premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not humble or brave is not old or curious.
Everyone who is either kind or wise is either old or generous and vice versa.
Everyone who is both brave and patient is not happy and vice versa.
Everyone who is not funny or creative is wise or creative.
Everyone who is not generous is not old and vice versa.
Everyone who is both calm and not funny is quiet.
If someone is calm then someone is not humble and vice versa.
If someone is both not happy and old then mary is either not rich or strong and vice versa.
Everyone who is not curious is strong.
Everyone who is generous or not creative is not patient or strong.
Everyone who is strong or funny is strong or wise and vice versa.
Everyone who is either old or strong is not calm and vice versa.
Everyone who is not funny is either not calm or not humble and vice versa.
Everyone who is not funny is either not old or not generous and vice versa.
If someone is both not curious and generous then lucy is not generous or old and vice versa.
Everyone who is either not quiet or not rich is funny or not funny.
Susan is wise or quiet.
Someone is both patient and not quiet.
Fred is both brave and not old.
Someone is either not humble or quiet.
Someone is either not patient or funny.
Someone is both tall and wise.
Someone is not kind.
Lucy is not humble. | Susan is wise. | neutral | (![X]:((~humble(X)|brave(X))=>(~old(X)|curious(X))))&
(![X]:((kind(X)<~>wise(X))<=>(old(X)<~>generous(X))))&
(![X]:((brave(X)&patient(X))<=>~happy(X)))&
(![X]:((~funny(X)|creative(X))=>(wise(X)|creative(X))))&
(![X]:(~generous(X)<=>~old(X)))&
(![X]:((calm(X)&~funny(X))=>quiet(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&old(X))))<=>((~rich(mary)<~>strong(mary))))&
(![X]:(~curious(X)=>strong(X)))&
(![X]:((generous(X)|~creative(X))=>(~patient(X)|strong(X))))&
(![X]:((strong(X)|funny(X))<=>(strong(X)|wise(X))))&
(![X]:((old(X)<~>strong(X))<=>~calm(X)))&
(![X]:(~funny(X)<=>(~calm(X)<~>~humble(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~generous(X))))&
((?[X]:((~curious(X)&generous(X))))<=>((~generous(lucy)|old(lucy))))&
(![X]:((~quiet(X)<~>~rich(X))=>(funny(X)|~funny(X))))&
((wise(susan)|quiet(susan)))&
(?[X]:((patient(X)&~quiet(X))))&
((brave(fred)&~old(fred)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:(~kind(X)))&
(~humble(lucy)) | wise(susan) | [] | null | 0 |
If someone is both old and generous then paul is old or not happy. If someone is both curious and not curious then fred is both happy and not old. Everyone who is not rich or calm is not quiet and vice versa. If mary is not humble then fred is brave. If someone is both funny and patient then alice is not kind or wise. Everyone who is either not creative or quiet is both not funny and not kind and vice versa. If someone is not creative then someone is not curious or quiet and vice versa. Everyone who is humble is either not rich or not calm and vice versa. Everyone who is strong or kind is either not generous or strong. Everyone who is both not funny and funny is both happy and old. Everyone who is both happy and humble is either not quiet or humble. If paul is not brave then someone is either not creative or not curious and vice versa. Everyone who is either generous or kind is both not tall and not funny. If someone is not calm or quiet then paul is either happy or not funny and vice versa. Everyone who is both brave and old is both not quiet and funny and vice versa. Everyone who is not humble or creative is either not funny or wise and vice versa. Someone is either not creative or brave. Fred is generous or brave. Someone is either quiet or tall. Someone is quiet or generous. Someone is both strong and not kind. Someone is not strong. Mary is kind or calm. Someone is both not humble and wise. | Mary is not old. | neutral | ((?[X]:((old(X)&generous(X))))=>((old(paul)|~happy(paul))))&
((?[X]:((curious(X)&~curious(X))))=>((happy(fred)&~old(fred))))&
(![X]:((~rich(X)|calm(X))<=>~quiet(X)))&
((~humble(mary))=>(brave(fred)))&
((?[X]:((funny(X)&patient(X))))=>((~kind(alice)|wise(alice))))&
(![X]:((~creative(X)<~>quiet(X))<=>(~funny(X)&~kind(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:(humble(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((strong(X)|kind(X))=>(~generous(X)<~>strong(X))))&
(![X]:((~funny(X)&funny(X))=>(happy(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>(~quiet(X)<~>humble(X))))&
((~brave(paul))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((generous(X)<~>kind(X))=>(~tall(X)&~funny(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>((happy(paul)<~>~funny(paul))))&
(![X]:((brave(X)&old(X))<=>(~quiet(X)&funny(X))))&
(![X]:((~humble(X)|creative(X))<=>(~funny(X)<~>wise(X))))&
(?[X]:((~creative(X)<~>brave(X))))&
((generous(fred)|brave(fred)))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:(~strong(X)))&
((kind(mary)|calm(mary)))&
(?[X]:((~humble(X)&wise(X)))) | ~old(mary) | [] | null | 0 |
If someone is either not funny or not quiet then someone is both not creative and humble and vice versa. Everyone who is either not strong or not quiet is calm. If someone is either not kind or not tall then alice is both kind and not happy and vice versa. Everyone who is wise is both rich and not happy. If alice is wise then someone is not patient or rich. If mary is either not humble or generous then someone is strong. Everyone who is strong is not tall or not generous. Everyone who is not wise is not funny or patient. Everyone who is not tall or not strong is old. Everyone who is either humble or not humble is both funny and quiet. If someone is either not rich or funny then alice is either strong or happy and vice versa. Everyone who is strong is patient. If lucy is both quiet and not tall then someone is kind or patient. If someone is both not generous and wise then paul is not tall. Everyone who is not old or generous is not quiet. Everyone who is both wise and calm is not generous or humble and vice versa. Fred is wise. Someone is wise or not brave. Someone is both not happy and not curious. John is not patient or happy. Someone is either not happy or generous. Someone is both creative and not generous. Someone is both not happy and funny. Someone is not creative. | John is old. | entailment | ((?[X]:((~funny(X)<~>~quiet(X))))<=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>calm(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((kind(alice)&~happy(alice))))&
(![X]:(wise(X)=>(rich(X)&~happy(X))))&
((wise(alice))=>(?[X]:((~patient(X)|rich(X)))))&
(((~humble(mary)<~>generous(mary)))=>(?[X]:(strong(X))))&
(![X]:(strong(X)=>(~tall(X)|~generous(X))))&
(![X]:(~wise(X)=>(~funny(X)|patient(X))))&
(![X]:((~tall(X)|~strong(X))=>old(X)))&
(![X]:((humble(X)<~>~humble(X))=>(funny(X)&quiet(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>((strong(alice)<~>happy(alice))))&
(![X]:(strong(X)=>patient(X)))&
(((quiet(lucy)&~tall(lucy)))=>(?[X]:((kind(X)|patient(X)))))&
((?[X]:((~generous(X)&wise(X))))=>(~tall(paul)))&
(![X]:((~old(X)|generous(X))=>~quiet(X)))&
(![X]:((wise(X)&calm(X))<=>(~generous(X)|humble(X))))&
(wise(fred))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((~happy(X)&~curious(X))))&
((~patient(john)|happy(john)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(~creative(X))) | old(john) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4447004218460497705908871
% SZS output start Proof for 4447004218460497705908871
10. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (quiet(X0) & funny(X0))) [input p9]
15. ! [X0] : ((generous(X0) | ~old(X0)) => ~quiet(X0)) [input p14]
25. ~old(john) [input hypothesis]
38. ! [X0] : ((quiet(X0) & funny(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 10]
43. ! [X0] : (~quiet(X0) | (~generous(X0) & old(X0))) [ennf transformation 15]
60. ! [X0] : ((quiet(X0) & funny(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 38]
105. quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 60]
106. quiet(X0) | humble(X0) | humble(X0) [cnf transformation 60]
118. ~quiet(X0) | old(X0) [cnf transformation 43]
135. ~old(john) [cnf transformation 25]
138. quiet(X0) | ~humble(X0) [duplicate literal removal 105]
139. quiet(X0) | humble(X0) [duplicate literal removal 106]
226. quiet(X0) [subsumption resolution 138,139]
270. old(X0) [subsumption resolution 118,226]
283. $false [subsumption resolution 135,270]
% SZS output end Proof for 4447004218460497705908871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or wise then someone is either rich or happy and vice versa. Everyone who is not generous or curious is either funny or not old. Everyone who is patient or old is old or strong and vice versa. Everyone who is both not funny and kind is old or not generous. Everyone who is either calm or not tall is either not funny or strong and vice versa. If susan is both not kind and generous then susan is both kind and not wise. Everyone who is not generous is not rich or old and vice versa. If fred is both humble and patient then someone is both generous and not funny. Everyone who is both not kind and not happy is not rich and vice versa. Everyone who is both creative and not kind is either not calm or brave and vice versa. If john is both not curious and not calm then someone is happy or curious and vice versa. Everyone who is not humble or humble is both not tall and funny. Everyone who is either not humble or curious is both curious and not generous. If someone is not generous then someone is either not quiet or patient. Everyone who is both not kind and not strong is not kind. If someone is either curious or kind then someone is generous and vice versa. Lucy is rich. Fred is generous or not funny. Someone is either not funny or not creative. Someone is old or quiet. Someone is curious. Someone is either humble or funny. Someone is not creative. Susan is not quiet. | Fred is not calm. | contradiction | ((?[X]:((~humble(X)<~>wise(X))))<=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~generous(X)|curious(X))=>(funny(X)<~>~old(X))))&
(![X]:((patient(X)|old(X))<=>(old(X)|strong(X))))&
(![X]:((~funny(X)&kind(X))=>(old(X)|~generous(X))))&
(![X]:((calm(X)<~>~tall(X))<=>(~funny(X)<~>strong(X))))&
(((~kind(susan)&generous(susan)))=>((kind(susan)&~wise(susan))))&
(![X]:(~generous(X)<=>(~rich(X)|old(X))))&
(((humble(fred)&patient(fred)))=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((~kind(X)&~happy(X))<=>~rich(X)))&
(![X]:((creative(X)&~kind(X))<=>(~calm(X)<~>brave(X))))&
(((~curious(john)&~calm(john)))<=>(?[X]:((happy(X)|curious(X)))))&
(![X]:((~humble(X)|humble(X))=>(~tall(X)&funny(X))))&
(![X]:((~humble(X)<~>curious(X))=>(curious(X)&~generous(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((~kind(X)&~strong(X))=>~kind(X)))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:(generous(X))))&
(rich(lucy))&
((generous(fred)|~funny(fred)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)<~>funny(X))))&
(?[X]:(~creative(X)))&
(~quiet(susan)) | ~calm(fred) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8659856335415385074180817
% SZS output start Proof for 8659856335415385074180817
2. ! [X0] : ((curious(X0) | ~generous(X0)) => (funny(X0) <~> ~old(X0))) [input p1]
3. ! [X0] : ((old(X0) | patient(X0)) <=> (strong(X0) | old(X0))) [input p2]
5. ! [X0] : ((calm(X0) <~> ~tall(X0)) <=> (~funny(X0) <~> strong(X0))) [input p4]
7. ! [X0] : (~generous(X0) <=> (old(X0) | ~rich(X0))) [input p6]
8. (patient(fred) & humble(fred)) => ? [X0] : (~funny(X0) & generous(X0)) [input p7]
12. ! [X0] : ((humble(X0) | ~humble(X0)) => (funny(X0) & ~tall(X0))) [input p11]
13. ! [X0] : ((~humble(X0) <~> curious(X0)) => (~generous(X0) & curious(X0))) [input p12]
18. ~funny(fred) | generous(fred) [input p17]
25. ~calm(fred) [input hypothesis]
29. ! [X0] : ((funny(X0) <~> ~old(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 2]
34. ? [X0] : (~funny(X0) & generous(X0)) | (~patient(fred) | ~humble(fred)) [ennf transformation 8]
35. ? [X0] : (~funny(X0) & generous(X0)) | ~patient(fred) | ~humble(fred) [flattening 34]
36. ! [X0] : ((funny(X0) & ~tall(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 12]
37. ! [X0] : ((~generous(X0) & curious(X0)) | (~humble(X0) <=> curious(X0))) [ennf transformation 13]
46. ! [X0] : (((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (~curious(X0) & generous(X0))) [nnf transformation 29]
47. ! [X0] : (((old(X0) | patient(X0)) | (~strong(X0) & ~old(X0))) & ((strong(X0) | old(X0)) | (~old(X0) & ~patient(X0)))) [nnf transformation 3]
48. ! [X0] : ((old(X0) | patient(X0) | (~strong(X0) & ~old(X0))) & (strong(X0) | old(X0) | (~old(X0) & ~patient(X0)))) [flattening 47]
49. ! [X0] : ((((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0)))) & (((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0))))) [nnf transformation 5]
50. ! [X0] : ((~generous(X0) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | generous(X0))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | generous(X0))) [flattening 50]
52. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK2) & generous(sK2)) [choice axiom]
53. (~funny(sK2) & generous(sK2)) | ~patient(fred) | ~humble(fred) [skolemisation 35,52]
63. ! [X0] : ((~generous(X0) & curious(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0)))) [nnf transformation 37]
96. ~funny(X0) | old(X0) | ~curious(X0) [cnf transformation 46]
100. ~strong(X0) | patient(X0) | old(X0) [cnf transformation 48]
103. ~funny(X0) | strong(X0) | calm(X0) | tall(X0) [cnf transformation 49]
114. ~old(X0) | ~generous(X0) [cnf transformation 51]
116. ~funny(sK2) | ~patient(fred) | ~humble(fred) [cnf transformation 53]
131. ~tall(X0) | humble(X0) [cnf transformation 36]
132. ~tall(X0) | ~humble(X0) [cnf transformation 36]
133. funny(X0) | humble(X0) [cnf transformation 36]
134. ~humble(X0) | funny(X0) [cnf transformation 36]
135. curious(X0) | curious(X0) | humble(X0) [cnf transformation 63]
147. ~funny(fred) | generous(fred) [cnf transformation 18]
156. ~calm(fred) [cnf transformation 25]
157. curious(X0) | humble(X0) [duplicate literal removal 135]
210. 12 <=> humble(fred) [avatar definition]
214. 13 <=> patient(fred) [avatar definition]
216. ~patient(fred) <- (~13) [avatar component clause 214]
218. 14 <=> funny(sK2) [avatar definition]
220. ~funny(sK2) <- (~14) [avatar component clause 218]
221. ~12 | ~13 | ~14 [avatar split clause 116,218,214,210]
255. funny(X0) [subsumption resolution 133,134]
256. ~tall(X0) [subsumption resolution 131,132]
295. generous(fred) [subsumption resolution 147,255]
326. ~curious(X0) | old(X0) [resolution 96,255]
329. old(X0) | humble(X0) [resolution 326,157]
465. strong(X0) | calm(X0) | tall(X0) [resolution 103,255]
466. calm(X0) | strong(X0) [subsumption resolution 465,256]
495. strong(fred) [resolution 466,156]
500. patient(fred) | old(fred) [resolution 495,100]
501. old(fred) <- (~13) [subsumption resolution 500,216]
526. ~generous(X2) | humble(X2) [resolution 329,114]
529. ~generous(fred) <- (~13) [resolution 501,114]
530. $false <- (~13) [subsumption resolution 529,295]
531. 13 [avatar contradiction clause 530]
553. humble(fred) [resolution 526,295]
557. 12 [avatar split clause 553,210]
558. $false <- (~14) [subsumption resolution 220,255]
559. 14 [avatar contradiction clause 558]
560. $false [avatar sat refutation 221,531,557,559]
% SZS output end Proof for 8659856335415385074180817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is both strong and curious then someone is old and vice versa.
Everyone who is either rich or not humble is either not kind or not wise.
If someone is either not wise or wise then susan is not strong.
If someone is both curious and not funny then someone is both funny and not old.
Everyone who is humble is either not brave or not generous and vice versa.
If someone is creative then alice is either not funny or not kind and vice versa.
If someone is either funny or not patient then paul is both generous and wise and vice versa.
Everyone who is both not rich and quiet is not patient or old and vice versa.
If paul is calm or old then someone is tall.
Everyone who is not rich or patient is humble and vice versa.
Everyone who is not funny or quiet is old.
Everyone who is either humble or not generous is not wise and vice versa.
If someone is both not funny and not strong then john is brave and vice versa.
If someone is either tall or not rich then someone is not quiet.
If alice is tall or strong then someone is tall.
Someone is calm or curious.
Someone is both tall and not wise.
Mary is either not humble or wise.
Mary is curious or not patient.
Fred is happy. | John is quiet. | entailment | (((strong(john)&curious(john)))<=>(?[X]:(old(X))))&
(![X]:((rich(X)<~>~humble(X))=>(~kind(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>(~strong(susan)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:((funny(X)&~old(X)))))&
(![X]:(humble(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(creative(X)))<=>((~funny(alice)<~>~kind(alice))))&
((?[X]:((funny(X)<~>~patient(X))))<=>((generous(paul)&wise(paul))))&
(![X]:((~rich(X)&quiet(X))<=>(~patient(X)|old(X))))&
(((calm(paul)|old(paul)))=>(?[X]:(tall(X))))&
(![X]:((~rich(X)|patient(X))<=>humble(X)))&
(![X]:((~funny(X)|quiet(X))=>old(X)))&
(![X]:((humble(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((~funny(X)&~strong(X))))<=>(brave(john)))&
((?[X]:((tall(X)<~>~rich(X))))=>(?[X]:(~quiet(X))))&
(((tall(alice)|strong(alice)))=>(?[X]:(tall(X))))&
(?[X]:((calm(X)|curious(X))))&
(?[X]:((tall(X)&~wise(X))))&
((~humble(mary)<~>wise(mary)))&
((curious(mary)|~patient(mary)))&
(happy(fred)) | quiet(john) | [
"p0",
"p3",
"p6",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5069275422811693277946314
% SZS output start Proof for 5069275422811693277946314
1. (curious(john) & strong(john)) <=> ? [X0] : old(X0) [input p0]
4. ? [X0] : (~funny(X0) & curious(X0)) => ? [X0] : (~old(X0) & funny(X0)) [input p3]
7. ? [X0] : (funny(X0) <~> ~patient(X0)) <=> (wise(paul) & generous(paul)) [input p6]
8. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (old(X0) | ~patient(X0))) [input p7]
10. ! [X0] : ((patient(X0) | ~rich(X0)) <=> humble(X0)) [input p9]
11. ! [X0] : ((quiet(X0) | ~funny(X0)) => old(X0)) [input p10]
12. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p11]
21. ~quiet(john) [input hypothesis]
22. ? [X0] : (~funny(X0) & curious(X0)) => ? [X1] : (~old(X1) & funny(X1)) [rectify 4]
27. ? [X1] : (~old(X1) & funny(X1)) | ! [X0] : (funny(X0) | ~curious(X0)) [ennf transformation 22]
29. ! [X0] : (old(X0) | (~quiet(X0) & funny(X0))) [ennf transformation 11]
32. ((curious(john) & strong(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~curious(john) | ~strong(john))) [nnf transformation 1]
33. ((curious(john) & strong(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~curious(john) | ~strong(john)) [flattening 32]
34. ((curious(john) & strong(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~curious(john) | ~strong(john)) [rectify 33]
35. ? [X1] : old(X1) => old(sK0) [choice axiom]
36. ((curious(john) & strong(john)) | ! [X0] : ~old(X0)) & (old(sK0) | ~curious(john) | ~strong(john)) [skolemisation 34,35]
39. ? [X0] : (~old(X0) & funny(X0)) | ! [X1] : (funny(X1) | ~curious(X1)) [rectify 27]
40. ? [X0] : (~old(X0) & funny(X0)) => (~old(sK1) & funny(sK1)) [choice axiom]
41. (~old(sK1) & funny(sK1)) | ! [X1] : (funny(X1) | ~curious(X1)) [skolemisation 39,40]
47. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~wise(paul) | ~generous(paul))) & ((wise(paul) & generous(paul)) | ! [X0] : ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) [nnf transformation 7]
48. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X0] : ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) [flattening 47]
49. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) [rectify 48]
50. ? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) => ((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) [choice axiom]
51. (((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) [skolemisation 49,50]
52. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 8]
53. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~quiet(X0) | rich(X0))) [flattening 52]
56. ! [X0] : (((patient(X0) | ~rich(X0)) | ~humble(X0)) & (humble(X0) | (~patient(X0) & rich(X0)))) [nnf transformation 10]
57. ! [X0] : ((patient(X0) | ~rich(X0) | ~humble(X0)) & (humble(X0) | (~patient(X0) & rich(X0)))) [flattening 56]
58. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | wise(X0)) & (~wise(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 12]
76. curious(john) | ~old(X0) [cnf transformation 36]
84. ~old(sK1) | funny(X1) | ~curious(X1) [cnf transformation 41]
93. generous(paul) | ~patient(X1) | ~funny(X1) [cnf transformation 51]
95. wise(paul) | ~patient(X1) | ~funny(X1) [cnf transformation 51]
101. ~rich(X0) | ~old(X0) [cnf transformation 53]
102. quiet(X0) | patient(X0) [cnf transformation 53]
106. humble(X0) | rich(X0) [cnf transformation 57]
107. ~patient(X0) | humble(X0) [cnf transformation 57]
109. funny(X0) | old(X0) [cnf transformation 29]
110. ~quiet(X0) | old(X0) [cnf transformation 29]
111. ~generous(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 58]
128. ~quiet(john) [cnf transformation 21]
132. 1 <=> ! [X0] : ~old(X0) [avatar definition]
133. ~old(X0) <- (1) [avatar component clause 132]
135. 2 <=> curious(john) [avatar definition]
137. curious(john) <- (2) [avatar component clause 135]
138. 1 | 2 [avatar split clause 76,135,132]
162. 8 <=> ! [X1] : (funny(X1) | ~curious(X1)) [avatar definition]
163. ~curious(X1) | funny(X1) <- (8) [avatar component clause 162]
165. 9 <=> old(sK1) [avatar definition]
167. ~old(sK1) <- (~9) [avatar component clause 165]
168. 8 | ~9 [avatar split clause 84,165,162]
194. 15 <=> generous(paul) [avatar definition]
195. generous(paul) <- (15) [avatar component clause 194]
198. 16 <=> wise(paul) [avatar definition]
199. wise(paul) <- (16) [avatar component clause 198]
216. 20 <=> ! [X1] : (~patient(X1) | ~funny(X1)) [avatar definition]
217. ~patient(X1) | ~funny(X1) <- (20) [avatar component clause 216]
218. 20 | 16 [avatar split clause 95,198,216]
220. 20 | 15 [avatar split clause 93,194,216]
222. 21 <=> old(paul) [avatar definition]
223. old(paul) <- (21) [avatar component clause 222]
224. ~old(paul) <- (~21) [avatar component clause 222]
307. patient(john) [resolution 102,128]
320. patient(X0) | old(X0) [resolution 110,102]
323. funny(john) <- (2, 8) [resolution 163,137]
327. 40 <=> humble(paul) [avatar definition]
329. ~humble(paul) <- (~40) [avatar component clause 327]
353. ~wise(paul) | ~humble(paul) <- (15) [resolution 111,195]
438. humble(X0) | old(X0) [resolution 320,107]
472. old(paul) <- (~40) [resolution 438,329]
474. $false <- (~21, ~40) [subsumption resolution 472,224]
475. 21 | 40 [avatar contradiction clause 474]
477. 55 <=> rich(paul) [avatar definition]
478. rich(paul) <- (55) [avatar component clause 477]
485. ~humble(paul) <- (15, 16) [subsumption resolution 353,199]
486. ~40 | ~15 | ~16 [avatar split clause 485,198,194,327]
490. rich(paul) <- (~40) [resolution 329,106]
491. 55 | 40 [avatar split clause 490,327,477]
493. ~old(paul) <- (55) [resolution 478,101]
495. $false <- (21, 55) [subsumption resolution 493,223]
496. ~21 | ~55 [avatar contradiction clause 495]
510. ~funny(john) <- (20) [resolution 217,307]
513. ~funny(X1) | old(X1) <- (20) [resolution 217,320]
514. $false <- (2, 8, 20) [subsumption resolution 510,323]
515. ~2 | ~8 | ~20 [avatar contradiction clause 514]
516. old(X1) <- (20) [subsumption resolution 513,109]
517. $false <- (~9, 20) [subsumption resolution 167,516]
518. 9 | ~20 [avatar contradiction clause 517]
519. $false <- (1, 20) [subsumption resolution 133,516]
520. ~1 | ~20 [avatar contradiction clause 519]
521. $false [avatar sat refutation 138,168,218,220,475,486,491,496,515,518,520]
% SZS output end Proof for 5069275422811693277946314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not happy is brave and vice versa. Everyone who is quiet or patient is not strong. Everyone who is either calm or not funny is both not curious and not generous. Everyone who is not generous or creative is either brave or kind and vice versa. Everyone who is humble or not rich is not rich or not brave. Everyone who is both patient and calm is either not funny or not kind and vice versa. Everyone who is brave is not funny or not calm. Everyone who is creative is not funny or not wise and vice versa. Everyone who is not tall or funny is tall or generous and vice versa. Everyone who is brave or not funny is not curious or not calm. Everyone who is strong or quiet is both patient and not strong. Everyone who is both humble and not rich is both generous and quiet and vice versa. If lucy is quiet or not curious then someone is humble. If susan is not kind then someone is creative and vice versa. Everyone who is both quiet and funny is both brave and generous and vice versa. Everyone who is both not wise and quiet is not happy and vice versa. Someone is both not tall and patient. Someone is happy. Susan is tall or not quiet. Susan is either kind or not calm. Someone is either patient or not curious. | Lucy is not wise. | contradiction | (![X]:((humble(X)<~>~happy(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))=>~strong(X)))&
(![X]:((calm(X)<~>~funny(X))=>(~curious(X)&~generous(X))))&
(![X]:((~generous(X)|creative(X))<=>(brave(X)<~>kind(X))))&
(![X]:((humble(X)|~rich(X))=>(~rich(X)|~brave(X))))&
(![X]:((patient(X)&calm(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(brave(X)=>(~funny(X)|~calm(X))))&
(![X]:(creative(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~tall(X)|funny(X))<=>(tall(X)|generous(X))))&
(![X]:((brave(X)|~funny(X))=>(~curious(X)|~calm(X))))&
(![X]:((strong(X)|quiet(X))=>(patient(X)&~strong(X))))&
(![X]:((humble(X)&~rich(X))<=>(generous(X)&quiet(X))))&
(((quiet(lucy)|~curious(lucy)))=>(?[X]:(humble(X))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)&funny(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)&quiet(X))<=>~happy(X)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:(happy(X)))&
((tall(susan)|~quiet(susan)))&
((kind(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>~curious(X)))) | ~wise(lucy) | [
"p3",
"p5",
"p7",
"p8",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7211837808167163055396978
% SZS output start Proof for 7211837808167163055396978
4. ! [X0] : ((creative(X0) | ~generous(X0)) <=> (brave(X0) <~> kind(X0))) [input p3]
6. ! [X0] : ((calm(X0) & patient(X0)) <=> (~funny(X0) <~> ~kind(X0))) [input p5]
8. ! [X0] : (creative(X0) <=> (~wise(X0) | ~funny(X0))) [input p7]
9. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (generous(X0) | tall(X0))) [input p8]
14. ~kind(susan) <=> ? [X0] : creative(X0) [input p13]
15. ! [X0] : ((funny(X0) & quiet(X0)) <=> (generous(X0) & brave(X0))) [input p14]
20. kind(susan) <~> ~calm(susan) [input p19]
22. ~wise(lucy) [input hypothesis]
36. ! [X0] : (((creative(X0) | ~generous(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~creative(X0) & generous(X0)))) [nnf transformation 4]
37. ! [X0] : ((creative(X0) | ~generous(X0) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~creative(X0) & generous(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (~calm(X0) | ~patient(X0)))) [nnf transformation 6]
39. ! [X0] : (((calm(X0) & patient(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ~calm(X0) | ~patient(X0))) [flattening 38]
40. ! [X0] : ((creative(X0) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | ~creative(X0))) [nnf transformation 8]
41. ! [X0] : ((creative(X0) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~creative(X0))) [flattening 40]
42. ! [X0] : (((funny(X0) | ~tall(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 9]
43. ! [X0] : ((funny(X0) | ~tall(X0) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | (~funny(X0) & tall(X0)))) [flattening 42]
48. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | kind(susan)) [nnf transformation 14]
49. (~kind(susan) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | kind(susan)) [rectify 48]
50. ? [X1] : creative(X1) => creative(sK1) [choice axiom]
51. (~kind(susan) | ! [X0] : ~creative(X0)) & (creative(sK1) | kind(susan)) [skolemisation 49,50]
52. ! [X0] : (((funny(X0) & quiet(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 15]
53. ! [X0] : (((funny(X0) & quiet(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 52]
60. (calm(susan) | ~kind(susan)) & (~calm(susan) | kind(susan)) [nnf transformation 20]
73. ~creative(X0) | brave(X0) | kind(X0) [cnf transformation 37]
85. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 39]
88. creative(X0) | funny(X0) [cnf transformation 41]
89. wise(X0) | creative(X0) [cnf transformation 41]
90. generous(X0) | tall(X0) | tall(X0) [cnf transformation 43]
92. funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
104. ~kind(susan) | ~creative(X0) [cnf transformation 51]
108. ~generous(X0) | funny(X0) | ~brave(X0) [cnf transformation 53]
116. ~calm(susan) | kind(susan) [cnf transformation 60]
120. ~wise(lucy) [cnf transformation 22]
121. tall(X0) | generous(X0) [duplicate literal removal 90]
122. ~tall(X0) | funny(X0) [duplicate literal removal 92]
139. 4 <=> ! [X0] : ~creative(X0) [avatar definition]
140. ~creative(X0) <- (4) [avatar component clause 139]
142. 5 <=> kind(susan) [avatar definition]
144. ~kind(susan) <- (~5) [avatar component clause 142]
145. 4 | ~5 [avatar split clause 104,142,139]
161. 9 <=> calm(susan) [avatar definition]
162. ~calm(susan) <- (~9) [avatar component clause 161]
165. 5 | ~9 [avatar split clause 116,161,142]
176. creative(lucy) [resolution 89,120]
181. generous(X0) | funny(X0) [resolution 122,121]
248. kind(X1) | brave(X1) | funny(X1) [resolution 73,88]
268. $false <- (4) [resolution 140,176]
271. ~4 [avatar contradiction clause 268]
385. funny(X0) | ~brave(X0) | funny(X0) [resolution 108,181]
387. funny(X0) | ~brave(X0) [duplicate literal removal 385]
464. brave(susan) | funny(susan) <- (~5) [resolution 248,144]
482. funny(susan) <- (~5) [subsumption resolution 464,387]
527. calm(susan) | kind(susan) <- (~5) [resolution 482,85]
532. kind(susan) <- (~5, ~9) [subsumption resolution 527,162]
533. $false <- (~5, ~9) [subsumption resolution 532,144]
534. 5 | 9 [avatar contradiction clause 533]
535. $false [avatar sat refutation 145,165,271,534]
% SZS output end Proof for 7211837808167163055396978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny and not kind is either not calm or not funny.
Everyone who is not brave is not rich.
If susan is both kind and not strong then alice is both creative and not calm.
If someone is either not brave or kind then lucy is wise or quiet.
Everyone who is both rich and not tall is not kind or not old.
If fred is not rich or generous then someone is both funny and tall.
Everyone who is either generous or not humble is quiet and vice versa.
Everyone who is either not rich or not calm is not rich or not humble.
If susan is not brave or tall then someone is not curious and vice versa.
Everyone who is either not creative or not brave is not humble.
Everyone who is not happy is patient or not quiet.
Everyone who is both not humble and not brave is both not curious and not generous.
Everyone who is not generous is either not rich or not calm.
Everyone who is both humble and not brave is either not calm or not curious.
Everyone who is both humble and wise is both kind and brave.
If susan is not calm then paul is either curious or brave.
Someone is not funny or not strong.
Someone is either quiet or not quiet.
Susan is either tall or strong.
Someone is both happy and creative.
Someone is generous or not old.
John is patient or not patient.
Mary is either not tall or not curious.
John is patient or not humble. | Susan is humble. | neutral | (![X]:((~funny(X)&~kind(X))=>(~calm(X)<~>~funny(X))))&
(![X]:(~brave(X)=>~rich(X)))&
(((kind(susan)&~strong(susan)))=>((creative(alice)&~calm(alice))))&
((?[X]:((~brave(X)<~>kind(X))))=>((wise(lucy)|quiet(lucy))))&
(![X]:((rich(X)&~tall(X))=>(~kind(X)|~old(X))))&
(((~rich(fred)|generous(fred)))=>(?[X]:((funny(X)&tall(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>quiet(X)))&
(![X]:((~rich(X)<~>~calm(X))=>(~rich(X)|~humble(X))))&
(((~brave(susan)|tall(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((~creative(X)<~>~brave(X))=>~humble(X)))&
(![X]:(~happy(X)=>(patient(X)|~quiet(X))))&
(![X]:((~humble(X)&~brave(X))=>(~curious(X)&~generous(X))))&
(![X]:(~generous(X)=>(~rich(X)<~>~calm(X))))&
(![X]:((humble(X)&~brave(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((humble(X)&wise(X))=>(kind(X)&brave(X))))&
((~calm(susan))=>((curious(paul)<~>brave(paul))))&
(?[X]:((~funny(X)|~strong(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((tall(susan)<~>strong(susan)))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((generous(X)|~old(X))))&
((patient(john)|~patient(john)))&
((~tall(mary)<~>~curious(mary)))&
((patient(john)|~humble(john))) | humble(susan) | [] | null | 0 |
If someone is not patient or kind then susan is either not brave or patient. If someone is tall or happy then someone is not happy and vice versa. Everyone who is either patient or happy is not happy or humble and vice versa. If someone is either curious or rich then lucy is either not funny or not rich and vice versa. Everyone who is both humble and not strong is both not patient and funny. Everyone who is both generous and not old is generous and vice versa. Everyone who is both generous and not rich is both funny and brave. Everyone who is curious is both not creative and not patient. Everyone who is wise is either not old or not humble and vice versa. Everyone who is not wise or funny is either not rich or not funny. Everyone who is not kind or not strong is not creative or curious and vice versa. If someone is either not calm or calm then someone is both humble and kind. Everyone who is either strong or not patient is patient. Everyone who is either creative or not tall is both curious and not brave and vice versa. Everyone who is either strong or not funny is either not tall or not calm. Fred is old. Someone is either generous or humble. John is both kind and old. Someone is generous. Someone is curious. John is either not creative or strong. | Susan is patient. | neutral | ((?[X]:((~patient(X)|kind(X))))=>((~brave(susan)<~>patient(susan))))&
((?[X]:((tall(X)|happy(X))))<=>(?[X]:(~happy(X))))&
(![X]:((patient(X)<~>happy(X))<=>(~happy(X)|humble(X))))&
((?[X]:((curious(X)<~>rich(X))))<=>((~funny(lucy)<~>~rich(lucy))))&
(![X]:((humble(X)&~strong(X))=>(~patient(X)&funny(X))))&
(![X]:((generous(X)&~old(X))<=>generous(X)))&
(![X]:((generous(X)&~rich(X))=>(funny(X)&brave(X))))&
(![X]:(curious(X)=>(~creative(X)&~patient(X))))&
(![X]:(wise(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~wise(X)|funny(X))=>(~rich(X)<~>~funny(X))))&
(![X]:((~kind(X)|~strong(X))<=>(~creative(X)|curious(X))))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((strong(X)<~>~patient(X))=>patient(X)))&
(![X]:((creative(X)<~>~tall(X))<=>(curious(X)&~brave(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~tall(X)<~>~calm(X))))&
(old(fred))&
(?[X]:((generous(X)<~>humble(X))))&
((kind(john)&old(john)))&
(?[X]:(generous(X)))&
(?[X]:(curious(X)))&
((~creative(john)<~>strong(john))) | patient(susan) | [] | null | 0 |
Everyone who is both not funny and not humble is either not brave or not tall and vice versa. Everyone who is strong or not humble is both not curious and happy. Everyone who is both not rich and not tall is not wise. Everyone who is wise is strong or not wise and vice versa. If someone is humble or funny then john is either not wise or not old and vice versa. If susan is either rich or old then someone is wise or patient. If lucy is both happy and not kind then someone is patient. If john is both funny and not patient then someone is not funny and vice versa. Everyone who is not strong is both quiet and funny. Everyone who is not rich or not old is wise or not wise and vice versa. Everyone who is either creative or not wise is not funny. If someone is not patient or happy then fred is both tall and not kind and vice versa. Everyone who is both old and not humble is either brave or not funny and vice versa. Everyone who is either calm or kind is tall. Alice is either tall or kind. Someone is both not humble and brave. Mary is both rich and funny. Someone is either not happy or brave. Someone is either patient or not patient. Alice is both not humble and funny. | Lucy is not wise. | contradiction | (![X]:((~funny(X)&~humble(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((strong(X)|~humble(X))=>(~curious(X)&happy(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
(![X]:(wise(X)<=>(strong(X)|~wise(X))))&
((?[X]:((humble(X)|funny(X))))<=>((~wise(john)<~>~old(john))))&
(((rich(susan)<~>old(susan)))=>(?[X]:((wise(X)|patient(X)))))&
(((happy(lucy)&~kind(lucy)))=>(?[X]:(patient(X))))&
(((funny(john)&~patient(john)))<=>(?[X]:(~funny(X))))&
(![X]:(~strong(X)=>(quiet(X)&funny(X))))&
(![X]:((~rich(X)|~old(X))<=>(wise(X)|~wise(X))))&
(![X]:((creative(X)<~>~wise(X))=>~funny(X)))&
((?[X]:((~patient(X)|happy(X))))<=>((tall(fred)&~kind(fred))))&
(![X]:((old(X)&~humble(X))<=>(brave(X)<~>~funny(X))))&
(![X]:((calm(X)<~>kind(X))=>tall(X)))&
((tall(alice)<~>kind(alice)))&
(?[X]:((~humble(X)&brave(X))))&
((rich(mary)&funny(mary)))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
((~humble(alice)&funny(alice))) | ~wise(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8505859055325314426976978
% SZS output start Proof for 8505859055325314426976978
4. ! [X0] : (wise(X0) <=> (~wise(X0) | strong(X0))) [input p3]
21. ~wise(lucy) [input hypothesis]
35. ! [X0] : ((wise(X0) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | ~wise(X0))) [nnf transformation 4]
36. ! [X0] : ((wise(X0) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | ~wise(X0))) [flattening 35]
82. wise(X0) | wise(X0) [cnf transformation 36]
127. ~wise(lucy) [cnf transformation 21]
129. wise(X0) [duplicate literal removal 82]
235. $false [subsumption resolution 127,129]
% SZS output end Proof for 8505859055325314426976978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not old or patient then someone is not wise or not strong and vice versa. Everyone who is happy is both not curious and funny and vice versa. If alice is both not tall and not happy then someone is not brave or brave and vice versa. Everyone who is not curious is humble or not old. If mary is either humble or not wise then someone is not tall and vice versa. Everyone who is generous or curious is happy and vice versa. Everyone who is not kind is both not old and not brave. If someone is not brave then mary is both not happy and not humble. Everyone who is brave or not calm is either quiet or tall. If fred is both not strong and generous then someone is not happy. If paul is not calm then someone is brave and vice versa. Everyone who is either kind or not happy is not brave and vice versa. If fred is curious or not patient then someone is creative or old. If alice is kind or not strong then paul is either not quiet or generous. If someone is strong then someone is calm. Everyone who is not wise or old is not funny or not happy. Lucy is not happy or not kind. Someone is strong. Someone is not kind. Lucy is either brave or not creative. Someone is not creative. Lucy is both kind and humble. Someone is both strong and happy. | Mary is wise. | contradiction | (((~old(mary)<~>patient(mary)))<=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:(happy(X)<=>(~curious(X)&funny(X))))&
(((~tall(alice)&~happy(alice)))<=>(?[X]:((~brave(X)|brave(X)))))&
(![X]:(~curious(X)=>(humble(X)|~old(X))))&
(((humble(mary)<~>~wise(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((generous(X)|curious(X))<=>happy(X)))&
(![X]:(~kind(X)=>(~old(X)&~brave(X))))&
((?[X]:(~brave(X)))=>((~happy(mary)&~humble(mary))))&
(![X]:((brave(X)|~calm(X))=>(quiet(X)<~>tall(X))))&
(((~strong(fred)&generous(fred)))=>(?[X]:(~happy(X))))&
((~calm(paul))<=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>~happy(X))<=>~brave(X)))&
(((curious(fred)|~patient(fred)))=>(?[X]:((creative(X)|old(X)))))&
(((kind(alice)|~strong(alice)))=>((~quiet(paul)<~>generous(paul))))&
((?[X]:(strong(X)))=>(?[X]:(calm(X))))&
(![X]:((~wise(X)|old(X))=>(~funny(X)|~happy(X))))&
((~happy(lucy)|~kind(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(~kind(X)))&
((brave(lucy)<~>~creative(lucy)))&
(?[X]:(~creative(X)))&
((kind(lucy)&humble(lucy)))&
(?[X]:((strong(X)&happy(X)))) | wise(mary) | [
"p2",
"p4",
"p6",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5424521528868096990156143
% SZS output start Proof for 5424521528868096990156143
3. (~happy(alice) & ~tall(alice)) <=> ? [X0] : (brave(X0) | ~brave(X0)) [input p2]
5. (humble(mary) <~> ~wise(mary)) <=> ? [X0] : ~tall(X0) [input p4]
7. ! [X0] : (~kind(X0) => (~brave(X0) & ~old(X0))) [input p6]
8. ? [X0] : ~brave(X0) => (~humble(mary) & ~happy(mary)) [input p7]
19. ? [X0] : ~kind(X0) [input p18]
24. wise(mary) [input hypothesis]
28. ! [X0] : ((~brave(X0) & ~old(X0)) | kind(X0)) [ennf transformation 7]
29. (~humble(mary) & ~happy(mary)) | ! [X0] : brave(X0) [ennf transformation 8]
44. ((~happy(alice) & ~tall(alice)) | ! [X0] : (~brave(X0) & brave(X0))) & (? [X0] : (brave(X0) | ~brave(X0)) | (happy(alice) | tall(alice))) [nnf transformation 3]
45. ((~happy(alice) & ~tall(alice)) | ! [X0] : (~brave(X0) & brave(X0))) & (? [X0] : (brave(X0) | ~brave(X0)) | happy(alice) | tall(alice)) [flattening 44]
46. ((~happy(alice) & ~tall(alice)) | ! [X0] : (~brave(X0) & brave(X0))) & (? [X1] : (brave(X1) | ~brave(X1)) | happy(alice) | tall(alice)) [rectify 45]
47. ? [X1] : (brave(X1) | ~brave(X1)) => (brave(sK1) | ~brave(sK1)) [choice axiom]
48. ((~happy(alice) & ~tall(alice)) | ! [X0] : (~brave(X0) & brave(X0))) & ((brave(sK1) | ~brave(sK1)) | happy(alice) | tall(alice)) [skolemisation 46,47]
49. (((wise(mary) | ~humble(mary)) & (~wise(mary) | humble(mary))) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ((humble(mary) | wise(mary)) & (~wise(mary) | ~humble(mary)))) [nnf transformation 5]
50. (((wise(mary) | ~humble(mary)) & (~wise(mary) | humble(mary))) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ((humble(mary) | wise(mary)) & (~wise(mary) | ~humble(mary)))) [rectify 49]
51. ? [X1] : ~tall(X1) => ~tall(sK2) [choice axiom]
52. (((wise(mary) | ~humble(mary)) & (~wise(mary) | humble(mary))) | ! [X0] : tall(X0)) & (~tall(sK2) | ((humble(mary) | wise(mary)) & (~wise(mary) | ~humble(mary)))) [skolemisation 50,51]
71. ? [X0] : ~kind(X0) => ~kind(sK8) [choice axiom]
72. ~kind(sK8) [skolemisation 19,71]
88. ~tall(alice) | brave(X0) [cnf transformation 48]
95. ~wise(mary) | humble(mary) | tall(X0) [cnf transformation 52]
101. ~brave(X0) | kind(X0) [cnf transformation 28]
103. ~humble(mary) | brave(X0) [cnf transformation 29]
126. ~kind(sK8) [cnf transformation 72]
134. wise(mary) [cnf transformation 24]
172. 9 <=> ! [X0] : brave(X0) [avatar definition]
173. brave(X0) <- (9) [avatar component clause 172]
176. 10 <=> tall(alice) [avatar definition]
178. ~tall(alice) <- (~10) [avatar component clause 176]
180. 9 | ~10 [avatar split clause 88,176,172]
182. 11 <=> ! [X0] : tall(X0) [avatar definition]
183. tall(X0) <- (11) [avatar component clause 182]
185. 12 <=> humble(mary) [avatar definition]
189. 13 <=> wise(mary) [avatar definition]
193. 11 | 12 | ~13 [avatar split clause 95,189,185,182]
202. 9 | ~12 [avatar split clause 103,185,172]
287. 13 [avatar split clause 134,189]
288. $false <- (~10, 11) [subsumption resolution 178,183]
289. 10 | ~11 [avatar contradiction clause 288]
299. kind(X0) <- (9) [resolution 101,173]
300. $false <- (9) [resolution 299,126]
301. ~9 [avatar contradiction clause 300]
302. $false [avatar sat refutation 180,193,202,287,289,301]
% SZS output end Proof for 5424521528868096990156143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is either not old or rich and vice versa.
Everyone who is either patient or curious is either not quiet or humble.
Everyone who is curious or patient is both not generous and tall and vice versa.
If lucy is not old then someone is not kind and vice versa.
Everyone who is both patient and strong is not happy and vice versa.
Everyone who is both not rich and generous is funny and vice versa.
If someone is humble or creative then someone is both not calm and not wise and vice versa.
Everyone who is generous is either kind or not wise.
Everyone who is both humble and not brave is either calm or not funny.
If mary is both not happy and brave then someone is either not funny or funny and vice versa.
Everyone who is not strong is brave.
If someone is not old then lucy is both not tall and humble and vice versa.
Everyone who is both not calm and not strong is either not patient or kind.
If mary is not happy or curious then lucy is both humble and not patient and vice versa.
If someone is both not humble and quiet then someone is quiet and vice versa.
Everyone who is both tall and funny is not generous.
Alice is patient.
Someone is rich or not wise.
Someone is calm.
Someone is both brave and not kind.
Someone is curious.
Someone is old.
Someone is curious or not happy.
Susan is not humble or kind. | Lucy is humble. | entailment | ((generous(paul))<=>(?[X]:((~old(X)<~>rich(X)))))&
(![X]:((patient(X)<~>curious(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((curious(X)|patient(X))<=>(~generous(X)&tall(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((patient(X)&strong(X))<=>~happy(X)))&
(![X]:((~rich(X)&generous(X))<=>funny(X)))&
((?[X]:((humble(X)|creative(X))))<=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:(generous(X)=>(kind(X)<~>~wise(X))))&
(![X]:((humble(X)&~brave(X))=>(calm(X)<~>~funny(X))))&
(((~happy(mary)&brave(mary)))<=>(?[X]:((~funny(X)<~>funny(X)))))&
(![X]:(~strong(X)=>brave(X)))&
((?[X]:(~old(X)))<=>((~tall(lucy)&humble(lucy))))&
(![X]:((~calm(X)&~strong(X))=>(~patient(X)<~>kind(X))))&
(((~happy(mary)|curious(mary)))<=>((humble(lucy)&~patient(lucy))))&
((?[X]:((~humble(X)&quiet(X))))<=>(?[X]:(quiet(X))))&
(![X]:((tall(X)&funny(X))=>~generous(X)))&
(patient(alice))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:(curious(X)))&
(?[X]:(old(X)))&
(?[X]:((curious(X)|~happy(X))))&
((~humble(susan)|kind(susan))) | humble(lucy) | [
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7984493582714194245511407
% SZS output start Proof for 7984493582714194245511407
10. (brave(mary) & ~happy(mary)) <=> ? [X0] : (~funny(X0) <~> funny(X0)) [input p9]
14. (curious(mary) | ~happy(mary)) <=> (~patient(lucy) & humble(lucy)) [input p13]
25. ~humble(lucy) [input hypothesis]
59. ((brave(mary) & ~happy(mary)) | ! [X0] : ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (? [X0] : ((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~brave(mary) | happy(mary))) [nnf transformation 10]
60. ((brave(mary) & ~happy(mary)) | ! [X0] : ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (? [X0] : ((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~brave(mary) | happy(mary)) [flattening 59]
61. ((brave(mary) & ~happy(mary)) | ! [X0] : ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (? [X1] : ((~funny(X1) | funny(X1)) & (funny(X1) | ~funny(X1))) | ~brave(mary) | happy(mary)) [rectify 60]
62. ? [X1] : ((~funny(X1) | funny(X1)) & (funny(X1) | ~funny(X1))) => ((~funny(sK4) | funny(sK4)) & (funny(sK4) | ~funny(sK4))) [choice axiom]
63. ((brave(mary) & ~happy(mary)) | ! [X0] : ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(sK4) | funny(sK4)) & (funny(sK4) | ~funny(sK4))) | ~brave(mary) | happy(mary)) [skolemisation 61,62]
70. ((curious(mary) | ~happy(mary)) | (patient(lucy) | ~humble(lucy))) & ((~patient(lucy) & humble(lucy)) | (~curious(mary) & happy(mary))) [nnf transformation 14]
71. (curious(mary) | ~happy(mary) | patient(lucy) | ~humble(lucy)) & ((~patient(lucy) & humble(lucy)) | (~curious(mary) & happy(mary))) [flattening 70]
121. ~happy(mary) | funny(X0) | funny(X0) [cnf transformation 63]
122. ~happy(mary) | ~funny(X0) | ~funny(X0) [cnf transformation 63]
131. humble(lucy) | happy(mary) [cnf transformation 71]
149. ~humble(lucy) [cnf transformation 25]
150. ~happy(mary) | funny(X0) [duplicate literal removal 121]
151. ~happy(mary) | ~funny(X0) [duplicate literal removal 122]
220. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
221. ~funny(X0) <- (16) [avatar component clause 220]
228. 18 <=> ! [X0] : funny(X0) [avatar definition]
229. funny(X0) <- (18) [avatar component clause 228]
232. 19 <=> happy(mary) [avatar definition]
235. 16 | ~19 [avatar split clause 151,232,220]
236. 18 | ~19 [avatar split clause 150,232,228]
242. 21 <=> humble(lucy) [avatar definition]
267. 19 | 21 [avatar split clause 131,242,232]
317. ~21 [avatar split clause 149,242]
318. $false <- (16, 18) [subsumption resolution 221,229]
319. ~16 | ~18 [avatar contradiction clause 318]
324. $false [avatar sat refutation 235,236,267,317,319]
% SZS output end Proof for 7984493582714194245511407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or not funny then someone is not happy.
If john is both rich and funny then someone is either not happy or not tall.
Everyone who is patient is either not kind or not generous and vice versa.
Everyone who is old is strong or not humble and vice versa.
If someone is either curious or not old then someone is both strong and not patient.
If mary is either old or not tall then someone is brave.
Everyone who is not generous or old is not happy.
If someone is both quiet and not rich then someone is either patient or happy.
Everyone who is not rich or not happy is not rich and vice versa.
If someone is either generous or not calm then john is not rich or strong.
If someone is either tall or not calm then paul is not happy or quiet and vice versa.
Everyone who is not strong or wise is either wise or not strong and vice versa.
Everyone who is not kind is either not quiet or not patient and vice versa.
Everyone who is not rich is generous or not wise and vice versa.
If someone is both strong and not rich then someone is both calm and not quiet.
Everyone who is both not patient and funny is creative or funny and vice versa.
Mary is either quiet or not wise.
Mary is not creative.
Someone is not brave.
Someone is not humble or funny.
John is either not creative or creative.
Someone is strong or quiet.
Someone is quiet or not calm.
Lucy is not tall. | Mary is not wise. | entailment | ((?[X]:((funny(X)<~>~funny(X))))=>(?[X]:(~happy(X))))&
(((rich(john)&funny(john)))=>(?[X]:((~happy(X)<~>~tall(X)))))&
(![X]:(patient(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:(old(X)<=>(strong(X)|~humble(X))))&
((?[X]:((curious(X)<~>~old(X))))=>(?[X]:((strong(X)&~patient(X)))))&
(((old(mary)<~>~tall(mary)))=>(?[X]:(brave(X))))&
(![X]:((~generous(X)|old(X))=>~happy(X)))&
((?[X]:((quiet(X)&~rich(X))))=>(?[X]:((patient(X)<~>happy(X)))))&
(![X]:((~rich(X)|~happy(X))<=>~rich(X)))&
((?[X]:((generous(X)<~>~calm(X))))=>((~rich(john)|strong(john))))&
((?[X]:((tall(X)<~>~calm(X))))<=>((~happy(paul)|quiet(paul))))&
(![X]:((~strong(X)|wise(X))<=>(wise(X)<~>~strong(X))))&
(![X]:(~kind(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:(~rich(X)<=>(generous(X)|~wise(X))))&
((?[X]:((strong(X)&~rich(X))))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~patient(X)&funny(X))<=>(creative(X)|funny(X))))&
((quiet(mary)<~>~wise(mary)))&
(~creative(mary))&
(?[X]:(~brave(X)))&
(?[X]:((~humble(X)|funny(X))))&
((~creative(john)<~>creative(john)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((quiet(X)|~calm(X))))&
(~tall(lucy)) | ~wise(mary) | [
"p2",
"p3",
"p6",
"p8",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1594996588867003440618771
% SZS output start Proof for 1594996588867003440618771
3. ! [X0] : (patient(X0) <=> (~kind(X0) <~> ~generous(X0))) [input p2]
4. ! [X0] : (old(X0) <=> (~humble(X0) | strong(X0))) [input p3]
7. ! [X0] : ((old(X0) | ~generous(X0)) => ~happy(X0)) [input p6]
9. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> ~rich(X0)) [input p8]
12. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p11]
13. ! [X0] : (~kind(X0) <=> (~quiet(X0) <~> ~patient(X0))) [input p12]
14. ! [X0] : (~rich(X0) <=> (~wise(X0) | generous(X0))) [input p13]
17. quiet(mary) <~> ~wise(mary) [input p16]
25. wise(mary) [input hypothesis]
35. ! [X0] : (~happy(X0) | (~old(X0) & generous(X0))) [ennf transformation 7]
47. ! [X0] : ((patient(X0) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ~patient(X0))) [nnf transformation 3]
48. ! [X0] : ((old(X0) | (humble(X0) & ~strong(X0))) & ((~humble(X0) | strong(X0)) | ~old(X0))) [nnf transformation 4]
49. ! [X0] : ((old(X0) | (humble(X0) & ~strong(X0))) & (~humble(X0) | strong(X0) | ~old(X0))) [flattening 48]
61. ! [X0] : (((~happy(X0) | ~rich(X0)) | rich(X0)) & (~rich(X0) | (happy(X0) & rich(X0)))) [nnf transformation 9]
62. ! [X0] : ((~happy(X0) | ~rich(X0) | rich(X0)) & (~rich(X0) | (happy(X0) & rich(X0)))) [flattening 61]
69. ! [X0] : (((wise(X0) | ~strong(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (~wise(X0) & strong(X0)))) [nnf transformation 12]
70. ! [X0] : ((wise(X0) | ~strong(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (~wise(X0) & strong(X0)))) [flattening 69]
71. ! [X0] : ((~kind(X0) | ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | kind(X0))) [nnf transformation 13]
72. ! [X0] : ((~rich(X0) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | rich(X0))) [nnf transformation 14]
73. ! [X0] : ((~rich(X0) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | rich(X0))) [flattening 72]
79. (wise(mary) | ~quiet(mary)) & (~wise(mary) | quiet(mary)) [nnf transformation 17]
93. ~generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 47]
95. ~generous(X0) | patient(X0) | kind(X0) [cnf transformation 47]
98. ~strong(X0) | old(X0) [cnf transformation 49]
107. ~old(X0) | ~happy(X0) [cnf transformation 35]
111. ~rich(X0) | happy(X0) [cnf transformation 62]
124. strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 70]
127. ~quiet(X0) | ~patient(X0) | kind(X0) [cnf transformation 71]
130. ~quiet(X0) | ~kind(X0) | patient(X0) [cnf transformation 71]
131. ~wise(X0) | generous(X0) | rich(X0) [cnf transformation 73]
141. ~wise(mary) | quiet(mary) [cnf transformation 79]
151. wise(mary) [cnf transformation 25]
153. ~wise(X0) | strong(X0) [duplicate literal removal 124]
211. 13 <=> old(mary) [avatar definition]
213. old(mary) <- (13) [avatar component clause 211]
287. 30 <=> quiet(mary) [avatar definition]
288. quiet(mary) <- (30) [avatar component clause 287]
291. 31 <=> wise(mary) [avatar definition]
293. wise(mary) <- (31) [avatar component clause 291]
295. 30 | ~31 [avatar split clause 141,291,287]
323. 31 [avatar split clause 151,291]
328. strong(mary) <- (31) [resolution 153,293]
329. old(mary) <- (31) [resolution 328,98]
332. 13 | ~31 [avatar split clause 329,291,211]
333. ~happy(mary) <- (13) [resolution 213,107]
367. ~patient(mary) | kind(mary) <- (30) [resolution 127,288]
369. 40 <=> kind(mary) [avatar definition]
370. ~kind(mary) <- (~40) [avatar component clause 369]
371. kind(mary) <- (40) [avatar component clause 369]
373. 41 <=> patient(mary) [avatar definition]
374. patient(mary) <- (41) [avatar component clause 373]
375. ~patient(mary) <- (~41) [avatar component clause 373]
376. 40 | ~41 | ~30 [avatar split clause 367,287,373,369]
415. ~kind(mary) | patient(mary) <- (30) [resolution 130,288]
423. generous(mary) | rich(mary) <- (31) [resolution 131,293]
429. 47 <=> rich(mary) [avatar definition]
431. rich(mary) <- (47) [avatar component clause 429]
433. 48 <=> generous(mary) [avatar definition]
435. generous(mary) <- (48) [avatar component clause 433]
436. 47 | 48 | ~31 [avatar split clause 423,291,433,429]
439. patient(mary) | kind(mary) <- (48) [resolution 435,95]
442. kind(mary) <- (~41, 48) [subsumption resolution 439,375]
443. $false <- (~40, ~41, 48) [subsumption resolution 442,370]
444. 40 | 41 | ~48 [avatar contradiction clause 443]
447. happy(mary) <- (47) [resolution 431,111]
448. $false <- (13, 47) [subsumption resolution 447,333]
449. ~13 | ~47 [avatar contradiction clause 448]
450. 41 | ~40 | ~30 [avatar split clause 415,287,369,373]
456. ~kind(mary) | ~patient(mary) <- (48) [resolution 435,93]
458. ~patient(mary) <- (40, 48) [subsumption resolution 456,371]
459. $false <- (40, 41, 48) [subsumption resolution 458,374]
460. ~40 | ~41 | ~48 [avatar contradiction clause 459]
461. $false [avatar sat refutation 295,323,332,376,436,444,449,450,460]
% SZS output end Proof for 1594996588867003440618771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either not generous or not wise.
Everyone who is both curious and not creative is both not rich and old and vice versa.
Everyone who is either rich or not kind is old or not wise and vice versa.
Everyone who is both not patient and not wise is funny and vice versa.
Everyone who is not curious or funny is both not calm and wise.
Everyone who is old or not strong is tall.
Everyone who is either not old or not quiet is not curious.
If alice is wise or quiet then someone is either tall or curious.
Everyone who is not kind is both strong and calm.
Everyone who is not creative is not brave and vice versa.
Everyone who is both not quiet and not patient is patient or not calm.
Everyone who is humble or quiet is either old or not happy.
Everyone who is not funny is both rich and not wise.
Everyone who is not funny is funny or patient and vice versa.
Everyone who is not tall or happy is rich or strong.
John is not funny.
Someone is either not strong or not tall.
Someone is not tall or not brave.
Lucy is both happy and humble.
John is not calm or not old.
Susan is not curious or not strong. | Lucy is rich. | entailment | (![X]:(kind(X)=>(~generous(X)<~>~wise(X))))&
(![X]:((curious(X)&~creative(X))<=>(~rich(X)&old(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(old(X)|~wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>funny(X)))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)&wise(X))))&
(![X]:((old(X)|~strong(X))=>tall(X)))&
(![X]:((~old(X)<~>~quiet(X))=>~curious(X)))&
(((wise(alice)|quiet(alice)))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~kind(X)=>(strong(X)&calm(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~quiet(X)&~patient(X))=>(patient(X)|~calm(X))))&
(![X]:((humble(X)|quiet(X))=>(old(X)<~>~happy(X))))&
(![X]:(~funny(X)=>(rich(X)&~wise(X))))&
(![X]:(~funny(X)<=>(funny(X)|patient(X))))&
(![X]:((~tall(X)|happy(X))=>(rich(X)|strong(X))))&
(~funny(john))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((~tall(X)|~brave(X))))&
((happy(lucy)&humble(lucy)))&
((~calm(john)|~old(john)))&
((~curious(susan)|~strong(susan))) | rich(lucy) | [
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7026595619658833897660548
% SZS output start Proof for 7026595619658833897660548
4. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> funny(X0)) [input p3]
5. ! [X0] : ((funny(X0) | ~curious(X0)) => (wise(X0) & ~calm(X0))) [input p4]
13. ! [X0] : (~funny(X0) => (~wise(X0) & rich(X0))) [input p12]
22. ~rich(lucy) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~calm(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 5]
32. ! [X0] : ((~wise(X0) & rich(X0)) | funny(X0)) [ennf transformation 13]
40. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) | patient(X0)))) [nnf transformation 4]
41. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | wise(X0) | patient(X0))) [flattening 40]
69. ~wise(X0) | ~funny(X0) [cnf transformation 41]
73. wise(X0) | ~funny(X0) [cnf transformation 24]
91. rich(X0) | funny(X0) [cnf transformation 32]
106. ~rich(lucy) [cnf transformation 22]
110. ~funny(X0) [subsumption resolution 73,69]
132. rich(X0) [subsumption resolution 91,110]
170. $false [subsumption resolution 106,132]
% SZS output end Proof for 7026595619658833897660548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both not wise and not quiet and vice versa.
Everyone who is generous is both old and funny and vice versa.
If someone is not old then paul is either not kind or not quiet.
Everyone who is not strong or humble is kind or not humble.
If someone is either not humble or not brave then susan is either not strong or not patient and vice versa.
Everyone who is both creative and not generous is strong.
Everyone who is both wise and not creative is not generous or not quiet.
If alice is brave or patient then john is not humble or not generous and vice versa.
Everyone who is both strong and not tall is funny or not tall and vice versa.
If someone is not calm then someone is not kind or not generous and vice versa.
Everyone who is creative or calm is kind.
Everyone who is either calm or tall is both not old and not curious.
If someone is either not patient or not funny then someone is funny or humble and vice versa.
If lucy is creative or not humble then someone is kind.
If someone is either not strong or not curious then lucy is either happy or not kind and vice versa.
Everyone who is rich or not creative is brave or not rich and vice versa.
Someone is creative.
Someone is quiet.
Fred is not generous or not patient.
Someone is kind.
Someone is not humble or humble.
Lucy is not brave.
Someone is old or not creative. | Alice is brave. | neutral | (![X]:(wise(X)<=>(~wise(X)&~quiet(X))))&
(![X]:(generous(X)<=>(old(X)&funny(X))))&
((?[X]:(~old(X)))=>((~kind(paul)<~>~quiet(paul))))&
(![X]:((~strong(X)|humble(X))=>(kind(X)|~humble(X))))&
((?[X]:((~humble(X)<~>~brave(X))))<=>((~strong(susan)<~>~patient(susan))))&
(![X]:((creative(X)&~generous(X))=>strong(X)))&
(![X]:((wise(X)&~creative(X))=>(~generous(X)|~quiet(X))))&
(((brave(alice)|patient(alice)))<=>((~humble(john)|~generous(john))))&
(![X]:((strong(X)&~tall(X))<=>(funny(X)|~tall(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((creative(X)|calm(X))=>kind(X)))&
(![X]:((calm(X)<~>tall(X))=>(~old(X)&~curious(X))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((funny(X)|humble(X)))))&
(((creative(lucy)|~humble(lucy)))=>(?[X]:(kind(X))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>((happy(lucy)<~>~kind(lucy))))&
(![X]:((rich(X)|~creative(X))<=>(brave(X)|~rich(X))))&
(?[X]:(creative(X)))&
(?[X]:(quiet(X)))&
((~generous(fred)|~patient(fred)))&
(?[X]:(kind(X)))&
(?[X]:((~humble(X)|humble(X))))&
(~brave(lucy))&
(?[X]:((old(X)|~creative(X)))) | brave(alice) | [] | null | 0 |
Everyone who is not rich or happy is kind and vice versa.
If someone is kind then lucy is either strong or tall.
If someone is not strong or funny then someone is not humble or not happy and vice versa.
Everyone who is strong or old is either not old or funny.
If someone is brave or not calm then someone is not quiet or happy.
Everyone who is humble or calm is not creative and vice versa.
Everyone who is strong is not old.
If someone is both patient and strong then someone is either brave or not humble.
Everyone who is not generous or not patient is not calm.
Everyone who is generous or not curious is both happy and not creative and vice versa.
If john is not happy or not brave then someone is tall or calm.
If alice is brave or curious then lucy is either not tall or calm.
Everyone who is either not calm or humble is not creative or creative and vice versa.
Everyone who is both tall and not strong is both tall and not generous.
Everyone who is both calm and rich is not old or generous and vice versa.
Everyone who is either kind or not wise is wise and vice versa.
Alice is both humble and patient.
Someone is not funny or creative.
Someone is creative or wise.
Alice is tall or not calm.
Someone is both rich and wise.
Someone is patient.
Someone is both not generous and funny. | Alice is not funny. | entailment | (![X]:((~rich(X)|happy(X))<=>kind(X)))&
((?[X]:(kind(X)))=>((strong(lucy)<~>tall(lucy))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((strong(X)|old(X))=>(~old(X)<~>funny(X))))&
((?[X]:((brave(X)|~calm(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((humble(X)|calm(X))<=>~creative(X)))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((~generous(X)|~patient(X))=>~calm(X)))&
(![X]:((generous(X)|~curious(X))<=>(happy(X)&~creative(X))))&
(((~happy(john)|~brave(john)))=>(?[X]:((tall(X)|calm(X)))))&
(((brave(alice)|curious(alice)))=>((~tall(lucy)<~>calm(lucy))))&
(![X]:((~calm(X)<~>humble(X))<=>(~creative(X)|creative(X))))&
(![X]:((tall(X)&~strong(X))=>(tall(X)&~generous(X))))&
(![X]:((calm(X)&rich(X))<=>(~old(X)|generous(X))))&
(![X]:((kind(X)<~>~wise(X))<=>wise(X)))&
((humble(alice)&patient(alice)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((creative(X)|wise(X))))&
((tall(alice)|~calm(alice)))&
(?[X]:((rich(X)&wise(X))))&
(?[X]:(patient(X)))&
(?[X]:((~generous(X)&funny(X)))) | ~funny(alice) | [
"p1",
"p3",
"p5",
"p6",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5247511804328289876150016
% SZS output start Proof for 5247511804328289876150016
2. ? [X0] : kind(X0) => (strong(lucy) <~> tall(lucy)) [input p1]
4. ! [X0] : ((old(X0) | strong(X0)) => (~old(X0) <~> funny(X0))) [input p3]
6. ! [X0] : ((calm(X0) | humble(X0)) <=> ~creative(X0)) [input p5]
7. ! [X0] : (strong(X0) => ~old(X0)) [input p6]
9. ! [X0] : ((~patient(X0) | ~generous(X0)) => ~calm(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | generous(X0)) <=> (~creative(X0) & happy(X0))) [input p9]
12. (curious(alice) | brave(alice)) => (~tall(lucy) <~> calm(lucy)) [input p11]
13. ! [X0] : ((~calm(X0) <~> humble(X0)) <=> (creative(X0) | ~creative(X0))) [input p12]
14. ! [X0] : ((~strong(X0) & tall(X0)) => (~generous(X0) & tall(X0))) [input p13]
15. ! [X0] : ((rich(X0) & calm(X0)) <=> (generous(X0) | ~old(X0))) [input p14]
16. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> wise(X0)) [input p15]
20. ~calm(alice) | tall(alice) [input p19]
24. funny(alice) [input hypothesis]
29. (strong(lucy) <~> tall(lucy)) | ! [X0] : ~kind(X0) [ennf transformation 2]
30. ! [X0] : ((~old(X0) <~> funny(X0)) | (~old(X0) & ~strong(X0))) [ennf transformation 4]
31. ! [X0] : (~old(X0) | ~strong(X0)) [ennf transformation 7]
33. ! [X0] : (~calm(X0) | (patient(X0) & generous(X0))) [ennf transformation 9]
35. (~tall(lucy) <~> calm(lucy)) | (~curious(alice) & ~brave(alice)) [ennf transformation 12]
36. ! [X0] : ((~generous(X0) & tall(X0)) | (strong(X0) | ~tall(X0))) [ennf transformation 14]
37. ! [X0] : ((~generous(X0) & tall(X0)) | strong(X0) | ~tall(X0)) [flattening 36]
40. ((~tall(lucy) | ~strong(lucy)) & (tall(lucy) | strong(lucy))) | ! [X0] : ~kind(X0) [nnf transformation 29]
46. ! [X0] : (((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | (~old(X0) & ~strong(X0))) [nnf transformation 30]
47. ! [X0] : (((calm(X0) | humble(X0)) | creative(X0)) & (~creative(X0) | (~calm(X0) & ~humble(X0)))) [nnf transformation 6]
48. ! [X0] : ((calm(X0) | humble(X0) | creative(X0)) & (~creative(X0) | (~calm(X0) & ~humble(X0)))) [flattening 47]
53. ! [X0] : (((~curious(X0) | generous(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (curious(X0) & ~generous(X0)))) [nnf transformation 10]
54. ! [X0] : ((~curious(X0) | generous(X0) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | (curious(X0) & ~generous(X0)))) [flattening 53]
57. ((~calm(lucy) | tall(lucy)) & (calm(lucy) | ~tall(lucy))) | (~curious(alice) & ~brave(alice)) [nnf transformation 35]
58. ! [X0] : ((((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))))) [flattening 58]
60. ! [X0] : (((rich(X0) & calm(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (~rich(X0) | ~calm(X0)))) [nnf transformation 15]
61. ! [X0] : (((rich(X0) & calm(X0)) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | ~rich(X0) | ~calm(X0))) [flattening 60]
62. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | ~wise(X0)) & (wise(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 16]
76. tall(lucy) | strong(lucy) | ~kind(X0) [cnf transformation 40]
77. ~tall(lucy) | ~strong(lucy) | ~kind(X0) [cnf transformation 40]
84. ~funny(X0) | old(X0) | ~strong(X0) [cnf transformation 46]
88. creative(X0) | humble(X0) | calm(X0) [cnf transformation 48]
89. ~old(X0) | ~strong(X0) [cnf transformation 31]
92. ~calm(X0) | generous(X0) [cnf transformation 33]
97. ~creative(X0) | curious(X0) [cnf transformation 54]
102. calm(lucy) | ~tall(lucy) | ~curious(alice) [cnf transformation 57]
104. ~calm(lucy) | tall(lucy) | ~curious(alice) [cnf transformation 57]
109. ~humble(X0) | calm(X0) | creative(X0) [cnf transformation 59]
112. ~generous(X0) | strong(X0) | ~tall(X0) [cnf transformation 37]
114. calm(X0) | old(X0) [cnf transformation 61]
119. wise(X0) | kind(X0) | wise(X0) [cnf transformation 62]
120. ~wise(X0) | kind(X0) | ~wise(X0) [cnf transformation 62]
126. ~calm(alice) | tall(alice) [cnf transformation 20]
132. funny(alice) [cnf transformation 24]
133. wise(X0) | kind(X0) [duplicate literal removal 119]
134. ~wise(X0) | kind(X0) [duplicate literal removal 120]
137. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
138. ~kind(X0) <- (1) [avatar component clause 137]
140. 2 <=> strong(lucy) [avatar definition]
141. strong(lucy) <- (2) [avatar component clause 140]
144. 3 <=> tall(lucy) [avatar definition]
147. 1 | ~2 | ~3 [avatar split clause 77,144,140,137]
148. 1 | 2 | 3 [avatar split clause 76,144,140,137]
213. 19 <=> curious(alice) [avatar definition]
215. ~curious(alice) <- (~19) [avatar component clause 213]
217. 20 <=> calm(lucy) [avatar definition]
218. calm(lucy) <- (20) [avatar component clause 217]
219. ~calm(lucy) <- (~20) [avatar component clause 217]
220. ~19 | 3 | ~20 [avatar split clause 104,217,144,213]
226. ~19 | ~3 | 20 [avatar split clause 102,217,144,213]
228. creative(X0) | calm(X0) [subsumption resolution 109,88]
230. kind(X0) [subsumption resolution 133,134]
250. 26 <=> tall(alice) [avatar definition]
252. tall(alice) <- (26) [avatar component clause 250]
254. 27 <=> calm(alice) [avatar definition]
255. calm(alice) <- (27) [avatar component clause 254]
257. 26 | ~27 [avatar split clause 126,254,250]
263. old(lucy) <- (~20) [resolution 114,219]
266. ~strong(lucy) <- (~20) [resolution 263,89]
267. $false <- (2, ~20) [subsumption resolution 266,141]
268. ~2 | 20 [avatar contradiction clause 267]
271. generous(lucy) <- (20) [resolution 218,92]
284. curious(X0) | calm(X0) [resolution 228,97]
295. old(alice) | ~strong(alice) [resolution 84,132]
302. strong(lucy) | ~tall(lucy) <- (20) [resolution 112,271]
317. calm(alice) <- (~19) [resolution 284,215]
321. 27 | 19 [avatar split clause 317,213,254]
322. ~strong(alice) [subsumption resolution 295,89]
324. generous(alice) <- (27) [resolution 255,92]
325. strong(alice) | ~tall(alice) <- (27) [resolution 324,112]
330. ~tall(alice) <- (27) [subsumption resolution 325,322]
331. $false <- (26, 27) [subsumption resolution 330,252]
332. ~26 | ~27 [avatar contradiction clause 331]
333. ~3 | 2 | ~20 [avatar split clause 302,217,140,144]
334. $false <- (1) [subsumption resolution 138,230]
335. ~1 [avatar contradiction clause 334]
336. $false [avatar sat refutation 147,148,220,226,257,268,321,332,333,335]
% SZS output end Proof for 5247511804328289876150016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either rich or not happy then fred is either not wise or brave. Everyone who is not quiet is both not brave and not creative and vice versa. Everyone who is brave is not strong or wise. Everyone who is either quiet or wise is not humble or quiet. If someone is either not generous or brave then fred is happy or generous. Everyone who is either curious or not creative is not generous. Everyone who is either strong or not calm is both not kind and not generous and vice versa. If fred is either creative or calm then someone is both not quiet and not patient. Everyone who is both not humble and not creative is both generous and not strong. Everyone who is both not wise and not brave is either happy or generous. Everyone who is humble or not creative is both rich and not calm. If someone is both not generous and generous then someone is not old or patient and vice versa. Everyone who is both not wise and wise is both creative and curious. Everyone who is rich or not happy is both not patient and not wise. If someone is both curious and strong then alice is either happy or not generous. If alice is both not old and brave then mary is not curious and vice versa. Someone is kind or strong. Lucy is either kind or not humble. Someone is both generous and not funny. John is either not rich or patient. Susan is both generous and not quiet. Someone is both not creative and not funny. Someone is kind or rich. Someone is either not brave or happy. | John is humble. | contradiction | (((rich(john)<~>~happy(john)))=>((~wise(fred)<~>brave(fred))))&
(![X]:(~quiet(X)<=>(~brave(X)&~creative(X))))&
(![X]:(brave(X)=>(~strong(X)|wise(X))))&
(![X]:((quiet(X)<~>wise(X))=>(~humble(X)|quiet(X))))&
((?[X]:((~generous(X)<~>brave(X))))=>((happy(fred)|generous(fred))))&
(![X]:((curious(X)<~>~creative(X))=>~generous(X)))&
(![X]:((strong(X)<~>~calm(X))<=>(~kind(X)&~generous(X))))&
(((creative(fred)<~>calm(fred)))=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((~humble(X)&~creative(X))=>(generous(X)&~strong(X))))&
(![X]:((~wise(X)&~brave(X))=>(happy(X)<~>generous(X))))&
(![X]:((humble(X)|~creative(X))=>(rich(X)&~calm(X))))&
((?[X]:((~generous(X)&generous(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((~wise(X)&wise(X))=>(creative(X)&curious(X))))&
(![X]:((rich(X)|~happy(X))=>(~patient(X)&~wise(X))))&
((?[X]:((curious(X)&strong(X))))=>((happy(alice)<~>~generous(alice))))&
(((~old(alice)&brave(alice)))<=>(~curious(mary)))&
(?[X]:((kind(X)|strong(X))))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((generous(X)&~funny(X))))&
((~rich(john)<~>patient(john)))&
((generous(susan)&~quiet(susan)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:((~brave(X)<~>happy(X)))) | humble(john) | [
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 781194997455015133359275
% SZS output start Proof for 781194997455015133359275
11. ! [X0] : ((~creative(X0) | humble(X0)) => (~calm(X0) & rich(X0))) [input p10]
14. ! [X0] : ((~happy(X0) | rich(X0)) => (~wise(X0) & ~patient(X0))) [input p13]
20. ~rich(john) <~> patient(john) [input p19]
25. humble(john) [input hypothesis]
42. ! [X0] : ((~calm(X0) & rich(X0)) | (creative(X0) & ~humble(X0))) [ennf transformation 11]
45. ! [X0] : ((~wise(X0) & ~patient(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 14]
72. (~patient(john) | rich(john)) & (patient(john) | ~rich(john)) [nnf transformation 20]
108. ~humble(X0) | rich(X0) [cnf transformation 42]
119. ~patient(X0) | ~rich(X0) [cnf transformation 45]
132. patient(john) | ~rich(john) [cnf transformation 72]
133. ~patient(john) | rich(john) [cnf transformation 72]
140. humble(john) [cnf transformation 25]
147. 2 <=> rich(john) [avatar definition]
148. ~rich(john) <- (~2) [avatar component clause 147]
259. ~patient(john) [subsumption resolution 133,119]
260. ~rich(john) [subsumption resolution 132,259]
261. ~2 [avatar split clause 260,147]
281. rich(john) [resolution 108,140]
282. $false <- (~2) [subsumption resolution 281,148]
283. 2 [avatar contradiction clause 282]
284. $false [avatar sat refutation 261,283]
% SZS output end Proof for 781194997455015133359275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then someone is not quiet. Everyone who is not calm or tall is not patient or not creative and vice versa. If alice is not rich then someone is not calm. Everyone who is not wise is not brave. Everyone who is either not old or patient is rich and vice versa. If someone is either not humble or not curious then john is both old and not creative and vice versa. If someone is kind or not quiet then someone is not brave or wise. Everyone who is either calm or wise is old and vice versa. Everyone who is both not old and brave is both rich and not tall and vice versa. If mary is both tall and generous then someone is calm or not creative and vice versa. If fred is humble or calm then susan is both not rich and happy and vice versa. Everyone who is both creative and calm is not curious or not kind and vice versa. Everyone who is both funny and patient is both funny and not wise and vice versa. If someone is not curious then fred is happy or not creative. Everyone who is patient or not tall is curious or calm. Everyone who is either brave or not strong is both rich and not patient and vice versa. Susan is not humble or not patient. Mary is not calm. Someone is not brave. John is either not wise or calm. Lucy is both not generous and happy. Alice is creative or not wise. Alice is either wise or not patient. Alice is either tall or rich. | Mary is humble. | entailment | ((?[X]:(tall(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~calm(X)|tall(X))<=>(~patient(X)|~creative(X))))&
((~rich(alice))=>(?[X]:(~calm(X))))&
(![X]:(~wise(X)=>~brave(X)))&
(![X]:((~old(X)<~>patient(X))<=>rich(X)))&
((?[X]:((~humble(X)<~>~curious(X))))<=>((old(john)&~creative(john))))&
((?[X]:((kind(X)|~quiet(X))))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((calm(X)<~>wise(X))<=>old(X)))&
(![X]:((~old(X)&brave(X))<=>(rich(X)&~tall(X))))&
(((tall(mary)&generous(mary)))<=>(?[X]:((calm(X)|~creative(X)))))&
(((humble(fred)|calm(fred)))<=>((~rich(susan)&happy(susan))))&
(![X]:((creative(X)&calm(X))<=>(~curious(X)|~kind(X))))&
(![X]:((funny(X)&patient(X))<=>(funny(X)&~wise(X))))&
((?[X]:(~curious(X)))=>((happy(fred)|~creative(fred))))&
(![X]:((patient(X)|~tall(X))=>(curious(X)|calm(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(rich(X)&~patient(X))))&
((~humble(susan)|~patient(susan)))&
(~calm(mary))&
(?[X]:(~brave(X)))&
((~wise(john)<~>calm(john)))&
((~generous(lucy)&happy(lucy)))&
((creative(alice)|~wise(alice)))&
((wise(alice)<~>~patient(alice)))&
((tall(alice)<~>rich(alice))) | humble(mary) | [
"p5",
"p7",
"p11",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6454090846834859751628991
% SZS output start Proof for 6454090846834859751628991
6. ? [X0] : (~humble(X0) <~> ~curious(X0)) <=> (~creative(john) & old(john)) [input p5]
8. ! [X0] : ((calm(X0) <~> wise(X0)) <=> old(X0)) [input p7]
12. ! [X0] : ((calm(X0) & creative(X0)) <=> (~kind(X0) | ~curious(X0))) [input p11]
18. ~calm(mary) [input p17]
20. ~wise(john) <~> calm(john) [input p19]
25. ~humble(mary) [input hypothesis]
44. (? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (creative(john) | ~old(john))) & ((~creative(john) & old(john)) | ! [X0] : ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) [nnf transformation 6]
45. (? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | creative(john) | ~old(john)) & ((~creative(john) & old(john)) | ! [X0] : ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) [flattening 44]
46. (? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | creative(john) | ~old(john)) & ((~creative(john) & old(john)) | ! [X1] : ((~humble(X1) | curious(X1)) & (~curious(X1) | humble(X1)))) [rectify 45]
47. ? [X0] : ((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) => ((curious(sK2) | humble(sK2)) & (~curious(sK2) | ~humble(sK2))) [choice axiom]
48. (((curious(sK2) | humble(sK2)) & (~curious(sK2) | ~humble(sK2))) | creative(john) | ~old(john)) & ((~creative(john) & old(john)) | ! [X1] : ((~humble(X1) | curious(X1)) & (~curious(X1) | humble(X1)))) [skolemisation 46,47]
52. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ~old(X0)) & (old(X0) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [nnf transformation 8]
62. ! [X0] : (((calm(X0) & creative(X0)) | (kind(X0) & curious(X0))) & ((~kind(X0) | ~curious(X0)) | (~calm(X0) | ~creative(X0)))) [nnf transformation 12]
63. ! [X0] : (((calm(X0) & creative(X0)) | (kind(X0) & curious(X0))) & (~kind(X0) | ~curious(X0) | ~calm(X0) | ~creative(X0))) [flattening 62]
70. (~calm(john) | wise(john)) & (calm(john) | ~wise(john)) [nnf transformation 20]
84. old(john) | ~curious(X1) | humble(X1) [cnf transformation 48]
94. ~old(X0) | calm(X0) | wise(X0) [cnf transformation 52]
95. ~old(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 52]
113. curious(X0) | calm(X0) [cnf transformation 63]
129. ~calm(mary) [cnf transformation 18]
131. calm(john) | ~wise(john) [cnf transformation 70]
132. ~calm(john) | wise(john) [cnf transformation 70]
140. ~humble(mary) [cnf transformation 25]
159. 5 <=> old(john) [avatar definition]
160. old(john) <- (5) [avatar component clause 159]
181. 10 <=> ! [X1] : (~curious(X1) | humble(X1)) [avatar definition]
182. ~curious(X1) | humble(X1) <- (10) [avatar component clause 181]
185. 10 | 5 [avatar split clause 84,159,181]
256. 26 <=> wise(john) [avatar definition]
258. wise(john) <- (26) [avatar component clause 256]
260. 27 <=> calm(john) [avatar definition]
261. calm(john) <- (27) [avatar component clause 260]
263. 26 | ~27 [avatar split clause 132,260,256]
264. ~26 | 27 [avatar split clause 131,260,256]
297. humble(X0) | calm(X0) <- (10) [resolution 182,113]
300. calm(mary) <- (10) [resolution 297,140]
302. $false <- (10) [subsumption resolution 300,129]
303. ~10 [avatar contradiction clause 302]
349. calm(john) | wise(john) <- (5) [resolution 94,160]
354. 26 | 27 | ~5 [avatar split clause 349,159,260,256]
360. ~calm(john) | ~wise(john) <- (5) [resolution 95,160]
362. ~wise(john) <- (5, 27) [subsumption resolution 360,261]
363. $false <- (5, 26, 27) [subsumption resolution 362,258]
364. ~5 | ~26 | ~27 [avatar contradiction clause 363]
365. $false [avatar sat refutation 185,263,264,303,354,364]
% SZS output end Proof for 6454090846834859751628991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not creative then mary is not wise or tall and vice versa.
Everyone who is either not happy or not patient is either happy or not brave.
If someone is not strong or not tall then john is either not curious or not tall.
Everyone who is both old and calm is either not curious or rich and vice versa.
Everyone who is either not strong or patient is kind and vice versa.
If lucy is quiet or not wise then someone is either not calm or quiet.
Everyone who is happy or not humble is both not rich and not generous.
If paul is not rich then paul is curious.
If someone is either not rich or calm then lucy is not calm or wise.
Everyone who is rich or tall is either old or humble.
If someone is funny or humble then alice is both humble and calm.
If someone is not quiet then mary is both rich and patient and vice versa.
If someone is calm then someone is both creative and calm.
Everyone who is happy is not tall or not brave and vice versa.
If someone is both not tall and happy then paul is not old and vice versa.
Everyone who is happy or patient is either not tall or brave.
Someone is both not strong and calm.
Someone is not kind or creative.
Paul is creative or strong.
John is not curious.
Paul is both not creative and not generous.
Someone is both not wise and happy.
Someone is both not creative and kind.
Mary is either not rich or not generous. | Paul is not quiet. | contradiction | ((?[X]:((kind(X)|~creative(X))))<=>((~wise(mary)|tall(mary))))&
(![X]:((~happy(X)<~>~patient(X))=>(happy(X)<~>~brave(X))))&
((?[X]:((~strong(X)|~tall(X))))=>((~curious(john)<~>~tall(john))))&
(![X]:((old(X)&calm(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((~strong(X)<~>patient(X))<=>kind(X)))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:((happy(X)|~humble(X))=>(~rich(X)&~generous(X))))&
((~rich(paul))=>(curious(paul)))&
((?[X]:((~rich(X)<~>calm(X))))=>((~calm(lucy)|wise(lucy))))&
(![X]:((rich(X)|tall(X))=>(old(X)<~>humble(X))))&
((?[X]:((funny(X)|humble(X))))=>((humble(alice)&calm(alice))))&
((?[X]:(~quiet(X)))<=>((rich(mary)&patient(mary))))&
((?[X]:(calm(X)))=>(?[X]:((creative(X)&calm(X)))))&
(![X]:(happy(X)<=>(~tall(X)|~brave(X))))&
((?[X]:((~tall(X)&happy(X))))<=>(~old(paul)))&
(![X]:((happy(X)|patient(X))=>(~tall(X)<~>brave(X))))&
(?[X]:((~strong(X)&calm(X))))&
(?[X]:((~kind(X)|creative(X))))&
((creative(paul)|strong(paul)))&
(~curious(john))&
((~creative(paul)&~generous(paul)))&
(?[X]:((~wise(X)&happy(X))))&
(?[X]:((~creative(X)&kind(X))))&
((~rich(mary)<~>~generous(mary))) | ~quiet(paul) | [
"p1",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6543173834799981650111671
% SZS output start Proof for 6543173834799981650111671
2. ! [X0] : ((~happy(X0) <~> ~patient(X0)) => (happy(X0) <~> ~brave(X0))) [input p1]
7. ! [X0] : ((~humble(X0) | happy(X0)) => (~generous(X0) & ~rich(X0))) [input p6]
12. ? [X0] : ~quiet(X0) <=> (patient(mary) & rich(mary)) [input p11]
14. ! [X0] : (happy(X0) <=> (~brave(X0) | ~tall(X0))) [input p13]
25. ~quiet(paul) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> ~brave(X0)) | (~happy(X0) <=> ~patient(X0))) [ennf transformation 2]
31. ! [X0] : ((~generous(X0) & ~rich(X0)) | (humble(X0) & ~happy(X0))) [ennf transformation 7]
44. ! [X0] : (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) [nnf transformation 28]
54. (? [X0] : ~quiet(X0) | (~patient(mary) | ~rich(mary))) & ((patient(mary) & rich(mary)) | ! [X0] : quiet(X0)) [nnf transformation 12]
55. (? [X0] : ~quiet(X0) | ~patient(mary) | ~rich(mary)) & ((patient(mary) & rich(mary)) | ! [X0] : quiet(X0)) [flattening 54]
56. (? [X0] : ~quiet(X0) | ~patient(mary) | ~rich(mary)) & ((patient(mary) & rich(mary)) | ! [X1] : quiet(X1)) [rectify 55]
57. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
58. (~quiet(sK2) | ~patient(mary) | ~rich(mary)) & ((patient(mary) & rich(mary)) | ! [X1] : quiet(X1)) [skolemisation 56,57]
62. ! [X0] : ((happy(X0) | (brave(X0) & tall(X0))) & ((~brave(X0) | ~tall(X0)) | ~happy(X0))) [nnf transformation 14]
63. ! [X0] : ((happy(X0) | (brave(X0) & tall(X0))) & (~brave(X0) | ~tall(X0) | ~happy(X0))) [flattening 62]
82. ~brave(X0) | happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 44]
104. ~rich(X0) | ~happy(X0) [cnf transformation 31]
117. rich(mary) | quiet(X1) [cnf transformation 58]
118. patient(mary) | quiet(X1) [cnf transformation 58]
124. brave(X0) | happy(X0) [cnf transformation 63]
145. ~quiet(paul) [cnf transformation 25]
146. ~brave(X0) | happy(X0) | ~patient(X0) [duplicate literal removal 82]
248. 23 <=> rich(mary) [avatar definition]
249. rich(mary) <- (23) [avatar component clause 248]
252. 24 <=> patient(mary) [avatar definition]
253. patient(mary) <- (24) [avatar component clause 252]
261. 26 <=> ! [X1] : quiet(X1) [avatar definition]
262. quiet(X1) <- (26) [avatar component clause 261]
263. 26 | 24 [avatar split clause 118,252,261]
264. 26 | 23 [avatar split clause 117,248,261]
345. $false <- (26) [resolution 262,145]
350. ~26 [avatar contradiction clause 345]
354. ~happy(mary) <- (23) [resolution 249,104]
443. happy(X0) | ~patient(X0) | happy(X0) [resolution 146,124]
445. ~patient(X0) | happy(X0) [duplicate literal removal 443]
518. happy(mary) <- (24) [resolution 445,253]
521. $false <- (23, 24) [subsumption resolution 518,354]
522. ~23 | ~24 [avatar contradiction clause 521]
523. $false [avatar sat refutation 263,264,350,522]
% SZS output end Proof for 6543173834799981650111671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both tall and rich.
If someone is either patient or funny then fred is both not old and not quiet.
Everyone who is either old or curious is either strong or not funny.
Everyone who is not rich or old is not strong.
Everyone who is either not creative or funny is either generous or funny and vice versa.
Everyone who is not patient is not creative and vice versa.
If someone is either not funny or not calm then fred is wise or generous and vice versa.
If someone is both not generous and not patient then someone is both not wise and brave and vice versa.
If john is wise then alice is either not creative or humble.
Everyone who is calm or not funny is kind or not humble and vice versa.
If alice is both not generous and brave then fred is not brave.
Everyone who is not curious or funny is either not patient or not humble.
Everyone who is both not curious and not funny is not tall and vice versa.
If someone is not rich or not kind then john is either not patient or not old and vice versa.
If alice is either not brave or tall then someone is strong and vice versa.
Everyone who is rich is brave or happy and vice versa.
Susan is both humble and not old.
Alice is either creative or funny.
Mary is both not strong and not old.
Lucy is not tall.
Mary is either not tall or strong.
John is not tall.
Paul is not brave or brave.
Someone is both not patient and wise. | Mary is not creative. | entailment | (![X]:(~humble(X)=>(tall(X)&rich(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((~old(fred)&~quiet(fred))))&
(![X]:((old(X)<~>curious(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~rich(X)|old(X))=>~strong(X)))&
(![X]:((~creative(X)<~>funny(X))<=>(generous(X)<~>funny(X))))&
(![X]:(~patient(X)<=>~creative(X)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((wise(fred)|generous(fred))))&
((?[X]:((~generous(X)&~patient(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
((wise(john))=>((~creative(alice)<~>humble(alice))))&
(![X]:((calm(X)|~funny(X))<=>(kind(X)|~humble(X))))&
(((~generous(alice)&brave(alice)))=>(~brave(fred)))&
(![X]:((~curious(X)|funny(X))=>(~patient(X)<~>~humble(X))))&
(![X]:((~curious(X)&~funny(X))<=>~tall(X)))&
((?[X]:((~rich(X)|~kind(X))))<=>((~patient(john)<~>~old(john))))&
(((~brave(alice)<~>tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:(rich(X)<=>(brave(X)|happy(X))))&
((humble(susan)&~old(susan)))&
((creative(alice)<~>funny(alice)))&
((~strong(mary)&~old(mary)))&
(~tall(lucy))&
((~tall(mary)<~>strong(mary)))&
(~tall(john))&
((~brave(paul)|brave(paul)))&
(?[X]:((~patient(X)&wise(X)))) | ~creative(mary) | [
"p0",
"p5",
"p11",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5941335000327271238265345
% SZS output start Proof for 5941335000327271238265345
1. ! [X0] : (~humble(X0) => (rich(X0) & tall(X0))) [input p0]
6. ! [X0] : (~patient(X0) <=> ~creative(X0)) [input p5]
12. ! [X0] : ((funny(X0) | ~curious(X0)) => (~patient(X0) <~> ~humble(X0))) [input p11]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> ~tall(X0)) [input p12]
19. ~old(mary) & ~strong(mary) [input p18]
21. ~tall(mary) <~> strong(mary) [input p20]
25. creative(mary) [input hypothesis]
28. ! [X0] : ((rich(X0) & tall(X0)) | humble(X0)) [ennf transformation 1]
35. ! [X0] : ((~patient(X0) <~> ~humble(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 12]
39. ! [X0] : ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))) [nnf transformation 6]
53. ! [X0] : (((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | (~funny(X0) & curious(X0))) [nnf transformation 35]
54. ! [X0] : (((~funny(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) | curious(X0)))) [nnf transformation 13]
55. ! [X0] : (((~funny(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | funny(X0) | curious(X0))) [flattening 54]
67. (~strong(mary) | tall(mary)) & (strong(mary) | ~tall(mary)) [nnf transformation 21]
70. tall(X0) | humble(X0) [cnf transformation 28]
88. ~creative(X0) | patient(X0) [cnf transformation 39]
107. ~patient(X0) | ~humble(X0) | curious(X0) [cnf transformation 53]
112. ~curious(X0) | tall(X0) [cnf transformation 55]
131. ~strong(mary) [cnf transformation 19]
134. strong(mary) | ~tall(mary) [cnf transformation 67]
140. creative(mary) [cnf transformation 25]
289. ~tall(mary) [subsumption resolution 134,131]
292. humble(mary) [resolution 70,289]
296. patient(mary) [resolution 88,140]
366. ~humble(mary) | curious(mary) [resolution 107,296]
369. curious(mary) [subsumption resolution 366,292]
449. tall(mary) [resolution 369,112]
450. $false [subsumption resolution 449,289]
% SZS output end Proof for 5941335000327271238265345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is brave then susan is both not tall and not happy and vice versa. Everyone who is not tall is both wise and generous. If alice is curious then someone is curious or not tall and vice versa. If susan is both not funny and not calm then someone is either not curious or not strong and vice versa. If someone is either not creative or generous then paul is tall or patient. Everyone who is rich is humble. Everyone who is both rich and generous is not old or not quiet. Everyone who is wise is both not wise and old and vice versa. Everyone who is both not happy and not funny is not funny or patient and vice versa. Everyone who is not creative is not curious or not old and vice versa. If susan is both not strong and not quiet then someone is either funny or not happy and vice versa. If someone is funny or calm then alice is either creative or not brave and vice versa. Everyone who is not old is kind. Everyone who is not generous is tall or not strong and vice versa. If someone is old or not brave then susan is not patient or not kind and vice versa. Someone is either not generous or brave. Someone is funny. Susan is funny. Alice is either calm or not strong. Paul is both not funny and not curious. Someone is either not curious or not humble. Lucy is both happy and kind. Lucy is either humble or not calm. | Susan is creative. | contradiction | ((brave(alice))<=>((~tall(susan)&~happy(susan))))&
(![X]:(~tall(X)=>(wise(X)&generous(X))))&
((curious(alice))<=>(?[X]:((curious(X)|~tall(X)))))&
(((~funny(susan)&~calm(susan)))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:((~creative(X)<~>generous(X))))=>((tall(paul)|patient(paul))))&
(![X]:(rich(X)=>humble(X)))&
(![X]:((rich(X)&generous(X))=>(~old(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~wise(X)&old(X))))&
(![X]:((~happy(X)&~funny(X))<=>(~funny(X)|patient(X))))&
(![X]:(~creative(X)<=>(~curious(X)|~old(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((creative(alice)<~>~brave(alice))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~generous(X)<=>(tall(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))<=>((~patient(susan)|~kind(susan))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:(funny(X)))&
(funny(susan))&
((calm(alice)<~>~strong(alice)))&
((~funny(paul)&~curious(paul)))&
(?[X]:((~curious(X)<~>~humble(X))))&
((happy(lucy)&kind(lucy)))&
((humble(lucy)<~>~calm(lucy))) | creative(susan) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 289049173358055893252645
% SZS output start Proof for 289049173358055893252645
8. ! [X0] : (wise(X0) <=> (old(X0) & ~wise(X0))) [input p7]
10. ! [X0] : (~creative(X0) <=> (~old(X0) | ~curious(X0))) [input p9]
24. creative(susan) [input hypothesis]
43. ! [X0] : ((wise(X0) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 8]
44. ! [X0] : ((wise(X0) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ~wise(X0))) [flattening 43]
47. ! [X0] : ((~creative(X0) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | creative(X0))) [nnf transformation 10]
48. ! [X0] : ((~creative(X0) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | creative(X0))) [flattening 47]
91. ~wise(X0) | ~wise(X0) [cnf transformation 44]
93. wise(X0) | ~old(X0) | wise(X0) [cnf transformation 44]
101. ~creative(X0) | old(X0) [cnf transformation 48]
136. creative(susan) [cnf transformation 24]
137. ~wise(X0) [duplicate literal removal 91]
138. ~old(X0) | wise(X0) [duplicate literal removal 93]
352. old(susan) [resolution 101,136]
355. wise(susan) [resolution 138,352]
356. $false [subsumption resolution 355,137]
% SZS output end Proof for 289049173358055893252645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not old then lucy is not creative or kind and vice versa. Everyone who is either generous or happy is both quiet and not happy. If mary is kind then someone is tall and vice versa. Everyone who is not creative or tall is quiet and vice versa. If someone is calm then paul is both not tall and kind and vice versa. If paul is either curious or not kind then paul is rich. Everyone who is funny is tall. Everyone who is wise or tall is either not kind or not funny. If someone is brave then fred is rich or quiet and vice versa. Everyone who is not old or not tall is both generous and wise. If someone is strong or not creative then fred is both not curious and rich and vice versa. If susan is funny then john is patient or kind. If john is not calm or tall then mary is brave. If someone is rich then mary is either not patient or strong and vice versa. Everyone who is brave or rich is not quiet or not brave. Everyone who is funny or not strong is either patient or creative and vice versa. Someone is not funny. Someone is either rich or not old. Someone is either not generous or not funny. John is either humble or not strong. John is creative or happy. Someone is either not humble or brave. Someone is old or not quiet. Paul is patient. | Mary is brave. | neutral | ((~old(susan))<=>((~creative(lucy)|kind(lucy))))&
(![X]:((generous(X)<~>happy(X))=>(quiet(X)&~happy(X))))&
((kind(mary))<=>(?[X]:(tall(X))))&
(![X]:((~creative(X)|tall(X))<=>quiet(X)))&
((?[X]:(calm(X)))<=>((~tall(paul)&kind(paul))))&
(((curious(paul)<~>~kind(paul)))=>(rich(paul)))&
(![X]:(funny(X)=>tall(X)))&
(![X]:((wise(X)|tall(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:(brave(X)))<=>((rich(fred)|quiet(fred))))&
(![X]:((~old(X)|~tall(X))=>(generous(X)&wise(X))))&
((?[X]:((strong(X)|~creative(X))))<=>((~curious(fred)&rich(fred))))&
((funny(susan))=>((patient(john)|kind(john))))&
(((~calm(john)|tall(john)))=>(brave(mary)))&
((?[X]:(rich(X)))<=>((~patient(mary)<~>strong(mary))))&
(![X]:((brave(X)|rich(X))=>(~quiet(X)|~brave(X))))&
(![X]:((funny(X)|~strong(X))<=>(patient(X)<~>creative(X))))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
((humble(john)<~>~strong(john)))&
((creative(john)|happy(john)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((old(X)|~quiet(X))))&
(patient(paul)) | brave(mary) | [] | null | 0 |
Everyone who is calm or not wise is both not calm and not strong and vice versa.
If susan is both funny and kind then someone is both quiet and not old.
Everyone who is either not patient or quiet is both not kind and generous.
If fred is not wise or wise then someone is both not rich and strong.
If john is not rich then mary is either curious or not rich and vice versa.
Everyone who is both not brave and not wise is both happy and not tall and vice versa.
Everyone who is both not kind and humble is not happy or not quiet.
Everyone who is either not quiet or kind is either not wise or not humble.
If someone is not kind then lucy is not curious and vice versa.
If lucy is either not happy or not humble then mary is calm and vice versa.
Everyone who is both not humble and not tall is both tall and generous and vice versa.
Everyone who is not patient or not curious is both not brave and patient and vice versa.
If someone is both creative and curious then someone is either not curious or not tall.
If mary is either quiet or old then someone is generous or creative and vice versa.
Everyone who is both rich and humble is not quiet or not curious.
Someone is not happy or not creative.
Someone is strong.
Lucy is not quiet.
Someone is both not curious and not strong.
John is not old.
Mary is both not curious and not wise.
Someone is kind or not curious.
Fred is either curious or calm. | Mary is humble. | entailment | (![X]:((calm(X)|~wise(X))<=>(~calm(X)&~strong(X))))&
(((funny(susan)&kind(susan)))=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>(~kind(X)&generous(X))))&
(((~wise(fred)|wise(fred)))=>(?[X]:((~rich(X)&strong(X)))))&
((~rich(john))<=>((curious(mary)<~>~rich(mary))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)&~tall(X))))&
(![X]:((~kind(X)&humble(X))=>(~happy(X)|~quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(~wise(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>(~curious(lucy)))&
(((~happy(lucy)<~>~humble(lucy)))<=>(calm(mary)))&
(![X]:((~humble(X)&~tall(X))<=>(tall(X)&generous(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~brave(X)&patient(X))))&
((?[X]:((creative(X)&curious(X))))=>(?[X]:((~curious(X)<~>~tall(X)))))&
(((quiet(mary)<~>old(mary)))<=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((rich(X)&humble(X))=>(~quiet(X)|~curious(X))))&
(?[X]:((~happy(X)|~creative(X))))&
(?[X]:(strong(X)))&
(~quiet(lucy))&
(?[X]:((~curious(X)&~strong(X))))&
(~old(john))&
((~curious(mary)&~wise(mary)))&
(?[X]:((kind(X)|~curious(X))))&
((curious(fred)<~>calm(fred))) | humble(mary) | [
"p5",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 594526753750996660971734
% SZS output start Proof for 594526753750996660971734
6. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> (~tall(X0) & happy(X0))) [input p5]
11. ! [X0] : ((~tall(X0) & ~humble(X0)) <=> (generous(X0) & tall(X0))) [input p10]
12. ! [X0] : ((~curious(X0) | ~patient(X0)) <=> (patient(X0) & ~brave(X0))) [input p11]
21. ~wise(mary) & ~curious(mary) [input p20]
24. ~humble(mary) [input hypothesis]
41. ! [X0] : (((~wise(X0) & ~brave(X0)) | (tall(X0) | ~happy(X0))) & ((~tall(X0) & happy(X0)) | (wise(X0) | brave(X0)))) [nnf transformation 6]
42. ! [X0] : (((~wise(X0) & ~brave(X0)) | tall(X0) | ~happy(X0)) & ((~tall(X0) & happy(X0)) | wise(X0) | brave(X0))) [flattening 41]
49. ! [X0] : (((~tall(X0) & ~humble(X0)) | (~generous(X0) | ~tall(X0))) & ((generous(X0) & tall(X0)) | (tall(X0) | humble(X0)))) [nnf transformation 11]
50. ! [X0] : (((~tall(X0) & ~humble(X0)) | ~generous(X0) | ~tall(X0)) & ((generous(X0) & tall(X0)) | tall(X0) | humble(X0))) [flattening 49]
51. ! [X0] : (((~curious(X0) | ~patient(X0)) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | (curious(X0) & patient(X0)))) [nnf transformation 12]
52. ! [X0] : ((~curious(X0) | ~patient(X0) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | (curious(X0) & patient(X0)))) [flattening 51]
88. ~tall(X0) | wise(X0) | brave(X0) [cnf transformation 42]
102. tall(X0) | tall(X0) | humble(X0) [cnf transformation 50]
107. ~brave(X0) | curious(X0) [cnf transformation 52]
126. ~curious(mary) [cnf transformation 21]
127. ~wise(mary) [cnf transformation 21]
131. ~humble(mary) [cnf transformation 24]
134. humble(X0) | tall(X0) [duplicate literal removal 102]
159. 5 <=> curious(mary) [avatar definition]
160. ~curious(mary) <- (~5) [avatar component clause 159]
245. ~5 [avatar split clause 126,159]
264. tall(mary) [resolution 134,131]
282. wise(mary) | brave(mary) [resolution 88,264]
284. brave(mary) [subsumption resolution 282,127]
286. curious(mary) [resolution 284,107]
287. $false <- (~5) [subsumption resolution 286,160]
288. 5 [avatar contradiction clause 287]
289. $false [avatar sat refutation 245,288]
% SZS output end Proof for 594526753750996660971734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is not old.
If fred is not strong then john is not brave and vice versa.
Everyone who is not patient is both tall and not happy and vice versa.
If mary is wise or not quiet then paul is either not calm or brave and vice versa.
Everyone who is generous or not strong is both not quiet and kind and vice versa.
Everyone who is either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
Someone is both not rich and not wise.
Lucy is either not generous or generous.
Alice is either generous or not old.
Paul is either not rich or old. | Mary is not curious. | contradiction | (![X]:((~creative(X)<~>brave(X))=>~old(X)))&
((~strong(fred))<=>(~brave(john)))&
(![X]:(~patient(X)<=>(tall(X)&~happy(X))))&
(((wise(mary)|~quiet(mary)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((generous(X)|~strong(X))<=>(~quiet(X)&kind(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
(?[X]:((~rich(X)&~wise(X))))&
((~generous(lucy)<~>generous(lucy)))&
((generous(alice)<~>~old(alice)))&
((~rich(paul)<~>old(paul))) | ~curious(mary) | [
"p2",
"p5",
"p6",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6147439716875888712569568
% SZS output start Proof for 6147439716875888712569568
3. ! [X0] : (~patient(X0) <=> (~happy(X0) & tall(X0))) [input p2]
6. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (~funny(X0) & ~patient(X0))) [input p5]
7. ! [X0] : ((calm(X0) <~> curious(X0)) => (~happy(X0) & ~kind(X0))) [input p6]
11. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p10]
12. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p11]
13. ! [X0] : ((calm(X0) & happy(X0)) => (strong(X0) & ~quiet(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p13]
21. ~curious(mary) [input hypothesis]
25. ! [X0] : ((~happy(X0) & ~kind(X0)) | (calm(X0) <=> curious(X0))) [ennf transformation 7]
27. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 12]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | (~calm(X0) | ~happy(X0))) [ennf transformation 13]
29. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~calm(X0) | ~happy(X0)) [flattening 28]
32. ! [X0] : ((~patient(X0) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | patient(X0))) [nnf transformation 3]
33. ! [X0] : ((~patient(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | patient(X0))) [flattening 32]
38. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 6]
39. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 38]
40. ! [X0] : ((~happy(X0) & ~kind(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) [nnf transformation 25]
49. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 11]
50. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 14]
51. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 50]
66. tall(X0) | patient(X0) [cnf transformation 33]
68. ~tall(X0) | happy(X0) | ~patient(X0) [cnf transformation 33]
81. ~patient(X0) | tall(X0) | funny(X0) [cnf transformation 39]
82. ~funny(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 39]
85. funny(X0) | ~tall(X0) | funny(X0) | patient(X0) [cnf transformation 39]
86. ~kind(X0) | curious(X0) | ~calm(X0) [cnf transformation 40]
104. ~funny(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 49]
107. funny(X0) | ~patient(X0) | calm(X0) [cnf transformation 49]
108. calm(X0) | creative(X0) [cnf transformation 27]
109. ~happy(X0) | calm(X0) [cnf transformation 27]
110. ~quiet(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 29]
113. kind(X0) | quiet(X0) [cnf transformation 51]
116. ~funny(X0) | ~creative(X0) [cnf transformation 51]
131. ~curious(mary) [cnf transformation 21]
134. ~funny(X0) | ~tall(X0) [duplicate literal removal 82]
135. funny(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 85]
159. 6 <=> quiet(mary) [avatar definition]
160. quiet(mary) <- (6) [avatar component clause 159]
168. funny(X0) | patient(X0) [subsumption resolution 135,66]
169. funny(X0) | tall(X0) [subsumption resolution 81,168]
193. funny(X0) | calm(X0) [subsumption resolution 107,168]
196. ~quiet(X0) | ~happy(X0) [subsumption resolution 110,109]
259. patient(X0) | ~tall(X0) [resolution 168,134]
262. patient(X0) [subsumption resolution 259,66]
267. calm(X1) | ~creative(X1) [resolution 193,116]
269. calm(X1) [subsumption resolution 267,108]
276. ~happy(mary) <- (6) [resolution 196,160]
290. curious(X0) | ~calm(X0) | quiet(X0) [resolution 86,113]
292. curious(X0) | quiet(X0) [subsumption resolution 290,269]
303. quiet(mary) [resolution 292,131]
316. ~calm(X1) | ~patient(X1) | tall(X1) [resolution 104,169]
319. ~patient(X1) | tall(X1) [subsumption resolution 316,269]
320. tall(X1) [subsumption resolution 319,262]
331. happy(X2) | ~patient(X2) [resolution 320,68]
332. happy(X2) [subsumption resolution 331,262]
349. $false <- (6) [resolution 332,276]
354. ~6 [avatar contradiction clause 349]
355. 6 [avatar split clause 303,159]
356. $false [avatar sat refutation 354,355]
% SZS output end Proof for 6147439716875888712569568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both quiet and not tall is either happy or not creative.
Everyone who is both not calm and happy is rich.
Everyone who is both rich and kind is generous or not old and vice versa.
If susan is either humble or not curious then someone is both not quiet and quiet and vice versa.
If someone is both not funny and not wise then someone is either not generous or not happy and vice versa.
Everyone who is not curious is either humble or not strong.
If someone is not humble or not quiet then alice is both not brave and not happy and vice versa.
If mary is either not old or wise then mary is creative or calm and vice versa.
If someone is not happy or not strong then someone is not patient or tall.
Everyone who is both old and not calm is either not brave or not quiet and vice versa.
If someone is quiet then alice is both not patient and not happy and vice versa.
Everyone who is either not brave or not happy is humble.
If someone is both old and quiet then paul is funny.
Everyone who is not creative or brave is either not curious or quiet.
Everyone who is both not rich and not happy is creative or rich and vice versa.
If someone is not old or old then paul is both not funny and not generous and vice versa.
Someone is not kind or curious.
Alice is both not generous and not kind.
Someone is either not creative or humble.
Alice is not funny.
Someone is not tall or happy.
Someone is both not funny and strong.
John is either patient or not strong. | Susan is funny. | neutral | (![X]:((quiet(X)&~tall(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(![X]:((rich(X)&kind(X))<=>(generous(X)|~old(X))))&
(((humble(susan)<~>~curious(susan)))<=>(?[X]:((~quiet(X)&quiet(X)))))&
((?[X]:((~funny(X)&~wise(X))))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~curious(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~brave(alice)&~happy(alice))))&
(((~old(mary)<~>wise(mary)))<=>((creative(mary)|calm(mary))))&
((?[X]:((~happy(X)|~strong(X))))=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((old(X)&~calm(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))<=>((~patient(alice)&~happy(alice))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
((?[X]:((old(X)&quiet(X))))=>(funny(paul)))&
(![X]:((~creative(X)|brave(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~rich(X)&~happy(X))<=>(creative(X)|rich(X))))&
((?[X]:((~old(X)|old(X))))<=>((~funny(paul)&~generous(paul))))&
(?[X]:((~kind(X)|curious(X))))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~creative(X)<~>humble(X))))&
(~funny(alice))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~funny(X)&strong(X))))&
((patient(john)<~>~strong(john))) | funny(susan) | [] | null | 0 |
If someone is not old or creative then someone is either not rich or not humble.
Everyone who is not brave is humble and vice versa.
Everyone who is either funny or not patient is not tall.
Everyone who is both not strong and quiet is not generous and vice versa.
If paul is both not patient and funny then someone is not quiet or not old.
Everyone who is patient or funny is not strong.
Everyone who is either old or patient is both not rich and not happy.
If lucy is not old then mary is patient and vice versa.
If lucy is funny then alice is either not generous or calm.
If john is wise or not old then someone is both not humble and not generous.
Everyone who is calm or generous is old and vice versa.
Everyone who is patient or not rich is not humble and vice versa.
If someone is happy or not patient then someone is kind or not kind and vice versa.
Everyone who is calm or funny is not curious or funny and vice versa.
If mary is strong or not curious then someone is not generous and vice versa.
If john is both not quiet and not patient then someone is either not creative or wise.
Lucy is old.
Alice is old.
Lucy is either kind or not humble.
Someone is both not funny and old.
Fred is either not rich or wise.
Alice is calm.
Someone is creative or not humble.
Someone is not kind. | Lucy is not kind. | entailment | ((?[X]:((~old(X)|creative(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:(~brave(X)<=>humble(X)))&
(![X]:((funny(X)<~>~patient(X))=>~tall(X)))&
(![X]:((~strong(X)&quiet(X))<=>~generous(X)))&
(((~patient(paul)&funny(paul)))=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
((~old(lucy))<=>(patient(mary)))&
((funny(lucy))=>((~generous(alice)<~>calm(alice))))&
(((wise(john)|~old(john)))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((calm(X)|generous(X))<=>old(X)))&
(![X]:((patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
(((~quiet(john)&~patient(john)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(old(lucy))&
(old(alice))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~funny(X)&old(X))))&
((~rich(fred)<~>wise(fred)))&
(calm(alice))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:(~kind(X))) | ~kind(lucy) | [
"p6",
"p11",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 538033550458095882491012
% SZS output start Proof for 538033550458095882491012
7. ! [X0] : ((old(X0) <~> patient(X0)) => (~happy(X0) & ~rich(X0))) [input p6]
12. ! [X0] : ((~rich(X0) | patient(X0)) <=> ~humble(X0)) [input p11]
17. old(lucy) [input p16]
19. kind(lucy) <~> ~humble(lucy) [input p18]
25. kind(lucy) [input hypothesis]
33. ! [X0] : ((~happy(X0) & ~rich(X0)) | (old(X0) <=> patient(X0))) [ennf transformation 7]
46. ! [X0] : ((~happy(X0) & ~rich(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) [nnf transformation 33]
53. ! [X0] : (((~rich(X0) | patient(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~patient(X0)))) [nnf transformation 12]
54. ! [X0] : ((~rich(X0) | patient(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~patient(X0)))) [flattening 53]
70. (humble(lucy) | ~kind(lucy)) & (~humble(lucy) | kind(lucy)) [nnf transformation 19]
88. ~rich(X0) | patient(X0) | ~old(X0) [cnf transformation 46]
103. ~patient(X0) | ~humble(X0) [cnf transformation 54]
104. ~humble(X0) | rich(X0) [cnf transformation 54]
119. old(lucy) [cnf transformation 17]
122. humble(lucy) | ~kind(lucy) [cnf transformation 70]
130. kind(lucy) [cnf transformation 25]
171. 10 <=> old(lucy) [avatar definition]
172. old(lucy) <- (10) [avatar component clause 171]
262. 10 [avatar split clause 119,171]
264. 30 <=> kind(lucy) [avatar definition]
268. 31 <=> humble(lucy) [avatar definition]
270. humble(lucy) <- (31) [avatar component clause 268]
271. ~30 | 31 [avatar split clause 122,268,264]
293. 30 [avatar split clause 130,264]
298. rich(lucy) <- (31) [resolution 104,270]
301. patient(lucy) | ~old(lucy) <- (31) [resolution 88,298]
311. patient(lucy) <- (10, 31) [subsumption resolution 301,172]
313. ~humble(lucy) <- (10, 31) [resolution 311,103]
314. $false <- (10, 31) [subsumption resolution 313,270]
315. ~10 | ~31 [avatar contradiction clause 314]
316. $false [avatar sat refutation 262,271,293,315]
% SZS output end Proof for 538033550458095882491012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not strong is not humble or not brave and vice versa.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
If fred is either not quiet or quiet then alice is not tall and vice versa.
Everyone who is both not wise and curious is both not quiet and not old.
If susan is both not brave and curious then lucy is both calm and not strong.
Someone is not happy.
Fred is creative.
John is both creative and not generous.
Mary is both brave and funny.
Alice is rich or not curious. | Alice is funny. | entailment | (![X]:((~brave(X)<~>~strong(X))<=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
(((~quiet(fred)<~>quiet(fred)))<=>(~tall(alice)))&
(![X]:((~wise(X)&curious(X))=>(~quiet(X)&~old(X))))&
(((~brave(susan)&curious(susan)))=>((calm(lucy)&~strong(lucy))))&
(?[X]:(~happy(X)))&
(creative(fred))&
((creative(john)&~generous(john)))&
((brave(mary)&funny(mary)))&
((rich(alice)|~curious(alice))) | funny(alice) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5320064886560189334838759
% SZS output start Proof for 5320064886560189334838759
9. ! [X0] : ((~wise(X0) | ~funny(X0)) => (~wise(X0) & strong(X0))) [input p8]
11. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p10]
21. ~funny(alice) [input hypothesis]
26. ! [X0] : ((~wise(X0) & strong(X0)) | (wise(X0) & funny(X0))) [ennf transformation 9]
57. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 11]
58. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 57]
104. ~wise(X0) | funny(X0) [cnf transformation 26]
111. ~tall(X0) | wise(X0) [cnf transformation 58]
113. tall(X0) | wise(X0) [cnf transformation 58]
131. ~funny(alice) [cnf transformation 21]
228. wise(X0) [subsumption resolution 111,113]
262. funny(X1) [resolution 104,228]
264. $false [resolution 262,131]
% SZS output end Proof for 5320064886560189334838759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or creative then lucy is old or not brave.
Everyone who is both not strong and not wise is humble.
Everyone who is calm is both not generous and not humble and vice versa.
Everyone who is both not old and not rich is both wise and not quiet and vice versa.
Everyone who is not rich is generous or not funny and vice versa.
Everyone who is either happy or strong is patient.
Everyone who is wise is not generous or not humble.
If someone is curious or not quiet then someone is either not tall or not patient.
Everyone who is both not calm and tall is both patient and strong.
If susan is not brave or strong then someone is both not quiet and strong and vice versa.
Everyone who is either not strong or not curious is both not quiet and generous.
Everyone who is either not funny or patient is both not patient and not quiet.
If fred is not patient or not quiet then someone is either generous or not quiet and vice versa.
Everyone who is funny is not tall or not curious and vice versa.
If someone is either not funny or strong then paul is not curious.
Everyone who is not humble or kind is not tall.
Someone is curious or not strong.
Someone is both not generous and wise.
Someone is brave or not curious.
Mary is either not brave or wise.
Someone is both calm and not happy.
Someone is not happy.
Someone is brave. | Lucy is not tall. | entailment | ((?[X]:((humble(X)<~>creative(X))))=>((old(lucy)|~brave(lucy))))&
(![X]:((~strong(X)&~wise(X))=>humble(X)))&
(![X]:(calm(X)<=>(~generous(X)&~humble(X))))&
(![X]:((~old(X)&~rich(X))<=>(wise(X)&~quiet(X))))&
(![X]:(~rich(X)<=>(generous(X)|~funny(X))))&
(![X]:((happy(X)<~>strong(X))=>patient(X)))&
(![X]:(wise(X)=>(~generous(X)|~humble(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((~calm(X)&tall(X))=>(patient(X)&strong(X))))&
(((~brave(susan)|strong(susan)))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((~strong(X)<~>~curious(X))=>(~quiet(X)&generous(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~patient(X)&~quiet(X))))&
(((~patient(fred)|~quiet(fred)))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:(funny(X)<=>(~tall(X)|~curious(X))))&
((?[X]:((~funny(X)<~>strong(X))))=>(~curious(paul)))&
(![X]:((~humble(X)|kind(X))=>~tall(X)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((brave(X)|~curious(X))))&
((~brave(mary)<~>wise(mary)))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:(brave(X))) | ~tall(lucy) | [
"p2",
"p7",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1064406384876950512447258
% SZS output start Proof for 1064406384876950512447258
3. ! [X0] : (calm(X0) <=> (~humble(X0) & ~generous(X0))) [input p2]
8. ? [X0] : (~quiet(X0) | curious(X0)) => ? [X0] : (~tall(X0) <~> ~patient(X0)) [input p7]
9. ! [X0] : ((tall(X0) & ~calm(X0)) => (strong(X0) & patient(X0))) [input p8]
11. ! [X0] : ((~strong(X0) <~> ~curious(X0)) => (generous(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> patient(X0)) => (~quiet(X0) & ~patient(X0))) [input p11]
14. ! [X0] : (funny(X0) <=> (~curious(X0) | ~tall(X0))) [input p13]
16. ! [X0] : ((kind(X0) | ~humble(X0)) => ~tall(X0)) [input p15]
24. tall(lucy) [input hypothesis]
25. ? [X0] : (~quiet(X0) | curious(X0)) => ? [X1] : (~tall(X1) <~> ~patient(X1)) [rectify 8]
26. ! [X0] : (calm(X0) => (~humble(X0) & ~generous(X0))) [unused predicate definition removal 3]
27. ! [X0] : (~humble(X0) => ~tall(X0)) [pure predicate removal 16]
32. ! [X0] : ((~humble(X0) & ~generous(X0)) | ~calm(X0)) [ennf transformation 26]
36. ? [X1] : (~tall(X1) <~> ~patient(X1)) | ! [X0] : (quiet(X0) & ~curious(X0)) [ennf transformation 25]
37. ! [X0] : ((strong(X0) & patient(X0)) | (~tall(X0) | calm(X0))) [ennf transformation 9]
38. ! [X0] : ((strong(X0) & patient(X0)) | ~tall(X0) | calm(X0)) [flattening 37]
39. ! [X0] : ((generous(X0) & ~quiet(X0)) | (~strong(X0) <=> ~curious(X0))) [ennf transformation 11]
40. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (~funny(X0) <=> patient(X0))) [ennf transformation 12]
42. ! [X0] : (~tall(X0) | humble(X0)) [ennf transformation 27]
49. ? [X1] : ((patient(X1) | tall(X1)) & (~patient(X1) | ~tall(X1))) | ! [X0] : (quiet(X0) & ~curious(X0)) [nnf transformation 36]
50. ? [X0] : ((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) & ~curious(X1)) [rectify 49]
51. ? [X0] : ((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) => ((patient(sK0) | tall(sK0)) & (~patient(sK0) | ~tall(sK0))) [choice axiom]
52. ((patient(sK0) | tall(sK0)) & (~patient(sK0) | ~tall(sK0))) | ! [X1] : (quiet(X1) & ~curious(X1)) [skolemisation 50,51]
58. ! [X0] : ((generous(X0) & ~quiet(X0)) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0)))) [nnf transformation 39]
59. ! [X0] : ((~quiet(X0) & ~patient(X0)) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) [nnf transformation 40]
65. ! [X0] : ((funny(X0) | (curious(X0) & tall(X0))) & ((~curious(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 14]
66. ! [X0] : ((funny(X0) | (curious(X0) & tall(X0))) & (~curious(X0) | ~tall(X0) | ~funny(X0))) [flattening 65]
85. ~calm(X0) | ~humble(X0) [cnf transformation 32]
96. ~patient(sK0) | ~tall(sK0) | ~curious(X1) [cnf transformation 52]
97. ~patient(sK0) | ~tall(sK0) | quiet(X1) [cnf transformation 52]
98. patient(sK0) | tall(sK0) | ~curious(X1) [cnf transformation 52]
99. patient(sK0) | tall(sK0) | quiet(X1) [cnf transformation 52]
100. ~tall(X0) | patient(X0) | calm(X0) [cnf transformation 38]
101. ~tall(X0) | strong(X0) | calm(X0) [cnf transformation 38]
108. ~quiet(X0) | ~strong(X0) | curious(X0) [cnf transformation 58]
112. ~patient(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 59]
122. tall(X0) | funny(X0) [cnf transformation 66]
126. ~tall(X0) | humble(X0) [cnf transformation 42]
137. tall(lucy) [cnf transformation 24]
138. ~patient(X0) | ~funny(X0) [duplicate literal removal 112]
156. 5 <=> ! [X1] : quiet(X1) [avatar definition]
157. quiet(X1) <- (5) [avatar component clause 156]
159. 6 <=> tall(sK0) [avatar definition]
160. ~tall(sK0) <- (~6) [avatar component clause 159]
161. tall(sK0) <- (6) [avatar component clause 159]
163. 7 <=> patient(sK0) [avatar definition]
164. ~patient(sK0) <- (~7) [avatar component clause 163]
165. patient(sK0) <- (7) [avatar component clause 163]
166. 5 | 6 | 7 [avatar split clause 99,163,159,156]
168. 8 <=> ! [X1] : ~curious(X1) [avatar definition]
169. ~curious(X1) <- (8) [avatar component clause 168]
170. 8 | 6 | 7 [avatar split clause 98,163,159,168]
171. 5 | ~6 | ~7 [avatar split clause 97,163,159,156]
172. 8 | ~6 | ~7 [avatar split clause 96,163,159,168]
268. humble(lucy) [resolution 126,137]
269. humble(sK0) <- (6) [resolution 126,161]
331. patient(sK0) | calm(sK0) <- (6) [resolution 100,161]
334. 39 <=> calm(lucy) [avatar definition]
336. calm(lucy) <- (39) [avatar component clause 334]
342. calm(sK0) <- (6, ~7) [subsumption resolution 331,164]
343. strong(lucy) | calm(lucy) [resolution 101,137]
346. ~humble(lucy) <- (39) [resolution 336,85]
347. $false <- (39) [subsumption resolution 346,268]
348. ~39 [avatar contradiction clause 347]
350. 41 <=> strong(lucy) [avatar definition]
352. strong(lucy) <- (41) [avatar component clause 350]
353. 39 | 41 [avatar split clause 343,350,334]
383. ~humble(sK0) <- (6, ~7) [resolution 342,85]
384. $false <- (6, ~7) [subsumption resolution 383,269]
385. ~6 | 7 [avatar contradiction clause 384]
386. funny(sK0) <- (~6) [resolution 160,122]
387. ~funny(sK0) <- (7) [resolution 165,138]
388. $false <- (~6, 7) [subsumption resolution 387,386]
389. 6 | ~7 [avatar contradiction clause 388]
391. ~strong(X0) | curious(X0) <- (5) [resolution 157,108]
394. ~strong(X0) <- (5, 8) [subsumption resolution 391,169]
441. $false <- (5, 8, 41) [resolution 394,352]
442. ~5 | ~8 | ~41 [avatar contradiction clause 441]
443. $false [avatar sat refutation 166,170,171,172,348,353,385,389,442]
% SZS output end Proof for 1064406384876950512447258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or strong is either rich or not humble and vice versa.
If alice is not funny then mary is brave or curious and vice versa.
Everyone who is not happy or not calm is both not old and not creative.
If mary is kind or rich then alice is both quiet and not funny and vice versa.
Everyone who is either rich or not generous is both patient and not happy.
Everyone who is strong is both not calm and kind.
Everyone who is not happy is creative or not humble.
Everyone who is not generous is not tall or not generous.
Everyone who is both patient and not humble is strong and vice versa.
If someone is tall then someone is both rich and not generous and vice versa.
Everyone who is both wise and not brave is both humble and strong and vice versa.
If someone is not creative or humble then someone is generous or tall.
Everyone who is humble or calm is not brave.
Everyone who is either humble or old is not generous and vice versa.
If alice is either patient or not brave then someone is both not creative and happy and vice versa.
If someone is both happy and not creative then someone is not quiet and vice versa.
Mary is either not tall or kind.
Someone is wise or creative.
Lucy is quiet or humble.
John is either wise or curious.
Mary is curious or humble.
Someone is either not humble or not generous.
Alice is both not tall and not kind.
Someone is calm. | Mary is happy. | neutral | (![X]:((kind(X)<~>strong(X))<=>(rich(X)<~>~humble(X))))&
((~funny(alice))<=>((brave(mary)|curious(mary))))&
(![X]:((~happy(X)|~calm(X))=>(~old(X)&~creative(X))))&
(((kind(mary)|rich(mary)))<=>((quiet(alice)&~funny(alice))))&
(![X]:((rich(X)<~>~generous(X))=>(patient(X)&~happy(X))))&
(![X]:(strong(X)=>(~calm(X)&kind(X))))&
(![X]:(~happy(X)=>(creative(X)|~humble(X))))&
(![X]:(~generous(X)=>(~tall(X)|~generous(X))))&
(![X]:((patient(X)&~humble(X))<=>strong(X)))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((wise(X)&~brave(X))<=>(humble(X)&strong(X))))&
((?[X]:((~creative(X)|humble(X))))=>(?[X]:((generous(X)|tall(X)))))&
(![X]:((humble(X)|calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>old(X))<=>~generous(X)))&
(((patient(alice)<~>~brave(alice)))<=>(?[X]:((~creative(X)&happy(X)))))&
((?[X]:((happy(X)&~creative(X))))<=>(?[X]:(~quiet(X))))&
((~tall(mary)<~>kind(mary)))&
(?[X]:((wise(X)|creative(X))))&
((quiet(lucy)|humble(lucy)))&
((wise(john)<~>curious(john)))&
((curious(mary)|humble(mary)))&
(?[X]:((~humble(X)<~>~generous(X))))&
((~tall(alice)&~kind(alice)))&
(?[X]:(calm(X))) | happy(mary) | [] | null | 0 |
Everyone who is kind or not brave is both not strong and not brave.
If susan is tall or not happy then someone is both creative and wise and vice versa.
Everyone who is not curious or patient is both brave and not generous and vice versa.
Everyone who is either funny or quiet is either old or not tall and vice versa.
Everyone who is not generous is wise.
Everyone who is not strong is both not humble and generous.
Everyone who is kind is not brave.
Everyone who is both old and not creative is happy and vice versa.
If someone is both not brave and humble then alice is calm.
If alice is both not wise and old then someone is both humble and not happy.
Everyone who is not patient is either curious or old.
If someone is not quiet or old then someone is both not wise and not kind and vice versa.
Everyone who is not humble or generous is not wise or quiet.
If someone is funny or not tall then someone is either kind or strong and vice versa.
If fred is either not tall or brave then john is happy.
Everyone who is either not funny or not strong is either patient or creative.
Someone is humble or creative.
Susan is either not patient or not strong.
Fred is not creative or not rich.
Someone is patient.
Alice is happy.
Someone is both not generous and strong.
Someone is either creative or not old. | Fred is not wise. | neutral | (![X]:((kind(X)|~brave(X))=>(~strong(X)&~brave(X))))&
(((tall(susan)|~happy(susan)))<=>(?[X]:((creative(X)&wise(X)))))&
(![X]:((~curious(X)|patient(X))<=>(brave(X)&~generous(X))))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~generous(X)=>wise(X)))&
(![X]:(~strong(X)=>(~humble(X)&generous(X))))&
(![X]:(kind(X)=>~brave(X)))&
(![X]:((old(X)&~creative(X))<=>happy(X)))&
((?[X]:((~brave(X)&humble(X))))=>(calm(alice)))&
(((~wise(alice)&old(alice)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:(~patient(X)=>(curious(X)<~>old(X))))&
((?[X]:((~quiet(X)|old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((~humble(X)|generous(X))=>(~wise(X)|quiet(X))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((kind(X)<~>strong(X)))))&
(((~tall(fred)<~>brave(fred)))=>(happy(john)))&
(![X]:((~funny(X)<~>~strong(X))=>(patient(X)<~>creative(X))))&
(?[X]:((humble(X)|creative(X))))&
((~patient(susan)<~>~strong(susan)))&
((~creative(fred)|~rich(fred)))&
(?[X]:(patient(X)))&
(happy(alice))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:((creative(X)<~>~old(X)))) | ~wise(fred) | [] | null | 0 |
Everyone who is quiet is not funny and vice versa. Everyone who is both not kind and happy is not wise or not humble and vice versa. Everyone who is both not generous and strong is not wise. If mary is both not kind and humble then someone is not creative or curious. Everyone who is both not rich and creative is not old and vice versa. Everyone who is curious or wise is brave or not wise. Everyone who is funny is wise or quiet. Everyone who is both not kind and old is either not generous or not curious. If someone is both not strong and funny then someone is either kind or not strong. Everyone who is either not wise or old is not old. If fred is either quiet or not wise then lucy is both not funny and rich and vice versa. Everyone who is either patient or not tall is happy or not happy. If someone is calm or kind then alice is both kind and not old. Everyone who is not patient or humble is either not creative or not brave. Everyone who is both not brave and not happy is not old or strong and vice versa. Everyone who is rich or patient is both not humble and not kind. Someone is curious. Mary is rich or not generous. Paul is both not generous and humble. Susan is not creative. Someone is not quiet or generous. Fred is either quiet or strong. | Paul is brave. | entailment | (![X]:(quiet(X)<=>~funny(X)))&
(![X]:((~kind(X)&happy(X))<=>(~wise(X)|~humble(X))))&
(![X]:((~generous(X)&strong(X))=>~wise(X)))&
(((~kind(mary)&humble(mary)))=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((~rich(X)&creative(X))<=>~old(X)))&
(![X]:((curious(X)|wise(X))=>(brave(X)|~wise(X))))&
(![X]:(funny(X)=>(wise(X)|quiet(X))))&
(![X]:((~kind(X)&old(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((kind(X)<~>~strong(X)))))&
(![X]:((~wise(X)<~>old(X))=>~old(X)))&
(((quiet(fred)<~>~wise(fred)))<=>((~funny(lucy)&rich(lucy))))&
(![X]:((patient(X)<~>~tall(X))=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|kind(X))))=>((kind(alice)&~old(alice))))&
(![X]:((~patient(X)|humble(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~old(X)|strong(X))))&
(![X]:((rich(X)|patient(X))=>(~humble(X)&~kind(X))))&
(?[X]:(curious(X)))&
((rich(mary)|~generous(mary)))&
((~generous(paul)&humble(paul)))&
(~creative(susan))&
(?[X]:((~quiet(X)|generous(X))))&
((quiet(fred)<~>strong(fred))) | brave(paul) | [
"p1",
"p4",
"p5",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4445684651784883121961803
% SZS output start Proof for 4445684651784883121961803
2. ! [X0] : ((happy(X0) & ~kind(X0)) <=> (~humble(X0) | ~wise(X0))) [input p1]
5. ! [X0] : ((creative(X0) & ~rich(X0)) <=> ~old(X0)) [input p4]
6. ! [X0] : ((wise(X0) | curious(X0)) => (~wise(X0) | brave(X0))) [input p5]
14. ! [X0] : ((humble(X0) | ~patient(X0)) => (~creative(X0) <~> ~brave(X0))) [input p13]
15. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (strong(X0) | ~old(X0))) [input p14]
16. ! [X0] : ((patient(X0) | rich(X0)) => (~kind(X0) & ~humble(X0))) [input p15]
19. humble(paul) & ~generous(paul) [input p18]
23. ~brave(paul) [input hypothesis]
30. ! [X0] : ((~wise(X0) | brave(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 6]
31. ! [X0] : (~wise(X0) | brave(X0) | (~wise(X0) & ~curious(X0))) [flattening 30]
41. ! [X0] : ((~creative(X0) <~> ~brave(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 14]
42. ! [X0] : ((~kind(X0) & ~humble(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 16]
44. ! [X0] : (((happy(X0) & ~kind(X0)) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | (~happy(X0) | kind(X0)))) [nnf transformation 2]
45. ! [X0] : (((happy(X0) & ~kind(X0)) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | ~happy(X0) | kind(X0))) [flattening 44]
48. ! [X0] : (((creative(X0) & ~rich(X0)) | old(X0)) & (~old(X0) | (~creative(X0) | rich(X0)))) [nnf transformation 5]
49. ! [X0] : (((creative(X0) & ~rich(X0)) | old(X0)) & (~old(X0) | ~creative(X0) | rich(X0))) [flattening 48]
59. ! [X0] : (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | (~humble(X0) & patient(X0))) [nnf transformation 41]
60. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 15]
61. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | happy(X0) | brave(X0))) [flattening 60]
72. wise(X0) | happy(X0) [cnf transformation 45]
76. ~old(X0) | ~creative(X0) | rich(X0) [cnf transformation 49]
80. ~wise(X0) | brave(X0) | ~wise(X0) [cnf transformation 31]
101. ~humble(X0) | creative(X0) | brave(X0) [cnf transformation 59]
103. ~brave(X0) | old(X0) [cnf transformation 61]
105. ~happy(X0) | old(X0) [cnf transformation 61]
107. ~rich(X0) | ~humble(X0) [cnf transformation 42]
114. humble(paul) [cnf transformation 19]
119. ~brave(paul) [cnf transformation 23]
121. ~wise(X0) | brave(X0) [duplicate literal removal 80]
217. brave(X0) | happy(X0) [resolution 121,72]
234. happy(X2) | old(X2) [resolution 217,103]
237. old(X2) [subsumption resolution 234,105]
244. creative(paul) | brave(paul) [resolution 101,114]
246. creative(paul) [subsumption resolution 244,119]
266. ~creative(X1) | rich(X1) [resolution 237,76]
308. rich(paul) [resolution 266,246]
313. ~humble(paul) [resolution 308,107]
315. $false [subsumption resolution 313,114]
% SZS output end Proof for 4445684651784883121961803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not funny is both happy and not curious and vice versa.
If susan is not curious then someone is either not tall or kind.
If someone is tall then lucy is either not rich or curious.
If someone is both creative and not tall then someone is both not funny and curious.
Everyone who is strong is not funny or not wise and vice versa.
If someone is either funny or brave then alice is not tall or wise.
If someone is not creative then john is either not humble or not rich and vice versa.
Everyone who is either not happy or creative is both funny and not patient and vice versa.
If alice is not creative then someone is either not creative or not calm and vice versa.
Everyone who is either not humble or old is both not kind and creative.
If susan is tall or not strong then someone is not old.
Everyone who is both creative and not strong is either brave or not rich and vice versa.
Everyone who is both tall and not curious is either tall or not funny.
If susan is both curious and not happy then someone is not old and vice versa.
Everyone who is not kind is old or not patient.
Everyone who is not happy or not humble is not generous and vice versa.
Someone is brave or not patient.
Someone is either not curious or humble.
Someone is not kind.
Someone is not wise.
Someone is not generous.
Susan is funny.
Alice is not creative.
Lucy is strong or not wise. | Lucy is not brave. | neutral | (![X]:((~old(X)|~funny(X))<=>(happy(X)&~curious(X))))&
((~curious(susan))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(tall(X)))=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:(strong(X)<=>(~funny(X)|~wise(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((~tall(alice)|wise(alice))))&
((?[X]:(~creative(X)))<=>((~humble(john)<~>~rich(john))))&
(![X]:((~happy(X)<~>creative(X))<=>(funny(X)&~patient(X))))&
((~creative(alice))<=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>old(X))=>(~kind(X)&creative(X))))&
(((tall(susan)|~strong(susan)))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~strong(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)<~>~funny(X))))&
(((curious(susan)&~happy(susan)))<=>(?[X]:(~old(X))))&
(![X]:(~kind(X)=>(old(X)|~patient(X))))&
(![X]:((~happy(X)|~humble(X))<=>~generous(X)))&
(?[X]:((brave(X)|~patient(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:(~generous(X)))&
(funny(susan))&
(~creative(alice))&
((strong(lucy)|~wise(lucy))) | ~brave(lucy) | [] | null | 0 |
If alice is both not kind and not humble then someone is both strong and not tall and vice versa.
If lucy is old then someone is either old or not calm.
Everyone who is not funny or humble is happy or generous and vice versa.
If someone is humble or not brave then someone is not wise or not happy.
Everyone who is both not humble and kind is curious.
Everyone who is not quiet is both rich and kind.
Everyone who is either kind or not kind is both calm and generous and vice versa.
If lucy is both not rich and not generous then someone is tall or not humble.
Everyone who is either not funny or quiet is generous and vice versa.
If someone is both not wise and tall then someone is both not humble and not curious.
If someone is not kind or not strong then fred is both not brave and not wise and vice versa.
If someone is not old then someone is either strong or patient and vice versa.
If someone is not calm then someone is both not creative and quiet.
Everyone who is not old is not happy or not rich and vice versa.
If someone is not quiet then alice is not happy or calm and vice versa.
Everyone who is not rich is not brave and vice versa.
Someone is either generous or not funny.
Alice is either funny or not curious.
Someone is either tall or rich.
Lucy is either quiet or humble.
Susan is not wise.
Someone is not old.
Someone is not calm or not quiet.
Someone is patient. | Fred is not quiet. | contradiction | (((~kind(alice)&~humble(alice)))<=>(?[X]:((strong(X)&~tall(X)))))&
((old(lucy))=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~funny(X)|humble(X))<=>(happy(X)|generous(X))))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:((~humble(X)&kind(X))=>curious(X)))&
(![X]:(~quiet(X)=>(rich(X)&kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(calm(X)&generous(X))))&
(((~rich(lucy)&~generous(lucy)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~funny(X)<~>quiet(X))<=>generous(X)))&
((?[X]:((~wise(X)&tall(X))))=>(?[X]:((~humble(X)&~curious(X)))))&
((?[X]:((~kind(X)|~strong(X))))<=>((~brave(fred)&~wise(fred))))&
((?[X]:(~old(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:(~old(X)<=>(~happy(X)|~rich(X))))&
((?[X]:(~quiet(X)))<=>((~happy(alice)|calm(alice))))&
(![X]:(~rich(X)<=>~brave(X)))&
(?[X]:((generous(X)<~>~funny(X))))&
((funny(alice)<~>~curious(alice)))&
(?[X]:((tall(X)<~>rich(X))))&
((quiet(lucy)<~>humble(lucy)))&
(~wise(susan))&
(?[X]:(~old(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:(patient(X))) | ~quiet(fred) | [
"p0",
"p4",
"p5",
"p9",
"p10",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6136028283885706473723923
% SZS output start Proof for 6136028283885706473723923
1. (~humble(alice) & ~kind(alice)) <=> ? [X0] : (~tall(X0) & strong(X0)) [input p0]
5. ! [X0] : ((kind(X0) & ~humble(X0)) => curious(X0)) [input p4]
6. ! [X0] : (~quiet(X0) => (kind(X0) & rich(X0))) [input p5]
10. ? [X0] : (tall(X0) & ~wise(X0)) => ? [X0] : (~curious(X0) & ~humble(X0)) [input p9]
11. ? [X0] : (~strong(X0) | ~kind(X0)) <=> (~wise(fred) & ~brave(fred)) [input p10]
16. ! [X0] : (~rich(X0) <=> ~brave(X0)) [input p15]
21. ~wise(susan) [input p20]
25. ~quiet(fred) [input hypothesis]
27. ? [X0] : (tall(X0) & ~wise(X0)) => ? [X1] : (~curious(X1) & ~humble(X1)) [rectify 10]
33. ! [X0] : (curious(X0) | (~kind(X0) | humble(X0))) [ennf transformation 5]
34. ! [X0] : (curious(X0) | ~kind(X0) | humble(X0)) [flattening 33]
35. ! [X0] : ((kind(X0) & rich(X0)) | quiet(X0)) [ennf transformation 6]
38. ? [X1] : (~curious(X1) & ~humble(X1)) | ! [X0] : (~tall(X0) | wise(X0)) [ennf transformation 27]
40. ((~humble(alice) & ~kind(alice)) | ! [X0] : (tall(X0) | ~strong(X0))) & (? [X0] : (~tall(X0) & strong(X0)) | (humble(alice) | kind(alice))) [nnf transformation 1]
41. ((~humble(alice) & ~kind(alice)) | ! [X0] : (tall(X0) | ~strong(X0))) & (? [X0] : (~tall(X0) & strong(X0)) | humble(alice) | kind(alice)) [flattening 40]
42. ((~humble(alice) & ~kind(alice)) | ! [X0] : (tall(X0) | ~strong(X0))) & (? [X1] : (~tall(X1) & strong(X1)) | humble(alice) | kind(alice)) [rectify 41]
43. ? [X1] : (~tall(X1) & strong(X1)) => (~tall(sK0) & strong(sK0)) [choice axiom]
44. ((~humble(alice) & ~kind(alice)) | ! [X0] : (tall(X0) | ~strong(X0))) & ((~tall(sK0) & strong(sK0)) | humble(alice) | kind(alice)) [skolemisation 42,43]
58. ? [X0] : (~curious(X0) & ~humble(X0)) | ! [X1] : (~tall(X1) | wise(X1)) [rectify 38]
59. ? [X0] : (~curious(X0) & ~humble(X0)) => (~curious(sK4) & ~humble(sK4)) [choice axiom]
60. (~curious(sK4) & ~humble(sK4)) | ! [X1] : (~tall(X1) | wise(X1)) [skolemisation 58,59]
61. (? [X0] : (~strong(X0) | ~kind(X0)) | (wise(fred) | brave(fred))) & ((~wise(fred) & ~brave(fred)) | ! [X0] : (strong(X0) & kind(X0))) [nnf transformation 11]
62. (? [X0] : (~strong(X0) | ~kind(X0)) | wise(fred) | brave(fred)) & ((~wise(fred) & ~brave(fred)) | ! [X0] : (strong(X0) & kind(X0))) [flattening 61]
63. (? [X0] : (~strong(X0) | ~kind(X0)) | wise(fred) | brave(fred)) & ((~wise(fred) & ~brave(fred)) | ! [X1] : (strong(X1) & kind(X1))) [rectify 62]
64. ? [X0] : (~strong(X0) | ~kind(X0)) => (~strong(sK5) | ~kind(sK5)) [choice axiom]
65. ((~strong(sK5) | ~kind(sK5)) | wise(fred) | brave(fred)) & ((~wise(fred) & ~brave(fred)) | ! [X1] : (strong(X1) & kind(X1))) [skolemisation 63,64]
81. ! [X0] : ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0))) [nnf transformation 16]
98. ~kind(alice) | tall(X0) | ~strong(X0) [cnf transformation 44]
108. ~kind(X0) | curious(X0) | humble(X0) [cnf transformation 34]
109. rich(X0) | quiet(X0) [cnf transformation 35]
122. ~humble(sK4) | ~tall(X1) | wise(X1) [cnf transformation 60]
123. ~curious(sK4) | ~tall(X1) | wise(X1) [cnf transformation 60]
124. ~brave(fred) | kind(X1) [cnf transformation 65]
125. ~brave(fred) | strong(X1) [cnf transformation 65]
141. ~rich(X0) | brave(X0) [cnf transformation 81]
150. ~wise(susan) [cnf transformation 21]
154. ~quiet(fred) [cnf transformation 25]
160. 1 <=> ! [X0] : (tall(X0) | ~strong(X0)) [avatar definition]
161. tall(X0) | ~strong(X0) <- (1) [avatar component clause 160]
168. 3 <=> kind(alice) [avatar definition]
170. ~kind(alice) <- (~3) [avatar component clause 168]
171. 1 | ~3 [avatar split clause 98,168,160]
217. 13 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
218. ~tall(X1) | wise(X1) <- (13) [avatar component clause 217]
220. 14 <=> curious(sK4) [avatar definition]
222. ~curious(sK4) <- (~14) [avatar component clause 220]
223. 13 | ~14 [avatar split clause 123,220,217]
225. 15 <=> humble(sK4) [avatar definition]
227. ~humble(sK4) <- (~15) [avatar component clause 225]
228. 13 | ~15 [avatar split clause 122,225,217]
230. 16 <=> brave(fred) [avatar definition]
247. 20 <=> ! [X1] : strong(X1) [avatar definition]
248. strong(X1) <- (20) [avatar component clause 247]
251. 21 <=> ! [X1] : kind(X1) [avatar definition]
252. kind(X1) <- (21) [avatar component clause 251]
254. 20 | ~16 [avatar split clause 125,230,247]
255. 21 | ~16 [avatar split clause 124,230,251]
322. quiet(X0) | brave(X0) [resolution 141,109]
331. brave(fred) [resolution 322,154]
336. 16 [avatar split clause 331,230]
340. $false <- (~3, 21) [resolution 252,170]
341. 3 | ~21 [avatar contradiction clause 340]
342. tall(X0) <- (1, 20) [subsumption resolution 161,248]
350. curious(X0) | humble(X0) <- (21) [resolution 108,252]
389. humble(sK4) <- (~14, 21) [resolution 350,222]
391. $false <- (~14, ~15, 21) [subsumption resolution 389,227]
392. 14 | 15 | ~21 [avatar contradiction clause 391]
395. wise(X1) <- (1, 13, 20) [subsumption resolution 218,342]
403. $false <- (1, 13, 20) [resolution 395,150]
408. ~1 | ~13 | ~20 [avatar contradiction clause 403]
409. $false [avatar sat refutation 171,223,228,254,255,336,341,392,408]
% SZS output end Proof for 6136028283885706473723923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not creative is not quiet and vice versa.
Everyone who is both not tall and humble is generous or calm.
Everyone who is not kind or old is either not rich or curious.
Everyone who is happy is either not strong or curious and vice versa.
Everyone who is not curious or kind is either not patient or not rich.
Everyone who is strong is both not funny and wise and vice versa.
If someone is either creative or funny then mary is either not quiet or not old.
Everyone who is both wise and not generous is not rich or kind.
Everyone who is either calm or humble is both happy and not kind and vice versa.
If susan is not tall or not generous then someone is either curious or not curious.
Everyone who is not wise is not patient or rich.
Everyone who is happy is either not strong or patient and vice versa.
Everyone who is both creative and tall is funny or not creative and vice versa.
Everyone who is either not calm or tall is patient or happy and vice versa.
If paul is both not generous and funny then someone is both quiet and happy.
Everyone who is calm or not calm is either not brave or strong.
Someone is tall or old.
Paul is either not tall or not quiet.
Paul is either not patient or not calm.
Mary is not wise.
Susan is both not calm and brave.
Someone is not curious.
Lucy is not rich. | Susan is not patient. | contradiction | (![X]:((~generous(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((~tall(X)&humble(X))=>(generous(X)|calm(X))))&
(![X]:((~kind(X)|old(X))=>(~rich(X)<~>curious(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~curious(X)|kind(X))=>(~patient(X)<~>~rich(X))))&
(![X]:(strong(X)<=>(~funny(X)&wise(X))))&
((?[X]:((creative(X)<~>funny(X))))=>((~quiet(mary)<~>~old(mary))))&
(![X]:((wise(X)&~generous(X))=>(~rich(X)|kind(X))))&
(![X]:((calm(X)<~>humble(X))<=>(happy(X)&~kind(X))))&
(((~tall(susan)|~generous(susan)))=>(?[X]:((curious(X)<~>~curious(X)))))&
(![X]:(~wise(X)=>(~patient(X)|rich(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>patient(X))))&
(![X]:((creative(X)&tall(X))<=>(funny(X)|~creative(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(patient(X)|happy(X))))&
(((~generous(paul)&funny(paul)))=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((calm(X)|~calm(X))=>(~brave(X)<~>strong(X))))&
(?[X]:((tall(X)|old(X))))&
((~tall(paul)<~>~quiet(paul)))&
((~patient(paul)<~>~calm(paul)))&
(~wise(mary))&
((~calm(susan)&brave(susan)))&
(?[X]:(~curious(X)))&
(~rich(lucy)) | ~patient(susan) | [
"p5",
"p11",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 582839200384576629982106
% SZS output start Proof for 582839200384576629982106
6. ! [X0] : (strong(X0) <=> (wise(X0) & ~funny(X0))) [input p5]
12. ! [X0] : (happy(X0) <=> (~strong(X0) <~> patient(X0))) [input p11]
13. ! [X0] : ((tall(X0) & creative(X0)) <=> (~creative(X0) | funny(X0))) [input p12]
14. ! [X0] : ((~calm(X0) <~> tall(X0)) <=> (happy(X0) | patient(X0))) [input p13]
16. ! [X0] : ((~calm(X0) | calm(X0)) => (~brave(X0) <~> strong(X0))) [input p15]
21. brave(susan) & ~calm(susan) [input p20]
24. ~patient(susan) [input hypothesis]
37. ! [X0] : ((~brave(X0) <~> strong(X0)) | (calm(X0) & ~calm(X0))) [ennf transformation 16]
42. ! [X0] : ((strong(X0) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 6]
43. ! [X0] : ((strong(X0) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~strong(X0))) [flattening 42]
50. ! [X0] : ((happy(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 12]
51. ! [X0] : (((tall(X0) & creative(X0)) | (creative(X0) & ~funny(X0))) & ((~creative(X0) | funny(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 13]
52. ! [X0] : (((tall(X0) & creative(X0)) | (creative(X0) & ~funny(X0))) & (~creative(X0) | funny(X0) | ~tall(X0) | ~creative(X0))) [flattening 51]
53. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [flattening 53]
57. ! [X0] : (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (calm(X0) & ~calm(X0))) [nnf transformation 37]
81. ~funny(X0) | ~strong(X0) [cnf transformation 43]
100. ~strong(X0) | patient(X0) | ~happy(X0) [cnf transformation 50]
104. ~creative(X0) | funny(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 52]
106. creative(X0) | creative(X0) [cnf transformation 52]
109. patient(X0) | happy(X0) | tall(X0) | calm(X0) [cnf transformation 54]
117. strong(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 57]
118. ~brave(X0) | strong(X0) | calm(X0) [cnf transformation 57]
127. ~calm(susan) [cnf transformation 21]
128. brave(susan) [cnf transformation 21]
131. ~patient(susan) [cnf transformation 24]
132. ~creative(X0) | funny(X0) | ~tall(X0) [duplicate literal removal 104]
133. creative(X0) [duplicate literal removal 106]
152. ~tall(X0) | funny(X0) [subsumption resolution 132,133]
172. ~brave(X0) | strong(X0) [subsumption resolution 117,118]
212. strong(susan) [resolution 172,128]
235. 15 <=> happy(susan) [avatar definition]
237. ~happy(susan) <- (~15) [avatar component clause 235]
307. patient(susan) | ~happy(susan) [resolution 100,212]
411. happy(susan) | tall(susan) | calm(susan) [resolution 109,131]
422. tall(susan) | calm(susan) <- (~15) [subsumption resolution 411,237]
423. tall(susan) <- (~15) [subsumption resolution 422,127]
425. funny(susan) <- (~15) [resolution 423,152]
427. ~strong(susan) <- (~15) [resolution 425,81]
428. $false <- (~15) [subsumption resolution 427,212]
429. 15 [avatar contradiction clause 428]
436. ~happy(susan) [subsumption resolution 307,131]
437. ~15 [avatar split clause 436,235]
453. $false [avatar sat refutation 429,437]
% SZS output end Proof for 582839200384576629982106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not wise and not patient then alice is either brave or happy and vice versa.
If mary is not humble then someone is both not wise and tall.
Everyone who is not generous or strong is either brave or rich.
Everyone who is happy or not funny is both happy and rich.
Everyone who is happy or curious is not patient and vice versa.
If mary is either strong or creative then mary is not tall or wise.
Everyone who is rich is generous.
If mary is both not patient and not brave then someone is both not quiet and not strong and vice versa.
Everyone who is creative or not quiet is either not wise or not happy.
If someone is not rich or humble then someone is not calm.
Everyone who is creative is not patient.
Everyone who is wise is old.
Everyone who is both not kind and wise is rich and vice versa.
Everyone who is not funny or not tall is either not calm or strong and vice versa.
If paul is either not wise or not funny then someone is not brave or wise and vice versa.
If someone is not tall or curious then lucy is not tall or not strong.
Mary is rich.
John is both not rich and old.
Someone is either not calm or brave.
Susan is kind or not kind.
Someone is either not strong or funny.
Someone is both not tall and patient.
Mary is both wise and not calm.
Paul is not wise or patient. | Paul is not rich. | entailment | (((~wise(alice)&~patient(alice)))<=>((brave(alice)<~>happy(alice))))&
((~humble(mary))=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((~generous(X)|strong(X))=>(brave(X)<~>rich(X))))&
(![X]:((happy(X)|~funny(X))=>(happy(X)&rich(X))))&
(![X]:((happy(X)|curious(X))<=>~patient(X)))&
(((strong(mary)<~>creative(mary)))=>((~tall(mary)|wise(mary))))&
(![X]:(rich(X)=>generous(X)))&
(((~patient(mary)&~brave(mary)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((creative(X)|~quiet(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:(~calm(X))))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~kind(X)&wise(X))<=>rich(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~calm(X)<~>strong(X))))&
(((~wise(paul)<~>~funny(paul)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~tall(lucy)|~strong(lucy))))&
(rich(mary))&
((~rich(john)&old(john)))&
(?[X]:((~calm(X)<~>brave(X))))&
((kind(susan)|~kind(susan)))&
(?[X]:((~strong(X)<~>funny(X))))&
(?[X]:((~tall(X)&patient(X))))&
((wise(mary)&~calm(mary)))&
((~wise(paul)|patient(paul))) | ~rich(paul) | [
"p3",
"p4",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6149548407513567231603926
% SZS output start Proof for 6149548407513567231603926
4. ! [X0] : ((~funny(X0) | happy(X0)) => (rich(X0) & happy(X0))) [input p3]
5. ! [X0] : ((curious(X0) | happy(X0)) <=> ~patient(X0)) [input p4]
13. ! [X0] : ((wise(X0) & ~kind(X0)) <=> rich(X0)) [input p12]
15. (~wise(paul) <~> ~funny(paul)) <=> ? [X0] : (wise(X0) | ~brave(X0)) [input p14]
24. patient(paul) | ~wise(paul) [input p23]
25. rich(paul) [input hypothesis]
33. ! [X0] : ((rich(X0) & happy(X0)) | (funny(X0) & ~happy(X0))) [ennf transformation 4]
46. ! [X0] : (((curious(X0) | happy(X0)) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~happy(X0)))) [nnf transformation 5]
47. ! [X0] : ((curious(X0) | happy(X0) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~happy(X0)))) [flattening 46]
58. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 13]
59. ! [X0] : (((wise(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~wise(X0) | kind(X0))) [flattening 58]
62. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X0] : (wise(X0) | ~brave(X0)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [nnf transformation 15]
63. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X1] : (wise(X1) | ~brave(X1)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [rectify 62]
64. ? [X1] : (wise(X1) | ~brave(X1)) => (wise(sK3) | ~brave(sK3)) [choice axiom]
65. (((funny(paul) | wise(paul)) & (~funny(paul) | ~wise(paul))) | ! [X0] : (~wise(X0) & brave(X0))) & ((wise(sK3) | ~brave(sK3)) | ((~wise(paul) | funny(paul)) & (~funny(paul) | wise(paul)))) [skolemisation 63,64]
85. funny(X0) | happy(X0) [cnf transformation 33]
88. ~happy(X0) | ~patient(X0) [cnf transformation 47]
106. ~rich(X0) | wise(X0) [cnf transformation 59]
116. ~funny(paul) | ~wise(paul) | ~wise(X0) [cnf transformation 65]
132. patient(paul) | ~wise(paul) [cnf transformation 24]
133. rich(paul) [cnf transformation 25]
224. 20 <=> ! [X0] : ~wise(X0) [avatar definition]
225. ~wise(X0) <- (20) [avatar component clause 224]
227. 21 <=> wise(paul) [avatar definition]
229. wise(paul) <- (21) [avatar component clause 227]
231. 22 <=> funny(paul) [avatar definition]
232. ~funny(paul) <- (~22) [avatar component clause 231]
239. 20 | ~21 | ~22 [avatar split clause 116,231,227,224]
289. 34 <=> patient(paul) [avatar definition]
291. patient(paul) <- (34) [avatar component clause 289]
292. ~21 | 34 [avatar split clause 132,289,227]
298. wise(paul) [resolution 106,133]
302. 21 [avatar split clause 298,227]
304. happy(paul) <- (~22) [resolution 232,85]
305. ~patient(paul) <- (~22) [resolution 304,88]
307. $false <- (~22, 34) [subsumption resolution 305,291]
308. 22 | ~34 [avatar contradiction clause 307]
310. $false <- (20, 21) [resolution 225,229]
311. ~20 | ~21 [avatar contradiction clause 310]
313. $false [avatar sat refutation 239,292,302,308,311]
% SZS output end Proof for 6149548407513567231603926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or creative.
Everyone who is not old is not brave and vice versa.
Everyone who is both not old and wise is rich or not old.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich.
Someone is happy or strong. | Fred is not strong. | neutral | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|creative(X)))))&
(![X]:(~old(X)<=>~brave(X)))&
(![X]:((~old(X)&wise(X))=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan)))&
(?[X]:((happy(X)|strong(X)))) | ~strong(fred) | [] | null | 0 |
Everyone who is funny or old is both not brave and creative. Everyone who is both not calm and strong is happy or not quiet and vice versa. Everyone who is not brave is either not calm or happy. Everyone who is both not calm and calm is either not funny or curious. If someone is kind or not tall then paul is rich or not tall. Everyone who is both strong and not calm is both not humble and happy. Everyone who is either not brave or generous is not rich or not brave and vice versa. Everyone who is either wise or happy is either not humble or not strong and vice versa. If lucy is not wise then mary is not strong and vice versa. If someone is not strong then alice is both strong and happy. Everyone who is not humble or not tall is not happy and vice versa. Everyone who is both old and kind is either patient or old and vice versa. If someone is both patient and not calm then john is not humble and vice versa. If lucy is either not humble or not creative then fred is either quiet or not kind. If someone is both rich and not old then someone is calm or strong and vice versa. Alice is not kind. Paul is either rich or humble. Fred is kind or strong. Someone is both calm and not patient. Paul is not humble. Someone is funny or not wise. Someone is brave or funny. | John is not wise. | entailment | (![X]:((funny(X)|old(X))=>(~brave(X)&creative(X))))&
(![X]:((~calm(X)&strong(X))<=>(happy(X)|~quiet(X))))&
(![X]:(~brave(X)=>(~calm(X)<~>happy(X))))&
(![X]:((~calm(X)&calm(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((kind(X)|~tall(X))))=>((rich(paul)|~tall(paul))))&
(![X]:((strong(X)&~calm(X))=>(~humble(X)&happy(X))))&
(![X]:((~brave(X)<~>generous(X))<=>(~rich(X)|~brave(X))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)<~>~strong(X))))&
((~wise(lucy))<=>(~strong(mary)))&
((?[X]:(~strong(X)))=>((strong(alice)&happy(alice))))&
(![X]:((~humble(X)|~tall(X))<=>~happy(X)))&
(![X]:((old(X)&kind(X))<=>(patient(X)<~>old(X))))&
((?[X]:((patient(X)&~calm(X))))<=>(~humble(john)))&
(((~humble(lucy)<~>~creative(lucy)))=>((quiet(fred)<~>~kind(fred))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(~kind(alice))&
((rich(paul)<~>humble(paul)))&
((kind(fred)|strong(fred)))&
(?[X]:((calm(X)&~patient(X))))&
(~humble(paul))&
(?[X]:((funny(X)|~wise(X))))&
(?[X]:((brave(X)|funny(X)))) | ~wise(john) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2973287425833617447742661
% SZS output start Proof for 2973287425833617447742661
1. ! [X0] : ((old(X0) | funny(X0)) => (creative(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (~quiet(X0) | happy(X0))) [input p1]
3. ! [X0] : (~brave(X0) => (~calm(X0) <~> happy(X0))) [input p2]
6. ! [X0] : ((~calm(X0) & strong(X0)) => (happy(X0) & ~humble(X0))) [input p5]
8. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p7]
10. ? [X0] : ~strong(X0) => (happy(alice) & strong(alice)) [input p9]
11. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((kind(X0) & old(X0)) <=> (patient(X0) <~> old(X0))) [input p11]
13. ? [X0] : (~calm(X0) & patient(X0)) <=> ~humble(john) [input p12]
23. wise(john) [input hypothesis]
25. ! [X0] : ((creative(X0) & ~brave(X0)) | (~old(X0) & ~funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~calm(X0) <~> happy(X0)) | brave(X0)) [ennf transformation 3]
31. ! [X0] : ((happy(X0) & ~humble(X0)) | (calm(X0) | ~strong(X0))) [ennf transformation 6]
32. ! [X0] : ((happy(X0) & ~humble(X0)) | calm(X0) | ~strong(X0)) [flattening 31]
33. (happy(alice) & strong(alice)) | ! [X0] : strong(X0) [ennf transformation 10]
35. ! [X0] : (((strong(X0) & ~calm(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (~strong(X0) | calm(X0)))) [nnf transformation 2]
36. ! [X0] : (((strong(X0) & ~calm(X0)) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | ~strong(X0) | calm(X0))) [flattening 35]
37. ! [X0] : (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | brave(X0)) [nnf transformation 26]
41. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 8]
43. ! [X0] : (((~tall(X0) | ~humble(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) & humble(X0)))) [nnf transformation 11]
44. ! [X0] : ((~tall(X0) | ~humble(X0) | happy(X0)) & (~happy(X0) | (tall(X0) & humble(X0)))) [flattening 43]
45. ! [X0] : (((kind(X0) & old(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 12]
46. ! [X0] : (((kind(X0) & old(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~kind(X0) | ~old(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) & patient(X0)) | humble(john)) & (~humble(john) | ! [X0] : (calm(X0) | ~patient(X0))) [nnf transformation 13]
48. (? [X0] : (~calm(X0) & patient(X0)) | humble(john)) & (~humble(john) | ! [X1] : (calm(X1) | ~patient(X1))) [rectify 47]
49. ? [X0] : (~calm(X0) & patient(X0)) => (~calm(sK0) & patient(sK0)) [choice axiom]
50. ((~calm(sK0) & patient(sK0)) | humble(john)) & (~humble(john) | ! [X1] : (calm(X1) | ~patient(X1))) [skolemisation 48,49]
65. ~brave(X0) | ~old(X0) [cnf transformation 25]
69. ~happy(X0) | ~calm(X0) [cnf transformation 36]
73. happy(X0) | ~calm(X0) | brave(X0) [cnf transformation 37]
74. ~happy(X0) | calm(X0) | brave(X0) [cnf transformation 37]
79. ~humble(X0) | calm(X0) | ~strong(X0) [cnf transformation 32]
80. ~strong(X0) | calm(X0) | happy(X0) [cnf transformation 32]
87. ~wise(X0) | ~humble(X0) | happy(X0) | ~strong(X0) [cnf transformation 41]
97. strong(alice) | strong(X0) [cnf transformation 33]
98. happy(alice) | strong(X0) [cnf transformation 33]
99. ~happy(X0) | humble(X0) [cnf transformation 44]
104. old(X0) | old(X0) | ~patient(X0) [cnf transformation 46]
109. patient(sK0) | humble(john) [cnf transformation 50]
129. wise(john) [cnf transformation 23]
131. ~patient(X0) | old(X0) [duplicate literal removal 104]
134. ~happy(X0) | brave(X0) [subsumption resolution 74,69]
135. ~calm(X0) | brave(X0) [subsumption resolution 73,134]
168. 7 <=> ! [X0] : strong(X0) [avatar definition]
169. strong(X0) <- (7) [avatar component clause 168]
171. 8 <=> happy(alice) [avatar definition]
173. happy(alice) <- (8) [avatar component clause 171]
174. 7 | 8 [avatar split clause 98,171,168]
176. 9 <=> strong(alice) [avatar definition]
178. strong(alice) <- (9) [avatar component clause 176]
179. 7 | 9 [avatar split clause 97,176,168]
182. 10 <=> humble(john) [avatar definition]
191. 12 <=> patient(sK0) [avatar definition]
193. patient(sK0) <- (12) [avatar component clause 191]
194. 10 | 12 [avatar split clause 109,191,182]
295. old(sK0) <- (12) [resolution 131,193]
314. happy(X0) | calm(X0) <- (7) [resolution 80,169]
360. ~humble(john) | happy(john) | ~strong(john) [resolution 87,129]
362. calm(X0) | brave(X0) <- (7) [resolution 314,134]
364. humble(X2) | calm(X2) <- (7) [resolution 314,99]
368. brave(X0) <- (7) [subsumption resolution 362,135]
380. ~old(X1) <- (7) [resolution 368,65]
395. calm(X3) | calm(X3) | ~strong(X3) <- (7) [resolution 364,79]
399. calm(X3) | ~strong(X3) <- (7) [duplicate literal removal 395]
401. calm(X3) <- (7) [subsumption resolution 399,169]
402. $false <- (7, 12) [resolution 380,295]
403. ~7 | ~12 [avatar contradiction clause 402]
404. ~humble(john) | happy(john) <- (7) [subsumption resolution 360,169]
406. 37 <=> happy(john) [avatar definition]
408. happy(john) <- (37) [avatar component clause 406]
409. 37 | ~10 | ~7 [avatar split clause 404,168,182,406]
418. ~calm(john) <- (37) [resolution 408,69]
419. $false <- (7, 37) [subsumption resolution 418,401]
420. ~7 | ~37 [avatar contradiction clause 419]
461. humble(alice) <- (8) [resolution 173,99]
463. ~calm(alice) <- (8) [resolution 173,69]
484. calm(alice) | ~strong(alice) <- (8) [resolution 461,79]
486. ~strong(alice) <- (8) [subsumption resolution 484,463]
487. $false <- (8, 9) [subsumption resolution 486,178]
488. ~8 | ~9 [avatar contradiction clause 487]
489. $false [avatar sat refutation 174,179,194,403,409,420,488]
% SZS output end Proof for 2973287425833617447742661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either patient or not humble then someone is wise.
If someone is both strong and not old then alice is not strong and vice versa.
If someone is patient then alice is both not old and wise.
If john is not humble or curious then someone is not rich or not old.
Everyone who is rich is either not humble or not curious and vice versa.
If lucy is not strong or not generous then paul is either not old or generous and vice versa.
Everyone who is not creative or not strong is not patient or calm and vice versa.
If someone is not quiet then mary is tall or not happy and vice versa.
If lucy is curious or happy then paul is either not funny or rich.
If someone is curious then someone is not tall and vice versa.
If paul is humble or not tall then paul is funny.
If paul is generous then fred is not calm or not patient and vice versa.
If susan is both calm and not generous then someone is not humble or calm.
Everyone who is not kind or generous is strong or not strong.
If lucy is kind or happy then alice is both not happy and not kind.
Someone is either not patient or not wise.
Mary is curious or rich.
Susan is not curious or calm.
Mary is not patient or not generous.
Paul is both happy and not humble.
Someone is either funny or not wise.
Someone is tall or kind.
Fred is generous. | Fred is not tall. | neutral | (((patient(mary)<~>~humble(mary)))=>(?[X]:(wise(X))))&
((?[X]:((strong(X)&~old(X))))<=>(~strong(alice)))&
((?[X]:(patient(X)))=>((~old(alice)&wise(alice))))&
(((~humble(john)|curious(john)))=>(?[X]:((~rich(X)|~old(X)))))&
(![X]:(rich(X)<=>(~humble(X)<~>~curious(X))))&
(((~strong(lucy)|~generous(lucy)))<=>((~old(paul)<~>generous(paul))))&
(![X]:((~creative(X)|~strong(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~quiet(X)))<=>((tall(mary)|~happy(mary))))&
(((curious(lucy)|happy(lucy)))=>((~funny(paul)<~>rich(paul))))&
((?[X]:(curious(X)))<=>(?[X]:(~tall(X))))&
(((humble(paul)|~tall(paul)))=>(funny(paul)))&
((generous(paul))<=>((~calm(fred)|~patient(fred))))&
(((calm(susan)&~generous(susan)))=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((~kind(X)|generous(X))=>(strong(X)|~strong(X))))&
(((kind(lucy)|happy(lucy)))=>((~happy(alice)&~kind(alice))))&
(?[X]:((~patient(X)<~>~wise(X))))&
((curious(mary)|rich(mary)))&
((~curious(susan)|calm(susan)))&
((~patient(mary)|~generous(mary)))&
((happy(paul)&~humble(paul)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((tall(X)|kind(X))))&
(generous(fred)) | ~tall(fred) | [] | null | 0 |
Everyone who is creative is both not tall and quiet and vice versa.
Everyone who is patient or not creative is both generous and happy.
If alice is either not kind or not generous then fred is either brave or not happy and vice versa.
Everyone who is funny or not quiet is both not strong and quiet and vice versa.
If mary is creative or not brave then someone is not tall or quiet and vice versa.
Everyone who is creative is not tall or not curious.
If someone is not generous then someone is both not calm and funny and vice versa.
If lucy is not wise or old then someone is old or patient.
Everyone who is either old or not creative is creative.
Everyone who is wise or not curious is not humble.
Everyone who is not wise or not funny is curious or humble and vice versa.
If paul is not curious then susan is either not generous or not quiet and vice versa.
If alice is either not happy or wise then john is both not happy and rich.
Everyone who is both not calm and not rich is old and vice versa.
Everyone who is not calm or not wise is either creative or not rich and vice versa.
If alice is either old or happy then someone is either brave or not funny.
Someone is both curious and strong.
Paul is both not old and not strong.
Mary is brave.
Mary is happy or rich.
Fred is both quiet and not wise.
Fred is either happy or not tall.
Someone is wise or brave. | Fred is not tall. | neutral | (![X]:(creative(X)<=>(~tall(X)&quiet(X))))&
(![X]:((patient(X)|~creative(X))=>(generous(X)&happy(X))))&
(((~kind(alice)<~>~generous(alice)))<=>((brave(fred)<~>~happy(fred))))&
(![X]:((funny(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
(((creative(mary)|~brave(mary)))<=>(?[X]:((~tall(X)|quiet(X)))))&
(![X]:(creative(X)=>(~tall(X)|~curious(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~calm(X)&funny(X)))))&
(((~wise(lucy)|old(lucy)))=>(?[X]:((old(X)|patient(X)))))&
(![X]:((old(X)<~>~creative(X))=>creative(X)))&
(![X]:((wise(X)|~curious(X))=>~humble(X)))&
(![X]:((~wise(X)|~funny(X))<=>(curious(X)|humble(X))))&
((~curious(paul))<=>((~generous(susan)<~>~quiet(susan))))&
(((~happy(alice)<~>wise(alice)))=>((~happy(john)&rich(john))))&
(![X]:((~calm(X)&~rich(X))<=>old(X)))&
(![X]:((~calm(X)|~wise(X))<=>(creative(X)<~>~rich(X))))&
(((old(alice)<~>happy(alice)))=>(?[X]:((brave(X)<~>~funny(X)))))&
(?[X]:((curious(X)&strong(X))))&
((~old(paul)&~strong(paul)))&
(brave(mary))&
((happy(mary)|rich(mary)))&
((quiet(fred)&~wise(fred)))&
((happy(fred)<~>~tall(fred)))&
(?[X]:((wise(X)|brave(X)))) | ~tall(fred) | [] | null | 0 |
If someone is either old or not brave then paul is old or not humble.
If susan is either not rich or not creative then susan is both not quiet and funny.
If someone is wise then lucy is either rich or calm and vice versa.
Everyone who is strong or not kind is brave or old.
Everyone who is generous or not generous is both not patient and not funny and vice versa.
If someone is both not humble and funny then someone is either rich or tall and vice versa.
Everyone who is not generous or funny is both kind and not humble and vice versa.
Everyone who is both old and generous is old.
If someone is both humble and funny then someone is not generous.
Everyone who is either quiet or creative is not rich or brave and vice versa.
Everyone who is not calm is tall.
If someone is kind then susan is either quiet or rich and vice versa.
Everyone who is not creative or generous is either not old or not patient and vice versa.
Everyone who is rich is not wise or not happy and vice versa.
If susan is kind or not happy then someone is calm or patient and vice versa.
If fred is either old or humble then someone is generous or strong and vice versa.
Alice is not rich or not old.
Someone is either not quiet or not calm.
Someone is quiet or not generous.
Susan is both calm and not strong.
Someone is either strong or not quiet.
Someone is either not rich or strong.
Someone is both calm and not humble.
Fred is either creative or generous. | Susan is not patient. | entailment | ((?[X]:((old(X)<~>~brave(X))))=>((old(paul)|~humble(paul))))&
(((~rich(susan)<~>~creative(susan)))=>((~quiet(susan)&funny(susan))))&
((?[X]:(wise(X)))<=>((rich(lucy)<~>calm(lucy))))&
(![X]:((strong(X)|~kind(X))=>(brave(X)|old(X))))&
(![X]:((generous(X)|~generous(X))<=>(~patient(X)&~funny(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((~generous(X)|funny(X))<=>(kind(X)&~humble(X))))&
(![X]:((old(X)&generous(X))=>old(X)))&
((?[X]:((humble(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(~rich(X)|brave(X))))&
(![X]:(~calm(X)=>tall(X)))&
((?[X]:(kind(X)))<=>((quiet(susan)<~>rich(susan))))&
(![X]:((~creative(X)|generous(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(rich(X)<=>(~wise(X)|~happy(X))))&
(((kind(susan)|~happy(susan)))<=>(?[X]:((calm(X)|patient(X)))))&
(((old(fred)<~>humble(fred)))<=>(?[X]:((generous(X)|strong(X)))))&
((~rich(alice)|~old(alice)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:((quiet(X)|~generous(X))))&
((calm(susan)&~strong(susan)))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:((calm(X)&~humble(X))))&
((creative(fred)<~>generous(fred))) | ~patient(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5573789098905106169765361
% SZS output start Proof for 5573789098905106169765361
5. ! [X0] : ((~generous(X0) | generous(X0)) <=> (~funny(X0) & ~patient(X0))) [input p4]
25. patient(susan) [input hypothesis]
43. ! [X0] : (((~generous(X0) | generous(X0)) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((~generous(X0) | generous(X0) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | (generous(X0) & ~generous(X0)))) [flattening 43]
100. ~patient(X0) | ~generous(X0) [cnf transformation 44]
101. ~patient(X0) | generous(X0) [cnf transformation 44]
162. patient(susan) [cnf transformation 25]
219. ~patient(X0) [subsumption resolution 100,101]
343. $false [subsumption resolution 162,219]
% SZS output end Proof for 5573789098905106169765361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and strong is old and vice versa. Everyone who is both patient and not kind is not kind. Everyone who is either not happy or strong is happy or humble and vice versa. If someone is humble or not wise then someone is rich. Everyone who is not patient is either not quiet or kind and vice versa. If someone is either strong or calm then susan is curious or not generous and vice versa. If someone is quiet then alice is not wise or not strong. Everyone who is both not curious and not brave is either creative or not wise and vice versa. Everyone who is calm is both not wise and happy and vice versa. Everyone who is either not kind or happy is not old. If fred is both not generous and not curious then someone is not curious. If john is not curious or humble then someone is both quiet and not calm. Everyone who is old or humble is both curious and brave. If mary is either quiet or not patient then someone is not rich. Everyone who is not old or not creative is both quiet and not curious and vice versa. If mary is both tall and not happy then someone is tall or not rich and vice versa. John is not tall or not kind. Paul is both kind and not calm. Someone is not humble or not happy. Alice is not strong or not quiet. John is not curious. Susan is either curious or not wise. Fred is both happy and not humble. Mary is not patient. | Mary is not patient. | entailment | (![X]:((humble(X)&strong(X))<=>old(X)))&
(![X]:((patient(X)&~kind(X))=>~kind(X)))&
(![X]:((~happy(X)<~>strong(X))<=>(happy(X)|humble(X))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>kind(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>((curious(susan)|~generous(susan))))&
((?[X]:(quiet(X)))=>((~wise(alice)|~strong(alice))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:(calm(X)<=>(~wise(X)&happy(X))))&
(![X]:((~kind(X)<~>happy(X))=>~old(X)))&
(((~generous(fred)&~curious(fred)))=>(?[X]:(~curious(X))))&
(((~curious(john)|humble(john)))=>(?[X]:((quiet(X)&~calm(X)))))&
(![X]:((old(X)|humble(X))=>(curious(X)&brave(X))))&
(((quiet(mary)<~>~patient(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)|~creative(X))<=>(quiet(X)&~curious(X))))&
(((tall(mary)&~happy(mary)))<=>(?[X]:((tall(X)|~rich(X)))))&
((~tall(john)|~kind(john)))&
((kind(paul)&~calm(paul)))&
(?[X]:((~humble(X)|~happy(X))))&
((~strong(alice)|~quiet(alice)))&
(~curious(john))&
((curious(susan)<~>~wise(susan)))&
((happy(fred)&~humble(fred)))&
(~patient(mary)) | ~patient(mary) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6468001782245648834362160
% SZS output start Proof for 6468001782245648834362160
24. ~patient(mary) [input p23]
25. patient(mary) [input hypothesis]
138. ~patient(mary) [cnf transformation 24]
139. patient(mary) [cnf transformation 25]
229. 20 <=> patient(mary) [avatar definition]
299. ~20 [avatar split clause 138,229]
300. 20 [avatar split clause 139,229]
301. $false [avatar sat refutation 299,300]
% SZS output end Proof for 6468001782245648834362160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not rich then mary is quiet or not old and vice versa. Everyone who is both not patient and quiet is not happy. Everyone who is old or kind is old and vice versa. If susan is either generous or not quiet then lucy is not rich. Everyone who is wise is creative or happy and vice versa. Everyone who is funny is both not creative and generous and vice versa. If paul is either tall or not creative then lucy is calm or not creative and vice versa. Everyone who is not happy or not humble is rich and vice versa. If someone is not strong or creative then mary is not rich and vice versa. If someone is both calm and not humble then fred is either not humble or funny. Everyone who is brave is either not patient or calm. Everyone who is kind or not creative is not curious or kind and vice versa. If lucy is both strong and old then someone is both quiet and strong. Everyone who is old is both not humble and not funny. If someone is not patient then fred is not happy. Everyone who is old is happy or not kind and vice versa. Someone is either not humble or not strong. Mary is not kind or wise. John is not happy. Alice is curious or not curious. Someone is either not old or kind. Someone is either not generous or quiet. | Alice is patient. | neutral | ((?[X]:((~brave(X)<~>~rich(X))))<=>((quiet(mary)|~old(mary))))&
(![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X)))) | patient(alice) | [] | null | 0 |
Everyone who is not rich or not humble is tall and vice versa.
If alice is both humble and tall then someone is both rich and curious.
If mary is either wise or funny then alice is either not rich or brave.
Everyone who is brave is kind.
Everyone who is calm is both humble and happy and vice versa.
Everyone who is not brave or not wise is not strong.
Everyone who is either not patient or humble is either not strong or calm.
If susan is both not creative and not kind then fred is either strong or not generous and vice versa.
If someone is either quiet or not creative then mary is either kind or generous and vice versa.
Everyone who is not wise is brave or not funny.
Everyone who is not wise is curious or tall and vice versa.
Everyone who is not happy or strong is either not brave or not old and vice versa.
Everyone who is rich is creative.
Everyone who is calm is not rich.
If someone is either happy or not funny then someone is both tall and not brave and vice versa.
Everyone who is not funny or not wise is not curious or rich.
Someone is either not old or wise.
Someone is not humble or quiet.
Someone is old or tall.
Someone is kind or not rich.
John is curious.
John is quiet.
Susan is generous or wise. | John is not strong. | entailment | (![X]:((~rich(X)|~humble(X))<=>tall(X)))&
(((humble(alice)&tall(alice)))=>(?[X]:((rich(X)&curious(X)))))&
(((wise(mary)<~>funny(mary)))=>((~rich(alice)<~>brave(alice))))&
(![X]:(brave(X)=>kind(X)))&
(![X]:(calm(X)<=>(humble(X)&happy(X))))&
(![X]:((~brave(X)|~wise(X))=>~strong(X)))&
(![X]:((~patient(X)<~>humble(X))=>(~strong(X)<~>calm(X))))&
(((~creative(susan)&~kind(susan)))<=>((strong(fred)<~>~generous(fred))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>((kind(mary)<~>generous(mary))))&
(![X]:(~wise(X)=>(brave(X)|~funny(X))))&
(![X]:(~wise(X)<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)|strong(X))<=>(~brave(X)<~>~old(X))))&
(![X]:(rich(X)=>creative(X)))&
(![X]:(calm(X)=>~rich(X)))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~funny(X)|~wise(X))=>(~curious(X)|rich(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((kind(X)|~rich(X))))&
(curious(john))&
(quiet(john))&
((generous(susan)|wise(susan))) | ~strong(john) | [
"p5",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5633889196972553642448524
% SZS output start Proof for 5633889196972553642448524
6. ! [X0] : ((~wise(X0) | ~brave(X0)) => ~strong(X0)) [input p5]
11. ! [X0] : (~wise(X0) <=> (tall(X0) | curious(X0))) [input p10]
21. curious(john) [input p20]
24. strong(john) [input hypothesis]
30. ! [X0] : (~strong(X0) | (wise(X0) & brave(X0))) [ennf transformation 6]
52. ! [X0] : ((~wise(X0) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((~wise(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | wise(X0))) [flattening 52]
84. ~strong(X0) | wise(X0) [cnf transformation 30]
105. ~wise(X0) | ~curious(X0) [cnf transformation 53]
128. curious(john) [cnf transformation 21]
131. strong(john) [cnf transformation 24]
306. wise(john) [resolution 84,131]
307. ~curious(john) [resolution 105,306]
308. $false [subsumption resolution 307,128]
% SZS output end Proof for 5633889196972553642448524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not kind is curious or patient and vice versa. If alice is not funny or strong then someone is not strong or creative. Everyone who is both not old and quiet is both not old and not humble and vice versa. Everyone who is not creative is either curious or calm. If mary is either curious or not funny then mary is both quiet and strong and vice versa. Everyone who is either not patient or humble is both not tall and not old and vice versa. If susan is creative then someone is both quiet and not quiet. If susan is either not patient or tall then someone is not creative or not funny and vice versa. If susan is both wise and humble then lucy is both not creative and tall and vice versa. Everyone who is both humble and curious is not creative and vice versa. Everyone who is brave or not happy is not patient or not strong. Everyone who is not patient is curious or creative and vice versa. If someone is patient or kind then someone is patient or happy. If lucy is either wise or not generous then john is not old or not tall. Someone is tall. Someone is either not generous or patient. Someone is not happy or not humble. Someone is funny or not kind. Mary is rich or not quiet. John is old or generous. Someone is both happy and tall. | Susan is not tall. | entailment | (![X]:((~wise(X)&~kind(X))<=>(curious(X)|patient(X))))&
(((~funny(alice)|strong(alice)))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((~old(X)&quiet(X))<=>(~old(X)&~humble(X))))&
(![X]:(~creative(X)=>(curious(X)<~>calm(X))))&
(((curious(mary)<~>~funny(mary)))<=>((quiet(mary)&strong(mary))))&
(![X]:((~patient(X)<~>humble(X))<=>(~tall(X)&~old(X))))&
((creative(susan))=>(?[X]:((quiet(X)&~quiet(X)))))&
(((~patient(susan)<~>tall(susan)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((wise(susan)&humble(susan)))<=>((~creative(lucy)&tall(lucy))))&
(![X]:((humble(X)&curious(X))<=>~creative(X)))&
(![X]:((brave(X)|~happy(X))=>(~patient(X)|~strong(X))))&
(![X]:(~patient(X)<=>(curious(X)|creative(X))))&
((?[X]:((patient(X)|kind(X))))=>(?[X]:((patient(X)|happy(X)))))&
(((wise(lucy)<~>~generous(lucy)))=>((~old(john)|~tall(john))))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)<~>patient(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((funny(X)|~kind(X))))&
((rich(mary)|~quiet(mary)))&
((old(john)|generous(john)))&
(?[X]:((happy(X)&tall(X)))) | ~tall(susan) | [
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 182090017112391161969313
% SZS output start Proof for 182090017112391161969313
7. creative(susan) => ? [X0] : (~quiet(X0) & quiet(X0)) [input p6]
8. (~patient(susan) <~> tall(susan)) <=> ? [X0] : (~funny(X0) | ~creative(X0)) [input p7]
10. ! [X0] : ((curious(X0) & humble(X0)) <=> ~creative(X0)) [input p9]
12. ! [X0] : (~patient(X0) <=> (creative(X0) | curious(X0))) [input p11]
22. tall(susan) [input hypothesis]
28. ? [X0] : (~quiet(X0) & quiet(X0)) | ~creative(susan) [ennf transformation 7]
45. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK1) & quiet(sK1)) [choice axiom]
46. (~quiet(sK1) & quiet(sK1)) | ~creative(susan) [skolemisation 28,45]
47. (((~tall(susan) | patient(susan)) & (tall(susan) | ~patient(susan))) | ! [X0] : (funny(X0) & creative(X0))) & (? [X0] : (~funny(X0) | ~creative(X0)) | ((~patient(susan) | ~tall(susan)) & (tall(susan) | patient(susan)))) [nnf transformation 8]
48. (((~tall(susan) | patient(susan)) & (tall(susan) | ~patient(susan))) | ! [X0] : (funny(X0) & creative(X0))) & (? [X1] : (~funny(X1) | ~creative(X1)) | ((~patient(susan) | ~tall(susan)) & (tall(susan) | patient(susan)))) [rectify 47]
49. ? [X1] : (~funny(X1) | ~creative(X1)) => (~funny(sK2) | ~creative(sK2)) [choice axiom]
50. (((~tall(susan) | patient(susan)) & (tall(susan) | ~patient(susan))) | ! [X0] : (funny(X0) & creative(X0))) & ((~funny(sK2) | ~creative(sK2)) | ((~patient(susan) | ~tall(susan)) & (tall(susan) | patient(susan)))) [skolemisation 48,49]
53. ! [X0] : (((curious(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | (~curious(X0) | ~humble(X0)))) [nnf transformation 10]
54. ! [X0] : (((curious(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | ~curious(X0) | ~humble(X0))) [flattening 53]
55. ! [X0] : ((~patient(X0) | (~creative(X0) & ~curious(X0))) & ((creative(X0) | curious(X0)) | patient(X0))) [nnf transformation 12]
56. ! [X0] : ((~patient(X0) | (~creative(X0) & ~curious(X0))) & (creative(X0) | curious(X0) | patient(X0))) [flattening 55]
97. quiet(sK1) | ~creative(susan) [cnf transformation 46]
98. ~quiet(sK1) | ~creative(susan) [cnf transformation 46]
103. ~tall(susan) | patient(susan) | creative(X0) [cnf transformation 50]
111. creative(X0) | curious(X0) [cnf transformation 54]
114. ~patient(X0) | ~curious(X0) [cnf transformation 56]
128. tall(susan) [cnf transformation 22]
170. 9 <=> creative(susan) [avatar definition]
172. ~creative(susan) <- (~9) [avatar component clause 170]
174. 10 <=> quiet(sK1) [avatar definition]
177. ~9 | ~10 [avatar split clause 98,174,170]
178. ~9 | 10 [avatar split clause 97,174,170]
183. 12 <=> patient(susan) [avatar definition]
185. patient(susan) <- (12) [avatar component clause 183]
187. 13 <=> tall(susan) [avatar definition]
192. 14 <=> ! [X0] : creative(X0) [avatar definition]
193. creative(X0) <- (14) [avatar component clause 192]
194. 14 | 12 | ~13 [avatar split clause 103,187,183,192]
294. 13 [avatar split clause 128,187]
303. curious(susan) <- (~9) [resolution 111,172]
305. ~curious(susan) <- (12) [resolution 114,185]
307. $false <- (~9, 12) [subsumption resolution 305,303]
308. 9 | ~12 [avatar contradiction clause 307]
311. $false <- (~9, 14) [resolution 193,172]
314. 9 | ~14 [avatar contradiction clause 311]
315. $false [avatar sat refutation 177,178,194,294,308,314]
% SZS output end Proof for 182090017112391161969313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or calm is both not humble and generous and vice versa. If john is either not funny or not calm then lucy is calm or funny and vice versa. Everyone who is either funny or brave is either patient or happy. Everyone who is both humble and not calm is both brave and not generous. Everyone who is either not patient or creative is curious or patient and vice versa. If mary is funny then paul is either not generous or humble and vice versa. Everyone who is curious or not tall is kind and vice versa. If someone is not strong or not rich then someone is either happy or not rich. If fred is either calm or curious then lucy is both kind and not calm and vice versa. If someone is either happy or creative then susan is not old or not kind. If mary is not funny or calm then someone is not patient or wise. If someone is both happy and not generous then susan is both rich and not calm. Everyone who is not old or not calm is old. Everyone who is not old is either patient or kind and vice versa. If someone is not quiet or humble then alice is not patient. John is old. Someone is not generous or not old. Someone is generous or strong. John is old or not strong. Susan is not calm. Mary is funny or patient. Someone is happy or generous. | Susan is calm. | contradiction | (![X]:((humble(X)|calm(X))<=>(~humble(X)&generous(X))))&
(((~funny(john)<~>~calm(john)))<=>((calm(lucy)|funny(lucy))))&
(![X]:((funny(X)<~>brave(X))=>(patient(X)<~>happy(X))))&
(![X]:((humble(X)&~calm(X))=>(brave(X)&~generous(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(curious(X)|patient(X))))&
((funny(mary))<=>((~generous(paul)<~>humble(paul))))&
(![X]:((curious(X)|~tall(X))<=>kind(X)))&
((?[X]:((~strong(X)|~rich(X))))=>(?[X]:((happy(X)<~>~rich(X)))))&
(((calm(fred)<~>curious(fred)))<=>((kind(lucy)&~calm(lucy))))&
((?[X]:((happy(X)<~>creative(X))))=>((~old(susan)|~kind(susan))))&
(((~funny(mary)|calm(mary)))=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((happy(X)&~generous(X))))=>((rich(susan)&~calm(susan))))&
(![X]:((~old(X)|~calm(X))=>old(X)))&
(![X]:(~old(X)<=>(patient(X)<~>kind(X))))&
((?[X]:((~quiet(X)|humble(X))))=>(~patient(alice)))&
(old(john))&
(?[X]:((~generous(X)|~old(X))))&
(?[X]:((generous(X)|strong(X))))&
((old(john)|~strong(john)))&
(~calm(susan))&
((funny(mary)|patient(mary)))&
(?[X]:((happy(X)|generous(X)))) | calm(susan) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 133609010660658931527750
% SZS output start Proof for 133609010660658931527750
20. ~calm(susan) [input p19]
23. calm(susan) [input hypothesis]
115. ~calm(susan) [cnf transformation 20]
118. calm(susan) [cnf transformation 23]
215. 19 <=> calm(susan) [avatar definition]
236. ~19 [avatar split clause 115,215]
251. 19 [avatar split clause 118,215]
252. $false [avatar sat refutation 236,251]
% SZS output end Proof for 133609010660658931527750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and creative then susan is not happy.
If paul is not happy then someone is not generous or brave.
If susan is both not creative and not curious then someone is either funny or calm and vice versa.
If alice is either not wise or brave then alice is creative and vice versa.
Everyone who is not calm is either not patient or quiet.
If mary is patient then someone is both tall and curious and vice versa.
If someone is old then john is both not tall and happy.
Everyone who is both generous and quiet is both not curious and not funny.
Everyone who is not humble is either not curious or brave and vice versa.
Everyone who is creative is both tall and kind and vice versa.
If paul is not rich or patient then fred is not old and vice versa.
If someone is funny then lucy is both not happy and humble and vice versa.
Everyone who is not creative or tall is both calm and not curious and vice versa.
If susan is either calm or not kind then someone is both happy and not wise.
If someone is either not patient or not curious then someone is either not calm or creative and vice versa.
Everyone who is not strong or not curious is brave.
Someone is either calm or curious.
Paul is either strong or wise.
Alice is either not kind or wise.
Susan is old or brave.
Susan is not rich.
Alice is not tall.
Alice is not creative.
John is funny or tall. | Alice is kind. | contradiction | ((?[X]:((old(X)&creative(X))))=>(~happy(susan)))&
((~happy(paul))=>(?[X]:((~generous(X)|brave(X)))))&
(((~creative(susan)&~curious(susan)))<=>(?[X]:((funny(X)<~>calm(X)))))&
(((~wise(alice)<~>brave(alice)))<=>(creative(alice)))&
(![X]:(~calm(X)=>(~patient(X)<~>quiet(X))))&
((patient(mary))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:(old(X)))=>((~tall(john)&happy(john))))&
(![X]:((generous(X)&quiet(X))=>(~curious(X)&~funny(X))))&
(![X]:(~humble(X)<=>(~curious(X)<~>brave(X))))&
(![X]:(creative(X)<=>(tall(X)&kind(X))))&
(((~rich(paul)|patient(paul)))<=>(~old(fred)))&
((?[X]:(funny(X)))<=>((~happy(lucy)&humble(lucy))))&
(![X]:((~creative(X)|tall(X))<=>(calm(X)&~curious(X))))&
(((calm(susan)<~>~kind(susan)))=>(?[X]:((happy(X)&~wise(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~strong(X)|~curious(X))=>brave(X)))&
(?[X]:((calm(X)<~>curious(X))))&
((strong(paul)<~>wise(paul)))&
((~kind(alice)<~>wise(alice)))&
((old(susan)|brave(susan)))&
(~rich(susan))&
(~tall(alice))&
(~creative(alice))&
((funny(john)|tall(john))) | kind(alice) | [
"p3",
"p12",
"p15",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3562547856534830780536972
% SZS output start Proof for 3562547856534830780536972
4. (~wise(alice) <~> brave(alice)) <=> creative(alice) [input p3]
13. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (~curious(X0) & calm(X0))) [input p12]
16. ! [X0] : ((~curious(X0) | ~strong(X0)) => brave(X0)) [input p15]
19. ~kind(alice) <~> wise(alice) [input p18]
23. ~creative(alice) [input p22]
25. kind(alice) [input hypothesis]
33. ! [X0] : (brave(X0) | (curious(X0) & strong(X0))) [ennf transformation 16]
39. (((~brave(alice) | wise(alice)) & (brave(alice) | ~wise(alice))) | ~creative(alice)) & (creative(alice) | ((~wise(alice) | ~brave(alice)) & (brave(alice) | wise(alice)))) [nnf transformation 4]
55. ! [X0] : (((tall(X0) | ~creative(X0)) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | (~tall(X0) & creative(X0)))) [nnf transformation 13]
56. ! [X0] : ((tall(X0) | ~creative(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | (~tall(X0) & creative(X0)))) [flattening 55]
69. (~wise(alice) | kind(alice)) & (wise(alice) | ~kind(alice)) [nnf transformation 19]
78. creative(alice) | ~wise(alice) | ~brave(alice) [cnf transformation 39]
103. ~curious(X0) | creative(X0) [cnf transformation 56]
119. curious(X0) | brave(X0) [cnf transformation 33]
124. wise(alice) | ~kind(alice) [cnf transformation 69]
129. ~creative(alice) [cnf transformation 23]
131. kind(alice) [cnf transformation 25]
169. 9 <=> creative(alice) [avatar definition]
171. ~creative(alice) <- (~9) [avatar component clause 169]
173. 10 <=> wise(alice) [avatar definition]
177. 11 <=> brave(alice) [avatar definition]
179. ~brave(alice) <- (~11) [avatar component clause 177]
182. ~11 | ~10 | 9 [avatar split clause 78,169,173,177]
325. 41 <=> kind(alice) [avatar definition]
329. ~41 | 10 [avatar split clause 124,173,325]
339. ~9 [avatar split clause 129,169]
345. 41 [avatar split clause 131,325]
360. brave(X0) | creative(X0) [resolution 119,103]
426. creative(alice) <- (~11) [resolution 360,179]
429. $false <- (~9, ~11) [subsumption resolution 426,171]
430. 9 | 11 [avatar contradiction clause 429]
432. $false [avatar sat refutation 182,329,339,345,430]
% SZS output end Proof for 3562547856534830780536972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.045 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both curious and not old. If someone is not happy then paul is quiet or humble. If paul is generous then someone is either rich or not humble and vice versa. If john is not humble or not old then someone is old or generous. Everyone who is both not patient and not calm is calm or not creative. If someone is either strong or funny then someone is happy or not old and vice versa. Everyone who is not creative is both calm and not rich. Everyone who is kind or not funny is either creative or not quiet. If someone is creative or kind then alice is either not humble or old. Everyone who is not humble is tall. If someone is either humble or not creative then someone is both not rich and funny and vice versa. If fred is both old and happy then someone is either not funny or not strong and vice versa. Everyone who is not funny is not generous and vice versa. If fred is either not wise or patient then lucy is either not kind or old and vice versa. If fred is humble then someone is not kind or not rich. Everyone who is both calm and not tall is not humble or generous and vice versa. Mary is both rich and quiet. Alice is either humble or rich. Paul is creative or quiet. Someone is calm or generous. Someone is either not patient or tall. Mary is either quiet or not happy. | Paul is tall. | contradiction | (![X]:(~old(X)=>(curious(X)&~old(X))))&
((?[X]:(~happy(X)))=>((quiet(paul)|humble(paul))))&
((generous(paul))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~humble(john)|~old(john)))=>(?[X]:((old(X)|generous(X)))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~creative(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:(~creative(X)=>(calm(X)&~rich(X))))&
(![X]:((kind(X)|~funny(X))=>(creative(X)<~>~quiet(X))))&
((?[X]:((creative(X)|kind(X))))=>((~humble(alice)<~>old(alice))))&
(![X]:(~humble(X)=>tall(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
(((old(fred)&happy(fred)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~funny(X)<=>~generous(X)))&
(((~wise(fred)<~>patient(fred)))<=>((~kind(lucy)<~>old(lucy))))&
((humble(fred))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((calm(X)&~tall(X))<=>(~humble(X)|generous(X))))&
((rich(mary)&quiet(mary)))&
((humble(alice)<~>rich(alice)))&
((creative(paul)|quiet(paul)))&
(?[X]:((calm(X)|generous(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((quiet(mary)<~>~happy(mary))) | tall(paul) | [
"p2",
"p9",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2364339965817812687598953
% SZS output start Proof for 2364339965817812687598953
3. generous(paul) <=> ? [X0] : (rich(X0) <~> ~humble(X0)) [input p2]
10. ! [X0] : (~humble(X0) => tall(X0)) [input p9]
16. ! [X0] : ((~tall(X0) & calm(X0)) <=> (generous(X0) | ~humble(X0))) [input p15]
17. quiet(mary) & rich(mary) [input p16]
23. tall(paul) [input hypothesis]
36. ! [X0] : (tall(X0) | humble(X0)) [ennf transformation 10]
38. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X0] : ((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~generous(paul)) [nnf transformation 3]
39. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) | ~generous(paul)) [rectify 38]
40. ? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) => ((humble(sK0) | ~rich(sK0)) & (~humble(sK0) | rich(sK0))) [choice axiom]
41. (generous(paul) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(sK0) | ~rich(sK0)) & (~humble(sK0) | rich(sK0))) | ~generous(paul)) [skolemisation 39,40]
65. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 16]
66. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | tall(X0) | ~calm(X0))) [flattening 65]
78. generous(paul) | ~humble(X0) | ~rich(X0) [cnf transformation 41]
99. tall(X0) | humble(X0) [cnf transformation 36]
126. ~tall(X0) | humble(X0) [cnf transformation 66]
127. ~tall(X0) | ~generous(X0) [cnf transformation 66]
128. rich(mary) [cnf transformation 17]
138. tall(paul) [cnf transformation 23]
156. 5 <=> generous(paul) [avatar definition]
158. generous(paul) <- (5) [avatar component clause 156]
161. 6 <=> ! [X0] : (~humble(X0) | ~rich(X0)) [avatar definition]
162. ~humble(X0) | ~rich(X0) <- (6) [avatar component clause 161]
163. 6 | 5 [avatar split clause 78,156,161]
334. humble(X0) [subsumption resolution 126,99]
362. ~rich(X0) <- (6) [subsumption resolution 162,334]
363. $false <- (6) [resolution 362,128]
364. ~6 [avatar contradiction clause 363]
375. ~generous(paul) [resolution 127,138]
377. $false <- (5) [subsumption resolution 375,158]
378. ~5 [avatar contradiction clause 377]
379. $false [avatar sat refutation 163,364,378]
% SZS output end Proof for 2364339965817812687598953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either generous or old then fred is both not curious and happy.
If john is wise then susan is both calm and creative.
Everyone who is wise or not brave is not patient.
Everyone who is rich is not strong or tall and vice versa.
Everyone who is both not calm and not funny is brave or not strong.
Everyone who is strong is happy or not strong.
If someone is either humble or not calm then mary is not humble or quiet.
If someone is either rich or not kind then someone is either brave or patient and vice versa.
If someone is not kind or not generous then someone is not rich or tall and vice versa.
If someone is not funny or patient then someone is wise or not brave.
Everyone who is both not kind and not calm is not calm and vice versa.
Everyone who is either not creative or calm is either not tall or funny and vice versa.
Everyone who is both not creative and not kind is rich and vice versa.
If mary is not old or not happy then john is either not brave or not rich and vice versa.
Everyone who is wise or not strong is brave or not rich.
Everyone who is patient or quiet is both quiet and wise.
Paul is generous.
Paul is either not wise or not calm.
Mary is either not strong or tall.
Mary is not wise.
Lucy is either brave or curious.
Someone is rich or funny. | Lucy is not generous. | neutral | (((generous(paul)<~>old(paul)))=>((~curious(fred)&happy(fred))))&
((wise(john))=>((calm(susan)&creative(susan))))&
(![X]:((wise(X)|~brave(X))=>~patient(X)))&
(![X]:(rich(X)<=>(~strong(X)|tall(X))))&
(![X]:((~calm(X)&~funny(X))=>(brave(X)|~strong(X))))&
(![X]:(strong(X)=>(happy(X)|~strong(X))))&
((?[X]:((humble(X)<~>~calm(X))))=>((~humble(mary)|quiet(mary))))&
((?[X]:((rich(X)<~>~kind(X))))<=>(?[X]:((brave(X)<~>patient(X)))))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((~rich(X)|tall(X)))))&
((?[X]:((~funny(X)|patient(X))))=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:((~kind(X)&~calm(X))<=>~calm(X)))&
(![X]:((~creative(X)<~>calm(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~creative(X)&~kind(X))<=>rich(X)))&
(((~old(mary)|~happy(mary)))<=>((~brave(john)<~>~rich(john))))&
(![X]:((wise(X)|~strong(X))=>(brave(X)|~rich(X))))&
(![X]:((patient(X)|quiet(X))=>(quiet(X)&wise(X))))&
(generous(paul))&
((~wise(paul)<~>~calm(paul)))&
((~strong(mary)<~>tall(mary)))&
(~wise(mary))&
((brave(lucy)<~>curious(lucy)))&
(?[X]:((rich(X)|funny(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is both not calm and not rich is both not kind and not creative.
If someone is not curious then someone is either not strong or wise.
Everyone who is either not strong or not happy is not curious and vice versa.
Everyone who is wise is either generous or not happy.
If someone is not funny or not kind then someone is not tall.
Everyone who is either tall or not humble is both tall and calm and vice versa.
If mary is either not rich or patient then lucy is both funny and not old and vice versa.
Everyone who is not tall or not wise is both calm and not kind.
If someone is strong then fred is both not funny and rich.
Everyone who is calm or not quiet is either tall or not rich and vice versa.
Everyone who is both brave and not generous is both not curious and calm.
If lucy is either strong or not brave then someone is not creative.
If paul is not strong then someone is both creative and brave.
If mary is both old and happy then someone is both not wise and quiet.
Everyone who is both not kind and creative is either wise or kind and vice versa.
Everyone who is both wise and creative is either calm or curious.
Someone is brave or not happy.
Someone is both kind and not patient.
Fred is not curious.
Alice is not old or patient.
Someone is either not funny or rich.
Someone is either old or not creative.
John is not curious or not creative.
Fred is either not rich or not strong. | Fred is not happy. | contradiction | (![X]:((~calm(X)&~rich(X))=>(~kind(X)&~creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~strong(X)<~>~happy(X))<=>~curious(X)))&
(![X]:(wise(X)=>(generous(X)<~>~happy(X))))&
((?[X]:((~funny(X)|~kind(X))))=>(?[X]:(~tall(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(tall(X)&calm(X))))&
(((~rich(mary)<~>patient(mary)))<=>((funny(lucy)&~old(lucy))))&
(![X]:((~tall(X)|~wise(X))=>(calm(X)&~kind(X))))&
((?[X]:(strong(X)))=>((~funny(fred)&rich(fred))))&
(![X]:((calm(X)|~quiet(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((brave(X)&~generous(X))=>(~curious(X)&calm(X))))&
(((strong(lucy)<~>~brave(lucy)))=>(?[X]:(~creative(X))))&
((~strong(paul))=>(?[X]:((creative(X)&brave(X)))))&
(((old(mary)&happy(mary)))=>(?[X]:((~wise(X)&quiet(X)))))&
(![X]:((~kind(X)&creative(X))<=>(wise(X)<~>kind(X))))&
(![X]:((wise(X)&creative(X))=>(calm(X)<~>curious(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((kind(X)&~patient(X))))&
(~curious(fred))&
((~old(alice)|patient(alice)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((old(X)<~>~creative(X))))&
((~curious(john)|~creative(john)))&
((~rich(fred)<~>~strong(fred))) | ~happy(fred) | [
"p2",
"p8",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8594937594506562961659862
% SZS output start Proof for 8594937594506562961659862
3. ! [X0] : ((~strong(X0) <~> ~happy(X0)) <=> ~curious(X0)) [input p2]
9. ? [X0] : strong(X0) => (rich(fred) & ~funny(fred)) [input p8]
19. ~curious(fred) [input p18]
24. ~rich(fred) <~> ~strong(fred) [input p23]
25. ~happy(fred) [input hypothesis]
34. (rich(fred) & ~funny(fred)) | ! [X0] : ~strong(X0) [ennf transformation 9]
47. ! [X0] : ((((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | curious(X0)) & (~curious(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0))))) [nnf transformation 3]
78. (strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred)) [nnf transformation 24]
86. happy(X0) | strong(X0) | curious(X0) [cnf transformation 47]
108. rich(fred) | ~strong(X0) [cnf transformation 34]
134. ~curious(fred) [cnf transformation 19]
141. ~strong(fred) | ~rich(fred) [cnf transformation 78]
143. ~happy(fred) [cnf transformation 25]
196. 11 <=> ! [X0] : ~strong(X0) [avatar definition]
197. ~strong(X0) <- (11) [avatar component clause 196]
199. 12 <=> rich(fred) [avatar definition]
202. 11 | 12 [avatar split clause 108,199,196]
307. 34 <=> strong(fred) [avatar definition]
309. strong(fred) <- (34) [avatar component clause 307]
311. ~12 | ~34 [avatar split clause 141,307,199]
337. strong(fred) | curious(fred) [resolution 86,143]
355. strong(fred) [subsumption resolution 337,134]
356. 34 [avatar split clause 355,307]
374. $false <- (11, 34) [resolution 309,197]
376. ~11 | ~34 [avatar contradiction clause 374]
377. $false [avatar sat refutation 202,311,356,376]
% SZS output end Proof for 8594937594506562961659862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave or not curious then someone is either creative or calm. Everyone who is patient is either curious or generous. Everyone who is not calm is not humble or strong. If fred is happy or not happy then paul is brave or generous and vice versa. If alice is not funny then someone is not old and vice versa. If someone is both not patient and old then mary is humble or calm. If someone is tall or kind then john is not brave or not generous and vice versa. If someone is not brave or tall then susan is not creative and vice versa. If someone is not tall then alice is tall or not tall and vice versa. Everyone who is either not patient or patient is not wise and vice versa. Everyone who is either not old or not rich is both patient and brave. Everyone who is either generous or humble is both wise and not curious. If susan is not funny then lucy is both strong and generous. If someone is not humble or not curious then mary is quiet. If someone is both not funny and not rich then someone is not strong or creative. If someone is either brave or rich then lucy is not happy or not quiet. Someone is curious. Someone is not rich. Paul is both rich and patient. John is both curious and happy. Someone is both not curious and calm. Susan is both creative and not wise. Someone is either not generous or not brave. Someone is either kind or old. | Mary is wise. | contradiction | ((?[X]:((brave(X)|~curious(X))))=>(?[X]:((creative(X)<~>calm(X)))))&
(![X]:(patient(X)=>(curious(X)<~>generous(X))))&
(![X]:(~calm(X)=>(~humble(X)|strong(X))))&
(((happy(fred)|~happy(fred)))<=>((brave(paul)|generous(paul))))&
((~funny(alice))<=>(?[X]:(~old(X))))&
((?[X]:((~patient(X)&old(X))))=>((humble(mary)|calm(mary))))&
((?[X]:((tall(X)|kind(X))))<=>((~brave(john)|~generous(john))))&
((?[X]:((~brave(X)|tall(X))))<=>(~creative(susan)))&
((?[X]:(~tall(X)))<=>((tall(alice)|~tall(alice))))&
(![X]:((~patient(X)<~>patient(X))<=>~wise(X)))&
(![X]:((~old(X)<~>~rich(X))=>(patient(X)&brave(X))))&
(![X]:((generous(X)<~>humble(X))=>(wise(X)&~curious(X))))&
((~funny(susan))=>((strong(lucy)&generous(lucy))))&
((?[X]:((~humble(X)|~curious(X))))=>(quiet(mary)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~strong(X)|creative(X)))))&
((?[X]:((brave(X)<~>rich(X))))=>((~happy(lucy)|~quiet(lucy))))&
(?[X]:(curious(X)))&
(?[X]:(~rich(X)))&
((rich(paul)&patient(paul)))&
((curious(john)&happy(john)))&
(?[X]:((~curious(X)&calm(X))))&
((creative(susan)&~wise(susan)))&
(?[X]:((~generous(X)<~>~brave(X))))&
(?[X]:((kind(X)<~>old(X)))) | wise(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7514225817027896615269268
% SZS output start Proof for 7514225817027896615269268
10. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> ~wise(X0)) [input p9]
25. wise(mary) [input hypothesis]
66. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | wise(X0)) & (~wise(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 10]
109. ~wise(X0) | patient(X0) | patient(X0) [cnf transformation 66]
110. ~wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 66]
142. wise(mary) [cnf transformation 25]
143. ~wise(X0) | patient(X0) [duplicate literal removal 109]
144. ~wise(X0) | ~patient(X0) [duplicate literal removal 110]
256. ~wise(X0) [subsumption resolution 143,144]
331. $false [subsumption resolution 142,256]
% SZS output end Proof for 7514225817027896615269268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not strong then fred is not strong or not patient. If john is not curious or not wise then someone is not calm or rich. If someone is rich then someone is both creative and humble. Everyone who is either not funny or happy is either not curious or not humble. Everyone who is either curious or not generous is wise and vice versa. Everyone who is either brave or not humble is both tall and not tall. If fred is both not calm and old then someone is not brave and vice versa. If lucy is both not tall and tall then someone is not generous or not humble and vice versa. Everyone who is either not generous or humble is both not curious and strong and vice versa. If someone is rich or not patient then someone is either not calm or generous and vice versa. If lucy is not funny then lucy is not rich or not calm. If someone is generous or brave then someone is either curious or kind and vice versa. If someone is either patient or calm then susan is both not curious and not wise. If someone is creative then someone is creative or funny. Everyone who is kind is either humble or not generous and vice versa. Mary is either patient or not strong. Paul is tall. Someone is not brave. Someone is both humble and patient. Someone is not curious. John is not happy. Someone is creative. | Fred is wise. | contradiction | (((funny(lucy)<~>~strong(lucy)))=>((~strong(fred)|~patient(fred))))&
(((~curious(john)|~wise(john)))=>(?[X]:((~calm(X)|rich(X)))))&
((?[X]:(rich(X)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((~funny(X)<~>happy(X))=>(~curious(X)<~>~humble(X))))&
(![X]:((curious(X)<~>~generous(X))<=>wise(X)))&
(![X]:((brave(X)<~>~humble(X))=>(tall(X)&~tall(X))))&
(((~calm(fred)&old(fred)))<=>(?[X]:(~brave(X))))&
(((~tall(lucy)&tall(lucy)))<=>(?[X]:((~generous(X)|~humble(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~curious(X)&strong(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~calm(X)<~>generous(X)))))&
((~funny(lucy))=>((~rich(lucy)|~calm(lucy))))&
((?[X]:((generous(X)|brave(X))))<=>(?[X]:((curious(X)<~>kind(X)))))&
((?[X]:((patient(X)<~>calm(X))))=>((~curious(susan)&~wise(susan))))&
((?[X]:(creative(X)))=>(?[X]:((creative(X)|funny(X)))))&
(![X]:(kind(X)<=>(humble(X)<~>~generous(X))))&
((patient(mary)<~>~strong(mary)))&
(tall(paul))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)&patient(X))))&
(?[X]:(~curious(X)))&
(~happy(john))&
(?[X]:(creative(X))) | wise(fred) | [
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4334862418861801715739926
% SZS output start Proof for 4334862418861801715739926
5. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> wise(X0)) [input p4]
8. (tall(lucy) & ~tall(lucy)) <=> ? [X0] : (~humble(X0) | ~generous(X0)) [input p7]
9. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (strong(X0) & ~curious(X0))) [input p8]
23. wise(fred) [input hypothesis]
45. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | ~wise(X0)) & (wise(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 5]
52. ((tall(lucy) & ~tall(lucy)) | ! [X0] : (humble(X0) & generous(X0))) & (? [X0] : (~humble(X0) | ~generous(X0)) | (~tall(lucy) | tall(lucy))) [nnf transformation 8]
53. ((tall(lucy) & ~tall(lucy)) | ! [X0] : (humble(X0) & generous(X0))) & (? [X0] : (~humble(X0) | ~generous(X0)) | ~tall(lucy) | tall(lucy)) [flattening 52]
54. ((tall(lucy) & ~tall(lucy)) | ! [X0] : (humble(X0) & generous(X0))) & (? [X1] : (~humble(X1) | ~generous(X1)) | ~tall(lucy) | tall(lucy)) [rectify 53]
55. ? [X1] : (~humble(X1) | ~generous(X1)) => (~humble(sK3) | ~generous(sK3)) [choice axiom]
56. ((tall(lucy) & ~tall(lucy)) | ! [X0] : (humble(X0) & generous(X0))) & ((~humble(sK3) | ~generous(sK3)) | ~tall(lucy) | tall(lucy)) [skolemisation 54,55]
57. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~strong(X0) | curious(X0))) & ((strong(X0) & ~curious(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~strong(X0) | curious(X0)) & ((strong(X0) & ~curious(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [flattening 57]
95. ~generous(X0) | curious(X0) | ~wise(X0) [cnf transformation 45]
105. ~tall(lucy) | generous(X0) [cnf transformation 56]
106. ~tall(lucy) | humble(X0) [cnf transformation 56]
107. tall(lucy) | generous(X0) [cnf transformation 56]
108. tall(lucy) | humble(X0) [cnf transformation 56]
110. ~generous(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 58]
146. wise(fred) [cnf transformation 23]
217. 16 <=> ! [X0] : humble(X0) [avatar definition]
218. humble(X0) <- (16) [avatar component clause 217]
220. 17 <=> tall(lucy) [avatar definition]
223. 16 | 17 [avatar split clause 108,220,217]
225. 18 <=> ! [X0] : generous(X0) [avatar definition]
226. generous(X0) <- (18) [avatar component clause 225]
227. 18 | 17 [avatar split clause 107,220,225]
228. 16 | ~17 [avatar split clause 106,220,217]
229. 18 | ~17 [avatar split clause 105,220,225]
365. ~wise(X1) | curious(X1) <- (18) [resolution 95,226]
368. curious(fred) <- (18) [resolution 365,146]
378. ~curious(X1) | ~humble(X1) <- (18) [resolution 110,226]
380. ~curious(X1) <- (16, 18) [subsumption resolution 378,218]
385. $false <- (16, 18) [resolution 380,368]
386. ~16 | ~18 [avatar contradiction clause 385]
388. $false [avatar sat refutation 223,227,228,229,386]
% SZS output end Proof for 4334862418861801715739926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is not humble then someone is brave and vice versa. Everyone who is both not patient and not rich is tall and vice versa. If someone is not strong or not brave then someone is either curious or tall. Everyone who is tall or not calm is not brave. If someone is not generous then someone is curious and vice versa. If john is humble then someone is both tall and not patient and vice versa. If susan is both not rich and not funny then mary is not funny or patient and vice versa. If someone is calm then lucy is either not wise or not creative and vice versa. Everyone who is curious or not generous is either old or funny. Everyone who is not creative or old is both not funny and tall. If mary is either not humble or not creative then someone is either not kind or patient and vice versa. If someone is both happy and not funny then someone is not wise and vice versa. If lucy is kind then someone is either not wise or not calm. If someone is not generous or brave then someone is not tall or not calm. Everyone who is quiet or not generous is both calm and not old and vice versa. Everyone who is not brave is kind or not wise. Lucy is not wise or not rich. John is not humble. Someone is happy or not strong. Someone is humble or not curious. Someone is not quiet. Susan is both calm and not tall. Susan is either not humble or happy. Someone is strong or tall. | Lucy is tall. | contradiction | ((~humble(lucy))<=>(?[X]:(brave(X))))&
(![X]:((~patient(X)&~rich(X))<=>tall(X)))&
((?[X]:((~strong(X)|~brave(X))))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((tall(X)|~calm(X))=>~brave(X)))&
((?[X]:(~generous(X)))<=>(?[X]:(curious(X))))&
((humble(john))<=>(?[X]:((tall(X)&~patient(X)))))&
(((~rich(susan)&~funny(susan)))<=>((~funny(mary)|patient(mary))))&
((?[X]:(calm(X)))<=>((~wise(lucy)<~>~creative(lucy))))&
(![X]:((curious(X)|~generous(X))=>(old(X)<~>funny(X))))&
(![X]:((~creative(X)|old(X))=>(~funny(X)&tall(X))))&
(((~humble(mary)<~>~creative(mary)))<=>(?[X]:((~kind(X)<~>patient(X)))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:(~wise(X))))&
((kind(lucy))=>(?[X]:((~wise(X)<~>~calm(X)))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(~brave(X)=>(kind(X)|~wise(X))))&
((~wise(lucy)|~rich(lucy)))&
(~humble(john))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~quiet(X)))&
((calm(susan)&~tall(susan)))&
((~humble(susan)<~>happy(susan)))&
(?[X]:((strong(X)|tall(X)))) | tall(lucy) | [
"p1",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9079298171862451781290145
% SZS output start Proof for 9079298171862451781290145
2. ! [X0] : ((~rich(X0) & ~patient(X0)) <=> tall(X0)) [input p1]
6. humble(john) <=> ? [X0] : (~patient(X0) & tall(X0)) [input p5]
18. ~humble(john) [input p17]
25. tall(lucy) [input hypothesis]
42. ! [X0] : (((~rich(X0) & ~patient(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) | patient(X0)))) [nnf transformation 2]
43. ! [X0] : (((~rich(X0) & ~patient(X0)) | ~tall(X0)) & (tall(X0) | rich(X0) | patient(X0))) [flattening 42]
53. (humble(john) | ! [X0] : (patient(X0) | ~tall(X0))) & (? [X0] : (~patient(X0) & tall(X0)) | ~humble(john)) [nnf transformation 6]
54. (humble(john) | ! [X0] : (patient(X0) | ~tall(X0))) & (? [X1] : (~patient(X1) & tall(X1)) | ~humble(john)) [rectify 53]
55. ? [X1] : (~patient(X1) & tall(X1)) => (~patient(sK4) & tall(sK4)) [choice axiom]
56. (humble(john) | ! [X0] : (patient(X0) | ~tall(X0))) & ((~patient(sK4) & tall(sK4)) | ~humble(john)) [skolemisation 54,55]
93. ~patient(X0) | ~tall(X0) [cnf transformation 43]
105. humble(john) | patient(X0) | ~tall(X0) [cnf transformation 56]
145. ~humble(john) [cnf transformation 18]
154. tall(lucy) [cnf transformation 25]
202. humble(john) | ~tall(X0) [subsumption resolution 105,93]
204. 12 <=> ! [X0] : ~tall(X0) [avatar definition]
205. ~tall(X0) <- (12) [avatar component clause 204]
207. 13 <=> humble(john) [avatar definition]
210. 12 | 13 [avatar split clause 202,207,204]
341. ~13 [avatar split clause 145,207]
385. $false <- (12) [resolution 205,154]
386. ~12 [avatar contradiction clause 385]
387. $false [avatar sat refutation 210,341,386]
% SZS output end Proof for 9079298171862451781290145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not patient is both not patient and rich and vice versa. Everyone who is calm or not creative is tall and vice versa. Everyone who is patient or creative is not brave. If susan is either not kind or old then lucy is rich or kind and vice versa. If someone is not patient then someone is both curious and not patient. If john is creative or not rich then someone is either not curious or curious and vice versa. Everyone who is either not kind or tall is not strong or kind. Everyone who is both strong and not wise is both generous and not tall. If someone is not tall or tall then someone is wise. If mary is not happy or creative then someone is both not funny and not brave and vice versa. Everyone who is either kind or creative is both patient and not quiet. If someone is not brave then alice is both not tall and not kind and vice versa. If john is both tall and generous then paul is curious or not tall. Everyone who is either not kind or not old is not strong or not quiet. If someone is quiet or not quiet then lucy is patient. Everyone who is not funny or not kind is calm or not funny. Mary is either not rich or not quiet. Susan is either not tall or tall. Someone is curious or humble. Alice is either curious or calm. Susan is old or generous. | Paul is quiet. | neutral | (![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(![X]:((calm(X)|~creative(X))<=>tall(X)))&
(![X]:((patient(X)|creative(X))=>~brave(X)))&
(((~kind(susan)<~>old(susan)))<=>((rich(lucy)|kind(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:((curious(X)&~patient(X)))))&
(((creative(john)|~rich(john)))<=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:((~kind(X)<~>tall(X))=>(~strong(X)|kind(X))))&
(![X]:((strong(X)&~wise(X))=>(generous(X)&~tall(X))))&
((?[X]:((~tall(X)|tall(X))))=>(?[X]:(wise(X))))&
(((~happy(mary)|creative(mary)))<=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((kind(X)<~>creative(X))=>(patient(X)&~quiet(X))))&
((?[X]:(~brave(X)))<=>((~tall(alice)&~kind(alice))))&
(((tall(john)&generous(john)))=>((curious(paul)|~tall(paul))))&
(![X]:((~kind(X)<~>~old(X))=>(~strong(X)|~quiet(X))))&
((?[X]:((quiet(X)|~quiet(X))))=>(patient(lucy)))&
(![X]:((~funny(X)|~kind(X))=>(calm(X)|~funny(X))))&
((~rich(mary)<~>~quiet(mary)))&
((~tall(susan)<~>tall(susan)))&
(?[X]:((curious(X)|humble(X))))&
((curious(alice)<~>calm(alice)))&
((old(susan)|generous(susan))) | quiet(paul) | [] | null | 0 |
If lucy is both old and kind then lucy is old or wise. Everyone who is both not rich and not tall is not quiet or not generous and vice versa. If susan is humble or not happy then someone is both old and humble and vice versa. Everyone who is funny is either quiet or not calm. Everyone who is rich or generous is not old and vice versa. Everyone who is not curious is either happy or generous and vice versa. Everyone who is not patient or not rich is both kind and not old and vice versa. If someone is not brave or brave then someone is not happy. If someone is humble or not creative then fred is either not old or brave and vice versa. Everyone who is both not tall and strong is either not wise or not tall. Everyone who is not strong or funny is not brave and vice versa. Everyone who is both old and calm is creative or not brave. If someone is either not creative or calm then john is both humble and creative. Everyone who is both not tall and creative is either strong or rich. If someone is not humble then someone is creative. If someone is either not humble or strong then someone is old or not strong and vice versa. Someone is either patient or happy. Someone is not old or old. Lucy is kind. Someone is either funny or rich. Lucy is both not calm and creative. Someone is not brave. Someone is not brave or wise. John is not humble. | Susan is not curious. | contradiction | (((old(lucy)&kind(lucy)))=>((old(lucy)|wise(lucy))))&
(![X]:((~rich(X)&~tall(X))<=>(~quiet(X)|~generous(X))))&
(((humble(susan)|~happy(susan)))<=>(?[X]:((old(X)&humble(X)))))&
(![X]:(funny(X)=>(quiet(X)<~>~calm(X))))&
(![X]:((rich(X)|generous(X))<=>~old(X)))&
(![X]:(~curious(X)<=>(happy(X)<~>generous(X))))&
(![X]:((~patient(X)|~rich(X))<=>(kind(X)&~old(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~happy(X))))&
((?[X]:((humble(X)|~creative(X))))<=>((~old(fred)<~>brave(fred))))&
(![X]:((~tall(X)&strong(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((~strong(X)|funny(X))<=>~brave(X)))&
(![X]:((old(X)&calm(X))=>(creative(X)|~brave(X))))&
((?[X]:((~creative(X)<~>calm(X))))=>((humble(john)&creative(john))))&
(![X]:((~tall(X)&creative(X))=>(strong(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:(creative(X))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((old(X)|~strong(X)))))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((~old(X)|old(X))))&
(kind(lucy))&
(?[X]:((funny(X)<~>rich(X))))&
((~calm(lucy)&creative(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|wise(X))))&
(~humble(john)) | ~curious(susan) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5003585655092460648261936
% SZS output start Proof for 5003585655092460648261936
2. ! [X0] : ((~tall(X0) & ~rich(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p1]
3. (~happy(susan) | humble(susan)) <=> ? [X0] : (humble(X0) & old(X0)) [input p2]
5. ! [X0] : ((generous(X0) | rich(X0)) <=> ~old(X0)) [input p4]
6. ! [X0] : (~curious(X0) <=> (happy(X0) <~> generous(X0))) [input p5]
7. ! [X0] : ((~rich(X0) | ~patient(X0)) <=> (~old(X0) & kind(X0))) [input p6]
25. ~curious(susan) [input hypothesis]
29. ! [X0] : (~curious(X0) => (happy(X0) <~> generous(X0))) [unused predicate definition removal 6]
33. ! [X0] : ((happy(X0) <~> generous(X0)) | curious(X0)) [ennf transformation 29]
43. ! [X0] : (((~tall(X0) & ~rich(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (tall(X0) | rich(X0)))) [nnf transformation 2]
44. ! [X0] : (((~tall(X0) & ~rich(X0)) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | tall(X0) | rich(X0))) [flattening 43]
45. ((~happy(susan) | humble(susan)) | ! [X0] : (~humble(X0) | ~old(X0))) & (? [X0] : (humble(X0) & old(X0)) | (happy(susan) & ~humble(susan))) [nnf transformation 3]
46. (~happy(susan) | humble(susan) | ! [X0] : (~humble(X0) | ~old(X0))) & (? [X0] : (humble(X0) & old(X0)) | (happy(susan) & ~humble(susan))) [flattening 45]
47. (~happy(susan) | humble(susan) | ! [X0] : (~humble(X0) | ~old(X0))) & (? [X1] : (humble(X1) & old(X1)) | (happy(susan) & ~humble(susan))) [rectify 46]
48. ? [X1] : (humble(X1) & old(X1)) => (humble(sK0) & old(sK0)) [choice axiom]
49. (~happy(susan) | humble(susan) | ! [X0] : (~humble(X0) | ~old(X0))) & ((humble(sK0) & old(sK0)) | (happy(susan) & ~humble(susan))) [skolemisation 47,48]
51. ! [X0] : (((generous(X0) | rich(X0)) | old(X0)) & (~old(X0) | (~generous(X0) & ~rich(X0)))) [nnf transformation 5]
52. ! [X0] : ((generous(X0) | rich(X0) | old(X0)) & (~old(X0) | (~generous(X0) & ~rich(X0)))) [flattening 51]
53. ! [X0] : (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | curious(X0)) [nnf transformation 33]
54. ! [X0] : (((~rich(X0) | ~patient(X0)) | (old(X0) | ~kind(X0))) & ((~old(X0) & kind(X0)) | (rich(X0) & patient(X0)))) [nnf transformation 7]
55. ! [X0] : ((~rich(X0) | ~patient(X0) | old(X0) | ~kind(X0)) & ((~old(X0) & kind(X0)) | (rich(X0) & patient(X0)))) [flattening 54]
91. ~rich(X0) | generous(X0) [cnf transformation 44]
95. old(sK0) | happy(susan) [cnf transformation 49]
101. ~rich(X0) | ~old(X0) [cnf transformation 52]
103. generous(X0) | rich(X0) | old(X0) [cnf transformation 52]
105. ~happy(X0) | ~generous(X0) | curious(X0) [cnf transformation 53]
109. ~old(X0) | rich(X0) [cnf transformation 55]
149. ~curious(susan) [cnf transformation 25]
159. 3 <=> happy(susan) [avatar definition]
160. happy(susan) <- (3) [avatar component clause 159]
170. 5 <=> old(sK0) [avatar definition]
172. old(sK0) <- (5) [avatar component clause 170]
173. 3 | 5 [avatar split clause 95,170,159]
175. generous(X0) | old(X0) [subsumption resolution 103,91]
177. ~old(X0) [subsumption resolution 109,101]
299. $false <- (5) [subsumption resolution 172,177]
300. ~5 [avatar contradiction clause 299]
333. ~generous(susan) | curious(susan) <- (3) [resolution 105,160]
334. ~generous(susan) <- (3) [subsumption resolution 333,149]
335. old(susan) <- (3) [resolution 334,175]
336. $false <- (3) [subsumption resolution 335,177]
337. ~3 [avatar contradiction clause 336]
338. $false [avatar sat refutation 173,300,337]
% SZS output end Proof for 5003585655092460648261936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not creative is not patient and vice versa.
If someone is old then mary is both humble and not quiet and vice versa.
If john is both strong and curious then paul is either not old or not rich and vice versa.
Everyone who is either generous or humble is either calm or not curious.
Everyone who is not generous or rich is kind and vice versa.
Everyone who is either not patient or creative is creative.
If someone is not rich then susan is brave.
Everyone who is humble or funny is not old and vice versa.
Everyone who is not kind is rich or not old and vice versa.
Everyone who is either not brave or not rich is either not calm or curious.
If someone is either humble or tall then someone is both rich and brave and vice versa.
Everyone who is either not creative or tall is generous.
If mary is both not happy and not creative then lucy is both brave and old and vice versa.
Everyone who is not humble or not curious is not calm and vice versa.
Everyone who is kind is patient.
Everyone who is kind or generous is creative.
Someone is tall or patient.
Fred is both not old and curious.
Mary is both not strong and tall.
Susan is either happy or quiet.
Paul is either not kind or tall.
Someone is not strong.
John is both humble and patient.
Someone is wise or calm. | Susan is not brave. | contradiction | (![X]:((~tall(X)<~>~creative(X))<=>~patient(X)))&
((?[X]:(old(X)))<=>((humble(mary)&~quiet(mary))))&
(((strong(john)&curious(john)))<=>((~old(paul)<~>~rich(paul))))&
(![X]:((generous(X)<~>humble(X))=>(calm(X)<~>~curious(X))))&
(![X]:((~generous(X)|rich(X))<=>kind(X)))&
(![X]:((~patient(X)<~>creative(X))=>creative(X)))&
((?[X]:(~rich(X)))=>(brave(susan)))&
(![X]:((humble(X)|funny(X))<=>~old(X)))&
(![X]:(~kind(X)<=>(rich(X)|~old(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(~calm(X)<~>curious(X))))&
((?[X]:((humble(X)<~>tall(X))))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~creative(X)<~>tall(X))=>generous(X)))&
(((~happy(mary)&~creative(mary)))<=>((brave(lucy)&old(lucy))))&
(![X]:((~humble(X)|~curious(X))<=>~calm(X)))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((kind(X)|generous(X))=>creative(X)))&
(?[X]:((tall(X)|patient(X))))&
((~old(fred)&curious(fred)))&
((~strong(mary)&tall(mary)))&
((happy(susan)<~>quiet(susan)))&
((~kind(paul)<~>tall(paul)))&
(?[X]:(~strong(X)))&
((humble(john)&patient(john)))&
(?[X]:((wise(X)|calm(X)))) | ~brave(susan) | [
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4195761786750499617358910
% SZS output start Proof for 4195761786750499617358910
5. ! [X0] : ((rich(X0) | ~generous(X0)) <=> kind(X0)) [input p4]
7. ? [X0] : ~rich(X0) => brave(susan) [input p6]
9. ! [X0] : (~kind(X0) <=> (~old(X0) | rich(X0))) [input p8]
25. ~brave(susan) [input hypothesis]
30. brave(susan) | ! [X0] : rich(X0) [ennf transformation 7]
44. ! [X0] : (((rich(X0) | ~generous(X0)) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | ~generous(X0) | ~kind(X0)) & (kind(X0) | (~rich(X0) & generous(X0)))) [flattening 44]
49. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | kind(X0))) [nnf transformation 9]
50. ! [X0] : ((~kind(X0) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | kind(X0))) [flattening 49]
86. kind(X0) | ~rich(X0) [cnf transformation 45]
90. brave(susan) | rich(X0) [cnf transformation 30]
95. ~kind(X0) | ~rich(X0) [cnf transformation 50]
131. ~brave(susan) [cnf transformation 25]
174. 9 <=> ! [X0] : rich(X0) [avatar definition]
175. rich(X0) <- (9) [avatar component clause 174]
177. 10 <=> brave(susan) [avatar definition]
180. 9 | 10 [avatar split clause 90,177,174]
181. ~rich(X0) [subsumption resolution 95,86]
250. ~10 [avatar split clause 131,177]
251. $false <- (9) [subsumption resolution 175,181]
252. ~9 [avatar contradiction clause 251]
253. $false [avatar sat refutation 180,250,252]
% SZS output end Proof for 4195761786750499617358910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then someone is funny.
Everyone who is not calm is both rich and old.
Everyone who is not old is not happy.
Everyone who is strong or not curious is old.
If someone is both wise and not generous then lucy is not patient or not quiet and vice versa.
Everyone who is not calm or not humble is both not kind and tall.
Everyone who is humble or not generous is not rich or not tall.
Everyone who is not tall or calm is either not patient or humble and vice versa.
Everyone who is both not happy and not old is tall and vice versa.
Everyone who is either creative or rich is generous or not rich and vice versa.
If someone is not humble or not wise then someone is quiet.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
Someone is both not patient and brave.
Fred is not tall.
Paul is both calm and strong.
Fred is either strong or not generous.
Someone is rich or not kind.
Someone is either not rich or happy.
Paul is patient or tall. | Paul is not tall. | entailment | ((?[X]:(~tall(X)))=>(?[X]:(funny(X))))&
(![X]:(~calm(X)=>(rich(X)&old(X))))&
(![X]:(~old(X)=>~happy(X)))&
(![X]:((strong(X)|~curious(X))=>old(X)))&
((?[X]:((wise(X)&~generous(X))))<=>((~patient(lucy)|~quiet(lucy))))&
(![X]:((~calm(X)|~humble(X))=>(~kind(X)&tall(X))))&
(![X]:((humble(X)|~generous(X))=>(~rich(X)|~tall(X))))&
(![X]:((~tall(X)|calm(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((~happy(X)&~old(X))<=>tall(X)))&
(![X]:((creative(X)<~>rich(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(?[X]:((~patient(X)&brave(X))))&
(~tall(fred))&
((calm(paul)&strong(paul)))&
((strong(fred)<~>~generous(fred)))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
((patient(paul)|tall(paul))) | ~tall(paul) | [
"p3",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3682395299027865215336413
% SZS output start Proof for 3682395299027865215336413
4. ! [X0] : ((~curious(X0) | strong(X0)) => old(X0)) [input p3]
9. ! [X0] : ((~old(X0) & ~happy(X0)) <=> tall(X0)) [input p8]
19. strong(paul) & calm(paul) [input p18]
24. tall(paul) [input hypothesis]
29. ! [X0] : (strong(X0) => old(X0)) [pure predicate removal 4]
33. ! [X0] : (old(X0) | ~strong(X0)) [ennf transformation 29]
47. ! [X0] : (((~old(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | (old(X0) | happy(X0)))) [nnf transformation 9]
48. ! [X0] : (((~old(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | old(X0) | happy(X0))) [flattening 47]
84. ~strong(X0) | old(X0) [cnf transformation 33]
104. ~old(X0) | ~tall(X0) [cnf transformation 48]
133. strong(paul) [cnf transformation 19]
140. tall(paul) [cnf transformation 24]
300. old(paul) [resolution 84,133]
307. ~tall(paul) [resolution 104,300]
310. $false [subsumption resolution 307,140]
% SZS output end Proof for 3682395299027865215336413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not kind is funny. Everyone who is both patient and not quiet is not curious and vice versa. Everyone who is wise is not rich or not calm and vice versa. If someone is both rich and not curious then john is both brave and creative. If john is either generous or not happy then lucy is both old and happy and vice versa. Everyone who is rich or generous is humble or not generous and vice versa. If someone is not wise or not curious then someone is not curious. Everyone who is either kind or not generous is both not wise and creative and vice versa. Everyone who is either brave or curious is brave. Everyone who is rich is not rich or rich and vice versa. If someone is not funny then someone is either tall or old and vice versa. If john is tall then john is either generous or not generous and vice versa. If susan is not wise then alice is kind. Everyone who is either creative or wise is not humble or funny and vice versa. If someone is both not patient and curious then paul is curious and vice versa. Mary is both funny and not tall. Lucy is both brave and not humble. Someone is either not funny or quiet. Someone is not patient. Alice is not calm. | John is not generous. | neutral | (![X]:((curious(X)|~kind(X))=>funny(X)))&
(![X]:((patient(X)&~quiet(X))<=>~curious(X)))&
(![X]:(wise(X)<=>(~rich(X)|~calm(X))))&
((?[X]:((rich(X)&~curious(X))))=>((brave(john)&creative(john))))&
(((generous(john)<~>~happy(john)))<=>((old(lucy)&happy(lucy))))&
(![X]:((rich(X)|generous(X))<=>(humble(X)|~generous(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~wise(X)&creative(X))))&
(![X]:((brave(X)<~>curious(X))=>brave(X)))&
(![X]:(rich(X)<=>(~rich(X)|rich(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((tall(X)<~>old(X)))))&
((tall(john))<=>((generous(john)<~>~generous(john))))&
((~wise(susan))=>(kind(alice)))&
(![X]:((creative(X)<~>wise(X))<=>(~humble(X)|funny(X))))&
((?[X]:((~patient(X)&curious(X))))<=>(curious(paul)))&
((funny(mary)&~tall(mary)))&
((brave(lucy)&~humble(lucy)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:(~patient(X)))&
(~calm(alice)) | ~generous(john) | [] | null | 0 |
Everyone who is either patient or curious is not old or not funny and vice versa.
Everyone who is not kind or not wise is generous and vice versa.
Everyone who is kind is creative or not curious and vice versa.
If john is both humble and patient then someone is both generous and not rich and vice versa.
If alice is old then fred is either not calm or not happy.
Everyone who is not patient or not quiet is not funny and vice versa.
Everyone who is not curious or calm is happy and vice versa.
If someone is both creative and tall then someone is either not patient or not tall.
Everyone who is both curious and tall is not quiet and vice versa.
If susan is not creative then mary is calm and vice versa.
Everyone who is both not rich and not curious is either calm or not kind and vice versa.
If fred is either funny or not kind then someone is curious.
Everyone who is creative or wise is either wise or kind.
If susan is either not old or not curious then susan is both not patient and calm and vice versa.
Everyone who is not patient is either kind or calm and vice versa.
Everyone who is not strong is both calm and not tall and vice versa.
Someone is either strong or rich.
Someone is both not rich and quiet.
Someone is not brave or not patient.
Someone is not funny.
Mary is calm.
John is not strong or old. | John is not wise. | entailment | (![X]:((patient(X)<~>curious(X))<=>(~old(X)|~funny(X))))&
(![X]:((~kind(X)|~wise(X))<=>generous(X)))&
(![X]:(kind(X)<=>(creative(X)|~curious(X))))&
(((humble(john)&patient(john)))<=>(?[X]:((generous(X)&~rich(X)))))&
((old(alice))=>((~calm(fred)<~>~happy(fred))))&
(![X]:((~patient(X)|~quiet(X))<=>~funny(X)))&
(![X]:((~curious(X)|calm(X))<=>happy(X)))&
((?[X]:((creative(X)&tall(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((curious(X)&tall(X))<=>~quiet(X)))&
((~creative(susan))<=>(calm(mary)))&
(![X]:((~rich(X)&~curious(X))<=>(calm(X)<~>~kind(X))))&
(((funny(fred)<~>~kind(fred)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|wise(X))=>(wise(X)<~>kind(X))))&
(((~old(susan)<~>~curious(susan)))<=>((~patient(susan)&calm(susan))))&
(![X]:(~patient(X)<=>(kind(X)<~>calm(X))))&
(![X]:(~strong(X)<=>(calm(X)&~tall(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~rich(X)&quiet(X))))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:(~funny(X)))&
(calm(mary))&
((~strong(john)|old(john))) | ~wise(john) | [
"p1",
"p2",
"p3",
"p10",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 572073005965928831146081
% SZS output start Proof for 572073005965928831146081
2. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> generous(X0)) [input p1]
3. ! [X0] : (kind(X0) <=> (~curious(X0) | creative(X0))) [input p2]
4. (patient(john) & humble(john)) <=> ? [X0] : (~rich(X0) & generous(X0)) [input p3]
11. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p10]
13. ! [X0] : ((wise(X0) | creative(X0)) => (wise(X0) <~> kind(X0))) [input p12]
15. ! [X0] : (~patient(X0) <=> (kind(X0) <~> calm(X0))) [input p14]
18. ? [X0] : (quiet(X0) & ~rich(X0)) [input p17]
23. wise(john) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> kind(X0)) | (~wise(X0) & ~creative(X0))) [ennf transformation 13]
32. ! [X0] : (((~wise(X0) | ~kind(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & kind(X0)))) [nnf transformation 2]
33. ! [X0] : ((~wise(X0) | ~kind(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & kind(X0)))) [flattening 32]
34. ! [X0] : ((kind(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~kind(X0))) [nnf transformation 3]
35. ! [X0] : ((kind(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~kind(X0))) [flattening 34]
36. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X0] : (~rich(X0) & generous(X0)) | (~patient(john) | ~humble(john))) [nnf transformation 4]
37. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X0] : (~rich(X0) & generous(X0)) | ~patient(john) | ~humble(john)) [flattening 36]
38. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X1] : (~rich(X1) & generous(X1)) | ~patient(john) | ~humble(john)) [rectify 37]
39. ? [X1] : (~rich(X1) & generous(X1)) => (~rich(sK0) & generous(sK0)) [choice axiom]
40. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & ((~rich(sK0) & generous(sK0)) | ~patient(john) | ~humble(john)) [skolemisation 38,39]
53. ! [X0] : (((~curious(X0) & ~rich(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (curious(X0) | rich(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~rich(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | curious(X0) | rich(X0))) [flattening 53]
58. ! [X0] : (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~wise(X0) & ~creative(X0))) [nnf transformation 29]
61. ! [X0] : ((~patient(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | patient(X0))) [nnf transformation 15]
67. ? [X0] : (quiet(X0) & ~rich(X0)) => (quiet(sK4) & ~rich(sK4)) [choice axiom]
68. quiet(sK4) & ~rich(sK4) [skolemisation 18,67]
77. generous(X0) | kind(X0) [cnf transformation 33]
78. generous(X0) | wise(X0) [cnf transformation 33]
82. kind(X0) | curious(X0) [cnf transformation 35]
86. patient(john) | rich(X0) | ~generous(X0) [cnf transformation 40]
107. ~curious(X0) | calm(X0) | kind(X0) [cnf transformation 54]
113. ~kind(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 58]
123. ~patient(X0) | kind(X0) | ~calm(X0) [cnf transformation 61]
129. ~rich(sK4) [cnf transformation 68]
134. wise(john) [cnf transformation 23]
135. ~wise(X0) | ~kind(X0) [duplicate literal removal 113]
137. 1 <=> ! [X0] : (rich(X0) | ~generous(X0)) [avatar definition]
138. ~generous(X0) | rich(X0) <- (1) [avatar component clause 137]
140. 2 <=> patient(john) [avatar definition]
142. patient(john) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 86,140,137]
196. calm(X0) | kind(X0) [subsumption resolution 107,82]
232. ~patient(X0) | kind(X0) [subsumption resolution 123,196]
258. ~kind(john) [resolution 135,134]
262. kind(john) <- (2) [resolution 232,142]
263. $false <- (2) [subsumption resolution 262,258]
264. ~2 [avatar contradiction clause 263]
266. rich(X0) | wise(X0) <- (1) [resolution 138,78]
267. rich(X1) | kind(X1) <- (1) [resolution 138,77]
477. wise(sK4) <- (1) [resolution 266,129]
482. kind(sK4) <- (1) [resolution 267,129]
547. ~kind(sK4) <- (1) [resolution 477,135]
548. $false <- (1) [subsumption resolution 547,482]
549. ~1 [avatar contradiction clause 548]
550. $false [avatar sat refutation 143,264,549]
% SZS output end Proof for 572073005965928831146081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or creative is calm or creative. Everyone who is not curious is not strong or quiet. Everyone who is not happy or kind is not brave or not rich. Everyone who is both rich and not funny is funny or brave and vice versa. Everyone who is either patient or kind is creative. If someone is either quiet or not strong then lucy is either not generous or not kind. Everyone who is not tall is generous. If paul is strong or not funny then fred is both not creative and not rich and vice versa. Everyone who is either not brave or kind is either not quiet or not old and vice versa. If alice is either tall or not tall then someone is not wise or patient. Everyone who is not happy or not humble is not happy. Everyone who is not curious is both not wise and brave and vice versa. If someone is humble or strong then mary is curious or calm and vice versa. Everyone who is both brave and strong is both humble and calm and vice versa. If someone is quiet then mary is brave or patient and vice versa. Alice is patient. Someone is either not funny or not happy. Someone is not quiet or generous. Someone is either kind or quiet. Someone is tall. Fred is either not tall or brave. Someone is either creative or strong. Someone is not generous. | Fred is not happy. | entailment | (![X]:((~funny(X)|creative(X))=>(calm(X)|creative(X))))&
(![X]:(~curious(X)=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)|kind(X))=>(~brave(X)|~rich(X))))&
(![X]:((rich(X)&~funny(X))<=>(funny(X)|brave(X))))&
(![X]:((patient(X)<~>kind(X))=>creative(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>((~generous(lucy)<~>~kind(lucy))))&
(![X]:(~tall(X)=>generous(X)))&
(((strong(paul)|~funny(paul)))<=>((~creative(fred)&~rich(fred))))&
(![X]:((~brave(X)<~>kind(X))<=>(~quiet(X)<~>~old(X))))&
(((tall(alice)<~>~tall(alice)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~happy(X)|~humble(X))=>~happy(X)))&
(![X]:(~curious(X)<=>(~wise(X)&brave(X))))&
((?[X]:((humble(X)|strong(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((brave(X)&strong(X))<=>(humble(X)&calm(X))))&
((?[X]:(quiet(X)))<=>((brave(mary)|patient(mary))))&
(patient(alice))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:(tall(X)))&
((~tall(fred)<~>brave(fred)))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:(~generous(X))) | ~happy(fred) | [
"p0",
"p3",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 604088831514628981834529
% SZS output start Proof for 604088831514628981834529
1. ! [X0] : ((creative(X0) | ~funny(X0)) => (creative(X0) | calm(X0))) [input p0]
4. ! [X0] : ((~funny(X0) & rich(X0)) <=> (brave(X0) | funny(X0))) [input p3]
8. (~funny(paul) | strong(paul)) <=> (~rich(fred) & ~creative(fred)) [input p7]
11. ! [X0] : ((~humble(X0) | ~happy(X0)) => ~happy(X0)) [input p10]
14. ! [X0] : ((strong(X0) & brave(X0)) <=> (calm(X0) & humble(X0))) [input p13]
24. happy(fred) [input hypothesis]
25. ! [X0] : ((creative(X0) | calm(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 1]
26. ! [X0] : (creative(X0) | calm(X0) | (~creative(X0) & funny(X0))) [flattening 25]
35. ! [X0] : (~happy(X0) | (humble(X0) & happy(X0))) [ennf transformation 11]
36. ! [X0] : (((~funny(X0) & rich(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (funny(X0) | ~rich(X0)))) [nnf transformation 4]
37. ! [X0] : (((~funny(X0) & rich(X0)) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | funny(X0) | ~rich(X0))) [flattening 36]
40. ((~funny(paul) | strong(paul)) | (rich(fred) | creative(fred))) & ((~rich(fred) & ~creative(fred)) | (funny(paul) & ~strong(paul))) [nnf transformation 8]
41. (~funny(paul) | strong(paul) | rich(fred) | creative(fred)) & ((~rich(fred) & ~creative(fred)) | (funny(paul) & ~strong(paul))) [flattening 40]
53. ! [X0] : (((strong(X0) & brave(X0)) | (~calm(X0) | ~humble(X0))) & ((calm(X0) & humble(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 14]
54. ! [X0] : (((strong(X0) & brave(X0)) | ~calm(X0) | ~humble(X0)) & ((calm(X0) & humble(X0)) | ~strong(X0) | ~brave(X0))) [flattening 53]
76. calm(X0) | creative(X0) | funny(X0) [cnf transformation 26]
83. ~brave(X0) | rich(X0) [cnf transformation 37]
84. ~funny(X0) | ~funny(X0) [cnf transformation 37]
94. ~creative(fred) | funny(paul) [cnf transformation 41]
96. ~rich(fred) | funny(paul) [cnf transformation 41]
109. ~happy(X0) | humble(X0) [cnf transformation 35]
119. ~humble(X0) | ~calm(X0) | brave(X0) [cnf transformation 54]
136. happy(fred) [cnf transformation 24]
140. ~funny(X0) [duplicate literal removal 84]
160. ~rich(fred) [subsumption resolution 96,140]
161. ~creative(fred) [subsumption resolution 94,140]
245. 23 <=> brave(fred) [avatar definition]
246. brave(fred) <- (23) [avatar component clause 245]
247. ~brave(fred) <- (~23) [avatar component clause 245]
261. humble(fred) [resolution 109,136]
332. ~calm(fred) | brave(fred) [resolution 119,261]
343. ~calm(fred) <- (~23) [subsumption resolution 332,247]
369. creative(fred) | funny(fred) <- (~23) [resolution 343,76]
370. funny(fred) <- (~23) [subsumption resolution 369,161]
371. $false <- (~23) [subsumption resolution 370,140]
372. 23 [avatar contradiction clause 371]
387. rich(fred) <- (23) [resolution 246,83]
391. $false <- (23) [subsumption resolution 387,160]
392. ~23 [avatar contradiction clause 391]
393. $false [avatar sat refutation 372,392]
% SZS output end Proof for 604088831514628981834529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or quiet is either not humble or patient.
If susan is funny then mary is wise or not curious.
If mary is funny or not humble then fred is either quiet or calm.
If fred is either not brave or old then john is generous.
Everyone who is calm or not curious is brave or not wise and vice versa.
Everyone who is either not creative or not calm is kind and vice versa.
Everyone who is either kind or not strong is not creative or old and vice versa.
If fred is tall then john is old.
If someone is both wise and not strong then someone is both not strong and not brave and vice versa.
Everyone who is not patient is not creative.
If paul is both not creative and happy then alice is either patient or brave.
If someone is brave or generous then someone is either not creative or not calm and vice versa.
If fred is either not creative or curious then alice is either not humble or old and vice versa.
Everyone who is wise or happy is rich.
Everyone who is either not wise or not happy is either not creative or not rich.
Everyone who is not strong is either wise or brave.
Alice is generous.
Someone is not calm.
Susan is not funny or curious.
Someone is quiet.
Someone is either curious or not old.
Alice is not strong or humble.
Someone is happy.
Someone is either tall or not calm. | Alice is not humble. | neutral | (![X]:((~rich(X)|quiet(X))=>(~humble(X)<~>patient(X))))&
((funny(susan))=>((wise(mary)|~curious(mary))))&
(((funny(mary)|~humble(mary)))=>((quiet(fred)<~>calm(fred))))&
(((~brave(fred)<~>old(fred)))=>(generous(john)))&
(![X]:((calm(X)|~curious(X))<=>(brave(X)|~wise(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>kind(X)))&
(![X]:((kind(X)<~>~strong(X))<=>(~creative(X)|old(X))))&
((tall(fred))=>(old(john)))&
((?[X]:((wise(X)&~strong(X))))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:(~patient(X)=>~creative(X)))&
(((~creative(paul)&happy(paul)))=>((patient(alice)<~>brave(alice))))&
((?[X]:((brave(X)|generous(X))))<=>(?[X]:((~creative(X)<~>~calm(X)))))&
(((~creative(fred)<~>curious(fred)))<=>((~humble(alice)<~>old(alice))))&
(![X]:((wise(X)|happy(X))=>rich(X)))&
(![X]:((~wise(X)<~>~happy(X))=>(~creative(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(wise(X)<~>brave(X))))&
(generous(alice))&
(?[X]:(~calm(X)))&
((~funny(susan)|curious(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((curious(X)<~>~old(X))))&
((~strong(alice)|humble(alice)))&
(?[X]:(happy(X)))&
(?[X]:((tall(X)<~>~calm(X)))) | ~humble(alice) | [] | null | 0 |
If alice is not funny then someone is either not happy or not funny.
If mary is rich or not rich then paul is not kind or not rich.
If someone is not wise or not tall then someone is either not patient or not humble.
Everyone who is not strong or not wise is both calm and not generous.
Everyone who is either not kind or old is both funny and generous and vice versa.
Everyone who is wise or not quiet is kind.
Everyone who is either not curious or rich is either not funny or creative and vice versa.
If paul is quiet or not wise then lucy is either old or not old.
If alice is happy then paul is not old and vice versa.
Everyone who is happy or patient is either not tall or brave.
Everyone who is either not strong or calm is not kind or creative.
If someone is not quiet or not strong then susan is both not creative and generous and vice versa.
Everyone who is not happy or creative is both not old and not brave.
If lucy is not wise or not brave then john is either not funny or not quiet.
Everyone who is both not curious and not humble is generous.
Someone is not patient.
Someone is both not rich and not patient.
Someone is not old or brave.
Fred is either not quiet or calm.
Mary is either not funny or patient.
Fred is either kind or curious.
Someone is not wise or not happy.
Alice is either not curious or kind. | Mary is not calm. | neutral | ((~funny(alice))=>(?[X]:((~happy(X)<~>~funny(X)))))&
(((rich(mary)|~rich(mary)))=>((~kind(paul)|~rich(paul))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(![X]:((~strong(X)|~wise(X))=>(calm(X)&~generous(X))))&
(![X]:((~kind(X)<~>old(X))<=>(funny(X)&generous(X))))&
(![X]:((wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~curious(X)<~>rich(X))<=>(~funny(X)<~>creative(X))))&
(((quiet(paul)|~wise(paul)))=>((old(lucy)<~>~old(lucy))))&
((happy(alice))<=>(~old(paul)))&
(![X]:((happy(X)|patient(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~strong(X)<~>calm(X))=>(~kind(X)|creative(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~creative(susan)&generous(susan))))&
(![X]:((~happy(X)|creative(X))=>(~old(X)&~brave(X))))&
(((~wise(lucy)|~brave(lucy)))=>((~funny(john)<~>~quiet(john))))&
(![X]:((~curious(X)&~humble(X))=>generous(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((~old(X)|brave(X))))&
((~quiet(fred)<~>calm(fred)))&
((~funny(mary)<~>patient(mary)))&
((kind(fred)<~>curious(fred)))&
(?[X]:((~wise(X)|~happy(X))))&
((~curious(alice)<~>kind(alice))) | ~calm(mary) | [] | null | 0 |
Everyone who is calm or funny is humble and vice versa. Everyone who is both not old and not happy is not patient or not happy. If susan is either strong or not curious then lucy is brave and vice versa. Everyone who is both not patient and not tall is happy or not brave. Everyone who is not quiet is both curious and not calm. If someone is either rich or not old then lucy is either not kind or not strong and vice versa. If fred is both not quiet and not brave then fred is both not tall and quiet. If someone is not tall then mary is either calm or not generous and vice versa. Everyone who is both not generous and creative is not curious and vice versa. If fred is either not happy or not humble then paul is not rich. Everyone who is not patient is quiet or not strong and vice versa. Everyone who is both not curious and not quiet is either not brave or kind and vice versa. If someone is both not generous and not calm then lucy is not curious or not humble. Everyone who is either not tall or not quiet is either creative or not humble and vice versa. Everyone who is either not patient or creative is not kind or not generous. If someone is rich then someone is either not calm or not wise and vice versa. Someone is curious or not brave. Someone is not humble. John is generous or quiet. Someone is either funny or not curious. Fred is not old. Someone is not happy or generous. Susan is both not patient and strong. | John is not wise. | neutral | (![X]:((calm(X)|funny(X))<=>humble(X)))&
(![X]:((~old(X)&~happy(X))=>(~patient(X)|~happy(X))))&
(((strong(susan)<~>~curious(susan)))<=>(brave(lucy)))&
(![X]:((~patient(X)&~tall(X))=>(happy(X)|~brave(X))))&
(![X]:(~quiet(X)=>(curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~old(X))))<=>((~kind(lucy)<~>~strong(lucy))))&
(((~quiet(fred)&~brave(fred)))=>((~tall(fred)&quiet(fred))))&
((?[X]:(~tall(X)))<=>((calm(mary)<~>~generous(mary))))&
(![X]:((~generous(X)&creative(X))<=>~curious(X)))&
(((~happy(fred)<~>~humble(fred)))=>(~rich(paul)))&
(![X]:(~patient(X)<=>(quiet(X)|~strong(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:((~generous(X)&~calm(X))))=>((~curious(lucy)|~humble(lucy))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~kind(X)|~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:(~humble(X)))&
((generous(john)|quiet(john)))&
(?[X]:((funny(X)<~>~curious(X))))&
(~old(fred))&
(?[X]:((~happy(X)|generous(X))))&
((~patient(susan)&strong(susan))) | ~wise(john) | [] | null | 0 |
If someone is either old or funny then someone is humble or not tall and vice versa.
If someone is both humble and not curious then paul is both not calm and not happy and vice versa.
Everyone who is old or happy is both not patient and not funny and vice versa.
If someone is either patient or generous then lucy is kind and vice versa.
If alice is kind or quiet then someone is either old or brave.
Everyone who is either not brave or funny is either curious or wise and vice versa.
If someone is not generous then someone is both not creative and kind and vice versa.
If someone is both not patient and patient then alice is either strong or not creative.
Everyone who is both funny and not happy is either not calm or tall.
If someone is either wise or strong then someone is humble or not wise and vice versa.
Everyone who is both not patient and not happy is tall or not rich and vice versa.
If lucy is not calm or not humble then paul is either funny or not strong.
If susan is both not patient and curious then someone is either not brave or generous.
If lucy is either patient or not brave then paul is not strong and vice versa.
If someone is not brave then john is either not patient or not kind.
Everyone who is not happy is either tall or rich.
John is either not rich or kind.
Someone is both not calm and kind.
Someone is not brave or kind.
Fred is not quiet.
Alice is rich.
Someone is both not wise and quiet.
Someone is either not quiet or not creative.
Someone is either kind or calm. | Alice is not tall. | entailment | ((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
((?[X]:((humble(X)&~curious(X))))<=>((~calm(paul)&~happy(paul))))&
(![X]:((old(X)|happy(X))<=>(~patient(X)&~funny(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(kind(lucy)))&
(((kind(alice)|quiet(alice)))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((~brave(X)<~>funny(X))<=>(curious(X)<~>wise(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((~patient(X)&patient(X))))=>((strong(alice)<~>~creative(alice))))&
(![X]:((funny(X)&~happy(X))=>(~calm(X)<~>tall(X))))&
((?[X]:((wise(X)<~>strong(X))))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(tall(X)|~rich(X))))&
(((~calm(lucy)|~humble(lucy)))=>((funny(paul)<~>~strong(paul))))&
(((~patient(susan)&curious(susan)))=>(?[X]:((~brave(X)<~>generous(X)))))&
(((patient(lucy)<~>~brave(lucy)))<=>(~strong(paul)))&
((?[X]:(~brave(X)))=>((~patient(john)<~>~kind(john))))&
(![X]:(~happy(X)=>(tall(X)<~>rich(X))))&
((~rich(john)<~>kind(john)))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((~brave(X)|kind(X))))&
(~quiet(fred))&
(rich(alice))&
(?[X]:((~wise(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:((kind(X)<~>calm(X)))) | ~tall(alice) | [
"p10",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 857945645693850058807993
% SZS output start Proof for 857945645693850058807993
11. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (~rich(X0) | tall(X0))) [input p10]
16. ! [X0] : (~happy(X0) => (tall(X0) <~> rich(X0))) [input p15]
21. rich(alice) [input p20]
25. tall(alice) [input hypothesis]
37. ! [X0] : ((tall(X0) <~> rich(X0)) | happy(X0)) [ennf transformation 16]
70. ! [X0] : (((~happy(X0) & ~patient(X0)) | (rich(X0) & ~tall(X0))) & ((~rich(X0) | tall(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 11]
71. ! [X0] : (((~happy(X0) & ~patient(X0)) | (rich(X0) & ~tall(X0))) & (~rich(X0) | tall(X0) | happy(X0) | patient(X0))) [flattening 70]
78. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | happy(X0)) [nnf transformation 37]
139. ~happy(X0) | ~tall(X0) [cnf transformation 71]
154. ~rich(X0) | ~tall(X0) | happy(X0) [cnf transformation 78]
161. rich(alice) [cnf transformation 21]
168. tall(alice) [cnf transformation 25]
385. ~rich(X0) | ~tall(X0) [subsumption resolution 154,139]
454. ~tall(alice) [resolution 385,161]
457. $false [subsumption resolution 454,168]
% SZS output end Proof for 857945645693850058807993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not calm is not generous. Everyone who is humble is both not humble and creative and vice versa. If someone is not funny or not tall then john is not kind or not tall. Everyone who is old is strong or brave. Everyone who is not old is both patient and rich and vice versa. Everyone who is both not humble and not tall is wise or not tall. If alice is not happy then paul is both funny and calm. If mary is either not rich or patient then someone is both not happy and calm and vice versa. If lucy is not humble then alice is generous or not quiet. If someone is not calm or not quiet then someone is not brave or not strong. Everyone who is both not happy and strong is either happy or not quiet. If alice is either not rich or rich then paul is not creative. Everyone who is not tall or generous is calm and vice versa. If paul is either not patient or not funny then someone is both rich and generous and vice versa. If someone is not curious or humble then john is wise. Everyone who is curious is not happy. Alice is both old and funny. John is strong. Someone is both calm and not curious. Someone is either funny or old. Someone is either not humble or not curious. Someone is not patient or not old. Lucy is either generous or not tall. | Alice is not creative. | entailment | (![X]:((wise(X)<~>~calm(X))=>~generous(X)))&
(![X]:(humble(X)<=>(~humble(X)&creative(X))))&
((?[X]:((~funny(X)|~tall(X))))=>((~kind(john)|~tall(john))))&
(![X]:(old(X)=>(strong(X)|brave(X))))&
(![X]:(~old(X)<=>(patient(X)&rich(X))))&
(![X]:((~humble(X)&~tall(X))=>(wise(X)|~tall(X))))&
((~happy(alice))=>((funny(paul)&calm(paul))))&
(((~rich(mary)<~>patient(mary)))<=>(?[X]:((~happy(X)&calm(X)))))&
((~humble(lucy))=>((generous(alice)|~quiet(alice))))&
((?[X]:((~calm(X)|~quiet(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((~happy(X)&strong(X))=>(happy(X)<~>~quiet(X))))&
(((~rich(alice)<~>rich(alice)))=>(~creative(paul)))&
(![X]:((~tall(X)|generous(X))<=>calm(X)))&
(((~patient(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&generous(X)))))&
((?[X]:((~curious(X)|humble(X))))=>(wise(john)))&
(![X]:(curious(X)=>~happy(X)))&
((old(alice)&funny(alice)))&
(strong(john))&
(?[X]:((calm(X)&~curious(X))))&
(?[X]:((funny(X)<~>old(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((~patient(X)|~old(X))))&
((generous(lucy)<~>~tall(lucy))) | ~creative(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3573039416936161632953718
% SZS output start Proof for 3573039416936161632953718
2. ! [X0] : (humble(X0) <=> (creative(X0) & ~humble(X0))) [input p1]
24. creative(alice) [input hypothesis]
42. ! [X0] : ((humble(X0) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | ~humble(X0))) [nnf transformation 2]
43. ! [X0] : ((humble(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | ~humble(X0))) [flattening 42]
74. ~humble(X0) | ~humble(X0) [cnf transformation 43]
76. humble(X0) | ~creative(X0) | humble(X0) [cnf transformation 43]
121. creative(alice) [cnf transformation 24]
125. ~humble(X0) [duplicate literal removal 74]
126. ~creative(X0) | humble(X0) [duplicate literal removal 76]
266. humble(alice) [resolution 126,121]
267. $false [subsumption resolution 266,125]
% SZS output end Proof for 3573039416936161632953718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or not kind then mary is happy and vice versa.
If someone is either not quiet or generous then alice is not happy or not curious and vice versa.
If susan is not patient or creative then john is not curious and vice versa.
If someone is strong or patient then someone is not patient or not wise.
Everyone who is both funny and strong is either old or not rich.
Everyone who is not generous is tall and vice versa.
Everyone who is both rich and not tall is not curious and vice versa.
Everyone who is either funny or quiet is not quiet.
If paul is both not calm and not curious then someone is either not curious or generous and vice versa.
Everyone who is either not generous or not old is both humble and not generous.
Everyone who is not kind is either humble or not funny.
If someone is not calm then someone is rich or funny and vice versa.
If mary is not rich then someone is brave or humble and vice versa.
If fred is either not brave or not generous then lucy is strong and vice versa.
If alice is not funny then someone is not funny and vice versa.
Everyone who is calm or not curious is quiet or not rich and vice versa.
Someone is not kind or not generous.
Someone is not patient or brave.
Someone is both not wise and funny.
Mary is either old or not tall.
Someone is not rich.
Susan is not kind or curious.
Mary is either not rich or creative.
Lucy is not rich. | Mary is calm. | entailment | ((?[X]:((tall(X)<~>~kind(X))))<=>(happy(mary)))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((~happy(alice)|~curious(alice))))&
(((~patient(susan)|creative(susan)))<=>(~curious(john)))&
((?[X]:((strong(X)|patient(X))))=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((funny(X)&strong(X))=>(old(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>tall(X)))&
(![X]:((rich(X)&~tall(X))<=>~curious(X)))&
(![X]:((funny(X)<~>quiet(X))=>~quiet(X)))&
(((~calm(paul)&~curious(paul)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:((~generous(X)<~>~old(X))=>(humble(X)&~generous(X))))&
(![X]:(~kind(X)=>(humble(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((rich(X)|funny(X)))))&
((~rich(mary))<=>(?[X]:((brave(X)|humble(X)))))&
(((~brave(fred)<~>~generous(fred)))<=>(strong(lucy)))&
((~funny(alice))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)|~curious(X))<=>(quiet(X)|~rich(X))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((~wise(X)&funny(X))))&
((old(mary)<~>~tall(mary)))&
(?[X]:(~rich(X)))&
((~kind(susan)|curious(susan)))&
((~rich(mary)<~>creative(mary)))&
(~rich(lucy)) | calm(mary) | [
"p5",
"p6",
"p9",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2339872453100932355479015
% SZS output start Proof for 2339872453100932355479015
6. ! [X0] : (~generous(X0) <=> tall(X0)) [input p5]
7. ! [X0] : ((~tall(X0) & rich(X0)) <=> ~curious(X0)) [input p6]
10. ! [X0] : ((~generous(X0) <~> ~old(X0)) => (~generous(X0) & humble(X0))) [input p9]
13. ~rich(mary) <=> ? [X0] : (humble(X0) | brave(X0)) [input p12]
16. ! [X0] : ((~curious(X0) | calm(X0)) <=> (~rich(X0) | quiet(X0))) [input p15]
20. old(mary) <~> ~tall(mary) [input p19]
25. ~calm(mary) [input hypothesis]
33. ! [X0] : ((~generous(X0) & humble(X0)) | (~generous(X0) <=> ~old(X0))) [ennf transformation 10]
47. ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))) [nnf transformation 6]
48. ! [X0] : (((~tall(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | (tall(X0) | ~rich(X0)))) [nnf transformation 7]
49. ! [X0] : (((~tall(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | tall(X0) | ~rich(X0))) [flattening 48]
56. ! [X0] : ((~generous(X0) & humble(X0)) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) [nnf transformation 33]
63. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & (? [X0] : (humble(X0) | brave(X0)) | rich(mary)) [nnf transformation 13]
64. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & (? [X1] : (humble(X1) | brave(X1)) | rich(mary)) [rectify 63]
65. ? [X1] : (humble(X1) | brave(X1)) => (humble(sK5) | brave(sK5)) [choice axiom]
66. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & ((humble(sK5) | brave(sK5)) | rich(mary)) [skolemisation 64,65]
72. ! [X0] : (((~curious(X0) | calm(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (curious(X0) & ~calm(X0)))) [nnf transformation 16]
73. ! [X0] : ((~curious(X0) | calm(X0) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | (curious(X0) & ~calm(X0)))) [flattening 72]
80. (tall(mary) | ~old(mary)) & (~tall(mary) | old(mary)) [nnf transformation 20]
99. generous(X0) | tall(X0) [cnf transformation 47]
100. ~generous(X0) | ~tall(X0) [cnf transformation 47]
102. rich(X0) | curious(X0) [cnf transformation 49]
112. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 56]
115. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 56]
123. ~rich(mary) | ~humble(X0) [cnf transformation 66]
133. ~curious(X0) | calm(X0) | rich(X0) [cnf transformation 73]
137. ~tall(mary) | old(mary) [cnf transformation 80]
138. tall(mary) | ~old(mary) [cnf transformation 80]
144. ~calm(mary) [cnf transformation 25]
145. ~generous(X0) | old(X0) [duplicate literal removal 115]
265. 27 <=> ! [X0] : ~humble(X0) [avatar definition]
266. ~humble(X0) <- (27) [avatar component clause 265]
268. 28 <=> rich(mary) [avatar definition]
271. 27 | ~28 [avatar split clause 123,268,265]
314. calm(X0) | rich(X0) [subsumption resolution 133,102]
335. 42 <=> old(mary) [avatar definition]
336. old(mary) <- (42) [avatar component clause 335]
337. ~old(mary) <- (~42) [avatar component clause 335]
339. 43 <=> tall(mary) [avatar definition]
340. ~tall(mary) <- (~43) [avatar component clause 339]
341. tall(mary) <- (43) [avatar component clause 339]
342. ~42 | 43 [avatar split clause 138,339,335]
343. 42 | ~43 [avatar split clause 137,339,335]
379. old(X0) | tall(X0) [resolution 145,99]
397. rich(mary) [resolution 314,144]
401. 28 [avatar split clause 397,268]
522. tall(mary) <- (~42) [resolution 379,337]
525. $false <- (~42, ~43) [subsumption resolution 522,340]
526. 42 | 43 [avatar contradiction clause 525]
533. humble(mary) | generous(mary) <- (42) [resolution 336,112]
534. generous(mary) <- (27, 42) [subsumption resolution 533,266]
546. ~tall(mary) <- (27, 42) [resolution 534,100]
547. $false <- (27, 42, 43) [subsumption resolution 546,341]
548. ~27 | ~42 | ~43 [avatar contradiction clause 547]
549. $false [avatar sat refutation 271,342,343,401,526,548]
% SZS output end Proof for 2339872453100932355479015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either not funny or not strong and vice versa. If someone is happy then alice is both quiet and calm. If mary is either not patient or not happy then fred is not wise or quiet and vice versa. If someone is either happy or not brave then someone is either patient or not brave. Everyone who is both generous and strong is curious or not kind. If someone is not brave then lucy is either humble or not curious. If fred is either not kind or not wise then someone is either not happy or curious. If someone is kind then fred is curious or not creative and vice versa. If someone is either quiet or brave then fred is either not humble or curious. Everyone who is both quiet and calm is not patient. If fred is both tall and not funny then alice is not old or not calm and vice versa. Everyone who is either not humble or tall is both quiet and not curious. If john is kind or not curious then someone is not kind or not generous. Everyone who is kind or curious is both happy and not calm and vice versa. If alice is either quiet or not quiet then mary is curious or not quiet. Everyone who is brave is not generous or curious and vice versa. Someone is not quiet or not patient. Mary is both strong and quiet. Someone is either not humble or wise. Fred is not happy. Someone is either not strong or quiet. Someone is humble or wise. Someone is funny or happy. Someone is not brave. | Alice is not patient. | entailment | (![X]:(~happy(X)<=>(~funny(X)<~>~strong(X))))&
((?[X]:(happy(X)))=>((quiet(alice)&calm(alice))))&
(((~patient(mary)<~>~happy(mary)))<=>((~wise(fred)|quiet(fred))))&
((?[X]:((happy(X)<~>~brave(X))))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((generous(X)&strong(X))=>(curious(X)|~kind(X))))&
((?[X]:(~brave(X)))=>((humble(lucy)<~>~curious(lucy))))&
(((~kind(fred)<~>~wise(fred)))=>(?[X]:((~happy(X)<~>curious(X)))))&
((?[X]:(kind(X)))<=>((curious(fred)|~creative(fred))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~humble(fred)<~>curious(fred))))&
(![X]:((quiet(X)&calm(X))=>~patient(X)))&
(((tall(fred)&~funny(fred)))<=>((~old(alice)|~calm(alice))))&
(![X]:((~humble(X)<~>tall(X))=>(quiet(X)&~curious(X))))&
(((kind(john)|~curious(john)))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((kind(X)|curious(X))<=>(happy(X)&~calm(X))))&
(((quiet(alice)<~>~quiet(alice)))=>((curious(mary)|~quiet(mary))))&
(![X]:(brave(X)<=>(~generous(X)|curious(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
((strong(mary)&quiet(mary)))&
(?[X]:((~humble(X)<~>wise(X))))&
(~happy(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:(~brave(X))) | ~patient(alice) | [
"p1",
"p9",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3017474871510964018219906
% SZS output start Proof for 3017474871510964018219906
2. ? [X0] : happy(X0) => (calm(alice) & quiet(alice)) [input p1]
10. ! [X0] : ((calm(X0) & quiet(X0)) => ~patient(X0)) [input p9]
14. ! [X0] : ((curious(X0) | kind(X0)) <=> (~calm(X0) & happy(X0))) [input p13]
15. (quiet(alice) <~> ~quiet(alice)) => (~quiet(mary) | curious(mary)) [input p14]
18. quiet(mary) & strong(mary) [input p17]
25. patient(alice) [input hypothesis]
27. (calm(alice) & quiet(alice)) | ! [X0] : ~happy(X0) [ennf transformation 2]
34. ! [X0] : (~patient(X0) | (~calm(X0) | ~quiet(X0))) [ennf transformation 10]
35. ! [X0] : (~patient(X0) | ~calm(X0) | ~quiet(X0)) [flattening 34]
38. (~quiet(mary) | curious(mary)) | (quiet(alice) <=> ~quiet(alice)) [ennf transformation 15]
39. ~quiet(mary) | curious(mary) | (quiet(alice) <=> ~quiet(alice)) [flattening 38]
62. ! [X0] : (((curious(X0) | kind(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (~curious(X0) & ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((curious(X0) | kind(X0) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | (~curious(X0) & ~kind(X0)))) [flattening 62]
64. ~quiet(mary) | curious(mary) | ((quiet(alice) | quiet(alice)) & (~quiet(alice) | ~quiet(alice))) [nnf transformation 39]
85. quiet(alice) | ~happy(X0) [cnf transformation 27]
86. calm(alice) | ~happy(X0) [cnf transformation 27]
111. ~patient(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 35]
124. ~curious(X0) | happy(X0) [cnf transformation 63]
128. ~quiet(mary) | curious(mary) | ~quiet(alice) | ~quiet(alice) [cnf transformation 64]
129. ~quiet(mary) | curious(mary) | quiet(alice) | quiet(alice) [cnf transformation 64]
135. quiet(mary) [cnf transformation 18]
144. patient(alice) [cnf transformation 25]
145. ~quiet(mary) | curious(mary) | ~quiet(alice) [duplicate literal removal 128]
146. ~quiet(mary) | curious(mary) | quiet(alice) [duplicate literal removal 129]
148. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
149. ~happy(X0) <- (1) [avatar component clause 148]
151. 2 <=> calm(alice) [avatar definition]
153. calm(alice) <- (2) [avatar component clause 151]
154. 1 | 2 [avatar split clause 86,151,148]
156. 3 <=> quiet(alice) [avatar definition]
159. 1 | 3 [avatar split clause 85,156,148]
169. 6 <=> happy(mary) [avatar definition]
171. happy(mary) <- (6) [avatar component clause 169]
297. 32 <=> curious(mary) [avatar definition]
299. curious(mary) <- (32) [avatar component clause 297]
301. 33 <=> quiet(mary) [avatar definition]
304. 3 | 32 | ~33 [avatar split clause 146,301,297,156]
305. ~3 | 32 | ~33 [avatar split clause 145,301,297,156]
315. 33 [avatar split clause 135,301]
355. happy(mary) <- (32) [resolution 124,299]
358. 6 | ~32 [avatar split clause 355,297,169]
390. ~calm(alice) | ~quiet(alice) [resolution 111,144]
391. ~quiet(alice) <- (2) [subsumption resolution 390,153]
394. ~3 | ~2 [avatar split clause 391,151,156]
395. $false <- (1, 6) [resolution 149,171]
398. ~1 | ~6 [avatar contradiction clause 395]
399. $false [avatar sat refutation 154,159,304,305,315,358,394,398]
% SZS output end Proof for 3017474871510964018219906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich then paul is humble or generous and vice versa.
If alice is either funny or calm then mary is both strong and rich and vice versa.
Everyone who is rich or not funny is strong.
If alice is not curious then someone is not patient and vice versa.
If someone is both humble and kind then alice is both generous and not funny.
If someone is either not creative or kind then alice is both generous and not patient and vice versa.
Everyone who is both strong and tall is either not strong or not calm and vice versa.
Everyone who is both calm and not strong is brave and vice versa.
Everyone who is either not strong or not happy is both not quiet and not curious.
Everyone who is either rich or not patient is rich and vice versa.
If lucy is not humble then someone is not curious.
If someone is either patient or not patient then lucy is both not creative and happy.
Everyone who is rich or quiet is brave or old.
Everyone who is generous is either not curious or not creative.
Everyone who is either funny or generous is either brave or not funny.
If someone is not brave then someone is both humble and quiet.
Someone is either humble or not creative.
Someone is either not rich or not humble.
Someone is generous.
Alice is not tall or rich.
Someone is not generous.
Paul is not rich.
Someone is either not old or happy.
Someone is quiet or not brave. | Alice is patient. | entailment | ((?[X]:(~rich(X)))<=>((humble(paul)|generous(paul))))&
(((funny(alice)<~>calm(alice)))<=>((strong(mary)&rich(mary))))&
(![X]:((rich(X)|~funny(X))=>strong(X)))&
((~curious(alice))<=>(?[X]:(~patient(X))))&
((?[X]:((humble(X)&kind(X))))=>((generous(alice)&~funny(alice))))&
((?[X]:((~creative(X)<~>kind(X))))<=>((generous(alice)&~patient(alice))))&
(![X]:((strong(X)&tall(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((calm(X)&~strong(X))<=>brave(X)))&
(![X]:((~strong(X)<~>~happy(X))=>(~quiet(X)&~curious(X))))&
(![X]:((rich(X)<~>~patient(X))<=>rich(X)))&
((~humble(lucy))=>(?[X]:(~curious(X))))&
((?[X]:((patient(X)<~>~patient(X))))=>((~creative(lucy)&happy(lucy))))&
(![X]:((rich(X)|quiet(X))=>(brave(X)|old(X))))&
(![X]:(generous(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>(brave(X)<~>~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)&quiet(X)))))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:(generous(X)))&
((~tall(alice)|rich(alice)))&
(?[X]:(~generous(X)))&
(~rich(paul))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((quiet(X)|~brave(X)))) | patient(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7000413507285749081200916
% SZS output start Proof for 7000413507285749081200916
10. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> rich(X0)) [input p9]
25. ~patient(alice) [input hypothesis]
58. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ~rich(X0)) & (rich(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 10]
117. rich(X0) | rich(X0) | patient(X0) [cnf transformation 58]
119. patient(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
146. ~patient(alice) [cnf transformation 25]
153. rich(X0) | patient(X0) [duplicate literal removal 117]
154. patient(X0) | ~rich(X0) [duplicate literal removal 119]
198. 9 <=> ! [X0] : patient(X0) [avatar definition]
199. patient(X0) <- (9) [avatar component clause 198]
220. 14 <=> patient(alice) [avatar definition]
221. ~patient(alice) <- (~14) [avatar component clause 220]
244. patient(X0) [subsumption resolution 153,154]
245. 9 [avatar split clause 244,198]
331. ~14 [avatar split clause 146,220]
334. $false <- (9, ~14) [resolution 221,199]
335. ~9 | 14 [avatar contradiction clause 334]
336. $false [avatar sat refutation 245,331,335]
% SZS output end Proof for 7000413507285749081200916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not tall or not strong and vice versa.
If someone is either not wise or not old then john is kind.
If someone is both not calm and funny then alice is not old.
Everyone who is either creative or patient is not tall and vice versa.
Everyone who is not kind is either not creative or patient and vice versa.
Everyone who is wise is not generous or tall and vice versa.
If someone is not humble or not rich then someone is patient or old.
If someone is either quiet or not happy then someone is happy and vice versa.
Everyone who is both quiet and not kind is both not quiet and not humble and vice versa.
Everyone who is either not happy or strong is both strong and not wise.
If susan is either not quiet or calm then someone is both not rich and not calm and vice versa.
Everyone who is not calm is brave or not patient.
Everyone who is not funny is either not kind or not brave.
Everyone who is quiet or not kind is both quiet and tall and vice versa.
If john is not humble then someone is curious or patient and vice versa.
If someone is not tall then alice is either not calm or not brave.
Someone is not curious or calm.
Mary is both not old and not calm.
Someone is both not strong and not patient.
Someone is creative or not old.
Lucy is not old or not wise.
Paul is not tall or generous. | Lucy is not curious. | entailment | (![X]:((~brave(X)|curious(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>(kind(john)))&
((?[X]:((~calm(X)&funny(X))))=>(~old(alice)))&
(![X]:((creative(X)<~>patient(X))<=>~tall(X)))&
(![X]:(~kind(X)<=>(~creative(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~generous(X)|tall(X))))&
((?[X]:((~humble(X)|~rich(X))))=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((quiet(X)<~>~happy(X))))<=>(?[X]:(happy(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~quiet(X)&~humble(X))))&
(![X]:((~happy(X)<~>strong(X))=>(strong(X)&~wise(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:((~rich(X)&~calm(X)))))&
(![X]:(~calm(X)=>(brave(X)|~patient(X))))&
(![X]:(~funny(X)=>(~kind(X)<~>~brave(X))))&
(![X]:((quiet(X)|~kind(X))<=>(quiet(X)&tall(X))))&
((~humble(john))<=>(?[X]:((curious(X)|patient(X)))))&
((?[X]:(~tall(X)))=>((~calm(alice)<~>~brave(alice))))&
(?[X]:((~curious(X)|calm(X))))&
((~old(mary)&~calm(mary)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((creative(X)|~old(X))))&
((~old(lucy)|~wise(lucy)))&
((~tall(paul)|generous(paul))) | ~curious(lucy) | [
"p3",
"p4",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8988733487127544537782406
% SZS output start Proof for 8988733487127544537782406
4. ! [X0] : ((creative(X0) <~> patient(X0)) <=> ~tall(X0)) [input p3]
5. ! [X0] : (~kind(X0) <=> (~creative(X0) <~> patient(X0))) [input p4]
9. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~humble(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : ((~kind(X0) | quiet(X0)) <=> (tall(X0) & quiet(X0))) [input p13]
15. ~humble(john) <=> ? [X0] : (patient(X0) | curious(X0)) [input p14]
23. curious(lucy) [input hypothesis]
37. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | tall(X0)) & (~tall(X0) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [nnf transformation 4]
38. ! [X0] : ((~kind(X0) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | kind(X0))) [nnf transformation 5]
49. ! [X0] : (((~kind(X0) & quiet(X0)) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 9]
50. ! [X0] : (((~kind(X0) & quiet(X0)) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | kind(X0) | ~quiet(X0))) [flattening 49]
57. ! [X0] : (((~kind(X0) | quiet(X0)) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | (kind(X0) & ~quiet(X0)))) [nnf transformation 14]
58. ! [X0] : ((~kind(X0) | quiet(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | (kind(X0) & ~quiet(X0)))) [flattening 57]
59. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & (? [X0] : (patient(X0) | curious(X0)) | humble(john)) [nnf transformation 15]
60. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & (? [X1] : (patient(X1) | curious(X1)) | humble(john)) [rectify 59]
61. ? [X1] : (patient(X1) | curious(X1)) => (patient(sK4) | curious(sK4)) [choice axiom]
62. (~humble(john) | ! [X0] : (~patient(X0) & ~curious(X0))) & ((patient(sK4) | curious(sK4)) | humble(john)) [skolemisation 60,61]
77. ~creative(X0) | patient(X0) | ~tall(X0) [cnf transformation 37]
78. ~patient(X0) | creative(X0) | ~tall(X0) [cnf transformation 37]
83. ~kind(X0) | patient(X0) | creative(X0) [cnf transformation 38]
84. ~patient(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 38]
94. ~quiet(X0) | kind(X0) | ~quiet(X0) [cnf transformation 50]
96. quiet(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
112. quiet(X0) | kind(X0) [cnf transformation 58]
113. ~quiet(X0) | tall(X0) [cnf transformation 58]
117. ~humble(john) | ~curious(X0) [cnf transformation 62]
129. curious(lucy) [cnf transformation 23]
131. ~quiet(X0) | kind(X0) [duplicate literal removal 94]
132. quiet(X0) | humble(X0) [duplicate literal removal 96]
219. kind(X0) [subsumption resolution 112,131]
224. 22 <=> humble(john) [avatar definition]
226. ~humble(john) <- (~22) [avatar component clause 224]
229. 23 <=> ! [X0] : ~curious(X0) [avatar definition]
230. ~curious(X0) <- (23) [avatar component clause 229]
231. 23 | ~22 [avatar split clause 117,224,229]
292. $false <- (23) [resolution 230,129]
293. ~23 [avatar contradiction clause 292]
300. humble(X1) | tall(X1) [resolution 132,113]
312. tall(john) <- (~22) [resolution 300,226]
335. patient(X1) | creative(X1) [resolution 83,219]
373. creative(X3) | creative(X3) | ~tall(X3) [resolution 335,78]
374. ~tall(X3) | creative(X3) [duplicate literal removal 373]
420. creative(john) <- (~22) [resolution 374,312]
425. patient(john) | ~tall(john) <- (~22) [resolution 420,77]
426. patient(john) <- (~22) [subsumption resolution 425,312]
438. ~creative(john) | ~kind(john) <- (~22) [resolution 426,84]
442. ~kind(john) <- (~22) [subsumption resolution 438,420]
443. $false <- (~22) [subsumption resolution 442,219]
444. 22 [avatar contradiction clause 443]
445. $false [avatar sat refutation 231,293,444]
% SZS output end Proof for 8988733487127544537782406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both strong and not creative then fred is both creative and wise.
Everyone who is curious is not tall or not rich and vice versa.
Everyone who is quiet or not strong is both not patient and not creative.
Everyone who is both rich and not creative is both not happy and not quiet.
If someone is both brave and happy then someone is both not brave and not rich and vice versa.
Everyone who is not wise or funny is both funny and not creative.
Everyone who is not wise is either old or not curious.
If someone is funny or not quiet then alice is both calm and not brave.
Everyone who is not quiet or brave is both calm and not creative.
If mary is either not rich or not curious then someone is both rich and strong and vice versa.
Everyone who is not kind or humble is old or not generous and vice versa.
If someone is not calm then someone is not creative.
Everyone who is not wise is both not curious and not calm and vice versa.
If paul is creative or not brave then paul is not happy and vice versa.
If someone is either old or patient then someone is happy.
If lucy is not calm or not kind then someone is not old or brave and vice versa.
Susan is not strong.
Someone is wise or not generous.
Someone is not creative.
Someone is either not kind or not funny.
Paul is not brave or not creative.
Someone is both calm and not kind.
Someone is both not happy and not funny. | Mary is not curious. | contradiction | ((?[X]:((strong(X)&~creative(X))))=>((creative(fred)&wise(fred))))&
(![X]:(curious(X)<=>(~tall(X)|~rich(X))))&
(![X]:((quiet(X)|~strong(X))=>(~patient(X)&~creative(X))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)&~quiet(X))))&
((?[X]:((brave(X)&happy(X))))<=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((~wise(X)|funny(X))=>(funny(X)&~creative(X))))&
(![X]:(~wise(X)=>(old(X)<~>~curious(X))))&
((?[X]:((funny(X)|~quiet(X))))=>((calm(alice)&~brave(alice))))&
(![X]:((~quiet(X)|brave(X))=>(calm(X)&~creative(X))))&
(((~rich(mary)<~>~curious(mary)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~kind(X)|humble(X))<=>(old(X)|~generous(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~creative(X))))&
(![X]:(~wise(X)<=>(~curious(X)&~calm(X))))&
(((creative(paul)|~brave(paul)))<=>(~happy(paul)))&
((?[X]:((old(X)<~>patient(X))))=>(?[X]:(happy(X))))&
(((~calm(lucy)|~kind(lucy)))<=>(?[X]:((~old(X)|brave(X)))))&
(~strong(susan))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~kind(X)<~>~funny(X))))&
((~brave(paul)|~creative(paul)))&
(?[X]:((calm(X)&~kind(X))))&
(?[X]:((~happy(X)&~funny(X)))) | ~curious(mary) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8120513464129223208499156
% SZS output start Proof for 8120513464129223208499156
1. ? [X0] : (~creative(X0) & strong(X0)) => (wise(fred) & creative(fred)) [input p0]
2. ! [X0] : (curious(X0) <=> (~rich(X0) | ~tall(X0))) [input p1]
3. ! [X0] : ((~strong(X0) | quiet(X0)) => (~creative(X0) & ~patient(X0))) [input p2]
9. ! [X0] : ((brave(X0) | ~quiet(X0)) => (~creative(X0) & calm(X0))) [input p8]
10. (~rich(mary) <~> ~curious(mary)) <=> ? [X0] : (strong(X0) & rich(X0)) [input p9]
24. ~curious(mary) [input hypothesis]
29. (wise(fred) & creative(fred)) | ! [X0] : (creative(X0) | ~strong(X0)) [ennf transformation 1]
30. ! [X0] : ((~creative(X0) & ~patient(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 3]
36. ! [X0] : ((~creative(X0) & calm(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 9]
41. ! [X0] : ((curious(X0) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ~curious(X0))) [nnf transformation 2]
42. ! [X0] : ((curious(X0) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ~curious(X0))) [flattening 41]
49. (((curious(mary) | rich(mary)) & (~curious(mary) | ~rich(mary))) | ! [X0] : (~strong(X0) | ~rich(X0))) & (? [X0] : (strong(X0) & rich(X0)) | ((~rich(mary) | curious(mary)) & (~curious(mary) | rich(mary)))) [nnf transformation 10]
50. (((curious(mary) | rich(mary)) & (~curious(mary) | ~rich(mary))) | ! [X0] : (~strong(X0) | ~rich(X0))) & (? [X1] : (strong(X1) & rich(X1)) | ((~rich(mary) | curious(mary)) & (~curious(mary) | rich(mary)))) [rectify 49]
51. ? [X1] : (strong(X1) & rich(X1)) => (strong(sK2) & rich(sK2)) [choice axiom]
52. (((curious(mary) | rich(mary)) & (~curious(mary) | ~rich(mary))) | ! [X0] : (~strong(X0) | ~rich(X0))) & ((strong(sK2) & rich(sK2)) | ((~rich(mary) | curious(mary)) & (~curious(mary) | rich(mary)))) [skolemisation 50,51]
80. creative(fred) | creative(X0) | ~strong(X0) [cnf transformation 29]
84. curious(X0) | rich(X0) [cnf transformation 42]
87. ~creative(X0) | ~quiet(X0) [cnf transformation 30]
107. ~creative(X0) | quiet(X0) [cnf transformation 36]
112. strong(sK2) | ~rich(mary) | curious(mary) [cnf transformation 52]
140. ~curious(mary) [cnf transformation 24]
142. 1 <=> ! [X0] : (creative(X0) | ~strong(X0)) [avatar definition]
143. creative(X0) | ~strong(X0) <- (1) [avatar component clause 142]
150. 3 <=> creative(fred) [avatar definition]
152. creative(fred) <- (3) [avatar component clause 150]
153. 1 | 3 [avatar split clause 80,150,142]
199. ~creative(X0) [subsumption resolution 107,87]
208. 16 <=> curious(mary) [avatar definition]
212. strong(sK2) | curious(mary) [subsumption resolution 112,84]
214. 17 <=> strong(sK2) [avatar definition]
216. strong(sK2) <- (17) [avatar component clause 214]
217. 16 | 17 [avatar split clause 212,214,208]
296. ~16 [avatar split clause 140,208]
297. $false <- (3) [subsumption resolution 152,199]
298. ~3 [avatar contradiction clause 297]
299. ~strong(X0) <- (1) [subsumption resolution 143,199]
300. $false <- (1, 17) [resolution 299,216]
301. ~1 | ~17 [avatar contradiction clause 300]
302. $false [avatar sat refutation 153,217,296,298,301]
% SZS output end Proof for 8120513464129223208499156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or rich then someone is both wise and not tall.
If someone is humble then susan is either not wise or patient and vice versa.
Everyone who is calm or not humble is either not funny or old.
Everyone who is not patient or not brave is creative.
If someone is not quiet or not brave then alice is either not happy or creative.
If mary is not tall then someone is not calm or not patient.
If someone is curious then someone is both not funny and not humble.
Everyone who is generous or kind is not creative or happy and vice versa.
Everyone who is both not strong and not old is not rich.
Everyone who is curious or quiet is happy and vice versa.
Everyone who is old is not tall or brave and vice versa.
Everyone who is kind is tall and vice versa.
Everyone who is both not brave and not tall is both happy and not strong and vice versa.
Everyone who is not quiet or not happy is both not rich and not generous.
Everyone who is not brave is not happy and vice versa.
If someone is either not rich or not patient then someone is funny or old.
Mary is either not curious or not old.
Someone is both wise and generous.
Paul is either funny or rich.
Someone is either not quiet or not tall.
Someone is both not humble and not patient.
Someone is happy.
Someone is not generous or old. | Mary is not strong. | contradiction | (((~wise(mary)|rich(mary)))=>(?[X]:((wise(X)&~tall(X)))))&
((?[X]:(humble(X)))<=>((~wise(susan)<~>patient(susan))))&
(![X]:((calm(X)|~humble(X))=>(~funny(X)<~>old(X))))&
(![X]:((~patient(X)|~brave(X))=>creative(X)))&
((?[X]:((~quiet(X)|~brave(X))))=>((~happy(alice)<~>creative(alice))))&
((~tall(mary))=>(?[X]:((~calm(X)|~patient(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:((generous(X)|kind(X))<=>(~creative(X)|happy(X))))&
(![X]:((~strong(X)&~old(X))=>~rich(X)))&
(![X]:((curious(X)|quiet(X))<=>happy(X)))&
(![X]:(old(X)<=>(~tall(X)|brave(X))))&
(![X]:(kind(X)<=>tall(X)))&
(![X]:((~brave(X)&~tall(X))<=>(happy(X)&~strong(X))))&
(![X]:((~quiet(X)|~happy(X))=>(~rich(X)&~generous(X))))&
(![X]:(~brave(X)<=>~happy(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:((funny(X)|old(X)))))&
((~curious(mary)<~>~old(mary)))&
(?[X]:((wise(X)&generous(X))))&
((funny(paul)<~>rich(paul)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((~generous(X)|old(X)))) | ~strong(mary) | [
"p3",
"p7",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 133713580867168696131212
% SZS output start Proof for 133713580867168696131212
4. ! [X0] : ((~brave(X0) | ~patient(X0)) => creative(X0)) [input p3]
8. ! [X0] : ((kind(X0) | generous(X0)) <=> (happy(X0) | ~creative(X0))) [input p7]
12. ! [X0] : (kind(X0) <=> tall(X0)) [input p11]
13. ! [X0] : ((~tall(X0) & ~brave(X0)) <=> (~strong(X0) & happy(X0))) [input p12]
14. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~generous(X0) & ~rich(X0))) [input p13]
15. ! [X0] : (~brave(X0) <=> ~happy(X0)) [input p14]
24. ~strong(mary) [input hypothesis]
31. ! [X0] : (creative(X0) | (brave(X0) & patient(X0))) [ennf transformation 4]
36. ! [X0] : ((~generous(X0) & ~rich(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 14]
49. ! [X0] : (((kind(X0) | generous(X0)) | (~happy(X0) & creative(X0))) & ((happy(X0) | ~creative(X0)) | (~kind(X0) & ~generous(X0)))) [nnf transformation 8]
50. ! [X0] : ((kind(X0) | generous(X0) | (~happy(X0) & creative(X0))) & (happy(X0) | ~creative(X0) | (~kind(X0) & ~generous(X0)))) [flattening 49]
55. ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0))) [nnf transformation 12]
56. ! [X0] : (((~tall(X0) & ~brave(X0)) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | (tall(X0) | brave(X0)))) [nnf transformation 13]
57. ! [X0] : (((~tall(X0) & ~brave(X0)) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | tall(X0) | brave(X0))) [flattening 56]
58. ! [X0] : ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))) [nnf transformation 15]
87. creative(X0) | brave(X0) [cnf transformation 31]
95. ~kind(X0) | ~creative(X0) | happy(X0) [cnf transformation 50]
97. ~happy(X0) | generous(X0) | kind(X0) [cnf transformation 50]
106. ~tall(X0) | kind(X0) [cnf transformation 55]
107. happy(X0) | tall(X0) | brave(X0) [cnf transformation 57]
109. ~happy(X0) | strong(X0) | ~brave(X0) [cnf transformation 57]
110. ~happy(X0) | strong(X0) | ~tall(X0) [cnf transformation 57]
114. ~generous(X0) | happy(X0) [cnf transformation 36]
115. ~happy(X0) | brave(X0) [cnf transformation 58]
116. ~brave(X0) | happy(X0) [cnf transformation 58]
131. ~strong(mary) [cnf transformation 24]
398. tall(X1) | brave(X1) | generous(X1) | kind(X1) [resolution 107,97]
399. tall(X2) | brave(X2) | brave(X2) [resolution 107,115]
400. brave(X2) | tall(X2) [duplicate literal removal 399]
401. kind(X1) | generous(X1) | brave(X1) [subsumption resolution 398,106]
420. happy(X0) | tall(X0) [resolution 400,116]
463. generous(X0) | brave(X0) | ~creative(X0) | happy(X0) [resolution 401,95]
465. generous(X0) | ~creative(X0) | happy(X0) [subsumption resolution 463,116]
466. ~creative(X0) | happy(X0) [subsumption resolution 465,114]
492. tall(X1) | strong(X1) | ~brave(X1) [resolution 420,109]
496. strong(X1) | tall(X1) [subsumption resolution 492,400]
498. happy(X0) | brave(X0) [resolution 466,87]
501. happy(X0) [subsumption resolution 498,116]
509. strong(X0) | ~tall(X0) [resolution 501,110]
514. strong(X0) [subsumption resolution 509,496]
541. $false [resolution 514,131]
% SZS output end Proof for 133713580867168696131212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not rich or not patient is both happy and rich and vice versa.
If someone is happy or quiet then fred is both not creative and not tall and vice versa.
Everyone who is both not calm and old is both not curious and not funny.
If someone is either not wise or kind then lucy is both quiet and not calm and vice versa.
Everyone who is both not strong and not quiet is either not tall or tall and vice versa.
Everyone who is humble or not kind is not rich and vice versa.
If someone is either rich or not funny then someone is not creative or not generous and vice versa.
Everyone who is not quiet or creative is both not generous and not patient and vice versa.
If someone is either quiet or creative then john is not brave and vice versa.
Everyone who is either not rich or not happy is either brave or curious and vice versa.
If someone is either patient or wise then alice is not curious or not old and vice versa.
Everyone who is curious or not quiet is both brave and not humble.
Everyone who is both not wise and creative is not kind.
Everyone who is happy or not strong is curious or not rich.
Someone is not quiet.
Someone is not rich or not creative.
Paul is either not humble or old.
Mary is not humble. | Fred is wise. | contradiction | (![X]:((~rich(X)|~patient(X))<=>(happy(X)&rich(X))))&
((?[X]:((happy(X)|quiet(X))))<=>((~creative(fred)&~tall(fred))))&
(![X]:((~calm(X)&old(X))=>(~curious(X)&~funny(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((quiet(lucy)&~calm(lucy))))&
(![X]:((~strong(X)&~quiet(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((humble(X)|~kind(X))<=>~rich(X)))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((~quiet(X)|creative(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(~brave(john)))&
(![X]:((~rich(X)<~>~happy(X))<=>(brave(X)<~>curious(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>((~curious(alice)|~old(alice))))&
(![X]:((curious(X)|~quiet(X))=>(brave(X)&~humble(X))))&
(![X]:((~wise(X)&creative(X))=>~kind(X)))&
(![X]:((happy(X)|~strong(X))=>(curious(X)|~rich(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|~creative(X))))&
((~humble(paul)<~>old(paul)))&
(~humble(mary)) | wise(fred) | [
"p0",
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6941503488967272395562107
% SZS output start Proof for 6941503488967272395562107
1. ! [X0] : ((~patient(X0) | ~rich(X0)) <=> (rich(X0) & happy(X0))) [input p0]
4. ? [X0] : (~wise(X0) <~> kind(X0)) <=> (~calm(lucy) & quiet(lucy)) [input p3]
5. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> (~tall(X0) <~> tall(X0))) [input p4]
6. ! [X0] : ((~kind(X0) | humble(X0)) <=> ~rich(X0)) [input p5]
19. wise(fred) [input hypothesis]
28. ! [X0] : (((~patient(X0) | ~rich(X0)) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | (patient(X0) & rich(X0)))) [nnf transformation 1]
29. ! [X0] : ((~patient(X0) | ~rich(X0) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | (patient(X0) & rich(X0)))) [flattening 28]
35. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (calm(lucy) | ~quiet(lucy))) & ((~calm(lucy) & quiet(lucy)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 4]
36. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | calm(lucy) | ~quiet(lucy)) & ((~calm(lucy) & quiet(lucy)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [flattening 35]
37. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | calm(lucy) | ~quiet(lucy)) & ((~calm(lucy) & quiet(lucy)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [rectify 36]
38. ? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) => ((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) [choice axiom]
39. (((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) | calm(lucy) | ~quiet(lucy)) & ((~calm(lucy) & quiet(lucy)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [skolemisation 37,38]
40. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (quiet(X0) | strong(X0)))) [nnf transformation 5]
41. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | quiet(X0) | strong(X0))) [flattening 40]
42. ! [X0] : (((~kind(X0) | humble(X0)) | rich(X0)) & (~rich(X0) | (kind(X0) & ~humble(X0)))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | humble(X0) | rich(X0)) & (~rich(X0) | (kind(X0) & ~humble(X0)))) [flattening 42]
68. rich(X0) | rich(X0) [cnf transformation 29]
79. quiet(lucy) | ~wise(X1) | ~kind(X1) [cnf transformation 39]
88. ~quiet(X0) | tall(X0) | tall(X0) [cnf transformation 41]
89. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
91. ~rich(X0) | kind(X0) [cnf transformation 43]
134. wise(fred) [cnf transformation 19]
137. ~quiet(X0) | tall(X0) [duplicate literal removal 88]
138. ~quiet(X0) | ~tall(X0) [duplicate literal removal 89]
139. rich(X0) [duplicate literal removal 68]
159. 5 <=> ! [X1] : ~quiet(X1) [avatar definition]
160. ~quiet(X1) <- (5) [avatar component clause 159]
169. 7 <=> quiet(lucy) [avatar definition]
170. quiet(lucy) <- (7) [avatar component clause 169]
187. 11 <=> ! [X1] : (~wise(X1) | ~kind(X1)) [avatar definition]
188. ~wise(X1) | ~kind(X1) <- (11) [avatar component clause 187]
194. 11 | 7 [avatar split clause 79,169,187]
196. ~quiet(X0) [subsumption resolution 137,138]
197. 5 [avatar split clause 196,159]
199. kind(X0) [subsumption resolution 91,139]
291. $false <- (5, 7) [resolution 170,160]
292. ~5 | ~7 [avatar contradiction clause 291]
293. ~wise(X1) <- (11) [subsumption resolution 188,199]
296. $false <- (11) [resolution 293,134]
299. ~11 [avatar contradiction clause 296]
300. $false [avatar sat refutation 194,197,292,299]
% SZS output end Proof for 6941503488967272395562107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or kind is not old or rich and vice versa. If someone is both patient and happy then john is rich. If mary is funny then someone is not wise or not strong. Everyone who is curious or not old is brave or not wise. Everyone who is tall is not generous and vice versa. Everyone who is brave is patient and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Everyone who is either not curious or not brave is curious or funny and vice versa. Everyone who is not curious or not calm is not calm and vice versa. Everyone who is either rich or curious is brave or not quiet and vice versa. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. Susan is either not generous or rich. Someone is either not calm or not quiet. Fred is either rich or curious. | Alice is not wise. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(~old(X)|rich(X))))&
((?[X]:((patient(X)&happy(X))))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((rich(fred)<~>curious(fred))) | ~wise(alice) | [
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 159650007291083789348421
% SZS output start Proof for 159650007291083789348421
4. ! [X0] : ((~old(X0) | curious(X0)) => (~wise(X0) | brave(X0))) [input p3]
12. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p11]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p12]
15. ~tall(alice) & calm(alice) [input p14]
21. wise(alice) [input hypothesis]
24. ! [X0] : ((~wise(X0) | brave(X0)) | (old(X0) & ~curious(X0))) [ennf transformation 4]
25. ! [X0] : (~wise(X0) | brave(X0) | (old(X0) & ~curious(X0))) [flattening 24]
45. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 12]
46. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 45]
47. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 13]
48. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 47]
66. ~curious(X0) | brave(X0) | ~wise(X0) [cnf transformation 25]
94. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
98. ~calm(X0) | curious(X0) [cnf transformation 48]
107. calm(alice) [cnf transformation 15]
118. wise(alice) [cnf transformation 21]
120. ~brave(X0) | ~curious(X0) [duplicate literal removal 94]
219. curious(alice) [resolution 98,107]
274. brave(alice) | ~wise(alice) [resolution 66,219]
276. brave(alice) [subsumption resolution 274,118]
344. ~curious(alice) [resolution 276,120]
352. $false [subsumption resolution 344,219]
% SZS output end Proof for 159650007291083789348421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or generous is not brave.
Everyone who is both quiet and not humble is brave.
Everyone who is not strong or not brave is either tall or not humble and vice versa.
If fred is either quiet or not calm then fred is both not wise and brave.
Everyone who is either happy or not funny is either tall or creative.
If paul is both not strong and quiet then someone is not patient.
Everyone who is both not creative and strong is rich or not curious and vice versa.
If john is funny then someone is either not funny or curious and vice versa.
If someone is old or not kind then someone is both creative and not rich and vice versa.
If alice is both kind and strong then paul is either brave or not patient and vice versa.
If someone is not wise then someone is strong or wise.
If mary is both not brave and not old then someone is both not curious and not calm and vice versa.
If someone is either not creative or not curious then someone is both not rich and humble.
If paul is not curious then paul is not calm or not curious.
Everyone who is both curious and old is not tall and vice versa.
Everyone who is funny is not wise.
Lucy is both not strong and patient.
Someone is both not funny and quiet.
Someone is both not tall and wise.
Fred is either not calm or not old.
Fred is both rich and wise.
John is wise or brave.
Susan is either strong or happy.
Susan is both not kind and not wise. | Alice is not curious. | neutral | (![X]:((~calm(X)|generous(X))=>~brave(X)))&
(![X]:((quiet(X)&~humble(X))=>brave(X)))&
(![X]:((~strong(X)|~brave(X))<=>(tall(X)<~>~humble(X))))&
(((quiet(fred)<~>~calm(fred)))=>((~wise(fred)&brave(fred))))&
(![X]:((happy(X)<~>~funny(X))=>(tall(X)<~>creative(X))))&
(((~strong(paul)&quiet(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~creative(X)&strong(X))<=>(rich(X)|~curious(X))))&
((funny(john))<=>(?[X]:((~funny(X)<~>curious(X)))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:((creative(X)&~rich(X)))))&
(((kind(alice)&strong(alice)))<=>((brave(paul)<~>~patient(paul))))&
((?[X]:(~wise(X)))=>(?[X]:((strong(X)|wise(X)))))&
(((~brave(mary)&~old(mary)))<=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~creative(X)<~>~curious(X))))=>(?[X]:((~rich(X)&humble(X)))))&
((~curious(paul))=>((~calm(paul)|~curious(paul))))&
(![X]:((curious(X)&old(X))<=>~tall(X)))&
(![X]:(funny(X)=>~wise(X)))&
((~strong(lucy)&patient(lucy)))&
(?[X]:((~funny(X)&quiet(X))))&
(?[X]:((~tall(X)&wise(X))))&
((~calm(fred)<~>~old(fred)))&
((rich(fred)&wise(fred)))&
((wise(john)|brave(john)))&
((strong(susan)<~>happy(susan)))&
((~kind(susan)&~wise(susan))) | ~curious(alice) | [] | null | 0 |
Everyone who is both patient and wise is strong and vice versa.
If mary is either calm or funny then someone is either brave or not humble and vice versa.
Everyone who is both patient and not quiet is both funny and calm.
Everyone who is either old or curious is either not quiet or calm.
Everyone who is both not creative and humble is not brave or not happy and vice versa.
Everyone who is quiet is either brave or creative and vice versa.
Everyone who is funny is curious.
Everyone who is old is happy and vice versa.
Everyone who is not tall or not funny is happy or not old and vice versa.
If someone is either not patient or patient then mary is not tall or not rich and vice versa.
Everyone who is either not old or old is either happy or rich.
If paul is calm or tall then mary is calm.
If someone is both curious and tall then someone is happy or not brave and vice versa.
Everyone who is both rich and not tall is not generous or not funny and vice versa.
Everyone who is funny is either happy or not patient.
If someone is both generous and funny then mary is quiet.
Someone is either not brave or brave.
Alice is curious or not curious.
Someone is both not tall and not calm.
Fred is both wise and not patient.
Alice is wise. | Mary is not quiet. | contradiction | (![X]:((patient(X)&wise(X))<=>strong(X)))&
(((calm(mary)<~>funny(mary)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((patient(X)&~quiet(X))=>(funny(X)&calm(X))))&
(![X]:((old(X)<~>curious(X))=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(~brave(X)|~happy(X))))&
(![X]:(quiet(X)<=>(brave(X)<~>creative(X))))&
(![X]:(funny(X)=>curious(X)))&
(![X]:(old(X)<=>happy(X)))&
(![X]:((~tall(X)|~funny(X))<=>(happy(X)|~old(X))))&
((?[X]:((~patient(X)<~>patient(X))))<=>((~tall(mary)|~rich(mary))))&
(![X]:((~old(X)<~>old(X))=>(happy(X)<~>rich(X))))&
(((calm(paul)|tall(paul)))=>(calm(mary)))&
((?[X]:((curious(X)&tall(X))))<=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:((rich(X)&~tall(X))<=>(~generous(X)|~funny(X))))&
(![X]:(funny(X)=>(happy(X)<~>~patient(X))))&
((?[X]:((generous(X)&funny(X))))=>(quiet(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
((curious(alice)|~curious(alice)))&
(?[X]:((~tall(X)&~calm(X))))&
((wise(fred)&~patient(fred)))&
(wise(alice)) | ~quiet(mary) | [
"p4",
"p5",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4574331842110945110818028
% SZS output start Proof for 4574331842110945110818028
5. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (~happy(X0) | ~brave(X0))) [input p4]
6. ! [X0] : (quiet(X0) <=> (brave(X0) <~> creative(X0))) [input p5]
13. ? [X0] : (tall(X0) & curious(X0)) <=> ? [X0] : (~brave(X0) | happy(X0)) [input p12]
14. ! [X0] : ((~tall(X0) & rich(X0)) <=> (~funny(X0) | ~generous(X0))) [input p13]
16. ? [X0] : (funny(X0) & generous(X0)) => quiet(mary) [input p15]
22. ~quiet(mary) [input hypothesis]
23. ? [X0] : (tall(X0) & curious(X0)) <=> ? [X1] : (~brave(X1) | happy(X1)) [rectify 13]
33. quiet(mary) | ! [X0] : (~funny(X0) | ~generous(X0)) [ennf transformation 16]
39. ! [X0] : (((humble(X0) & ~creative(X0)) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 5]
40. ! [X0] : (((humble(X0) & ~creative(X0)) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | ~humble(X0) | creative(X0))) [flattening 39]
41. ! [X0] : ((quiet(X0) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0)))) & (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | ~quiet(X0))) [nnf transformation 6]
51. (? [X0] : (tall(X0) & curious(X0)) | ! [X1] : (brave(X1) & ~happy(X1))) & (? [X1] : (~brave(X1) | happy(X1)) | ! [X0] : (~tall(X0) | ~curious(X0))) [nnf transformation 23]
52. (? [X0] : (tall(X0) & curious(X0)) | ! [X1] : (brave(X1) & ~happy(X1))) & (? [X2] : (~brave(X2) | happy(X2)) | ! [X3] : (~tall(X3) | ~curious(X3))) [rectify 51]
53. ? [X0] : (tall(X0) & curious(X0)) => (tall(sK2) & curious(sK2)) [choice axiom]
54. ? [X2] : (~brave(X2) | happy(X2)) => (~brave(sK3) | happy(sK3)) [choice axiom]
55. ((tall(sK2) & curious(sK2)) | ! [X1] : (brave(X1) & ~happy(X1))) & ((~brave(sK3) | happy(sK3)) | ! [X3] : (~tall(X3) | ~curious(X3))) [skolemisation 52,54,53]
56. ! [X0] : (((~tall(X0) & rich(X0)) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | (tall(X0) | ~rich(X0)))) [nnf transformation 14]
57. ! [X0] : (((~tall(X0) & rich(X0)) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | tall(X0) | ~rich(X0))) [flattening 56]
80. ~creative(X0) | happy(X0) [cnf transformation 40]
85. ~brave(X0) | creative(X0) | quiet(X0) [cnf transformation 41]
109. tall(sK2) | ~happy(X1) [cnf transformation 55]
110. tall(sK2) | brave(X1) [cnf transformation 55]
114. ~tall(X0) | generous(X0) [cnf transformation 57]
115. ~tall(X0) | funny(X0) [cnf transformation 57]
118. quiet(mary) | ~funny(X0) | ~generous(X0) [cnf transformation 33]
125. ~quiet(mary) [cnf transformation 22]
194. 13 <=> ! [X1] : brave(X1) [avatar definition]
195. brave(X1) <- (13) [avatar component clause 194]
197. 14 <=> tall(sK2) [avatar definition]
199. tall(sK2) <- (14) [avatar component clause 197]
200. 13 | 14 [avatar split clause 110,197,194]
202. 15 <=> ! [X1] : ~happy(X1) [avatar definition]
203. ~happy(X1) <- (15) [avatar component clause 202]
204. 15 | 14 [avatar split clause 109,197,202]
224. 20 <=> ! [X0] : (~funny(X0) | ~generous(X0)) [avatar definition]
225. ~generous(X0) | ~funny(X0) <- (20) [avatar component clause 224]
227. 21 <=> quiet(mary) [avatar definition]
228. ~quiet(mary) <- (~21) [avatar component clause 227]
230. 20 | 21 [avatar split clause 118,227,224]
231. ~21 [avatar split clause 125,227]
239. generous(sK2) <- (14) [resolution 114,199]
240. funny(sK2) <- (14) [resolution 115,199]
245. ~funny(sK2) <- (14, 20) [resolution 225,239]
247. $false <- (14, 20) [subsumption resolution 245,240]
248. ~14 | ~20 [avatar contradiction clause 247]
251. creative(X0) | quiet(X0) <- (13) [resolution 85,195]
264. quiet(X1) | happy(X1) <- (13) [resolution 251,80]
266. quiet(X1) <- (13, 15) [subsumption resolution 264,203]
267. $false <- (13, 15, ~21) [resolution 266,228]
269. ~13 | ~15 | 21 [avatar contradiction clause 267]
270. $false [avatar sat refutation 200,204,230,231,248,269]
% SZS output end Proof for 4574331842110945110818028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not quiet or funny then someone is either not generous or not calm and vice versa.
Everyone who is wise or generous is both not rich and not tall.
If someone is both quiet and not generous then mary is either not quiet or brave and vice versa.
Everyone who is both calm and patient is either wise or not tall and vice versa.
Everyone who is not brave is not calm and vice versa.
If fred is either not strong or not generous then someone is not tall or old.
Everyone who is either rich or happy is both not quiet and not brave and vice versa.
Everyone who is both not wise and not old is not humble or kind.
Everyone who is either rich or not creative is either creative or tall.
If john is both not old and not quiet then alice is both not funny and calm and vice versa.
Everyone who is not wise is curious or not quiet.
Everyone who is both curious and not calm is wise.
If someone is either not rich or kind then someone is both not rich and wise and vice versa.
If someone is both calm and brave then someone is both quiet and not patient.
Everyone who is humble or quiet is quiet or not creative.
If someone is both calm and not generous then susan is not generous and vice versa.
Susan is not old.
Someone is both not tall and not strong.
Mary is kind or humble.
Someone is not brave or not patient.
Someone is either not quiet or not patient.
Someone is calm.
Someone is brave.
Someone is either not calm or not strong. | Fred is not strong. | neutral | (((~quiet(susan)|funny(susan)))<=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((wise(X)|generous(X))=>(~rich(X)&~tall(X))))&
((?[X]:((quiet(X)&~generous(X))))<=>((~quiet(mary)<~>brave(mary))))&
(![X]:((calm(X)&patient(X))<=>(wise(X)<~>~tall(X))))&
(![X]:(~brave(X)<=>~calm(X)))&
(((~strong(fred)<~>~generous(fred)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((rich(X)<~>happy(X))<=>(~quiet(X)&~brave(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)|kind(X))))&
(![X]:((rich(X)<~>~creative(X))=>(creative(X)<~>tall(X))))&
(((~old(john)&~quiet(john)))<=>((~funny(alice)&calm(alice))))&
(![X]:(~wise(X)=>(curious(X)|~quiet(X))))&
(![X]:((curious(X)&~calm(X))=>wise(X)))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((calm(X)&brave(X))))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((humble(X)|quiet(X))=>(quiet(X)|~creative(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(~generous(susan)))&
(~old(susan))&
(?[X]:((~tall(X)&~strong(X))))&
((kind(mary)|humble(mary)))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:((~quiet(X)<~>~patient(X))))&
(?[X]:(calm(X)))&
(?[X]:(brave(X)))&
(?[X]:((~calm(X)<~>~strong(X)))) | ~strong(fred) | [] | null | 0 |
If someone is not quiet then someone is not strong or not quiet and vice versa.
If mary is both not kind and humble then someone is either tall or not tall and vice versa.
If john is either creative or not old then someone is both old and kind.
Everyone who is either generous or not humble is either not creative or old and vice versa.
Everyone who is either happy or not funny is both patient and not quiet.
If someone is calm or quiet then someone is both humble and not old.
If someone is either not happy or strong then someone is either brave or rich and vice versa.
Everyone who is not kind is both generous and not creative and vice versa.
Everyone who is not humble or not brave is both not old and happy and vice versa.
If susan is funny then someone is either not old or brave.
Everyone who is both not creative and not generous is both tall and not old.
Everyone who is not kind or funny is rich.
Everyone who is not strong or not kind is both happy and not curious.
If mary is either calm or not creative then susan is either creative or not kind and vice versa.
Everyone who is not calm is both not wise and old and vice versa.
If someone is either curious or generous then someone is either not generous or not strong.
Someone is either kind or not brave.
Someone is either not wise or old.
Someone is either not curious or not wise.
Someone is both not happy and patient.
Someone is humble.
Someone is not calm.
Alice is funny. | Alice is not rich. | contradiction | ((?[X]:(~quiet(X)))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(((~kind(mary)&humble(mary)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(((creative(john)<~>~old(john)))=>(?[X]:((old(X)&kind(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>(~creative(X)<~>old(X))))&
(![X]:((happy(X)<~>~funny(X))=>(patient(X)&~quiet(X))))&
((?[X]:((calm(X)|quiet(X))))=>(?[X]:((humble(X)&~old(X)))))&
((?[X]:((~happy(X)<~>strong(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(generous(X)&~creative(X))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)&happy(X))))&
((funny(susan))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~creative(X)&~generous(X))=>(tall(X)&~old(X))))&
(![X]:((~kind(X)|funny(X))=>rich(X)))&
(![X]:((~strong(X)|~kind(X))=>(happy(X)&~curious(X))))&
(((calm(mary)<~>~creative(mary)))<=>((creative(susan)<~>~kind(susan))))&
(![X]:(~calm(X)<=>(~wise(X)&old(X))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(?[X]:((kind(X)<~>~brave(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:(humble(X)))&
(?[X]:(~calm(X)))&
(funny(alice)) | ~rich(alice) | [
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3532907930954937908239344
% SZS output start Proof for 3532907930954937908239344
12. ! [X0] : ((funny(X0) | ~kind(X0)) => rich(X0)) [input p11]
23. funny(alice) [input p22]
24. ~rich(alice) [input hypothesis]
37. ! [X0] : (rich(X0) | (~funny(X0) & kind(X0))) [ennf transformation 12]
140. ~funny(X0) | rich(X0) [cnf transformation 37]
169. funny(alice) [cnf transformation 23]
170. ~rich(alice) [cnf transformation 24]
382. rich(alice) [resolution 140,169]
383. $false [subsumption resolution 382,170]
% SZS output end Proof for 3532907930954937908239344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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 8699611147714837172330617
% SZS output start Proof for 8699611147714837172330617
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 8699611147714837172330617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then someone is not strong. Everyone who is either strong or wise is either not kind or calm and vice versa. Everyone who is either kind or tall is either creative or not kind. Everyone who is not wise is not calm or patient and vice versa. If lucy is either not patient or not funny then mary is not happy and vice versa. If someone is both not old and not kind then alice is rich or not brave and vice versa. If lucy is both not humble and tall then mary is both not rich and not kind. Everyone who is either humble or not rich is not old or not brave. If someone is both not wise and rich then paul is either not generous or quiet. If alice is not happy then someone is either curious or not brave and vice versa. If someone is both old and not kind then someone is not curious or generous and vice versa. If someone is either creative or quiet then someone is not old and vice versa. Everyone who is not wise is quiet or not creative and vice versa. Everyone who is not patient is either not calm or not quiet. Everyone who is either not rich or brave is both kind and rich and vice versa. Everyone who is wise is either wise or not wise and vice versa. Lucy is either funny or not brave. Mary is either tall or not happy. Alice is not humble. Someone is either not happy or curious. Someone is both humble and not quiet. Someone is either curious or not funny. Lucy is not curious or not generous. | Fred is patient. | contradiction | ((happy(fred))=>(?[X]:(~strong(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~kind(X)<~>calm(X))))&
(![X]:((kind(X)<~>tall(X))=>(creative(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>(~calm(X)|patient(X))))&
(((~patient(lucy)<~>~funny(lucy)))<=>(~happy(mary)))&
((?[X]:((~old(X)&~kind(X))))<=>((rich(alice)|~brave(alice))))&
(((~humble(lucy)&tall(lucy)))=>((~rich(mary)&~kind(mary))))&
(![X]:((humble(X)<~>~rich(X))=>(~old(X)|~brave(X))))&
((?[X]:((~wise(X)&rich(X))))=>((~generous(paul)<~>quiet(paul))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
((funny(lucy)<~>~brave(lucy)))&
((tall(mary)<~>~happy(mary)))&
(~humble(alice))&
(?[X]:((~happy(X)<~>curious(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((curious(X)<~>~funny(X))))&
((~curious(lucy)|~generous(lucy))) | patient(fred) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 804751251421391800123819
% SZS output start Proof for 804751251421391800123819
4. ! [X0] : (~wise(X0) <=> (patient(X0) | ~calm(X0))) [input p3]
16. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p15]
24. patient(fred) [input hypothesis]
39. ! [X0] : ((~wise(X0) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | wise(X0))) [nnf transformation 4]
40. ! [X0] : ((~wise(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | wise(X0))) [flattening 39]
68. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 16]
94. ~patient(X0) | ~wise(X0) [cnf transformation 40]
137. wise(X0) | wise(X0) | wise(X0) [cnf transformation 68]
150. patient(fred) [cnf transformation 24]
154. wise(X0) [duplicate literal removal 137]
369. ~wise(fred) [resolution 94,150]
371. $false [subsumption resolution 369,154]
% SZS output end Proof for 804751251421391800123819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not humble or not kind and vice versa.
If alice is wise then mary is either kind or strong.
If someone is both humble and not humble then susan is tall.
Everyone who is not brave or happy is both kind and not strong.
If someone is creative then mary is either brave or creative.
Everyone who is both brave and not old is either not calm or tall and vice versa.
If someone is not humble or brave then alice is tall or not generous.
If john is rich then susan is not old and vice versa.
Everyone who is both rich and quiet is kind.
Everyone who is both calm and humble is both old and humble and vice versa.
Everyone who is not kind or quiet is not happy and vice versa.
Everyone who is not funny is either curious or old and vice versa.
If someone is not kind or happy then john is either humble or not calm.
Everyone who is patient is either not humble or not funny.
If someone is not rich then paul is both tall and not patient.
Everyone who is both rich and not patient is either humble or not generous and vice versa.
John is both tall and not happy.
Someone is either not happy or quiet.
Someone is calm or not old.
Someone is strong.
Someone is rich.
Paul is not curious or not humble.
Paul is curious or not happy. | John is not creative. | contradiction | (![X]:(creative(X)<=>(~humble(X)|~kind(X))))&
((wise(alice))=>((kind(mary)<~>strong(mary))))&
((?[X]:((humble(X)&~humble(X))))=>(tall(susan)))&
(![X]:((~brave(X)|happy(X))=>(kind(X)&~strong(X))))&
((?[X]:(creative(X)))=>((brave(mary)<~>creative(mary))))&
(![X]:((brave(X)&~old(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((~humble(X)|brave(X))))=>((tall(alice)|~generous(alice))))&
((rich(john))<=>(~old(susan)))&
(![X]:((rich(X)&quiet(X))=>kind(X)))&
(![X]:((calm(X)&humble(X))<=>(old(X)&humble(X))))&
(![X]:((~kind(X)|quiet(X))<=>~happy(X)))&
(![X]:(~funny(X)<=>(curious(X)<~>old(X))))&
((?[X]:((~kind(X)|happy(X))))=>((humble(john)<~>~calm(john))))&
(![X]:(patient(X)=>(~humble(X)<~>~funny(X))))&
((?[X]:(~rich(X)))=>((tall(paul)&~patient(paul))))&
(![X]:((rich(X)&~patient(X))<=>(humble(X)<~>~generous(X))))&
((tall(john)&~happy(john)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:(strong(X)))&
(?[X]:(rich(X)))&
((~curious(paul)|~humble(paul)))&
((curious(paul)|~happy(paul))) | ~creative(john) | [
"p0",
"p5",
"p9",
"p10",
"p12",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4254879034168376404121390
% SZS output start Proof for 4254879034168376404121390
1. ! [X0] : (creative(X0) <=> (~kind(X0) | ~humble(X0))) [input p0]
6. ! [X0] : ((~old(X0) & brave(X0)) <=> (~calm(X0) <~> tall(X0))) [input p5]
10. ! [X0] : ((humble(X0) & calm(X0)) <=> (humble(X0) & old(X0))) [input p9]
11. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> ~happy(X0)) [input p10]
13. ? [X0] : (happy(X0) | ~kind(X0)) => (humble(john) <~> ~calm(john)) [input p12]
17. ~happy(john) & tall(john) [input p16]
18. ? [X0] : (~happy(X0) <~> quiet(X0)) [input p17]
24. ~creative(john) [input hypothesis]
33. (humble(john) <~> ~calm(john)) | ! [X0] : (~happy(X0) & kind(X0)) [ennf transformation 13]
36. ! [X0] : ((creative(X0) | (kind(X0) & humble(X0))) & ((~kind(X0) | ~humble(X0)) | ~creative(X0))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | (kind(X0) & humble(X0))) & (~kind(X0) | ~humble(X0) | ~creative(X0))) [flattening 36]
39. ! [X0] : (((~old(X0) & brave(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0)))) & (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (old(X0) | ~brave(X0)))) [nnf transformation 6]
40. ! [X0] : (((~old(X0) & brave(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0)))) & (((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | old(X0) | ~brave(X0))) [flattening 39]
42. ! [X0] : (((humble(X0) & calm(X0)) | (~humble(X0) | ~old(X0))) & ((humble(X0) & old(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 10]
43. ! [X0] : (((humble(X0) & calm(X0)) | ~humble(X0) | ~old(X0)) & ((humble(X0) & old(X0)) | ~humble(X0) | ~calm(X0))) [flattening 42]
44. ! [X0] : (((quiet(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (~quiet(X0) & kind(X0)))) [nnf transformation 11]
45. ! [X0] : ((quiet(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (~quiet(X0) & kind(X0)))) [flattening 44]
47. ((calm(john) | ~humble(john)) & (~calm(john) | humble(john))) | ! [X0] : (~happy(X0) & kind(X0)) [nnf transformation 33]
51. ? [X0] : ((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) [nnf transformation 18]
52. ? [X0] : ((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) => ((~quiet(sK0) | happy(sK0)) & (quiet(sK0) | ~happy(sK0))) [choice axiom]
53. (~quiet(sK0) | happy(sK0)) & (quiet(sK0) | ~happy(sK0)) [skolemisation 51,52]
61. humble(X0) | creative(X0) [cnf transformation 37]
75. ~calm(X0) | ~old(X0) | ~tall(X0) [cnf transformation 40]
81. ~calm(X0) | ~humble(X0) | old(X0) [cnf transformation 43]
86. ~quiet(X0) | ~happy(X0) [cnf transformation 45]
87. ~kind(X0) | quiet(X0) | happy(X0) [cnf transformation 45]
94. calm(john) | ~humble(john) | kind(X0) [cnf transformation 47]
95. calm(john) | ~humble(john) | ~happy(X0) [cnf transformation 47]
106. tall(john) [cnf transformation 17]
109. ~quiet(sK0) | happy(sK0) [cnf transformation 53]
115. ~creative(john) [cnf transformation 24]
156. 10 <=> ! [X0] : ~happy(X0) [avatar definition]
157. ~happy(X0) <- (10) [avatar component clause 156]
159. 11 <=> humble(john) [avatar definition]
160. humble(john) <- (11) [avatar component clause 159]
161. ~humble(john) <- (~11) [avatar component clause 159]
163. 12 <=> calm(john) [avatar definition]
165. calm(john) <- (12) [avatar component clause 163]
166. 10 | ~11 | 12 [avatar split clause 95,163,159,156]
168. 13 <=> ! [X0] : kind(X0) [avatar definition]
169. kind(X0) <- (13) [avatar component clause 168]
170. 13 | ~11 | 12 [avatar split clause 94,163,159,168]
186. ~quiet(sK0) [subsumption resolution 109,86]
213. creative(john) <- (~11) [resolution 61,161]
215. $false <- (~11) [subsumption resolution 213,115]
216. 11 [avatar contradiction clause 215]
223. ~old(john) | ~tall(john) <- (12) [resolution 75,165]
225. ~old(john) <- (12) [subsumption resolution 223,106]
226. ~humble(john) | old(john) <- (12) [resolution 81,165]
228. old(john) <- (11, 12) [subsumption resolution 226,160]
229. $false <- (11, 12) [subsumption resolution 228,225]
230. ~11 | ~12 [avatar contradiction clause 229]
235. quiet(X0) | happy(X0) <- (13) [resolution 87,169]
237. quiet(X0) <- (10, 13) [subsumption resolution 235,157]
238. $false <- (10, 13) [resolution 237,186]
241. ~10 | ~13 [avatar contradiction clause 238]
242. $false [avatar sat refutation 166,170,216,230,241]
% SZS output end Proof for 4254879034168376404121390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or humble then alice is both funny and humble. Everyone who is either not brave or not kind is not creative or quiet and vice versa. Everyone who is creative is either not brave or curious. Everyone who is generous or patient is not patient or not kind and vice versa. Everyone who is both wise and not quiet is not brave or not quiet. Everyone who is either not curious or not rich is either kind or not generous and vice versa. Everyone who is either not calm or funny is both not happy and tall. Everyone who is not strong is both patient and old. Everyone who is either not wise or humble is both not old and humble and vice versa. Everyone who is both not rich and not kind is both wise and happy and vice versa. If susan is both old and tall then lucy is both not brave and brave and vice versa. Everyone who is either not old or patient is not old or not creative and vice versa. If someone is either curious or not wise then mary is both not old and not kind and vice versa. Everyone who is both not humble and old is wise or kind. Everyone who is either not kind or strong is both not wise and calm and vice versa. Everyone who is generous is both patient and funny. John is either humble or happy. Someone is not creative. Someone is happy. Mary is not creative or not brave. Someone is creative or not rich. Someone is quiet. Paul is not calm or not tall. Someone is both calm and curious. | Mary is kind. | contradiction | ((?[X]:((~old(X)<~>humble(X))))=>((funny(alice)&humble(alice))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~creative(X)|quiet(X))))&
(![X]:(creative(X)=>(~brave(X)<~>curious(X))))&
(![X]:((generous(X)|patient(X))<=>(~patient(X)|~kind(X))))&
(![X]:((wise(X)&~quiet(X))=>(~brave(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~rich(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>funny(X))=>(~happy(X)&tall(X))))&
(![X]:(~strong(X)=>(patient(X)&old(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(~old(X)&humble(X))))&
(![X]:((~rich(X)&~kind(X))<=>(wise(X)&happy(X))))&
(((old(susan)&tall(susan)))<=>((~brave(lucy)&brave(lucy))))&
(![X]:((~old(X)<~>patient(X))<=>(~old(X)|~creative(X))))&
((?[X]:((curious(X)<~>~wise(X))))<=>((~old(mary)&~kind(mary))))&
(![X]:((~humble(X)&old(X))=>(wise(X)|kind(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(~wise(X)&calm(X))))&
(![X]:(generous(X)=>(patient(X)&funny(X))))&
((humble(john)<~>happy(john)))&
(?[X]:(~creative(X)))&
(?[X]:(happy(X)))&
((~creative(mary)|~brave(mary)))&
(?[X]:((creative(X)|~rich(X))))&
(?[X]:(quiet(X)))&
((~calm(paul)|~tall(paul)))&
(?[X]:((calm(X)&curious(X)))) | kind(mary) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1490880504976251542150889
% SZS output start Proof for 1490880504976251542150889
4. ! [X0] : ((patient(X0) | generous(X0)) <=> (~kind(X0) | ~patient(X0))) [input p3]
16. ! [X0] : (generous(X0) => (funny(X0) & patient(X0))) [input p15]
25. kind(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) & patient(X0)) | ~generous(X0)) [ennf transformation 16]
39. ! [X0] : (((patient(X0) | generous(X0)) | (kind(X0) & patient(X0))) & ((~kind(X0) | ~patient(X0)) | (~patient(X0) & ~generous(X0)))) [nnf transformation 4]
40. ! [X0] : ((patient(X0) | generous(X0) | (kind(X0) & patient(X0))) & (~kind(X0) | ~patient(X0) | (~patient(X0) & ~generous(X0)))) [flattening 39]
82. ~kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 40]
83. patient(X0) | generous(X0) | patient(X0) [cnf transformation 40]
133. patient(X0) | ~generous(X0) [cnf transformation 34]
145. kind(mary) [cnf transformation 25]
150. ~patient(X0) | ~kind(X0) [duplicate literal removal 82]
151. patient(X0) | generous(X0) [duplicate literal removal 83]
190. 9 <=> kind(mary) [avatar definition]
192. kind(mary) <- (9) [avatar component clause 190]
213. patient(X0) [subsumption resolution 133,151]
251. 9 [avatar split clause 145,190]
253. ~kind(X0) [resolution 150,213]
254. $false <- (9) [resolution 253,192]
255. ~9 [avatar contradiction clause 254]
256. $false [avatar sat refutation 251,255]
% SZS output end Proof for 1490880504976251542150889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or patient is old.
Everyone who is old or not kind is both calm and generous and vice versa.
Everyone who is either not rich or wise is both not humble and curious and vice versa.
If someone is not creative or not calm then susan is either not old or not strong and vice versa.
Everyone who is old is either quiet or not strong.
Everyone who is not strong is either kind or not calm.
If someone is not curious then someone is either not brave or quiet and vice versa.
Everyone who is either curious or funny is both brave and curious.
Everyone who is both not rich and brave is not generous.
If john is both not happy and kind then someone is either not funny or brave.
Everyone who is both funny and not brave is wise or not calm.
If fred is humble then lucy is both wise and not patient.
Everyone who is either not old or calm is both not curious and patient and vice versa.
Everyone who is wise is either not kind or happy.
If lucy is not patient or old then alice is brave and vice versa.
If someone is not humble then someone is not curious or not old.
Someone is wise.
Someone is both calm and wise.
Mary is not strong or not kind.
Someone is either not humble or kind.
Someone is creative.
John is both old and wise.
Someone is not curious.
Paul is either not strong or not funny. | John is not brave. | entailment | (![X]:((~calm(X)|patient(X))=>old(X)))&
(![X]:((old(X)|~kind(X))<=>(calm(X)&generous(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>((~old(susan)<~>~strong(susan))))&
(![X]:(old(X)=>(quiet(X)<~>~strong(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~calm(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))=>(brave(X)&curious(X))))&
(![X]:((~rich(X)&brave(X))=>~generous(X)))&
(((~happy(john)&kind(john)))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((funny(X)&~brave(X))=>(wise(X)|~calm(X))))&
((humble(fred))=>((wise(lucy)&~patient(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&patient(X))))&
(![X]:(wise(X)=>(~kind(X)<~>happy(X))))&
(((~patient(lucy)|old(lucy)))<=>(brave(alice)))&
((?[X]:(~humble(X)))=>(?[X]:((~curious(X)|~old(X)))))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)|~kind(mary)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(creative(X)))&
((old(john)&wise(john)))&
(?[X]:(~curious(X)))&
((~strong(paul)<~>~funny(paul))) | ~brave(john) | [
"p0",
"p1",
"p2",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3429490703120945063986736
% SZS output start Proof for 3429490703120945063986736
1. ! [X0] : ((patient(X0) | ~calm(X0)) => old(X0)) [input p0]
2. ! [X0] : ((~kind(X0) | old(X0)) <=> (generous(X0) & calm(X0))) [input p1]
3. ! [X0] : ((~rich(X0) <~> wise(X0)) <=> (curious(X0) & ~humble(X0))) [input p2]
9. ! [X0] : ((brave(X0) & ~rich(X0)) => ~generous(X0)) [input p8]
13. ! [X0] : ((~old(X0) <~> calm(X0)) <=> (patient(X0) & ~curious(X0))) [input p12]
22. wise(john) & old(john) [input p21]
25. brave(john) [input hypothesis]
28. ! [X0] : (old(X0) | (~patient(X0) & calm(X0))) [ennf transformation 1]
32. ! [X0] : (~generous(X0) | (~brave(X0) | rich(X0))) [ennf transformation 9]
33. ! [X0] : (~generous(X0) | ~brave(X0) | rich(X0)) [flattening 32]
41. ! [X0] : (((~kind(X0) | old(X0)) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~kind(X0) | old(X0) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | (kind(X0) & ~old(X0)))) [flattening 41]
43. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [nnf transformation 3]
44. ! [X0] : ((((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0))))) [flattening 43]
60. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [flattening 60]
80. old(X0) | calm(X0) [cnf transformation 28]
82. calm(X0) | ~old(X0) [cnf transformation 42]
84. ~old(X0) | generous(X0) [cnf transformation 42]
90. ~wise(X0) | ~rich(X0) | curious(X0) [cnf transformation 44]
111. ~brave(X0) | ~generous(X0) | rich(X0) [cnf transformation 33]
118. ~curious(X0) | ~old(X0) | ~calm(X0) [cnf transformation 61]
136. old(john) [cnf transformation 22]
137. wise(john) [cnf transformation 22]
141. brave(john) [cnf transformation 25]
144. calm(X0) [subsumption resolution 82,80]
226. ~curious(X0) | ~old(X0) [subsumption resolution 118,144]
276. generous(john) [resolution 84,136]
308. ~rich(john) | curious(john) [resolution 90,137]
328. 34 <=> curious(john) [avatar definition]
330. curious(john) <- (34) [avatar component clause 328]
332. 35 <=> rich(john) [avatar definition]
335. 34 | ~35 [avatar split clause 308,332,328]
352. ~generous(john) | rich(john) [resolution 111,141]
354. rich(john) [subsumption resolution 352,276]
366. 35 [avatar split clause 354,332]
399. ~old(john) <- (34) [resolution 330,226]
400. $false <- (34) [subsumption resolution 399,136]
401. ~34 [avatar contradiction clause 400]
402. $false [avatar sat refutation 335,366,401]
% SZS output end Proof for 3429490703120945063986736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not patient then someone is either not creative or rich.
Everyone who is either not generous or not quiet is calm and vice versa.
Everyone who is old is both not quiet and not generous and vice versa.
If someone is either not strong or calm then someone is creative or wise.
Everyone who is either not generous or not tall is both not happy and kind.
Everyone who is either tall or not happy is both brave and old and vice versa.
Everyone who is both rich and not rich is both rich and old and vice versa.
Everyone who is generous or funny is not rich and vice versa.
If someone is not calm then alice is both not calm and not old.
Everyone who is creative is not calm.
If someone is either wise or not strong then john is not old or wise.
Everyone who is both wise and humble is not kind and vice versa.
If fred is both not tall and wise then someone is both not funny and funny.
If someone is both not creative and not patient then alice is both old and not funny and vice versa.
Everyone who is generous is either not strong or generous and vice versa.
If someone is not funny then someone is not rich or patient and vice versa.
Someone is both wise and not patient.
Someone is both happy and rich.
Someone is both tall and not quiet.
Someone is brave or not creative.
Fred is both not kind and strong.
Someone is calm.
Someone is strong.
Susan is either not old or generous. | John is old. | neutral | ((?[X]:((calm(X)&~patient(X))))=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:((~generous(X)<~>~quiet(X))<=>calm(X)))&
(![X]:(old(X)<=>(~quiet(X)&~generous(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(~happy(X)&kind(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(brave(X)&old(X))))&
(![X]:((rich(X)&~rich(X))<=>(rich(X)&old(X))))&
(![X]:((generous(X)|funny(X))<=>~rich(X)))&
((?[X]:(~calm(X)))=>((~calm(alice)&~old(alice))))&
(![X]:(creative(X)=>~calm(X)))&
((?[X]:((wise(X)<~>~strong(X))))=>((~old(john)|wise(john))))&
(![X]:((wise(X)&humble(X))<=>~kind(X)))&
(((~tall(fred)&wise(fred)))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((~creative(X)&~patient(X))))<=>((old(alice)&~funny(alice))))&
(![X]:(generous(X)<=>(~strong(X)<~>generous(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~rich(X)|patient(X)))))&
(?[X]:((wise(X)&~patient(X))))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((brave(X)|~creative(X))))&
((~kind(fred)&strong(fred)))&
(?[X]:(calm(X)))&
(?[X]:(strong(X)))&
((~old(susan)<~>generous(susan))) | old(john) | [] | null | 0 |
Everyone who is not curious or calm is either humble or patient and vice versa. Everyone who is both tall and curious is either calm or humble. Everyone who is strong or not tall is either wise or not strong. If someone is either not curious or not generous then mary is not rich. Everyone who is either not rich or not happy is funny or calm and vice versa. If john is kind or tall then susan is not humble. If mary is either calm or tall then susan is not generous. Everyone who is not rich or patient is either kind or not strong. Everyone who is strong is not wise or not humble. Everyone who is not patient is either brave or not humble. Everyone who is quiet is calm. If someone is either patient or brave then lucy is happy or not calm. If mary is both not humble and calm then someone is either patient or not tall and vice versa. Everyone who is either not creative or brave is happy or not tall. If alice is rich or wise then john is funny. Everyone who is either not tall or quiet is not humble and vice versa. Lucy is either calm or not kind. Someone is not brave. Lucy is happy or not curious. Susan is either not old or not tall. Susan is creative or not happy. Lucy is calm. Someone is humble or tall. Lucy is both rich and calm. | Lucy is not strong. | contradiction | (![X]:((~curious(X)|calm(X))<=>(humble(X)<~>patient(X))))&
(![X]:((tall(X)&curious(X))=>(calm(X)<~>humble(X))))&
(![X]:((strong(X)|~tall(X))=>(wise(X)<~>~strong(X))))&
((?[X]:((~curious(X)<~>~generous(X))))=>(~rich(mary)))&
(![X]:((~rich(X)<~>~happy(X))<=>(funny(X)|calm(X))))&
(((kind(john)|tall(john)))=>(~humble(susan)))&
(((calm(mary)<~>tall(mary)))=>(~generous(susan)))&
(![X]:((~rich(X)|patient(X))=>(kind(X)<~>~strong(X))))&
(![X]:(strong(X)=>(~wise(X)|~humble(X))))&
(![X]:(~patient(X)=>(brave(X)<~>~humble(X))))&
(![X]:(quiet(X)=>calm(X)))&
((?[X]:((patient(X)<~>brave(X))))=>((happy(lucy)|~calm(lucy))))&
(((~humble(mary)&calm(mary)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((~creative(X)<~>brave(X))=>(happy(X)|~tall(X))))&
(((rich(alice)|wise(alice)))=>(funny(john)))&
(![X]:((~tall(X)<~>quiet(X))<=>~humble(X)))&
((calm(lucy)<~>~kind(lucy)))&
(?[X]:(~brave(X)))&
((happy(lucy)|~curious(lucy)))&
((~old(susan)<~>~tall(susan)))&
((creative(susan)|~happy(susan)))&
(calm(lucy))&
(?[X]:((humble(X)|tall(X))))&
((rich(lucy)&calm(lucy))) | ~strong(lucy) | [
"p0",
"p4",
"p7",
"p9",
"p11",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8145429148057819504850460
% SZS output start Proof for 8145429148057819504850460
1. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (humble(X0) <~> patient(X0))) [input p0]
5. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> (calm(X0) | funny(X0))) [input p4]
8. ! [X0] : ((patient(X0) | ~rich(X0)) => (kind(X0) <~> ~strong(X0))) [input p7]
10. ! [X0] : (~patient(X0) => (brave(X0) <~> ~humble(X0))) [input p9]
12. ? [X0] : (patient(X0) <~> brave(X0)) => (~calm(lucy) | happy(lucy)) [input p11]
17. calm(lucy) <~> ~kind(lucy) [input p16]
24. calm(lucy) & rich(lucy) [input p23]
25. ~strong(lucy) [input hypothesis]
32. ! [X0] : ((kind(X0) <~> ~strong(X0)) | (~patient(X0) & rich(X0))) [ennf transformation 8]
35. ! [X0] : ((brave(X0) <~> ~humble(X0)) | patient(X0)) [ennf transformation 10]
37. (~calm(lucy) | happy(lucy)) | ! [X0] : (patient(X0) <=> brave(X0)) [ennf transformation 12]
38. ~calm(lucy) | happy(lucy) | ! [X0] : (patient(X0) <=> brave(X0)) [flattening 37]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~calm(X0) & curious(X0)))) [nnf transformation 1]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~calm(X0) & curious(X0)))) [flattening 42]
47. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 5]
48. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [flattening 47]
50. ! [X0] : (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (~patient(X0) & rich(X0))) [nnf transformation 32]
51. ! [X0] : (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | patient(X0)) [nnf transformation 35]
52. ~calm(lucy) | happy(lucy) | ! [X0] : ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))) [nnf transformation 38]
60. (kind(lucy) | ~calm(lucy)) & (~kind(lucy) | calm(lucy)) [nnf transformation 17]
67. ~calm(X0) | humble(X0) | patient(X0) [cnf transformation 43]
83. ~happy(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 48]
93. ~kind(X0) | strong(X0) | ~patient(X0) [cnf transformation 50]
95. ~humble(X0) | brave(X0) | patient(X0) [cnf transformation 51]
99. ~calm(lucy) | happy(lucy) | patient(X0) | ~brave(X0) [cnf transformation 52]
115. kind(lucy) | ~calm(lucy) [cnf transformation 60]
123. rich(lucy) [cnf transformation 24]
124. calm(lucy) [cnf transformation 24]
125. ~strong(lucy) [cnf transformation 25]
169. 10 <=> ! [X0] : (patient(X0) | ~brave(X0)) [avatar definition]
170. ~brave(X0) | patient(X0) <- (10) [avatar component clause 169]
172. 11 <=> happy(lucy) [avatar definition]
174. happy(lucy) <- (11) [avatar component clause 172]
176. 12 <=> calm(lucy) [avatar definition]
177. calm(lucy) <- (12) [avatar component clause 176]
179. 10 | 11 | ~12 [avatar split clause 99,176,172,169]
223. 22 <=> kind(lucy) [avatar definition]
225. kind(lucy) <- (22) [avatar component clause 223]
226. ~12 | 22 [avatar split clause 115,223,176]
262. 12 [avatar split clause 124,176]
276. humble(lucy) | patient(lucy) <- (12) [resolution 67,177]
278. 32 <=> patient(lucy) [avatar definition]
279. ~patient(lucy) <- (~32) [avatar component clause 278]
282. 33 <=> humble(lucy) [avatar definition]
284. humble(lucy) <- (33) [avatar component clause 282]
285. 32 | 33 | ~12 [avatar split clause 276,176,282,278]
299. ~rich(lucy) | ~calm(lucy) <- (11) [resolution 83,174]
300. ~calm(lucy) <- (11) [subsumption resolution 299,123]
301. $false <- (11, 12) [subsumption resolution 300,177]
302. ~11 | ~12 [avatar contradiction clause 301]
312. strong(lucy) | ~patient(lucy) <- (22) [resolution 93,225]
313. ~patient(lucy) <- (22) [subsumption resolution 312,125]
316. ~32 | ~22 [avatar split clause 313,223,278]
322. brave(lucy) | patient(lucy) <- (33) [resolution 284,95]
323. brave(lucy) <- (~32, 33) [subsumption resolution 322,279]
374. patient(lucy) <- (10, ~32, 33) [resolution 323,170]
375. $false <- (10, ~32, 33) [subsumption resolution 374,279]
376. ~10 | 32 | ~33 [avatar contradiction clause 375]
377. $false [avatar sat refutation 179,226,262,285,302,316,376]
% SZS output end Proof for 8145429148057819504850460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either generous or calm then susan is not old or not humble and vice versa.
Everyone who is not creative is not generous or kind and vice versa.
If someone is both not tall and quiet then someone is both not kind and not wise and vice versa.
If someone is not kind then lucy is either creative or old.
Everyone who is either not curious or wise is both wise and not curious and vice versa.
Everyone who is not happy is generous or tall and vice versa.
Everyone who is either not old or generous is generous and vice versa.
If someone is not brave or generous then mary is not patient.
If someone is either not generous or curious then someone is not generous or not brave.
Everyone who is not brave or not old is both old and strong.
If paul is both happy and kind then mary is kind and vice versa.
Everyone who is brave or curious is either not tall or not rich and vice versa.
Everyone who is either strong or tall is both not creative and not generous.
If someone is not creative then fred is not tall and vice versa.
Everyone who is either not tall or quiet is not quiet or wise and vice versa.
If someone is brave then susan is generous or not curious.
Someone is not old or not tall.
Paul is both rich and not calm.
Mary is either not wise or not strong.
John is not quiet.
Paul is both curious and not calm.
Susan is not brave.
Susan is humble. | Paul is not strong. | contradiction | (((generous(susan)<~>calm(susan)))<=>((~old(susan)|~humble(susan))))&
(![X]:(~creative(X)<=>(~generous(X)|kind(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:((~kind(X)&~wise(X)))))&
((?[X]:(~kind(X)))=>((creative(lucy)<~>old(lucy))))&
(![X]:((~curious(X)<~>wise(X))<=>(wise(X)&~curious(X))))&
(![X]:(~happy(X)<=>(generous(X)|tall(X))))&
(![X]:((~old(X)<~>generous(X))<=>generous(X)))&
((?[X]:((~brave(X)|generous(X))))=>(~patient(mary)))&
((?[X]:((~generous(X)<~>curious(X))))=>(?[X]:((~generous(X)|~brave(X)))))&
(![X]:((~brave(X)|~old(X))=>(old(X)&strong(X))))&
(((happy(paul)&kind(paul)))<=>(kind(mary)))&
(![X]:((brave(X)|curious(X))<=>(~tall(X)<~>~rich(X))))&
(![X]:((strong(X)<~>tall(X))=>(~creative(X)&~generous(X))))&
((?[X]:(~creative(X)))<=>(~tall(fred)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~quiet(X)|wise(X))))&
((?[X]:(brave(X)))=>((generous(susan)|~curious(susan))))&
(?[X]:((~old(X)|~tall(X))))&
((rich(paul)&~calm(paul)))&
((~wise(mary)<~>~strong(mary)))&
(~quiet(john))&
((curious(paul)&~calm(paul)))&
(~brave(susan))&
(humble(susan)) | ~strong(paul) | [
"p4",
"p9",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3179982405918258711499350
% SZS output start Proof for 3179982405918258711499350
5. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (~curious(X0) & wise(X0))) [input p4]
10. ! [X0] : ((~old(X0) | ~brave(X0)) => (strong(X0) & old(X0))) [input p9]
13. ! [X0] : ((strong(X0) <~> tall(X0)) => (~generous(X0) & ~creative(X0))) [input p12]
15. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (wise(X0) | ~quiet(X0))) [input p14]
16. ? [X0] : brave(X0) => (~curious(susan) | generous(susan)) [input p15]
22. ~brave(susan) [input p21]
24. ~strong(paul) [input hypothesis]
30. ! [X0] : ((strong(X0) & old(X0)) | (old(X0) & brave(X0))) [ennf transformation 10]
31. ! [X0] : ((~generous(X0) & ~creative(X0)) | (strong(X0) <=> tall(X0))) [ennf transformation 13]
32. (~curious(susan) | generous(susan)) | ! [X0] : ~brave(X0) [ennf transformation 16]
33. ~curious(susan) | generous(susan) | ! [X0] : ~brave(X0) [flattening 32]
44. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [flattening 44]
57. ! [X0] : ((~generous(X0) & ~creative(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) [nnf transformation 31]
62. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 15]
63. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 62]
82. wise(X0) | wise(X0) | curious(X0) [cnf transformation 45]
85. ~curious(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 45]
87. ~wise(X0) | curious(X0) | curious(X0) | ~wise(X0) [cnf transformation 45]
99. strong(X0) | brave(X0) [cnf transformation 30]
112. ~strong(X0) | tall(X0) | ~generous(X0) [cnf transformation 57]
117. wise(X0) | ~quiet(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 63]
118. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 63]
122. ~curious(susan) | generous(susan) | ~brave(X0) [cnf transformation 33]
131. ~brave(susan) [cnf transformation 22]
133. ~strong(paul) [cnf transformation 24]
134. wise(X0) | ~quiet(X0) | ~tall(X0) [duplicate literal removal 117]
135. ~tall(X0) | quiet(X0) [duplicate literal removal 118]
139. wise(X0) | curious(X0) [duplicate literal removal 82]
140. ~curious(X0) | ~wise(X0) [duplicate literal removal 85]
141. ~wise(X0) | curious(X0) [duplicate literal removal 87]
147. 2 <=> generous(susan) [avatar definition]
148. generous(susan) <- (2) [avatar component clause 147]
203. ~wise(X0) [subsumption resolution 140,141]
204. curious(X0) [subsumption resolution 139,203]
249. ~quiet(X0) | ~tall(X0) [subsumption resolution 134,203]
250. ~tall(X0) [subsumption resolution 249,135]
251. generous(susan) | ~brave(X0) [subsumption resolution 122,204]
253. 23 <=> ! [X0] : ~brave(X0) [avatar definition]
254. ~brave(X0) <- (23) [avatar component clause 253]
255. 23 | 2 [avatar split clause 251,147,253]
278. brave(paul) [resolution 99,133]
279. $false <- (23) [subsumption resolution 278,254]
280. ~23 [avatar contradiction clause 279]
290. tall(X0) | ~generous(X0) | brave(X0) [resolution 112,99]
292. ~generous(X0) | brave(X0) [subsumption resolution 290,250]
293. brave(susan) <- (2) [resolution 292,148]
294. $false <- (2) [subsumption resolution 293,131]
295. ~2 [avatar contradiction clause 294]
296. $false [avatar sat refutation 255,280,295]
% SZS output end Proof for 3179982405918258711499350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or calm is either not quiet or not calm. If someone is both not quiet and not creative then someone is not kind. If someone is both curious and not funny then someone is either brave or not generous. If someone is not old then someone is creative and vice versa. If someone is not patient then someone is both not happy and not tall and vice versa. If someone is not rich or not generous then someone is either humble or not brave. Everyone who is humble or not humble is kind or old. If someone is tall then someone is calm. If mary is wise then paul is both brave and tall and vice versa. If john is both generous and not humble then alice is both strong and funny and vice versa. Everyone who is not happy is both not happy and tall. Everyone who is both not funny and kind is either not patient or not rich and vice versa. Everyone who is funny or not funny is not creative. Everyone who is both not tall and not kind is not funny or rich and vice versa. If paul is not strong or not rich then susan is both old and rich and vice versa. If someone is either not humble or kind then alice is not happy or not humble. Someone is either not old or not wise. Someone is either generous or not strong. Paul is either funny or not calm. Someone is not curious or brave. Someone is both generous and not creative. John is either not happy or not wise. | Mary is wise. | contradiction | (![X]:((~brave(X)<~>calm(X))=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:((brave(X)<~>~generous(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(creative(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:((~rich(X)|~generous(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((humble(X)|~humble(X))=>(kind(X)|old(X))))&
((?[X]:(tall(X)))=>(?[X]:(calm(X))))&
((wise(mary))<=>((brave(paul)&tall(paul))))&
(((generous(john)&~humble(john)))<=>((strong(alice)&funny(alice))))&
(![X]:(~happy(X)=>(~happy(X)&tall(X))))&
(![X]:((~funny(X)&kind(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((funny(X)|~funny(X))=>~creative(X)))&
(![X]:((~tall(X)&~kind(X))<=>(~funny(X)|rich(X))))&
(((~strong(paul)|~rich(paul)))<=>((old(susan)&rich(susan))))&
((?[X]:((~humble(X)<~>kind(X))))=>((~happy(alice)|~humble(alice))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
((funny(paul)<~>~calm(paul)))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:((generous(X)&~creative(X))))&
((~happy(john)<~>~wise(john))) | wise(mary) | [
"p4",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7447512120785866378535010
% SZS output start Proof for 7447512120785866378535010
5. ? [X0] : ~patient(X0) <=> ? [X0] : (~tall(X0) & ~happy(X0)) [input p4]
9. wise(mary) <=> (tall(paul) & brave(paul)) [input p8]
11. ! [X0] : (~happy(X0) => (tall(X0) & ~happy(X0))) [input p10]
12. ! [X0] : ((kind(X0) & ~funny(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p11]
14. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (rich(X0) | ~funny(X0))) [input p13]
23. wise(mary) [input hypothesis]
27. ? [X0] : ~patient(X0) <=> ? [X1] : (~tall(X1) & ~happy(X1)) [rectify 5]
38. ! [X0] : ((tall(X0) & ~happy(X0)) | happy(X0)) [ennf transformation 11]
51. (? [X0] : ~patient(X0) | ! [X1] : (tall(X1) | happy(X1))) & (? [X1] : (~tall(X1) & ~happy(X1)) | ! [X0] : patient(X0)) [nnf transformation 27]
52. (? [X0] : ~patient(X0) | ! [X1] : (tall(X1) | happy(X1))) & (? [X2] : (~tall(X2) & ~happy(X2)) | ! [X3] : patient(X3)) [rectify 51]
53. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
54. ? [X2] : (~tall(X2) & ~happy(X2)) => (~tall(sK4) & ~happy(sK4)) [choice axiom]
55. (~patient(sK3) | ! [X1] : (tall(X1) | happy(X1))) & ((~tall(sK4) & ~happy(sK4)) | ! [X3] : patient(X3)) [skolemisation 52,54,53]
63. (wise(mary) | (~tall(paul) | ~brave(paul))) & ((tall(paul) & brave(paul)) | ~wise(mary)) [nnf transformation 9]
64. (wise(mary) | ~tall(paul) | ~brave(paul)) & ((tall(paul) & brave(paul)) | ~wise(mary)) [flattening 63]
67. ! [X0] : (((kind(X0) & ~funny(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (~kind(X0) | funny(X0)))) [nnf transformation 12]
68. ! [X0] : (((kind(X0) & ~funny(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | ~kind(X0) | funny(X0))) [flattening 67]
69. ! [X0] : (((~kind(X0) & ~tall(X0)) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 14]
70. ! [X0] : (((~kind(X0) & ~tall(X0)) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | kind(X0) | tall(X0))) [flattening 69]
91. ~happy(sK4) | patient(X3) [cnf transformation 55]
92. ~tall(sK4) | patient(X3) [cnf transformation 55]
102. tall(paul) | ~wise(mary) [cnf transformation 64]
109. tall(X0) | happy(X0) [cnf transformation 38]
113. ~patient(X0) | ~funny(X0) | rich(X0) [cnf transformation 68]
119. ~tall(X0) | funny(X0) [cnf transformation 70]
120. ~rich(X0) | ~tall(X0) [cnf transformation 70]
140. wise(mary) [cnf transformation 23]
168. 7 <=> ! [X1] : (tall(X1) | happy(X1)) [avatar definition]
169. tall(X1) | happy(X1) <- (7) [avatar component clause 168]
176. 9 <=> ! [X3] : patient(X3) [avatar definition]
177. patient(X3) <- (9) [avatar component clause 176]
179. 10 <=> tall(sK4) [avatar definition]
181. ~tall(sK4) <- (~10) [avatar component clause 179]
182. 9 | ~10 [avatar split clause 92,179,176]
184. 11 <=> happy(sK4) [avatar definition]
186. ~happy(sK4) <- (~11) [avatar component clause 184]
187. 9 | ~11 [avatar split clause 91,184,176]
220. 19 <=> tall(paul) [avatar definition]
221. tall(paul) <- (19) [avatar component clause 220]
224. 20 <=> wise(mary) [avatar definition]
228. ~20 | 19 [avatar split clause 102,220,224]
250. 7 [avatar split clause 109,168]
266. 28 <=> rich(paul) [avatar definition]
267. rich(paul) <- (28) [avatar component clause 266]
311. 37 <=> funny(paul) [avatar definition]
312. funny(paul) <- (37) [avatar component clause 311]
330. 20 [avatar split clause 140,224]
334. funny(paul) <- (19) [resolution 119,221]
337. 37 | ~19 [avatar split clause 334,220,311]
340. happy(sK4) <- (7, ~10) [resolution 169,181]
343. $false <- (7, ~10, ~11) [subsumption resolution 340,186]
344. ~7 | 10 | 11 [avatar contradiction clause 343]
351. ~funny(X0) | rich(X0) <- (9) [resolution 113,177]
352. rich(paul) <- (9, 37) [resolution 351,312]
357. 28 | ~9 | ~37 [avatar split clause 352,311,176,266]
360. ~tall(paul) <- (28) [resolution 267,120]
361. $false <- (19, 28) [subsumption resolution 360,221]
362. ~19 | ~28 [avatar contradiction clause 361]
363. $false [avatar sat refutation 182,187,228,250,330,337,344,357,362]
% SZS output end Proof for 7447512120785866378535010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or old is either quiet or not quiet and vice versa.
If someone is not funny or not curious then paul is not wise.
Everyone who is not generous or not tall is either curious or not calm.
If someone is both brave and not strong then lucy is not creative and vice versa.
Everyone who is not tall or tall is not strong.
Everyone who is both wise and not happy is not quiet or wise and vice versa.
If someone is either not wise or kind then susan is brave and vice versa.
Everyone who is not funny is either not generous or not tall and vice versa.
Everyone who is patient or creative is not brave or not funny and vice versa.
Everyone who is not funny is not humble and vice versa.
Everyone who is both not patient and not curious is not brave or not curious and vice versa.
If paul is either humble or old then someone is either not quiet or happy.
Everyone who is not strong or happy is both not creative and not quiet and vice versa.
If susan is both not old and not happy then lucy is both quiet and not calm and vice versa.
If someone is either humble or not wise then someone is not old or patient and vice versa.
Everyone who is not brave is both not wise and not humble and vice versa.
Fred is not kind or not patient.
Paul is either not happy or not tall.
Someone is either calm or humble.
Lucy is either not humble or not strong.
Someone is not rich. | Susan is not kind. | neutral | (![X]:((tall(X)|old(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~funny(X)|~curious(X))))=>(~wise(paul)))&
(![X]:((~generous(X)|~tall(X))=>(curious(X)<~>~calm(X))))&
((?[X]:((brave(X)&~strong(X))))<=>(~creative(lucy)))&
(![X]:((~tall(X)|tall(X))=>~strong(X)))&
(![X]:((wise(X)&~happy(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(brave(susan)))&
(![X]:(~funny(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((patient(X)|creative(X))<=>(~brave(X)|~funny(X))))&
(![X]:(~funny(X)<=>~humble(X)))&
(![X]:((~patient(X)&~curious(X))<=>(~brave(X)|~curious(X))))&
(((humble(paul)<~>old(paul)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~strong(X)|happy(X))<=>(~creative(X)&~quiet(X))))&
(((~old(susan)&~happy(susan)))<=>((quiet(lucy)&~calm(lucy))))&
((?[X]:((humble(X)<~>~wise(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:(~brave(X)<=>(~wise(X)&~humble(X))))&
((~kind(fred)|~patient(fred)))&
((~happy(paul)<~>~tall(paul)))&
(?[X]:((calm(X)<~>humble(X))))&
((~humble(lucy)<~>~strong(lucy)))&
(?[X]:(~rich(X))) | ~kind(susan) | [] | null | 0 |
Everyone who is creative is both not patient and not rich.
If fred is either not calm or patient then fred is kind or creative.
Everyone who is either not old or old is not generous or wise.
If someone is not rich or not funny then fred is both tall and strong and vice versa.
Everyone who is kind or humble is both not happy and funny and vice versa.
Everyone who is not generous is either not kind or generous.
Everyone who is calm or generous is both calm and not humble and vice versa.
If paul is strong then someone is either calm or not humble and vice versa.
If someone is calm or brave then alice is both wise and not kind and vice versa.
Everyone who is not old or quiet is both not calm and humble and vice versa.
Everyone who is both not calm and patient is not old or brave and vice versa.
Everyone who is either not calm or rich is both not creative and curious and vice versa.
If mary is both tall and not strong then someone is either not happy or not rich and vice versa.
If susan is calm then fred is not generous or not curious.
Everyone who is curious or not calm is kind and vice versa.
Everyone who is not happy or generous is both kind and not funny and vice versa.
John is strong.
Fred is not brave.
Alice is old or not old.
Paul is either not humble or brave.
Someone is wise. | John is not brave. | entailment | (![X]:(creative(X)=>(~patient(X)&~rich(X))))&
(((~calm(fred)<~>patient(fred)))=>((kind(fred)|creative(fred))))&
(![X]:((~old(X)<~>old(X))=>(~generous(X)|wise(X))))&
((?[X]:((~rich(X)|~funny(X))))<=>((tall(fred)&strong(fred))))&
(![X]:((kind(X)|humble(X))<=>(~happy(X)&funny(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>generous(X))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~humble(X))))&
((strong(paul))<=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((calm(X)|brave(X))))<=>((wise(alice)&~kind(alice))))&
(![X]:((~old(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~old(X)|brave(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~creative(X)&curious(X))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((calm(susan))=>((~generous(fred)|~curious(fred))))&
(![X]:((curious(X)|~calm(X))<=>kind(X)))&
(![X]:((~happy(X)|generous(X))<=>(kind(X)&~funny(X))))&
(strong(john))&
(~brave(fred))&
((old(alice)|~old(alice)))&
((~humble(paul)<~>brave(paul)))&
(?[X]:(wise(X))) | ~brave(john) | [
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7692099910084624740622384
% SZS output start Proof for 7692099910084624740622384
6. ! [X0] : (~generous(X0) => (~kind(X0) <~> generous(X0))) [input p5]
7. ! [X0] : ((generous(X0) | calm(X0)) <=> (~humble(X0) & calm(X0))) [input p6]
11. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (brave(X0) | ~old(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | curious(X0)) <=> kind(X0)) [input p14]
22. brave(john) [input hypothesis]
28. ! [X0] : ((~kind(X0) <~> generous(X0)) | generous(X0)) [ennf transformation 6]
40. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | generous(X0)) [nnf transformation 28]
41. ! [X0] : (((generous(X0) | calm(X0)) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 7]
42. ! [X0] : ((generous(X0) | calm(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 41]
54. ! [X0] : (((patient(X0) & ~calm(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (~patient(X0) | calm(X0)))) [nnf transformation 11]
55. ! [X0] : (((patient(X0) & ~calm(X0)) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | ~patient(X0) | calm(X0))) [flattening 54]
63. ! [X0] : (((~calm(X0) | curious(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~curious(X0)))) [nnf transformation 15]
64. ! [X0] : ((~calm(X0) | curious(X0) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~curious(X0)))) [flattening 63]
86. generous(X0) | ~kind(X0) | generous(X0) [cnf transformation 40]
89. ~generous(X0) | calm(X0) [cnf transformation 42]
109. ~brave(X0) | ~calm(X0) [cnf transformation 55]
126. kind(X0) | calm(X0) [cnf transformation 64]
139. brave(john) [cnf transformation 22]
140. ~kind(X0) | generous(X0) [duplicate literal removal 86]
297. ~calm(john) [resolution 109,139]
305. generous(X0) | calm(X0) [resolution 140,126]
306. calm(X0) [subsumption resolution 305,89]
308. $false [resolution 306,297]
% SZS output end Proof for 7692099910084624740622384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then paul is not strong and vice versa.
If john is brave then lucy is either not rich or generous and vice versa.
If someone is not old then someone is either happy or not wise and vice versa.
If mary is both creative and not curious then someone is either not rich or not brave.
Everyone who is not patient or not quiet is quiet or calm and vice versa.
If someone is rich or not kind then someone is old.
Everyone who is wise is not humble and vice versa.
Everyone who is not strong or not wise is both funny and patient.
Everyone who is both funny and not creative is not wise or not old and vice versa.
If mary is creative then someone is not brave and vice versa.
Everyone who is tall is both not happy and happy and vice versa.
Everyone who is quiet is either not creative or patient.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
Someone is not rich or not kind.
Alice is both quiet and not patient.
Someone is calm or not old.
Lucy is either kind or not kind.
Someone is wise or funny.
Someone is either patient or funny. | Alice is creative. | contradiction | ((?[X]:(old(X)))<=>(~strong(paul)))&
((brave(john))<=>((~rich(lucy)<~>generous(lucy))))&
((?[X]:(~old(X)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(((creative(mary)&~curious(mary)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(quiet(X)|calm(X))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>~humble(X)))&
(![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
(?[X]:((~rich(X)|~kind(X))))&
((quiet(alice)&~patient(alice)))&
(?[X]:((calm(X)|~old(X))))&
((kind(lucy)<~>~kind(lucy)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:((patient(X)<~>funny(X)))) | creative(alice) | [
"p4",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6905202340919214918727091
% SZS output start Proof for 6905202340919214918727091
5. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> (calm(X0) | quiet(X0))) [input p4]
12. ! [X0] : (quiet(X0) => (~creative(X0) <~> patient(X0))) [input p11]
18. ~patient(alice) & quiet(alice) [input p17]
23. creative(alice) [input hypothesis]
29. ! [X0] : ((~creative(X0) <~> patient(X0)) | ~quiet(X0)) [ennf transformation 12]
42. ! [X0] : (((~quiet(X0) | ~patient(X0)) | (~calm(X0) & ~quiet(X0))) & ((calm(X0) | quiet(X0)) | (quiet(X0) & patient(X0)))) [nnf transformation 5]
43. ! [X0] : ((~quiet(X0) | ~patient(X0) | (~calm(X0) & ~quiet(X0))) & (calm(X0) | quiet(X0) | (quiet(X0) & patient(X0)))) [flattening 42]
54. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~quiet(X0)) [nnf transformation 29]
83. ~quiet(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 43]
100. patient(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 54]
116. quiet(alice) [cnf transformation 18]
124. creative(alice) [cnf transformation 23]
128. ~quiet(X0) | ~patient(X0) [duplicate literal removal 83]
208. ~quiet(X0) | ~creative(X0) [subsumption resolution 100,128]
256. ~creative(alice) [resolution 208,116]
259. $false [subsumption resolution 256,124]
% SZS output end Proof for 6905202340919214918727091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or curious is both patient and not humble and vice versa.
If someone is either not happy or happy then mary is either not happy or creative.
If someone is either not calm or creative then someone is both not brave and old and vice versa.
If fred is both tall and not tall then someone is not generous and vice versa.
If someone is curious or not rich then someone is both strong and not calm.
If mary is either not rich or brave then paul is either not wise or not old.
Everyone who is either not old or not tall is either not old or humble and vice versa.
If susan is both not brave and not old then mary is funny or not creative.
If someone is not rich or rich then mary is patient and vice versa.
Everyone who is both rich and not patient is both not patient and rich and vice versa.
If mary is both wise and not happy then someone is either patient or calm and vice versa.
If john is either curious or not rich then mary is either generous or strong and vice versa.
Everyone who is either not happy or not funny is either patient or rich and vice versa.
Everyone who is not old is either not brave or happy and vice versa.
Everyone who is both rich and not happy is not wise or not tall.
Paul is brave.
Someone is not quiet or not wise.
Someone is creative or funny.
Someone is rich.
Paul is strong or rich.
Someone is both not wise and not quiet.
Mary is tall or not strong.
Paul is not creative. | Paul is not old. | neutral | (![X]:((calm(X)|curious(X))<=>(patient(X)&~humble(X))))&
((?[X]:((~happy(X)<~>happy(X))))=>((~happy(mary)<~>creative(mary))))&
((?[X]:((~calm(X)<~>creative(X))))<=>(?[X]:((~brave(X)&old(X)))))&
(((tall(fred)&~tall(fred)))<=>(?[X]:(~generous(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:((strong(X)&~calm(X)))))&
(((~rich(mary)<~>brave(mary)))=>((~wise(paul)<~>~old(paul))))&
(![X]:((~old(X)<~>~tall(X))<=>(~old(X)<~>humble(X))))&
(((~brave(susan)&~old(susan)))=>((funny(mary)|~creative(mary))))&
((?[X]:((~rich(X)|rich(X))))<=>(patient(mary)))&
(![X]:((rich(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(((wise(mary)&~happy(mary)))<=>(?[X]:((patient(X)<~>calm(X)))))&
(((curious(john)<~>~rich(john)))<=>((generous(mary)<~>strong(mary))))&
(![X]:((~happy(X)<~>~funny(X))<=>(patient(X)<~>rich(X))))&
(![X]:(~old(X)<=>(~brave(X)<~>happy(X))))&
(![X]:((rich(X)&~happy(X))=>(~wise(X)|~tall(X))))&
(brave(paul))&
(?[X]:((~quiet(X)|~wise(X))))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:(rich(X)))&
((strong(paul)|rich(paul)))&
(?[X]:((~wise(X)&~quiet(X))))&
((tall(mary)|~strong(mary)))&
(~creative(paul)) | ~old(paul) | [] | null | 0 |
If mary is rich or not patient then lucy is both not curious and not funny and vice versa.
Everyone who is not wise or patient is strong or not happy.
Everyone who is either funny or not calm is not quiet.
If someone is both kind and wise then susan is both strong and rich.
If someone is not brave or curious then someone is not kind.
Everyone who is not tall or not curious is either not humble or old and vice versa.
If someone is either not patient or kind then someone is not quiet or wise and vice versa.
Everyone who is quiet is both not old and not tall.
Everyone who is both not patient and patient is humble.
If lucy is both not strong and humble then mary is both quiet and not generous and vice versa.
Everyone who is calm is either not quiet or wise and vice versa.
Everyone who is either not wise or wise is not happy and vice versa.
If someone is either not creative or not patient then susan is either not curious or not humble and vice versa.
If mary is strong or not brave then someone is not brave or generous and vice versa.
Everyone who is wise or not rich is either not humble or calm and vice versa.
If susan is not patient then someone is either not funny or not wise.
Mary is either not wise or not patient.
Lucy is both calm and curious.
Mary is kind.
Mary is not wise or not generous.
Someone is both not strong and brave.
Someone is not quiet.
Lucy is not quiet or not wise.
Fred is not funny or strong. | Lucy is patient. | neutral | (((rich(mary)|~patient(mary)))<=>((~curious(lucy)&~funny(lucy))))&
(![X]:((~wise(X)|patient(X))=>(strong(X)|~happy(X))))&
(![X]:((funny(X)<~>~calm(X))=>~quiet(X)))&
((?[X]:((kind(X)&wise(X))))=>((strong(susan)&rich(susan))))&
((?[X]:((~brave(X)|curious(X))))=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)|~curious(X))<=>(~humble(X)<~>old(X))))&
((?[X]:((~patient(X)<~>kind(X))))<=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:(quiet(X)=>(~old(X)&~tall(X))))&
(![X]:((~patient(X)&patient(X))=>humble(X)))&
(((~strong(lucy)&humble(lucy)))<=>((quiet(mary)&~generous(mary))))&
(![X]:(calm(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:((~wise(X)<~>wise(X))<=>~happy(X)))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((~curious(susan)<~>~humble(susan))))&
(((strong(mary)|~brave(mary)))<=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((wise(X)|~rich(X))<=>(~humble(X)<~>calm(X))))&
((~patient(susan))=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~wise(mary)<~>~patient(mary)))&
((calm(lucy)&curious(lucy)))&
(kind(mary))&
((~wise(mary)|~generous(mary)))&
(?[X]:((~strong(X)&brave(X))))&
(?[X]:(~quiet(X)))&
((~quiet(lucy)|~wise(lucy)))&
((~funny(fred)|strong(fred))) | patient(lucy) | [] | null | 0 |
Everyone who is both not creative and not humble is tall.
If someone is not happy or not generous then alice is wise and vice versa.
Everyone who is curious or not old is not wise or not strong and vice versa.
If lucy is not curious then susan is either curious or quiet and vice versa.
If paul is both not patient and patient then someone is not patient or not brave.
If fred is calm then lucy is either wise or not tall.
If someone is either brave or not strong then someone is not brave.
Everyone who is both not happy and not rich is generous or tall.
Everyone who is not curious is not wise and vice versa.
If someone is either not rich or calm then someone is strong.
Everyone who is both patient and funny is both not wise and not tall and vice versa.
Everyone who is either quiet or calm is not tall.
If alice is either patient or not strong then lucy is either not old or not generous and vice versa.
Everyone who is both creative and not patient is both rich and not strong and vice versa.
If paul is not rich or not patient then paul is not calm.
Everyone who is calm is both not wise and humble and vice versa.
John is both not kind and not happy.
John is both not rich and not funny.
Paul is either not happy or calm.
Someone is either not calm or not rich.
Lucy is both creative and not calm.
Someone is not kind.
Mary is either not quiet or not patient.
Alice is either not wise or not humble. | Alice is not strong. | entailment | (![X]:((~creative(X)&~humble(X))=>tall(X)))&
((?[X]:((~happy(X)|~generous(X))))<=>(wise(alice)))&
(![X]:((curious(X)|~old(X))<=>(~wise(X)|~strong(X))))&
((~curious(lucy))<=>((curious(susan)<~>quiet(susan))))&
(((~patient(paul)&patient(paul)))=>(?[X]:((~patient(X)|~brave(X)))))&
((calm(fred))=>((wise(lucy)<~>~tall(lucy))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:(~brave(X))))&
(![X]:((~happy(X)&~rich(X))=>(generous(X)|tall(X))))&
(![X]:(~curious(X)<=>~wise(X)))&
((?[X]:((~rich(X)<~>calm(X))))=>(?[X]:(strong(X))))&
(![X]:((patient(X)&funny(X))<=>(~wise(X)&~tall(X))))&
(![X]:((quiet(X)<~>calm(X))=>~tall(X)))&
(((patient(alice)<~>~strong(alice)))<=>((~old(lucy)<~>~generous(lucy))))&
(![X]:((creative(X)&~patient(X))<=>(rich(X)&~strong(X))))&
(((~rich(paul)|~patient(paul)))=>(~calm(paul)))&
(![X]:(calm(X)<=>(~wise(X)&humble(X))))&
((~kind(john)&~happy(john)))&
((~rich(john)&~funny(john)))&
((~happy(paul)<~>calm(paul)))&
(?[X]:((~calm(X)<~>~rich(X))))&
((creative(lucy)&~calm(lucy)))&
(?[X]:(~kind(X)))&
((~quiet(mary)<~>~patient(mary)))&
((~wise(alice)<~>~humble(alice))) | ~strong(alice) | [
"p1",
"p2",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8465486545843339051510430
% SZS output start Proof for 8465486545843339051510430
2. ? [X0] : (~generous(X0) | ~happy(X0)) <=> wise(alice) [input p1]
3. ! [X0] : ((~old(X0) | curious(X0)) <=> (~strong(X0) | ~wise(X0))) [input p2]
9. ! [X0] : (~curious(X0) <=> ~wise(X0)) [input p8]
17. ~happy(john) & ~kind(john) [input p16]
25. strong(alice) [input hypothesis]
28. ~happy(john) [pure predicate removal 17]
41. (? [X0] : (~generous(X0) | ~happy(X0)) | ~wise(alice)) & (wise(alice) | ! [X0] : (generous(X0) & happy(X0))) [nnf transformation 2]
42. (? [X0] : (~generous(X0) | ~happy(X0)) | ~wise(alice)) & (wise(alice) | ! [X1] : (generous(X1) & happy(X1))) [rectify 41]
43. ? [X0] : (~generous(X0) | ~happy(X0)) => (~generous(sK0) | ~happy(sK0)) [choice axiom]
44. ((~generous(sK0) | ~happy(sK0)) | ~wise(alice)) & (wise(alice) | ! [X1] : (generous(X1) & happy(X1))) [skolemisation 42,43]
45. ! [X0] : (((~old(X0) | curious(X0)) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | (old(X0) & ~curious(X0)))) [nnf transformation 3]
46. ! [X0] : ((~old(X0) | curious(X0) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | (old(X0) & ~curious(X0)))) [flattening 45]
55. ! [X0] : ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0))) [nnf transformation 9]
75. wise(alice) | happy(X1) [cnf transformation 44]
78. ~strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 46]
92. ~wise(X0) | curious(X0) [cnf transformation 55]
119. ~happy(john) [cnf transformation 28]
132. strong(alice) [cnf transformation 25]
134. 1 <=> wise(alice) [avatar definition]
135. wise(alice) <- (1) [avatar component clause 134]
151. 5 <=> ! [X1] : happy(X1) [avatar definition]
152. happy(X1) <- (5) [avatar component clause 151]
153. 5 | 1 [avatar split clause 75,134,151]
221. 21 <=> strong(alice) [avatar definition]
223. strong(alice) <- (21) [avatar component clause 221]
278. 21 [avatar split clause 132,221]
279. $false <- (5) [resolution 152,119]
280. ~5 [avatar contradiction clause 279]
283. curious(alice) <- (1) [resolution 92,135]
288. ~wise(alice) | ~curious(alice) <- (21) [resolution 78,223]
290. ~curious(alice) <- (1, 21) [subsumption resolution 288,135]
291. $false <- (1, 21) [subsumption resolution 290,283]
292. ~1 | ~21 [avatar contradiction clause 291]
293. $false [avatar sat refutation 153,278,280,292]
% SZS output end Proof for 8465486545843339051510430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either funny or not tall and vice versa. Everyone who is quiet is both not creative and funny. Everyone who is not kind or not generous is not strong. Everyone who is both curious and not old is either old or rich. If someone is happy or not happy then fred is not wise. If mary is both not kind and humble then john is both quiet and wise. If someone is generous or curious then someone is both not generous and not humble and vice versa. If john is both kind and tall then someone is quiet. Everyone who is calm is both funny and brave. Everyone who is not quiet is calm or not rich and vice versa. If mary is either not old or not patient then mary is either not old or not curious. If mary is both not calm and generous then susan is both not humble and not patient and vice versa. If paul is generous then fred is not generous. If someone is creative then someone is either tall or not humble. If susan is both not creative and calm then someone is quiet or not kind. If someone is both old and not happy then mary is tall. Lucy is quiet. Fred is either kind or brave. Someone is happy or not humble. Someone is both not kind and not quiet. Someone is either not funny or tall. Susan is either creative or strong. Paul is not strong. Alice is both patient and calm. | Lucy is creative. | contradiction | (![X]:(~humble(X)<=>(funny(X)<~>~tall(X))))&
(![X]:(quiet(X)=>(~creative(X)&funny(X))))&
(![X]:((~kind(X)|~generous(X))=>~strong(X)))&
(![X]:((curious(X)&~old(X))=>(old(X)<~>rich(X))))&
((?[X]:((happy(X)|~happy(X))))=>(~wise(fred)))&
(((~kind(mary)&humble(mary)))=>((quiet(john)&wise(john))))&
((?[X]:((generous(X)|curious(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(((kind(john)&tall(john)))=>(?[X]:(quiet(X))))&
(![X]:(calm(X)=>(funny(X)&brave(X))))&
(![X]:(~quiet(X)<=>(calm(X)|~rich(X))))&
(((~old(mary)<~>~patient(mary)))=>((~old(mary)<~>~curious(mary))))&
(((~calm(mary)&generous(mary)))<=>((~humble(susan)&~patient(susan))))&
((generous(paul))=>(~generous(fred)))&
((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~creative(susan)&calm(susan)))=>(?[X]:((quiet(X)|~kind(X)))))&
((?[X]:((old(X)&~happy(X))))=>(tall(mary)))&
(quiet(lucy))&
((kind(fred)<~>brave(fred)))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:((~kind(X)&~quiet(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
((creative(susan)<~>strong(susan)))&
(~strong(paul))&
((patient(alice)&calm(alice))) | creative(lucy) | [
"p1",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6215573598739878060919281
% SZS output start Proof for 6215573598739878060919281
2. ! [X0] : (quiet(X0) => (funny(X0) & ~creative(X0))) [input p1]
17. quiet(lucy) [input p16]
25. creative(lucy) [input hypothesis]
28. ! [X0] : ((funny(X0) & ~creative(X0)) | ~quiet(X0)) [ennf transformation 2]
77. ~creative(X0) | ~quiet(X0) [cnf transformation 28]
111. quiet(lucy) [cnf transformation 17]
124. creative(lucy) [cnf transformation 25]
317. ~quiet(lucy) [resolution 77,124]
319. $false [subsumption resolution 317,111]
% SZS output end Proof for 6215573598739878060919281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not humble is both not calm and not generous. Everyone who is happy or kind is either wise or happy. If someone is both quiet and wise then someone is either not wise or tall and vice versa. If fred is either curious or not strong then someone is not rich. If lucy is not humble then someone is either brave or not curious. If paul is either not strong or not happy then someone is both patient and not rich. If someone is tall or rich then someone is humble or patient. Everyone who is tall or not funny is both humble and tall and vice versa. If mary is both old and humble then alice is not patient. Everyone who is curious or not funny is creative or not happy. If paul is not curious then someone is both not funny and not old and vice versa. If someone is not old or not curious then someone is not kind or wise and vice versa. Everyone who is strong or rich is rich. Everyone who is kind or not funny is not kind. If john is brave then paul is both not happy and not rich and vice versa. Everyone who is kind is either not brave or not calm. Mary is not tall. Paul is either not wise or not generous. Alice is either not curious or curious. Someone is either kind or not brave. Someone is both not generous and not kind. Someone is either quiet or not wise. | Lucy is kind. | contradiction | (![X]:((humble(X)<~>~humble(X))=>(~calm(X)&~generous(X))))&
(![X]:((happy(X)|kind(X))=>(wise(X)<~>happy(X))))&
((?[X]:((quiet(X)&wise(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
(((curious(fred)<~>~strong(fred)))=>(?[X]:(~rich(X))))&
((~humble(lucy))=>(?[X]:((brave(X)<~>~curious(X)))))&
(((~strong(paul)<~>~happy(paul)))=>(?[X]:((patient(X)&~rich(X)))))&
((?[X]:((tall(X)|rich(X))))=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((tall(X)|~funny(X))<=>(humble(X)&tall(X))))&
(((old(mary)&humble(mary)))=>(~patient(alice)))&
(![X]:((curious(X)|~funny(X))=>(creative(X)|~happy(X))))&
((~curious(paul))<=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((~old(X)|~curious(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
(![X]:((strong(X)|rich(X))=>rich(X)))&
(![X]:((kind(X)|~funny(X))=>~kind(X)))&
((brave(john))<=>((~happy(paul)&~rich(paul))))&
(![X]:(kind(X)=>(~brave(X)<~>~calm(X))))&
(~tall(mary))&
((~wise(paul)<~>~generous(paul)))&
((~curious(alice)<~>curious(alice)))&
(?[X]:((kind(X)<~>~brave(X))))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((quiet(X)<~>~wise(X)))) | kind(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4585727739749121176180101
% SZS output start Proof for 4585727739749121176180101
14. ! [X0] : ((~funny(X0) | kind(X0)) => ~kind(X0)) [input p13]
23. kind(lucy) [input hypothesis]
37. ! [X0] : (~kind(X0) | (funny(X0) & ~kind(X0))) [ennf transformation 14]
121. ~kind(X0) | ~kind(X0) [cnf transformation 37]
139. kind(lucy) [cnf transformation 23]
140. ~kind(X0) [duplicate literal removal 121]
329. $false [subsumption resolution 139,140]
% SZS output end Proof for 4585727739749121176180101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or quiet then paul is humble or creative and vice versa.
If someone is not brave or humble then someone is either not creative or not quiet.
Everyone who is not happy is not tall and vice versa.
If lucy is either not funny or rich then john is either patient or not tall and vice versa.
Everyone who is not curious or not kind is either tall or quiet.
If alice is old or not strong then someone is not patient or old and vice versa.
Everyone who is wise or brave is either not happy or brave.
Everyone who is not patient or creative is both not rich and not strong.
If someone is rich or not humble then someone is both not kind and rich and vice versa.
If susan is both not strong and generous then lucy is both quiet and not calm and vice versa.
If mary is not old then someone is either not strong or wise.
If susan is either generous or not strong then lucy is not tall or brave.
If paul is not humble then lucy is not old or old and vice versa.
Everyone who is either not happy or wise is both not rich and not funny and vice versa.
Everyone who is humble or brave is both curious and wise.
Everyone who is wise or not kind is not humble or wise.
Paul is both not creative and not rich.
Paul is either not creative or curious.
Someone is either not calm or curious.
John is strong.
Mary is either not brave or not strong.
Someone is not generous or strong.
Someone is not kind or old.
Susan is either not kind or old. | Paul is funny. | entailment | ((?[X]:((~calm(X)|quiet(X))))<=>((humble(paul)|creative(paul))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:(~happy(X)<=>~tall(X)))&
(((~funny(lucy)<~>rich(lucy)))<=>((patient(john)<~>~tall(john))))&
(![X]:((~curious(X)|~kind(X))=>(tall(X)<~>quiet(X))))&
(((old(alice)|~strong(alice)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((wise(X)|brave(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~patient(X)|creative(X))=>(~rich(X)&~strong(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
(((~strong(susan)&generous(susan)))<=>((quiet(lucy)&~calm(lucy))))&
((~old(mary))=>(?[X]:((~strong(X)<~>wise(X)))))&
(((generous(susan)<~>~strong(susan)))=>((~tall(lucy)|brave(lucy))))&
((~humble(paul))<=>((~old(lucy)|old(lucy))))&
(![X]:((~happy(X)<~>wise(X))<=>(~rich(X)&~funny(X))))&
(![X]:((humble(X)|brave(X))=>(curious(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>(~humble(X)|wise(X))))&
((~creative(paul)&~rich(paul)))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((~calm(X)<~>curious(X))))&
(strong(john))&
((~brave(mary)<~>~strong(mary)))&
(?[X]:((~generous(X)|strong(X))))&
(?[X]:((~kind(X)|old(X))))&
((~kind(susan)<~>old(susan))) | funny(paul) | [
"p0",
"p2",
"p4",
"p6",
"p12",
"p13",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5297142982677356968506384
% SZS output start Proof for 5297142982677356968506384
1. ? [X0] : (quiet(X0) | ~calm(X0)) <=> (creative(paul) | humble(paul)) [input p0]
3. ! [X0] : (~happy(X0) <=> ~tall(X0)) [input p2]
5. ! [X0] : ((~kind(X0) | ~curious(X0)) => (tall(X0) <~> quiet(X0))) [input p4]
7. ! [X0] : ((brave(X0) | wise(X0)) => (~happy(X0) <~> brave(X0))) [input p6]
13. ~humble(paul) <=> (old(lucy) | ~old(lucy)) [input p12]
14. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (~funny(X0) & ~rich(X0))) [input p13]
15. ! [X0] : ((brave(X0) | humble(X0)) => (wise(X0) & curious(X0))) [input p14]
17. ~rich(paul) & ~creative(paul) [input p16]
18. ~creative(paul) <~> curious(paul) [input p17]
25. ~funny(paul) [input hypothesis]
29. ! [X0] : ((tall(X0) <~> quiet(X0)) | (kind(X0) & curious(X0))) [ennf transformation 5]
30. ! [X0] : ((~happy(X0) <~> brave(X0)) | (~brave(X0) & ~wise(X0))) [ennf transformation 7]
35. ! [X0] : ((wise(X0) & curious(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 15]
38. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & ((creative(paul) | humble(paul)) | ! [X0] : (~quiet(X0) & calm(X0))) [nnf transformation 1]
39. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X0] : (~quiet(X0) & calm(X0))) [flattening 38]
40. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X1] : (~quiet(X1) & calm(X1))) [rectify 39]
41. ? [X0] : (quiet(X0) | ~calm(X0)) => (quiet(sK0) | ~calm(sK0)) [choice axiom]
42. ((quiet(sK0) | ~calm(sK0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X1] : (~quiet(X1) & calm(X1))) [skolemisation 40,41]
47. ! [X0] : ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))) [nnf transformation 3]
49. ! [X0] : (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (kind(X0) & curious(X0))) [nnf transformation 29]
55. ! [X0] : (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~brave(X0) & ~wise(X0))) [nnf transformation 30]
67. (~humble(paul) | (~old(lucy) & old(lucy))) & ((old(lucy) | ~old(lucy)) | humble(paul)) [nnf transformation 13]
68. (~humble(paul) | (~old(lucy) & old(lucy))) & (old(lucy) | ~old(lucy) | humble(paul)) [flattening 67]
69. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) | rich(X0))) & ((~funny(X0) & ~rich(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 14]
70. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | funny(X0) | rich(X0)) & ((~funny(X0) & ~rich(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 69]
71. (~curious(paul) | creative(paul)) & (curious(paul) | ~creative(paul)) [nnf transformation 18]
82. creative(paul) | humble(paul) | ~quiet(X1) [cnf transformation 42]
89. ~tall(X0) | happy(X0) [cnf transformation 47]
99. curious(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
107. ~wise(X0) | ~happy(X0) | brave(X0) [cnf transformation 55]
129. ~humble(paul) | old(lucy) [cnf transformation 68]
130. ~humble(paul) | ~old(lucy) [cnf transformation 68]
135. ~happy(X0) | wise(X0) | funny(X0) | rich(X0) [cnf transformation 70]
138. ~brave(X0) | curious(X0) [cnf transformation 35]
143. ~creative(paul) [cnf transformation 17]
144. ~rich(paul) [cnf transformation 17]
146. ~curious(paul) | creative(paul) [cnf transformation 71]
156. ~funny(paul) [cnf transformation 25]
159. 1 <=> creative(paul) [avatar definition]
172. 4 <=> humble(paul) [avatar definition]
177. 5 <=> ! [X1] : ~quiet(X1) [avatar definition]
178. ~quiet(X1) <- (5) [avatar component clause 177]
179. 5 | 4 | 1 [avatar split clause 82,159,172,177]
327. 37 <=> old(lucy) [avatar definition]
330. ~37 | ~4 [avatar split clause 130,172,327]
331. 37 | ~4 [avatar split clause 129,172,327]
332. ~1 [avatar split clause 143,159]
334. 38 <=> curious(paul) [avatar definition]
336. ~curious(paul) <- (~38) [avatar component clause 334]
337. 1 | ~38 [avatar split clause 146,334,159]
401. tall(paul) | quiet(paul) <- (~38) [resolution 99,336]
402. tall(paul) <- (5, ~38) [subsumption resolution 401,178]
410. happy(paul) <- (5, ~38) [resolution 402,89]
436. wise(paul) | funny(paul) | rich(paul) <- (5, ~38) [resolution 135,410]
441. wise(paul) | rich(paul) <- (5, ~38) [subsumption resolution 436,156]
442. wise(paul) <- (5, ~38) [subsumption resolution 441,144]
510. ~happy(paul) | brave(paul) <- (5, ~38) [resolution 442,107]
511. brave(paul) <- (5, ~38) [subsumption resolution 510,410]
514. curious(paul) <- (5, ~38) [resolution 511,138]
515. $false <- (5, ~38) [subsumption resolution 514,336]
516. ~5 | 38 [avatar contradiction clause 515]
517. $false [avatar sat refutation 179,330,331,332,337,516]
% SZS output end Proof for 5297142982677356968506384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or curious is not funny and vice versa.
If someone is not old or calm then susan is not happy.
Everyone who is either happy or kind is strong.
If someone is not calm or not tall then john is either rich or old and vice versa.
If alice is both not brave and happy then someone is both not curious and kind and vice versa.
If susan is not calm then someone is old and vice versa.
If someone is quiet then mary is not funny.
Everyone who is both funny and not wise is not old and vice versa.
Everyone who is either happy or not rich is not creative or not patient.
Everyone who is either not strong or not patient is both not brave and not humble and vice versa.
If someone is humble then someone is brave and vice versa.
Everyone who is not calm or old is not humble.
Everyone who is not funny is happy and vice versa.
If someone is not funny or happy then mary is tall.
Everyone who is brave is both funny and not happy and vice versa.
Everyone who is not funny is brave.
Susan is either quiet or not strong.
Lucy is either not strong or not funny.
Fred is both creative and not rich.
Someone is both not creative and strong.
John is not kind or not funny.
Alice is either happy or old.
Someone is not patient.
Someone is not kind. | Fred is curious. | contradiction | (![X]:((strong(X)<~>curious(X))<=>~funny(X)))&
((?[X]:((~old(X)|calm(X))))=>(~happy(susan)))&
(![X]:((happy(X)<~>kind(X))=>strong(X)))&
((?[X]:((~calm(X)|~tall(X))))<=>((rich(john)<~>old(john))))&
(((~brave(alice)&happy(alice)))<=>(?[X]:((~curious(X)&kind(X)))))&
((~calm(susan))<=>(?[X]:(old(X))))&
((?[X]:(quiet(X)))=>(~funny(mary)))&
(![X]:((funny(X)&~wise(X))<=>~old(X)))&
(![X]:((happy(X)<~>~rich(X))=>(~creative(X)|~patient(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~brave(X)&~humble(X))))&
((?[X]:(humble(X)))<=>(?[X]:(brave(X))))&
(![X]:((~calm(X)|old(X))=>~humble(X)))&
(![X]:(~funny(X)<=>happy(X)))&
((?[X]:((~funny(X)|happy(X))))=>(tall(mary)))&
(![X]:(brave(X)<=>(funny(X)&~happy(X))))&
(![X]:(~funny(X)=>brave(X)))&
((quiet(susan)<~>~strong(susan)))&
((~strong(lucy)<~>~funny(lucy)))&
((creative(fred)&~rich(fred)))&
(?[X]:((~creative(X)&strong(X))))&
((~kind(john)|~funny(john)))&
((happy(alice)<~>old(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(~kind(X))) | curious(fred) | [
"p0",
"p8",
"p9",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3164526778183966382449676
% SZS output start Proof for 3164526778183966382449676
1. ! [X0] : ((strong(X0) <~> curious(X0)) <=> ~funny(X0)) [input p0]
9. ! [X0] : ((happy(X0) <~> ~rich(X0)) => (~patient(X0) | ~creative(X0))) [input p8]
10. ! [X0] : ((~strong(X0) <~> ~patient(X0)) <=> (~humble(X0) & ~brave(X0))) [input p9]
13. ! [X0] : (~funny(X0) <=> happy(X0)) [input p12]
15. ! [X0] : (brave(X0) <=> (~happy(X0) & funny(X0))) [input p14]
16. ! [X0] : (~funny(X0) => brave(X0)) [input p15]
19. ~rich(fred) & creative(fred) [input p18]
25. curious(fred) [input hypothesis]
30. ! [X0] : ((~patient(X0) | ~creative(X0)) | (happy(X0) <=> ~rich(X0))) [ennf transformation 9]
31. ! [X0] : (~patient(X0) | ~creative(X0) | (happy(X0) <=> ~rich(X0))) [flattening 30]
34. ! [X0] : (brave(X0) | funny(X0)) [ennf transformation 16]
35. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | funny(X0)) & (~funny(X0) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [nnf transformation 1]
52. ! [X0] : (~patient(X0) | ~creative(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) [nnf transformation 31]
53. ! [X0] : ((((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))))) [nnf transformation 10]
54. ! [X0] : ((((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))))) [flattening 53]
60. ! [X0] : ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))) [nnf transformation 13]
61. ! [X0] : ((brave(X0) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | ~brave(X0))) [nnf transformation 15]
62. ! [X0] : ((brave(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | ~brave(X0))) [flattening 61]
73. ~funny(X0) | strong(X0) | ~curious(X0) [cnf transformation 35]
97. ~patient(X0) | ~creative(X0) | happy(X0) | rich(X0) [cnf transformation 52]
99. ~brave(X0) | ~strong(X0) | patient(X0) [cnf transformation 54]
108. happy(X0) | funny(X0) [cnf transformation 60]
109. ~happy(X0) | ~funny(X0) [cnf transformation 60]
112. ~brave(X0) | funny(X0) [cnf transformation 62]
114. brave(X0) | happy(X0) | ~funny(X0) [cnf transformation 62]
115. brave(X0) | funny(X0) [cnf transformation 34]
120. creative(fred) [cnf transformation 19]
121. ~rich(fred) [cnf transformation 19]
129. curious(fred) [cnf transformation 25]
239. 26 <=> ! [X0] : funny(X0) [avatar definition]
240. funny(X0) <- (26) [avatar component clause 239]
242. brave(X0) | happy(X0) [subsumption resolution 114,108]
243. funny(X0) [subsumption resolution 115,112]
244. 26 [avatar split clause 243,239]
326. ~curious(X0) | strong(X0) <- (26) [resolution 73,240]
344. ~strong(X0) | patient(X0) | happy(X0) [resolution 99,242]
378. strong(fred) <- (26) [resolution 326,129]
388. patient(fred) | happy(fred) <- (26) [resolution 344,378]
399. 42 <=> happy(fred) [avatar definition]
400. ~happy(fred) <- (~42) [avatar component clause 399]
401. happy(fred) <- (42) [avatar component clause 399]
403. 43 <=> patient(fred) [avatar definition]
405. patient(fred) <- (43) [avatar component clause 403]
406. 42 | 43 | ~26 [avatar split clause 388,239,403,399]
476. ~funny(fred) <- (42) [resolution 401,109]
477. $false <- (26, 42) [subsumption resolution 476,240]
478. ~26 | ~42 [avatar contradiction clause 477]
482. ~creative(fred) | happy(fred) | rich(fred) <- (43) [resolution 405,97]
495. happy(fred) | rich(fred) <- (43) [subsumption resolution 482,120]
496. rich(fred) <- (~42, 43) [subsumption resolution 495,400]
497. $false <- (~42, 43) [subsumption resolution 496,121]
498. 42 | ~43 [avatar contradiction clause 497]
499. $false [avatar sat refutation 244,406,478,498]
% SZS output end Proof for 3164526778183966382449676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or tall is both old and not brave and vice versa.
Everyone who is both happy and old is either patient or happy.
Everyone who is either not strong or not kind is either not kind or not quiet and vice versa.
Everyone who is not calm or not wise is both not calm and not curious.
Everyone who is either not patient or not generous is either not creative or tall.
If fred is not creative then someone is not tall or not wise.
If someone is either happy or rich then someone is not strong or not brave and vice versa.
Everyone who is not rich or not happy is generous.
Everyone who is either quiet or not generous is both old and tall and vice versa.
If someone is either rich or not kind then fred is not quiet.
Everyone who is either not old or happy is both not happy and creative and vice versa.
If someone is either quiet or curious then susan is rich.
Everyone who is brave is not rich.
Everyone who is either not generous or not old is both not old and kind.
If someone is kind then someone is not old and vice versa.
If someone is not generous then someone is either rich or not brave.
Mary is both not happy and humble.
Someone is tall or strong.
Someone is brave.
John is both not creative and rich.
Someone is either strong or generous.
Paul is both not kind and humble.
Someone is either not brave or not creative. | Susan is happy. | contradiction | (![X]:((happy(X)|tall(X))<=>(old(X)&~brave(X))))&
(![X]:((happy(X)&old(X))=>(patient(X)<~>happy(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~kind(X)<~>~quiet(X))))&
(![X]:((~calm(X)|~wise(X))=>(~calm(X)&~curious(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(~creative(X)<~>tall(X))))&
((~creative(fred))=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((happy(X)<~>rich(X))))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((~rich(X)|~happy(X))=>generous(X)))&
(![X]:((quiet(X)<~>~generous(X))<=>(old(X)&tall(X))))&
((?[X]:((rich(X)<~>~kind(X))))=>(~quiet(fred)))&
(![X]:((~old(X)<~>happy(X))<=>(~happy(X)&creative(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>(rich(susan)))&
(![X]:(brave(X)=>~rich(X)))&
(![X]:((~generous(X)<~>~old(X))=>(~old(X)&kind(X))))&
((?[X]:(kind(X)))<=>(?[X]:(~old(X))))&
((?[X]:(~generous(X)))=>(?[X]:((rich(X)<~>~brave(X)))))&
((~happy(mary)&humble(mary)))&
(?[X]:((tall(X)|strong(X))))&
(?[X]:(brave(X)))&
((~creative(john)&rich(john)))&
(?[X]:((strong(X)<~>generous(X))))&
((~kind(paul)&humble(paul)))&
(?[X]:((~brave(X)<~>~creative(X)))) | happy(susan) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1376251525735070010847891
% SZS output start Proof for 1376251525735070010847891
1. ! [X0] : ((tall(X0) | happy(X0)) <=> (~brave(X0) & old(X0))) [input p0]
11. ! [X0] : ((~old(X0) <~> happy(X0)) <=> (creative(X0) & ~happy(X0))) [input p10]
24. happy(susan) [input hypothesis]
41. ! [X0] : (((tall(X0) | happy(X0)) | (brave(X0) | ~old(X0))) & ((~brave(X0) & old(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 1]
42. ! [X0] : ((tall(X0) | happy(X0) | brave(X0) | ~old(X0)) & ((~brave(X0) & old(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 41]
56. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~creative(X0) | happy(X0))) & ((creative(X0) & ~happy(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 11]
57. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~creative(X0) | happy(X0)) & ((creative(X0) & ~happy(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [flattening 56]
79. old(X0) | ~happy(X0) [cnf transformation 42]
120. ~happy(X0) | ~old(X0) | ~happy(X0) [cnf transformation 57]
146. happy(susan) [cnf transformation 24]
148. ~happy(X0) | ~old(X0) [duplicate literal removal 120]
221. ~happy(X0) [subsumption resolution 148,79]
294. $false [subsumption resolution 146,221]
% SZS output end Proof for 1376251525735070010847891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not tall and not humble then someone is brave or kind.
If mary is strong or calm then lucy is either calm or not kind and vice versa.
If mary is brave or not curious then someone is both not old and not generous and vice versa.
Everyone who is both patient and curious is either old or not old and vice versa.
Everyone who is both not old and not kind is not funny or not creative and vice versa.
Everyone who is not humble or wise is both tall and not kind and vice versa.
Everyone who is either not happy or not tall is curious.
Everyone who is both not generous and generous is both strong and not tall and vice versa.
Everyone who is either patient or not happy is either happy or not funny.
If someone is either kind or generous then someone is both funny and not quiet and vice versa.
If susan is either creative or not brave then susan is either generous or not kind.
If lucy is kind then paul is funny and vice versa.
If someone is both rich and kind then someone is quiet and vice versa.
Everyone who is both kind and tall is patient.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
Someone is either not old or not kind.
Lucy is either curious or happy.
Lucy is either creative or not generous.
Paul is either not kind or quiet.
Someone is both not old and quiet.
Someone is not old.
Someone is either old or wise. | Lucy is not strong. | neutral | (((~tall(susan)&~humble(susan)))=>(?[X]:((brave(X)|kind(X)))))&
(((strong(mary)|calm(mary)))<=>((calm(lucy)<~>~kind(lucy))))&
(((brave(mary)|~curious(mary)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((patient(X)&curious(X))<=>(old(X)<~>~old(X))))&
(![X]:((~old(X)&~kind(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~humble(X)|wise(X))<=>(tall(X)&~kind(X))))&
(![X]:((~happy(X)<~>~tall(X))=>curious(X)))&
(![X]:((~generous(X)&generous(X))<=>(strong(X)&~tall(X))))&
(![X]:((patient(X)<~>~happy(X))=>(happy(X)<~>~funny(X))))&
((?[X]:((kind(X)<~>generous(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((creative(susan)<~>~brave(susan)))=>((generous(susan)<~>~kind(susan))))&
((kind(lucy))<=>(funny(paul)))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&tall(X))=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:((~old(X)<~>~kind(X))))&
((curious(lucy)<~>happy(lucy)))&
((creative(lucy)<~>~generous(lucy)))&
((~kind(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:((old(X)<~>wise(X)))) | ~strong(lucy) | [] | null | 0 |
If someone is not patient then someone is not creative or quiet.
Everyone who is not tall is both not rich and humble and vice versa.
If paul is either strong or happy then someone is strong or patient.
Everyone who is either not creative or kind is both not humble and not creative and vice versa.
If someone is both curious and not creative then john is not quiet.
If someone is brave then fred is both funny and not patient and vice versa.
Everyone who is both not creative and not patient is both not strong and not tall and vice versa.
Everyone who is both rich and not tall is wise.
Everyone who is both strong and curious is either not old or not calm and vice versa.
If alice is tall or brave then someone is not funny.
If someone is both old and not quiet then someone is either not strong or not funny.
Everyone who is either not curious or not generous is quiet or wise and vice versa.
Everyone who is kind is creative and vice versa.
If john is not humble or generous then mary is not calm.
If fred is funny or not strong then paul is either brave or not curious.
If mary is both not generous and kind then alice is either tall or strong.
Mary is rich.
Someone is either not old or patient.
Someone is both generous and quiet.
Someone is patient.
Someone is rich. | Mary is not calm. | entailment | ((?[X]:(~patient(X)))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:(~tall(X)<=>(~rich(X)&humble(X))))&
(((strong(paul)<~>happy(paul)))=>(?[X]:((strong(X)|patient(X)))))&
(![X]:((~creative(X)<~>kind(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((curious(X)&~creative(X))))=>(~quiet(john)))&
((?[X]:(brave(X)))<=>((funny(fred)&~patient(fred))))&
(![X]:((~creative(X)&~patient(X))<=>(~strong(X)&~tall(X))))&
(![X]:((rich(X)&~tall(X))=>wise(X)))&
(![X]:((strong(X)&curious(X))<=>(~old(X)<~>~calm(X))))&
(((tall(alice)|brave(alice)))=>(?[X]:(~funny(X))))&
((?[X]:((old(X)&~quiet(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(quiet(X)|wise(X))))&
(![X]:(kind(X)<=>creative(X)))&
(((~humble(john)|generous(john)))=>(~calm(mary)))&
(((funny(fred)|~strong(fred)))=>((brave(paul)<~>~curious(paul))))&
(((~generous(mary)&kind(mary)))=>((tall(alice)<~>strong(alice))))&
(rich(mary))&
(?[X]:((~old(X)<~>patient(X))))&
(?[X]:((generous(X)&quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:(rich(X))) | ~calm(mary) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6194427336049541679869551
% SZS output start Proof for 6194427336049541679869551
4. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> (~creative(X0) & ~humble(X0))) [input p3]
13. ! [X0] : (kind(X0) <=> creative(X0)) [input p12]
14. (generous(john) | ~humble(john)) => ~calm(mary) [input p13]
22. calm(mary) [input hypothesis]
32. ~calm(mary) | (~generous(john) & humble(john)) [ennf transformation 14]
44. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 4]
45. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [flattening 44]
63. ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))) [nnf transformation 13]
81. ~humble(X0) | kind(X0) | creative(X0) [cnf transformation 45]
84. ~creative(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 45]
112. creative(X0) | ~kind(X0) [cnf transformation 63]
113. kind(X0) | ~creative(X0) [cnf transformation 63]
114. ~calm(mary) | humble(john) [cnf transformation 32]
129. calm(mary) [cnf transformation 22]
130. ~kind(X0) | ~creative(X0) [duplicate literal removal 84]
215. ~creative(X0) [subsumption resolution 113,130]
216. ~kind(X0) [subsumption resolution 112,215]
222. 21 <=> calm(mary) [avatar definition]
227. 22 <=> humble(john) [avatar definition]
229. humble(john) <- (22) [avatar component clause 227]
230. 22 | ~21 [avatar split clause 114,222,227]
257. 21 [avatar split clause 129,222]
271. kind(john) | creative(john) <- (22) [resolution 81,229]
273. creative(john) <- (22) [subsumption resolution 271,216]
274. $false <- (22) [subsumption resolution 273,215]
275. ~22 [avatar contradiction clause 274]
278. $false [avatar sat refutation 230,257,275]
% SZS output end Proof for 6194427336049541679869551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either quiet or not curious. If someone is old or kind then someone is funny and vice versa. If someone is brave or generous then someone is either not patient or kind. Everyone who is strong or patient is calm. Everyone who is either humble or wise is not calm. If mary is either quiet or not calm then someone is both not generous and brave and vice versa. Everyone who is both not funny and old is either wise or rich. If lucy is curious or not generous then paul is either tall or not kind. Everyone who is rich or not rich is both wise and curious and vice versa. Everyone who is either kind or not curious is both quiet and not quiet. Everyone who is both funny and happy is either creative or funny. Everyone who is either not curious or not generous is strong and vice versa. Everyone who is creative is funny or not curious. Everyone who is either strong or not strong is funny and vice versa. Everyone who is not generous or tall is strong. Someone is either not happy or brave. John is both brave and patient. Someone is either calm or rich. Someone is funny or not funny. Alice is either not brave or curious. Lucy is not kind or wise. Someone is both humble and brave. | Paul is rich. | neutral | (![X]:(~happy(X)=>(quiet(X)<~>~curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)|patient(X))=>calm(X)))&
(![X]:((humble(X)<~>wise(X))=>~calm(X)))&
(((quiet(mary)<~>~calm(mary)))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~funny(X)&old(X))=>(wise(X)<~>rich(X))))&
(((curious(lucy)|~generous(lucy)))=>((tall(paul)<~>~kind(paul))))&
(![X]:((rich(X)|~rich(X))<=>(wise(X)&curious(X))))&
(![X]:((kind(X)<~>~curious(X))=>(quiet(X)&~quiet(X))))&
(![X]:((funny(X)&happy(X))=>(creative(X)<~>funny(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>strong(X)))&
(![X]:(creative(X)=>(funny(X)|~curious(X))))&
(![X]:((strong(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~generous(X)|tall(X))=>strong(X)))&
(?[X]:((~happy(X)<~>brave(X))))&
((brave(john)&patient(john)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((funny(X)|~funny(X))))&
((~brave(alice)<~>curious(alice)))&
((~kind(lucy)|wise(lucy)))&
(?[X]:((humble(X)&brave(X)))) | rich(paul) | [] | null | 0 |
Everyone who is not happy is both curious and not patient. If john is not humble or happy then someone is humble. Everyone who is calm is generous or patient. If mary is not creative or old then fred is both wise and happy. If someone is rich or happy then someone is both not patient and patient. Everyone who is not quiet or not creative is either old or generous and vice versa. Everyone who is not brave is quiet and vice versa. Everyone who is not strong or tall is either tall or humble and vice versa. Everyone who is both wise and not generous is either not calm or not old and vice versa. Everyone who is either humble or curious is not calm and vice versa. Everyone who is either kind or brave is both not generous and tall and vice versa. Everyone who is either not curious or not funny is old or not quiet. If fred is strong then alice is humble. Everyone who is creative is either funny or not quiet. Someone is both wise and funny. Paul is creative or not creative. Alice is curious. | Alice is not calm. | neutral | (![X]:(~happy(X)=>(curious(X)&~patient(X))))&
(((~humble(john)|happy(john)))=>(?[X]:(humble(X))))&
(![X]:(calm(X)=>(generous(X)|patient(X))))&
(((~creative(mary)|old(mary)))=>((wise(fred)&happy(fred))))&
((?[X]:((rich(X)|happy(X))))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~quiet(X)|~creative(X))<=>(old(X)<~>generous(X))))&
(![X]:(~brave(X)<=>quiet(X)))&
(![X]:((~strong(X)|tall(X))<=>(tall(X)<~>humble(X))))&
(![X]:((wise(X)&~generous(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((humble(X)<~>curious(X))<=>~calm(X)))&
(![X]:((kind(X)<~>brave(X))<=>(~generous(X)&tall(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(old(X)|~quiet(X))))&
((strong(fred))=>(humble(alice)))&
(![X]:(creative(X)=>(funny(X)<~>~quiet(X))))&
(?[X]:((wise(X)&funny(X))))&
((creative(paul)|~creative(paul)))&
(curious(alice)) | ~calm(alice) | [] | null | 0 |
If alice is not tall or not patient then john is both not kind and not humble and vice versa.
Everyone who is both not tall and patient is both strong and happy.
If someone is both not funny and not creative then alice is both not rich and humble and vice versa.
Everyone who is either patient or creative is either humble or not old.
If someone is strong then paul is not kind.
Everyone who is not rich is both not calm and happy and vice versa.
If someone is either not quiet or not curious then someone is either humble or not patient.
If john is either kind or creative then someone is either not creative or not generous.
Everyone who is happy is both not calm and not tall and vice versa.
If paul is both not wise and curious then susan is both rich and happy and vice versa.
If someone is not strong then someone is not tall or not wise.
Everyone who is not patient is rich or old.
Everyone who is either quiet or patient is not brave or patient.
If alice is both not patient and not strong then susan is generous or not calm and vice versa.
Everyone who is not happy or wise is old or calm.
Everyone who is not humble is funny.
Alice is not curious.
Someone is not old or generous.
Paul is not rich.
Someone is both not patient and not humble.
Someone is both not happy and quiet.
Someone is both brave and calm.
Someone is not calm.
Mary is wise or not quiet. | John is not kind. | neutral | (((~tall(alice)|~patient(alice)))<=>((~kind(john)&~humble(john))))&
(![X]:((~tall(X)&patient(X))=>(strong(X)&happy(X))))&
((?[X]:((~funny(X)&~creative(X))))<=>((~rich(alice)&humble(alice))))&
(![X]:((patient(X)<~>creative(X))=>(humble(X)<~>~old(X))))&
((?[X]:(strong(X)))=>(~kind(paul)))&
(![X]:(~rich(X)<=>(~calm(X)&happy(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>~patient(X)))))&
(((kind(john)<~>creative(john)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
(![X]:(happy(X)<=>(~calm(X)&~tall(X))))&
(((~wise(paul)&curious(paul)))<=>((rich(susan)&happy(susan))))&
((?[X]:(~strong(X)))=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(~patient(X)=>(rich(X)|old(X))))&
(![X]:((quiet(X)<~>patient(X))=>(~brave(X)|patient(X))))&
(((~patient(alice)&~strong(alice)))<=>((generous(susan)|~calm(susan))))&
(![X]:((~happy(X)|wise(X))=>(old(X)|calm(X))))&
(![X]:(~humble(X)=>funny(X)))&
(~curious(alice))&
(?[X]:((~old(X)|generous(X))))&
(~rich(paul))&
(?[X]:((~patient(X)&~humble(X))))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:(~calm(X)))&
((wise(mary)|~quiet(mary))) | ~kind(john) | [] | null | 0 |
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