premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both funny and not old is both not strong and not patient. Everyone who is both not tall and not strong is both tall and not kind and vice versa. If someone is both not funny and old then paul is both tall and kind. Everyone who is both not rich and creative is curious and vice versa. Everyone who is strong or not kind is both strong and generous and vice versa. If someone is either not humble or not creative then someone is either not curious or not quiet. If someone is both not funny and not quiet then lucy is patient and vice versa. If someone is strong or tall then lucy is both tall and humble. If someone is both not wise and not patient then lucy is both creative and not old. Everyone who is either old or not rich is not quiet or funny and vice versa. Everyone who is brave or calm is funny. If someone is old or happy then fred is both rich and not generous. Everyone who is either not happy or not brave is not humble or wise and vice versa. Everyone who is strong is not patient. If alice is either generous or not strong then someone is not calm. If someone is either creative or not kind then mary is both wise and calm. Someone is either rich or calm. Someone is both not quiet and calm. John is funny. Alice is funny. Someone is either old or generous. John is not calm or wise. Someone is generous or not happy. Susan is both not rich and not brave. | Mary is not wise. | neutral | (![X]:((funny(X)&~old(X))=>(~strong(X)&~patient(X))))&
(![X]:((~tall(X)&~strong(X))<=>(tall(X)&~kind(X))))&
((?[X]:((~funny(X)&old(X))))=>((tall(paul)&kind(paul))))&
(![X]:((~rich(X)&creative(X))<=>curious(X)))&
(![X]:((strong(X)|~kind(X))<=>(strong(X)&generous(X))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(patient(lucy)))&
((?[X]:((strong(X)|tall(X))))=>((tall(lucy)&humble(lucy))))&
((?[X]:((~wise(X)&~patient(X))))=>((creative(lucy)&~old(lucy))))&
(![X]:((old(X)<~>~rich(X))<=>(~quiet(X)|funny(X))))&
(![X]:((brave(X)|calm(X))=>funny(X)))&
((?[X]:((old(X)|happy(X))))=>((rich(fred)&~generous(fred))))&
(![X]:((~happy(X)<~>~brave(X))<=>(~humble(X)|wise(X))))&
(![X]:(strong(X)=>~patient(X)))&
(((generous(alice)<~>~strong(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((creative(X)<~>~kind(X))))=>((wise(mary)&calm(mary))))&
(?[X]:((rich(X)<~>calm(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(funny(john))&
(funny(alice))&
(?[X]:((old(X)<~>generous(X))))&
((~calm(john)|wise(john)))&
(?[X]:((generous(X)|~happy(X))))&
((~rich(susan)&~brave(susan))) | ~wise(mary) | [] | null | 0 |
Everyone who is either not generous or not strong is either not rich or old and vice versa.
If someone is either tall or not quiet then lucy is both not strong and old.
Everyone who is both tall and patient is happy and vice versa.
Everyone who is not funny is either not patient or not wise and vice versa.
If someone is both not old and wise then someone is either rich or creative and vice versa.
If alice is both not patient and humble then susan is either not wise or not happy and vice versa.
Everyone who is wise or rich is either rich or not curious.
Everyone who is not strong or not patient is calm or not brave.
If someone is not curious or not creative then lucy is creative or brave and vice versa.
Everyone who is both old and not humble is patient.
If john is either tall or funny then someone is either rich or not wise and vice versa.
Everyone who is creative is not happy or quiet and vice versa.
Everyone who is not patient is not brave and vice versa.
Everyone who is either curious or not happy is both strong and calm and vice versa.
If john is patient or creative then john is either patient or strong.
Everyone who is both not brave and not quiet is either not old or not calm and vice versa.
Alice is not quiet or not tall.
Someone is not tall.
Alice is strong or tall.
Susan is not calm or not patient.
Fred is both not curious and kind.
Someone is either calm or not wise.
Someone is either calm or not tall.
Someone is either not kind or not curious. | Fred is not calm. | neutral | (![X]:((~generous(X)<~>~strong(X))<=>(~rich(X)<~>old(X))))&
((?[X]:((tall(X)<~>~quiet(X))))=>((~strong(lucy)&old(lucy))))&
(![X]:((tall(X)&patient(X))<=>happy(X)))&
(![X]:(~funny(X)<=>(~patient(X)<~>~wise(X))))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
(((~patient(alice)&humble(alice)))<=>((~wise(susan)<~>~happy(susan))))&
(![X]:((wise(X)|rich(X))=>(rich(X)<~>~curious(X))))&
(![X]:((~strong(X)|~patient(X))=>(calm(X)|~brave(X))))&
((?[X]:((~curious(X)|~creative(X))))<=>((creative(lucy)|brave(lucy))))&
(![X]:((old(X)&~humble(X))=>patient(X)))&
(((tall(john)<~>funny(john)))<=>(?[X]:((rich(X)<~>~wise(X)))))&
(![X]:(creative(X)<=>(~happy(X)|quiet(X))))&
(![X]:(~patient(X)<=>~brave(X)))&
(![X]:((curious(X)<~>~happy(X))<=>(strong(X)&calm(X))))&
(((patient(john)|creative(john)))=>((patient(john)<~>strong(john))))&
(![X]:((~brave(X)&~quiet(X))<=>(~old(X)<~>~calm(X))))&
((~quiet(alice)|~tall(alice)))&
(?[X]:(~tall(X)))&
((strong(alice)|tall(alice)))&
((~calm(susan)|~patient(susan)))&
((~curious(fred)&kind(fred)))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((~kind(X)<~>~curious(X)))) | ~calm(fred) | [] | null | 0 |
If mary is both not old and not funny then susan is not humble or wise.
If someone is patient or not strong then john is both not creative and not humble and vice versa.
If someone is not curious then someone is not brave or wise.
If someone is not strong then lucy is both not old and not funny and vice versa.
Everyone who is both not humble and kind is not rich and vice versa.
Everyone who is both old and not old is either not happy or not tall and vice versa.
Everyone who is not curious or generous is both wise and kind and vice versa.
If someone is both quiet and not curious then fred is both humble and quiet.
Everyone who is funny is both not tall and brave and vice versa.
If lucy is creative or calm then alice is not curious.
If someone is both not rich and tall then someone is creative or generous and vice versa.
Everyone who is not rich is both quiet and kind and vice versa.
If someone is funny then someone is not humble or not tall and vice versa.
If someone is either patient or not wise then someone is not curious or not rich and vice versa.
Everyone who is both not creative and brave is not wise or curious and vice versa.
Everyone who is not generous is calm or not curious and vice versa.
Alice is strong.
Someone is either creative or brave.
Lucy is either curious or not generous.
Paul is not kind or not funny.
Someone is both not old and quiet.
Alice is not old or not curious.
Someone is not creative.
Fred is not strong or kind. | Lucy is kind. | entailment | (((~old(mary)&~funny(mary)))=>((~humble(susan)|wise(susan))))&
((?[X]:((patient(X)|~strong(X))))<=>((~creative(john)&~humble(john))))&
((?[X]:(~curious(X)))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:(~strong(X)))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~humble(X)&kind(X))<=>~rich(X)))&
(![X]:((old(X)&~old(X))<=>(~happy(X)<~>~tall(X))))&
(![X]:((~curious(X)|generous(X))<=>(wise(X)&kind(X))))&
((?[X]:((quiet(X)&~curious(X))))=>((humble(fred)&quiet(fred))))&
(![X]:(funny(X)<=>(~tall(X)&brave(X))))&
(((creative(lucy)|calm(lucy)))=>(~curious(alice)))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:(~rich(X)<=>(quiet(X)&kind(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:((~creative(X)&brave(X))<=>(~wise(X)|curious(X))))&
(![X]:(~generous(X)<=>(calm(X)|~curious(X))))&
(strong(alice))&
(?[X]:((creative(X)<~>brave(X))))&
((curious(lucy)<~>~generous(lucy)))&
((~kind(paul)|~funny(paul)))&
(?[X]:((~old(X)&quiet(X))))&
((~old(alice)|~curious(alice)))&
(?[X]:(~creative(X)))&
((~strong(fred)|kind(fred))) | kind(lucy) | [
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 522538583380794599427895
% SZS output start Proof for 522538583380794599427895
7. ! [X0] : ((generous(X0) | ~curious(X0)) <=> (kind(X0) & wise(X0))) [input p6]
19. curious(lucy) <~> ~generous(lucy) [input p18]
25. ~kind(lucy) [input hypothesis]
52. ! [X0] : (((generous(X0) | ~curious(X0)) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | (~generous(X0) & curious(X0)))) [nnf transformation 7]
53. ! [X0] : ((generous(X0) | ~curious(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | (~generous(X0) & curious(X0)))) [flattening 52]
80. (generous(lucy) | ~curious(lucy)) & (~generous(lucy) | curious(lucy)) [nnf transformation 19]
106. kind(X0) | curious(X0) [cnf transformation 53]
107. ~generous(X0) | kind(X0) [cnf transformation 53]
145. generous(lucy) | ~curious(lucy) [cnf transformation 80]
152. ~kind(lucy) [cnf transformation 25]
350. 45 <=> curious(lucy) [avatar definition]
354. 46 <=> generous(lucy) [avatar definition]
356. generous(lucy) <- (46) [avatar component clause 354]
357. ~45 | 46 [avatar split clause 145,354,350]
385. curious(lucy) [resolution 106,152]
389. 45 [avatar split clause 385,350]
391. kind(lucy) <- (46) [resolution 107,356]
392. $false <- (46) [subsumption resolution 391,152]
393. ~46 [avatar contradiction clause 392]
394. $false [avatar sat refutation 357,389,393]
% SZS output end Proof for 522538583380794599427895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not humble is either not curious or not brave. If someone is not wise then susan is curious. If someone is both not strong and not kind then someone is not humble or funny. Everyone who is either happy or not calm is either not generous or not old. If alice is humble or old then someone is both not happy and brave and vice versa. If john is either not quiet or not generous then john is both not wise and not generous. Everyone who is both not generous and wise is both brave and not patient. If lucy is not humble then mary is either not rich or generous. Everyone who is both old and rich is humble or brave and vice versa. Everyone who is creative is not calm and vice versa. Everyone who is curious is creative. Everyone who is not tall is calm or brave. If john is not rich or not kind then alice is both not quiet and quiet. Everyone who is funny is not generous or rich and vice versa. If susan is both not curious and strong then someone is both strong and humble and vice versa. Everyone who is strong or not happy is not rich and vice versa. Someone is not quiet. Mary is not generous or not happy. Someone is not generous. Lucy is both not kind and not quiet. Someone is not kind or curious. | Alice is not calm. | entailment | (![X]:((~creative(X)&~humble(X))=>(~curious(X)<~>~brave(X))))&
((?[X]:(~wise(X)))=>(curious(susan)))&
((?[X]:((~strong(X)&~kind(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(~generous(X)<~>~old(X))))&
(((humble(alice)|old(alice)))<=>(?[X]:((~happy(X)&brave(X)))))&
(((~quiet(john)<~>~generous(john)))=>((~wise(john)&~generous(john))))&
(![X]:((~generous(X)&wise(X))=>(brave(X)&~patient(X))))&
((~humble(lucy))=>((~rich(mary)<~>generous(mary))))&
(![X]:((old(X)&rich(X))<=>(humble(X)|brave(X))))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:(curious(X)=>creative(X)))&
(![X]:(~tall(X)=>(calm(X)|brave(X))))&
(((~rich(john)|~kind(john)))=>((~quiet(alice)&quiet(alice))))&
(![X]:(funny(X)<=>(~generous(X)|rich(X))))&
(((~curious(susan)&strong(susan)))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((strong(X)|~happy(X))<=>~rich(X)))&
(?[X]:(~quiet(X)))&
((~generous(mary)|~happy(mary)))&
(?[X]:(~generous(X)))&
((~kind(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)|curious(X)))) | ~calm(alice) | [
"p0",
"p4",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1424288065059354329228875
% SZS output start Proof for 1424288065059354329228875
1. ! [X0] : ((~humble(X0) & ~creative(X0)) => (~curious(X0) <~> ~brave(X0))) [input p0]
5. (old(alice) | humble(alice)) <=> ? [X0] : (brave(X0) & ~happy(X0)) [input p4]
9. ! [X0] : ((rich(X0) & old(X0)) <=> (brave(X0) | humble(X0))) [input p8]
10. ! [X0] : (creative(X0) <=> ~calm(X0)) [input p9]
11. ! [X0] : (curious(X0) => creative(X0)) [input p10]
16. ! [X0] : ((~happy(X0) | strong(X0)) <=> ~rich(X0)) [input p15]
22. calm(alice) [input hypothesis]
25. ! [X0] : (creative(X0) => ~calm(X0)) [unused predicate definition removal 10]
28. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | (humble(X0) | creative(X0))) [ennf transformation 1]
29. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | humble(X0) | creative(X0)) [flattening 28]
37. ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 25]
38. ! [X0] : (creative(X0) | ~curious(X0)) [ennf transformation 11]
42. ! [X0] : (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | humble(X0) | creative(X0)) [nnf transformation 29]
47. ((old(alice) | humble(alice)) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X0] : (brave(X0) & ~happy(X0)) | (~old(alice) & ~humble(alice))) [nnf transformation 5]
48. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X0] : (brave(X0) & ~happy(X0)) | (~old(alice) & ~humble(alice))) [flattening 47]
49. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X1] : (brave(X1) & ~happy(X1)) | (~old(alice) & ~humble(alice))) [rectify 48]
50. ? [X1] : (brave(X1) & ~happy(X1)) => (brave(sK1) & ~happy(sK1)) [choice axiom]
51. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & ((brave(sK1) & ~happy(sK1)) | (~old(alice) & ~humble(alice))) [skolemisation 49,50]
54. ! [X0] : (((rich(X0) & old(X0)) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | (~rich(X0) | ~old(X0)))) [nnf transformation 9]
55. ! [X0] : (((rich(X0) & old(X0)) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ~rich(X0) | ~old(X0))) [flattening 54]
61. ! [X0] : (((~happy(X0) | strong(X0)) | rich(X0)) & (~rich(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 16]
62. ! [X0] : ((~happy(X0) | strong(X0) | rich(X0)) & (~rich(X0) | (happy(X0) & ~strong(X0)))) [flattening 61]
70. brave(X0) | curious(X0) | humble(X0) | creative(X0) [cnf transformation 42]
78. ~happy(sK1) | ~old(alice) [cnf transformation 51]
80. brave(sK1) | ~old(alice) [cnf transformation 51]
90. ~humble(X0) | old(X0) [cnf transformation 55]
91. ~brave(X0) | old(X0) [cnf transformation 55]
93. ~brave(X0) | rich(X0) [cnf transformation 55]
94. ~calm(X0) | ~creative(X0) [cnf transformation 37]
95. ~curious(X0) | creative(X0) [cnf transformation 38]
106. ~rich(X0) | happy(X0) [cnf transformation 62]
114. calm(alice) [cnf transformation 22]
144. 8 <=> old(alice) [avatar definition]
145. ~old(alice) <- (~8) [avatar component clause 144]
149. 9 <=> brave(sK1) [avatar definition]
151. brave(sK1) <- (9) [avatar component clause 149]
152. ~8 | 9 [avatar split clause 80,149,144]
155. 10 <=> happy(sK1) [avatar definition]
157. ~happy(sK1) <- (~10) [avatar component clause 155]
158. ~8 | ~10 [avatar split clause 78,155,144]
238. ~creative(alice) [resolution 94,114]
246. curious(X3) | humble(X3) | creative(X3) | old(X3) [resolution 70,91]
251. curious(X3) | creative(X3) | old(X3) [subsumption resolution 246,90]
252. old(X3) | creative(X3) [subsumption resolution 251,95]
271. creative(alice) <- (~8) [resolution 252,145]
274. $false <- (~8) [subsumption resolution 271,238]
275. 8 [avatar contradiction clause 274]
281. rich(sK1) <- (9) [resolution 151,93]
285. happy(sK1) <- (9) [resolution 281,106]
287. $false <- (9, ~10) [subsumption resolution 285,157]
288. ~9 | 10 [avatar contradiction clause 287]
289. $false [avatar sat refutation 152,158,275,288]
% SZS output end Proof for 1424288065059354329228875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not strong is both strong and humble.
If someone is not curious or not patient then paul is both creative and wise and vice versa.
If someone is either old or not quiet then lucy is rich or not strong and vice versa.
If susan is both not strong and not patient then paul is both not curious and not humble and vice versa.
If lucy is both calm and not generous then someone is both strong and curious.
Everyone who is either creative or not tall is not creative and vice versa.
Everyone who is both brave and humble is either not calm or quiet.
If alice is either creative or quiet then someone is not curious or generous.
Everyone who is not humble or not kind is not patient and vice versa.
Everyone who is not humble or not creative is rich or wise and vice versa.
Everyone who is calm or not wise is both not patient and not calm and vice versa.
If paul is creative or brave then someone is not humble and vice versa.
Everyone who is both brave and tall is not rich.
Everyone who is either generous or not rich is both not kind and not humble and vice versa.
If someone is both strong and not old then john is quiet and vice versa.
Everyone who is both curious and not brave is quiet or tall.
Lucy is not tall or generous.
Someone is funny or old.
John is both not quiet and not happy.
Lucy is not happy.
Someone is happy or generous.
Mary is either brave or not calm.
Someone is rich. | John is not curious. | contradiction | (![X]:((brave(X)&~strong(X))=>(strong(X)&humble(X))))&
((?[X]:((~curious(X)|~patient(X))))<=>((creative(paul)&wise(paul))))&
((?[X]:((old(X)<~>~quiet(X))))<=>((rich(lucy)|~strong(lucy))))&
(((~strong(susan)&~patient(susan)))<=>((~curious(paul)&~humble(paul))))&
(((calm(lucy)&~generous(lucy)))=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((creative(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((brave(X)&humble(X))=>(~calm(X)<~>quiet(X))))&
(((creative(alice)<~>quiet(alice)))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~humble(X)|~kind(X))<=>~patient(X)))&
(![X]:((~humble(X)|~creative(X))<=>(rich(X)|wise(X))))&
(![X]:((calm(X)|~wise(X))<=>(~patient(X)&~calm(X))))&
(((creative(paul)|brave(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&tall(X))=>~rich(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((strong(X)&~old(X))))<=>(quiet(john)))&
(![X]:((curious(X)&~brave(X))=>(quiet(X)|tall(X))))&
((~tall(lucy)|generous(lucy)))&
(?[X]:((funny(X)|old(X))))&
((~quiet(john)&~happy(john)))&
(~happy(lucy))&
(?[X]:((happy(X)|generous(X))))&
((brave(mary)<~>~calm(mary)))&
(?[X]:(rich(X))) | ~curious(john) | [
"p1",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 953443816872631201858349
% SZS output start Proof for 953443816872631201858349
2. ? [X0] : (~patient(X0) | ~curious(X0)) <=> (wise(paul) & creative(paul)) [input p1]
9. ! [X0] : ((~kind(X0) | ~humble(X0)) <=> ~patient(X0)) [input p8]
10. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (wise(X0) | rich(X0))) [input p9]
11. ! [X0] : ((~wise(X0) | calm(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
24. ~curious(john) [input hypothesis]
37. (? [X0] : (~patient(X0) | ~curious(X0)) | (~wise(paul) | ~creative(paul))) & ((wise(paul) & creative(paul)) | ! [X0] : (patient(X0) & curious(X0))) [nnf transformation 2]
38. (? [X0] : (~patient(X0) | ~curious(X0)) | ~wise(paul) | ~creative(paul)) & ((wise(paul) & creative(paul)) | ! [X0] : (patient(X0) & curious(X0))) [flattening 37]
39. (? [X0] : (~patient(X0) | ~curious(X0)) | ~wise(paul) | ~creative(paul)) & ((wise(paul) & creative(paul)) | ! [X1] : (patient(X1) & curious(X1))) [rectify 38]
40. ? [X0] : (~patient(X0) | ~curious(X0)) => (~patient(sK0) | ~curious(sK0)) [choice axiom]
41. ((~patient(sK0) | ~curious(sK0)) | ~wise(paul) | ~creative(paul)) & ((wise(paul) & creative(paul)) | ! [X1] : (patient(X1) & curious(X1))) [skolemisation 39,40]
56. ! [X0] : (((~kind(X0) | ~humble(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & humble(X0)))) [nnf transformation 9]
57. ! [X0] : ((~kind(X0) | ~humble(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & humble(X0)))) [flattening 56]
58. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~wise(X0) & ~rich(X0))) & ((wise(X0) | rich(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 10]
59. ! [X0] : ((~creative(X0) | ~humble(X0) | (~wise(X0) & ~rich(X0))) & (wise(X0) | rich(X0) | (creative(X0) & humble(X0)))) [flattening 58]
60. ! [X0] : (((~wise(X0) | calm(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (wise(X0) & ~calm(X0)))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | calm(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (wise(X0) & ~calm(X0)))) [flattening 60]
80. creative(paul) | curious(X1) [cnf transformation 41]
82. wise(paul) | curious(X1) [cnf transformation 41]
105. ~patient(X0) | humble(X0) [cnf transformation 57]
111. ~wise(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 59]
114. ~calm(X0) | ~calm(X0) [cnf transformation 61]
116. ~wise(X0) | calm(X0) | calm(X0) | patient(X0) [cnf transformation 61]
139. ~curious(john) [cnf transformation 24]
140. ~calm(X0) [duplicate literal removal 114]
141. ~wise(X0) | calm(X0) | patient(X0) [duplicate literal removal 116]
146. 1 <=> creative(paul) [avatar definition]
147. creative(paul) <- (1) [avatar component clause 146]
150. 2 <=> wise(paul) [avatar definition]
151. wise(paul) <- (2) [avatar component clause 150]
167. 6 <=> ! [X1] : curious(X1) [avatar definition]
168. curious(X1) <- (6) [avatar component clause 167]
169. 6 | 2 [avatar split clause 82,150,167]
171. 6 | 1 [avatar split clause 80,146,167]
205. 14 <=> humble(paul) [avatar definition]
206. ~humble(paul) <- (~14) [avatar component clause 205]
303. $false <- (6) [resolution 168,139]
304. ~6 [avatar contradiction clause 303]
325. ~humble(paul) | ~creative(paul) <- (2) [resolution 111,151]
331. ~humble(paul) <- (1, 2) [subsumption resolution 325,147]
332. ~14 | ~1 | ~2 [avatar split clause 331,150,146,205]
346. calm(paul) | patient(paul) <- (2) [resolution 141,151]
347. patient(paul) <- (2) [subsumption resolution 346,140]
350. humble(paul) <- (2) [resolution 347,105]
351. $false <- (2, ~14) [subsumption resolution 350,206]
352. ~2 | 14 [avatar contradiction clause 351]
353. $false [avatar sat refutation 169,171,304,332,352]
% SZS output end Proof for 953443816872631201858349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then fred is both not strong and not curious. Everyone who is either brave or strong is either not strong or not rich. Everyone who is tall is both not rich and happy. Everyone who is not funny or strong is both creative and not brave. Everyone who is not brave or not quiet is both not humble and not calm and vice versa. If someone is either humble or not kind then someone is both not humble and rich and vice versa. If someone is not strong or not calm then someone is not generous. If fred is wise or quiet then john is wise. If fred is creative or not rich then susan is either calm or not quiet. Everyone who is either not rich or not humble is not tall or not quiet. Everyone who is either tall or generous is not quiet and vice versa. Everyone who is both not kind and not creative is either rich or wise and vice versa. Everyone who is kind is patient. If mary is old then susan is not wise or not calm. Everyone who is not generous is not kind and vice versa. Paul is funny. Someone is calm. Someone is not humble or not curious. Lucy is not rich or not kind. John is not kind or not creative. Someone is not funny. Susan is humble. John is curious. | Lucy is happy. | neutral | ((strong(mary))=>((~strong(fred)&~curious(fred))))&
(![X]:((brave(X)<~>strong(X))=>(~strong(X)<~>~rich(X))))&
(![X]:(tall(X)=>(~rich(X)&happy(X))))&
(![X]:((~funny(X)|strong(X))=>(creative(X)&~brave(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~generous(X))))&
(((wise(fred)|quiet(fred)))=>(wise(john)))&
(((creative(fred)|~rich(fred)))=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
(funny(paul))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)|~curious(X))))&
((~rich(lucy)|~kind(lucy)))&
((~kind(john)|~creative(john)))&
(?[X]:(~funny(X)))&
(humble(susan))&
(curious(john)) | happy(lucy) | [] | null | 0 |
Everyone who is not brave is either not happy or not brave.
If paul is rich then paul is not wise or not generous and vice versa.
Everyone who is not kind is happy and vice versa.
If john is both wise and not calm then someone is patient or not brave.
Everyone who is generous is both not humble and not happy.
Everyone who is tall or not brave is both tall and not curious.
If someone is either creative or not humble then someone is not happy or old and vice versa.
Everyone who is both not generous and humble is both happy and brave.
Everyone who is either not generous or not old is both not kind and not curious and vice versa.
If someone is both not happy and not calm then someone is either calm or rich and vice versa.
Everyone who is not brave is strong.
Everyone who is tall is both not wise and not funny.
Everyone who is either not humble or old is both not rich and not old.
Everyone who is wise or patient is not tall or not rich and vice versa.
Everyone who is strong or not generous is not rich.
If someone is both generous and not brave then susan is either not curious or not brave.
Someone is either not strong or generous.
Someone is not humble or rich.
John is not generous.
Paul is both not tall and not rich.
Someone is both not old and not creative.
Someone is quiet.
Someone is either kind or calm.
Lucy is not generous or not quiet. | Paul is not humble. | entailment | (![X]:(~brave(X)=>(~happy(X)<~>~brave(X))))&
((rich(paul))<=>((~wise(paul)|~generous(paul))))&
(![X]:(~kind(X)<=>happy(X)))&
(((wise(john)&~calm(john)))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:(generous(X)=>(~humble(X)&~happy(X))))&
(![X]:((tall(X)|~brave(X))=>(tall(X)&~curious(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((~generous(X)&humble(X))=>(happy(X)&brave(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~kind(X)&~curious(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(![X]:(tall(X)=>(~wise(X)&~funny(X))))&
(![X]:((~humble(X)<~>old(X))=>(~rich(X)&~old(X))))&
(![X]:((wise(X)|patient(X))<=>(~tall(X)|~rich(X))))&
(![X]:((strong(X)|~generous(X))=>~rich(X)))&
((?[X]:((generous(X)&~brave(X))))=>((~curious(susan)<~>~brave(susan))))&
(?[X]:((~strong(X)<~>generous(X))))&
(?[X]:((~humble(X)|rich(X))))&
(~generous(john))&
((~tall(paul)&~rich(paul)))&
(?[X]:((~old(X)&~creative(X))))&
(?[X]:(quiet(X)))&
(?[X]:((kind(X)<~>calm(X))))&
((~generous(lucy)|~quiet(lucy))) | ~humble(paul) | [
"p1",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8157420188603361989451277
% SZS output start Proof for 8157420188603361989451277
2. rich(paul) <=> (~generous(paul) | ~wise(paul)) [input p1]
5. ! [X0] : (generous(X0) => (~happy(X0) & ~humble(X0))) [input p4]
20. ~rich(paul) & ~tall(paul) [input p19]
25. humble(paul) [input hypothesis]
32. ! [X0] : ((~happy(X0) & ~humble(X0)) | ~generous(X0)) [ennf transformation 5]
42. (rich(paul) | (generous(paul) & wise(paul))) & ((~generous(paul) | ~wise(paul)) | ~rich(paul)) [nnf transformation 2]
43. (rich(paul) | (generous(paul) & wise(paul))) & (~generous(paul) | ~wise(paul) | ~rich(paul)) [flattening 42]
79. rich(paul) | generous(paul) [cnf transformation 43]
83. ~humble(X0) | ~generous(X0) [cnf transformation 32]
128. ~rich(paul) [cnf transformation 20]
135. humble(paul) [cnf transformation 25]
139. 1 <=> generous(paul) [avatar definition]
141. generous(paul) <- (1) [avatar component clause 139]
143. 2 <=> rich(paul) [avatar definition]
146. 1 | 2 [avatar split clause 79,143,139]
271. ~2 [avatar split clause 128,143]
293. ~generous(paul) [resolution 83,135]
294. $false <- (1) [subsumption resolution 293,141]
295. ~1 [avatar contradiction clause 294]
296. $false [avatar sat refutation 146,271,295]
% SZS output end Proof for 8157420188603361989451277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not creative is brave or not curious.
Everyone who is generous or humble is both tall and not tall and vice versa.
If john is happy then someone is both wise and not wise and vice versa.
Everyone who is either humble or wise is not happy.
If someone is kind then someone is either curious or not quiet and vice versa.
Everyone who is both not strong and calm is not tall and vice versa.
If lucy is both strong and not tall then someone is curious or brave and vice versa.
If alice is both not calm and not rich then someone is either not kind or not patient and vice versa.
Everyone who is patient or generous is either brave or patient and vice versa.
Everyone who is not calm is humble.
Everyone who is both not quiet and old is not generous.
If someone is not generous or patient then someone is not kind or creative and vice versa.
Everyone who is curious is not rich or not humble.
If fred is either not tall or humble then someone is not brave or not kind and vice versa.
If paul is either not humble or creative then mary is both curious and funny.
Susan is both happy and not generous.
Susan is either not funny or kind.
Someone is not patient.
Someone is kind or funny.
Alice is strong.
Alice is not quiet or not strong.
John is not humble. | Susan is happy. | entailment | (![X]:((generous(X)&~creative(X))=>(brave(X)|~curious(X))))&
(![X]:((generous(X)|humble(X))<=>(tall(X)&~tall(X))))&
((happy(john))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((humble(X)<~>wise(X))=>~happy(X)))&
((?[X]:(kind(X)))<=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:((~strong(X)&calm(X))<=>~tall(X)))&
(((strong(lucy)&~tall(lucy)))<=>(?[X]:((curious(X)|brave(X)))))&
(((~calm(alice)&~rich(alice)))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((patient(X)|generous(X))<=>(brave(X)<~>patient(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((~quiet(X)&old(X))=>~generous(X)))&
((?[X]:((~generous(X)|patient(X))))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:(curious(X)=>(~rich(X)|~humble(X))))&
(((~tall(fred)<~>humble(fred)))<=>(?[X]:((~brave(X)|~kind(X)))))&
(((~humble(paul)<~>creative(paul)))=>((curious(mary)&funny(mary))))&
((happy(susan)&~generous(susan)))&
((~funny(susan)<~>kind(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)|funny(X))))&
(strong(alice))&
((~quiet(alice)|~strong(alice)))&
(~humble(john)) | happy(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1545020808239141130543084
% SZS output start Proof for 1545020808239141130543084
16. ~generous(susan) & happy(susan) [input p15]
23. ~happy(susan) [input hypothesis]
126. happy(susan) [cnf transformation 16]
135. ~happy(susan) [cnf transformation 23]
300. $false [subsumption resolution 135,126]
% SZS output end Proof for 1545020808239141130543084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm then someone is either quiet or wise and vice versa. If mary is both brave and not wise then john is creative and vice versa. If someone is not generous then alice is not funny. Everyone who is calm or humble is strong or not tall. Everyone who is not tall is rich. If someone is either not humble or kind then susan is both not generous and not humble. If lucy is either funny or kind then fred is both humble and not wise. Everyone who is both not quiet and not kind is both creative and not tall. If someone is not creative then someone is either funny or strong. Everyone who is both brave and not curious is quiet or wise and vice versa. If someone is both humble and not kind then someone is either not strong or not quiet and vice versa. Everyone who is either not funny or not happy is not wise or happy and vice versa. If paul is both rich and not wise then paul is generous and vice versa. Everyone who is not wise or brave is not generous. Everyone who is old or not rich is either not curious or creative. If john is both not quiet and quiet then someone is brave and vice versa. Someone is either curious or kind. Someone is either not kind or not happy. Lucy is not creative or tall. Paul is both curious and kind. Paul is happy. Someone is not creative. Susan is strong. | Lucy is creative. | neutral | ((calm(fred))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(((brave(mary)&~wise(mary)))<=>(creative(john)))&
((?[X]:(~generous(X)))=>(~funny(alice)))&
(![X]:((calm(X)|humble(X))=>(strong(X)|~tall(X))))&
(![X]:(~tall(X)=>rich(X)))&
((?[X]:((~humble(X)<~>kind(X))))=>((~generous(susan)&~humble(susan))))&
(((funny(lucy)<~>kind(lucy)))=>((humble(fred)&~wise(fred))))&
(![X]:((~quiet(X)&~kind(X))=>(creative(X)&~tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:((brave(X)&~curious(X))<=>(quiet(X)|wise(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~wise(X)|happy(X))))&
(((rich(paul)&~wise(paul)))<=>(generous(paul)))&
(![X]:((~wise(X)|brave(X))=>~generous(X)))&
(![X]:((old(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
(((~quiet(john)&quiet(john)))<=>(?[X]:(brave(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~creative(lucy)|tall(lucy)))&
((curious(paul)&kind(paul)))&
(happy(paul))&
(?[X]:(~creative(X)))&
(strong(susan)) | creative(lucy) | [] | null | 0 |
If fred is either not strong or not happy then someone is both not strong and creative and vice versa. Everyone who is not old or not creative is both patient and not calm. If someone is not calm or not tall then john is both not happy and not rich and vice versa. Everyone who is not happy or tall is both funny and not brave and vice versa. If susan is old or not funny then john is either old or not brave and vice versa. Everyone who is both wise and patient is either not strong or not tall and vice versa. If someone is old or not brave then john is both funny and not kind and vice versa. Everyone who is kind is either kind or not generous and vice versa. If paul is creative or generous then lucy is either not happy or patient and vice versa. If someone is not funny then john is calm or not strong and vice versa. If someone is creative or humble then mary is wise. Everyone who is not kind or not rich is either not strong or patient and vice versa. If lucy is either not rich or not strong then alice is both creative and strong. Everyone who is both wise and not calm is either generous or tall. Everyone who is both wise and not calm is both old and not strong. Someone is not humble or brave. John is either not old or generous. John is not creative or creative. Someone is curious or generous. | Alice is generous. | entailment | (((~strong(fred)<~>~happy(fred)))<=>(?[X]:((~strong(X)&creative(X)))))&
(![X]:((~old(X)|~creative(X))=>(patient(X)&~calm(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>((~happy(john)&~rich(john))))&
(![X]:((~happy(X)|tall(X))<=>(funny(X)&~brave(X))))&
(((old(susan)|~funny(susan)))<=>((old(john)<~>~brave(john))))&
(![X]:((wise(X)&patient(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((old(X)|~brave(X))))<=>((funny(john)&~kind(john))))&
(![X]:(kind(X)<=>(kind(X)<~>~generous(X))))&
(((creative(paul)|generous(paul)))<=>((~happy(lucy)<~>patient(lucy))))&
((?[X]:(~funny(X)))<=>((calm(john)|~strong(john))))&
((?[X]:((creative(X)|humble(X))))=>(wise(mary)))&
(![X]:((~kind(X)|~rich(X))<=>(~strong(X)<~>patient(X))))&
(((~rich(lucy)<~>~strong(lucy)))=>((creative(alice)&strong(alice))))&
(![X]:((wise(X)&~calm(X))=>(generous(X)<~>tall(X))))&
(![X]:((wise(X)&~calm(X))=>(old(X)&~strong(X))))&
(?[X]:((~humble(X)|brave(X))))&
((~old(john)<~>generous(john)))&
((~creative(john)|creative(john)))&
(?[X]:((curious(X)|generous(X)))) | generous(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 158288731762369877988278
% SZS output start Proof for 158288731762369877988278
8. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~generous(X0))) [input p7]
20. ~generous(alice) [input hypothesis]
51. ! [X0] : ((kind(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0)))) & (((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 8]
102. generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 51]
104. kind(X0) | kind(X0) | generous(X0) [cnf transformation 51]
132. ~generous(alice) [cnf transformation 20]
133. generous(X0) | ~kind(X0) [duplicate literal removal 102]
134. kind(X0) | generous(X0) [duplicate literal removal 104]
236. generous(X0) [subsumption resolution 133,134]
305. $false [subsumption resolution 132,236]
% SZS output end Proof for 158288731762369877988278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not quiet is either not brave or not curious and vice versa.
Everyone who is not humble or kind is curious or not curious and vice versa.
If lucy is both wise and curious then paul is either funny or tall and vice versa.
If paul is not tall or not kind then mary is tall.
Everyone who is either not calm or not old is both not humble and humble and vice versa.
Everyone who is funny is both humble and patient and vice versa.
If alice is not quiet or not happy then alice is either not funny or curious and vice versa.
Everyone who is not old is old.
Everyone who is tall or not happy is either not humble or not happy.
If someone is either curious or quiet then someone is not funny.
Everyone who is either not kind or not patient is both happy and not happy.
Everyone who is both creative and not brave is not brave or not wise.
Everyone who is either curious or generous is not wise or kind and vice versa.
If mary is both not funny and wise then fred is both not wise and not old and vice versa.
If someone is curious then susan is not strong and vice versa.
If someone is both kind and not strong then someone is both not humble and not funny and vice versa.
Fred is funny.
Alice is wise or strong.
Someone is not generous.
Paul is not quiet.
Someone is either tall or not tall.
Paul is not calm or wise.
Someone is either not brave or calm. | Paul is generous. | neutral | (![X]:((curious(X)<~>~quiet(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~humble(X)|kind(X))<=>(curious(X)|~curious(X))))&
(((wise(lucy)&curious(lucy)))<=>((funny(paul)<~>tall(paul))))&
(((~tall(paul)|~kind(paul)))=>(tall(mary)))&
(![X]:((~calm(X)<~>~old(X))<=>(~humble(X)&humble(X))))&
(![X]:(funny(X)<=>(humble(X)&patient(X))))&
(((~quiet(alice)|~happy(alice)))<=>((~funny(alice)<~>curious(alice))))&
(![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)|~happy(X))=>(~humble(X)<~>~happy(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>~patient(X))=>(happy(X)&~happy(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)|~wise(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~wise(X)|kind(X))))&
(((~funny(mary)&wise(mary)))<=>((~wise(fred)&~old(fred))))&
((?[X]:(curious(X)))<=>(~strong(susan)))&
((?[X]:((kind(X)&~strong(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(funny(fred))&
((wise(alice)|strong(alice)))&
(?[X]:(~generous(X)))&
(~quiet(paul))&
(?[X]:((tall(X)<~>~tall(X))))&
((~calm(paul)|wise(paul)))&
(?[X]:((~brave(X)<~>calm(X)))) | generous(paul) | [] | null | 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. | Lucy is not patient. | neutral | ((?[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)))) | ~patient(lucy) | [] | null | 0 |
Everyone who is either not rich or not strong is both wise and not rich.
Everyone who is not generous or not calm is not humble or generous.
If lucy is both curious and patient then someone is creative and vice versa.
If someone is not tall then someone is either not curious or not wise.
If alice is funny then fred is not tall.
If lucy is both not kind and not patient then susan is not humble or generous and vice versa.
If lucy is both brave and not tall then someone is both calm and kind.
Everyone who is quiet or not old is quiet and vice versa.
If paul is not rich then alice is both not kind and strong and vice versa.
Everyone who is both not brave and not strong is either not quiet or humble.
Everyone who is not happy is either humble or tall.
Everyone who is either not patient or funny is either rich or not generous and vice versa.
If someone is either patient or happy then someone is humble and vice versa.
Everyone who is either not strong or not tall is both not old and not happy and vice versa.
Everyone who is either strong or generous is both not humble and not kind and vice versa.
Everyone who is either wise or not quiet is not kind or tall.
Mary is both calm and not curious.
Someone is either not kind or quiet.
Someone is not curious or old.
Susan is both generous and not patient.
Susan is kind or happy.
Lucy is not wise or not creative.
Paul is not kind. | Alice is creative. | contradiction | (![X]:((~rich(X)<~>~strong(X))=>(wise(X)&~rich(X))))&
(![X]:((~generous(X)|~calm(X))=>(~humble(X)|generous(X))))&
(((curious(lucy)&patient(lucy)))<=>(?[X]:(creative(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
((funny(alice))=>(~tall(fred)))&
(((~kind(lucy)&~patient(lucy)))<=>((~humble(susan)|generous(susan))))&
(((brave(lucy)&~tall(lucy)))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((quiet(X)|~old(X))<=>quiet(X)))&
((~rich(paul))<=>((~kind(alice)&strong(alice))))&
(![X]:((~brave(X)&~strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:(~happy(X)=>(humble(X)<~>tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~old(X)&~happy(X))))&
(![X]:((strong(X)<~>generous(X))<=>(~humble(X)&~kind(X))))&
(![X]:((wise(X)<~>~quiet(X))=>(~kind(X)|tall(X))))&
((calm(mary)&~curious(mary)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((~curious(X)|old(X))))&
((generous(susan)&~patient(susan)))&
((kind(susan)|happy(susan)))&
((~wise(lucy)|~creative(lucy)))&
(~kind(paul)) | creative(alice) | [
"p2",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6959408145320364503335649
% SZS output start Proof for 6959408145320364503335649
3. (patient(lucy) & curious(lucy)) <=> ? [X0] : creative(X0) [input p2]
6. (~patient(lucy) & ~kind(lucy)) <=> (generous(susan) | ~humble(susan)) [input p5]
20. ~patient(susan) & generous(susan) [input p19]
24. creative(alice) [input hypothesis]
43. ((patient(lucy) & curious(lucy)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (~patient(lucy) | ~curious(lucy))) [nnf transformation 3]
44. ((patient(lucy) & curious(lucy)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | ~patient(lucy) | ~curious(lucy)) [flattening 43]
45. ((patient(lucy) & curious(lucy)) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | ~patient(lucy) | ~curious(lucy)) [rectify 44]
46. ? [X1] : creative(X1) => creative(sK0) [choice axiom]
47. ((patient(lucy) & curious(lucy)) | ! [X0] : ~creative(X0)) & (creative(sK0) | ~patient(lucy) | ~curious(lucy)) [skolemisation 45,46]
52. ((~patient(lucy) & ~kind(lucy)) | (~generous(susan) & humble(susan))) & ((generous(susan) | ~humble(susan)) | (patient(lucy) | kind(lucy))) [nnf transformation 6]
53. ((~patient(lucy) & ~kind(lucy)) | (~generous(susan) & humble(susan))) & (generous(susan) | ~humble(susan) | patient(lucy) | kind(lucy)) [flattening 52]
85. patient(lucy) | ~creative(X0) [cnf transformation 47]
93. ~patient(lucy) | ~generous(susan) [cnf transformation 53]
135. generous(susan) [cnf transformation 20]
140. creative(alice) [cnf transformation 24]
144. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
145. ~creative(X0) <- (1) [avatar component clause 144]
147. 2 <=> patient(lucy) [avatar definition]
150. 1 | 2 [avatar split clause 85,147,144]
184. 10 <=> generous(susan) [avatar definition]
187. ~10 | ~2 [avatar split clause 93,147,184]
273. 10 [avatar split clause 135,184]
292. $false <- (1) [resolution 145,140]
293. ~1 [avatar contradiction clause 292]
294. $false [avatar sat refutation 150,187,273,293]
% SZS output end Proof for 6959408145320364503335649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not brave is both not rich and brave.
If mary is either creative or calm then someone is not strong or creative and vice versa.
If paul is tall or wise then someone is both not funny and not quiet.
Everyone who is kind is wise or curious.
If someone is not brave or quiet then someone is both patient and not strong and vice versa.
If fred is not old or kind then someone is either not tall or curious and vice versa.
If someone is humble then paul is both not quiet and not kind and vice versa.
If someone is either curious or quiet then someone is strong or old.
If someone is both not quiet and not rich then someone is both brave and not humble.
Everyone who is both humble and not patient is both quiet and humble and vice versa.
If someone is either not creative or brave then someone is both not wise and not humble and vice versa.
If someone is strong or rich then someone is tall or wise.
Everyone who is both not rich and old is tall.
Everyone who is either not curious or not patient is not wise or kind.
If someone is not brave then someone is not rich and vice versa.
Everyone who is not tall is brave and vice versa.
Alice is either not generous or not calm.
Fred is not old or not happy.
Alice is both kind and old.
John is both not calm and not generous.
Fred is not happy.
Alice is either wise or old.
John is both old and not wise. | Alice is tall. | contradiction | (![X]:((happy(X)|~brave(X))=>(~rich(X)&brave(X))))&
(((creative(mary)<~>calm(mary)))<=>(?[X]:((~strong(X)|creative(X)))))&
(((tall(paul)|wise(paul)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(kind(X)=>(wise(X)|curious(X))))&
((?[X]:((~brave(X)|quiet(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(((~old(fred)|kind(fred)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:(humble(X)))<=>((~quiet(paul)&~kind(paul))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((strong(X)|old(X)))))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((brave(X)&~humble(X)))))&
(![X]:((humble(X)&~patient(X))<=>(quiet(X)&humble(X))))&
((?[X]:((~creative(X)<~>brave(X))))<=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((strong(X)|rich(X))))=>(?[X]:((tall(X)|wise(X)))))&
(![X]:((~rich(X)&old(X))=>tall(X)))&
(![X]:((~curious(X)<~>~patient(X))=>(~wise(X)|kind(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(~rich(X))))&
(![X]:(~tall(X)<=>brave(X)))&
((~generous(alice)<~>~calm(alice)))&
((~old(fred)|~happy(fred)))&
((kind(alice)&old(alice)))&
((~calm(john)&~generous(john)))&
(~happy(fred))&
((wise(alice)<~>old(alice)))&
((old(john)&~wise(john))) | tall(alice) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1434844973721675838847142
% SZS output start Proof for 1434844973721675838847142
1. ! [X0] : ((~brave(X0) | happy(X0)) => (brave(X0) & ~rich(X0))) [input p0]
16. ! [X0] : (~tall(X0) <=> brave(X0)) [input p15]
24. tall(alice) [input hypothesis]
33. ! [X0] : (~brave(X0) => (brave(X0) & ~rich(X0))) [pure predicate removal 1]
35. ! [X0] : ((brave(X0) & ~rich(X0)) | brave(X0)) [ennf transformation 33]
90. ! [X0] : ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0))) [nnf transformation 16]
94. brave(X0) | brave(X0) [cnf transformation 35]
140. ~tall(X0) | ~brave(X0) [cnf transformation 90]
151. tall(alice) [cnf transformation 24]
152. brave(X0) [duplicate literal removal 94]
325. ~tall(X0) [subsumption resolution 140,152]
337. $false [subsumption resolution 151,325]
% SZS output end Proof for 1434844973721675838847142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and tall is not creative and vice versa.
If someone is humble or funny then lucy is either not brave or not humble.
If paul is not curious or funny then paul is not kind or not tall.
If fred is not rich then someone is wise.
If someone is calm then paul is generous and vice versa.
If someone is happy then alice is both old and not calm.
Everyone who is generous or not funny is not creative.
If someone is either happy or funny then susan is both generous and happy and vice versa.
If someone is old then lucy is both rich and not rich and vice versa.
Everyone who is both humble and not kind is both not calm and not patient and vice versa.
Everyone who is wise or not kind is either wise or not curious.
If someone is either happy or not humble then someone is either not brave or creative and vice versa.
If paul is not funny then john is either not tall or quiet.
If someone is brave or not brave then someone is either not kind or not generous and vice versa.
Everyone who is both generous and curious is not generous or not strong.
Fred is both not kind and quiet.
Alice is not funny.
Someone is either not happy or not kind.
Someone is kind.
Alice is curious.
Someone is both kind and not humble.
Fred is kind or humble. | Susan is not patient. | entailment | (![X]:((~patient(X)&tall(X))<=>~creative(X)))&
((?[X]:((humble(X)|funny(X))))=>((~brave(lucy)<~>~humble(lucy))))&
(((~curious(paul)|funny(paul)))=>((~kind(paul)|~tall(paul))))&
((~rich(fred))=>(?[X]:(wise(X))))&
((?[X]:(calm(X)))<=>(generous(paul)))&
((?[X]:(happy(X)))=>((old(alice)&~calm(alice))))&
(![X]:((generous(X)|~funny(X))=>~creative(X)))&
((?[X]:((happy(X)<~>funny(X))))<=>((generous(susan)&happy(susan))))&
((?[X]:(old(X)))<=>((rich(lucy)&~rich(lucy))))&
(![X]:((humble(X)&~kind(X))<=>(~calm(X)&~patient(X))))&
(![X]:((wise(X)|~kind(X))=>(wise(X)<~>~curious(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((~funny(paul))=>((~tall(john)<~>quiet(john))))&
((?[X]:((brave(X)|~brave(X))))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(![X]:((generous(X)&curious(X))=>(~generous(X)|~strong(X))))&
((~kind(fred)&quiet(fred)))&
(~funny(alice))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:(kind(X)))&
(curious(alice))&
(?[X]:((kind(X)&~humble(X))))&
((kind(fred)|humble(fred))) | ~patient(susan) | [
"p0",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8142752952595722716285703
% SZS output start Proof for 8142752952595722716285703
1. ! [X0] : ((tall(X0) & ~patient(X0)) <=> ~creative(X0)) [input p0]
6. ? [X0] : happy(X0) => (~calm(alice) & old(alice)) [input p5]
7. ! [X0] : ((~funny(X0) | generous(X0)) => ~creative(X0)) [input p6]
8. ? [X0] : (happy(X0) <~> funny(X0)) <=> (happy(susan) & generous(susan)) [input p7]
9. ? [X0] : old(X0) <=> (~rich(lucy) & rich(lucy)) [input p8]
23. patient(susan) [input hypothesis]
31. (~calm(alice) & old(alice)) | ! [X0] : ~happy(X0) [ennf transformation 6]
32. ! [X0] : (~creative(X0) | (funny(X0) & ~generous(X0))) [ennf transformation 7]
35. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (~tall(X0) | patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | ~tall(X0) | patient(X0))) [flattening 35]
44. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | (~happy(susan) | ~generous(susan))) & ((happy(susan) & generous(susan)) | ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [nnf transformation 8]
45. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [flattening 44]
46. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X1] : ((happy(X1) | ~funny(X1)) & (funny(X1) | ~happy(X1)))) [rectify 45]
47. ? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) => ((~funny(sK2) | ~happy(sK2)) & (funny(sK2) | happy(sK2))) [choice axiom]
48. (((~funny(sK2) | ~happy(sK2)) & (funny(sK2) | happy(sK2))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X1] : ((happy(X1) | ~funny(X1)) & (funny(X1) | ~happy(X1)))) [skolemisation 46,47]
49. (? [X0] : old(X0) | (rich(lucy) | ~rich(lucy))) & ((~rich(lucy) & rich(lucy)) | ! [X0] : ~old(X0)) [nnf transformation 9]
50. (? [X0] : old(X0) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X0] : ~old(X0)) [flattening 49]
51. (? [X0] : old(X0) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X1] : ~old(X1)) [rectify 50]
52. ? [X0] : old(X0) => old(sK3) [choice axiom]
53. (old(sK3) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X1] : ~old(X1)) [skolemisation 51,52]
76. ~patient(X0) | creative(X0) [cnf transformation 36]
87. old(alice) | ~happy(X0) [cnf transformation 31]
89. ~generous(X0) | ~creative(X0) [cnf transformation 32]
90. ~creative(X0) | funny(X0) [cnf transformation 32]
92. generous(susan) | happy(X1) | ~funny(X1) [cnf transformation 48]
97. rich(lucy) | ~old(X1) [cnf transformation 53]
98. ~rich(lucy) | ~old(X1) [cnf transformation 53]
134. patient(susan) [cnf transformation 23]
195. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
196. ~happy(X0) <- (14) [avatar component clause 195]
203. 16 <=> old(alice) [avatar definition]
205. old(alice) <- (16) [avatar component clause 203]
206. 14 | 16 [avatar split clause 87,203,195]
208. 17 <=> generous(susan) [avatar definition]
209. generous(susan) <- (17) [avatar component clause 208]
212. 18 <=> happy(susan) [avatar definition]
213. happy(susan) <- (18) [avatar component clause 212]
214. ~happy(susan) <- (~18) [avatar component clause 212]
226. 21 <=> ! [X1] : (happy(X1) | ~funny(X1)) [avatar definition]
227. ~funny(X1) | happy(X1) <- (21) [avatar component clause 226]
233. 21 | 17 [avatar split clause 92,208,226]
236. 23 <=> ! [X1] : ~old(X1) [avatar definition]
237. ~old(X1) <- (23) [avatar component clause 236]
239. 24 <=> rich(lucy) [avatar definition]
242. 23 | ~24 [avatar split clause 98,239,236]
243. 23 | 24 [avatar split clause 97,239,236]
319. $false <- (14, 18) [resolution 213,196]
320. ~14 | ~18 [avatar contradiction clause 319]
321. $false <- (16, 23) [subsumption resolution 205,237]
322. ~16 | ~23 [avatar contradiction clause 321]
327. creative(susan) [resolution 76,134]
330. ~creative(susan) <- (17) [resolution 89,209]
331. $false <- (17) [subsumption resolution 330,327]
332. ~17 [avatar contradiction clause 331]
334. funny(susan) [resolution 90,327]
337. happy(susan) <- (21) [resolution 227,334]
338. $false <- (~18, 21) [subsumption resolution 337,214]
339. 18 | ~21 [avatar contradiction clause 338]
340. $false [avatar sat refutation 206,233,242,243,320,322,332,339]
% SZS output end Proof for 8142752952595722716285703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not old is either not patient or curious and vice versa. Everyone who is either creative or happy is not tall and vice versa. If someone is quiet or brave then someone is both creative and not happy and vice versa. Everyone who is either not quiet or not curious is not funny or patient. Everyone who is both rich and not creative is both strong and not humble. If fred is either not calm or rich then someone is both strong and calm. If someone is either generous or funny then john is both generous and patient and vice versa. Everyone who is not humble is both strong and curious and vice versa. Everyone who is rich or not strong is not kind. Everyone who is rich is old and vice versa. If fred is both funny and not calm then someone is kind or not quiet and vice versa. Everyone who is not quiet or happy is both patient and generous and vice versa. If someone is happy then mary is either kind or not patient and vice versa. If someone is not humble or not patient then someone is not kind or happy. Everyone who is both not brave and humble is not happy or old and vice versa. Everyone who is either not calm or kind is both not wise and not funny. Someone is either brave or creative. Someone is either not wise or old. Fred is old. Someone is happy or not strong. Someone is old or not curious. Susan is either brave or not rich. Someone is tall or not humble. | Susan is not strong. | neutral | (![X]:((old(X)&~old(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((creative(X)<~>happy(X))<=>~tall(X)))&
((?[X]:((quiet(X)|brave(X))))<=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~funny(X)|patient(X))))&
(![X]:((rich(X)&~creative(X))=>(strong(X)&~humble(X))))&
(((~calm(fred)<~>rich(fred)))=>(?[X]:((strong(X)&calm(X)))))&
((?[X]:((generous(X)<~>funny(X))))<=>((generous(john)&patient(john))))&
(![X]:(~humble(X)<=>(strong(X)&curious(X))))&
(![X]:((rich(X)|~strong(X))=>~kind(X)))&
(![X]:(rich(X)<=>old(X)))&
(((funny(fred)&~calm(fred)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~quiet(X)|happy(X))<=>(patient(X)&generous(X))))&
((?[X]:(happy(X)))<=>((kind(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~brave(X)&humble(X))<=>(~happy(X)|old(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~wise(X)&~funny(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(old(fred))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((old(X)|~curious(X))))&
((brave(susan)<~>~rich(susan)))&
(?[X]:((tall(X)|~humble(X)))) | ~strong(susan) | [] | null | 0 |
If someone is both not strong and happy then lucy is not brave or creative. If someone is humble or not generous then someone is both strong and not wise and vice versa. Everyone who is generous is calm or not old and vice versa. Everyone who is both not wise and not curious is quiet and vice versa. Everyone who is both rich and happy is wise or old. Everyone who is either not tall or not old is either not wise or humble. If someone is either not rich or rich then someone is not happy or not old and vice versa. If someone is not humble or not funny then someone is brave or not strong. If susan is either not funny or quiet then alice is either strong or rich and vice versa. Everyone who is calm or not creative is both not generous and creative and vice versa. If mary is not curious then someone is either old or brave. If someone is both old and rich then alice is not brave or quiet. Everyone who is not creative is not quiet and vice versa. Everyone who is both not patient and generous is either not happy or not curious. Everyone who is either not tall or curious is either patient or kind and vice versa. Someone is either humble or not tall. Someone is not rich or not brave. Lucy is wise or happy. Someone is both creative and strong. Paul is brave. | Mary is calm. | contradiction | ((?[X]:((~strong(X)&happy(X))))=>((~brave(lucy)|creative(lucy))))&
((?[X]:((humble(X)|~generous(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|~old(X))))&
(![X]:((~wise(X)&~curious(X))<=>quiet(X)))&
(![X]:((rich(X)&happy(X))=>(wise(X)|old(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(((~funny(susan)<~>quiet(susan)))<=>((strong(alice)<~>rich(alice))))&
(![X]:((calm(X)|~creative(X))<=>(~generous(X)&creative(X))))&
((~curious(mary))=>(?[X]:((old(X)<~>brave(X)))))&
((?[X]:((old(X)&rich(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)&generous(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(patient(X)<~>kind(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~brave(X))))&
((wise(lucy)|happy(lucy)))&
(?[X]:((creative(X)&strong(X))))&
(brave(paul)) | calm(mary) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6339288692735620773335088
% SZS output start Proof for 6339288692735620773335088
3. ! [X0] : (generous(X0) <=> (~old(X0) | calm(X0))) [input p2]
10. ! [X0] : ((~creative(X0) | calm(X0)) <=> (creative(X0) & ~generous(X0))) [input p9]
21. calm(mary) [input hypothesis]
41. ! [X0] : ((generous(X0) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | ~generous(X0))) [nnf transformation 3]
42. ! [X0] : ((generous(X0) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~generous(X0))) [flattening 41]
55. ! [X0] : (((~creative(X0) | calm(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [nnf transformation 10]
56. ! [X0] : ((~creative(X0) | calm(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [flattening 55]
77. generous(X0) | ~calm(X0) [cnf transformation 42]
103. ~generous(X0) | ~calm(X0) [cnf transformation 56]
130. calm(mary) [cnf transformation 21]
234. ~calm(X0) [subsumption resolution 103,77]
290. $false [subsumption resolution 130,234]
% SZS output end Proof for 6339288692735620773335088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or quiet is not strong or not tall.
If someone is happy then someone is wise and vice versa.
If fred is rich or brave then someone is either kind or not calm and vice versa.
Everyone who is not funny or creative is both not quiet and kind.
Everyone who is either curious or happy is either not humble or creative.
If mary is funny or quiet then someone is both not kind and old and vice versa.
If someone is tall then alice is both brave and not patient and vice versa.
Everyone who is both tall and not wise is either brave or wise and vice versa.
If someone is not brave then mary is strong.
Everyone who is kind or rich is either wise or not quiet.
If someone is either curious or creative then susan is both quiet and brave.
Everyone who is not wise or wise is both generous and patient and vice versa.
Everyone who is either rich or funny is not patient.
Everyone who is both strong and curious is either kind or not tall.
Someone is humble or old.
Paul is either not kind or creative.
Alice is strong or not happy.
Mary is not strong or curious.
Someone is both not happy and patient.
Susan is either not happy or not patient.
Alice is not quiet. | Susan is rich. | entailment | (![X]:((~funny(X)<~>quiet(X))=>(~strong(X)|~tall(X))))&
((?[X]:(happy(X)))<=>(?[X]:(wise(X))))&
(((rich(fred)|brave(fred)))<=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~funny(X)|creative(X))=>(~quiet(X)&kind(X))))&
(![X]:((curious(X)<~>happy(X))=>(~humble(X)<~>creative(X))))&
(((funny(mary)|quiet(mary)))<=>(?[X]:((~kind(X)&old(X)))))&
((?[X]:(tall(X)))<=>((brave(alice)&~patient(alice))))&
(![X]:((tall(X)&~wise(X))<=>(brave(X)<~>wise(X))))&
((?[X]:(~brave(X)))=>(strong(mary)))&
(![X]:((kind(X)|rich(X))=>(wise(X)<~>~quiet(X))))&
((?[X]:((curious(X)<~>creative(X))))=>((quiet(susan)&brave(susan))))&
(![X]:((~wise(X)|wise(X))<=>(generous(X)&patient(X))))&
(![X]:((rich(X)<~>funny(X))=>~patient(X)))&
(![X]:((strong(X)&curious(X))=>(kind(X)<~>~tall(X))))&
(?[X]:((humble(X)|old(X))))&
((~kind(paul)<~>creative(paul)))&
((strong(alice)|~happy(alice)))&
((~strong(mary)|curious(mary)))&
(?[X]:((~happy(X)&patient(X))))&
((~happy(susan)<~>~patient(susan)))&
(~quiet(alice)) | rich(susan) | [
"p3",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5970113340438114033765268
% SZS output start Proof for 5970113340438114033765268
4. ! [X0] : ((creative(X0) | ~funny(X0)) => (kind(X0) & ~quiet(X0))) [input p3]
7. ? [X0] : tall(X0) <=> (~patient(alice) & brave(alice)) [input p6]
8. ! [X0] : ((~wise(X0) & tall(X0)) <=> (brave(X0) <~> wise(X0))) [input p7]
9. ? [X0] : ~brave(X0) => strong(mary) [input p8]
10. ! [X0] : ((rich(X0) | kind(X0)) => (wise(X0) <~> ~quiet(X0))) [input p9]
11. ? [X0] : (curious(X0) <~> creative(X0)) => (brave(susan) & quiet(susan)) [input p10]
12. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (patient(X0) & generous(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> funny(X0)) => ~patient(X0)) [input p12]
14. ! [X0] : ((curious(X0) & strong(X0)) => (kind(X0) <~> ~tall(X0))) [input p13]
18. curious(mary) | ~strong(mary) [input p17]
22. ~rich(susan) [input hypothesis]
26. ! [X0] : ((kind(X0) & ~quiet(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 4]
28. strong(mary) | ! [X0] : brave(X0) [ennf transformation 9]
29. ! [X0] : ((wise(X0) <~> ~quiet(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 10]
30. (brave(susan) & quiet(susan)) | ! [X0] : (curious(X0) <=> creative(X0)) [ennf transformation 11]
31. ! [X0] : (~patient(X0) | (rich(X0) <=> funny(X0))) [ennf transformation 13]
32. ! [X0] : ((kind(X0) <~> ~tall(X0)) | (~curious(X0) | ~strong(X0))) [ennf transformation 14]
33. ! [X0] : ((kind(X0) <~> ~tall(X0)) | ~curious(X0) | ~strong(X0)) [flattening 32]
51. (? [X0] : tall(X0) | (patient(alice) | ~brave(alice))) & ((~patient(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [nnf transformation 7]
52. (? [X0] : tall(X0) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [flattening 51]
53. (? [X0] : tall(X0) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [rectify 52]
54. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
55. (tall(sK4) | patient(alice) | ~brave(alice)) & ((~patient(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [skolemisation 53,54]
56. ! [X0] : (((~wise(X0) & tall(X0)) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | (wise(X0) | ~tall(X0)))) [nnf transformation 8]
57. ! [X0] : (((~wise(X0) & tall(X0)) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | wise(X0) | ~tall(X0))) [flattening 56]
58. ! [X0] : (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~rich(X0) & ~kind(X0))) [nnf transformation 29]
59. (brave(susan) & quiet(susan)) | ! [X0] : ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))) [nnf transformation 30]
60. ! [X0] : (((wise(X0) | ~wise(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (~wise(X0) & wise(X0)))) [nnf transformation 12]
61. ! [X0] : ((wise(X0) | ~wise(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (~wise(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (~patient(X0) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) [nnf transformation 31]
63. ! [X0] : (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ~curious(X0) | ~strong(X0)) [nnf transformation 33]
80. ~quiet(X0) | funny(X0) [cnf transformation 26]
82. kind(X0) | funny(X0) [cnf transformation 26]
83. ~creative(X0) | kind(X0) [cnf transformation 26]
94. ~patient(alice) | ~tall(X1) [cnf transformation 55]
98. ~brave(X0) | wise(X0) | tall(X0) [cnf transformation 57]
102. strong(mary) | brave(X0) [cnf transformation 28]
105. ~kind(X0) | ~wise(X0) | quiet(X0) [cnf transformation 58]
107. quiet(susan) | creative(X0) | ~curious(X0) [cnf transformation 59]
113. patient(X0) | wise(X0) [cnf transformation 61]
114. ~wise(X0) | patient(X0) [cnf transformation 61]
117. ~patient(X0) | rich(X0) | ~funny(X0) [cnf transformation 62]
119. ~curious(X0) | ~kind(X0) | tall(X0) | ~strong(X0) [cnf transformation 63]
124. curious(mary) | ~strong(mary) [cnf transformation 18]
130. ~rich(susan) [cnf transformation 22]
207. 17 <=> patient(alice) [avatar definition]
208. ~patient(alice) <- (~17) [avatar component clause 207]
216. 19 <=> ! [X1] : ~tall(X1) [avatar definition]
217. ~tall(X1) <- (19) [avatar component clause 216]
218. 19 | ~17 [avatar split clause 94,207,216]
222. 20 <=> ! [X0] : brave(X0) [avatar definition]
223. brave(X0) <- (20) [avatar component clause 222]
225. 21 <=> strong(mary) [avatar definition]
227. strong(mary) <- (21) [avatar component clause 225]
228. 20 | 21 [avatar split clause 102,225,222]
238. 24 <=> ! [X0] : (creative(X0) | ~curious(X0)) [avatar definition]
239. ~curious(X0) | creative(X0) <- (24) [avatar component clause 238]
242. 25 <=> quiet(susan) [avatar definition]
244. quiet(susan) <- (25) [avatar component clause 242]
246. 24 | 25 [avatar split clause 107,242,238]
247. patient(X0) [subsumption resolution 113,114]
249. ~funny(X0) | rich(X0) [subsumption resolution 117,247]
279. 32 <=> curious(mary) [avatar definition]
281. curious(mary) <- (32) [avatar component clause 279]
282. ~21 | 32 [avatar split clause 124,279,225]
284. $false <- (~17) [subsumption resolution 208,247]
285. 17 [avatar contradiction clause 284]
311. creative(mary) <- (24, 32) [resolution 281,239]
313. kind(mary) <- (24, 32) [resolution 311,83]
323. ~wise(X0) | quiet(X0) | funny(X0) [resolution 105,82]
338. ~kind(mary) | tall(mary) | ~strong(mary) <- (32) [resolution 119,281]
339. tall(mary) | ~strong(mary) <- (24, 32) [subsumption resolution 338,313]
340. ~strong(mary) <- (19, 24, 32) [subsumption resolution 339,217]
341. $false <- (19, 21, 24, 32) [subsumption resolution 340,227]
342. ~19 | ~21 | ~24 | ~32 [avatar contradiction clause 341]
395. ~wise(X0) | funny(X0) [subsumption resolution 323,80]
413. wise(X0) | tall(X0) <- (20) [resolution 223,98]
416. wise(X0) <- (19, 20) [subsumption resolution 413,217]
417. funny(susan) <- (25) [resolution 244,80]
457. rich(susan) <- (25) [resolution 417,249]
458. $false <- (25) [subsumption resolution 457,130]
459. ~25 [avatar contradiction clause 458]
474. funny(X0) <- (19, 20) [resolution 395,416]
476. rich(X0) <- (19, 20) [resolution 474,249]
515. $false <- (19, 20) [resolution 476,130]
521. ~19 | ~20 [avatar contradiction clause 515]
523. $false [avatar sat refutation 218,228,246,282,285,342,459,521]
% SZS output end Proof for 5970113340438114033765268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is either not creative or tall then someone is either not creative or not rich and vice versa.
Everyone who is not wise or not creative is not brave and vice versa.
If mary is tall or not kind then fred is both old and not tall.
If someone is patient or happy then someone is either not quiet or creative.
Everyone who is either not humble or not happy is not creative and vice versa.
Everyone who is not curious or not happy is happy and vice versa.
If paul is either tall or not patient then john is either patient or not generous.
If someone is humble or generous then john is either quiet or brave.
Everyone who is either calm or not curious is either not humble or curious.
If someone is both not patient and old then someone is tall or not funny.
Everyone who is either brave or not wise is both humble and not patient and vice versa.
Everyone who is strong or not humble is either generous or wise and vice versa.
If someone is happy then someone is either humble or not brave.
If alice is both humble and tall then someone is either quiet or not funny and vice versa.
If someone is either not funny or kind then someone is humble.
If someone is not patient then someone is either rich or strong and vice versa.
Paul is both brave and old.
Mary is either not curious or curious.
Someone is both not curious and quiet.
John is either tall or calm.
Someone is either not humble or not curious.
Lucy is not calm.
Someone is not brave or not strong.
Paul is generous or not old. | Paul is creative. | entailment | (((~creative(paul)<~>tall(paul)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~wise(X)|~creative(X))<=>~brave(X)))&
(((tall(mary)|~kind(mary)))=>((old(fred)&~tall(fred))))&
((?[X]:((patient(X)|happy(X))))=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((~humble(X)<~>~happy(X))<=>~creative(X)))&
(![X]:((~curious(X)|~happy(X))<=>happy(X)))&
(((tall(paul)<~>~patient(paul)))=>((patient(john)<~>~generous(john))))&
((?[X]:((humble(X)|generous(X))))=>((quiet(john)<~>brave(john))))&
(![X]:((calm(X)<~>~curious(X))=>(~humble(X)<~>curious(X))))&
((?[X]:((~patient(X)&old(X))))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((brave(X)<~>~wise(X))<=>(humble(X)&~patient(X))))&
(![X]:((strong(X)|~humble(X))<=>(generous(X)<~>wise(X))))&
((?[X]:(happy(X)))=>(?[X]:((humble(X)<~>~brave(X)))))&
(((humble(alice)&tall(alice)))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
((?[X]:((~funny(X)<~>kind(X))))=>(?[X]:(humble(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((rich(X)<~>strong(X)))))&
((brave(paul)&old(paul)))&
((~curious(mary)<~>curious(mary)))&
(?[X]:((~curious(X)&quiet(X))))&
((tall(john)<~>calm(john)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(~calm(lucy))&
(?[X]:((~brave(X)|~strong(X))))&
((generous(paul)|~old(paul))) | creative(paul) | [
"p1",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1235727742394576233733149
% SZS output start Proof for 1235727742394576233733149
2. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> ~brave(X0)) [input p1]
17. old(paul) & brave(paul) [input p16]
25. ~creative(paul) [input hypothesis]
43. ! [X0] : (((~creative(X0) | ~wise(X0)) | brave(X0)) & (~brave(X0) | (creative(X0) & wise(X0)))) [nnf transformation 2]
44. ! [X0] : ((~creative(X0) | ~wise(X0) | brave(X0)) & (~brave(X0) | (creative(X0) & wise(X0)))) [flattening 43]
98. ~brave(X0) | creative(X0) [cnf transformation 44]
154. brave(paul) [cnf transformation 17]
167. ~creative(paul) [cnf transformation 25]
176. 2 <=> creative(paul) [avatar definition]
177. ~creative(paul) <- (~2) [avatar component clause 176]
397. ~2 [avatar split clause 167,176]
403. creative(paul) [resolution 98,154]
404. $false <- (~2) [subsumption resolution 403,177]
405. 2 [avatar contradiction clause 404]
406. $false [avatar sat refutation 397,405]
% SZS output end Proof for 1235727742394576233733149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not kind and not tall then fred is tall and vice versa. Everyone who is either kind or strong is not happy. Everyone who is humble or not brave is both wise and not brave and vice versa. If susan is old or tall then mary is quiet or not kind. Everyone who is wise or curious is either generous or not happy. If someone is either humble or not quiet then lucy is not curious. If someone is not generous then lucy is both not creative and kind and vice versa. Everyone who is not calm or not patient is either not generous or tall. Everyone who is not quiet is tall or not kind. If someone is either not old or quiet then alice is both not strong and not creative and vice versa. Everyone who is both humble and curious is either old or patient and vice versa. If paul is both not quiet and happy then susan is either patient or not old and vice versa. Everyone who is not calm or quiet is either not old or old and vice versa. If someone is humble then mary is brave. Everyone who is not wise or strong is either patient or creative and vice versa. Everyone who is not brave is both quiet and not creative. Someone is either not generous or kind. Susan is wise. Paul is humble. Someone is not calm. Someone is humble. Susan is both old and not strong. Someone is either happy or patient. Someone is both not curious and not wise. | Paul is happy. | neutral | ((?[X]:((~kind(X)&~tall(X))))<=>(tall(fred)))&
(![X]:((kind(X)<~>strong(X))=>~happy(X)))&
(![X]:((humble(X)|~brave(X))<=>(wise(X)&~brave(X))))&
(((old(susan)|tall(susan)))=>((quiet(mary)|~kind(mary))))&
(![X]:((wise(X)|curious(X))=>(generous(X)<~>~happy(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(~curious(lucy)))&
((?[X]:(~generous(X)))<=>((~creative(lucy)&kind(lucy))))&
(![X]:((~calm(X)|~patient(X))=>(~generous(X)<~>tall(X))))&
(![X]:(~quiet(X)=>(tall(X)|~kind(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((~strong(alice)&~creative(alice))))&
(![X]:((humble(X)&curious(X))<=>(old(X)<~>patient(X))))&
(((~quiet(paul)&happy(paul)))<=>((patient(susan)<~>~old(susan))))&
(![X]:((~calm(X)|quiet(X))<=>(~old(X)<~>old(X))))&
((?[X]:(humble(X)))=>(brave(mary)))&
(![X]:((~wise(X)|strong(X))<=>(patient(X)<~>creative(X))))&
(![X]:(~brave(X)=>(quiet(X)&~creative(X))))&
(?[X]:((~generous(X)<~>kind(X))))&
(wise(susan))&
(humble(paul))&
(?[X]:(~calm(X)))&
(?[X]:(humble(X)))&
((old(susan)&~strong(susan)))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~curious(X)&~wise(X)))) | happy(paul) | [] | null | 0 |
Everyone who is both patient and not generous is both quiet and not happy and vice versa.
Everyone who is both not patient and not kind is not strong and vice versa.
Everyone who is patient or rich is curious.
If paul is either kind or not tall then someone is both humble and not curious.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Everyone who is not rich or wise is not generous and vice versa.
If someone is quiet or not generous then alice is old and vice versa.
Everyone who is both funny and not kind is both not happy and old.
Everyone who is not creative is not brave and vice versa.
Someone is both not calm and not patient.
Susan is not humble.
Someone is both funny and humble.
Someone is both not wise and not curious.
Susan is tall or not curious.
Someone is both not patient and quiet.
Someone is either wise or patient.
Fred is both wise and quiet. | Paul is not rich. | neutral | (![X]:((patient(X)&~generous(X))<=>(quiet(X)&~happy(X))))&
(![X]:((~patient(X)&~kind(X))<=>~strong(X)))&
(![X]:((patient(X)|rich(X))=>curious(X)))&
(((kind(paul)<~>~tall(paul)))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(![X]:((~rich(X)|wise(X))<=>~generous(X)))&
((?[X]:((quiet(X)|~generous(X))))<=>(old(alice)))&
(![X]:((funny(X)&~kind(X))=>(~happy(X)&old(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(~humble(susan))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((tall(susan)|~curious(susan)))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((wise(X)<~>patient(X))))&
((wise(fred)&quiet(fred))) | ~rich(paul) | [] | null | 0 |
Everyone who is either not rich or not humble is both not old and not funny and vice versa. Everyone who is strong is both not calm and old. Everyone who is either brave or not kind is either not kind or quiet. Everyone who is not generous is either not happy or not quiet. If lucy is brave or not tall then someone is either humble or not patient and vice versa. If fred is both quiet and strong then someone is both strong and not creative. Everyone who is either not patient or curious is either humble or quiet and vice versa. If mary is either creative or not funny then john is both not calm and generous and vice versa. Everyone who is either funny or brave is either not quiet or funny and vice versa. If paul is both calm and not creative then mary is either tall or creative and vice versa. If susan is brave then john is either strong or not happy. If fred is either strong or not patient then someone is not creative and vice versa. Everyone who is quiet is either not calm or not rich and vice versa. Everyone who is either not rich or not creative is either not humble or not quiet. If someone is not kind or creative then susan is both not tall and quiet. Everyone who is not humble is either curious or rich. Someone is either not brave or not humble. Someone is funny. Someone is both funny and old. Someone is both not quiet and happy. Someone is generous or brave. Lucy is both not generous and patient. Someone is rich or not creative. | John is not quiet. | neutral | (![X]:((~rich(X)<~>~humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(strong(X)=>(~calm(X)&old(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~kind(X)<~>quiet(X))))&
(![X]:(~generous(X)=>(~happy(X)<~>~quiet(X))))&
(((brave(lucy)|~tall(lucy)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(((quiet(fred)&strong(fred)))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~patient(X)<~>curious(X))<=>(humble(X)<~>quiet(X))))&
(((creative(mary)<~>~funny(mary)))<=>((~calm(john)&generous(john))))&
(![X]:((funny(X)<~>brave(X))<=>(~quiet(X)<~>funny(X))))&
(((calm(paul)&~creative(paul)))<=>((tall(mary)<~>creative(mary))))&
((brave(susan))=>((strong(john)<~>~happy(john))))&
(((strong(fred)<~>~patient(fred)))<=>(?[X]:(~creative(X))))&
(![X]:(quiet(X)<=>(~calm(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>~creative(X))=>(~humble(X)<~>~quiet(X))))&
((?[X]:((~kind(X)|creative(X))))=>((~tall(susan)&quiet(susan))))&
(![X]:(~humble(X)=>(curious(X)<~>rich(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((generous(X)|brave(X))))&
((~generous(lucy)&patient(lucy)))&
(?[X]:((rich(X)|~creative(X)))) | ~quiet(john) | [] | null | 0 |
If someone is both not tall and strong then someone is either strong or funny.
Everyone who is not brave or funny is either not curious or not kind and vice versa.
If paul is wise then someone is not rich and vice versa.
Everyone who is both not calm and not patient is not generous or not strong and vice versa.
Everyone who is either not kind or not generous is either not creative or curious and vice versa.
Everyone who is wise is either creative or patient.
Everyone who is wise or kind is not humble.
If paul is either not kind or curious then someone is not calm and vice versa.
Everyone who is not calm or not creative is both creative and strong and vice versa.
If john is funny or not calm then alice is either not happy or not humble.
Everyone who is strong is both humble and not old and vice versa.
If someone is either patient or not kind then someone is calm or not calm and vice versa.
If someone is creative or calm then someone is happy.
If fred is not patient then someone is both not generous and not patient and vice versa.
Everyone who is either not old or rich is either patient or not creative and vice versa.
Someone is rich.
Mary is rich.
Someone is tall or strong.
Mary is patient or creative.
Someone is quiet. | Paul is not funny. | entailment | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~brave(X)|funny(X))<=>(~curious(X)<~>~kind(X))))&
((wise(paul))<=>(?[X]:(~rich(X))))&
(![X]:((~calm(X)&~patient(X))<=>(~generous(X)|~strong(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~creative(X)<~>curious(X))))&
(![X]:(wise(X)=>(creative(X)<~>patient(X))))&
(![X]:((wise(X)|kind(X))=>~humble(X)))&
(((~kind(paul)<~>curious(paul)))<=>(?[X]:(~calm(X))))&
(![X]:((~calm(X)|~creative(X))<=>(creative(X)&strong(X))))&
(((funny(john)|~calm(john)))=>((~happy(alice)<~>~humble(alice))))&
(![X]:(strong(X)<=>(humble(X)&~old(X))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:((calm(X)|~calm(X)))))&
((?[X]:((creative(X)|calm(X))))=>(?[X]:(happy(X))))&
((~patient(fred))<=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(patient(X)<~>~creative(X))))&
(?[X]:(rich(X)))&
(rich(mary))&
(?[X]:((tall(X)|strong(X))))&
((patient(mary)|creative(mary)))&
(?[X]:(quiet(X))) | ~funny(paul) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3402359630861315381227031
% SZS output start Proof for 3402359630861315381227031
2. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (~curious(X0) <~> ~kind(X0))) [input p1]
4. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (~strong(X0) | ~generous(X0))) [input p3]
7. ! [X0] : ((kind(X0) | wise(X0)) => ~humble(X0)) [input p6]
8. (~kind(paul) <~> curious(paul)) <=> ? [X0] : ~calm(X0) [input p7]
9. ! [X0] : ((~creative(X0) | ~calm(X0)) <=> (strong(X0) & creative(X0))) [input p8]
11. ! [X0] : (strong(X0) <=> (~old(X0) & humble(X0))) [input p10]
21. funny(paul) [input hypothesis]
29. ! [X0] : (~humble(X0) | (~kind(X0) & ~wise(X0))) [ennf transformation 7]
32. ! [X0] : (((funny(X0) | ~brave(X0)) | ((~curious(X0) | kind(X0)) & (~kind(X0) | curious(X0)))) & (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 2]
33. ! [X0] : ((funny(X0) | ~brave(X0) | ((~curious(X0) | kind(X0)) & (~kind(X0) | curious(X0)))) & (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | (~funny(X0) & brave(X0)))) [flattening 32]
38. ! [X0] : (((~patient(X0) & ~calm(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (patient(X0) | calm(X0)))) [nnf transformation 4]
39. ! [X0] : (((~patient(X0) & ~calm(X0)) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | patient(X0) | calm(X0))) [flattening 38]
42. (((~curious(paul) | kind(paul)) & (curious(paul) | ~kind(paul))) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ((~kind(paul) | ~curious(paul)) & (curious(paul) | kind(paul)))) [nnf transformation 8]
43. (((~curious(paul) | kind(paul)) & (curious(paul) | ~kind(paul))) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ((~kind(paul) | ~curious(paul)) & (curious(paul) | kind(paul)))) [rectify 42]
44. ? [X1] : ~calm(X1) => ~calm(sK1) [choice axiom]
45. (((~curious(paul) | kind(paul)) & (curious(paul) | ~kind(paul))) | ! [X0] : calm(X0)) & (~calm(sK1) | ((~kind(paul) | ~curious(paul)) & (curious(paul) | kind(paul)))) [skolemisation 43,44]
46. ! [X0] : (((~creative(X0) | ~calm(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (creative(X0) & calm(X0)))) [nnf transformation 9]
47. ! [X0] : ((~creative(X0) | ~calm(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (creative(X0) & calm(X0)))) [flattening 46]
49. ! [X0] : ((strong(X0) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 11]
50. ! [X0] : ((strong(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | ~strong(X0))) [flattening 49]
69. ~funny(X0) | curious(X0) | kind(X0) [cnf transformation 33]
76. ~calm(X0) | strong(X0) [cnf transformation 39]
90. ~humble(X0) | ~kind(X0) [cnf transformation 29]
94. ~curious(paul) | kind(paul) | calm(X0) [cnf transformation 45]
96. creative(X0) | creative(X0) [cnf transformation 47]
97. strong(X0) | calm(X0) [cnf transformation 47]
99. ~creative(X0) | ~calm(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 47]
104. humble(X0) | ~strong(X0) [cnf transformation 50]
129. funny(paul) [cnf transformation 21]
130. creative(X0) [duplicate literal removal 96]
131. ~creative(X0) | ~calm(X0) | ~strong(X0) [duplicate literal removal 99]
146. 4 <=> ! [X0] : calm(X0) [avatar definition]
147. calm(X0) <- (4) [avatar component clause 146]
149. 5 <=> kind(paul) [avatar definition]
150. ~kind(paul) <- (~5) [avatar component clause 149]
151. kind(paul) <- (5) [avatar component clause 149]
153. 6 <=> curious(paul) [avatar definition]
156. 4 | 5 | ~6 [avatar split clause 94,153,149,146]
164. ~creative(X0) | ~calm(X0) [subsumption resolution 131,76]
165. strong(X0) [subsumption resolution 97,76]
187. humble(X0) [subsumption resolution 104,165]
198. 14 <=> ! [X1] : ~calm(X1) [avatar definition]
199. ~calm(X1) <- (14) [avatar component clause 198]
242. ~kind(X0) [resolution 90,187]
244. ~calm(X1) [resolution 164,130]
245. 14 [avatar split clause 244,198]
273. curious(paul) | kind(paul) [resolution 69,129]
277. curious(paul) <- (~5) [subsumption resolution 273,150]
278. 6 | 5 [avatar split clause 277,149,153]
279. $false <- (4, 14) [subsumption resolution 147,199]
280. ~4 | ~14 [avatar contradiction clause 279]
281. $false <- (5) [subsumption resolution 151,242]
282. ~5 [avatar contradiction clause 281]
283. $false [avatar sat refutation 156,245,278,280,282]
% SZS output end Proof for 3402359630861315381227031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both happy and not wise and vice versa.
Everyone who is both kind and not creative is not calm and vice versa.
Everyone who is not patient or quiet is both rich and generous.
If john is either brave or not calm then alice is either old or not brave.
Everyone who is humble or tall is quiet or not humble and vice versa.
Everyone who is either not rich or not tall is either not wise or not tall and vice versa.
Everyone who is creative is either happy or calm.
If lucy is not strong then alice is both not creative and not wise and vice versa.
If someone is both creative and quiet then someone is both not calm and calm.
If someone is either humble or happy then someone is both not quiet and happy and vice versa.
Everyone who is either kind or funny is quiet or not generous and vice versa.
Everyone who is either old or not humble is either brave or not old.
Everyone who is both not brave and tall is calm.
Everyone who is creative is either not calm or quiet.
Everyone who is not calm is both tall and not brave.
Mary is both old and calm.
Someone is either not funny or wise.
Paul is not humble.
Someone is not strong or funny. | Lucy is tall. | entailment | (![X]:(wise(X)<=>(happy(X)&~wise(X))))&
(![X]:((kind(X)&~creative(X))<=>~calm(X)))&
(![X]:((~patient(X)|quiet(X))=>(rich(X)&generous(X))))&
(((brave(john)<~>~calm(john)))=>((old(alice)<~>~brave(alice))))&
(![X]:((humble(X)|tall(X))<=>(quiet(X)|~humble(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:(creative(X)=>(happy(X)<~>calm(X))))&
((~strong(lucy))<=>((~creative(alice)&~wise(alice))))&
((?[X]:((creative(X)&quiet(X))))=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:((humble(X)<~>happy(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
(![X]:((kind(X)<~>funny(X))<=>(quiet(X)|~generous(X))))&
(![X]:((old(X)<~>~humble(X))=>(brave(X)<~>~old(X))))&
(![X]:((~brave(X)&tall(X))=>calm(X)))&
(![X]:(creative(X)=>(~calm(X)<~>quiet(X))))&
(![X]:(~calm(X)=>(tall(X)&~brave(X))))&
((old(mary)&calm(mary)))&
(?[X]:((~funny(X)<~>wise(X))))&
(~humble(paul))&
(?[X]:((~strong(X)|funny(X)))) | tall(lucy) | [
"p0",
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1545327955484909414772898
% SZS output start Proof for 1545327955484909414772898
1. ! [X0] : (wise(X0) <=> (~wise(X0) & happy(X0))) [input p0]
3. ! [X0] : ((quiet(X0) | ~patient(X0)) => (generous(X0) & rich(X0))) [input p2]
5. ! [X0] : ((tall(X0) | humble(X0)) <=> (~humble(X0) | quiet(X0))) [input p4]
6. ! [X0] : ((~rich(X0) <~> ~tall(X0)) <=> (~wise(X0) <~> ~tall(X0))) [input p5]
20. ~tall(lucy) [input hypothesis]
23. ! [X0] : (quiet(X0) => (generous(X0) & rich(X0))) [pure predicate removal 3]
24. ! [X0] : ((generous(X0) & rich(X0)) | ~quiet(X0)) [ennf transformation 23]
33. ! [X0] : ((wise(X0) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | ~wise(X0))) [nnf transformation 1]
34. ! [X0] : ((wise(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ~wise(X0))) [flattening 33]
38. ! [X0] : (((tall(X0) | humble(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (~tall(X0) & ~humble(X0)))) [nnf transformation 5]
39. ! [X0] : ((tall(X0) | humble(X0) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | (~tall(X0) & ~humble(X0)))) [flattening 38]
40. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [nnf transformation 6]
62. ~wise(X0) | ~wise(X0) [cnf transformation 34]
67. ~quiet(X0) | rich(X0) [cnf transformation 24]
73. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 39]
76. tall(X0) | humble(X0) | humble(X0) [cnf transformation 39]
80. tall(X0) | wise(X0) | ~rich(X0) | tall(X0) [cnf transformation 40]
81. ~tall(X0) | ~rich(X0) | ~tall(X0) | wise(X0) [cnf transformation 40]
119. ~tall(lucy) [cnf transformation 20]
123. tall(X0) | wise(X0) | ~rich(X0) [duplicate literal removal 80]
124. ~tall(X0) | ~rich(X0) | wise(X0) [duplicate literal removal 81]
126. ~humble(X0) | quiet(X0) [duplicate literal removal 73]
127. tall(X0) | humble(X0) [duplicate literal removal 76]
128. ~wise(X0) [duplicate literal removal 62]
150. ~tall(X0) | ~rich(X0) [subsumption resolution 124,128]
151. tall(X0) | ~rich(X0) [subsumption resolution 123,128]
152. ~rich(X0) [subsumption resolution 151,150]
219. humble(lucy) [resolution 127,119]
225. quiet(lucy) [resolution 219,126]
227. rich(lucy) [resolution 225,67]
228. $false [subsumption resolution 227,152]
% SZS output end Proof for 1545327955484909414772898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not old and brave then lucy is both not funny and patient and vice versa. Everyone who is not brave is quiet or wise and vice versa. If someone is either not happy or not creative then alice is either not old or humble. If someone is wise or brave then someone is both old and not wise and vice versa. Everyone who is old or funny is quiet or kind. Everyone who is either strong or calm is generous. If mary is not happy then mary is quiet or not curious. Everyone who is both not calm and generous is either calm or generous and vice versa. Everyone who is either strong or creative is rich. Everyone who is not happy is both not wise and not kind and vice versa. Everyone who is not rich is either tall or quiet and vice versa. If someone is both not kind and brave then someone is happy or not strong. Everyone who is both not patient and not happy is not calm and vice versa. If someone is both funny and not rich then lucy is strong or not happy and vice versa. If susan is calm or not old then mary is humble. Everyone who is both funny and generous is funny or happy. Paul is rich or not curious. Lucy is not humble or curious. Lucy is both not funny and not tall. Someone is old. Someone is wise or not generous. Lucy is both not kind and happy. Someone is patient or not rich. | Lucy is not brave. | entailment | (((~old(alice)&brave(alice)))<=>((~funny(lucy)&patient(lucy))))&
(![X]:(~brave(X)<=>(quiet(X)|wise(X))))&
((?[X]:((~happy(X)<~>~creative(X))))=>((~old(alice)<~>humble(alice))))&
((?[X]:((wise(X)|brave(X))))<=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((old(X)|funny(X))=>(quiet(X)|kind(X))))&
(![X]:((strong(X)<~>calm(X))=>generous(X)))&
((~happy(mary))=>((quiet(mary)|~curious(mary))))&
(![X]:((~calm(X)&generous(X))<=>(calm(X)<~>generous(X))))&
(![X]:((strong(X)<~>creative(X))=>rich(X)))&
(![X]:(~happy(X)<=>(~wise(X)&~kind(X))))&
(![X]:(~rich(X)<=>(tall(X)<~>quiet(X))))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((happy(X)|~strong(X)))))&
(![X]:((~patient(X)&~happy(X))<=>~calm(X)))&
((?[X]:((funny(X)&~rich(X))))<=>((strong(lucy)|~happy(lucy))))&
(((calm(susan)|~old(susan)))=>(humble(mary)))&
(![X]:((funny(X)&generous(X))=>(funny(X)|happy(X))))&
((rich(paul)|~curious(paul)))&
((~humble(lucy)|curious(lucy)))&
((~funny(lucy)&~tall(lucy)))&
(?[X]:(old(X)))&
(?[X]:((wise(X)|~generous(X))))&
((~kind(lucy)&happy(lucy)))&
(?[X]:((patient(X)|~rich(X)))) | ~brave(lucy) | [
"p1",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4364370712055895831407466
% SZS output start Proof for 4364370712055895831407466
2. ! [X0] : (~brave(X0) <=> (wise(X0) | quiet(X0))) [input p1]
10. ! [X0] : (~happy(X0) <=> (~kind(X0) & ~wise(X0))) [input p9]
22. happy(lucy) & ~kind(lucy) [input p21]
24. brave(lucy) [input hypothesis]
40. ! [X0] : ((~brave(X0) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | brave(X0))) [nnf transformation 2]
41. ! [X0] : ((~brave(X0) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | brave(X0))) [flattening 40]
52. ! [X0] : ((~happy(X0) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 10]
53. ! [X0] : ((~happy(X0) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | happy(X0))) [flattening 52]
77. ~wise(X0) | ~brave(X0) [cnf transformation 41]
102. ~happy(X0) | kind(X0) | wise(X0) [cnf transformation 53]
125. ~kind(lucy) [cnf transformation 22]
126. happy(lucy) [cnf transformation 22]
128. brave(lucy) [cnf transformation 24]
223. 21 <=> happy(lucy) [avatar definition]
225. happy(lucy) <- (21) [avatar component clause 223]
288. 21 [avatar split clause 126,223]
368. kind(lucy) | wise(lucy) <- (21) [resolution 102,225]
370. wise(lucy) <- (21) [subsumption resolution 368,125]
393. ~brave(lucy) <- (21) [resolution 370,77]
394. $false <- (21) [subsumption resolution 393,128]
395. ~21 [avatar contradiction clause 394]
396. $false [avatar sat refutation 288,395]
% SZS output end Proof for 4364370712055895831407466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or happy is either patient or rich. If someone is either not brave or brave then someone is not quiet. If john is creative or quiet then someone is either not curious or not funny. Everyone who is wise or not quiet is either curious or not curious. Everyone who is old is not wise and vice versa. Everyone who is creative is either not curious or not kind and vice versa. Everyone who is either not generous or creative is either not creative or not strong and vice versa. If paul is not strong or curious then someone is either not tall or patient. Everyone who is not curious is not patient or not wise. Everyone who is both not old and generous is funny or patient and vice versa. If someone is both funny and not funny then john is not kind. If alice is humble or generous then someone is either not generous or not wise and vice versa. If mary is both not funny and curious then alice is either rich or not calm and vice versa. Everyone who is creative is both not creative and humble. Everyone who is not brave or wise is both wise and not generous and vice versa. Everyone who is humble or brave is not brave or not tall and vice versa. Someone is either old or calm. Lucy is not quiet or not funny. Someone is either not rich or not happy. Someone is either happy or not calm. Lucy is not brave. Paul is not quiet or kind. Susan is either not strong or tall. | John is calm. | neutral | (![X]:((~curious(X)|happy(X))=>(patient(X)<~>rich(X))))&
((?[X]:((~brave(X)<~>brave(X))))=>(?[X]:(~quiet(X))))&
(((creative(john)|quiet(john)))=>(?[X]:((~curious(X)<~>~funny(X)))))&
(![X]:((wise(X)|~quiet(X))=>(curious(X)<~>~curious(X))))&
(![X]:(old(X)<=>~wise(X)))&
(![X]:(creative(X)<=>(~curious(X)<~>~kind(X))))&
(![X]:((~generous(X)<~>creative(X))<=>(~creative(X)<~>~strong(X))))&
(((~strong(paul)|curious(paul)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:(~curious(X)=>(~patient(X)|~wise(X))))&
(![X]:((~old(X)&generous(X))<=>(funny(X)|patient(X))))&
((?[X]:((funny(X)&~funny(X))))=>(~kind(john)))&
(((humble(alice)|generous(alice)))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
(((~funny(mary)&curious(mary)))<=>((rich(alice)<~>~calm(alice))))&
(![X]:(creative(X)=>(~creative(X)&humble(X))))&
(![X]:((~brave(X)|wise(X))<=>(wise(X)&~generous(X))))&
(![X]:((humble(X)|brave(X))<=>(~brave(X)|~tall(X))))&
(?[X]:((old(X)<~>calm(X))))&
((~quiet(lucy)|~funny(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((happy(X)<~>~calm(X))))&
(~brave(lucy))&
((~quiet(paul)|kind(paul)))&
((~strong(susan)<~>tall(susan))) | calm(john) | [] | null | 0 |
Everyone who is either not old or not patient is wise or not happy.
Everyone who is happy is not generous and vice versa.
Everyone who is not quiet is either not happy or not calm.
Everyone who is wise is humble or quiet and vice versa.
If someone is not creative then someone is not happy or not kind and vice versa.
If john is curious then someone is both not happy and calm and vice versa.
If fred is old or quiet then fred is either happy or not happy and vice versa.
Everyone who is either curious or wise is both calm and not rich.
Everyone who is either not wise or tall is generous and vice versa.
If someone is not tall then alice is either quiet or generous.
If someone is either not brave or tall then paul is generous or creative and vice versa.
Everyone who is not happy or not curious is humble and vice versa.
If mary is not funny then someone is funny.
If lucy is either calm or not creative then someone is not happy and vice versa.
Everyone who is happy is not kind or not rich.
If susan is wise then john is both not rich and not tall.
Someone is creative.
Mary is either creative or humble.
Lucy is either strong or curious.
Mary is either quiet or brave.
Alice is strong.
Someone is either not humble or not funny.
Paul is both not patient and kind.
Fred is not rich. | John is wise. | entailment | (![X]:((~old(X)<~>~patient(X))=>(wise(X)|~happy(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:(~quiet(X)=>(~happy(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(humble(X)|quiet(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~happy(X)|~kind(X)))))&
((curious(john))<=>(?[X]:((~happy(X)&calm(X)))))&
(((old(fred)|quiet(fred)))<=>((happy(fred)<~>~happy(fred))))&
(![X]:((curious(X)<~>wise(X))=>(calm(X)&~rich(X))))&
(![X]:((~wise(X)<~>tall(X))<=>generous(X)))&
((?[X]:(~tall(X)))=>((quiet(alice)<~>generous(alice))))&
((?[X]:((~brave(X)<~>tall(X))))<=>((generous(paul)|creative(paul))))&
(![X]:((~happy(X)|~curious(X))<=>humble(X)))&
((~funny(mary))=>(?[X]:(funny(X))))&
(((calm(lucy)<~>~creative(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:(happy(X)=>(~kind(X)|~rich(X))))&
((wise(susan))=>((~rich(john)&~tall(john))))&
(?[X]:(creative(X)))&
((creative(mary)<~>humble(mary)))&
((strong(lucy)<~>curious(lucy)))&
((quiet(mary)<~>brave(mary)))&
(strong(alice))&
(?[X]:((~humble(X)<~>~funny(X))))&
((~patient(paul)&kind(paul)))&
(~rich(fred)) | wise(john) | [
"p2",
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7009015599340241254531001
% SZS output start Proof for 7009015599340241254531001
3. ! [X0] : (~quiet(X0) => (~happy(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> (quiet(X0) | humble(X0))) [input p3]
8. ! [X0] : ((curious(X0) <~> wise(X0)) => (~rich(X0) & calm(X0))) [input p7]
12. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> humble(X0)) [input p11]
25. ~wise(john) [input hypothesis]
27. ! [X0] : ((curious(X0) <~> wise(X0)) => calm(X0)) [pure predicate removal 8]
33. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | quiet(X0)) [ennf transformation 3]
34. ! [X0] : (calm(X0) | (curious(X0) <=> wise(X0))) [ennf transformation 27]
40. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | quiet(X0)) [nnf transformation 33]
41. ! [X0] : ((wise(X0) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | ~wise(X0))) [nnf transformation 4]
42. ! [X0] : ((wise(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ~wise(X0))) [flattening 41]
54. ! [X0] : (calm(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) [nnf transformation 34]
62. ! [X0] : (((~curious(X0) | ~happy(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & happy(X0)))) [nnf transformation 12]
63. ! [X0] : ((~curious(X0) | ~happy(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & happy(X0)))) [flattening 62]
82. ~calm(X0) | ~happy(X0) | quiet(X0) [cnf transformation 40]
85. ~humble(X0) | wise(X0) [cnf transformation 42]
86. ~quiet(X0) | wise(X0) [cnf transformation 42]
99. ~curious(X0) | wise(X0) | calm(X0) [cnf transformation 54]
113. humble(X0) | happy(X0) [cnf transformation 63]
114. curious(X0) | humble(X0) [cnf transformation 63]
134. ~wise(john) [cnf transformation 25]
316. happy(X0) | wise(X0) [resolution 113,85]
347. wise(X0) | calm(X0) | humble(X0) [resolution 99,114]
349. calm(X0) | wise(X0) [subsumption resolution 347,85]
491. wise(X0) | ~happy(X0) | quiet(X0) [resolution 349,82]
492. wise(X0) | quiet(X0) [subsumption resolution 491,316]
493. wise(X0) [subsumption resolution 492,86]
559. $false [resolution 493,134]
% SZS output end Proof for 7009015599340241254531001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not funny is either generous or funny and vice versa.
If someone is not kind or curious then fred is not wise and vice versa.
If lucy is creative then susan is both not quiet and not rich and vice versa.
If john is tall then alice is either curious or not patient.
If someone is either rich or wise then someone is both old and quiet and vice versa.
Everyone who is either tall or happy is either not creative or not happy.
Everyone who is either patient or not generous is both not patient and not rich and vice versa.
Everyone who is either not tall or happy is both happy and wise.
If someone is both not tall and creative then someone is funny and vice versa.
Everyone who is either curious or not old is not rich or not generous and vice versa.
Everyone who is either quiet or generous is both tall and old and vice versa.
If someone is not kind or not generous then fred is either kind or brave.
If susan is not funny then mary is both old and not tall and vice versa.
Everyone who is both not generous and not tall is not kind or quiet and vice versa.
If mary is not patient then someone is either brave or strong and vice versa.
If paul is strong or brave then mary is both not creative and humble and vice versa.
Someone is not brave.
Someone is funny or happy.
Alice is not calm.
Susan is either not happy or not calm.
Someone is both not funny and creative.
Lucy is not happy or not funny.
Someone is either kind or not happy.
John is wise or not quiet. | Fred is not curious. | entailment | (![X]:((brave(X)&~funny(X))<=>(generous(X)<~>funny(X))))&
((?[X]:((~kind(X)|curious(X))))<=>(~wise(fred)))&
((creative(lucy))<=>((~quiet(susan)&~rich(susan))))&
((tall(john))=>((curious(alice)<~>~patient(alice))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((tall(X)<~>happy(X))=>(~creative(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~patient(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))=>(happy(X)&wise(X))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:(funny(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(tall(X)&old(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((kind(fred)<~>brave(fred))))&
((~funny(susan))<=>((old(mary)&~tall(mary))))&
(![X]:((~generous(X)&~tall(X))<=>(~kind(X)|quiet(X))))&
((~patient(mary))<=>(?[X]:((brave(X)<~>strong(X)))))&
(((strong(paul)|brave(paul)))<=>((~creative(mary)&humble(mary))))&
(?[X]:(~brave(X)))&
(?[X]:((funny(X)|happy(X))))&
(~calm(alice))&
((~happy(susan)<~>~calm(susan)))&
(?[X]:((~funny(X)&creative(X))))&
((~happy(lucy)|~funny(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
((wise(john)|~quiet(john))) | ~curious(fred) | [
"p0",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8411986504089727022299392
% SZS output start Proof for 8411986504089727022299392
1. ! [X0] : ((~funny(X0) & brave(X0)) <=> (generous(X0) <~> funny(X0))) [input p0]
5. ? [X0] : (rich(X0) <~> wise(X0)) <=> ? [X0] : (quiet(X0) & old(X0)) [input p4]
6. ! [X0] : ((tall(X0) <~> happy(X0)) => (~creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) <~> happy(X0)) => (wise(X0) & happy(X0))) [input p7]
9. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X0] : funny(X0) [input p8]
10. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> (~generous(X0) | ~rich(X0))) [input p9]
11. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (old(X0) & tall(X0))) [input p10]
12. ? [X0] : (~generous(X0) | ~kind(X0)) => (kind(fred) <~> brave(fred)) [input p11]
14. ! [X0] : ((~tall(X0) & ~generous(X0)) <=> (quiet(X0) | ~kind(X0))) [input p13]
17. ? [X0] : ~brave(X0) [input p16]
25. curious(fred) [input hypothesis]
26. ? [X0] : (rich(X0) <~> wise(X0)) <=> ? [X1] : (quiet(X1) & old(X1)) [rectify 5]
27. ? [X0] : (creative(X0) & ~tall(X0)) <=> ? [X1] : funny(X1) [rectify 9]
29. ! [X0] : ((~creative(X0) <~> ~happy(X0)) | (tall(X0) <=> happy(X0))) [ennf transformation 6]
30. ! [X0] : ((wise(X0) & happy(X0)) | (~tall(X0) <=> happy(X0))) [ennf transformation 8]
31. (kind(fred) <~> brave(fred)) | ! [X0] : (generous(X0) & kind(X0)) [ennf transformation 12]
32. ! [X0] : (((~funny(X0) & brave(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) & (((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (funny(X0) | ~brave(X0)))) [nnf transformation 1]
33. ! [X0] : (((~funny(X0) & brave(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) & (((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | funny(X0) | ~brave(X0))) [flattening 32]
41. (? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | ! [X1] : (~quiet(X1) | ~old(X1))) & (? [X1] : (quiet(X1) & old(X1)) | ! [X0] : ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0)))) [nnf transformation 26]
42. (? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | ! [X1] : (~quiet(X1) | ~old(X1))) & (? [X2] : (quiet(X2) & old(X2)) | ! [X3] : ((rich(X3) | ~wise(X3)) & (wise(X3) | ~rich(X3)))) [rectify 41]
43. ? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) => ((~wise(sK1) | ~rich(sK1)) & (wise(sK1) | rich(sK1))) [choice axiom]
44. ? [X2] : (quiet(X2) & old(X2)) => (quiet(sK2) & old(sK2)) [choice axiom]
45. (((~wise(sK1) | ~rich(sK1)) & (wise(sK1) | rich(sK1))) | ! [X1] : (~quiet(X1) | ~old(X1))) & ((quiet(sK2) & old(sK2)) | ! [X3] : ((rich(X3) | ~wise(X3)) & (wise(X3) | ~rich(X3)))) [skolemisation 42,44,43]
46. ! [X0] : (((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) [nnf transformation 29]
49. ! [X0] : ((wise(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) [nnf transformation 30]
50. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : (~creative(X0) | tall(X0))) [nnf transformation 27]
51. (? [X0] : (creative(X0) & ~tall(X0)) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : (~creative(X3) | tall(X3))) [rectify 50]
52. ? [X0] : (creative(X0) & ~tall(X0)) => (creative(sK3) & ~tall(sK3)) [choice axiom]
53. ? [X2] : funny(X2) => funny(sK4) [choice axiom]
54. ((creative(sK3) & ~tall(sK3)) | ! [X1] : ~funny(X1)) & (funny(sK4) | ! [X3] : (~creative(X3) | tall(X3))) [skolemisation 51,53,52]
55. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 10]
56. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [flattening 55]
57. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 11]
58. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 57]
59. ((~brave(fred) | ~kind(fred)) & (brave(fred) | kind(fred))) | ! [X0] : (generous(X0) & kind(X0)) [nnf transformation 31]
62. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (tall(X0) | generous(X0)))) [nnf transformation 14]
63. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | tall(X0) | generous(X0))) [flattening 62]
70. ? [X0] : ~brave(X0) => ~brave(sK6) [choice axiom]
71. ~brave(sK6) [skolemisation 17,70]
80. funny(X0) | generous(X0) | funny(X0) | ~brave(X0) [cnf transformation 33]
82. ~generous(X0) | funny(X0) | brave(X0) [cnf transformation 33]
85. ~funny(X0) | generous(X0) | ~funny(X0) [cnf transformation 33]
96. quiet(sK2) | wise(X3) | ~rich(X3) [cnf transformation 45]
97. quiet(sK2) | rich(X3) | ~wise(X3) [cnf transformation 45]
98. wise(sK1) | rich(sK1) | ~quiet(X1) | ~old(X1) [cnf transformation 45]
99. ~wise(sK1) | ~rich(sK1) | ~quiet(X1) | ~old(X1) [cnf transformation 45]
101. ~happy(X0) | ~creative(X0) | tall(X0) | ~happy(X0) [cnf transformation 46]
110. happy(X0) | happy(X0) | tall(X0) [cnf transformation 49]
115. ~tall(sK3) | ~funny(X1) [cnf transformation 54]
116. creative(sK3) | ~funny(X1) [cnf transformation 54]
122. ~curious(X0) | old(X0) | generous(X0) [cnf transformation 56]
123. ~quiet(X0) | generous(X0) | tall(X0) [cnf transformation 58]
127. ~old(X0) | quiet(X0) | generous(X0) | ~tall(X0) [cnf transformation 58]
129. brave(fred) | kind(fred) | kind(X0) [cnf transformation 59]
132. ~brave(fred) | ~kind(fred) | generous(X0) [cnf transformation 59]
136. quiet(X0) | ~kind(X0) | tall(X0) | generous(X0) [cnf transformation 63]
137. ~generous(X0) | kind(X0) [cnf transformation 63]
138. ~quiet(X0) | ~generous(X0) [cnf transformation 63]
140. ~tall(X0) | ~quiet(X0) [cnf transformation 63]
150. ~brave(sK6) [cnf transformation 71]
161. curious(fred) [cnf transformation 25]
162. happy(X0) | tall(X0) [duplicate literal removal 110]
165. ~happy(X0) | ~creative(X0) | tall(X0) [duplicate literal removal 101]
167. funny(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 80]
168. ~funny(X0) | generous(X0) [duplicate literal removal 85]
169. ~brave(X0) | generous(X0) [subsumption resolution 167,168]
188. 5 <=> ! [X1] : kind(X1) [avatar definition]
189. kind(X1) <- (5) [avatar component clause 188]
221. 12 <=> ! [X1] : (~quiet(X1) | ~old(X1)) [avatar definition]
222. ~old(X1) | ~quiet(X1) <- (12) [avatar component clause 221]
224. 13 <=> rich(sK1) [avatar definition]
225. rich(sK1) <- (13) [avatar component clause 224]
228. 14 <=> wise(sK1) [avatar definition]
229. wise(sK1) <- (14) [avatar component clause 228]
230. ~wise(sK1) <- (~14) [avatar component clause 228]
231. 12 | ~13 | ~14 [avatar split clause 99,228,224,221]
232. 12 | 13 | 14 [avatar split clause 98,228,224,221]
234. 15 <=> ! [X3] : (rich(X3) | ~wise(X3)) [avatar definition]
235. ~wise(X3) | rich(X3) <- (15) [avatar component clause 234]
237. 16 <=> quiet(sK2) [avatar definition]
239. quiet(sK2) <- (16) [avatar component clause 237]
240. 15 | 16 [avatar split clause 97,237,234]
242. 17 <=> ! [X3] : (wise(X3) | ~rich(X3)) [avatar definition]
243. ~rich(X3) | wise(X3) <- (17) [avatar component clause 242]
244. 17 | 16 [avatar split clause 96,237,242]
252. 19 <=> ! [X1] : ~funny(X1) [avatar definition]
253. ~funny(X1) <- (19) [avatar component clause 252]
255. 20 <=> creative(sK3) [avatar definition]
257. creative(sK3) <- (20) [avatar component clause 255]
258. 19 | 20 [avatar split clause 116,255,252]
260. 21 <=> tall(sK3) [avatar definition]
262. ~tall(sK3) <- (~21) [avatar component clause 260]
263. 19 | ~21 [avatar split clause 115,260,252]
265. 22 <=> ! [X3] : (~creative(X3) | tall(X3)) [avatar definition]
266. ~creative(X3) | tall(X3) <- (22) [avatar component clause 265]
273. 24 <=> ! [X0] : generous(X0) [avatar definition]
274. generous(X0) <- (24) [avatar component clause 273]
276. 25 <=> kind(fred) [avatar definition]
277. kind(fred) <- (25) [avatar component clause 276]
278. ~kind(fred) <- (~25) [avatar component clause 276]
280. 26 <=> brave(fred) [avatar definition]
281. brave(fred) <- (26) [avatar component clause 280]
282. ~brave(fred) <- (~26) [avatar component clause 280]
283. 24 | ~25 | ~26 [avatar split clause 132,280,276,273]
286. 5 | 25 | 26 [avatar split clause 129,280,276,188]
302. ~kind(X0) | tall(X0) | generous(X0) [subsumption resolution 136,123]
413. tall(sK3) <- (20, 22) [resolution 266,257]
414. $false <- (20, ~21, 22) [subsumption resolution 413,262]
415. ~20 | 21 | ~22 [avatar contradiction clause 414]
478. 57 <=> old(fred) [avatar definition]
480. old(fred) <- (57) [avatar component clause 478]
482. old(fred) | generous(fred) [resolution 122,161]
484. 58 <=> generous(fred) [avatar definition]
486. generous(fred) <- (58) [avatar component clause 484]
487. 58 | 57 [avatar split clause 482,478,484]
566. ~creative(X1) | tall(X1) | tall(X1) [resolution 165,162]
568. ~creative(X1) | tall(X1) [duplicate literal removal 566]
577. tall(fred) | generous(fred) <- (25) [resolution 302,277]
581. 67 <=> tall(fred) [avatar definition]
583. tall(fred) <- (67) [avatar component clause 581]
584. 58 | 67 | ~25 [avatar split clause 577,276,581,484]
587. generous(fred) <- (26) [resolution 281,169]
588. 58 | ~26 [avatar split clause 587,280,484]
608. generous(sK2) | tall(sK2) <- (16) [resolution 239,123]
609. ~generous(sK2) <- (16) [resolution 239,138]
611. 70 <=> tall(sK2) [avatar definition]
613. tall(sK2) <- (70) [avatar component clause 611]
615. 71 <=> generous(sK2) [avatar definition]
618. 70 | 71 | ~16 [avatar split clause 608,237,615,611]
619. ~71 | ~16 [avatar split clause 609,237,615]
629. wise(sK1) <- (13, 17) [resolution 225,243]
639. $false <- (13, ~14, 17) [subsumption resolution 629,230]
640. ~13 | 14 | ~17 [avatar contradiction clause 639]
648. funny(fred) | brave(fred) <- (58) [resolution 486,82]
649. kind(fred) <- (58) [resolution 486,137]
653. 74 <=> quiet(fred) [avatar definition]
654. ~quiet(fred) <- (~74) [avatar component clause 653]
655. quiet(fred) <- (74) [avatar component clause 653]
657. brave(fred) <- (19, 58) [subsumption resolution 648,253]
658. $false <- (19, ~26, 58) [subsumption resolution 657,282]
659. ~19 | 26 | ~58 [avatar contradiction clause 658]
662. 22 [avatar split clause 568,265]
664. 25 | ~58 [avatar split clause 649,484,276]
684. $false <- (5, ~25) [resolution 278,189]
685. ~5 | 25 [avatar contradiction clause 684]
720. quiet(fred) | generous(fred) | ~tall(fred) <- (57) [resolution 127,480]
725. ~quiet(sK2) <- (70) [resolution 613,140]
738. ~16 | ~70 [avatar split clause 725,611,237]
739. rich(sK1) <- (14, 15) [resolution 229,235]
740. ~quiet(fred) <- (12, 57) [resolution 222,480]
744. $false <- (12, 57, 74) [subsumption resolution 740,655]
745. ~12 | ~57 | ~74 [avatar contradiction clause 744]
746. 13 | ~14 | ~15 [avatar split clause 739,234,228,224]
765. generous(fred) | ~tall(fred) <- (57, ~74) [subsumption resolution 720,654]
766. generous(fred) <- (57, 67, ~74) [subsumption resolution 765,583]
767. 58 | ~57 | ~67 | 74 [avatar split clause 766,653,581,478,484]
809. funny(X3) | brave(X3) <- (24) [resolution 274,82]
811. brave(X3) <- (19, 24) [subsumption resolution 809,253]
853. $false <- (19, 24) [resolution 811,150]
854. ~19 | ~24 [avatar contradiction clause 853]
856. $false [avatar sat refutation 231,232,240,244,258,263,283,286,415,487,584,588,618,619,640,659,662,664,685,738,745,746,767,854]
% SZS output end Proof for 8411986504089727022299392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not brave is either happy or tall.
If someone is not creative then fred is not wise.
If someone is happy or not wise then someone is both old and kind and vice versa.
Everyone who is both not happy and not quiet is old or tall and vice versa.
Everyone who is not humble or not brave is funny.
If john is not wise then someone is either rich or patient.
Everyone who is calm or not rich is not patient.
Everyone who is both not strong and not old is not quiet or not kind and vice versa.
Everyone who is not patient is creative and vice versa.
Everyone who is humble or quiet is not generous or quiet.
If someone is old or not patient then susan is either funny or not curious and vice versa.
If someone is not brave then someone is not humble and vice versa.
Everyone who is not humble or calm is either humble or not wise.
Lucy is both not quiet and rich.
Paul is happy or not happy.
Mary is both not kind and tall.
John is calm.
John is not patient or humble.
Fred is not old. | Mary is happy. | contradiction | (![X]:((brave(X)|~brave(X))=>(happy(X)<~>tall(X))))&
((?[X]:(~creative(X)))=>(~wise(fred)))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:((old(X)&kind(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(old(X)|tall(X))))&
(![X]:((~humble(X)|~brave(X))=>funny(X)))&
((~wise(john))=>(?[X]:((rich(X)<~>patient(X)))))&
(![X]:((calm(X)|~rich(X))=>~patient(X)))&
(![X]:((~strong(X)&~old(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:((humble(X)|quiet(X))=>(~generous(X)|quiet(X))))&
((?[X]:((old(X)|~patient(X))))<=>((funny(susan)<~>~curious(susan))))&
((?[X]:(~brave(X)))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|calm(X))=>(humble(X)<~>~wise(X))))&
((~quiet(lucy)&rich(lucy)))&
((happy(paul)|~happy(paul)))&
((~kind(mary)&tall(mary)))&
(calm(john))&
((~patient(john)|humble(john)))&
(~old(fred)) | happy(mary) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3530421585628111821538668
% SZS output start Proof for 3530421585628111821538668
3. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X0] : (kind(X0) & old(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (tall(X0) | old(X0))) [input p3]
8. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p7]
20. happy(mary) [input hypothesis]
21. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X1] : (kind(X1) & old(X1)) [rectify 3]
31. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X1] : (kind(X1) & old(X1)) | ! [X0] : (wise(X0) & ~happy(X0))) [nnf transformation 21]
32. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X2] : (kind(X2) & old(X2)) | ! [X3] : (wise(X3) & ~happy(X3))) [rectify 31]
33. ? [X0] : (~wise(X0) | happy(X0)) => (~wise(sK0) | happy(sK0)) [choice axiom]
34. ? [X2] : (kind(X2) & old(X2)) => (kind(sK1) & old(sK1)) [choice axiom]
35. ((~wise(sK0) | happy(sK0)) | ! [X1] : (~kind(X1) | ~old(X1))) & ((kind(sK1) & old(sK1)) | ! [X3] : (wise(X3) & ~happy(X3))) [skolemisation 32,34,33]
36. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 4]
37. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | quiet(X0) | happy(X0))) [flattening 36]
41. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (old(X0) | strong(X0)))) [nnf transformation 8]
42. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | old(X0) | strong(X0))) [flattening 41]
59. old(sK1) | ~happy(X3) [cnf transformation 35]
67. ~quiet(X0) | ~old(X0) [cnf transformation 37]
78. ~old(X0) | quiet(X0) [cnf transformation 42]
102. happy(mary) [cnf transformation 20]
135. 8 <=> ! [X3] : ~happy(X3) [avatar definition]
136. ~happy(X3) <- (8) [avatar component clause 135]
139. 9 <=> old(sK1) [avatar definition]
141. old(sK1) <- (9) [avatar component clause 139]
143. 8 | 9 [avatar split clause 59,139,135]
158. ~old(X0) [subsumption resolution 78,67]
210. $false <- (9) [subsumption resolution 141,158]
211. ~9 [avatar contradiction clause 210]
214. $false <- (8) [resolution 136,102]
215. ~8 [avatar contradiction clause 214]
216. $false [avatar sat refutation 143,211,215]
% SZS output end Proof for 3530421585628111821538668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both rich and creative then someone is not kind or not creative and vice versa. If someone is both quiet and creative then alice is either not happy or generous. Everyone who is not humble is both not curious and not old and vice versa. If paul is either creative or humble then someone is not funny or calm. Everyone who is not wise is both patient and not kind. If someone is either creative or generous then someone is brave. If someone is quiet or not funny then susan is not strong or not old and vice versa. Everyone who is either quiet or not humble is either not rich or patient and vice versa. Everyone who is both not wise and quiet is either old or tall and vice versa. Everyone who is happy or not humble is funny or curious and vice versa. If alice is humble then paul is not brave or generous. If someone is either not strong or not patient then mary is not humble. Everyone who is brave is not funny or not generous. Everyone who is humble or brave is not old or funny and vice versa. Everyone who is not quiet is either not kind or not curious. If someone is quiet or not tall then susan is either not generous or not old. Mary is either kind or brave. Someone is both funny and not patient. Someone is both not quiet and old. Lucy is either tall or kind. Alice is old. Fred is both not brave and calm. Someone is either not quiet or happy. Someone is not creative. | Alice is happy. | entailment | (((rich(fred)&creative(fred)))<=>(?[X]:((~kind(X)|~creative(X)))))&
((?[X]:((quiet(X)&creative(X))))=>((~happy(alice)<~>generous(alice))))&
(![X]:(~humble(X)<=>(~curious(X)&~old(X))))&
(((creative(paul)<~>humble(paul)))=>(?[X]:((~funny(X)|calm(X)))))&
(![X]:(~wise(X)=>(patient(X)&~kind(X))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:(brave(X))))&
((?[X]:((quiet(X)|~funny(X))))<=>((~strong(susan)|~old(susan))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((~wise(X)&quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((happy(X)|~humble(X))<=>(funny(X)|curious(X))))&
((humble(alice))=>((~brave(paul)|generous(paul))))&
((?[X]:((~strong(X)<~>~patient(X))))=>(~humble(mary)))&
(![X]:(brave(X)=>(~funny(X)|~generous(X))))&
(![X]:((humble(X)|brave(X))<=>(~old(X)|funny(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>~curious(X))))&
((?[X]:((quiet(X)|~tall(X))))=>((~generous(susan)<~>~old(susan))))&
((kind(mary)<~>brave(mary)))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:((~quiet(X)&old(X))))&
((tall(lucy)<~>kind(lucy)))&
(old(alice))&
((~brave(fred)&calm(fred)))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:(~creative(X))) | happy(alice) | [
"p2",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5998819440077021920338367
% SZS output start Proof for 5998819440077021920338367
3. ! [X0] : (~humble(X0) <=> (~old(X0) & ~curious(X0))) [input p2]
10. ! [X0] : ((~humble(X0) | happy(X0)) <=> (curious(X0) | funny(X0))) [input p9]
14. ! [X0] : ((brave(X0) | humble(X0)) <=> (funny(X0) | ~old(X0))) [input p13]
21. old(alice) [input p20]
25. ~happy(alice) [input hypothesis]
45. ! [X0] : ((~humble(X0) | (old(X0) | curious(X0))) & ((~old(X0) & ~curious(X0)) | humble(X0))) [nnf transformation 3]
46. ! [X0] : ((~humble(X0) | old(X0) | curious(X0)) & ((~old(X0) & ~curious(X0)) | humble(X0))) [flattening 45]
59. ! [X0] : (((~humble(X0) | happy(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (humble(X0) & ~happy(X0)))) [nnf transformation 10]
60. ! [X0] : ((~humble(X0) | happy(X0) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | (humble(X0) & ~happy(X0)))) [flattening 59]
62. ! [X0] : (((brave(X0) | humble(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~brave(X0) & ~humble(X0)))) [nnf transformation 14]
63. ! [X0] : ((brave(X0) | humble(X0) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | (~brave(X0) & ~humble(X0)))) [flattening 62]
85. ~old(X0) | humble(X0) [cnf transformation 46]
111. ~funny(X0) | happy(X0) | ~humble(X0) [cnf transformation 60]
117. funny(X0) | ~old(X0) | ~humble(X0) [cnf transformation 63]
135. old(alice) [cnf transformation 21]
140. ~happy(alice) [cnf transformation 25]
172. 8 <=> happy(alice) [avatar definition]
173. ~happy(alice) <- (~8) [avatar component clause 172]
222. 19 <=> humble(alice) [avatar definition]
223. humble(alice) <- (19) [avatar component clause 222]
247. ~old(X0) | funny(X0) [subsumption resolution 117,85]
289. ~8 [avatar split clause 140,172]
291. humble(alice) [resolution 85,135]
293. 19 [avatar split clause 291,222]
305. funny(alice) [resolution 247,135]
412. happy(alice) | ~humble(alice) [resolution 111,305]
416. ~humble(alice) <- (~8) [subsumption resolution 412,173]
417. $false <- (~8, 19) [subsumption resolution 416,223]
418. 8 | ~19 [avatar contradiction clause 417]
438. $false [avatar sat refutation 289,293,418]
% SZS output end Proof for 5998819440077021920338367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is kind then someone is not funny or not curious.
If someone is either old or rich then fred is old or brave and vice versa.
If someone is not funny then someone is either not calm or tall.
Everyone who is either generous or not strong is not wise or not funny and vice versa.
If someone is both strong and creative then fred is not calm and vice versa.
If someone is both generous and quiet then someone is not kind or not calm and vice versa.
Everyone who is funny is not funny or brave.
If fred is not rich then someone is either not tall or not humble and vice versa.
Everyone who is strong or not patient is not creative or humble and vice versa.
Everyone who is both generous and tall is rich or creative and vice versa.
Everyone who is generous or not wise is not generous.
Everyone who is both wise and not patient is wise or not brave.
Everyone who is both not creative and curious is either old or creative and vice versa.
If someone is both creative and happy then paul is both rich and brave and vice versa.
Everyone who is both not old and not creative is creative.
If paul is both not funny and rich then someone is kind or wise.
Paul is not funny or not happy.
Someone is not wise or not calm.
Paul is not old or not funny.
Someone is both funny and patient.
Mary is patient.
Someone is either not happy or not patient. | Paul is not happy. | neutral | ((kind(lucy))=>(?[X]:((~funny(X)|~curious(X)))))&
((?[X]:((old(X)<~>rich(X))))<=>((old(fred)|brave(fred))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((generous(X)<~>~strong(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((strong(X)&creative(X))))<=>(~calm(fred)))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(funny(X)=>(~funny(X)|brave(X))))&
((~rich(fred))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~creative(X)|humble(X))))&
(![X]:((generous(X)&tall(X))<=>(rich(X)|creative(X))))&
(![X]:((generous(X)|~wise(X))=>~generous(X)))&
(![X]:((wise(X)&~patient(X))=>(wise(X)|~brave(X))))&
(![X]:((~creative(X)&curious(X))<=>(old(X)<~>creative(X))))&
((?[X]:((creative(X)&happy(X))))<=>((rich(paul)&brave(paul))))&
(![X]:((~old(X)&~creative(X))=>creative(X)))&
(((~funny(paul)&rich(paul)))=>(?[X]:((kind(X)|wise(X)))))&
((~funny(paul)|~happy(paul)))&
(?[X]:((~wise(X)|~calm(X))))&
((~old(paul)|~funny(paul)))&
(?[X]:((funny(X)&patient(X))))&
(patient(mary))&
(?[X]:((~happy(X)<~>~patient(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is both not calm and not wise is not generous or happy.
If someone is calm then mary is either humble or not rich.
Everyone who is both creative and not brave is both not brave and generous.
Everyone who is both kind and not calm is not wise.
If someone is brave then mary is either not funny or creative and vice versa.
Everyone who is rich is both generous and creative and vice versa.
If someone is not curious then alice is both not tall and not calm and vice versa.
If fred is both strong and rich then someone is funny.
Everyone who is both not brave and generous is either not funny or not happy and vice versa.
Everyone who is either not wise or not tall is either quiet or not brave and vice versa.
Everyone who is not brave or not kind is creative or not quiet.
Everyone who is either not brave or kind is not curious.
If fred is tall or strong then john is both brave and not rich and vice versa.
Everyone who is either not calm or not funny is quiet or not creative and vice versa.
Everyone who is not funny is both creative and not rich and vice versa.
Everyone who is not tall is not humble and vice versa.
Someone is not strong or not brave.
Someone is both not wise and tall.
Someone is either wise or not quiet.
Paul is either not strong or old.
Fred is both not humble and not funny.
Someone is either old or curious.
Someone is both patient and calm.
Someone is both kind and old. | Fred is strong. | neutral | (![X]:((~calm(X)&~wise(X))=>(~generous(X)|happy(X))))&
((?[X]:(calm(X)))=>((humble(mary)<~>~rich(mary))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)&generous(X))))&
(![X]:((kind(X)&~calm(X))=>~wise(X)))&
((?[X]:(brave(X)))<=>((~funny(mary)<~>creative(mary))))&
(![X]:(rich(X)<=>(generous(X)&creative(X))))&
((?[X]:(~curious(X)))<=>((~tall(alice)&~calm(alice))))&
(((strong(fred)&rich(fred)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)&generous(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~tall(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~brave(X)|~kind(X))=>(creative(X)|~quiet(X))))&
(![X]:((~brave(X)<~>kind(X))=>~curious(X)))&
(((tall(fred)|strong(fred)))<=>((brave(john)&~rich(john))))&
(![X]:((~calm(X)<~>~funny(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~funny(X)<=>(creative(X)&~rich(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((wise(X)<~>~quiet(X))))&
((~strong(paul)<~>old(paul)))&
((~humble(fred)&~funny(fred)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((kind(X)&old(X)))) | strong(fred) | [] | null | 0 |
If someone is both not wise and not generous then alice is both kind and not happy. Everyone who is creative or happy is both not calm and happy. If john is both kind and not kind then someone is not rich and vice versa. If someone is generous then lucy is not wise or calm and vice versa. If someone is either not calm or humble then lucy is either rich or strong. If lucy is not kind or wise then fred is patient or not strong and vice versa. Everyone who is not curious or not patient is either tall or not humble and vice versa. Everyone who is either not creative or tall is either not brave or old and vice versa. If someone is not humble then paul is generous or old. Everyone who is both tall and generous is both happy and old. Everyone who is humble or tall is either happy or not generous and vice versa. If someone is either not brave or humble then mary is curious. If paul is not curious then alice is not rich and vice versa. If alice is both old and not patient then lucy is not kind. If john is both not calm and not generous then someone is wise and vice versa. Everyone who is rich or creative is happy. Someone is either kind or not generous. Mary is either not curious or not creative. Fred is not strong or strong. Someone is both generous and rich. Someone is either tall or kind. Mary is either not strong or not calm. Fred is both tall and not patient. Someone is quiet. | John is calm. | contradiction | ((?[X]:((~wise(X)&~generous(X))))=>((kind(alice)&~happy(alice))))&
(![X]:((creative(X)|happy(X))=>(~calm(X)&happy(X))))&
(((kind(john)&~kind(john)))<=>(?[X]:(~rich(X))))&
((?[X]:(generous(X)))<=>((~wise(lucy)|calm(lucy))))&
((?[X]:((~calm(X)<~>humble(X))))=>((rich(lucy)<~>strong(lucy))))&
(((~kind(lucy)|wise(lucy)))<=>((patient(fred)|~strong(fred))))&
(![X]:((~curious(X)|~patient(X))<=>(tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>tall(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~humble(X)))=>((generous(paul)|old(paul))))&
(![X]:((tall(X)&generous(X))=>(happy(X)&old(X))))&
(![X]:((humble(X)|tall(X))<=>(happy(X)<~>~generous(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>(curious(mary)))&
((~curious(paul))<=>(~rich(alice)))&
(((old(alice)&~patient(alice)))=>(~kind(lucy)))&
(((~calm(john)&~generous(john)))<=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
(?[X]:((kind(X)<~>~generous(X))))&
((~curious(mary)<~>~creative(mary)))&
((~strong(fred)|strong(fred)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((tall(X)<~>kind(X))))&
((~strong(mary)<~>~calm(mary)))&
((tall(fred)&~patient(fred)))&
(?[X]:(quiet(X))) | calm(john) | [
"p1",
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3798528743829381194190845
% SZS output start Proof for 3798528743829381194190845
2. ! [X0] : ((happy(X0) | creative(X0)) => (happy(X0) & ~calm(X0))) [input p1]
3. (~kind(john) & kind(john)) <=> ? [X0] : ~rich(X0) [input p2]
16. ! [X0] : ((creative(X0) | rich(X0)) => happy(X0)) [input p15]
25. calm(john) [input hypothesis]
28. ! [X0] : ((happy(X0) & ~calm(X0)) | (~happy(X0) & ~creative(X0))) [ennf transformation 2]
37. ! [X0] : (happy(X0) | (~creative(X0) & ~rich(X0))) [ennf transformation 16]
38. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (kind(john) | ~kind(john))) [nnf transformation 3]
39. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | kind(john) | ~kind(john)) [flattening 38]
40. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | kind(john) | ~kind(john)) [rectify 39]
41. ? [X1] : ~rich(X1) => ~rich(sK0) [choice axiom]
42. ((~kind(john) & kind(john)) | ! [X0] : rich(X0)) & (~rich(sK0) | kind(john) | ~kind(john)) [skolemisation 40,41]
76. ~calm(X0) | ~happy(X0) [cnf transformation 28]
80. kind(john) | rich(X0) [cnf transformation 42]
81. ~kind(john) | rich(X0) [cnf transformation 42]
124. ~rich(X0) | happy(X0) [cnf transformation 37]
139. calm(john) [cnf transformation 25]
154. 4 <=> ! [X0] : rich(X0) [avatar definition]
155. rich(X0) <- (4) [avatar component clause 154]
157. 5 <=> kind(john) [avatar definition]
160. 4 | ~5 [avatar split clause 81,157,154]
161. 4 | 5 [avatar split clause 80,157,154]
266. 29 <=> calm(john) [avatar definition]
267. calm(john) <- (29) [avatar component clause 266]
312. 29 [avatar split clause 139,266]
316. ~happy(john) <- (29) [resolution 76,267]
318. happy(X0) <- (4) [resolution 124,155]
323. $false <- (4, 29) [resolution 318,316]
324. ~4 | ~29 [avatar contradiction clause 323]
326. $false [avatar sat refutation 160,161,312,324]
% SZS output end Proof for 3798528743829381194190845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and wise then john is old.
If fred is wise or not strong then someone is both not creative and wise and vice versa.
Everyone who is either rich or creative is both not calm and tall and vice versa.
Everyone who is both curious and quiet is not brave and vice versa.
If someone is happy or not kind then john is not old.
Everyone who is wise is both not happy and not wise.
If someone is not curious then someone is both not quiet and rich and vice versa.
Everyone who is either not curious or funny is funny or not rich.
Everyone who is not curious or not strong is not quiet or not happy.
Everyone who is generous or not quiet is both creative and tall.
If fred is not calm or kind then someone is both wise and not tall.
Everyone who is not generous or wise is tall or generous and vice versa.
If paul is either not brave or not funny then mary is either tall or not curious and vice versa.
Everyone who is either not creative or not calm is not quiet and vice versa.
Everyone who is both curious and not creative is both humble and strong and vice versa.
Everyone who is patient is either not calm or generous and vice versa.
Lucy is both patient and not kind.
Someone is both not quiet and brave.
Someone is either quiet or old.
Someone is funny or happy.
Paul is not wise.
Someone is either curious or quiet. | John is strong. | neutral | ((?[X]:((~kind(X)&wise(X))))=>(old(john)))&
(((wise(fred)|~strong(fred)))<=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(~calm(X)&tall(X))))&
(![X]:((curious(X)&quiet(X))<=>~brave(X)))&
((?[X]:((happy(X)|~kind(X))))=>(~old(john)))&
(![X]:(wise(X)=>(~happy(X)&~wise(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((~curious(X)<~>funny(X))=>(funny(X)|~rich(X))))&
(![X]:((~curious(X)|~strong(X))=>(~quiet(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(creative(X)&tall(X))))&
(((~calm(fred)|kind(fred)))=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~generous(X)|wise(X))<=>(tall(X)|generous(X))))&
(((~brave(paul)<~>~funny(paul)))<=>((tall(mary)<~>~curious(mary))))&
(![X]:((~creative(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((curious(X)&~creative(X))<=>(humble(X)&strong(X))))&
(![X]:(patient(X)<=>(~calm(X)<~>generous(X))))&
((patient(lucy)&~kind(lucy)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((quiet(X)<~>old(X))))&
(?[X]:((funny(X)|happy(X))))&
(~wise(paul))&
(?[X]:((curious(X)<~>quiet(X)))) | strong(john) | [] | null | 0 |
If someone is both rich and quiet then paul is either not patient or not brave and vice versa.
Everyone who is not curious or wise is either not creative or not rich and vice versa.
Everyone who is not humble or not happy is both old and not calm.
If alice is either not brave or old then lucy is rich.
Everyone who is generous is both not rich and not happy and vice versa.
Everyone who is brave or not generous is both humble and patient and vice versa.
Everyone who is not generous or kind is not quiet and vice versa.
Everyone who is either tall or curious is either not creative or rich and vice versa.
If lucy is kind or not humble then lucy is either not curious or not happy and vice versa.
Everyone who is curious or brave is both not rich and not kind and vice versa.
Everyone who is both not funny and wise is not happy or not old and vice versa.
If mary is either quiet or not kind then someone is either creative or not quiet.
Everyone who is both tall and rich is curious or not funny and vice versa.
Everyone who is tall or quiet is either not calm or not generous and vice versa.
If paul is not happy or not rich then mary is not quiet or funny.
Someone is tall or strong.
Lucy is wise.
Someone is both wise and not rich.
Someone is not creative.
Someone is either not funny or not tall.
Someone is both not creative and strong.
Someone is either not tall or curious.
Someone is either not tall or not kind. | Alice is not funny. | contradiction | ((?[X]:((rich(X)&quiet(X))))<=>((~patient(paul)<~>~brave(paul))))&
(![X]:((~curious(X)|wise(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((~humble(X)|~happy(X))=>(old(X)&~calm(X))))&
(((~brave(alice)<~>old(alice)))=>(rich(lucy)))&
(![X]:(generous(X)<=>(~rich(X)&~happy(X))))&
(![X]:((brave(X)|~generous(X))<=>(humble(X)&patient(X))))&
(![X]:((~generous(X)|kind(X))<=>~quiet(X)))&
(![X]:((tall(X)<~>curious(X))<=>(~creative(X)<~>rich(X))))&
(((kind(lucy)|~humble(lucy)))<=>((~curious(lucy)<~>~happy(lucy))))&
(![X]:((curious(X)|brave(X))<=>(~rich(X)&~kind(X))))&
(![X]:((~funny(X)&wise(X))<=>(~happy(X)|~old(X))))&
(((quiet(mary)<~>~kind(mary)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)&rich(X))<=>(curious(X)|~funny(X))))&
(![X]:((tall(X)|quiet(X))<=>(~calm(X)<~>~generous(X))))&
(((~happy(paul)|~rich(paul)))=>((~quiet(mary)|funny(mary))))&
(?[X]:((tall(X)|strong(X))))&
(wise(lucy))&
(?[X]:((wise(X)&~rich(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~tall(X))))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:((~tall(X)<~>~kind(X)))) | ~funny(alice) | [
"p1",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1443008255070304690289527
% SZS output start Proof for 1443008255070304690289527
2. ! [X0] : ((wise(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p1]
8. ! [X0] : ((tall(X0) <~> curious(X0)) <=> (~creative(X0) <~> rich(X0))) [input p7]
10. ! [X0] : ((brave(X0) | curious(X0)) <=> (~kind(X0) & ~rich(X0))) [input p9]
13. ! [X0] : ((rich(X0) & tall(X0)) <=> (~funny(X0) | curious(X0))) [input p12]
24. ~funny(alice) [input hypothesis]
36. ! [X0] : (((wise(X0) | ~curious(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~wise(X0) & curious(X0)))) [nnf transformation 2]
37. ! [X0] : ((wise(X0) | ~curious(X0) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~wise(X0) & curious(X0)))) [flattening 36]
45. ! [X0] : ((((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))))) [nnf transformation 8]
48. ! [X0] : (((brave(X0) | curious(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 10]
49. ! [X0] : ((brave(X0) | curious(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 48]
55. ! [X0] : (((rich(X0) & tall(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (~rich(X0) | ~tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((rich(X0) & tall(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~rich(X0) | ~tall(X0))) [flattening 55]
80. ~creative(X0) | ~rich(X0) | curious(X0) [cnf transformation 37]
105. ~rich(X0) | creative(X0) | curious(X0) | ~tall(X0) [cnf transformation 45]
110. ~curious(X0) | ~tall(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 45]
117. ~curious(X0) | ~rich(X0) [cnf transformation 49]
133. funny(X0) | tall(X0) [cnf transformation 56]
134. rich(X0) | ~curious(X0) [cnf transformation 56]
135. funny(X0) | rich(X0) [cnf transformation 56]
155. ~funny(alice) [cnf transformation 24]
195. ~tall(X0) | ~creative(X0) | ~rich(X0) [subsumption resolution 110,80]
197. ~tall(X0) | curious(X0) | ~rich(X0) [subsumption resolution 105,195]
239. ~curious(X0) [subsumption resolution 134,117]
285. tall(alice) [resolution 133,155]
292. rich(alice) [resolution 135,155]
368. curious(alice) | ~rich(alice) [resolution 197,285]
369. ~rich(alice) [subsumption resolution 368,239]
370. $false [subsumption resolution 369,292]
% SZS output end Proof for 1443008255070304690289527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not funny is generous or not patient and vice versa. Everyone who is tall or not humble is not brave or tall and vice versa. Everyone who is not curious or quiet is either not strong or not creative. Everyone who is not old or not calm is not brave. If someone is both not tall and kind then someone is wise. If susan is not tall or wise then someone is not funny or not wise and vice versa. If susan is both not wise and not kind then someone is not funny or not kind and vice versa. If someone is not humble then fred is not rich or not kind. Everyone who is humble is either not humble or not calm. If someone is either curious or not happy then someone is either not rich or not funny. If fred is both not generous and tall then someone is not happy. Everyone who is not strong is calm or not curious. If someone is not strong then someone is either not wise or strong and vice versa. Everyone who is either tall or kind is not calm or not creative and vice versa. Everyone who is not rich is not quiet or not tall and vice versa. If someone is both not brave and not strong then someone is either not happy or not patient and vice versa. Someone is either not funny or not brave. Fred is not strong. Lucy is either not rich or not patient. Someone is tall. Someone is kind. Someone is not curious. John is calm. | Lucy is not funny. | neutral | (![X]:((~quiet(X)|~funny(X))<=>(generous(X)|~patient(X))))&
(![X]:((tall(X)|~humble(X))<=>(~brave(X)|tall(X))))&
(![X]:((~curious(X)|quiet(X))=>(~strong(X)<~>~creative(X))))&
(![X]:((~old(X)|~calm(X))=>~brave(X)))&
((?[X]:((~tall(X)&kind(X))))=>(?[X]:(wise(X))))&
(((~tall(susan)|wise(susan)))<=>(?[X]:((~funny(X)|~wise(X)))))&
(((~wise(susan)&~kind(susan)))<=>(?[X]:((~funny(X)|~kind(X)))))&
((?[X]:(~humble(X)))=>((~rich(fred)|~kind(fred))))&
(![X]:(humble(X)=>(~humble(X)<~>~calm(X))))&
((?[X]:((curious(X)<~>~happy(X))))=>(?[X]:((~rich(X)<~>~funny(X)))))&
(((~generous(fred)&tall(fred)))=>(?[X]:(~happy(X))))&
(![X]:(~strong(X)=>(calm(X)|~curious(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((tall(X)<~>kind(X))<=>(~calm(X)|~creative(X))))&
(![X]:(~rich(X)<=>(~quiet(X)|~tall(X))))&
((?[X]:((~brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(?[X]:((~funny(X)<~>~brave(X))))&
(~strong(fred))&
((~rich(lucy)<~>~patient(lucy)))&
(?[X]:(tall(X)))&
(?[X]:(kind(X)))&
(?[X]:(~curious(X)))&
(calm(john)) | ~funny(lucy) | [] | null | 0 |
Everyone who is either not creative or not tall is rich and vice versa. Everyone who is both not curious and not calm is tall or generous and vice versa. Everyone who is both not funny and old is both not happy and not funny and vice versa. If someone is either rich or not quiet then paul is both tall and not creative and vice versa. If lucy is both tall and not wise then fred is both rich and not generous and vice versa. Everyone who is both not strong and not curious is both not tall and strong. Everyone who is patient or brave is both not kind and not patient. Everyone who is either curious or wise is rich and vice versa. If fred is both old and not wise then paul is both patient and not curious. Everyone who is either strong or not tall is humble. If someone is both calm and not strong then someone is both not curious and curious and vice versa. Everyone who is quiet is calm or humble and vice versa. Everyone who is calm is both not tall and brave and vice versa. If paul is either generous or not happy then someone is not old or not quiet and vice versa. Everyone who is not wise or kind is either not rich or funny and vice versa. Everyone who is both not generous and not rich is either not strong or not curious. Someone is quiet or kind. Someone is both calm and not generous. Someone is not rich or not generous. Someone is not wise or patient. Someone is both quiet and not generous. Mary is not kind. Someone is either not rich or old. Someone is calm or not wise. | Paul is not patient. | entailment | (![X]:((~creative(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~curious(X)&~calm(X))<=>(tall(X)|generous(X))))&
(![X]:((~funny(X)&old(X))<=>(~happy(X)&~funny(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(paul)&~creative(paul))))&
(((tall(lucy)&~wise(lucy)))<=>((rich(fred)&~generous(fred))))&
(![X]:((~strong(X)&~curious(X))=>(~tall(X)&strong(X))))&
(![X]:((patient(X)|brave(X))=>(~kind(X)&~patient(X))))&
(![X]:((curious(X)<~>wise(X))<=>rich(X)))&
(((old(fred)&~wise(fred)))=>((patient(paul)&~curious(paul))))&
(![X]:((strong(X)<~>~tall(X))=>humble(X)))&
((?[X]:((calm(X)&~strong(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:(quiet(X)<=>(calm(X)|humble(X))))&
(![X]:(calm(X)<=>(~tall(X)&brave(X))))&
(((generous(paul)<~>~happy(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((~wise(X)|kind(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~generous(X)&~rich(X))=>(~strong(X)<~>~curious(X))))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((calm(X)&~generous(X))))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:((quiet(X)&~generous(X))))&
(~kind(mary))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:((calm(X)|~wise(X)))) | ~patient(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5377216963919347064307200
% SZS output start Proof for 5377216963919347064307200
7. ! [X0] : ((brave(X0) | patient(X0)) => (~patient(X0) & ~kind(X0))) [input p6]
25. patient(paul) [input hypothesis]
29. ! [X0] : ((~patient(X0) & ~kind(X0)) | (~brave(X0) & ~patient(X0))) [ennf transformation 7]
107. ~patient(X0) | ~patient(X0) [cnf transformation 29]
152. patient(paul) [cnf transformation 25]
153. ~patient(X0) [duplicate literal removal 107]
294. $false [subsumption resolution 152,153]
% SZS output end Proof for 5377216963919347064307200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and old is strong.
Everyone who is either brave or not quiet is either not quiet or happy and vice versa.
Everyone who is humble is either wise or rich and vice versa.
If someone is calm or creative then alice is not generous or strong and vice versa.
If lucy is funny then alice is both humble and happy and vice versa.
Everyone who is not tall is calm and vice versa.
If alice is both creative and not generous then someone is both funny and kind and vice versa.
Everyone who is not strong or patient is curious or not happy and vice versa.
Everyone who is both not brave and humble is not quiet.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Everyone who is both old and generous is kind.
Someone is not funny or strong.
Alice is old or not kind.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave.
Lucy is patient.
Someone is kind. | Alice is curious. | neutral | (![X]:((~happy(X)&old(X))=>strong(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>((~generous(alice)|strong(alice))))&
((funny(lucy))<=>((humble(alice)&happy(alice))))&
(![X]:(~tall(X)<=>calm(X)))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((~strong(X)|patient(X))<=>(curious(X)|~happy(X))))&
(![X]:((~brave(X)&humble(X))=>~quiet(X)))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(?[X]:((~funny(X)|strong(X))))&
((old(alice)|~kind(alice)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary)))&
(patient(lucy))&
(?[X]:(kind(X))) | curious(alice) | [] | null | 0 |
Everyone who is not tall or not creative is both not strong and generous and vice versa.
Everyone who is either quiet or not quiet is rich or not quiet.
Everyone who is both kind and not old is both not kind and not rich.
If lucy is both quiet and wise then someone is either not funny or not creative.
Everyone who is both not strong and funny is both not curious and not calm and vice versa.
Everyone who is either not calm or strong is patient or rich and vice versa.
If john is not patient then john is tall or not patient.
Everyone who is not quiet or humble is both not funny and patient.
Everyone who is both not creative and not quiet is either generous or humble and vice versa.
Everyone who is either strong or not patient is patient.
Everyone who is either not strong or not brave is either not kind or not rich and vice versa.
Everyone who is both curious and kind is either not funny or not wise.
Everyone who is not kind or wise is either not humble or not curious and vice versa.
Everyone who is not old or kind is generous or tall and vice versa.
If someone is not patient or creative then mary is not tall or not wise.
Everyone who is either not strong or not rich is not strong or tall.
John is both quiet and brave.
Fred is strong or patient.
Someone is either patient or tall.
Mary is both tall and funny.
Fred is not patient or not old.
Someone is patient or not generous.
Someone is wise. | Mary is rich. | entailment | (![X]:((~tall(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(rich(X)|~quiet(X))))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&~rich(X))))&
(((quiet(lucy)&wise(lucy)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(patient(X)|rich(X))))&
((~patient(john))=>((tall(john)|~patient(john))))&
(![X]:((~quiet(X)|humble(X))=>(~funny(X)&patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)<~>humble(X))))&
(![X]:((strong(X)<~>~patient(X))=>patient(X)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((curious(X)&kind(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~old(X)|kind(X))<=>(generous(X)|tall(X))))&
((?[X]:((~patient(X)|creative(X))))=>((~tall(mary)|~wise(mary))))&
(![X]:((~strong(X)<~>~rich(X))=>(~strong(X)|tall(X))))&
((quiet(john)&brave(john)))&
((strong(fred)|patient(fred)))&
(?[X]:((patient(X)<~>tall(X))))&
((tall(mary)&funny(mary)))&
((~patient(fred)|~old(fred)))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:(wise(X))) | rich(mary) | [
"p1",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9096255237752081898617762
% SZS output start Proof for 9096255237752081898617762
2. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (~quiet(X0) | rich(X0))) [input p1]
8. ! [X0] : ((humble(X0) | ~quiet(X0)) => (patient(X0) & ~funny(X0))) [input p7]
20. funny(mary) & tall(mary) [input p19]
24. ~rich(mary) [input hypothesis]
25. ! [X0] : ((~quiet(X0) | rich(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 2]
26. ! [X0] : (~quiet(X0) | rich(X0) | (quiet(X0) <=> ~quiet(X0))) [flattening 25]
33. ! [X0] : ((patient(X0) & ~funny(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 8]
43. ! [X0] : (~quiet(X0) | rich(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 26]
73. ~quiet(X0) | rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 43]
90. ~funny(X0) | quiet(X0) [cnf transformation 33]
132. funny(mary) [cnf transformation 20]
136. ~rich(mary) [cnf transformation 24]
140. ~quiet(X0) | rich(X0) [duplicate literal removal 73]
209. quiet(mary) [resolution 90,132]
215. rich(mary) [resolution 140,209]
217. $false [subsumption resolution 215,136]
% SZS output end Proof for 9096255237752081898617762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old then someone is not funny and vice versa.
Everyone who is both creative and not humble is quiet or strong.
Everyone who is not creative or not tall is not patient or brave and vice versa.
Everyone who is both not generous and funny is either not creative or quiet and vice versa.
Everyone who is either humble or strong is not old.
If john is either happy or tall then paul is patient or tall.
Everyone who is both funny and curious is either humble or not kind.
Everyone who is both generous and kind is curious or brave and vice versa.
Everyone who is happy or funny is patient and vice versa.
If mary is either not creative or not rich then lucy is not kind and vice versa.
Everyone who is curious is generous.
Everyone who is both not strong and not kind is not humble.
If lucy is both not creative and not generous then someone is not curious and vice versa.
If someone is wise or patient then john is funny and vice versa.
If alice is both humble and happy then someone is not wise and vice versa.
If someone is old then alice is not strong or not humble and vice versa.
Susan is not creative.
Fred is either not funny or not creative.
Someone is not happy.
Paul is not calm.
Someone is not patient or not strong.
Fred is either generous or not humble.
Mary is both not tall and not curious.
Someone is both curious and creative. | Mary is curious. | contradiction | ((~old(mary))<=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&~humble(X))=>(quiet(X)|strong(X))))&
(![X]:((~creative(X)|~tall(X))<=>(~patient(X)|brave(X))))&
(![X]:((~generous(X)&funny(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((humble(X)<~>strong(X))=>~old(X)))&
(((happy(john)<~>tall(john)))=>((patient(paul)|tall(paul))))&
(![X]:((funny(X)&curious(X))=>(humble(X)<~>~kind(X))))&
(![X]:((generous(X)&kind(X))<=>(curious(X)|brave(X))))&
(![X]:((happy(X)|funny(X))<=>patient(X)))&
(((~creative(mary)<~>~rich(mary)))<=>(~kind(lucy)))&
(![X]:(curious(X)=>generous(X)))&
(![X]:((~strong(X)&~kind(X))=>~humble(X)))&
(((~creative(lucy)&~generous(lucy)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|patient(X))))<=>(funny(john)))&
(((humble(alice)&happy(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:(old(X)))<=>((~strong(alice)|~humble(alice))))&
(~creative(susan))&
((~funny(fred)<~>~creative(fred)))&
(?[X]:(~happy(X)))&
(~calm(paul))&
(?[X]:((~patient(X)|~strong(X))))&
((generous(fred)<~>~humble(fred)))&
((~tall(mary)&~curious(mary)))&
(?[X]:((curious(X)&creative(X)))) | curious(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4405401637554278516506305
% SZS output start Proof for 4405401637554278516506305
23. ~curious(mary) & ~tall(mary) [input p22]
25. curious(mary) [input hypothesis]
133. ~curious(mary) [cnf transformation 23]
136. curious(mary) [cnf transformation 25]
284. $false [subsumption resolution 136,133]
% SZS output end Proof for 4405401637554278516506305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not happy is rich.
Everyone who is not quiet is wise.
If john is generous or not rich then mary is either quiet or patient.
If someone is not quiet or strong then john is old or not wise.
If someone is quiet or patient then paul is not humble and vice versa.
If someone is both humble and happy then someone is both curious and not patient and vice versa.
Everyone who is both not strong and humble is both not creative and curious and vice versa.
If someone is old or kind then someone is both not brave and not creative and vice versa.
Everyone who is both funny and calm is not humble and vice versa.
If someone is either not brave or not tall then alice is not quiet or brave.
Everyone who is not curious is both calm and not strong and vice versa.
Everyone who is calm or creative is quiet or strong.
Everyone who is both not brave and tall is either creative or brave and vice versa.
Everyone who is quiet or humble is both not calm and not tall and vice versa.
Everyone who is both kind and humble is either not curious or not tall.
Susan is both not old and not kind.
Someone is not humble or patient. | Alice is humble. | neutral | (![X]:((creative(X)|~happy(X))=>rich(X)))&
(![X]:(~quiet(X)=>wise(X)))&
(((generous(john)|~rich(john)))=>((quiet(mary)<~>patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))=>((old(john)|~wise(john))))&
((?[X]:((quiet(X)|patient(X))))<=>(~humble(paul)))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~strong(X)&humble(X))<=>(~creative(X)&curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((funny(X)&calm(X))<=>~humble(X)))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~quiet(alice)|brave(alice))))&
(![X]:(~curious(X)<=>(calm(X)&~strong(X))))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|strong(X))))&
(![X]:((~brave(X)&tall(X))<=>(creative(X)<~>brave(X))))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)&~tall(X))))&
(![X]:((kind(X)&humble(X))=>(~curious(X)<~>~tall(X))))&
((~old(susan)&~kind(susan)))&
(?[X]:((~humble(X)|patient(X)))) | humble(alice) | [] | null | 0 |
If someone is not strong or not creative then john is both not creative and wise and vice versa.
Everyone who is kind or not humble is both not quiet and calm and vice versa.
If someone is both brave and calm then mary is patient or not generous and vice versa.
Everyone who is not old or not humble is not tall or happy and vice versa.
Everyone who is both curious and quiet is not brave.
Everyone who is not old is both not tall and not happy.
If someone is brave or not creative then susan is both brave and not kind and vice versa.
Everyone who is not calm or not humble is not tall and vice versa.
Everyone who is not funny or kind is either not patient or humble and vice versa.
If someone is either not patient or not creative then someone is humble and vice versa.
Everyone who is either not curious or curious is rich and vice versa.
Everyone who is either happy or not creative is both not brave and funny and vice versa.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
John is either not happy or not calm.
Alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is both not strong and not patient.
Mary is both brave and not calm.
Someone is either not generous or humble. | John is not funny. | contradiction | ((?[X]:((~strong(X)|~creative(X))))<=>((~creative(john)&wise(john))))&
(![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
((~happy(john)<~>~calm(john)))&
(~tall(alice))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X)))) | ~funny(john) | [
"p0",
"p1",
"p5",
"p9",
"p11",
"p13",
"p15",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6561228699964527023573368
% SZS output start Proof for 6561228699964527023573368
1. ? [X0] : (~creative(X0) | ~strong(X0)) <=> (wise(john) & ~creative(john)) [input p0]
2. ! [X0] : ((~humble(X0) | kind(X0)) <=> (calm(X0) & ~quiet(X0))) [input p1]
6. ! [X0] : (~old(X0) => (~happy(X0) & ~tall(X0))) [input p5]
10. ? [X0] : (~patient(X0) <~> ~creative(X0)) <=> ? [X0] : humble(X0) [input p9]
12. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (funny(X0) & ~brave(X0))) [input p11]
14. ! [X0] : (~patient(X0) => (~old(X0) & ~creative(X0))) [input p13]
16. ! [X0] : ((curious(X0) | happy(X0)) => (~calm(X0) <~> old(X0))) [input p15]
17. ~happy(john) <~> ~calm(john) [input p16]
23. ~calm(mary) & brave(mary) [input p22]
25. ~funny(john) [input hypothesis]
26. ? [X0] : (~patient(X0) <~> ~creative(X0)) <=> ? [X1] : humble(X1) [rectify 10]
29. ! [X0] : ((~happy(X0) & ~tall(X0)) | old(X0)) [ennf transformation 6]
31. ! [X0] : ((~old(X0) & ~creative(X0)) | patient(X0)) [ennf transformation 14]
34. ! [X0] : ((~calm(X0) <~> old(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 16]
35. (? [X0] : (~creative(X0) | ~strong(X0)) | (~wise(john) | creative(john))) & ((wise(john) & ~creative(john)) | ! [X0] : (creative(X0) & strong(X0))) [nnf transformation 1]
36. (? [X0] : (~creative(X0) | ~strong(X0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X0] : (creative(X0) & strong(X0))) [flattening 35]
37. (? [X0] : (~creative(X0) | ~strong(X0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X1] : (creative(X1) & strong(X1))) [rectify 36]
38. ? [X0] : (~creative(X0) | ~strong(X0)) => (~creative(sK0) | ~strong(sK0)) [choice axiom]
39. ((~creative(sK0) | ~strong(sK0)) | ~wise(john) | creative(john)) & ((wise(john) & ~creative(john)) | ! [X1] : (creative(X1) & strong(X1))) [skolemisation 37,38]
40. ! [X0] : (((~humble(X0) | kind(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (humble(X0) & ~kind(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | kind(X0) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | (humble(X0) & ~kind(X0)))) [flattening 40]
58. (? [X0] : ((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ! [X1] : ~humble(X1)) & (? [X1] : humble(X1) | ! [X0] : ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) [nnf transformation 26]
59. (? [X0] : ((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ! [X1] : ~humble(X1)) & (? [X2] : humble(X2) | ! [X3] : ((~patient(X3) | creative(X3)) & (~creative(X3) | patient(X3)))) [rectify 58]
60. ? [X0] : ((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) => ((creative(sK3) | patient(sK3)) & (~creative(sK3) | ~patient(sK3))) [choice axiom]
61. ? [X2] : humble(X2) => humble(sK4) [choice axiom]
62. (((creative(sK3) | patient(sK3)) & (~creative(sK3) | ~patient(sK3))) | ! [X1] : ~humble(X1)) & (humble(sK4) | ! [X3] : ((~patient(X3) | creative(X3)) & (~creative(X3) | patient(X3)))) [skolemisation 59,61,60]
64. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 12]
65. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [flattening 64]
66. ! [X0] : (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (~curious(X0) & ~happy(X0))) [nnf transformation 34]
67. (calm(john) | happy(john)) & (~calm(john) | ~happy(john)) [nnf transformation 17]
81. ~creative(john) | creative(X1) [cnf transformation 39]
88. calm(X0) | humble(X0) [cnf transformation 41]
101. ~happy(X0) | old(X0) [cnf transformation 29]
118. ~creative(sK3) | ~patient(sK3) | ~humble(X1) [cnf transformation 62]
127. funny(X0) | happy(X0) | creative(X0) [cnf transformation 65]
134. ~creative(X0) | patient(X0) [cnf transformation 31]
139. ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 66]
141. ~calm(john) | ~happy(john) [cnf transformation 67]
142. calm(john) | happy(john) [cnf transformation 67]
153. ~calm(mary) [cnf transformation 23]
156. ~funny(john) [cnf transformation 25]
160. 1 <=> creative(john) [avatar definition]
161. ~creative(john) <- (~1) [avatar component clause 160]
177. 5 <=> ! [X1] : creative(X1) [avatar definition]
178. creative(X1) <- (5) [avatar component clause 177]
184. 5 | ~1 [avatar split clause 81,160,177]
235. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
236. ~humble(X1) <- (17) [avatar component clause 235]
238. 18 <=> patient(sK3) [avatar definition]
239. ~patient(sK3) <- (~18) [avatar component clause 238]
242. 19 <=> creative(sK3) [avatar definition]
243. ~creative(sK3) <- (~19) [avatar component clause 242]
244. creative(sK3) <- (19) [avatar component clause 242]
246. 17 | ~18 | ~19 [avatar split clause 118,242,238,235]
256. 22 <=> ! [X3] : (~creative(X3) | patient(X3)) [avatar definition]
257. ~creative(X3) | patient(X3) <- (22) [avatar component clause 256]
280. 22 [avatar split clause 134,256]
281. ~happy(X0) | calm(X0) [subsumption resolution 139,101]
282. calm(john) [subsumption resolution 142,281]
283. ~happy(john) [subsumption resolution 141,282]
311. humble(mary) [resolution 88,153]
313. $false <- (17) [subsumption resolution 311,236]
314. ~17 [avatar contradiction clause 313]
382. patient(sK3) <- (19, 22) [resolution 244,257]
383. $false <- (~18, 19, 22) [subsumption resolution 382,239]
384. 18 | ~19 | ~22 [avatar contradiction clause 383]
476. $false <- (5, ~19) [resolution 178,243]
477. ~5 | 19 [avatar contradiction clause 476]
486. happy(john) | creative(john) [resolution 127,156]
488. creative(john) [subsumption resolution 486,283]
489. $false <- (~1) [subsumption resolution 488,161]
490. 1 [avatar contradiction clause 489]
500. $false [avatar sat refutation 184,246,280,314,384,477,490]
% SZS output end Proof for 6561228699964527023573368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is brave then paul is generous or not rich and vice versa.
Everyone who is either tall or not kind is both patient and strong and vice versa.
Everyone who is generous is both not tall and old and vice versa.
If lucy is old or not strong then susan is both old and not curious.
If susan is not kind then someone is creative and vice versa.
If someone is generous or not old then someone is not kind and vice versa.
Everyone who is not funny is kind and vice versa.
If someone is wise or not generous then john is both kind and not brave and vice versa.
Everyone who is both kind and not strong is not old and vice versa.
If someone is both funny and not quiet then alice is not curious or not patient and vice versa.
If fred is wise then lucy is not happy.
If john is not humble or not quiet then paul is both not old and not creative and vice versa.
If lucy is quiet then someone is both quiet and not happy.
Everyone who is either not strong or strong is funny.
If mary is both curious and not quiet then someone is old or not strong.
Someone is both not tall and not wise.
Someone is calm.
Susan is either not humble or not creative.
Someone is not kind.
Someone is quiet or kind. | John is not happy. | neutral | ((brave(susan))<=>((generous(paul)|~rich(paul))))&
(![X]:((tall(X)<~>~kind(X))<=>(patient(X)&strong(X))))&
(![X]:(generous(X)<=>(~tall(X)&old(X))))&
(((old(lucy)|~strong(lucy)))=>((old(susan)&~curious(susan))))&
((~kind(susan))<=>(?[X]:(creative(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~funny(X)<=>kind(X)))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(john)&~brave(john))))&
(![X]:((kind(X)&~strong(X))<=>~old(X)))&
((?[X]:((funny(X)&~quiet(X))))<=>((~curious(alice)|~patient(alice))))&
((wise(fred))=>(~happy(lucy)))&
(((~humble(john)|~quiet(john)))<=>((~old(paul)&~creative(paul))))&
((quiet(lucy))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:(calm(X)))&
((~humble(susan)<~>~creative(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)|kind(X)))) | ~happy(john) | [] | null | 0 |
If someone is either funny or quiet then paul is either humble or not brave and vice versa.
Everyone who is both not calm and humble is not rich and vice versa.
If someone is either generous or funny then paul is happy or tall and vice versa.
Everyone who is quiet is either not calm or kind and vice versa.
If mary is either not tall or creative then mary is curious.
If someone is not funny then lucy is either funny or not humble.
If someone is creative then alice is either not creative or not rich and vice versa.
Everyone who is both calm and tall is either calm or not curious.
If mary is wise or not creative then someone is both quiet and not strong and vice versa.
Everyone who is either humble or patient is either not tall or not brave.
Everyone who is either not rich or generous is either strong or not brave.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Susan is not patient or not quiet.
Someone is either not funny or quiet.
Mary is not brave or not creative.
Paul is both kind and not strong.
Fred is not calm.
Susan is creative or tall.
Someone is both generous and not strong. | Susan is not creative. | neutral | ((?[X]:((funny(X)<~>quiet(X))))<=>((humble(paul)<~>~brave(paul))))&
(![X]:((~calm(X)&humble(X))<=>~rich(X)))&
((?[X]:((generous(X)<~>funny(X))))<=>((happy(paul)|tall(paul))))&
(![X]:(quiet(X)<=>(~calm(X)<~>kind(X))))&
(((~tall(mary)<~>creative(mary)))=>(curious(mary)))&
((?[X]:(~funny(X)))=>((funny(lucy)<~>~humble(lucy))))&
((?[X]:(creative(X)))<=>((~creative(alice)<~>~rich(alice))))&
(![X]:((calm(X)&tall(X))=>(calm(X)<~>~curious(X))))&
(((wise(mary)|~creative(mary)))<=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~rich(X)<~>generous(X))=>(strong(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
((~patient(susan)|~quiet(susan)))&
(?[X]:((~funny(X)<~>quiet(X))))&
((~brave(mary)|~creative(mary)))&
((kind(paul)&~strong(paul)))&
(~calm(fred))&
((creative(susan)|tall(susan)))&
(?[X]:((generous(X)&~strong(X)))) | ~creative(susan) | [] | null | 0 |
If mary is both generous and not old then someone is either old or not tall and vice versa.
Everyone who is old is either brave or wise.
If someone is either not happy or not funny then someone is either not old or funny and vice versa.
If someone is brave then someone is not strong.
Everyone who is either tall or rich is both patient and not creative.
If paul is both not rich and not old then someone is patient or not curious and vice versa.
Everyone who is either not wise or not curious is not old.
If someone is either not quiet or strong then someone is both not wise and happy.
If someone is not generous or not happy then john is creative and vice versa.
Everyone who is either rich or not patient is both not patient and tall and vice versa.
Everyone who is either rich or not wise is either generous or not humble and vice versa.
Everyone who is either brave or not curious is creative and vice versa.
If someone is either not creative or not humble then susan is either not brave or not strong.
If someone is not old then someone is both curious and not tall.
If alice is both not wise and generous then susan is either kind or old.
Everyone who is tall or not strong is both not strong and not tall and vice versa.
Someone is both humble and not calm.
Fred is either generous or not calm.
Someone is either not rich or brave.
Paul is both not humble and not tall.
John is either quiet or not creative.
Someone is brave or rich. | Paul is calm. | neutral | (((generous(mary)&~old(mary)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(old(X)=>(brave(X)<~>wise(X))))&
((?[X]:((~happy(X)<~>~funny(X))))<=>(?[X]:((~old(X)<~>funny(X)))))&
((?[X]:(brave(X)))=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>rich(X))=>(patient(X)&~creative(X))))&
(((~rich(paul)&~old(paul)))<=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:((~wise(X)<~>~curious(X))=>~old(X)))&
((?[X]:((~quiet(X)<~>strong(X))))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((~generous(X)|~happy(X))))<=>(creative(john)))&
(![X]:((rich(X)<~>~patient(X))<=>(~patient(X)&tall(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(generous(X)<~>~humble(X))))&
(![X]:((brave(X)<~>~curious(X))<=>creative(X)))&
((?[X]:((~creative(X)<~>~humble(X))))=>((~brave(susan)<~>~strong(susan))))&
((?[X]:(~old(X)))=>(?[X]:((curious(X)&~tall(X)))))&
(((~wise(alice)&generous(alice)))=>((kind(susan)<~>old(susan))))&
(![X]:((tall(X)|~strong(X))<=>(~strong(X)&~tall(X))))&
(?[X]:((humble(X)&~calm(X))))&
((generous(fred)<~>~calm(fred)))&
(?[X]:((~rich(X)<~>brave(X))))&
((~humble(paul)&~tall(paul)))&
((quiet(john)<~>~creative(john)))&
(?[X]:((brave(X)|rich(X)))) | calm(paul) | [] | null | 0 |
Everyone who is not old or happy is kind or creative.
Everyone who is either not humble or humble is both not brave and creative.
If someone is not strong or not tall then someone is creative.
Everyone who is either old or not generous is either not strong or quiet.
If someone is both not old and tall then someone is either not curious or kind.
Everyone who is both old and humble is brave and vice versa.
If someone is not humble or not creative then someone is both rich and funny.
If lucy is both not happy and not kind then someone is not tall or not creative.
Everyone who is not tall or not rich is funny.
If mary is both not rich and happy then mary is both funny and not patient and vice versa.
Everyone who is not humble is quiet and vice versa.
Everyone who is not brave is generous or not brave and vice versa.
If alice is kind then someone is kind and vice versa.
Everyone who is not kind or not calm is humble and vice versa.
Everyone who is not calm or not rich is not humble or not kind and vice versa.
If someone is either not quiet or not creative then someone is not creative or wise and vice versa.
Someone is calm.
Mary is not humble or not wise.
Someone is quiet or strong.
Alice is happy or creative.
Lucy is either not funny or not quiet.
Someone is curious or calm.
Lucy is not kind or not curious.
Alice is both creative and tall. | Mary is not happy. | neutral | (![X]:((~old(X)|happy(X))=>(kind(X)|creative(X))))&
(![X]:((~humble(X)<~>humble(X))=>(~brave(X)&creative(X))))&
((?[X]:((~strong(X)|~tall(X))))=>(?[X]:(creative(X))))&
(![X]:((old(X)<~>~generous(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((old(X)&humble(X))<=>brave(X)))&
((?[X]:((~humble(X)|~creative(X))))=>(?[X]:((rich(X)&funny(X)))))&
(((~happy(lucy)&~kind(lucy)))=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((~tall(X)|~rich(X))=>funny(X)))&
(((~rich(mary)&happy(mary)))<=>((funny(mary)&~patient(mary))))&
(![X]:(~humble(X)<=>quiet(X)))&
(![X]:(~brave(X)<=>(generous(X)|~brave(X))))&
((kind(alice))<=>(?[X]:(kind(X))))&
(![X]:((~kind(X)|~calm(X))<=>humble(X)))&
(![X]:((~calm(X)|~rich(X))<=>(~humble(X)|~kind(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))<=>(?[X]:((~creative(X)|wise(X)))))&
(?[X]:(calm(X)))&
((~humble(mary)|~wise(mary)))&
(?[X]:((quiet(X)|strong(X))))&
((happy(alice)|creative(alice)))&
((~funny(lucy)<~>~quiet(lucy)))&
(?[X]:((curious(X)|calm(X))))&
((~kind(lucy)|~curious(lucy)))&
((creative(alice)&tall(alice))) | ~happy(mary) | [] | null | 0 |
Everyone who is either not strong or not old is calm or brave. Everyone who is either kind or not generous is either not creative or not humble and vice versa. Everyone who is not quiet is both not calm and not quiet and vice versa. Everyone who is quiet is either not strong or not old and vice versa. Everyone who is not kind is not calm or brave and vice versa. Everyone who is happy or rich is both not brave and calm. Everyone who is either happy or quiet is either patient or generous and vice versa. If fred is both not patient and creative then someone is either not patient or not wise and vice versa. Everyone who is either not curious or not generous is not calm or not rich and vice versa. If someone is both not rich and not humble then someone is not strong or wise. Everyone who is both happy and rich is not old or not curious and vice versa. If mary is not brave then lucy is rich or not brave. Everyone who is both not creative and not strong is not curious or not calm. If someone is not tall then mary is either not kind or not wise and vice versa. Everyone who is either not funny or not rich is not tall. If someone is brave or not humble then fred is both not brave and patient. Someone is not happy. Someone is either calm or wise. Someone is not patient or not happy. Lucy is both not calm and funny. Susan is not happy or rich. Someone is either calm or kind. Someone is both tall and not quiet. John is both calm and not funny. | Fred is curious. | entailment | (![X]:((~strong(X)<~>~old(X))=>(calm(X)|brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~calm(X)&~quiet(X))))&
(![X]:(quiet(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(~calm(X)|brave(X))))&
(![X]:((happy(X)|rich(X))=>(~brave(X)&calm(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(patient(X)<~>generous(X))))&
(((~patient(fred)&creative(fred)))<=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~calm(X)|~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((happy(X)&rich(X))<=>(~old(X)|~curious(X))))&
((~brave(mary))=>((rich(lucy)|~brave(lucy))))&
(![X]:((~creative(X)&~strong(X))=>(~curious(X)|~calm(X))))&
((?[X]:(~tall(X)))<=>((~kind(mary)<~>~wise(mary))))&
(![X]:((~funny(X)<~>~rich(X))=>~tall(X)))&
((?[X]:((brave(X)|~humble(X))))=>((~brave(fred)&patient(fred))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>wise(X))))&
(?[X]:((~patient(X)|~happy(X))))&
((~calm(lucy)&funny(lucy)))&
((~happy(susan)|rich(susan)))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((tall(X)&~quiet(X))))&
((calm(john)&~funny(john))) | curious(fred) | [
"p2",
"p4",
"p5",
"p6",
"p8",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2958642258029877924444899
% SZS output start Proof for 2958642258029877924444899
3. ! [X0] : (~quiet(X0) <=> (~quiet(X0) & ~calm(X0))) [input p2]
5. ! [X0] : (~kind(X0) <=> (brave(X0) | ~calm(X0))) [input p4]
6. ! [X0] : ((rich(X0) | happy(X0)) => (calm(X0) & ~brave(X0))) [input p5]
7. ! [X0] : ((happy(X0) <~> quiet(X0)) <=> (patient(X0) <~> generous(X0))) [input p6]
9. ! [X0] : ((~curious(X0) <~> ~generous(X0)) <=> (~rich(X0) | ~calm(X0))) [input p8]
11. ! [X0] : ((rich(X0) & happy(X0)) <=> (~curious(X0) | ~old(X0))) [input p10]
16. ? [X0] : (~humble(X0) | brave(X0)) => (patient(fred) & ~brave(fred)) [input p15]
22. ? [X0] : (calm(X0) <~> kind(X0)) [input p21]
25. ~curious(fred) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~brave(X0)) | (~rich(X0) & ~happy(X0))) [ennf transformation 6]
36. (patient(fred) & ~brave(fred)) | ! [X0] : (humble(X0) & ~brave(X0)) [ennf transformation 16]
39. ! [X0] : ((~quiet(X0) | (quiet(X0) | calm(X0))) & ((~quiet(X0) & ~calm(X0)) | quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((~quiet(X0) | quiet(X0) | calm(X0)) & ((~quiet(X0) & ~calm(X0)) | quiet(X0))) [flattening 39]
42. ! [X0] : ((~kind(X0) | (~brave(X0) & calm(X0))) & ((brave(X0) | ~calm(X0)) | kind(X0))) [nnf transformation 5]
43. ! [X0] : ((~kind(X0) | (~brave(X0) & calm(X0))) & (brave(X0) | ~calm(X0) | kind(X0))) [flattening 42]
44. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [nnf transformation 7]
50. ! [X0] : ((((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | (rich(X0) & calm(X0))) & ((~rich(X0) | ~calm(X0)) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0))))) [nnf transformation 9]
51. ! [X0] : ((((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | (rich(X0) & calm(X0))) & (~rich(X0) | ~calm(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0))))) [flattening 50]
55. ! [X0] : (((rich(X0) & happy(X0)) | (curious(X0) & old(X0))) & ((~curious(X0) | ~old(X0)) | (~rich(X0) | ~happy(X0)))) [nnf transformation 11]
56. ! [X0] : (((rich(X0) & happy(X0)) | (curious(X0) & old(X0))) & (~curious(X0) | ~old(X0) | ~rich(X0) | ~happy(X0))) [flattening 55]
69. ? [X0] : ((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) [nnf transformation 22]
70. ? [X0] : ((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) => ((~kind(sK6) | ~calm(sK6)) & (kind(sK6) | calm(sK6))) [choice axiom]
71. (~kind(sK6) | ~calm(sK6)) & (kind(sK6) | calm(sK6)) [skolemisation 69,70]
84. ~calm(X0) | quiet(X0) [cnf transformation 40]
91. ~calm(X0) | brave(X0) | kind(X0) [cnf transformation 43]
92. ~kind(X0) | calm(X0) [cnf transformation 43]
96. ~happy(X0) | calm(X0) [cnf transformation 29]
97. ~rich(X0) | calm(X0) [cnf transformation 29]
104. ~patient(X0) | ~happy(X0) | generous(X0) | ~quiet(X0) [cnf transformation 44]
112. ~rich(X0) | ~calm(X0) | ~generous(X0) | curious(X0) [cnf transformation 51]
121. curious(X0) | happy(X0) [cnf transformation 56]
123. curious(X0) | rich(X0) [cnf transformation 56]
134. patient(fred) | ~brave(X0) [cnf transformation 36]
143. kind(sK6) | calm(sK6) [cnf transformation 71]
144. ~kind(sK6) | ~calm(sK6) [cnf transformation 71]
149. ~curious(fred) [cnf transformation 25]
163. 4 <=> patient(fred) [avatar definition]
164. patient(fred) <- (4) [avatar component clause 163]
179. ~rich(X0) | ~generous(X0) | curious(X0) [subsumption resolution 112,97]
226. 17 <=> ! [X0] : ~brave(X0) [avatar definition]
227. ~brave(X0) <- (17) [avatar component clause 226]
228. 17 | 4 [avatar split clause 134,163,226]
263. ~kind(sK6) [subsumption resolution 144,92]
264. calm(sK6) [subsumption resolution 143,263]
272. happy(fred) [resolution 121,149]
275. rich(fred) [resolution 123,149]
276. calm(fred) [resolution 272,96]
320. quiet(fred) [resolution 276,84]
355. brave(sK6) | kind(sK6) [resolution 91,264]
358. kind(sK6) <- (17) [subsumption resolution 355,227]
359. $false <- (17) [subsumption resolution 358,263]
360. ~17 [avatar contradiction clause 359]
432. ~generous(fred) | curious(fred) [resolution 179,275]
433. ~generous(fred) [subsumption resolution 432,149]
588. ~happy(fred) | generous(fred) | ~quiet(fred) <- (4) [resolution 104,164]
591. generous(fred) | ~quiet(fred) <- (4) [subsumption resolution 588,272]
592. ~quiet(fred) <- (4) [subsumption resolution 591,433]
593. $false <- (4) [subsumption resolution 592,320]
594. ~4 [avatar contradiction clause 593]
598. $false [avatar sat refutation 228,360,594]
% SZS output end Proof for 2958642258029877924444899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not curious is not curious.
Everyone who is either calm or generous is tall.
Everyone who is not brave is both kind and not strong and vice versa.
Everyone who is either quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Someone is creative or patient.
Someone is not wise or not calm.
Lucy is either tall or not funny.
Someone is either tall or not humble.
Someone is both not curious and quiet.
Fred is not curious or brave.
Mary is both not patient and not creative. | Paul is funny. | neutral | (![X]:((old(X)|~curious(X))=>~curious(X)))&
(![X]:((calm(X)<~>generous(X))=>tall(X)))&
(![X]:(~brave(X)<=>(kind(X)&~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary))) | funny(paul) | [] | null | 0 |
If someone is both creative and not old then someone is not brave or funny.
Everyone who is not rich is both not happy and brave.
Everyone who is not humble is either not happy or brave and vice versa.
If someone is patient or rich then someone is either not patient or not quiet.
Everyone who is brave or not strong is either not rich or not patient and vice versa.
If mary is not patient or wise then someone is both not creative and not curious and vice versa.
Everyone who is either humble or not tall is not rich or not tall.
If paul is either not rich or not calm then someone is either kind or tall and vice versa.
Everyone who is both not strong and not funny is not creative or not patient.
Everyone who is calm or strong is not generous or not humble.
If someone is not curious or not quiet then someone is brave or happy and vice versa.
If someone is quiet or kind then alice is both not rich and curious.
Everyone who is either not humble or wise is both not happy and humble.
Everyone who is quiet or patient is not quiet and vice versa.
If someone is tall or patient then someone is either not calm or not brave and vice versa.
Everyone who is both strong and not quiet is both not tall and not strong and vice versa.
Someone is either tall or generous.
Someone is either not kind or old.
Fred is either not patient or not calm.
Someone is either not funny or not rich.
Susan is either generous or not rich.
Fred is not curious.
Someone is both not quiet and wise.
Susan is both curious and not happy. | Alice is not brave. | contradiction | ((?[X]:((creative(X)&~old(X))))=>(?[X]:((~brave(X)|funny(X)))))&
(![X]:(~rich(X)=>(~happy(X)&brave(X))))&
(![X]:(~humble(X)<=>(~happy(X)<~>brave(X))))&
((?[X]:((patient(X)|rich(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((brave(X)|~strong(X))<=>(~rich(X)<~>~patient(X))))&
(((~patient(mary)|wise(mary)))<=>(?[X]:((~creative(X)&~curious(X)))))&
(![X]:((humble(X)<~>~tall(X))=>(~rich(X)|~tall(X))))&
(((~rich(paul)<~>~calm(paul)))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:((~strong(X)&~funny(X))=>(~creative(X)|~patient(X))))&
(![X]:((calm(X)|strong(X))=>(~generous(X)|~humble(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((quiet(X)|kind(X))))=>((~rich(alice)&curious(alice))))&
(![X]:((~humble(X)<~>wise(X))=>(~happy(X)&humble(X))))&
(![X]:((quiet(X)|patient(X))<=>~quiet(X)))&
((?[X]:((tall(X)|patient(X))))<=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((strong(X)&~quiet(X))<=>(~tall(X)&~strong(X))))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((~kind(X)<~>old(X))))&
((~patient(fred)<~>~calm(fred)))&
(?[X]:((~funny(X)<~>~rich(X))))&
((generous(susan)<~>~rich(susan)))&
(~curious(fred))&
(?[X]:((~quiet(X)&wise(X))))&
((curious(susan)&~happy(susan))) | ~brave(alice) | [
"p1",
"p4",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4576725236308079615742053
% SZS output start Proof for 4576725236308079615742053
2. ! [X0] : (~rich(X0) => (brave(X0) & ~happy(X0))) [input p1]
5. ! [X0] : ((~strong(X0) | brave(X0)) <=> (~rich(X0) <~> ~patient(X0))) [input p4]
14. ! [X0] : ((patient(X0) | quiet(X0)) <=> ~quiet(X0)) [input p13]
16. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (~strong(X0) & ~tall(X0))) [input p15]
25. ~brave(alice) [input hypothesis]
31. ! [X0] : ((brave(X0) & ~happy(X0)) | rich(X0)) [ennf transformation 2]
49. ! [X0] : (((~strong(X0) | brave(X0)) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0)))) & (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (strong(X0) & ~brave(X0)))) [nnf transformation 5]
50. ! [X0] : ((~strong(X0) | brave(X0) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0)))) & (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (strong(X0) & ~brave(X0)))) [flattening 49]
67. ! [X0] : (((patient(X0) | quiet(X0)) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & ~quiet(X0)))) [nnf transformation 14]
68. ! [X0] : ((patient(X0) | quiet(X0) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & ~quiet(X0)))) [flattening 67]
74. ! [X0] : (((~quiet(X0) & strong(X0)) | (strong(X0) | tall(X0))) & ((~strong(X0) & ~tall(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 16]
75. ! [X0] : (((~quiet(X0) & strong(X0)) | strong(X0) | tall(X0)) & ((~strong(X0) & ~tall(X0)) | quiet(X0) | ~strong(X0))) [flattening 74]
91. rich(X0) | brave(X0) [cnf transformation 31]
101. ~patient(X0) | ~rich(X0) | strong(X0) [cnf transformation 50]
136. ~quiet(X0) | ~quiet(X0) [cnf transformation 68]
138. patient(X0) | quiet(X0) | quiet(X0) [cnf transformation 68]
146. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 75]
164. ~brave(alice) [cnf transformation 25]
165. ~strong(X0) | quiet(X0) [duplicate literal removal 146]
167. ~quiet(X0) [duplicate literal removal 136]
168. quiet(X0) | patient(X0) [duplicate literal removal 138]
298. 29 <=> ! [X0] : ~quiet(X0) [avatar definition]
299. ~quiet(X0) <- (29) [avatar component clause 298]
302. 30 <=> rich(alice) [avatar definition]
303. rich(alice) <- (30) [avatar component clause 302]
304. ~rich(alice) <- (~30) [avatar component clause 302]
307. 29 [avatar split clause 167,298]
403. brave(alice) <- (~30) [resolution 304,91]
404. $false <- (~30) [subsumption resolution 403,164]
405. 30 [avatar contradiction clause 404]
413. patient(X1) <- (29) [resolution 168,299]
472. ~rich(X0) | strong(X0) <- (29) [resolution 101,413]
581. strong(alice) <- (29, 30) [resolution 472,303]
584. quiet(alice) <- (29, 30) [resolution 581,165]
585. $false <- (29, 30) [subsumption resolution 584,299]
586. ~29 | ~30 [avatar contradiction clause 585]
587. $false [avatar sat refutation 307,405,586]
% SZS output end Proof for 4576725236308079615742053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and calm then someone is either not wise or strong and vice versa.
If someone is both not humble and funny then someone is both kind and wise and vice versa.
If someone is either old or wise then someone is either brave or not creative.
Everyone who is not funny is rich or not tall and vice versa.
If lucy is both patient and not calm then someone is either calm or not strong.
Everyone who is patient is either not old or strong.
Everyone who is either generous or brave is not generous or not curious and vice versa.
If mary is both generous and not happy then paul is strong and vice versa.
Everyone who is not tall is both not quiet and funny and vice versa.
Everyone who is generous or not strong is humble or not creative.
If someone is quiet or creative then paul is not quiet.
If paul is both not generous and generous then someone is either generous or patient.
If alice is not old then someone is either not humble or not calm.
If someone is either not brave or strong then someone is happy or not happy.
If someone is both not old and rich then someone is either kind or not calm.
If lucy is both not curious and not strong then someone is humble and vice versa.
Paul is not happy.
Mary is not happy or generous.
Lucy is not old.
Paul is either brave or patient.
Someone is either rich or tall.
Fred is not wise.
Lucy is either tall or humble.
Someone is either generous or not creative. | Lucy is humble. | contradiction | ((?[X]:((~rich(X)&calm(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((kind(X)&wise(X)))))&
((?[X]:((old(X)<~>wise(X))))=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:(~funny(X)<=>(rich(X)|~tall(X))))&
(((patient(lucy)&~calm(lucy)))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:(patient(X)=>(~old(X)<~>strong(X))))&
(![X]:((generous(X)<~>brave(X))<=>(~generous(X)|~curious(X))))&
(((generous(mary)&~happy(mary)))<=>(strong(paul)))&
(![X]:(~tall(X)<=>(~quiet(X)&funny(X))))&
(![X]:((generous(X)|~strong(X))=>(humble(X)|~creative(X))))&
((?[X]:((quiet(X)|creative(X))))=>(~quiet(paul)))&
(((~generous(paul)&generous(paul)))=>(?[X]:((generous(X)<~>patient(X)))))&
((~old(alice))=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((happy(X)|~happy(X)))))&
((?[X]:((~old(X)&rich(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(((~curious(lucy)&~strong(lucy)))<=>(?[X]:(humble(X))))&
(~happy(paul))&
((~happy(mary)|generous(mary)))&
(~old(lucy))&
((brave(paul)<~>patient(paul)))&
(?[X]:((rich(X)<~>tall(X))))&
(~wise(fred))&
((tall(lucy)<~>humble(lucy)))&
(?[X]:((generous(X)<~>~creative(X)))) | humble(lucy) | [
"p3",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 428652301673975335144312
% SZS output start Proof for 428652301673975335144312
4. ! [X0] : (~funny(X0) <=> (~tall(X0) | rich(X0))) [input p3]
9. ! [X0] : (~tall(X0) <=> (funny(X0) & ~quiet(X0))) [input p8]
23. tall(lucy) <~> humble(lucy) [input p22]
25. humble(lucy) [input hypothesis]
57. ! [X0] : ((~funny(X0) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | funny(X0))) [nnf transformation 4]
58. ! [X0] : ((~funny(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | funny(X0))) [flattening 57]
67. ! [X0] : ((~tall(X0) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | tall(X0))) [nnf transformation 9]
68. ! [X0] : ((~tall(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | tall(X0))) [flattening 67]
92. (~humble(lucy) | ~tall(lucy)) & (humble(lucy) | tall(lucy)) [nnf transformation 23]
112. ~funny(X0) | tall(X0) [cnf transformation 58]
127. funny(X0) | tall(X0) [cnf transformation 68]
153. ~humble(lucy) | ~tall(lucy) [cnf transformation 92]
156. humble(lucy) [cnf transformation 25]
269. tall(X0) [subsumption resolution 127,112]
339. ~humble(lucy) [subsumption resolution 153,269]
350. $false [subsumption resolution 156,339]
% SZS output end Proof for 428652301673975335144312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not creative or not happy. Everyone who is either not humble or not tall is both happy and wise. Everyone who is not brave is curious or not rich. Everyone who is generous or not rich is not kind. Everyone who is both not happy and calm is either brave or not brave and vice versa. Everyone who is not old or rich is both curious and wise and vice versa. Everyone who is either not rich or not generous is not old or calm and vice versa. If someone is happy then someone is both not old and not happy and vice versa. If lucy is not patient then lucy is wise and vice versa. Everyone who is not funny or curious is either not brave or calm. Everyone who is both not strong and generous is both calm and creative. Everyone who is not happy or not humble is brave or not humble. Everyone who is both not rich and not kind is curious. If someone is not brave or not rich then susan is not generous and vice versa. Everyone who is both creative and not humble is both brave and not wise and vice versa. Everyone who is either not wise or strong is happy or creative and vice versa. Paul is either not quiet or not rich. Someone is both patient and not quiet. Alice is not kind or creative. Fred is not funny. Someone is not tall. Someone is both calm and rich. | Fred is rich. | neutral | (![X]:(~humble(X)=>(~creative(X)<~>~happy(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(happy(X)&wise(X))))&
(![X]:(~brave(X)=>(curious(X)|~rich(X))))&
(![X]:((generous(X)|~rich(X))=>~kind(X)))&
(![X]:((~happy(X)&calm(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((~old(X)|rich(X))<=>(curious(X)&wise(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~old(X)&~happy(X)))))&
((~patient(lucy))<=>(wise(lucy)))&
(![X]:((~funny(X)|curious(X))=>(~brave(X)<~>calm(X))))&
(![X]:((~strong(X)&generous(X))=>(calm(X)&creative(X))))&
(![X]:((~happy(X)|~humble(X))=>(brave(X)|~humble(X))))&
(![X]:((~rich(X)&~kind(X))=>curious(X)))&
((?[X]:((~brave(X)|~rich(X))))<=>(~generous(susan)))&
(![X]:((creative(X)&~humble(X))<=>(brave(X)&~wise(X))))&
(![X]:((~wise(X)<~>strong(X))<=>(happy(X)|creative(X))))&
((~quiet(paul)<~>~rich(paul)))&
(?[X]:((patient(X)&~quiet(X))))&
((~kind(alice)|creative(alice)))&
(~funny(fred))&
(?[X]:(~tall(X)))&
(?[X]:((calm(X)&rich(X)))) | rich(fred) | [] | null | 0 |
Everyone who is either not patient or not funny is old.
Everyone who is both rich and calm is either not tall or not curious.
If mary is both strong and not creative then mary is either tall or not creative.
Everyone who is either not happy or not old is both not wise and curious.
If someone is not tall or not patient then fred is not brave or generous and vice versa.
Everyone who is either happy or not patient is brave and vice versa.
Everyone who is either funny or not generous is old or not brave and vice versa.
Everyone who is kind is either not rich or quiet and vice versa.
Everyone who is not humble or wise is strong and vice versa.
Everyone who is both humble and brave is not strong.
If lucy is both humble and curious then mary is patient or tall and vice versa.
Everyone who is not tall is quiet or patient.
If paul is not kind then john is not tall or calm and vice versa.
Everyone who is not happy or brave is patient or not strong and vice versa.
If mary is funny then susan is tall or not rich and vice versa.
Everyone who is both not brave and not creative is rich and vice versa.
Someone is strong or patient.
Someone is either not strong or strong.
Lucy is both generous and humble.
Paul is not wise.
Mary is not curious or not generous.
Someone is both brave and not humble.
Someone is old. | Paul is strong. | neutral | (![X]:((~patient(X)<~>~funny(X))=>old(X)))&
(![X]:((rich(X)&calm(X))=>(~tall(X)<~>~curious(X))))&
(((strong(mary)&~creative(mary)))=>((tall(mary)<~>~creative(mary))))&
(![X]:((~happy(X)<~>~old(X))=>(~wise(X)&curious(X))))&
((?[X]:((~tall(X)|~patient(X))))<=>((~brave(fred)|generous(fred))))&
(![X]:((happy(X)<~>~patient(X))<=>brave(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(old(X)|~brave(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>quiet(X))))&
(![X]:((~humble(X)|wise(X))<=>strong(X)))&
(![X]:((humble(X)&brave(X))=>~strong(X)))&
(((humble(lucy)&curious(lucy)))<=>((patient(mary)|tall(mary))))&
(![X]:(~tall(X)=>(quiet(X)|patient(X))))&
((~kind(paul))<=>((~tall(john)|calm(john))))&
(![X]:((~happy(X)|brave(X))<=>(patient(X)|~strong(X))))&
((funny(mary))<=>((tall(susan)|~rich(susan))))&
(![X]:((~brave(X)&~creative(X))<=>rich(X)))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
((generous(lucy)&humble(lucy)))&
(~wise(paul))&
((~curious(mary)|~generous(mary)))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:(old(X))) | strong(paul) | [] | null | 0 |
If alice is not rich or not strong then lucy is rich. Everyone who is not patient or not creative is generous. Everyone who is humble or not happy is both humble and not humble and vice versa. Everyone who is both happy and generous is both not wise and old. If someone is not wise then lucy is both not brave and curious. Everyone who is not old or old is either rich or curious and vice versa. If john is both not generous and not curious then someone is old. If someone is creative or not creative then mary is either not creative or not old and vice versa. Everyone who is both creative and not kind is both tall and not patient. If paul is both kind and quiet then someone is not humble and vice versa. If someone is not patient then someone is both not tall and not patient and vice versa. If john is happy or not calm then paul is wise. Everyone who is either not happy or calm is either happy or humble. Everyone who is either strong or not humble is either happy or tall and vice versa. Everyone who is both calm and funny is both happy and not curious and vice versa. Everyone who is not funny is either humble or not wise and vice versa. Someone is both happy and not strong. Someone is not creative. Someone is both rich and patient. Lucy is either not quiet or humble. Someone is not humble. Someone is either kind or generous. | Paul is not creative. | contradiction | (((~rich(alice)|~strong(alice)))=>(rich(lucy)))&
(![X]:((~patient(X)|~creative(X))=>generous(X)))&
(![X]:((humble(X)|~happy(X))<=>(humble(X)&~humble(X))))&
(![X]:((happy(X)&generous(X))=>(~wise(X)&old(X))))&
((?[X]:(~wise(X)))=>((~brave(lucy)&curious(lucy))))&
(![X]:((~old(X)|old(X))<=>(rich(X)<~>curious(X))))&
(((~generous(john)&~curious(john)))=>(?[X]:(old(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(mary)<~>~old(mary))))&
(![X]:((creative(X)&~kind(X))=>(tall(X)&~patient(X))))&
(((kind(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(((happy(john)|~calm(john)))=>(wise(paul)))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)<~>humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)<~>tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)&patient(X))))&
((~quiet(lucy)<~>humble(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)<~>generous(X)))) | ~creative(paul) | [
"p1",
"p2",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1684834881846182190744242
% SZS output start Proof for 1684834881846182190744242
2. ! [X0] : ((~creative(X0) | ~patient(X0)) => generous(X0)) [input p1]
3. ! [X0] : ((~happy(X0) | humble(X0)) <=> (~humble(X0) & humble(X0))) [input p2]
4. ! [X0] : ((generous(X0) & happy(X0)) => (old(X0) & ~wise(X0))) [input p3]
12. (~calm(john) | happy(john)) => wise(paul) [input p11]
23. ~creative(paul) [input hypothesis]
27. ! [X0] : (generous(X0) | (creative(X0) & patient(X0))) [ennf transformation 2]
28. ! [X0] : ((old(X0) & ~wise(X0)) | (~generous(X0) | ~happy(X0))) [ennf transformation 4]
29. ! [X0] : ((old(X0) & ~wise(X0)) | ~generous(X0) | ~happy(X0)) [flattening 28]
35. wise(paul) | (calm(john) & ~happy(john)) [ennf transformation 12]
37. ! [X0] : (((~happy(X0) | humble(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 3]
38. ! [X0] : ((~happy(X0) | humble(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (happy(X0) & ~humble(X0)))) [flattening 37]
77. generous(X0) | creative(X0) [cnf transformation 27]
79. humble(X0) | happy(X0) [cnf transformation 38]
80. ~humble(X0) | ~humble(X0) [cnf transformation 38]
83. ~wise(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 29]
107. wise(paul) | ~happy(john) [cnf transformation 35]
139. ~creative(paul) [cnf transformation 23]
142. ~humble(X0) [duplicate literal removal 80]
158. happy(X0) [subsumption resolution 79,142]
160. ~wise(X0) | ~generous(X0) [subsumption resolution 83,158]
230. 19 <=> wise(paul) [avatar definition]
232. wise(paul) <- (19) [avatar component clause 230]
234. wise(paul) [subsumption resolution 107,158]
235. 19 [avatar split clause 234,230]
261. ~generous(paul) <- (19) [resolution 160,232]
273. creative(paul) <- (19) [resolution 261,77]
275. $false <- (19) [subsumption resolution 273,139]
276. ~19 [avatar contradiction clause 275]
277. $false [avatar sat refutation 235,276]
% SZS output end Proof for 1684834881846182190744242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or humble is both rich and not curious and vice versa.
If lucy is not kind then lucy is both happy and not old and vice versa.
If john is both curious and brave then someone is not creative or not brave and vice versa.
If paul is not tall then someone is not curious.
If lucy is funny then someone is both brave and not tall and vice versa.
If someone is both kind and not humble then someone is quiet.
If someone is both calm and wise then someone is both not creative and humble and vice versa.
Everyone who is not brave or curious is not funny.
Everyone who is not funny or quiet is not calm or funny.
Everyone who is patient or not calm is either quiet or tall and vice versa.
If paul is not humble then someone is not happy or not old and vice versa.
If fred is either patient or brave then fred is either not funny or creative.
Everyone who is old or not patient is both kind and not generous and vice versa.
If someone is both curious and old then paul is not old or strong and vice versa.
Everyone who is both not kind and not creative is both not creative and humble and vice versa.
If mary is either not generous or curious then someone is either not curious or rich.
Alice is both calm and humble.
Fred is both not brave and rich.
Paul is kind.
Someone is funny or humble.
Someone is not brave or not happy.
Susan is curious.
Someone is not tall or not happy. | Susan is calm. | contradiction | (![X]:((~patient(X)|humble(X))<=>(rich(X)&~curious(X))))&
((~kind(lucy))<=>((happy(lucy)&~old(lucy))))&
(((curious(john)&brave(john)))<=>(?[X]:((~creative(X)|~brave(X)))))&
((~tall(paul))=>(?[X]:(~curious(X))))&
((funny(lucy))<=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((~brave(X)|curious(X))=>~funny(X)))&
(![X]:((~funny(X)|quiet(X))=>(~calm(X)|funny(X))))&
(![X]:((patient(X)|~calm(X))<=>(quiet(X)<~>tall(X))))&
((~humble(paul))<=>(?[X]:((~happy(X)|~old(X)))))&
(((patient(fred)<~>brave(fred)))=>((~funny(fred)<~>creative(fred))))&
(![X]:((old(X)|~patient(X))<=>(kind(X)&~generous(X))))&
((?[X]:((curious(X)&old(X))))<=>((~old(paul)|strong(paul))))&
(![X]:((~kind(X)&~creative(X))<=>(~creative(X)&humble(X))))&
(((~generous(mary)<~>curious(mary)))=>(?[X]:((~curious(X)<~>rich(X)))))&
((calm(alice)&humble(alice)))&
((~brave(fred)&rich(fred)))&
(kind(paul))&
(?[X]:((funny(X)|humble(X))))&
(?[X]:((~brave(X)|~happy(X))))&
(curious(susan))&
(?[X]:((~tall(X)|~happy(X)))) | calm(susan) | [
"p7",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 239274387700239751430765
% SZS output start Proof for 239274387700239751430765
8. ! [X0] : ((curious(X0) | ~brave(X0)) => ~funny(X0)) [input p7]
9. ! [X0] : ((quiet(X0) | ~funny(X0)) => (funny(X0) | ~calm(X0))) [input p8]
22. curious(susan) [input p21]
24. calm(susan) [input hypothesis]
29. ! [X0] : (~funny(X0) | (~curious(X0) & brave(X0))) [ennf transformation 8]
30. ! [X0] : ((funny(X0) | ~calm(X0)) | (~quiet(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : (funny(X0) | ~calm(X0) | (~quiet(X0) & funny(X0))) [flattening 30]
105. ~funny(X0) | ~curious(X0) [cnf transformation 29]
106. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 31]
146. curious(susan) [cnf transformation 22]
148. calm(susan) [cnf transformation 24]
149. ~calm(X0) | funny(X0) [duplicate literal removal 106]
379. funny(susan) [resolution 149,148]
385. ~curious(susan) [resolution 379,105]
387. $false [subsumption resolution 385,146]
% SZS output end Proof for 239274387700239751430765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious then john is either not humble or not funny and vice versa. If fred is both not curious and not patient then someone is both tall and happy. If paul is both not happy and not quiet then mary is both not strong and not creative. If susan is both not kind and not wise then lucy is both quiet and not quiet. If someone is not kind then someone is old or not creative and vice versa. Everyone who is not curious is old or funny and vice versa. If fred is both funny and not humble then someone is rich. Everyone who is both not patient and creative is calm or quiet. Everyone who is not creative or happy is both creative and not brave and vice versa. If mary is not funny then someone is either generous or humble and vice versa. Everyone who is either not generous or not humble is not creative. If alice is either not curious or kind then fred is both quiet and funny and vice versa. If someone is either not happy or not funny then fred is curious or kind. If someone is not kind then fred is either curious or not kind. If someone is either quiet or rich then someone is either not humble or not old and vice versa. Everyone who is not humble is both not creative and not generous and vice versa. Someone is either not wise or generous. Mary is not curious. Someone is calm or not calm. Paul is both wise and not quiet. John is either rich or curious. Someone is humble. Someone is either brave or not quiet. Someone is both not calm and humble. | John is creative. | entailment | ((?[X]:((wise(X)|curious(X))))<=>((~humble(john)<~>~funny(john))))&
(((~curious(fred)&~patient(fred)))=>(?[X]:((tall(X)&happy(X)))))&
(((~happy(paul)&~quiet(paul)))=>((~strong(mary)&~creative(mary))))&
(((~kind(susan)&~wise(susan)))=>((quiet(lucy)&~quiet(lucy))))&
((?[X]:(~kind(X)))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:(~curious(X)<=>(old(X)|funny(X))))&
(((funny(fred)&~humble(fred)))=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&creative(X))=>(calm(X)|quiet(X))))&
(![X]:((~creative(X)|happy(X))<=>(creative(X)&~brave(X))))&
((~funny(mary))<=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>~creative(X)))&
(((~curious(alice)<~>kind(alice)))<=>((quiet(fred)&funny(fred))))&
((?[X]:((~happy(X)<~>~funny(X))))=>((curious(fred)|kind(fred))))&
((?[X]:(~kind(X)))=>((curious(fred)<~>~kind(fred))))&
((?[X]:((quiet(X)<~>rich(X))))<=>(?[X]:((~humble(X)<~>~old(X)))))&
(![X]:(~humble(X)<=>(~creative(X)&~generous(X))))&
(?[X]:((~wise(X)<~>generous(X))))&
(~curious(mary))&
(?[X]:((calm(X)|~calm(X))))&
((wise(paul)&~quiet(paul)))&
((rich(john)<~>curious(john)))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:((~calm(X)&humble(X)))) | creative(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 725642548842196861080066
% SZS output start Proof for 725642548842196861080066
9. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~brave(X0) & creative(X0))) [input p8]
25. ~creative(john) [input hypothesis]
55. ! [X0] : (((happy(X0) | ~creative(X0)) | (brave(X0) | ~creative(X0))) & ((~brave(X0) & creative(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 9]
56. ! [X0] : ((happy(X0) | ~creative(X0) | brave(X0) | ~creative(X0)) & ((~brave(X0) & creative(X0)) | (~happy(X0) & creative(X0)))) [flattening 55]
102. creative(X0) | creative(X0) [cnf transformation 56]
147. ~creative(john) [cnf transformation 25]
148. creative(X0) [duplicate literal removal 102]
206. 13 <=> ! [X1] : creative(X1) [avatar definition]
207. creative(X1) <- (13) [avatar component clause 206]
242. 13 [avatar split clause 148,206]
375. $false <- (13) [resolution 207,147]
376. ~13 [avatar contradiction clause 375]
377. $false [avatar sat refutation 242,376]
% SZS output end Proof for 725642548842196861080066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and happy then susan is curious or calm.
Everyone who is generous is both not brave and not creative.
If someone is both not generous and not wise then fred is both rich and creative.
Everyone who is either not curious or wise is not quiet and vice versa.
Everyone who is both kind and not kind is not patient or old and vice versa.
If lucy is either not funny or not humble then someone is not brave or humble and vice versa.
Everyone who is brave or strong is not brave and vice versa.
Everyone who is both rich and not tall is either tall or not tall.
If someone is not funny or not strong then someone is humble or not quiet.
Everyone who is either not strong or strong is either creative or not humble.
If someone is funny then alice is either not rich or not happy and vice versa.
If alice is rich then mary is curious and vice versa.
Everyone who is both quiet and curious is not calm or calm.
Everyone who is not generous or funny is not creative.
If john is either tall or quiet then john is generous and vice versa.
Everyone who is not calm or calm is either not kind or humble.
Someone is not happy.
Lucy is both wise and not brave.
Someone is either rich or not rich.
Someone is funny.
Alice is funny.
Someone is either curious or creative. | Susan is not creative. | entailment | ((?[X]:((brave(X)&happy(X))))=>((curious(susan)|calm(susan))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
((?[X]:((~generous(X)&~wise(X))))=>((rich(fred)&creative(fred))))&
(![X]:((~curious(X)<~>wise(X))<=>~quiet(X)))&
(![X]:((kind(X)&~kind(X))<=>(~patient(X)|old(X))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((brave(X)|strong(X))<=>~brave(X)))&
(![X]:((rich(X)&~tall(X))=>(tall(X)<~>~tall(X))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>((~rich(alice)<~>~happy(alice))))&
((rich(alice))<=>(curious(mary)))&
(![X]:((quiet(X)&curious(X))=>(~calm(X)|calm(X))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(((tall(john)<~>quiet(john)))<=>(generous(john)))&
(![X]:((~calm(X)|calm(X))=>(~kind(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((wise(lucy)&~brave(lucy)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
(funny(alice))&
(?[X]:((curious(X)<~>creative(X)))) | ~creative(susan) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4000089063215906079223915
% SZS output start Proof for 4000089063215906079223915
2. ! [X0] : (generous(X0) => (~creative(X0) & ~brave(X0))) [input p1]
14. ! [X0] : ((funny(X0) | ~generous(X0)) => ~creative(X0)) [input p13]
23. creative(susan) [input hypothesis]
27. ! [X0] : ((~creative(X0) & ~brave(X0)) | ~generous(X0)) [ennf transformation 2]
35. ! [X0] : (~creative(X0) | (~funny(X0) & generous(X0))) [ennf transformation 14]
70. ~creative(X0) | ~generous(X0) [cnf transformation 27]
106. ~creative(X0) | generous(X0) [cnf transformation 35]
125. creative(susan) [cnf transformation 23]
232. ~creative(X0) [subsumption resolution 106,70]
252. $false [subsumption resolution 125,232]
% SZS output end Proof for 4000089063215906079223915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or kind is both not humble and not happy.
Everyone who is rich or creative is both generous and not quiet and vice versa.
If someone is either patient or creative then alice is both generous and not patient.
If paul is either not old or not tall then paul is both not wise and not calm and vice versa.
If someone is humble then someone is brave or not strong and vice versa.
If mary is strong then someone is either not tall or not funny and vice versa.
If john is either not humble or wise then paul is strong or not creative.
Everyone who is rich or not kind is rich or not wise.
Everyone who is either curious or not calm is both not brave and not patient and vice versa.
Everyone who is not happy or funny is kind.
Everyone who is both not strong and brave is not old or not calm and vice versa.
If someone is not kind or not patient then someone is not rich.
If someone is not tall or quiet then someone is either not rich or patient and vice versa.
Everyone who is rich or not rich is both curious and generous.
Everyone who is either not happy or not quiet is kind and vice versa.
Everyone who is quiet or not humble is not kind.
John is quiet.
Someone is either patient or not old.
Lucy is either not strong or patient.
Fred is not brave or patient.
Mary is not rich or not calm.
Someone is not patient or not kind.
Someone is not patient or not tall.
Someone is either rich or brave. | Lucy is not strong. | entailment | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((rich(X)|creative(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((patient(X)<~>creative(X))))=>((generous(alice)&~patient(alice))))&
(((~old(paul)<~>~tall(paul)))<=>((~wise(paul)&~calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((brave(X)|~strong(X)))))&
((strong(mary))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
(((~humble(john)<~>wise(john)))=>((strong(paul)|~creative(paul))))&
(![X]:((rich(X)|~kind(X))=>(rich(X)|~wise(X))))&
(![X]:((curious(X)<~>~calm(X))<=>(~brave(X)&~patient(X))))&
(![X]:((~happy(X)|funny(X))=>kind(X)))&
(![X]:((~strong(X)&brave(X))<=>(~old(X)|~calm(X))))&
((?[X]:((~kind(X)|~patient(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((rich(X)|~rich(X))=>(curious(X)&generous(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((quiet(X)|~humble(X))=>~kind(X)))&
(quiet(john))&
(?[X]:((patient(X)<~>~old(X))))&
((~strong(lucy)<~>patient(lucy)))&
((~brave(fred)|patient(fred)))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>brave(X)))) | ~strong(lucy) | [
"p8",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7442002781214532410612543
% SZS output start Proof for 7442002781214532410612543
9. ! [X0] : ((curious(X0) <~> ~calm(X0)) <=> (~patient(X0) & ~brave(X0))) [input p8]
11. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~calm(X0) | ~old(X0))) [input p10]
14. ! [X0] : ((~rich(X0) | rich(X0)) => (generous(X0) & curious(X0))) [input p13]
19. ~strong(lucy) <~> patient(lucy) [input p18]
25. strong(lucy) [input hypothesis]
37. ! [X0] : ((generous(X0) & curious(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 14]
55. ! [X0] : ((((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | (patient(X0) | brave(X0))) & ((~patient(X0) & ~brave(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))))) [nnf transformation 9]
56. ! [X0] : ((((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | patient(X0) | brave(X0)) & ((~patient(X0) & ~brave(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))))) [flattening 55]
57. ! [X0] : (((brave(X0) & ~strong(X0)) | (calm(X0) & old(X0))) & ((~calm(X0) | ~old(X0)) | (~brave(X0) | strong(X0)))) [nnf transformation 11]
58. ! [X0] : (((brave(X0) & ~strong(X0)) | (calm(X0) & old(X0))) & (~calm(X0) | ~old(X0) | ~brave(X0) | strong(X0))) [flattening 57]
71. (~patient(lucy) | strong(lucy)) & (patient(lucy) | ~strong(lucy)) [nnf transformation 19]
111. ~curious(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 56]
119. ~strong(X0) | calm(X0) [cnf transformation 58]
130. curious(X0) | ~rich(X0) [cnf transformation 37]
131. curious(X0) | rich(X0) [cnf transformation 37]
143. patient(lucy) | ~strong(lucy) [cnf transformation 71]
151. strong(lucy) [cnf transformation 25]
303. curious(X0) [subsumption resolution 130,131]
316. 37 <=> strong(lucy) [avatar definition]
318. strong(lucy) <- (37) [avatar component clause 316]
320. 38 <=> patient(lucy) [avatar definition]
321. patient(lucy) <- (38) [avatar component clause 320]
324. ~37 | 38 [avatar split clause 143,320,316]
371. 37 [avatar split clause 151,316]
375. calm(lucy) <- (37) [resolution 119,318]
450. ~calm(X1) | ~patient(X1) [resolution 111,303]
481. ~patient(lucy) <- (37) [resolution 450,375]
485. $false <- (37, 38) [subsumption resolution 481,321]
486. ~37 | ~38 [avatar contradiction clause 485]
488. $false [avatar sat refutation 324,371,486]
% SZS output end Proof for 7442002781214532410612543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or not kind then someone is not tall or not rich and vice versa. If someone is wise then paul is not strong. If alice is either funny or happy then paul is humble or rich and vice versa. If someone is curious or kind then susan is wise and vice versa. Everyone who is happy is not creative and vice versa. Everyone who is not rich or not kind is either not generous or not happy. Everyone who is both not kind and not curious is both not strong and not old. If lucy is funny then someone is both generous and not quiet and vice versa. Everyone who is not funny is strong and vice versa. Everyone who is not brave is both strong and not patient. Everyone who is either not happy or not strong is either funny or not curious. If alice is either happy or not happy then susan is either not strong or not rich and vice versa. Everyone who is not old is creative or old. Everyone who is brave or not curious is either curious or not rich. If someone is creative or wise then someone is not old. Everyone who is either not calm or not quiet is calm and vice versa. Someone is either old or quiet. Someone is funny. Someone is patient. Someone is curious. Paul is calm. Susan is rich or quiet. Someone is not wise or not patient. John is either creative or brave. | Susan is strong. | contradiction | ((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~tall(X)|~rich(X)))))&
((?[X]:(wise(X)))=>(~strong(paul)))&
(((funny(alice)<~>happy(alice)))<=>((humble(paul)|rich(paul))))&
((?[X]:((curious(X)|kind(X))))<=>(wise(susan)))&
(![X]:(happy(X)<=>~creative(X)))&
(![X]:((~rich(X)|~kind(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~kind(X)&~curious(X))=>(~strong(X)&~old(X))))&
((funny(lucy))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:(~funny(X)<=>strong(X)))&
(![X]:(~brave(X)=>(strong(X)&~patient(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(funny(X)<~>~curious(X))))&
(((happy(alice)<~>~happy(alice)))<=>((~strong(susan)<~>~rich(susan))))&
(![X]:(~old(X)=>(creative(X)|old(X))))&
(![X]:((brave(X)|~curious(X))=>(curious(X)<~>~rich(X))))&
((?[X]:((creative(X)|wise(X))))=>(?[X]:(~old(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>calm(X)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:(funny(X)))&
(?[X]:(patient(X)))&
(?[X]:(curious(X)))&
(calm(paul))&
((rich(susan)|quiet(susan)))&
(?[X]:((~wise(X)|~patient(X))))&
((creative(john)<~>brave(john))) | strong(susan) | [
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 872192304757895542450155
% SZS output start Proof for 872192304757895542450155
12. (happy(alice) <~> ~happy(alice)) <=> (~strong(susan) <~> ~rich(susan)) [input p11]
16. ! [X0] : ((~calm(X0) <~> ~quiet(X0)) <=> calm(X0)) [input p15]
22. quiet(susan) | rich(susan) [input p21]
25. strong(susan) [input hypothesis]
57. (((happy(alice) | ~happy(alice)) & (~happy(alice) | happy(alice))) | ((~strong(susan) | rich(susan)) & (~rich(susan) | strong(susan)))) & (((rich(susan) | strong(susan)) & (~rich(susan) | ~strong(susan))) | ((happy(alice) | happy(alice)) & (~happy(alice) | ~happy(alice)))) [nnf transformation 12]
62. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | ~calm(X0)) & (calm(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [nnf transformation 16]
110. ~rich(susan) | ~strong(susan) | ~happy(alice) | ~happy(alice) [cnf transformation 57]
111. ~rich(susan) | ~strong(susan) | happy(alice) | happy(alice) [cnf transformation 57]
125. calm(X0) | ~quiet(X0) | calm(X0) [cnf transformation 62]
127. ~quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 62]
135. quiet(susan) | rich(susan) [cnf transformation 22]
139. strong(susan) [cnf transformation 25]
140. calm(X0) | ~quiet(X0) [duplicate literal removal 125]
141. ~quiet(X0) | ~calm(X0) [duplicate literal removal 127]
144. ~rich(susan) | ~strong(susan) | ~happy(alice) [duplicate literal removal 110]
145. ~rich(susan) | ~strong(susan) | happy(alice) [duplicate literal removal 111]
199. 13 <=> happy(alice) [avatar definition]
254. 24 <=> strong(susan) [avatar definition]
258. 25 <=> rich(susan) [avatar definition]
263. 13 | ~24 | ~25 [avatar split clause 145,258,254,199]
264. ~13 | ~24 | ~25 [avatar split clause 144,258,254,199]
274. ~quiet(X0) [subsumption resolution 140,141]
276. rich(susan) [subsumption resolution 135,274]
277. 25 [avatar split clause 276,258]
297. 24 [avatar split clause 139,254]
298. $false [avatar sat refutation 263,264,277,297]
% SZS output end Proof for 872192304757895542450155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old is either not happy or tall.
Everyone who is both not funny and calm is both not old and not happy and vice versa.
If someone is not generous or not strong then someone is not kind or not old.
Everyone who is both not patient and curious is either not wise or not quiet.
Everyone who is both patient and curious is quiet or not brave and vice versa.
Everyone who is both tall and old is either not strong or generous and vice versa.
Everyone who is not funny or not strong is both happy and not strong.
Everyone who is both curious and not calm is both not kind and generous and vice versa.
Everyone who is not creative is old or generous and vice versa.
Everyone who is either not old or not rich is humble and vice versa.
If someone is not tall then someone is kind or not humble and vice versa.
If someone is not kind then someone is generous.
If someone is creative or not old then someone is calm.
If alice is not humble then paul is both kind and not brave.
Everyone who is humble is wise and vice versa.
If someone is either not wise or quiet then alice is not happy or humble and vice versa.
Someone is calm or funny.
Mary is either not generous or not rich.
John is generous or not brave.
Someone is both not quiet and not patient.
Someone is both not wise and not creative.
John is both rich and quiet.
Someone is both brave and calm. | Alice is not kind. | neutral | (![X]:((curious(X)<~>~old(X))=>(~happy(X)<~>tall(X))))&
(![X]:((~funny(X)&calm(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((~patient(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((patient(X)&curious(X))<=>(quiet(X)|~brave(X))))&
(![X]:((tall(X)&old(X))<=>(~strong(X)<~>generous(X))))&
(![X]:((~funny(X)|~strong(X))=>(happy(X)&~strong(X))))&
(![X]:((curious(X)&~calm(X))<=>(~kind(X)&generous(X))))&
(![X]:(~creative(X)<=>(old(X)|generous(X))))&
(![X]:((~old(X)<~>~rich(X))<=>humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((kind(X)|~humble(X)))))&
((?[X]:(~kind(X)))=>(?[X]:(generous(X))))&
((?[X]:((creative(X)|~old(X))))=>(?[X]:(calm(X))))&
((~humble(alice))=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)<=>wise(X)))&
((?[X]:((~wise(X)<~>quiet(X))))<=>((~happy(alice)|humble(alice))))&
(?[X]:((calm(X)|funny(X))))&
((~generous(mary)<~>~rich(mary)))&
((generous(john)|~brave(john)))&
(?[X]:((~quiet(X)&~patient(X))))&
(?[X]:((~wise(X)&~creative(X))))&
((rich(john)&quiet(john)))&
(?[X]:((brave(X)&calm(X)))) | ~kind(alice) | [] | null | 0 |
Everyone who is both calm and curious is not kind.
Everyone who is both not brave and brave is both not rich and creative and vice versa.
If someone is not happy then someone is either generous or not patient and vice versa.
Everyone who is kind is either not generous or old.
If lucy is not rich or not funny then susan is not creative or not happy and vice versa.
Everyone who is not patient is either creative or calm and vice versa.
If lucy is not quiet or wise then lucy is either not funny or strong and vice versa.
If someone is both calm and creative then fred is not rich and vice versa.
Everyone who is both happy and not patient is both generous and not tall.
Everyone who is either patient or creative is not strong or happy.
If someone is not old then alice is both brave and not generous.
Everyone who is either curious or not calm is curious or not rich.
If someone is either brave or not happy then fred is not humble.
If paul is calm or strong then john is not tall or not curious.
Everyone who is both strong and tall is both rich and not old.
If paul is not calm then someone is brave.
Alice is either not patient or wise.
Someone is either not humble or brave.
Someone is both not humble and wise.
Alice is funny.
Someone is not curious.
Paul is either old or strong.
Alice is not tall or quiet.
Someone is kind or not curious. | Alice is not patient. | neutral | (![X]:((calm(X)&curious(X))=>~kind(X)))&
(![X]:((~brave(X)&brave(X))<=>(~rich(X)&creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:(kind(X)=>(~generous(X)<~>old(X))))&
(((~rich(lucy)|~funny(lucy)))<=>((~creative(susan)|~happy(susan))))&
(![X]:(~patient(X)<=>(creative(X)<~>calm(X))))&
(((~quiet(lucy)|wise(lucy)))<=>((~funny(lucy)<~>strong(lucy))))&
((?[X]:((calm(X)&creative(X))))<=>(~rich(fred)))&
(![X]:((happy(X)&~patient(X))=>(generous(X)&~tall(X))))&
(![X]:((patient(X)<~>creative(X))=>(~strong(X)|happy(X))))&
((?[X]:(~old(X)))=>((brave(alice)&~generous(alice))))&
(![X]:((curious(X)<~>~calm(X))=>(curious(X)|~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))=>(~humble(fred)))&
(((calm(paul)|strong(paul)))=>((~tall(john)|~curious(john))))&
(![X]:((strong(X)&tall(X))=>(rich(X)&~old(X))))&
((~calm(paul))=>(?[X]:(brave(X))))&
((~patient(alice)<~>wise(alice)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((~humble(X)&wise(X))))&
(funny(alice))&
(?[X]:(~curious(X)))&
((old(paul)<~>strong(paul)))&
((~tall(alice)|quiet(alice)))&
(?[X]:((kind(X)|~curious(X)))) | ~patient(alice) | [] | null | 0 |
Everyone who is rich is not creative.
If someone is both not creative and not old then lucy is not quiet and vice versa.
If mary is strong or funny then someone is both not generous and not rich and vice versa.
Everyone who is both not curious and patient is happy and vice versa.
If paul is not old then someone is both not kind and not curious and vice versa.
Everyone who is either rich or not humble is both kind and humble.
If alice is not happy or not brave then susan is either not quiet or generous.
If mary is not tall then someone is not curious or funny.
If susan is either not quiet or not generous then someone is either not rich or generous and vice versa.
If susan is both not tall and not wise then someone is both humble and not old.
If someone is either funny or tall then someone is calm and vice versa.
Everyone who is either quiet or generous is not rich or curious.
Everyone who is both not calm and wise is both patient and not patient.
If john is both quiet and patient then lucy is either not tall or not patient and vice versa.
Everyone who is kind or quiet is humble and vice versa.
If paul is both not wise and not creative then someone is both not old and happy.
Someone is both curious and not generous.
Fred is tall.
Fred is calm.
Someone is not curious or rich.
Lucy is not patient.
Mary is both not creative and funny.
Someone is both not quiet and not creative. | Alice is patient. | entailment | (![X]:(rich(X)=>~creative(X)))&
((?[X]:((~creative(X)&~old(X))))<=>(~quiet(lucy)))&
(((strong(mary)|funny(mary)))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~curious(X)&patient(X))<=>happy(X)))&
((~old(paul))<=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((rich(X)<~>~humble(X))=>(kind(X)&humble(X))))&
(((~happy(alice)|~brave(alice)))=>((~quiet(susan)<~>generous(susan))))&
((~tall(mary))=>(?[X]:((~curious(X)|funny(X)))))&
(((~quiet(susan)<~>~generous(susan)))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(((~tall(susan)&~wise(susan)))=>(?[X]:((humble(X)&~old(X)))))&
((?[X]:((funny(X)<~>tall(X))))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)|curious(X))))&
(![X]:((~calm(X)&wise(X))=>(patient(X)&~patient(X))))&
(((quiet(john)&patient(john)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:((kind(X)|quiet(X))<=>humble(X)))&
(((~wise(paul)&~creative(paul)))=>(?[X]:((~old(X)&happy(X)))))&
(?[X]:((curious(X)&~generous(X))))&
(tall(fred))&
(calm(fred))&
(?[X]:((~curious(X)|rich(X))))&
(~patient(lucy))&
((~creative(mary)&funny(mary)))&
(?[X]:((~quiet(X)&~creative(X)))) | patient(alice) | [
"p2",
"p3",
"p6",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3745674570224525630678262
% SZS output start Proof for 3745674570224525630678262
3. (funny(mary) | strong(mary)) <=> ? [X0] : (~rich(X0) & ~generous(X0)) [input p2]
4. ! [X0] : ((patient(X0) & ~curious(X0)) <=> happy(X0)) [input p3]
7. (~brave(alice) | ~happy(alice)) => (~quiet(susan) <~> generous(susan)) [input p6]
9. (~quiet(susan) <~> ~generous(susan)) <=> ? [X0] : (~rich(X0) <~> generous(X0)) [input p8]
22. funny(mary) & ~creative(mary) [input p21]
24. ~patient(alice) [input hypothesis]
26. ! [X0] : (happy(X0) => (patient(X0) & ~curious(X0))) [unused predicate definition removal 4]
27. ~happy(alice) => (~quiet(susan) <~> generous(susan)) [pure predicate removal 7]
29. ! [X0] : ((patient(X0) & ~curious(X0)) | ~happy(X0)) [ennf transformation 26]
31. (~quiet(susan) <~> generous(susan)) | happy(alice) [ennf transformation 27]
45. ((funny(mary) | strong(mary)) | ! [X0] : (rich(X0) | generous(X0))) & (? [X0] : (~rich(X0) & ~generous(X0)) | (~funny(mary) & ~strong(mary))) [nnf transformation 3]
46. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & (? [X0] : (~rich(X0) & ~generous(X0)) | (~funny(mary) & ~strong(mary))) [flattening 45]
47. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & (? [X1] : (~rich(X1) & ~generous(X1)) | (~funny(mary) & ~strong(mary))) [rectify 46]
48. ? [X1] : (~rich(X1) & ~generous(X1)) => (~rich(sK1) & ~generous(sK1)) [choice axiom]
49. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & ((~rich(sK1) & ~generous(sK1)) | (~funny(mary) & ~strong(mary))) [skolemisation 47,48]
55. ((~generous(susan) | quiet(susan)) & (generous(susan) | ~quiet(susan))) | happy(alice) [nnf transformation 31]
58. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X0] : ((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [nnf transformation 9]
59. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [rectify 58]
60. ? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) => ((~generous(sK4) | rich(sK4)) & (generous(sK4) | ~rich(sK4))) [choice axiom]
61. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(sK4) | rich(sK4)) & (generous(sK4) | ~rich(sK4))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [skolemisation 59,60]
87. ~generous(sK1) | ~funny(mary) [cnf transformation 49]
89. ~rich(sK1) | ~funny(mary) [cnf transformation 49]
92. ~happy(X0) | patient(X0) [cnf transformation 29]
100. generous(susan) | ~quiet(susan) | happy(alice) [cnf transformation 55]
101. ~generous(susan) | quiet(susan) | happy(alice) [cnf transformation 55]
107. ~generous(susan) | ~quiet(susan) | generous(X0) | rich(X0) [cnf transformation 61]
109. generous(susan) | quiet(susan) | generous(X0) | rich(X0) [cnf transformation 61]
139. funny(mary) [cnf transformation 22]
142. ~patient(alice) [cnf transformation 24]
163. 5 <=> ! [X0] : (rich(X0) | generous(X0)) [avatar definition]
164. generous(X0) | rich(X0) <- (5) [avatar component clause 163]
170. 7 <=> funny(mary) [avatar definition]
175. 8 <=> rich(sK1) [avatar definition]
177. ~rich(sK1) <- (~8) [avatar component clause 175]
178. ~7 | ~8 [avatar split clause 89,175,170]
181. 9 <=> generous(sK1) [avatar definition]
183. ~generous(sK1) <- (~9) [avatar component clause 181]
184. ~7 | ~9 [avatar split clause 87,181,170]
205. 14 <=> happy(alice) [avatar definition]
207. happy(alice) <- (14) [avatar component clause 205]
209. 15 <=> quiet(susan) [avatar definition]
213. 16 <=> generous(susan) [avatar definition]
216. 14 | 15 | ~16 [avatar split clause 101,213,209,205]
217. 14 | ~15 | 16 [avatar split clause 100,213,209,205]
235. 5 | 15 | 16 [avatar split clause 109,213,209,163]
237. 5 | ~15 | ~16 [avatar split clause 107,213,209,163]
344. 7 [avatar split clause 139,170]
348. patient(alice) <- (14) [resolution 92,207]
349. $false <- (14) [subsumption resolution 348,142]
350. ~14 [avatar contradiction clause 349]
352. rich(sK1) <- (5, ~9) [resolution 164,183]
355. $false <- (5, ~8, ~9) [subsumption resolution 352,177]
356. ~5 | 8 | 9 [avatar contradiction clause 355]
359. $false [avatar sat refutation 178,184,216,217,235,237,344,350,356]
% SZS output end Proof for 3745674570224525630678262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both quiet and not kind and vice versa. Everyone who is not wise is both funny and not old. Everyone who is not quiet is either tall or calm. If mary is happy or humble then mary is both funny and not wise and vice versa. Everyone who is either not creative or not generous is both not strong and not happy and vice versa. If alice is kind or creative then fred is creative and vice versa. If someone is either wise or old then someone is not wise or creative. Everyone who is both not strong and not tall is quiet or strong. Everyone who is curious is not wise or tall. If someone is brave or not curious then someone is both not tall and not patient. Everyone who is either tall or funny is creative or old and vice versa. Everyone who is not tall is humble and vice versa. Everyone who is not wise or kind is rich. Everyone who is quiet is kind or quiet. If john is not generous or patient then someone is tall. Everyone who is kind is both not patient and not calm. Someone is generous. John is wise or brave. Someone is either not quiet or wise. Someone is both not happy and not old. Lucy is either not patient or happy. Someone is not brave or not funny. Someone is not strong or rich. Someone is either tall or wise. | Alice is creative. | neutral | (![X]:(~rich(X)<=>(quiet(X)&~kind(X))))&
(![X]:(~wise(X)=>(funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(tall(X)<~>calm(X))))&
(((happy(mary)|humble(mary)))<=>((funny(mary)&~wise(mary))))&
(![X]:((~creative(X)<~>~generous(X))<=>(~strong(X)&~happy(X))))&
(((kind(alice)|creative(alice)))<=>(creative(fred)))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((~strong(X)&~tall(X))=>(quiet(X)|strong(X))))&
(![X]:(curious(X)=>(~wise(X)|tall(X))))&
((?[X]:((brave(X)|~curious(X))))=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(creative(X)|old(X))))&
(![X]:(~tall(X)<=>humble(X)))&
(![X]:((~wise(X)|kind(X))=>rich(X)))&
(![X]:(quiet(X)=>(kind(X)|quiet(X))))&
(((~generous(john)|patient(john)))=>(?[X]:(tall(X))))&
(![X]:(kind(X)=>(~patient(X)&~calm(X))))&
(?[X]:(generous(X)))&
((wise(john)|brave(john)))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((~happy(X)&~old(X))))&
((~patient(lucy)<~>happy(lucy)))&
(?[X]:((~brave(X)|~funny(X))))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:((tall(X)<~>wise(X)))) | creative(alice) | [] | null | 0 |
If lucy is curious then john is both funny and not calm. Everyone who is both humble and not wise is not tall or tall and vice versa. Everyone who is brave or not humble is either old or not generous. Everyone who is either not wise or old is both not creative and not strong and vice versa. If someone is quiet then someone is either quiet or calm. If someone is both not rich and curious then someone is both not happy and not generous and vice versa. If lucy is both not old and rich then someone is strong or calm and vice versa. Everyone who is both not strong and not rich is not old or quiet and vice versa. If alice is not strong then someone is either not kind or wise and vice versa. If alice is wise then alice is creative or not patient and vice versa. If someone is not humble then someone is generous. If someone is either tall or humble then fred is both not quiet and not humble and vice versa. Everyone who is both not calm and not happy is not curious and vice versa. Everyone who is humble or not rich is not happy or generous. Everyone who is old or generous is either rich or not happy. Paul is funny. Someone is not calm or humble. Someone is either not wise or not happy. Someone is brave or not old. Someone is tall or old. Susan is not strong. | Fred is generous. | entailment | ((curious(lucy))=>((funny(john)&~calm(john))))&
(![X]:((humble(X)&~wise(X))<=>(~tall(X)|tall(X))))&
(![X]:((brave(X)|~humble(X))=>(old(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>old(X))<=>(~creative(X)&~strong(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)<~>calm(X)))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((~happy(X)&~generous(X)))))&
(((~old(lucy)&rich(lucy)))<=>(?[X]:((strong(X)|calm(X)))))&
(![X]:((~strong(X)&~rich(X))<=>(~old(X)|quiet(X))))&
((~strong(alice))<=>(?[X]:((~kind(X)<~>wise(X)))))&
((wise(alice))<=>((creative(alice)|~patient(alice))))&
((?[X]:(~humble(X)))=>(?[X]:(generous(X))))&
((?[X]:((tall(X)<~>humble(X))))<=>((~quiet(fred)&~humble(fred))))&
(![X]:((~calm(X)&~happy(X))<=>~curious(X)))&
(![X]:((humble(X)|~rich(X))=>(~happy(X)|generous(X))))&
(![X]:((old(X)|generous(X))=>(rich(X)<~>~happy(X))))&
(funny(paul))&
(?[X]:((~calm(X)|humble(X))))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:((tall(X)|old(X))))&
(~strong(susan)) | generous(fred) | [
"p1",
"p5",
"p6",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4545727056369993890400859
% SZS output start Proof for 4545727056369993890400859
2. ! [X0] : ((~wise(X0) & humble(X0)) <=> (tall(X0) | ~tall(X0))) [input p1]
6. ? [X0] : (curious(X0) & ~rich(X0)) <=> ? [X0] : (~generous(X0) & ~happy(X0)) [input p5]
7. (rich(lucy) & ~old(lucy)) <=> ? [X0] : (calm(X0) | strong(X0)) [input p6]
8. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (quiet(X0) | ~old(X0))) [input p7]
13. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> ~curious(X0)) [input p12]
14. ! [X0] : ((~rich(X0) | humble(X0)) => (generous(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((generous(X0) | old(X0)) => (rich(X0) <~> ~happy(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
24. ? [X0] : (curious(X0) & ~rich(X0)) <=> ? [X1] : (~generous(X1) & ~happy(X1)) [rectify 6]
32. ! [X0] : ((generous(X0) | ~happy(X0)) | (rich(X0) & ~humble(X0))) [ennf transformation 14]
33. ! [X0] : (generous(X0) | ~happy(X0) | (rich(X0) & ~humble(X0))) [flattening 32]
34. ! [X0] : ((rich(X0) <~> ~happy(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 15]
35. ! [X0] : (((~wise(X0) & humble(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (wise(X0) | ~humble(X0)))) [nnf transformation 2]
36. ! [X0] : (((~wise(X0) & humble(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | wise(X0) | ~humble(X0))) [flattening 35]
44. (? [X0] : (curious(X0) & ~rich(X0)) | ! [X1] : (generous(X1) | happy(X1))) & (? [X1] : (~generous(X1) & ~happy(X1)) | ! [X0] : (~curious(X0) | rich(X0))) [nnf transformation 24]
45. (? [X0] : (curious(X0) & ~rich(X0)) | ! [X1] : (generous(X1) | happy(X1))) & (? [X2] : (~generous(X2) & ~happy(X2)) | ! [X3] : (~curious(X3) | rich(X3))) [rectify 44]
46. ? [X0] : (curious(X0) & ~rich(X0)) => (curious(sK1) & ~rich(sK1)) [choice axiom]
47. ? [X2] : (~generous(X2) & ~happy(X2)) => (~generous(sK2) & ~happy(sK2)) [choice axiom]
48. ((curious(sK1) & ~rich(sK1)) | ! [X1] : (generous(X1) | happy(X1))) & ((~generous(sK2) & ~happy(sK2)) | ! [X3] : (~curious(X3) | rich(X3))) [skolemisation 45,47,46]
49. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X0] : (calm(X0) | strong(X0)) | (~rich(lucy) | old(lucy))) [nnf transformation 7]
50. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X0] : (calm(X0) | strong(X0)) | ~rich(lucy) | old(lucy)) [flattening 49]
51. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & (? [X1] : (calm(X1) | strong(X1)) | ~rich(lucy) | old(lucy)) [rectify 50]
52. ? [X1] : (calm(X1) | strong(X1)) => (calm(sK3) | strong(sK3)) [choice axiom]
53. ((rich(lucy) & ~old(lucy)) | ! [X0] : (~calm(X0) & ~strong(X0))) & ((calm(sK3) | strong(sK3)) | ~rich(lucy) | old(lucy)) [skolemisation 51,52]
54. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 8]
55. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | rich(X0) | strong(X0))) [flattening 54]
70. ! [X0] : (((~happy(X0) & ~calm(X0)) | curious(X0)) & (~curious(X0) | (happy(X0) | calm(X0)))) [nnf transformation 13]
71. ! [X0] : (((~happy(X0) & ~calm(X0)) | curious(X0)) & (~curious(X0) | happy(X0) | calm(X0))) [flattening 70]
72. ! [X0] : (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~generous(X0) & ~old(X0))) [nnf transformation 34]
84. humble(X0) | tall(X0) [cnf transformation 36]
85. ~tall(X0) | humble(X0) [cnf transformation 36]
102. ~rich(sK1) | generous(X1) | happy(X1) [cnf transformation 48]
103. curious(sK1) | generous(X1) | happy(X1) [cnf transformation 48]
106. ~old(lucy) | ~calm(X0) [cnf transformation 53]
108. rich(lucy) | ~calm(X0) [cnf transformation 53]
112. ~rich(X0) | old(X0) [cnf transformation 55]
128. ~curious(X0) | happy(X0) | calm(X0) [cnf transformation 71]
131. generous(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 33]
132. generous(X0) | ~happy(X0) | rich(X0) [cnf transformation 33]
134. ~happy(X0) | rich(X0) | ~generous(X0) [cnf transformation 72]
143. ~generous(fred) [cnf transformation 22]
154. humble(X0) [subsumption resolution 84,85]
172. 6 <=> ! [X1] : (generous(X1) | happy(X1)) [avatar definition]
173. generous(X1) | happy(X1) <- (6) [avatar component clause 172]
175. 7 <=> curious(sK1) [avatar definition]
177. curious(sK1) <- (7) [avatar component clause 175]
178. 6 | 7 [avatar split clause 103,175,172]
180. 8 <=> rich(sK1) [avatar definition]
182. ~rich(sK1) <- (~8) [avatar component clause 180]
183. 6 | ~8 [avatar split clause 102,180,172]
198. 12 <=> ! [X0] : ~calm(X0) [avatar definition]
199. ~calm(X0) <- (12) [avatar component clause 198]
201. 13 <=> rich(lucy) [avatar definition]
203. rich(lucy) <- (13) [avatar component clause 201]
204. 12 | 13 [avatar split clause 108,201,198]
210. 15 <=> old(lucy) [avatar definition]
212. ~old(lucy) <- (~15) [avatar component clause 210]
213. 12 | ~15 [avatar split clause 106,210,198]
243. ~happy(X0) | generous(X0) [subsumption resolution 131,154]
245. ~happy(X0) | rich(X0) [subsumption resolution 134,132]
256. generous(X1) <- (6) [subsumption resolution 173,243]
257. $false <- (6) [resolution 256,143]
260. ~6 [avatar contradiction clause 257]
280. happy(sK1) | calm(sK1) <- (7) [resolution 128,177]
282. happy(sK1) <- (7, 12) [subsumption resolution 280,199]
283. rich(sK1) <- (7, 12) [resolution 282,245]
286. $false <- (7, ~8, 12) [subsumption resolution 283,182]
287. ~7 | 8 | ~12 [avatar contradiction clause 286]
301. old(lucy) <- (13) [resolution 203,112]
302. $false <- (13, ~15) [subsumption resolution 301,212]
303. ~13 | 15 [avatar contradiction clause 302]
304. $false [avatar sat refutation 178,183,204,213,260,287,303]
% SZS output end Proof for 4545727056369993890400859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or rich then someone is strong. Everyone who is both not rich and rich is both generous and not strong. Everyone who is both quiet and not quiet is both not brave and strong and vice versa. If someone is generous then someone is both not strong and not tall and vice versa. If someone is not old or not funny then alice is either not brave or not strong and vice versa. If someone is brave then mary is curious or not rich. Everyone who is old is wise. Everyone who is either humble or not funny is creative and vice versa. If someone is both wise and quiet then lucy is both brave and generous. Everyone who is not brave or not humble is happy. If someone is curious or funny then someone is not wise and vice versa. If someone is not brave or not patient then someone is either not tall or humble and vice versa. If someone is both calm and not creative then someone is quiet or curious. Everyone who is not calm or not old is rich and vice versa. If john is either quiet or generous then someone is either not quiet or rich. Everyone who is both generous and not creative is both curious and happy. Someone is brave or patient. Someone is not brave. Someone is not creative. Alice is funny. Fred is generous or rich. Someone is either not happy or not rich. Paul is both not generous and old. Someone is not funny or humble. | Alice is not strong. | entailment | ((?[X]:((happy(X)<~>rich(X))))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)&rich(X))=>(generous(X)&~strong(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(~brave(X)&strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~strong(X)&~tall(X)))))&
((?[X]:((~old(X)|~funny(X))))<=>((~brave(alice)<~>~strong(alice))))&
((?[X]:(brave(X)))=>((curious(mary)|~rich(mary))))&
(![X]:(old(X)=>wise(X)))&
(![X]:((humble(X)<~>~funny(X))<=>creative(X)))&
((?[X]:((wise(X)&quiet(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:((~brave(X)|~humble(X))=>happy(X)))&
((?[X]:((curious(X)|funny(X))))<=>(?[X]:(~wise(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((~tall(X)<~>humble(X)))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~calm(X)|~old(X))<=>rich(X)))&
(((quiet(john)<~>generous(john)))=>(?[X]:((~quiet(X)<~>rich(X)))))&
(![X]:((generous(X)&~creative(X))=>(curious(X)&happy(X))))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~creative(X)))&
(funny(alice))&
((generous(fred)|rich(fred)))&
(?[X]:((~happy(X)<~>~rich(X))))&
((~generous(paul)&old(paul)))&
(?[X]:((~funny(X)|humble(X)))) | ~strong(alice) | [
"p2",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4341419674151314380945268
% SZS output start Proof for 4341419674151314380945268
3. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (strong(X0) & ~brave(X0))) [input p2]
5. ? [X0] : (~funny(X0) | ~old(X0)) <=> (~brave(alice) <~> ~strong(alice)) [input p4]
7. ! [X0] : (old(X0) => wise(X0)) [input p6]
11. ? [X0] : (funny(X0) | curious(X0)) <=> ? [X0] : ~wise(X0) [input p10]
25. strong(alice) [input hypothesis]
28. ? [X0] : (funny(X0) | curious(X0)) <=> ? [X1] : ~wise(X1) [rectify 11]
36. ! [X0] : (wise(X0) | ~old(X0)) [ennf transformation 7]
47. ! [X0] : (((~quiet(X0) & quiet(X0)) | (~strong(X0) | brave(X0))) & ((strong(X0) & ~brave(X0)) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 3]
48. ! [X0] : (((~quiet(X0) & quiet(X0)) | ~strong(X0) | brave(X0)) & ((strong(X0) & ~brave(X0)) | quiet(X0) | ~quiet(X0))) [flattening 47]
54. (? [X0] : (~funny(X0) | ~old(X0)) | ((~brave(alice) | strong(alice)) & (~strong(alice) | brave(alice)))) & (((strong(alice) | brave(alice)) & (~strong(alice) | ~brave(alice))) | ! [X0] : (funny(X0) & old(X0))) [nnf transformation 5]
55. (? [X0] : (~funny(X0) | ~old(X0)) | ((~brave(alice) | strong(alice)) & (~strong(alice) | brave(alice)))) & (((strong(alice) | brave(alice)) & (~strong(alice) | ~brave(alice))) | ! [X1] : (funny(X1) & old(X1))) [rectify 54]
56. ? [X0] : (~funny(X0) | ~old(X0)) => (~funny(sK3) | ~old(sK3)) [choice axiom]
57. ((~funny(sK3) | ~old(sK3)) | ((~brave(alice) | strong(alice)) & (~strong(alice) | brave(alice)))) & (((strong(alice) | brave(alice)) & (~strong(alice) | ~brave(alice))) | ! [X1] : (funny(X1) & old(X1))) [skolemisation 55,56]
59. (? [X0] : (funny(X0) | curious(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~funny(X0) & ~curious(X0))) [nnf transformation 28]
60. (? [X0] : (funny(X0) | curious(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~funny(X3) & ~curious(X3))) [rectify 59]
61. ? [X0] : (funny(X0) | curious(X0)) => (funny(sK4) | curious(sK4)) [choice axiom]
62. ? [X2] : ~wise(X2) => ~wise(sK5) [choice axiom]
63. ((funny(sK4) | curious(sK4)) | ! [X1] : wise(X1)) & (~wise(sK5) | ! [X3] : (~funny(X3) & ~curious(X3))) [skolemisation 60,62,61]
94. quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 48]
95. ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 48]
99. ~strong(alice) | ~brave(alice) | old(X1) [cnf transformation 57]
100. ~strong(alice) | ~brave(alice) | funny(X1) [cnf transformation 57]
106. ~old(X0) | wise(X0) [cnf transformation 36]
116. ~wise(sK5) | ~funny(X3) [cnf transformation 63]
144. strong(alice) [cnf transformation 25]
157. ~strong(X0) | brave(X0) [subsumption resolution 94,95]
180. 9 <=> strong(alice) [avatar definition]
198. 13 <=> ! [X1] : funny(X1) [avatar definition]
199. funny(X1) <- (13) [avatar component clause 198]
203. 14 <=> ! [X1] : old(X1) [avatar definition]
204. old(X1) <- (14) [avatar component clause 203]
206. ~strong(alice) | funny(X1) [subsumption resolution 100,157]
207. 13 | ~9 [avatar split clause 206,180,198]
208. ~strong(alice) | old(X1) [subsumption resolution 99,157]
209. 14 | ~9 [avatar split clause 208,180,203]
236. 21 <=> ! [X1] : wise(X1) [avatar definition]
237. wise(X1) <- (21) [avatar component clause 236]
248. 24 <=> ! [X3] : ~funny(X3) [avatar definition]
249. ~funny(X3) <- (24) [avatar component clause 248]
251. 25 <=> wise(sK5) [avatar definition]
253. ~wise(sK5) <- (~25) [avatar component clause 251]
254. 24 | ~25 [avatar split clause 116,251,248]
362. 9 [avatar split clause 144,180]
364. $false <- (21, ~25) [resolution 253,237]
365. ~21 | 25 [avatar contradiction clause 364]
369. wise(X0) <- (14) [resolution 106,204]
370. 21 | ~14 [avatar split clause 369,203,236]
371. $false <- (13, 24) [subsumption resolution 249,199]
372. ~13 | ~24 [avatar contradiction clause 371]
373. $false [avatar sat refutation 207,209,254,362,365,370,372]
% SZS output end Proof for 4341419674151314380945268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or not creative is either tall or wise.
Everyone who is both not patient and rich is brave or not calm and vice versa.
If someone is either wise or not happy then someone is rich or not happy and vice versa.
If john is either happy or not quiet then someone is either patient or not happy.
Everyone who is humble is not kind or humble and vice versa.
Everyone who is not strong or not generous is tall.
Everyone who is either not funny or not brave is happy or old.
If someone is either not patient or not tall then paul is either tall or generous.
Everyone who is not rich or calm is either not creative or not kind and vice versa.
If someone is not generous or not kind then someone is both brave and creative and vice versa.
Everyone who is either wise or happy is not calm.
If john is not strong or funny then someone is both generous and kind.
Everyone who is either brave or calm is both tall and not humble and vice versa.
If someone is either not tall or generous then paul is quiet.
Everyone who is not old is calm and vice versa.
If someone is not strong then someone is creative.
Lucy is either rich or not happy.
John is not happy or not funny.
Someone is either not old or patient.
Someone is both calm and rich.
Someone is old.
Fred is either not rich or not happy.
Lucy is not quiet.
Susan is calm or not curious. | Lucy is quiet. | contradiction | (![X]:((~patient(X)<~>~creative(X))=>(tall(X)<~>wise(X))))&
(![X]:((~patient(X)&rich(X))<=>(brave(X)|~calm(X))))&
((?[X]:((wise(X)<~>~happy(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
(((happy(john)<~>~quiet(john)))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:(humble(X)<=>(~kind(X)|humble(X))))&
(![X]:((~strong(X)|~generous(X))=>tall(X)))&
(![X]:((~funny(X)<~>~brave(X))=>(happy(X)|old(X))))&
((?[X]:((~patient(X)<~>~tall(X))))=>((tall(paul)<~>generous(paul))))&
(![X]:((~rich(X)|calm(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((~generous(X)|~kind(X))))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((wise(X)<~>happy(X))=>~calm(X)))&
(((~strong(john)|funny(john)))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(tall(X)&~humble(X))))&
((?[X]:((~tall(X)<~>generous(X))))=>(quiet(paul)))&
(![X]:(~old(X)<=>calm(X)))&
((?[X]:(~strong(X)))=>(?[X]:(creative(X))))&
((rich(lucy)<~>~happy(lucy)))&
((~happy(john)|~funny(john)))&
(?[X]:((~old(X)<~>patient(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:(old(X)))&
((~rich(fred)<~>~happy(fred)))&
(~quiet(lucy))&
((calm(susan)|~curious(susan))) | quiet(lucy) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1638017491260146574529352
% SZS output start Proof for 1638017491260146574529352
23. ~quiet(lucy) [input p22]
25. quiet(lucy) [input hypothesis]
144. ~quiet(lucy) [cnf transformation 23]
145. quiet(lucy) [cnf transformation 25]
301. $false [subsumption resolution 145,144]
% SZS output end Proof for 1638017491260146574529352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not creative is brave or quiet.
If john is brave then someone is not happy.
Everyone who is both not kind and old is both happy and rich and vice versa.
If someone is not rich then someone is both not quiet and rich and vice versa.
Everyone who is both creative and humble is curious.
Everyone who is not brave or not patient is either curious or not patient.
Everyone who is either not strong or kind is either brave or creative.
If someone is both not old and patient then paul is both rich and brave.
If someone is generous then someone is rich and vice versa.
Everyone who is funny or rich is patient and vice versa.
Everyone who is old is either not creative or not humble.
If susan is both not creative and quiet then someone is not rich or not patient.
Everyone who is quiet or old is not tall or funny.
Everyone who is old is not rich and vice versa.
Everyone who is either humble or rich is both not calm and quiet.
If fred is either curious or not generous then alice is either patient or not generous.
Fred is quiet or kind.
Lucy is not humble or wise.
Someone is not creative.
Someone is not happy or patient.
Someone is not old or wise.
Someone is either curious or not rich.
Mary is both old and funny.
Someone is funny or not wise. | Paul is not patient. | contradiction | (![X]:((rich(X)&~creative(X))=>(brave(X)|quiet(X))))&
((brave(john))=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)&old(X))<=>(happy(X)&rich(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((creative(X)&humble(X))=>curious(X)))&
(![X]:((~brave(X)|~patient(X))=>(curious(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>kind(X))=>(brave(X)<~>creative(X))))&
((?[X]:((~old(X)&patient(X))))=>((rich(paul)&brave(paul))))&
((?[X]:(generous(X)))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)|rich(X))<=>patient(X)))&
(![X]:(old(X)=>(~creative(X)<~>~humble(X))))&
(((~creative(susan)&quiet(susan)))=>(?[X]:((~rich(X)|~patient(X)))))&
(![X]:((quiet(X)|old(X))=>(~tall(X)|funny(X))))&
(![X]:(old(X)<=>~rich(X)))&
(![X]:((humble(X)<~>rich(X))=>(~calm(X)&quiet(X))))&
(((curious(fred)<~>~generous(fred)))=>((patient(alice)<~>~generous(alice))))&
((quiet(fred)|kind(fred)))&
((~humble(lucy)|wise(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((curious(X)<~>~rich(X))))&
((old(mary)&funny(mary)))&
(?[X]:((funny(X)|~wise(X)))) | ~patient(paul) | [
"p3",
"p7",
"p9",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2300307554686995598309048
% SZS output start Proof for 2300307554686995598309048
4. ? [X0] : ~rich(X0) <=> ? [X0] : (rich(X0) & ~quiet(X0)) [input p3]
8. ? [X0] : (patient(X0) & ~old(X0)) => (brave(paul) & rich(paul)) [input p7]
10. ! [X0] : ((rich(X0) | funny(X0)) <=> patient(X0)) [input p9]
14. ! [X0] : (old(X0) <=> ~rich(X0)) [input p13]
23. funny(mary) & old(mary) [input p22]
25. ~patient(paul) [input hypothesis]
26. ? [X0] : ~rich(X0) <=> ? [X1] : (rich(X1) & ~quiet(X1)) [rectify 4]
37. (brave(paul) & rich(paul)) | ! [X0] : (~patient(X0) | old(X0)) [ennf transformation 8]
47. (? [X0] : ~rich(X0) | ! [X1] : (~rich(X1) | quiet(X1))) & (? [X1] : (rich(X1) & ~quiet(X1)) | ! [X0] : rich(X0)) [nnf transformation 26]
48. (? [X0] : ~rich(X0) | ! [X1] : (~rich(X1) | quiet(X1))) & (? [X2] : (rich(X2) & ~quiet(X2)) | ! [X3] : rich(X3)) [rectify 47]
49. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
50. ? [X2] : (rich(X2) & ~quiet(X2)) => (rich(sK2) & ~quiet(sK2)) [choice axiom]
51. (~rich(sK1) | ! [X1] : (~rich(X1) | quiet(X1))) & ((rich(sK2) & ~quiet(sK2)) | ! [X3] : rich(X3)) [skolemisation 48,50,49]
59. ! [X0] : (((rich(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (~rich(X0) & ~funny(X0)))) [nnf transformation 10]
60. ! [X0] : ((rich(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (~rich(X0) & ~funny(X0)))) [flattening 59]
64. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 14]
85. rich(sK2) | rich(X3) [cnf transformation 51]
96. rich(paul) | ~patient(X0) | old(X0) [cnf transformation 37]
101. ~rich(X0) | patient(X0) [cnf transformation 60]
106. ~old(X0) | ~rich(X0) [cnf transformation 64]
121. old(mary) [cnf transformation 23]
124. ~patient(paul) [cnf transformation 25]
144. 5 <=> ! [X3] : rich(X3) [avatar definition]
145. rich(X3) <- (5) [avatar component clause 144]
147. 6 <=> rich(sK2) [avatar definition]
149. rich(sK2) <- (6) [avatar component clause 147]
150. 5 | 6 [avatar split clause 85,147,144]
157. 8 <=> ! [X0] : (~patient(X0) | old(X0)) [avatar definition]
158. ~patient(X0) | old(X0) <- (8) [avatar component clause 157]
165. 10 <=> rich(paul) [avatar definition]
167. rich(paul) <- (10) [avatar component clause 165]
168. 8 | 10 [avatar split clause 96,165,157]
281. patient(sK2) <- (6) [resolution 101,149]
283. ~rich(mary) [resolution 106,121]
293. patient(paul) <- (10) [resolution 167,101]
294. $false <- (10) [subsumption resolution 293,124]
295. ~10 [avatar contradiction clause 294]
298. old(sK2) <- (6, 8) [resolution 158,281]
300. ~rich(sK2) <- (6, 8) [resolution 298,106]
301. $false <- (6, 8) [subsumption resolution 300,149]
302. ~6 | ~8 [avatar contradiction clause 301]
305. $false <- (5) [resolution 145,283]
314. ~5 [avatar contradiction clause 305]
316. $false [avatar sat refutation 150,168,295,302,314]
% SZS output end Proof for 2300307554686995598309048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not humble or not calm then fred is both rich and not generous and vice versa.
Everyone who is not strong or quiet is both not rich and humble.
If someone is not funny or not rich then lucy is both funny and calm.
Everyone who is either humble or not funny is either not brave or funny and vice versa.
If paul is both strong and not generous then someone is both not wise and kind and vice versa.
If fred is both not curious and rich then someone is curious or rich and vice versa.
Everyone who is both strong and humble is both old and not quiet.
If john is humble then someone is either curious or kind and vice versa.
If someone is both not strong and happy then susan is either wise or humble.
Everyone who is patient is either not funny or calm.
If lucy is not creative or not funny then paul is both not strong and strong.
If someone is not creative or not rich then someone is brave and vice versa.
Everyone who is either not curious or calm is both old and not calm.
If someone is not calm or funny then someone is both not humble and calm and vice versa.
Everyone who is either not creative or strong is not rich or brave.
Everyone who is not calm or curious is either happy or rich.
Fred is not rich or not wise.
Someone is either tall or not curious.
Someone is either curious or humble.
Someone is both calm and not old.
Mary is both brave and not wise.
Someone is either not creative or tall.
Mary is both not quiet and not funny.
Someone is either generous or not humble. | Fred is not wise. | entailment | ((?[X]:((~humble(X)<~>~calm(X))))<=>((rich(fred)&~generous(fred))))&
(![X]:((~strong(X)|quiet(X))=>(~rich(X)&humble(X))))&
((?[X]:((~funny(X)|~rich(X))))=>((funny(lucy)&calm(lucy))))&
(![X]:((humble(X)<~>~funny(X))<=>(~brave(X)<~>funny(X))))&
(((strong(paul)&~generous(paul)))<=>(?[X]:((~wise(X)&kind(X)))))&
(((~curious(fred)&rich(fred)))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((strong(X)&humble(X))=>(old(X)&~quiet(X))))&
((humble(john))<=>(?[X]:((curious(X)<~>kind(X)))))&
((?[X]:((~strong(X)&happy(X))))=>((wise(susan)<~>humble(susan))))&
(![X]:(patient(X)=>(~funny(X)<~>calm(X))))&
(((~creative(lucy)|~funny(lucy)))=>((~strong(paul)&strong(paul))))&
((?[X]:((~creative(X)|~rich(X))))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)<~>calm(X))=>(old(X)&~calm(X))))&
((?[X]:((~calm(X)|funny(X))))<=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((~creative(X)<~>strong(X))=>(~rich(X)|brave(X))))&
(![X]:((~calm(X)|curious(X))=>(happy(X)<~>rich(X))))&
((~rich(fred)|~wise(fred)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((calm(X)&~old(X))))&
((brave(mary)&~wise(mary)))&
(?[X]:((~creative(X)<~>tall(X))))&
((~quiet(mary)&~funny(mary)))&
(?[X]:((generous(X)<~>~humble(X)))) | ~wise(fred) | [
"p0",
"p2",
"p13",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7961877098041818544594327
% SZS output start Proof for 7961877098041818544594327
1. ? [X0] : (~humble(X0) <~> ~calm(X0)) <=> (~generous(fred) & rich(fred)) [input p0]
3. ? [X0] : (~rich(X0) | ~funny(X0)) => (calm(lucy) & funny(lucy)) [input p2]
14. ? [X0] : (funny(X0) | ~calm(X0)) <=> ? [X0] : (calm(X0) & ~humble(X0)) [input p13]
17. ~wise(fred) | ~rich(fred) [input p16]
23. ~funny(mary) & ~quiet(mary) [input p22]
25. wise(fred) [input hypothesis]
27. ? [X0] : (funny(X0) | ~calm(X0)) <=> ? [X1] : (calm(X1) & ~humble(X1)) [rectify 14]
31. ~funny(mary) [pure predicate removal 23]
33. (calm(lucy) & funny(lucy)) | ! [X0] : (rich(X0) & funny(X0)) [ennf transformation 3]
42. (? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | (generous(fred) | ~rich(fred))) & ((~generous(fred) & rich(fred)) | ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 1]
43. (? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | generous(fred) | ~rich(fred)) & ((~generous(fred) & rich(fred)) | ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [flattening 42]
44. (? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | generous(fred) | ~rich(fred)) & ((~generous(fred) & rich(fred)) | ! [X1] : ((~humble(X1) | calm(X1)) & (~calm(X1) | humble(X1)))) [rectify 43]
45. ? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) => ((calm(sK0) | humble(sK0)) & (~calm(sK0) | ~humble(sK0))) [choice axiom]
46. (((calm(sK0) | humble(sK0)) & (~calm(sK0) | ~humble(sK0))) | generous(fred) | ~rich(fred)) & ((~generous(fred) & rich(fred)) | ! [X1] : ((~humble(X1) | calm(X1)) & (~calm(X1) | humble(X1)))) [skolemisation 44,45]
69. (? [X0] : (funny(X0) | ~calm(X0)) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X1] : (calm(X1) & ~humble(X1)) | ! [X0] : (~funny(X0) & calm(X0))) [nnf transformation 27]
70. (? [X0] : (funny(X0) | ~calm(X0)) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X2] : (calm(X2) & ~humble(X2)) | ! [X3] : (~funny(X3) & calm(X3))) [rectify 69]
71. ? [X0] : (funny(X0) | ~calm(X0)) => (funny(sK6) | ~calm(sK6)) [choice axiom]
72. ? [X2] : (calm(X2) & ~humble(X2)) => (calm(sK7) & ~humble(sK7)) [choice axiom]
73. ((funny(sK6) | ~calm(sK6)) | ! [X1] : (~calm(X1) | humble(X1))) & ((calm(sK7) & ~humble(sK7)) | ! [X3] : (~funny(X3) & calm(X3))) [skolemisation 70,72,71]
90. rich(fred) | ~calm(X1) | humble(X1) [cnf transformation 46]
98. funny(lucy) | funny(X0) [cnf transformation 33]
138. ~humble(sK7) | ~funny(X3) [cnf transformation 73]
140. calm(sK7) | ~funny(X3) [cnf transformation 73]
148. ~wise(fred) | ~rich(fred) [cnf transformation 17]
159. ~funny(mary) [cnf transformation 31]
162. wise(fred) [cnf transformation 25]
169. 1 <=> rich(fred) [avatar definition]
191. 6 <=> ! [X1] : (~calm(X1) | humble(X1)) [avatar definition]
192. ~calm(X1) | humble(X1) <- (6) [avatar component clause 191]
195. 6 | 1 [avatar split clause 90,169,191]
205. 9 <=> ! [X0] : funny(X0) [avatar definition]
206. funny(X0) <- (9) [avatar component clause 205]
209. 10 <=> funny(lucy) [avatar definition]
211. funny(lucy) <- (10) [avatar component clause 209]
213. 9 | 10 [avatar split clause 98,209,205]
336. 37 <=> ! [X3] : ~funny(X3) [avatar definition]
337. ~funny(X3) <- (37) [avatar component clause 336]
339. 38 <=> calm(sK7) [avatar definition]
341. calm(sK7) <- (38) [avatar component clause 339]
342. 37 | 38 [avatar split clause 140,339,336]
348. 40 <=> humble(sK7) [avatar definition]
350. ~humble(sK7) <- (~40) [avatar component clause 348]
351. 37 | ~40 [avatar split clause 138,348,336]
355. 41 <=> wise(fred) [avatar definition]
358. ~1 | ~41 [avatar split clause 148,355,169]
399. 41 [avatar split clause 162,355]
402. $false <- (9) [resolution 206,159]
403. ~9 [avatar contradiction clause 402]
410. humble(sK7) <- (6, 38) [resolution 192,341]
412. $false <- (6, 38, ~40) [subsumption resolution 410,350]
413. ~6 | ~38 | 40 [avatar contradiction clause 412]
416. $false <- (10, 37) [resolution 337,211]
417. ~10 | ~37 [avatar contradiction clause 416]
418. $false [avatar sat refutation 195,213,342,351,358,399,403,413,417]
% SZS output end Proof for 7961877098041818544594327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not humble is kind.
If someone is not creative then lucy is not funny or not calm and vice versa.
Everyone who is wise or calm is both not quiet and not kind.
Everyone who is either wise or not tall is not patient or not generous.
Everyone who is kind is either not funny or not curious.
Everyone who is both not wise and not old is either generous or not rich.
Everyone who is either kind or calm is not curious and vice versa.
Everyone who is not humble is either not wise or humble.
If mary is kind then alice is tall or not curious and vice versa.
If john is both strong and not strong then someone is both curious and quiet and vice versa.
Everyone who is either tall or funny is both not calm and not curious and vice versa.
Everyone who is either quiet or strong is calm or not wise.
If someone is not wise or not humble then alice is both funny and quiet.
Everyone who is not rich is either tall or creative and vice versa.
If someone is not kind or generous then alice is brave or not quiet.
If paul is not creative then lucy is brave or quiet and vice versa.
Someone is both funny and not tall.
Someone is either not patient or not generous.
Someone is not kind.
Alice is not generous.
Fred is either patient or strong.
Someone is not quiet or not brave.
Paul is not quiet.
Paul is both not strong and brave. | Mary is not calm. | entailment | (![X]:((quiet(X)<~>~humble(X))=>kind(X)))&
((?[X]:(~creative(X)))<=>((~funny(lucy)|~calm(lucy))))&
(![X]:((wise(X)|calm(X))=>(~quiet(X)&~kind(X))))&
(![X]:((wise(X)<~>~tall(X))=>(~patient(X)|~generous(X))))&
(![X]:(kind(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~wise(X)&~old(X))=>(generous(X)<~>~rich(X))))&
(![X]:((kind(X)<~>calm(X))<=>~curious(X)))&
(![X]:(~humble(X)=>(~wise(X)<~>humble(X))))&
((kind(mary))<=>((tall(alice)|~curious(alice))))&
(((strong(john)&~strong(john)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(calm(X)|~wise(X))))&
((?[X]:((~wise(X)|~humble(X))))=>((funny(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((~kind(X)|generous(X))))=>((brave(alice)|~quiet(alice))))&
((~creative(paul))<=>((brave(lucy)|quiet(lucy))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:(~kind(X)))&
(~generous(alice))&
((patient(fred)<~>strong(fred)))&
(?[X]:((~quiet(X)|~brave(X))))&
(~quiet(paul))&
((~strong(paul)&brave(paul))) | ~calm(mary) | [
"p2",
"p6",
"p8",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2530500612307269179179090
% SZS output start Proof for 2530500612307269179179090
3. ! [X0] : ((calm(X0) | wise(X0)) => (~kind(X0) & ~quiet(X0))) [input p2]
7. ! [X0] : ((kind(X0) <~> calm(X0)) <=> ~curious(X0)) [input p6]
9. kind(mary) <=> (~curious(alice) | tall(alice)) [input p8]
11. ! [X0] : ((tall(X0) <~> funny(X0)) <=> (~curious(X0) & ~calm(X0))) [input p10]
13. ? [X0] : (~humble(X0) | ~wise(X0)) => (quiet(alice) & funny(alice)) [input p12]
17. ? [X0] : (~tall(X0) & funny(X0)) [input p16]
25. calm(mary) [input hypothesis]
28. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (~calm(X0) & ~wise(X0))) [ennf transformation 3]
35. (quiet(alice) & funny(alice)) | ! [X0] : (humble(X0) & wise(X0)) [ennf transformation 13]
46. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | curious(X0)) & (~curious(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [nnf transformation 7]
48. (kind(mary) | (curious(alice) & ~tall(alice))) & ((~curious(alice) | tall(alice)) | ~kind(mary)) [nnf transformation 9]
49. (kind(mary) | (curious(alice) & ~tall(alice))) & (~curious(alice) | tall(alice) | ~kind(mary)) [flattening 48]
55. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [flattening 55]
60. ? [X0] : (~tall(X0) & funny(X0)) => (~tall(sK2) & funny(sK2)) [choice axiom]
61. ~tall(sK2) & funny(sK2) [skolemisation 17,60]
77. ~wise(X0) | ~kind(X0) [cnf transformation 28]
78. ~calm(X0) | ~kind(X0) [cnf transformation 28]
85. curious(X0) | kind(X0) | calm(X0) [cnf transformation 46]
90. kind(mary) | ~tall(alice) [cnf transformation 49]
91. kind(mary) | curious(alice) [cnf transformation 49]
97. ~calm(X0) | tall(X0) | ~funny(X0) [cnf transformation 56]
99. ~curious(X0) | tall(X0) | ~funny(X0) [cnf transformation 56]
104. funny(alice) | wise(X0) [cnf transformation 35]
113. funny(sK2) [cnf transformation 61]
114. ~tall(sK2) [cnf transformation 61]
125. calm(mary) [cnf transformation 25]
148. 5 <=> curious(alice) [avatar definition]
150. curious(alice) <- (5) [avatar component clause 148]
152. 6 <=> kind(mary) [avatar definition]
155. 5 | 6 [avatar split clause 91,152,148]
157. 7 <=> tall(alice) [avatar definition]
159. ~tall(alice) <- (~7) [avatar component clause 157]
160. ~7 | 6 [avatar split clause 90,152,157]
181. 12 <=> ! [X0] : wise(X0) [avatar definition]
182. wise(X0) <- (12) [avatar component clause 181]
185. 13 <=> funny(alice) [avatar definition]
189. 12 | 13 [avatar split clause 104,185,181]
250. ~kind(mary) [resolution 78,125]
256. ~6 [avatar split clause 250,152]
261. ~kind(X1) <- (12) [resolution 182,77]
288. tall(alice) | ~funny(alice) <- (5) [resolution 99,150]
289. tall(X0) | ~funny(X0) | kind(X0) | calm(X0) [resolution 99,85]
290. ~funny(alice) <- (5, ~7) [subsumption resolution 288,159]
293. tall(X0) | ~funny(X0) | calm(X0) <- (12) [subsumption resolution 289,261]
294. ~funny(X0) | tall(X0) <- (12) [subsumption resolution 293,97]
295. ~13 | ~5 | 7 [avatar split clause 290,157,148,185]
296. tall(sK2) <- (12) [resolution 294,113]
297. $false <- (12) [subsumption resolution 296,114]
298. ~12 [avatar contradiction clause 297]
299. $false [avatar sat refutation 155,160,189,256,295,298]
% SZS output end Proof for 2530500612307269179179090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or not rich then paul is both happy and not quiet.
If someone is both not wise and not happy then lucy is either patient or not rich and vice versa.
Everyone who is patient or tall is not quiet and vice versa.
If fred is both patient and not generous then susan is either strong or curious and vice versa.
Everyone who is not old or calm is not happy or patient.
Everyone who is either not curious or not humble is not wise.
Everyone who is either not brave or quiet is both wise and not quiet and vice versa.
Everyone who is strong is not curious and vice versa.
If alice is rich then someone is funny or not quiet.
Everyone who is not generous or not quiet is both not generous and wise.
Everyone who is either not tall or old is either not curious or not quiet and vice versa.
If john is creative or tall then someone is both curious and patient and vice versa.
Everyone who is both funny and patient is not happy or not humble.
Everyone who is not strong or not brave is patient or not happy and vice versa.
Everyone who is either tall or not generous is patient or not patient and vice versa.
If someone is either not creative or tall then someone is either curious or not patient and vice versa.
Alice is both not kind and not brave.
Someone is brave or kind.
Susan is not patient.
Someone is either humble or strong.
Susan is calm.
Lucy is curious or not creative.
Paul is both humble and not old. | Paul is not old. | entailment | ((?[X]:((funny(X)|~rich(X))))=>((happy(paul)&~quiet(paul))))&
((?[X]:((~wise(X)&~happy(X))))<=>((patient(lucy)<~>~rich(lucy))))&
(![X]:((patient(X)|tall(X))<=>~quiet(X)))&
(((patient(fred)&~generous(fred)))<=>((strong(susan)<~>curious(susan))))&
(![X]:((~old(X)|calm(X))=>(~happy(X)|patient(X))))&
(![X]:((~curious(X)<~>~humble(X))=>~wise(X)))&
(![X]:((~brave(X)<~>quiet(X))<=>(wise(X)&~quiet(X))))&
(![X]:(strong(X)<=>~curious(X)))&
((rich(alice))=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((~generous(X)|~quiet(X))=>(~generous(X)&wise(X))))&
(![X]:((~tall(X)<~>old(X))<=>(~curious(X)<~>~quiet(X))))&
(((creative(john)|tall(john)))<=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((funny(X)&patient(X))=>(~happy(X)|~humble(X))))&
(![X]:((~strong(X)|~brave(X))<=>(patient(X)|~happy(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(patient(X)|~patient(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((~kind(alice)&~brave(alice)))&
(?[X]:((brave(X)|kind(X))))&
(~patient(susan))&
(?[X]:((humble(X)<~>strong(X))))&
(calm(susan))&
((curious(lucy)|~creative(lucy)))&
((humble(paul)&~old(paul))) | ~old(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5466187767495513005633147
% SZS output start Proof for 5466187767495513005633147
23. ~old(paul) & humble(paul) [input p22]
24. old(paul) [input hypothesis]
145. ~old(paul) [cnf transformation 23]
146. old(paul) [cnf transformation 24]
318. $false [subsumption resolution 146,145]
% SZS output end Proof for 5466187767495513005633147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is old or not kind. If someone is both brave and quiet then someone is both happy and not generous. Everyone who is funny is both calm and not brave. Everyone who is funny is both not calm and not patient. If paul is brave then someone is either creative or patient and vice versa. Everyone who is wise or quiet is both not old and strong. If someone is either not funny or not wise then lucy is not old or creative and vice versa. If fred is either rich or kind then someone is either happy or not rich and vice versa. If someone is not patient or wise then someone is either not creative or quiet and vice versa. Everyone who is both curious and wise is not humble. If someone is both funny and calm then paul is not patient or funny and vice versa. Everyone who is not quiet or not humble is either old or happy. Everyone who is both rich and not creative is both not humble and not tall and vice versa. Everyone who is not strong or brave is not humble or not rich and vice versa. If someone is strong or old then someone is not curious or humble. Everyone who is wise or not funny is both not humble and not tall and vice versa. John is both not happy and not wise. Mary is not humble or strong. Someone is both not calm and not humble. Mary is old or not strong. Someone is both not tall and quiet. Someone is either wise or strong. Someone is both happy and strong. | John is old. | entailment | ((~funny(susan))=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((brave(X)&quiet(X))))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:(funny(X)=>(calm(X)&~brave(X))))&
(![X]:(funny(X)=>(~calm(X)&~patient(X))))&
((brave(paul))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((wise(X)|quiet(X))=>(~old(X)&strong(X))))&
((?[X]:((~funny(X)<~>~wise(X))))<=>((~old(lucy)|creative(lucy))))&
(((rich(fred)<~>kind(fred)))<=>(?[X]:((happy(X)<~>~rich(X)))))&
((?[X]:((~patient(X)|wise(X))))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:((curious(X)&wise(X))=>~humble(X)))&
((?[X]:((funny(X)&calm(X))))<=>((~patient(paul)|funny(paul))))&
(![X]:((~quiet(X)|~humble(X))=>(old(X)<~>happy(X))))&
(![X]:((rich(X)&~creative(X))<=>(~humble(X)&~tall(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~rich(X))))&
((?[X]:((strong(X)|old(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((wise(X)|~funny(X))<=>(~humble(X)&~tall(X))))&
((~happy(john)&~wise(john)))&
((~humble(mary)|strong(mary)))&
(?[X]:((~calm(X)&~humble(X))))&
((old(mary)|~strong(mary)))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:((wise(X)<~>strong(X))))&
(?[X]:((happy(X)&strong(X)))) | old(john) | [
"p2",
"p3",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4251370966438837911337248
% SZS output start Proof for 4251370966438837911337248
3. ! [X0] : (funny(X0) => (~brave(X0) & calm(X0))) [input p2]
4. ! [X0] : (funny(X0) => (~patient(X0) & ~calm(X0))) [input p3]
12. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (old(X0) <~> happy(X0))) [input p11]
16. ! [X0] : ((~funny(X0) | wise(X0)) <=> (~tall(X0) & ~humble(X0))) [input p15]
17. ~wise(john) & ~happy(john) [input p16]
24. ~old(john) [input hypothesis]
33. ! [X0] : ((~brave(X0) & calm(X0)) | ~funny(X0)) [ennf transformation 3]
34. ! [X0] : ((~patient(X0) & ~calm(X0)) | ~funny(X0)) [ennf transformation 4]
36. ! [X0] : ((old(X0) <~> happy(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 12]
65. ! [X0] : (((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (humble(X0) & quiet(X0))) [nnf transformation 36]
70. ! [X0] : (((~funny(X0) | wise(X0)) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | (funny(X0) & ~wise(X0)))) [nnf transformation 16]
71. ! [X0] : ((~funny(X0) | wise(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | (funny(X0) & ~wise(X0)))) [flattening 70]
83. ~funny(X0) | calm(X0) [cnf transformation 33]
85. ~calm(X0) | ~funny(X0) [cnf transformation 34]
121. humble(X0) | old(X0) | happy(X0) [cnf transformation 65]
133. ~humble(X0) | funny(X0) [cnf transformation 71]
137. ~happy(john) [cnf transformation 17]
149. ~old(john) [cnf transformation 24]
171. ~funny(X0) [subsumption resolution 85,83]
289. ~humble(X0) [subsumption resolution 133,171]
332. happy(X0) | old(X0) [resolution 121,289]
338. old(john) [resolution 332,137]
341. $false [subsumption resolution 338,149]
% SZS output end Proof for 4251370966438837911337248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and not happy then mary is both not humble and not strong and vice versa. Everyone who is rich or humble is patient and vice versa. If lucy is both funny and not creative then someone is either not quiet or wise and vice versa. If john is not wise then mary is both not funny and patient and vice versa. Everyone who is both not old and not generous is both calm and not patient. Everyone who is both generous and not funny is either not quiet or not patient and vice versa. If mary is either curious or not calm then fred is either happy or calm. Everyone who is not strong or funny is either not happy or curious and vice versa. If alice is either not creative or rich then fred is both not calm and creative. Everyone who is not patient is both creative and not strong. If fred is happy then someone is humble or not strong and vice versa. If someone is rich or old then someone is not generous or kind. Everyone who is both generous and wise is both rich and wise. Everyone who is strong or not kind is not curious and vice versa. If mary is either tall or patient then john is both rich and not calm and vice versa. If susan is both tall and old then mary is creative. Someone is both calm and not strong. Susan is either quiet or calm. Susan is happy. Someone is both rich and old. Someone is either brave or old. Someone is not quiet or calm. Mary is both not brave and kind. | Fred is rich. | neutral | ((?[X]:((kind(X)&~happy(X))))<=>((~humble(mary)&~strong(mary))))&
(![X]:((rich(X)|humble(X))<=>patient(X)))&
(((funny(lucy)&~creative(lucy)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((~wise(john))<=>((~funny(mary)&patient(mary))))&
(![X]:((~old(X)&~generous(X))=>(calm(X)&~patient(X))))&
(![X]:((generous(X)&~funny(X))<=>(~quiet(X)<~>~patient(X))))&
(((curious(mary)<~>~calm(mary)))=>((happy(fred)<~>calm(fred))))&
(![X]:((~strong(X)|funny(X))<=>(~happy(X)<~>curious(X))))&
(((~creative(alice)<~>rich(alice)))=>((~calm(fred)&creative(fred))))&
(![X]:(~patient(X)=>(creative(X)&~strong(X))))&
((happy(fred))<=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((rich(X)|old(X))))=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((generous(X)&wise(X))=>(rich(X)&wise(X))))&
(![X]:((strong(X)|~kind(X))<=>~curious(X)))&
(((tall(mary)<~>patient(mary)))<=>((rich(john)&~calm(john))))&
(((tall(susan)&old(susan)))=>(creative(mary)))&
(?[X]:((calm(X)&~strong(X))))&
((quiet(susan)<~>calm(susan)))&
(happy(susan))&
(?[X]:((rich(X)&old(X))))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((~brave(mary)&kind(mary))) | rich(fred) | [] | null | 0 |
Everyone who is not rich is not brave.
Everyone who is either happy or not creative is not happy and vice versa.
If someone is both not calm and humble then someone is not patient or rich.
If someone is not rich or not creative then john is not funny or not happy and vice versa.
If someone is either wise or kind then someone is patient.
If john is happy then someone is not rich or generous and vice versa.
Everyone who is patient is not brave.
Everyone who is not kind is both not rich and curious.
If paul is both not kind and not quiet then someone is either happy or creative and vice versa.
If someone is wise then someone is not funny or not tall.
If mary is both funny and not creative then lucy is creative.
If john is funny or not old then someone is both happy and kind and vice versa.
Everyone who is both old and funny is either wise or not kind and vice versa.
Everyone who is both calm and not wise is either funny or calm and vice versa.
If someone is both not calm and rich then fred is old or quiet.
Everyone who is either funny or not rich is either not patient or brave.
Susan is both old and happy.
Someone is patient.
Someone is not happy.
Someone is not funny or not creative.
John is both happy and humble.
Mary is calm or tall.
Mary is either funny or happy.
Someone is not curious. | Lucy is not creative. | entailment | (![X]:(~rich(X)=>~brave(X)))&
(![X]:((happy(X)<~>~creative(X))<=>~happy(X)))&
((?[X]:((~calm(X)&humble(X))))=>(?[X]:((~patient(X)|rich(X)))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~funny(john)|~happy(john))))&
((?[X]:((wise(X)<~>kind(X))))=>(?[X]:(patient(X))))&
((happy(john))<=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:(patient(X)=>~brave(X)))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(((~kind(paul)&~quiet(paul)))<=>(?[X]:((happy(X)<~>creative(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~funny(X)|~tall(X)))))&
(((funny(mary)&~creative(mary)))=>(creative(lucy)))&
(((funny(john)|~old(john)))<=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((old(X)&funny(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((calm(X)&~wise(X))<=>(funny(X)<~>calm(X))))&
((?[X]:((~calm(X)&rich(X))))=>((old(fred)|quiet(fred))))&
(![X]:((funny(X)<~>~rich(X))=>(~patient(X)<~>brave(X))))&
((old(susan)&happy(susan)))&
(?[X]:(patient(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)|~creative(X))))&
((happy(john)&humble(john)))&
((calm(mary)|tall(mary)))&
((funny(mary)<~>happy(mary)))&
(?[X]:(~curious(X))) | ~creative(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6715598229467641614927789
% SZS output start Proof for 6715598229467641614927789
2. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> ~happy(X0)) [input p1]
25. creative(lucy) [input hypothesis]
40. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 2]
85. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 40]
87. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 40]
143. creative(lucy) [cnf transformation 25]
146. ~happy(X0) | ~creative(X0) [duplicate literal removal 85]
147. ~creative(X0) | happy(X0) [duplicate literal removal 87]
148. ~creative(X0) [subsumption resolution 146,147]
284. $false [subsumption resolution 143,148]
% SZS output end Proof for 6715598229467641614927789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble is not curious and vice versa.
If someone is both not old and not funny then someone is either not funny or wise and vice versa.
Everyone who is either not patient or not strong is happy or funny.
Everyone who is both not kind and tall is both happy and tall and vice versa.
If someone is both not happy and happy then someone is quiet and vice versa.
Everyone who is generous or old is not happy or not brave and vice versa.
If someone is not rich then someone is either patient or funny and vice versa.
If lucy is both not humble and not generous then someone is not wise or patient and vice versa.
If lucy is both not funny and kind then alice is patient or rich.
Everyone who is either not generous or not patient is both strong and happy and vice versa.
Everyone who is brave is either not kind or not tall and vice versa.
If someone is either not humble or not rich then someone is not funny and vice versa.
If susan is not quiet or happy then someone is both strong and not calm.
Everyone who is humble or strong is either curious or not rich.
Everyone who is not happy is not curious or old.
Everyone who is both rich and wise is either not tall or not humble and vice versa.
Someone is either wise or creative.
Someone is not wise or rich.
John is wise.
Someone is curious.
Someone is either brave or patient.
Susan is both funny and not creative.
Lucy is strong or not rich. | Susan is strong. | neutral | (![X]:((~creative(X)|~humble(X))<=>~curious(X)))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(![X]:((~patient(X)<~>~strong(X))=>(happy(X)|funny(X))))&
(![X]:((~kind(X)&tall(X))<=>(happy(X)&tall(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|old(X))<=>(~happy(X)|~brave(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:((~wise(X)|patient(X)))))&
(((~funny(lucy)&kind(lucy)))=>((patient(alice)|rich(alice))))&
(![X]:((~generous(X)<~>~patient(X))<=>(strong(X)&happy(X))))&
(![X]:(brave(X)<=>(~kind(X)<~>~tall(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:(~funny(X))))&
(((~quiet(susan)|happy(susan)))=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~curious(X)|old(X))))&
(![X]:((rich(X)&wise(X))<=>(~tall(X)<~>~humble(X))))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((~wise(X)|rich(X))))&
(wise(john))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((funny(susan)&~creative(susan)))&
((strong(lucy)|~rich(lucy))) | strong(susan) | [] | null | 0 |
If someone is either not humble or not patient then someone is calm and vice versa.
If someone is either not strong or not patient then paul is both generous and rich and vice versa.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Susan is not kind or curious.
Someone is old. | Fred is creative. | contradiction | ((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((generous(paul)&rich(paul))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X))) | creative(fred) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4757240879726563772475999
% SZS output start Proof for 4757240879726563772475999
1. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X0] : calm(X0) [input p0]
2. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> (rich(paul) & generous(paul)) [input p1]
5. ! [X0] : (brave(X0) <=> (~generous(X0) <~> humble(X0))) [input p4]
6. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | creative(X0)) => brave(X0)) [input p7]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p8]
12. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p11]
21. creative(fred) [input hypothesis]
22. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X1] : calm(X1) [rectify 1]
24. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 12]
25. ! [X0] : (brave(X0) => (~generous(X0) <~> humble(X0))) [unused predicate definition removal 5]
28. ! [X0] : ((~generous(X0) <~> humble(X0)) | ~brave(X0)) [ennf transformation 25]
29. ! [X0] : (brave(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 8]
37. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 22]
38. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) => ((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) [choice axiom]
40. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
41. (((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [skolemisation 38,40,39]
42. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~rich(paul) | ~generous(paul))) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 2]
43. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [flattening 42]
44. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [rectify 43]
45. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) [choice axiom]
46. (((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [skolemisation 44,45]
47. ! [X0] : (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~brave(X0)) [nnf transformation 28]
48. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 6]
49. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 48]
52. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 9]
53. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 52]
58. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 24]
59. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 58]
60. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK4) & generous(sK4)) [choice axiom]
61. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
62. ((~funny(sK4) & generous(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 59,61,60]
69. calm(sK1) | ~patient(X3) | humble(X3) [cnf transformation 41]
74. generous(paul) | ~strong(X1) | patient(X1) [cnf transformation 46]
80. ~brave(X0) | generous(X0) | ~humble(X0) [cnf transformation 47]
82. ~strong(X0) | generous(X0) | ~calm(X0) | curious(X0) [cnf transformation 49]
93. ~creative(X0) | brave(X0) [cnf transformation 29]
95. strong(X0) | strong(X0) [cnf transformation 53]
97. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
106. generous(sK4) | ~curious(X1) [cnf transformation 62]
125. creative(fred) [cnf transformation 21]
126. strong(X0) [duplicate literal removal 95]
127. ~generous(X0) | ~strong(X0) [duplicate literal removal 97]
147. 5 <=> calm(sK1) [avatar definition]
149. calm(sK1) <- (5) [avatar component clause 147]
152. 6 <=> ! [X3] : (~patient(X3) | humble(X3)) [avatar definition]
153. ~patient(X3) | humble(X3) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 69,147,152]
156. 7 <=> generous(paul) [avatar definition]
157. generous(paul) <- (7) [avatar component clause 156]
174. 11 <=> ! [X1] : (~strong(X1) | patient(X1)) [avatar definition]
175. ~strong(X1) | patient(X1) <- (11) [avatar component clause 174]
181. 11 | 7 [avatar split clause 74,156,174]
209. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
210. ~curious(X1) <- (18) [avatar component clause 209]
217. 20 <=> generous(sK4) [avatar definition]
219. generous(sK4) <- (20) [avatar component clause 217]
220. 18 | 20 [avatar split clause 106,217,209]
274. brave(fred) [resolution 93,125]
278. ~strong(paul) <- (7) [resolution 127,157]
280. $false <- (7) [subsumption resolution 278,126]
281. ~7 [avatar contradiction clause 280]
282. patient(X1) <- (11) [subsumption resolution 175,126]
296. 34 <=> generous(fred) [avatar definition]
297. generous(fred) <- (34) [avatar component clause 296]
300. generous(fred) | ~humble(fred) [resolution 80,274]
318. generous(X0) | ~calm(X0) | curious(X0) [resolution 82,126]
319. ~calm(X0) | generous(X0) <- (18) [subsumption resolution 318,210]
320. generous(sK1) <- (5, 18) [resolution 319,149]
343. ~strong(sK1) <- (5, 18) [resolution 320,127]
344. $false <- (5, 18) [subsumption resolution 343,126]
345. ~5 | ~18 [avatar contradiction clause 344]
349. ~strong(sK4) <- (20) [resolution 219,127]
361. $false <- (20) [subsumption resolution 349,126]
362. ~20 [avatar contradiction clause 361]
363. humble(X3) <- (6, 11) [subsumption resolution 153,282]
376. generous(fred) <- (6, 11) [subsumption resolution 300,363]
377. 34 | ~6 | ~11 [avatar split clause 376,174,152,296]
404. ~strong(fred) <- (34) [resolution 297,127]
418. $false <- (34) [subsumption resolution 404,126]
419. ~34 [avatar contradiction clause 418]
420. $false [avatar sat refutation 154,181,220,281,345,362,377,419]
% SZS output end Proof for 4757240879726563772475999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not brave and kind then someone is generous.
If someone is wise or not calm then someone is both not curious and not strong.
Everyone who is both not calm and curious is either brave or not strong.
Everyone who is both not happy and not quiet is either not funny or rich.
Everyone who is both not tall and not brave is not old or humble and vice versa.
If paul is both not curious and not strong then someone is both happy and humble.
Everyone who is calm or brave is both not humble and creative and vice versa.
Everyone who is either not calm or not wise is either humble or not kind and vice versa.
Everyone who is not wise is either wise or creative and vice versa.
If lucy is either not old or not patient then lucy is both not wise and creative.
Everyone who is quiet or not generous is humble.
If john is calm then fred is not tall and vice versa.
Everyone who is both curious and calm is both generous and brave.
If someone is either not tall or tall then paul is not kind.
Everyone who is both patient and tall is either not patient or not kind and vice versa.
If lucy is either old or not old then someone is calm and vice versa.
Susan is kind.
Susan is quiet.
Susan is both not funny and patient.
John is both happy and calm.
Mary is either not strong or quiet.
Someone is strong.
Someone is not brave or not tall. | Susan is calm. | contradiction | (((~brave(alice)&kind(alice)))=>(?[X]:(generous(X))))&
((?[X]:((wise(X)|~calm(X))))=>(?[X]:((~curious(X)&~strong(X)))))&
(![X]:((~calm(X)&curious(X))=>(brave(X)<~>~strong(X))))&
(![X]:((~happy(X)&~quiet(X))=>(~funny(X)<~>rich(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~old(X)|humble(X))))&
(((~curious(paul)&~strong(paul)))=>(?[X]:((happy(X)&humble(X)))))&
(![X]:((calm(X)|brave(X))<=>(~humble(X)&creative(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(humble(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>(wise(X)<~>creative(X))))&
(((~old(lucy)<~>~patient(lucy)))=>((~wise(lucy)&creative(lucy))))&
(![X]:((quiet(X)|~generous(X))=>humble(X)))&
((calm(john))<=>(~tall(fred)))&
(![X]:((curious(X)&calm(X))=>(generous(X)&brave(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>(~kind(paul)))&
(![X]:((patient(X)&tall(X))<=>(~patient(X)<~>~kind(X))))&
(((old(lucy)<~>~old(lucy)))<=>(?[X]:(calm(X))))&
(kind(susan))&
(quiet(susan))&
((~funny(susan)&patient(susan)))&
((happy(john)&calm(john)))&
((~strong(mary)<~>quiet(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~brave(X)|~tall(X)))) | calm(susan) | [
"p6",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3372900341160219346644917
% SZS output start Proof for 3372900341160219346644917
7. ! [X0] : ((brave(X0) | calm(X0)) <=> (creative(X0) & ~humble(X0))) [input p6]
11. ! [X0] : ((~generous(X0) | quiet(X0)) => humble(X0)) [input p10]
18. quiet(susan) [input p17]
24. calm(susan) [input hypothesis]
30. ! [X0] : (quiet(X0) => humble(X0)) [pure predicate removal 11]
39. ! [X0] : (humble(X0) | ~quiet(X0)) [ennf transformation 30]
51. ! [X0] : (((brave(X0) | calm(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 7]
52. ! [X0] : ((brave(X0) | calm(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (~brave(X0) & ~calm(X0)))) [flattening 51]
81. ~humble(X0) | ~calm(X0) [cnf transformation 52]
102. ~quiet(X0) | humble(X0) [cnf transformation 39]
119. quiet(susan) [cnf transformation 18]
126. calm(susan) [cnf transformation 24]
237. humble(susan) [resolution 102,119]
239. ~calm(susan) [resolution 237,81]
242. $false [subsumption resolution 239,126]
% SZS output end Proof for 3372900341160219346644917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both creative and calm then susan is not generous and vice versa.
Everyone who is generous is strong.
If someone is not strong or funny then someone is not calm or calm and vice versa.
Everyone who is not creative or not humble is either kind or quiet.
If someone is both tall and patient then john is not funny and vice versa.
If john is both not humble and rich then fred is either not funny or not wise.
Everyone who is both not kind and curious is either not happy or brave and vice versa.
If someone is humble or patient then someone is either generous or brave.
Everyone who is not kind or not funny is either not strong or calm.
Everyone who is humble is patient or not patient.
Everyone who is either not happy or not rich is not strong or not brave.
Everyone who is not old is either rich or not curious and vice versa.
Everyone who is either not happy or not wise is both wise and not brave and vice versa.
If mary is either old or not tall then john is wise.
Everyone who is not quiet or not generous is wise or not wise and vice versa.
Everyone who is both not brave and not generous is either tall or generous.
John is not funny or generous.
Fred is not old.
Susan is not rich.
Lucy is generous or not rich.
Fred is both generous and brave.
Someone is strong.
Lucy is not tall or quiet.
Someone is both funny and creative. | Fred is wise. | neutral | (((creative(susan)&calm(susan)))<=>(~generous(susan)))&
(![X]:(generous(X)=>strong(X)))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((~creative(X)|~humble(X))=>(kind(X)<~>quiet(X))))&
((?[X]:((tall(X)&patient(X))))<=>(~funny(john)))&
(((~humble(john)&rich(john)))=>((~funny(fred)<~>~wise(fred))))&
(![X]:((~kind(X)&curious(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((humble(X)|patient(X))))=>(?[X]:((generous(X)<~>brave(X)))))&
(![X]:((~kind(X)|~funny(X))=>(~strong(X)<~>calm(X))))&
(![X]:(humble(X)=>(patient(X)|~patient(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~strong(X)|~brave(X))))&
(![X]:(~old(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>(wise(X)&~brave(X))))&
(((old(mary)<~>~tall(mary)))=>(wise(john)))&
(![X]:((~quiet(X)|~generous(X))<=>(wise(X)|~wise(X))))&
(![X]:((~brave(X)&~generous(X))=>(tall(X)<~>generous(X))))&
((~funny(john)|generous(john)))&
(~old(fred))&
(~rich(susan))&
((generous(lucy)|~rich(lucy)))&
((generous(fred)&brave(fred)))&
(?[X]:(strong(X)))&
((~tall(lucy)|quiet(lucy)))&
(?[X]:((funny(X)&creative(X)))) | wise(fred) | [] | null | 0 |
Everyone who is generous or tall is both not wise and not old.
Everyone who is wise or generous is not tall or curious.
If someone is either not humble or humble then someone is both patient and not curious.
Everyone who is either not funny or quiet is both calm and creative.
If someone is not brave then someone is not kind.
Everyone who is both not rich and not happy is patient or kind and vice versa.
If paul is not humble then alice is either not generous or happy and vice versa.
Everyone who is not brave or strong is both old and happy.
If someone is tall then lucy is either not old or creative.
Everyone who is not wise or not funny is both strong and not calm.
Everyone who is not happy or not old is not old or not kind.
Everyone who is both not humble and humble is not wise.
Everyone who is either old or curious is both not calm and not funny.
Everyone who is either patient or calm is not brave.
If someone is either not old or calm then paul is either humble or wise.
If someone is creative then someone is either wise or not old and vice versa.
Someone is not old.
Someone is either kind or not patient.
Someone is both not curious and funny.
Someone is kind or not rich.
John is funny.
Someone is both not tall and not calm.
Someone is either old or not funny.
Someone is old or quiet. | Alice is happy. | neutral | (![X]:((generous(X)|tall(X))=>(~wise(X)&~old(X))))&
(![X]:((wise(X)|generous(X))=>(~tall(X)|curious(X))))&
((?[X]:((~humble(X)<~>humble(X))))=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~funny(X)<~>quiet(X))=>(calm(X)&creative(X))))&
((?[X]:(~brave(X)))=>(?[X]:(~kind(X))))&
(![X]:((~rich(X)&~happy(X))<=>(patient(X)|kind(X))))&
((~humble(paul))<=>((~generous(alice)<~>happy(alice))))&
(![X]:((~brave(X)|strong(X))=>(old(X)&happy(X))))&
((?[X]:(tall(X)))=>((~old(lucy)<~>creative(lucy))))&
(![X]:((~wise(X)|~funny(X))=>(strong(X)&~calm(X))))&
(![X]:((~happy(X)|~old(X))=>(~old(X)|~kind(X))))&
(![X]:((~humble(X)&humble(X))=>~wise(X)))&
(![X]:((old(X)<~>curious(X))=>(~calm(X)&~funny(X))))&
(![X]:((patient(X)<~>calm(X))=>~brave(X)))&
((?[X]:((~old(X)<~>calm(X))))=>((humble(paul)<~>wise(paul))))&
((?[X]:(creative(X)))<=>(?[X]:((wise(X)<~>~old(X)))))&
(?[X]:(~old(X)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((kind(X)|~rich(X))))&
(funny(john))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:((old(X)|quiet(X)))) | happy(alice) | [] | null | 0 |
Everyone who is not wise is old.
Everyone who is not calm or calm is happy or not old.
Everyone who is both happy and not old is not brave or not quiet and vice versa.
If lucy is funny then alice is not curious and vice versa.
Everyone who is either not calm or not wise is not curious or not rich and vice versa.
If john is kind then someone is both not happy and not creative.
Everyone who is both not strong and old is happy or not strong.
Everyone who is either patient or not quiet is not happy or happy and vice versa.
If john is old then john is both not old and not funny.
Everyone who is not funny or not generous is either not funny or humble and vice versa.
Everyone who is not patient or tall is not tall.
Everyone who is generous is curious and vice versa.
If someone is both not patient and generous then someone is both not patient and strong and vice versa.
If alice is either not patient or old then someone is both not quiet and not wise and vice versa.
If alice is not patient then someone is happy and vice versa.
If fred is not calm then someone is brave.
Someone is old or strong.
Susan is either not creative or old.
Paul is not curious.
John is both patient and not strong.
Someone is either not strong or not calm.
Someone is not kind or wise.
Fred is not tall or not creative.
Mary is either not strong or funny. | Susan is brave. | entailment | (![X]:(~wise(X)=>old(X)))&
(![X]:((~calm(X)|calm(X))=>(happy(X)|~old(X))))&
(![X]:((happy(X)&~old(X))<=>(~brave(X)|~quiet(X))))&
((funny(lucy))<=>(~curious(alice)))&
(![X]:((~calm(X)<~>~wise(X))<=>(~curious(X)|~rich(X))))&
((kind(john))=>(?[X]:((~happy(X)&~creative(X)))))&
(![X]:((~strong(X)&old(X))=>(happy(X)|~strong(X))))&
(![X]:((patient(X)<~>~quiet(X))<=>(~happy(X)|happy(X))))&
((old(john))=>((~old(john)&~funny(john))))&
(![X]:((~funny(X)|~generous(X))<=>(~funny(X)<~>humble(X))))&
(![X]:((~patient(X)|tall(X))=>~tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
((?[X]:((~patient(X)&generous(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
(((~patient(alice)<~>old(alice)))<=>(?[X]:((~quiet(X)&~wise(X)))))&
((~patient(alice))<=>(?[X]:(happy(X))))&
((~calm(fred))=>(?[X]:(brave(X))))&
(?[X]:((old(X)|strong(X))))&
((~creative(susan)<~>old(susan)))&
(~curious(paul))&
((patient(john)&~strong(john)))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:((~kind(X)|wise(X))))&
((~tall(fred)|~creative(fred)))&
((~strong(mary)<~>funny(mary))) | brave(susan) | [
"p0",
"p2",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4141807441383670016409846
% SZS output start Proof for 4141807441383670016409846
1. ! [X0] : (~wise(X0) => old(X0)) [input p0]
3. ! [X0] : ((~old(X0) & happy(X0)) <=> (~quiet(X0) | ~brave(X0))) [input p2]
8. ! [X0] : ((patient(X0) <~> ~quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p7]
14. (~patient(alice) <~> old(alice)) <=> ? [X0] : (~wise(X0) & ~quiet(X0)) [input p13]
15. ~patient(alice) <=> ? [X0] : happy(X0) [input p14]
25. ~brave(susan) [input hypothesis]
31. ! [X0] : (old(X0) | wise(X0)) [ennf transformation 1]
38. ! [X0] : (((~old(X0) & happy(X0)) | (quiet(X0) & brave(X0))) & ((~quiet(X0) | ~brave(X0)) | (old(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((~old(X0) & happy(X0)) | (quiet(X0) & brave(X0))) & (~quiet(X0) | ~brave(X0) | old(X0) | ~happy(X0))) [flattening 38]
43. ! [X0] : ((((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0))))) [nnf transformation 8]
44. ! [X0] : ((((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0))))) [flattening 43]
53. (((~old(alice) | patient(alice)) & (old(alice) | ~patient(alice))) | ! [X0] : (wise(X0) | quiet(X0))) & (? [X0] : (~wise(X0) & ~quiet(X0)) | ((~patient(alice) | ~old(alice)) & (old(alice) | patient(alice)))) [nnf transformation 14]
54. (((~old(alice) | patient(alice)) & (old(alice) | ~patient(alice))) | ! [X0] : (wise(X0) | quiet(X0))) & (? [X1] : (~wise(X1) & ~quiet(X1)) | ((~patient(alice) | ~old(alice)) & (old(alice) | patient(alice)))) [rectify 53]
55. ? [X1] : (~wise(X1) & ~quiet(X1)) => (~wise(sK2) & ~quiet(sK2)) [choice axiom]
56. (((~old(alice) | patient(alice)) & (old(alice) | ~patient(alice))) | ! [X0] : (wise(X0) | quiet(X0))) & ((~wise(sK2) & ~quiet(sK2)) | ((~patient(alice) | ~old(alice)) & (old(alice) | patient(alice)))) [skolemisation 54,55]
57. (~patient(alice) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | patient(alice)) [nnf transformation 15]
58. (~patient(alice) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | patient(alice)) [rectify 57]
59. ? [X1] : happy(X1) => happy(sK3) [choice axiom]
60. (~patient(alice) | ! [X0] : ~happy(X0)) & (happy(sK3) | patient(alice)) [skolemisation 58,59]
70. old(X0) | wise(X0) [cnf transformation 31]
74. brave(X0) | happy(X0) [cnf transformation 39]
77. ~old(X0) | quiet(X0) [cnf transformation 39]
89. ~quiet(X0) | patient(X0) | happy(X0) [cnf transformation 44]
90. ~quiet(X0) | patient(X0) | ~happy(X0) [cnf transformation 44]
107. ~quiet(sK2) | old(alice) | patient(alice) [cnf transformation 56]
109. ~wise(sK2) | old(alice) | patient(alice) [cnf transformation 56]
114. ~patient(alice) | ~happy(X0) [cnf transformation 60]
126. ~brave(susan) [cnf transformation 25]
142. ~quiet(X0) | patient(X0) [subsumption resolution 89,90]
180. 11 <=> ! [X0] : (wise(X0) | quiet(X0)) [avatar definition]
181. quiet(X0) | wise(X0) <- (11) [avatar component clause 180]
183. 12 <=> patient(alice) [avatar definition]
184. ~patient(alice) <- (~12) [avatar component clause 183]
187. 13 <=> old(alice) [avatar definition]
188. old(alice) <- (13) [avatar component clause 187]
193. 14 <=> wise(sK2) [avatar definition]
195. ~wise(sK2) <- (~14) [avatar component clause 193]
197. 12 | 13 | ~14 [avatar split clause 109,193,187,183]
199. 15 <=> quiet(sK2) [avatar definition]
201. ~quiet(sK2) <- (~15) [avatar component clause 199]
203. 12 | 13 | ~15 [avatar split clause 107,199,187,183]
205. 16 <=> ! [X0] : ~happy(X0) [avatar definition]
206. ~happy(X0) <- (16) [avatar component clause 205]
207. 16 | ~12 [avatar split clause 114,183,205]
264. happy(susan) [resolution 74,126]
265. $false <- (16) [subsumption resolution 264,206]
266. ~16 [avatar contradiction clause 265]
271. quiet(X0) | wise(X0) [resolution 77,70]
282. wise(sK2) <- (11, ~15) [resolution 181,201]
284. $false <- (11, ~14, ~15) [subsumption resolution 282,195]
285. ~11 | 14 | 15 [avatar contradiction clause 284]
286. 11 [avatar split clause 271,180]
288. quiet(alice) <- (13) [resolution 188,77]
292. patient(alice) <- (13) [resolution 288,142]
293. $false <- (~12, 13) [subsumption resolution 292,184]
294. 12 | ~13 [avatar contradiction clause 293]
295. $false [avatar sat refutation 197,203,207,266,285,286,294]
% SZS output end Proof for 4141807441383670016409846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not patient is either not tall or not brave. If someone is tall then fred is either not tall or brave. Everyone who is both not strong and funny is either not kind or not wise and vice versa. If mary is not funny or brave then paul is not curious and vice versa. Everyone who is kind is not patient. Everyone who is brave or not generous is both not humble and kind. If lucy is creative then someone is both not creative and not quiet and vice versa. If someone is both not kind and tall then paul is both not patient and not happy. If lucy is brave then someone is not generous and vice versa. Everyone who is not happy or generous is not strong. If lucy is not patient or quiet then alice is rich or humble and vice versa. Everyone who is not happy or curious is patient and vice versa. Everyone who is not curious is happy and vice versa. If john is happy then someone is both not calm and not quiet and vice versa. Everyone who is quiet or curious is tall. Lucy is generous. Someone is old. Someone is either not patient or not strong. Someone is either quiet or not wise. Fred is not wise. | Mary is not humble. | entailment | (![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~brave(X))))&
((?[X]:(tall(X)))=>((~tall(fred)<~>brave(fred))))&
(![X]:((~strong(X)&funny(X))<=>(~kind(X)<~>~wise(X))))&
(((~funny(mary)|brave(mary)))<=>(~curious(paul)))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((brave(X)|~generous(X))=>(~humble(X)&kind(X))))&
((creative(lucy))<=>(?[X]:((~creative(X)&~quiet(X)))))&
((?[X]:((~kind(X)&tall(X))))=>((~patient(paul)&~happy(paul))))&
((brave(lucy))<=>(?[X]:(~generous(X))))&
(![X]:((~happy(X)|generous(X))=>~strong(X)))&
(((~patient(lucy)|quiet(lucy)))<=>((rich(alice)|humble(alice))))&
(![X]:((~happy(X)|curious(X))<=>patient(X)))&
(![X]:(~curious(X)<=>happy(X)))&
((happy(john))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((quiet(X)|curious(X))=>tall(X)))&
(generous(lucy))&
(?[X]:(old(X)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((quiet(X)<~>~wise(X))))&
(~wise(fred)) | ~humble(mary) | [
"p0",
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4896384665302141519350826
% SZS output start Proof for 4896384665302141519350826
1. ! [X0] : ((patient(X0) <~> ~patient(X0)) => (~tall(X0) <~> ~brave(X0))) [input p0]
2. ? [X0] : tall(X0) => (~tall(fred) <~> brave(fred)) [input p1]
6. ! [X0] : ((~generous(X0) | brave(X0)) => (kind(X0) & ~humble(X0))) [input p5]
21. humble(mary) [input hypothesis]
23. ! [X0] : ((~tall(X0) <~> ~brave(X0)) | (patient(X0) <=> ~patient(X0))) [ennf transformation 1]
24. (~tall(fred) <~> brave(fred)) | ! [X0] : ~tall(X0) [ennf transformation 2]
26. ! [X0] : ((kind(X0) & ~humble(X0)) | (generous(X0) & ~brave(X0))) [ennf transformation 6]
30. ! [X0] : (((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 23]
31. ((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : ~tall(X0) [nnf transformation 24]
59. ~brave(X0) | ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 30]
60. ~brave(X0) | ~tall(X0) | patient(X0) | patient(X0) [cnf transformation 30]
61. brave(X0) | tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 30]
62. brave(X0) | tall(X0) | patient(X0) | patient(X0) [cnf transformation 30]
63. brave(fred) | ~tall(fred) | ~tall(X0) [cnf transformation 31]
64. ~brave(fred) | tall(fred) | ~tall(X0) [cnf transformation 31]
75. ~humble(X0) | ~brave(X0) [cnf transformation 26]
108. humble(mary) [cnf transformation 21]
109. ~brave(X0) | ~tall(X0) | ~patient(X0) [duplicate literal removal 59]
110. ~brave(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 60]
111. brave(X0) | tall(X0) | ~patient(X0) [duplicate literal removal 61]
112. brave(X0) | tall(X0) | patient(X0) [duplicate literal removal 62]
113. brave(X0) | tall(X0) [subsumption resolution 111,112]
114. ~brave(X0) | ~tall(X0) [subsumption resolution 109,110]
115. ~brave(fred) | ~tall(X0) [subsumption resolution 64,114]
117. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
118. ~tall(X0) <- (1) [avatar component clause 117]
120. 2 <=> brave(fred) [avatar definition]
123. 1 | ~2 [avatar split clause 115,120,117]
124. brave(fred) | ~tall(X0) [subsumption resolution 63,113]
125. 1 | 2 [avatar split clause 124,120,117]
135. 5 <=> brave(mary) [avatar definition]
136. ~brave(mary) <- (~5) [avatar component clause 135]
243. ~brave(mary) [resolution 75,108]
245. ~5 [avatar split clause 243,135]
265. tall(mary) <- (~5) [resolution 113,136]
269. $false <- (1, ~5) [subsumption resolution 265,118]
270. ~1 | 5 [avatar contradiction clause 269]
275. $false [avatar sat refutation 123,125,245,270]
% SZS output end Proof for 4896384665302141519350826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny is either not old or old and vice versa. If john is not quiet or not happy then alice is wise. Everyone who is either happy or not kind is not strong or brave. Everyone who is either not happy or not curious is either not quiet or happy and vice versa. Everyone who is both curious and not curious is both not curious and calm. Everyone who is either creative or humble is not wise or quiet and vice versa. Everyone who is both not strong and not kind is quiet or not quiet and vice versa. Everyone who is curious is either funny or not wise and vice versa. Everyone who is either quiet or not rich is either wise or kind and vice versa. If someone is humble then someone is rich or happy. If susan is either tall or not tall then fred is both old and not calm and vice versa. Everyone who is either not rich or not old is either old or not kind and vice versa. Everyone who is either curious or humble is both happy and calm. If lucy is rich then alice is either quiet or creative and vice versa. Everyone who is both rich and not wise is strong and vice versa. Everyone who is not tall is not funny. Alice is either curious or generous. Mary is happy or old. Fred is not strong or humble. Someone is both creative and happy. Mary is not strong or not brave. Someone is not happy or not creative. Alice is both quiet and not funny. | John is curious. | contradiction | (![X]:((~calm(X)|~funny(X))<=>(~old(X)<~>old(X))))&
(((~quiet(john)|~happy(john)))=>(wise(alice)))&
(![X]:((happy(X)<~>~kind(X))=>(~strong(X)|brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((curious(X)&~curious(X))=>(~curious(X)&calm(X))))&
(![X]:((creative(X)<~>humble(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~strong(X)&~kind(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(curious(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((rich(X)|happy(X)))))&
(((tall(susan)<~>~tall(susan)))<=>((old(fred)&~calm(fred))))&
(![X]:((~rich(X)<~>~old(X))<=>(old(X)<~>~kind(X))))&
(![X]:((curious(X)<~>humble(X))=>(happy(X)&calm(X))))&
((rich(lucy))<=>((quiet(alice)<~>creative(alice))))&
(![X]:((rich(X)&~wise(X))<=>strong(X)))&
(![X]:(~tall(X)=>~funny(X)))&
((curious(alice)<~>generous(alice)))&
((happy(mary)|old(mary)))&
((~strong(fred)|humble(fred)))&
(?[X]:((creative(X)&happy(X))))&
((~strong(mary)|~brave(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((quiet(alice)&~funny(alice))) | curious(john) | [
"p3",
"p6",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7503977931170326124924388
% SZS output start Proof for 7503977931170326124924388
4. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (~quiet(X0) <~> happy(X0))) [input p3]
7. ! [X0] : ((~kind(X0) & ~strong(X0)) <=> (~quiet(X0) | quiet(X0))) [input p6]
9. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (wise(X0) <~> kind(X0))) [input p8]
12. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (old(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~wise(X0) & rich(X0)) <=> strong(X0)) [input p14]
24. curious(john) [input hypothesis]
37. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 4]
40. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | (kind(X0) | strong(X0)))) [nnf transformation 7]
41. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | kind(X0) | strong(X0))) [flattening 40]
43. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 9]
49. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 12]
52. ! [X0] : (((~wise(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | (wise(X0) | ~rich(X0)))) [nnf transformation 15]
53. ! [X0] : (((~wise(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | wise(X0) | ~rich(X0))) [flattening 52]
69. happy(X0) | ~quiet(X0) | ~curious(X0) | happy(X0) [cnf transformation 37]
74. ~curious(X0) | ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 37]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 41]
87. ~strong(X0) | quiet(X0) [cnf transformation 41]
88. ~kind(X0) | ~quiet(X0) [cnf transformation 41]
89. ~kind(X0) | quiet(X0) [cnf transformation 41]
98. ~rich(X0) | quiet(X0) | kind(X0) | ~wise(X0) [cnf transformation 43]
111. kind(X0) | ~old(X0) | ~old(X0) | rich(X0) [cnf transformation 49]
116. old(X0) | rich(X0) | old(X0) | kind(X0) [cnf transformation 49]
125. strong(X0) | wise(X0) | ~rich(X0) [cnf transformation 53]
139. curious(john) [cnf transformation 24]
141. kind(X0) | ~old(X0) | rich(X0) [duplicate literal removal 111]
143. old(X0) | rich(X0) | kind(X0) [duplicate literal removal 116]
149. happy(X0) | ~quiet(X0) | ~curious(X0) [duplicate literal removal 69]
151. ~curious(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 74]
166. 3 <=> quiet(john) [avatar definition]
167. ~quiet(john) <- (~3) [avatar component clause 166]
171. ~curious(X0) | ~quiet(X0) [subsumption resolution 149,151]
172. ~kind(X0) [subsumption resolution 88,89]
173. ~strong(X0) [subsumption resolution 86,87]
175. ~rich(X0) | quiet(X0) | ~wise(X0) [subsumption resolution 98,172]
206. rich(X0) | old(X0) [subsumption resolution 143,172]
207. ~old(X0) | rich(X0) [subsumption resolution 141,172]
208. rich(X0) [subsumption resolution 207,206]
221. wise(X0) | ~rich(X0) [subsumption resolution 125,173]
222. wise(X0) [subsumption resolution 221,208]
252. ~quiet(john) [resolution 171,139]
255. ~3 [avatar split clause 252,166]
321. quiet(X1) | ~wise(X1) [resolution 175,208]
323. quiet(X1) [subsumption resolution 321,222]
326. $false <- (~3) [resolution 323,167]
328. 3 [avatar contradiction clause 326]
329. $false [avatar sat refutation 255,328]
% SZS output end Proof for 7503977931170326124924388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or funny is both not curious and kind.
If someone is either happy or curious then mary is both not rich and old and vice versa.
If someone is both strong and not tall then someone is patient.
Everyone who is either not rich or funny is not curious or tall.
Everyone who is patient is not happy and vice versa.
If paul is either not old or kind then someone is not rich or not curious.
Everyone who is not funny or not humble is either humble or old.
If susan is either humble or patient then someone is not generous.
Everyone who is both patient and not kind is either not kind or curious and vice versa.
If mary is funny or not patient then paul is brave or not curious and vice versa.
Everyone who is old or not wise is either wise or curious and vice versa.
If someone is not patient or not happy then paul is both not patient and not brave and vice versa.
Everyone who is both not tall and not curious is curious or funny.
Everyone who is tall or old is not tall and vice versa.
Everyone who is both not kind and not generous is either not happy or not old and vice versa.
If someone is either not patient or creative then someone is not brave or strong.
John is funny.
Mary is not patient.
Someone is not quiet.
Paul is both not humble and not generous.
Someone is both not quiet and rich.
Fred is not humble or not wise. | Mary is rich. | contradiction | (![X]:((~rich(X)<~>funny(X))=>(~curious(X)&kind(X))))&
((?[X]:((happy(X)<~>curious(X))))<=>((~rich(mary)&old(mary))))&
((?[X]:((strong(X)&~tall(X))))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)<~>funny(X))=>(~curious(X)|tall(X))))&
(![X]:(patient(X)<=>~happy(X)))&
(((~old(paul)<~>kind(paul)))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((~funny(X)|~humble(X))=>(humble(X)<~>old(X))))&
(((humble(susan)<~>patient(susan)))=>(?[X]:(~generous(X))))&
(![X]:((patient(X)&~kind(X))<=>(~kind(X)<~>curious(X))))&
(((funny(mary)|~patient(mary)))<=>((brave(paul)|~curious(paul))))&
(![X]:((old(X)|~wise(X))<=>(wise(X)<~>curious(X))))&
((?[X]:((~patient(X)|~happy(X))))<=>((~patient(paul)&~brave(paul))))&
(![X]:((~tall(X)&~curious(X))=>(curious(X)|funny(X))))&
(![X]:((tall(X)|old(X))<=>~tall(X)))&
(![X]:((~kind(X)&~generous(X))<=>(~happy(X)<~>~old(X))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((~brave(X)|strong(X)))))&
(funny(john))&
(~patient(mary))&
(?[X]:(~quiet(X)))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~quiet(X)&rich(X))))&
((~humble(fred)|~wise(fred))) | rich(mary) | [
"p1",
"p4",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8313476244311584843756009
% SZS output start Proof for 8313476244311584843756009
2. ? [X0] : (happy(X0) <~> curious(X0)) <=> (old(mary) & ~rich(mary)) [input p1]
5. ! [X0] : (patient(X0) <=> ~happy(X0)) [input p4]
10. (~patient(mary) | funny(mary)) <=> (~curious(paul) | brave(paul)) [input p9]
12. ? [X0] : (~happy(X0) | ~patient(X0)) <=> (~brave(paul) & ~patient(paul)) [input p11]
18. ~patient(mary) [input p17]
23. rich(mary) [input hypothesis]
39. (? [X0] : ((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | (~old(mary) | rich(mary))) & ((old(mary) & ~rich(mary)) | ! [X0] : ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0)))) [nnf transformation 2]
40. (? [X0] : ((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | ~old(mary) | rich(mary)) & ((old(mary) & ~rich(mary)) | ! [X0] : ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0)))) [flattening 39]
41. (? [X0] : ((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | ~old(mary) | rich(mary)) & ((old(mary) & ~rich(mary)) | ! [X1] : ((happy(X1) | ~curious(X1)) & (curious(X1) | ~happy(X1)))) [rectify 40]
42. ? [X0] : ((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) => ((~curious(sK0) | ~happy(sK0)) & (curious(sK0) | happy(sK0))) [choice axiom]
43. (((~curious(sK0) | ~happy(sK0)) & (curious(sK0) | happy(sK0))) | ~old(mary) | rich(mary)) & ((old(mary) & ~rich(mary)) | ! [X1] : ((happy(X1) | ~curious(X1)) & (curious(X1) | ~happy(X1)))) [skolemisation 41,42]
48. ! [X0] : ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))) [nnf transformation 5]
58. ((~patient(mary) | funny(mary)) | (curious(paul) & ~brave(paul))) & ((~curious(paul) | brave(paul)) | (patient(mary) & ~funny(mary))) [nnf transformation 10]
59. (~patient(mary) | funny(mary) | (curious(paul) & ~brave(paul))) & (~curious(paul) | brave(paul) | (patient(mary) & ~funny(mary))) [flattening 58]
62. (? [X0] : (~happy(X0) | ~patient(X0)) | (brave(paul) | patient(paul))) & ((~brave(paul) & ~patient(paul)) | ! [X0] : (happy(X0) & patient(X0))) [nnf transformation 12]
63. (? [X0] : (~happy(X0) | ~patient(X0)) | brave(paul) | patient(paul)) & ((~brave(paul) & ~patient(paul)) | ! [X0] : (happy(X0) & patient(X0))) [flattening 62]
64. (? [X0] : (~happy(X0) | ~patient(X0)) | brave(paul) | patient(paul)) & ((~brave(paul) & ~patient(paul)) | ! [X1] : (happy(X1) & patient(X1))) [rectify 63]
65. ? [X0] : (~happy(X0) | ~patient(X0)) => (~happy(sK4) | ~patient(sK4)) [choice axiom]
66. ((~happy(sK4) | ~patient(sK4)) | brave(paul) | patient(paul)) & ((~brave(paul) & ~patient(paul)) | ! [X1] : (happy(X1) & patient(X1))) [skolemisation 64,65]
81. ~rich(mary) | curious(X1) | ~happy(X1) [cnf transformation 43]
91. patient(X0) | happy(X0) [cnf transformation 48]
107. ~curious(paul) | brave(paul) | patient(mary) [cnf transformation 59]
116. ~patient(paul) | patient(X1) [cnf transformation 66]
118. ~brave(paul) | patient(X1) [cnf transformation 66]
134. ~patient(mary) [cnf transformation 18]
139. rich(mary) [cnf transformation 23]
149. 1 <=> rich(mary) [avatar definition]
171. 6 <=> ! [X1] : (curious(X1) | ~happy(X1)) [avatar definition]
172. ~happy(X1) | curious(X1) <- (6) [avatar component clause 171]
175. 6 | ~1 [avatar split clause 81,149,171]
218. 16 <=> curious(paul) [avatar definition]
226. 18 <=> patient(mary) [avatar definition]
228. ~patient(mary) <- (~18) [avatar component clause 226]
231. 19 <=> brave(paul) [avatar definition]
235. 18 | 19 | ~16 [avatar split clause 107,218,231,226]
242. 21 <=> ! [X1] : patient(X1) [avatar definition]
243. patient(X1) <- (21) [avatar component clause 242]
244. 21 | ~19 [avatar split clause 118,231,242]
246. 22 <=> patient(paul) [avatar definition]
248. ~patient(paul) <- (~22) [avatar component clause 246]
250. 21 | ~22 [avatar split clause 116,246,242]
267. ~18 [avatar split clause 134,226]
277. 1 [avatar split clause 139,149]
280. happy(paul) <- (~22) [resolution 91,248]
288. curious(paul) <- (6, ~22) [resolution 172,280]
291. 16 | ~6 | 22 [avatar split clause 288,246,171,218]
294. $false <- (~18, 21) [resolution 243,228]
298. 18 | ~21 [avatar contradiction clause 294]
301. $false [avatar sat refutation 175,235,244,250,267,277,291,298]
% SZS output end Proof for 8313476244311584843756009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not happy or brave then lucy is either not humble or humble.
Everyone who is both not wise and not patient is either strong or old and vice versa.
Everyone who is calm or not creative is either not old or not curious.
Everyone who is both not wise and not old is both not humble and not kind.
Everyone who is not brave or not funny is not calm.
If someone is not generous or not kind then lucy is not funny and vice versa.
If paul is not patient or humble then someone is patient or not funny and vice versa.
Everyone who is both happy and not wise is both rich and happy.
Everyone who is both not curious and not creative is generous.
If paul is either brave or not quiet then susan is not rich or not strong and vice versa.
Everyone who is either creative or not happy is not tall or wise and vice versa.
If susan is not wise then someone is not strong or not patient.
If someone is either not old or not quiet then someone is both funny and not curious and vice versa.
If fred is both not wise and patient then alice is either strong or not wise and vice versa.
Everyone who is both quiet and not kind is brave or not happy and vice versa.
Someone is either not happy or kind.
Paul is old.
John is not happy or not calm.
Mary is either not tall or generous.
Mary is brave.
Someone is not old.
John is tall.
Alice is both not old and humble. | John is generous. | neutral | (((~happy(susan)|brave(susan)))=>((~humble(lucy)<~>humble(lucy))))&
(![X]:((~wise(X)&~patient(X))<=>(strong(X)<~>old(X))))&
(![X]:((calm(X)|~creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)|~funny(X))=>~calm(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>(~funny(lucy)))&
(((~patient(paul)|humble(paul)))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>generous(X)))&
(((brave(paul)<~>~quiet(paul)))<=>((~rich(susan)|~strong(susan))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)|wise(X))))&
((~wise(susan))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~wise(fred)&patient(fred)))<=>((strong(alice)<~>~wise(alice))))&
(![X]:((quiet(X)&~kind(X))<=>(brave(X)|~happy(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
(old(paul))&
((~happy(john)|~calm(john)))&
((~tall(mary)<~>generous(mary)))&
(brave(mary))&
(?[X]:(~old(X)))&
(tall(john))&
((~old(alice)&humble(alice))) | generous(john) | [] | null | 0 |
Everyone who is both not generous and strong is not rich or not curious. Everyone who is wise is kind and vice versa. If someone is quiet then alice is both creative and not old and vice versa. Everyone who is either brave or not patient is old or wise. Everyone who is patient is not strong or not brave and vice versa. Everyone who is both wise and happy is not old or kind and vice versa. Everyone who is either not old or not curious is not wise or not funny and vice versa. If someone is either not strong or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. If alice is calm or rich then fred is not humble or curious and vice versa. Everyone who is generous or not happy is both tall and wise and vice versa. John is creative or rich. Someone is either quiet or kind. Lucy is not calm or patient. Someone is both funny and not kind. Fred is both brave and not patient. Someone is strong. John is not curious or old. Paul is strong or not calm. | Paul is strong. | neutral | (![X]:((~generous(X)&strong(X))=>(~rich(X)|~curious(X))))&
(![X]:(wise(X)<=>kind(X)))&
((?[X]:(quiet(X)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
((creative(john)|rich(john)))&
(?[X]:((quiet(X)<~>kind(X))))&
((~calm(lucy)|patient(lucy)))&
(?[X]:((funny(X)&~kind(X))))&
((brave(fred)&~patient(fred)))&
(?[X]:(strong(X)))&
((~curious(john)|old(john)))&
((strong(paul)|~calm(paul))) | strong(paul) | [] | null | 0 |
Everyone who is not quiet or generous is both strong and not brave and vice versa.
If someone is both generous and old then someone is both strong and rich and vice versa.
Everyone who is either calm or wise is humble or not rich.
Everyone who is not brave is either not curious or not patient.
Everyone who is not kind is both not tall and brave and vice versa.
Everyone who is either humble or rich is generous or humble and vice versa.
Everyone who is either not humble or not funny is either not old or strong and vice versa.
If someone is either patient or quiet then someone is tall and vice versa.
Everyone who is both kind and not quiet is old.
Everyone who is both not patient and wise is either not rich or wise and vice versa.
If someone is not brave or not kind then susan is not calm and vice versa.
Everyone who is not funny or funny is either not calm or not tall and vice versa.
If someone is not kind then someone is not strong and vice versa.
If someone is not quiet or happy then someone is not tall or not kind.
If susan is either not old or not creative then someone is either curious or funny.
Lucy is happy or kind.
Fred is not humble or funny.
Susan is either quiet or humble.
Someone is either generous or creative.
Someone is brave.
John is funny or rich.
Susan is patient or wise.
Someone is not patient or not generous. | Fred is not generous. | neutral | (![X]:((~quiet(X)|generous(X))<=>(strong(X)&~brave(X))))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((calm(X)<~>wise(X))=>(humble(X)|~rich(X))))&
(![X]:(~brave(X)=>(~curious(X)<~>~patient(X))))&
(![X]:(~kind(X)<=>(~tall(X)&brave(X))))&
(![X]:((humble(X)<~>rich(X))<=>(generous(X)|humble(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~old(X)<~>strong(X))))&
((?[X]:((patient(X)<~>quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~quiet(X))=>old(X)))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~calm(susan)))&
(![X]:((~funny(X)|funny(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(~strong(X))))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(((~old(susan)<~>~creative(susan)))=>(?[X]:((curious(X)<~>funny(X)))))&
((happy(lucy)|kind(lucy)))&
((~humble(fred)|funny(fred)))&
((quiet(susan)<~>humble(susan)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(brave(X)))&
((funny(john)|rich(john)))&
((patient(susan)|wise(susan)))&
(?[X]:((~patient(X)|~generous(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is not old is either quiet or generous.
Everyone who is both calm and not old is wise or not funny.
Everyone who is either not rich or not kind is not curious.
Everyone who is either not curious or kind is kind and vice versa.
If alice is both rich and not quiet then lucy is either not brave or kind.
If fred is not funny then someone is kind and vice versa.
If someone is not strong or quiet then fred is both not wise and quiet and vice versa.
If someone is happy then someone is not calm and vice versa.
If someone is not kind then susan is not rich or kind.
Everyone who is both tall and funny is not calm or not happy and vice versa.
If someone is patient then john is curious or not strong and vice versa.
Everyone who is both funny and not humble is either patient or not calm.
If susan is either not strong or curious then someone is not humble and vice versa.
If john is not happy then alice is either strong or not funny.
If lucy is not rich then someone is either happy or not quiet.
Everyone who is not wise or quiet is both not kind and funny and vice versa.
Someone is either humble or not rich.
Lucy is rich or old.
John is creative or patient.
Someone is both rich and curious.
Someone is both wise and old.
Lucy is either kind or not humble.
Someone is not humble or not curious.
Alice is either wise or not generous. | Lucy is not quiet. | entailment | (![X]:(~old(X)=>(quiet(X)<~>generous(X))))&
(![X]:((calm(X)&~old(X))=>(wise(X)|~funny(X))))&
(![X]:((~rich(X)<~>~kind(X))=>~curious(X)))&
(![X]:((~curious(X)<~>kind(X))<=>kind(X)))&
(((rich(alice)&~quiet(alice)))=>((~brave(lucy)<~>kind(lucy))))&
((~funny(fred))<=>(?[X]:(kind(X))))&
((?[X]:((~strong(X)|quiet(X))))<=>((~wise(fred)&quiet(fred))))&
((?[X]:(happy(X)))<=>(?[X]:(~calm(X))))&
((?[X]:(~kind(X)))=>((~rich(susan)|kind(susan))))&
(![X]:((tall(X)&funny(X))<=>(~calm(X)|~happy(X))))&
((?[X]:(patient(X)))<=>((curious(john)|~strong(john))))&
(![X]:((funny(X)&~humble(X))=>(patient(X)<~>~calm(X))))&
(((~strong(susan)<~>curious(susan)))<=>(?[X]:(~humble(X))))&
((~happy(john))=>((strong(alice)<~>~funny(alice))))&
((~rich(lucy))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(![X]:((~wise(X)|quiet(X))<=>(~kind(X)&funny(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
((rich(lucy)|old(lucy)))&
((creative(john)|patient(john)))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((wise(X)&old(X))))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~humble(X)|~curious(X))))&
((wise(alice)<~>~generous(alice))) | ~quiet(lucy) | [
"p2",
"p3",
"p5",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6900882475059799285487519
% SZS output start Proof for 6900882475059799285487519
3. ! [X0] : ((~rich(X0) <~> ~kind(X0)) => ~curious(X0)) [input p2]
4. ! [X0] : ((~curious(X0) <~> kind(X0)) <=> kind(X0)) [input p3]
6. ~funny(fred) <=> ? [X0] : kind(X0) [input p5]
7. ? [X0] : (quiet(X0) | ~strong(X0)) <=> (quiet(fred) & ~wise(fred)) [input p6]
16. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (funny(X0) & ~kind(X0))) [input p15]
20. ? [X0] : (curious(X0) & rich(X0)) [input p19]
25. quiet(lucy) [input hypothesis]
32. ! [X0] : (~curious(X0) | (~rich(X0) <=> ~kind(X0))) [ennf transformation 3]
41. ! [X0] : (~curious(X0) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) [nnf transformation 32]
42. ! [X0] : ((((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | ~kind(X0)) & (kind(X0) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0))))) [nnf transformation 4]
44. (~funny(fred) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | funny(fred)) [nnf transformation 6]
45. (~funny(fred) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | funny(fred)) [rectify 44]
46. ? [X1] : kind(X1) => kind(sK0) [choice axiom]
47. (~funny(fred) | ! [X0] : ~kind(X0)) & (kind(sK0) | funny(fred)) [skolemisation 45,46]
48. (? [X0] : (quiet(X0) | ~strong(X0)) | (~quiet(fred) | wise(fred))) & ((quiet(fred) & ~wise(fred)) | ! [X0] : (~quiet(X0) & strong(X0))) [nnf transformation 7]
49. (? [X0] : (quiet(X0) | ~strong(X0)) | ~quiet(fred) | wise(fred)) & ((quiet(fred) & ~wise(fred)) | ! [X0] : (~quiet(X0) & strong(X0))) [flattening 48]
50. (? [X0] : (quiet(X0) | ~strong(X0)) | ~quiet(fred) | wise(fred)) & ((quiet(fred) & ~wise(fred)) | ! [X1] : (~quiet(X1) & strong(X1))) [rectify 49]
51. ? [X0] : (quiet(X0) | ~strong(X0)) => (quiet(sK1) | ~strong(sK1)) [choice axiom]
52. ((quiet(sK1) | ~strong(sK1)) | ~quiet(fred) | wise(fred)) & ((quiet(fred) & ~wise(fred)) | ! [X1] : (~quiet(X1) & strong(X1))) [skolemisation 50,51]
74. ! [X0] : (((quiet(X0) | ~wise(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 16]
75. ! [X0] : ((quiet(X0) | ~wise(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | (~quiet(X0) & wise(X0)))) [flattening 74]
79. ? [X0] : (curious(X0) & rich(X0)) => (curious(sK8) & rich(sK8)) [choice axiom]
80. curious(sK8) & rich(sK8) [skolemisation 20,79]
88. ~curious(X0) | ~rich(X0) | kind(X0) [cnf transformation 41]
89. kind(X0) | kind(X0) | curious(X0) [cnf transformation 42]
92. ~kind(X0) | curious(X0) | ~kind(X0) [cnf transformation 42]
96. ~funny(fred) | ~kind(X0) [cnf transformation 47]
98. ~wise(fred) | ~quiet(X1) [cnf transformation 52]
125. funny(X0) | wise(X0) [cnf transformation 75]
130. rich(sK8) [cnf transformation 80]
138. quiet(lucy) [cnf transformation 25]
139. kind(X0) | curious(X0) [duplicate literal removal 89]
140. ~kind(X0) | curious(X0) [duplicate literal removal 92]
141. curious(X0) [subsumption resolution 139,140]
161. 5 <=> ! [X0] : ~kind(X0) [avatar definition]
162. ~kind(X0) <- (5) [avatar component clause 161]
164. 6 <=> funny(fred) [avatar definition]
166. ~funny(fred) <- (~6) [avatar component clause 164]
167. 5 | ~6 [avatar split clause 96,164,161]
174. 8 <=> wise(fred) [avatar definition]
191. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
192. ~quiet(X1) <- (12) [avatar component clause 191]
198. 12 | ~8 [avatar split clause 98,174,191]
322. ~rich(X0) | kind(X0) [resolution 88,141]
323. ~rich(X0) <- (5) [subsumption resolution 322,162]
324. $false <- (5) [resolution 323,130]
325. ~5 [avatar contradiction clause 324]
327. wise(fred) <- (~6) [resolution 166,125]
331. 8 | 6 [avatar split clause 327,164,174]
335. $false <- (12) [resolution 192,138]
336. ~12 [avatar contradiction clause 335]
337. $false [avatar sat refutation 167,198,325,331,336]
% SZS output end Proof for 6900882475059799285487519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and quiet is not tall.
If someone is brave or not happy then someone is not strong or kind and vice versa.
Everyone who is creative is kind or wise and vice versa.
Everyone who is not strong is both creative and wise.
Everyone who is both not generous and generous is tall or calm.
If john is both tall and not wise then lucy is brave and vice versa.
Everyone who is funny or not strong is either kind or not calm and vice versa.
If mary is generous or not funny then john is not brave and vice versa.
Everyone who is both old and funny is not rich or curious and vice versa.
If paul is both tall and kind then someone is both humble and wise.
If paul is both generous and calm then someone is both quiet and generous.
Everyone who is patient is not patient or not old and vice versa.
Everyone who is both not rich and calm is not creative or not funny and vice versa.
If fred is both kind and wise then someone is brave or generous.
If paul is both not kind and quiet then someone is either not wise or not tall and vice versa.
Everyone who is both not generous and not brave is either not brave or not funny.
Alice is kind.
Susan is either generous or not quiet.
Someone is not creative or strong.
Fred is either generous or brave.
Someone is generous or creative. | Paul is not humble. | neutral | (![X]:((curious(X)&quiet(X))=>~tall(X)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:(creative(X)<=>(kind(X)|wise(X))))&
(![X]:(~strong(X)=>(creative(X)&wise(X))))&
(![X]:((~generous(X)&generous(X))=>(tall(X)|calm(X))))&
(((tall(john)&~wise(john)))<=>(brave(lucy)))&
(![X]:((funny(X)|~strong(X))<=>(kind(X)<~>~calm(X))))&
(((generous(mary)|~funny(mary)))<=>(~brave(john)))&
(![X]:((old(X)&funny(X))<=>(~rich(X)|curious(X))))&
(((tall(paul)&kind(paul)))=>(?[X]:((humble(X)&wise(X)))))&
(((generous(paul)&calm(paul)))=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:(patient(X)<=>(~patient(X)|~old(X))))&
(![X]:((~rich(X)&calm(X))<=>(~creative(X)|~funny(X))))&
(((kind(fred)&wise(fred)))=>(?[X]:((brave(X)|generous(X)))))&
(((~kind(paul)&quiet(paul)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~generous(X)&~brave(X))=>(~brave(X)<~>~funny(X))))&
(kind(alice))&
((generous(susan)<~>~quiet(susan)))&
(?[X]:((~creative(X)|strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((generous(X)|creative(X)))) | ~humble(paul) | [] | null | 0 |
If lucy is not calm then john is both humble and tall.
If someone is both not brave and happy then alice is both not strong and quiet.
If alice is humble then someone is patient or rich and vice versa.
Everyone who is either not kind or calm is both not tall and not rich and vice versa.
If someone is not tall then someone is either not rich or not brave.
If someone is not generous then someone is not old.
Everyone who is both quiet and not tall is not quiet and vice versa.
Everyone who is both not rich and curious is either tall or not quiet and vice versa.
If lucy is both not kind and not old then someone is either not kind or wise.
If alice is either not old or not wise then alice is quiet or patient and vice versa.
If alice is brave or strong then paul is not patient and vice versa.
Everyone who is either not generous or kind is not strong.
If someone is patient then someone is calm or not generous.
Everyone who is both generous and not wise is either old or happy.
Everyone who is not funny is both funny and not patient and vice versa.
Everyone who is generous or not calm is both not quiet and funny and vice versa.
Fred is either not strong or not brave.
John is tall or not curious.
Someone is not wise.
Someone is either brave or not brave.
Someone is quiet. | John is generous. | contradiction | ((~calm(lucy))=>((humble(john)&tall(john))))&
((?[X]:((~brave(X)&happy(X))))=>((~strong(alice)&quiet(alice))))&
((humble(alice))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~tall(X)&~rich(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)&~tall(X))<=>~quiet(X)))&
(![X]:((~rich(X)&curious(X))<=>(tall(X)<~>~quiet(X))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(((~old(alice)<~>~wise(alice)))<=>((quiet(alice)|patient(alice))))&
(((brave(alice)|strong(alice)))<=>(~patient(paul)))&
(![X]:((~generous(X)<~>kind(X))=>~strong(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((generous(X)&~wise(X))=>(old(X)<~>happy(X))))&
(![X]:(~funny(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)|~calm(X))<=>(~quiet(X)&funny(X))))&
((~strong(fred)<~>~brave(fred)))&
((tall(john)|~curious(john)))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:(quiet(X))) | generous(john) | [
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 668724406418048870271166
% SZS output start Proof for 668724406418048870271166
7. ! [X0] : ((~tall(X0) & quiet(X0)) <=> ~quiet(X0)) [input p6]
16. ! [X0] : ((~calm(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p15]
22. generous(john) [input hypothesis]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | (tall(X0) | ~quiet(X0)))) [nnf transformation 7]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | tall(X0) | ~quiet(X0))) [flattening 49]
67. ! [X0] : (((~calm(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [flattening 67]
94. quiet(X0) | quiet(X0) [cnf transformation 50]
121. ~quiet(X0) | ~generous(X0) [cnf transformation 68]
133. generous(john) [cnf transformation 22]
137. quiet(X0) [duplicate literal removal 94]
269. ~generous(X0) [subsumption resolution 121,137]
285. $false [subsumption resolution 133,269]
% SZS output end Proof for 668724406418048870271166
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not quiet then john is both not generous and not kind. Everyone who is wise or rich is either not happy or not rich and vice versa. Everyone who is not kind or happy is both not old and wise. Everyone who is quiet is kind or not humble. Everyone who is either generous or kind is kind or humble. If someone is kind or wise then someone is happy. If john is not patient then john is both rich and humble and vice versa. If someone is both tall and patient then someone is calm and vice versa. Everyone who is both not wise and calm is not kind. If alice is both not strong and happy then someone is not curious or not rich. If someone is generous then alice is happy. Everyone who is not happy or humble is either not happy or kind. Everyone who is not curious is either not generous or wise and vice versa. If alice is rich then alice is not creative or brave and vice versa. Everyone who is both not happy and humble is curious and vice versa. If fred is not curious or not funny then someone is both not rich and not curious and vice versa. Fred is old or not funny. Fred is either not curious or brave. Someone is both rich and wise. Fred is both creative and not generous. Mary is not old. Someone is strong or wise. Someone is either funny or not curious. Someone is either happy or calm. | Mary is wise. | entailment | ((?[X]:((strong(X)|~quiet(X))))=>((~generous(john)&~kind(john))))&
(![X]:((wise(X)|rich(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((~kind(X)|happy(X))=>(~old(X)&wise(X))))&
(![X]:(quiet(X)=>(kind(X)|~humble(X))))&
(![X]:((generous(X)<~>kind(X))=>(kind(X)|humble(X))))&
((?[X]:((kind(X)|wise(X))))=>(?[X]:(happy(X))))&
((~patient(john))<=>((rich(john)&humble(john))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:(calm(X))))&
(![X]:((~wise(X)&calm(X))=>~kind(X)))&
(((~strong(alice)&happy(alice)))=>(?[X]:((~curious(X)|~rich(X)))))&
((?[X]:(generous(X)))=>(happy(alice)))&
(![X]:((~happy(X)|humble(X))=>(~happy(X)<~>kind(X))))&
(![X]:(~curious(X)<=>(~generous(X)<~>wise(X))))&
((rich(alice))<=>((~creative(alice)|brave(alice))))&
(![X]:((~happy(X)&humble(X))<=>curious(X)))&
(((~curious(fred)|~funny(fred)))<=>(?[X]:((~rich(X)&~curious(X)))))&
((old(fred)|~funny(fred)))&
((~curious(fred)<~>brave(fred)))&
(?[X]:((rich(X)&wise(X))))&
((creative(fred)&~generous(fred)))&
(~old(mary))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((funny(X)<~>~curious(X))))&
(?[X]:((happy(X)<~>calm(X)))) | wise(mary) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 288128496463229768880966
% SZS output start Proof for 288128496463229768880966
3. ! [X0] : ((happy(X0) | ~kind(X0)) => (wise(X0) & ~old(X0))) [input p2]
12. ! [X0] : ((humble(X0) | ~happy(X0)) => (~happy(X0) <~> kind(X0))) [input p11]
25. ~wise(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~old(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 3]
40. ! [X0] : ((~happy(X0) <~> kind(X0)) | (~humble(X0) & happy(X0))) [ennf transformation 12]
56. ! [X0] : (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (~humble(X0) & happy(X0))) [nnf transformation 40]
90. wise(X0) | kind(X0) [cnf transformation 29]
91. ~happy(X0) | wise(X0) [cnf transformation 29]
108. ~kind(X0) | happy(X0) | happy(X0) [cnf transformation 56]
138. ~wise(mary) [cnf transformation 25]
139. ~kind(X0) | happy(X0) [duplicate literal removal 108]
310. kind(mary) [resolution 90,138]
314. happy(mary) [resolution 139,310]
315. wise(mary) [resolution 314,91]
316. $false [subsumption resolution 315,138]
% SZS output end Proof for 288128496463229768880966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not curious is not brave and vice versa. If someone is both strong and brave then someone is not brave or not kind. Everyone who is quiet or calm is both not humble and wise and vice versa. Everyone who is either not quiet or not happy is not patient. If someone is both happy and funny then someone is strong. Everyone who is both patient and not rich is humble and vice versa. Everyone who is both not rich and not quiet is not calm or not brave and vice versa. If someone is rich then someone is strong. Everyone who is not rich or not kind is not quiet and vice versa. Everyone who is both happy and not happy is kind and vice versa. If alice is funny then mary is either not humble or generous. If john is old then someone is not creative or patient. If lucy is not creative or not funny then alice is either not strong or curious and vice versa. If john is rich then lucy is either curious or humble. Everyone who is both generous and not happy is not quiet. If someone is both curious and funny then susan is old and vice versa. Someone is rich or not rich. Mary is either not patient or not wise. Fred is not old or not wise. Susan is both strong and not brave. Fred is both brave and not generous. Someone is both not quiet and not rich. | Fred is not wise. | neutral | (![X]:((calm(X)|~curious(X))<=>~brave(X)))&
((?[X]:((strong(X)&brave(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~humble(X)&wise(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>~patient(X)))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(strong(X))))&
(![X]:((patient(X)&~rich(X))<=>humble(X)))&
(![X]:((~rich(X)&~quiet(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(rich(X)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)|~kind(X))<=>~quiet(X)))&
(![X]:((happy(X)&~happy(X))<=>kind(X)))&
((funny(alice))=>((~humble(mary)<~>generous(mary))))&
((old(john))=>(?[X]:((~creative(X)|patient(X)))))&
(((~creative(lucy)|~funny(lucy)))<=>((~strong(alice)<~>curious(alice))))&
((rich(john))=>((curious(lucy)<~>humble(lucy))))&
(![X]:((generous(X)&~happy(X))=>~quiet(X)))&
((?[X]:((curious(X)&funny(X))))<=>(old(susan)))&
(?[X]:((rich(X)|~rich(X))))&
((~patient(mary)<~>~wise(mary)))&
((~old(fred)|~wise(fred)))&
((strong(susan)&~brave(susan)))&
((brave(fred)&~generous(fred)))&
(?[X]:((~quiet(X)&~rich(X)))) | ~wise(fred) | [] | null | 0 |
If susan is old or patient then someone is both not old and kind and vice versa. Everyone who is both old and generous is either not brave or not quiet and vice versa. Everyone who is patient is both funny and not old. If susan is either not strong or not wise then fred is calm. Everyone who is either not generous or wise is both strong and not humble. Everyone who is calm is curious and vice versa. Everyone who is happy or not kind is not old or not happy and vice versa. If alice is old or not calm then someone is calm or rich. If susan is both not old and not kind then fred is both not kind and happy. Everyone who is kind or patient is both creative and tall. If someone is both not patient and not happy then susan is not calm. Everyone who is both not old and not strong is not rich and vice versa. If fred is either not curious or kind then alice is both rich and not rich and vice versa. If alice is tall then alice is either not funny or kind. Everyone who is not kind or funny is not brave. If susan is not calm or not curious then fred is both funny and not creative and vice versa. Someone is not wise or funny. Alice is not kind or brave. Someone is both not generous and not calm. Susan is either not humble or not old. Someone is both quiet and humble. John is generous. Mary is not curious or quiet. Someone is old. | Susan is not brave. | entailment | (((old(susan)|patient(susan)))<=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((old(X)&generous(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:(patient(X)=>(funny(X)&~old(X))))&
(((~strong(susan)<~>~wise(susan)))=>(calm(fred)))&
(![X]:((~generous(X)<~>wise(X))=>(strong(X)&~humble(X))))&
(![X]:(calm(X)<=>curious(X)))&
(![X]:((happy(X)|~kind(X))<=>(~old(X)|~happy(X))))&
(((old(alice)|~calm(alice)))=>(?[X]:((calm(X)|rich(X)))))&
(((~old(susan)&~kind(susan)))=>((~kind(fred)&happy(fred))))&
(![X]:((kind(X)|patient(X))=>(creative(X)&tall(X))))&
((?[X]:((~patient(X)&~happy(X))))=>(~calm(susan)))&
(![X]:((~old(X)&~strong(X))<=>~rich(X)))&
(((~curious(fred)<~>kind(fred)))<=>((rich(alice)&~rich(alice))))&
((tall(alice))=>((~funny(alice)<~>kind(alice))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(((~calm(susan)|~curious(susan)))<=>((funny(fred)&~creative(fred))))&
(?[X]:((~wise(X)|funny(X))))&
((~kind(alice)|brave(alice)))&
(?[X]:((~generous(X)&~calm(X))))&
((~humble(susan)<~>~old(susan)))&
(?[X]:((quiet(X)&humble(X))))&
(generous(john))&
((~curious(mary)|quiet(mary)))&
(?[X]:(old(X))) | ~brave(susan) | [
"p0",
"p2",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4984693972068213462904808
% SZS output start Proof for 4984693972068213462904808
1. (patient(susan) | old(susan)) <=> ? [X0] : (kind(X0) & ~old(X0)) [input p0]
3. ! [X0] : (patient(X0) => (~old(X0) & funny(X0))) [input p2]
7. ! [X0] : ((~kind(X0) | happy(X0)) <=> (~happy(X0) | ~old(X0))) [input p6]
15. ! [X0] : ((funny(X0) | ~kind(X0)) => ~brave(X0)) [input p14]
25. brave(susan) [input hypothesis]
26. ! [X0] : ((~old(X0) & funny(X0)) | ~patient(X0)) [ennf transformation 3]
35. ! [X0] : (~brave(X0) | (~funny(X0) & kind(X0))) [ennf transformation 15]
36. ((patient(susan) | old(susan)) | ! [X0] : (~kind(X0) | old(X0))) & (? [X0] : (kind(X0) & ~old(X0)) | (~patient(susan) & ~old(susan))) [nnf transformation 1]
37. (patient(susan) | old(susan) | ! [X0] : (~kind(X0) | old(X0))) & (? [X0] : (kind(X0) & ~old(X0)) | (~patient(susan) & ~old(susan))) [flattening 36]
38. (patient(susan) | old(susan) | ! [X0] : (~kind(X0) | old(X0))) & (? [X1] : (kind(X1) & ~old(X1)) | (~patient(susan) & ~old(susan))) [rectify 37]
39. ? [X1] : (kind(X1) & ~old(X1)) => (kind(sK0) & ~old(sK0)) [choice axiom]
40. (patient(susan) | old(susan) | ! [X0] : (~kind(X0) | old(X0))) & ((kind(sK0) & ~old(sK0)) | (~patient(susan) & ~old(susan))) [skolemisation 38,39]
46. ! [X0] : (((~kind(X0) | happy(X0)) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | (kind(X0) & ~happy(X0)))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | happy(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | (kind(X0) & ~happy(X0)))) [flattening 46]
70. patient(susan) | old(susan) | ~kind(X0) | old(X0) [cnf transformation 40]
77. ~patient(X0) | funny(X0) [cnf transformation 26]
87. ~happy(X0) | ~old(X0) | ~happy(X0) [cnf transformation 47]
90. ~kind(X0) | happy(X0) | happy(X0) [cnf transformation 47]
111. ~brave(X0) | kind(X0) [cnf transformation 35]
112. ~funny(X0) | ~brave(X0) [cnf transformation 35]
129. brave(susan) [cnf transformation 25]
130. ~happy(X0) | ~old(X0) [duplicate literal removal 87]
131. ~kind(X0) | happy(X0) [duplicate literal removal 90]
133. 1 <=> ! [X0] : (~kind(X0) | old(X0)) [avatar definition]
134. ~kind(X0) | old(X0) <- (1) [avatar component clause 133]
136. 2 <=> old(susan) [avatar definition]
137. ~old(susan) <- (~2) [avatar component clause 136]
140. 3 <=> patient(susan) [avatar definition]
142. patient(susan) <- (3) [avatar component clause 140]
143. 1 | 2 | 3 [avatar split clause 70,140,136,133]
189. 13 <=> kind(susan) [avatar definition]
191. kind(susan) <- (13) [avatar component clause 189]
296. kind(susan) [resolution 111,129]
297. 13 [avatar split clause 296,189]
302. happy(susan) <- (13) [resolution 131,191]
315. ~old(susan) <- (13) [resolution 302,130]
318. ~2 | ~13 [avatar split clause 315,189,136]
325. old(susan) <- (1, 13) [resolution 134,191]
328. $false <- (1, ~2, 13) [subsumption resolution 325,137]
329. ~1 | 2 | ~13 [avatar contradiction clause 328]
333. funny(susan) <- (3) [resolution 142,77]
354. ~brave(susan) <- (3) [resolution 333,112]
355. $false <- (3) [subsumption resolution 354,129]
356. ~3 [avatar contradiction clause 355]
357. $false [avatar sat refutation 143,297,318,329,356]
% SZS output end Proof for 4984693972068213462904808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and humble is both happy and tall and vice versa.
Everyone who is calm is either not wise or happy and vice versa.
Everyone who is kind or not calm is not generous and vice versa.
If someone is not happy then paul is creative or not creative.
If someone is creative or not curious then someone is both humble and strong.
Everyone who is both kind and not generous is creative.
If someone is both calm and wise then someone is both curious and not calm and vice versa.
If mary is both creative and not creative then someone is either not strong or calm and vice versa.
Everyone who is not rich is rich.
If someone is both patient and not old then someone is both not wise and kind and vice versa.
Everyone who is wise or patient is both not wise and not generous.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Fred is quiet.
Someone is either not quiet or strong.
Mary is tall or not funny.
Paul is either curious or humble. | Mary is not generous. | contradiction | (![X]:((~patient(X)&humble(X))<=>(happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~wise(X)<~>happy(X))))&
(![X]:((kind(X)|~calm(X))<=>~generous(X)))&
((?[X]:(~happy(X)))=>((creative(paul)|~creative(paul))))&
((?[X]:((creative(X)|~curious(X))))=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((kind(X)&~generous(X))=>creative(X)))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~rich(X)=>rich(X)))&
((?[X]:((patient(X)&~old(X))))<=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:((wise(X)|patient(X))=>(~wise(X)&~generous(X))))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>strong(X))))&
((tall(mary)|~funny(mary)))&
((curious(paul)<~>humble(paul))) | ~generous(mary) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4869096425186493059747565
% SZS output start Proof for 4869096425186493059747565
2. ! [X0] : (calm(X0) <=> (~wise(X0) <~> happy(X0))) [input p1]
3. ! [X0] : ((~calm(X0) | kind(X0)) <=> ~generous(X0)) [input p2]
5. ? [X0] : (~curious(X0) | creative(X0)) => ? [X0] : (strong(X0) & humble(X0)) [input p4]
6. ! [X0] : ((~generous(X0) & kind(X0)) => creative(X0)) [input p5]
7. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X0] : (~calm(X0) & curious(X0)) [input p6]
8. (~creative(mary) & creative(mary)) <=> ? [X0] : (~strong(X0) <~> calm(X0)) [input p7]
10. ? [X0] : (~old(X0) & patient(X0)) <=> ? [X0] : (kind(X0) & ~wise(X0)) [input p9]
11. ! [X0] : ((patient(X0) | wise(X0)) => (~generous(X0) & ~wise(X0))) [input p10]
15. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p14]
16. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p15]
21. ~generous(mary) [input hypothesis]
22. ? [X0] : (~curious(X0) | creative(X0)) => ? [X1] : (strong(X1) & humble(X1)) [rectify 5]
23. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X1] : (~calm(X1) & curious(X1)) [rectify 7]
24. ? [X0] : (~old(X0) & patient(X0)) <=> ? [X1] : (kind(X1) & ~wise(X1)) [rectify 10]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 16]
28. ? [X1] : (strong(X1) & humble(X1)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 22]
29. ! [X0] : (creative(X0) | (generous(X0) | ~kind(X0))) [ennf transformation 6]
30. ! [X0] : (creative(X0) | generous(X0) | ~kind(X0)) [flattening 29]
32. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~patient(X0) & ~wise(X0))) [ennf transformation 11]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 15]
37. ! [X0] : ((calm(X0) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0)))) & (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ~calm(X0))) [nnf transformation 2]
38. ! [X0] : (((~calm(X0) | kind(X0)) | generous(X0)) & (~generous(X0) | (calm(X0) & ~kind(X0)))) [nnf transformation 3]
39. ! [X0] : ((~calm(X0) | kind(X0) | generous(X0)) & (~generous(X0) | (calm(X0) & ~kind(X0)))) [flattening 38]
40. ? [X0] : (strong(X0) & humble(X0)) | ! [X1] : (curious(X1) & ~creative(X1)) [rectify 28]
41. ? [X0] : (strong(X0) & humble(X0)) => (strong(sK0) & humble(sK0)) [choice axiom]
42. (strong(sK0) & humble(sK0)) | ! [X1] : (curious(X1) & ~creative(X1)) [skolemisation 40,41]
43. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X1] : (~calm(X1) & curious(X1)) | ! [X0] : (~wise(X0) | ~calm(X0))) [nnf transformation 23]
44. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X2] : (~calm(X2) & curious(X2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [rectify 43]
45. ? [X0] : (wise(X0) & calm(X0)) => (wise(sK1) & calm(sK1)) [choice axiom]
46. ? [X2] : (~calm(X2) & curious(X2)) => (~calm(sK2) & curious(sK2)) [choice axiom]
47. ((wise(sK1) & calm(sK1)) | ! [X1] : (calm(X1) | ~curious(X1))) & ((~calm(sK2) & curious(sK2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [skolemisation 44,46,45]
48. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (creative(mary) | ~creative(mary))) [nnf transformation 8]
49. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | creative(mary) | ~creative(mary)) [flattening 48]
50. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) | creative(mary) | ~creative(mary)) [rectify 49]
51. ? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) => ((~calm(sK3) | strong(sK3)) & (calm(sK3) | ~strong(sK3))) [choice axiom]
52. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(sK3) | strong(sK3)) & (calm(sK3) | ~strong(sK3))) | creative(mary) | ~creative(mary)) [skolemisation 50,51]
53. (? [X0] : (~old(X0) & patient(X0)) | ! [X1] : (~kind(X1) | wise(X1))) & (? [X1] : (kind(X1) & ~wise(X1)) | ! [X0] : (old(X0) | ~patient(X0))) [nnf transformation 24]
54. (? [X0] : (~old(X0) & patient(X0)) | ! [X1] : (~kind(X1) | wise(X1))) & (? [X2] : (kind(X2) & ~wise(X2)) | ! [X3] : (old(X3) | ~patient(X3))) [rectify 53]
55. ? [X0] : (~old(X0) & patient(X0)) => (~old(sK4) & patient(sK4)) [choice axiom]
56. ? [X2] : (kind(X2) & ~wise(X2)) => (kind(sK5) & ~wise(sK5)) [choice axiom]
57. ((~old(sK4) & patient(sK4)) | ! [X1] : (~kind(X1) | wise(X1))) & ((kind(sK5) & ~wise(sK5)) | ! [X3] : (old(X3) | ~patient(X3))) [skolemisation 54,56,55]
65. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
66. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (old(X0) | humble(X0)) => (old(sK7) | humble(sK7)) [choice axiom]
68. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK8) & happy(sK8)) [choice axiom]
69. ((old(sK7) | humble(sK7)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK8) & happy(sK8)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 66,68,67]
80. wise(X0) | happy(X0) | calm(X0) [cnf transformation 37]
82. ~generous(X0) | ~kind(X0) [cnf transformation 39]
84. ~calm(X0) | kind(X0) | generous(X0) [cnf transformation 39]
88. strong(sK0) | ~creative(X1) [cnf transformation 42]
89. strong(sK0) | curious(X1) [cnf transformation 42]
90. creative(X0) | generous(X0) | ~kind(X0) [cnf transformation 30]
94. wise(sK1) | calm(X1) | ~curious(X1) [cnf transformation 47]
98. creative(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 52]
100. ~creative(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 52]
103. kind(sK5) | old(X3) | ~patient(X3) [cnf transformation 57]
104. patient(sK4) | ~kind(X1) | wise(X1) [cnf transformation 57]
106. ~wise(X0) | ~wise(X0) [cnf transformation 32]
122. ~happy(X0) | calm(X0) [cnf transformation 34]
127. ~calm(sK8) | ~old(X3) [cnf transformation 69]
135. ~generous(mary) [cnf transformation 21]
137. ~wise(X0) [duplicate literal removal 106]
140. 1 <=> ! [X1] : curious(X1) [avatar definition]
141. curious(X1) <- (1) [avatar component clause 140]
143. 2 <=> strong(sK0) [avatar definition]
145. strong(sK0) <- (2) [avatar component clause 143]
146. 1 | 2 [avatar split clause 89,143,140]
148. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
149. ~creative(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 88,143,148]
157. ~kind(X0) | creative(X0) [subsumption resolution 90,82]
159. 5 <=> ! [X1] : (calm(X1) | ~curious(X1)) [avatar definition]
160. ~curious(X1) | calm(X1) <- (5) [avatar component clause 159]
162. 6 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (6) [avatar component clause 162]
165. 5 | 6 [avatar split clause 94,162,159]
185. 11 <=> ! [X0] : (~strong(X0) | ~calm(X0)) [avatar definition]
186. ~strong(X0) | ~calm(X0) <- (11) [avatar component clause 185]
188. 12 <=> creative(mary) [avatar definition]
191. 11 | ~12 [avatar split clause 100,188,185]
196. 11 | 12 [avatar split clause 98,188,185]
199. 14 <=> ! [X1] : (~kind(X1) | wise(X1)) [avatar definition]
200. ~kind(X1) | wise(X1) <- (14) [avatar component clause 199]
207. 16 <=> patient(sK4) [avatar definition]
209. patient(sK4) <- (16) [avatar component clause 207]
210. 14 | 16 [avatar split clause 104,207,199]
212. 17 <=> ! [X3] : (old(X3) | ~patient(X3)) [avatar definition]
213. old(X3) | ~patient(X3) <- (17) [avatar component clause 212]
215. 18 <=> kind(sK5) [avatar definition]
217. kind(sK5) <- (18) [avatar component clause 215]
218. 17 | 18 [avatar split clause 103,215,212]
250. 25 <=> ! [X3] : ~old(X3) [avatar definition]
251. ~old(X3) <- (25) [avatar component clause 250]
253. 26 <=> calm(sK8) [avatar definition]
255. ~calm(sK8) <- (~26) [avatar component clause 253]
256. 25 | ~26 [avatar split clause 127,253,250]
297. ~patient(X3) <- (17, 25) [subsumption resolution 213,251]
298. ~kind(X1) <- (14) [subsumption resolution 200,137]
301. calm(X0) <- (1, 5) [resolution 160,141]
316. happy(X2) | calm(X2) [resolution 80,137]
320. kind(X0) | generous(X0) <- (1, 5) [resolution 84,301]
321. generous(X0) <- (1, 5, 14) [subsumption resolution 320,298]
322. $false <- (1, 5, 14) [resolution 321,135]
327. ~1 | ~5 | ~14 [avatar contradiction clause 322]
329. $false <- (6) [subsumption resolution 164,137]
330. ~6 [avatar contradiction clause 329]
331. $false <- (16, 17, 25) [subsumption resolution 209,297]
332. ~16 | ~17 | ~25 [avatar contradiction clause 331]
333. creative(sK5) <- (18) [resolution 217,157]
334. $false <- (3, 18) [subsumption resolution 333,149]
335. ~3 | ~18 [avatar contradiction clause 334]
345. calm(X1) <- (1, 5) [subsumption resolution 160,141]
348. $false <- (1, 5, ~26) [subsumption resolution 255,345]
349. ~1 | ~5 | 26 [avatar contradiction clause 348]
350. calm(X2) [subsumption resolution 316,122]
356. ~calm(sK0) <- (2, 11) [resolution 145,186]
357. $false <- (2, 11) [subsumption resolution 356,350]
358. ~2 | ~11 [avatar contradiction clause 357]
359. $false [avatar sat refutation 146,150,165,191,196,210,218,256,327,330,332,335,349,358]
% SZS output end Proof for 4869096425186493059747565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or wise is patient and vice versa. Everyone who is creative or not old is funny. If alice is either tall or not generous then someone is not strong or generous and vice versa. Everyone who is not quiet is both not curious and brave and vice versa. If alice is strong then fred is not calm or not kind and vice versa. If fred is both not wise and curious then susan is both not brave and not happy and vice versa. If john is not calm then someone is either curious or rich. Everyone who is wise or not quiet is both not rich and creative. If someone is both calm and patient then alice is not happy or quiet. If susan is not brave or humble then alice is not happy or not generous and vice versa. Everyone who is either humble or quiet is either not patient or curious and vice versa. Everyone who is both not patient and not brave is not curious or not tall and vice versa. Everyone who is either not happy or humble is not rich and vice versa. Everyone who is strong is not curious and vice versa. Everyone who is either old or strong is either not funny or patient and vice versa. Everyone who is both rich and kind is both not quiet and brave. Someone is not old or creative. Someone is both strong and not happy. Someone is either not strong or humble. Someone is either not kind or brave. John is creative. Susan is humble or not wise. Mary is either not curious or brave. John is both creative and patient. | Alice is funny. | entailment | (![X]:((~strong(X)<~>wise(X))<=>patient(X)))&
(![X]:((creative(X)|~old(X))=>funny(X)))&
(((tall(alice)<~>~generous(alice)))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(~quiet(X)<=>(~curious(X)&brave(X))))&
((strong(alice))<=>((~calm(fred)|~kind(fred))))&
(((~wise(fred)&curious(fred)))<=>((~brave(susan)&~happy(susan))))&
((~calm(john))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&creative(X))))&
((?[X]:((calm(X)&patient(X))))=>((~happy(alice)|quiet(alice))))&
(((~brave(susan)|humble(susan)))<=>((~happy(alice)|~generous(alice))))&
(![X]:((humble(X)<~>quiet(X))<=>(~patient(X)<~>curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~rich(X)))&
(![X]:(strong(X)<=>~curious(X)))&
(![X]:((old(X)<~>strong(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((rich(X)&kind(X))=>(~quiet(X)&brave(X))))&
(?[X]:((~old(X)|creative(X))))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(creative(john))&
((humble(susan)|~wise(susan)))&
((~curious(mary)<~>brave(mary)))&
((creative(john)&patient(john))) | funny(alice) | [
"p0",
"p1",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1477427730331876646166780
% SZS output start Proof for 1477427730331876646166780
1. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : ((~old(X0) | creative(X0)) => funny(X0)) [input p1]
8. ! [X0] : ((~quiet(X0) | wise(X0)) => (creative(X0) & ~rich(X0))) [input p7]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~tall(X0) | ~curious(X0))) [input p11]
14. ! [X0] : (strong(X0) <=> ~curious(X0)) [input p13]
15. ! [X0] : ((old(X0) <~> strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p14]
25. ~funny(alice) [input hypothesis]
26. ! [X0] : (funny(X0) | (old(X0) & ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((creative(X0) & ~rich(X0)) | (quiet(X0) & ~wise(X0))) [ennf transformation 8]
33. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0)) & (patient(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 1]
50. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & ~patient(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | brave(X0) | patient(X0))) [flattening 50]
53. ! [X0] : ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))) [nnf transformation 14]
54. ! [X0] : ((((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))))) [nnf transformation 15]
66. patient(X0) | wise(X0) | strong(X0) [cnf transformation 33]
70. ~creative(X0) | funny(X0) [cnf transformation 26]
71. funny(X0) | old(X0) [cnf transformation 26]
92. ~wise(X0) | creative(X0) [cnf transformation 28]
108. ~patient(X0) | curious(X0) [cnf transformation 51]
116. ~curious(X0) | ~strong(X0) [cnf transformation 53]
120. ~patient(X0) | funny(X0) | strong(X0) | ~old(X0) [cnf transformation 54]
124. ~strong(X0) | ~old(X0) | patient(X0) | funny(X0) [cnf transformation 54]
141. ~funny(alice) [cnf transformation 25]
175. 8 <=> strong(alice) [avatar definition]
176. ~strong(alice) <- (~8) [avatar component clause 175]
177. strong(alice) <- (8) [avatar component clause 175]
243. ~strong(X0) | patient(X0) | funny(X0) [subsumption resolution 124,71]
245. ~patient(X0) | funny(X0) | strong(X0) [subsumption resolution 120,71]
394. funny(X0) | strong(X0) | wise(X0) | strong(X0) [resolution 245,66]
395. funny(X0) | strong(X0) | wise(X0) [duplicate literal removal 394]
491. strong(alice) | wise(alice) [resolution 395,141]
558. wise(alice) <- (~8) [subsumption resolution 491,176]
564. 44 <=> patient(alice) [avatar definition]
566. patient(alice) <- (44) [avatar component clause 564]
573. creative(alice) <- (~8) [resolution 558,92]
616. funny(alice) <- (~8) [resolution 573,70]
617. $false <- (~8) [subsumption resolution 616,141]
618. 8 [avatar contradiction clause 617]
626. patient(alice) | funny(alice) <- (8) [resolution 177,243]
630. patient(alice) <- (8) [subsumption resolution 626,141]
631. 44 | ~8 [avatar split clause 630,175,564]
637. curious(alice) <- (44) [resolution 566,108]
651. ~strong(alice) <- (44) [resolution 637,116]
653. $false <- (8, 44) [subsumption resolution 651,177]
654. ~8 | ~44 [avatar contradiction clause 653]
655. $false [avatar sat refutation 618,631,654]
% SZS output end Proof for 1477427730331876646166780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not generous is not rich. If paul is quiet or not old then lucy is both not patient and old. Everyone who is either quiet or not generous is either strong or not brave and vice versa. If someone is both rich and tall then paul is not happy or humble. Everyone who is both brave and kind is not quiet and vice versa. If someone is strong then susan is either funny or not funny and vice versa. If someone is either wise or tall then someone is both not quiet and not curious and vice versa. If mary is not quiet or rich then someone is either not patient or strong and vice versa. Everyone who is not strong is both not generous and not funny and vice versa. If someone is rich then alice is not creative or not strong and vice versa. If someone is not quiet or not humble then alice is funny. Everyone who is either patient or not generous is either not happy or tall and vice versa. If alice is both not happy and not generous then someone is both not brave and not kind. Everyone who is either quiet or strong is both humble and not quiet. Everyone who is either humble or not curious is happy. Everyone who is not tall or not generous is either tall or old. Someone is either not generous or not creative. Someone is not funny or quiet. Someone is not curious. Someone is either not wise or not calm. Someone is either humble or quiet. Someone is both not creative and patient. | Alice is not rich. | neutral | (![X]:((~happy(X)<~>~generous(X))=>~rich(X)))&
(((quiet(paul)|~old(paul)))=>((~patient(lucy)&old(lucy))))&
(![X]:((quiet(X)<~>~generous(X))<=>(strong(X)<~>~brave(X))))&
((?[X]:((rich(X)&tall(X))))=>((~happy(paul)|humble(paul))))&
(![X]:((brave(X)&kind(X))<=>~quiet(X)))&
((?[X]:(strong(X)))<=>((funny(susan)<~>~funny(susan))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((~quiet(X)&~curious(X)))))&
(((~quiet(mary)|rich(mary)))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:(~strong(X)<=>(~generous(X)&~funny(X))))&
((?[X]:(rich(X)))<=>((~creative(alice)|~strong(alice))))&
((?[X]:((~quiet(X)|~humble(X))))=>(funny(alice)))&
(![X]:((patient(X)<~>~generous(X))<=>(~happy(X)<~>tall(X))))&
(((~happy(alice)&~generous(alice)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((quiet(X)<~>strong(X))=>(humble(X)&~quiet(X))))&
(![X]:((humble(X)<~>~curious(X))=>happy(X)))&
(![X]:((~tall(X)|~generous(X))=>(tall(X)<~>old(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)<~>~calm(X))))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((~creative(X)&patient(X)))) | ~rich(alice) | [] | null | 0 |
If john is either not calm or wise then someone is not tall or not calm.
If paul is either not humble or not funny then someone is either not brave or not generous.
If mary is not kind then someone is both not rich and not curious and vice versa.
If someone is not tall or not calm then paul is both not calm and not generous.
If someone is either not quiet or happy then fred is not brave and vice versa.
If susan is not humble or not happy then fred is funny or strong.
Everyone who is not rich or not curious is not kind or kind.
Everyone who is not patient is not brave and vice versa.
If someone is either generous or tall then someone is not wise or not old.
If someone is either not wise or curious then someone is either not tall or quiet.
Everyone who is not happy is not old or not rich and vice versa.
If someone is not tall then john is creative or not brave.
If someone is either not old or kind then someone is both not funny and not wise and vice versa.
If lucy is not humble then paul is not strong or creative and vice versa.
If susan is kind then mary is patient and vice versa.
Everyone who is not brave or curious is not wise or funny.
Mary is tall.
Fred is both kind and not strong.
Someone is either not brave or not creative.
Lucy is not quiet or wise.
Lucy is both not rich and old.
Paul is not kind or not generous.
Alice is either not rich or not humble.
Someone is patient. | Fred is not strong. | entailment | (((~calm(john)<~>wise(john)))=>(?[X]:((~tall(X)|~calm(X)))))&
(((~humble(paul)<~>~funny(paul)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
((~kind(mary))<=>(?[X]:((~rich(X)&~curious(X)))))&
((?[X]:((~tall(X)|~calm(X))))=>((~calm(paul)&~generous(paul))))&
((?[X]:((~quiet(X)<~>happy(X))))<=>(~brave(fred)))&
(((~humble(susan)|~happy(susan)))=>((funny(fred)|strong(fred))))&
(![X]:((~rich(X)|~curious(X))=>(~kind(X)|kind(X))))&
(![X]:(~patient(X)<=>~brave(X)))&
((?[X]:((generous(X)<~>tall(X))))=>(?[X]:((~wise(X)|~old(X)))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:(~happy(X)<=>(~old(X)|~rich(X))))&
((?[X]:(~tall(X)))=>((creative(john)|~brave(john))))&
((?[X]:((~old(X)<~>kind(X))))<=>(?[X]:((~funny(X)&~wise(X)))))&
((~humble(lucy))<=>((~strong(paul)|creative(paul))))&
((kind(susan))<=>(patient(mary)))&
(![X]:((~brave(X)|curious(X))=>(~wise(X)|funny(X))))&
(tall(mary))&
((kind(fred)&~strong(fred)))&
(?[X]:((~brave(X)<~>~creative(X))))&
((~quiet(lucy)|wise(lucy)))&
((~rich(lucy)&old(lucy)))&
((~kind(paul)|~generous(paul)))&
((~rich(alice)<~>~humble(alice)))&
(?[X]:(patient(X))) | ~strong(fred) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4761138619394478836101455
% SZS output start Proof for 4761138619394478836101455
18. ~strong(fred) & kind(fred) [input p17]
25. strong(fred) [input hypothesis]
129. ~strong(fred) [cnf transformation 18]
139. strong(fred) [cnf transformation 25]
245. 24 <=> strong(fred) [avatar definition]
353. ~24 [avatar split clause 129,245]
388. 24 [avatar split clause 139,245]
389. $false [avatar sat refutation 353,388]
% SZS output end Proof for 4761138619394478836101455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and wise is not quiet or quiet and vice versa. If someone is either humble or patient then paul is old. Everyone who is not strong or kind is both wise and happy and vice versa. Everyone who is not calm or not happy is wise or curious. Everyone who is both kind and not humble is not strong or not patient and vice versa. If someone is both old and humble then someone is either not humble or wise. If someone is both strong and funny then someone is either curious or old and vice versa. If susan is either not humble or generous then someone is not strong and vice versa. If lucy is either not strong or brave then lucy is either funny or rich. Everyone who is both patient and curious is generous and vice versa. Everyone who is calm is creative and vice versa. Everyone who is both not calm and not humble is both wise and not curious and vice versa. Everyone who is both not strong and old is both curious and not happy. Everyone who is not wise or not curious is not old and vice versa. Everyone who is generous or not strong is either curious or wise. If someone is calm or not generous then john is happy or brave. Someone is either not curious or old. Someone is either not patient or not generous. Mary is both happy and funny. Susan is not creative or tall. Someone is either generous or not patient. Susan is both funny and not tall. | John is not humble. | entailment | (![X]:((happy(X)&wise(X))<=>(~quiet(X)|quiet(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(old(paul)))&
(![X]:((~strong(X)|kind(X))<=>(wise(X)&happy(X))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)|curious(X))))&
(![X]:((kind(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~humble(X)<~>wise(X)))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((curious(X)<~>old(X)))))&
(((~humble(susan)<~>generous(susan)))<=>(?[X]:(~strong(X))))&
(((~strong(lucy)<~>brave(lucy)))=>((funny(lucy)<~>rich(lucy))))&
(![X]:((patient(X)&curious(X))<=>generous(X)))&
(![X]:(calm(X)<=>creative(X)))&
(![X]:((~calm(X)&~humble(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)&old(X))=>(curious(X)&~happy(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((generous(X)|~strong(X))=>(curious(X)<~>wise(X))))&
((?[X]:((calm(X)|~generous(X))))=>((happy(john)|brave(john))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
((happy(mary)&funny(mary)))&
((~creative(susan)|tall(susan)))&
(?[X]:((generous(X)<~>~patient(X))))&
((funny(susan)&~tall(susan))) | ~humble(john) | [
"p0",
"p4",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4265345121814301923681829
% SZS output start Proof for 4265345121814301923681829
1. ! [X0] : ((wise(X0) & happy(X0)) <=> (quiet(X0) | ~quiet(X0))) [input p0]
5. ! [X0] : ((~humble(X0) & kind(X0)) <=> (~patient(X0) | ~strong(X0))) [input p4]
10. ! [X0] : ((curious(X0) & patient(X0)) <=> generous(X0)) [input p9]
12. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> (~curious(X0) & wise(X0))) [input p11]
15. ! [X0] : ((~strong(X0) | generous(X0)) => (curious(X0) <~> wise(X0))) [input p14]
23. humble(john) [input hypothesis]
33. ! [X0] : ((curious(X0) <~> wise(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 15]
36. ! [X0] : (((wise(X0) & happy(X0)) | (~quiet(X0) & quiet(X0))) & ((quiet(X0) | ~quiet(X0)) | (~wise(X0) | ~happy(X0)))) [nnf transformation 1]
37. ! [X0] : (((wise(X0) & happy(X0)) | (~quiet(X0) & quiet(X0))) & (quiet(X0) | ~quiet(X0) | ~wise(X0) | ~happy(X0))) [flattening 36]
41. ! [X0] : (((~humble(X0) & kind(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (humble(X0) | ~kind(X0)))) [nnf transformation 5]
42. ! [X0] : (((~humble(X0) & kind(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | humble(X0) | ~kind(X0))) [flattening 41]
57. ! [X0] : (((curious(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) | ~patient(X0)))) [nnf transformation 10]
58. ! [X0] : (((curious(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | ~curious(X0) | ~patient(X0))) [flattening 57]
60. ! [X0] : (((~humble(X0) & ~calm(X0)) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | (humble(X0) | calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((~humble(X0) & ~calm(X0)) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | humble(X0) | calm(X0))) [flattening 60]
64. ! [X0] : (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 33]
77. wise(X0) | quiet(X0) [cnf transformation 37]
78. ~quiet(X0) | wise(X0) [cnf transformation 37]
92. ~humble(X0) | patient(X0) [cnf transformation 42]
109. ~curious(X0) | generous(X0) | ~patient(X0) [cnf transformation 58]
111. ~generous(X0) | curious(X0) [cnf transformation 58]
117. ~humble(X0) | curious(X0) | ~wise(X0) [cnf transformation 61]
125. ~wise(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 64]
140. humble(john) [cnf transformation 23]
141. wise(X0) [subsumption resolution 77,78]
152. 3 <=> ! [X0] : (patient(X0) | ~humble(X0)) [avatar definition]
153. ~humble(X0) | patient(X0) <- (3) [avatar component clause 152]
157. 3 [avatar split clause 92,152]
239. ~humble(X0) | curious(X0) [subsumption resolution 117,141]
246. ~curious(X0) | ~generous(X0) [subsumption resolution 125,141]
247. ~generous(X0) [subsumption resolution 246,111]
271. patient(john) <- (3) [resolution 153,140]
278. curious(john) [resolution 239,140]
295. generous(john) | ~patient(john) [resolution 109,278]
298. ~patient(john) [subsumption resolution 295,247]
299. $false <- (3) [subsumption resolution 298,271]
300. ~3 [avatar contradiction clause 299]
304. $false [avatar sat refutation 157,300]
% SZS output end Proof for 4265345121814301923681829
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm or not humble then someone is not happy or not old.
Everyone who is not funny or curious is not strong and vice versa.
Everyone who is not funny is both not tall and not patient.
Everyone who is both not tall and generous is not humble or brave and vice versa.
If someone is both not old and kind then someone is old or not brave.
Everyone who is happy or not strong is not calm and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is both wise and not curious is either patient or not happy and vice versa.
If someone is not tall or not wise then someone is both patient and not wise.
Everyone who is either humble or not old is both brave and funny and vice versa.
Everyone who is funny is both not kind and humble.
If someone is either not wise or not brave then paul is not humble and vice versa.
Everyone who is not quiet is either not tall or not quiet and vice versa.
If susan is either old or strong then susan is happy.
Everyone who is either creative or not generous is not generous or not wise.
If someone is not old then someone is both not strong and quiet.
Alice is quiet or funny.
Alice is funny or not kind.
Someone is both not calm and creative.
Someone is either brave or not happy.
Lucy is patient or not rich.
Someone is tall. | Susan is not wise. | entailment | (((~calm(lucy)|~humble(lucy)))=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~funny(X)|curious(X))<=>~strong(X)))&
(![X]:(~funny(X)=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&generous(X))<=>(~humble(X)|brave(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>~calm(X)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)&~curious(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&funny(X))))&
(![X]:(funny(X)=>(~kind(X)&humble(X))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~quiet(X))))&
(((old(susan)<~>strong(susan)))=>(happy(susan)))&
(![X]:((creative(X)<~>~generous(X))=>(~generous(X)|~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((~strong(X)&quiet(X)))))&
((quiet(alice)|funny(alice)))&
((funny(alice)|~kind(alice)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(lucy)|~rich(lucy)))&
(?[X]:(tall(X))) | ~wise(susan) | [
"p3",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4960772807771129702218837
% SZS output start Proof for 4960772807771129702218837
4. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (brave(X0) | ~humble(X0))) [input p3]
12. ? [X0] : (~wise(X0) <~> ~brave(X0)) <=> ~humble(paul) [input p11]
13. ! [X0] : (~quiet(X0) <=> (~tall(X0) <~> ~quiet(X0))) [input p12]
23. wise(susan) [input hypothesis]
43. ! [X0] : (((generous(X0) & ~tall(X0)) | (~brave(X0) & humble(X0))) & ((brave(X0) | ~humble(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 4]
44. ! [X0] : (((generous(X0) & ~tall(X0)) | (~brave(X0) & humble(X0))) & (brave(X0) | ~humble(X0) | ~generous(X0) | tall(X0))) [flattening 43]
55. (? [X0] : ((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | humble(paul)) & (~humble(paul) | ! [X0] : ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) [nnf transformation 12]
56. (? [X0] : ((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | humble(paul)) & (~humble(paul) | ! [X1] : ((~wise(X1) | brave(X1)) & (~brave(X1) | wise(X1)))) [rectify 55]
57. ? [X0] : ((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) => ((brave(sK2) | wise(sK2)) & (~brave(sK2) | ~wise(sK2))) [choice axiom]
58. (((brave(sK2) | wise(sK2)) & (~brave(sK2) | ~wise(sK2))) | humble(paul)) & (~humble(paul) | ! [X1] : ((~wise(X1) | brave(X1)) & (~brave(X1) | wise(X1)))) [skolemisation 56,57]
59. ! [X0] : ((~quiet(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | quiet(X0))) [nnf transformation 13]
80. ~tall(X0) | humble(X0) [cnf transformation 44]
81. ~brave(X0) | ~tall(X0) [cnf transformation 44]
107. ~humble(paul) | ~wise(X1) | brave(X1) [cnf transformation 58]
111. quiet(X0) | tall(X0) | quiet(X0) [cnf transformation 59]
112. ~quiet(X0) | ~quiet(X0) | tall(X0) [cnf transformation 59]
126. wise(susan) [cnf transformation 23]
128. quiet(X0) | tall(X0) [duplicate literal removal 111]
129. ~quiet(X0) | tall(X0) [duplicate literal removal 112]
157. 7 <=> ! [X1] : tall(X1) [avatar definition]
158. tall(X1) <- (7) [avatar component clause 157]
167. 9 <=> humble(paul) [avatar definition]
168. ~humble(paul) <- (~9) [avatar component clause 167]
181. 12 <=> ! [X1] : (~wise(X1) | brave(X1)) [avatar definition]
182. ~wise(X1) | brave(X1) <- (12) [avatar component clause 181]
183. 12 | ~9 [avatar split clause 107,167,181]
188. tall(X0) [subsumption resolution 128,129]
189. 7 [avatar split clause 188,157]
243. humble(X0) <- (7) [resolution 80,158]
244. $false <- (7, ~9) [resolution 243,168]
245. ~7 | 9 [avatar contradiction clause 244]
266. brave(susan) <- (12) [resolution 182,126]
271. ~tall(susan) <- (12) [resolution 266,81]
272. $false <- (7, 12) [subsumption resolution 271,158]
273. ~7 | ~12 [avatar contradiction clause 272]
274. $false [avatar sat refutation 183,189,245,273]
% SZS output end Proof for 4960772807771129702218837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not wise is both not rich and generous and vice versa.
Everyone who is both happy and brave is quiet and vice versa.
If mary is either happy or calm then paul is rich and vice versa.
Everyone who is both old and strong is not kind or tall.
If john is calm or strong then someone is not happy and vice versa.
If someone is not old then someone is either not funny or not brave.
Everyone who is either not funny or not creative is both kind and funny.
Everyone who is humble is both not strong and tall and vice versa.
Everyone who is not wise or not humble is generous.
Everyone who is not creative or strong is happy.
Everyone who is not kind or not tall is either not happy or not strong.
Everyone who is quiet is wise.
Everyone who is both not rich and calm is both not old and rich and vice versa.
Everyone who is quiet or not strong is calm and vice versa.
If susan is either patient or happy then john is either not creative or rich and vice versa.
Everyone who is not creative or not tall is either not quiet or creative and vice versa.
Paul is either not generous or humble.
John is not rich or not funny.
Fred is both not brave and rich.
Susan is not humble or not curious.
Someone is both not brave and patient.
Someone is old or not curious. | Fred is not curious. | neutral | (![X]:((happy(X)|~wise(X))<=>(~rich(X)&generous(X))))&
(![X]:((happy(X)&brave(X))<=>quiet(X)))&
(((happy(mary)<~>calm(mary)))<=>(rich(paul)))&
(![X]:((old(X)&strong(X))=>(~kind(X)|tall(X))))&
(((calm(john)|strong(john)))<=>(?[X]:(~happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(kind(X)&funny(X))))&
(![X]:(humble(X)<=>(~strong(X)&tall(X))))&
(![X]:((~wise(X)|~humble(X))=>generous(X)))&
(![X]:((~creative(X)|strong(X))=>happy(X)))&
(![X]:((~kind(X)|~tall(X))=>(~happy(X)<~>~strong(X))))&
(![X]:(quiet(X)=>wise(X)))&
(![X]:((~rich(X)&calm(X))<=>(~old(X)&rich(X))))&
(![X]:((quiet(X)|~strong(X))<=>calm(X)))&
(((patient(susan)<~>happy(susan)))<=>((~creative(john)<~>rich(john))))&
(![X]:((~creative(X)|~tall(X))<=>(~quiet(X)<~>creative(X))))&
((~generous(paul)<~>humble(paul)))&
((~rich(john)|~funny(john)))&
((~brave(fred)&rich(fred)))&
((~humble(susan)|~curious(susan)))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:((old(X)|~curious(X)))) | ~curious(fred) | [] | null | 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. | Lucy is not kind. | neutral | ((?[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)))) | ~kind(lucy) | [] | null | 0 |
Everyone who is either not calm or not strong is not old or happy.
Everyone who is old is not brave or not happy.
If paul is either funny or not tall then john is either not patient or quiet and vice versa.
Everyone who is not kind is not calm and vice versa.
Everyone who is both strong and not curious is both generous and kind and vice versa.
If someone is old then lucy is not wise.
If someone is either kind or happy then alice is either not creative or not humble and vice versa.
If someone is creative then susan is not strong and vice versa.
If someone is not happy or not curious then john is not humble.
If someone is not rich then someone is either tall or not wise.
Everyone who is either happy or curious is creative and vice versa.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
Mary is curious or brave.
Someone is generous.
Someone is old or rich.
Alice is both not curious and not strong.
John is creative or wise.
Lucy is not quiet or not wise.
John is either not kind or not humble. | Mary is brave. | entailment | (![X]:((~calm(X)<~>~strong(X))=>(~old(X)|happy(X))))&
(![X]:(old(X)=>(~brave(X)|~happy(X))))&
(((funny(paul)<~>~tall(paul)))<=>((~patient(john)<~>quiet(john))))&
(![X]:(~kind(X)<=>~calm(X)))&
(![X]:((strong(X)&~curious(X))<=>(generous(X)&kind(X))))&
((?[X]:(old(X)))=>(~wise(lucy)))&
((?[X]:((kind(X)<~>happy(X))))<=>((~creative(alice)<~>~humble(alice))))&
((?[X]:(creative(X)))<=>(~strong(susan)))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
((curious(mary)|brave(mary)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)|rich(X))))&
((~curious(alice)&~strong(alice)))&
((creative(john)|wise(john)))&
((~quiet(lucy)|~wise(lucy)))&
((~kind(john)<~>~humble(john))) | brave(mary) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7704964865184630113480682
% SZS output start Proof for 7704964865184630113480682
16. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p15]
17. brave(mary) | curious(mary) [input p16]
24. ~brave(mary) [input hypothesis]
38. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 16]
107. ~curious(X0) | wise(X0) [cnf transformation 38]
108. ~wise(X0) | ~wise(X0) [cnf transformation 38]
110. brave(mary) | curious(mary) [cnf transformation 17]
118. ~brave(mary) [cnf transformation 24]
119. ~wise(X0) [duplicate literal removal 108]
218. ~curious(X0) [subsumption resolution 107,119]
219. brave(mary) [subsumption resolution 110,218]
227. $false [subsumption resolution 118,219]
% SZS output end Proof for 7704964865184630113480682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not quiet or quiet.
Everyone who is either patient or not funny is funny and vice versa.
If someone is either rich or not quiet then paul is not humble.
If someone is either strong or curious then someone is not funny or not wise.
Everyone who is either funny or wise is patient.
Everyone who is either humble or not generous is not creative and vice versa.
Everyone who is either humble or not tall is either brave or not rich and vice versa.
Everyone who is either quiet or not old is strong.
If someone is not happy or not curious then fred is both wise and not wise.
Everyone who is both not old and wise is happy.
If someone is not kind or not curious then lucy is generous or not patient and vice versa.
If someone is either not kind or not quiet then someone is both calm and not patient and vice versa.
Everyone who is patient is either calm or not creative.
If susan is both not calm and not strong then someone is not humble and vice versa.
If john is both not happy and not brave then john is both calm and not kind and vice versa.
Everyone who is both quiet and funny is not calm and vice versa.
Lucy is both not quiet and creative.
Someone is strong or old.
Someone is rich.
Someone is not generous or tall.
Someone is either not happy or not strong.
John is either generous or not kind.
Lucy is curious or not rich. | John is not patient. | contradiction | (![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:((patient(X)<~>~funny(X))<=>funny(X)))&
((?[X]:((rich(X)<~>~quiet(X))))=>(~humble(paul)))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((funny(X)<~>wise(X))=>patient(X)))&
(![X]:((humble(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>strong(X)))&
((?[X]:((~happy(X)|~curious(X))))=>((wise(fred)&~wise(fred))))&
(![X]:((~old(X)&wise(X))=>happy(X)))&
((?[X]:((~kind(X)|~curious(X))))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(patient(X)=>(calm(X)<~>~creative(X))))&
(((~calm(susan)&~strong(susan)))<=>(?[X]:(~humble(X))))&
(((~happy(john)&~brave(john)))<=>((calm(john)&~kind(john))))&
(![X]:((quiet(X)&funny(X))<=>~calm(X)))&
((~quiet(lucy)&creative(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|tall(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((generous(john)<~>~kind(john)))&
((curious(lucy)|~rich(lucy))) | ~patient(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8163526598769354755927380
% SZS output start Proof for 8163526598769354755927380
2. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> funny(X0)) [input p1]
24. ~patient(john) [input hypothesis]
37. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 2]
80. funny(X0) | patient(X0) | funny(X0) [cnf transformation 37]
81. ~funny(X0) | patient(X0) | ~funny(X0) [cnf transformation 37]
140. ~patient(john) [cnf transformation 24]
141. funny(X0) | patient(X0) [duplicate literal removal 80]
142. ~funny(X0) | patient(X0) [duplicate literal removal 81]
143. patient(X0) [subsumption resolution 141,142]
291. $false [subsumption resolution 140,143]
% SZS output end Proof for 8163526598769354755927380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.