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 curious or calm is either tall or not brave. Everyone who is both calm and funny is either not rich or funny and vice versa. Everyone who is creative or not happy is both quiet and not old. If paul is patient then someone is both not patient and patient and vice versa. Everyone who is both not rich and not humble is not patient and vice versa. If someone is humble then someone is not happy. If someone is not quiet then someone is rich and vice versa. Everyone who is either not funny or strong is not generous. Everyone who is curious is rich and vice versa. Everyone who is creative or not brave is either not humble or rich. Everyone who is either generous or not humble is either not creative or quiet and vice versa. Everyone who is not calm or quiet is not strong and vice versa. If alice is either brave or strong then someone is brave. Everyone who is either not curious or tall is not funny and vice versa. Everyone who is either calm or creative is strong. Paul is funny. Lucy is both curious and tall. Paul is not wise. Someone is not curious or funny. John is humble. Mary is either not curious or creative. Someone is both not brave and not kind. Susan is not funny or funny. | John is not humble. | contradiction | (![X]:((curious(X)|calm(X))=>(tall(X)<~>~brave(X))))&
(![X]:((calm(X)&funny(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((creative(X)|~happy(X))=>(quiet(X)&~old(X))))&
((patient(paul))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~rich(X)&~humble(X))<=>~patient(X)))&
((?[X]:(humble(X)))=>(?[X]:(~happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(rich(X))))&
(![X]:((~funny(X)<~>strong(X))=>~generous(X)))&
(![X]:(curious(X)<=>rich(X)))&
(![X]:((creative(X)|~brave(X))=>(~humble(X)<~>rich(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((~calm(X)|quiet(X))<=>~strong(X)))&
(((brave(alice)<~>strong(alice)))=>(?[X]:(brave(X))))&
(![X]:((~curious(X)<~>tall(X))<=>~funny(X)))&
(![X]:((calm(X)<~>creative(X))=>strong(X)))&
(funny(paul))&
((curious(lucy)&tall(lucy)))&
(~wise(paul))&
(?[X]:((~curious(X)|funny(X))))&
(humble(john))&
((~curious(mary)<~>creative(mary)))&
(?[X]:((~brave(X)&~kind(X))))&
((~funny(susan)|funny(susan))) | ~humble(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3643586492027024343397134
% SZS output start Proof for 3643586492027024343397134
20. humble(john) [input p19]
24. ~humble(john) [input hypothesis]
122. humble(john) [cnf transformation 20]
127. ~humble(john) [cnf transformation 24]
203. $false [subsumption resolution 127,122]
% SZS output end Proof for 3643586492027024343397134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not curious is generous and vice versa.
Everyone who is not kind is not quiet or not humble and vice versa.
Everyone who is both generous and happy is both kind and not kind and vice versa.
Everyone who is happy or tall is both wise and curious and vice versa.
Everyone who is not creative or wise is either humble or wise and vice versa.
If mary is either calm or curious then someone is strong.
If mary is either not patient or wise then someone is not kind.
If someone is strong then alice is both not old and strong.
If someone is both quiet and not tall then john is either funny or rich and vice versa.
If alice is not creative or patient then fred is not strong and vice versa.
Everyone who is rich or not calm is rich or curious.
Everyone who is both patient and not creative is either rich or not funny.
Everyone who is either not creative or not quiet is happy and vice versa.
If alice is either not patient or wise then paul is not creative.
If paul is quiet or strong then mary is either not old or not funny.
If paul is either not happy or not rich then someone is rich or not patient and vice versa.
Paul is not rich.
Someone is strong.
Alice is tall or not patient.
Someone is either funny or not happy.
Someone is either not old or calm.
Lucy is either not strong or not calm.
Someone is both not old and not creative.
Mary is quiet. | Alice is kind. | contradiction | (![X]:((~kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:(~kind(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((generous(X)&happy(X))<=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|tall(X))<=>(wise(X)&curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(humble(X)<~>wise(X))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(strong(X)))=>((~old(alice)&strong(alice))))&
((?[X]:((quiet(X)&~tall(X))))<=>((funny(john)<~>rich(john))))&
(((~creative(alice)|patient(alice)))<=>(~strong(fred)))&
(![X]:((rich(X)|~calm(X))=>(rich(X)|curious(X))))&
(![X]:((patient(X)&~creative(X))=>(rich(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>happy(X)))&
(((~patient(alice)<~>wise(alice)))=>(~creative(paul)))&
(((quiet(paul)|strong(paul)))=>((~old(mary)<~>~funny(mary))))&
(((~happy(paul)<~>~rich(paul)))<=>(?[X]:((rich(X)|~patient(X)))))&
(~rich(paul))&
(?[X]:(strong(X)))&
((tall(alice)|~patient(alice)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(lucy)<~>~calm(lucy)))&
(?[X]:((~old(X)&~creative(X))))&
(quiet(mary)) | kind(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4272641683763792378899481
% SZS output start Proof for 4272641683763792378899481
1. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : (~kind(X0) <=> (~humble(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((happy(X0) & generous(X0)) <=> (~kind(X0) & kind(X0))) [input p2]
4. ! [X0] : ((tall(X0) | happy(X0)) <=> (curious(X0) & wise(X0))) [input p3]
5. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (humble(X0) <~> wise(X0))) [input p4]
16. (~happy(paul) <~> ~rich(paul)) <=> ? [X0] : (~patient(X0) | rich(X0)) [input p15]
17. ~rich(paul) [input p16]
19. ~patient(alice) | tall(alice) [input p18]
25. kind(alice) [input hypothesis]
35. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~generous(X0)) & (generous(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 1]
36. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | kind(X0))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | kind(X0))) [flattening 36]
38. ! [X0] : (((happy(X0) & generous(X0)) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & generous(X0)) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ~happy(X0) | ~generous(X0))) [flattening 38]
40. ! [X0] : (((tall(X0) | happy(X0)) | (~curious(X0) | ~wise(X0))) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | happy(X0) | ~curious(X0) | ~wise(X0)) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 40]
42. ! [X0] : (((wise(X0) | ~creative(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 5]
43. ! [X0] : ((wise(X0) | ~creative(X0) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [flattening 42]
60. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X0] : (~patient(X0) | rich(X0)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [nnf transformation 16]
61. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X1] : (~patient(X1) | rich(X1)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [rectify 60]
62. ? [X1] : (~patient(X1) | rich(X1)) => (~patient(sK3) | rich(sK3)) [choice axiom]
63. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & ((~patient(sK3) | rich(sK3)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [skolemisation 61,62]
75. ~curious(X0) | generous(X0) | kind(X0) [cnf transformation 35]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
82. kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
83. ~kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
86. ~happy(X0) | wise(X0) [cnf transformation 41]
87. ~tall(X0) | wise(X0) [cnf transformation 41]
88. ~happy(X0) | curious(X0) [cnf transformation 41]
94. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
131. rich(paul) | happy(paul) | patient(X0) [cnf transformation 63]
132. ~rich(paul) [cnf transformation 17]
134. ~patient(alice) | tall(alice) [cnf transformation 19]
144. kind(alice) [cnf transformation 25]
145. ~wise(X0) | ~humble(X0) [duplicate literal removal 94]
147. ~happy(X0) | ~generous(X0) [subsumption resolution 82,83]
223. 17 <=> patient(alice) [avatar definition]
224. ~patient(alice) <- (~17) [avatar component clause 223]
230. 18 <=> wise(alice) [avatar definition]
231. wise(alice) <- (18) [avatar component clause 230]
260. 24 <=> ! [X0] : patient(X0) [avatar definition]
261. patient(X0) <- (24) [avatar component clause 260]
263. 25 <=> happy(paul) [avatar definition]
265. happy(paul) <- (25) [avatar component clause 263]
267. 26 <=> rich(paul) [avatar definition]
270. 24 | 25 | 26 [avatar split clause 131,267,263,260]
287. ~26 [avatar split clause 132,267]
289. 30 <=> tall(alice) [avatar definition]
291. tall(alice) <- (30) [avatar component clause 289]
292. 30 | ~17 [avatar split clause 134,223,289]
326. humble(alice) [resolution 81,144]
327. wise(paul) <- (25) [resolution 86,265]
328. curious(paul) <- (25) [resolution 88,265]
329. ~humble(paul) <- (25) [resolution 145,327]
330. ~generous(paul) <- (25) [resolution 147,265]
331. generous(paul) | kind(paul) <- (25) [resolution 75,328]
332. kind(paul) <- (25) [subsumption resolution 331,330]
348. humble(paul) <- (25) [resolution 332,81]
350. $false <- (25) [subsumption resolution 348,329]
351. ~25 [avatar contradiction clause 350]
354. $false <- (~17, 24) [resolution 261,224]
357. 17 | ~24 [avatar contradiction clause 354]
361. wise(alice) <- (30) [resolution 291,87]
364. 18 | ~30 [avatar split clause 361,289,230]
366. ~humble(alice) <- (18) [resolution 231,145]
367. $false <- (18) [subsumption resolution 366,326]
368. ~18 [avatar contradiction clause 367]
369. $false [avatar sat refutation 270,287,292,351,357,364,368]
% SZS output end Proof for 4272641683763792378899481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or kind is not old or strong. Everyone who is both not humble and not creative is not patient or old. If susan is both not old and not tall then someone is both not happy and old. Everyone who is patient or rich is not patient and vice versa. If mary is not generous or patient then someone is either quiet or funny. Everyone who is not generous or strong is rich or not old. If alice is either not funny or happy then someone is either brave or not wise and vice versa. If someone is not rich then alice is not brave and vice versa. Everyone who is either not creative or quiet is humble or not patient. Everyone who is not old is both not brave and old and vice versa. Everyone who is either patient or tall is both curious and not rich and vice versa. Everyone who is both calm and patient is either not calm or patient. Everyone who is either not happy or kind is calm. Everyone who is wise or generous is not strong or curious and vice versa. Everyone who is either not old or old is not strong. Someone is not funny or strong. Someone is both creative and not calm. John is not tall or brave. Someone is both not creative and not generous. Susan is not happy. Alice is both not creative and kind. | John is creative. | neutral | (![X]:((~tall(X)<~>kind(X))=>(~old(X)|strong(X))))&
(![X]:((~humble(X)&~creative(X))=>(~patient(X)|old(X))))&
(((~old(susan)&~tall(susan)))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((patient(X)|rich(X))<=>~patient(X)))&
(((~generous(mary)|patient(mary)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~generous(X)|strong(X))=>(rich(X)|~old(X))))&
(((~funny(alice)<~>happy(alice)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:(~old(X)<=>(~brave(X)&old(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
(![X]:((~happy(X)<~>kind(X))=>calm(X)))&
(![X]:((wise(X)|generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((~old(X)<~>old(X))=>~strong(X)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~tall(john)|brave(john)))&
(?[X]:((~creative(X)&~generous(X))))&
(~happy(susan))&
((~creative(alice)&kind(alice))) | creative(john) | [] | null | 0 |
If alice is quiet then paul is either funny or not wise and vice versa.
If someone is both not happy and not funny then fred is both not rich and not humble and vice versa.
If someone is not quiet then john is rich and vice versa.
If someone is not humble then mary is either quiet or not funny and vice versa.
Everyone who is either tall or not wise is not rich or rich.
Everyone who is not wise is happy.
Everyone who is either not happy or not kind is either wise or old and vice versa.
If someone is not creative or funny then paul is either not curious or old.
Everyone who is not kind is creative and vice versa.
Everyone who is either curious or not generous is both quiet and not happy and vice versa.
Everyone who is funny or not curious is generous or tall and vice versa.
If someone is both happy and quiet then someone is both not wise and quiet and vice versa.
If john is not brave or not quiet then john is not happy and vice versa.
Everyone who is either brave or not old is both not tall and not quiet.
Everyone who is either creative or not creative is not quiet or curious.
Everyone who is funny or not generous is both not kind and brave.
Fred is creative.
Paul is either patient or humble.
Mary is not happy.
Someone is not quiet.
Fred is either not generous or not old.
Susan is not funny.
Someone is calm or not quiet.
Susan is not brave or rich. | Paul is not quiet. | entailment | ((quiet(alice))<=>((funny(paul)<~>~wise(paul))))&
((?[X]:((~happy(X)&~funny(X))))<=>((~rich(fred)&~humble(fred))))&
((?[X]:(~quiet(X)))<=>(rich(john)))&
((?[X]:(~humble(X)))<=>((quiet(mary)<~>~funny(mary))))&
(![X]:((tall(X)<~>~wise(X))=>(~rich(X)|rich(X))))&
(![X]:(~wise(X)=>happy(X)))&
(![X]:((~happy(X)<~>~kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:((~creative(X)|funny(X))))=>((~curious(paul)<~>old(paul))))&
(![X]:(~kind(X)<=>creative(X)))&
(![X]:((curious(X)<~>~generous(X))<=>(quiet(X)&~happy(X))))&
(![X]:((funny(X)|~curious(X))<=>(generous(X)|tall(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((~wise(X)&quiet(X)))))&
(((~brave(john)|~quiet(john)))<=>(~happy(john)))&
(![X]:((brave(X)<~>~old(X))=>(~tall(X)&~quiet(X))))&
(![X]:((creative(X)<~>~creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((funny(X)|~generous(X))=>(~kind(X)&brave(X))))&
(creative(fred))&
((patient(paul)<~>humble(paul)))&
(~happy(mary))&
(?[X]:(~quiet(X)))&
((~generous(fred)<~>~old(fred)))&
(~funny(susan))&
(?[X]:((calm(X)|~quiet(X))))&
((~brave(susan)|rich(susan))) | ~quiet(paul) | [
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2972072155621489867844998
% SZS output start Proof for 2972072155621489867844998
6. ! [X0] : (~wise(X0) => happy(X0)) [input p5]
7. ! [X0] : ((~happy(X0) <~> ~kind(X0)) <=> (wise(X0) <~> old(X0))) [input p6]
8. ? [X0] : (funny(X0) | ~creative(X0)) => (~curious(paul) <~> old(paul)) [input p7]
9. ! [X0] : (~kind(X0) <=> creative(X0)) [input p8]
10. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> (~happy(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((~curious(X0) | funny(X0)) <=> (tall(X0) | generous(X0))) [input p10]
12. ? [X0] : (quiet(X0) & happy(X0)) <=> ? [X0] : (quiet(X0) & ~wise(X0)) [input p11]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) => (~quiet(X0) & ~tall(X0))) [input p13]
15. ! [X0] : ((creative(X0) <~> ~creative(X0)) => (curious(X0) | ~quiet(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | funny(X0)) => (brave(X0) & ~kind(X0))) [input p15]
25. quiet(paul) [input hypothesis]
26. ? [X0] : (quiet(X0) & happy(X0)) <=> ? [X1] : (quiet(X1) & ~wise(X1)) [rectify 12]
30. ! [X0] : (happy(X0) | wise(X0)) [ennf transformation 6]
31. (~curious(paul) <~> old(paul)) | ! [X0] : (~funny(X0) & creative(X0)) [ennf transformation 8]
32. ! [X0] : ((~quiet(X0) & ~tall(X0)) | (brave(X0) <=> ~old(X0))) [ennf transformation 14]
33. ! [X0] : ((curious(X0) | ~quiet(X0)) | (creative(X0) <=> ~creative(X0))) [ennf transformation 15]
34. ! [X0] : (curious(X0) | ~quiet(X0) | (creative(X0) <=> ~creative(X0))) [flattening 33]
35. ! [X0] : ((brave(X0) & ~kind(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 16]
51. ! [X0] : ((((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))))) [nnf transformation 7]
52. ((~old(paul) | curious(paul)) & (old(paul) | ~curious(paul))) | ! [X0] : (~funny(X0) & creative(X0)) [nnf transformation 31]
53. ! [X0] : ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))) [nnf transformation 9]
54. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (happy(X0) | ~quiet(X0))) & ((~happy(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 10]
55. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | happy(X0) | ~quiet(X0)) & ((~happy(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [flattening 54]
56. ! [X0] : (((~curious(X0) | funny(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (curious(X0) & ~funny(X0)))) [nnf transformation 11]
57. ! [X0] : ((~curious(X0) | funny(X0) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | (curious(X0) & ~funny(X0)))) [flattening 56]
58. (? [X0] : (quiet(X0) & happy(X0)) | ! [X1] : (~quiet(X1) | wise(X1))) & (? [X1] : (quiet(X1) & ~wise(X1)) | ! [X0] : (~quiet(X0) | ~happy(X0))) [nnf transformation 26]
59. (? [X0] : (quiet(X0) & happy(X0)) | ! [X1] : (~quiet(X1) | wise(X1))) & (? [X2] : (quiet(X2) & ~wise(X2)) | ! [X3] : (~quiet(X3) | ~happy(X3))) [rectify 58]
60. ? [X0] : (quiet(X0) & happy(X0)) => (quiet(sK3) & happy(sK3)) [choice axiom]
61. ? [X2] : (quiet(X2) & ~wise(X2)) => (quiet(sK4) & ~wise(sK4)) [choice axiom]
62. ((quiet(sK3) & happy(sK3)) | ! [X1] : (~quiet(X1) | wise(X1))) & ((quiet(sK4) & ~wise(sK4)) | ! [X3] : (~quiet(X3) | ~happy(X3))) [skolemisation 59,61,60]
65. ! [X0] : ((~quiet(X0) & ~tall(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) [nnf transformation 32]
66. ! [X0] : (curious(X0) | ~quiet(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 34]
87. happy(X0) | wise(X0) [cnf transformation 30]
89. old(X0) | wise(X0) | ~happy(X0) | kind(X0) [cnf transformation 51]
96. old(paul) | ~curious(paul) | creative(X0) [cnf transformation 52]
97. old(paul) | ~curious(paul) | ~funny(X0) [cnf transformation 52]
101. ~creative(X0) | ~kind(X0) [cnf transformation 53]
107. ~curious(X0) | generous(X0) | happy(X0) | ~quiet(X0) [cnf transformation 55]
110. ~generous(X0) | funny(X0) | ~curious(X0) [cnf transformation 57]
112. ~wise(sK4) | ~quiet(X3) | ~happy(X3) [cnf transformation 62]
113. quiet(sK4) | ~quiet(X3) | ~happy(X3) [cnf transformation 62]
121. ~brave(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 65]
123. curious(X0) | ~quiet(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 66]
124. curious(X0) | ~quiet(X0) | creative(X0) | creative(X0) [cnf transformation 66]
127. ~funny(X0) | brave(X0) [cnf transformation 35]
128. brave(X0) | generous(X0) [cnf transformation 35]
138. quiet(paul) [cnf transformation 25]
139. curious(X0) | ~quiet(X0) | ~creative(X0) [duplicate literal removal 123]
140. ~quiet(X0) | curious(X0) | creative(X0) [duplicate literal removal 124]
146. 2 <=> funny(paul) [avatar definition]
148. funny(paul) <- (2) [avatar component clause 146]
215. old(X0) | wise(X0) | kind(X0) [subsumption resolution 89,87]
217. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
218. ~funny(X0) <- (16) [avatar component clause 217]
220. 17 <=> curious(paul) [avatar definition]
222. curious(paul) <- (17) [avatar component clause 220]
224. 18 <=> old(paul) [avatar definition]
225. old(paul) <- (18) [avatar component clause 224]
229. 19 <=> ! [X0] : creative(X0) [avatar definition]
230. creative(X0) <- (19) [avatar component clause 229]
232. 16 | ~17 | 18 [avatar split clause 97,224,220,217]
233. 19 | ~17 | 18 [avatar split clause 96,224,220,229]
248. 23 <=> ! [X3] : (~quiet(X3) | ~happy(X3)) [avatar definition]
249. ~happy(X3) | ~quiet(X3) <- (23) [avatar component clause 248]
251. 24 <=> quiet(sK4) [avatar definition]
253. quiet(sK4) <- (24) [avatar component clause 251]
254. 23 | 24 [avatar split clause 113,251,248]
256. 25 <=> wise(sK4) [avatar definition]
258. ~wise(sK4) <- (~25) [avatar component clause 256]
259. 23 | ~25 [avatar split clause 112,256,248]
275. ~quiet(X0) | curious(X0) [subsumption resolution 139,140]
321. curious(paul) [resolution 275,138]
326. 17 [avatar split clause 321,220]
367. 41 <=> generous(paul) [avatar definition]
368. ~generous(paul) <- (~41) [avatar component clause 367]
369. generous(paul) <- (41) [avatar component clause 367]
413. ~old(X0) | ~quiet(X0) | generous(X0) [resolution 121,128]
437. 52 <=> old(sK4) [avatar definition]
438. ~old(sK4) <- (~52) [avatar component clause 437]
439. old(sK4) <- (52) [avatar component clause 437]
469. 56 <=> happy(paul) [avatar definition]
471. happy(paul) <- (56) [avatar component clause 469]
503. generous(paul) | happy(paul) | ~quiet(paul) <- (17) [resolution 107,222]
508. funny(paul) | ~curious(paul) <- (41) [resolution 369,110]
514. funny(paul) <- (17, 41) [subsumption resolution 508,222]
515. 2 | ~17 | ~41 [avatar split clause 514,367,220,146]
517. brave(paul) <- (2) [resolution 148,127]
552. curious(sK4) <- (24) [resolution 253,275]
558. 62 <=> curious(sK4) [avatar definition]
560. curious(sK4) <- (62) [avatar component clause 558]
562. 62 | ~24 [avatar split clause 552,251,558]
603. 69 <=> kind(sK4) [avatar definition]
604. kind(sK4) <- (69) [avatar component clause 603]
605. ~kind(sK4) <- (~69) [avatar component clause 603]
624. ~old(paul) | ~quiet(paul) <- (2) [resolution 517,121]
629. ~old(paul) <- (2) [subsumption resolution 624,138]
630. ~18 | ~2 [avatar split clause 629,146,224]
631. $false <- (2, 16) [resolution 218,148]
632. ~2 | ~16 [avatar contradiction clause 631]
634. generous(paul) | happy(paul) <- (17) [subsumption resolution 503,138]
635. 56 | 41 | ~17 [avatar split clause 634,220,367,469]
638. ~kind(X0) <- (19) [resolution 230,101]
649. 70 <=> generous(sK4) [avatar definition]
650. ~generous(sK4) <- (~70) [avatar component clause 649]
651. generous(sK4) <- (70) [avatar component clause 649]
666. ~quiet(sK4) | generous(sK4) <- (52) [resolution 413,439]
683. funny(sK4) | ~curious(sK4) <- (70) [resolution 651,110]
686. ~curious(sK4) <- (16, 70) [subsumption resolution 683,218]
687. $false <- (16, 62, 70) [subsumption resolution 686,560]
688. ~16 | ~62 | ~70 [avatar contradiction clause 687]
693. ~quiet(sK4) <- (52, ~70) [subsumption resolution 666,650]
694. ~24 | ~52 | 70 [avatar split clause 693,649,437,251]
701. ~quiet(paul) <- (23, 56) [resolution 249,471]
705. $false <- (23, 56) [subsumption resolution 701,138]
706. ~23 | ~56 [avatar contradiction clause 705]
716. wise(sK4) | kind(sK4) <- (~52) [resolution 438,215]
718. kind(sK4) <- (~25, ~52) [subsumption resolution 716,258]
719. $false <- (~25, ~52, ~69) [subsumption resolution 718,605]
720. 25 | 52 | 69 [avatar contradiction clause 719]
723. $false <- (19, 69) [subsumption resolution 604,638]
724. ~19 | ~69 [avatar contradiction clause 723]
734. ~quiet(paul) | generous(paul) <- (18) [resolution 225,413]
739. generous(paul) <- (18) [subsumption resolution 734,138]
740. $false <- (18, ~41) [subsumption resolution 739,368]
741. ~18 | 41 [avatar contradiction clause 740]
742. $false [avatar sat refutation 232,233,254,259,326,515,562,630,632,635,688,694,706,720,724,741]
% SZS output end Proof for 2972072155621489867844998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or wise then someone is tall or not creative. If susan is either patient or funny then someone is not funny and vice versa. Everyone who is both not wise and creative is old or not funny. If someone is creative then someone is either not curious or curious and vice versa. If john is rich then fred is not calm. If someone is either humble or not patient then mary is not strong and vice versa. Everyone who is either happy or funny is both humble and not old and vice versa. Everyone who is creative or funny is either curious or happy. If someone is not kind then john is tall and vice versa. If someone is not strong or humble then john is not wise or not happy. Everyone who is both not strong and humble is either strong or rich. If someone is not humble then susan is both humble and not strong. Everyone who is both rich and not quiet is curious. Everyone who is both not funny and happy is either not happy or not kind and vice versa. Everyone who is both generous and not humble is not generous. Everyone who is not generous or not rich is both not wise and creative. Someone is not funny or not calm. Someone is funny. Someone is not happy. Mary is not generous or generous. Susan is either not tall or not calm. Fred is either creative or calm. John is both calm and not humble. Mary is either happy or old. | Susan is not rich. | contradiction | (((~brave(lucy)|wise(lucy)))=>(?[X]:((tall(X)|~creative(X)))))&
(((patient(susan)<~>funny(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)&creative(X))=>(old(X)|~funny(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)<~>curious(X)))))&
((rich(john))=>(~calm(fred)))&
((?[X]:((humble(X)<~>~patient(X))))<=>(~strong(mary)))&
(![X]:((happy(X)<~>funny(X))<=>(humble(X)&~old(X))))&
(![X]:((creative(X)|funny(X))=>(curious(X)<~>happy(X))))&
((?[X]:(~kind(X)))<=>(tall(john)))&
((?[X]:((~strong(X)|humble(X))))=>((~wise(john)|~happy(john))))&
(![X]:((~strong(X)&humble(X))=>(strong(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>((humble(susan)&~strong(susan))))&
(![X]:((rich(X)&~quiet(X))=>curious(X)))&
(![X]:((~funny(X)&happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((generous(X)&~humble(X))=>~generous(X)))&
(![X]:((~generous(X)|~rich(X))=>(~wise(X)&creative(X))))&
(?[X]:((~funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:(~happy(X)))&
((~generous(mary)|generous(mary)))&
((~tall(susan)<~>~calm(susan)))&
((creative(fred)<~>calm(fred)))&
((calm(john)&~humble(john)))&
((happy(mary)<~>old(mary))) | ~rich(susan) | [
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5553024041014280904824649
% SZS output start Proof for 5553024041014280904824649
11. ! [X0] : ((humble(X0) & ~strong(X0)) => (strong(X0) <~> rich(X0))) [input p10]
12. ? [X0] : ~humble(X0) => (~strong(susan) & humble(susan)) [input p11]
23. ~humble(john) & calm(john) [input p22]
25. ~rich(susan) [input hypothesis]
36. ! [X0] : ((strong(X0) <~> rich(X0)) | (~humble(X0) | strong(X0))) [ennf transformation 11]
37. ! [X0] : ((strong(X0) <~> rich(X0)) | ~humble(X0) | strong(X0)) [flattening 36]
38. (~strong(susan) & humble(susan)) | ! [X0] : humble(X0) [ennf transformation 12]
64. ! [X0] : (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | ~humble(X0) | strong(X0)) [nnf transformation 37]
105. rich(X0) | strong(X0) | ~humble(X0) | strong(X0) [cnf transformation 64]
107. humble(susan) | humble(X0) [cnf transformation 38]
108. ~strong(susan) | humble(X0) [cnf transformation 38]
129. ~humble(john) [cnf transformation 23]
132. ~rich(susan) [cnf transformation 25]
136. ~humble(X0) | strong(X0) | rich(X0) [duplicate literal removal 105]
244. 25 <=> ! [X0] : humble(X0) [avatar definition]
245. humble(X0) <- (25) [avatar component clause 244]
247. 26 <=> strong(susan) [avatar definition]
249. ~strong(susan) <- (~26) [avatar component clause 247]
250. 25 | ~26 [avatar split clause 108,247,244]
252. 27 <=> humble(susan) [avatar definition]
254. humble(susan) <- (27) [avatar component clause 252]
255. 25 | 27 [avatar split clause 107,252,244]
296. $false <- (25) [resolution 245,129]
297. ~25 [avatar contradiction clause 296]
444. strong(susan) | rich(susan) <- (27) [resolution 136,254]
447. rich(susan) <- (~26, 27) [subsumption resolution 444,249]
448. $false <- (~26, 27) [subsumption resolution 447,132]
449. 26 | ~27 [avatar contradiction clause 448]
468. $false [avatar sat refutation 250,255,297,449]
% SZS output end Proof for 5553024041014280904824649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not strong or not happy then someone is humble or not strong.
Everyone who is both old and not humble is not quiet or not strong.
Everyone who is both strong and tall is not humble or kind.
Everyone who is not old is generous.
If alice is both curious and not rich then paul is not patient or creative.
Everyone who is both generous and humble is both generous and wise and vice versa.
If mary is either patient or not happy then mary is both happy and creative.
Everyone who is kind or not brave is either not quiet or not curious and vice versa.
Everyone who is both happy and not wise is both not generous and not brave and vice versa.
If lucy is either not patient or humble then someone is both creative and not brave.
If someone is humble then someone is not brave and vice versa.
If fred is both patient and not curious then someone is quiet and vice versa.
If john is not brave or not happy then susan is not creative and vice versa.
Everyone who is not patient or not quiet is not tall or not strong and vice versa.
If someone is both wise and kind then someone is wise and vice versa.
If someone is either not brave or happy then susan is either not generous or not strong.
Someone is rich.
Someone is both rich and not brave.
Fred is both not curious and happy.
Someone is either happy or rich.
Susan is either rich or not tall.
Paul is both not patient and happy.
Alice is both creative and not wise.
Someone is either quiet or not strong. | Paul is patient. | contradiction | (((~strong(alice)<~>~happy(alice)))=>(?[X]:((humble(X)|~strong(X)))))&
(![X]:((old(X)&~humble(X))=>(~quiet(X)|~strong(X))))&
(![X]:((strong(X)&tall(X))=>(~humble(X)|kind(X))))&
(![X]:(~old(X)=>generous(X)))&
(((curious(alice)&~rich(alice)))=>((~patient(paul)|creative(paul))))&
(![X]:((generous(X)&humble(X))<=>(generous(X)&wise(X))))&
(((patient(mary)<~>~happy(mary)))=>((happy(mary)&creative(mary))))&
(![X]:((kind(X)|~brave(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((happy(X)&~wise(X))<=>(~generous(X)&~brave(X))))&
(((~patient(lucy)<~>humble(lucy)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:(humble(X)))<=>(?[X]:(~brave(X))))&
(((patient(fred)&~curious(fred)))<=>(?[X]:(quiet(X))))&
(((~brave(john)|~happy(john)))<=>(~creative(susan)))&
(![X]:((~patient(X)|~quiet(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((wise(X)&kind(X))))<=>(?[X]:(wise(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>((~generous(susan)<~>~strong(susan))))&
(?[X]:(rich(X)))&
(?[X]:((rich(X)&~brave(X))))&
((~curious(fred)&happy(fred)))&
(?[X]:((happy(X)<~>rich(X))))&
((rich(susan)<~>~tall(susan)))&
((~patient(paul)&happy(paul)))&
((creative(alice)&~wise(alice)))&
(?[X]:((quiet(X)<~>~strong(X)))) | patient(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4677115302437435899525236
% SZS output start Proof for 4677115302437435899525236
22. happy(paul) & ~patient(paul) [input p21]
25. patient(paul) [input hypothesis]
139. ~patient(paul) [cnf transformation 22]
145. patient(paul) [cnf transformation 25]
174. 7 <=> patient(paul) [avatar definition]
326. ~7 [avatar split clause 139,174]
337. 7 [avatar split clause 145,174]
338. $false [avatar sat refutation 326,337]
% SZS output end Proof for 4677115302437435899525236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not funny is patient and vice versa. Everyone who is brave or not kind is either wise or not brave and vice versa. Everyone who is either not happy or patient is both tall and funny. If paul is strong or curious then john is both strong and happy. If lucy is tall then someone is not humble or old and vice versa. Everyone who is both not quiet and brave is either not wise or funny. Everyone who is both calm and not creative is not curious. Everyone who is both not patient and not strong is generous and vice versa. Everyone who is not old or wise is both patient and not kind and vice versa. Everyone who is not old is patient or generous and vice versa. Everyone who is both tall and not quiet is curious or not humble. Everyone who is curious or strong is either strong or generous. If someone is quiet or funny then lucy is either humble or not humble. Everyone who is generous is brave and vice versa. Everyone who is either calm or creative is brave or not brave. Everyone who is both not funny and not humble is generous or curious and vice versa. Mary is both funny and not patient. Lucy is happy or not wise. Someone is not calm. John is not quiet or old. Someone is not happy. Someone is either generous or patient. John is either not humble or creative. | Mary is not generous. | entailment | (![X]:((humble(X)<~>~funny(X))<=>patient(X)))&
(![X]:((brave(X)|~kind(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>patient(X))=>(tall(X)&funny(X))))&
(((strong(paul)|curious(paul)))=>((strong(john)&happy(john))))&
((tall(lucy))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((~quiet(X)&brave(X))=>(~wise(X)<~>funny(X))))&
(![X]:((calm(X)&~creative(X))=>~curious(X)))&
(![X]:((~patient(X)&~strong(X))<=>generous(X)))&
(![X]:((~old(X)|wise(X))<=>(patient(X)&~kind(X))))&
(![X]:(~old(X)<=>(patient(X)|generous(X))))&
(![X]:((tall(X)&~quiet(X))=>(curious(X)|~humble(X))))&
(![X]:((curious(X)|strong(X))=>(strong(X)<~>generous(X))))&
((?[X]:((quiet(X)|funny(X))))=>((humble(lucy)<~>~humble(lucy))))&
(![X]:(generous(X)<=>brave(X)))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|~brave(X))))&
(![X]:((~funny(X)&~humble(X))<=>(generous(X)|curious(X))))&
((funny(mary)&~patient(mary)))&
((happy(lucy)|~wise(lucy)))&
(?[X]:(~calm(X)))&
((~quiet(john)|old(john)))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)<~>patient(X))))&
((~humble(john)<~>creative(john))) | ~generous(mary) | [
"p8",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8198905376837784014292791
% SZS output start Proof for 8198905376837784014292791
9. ! [X0] : ((wise(X0) | ~old(X0)) <=> (~kind(X0) & patient(X0))) [input p8]
10. ! [X0] : (~old(X0) <=> (generous(X0) | patient(X0))) [input p9]
17. ~patient(mary) & funny(mary) [input p16]
24. generous(mary) [input hypothesis]
48. ! [X0] : (((wise(X0) | ~old(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 9]
49. ! [X0] : ((wise(X0) | ~old(X0) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | (~wise(X0) & old(X0)))) [flattening 48]
50. ! [X0] : ((~old(X0) | (~generous(X0) & ~patient(X0))) & ((generous(X0) | patient(X0)) | old(X0))) [nnf transformation 10]
51. ! [X0] : ((~old(X0) | (~generous(X0) & ~patient(X0))) & (generous(X0) | patient(X0) | old(X0))) [flattening 50]
93. old(X0) | patient(X0) [cnf transformation 49]
100. ~generous(X0) | ~old(X0) [cnf transformation 51]
120. ~patient(mary) [cnf transformation 17]
129. generous(mary) [cnf transformation 24]
218. ~old(mary) [resolution 100,129]
222. patient(mary) [resolution 218,93]
223. $false [subsumption resolution 222,120]
% SZS output end Proof for 8198905376837784014292791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not kind or not tall then fred is not quiet or not wise and vice versa.
Everyone who is either tall or not calm is either kind or rich.
Everyone who is not generous is not strong.
If fred is not calm then someone is not funny.
Everyone who is either not brave or not old is both strong and not kind and vice versa.
If mary is rich or not tall then alice is not quiet.
If someone is tall or not curious then someone is tall or humble and vice versa.
If mary is either not patient or tall then someone is not curious.
Everyone who is not tall or quiet is either not funny or not old and vice versa.
Everyone who is not generous or not calm is either wise or strong.
Everyone who is curious is not happy.
If alice is curious or not strong then fred is both not humble and not rich.
If someone is not happy or not kind then mary is not funny or rich.
If someone is either not calm or not curious then someone is rich or generous.
Everyone who is humble or not calm is both old and not rich and vice versa.
Everyone who is not strong or not kind is tall and vice versa.
Someone is both not humble and not kind.
Someone is curious.
Someone is not brave or kind.
Lucy is either patient or not brave.
Someone is either humble or not quiet.
Fred is both not rich and funny.
Someone is both not kind and happy.
Mary is both not old and not kind. | Lucy is not curious. | neutral | (((~kind(susan)<~>~tall(susan)))<=>((~quiet(fred)|~wise(fred))))&
(![X]:((tall(X)<~>~calm(X))=>(kind(X)<~>rich(X))))&
(![X]:(~generous(X)=>~strong(X)))&
((~calm(fred))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(strong(X)&~kind(X))))&
(((rich(mary)|~tall(mary)))=>(~quiet(alice)))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((tall(X)|humble(X)))))&
(((~patient(mary)<~>tall(mary)))=>(?[X]:(~curious(X))))&
(![X]:((~tall(X)|quiet(X))<=>(~funny(X)<~>~old(X))))&
(![X]:((~generous(X)|~calm(X))=>(wise(X)<~>strong(X))))&
(![X]:(curious(X)=>~happy(X)))&
(((curious(alice)|~strong(alice)))=>((~humble(fred)&~rich(fred))))&
((?[X]:((~happy(X)|~kind(X))))=>((~funny(mary)|rich(mary))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((humble(X)|~calm(X))<=>(old(X)&~rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>tall(X)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)|kind(X))))&
((patient(lucy)<~>~brave(lucy)))&
(?[X]:((humble(X)<~>~quiet(X))))&
((~rich(fred)&funny(fred)))&
(?[X]:((~kind(X)&happy(X))))&
((~old(mary)&~kind(mary))) | ~curious(lucy) | [] | null | 0 |
Everyone who is not strong or strong is wise or not creative and vice versa.
If mary is either wise or calm then someone is not calm or not funny and vice versa.
Everyone who is either calm or not funny is not calm or not rich.
If someone is not quiet then paul is strong or not calm.
If fred is either old or wise then susan is tall or patient.
If someone is quiet or wise then someone is either wise or not quiet.
Everyone who is wise or patient is patient and vice versa.
Everyone who is both quiet and not tall is brave or quiet.
Everyone who is not old or not rich is wise or not brave.
If fred is both not calm and not happy then paul is either not tall or humble and vice versa.
If alice is not patient then lucy is both strong and not quiet and vice versa.
If someone is both strong and funny then someone is not funny and vice versa.
Everyone who is calm or tall is happy and vice versa.
If someone is either not strong or not kind then someone is both not patient and not generous.
Everyone who is either creative or not quiet is not tall.
Everyone who is either not strong or not old is either generous or not old.
Someone is both old and creative.
Fred is both happy and not generous.
Fred is not kind or not wise.
John is both patient and brave.
Someone is both wise and not strong.
Fred is not old or tall.
Someone is either curious or not humble.
Susan is old or tall. | John is not brave. | contradiction | (![X]:((~strong(X)|strong(X))<=>(wise(X)|~creative(X))))&
(((wise(mary)<~>calm(mary)))<=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((calm(X)<~>~funny(X))=>(~calm(X)|~rich(X))))&
((?[X]:(~quiet(X)))=>((strong(paul)|~calm(paul))))&
(((old(fred)<~>wise(fred)))=>((tall(susan)|patient(susan))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((wise(X)|patient(X))<=>patient(X)))&
(![X]:((quiet(X)&~tall(X))=>(brave(X)|quiet(X))))&
(![X]:((~old(X)|~rich(X))=>(wise(X)|~brave(X))))&
(((~calm(fred)&~happy(fred)))<=>((~tall(paul)<~>humble(paul))))&
((~patient(alice))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)|tall(X))<=>happy(X)))&
((?[X]:((~strong(X)<~>~kind(X))))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((creative(X)<~>~quiet(X))=>~tall(X)))&
(![X]:((~strong(X)<~>~old(X))=>(generous(X)<~>~old(X))))&
(?[X]:((old(X)&creative(X))))&
((happy(fred)&~generous(fred)))&
((~kind(fred)|~wise(fred)))&
((patient(john)&brave(john)))&
(?[X]:((wise(X)&~strong(X))))&
((~old(fred)|tall(fred)))&
(?[X]:((curious(X)<~>~humble(X))))&
((old(susan)|tall(susan))) | ~brave(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7750596160724287680474379
% SZS output start Proof for 7750596160724287680474379
20. brave(john) & patient(john) [input p19]
25. ~brave(john) [input hypothesis]
137. brave(john) [cnf transformation 20]
144. ~brave(john) [cnf transformation 25]
324. $false [subsumption resolution 144,137]
% SZS output end Proof for 7750596160724287680474379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not old is strong or quiet. If someone is either strong or not wise then mary is creative. Everyone who is both funny and strong is curious or not rich and vice versa. If alice is wise then someone is rich or not quiet. Everyone who is either kind or not old is either curious or not wise and vice versa. Everyone who is not calm or wise is either quiet or calm and vice versa. Everyone who is both not humble and not kind is either not wise or strong and vice versa. If someone is either not curious or quiet then someone is calm or not brave. Everyone who is both not creative and not curious is happy or not old and vice versa. Everyone who is not patient or not wise is not strong. If someone is either not funny or not old then john is not old or tall. Everyone who is either not generous or generous is both not tall and not brave and vice versa. Everyone who is tall is rich or quiet and vice versa. Everyone who is both kind and tall is not humble or patient. If someone is both not quiet and not curious then paul is either tall or not brave and vice versa. Someone is either not tall or not strong. Someone is strong. Lucy is calm or quiet. Alice is generous or not wise. Someone is old or generous. | John is not strong. | contradiction | (![X]:((strong(X)&~old(X))=>(strong(X)|quiet(X))))&
((?[X]:((strong(X)<~>~wise(X))))=>(creative(mary)))&
(![X]:((funny(X)&strong(X))<=>(curious(X)|~rich(X))))&
((wise(alice))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)<~>~old(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|wise(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~wise(X)<~>strong(X))))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~curious(X))<=>(happy(X)|~old(X))))&
(![X]:((~patient(X)|~wise(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>((~old(john)|tall(john))))&
(![X]:((~generous(X)<~>generous(X))<=>(~tall(X)&~brave(X))))&
(![X]:(tall(X)<=>(rich(X)|quiet(X))))&
(![X]:((kind(X)&tall(X))=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((tall(paul)<~>~brave(paul))))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:(strong(X)))&
((calm(lucy)|quiet(lucy)))&
((generous(alice)|~wise(alice)))&
(?[X]:((old(X)|generous(X)))) | ~strong(john) | [
"p2",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5202274333404779713105244
% SZS output start Proof for 5202274333404779713105244
3. ! [X0] : ((strong(X0) & funny(X0)) <=> (~rich(X0) | curious(X0))) [input p2]
12. ! [X0] : ((~generous(X0) <~> generous(X0)) <=> (~brave(X0) & ~tall(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (quiet(X0) | rich(X0))) [input p12]
21. ~strong(john) [input hypothesis]
34. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 3]
35. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ~strong(X0) | ~funny(X0))) [flattening 34]
50. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [nnf transformation 12]
51. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [flattening 50]
52. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 13]
53. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~tall(X0))) [flattening 52]
72. rich(X0) | strong(X0) [cnf transformation 35]
104. ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 51]
105. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 51]
111. tall(X0) | ~rich(X0) [cnf transformation 53]
125. ~strong(john) [cnf transformation 21]
126. ~tall(X0) | generous(X0) [duplicate literal removal 104]
127. ~tall(X0) | ~generous(X0) [duplicate literal removal 105]
190. ~tall(X0) [subsumption resolution 126,127]
192. ~rich(X0) [subsumption resolution 111,190]
211. strong(X0) [resolution 72,192]
212. $false [resolution 211,125]
% SZS output end Proof for 5202274333404779713105244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is curious and vice versa. If john is both not brave and not wise then someone is either humble or not strong. If someone is humble or not happy then someone is either patient or not old and vice versa. If fred is not strong or not generous then john is not tall or not kind and vice versa. If lucy is not rich then someone is not patient and vice versa. Everyone who is not curious or patient is not humble. If mary is both tall and happy then susan is either quiet or not strong. If someone is both not funny and not rich then someone is not kind or patient. If someone is funny then someone is not quiet. Everyone who is either not brave or rich is kind or calm and vice versa. Everyone who is both strong and not rich is both not tall and not strong and vice versa. Everyone who is both not wise and not rich is either not curious or not rich and vice versa. Everyone who is both not curious and not kind is either old or not kind. If someone is either not wise or not curious then john is both not patient and quiet and vice versa. If susan is rich or not quiet then alice is both not funny and quiet. Everyone who is either not generous or not rich is either tall or not happy and vice versa. Someone is both funny and not strong. Mary is either not strong or not kind. Fred is curious. Someone is quiet. Someone is either not quiet or rich. Mary is not kind or not tall. Someone is not tall or strong. Alice is both not tall and not happy. | Fred is not curious. | contradiction | (![X]:((~creative(X)&patient(X))<=>curious(X)))&
(((~brave(john)&~wise(john)))=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((humble(X)|~happy(X))))<=>(?[X]:((patient(X)<~>~old(X)))))&
(((~strong(fred)|~generous(fred)))<=>((~tall(john)|~kind(john))))&
((~rich(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)|patient(X))=>~humble(X)))&
(((tall(mary)&happy(mary)))=>((quiet(susan)<~>~strong(susan))))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:(funny(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(kind(X)|calm(X))))&
(![X]:((strong(X)&~rich(X))<=>(~tall(X)&~strong(X))))&
(![X]:((~wise(X)&~rich(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:((~curious(X)&~kind(X))=>(old(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((~patient(john)&quiet(john))))&
(((rich(susan)|~quiet(susan)))=>((~funny(alice)&quiet(alice))))&
(![X]:((~generous(X)<~>~rich(X))<=>(tall(X)<~>~happy(X))))&
(?[X]:((funny(X)&~strong(X))))&
((~strong(mary)<~>~kind(mary)))&
(curious(fred))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)<~>rich(X))))&
((~kind(mary)|~tall(mary)))&
(?[X]:((~tall(X)|strong(X))))&
((~tall(alice)&~happy(alice))) | ~curious(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4311686550581199106434741
% SZS output start Proof for 4311686550581199106434741
19. curious(fred) [input p18]
25. ~curious(fred) [input hypothesis]
148. curious(fred) [cnf transformation 19]
156. ~curious(fred) [cnf transformation 25]
355. $false [subsumption resolution 156,148]
% SZS output end Proof for 4311686550581199106434741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both curious and brave then fred is either not patient or not creative and vice versa.
If someone is both creative and not calm then someone is both rich and happy and vice versa.
Everyone who is not generous or not calm is both not old and calm.
If mary is happy then someone is not quiet or old and vice versa.
If paul is not humble or not brave then someone is not wise or generous and vice versa.
If paul is strong or not strong then someone is rich.
Everyone who is either not old or not kind is quiet or not patient and vice versa.
If someone is not kind or not brave then someone is either not humble or quiet and vice versa.
If someone is not rich then someone is not creative.
Everyone who is curious is either not funny or not old and vice versa.
If john is both rich and not generous then someone is both not quiet and wise and vice versa.
If someone is either not quiet or curious then someone is either not curious or not brave and vice versa.
Everyone who is not kind or quiet is both not brave and not kind and vice versa.
If someone is both creative and not humble then someone is either not patient or not brave and vice versa.
Everyone who is both creative and not creative is either not wise or not calm and vice versa.
Everyone who is either kind or rich is wise.
Someone is either not old or calm.
Someone is patient or generous.
Someone is not kind or not patient.
Someone is either quiet or generous.
Susan is both not brave and tall.
Paul is either not curious or calm.
Lucy is either brave or not rich. | John is not quiet. | entailment | (((curious(fred)&brave(fred)))<=>((~patient(fred)<~>~creative(fred))))&
((?[X]:((creative(X)&~calm(X))))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((~generous(X)|~calm(X))=>(~old(X)&calm(X))))&
((happy(mary))<=>(?[X]:((~quiet(X)|old(X)))))&
(((~humble(paul)|~brave(paul)))<=>(?[X]:((~wise(X)|generous(X)))))&
(((strong(paul)|~strong(paul)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(quiet(X)|~patient(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
((?[X]:(~rich(X)))=>(?[X]:(~creative(X))))&
(![X]:(curious(X)<=>(~funny(X)<~>~old(X))))&
(((rich(john)&~generous(john)))<=>(?[X]:((~quiet(X)&wise(X)))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((~kind(X)|quiet(X))<=>(~brave(X)&~kind(X))))&
((?[X]:((creative(X)&~humble(X))))<=>(?[X]:((~patient(X)<~>~brave(X)))))&
(![X]:((creative(X)&~creative(X))<=>(~wise(X)<~>~calm(X))))&
(![X]:((kind(X)<~>rich(X))=>wise(X)))&
(?[X]:((~old(X)<~>calm(X))))&
(?[X]:((patient(X)|generous(X))))&
(?[X]:((~kind(X)|~patient(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((~brave(susan)&tall(susan)))&
((~curious(paul)<~>calm(paul)))&
((brave(lucy)<~>~rich(lucy))) | ~quiet(john) | [
"p2",
"p6",
"p10",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4679641350225074682725743
% SZS output start Proof for 4679641350225074682725743
3. ! [X0] : ((~calm(X0) | ~generous(X0)) => (calm(X0) & ~old(X0))) [input p2]
7. ! [X0] : ((~old(X0) <~> ~kind(X0)) <=> (~patient(X0) | quiet(X0))) [input p6]
11. (~generous(john) & rich(john)) <=> ? [X0] : (wise(X0) & ~quiet(X0)) [input p10]
13. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> (~kind(X0) & ~brave(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~wise(X0) <~> ~calm(X0))) [input p14]
20. ? [X0] : (quiet(X0) <~> generous(X0)) [input p19]
24. quiet(john) [input hypothesis]
31. ! [X0] : ((calm(X0) & ~old(X0)) | (calm(X0) & generous(X0))) [ennf transformation 3]
53. ! [X0] : ((((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0))))) [nnf transformation 7]
54. ! [X0] : ((((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0))))) [flattening 53]
64. ((~generous(john) & rich(john)) | ! [X0] : (~wise(X0) | quiet(X0))) & (? [X0] : (wise(X0) & ~quiet(X0)) | (generous(john) | ~rich(john))) [nnf transformation 11]
65. ((~generous(john) & rich(john)) | ! [X0] : (~wise(X0) | quiet(X0))) & (? [X0] : (wise(X0) & ~quiet(X0)) | generous(john) | ~rich(john)) [flattening 64]
66. ((~generous(john) & rich(john)) | ! [X0] : (~wise(X0) | quiet(X0))) & (? [X1] : (wise(X1) & ~quiet(X1)) | generous(john) | ~rich(john)) [rectify 65]
67. ? [X1] : (wise(X1) & ~quiet(X1)) => (wise(sK8) & ~quiet(sK8)) [choice axiom]
68. ((~generous(john) & rich(john)) | ! [X0] : (~wise(X0) | quiet(X0))) & ((wise(sK8) & ~quiet(sK8)) | generous(john) | ~rich(john)) [skolemisation 66,67]
74. ! [X0] : (((quiet(X0) | ~kind(X0)) | (kind(X0) | brave(X0))) & ((~kind(X0) & ~brave(X0)) | (~quiet(X0) & kind(X0)))) [nnf transformation 13]
75. ! [X0] : ((quiet(X0) | ~kind(X0) | kind(X0) | brave(X0)) & ((~kind(X0) & ~brave(X0)) | (~quiet(X0) & kind(X0)))) [flattening 74]
81. ! [X0] : (((~creative(X0) & creative(X0)) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | (creative(X0) | ~creative(X0)))) [nnf transformation 15]
82. ! [X0] : (((~creative(X0) & creative(X0)) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | creative(X0) | ~creative(X0))) [flattening 81]
91. ? [X0] : ((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) [nnf transformation 20]
92. ? [X0] : ((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) => ((~generous(sK16) | ~quiet(sK16)) & (generous(sK16) | quiet(sK16))) [choice axiom]
93. (~generous(sK16) | ~quiet(sK16)) & (generous(sK16) | quiet(sK16)) [skolemisation 91,92]
106. ~old(X0) | generous(X0) [cnf transformation 31]
109. calm(X0) | calm(X0) [cnf transformation 31]
123. ~quiet(X0) | old(X0) | kind(X0) [cnf transformation 54]
139. ~generous(john) | ~wise(X0) | quiet(X0) [cnf transformation 68]
151. ~kind(X0) | ~quiet(X0) [cnf transformation 75]
161. creative(X0) | ~calm(X0) | wise(X0) [cnf transformation 82]
163. ~creative(X0) | ~calm(X0) | wise(X0) [cnf transformation 82]
172. ~generous(sK16) | ~quiet(sK16) [cnf transformation 93]
178. quiet(john) [cnf transformation 24]
179. calm(X0) [duplicate literal removal 109]
237. 13 <=> ! [X0] : quiet(X0) [avatar definition]
238. quiet(X0) <- (13) [avatar component clause 237]
262. 19 <=> ! [X0] : wise(X0) [avatar definition]
263. wise(X0) <- (19) [avatar component clause 262]
328. 34 <=> ! [X0] : (~wise(X0) | quiet(X0)) [avatar definition]
329. ~wise(X0) | quiet(X0) <- (34) [avatar component clause 328]
331. 35 <=> generous(john) [avatar definition]
334. 34 | ~35 [avatar split clause 139,331,328]
417. ~creative(X0) | wise(X0) [subsumption resolution 163,179]
418. creative(X0) | wise(X0) [subsumption resolution 161,179]
419. wise(X0) [subsumption resolution 418,417]
420. 19 [avatar split clause 419,262]
441. 58 <=> quiet(sK16) [avatar definition]
442. quiet(sK16) <- (58) [avatar component clause 441]
443. ~quiet(sK16) <- (~58) [avatar component clause 441]
445. 59 <=> generous(sK16) [avatar definition]
447. ~generous(sK16) <- (~59) [avatar component clause 445]
448. ~58 | ~59 [avatar split clause 172,445,441]
494. old(john) | kind(john) [resolution 123,178]
495. old(sK16) | kind(sK16) <- (58) [resolution 123,442]
497. 62 <=> kind(john) [avatar definition]
499. kind(john) <- (62) [avatar component clause 497]
501. 63 <=> old(john) [avatar definition]
503. old(john) <- (63) [avatar component clause 501]
504. 62 | 63 [avatar split clause 494,501,497]
506. 64 <=> kind(sK16) [avatar definition]
508. kind(sK16) <- (64) [avatar component clause 506]
510. 65 <=> old(sK16) [avatar definition]
512. old(sK16) <- (65) [avatar component clause 510]
513. 64 | 65 | ~58 [avatar split clause 495,441,510,506]
557. ~quiet(john) <- (62) [resolution 499,151]
565. $false <- (62) [subsumption resolution 557,178]
566. ~62 [avatar contradiction clause 565]
590. generous(john) <- (63) [resolution 503,106]
593. 35 | ~63 [avatar split clause 590,501,331]
594. quiet(X0) <- (19, 34) [subsumption resolution 329,263]
595. 13 | ~19 | ~34 [avatar split clause 594,328,262,237]
601. $false <- (13, ~58) [resolution 238,443]
602. ~13 | 58 [avatar contradiction clause 601]
633. ~quiet(sK16) <- (64) [resolution 508,151]
641. $false <- (13, 64) [subsumption resolution 633,238]
642. ~13 | ~64 [avatar contradiction clause 641]
685. generous(sK16) <- (65) [resolution 512,106]
695. $false <- (~59, 65) [subsumption resolution 685,447]
696. 59 | ~65 [avatar contradiction clause 695]
697. $false [avatar sat refutation 334,420,448,504,513,566,593,595,602,642,696]
% SZS output end Proof for 4679641350225074682725743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is both happy and humble and vice versa.
Everyone who is both patient and old is not funny or not old.
If someone is both not happy and kind then fred is both funny and brave and vice versa.
If someone is curious then someone is not creative or funny and vice versa.
If someone is not creative or calm then someone is not tall or not quiet and vice versa.
Everyone who is not curious or old is both creative and not funny.
If susan is kind then paul is generous or rich and vice versa.
Everyone who is humble is either not calm or happy and vice versa.
Everyone who is patient is humble or patient and vice versa.
Everyone who is both not brave and not tall is wise.
Everyone who is kind is either not funny or creative.
Everyone who is both not humble and not creative is either brave or patient.
Everyone who is either humble or calm is either humble or not kind.
If someone is either tall or not funny then someone is either funny or curious and vice versa.
Everyone who is either not curious or not calm is both not rich and not funny.
Everyone who is calm or not happy is both not creative and not kind.
Someone is funny or creative.
Someone is either humble or rich.
Someone is not quiet or happy.
Someone is both not happy and not humble.
Someone is wise.
John is not brave.
Paul is either strong or wise.
Someone is curious. | John is not humble. | neutral | (![X]:((~strong(X)|~generous(X))<=>(happy(X)&humble(X))))&
(![X]:((patient(X)&old(X))=>(~funny(X)|~old(X))))&
((?[X]:((~happy(X)&kind(X))))<=>((funny(fred)&brave(fred))))&
((?[X]:(curious(X)))<=>(?[X]:((~creative(X)|funny(X)))))&
((?[X]:((~creative(X)|calm(X))))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((~curious(X)|old(X))=>(creative(X)&~funny(X))))&
((kind(susan))<=>((generous(paul)|rich(paul))))&
(![X]:(humble(X)<=>(~calm(X)<~>happy(X))))&
(![X]:(patient(X)<=>(humble(X)|patient(X))))&
(![X]:((~brave(X)&~tall(X))=>wise(X)))&
(![X]:(kind(X)=>(~funny(X)<~>creative(X))))&
(![X]:((~humble(X)&~creative(X))=>(brave(X)<~>patient(X))))&
(![X]:((humble(X)<~>calm(X))=>(humble(X)<~>~kind(X))))&
((?[X]:((tall(X)<~>~funny(X))))<=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>(~rich(X)&~funny(X))))&
(![X]:((calm(X)|~happy(X))=>(~creative(X)&~kind(X))))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((humble(X)<~>rich(X))))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:(wise(X)))&
(~brave(john))&
((strong(paul)<~>wise(paul)))&
(?[X]:(curious(X))) | ~humble(john) | [] | null | 0 |
Everyone who is both curious and quiet is either humble or not old and vice versa. If someone is either not curious or not tall then someone is either rich or strong and vice versa. Everyone who is brave or not creative is both not generous and funny. Everyone who is not creative or patient is both curious and kind and vice versa. If someone is either funny or tall then fred is both tall and kind. If fred is not creative then someone is not curious. If lucy is old then paul is either not generous or not kind. If someone is patient then mary is brave. If lucy is curious or happy then john is both not generous and not brave and vice versa. Everyone who is creative is not old. Everyone who is funny is both rich and not happy. If mary is either strong or not strong then mary is both not tall and rich and vice versa. If someone is tall or not creative then fred is both not tall and not wise and vice versa. Everyone who is not kind is either not happy or generous and vice versa. Everyone who is calm is strong and vice versa. Everyone who is tall or not tall is either calm or quiet. Susan is either not funny or creative. Alice is either not brave or not happy. Someone is not creative or not wise. Mary is not humble or not quiet. Lucy is quiet or not funny. Lucy is not strong or not kind. | John is not creative. | contradiction | (![X]:((curious(X)&quiet(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((~curious(X)<~>~tall(X))))<=>(?[X]:((rich(X)<~>strong(X)))))&
(![X]:((brave(X)|~creative(X))=>(~generous(X)&funny(X))))&
(![X]:((~creative(X)|patient(X))<=>(curious(X)&kind(X))))&
((?[X]:((funny(X)<~>tall(X))))=>((tall(fred)&kind(fred))))&
((~creative(fred))=>(?[X]:(~curious(X))))&
((old(lucy))=>((~generous(paul)<~>~kind(paul))))&
((?[X]:(patient(X)))=>(brave(mary)))&
(((curious(lucy)|happy(lucy)))<=>((~generous(john)&~brave(john))))&
(![X]:(creative(X)=>~old(X)))&
(![X]:(funny(X)=>(rich(X)&~happy(X))))&
(((strong(mary)<~>~strong(mary)))<=>((~tall(mary)&rich(mary))))&
((?[X]:((tall(X)|~creative(X))))<=>((~tall(fred)&~wise(fred))))&
(![X]:(~kind(X)<=>(~happy(X)<~>generous(X))))&
(![X]:(calm(X)<=>strong(X)))&
(![X]:((tall(X)|~tall(X))=>(calm(X)<~>quiet(X))))&
((~funny(susan)<~>creative(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~creative(X)|~wise(X))))&
((~humble(mary)|~quiet(mary)))&
((quiet(lucy)|~funny(lucy)))&
((~strong(lucy)|~kind(lucy))) | ~creative(john) | [
"p2",
"p3",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5530785096146794523521700
% SZS output start Proof for 5530785096146794523521700
3. ! [X0] : ((~creative(X0) | brave(X0)) => (funny(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((patient(X0) | ~creative(X0)) <=> (kind(X0) & curious(X0))) [input p3]
11. ! [X0] : (funny(X0) => (~happy(X0) & rich(X0))) [input p10]
14. ! [X0] : (~kind(X0) <=> (~happy(X0) <~> generous(X0))) [input p13]
23. ~creative(john) [input hypothesis]
25. ! [X0] : ((funny(X0) & ~generous(X0)) | (creative(X0) & ~brave(X0))) [ennf transformation 3]
31. ! [X0] : ((~happy(X0) & rich(X0)) | ~funny(X0)) [ennf transformation 11]
40. ! [X0] : (((patient(X0) | ~creative(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (~patient(X0) & creative(X0)))) [nnf transformation 4]
41. ! [X0] : ((patient(X0) | ~creative(X0) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | (~patient(X0) & creative(X0)))) [flattening 40]
55. ! [X0] : ((~kind(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | kind(X0))) [nnf transformation 14]
77. ~generous(X0) | creative(X0) [cnf transformation 25]
79. funny(X0) | creative(X0) [cnf transformation 25]
82. kind(X0) | creative(X0) [cnf transformation 41]
100. ~happy(X0) | ~funny(X0) [cnf transformation 31]
114. ~kind(X0) | generous(X0) | happy(X0) [cnf transformation 55]
130. ~creative(john) [cnf transformation 23]
271. 30 <=> ! [X1] : creative(X1) [avatar definition]
272. creative(X1) <- (30) [avatar component clause 271]
388. generous(X0) | happy(X0) | creative(X0) [resolution 114,82]
389. happy(X0) | creative(X0) [subsumption resolution 388,77]
428. creative(X2) | ~funny(X2) [resolution 389,100]
429. creative(X2) [subsumption resolution 428,79]
430. 30 [avatar split clause 429,271]
432. $false <- (30) [resolution 272,130]
437. ~30 [avatar contradiction clause 432]
438. $false [avatar sat refutation 430,437]
% SZS output end Proof for 5530785096146794523521700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and brave is either creative or curious. If someone is not creative then susan is humble. Everyone who is quiet or not strong is either not tall or calm. Everyone who is tall or kind is generous and vice versa. Everyone who is both not tall and not quiet is brave. If john is not humble or patient then someone is rich or not generous. If someone is not humble then someone is not old and vice versa. If someone is both calm and not wise then alice is not wise or creative. Everyone who is both not patient and not humble is either not curious or calm. If mary is patient or wise then lucy is both not calm and quiet. Everyone who is kind or humble is both not creative and kind. Everyone who is either quiet or brave is either not tall or humble and vice versa. Everyone who is either humble or kind is brave and vice versa. Everyone who is wise or quiet is not rich or strong. If paul is brave then someone is happy and vice versa. Everyone who is calm is both kind and patient. Someone is not funny. Lucy is both generous and not kind. Someone is both not kind and old. Lucy is either curious or calm. Susan is either calm or quiet. Mary is not funny or not wise. Someone is either not wise or not happy. Susan is not humble. | Paul is happy. | contradiction | (![X]:((~patient(X)&brave(X))=>(creative(X)<~>curious(X))))&
((?[X]:(~creative(X)))=>(humble(susan)))&
(![X]:((quiet(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:((tall(X)|kind(X))<=>generous(X)))&
(![X]:((~tall(X)&~quiet(X))=>brave(X)))&
(((~humble(john)|patient(john)))=>(?[X]:((rich(X)|~generous(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((calm(X)&~wise(X))))=>((~wise(alice)|creative(alice))))&
(![X]:((~patient(X)&~humble(X))=>(~curious(X)<~>calm(X))))&
(((patient(mary)|wise(mary)))=>((~calm(lucy)&quiet(lucy))))&
(![X]:((kind(X)|humble(X))=>(~creative(X)&kind(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(?[X]:(~funny(X)))&
((generous(lucy)&~kind(lucy)))&
(?[X]:((~kind(X)&old(X))))&
((curious(lucy)<~>calm(lucy)))&
((calm(susan)<~>quiet(susan)))&
((~funny(mary)|~wise(mary)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(~humble(susan)) | happy(paul) | [
"p1",
"p10",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2226763812322122260465471
% SZS output start Proof for 2226763812322122260465471
2. ? [X0] : ~creative(X0) => humble(susan) [input p1]
11. ! [X0] : ((humble(X0) | kind(X0)) => (kind(X0) & ~creative(X0))) [input p10]
13. ! [X0] : ((humble(X0) <~> kind(X0)) <=> brave(X0)) [input p12]
15. brave(paul) <=> ? [X0] : happy(X0) [input p14]
24. ~humble(susan) [input p23]
25. happy(paul) [input hypothesis]
35. humble(susan) | ! [X0] : creative(X0) [ennf transformation 2]
46. ! [X0] : ((kind(X0) & ~creative(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 11]
57. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~brave(X0)) & (brave(X0) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 13]
58. (brave(paul) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~brave(paul)) [nnf transformation 15]
59. (brave(paul) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~brave(paul)) [rectify 58]
60. ? [X1] : happy(X1) => happy(sK2) [choice axiom]
61. (brave(paul) | ! [X0] : ~happy(X0)) & (happy(sK2) | ~brave(paul)) [skolemisation 59,60]
71. humble(susan) | creative(X0) [cnf transformation 35]
85. ~kind(X0) | ~creative(X0) [cnf transformation 46]
88. ~humble(X0) | kind(X0) [cnf transformation 46]
99. kind(X0) | humble(X0) | ~brave(X0) [cnf transformation 57]
100. ~kind(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 57]
102. brave(paul) | ~happy(X0) [cnf transformation 61]
115. ~humble(susan) [cnf transformation 24]
116. happy(paul) [cnf transformation 25]
118. 1 <=> ! [X0] : creative(X0) [avatar definition]
119. creative(X0) <- (1) [avatar component clause 118]
121. 2 <=> humble(susan) [avatar definition]
124. 1 | 2 [avatar split clause 71,121,118]
176. ~humble(X0) | ~brave(X0) [subsumption resolution 100,88]
177. ~brave(X0) | kind(X0) [subsumption resolution 99,176]
179. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
180. ~happy(X0) <- (14) [avatar component clause 179]
182. 15 <=> brave(paul) [avatar definition]
184. brave(paul) <- (15) [avatar component clause 182]
185. 14 | 15 [avatar split clause 102,182,179]
217. ~2 [avatar split clause 115,121]
218. $false <- (14) [resolution 180,116]
219. ~14 [avatar contradiction clause 218]
228. kind(paul) <- (15) [resolution 177,184]
229. ~creative(paul) <- (15) [resolution 228,85]
230. $false <- (1, 15) [subsumption resolution 229,119]
231. ~1 | ~15 [avatar contradiction clause 230]
232. $false [avatar sat refutation 124,185,217,219,231]
% SZS output end Proof for 2226763812322122260465471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or strong is both not old and calm and vice versa.
Everyone who is patient is both funny and tall.
If mary is not quiet then mary is either strong or happy.
If mary is either kind or rich then alice is not funny or wise.
If someone is funny then someone is not humble and vice versa.
Everyone who is either funny or calm is humble.
If john is both not wise and calm then fred is not humble or not curious and vice versa.
Everyone who is either not patient or not kind is generous and vice versa.
If susan is either not curious or not happy then someone is both curious and creative.
Everyone who is old is both not tall and not brave and vice versa.
If someone is both calm and not happy then fred is both quiet and rich.
If john is either strong or humble then mary is not creative or not curious and vice versa.
Everyone who is both not strong and not humble is happy or not tall and vice versa.
If mary is calm or curious then mary is either tall or curious and vice versa.
Everyone who is both not strong and brave is both not tall and not creative and vice versa.
Everyone who is not funny or not brave is not quiet.
Someone is both not generous and not creative.
Someone is not funny.
Fred is either strong or not generous.
Someone is not tall.
John is not strong or happy.
Alice is happy or strong.
Paul is either not patient or wise.
Susan is kind or not calm. | John is humble. | entailment | (![X]:((~strong(X)<~>strong(X))<=>(~old(X)&calm(X))))&
(![X]:(patient(X)=>(funny(X)&tall(X))))&
((~quiet(mary))=>((strong(mary)<~>happy(mary))))&
(((kind(mary)<~>rich(mary)))=>((~funny(alice)|wise(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~humble(X))))&
(![X]:((funny(X)<~>calm(X))=>humble(X)))&
(((~wise(john)&calm(john)))<=>((~humble(fred)|~curious(fred))))&
(![X]:((~patient(X)<~>~kind(X))<=>generous(X)))&
(((~curious(susan)<~>~happy(susan)))=>(?[X]:((curious(X)&creative(X)))))&
(![X]:(old(X)<=>(~tall(X)&~brave(X))))&
((?[X]:((calm(X)&~happy(X))))=>((quiet(fred)&rich(fred))))&
(((strong(john)<~>humble(john)))<=>((~creative(mary)|~curious(mary))))&
(![X]:((~strong(X)&~humble(X))<=>(happy(X)|~tall(X))))&
(((calm(mary)|curious(mary)))<=>((tall(mary)<~>curious(mary))))&
(![X]:((~strong(X)&brave(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~funny(X)|~brave(X))=>~quiet(X)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:(~funny(X)))&
((strong(fred)<~>~generous(fred)))&
(?[X]:(~tall(X)))&
((~strong(john)|happy(john)))&
((happy(alice)|strong(alice)))&
((~patient(paul)<~>wise(paul)))&
((kind(susan)|~calm(susan))) | humble(john) | [
"p0",
"p9",
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6223252770718986295465684
% SZS output start Proof for 6223252770718986295465684
1. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (calm(X0) & ~old(X0))) [input p0]
10. ! [X0] : (old(X0) <=> (~brave(X0) & ~tall(X0))) [input p9]
12. (strong(john) <~> humble(john)) <=> (~curious(mary) | ~creative(mary)) [input p11]
13. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (~tall(X0) | happy(X0))) [input p12]
14. (curious(mary) | calm(mary)) <=> (tall(mary) <~> curious(mary)) [input p13]
15. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~creative(X0) & ~tall(X0))) [input p14]
21. happy(john) | ~strong(john) [input p20]
25. ~humble(john) [input hypothesis]
35. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 35]
51. ! [X0] : ((old(X0) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | ~old(X0))) [nnf transformation 10]
52. ! [X0] : ((old(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | ~old(X0))) [flattening 51]
53. (((~humble(john) | ~strong(john)) & (humble(john) | strong(john))) | (curious(mary) & creative(mary))) & ((~curious(mary) | ~creative(mary)) | ((strong(john) | ~humble(john)) & (humble(john) | ~strong(john)))) [nnf transformation 12]
54. (((~humble(john) | ~strong(john)) & (humble(john) | strong(john))) | (curious(mary) & creative(mary))) & (~curious(mary) | ~creative(mary) | ((strong(john) | ~humble(john)) & (humble(john) | ~strong(john)))) [flattening 53]
55. ! [X0] : (((~humble(X0) & ~strong(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 13]
56. ! [X0] : (((~humble(X0) & ~strong(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | humble(X0) | strong(X0))) [flattening 55]
57. ((curious(mary) | calm(mary)) | ((tall(mary) | ~curious(mary)) & (curious(mary) | ~tall(mary)))) & (((~curious(mary) | ~tall(mary)) & (curious(mary) | tall(mary))) | (~curious(mary) & ~calm(mary))) [nnf transformation 14]
58. (curious(mary) | calm(mary) | ((tall(mary) | ~curious(mary)) & (curious(mary) | ~tall(mary)))) & (((~curious(mary) | ~tall(mary)) & (curious(mary) | tall(mary))) | (~curious(mary) & ~calm(mary))) [flattening 57]
59. ! [X0] : (((brave(X0) & ~strong(X0)) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | (~brave(X0) | strong(X0)))) [nnf transformation 15]
60. ! [X0] : (((brave(X0) & ~strong(X0)) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ~brave(X0) | strong(X0))) [flattening 59]
69. ~old(X0) | strong(X0) | strong(X0) [cnf transformation 36]
70. ~old(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 36]
71. calm(X0) | strong(X0) | strong(X0) [cnf transformation 36]
72. calm(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 36]
100. old(X0) | brave(X0) | tall(X0) [cnf transformation 52]
105. humble(john) | strong(john) | creative(mary) [cnf transformation 54]
106. humble(john) | strong(john) | curious(mary) [cnf transformation 54]
110. ~happy(X0) | ~strong(X0) [cnf transformation 56]
111. ~strong(X0) | tall(X0) [cnf transformation 56]
116. ~curious(mary) | ~tall(mary) | ~calm(mary) [cnf transformation 58]
121. ~brave(X0) | ~creative(X0) | strong(X0) [cnf transformation 60]
132. happy(john) | ~strong(john) [cnf transformation 21]
137. ~humble(john) [cnf transformation 25]
140. ~old(X0) | strong(X0) [duplicate literal removal 69]
141. ~old(X0) | ~strong(X0) [duplicate literal removal 70]
142. calm(X0) | strong(X0) [duplicate literal removal 71]
143. ~strong(X0) | calm(X0) [duplicate literal removal 72]
144. calm(X0) [subsumption resolution 142,143]
145. ~old(X0) [subsumption resolution 140,141]
231. brave(X0) | tall(X0) [subsumption resolution 100,145]
248. 22 <=> curious(mary) [avatar definition]
252. 23 <=> strong(john) [avatar definition]
256. 24 <=> humble(john) [avatar definition]
261. 25 <=> creative(mary) [avatar definition]
263. creative(mary) <- (25) [avatar component clause 261]
265. 22 | 23 | 24 [avatar split clause 106,256,252,248]
266. 25 | 23 | 24 [avatar split clause 105,256,252,261]
270. 26 <=> tall(mary) [avatar definition]
272. ~tall(mary) <- (~26) [avatar component clause 270]
274. ~curious(mary) | ~tall(mary) [subsumption resolution 116,144]
275. ~26 | ~22 [avatar split clause 274,248,270]
288. ~strong(john) [subsumption resolution 132,110]
289. ~23 [avatar split clause 288,252]
310. ~24 [avatar split clause 137,256]
347. ~creative(X0) | strong(X0) | tall(X0) [resolution 121,231]
349. ~creative(X0) | tall(X0) [subsumption resolution 347,111]
376. tall(mary) <- (25) [resolution 349,263]
377. $false <- (25, ~26) [subsumption resolution 376,272]
378. ~25 | 26 [avatar contradiction clause 377]
379. $false [avatar sat refutation 265,266,275,289,310,378]
% SZS output end Proof for 6223252770718986295465684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either old or not tall then someone is both patient and not happy.
If someone is not wise or not quiet then john is both calm and rich and vice versa.
Everyone who is both not happy and brave is not old and vice versa.
Everyone who is either creative or not tall is both strong and not old.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Fred is not generous or not quiet.
Someone is both patient and not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous. | Susan is creative. | contradiction | (((old(alice)<~>~tall(alice)))=>(?[X]:((patient(X)&~happy(X)))))&
((?[X]:((~wise(X)|~quiet(X))))<=>((calm(john)&rich(john))))&
(![X]:((~happy(X)&brave(X))<=>~old(X)))&
(![X]:((creative(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
((~generous(fred)|~quiet(fred)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X)))) | creative(susan) | [
"p3",
"p5",
"p6",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3780450516482705462131678
% SZS output start Proof for 3780450516482705462131678
4. ! [X0] : ((creative(X0) <~> ~tall(X0)) => (~old(X0) & strong(X0))) [input p3]
6. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (~humble(X0) & ~brave(X0))) [input p6]
11. ! [X0] : (~brave(X0) <=> (funny(X0) | ~wise(X0))) [input p10]
15. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (~tall(X0) & ~funny(X0))) [input p14]
16. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p15]
25. creative(susan) [input hypothesis]
27. ! [X0] : ((~old(X0) & strong(X0)) | (creative(X0) <=> ~tall(X0))) [ennf transformation 4]
30. ! [X0] : ((~humble(X0) & ~brave(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 7]
47. ! [X0] : ((~old(X0) & strong(X0)) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0)))) [nnf transformation 27]
49. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | ~humble(X0)))) [nnf transformation 6]
50. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | ~humble(X0))) [flattening 49]
51. ! [X0] : ((~humble(X0) & ~brave(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 30]
61. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 11]
62. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | brave(X0))) [flattening 61]
63. ! [X0] : (((~old(X0) & ~funny(X0)) | (tall(X0) | funny(X0))) & ((~tall(X0) & ~funny(X0)) | (old(X0) | funny(X0)))) [nnf transformation 15]
64. ! [X0] : (((~old(X0) & ~funny(X0)) | tall(X0) | funny(X0)) & ((~tall(X0) & ~funny(X0)) | old(X0) | funny(X0))) [flattening 63]
65. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 16]
93. ~creative(X0) | ~tall(X0) | ~old(X0) [cnf transformation 47]
99. ~creative(X0) | humble(X0) | old(X0) [cnf transformation 50]
106. ~humble(X0) | brave(X0) | tall(X0) [cnf transformation 51]
126. ~funny(X0) | ~brave(X0) [cnf transformation 62]
134. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 64]
135. ~old(X0) | humble(X0) [cnf transformation 65]
136. ~humble(X0) | old(X0) [cnf transformation 65]
151. creative(susan) [cnf transformation 25]
201. 11 <=> funny(susan) [avatar definition]
203. funny(susan) <- (11) [avatar component clause 201]
324. 34 <=> tall(susan) [avatar definition]
329. ~tall(susan) | ~old(susan) [resolution 93,151]
378. humble(susan) | old(susan) [resolution 99,151]
379. humble(susan) [subsumption resolution 378,135]
417. brave(susan) | tall(susan) [resolution 379,106]
419. old(susan) [resolution 379,136]
678. tall(susan) | funny(susan) [resolution 419,134]
691. 11 | 34 [avatar split clause 678,324,201]
701. 70 <=> brave(susan) [avatar definition]
703. brave(susan) <- (70) [avatar component clause 701]
704. 34 | 70 [avatar split clause 417,701,324]
705. ~tall(susan) [subsumption resolution 329,419]
706. ~34 [avatar split clause 705,324]
707. ~brave(susan) <- (11) [resolution 203,126]
708. $false <- (11, 70) [subsumption resolution 707,703]
709. ~11 | ~70 [avatar contradiction clause 708]
710. $false [avatar sat refutation 691,704,706,709]
% SZS output end Proof for 3780450516482705462131678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not humble or calm and vice versa.
If alice is calm then alice is both wise and quiet.
Everyone who is both not curious and happy is either old or not strong.
Everyone who is both kind and curious is not curious and vice versa.
Everyone who is either not patient or funny is both patient and brave.
Everyone who is not generous is both not brave and not quiet.
If someone is quiet or not patient then someone is wise or not happy.
If lucy is both tall and not generous then someone is not generous and vice versa.
If susan is calm or not brave then someone is either quiet or kind and vice versa.
Everyone who is both brave and not generous is not generous or not happy and vice versa.
Everyone who is either not old or happy is both patient and not curious and vice versa.
Everyone who is both not funny and not calm is funny.
If someone is both not funny and not rich then someone is either patient or happy.
If mary is creative then susan is both old and calm and vice versa.
Everyone who is brave is not creative or not rich.
Everyone who is either tall or not rich is generous.
Someone is either curious or not wise.
Fred is not funny or not happy.
Someone is either not quiet or not old.
Fred is either not brave or not strong.
Someone is funny.
Paul is happy or not quiet.
Someone is happy.
Mary is either not quiet or creative. | Mary is not old. | entailment | (![X]:(~rich(X)<=>(~humble(X)<~>calm(X))))&
((calm(alice))=>((wise(alice)&quiet(alice))))&
(![X]:((~curious(X)&happy(X))=>(old(X)<~>~strong(X))))&
(![X]:((kind(X)&curious(X))<=>~curious(X)))&
(![X]:((~patient(X)<~>funny(X))=>(patient(X)&brave(X))))&
(![X]:(~generous(X)=>(~brave(X)&~quiet(X))))&
((?[X]:((quiet(X)|~patient(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(((tall(lucy)&~generous(lucy)))<=>(?[X]:(~generous(X))))&
(((calm(susan)|~brave(susan)))<=>(?[X]:((quiet(X)<~>kind(X)))))&
(![X]:((brave(X)&~generous(X))<=>(~generous(X)|~happy(X))))&
(![X]:((~old(X)<~>happy(X))<=>(patient(X)&~curious(X))))&
(![X]:((~funny(X)&~calm(X))=>funny(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((patient(X)<~>happy(X)))))&
((creative(mary))<=>((old(susan)&calm(susan))))&
(![X]:(brave(X)=>(~creative(X)|~rich(X))))&
(![X]:((tall(X)<~>~rich(X))=>generous(X)))&
(?[X]:((curious(X)<~>~wise(X))))&
((~funny(fred)|~happy(fred)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~brave(fred)<~>~strong(fred)))&
(?[X]:(funny(X)))&
((happy(paul)|~quiet(paul)))&
(?[X]:(happy(X)))&
((~quiet(mary)<~>creative(mary))) | ~old(mary) | [
"p3",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4850375565749626551943392
% SZS output start Proof for 4850375565749626551943392
4. ! [X0] : ((curious(X0) & kind(X0)) <=> ~curious(X0)) [input p3]
6. ! [X0] : (~generous(X0) => (~quiet(X0) & ~brave(X0))) [input p5]
10. ! [X0] : ((~generous(X0) & brave(X0)) <=> (~happy(X0) | ~generous(X0))) [input p9]
11. ! [X0] : ((~old(X0) <~> happy(X0)) <=> (~curious(X0) & patient(X0))) [input p10]
25. old(mary) [input hypothesis]
32. ! [X0] : ((~quiet(X0) & ~brave(X0)) | generous(X0)) [ennf transformation 6]
42. ! [X0] : (((curious(X0) & kind(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | ~kind(X0)))) [nnf transformation 4]
43. ! [X0] : (((curious(X0) & kind(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | ~kind(X0))) [flattening 42]
58. ! [X0] : (((~generous(X0) & brave(X0)) | (happy(X0) & generous(X0))) & ((~happy(X0) | ~generous(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 10]
59. ! [X0] : (((~generous(X0) & brave(X0)) | (happy(X0) & generous(X0))) & (~happy(X0) | ~generous(X0) | generous(X0) | ~brave(X0))) [flattening 58]
60. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 11]
61. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [flattening 60]
91. curious(X0) | curious(X0) [cnf transformation 43]
96. ~brave(X0) | generous(X0) [cnf transformation 32]
110. brave(X0) | generous(X0) [cnf transformation 59]
113. ~generous(X0) | happy(X0) [cnf transformation 59]
117. ~curious(X0) | ~old(X0) | ~happy(X0) [cnf transformation 61]
141. old(mary) [cnf transformation 25]
145. curious(X0) [duplicate literal removal 91]
178. 8 <=> ! [X0] : generous(X0) [avatar definition]
179. generous(X0) <- (8) [avatar component clause 178]
213. generous(X0) [subsumption resolution 110,96]
214. 8 [avatar split clause 213,178]
215. ~old(X0) | ~happy(X0) [subsumption resolution 117,145]
293. happy(X0) <- (8) [resolution 113,179]
300. ~happy(mary) [resolution 215,141]
301. $false <- (8) [subsumption resolution 300,293]
302. ~8 [avatar contradiction clause 301]
303. $false [avatar sat refutation 214,302]
% SZS output end Proof for 4850375565749626551943392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not 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. | Fred is not generous. | 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)) | ~generous(fred) | [] | null | 0 |
If fred is either patient or not rich then someone is tall or not funny.
Everyone who is not old is not curious.
If alice is either calm or quiet then susan is not funny or not strong.
Everyone who is both not rich and quiet is both not funny and old and vice versa.
Everyone who is quiet is either happy or not quiet and vice versa.
If mary is not brave or not funny then lucy is either creative or wise.
Everyone who is brave or not kind is either happy or not tall and vice versa.
Everyone who is both not tall and not old is either not wise or not brave and vice versa.
Everyone who is not wise is either brave or not tall.
If someone is both brave and not funny then someone is not old or not funny.
Everyone who is both wise and not rich is both not strong and not generous and vice versa.
If someone is not happy or happy then alice is patient or rich and vice versa.
Everyone who is rich is brave or not rich and vice versa.
Everyone who is either not generous or wise is wise or not brave and vice versa.
Everyone who is tall or not tall is either not funny or kind.
Everyone who is old is either kind or not kind and vice versa.
Someone is not humble or funny.
Lucy is both not quiet and funny.
Fred is old.
Susan is wise or not old.
Susan is not creative or not generous. | Fred is brave. | entailment | (((patient(fred)<~>~rich(fred)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:(~old(X)=>~curious(X)))&
(((calm(alice)<~>quiet(alice)))=>((~funny(susan)|~strong(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(~funny(X)&old(X))))&
(![X]:(quiet(X)<=>(happy(X)<~>~quiet(X))))&
(((~brave(mary)|~funny(mary)))=>((creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)|~kind(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~tall(X)&~old(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(brave(X)<~>~tall(X))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((wise(X)&~rich(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((~happy(X)|happy(X))))<=>((patient(alice)|rich(alice))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(wise(X)|~brave(X))))&
(![X]:((tall(X)|~tall(X))=>(~funny(X)<~>kind(X))))&
(![X]:(old(X)<=>(kind(X)<~>~kind(X))))&
(?[X]:((~humble(X)|funny(X))))&
((~quiet(lucy)&funny(lucy)))&
(old(fred))&
((wise(susan)|~old(susan)))&
((~creative(susan)|~generous(susan))) | brave(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8269386295873578221333734
% SZS output start Proof for 8269386295873578221333734
13. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p12]
22. ~brave(fred) [input hypothesis]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 13]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
101. ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
103. rich(X0) | rich(X0) [cnf transformation 57]
123. ~brave(fred) [cnf transformation 22]
128. ~rich(X0) | brave(X0) [duplicate literal removal 101]
129. rich(X0) [duplicate literal removal 103]
217. brave(X0) [subsumption resolution 128,129]
232. $false [subsumption resolution 123,217]
% SZS output end Proof for 8269386295873578221333734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or strong is strong or curious and vice versa. If someone is either not creative or curious then lucy is not generous or not brave. Everyone who is both not creative and not calm is either not kind or not quiet and vice versa. If someone is not old or not brave then someone is not quiet or funny. If someone is not generous or not wise then susan is either not kind or old. If someone is not curious or not humble then mary is both rich and patient. Everyone who is either patient or not strong is both not rich and funny and vice versa. Everyone who is either kind or funny is either not wise or old and vice versa. Everyone who is rich or not creative is patient or not funny. Everyone who is not wise is either not brave or kind. If lucy is both not wise and not calm then someone is both not humble and not strong. If alice is strong then alice is both calm and not tall. If paul is not strong or not kind then someone is wise. If someone is tall then fred is both tall and quiet. Everyone who is both quiet and brave is patient. Everyone who is both not creative and not quiet is not funny. Someone is both old and wise. Someone is strong or patient. Someone is either funny or creative. Someone is not creative or humble. Susan is funny. Someone is not wise. John is not humble. Someone is not creative. | Mary is not rich. | contradiction | (![X]:((happy(X)<~>strong(X))<=>(strong(X)|curious(X))))&
((?[X]:((~creative(X)<~>curious(X))))=>((~generous(lucy)|~brave(lucy))))&
(![X]:((~creative(X)&~calm(X))<=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:((~generous(X)|~wise(X))))=>((~kind(susan)<~>old(susan))))&
((?[X]:((~curious(X)|~humble(X))))=>((rich(mary)&patient(mary))))&
(![X]:((patient(X)<~>~strong(X))<=>(~rich(X)&funny(X))))&
(![X]:((kind(X)<~>funny(X))<=>(~wise(X)<~>old(X))))&
(![X]:((rich(X)|~creative(X))=>(patient(X)|~funny(X))))&
(![X]:(~wise(X)=>(~brave(X)<~>kind(X))))&
(((~wise(lucy)&~calm(lucy)))=>(?[X]:((~humble(X)&~strong(X)))))&
((strong(alice))=>((calm(alice)&~tall(alice))))&
(((~strong(paul)|~kind(paul)))=>(?[X]:(wise(X))))&
((?[X]:(tall(X)))=>((tall(fred)&quiet(fred))))&
(![X]:((quiet(X)&brave(X))=>patient(X)))&
(![X]:((~creative(X)&~quiet(X))=>~funny(X)))&
(?[X]:((old(X)&wise(X))))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:((~creative(X)|humble(X))))&
(funny(susan))&
(?[X]:(~wise(X)))&
(~humble(john))&
(?[X]:(~creative(X))) | ~rich(mary) | [
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1052265744483700132790510
% SZS output start Proof for 1052265744483700132790510
6. ? [X0] : (~humble(X0) | ~curious(X0)) => (patient(mary) & rich(mary)) [input p5]
23. ~humble(john) [input p22]
25. ~rich(mary) [input hypothesis]
31. (patient(mary) & rich(mary)) | ! [X0] : (humble(X0) & curious(X0)) [ennf transformation 6]
95. rich(mary) | humble(X0) [cnf transformation 31]
134. ~humble(john) [cnf transformation 23]
136. ~rich(mary) [cnf transformation 25]
191. 13 <=> ! [X0] : humble(X0) [avatar definition]
192. humble(X0) <- (13) [avatar component clause 191]
203. 16 <=> rich(mary) [avatar definition]
206. 13 | 16 [avatar split clause 95,203,191]
295. ~16 [avatar split clause 136,203]
296. $false <- (13) [resolution 192,134]
297. ~13 [avatar contradiction clause 296]
298. $false [avatar sat refutation 206,295,297]
% SZS output end Proof for 1052265744483700132790510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not brave is both rich and not brave and vice versa.
If someone is not tall or curious then someone is not funny.
Everyone who is not funny is either not tall or generous and vice versa.
If john is either old or generous then someone is both brave and humble and vice versa.
Everyone who is both strong and not strong is either not old or happy.
Everyone who is either generous or patient is quiet or not rich and vice versa.
If someone is either not happy or curious then paul is not generous or wise and vice versa.
If lucy is not calm then john is not generous or curious and vice versa.
Everyone who is not calm or not happy is either not kind or quiet and vice versa.
Everyone who is both not strong and quiet is strong and vice versa.
Everyone who is not rich is both not creative and not quiet and vice versa.
Everyone who is both not tall and strong is generous or not wise and vice versa.
If alice is wise then someone is either old or not patient.
If susan is both brave and not quiet then someone is old or calm and vice versa.
Everyone who is either rich or funny is creative and vice versa.
Everyone who is both strong and not generous is either not wise or not curious and vice versa.
Someone is either not calm or not happy.
Someone is not tall.
Someone is both humble and rich.
Fred is quiet or not quiet.
Someone is both not strong and calm.
Someone is both wise and not tall. | Lucy is kind. | contradiction | (![X]:((quiet(X)|~brave(X))<=>(rich(X)&~brave(X))))&
((?[X]:((~tall(X)|curious(X))))=>(?[X]:(~funny(X))))&
(![X]:(~funny(X)<=>(~tall(X)<~>generous(X))))&
(((old(john)<~>generous(john)))<=>(?[X]:((brave(X)&humble(X)))))&
(![X]:((strong(X)&~strong(X))=>(~old(X)<~>happy(X))))&
(![X]:((generous(X)<~>patient(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((~happy(X)<~>curious(X))))<=>((~generous(paul)|wise(paul))))&
((~calm(lucy))<=>((~generous(john)|curious(john))))&
(![X]:((~calm(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((~strong(X)&quiet(X))<=>strong(X)))&
(![X]:(~rich(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((~tall(X)&strong(X))<=>(generous(X)|~wise(X))))&
((wise(alice))=>(?[X]:((old(X)<~>~patient(X)))))&
(((brave(susan)&~quiet(susan)))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((rich(X)<~>funny(X))<=>creative(X)))&
(![X]:((strong(X)&~generous(X))<=>(~wise(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((humble(X)&rich(X))))&
((quiet(fred)|~quiet(fred)))&
(?[X]:((~strong(X)&calm(X))))&
(?[X]:((wise(X)&~tall(X)))) | kind(lucy) | [
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1615930532249640238538857
% SZS output start Proof for 1615930532249640238538857
8. ~calm(lucy) <=> (curious(john) | ~generous(john)) [input p7]
9. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> strong(X0)) [input p9]
12. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~wise(X0) | generous(X0))) [input p11]
23. kind(lucy) [input hypothesis]
47. (~calm(lucy) | (~curious(john) & generous(john))) & ((curious(john) | ~generous(john)) | calm(lucy)) [nnf transformation 8]
48. (~calm(lucy) | (~curious(john) & generous(john))) & (curious(john) | ~generous(john) | calm(lucy)) [flattening 47]
49. ! [X0] : (((~happy(X0) | ~calm(X0)) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (happy(X0) & calm(X0)))) [nnf transformation 9]
50. ! [X0] : ((~happy(X0) | ~calm(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (happy(X0) & calm(X0)))) [flattening 49]
51. ! [X0] : (((quiet(X0) & ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~quiet(X0) | strong(X0)))) [nnf transformation 10]
52. ! [X0] : (((quiet(X0) & ~strong(X0)) | ~strong(X0)) & (strong(X0) | ~quiet(X0) | strong(X0))) [flattening 51]
55. ! [X0] : (((strong(X0) & ~tall(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 12]
56. ! [X0] : (((strong(X0) & ~tall(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | ~strong(X0) | tall(X0))) [flattening 55]
111. ~calm(lucy) | generous(john) [cnf transformation 48]
113. ~kind(X0) | quiet(X0) | calm(X0) [cnf transformation 50]
119. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 52]
120. ~strong(X0) | ~strong(X0) [cnf transformation 52]
128. strong(X0) | ~generous(X0) [cnf transformation 56]
157. kind(lucy) [cnf transformation 23]
158. strong(X0) | ~quiet(X0) [duplicate literal removal 119]
159. ~strong(X0) [duplicate literal removal 120]
180. 6 <=> generous(john) [avatar definition]
181. generous(john) <- (6) [avatar component clause 180]
230. 16 <=> calm(lucy) [avatar definition]
234. 6 | ~16 [avatar split clause 111,230,180]
236. ~quiet(X0) [subsumption resolution 158,159]
239. ~generous(X0) [subsumption resolution 128,159]
313. quiet(lucy) | calm(lucy) [resolution 113,157]
314. calm(lucy) [subsumption resolution 313,236]
317. 16 [avatar split clause 314,230]
320. $false <- (6) [subsumption resolution 181,239]
321. ~6 [avatar contradiction clause 320]
322. $false [avatar sat refutation 234,317,321]
% SZS output end Proof for 1615930532249640238538857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both not kind and not funny and vice versa. Everyone who is both not old and not quiet is either not tall or funny. If someone is tall or not curious then mary is not humble. Everyone who is calm or not brave is not funny and vice versa. Everyone who is quiet is curious and vice versa. If someone is not strong or humble then someone is both not happy and not quiet and vice versa. Everyone who is strong or not wise is either quiet or not generous. Everyone who is creative or not calm is either old or not old. Everyone who is humble is both not strong and not humble and vice versa. Everyone who is both old and strong is both funny and brave and vice versa. If someone is either wise or not rich then someone is both generous and not creative. Everyone who is not happy is not brave. If someone is either not creative or patient then someone is not humble and vice versa. If lucy is either not funny or wise then susan is either not patient or strong. If alice is not curious then susan is not creative or not humble. If someone is quiet or not tall then mary is calm. Someone is either not calm or not happy. Alice is either old or not funny. Susan is not happy or calm. Mary is either quiet or not calm. Someone is patient. Someone is not quiet or strong. Someone is both tall and strong. Someone is funny. | Susan is funny. | contradiction | (![X]:(~old(X)<=>(~kind(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))=>(~tall(X)<~>funny(X))))&
((?[X]:((tall(X)|~curious(X))))=>(~humble(mary)))&
(![X]:((calm(X)|~brave(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>curious(X)))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((strong(X)|~wise(X))=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)|~calm(X))=>(old(X)<~>~old(X))))&
(![X]:(humble(X)<=>(~strong(X)&~humble(X))))&
(![X]:((old(X)&strong(X))<=>(funny(X)&brave(X))))&
((?[X]:((wise(X)<~>~rich(X))))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:(~happy(X)=>~brave(X)))&
((?[X]:((~creative(X)<~>patient(X))))<=>(?[X]:(~humble(X))))&
(((~funny(lucy)<~>wise(lucy)))=>((~patient(susan)<~>strong(susan))))&
((~curious(alice))=>((~creative(susan)|~humble(susan))))&
((?[X]:((quiet(X)|~tall(X))))=>(calm(mary)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((old(alice)<~>~funny(alice)))&
((~happy(susan)|calm(susan)))&
((quiet(mary)<~>~calm(mary)))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:(funny(X))) | funny(susan) | [
"p3",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7784127115170201627985721
% SZS output start Proof for 7784127115170201627985721
4. ! [X0] : ((~brave(X0) | calm(X0)) <=> ~funny(X0)) [input p3]
12. ! [X0] : (~happy(X0) => ~brave(X0)) [input p11]
19. calm(susan) | ~happy(susan) [input p18]
25. funny(susan) [input hypothesis]
35. ! [X0] : (~brave(X0) | happy(X0)) [ennf transformation 12]
43. ! [X0] : (((~brave(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (brave(X0) & ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : ((~brave(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (brave(X0) & ~calm(X0)))) [flattening 43]
87. ~calm(X0) | ~funny(X0) [cnf transformation 44]
88. ~funny(X0) | brave(X0) [cnf transformation 44]
116. ~brave(X0) | happy(X0) [cnf transformation 35]
132. calm(susan) | ~happy(susan) [cnf transformation 19]
140. funny(susan) [cnf transformation 25]
296. 35 <=> happy(susan) [avatar definition]
300. 36 <=> calm(susan) [avatar definition]
302. calm(susan) <- (36) [avatar component clause 300]
303. ~35 | 36 [avatar split clause 132,300,296]
323. brave(susan) [resolution 88,140]
326. happy(susan) [resolution 116,323]
329. 35 [avatar split clause 326,296]
330. ~funny(susan) <- (36) [resolution 302,87]
331. $false <- (36) [subsumption resolution 330,140]
332. ~36 [avatar contradiction clause 331]
333. $false [avatar sat refutation 303,329,332]
% SZS output end Proof for 7784127115170201627985721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not wise is brave and vice versa.
Everyone who is rich is quiet or kind.
If someone is either not funny or not strong then fred is not old and vice versa.
Everyone who is both generous and quiet is either humble or not humble.
If someone is both not tall and happy then lucy is not patient or quiet.
Everyone who is both not patient and not rich is strong.
Everyone who is both rich and strong is both not funny and wise and vice versa.
Everyone who is both not creative and humble is either not calm or funny.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Everyone who is not quiet is not kind.
Everyone who is not quiet or patient is either not calm or brave and vice versa.
If someone is rich then someone is either creative or generous and vice versa.
If lucy is not curious then someone is both wise and not strong and vice versa.
If someone is curious or not creative then someone is not wise or not funny and vice versa.
If someone is quiet or funny then someone is not quiet or tall and vice versa.
Lucy is either not quiet or not tall.
Fred is rich.
Alice is either not funny or wise.
Someone is both creative and rich.
Someone is either not brave or wise.
Someone is patient.
Alice is not wise.
Someone is both not brave and not old. | Fred is not quiet. | contradiction | (![X]:((strong(X)|~wise(X))<=>brave(X)))&
(![X]:(rich(X)=>(quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(~old(fred)))&
(![X]:((generous(X)&quiet(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~tall(X)&happy(X))))=>((~patient(lucy)|quiet(lucy))))&
(![X]:((~patient(X)&~rich(X))=>strong(X)))&
(![X]:((rich(X)&strong(X))<=>(~funny(X)&wise(X))))&
(![X]:((~creative(X)&humble(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((~quiet(X)|patient(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~curious(lucy))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((curious(X)|~creative(X))))<=>(?[X]:((~wise(X)|~funny(X)))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(fred))&
((~funny(alice)<~>wise(alice)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(patient(X)))&
(~wise(alice))&
(?[X]:((~brave(X)&~old(X)))) | ~quiet(fred) | [
"p1",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 808174181085874787888530
% SZS output start Proof for 808174181085874787888530
2. ! [X0] : (rich(X0) => (kind(X0) | quiet(X0))) [input p1]
11. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p10]
18. rich(fred) [input p17]
25. ~quiet(fred) [input hypothesis]
31. ! [X0] : ((kind(X0) | quiet(X0)) | ~rich(X0)) [ennf transformation 2]
32. ! [X0] : (kind(X0) | quiet(X0) | ~rich(X0)) [flattening 31]
40. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 11]
88. ~rich(X0) | quiet(X0) | kind(X0) [cnf transformation 32]
109. ~kind(X0) | quiet(X0) [cnf transformation 40]
133. rich(fred) [cnf transformation 18]
144. ~quiet(fred) [cnf transformation 25]
318. quiet(fred) | kind(fred) [resolution 88,133]
321. kind(fred) [subsumption resolution 318,144]
324. quiet(fred) [resolution 321,109]
325. $false [subsumption resolution 324,144]
% SZS output end Proof for 808174181085874787888530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet and not creative is tall or not strong and vice versa.
If fred is creative then susan is not generous.
If lucy is both rich and curious then john is strong and vice versa.
Everyone who is either creative or not patient is old or not brave.
Everyone who is calm or not humble is either creative or not happy.
Everyone who is both not rich and curious is both not patient and not quiet.
Everyone who is not quiet or old is humble.
Everyone who is both rich and brave is either strong or not strong and vice versa.
Everyone who is either quiet or strong is both not patient and happy.
If alice is either funny or rich then alice is not quiet and vice versa.
Everyone who is calm is generous and vice versa.
If mary is both strong and not funny then someone is tall and vice versa.
If someone is both kind and brave then mary is not rich or generous and vice versa.
If mary is either quiet or not quiet then mary is not calm and vice versa.
If someone is calm or not happy then john is both not generous and not patient and vice versa.
If someone is both old and not quiet then someone is funny.
John is creative.
Someone is either not brave or patient.
Alice is either happy or tall.
John is either not humble or kind.
Someone is not curious or humble.
Someone is calm.
Susan is either not funny or wise. | John is not humble. | entailment | (![X]:((~quiet(X)&~creative(X))<=>(tall(X)|~strong(X))))&
((creative(fred))=>(~generous(susan)))&
(((rich(lucy)&curious(lucy)))<=>(strong(john)))&
(![X]:((creative(X)<~>~patient(X))=>(old(X)|~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(creative(X)<~>~happy(X))))&
(![X]:((~rich(X)&curious(X))=>(~patient(X)&~quiet(X))))&
(![X]:((~quiet(X)|old(X))=>humble(X)))&
(![X]:((rich(X)&brave(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~patient(X)&happy(X))))&
(((funny(alice)<~>rich(alice)))<=>(~quiet(alice)))&
(![X]:(calm(X)<=>generous(X)))&
(((strong(mary)&~funny(mary)))<=>(?[X]:(tall(X))))&
((?[X]:((kind(X)&brave(X))))<=>((~rich(mary)|generous(mary))))&
(((quiet(mary)<~>~quiet(mary)))<=>(~calm(mary)))&
((?[X]:((calm(X)|~happy(X))))<=>((~generous(john)&~patient(john))))&
((?[X]:((old(X)&~quiet(X))))=>(?[X]:(funny(X))))&
(creative(john))&
(?[X]:((~brave(X)<~>patient(X))))&
((happy(alice)<~>tall(alice)))&
((~humble(john)<~>kind(john)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:(calm(X)))&
((~funny(susan)<~>wise(susan))) | ~humble(john) | [
"p7",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3409050605065310574259502
% SZS output start Proof for 3409050605065310574259502
8. ! [X0] : ((brave(X0) & rich(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> generous(X0)) [input p10]
13. ? [X0] : (brave(X0) & kind(X0)) <=> (generous(mary) | ~rich(mary)) [input p12]
14. (quiet(mary) <~> ~quiet(mary)) <=> ~calm(mary) [input p13]
20. ~humble(john) <~> kind(john) [input p19]
24. humble(john) [input hypothesis]
41. ! [X0] : (((brave(X0) & rich(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~brave(X0) | ~rich(X0)))) [nnf transformation 8]
42. ! [X0] : (((brave(X0) & rich(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~brave(X0) | ~rich(X0))) [flattening 41]
45. ! [X0] : ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))) [nnf transformation 11]
51. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & ((generous(mary) | ~rich(mary)) | ! [X0] : (~brave(X0) | ~kind(X0))) [nnf transformation 13]
52. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X0] : (~brave(X0) | ~kind(X0))) [flattening 51]
53. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X1] : (~brave(X1) | ~kind(X1))) [rectify 52]
54. ? [X0] : (brave(X0) & kind(X0)) => (brave(sK1) & kind(sK1)) [choice axiom]
55. ((brave(sK1) & kind(sK1)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X1] : (~brave(X1) | ~kind(X1))) [skolemisation 53,54]
56. (((quiet(mary) | ~quiet(mary)) & (~quiet(mary) | quiet(mary))) | calm(mary)) & (~calm(mary) | ((quiet(mary) | quiet(mary)) & (~quiet(mary) | ~quiet(mary)))) [nnf transformation 14]
69. (~kind(john) | humble(john)) & (kind(john) | ~humble(john)) [nnf transformation 20]
96. rich(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
97. rich(X0) | strong(X0) | strong(X0) [cnf transformation 42]
98. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
99. brave(X0) | strong(X0) | strong(X0) [cnf transformation 42]
109. ~generous(X0) | calm(X0) [cnf transformation 45]
113. generous(mary) | ~rich(mary) | ~brave(X1) | ~kind(X1) [cnf transformation 55]
118. ~calm(mary) | ~quiet(mary) | ~quiet(mary) [cnf transformation 56]
119. ~calm(mary) | quiet(mary) | quiet(mary) [cnf transformation 56]
133. kind(john) | ~humble(john) [cnf transformation 69]
139. humble(john) [cnf transformation 24]
140. ~calm(mary) | ~quiet(mary) [duplicate literal removal 118]
141. ~calm(mary) | quiet(mary) [duplicate literal removal 119]
142. rich(X0) | ~strong(X0) [duplicate literal removal 96]
143. rich(X0) | strong(X0) [duplicate literal removal 97]
144. brave(X0) | ~strong(X0) [duplicate literal removal 98]
145. brave(X0) | strong(X0) [duplicate literal removal 99]
170. brave(X0) [subsumption resolution 144,145]
171. rich(X0) [subsumption resolution 142,143]
203. 12 <=> generous(mary) [avatar definition]
204. generous(mary) <- (12) [avatar component clause 203]
211. generous(mary) | ~brave(X1) | ~kind(X1) [subsumption resolution 113,171]
212. generous(mary) | ~kind(X1) [subsumption resolution 211,170]
214. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
215. ~kind(X1) <- (14) [avatar component clause 214]
216. 14 | 12 [avatar split clause 212,203,214]
218. 15 <=> quiet(mary) [avatar definition]
222. 16 <=> calm(mary) [avatar definition]
224. ~calm(mary) <- (~16) [avatar component clause 222]
225. 15 | ~16 [avatar split clause 141,222,218]
226. ~15 | ~16 [avatar split clause 140,222,218]
274. 27 <=> humble(john) [avatar definition]
278. 28 <=> kind(john) [avatar definition]
279. kind(john) <- (28) [avatar component clause 278]
282. ~27 | 28 [avatar split clause 133,278,274]
302. 27 [avatar split clause 139,274]
308. calm(mary) <- (12) [resolution 109,204]
310. $false <- (12, ~16) [subsumption resolution 308,224]
311. ~12 | 16 [avatar contradiction clause 310]
313. $false <- (14, 28) [resolution 215,279]
314. ~14 | ~28 [avatar contradiction clause 313]
316. $false [avatar sat refutation 216,225,226,282,302,311,314]
% SZS output end Proof for 3409050605065310574259502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If mary is kind or strong then fred is curious.
Everyone who is either not creative or strong is creative.
If lucy is both quiet and not generous then someone is not rich.
If paul is not happy then someone is quiet and vice versa.
Everyone who is not rich is both generous and rich and vice versa.
Everyone who is not rich is both creative and not old and vice versa.
Everyone who is strong or kind is either not curious or patient and vice versa.
If lucy is both not quiet and wise then someone is either not tall or not calm and vice versa.
Everyone who is patient or not calm is not kind.
If mary is not rich then mary is not happy or not patient and vice versa.
Everyone who is both quiet and not rich is both not funny and rich.
Everyone who is either not strong or patient is both not funny and not strong.
If fred is patient or happy then lucy is rich or not tall and vice versa.
If paul is quiet then alice is creative and vice versa.
If someone is not funny then paul is both not humble and not wise.
If alice is not patient then someone is both not generous and not humble.
Alice is both curious and happy.
Fred is either funny or not old.
John is tall or not calm.
Paul is either creative or not tall.
Mary is both quiet and brave.
Lucy is curious or not generous.
Someone is happy. | Paul is not wise. | entailment | (((kind(mary)|strong(mary)))=>(curious(fred)))&
(![X]:((~creative(X)<~>strong(X))=>creative(X)))&
(((quiet(lucy)&~generous(lucy)))=>(?[X]:(~rich(X))))&
((~happy(paul))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>(generous(X)&rich(X))))&
(![X]:(~rich(X)<=>(creative(X)&~old(X))))&
(![X]:((strong(X)|kind(X))<=>(~curious(X)<~>patient(X))))&
(((~quiet(lucy)&wise(lucy)))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((patient(X)|~calm(X))=>~kind(X)))&
((~rich(mary))<=>((~happy(mary)|~patient(mary))))&
(![X]:((quiet(X)&~rich(X))=>(~funny(X)&rich(X))))&
(![X]:((~strong(X)<~>patient(X))=>(~funny(X)&~strong(X))))&
(((patient(fred)|happy(fred)))<=>((rich(lucy)|~tall(lucy))))&
((quiet(paul))<=>(creative(alice)))&
((?[X]:(~funny(X)))=>((~humble(paul)&~wise(paul))))&
((~patient(alice))=>(?[X]:((~generous(X)&~humble(X)))))&
((curious(alice)&happy(alice)))&
((funny(fred)<~>~old(fred)))&
((tall(john)|~calm(john)))&
((creative(paul)<~>~tall(paul)))&
((quiet(mary)&brave(mary)))&
((curious(lucy)|~generous(lucy)))&
(?[X]:(happy(X))) | ~wise(paul) | [
"p6",
"p8",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5409614074424288072399095
% SZS output start Proof for 5409614074424288072399095
7. ! [X0] : ((kind(X0) | strong(X0)) <=> (~curious(X0) <~> patient(X0))) [input p6]
9. ! [X0] : ((~calm(X0) | patient(X0)) => ~kind(X0)) [input p8]
12. ! [X0] : ((~strong(X0) <~> patient(X0)) => (~strong(X0) & ~funny(X0))) [input p11]
15. ? [X0] : ~funny(X0) => (~wise(paul) & ~humble(paul)) [input p14]
17. happy(alice) & curious(alice) [input p16]
24. wise(paul) [input hypothesis]
27. ? [X0] : ~funny(X0) => ~wise(paul) [pure predicate removal 15]
32. ! [X0] : (~kind(X0) | (calm(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : ((~strong(X0) & ~funny(X0)) | (~strong(X0) <=> patient(X0))) [ennf transformation 12]
36. ~wise(paul) | ! [X0] : funny(X0) [ennf transformation 27]
49. ! [X0] : (((kind(X0) | strong(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~kind(X0) & ~strong(X0)))) [nnf transformation 7]
50. ! [X0] : ((kind(X0) | strong(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (~kind(X0) & ~strong(X0)))) [flattening 49]
58. ! [X0] : ((~strong(X0) & ~funny(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) [nnf transformation 35]
81. ~curious(X0) | patient(X0) | ~strong(X0) [cnf transformation 50]
86. ~patient(X0) | strong(X0) | ~curious(X0) | kind(X0) [cnf transformation 50]
93. ~patient(X0) | ~kind(X0) [cnf transformation 32]
100. ~funny(X0) | patient(X0) | strong(X0) [cnf transformation 58]
103. ~strong(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 58]
110. ~wise(paul) | funny(X0) [cnf transformation 36]
112. curious(alice) [cnf transformation 17]
122. wise(paul) [cnf transformation 24]
123. ~patient(X0) | ~strong(X0) [duplicate literal removal 103]
221. 20 <=> ! [X0] : funny(X0) [avatar definition]
222. funny(X0) <- (20) [avatar component clause 221]
224. 21 <=> wise(paul) [avatar definition]
227. 20 | ~21 [avatar split clause 110,224,221]
271. 21 [avatar split clause 122,224]
284. patient(alice) | ~strong(alice) [resolution 81,112]
287. ~strong(alice) [subsumption resolution 284,123]
295. patient(X0) | strong(X0) <- (20) [resolution 100,222]
299. ~kind(X3) | strong(X3) <- (20) [resolution 295,93]
309. strong(X1) | ~curious(X1) | kind(X1) | strong(X1) <- (20) [resolution 86,295]
310. strong(X1) | ~curious(X1) | kind(X1) <- (20) [duplicate literal removal 309]
317. ~curious(X1) | strong(X1) <- (20) [subsumption resolution 310,299]
318. strong(alice) <- (20) [resolution 317,112]
319. $false <- (20) [subsumption resolution 318,287]
320. ~20 [avatar contradiction clause 319]
321. $false [avatar sat refutation 227,271,320]
% SZS output end Proof for 5409614074424288072399095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not curious then someone is creative or old and vice versa.
If someone is brave then john is kind or brave.
Everyone who is both not old and old is not quiet and vice versa.
Everyone who is both not happy and generous is both not humble and creative and vice versa.
Everyone who is generous is funny or humble.
If someone is not rich then someone is not wise or not patient and vice versa.
If mary is either not happy or not funny then someone is both patient and not wise and vice versa.
Everyone who is funny or generous is both curious and calm and vice versa.
If lucy is either not strong or not curious then fred is happy.
Everyone who is not rich or not happy is tall or creative.
If alice is both old and patient then susan is either kind or calm and vice versa.
Everyone who is both not kind and not happy is not curious or tall.
Everyone who is both curious and not funny is either wise or not strong and vice versa.
Everyone who is either quiet or calm is quiet and vice versa.
Everyone who is either generous or brave is either patient or not kind and vice versa.
Everyone who is either not quiet or not strong is either curious or tall and vice versa.
Susan is not strong.
Susan is both not rich and brave.
Fred is generous or not strong.
Paul is rich or kind.
Someone is not tall.
Paul is humble or strong. | Mary is not strong. | neutral | ((~curious(fred))<=>(?[X]:((creative(X)|old(X)))))&
((?[X]:(brave(X)))=>((kind(john)|brave(john))))&
(![X]:((~old(X)&old(X))<=>~quiet(X)))&
(![X]:((~happy(X)&generous(X))<=>(~humble(X)&creative(X))))&
(![X]:(generous(X)=>(funny(X)|humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)|~patient(X)))))&
(((~happy(mary)<~>~funny(mary)))<=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((funny(X)|generous(X))<=>(curious(X)&calm(X))))&
(((~strong(lucy)<~>~curious(lucy)))=>(happy(fred)))&
(![X]:((~rich(X)|~happy(X))=>(tall(X)|creative(X))))&
(((old(alice)&patient(alice)))<=>((kind(susan)<~>calm(susan))))&
(![X]:((~kind(X)&~happy(X))=>(~curious(X)|tall(X))))&
(![X]:((curious(X)&~funny(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>calm(X))<=>quiet(X)))&
(![X]:((generous(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(curious(X)<~>tall(X))))&
(~strong(susan))&
((~rich(susan)&brave(susan)))&
((generous(fred)|~strong(fred)))&
((rich(paul)|kind(paul)))&
(?[X]:(~tall(X)))&
((humble(paul)|strong(paul))) | ~strong(mary) | [] | null | 0 |
Everyone who is both rich and patient is curious or not patient. Everyone who is tall or brave is brave and vice versa. Everyone who is both not quiet and calm is either patient or happy. Everyone who is not generous or not quiet is not kind. Everyone who is quiet is both not quiet and strong. Everyone who is not wise is both not wise and rich. If someone is tall or not wise then mary is either brave or curious and vice versa. Everyone who is both not wise and curious is both not curious and not rich. If fred is brave or kind then alice is both kind and old and vice versa. If someone is not humble then john is both kind and not patient and vice versa. Everyone who is not wise is strong or humble and vice versa. If someone is either creative or humble then someone is not curious or not happy. If john is not creative or kind then lucy is either humble or not old and vice versa. Everyone who is generous or humble is either not calm or happy and vice versa. Everyone who is either not curious or old is both not old and not humble and vice versa. Everyone who is not funny or creative is patient or kind and vice versa. Someone is not kind. Someone is tall. John is not creative or not wise. Susan is not tall. | Fred is not curious. | entailment | (![X]:((rich(X)&patient(X))=>(curious(X)|~patient(X))))&
(![X]:((tall(X)|brave(X))<=>brave(X)))&
(![X]:((~quiet(X)&calm(X))=>(patient(X)<~>happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>~kind(X)))&
(![X]:(quiet(X)=>(~quiet(X)&strong(X))))&
(![X]:(~wise(X)=>(~wise(X)&rich(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((brave(mary)<~>curious(mary))))&
(![X]:((~wise(X)&curious(X))=>(~curious(X)&~rich(X))))&
(((brave(fred)|kind(fred)))<=>((kind(alice)&old(alice))))&
((?[X]:(~humble(X)))<=>((kind(john)&~patient(john))))&
(![X]:(~wise(X)<=>(strong(X)|humble(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(((~creative(john)|kind(john)))<=>((humble(lucy)<~>~old(lucy))))&
(![X]:((generous(X)|humble(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)&~humble(X))))&
(![X]:((~funny(X)|creative(X))<=>(patient(X)|kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(tall(X)))&
((~creative(john)|~wise(john)))&
(~tall(susan)) | ~curious(fred) | [
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1634102358468193070607967
% SZS output start Proof for 1634102358468193070607967
4. ! [X0] : ((~quiet(X0) | ~generous(X0)) => ~kind(X0)) [input p3]
5. ! [X0] : (quiet(X0) => (strong(X0) & ~quiet(X0))) [input p4]
6. ! [X0] : (~wise(X0) => (rich(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((curious(X0) & ~wise(X0)) => (~rich(X0) & ~curious(X0))) [input p7]
10. ? [X0] : ~humble(X0) <=> (~patient(john) & kind(john)) [input p9]
11. ! [X0] : (~wise(X0) <=> (humble(X0) | strong(X0))) [input p10]
21. curious(fred) [input hypothesis]
27. ! [X0] : (~kind(X0) | (quiet(X0) & generous(X0))) [ennf transformation 4]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~quiet(X0)) [ennf transformation 5]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | wise(X0)) [ennf transformation 6]
30. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~curious(X0) | wise(X0))) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & ~curious(X0)) | ~curious(X0) | wise(X0)) [flattening 30]
42. (? [X0] : ~humble(X0) | (patient(john) | ~kind(john))) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [nnf transformation 10]
43. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [flattening 42]
44. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [rectify 43]
45. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
46. (~humble(sK1) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [skolemisation 44,45]
47. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | wise(X0))) [nnf transformation 11]
48. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | wise(X0))) [flattening 47]
72. ~kind(X0) | quiet(X0) [cnf transformation 27]
73. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
76. wise(X0) | rich(X0) [cnf transformation 29]
84. ~rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
90. kind(john) | humble(X1) [cnf transformation 46]
95. ~humble(X0) | ~wise(X0) [cnf transformation 48]
124. curious(fred) [cnf transformation 21]
128. ~quiet(X0) [duplicate literal removal 73]
158. ~curious(X0) | wise(X0) [subsumption resolution 84,76]
181. 11 <=> kind(john) [avatar definition]
182. kind(john) <- (11) [avatar component clause 181]
194. 14 <=> ! [X1] : humble(X1) [avatar definition]
195. humble(X1) <- (14) [avatar component clause 194]
197. 14 | 11 [avatar split clause 90,181,194]
239. quiet(john) <- (11) [resolution 72,182]
240. $false <- (11) [subsumption resolution 239,128]
241. ~11 [avatar contradiction clause 240]
249. ~wise(X0) <- (14) [resolution 95,195]
252. wise(fred) [resolution 158,124]
253. $false <- (14) [subsumption resolution 252,249]
254. ~14 [avatar contradiction clause 253]
255. $false [avatar sat refutation 197,241,254]
% SZS output end Proof for 1634102358468193070607967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both funny and not patient.
Everyone who is either humble or rich is quiet and vice versa.
If fred is both rich and curious then mary is not old or calm and vice versa.
Everyone who is old is either not strong or wise and vice versa.
Everyone who is patient or generous is funny or rich and vice versa.
Everyone who is not wise is either not quiet or humble and vice versa.
Everyone who is both happy and not old is not funny or generous.
If someone is not patient or not creative then someone is calm and vice versa.
If someone is both not creative and generous then someone is wise.
Everyone who is either generous or rich is either not tall or not generous and vice versa.
If paul is either not kind or wise then someone is not funny and vice versa.
Everyone who is not rich or not wise is curious and vice versa.
If someone is both not funny and not humble then lucy is both strong and not calm and vice versa.
Everyone who is either calm or old is old and vice versa.
If john is either tall or funny then john is not patient or strong.
If someone is not creative or humble then john is creative or not strong.
Someone is not quiet.
Someone is kind or generous.
Someone is brave.
Someone is both creative and generous.
Someone is not wise or not strong.
Someone is not generous. | John is calm. | contradiction | (![X]:(~kind(X)=>(funny(X)&~patient(X))))&
(![X]:((humble(X)<~>rich(X))<=>quiet(X)))&
(((rich(fred)&curious(fred)))<=>((~old(mary)|calm(mary))))&
(![X]:(old(X)<=>(~strong(X)<~>wise(X))))&
(![X]:((patient(X)|generous(X))<=>(funny(X)|rich(X))))&
(![X]:(~wise(X)<=>(~quiet(X)<~>humble(X))))&
(![X]:((happy(X)&~old(X))=>(~funny(X)|generous(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>~generous(X))))&
(((~kind(paul)<~>wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)|~wise(X))<=>curious(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>((strong(lucy)&~calm(lucy))))&
(![X]:((calm(X)<~>old(X))<=>old(X)))&
(((tall(john)<~>funny(john)))=>((~patient(john)|strong(john))))&
((?[X]:((~creative(X)|humble(X))))=>((creative(john)|~strong(john))))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:(~generous(X))) | calm(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3144433973663871880740412
% SZS output start Proof for 3144433973663871880740412
14. ! [X0] : ((calm(X0) <~> old(X0)) <=> old(X0)) [input p13]
23. calm(john) [input hypothesis]
61. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ~old(X0)) & (old(X0) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 14]
119. old(X0) | old(X0) | ~calm(X0) [cnf transformation 61]
122. ~old(X0) | ~calm(X0) | ~old(X0) [cnf transformation 61]
133. calm(john) [cnf transformation 23]
134. old(X0) | ~calm(X0) [duplicate literal removal 119]
135. ~old(X0) | ~calm(X0) [duplicate literal removal 122]
162. 5 <=> ! [X1] : ~calm(X1) [avatar definition]
163. ~calm(X1) <- (5) [avatar component clause 162]
237. ~calm(X0) [subsumption resolution 134,135]
238. 5 [avatar split clause 237,162]
284. $false <- (5) [resolution 163,133]
285. ~5 [avatar contradiction clause 284]
286. $false [avatar sat refutation 238,285]
% SZS output end Proof for 3144433973663871880740412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not wise is not kind and vice versa. If john is calm then lucy is both humble and kind. If someone is rich or not quiet then someone is old and vice versa. Everyone who is either not rich or not curious is either not old or rich and vice versa. Everyone who is curious is rich and vice versa. Everyone who is both strong and not patient is rich. If fred is both patient and quiet then fred is not brave or not strong. Everyone who is not generous is not creative or curious and vice versa. Everyone who is strong is both not strong and not old. Everyone who is not creative or kind is either happy or kind. If lucy is either brave or not calm then alice is funny and vice versa. Everyone who is either creative or patient is not quiet and vice versa. Everyone who is either generous or not happy is not humble. If someone is both not generous and quiet then someone is kind or not funny and vice versa. Everyone who is both not funny and not quiet is not calm. If someone is not happy or not patient then alice is curious or not rich. Alice is not humble or funny. Fred is either tall or not humble. Fred is both old and kind. Someone is happy or not wise. Someone is kind. Paul is either not brave or old. Someone is either not happy or rich. Someone is both not generous and humble. | Paul is strong. | contradiction | (![X]:((curious(X)<~>~wise(X))<=>~kind(X)))&
((calm(john))=>((humble(lucy)&kind(lucy))))&
((?[X]:((rich(X)|~quiet(X))))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)<~>~curious(X))<=>(~old(X)<~>rich(X))))&
(![X]:(curious(X)<=>rich(X)))&
(![X]:((strong(X)&~patient(X))=>rich(X)))&
(((patient(fred)&quiet(fred)))=>((~brave(fred)|~strong(fred))))&
(![X]:(~generous(X)<=>(~creative(X)|curious(X))))&
(![X]:(strong(X)=>(~strong(X)&~old(X))))&
(![X]:((~creative(X)|kind(X))=>(happy(X)<~>kind(X))))&
(((brave(lucy)<~>~calm(lucy)))<=>(funny(alice)))&
(![X]:((creative(X)<~>patient(X))<=>~quiet(X)))&
(![X]:((generous(X)<~>~happy(X))=>~humble(X)))&
((?[X]:((~generous(X)&quiet(X))))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~funny(X)&~quiet(X))=>~calm(X)))&
((?[X]:((~happy(X)|~patient(X))))=>((curious(alice)|~rich(alice))))&
((~humble(alice)|funny(alice)))&
((tall(fred)<~>~humble(fred)))&
((old(fred)&kind(fred)))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:(kind(X)))&
((~brave(paul)<~>old(paul)))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:((~generous(X)&humble(X)))) | strong(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2263940149140126230521398
% SZS output start Proof for 2263940149140126230521398
9. ! [X0] : (strong(X0) => (~old(X0) & ~strong(X0))) [input p8]
25. strong(paul) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~strong(X0)) | ~strong(X0)) [ennf transformation 9]
94. ~strong(X0) | ~strong(X0) [cnf transformation 33]
131. strong(paul) [cnf transformation 25]
133. ~strong(X0) [duplicate literal removal 94]
285. $false [subsumption resolution 131,133]
% SZS output end Proof for 2263940149140126230521398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or not old then someone is not old.
Everyone who is both not tall and not wise is creative and vice versa.
If someone is either quiet or happy then lucy is wise or not wise.
If someone is both rich and happy then paul is not brave.
If alice is not quiet then lucy is wise or creative.
If someone is calm then alice is not patient and vice versa.
If someone is not old then susan is either happy or curious.
Everyone who is either generous or quiet is not quiet or not patient and vice versa.
Everyone who is not happy is either generous or not rich and vice versa.
Everyone who is not brave is not happy or not old and vice versa.
Everyone who is not brave or patient is both tall and funny.
Everyone who is not brave or not kind is not humble or wise and vice versa.
If someone is old then mary is not old.
If susan is either creative or not kind then someone is not patient or strong.
If someone is either calm or not wise then fred is both not humble and patient.
Everyone who is either creative or brave is either kind or not strong and vice versa.
Susan is both not old and kind.
John is both kind and rich.
Someone is not kind.
Fred is not quiet.
Someone is both old and not funny.
Susan is either not rich or creative.
Someone is both brave and patient. | Mary is funny. | entailment | (((~tall(fred)<~>~old(fred)))=>(?[X]:(~old(X))))&
(![X]:((~tall(X)&~wise(X))<=>creative(X)))&
((?[X]:((quiet(X)<~>happy(X))))=>((wise(lucy)|~wise(lucy))))&
((?[X]:((rich(X)&happy(X))))=>(~brave(paul)))&
((~quiet(alice))=>((wise(lucy)|creative(lucy))))&
((?[X]:(calm(X)))<=>(~patient(alice)))&
((?[X]:(~old(X)))=>((happy(susan)<~>curious(susan))))&
(![X]:((generous(X)<~>quiet(X))<=>(~quiet(X)|~patient(X))))&
(![X]:(~happy(X)<=>(generous(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>(~happy(X)|~old(X))))&
(![X]:((~brave(X)|patient(X))=>(tall(X)&funny(X))))&
(![X]:((~brave(X)|~kind(X))<=>(~humble(X)|wise(X))))&
((?[X]:(old(X)))=>(~old(mary)))&
(((creative(susan)<~>~kind(susan)))=>(?[X]:((~patient(X)|strong(X)))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~humble(fred)&patient(fred))))&
(![X]:((creative(X)<~>brave(X))<=>(kind(X)<~>~strong(X))))&
((~old(susan)&kind(susan)))&
((kind(john)&rich(john)))&
(?[X]:(~kind(X)))&
(~quiet(fred))&
(?[X]:((old(X)&~funny(X))))&
((~rich(susan)<~>creative(susan)))&
(?[X]:((brave(X)&patient(X)))) | funny(mary) | [
"p9",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7944359086555289769748586
% SZS output start Proof for 7944359086555289769748586
10. ! [X0] : (~brave(X0) <=> (~old(X0) | ~happy(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~brave(X0)) => (funny(X0) & tall(X0))) [input p10]
13. ? [X0] : old(X0) => ~old(mary) [input p12]
21. ? [X0] : (~funny(X0) & old(X0)) [input p20]
24. ~funny(mary) [input hypothesis]
32. ! [X0] : ((funny(X0) & tall(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 11]
33. ~old(mary) | ! [X0] : ~old(X0) [ennf transformation 13]
50. ! [X0] : ((~brave(X0) | (old(X0) & happy(X0))) & ((~old(X0) | ~happy(X0)) | brave(X0))) [nnf transformation 10]
51. ! [X0] : ((~brave(X0) | (old(X0) & happy(X0))) & (~old(X0) | ~happy(X0) | brave(X0))) [flattening 50]
61. ? [X0] : (~funny(X0) & old(X0)) => (~funny(sK4) & old(sK4)) [choice axiom]
62. ~funny(sK4) & old(sK4) [skolemisation 21,61]
91. ~brave(X0) | old(X0) [cnf transformation 51]
94. funny(X0) | brave(X0) [cnf transformation 32]
100. ~old(mary) | ~old(X0) [cnf transformation 33]
121. old(sK4) [cnf transformation 62]
127. ~funny(mary) [cnf transformation 24]
193. 15 <=> ! [X0] : ~old(X0) [avatar definition]
194. ~old(X0) <- (15) [avatar component clause 193]
196. 16 <=> old(mary) [avatar definition]
199. 15 | ~16 [avatar split clause 100,196,193]
257. brave(mary) [resolution 94,127]
261. old(mary) [resolution 257,91]
265. 16 [avatar split clause 261,196]
266. $false <- (15) [resolution 194,121]
271. ~15 [avatar contradiction clause 266]
272. $false [avatar sat refutation 199,265,271]
% SZS output end Proof for 7944359086555289769748586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not tall then someone is not kind or kind and vice versa. Everyone who is rich or not happy is either not curious or not calm and vice versa. Everyone who is calm is either curious or strong. If mary is curious or kind then paul is not patient. Everyone who is not strong or patient is not generous and vice versa. If lucy is wise or funny then someone is both happy and old and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. Someone is either funny or not calm. Lucy is not wise or calm. Susan is rich. Susan is not calm. Someone is both humble and rich. Someone is generous or wise. | Fred is calm. | contradiction | ((~tall(fred))<=>(?[X]:((~kind(X)|kind(X)))))&
(![X]:((rich(X)|~happy(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:(calm(X)=>(curious(X)<~>strong(X))))&
(((curious(mary)|kind(mary)))=>(~patient(paul)))&
(![X]:((~strong(X)|patient(X))<=>~generous(X)))&
(((wise(lucy)|funny(lucy)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X)))) | calm(fred) | [
"p0",
"p2",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4618491948531740306229544
% SZS output start Proof for 4618491948531740306229544
1. ~tall(fred) <=> ? [X0] : (kind(X0) | ~kind(X0)) [input p0]
3. ! [X0] : (calm(X0) => (curious(X0) <~> strong(X0))) [input p2]
8. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p7]
13. ! [X0] : (~strong(X0) <=> (funny(X0) & ~brave(X0))) [input p12]
14. ! [X0] : ((quiet(X0) | calm(X0)) <=> (wise(X0) & ~funny(X0))) [input p13]
15. ! [X0] : (~generous(X0) <=> (curious(X0) & humble(X0))) [input p14]
22. calm(fred) [input hypothesis]
23. ! [X0] : ((curious(X0) <~> strong(X0)) | ~calm(X0)) [ennf transformation 3]
26. ! [X0] : ((tall(X0) & ~curious(X0)) | (~old(X0) & ~generous(X0))) [ennf transformation 8]
29. (~tall(fred) | ! [X0] : (~kind(X0) & kind(X0))) & (? [X0] : (kind(X0) | ~kind(X0)) | tall(fred)) [nnf transformation 1]
30. (~tall(fred) | ! [X0] : (~kind(X0) & kind(X0))) & (? [X1] : (kind(X1) | ~kind(X1)) | tall(fred)) [rectify 29]
31. ? [X1] : (kind(X1) | ~kind(X1)) => (kind(sK0) | ~kind(sK0)) [choice axiom]
32. (~tall(fred) | ! [X0] : (~kind(X0) & kind(X0))) & ((kind(sK0) | ~kind(sK0)) | tall(fred)) [skolemisation 30,31]
35. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | ~calm(X0)) [nnf transformation 23]
52. ! [X0] : ((~strong(X0) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | strong(X0))) [nnf transformation 13]
53. ! [X0] : ((~strong(X0) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | strong(X0))) [flattening 52]
54. ! [X0] : (((quiet(X0) | calm(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 14]
55. ! [X0] : ((quiet(X0) | calm(X0) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 54]
56. ! [X0] : ((~generous(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | generous(X0))) [nnf transformation 15]
57. ! [X0] : ((~generous(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | generous(X0))) [flattening 56]
66. ~tall(fred) | kind(X0) [cnf transformation 32]
67. ~tall(fred) | ~kind(X0) [cnf transformation 32]
75. ~strong(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 35]
90. ~generous(X0) | tall(X0) [cnf transformation 26]
110. funny(X0) | strong(X0) [cnf transformation 53]
112. ~funny(X0) | ~calm(X0) [cnf transformation 55]
118. generous(X0) | curious(X0) [cnf transformation 57]
128. calm(fred) [cnf transformation 22]
130. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
131. ~kind(X0) <- (1) [avatar component clause 130]
133. 2 <=> tall(fred) [avatar definition]
135. ~tall(fred) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 67,133,130]
138. 3 <=> ! [X0] : kind(X0) [avatar definition]
139. kind(X0) <- (3) [avatar component clause 138]
140. 3 | ~2 [avatar split clause 66,133,138]
260. ~calm(X0) | strong(X0) [resolution 112,110]
266. curious(X0) | tall(X0) [resolution 118,90]
283. 27 <=> curious(fred) [avatar definition]
285. ~curious(fred) <- (~27) [avatar component clause 283]
442. strong(fred) [resolution 260,128]
450. tall(fred) <- (~27) [resolution 266,285]
457. $false <- (~2, ~27) [subsumption resolution 450,135]
458. 2 | 27 [avatar contradiction clause 457]
462. ~curious(fred) | ~calm(fred) [resolution 442,75]
477. ~curious(fred) [subsumption resolution 462,128]
478. ~27 [avatar split clause 477,283]
479. $false <- (1, 3) [subsumption resolution 131,139]
480. ~1 | ~3 [avatar contradiction clause 479]
481. $false [avatar sat refutation 136,140,458,478,480]
% SZS output end Proof for 4618491948531740306229544
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either kind or not curious then someone is creative or patient.
Everyone who is either not creative or rich is brave or not wise and vice versa.
If susan is funny or happy then john is either not strong or not rich and vice versa.
Everyone who is either not funny or calm is not brave or rich and vice versa.
Everyone who is not calm is funny or brave and vice versa.
Everyone who is not patient is either rich or not curious.
Everyone who is not quiet is generous or not generous.
If alice is rich or not patient then someone is not funny or not patient and vice versa.
Everyone who is not strong or creative is wise and vice versa.
Everyone who is creative is not old.
If fred is quiet or not funny then alice is both wise and not happy.
Everyone who is either not wise or not tall is either patient or not strong.
Everyone who is not brave is not wise and vice versa.
If paul is not wise or happy then someone is not quiet and vice versa.
Everyone who is either not kind or funny is both funny and not tall and vice versa.
Everyone who is kind or patient is either not rich or wise.
Susan is both wise and not curious.
Someone is tall.
Paul is both happy and not rich.
Someone is not happy.
Mary is not generous.
Someone is not wise or old.
John is either brave or not quiet.
Someone is either calm or tall. | Paul is not funny. | contradiction | (((kind(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~creative(X)<~>rich(X))<=>(brave(X)|~wise(X))))&
(((funny(susan)|happy(susan)))<=>((~strong(john)<~>~rich(john))))&
(![X]:((~funny(X)<~>calm(X))<=>(~brave(X)|rich(X))))&
(![X]:(~calm(X)<=>(funny(X)|brave(X))))&
(![X]:(~patient(X)=>(rich(X)<~>~curious(X))))&
(![X]:(~quiet(X)=>(generous(X)|~generous(X))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~strong(X)|creative(X))<=>wise(X)))&
(![X]:(creative(X)=>~old(X)))&
(((quiet(fred)|~funny(fred)))=>((wise(alice)&~happy(alice))))&
(![X]:((~wise(X)<~>~tall(X))=>(patient(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>~wise(X)))&
(((~wise(paul)|happy(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(funny(X)&~tall(X))))&
(![X]:((kind(X)|patient(X))=>(~rich(X)<~>wise(X))))&
((wise(susan)&~curious(susan)))&
(?[X]:(tall(X)))&
((happy(paul)&~rich(paul)))&
(?[X]:(~happy(X)))&
(~generous(mary))&
(?[X]:((~wise(X)|old(X))))&
((brave(john)<~>~quiet(john)))&
(?[X]:((calm(X)<~>tall(X)))) | ~funny(paul) | [
"p3",
"p4",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4341724547938282490719357
% SZS output start Proof for 4341724547938282490719357
4. ! [X0] : ((~funny(X0) <~> calm(X0)) <=> (rich(X0) | ~brave(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (brave(X0) | funny(X0))) [input p4]
13. ! [X0] : (~brave(X0) <=> ~wise(X0)) [input p12]
15. ! [X0] : ((~kind(X0) <~> funny(X0)) <=> (~tall(X0) & funny(X0))) [input p14]
16. ! [X0] : ((patient(X0) | kind(X0)) => (~rich(X0) <~> wise(X0))) [input p15]
19. ~rich(paul) & happy(paul) [input p18]
25. ~funny(paul) [input hypothesis]
33. ! [X0] : ((~rich(X0) <~> wise(X0)) | (~patient(X0) & ~kind(X0))) [ennf transformation 16]
41. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & ((rich(X0) | ~brave(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & (rich(X0) | ~brave(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [flattening 41]
43. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | calm(X0))) [nnf transformation 5]
44. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | calm(X0))) [flattening 43]
54. ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))) [nnf transformation 13]
60. ! [X0] : ((((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))))) [flattening 60]
62. ! [X0] : (((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (~patient(X0) & ~kind(X0))) [nnf transformation 33]
89. ~funny(X0) | calm(X0) | brave(X0) [cnf transformation 42]
91. ~calm(X0) | funny(X0) | brave(X0) [cnf transformation 42]
93. brave(X0) | funny(X0) | calm(X0) [cnf transformation 44]
94. ~calm(X0) | ~funny(X0) [cnf transformation 44]
116. ~brave(X0) | wise(X0) [cnf transformation 54]
120. funny(X0) | funny(X0) | kind(X0) [cnf transformation 61]
128. ~wise(X0) | rich(X0) | ~kind(X0) [cnf transformation 62]
134. ~rich(paul) [cnf transformation 19]
142. ~funny(paul) [cnf transformation 25]
143. funny(X0) | kind(X0) [duplicate literal removal 120]
150. 2 <=> kind(paul) [avatar definition]
152. kind(paul) <- (2) [avatar component clause 150]
185. calm(X0) | brave(X0) [subsumption resolution 93,89]
290. kind(paul) [resolution 143,142]
295. ~funny(X1) | brave(X1) [resolution 185,94]
335. funny(X0) | brave(X0) | brave(X0) [resolution 91,185]
336. funny(X0) | brave(X0) [duplicate literal removal 335]
340. brave(X0) [subsumption resolution 336,295]
344. wise(X2) [resolution 340,116]
401. ~kind(X0) | rich(X0) [resolution 128,344]
504. rich(paul) <- (2) [resolution 401,152]
508. $false <- (2) [subsumption resolution 504,134]
509. ~2 [avatar contradiction clause 508]
510. 2 [avatar split clause 290,150]
511. $false [avatar sat refutation 509,510]
% SZS output end Proof for 4341724547938282490719357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not humble is either strong or old.
If someone is either not happy or not humble then someone is either not funny or quiet and vice versa.
Everyone who is not old is not quiet or not calm.
Everyone who is either not quiet or not kind is calm or not kind and vice versa.
If alice is funny then alice is wise.
Everyone who is either not tall or not quiet is both old and not creative and vice versa.
If fred is patient then someone is not wise or not brave and vice versa.
Everyone who is not funny is not old or tall and vice versa.
If john is both happy and not funny then fred is both kind and not kind and vice versa.
Everyone who is not calm or wise is kind.
If someone is tall or old then fred is both calm and creative and vice versa.
Everyone who is brave is either not patient or not tall.
If john is either not generous or not strong then susan is not curious.
If someone is not curious then paul is either brave or not generous.
Everyone who is not happy is either happy or not creative and vice versa.
If fred is both not generous and creative then susan is not creative or not wise.
Someone is old or not patient.
Someone is not happy or brave.
Someone is either brave or kind.
Someone is both kind and not creative.
Someone is not patient or not strong. | Paul is calm. | entailment | (![X]:((calm(X)|~humble(X))=>(strong(X)<~>old(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
(![X]:(~old(X)=>(~quiet(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(calm(X)|~kind(X))))&
((funny(alice))=>(wise(alice)))&
(![X]:((~tall(X)<~>~quiet(X))<=>(old(X)&~creative(X))))&
((patient(fred))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~funny(X)<=>(~old(X)|tall(X))))&
(((happy(john)&~funny(john)))<=>((kind(fred)&~kind(fred))))&
(![X]:((~calm(X)|wise(X))=>kind(X)))&
((?[X]:((tall(X)|old(X))))<=>((calm(fred)&creative(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>~tall(X))))&
(((~generous(john)<~>~strong(john)))=>(~curious(susan)))&
((?[X]:(~curious(X)))=>((brave(paul)<~>~generous(paul))))&
(![X]:(~happy(X)<=>(happy(X)<~>~creative(X))))&
(((~generous(fred)&creative(fred)))=>((~creative(susan)|~wise(susan))))&
(?[X]:((old(X)|~patient(X))))&
(?[X]:((~happy(X)|brave(X))))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:((~patient(X)|~strong(X)))) | calm(paul) | [
"p3",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5067175066404644265877672
% SZS output start Proof for 5067175066404644265877672
4. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (~kind(X0) | calm(X0))) [input p3]
6. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> (~creative(X0) & old(X0))) [input p5]
11. ? [X0] : (old(X0) | tall(X0)) <=> (creative(fred) & calm(fred)) [input p10]
15. ! [X0] : (~happy(X0) <=> (happy(X0) <~> ~creative(X0))) [input p14]
22. ~calm(paul) [input hypothesis]
40. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 4]
41. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [flattening 40]
42. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 6]
43. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [flattening 42]
52. (? [X0] : (old(X0) | tall(X0)) | (~creative(fred) | ~calm(fred))) & ((creative(fred) & calm(fred)) | ! [X0] : (~old(X0) & ~tall(X0))) [nnf transformation 11]
53. (? [X0] : (old(X0) | tall(X0)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X0] : (~old(X0) & ~tall(X0))) [flattening 52]
54. (? [X0] : (old(X0) | tall(X0)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X1] : (~old(X1) & ~tall(X1))) [rectify 53]
55. ? [X0] : (old(X0) | tall(X0)) => (old(sK3) | tall(sK3)) [choice axiom]
56. ((old(sK3) | tall(sK3)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X1] : (~old(X1) & ~tall(X1))) [skolemisation 54,55]
60. ! [X0] : ((~happy(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | happy(X0))) [nnf transformation 15]
85. ~kind(X0) | calm(X0) | ~kind(X0) | quiet(X0) [cnf transformation 41]
90. kind(X0) | quiet(X0) | kind(X0) [cnf transformation 41]
92. ~quiet(X0) | old(X0) | tall(X0) [cnf transformation 43]
112. creative(fred) | ~tall(X1) [cnf transformation 56]
113. creative(fred) | ~old(X1) [cnf transformation 56]
121. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 60]
123. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 60]
133. ~calm(paul) [cnf transformation 22]
134. ~creative(X0) | happy(X0) [duplicate literal removal 121]
135. ~creative(X0) | ~happy(X0) [duplicate literal removal 123]
136. ~kind(X0) | calm(X0) | quiet(X0) [duplicate literal removal 85]
137. kind(X0) | quiet(X0) [duplicate literal removal 90]
174. quiet(X0) | calm(X0) [subsumption resolution 136,137]
224. 20 <=> creative(fred) [avatar definition]
225. creative(fred) <- (20) [avatar component clause 224]
237. 23 <=> ! [X1] : ~old(X1) [avatar definition]
238. ~old(X1) <- (23) [avatar component clause 237]
239. 23 | 20 [avatar split clause 113,224,237]
241. 24 <=> ! [X1] : ~tall(X1) [avatar definition]
242. ~tall(X1) <- (24) [avatar component clause 241]
243. 24 | 20 [avatar split clause 112,224,241]
273. ~creative(X0) [subsumption resolution 134,135]
311. $false <- (20) [subsumption resolution 225,273]
312. ~20 [avatar contradiction clause 311]
356. old(X0) | tall(X0) | calm(X0) [resolution 92,174]
357. tall(X0) | calm(X0) <- (23) [subsumption resolution 356,238]
358. calm(X0) <- (23, 24) [subsumption resolution 357,242]
360. $false <- (23, 24) [resolution 358,133]
364. ~23 | ~24 [avatar contradiction clause 360]
366. $false [avatar sat refutation 239,243,312,364]
% SZS output end Proof for 5067175066404644265877672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not funny and calm then someone is not wise or curious and vice versa.
If alice is not creative then mary is quiet or not brave and vice versa.
Everyone who is either wise or not kind is not wise or not generous.
Everyone who is curious is both not old and not happy.
If susan is not kind or quiet then someone is not strong.
If alice is both not rich and wise then paul is not creative or patient and vice versa.
Everyone who is either kind or quiet is both not kind and humble and vice versa.
Everyone who is not creative is not rich or rich and vice versa.
If alice is either funny or old then susan is both not strong and not old and vice versa.
Everyone who is not humble is both creative and not old and vice versa.
Everyone who is wise is patient and vice versa.
Everyone who is either not happy or humble is funny and vice versa.
Everyone who is both not creative and quiet is kind or not kind.
If someone is tall then someone is patient or generous.
Everyone who is not generous is old.
If someone is either calm or kind then paul is both funny and kind and vice versa.
Someone is happy or curious.
Someone is not strong or humble.
Someone is not brave.
Mary is kind.
Lucy is patient.
Fred is not old.
Someone is happy or not old.
Someone is humble. | Fred is quiet. | entailment | (((~funny(mary)&calm(mary)))<=>(?[X]:((~wise(X)|curious(X)))))&
((~creative(alice))<=>((quiet(mary)|~brave(mary))))&
(![X]:((wise(X)<~>~kind(X))=>(~wise(X)|~generous(X))))&
(![X]:(curious(X)=>(~old(X)&~happy(X))))&
(((~kind(susan)|quiet(susan)))=>(?[X]:(~strong(X))))&
(((~rich(alice)&wise(alice)))<=>((~creative(paul)|patient(paul))))&
(![X]:((kind(X)<~>quiet(X))<=>(~kind(X)&humble(X))))&
(![X]:(~creative(X)<=>(~rich(X)|rich(X))))&
(((funny(alice)<~>old(alice)))<=>((~strong(susan)&~old(susan))))&
(![X]:(~humble(X)<=>(creative(X)&~old(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((~happy(X)<~>humble(X))<=>funny(X)))&
(![X]:((~creative(X)&quiet(X))=>(kind(X)|~kind(X))))&
((?[X]:(tall(X)))=>(?[X]:((patient(X)|generous(X)))))&
(![X]:(~generous(X)=>old(X)))&
((?[X]:((calm(X)<~>kind(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~strong(X)|humble(X))))&
(?[X]:(~brave(X)))&
(kind(mary))&
(patient(lucy))&
(~old(fred))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:(humble(X))) | quiet(fred) | [
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 54632175925428287955432
% SZS output start Proof for 54632175925428287955432
7. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> (humble(X0) & ~kind(X0))) [input p6]
8. ! [X0] : (~creative(X0) <=> (rich(X0) | ~rich(X0))) [input p7]
10. ! [X0] : (~humble(X0) <=> (~old(X0) & creative(X0))) [input p9]
25. ~quiet(fred) [input hypothesis]
47. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [flattening 47]
49. ! [X0] : ((~creative(X0) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | creative(X0))) [nnf transformation 8]
50. ! [X0] : ((~creative(X0) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | creative(X0))) [flattening 49]
53. ! [X0] : ((~humble(X0) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | humble(X0))) [nnf transformation 10]
54. ! [X0] : ((~humble(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | humble(X0))) [flattening 53]
91. ~kind(X0) | quiet(X0) | ~kind(X0) [cnf transformation 48]
95. quiet(X0) | kind(X0) | ~humble(X0) | kind(X0) [cnf transformation 48]
98. ~creative(X0) | rich(X0) [cnf transformation 50]
99. ~rich(X0) | ~creative(X0) [cnf transformation 50]
106. creative(X0) | humble(X0) [cnf transformation 54]
131. ~quiet(fred) [cnf transformation 25]
132. ~kind(X0) | quiet(X0) [duplicate literal removal 91]
133. ~humble(X0) | kind(X0) | quiet(X0) [duplicate literal removal 95]
212. ~creative(X0) [subsumption resolution 98,99]
235. humble(X0) [subsumption resolution 106,212]
306. kind(X0) | quiet(X0) [resolution 133,235]
307. quiet(X0) [subsumption resolution 306,132]
331. $false [resolution 307,131]
% SZS output end Proof for 54632175925428287955432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not old is not quiet and vice versa. If lucy is not old or brave then paul is both brave and not humble. If someone is both not curious and strong then lucy is not tall or not rich. Everyone who is strong or brave is old or strong. Everyone who is either humble or kind is either not rich or old and vice versa. If someone is not brave or not humble then someone is not creative or rich and vice versa. Everyone who is either not patient or humble is either old or curious and vice versa. If john is both not brave and not funny then alice is either funny or patient and vice versa. If someone is calm or wise then someone is not strong or calm. Everyone who is both not happy and creative is wise or brave and vice versa. Everyone who is either brave or not patient is either brave or wise. Everyone who is happy or not wise is both brave and not brave and vice versa. Everyone who is either funny or not kind is kind and vice versa. Everyone who is not generous or quiet is both strong and not tall. Everyone who is not rich or not tall is quiet or patient and vice versa. If john is not generous then paul is both quiet and old and vice versa. Someone is not calm or not rich. Someone is not patient. Mary is calm. Alice is generous or not quiet. Someone is either tall or not funny. Someone is calm or humble. Paul is both not old and curious. Someone is either wise or not brave. | John is creative. | entailment | (![X]:((wise(X)<~>~old(X))<=>~quiet(X)))&
(((~old(lucy)|brave(lucy)))=>((brave(paul)&~humble(paul))))&
((?[X]:((~curious(X)&strong(X))))=>((~tall(lucy)|~rich(lucy))))&
(![X]:((strong(X)|brave(X))=>(old(X)|strong(X))))&
(![X]:((humble(X)<~>kind(X))<=>(~rich(X)<~>old(X))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:(~patient(X)))&
(calm(mary))&
((generous(alice)|~quiet(alice)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((calm(X)|humble(X))))&
((~old(paul)&curious(paul)))&
(?[X]:((wise(X)<~>~brave(X)))) | creative(john) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4778472731061530261187934
% SZS output start Proof for 4778472731061530261187934
10. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (brave(X0) | wise(X0))) [input p9]
12. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p11]
25. ~creative(john) [input hypothesis]
49. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 10]
50. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~creative(X0) | happy(X0))) [flattening 49]
52. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 12]
53. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 52]
113. ~wise(X0) | creative(X0) [cnf transformation 50]
120. brave(X0) | wise(X0) [cnf transformation 53]
122. ~brave(X0) | wise(X0) [cnf transformation 53]
150. ~creative(john) [cnf transformation 25]
200. 11 <=> ! [X1] : creative(X1) [avatar definition]
201. creative(X1) <- (11) [avatar component clause 200]
257. wise(X0) [subsumption resolution 120,122]
309. creative(X0) [resolution 113,257]
310. 11 [avatar split clause 309,200]
311. $false <- (11) [resolution 201,150]
314. ~11 [avatar contradiction clause 311]
315. $false [avatar sat refutation 310,314]
% SZS output end Proof for 4778472731061530261187934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not rich then paul is both curious and not happy.
If susan is tall or not rich then mary is both rich and not tall.
If susan is either creative or not brave then someone is either rich or curious.
If susan is not rich or not curious then mary is both tall and strong and vice versa.
Everyone who is not calm is not generous and vice versa.
If fred is not funny or not curious then someone is not creative and vice versa.
Everyone who is rich or strong is both happy and not creative.
If someone is both not happy and patient then mary is not generous or calm and vice versa.
Everyone who is either creative or calm is both old and wise.
Everyone who is both curious and quiet is both not curious and strong.
Everyone who is not old is wise and vice versa.
Everyone who is not patient or brave is either not humble or kind and vice versa.
If someone is either not kind or not brave then someone is not rich or not kind.
If someone is not rich then someone is curious or not creative and vice versa.
Everyone who is curious is not rich.
If someone is curious then someone is tall or not funny and vice versa.
John is either creative or funny.
Someone is either strong or not kind.
Susan is not funny or quiet.
Susan is brave or wise.
Lucy is tall or not happy.
Someone is both not creative and old.
Someone is both not tall and strong.
Mary is both not wise and humble. | Mary is happy. | entailment | ((?[X]:((~funny(X)|~rich(X))))=>((curious(paul)&~happy(paul))))&
(((tall(susan)|~rich(susan)))=>((rich(mary)&~tall(mary))))&
(((creative(susan)<~>~brave(susan)))=>(?[X]:((rich(X)<~>curious(X)))))&
(((~rich(susan)|~curious(susan)))<=>((tall(mary)&strong(mary))))&
(![X]:(~calm(X)<=>~generous(X)))&
(((~funny(fred)|~curious(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((rich(X)|strong(X))=>(happy(X)&~creative(X))))&
((?[X]:((~happy(X)&patient(X))))<=>((~generous(mary)|calm(mary))))&
(![X]:((creative(X)<~>calm(X))=>(old(X)&wise(X))))&
(![X]:((curious(X)&quiet(X))=>(~curious(X)&strong(X))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~patient(X)|brave(X))<=>(~humble(X)<~>kind(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(curious(X)=>~rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((tall(X)|~funny(X)))))&
((creative(john)<~>funny(john)))&
(?[X]:((strong(X)<~>~kind(X))))&
((~funny(susan)|quiet(susan)))&
((brave(susan)|wise(susan)))&
((tall(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((~tall(X)&strong(X))))&
((~wise(mary)&humble(mary))) | happy(mary) | [
"p3",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5536824522730199578681953
% SZS output start Proof for 5536824522730199578681953
4. (~curious(susan) | ~rich(susan)) <=> (strong(mary) & tall(mary)) [input p3]
7. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) & happy(X0))) [input p6]
15. ! [X0] : (curious(X0) => ~rich(X0)) [input p14]
25. ~happy(mary) [input hypothesis]
33. ! [X0] : ((~creative(X0) & happy(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 7]
39. ! [X0] : (~rich(X0) | ~curious(X0)) [ennf transformation 15]
43. ((~curious(susan) | ~rich(susan)) | (~strong(mary) | ~tall(mary))) & ((strong(mary) & tall(mary)) | (curious(susan) & rich(susan))) [nnf transformation 4]
44. (~curious(susan) | ~rich(susan) | ~strong(mary) | ~tall(mary)) & ((strong(mary) & tall(mary)) | (curious(susan) & rich(susan))) [flattening 43]
95. strong(mary) | rich(susan) [cnf transformation 44]
96. strong(mary) | curious(susan) [cnf transformation 44]
104. ~strong(X0) | happy(X0) [cnf transformation 33]
130. ~curious(X0) | ~rich(X0) [cnf transformation 39]
147. ~happy(mary) [cnf transformation 25]
168. 5 <=> rich(susan) [avatar definition]
170. rich(susan) <- (5) [avatar component clause 168]
208. 13 <=> strong(mary) [avatar definition]
209. strong(mary) <- (13) [avatar component clause 208]
212. 14 <=> curious(susan) [avatar definition]
213. curious(susan) <- (14) [avatar component clause 212]
216. 14 | 13 [avatar split clause 96,208,212]
217. 5 | 13 [avatar split clause 95,208,168]
355. happy(mary) <- (13) [resolution 104,209]
356. $false <- (13) [subsumption resolution 355,147]
357. ~13 [avatar contradiction clause 356]
362. ~rich(susan) <- (14) [resolution 130,213]
363. $false <- (5, 14) [subsumption resolution 362,170]
364. ~5 | ~14 [avatar contradiction clause 363]
365. $false [avatar sat refutation 216,217,357,364]
% SZS output end Proof for 5536824522730199578681953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not tall and humble then someone is not old.
If lucy is both creative and funny then someone is not funny.
Everyone who is funny or not calm is curious.
Everyone who is creative or not wise is brave or quiet.
If someone is both happy and rich then someone is either not humble or not kind.
Everyone who is either tall or rich is both wise and funny.
Everyone who is not happy is not calm and vice versa.
Everyone who is generous is not curious or not old and vice versa.
Everyone who is either not kind or rich is funny and vice versa.
If paul is both not happy and happy then alice is not old or not calm.
Everyone who is wise is not curious or creative.
If paul is both not quiet and strong then alice is either strong or not happy.
Everyone who is both not kind and old is either rich or not calm and vice versa.
If someone is not wise or not tall then someone is not old.
If someone is not curious or not calm then someone is not old and vice versa.
If susan is either funny or old then lucy is not brave or happy.
Susan is either generous or not calm.
Someone is not kind.
Lucy is both not kind and not creative.
Someone is either not wise or creative.
Lucy is old.
Someone is not rich or wise.
Alice is both calm and patient.
Paul is not curious. | Lucy is quiet. | neutral | (((~tall(susan)&humble(susan)))=>(?[X]:(~old(X))))&
(((creative(lucy)&funny(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((funny(X)|~calm(X))=>curious(X)))&
(![X]:((creative(X)|~wise(X))=>(brave(X)|quiet(X))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((~humble(X)<~>~kind(X)))))&
(![X]:((tall(X)<~>rich(X))=>(wise(X)&funny(X))))&
(![X]:(~happy(X)<=>~calm(X)))&
(![X]:(generous(X)<=>(~curious(X)|~old(X))))&
(![X]:((~kind(X)<~>rich(X))<=>funny(X)))&
(((~happy(paul)&happy(paul)))=>((~old(alice)|~calm(alice))))&
(![X]:(wise(X)=>(~curious(X)|creative(X))))&
(((~quiet(paul)&strong(paul)))=>((strong(alice)<~>~happy(alice))))&
(![X]:((~kind(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:(~old(X))))&
((?[X]:((~curious(X)|~calm(X))))<=>(?[X]:(~old(X))))&
(((funny(susan)<~>old(susan)))=>((~brave(lucy)|happy(lucy))))&
((generous(susan)<~>~calm(susan)))&
(?[X]:(~kind(X)))&
((~kind(lucy)&~creative(lucy)))&
(?[X]:((~wise(X)<~>creative(X))))&
(old(lucy))&
(?[X]:((~rich(X)|wise(X))))&
((calm(alice)&patient(alice)))&
(~curious(paul)) | quiet(lucy) | [] | null | 0 |
If john is not strong then john is not rich or not creative and vice versa.
Everyone who is not happy or creative is either not patient or rich.
If someone is creative or not happy then paul is brave or rich and vice versa.
Everyone who is not happy or not calm is not happy or not rich.
If someone is either quiet or not brave then someone is not old or not brave.
If alice is calm or not creative then lucy is tall.
Everyone who is either curious or creative is not funny.
If someone is patient or happy then fred is not strong.
Everyone who is both tall and not generous is calm.
If someone is not wise or creative then someone is patient and vice versa.
Everyone who is not strong or not generous is both kind and not rich and vice versa.
Everyone who is either not patient or not happy is not strong or patient and vice versa.
Everyone who is funny is not quiet or not kind.
Everyone who is either not strong or not generous is humble.
Everyone who is both brave and not tall is patient or wise and vice versa.
Someone is not happy or curious.
Lucy is not humble or not old.
Fred is both not curious and humble.
Lucy is brave.
Someone is either rich or kind.
Paul is humble.
Someone is not curious. | Fred is creative. | neutral | ((~strong(john))<=>((~rich(john)|~creative(john))))&
(![X]:((~happy(X)|creative(X))=>(~patient(X)<~>rich(X))))&
((?[X]:((creative(X)|~happy(X))))<=>((brave(paul)|rich(paul))))&
(![X]:((~happy(X)|~calm(X))=>(~happy(X)|~rich(X))))&
((?[X]:((quiet(X)<~>~brave(X))))=>(?[X]:((~old(X)|~brave(X)))))&
(((calm(alice)|~creative(alice)))=>(tall(lucy)))&
(![X]:((curious(X)<~>creative(X))=>~funny(X)))&
((?[X]:((patient(X)|happy(X))))=>(~strong(fred)))&
(![X]:((tall(X)&~generous(X))=>calm(X)))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~strong(X)|~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(![X]:(funny(X)=>(~quiet(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>humble(X)))&
(![X]:((brave(X)&~tall(X))<=>(patient(X)|wise(X))))&
(?[X]:((~happy(X)|curious(X))))&
((~humble(lucy)|~old(lucy)))&
((~curious(fred)&humble(fred)))&
(brave(lucy))&
(?[X]:((rich(X)<~>kind(X))))&
(humble(paul))&
(?[X]:(~curious(X))) | creative(fred) | [] | null | 0 |
If someone is either rich or funny then someone is either not tall or not old and vice versa.
If mary is both not kind and curious then fred is brave.
If susan is either not wise or brave then alice is quiet or not humble and vice versa.
Everyone who is happy or generous is quiet or patient and vice versa.
Everyone who is generous is strong or humble and vice versa.
If mary is not wise or not funny then someone is either creative or not generous.
Everyone who is calm is not patient or not quiet.
Everyone who is either wise or funny is either happy or not rich and vice versa.
Everyone who is not generous is not wise or not happy and vice versa.
Everyone who is either not creative or not wise is not tall or not humble.
If someone is curious or wise then susan is tall or not humble.
If someone is either quiet or not generous then lucy is not humble or tall.
If someone is not humble then susan is not brave.
Everyone who is not wise is strong or not rich and vice versa.
If paul is patient or not funny then john is either not tall or not wise and vice versa.
If alice is either not kind or strong then someone is either not wise or not generous.
Someone is both calm and patient.
Alice is not creative.
Someone is kind or not patient.
Someone is both not funny and not old.
Fred is either quiet or not quiet.
Susan is brave or strong.
Lucy is not quiet or brave.
Fred is either rich or not generous. | Alice is not funny. | entailment | ((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~kind(mary)&curious(mary)))=>(brave(fred)))&
(((~wise(susan)<~>brave(susan)))<=>((quiet(alice)|~humble(alice))))&
(![X]:((happy(X)|generous(X))<=>(quiet(X)|patient(X))))&
(![X]:(generous(X)<=>(strong(X)|humble(X))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~wise(X)|~happy(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~tall(X)|~humble(X))))&
((?[X]:((curious(X)|wise(X))))=>((tall(susan)|~humble(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>((~humble(lucy)|tall(lucy))))&
((?[X]:(~humble(X)))=>(~brave(susan)))&
(![X]:(~wise(X)<=>(strong(X)|~rich(X))))&
(((patient(paul)|~funny(paul)))<=>((~tall(john)<~>~wise(john))))&
(((~kind(alice)<~>strong(alice)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(?[X]:((calm(X)&patient(X))))&
(~creative(alice))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:((~funny(X)&~old(X))))&
((quiet(fred)<~>~quiet(fred)))&
((brave(susan)|strong(susan)))&
((~quiet(lucy)|brave(lucy)))&
((rich(fred)<~>~generous(fred))) | ~funny(alice) | [
"p4",
"p7",
"p8",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 731223576340820489236621
% SZS output start Proof for 731223576340820489236621
5. ! [X0] : (generous(X0) <=> (humble(X0) | strong(X0))) [input p4]
8. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (happy(X0) <~> ~rich(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~wise(X0))) [input p8]
13. ? [X0] : ~humble(X0) => ~brave(susan) [input p12]
14. ! [X0] : (~wise(X0) <=> (~rich(X0) | strong(X0))) [input p13]
22. strong(susan) | brave(susan) [input p21]
25. funny(alice) [input hypothesis]
38. ~brave(susan) | ! [X0] : humble(X0) [ennf transformation 13]
49. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 5]
50. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ~generous(X0))) [flattening 49]
54. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 8]
55. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 9]
56. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | generous(X0))) [flattening 55]
59. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | wise(X0))) [nnf transformation 14]
60. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | wise(X0))) [flattening 59]
93. ~strong(X0) | generous(X0) [cnf transformation 50]
94. ~humble(X0) | generous(X0) [cnf transformation 50]
106. ~happy(X0) | ~wise(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 54]
109. ~generous(X0) | wise(X0) [cnf transformation 56]
110. ~generous(X0) | happy(X0) [cnf transformation 56]
116. ~brave(susan) | humble(X0) [cnf transformation 38]
118. ~strong(X0) | ~wise(X0) [cnf transformation 60]
119. ~wise(X0) | rich(X0) [cnf transformation 60]
138. strong(susan) | brave(susan) [cnf transformation 22]
142. funny(alice) [cnf transformation 25]
184. 10 <=> wise(susan) [avatar definition]
185. ~wise(susan) <- (~10) [avatar component clause 184]
188. 11 <=> brave(susan) [avatar definition]
250. 24 <=> ! [X0] : humble(X0) [avatar definition]
251. humble(X0) <- (24) [avatar component clause 250]
252. 24 | ~11 [avatar split clause 116,188,250]
309. 35 <=> strong(susan) [avatar definition]
311. strong(susan) <- (35) [avatar component clause 309]
312. 11 | 35 [avatar split clause 138,309,188]
348. generous(susan) <- (35) [resolution 311,93]
359. ~wise(susan) <- (35) [resolution 118,311]
364. ~10 | ~35 [avatar split clause 359,309,184]
367. wise(susan) <- (35) [resolution 348,109]
368. $false <- (~10, 35) [subsumption resolution 367,185]
369. 10 | ~35 [avatar contradiction clause 368]
373. generous(X0) <- (24) [resolution 251,94]
405. happy(X1) <- (24) [resolution 373,110]
406. wise(X2) <- (24) [resolution 373,109]
456. ~wise(X0) | ~rich(X0) | ~funny(X0) <- (24) [resolution 106,405]
461. ~funny(X0) | ~rich(X0) <- (24) [subsumption resolution 456,406]
463. rich(X1) <- (24) [resolution 406,119]
487. ~rich(alice) <- (24) [resolution 461,142]
488. $false <- (24) [subsumption resolution 487,463]
489. ~24 [avatar contradiction clause 488]
490. $false [avatar sat refutation 252,312,364,369,489]
% SZS output end Proof for 731223576340820489236621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or old then someone is both creative and not quiet. Everyone who is both not strong and old is not tall and vice versa. If john is not strong or wise then fred is not generous or creative. Everyone who is both not calm and not rich is either not curious or not generous. If lucy is both rich and not curious then someone is not calm or old. Everyone who is not happy is not old and vice versa. If mary is not tall then someone is either humble or not generous. If mary is funny or not strong then someone is both rich and not wise. If lucy is happy or brave then lucy is either curious or kind. Everyone who is either not calm or quiet is not patient or strong. Everyone who is either not generous or kind is generous and vice versa. Everyone who is both generous and humble is happy. Everyone who is funny is not funny. Everyone who is both funny and not humble is either curious or not happy. Everyone who is humble or not old is not curious or strong and vice versa. If someone is either not patient or not generous then mary is old or not tall. Lucy is not tall. Alice is both rich and not calm. Mary is both not generous and rich. Someone is either generous or not happy. Fred is strong. Someone is either not creative or funny. | Lucy is humble. | entailment | ((?[X]:((humble(X)|old(X))))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:((~strong(X)&old(X))<=>~tall(X)))&
(((~strong(john)|wise(john)))=>((~generous(fred)|creative(fred))))&
(![X]:((~calm(X)&~rich(X))=>(~curious(X)<~>~generous(X))))&
(((rich(lucy)&~curious(lucy)))=>(?[X]:((~calm(X)|old(X)))))&
(![X]:(~happy(X)<=>~old(X)))&
((~tall(mary))=>(?[X]:((humble(X)<~>~generous(X)))))&
(((funny(mary)|~strong(mary)))=>(?[X]:((rich(X)&~wise(X)))))&
(((happy(lucy)|brave(lucy)))=>((curious(lucy)<~>kind(lucy))))&
(![X]:((~calm(X)<~>quiet(X))=>(~patient(X)|strong(X))))&
(![X]:((~generous(X)<~>kind(X))<=>generous(X)))&
(![X]:((generous(X)&humble(X))=>happy(X)))&
(![X]:(funny(X)=>~funny(X)))&
(![X]:((funny(X)&~humble(X))=>(curious(X)<~>~happy(X))))&
(![X]:((humble(X)|~old(X))<=>(~curious(X)|strong(X))))&
((?[X]:((~patient(X)<~>~generous(X))))=>((old(mary)|~tall(mary))))&
(~tall(lucy))&
((rich(alice)&~calm(alice)))&
((~generous(mary)&rich(mary)))&
(?[X]:((generous(X)<~>~happy(X))))&
(strong(fred))&
(?[X]:((~creative(X)<~>funny(X)))) | humble(lucy) | [
"p1",
"p5",
"p8",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4372255350800593263929367
% SZS output start Proof for 4372255350800593263929367
2. ! [X0] : ((old(X0) & ~strong(X0)) <=> ~tall(X0)) [input p1]
6. ! [X0] : (~happy(X0) <=> ~old(X0)) [input p5]
9. (brave(lucy) | happy(lucy)) => (curious(lucy) <~> kind(lucy)) [input p8]
11. ! [X0] : ((~generous(X0) <~> kind(X0)) <=> generous(X0)) [input p10]
15. ! [X0] : ((~old(X0) | humble(X0)) <=> (strong(X0) | ~curious(X0))) [input p14]
17. ~tall(lucy) [input p16]
23. ~humble(lucy) [input hypothesis]
25. happy(lucy) => (curious(lucy) <~> kind(lucy)) [pure predicate removal 9]
37. (curious(lucy) <~> kind(lucy)) | ~happy(lucy) [ennf transformation 25]
50. ! [X0] : (((old(X0) & ~strong(X0)) | tall(X0)) & (~tall(X0) | (~old(X0) | strong(X0)))) [nnf transformation 2]
51. ! [X0] : (((old(X0) & ~strong(X0)) | tall(X0)) & (~tall(X0) | ~old(X0) | strong(X0))) [flattening 50]
55. ! [X0] : ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))) [nnf transformation 6]
61. ((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ~happy(lucy) [nnf transformation 37]
63. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | ~generous(X0)) & (generous(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [nnf transformation 11]
65. ! [X0] : (((~old(X0) | humble(X0)) | (~strong(X0) & curious(X0))) & ((strong(X0) | ~curious(X0)) | (old(X0) & ~humble(X0)))) [nnf transformation 15]
66. ! [X0] : ((~old(X0) | humble(X0) | (~strong(X0) & curious(X0))) & (strong(X0) | ~curious(X0) | (old(X0) & ~humble(X0)))) [flattening 65]
80. tall(X0) | old(X0) [cnf transformation 51]
85. ~old(X0) | happy(X0) [cnf transformation 55]
92. ~kind(lucy) | ~curious(lucy) | ~happy(lucy) [cnf transformation 61]
95. generous(X0) | kind(X0) | generous(X0) [cnf transformation 63]
97. kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 63]
105. ~old(X0) | humble(X0) | curious(X0) [cnf transformation 66]
109. ~tall(lucy) [cnf transformation 17]
119. ~humble(lucy) [cnf transformation 23]
121. generous(X0) | kind(X0) [duplicate literal removal 95]
122. ~generous(X0) | kind(X0) [duplicate literal removal 97]
159. 9 <=> curious(lucy) [avatar definition]
160. ~curious(lucy) <- (~9) [avatar component clause 159]
200. 18 <=> happy(lucy) [avatar definition]
204. 19 <=> kind(lucy) [avatar definition]
206. ~kind(lucy) <- (~19) [avatar component clause 204]
207. ~18 | ~9 | ~19 [avatar split clause 92,204,159,200]
209. kind(X0) [subsumption resolution 121,122]
238. old(lucy) [resolution 80,109]
240. happy(lucy) [resolution 238,85]
243. 18 [avatar split clause 240,200]
244. $false <- (~19) [subsumption resolution 206,209]
245. 19 [avatar contradiction clause 244]
252. humble(lucy) | curious(lucy) [resolution 105,238]
262. curious(lucy) [subsumption resolution 252,119]
263. $false <- (~9) [subsumption resolution 262,160]
264. 9 [avatar contradiction clause 263]
265. $false [avatar sat refutation 207,243,245,264]
% SZS output end Proof for 4372255350800593263929367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not calm and vice versa.
Everyone who is not calm or curious is not strong and vice versa.
If someone is either tall or quiet then susan is not rich or happy.
If someone is not funny or creative then alice is both curious and creative and vice versa.
Everyone who is either wise or quiet is either not creative or not humble.
Everyone who is not tall is not patient or rich.
Everyone who is generous is either not curious or not tall and vice versa.
Everyone who is strong is patient and vice versa.
If mary is both not old and not quiet then someone is wise or not creative.
Everyone who is not old or tall is rich or kind.
Everyone who is not kind is both happy and curious.
If someone is either kind or wise then lucy is either not strong or calm.
Everyone who is not humble or not happy is funny and vice versa.
Everyone who is both calm and funny is not brave or not creative.
Everyone who is either not generous or strong is tall or kind and vice versa.
If alice is funny or calm then alice is not creative and vice versa.
Someone is either rich or not rich.
Someone is both quiet and not happy.
Someone is not quiet.
Someone is either patient or funny.
Someone is old.
Someone is both generous and not patient.
Someone is either quiet or not humble.
Mary is not strong. | Mary is brave. | neutral | (![X]:(~brave(X)<=>~calm(X)))&
(![X]:((~calm(X)|curious(X))<=>~strong(X)))&
((?[X]:((tall(X)<~>quiet(X))))=>((~rich(susan)|happy(susan))))&
((?[X]:((~funny(X)|creative(X))))<=>((curious(alice)&creative(alice))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(~patient(X)|rich(X))))&
(![X]:(generous(X)<=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>patient(X)))&
(((~old(mary)&~quiet(mary)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~old(X)|tall(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)=>(happy(X)&curious(X))))&
((?[X]:((kind(X)<~>wise(X))))=>((~strong(lucy)<~>calm(lucy))))&
(![X]:((~humble(X)|~happy(X))<=>funny(X)))&
(![X]:((calm(X)&funny(X))=>(~brave(X)|~creative(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)|kind(X))))&
(((funny(alice)|calm(alice)))<=>(~creative(alice)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(~strong(mary)) | brave(mary) | [] | null | 0 |
Everyone who is either old or calm is creative or happy.
Everyone who is either old or not generous is not tall or not rich.
If paul is both brave and not generous then john is not curious and vice versa.
If someone is not funny then mary is not generous or not curious.
If someone is brave or not quiet then fred is both not patient and not happy and vice versa.
Everyone who is rich or not old is both not wise and not strong.
Everyone who is either not patient or kind is not creative or not generous and vice versa.
Everyone who is either not kind or kind is both not rich and not wise.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
Everyone who is either patient or not kind is either calm or not wise.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Fred is either generous or brave.
Someone is either not wise or not patient.
Someone is either not curious or not funny.
John is calm or strong. | Paul is rich. | contradiction | (![X]:((old(X)<~>calm(X))=>(creative(X)|happy(X))))&
(![X]:((old(X)<~>~generous(X))=>(~tall(X)|~rich(X))))&
(((brave(paul)&~generous(paul)))<=>(~curious(john)))&
((?[X]:(~funny(X)))=>((~generous(mary)|~curious(mary))))&
((?[X]:((brave(X)|~quiet(X))))<=>((~patient(fred)&~happy(fred))))&
(![X]:((rich(X)|~old(X))=>(~wise(X)&~strong(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~generous(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~rich(X)&~wise(X))))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~kind(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((calm(john)|strong(john))) | rich(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8133030448975858472113701
% SZS output start Proof for 8133030448975858472113701
8. ! [X0] : ((~kind(X0) <~> kind(X0)) => (~wise(X0) & ~rich(X0))) [input p7]
21. rich(paul) [input hypothesis]
28. ! [X0] : ((~wise(X0) & ~rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 8]
42. ! [X0] : ((~wise(X0) & ~rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 28]
90. ~rich(X0) | kind(X0) | kind(X0) [cnf transformation 42]
91. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
132. rich(paul) [cnf transformation 21]
135. ~rich(X0) | kind(X0) [duplicate literal removal 90]
136. ~rich(X0) | ~kind(X0) [duplicate literal removal 91]
194. ~rich(X0) [subsumption resolution 135,136]
269. $false [subsumption resolution 132,194]
% SZS output end Proof for 8133030448975858472113701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or patient is either strong or not tall.
If mary is curious then john is not tall.
Everyone who is not calm or rich is not generous and vice versa.
If someone is both happy and not tall then someone is not kind.
Everyone who is both wise and not old is both not humble and not brave.
If alice is not rich or not brave then someone is curious and vice versa.
Everyone who is generous or kind is tall and vice versa.
Everyone who is both not rich and not old is not rich or not happy and vice versa.
Everyone who is both not calm and wise is either humble or tall and vice versa.
Everyone who is either humble or curious is both not calm and strong.
If lucy is both patient and rich then john is both not tall and humble and vice versa.
Everyone who is not old is happy and vice versa.
Everyone who is not kind or generous is both not creative and not calm.
If john is not strong or humble then someone is not funny or not curious.
If someone is not calm then someone is not kind or rich and vice versa.
If alice is not calm then lucy is either generous or not tall and vice versa.
Lucy is not humble.
Susan is not tall.
John is both brave and funny.
Paul is old or kind.
Mary is either not calm or strong.
Lucy is either not rich or not humble.
Paul is rich.
Someone is either rich or not generous. | Alice is not generous. | entailment | (![X]:((humble(X)<~>patient(X))=>(strong(X)<~>~tall(X))))&
((curious(mary))=>(~tall(john)))&
(![X]:((~calm(X)|rich(X))<=>~generous(X)))&
((?[X]:((happy(X)&~tall(X))))=>(?[X]:(~kind(X))))&
(![X]:((wise(X)&~old(X))=>(~humble(X)&~brave(X))))&
(((~rich(alice)|~brave(alice)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)|kind(X))<=>tall(X)))&
(![X]:((~rich(X)&~old(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~calm(X)&wise(X))<=>(humble(X)<~>tall(X))))&
(![X]:((humble(X)<~>curious(X))=>(~calm(X)&strong(X))))&
(((patient(lucy)&rich(lucy)))<=>((~tall(john)&humble(john))))&
(![X]:(~old(X)<=>happy(X)))&
(![X]:((~kind(X)|generous(X))=>(~creative(X)&~calm(X))))&
(((~strong(john)|humble(john)))=>(?[X]:((~funny(X)|~curious(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:((~kind(X)|rich(X)))))&
((~calm(alice))<=>((generous(lucy)<~>~tall(lucy))))&
(~humble(lucy))&
(~tall(susan))&
((brave(john)&funny(john)))&
((old(paul)|kind(paul)))&
((~calm(mary)<~>strong(mary)))&
((~rich(lucy)<~>~humble(lucy)))&
(rich(paul))&
(?[X]:((rich(X)<~>~generous(X)))) | ~generous(alice) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 337417420568584651456600
% SZS output start Proof for 337417420568584651456600
3. ! [X0] : ((rich(X0) | ~calm(X0)) <=> ~generous(X0)) [input p2]
13. ! [X0] : ((generous(X0) | ~kind(X0)) => (~calm(X0) & ~creative(X0))) [input p12]
25. generous(alice) [input hypothesis]
28. ! [X0] : ((generous(X0) | ~kind(X0)) => ~calm(X0)) [pure predicate removal 13]
35. ! [X0] : (~calm(X0) | (~generous(X0) & kind(X0))) [ennf transformation 28]
38. ! [X0] : (((rich(X0) | ~calm(X0)) | generous(X0)) & (~generous(X0) | (~rich(X0) & calm(X0)))) [nnf transformation 3]
39. ! [X0] : ((rich(X0) | ~calm(X0) | generous(X0)) & (~generous(X0) | (~rich(X0) & calm(X0)))) [flattening 38]
76. ~generous(X0) | calm(X0) [cnf transformation 39]
110. ~calm(X0) | ~generous(X0) [cnf transformation 35]
132. generous(alice) [cnf transformation 25]
186. ~generous(X0) [subsumption resolution 110,76]
251. $false [subsumption resolution 132,186]
% SZS output end Proof for 337417420568584651456600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is not calm.
Everyone who is not creative is both not tall and tall and vice versa.
Everyone who is happy is either wise or not calm and vice versa.
If someone is happy or generous then paul is wise or calm.
If someone is either not rich or patient then alice is curious.
Everyone who is not rich is tall or not calm and vice versa.
Everyone who is not happy or not strong is both not funny and strong.
Everyone who is not curious is strong or quiet and vice versa.
Everyone who is not patient is either kind or creative and vice versa.
If paul is not generous or not tall then paul is not wise or humble and vice versa.
Everyone who is both kind and not wise is not wise or generous and vice versa.
Everyone who is both not rich and not calm is both not creative and humble.
If someone is old then someone is either not quiet or not tall.
If mary is either not rich or funny then someone is either generous or strong.
Everyone who is brave is not patient.
Everyone who is not wise or strong is not patient.
Lucy is either generous or not old.
Fred is either not old or not creative.
Someone is not generous.
Alice is both not funny and happy.
Someone is either wise or humble.
John is either funny or not patient. | Mary is funny. | neutral | (![X]:((calm(X)<~>~old(X))=>~calm(X)))&
(![X]:(~creative(X)<=>(~tall(X)&tall(X))))&
(![X]:(happy(X)<=>(wise(X)<~>~calm(X))))&
((?[X]:((happy(X)|generous(X))))=>((wise(paul)|calm(paul))))&
((?[X]:((~rich(X)<~>patient(X))))=>(curious(alice)))&
(![X]:(~rich(X)<=>(tall(X)|~calm(X))))&
(![X]:((~happy(X)|~strong(X))=>(~funny(X)&strong(X))))&
(![X]:(~curious(X)<=>(strong(X)|quiet(X))))&
(![X]:(~patient(X)<=>(kind(X)<~>creative(X))))&
(((~generous(paul)|~tall(paul)))<=>((~wise(paul)|humble(paul))))&
(![X]:((kind(X)&~wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((~rich(X)&~calm(X))=>(~creative(X)&humble(X))))&
((?[X]:(old(X)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(((~rich(mary)<~>funny(mary)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(brave(X)=>~patient(X)))&
(![X]:((~wise(X)|strong(X))=>~patient(X)))&
((generous(lucy)<~>~old(lucy)))&
((~old(fred)<~>~creative(fred)))&
(?[X]:(~generous(X)))&
((~funny(alice)&happy(alice)))&
(?[X]:((wise(X)<~>humble(X))))&
((funny(john)<~>~patient(john))) | funny(mary) | [] | null | 0 |
Everyone who is patient or creative is not patient or curious. If lucy is not brave then someone is wise and vice versa. If mary is both not funny and not tall then someone is either not old or calm. Everyone who is happy or strong is either not creative or calm. Everyone who is quiet is not rich or calm and vice versa. Everyone who is brave is either generous or brave and vice versa. Everyone who is both not generous and not quiet is old and vice versa. Everyone who is both not humble and not brave is not wise. If lucy is humble or not generous then paul is both not kind and not old. If john is not funny then someone is both not calm and curious. Everyone who is funny is either not calm or curious. Everyone who is either not creative or calm is both wise and creative. If someone is curious or rich then someone is both not calm and not quiet and vice versa. If someone is not funny then susan is either funny or quiet and vice versa. Everyone who is brave or not quiet is both quiet and not creative. Everyone who is curious or quiet is not tall or not quiet. Paul is generous or wise. Susan is not quiet or not tall. Fred is both not old and not strong. Mary is both not rich and not happy. Someone is not tall. Someone is both not funny and strong. Someone is not creative or not patient. Fred is either not calm or generous. | Mary is not curious. | entailment | (![X]:((patient(X)|creative(X))=>(~patient(X)|curious(X))))&
((~brave(lucy))<=>(?[X]:(wise(X))))&
(((~funny(mary)&~tall(mary)))=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((happy(X)|strong(X))=>(~creative(X)<~>calm(X))))&
(![X]:(quiet(X)<=>(~rich(X)|calm(X))))&
(![X]:(brave(X)<=>(generous(X)<~>brave(X))))&
(![X]:((~generous(X)&~quiet(X))<=>old(X)))&
(![X]:((~humble(X)&~brave(X))=>~wise(X)))&
(((humble(lucy)|~generous(lucy)))=>((~kind(paul)&~old(paul))))&
((~funny(john))=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(funny(X)=>(~calm(X)<~>curious(X))))&
(![X]:((~creative(X)<~>calm(X))=>(wise(X)&creative(X))))&
((?[X]:((curious(X)|rich(X))))<=>(?[X]:((~calm(X)&~quiet(X)))))&
((?[X]:(~funny(X)))<=>((funny(susan)<~>quiet(susan))))&
(![X]:((brave(X)|~quiet(X))=>(quiet(X)&~creative(X))))&
(![X]:((curious(X)|quiet(X))=>(~tall(X)|~quiet(X))))&
((generous(paul)|wise(paul)))&
((~quiet(susan)|~tall(susan)))&
((~old(fred)&~strong(fred)))&
((~rich(mary)&~happy(mary)))&
(?[X]:(~tall(X)))&
(?[X]:((~funny(X)&strong(X))))&
(?[X]:((~creative(X)|~patient(X))))&
((~calm(fred)<~>generous(fred))) | ~curious(mary) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3941733350919028619892239
% SZS output start Proof for 3941733350919028619892239
13. ? [X0] : (rich(X0) | curious(X0)) <=> ? [X0] : (~quiet(X0) & ~calm(X0)) [input p12]
15. ! [X0] : ((~quiet(X0) | brave(X0)) => (~creative(X0) & quiet(X0))) [input p14]
25. curious(mary) [input hypothesis]
26. ? [X0] : (rich(X0) | curious(X0)) <=> ? [X1] : (~quiet(X1) & ~calm(X1)) [rectify 13]
41. ! [X0] : ((~creative(X0) & quiet(X0)) | (quiet(X0) & ~brave(X0))) [ennf transformation 15]
61. (? [X0] : (rich(X0) | curious(X0)) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X1] : (~quiet(X1) & ~calm(X1)) | ! [X0] : (~rich(X0) & ~curious(X0))) [nnf transformation 26]
62. (? [X0] : (rich(X0) | curious(X0)) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X2] : (~quiet(X2) & ~calm(X2)) | ! [X3] : (~rich(X3) & ~curious(X3))) [rectify 61]
63. ? [X0] : (rich(X0) | curious(X0)) => (rich(sK3) | curious(sK3)) [choice axiom]
64. ? [X2] : (~quiet(X2) & ~calm(X2)) => (~quiet(sK4) & ~calm(sK4)) [choice axiom]
65. ((rich(sK3) | curious(sK3)) | ! [X1] : (quiet(X1) | calm(X1))) & ((~quiet(sK4) & ~calm(sK4)) | ! [X3] : (~rich(X3) & ~curious(X3))) [skolemisation 62,64,63]
104. ~quiet(sK4) | ~curious(X3) [cnf transformation 65]
112. quiet(X0) | quiet(X0) [cnf transformation 41]
127. curious(mary) [cnf transformation 25]
129. quiet(X0) [duplicate literal removal 112]
183. 11 <=> ! [X1] : quiet(X1) [avatar definition]
184. quiet(X1) <- (11) [avatar component clause 183]
198. 15 <=> quiet(sK4) [avatar definition]
200. ~quiet(sK4) <- (~15) [avatar component clause 198]
203. 16 <=> ! [X3] : ~curious(X3) [avatar definition]
204. ~curious(X3) <- (16) [avatar component clause 203]
205. 16 | ~15 [avatar split clause 104,198,203]
231. 11 [avatar split clause 129,183]
234. $false <- (11, ~15) [resolution 200,184]
235. ~11 | 15 [avatar contradiction clause 234]
236. $false <- (16) [resolution 204,127]
237. ~16 [avatar contradiction clause 236]
238. $false [avatar sat refutation 205,231,235,237]
% SZS output end Proof for 3941733350919028619892239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not quiet then someone is happy.
If someone is either not happy or quiet then someone is either happy or not generous.
Everyone who is both not curious and creative is both not calm and not generous and vice versa.
If someone is generous or creative then lucy is either not humble or not curious and vice versa.
Everyone who is either not happy or not patient is both not generous and happy and vice versa.
Everyone who is not generous or not old is both funny and old.
If someone is both not creative and generous then someone is not rich and vice versa.
Everyone who is wise or not creative is not tall or humble.
Everyone who is either not creative or not wise is both not generous and not calm.
If john is either not quiet or not strong then lucy is either not kind or not happy and vice versa.
Everyone who is wise is not humble or not brave and vice versa.
Everyone who is both not funny and creative is either not wise or not patient and vice versa.
Everyone who is both generous and not kind is both rich and not calm and vice versa.
If fred is either quiet or wise then someone is either funny or not old.
If someone is not brave or wise then lucy is not strong.
Everyone who is both not tall and not happy is both old and curious.
Someone is strong or funny.
Someone is strong.
Someone is either generous or not rich.
Someone is either not strong or wise.
Fred is tall or not strong.
John is either not kind or generous.
Fred is creative or not strong.
Someone is not happy or not curious. | Fred is tall. | neutral | ((~quiet(lucy))=>(?[X]:(happy(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((~curious(X)&creative(X))<=>(~calm(X)&~generous(X))))&
((?[X]:((generous(X)|creative(X))))<=>((~humble(lucy)<~>~curious(lucy))))&
(![X]:((~happy(X)<~>~patient(X))<=>(~generous(X)&happy(X))))&
(![X]:((~generous(X)|~old(X))=>(funny(X)&old(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((wise(X)|~creative(X))=>(~tall(X)|humble(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~generous(X)&~calm(X))))&
(((~quiet(john)<~>~strong(john)))<=>((~kind(lucy)<~>~happy(lucy))))&
(![X]:(wise(X)<=>(~humble(X)|~brave(X))))&
(![X]:((~funny(X)&creative(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((generous(X)&~kind(X))<=>(rich(X)&~calm(X))))&
(((quiet(fred)<~>wise(fred)))=>(?[X]:((funny(X)<~>~old(X)))))&
((?[X]:((~brave(X)|wise(X))))=>(~strong(lucy)))&
(![X]:((~tall(X)&~happy(X))=>(old(X)&curious(X))))&
(?[X]:((strong(X)|funny(X))))&
(?[X]:(strong(X)))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~strong(X)<~>wise(X))))&
((tall(fred)|~strong(fred)))&
((~kind(john)<~>generous(john)))&
((creative(fred)|~strong(fred)))&
(?[X]:((~happy(X)|~curious(X)))) | tall(fred) | [] | null | 0 |
Everyone who is not brave or not happy is happy.
Everyone who is creative is both strong and not tall.
Everyone who is both not tall and not patient is both kind and strong and vice versa.
If someone is either not strong or not quiet then someone is not calm.
Everyone who is quiet is not wise.
Everyone who is rich or not happy is either not quiet or not creative.
Everyone who is either kind or humble is either tall or not kind and vice versa.
Everyone who is patient is both not curious and happy and vice versa.
Everyone who is not old is kind and vice versa.
If someone is not rich then someone is either tall or not creative.
Everyone who is either calm or not happy is either old or not calm.
Everyone who is either rich or old is either not calm or old.
If lucy is both not curious and not tall then someone is both funny and old and vice versa.
If someone is not quiet then john is both humble and not creative.
If someone is both not humble and patient then someone is not happy and vice versa.
Everyone who is not happy is not rich and vice versa.
Susan is either rich or patient.
John is either not patient or not wise.
John is either curious or not funny.
Someone is not kind.
Lucy is generous.
Someone is either quiet or tall.
Someone is either generous or not curious. | John is not patient. | contradiction | (![X]:((~brave(X)|~happy(X))=>happy(X)))&
(![X]:(creative(X)=>(strong(X)&~tall(X))))&
(![X]:((~tall(X)&~patient(X))<=>(kind(X)&strong(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))=>(?[X]:(~calm(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((kind(X)<~>humble(X))<=>(tall(X)<~>~kind(X))))&
(![X]:(patient(X)<=>(~curious(X)&happy(X))))&
(![X]:(~old(X)<=>kind(X)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((calm(X)<~>~happy(X))=>(old(X)<~>~calm(X))))&
(![X]:((rich(X)<~>old(X))=>(~calm(X)<~>old(X))))&
(((~curious(lucy)&~tall(lucy)))<=>(?[X]:((funny(X)&old(X)))))&
((?[X]:(~quiet(X)))=>((humble(john)&~creative(john))))&
((?[X]:((~humble(X)&patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:(~happy(X)<=>~rich(X)))&
((rich(susan)<~>patient(susan)))&
((~patient(john)<~>~wise(john)))&
((curious(john)<~>~funny(john)))&
(?[X]:(~kind(X)))&
(generous(lucy))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((generous(X)<~>~curious(X)))) | ~patient(john) | [
"p0",
"p4",
"p5",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 91844001465014363750404
% SZS output start Proof for 91844001465014363750404
1. ! [X0] : ((~happy(X0) | ~brave(X0)) => happy(X0)) [input p0]
5. ! [X0] : (quiet(X0) => ~wise(X0)) [input p4]
6. ! [X0] : ((~happy(X0) | rich(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p5]
14. ? [X0] : ~quiet(X0) => (~creative(john) & humble(john)) [input p13]
16. ! [X0] : (~happy(X0) <=> ~rich(X0)) [input p15]
18. ~patient(john) <~> ~wise(john) [input p17]
24. ~patient(john) [input hypothesis]
28. ! [X0] : (~happy(X0) => happy(X0)) [pure predicate removal 1]
29. ! [X0] : (happy(X0) | happy(X0)) [ennf transformation 28]
32. ! [X0] : (~wise(X0) | ~quiet(X0)) [ennf transformation 5]
33. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 6]
37. (~creative(john) & humble(john)) | ! [X0] : quiet(X0) [ennf transformation 14]
44. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (happy(X0) & ~rich(X0))) [nnf transformation 33]
65. ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))) [nnf transformation 16]
67. (wise(john) | patient(john)) & (~wise(john) | ~patient(john)) [nnf transformation 18]
77. happy(X0) | happy(X0) [cnf transformation 29]
86. ~wise(X0) | ~quiet(X0) [cnf transformation 32]
89. ~rich(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
119. ~creative(john) | quiet(X0) [cnf transformation 37]
124. ~happy(X0) | rich(X0) [cnf transformation 65]
128. wise(john) | patient(john) [cnf transformation 67]
137. ~patient(john) [cnf transformation 24]
146. happy(X0) [duplicate literal removal 77]
164. 4 <=> ! [X1] : rich(X1) [avatar definition]
165. rich(X1) <- (4) [avatar component clause 164]
202. 12 <=> ! [X0] : quiet(X0) [avatar definition]
203. quiet(X0) <- (12) [avatar component clause 202]
205. 13 <=> creative(john) [avatar definition]
207. ~creative(john) <- (~13) [avatar component clause 205]
208. 12 | ~13 [avatar split clause 119,205,202]
215. rich(X0) [subsumption resolution 124,146]
216. 4 [avatar split clause 215,164]
228. 17 <=> patient(john) [avatar definition]
232. 18 <=> wise(john) [avatar definition]
234. wise(john) <- (18) [avatar component clause 232]
235. 17 | 18 [avatar split clause 128,232,228]
267. ~17 [avatar split clause 137,228]
269. ~quiet(john) <- (18) [resolution 86,234]
270. $false <- (12, 18) [subsumption resolution 269,203]
271. ~12 | ~18 [avatar contradiction clause 270]
318. quiet(X0) | creative(X0) <- (4) [resolution 89,165]
326. creative(john) <- (4, 18) [resolution 318,269]
328. $false <- (4, ~13, 18) [subsumption resolution 326,207]
329. ~4 | 13 | ~18 [avatar contradiction clause 328]
330. $false [avatar sat refutation 208,216,235,267,271,329]
% SZS output end Proof for 91844001465014363750404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and curious is both not creative and kind and vice versa.
Everyone who is both humble and not curious is both humble and not tall and vice versa.
Everyone who is not curious or not creative is not funny and vice versa.
If john is either brave or kind then john is either not creative or not calm.
If lucy is not strong then susan is both not funny and patient.
If susan is not wise or not brave then susan is either quiet or not generous.
Everyone who is both humble and not quiet is either not funny or humble.
If someone is either not old or not wise then lucy is generous.
Everyone who is both quiet and old is both not patient and not curious.
Everyone who is not quiet or wise is either old or not happy.
If john is not brave or not old then susan is not calm and vice versa.
Everyone who is not old or not tall is both not old and tall and vice versa.
If fred is either not creative or kind then lucy is either not patient or calm and vice versa.
Everyone who is both tall and not old is not rich.
If alice is old or not quiet then alice is not quiet and vice versa.
If someone is either not strong or not humble then lucy is tall and vice versa.
Susan is either old or not generous.
Alice is either humble or not rich.
Someone is either generous or not generous.
Someone is either humble or calm.
Someone is not curious or funny.
John is not curious. | Alice is old. | neutral | (![X]:((strong(X)&curious(X))<=>(~creative(X)&kind(X))))&
(![X]:((humble(X)&~curious(X))<=>(humble(X)&~tall(X))))&
(![X]:((~curious(X)|~creative(X))<=>~funny(X)))&
(((brave(john)<~>kind(john)))=>((~creative(john)<~>~calm(john))))&
((~strong(lucy))=>((~funny(susan)&patient(susan))))&
(((~wise(susan)|~brave(susan)))=>((quiet(susan)<~>~generous(susan))))&
(![X]:((humble(X)&~quiet(X))=>(~funny(X)<~>humble(X))))&
((?[X]:((~old(X)<~>~wise(X))))=>(generous(lucy)))&
(![X]:((quiet(X)&old(X))=>(~patient(X)&~curious(X))))&
(![X]:((~quiet(X)|wise(X))=>(old(X)<~>~happy(X))))&
(((~brave(john)|~old(john)))<=>(~calm(susan)))&
(![X]:((~old(X)|~tall(X))<=>(~old(X)&tall(X))))&
(((~creative(fred)<~>kind(fred)))<=>((~patient(lucy)<~>calm(lucy))))&
(![X]:((tall(X)&~old(X))=>~rich(X)))&
(((old(alice)|~quiet(alice)))<=>(~quiet(alice)))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(tall(lucy)))&
((old(susan)<~>~generous(susan)))&
((humble(alice)<~>~rich(alice)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:((~curious(X)|funny(X))))&
(~curious(john)) | old(alice) | [] | null | 0 |
If john is patient then alice is either not rich or old and vice versa. If mary is not creative then someone is not curious. Everyone who is not wise or rich is not patient or humble. If paul is both not kind and not rich then susan is not funny and vice versa. If paul is curious then fred is wise. Everyone who is both not wise and not funny is either wise or not strong. Everyone who is not happy is humble. Everyone who is creative or strong is both not old and not wise. If alice is not brave then fred is kind and vice versa. Everyone who is not quiet or humble is not funny. Everyone who is both funny and not kind is not old. Everyone who is not patient or generous is strong. Everyone who is both old and not happy is old and vice versa. If someone is both not quiet and strong then someone is creative or not quiet and vice versa. Everyone who is either not curious or not wise is not generous and vice versa. If alice is both not brave and strong then john is kind or not happy and vice versa. Lucy is both patient and brave. Someone is not generous or patient. Someone is both not strong and not creative. Someone is either not wise or not curious. John is either not happy or not quiet. John is tall or curious. Someone is either kind or funny. | John is not creative. | entailment | ((patient(john))<=>((~rich(alice)<~>old(alice))))&
((~creative(mary))=>(?[X]:(~curious(X))))&
(![X]:((~wise(X)|rich(X))=>(~patient(X)|humble(X))))&
(((~kind(paul)&~rich(paul)))<=>(~funny(susan)))&
((curious(paul))=>(wise(fred)))&
(![X]:((~wise(X)&~funny(X))=>(wise(X)<~>~strong(X))))&
(![X]:(~happy(X)=>humble(X)))&
(![X]:((creative(X)|strong(X))=>(~old(X)&~wise(X))))&
((~brave(alice))<=>(kind(fred)))&
(![X]:((~quiet(X)|humble(X))=>~funny(X)))&
(![X]:((funny(X)&~kind(X))=>~old(X)))&
(![X]:((~patient(X)|generous(X))=>strong(X)))&
(![X]:((old(X)&~happy(X))<=>old(X)))&
((?[X]:((~quiet(X)&strong(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>~generous(X)))&
(((~brave(alice)&strong(alice)))<=>((kind(john)|~happy(john))))&
((patient(lucy)&brave(lucy)))&
(?[X]:((~generous(X)|patient(X))))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~wise(X)<~>~curious(X))))&
((~happy(john)<~>~quiet(john)))&
((tall(john)|curious(john)))&
(?[X]:((kind(X)<~>funny(X)))) | ~creative(john) | [
"p5",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4892401676315544474841432
% SZS output start Proof for 4892401676315544474841432
6. ! [X0] : ((~funny(X0) & ~wise(X0)) => (wise(X0) <~> ~strong(X0))) [input p5]
8. ! [X0] : ((strong(X0) | creative(X0)) => (~wise(X0) & ~old(X0))) [input p7]
10. ! [X0] : ((humble(X0) | ~quiet(X0)) => ~funny(X0)) [input p9]
14. ? [X0] : (strong(X0) & ~quiet(X0)) <=> ? [X0] : (~quiet(X0) | creative(X0)) [input p13]
24. creative(john) [input hypothesis]
25. ? [X0] : (strong(X0) & ~quiet(X0)) <=> ? [X1] : (~quiet(X1) | creative(X1)) [rectify 14]
32. ! [X0] : ((wise(X0) <~> ~strong(X0)) | (funny(X0) | wise(X0))) [ennf transformation 6]
33. ! [X0] : ((wise(X0) <~> ~strong(X0)) | funny(X0) | wise(X0)) [flattening 32]
35. ! [X0] : ((~wise(X0) & ~old(X0)) | (~strong(X0) & ~creative(X0))) [ennf transformation 8]
36. ! [X0] : (~funny(X0) | (~humble(X0) & quiet(X0))) [ennf transformation 10]
46. ! [X0] : (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | funny(X0) | wise(X0)) [nnf transformation 33]
50. (? [X0] : (strong(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) & ~creative(X1))) & (? [X1] : (~quiet(X1) | creative(X1)) | ! [X0] : (~strong(X0) | quiet(X0))) [nnf transformation 25]
51. (? [X0] : (strong(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) & ~creative(X1))) & (? [X2] : (~quiet(X2) | creative(X2)) | ! [X3] : (~strong(X3) | quiet(X3))) [rectify 50]
52. ? [X0] : (strong(X0) & ~quiet(X0)) => (strong(sK1) & ~quiet(sK1)) [choice axiom]
53. ? [X2] : (~quiet(X2) | creative(X2)) => (~quiet(sK2) | creative(sK2)) [choice axiom]
54. ((strong(sK1) & ~quiet(sK1)) | ! [X1] : (quiet(X1) & ~creative(X1))) & ((~quiet(sK2) | creative(sK2)) | ! [X3] : (~strong(X3) | quiet(X3))) [skolemisation 51,53,52]
80. ~strong(X0) | wise(X0) | funny(X0) | wise(X0) [cnf transformation 46]
86. ~strong(X0) | ~wise(X0) [cnf transformation 35]
89. ~funny(X0) | quiet(X0) [cnf transformation 36]
98. ~quiet(sK1) | ~creative(X1) [cnf transformation 54]
100. strong(sK1) | ~creative(X1) [cnf transformation 54]
120. creative(john) [cnf transformation 24]
121. ~strong(X0) | wise(X0) | funny(X0) [duplicate literal removal 80]
185. 14 <=> strong(sK1) [avatar definition]
187. strong(sK1) <- (14) [avatar component clause 185]
190. 15 <=> ! [X1] : ~creative(X1) [avatar definition]
191. ~creative(X1) <- (15) [avatar component clause 190]
192. 15 | 14 [avatar split clause 100,185,190]
194. 16 <=> quiet(sK1) [avatar definition]
198. 15 | ~16 [avatar split clause 98,194,190]
266. ~wise(sK1) <- (14) [resolution 86,187]
354. wise(sK1) | funny(sK1) <- (14) [resolution 121,187]
357. funny(sK1) <- (14) [subsumption resolution 354,266]
366. quiet(sK1) <- (14) [resolution 357,89]
369. 16 | ~14 [avatar split clause 366,185,194]
374. $false <- (15) [resolution 191,120]
375. ~15 [avatar contradiction clause 374]
376. $false [avatar sat refutation 192,198,369,375]
% SZS output end Proof for 4892401676315544474841432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not curious is patient and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is either brave or not patient is either tall or not humble.
If fred is not patient then someone is either not brave or not wise and vice versa.
Everyone who is either not brave or not patient is both happy and rich and vice versa.
Everyone who is generous is either not kind or tall.
Everyone who is either tall or not tall is either not generous or not humble and vice versa.
Everyone who is either rich or wise is not kind or strong.
If someone is either not old or kind then alice is either rich or quiet and vice versa.
Everyone who is tall is both strong and funny and vice versa.
Everyone who is not rich is not funny or strong.
Everyone who is either not curious or rich is both not patient and quiet.
If paul is either quiet or generous then lucy is both creative and happy and vice versa.
Everyone who is either strong or old is both brave and old and vice versa.
Everyone who is humble is wise.
Everyone who is humble or not strong is both not rich and brave and vice versa.
Mary is strong or old.
Someone is both old and strong.
Someone is not humble.
Mary is not quiet or funny.
Someone is generous or not wise. | Paul is not strong. | contradiction | (![X]:((funny(X)&~curious(X))<=>patient(X)))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:((brave(X)<~>~patient(X))=>(tall(X)<~>~humble(X))))&
((~patient(fred))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((~brave(X)<~>~patient(X))<=>(happy(X)&rich(X))))&
(![X]:(generous(X)=>(~kind(X)<~>tall(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((rich(X)<~>wise(X))=>(~kind(X)|strong(X))))&
((?[X]:((~old(X)<~>kind(X))))<=>((rich(alice)<~>quiet(alice))))&
(![X]:(tall(X)<=>(strong(X)&funny(X))))&
(![X]:(~rich(X)=>(~funny(X)|strong(X))))&
(![X]:((~curious(X)<~>rich(X))=>(~patient(X)&quiet(X))))&
(((quiet(paul)<~>generous(paul)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>old(X))<=>(brave(X)&old(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((humble(X)|~strong(X))<=>(~rich(X)&brave(X))))&
((strong(mary)|old(mary)))&
(?[X]:((old(X)&strong(X))))&
(?[X]:(~humble(X)))&
((~quiet(mary)|funny(mary)))&
(?[X]:((generous(X)|~wise(X)))) | ~strong(paul) | [
"p0",
"p4",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6554111895982147785653178
% SZS output start Proof for 6554111895982147785653178
1. ! [X0] : ((~curious(X0) & funny(X0)) <=> patient(X0)) [input p0]
5. ! [X0] : ((~brave(X0) <~> ~patient(X0)) <=> (rich(X0) & happy(X0))) [input p4]
12. ! [X0] : ((~curious(X0) <~> rich(X0)) => (quiet(X0) & ~patient(X0))) [input p11]
16. ! [X0] : ((~strong(X0) | humble(X0)) <=> (brave(X0) & ~rich(X0))) [input p15]
22. ~strong(paul) [input hypothesis]
29. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~curious(X0) <=> rich(X0))) [ennf transformation 12]
31. ! [X0] : (((~curious(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 1]
32. ! [X0] : (((~curious(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | curious(X0) | ~funny(X0))) [flattening 31]
39. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [nnf transformation 5]
40. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [flattening 39]
50. ! [X0] : ((quiet(X0) & ~patient(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) [nnf transformation 29]
55. ! [X0] : (((~strong(X0) | humble(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (strong(X0) & ~humble(X0)))) [nnf transformation 16]
56. ! [X0] : ((~strong(X0) | humble(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (strong(X0) & ~humble(X0)))) [flattening 55]
65. ~patient(X0) | ~curious(X0) [cnf transformation 32]
79. ~brave(X0) | rich(X0) | patient(X0) [cnf transformation 40]
106. ~patient(X0) | rich(X0) | curious(X0) [cnf transformation 50]
124. ~rich(X0) | strong(X0) [cnf transformation 56]
126. strong(X0) | brave(X0) [cnf transformation 56]
134. ~strong(paul) [cnf transformation 22]
197. ~patient(X0) | rich(X0) [subsumption resolution 106,65]
243. brave(paul) [resolution 126,134]
257. rich(paul) | patient(paul) [resolution 79,243]
260. rich(paul) [subsumption resolution 257,197]
263. strong(paul) [resolution 260,124]
265. $false [subsumption resolution 263,134]
% SZS output end Proof for 6554111895982147785653178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not calm is either humble or old and vice versa.
Everyone who is both not strong and tall is either not old or happy and vice versa.
If lucy is rich or not funny then someone is either calm or not curious.
Everyone who is humble or tall is both not strong and curious.
If mary is both funny and patient then someone is both not funny and curious.
Everyone who is either not tall or happy is old or not wise.
If lucy is both not creative and old then john is not kind and vice versa.
If someone is wise or not humble then fred is either not brave or not curious.
Everyone who is strong or not kind is both not strong and happy and vice versa.
Everyone who is either old or not happy is either not wise or quiet.
Everyone who is not old is both not brave and calm.
Everyone who is not calm is not happy or not generous.
Everyone who is either brave or calm is either creative or rich and vice versa.
Everyone who is either happy or old is either tall or not old and vice versa.
If someone is either generous or humble then someone is not humble or not old and vice versa.
Everyone who is not calm or not happy is either quiet or humble.
Someone is both creative and funny.
Mary is both curious and not humble.
Lucy is both not generous and wise.
Lucy is not rich or creative.
Someone is happy or not old.
Susan is either not patient or wise.
Someone is not old. | John is not wise. | contradiction | (![X]:((old(X)<~>~calm(X))<=>(humble(X)<~>old(X))))&
(![X]:((~strong(X)&tall(X))<=>(~old(X)<~>happy(X))))&
(((rich(lucy)|~funny(lucy)))=>(?[X]:((calm(X)<~>~curious(X)))))&
(![X]:((humble(X)|tall(X))=>(~strong(X)&curious(X))))&
(((funny(mary)&patient(mary)))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:((~tall(X)<~>happy(X))=>(old(X)|~wise(X))))&
(((~creative(lucy)&old(lucy)))<=>(~kind(john)))&
((?[X]:((wise(X)|~humble(X))))=>((~brave(fred)<~>~curious(fred))))&
(![X]:((strong(X)|~kind(X))<=>(~strong(X)&happy(X))))&
(![X]:((old(X)<~>~happy(X))=>(~wise(X)<~>quiet(X))))&
(![X]:(~old(X)=>(~brave(X)&calm(X))))&
(![X]:(~calm(X)=>(~happy(X)|~generous(X))))&
(![X]:((brave(X)<~>calm(X))<=>(creative(X)<~>rich(X))))&
(![X]:((happy(X)<~>old(X))<=>(tall(X)<~>~old(X))))&
((?[X]:((generous(X)<~>humble(X))))<=>(?[X]:((~humble(X)|~old(X)))))&
(![X]:((~calm(X)|~happy(X))=>(quiet(X)<~>humble(X))))&
(?[X]:((creative(X)&funny(X))))&
((curious(mary)&~humble(mary)))&
((~generous(lucy)&wise(lucy)))&
((~rich(lucy)|creative(lucy)))&
(?[X]:((happy(X)|~old(X))))&
((~patient(susan)<~>wise(susan)))&
(?[X]:(~old(X))) | ~wise(john) | [
"p0",
"p1",
"p6",
"p8",
"p9",
"p10",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7109730629808403232640985
% SZS output start Proof for 7109730629808403232640985
1. ! [X0] : ((old(X0) <~> ~calm(X0)) <=> (humble(X0) <~> old(X0))) [input p0]
2. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (~old(X0) <~> happy(X0))) [input p1]
7. (old(lucy) & ~creative(lucy)) <=> ~kind(john) [input p6]
9. ! [X0] : ((~kind(X0) | strong(X0)) <=> (happy(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~wise(X0) <~> quiet(X0))) [input p9]
11. ! [X0] : (~old(X0) => (calm(X0) & ~brave(X0))) [input p10]
13. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (creative(X0) <~> rich(X0))) [input p12]
14. ! [X0] : ((happy(X0) <~> old(X0)) <=> (tall(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~happy(X0) | ~calm(X0)) => (quiet(X0) <~> humble(X0))) [input p15]
20. creative(lucy) | ~rich(lucy) [input p19]
24. ~wise(john) [input hypothesis]
33. ! [X0] : ((~wise(X0) <~> quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10]
34. ! [X0] : ((calm(X0) & ~brave(X0)) | old(X0)) [ennf transformation 11]
37. ! [X0] : ((quiet(X0) <~> humble(X0)) | (happy(X0) & calm(X0))) [ennf transformation 16]
38. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) & (((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [nnf transformation 1]
39. ! [X0] : (((tall(X0) & ~strong(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~tall(X0) | strong(X0)))) [nnf transformation 2]
40. ! [X0] : (((tall(X0) & ~strong(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~tall(X0) | strong(X0))) [flattening 39]
47. ((old(lucy) & ~creative(lucy)) | kind(john)) & (~kind(john) | (~old(lucy) | creative(lucy))) [nnf transformation 7]
48. ((old(lucy) & ~creative(lucy)) | kind(john)) & (~kind(john) | ~old(lucy) | creative(lucy)) [flattening 47]
50. ! [X0] : (((~kind(X0) | strong(X0)) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | (kind(X0) & ~strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((~kind(X0) | strong(X0) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | (kind(X0) & ~strong(X0)))) [flattening 50]
52. ! [X0] : (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 33]
53. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 13]
54. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 14]
60. ! [X0] : (((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (happy(X0) & calm(X0))) [nnf transformation 37]
72. ~calm(X0) | old(X0) | old(X0) | ~humble(X0) [cnf transformation 38]
76. ~tall(X0) | ~old(X0) | happy(X0) | strong(X0) [cnf transformation 40]
80. happy(X0) | tall(X0) | old(X0) [cnf transformation 40]
81. ~happy(X0) | ~old(X0) | tall(X0) [cnf transformation 40]
95. ~creative(lucy) | kind(john) [cnf transformation 48]
101. ~strong(X0) | ~strong(X0) [cnf transformation 51]
105. ~kind(X0) | strong(X0) | ~happy(X0) | strong(X0) [cnf transformation 51]
109. ~quiet(X0) | wise(X0) | old(X0) | happy(X0) [cnf transformation 52]
110. ~brave(X0) | old(X0) [cnf transformation 34]
111. calm(X0) | old(X0) [cnf transformation 34]
114. ~calm(X0) | creative(X0) | brave(X0) | rich(X0) [cnf transformation 53]
122. ~old(X0) | tall(X0) | happy(X0) | ~old(X0) [cnf transformation 54]
127. ~old(X0) | ~happy(X0) | ~old(X0) | ~tall(X0) [cnf transformation 54]
136. quiet(X0) | humble(X0) | happy(X0) [cnf transformation 60]
145. creative(lucy) | ~rich(lucy) [cnf transformation 20]
150. ~wise(john) [cnf transformation 24]
151. ~old(X0) | tall(X0) | happy(X0) [duplicate literal removal 122]
154. ~old(X0) | ~happy(X0) | ~tall(X0) [duplicate literal removal 127]
155. ~strong(X0) [duplicate literal removal 101]
156. ~kind(X0) | strong(X0) | ~happy(X0) [duplicate literal removal 105]
159. ~humble(X0) | old(X0) | ~calm(X0) [duplicate literal removal 72]
177. 4 <=> rich(lucy) [avatar definition]
179. ~rich(lucy) <- (~4) [avatar component clause 177]
202. 9 <=> kind(john) [avatar definition]
204. kind(john) <- (9) [avatar component clause 202]
206. 10 <=> old(lucy) [avatar definition]
207. ~old(lucy) <- (~10) [avatar component clause 206]
208. old(lucy) <- (10) [avatar component clause 206]
211. 11 <=> creative(lucy) [avatar definition]
213. ~creative(lucy) <- (~11) [avatar component clause 211]
214. 9 | ~11 [avatar split clause 95,211,202]
234. ~happy(X0) | ~old(X0) [subsumption resolution 154,81]
236. happy(X0) | tall(X0) [subsumption resolution 151,80]
269. ~4 | 11 [avatar split clause 145,211,177]
298. ~old(X1) | tall(X1) [resolution 236,234]
308. tall(lucy) <- (10) [resolution 298,208]
332. ~old(lucy) | happy(lucy) | strong(lucy) <- (10) [resolution 76,308]
334. happy(lucy) | strong(lucy) <- (10) [subsumption resolution 332,208]
335. happy(lucy) <- (10) [subsumption resolution 334,155]
346. ~old(lucy) <- (10) [resolution 335,234]
349. $false <- (10) [subsumption resolution 346,208]
350. ~10 [avatar contradiction clause 349]
351. strong(john) | ~happy(john) <- (9) [resolution 204,156]
352. ~happy(john) <- (9) [subsumption resolution 351,155]
354. tall(john) | old(john) <- (9) [resolution 352,80]
356. tall(john) <- (9) [subsumption resolution 354,298]
358. ~old(john) | happy(john) | strong(john) <- (9) [resolution 356,76]
361. ~old(john) | strong(john) <- (9) [subsumption resolution 358,352]
362. ~old(john) <- (9) [subsumption resolution 361,155]
382. wise(X0) | old(X0) | happy(X0) | humble(X0) | happy(X0) [resolution 109,136]
383. wise(X0) | old(X0) | happy(X0) | humble(X0) [duplicate literal removal 382]
393. creative(X0) | brave(X0) | rich(X0) | old(X0) [resolution 114,111]
398. creative(X0) | rich(X0) | old(X0) [subsumption resolution 393,110]
479. rich(lucy) | old(lucy) <- (~11) [resolution 398,213]
483. old(lucy) <- (~4, ~11) [subsumption resolution 479,179]
484. $false <- (~4, ~10, ~11) [subsumption resolution 483,207]
485. 4 | 10 | 11 [avatar contradiction clause 484]
511. old(john) | happy(john) | humble(john) [resolution 383,150]
518. happy(john) | humble(john) <- (9) [subsumption resolution 511,362]
519. humble(john) <- (9) [subsumption resolution 518,352]
546. old(john) | ~calm(john) <- (9) [resolution 519,159]
549. ~calm(john) <- (9) [subsumption resolution 546,362]
616. old(john) <- (9) [resolution 549,111]
617. $false <- (9) [subsumption resolution 616,362]
618. ~9 [avatar contradiction clause 617]
619. $false [avatar sat refutation 214,269,350,485,618]
% SZS output end Proof for 7109730629808403232640985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not brave is generous or calm. If someone is strong or calm then fred is brave. If someone is not creative or not wise then mary is both not strong and not quiet. If someone is either not tall or not quiet then someone is either happy or wise. Everyone who is both rich and not patient is either old or not happy and vice versa. If john is not kind or not old then someone is both not kind and old. If someone is tall or not tall then someone is either brave or quiet and vice versa. Everyone who is either not funny or not patient is happy or not brave. If someone is either quiet or strong then someone is either not humble or not brave. Everyone who is both not happy and not patient is either not wise or not quiet and vice versa. If lucy is funny then someone is not patient and vice versa. Everyone who is either old or not wise is both not calm and not old and vice versa. Everyone who is either tall or not calm is not quiet and vice versa. Everyone who is either not funny or not tall is both brave and funny. Everyone who is not funny or not tall is either not tall or calm and vice versa. If someone is either happy or kind then someone is either patient or not funny and vice versa. Someone is either strong or not humble. Alice is both not rich and quiet. Someone is either rich or not calm. John is not strong or not patient. Susan is both kind and not brave. Fred is either funny or not creative. | Mary is wise. | contradiction | (![X]:((rich(X)&~brave(X))=>(generous(X)|calm(X))))&
((?[X]:((strong(X)|calm(X))))=>(brave(fred)))&
((?[X]:((~creative(X)|~wise(X))))=>((~strong(mary)&~quiet(mary))))&
((?[X]:((~tall(X)<~>~quiet(X))))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:((rich(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~kind(john)|~old(john)))=>(?[X]:((~kind(X)&old(X)))))&
((?[X]:((tall(X)|~tall(X))))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~funny(X)<~>~patient(X))=>(happy(X)|~brave(X))))&
((?[X]:((quiet(X)<~>strong(X))))=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(~wise(X)<~>~quiet(X))))&
((funny(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~calm(X)&~old(X))))&
(![X]:((tall(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~funny(X)<~>~tall(X))=>(brave(X)&funny(X))))&
(![X]:((~funny(X)|~tall(X))<=>(~tall(X)<~>calm(X))))&
((?[X]:((happy(X)<~>kind(X))))<=>(?[X]:((patient(X)<~>~funny(X)))))&
(?[X]:((strong(X)<~>~humble(X))))&
((~rich(alice)&quiet(alice)))&
(?[X]:((rich(X)<~>~calm(X))))&
((~strong(john)|~patient(john)))&
((kind(susan)&~brave(susan)))&
((funny(fred)<~>~creative(fred))) | wise(mary) | [
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6152704947306209611150348
% SZS output start Proof for 6152704947306209611150348
12. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (~old(X0) & ~calm(X0))) [input p11]
14. ! [X0] : ((~funny(X0) <~> ~tall(X0)) => (funny(X0) & brave(X0))) [input p13]
15. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~tall(X0) <~> calm(X0))) [input p14]
23. wise(mary) [input hypothesis]
36. ! [X0] : ((funny(X0) & brave(X0)) | (~funny(X0) <=> ~tall(X0))) [ennf transformation 14]
61. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | calm(X0))) & ((~old(X0) & ~calm(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 12]
62. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | calm(X0)) & ((~old(X0) & ~calm(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [flattening 61]
64. ! [X0] : ((funny(X0) & brave(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) [nnf transformation 36]
65. ! [X0] : (((~tall(X0) | ~funny(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) & (((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (tall(X0) & funny(X0)))) [nnf transformation 15]
66. ! [X0] : ((~tall(X0) | ~funny(X0) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) & (((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (tall(X0) & funny(X0)))) [flattening 65]
121. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 62]
123. ~wise(X0) | old(X0) | old(X0) | calm(X0) [cnf transformation 62]
131. funny(X0) | ~tall(X0) | funny(X0) [cnf transformation 64]
136. ~calm(X0) | tall(X0) | tall(X0) [cnf transformation 66]
138. ~tall(X0) | ~funny(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 66]
158. wise(mary) [cnf transformation 23]
159. ~calm(X0) | tall(X0) [duplicate literal removal 136]
160. ~tall(X0) | ~funny(X0) | ~calm(X0) [duplicate literal removal 138]
161. ~tall(X0) | funny(X0) [duplicate literal removal 131]
162. ~old(X0) | ~wise(X0) [duplicate literal removal 121]
163. ~wise(X0) | old(X0) | calm(X0) [duplicate literal removal 123]
165. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
166. ~calm(X0) <- (1) [avatar component clause 165]
281. ~tall(X0) | ~calm(X0) [subsumption resolution 160,161]
282. ~calm(X0) [subsumption resolution 159,281]
283. 1 [avatar split clause 282,165]
438. old(mary) | calm(mary) [resolution 163,158]
439. old(mary) <- (1) [subsumption resolution 438,166]
471. ~wise(mary) <- (1) [resolution 439,162]
487. $false <- (1) [subsumption resolution 471,158]
488. ~1 [avatar contradiction clause 487]
489. $false [avatar sat refutation 283,488]
% SZS output end Proof for 6152704947306209611150348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or happy is kind.
Everyone who is both not rich and old is both not calm and old and vice versa.
Everyone who is patient is either not patient or patient and vice versa.
Everyone who is either not old or not happy is old or not calm and vice versa.
Everyone who is both strong and not rich is both kind and quiet and vice versa.
Everyone who is either not happy or not tall is either not old or creative.
If paul is either not quiet or not happy then someone is both not strong and tall.
Everyone who is either not humble or not old is both patient and humble.
Everyone who is happy or not creative is both creative and quiet.
Everyone who is either not creative or not old is both patient and not old.
If mary is either patient or old then someone is happy and vice versa.
If someone is both not wise and not funny then someone is either wise or generous.
Everyone who is not generous or old is brave.
Everyone who is both not happy and generous is either not humble or not strong and vice versa.
Everyone who is not creative is either not calm or not quiet.
Someone is either not happy or strong.
Alice is not happy or not tall.
John is either not rich or not kind.
Lucy is either not creative or not quiet.
Someone is brave.
Susan is strong. | Lucy is not creative. | contradiction | (![X]:((strong(X)<~>happy(X))=>kind(X)))&
(![X]:((~rich(X)&old(X))<=>(~calm(X)&old(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(old(X)|~calm(X))))&
(![X]:((strong(X)&~rich(X))<=>(kind(X)&quiet(X))))&
(![X]:((~happy(X)<~>~tall(X))=>(~old(X)<~>creative(X))))&
(((~quiet(paul)<~>~happy(paul)))=>(?[X]:((~strong(X)&tall(X)))))&
(![X]:((~humble(X)<~>~old(X))=>(patient(X)&humble(X))))&
(![X]:((happy(X)|~creative(X))=>(creative(X)&quiet(X))))&
(![X]:((~creative(X)<~>~old(X))=>(patient(X)&~old(X))))&
(((patient(mary)<~>old(mary)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)&~funny(X))))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((~generous(X)|old(X))=>brave(X)))&
(![X]:((~happy(X)&generous(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~creative(X)=>(~calm(X)<~>~quiet(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
((~happy(alice)|~tall(alice)))&
((~rich(john)<~>~kind(john)))&
((~creative(lucy)<~>~quiet(lucy)))&
(?[X]:(brave(X)))&
(strong(susan)) | ~creative(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5616623282702203005293550
% SZS output start Proof for 5616623282702203005293550
9. ! [X0] : ((~creative(X0) | happy(X0)) => (quiet(X0) & creative(X0))) [input p8]
22. ~creative(lucy) [input hypothesis]
31. ! [X0] : ((quiet(X0) & creative(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 9]
93. creative(X0) | creative(X0) [cnf transformation 31]
120. ~creative(lucy) [cnf transformation 22]
122. creative(X0) [duplicate literal removal 93]
198. $false [subsumption resolution 120,122]
% SZS output end Proof for 5616623282702203005293550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is both kind and not brave.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Fred is either rich or curious. | Susan is kind. | contradiction | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:((kind(X)&~brave(X)))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
((rich(fred)<~>curious(fred))) | kind(susan) | [
"p0",
"p2",
"p3",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3617023889371092781161892
% SZS output start Proof for 3617023889371092781161892
1. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (calm(X0) & creative(X0))) [input p0]
3. ! [X0] : ((kind(X0) | ~kind(X0)) => (calm(X0) <~> tall(X0))) [input p2]
4. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p3]
7. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p6]
8. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p7]
11. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p10]
20. kind(susan) [input hypothesis]
23. ! [X0] : ((calm(X0) <~> tall(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 3]
25. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 11]
26. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 1]
27. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 26]
31. ! [X0] : (((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~kind(X0) & kind(X0))) [nnf transformation 23]
32. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 4]
33. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 32]
38. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 7]
39. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 38]
40. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 8]
41. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 40]
62. ~kind(X0) | ~wise(X0) | calm(X0) [cnf transformation 27]
67. tall(X0) | calm(X0) | kind(X0) [cnf transformation 31]
68. ~kind(X0) | calm(X0) | tall(X0) [cnf transformation 31]
69. ~tall(X0) | ~calm(X0) | kind(X0) [cnf transformation 31]
70. ~tall(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 31]
75. ~patient(X0) | strong(X0) [cnf transformation 33]
88. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 39]
90. brave(X0) | patient(X0) | strong(X0) [cnf transformation 39]
94. ~strong(X0) | ~kind(X0) [cnf transformation 41]
105. ~brave(X0) | wise(X0) [cnf transformation 25]
131. kind(susan) [cnf transformation 20]
147. ~tall(X0) | ~calm(X0) [subsumption resolution 69,70]
148. tall(X0) | calm(X0) [subsumption resolution 67,68]
149. strong(X0) | brave(X0) [subsumption resolution 90,75]
151. ~calm(X0) | strong(X0) [subsumption resolution 88,75]
154. 4 <=> tall(susan) [avatar definition]
155. ~tall(susan) <- (~4) [avatar component clause 154]
156. tall(susan) <- (4) [avatar component clause 154]
235. calm(susan) <- (~4) [resolution 148,155]
240. ~kind(X1) | brave(X1) [resolution 149,94]
244. strong(susan) <- (~4) [resolution 151,235]
257. ~kind(susan) <- (~4) [resolution 244,94]
258. $false <- (~4) [subsumption resolution 257,131]
259. 4 [avatar contradiction clause 258]
260. ~calm(susan) <- (4) [resolution 156,147]
271. 17 <=> wise(susan) [avatar definition]
287. ~wise(susan) | calm(susan) [resolution 62,131]
472. brave(susan) [resolution 240,131]
572. wise(susan) [resolution 472,105]
575. 17 [avatar split clause 572,271]
576. ~wise(susan) <- (4) [subsumption resolution 287,260]
577. ~17 | ~4 [avatar split clause 576,154,271]
578. $false [avatar sat refutation 259,575,577]
% SZS output end Proof for 3617023889371092781161892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not tall is both strong and happy and vice versa.
If susan is either happy or not wise then paul is either old or not wise.
If john is not funny or not old then someone is calm or not curious and vice versa.
If fred is calm then alice is rich and vice versa.
Everyone who is tall or old is either not tall or not brave and vice versa.
Everyone who is not tall is not kind or creative and vice versa.
Everyone who is not tall or not quiet is not humble.
Everyone who is kind or humble is humble.
If alice is either happy or rich then paul is either brave or old and vice versa.
Everyone who is either not patient or quiet is happy.
If someone is not generous or brave then someone is curious or not quiet and vice versa.
If someone is either strong or not humble then someone is generous or kind and vice versa.
If mary is both strong and not brave then someone is both funny and quiet and vice versa.
Everyone who is not old is both wise and kind.
Everyone who is generous is both not kind and not calm and vice versa.
Everyone who is either not kind or wise is either not quiet or not creative.
Someone is both not rich and wise.
John is not creative.
Someone is rich or not old.
Mary is both not humble and not patient.
Fred is calm or wise. | Fred is generous. | contradiction | (![X]:((~happy(X)|~tall(X))<=>(strong(X)&happy(X))))&
(((happy(susan)<~>~wise(susan)))=>((old(paul)<~>~wise(paul))))&
(((~funny(john)|~old(john)))<=>(?[X]:((calm(X)|~curious(X)))))&
((calm(fred))<=>(rich(alice)))&
(![X]:((tall(X)|old(X))<=>(~tall(X)<~>~brave(X))))&
(![X]:(~tall(X)<=>(~kind(X)|creative(X))))&
(![X]:((~tall(X)|~quiet(X))=>~humble(X)))&
(![X]:((kind(X)|humble(X))=>humble(X)))&
(((happy(alice)<~>rich(alice)))<=>((brave(paul)<~>old(paul))))&
(![X]:((~patient(X)<~>quiet(X))=>happy(X)))&
((?[X]:((~generous(X)|brave(X))))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:((strong(X)<~>~humble(X))))<=>(?[X]:((generous(X)|kind(X)))))&
(((strong(mary)&~brave(mary)))<=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:(~old(X)=>(wise(X)&kind(X))))&
(![X]:(generous(X)<=>(~kind(X)&~calm(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~quiet(X)<~>~creative(X))))&
(?[X]:((~rich(X)&wise(X))))&
(~creative(john))&
(?[X]:((rich(X)|~old(X))))&
((~humble(mary)&~patient(mary)))&
((calm(fred)|wise(fred))) | generous(fred) | [
"p0",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7396045836922521558934875
% SZS output start Proof for 7396045836922521558934875
1. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (happy(X0) & strong(X0))) [input p0]
6. ! [X0] : (~tall(X0) <=> (creative(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | ~tall(X0)) => ~humble(X0)) [input p6]
8. ! [X0] : ((humble(X0) | kind(X0)) => humble(X0)) [input p7]
12. ? [X0] : (strong(X0) <~> ~humble(X0)) <=> ? [X0] : (kind(X0) | generous(X0)) [input p11]
22. generous(fred) [input hypothesis]
24. ? [X0] : (strong(X0) <~> ~humble(X0)) <=> ? [X1] : (kind(X1) | generous(X1)) [rectify 12]
26. ! [X0] : (~humble(X0) | (quiet(X0) & tall(X0))) [ennf transformation 7]
27. ! [X0] : (humble(X0) | (~humble(X0) & ~kind(X0))) [ennf transformation 8]
31. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 1]
32. ! [X0] : ((~tall(X0) | ~happy(X0) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | (tall(X0) & happy(X0)))) [flattening 31]
42. ! [X0] : ((~tall(X0) | (~creative(X0) & kind(X0))) & ((creative(X0) | ~kind(X0)) | tall(X0))) [nnf transformation 6]
43. ! [X0] : ((~tall(X0) | (~creative(X0) & kind(X0))) & (creative(X0) | ~kind(X0) | tall(X0))) [flattening 42]
51. (? [X0] : ((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ! [X1] : (~kind(X1) & ~generous(X1))) & (? [X1] : (kind(X1) | generous(X1)) | ! [X0] : ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) [nnf transformation 24]
52. (? [X0] : ((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ! [X1] : (~kind(X1) & ~generous(X1))) & (? [X2] : (kind(X2) | generous(X2)) | ! [X3] : ((strong(X3) | humble(X3)) & (~humble(X3) | ~strong(X3)))) [rectify 51]
53. ? [X0] : ((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) => ((humble(sK3) | ~strong(sK3)) & (~humble(sK3) | strong(sK3))) [choice axiom]
54. ? [X2] : (kind(X2) | generous(X2)) => (kind(sK4) | generous(sK4)) [choice axiom]
55. (((humble(sK3) | ~strong(sK3)) & (~humble(sK3) | strong(sK3))) | ! [X1] : (~kind(X1) & ~generous(X1))) & ((kind(sK4) | generous(sK4)) | ! [X3] : ((strong(X3) | humble(X3)) & (~humble(X3) | ~strong(X3)))) [skolemisation 52,54,53]
69. strong(X0) | tall(X0) [cnf transformation 32]
70. happy(X0) | happy(X0) [cnf transformation 32]
72. ~tall(X0) | ~happy(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 32]
90. ~tall(X0) | kind(X0) [cnf transformation 43]
92. ~humble(X0) | tall(X0) [cnf transformation 26]
94. ~kind(X0) | humble(X0) [cnf transformation 27]
112. ~humble(sK3) | strong(sK3) | ~generous(X1) [cnf transformation 55]
114. humble(sK3) | ~strong(sK3) | ~generous(X1) [cnf transformation 55]
136. generous(fred) [cnf transformation 22]
139. happy(X0) [duplicate literal removal 70]
140. ~strong(X0) | ~happy(X0) | ~tall(X0) [duplicate literal removal 72]
241. 22 <=> strong(sK3) [avatar definition]
242. strong(sK3) <- (22) [avatar component clause 241]
243. ~strong(sK3) <- (~22) [avatar component clause 241]
245. 23 <=> humble(sK3) [avatar definition]
246. ~humble(sK3) <- (~23) [avatar component clause 245]
247. humble(sK3) <- (23) [avatar component clause 245]
250. 24 <=> ! [X1] : ~generous(X1) [avatar definition]
251. ~generous(X1) <- (24) [avatar component clause 250]
252. 24 | ~22 | 23 [avatar split clause 114,245,241,250]
254. 24 | 22 | ~23 [avatar split clause 112,245,241,250]
308. tall(sK3) <- (~22) [resolution 69,243]
310. kind(sK3) <- (~22) [resolution 90,308]
313. humble(sK3) <- (~22) [resolution 94,310]
315. $false <- (~22, ~23) [subsumption resolution 313,246]
316. 22 | 23 [avatar contradiction clause 315]
320. tall(sK3) <- (23) [resolution 247,92]
386. ~happy(sK3) | ~tall(sK3) <- (22) [resolution 140,242]
388. ~tall(sK3) <- (22) [subsumption resolution 386,139]
389. $false <- (22, 23) [subsumption resolution 388,320]
390. ~22 | ~23 [avatar contradiction clause 389]
394. $false <- (24) [resolution 251,136]
398. ~24 [avatar contradiction clause 394]
400. $false [avatar sat refutation 252,254,316,390,398]
% SZS output end Proof for 7396045836922521558934875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old is creative.
Everyone who is either calm or patient is curious and vice versa.
Everyone who is creative is either tall or not rich.
Everyone who is either not humble or not happy is both generous and calm.
Everyone who is either not wise or patient is either not curious or rich.
Everyone who is funny is brave and vice versa.
Everyone who is not creative or not funny is not tall or wise and vice versa.
Everyone who is not happy is both old and tall and vice versa.
Everyone who is either not kind or not old is not quiet.
Everyone who is both not rich and not humble is either not curious or wise.
Everyone who is curious is not patient.
Everyone who is either quiet or old is not happy and vice versa.
Everyone who is both not generous and kind is not strong.
Everyone who is not humble is both not patient and not brave and vice versa.
Everyone who is happy or wise is patient or generous.
Everyone who is quiet is both brave and not old and vice versa.
Fred is not tall or not humble.
Someone is curious.
Someone is both curious and kind.
Someone is not strong or not brave.
Fred is both patient and not curious.
John is not funny.
Someone is not kind or patient.
Someone is both not funny and calm. | Fred is not rich. | entailment | (![X]:((happy(X)|old(X))=>creative(X)))&
(![X]:((calm(X)<~>patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(generous(X)&calm(X))))&
(![X]:((~wise(X)<~>patient(X))=>(~curious(X)<~>rich(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~creative(X)|~funny(X))<=>(~tall(X)|wise(X))))&
(![X]:(~happy(X)<=>(old(X)&tall(X))))&
(![X]:((~kind(X)<~>~old(X))=>~quiet(X)))&
(![X]:((~rich(X)&~humble(X))=>(~curious(X)<~>wise(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((quiet(X)<~>old(X))<=>~happy(X)))&
(![X]:((~generous(X)&kind(X))=>~strong(X)))&
(![X]:(~humble(X)<=>(~patient(X)&~brave(X))))&
(![X]:((happy(X)|wise(X))=>(patient(X)|generous(X))))&
(![X]:(quiet(X)<=>(brave(X)&~old(X))))&
((~tall(fred)|~humble(fred)))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:((~strong(X)|~brave(X))))&
((patient(fred)&~curious(fred)))&
(~funny(john))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((~funny(X)&calm(X)))) | ~rich(fred) | [
"p0",
"p2",
"p7",
"p13",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1295184552567140343264244
% SZS output start Proof for 1295184552567140343264244
1. ! [X0] : ((old(X0) | happy(X0)) => creative(X0)) [input p0]
3. ! [X0] : (creative(X0) => (tall(X0) <~> ~rich(X0))) [input p2]
8. ! [X0] : (~happy(X0) <=> (tall(X0) & old(X0))) [input p7]
14. ! [X0] : (~humble(X0) <=> (~brave(X0) & ~patient(X0))) [input p13]
17. ~humble(fred) | ~tall(fred) [input p16]
21. ~curious(fred) & patient(fred) [input p20]
25. rich(fred) [input hypothesis]
30. ! [X0] : (creative(X0) | (~old(X0) & ~happy(X0))) [ennf transformation 1]
31. ! [X0] : ((tall(X0) <~> ~rich(X0)) | ~creative(X0)) [ennf transformation 3]
39. ! [X0] : (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ~creative(X0)) [nnf transformation 31]
45. ! [X0] : ((~happy(X0) | (~tall(X0) | ~old(X0))) & ((tall(X0) & old(X0)) | happy(X0))) [nnf transformation 8]
46. ! [X0] : ((~happy(X0) | ~tall(X0) | ~old(X0)) & ((tall(X0) & old(X0)) | happy(X0))) [flattening 45]
50. ! [X0] : ((~humble(X0) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | humble(X0))) [nnf transformation 14]
51. ! [X0] : ((~humble(X0) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | humble(X0))) [flattening 50]
62. ~happy(X0) | creative(X0) [cnf transformation 30]
63. ~old(X0) | creative(X0) [cnf transformation 30]
68. ~rich(X0) | tall(X0) | ~creative(X0) [cnf transformation 39]
82. old(X0) | happy(X0) [cnf transformation 46]
94. ~patient(X0) | humble(X0) [cnf transformation 51]
100. ~humble(fred) | ~tall(fred) [cnf transformation 17]
104. patient(fred) [cnf transformation 21]
110. rich(fred) [cnf transformation 25]
116. 1 <=> tall(fred) [avatar definition]
118. ~tall(fred) <- (~1) [avatar component clause 116]
120. 2 <=> humble(fred) [avatar definition]
123. ~1 | ~2 [avatar split clause 100,120,116]
133. happy(X0) | creative(X0) [resolution 82,63]
134. creative(X0) [subsumption resolution 133,62]
139. humble(fred) [resolution 94,104]
140. 2 [avatar split clause 139,120]
165. tall(fred) | ~creative(fred) [resolution 68,110]
166. ~creative(fred) <- (~1) [subsumption resolution 165,118]
167. $false <- (~1) [subsumption resolution 166,134]
168. 1 [avatar contradiction clause 167]
169. $false [avatar sat refutation 123,140,168]
% SZS output end Proof for 1295184552567140343264244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not creative and vice versa.
If someone is either strong or not curious then someone is not kind.
If alice is quiet then paul is either not generous or tall and vice versa.
If alice is tall then someone is patient or not rich.
Everyone who is either tall or creative is both not funny and not rich and vice versa.
If someone is both not generous and generous then someone is both not happy and patient.
Everyone who is not curious or not old is brave and vice versa.
If paul is both rich and not brave then fred is strong or not generous.
If someone is either wise or not strong then lucy is both calm and not strong.
If someone is both not strong and funny then lucy is either not creative or wise and vice versa.
If fred is both wise and happy then john is not old or not brave.
Everyone who is not brave is happy or old.
Everyone who is not quiet is both creative and curious and vice versa.
If paul is strong then paul is both not calm and not curious and vice versa.
If john is not calm then someone is creative and vice versa.
Everyone who is rich or kind is both old and not kind and vice versa.
Someone is not funny or not happy.
John is funny or humble.
John is either strong or not tall.
Fred is strong.
Someone is both old and not creative.
Someone is humble.
Someone is both not curious and not calm.
John is either not brave or not strong. | John is not tall. | entailment | (![X]:(~kind(X)<=>~creative(X)))&
((?[X]:((strong(X)<~>~curious(X))))=>(?[X]:(~kind(X))))&
((quiet(alice))<=>((~generous(paul)<~>tall(paul))))&
((tall(alice))=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((tall(X)<~>creative(X))<=>(~funny(X)&~rich(X))))&
((?[X]:((~generous(X)&generous(X))))=>(?[X]:((~happy(X)&patient(X)))))&
(![X]:((~curious(X)|~old(X))<=>brave(X)))&
(((rich(paul)&~brave(paul)))=>((strong(fred)|~generous(fred))))&
((?[X]:((wise(X)<~>~strong(X))))=>((calm(lucy)&~strong(lucy))))&
((?[X]:((~strong(X)&funny(X))))<=>((~creative(lucy)<~>wise(lucy))))&
(((wise(fred)&happy(fred)))=>((~old(john)|~brave(john))))&
(![X]:(~brave(X)=>(happy(X)|old(X))))&
(![X]:(~quiet(X)<=>(creative(X)&curious(X))))&
((strong(paul))<=>((~calm(paul)&~curious(paul))))&
((~calm(john))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|kind(X))<=>(old(X)&~kind(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((funny(john)|humble(john)))&
((strong(john)<~>~tall(john)))&
(strong(fred))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:(humble(X)))&
(?[X]:((~curious(X)&~calm(X))))&
((~brave(john)<~>~strong(john))) | ~tall(john) | [
"p0",
"p4",
"p6",
"p14",
"p15",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 496447598822685435799361
% SZS output start Proof for 496447598822685435799361
1. ! [X0] : (~kind(X0) <=> ~creative(X0)) [input p0]
5. ! [X0] : ((tall(X0) <~> creative(X0)) <=> (~rich(X0) & ~funny(X0))) [input p4]
7. ! [X0] : ((~old(X0) | ~curious(X0)) <=> brave(X0)) [input p6]
15. ~calm(john) <=> ? [X0] : creative(X0) [input p14]
16. ! [X0] : ((kind(X0) | rich(X0)) <=> (~kind(X0) & old(X0))) [input p15]
19. strong(john) <~> ~tall(john) [input p18]
24. ~brave(john) <~> ~strong(john) [input p23]
25. tall(john) [input hypothesis]
41. ! [X0] : ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))) [nnf transformation 1]
47. ! [X0] : ((((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0))))) [nnf transformation 5]
48. ! [X0] : ((((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0))))) [flattening 47]
52. ! [X0] : (((~old(X0) | ~curious(X0)) | ~brave(X0)) & (brave(X0) | (old(X0) & curious(X0)))) [nnf transformation 7]
53. ! [X0] : ((~old(X0) | ~curious(X0) | ~brave(X0)) & (brave(X0) | (old(X0) & curious(X0)))) [flattening 52]
63. (~calm(john) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | calm(john)) [nnf transformation 15]
64. (~calm(john) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | calm(john)) [rectify 63]
65. ? [X1] : creative(X1) => creative(sK3) [choice axiom]
66. (~calm(john) | ! [X0] : ~creative(X0)) & (creative(sK3) | calm(john)) [skolemisation 64,65]
67. ! [X0] : (((kind(X0) | rich(X0)) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 16]
68. ! [X0] : ((kind(X0) | rich(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 67]
71. (tall(john) | ~strong(john)) & (~tall(john) | strong(john)) [nnf transformation 19]
76. (strong(john) | brave(john)) & (~strong(john) | ~brave(john)) [nnf transformation 24]
77. ~creative(X0) | kind(X0) [cnf transformation 41]
87. ~rich(X0) | creative(X0) | ~tall(X0) [cnf transformation 48]
93. brave(X0) | old(X0) [cnf transformation 53]
114. creative(sK3) | calm(john) [cnf transformation 66]
115. ~calm(john) | ~creative(X0) [cnf transformation 66]
119. ~kind(X0) | ~kind(X0) [cnf transformation 68]
120. kind(X0) | rich(X0) | kind(X0) | ~old(X0) [cnf transformation 68]
122. ~tall(john) | strong(john) [cnf transformation 71]
129. ~strong(john) | ~brave(john) [cnf transformation 76]
131. tall(john) [cnf transformation 25]
132. ~kind(X0) [duplicate literal removal 119]
133. ~old(X0) | rich(X0) | kind(X0) [duplicate literal removal 120]
231. 22 <=> old(john) [avatar definition]
232. old(john) <- (22) [avatar component clause 231]
235. 23 <=> brave(john) [avatar definition]
237. ~brave(john) <- (~23) [avatar component clause 235]
255. 27 <=> ! [X0] : ~creative(X0) [avatar definition]
256. ~creative(X0) <- (27) [avatar component clause 255]
258. 28 <=> calm(john) [avatar definition]
261. 27 | ~28 [avatar split clause 115,258,255]
263. 29 <=> creative(sK3) [avatar definition]
265. creative(sK3) <- (29) [avatar component clause 263]
266. 28 | 29 [avatar split clause 114,263,258]
277. 32 <=> strong(john) [avatar definition]
281. 33 <=> tall(john) [avatar definition]
283. tall(john) <- (33) [avatar component clause 281]
285. 32 | ~33 [avatar split clause 122,281,277]
288. ~23 | ~32 [avatar split clause 129,277,235]
289. 33 [avatar split clause 131,281]
291. old(john) <- (~23) [resolution 93,237]
292. 22 | 23 [avatar split clause 291,235,231]
307. rich(john) | kind(john) <- (22) [resolution 133,232]
309. rich(john) <- (22) [subsumption resolution 307,132]
332. creative(john) | ~tall(john) <- (22) [resolution 309,87]
334. ~tall(john) <- (22, 27) [subsumption resolution 332,256]
335. $false <- (22, 27, 33) [subsumption resolution 334,283]
336. ~22 | ~27 | ~33 [avatar contradiction clause 335]
366. kind(sK3) <- (29) [resolution 265,77]
367. $false <- (29) [subsumption resolution 366,132]
368. ~29 [avatar contradiction clause 367]
369. $false [avatar sat refutation 261,266,285,288,289,292,336,368]
% SZS output end Proof for 496447598822685435799361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or not calm then someone is both not creative and humble.
Everyone who is both humble and not kind is either not funny or wise and vice versa.
Everyone who is both creative and curious is either not generous or not funny.
Everyone who is happy or not wise is both brave and not happy.
If someone is not kind then alice is both not patient and not brave.
Everyone who is both funny and not happy is either not curious or not strong.
Everyone who is both strong and not old is not funny and vice versa.
If someone is rich or not patient then fred is either not patient or tall.
If john is both not kind and creative then someone is both kind and generous.
Everyone who is not patient is either not wise or not tall and vice versa.
Everyone who is curious is either kind or tall.
If someone is either kind or brave then someone is not generous and vice versa.
If someone is not funny or not creative then lucy is both curious and not funny and vice versa.
If someone is calm then someone is either not brave or creative and vice versa.
If someone is both brave and humble then someone is both calm and wise and vice versa.
Everyone who is both not creative and not quiet is generous or kind.
Someone is creative or kind.
Mary is not patient or creative.
Susan is patient or not strong.
Someone is either not wise or not tall.
Someone is patient.
Someone is either curious or not strong.
Paul is both not kind and not calm.
Someone is both creative and calm. | Lucy is not funny. | entailment | (((~patient(alice)<~>~calm(alice)))=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((humble(X)&~kind(X))<=>(~funny(X)<~>wise(X))))&
(![X]:((creative(X)&curious(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((happy(X)|~wise(X))=>(brave(X)&~happy(X))))&
((?[X]:(~kind(X)))=>((~patient(alice)&~brave(alice))))&
(![X]:((funny(X)&~happy(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((strong(X)&~old(X))<=>~funny(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~patient(fred)<~>tall(fred))))&
(((~kind(john)&creative(john)))=>(?[X]:((kind(X)&generous(X)))))&
(![X]:(~patient(X)<=>(~wise(X)<~>~tall(X))))&
(![X]:(curious(X)=>(kind(X)<~>tall(X))))&
((?[X]:((kind(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(lucy)&~funny(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:((brave(X)&humble(X))))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)|kind(X))))&
(?[X]:((creative(X)|kind(X))))&
((~patient(mary)|creative(mary)))&
((patient(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~tall(X))))&
(?[X]:(patient(X)))&
(?[X]:((curious(X)<~>~strong(X))))&
((~kind(paul)&~calm(paul)))&
(?[X]:((creative(X)&calm(X)))) | ~funny(lucy) | [
"p3",
"p5",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8756561479902176228460029
% SZS output start Proof for 8756561479902176228460029
4. ! [X0] : ((~wise(X0) | happy(X0)) => (~happy(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~happy(X0) & funny(X0)) => (~curious(X0) <~> ~strong(X0))) [input p5]
13. ? [X0] : (~creative(X0) | ~funny(X0)) <=> (~funny(lucy) & curious(lucy)) [input p12]
22. ? [X0] : (curious(X0) <~> ~strong(X0)) [input p21]
25. funny(lucy) [input hypothesis]
34. ! [X0] : ((~happy(X0) & brave(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 4]
36. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | (happy(X0) | ~funny(X0))) [ennf transformation 6]
37. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | happy(X0) | ~funny(X0)) [flattening 36]
48. ! [X0] : (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | happy(X0) | ~funny(X0)) [nnf transformation 37]
61. (? [X0] : (~creative(X0) | ~funny(X0)) | (funny(lucy) | ~curious(lucy))) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [nnf transformation 13]
62. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X0] : (creative(X0) & funny(X0))) [flattening 61]
63. (? [X0] : (~creative(X0) | ~funny(X0)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [rectify 62]
64. ? [X0] : (~creative(X0) | ~funny(X0)) => (~creative(sK4) | ~funny(sK4)) [choice axiom]
65. ((~creative(sK4) | ~funny(sK4)) | funny(lucy) | ~curious(lucy)) & ((~funny(lucy) & curious(lucy)) | ! [X1] : (creative(X1) & funny(X1))) [skolemisation 63,64]
83. ? [X0] : ((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) [nnf transformation 22]
84. ? [X0] : ((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) => ((strong(sK12) | ~curious(sK12)) & (~strong(sK12) | curious(sK12))) [choice axiom]
85. (strong(sK12) | ~curious(sK12)) & (~strong(sK12) | curious(sK12)) [skolemisation 83,84]
102. ~happy(X0) | ~happy(X0) [cnf transformation 34]
106. ~strong(X0) | ~curious(X0) | happy(X0) | ~funny(X0) [cnf transformation 48]
107. strong(X0) | curious(X0) | happy(X0) | ~funny(X0) [cnf transformation 48]
127. ~funny(lucy) | funny(X1) [cnf transformation 65]
144. ~strong(sK12) | curious(sK12) [cnf transformation 85]
145. strong(sK12) | ~curious(sK12) [cnf transformation 85]
150. funny(lucy) [cnf transformation 25]
151. ~happy(X0) [duplicate literal removal 102]
181. ~funny(X0) | curious(X0) | strong(X0) [subsumption resolution 107,151]
182. ~strong(X0) | ~curious(X0) | ~funny(X0) [subsumption resolution 106,151]
244. 21 <=> funny(lucy) [avatar definition]
261. 25 <=> ! [X1] : funny(X1) [avatar definition]
262. funny(X1) <- (25) [avatar component clause 261]
263. 25 | ~21 [avatar split clause 127,244,261]
355. 46 <=> curious(sK12) [avatar definition]
356. curious(sK12) <- (46) [avatar component clause 355]
357. ~curious(sK12) <- (~46) [avatar component clause 355]
359. 47 <=> strong(sK12) [avatar definition]
360. ~strong(sK12) <- (~47) [avatar component clause 359]
361. strong(sK12) <- (47) [avatar component clause 359]
362. ~46 | 47 [avatar split clause 145,359,355]
363. 46 | ~47 [avatar split clause 144,359,355]
364. 21 [avatar split clause 150,244]
424. strong(X0) | curious(X0) <- (25) [resolution 181,262]
431. curious(sK12) <- (25, ~47) [resolution 424,360]
434. $false <- (25, ~46, ~47) [subsumption resolution 431,357]
435. ~25 | 46 | 47 [avatar contradiction clause 434]
447. ~curious(sK12) | ~funny(sK12) <- (47) [resolution 361,182]
449. ~funny(sK12) <- (46, 47) [subsumption resolution 447,356]
450. $false <- (25, 46, 47) [subsumption resolution 449,262]
451. ~25 | ~46 | ~47 [avatar contradiction clause 450]
453. $false [avatar sat refutation 263,362,363,364,435,451]
% SZS output end Proof for 8756561479902176228460029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either quiet or wise then alice is both humble and not humble.
If paul is either quiet or not happy then someone is not brave or patient.
If john is either generous or calm then someone is either not calm or not tall.
Everyone who is humble or calm is not strong.
If paul is both humble and not creative then someone is not strong or creative.
Everyone who is either not curious or not rich is both funny and not happy.
Everyone who is either not old or not kind is either wise or generous and vice versa.
Everyone who is wise or not brave is not brave or not old and vice versa.
If someone is creative or generous then someone is not humble and vice versa.
Everyone who is both happy and not happy is either not old or not creative and vice versa.
If someone is both not quiet and not patient then fred is quiet or strong and vice versa.
If someone is not curious or not old then lucy is either creative or old and vice versa.
Everyone who is not calm or calm is not creative or not happy and vice versa.
Everyone who is calm or curious is not funny.
If someone is not calm then alice is both quiet and not curious.
Someone is either wise or brave.
Someone is tall or not rich.
Someone is funny or quiet.
Someone is either curious or kind.
Susan is either not quiet or happy.
Someone is either rich or strong.
Someone is humble or not rich.
Lucy is not happy. | Alice is happy. | contradiction | (((quiet(fred)<~>wise(fred)))=>((humble(alice)&~humble(alice))))&
(((quiet(paul)<~>~happy(paul)))=>(?[X]:((~brave(X)|patient(X)))))&
(((generous(john)<~>calm(john)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:((humble(X)|calm(X))=>~strong(X)))&
(((humble(paul)&~creative(paul)))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(wise(X)<~>generous(X))))&
(![X]:((wise(X)|~brave(X))<=>(~brave(X)|~old(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)&~happy(X))<=>(~old(X)<~>~creative(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>((quiet(fred)|strong(fred))))&
((?[X]:((~curious(X)|~old(X))))<=>((creative(lucy)<~>old(lucy))))&
(![X]:((~calm(X)|calm(X))<=>(~creative(X)|~happy(X))))&
(![X]:((calm(X)|curious(X))=>~funny(X)))&
((?[X]:(~calm(X)))=>((quiet(alice)&~curious(alice))))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((funny(X)|quiet(X))))&
(?[X]:((curious(X)<~>kind(X))))&
((~quiet(susan)<~>happy(susan)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((humble(X)|~rich(X))))&
(~happy(lucy)) | happy(alice) | [
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 312477153267636036511786
% SZS output start Proof for 312477153267636036511786
10. ! [X0] : ((~happy(X0) & happy(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p9]
12. ? [X0] : (~old(X0) | ~curious(X0)) <=> (creative(lucy) <~> old(lucy)) [input p11]
13. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (~happy(X0) | ~creative(X0))) [input p12]
24. happy(alice) [input hypothesis]
53. ! [X0] : (((~happy(X0) & happy(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (happy(X0) | ~happy(X0)))) [nnf transformation 10]
54. ! [X0] : (((~happy(X0) & happy(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | happy(X0) | ~happy(X0))) [flattening 53]
60. (? [X0] : (~old(X0) | ~curious(X0)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X0] : (old(X0) & curious(X0))) [nnf transformation 12]
61. (? [X0] : (~old(X0) | ~curious(X0)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X1] : (old(X1) & curious(X1))) [rectify 60]
62. ? [X0] : (~old(X0) | ~curious(X0)) => (~old(sK6) | ~curious(sK6)) [choice axiom]
63. ((~old(sK6) | ~curious(sK6)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X1] : (old(X1) & curious(X1))) [skolemisation 61,62]
64. ! [X0] : (((calm(X0) | ~calm(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~calm(X0) & calm(X0)))) [nnf transformation 13]
65. ! [X0] : ((calm(X0) | ~calm(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | (~calm(X0) & calm(X0)))) [flattening 64]
116. happy(X0) | ~creative(X0) | old(X0) [cnf transformation 54]
117. happy(X0) | ~old(X0) | creative(X0) [cnf transformation 54]
118. ~happy(X0) | ~creative(X0) | old(X0) [cnf transformation 54]
119. ~happy(X0) | ~old(X0) | creative(X0) [cnf transformation 54]
126. old(lucy) | creative(lucy) | old(X1) [cnf transformation 63]
128. ~old(lucy) | ~creative(lucy) | old(X1) [cnf transformation 63]
131. ~happy(X0) | ~creative(X0) | calm(X0) [cnf transformation 65]
132. ~happy(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 65]
151. happy(alice) [cnf transformation 24]
247. ~old(X0) | creative(X0) [subsumption resolution 117,119]
248. ~creative(X0) | old(X0) [subsumption resolution 116,118]
269. ~creative(lucy) | old(X1) [subsumption resolution 128,248]
271. 26 <=> ! [X1] : old(X1) [avatar definition]
272. old(X1) <- (26) [avatar component clause 271]
274. 27 <=> creative(lucy) [avatar definition]
277. 26 | ~27 [avatar split clause 269,274,271]
283. creative(lucy) | old(X1) [subsumption resolution 126,247]
284. 26 | 27 [avatar split clause 283,274,271]
287. ~creative(X0) | ~happy(X0) [subsumption resolution 131,132]
379. creative(X0) <- (26) [resolution 247,272]
383. ~happy(X0) <- (26) [resolution 287,379]
385. $false <- (26) [resolution 383,151]
386. ~26 [avatar contradiction clause 385]
387. $false [avatar sat refutation 277,284,386]
% SZS output end Proof for 312477153267636036511786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and creative is not patient. If alice is both not generous and strong then someone is either wise or not brave and vice versa. If paul is not creative or not generous then john is both not old and not curious and vice versa. Everyone who is not happy is not funny and vice versa. Everyone who is either not tall or patient is both not funny and rich and vice versa. Everyone who is both strong and not wise is not happy and vice versa. Everyone who is either strong or happy is tall. Everyone who is not rich is both curious and humble and vice versa. If someone is old or not patient then someone is tall and vice versa. Everyone who is not happy is happy or not quiet and vice versa. Everyone who is either not happy or brave is both not happy and not old. If someone is not rich or wise then someone is not strong or not generous and vice versa. If someone is curious then john is both not calm and not humble. Everyone who is kind is not old or not funny. Everyone who is calm or patient is not brave or funny. Everyone who is both creative and kind is old and vice versa. Lucy is not quiet or not rich. Fred is either not humble or not brave. Someone is not creative. Alice is either humble or not tall. Susan is both old and kind. Someone is either not funny or not generous. | Fred is humble. | entailment | (![X]:((~funny(X)&creative(X))=>~patient(X)))&
(((~generous(alice)&strong(alice)))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(((~creative(paul)|~generous(paul)))<=>((~old(john)&~curious(john))))&
(![X]:(~happy(X)<=>~funny(X)))&
(![X]:((~tall(X)<~>patient(X))<=>(~funny(X)&rich(X))))&
(![X]:((strong(X)&~wise(X))<=>~happy(X)))&
(![X]:((strong(X)<~>happy(X))=>tall(X)))&
(![X]:(~rich(X)<=>(curious(X)&humble(X))))&
((?[X]:((old(X)|~patient(X))))<=>(?[X]:(tall(X))))&
(![X]:(~happy(X)<=>(happy(X)|~quiet(X))))&
(![X]:((~happy(X)<~>brave(X))=>(~happy(X)&~old(X))))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
((?[X]:(curious(X)))=>((~calm(john)&~humble(john))))&
(![X]:(kind(X)=>(~old(X)|~funny(X))))&
(![X]:((calm(X)|patient(X))=>(~brave(X)|funny(X))))&
(![X]:((creative(X)&kind(X))<=>old(X)))&
((~quiet(lucy)|~rich(lucy)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:(~creative(X)))&
((humble(alice)<~>~tall(alice)))&
((old(susan)&kind(susan)))&
(?[X]:((~funny(X)<~>~generous(X)))) | humble(fred) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2157880155917505384302570
% SZS output start Proof for 2157880155917505384302570
4. ! [X0] : (~happy(X0) <=> ~funny(X0)) [input p3]
5. ! [X0] : ((~tall(X0) <~> patient(X0)) <=> (rich(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((~wise(X0) & strong(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : ((strong(X0) <~> happy(X0)) => tall(X0)) [input p6]
8. ! [X0] : (~rich(X0) <=> (humble(X0) & curious(X0))) [input p7]
10. ! [X0] : (~happy(X0) <=> (~quiet(X0) | happy(X0))) [input p9]
15. ! [X0] : ((patient(X0) | calm(X0)) => (funny(X0) | ~brave(X0))) [input p14]
18. ~humble(fred) <~> ~brave(fred) [input p17]
23. ~humble(fred) [input hypothesis]
26. ! [X0] : (patient(X0) => (funny(X0) | ~brave(X0))) [pure predicate removal 15]
30. ! [X0] : (tall(X0) | (strong(X0) <=> happy(X0))) [ennf transformation 7]
35. ! [X0] : ((funny(X0) | ~brave(X0)) | ~patient(X0)) [ennf transformation 26]
36. ! [X0] : (funny(X0) | ~brave(X0) | ~patient(X0)) [flattening 35]
44. ! [X0] : ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))) [nnf transformation 4]
45. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [flattening 45]
47. ! [X0] : (((~wise(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | (wise(X0) | ~strong(X0)))) [nnf transformation 6]
48. ! [X0] : (((~wise(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | wise(X0) | ~strong(X0))) [flattening 47]
49. ! [X0] : (tall(X0) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) [nnf transformation 30]
50. ! [X0] : ((~rich(X0) | (~humble(X0) | ~curious(X0))) & ((humble(X0) & curious(X0)) | rich(X0))) [nnf transformation 8]
51. ! [X0] : ((~rich(X0) | ~humble(X0) | ~curious(X0)) & ((humble(X0) & curious(X0)) | rich(X0))) [flattening 50]
57. ! [X0] : ((~happy(X0) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | happy(X0))) [nnf transformation 10]
58. ! [X0] : ((~happy(X0) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | happy(X0))) [flattening 57]
67. (brave(fred) | humble(fred)) & (~brave(fred) | ~humble(fred)) [nnf transformation 18]
86. ~funny(X0) | happy(X0) [cnf transformation 44]
92. ~rich(X0) | ~tall(X0) | patient(X0) | funny(X0) [cnf transformation 46]
95. happy(X0) | strong(X0) [cnf transformation 48]
97. tall(X0) | happy(X0) | ~strong(X0) [cnf transformation 49]
98. tall(X0) | strong(X0) | ~happy(X0) [cnf transformation 49]
100. humble(X0) | rich(X0) [cnf transformation 51]
106. ~happy(X0) | ~happy(X0) [cnf transformation 58]
118. ~brave(X0) | funny(X0) | ~patient(X0) [cnf transformation 36]
124. brave(fred) | humble(fred) [cnf transformation 67]
132. ~humble(fred) [cnf transformation 23]
135. ~happy(X0) [duplicate literal removal 106]
185. tall(X0) | strong(X0) [subsumption resolution 98,95]
186. tall(X0) | happy(X0) [subsumption resolution 97,185]
254. 27 <=> humble(fred) [avatar definition]
255. ~humble(fred) <- (~27) [avatar component clause 254]
258. 28 <=> brave(fred) [avatar definition]
260. brave(fred) <- (28) [avatar component clause 258]
261. 27 | 28 [avatar split clause 124,258,254]
283. ~27 [avatar split clause 132,254]
294. rich(fred) <- (~27) [resolution 100,255]
371. funny(fred) | ~patient(fred) <- (28) [resolution 118,260]
374. 42 <=> patient(fred) [avatar definition]
376. ~patient(fred) <- (~42) [avatar component clause 374]
378. 43 <=> funny(fred) [avatar definition]
380. funny(fred) <- (43) [avatar component clause 378]
381. ~42 | 43 | ~28 [avatar split clause 371,258,378,374]
387. ~tall(fred) | patient(fred) | funny(fred) <- (~27) [resolution 92,294]
402. ~tall(fred) | funny(fred) <- (~27, ~42) [subsumption resolution 387,376]
404. 47 <=> tall(fred) [avatar definition]
406. ~tall(fred) <- (~47) [avatar component clause 404]
407. 43 | ~47 | 27 | 42 [avatar split clause 402,374,254,404,378]
443. happy(fred) <- (~47) [resolution 406,186]
445. $false <- (~47) [subsumption resolution 443,135]
446. 47 [avatar contradiction clause 445]
448. happy(fred) <- (43) [resolution 380,86]
449. $false <- (43) [subsumption resolution 448,135]
450. ~43 [avatar contradiction clause 449]
451. $false [avatar sat refutation 261,283,381,407,446,450]
% SZS output end Proof for 2157880155917505384302570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not tall or not funny and vice versa.
If someone is both not funny and funny then someone is wise or not curious and vice versa.
If alice is calm then someone is both strong and calm.
Everyone who is either not calm or not kind is either curious or brave and vice versa.
If someone is not humble or not tall then lucy is either quiet or not happy and vice versa.
If someone is not wise or not generous then susan is patient or calm and vice versa.
If lucy is not generous or not old then someone is both not strong and not funny.
Everyone who is not creative or rich is not kind or patient and vice versa.
If someone is either not humble or not patient then susan is not quiet and vice versa.
Everyone who is both old and curious is either not curious or creative and vice versa.
Everyone who is both not happy and not calm is either not rich or not patient.
If someone is either happy or old then someone is both not humble and happy.
Everyone who is not wise or not creative is not quiet or not brave and vice versa.
Everyone who is not patient is generous or not brave.
Someone is brave.
Mary is both strong and kind.
Someone is both not generous and not patient.
Someone is not rich.
John is either not rich or brave.
Someone is not old or not strong. | John is wise. | contradiction | (![X]:(~curious(X)<=>(~tall(X)|~funny(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:((wise(X)|~curious(X)))))&
((calm(alice))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:((~calm(X)<~>~kind(X))<=>(curious(X)<~>brave(X))))&
((?[X]:((~humble(X)|~tall(X))))<=>((quiet(lucy)<~>~happy(lucy))))&
((?[X]:((~wise(X)|~generous(X))))<=>((patient(susan)|calm(susan))))&
(((~generous(lucy)|~old(lucy)))=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~creative(X)|rich(X))<=>(~kind(X)|patient(X))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(~quiet(susan)))&
(![X]:((old(X)&curious(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~happy(X)&~calm(X))=>(~rich(X)<~>~patient(X))))&
((?[X]:((happy(X)<~>old(X))))=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:((~wise(X)|~creative(X))<=>(~quiet(X)|~brave(X))))&
(![X]:(~patient(X)=>(generous(X)|~brave(X))))&
(?[X]:(brave(X)))&
((strong(mary)&kind(mary)))&
(?[X]:((~generous(X)&~patient(X))))&
(?[X]:(~rich(X)))&
((~rich(john)<~>brave(john)))&
(?[X]:((~old(X)|~strong(X)))) | wise(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2327158247292921401425636
% SZS output start Proof for 2327158247292921401425636
2. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X0] : (~curious(X0) | wise(X0)) [input p1]
21. wise(john) [input hypothesis]
22. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X1] : (~curious(X1) | wise(X1)) [rectify 2]
33. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : (curious(X1) & ~wise(X1))) & (? [X1] : (~curious(X1) | wise(X1)) | ! [X0] : (~funny(X0) | funny(X0))) [nnf transformation 22]
34. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : (curious(X1) & ~wise(X1))) & (? [X2] : (~curious(X2) | wise(X2)) | ! [X3] : (~funny(X3) | funny(X3))) [rectify 33]
35. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK0) & ~funny(sK0)) [choice axiom]
36. ? [X2] : (~curious(X2) | wise(X2)) => (~curious(sK1) | wise(sK1)) [choice axiom]
37. ((funny(sK0) & ~funny(sK0)) | ! [X1] : (curious(X1) & ~wise(X1))) & ((~curious(sK1) | wise(sK1)) | ! [X3] : (~funny(X3) | funny(X3))) [skolemisation 34,36,35]
80. ~funny(sK0) | ~wise(X1) [cnf transformation 37]
82. funny(sK0) | ~wise(X1) [cnf transformation 37]
142. wise(john) [cnf transformation 21]
149. 2 <=> funny(sK0) [avatar definition]
154. 3 <=> ! [X1] : ~wise(X1) [avatar definition]
155. ~wise(X1) <- (3) [avatar component clause 154]
156. 3 | 2 [avatar split clause 82,149,154]
158. 3 | ~2 [avatar split clause 80,149,154]
307. $false <- (3) [resolution 155,142]
308. ~3 [avatar contradiction clause 307]
309. $false [avatar sat refutation 156,158,308]
% SZS output end Proof for 2327158247292921401425636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or tall then someone is not wise or curious.
Everyone who is either not wise or patient is strong and vice versa.
If someone is not tall then alice is either creative or not old and vice versa.
If someone is not creative then susan is both not kind and rich.
If someone is not tall or not curious then someone is not kind or funny.
If someone is not generous or happy then fred is funny.
Everyone who is strong or calm is both happy and old.
Everyone who is old is strong and vice versa.
Everyone who is both not brave and not curious is both strong and happy and vice versa.
Everyone who is both not humble and tall is both not kind and not humble.
Everyone who is not strong is patient or not curious.
Everyone who is not calm or not curious is both not humble and brave.
Everyone who is old is both not rich and not tall.
Everyone who is either old or not generous is either tall or curious and vice versa.
If someone is either not happy or old then lucy is either not generous or patient.
Everyone who is wise or not brave is either patient or quiet and vice versa.
Someone is both kind and not generous.
Someone is either generous or rich.
Someone is either generous or brave.
John is either not funny or happy. | Alice is not rich. | neutral | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>strong(X)))&
((?[X]:(~tall(X)))<=>((creative(alice)<~>~old(alice))))&
((?[X]:(~creative(X)))=>((~kind(susan)&rich(susan))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((~generous(X)|happy(X))))=>(funny(fred)))&
(![X]:((strong(X)|calm(X))=>(happy(X)&old(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)&happy(X))))&
(![X]:((~humble(X)&tall(X))=>(~kind(X)&~humble(X))))&
(![X]:(~strong(X)=>(patient(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~humble(X)&brave(X))))&
(![X]:(old(X)=>(~rich(X)&~tall(X))))&
(![X]:((old(X)<~>~generous(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>old(X))))=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((wise(X)|~brave(X))<=>(patient(X)<~>quiet(X))))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((~funny(john)<~>happy(john))) | ~rich(alice) | [] | null | 0 |
If someone is rich then mary is patient and vice versa.
Everyone who is either calm or not calm is both not funny and curious and vice versa.
Everyone who is both generous and patient is either not strong or not humble and vice versa.
Everyone who is either not quiet or not generous is both kind and tall.
Everyone who is either not quiet or strong is both kind and not kind.
If paul is either not humble or not funny then someone is calm or not funny and vice versa.
Everyone who is either rich or not old is both calm and quiet.
Everyone who is either not tall or creative is not patient and vice versa.
Everyone who is not quiet is either not funny or not generous and vice versa.
Everyone who is both wise and patient is either not quiet or rich.
Everyone who is both humble and happy is quiet.
If lucy is both kind and not wise then someone is either tall or not happy and vice versa.
Everyone who is not happy is either funny or not rich and vice versa.
If alice is either calm or happy then alice is happy and vice versa.
If someone is either not patient or not brave then susan is both not tall and kind and vice versa.
Someone is both happy and calm.
Susan is not generous.
Lucy is old.
Susan is old or not calm.
Someone is old or brave. | Paul is not patient. | entailment | ((?[X]:(rich(X)))<=>(patient(mary)))&
(![X]:((calm(X)<~>~calm(X))<=>(~funny(X)&curious(X))))&
(![X]:((generous(X)&patient(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>(kind(X)&tall(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(kind(X)&~kind(X))))&
(((~humble(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:((rich(X)<~>~old(X))=>(calm(X)&quiet(X))))&
(![X]:((~tall(X)<~>creative(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~generous(X))))&
(![X]:((wise(X)&patient(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((humble(X)&happy(X))=>quiet(X)))&
(((kind(lucy)&~wise(lucy)))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:(~happy(X)<=>(funny(X)<~>~rich(X))))&
(((calm(alice)<~>happy(alice)))<=>(happy(alice)))&
((?[X]:((~patient(X)<~>~brave(X))))<=>((~tall(susan)&kind(susan))))&
(?[X]:((happy(X)&calm(X))))&
(~generous(susan))&
(old(lucy))&
((old(susan)|~calm(susan)))&
(?[X]:((old(X)|brave(X)))) | ~patient(paul) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6039875821580317334293470
% SZS output start Proof for 6039875821580317334293470
2. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (curious(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((patient(X0) & generous(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p2]
5. ! [X0] : ((~quiet(X0) <~> strong(X0)) => (~kind(X0) & kind(X0))) [input p4]
6. (~humble(paul) <~> ~funny(paul)) <=> ? [X0] : (~funny(X0) | calm(X0)) [input p5]
9. ! [X0] : (~quiet(X0) <=> (~funny(X0) <~> ~generous(X0))) [input p8]
21. patient(paul) [input hypothesis]
23. ! [X0] : ((~kind(X0) & kind(X0)) | (~quiet(X0) <=> strong(X0))) [ennf transformation 5]
33. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (~curious(X0) | funny(X0))) & ((curious(X0) & ~funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 2]
34. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~curious(X0) | funny(X0)) & ((curious(X0) & ~funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [flattening 33]
35. ! [X0] : (((patient(X0) & generous(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~patient(X0) | ~generous(X0)))) [nnf transformation 3]
36. ! [X0] : (((patient(X0) & generous(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~patient(X0) | ~generous(X0))) [flattening 35]
38. ! [X0] : ((~kind(X0) & kind(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) [nnf transformation 23]
39. (((funny(paul) | humble(paul)) & (~funny(paul) | ~humble(paul))) | ! [X0] : (funny(X0) & ~calm(X0))) & (? [X0] : (~funny(X0) | calm(X0)) | ((~humble(paul) | funny(paul)) & (~funny(paul) | humble(paul)))) [nnf transformation 6]
40. (((funny(paul) | humble(paul)) & (~funny(paul) | ~humble(paul))) | ! [X0] : (funny(X0) & ~calm(X0))) & (? [X1] : (~funny(X1) | calm(X1)) | ((~humble(paul) | funny(paul)) & (~funny(paul) | humble(paul)))) [rectify 39]
41. ? [X1] : (~funny(X1) | calm(X1)) => (~funny(sK1) | calm(sK1)) [choice axiom]
42. (((funny(paul) | humble(paul)) & (~funny(paul) | ~humble(paul))) | ! [X0] : (funny(X0) & ~calm(X0))) & ((~funny(sK1) | calm(sK1)) | ((~humble(paul) | funny(paul)) & (~funny(paul) | humble(paul)))) [skolemisation 40,41]
45. ! [X0] : ((~quiet(X0) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | quiet(X0))) [nnf transformation 9]
65. ~funny(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 34]
66. ~funny(X0) | calm(X0) | calm(X0) [cnf transformation 34]
71. ~humble(X0) | ~strong(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 36]
73. ~humble(X0) | generous(X0) | strong(X0) [cnf transformation 36]
81. kind(X0) | strong(X0) | quiet(X0) [cnf transformation 38]
82. kind(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 38]
83. ~kind(X0) | strong(X0) | quiet(X0) [cnf transformation 38]
84. ~kind(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 38]
90. funny(paul) | humble(paul) | funny(X0) [cnf transformation 42]
100. generous(X0) | funny(X0) | quiet(X0) [cnf transformation 45]
101. ~quiet(X0) | ~generous(X0) | funny(X0) [cnf transformation 45]
132. patient(paul) [cnf transformation 21]
135. ~funny(X0) | ~calm(X0) [duplicate literal removal 65]
136. ~funny(X0) | calm(X0) [duplicate literal removal 66]
153. ~funny(X0) [subsumption resolution 135,136]
154. ~quiet(X0) | ~strong(X0) [subsumption resolution 82,84]
155. quiet(X0) | strong(X0) [subsumption resolution 81,83]
156. humble(paul) | funny(X0) [subsumption resolution 90,153]
157. humble(paul) [subsumption resolution 156,153]
158. ~quiet(X0) | ~generous(X0) [subsumption resolution 101,153]
159. quiet(X0) | generous(X0) [subsumption resolution 100,153]
247. ~generous(X0) | strong(X0) [resolution 158,155]
249. ~strong(X1) | generous(X1) [resolution 159,154]
259. generous(paul) | strong(paul) [resolution 73,157]
260. strong(paul) [subsumption resolution 259,247]
266. generous(paul) [resolution 249,260]
441. ~strong(paul) | ~patient(paul) | ~generous(paul) [resolution 71,157]
442. ~patient(paul) | ~generous(paul) [subsumption resolution 441,260]
443. ~generous(paul) [subsumption resolution 442,132]
444. $false [subsumption resolution 443,266]
% SZS output end Proof for 6039875821580317334293470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not strong is either creative or not generous.
If someone is either rich or not generous then john is either old or wise.
Everyone who is curious is either rich or not generous.
Everyone who is either not happy or not humble is both quiet and happy.
Everyone who is both creative and tall is patient or not calm.
Everyone who is both kind and funny is humble and vice versa.
If fred is both not curious and not brave then someone is creative or not rich and vice versa.
If someone is old or strong then someone is not rich.
If mary is either brave or not strong then mary is either not happy or curious and vice versa.
If fred is both not generous and not curious then susan is not brave or creative.
Everyone who is both not curious and not tall is happy or patient and vice versa.
If someone is brave or creative then paul is both not quiet and creative.
Everyone who is both not happy and creative is not tall or calm and vice versa.
Everyone who is either brave or kind is humble.
If someone is either not wise or tall then someone is both rich and wise and vice versa.
If paul is either not strong or generous then john is either humble or creative and vice versa.
Someone is old.
Someone is not funny or old.
Someone is either strong or tall.
John is tall or wise.
Someone is both calm and not wise.
Someone is either not happy or calm.
Fred is either not old or not happy.
Susan is both not quiet and not patient. | Paul is not creative. | contradiction | (![X]:((calm(X)<~>~strong(X))=>(creative(X)<~>~generous(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>((old(john)<~>wise(john))))&
(![X]:(curious(X)=>(rich(X)<~>~generous(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)&tall(X))=>(patient(X)|~calm(X))))&
(![X]:((kind(X)&funny(X))<=>humble(X)))&
(((~curious(fred)&~brave(fred)))<=>(?[X]:((creative(X)|~rich(X)))))&
((?[X]:((old(X)|strong(X))))=>(?[X]:(~rich(X))))&
(((brave(mary)<~>~strong(mary)))<=>((~happy(mary)<~>curious(mary))))&
(((~generous(fred)&~curious(fred)))=>((~brave(susan)|creative(susan))))&
(![X]:((~curious(X)&~tall(X))<=>(happy(X)|patient(X))))&
((?[X]:((brave(X)|creative(X))))=>((~quiet(paul)&creative(paul))))&
(![X]:((~happy(X)&creative(X))<=>(~tall(X)|calm(X))))&
(![X]:((brave(X)<~>kind(X))=>humble(X)))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((rich(X)&wise(X)))))&
(((~strong(paul)<~>generous(paul)))<=>((humble(john)<~>creative(john))))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)|old(X))))&
(?[X]:((strong(X)<~>tall(X))))&
((tall(john)|wise(john)))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((~happy(X)<~>calm(X))))&
((~old(fred)<~>~happy(fred)))&
((~quiet(susan)&~patient(susan))) | ~creative(paul) | [
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8494822454016513946411385
% SZS output start Proof for 8494822454016513946411385
12. ? [X0] : (creative(X0) | brave(X0)) => (creative(paul) & ~quiet(paul)) [input p11]
13. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (calm(X0) | ~tall(X0))) [input p12]
21. ? [X0] : (~wise(X0) & calm(X0)) [input p20]
25. ~creative(paul) [input hypothesis]
37. (creative(paul) & ~quiet(paul)) | ! [X0] : (~creative(X0) & ~brave(X0)) [ennf transformation 12]
56. ! [X0] : (((creative(X0) & ~happy(X0)) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 13]
57. ! [X0] : (((creative(X0) & ~happy(X0)) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | ~creative(X0) | happy(X0))) [flattening 56]
72. ? [X0] : (~wise(X0) & calm(X0)) => (~wise(sK7) & calm(sK7)) [choice axiom]
73. ~wise(sK7) & calm(sK7) [skolemisation 21,72]
120. creative(paul) | ~creative(X0) [cnf transformation 37]
125. ~calm(X0) | creative(X0) [cnf transformation 57]
147. calm(sK7) [cnf transformation 73]
155. ~creative(paul) [cnf transformation 25]
184. 7 <=> ! [X0] : ~creative(X0) [avatar definition]
185. ~creative(X0) <- (7) [avatar component clause 184]
252. 21 <=> creative(paul) [avatar definition]
255. 7 | 21 [avatar split clause 120,252,184]
350. ~21 [avatar split clause 155,252]
364. creative(sK7) [resolution 125,147]
365. $false <- (7) [subsumption resolution 364,185]
366. ~7 [avatar contradiction clause 365]
367. $false [avatar sat refutation 255,350,366]
% SZS output end Proof for 8494822454016513946411385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not old is not quiet.
If someone is not strong or happy then someone is either tall or not strong.
If fred is tall then someone is calm or humble and vice versa.
Everyone who is both tall and not patient is rich and vice versa.
If someone is either not generous or not curious then someone is kind.
Everyone who is both not patient and brave is not quiet and vice versa.
Everyone who is either not generous or not humble is both creative and not happy and vice versa.
Everyone who is patient or creative is both humble and not patient and vice versa.
Everyone who is both old and not funny is either patient or happy.
If john is both not curious and not calm then john is either generous or not strong.
Everyone who is not wise or not creative is curious or not tall.
Everyone who is not happy or patient is humble and vice versa.
If paul is not kind then mary is either not old or old.
If mary is happy or not patient then john is happy and vice versa.
If paul is both humble and not happy then someone is both strong and not curious and vice versa.
If paul is both tall and not curious then someone is not curious or not kind and vice versa.
Lucy is both not curious and not wise.
Someone is either quiet or not tall.
Someone is both creative and not quiet.
Paul is funny or strong.
Someone is both not quiet and creative.
Fred is both calm and humble. | Paul is not rich. | contradiction | (![X]:((kind(X)|~old(X))=>~quiet(X)))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((tall(X)<~>~strong(X)))))&
((tall(fred))<=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((tall(X)&~patient(X))<=>rich(X)))&
((?[X]:((~generous(X)<~>~curious(X))))=>(?[X]:(kind(X))))&
(![X]:((~patient(X)&brave(X))<=>~quiet(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(creative(X)&~happy(X))))&
(![X]:((patient(X)|creative(X))<=>(humble(X)&~patient(X))))&
(![X]:((old(X)&~funny(X))=>(patient(X)<~>happy(X))))&
(((~curious(john)&~calm(john)))=>((generous(john)<~>~strong(john))))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)|~tall(X))))&
(![X]:((~happy(X)|patient(X))<=>humble(X)))&
((~kind(paul))=>((~old(mary)<~>old(mary))))&
(((happy(mary)|~patient(mary)))<=>(happy(john)))&
(((humble(paul)&~happy(paul)))<=>(?[X]:((strong(X)&~curious(X)))))&
(((tall(paul)&~curious(paul)))<=>(?[X]:((~curious(X)|~kind(X)))))&
((~curious(lucy)&~wise(lucy)))&
(?[X]:((quiet(X)<~>~tall(X))))&
(?[X]:((creative(X)&~quiet(X))))&
((funny(paul)|strong(paul)))&
(?[X]:((~quiet(X)&creative(X))))&
((calm(fred)&humble(fred))) | ~rich(paul) | [
"p3",
"p7",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7426430917108158478428835
% SZS output start Proof for 7426430917108158478428835
4. ! [X0] : ((~patient(X0) & tall(X0)) <=> rich(X0)) [input p3]
8. ! [X0] : ((creative(X0) | patient(X0)) <=> (~patient(X0) & humble(X0))) [input p7]
16. (~curious(paul) & tall(paul)) <=> ? [X0] : (~kind(X0) | ~curious(X0)) [input p15]
17. ~wise(lucy) & ~curious(lucy) [input p16]
23. ~rich(paul) [input hypothesis]
26. ! [X0] : ((~patient(X0) & tall(X0)) => rich(X0)) [unused predicate definition removal 4]
31. ! [X0] : (rich(X0) | (patient(X0) | ~tall(X0))) [ennf transformation 26]
32. ! [X0] : (rich(X0) | patient(X0) | ~tall(X0)) [flattening 31]
55. ! [X0] : (((creative(X0) | patient(X0)) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | (~creative(X0) & ~patient(X0)))) [nnf transformation 8]
56. ! [X0] : ((creative(X0) | patient(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | (~creative(X0) & ~patient(X0)))) [flattening 55]
68. ((~curious(paul) & tall(paul)) | ! [X0] : (kind(X0) & curious(X0))) & (? [X0] : (~kind(X0) | ~curious(X0)) | (curious(paul) | ~tall(paul))) [nnf transformation 16]
69. ((~curious(paul) & tall(paul)) | ! [X0] : (kind(X0) & curious(X0))) & (? [X0] : (~kind(X0) | ~curious(X0)) | curious(paul) | ~tall(paul)) [flattening 68]
70. ((~curious(paul) & tall(paul)) | ! [X0] : (kind(X0) & curious(X0))) & (? [X1] : (~kind(X1) | ~curious(X1)) | curious(paul) | ~tall(paul)) [rectify 69]
71. ? [X1] : (~kind(X1) | ~curious(X1)) => (~kind(sK4) | ~curious(sK4)) [choice axiom]
72. ((~curious(paul) & tall(paul)) | ! [X0] : (kind(X0) & curious(X0))) & ((~kind(sK4) | ~curious(sK4)) | curious(paul) | ~tall(paul)) [skolemisation 70,71]
89. ~tall(X0) | patient(X0) | rich(X0) [cnf transformation 32]
103. ~patient(X0) | ~patient(X0) [cnf transformation 56]
123. tall(paul) | curious(X0) [cnf transformation 72]
127. ~curious(lucy) [cnf transformation 17]
137. ~rich(paul) [cnf transformation 23]
138. ~patient(X0) [duplicate literal removal 103]
245. 24 <=> ! [X0] : curious(X0) [avatar definition]
246. curious(X0) <- (24) [avatar component clause 245]
249. 25 <=> tall(paul) [avatar definition]
251. tall(paul) <- (25) [avatar component clause 249]
253. 24 | 25 [avatar split clause 123,249,245]
277. $false <- (24) [resolution 246,127]
278. ~24 [avatar contradiction clause 277]
292. patient(paul) | rich(paul) <- (25) [resolution 89,251]
294. rich(paul) <- (25) [subsumption resolution 292,138]
295. $false <- (25) [subsumption resolution 294,137]
296. ~25 [avatar contradiction clause 295]
297. $false [avatar sat refutation 253,278,296]
% SZS output end Proof for 7426430917108158478428835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either old or not rich then mary is either humble or not rich and vice versa.
If someone is not curious or creative then alice is strong.
Everyone who is calm or humble is both not wise and not happy and vice versa.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
If someone is both happy and calm then alice is either not brave or curious and vice versa.
If someone is either not brave or generous then fred is quiet and vice versa.
Someone is either quiet or not funny.
Someone is funny.
Alice is either not tall or not patient.
Someone is both quiet and not creative.
Susan is not brave.
Someone is humble or calm.
Someone is creative.
Someone is not humble or not patient. | Alice is brave. | contradiction | (((old(paul)<~>~rich(paul)))<=>((humble(mary)<~>~rich(mary))))&
((?[X]:((~curious(X)|creative(X))))=>(strong(alice)))&
(![X]:((calm(X)|humble(X))<=>(~wise(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:(funny(X)))&
((~tall(alice)<~>~patient(alice)))&
(?[X]:((quiet(X)&~creative(X))))&
(~brave(susan))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~patient(X)))) | brave(alice) | [
"p2",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 473277619394179867713932
% SZS output start Proof for 473277619394179867713932
3. ! [X0] : ((humble(X0) | calm(X0)) <=> (~happy(X0) & ~wise(X0))) [input p2]
8. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p7]
15. ? [X0] : (calm(X0) & happy(X0)) <=> (~brave(alice) <~> curious(alice)) [input p14]
25. brave(alice) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 8]
38. ! [X0] : (((humble(X0) | calm(X0)) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 3]
39. ! [X0] : ((humble(X0) | calm(X0) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 38]
55. (? [X0] : (calm(X0) & happy(X0)) | ((~brave(alice) | ~curious(alice)) & (curious(alice) | brave(alice)))) & (((~curious(alice) | brave(alice)) & (curious(alice) | ~brave(alice))) | ! [X0] : (~calm(X0) | ~happy(X0))) [nnf transformation 15]
56. (? [X0] : (calm(X0) & happy(X0)) | ((~brave(alice) | ~curious(alice)) & (curious(alice) | brave(alice)))) & (((~curious(alice) | brave(alice)) & (curious(alice) | ~brave(alice))) | ! [X1] : (~calm(X1) | ~happy(X1))) [rectify 55]
57. ? [X0] : (calm(X0) & happy(X0)) => (calm(sK2) & happy(sK2)) [choice axiom]
58. ((calm(sK2) & happy(sK2)) | ((~brave(alice) | ~curious(alice)) & (curious(alice) | brave(alice)))) & (((~curious(alice) | brave(alice)) & (curious(alice) | ~brave(alice))) | ! [X1] : (~calm(X1) | ~happy(X1))) [skolemisation 56,57]
89. ~happy(X0) | ~calm(X0) [cnf transformation 39]
109. ~brave(X0) | curious(X0) [cnf transformation 30]
132. happy(sK2) | ~brave(alice) | ~curious(alice) [cnf transformation 58]
134. calm(sK2) | ~brave(alice) | ~curious(alice) [cnf transformation 58]
150. brave(alice) [cnf transformation 25]
218. calm(sK2) | ~brave(alice) [subsumption resolution 134,109]
220. 13 <=> brave(alice) [avatar definition]
224. 14 <=> calm(sK2) [avatar definition]
226. calm(sK2) <- (14) [avatar component clause 224]
227. ~13 | 14 [avatar split clause 218,224,220]
234. happy(sK2) | ~brave(alice) [subsumption resolution 132,109]
236. 16 <=> happy(sK2) [avatar definition]
238. happy(sK2) <- (16) [avatar component clause 236]
239. ~13 | 16 [avatar split clause 234,236,220]
302. 13 [avatar split clause 150,220]
305. ~calm(sK2) <- (16) [resolution 89,238]
306. $false <- (14, 16) [subsumption resolution 305,226]
307. ~14 | ~16 [avatar contradiction clause 306]
308. $false [avatar sat refutation 227,239,302,307]
% SZS output end Proof for 473277619394179867713932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not creative is both not patient and wise and vice versa.
If someone is not kind then someone is kind and vice versa.
If fred is both creative and not humble then someone is curious or patient and vice versa.
Everyone who is both not funny and not strong is patient or curious and vice versa.
If someone is both wise and calm then fred is both patient and not brave.
If john is not humble or not quiet then someone is either not kind or old.
Everyone who is both not humble and creative is either not funny or not patient and vice versa.
If someone is both not happy and not calm then mary is quiet or patient and vice versa.
If someone is not humble then fred is not kind or generous and vice versa.
Everyone who is both not creative and not rich is curious or rich.
Everyone who is not calm or not brave is either not rich or rich and vice versa.
Everyone who is not humble is either brave or calm and vice versa.
If fred is both not tall and calm then someone is both patient and not creative.
Everyone who is either funny or not humble is strong or not patient and vice versa.
Everyone who is either humble or not strong is humble and vice versa.
Everyone who is both curious and not generous is either not quiet or rich and vice versa.
Someone is either not happy or not generous.
Someone is both not creative and not calm.
Someone is not quiet.
Someone is rich or not brave. | John is quiet. | contradiction | (![X]:((~generous(X)|~creative(X))<=>(~patient(X)&wise(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X)))) | quiet(john) | [
"p3",
"p6",
"p9",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6243963094484113002773940
% SZS output start Proof for 6243963094484113002773940
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p3]
7. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p6]
10. ! [X0] : ((~rich(X0) & ~creative(X0)) => (rich(X0) | curious(X0))) [input p9]
14. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p13]
15. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> humble(X0)) [input p14]
16. ! [X0] : ((~generous(X0) & curious(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p15]
21. quiet(john) [input hypothesis]
26. ! [X0] : ((rich(X0) | curious(X0)) | (rich(X0) | creative(X0))) [ennf transformation 10]
27. ! [X0] : (rich(X0) | curious(X0) | rich(X0) | creative(X0)) [flattening 26]
40. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 40]
45. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 45]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 14]
61. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 60]
62. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (generous(X0) | ~curious(X0)))) [nnf transformation 16]
64. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | generous(X0) | ~curious(X0))) [flattening 63]
87. ~funny(X0) | ~patient(X0) [cnf transformation 41]
89. ~strong(X0) | ~patient(X0) [cnf transformation 41]
90. ~strong(X0) | ~curious(X0) [cnf transformation 41]
98. ~creative(X0) | funny(X0) | patient(X0) | humble(X0) [cnf transformation 46]
99. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 46]
100. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 46]
111. rich(X0) | curious(X0) | rich(X0) | creative(X0) [cnf transformation 27]
123. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 61]
125. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 61]
127. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 61]
129. humble(X0) | humble(X0) | strong(X0) [cnf transformation 62]
135. ~rich(X0) | ~quiet(X0) | curious(X0) [cnf transformation 64]
144. quiet(john) [cnf transformation 21]
145. humble(X0) | strong(X0) [duplicate literal removal 129]
149. rich(X0) | curious(X0) | creative(X0) [duplicate literal removal 111]
167. 5 <=> ! [X0] : ~patient(X0) [avatar definition]
168. ~patient(X0) <- (5) [avatar component clause 167]
175. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
176. ~curious(X0) <- (7) [avatar component clause 175]
207. 14 <=> quiet(john) [avatar definition]
209. quiet(john) <- (14) [avatar component clause 207]
227. ~funny(X0) | ~humble(X0) [subsumption resolution 100,87]
228. ~humble(X0) | ~patient(X0) [subsumption resolution 99,227]
274. humble(X0) | ~funny(X0) [subsumption resolution 127,87]
275. ~funny(X0) [subsumption resolution 274,227]
276. ~humble(X0) | patient(X0) [subsumption resolution 125,275]
277. ~humble(X0) [subsumption resolution 276,228]
278. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 123,275]
279. ~patient(X0) | strong(X0) [subsumption resolution 278,277]
280. ~patient(X0) [subsumption resolution 279,89]
281. 5 [avatar split clause 280,167]
282. strong(X0) [subsumption resolution 145,277]
302. 14 [avatar split clause 144,207]
310. ~curious(X0) [resolution 90,282]
331. curious(X2) | creative(X2) | ~quiet(X2) | curious(X2) [resolution 149,135]
332. curious(X2) | creative(X2) | ~quiet(X2) [duplicate literal removal 331]
334. ~quiet(X2) | creative(X2) <- (7) [subsumption resolution 332,176]
337. creative(john) <- (7, 14) [resolution 334,209]
343. funny(john) | patient(john) | humble(john) <- (7, 14) [resolution 98,337]
348. patient(john) | humble(john) <- (7, 14) [subsumption resolution 343,275]
349. humble(john) <- (5, 7, 14) [subsumption resolution 348,168]
350. $false <- (5, 7, 14) [subsumption resolution 349,277]
351. ~5 | ~7 | ~14 [avatar contradiction clause 350]
352. 7 [avatar split clause 310,175]
355. $false [avatar sat refutation 281,302,351,352]
% SZS output end Proof for 6243963094484113002773940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and creative is either not quiet or not tall and vice versa. If someone is not curious or not generous then john is not tall or not quiet and vice versa. Everyone who is either not kind or not funny is curious or wise and vice versa. If someone is not creative then someone is both kind and wise and vice versa. If fred is both not kind and not rich then someone is not curious and vice versa. Everyone who is rich or not wise is not brave and vice versa. Everyone who is not creative or old is both wise and not kind. Everyone who is both not calm and creative is not quiet or generous and vice versa. Everyone who is both wise and patient is brave or not happy and vice versa. If fred is brave or not rich then someone is tall and vice versa. If someone is generous or happy then lucy is not creative or not generous. 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 both not kind and calm. 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. | John is not tall. | contradiction | (![X]:((~calm(X)&creative(X))<=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((~tall(john)|~quiet(john))))&
(![X]:((~kind(X)<~>~funny(X))<=>(curious(X)|wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~kind(fred)&~rich(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~wise(X))<=>~brave(X)))&
(![X]:((~creative(X)|old(X))=>(wise(X)&~kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((wise(X)&patient(X))<=>(brave(X)|~happy(X))))&
(((brave(fred)|~rich(fred)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)|happy(X))))=>((~creative(lucy)|~generous(lucy))))&
(![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))))&
((~kind(mary)&calm(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))) | ~tall(john) | [
"p0",
"p4",
"p6",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5316947691142955738740842
% SZS output start Proof for 5316947691142955738740842
1. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~quiet(X0) <~> ~tall(X0))) [input p0]
5. (~rich(fred) & ~kind(fred)) <=> ? [X0] : ~curious(X0) [input p4]
7. ! [X0] : ((old(X0) | ~creative(X0)) => (~kind(X0) & wise(X0))) [input p6]
8. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (generous(X0) | ~quiet(X0))) [input p7]
13. ? [X0] : (~kind(X0) | ~happy(X0)) => (~quiet(john) & generous(john)) [input p12]
16. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p15]
24. ~tall(john) [input hypothesis]
26. ! [X0] : ((~kind(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 7]
29. (~quiet(john) & generous(john)) | ! [X0] : (kind(X0) & happy(X0)) [ennf transformation 13]
33. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 16]
34. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 1]
35. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~creative(X0) | calm(X0))) [flattening 34]
48. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (rich(fred) | kind(fred))) [nnf transformation 5]
49. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | rich(fred) | kind(fred)) [flattening 48]
50. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | rich(fred) | kind(fred)) [rectify 49]
51. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
52. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (~curious(sK3) | rich(fred) | kind(fred)) [skolemisation 50,51]
55. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | calm(X0))) [flattening 55]
73. ~creative(X0) | quiet(X0) | tall(X0) | calm(X0) [cnf transformation 35]
92. ~kind(fred) | curious(X0) [cnf transformation 52]
97. wise(X0) | creative(X0) [cnf transformation 26]
102. ~calm(X0) | quiet(X0) [cnf transformation 56]
123. ~quiet(john) | kind(X0) [cnf transformation 29]
130. ~curious(X0) | wise(X0) [cnf transformation 33]
131. ~wise(X0) | ~wise(X0) [cnf transformation 33]
143. ~tall(john) [cnf transformation 24]
144. ~wise(X0) [duplicate literal removal 131]
146. 1 <=> quiet(john) [avatar definition]
147. ~quiet(john) <- (~1) [avatar component clause 146]
159. 4 <=> tall(john) [avatar definition]
160. ~tall(john) <- (~4) [avatar component clause 159]
168. 6 <=> ! [X1] : curious(X1) [avatar definition]
169. curious(X1) <- (6) [avatar component clause 168]
180. 9 <=> ! [X3] : creative(X3) [avatar definition]
181. creative(X3) <- (9) [avatar component clause 180]
198. 13 <=> kind(fred) [avatar definition]
200. ~kind(fred) <- (~13) [avatar component clause 198]
201. 6 | ~13 [avatar split clause 92,198,168]
237. 21 <=> ! [X0] : kind(X0) [avatar definition]
238. kind(X0) <- (21) [avatar component clause 237]
239. 21 | ~1 [avatar split clause 123,146,237]
250. ~curious(X0) [subsumption resolution 130,144]
270. ~4 [avatar split clause 143,159]
273. $false <- (6) [subsumption resolution 169,250]
274. ~6 [avatar contradiction clause 273]
277. $false <- (~13, 21) [subsumption resolution 200,238]
278. 13 | ~21 [avatar contradiction clause 277]
279. creative(X0) [resolution 97,144]
318. quiet(X0) | tall(X0) | calm(X0) <- (9) [resolution 73,181]
319. tall(X0) | quiet(X0) <- (9) [subsumption resolution 318,102]
320. quiet(john) <- (~4, 9) [resolution 319,160]
326. $false <- (~1, ~4, 9) [subsumption resolution 320,147]
327. 1 | 4 | ~9 [avatar contradiction clause 326]
329. 9 [avatar split clause 279,180]
332. $false [avatar sat refutation 201,239,270,274,278,327,329]
% SZS output end Proof for 5316947691142955738740842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or humble is not strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
If someone is curious or not wise then someone is not rich.
Everyone who is not curious is creative or not patient and vice versa.
Everyone who is old or not quiet is either not creative or not curious and vice versa.
If someone is both not generous and not funny then someone is not quiet.
Everyone who is quiet or not curious is both not funny and generous and vice versa.
If fred is both humble and not creative then someone is brave or not curious and vice versa.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Someone is calm or not happy.
Someone is both wise and not kind.
Someone is calm or wise.
John is generous or not humble.
Alice is both creative and not quiet.
John is either calm or patient.
Someone is either wise or not humble.
Someone is old. | John is not quiet. | entailment | (![X]:((~creative(X)<~>humble(X))<=>(~strong(X)|~patient(X))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~funny(X)&generous(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((brave(X)|~curious(X)))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(?[X]:((calm(X)|~happy(X))))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((calm(X)|wise(X))))&
((generous(john)|~humble(john)))&
((creative(alice)&~quiet(alice)))&
((calm(john)<~>patient(john)))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:(old(X))) | ~quiet(john) | [
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7645190949057696449907389
% SZS output start Proof for 7645190949057696449907389
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (generous(X0) & ~funny(X0))) [input p9]
12. generous(fred) <=> funny(john) [input p11]
13. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p12]
15. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p14]
25. quiet(john) [input hypothesis]
54. ! [X0] : (((~curious(X0) | quiet(X0)) | (~generous(X0) | funny(X0))) & ((generous(X0) & ~funny(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
55. ! [X0] : ((~curious(X0) | quiet(X0) | ~generous(X0) | funny(X0)) & ((generous(X0) & ~funny(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 54]
61. (generous(fred) | ~funny(john)) & (funny(john) | ~generous(fred)) [nnf transformation 12]
62. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 13]
63. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 62]
65. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 15]
66. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 65]
110. ~funny(X0) | ~quiet(X0) [cnf transformation 55]
120. funny(john) | ~generous(fred) [cnf transformation 61]
124. ~strong(X0) | generous(X0) [cnf transformation 63]
129. strong(X0) | generous(X0) [cnf transformation 66]
145. quiet(john) [cnf transformation 25]
218. 17 <=> funny(john) [avatar definition]
219. funny(john) <- (17) [avatar component clause 218]
222. 18 <=> generous(fred) [avatar definition]
223. ~generous(fred) <- (~18) [avatar component clause 222]
226. ~18 | 17 [avatar split clause 120,218,222]
239. generous(X0) [subsumption resolution 129,124]
279. $false <- (~18) [subsumption resolution 223,239]
280. 18 [avatar contradiction clause 279]
287. ~quiet(john) <- (17) [resolution 110,219]
288. $false <- (17) [subsumption resolution 287,145]
289. ~17 [avatar contradiction clause 288]
290. $false [avatar sat refutation 226,280,289]
% SZS output end Proof for 7645190949057696449907389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not calm or not creative then someone is patient and vice versa.
Everyone who is both strong and happy is not creative or funny and vice versa.
Everyone who is both generous and humble is both not happy and not kind.
If mary is both kind and not brave then lucy is both kind and not calm and vice versa.
If john is either happy or quiet then someone is either not strong or not happy and vice versa.
Everyone who is kind is not brave or not generous and vice versa.
If someone is either happy or not rich then someone is not patient.
If someone is not wise or funny then someone is not brave.
Everyone who is not kind or not curious is either not curious or tall and vice versa.
If someone is brave or strong then someone is not patient.
Everyone who is either calm or not humble is not kind or creative.
If someone is both quiet and not generous then someone is happy.
Everyone who is both happy and not patient is humble or not humble.
Everyone who is not generous is either kind or humble.
Everyone who is both tall and not creative is calm or not patient.
Everyone who is happy or patient is both humble and not kind.
Fred is not creative or not strong.
Someone is not strong or not happy.
Someone is not wise or not generous.
Someone is not old.
Alice is not funny.
Someone is not funny or not creative.
Someone is either generous or not curious.
John is either not quiet or kind. | Mary is funny. | contradiction | (((~calm(paul)<~>~creative(paul)))<=>(?[X]:(patient(X))))&
(![X]:((strong(X)&happy(X))<=>(~creative(X)|funny(X))))&
(![X]:((generous(X)&humble(X))=>(~happy(X)&~kind(X))))&
(((kind(mary)&~brave(mary)))<=>((kind(lucy)&~calm(lucy))))&
(((happy(john)<~>quiet(john)))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(![X]:(kind(X)<=>(~brave(X)|~generous(X))))&
((?[X]:((happy(X)<~>~rich(X))))=>(?[X]:(~patient(X))))&
((?[X]:((~wise(X)|funny(X))))=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)|~curious(X))<=>(~curious(X)<~>tall(X))))&
((?[X]:((brave(X)|strong(X))))=>(?[X]:(~patient(X))))&
(![X]:((calm(X)<~>~humble(X))=>(~kind(X)|creative(X))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:(happy(X))))&
(![X]:((happy(X)&~patient(X))=>(humble(X)|~humble(X))))&
(![X]:(~generous(X)=>(kind(X)<~>humble(X))))&
(![X]:((tall(X)&~creative(X))=>(calm(X)|~patient(X))))&
(![X]:((happy(X)|patient(X))=>(humble(X)&~kind(X))))&
((~creative(fred)|~strong(fred)))&
(?[X]:((~strong(X)|~happy(X))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:(~old(X)))&
(~funny(alice))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
((~quiet(john)<~>kind(john))) | funny(mary) | [
"p1",
"p2",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3451138465830207582515253
% SZS output start Proof for 3451138465830207582515253
2. ! [X0] : ((happy(X0) & strong(X0)) <=> (funny(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((humble(X0) & generous(X0)) => (~kind(X0) & ~happy(X0))) [input p2]
6. ! [X0] : (kind(X0) <=> (~generous(X0) | ~brave(X0))) [input p5]
16. ! [X0] : ((patient(X0) | happy(X0)) => (~kind(X0) & humble(X0))) [input p15]
25. funny(mary) [input hypothesis]
31. ! [X0] : ((~kind(X0) & ~happy(X0)) | (~humble(X0) | ~generous(X0))) [ennf transformation 3]
32. ! [X0] : ((~kind(X0) & ~happy(X0)) | ~humble(X0) | ~generous(X0)) [flattening 31]
44. ! [X0] : ((~kind(X0) & humble(X0)) | (~patient(X0) & ~happy(X0))) [ennf transformation 16]
49. ! [X0] : (((happy(X0) & strong(X0)) | (~funny(X0) & creative(X0))) & ((funny(X0) | ~creative(X0)) | (~happy(X0) | ~strong(X0)))) [nnf transformation 2]
50. ! [X0] : (((happy(X0) & strong(X0)) | (~funny(X0) & creative(X0))) & (funny(X0) | ~creative(X0) | ~happy(X0) | ~strong(X0))) [flattening 49]
57. ! [X0] : ((kind(X0) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | ~kind(X0))) [nnf transformation 6]
58. ! [X0] : ((kind(X0) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | ~kind(X0))) [flattening 57]
94. ~funny(X0) | happy(X0) [cnf transformation 50]
95. ~humble(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 32]
111. kind(X0) | generous(X0) [cnf transformation 58]
131. ~happy(X0) | humble(X0) [cnf transformation 44]
133. ~kind(X0) | ~happy(X0) [cnf transformation 44]
144. funny(mary) [cnf transformation 25]
180. 8 <=> kind(mary) [avatar definition]
181. ~kind(mary) <- (~8) [avatar component clause 180]
182. kind(mary) <- (8) [avatar component clause 180]
318. happy(mary) [resolution 94,144]
321. generous(mary) <- (~8) [resolution 111,181]
324. humble(mary) [resolution 131,318]
338. ~happy(mary) | ~generous(mary) [resolution 95,324]
340. ~generous(mary) [subsumption resolution 338,318]
341. $false <- (~8) [subsumption resolution 340,321]
342. 8 [avatar contradiction clause 341]
349. ~happy(mary) <- (8) [resolution 182,133]
352. $false <- (8) [subsumption resolution 349,318]
353. ~8 [avatar contradiction clause 352]
354. $false [avatar sat refutation 342,353]
% SZS output end Proof for 3451138465830207582515253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and generous then someone is funny.
Everyone who is either not calm or not kind is not strong.
If alice is either not tall or not patient then someone is not quiet or not curious and vice versa.
If someone is both not strong and not old then someone is either tall or strong.
Everyone who is both not creative and not tall is not rich.
Everyone who is either quiet or not curious is not humble or humble and vice versa.
Everyone who is both not tall and not generous is both rich and generous and vice versa.
Everyone who is either strong or not tall is strong and vice versa.
Everyone who is both not tall and humble is not calm or humble and vice versa.
Everyone who is creative is both not calm and old.
Everyone who is not wise is both not generous and not happy and vice versa.
Everyone who is not funny is both not calm and not curious and vice versa.
Everyone who is both quiet and not kind is either not rich or generous.
Everyone who is not old is either not kind or rich and vice versa.
If fred is either not strong or not generous then someone is brave and vice versa.
Everyone who is either strong or not creative is either not brave or patient.
Fred is not funny or strong.
Someone is both not happy and not curious.
Someone is not rich.
Someone is not funny or kind.
Mary is wise or happy.
Susan is either brave or calm.
Someone is both not kind and funny. | Fred is not kind. | contradiction | ((?[X]:((humble(X)&generous(X))))=>(?[X]:(funny(X))))&
(![X]:((~calm(X)<~>~kind(X))=>~strong(X)))&
(((~tall(alice)<~>~patient(alice)))<=>(?[X]:((~quiet(X)|~curious(X)))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((~creative(X)&~tall(X))=>~rich(X)))&
(![X]:((quiet(X)<~>~curious(X))<=>(~humble(X)|humble(X))))&
(![X]:((~tall(X)&~generous(X))<=>(rich(X)&generous(X))))&
(![X]:((strong(X)<~>~tall(X))<=>strong(X)))&
(![X]:((~tall(X)&humble(X))<=>(~calm(X)|humble(X))))&
(![X]:(creative(X)=>(~calm(X)&old(X))))&
(![X]:(~wise(X)<=>(~generous(X)&~happy(X))))&
(![X]:(~funny(X)<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)&~kind(X))=>(~rich(X)<~>generous(X))))&
(![X]:(~old(X)<=>(~kind(X)<~>rich(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(brave(X))))&
(![X]:((strong(X)<~>~creative(X))=>(~brave(X)<~>patient(X))))&
((~funny(fred)|strong(fred)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~funny(X)|kind(X))))&
((wise(mary)|happy(mary)))&
((brave(susan)<~>calm(susan)))&
(?[X]:((~kind(X)&funny(X)))) | ~kind(fred) | [
"p1",
"p7",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4289541416848033588982697
% SZS output start Proof for 4289541416848033588982697
2. ! [X0] : ((~calm(X0) <~> ~kind(X0)) => ~strong(X0)) [input p1]
8. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> strong(X0)) [input p7]
9. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (humble(X0) | ~calm(X0))) [input p8]
12. ! [X0] : (~funny(X0) <=> (~curious(X0) & ~calm(X0))) [input p11]
17. strong(fred) | ~funny(fred) [input p16]
24. ~kind(fred) [input hypothesis]
30. ! [X0] : (~strong(X0) | (~calm(X0) <=> ~kind(X0))) [ennf transformation 2]
44. ! [X0] : (~strong(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) [nnf transformation 30]
57. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | ~strong(X0)) & (strong(X0) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 8]
58. ! [X0] : (((humble(X0) & ~tall(X0)) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 9]
59. ! [X0] : (((humble(X0) & ~tall(X0)) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | ~humble(X0) | tall(X0))) [flattening 58]
60. ! [X0] : ((~funny(X0) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | funny(X0))) [nnf transformation 12]
61. ! [X0] : ((~funny(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | funny(X0))) [flattening 60]
80. ~strong(X0) | ~calm(X0) | kind(X0) [cnf transformation 44]
101. strong(X0) | strong(X0) | tall(X0) [cnf transformation 57]
103. tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 57]
105. ~tall(X0) | calm(X0) [cnf transformation 59]
112. ~calm(X0) | funny(X0) [cnf transformation 61]
127. strong(fred) | ~funny(fred) [cnf transformation 17]
137. ~kind(fred) [cnf transformation 24]
138. strong(X0) | tall(X0) [duplicate literal removal 101]
139. ~strong(X0) | tall(X0) [duplicate literal removal 103]
193. tall(X0) [subsumption resolution 138,139]
195. calm(X0) [subsumption resolution 105,193]
197. funny(X0) [subsumption resolution 112,195]
204. 13 <=> strong(fred) [avatar definition]
206. strong(fred) <- (13) [avatar component clause 204]
221. strong(fred) [subsumption resolution 127,197]
222. 13 [avatar split clause 221,204]
236. ~calm(fred) | kind(fred) <- (13) [resolution 80,206]
237. kind(fred) <- (13) [subsumption resolution 236,195]
238. $false <- (13) [subsumption resolution 237,137]
239. ~13 [avatar contradiction clause 238]
240. $false [avatar sat refutation 222,239]
% SZS output end Proof for 4289541416848033588982697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not creative is patient and vice versa.
If someone is not old then susan is calm or curious and vice versa.
If someone is old then lucy is both not calm and not generous.
Everyone who is either kind or generous is not creative or not calm and vice versa.
Everyone who is either not quiet or old is not wise.
Everyone who is not creative is either not kind or not generous and vice versa.
If someone is not strong then someone is brave and vice versa.
If someone is not curious then susan is either not kind or happy and vice versa.
Everyone who is not patient is patient or not quiet and vice versa.
Everyone who is not happy or not rich is generous or calm and vice versa.
If someone is either not humble or strong then susan is either not brave or not quiet and vice versa.
Everyone who is quiet is not creative or not happy and vice versa.
If someone is both not wise and not old then susan is not kind or not old.
If someone is both not tall and not old then fred is strong and vice versa.
Everyone who is not patient is both happy and not funny.
Everyone who is not creative or not calm is not curious or brave and vice versa.
John is not old.
Someone is not humble.
Someone is not funny.
Someone is rich or not old.
Someone is either not old or kind. | Susan is kind. | contradiction | (![X]:((wise(X)&~creative(X))<=>patient(X)))&
((?[X]:(~old(X)))<=>((calm(susan)|curious(susan))))&
((?[X]:(old(X)))=>((~calm(lucy)&~generous(lucy))))&
(![X]:((kind(X)<~>generous(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~quiet(X)<~>old(X))=>~wise(X)))&
(![X]:(~creative(X)<=>(~kind(X)<~>~generous(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(brave(X))))&
((?[X]:(~curious(X)))<=>((~kind(susan)<~>happy(susan))))&
(![X]:(~patient(X)<=>(patient(X)|~quiet(X))))&
(![X]:((~happy(X)|~rich(X))<=>(generous(X)|calm(X))))&
((?[X]:((~humble(X)<~>strong(X))))<=>((~brave(susan)<~>~quiet(susan))))&
(![X]:(quiet(X)<=>(~creative(X)|~happy(X))))&
((?[X]:((~wise(X)&~old(X))))=>((~kind(susan)|~old(susan))))&
((?[X]:((~tall(X)&~old(X))))<=>(strong(fred)))&
(![X]:(~patient(X)=>(happy(X)&~funny(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~curious(X)|brave(X))))&
(~old(john))&
(?[X]:(~humble(X)))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((~old(X)<~>kind(X)))) | kind(susan) | [
"p3",
"p5",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 905882523104805133833895
% SZS output start Proof for 905882523104805133833895
4. ! [X0] : ((kind(X0) <~> generous(X0)) <=> (~calm(X0) | ~creative(X0))) [input p3]
6. ! [X0] : (~creative(X0) <=> (~kind(X0) <~> ~generous(X0))) [input p5]
8. ? [X0] : ~curious(X0) <=> (~kind(susan) <~> happy(susan)) [input p7]
9. ! [X0] : (~patient(X0) <=> (~quiet(X0) | patient(X0))) [input p8]
12. ! [X0] : (quiet(X0) <=> (~happy(X0) | ~creative(X0))) [input p11]
16. ! [X0] : ((~calm(X0) | ~creative(X0)) <=> (brave(X0) | ~curious(X0))) [input p15]
22. kind(susan) [input hypothesis]
38. ! [X0] : ((((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))))) [flattening 38]
41. ! [X0] : ((~creative(X0) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | creative(X0))) [nnf transformation 6]
47. (? [X0] : ~curious(X0) | ((~kind(susan) | ~happy(susan)) & (happy(susan) | kind(susan)))) & (((~happy(susan) | kind(susan)) & (happy(susan) | ~kind(susan))) | ! [X0] : curious(X0)) [nnf transformation 8]
48. (? [X0] : ~curious(X0) | ((~kind(susan) | ~happy(susan)) & (happy(susan) | kind(susan)))) & (((~happy(susan) | kind(susan)) & (happy(susan) | ~kind(susan))) | ! [X1] : curious(X1)) [rectify 47]
49. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
50. (~curious(sK3) | ((~kind(susan) | ~happy(susan)) & (happy(susan) | kind(susan)))) & (((~happy(susan) | kind(susan)) & (happy(susan) | ~kind(susan))) | ! [X1] : curious(X1)) [skolemisation 48,49]
51. ! [X0] : ((~patient(X0) | (quiet(X0) & ~patient(X0))) & ((~quiet(X0) | patient(X0)) | patient(X0))) [nnf transformation 9]
52. ! [X0] : ((~patient(X0) | (quiet(X0) & ~patient(X0))) & (~quiet(X0) | patient(X0) | patient(X0))) [flattening 51]
59. ! [X0] : ((quiet(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | ~quiet(X0))) [nnf transformation 12]
60. ! [X0] : ((quiet(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~quiet(X0))) [flattening 59]
65. ! [X0] : (((~calm(X0) | ~creative(X0)) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | (calm(X0) & creative(X0)))) [nnf transformation 16]
66. ! [X0] : ((~calm(X0) | ~creative(X0) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | (calm(X0) & creative(X0)))) [flattening 65]
85. kind(X0) | generous(X0) | calm(X0) [cnf transformation 39]
87. ~kind(X0) | ~generous(X0) | calm(X0) [cnf transformation 39]
92. ~generous(X0) | ~creative(X0) | kind(X0) [cnf transformation 41]
93. ~kind(X0) | ~creative(X0) | generous(X0) [cnf transformation 41]
99. ~curious(sK3) | ~kind(susan) | ~happy(susan) [cnf transformation 50]
100. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 52]
101. ~patient(X0) | ~patient(X0) [cnf transformation 52]
116. quiet(X0) | creative(X0) [cnf transformation 60]
117. quiet(X0) | happy(X0) [cnf transformation 60]
125. ~calm(X0) | ~creative(X0) | curious(X0) [cnf transformation 66]
132. kind(susan) [cnf transformation 22]
133. ~quiet(X0) | patient(X0) [duplicate literal removal 100]
134. ~patient(X0) [duplicate literal removal 101]
183. 12 <=> happy(susan) [avatar definition]
185. ~happy(susan) <- (~12) [avatar component clause 183]
187. 13 <=> kind(susan) [avatar definition]
191. 14 <=> curious(sK3) [avatar definition]
193. ~curious(sK3) <- (~14) [avatar component clause 191]
194. ~12 | ~13 | ~14 [avatar split clause 99,191,187,183]
197. 15 <=> ! [X1] : curious(X1) [avatar definition]
198. curious(X1) <- (15) [avatar component clause 197]
201. ~quiet(X0) [subsumption resolution 133,134]
228. happy(X0) [subsumption resolution 117,201]
229. creative(X0) [subsumption resolution 116,201]
257. ~calm(X0) | curious(X0) [subsumption resolution 125,229]
277. 13 [avatar split clause 132,187]
317. ~creative(X0) | generous(X0) | generous(X0) | calm(X0) [resolution 93,85]
321. ~creative(X0) | generous(X0) | calm(X0) [duplicate literal removal 317]
323. generous(X0) | calm(X0) [subsumption resolution 321,229]
334. calm(X0) | ~creative(X0) | kind(X0) [resolution 323,92]
337. kind(X0) | calm(X0) [subsumption resolution 334,229]
345. calm(X1) | ~generous(X1) | calm(X1) [resolution 337,87]
348. calm(X1) | ~generous(X1) [duplicate literal removal 345]
349. calm(X1) [subsumption resolution 348,323]
356. curious(X0) [resolution 349,257]
359. 15 [avatar split clause 356,197]
364. $false <- (~14, 15) [resolution 198,193]
366. 14 | ~15 [avatar contradiction clause 364]
367. $false <- (~12) [subsumption resolution 185,228]
368. 12 [avatar contradiction clause 367]
369. $false [avatar sat refutation 194,277,359,366,368]
% SZS output end Proof for 905882523104805133833895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and funny is tall and vice versa. Everyone who is wise is not calm or not funny and vice versa. If susan is kind then someone is not quiet or calm. If alice is either not strong or happy then someone is strong or not tall. If paul is calm then susan is not curious and vice versa. Everyone who is both humble and calm is not old or not kind. If lucy is both not wise and not curious then fred is both not humble and not old and vice versa. Everyone who is not humble is either calm or kind and vice versa. Everyone who is either not strong or curious is either not creative or not quiet and vice versa. Everyone who is curious is not calm or happy and vice versa. If paul is tall or old then alice is not generous. Everyone who is either not humble or quiet is both not calm and calm. If someone is calm then someone is both tall and wise. Everyone who is both rich and kind is not generous or not humble. If susan is brave or not happy then fred is both not generous and not tall and vice versa. Everyone who is not generous or generous is not patient and vice versa. Paul is not old. Someone is either not strong or kind. Paul is generous or not curious. Mary is patient or tall. Lucy is either humble or old. Fred is not funny or funny. Someone is either not curious or kind. John is not quiet. | Alice is not generous. | neutral | (![X]:((~old(X)&funny(X))<=>tall(X)))&
(![X]:(wise(X)<=>(~calm(X)|~funny(X))))&
((kind(susan))=>(?[X]:((~quiet(X)|calm(X)))))&
(((~strong(alice)<~>happy(alice)))=>(?[X]:((strong(X)|~tall(X)))))&
((calm(paul))<=>(~curious(susan)))&
(![X]:((humble(X)&calm(X))=>(~old(X)|~kind(X))))&
(((~wise(lucy)&~curious(lucy)))<=>((~humble(fred)&~old(fred))))&
(![X]:(~humble(X)<=>(calm(X)<~>kind(X))))&
(![X]:((~strong(X)<~>curious(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:(curious(X)<=>(~calm(X)|happy(X))))&
(((tall(paul)|old(paul)))=>(~generous(alice)))&
(![X]:((~humble(X)<~>quiet(X))=>(~calm(X)&calm(X))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)&wise(X)))))&
(![X]:((rich(X)&kind(X))=>(~generous(X)|~humble(X))))&
(((brave(susan)|~happy(susan)))<=>((~generous(fred)&~tall(fred))))&
(![X]:((~generous(X)|generous(X))<=>~patient(X)))&
(~old(paul))&
(?[X]:((~strong(X)<~>kind(X))))&
((generous(paul)|~curious(paul)))&
((patient(mary)|tall(mary)))&
((humble(lucy)<~>old(lucy)))&
((~funny(fred)|funny(fred)))&
(?[X]:((~curious(X)<~>kind(X))))&
(~quiet(john)) | ~generous(alice) | [] | null | 0 |
If someone is either generous or not curious then someone is either not tall or not patient and vice versa.
If mary is either not humble or not kind then someone is not funny or not rich.
If someone is not old then alice is generous or old.
If someone is either not creative or curious then someone is not old or not happy and vice versa.
If john is either happy or calm then someone is kind.
Everyone who is rich or strong is tall and vice versa.
Everyone who is both old and not humble is either brave or not strong and vice versa.
Everyone who is patient or old is either generous or not curious and vice versa.
Everyone who is curious is both tall and not brave.
If someone is not wise or creative then someone is creative or not rich and vice versa.
If someone is humble or wise then someone is either wise or not funny.
Everyone who is brave or not calm is not generous or happy and vice versa.
If someone is either not tall or old then paul is both tall and not brave and vice versa.
Everyone who is both old and not happy is either not creative or not old and vice versa.
Everyone who is strong is either not brave or not creative.
If paul is wise then someone is both funny and creative.
Someone is not curious or not creative.
Someone is rich.
Mary is funny.
John is either old or patient.
Someone is both rich and not patient.
Someone is kind.
Alice is either curious or brave. | Alice is old. | neutral | ((?[X]:((generous(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~patient(X)))))&
(((~humble(mary)<~>~kind(mary)))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:(~old(X)))=>((generous(alice)|old(alice))))&
((?[X]:((~creative(X)<~>curious(X))))<=>(?[X]:((~old(X)|~happy(X)))))&
(((happy(john)<~>calm(john)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)|strong(X))<=>tall(X)))&
(![X]:((old(X)&~humble(X))<=>(brave(X)<~>~strong(X))))&
(![X]:((patient(X)|old(X))<=>(generous(X)<~>~curious(X))))&
(![X]:(curious(X)=>(tall(X)&~brave(X))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((creative(X)|~rich(X)))))&
((?[X]:((humble(X)|wise(X))))=>(?[X]:((wise(X)<~>~funny(X)))))&
(![X]:((brave(X)|~calm(X))<=>(~generous(X)|happy(X))))&
((?[X]:((~tall(X)<~>old(X))))<=>((tall(paul)&~brave(paul))))&
(![X]:((old(X)&~happy(X))<=>(~creative(X)<~>~old(X))))&
(![X]:(strong(X)=>(~brave(X)<~>~creative(X))))&
((wise(paul))=>(?[X]:((funny(X)&creative(X)))))&
(?[X]:((~curious(X)|~creative(X))))&
(?[X]:(rich(X)))&
(funny(mary))&
((old(john)<~>patient(john)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:(kind(X)))&
((curious(alice)<~>brave(alice))) | old(alice) | [] | null | 0 |
Everyone who is both not brave and not kind is either curious or not funny and vice versa.
If mary is not kind or not creative then someone is wise and vice versa.
If someone is not kind or not humble then alice is both not brave and brave.
Everyone who is either patient or quiet is either tall or not creative and vice versa.
If lucy is either kind or curious then paul is either rich or not happy.
If lucy is both not patient and not wise then paul is rich and vice versa.
If paul is not wise then someone is kind and vice versa.
If mary is generous then alice is calm or not old and vice versa.
Everyone who is patient or wise is either brave or wise.
Everyone who is wise or not quiet is tall or not calm and vice versa.
If john is rich then alice is both not creative and quiet.
Everyone who is not wise or not curious is not old and vice versa.
If lucy is not creative or calm then someone is both strong and not rich and vice versa.
If susan is not tall or rich then someone is either not strong or tall and vice versa.
Everyone who is either not creative or old is either not creative or curious and vice versa.
Paul is both not creative and not brave.
Someone is wise.
Someone is both not generous and not curious.
Susan is either not generous or curious.
Someone is either not brave or wise.
Someone is either old or not brave.
Someone is not humble or tall. | Mary is not kind. | contradiction | (![X]:((~brave(X)&~kind(X))<=>(curious(X)<~>~funny(X))))&
(((~kind(mary)|~creative(mary)))<=>(?[X]:(wise(X))))&
((?[X]:((~kind(X)|~humble(X))))=>((~brave(alice)&brave(alice))))&
(![X]:((patient(X)<~>quiet(X))<=>(tall(X)<~>~creative(X))))&
(((kind(lucy)<~>curious(lucy)))=>((rich(paul)<~>~happy(paul))))&
(((~patient(lucy)&~wise(lucy)))<=>(rich(paul)))&
((~wise(paul))<=>(?[X]:(kind(X))))&
((generous(mary))<=>((calm(alice)|~old(alice))))&
(![X]:((patient(X)|wise(X))=>(brave(X)<~>wise(X))))&
(![X]:((wise(X)|~quiet(X))<=>(tall(X)|~calm(X))))&
((rich(john))=>((~creative(alice)&quiet(alice))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(((~creative(lucy)|calm(lucy)))<=>(?[X]:((strong(X)&~rich(X)))))&
(((~tall(susan)|rich(susan)))<=>(?[X]:((~strong(X)<~>tall(X)))))&
(![X]:((~creative(X)<~>old(X))<=>(~creative(X)<~>curious(X))))&
((~creative(paul)&~brave(paul)))&
(?[X]:(wise(X)))&
(?[X]:((~generous(X)&~curious(X))))&
((~generous(susan)<~>curious(susan)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~humble(X)|tall(X)))) | ~kind(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5611255676027573591780746
% SZS output start Proof for 5611255676027573591780746
3. ? [X0] : (~humble(X0) | ~kind(X0)) => (brave(alice) & ~brave(alice)) [input p2]
23. ~kind(mary) [input hypothesis]
24. (brave(alice) & ~brave(alice)) | ! [X0] : (humble(X0) & kind(X0)) [ennf transformation 3]
83. ~brave(alice) | kind(X0) [cnf transformation 24]
85. brave(alice) | kind(X0) [cnf transformation 24]
151. ~kind(mary) [cnf transformation 23]
161. 2 <=> kind(mary) [avatar definition]
163. ~kind(mary) <- (~2) [avatar component clause 161]
179. 6 <=> brave(alice) [avatar definition]
184. 7 <=> ! [X0] : kind(X0) [avatar definition]
185. kind(X0) <- (7) [avatar component clause 184]
186. 7 | 6 [avatar split clause 85,179,184]
188. 7 | ~6 [avatar split clause 83,179,184]
346. ~2 [avatar split clause 151,161]
351. $false <- (~2, 7) [resolution 185,163]
352. 2 | ~7 [avatar contradiction clause 351]
353. $false [avatar sat refutation 186,188,346,352]
% SZS output end Proof for 5611255676027573591780746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both creative and not happy then john is not tall and vice versa. Everyone who is either tall or not humble is either calm or not humble. Everyone who is both not old and not calm is both not wise and not funny. Everyone who is rich is not rich. If fred is creative or strong then someone is old or brave and vice versa. If someone is generous or not generous then someone is humble or not happy and vice versa. Everyone who is both strong and patient is either not rich or not curious. If someone is either strong or not rich then someone is happy or creative and vice versa. If mary is either patient or not generous then mary is old. If susan is not kind then someone is either not old or not funny and vice versa. If john is both not generous and generous then someone is not wise. If john is either not strong or not kind then fred is either patient or calm. If someone is kind or happy then john is either not rich or strong and vice versa. Everyone who is both not kind and funny is either kind or happy and vice versa. If someone is not wise or creative then alice is both not strong and wise and vice versa. If someone is either not brave or generous then someone is both brave and wise and vice versa. Alice is wise or not patient. Someone is not quiet or rich. Fred is rich or not quiet. Fred is not old or not rich. Alice is not tall or not rich. Someone is not calm. Susan is not old or not curious. | Alice is strong. | neutral | (((creative(john)&~happy(john)))<=>(~tall(john)))&
(![X]:((tall(X)<~>~humble(X))=>(calm(X)<~>~humble(X))))&
(![X]:((~old(X)&~calm(X))=>(~wise(X)&~funny(X))))&
(![X]:(rich(X)=>~rich(X)))&
(((creative(fred)|strong(fred)))<=>(?[X]:((old(X)|brave(X)))))&
((?[X]:((generous(X)|~generous(X))))<=>(?[X]:((humble(X)|~happy(X)))))&
(![X]:((strong(X)&patient(X))=>(~rich(X)<~>~curious(X))))&
((?[X]:((strong(X)<~>~rich(X))))<=>(?[X]:((happy(X)|creative(X)))))&
(((patient(mary)<~>~generous(mary)))=>(old(mary)))&
((~kind(susan))<=>(?[X]:((~old(X)<~>~funny(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:(~wise(X))))&
(((~strong(john)<~>~kind(john)))=>((patient(fred)<~>calm(fred))))&
((?[X]:((kind(X)|happy(X))))<=>((~rich(john)<~>strong(john))))&
(![X]:((~kind(X)&funny(X))<=>(kind(X)<~>happy(X))))&
((?[X]:((~wise(X)|creative(X))))<=>((~strong(alice)&wise(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(?[X]:((brave(X)&wise(X)))))&
((wise(alice)|~patient(alice)))&
(?[X]:((~quiet(X)|rich(X))))&
((rich(fred)|~quiet(fred)))&
((~old(fred)|~rich(fred)))&
((~tall(alice)|~rich(alice)))&
(?[X]:(~calm(X)))&
((~old(susan)|~curious(susan))) | strong(alice) | [] | null | 0 |
Everyone who is either not brave or not patient is both calm and not kind and vice versa.
Everyone who is either creative or strong is both not rich and generous and vice versa.
Everyone who is both calm and not wise is tall or not brave.
If fred is both not creative and not wise then alice is either not brave or old.
If someone is wise then alice is either not old or tall.
If someone is generous or not rich then john is both not generous and kind and vice versa.
If someone is both happy and not old then someone is either curious or wise and vice versa.
If mary is both not humble and old then someone is not calm or not kind and vice versa.
If someone is both not quiet and tall then someone is both not patient and brave and vice versa.
Everyone who is either patient or not old is both patient and calm.
If someone is either strong or happy then mary is not calm or curious.
Everyone who is not brave is either happy or brave.
Everyone who is not happy or patient is both not strong and not happy.
Everyone who is either strong or not calm is humble and vice versa.
Everyone who is not patient or patient is both patient and not strong.
Everyone who is either not creative or quiet is both brave and funny.
Someone is not humble or tall.
Fred is not funny.
Someone is curious.
Lucy is either not wise or not quiet.
Someone is rich. | John is not kind. | neutral | (![X]:((~brave(X)<~>~patient(X))<=>(calm(X)&~kind(X))))&
(![X]:((creative(X)<~>strong(X))<=>(~rich(X)&generous(X))))&
(![X]:((calm(X)&~wise(X))=>(tall(X)|~brave(X))))&
(((~creative(fred)&~wise(fred)))=>((~brave(alice)<~>old(alice))))&
((?[X]:(wise(X)))=>((~old(alice)<~>tall(alice))))&
((?[X]:((generous(X)|~rich(X))))<=>((~generous(john)&kind(john))))&
((?[X]:((happy(X)&~old(X))))<=>(?[X]:((curious(X)<~>wise(X)))))&
(((~humble(mary)&old(mary)))<=>(?[X]:((~calm(X)|~kind(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:((~patient(X)&brave(X)))))&
(![X]:((patient(X)<~>~old(X))=>(patient(X)&calm(X))))&
((?[X]:((strong(X)<~>happy(X))))=>((~calm(mary)|curious(mary))))&
(![X]:(~brave(X)=>(happy(X)<~>brave(X))))&
(![X]:((~happy(X)|patient(X))=>(~strong(X)&~happy(X))))&
(![X]:((strong(X)<~>~calm(X))<=>humble(X)))&
(![X]:((~patient(X)|patient(X))=>(patient(X)&~strong(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(brave(X)&funny(X))))&
(?[X]:((~humble(X)|tall(X))))&
(~funny(fred))&
(?[X]:(curious(X)))&
((~wise(lucy)<~>~quiet(lucy)))&
(?[X]:(rich(X))) | ~kind(john) | [] | null | 0 |
Everyone who is old or not generous is both wise and creative and vice versa. Everyone who is both patient and not funny is either not rich or old. If someone is either curious or not kind then alice is humble or not quiet and vice versa. If someone is both not patient and not funny then someone is both brave and not tall and vice versa. Everyone who is rich is happy. If someone is not kind or not funny then paul is not quiet and vice versa. Everyone who is either funny or not quiet is not strong. Everyone who is not strong is both wise and not old and vice versa. If mary is patient then someone is both not brave and not calm. If someone is not quiet then alice is old. If someone is both not quiet and not calm then someone is not wise and vice versa. If susan is either not funny or quiet then mary is strong and vice versa. If someone is curious then someone is both not patient and strong. If john is not patient then lucy is both not curious and humble and vice versa. If someone is not happy then john is both not calm and not curious. If john is both not wise and not funny then someone is both not kind and not quiet. Someone is both not tall and happy. Someone is either not humble or not quiet. Someone is not quiet. Mary is either not humble or not kind. Susan is either creative or strong. Someone is wise or not rich. John is either curious or happy. Someone is curious. | Susan is old. | contradiction | (![X]:((old(X)|~generous(X))<=>(wise(X)&creative(X))))&
(![X]:((patient(X)&~funny(X))=>(~rich(X)<~>old(X))))&
((?[X]:((curious(X)<~>~kind(X))))<=>((humble(alice)|~quiet(alice))))&
((?[X]:((~patient(X)&~funny(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:(rich(X)=>happy(X)))&
((?[X]:((~kind(X)|~funny(X))))<=>(~quiet(paul)))&
(![X]:((funny(X)<~>~quiet(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(wise(X)&~old(X))))&
((patient(mary))=>(?[X]:((~brave(X)&~calm(X)))))&
((?[X]:(~quiet(X)))=>(old(alice)))&
((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:(~wise(X))))&
(((~funny(susan)<~>quiet(susan)))<=>(strong(mary)))&
((?[X]:(curious(X)))=>(?[X]:((~patient(X)&strong(X)))))&
((~patient(john))<=>((~curious(lucy)&humble(lucy))))&
((?[X]:(~happy(X)))=>((~calm(john)&~curious(john))))&
(((~wise(john)&~funny(john)))=>(?[X]:((~kind(X)&~quiet(X)))))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
((~humble(mary)<~>~kind(mary)))&
((creative(susan)<~>strong(susan)))&
(?[X]:((wise(X)|~rich(X))))&
((curious(john)<~>happy(john)))&
(?[X]:(curious(X))) | old(susan) | [
"p0",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1846207167177404128869079
% SZS output start Proof for 1846207167177404128869079
1. ! [X0] : ((~generous(X0) | old(X0)) <=> (creative(X0) & wise(X0))) [input p0]
8. ! [X0] : (~strong(X0) <=> (~old(X0) & wise(X0))) [input p7]
21. creative(susan) <~> strong(susan) [input p20]
25. old(susan) [input hypothesis]
39. ! [X0] : (((~generous(X0) | old(X0)) | (~creative(X0) | ~wise(X0))) & ((creative(X0) & wise(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((~generous(X0) | old(X0) | ~creative(X0) | ~wise(X0)) & ((creative(X0) & wise(X0)) | (generous(X0) & ~old(X0)))) [flattening 39]
57. ! [X0] : ((~strong(X0) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | strong(X0))) [nnf transformation 8]
58. ! [X0] : ((~strong(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | strong(X0))) [flattening 57]
82. (~strong(susan) | ~creative(susan)) & (strong(susan) | creative(susan)) [nnf transformation 21]
90. ~old(X0) | creative(X0) [cnf transformation 40]
112. ~old(X0) | strong(X0) [cnf transformation 58]
141. ~strong(susan) | ~creative(susan) [cnf transformation 82]
146. old(susan) [cnf transformation 25]
361. 48 <=> creative(susan) [avatar definition]
365. 49 <=> strong(susan) [avatar definition]
368. ~48 | ~49 [avatar split clause 141,365,361]
396. creative(susan) [resolution 90,146]
399. strong(susan) [resolution 112,146]
403. 48 [avatar split clause 396,361]
404. 49 [avatar split clause 399,365]
405. $false [avatar sat refutation 368,403,404]
% SZS output end Proof for 1846207167177404128869079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or curious is either not generous or rich and vice versa.
If fred is not happy or rich then mary is wise.
If alice is both brave and not creative then john is calm.
Everyone who is both not old and old is both humble and tall.
If lucy is generous or not calm then someone is both strong and rich.
Everyone who is both patient and curious is either not calm or rich.
Everyone who is not quiet or not curious is either quiet or tall.
Everyone who is both not old and creative is not strong and vice versa.
Everyone who is both not wise and generous is patient.
If paul is not patient or old then someone is curious.
Everyone who is not calm or not tall is kind.
If someone is both brave and tall then someone is not brave.
Everyone who is generous is both not old and happy.
Everyone who is both curious and not old is strong and vice versa.
If paul is strong then someone is either not brave or not kind and vice versa.
If susan is happy or not kind then someone is either kind or not old and vice versa.
Paul is either not generous or not happy.
Someone is wise.
John is patient or funny.
Someone is not humble or curious.
Lucy is not curious or tall.
Someone is both brave and not patient.
Someone is both not patient and not kind.
Someone is not creative. | Paul is rich. | contradiction | (![X]:((~strong(X)|curious(X))<=>(~generous(X)<~>rich(X))))&
(((~happy(fred)|rich(fred)))=>(wise(mary)))&
(((brave(alice)&~creative(alice)))=>(calm(john)))&
(![X]:((~old(X)&old(X))=>(humble(X)&tall(X))))&
(((generous(lucy)|~calm(lucy)))=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((patient(X)&curious(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)|~curious(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~old(X)&creative(X))<=>~strong(X)))&
(![X]:((~wise(X)&generous(X))=>patient(X)))&
(((~patient(paul)|old(paul)))=>(?[X]:(curious(X))))&
(![X]:((~calm(X)|~tall(X))=>kind(X)))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:(~brave(X))))&
(![X]:(generous(X)=>(~old(X)&happy(X))))&
(![X]:((curious(X)&~old(X))<=>strong(X)))&
((strong(paul))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((happy(susan)|~kind(susan)))<=>(?[X]:((kind(X)<~>~old(X)))))&
((~generous(paul)<~>~happy(paul)))&
(?[X]:(wise(X)))&
((patient(john)|funny(john)))&
(?[X]:((~humble(X)|curious(X))))&
((~curious(lucy)|tall(lucy)))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((~patient(X)&~kind(X))))&
(?[X]:(~creative(X))) | rich(paul) | [
"p0",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 465763014038237962513014
% SZS output start Proof for 465763014038237962513014
1. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~generous(X0) <~> rich(X0))) [input p0]
13. ! [X0] : (generous(X0) => (happy(X0) & ~old(X0))) [input p12]
14. ! [X0] : ((~old(X0) & curious(X0)) <=> strong(X0)) [input p13]
17. ~generous(paul) <~> ~happy(paul) [input p16]
25. rich(paul) [input hypothesis]
42. ! [X0] : ((happy(X0) & ~old(X0)) | ~generous(X0)) [ennf transformation 13]
43. ! [X0] : (((curious(X0) | ~strong(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~curious(X0) & strong(X0)))) [nnf transformation 1]
44. ! [X0] : ((curious(X0) | ~strong(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~curious(X0) & strong(X0)))) [flattening 43]
56. ! [X0] : (((~old(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) | ~curious(X0)))) [nnf transformation 14]
57. ! [X0] : (((~old(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | old(X0) | ~curious(X0))) [flattening 56]
67. (happy(paul) | generous(paul)) & (~happy(paul) | ~generous(paul)) [nnf transformation 17]
78. ~rich(X0) | generous(X0) | strong(X0) [cnf transformation 44]
79. ~rich(X0) | generous(X0) | ~curious(X0) [cnf transformation 44]
104. ~generous(X0) | happy(X0) [cnf transformation 42]
106. ~strong(X0) | curious(X0) [cnf transformation 57]
118. ~happy(paul) | ~generous(paul) [cnf transformation 67]
119. happy(paul) | generous(paul) [cnf transformation 67]
127. rich(paul) [cnf transformation 25]
190. 14 <=> strong(paul) [avatar definition]
192. strong(paul) <- (14) [avatar component clause 190]
229. happy(paul) [subsumption resolution 119,104]
230. ~generous(paul) [subsumption resolution 118,229]
264. generous(paul) | strong(paul) [resolution 78,127]
265. strong(paul) [subsumption resolution 264,230]
268. 14 [avatar split clause 265,190]
269. curious(paul) <- (14) [resolution 192,106]
275. generous(paul) | ~curious(paul) [resolution 79,127]
276. ~curious(paul) [subsumption resolution 275,230]
277. $false <- (14) [subsumption resolution 276,269]
278. ~14 [avatar contradiction clause 277]
279. $false [avatar sat refutation 268,278]
% SZS output end Proof for 465763014038237962513014
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or generous is either not wise or curious. Everyone who is both not old and not generous is either kind or funny. If susan is humble then john is either humble or not happy and vice versa. If someone is either old or not kind then paul is both curious and creative. Everyone who is both not happy and not curious is not patient. Everyone who is not happy or funny is both patient and not generous. If alice is both wise and not happy then someone is either rich or kind. If susan is not curious then john is generous and vice versa. Everyone who is both not rich and strong is not patient and vice versa. If someone is both wise and not wise then susan is patient or not happy. Everyone who is not quiet is either generous or not happy. Everyone who is both happy and not funny is either generous or not funny and vice versa. If someone is either not brave or not kind then someone is not calm or curious. Everyone who is both not humble and generous is either generous or kind and vice versa. If someone is not humble then someone is wise or generous and vice versa. Everyone who is not patient is either kind or curious. Someone is either not humble or old. John is not generous. Someone is not strong or not quiet. John is both not tall and not brave. Someone is either not creative or curious. Fred is not creative. Someone is either strong or not old. Someone is not brave. | Alice is kind. | contradiction | (![X]:((~old(X)<~>generous(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~old(X)&~generous(X))=>(kind(X)<~>funny(X))))&
((humble(susan))<=>((humble(john)<~>~happy(john))))&
((?[X]:((old(X)<~>~kind(X))))=>((curious(paul)&creative(paul))))&
(![X]:((~happy(X)&~curious(X))=>~patient(X)))&
(![X]:((~happy(X)|funny(X))=>(patient(X)&~generous(X))))&
(((wise(alice)&~happy(alice)))=>(?[X]:((rich(X)<~>kind(X)))))&
((~curious(susan))<=>(generous(john)))&
(![X]:((~rich(X)&strong(X))<=>~patient(X)))&
((?[X]:((wise(X)&~wise(X))))=>((patient(susan)|~happy(susan))))&
(![X]:(~quiet(X)=>(generous(X)<~>~happy(X))))&
(![X]:((happy(X)&~funny(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>~kind(X))))=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:((~humble(X)&generous(X))<=>(generous(X)<~>kind(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(~patient(X)=>(kind(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>old(X))))&
(~generous(john))&
(?[X]:((~strong(X)|~quiet(X))))&
((~tall(john)&~brave(john)))&
(?[X]:((~creative(X)<~>curious(X))))&
(~creative(fred))&
(?[X]:((strong(X)<~>~old(X))))&
(?[X]:(~brave(X))) | kind(alice) | [
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 269385159082856096620311
% SZS output start Proof for 269385159082856096620311
6. ! [X0] : ((funny(X0) | ~happy(X0)) => (~generous(X0) & patient(X0))) [input p5]
12. ! [X0] : ((~funny(X0) & happy(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p11]
14. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (generous(X0) <~> kind(X0))) [input p13]
25. kind(alice) [input hypothesis]
38. ! [X0] : ((~generous(X0) & patient(X0)) | (~funny(X0) & happy(X0))) [ennf transformation 6]
56. ! [X0] : (((~funny(X0) & happy(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (funny(X0) | ~happy(X0)))) [nnf transformation 12]
57. ! [X0] : (((~funny(X0) & happy(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | funny(X0) | ~happy(X0))) [flattening 56]
58. ! [X0] : (((generous(X0) & ~humble(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (~generous(X0) | humble(X0)))) [nnf transformation 14]
59. ! [X0] : (((generous(X0) & ~humble(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ~generous(X0) | humble(X0))) [flattening 58]
94. ~generous(X0) | happy(X0) [cnf transformation 38]
95. ~generous(X0) | ~funny(X0) [cnf transformation 38]
107. funny(X0) | ~generous(X0) | funny(X0) | ~happy(X0) [cnf transformation 57]
117. generous(X0) | generous(X0) | ~kind(X0) [cnf transformation 59]
132. kind(alice) [cnf transformation 25]
134. generous(X0) | ~kind(X0) [duplicate literal removal 117]
135. funny(X0) | ~generous(X0) | ~happy(X0) [duplicate literal removal 107]
200. ~generous(X0) | ~happy(X0) [subsumption resolution 135,95]
201. ~generous(X0) [subsumption resolution 200,94]
202. ~kind(X0) [subsumption resolution 134,201]
260. $false [subsumption resolution 132,202]
% SZS output end Proof for 269385159082856096620311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not wise or not strong then someone is both not generous and curious.
Everyone who is not old or not quiet is both patient and calm.
If susan is either not calm or quiet then someone is not curious.
If alice is kind then someone is not humble.
Everyone who is not quiet or patient is both not curious and not funny.
Everyone who is old or calm is creative or brave and vice versa.
Everyone who is not happy is kind or quiet and vice versa.
If someone is both not old and patient then someone is both rich and not quiet and vice versa.
If someone is not quiet or rich then someone is both not calm and humble.
Everyone who is old is not tall or happy and vice versa.
Everyone who is kind or old is both quiet and strong and vice versa.
If someone is not creative or not calm then someone is not creative and vice versa.
If alice is both not patient and not old then fred is both not funny and not brave.
If lucy is either kind or not rich then fred is tall.
If someone is not creative then someone is either old or funny and vice versa.
If someone is quiet or not wise then alice is not rich.
John is not funny.
Paul is humble.
Someone is not curious or not calm.
John is creative.
Susan is both curious and not calm.
Someone is either curious or humble.
Someone is both kind and not brave. | Fred is not old. | contradiction | (((~wise(alice)|~strong(alice)))=>(?[X]:((~generous(X)&curious(X)))))&
(![X]:((~old(X)|~quiet(X))=>(patient(X)&calm(X))))&
(((~calm(susan)<~>quiet(susan)))=>(?[X]:(~curious(X))))&
((kind(alice))=>(?[X]:(~humble(X))))&
(![X]:((~quiet(X)|patient(X))=>(~curious(X)&~funny(X))))&
(![X]:((old(X)|calm(X))<=>(creative(X)|brave(X))))&
(![X]:(~happy(X)<=>(kind(X)|quiet(X))))&
((?[X]:((~old(X)&patient(X))))<=>(?[X]:((rich(X)&~quiet(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:(old(X)<=>(~tall(X)|happy(X))))&
(![X]:((kind(X)|old(X))<=>(quiet(X)&strong(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>(?[X]:(~creative(X))))&
(((~patient(alice)&~old(alice)))=>((~funny(fred)&~brave(fred))))&
(((kind(lucy)<~>~rich(lucy)))=>(tall(fred)))&
((?[X]:(~creative(X)))<=>(?[X]:((old(X)<~>funny(X)))))&
((?[X]:((quiet(X)|~wise(X))))=>(~rich(alice)))&
(~funny(john))&
(humble(paul))&
(?[X]:((~curious(X)|~calm(X))))&
(creative(john))&
((curious(susan)&~calm(susan)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((kind(X)&~brave(X)))) | ~old(fred) | [
"p1",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9031886457065212866884687
% SZS output start Proof for 9031886457065212866884687
2. ! [X0] : ((~quiet(X0) | ~old(X0)) => (calm(X0) & patient(X0))) [input p1]
7. ! [X0] : (~happy(X0) <=> (quiet(X0) | kind(X0))) [input p6]
8. ? [X0] : (patient(X0) & ~old(X0)) <=> ? [X0] : (~quiet(X0) & rich(X0)) [input p7]
10. ! [X0] : (old(X0) <=> (happy(X0) | ~tall(X0))) [input p9]
11. ! [X0] : ((old(X0) | kind(X0)) <=> (strong(X0) & quiet(X0))) [input p10]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (patient(X0) & ~old(X0)) <=> ? [X1] : (~quiet(X1) & rich(X1)) [rectify 8]
33. ! [X0] : ((calm(X0) & patient(X0)) | (quiet(X0) & old(X0))) [ennf transformation 2]
51. ! [X0] : ((~happy(X0) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | happy(X0))) [nnf transformation 7]
52. ! [X0] : ((~happy(X0) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | happy(X0))) [flattening 51]
53. (? [X0] : (patient(X0) & ~old(X0)) | ! [X1] : (quiet(X1) | ~rich(X1))) & (? [X1] : (~quiet(X1) & rich(X1)) | ! [X0] : (~patient(X0) | old(X0))) [nnf transformation 25]
54. (? [X0] : (patient(X0) & ~old(X0)) | ! [X1] : (quiet(X1) | ~rich(X1))) & (? [X2] : (~quiet(X2) & rich(X2)) | ! [X3] : (~patient(X3) | old(X3))) [rectify 53]
55. ? [X0] : (patient(X0) & ~old(X0)) => (patient(sK3) & ~old(sK3)) [choice axiom]
56. ? [X2] : (~quiet(X2) & rich(X2)) => (~quiet(sK4) & rich(sK4)) [choice axiom]
57. ((patient(sK3) & ~old(sK3)) | ! [X1] : (quiet(X1) | ~rich(X1))) & ((~quiet(sK4) & rich(sK4)) | ! [X3] : (~patient(X3) | old(X3))) [skolemisation 54,56,55]
61. ! [X0] : ((old(X0) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | ~old(X0))) [nnf transformation 10]
62. ! [X0] : ((old(X0) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~old(X0))) [flattening 61]
63. ! [X0] : (((old(X0) | kind(X0)) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 11]
64. ! [X0] : ((old(X0) | kind(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | (~old(X0) & ~kind(X0)))) [flattening 63]
84. patient(X0) | old(X0) [cnf transformation 33]
99. happy(X0) | kind(X0) | quiet(X0) [cnf transformation 52]
103. ~quiet(sK4) | ~patient(X3) | old(X3) [cnf transformation 57]
112. ~happy(X0) | old(X0) [cnf transformation 62]
113. ~kind(X0) | quiet(X0) [cnf transformation 64]
114. ~old(X0) | quiet(X0) [cnf transformation 64]
140. ~old(fred) [cnf transformation 24]
185. ~quiet(sK4) | old(X3) [subsumption resolution 103,84]
187. 11 <=> ! [X3] : old(X3) [avatar definition]
188. old(X3) <- (11) [avatar component clause 187]
190. 12 <=> quiet(sK4) [avatar definition]
192. ~quiet(sK4) <- (~12) [avatar component clause 190]
193. 11 | ~12 [avatar split clause 185,190,187]
209. 16 <=> ! [X1] : quiet(X1) [avatar definition]
210. quiet(X1) <- (16) [avatar component clause 209]
303. $false <- (11) [resolution 188,140]
304. ~11 [avatar contradiction clause 303]
382. $false <- (~12, 16) [resolution 210,192]
383. 12 | ~16 [avatar contradiction clause 382]
392. kind(X0) | quiet(X0) | old(X0) [resolution 99,112]
395. kind(X0) | quiet(X0) [subsumption resolution 392,114]
396. quiet(X0) [subsumption resolution 395,113]
397. 16 [avatar split clause 396,209]
398. $false [avatar sat refutation 193,304,383,397]
% SZS output end Proof for 9031886457065212866884687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not funny or patient then mary is both not rich and not wise and vice versa.
Everyone who is brave or generous is both not calm and not old.
Everyone who is both tall and not kind is both not calm and not brave and vice versa.
Everyone who is both not kind and rich is not tall and vice versa.
If alice is both old and not brave then someone is rich or old.
Everyone who is both not strong and not old is either funny or patient and vice versa.
If someone is not creative or old then fred is patient.
Everyone who is both brave and not happy is both not creative and happy.
Everyone who is quiet or rich is old or not funny.
Everyone who is not rich or not happy is either quiet or not brave.
Everyone who is either not kind or not curious is not kind.
If lucy is patient or not strong then someone is either not happy or not creative and vice versa.
If fred is either happy or not creative then mary is either not patient or quiet and vice versa.
If someone is either funny or not old then someone is both calm and not funny and vice versa.
If paul is either funny or not patient then susan is both not patient and old.
Everyone who is both curious and calm is not generous and vice versa.
Someone is not generous or generous.
John is not strong.
Mary is wise.
Someone is both not quiet and funny.
Someone is not strong.
Someone is not calm.
Someone is not quiet.
Someone is both quiet and not creative. | Mary is strong. | neutral | (((~funny(alice)<~>patient(alice)))<=>((~rich(mary)&~wise(mary))))&
(![X]:((brave(X)|generous(X))=>(~calm(X)&~old(X))))&
(![X]:((tall(X)&~kind(X))<=>(~calm(X)&~brave(X))))&
(![X]:((~kind(X)&rich(X))<=>~tall(X)))&
(((old(alice)&~brave(alice)))=>(?[X]:((rich(X)|old(X)))))&
(![X]:((~strong(X)&~old(X))<=>(funny(X)<~>patient(X))))&
((?[X]:((~creative(X)|old(X))))=>(patient(fred)))&
(![X]:((brave(X)&~happy(X))=>(~creative(X)&happy(X))))&
(![X]:((quiet(X)|rich(X))=>(old(X)|~funny(X))))&
(![X]:((~rich(X)|~happy(X))=>(quiet(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>~curious(X))=>~kind(X)))&
(((patient(lucy)|~strong(lucy)))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(((happy(fred)<~>~creative(fred)))<=>((~patient(mary)<~>quiet(mary))))&
((?[X]:((funny(X)<~>~old(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
(((funny(paul)<~>~patient(paul)))=>((~patient(susan)&old(susan))))&
(![X]:((curious(X)&calm(X))<=>~generous(X)))&
(?[X]:((~generous(X)|generous(X))))&
(~strong(john))&
(wise(mary))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~calm(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)&~creative(X)))) | strong(mary) | [] | null | 0 |
If someone is not quiet or not curious then someone is both brave and not patient.
If paul is not kind or not rich then someone is tall.
If lucy is both not creative and not brave then mary is not humble.
If susan is either curious or rich then someone is wise or tall and vice versa.
Everyone who is not rich or patient is not humble or not brave and vice versa.
If alice is either not wise or not strong then someone is both strong and curious and vice versa.
If someone is curious or not rich then someone is either not quiet or not funny.
If susan is either not kind or rich then john is either brave or not happy and vice versa.
Everyone who is both creative and not funny is both not curious and not generous and vice versa.
Everyone who is not generous or creative is either brave or kind and vice versa.
Everyone who is humble or not rich is not rich or not brave.
Everyone who is both patient and calm is either not funny or not kind and vice versa.
Everyone who is brave is not funny or not calm.
Everyone who is creative is not funny or not wise and vice versa.
Everyone who is not tall or funny is tall or generous and vice versa.
Everyone who is brave or not funny is not curious or not calm.
Someone is not creative.
Someone is happy.
Someone is both tall and curious.
Fred is both old and not creative.
Mary is either not brave or patient.
Alice is not calm.
Someone is not rich.
Someone is not happy or not generous. | Lucy is not creative. | neutral | ((?[X]:((~quiet(X)|~curious(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(((~kind(paul)|~rich(paul)))=>(?[X]:(tall(X))))&
(((~creative(lucy)&~brave(lucy)))=>(~humble(mary)))&
(((curious(susan)<~>rich(susan)))<=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~rich(X)|patient(X))<=>(~humble(X)|~brave(X))))&
(((~wise(alice)<~>~strong(alice)))<=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(((~kind(susan)<~>rich(susan)))<=>((brave(john)<~>~happy(john))))&
(![X]:((creative(X)&~funny(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~generous(X)|creative(X))<=>(brave(X)<~>kind(X))))&
(![X]:((humble(X)|~rich(X))=>(~rich(X)|~brave(X))))&
(![X]:((patient(X)&calm(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(brave(X)=>(~funny(X)|~calm(X))))&
(![X]:(creative(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~tall(X)|funny(X))<=>(tall(X)|generous(X))))&
(![X]:((brave(X)|~funny(X))=>(~curious(X)|~calm(X))))&
(?[X]:(~creative(X)))&
(?[X]:(happy(X)))&
(?[X]:((tall(X)&curious(X))))&
((old(fred)&~creative(fred)))&
((~brave(mary)<~>patient(mary)))&
(~calm(alice))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)|~generous(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is not tall or happy is not rich. If john is strong then alice is quiet. If someone is not calm then someone is not creative. If someone is either not patient or tall then lucy is either not generous or kind. Everyone who is not humble or not happy is both curious and not tall. Everyone who is both quiet and curious is both creative and not strong. If someone is humble then someone is not old. If someone is both not rich and quiet then john is not curious or curious. If fred is not old then someone is both not patient and not strong and vice versa. If fred is tall then someone is happy and vice versa. Everyone who is either not tall or patient is generous and vice versa. If someone is not happy or quiet then fred is not happy and vice versa. Everyone who is not rich is both not quiet and wise. If someone is either calm or curious then someone is either kind or happy and vice versa. If alice is either not strong or funny then someone is both not wise and tall and vice versa. Everyone who is humble or generous is both not strong and tall. Lucy is happy or quiet. Someone is not old. Alice is brave or humble. Fred is funny or not funny. John is humble or rich. Mary is both happy and humble. Alice is humble or not curious. Someone is either not strong or calm. | Fred is not humble. | contradiction | (![X]:((~tall(X)|happy(X))=>~rich(X)))&
((strong(john))=>(quiet(alice)))&
((?[X]:(~calm(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~patient(X)<~>tall(X))))=>((~generous(lucy)<~>kind(lucy))))&
(![X]:((~humble(X)|~happy(X))=>(curious(X)&~tall(X))))&
(![X]:((quiet(X)&curious(X))=>(creative(X)&~strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)&quiet(X))))=>((~curious(john)|curious(john))))&
((~old(fred))<=>(?[X]:((~patient(X)&~strong(X)))))&
((tall(fred))<=>(?[X]:(happy(X))))&
(![X]:((~tall(X)<~>patient(X))<=>generous(X)))&
((?[X]:((~happy(X)|quiet(X))))<=>(~happy(fred)))&
(![X]:(~rich(X)=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((~strong(alice)<~>funny(alice)))<=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((humble(X)|generous(X))=>(~strong(X)&tall(X))))&
((happy(lucy)|quiet(lucy)))&
(?[X]:(~old(X)))&
((brave(alice)|humble(alice)))&
((funny(fred)|~funny(fred)))&
((humble(john)|rich(john)))&
((happy(mary)&humble(mary)))&
((humble(alice)|~curious(alice)))&
(?[X]:((~strong(X)<~>calm(X)))) | ~humble(fred) | [
"p4",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8151862739986318913693264
% SZS output start Proof for 8151862739986318913693264
5. ! [X0] : ((~happy(X0) | ~humble(X0)) => (~tall(X0) & curious(X0))) [input p4]
10. tall(fred) <=> ? [X0] : happy(X0) [input p9]
22. humble(mary) & happy(mary) [input p21]
25. ~humble(fred) [input hypothesis]
34. ! [X0] : ((~tall(X0) & curious(X0)) | (happy(X0) & humble(X0))) [ennf transformation 5]
53. (tall(fred) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~tall(fred)) [nnf transformation 10]
54. (tall(fred) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~tall(fred)) [rectify 53]
55. ? [X1] : happy(X1) => happy(sK3) [choice axiom]
56. (tall(fred) | ! [X0] : ~happy(X0)) & (happy(sK3) | ~tall(fred)) [skolemisation 54,55]
86. ~tall(X0) | humble(X0) [cnf transformation 34]
96. tall(fred) | ~happy(X0) [cnf transformation 56]
128. happy(mary) [cnf transformation 22]
133. ~humble(fred) [cnf transformation 25]
196. 15 <=> ! [X0] : ~happy(X0) [avatar definition]
197. ~happy(X0) <- (15) [avatar component clause 196]
199. 16 <=> tall(fred) [avatar definition]
201. tall(fred) <- (16) [avatar component clause 199]
202. 15 | 16 [avatar split clause 96,199,196]
319. $false <- (15) [resolution 197,128]
320. ~15 [avatar contradiction clause 319]
323. humble(fred) <- (16) [resolution 86,201]
324. $false <- (16) [subsumption resolution 323,133]
325. ~16 [avatar contradiction clause 324]
326. $false [avatar sat refutation 202,320,325]
% SZS output end Proof for 8151862739986318913693264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or curious is not quiet or curious and vice versa.
Everyone who is both tall and happy is rich or not quiet and vice versa.
If fred is not strong then someone is creative or not wise and vice versa.
If john is both not kind and not strong then someone is not calm and vice versa.
If someone is both not wise and quiet then lucy is both not humble and generous.
Everyone who is either not funny or not humble is both not generous and curious.
Everyone who is not funny is either old or calm and vice versa.
If susan is tall then fred is either quiet or not humble and vice versa.
Everyone who is either not rich or calm is both brave and old and vice versa.
Everyone who is not generous is both not creative and funny.
Everyone who is creative is either brave or not generous.
If fred is quiet then someone is kind and vice versa.
If fred is either not generous or generous then lucy is either generous or not humble.
Everyone who is not wise or quiet is both not kind and strong.
Everyone who is both calm and not strong is wise and vice versa.
If paul is not wise then someone is curious.
Someone is either kind or not strong.
Someone is both humble and not creative.
Fred is either not kind or not rich.
Paul is either not humble or not tall.
Someone is calm.
Someone is either not creative or not strong.
Someone is humble. | Susan is not kind. | entailment | (![X]:((strong(X)|curious(X))<=>(~quiet(X)|curious(X))))&
(![X]:((tall(X)&happy(X))<=>(rich(X)|~quiet(X))))&
((~strong(fred))<=>(?[X]:((creative(X)|~wise(X)))))&
(((~kind(john)&~strong(john)))<=>(?[X]:(~calm(X))))&
((?[X]:((~wise(X)&quiet(X))))=>((~humble(lucy)&generous(lucy))))&
(![X]:((~funny(X)<~>~humble(X))=>(~generous(X)&curious(X))))&
(![X]:(~funny(X)<=>(old(X)<~>calm(X))))&
((tall(susan))<=>((quiet(fred)<~>~humble(fred))))&
(![X]:((~rich(X)<~>calm(X))<=>(brave(X)&old(X))))&
(![X]:(~generous(X)=>(~creative(X)&funny(X))))&
(![X]:(creative(X)=>(brave(X)<~>~generous(X))))&
((quiet(fred))<=>(?[X]:(kind(X))))&
(((~generous(fred)<~>generous(fred)))=>((generous(lucy)<~>~humble(lucy))))&
(![X]:((~wise(X)|quiet(X))=>(~kind(X)&strong(X))))&
(![X]:((calm(X)&~strong(X))<=>wise(X)))&
((~wise(paul))=>(?[X]:(curious(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((humble(X)&~creative(X))))&
((~kind(fred)<~>~rich(fred)))&
((~humble(paul)<~>~tall(paul)))&
(?[X]:(calm(X)))&
(?[X]:((~creative(X)<~>~strong(X))))&
(?[X]:(humble(X))) | ~kind(susan) | [
"p2",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8985280872848931945112272
% SZS output start Proof for 8985280872848931945112272
3. ~strong(fred) <=> ? [X0] : (~wise(X0) | creative(X0)) [input p2]
12. quiet(fred) <=> ? [X0] : kind(X0) [input p11]
14. ! [X0] : ((quiet(X0) | ~wise(X0)) => (strong(X0) & ~kind(X0))) [input p13]
15. ! [X0] : ((~strong(X0) & calm(X0)) <=> wise(X0)) [input p14]
24. kind(susan) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~kind(X0)) | (~quiet(X0) & wise(X0))) [ennf transformation 14]
36. (~strong(fred) | ! [X0] : (wise(X0) & ~creative(X0))) & (? [X0] : (~wise(X0) | creative(X0)) | strong(fred)) [nnf transformation 3]
37. (~strong(fred) | ! [X0] : (wise(X0) & ~creative(X0))) & (? [X1] : (~wise(X1) | creative(X1)) | strong(fred)) [rectify 36]
38. ? [X1] : (~wise(X1) | creative(X1)) => (~wise(sK0) | creative(sK0)) [choice axiom]
39. (~strong(fred) | ! [X0] : (wise(X0) & ~creative(X0))) & ((~wise(sK0) | creative(sK0)) | strong(fred)) [skolemisation 37,38]
51. (quiet(fred) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | ~quiet(fred)) [nnf transformation 12]
52. (quiet(fred) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | ~quiet(fred)) [rectify 51]
53. ? [X1] : kind(X1) => kind(sK2) [choice axiom]
54. (quiet(fred) | ! [X0] : ~kind(X0)) & (kind(sK2) | ~quiet(fred)) [skolemisation 52,53]
56. ! [X0] : (((~strong(X0) & calm(X0)) | ~wise(X0)) & (wise(X0) | (strong(X0) | ~calm(X0)))) [nnf transformation 15]
57. ! [X0] : (((~strong(X0) & calm(X0)) | ~wise(X0)) & (wise(X0) | strong(X0) | ~calm(X0))) [flattening 56]
85. ~strong(fred) | wise(X0) [cnf transformation 39]
114. quiet(fred) | ~kind(X0) [cnf transformation 54]
122. ~quiet(X0) | strong(X0) [cnf transformation 30]
125. ~wise(X0) | ~strong(X0) [cnf transformation 57]
139. kind(susan) [cnf transformation 24]
145. 1 <=> ! [X0] : wise(X0) [avatar definition]
146. wise(X0) <- (1) [avatar component clause 145]
148. 2 <=> strong(fred) [avatar definition]
149. strong(fred) <- (2) [avatar component clause 148]
151. 1 | ~2 [avatar split clause 85,148,145]
201. 14 <=> quiet(fred) [avatar definition]
203. quiet(fred) <- (14) [avatar component clause 201]
214. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
215. ~kind(X0) <- (16) [avatar component clause 214]
216. 16 | 14 [avatar split clause 114,201,214]
279. $false <- (16) [resolution 215,139]
280. ~16 [avatar contradiction clause 279]
297. strong(fred) <- (14) [resolution 122,203]
301. 2 | ~14 [avatar split clause 297,201,148]
314. ~strong(X0) <- (1) [resolution 125,146]
321. $false <- (1, 2) [resolution 314,149]
326. ~1 | ~2 [avatar contradiction clause 321]
327. $false [avatar sat refutation 151,216,280,301,326]
% SZS output end Proof for 8985280872848931945112272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is funny and vice versa.
If someone is rich then john is not patient.
If susan is not kind then alice is either not old or not creative.
If lucy is either old or not generous then someone is not patient or tall and vice versa.
Everyone who is either brave or old is not brave or strong and vice versa.
Everyone who is either kind or curious is not wise and vice versa.
Everyone who is either not happy or not kind is both humble and patient.
Everyone who is both not funny and not strong is not generous.
Everyone who is not old or not patient is both not strong and old.
Everyone who is either not brave or not calm is both happy and tall.
If lucy is either not funny or not old then someone is either not humble or generous and vice versa.
If fred is both wise and tall then someone is both strong and funny and vice versa.
Everyone who is either patient or strong is not patient or not strong and vice versa.
Everyone who is not happy is not generous or humble and vice versa.
If someone is old then paul is not strong.
Everyone who is not wise or not kind is both old and not creative and vice versa.
Someone is kind or quiet.
Alice is not funny.
Someone is both strong and creative.
John is happy.
Alice is funny or not strong.
Fred is both not creative and not brave.
Someone is brave. | John is kind. | entailment | (![X]:((~creative(X)&curious(X))<=>funny(X)))&
((?[X]:(rich(X)))=>(~patient(john)))&
((~kind(susan))=>((~old(alice)<~>~creative(alice))))&
(((old(lucy)<~>~generous(lucy)))<=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((brave(X)<~>old(X))<=>(~brave(X)|strong(X))))&
(![X]:((kind(X)<~>curious(X))<=>~wise(X)))&
(![X]:((~happy(X)<~>~kind(X))=>(humble(X)&patient(X))))&
(![X]:((~funny(X)&~strong(X))=>~generous(X)))&
(![X]:((~old(X)|~patient(X))=>(~strong(X)&old(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(happy(X)&tall(X))))&
(((~funny(lucy)<~>~old(lucy)))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(((wise(fred)&tall(fred)))<=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((patient(X)<~>strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:(~happy(X)<=>(~generous(X)|humble(X))))&
((?[X]:(old(X)))=>(~strong(paul)))&
(![X]:((~wise(X)|~kind(X))<=>(old(X)&~creative(X))))&
(?[X]:((kind(X)|quiet(X))))&
(~funny(alice))&
(?[X]:((strong(X)&creative(X))))&
(happy(john))&
((funny(alice)|~strong(alice)))&
((~creative(fred)&~brave(fred)))&
(?[X]:(brave(X))) | kind(john) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6100057786811634768786644
% SZS output start Proof for 6100057786811634768786644
7. ! [X0] : ((~happy(X0) <~> ~kind(X0)) => (patient(X0) & humble(X0))) [input p6]
14. ! [X0] : (~happy(X0) <=> (humble(X0) | ~generous(X0))) [input p13]
20. happy(john) [input p19]
24. ~kind(john) [input hypothesis]
28. ! [X0] : ((patient(X0) & humble(X0)) | (~happy(X0) <=> ~kind(X0))) [ennf transformation 7]
44. ! [X0] : ((patient(X0) & humble(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) [nnf transformation 28]
57. ! [X0] : ((~happy(X0) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | happy(X0))) [nnf transformation 14]
58. ! [X0] : ((~happy(X0) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | happy(X0))) [flattening 57]
87. ~happy(X0) | humble(X0) | kind(X0) [cnf transformation 44]
119. ~humble(X0) | ~happy(X0) [cnf transformation 58]
129. happy(john) [cnf transformation 20]
134. ~kind(john) [cnf transformation 24]
296. humble(john) | kind(john) [resolution 87,129]
298. humble(john) [subsumption resolution 296,134]
299. ~happy(john) [resolution 298,119]
300. $false [subsumption resolution 299,129]
% SZS output end Proof for 6100057786811634768786644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and humble then john is either not creative or not happy.
Everyone who is either happy or not happy is curious.
Everyone who is either not creative or not quiet is not quiet or happy.
If john is brave or not kind then paul is strong or not old and vice versa.
Everyone who is either not creative or generous is either not rich or not old and vice versa.
If alice is humble then someone is either not rich or humble and vice versa.
Everyone who is both not quiet and rich is both patient and not patient.
If someone is not funny or calm then someone is not funny or not calm and vice versa.
If someone is both not humble and not happy then susan is kind or wise.
If someone is both not old and wise then someone is both strong and happy and vice versa.
Everyone who is rich or tall is tall or not generous and vice versa.
If mary is either creative or not brave then someone is old.
Everyone who is not quiet or old is both funny and patient.
If someone is not humble or wise then someone is both kind and humble and vice versa.
If paul is humble then susan is quiet.
Someone is either strong or not quiet.
Someone is both not patient and strong.
Fred is both strong and creative.
Lucy is not patient.
Alice is either not funny or not kind.
Susan is both kind and strong.
Someone is either not quiet or not strong.
John is not humble. | Lucy is not old. | entailment | ((?[X]:((~brave(X)&humble(X))))=>((~creative(john)<~>~happy(john))))&
(![X]:((happy(X)<~>~happy(X))=>curious(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~quiet(X)|happy(X))))&
(((brave(john)|~kind(john)))<=>((strong(paul)|~old(paul))))&
(![X]:((~creative(X)<~>generous(X))<=>(~rich(X)<~>~old(X))))&
((humble(alice))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~quiet(X)&rich(X))=>(patient(X)&~patient(X))))&
((?[X]:((~funny(X)|calm(X))))<=>(?[X]:((~funny(X)|~calm(X)))))&
((?[X]:((~humble(X)&~happy(X))))=>((kind(susan)|wise(susan))))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((rich(X)|tall(X))<=>(tall(X)|~generous(X))))&
(((creative(mary)<~>~brave(mary)))=>(?[X]:(old(X))))&
(![X]:((~quiet(X)|old(X))=>(funny(X)&patient(X))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((kind(X)&humble(X)))))&
((humble(paul))=>(quiet(susan)))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&strong(X))))&
((strong(fred)&creative(fred)))&
(~patient(lucy))&
((~funny(alice)<~>~kind(alice)))&
((kind(susan)&strong(susan)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(~humble(john)) | ~old(lucy) | [
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4139380509967677956573062
% SZS output start Proof for 4139380509967677956573062
13. ! [X0] : ((old(X0) | ~quiet(X0)) => (patient(X0) & funny(X0))) [input p12]
19. ~patient(lucy) [input p18]
24. old(lucy) [input hypothesis]
37. ! [X0] : ((patient(X0) & funny(X0)) | (~old(X0) & quiet(X0))) [ennf transformation 13]
117. ~old(X0) | patient(X0) [cnf transformation 37]
130. ~patient(lucy) [cnf transformation 19]
138. old(lucy) [cnf transformation 24]
364. patient(lucy) [resolution 117,138]
365. $false [subsumption resolution 364,130]
% SZS output end Proof for 4139380509967677956573062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is old or funny then paul is both not tall and not wise.
Everyone who is either not brave or not patient is not kind or rich.
Everyone who is both not happy and not patient is not calm.
Everyone who is both curious and not kind is not kind.
If alice is either old or not curious then susan is either not rich or not kind.
If lucy is not funny or not old then someone is wise or old and vice versa.
If someone is either humble or rich then john is not brave.
If susan is both not rich and not happy then someone is generous or creative and vice versa.
Everyone who is not brave or not tall is either not calm or curious.
Everyone who is both calm and not tall is either not strong or curious and vice versa.
Everyone who is either generous or curious is both brave and wise.
Everyone who is both not tall and generous is either wise or calm and vice versa.
Everyone who is patient is tall.
Everyone who is not generous is not old or brave.
Everyone who is either not wise or not brave is either strong or not kind and vice versa.
If paul is not patient then someone is not old.
Someone is not creative.
Alice is curious or happy.
Fred is either not patient or generous.
Someone is either strong or not wise.
Mary is not rich or not kind.
Susan is both quiet and wise.
John is not strong.
Susan is strong. | John is not tall. | contradiction | (((old(john)|funny(john)))=>((~tall(paul)&~wise(paul))))&
(![X]:((~brave(X)<~>~patient(X))=>(~kind(X)|rich(X))))&
(![X]:((~happy(X)&~patient(X))=>~calm(X)))&
(![X]:((curious(X)&~kind(X))=>~kind(X)))&
(((old(alice)<~>~curious(alice)))=>((~rich(susan)<~>~kind(susan))))&
(((~funny(lucy)|~old(lucy)))<=>(?[X]:((wise(X)|old(X)))))&
((?[X]:((humble(X)<~>rich(X))))=>(~brave(john)))&
(((~rich(susan)&~happy(susan)))<=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((~brave(X)|~tall(X))=>(~calm(X)<~>curious(X))))&
(![X]:((calm(X)&~tall(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((generous(X)<~>curious(X))=>(brave(X)&wise(X))))&
(![X]:((~tall(X)&generous(X))<=>(wise(X)<~>calm(X))))&
(![X]:(patient(X)=>tall(X)))&
(![X]:(~generous(X)=>(~old(X)|brave(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>(strong(X)<~>~kind(X))))&
((~patient(paul))=>(?[X]:(~old(X))))&
(?[X]:(~creative(X)))&
((curious(alice)|happy(alice)))&
((~patient(fred)<~>generous(fred)))&
(?[X]:((strong(X)<~>~wise(X))))&
((~rich(mary)|~kind(mary)))&
((quiet(susan)&wise(susan)))&
(~strong(john))&
(strong(susan)) | ~tall(john) | [
"p8",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6570528781676763526937525
% SZS output start Proof for 6570528781676763526937525
9. ! [X0] : ((~tall(X0) | ~brave(X0)) => (~calm(X0) <~> curious(X0))) [input p8]
10. ! [X0] : ((~tall(X0) & calm(X0)) <=> (~strong(X0) <~> curious(X0))) [input p9]
23. ~strong(john) [input p22]
25. ~tall(john) [input hypothesis]
36. ! [X0] : ((~calm(X0) <~> curious(X0)) | (tall(X0) & brave(X0))) [ennf transformation 9]
55. ! [X0] : (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (tall(X0) & brave(X0))) [nnf transformation 36]
56. ! [X0] : (((~tall(X0) & calm(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (tall(X0) | ~calm(X0)))) [nnf transformation 10]
57. ! [X0] : (((~tall(X0) & calm(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | tall(X0) | ~calm(X0))) [flattening 56]
94. ~calm(X0) | curious(X0) | tall(X0) [cnf transformation 55]
96. ~curious(X0) | calm(X0) | tall(X0) [cnf transformation 55]
98. ~curious(X0) | strong(X0) | tall(X0) | ~calm(X0) [cnf transformation 57]
99. strong(X0) | curious(X0) | calm(X0) [cnf transformation 57]
132. ~strong(john) [cnf transformation 23]
134. ~tall(john) [cnf transformation 25]
236. ~calm(X0) | tall(X0) | strong(X0) [subsumption resolution 98,94]
300. curious(john) | calm(john) [resolution 99,132]
303. 35 <=> calm(john) [avatar definition]
305. calm(john) <- (35) [avatar component clause 303]
307. 36 <=> curious(john) [avatar definition]
309. curious(john) <- (36) [avatar component clause 307]
310. 35 | 36 [avatar split clause 300,307,303]
349. calm(john) | tall(john) <- (36) [resolution 309,96]
437. tall(john) | strong(john) <- (35) [resolution 236,305]
441. strong(john) <- (35) [subsumption resolution 437,134]
442. $false <- (35) [subsumption resolution 441,132]
443. ~35 [avatar contradiction clause 442]
444. calm(john) <- (36) [subsumption resolution 349,134]
445. 35 | ~36 [avatar split clause 444,307,303]
446. $false [avatar sat refutation 310,443,445]
% SZS output end Proof for 6570528781676763526937525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is strong then susan is not calm.
Everyone who is generous is not quiet or creative and vice versa.
If someone is not rich then lucy is either not old or not patient and vice versa.
Everyone who is both creative and not funny is both not quiet and brave.
Everyone who is not rich or patient is not brave.
If susan is brave then alice is both quiet and not wise and vice versa.
If alice is both strong and not quiet then someone is curious or not happy and vice versa.
If lucy is not curious then someone is quiet and vice versa.
If paul is either kind or not rich then mary is not happy or calm.
If paul is both creative and not old then alice is not curious or not kind and vice versa.
Everyone who is both not kind and rich is either not brave or not quiet.
Everyone who is not funny is not rich or creative.
If mary is not strong or not happy then someone is both not rich and rich and vice versa.
If susan is not brave then someone is both tall and not tall.
Everyone who is both not rich and not calm is not calm or not happy.
Everyone who is either not generous or not curious is not calm.
Alice is either not brave or kind.
Someone is not quiet or brave.
Lucy is both not humble and rich.
Someone is either not happy or patient.
Someone is not tall or creative.
Alice is funny or not kind.
Mary is not funny or not rich. | Lucy is happy. | entailment | ((strong(lucy))=>(~calm(susan)))&
(![X]:(generous(X)<=>(~quiet(X)|creative(X))))&
((?[X]:(~rich(X)))<=>((~old(lucy)<~>~patient(lucy))))&
(![X]:((creative(X)&~funny(X))=>(~quiet(X)&brave(X))))&
(![X]:((~rich(X)|patient(X))=>~brave(X)))&
((brave(susan))<=>((quiet(alice)&~wise(alice))))&
(((strong(alice)&~quiet(alice)))<=>(?[X]:((curious(X)|~happy(X)))))&
((~curious(lucy))<=>(?[X]:(quiet(X))))&
(((kind(paul)<~>~rich(paul)))=>((~happy(mary)|calm(mary))))&
(((creative(paul)&~old(paul)))<=>((~curious(alice)|~kind(alice))))&
(![X]:((~kind(X)&rich(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~rich(X)|creative(X))))&
(((~strong(mary)|~happy(mary)))<=>(?[X]:((~rich(X)&rich(X)))))&
((~brave(susan))=>(?[X]:((tall(X)&~tall(X)))))&
(![X]:((~rich(X)&~calm(X))=>(~calm(X)|~happy(X))))&
(![X]:((~generous(X)<~>~curious(X))=>~calm(X)))&
((~brave(alice)<~>kind(alice)))&
(?[X]:((~quiet(X)|brave(X))))&
((~humble(lucy)&rich(lucy)))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((~tall(X)|creative(X))))&
((funny(alice)|~kind(alice)))&
((~funny(mary)|~rich(mary))) | happy(lucy) | [
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6854874399960010356179067
% SZS output start Proof for 6854874399960010356179067
6. brave(susan) <=> (~wise(alice) & quiet(alice)) [input p5]
7. (~quiet(alice) & strong(alice)) <=> ? [X0] : (~happy(X0) | curious(X0)) [input p6]
14. ~brave(susan) => ? [X0] : (~tall(X0) & tall(X0)) [input p13]
24. ~happy(lucy) [input hypothesis]
36. ? [X0] : (~tall(X0) & tall(X0)) | brave(susan) [ennf transformation 14]
46. (brave(susan) | (wise(alice) | ~quiet(alice))) & ((~wise(alice) & quiet(alice)) | ~brave(susan)) [nnf transformation 6]
47. (brave(susan) | wise(alice) | ~quiet(alice)) & ((~wise(alice) & quiet(alice)) | ~brave(susan)) [flattening 46]
48. ((~quiet(alice) & strong(alice)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X0] : (~happy(X0) | curious(X0)) | (quiet(alice) | ~strong(alice))) [nnf transformation 7]
49. ((~quiet(alice) & strong(alice)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X0] : (~happy(X0) | curious(X0)) | quiet(alice) | ~strong(alice)) [flattening 48]
50. ((~quiet(alice) & strong(alice)) | ! [X0] : (happy(X0) & ~curious(X0))) & (? [X1] : (~happy(X1) | curious(X1)) | quiet(alice) | ~strong(alice)) [rectify 49]
51. ? [X1] : (~happy(X1) | curious(X1)) => (~happy(sK1) | curious(sK1)) [choice axiom]
52. ((~quiet(alice) & strong(alice)) | ! [X0] : (happy(X0) & ~curious(X0))) & ((~happy(sK1) | curious(sK1)) | quiet(alice) | ~strong(alice)) [skolemisation 50,51]
66. ? [X0] : (~tall(X0) & tall(X0)) => (~tall(sK4) & tall(sK4)) [choice axiom]
67. (~tall(sK4) & tall(sK4)) | brave(susan) [skolemisation 36,66]
89. quiet(alice) | ~brave(susan) [cnf transformation 47]
96. ~quiet(alice) | happy(X0) [cnf transformation 52]
114. tall(sK4) | brave(susan) [cnf transformation 67]
115. ~tall(sK4) | brave(susan) [cnf transformation 67]
128. ~happy(lucy) [cnf transformation 24]
158. 7 <=> quiet(alice) [avatar definition]
166. 9 <=> brave(susan) [avatar definition]
171. ~9 | 7 [avatar split clause 89,158,166]
173. 10 <=> ! [X0] : happy(X0) [avatar definition]
174. happy(X0) <- (10) [avatar component clause 173]
175. 10 | ~7 [avatar split clause 96,158,173]
261. 28 <=> tall(sK4) [avatar definition]
264. 9 | ~28 [avatar split clause 115,261,166]
265. 9 | 28 [avatar split clause 114,261,166]
316. $false <- (10) [resolution 174,128]
317. ~10 [avatar contradiction clause 316]
318. $false [avatar sat refutation 171,175,264,265,317]
% SZS output end Proof for 6854874399960010356179067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not humble and not calm then someone is both strong and patient.
If someone is both not old and not tall then someone is not humble or patient and vice versa.
If susan is either kind or curious then someone is either not humble or not curious.
Everyone who is kind or not rich is both strong and humble.
If susan is patient then someone is not kind or generous.
If someone is either funny or not happy then someone is either not calm or not humble.
Everyone who is either happy or curious is rich or not kind and vice versa.
Everyone who is both not happy and not rich is humble and vice versa.
Everyone who is both not creative and generous is both rich and creative and vice versa.
If fred is not wise or generous then mary is both not tall and not patient.
Everyone who is either patient or not kind is kind or brave and vice versa.
If someone is calm then alice is not calm or not rich.
If john is strong or patient then someone is both not quiet and brave.
If someone is rich or brave then mary is not wise or patient and vice versa.
Everyone who is calm or not quiet is not humble and vice versa.
If someone is either not creative or patient then someone is not rich or not curious and vice versa.
John is not happy or not funny.
Someone is funny.
Someone is not old or humble.
Susan is happy.
Fred is either quiet or not kind.
Susan is both not kind and not humble.
Someone is both quiet and generous.
Lucy is humble or not patient. | Mary is patient. | neutral | (((~humble(mary)&~calm(mary)))=>(?[X]:((strong(X)&patient(X)))))&
((?[X]:((~old(X)&~tall(X))))<=>(?[X]:((~humble(X)|patient(X)))))&
(((kind(susan)<~>curious(susan)))=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((kind(X)|~rich(X))=>(strong(X)&humble(X))))&
((patient(susan))=>(?[X]:((~kind(X)|generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((~calm(X)<~>~humble(X)))))&
(![X]:((happy(X)<~>curious(X))<=>(rich(X)|~kind(X))))&
(![X]:((~happy(X)&~rich(X))<=>humble(X)))&
(![X]:((~creative(X)&generous(X))<=>(rich(X)&creative(X))))&
(((~wise(fred)|generous(fred)))=>((~tall(mary)&~patient(mary))))&
(![X]:((patient(X)<~>~kind(X))<=>(kind(X)|brave(X))))&
((?[X]:(calm(X)))=>((~calm(alice)|~rich(alice))))&
(((strong(john)|patient(john)))=>(?[X]:((~quiet(X)&brave(X)))))&
((?[X]:((rich(X)|brave(X))))<=>((~wise(mary)|patient(mary))))&
(![X]:((calm(X)|~quiet(X))<=>~humble(X)))&
((?[X]:((~creative(X)<~>patient(X))))<=>(?[X]:((~rich(X)|~curious(X)))))&
((~happy(john)|~funny(john)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|humble(X))))&
(happy(susan))&
((quiet(fred)<~>~kind(fred)))&
((~kind(susan)&~humble(susan)))&
(?[X]:((quiet(X)&generous(X))))&
((humble(lucy)|~patient(lucy))) | patient(mary) | [] | null | 0 |
Everyone who is quiet or not curious is kind.
Everyone who is not old is not rich and vice versa.
If john is creative then paul is either not brave or not patient and vice versa.
Everyone who is both happy and not wise is not brave.
Everyone who is not generous is both curious and not curious and vice versa.
Everyone who is not strong is brave or not tall and vice versa.
Everyone who is either rich or old is not wise and vice versa.
Everyone who is calm or not strong is generous.
Everyone who is not happy is not old or not tall and vice versa.
If someone is both not tall and humble then alice is both not curious and brave and vice versa.
If john is either not wise or funny then paul is quiet or not kind and vice versa.
Everyone who is kind or humble is brave and vice versa.
Everyone who is both not patient and not old is humble and vice versa.
Everyone who is calm is either strong or not rich.
Everyone who is both strong and creative is wise and vice versa.
Everyone who is tall or patient is not curious or calm and vice versa.
Alice is not rich or tall.
Someone is quiet or not brave.
Someone is rich.
Susan is either tall or not creative. | Paul is wise. | entailment | (![X]:((quiet(X)|~curious(X))=>kind(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((creative(john))<=>((~brave(paul)<~>~patient(paul))))&
(![X]:((happy(X)&~wise(X))=>~brave(X)))&
(![X]:(~generous(X)<=>(curious(X)&~curious(X))))&
(![X]:(~strong(X)<=>(brave(X)|~tall(X))))&
(![X]:((rich(X)<~>old(X))<=>~wise(X)))&
(![X]:((calm(X)|~strong(X))=>generous(X)))&
(![X]:(~happy(X)<=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)&humble(X))))<=>((~curious(alice)&brave(alice))))&
(((~wise(john)<~>funny(john)))<=>((quiet(paul)|~kind(paul))))&
(![X]:((kind(X)|humble(X))<=>brave(X)))&
(![X]:((~patient(X)&~old(X))<=>humble(X)))&
(![X]:(calm(X)=>(strong(X)<~>~rich(X))))&
(![X]:((strong(X)&creative(X))<=>wise(X)))&
(![X]:((tall(X)|patient(X))<=>(~curious(X)|calm(X))))&
((~rich(alice)|tall(alice)))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:(rich(X)))&
((tall(susan)<~>~creative(susan))) | wise(paul) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1549341124901559942241436
% SZS output start Proof for 1549341124901559942241436
2. ! [X0] : (~old(X0) <=> ~rich(X0)) [input p1]
7. ! [X0] : ((rich(X0) <~> old(X0)) <=> ~wise(X0)) [input p6]
21. ~wise(paul) [input hypothesis]
33. ! [X0] : ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))) [nnf transformation 2]
37. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | wise(X0)) & (~wise(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [nnf transformation 7]
61. ~rich(X0) | old(X0) [cnf transformation 33]
62. ~old(X0) | rich(X0) [cnf transformation 33]
74. old(X0) | rich(X0) | wise(X0) [cnf transformation 37]
75. ~old(X0) | ~rich(X0) | wise(X0) [cnf transformation 37]
109. ~wise(paul) [cnf transformation 21]
126. ~rich(X0) | wise(X0) [subsumption resolution 75,61]
127. wise(X0) | old(X0) [subsumption resolution 74,126]
213. old(paul) [resolution 127,109]
217. rich(paul) [resolution 213,62]
261. wise(paul) [resolution 217,126]
263. $false [subsumption resolution 261,109]
% SZS output end Proof for 1549341124901559942241436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Mary is quiet. | contradiction | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | quiet(mary) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1624256474328391818227362
% SZS output start Proof for 1624256474328391818227362
5. ! [X0] : ((happy(X0) <~> brave(X0)) <=> (~patient(X0) <~> ~kind(X0))) [input p4]
6. ? [X0] : (wise(X0) <~> tall(X0)) <=> ? [X0] : (tall(X0) & happy(X0)) [input p5]
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p8]
11. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~humble(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((~funny(X0) | ~curious(X0)) <=> (~humble(X0) & ~brave(X0))) [input p11]
13. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (~curious(X0) | ~old(X0))) [input p12]
14. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p13]
22. quiet(mary) [input hypothesis]
24. ? [X0] : (wise(X0) <~> tall(X0)) <=> ? [X1] : (tall(X1) & happy(X1)) [rectify 6]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 9]
41. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 5]
42. (? [X0] : ((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) | ! [X1] : (~tall(X1) | ~happy(X1))) & (? [X1] : (tall(X1) & happy(X1)) | ! [X0] : ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) [nnf transformation 24]
43. (? [X0] : ((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) | ! [X1] : (~tall(X1) | ~happy(X1))) & (? [X2] : (tall(X2) & happy(X2)) | ! [X3] : ((wise(X3) | ~tall(X3)) & (tall(X3) | ~wise(X3)))) [rectify 42]
44. ? [X0] : ((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) => ((~tall(sK1) | ~wise(sK1)) & (tall(sK1) | wise(sK1))) [choice axiom]
45. ? [X2] : (tall(X2) & happy(X2)) => (tall(sK2) & happy(sK2)) [choice axiom]
46. (((~tall(sK1) | ~wise(sK1)) & (tall(sK1) | wise(sK1))) | ! [X1] : (~tall(X1) | ~happy(X1))) & ((tall(sK2) & happy(sK2)) | ! [X3] : ((wise(X3) | ~tall(X3)) & (tall(X3) | ~wise(X3)))) [skolemisation 43,45,44]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
49. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | brave(X0)) & (~brave(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 8]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | (humble(X0) & tall(X0))) & ((~humble(X0) | ~tall(X0)) | (~brave(X0) & happy(X0)))) [nnf transformation 11]
51. ! [X0] : ((brave(X0) | ~happy(X0) | (humble(X0) & tall(X0))) & (~humble(X0) | ~tall(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
52. ! [X0] : (((~funny(X0) | ~curious(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [nnf transformation 12]
53. ! [X0] : ((~funny(X0) | ~curious(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [flattening 52]
54. ! [X0] : (((~funny(X0) & ~patient(X0)) | (curious(X0) & old(X0))) & ((~curious(X0) | ~old(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 13]
55. ! [X0] : (((~funny(X0) & ~patient(X0)) | (curious(X0) & old(X0))) & (~curious(X0) | ~old(X0) | funny(X0) | patient(X0))) [flattening 54]
56. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 14]
57. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 56]
85. ~happy(X0) | patient(X0) | brave(X0) | kind(X0) [cnf transformation 41]
91. happy(sK2) | tall(X3) | ~wise(X3) [cnf transformation 46]
99. ~rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 48]
101. wise(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
102. wise(X0) | creative(X0) | creative(X0) [cnf transformation 48]
105. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 49]
108. ~quiet(X0) | ~brave(X0) [cnf transformation 32]
109. ~kind(X0) | patient(X0) [cnf transformation 32]
110. ~brave(X0) | patient(X0) [cnf transformation 32]
115. ~happy(X0) | brave(X0) | humble(X0) [cnf transformation 51]
118. ~humble(X0) | curious(X0) [cnf transformation 53]
123. ~patient(X0) | curious(X0) [cnf transformation 55]
127. ~patient(X0) | quiet(X0) [cnf transformation 57]
128. ~quiet(X0) | patient(X0) | ~tall(X0) [cnf transformation 57]
139. quiet(mary) [cnf transformation 22]
140. ~rich(X0) | ~creative(X0) [duplicate literal removal 99]
141. ~rich(X0) | creative(X0) [duplicate literal removal 100]
142. wise(X0) | ~creative(X0) [duplicate literal removal 101]
143. creative(X0) | wise(X0) [duplicate literal removal 102]
188. 10 <=> tall(mary) [avatar definition]
190. ~tall(mary) <- (~10) [avatar component clause 188]
233. 20 <=> ! [X3] : (tall(X3) | ~wise(X3)) [avatar definition]
234. tall(X3) | ~wise(X3) <- (20) [avatar component clause 233]
237. 21 <=> happy(sK2) [avatar definition]
239. happy(sK2) <- (21) [avatar component clause 237]
241. 20 | 21 [avatar split clause 91,237,233]
242. wise(X0) [subsumption resolution 142,143]
243. ~rich(X0) [subsumption resolution 140,141]
244. ~curious(X0) | brave(X0) [subsumption resolution 105,243]
266. tall(X3) <- (20) [subsumption resolution 234,242]
268. $false <- (~10, 20) [subsumption resolution 190,266]
269. 10 | ~20 [avatar contradiction clause 268]
273. ~brave(mary) [resolution 108,139]
277. patient(mary) | ~tall(mary) [resolution 128,139]
286. 26 <=> patient(mary) [avatar definition]
288. patient(mary) <- (26) [avatar component clause 286]
289. ~10 | 26 [avatar split clause 277,286,188]
306. 30 <=> curious(mary) [avatar definition]
308. curious(mary) <- (30) [avatar component clause 306]
321. brave(sK2) | humble(sK2) <- (21) [resolution 239,115]
324. 33 <=> humble(sK2) [avatar definition]
326. humble(sK2) <- (33) [avatar component clause 324]
328. 34 <=> brave(sK2) [avatar definition]
330. brave(sK2) <- (34) [avatar component clause 328]
331. 33 | 34 | ~21 [avatar split clause 321,237,328,324]
342. curious(mary) <- (26) [resolution 288,123]
344. 30 | ~26 [avatar split clause 342,286,306]
347. brave(mary) <- (30) [resolution 308,244]
348. $false <- (30) [subsumption resolution 347,273]
349. ~30 [avatar contradiction clause 348]
368. patient(sK2) | brave(sK2) | kind(sK2) <- (21) [resolution 85,239]
369. patient(sK2) | brave(sK2) <- (21) [subsumption resolution 368,109]
370. patient(sK2) <- (21) [subsumption resolution 369,110]
372. curious(sK2) <- (33) [resolution 326,118]
381. quiet(sK2) <- (21) [resolution 370,127]
392. brave(sK2) <- (33) [resolution 372,244]
395. 34 | ~33 [avatar split clause 392,324,328]
408. ~brave(sK2) <- (21) [resolution 381,108]
410. $false <- (21, 34) [subsumption resolution 408,330]
411. ~21 | ~34 [avatar contradiction clause 410]
414. $false [avatar sat refutation 241,269,289,331,344,349,395,411]
% SZS output end Proof for 1624256474328391818227362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not generous is both not rich and quiet. If mary is both curious and not tall then someone is both not funny and generous. If paul is both not kind and wise then fred is either not patient or not kind and vice versa. Everyone who is either not creative or not funny is both kind and patient and vice versa. Everyone who is not patient is either funny or not calm and vice versa. Everyone who is humble is either not creative or patient and vice versa. Everyone who is either curious or kind is not patient. If alice is both not kind and kind then john is either creative or not creative. Everyone who is not funny or calm is not happy or not creative and vice versa. Everyone who is humble is either not creative or happy. Everyone who is both quiet and not creative is not tall or not old and vice versa. If someone is creative or not kind then someone is not tall and vice versa. Everyone who is not tall or generous is not old or funny and vice versa. If fred is not patient then susan is not old. If someone is either creative or happy then susan is not brave or calm and vice versa. Paul is either tall or old. Someone is both creative and calm. Mary is both generous and not brave. Alice is not old or curious. Someone is kind. Someone is not generous. Someone is rich or happy. | Fred is happy. | neutral | (![X]:((~rich(X)|~generous(X))=>(~rich(X)&quiet(X))))&
(((curious(mary)&~tall(mary)))=>(?[X]:((~funny(X)&generous(X)))))&
(((~kind(paul)&wise(paul)))<=>((~patient(fred)<~>~kind(fred))))&
(![X]:((~creative(X)<~>~funny(X))<=>(kind(X)&patient(X))))&
(![X]:(~patient(X)<=>(funny(X)<~>~calm(X))))&
(![X]:(humble(X)<=>(~creative(X)<~>patient(X))))&
(![X]:((curious(X)<~>kind(X))=>~patient(X)))&
(((~kind(alice)&kind(alice)))=>((creative(john)<~>~creative(john))))&
(![X]:((~funny(X)|calm(X))<=>(~happy(X)|~creative(X))))&
(![X]:(humble(X)=>(~creative(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~tall(X)|~old(X))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|generous(X))<=>(~old(X)|funny(X))))&
((~patient(fred))=>(~old(susan)))&
((?[X]:((creative(X)<~>happy(X))))<=>((~brave(susan)|calm(susan))))&
((tall(paul)<~>old(paul)))&
(?[X]:((creative(X)&calm(X))))&
((generous(mary)&~brave(mary)))&
((~old(alice)|curious(alice)))&
(?[X]:(kind(X)))&
(?[X]:(~generous(X)))&
(?[X]:((rich(X)|happy(X)))) | happy(fred) | [] | null | 0 |
Everyone who is not humble or brave is patient or kind.
Everyone who is funny is quiet and vice versa.
Everyone who is both patient and generous is humble or funny.
If someone is both not generous and not calm then mary is both kind and happy and vice versa.
Everyone who is patient or funny is both generous and curious and vice versa.
Everyone who is calm or generous is both not brave and generous.
If someone is either tall or not funny then paul is both not kind and brave.
Everyone who is not calm or not strong is not old and vice versa.
Everyone who is both not humble and not funny is either funny or kind and vice versa.
If paul is both brave and not creative then someone is creative or not calm.
Everyone who is both not tall and funny is both not quiet and calm and vice versa.
Everyone who is wise is kind or brave.
Everyone who is generous or not calm is not rich.
If paul is generous then someone is curious.
If someone is brave then someone is either not kind or brave and vice versa.
If fred is not humble or curious then susan is curious or brave.
Alice is either not generous or curious.
Someone is either not kind or rich.
Lucy is not wise.
Someone is not quiet.
Fred is either not strong or not wise.
Someone is rich or not quiet. | Mary is not calm. | entailment | (![X]:((~humble(X)|brave(X))=>(patient(X)|kind(X))))&
(![X]:(funny(X)<=>quiet(X)))&
(![X]:((patient(X)&generous(X))=>(humble(X)|funny(X))))&
((?[X]:((~generous(X)&~calm(X))))<=>((kind(mary)&happy(mary))))&
(![X]:((patient(X)|funny(X))<=>(generous(X)&curious(X))))&
(![X]:((calm(X)|generous(X))=>(~brave(X)&generous(X))))&
((?[X]:((tall(X)<~>~funny(X))))=>((~kind(paul)&brave(paul))))&
(![X]:((~calm(X)|~strong(X))<=>~old(X)))&
(![X]:((~humble(X)&~funny(X))<=>(funny(X)<~>kind(X))))&
(((brave(paul)&~creative(paul)))=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~tall(X)&funny(X))<=>(~quiet(X)&calm(X))))&
(![X]:(wise(X)=>(kind(X)|brave(X))))&
(![X]:((generous(X)|~calm(X))=>~rich(X)))&
((generous(paul))=>(?[X]:(curious(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)<~>brave(X)))))&
(((~humble(fred)|curious(fred)))=>((curious(susan)|brave(susan))))&
((~generous(alice)<~>curious(alice)))&
(?[X]:((~kind(X)<~>rich(X))))&
(~wise(lucy))&
(?[X]:(~quiet(X)))&
((~strong(fred)<~>~wise(fred)))&
(?[X]:((rich(X)|~quiet(X)))) | ~calm(mary) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6803201804111863819863849
% SZS output start Proof for 6803201804111863819863849
1. ! [X0] : ((brave(X0) | ~humble(X0)) => (kind(X0) | patient(X0))) [input p0]
2. ! [X0] : (funny(X0) <=> quiet(X0)) [input p1]
5. ! [X0] : ((funny(X0) | patient(X0)) <=> (curious(X0) & generous(X0))) [input p4]
6. ! [X0] : ((generous(X0) | calm(X0)) => (generous(X0) & ~brave(X0))) [input p5]
7. ? [X0] : (tall(X0) <~> ~funny(X0)) => (brave(paul) & ~kind(paul)) [input p6]
11. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (calm(X0) & ~quiet(X0))) [input p10]
23. calm(mary) [input hypothesis]
26. ! [X0] : ((kind(X0) | patient(X0)) | (~brave(X0) & humble(X0))) [ennf transformation 1]
27. ! [X0] : (kind(X0) | patient(X0) | (~brave(X0) & humble(X0))) [flattening 26]
30. ! [X0] : ((generous(X0) & ~brave(X0)) | (~generous(X0) & ~calm(X0))) [ennf transformation 6]
31. (brave(paul) & ~kind(paul)) | ! [X0] : (tall(X0) <=> ~funny(X0)) [ennf transformation 7]
38. ! [X0] : ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))) [nnf transformation 2]
44. ! [X0] : (((funny(X0) | patient(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (~funny(X0) & ~patient(X0)))) [nnf transformation 5]
45. ! [X0] : ((funny(X0) | patient(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (~funny(X0) & ~patient(X0)))) [flattening 44]
46. (brave(paul) & ~kind(paul)) | ! [X0] : ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))) [nnf transformation 31]
49. ! [X0] : (((funny(X0) & ~tall(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (~funny(X0) | tall(X0)))) [nnf transformation 11]
50. ! [X0] : (((funny(X0) & ~tall(X0)) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ~funny(X0) | tall(X0))) [flattening 49]
68. ~brave(X0) | patient(X0) | kind(X0) [cnf transformation 27]
69. ~funny(X0) | quiet(X0) [cnf transformation 38]
70. ~quiet(X0) | funny(X0) [cnf transformation 38]
76. ~patient(X0) | generous(X0) [cnf transformation 45]
82. ~generous(X0) | ~brave(X0) [cnf transformation 30]
85. ~kind(paul) | ~funny(X0) | ~tall(X0) [cnf transformation 46]
87. brave(paul) | ~funny(X0) | ~tall(X0) [cnf transformation 46]
95. ~quiet(X0) | ~funny(X0) | tall(X0) [cnf transformation 50]
98. funny(X0) | ~calm(X0) | quiet(X0) [cnf transformation 50]
118. calm(mary) [cnf transformation 23]
148. 7 <=> brave(paul) [avatar definition]
150. brave(paul) <- (7) [avatar component clause 148]
153. 8 <=> ! [X0] : (~funny(X0) | ~tall(X0)) [avatar definition]
154. ~funny(X0) | ~tall(X0) <- (8) [avatar component clause 153]
155. 8 | 7 [avatar split clause 87,148,153]
157. 9 <=> kind(paul) [avatar definition]
159. ~kind(paul) <- (~9) [avatar component clause 157]
161. 8 | ~9 [avatar split clause 85,157,153]
163. ~calm(X0) | quiet(X0) [subsumption resolution 98,69]
164. ~funny(X0) | tall(X0) [subsumption resolution 95,69]
166. 10 <=> generous(paul) [avatar definition]
167. generous(paul) <- (10) [avatar component clause 166]
168. ~generous(paul) <- (~10) [avatar component clause 166]
269. ~funny(X0) <- (8) [subsumption resolution 154,164]
279. ~brave(paul) <- (10) [resolution 167,82]
286. quiet(mary) [resolution 163,118]
293. funny(mary) [resolution 286,70]
294. $false <- (8) [subsumption resolution 293,269]
295. ~8 [avatar contradiction clause 294]
296. ~7 | ~10 [avatar split clause 279,166,148]
304. patient(paul) | kind(paul) <- (7) [resolution 68,150]
314. patient(paul) <- (7, ~9) [subsumption resolution 304,159]
321. generous(paul) <- (7, ~9) [resolution 314,76]
322. $false <- (7, ~9, ~10) [subsumption resolution 321,168]
323. ~7 | 9 | 10 [avatar contradiction clause 322]
324. $false [avatar sat refutation 155,161,295,296,323]
% SZS output end Proof for 6803201804111863819863849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or quiet is either patient or generous.
Everyone who is both brave and humble is funny or happy.
If susan is brave or not brave then susan is either calm or brave and vice versa.
Everyone who is calm is not old and vice versa.
If paul is creative or funny then alice is either curious or not kind.
If someone is both not strong and brave then someone is curious.
If lucy is patient or wise then someone is strong and vice versa.
If lucy is either creative or generous then alice is not calm and vice versa.
Everyone who is either not creative or funny is both not brave and tall and vice versa.
Everyone who is either kind or not generous is both kind and not curious and vice versa.
Everyone who is funny is either not wise or not brave.
If someone is either brave or curious then john is not humble.
Everyone who is patient or generous is both quiet and curious.
If someone is rich or not old then someone is rich or not rich.
Everyone who is not curious or creative is either not calm or not humble.
If paul is not wise then alice is both not generous and funny.
Someone is funny or creative.
Mary is either not generous or not patient.
Someone is not rich or calm.
John is rich or not kind.
Someone is not patient or patient.
Alice is brave.
Paul is not rich or creative. | Lucy is wise. | neutral | (![X]:((~happy(X)|quiet(X))=>(patient(X)<~>generous(X))))&
(![X]:((brave(X)&humble(X))=>(funny(X)|happy(X))))&
(((brave(susan)|~brave(susan)))<=>((calm(susan)<~>brave(susan))))&
(![X]:(calm(X)<=>~old(X)))&
(((creative(paul)|funny(paul)))=>((curious(alice)<~>~kind(alice))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:(curious(X))))&
(((patient(lucy)|wise(lucy)))<=>(?[X]:(strong(X))))&
(((creative(lucy)<~>generous(lucy)))<=>(~calm(alice)))&
(![X]:((~creative(X)<~>funny(X))<=>(~brave(X)&tall(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(kind(X)&~curious(X))))&
(![X]:(funny(X)=>(~wise(X)<~>~brave(X))))&
((?[X]:((brave(X)<~>curious(X))))=>(~humble(john)))&
(![X]:((patient(X)|generous(X))=>(quiet(X)&curious(X))))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((~curious(X)|creative(X))=>(~calm(X)<~>~humble(X))))&
((~wise(paul))=>((~generous(alice)&funny(alice))))&
(?[X]:((funny(X)|creative(X))))&
((~generous(mary)<~>~patient(mary)))&
(?[X]:((~rich(X)|calm(X))))&
((rich(john)|~kind(john)))&
(?[X]:((~patient(X)|patient(X))))&
(brave(alice))&
((~rich(paul)|creative(paul))) | wise(lucy) | [] | null | 0 |
If someone is wise then paul is either not tall or kind.
Everyone who is not tall is not patient or curious.
If susan is either not funny or not curious then fred is either not wise or tall.
If someone is not old or kind then someone is not kind or not curious.
Everyone who is not patient is both quiet and not quiet and vice versa.
Everyone who is either curious or not creative is both not kind and not patient.
If someone is rich then lucy is both strong and not wise and vice versa.
If someone is not humble then someone is not happy.
Everyone who is not tall is both not kind and not old.
If someone is strong then fred is patient and vice versa.
If lucy is humble then someone is not kind or not patient.
Everyone who is wise is either not tall or not happy and vice versa.
Everyone who is both not quiet and not curious is either funny or not brave and vice versa.
If someone is patient then paul is not rich and vice versa.
Everyone who is either not funny or brave is kind or calm and vice versa.
Everyone who is not rich is old and vice versa.
Fred is funny.
Someone is wise.
Mary is both not brave and calm.
Someone is both kind and funny.
Someone is rich.
Someone is not rich or wise.
Paul is both not funny and not happy. | Paul is wise. | entailment | ((?[X]:(wise(X)))=>((~tall(paul)<~>kind(paul))))&
(![X]:(~tall(X)=>(~patient(X)|curious(X))))&
(((~funny(susan)<~>~curious(susan)))=>((~wise(fred)<~>tall(fred))))&
((?[X]:((~old(X)|kind(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:(~patient(X)<=>(quiet(X)&~quiet(X))))&
(![X]:((curious(X)<~>~creative(X))=>(~kind(X)&~patient(X))))&
((?[X]:(rich(X)))<=>((strong(lucy)&~wise(lucy))))&
((?[X]:(~humble(X)))=>(?[X]:(~happy(X))))&
(![X]:(~tall(X)=>(~kind(X)&~old(X))))&
((?[X]:(strong(X)))<=>(patient(fred)))&
((humble(lucy))=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:(wise(X)<=>(~tall(X)<~>~happy(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(funny(X)<~>~brave(X))))&
((?[X]:(patient(X)))<=>(~rich(paul)))&
(![X]:((~funny(X)<~>brave(X))<=>(kind(X)|calm(X))))&
(![X]:(~rich(X)<=>old(X)))&
(funny(fred))&
(?[X]:(wise(X)))&
((~brave(mary)&calm(mary)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|wise(X))))&
((~funny(paul)&~happy(paul))) | wise(paul) | [
"p4",
"p8",
"p11",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 574979090269823636125237
% SZS output start Proof for 574979090269823636125237
5. ! [X0] : (~patient(X0) <=> (~quiet(X0) & quiet(X0))) [input p4]
9. ! [X0] : (~tall(X0) => (~old(X0) & ~kind(X0))) [input p8]
12. ! [X0] : (wise(X0) <=> (~tall(X0) <~> ~happy(X0))) [input p11]
14. ? [X0] : patient(X0) <=> ~rich(paul) [input p13]
16. ! [X0] : (~rich(X0) <=> old(X0)) [input p15]
23. ~happy(paul) & ~funny(paul) [input p22]
24. ~wise(paul) [input hypothesis]
34. ! [X0] : ((~old(X0) & ~kind(X0)) | tall(X0)) [ennf transformation 9]
41. ! [X0] : ((~patient(X0) | (quiet(X0) | ~quiet(X0))) & ((~quiet(X0) & quiet(X0)) | patient(X0))) [nnf transformation 5]
42. ! [X0] : ((~patient(X0) | quiet(X0) | ~quiet(X0)) & ((~quiet(X0) & quiet(X0)) | patient(X0))) [flattening 41]
58. ! [X0] : ((wise(X0) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | ~wise(X0))) [nnf transformation 12]
61. (? [X0] : patient(X0) | rich(paul)) & (~rich(paul) | ! [X0] : ~patient(X0)) [nnf transformation 14]
62. (? [X0] : patient(X0) | rich(paul)) & (~rich(paul) | ! [X1] : ~patient(X1)) [rectify 61]
63. ? [X0] : patient(X0) => patient(sK5) [choice axiom]
64. (patient(sK5) | rich(paul)) & (~rich(paul) | ! [X1] : ~patient(X1)) [skolemisation 62,63]
67. ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))) [nnf transformation 16]
85. quiet(X0) | patient(X0) [cnf transformation 42]
86. ~quiet(X0) | patient(X0) [cnf transformation 42]
97. ~old(X0) | tall(X0) [cnf transformation 34]
104. ~tall(X0) | wise(X0) | happy(X0) [cnf transformation 58]
111. ~rich(paul) | ~patient(X1) [cnf transformation 64]
119. rich(X0) | old(X0) [cnf transformation 67]
130. ~happy(paul) [cnf transformation 23]
131. ~wise(paul) [cnf transformation 24]
136. 2 <=> tall(paul) [avatar definition]
138. tall(paul) <- (2) [avatar component clause 136]
181. patient(X0) [subsumption resolution 85,86]
221. ~rich(paul) [subsumption resolution 111,181]
232. old(paul) [resolution 119,221]
237. tall(paul) [resolution 232,97]
240. 2 [avatar split clause 237,136]
260. wise(paul) | happy(paul) <- (2) [resolution 104,138]
271. happy(paul) <- (2) [subsumption resolution 260,131]
272. $false <- (2) [subsumption resolution 271,130]
273. ~2 [avatar contradiction clause 272]
279. $false [avatar sat refutation 240,273]
% SZS output end Proof for 574979090269823636125237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and wise is either not quiet or wise and vice versa.
If someone is not funny or calm then john is not creative.
Everyone who is both kind and not happy is both not old and quiet and vice versa.
Everyone who is not patient is either tall or not patient and vice versa.
If someone is both brave and not old then paul is both wise and not patient and vice versa.
Everyone who is either strong or not rich is not old or not strong.
If paul is kind then lucy is not patient and vice versa.
If someone is rich then susan is not funny and vice versa.
Everyone who is patient is quiet or not tall.
If lucy is happy or funny then paul is both not happy and not quiet.
If mary is not strong then fred is both not rich and not old and vice versa.
Everyone who is either wise or not tall is not creative.
Everyone who is both humble and not strong is not wise.
If someone is not strong then lucy is strong.
Everyone who is strong is not old or happy.
If fred is happy or not happy then lucy is funny or not strong and vice versa.
Fred is wise or not brave.
Someone is tall or not tall.
Someone is both not curious and patient.
Someone is either not curious or not brave.
Someone is not humble.
Susan is not tall.
Mary is either generous or not patient.
Susan is either not creative or curious. | Paul is quiet. | contradiction | (![X]:((funny(X)&wise(X))<=>(~quiet(X)<~>wise(X))))&
((?[X]:((~funny(X)|calm(X))))=>(~creative(john)))&
(![X]:((kind(X)&~happy(X))<=>(~old(X)&quiet(X))))&
(![X]:(~patient(X)<=>(tall(X)<~>~patient(X))))&
((?[X]:((brave(X)&~old(X))))<=>((wise(paul)&~patient(paul))))&
(![X]:((strong(X)<~>~rich(X))=>(~old(X)|~strong(X))))&
((kind(paul))<=>(~patient(lucy)))&
((?[X]:(rich(X)))<=>(~funny(susan)))&
(![X]:(patient(X)=>(quiet(X)|~tall(X))))&
(((happy(lucy)|funny(lucy)))=>((~happy(paul)&~quiet(paul))))&
((~strong(mary))<=>((~rich(fred)&~old(fred))))&
(![X]:((wise(X)<~>~tall(X))=>~creative(X)))&
(![X]:((humble(X)&~strong(X))=>~wise(X)))&
((?[X]:(~strong(X)))=>(strong(lucy)))&
(![X]:(strong(X)=>(~old(X)|happy(X))))&
(((happy(fred)|~happy(fred)))<=>((funny(lucy)|~strong(lucy))))&
((wise(fred)|~brave(fred)))&
(?[X]:((tall(X)|~tall(X))))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:(~humble(X)))&
(~tall(susan))&
((generous(mary)<~>~patient(mary)))&
((~creative(susan)<~>curious(susan))) | quiet(paul) | [
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6719958266808793374173698
% SZS output start Proof for 6719958266808793374173698
10. (funny(lucy) | happy(lucy)) => (~quiet(paul) & ~happy(paul)) [input p9]
14. ? [X0] : ~strong(X0) => strong(lucy) [input p13]
16. (~happy(fred) | happy(fred)) <=> (~strong(lucy) | funny(lucy)) [input p15]
25. quiet(paul) [input hypothesis]
34. (~quiet(paul) & ~happy(paul)) | (~funny(lucy) & ~happy(lucy)) [ennf transformation 10]
36. strong(lucy) | ! [X0] : strong(X0) [ennf transformation 14]
58. ((~happy(fred) | happy(fred)) | (strong(lucy) & ~funny(lucy))) & ((~strong(lucy) | funny(lucy)) | (happy(fred) & ~happy(fred))) [nnf transformation 16]
59. (~happy(fred) | happy(fred) | (strong(lucy) & ~funny(lucy))) & (~strong(lucy) | funny(lucy) | (happy(fred) & ~happy(fred))) [flattening 58]
98. ~quiet(paul) | ~funny(lucy) [cnf transformation 34]
104. strong(lucy) | strong(X0) [cnf transformation 36]
106. ~strong(lucy) | funny(lucy) | ~happy(fred) [cnf transformation 59]
107. ~strong(lucy) | funny(lucy) | happy(fred) [cnf transformation 59]
121. quiet(paul) [cnf transformation 25]
184. 13 <=> funny(lucy) [avatar definition]
188. 14 <=> quiet(paul) [avatar definition]
191. ~13 | ~14 [avatar split clause 98,188,184]
220. 20 <=> ! [X0] : strong(X0) [avatar definition]
221. strong(X0) <- (20) [avatar component clause 220]
223. 21 <=> strong(lucy) [avatar definition]
224. ~strong(lucy) <- (~21) [avatar component clause 223]
226. 20 | 21 [avatar split clause 104,223,220]
228. 22 <=> happy(fred) [avatar definition]
231. 22 | 13 | ~21 [avatar split clause 107,223,184,228]
232. ~22 | 13 | ~21 [avatar split clause 106,223,184,228]
272. 14 [avatar split clause 121,188]
275. $false <- (20, ~21) [resolution 224,221]
276. ~20 | 21 [avatar contradiction clause 275]
277. $false [avatar sat refutation 191,226,231,232,272,276]
% SZS output end Proof for 6719958266808793374173698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not humble then someone is either not strong or not quiet and vice versa.
If someone is not generous then alice is both not patient and old.
Everyone who is calm or not happy is patient.
Everyone who is wise or not tall is both wise and not happy and vice versa.
Everyone who is wise is both happy and generous.
Everyone who is either quiet or not generous is patient or curious.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Everyone who is both generous and humble is either not wise or wise and vice versa.
If someone is both not brave and generous then fred is either not wise or not quiet and vice versa.
Everyone who is not curious or strong is both patient and not curious and vice versa.
Everyone who is not curious or not calm is both not quiet and not brave and vice versa.
If alice is not tall then lucy is not rich or not tall.
If someone is brave or not humble then john is patient.
Everyone who is not kind is not tall or happy.
Mary is both rich and not quiet.
Mary is either not rich or not happy.
Someone is not wise.
Lucy is rich or not strong. | Lucy is strong. | contradiction | ((?[X]:((happy(X)&~humble(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((?[X]:(~generous(X)))=>((~patient(alice)&old(alice))))&
(![X]:((calm(X)|~happy(X))=>patient(X)))&
(![X]:((wise(X)|~tall(X))<=>(wise(X)&~happy(X))))&
(![X]:(wise(X)=>(happy(X)&generous(X))))&
(![X]:((quiet(X)<~>~generous(X))=>(patient(X)|curious(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((generous(X)&humble(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((~curious(X)|strong(X))<=>(patient(X)&~curious(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&~brave(X))))&
((~tall(alice))=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((brave(X)|~humble(X))))=>(patient(john)))&
(![X]:(~kind(X)=>(~tall(X)|happy(X))))&
((rich(mary)&~quiet(mary)))&
((~rich(mary)<~>~happy(mary)))&
(?[X]:(~wise(X)))&
((rich(lucy)|~strong(lucy))) | strong(lucy) | [
"p0",
"p3",
"p4",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6353621153976408022223889
% SZS output start Proof for 6353621153976408022223889
1. ? [X0] : (~humble(X0) & happy(X0)) <=> ? [X0] : (~strong(X0) <~> ~quiet(X0)) [input p0]
4. ! [X0] : ((~tall(X0) | wise(X0)) <=> (~happy(X0) & wise(X0))) [input p3]
5. ! [X0] : (wise(X0) => (generous(X0) & happy(X0))) [input p4]
10. ! [X0] : ((humble(X0) & generous(X0)) <=> (~wise(X0) <~> wise(X0))) [input p9]
11. ? [X0] : (generous(X0) & ~brave(X0)) <=> (~wise(fred) <~> ~quiet(fred)) [input p10]
12. ! [X0] : ((strong(X0) | ~curious(X0)) <=> (~curious(X0) & patient(X0))) [input p11]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p12]
21. strong(lucy) [input hypothesis]
22. ? [X0] : (~humble(X0) & happy(X0)) <=> ? [X1] : (~strong(X1) <~> ~quiet(X1)) [rectify 1]
28. ! [X0] : ((generous(X0) & happy(X0)) | ~wise(X0)) [ennf transformation 5]
37. (? [X0] : (~humble(X0) & happy(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X1] : ((quiet(X1) | strong(X1)) & (~quiet(X1) | ~strong(X1))) | ! [X0] : (humble(X0) | ~happy(X0))) [nnf transformation 22]
38. (? [X0] : (~humble(X0) & happy(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) | ! [X3] : (humble(X3) | ~happy(X3))) [rectify 37]
39. ? [X0] : (~humble(X0) & happy(X0)) => (~humble(sK0) & happy(sK0)) [choice axiom]
40. ? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) => ((quiet(sK1) | strong(sK1)) & (~quiet(sK1) | ~strong(sK1))) [choice axiom]
41. ((~humble(sK0) & happy(sK0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (((quiet(sK1) | strong(sK1)) & (~quiet(sK1) | ~strong(sK1))) | ! [X3] : (humble(X3) | ~happy(X3))) [skolemisation 38,40,39]
42. ! [X0] : (((~tall(X0) | wise(X0)) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | (tall(X0) & ~wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((~tall(X0) | wise(X0) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | (tall(X0) & ~wise(X0)))) [flattening 42]
48. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 10]
49. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~humble(X0) | ~generous(X0))) [flattening 48]
50. (? [X0] : (generous(X0) & ~brave(X0)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X0] : (~generous(X0) | brave(X0))) [nnf transformation 11]
51. (? [X0] : (generous(X0) & ~brave(X0)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X1] : (~generous(X1) | brave(X1))) [rectify 50]
52. ? [X0] : (generous(X0) & ~brave(X0)) => (generous(sK2) & ~brave(sK2)) [choice axiom]
53. ((generous(sK2) & ~brave(sK2)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X1] : (~generous(X1) | brave(X1))) [skolemisation 51,52]
54. ! [X0] : (((strong(X0) | ~curious(X0)) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | (~strong(X0) & curious(X0)))) [nnf transformation 12]
55. ! [X0] : ((strong(X0) | ~curious(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | (~strong(X0) & curious(X0)))) [flattening 54]
56. ! [X0] : (((~calm(X0) | ~curious(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 13]
57. ! [X0] : ((~calm(X0) | ~curious(X0) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [flattening 56]
65. ~humble(sK0) | ~quiet(X1) | strong(X1) [cnf transformation 41]
72. ~wise(X0) | ~happy(X0) [cnf transformation 43]
75. happy(X0) | ~wise(X0) [cnf transformation 28]
87. generous(X0) | wise(X0) | wise(X0) [cnf transformation 49]
89. humble(X0) | wise(X0) | wise(X0) [cnf transformation 49]
92. quiet(fred) | wise(fred) | ~generous(X1) | brave(X1) [cnf transformation 53]
100. ~curious(X0) | ~strong(X0) [cnf transformation 55]
102. ~quiet(X0) | curious(X0) [cnf transformation 57]
104. ~brave(X0) | curious(X0) [cnf transformation 57]
116. strong(lucy) [cnf transformation 21]
117. generous(X0) | wise(X0) [duplicate literal removal 87]
119. humble(X0) | wise(X0) [duplicate literal removal 89]
125. 2 <=> humble(sK0) [avatar definition]
127. ~humble(sK0) <- (~2) [avatar component clause 125]
130. 3 <=> ! [X1] : (~quiet(X1) | strong(X1)) [avatar definition]
131. ~quiet(X1) | strong(X1) <- (3) [avatar component clause 130]
132. 3 | ~2 [avatar split clause 65,125,130]
153. 8 <=> ! [X0] : generous(X0) [avatar definition]
154. generous(X0) <- (8) [avatar component clause 153]
160. ~wise(X0) [subsumption resolution 75,72]
161. humble(X0) [subsumption resolution 119,160]
162. generous(X0) [subsumption resolution 117,160]
163. 8 [avatar split clause 162,153]
166. 10 <=> quiet(fred) [avatar definition]
167. quiet(fred) <- (10) [avatar component clause 166]
180. quiet(fred) | ~generous(X1) | brave(X1) [subsumption resolution 92,160]
182. 13 <=> ! [X1] : (~generous(X1) | brave(X1)) [avatar definition]
183. ~generous(X1) | brave(X1) <- (13) [avatar component clause 182]
184. 13 | 10 [avatar split clause 180,166,182]
208. 19 <=> strong(lucy) [avatar definition]
209. strong(lucy) <- (19) [avatar component clause 208]
212. 19 [avatar split clause 116,208]
213. $false <- (~2) [subsumption resolution 127,161]
214. 2 [avatar contradiction clause 213]
221. curious(fred) <- (10) [resolution 102,167]
223. ~strong(fred) <- (10) [resolution 221,100]
228. strong(fred) <- (3, 10) [resolution 131,167]
230. $false <- (3, 10) [subsumption resolution 228,223]
231. ~3 | ~10 [avatar contradiction clause 230]
232. brave(X1) <- (8, 13) [subsumption resolution 183,154]
238. curious(X1) <- (8, 13) [resolution 232,104]
246. ~strong(X0) <- (8, 13) [resolution 238,100]
271. $false <- (8, 13, 19) [resolution 246,209]
272. ~8 | ~13 | ~19 [avatar contradiction clause 271]
273. $false [avatar sat refutation 132,163,184,212,214,231,272]
% SZS output end Proof for 6353621153976408022223889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or creative then lucy is curious and vice versa.
If someone is kind or not happy then fred is not creative and vice versa.
Everyone who is not calm or strong is not humble or not strong.
If someone is patient or not rich then someone is either not creative or not kind and vice versa.
Everyone who is either happy or old is rich or happy and vice versa.
If someone is not wise then someone is either not wise or old.
Everyone who is happy is both quiet and not generous and vice versa.
Everyone who is patient is not wise or humble and vice versa.
Everyone who is patient or not kind is old.
If someone is happy then someone is not patient and vice versa.
Everyone who is both not old and not humble is either not curious or not brave and vice versa.
Everyone who is either calm or not wise is strong or kind.
Everyone who is not kind or not calm is either not generous or not calm and vice versa.
If lucy is both not wise and tall then someone is not tall or generous and vice versa.
If paul is not wise or not strong then someone is either not creative or brave.
If susan is not funny or strong then alice is not kind or not generous.
Someone is either calm or brave.
Paul is not old or wise.
Someone is either brave or not rich.
Susan is both quiet and not kind.
Lucy is both not happy and not creative.
Someone is both not curious and old.
Someone is both quiet and kind.
Paul is either tall or old. | Alice is rich. | entailment | ((?[X]:((~creative(X)|creative(X))))<=>(curious(lucy)))&
((?[X]:((kind(X)|~happy(X))))<=>(~creative(fred)))&
(![X]:((~calm(X)|strong(X))=>(~humble(X)|~strong(X))))&
((?[X]:((patient(X)|~rich(X))))<=>(?[X]:((~creative(X)<~>~kind(X)))))&
(![X]:((happy(X)<~>old(X))<=>(rich(X)|happy(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(happy(X)<=>(quiet(X)&~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)|humble(X))))&
(![X]:((patient(X)|~kind(X))=>old(X)))&
((?[X]:(happy(X)))<=>(?[X]:(~patient(X))))&
(![X]:((~old(X)&~humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((calm(X)<~>~wise(X))=>(strong(X)|kind(X))))&
(![X]:((~kind(X)|~calm(X))<=>(~generous(X)<~>~calm(X))))&
(((~wise(lucy)&tall(lucy)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((~wise(paul)|~strong(paul)))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((~funny(susan)|strong(susan)))=>((~kind(alice)|~generous(alice))))&
(?[X]:((calm(X)<~>brave(X))))&
((~old(paul)|wise(paul)))&
(?[X]:((brave(X)<~>~rich(X))))&
((quiet(susan)&~kind(susan)))&
((~happy(lucy)&~creative(lucy)))&
(?[X]:((~curious(X)&old(X))))&
(?[X]:((quiet(X)&kind(X))))&
((tall(paul)<~>old(paul))) | rich(alice) | [
"p4",
"p6",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 406555966714906665701196
% SZS output start Proof for 406555966714906665701196
5. ! [X0] : ((happy(X0) <~> old(X0)) <=> (happy(X0) | rich(X0))) [input p4]
7. ! [X0] : (happy(X0) <=> (~generous(X0) & quiet(X0))) [input p6]
9. ! [X0] : ((~kind(X0) | patient(X0)) => old(X0)) [input p8]
10. ? [X0] : happy(X0) <=> ? [X0] : ~patient(X0) [input p9]
13. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p12]
25. ~rich(alice) [input hypothesis]
28. ? [X0] : happy(X0) <=> ? [X1] : ~patient(X1) [rectify 10]
33. ! [X0] : (old(X0) | (kind(X0) & ~patient(X0))) [ennf transformation 9]
52. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 5]
53. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 52]
58. ! [X0] : ((happy(X0) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 7]
59. ! [X0] : ((happy(X0) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | ~happy(X0))) [flattening 58]
62. (? [X0] : happy(X0) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ~happy(X0)) [nnf transformation 28]
63. (? [X0] : happy(X0) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ~happy(X3)) [rectify 62]
64. ? [X0] : happy(X0) => happy(sK5) [choice axiom]
65. ? [X2] : ~patient(X2) => ~patient(sK6) [choice axiom]
66. (happy(sK5) | ! [X1] : patient(X1)) & (~patient(sK6) | ! [X3] : ~happy(X3)) [skolemisation 63,65,64]
70. ! [X0] : (((~calm(X0) | ~kind(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (calm(X0) & kind(X0)))) [nnf transformation 13]
71. ! [X0] : ((~calm(X0) | ~kind(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (calm(X0) & kind(X0)))) [flattening 70]
106. happy(X0) | rich(X0) | happy(X0) | ~old(X0) [cnf transformation 53]
110. ~old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 53]
114. ~generous(X0) | ~happy(X0) [cnf transformation 59]
119. ~patient(X0) | old(X0) [cnf transformation 33]
120. old(X0) | kind(X0) [cnf transformation 33]
122. happy(sK5) | patient(X1) [cnf transformation 66]
134. calm(X0) | generous(X0) | calm(X0) [cnf transformation 71]
135. ~calm(X0) | ~kind(X0) | ~calm(X0) | generous(X0) [cnf transformation 71]
162. ~rich(alice) [cnf transformation 25]
163. generous(X0) | calm(X0) [duplicate literal removal 134]
164. ~calm(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 135]
165. happy(X0) | rich(X0) | ~old(X0) [duplicate literal removal 106]
166. ~old(X0) | ~happy(X0) [duplicate literal removal 110]
218. 13 <=> ! [X3] : rich(X3) [avatar definition]
219. rich(X3) <- (13) [avatar component clause 218]
235. ~old(X0) | rich(X0) [subsumption resolution 165,166]
250. 20 <=> ! [X1] : patient(X1) [avatar definition]
251. patient(X1) <- (20) [avatar component clause 250]
253. 21 <=> happy(sK5) [avatar definition]
255. happy(sK5) <- (21) [avatar component clause 253]
256. 20 | 21 [avatar split clause 122,253,250]
367. ~happy(X0) | calm(X0) [resolution 163,114]
368. ~happy(X0) | kind(X0) [resolution 166,120]
569. calm(sK5) <- (21) [resolution 367,255]
572. kind(sK5) <- (21) [resolution 368,255]
595. ~kind(sK5) | generous(sK5) <- (21) [resolution 569,164]
596. generous(sK5) <- (21) [subsumption resolution 595,572]
615. ~happy(sK5) <- (21) [resolution 596,114]
616. $false <- (21) [subsumption resolution 615,255]
617. ~21 [avatar contradiction clause 616]
619. old(X1) <- (20) [resolution 251,119]
650. rich(X1) <- (20) [resolution 619,235]
658. 13 | ~20 [avatar split clause 650,250,218]
665. $false <- (13) [resolution 219,162]
668. ~13 [avatar contradiction clause 665]
669. $false [avatar sat refutation 256,617,658,668]
% SZS output end Proof for 406555966714906665701196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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