premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is wise then someone is brave.
Everyone who is both not brave and not kind is generous or strong and vice versa.
If mary is not generous then someone is either generous or not happy.
If someone is both not tall and old then susan is both happy and creative.
If lucy is brave then someone is both not creative and strong.
Everyone who is patient or strong is either not generous or tall.
If lucy is not strong or not patient then someone is tall or generous and vice versa.
If fred is both quiet and rich then someone is quiet.
Everyone who is both not happy and not strong is brave or humble.
Everyone who is either generous or wise is generous and vice versa.
Everyone who is not kind is happy and vice versa.
If john is not funny or funny then someone is not humble or happy.
If susan is quiet or not tall then someone is not funny or generous.
Everyone who is either not happy or humble is either strong or creative and vice versa.
Everyone who is both tall and generous is not wise or not funny and vice versa.
Everyone who is both not curious and not funny is not happy or not curious.
Susan is strong or curious.
Someone is both not old and not brave.
John is either not quiet or not humble.
Alice is not strong.
John is creative.
John is not creative or not patient.
Fred is not creative. | Fred is not kind. | entailment | ((?[X]:(wise(X)))=>(?[X]:(brave(X))))&
(![X]:((~brave(X)&~kind(X))<=>(generous(X)|strong(X))))&
((~generous(mary))=>(?[X]:((generous(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&old(X))))=>((happy(susan)&creative(susan))))&
((brave(lucy))=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((patient(X)|strong(X))=>(~generous(X)<~>tall(X))))&
(((~strong(lucy)|~patient(lucy)))<=>(?[X]:((tall(X)|generous(X)))))&
(((quiet(fred)&rich(fred)))=>(?[X]:(quiet(X))))&
(![X]:((~happy(X)&~strong(X))=>(brave(X)|humble(X))))&
(![X]:((generous(X)<~>wise(X))<=>generous(X)))&
(![X]:(~kind(X)<=>happy(X)))&
(((~funny(john)|funny(john)))=>(?[X]:((~humble(X)|happy(X)))))&
(((quiet(susan)|~tall(susan)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~happy(X)<~>humble(X))<=>(strong(X)<~>creative(X))))&
(![X]:((tall(X)&generous(X))<=>(~wise(X)|~funny(X))))&
(![X]:((~curious(X)&~funny(X))=>(~happy(X)|~curious(X))))&
((strong(susan)|curious(susan)))&
(?[X]:((~old(X)&~brave(X))))&
((~quiet(john)<~>~humble(john)))&
(~strong(alice))&
(creative(john))&
((~creative(john)|~patient(john)))&
(~creative(fred)) | ~kind(fred) | [
"p1",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 6741406639750362075147431
% SZS output start Proof for 6741406639750362075147431
2. ! [X0] : ((~kind(X0) & ~brave(X0)) <=> (strong(X0) | generous(X0))) [input p1]
10. ! [X0] : ((generous(X0) <~> wise(X0)) <=> generous(X0)) [input p9]
15. ! [X0] : ((generous(X0) & tall(X0)) <=> (~funny(X0) | ~wise(X0))) [input p14]
24. kind(fred) [input hypothesis]
42. ! [X0] : (((~kind(X0) & ~brave(X0)) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | (kind(X0) | brave(X0)))) [nnf transformation 2]
43. ! [X0] : (((~kind(X0) & ~brave(X0)) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | kind(X0) | brave(X0))) [flattening 42]
55. ! [X0] : ((((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | ~generous(X0)) & (generous(X0) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0))))) [nnf transformation 10]
62. ! [X0] : (((generous(X0) & tall(X0)) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((generous(X0) & tall(X0)) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | ~generous(X0) | ~tall(X0))) [flattening 62]
71. ~generous(X0) | ~kind(X0) [cnf transformation 43]
87. generous(X0) | generous(X0) | ~wise(X0) [cnf transformation 55]
89. ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 55]
107. generous(X0) | wise(X0) [cnf transformation 63]
118. kind(fred) [cnf transformation 24]
119. generous(X0) | ~wise(X0) [duplicate literal removal 87]
120. ~generous(X0) | ~wise(X0) [duplicate literal removal 89]
122. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
123. ~wise(X1) <- (1) [avatar component clause 122]
183. ~wise(X0) [subsumption resolution 119,120]
184. 1 [avatar split clause 183,122]
247. wise(X0) | ~kind(X0) [resolution 107,71]
250. ~kind(X0) <- (1) [subsumption resolution 247,123]
264. $false <- (1) [resolution 250,118]
265. ~1 [avatar contradiction clause 264]
266. $false [avatar sat refutation 184,265]
% SZS output end Proof for 6741406639750362075147431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or not strong then alice is either curious or not rich and vice versa. Everyone who is either rich or patient is not calm or old. Everyone who is not old is both patient and not rich and vice versa. If alice is not quiet then susan is not creative. If someone is old or not quiet then fred is brave and vice versa. Everyone who is both not old and brave is tall and vice versa. Everyone who is both not rich and happy is both not humble and kind and vice versa. Everyone who is not patient or not brave is both not creative and not wise. Everyone who is either tall or wise is not tall or quiet and vice versa. If john is either calm or not rich then someone is both not tall and not patient and vice versa. Everyone who is not patient is both generous and quiet. Everyone who is happy or strong is either tall or not wise and vice versa. Everyone who is both not kind and not tall is both patient and not brave. Everyone who is creative is either not kind or not curious. Everyone who is strong or not curious is both wise and not tall. If someone is both creative and not strong then someone is either old or not humble. Lucy is both not old and happy. Alice is not funny. Someone is both wise and rich. Alice is not quiet. Someone is either generous or quiet. Mary is either not curious or not humble. Someone is either creative or not old. Someone is generous. | Alice is kind. | entailment | (((~generous(susan)|~strong(susan)))<=>((curious(alice)<~>~rich(alice))))&
(![X]:((rich(X)<~>patient(X))=>(~calm(X)|old(X))))&
(![X]:(~old(X)<=>(patient(X)&~rich(X))))&
((~quiet(alice))=>(~creative(susan)))&
((?[X]:((old(X)|~quiet(X))))<=>(brave(fred)))&
(![X]:((~old(X)&brave(X))<=>tall(X)))&
(![X]:((~rich(X)&happy(X))<=>(~humble(X)&kind(X))))&
(![X]:((~patient(X)|~brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~tall(X)|quiet(X))))&
(((calm(john)<~>~rich(john)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:(~patient(X)=>(generous(X)&quiet(X))))&
(![X]:((happy(X)|strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~kind(X)&~tall(X))=>(patient(X)&~brave(X))))&
(![X]:(creative(X)=>(~kind(X)<~>~curious(X))))&
(![X]:((strong(X)|~curious(X))=>(wise(X)&~tall(X))))&
((?[X]:((creative(X)&~strong(X))))=>(?[X]:((old(X)<~>~humble(X)))))&
((~old(lucy)&happy(lucy)))&
(~funny(alice))&
(?[X]:((wise(X)&rich(X))))&
(~quiet(alice))&
(?[X]:((generous(X)<~>quiet(X))))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:(generous(X))) | kind(alice) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8595462959206710789564269
% SZS output start Proof for 8595462959206710789564269
1. (~strong(susan) | ~generous(susan)) <=> (curious(alice) <~> ~rich(alice)) [input p0]
3. ! [X0] : (~old(X0) <=> (~rich(X0) & patient(X0))) [input p2]
6. ! [X0] : ((brave(X0) & ~old(X0)) <=> tall(X0)) [input p5]
8. ! [X0] : ((~brave(X0) | ~patient(X0)) => (~wise(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((tall(X0) <~> wise(X0)) <=> (quiet(X0) | ~tall(X0))) [input p8]
12. ! [X0] : ((strong(X0) | happy(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : ((~tall(X0) & ~kind(X0)) => (~brave(X0) & patient(X0))) [input p12]
15. ! [X0] : ((~curious(X0) | strong(X0)) => (~tall(X0) & wise(X0))) [input p14]
25. ~kind(alice) [input hypothesis]
31. ! [X0] : ((~wise(X0) & ~creative(X0)) | (brave(X0) & patient(X0))) [ennf transformation 8]
33. ! [X0] : ((~brave(X0) & patient(X0)) | (tall(X0) | kind(X0))) [ennf transformation 13]
34. ! [X0] : ((~brave(X0) & patient(X0)) | tall(X0) | kind(X0)) [flattening 33]
36. ! [X0] : ((~tall(X0) & wise(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 15]
38. ((~strong(susan) | ~generous(susan)) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [nnf transformation 1]
39. (~strong(susan) | ~generous(susan) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [flattening 38]
41. ! [X0] : ((~old(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | old(X0))) [flattening 41]
47. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | (~brave(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | ~brave(X0) | old(X0))) [flattening 47]
51. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [nnf transformation 9]
52. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [flattening 51]
57. ! [X0] : (((strong(X0) | happy(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((strong(X0) | happy(X0) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [flattening 57]
78. rich(alice) | ~curious(alice) | strong(susan) [cnf transformation 39]
84. ~rich(X0) | old(X0) [cnf transformation 42]
91. ~tall(X0) | ~old(X0) [cnf transformation 48]
92. ~tall(X0) | brave(X0) [cnf transformation 48]
100. ~wise(X0) | brave(X0) [cnf transformation 31]
103. wise(X0) | tall(X0) | tall(X0) [cnf transformation 52]
116. ~wise(X0) | tall(X0) | ~strong(X0) [cnf transformation 58]
118. wise(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 58]
122. ~brave(X0) | tall(X0) | kind(X0) [cnf transformation 34]
127. ~tall(X0) | ~strong(X0) [cnf transformation 36]
128. ~tall(X0) | curious(X0) [cnf transformation 36]
143. ~kind(alice) [cnf transformation 25]
145. wise(X0) | tall(X0) [duplicate literal removal 103]
147. 1 <=> rich(alice) [avatar definition]
149. rich(alice) <- (1) [avatar component clause 147]
151. 2 <=> curious(alice) [avatar definition]
159. 4 <=> strong(susan) [avatar definition]
160. strong(susan) <- (4) [avatar component clause 159]
164. 4 | ~2 | 1 [avatar split clause 78,147,151,159]
224. ~strong(X0) | wise(X0) [subsumption resolution 118,145]
226. ~strong(X0) | tall(X0) [subsumption resolution 116,224]
228. ~strong(X0) [subsumption resolution 127,226]
287. tall(X0) | brave(X0) [resolution 145,100]
289. brave(X0) [subsumption resolution 287,92]
370. kind(X0) | tall(X0) [resolution 122,289]
411. tall(alice) [resolution 370,143]
417. curious(alice) [resolution 411,128]
419. ~old(alice) [resolution 411,91]
423. 2 [avatar split clause 417,151]
424. old(alice) <- (1) [resolution 149,84]
425. $false <- (1) [subsumption resolution 424,419]
426. ~1 [avatar contradiction clause 425]
427. $false <- (4) [subsumption resolution 160,228]
428. ~4 [avatar contradiction clause 427]
429. $false [avatar sat refutation 164,423,426,428]
% SZS output end Proof for 8595462959206710789564269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or creative then john is both not humble and patient and vice versa. Everyone who is strong is both humble and generous. If someone is both patient and quiet then someone is not funny. If someone is both not kind and creative then paul is either rich or not creative and vice versa. If someone is either not old or not kind then someone is strong or generous. If john is either not patient or not funny then someone is either kind or patient. If someone is both tall and not curious then susan is not old or strong and vice versa. Everyone who is not brave or not quiet is either not humble or funny. Everyone who is happy or not creative is either curious or generous and vice versa. Everyone who is either tall or not tall is brave and vice versa. If someone is strong then someone is either not creative or old and vice versa. If susan is both not calm and not wise then lucy is not brave and vice versa. Everyone who is not funny is not brave. Everyone who is calm is curious. Everyone who is either not patient or patient is strong or quiet. If someone is either not tall or not happy then someone is brave and vice versa. Someone is old or not strong. Someone is either humble or happy. Someone is not tall. Someone is either not happy or not patient. Mary is either not kind or kind. Susan is not funny or patient. Fred is curious or not funny. | Susan is not calm. | entailment | ((?[X]:((~brave(X)|creative(X))))<=>((~humble(john)&patient(john))))&
(![X]:(strong(X)=>(humble(X)&generous(X))))&
((?[X]:((patient(X)&quiet(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~kind(X)&creative(X))))<=>((rich(paul)<~>~creative(paul))))&
((?[X]:((~old(X)<~>~kind(X))))=>(?[X]:((strong(X)|generous(X)))))&
(((~patient(john)<~>~funny(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
((?[X]:((tall(X)&~curious(X))))<=>((~old(susan)|strong(susan))))&
(![X]:((~brave(X)|~quiet(X))=>(~humble(X)<~>funny(X))))&
(![X]:((happy(X)|~creative(X))<=>(curious(X)<~>generous(X))))&
(![X]:((tall(X)<~>~tall(X))<=>brave(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(((~calm(susan)&~wise(susan)))<=>(~brave(lucy)))&
(![X]:(~funny(X)=>~brave(X)))&
(![X]:(calm(X)=>curious(X)))&
(![X]:((~patient(X)<~>patient(X))=>(strong(X)|quiet(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:(brave(X))))&
(?[X]:((old(X)|~strong(X))))&
(?[X]:((humble(X)<~>happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~happy(X)<~>~patient(X))))&
((~kind(mary)<~>kind(mary)))&
((~funny(susan)|patient(susan)))&
((curious(fred)|~funny(fred))) | ~calm(susan) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p12",
"p13",
"p14",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4285651866494778743753021
% SZS output start Proof for 4285651866494778743753021
1. ? [X0] : (creative(X0) | ~brave(X0)) <=> (patient(john) & ~humble(john)) [input p0]
2. ! [X0] : (strong(X0) => (generous(X0) & humble(X0))) [input p1]
3. ? [X0] : (quiet(X0) & patient(X0)) => ? [X0] : ~funny(X0) [input p2]
9. ! [X0] : ((~creative(X0) | happy(X0)) <=> (curious(X0) <~> generous(X0))) [input p8]
10. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> brave(X0)) [input p9]
13. ! [X0] : (~funny(X0) => ~brave(X0)) [input p12]
14. ! [X0] : (calm(X0) => curious(X0)) [input p13]
15. ! [X0] : ((~patient(X0) <~> patient(X0)) => (quiet(X0) | strong(X0))) [input p14]
22. patient(susan) | ~funny(susan) [input p21]
24. calm(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) & patient(X0)) => ? [X1] : ~funny(X1) [rectify 3]
29. ! [X0] : ((generous(X0) & humble(X0)) | ~strong(X0)) [ennf transformation 2]
30. ? [X1] : ~funny(X1) | ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 25]
34. ! [X0] : (~brave(X0) | funny(X0)) [ennf transformation 13]
35. ! [X0] : (curious(X0) | ~calm(X0)) [ennf transformation 14]
36. ! [X0] : ((quiet(X0) | strong(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 15]
37. ! [X0] : (quiet(X0) | strong(X0) | (~patient(X0) <=> patient(X0))) [flattening 36]
38. (? [X0] : (creative(X0) | ~brave(X0)) | (~patient(john) | humble(john))) & ((patient(john) & ~humble(john)) | ! [X0] : (~creative(X0) & brave(X0))) [nnf transformation 1]
39. (? [X0] : (creative(X0) | ~brave(X0)) | ~patient(john) | humble(john)) & ((patient(john) & ~humble(john)) | ! [X0] : (~creative(X0) & brave(X0))) [flattening 38]
40. (? [X0] : (creative(X0) | ~brave(X0)) | ~patient(john) | humble(john)) & ((patient(john) & ~humble(john)) | ! [X1] : (~creative(X1) & brave(X1))) [rectify 39]
41. ? [X0] : (creative(X0) | ~brave(X0)) => (creative(sK0) | ~brave(sK0)) [choice axiom]
42. ((creative(sK0) | ~brave(sK0)) | ~patient(john) | humble(john)) & ((patient(john) & ~humble(john)) | ! [X1] : (~creative(X1) & brave(X1))) [skolemisation 40,41]
43. ? [X0] : ~funny(X0) | ! [X1] : (~quiet(X1) | ~patient(X1)) [rectify 30]
44. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
45. ~funny(sK1) | ! [X1] : (~quiet(X1) | ~patient(X1)) [skolemisation 43,44]
63. ! [X0] : (((~creative(X0) | happy(X0)) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | (creative(X0) & ~happy(X0)))) [nnf transformation 9]
64. ! [X0] : ((~creative(X0) | happy(X0) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | (creative(X0) & ~happy(X0)))) [flattening 63]
65. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~brave(X0)) & (brave(X0) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 10]
73. ! [X0] : (quiet(X0) | strong(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 37]
91. ~humble(john) | ~creative(X1) [cnf transformation 42]
93. patient(john) | ~creative(X1) [cnf transformation 42]
95. ~strong(X0) | humble(X0) [cnf transformation 29]
96. ~strong(X0) | generous(X0) [cnf transformation 29]
97. ~funny(sK1) | ~quiet(X1) | ~patient(X1) [cnf transformation 45]
122. ~curious(X0) | ~generous(X0) | creative(X0) [cnf transformation 64]
125. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
126. brave(X0) | tall(X0) | tall(X0) [cnf transformation 65]
136. ~brave(X0) | funny(X0) [cnf transformation 34]
137. ~calm(X0) | curious(X0) [cnf transformation 35]
138. quiet(X0) | strong(X0) | patient(X0) | patient(X0) [cnf transformation 73]
139. quiet(X0) | strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 73]
152. patient(susan) | ~funny(susan) [cnf transformation 22]
154. calm(susan) [cnf transformation 24]
155. quiet(X0) | strong(X0) | patient(X0) [duplicate literal removal 138]
156. quiet(X0) | strong(X0) | ~patient(X0) [duplicate literal removal 139]
157. brave(X0) | ~tall(X0) [duplicate literal removal 125]
158. tall(X0) | brave(X0) [duplicate literal removal 126]
160. 1 <=> humble(john) [avatar definition]
164. 2 <=> patient(john) [avatar definition]
165. patient(john) <- (2) [avatar component clause 164]
177. 5 <=> ! [X1] : ~creative(X1) [avatar definition]
178. ~creative(X1) <- (5) [avatar component clause 177]
179. 5 | 2 [avatar split clause 93,164,177]
181. 6 <=> ! [X1] : brave(X1) [avatar definition]
182. brave(X1) <- (6) [avatar component clause 181]
184. 5 | ~1 [avatar split clause 91,160,177]
187. 7 <=> ! [X1] : (~quiet(X1) | ~patient(X1)) [avatar definition]
188. ~quiet(X1) | ~patient(X1) <- (7) [avatar component clause 187]
190. 8 <=> funny(sK1) [avatar definition]
192. ~funny(sK1) <- (~8) [avatar component clause 190]
193. 7 | ~8 [avatar split clause 97,190,187]
250. 20 <=> strong(susan) [avatar definition]
251. strong(susan) <- (20) [avatar component clause 250]
273. brave(X0) [subsumption resolution 157,158]
274. 6 [avatar split clause 273,181]
310. 33 <=> calm(susan) [avatar definition]
311. calm(susan) <- (33) [avatar component clause 310]
315. quiet(X0) | strong(X0) [subsumption resolution 155,156]
371. 46 <=> funny(susan) [avatar definition]
373. ~funny(susan) <- (~46) [avatar component clause 371]
375. 47 <=> patient(susan) [avatar definition]
377. patient(susan) <- (47) [avatar component clause 375]
378. ~46 | 47 [avatar split clause 152,375,371]
388. 33 [avatar split clause 154,310]
399. generous(susan) <- (20) [resolution 96,251]
401. funny(X0) <- (6) [resolution 136,182]
403. curious(susan) <- (33) [resolution 137,311]
405. $false <- (6, ~8) [resolution 401,192]
406. $false <- (6, ~46) [resolution 401,373]
409. ~6 | 46 [avatar contradiction clause 406]
410. ~6 | 8 [avatar contradiction clause 405]
411. ~patient(X0) | strong(X0) <- (7) [resolution 188,315]
415. strong(john) <- (2, 7) [resolution 411,165]
416. strong(susan) <- (7, 47) [resolution 411,377]
421. humble(john) <- (2, 7) [resolution 415,95]
424. 1 | ~2 | ~7 [avatar split clause 421,187,164,160]
458. ~generous(susan) | creative(susan) <- (33) [resolution 122,403]
462. creative(susan) <- (20, 33) [subsumption resolution 458,399]
463. $false <- (5, 20, 33) [subsumption resolution 462,178]
464. ~5 | ~20 | ~33 [avatar contradiction clause 463]
466. 20 | ~7 | ~47 [avatar split clause 416,375,187,250]
467. $false [avatar sat refutation 179,184,193,274,378,388,409,410,424,464,466]
% SZS output end Proof for 4285651866494778743753021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not kind is both not rich and not happy and vice versa. If someone is not creative then paul is tall and vice versa. Everyone who is not calm is both not kind and patient and vice versa. Everyone who is either generous or happy is patient or not happy and vice versa. If mary is patient or not creative then lucy is wise and vice versa. Everyone who is both brave and old is not old or funny and vice versa. Everyone who is both creative and not creative is patient or strong and vice versa. Everyone who is calm or happy is generous. If someone is not strong then john is not calm or not quiet. If paul is both not generous and wise then mary is both wise and old and vice versa. Everyone who is patient is either strong or not generous and vice versa. If someone is both not generous and not strong then someone is not kind. If someone is either not wise or humble then someone is kind and vice versa. Everyone who is either not brave or not creative is both rich and not creative and vice versa. Lucy is not tall. Someone is not patient. Someone is both kind and brave. Someone is both not happy and old. Someone is rich. Someone is both generous and old. | Lucy is not calm. | contradiction | (![X]:((quiet(X)&~kind(X))<=>(~rich(X)&~happy(X))))&
((?[X]:(~creative(X)))<=>(tall(paul)))&
(![X]:(~calm(X)<=>(~kind(X)&patient(X))))&
(![X]:((generous(X)<~>happy(X))<=>(patient(X)|~happy(X))))&
(((patient(mary)|~creative(mary)))<=>(wise(lucy)))&
(![X]:((brave(X)&old(X))<=>(~old(X)|funny(X))))&
(![X]:((creative(X)&~creative(X))<=>(patient(X)|strong(X))))&
(![X]:((calm(X)|happy(X))=>generous(X)))&
((?[X]:(~strong(X)))=>((~calm(john)|~quiet(john))))&
(((~generous(paul)&wise(paul)))<=>((wise(mary)&old(mary))))&
(![X]:(patient(X)<=>(strong(X)<~>~generous(X))))&
((?[X]:((~generous(X)&~strong(X))))=>(?[X]:(~kind(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~creative(X))))&
(~tall(lucy))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~happy(X)&old(X))))&
(?[X]:(rich(X)))&
(?[X]:((generous(X)&old(X)))) | ~calm(lucy) | [
"p2",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 4048349843562728621483268
% SZS output start Proof for 4048349843562728621483268
3. ! [X0] : (~calm(X0) <=> (patient(X0) & ~kind(X0))) [input p2]
7. ! [X0] : ((~creative(X0) & creative(X0)) <=> (strong(X0) | patient(X0))) [input p6]
21. ~calm(lucy) [input hypothesis]
24. ! [X0] : (~calm(X0) => (patient(X0) & ~kind(X0))) [unused predicate definition removal 3]
25. ! [X0] : ((patient(X0) & ~kind(X0)) | calm(X0)) [ennf transformation 24]
42. ! [X0] : (((~creative(X0) & creative(X0)) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 7]
43. ! [X0] : (((~creative(X0) & creative(X0)) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | creative(X0) | ~creative(X0))) [flattening 42]
74. patient(X0) | calm(X0) [cnf transformation 25]
90. creative(X0) | ~patient(X0) [cnf transformation 43]
92. ~creative(X0) | ~patient(X0) [cnf transformation 43]
125. ~calm(lucy) [cnf transformation 21]
163. ~patient(X0) [subsumption resolution 90,92]
217. calm(X0) [resolution 74,163]
218. $false [resolution 217,125]
% SZS output end Proof for 4048349843562728621483268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and wise is quiet or not kind and vice versa.
Everyone who is calm or not rich is patient or not rich and vice versa.
If someone is either not creative or brave then alice is either not quiet or calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
If john is happy then someone is wise and vice versa.
Someone is not wise or happy.
Someone is either not generous or creative.
Someone is either rich or not creative.
Lucy is either not humble or humble.
Someone is either creative or not wise.
Fred is either rich or humble. | Fred is happy. | neutral | (![X]:((~tall(X)&wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:((calm(X)|~rich(X))<=>(patient(X)|~rich(X))))&
((?[X]:((~creative(X)<~>brave(X))))<=>((~quiet(alice)<~>calm(alice))))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
((happy(john))<=>(?[X]:(wise(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X))))&
((rich(fred)<~>humble(fred))) | happy(fred) | []
| null | 0 |
Everyone who is both strong and not creative is generous or not quiet. If someone is funny or not generous then john is both strong and not creative. If susan is calm then someone is not humble and vice versa. Everyone who is either not rich or not old is old or kind. Everyone who is not generous is happy or generous and vice versa. If someone is either not wise or not generous then someone is either not strong or not quiet. Everyone who is humble or tall is tall or funny and vice versa. Everyone who is either not brave or rich is not rich or patient and vice versa. Everyone who is wise or not patient is both curious and humble. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Someone is either tall or creative. Someone is both not calm and not humble. Someone is not curious or happy. Fred is either not happy or not rich. Someone is not happy or happy. Someone is either brave or kind. | John is curious. | entailment | (![X]:((strong(X)&~creative(X))=>(generous(X)|~quiet(X))))&
((?[X]:((funny(X)|~generous(X))))=>((strong(john)&~creative(john))))&
((calm(susan))<=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))<=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(?[X]:((tall(X)<~>creative(X))))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~curious(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X)))) | curious(john) | [
"p0",
"p1",
"p4",
"p8",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 4624840684361353523148749
% SZS output start Proof for 4624840684361353523148749
1. ! [X0] : ((~creative(X0) & strong(X0)) => (~quiet(X0) | generous(X0))) [input p0]
2. ? [X0] : (~generous(X0) | funny(X0)) => (~creative(john) & strong(john)) [input p1]
5. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p4]
9. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p9]
21. ~curious(john) [input hypothesis]
23. ! [X0] : ((~quiet(X0) | generous(X0)) | (creative(X0) | ~strong(X0))) [ennf transformation 1]
24. ! [X0] : (~quiet(X0) | generous(X0) | creative(X0) | ~strong(X0)) [flattening 23]
25. (~creative(john) & strong(john)) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 2]
29. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 9]
30. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 10]
36. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 5]
37. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 36]
70. ~quiet(X0) | generous(X0) | creative(X0) | ~strong(X0) [cnf transformation 24]
72. strong(john) | generous(X0) [cnf transformation 25]
74. ~creative(john) | generous(X0) [cnf transformation 25]
81. ~generous(X0) | ~generous(X0) [cnf transformation 37]
97. curious(X0) | patient(X0) [cnf transformation 29]
101. ~patient(X0) | quiet(X0) [cnf transformation 30]
138. ~curious(john) [cnf transformation 21]
142. ~generous(X0) [duplicate literal removal 81]
145. 1 <=> ! [X0] : generous(X0) [avatar definition]
146. generous(X0) <- (1) [avatar component clause 145]
148. 2 <=> creative(john) [avatar definition]
150. ~creative(john) <- (~2) [avatar component clause 148]
151. 1 | ~2 [avatar split clause 74,148,145]
157. 4 <=> strong(john) [avatar definition]
160. 1 | 4 [avatar split clause 72,157,145]
243. patient(john) [resolution 97,138]
244. quiet(john) [resolution 101,243]
394. generous(john) | creative(john) | ~strong(john) [resolution 70,244]
396. creative(john) | ~strong(john) [subsumption resolution 394,142]
397. ~strong(john) <- (~2) [subsumption resolution 396,150]
401. ~4 | 2 [avatar split clause 397,148,157]
402. $false <- (1) [subsumption resolution 146,142]
403. ~1 [avatar contradiction clause 402]
404. $false [avatar sat refutation 151,160,401,403]
% SZS output end Proof for 4624840684361353523148749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious is not tall.
Everyone who is either rich or not brave is both not quiet and patient.
Everyone who is both old and not brave is not old or brave.
Everyone who is not strong is old or not brave and vice versa.
If john is both not funny and not happy then paul is both patient and creative.
Everyone who is not tall or not calm is not rich.
If mary is strong or old then alice is calm and vice versa.
If paul is either not patient or calm then alice is both not kind and wise.
Everyone who is not tall is not kind or not old.
Everyone who is either not generous or humble is both strong and not funny.
Everyone who is either patient or not humble is both not strong and not humble and vice versa.
Everyone who is not creative is both not old and humble.
Everyone who is not generous is both humble and happy.
Everyone who is both not curious and not rich is curious or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Lucy is both wise and not funny.
Someone is both creative and not old.
Someone is either not funny or not strong.
Someone is old or patient.
Someone is old or not happy.
Someone is either not old or not humble.
Someone is tall or not curious. | John is not curious. | entailment | (![X]:((~wise(X)<~>curious(X))=>~tall(X)))&
(![X]:((rich(X)<~>~brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((old(X)&~brave(X))=>(~old(X)|brave(X))))&
(![X]:(~strong(X)<=>(old(X)|~brave(X))))&
(((~funny(john)&~happy(john)))=>((patient(paul)&creative(paul))))&
(![X]:((~tall(X)|~calm(X))=>~rich(X)))&
(((strong(mary)|old(mary)))<=>(calm(alice)))&
(((~patient(paul)<~>calm(paul)))=>((~kind(alice)&wise(alice))))&
(![X]:(~tall(X)=>(~kind(X)|~old(X))))&
(![X]:((~generous(X)<~>humble(X))=>(strong(X)&~funny(X))))&
(![X]:((patient(X)<~>~humble(X))<=>(~strong(X)&~humble(X))))&
(![X]:(~creative(X)=>(~old(X)&humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|funny(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
((wise(lucy)&~funny(lucy)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:((tall(X)|~curious(X)))) | ~curious(john) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 1033354717035350770686930
% SZS output start Proof for 1033354717035350770686930
14. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) | curious(X0))) [input p13]
24. curious(john) [input hypothesis]
53. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 14]
54. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 53]
98. ~curious(X0) | ~curious(X0) [cnf transformation 54]
115. curious(john) [cnf transformation 24]
117. ~curious(X0) [duplicate literal removal 98]
198. $false [subsumption resolution 115,117]
% SZS output end Proof for 1033354717035350770686930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If fred is old or creative then someone is old or not patient and vice versa. Everyone who is both strong and kind is not wise. If mary is rich then fred is wise and vice versa. If someone is not calm or funny then susan is either generous or not quiet. If alice is both kind and not patient then someone is not generous or not rich. Everyone who is both not happy and brave is either not humble or rich and vice versa. Everyone who is both not curious and not rich is curious or not generous and vice versa. If susan is not calm then john is both not curious and wise and vice versa. Everyone who is not tall or not happy is either patient or not generous and vice versa. Everyone who is both not tall and not calm is not quiet or funny. Everyone who is not curious or calm is either old or not tall and vice versa. Everyone who is calm is both rich and not generous and vice versa. Everyone who is both not humble and not strong is either generous or kind and vice versa. Everyone who is not humble or strong is either not quiet or quiet and vice versa. Everyone who is both brave and curious is both not strong and wise. Everyone who is either brave or calm is generous. Someone is quiet or not patient. Someone is both not wise and not calm. Someone is not wise or not funny. Someone is either calm or not kind. Someone is quiet or not happy. John is not tall. Paul is either not generous or kind. | John is not kind. | entailment | (((old(fred)|creative(fred)))<=>(?[X]:((old(X)|~patient(X)))))&
(![X]:((strong(X)&kind(X))=>~wise(X)))&
((rich(mary))<=>(wise(fred)))&
((?[X]:((~calm(X)|funny(X))))=>((generous(susan)<~>~quiet(susan))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(![X]:((~tall(X)|~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~tall(X)&~calm(X))=>(~quiet(X)|funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(old(X)<~>~tall(X))))&
(![X]:(calm(X)<=>(rich(X)&~generous(X))))&
(![X]:((~humble(X)&~strong(X))<=>(generous(X)<~>kind(X))))&
(![X]:((~humble(X)|strong(X))<=>(~quiet(X)<~>quiet(X))))&
(![X]:((brave(X)&curious(X))=>(~strong(X)&wise(X))))&
(![X]:((brave(X)<~>calm(X))=>generous(X)))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:((~wise(X)|~funny(X))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((quiet(X)|~happy(X))))&
(~tall(john))&
((~generous(paul)<~>kind(paul))) | ~kind(john) | [
"p1",
"p5",
"p6",
"p7",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7708136909353883493855643
% SZS output start Proof for 7708136909353883493855643
2. ! [X0] : ((kind(X0) & strong(X0)) => ~wise(X0)) [input p1]
6. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (~humble(X0) <~> rich(X0))) [input p5]
7. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (~generous(X0) | curious(X0))) [input p6]
8. ~calm(susan) <=> (wise(john) & ~curious(john)) [input p7]
12. ! [X0] : (calm(X0) <=> (~generous(X0) & rich(X0))) [input p11]
13. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (generous(X0) <~> kind(X0))) [input p12]
14. ! [X0] : ((strong(X0) | ~humble(X0)) <=> (~quiet(X0) <~> quiet(X0))) [input p13]
16. ! [X0] : ((brave(X0) <~> calm(X0)) => generous(X0)) [input p15]
24. kind(john) [input hypothesis]
25. ! [X0] : (~wise(X0) | (~kind(X0) | ~strong(X0))) [ennf transformation 2]
26. ! [X0] : (~wise(X0) | ~kind(X0) | ~strong(X0)) [flattening 25]
34. ! [X0] : (generous(X0) | (brave(X0) <=> calm(X0))) [ennf transformation 16]
44. ! [X0] : (((brave(X0) & ~happy(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 6]
45. ! [X0] : (((brave(X0) & ~happy(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | ~brave(X0) | happy(X0))) [flattening 44]
46. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 7]
47. ! [X0] : (((~rich(X0) & ~curious(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 46]
48. (~calm(susan) | (~wise(john) | curious(john))) & ((wise(john) & ~curious(john)) | calm(susan)) [nnf transformation 8]
49. (~calm(susan) | ~wise(john) | curious(john)) & ((wise(john) & ~curious(john)) | calm(susan)) [flattening 48]
54. ! [X0] : ((calm(X0) | (generous(X0) | ~rich(X0))) & ((~generous(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | generous(X0) | ~rich(X0)) & ((~generous(X0) & rich(X0)) | ~calm(X0))) [flattening 54]
56. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (strong(X0) | humble(X0)))) [nnf transformation 13]
57. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | strong(X0) | humble(X0))) [flattening 56]
58. ! [X0] : (((strong(X0) | ~humble(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~strong(X0) & humble(X0)))) [nnf transformation 14]
59. ! [X0] : ((strong(X0) | ~humble(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~strong(X0) & humble(X0)))) [flattening 58]
60. ! [X0] : (generous(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) [nnf transformation 34]
77. ~wise(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 26]
89. humble(X0) | rich(X0) | brave(X0) [cnf transformation 45]
91. ~generous(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 47]
92. ~curious(X0) | ~curious(X0) [cnf transformation 47]
95. ~rich(X0) | generous(X0) [cnf transformation 47]
97. wise(john) | calm(susan) [cnf transformation 49]
112. ~calm(X0) | rich(X0) [cnf transformation 55]
113. ~generous(X0) | ~calm(X0) [cnf transformation 55]
116. ~generous(X0) | ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 57]
125. strong(X0) | ~humble(X0) | quiet(X0) | quiet(X0) [cnf transformation 59]
126. strong(X0) | ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 59]
129. ~brave(X0) | calm(X0) | generous(X0) [cnf transformation 60]
141. kind(john) [cnf transformation 24]
142. strong(X0) | ~humble(X0) | quiet(X0) [duplicate literal removal 125]
143. ~humble(X0) | strong(X0) | ~quiet(X0) [duplicate literal removal 126]
144. ~generous(X0) | curious(X0) | rich(X0) [duplicate literal removal 91]
145. ~curious(X0) [duplicate literal removal 92]
186. 10 <=> generous(susan) [avatar definition]
187. generous(susan) <- (10) [avatar component clause 186]
217. ~generous(X0) | rich(X0) [subsumption resolution 144,145]
220. 17 <=> wise(john) [avatar definition]
221. wise(john) <- (17) [avatar component clause 220]
224. 18 <=> calm(susan) [avatar definition]
225. calm(susan) <- (18) [avatar component clause 224]
228. 18 | 17 [avatar split clause 97,220,224]
231. ~humble(X0) | strong(X0) [subsumption resolution 142,143]
285. brave(X1) | rich(X1) | strong(X1) [resolution 89,231]
294. rich(X0) | strong(X0) | calm(X0) | generous(X0) [resolution 285,129]
295. rich(X0) | strong(X0) | calm(X0) [subsumption resolution 294,217]
296. rich(X0) | strong(X0) [subsumption resolution 295,112]
300. generous(X0) | strong(X0) [resolution 296,95]
337. ~kind(X0) | strong(X0) | humble(X0) | strong(X0) [resolution 116,300]
338. ~kind(X0) | strong(X0) | humble(X0) [duplicate literal removal 337]
339. ~kind(X0) | strong(X0) [subsumption resolution 338,231]
380. rich(susan) <- (18) [resolution 225,112]
393. generous(susan) <- (18) [resolution 380,95]
396. 10 | ~18 [avatar split clause 393,224,186]
402. ~calm(susan) <- (10) [resolution 187,113]
423. ~18 | ~10 [avatar split clause 402,186,224]
432. ~kind(john) | ~strong(john) <- (17) [resolution 221,77]
433. ~strong(john) <- (17) [subsumption resolution 432,141]
450. strong(john) [resolution 339,141]
451. $false <- (17) [subsumption resolution 450,433]
452. ~17 [avatar contradiction clause 451]
453. $false [avatar sat refutation 228,396,423,452]
% SZS output end Proof for 7708136909353883493855643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or happy then someone is happy. Everyone who is happy or calm is not old and vice versa. Everyone who is both curious and not patient is not kind or not generous and vice versa. If lucy is both not rich and not old then john is either not quiet or generous and vice versa. If someone is not curious or not brave then alice is both not brave and not quiet and vice versa. Everyone who is not kind is both wise and not happy. If alice is brave or not strong then john is either not tall or curious and vice versa. If someone is either humble or wise then someone is strong or not kind and vice versa. Everyone who is either not funny or not creative is both not patient and calm. If paul is not funny or rich then lucy is quiet or not kind. If someone is either not humble or not generous then someone is both rich and not creative and vice versa. Everyone who is not rich is both not calm and not generous and vice versa. Everyone who is not generous is both old and funny. Everyone who is either kind or calm is either not happy or strong. If someone is either not quiet or patient then someone is both old and not creative and vice versa. Everyone who is both rich and not brave is either not rich or not funny and vice versa. Paul is not calm or quiet. Someone is either kind or not old. Someone is not quiet. Someone is not calm or not quiet. Lucy is both patient and rich. Someone is not funny or generous. | Alice is not tall. | neutral | ((?[X]:((~happy(X)|happy(X))))=>(?[X]:(happy(X))))&
(![X]:((happy(X)|calm(X))<=>~old(X)))&
(![X]:((curious(X)&~patient(X))<=>(~kind(X)|~generous(X))))&
(((~rich(lucy)&~old(lucy)))<=>((~quiet(john)<~>generous(john))))&
((?[X]:((~curious(X)|~brave(X))))<=>((~brave(alice)&~quiet(alice))))&
(![X]:(~kind(X)=>(wise(X)&~happy(X))))&
(((brave(alice)|~strong(alice)))<=>((~tall(john)<~>curious(john))))&
((?[X]:((humble(X)<~>wise(X))))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~patient(X)&calm(X))))&
(((~funny(paul)|rich(paul)))=>((quiet(lucy)|~kind(lucy))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(~rich(X)<=>(~calm(X)&~generous(X))))&
(![X]:(~generous(X)=>(old(X)&funny(X))))&
(![X]:((kind(X)<~>calm(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((~calm(paul)|quiet(paul)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
((patient(lucy)&rich(lucy)))&
(?[X]:((~funny(X)|generous(X)))) | ~tall(alice) | []
| null | 0 |
Everyone who is both humble and not happy is either not quiet or not calm and vice versa. If john is both not patient and not creative then someone is either not creative or tall and vice versa. If paul is not calm or not rich then someone is not curious and vice versa. Everyone who is both not rich and tall is not kind or not humble. If mary is happy or kind then john is both not generous and curious and vice versa. Everyone who is brave is either strong or patient and vice versa. Everyone who is either not happy or not rich is old and vice versa. Everyone who is not creative or not tall is either not calm or patient and vice versa. If john is both not old and not curious then lucy is either not happy or strong. If alice is patient then someone is not happy. If paul is not wise or not strong then someone is both quiet and not brave. Everyone who is brave is tall and vice versa. Everyone who is either strong or generous is creative or brave. Everyone who is either not happy or not old is both creative and not quiet. Everyone who is both quiet and wise is both not calm and strong. Everyone who is funny or not curious is strong or wise. Someone is either not kind or not old. John is not quiet or not tall. Someone is happy or strong. Fred is rich. Paul is not kind or not creative. Someone is not creative. Someone is rich or not quiet. Fred is happy. | Fred is not calm. | entailment | (![X]:((humble(X)&~happy(X))<=>(~quiet(X)<~>~calm(X))))&
(((~patient(john)&~creative(john)))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~calm(paul)|~rich(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)&tall(X))=>(~kind(X)|~humble(X))))&
(((happy(mary)|kind(mary)))<=>((~generous(john)&curious(john))))&
(![X]:(brave(X)<=>(strong(X)<~>patient(X))))&
(![X]:((~happy(X)<~>~rich(X))<=>old(X)))&
(![X]:((~creative(X)|~tall(X))<=>(~calm(X)<~>patient(X))))&
(((~old(john)&~curious(john)))=>((~happy(lucy)<~>strong(lucy))))&
((patient(alice))=>(?[X]:(~happy(X))))&
(((~wise(paul)|~strong(paul)))=>(?[X]:((quiet(X)&~brave(X)))))&
(![X]:(brave(X)<=>tall(X)))&
(![X]:((strong(X)<~>generous(X))=>(creative(X)|brave(X))))&
(![X]:((~happy(X)<~>~old(X))=>(creative(X)&~quiet(X))))&
(![X]:((quiet(X)&wise(X))=>(~calm(X)&strong(X))))&
(![X]:((funny(X)|~curious(X))=>(strong(X)|wise(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
((~quiet(john)|~tall(john)))&
(?[X]:((happy(X)|strong(X))))&
(rich(fred))&
((~kind(paul)|~creative(paul)))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)|~quiet(X))))&
(happy(fred)) | ~calm(fred) | [
"p0",
"p6",
"p13",
"p19",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 2406966449214953277374363
% SZS output start Proof for 2406966449214953277374363
1. ! [X0] : ((~happy(X0) & humble(X0)) <=> (~quiet(X0) <~> ~calm(X0))) [input p0]
7. ! [X0] : ((~happy(X0) <~> ~rich(X0)) <=> old(X0)) [input p6]
14. ! [X0] : ((~happy(X0) <~> ~old(X0)) => (~quiet(X0) & creative(X0))) [input p13]
20. rich(fred) [input p19]
24. happy(fred) [input p23]
25. calm(fred) [input hypothesis]
35. ! [X0] : ((~quiet(X0) & creative(X0)) | (~happy(X0) <=> ~old(X0))) [ennf transformation 14]
40. ! [X0] : (((~happy(X0) & humble(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) & (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (happy(X0) | ~humble(X0)))) [nnf transformation 1]
41. ! [X0] : (((~happy(X0) & humble(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) & (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | happy(X0) | ~humble(X0))) [flattening 40]
55. ! [X0] : ((((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ~old(X0)) & (old(X0) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))))) [nnf transformation 7]
65. ! [X0] : ((~quiet(X0) & creative(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) [nnf transformation 35]
79. ~calm(X0) | ~happy(X0) | quiet(X0) [cnf transformation 41]
102. ~old(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 55]
124. ~quiet(X0) | ~happy(X0) | old(X0) [cnf transformation 65]
132. rich(fred) [cnf transformation 20]
136. happy(fred) [cnf transformation 24]
137. calm(fred) [cnf transformation 25]
296. 34 <=> quiet(fred) [avatar definition]
298. quiet(fred) <- (34) [avatar component clause 296]
305. ~happy(fred) | quiet(fred) [resolution 79,137]
406. ~happy(fred) | old(fred) <- (34) [resolution 124,298]
407. old(fred) <- (34) [subsumption resolution 406,136]
417. ~happy(fred) | ~rich(fred) <- (34) [resolution 407,102]
418. ~rich(fred) <- (34) [subsumption resolution 417,136]
419. $false <- (34) [subsumption resolution 418,132]
420. ~34 [avatar contradiction clause 419]
421. quiet(fred) [subsumption resolution 305,136]
422. 34 [avatar split clause 421,296]
423. $false [avatar sat refutation 420,422]
% SZS output end Proof for 2406966449214953277374363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or old then john is not funny or happy and vice versa.
Everyone who is both old and not kind is either rich or curious.
Everyone who is tall is not patient or not rich.
If someone is generous then someone is patient.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Paul is humble. | contradiction | ((?[X]:((patient(X)|old(X))))<=>((~funny(john)|happy(john))))&
(![X]:((old(X)&~kind(X))=>(rich(X)<~>curious(X))))&
(![X]:(tall(X)=>(~patient(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | humble(paul) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5812760518101883598195576
% SZS output start Proof for 5812760518101883598195576
4. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p3]
6. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (tall(X0) | ~strong(X0))) [input p5]
8. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X0] : (~wise(X0) & generous(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (humble(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : ((rich(X0) & kind(X0)) <=> (~brave(X0) | old(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => calm(X0)) [input p13]
23. humble(paul) [input hypothesis]
24. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 4]
25. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X1] : (~wise(X1) & generous(X1)) [rectify 8]
30. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 24]
35. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : (~tall(X0) <=> ~wise(X0)) [ennf transformation 25]
36. ! [X0] : ((humble(X0) <~> ~old(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 9]
38. ! [X0] : (calm(X0) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
48. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 30]
49. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
50. patient(sK1) | ! [X1] : ~generous(X1) [skolemisation 48,49]
51. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [flattening 51]
53. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 35]
54. ? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) & generous(X0)) => (~wise(sK2) & generous(sK2)) [choice axiom]
56. (~wise(sK2) & generous(sK2)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [skolemisation 54,55]
57. ! [X0] : (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 36]
58. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~rich(X0) | ~kind(X0)))) [nnf transformation 10]
59. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~rich(X0) | ~kind(X0))) [flattening 58]
60. ! [X0] : (((patient(X0) | ~patient(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((patient(X0) | ~patient(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 60]
64. ! [X0] : (calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 38]
80. patient(sK1) | ~generous(X1) [cnf transformation 50]
83. ~strong(X0) | tall(X0) | wise(X0) | ~kind(X0) [cnf transformation 52]
88. ~wise(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 52]
91. generous(sK2) | ~wise(X1) | tall(X1) [cnf transformation 56]
92. generous(sK2) | ~tall(X1) | wise(X1) [cnf transformation 56]
98. ~humble(X0) | old(X0) | ~strong(X0) | patient(X0) [cnf transformation 57]
100. ~old(X0) | kind(X0) [cnf transformation 59]
105. ~patient(X0) | ~patient(X0) [cnf transformation 61]
106. ~calm(X0) | patient(X0) [cnf transformation 61]
107. ~calm(X0) | ~patient(X0) [cnf transformation 61]
118. calm(X0) | strong(X0) | ~humble(X0) [cnf transformation 64]
132. humble(paul) [cnf transformation 23]
134. ~patient(X0) [duplicate literal removal 105]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
163. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
164. ~generous(X1) <- (7) [avatar component clause 163]
166. 8 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (8) [avatar component clause 166]
169. 7 | 8 [avatar split clause 80,166,163]
187. 13 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
188. ~tall(X1) | wise(X1) <- (13) [avatar component clause 187]
195. 15 <=> ! [X1] : (~wise(X1) | tall(X1)) [avatar definition]
196. ~wise(X1) | tall(X1) <- (15) [avatar component clause 195]
199. 16 <=> generous(sK2) [avatar definition]
201. generous(sK2) <- (16) [avatar component clause 199]
202. 13 | 16 [avatar split clause 92,199,187]
203. 15 | 16 [avatar split clause 91,199,195]
204. ~calm(X0) [subsumption resolution 106,107]
205. 6 [avatar split clause 134,159]
209. 17 <=> kind(paul) [avatar definition]
210. ~kind(paul) <- (~17) [avatar component clause 209]
211. kind(paul) <- (17) [avatar component clause 209]
213. 18 <=> patient(paul) [avatar definition]
214. patient(paul) <- (18) [avatar component clause 213]
215. ~patient(paul) <- (~18) [avatar component clause 213]
224. ~humble(X0) | strong(X0) [subsumption resolution 118,204]
275. strong(paul) [resolution 224,132]
321. tall(paul) | wise(paul) | ~kind(paul) [resolution 83,275]
333. old(paul) | ~strong(paul) | patient(paul) [resolution 98,132]
335. old(paul) | patient(paul) [subsumption resolution 333,275]
336. old(paul) <- (~18) [subsumption resolution 335,215]
340. kind(paul) <- (~18) [resolution 336,100]
352. $false <- (~17, ~18) [subsumption resolution 340,210]
353. 17 | 18 [avatar contradiction clause 352]
354. wise(paul) | ~kind(paul) <- (13) [subsumption resolution 321,188]
356. 31 <=> wise(paul) [avatar definition]
358. wise(paul) <- (31) [avatar component clause 356]
359. ~17 | 31 | ~13 [avatar split clause 354,187,356,209]
361. $false <- (6, 18) [subsumption resolution 214,160]
362. ~6 | ~18 [avatar contradiction clause 361]
363. tall(paul) | wise(paul) <- (17) [subsumption resolution 321,211]
364. tall(paul) <- (15, 17) [subsumption resolution 363,196]
368. $false <- (7, 16) [subsumption resolution 201,164]
369. ~7 | ~16 [avatar contradiction clause 368]
370. $false <- (6, 8) [subsumption resolution 168,160]
371. ~6 | ~8 [avatar contradiction clause 370]
399. ~kind(paul) | ~tall(paul) <- (31) [resolution 358,88]
403. ~tall(paul) <- (17, 31) [subsumption resolution 399,211]
404. $false <- (15, 17, 31) [subsumption resolution 403,364]
405. ~15 | ~17 | ~31 [avatar contradiction clause 404]
407. $false [avatar sat refutation 169,202,203,205,353,359,362,369,371,405]
% SZS output end Proof for 5812760518101883598195576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient and quiet is not happy.
Everyone who is old or kind is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is either not generous or quiet.
Lucy is not funny or strong.
John is not kind or not funny. | Mary is brave. | neutral | (![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~funny(lucy)|strong(lucy)))&
((~kind(john)|~funny(john))) | brave(mary) | []
| null | 0 |
If someone is generous or not generous then john is either quiet or old.
If someone is either brave or tall then paul is either not rich or not patient and vice versa.
If someone is funny then someone is either not happy or rich and vice versa.
Everyone who is not kind is creative or not patient and vice versa.
Everyone who is both brave and curious is both not quiet and generous and vice versa.
If paul is both happy and funny then mary is not funny and vice versa.
Everyone who is either not old or generous is both calm and generous and vice versa.
Everyone who is either not patient or funny is not humble.
If paul is both curious and not kind then someone is not brave.
If someone is not patient then someone is both not brave and not old and vice versa.
If someone is both funny and not brave then paul is both kind and humble.
Everyone who is not strong is either creative or not strong and vice versa.
Everyone who is both strong and old is tall.
Everyone who is strong or not kind is either not funny or not tall and vice versa.
Everyone who is both not strong and tall is happy or kind and vice versa.
Everyone who is not quiet is not tall or generous and vice versa.
Susan is both happy and not strong.
Someone is either not quiet or tall.
Someone is not rich.
Susan is old.
Paul is not old.
Alice is both old and curious.
Paul is curious or not generous. | Alice is humble. | contradiction | ((?[X]:((generous(X)|~generous(X))))=>((quiet(john)<~>old(john))))&
((?[X]:((brave(X)<~>tall(X))))<=>((~rich(paul)<~>~patient(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(creative(X)|~patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~quiet(X)&generous(X))))&
(((happy(paul)&funny(paul)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>generous(X))<=>(calm(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>~humble(X)))&
(((curious(paul)&~kind(paul)))=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((?[X]:((funny(X)&~brave(X))))=>((kind(paul)&humble(paul))))&
(![X]:(~strong(X)<=>(creative(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))=>tall(X)))&
(![X]:((strong(X)|~kind(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~strong(X)&tall(X))<=>(happy(X)|kind(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|generous(X))))&
((happy(susan)&~strong(susan)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~rich(X)))&
(old(susan))&
(~old(paul))&
((old(alice)&curious(alice)))&
((curious(paul)|~generous(paul))) | humble(alice) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8690008933458523536908818
% SZS output start Proof for 8690008933458523536908818
4. ! [X0] : (~kind(X0) <=> (~patient(X0) | creative(X0))) [input p3]
5. ! [X0] : ((curious(X0) & brave(X0)) <=> (generous(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~old(X0) <~> generous(X0)) <=> (generous(X0) & calm(X0))) [input p6]
8. ! [X0] : ((~patient(X0) <~> funny(X0)) => ~humble(X0)) [input p7]
10. ? [X0] : ~patient(X0) <=> ? [X0] : (~old(X0) & ~brave(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (creative(X0) <~> ~strong(X0))) [input p11]
14. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p13]
15. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (kind(X0) | happy(X0))) [input p14]
16. ! [X0] : (~quiet(X0) <=> (generous(X0) | ~tall(X0))) [input p15]
24. humble(alice) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : (~old(X1) & ~brave(X1)) [rectify 10]
28. ! [X0] : (~humble(X0) | (~patient(X0) <=> funny(X0))) [ennf transformation 8]
44. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | kind(X0))) [nnf transformation 4]
45. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | kind(X0))) [flattening 44]
46. ! [X0] : (((curious(X0) & brave(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((curious(X0) & brave(X0)) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [flattening 50]
52. ! [X0] : (~humble(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) [nnf transformation 28]
55. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X1] : (~old(X1) & ~brave(X1)) | ! [X0] : patient(X0)) [nnf transformation 26]
56. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X2] : (~old(X2) & ~brave(X2)) | ! [X3] : patient(X3)) [rectify 55]
57. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
58. ? [X2] : (~old(X2) & ~brave(X2)) => (~old(sK5) & ~brave(sK5)) [choice axiom]
59. (~patient(sK4) | ! [X1] : (old(X1) | brave(X1))) & ((~old(sK5) & ~brave(sK5)) | ! [X3] : patient(X3)) [skolemisation 56,58,57]
60. ! [X0] : ((~strong(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | strong(X0))) [nnf transformation 12]
61. ! [X0] : (((~kind(X0) | strong(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : ((~kind(X0) | strong(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [flattening 61]
63. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & ((kind(X0) | happy(X0)) | (~tall(X0) | strong(X0)))) [nnf transformation 15]
64. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & (kind(X0) | happy(X0) | ~tall(X0) | strong(X0))) [flattening 63]
65. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | quiet(X0))) [flattening 65]
88. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 45]
93. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
100. generous(X0) | generous(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
107. ~brave(sK5) | patient(X3) [cnf transformation 59]
108. ~old(sK5) | patient(X3) [cnf transformation 59]
113. strong(X0) | ~creative(X0) | strong(X0) [cnf transformation 60]
114. ~strong(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 60]
120. kind(X0) | funny(X0) | tall(X0) [cnf transformation 62]
121. ~kind(X0) | strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 62]
125. ~strong(X0) | ~kind(X0) [cnf transformation 64]
127. ~kind(X0) | tall(X0) [cnf transformation 64]
130. ~quiet(X0) | ~generous(X0) [cnf transformation 66]
141. humble(alice) [cnf transformation 24]
142. strong(X0) | ~creative(X0) [duplicate literal removal 113]
143. ~strong(X0) | ~creative(X0) [duplicate literal removal 114]
144. old(X0) | generous(X0) [duplicate literal removal 100]
256. 25 <=> ! [X3] : patient(X3) [avatar definition]
257. patient(X3) <- (25) [avatar component clause 256]
259. 26 <=> old(sK5) [avatar definition]
261. ~old(sK5) <- (~26) [avatar component clause 259]
262. 25 | ~26 [avatar split clause 108,259,256]
264. 27 <=> brave(sK5) [avatar definition]
266. ~brave(sK5) <- (~27) [avatar component clause 264]
267. 25 | ~27 [avatar split clause 107,264,256]
277. ~creative(X0) [subsumption resolution 142,143]
294. generous(sK5) <- (~26) [resolution 144,261]
328. brave(sK5) | quiet(sK5) <- (~26) [resolution 93,294]
331. quiet(sK5) <- (~26, ~27) [subsumption resolution 328,266]
380. ~patient(alice) | ~funny(alice) [resolution 105,141]
403. funny(X0) | tall(X0) | tall(X0) [resolution 120,127]
405. funny(X0) | tall(X0) [duplicate literal removal 403]
437. ~generous(sK5) <- (~26, ~27) [resolution 331,130]
439. $false <- (~26, ~27) [subsumption resolution 437,294]
440. 26 | 27 [avatar contradiction clause 439]
452. creative(X0) | kind(X0) <- (25) [resolution 257,88]
454. kind(X0) <- (25) [subsumption resolution 452,277]
458. strong(X1) | ~tall(X1) | funny(X1) <- (25) [resolution 454,121]
462. strong(X1) | funny(X1) <- (25) [subsumption resolution 458,405]
526. funny(X4) | ~kind(X4) <- (25) [resolution 462,125]
530. funny(X4) <- (25) [subsumption resolution 526,454]
539. ~funny(alice) <- (25) [subsumption resolution 380,257]
540. $false <- (25) [subsumption resolution 539,530]
541. ~25 [avatar contradiction clause 540]
544. $false [avatar sat refutation 262,267,440,541]
% SZS output end Proof for 8690008933458523536908818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not quiet is either rich or calm.
Everyone who is not happy is both wise and quiet.
Everyone who is not humble or not rich is not creative and vice versa.
Everyone who is happy is not quiet and vice versa.
Everyone who is not creative or not funny is happy and vice versa.
If lucy is both not wise and generous then fred is either old or happy.
Everyone who is old or brave is either not rich or not old and vice versa.
If paul is either old or not tall then someone is both not tall and not funny and vice versa.
Everyone who is either old or patient is not wise.
If susan is either creative or humble then susan is not rich or not creative.
If someone is not wise or not calm then mary is funny and vice versa.
Everyone who is both not quiet and not patient is funny.
Everyone who is either not strong or happy is both happy and quiet.
If someone is curious then someone is not strong or not patient.
If someone is brave then mary is creative and vice versa.
If someone is not old then alice is either strong or not humble and vice versa.
Alice is rich or kind.
Someone is not rich or kind.
Mary is not calm.
Someone is wise.
Someone is both creative and tall.
Alice is not curious. | Mary is humble. | entailment | (![X]:((~generous(X)<~>~quiet(X))=>(rich(X)<~>calm(X))))&
(![X]:(~happy(X)=>(wise(X)&quiet(X))))&
(![X]:((~humble(X)|~rich(X))<=>~creative(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
(![X]:((~creative(X)|~funny(X))<=>happy(X)))&
(((~wise(lucy)&generous(lucy)))=>((old(fred)<~>happy(fred))))&
(![X]:((old(X)|brave(X))<=>(~rich(X)<~>~old(X))))&
(((old(paul)<~>~tall(paul)))<=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((old(X)<~>patient(X))=>~wise(X)))&
(((creative(susan)<~>humble(susan)))=>((~rich(susan)|~creative(susan))))&
((?[X]:((~wise(X)|~calm(X))))<=>(funny(mary)))&
(![X]:((~quiet(X)&~patient(X))=>funny(X)))&
(![X]:((~strong(X)<~>happy(X))=>(happy(X)&quiet(X))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:(brave(X)))<=>(creative(mary)))&
((?[X]:(~old(X)))<=>((strong(alice)<~>~humble(alice))))&
((rich(alice)|kind(alice)))&
(?[X]:((~rich(X)|kind(X))))&
(~calm(mary))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&tall(X))))&
(~curious(alice)) | humble(mary) | [
"p2",
"p6",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 2104247113232315798434149
% SZS output start Proof for 2104247113232315798434149
3. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> ~creative(X0)) [input p2]
7. ! [X0] : ((brave(X0) | old(X0)) <=> (~rich(X0) <~> ~old(X0))) [input p6]
15. ? [X0] : brave(X0) <=> creative(mary) [input p14]
21. ? [X0] : (tall(X0) & creative(X0)) [input p20]
23. ~humble(mary) [input hypothesis]
40. ! [X0] : (((~rich(X0) | ~humble(X0)) | creative(X0)) & (~creative(X0) | (rich(X0) & humble(X0)))) [nnf transformation 3]
41. ! [X0] : ((~rich(X0) | ~humble(X0) | creative(X0)) & (~creative(X0) | (rich(X0) & humble(X0)))) [flattening 40]
46. ! [X0] : (((brave(X0) | old(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~brave(X0) & ~old(X0)))) [nnf transformation 7]
47. ! [X0] : ((brave(X0) | old(X0) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~brave(X0) & ~old(X0)))) [flattening 46]
59. (? [X0] : brave(X0) | ~creative(mary)) & (creative(mary) | ! [X0] : ~brave(X0)) [nnf transformation 15]
60. (? [X0] : brave(X0) | ~creative(mary)) & (creative(mary) | ! [X1] : ~brave(X1)) [rectify 59]
61. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
62. (brave(sK2) | ~creative(mary)) & (creative(mary) | ! [X1] : ~brave(X1)) [skolemisation 60,61]
69. ? [X0] : (tall(X0) & creative(X0)) => (tall(sK5) & creative(sK5)) [choice axiom]
70. tall(sK5) & creative(sK5) [skolemisation 21,69]
77. ~creative(X0) | humble(X0) [cnf transformation 41]
78. ~creative(X0) | rich(X0) [cnf transformation 41]
87. ~old(X0) | ~rich(X0) | ~old(X0) [cnf transformation 47]
92. brave(X0) | old(X0) | ~rich(X0) | old(X0) [cnf transformation 47]
111. creative(mary) | ~brave(X1) [cnf transformation 62]
119. creative(sK5) [cnf transformation 70]
121. ~humble(mary) [cnf transformation 23]
124. ~old(X0) | ~rich(X0) [duplicate literal removal 87]
125. ~rich(X0) | old(X0) | brave(X0) [duplicate literal removal 92]
192. 15 <=> creative(mary) [avatar definition]
193. creative(mary) <- (15) [avatar component clause 192]
201. 17 <=> ! [X1] : ~brave(X1) [avatar definition]
202. ~brave(X1) <- (17) [avatar component clause 201]
203. 17 | 15 [avatar split clause 111,192,201]
224. humble(mary) <- (15) [resolution 77,193]
225. $false <- (15) [subsumption resolution 224,121]
226. ~15 [avatar contradiction clause 225]
229. rich(sK5) [resolution 78,119]
248. old(sK5) | brave(sK5) [resolution 125,229]
249. old(sK5) <- (17) [subsumption resolution 248,202]
251. ~rich(sK5) <- (17) [resolution 249,124]
261. $false <- (17) [subsumption resolution 251,229]
262. ~17 [avatar contradiction clause 261]
263. $false [avatar sat refutation 203,226,262]
% SZS output end Proof for 2104247113232315798434149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then alice is both not wise and not funny and vice versa.
If paul is not happy or not patient then john is not wise.
If susan is not kind or not tall then mary is brave and vice versa.
Everyone who is either not old or happy is not kind and vice versa.
If someone is either not wise or generous then someone is not patient.
Everyone who is tall is not rich and vice versa.
Everyone who is humble is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
If john is either not happy or curious then someone is quiet.
If someone is both calm and not creative then someone is both not patient and brave.
If someone is not patient then someone is quiet and vice versa.
Everyone who is either not tall or not patient is both not calm and tall.
Someone is either patient or quiet.
Alice is not happy or creative.
Susan is not rich.
Someone is curious or not happy.
Someone is either not happy or not strong.
Someone is quiet. | Alice is creative. | entailment | ((?[X]:(happy(X)))<=>((~wise(alice)&~funny(alice))))&
(((~happy(paul)|~patient(paul)))=>(~wise(john)))&
(((~kind(susan)|~tall(susan)))<=>(brave(mary)))&
(![X]:((~old(X)<~>happy(X))<=>~kind(X)))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:(~patient(X))))&
(![X]:(tall(X)<=>~rich(X)))&
(![X]:(humble(X)<=>(~wise(X)|~creative(X))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(((~happy(john)<~>curious(john)))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((~patient(X)&brave(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~calm(X)&tall(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
((~happy(alice)|creative(alice)))&
(~rich(susan))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(quiet(X))) | creative(alice) | [
"p9",
"p10",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 6625001148903968836242265
% SZS output start Proof for 6625001148903968836242265
10. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (patient(X0) & old(X0))) [input p9]
11. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p10]
18. creative(alice) | ~happy(alice) [input p17]
23. ~creative(alice) [input hypothesis]
52. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 10]
53. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 52]
54. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 11]
99. old(X0) | ~patient(X0) | old(X0) [cnf transformation 53]
102. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 53]
103. ~patient(X0) | ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 53]
106. happy(X0) | patient(X0) [cnf transformation 54]
119. creative(alice) | ~happy(alice) [cnf transformation 18]
125. ~creative(alice) [cnf transformation 23]
127. old(X0) | ~patient(X0) [duplicate literal removal 99]
128. patient(X0) | ~old(X0) [duplicate literal removal 102]
129. ~patient(X0) | ~old(X0) [duplicate literal removal 103]
189. ~old(X0) [subsumption resolution 128,129]
190. ~patient(X0) [subsumption resolution 127,189]
191. happy(X0) [subsumption resolution 106,190]
214. creative(alice) [subsumption resolution 119,191]
217. $false [subsumption resolution 125,214]
% SZS output end Proof for 6625001148903968836242265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both rich and not old and vice versa. Everyone who is both calm and old is either not strong or old. If paul is both not happy and strong then fred is both generous and not calm and vice versa. If paul is either not funny or wise then alice is either not tall or creative. Everyone who is both generous and brave is not calm. If someone is both curious and not old then lucy is both patient and not patient and vice versa. If someone is not strong then someone is both humble and creative and vice versa. If lucy is both kind and creative then someone is either not kind or kind and vice versa. Everyone who is not creative or old is rich or not curious and vice versa. Everyone who is happy or old is both not strong and not patient. Everyone who is both not calm and generous is either not curious or funny and vice versa. Everyone who is brave is either quiet or not quiet. Everyone who is not brave or patient is calm or old and vice versa. Everyone who is not creative is strong and vice versa. Everyone who is not old is not kind. If someone is either not wise or not curious then someone is not strong and vice versa. Someone is either not quiet or not brave. Susan is not rich. Susan is both strong and not funny. Someone is not kind or not tall. Someone is both wise and generous. Someone is not calm. Someone is not curious. Someone is both patient and quiet. | Susan is curious. | contradiction | (![X]:(funny(X)<=>(rich(X)&~old(X))))&
(![X]:((calm(X)&old(X))=>(~strong(X)<~>old(X))))&
(((~happy(paul)&strong(paul)))<=>((generous(fred)&~calm(fred))))&
(((~funny(paul)<~>wise(paul)))=>((~tall(alice)<~>creative(alice))))&
(![X]:((generous(X)&brave(X))=>~calm(X)))&
((?[X]:((curious(X)&~old(X))))<=>((patient(lucy)&~patient(lucy))))&
((?[X]:(~strong(X)))<=>(?[X]:((humble(X)&creative(X)))))&
(((kind(lucy)&creative(lucy)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:((~creative(X)|old(X))<=>(rich(X)|~curious(X))))&
(![X]:((happy(X)|old(X))=>(~strong(X)&~patient(X))))&
(![X]:((~calm(X)&generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:(brave(X)=>(quiet(X)<~>~quiet(X))))&
(![X]:((~brave(X)|patient(X))<=>(calm(X)|old(X))))&
(![X]:(~creative(X)<=>strong(X)))&
(![X]:(~old(X)=>~kind(X)))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(~strong(X))))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(~rich(susan))&
((strong(susan)&~funny(susan)))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((wise(X)&generous(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)&quiet(X)))) | curious(susan) | [
"p5",
"p9",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 3452768681070437205232005
% SZS output start Proof for 3452768681070437205232005
6. ? [X0] : (~old(X0) & curious(X0)) <=> (~patient(lucy) & patient(lucy)) [input p5]
10. ! [X0] : ((old(X0) | happy(X0)) => (~patient(X0) & ~strong(X0))) [input p9]
19. ~funny(susan) & strong(susan) [input p18]
25. curious(susan) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~strong(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 10]
42. (? [X0] : (~old(X0) & curious(X0)) | (patient(lucy) | ~patient(lucy))) & ((~patient(lucy) & patient(lucy)) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 6]
43. (? [X0] : (~old(X0) & curious(X0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X0] : (old(X0) | ~curious(X0))) [flattening 42]
44. (? [X0] : (~old(X0) & curious(X0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : (old(X1) | ~curious(X1))) [rectify 43]
45. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK0) & curious(sK0)) [choice axiom]
46. ((~old(sK0) & curious(sK0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : (old(X1) | ~curious(X1))) [skolemisation 44,45]
97. patient(lucy) | old(X1) | ~curious(X1) [cnf transformation 46]
98. ~patient(lucy) | old(X1) | ~curious(X1) [cnf transformation 46]
115. ~strong(X0) | ~old(X0) [cnf transformation 33]
140. strong(susan) [cnf transformation 19]
149. curious(susan) [cnf transformation 25]
196. 9 <=> ! [X1] : (old(X1) | ~curious(X1)) [avatar definition]
197. ~curious(X1) | old(X1) <- (9) [avatar component clause 196]
199. 10 <=> patient(lucy) [avatar definition]
202. 9 | ~10 [avatar split clause 98,199,196]
203. 9 | 10 [avatar split clause 97,199,196]
300. ~old(susan) [resolution 115,140]
313. old(susan) <- (9) [resolution 197,149]
322. $false <- (9) [subsumption resolution 313,300]
323. ~9 [avatar contradiction clause 322]
324. $false [avatar sat refutation 202,203,323]
% SZS output end Proof for 3452768681070437205232005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and humble then paul is both tall and not happy. Everyone who is both not brave and old is either patient or wise. Everyone who is not calm is both strong and old. If lucy is either not creative or not rich then someone is both generous and wise. If alice is patient then someone is not happy and vice versa. Everyone who is not strong or kind is both not rich and not patient and vice versa. Everyone who is not rich or not wise is both generous and quiet and vice versa. Everyone who is happy is creative and vice versa. If someone is both brave and not funny then someone is either curious or not kind. If mary is not rich or not wise then someone is happy. If john is old or funny then susan is either not wise or calm and vice versa. Everyone who is both not kind and old is not happy. If someone is both not wise and funny then fred is not creative or not strong. If someone is humble then someone is not strong and vice versa. Everyone who is either patient or humble is old. Everyone who is both not happy and generous is not humble or calm. Susan is not creative or not funny. Paul is either rich or not wise. Paul is both brave and not kind. Alice is not rich or humble. Someone is curious or brave. Someone is wise or not strong. Someone is not creative or curious. Fred is both patient and brave. | Susan is not rich. | neutral | ((?[X]:((curious(X)&humble(X))))=>((tall(paul)&~happy(paul))))&
(![X]:((~brave(X)&old(X))=>(patient(X)<~>wise(X))))&
(![X]:(~calm(X)=>(strong(X)&old(X))))&
(((~creative(lucy)<~>~rich(lucy)))=>(?[X]:((generous(X)&wise(X)))))&
((patient(alice))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)|kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~rich(X)|~wise(X))<=>(generous(X)&quiet(X))))&
(![X]:(happy(X)<=>creative(X)))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((curious(X)<~>~kind(X)))))&
(((~rich(mary)|~wise(mary)))=>(?[X]:(happy(X))))&
(((old(john)|funny(john)))<=>((~wise(susan)<~>calm(susan))))&
(![X]:((~kind(X)&old(X))=>~happy(X)))&
((?[X]:((~wise(X)&funny(X))))=>((~creative(fred)|~strong(fred))))&
((?[X]:(humble(X)))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)<~>humble(X))=>old(X)))&
(![X]:((~happy(X)&generous(X))=>(~humble(X)|calm(X))))&
((~creative(susan)|~funny(susan)))&
((rich(paul)<~>~wise(paul)))&
((brave(paul)&~kind(paul)))&
((~rich(alice)|humble(alice)))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((wise(X)|~strong(X))))&
(?[X]:((~creative(X)|curious(X))))&
((patient(fred)&brave(fred))) | ~rich(susan) | []
| null | 0 |
If mary is either rich or not strong then lucy is either not rich or not curious.
Everyone who is calm is either kind or happy.
If someone is both wise and creative then someone is patient or not calm.
Everyone who is either wise or not rich is old or not funny and vice versa.
If someone is not strong or not kind then mary is not wise and vice versa.
Everyone who is funny or not strong is both not generous and brave and vice versa.
Everyone who is both not kind and not happy is either not quiet or patient and vice versa.
Everyone who is either old or not creative is both not calm and tall and vice versa.
Everyone who is tall is not kind or happy and vice versa.
Everyone who is not patient or patient is both not humble and not funny and vice versa.
Everyone who is not old is both not funny and not calm and vice versa.
Everyone who is either not kind or happy is either not brave or not generous.
Everyone who is either not humble or not rich is either not tall or funny and vice versa.
Everyone who is not old or patient is not creative.
If someone is both not generous and funny then fred is both funny and not generous and vice versa.
If someone is rich then someone is not quiet and vice versa.
Someone is not brave or not generous.
Lucy is both strong and not happy.
Someone is not curious or not tall.
Someone is calm.
Fred is both not strong and not creative.
Someone is both rich and not quiet.
Fred is not tall or not humble. | Mary is not rich. | entailment | (((rich(mary)<~>~strong(mary)))=>((~rich(lucy)<~>~curious(lucy))))&
(![X]:(calm(X)=>(kind(X)<~>happy(X))))&
((?[X]:((wise(X)&creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((wise(X)<~>~rich(X))<=>(old(X)|~funny(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>(~wise(mary)))&
(![X]:((funny(X)|~strong(X))<=>(~generous(X)&brave(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((old(X)<~>~creative(X))<=>(~calm(X)&tall(X))))&
(![X]:(tall(X)<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((strong(lucy)&~happy(lucy)))&
(?[X]:((~curious(X)|~tall(X))))&
(?[X]:(calm(X)))&
((~strong(fred)&~creative(fred)))&
(?[X]:((rich(X)&~quiet(X))))&
((~tall(fred)|~humble(fred))) | ~rich(mary) | [
"p3",
"p4",
"p9",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 739053759390770569817900
% SZS output start Proof for 739053759390770569817900
4. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (~funny(X0) | old(X0))) [input p3]
5. ? [X0] : (~kind(X0) | ~strong(X0)) <=> ~wise(mary) [input p4]
10. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p9]
21. ~creative(fred) & ~strong(fred) [input p20]
24. rich(mary) [input hypothesis]
37. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 4]
38. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 37]
39. (? [X0] : (~kind(X0) | ~strong(X0)) | wise(mary)) & (~wise(mary) | ! [X0] : (kind(X0) & strong(X0))) [nnf transformation 5]
40. (? [X0] : (~kind(X0) | ~strong(X0)) | wise(mary)) & (~wise(mary) | ! [X1] : (kind(X1) & strong(X1))) [rectify 39]
41. ? [X0] : (~kind(X0) | ~strong(X0)) => (~kind(sK1) | ~strong(sK1)) [choice axiom]
42. ((~kind(sK1) | ~strong(sK1)) | wise(mary)) & (~wise(mary) | ! [X1] : (kind(X1) & strong(X1))) [skolemisation 40,41]
51. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 10]
52. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 51]
85. ~rich(X0) | wise(X0) | funny(X0) [cnf transformation 38]
88. ~wise(mary) | strong(X1) [cnf transformation 42]
113. ~funny(X0) | patient(X0) [cnf transformation 52]
114. ~funny(X0) | ~patient(X0) [cnf transformation 52]
144. ~strong(fred) [cnf transformation 21]
149. rich(mary) [cnf transformation 24]
155. 2 <=> rich(mary) [avatar definition]
157. rich(mary) <- (2) [avatar component clause 155]
183. 8 <=> wise(mary) [avatar definition]
200. 12 <=> ! [X1] : strong(X1) [avatar definition]
201. strong(X1) <- (12) [avatar component clause 200]
202. 12 | ~8 [avatar split clause 88,183,200]
203. ~funny(X0) [subsumption resolution 113,114]
244. 2 [avatar split clause 149,155]
281. wise(mary) | funny(mary) <- (2) [resolution 85,157]
291. wise(mary) <- (2) [subsumption resolution 281,203]
292. 8 | ~2 [avatar split clause 291,155,183]
297. $false <- (12) [resolution 201,144]
300. ~12 [avatar contradiction clause 297]
301. $false [avatar sat refutation 202,244,292,300]
% SZS output end Proof for 739053759390770569817900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is curious or tall then fred is not creative or not tall.
Everyone who is both not strong and old is not tall.
Everyone who is both happy and not old is kind or not calm and vice versa.
If someone is both not quiet and not old then alice is both not calm and not humble and vice versa.
If someone is either not wise or kind then john is both not calm and calm and vice versa.
Everyone who is funny is brave or not quiet.
Everyone who is not creative or not brave is calm or brave.
Everyone who is not happy or not old is both curious and not humble and vice versa.
Everyone who is not creative is both creative and not happy.
If someone is either not funny or old then someone is kind or tall.
Everyone who is both not humble and curious is either funny or wise.
If someone is both not funny and not wise then someone is both generous and not calm.
Everyone who is either not rich or not funny is either not creative or not rich and vice versa.
Everyone who is both patient and not rich is not creative or not strong.
Everyone who is both quiet and tall is not kind and vice versa.
If someone is old then paul is patient or not happy.
Fred is not curious or not calm.
Mary is either kind or rich.
Someone is both rich and calm.
John is both not old and not patient.
Lucy is both not calm and not rich.
Susan is both not patient and not quiet.
Mary is either generous or not kind. | John is funny. | entailment | (((curious(fred)|tall(fred)))=>((~creative(fred)|~tall(fred))))&
(![X]:((~strong(X)&old(X))=>~tall(X)))&
(![X]:((happy(X)&~old(X))<=>(kind(X)|~calm(X))))&
((?[X]:((~quiet(X)&~old(X))))<=>((~calm(alice)&~humble(alice))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((~calm(john)&calm(john))))&
(![X]:(funny(X)=>(brave(X)|~quiet(X))))&
(![X]:((~creative(X)|~brave(X))=>(calm(X)|brave(X))))&
(![X]:((~happy(X)|~old(X))<=>(curious(X)&~humble(X))))&
(![X]:(~creative(X)=>(creative(X)&~happy(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~humble(X)&curious(X))=>(funny(X)<~>wise(X))))&
((?[X]:((~funny(X)&~wise(X))))=>(?[X]:((generous(X)&~calm(X)))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((patient(X)&~rich(X))=>(~creative(X)|~strong(X))))&
(![X]:((quiet(X)&tall(X))<=>~kind(X)))&
((?[X]:(old(X)))=>((patient(paul)|~happy(paul))))&
((~curious(fred)|~calm(fred)))&
((kind(mary)<~>rich(mary)))&
(?[X]:((rich(X)&calm(X))))&
((~old(john)&~patient(john)))&
((~calm(lucy)&~rich(lucy)))&
((~patient(susan)&~quiet(susan)))&
((generous(mary)<~>~kind(mary))) | funny(john) | [
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 441765803621517706147666
% SZS output start Proof for 441765803621517706147666
9. ! [X0] : (~creative(X0) => (~happy(X0) & creative(X0))) [input p8]
13. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p12]
24. ~funny(john) [input hypothesis]
33. ! [X0] : ((~happy(X0) & creative(X0)) | creative(X0)) [ennf transformation 9]
64. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 13]
94. creative(X0) | creative(X0) [cnf transformation 33]
103. ~rich(X0) | ~creative(X0) | ~rich(X0) | funny(X0) [cnf transformation 64]
109. funny(X0) | rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 64]
128. ~funny(john) [cnf transformation 24]
129. ~rich(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 103]
132. funny(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 109]
133. creative(X0) [duplicate literal removal 94]
215. funny(X0) | rich(X0) [subsumption resolution 132,133]
216. ~rich(X0) | funny(X0) [subsumption resolution 129,133]
217. funny(X0) [subsumption resolution 216,215]
252. $false [subsumption resolution 128,217]
% SZS output end Proof for 441765803621517706147666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not tall then john is both not quiet and not happy and vice versa.
Everyone who is not happy is not curious and vice versa.
Everyone who is not quiet or brave is both kind and not curious and vice versa.
If someone is either humble or strong then mary is either generous or not happy.
If mary is not strong or rich then lucy is not creative or kind and vice versa.
If john is not creative or not generous then someone is not strong.
Everyone who is both curious and not patient is patient and vice versa.
If john is generous then someone is both not patient and creative and vice versa.
Everyone who is either not curious or not humble is both not calm and humble and vice versa.
If mary is either not brave or kind then someone is not creative and vice versa.
If someone is either strong or patient then mary is both not humble and generous and vice versa.
Everyone who is creative or generous is both rich and not wise.
Everyone who is either not rich or not brave is both tall and kind.
If susan is not curious or kind then someone is not creative and vice versa.
Everyone who is both not strong and funny is both not old and curious and vice versa.
Everyone who is either not rich or patient is not quiet or not old and vice versa.
Paul is not calm.
John is creative.
Someone is either rich or tall.
Someone is either patient or quiet.
Someone is either not calm or patient. | John is tall. | entailment | ((?[X]:((strong(X)|~tall(X))))<=>((~quiet(john)&~happy(john))))&
(![X]:(~happy(X)<=>~curious(X)))&
(![X]:((~quiet(X)|brave(X))<=>(kind(X)&~curious(X))))&
((?[X]:((humble(X)<~>strong(X))))=>((generous(mary)<~>~happy(mary))))&
(((~strong(mary)|rich(mary)))<=>((~creative(lucy)|kind(lucy))))&
(((~creative(john)|~generous(john)))=>(?[X]:(~strong(X))))&
(![X]:((curious(X)&~patient(X))<=>patient(X)))&
((generous(john))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:((~curious(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
(((~brave(mary)<~>kind(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((strong(X)<~>patient(X))))<=>((~humble(mary)&generous(mary))))&
(![X]:((creative(X)|generous(X))=>(rich(X)&~wise(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(tall(X)&kind(X))))&
(((~curious(susan)|kind(susan)))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&curious(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~quiet(X)|~old(X))))&
(~calm(paul))&
(creative(john))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((~calm(X)<~>patient(X)))) | tall(john) | [
"p0",
"p6",
"p11",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 697384357018332277360549
% SZS output start Proof for 697384357018332277360549
1. ? [X0] : (~tall(X0) | strong(X0)) <=> (~happy(john) & ~quiet(john)) [input p0]
7. ! [X0] : ((~patient(X0) & curious(X0)) <=> patient(X0)) [input p6]
12. ! [X0] : ((generous(X0) | creative(X0)) => (~wise(X0) & rich(X0))) [input p11]
16. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (~old(X0) | ~quiet(X0))) [input p15]
18. creative(john) [input p17]
22. ~tall(john) [input hypothesis]
23. ! [X0] : ((generous(X0) | creative(X0)) => rich(X0)) [pure predicate removal 12]
26. ! [X0] : (rich(X0) | (~generous(X0) & ~creative(X0))) [ennf transformation 23]
28. (? [X0] : (~tall(X0) | strong(X0)) | (happy(john) | quiet(john))) & ((~happy(john) & ~quiet(john)) | ! [X0] : (tall(X0) & ~strong(X0))) [nnf transformation 1]
29. (? [X0] : (~tall(X0) | strong(X0)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X0] : (tall(X0) & ~strong(X0))) [flattening 28]
30. (? [X0] : (~tall(X0) | strong(X0)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X1] : (tall(X1) & ~strong(X1))) [rectify 29]
31. ? [X0] : (~tall(X0) | strong(X0)) => (~tall(sK0) | strong(sK0)) [choice axiom]
32. ((~tall(sK0) | strong(sK0)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X1] : (tall(X1) & ~strong(X1))) [skolemisation 30,31]
41. ! [X0] : (((~patient(X0) & curious(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | ~curious(X0)))) [nnf transformation 7]
42. ! [X0] : (((~patient(X0) & curious(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | ~curious(X0))) [flattening 41]
66. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 16]
67. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [flattening 66]
78. ~quiet(john) | tall(X1) [cnf transformation 32]
101. ~patient(X0) | ~patient(X0) [cnf transformation 42]
121. ~creative(X0) | rich(X0) [cnf transformation 26]
136. patient(X0) | ~rich(X0) | quiet(X0) [cnf transformation 67]
141. creative(john) [cnf transformation 18]
148. ~tall(john) [cnf transformation 22]
152. ~patient(X0) [duplicate literal removal 101]
154. 1 <=> quiet(john) [avatar definition]
171. 5 <=> ! [X1] : tall(X1) [avatar definition]
172. tall(X1) <- (5) [avatar component clause 171]
178. 5 | ~1 [avatar split clause 78,154,171]
228. 17 <=> creative(john) [avatar definition]
230. creative(john) <- (17) [avatar component clause 228]
292. ~rich(X0) | quiet(X0) [subsumption resolution 136,152]
294. 17 [avatar split clause 141,228]
310. rich(john) <- (17) [resolution 121,230]
320. quiet(john) <- (17) [resolution 292,310]
324. 1 | ~17 [avatar split clause 320,228,154]
325. $false <- (5) [resolution 172,148]
330. ~5 [avatar contradiction clause 325]
331. $false [avatar sat refutation 178,294,324,330]
% SZS output end Proof for 697384357018332277360549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not brave is both not creative and rich.
Everyone who is either humble or old is humble.
Everyone who is tall or not strong is not old or brave and vice versa.
Everyone who is happy or not rich is rich or curious and vice versa.
Everyone who is either not funny or not strong is both kind and not patient and vice versa.
Everyone who is not curious is both not funny and strong and vice versa.
If fred is kind or old then someone is not rich and vice versa.
Everyone who is both wise and rich is both not curious and happy.
Everyone who is both calm and tall is either not kind or not curious.
If fred is both tall and funny then someone is both curious and not kind.
If someone is not humble then paul is not tall and vice versa.
Everyone who is both kind and strong is not humble and vice versa.
Everyone who is wise is both humble and not happy and vice versa.
If alice is both tall and not happy then paul is strong or humble and vice versa.
If someone is funny then john is funny or brave and vice versa.
If someone is either quiet or calm then someone is both not happy and humble.
Lucy is either not kind or not old.
Lucy is both not creative and strong.
Lucy is not strong or not patient.
Lucy is either generous or strong.
Alice is not brave or not kind.
Susan is not quiet or humble.
Paul is either not rich or rich. | Paul is curious. | entailment | (![X]:((~wise(X)&~brave(X))=>(~creative(X)&rich(X))))&
(![X]:((humble(X)<~>old(X))=>humble(X)))&
(![X]:((tall(X)|~strong(X))<=>(~old(X)|brave(X))))&
(![X]:((happy(X)|~rich(X))<=>(rich(X)|curious(X))))&
(![X]:((~funny(X)<~>~strong(X))<=>(kind(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~funny(X)&strong(X))))&
(((kind(fred)|old(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&rich(X))=>(~curious(X)&happy(X))))&
(![X]:((calm(X)&tall(X))=>(~kind(X)<~>~curious(X))))&
(((tall(fred)&funny(fred)))=>(?[X]:((curious(X)&~kind(X)))))&
((?[X]:(~humble(X)))<=>(~tall(paul)))&
(![X]:((kind(X)&strong(X))<=>~humble(X)))&
(![X]:(wise(X)<=>(humble(X)&~happy(X))))&
(((tall(alice)&~happy(alice)))<=>((strong(paul)|humble(paul))))&
((?[X]:(funny(X)))<=>((funny(john)|brave(john))))&
((?[X]:((quiet(X)<~>calm(X))))=>(?[X]:((~happy(X)&humble(X)))))&
((~kind(lucy)<~>~old(lucy)))&
((~creative(lucy)&strong(lucy)))&
((~strong(lucy)|~patient(lucy)))&
((generous(lucy)<~>strong(lucy)))&
((~brave(alice)|~kind(alice)))&
((~quiet(susan)|humble(susan)))&
((~rich(paul)<~>rich(paul))) | curious(paul) | [
"p1",
"p2",
"p4",
"p5",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 152145059942828047812034
% SZS output start Proof for 152145059942828047812034
2. ! [X0] : ((humble(X0) <~> old(X0)) => humble(X0)) [input p1]
3. ! [X0] : ((~strong(X0) | tall(X0)) <=> (brave(X0) | ~old(X0))) [input p2]
5. ! [X0] : ((~funny(X0) <~> ~strong(X0)) <=> (~patient(X0) & kind(X0))) [input p4]
6. ! [X0] : (~curious(X0) <=> (strong(X0) & ~funny(X0))) [input p5]
11. ? [X0] : ~humble(X0) <=> ~tall(paul) [input p10]
12. ! [X0] : ((strong(X0) & kind(X0)) <=> ~humble(X0)) [input p11]
24. ~curious(paul) [input hypothesis]
30. ! [X0] : (humble(X0) | (humble(X0) <=> old(X0))) [ennf transformation 2]
38. ! [X0] : (humble(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) [nnf transformation 30]
39. ! [X0] : (((~strong(X0) | tall(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (strong(X0) & ~tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((~strong(X0) | tall(X0) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | (strong(X0) & ~tall(X0)))) [flattening 39]
43. ! [X0] : ((((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0))))) [nnf transformation 5]
44. ! [X0] : ((((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0))))) [flattening 43]
45. ! [X0] : ((~curious(X0) | (~strong(X0) | funny(X0))) & ((strong(X0) & ~funny(X0)) | curious(X0))) [nnf transformation 6]
46. ! [X0] : ((~curious(X0) | ~strong(X0) | funny(X0)) & ((strong(X0) & ~funny(X0)) | curious(X0))) [flattening 45]
55. (? [X0] : ~humble(X0) | tall(paul)) & (~tall(paul) | ! [X0] : humble(X0)) [nnf transformation 11]
56. (? [X0] : ~humble(X0) | tall(paul)) & (~tall(paul) | ! [X1] : humble(X1)) [rectify 55]
57. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
58. (~humble(sK2) | tall(paul)) & (~tall(paul) | ! [X1] : humble(X1)) [skolemisation 56,57]
59. ! [X0] : (((strong(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | (~strong(X0) | ~kind(X0)))) [nnf transformation 12]
60. ! [X0] : (((strong(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | ~strong(X0) | ~kind(X0))) [flattening 59]
79. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 38]
82. ~strong(X0) | tall(X0) | old(X0) [cnf transformation 40]
88. ~strong(X0) | kind(X0) | funny(X0) [cnf transformation 44]
94. ~funny(X0) | curious(X0) [cnf transformation 46]
95. curious(X0) | strong(X0) [cnf transformation 46]
106. ~tall(paul) | humble(X1) [cnf transformation 58]
108. ~kind(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 60]
136. ~curious(paul) [cnf transformation 24]
139. ~old(X0) | humble(X0) [duplicate literal removal 79]
177. 9 <=> tall(paul) [avatar definition]
178. ~tall(paul) <- (~9) [avatar component clause 177]
186. 11 <=> ! [X1] : humble(X1) [avatar definition]
187. humble(X1) <- (11) [avatar component clause 186]
188. 11 | ~9 [avatar split clause 106,177,186]
190. 12 <=> humble(paul) [avatar definition]
192. ~humble(paul) <- (~12) [avatar component clause 190]
199. 14 <=> strong(paul) [avatar definition]
200. strong(paul) <- (14) [avatar component clause 199]
276. strong(paul) [resolution 95,136]
279. 14 [avatar split clause 276,199]
298. tall(paul) | old(paul) <- (14) [resolution 82,200]
301. old(paul) <- (~9, 14) [subsumption resolution 298,178]
309. humble(paul) <- (~9, 14) [resolution 301,139]
310. $false <- (~9, ~12, 14) [subsumption resolution 309,192]
311. 9 | 12 | ~14 [avatar contradiction clause 310]
332. kind(paul) | funny(paul) <- (14) [resolution 88,200]
335. 34 <=> funny(paul) [avatar definition]
337. funny(paul) <- (34) [avatar component clause 335]
339. 35 <=> kind(paul) [avatar definition]
341. kind(paul) <- (35) [avatar component clause 339]
342. 34 | 35 | ~14 [avatar split clause 332,199,339,335]
343. curious(paul) <- (34) [resolution 337,94]
344. $false <- (34) [subsumption resolution 343,136]
345. ~34 [avatar contradiction clause 344]
369. ~strong(paul) | ~humble(paul) <- (35) [resolution 108,341]
372. ~humble(paul) <- (14, 35) [subsumption resolution 369,200]
373. $false <- (11, 14, 35) [subsumption resolution 372,187]
374. ~11 | ~14 | ~35 [avatar contradiction clause 373]
378. ~12 | ~14 | ~35 [avatar split clause 372,339,199,190]
389. $false [avatar sat refutation 188,279,311,342,345,374,378]
% SZS output end Proof for 152145059942828047812034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not calm is not humble.
If susan is not generous or generous then mary is either not curious or generous.
Everyone who is not old or kind is either kind or not brave and vice versa.
If someone is not old or not generous then someone is either not brave or not generous.
Everyone who is both not funny and humble is both not strong and strong and vice versa.
If someone is not calm or generous then susan is both quiet and not generous and vice versa.
Everyone who is either not brave or funny is either strong or not old and vice versa.
Everyone who is both happy and funny is quiet.
Everyone who is tall or not humble is either calm or tall.
If someone is generous or wise then someone is patient.
If john is not calm or not creative then someone is either not calm or not generous.
If someone is not creative then someone is either not curious or creative and vice versa.
Everyone who is either humble or brave is not brave and vice versa.
If someone is not kind or not quiet then someone is brave and vice versa.
Everyone who is not creative or quiet is calm and vice versa.
If someone is both not tall and funny then alice is either not quiet or calm and vice versa.
Mary is not strong.
Paul is not quiet.
Alice is creative.
Alice is not brave or old.
Someone is both funny and quiet.
Lucy is either not strong or not calm. | Mary is not old. | entailment | (![X]:((~quiet(X)&~calm(X))=>~humble(X)))&
(((~generous(susan)|generous(susan)))=>((~curious(mary)<~>generous(mary))))&
(![X]:((~old(X)|kind(X))<=>(kind(X)<~>~brave(X))))&
((?[X]:((~old(X)|~generous(X))))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((~funny(X)&humble(X))<=>(~strong(X)&strong(X))))&
((?[X]:((~calm(X)|generous(X))))<=>((quiet(susan)&~generous(susan))))&
(![X]:((~brave(X)<~>funny(X))<=>(strong(X)<~>~old(X))))&
(![X]:((happy(X)&funny(X))=>quiet(X)))&
(![X]:((tall(X)|~humble(X))=>(calm(X)<~>tall(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:(patient(X))))&
(((~calm(john)|~creative(john)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~curious(X)<~>creative(X)))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
((?[X]:((~kind(X)|~quiet(X))))<=>(?[X]:(brave(X))))&
(![X]:((~creative(X)|quiet(X))<=>calm(X)))&
((?[X]:((~tall(X)&funny(X))))<=>((~quiet(alice)<~>calm(alice))))&
(~strong(mary))&
(~quiet(paul))&
(creative(alice))&
((~brave(alice)|old(alice)))&
(?[X]:((funny(X)&quiet(X))))&
((~strong(lucy)<~>~calm(lucy))) | ~old(mary) | [
"p2",
"p4",
"p6",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 148762622852632769610402
% SZS output start Proof for 148762622852632769610402
3. ! [X0] : ((kind(X0) | ~old(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p2]
5. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (strong(X0) & ~strong(X0))) [input p4]
7. ! [X0] : ((~brave(X0) <~> funny(X0)) <=> (strong(X0) <~> ~old(X0))) [input p6]
13. ! [X0] : ((humble(X0) <~> brave(X0)) <=> ~brave(X0)) [input p12]
17. ~strong(mary) [input p16]
23. old(mary) [input hypothesis]
37. ! [X0] : (((kind(X0) | ~old(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~kind(X0) & old(X0)))) [nnf transformation 3]
38. ! [X0] : ((kind(X0) | ~old(X0) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~kind(X0) & old(X0)))) [flattening 37]
43. ! [X0] : (((humble(X0) & ~funny(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 5]
44. ! [X0] : (((humble(X0) & ~funny(X0)) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ~humble(X0) | funny(X0))) [flattening 43]
50. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [nnf transformation 7]
60. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | brave(X0)) & (~brave(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 13]
83. brave(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
85. kind(X0) | ~old(X0) | kind(X0) | brave(X0) [cnf transformation 38]
90. ~strong(X0) | ~humble(X0) | funny(X0) [cnf transformation 44]
91. ~humble(X0) | strong(X0) | funny(X0) [cnf transformation 44]
100. ~funny(X0) | strong(X0) | ~brave(X0) | ~old(X0) [cnf transformation 50]
120. ~brave(X0) | humble(X0) | ~brave(X0) [cnf transformation 60]
121. brave(X0) | humble(X0) | brave(X0) [cnf transformation 60]
135. ~strong(mary) [cnf transformation 17]
143. old(mary) [cnf transformation 23]
144. ~brave(X0) | humble(X0) [duplicate literal removal 120]
145. brave(X0) | humble(X0) [duplicate literal removal 121]
147. ~kind(X0) | brave(X0) [duplicate literal removal 83]
148. ~old(X0) | kind(X0) | brave(X0) [duplicate literal removal 85]
183. ~humble(X0) | funny(X0) [subsumption resolution 90,91]
252. humble(X0) [subsumption resolution 144,145]
329. funny(X0) [resolution 183,252]
381. kind(mary) | brave(mary) [resolution 148,143]
391. ~brave(X0) | strong(X0) | ~old(X0) [resolution 100,329]
423. brave(mary) [subsumption resolution 381,147]
433. strong(mary) | ~old(mary) [resolution 391,423]
437. ~old(mary) [subsumption resolution 433,135]
438. $false [subsumption resolution 437,143]
% SZS output end Proof for 148762622852632769610402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not strong is not wise and vice versa. Everyone who is either not rich or not quiet is both brave and curious. Everyone who is creative or patient is either not quiet or not brave and vice versa. Everyone who is not generous is not kind or not creative and vice versa. Everyone who is either not patient or not creative is creative and vice versa. Everyone who is both curious and not quiet is wise and vice versa. Everyone who is not rich or creative is both old and rich and vice versa. Everyone who is either patient or strong is not humble and vice versa. Everyone who is not calm is either not kind or not rich and vice versa. If someone is not tall then susan is old or not happy. Everyone who is rich is old. Everyone who is both not brave and patient is not quiet or not patient. Everyone who is either not strong or rich is brave or calm. Everyone who is calm or not brave is not brave or funny and vice versa. If someone is both not tall and not creative then someone is either wise or funny and vice versa. If someone is both creative and not generous then john is both not creative and not tall and vice versa. Someone is either not creative or generous. Someone is both not patient and happy. Lucy is not patient. Someone is both rich and happy. John is not quiet or not brave. Someone is strong. | Lucy is not rich. | contradiction | (![X]:((~quiet(X)&~strong(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~quiet(X))=>(brave(X)&curious(X))))&
(![X]:((creative(X)|patient(X))<=>(~quiet(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~creative(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>creative(X)))&
(![X]:((curious(X)&~quiet(X))<=>wise(X)))&
(![X]:((~rich(X)|creative(X))<=>(old(X)&rich(X))))&
(![X]:((patient(X)<~>strong(X))<=>~humble(X)))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
((?[X]:(~tall(X)))=>((old(susan)|~happy(susan))))&
(![X]:(rich(X)=>old(X)))&
(![X]:((~brave(X)&patient(X))=>(~quiet(X)|~patient(X))))&
(![X]:((~strong(X)<~>rich(X))=>(brave(X)|calm(X))))&
(![X]:((calm(X)|~brave(X))<=>(~brave(X)|funny(X))))&
((?[X]:((~tall(X)&~creative(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((creative(X)&~generous(X))))<=>((~creative(john)&~tall(john))))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:((~patient(X)&happy(X))))&
(~patient(lucy))&
(?[X]:((rich(X)&happy(X))))&
((~quiet(john)|~brave(john)))&
(?[X]:(strong(X))) | ~rich(lucy) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 6776086871102575002323878
% SZS output start Proof for 6776086871102575002323878
7. ! [X0] : ((creative(X0) | ~rich(X0)) <=> (rich(X0) & old(X0))) [input p6]
23. ~rich(lucy) [input hypothesis]
43. ! [X0] : (((creative(X0) | ~rich(X0)) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | (~creative(X0) & rich(X0)))) [nnf transformation 7]
44. ! [X0] : ((creative(X0) | ~rich(X0) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | (~creative(X0) & rich(X0)))) [flattening 43]
93. rich(X0) | rich(X0) [cnf transformation 44]
128. ~rich(lucy) [cnf transformation 23]
130. rich(X0) [duplicate literal removal 93]
216. $false [subsumption resolution 128,130]
% SZS output end Proof for 6776086871102575002323878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both strong and not happy then someone is either not curious or not creative. Everyone who is both not wise and not old is not calm. If alice is both not old and not strong then lucy is either tall or rich and vice versa. If someone is creative or patient then someone is not kind or calm. If someone is tall then someone is either brave or kind. If someone is creative then someone is either tall or generous and vice versa. Everyone who is both not calm and not humble is calm or old and vice versa. If susan is both not happy and funny then susan is humble. If someone is either happy or patient then lucy is not calm or rich. Everyone who is brave or not humble is not brave and vice versa. If john is either old or humble then someone is funny or humble and vice versa. If someone is either old or not old then susan is patient. Everyone who is both not old and wise is either not kind or kind. Everyone who is both curious and not kind is not happy. Everyone who is both not happy and tall is not creative or strong. Everyone who is not old or not kind is both generous and old. Someone is patient or not humble. Someone is tall or not calm. Someone is both tall and not brave. Susan is not funny. Someone is quiet. Paul is not calm. Someone is either not tall or patient. Susan is either generous or creative. | Susan is patient. | entailment | (((strong(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((~wise(X)&~old(X))=>~calm(X)))&
(((~old(alice)&~strong(alice)))<=>((tall(lucy)<~>rich(lucy))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~kind(X)|calm(X)))))&
((?[X]:(tall(X)))=>(?[X]:((brave(X)<~>kind(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((~calm(X)&~humble(X))<=>(calm(X)|old(X))))&
(((~happy(susan)&funny(susan)))=>(humble(susan)))&
((?[X]:((happy(X)<~>patient(X))))=>((~calm(lucy)|rich(lucy))))&
(![X]:((brave(X)|~humble(X))<=>~brave(X)))&
(((old(john)<~>humble(john)))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((old(X)<~>~old(X))))=>(patient(susan)))&
(![X]:((~old(X)&wise(X))=>(~kind(X)<~>kind(X))))&
(![X]:((curious(X)&~kind(X))=>~happy(X)))&
(![X]:((~happy(X)&tall(X))=>(~creative(X)|strong(X))))&
(![X]:((~old(X)|~kind(X))=>(generous(X)&old(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((tall(X)|~calm(X))))&
(?[X]:((tall(X)&~brave(X))))&
(~funny(susan))&
(?[X]:(quiet(X)))&
(~calm(paul))&
(?[X]:((~tall(X)<~>patient(X))))&
((generous(susan)<~>creative(susan))) | patient(susan) | [
"p11",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7795753701982143632817600
% SZS output start Proof for 7795753701982143632817600
12. ? [X0] : (old(X0) <~> ~old(X0)) => patient(susan) [input p11]
16. ! [X0] : ((~kind(X0) | ~old(X0)) => (old(X0) & generous(X0))) [input p15]
25. ~patient(susan) [input hypothesis]
40. patient(susan) | ! [X0] : (old(X0) <=> ~old(X0)) [ennf transformation 12]
47. ! [X0] : ((old(X0) & generous(X0)) | (kind(X0) & old(X0))) [ennf transformation 16]
74. patient(susan) | ! [X0] : ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))) [nnf transformation 40]
120. patient(susan) | ~old(X0) | ~old(X0) [cnf transformation 74]
128. old(X0) | old(X0) [cnf transformation 47]
140. ~patient(susan) [cnf transformation 25]
141. old(X0) [duplicate literal removal 128]
142. patient(susan) | ~old(X0) [duplicate literal removal 120]
266. 26 <=> ! [X0] : old(X0) [avatar definition]
267. old(X0) <- (26) [avatar component clause 266]
269. 27 <=> patient(susan) [avatar definition]
274. 28 <=> ! [X0] : ~old(X0) [avatar definition]
275. ~old(X0) <- (28) [avatar component clause 274]
276. 28 | 27 [avatar split clause 142,269,274]
277. 26 [avatar split clause 141,266]
308. ~27 [avatar split clause 140,269]
309. $false <- (26, 28) [subsumption resolution 267,275]
310. ~26 | ~28 [avatar contradiction clause 309]
313. $false [avatar sat refutation 276,277,308,310]
% SZS output end Proof for 7795753701982143632817600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or funny is either quiet or wise and vice versa.
Everyone who is not creative or not strong is either creative or wise.
Everyone who is strong or not brave is creative.
Everyone who is either curious or old is both not strong and not funny.
Everyone who is not quiet is brave or generous and vice versa.
If paul is not rich then mary is either not humble or quiet.
Everyone who is strong or old is either not brave or not calm.
If mary is rich or not humble then mary is either generous or not curious.
Everyone who is brave or not kind is not patient and vice versa.
Everyone who is humble or not generous is brave or not patient and vice versa.
Everyone who is either not patient or not brave is either generous or funny and vice versa.
Everyone who is not kind is both not wise and tall.
Everyone who is either not generous or wise is not rich and vice versa.
Everyone who is either funny or not humble is not happy and vice versa.
If susan is both not humble and not kind then someone is both kind and curious and vice versa.
Fred is not old or not happy.
Mary is not old.
Lucy is old or tall.
Someone is either brave or calm.
Lucy is patient or strong.
Someone is strong.
Someone is either not kind or not old. | Susan is not kind. | neutral | (![X]:((~generous(X)<~>funny(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((~creative(X)|~strong(X))=>(creative(X)<~>wise(X))))&
(![X]:((strong(X)|~brave(X))=>creative(X)))&
(![X]:((curious(X)<~>old(X))=>(~strong(X)&~funny(X))))&
(![X]:(~quiet(X)<=>(brave(X)|generous(X))))&
((~rich(paul))=>((~humble(mary)<~>quiet(mary))))&
(![X]:((strong(X)|old(X))=>(~brave(X)<~>~calm(X))))&
(((rich(mary)|~humble(mary)))=>((generous(mary)<~>~curious(mary))))&
(![X]:((brave(X)|~kind(X))<=>~patient(X)))&
(![X]:((humble(X)|~generous(X))<=>(brave(X)|~patient(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(generous(X)<~>funny(X))))&
(![X]:(~kind(X)=>(~wise(X)&tall(X))))&
(![X]:((~generous(X)<~>wise(X))<=>~rich(X)))&
(![X]:((funny(X)<~>~humble(X))<=>~happy(X)))&
(((~humble(susan)&~kind(susan)))<=>(?[X]:((kind(X)&curious(X)))))&
((~old(fred)|~happy(fred)))&
(~old(mary))&
((old(lucy)|tall(lucy)))&
(?[X]:((brave(X)<~>calm(X))))&
((patient(lucy)|strong(lucy)))&
(?[X]:(strong(X)))&
(?[X]:((~kind(X)<~>~old(X)))) | ~kind(susan) | []
| null | 0 |
Everyone who is either happy or not funny is both humble and not tall and vice versa.
Everyone who is creative or not generous is both not strong and wise.
Everyone who is rich or not strong is humble.
If john is either not rich or not curious then john is old and vice versa.
If fred is both not wise and not strong then someone is patient.
Everyone who is not curious is tall and vice versa.
If mary is not kind or old then someone is both not rich and not happy.
If alice is not funny then susan is both kind and not old and vice versa.
If alice is not quiet or quiet then someone is strong or not happy and vice versa.
If someone is either not old or humble then paul is not strong.
Everyone who is brave or not generous is either brave or not creative and vice versa.
Everyone who is both not brave and not kind is not kind or not old.
Everyone who is not old is both humble and not old.
If paul is both not strong and not calm then someone is both rich and calm.
John is curious or not quiet.
Someone is not kind or humble.
Paul is humble.
Someone is either not funny or creative.
Mary is either not tall or not quiet.
Susan is either not curious or old. | Susan is funny. | neutral | (![X]:((happy(X)<~>~funny(X))<=>(humble(X)&~tall(X))))&
(![X]:((creative(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((rich(X)|~strong(X))=>humble(X)))&
(((~rich(john)<~>~curious(john)))<=>(old(john)))&
(((~wise(fred)&~strong(fred)))=>(?[X]:(patient(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(((~kind(mary)|old(mary)))=>(?[X]:((~rich(X)&~happy(X)))))&
((~funny(alice))<=>((kind(susan)&~old(susan))))&
(((~quiet(alice)|quiet(alice)))<=>(?[X]:((strong(X)|~happy(X)))))&
((?[X]:((~old(X)<~>humble(X))))=>(~strong(paul)))&
(![X]:((brave(X)|~generous(X))<=>(brave(X)<~>~creative(X))))&
(![X]:((~brave(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:(~old(X)=>(humble(X)&~old(X))))&
(((~strong(paul)&~calm(paul)))=>(?[X]:((rich(X)&calm(X)))))&
((curious(john)|~quiet(john)))&
(?[X]:((~kind(X)|humble(X))))&
(humble(paul))&
(?[X]:((~funny(X)<~>creative(X))))&
((~tall(mary)<~>~quiet(mary)))&
((~curious(susan)<~>old(susan))) | funny(susan) | []
| null | 0 |
If susan is kind then someone is either happy or not tall and vice versa.
If someone is both funny and not calm then susan is both not patient and generous.
Everyone who is quiet or not strong is not strong or not kind and vice versa.
If someone is both curious and kind then someone is both not rich and generous and vice versa.
If susan is both not quiet and not generous then someone is funny.
Everyone who is brave is not funny and vice versa.
Everyone who is calm is both not old and calm and vice versa.
If paul is not curious then john is patient and vice versa.
Everyone who is brave or not old is either not quiet or strong.
If john is not funny or not calm then someone is both not humble and not curious.
Everyone who is strong is both not strong and strong and vice versa.
Everyone who is both strong and funny is not quiet and vice versa.
If someone is both old and kind then lucy is either creative or not kind.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Lucy is either generous or tall.
John is not brave.
Someone is either not curious or strong.
Someone is wise.
Susan is not wise.
Someone is calm or not tall.
Paul is not humble or not calm.
Paul is both happy and not kind. | Lucy is funny. | entailment | ((kind(susan))<=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:((funny(X)&~calm(X))))=>((~patient(susan)&generous(susan))))&
(![X]:((quiet(X)|~strong(X))<=>(~strong(X)|~kind(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(((~quiet(susan)&~generous(susan)))=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:(calm(X)<=>(~old(X)&calm(X))))&
((~curious(paul))<=>(patient(john)))&
(![X]:((brave(X)|~old(X))=>(~quiet(X)<~>strong(X))))&
(((~funny(john)|~calm(john)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:(strong(X)<=>(~strong(X)&strong(X))))&
(![X]:((strong(X)&funny(X))<=>~quiet(X)))&
((?[X]:((old(X)&kind(X))))=>((creative(lucy)<~>~kind(lucy))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((generous(lucy)<~>tall(lucy)))&
(~brave(john))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(wise(X)))&
(~wise(susan))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul))) | funny(lucy) | [
"p5",
"p8",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1239036169469862622189177
% SZS output start Proof for 1239036169469862622189177
6. ! [X0] : (brave(X0) <=> ~funny(X0)) [input p5]
9. ! [X0] : ((~old(X0) | brave(X0)) => (~quiet(X0) <~> strong(X0))) [input p8]
11. ! [X0] : (strong(X0) <=> (strong(X0) & ~strong(X0))) [input p10]
12. ! [X0] : ((funny(X0) & strong(X0)) <=> ~quiet(X0)) [input p11]
25. ~funny(lucy) [input hypothesis]
33. ! [X0] : ((~quiet(X0) <~> strong(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 9]
54. ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))) [nnf transformation 6]
58. ! [X0] : (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (old(X0) & ~brave(X0))) [nnf transformation 33]
61. ! [X0] : ((strong(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 11]
62. ! [X0] : ((strong(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [flattening 61]
63. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) | ~strong(X0)))) [nnf transformation 12]
64. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | ~funny(X0) | ~strong(X0))) [flattening 63]
94. brave(X0) | funny(X0) [cnf transformation 54]
100. ~brave(X0) | ~quiet(X0) | strong(X0) [cnf transformation 58]
106. ~strong(X0) | ~strong(X0) [cnf transformation 62]
110. strong(X0) | quiet(X0) [cnf transformation 64]
131. ~funny(lucy) [cnf transformation 25]
132. ~strong(X0) [duplicate literal removal 106]
228. quiet(X0) [subsumption resolution 110,132]
282. ~quiet(X0) | strong(X0) | funny(X0) [resolution 100,94]
283. strong(X0) | funny(X0) [subsumption resolution 282,228]
284. funny(X0) [subsumption resolution 283,132]
285. $false [resolution 284,131]
% SZS output end Proof for 1239036169469862622189177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or wise is either not humble or tall and vice versa. Everyone who is not tall is both not wise and not strong. Everyone who is either funny or rich is calm or rich and vice versa. Everyone who is both strong and not wise is not funny or humble. Everyone who is both not brave and not strong is not funny or wise. If lucy is both not strong and not patient then paul is not humble and vice versa. If paul is either brave or not funny then someone is both calm and not quiet and vice versa. If mary is both not patient and brave then lucy is either tall or not tall. Everyone who is both not funny and curious is either kind or funny and vice versa. Everyone who is humble is both happy and kind and vice versa. Everyone who is both brave and not tall is not curious or tall. If john is not brave then john is both strong and not happy. Everyone who is strong or rich is both patient and rich. Everyone who is either kind or not kind is both wise and not strong. Everyone who is both not generous and not quiet is both funny and not kind. If someone is either not generous or humble then mary is either not generous or not humble and vice versa. Alice is either rich or not quiet. Someone is wise or not tall. Lucy is both generous and curious. Someone is not tall or not brave. Mary is funny or kind. John is either generous or kind. Someone is tall. | Mary is kind. | entailment | (![X]:((~tall(X)|wise(X))<=>(~humble(X)<~>tall(X))))&
(![X]:(~tall(X)=>(~wise(X)&~strong(X))))&
(![X]:((funny(X)<~>rich(X))<=>(calm(X)|rich(X))))&
(![X]:((strong(X)&~wise(X))=>(~funny(X)|humble(X))))&
(![X]:((~brave(X)&~strong(X))=>(~funny(X)|wise(X))))&
(((~strong(lucy)&~patient(lucy)))<=>(~humble(paul)))&
(((brave(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&~quiet(X)))))&
(((~patient(mary)&brave(mary)))=>((tall(lucy)<~>~tall(lucy))))&
(![X]:((~funny(X)&curious(X))<=>(kind(X)<~>funny(X))))&
(![X]:(humble(X)<=>(happy(X)&kind(X))))&
(![X]:((brave(X)&~tall(X))=>(~curious(X)|tall(X))))&
((~brave(john))=>((strong(john)&~happy(john))))&
(![X]:((strong(X)|rich(X))=>(patient(X)&rich(X))))&
(![X]:((kind(X)<~>~kind(X))=>(wise(X)&~strong(X))))&
(![X]:((~generous(X)&~quiet(X))=>(funny(X)&~kind(X))))&
((?[X]:((~generous(X)<~>humble(X))))<=>((~generous(mary)<~>~humble(mary))))&
((rich(alice)<~>~quiet(alice)))&
(?[X]:((wise(X)|~tall(X))))&
((generous(lucy)&curious(lucy)))&
(?[X]:((~tall(X)|~brave(X))))&
((funny(mary)|kind(mary)))&
((generous(john)<~>kind(john)))&
(?[X]:(tall(X))) | kind(mary) | [
"p8",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 113774804219485169785570
% SZS output start Proof for 113774804219485169785570
9. ! [X0] : ((curious(X0) & ~funny(X0)) <=> (kind(X0) <~> funny(X0))) [input p8]
21. kind(mary) | funny(mary) [input p20]
24. ~kind(mary) [input hypothesis]
50. ! [X0] : (((curious(X0) & ~funny(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~curious(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((curious(X0) & ~funny(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | ~curious(X0) | funny(X0))) [flattening 50]
97. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 51]
130. kind(mary) | funny(mary) [cnf transformation 21]
134. ~kind(mary) [cnf transformation 24]
141. ~funny(X0) | kind(X0) [duplicate literal removal 97]
253. kind(mary) [subsumption resolution 130,141]
264. $false [subsumption resolution 134,253]
% SZS output end Proof for 113774804219485169785570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not brave is strong and vice versa.
Everyone who is strong or not old is either wise or curious.
Everyone who is not tall or kind is old or not generous and vice versa.
If fred is both humble and not happy then lucy is not wise.
If someone is patient then alice is wise or not brave.
If someone is either tall or not brave then someone is both not quiet and not generous and vice versa.
If someone is creative or not strong then someone is rich.
If someone is not wise or quiet then someone is not brave or old and vice versa.
If someone is funny or tall then paul is not wise.
If someone is both kind and happy then mary is generous.
If someone is quiet then someone is not strong or not kind.
Everyone who is kind is both not brave and not curious and vice versa.
Everyone who is generous is calm or funny.
Everyone who is calm is not humble and vice versa.
If fred is both not old and creative then john is both humble and tall and vice versa.
If someone is not old or not curious then susan is both strong and not creative and vice versa.
John is either kind or rich.
Lucy is both happy and quiet.
Someone is both patient and calm.
Someone is both creative and happy.
Someone is creative or kind.
Susan is not wise.
Susan is both patient and creative. | Mary is creative. | neutral | (![X]:((~kind(X)|~brave(X))<=>strong(X)))&
(![X]:((strong(X)|~old(X))=>(wise(X)<~>curious(X))))&
(![X]:((~tall(X)|kind(X))<=>(old(X)|~generous(X))))&
(((humble(fred)&~happy(fred)))=>(~wise(lucy)))&
((?[X]:(patient(X)))=>((wise(alice)|~brave(alice))))&
((?[X]:((tall(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((?[X]:((creative(X)|~strong(X))))=>(?[X]:(rich(X))))&
((?[X]:((~wise(X)|quiet(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:((funny(X)|tall(X))))=>(~wise(paul)))&
((?[X]:((kind(X)&happy(X))))=>(generous(mary)))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:(kind(X)<=>(~brave(X)&~curious(X))))&
(![X]:(generous(X)=>(calm(X)|funny(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(((~old(fred)&creative(fred)))<=>((humble(john)&tall(john))))&
((?[X]:((~old(X)|~curious(X))))<=>((strong(susan)&~creative(susan))))&
((kind(john)<~>rich(john)))&
((happy(lucy)&quiet(lucy)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((creative(X)|kind(X))))&
(~wise(susan))&
((patient(susan)&creative(susan))) | creative(mary) | []
| null | 0 |
If susan is not quiet or not generous then someone is both patient and not curious.
Everyone who is either not calm or not happy is either not old or not wise and vice versa.
If paul is curious or not creative then paul is both not funny and not old and vice versa.
Everyone who is not brave is brave or not tall.
Everyone who is both not curious and happy is not tall and vice versa.
If someone is both not brave and not wise then someone is both not wise and not tall and vice versa.
If mary is both not rich and patient then someone is not humble.
Everyone who is creative or old is either brave or tall.
Everyone who is generous or happy is not wise and vice versa.
Everyone who is both funny and strong is both not calm and tall and vice versa.
Everyone who is brave is either kind or wise.
If someone is curious then susan is both not tall and not rich and vice versa.
Everyone who is either quiet or strong is either creative or tall.
Everyone who is not brave is both tall and not patient.
Everyone who is both old and not humble is both not happy and not humble and vice versa.
If mary is not wise or funny then fred is both not patient and not tall and vice versa.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Lucy is generous or not happy. | Mary is not old. | entailment | (((~quiet(susan)|~generous(susan)))=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~old(X)<~>~wise(X))))&
(((curious(paul)|~creative(paul)))<=>((~funny(paul)&~old(paul))))&
(![X]:(~brave(X)=>(brave(X)|~tall(X))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~rich(mary)&patient(mary)))=>(?[X]:(~humble(X))))&
(![X]:((creative(X)|old(X))=>(brave(X)<~>tall(X))))&
(![X]:((generous(X)|happy(X))<=>~wise(X)))&
(![X]:((funny(X)&strong(X))<=>(~calm(X)&tall(X))))&
(![X]:(brave(X)=>(kind(X)<~>wise(X))))&
((?[X]:(curious(X)))<=>((~tall(susan)&~rich(susan))))&
(![X]:((quiet(X)<~>strong(X))=>(creative(X)<~>tall(X))))&
(![X]:(~brave(X)=>(tall(X)&~patient(X))))&
(![X]:((old(X)&~humble(X))<=>(~happy(X)&~humble(X))))&
(((~wise(mary)|funny(mary)))<=>((~patient(fred)&~tall(fred))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((generous(lucy)|~happy(lucy))) | ~old(mary) | [
"p3",
"p4",
"p5",
"p7",
"p8",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2064780875566909944148433
% SZS output start Proof for 2064780875566909944148433
4. ! [X0] : (~brave(X0) => (~tall(X0) | brave(X0))) [input p3]
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X0] : (~tall(X0) & ~wise(X0)) [input p5]
8. ! [X0] : ((old(X0) | creative(X0)) => (brave(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> ~wise(X0)) [input p8]
14. ! [X0] : (~brave(X0) => (~patient(X0) & tall(X0))) [input p13]
16. (funny(mary) | ~wise(mary)) <=> (~tall(fred) & ~patient(fred)) [input p15]
22. old(mary) [input hypothesis]
23. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X1] : (~tall(X1) & ~wise(X1)) [rectify 6]
25. ! [X0] : ((~tall(X0) | brave(X0)) | brave(X0)) [ennf transformation 4]
26. ! [X0] : (~tall(X0) | brave(X0) | brave(X0)) [flattening 25]
29. ! [X0] : ((brave(X0) <~> tall(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
32. ! [X0] : ((~patient(X0) & tall(X0)) | brave(X0)) [ennf transformation 14]
38. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | ~happy(X0) | curious(X0))) [flattening 38]
40. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X1] : (~tall(X1) & ~wise(X1)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 23]
41. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X2] : (~tall(X2) & ~wise(X2)) | ! [X3] : (wise(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK1) & ~brave(sK1)) [choice axiom]
43. ? [X2] : (~tall(X2) & ~wise(X2)) => (~tall(sK2) & ~wise(sK2)) [choice axiom]
44. ((~wise(sK1) & ~brave(sK1)) | ! [X1] : (tall(X1) | wise(X1))) & ((~tall(sK2) & ~wise(sK2)) | ! [X3] : (wise(X3) | brave(X3))) [skolemisation 41,43,42]
47. ! [X0] : (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 29]
48. ! [X0] : (((happy(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((happy(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [flattening 48]
61. ((funny(mary) | ~wise(mary)) | (tall(fred) | patient(fred))) & ((~tall(fred) & ~patient(fred)) | (~funny(mary) & wise(mary))) [nnf transformation 16]
62. (funny(mary) | ~wise(mary) | tall(fred) | patient(fred)) & ((~tall(fred) & ~patient(fred)) | (~funny(mary) & wise(mary))) [flattening 61]
87. ~tall(X0) | brave(X0) | brave(X0) [cnf transformation 26]
90. tall(X0) | happy(X0) [cnf transformation 39]
93. ~brave(sK1) | tall(X1) | wise(X1) [cnf transformation 44]
99. ~tall(X0) | ~brave(X0) | ~old(X0) [cnf transformation 47]
101. ~wise(X0) | ~happy(X0) [cnf transformation 49]
116. tall(X0) | brave(X0) [cnf transformation 32]
124. ~tall(fred) | wise(mary) [cnf transformation 62]
133. old(mary) [cnf transformation 22]
134. ~tall(X0) | brave(X0) [duplicate literal removal 87]
177. 9 <=> ! [X1] : (tall(X1) | wise(X1)) [avatar definition]
178. tall(X1) | wise(X1) <- (9) [avatar component clause 177]
185. 11 <=> brave(sK1) [avatar definition]
187. ~brave(sK1) <- (~11) [avatar component clause 185]
188. 9 | ~11 [avatar split clause 93,185,177]
215. ~tall(X0) | ~old(X0) [subsumption resolution 99,134]
237. brave(X0) [subsumption resolution 116,134]
243. 23 <=> tall(fred) [avatar definition]
244. ~tall(fred) <- (~23) [avatar component clause 243]
247. 24 <=> wise(mary) [avatar definition]
248. wise(mary) <- (24) [avatar component clause 247]
256. 24 | ~23 [avatar split clause 124,243,247]
296. $false <- (~11) [subsumption resolution 187,237]
297. 11 [avatar contradiction clause 296]
301. happy(fred) <- (~23) [resolution 90,244]
310. wise(fred) <- (9, ~23) [resolution 178,244]
317. ~old(X1) | happy(X1) [resolution 215,90]
333. ~happy(fred) <- (9, ~23) [resolution 310,101]
335. $false <- (9, ~23) [subsumption resolution 333,301]
336. ~9 | 23 [avatar contradiction clause 335]
339. ~happy(mary) <- (24) [resolution 248,101]
419. happy(mary) [resolution 317,133]
422. $false <- (24) [subsumption resolution 419,339]
423. ~24 [avatar contradiction clause 422]
428. $false [avatar sat refutation 188,256,297,336,423]
% SZS output end Proof for 2064780875566909944148433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet then someone is brave and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is not happy or patient is not strong.
If john is either old or happy then john is either curious or happy and vice versa.
Everyone who is both not rich and old is curious or generous.
Everyone who is both not creative and creative is happy and vice versa.
If alice is humble then someone is both not wise and strong and vice versa.
Everyone who is not quiet is not calm.
Everyone who is both brave and curious is not tall or not rich and vice versa.
If paul is either not funny or not calm then someone is not quiet or not creative and vice versa.
Everyone who is either not strong or tall is both not kind and generous.
If someone is patient then mary is either humble or calm.
Everyone who is both not tall and patient is either not old or not brave and vice versa.
Everyone who is both not humble and brave is both not brave and not rich.
Everyone who is not generous is curious or not happy.
Paul is not old or not funny.
Paul is not funny or funny.
Susan is not wise.
Someone is humble or not brave.
Fred is not happy or not generous.
John is either rich or not generous.
Someone is both curious and not creative. | John is funny. | neutral | ((~quiet(paul))<=>(?[X]:(brave(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~happy(X)|patient(X))=>~strong(X)))&
(((old(john)<~>happy(john)))<=>((curious(john)<~>happy(john))))&
(![X]:((~rich(X)&old(X))=>(curious(X)|generous(X))))&
(![X]:((~creative(X)&creative(X))<=>happy(X)))&
((humble(alice))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:(~quiet(X)=>~calm(X)))&
(![X]:((brave(X)&curious(X))<=>(~tall(X)|~rich(X))))&
(((~funny(paul)<~>~calm(paul)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(~kind(X)&generous(X))))&
((?[X]:(patient(X)))=>((humble(mary)<~>calm(mary))))&
(![X]:((~tall(X)&patient(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((~humble(X)&brave(X))=>(~brave(X)&~rich(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((~old(paul)|~funny(paul)))&
((~funny(paul)|funny(paul)))&
(~wise(susan))&
(?[X]:((humble(X)|~brave(X))))&
((~happy(fred)|~generous(fred)))&
((rich(john)<~>~generous(john)))&
(?[X]:((curious(X)&~creative(X)))) | funny(john) | []
| null | 0 |
Everyone who is humble or not creative is either not calm or not rich.
If someone is either tall or not old then paul is both not quiet and funny.
Everyone who is either curious or old is both not kind and brave and vice versa.
If mary is either funny or strong then someone is both humble and not wise.
If someone is not rich then fred is either not creative or tall and vice versa.
If someone is either quiet or not quiet then someone is not wise or creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
Someone is not old or not quiet.
Someone is not rich or wise.
Lucy is either happy or not strong.
Someone is either not patient or old.
Someone is not happy or not tall. | Lucy is happy. | entailment | (![X]:((humble(X)|~creative(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((tall(X)<~>~old(X))))=>((~quiet(paul)&funny(paul))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~rich(X)|wise(X))))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((~happy(X)|~tall(X)))) | happy(lucy) | [
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 356989860374905122651678
% SZS output start Proof for 356989860374905122651678
13. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p12]
22. ~happy(lucy) [input hypothesis]
62. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 13]
63. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 62]
125. happy(X0) | ~old(X0) [cnf transformation 63]
126. happy(X0) | old(X0) [cnf transformation 63]
142. ~happy(lucy) [cnf transformation 22]
252. happy(X0) [subsumption resolution 125,126]
286. $false [subsumption resolution 142,252]
% SZS output end Proof for 356989860374905122651678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or brave is both not funny and old.
If lucy is both kind and funny then susan is either not tall or not kind.
If lucy is generous then alice is creative.
Everyone who is old is either patient or happy.
Everyone who is both not patient and not tall is wise or not curious and vice versa.
Everyone who is not humble is both not patient and not curious and vice versa.
Everyone who is strong or not old is both not humble and tall and vice versa.
If john is patient then someone is curious.
If someone is either not rich or not patient then someone is not rich or not brave and vice versa.
Everyone who is either not wise or not patient is not old and vice versa.
Everyone who is not quiet is both not patient and not curious.
Everyone who is not happy or not rich is curious and vice versa.
If someone is strong or not brave then alice is not funny or not humble.
If alice is generous then paul is both strong and old and vice versa.
Someone is not strong.
Paul is creative or not rich.
Alice is both not calm and not kind. | Alice is funny. | contradiction | (![X]:((~tall(X)|brave(X))=>(~funny(X)&old(X))))&
(((kind(lucy)&funny(lucy)))=>((~tall(susan)<~>~kind(susan))))&
((generous(lucy))=>(creative(alice)))&
(![X]:(old(X)=>(patient(X)<~>happy(X))))&
(![X]:((~patient(X)&~tall(X))<=>(wise(X)|~curious(X))))&
(![X]:(~humble(X)<=>(~patient(X)&~curious(X))))&
(![X]:((strong(X)|~old(X))<=>(~humble(X)&tall(X))))&
((patient(john))=>(?[X]:(curious(X))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~wise(X)<~>~patient(X))<=>~old(X)))&
(![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((~happy(X)|~rich(X))<=>curious(X)))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(?[X]:(~strong(X)))&
((creative(paul)|~rich(paul)))&
((~calm(alice)&~kind(alice))) | funny(alice) | [
"p0",
"p4",
"p5",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 469564508169990666569593
% SZS output start Proof for 469564508169990666569593
1. ! [X0] : ((brave(X0) | ~tall(X0)) => (old(X0) & ~funny(X0))) [input p0]
5. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (~curious(X0) | wise(X0))) [input p4]
6. ! [X0] : (~humble(X0) <=> (~curious(X0) & ~patient(X0))) [input p5]
13. ? [X0] : (~brave(X0) | strong(X0)) => (~humble(alice) | ~funny(alice)) [input p12]
18. funny(alice) [input hypothesis]
24. ! [X0] : ((old(X0) & ~funny(X0)) | (~brave(X0) & tall(X0))) [ennf transformation 1]
29. (~humble(alice) | ~funny(alice)) | ! [X0] : (brave(X0) & ~strong(X0)) [ennf transformation 13]
30. ~humble(alice) | ~funny(alice) | ! [X0] : (brave(X0) & ~strong(X0)) [flattening 29]
33. ! [X0] : (((~tall(X0) & ~patient(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (tall(X0) | patient(X0)))) [nnf transformation 5]
34. ! [X0] : (((~tall(X0) & ~patient(X0)) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | tall(X0) | patient(X0))) [flattening 33]
35. ! [X0] : ((~humble(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | humble(X0))) [nnf transformation 6]
36. ! [X0] : ((~humble(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | humble(X0))) [flattening 35]
53. ~funny(X0) | tall(X0) [cnf transformation 24]
54. ~funny(X0) | ~brave(X0) [cnf transformation 24]
65. ~tall(X0) | curious(X0) [cnf transformation 34]
67. ~curious(X0) | humble(X0) [cnf transformation 36]
89. ~humble(alice) | ~funny(alice) | brave(X0) [cnf transformation 30]
95. funny(alice) [cnf transformation 18]
125. 7 <=> ! [X1] : brave(X1) [avatar definition]
126. brave(X1) <- (7) [avatar component clause 125]
161. 15 <=> funny(alice) [avatar definition]
162. funny(alice) <- (15) [avatar component clause 161]
165. 16 <=> humble(alice) [avatar definition]
168. 7 | ~15 | ~16 [avatar split clause 89,165,161,125]
188. 15 [avatar split clause 95,161]
189. tall(alice) <- (15) [resolution 53,162]
190. ~brave(alice) <- (15) [resolution 54,162]
192. curious(alice) <- (15) [resolution 65,189]
194. humble(alice) <- (15) [resolution 67,192]
198. 16 | ~15 [avatar split clause 194,161,165]
199. $false <- (7, 15) [resolution 126,190]
201. ~7 | ~15 [avatar contradiction clause 199]
202. $false [avatar sat refutation 168,188,198,201]
% SZS output end Proof for 469564508169990666569593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both wise and not generous and vice versa. If mary is both wise and not kind then someone is either humble or brave. Everyone who is both happy and strong is not humble. Everyone who is not happy or not tall is not humble. Everyone who is either not brave or not happy is either not quiet or not happy. Everyone who is both quiet and not curious is either old or not strong. If someone is not funny then someone is both not calm and not brave. Everyone who is creative is not creative or happy. Everyone who is not strong is both not funny and not brave and vice versa. If mary is either quiet or generous then someone is old or not happy and vice versa. Everyone who is not quiet is either not quiet or funny. Everyone who is either not curious or not humble is both not tall and rich. Everyone who is either not creative or kind is either not quiet or not wise. Everyone who is either not kind or quiet is not calm or happy and vice versa. If lucy is not wise or not kind then someone is tall and vice versa. Someone is both strong and not humble. Someone is not funny. Alice is not wise or generous. Someone is both not calm and not tall. Someone is funny or humble. Lucy is both quiet and happy. Someone is brave or not calm. | Mary is not tall. | entailment | (![X]:(~wise(X)<=>(wise(X)&~generous(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((happy(X)&strong(X))=>~humble(X)))&
(![X]:((~happy(X)|~tall(X))=>~humble(X)))&
(![X]:((~brave(X)<~>~happy(X))=>(~quiet(X)<~>~happy(X))))&
(![X]:((quiet(X)&~curious(X))=>(old(X)<~>~strong(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:(creative(X)=>(~creative(X)|happy(X))))&
(![X]:(~strong(X)<=>(~funny(X)&~brave(X))))&
(((quiet(mary)<~>generous(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:(~quiet(X)=>(~quiet(X)<~>funny(X))))&
(![X]:((~curious(X)<~>~humble(X))=>(~tall(X)&rich(X))))&
(![X]:((~creative(X)<~>kind(X))=>(~quiet(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~calm(X)|happy(X))))&
(((~wise(lucy)|~kind(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:((strong(X)&~humble(X))))&
(?[X]:(~funny(X)))&
((~wise(alice)|generous(alice)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((funny(X)|humble(X))))&
((quiet(lucy)&happy(lucy)))&
(?[X]:((brave(X)|~calm(X)))) | ~tall(mary) | [
"p0",
"p13",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 2923652145731844256299263
% SZS output start Proof for 2923652145731844256299263
1. ! [X0] : (~wise(X0) <=> (~generous(X0) & wise(X0))) [input p0]
14. ! [X0] : ((~kind(X0) <~> quiet(X0)) <=> (happy(X0) | ~calm(X0))) [input p13]
15. (~kind(lucy) | ~wise(lucy)) <=> ? [X0] : tall(X0) [input p14]
21. happy(lucy) & quiet(lucy) [input p20]
23. tall(mary) [input hypothesis]
40. ! [X0] : ((~wise(X0) | (generous(X0) | ~wise(X0))) & ((~generous(X0) & wise(X0)) | wise(X0))) [nnf transformation 1]
41. ! [X0] : ((~wise(X0) | generous(X0) | ~wise(X0)) & ((~generous(X0) & wise(X0)) | wise(X0))) [flattening 40]
59. ! [X0] : ((((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0))))) [flattening 59]
61. ((~kind(lucy) | ~wise(lucy)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (kind(lucy) & wise(lucy))) [nnf transformation 15]
62. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (kind(lucy) & wise(lucy))) [flattening 61]
63. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | (kind(lucy) & wise(lucy))) [rectify 62]
64. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
65. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (tall(sK3) | (kind(lucy) & wise(lucy))) [skolemisation 63,64]
76. wise(X0) | wise(X0) [cnf transformation 41]
115. ~quiet(X0) | kind(X0) | ~happy(X0) [cnf transformation 60]
118. ~kind(lucy) | ~wise(lucy) | ~tall(X0) [cnf transformation 65]
126. quiet(lucy) [cnf transformation 21]
127. happy(lucy) [cnf transformation 21]
129. tall(mary) [cnf transformation 23]
134. wise(X0) [duplicate literal removal 76]
196. ~kind(lucy) | ~tall(X0) [subsumption resolution 118,134]
198. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
199. ~tall(X0) <- (13) [avatar component clause 198]
201. 14 <=> kind(lucy) [avatar definition]
203. ~kind(lucy) <- (~14) [avatar component clause 201]
204. 13 | ~14 [avatar split clause 196,201,198]
228. $false <- (13) [resolution 199,129]
229. ~13 [avatar contradiction clause 228]
293. kind(lucy) | ~happy(lucy) [resolution 115,126]
294. ~happy(lucy) <- (~14) [subsumption resolution 293,203]
295. $false <- (~14) [subsumption resolution 294,127]
296. 14 [avatar contradiction clause 295]
297. $false [avatar sat refutation 204,229,296]
% SZS output end Proof for 2923652145731844256299263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and calm is either not creative or not strong.
Everyone who is generous is old and vice versa.
Everyone who is not wise is both humble and not brave and vice versa.
If someone is both creative and not happy then someone is both not humble and not creative and vice versa.
Everyone who is not wise is both calm and not funny and vice versa.
Everyone who is either not calm or not rich is both not patient and not funny and vice versa.
Everyone who is both quiet and funny is both not tall and not wise.
Everyone who is not quiet is rich.
If someone is either patient or not patient then susan is both quiet and not old and vice versa.
If alice is both old and strong then someone is brave and vice versa.
If fred is not happy or generous then someone is both rich and not strong and vice versa.
Everyone who is either not calm or funny is either brave or not quiet.
If someone is either kind or not strong then someone is both not happy and not old and vice versa.
If someone is either not brave or not tall then susan is either strong or curious and vice versa.
Someone is wise or not tall.
Mary is both patient and quiet.
John is both quiet and patient.
John is creative or not wise.
Someone is not calm or not humble.
Lucy is tall or not creative.
Alice is not wise or brave.
Lucy is not rich or not kind. | Susan is funny. | contradiction | (![X]:((~rich(X)&calm(X))=>(~creative(X)<~>~strong(X))))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~wise(X)<=>(humble(X)&~brave(X))))&
((?[X]:((creative(X)&~happy(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:(~wise(X)<=>(calm(X)&~funny(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>(~patient(X)&~funny(X))))&
(![X]:((quiet(X)&funny(X))=>(~tall(X)&~wise(X))))&
(![X]:(~quiet(X)=>rich(X)))&
((?[X]:((patient(X)<~>~patient(X))))<=>((quiet(susan)&~old(susan))))&
(((old(alice)&strong(alice)))<=>(?[X]:(brave(X))))&
(((~happy(fred)|generous(fred)))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((~calm(X)<~>funny(X))=>(brave(X)<~>~quiet(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(?[X]:((~happy(X)&~old(X)))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>((strong(susan)<~>curious(susan))))&
(?[X]:((wise(X)|~tall(X))))&
((patient(mary)&quiet(mary)))&
((quiet(john)&patient(john)))&
((creative(john)|~wise(john)))&
(?[X]:((~calm(X)|~humble(X))))&
((tall(lucy)|~creative(lucy)))&
((~wise(alice)|brave(alice)))&
((~rich(lucy)|~kind(lucy))) | funny(susan) | [
"p4",
"p6",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 353084082084539831940841
% SZS output start Proof for 353084082084539831940841
5. ! [X0] : (~wise(X0) <=> (~funny(X0) & calm(X0))) [input p4]
7. ! [X0] : ((funny(X0) & quiet(X0)) => (~wise(X0) & ~tall(X0))) [input p6]
9. ? [X0] : (patient(X0) <~> ~patient(X0)) <=> (~old(susan) & quiet(susan)) [input p8]
23. funny(susan) [input hypothesis]
28. ! [X0] : ((~wise(X0) & ~tall(X0)) | (~funny(X0) | ~quiet(X0))) [ennf transformation 7]
29. ! [X0] : ((~wise(X0) & ~tall(X0)) | ~funny(X0) | ~quiet(X0)) [flattening 28]
41. ! [X0] : ((~wise(X0) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | wise(X0))) [nnf transformation 5]
42. ! [X0] : ((~wise(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | wise(X0))) [flattening 41]
45. (? [X0] : ((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (old(susan) | ~quiet(susan))) & ((~old(susan) & quiet(susan)) | ! [X0] : ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 9]
46. (? [X0] : ((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X0] : ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [flattening 45]
47. (? [X0] : ((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X1] : ((patient(X1) | patient(X1)) & (~patient(X1) | ~patient(X1)))) [rectify 46]
48. ? [X0] : ((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) => ((patient(sK2) | ~patient(sK2)) & (~patient(sK2) | patient(sK2))) [choice axiom]
49. (((patient(sK2) | ~patient(sK2)) & (~patient(sK2) | patient(sK2))) | old(susan) | ~quiet(susan)) & ((~old(susan) & quiet(susan)) | ! [X1] : ((patient(X1) | patient(X1)) & (~patient(X1) | ~patient(X1)))) [skolemisation 47,48]
86. ~funny(X0) | wise(X0) [cnf transformation 42]
95. ~wise(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 29]
97. quiet(susan) | ~patient(X1) | ~patient(X1) [cnf transformation 49]
98. quiet(susan) | patient(X1) | patient(X1) [cnf transformation 49]
139. funny(susan) [cnf transformation 23]
140. quiet(susan) | ~patient(X1) [duplicate literal removal 97]
141. quiet(susan) | patient(X1) [duplicate literal removal 98]
170. ~quiet(X0) | ~funny(X0) [subsumption resolution 95,86]
172. 7 <=> ! [X1] : patient(X1) [avatar definition]
173. patient(X1) <- (7) [avatar component clause 172]
180. 9 <=> ! [X1] : ~patient(X1) [avatar definition]
181. ~patient(X1) <- (9) [avatar component clause 180]
184. 10 <=> quiet(susan) [avatar definition]
186. quiet(susan) <- (10) [avatar component clause 184]
187. 7 | 10 [avatar split clause 141,184,172]
188. 9 | 10 [avatar split clause 140,184,180]
360. ~funny(susan) <- (10) [resolution 170,186]
363. $false <- (10) [subsumption resolution 360,139]
364. ~10 [avatar contradiction clause 363]
365. $false <- (7, 9) [subsumption resolution 173,181]
366. ~7 | ~9 [avatar contradiction clause 365]
367. $false [avatar sat refutation 187,188,364,366]
% SZS output end Proof for 353084082084539831940841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or not wise then someone is both not curious and strong.
If john is both not old and old then someone is both funny and not generous and vice versa.
If someone is not funny then alice is either not patient or rich.
Everyone who is both brave and not brave is both not wise and not tall.
Everyone who is not brave is funny and vice versa.
Everyone who is both tall and not old is either not wise or not humble and vice versa.
Everyone who is either not tall or generous is not curious or not generous and vice versa.
If susan is both not humble and not old then someone is either not creative or happy and vice versa.
Everyone who is both not kind and not humble is both humble and creative and vice versa.
Everyone who is both not generous and not curious is either not generous or not rich.
If someone is not tall then lucy is not humble or creative.
Everyone who is brave is both not curious and happy.
If someone is either not tall or calm then someone is both not tall and creative and vice versa.
If someone is either not generous or humble then someone is not rich or not generous.
If john is not funny then susan is either not creative or rich.
Everyone who is both not kind and happy is not kind.
Someone is patient.
Alice is not brave.
Susan is not patient or tall.
Someone is both not happy and humble.
Fred is kind.
Fred is not calm or kind.
Someone is not quiet or tall. | Fred is happy. | neutral | ((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((~curious(X)&strong(X)))))&
(((~old(john)&old(john)))<=>(?[X]:((funny(X)&~generous(X)))))&
((?[X]:(~funny(X)))=>((~patient(alice)<~>rich(alice))))&
(![X]:((brave(X)&~brave(X))=>(~wise(X)&~tall(X))))&
(![X]:(~brave(X)<=>funny(X)))&
(![X]:((tall(X)&~old(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((~tall(X)<~>generous(X))<=>(~curious(X)|~generous(X))))&
(((~humble(susan)&~old(susan)))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((~kind(X)&~humble(X))<=>(humble(X)&creative(X))))&
(![X]:((~generous(X)&~curious(X))=>(~generous(X)<~>~rich(X))))&
((?[X]:(~tall(X)))=>((~humble(lucy)|creative(lucy))))&
(![X]:(brave(X)=>(~curious(X)&happy(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(?[X]:((~tall(X)&creative(X)))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
((~funny(john))=>((~creative(susan)<~>rich(susan))))&
(![X]:((~kind(X)&happy(X))=>~kind(X)))&
(?[X]:(patient(X)))&
(~brave(alice))&
((~patient(susan)|tall(susan)))&
(?[X]:((~happy(X)&humble(X))))&
(kind(fred))&
((~calm(fred)|kind(fred)))&
(?[X]:((~quiet(X)|tall(X)))) | happy(fred) | []
| null | 0 |
If fred is both creative and not brave then alice is not old or calm.
If alice is not calm or curious then fred is not curious and vice versa.
Everyone who is rich or not strong is both tall and strong.
Everyone who is either not patient or patient is not rich or kind.
Everyone who is not wise is either not strong or happy and vice versa.
Everyone who is both creative and not creative is both strong and not old and vice versa.
If someone is not curious then someone is either not humble or rich and vice versa.
Everyone who is both funny and not generous is creative.
If someone is not tall or not patient then lucy is not brave.
Everyone who is both not old and brave is both kind and curious.
If paul is either not happy or not wise then alice is not tall or not curious and vice versa.
Everyone who is both rich and not tall is quiet or rich and vice versa.
If someone is calm then paul is not generous or wise and vice versa.
Everyone who is patient is either not patient or old.
Everyone who is both kind and not old is tall or generous and vice versa.
If alice is either old or not creative then someone is generous or not happy.
Alice is not tall.
Someone is not brave or not strong.
Susan is not generous.
Someone is not strong or not tall.
Someone is either funny or not funny.
Lucy is strong or curious. | Fred is not brave. | neutral | (((creative(fred)&~brave(fred)))=>((~old(alice)|calm(alice))))&
(((~calm(alice)|curious(alice)))<=>(~curious(fred)))&
(![X]:((rich(X)|~strong(X))=>(tall(X)&strong(X))))&
(![X]:((~patient(X)<~>patient(X))=>(~rich(X)|kind(X))))&
(![X]:(~wise(X)<=>(~strong(X)<~>happy(X))))&
(![X]:((creative(X)&~creative(X))<=>(strong(X)&~old(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((funny(X)&~generous(X))=>creative(X)))&
((?[X]:((~tall(X)|~patient(X))))=>(~brave(lucy)))&
(![X]:((~old(X)&brave(X))=>(kind(X)&curious(X))))&
(((~happy(paul)<~>~wise(paul)))<=>((~tall(alice)|~curious(alice))))&
(![X]:((rich(X)&~tall(X))<=>(quiet(X)|rich(X))))&
((?[X]:(calm(X)))<=>((~generous(paul)|wise(paul))))&
(![X]:(patient(X)=>(~patient(X)<~>old(X))))&
(![X]:((kind(X)&~old(X))<=>(tall(X)|generous(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((generous(X)|~happy(X)))))&
(~tall(alice))&
(?[X]:((~brave(X)|~strong(X))))&
(~generous(susan))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((funny(X)<~>~funny(X))))&
((strong(lucy)|curious(lucy))) | ~brave(fred) | []
| null | 0 |
If paul is strong then someone is not curious and vice versa.
Everyone who is both not happy and not funny is creative or not brave and vice versa.
Everyone who is creative or not tall is either happy or not curious and vice versa.
Everyone who is funny is wise or not generous.
Everyone who is not brave is humble and vice versa.
If someone is curious then someone is not humble or not calm and vice versa.
Everyone who is calm or not old is kind or brave.
Everyone who is both not strong and brave is either not creative or not patient and vice versa.
If someone is creative or curious then alice is both quiet and not strong and vice versa.
Everyone who is both not calm and happy is old or not patient and vice versa.
Everyone who is either humble or not quiet is patient and vice versa.
If someone is tall then someone is not rich or rich and vice versa.
If mary is either old or curious then someone is kind or not old.
If someone is both not strong and creative then mary is not patient or not humble.
Everyone who is funny is both creative and strong.
If someone is both not quiet and not generous then someone is not generous and vice versa.
Paul is calm.
Someone is creative.
Susan is not creative.
Someone is either rich or not calm.
Alice is not tall or tall.
John is both not brave and strong. | Susan is happy. | entailment | ((strong(paul))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~funny(X))<=>(creative(X)|~brave(X))))&
(![X]:((creative(X)|~tall(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(funny(X)=>(wise(X)|~generous(X))))&
(![X]:(~brave(X)<=>humble(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))&
(![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((?[X]:((~strong(X)&creative(X))))=>((~patient(mary)|~humble(mary))))&
(![X]:(funny(X)=>(creative(X)&strong(X))))&
((?[X]:((~quiet(X)&~generous(X))))<=>(?[X]:(~generous(X))))&
(calm(paul))&
(?[X]:(creative(X)))&
(~creative(susan))&
(?[X]:((rich(X)<~>~calm(X))))&
((~tall(alice)|tall(alice)))&
((~brave(john)&strong(john))) | happy(susan) | [
"p1",
"p7",
"p9",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 3299995373026730494987483
% SZS output start Proof for 3299995373026730494987483
2. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> (~brave(X0) | creative(X0))) [input p1]
8. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~creative(X0) <~> ~patient(X0))) [input p7]
10. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (~patient(X0) | old(X0))) [input p9]
15. ! [X0] : (funny(X0) => (strong(X0) & creative(X0))) [input p14]
19. ~creative(susan) [input p18]
23. ~happy(susan) [input hypothesis]
32. ! [X0] : ((strong(X0) & creative(X0)) | ~funny(X0)) [ennf transformation 15]
37. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (funny(X0) | happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | funny(X0) | happy(X0))) [flattening 37]
47. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~brave(X0) | strong(X0)))) [nnf transformation 8]
48. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ~brave(X0) | strong(X0))) [flattening 47]
54. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 10]
55. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~happy(X0) | calm(X0))) [flattening 54]
74. ~brave(X0) | creative(X0) | funny(X0) | happy(X0) [cnf transformation 38]
76. ~happy(X0) | brave(X0) [cnf transformation 38]
77. ~creative(X0) | ~funny(X0) [cnf transformation 38]
94. ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 48]
105. patient(X0) | happy(X0) [cnf transformation 55]
114. creative(X0) | ~funny(X0) [cnf transformation 32]
121. ~creative(susan) [cnf transformation 19]
127. ~happy(susan) [cnf transformation 23]
215. ~funny(X0) [subsumption resolution 114,77]
296. brave(X0) | creative(X0) | happy(X0) [resolution 94,105]
297. brave(X0) | creative(X0) [subsumption resolution 296,76]
546. creative(X1) | creative(X1) | funny(X1) | happy(X1) [resolution 297,74]
550. creative(X1) | funny(X1) | happy(X1) [duplicate literal removal 546]
553. creative(X1) | happy(X1) [subsumption resolution 550,215]
747. happy(susan) [resolution 553,121]
749. $false [subsumption resolution 747,127]
% SZS output end Proof for 3299995373026730494987483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or humble then fred is generous. If someone is strong or old then lucy is both not patient and not tall. If fred is humble then alice is patient or not humble. Everyone who is not generous or brave is not strong and vice versa. If someone is not funny or not generous then someone is either happy or not rich. Everyone who is not humble or not kind is either brave or curious and vice versa. If susan is not old then john is tall and vice versa. Everyone who is not curious or tall is both funny and rich. If someone is humble then lucy is not generous and vice versa. If paul is not generous or not old then mary is not happy and vice versa. Everyone who is quiet is curious or wise. Everyone who is either not strong or not patient is kind or funny. Everyone who is both not creative and not generous is either not quiet or not creative. If fred is both tall and not strong then mary is quiet or not kind and vice versa. Everyone who is either curious or rich is either not rich or not happy. If someone is strong or not wise then alice is wise or not kind. Someone is not curious. Someone is not brave. John is creative or not quiet. Fred is patient. Susan is either not creative or creative. Paul is both not strong and not generous. Someone is not creative or not calm. | Paul is not funny. | neutral | ((?[X]:((kind(X)|humble(X))))=>(generous(fred)))&
((?[X]:((strong(X)|old(X))))=>((~patient(lucy)&~tall(lucy))))&
((humble(fred))=>((patient(alice)|~humble(alice))))&
(![X]:((~generous(X)|brave(X))<=>~strong(X)))&
((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(brave(X)<~>curious(X))))&
((~old(susan))<=>(tall(john)))&
(![X]:((~curious(X)|tall(X))=>(funny(X)&rich(X))))&
((?[X]:(humble(X)))<=>(~generous(lucy)))&
(((~generous(paul)|~old(paul)))<=>(~happy(mary)))&
(![X]:(quiet(X)=>(curious(X)|wise(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(kind(X)|funny(X))))&
(![X]:((~creative(X)&~generous(X))=>(~quiet(X)<~>~creative(X))))&
(((tall(fred)&~strong(fred)))<=>((quiet(mary)|~kind(mary))))&
(![X]:((curious(X)<~>rich(X))=>(~rich(X)<~>~happy(X))))&
((?[X]:((strong(X)|~wise(X))))=>((wise(alice)|~kind(alice))))&
(?[X]:(~curious(X)))&
(?[X]:(~brave(X)))&
((creative(john)|~quiet(john)))&
(patient(fred))&
((~creative(susan)<~>creative(susan)))&
((~strong(paul)&~generous(paul)))&
(?[X]:((~creative(X)|~calm(X)))) | ~funny(paul) | []
| null | 0 |
Everyone who is not rich or not calm is patient and vice versa. Everyone who is not tall is both calm and not rich. If someone is both not happy and brave then someone is old and vice versa. Everyone who is quiet or generous is calm or humble and vice versa. Everyone who is patient or happy is not generous and vice versa. If alice is both not kind and not curious then someone is either not tall or not rich and vice versa. If someone is kind then paul is both not old and tall. If someone is either strong or rich then someone is either not creative or not patient. If someone is both not wise and curious then someone is either not creative or strong. If john is old or not humble then someone is both not rich and happy and vice versa. Everyone who is not patient or not happy is kind and vice versa. If susan is both not funny and not generous then someone is either not tall or not happy and vice versa. If someone is not wise then someone is either patient or not quiet and vice versa. If fred is calm then someone is either humble or not old and vice versa. If someone is not patient then someone is either not quiet or curious and vice versa. If fred is tall or generous then fred is not generous. Fred is rich. Someone is not funny. Someone is either patient or not calm. Susan is tall. Fred is not happy. Paul is generous. John is both old and not happy. Someone is patient or quiet. | Paul is not kind. | contradiction | (![X]:((~rich(X)|~calm(X))<=>patient(X)))&
(![X]:(~tall(X)=>(calm(X)&~rich(X))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:(old(X))))&
(![X]:((quiet(X)|generous(X))<=>(calm(X)|humble(X))))&
(![X]:((patient(X)|happy(X))<=>~generous(X)))&
(((~kind(alice)&~curious(alice)))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
((?[X]:(kind(X)))=>((~old(paul)&tall(paul))))&
((?[X]:((strong(X)<~>rich(X))))=>(?[X]:((~creative(X)<~>~patient(X)))))&
((?[X]:((~wise(X)&curious(X))))=>(?[X]:((~creative(X)<~>strong(X)))))&
(((old(john)|~humble(john)))<=>(?[X]:((~rich(X)&happy(X)))))&
(![X]:((~patient(X)|~happy(X))<=>kind(X)))&
(((~funny(susan)&~generous(susan)))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
((calm(fred))<=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((~quiet(X)<~>curious(X)))))&
(((tall(fred)|generous(fred)))=>(~generous(fred)))&
(rich(fred))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)<~>~calm(X))))&
(tall(susan))&
(~happy(fred))&
(generous(paul))&
((old(john)&~happy(john)))&
(?[X]:((patient(X)|quiet(X)))) | ~kind(paul) | [
"p4",
"p10",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 8916637420671536134205227
% SZS output start Proof for 8916637420671536134205227
5. ! [X0] : ((happy(X0) | patient(X0)) <=> ~generous(X0)) [input p4]
11. ! [X0] : ((~happy(X0) | ~patient(X0)) <=> kind(X0)) [input p10]
22. generous(paul) [input p21]
25. ~kind(paul) [input hypothesis]
45. ! [X0] : (((happy(X0) | patient(X0)) | generous(X0)) & (~generous(X0) | (~happy(X0) & ~patient(X0)))) [nnf transformation 5]
46. ! [X0] : ((happy(X0) | patient(X0) | generous(X0)) & (~generous(X0) | (~happy(X0) & ~patient(X0)))) [flattening 45]
65. ! [X0] : (((~happy(X0) | ~patient(X0)) | ~kind(X0)) & (kind(X0) | (happy(X0) & patient(X0)))) [nnf transformation 11]
66. ! [X0] : ((~happy(X0) | ~patient(X0) | ~kind(X0)) & (kind(X0) | (happy(X0) & patient(X0)))) [flattening 65]
105. ~generous(X0) | ~patient(X0) [cnf transformation 46]
127. kind(X0) | patient(X0) [cnf transformation 66]
156. generous(paul) [cnf transformation 22]
160. ~kind(paul) [cnf transformation 25]
398. ~patient(paul) [resolution 105,156]
402. patient(paul) [resolution 127,160]
404. $false [subsumption resolution 402,398]
% SZS output end Proof for 8916637420671536134205227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or funny is patient or old.
If someone is both not wise and tall then someone is both not kind and not funny and vice versa.
If someone is either not creative or rich then fred is wise or patient.
If someone is humble or not wise then someone is both not brave and calm and vice versa.
Everyone who is either calm or not strong is both curious and not wise.
Everyone who is not patient or generous is not curious.
If mary is either funny or humble then lucy is both creative and not patient and vice versa.
Everyone who is both creative and not rich is humble.
If someone is both not kind and creative then someone is wise and vice versa.
Everyone who is both not kind and not calm is either calm or patient and vice versa.
Everyone who is both not kind and not funny is not brave.
Everyone who is not generous or brave is not calm or curious and vice versa.
If lucy is either old or brave then alice is humble and vice versa.
Everyone who is either not happy or not creative is not curious or not old.
Everyone who is both not calm and not wise is not humble or humble.
If susan is both not patient and not funny then mary is not creative or generous.
Someone is not funny.
Lucy is either not brave or not rich.
Someone is either not generous or humble.
Someone is both tall and not creative.
Susan is not humble.
Mary is calm.
Susan is both quiet and generous.
Someone is rich. | Lucy is not patient. | neutral | (![X]:((patient(X)<~>funny(X))=>(patient(X)|old(X))))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
((?[X]:((~creative(X)<~>rich(X))))=>((wise(fred)|patient(fred))))&
((?[X]:((humble(X)|~wise(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((calm(X)<~>~strong(X))=>(curious(X)&~wise(X))))&
(![X]:((~patient(X)|generous(X))=>~curious(X)))&
(((funny(mary)<~>humble(mary)))<=>((creative(lucy)&~patient(lucy))))&
(![X]:((creative(X)&~rich(X))=>humble(X)))&
((?[X]:((~kind(X)&creative(X))))<=>(?[X]:(wise(X))))&
(![X]:((~kind(X)&~calm(X))<=>(calm(X)<~>patient(X))))&
(![X]:((~kind(X)&~funny(X))=>~brave(X)))&
(![X]:((~generous(X)|brave(X))<=>(~calm(X)|curious(X))))&
(((old(lucy)<~>brave(lucy)))<=>(humble(alice)))&
(![X]:((~happy(X)<~>~creative(X))=>(~curious(X)|~old(X))))&
(![X]:((~calm(X)&~wise(X))=>(~humble(X)|humble(X))))&
(((~patient(susan)&~funny(susan)))=>((~creative(mary)|generous(mary))))&
(?[X]:(~funny(X)))&
((~brave(lucy)<~>~rich(lucy)))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((tall(X)&~creative(X))))&
(~humble(susan))&
(calm(mary))&
((quiet(susan)&generous(susan)))&
(?[X]:(rich(X))) | ~patient(lucy) | []
| null | 0 |
Everyone who is both not patient and not brave is either not humble or calm and vice versa.
Everyone who is rich or creative is humble and vice versa.
If susan is both not brave and patient then mary is not humble or not calm.
If someone is both not quiet and old then someone is not quiet and vice versa.
Everyone who is brave is not funny.
If lucy is both happy and not tall then someone is both not humble and not patient.
Everyone who is not calm is either rich or humble.
If someone is not funny or happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
If mary is both patient and rich then someone is not patient or happy.
If john is not strong or brave then someone is not tall or not generous.
If john is both not wise and not humble then john is both happy and old and vice versa.
Everyone who is not curious or not patient is both quiet and curious and vice versa.
Everyone who is not tall is not rich.
Someone is both happy and quiet.
John is not rich or generous.
Someone is quiet.
Mary is either patient or tall.
Lucy is either not generous or strong.
Someone is either not old or not humble.
Susan is either creative or not brave.
Paul is not wise or tall. | Mary is curious. | entailment | (![X]:((~patient(X)&~brave(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((rich(X)|creative(X))<=>humble(X)))&
(((~brave(susan)&patient(susan)))=>((~humble(mary)|~calm(mary))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>~funny(X)))&
(((happy(lucy)&~tall(lucy)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:(~calm(X)=>(rich(X)<~>humble(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
(((patient(mary)&rich(mary)))=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(john)|brave(john)))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~wise(john)&~humble(john)))<=>((happy(john)&old(john))))&
(![X]:((~curious(X)|~patient(X))<=>(quiet(X)&curious(X))))&
(![X]:(~tall(X)=>~rich(X)))&
(?[X]:((happy(X)&quiet(X))))&
((~rich(john)|generous(john)))&
(?[X]:(quiet(X)))&
((patient(mary)<~>tall(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((~old(X)<~>~humble(X))))&
((creative(susan)<~>~brave(susan)))&
((~wise(paul)|tall(paul))) | curious(mary) | [
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 768440584810777866162660
% SZS output start Proof for 768440584810777866162660
15. ! [X0] : ((~patient(X0) | ~curious(X0)) <=> (curious(X0) & quiet(X0))) [input p14]
25. ~curious(mary) [input hypothesis]
66. ! [X0] : (((~patient(X0) | ~curious(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (patient(X0) & curious(X0)))) [nnf transformation 15]
67. ! [X0] : ((~patient(X0) | ~curious(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (patient(X0) & curious(X0)))) [flattening 66]
115. curious(X0) | curious(X0) [cnf transformation 67]
132. ~curious(mary) [cnf transformation 25]
133. curious(X0) [duplicate literal removal 115]
336. $false [subsumption resolution 132,133]
% SZS output end Proof for 768440584810777866162660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and humble then john is both rich and creative.
If mary is not funny or not generous then paul is both quiet and kind and vice versa.
If someone is both not tall and wise then fred is strong and vice versa.
If susan is brave then paul is both rich and not happy and vice versa.
Everyone who is not tall or humble is not wise and vice versa.
Everyone who is curious is generous.
If someone is not curious or humble then john is not tall.
If someone is patient or not tall then susan is strong or kind and vice versa.
If someone is either strong or calm then someone is calm or not rich and vice versa.
Everyone who is either not curious or generous is brave and vice versa.
Everyone who is calm or rich is either not happy or strong and vice versa.
Everyone who is either tall or not old is happy or not funny.
If someone is both tall and not happy then lucy is not calm.
Everyone who is not happy or quiet is either patient or humble and vice versa.
Everyone who is not generous or not old is quiet or not old and vice versa.
If susan is either tall or funny then someone is either not funny or not generous and vice versa.
Someone is either not creative or not generous.
Alice is both humble and not curious.
Mary is strong.
Lucy is either not old or old.
Mary is calm or patient.
Alice is wise or not tall.
Susan is kind.
Alice is rich or not wise. | Fred is not kind. | neutral | ((?[X]:((~happy(X)&humble(X))))=>((rich(john)&creative(john))))&
(((~funny(mary)|~generous(mary)))<=>((quiet(paul)&kind(paul))))&
((?[X]:((~tall(X)&wise(X))))<=>(strong(fred)))&
((brave(susan))<=>((rich(paul)&~happy(paul))))&
(![X]:((~tall(X)|humble(X))<=>~wise(X)))&
(![X]:(curious(X)=>generous(X)))&
((?[X]:((~curious(X)|humble(X))))=>(~tall(john)))&
((?[X]:((patient(X)|~tall(X))))<=>((strong(susan)|kind(susan))))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((~curious(X)<~>generous(X))<=>brave(X)))&
(![X]:((calm(X)|rich(X))<=>(~happy(X)<~>strong(X))))&
(![X]:((tall(X)<~>~old(X))=>(happy(X)|~funny(X))))&
((?[X]:((tall(X)&~happy(X))))=>(~calm(lucy)))&
(![X]:((~happy(X)|quiet(X))<=>(patient(X)<~>humble(X))))&
(![X]:((~generous(X)|~old(X))<=>(quiet(X)|~old(X))))&
(((tall(susan)<~>funny(susan)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
(?[X]:((~creative(X)<~>~generous(X))))&
((humble(alice)&~curious(alice)))&
(strong(mary))&
((~old(lucy)<~>old(lucy)))&
((calm(mary)|patient(mary)))&
((wise(alice)|~tall(alice)))&
(kind(susan))&
((rich(alice)|~wise(alice))) | ~kind(fred) | []
| null | 0 |
If someone is funny or patient then someone is not patient and vice versa.
Everyone who is quiet or not brave is both not old and wise.
Everyone who is both strong and not calm is not funny or funny and vice versa.
If someone is either not funny or not creative then fred is not wise or not creative and vice versa.
If john is either funny or humble then susan is not generous or quiet and vice versa.
If alice is tall then someone is not humble and vice versa.
Everyone who is either happy or quiet is not funny and vice versa.
Everyone who is either not humble or not tall is both not funny and not patient and vice versa.
If susan is funny or quiet then someone is either not funny or calm and vice versa.
Everyone who is not creative or not humble is either kind or not wise.
Everyone who is either not old or old is curious or not rich.
Everyone who is either calm or not creative is both quiet and tall and vice versa.
Everyone who is not old or not happy is funny and vice versa.
Everyone who is patient or curious is generous or brave and vice versa.
If someone is not humble then mary is not curious or not strong and vice versa.
Someone is both happy and not funny.
Fred is not curious.
John is either creative or kind.
Someone is not wise or rich.
Someone is both wise and happy.
Someone is not kind or not generous. | Susan is not funny. | contradiction | ((?[X]:((funny(X)|patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)|~brave(X))=>(~old(X)&wise(X))))&
(![X]:((strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((~wise(fred)|~creative(fred))))&
(((funny(john)<~>humble(john)))<=>((~generous(susan)|quiet(susan))))&
((tall(alice))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>quiet(X))<=>~funny(X)))&
(![X]:((~humble(X)<~>~tall(X))<=>(~funny(X)&~patient(X))))&
(((funny(susan)|quiet(susan)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((~creative(X)|~humble(X))=>(kind(X)<~>~wise(X))))&
(![X]:((~old(X)<~>old(X))=>(curious(X)|~rich(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(quiet(X)&tall(X))))&
(![X]:((~old(X)|~happy(X))<=>funny(X)))&
(![X]:((patient(X)|curious(X))<=>(generous(X)|brave(X))))&
((?[X]:(~humble(X)))<=>((~curious(mary)|~strong(mary))))&
(?[X]:((happy(X)&~funny(X))))&
(~curious(fred))&
((creative(john)<~>kind(john)))&
(?[X]:((~wise(X)|rich(X))))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:((~kind(X)|~generous(X)))) | ~funny(susan) | [
"p1",
"p2",
"p8",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2486785200885668495924792
% SZS output start Proof for 2486785200885668495924792
2. ! [X0] : ((~brave(X0) | quiet(X0)) => (wise(X0) & ~old(X0))) [input p1]
3. ! [X0] : ((~calm(X0) & strong(X0)) <=> (funny(X0) | ~funny(X0))) [input p2]
9. (quiet(susan) | funny(susan)) <=> ? [X0] : (~funny(X0) <~> calm(X0)) [input p8]
13. ! [X0] : ((~happy(X0) | ~old(X0)) <=> funny(X0)) [input p12]
16. ? [X0] : (~funny(X0) & happy(X0)) [input p15]
22. ~funny(susan) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~old(X0)) | (brave(X0) & ~quiet(X0))) [ennf transformation 2]
33. ! [X0] : (((~calm(X0) & strong(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~calm(X0) & strong(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | calm(X0) | ~strong(X0))) [flattening 33]
49. ((quiet(susan) | funny(susan)) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X0] : ((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~quiet(susan) & ~funny(susan))) [nnf transformation 9]
50. (quiet(susan) | funny(susan) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X0] : ((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~quiet(susan) & ~funny(susan))) [flattening 49]
51. (quiet(susan) | funny(susan) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X1] : ((~calm(X1) | funny(X1)) & (calm(X1) | ~funny(X1))) | (~quiet(susan) & ~funny(susan))) [rectify 50]
52. ? [X1] : ((~calm(X1) | funny(X1)) & (calm(X1) | ~funny(X1))) => ((~calm(sK4) | funny(sK4)) & (calm(sK4) | ~funny(sK4))) [choice axiom]
53. (quiet(susan) | funny(susan) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(sK4) | funny(sK4)) & (calm(sK4) | ~funny(sK4))) | (~quiet(susan) & ~funny(susan))) [skolemisation 51,52]
58. ! [X0] : (((~happy(X0) | ~old(X0)) | ~funny(X0)) & (funny(X0) | (happy(X0) & old(X0)))) [nnf transformation 13]
59. ! [X0] : ((~happy(X0) | ~old(X0) | ~funny(X0)) & (funny(X0) | (happy(X0) & old(X0)))) [flattening 58]
67. ? [X0] : (~funny(X0) & happy(X0)) => (~funny(sK6) & happy(sK6)) [choice axiom]
68. ~funny(sK6) & happy(sK6) [skolemisation 16,67]
79. ~old(X0) | ~quiet(X0) [cnf transformation 24]
86. ~calm(X0) | funny(X0) [cnf transformation 34]
87. ~calm(X0) | ~funny(X0) [cnf transformation 34]
116. quiet(susan) | funny(susan) | calm(X0) | funny(X0) [cnf transformation 53]
130. old(X0) | funny(X0) [cnf transformation 59]
141. ~funny(sK6) [cnf transformation 68]
149. ~funny(susan) [cnf transformation 22]
176. ~calm(X0) [subsumption resolution 86,87]
207. 13 <=> quiet(susan) [avatar definition]
208. quiet(susan) <- (13) [avatar component clause 207]
241. quiet(susan) | funny(susan) | funny(X0) [subsumption resolution 116,176]
243. 20 <=> ! [X0] : funny(X0) [avatar definition]
244. funny(X0) <- (20) [avatar component clause 243]
246. 21 <=> funny(susan) [avatar definition]
247. ~funny(susan) <- (~21) [avatar component clause 246]
249. 20 | 21 | 13 [avatar split clause 241,207,246,243]
301. ~21 [avatar split clause 149,246]
312. ~quiet(X1) | funny(X1) [resolution 130,79]
352. funny(susan) <- (13) [resolution 312,208]
354. $false <- (13, ~21) [subsumption resolution 352,247]
355. ~13 | 21 [avatar contradiction clause 354]
361. $false <- (20) [resolution 244,141]
364. ~20 [avatar contradiction clause 361]
369. $false [avatar sat refutation 249,301,355,364]
% SZS output end Proof for 2486785200885668495924792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both creative and generous then someone is either funny or tall.
If paul is both not calm and not creative then lucy is either old or calm.
Everyone who is brave is not generous and vice versa.
If paul is not calm then someone is either not wise or kind.
If john is either brave or not funny then alice is not old or not humble.
Everyone who is either strong or not strong is both not kind and not happy and vice versa.
Everyone who is either tall or not generous is both not patient and funny.
If lucy is both not quiet and not tall then susan is both strong and not brave.
Everyone who is either humble or generous is both creative and not wise.
Everyone who is both not kind and not wise is both not creative and not humble and vice versa.
If lucy is both brave and not creative then john is strong.
Everyone who is both rich and patient is not tall.
If someone is not funny or patient then someone is generous or not funny.
If susan is both not funny and not patient then alice is brave.
Everyone who is not curious or not happy is either calm or rich.
Everyone who is funny or old is either generous or not calm and vice versa.
Someone is quiet or old.
Alice is both not tall and calm.
Someone is curious.
Lucy is not tall.
Fred is either not old or wise.
Paul is both funny and calm.
Mary is both wise and not humble.
Someone is calm. | John is not quiet. | neutral | (((creative(paul)&generous(paul)))=>(?[X]:((funny(X)<~>tall(X)))))&
(((~calm(paul)&~creative(paul)))=>((old(lucy)<~>calm(lucy))))&
(![X]:(brave(X)<=>~generous(X)))&
((~calm(paul))=>(?[X]:((~wise(X)<~>kind(X)))))&
(((brave(john)<~>~funny(john)))=>((~old(alice)|~humble(alice))))&
(![X]:((strong(X)<~>~strong(X))<=>(~kind(X)&~happy(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~patient(X)&funny(X))))&
(((~quiet(lucy)&~tall(lucy)))=>((strong(susan)&~brave(susan))))&
(![X]:((humble(X)<~>generous(X))=>(creative(X)&~wise(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~creative(X)&~humble(X))))&
(((brave(lucy)&~creative(lucy)))=>(strong(john)))&
(![X]:((rich(X)&patient(X))=>~tall(X)))&
((?[X]:((~funny(X)|patient(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(((~funny(susan)&~patient(susan)))=>(brave(alice)))&
(![X]:((~curious(X)|~happy(X))=>(calm(X)<~>rich(X))))&
(![X]:((funny(X)|old(X))<=>(generous(X)<~>~calm(X))))&
(?[X]:((quiet(X)|old(X))))&
((~tall(alice)&calm(alice)))&
(?[X]:(curious(X)))&
(~tall(lucy))&
((~old(fred)<~>wise(fred)))&
((funny(paul)&calm(paul)))&
((wise(mary)&~humble(mary)))&
(?[X]:(calm(X))) | ~quiet(john) | []
| null | 0 |
If someone is both tall and curious then fred is tall.
Everyone who is tall is not funny and vice versa.
Everyone who is not creative is not calm or wise and vice versa.
If john is either not kind or humble then susan is kind and vice versa.
If someone is rich then someone is both not wise and not generous.
If someone is not kind or not curious then someone is brave and vice versa.
Everyone who is not strong or not tall is either not curious or kind and vice versa.
If someone is either humble or tall then someone is kind.
If someone is brave then someone is either brave or not funny and vice versa.
Everyone who is brave or old is not wise or not brave and vice versa.
If mary is not creative or not kind then john is humble or funny and vice versa.
If someone is both humble and not humble then susan is both not patient and not curious and vice versa.
Everyone who is not quiet is both not curious and not generous.
Everyone who is not wise is either generous or wise.
Everyone who is either not old or old is not generous.
If john is not brave or not tall then john is not kind or not rich.
Susan is not creative or not kind.
Someone is not patient or not tall.
Fred is not happy. | Fred is not calm. | neutral | ((?[X]:((tall(X)&curious(X))))=>(tall(fred)))&
(![X]:(tall(X)<=>~funny(X)))&
(![X]:(~creative(X)<=>(~calm(X)|wise(X))))&
(((~kind(john)<~>humble(john)))<=>(kind(susan)))&
((?[X]:(rich(X)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:(brave(X))))&
(![X]:((~strong(X)|~tall(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((brave(X)|old(X))<=>(~wise(X)|~brave(X))))&
(((~creative(mary)|~kind(mary)))<=>((humble(john)|funny(john))))&
((?[X]:((humble(X)&~humble(X))))<=>((~patient(susan)&~curious(susan))))&
(![X]:(~quiet(X)=>(~curious(X)&~generous(X))))&
(![X]:(~wise(X)=>(generous(X)<~>wise(X))))&
(![X]:((~old(X)<~>old(X))=>~generous(X)))&
(((~brave(john)|~tall(john)))=>((~kind(john)|~rich(john))))&
((~creative(susan)|~kind(susan)))&
(?[X]:((~patient(X)|~tall(X))))&
(~happy(fred)) | ~calm(fred) | []
| null | 0 |
Everyone who is both not funny and not humble is tall or rich.
Everyone who is either not humble or brave is generous and vice versa.
Everyone who is either not kind or kind is brave or wise and vice versa.
Everyone who is both not funny and not strong is calm and vice versa.
If someone is not funny then susan is either not brave or curious and vice versa.
If susan is not generous then someone is both patient and humble and vice versa.
If someone is old or strong then mary is funny and vice versa.
If john is not happy then susan is either curious or not brave.
Everyone who is quiet is both wise and not humble.
Everyone who is either not rich or rich is both not happy and not creative.
If someone is not tall or humble then someone is funny or not calm and vice versa.
Everyone who is both funny and creative is both not humble and brave and vice versa.
Everyone who is not brave is either funny or humble.
If paul is both not happy and not wise then fred is kind and vice versa.
Everyone who is both not curious and old is either not calm or humble and vice versa.
Everyone who is either generous or old is happy or not happy and vice versa.
Someone is either not kind or not curious.
Someone is either humble or not calm.
Alice is wise or not tall.
Someone is both not brave and patient.
Lucy is not kind. | Mary is not rich. | neutral | (![X]:((~funny(X)&~humble(X))=>(tall(X)|rich(X))))&
(![X]:((~humble(X)<~>brave(X))<=>generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(brave(X)|wise(X))))&
(![X]:((~funny(X)&~strong(X))<=>calm(X)))&
((?[X]:(~funny(X)))<=>((~brave(susan)<~>curious(susan))))&
((~generous(susan))<=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:((old(X)|strong(X))))<=>(funny(mary)))&
((~happy(john))=>((curious(susan)<~>~brave(susan))))&
(![X]:(quiet(X)=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((wise(alice)|~tall(alice)))&
(?[X]:((~brave(X)&patient(X))))&
(~kind(lucy)) | ~rich(mary) | []
| null | 0 |
Everyone who is not kind or not wise is not creative and vice versa. If mary is either strong or humble then john is either not quiet or not patient. If someone is humble then susan is not kind or not calm and vice versa. Everyone who is kind or not rich is both not patient and not happy. Everyone who is strong or not wise is both not humble and not calm. Everyone who is not rich or not funny is rich and vice versa. If someone is old or not generous then someone is creative and vice versa. If someone is quiet or old then someone is both curious and not curious. Everyone who is not generous or calm is both quiet and not generous and vice versa. Everyone who is both not funny and not quiet is both not old and brave. If someone is both not humble and brave then fred is not curious and vice versa. If fred is both not tall and not brave then someone is both old and calm. If mary is both funny and wise then fred is not funny or old. Everyone who is strong is either not happy or old and vice versa. If someone is generous then alice is either not quiet or patient. Alice is not curious. Someone is kind. John is not curious or not humble. Someone is curious. Fred is either not curious or not generous. | Susan is not wise. | neutral | (![X]:((~kind(X)|~wise(X))<=>~creative(X)))&
(((strong(mary)<~>humble(mary)))=>((~quiet(john)<~>~patient(john))))&
((?[X]:(humble(X)))<=>((~kind(susan)|~calm(susan))))&
(![X]:((kind(X)|~rich(X))=>(~patient(X)&~happy(X))))&
(![X]:((strong(X)|~wise(X))=>(~humble(X)&~calm(X))))&
(![X]:((~rich(X)|~funny(X))<=>rich(X)))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:(creative(X))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:((~generous(X)|calm(X))<=>(quiet(X)&~generous(X))))&
(![X]:((~funny(X)&~quiet(X))=>(~old(X)&brave(X))))&
((?[X]:((~humble(X)&brave(X))))<=>(~curious(fred)))&
(((~tall(fred)&~brave(fred)))=>(?[X]:((old(X)&calm(X)))))&
(((funny(mary)&wise(mary)))=>((~funny(fred)|old(fred))))&
(![X]:(strong(X)<=>(~happy(X)<~>old(X))))&
((?[X]:(generous(X)))=>((~quiet(alice)<~>patient(alice))))&
(~curious(alice))&
(?[X]:(kind(X)))&
((~curious(john)|~humble(john)))&
(?[X]:(curious(X)))&
((~curious(fred)<~>~generous(fred))) | ~wise(susan) | []
| null | 0 |
Everyone who is strong or not patient is rich or not calm and vice versa.
Everyone who is not brave or not humble is both not tall and humble.
If fred is not kind then lucy is both not tall and generous and vice versa.
Everyone who is not generous is curious.
Everyone who is either not funny or kind is either patient or kind.
Everyone who is either not strong or humble is both not wise and not patient.
Everyone who is old is both not generous and strong.
If someone is both humble and rich then paul is not brave and vice versa.
If someone is both not patient and wise then john is kind.
Everyone who is not humble or not curious is either not generous or not funny and vice versa.
Everyone who is either not generous or humble is either generous or kind and vice versa.
Everyone who is both humble and old is either not brave or quiet and vice versa.
If mary is both not calm and not strong then paul is both brave and rich.
Everyone who is either old or kind is quiet or not generous and vice versa.
If someone is both not old and old then someone is not creative or not wise.
Everyone who is either not patient or not brave is either generous or kind.
Mary is funny.
Lucy is brave or strong.
Alice is not kind.
Susan is either strong or generous.
Someone is not quiet.
Lucy is either curious or quiet.
John is brave. | Susan is not old. | entailment | (![X]:((strong(X)|~patient(X))<=>(rich(X)|~calm(X))))&
(![X]:((~brave(X)|~humble(X))=>(~tall(X)&humble(X))))&
((~kind(fred))<=>((~tall(lucy)&generous(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~funny(X)<~>kind(X))=>(patient(X)<~>kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(~wise(X)&~patient(X))))&
(![X]:(old(X)=>(~generous(X)&strong(X))))&
((?[X]:((humble(X)&rich(X))))<=>(~brave(paul)))&
((?[X]:((~patient(X)&wise(X))))=>(kind(john)))&
(![X]:((~humble(X)|~curious(X))<=>(~generous(X)<~>~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(generous(X)<~>kind(X))))&
(![X]:((humble(X)&old(X))<=>(~brave(X)<~>quiet(X))))&
(((~calm(mary)&~strong(mary)))=>((brave(paul)&rich(paul))))&
(![X]:((old(X)<~>kind(X))<=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((~creative(X)|~wise(X)))))&
(![X]:((~patient(X)<~>~brave(X))=>(generous(X)<~>kind(X))))&
(funny(mary))&
((brave(lucy)|strong(lucy)))&
(~kind(alice))&
((strong(susan)<~>generous(susan)))&
(?[X]:(~quiet(X)))&
((curious(lucy)<~>quiet(lucy)))&
(brave(john)) | ~old(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 6570517074084411633865806
% SZS output start Proof for 6570517074084411633865806
2. ! [X0] : ((~humble(X0) | ~brave(X0)) => (humble(X0) & ~tall(X0))) [input p1]
4. ! [X0] : (~generous(X0) => curious(X0)) [input p3]
5. ! [X0] : ((~funny(X0) <~> kind(X0)) => (patient(X0) <~> kind(X0))) [input p4]
6. ! [X0] : ((~strong(X0) <~> humble(X0)) => (~patient(X0) & ~wise(X0))) [input p5]
7. ! [X0] : (old(X0) => (strong(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (~generous(X0) <~> ~funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (generous(X0) <~> kind(X0))) [input p10]
24. old(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> humble(X0)) => ~patient(X0)) [pure predicate removal 6]
29. ! [X0] : ((humble(X0) & ~tall(X0)) | (humble(X0) & brave(X0))) [ennf transformation 2]
30. ! [X0] : (curious(X0) | generous(X0)) [ennf transformation 4]
31. ! [X0] : ((patient(X0) <~> kind(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 5]
32. ! [X0] : (~patient(X0) | (~strong(X0) <=> humble(X0))) [ennf transformation 27]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | ~old(X0)) [ennf transformation 7]
41. ! [X0] : (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 31]
42. ! [X0] : (~patient(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) [nnf transformation 32]
47. ! [X0] : (((~curious(X0) | ~humble(X0)) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [nnf transformation 10]
48. ! [X0] : ((~curious(X0) | ~humble(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [flattening 47]
49. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 11]
66. humble(X0) | humble(X0) [cnf transformation 29]
70. curious(X0) | generous(X0) [cnf transformation 30]
71. kind(X0) | patient(X0) | kind(X0) | funny(X0) [cnf transformation 41]
76. ~patient(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 42]
77. ~old(X0) | ~generous(X0) [cnf transformation 33]
78. ~old(X0) | strong(X0) [cnf transformation 33]
86. ~curious(X0) | ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 48]
91. ~kind(X0) | ~generous(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 49]
95. ~humble(X0) | generous(X0) | generous(X0) | ~kind(X0) [cnf transformation 49]
123. old(susan) [cnf transformation 24]
125. ~kind(X0) | ~generous(X0) | ~humble(X0) [duplicate literal removal 91]
127. ~humble(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
128. funny(X0) | patient(X0) | kind(X0) [duplicate literal removal 71]
130. humble(X0) [duplicate literal removal 66]
146. ~patient(X0) | ~strong(X0) [subsumption resolution 76,130]
162. ~curious(X0) | ~funny(X0) | generous(X0) [subsumption resolution 86,130]
163. ~funny(X0) | generous(X0) [subsumption resolution 162,70]
165. ~kind(X0) | generous(X0) [subsumption resolution 127,130]
166. ~kind(X0) | ~generous(X0) [subsumption resolution 125,130]
167. ~kind(X0) [subsumption resolution 166,165]
198. 12 <=> strong(susan) [avatar definition]
199. strong(susan) <- (12) [avatar component clause 198]
202. 13 <=> generous(susan) [avatar definition]
204. ~generous(susan) <- (~13) [avatar component clause 202]
217. ~generous(susan) [resolution 77,123]
218. strong(susan) [resolution 78,123]
256. patient(X1) | kind(X1) | generous(X1) [resolution 128,163]
258. generous(X1) | patient(X1) [subsumption resolution 256,167]
261. patient(susan) <- (~13) [resolution 258,204]
274. ~strong(susan) <- (~13) [resolution 261,146]
275. $false <- (12, ~13) [subsumption resolution 274,199]
276. ~12 | 13 [avatar contradiction clause 275]
277. 12 [avatar split clause 218,198]
278. ~13 [avatar split clause 217,202]
279. $false [avatar sat refutation 276,277,278]
% SZS output end Proof for 6570517074084411633865806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and tall is wise or not patient and vice versa.
If someone is not strong then someone is both not old and kind.
If someone is either not generous or patient then someone is both not curious and not brave and vice versa.
Everyone who is either wise or patient is either generous or not patient.
If someone is either not creative or brave then someone is not creative or not funny and vice versa.
Everyone who is both not wise and not curious is strong or not kind.
Everyone who is funny or not happy is either not rich or not old and vice versa.
Everyone who is either not happy or generous is not generous or not creative.
Everyone who is not strong or patient is generous and vice versa.
If someone is either not happy or quiet then someone is not curious or brave.
If someone is either quiet or not kind then john is not humble or not funny.
If someone is either not old or not curious then paul is either not rich or kind.
If paul is either generous or wise then someone is both not strong and not funny.
If susan is either curious or rich then someone is old.
Everyone who is either not generous or creative is not calm.
Lucy is either rich or funny.
Paul is either calm or rich.
Someone is happy or not old.
Mary is either not rich or not tall.
Someone is both not brave and not strong.
Lucy is wise.
Mary is either happy or quiet.
Someone is both not tall and calm. | John is patient. | neutral | (![X]:((old(X)&tall(X))<=>(wise(X)|~patient(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:((~generous(X)<~>patient(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((wise(X)<~>patient(X))=>(generous(X)<~>~patient(X))))&
((?[X]:((~creative(X)<~>brave(X))))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((~wise(X)&~curious(X))=>(strong(X)|~kind(X))))&
(![X]:((funny(X)|~happy(X))<=>(~rich(X)<~>~old(X))))&
(![X]:((~happy(X)<~>generous(X))=>(~generous(X)|~creative(X))))&
(![X]:((~strong(X)|patient(X))<=>generous(X)))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((~curious(X)|brave(X)))))&
((?[X]:((quiet(X)<~>~kind(X))))=>((~humble(john)|~funny(john))))&
((?[X]:((~old(X)<~>~curious(X))))=>((~rich(paul)<~>kind(paul))))&
(((generous(paul)<~>wise(paul)))=>(?[X]:((~strong(X)&~funny(X)))))&
(((curious(susan)<~>rich(susan)))=>(?[X]:(old(X))))&
(![X]:((~generous(X)<~>creative(X))=>~calm(X)))&
((rich(lucy)<~>funny(lucy)))&
((calm(paul)<~>rich(paul)))&
(?[X]:((happy(X)|~old(X))))&
((~rich(mary)<~>~tall(mary)))&
(?[X]:((~brave(X)&~strong(X))))&
(wise(lucy))&
((happy(mary)<~>quiet(mary)))&
(?[X]:((~tall(X)&calm(X)))) | patient(john) | []
| null | 0 |
If someone is strong or not funny then mary is not funny or not humble and vice versa.
Everyone who is curious is both not creative and strong.
If alice is not strong then someone is either not rich or not strong and vice versa.
Everyone who is either creative or happy is either not patient or not rich and vice versa.
Everyone who is not generous is tall and vice versa.
If paul is either happy or quiet then someone is not old and vice versa.
Everyone who is both not rich and not funny is not tall.
Everyone who is either not creative or quiet is both tall and happy and vice versa.
If john is generous or not creative then lucy is either generous or not tall and vice versa.
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.
Alice is generous.
Alice is both not funny and creative.
Lucy is both brave and not humble.
Someone is both not funny and calm.
Alice is either brave or not happy.
Susan is not humble or not happy. | Lucy is not quiet. | neutral | ((?[X]:((strong(X)|~funny(X))))<=>((~funny(mary)|~humble(mary))))&
(![X]:(curious(X)=>(~creative(X)&strong(X))))&
((~strong(alice))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((creative(X)<~>happy(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>tall(X)))&
(((happy(paul)<~>quiet(paul)))<=>(?[X]:(~old(X))))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(![X]:((~creative(X)<~>quiet(X))<=>(tall(X)&happy(X))))&
(((generous(john)|~creative(john)))<=>((generous(lucy)<~>~tall(lucy))))&
(((~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))))&
(generous(alice))&
((~funny(alice)&creative(alice)))&
((brave(lucy)&~humble(lucy)))&
(?[X]:((~funny(X)&calm(X))))&
((brave(alice)<~>~happy(alice)))&
((~humble(susan)|~happy(susan))) | ~quiet(lucy) | []
| null | 0 |
Everyone who is not strong or creative is not wise and vice versa.
Everyone who is both not funny and strong is either patient or kind.
Everyone who is both funny and happy is strong or happy and vice versa.
If someone is both funny and patient then paul is old.
Everyone who is not tall is both not calm and not happy.
If someone is either strong or not patient then someone is either not tall or humble.
Everyone who is not creative or old is curious or not wise and vice versa.
If mary is not kind then john is either not funny or strong.
If john is either not brave or not humble then someone is both not strong and old and vice versa.
Everyone who is not wise or old is either not strong or patient and vice versa.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is not humble is either patient or not kind and vice versa.
Everyone who is not calm is curious and vice versa.
If someone is both not kind and not strong then someone is both not calm and not generous and vice versa.
Everyone who is either wise or not old is both curious and not quiet.
If someone is either quiet or happy then someone is either not patient or not quiet.
Susan is brave or not quiet.
Susan is not old or funny.
Someone is both creative and not funny.
John is not tall.
Someone is both not curious and calm. | Mary is not creative. | neutral | (![X]:((~strong(X)|creative(X))<=>~wise(X)))&
(![X]:((~funny(X)&strong(X))=>(patient(X)<~>kind(X))))&
(![X]:((funny(X)&happy(X))<=>(strong(X)|happy(X))))&
((?[X]:((funny(X)&patient(X))))=>(old(paul)))&
(![X]:(~tall(X)=>(~calm(X)&~happy(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((~creative(X)|old(X))<=>(curious(X)|~wise(X))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
((brave(susan)|~quiet(susan)))&
((~old(susan)|funny(susan)))&
(?[X]:((creative(X)&~funny(X))))&
(~tall(john))&
(?[X]:((~curious(X)&calm(X)))) | ~creative(mary) | []
| null | 0 |
Everyone who is either strong or not generous is generous and vice versa.
If susan is not calm then someone is either not strong or not wise and vice versa.
Everyone who is either not wise or quiet is either not wise or curious.
Everyone who is either curious or not curious is either not tall or old and vice versa.
If someone is both rich and not old then someone is strong and vice versa.
If mary is happy then alice is both calm and not calm and vice versa.
If someone is not humble or not wise then fred is not patient and vice versa.
If someone is both not old and not creative then paul is not funny.
If fred is either tall or brave then lucy is either not creative or generous and vice versa.
If fred is both not funny and quiet then someone is both funny and rich and vice versa.
Everyone who is curious or wise is both calm and not tall.
Everyone who is brave or not kind is not kind or rich and vice versa.
If alice is generous or humble then paul is not calm.
If someone is either rich or kind then someone is wise and vice versa.
Someone is not kind or generous.
Paul is either kind or rich.
Someone is happy or not old.
Susan is either old or not funny.
Someone is either not wise or kind. | Susan is happy. | neutral | (![X]:((strong(X)<~>~generous(X))<=>generous(X)))&
((~calm(susan))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>(~wise(X)<~>curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:(strong(X))))&
((happy(mary))<=>((calm(alice)&~calm(alice))))&
((?[X]:((~humble(X)|~wise(X))))<=>(~patient(fred)))&
((?[X]:((~old(X)&~creative(X))))=>(~funny(paul)))&
(((tall(fred)<~>brave(fred)))<=>((~creative(lucy)<~>generous(lucy))))&
(((~funny(fred)&quiet(fred)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)&~tall(X))))&
(![X]:((brave(X)|~kind(X))<=>(~kind(X)|rich(X))))&
(((generous(alice)|humble(alice)))=>(~calm(paul)))&
((?[X]:((rich(X)<~>kind(X))))<=>(?[X]:(wise(X))))&
(?[X]:((~kind(X)|generous(X))))&
((kind(paul)<~>rich(paul)))&
(?[X]:((happy(X)|~old(X))))&
((old(susan)<~>~funny(susan)))&
(?[X]:((~wise(X)<~>kind(X)))) | happy(susan) | []
| null | 0 |
If paul is not curious then lucy is both not generous and not kind and vice versa.
Everyone who is either not curious or quiet is both not strong and generous and vice versa.
Everyone who is not old is curious or brave and vice versa.
Everyone who is both calm and not rich is both creative and not patient.
Everyone who is curious is strong or generous.
Everyone who is either creative or not strong is not tall.
If mary is either calm or not humble then fred is either not patient or old.
Everyone who is not funny is either not strong or not creative and vice versa.
If lucy is either happy or not funny then paul is not curious and vice versa.
Everyone who is either generous or not brave is either strong or not wise and vice versa.
If susan is either not wise or strong then john is either not creative or not calm and vice versa.
Everyone who is not tall is either old or not rich.
Everyone who is not wise is humble or not curious.
If lucy is both not rich and not old then lucy is not creative or not wise.
Everyone who is either calm or kind is funny or tall and vice versa.
If paul is both tall and creative then someone is both kind and not rich and vice versa.
Lucy is calm.
Someone is not brave or not funny.
Paul is generous.
Someone is both curious and not strong.
John is funny or kind.
Alice is curious or happy.
Someone is either not strong or not creative. | Lucy is not funny. | neutral | ((~curious(paul))<=>((~generous(lucy)&~kind(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>(~strong(X)&generous(X))))&
(![X]:(~old(X)<=>(curious(X)|brave(X))))&
(![X]:((calm(X)&~rich(X))=>(creative(X)&~patient(X))))&
(![X]:(curious(X)=>(strong(X)|generous(X))))&
(![X]:((creative(X)<~>~strong(X))=>~tall(X)))&
(((calm(mary)<~>~humble(mary)))=>((~patient(fred)<~>old(fred))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~creative(X))))&
(((happy(lucy)<~>~funny(lucy)))<=>(~curious(paul)))&
(![X]:((generous(X)<~>~brave(X))<=>(strong(X)<~>~wise(X))))&
(((~wise(susan)<~>strong(susan)))<=>((~creative(john)<~>~calm(john))))&
(![X]:(~tall(X)=>(old(X)<~>~rich(X))))&
(![X]:(~wise(X)=>(humble(X)|~curious(X))))&
(((~rich(lucy)&~old(lucy)))=>((~creative(lucy)|~wise(lucy))))&
(![X]:((calm(X)<~>kind(X))<=>(funny(X)|tall(X))))&
(((tall(paul)&creative(paul)))<=>(?[X]:((kind(X)&~rich(X)))))&
(calm(lucy))&
(?[X]:((~brave(X)|~funny(X))))&
(generous(paul))&
(?[X]:((curious(X)&~strong(X))))&
((funny(john)|kind(john)))&
((curious(alice)|happy(alice)))&
(?[X]:((~strong(X)<~>~creative(X)))) | ~funny(lucy) | []
| null | 0 |
Everyone who is both not creative and not humble is either not curious or not brave. If someone is not wise then susan is curious. If someone is both not strong and not kind then someone is not humble or funny. Everyone who is either happy or not calm is either not generous or not old. If alice is humble or old then someone is both not happy and brave and vice versa. If john is either not quiet or not generous then john is both not wise and not generous. Everyone who is both not generous and wise is both brave and not patient. If lucy is not humble then mary is either not rich or generous. Everyone who is both old and rich is humble or brave and vice versa. Everyone who is creative is not calm and vice versa. Everyone who is curious is creative. Everyone who is not tall is calm or brave. If john is not rich or not kind then alice is both not quiet and quiet. Everyone who is funny is not generous or rich and vice versa. If susan is both not curious and strong then someone is both strong and humble and vice versa. Everyone who is strong or not happy is not rich and vice versa. Someone is not quiet. Mary is not generous or not happy. Someone is not generous. Lucy is both not kind and not quiet. Someone is not kind or curious. | Alice is humble. | contradiction | (![X]:((~creative(X)&~humble(X))=>(~curious(X)<~>~brave(X))))&
((?[X]:(~wise(X)))=>(curious(susan)))&
((?[X]:((~strong(X)&~kind(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(~generous(X)<~>~old(X))))&
(((humble(alice)|old(alice)))<=>(?[X]:((~happy(X)&brave(X)))))&
(((~quiet(john)<~>~generous(john)))=>((~wise(john)&~generous(john))))&
(![X]:((~generous(X)&wise(X))=>(brave(X)&~patient(X))))&
((~humble(lucy))=>((~rich(mary)<~>generous(mary))))&
(![X]:((old(X)&rich(X))<=>(humble(X)|brave(X))))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:(curious(X)=>creative(X)))&
(![X]:(~tall(X)=>(calm(X)|brave(X))))&
(((~rich(john)|~kind(john)))=>((~quiet(alice)&quiet(alice))))&
(![X]:(funny(X)<=>(~generous(X)|rich(X))))&
(((~curious(susan)&strong(susan)))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((strong(X)|~happy(X))<=>~rich(X)))&
(?[X]:(~quiet(X)))&
((~generous(mary)|~happy(mary)))&
(?[X]:(~generous(X)))&
((~kind(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)|curious(X)))) | humble(alice) | [
"p4",
"p8",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 5395770882992986562301391
% SZS output start Proof for 5395770882992986562301391
5. (old(alice) | humble(alice)) <=> ? [X0] : (brave(X0) & ~happy(X0)) [input p4]
9. ! [X0] : ((rich(X0) & old(X0)) <=> (brave(X0) | humble(X0))) [input p8]
16. ! [X0] : ((~happy(X0) | strong(X0)) <=> ~rich(X0)) [input p15]
22. humble(alice) [input hypothesis]
47. ((old(alice) | humble(alice)) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X0] : (brave(X0) & ~happy(X0)) | (~old(alice) & ~humble(alice))) [nnf transformation 5]
48. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X0] : (brave(X0) & ~happy(X0)) | (~old(alice) & ~humble(alice))) [flattening 47]
49. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & (? [X1] : (brave(X1) & ~happy(X1)) | (~old(alice) & ~humble(alice))) [rectify 48]
50. ? [X1] : (brave(X1) & ~happy(X1)) => (brave(sK1) & ~happy(sK1)) [choice axiom]
51. (old(alice) | humble(alice) | ! [X0] : (~brave(X0) | happy(X0))) & ((brave(sK1) & ~happy(sK1)) | (~old(alice) & ~humble(alice))) [skolemisation 49,50]
54. ! [X0] : (((rich(X0) & old(X0)) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | (~rich(X0) | ~old(X0)))) [nnf transformation 9]
55. ! [X0] : (((rich(X0) & old(X0)) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ~rich(X0) | ~old(X0))) [flattening 54]
61. ! [X0] : (((~happy(X0) | strong(X0)) | rich(X0)) & (~rich(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 16]
62. ! [X0] : ((~happy(X0) | strong(X0) | rich(X0)) & (~rich(X0) | (happy(X0) & ~strong(X0)))) [flattening 61]
77. ~happy(sK1) | ~humble(alice) [cnf transformation 51]
79. brave(sK1) | ~humble(alice) [cnf transformation 51]
93. ~brave(X0) | rich(X0) [cnf transformation 55]
106. ~rich(X0) | happy(X0) [cnf transformation 62]
114. humble(alice) [cnf transformation 22]
140. 7 <=> humble(alice) [avatar definition]
149. 9 <=> brave(sK1) [avatar definition]
151. brave(sK1) <- (9) [avatar component clause 149]
153. ~7 | 9 [avatar split clause 79,149,140]
155. 10 <=> happy(sK1) [avatar definition]
157. ~happy(sK1) <- (~10) [avatar component clause 155]
159. ~7 | ~10 [avatar split clause 77,155,140]
238. 7 [avatar split clause 114,140]
243. rich(sK1) <- (9) [resolution 93,151]
250. happy(sK1) <- (9) [resolution 106,243]
251. $false <- (9, ~10) [subsumption resolution 250,157]
252. ~9 | 10 [avatar contradiction clause 251]
253. $false [avatar sat refutation 153,159,238,252]
% SZS output end Proof for 5395770882992986562301391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not patient is not calm or not brave and vice versa.
If john is not rich then someone is both rich and curious and vice versa.
If someone is patient then someone is either humble or not funny.
If susan is not old or calm then susan is old.
Everyone who is not old or generous is not brave and vice versa.
Everyone who is rich or not strong is curious or not tall and vice versa.
If lucy is both happy and quiet then mary is either not brave or not old and vice versa.
If mary is both curious and not funny then mary is brave or not funny and vice versa.
Everyone who is either not brave or not wise is either kind or not calm and vice versa.
If someone is either not creative or not generous then someone is old.
Everyone who is both brave and not calm is not kind or not wise and vice versa.
Everyone who is either brave or not happy is not tall or generous.
Everyone who is either not old or tall is both not generous and patient and vice versa.
Everyone who is both kind and brave is not patient.
If paul is strong then alice is quiet or not wise.
Everyone who is either funny or brave is either patient or happy and vice versa.
Someone is both tall and not creative.
John is funny or not creative.
Alice is not wise or patient.
John is both calm and not tall.
Someone is not wise.
Alice is not curious or wise. | Mary is not quiet. | neutral | (![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((~rich(john))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(((~old(susan)|calm(susan)))=>(old(susan)))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(((curious(mary)&~funny(mary)))<=>((brave(mary)|~funny(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((brave(X)&~calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((kind(X)&brave(X))=>~patient(X)))&
((strong(paul))=>((quiet(alice)|~wise(alice))))&
(![X]:((funny(X)<~>brave(X))<=>(patient(X)<~>happy(X))))&
(?[X]:((tall(X)&~creative(X))))&
((funny(john)|~creative(john)))&
((~wise(alice)|patient(alice)))&
((calm(john)&~tall(john)))&
(?[X]:(~wise(X)))&
((~curious(alice)|wise(alice))) | ~quiet(mary) | []
| null | 0 |
Everyone who is either not creative or humble is not funny and vice versa.
Everyone who is not funny is strong.
If fred is either not old or strong then someone is both not calm and calm.
Everyone who is either not brave or not kind is both not old and not rich and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Everyone who is either happy or not quiet is either wise or happy and vice versa.
If susan is both not humble and not rich then fred is not brave and vice versa.
If mary is not rich or not wise then someone is brave or happy.
Everyone who is either tall or humble is either strong or not creative and vice versa.
Someone is either not tall or tall.
Someone is not generous or not kind.
Fred is both not calm and not kind.
Someone is both not strong and not kind.
Paul is calm or not strong.
Paul is either strong or not happy.
Susan is not happy.
Someone is either not curious or wise. | Mary is not tall. | entailment | (![X]:((~creative(X)<~>humble(X))<=>~funny(X)))&
(![X]:(~funny(X)=>strong(X)))&
(((~old(fred)<~>strong(fred)))=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~old(X)&~rich(X))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(strong(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((~calm(fred)&~kind(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(paul)|~strong(paul)))&
((strong(paul)<~>~happy(paul)))&
(~happy(susan))&
(?[X]:((~curious(X)<~>wise(X)))) | ~tall(mary) | [
"p4",
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 1094514271653891815604620
% SZS output start Proof for 1094514271653891815604620
5. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p5]
25. tall(mary) [input hypothesis]
45. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 5]
46. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 45]
47. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
48. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 47]
94. ~quiet(X0) | ~tall(X0) [cnf transformation 46]
98. curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 48]
100. ~tall(X0) | ~curious(X0) | ~curious(X0) | quiet(X0) [cnf transformation 48]
151. tall(mary) [cnf transformation 25]
156. curious(X0) | ~tall(X0) [duplicate literal removal 98]
157. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 100]
174. ~tall(X0) | ~curious(X0) [subsumption resolution 157,94]
175. ~tall(X0) [subsumption resolution 156,174]
304. $false [subsumption resolution 151,175]
% SZS output end Proof for 1094514271653891815604620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and rich then mary is both funny and not humble.
Everyone who is either kind or calm is creative.
Everyone who is not old or wise is both calm and not wise.
If paul is strong then someone is not curious and vice versa.
Everyone who is both not happy and not funny is creative or not brave and vice versa.
Everyone who is creative or not tall is either happy or not curious and vice versa.
Everyone who is funny is wise or not generous.
Everyone who is not brave is humble and vice versa.
If someone is curious then someone is not humble or not calm and vice versa.
Everyone who is calm or not old is kind or brave.
Everyone who is both not strong and brave is either not creative or not patient and vice versa.
If someone is creative or curious then alice is both quiet and not strong and vice versa.
Everyone who is both not calm and happy is old or not patient and vice versa.
Everyone who is either humble or not quiet is patient and vice versa.
If someone is tall then someone is not rich or rich and vice versa.
If mary is either old or curious then someone is kind or not old.
Lucy is either not rich or creative.
Mary is not patient or not humble.
Lucy is funny.
Someone is not quiet or not generous.
Someone is not generous.
Paul is calm.
Someone is creative. | Paul is humble. | neutral | ((?[X]:((~patient(X)&rich(X))))=>((funny(mary)&~humble(mary))))&
(![X]:((kind(X)<~>calm(X))=>creative(X)))&
(![X]:((~old(X)|wise(X))=>(calm(X)&~wise(X))))&
((strong(paul))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~funny(X))<=>(creative(X)|~brave(X))))&
(![X]:((creative(X)|~tall(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(funny(X)=>(wise(X)|~generous(X))))&
(![X]:(~brave(X)<=>humble(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))&
(![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((~rich(lucy)<~>creative(lucy)))&
((~patient(mary)|~humble(mary)))&
(funny(lucy))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:(~generous(X)))&
(calm(paul))&
(?[X]:(creative(X))) | humble(paul) | []
| null | 0 |
Everyone who is strong is both not brave and not humble.
Everyone who is not calm is not funny.
Everyone who is not strong is both not brave and not calm and vice versa.
If alice is not rich then someone is either not happy or not quiet.
If someone is not kind then mary is not kind.
If mary is not wise or not generous then someone is either humble or not wise.
Everyone who is either rich or not wise is both tall and not generous.
Everyone who is both not patient and not wise is either generous or not wise.
If someone is either not funny or not happy then someone is not quiet or humble.
Everyone who is either not old or not brave is not creative or curious.
Everyone who is both not tall and not humble is either calm or not rich and vice versa.
Everyone who is not generous or not happy is both not rich and quiet.
If alice is generous or brave then someone is both quiet and tall and vice versa.
If mary is not calm then someone is humble or not generous and vice versa.
Everyone who is happy is both funny and rich and vice versa.
Everyone who is not strong or not creative is either funny or brave and vice versa.
Mary is quiet or not brave.
Someone is either not brave or not tall.
Susan is not old.
Someone is either brave or wise.
Fred is funny or tall.
John is both generous and creative. | John is not tall. | contradiction | (![X]:(strong(X)=>(~brave(X)&~humble(X))))&
(![X]:(~calm(X)=>~funny(X)))&
(![X]:(~strong(X)<=>(~brave(X)&~calm(X))))&
((~rich(alice))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
((?[X]:(~kind(X)))=>(~kind(mary)))&
(((~wise(mary)|~generous(mary)))=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:((rich(X)<~>~wise(X))=>(tall(X)&~generous(X))))&
(![X]:((~patient(X)&~wise(X))=>(generous(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>~happy(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~creative(X)|curious(X))))&
(![X]:((~tall(X)&~humble(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>(~rich(X)&quiet(X))))&
(((generous(alice)|brave(alice)))<=>(?[X]:((quiet(X)&tall(X)))))&
((~calm(mary))<=>(?[X]:((humble(X)|~generous(X)))))&
(![X]:(happy(X)<=>(funny(X)&rich(X))))&
(![X]:((~strong(X)|~creative(X))<=>(funny(X)<~>brave(X))))&
((quiet(mary)|~brave(mary)))&
(?[X]:((~brave(X)<~>~tall(X))))&
(~old(susan))&
(?[X]:((brave(X)<~>wise(X))))&
((funny(fred)|tall(fred)))&
((generous(john)&creative(john))) | ~tall(john) | [
"p0",
"p1",
"p2",
"p10",
"p11",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 7623675538074302718944872
% SZS output start Proof for 7623675538074302718944872
1. ! [X0] : (strong(X0) => (~humble(X0) & ~brave(X0))) [input p0]
2. ! [X0] : (~calm(X0) => ~funny(X0)) [input p1]
3. ! [X0] : (~strong(X0) <=> (~calm(X0) & ~brave(X0))) [input p2]
11. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (calm(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : ((~happy(X0) | ~generous(X0)) => (quiet(X0) & ~rich(X0))) [input p11]
14. ~calm(mary) <=> ? [X0] : (~generous(X0) | humble(X0)) [input p13]
15. ! [X0] : (happy(X0) <=> (rich(X0) & funny(X0))) [input p14]
16. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (funny(X0) <~> brave(X0))) [input p15]
22. creative(john) & generous(john) [input p21]
23. ~tall(john) [input hypothesis]
28. ! [X0] : ((~humble(X0) & ~brave(X0)) | ~strong(X0)) [ennf transformation 1]
29. ! [X0] : (~funny(X0) | calm(X0)) [ennf transformation 2]
35. ! [X0] : ((quiet(X0) & ~rich(X0)) | (happy(X0) & generous(X0))) [ennf transformation 12]
36. ! [X0] : ((~strong(X0) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | strong(X0))) [nnf transformation 3]
37. ! [X0] : ((~strong(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | strong(X0))) [flattening 36]
49. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (humble(X0) | tall(X0)))) [nnf transformation 11]
50. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | humble(X0) | tall(X0))) [flattening 49]
56. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & (? [X0] : (~generous(X0) | humble(X0)) | calm(mary)) [nnf transformation 14]
57. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & (? [X1] : (~generous(X1) | humble(X1)) | calm(mary)) [rectify 56]
58. ? [X1] : (~generous(X1) | humble(X1)) => (~generous(sK4) | humble(sK4)) [choice axiom]
59. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & ((~generous(sK4) | humble(sK4)) | calm(mary)) [skolemisation 57,58]
60. ! [X0] : ((happy(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ~happy(X0))) [nnf transformation 15]
61. ! [X0] : ((happy(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ~happy(X0))) [flattening 60]
62. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 16]
63. ! [X0] : ((~creative(X0) | ~strong(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (creative(X0) & strong(X0)))) [flattening 62]
70. ~brave(X0) | ~strong(X0) [cnf transformation 28]
72. ~funny(X0) | calm(X0) [cnf transformation 29]
73. ~brave(X0) | strong(X0) [cnf transformation 37]
74. ~calm(X0) | strong(X0) [cnf transformation 37]
75. ~strong(X0) | calm(X0) | brave(X0) [cnf transformation 37]
90. ~calm(X0) | rich(X0) | humble(X0) | tall(X0) [cnf transformation 50]
96. ~rich(X0) | happy(X0) [cnf transformation 35]
105. ~calm(mary) | ~humble(X0) [cnf transformation 59]
107. funny(X0) | ~happy(X0) [cnf transformation 61]
110. brave(X0) | funny(X0) | strong(X0) [cnf transformation 63]
114. ~creative(X0) | ~strong(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
123. creative(john) [cnf transformation 22]
124. ~tall(john) [cnf transformation 23]
125. ~strong(X0) | calm(X0) [subsumption resolution 75,70]
126. ~brave(X0) [subsumption resolution 73,70]
182. 13 <=> ! [X1] : (~happy(X1) | funny(X1)) [avatar definition]
183. ~happy(X1) | funny(X1) <- (13) [avatar component clause 182]
208. 19 <=> calm(mary) [avatar definition]
210. ~calm(mary) <- (~19) [avatar component clause 208]
213. 20 <=> ! [X0] : ~humble(X0) [avatar definition]
214. ~humble(X0) <- (20) [avatar component clause 213]
215. 20 | ~19 [avatar split clause 105,208,213]
225. 13 [avatar split clause 107,182]
226. ~creative(X0) | ~strong(X0) | ~funny(X0) [subsumption resolution 114,126]
228. funny(X0) | strong(X0) [subsumption resolution 110,126]
256. strong(X0) | calm(X0) [resolution 228,72]
257. calm(X0) [subsumption resolution 256,125]
258. $false <- (~19) [resolution 257,210]
259. strong(X0) [resolution 257,74]
260. 19 [avatar contradiction clause 258]
284. 28 <=> rich(john) [avatar definition]
286. rich(john) <- (28) [avatar component clause 284]
313. ~strong(john) | ~funny(john) [resolution 226,123]
315. ~funny(john) [subsumption resolution 313,259]
321. rich(X0) | humble(X0) | tall(X0) [resolution 90,257]
329. tall(X0) | rich(X0) <- (20) [subsumption resolution 321,214]
346. rich(john) <- (20) [resolution 329,124]
352. 28 | ~20 [avatar split clause 346,213,284]
356. happy(john) <- (28) [resolution 286,96]
358. funny(john) <- (13, 28) [resolution 356,183]
360. $false <- (13, 28) [subsumption resolution 358,315]
361. ~13 | ~28 [avatar contradiction clause 360]
362. $false [avatar sat refutation 215,225,260,352,361]
% SZS output end Proof for 7623675538074302718944872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and strong is not humble or wise and vice versa.
Everyone who is not strong is either not tall or not wise and vice versa.
If someone is not strong then lucy is either not generous or creative.
If someone is both creative and old then someone is old or not calm and vice versa.
Everyone who is not patient or kind is not strong and vice versa.
If someone is either not kind or calm then someone is rich and vice versa.
If someone is either humble or kind then susan is both calm and humble.
Everyone who is not quiet or quiet is either not funny or strong.
If someone is either not humble or not kind then lucy is curious.
Everyone who is not old is either funny or not wise.
If someone is either not quiet or curious then someone is either not calm or calm.
Everyone who is both calm and not calm is rich and vice versa.
Everyone who is both quiet and not calm is not happy and vice versa.
Everyone who is both patient and not quiet is both not patient and rich.
If alice is brave or not creative then someone is quiet or not patient and vice versa.
If john is not generous then susan is not generous or old and vice versa.
John is tall.
Someone is either not funny or not calm.
Someone is both not old and creative.
Someone is both wise and not kind.
Alice is not wise.
Lucy is tall.
Someone is humble or strong. | Lucy is not patient. | neutral | (![X]:((happy(X)&strong(X))<=>(~humble(X)|wise(X))))&
(![X]:(~strong(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:(~strong(X)))=>((~generous(lucy)<~>creative(lucy))))&
((?[X]:((creative(X)&old(X))))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:((~patient(X)|kind(X))<=>~strong(X)))&
((?[X]:((~kind(X)<~>calm(X))))<=>(?[X]:(rich(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((calm(susan)&humble(susan))))&
(![X]:((~quiet(X)|quiet(X))=>(~funny(X)<~>strong(X))))&
((?[X]:((~humble(X)<~>~kind(X))))=>(curious(lucy)))&
(![X]:(~old(X)=>(funny(X)<~>~wise(X))))&
((?[X]:((~quiet(X)<~>curious(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((calm(X)&~calm(X))<=>rich(X)))&
(![X]:((quiet(X)&~calm(X))<=>~happy(X)))&
(![X]:((patient(X)&~quiet(X))=>(~patient(X)&rich(X))))&
(((brave(alice)|~creative(alice)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((~generous(john))<=>((~generous(susan)|old(susan))))&
(tall(john))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((~old(X)&creative(X))))&
(?[X]:((wise(X)&~kind(X))))&
(~wise(alice))&
(tall(lucy))&
(?[X]:((humble(X)|strong(X)))) | ~patient(lucy) | []
| null | 0 |
If susan is not humble then paul is patient and vice versa. Everyone who is either happy or not old is both not happy and not quiet. Everyone who is old is either not kind or not quiet and vice versa. Everyone who is wise is both not strong and not calm. Everyone who is happy is not strong or patient and vice versa. If lucy is both quiet and kind then lucy is not calm or kind. Everyone who is either not quiet or not wise is either not funny or quiet and vice versa. If susan is both brave and not calm then paul is both tall and not creative and vice versa. Everyone who is both not funny and generous is not patient and vice versa. If someone is not calm or brave then someone is both not humble and rich and vice versa. Everyone who is rich is both not old and old and vice versa. Everyone who is both not humble and old is either not old or happy. If lucy is not generous then lucy is both not calm and tall and vice versa. Everyone who is happy or not kind is either creative or not kind and vice versa. If lucy is either not kind or quiet then alice is not rich. Susan is either curious or not generous. Someone is old or generous. Someone is patient or not calm. Someone is both humble and tall. Someone is happy. Lucy is not funny or quiet. | Susan is not strong. | neutral | ((~humble(susan))<=>(patient(paul)))&
(![X]:((happy(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
(![X]:(old(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:(wise(X)=>(~strong(X)&~calm(X))))&
(![X]:(happy(X)<=>(~strong(X)|patient(X))))&
(((quiet(lucy)&kind(lucy)))=>((~calm(lucy)|kind(lucy))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~funny(X)<~>quiet(X))))&
(((brave(susan)&~calm(susan)))<=>((tall(paul)&~creative(paul))))&
(![X]:((~funny(X)&generous(X))<=>~patient(X)))&
((?[X]:((~calm(X)|brave(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(rich(X)<=>(~old(X)&old(X))))&
(![X]:((~humble(X)&old(X))=>(~old(X)<~>happy(X))))&
((~generous(lucy))<=>((~calm(lucy)&tall(lucy))))&
(![X]:((happy(X)|~kind(X))<=>(creative(X)<~>~kind(X))))&
(((~kind(lucy)<~>quiet(lucy)))=>(~rich(alice)))&
((curious(susan)<~>~generous(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:(happy(X)))&
((~funny(lucy)|quiet(lucy))) | ~strong(susan) | []
| null | 0 |
Everyone who is both quiet and strong is both not happy and not kind.
If someone is either kind or not tall then mary is not tall.
If someone is not strong then someone is not tall.
Everyone who is either generous or not calm is both rich and quiet.
Everyone who is not quiet is either not humble or wise.
If someone is tall then someone is happy and vice versa.
If someone is both not creative and not patient then someone is curious or old.
If susan is either not kind or not calm then alice is either not happy or strong.
If mary is tall or not tall then paul is not wise and vice versa.
Everyone who is either patient or generous is not curious or not funny and vice versa.
If someone is either not old or not happy then john is either kind or funny and vice versa.
Everyone who is either not humble or not patient is either rich or not rich and vice versa.
Everyone who is not old or not tall is both rich and kind.
Everyone who is humble or wise is strong.
Everyone who is wise is creative or not generous and vice versa.
Everyone who is not old is either happy or calm and vice versa.
Paul is both not happy and not patient.
John is not funny.
Mary is tall or brave.
Fred is not curious.
Someone is not strong or not funny.
Mary is either not generous or funny.
Someone is creative or happy.
Alice is either curious or strong. | John is not creative. | contradiction | (![X]:((quiet(X)&strong(X))=>(~happy(X)&~kind(X))))&
((?[X]:((kind(X)<~>~tall(X))))=>(~tall(mary)))&
((?[X]:(~strong(X)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~calm(X))=>(rich(X)&quiet(X))))&
(![X]:(~quiet(X)=>(~humble(X)<~>wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((curious(X)|old(X)))))&
(((~kind(susan)<~>~calm(susan)))=>((~happy(alice)<~>strong(alice))))&
(((tall(mary)|~tall(mary)))<=>(~wise(paul)))&
(![X]:((patient(X)<~>generous(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((~old(X)<~>~happy(X))))<=>((kind(john)<~>funny(john))))&
(![X]:((~humble(X)<~>~patient(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((~old(X)|~tall(X))=>(rich(X)&kind(X))))&
(![X]:((humble(X)|wise(X))=>strong(X)))&
(![X]:(wise(X)<=>(creative(X)|~generous(X))))&
(![X]:(~old(X)<=>(happy(X)<~>calm(X))))&
((~happy(paul)&~patient(paul)))&
(~funny(john))&
((tall(mary)|brave(mary)))&
(~curious(fred))&
(?[X]:((~strong(X)|~funny(X))))&
((~generous(mary)<~>funny(mary)))&
(?[X]:((creative(X)|happy(X))))&
((curious(alice)<~>strong(alice))) | ~creative(john) | [
"p0",
"p4",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p16",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 5970358931141734365260904
% SZS output start Proof for 5970358931141734365260904
1. ! [X0] : ((strong(X0) & quiet(X0)) => (~kind(X0) & ~happy(X0))) [input p0]
5. ! [X0] : (~quiet(X0) => (~humble(X0) <~> wise(X0))) [input p4]
9. (~tall(mary) | tall(mary)) <=> ~wise(paul) [input p8]
10. ! [X0] : ((patient(X0) <~> generous(X0)) <=> (~funny(X0) | ~curious(X0))) [input p9]
11. ? [X0] : (~old(X0) <~> ~happy(X0)) <=> (kind(john) <~> funny(john)) [input p10]
12. ! [X0] : ((~humble(X0) <~> ~patient(X0)) <=> (rich(X0) <~> ~rich(X0))) [input p11]
13. ! [X0] : ((~tall(X0) | ~old(X0)) => (kind(X0) & rich(X0))) [input p12]
14. ! [X0] : ((wise(X0) | humble(X0)) => strong(X0)) [input p13]
15. ! [X0] : (wise(X0) <=> (~generous(X0) | creative(X0))) [input p14]
17. ~patient(paul) & ~happy(paul) [input p16]
18. ~funny(john) [input p17]
25. ~creative(john) [input hypothesis]
30. ! [X0] : ((~kind(X0) & ~happy(X0)) | (~strong(X0) | ~quiet(X0))) [ennf transformation 1]
31. ! [X0] : ((~kind(X0) & ~happy(X0)) | ~strong(X0) | ~quiet(X0)) [flattening 30]
35. ! [X0] : ((~humble(X0) <~> wise(X0)) | quiet(X0)) [ennf transformation 5]
38. ! [X0] : ((kind(X0) & rich(X0)) | (tall(X0) & old(X0))) [ennf transformation 13]
39. ! [X0] : (strong(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 14]
45. ! [X0] : (((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 35]
55. ((~tall(mary) | tall(mary)) | wise(paul)) & (~wise(paul) | (tall(mary) & ~tall(mary))) [nnf transformation 9]
56. (~tall(mary) | tall(mary) | wise(paul)) & (~wise(paul) | (tall(mary) & ~tall(mary))) [flattening 55]
57. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (funny(X0) & curious(X0))) & ((~funny(X0) | ~curious(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 10]
58. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (funny(X0) & curious(X0))) & (~funny(X0) | ~curious(X0) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [flattening 57]
59. (? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) [nnf transformation 11]
60. (? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X1] : ((~old(X1) | happy(X1)) & (~happy(X1) | old(X1)))) [rectify 59]
61. ? [X0] : ((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) => ((happy(sK4) | old(sK4)) & (~happy(sK4) | ~old(sK4))) [choice axiom]
62. (((happy(sK4) | old(sK4)) & (~happy(sK4) | ~old(sK4))) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X1] : ((~old(X1) | happy(X1)) & (~happy(X1) | old(X1)))) [skolemisation 60,61]
63. ! [X0] : ((((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) & (((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0))))) [nnf transformation 12]
64. ! [X0] : ((wise(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | ~wise(X0))) [nnf transformation 15]
65. ! [X0] : ((wise(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | ~wise(X0))) [flattening 64]
73. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 31]
74. ~kind(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 31]
82. ~humble(X0) | wise(X0) | quiet(X0) [cnf transformation 45]
83. ~wise(X0) | humble(X0) | quiet(X0) [cnf transformation 45]
91. ~wise(paul) | ~tall(mary) [cnf transformation 56]
92. ~wise(paul) | tall(mary) [cnf transformation 56]
97. funny(X0) | patient(X0) | generous(X0) [cnf transformation 58]
99. ~patient(X0) | ~generous(X0) | funny(X0) [cnf transformation 58]
101. funny(john) | kind(john) | ~old(X1) | happy(X1) [cnf transformation 62]
112. ~patient(X0) | ~humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
113. ~patient(X0) | ~humble(X0) | rich(X0) | rich(X0) [cnf transformation 63]
114. patient(X0) | humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
115. patient(X0) | humble(X0) | rich(X0) | rich(X0) [cnf transformation 63]
118. old(X0) | kind(X0) [cnf transformation 38]
120. ~humble(X0) | strong(X0) [cnf transformation 39]
121. ~wise(X0) | strong(X0) [cnf transformation 39]
122. ~wise(X0) | creative(X0) | ~generous(X0) [cnf transformation 65]
124. wise(X0) | generous(X0) [cnf transformation 65]
130. ~patient(paul) [cnf transformation 17]
131. ~funny(john) [cnf transformation 18]
139. ~creative(john) [cnf transformation 25]
140. ~patient(X0) | ~humble(X0) | ~rich(X0) [duplicate literal removal 112]
141. ~patient(X0) | ~humble(X0) | rich(X0) [duplicate literal removal 113]
142. patient(X0) | humble(X0) | ~rich(X0) [duplicate literal removal 114]
143. patient(X0) | humble(X0) | rich(X0) [duplicate literal removal 115]
148. 2 <=> tall(mary) [avatar definition]
213. 17 <=> wise(paul) [avatar definition]
215. ~wise(paul) <- (~17) [avatar component clause 213]
216. 2 | ~17 [avatar split clause 92,213,148]
217. ~2 | ~17 [avatar split clause 91,213,148]
219. 18 <=> funny(john) [avatar definition]
221. ~funny(john) <- (~18) [avatar component clause 219]
223. 19 <=> kind(john) [avatar definition]
225. kind(john) <- (19) [avatar component clause 223]
239. 22 <=> ! [X1] : (~old(X1) | happy(X1)) [avatar definition]
240. ~old(X1) | happy(X1) <- (22) [avatar component clause 239]
246. 22 | 19 | 18 [avatar split clause 101,219,223,239]
248. patient(X0) | humble(X0) [subsumption resolution 142,143]
249. ~patient(X0) | ~humble(X0) [subsumption resolution 140,141]
251. ~18 [avatar split clause 131,219]
294. generous(X0) | strong(X0) [resolution 124,121]
298. humble(paul) [resolution 248,130]
302. strong(paul) [resolution 298,120]
319. 33 <=> quiet(john) [avatar definition]
323. 34 <=> strong(john) [avatar definition]
364. wise(paul) | quiet(paul) [resolution 82,298]
365. quiet(paul) <- (~17) [subsumption resolution 364,215]
370. humble(X0) | quiet(X0) | generous(X0) [resolution 83,124]
406. patient(john) | generous(john) <- (~18) [resolution 97,221]
410. 48 <=> generous(john) [avatar definition]
411. ~generous(john) <- (~48) [avatar component clause 410]
412. generous(john) <- (48) [avatar component clause 410]
414. 49 <=> patient(john) [avatar definition]
416. patient(john) <- (49) [avatar component clause 414]
417. 48 | 49 | 18 [avatar split clause 406,219,414,410]
431. ~generous(X0) | funny(X0) | humble(X0) [resolution 99,248]
570. 60 <=> humble(john) [avatar definition]
571. ~humble(john) <- (~60) [avatar component clause 570]
572. humble(john) <- (60) [avatar component clause 570]
593. strong(john) <- (~48) [resolution 411,294]
594. 34 | 48 [avatar split clause 593,410,323]
598. ~humble(john) <- (49) [resolution 416,249]
604. ~60 | ~49 [avatar split clause 598,414,570]
668. quiet(john) | generous(john) <- (~60) [resolution 571,370]
678. quiet(john) <- (~48, ~60) [subsumption resolution 668,411]
679. 33 | 48 | 60 [avatar split clause 678,570,410,319]
723. ~strong(john) | ~quiet(john) <- (19) [resolution 225,74]
726. funny(john) | humble(john) <- (48) [resolution 412,431]
735. wise(john) | quiet(john) <- (60) [resolution 572,82]
736. strong(john) <- (60) [resolution 572,120]
740. 73 <=> wise(john) [avatar definition]
742. wise(john) <- (73) [avatar component clause 740]
743. 33 | 73 | ~60 [avatar split clause 735,570,740,319]
744. 34 | ~60 [avatar split clause 736,570,323]
745. ~33 | ~34 | ~19 [avatar split clause 723,223,323,319]
789. creative(john) | ~generous(john) <- (73) [resolution 742,122]
792. ~generous(john) <- (73) [subsumption resolution 789,139]
793. $false <- (48, 73) [subsumption resolution 792,412]
794. ~48 | ~73 [avatar contradiction clause 793]
798. humble(john) <- (~18, 48) [subsumption resolution 726,221]
799. 60 | 18 | ~48 [avatar split clause 798,410,219,570]
808. kind(X1) | happy(X1) <- (22) [resolution 240,118]
819. happy(X0) | ~strong(X0) | ~quiet(X0) <- (22) [resolution 808,74]
822. ~strong(X0) | ~quiet(X0) <- (22) [subsumption resolution 819,73]
876. ~quiet(paul) <- (22) [resolution 822,302]
882. $false <- (~17, 22) [subsumption resolution 876,365]
883. 17 | ~22 [avatar contradiction clause 882]
888. $false [avatar sat refutation 216,217,246,251,417,594,604,679,743,744,745,794,799,883]
% SZS output end Proof for 5970358931141734365260904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not curious or generous. Everyone who is both rich and generous is either tall or happy. Everyone who is both not kind and brave is not old. Everyone who is not old or calm is either brave or generous and vice versa. If paul is both not kind and tall then someone is strong or not rich and vice versa. If someone is either not funny or creative then someone is not funny. If someone is both not old and rich then alice is not happy and vice versa. Everyone who is both rich and happy is not creative or not rich. If susan is brave then someone is both generous and not generous and vice versa. Everyone who is not calm or curious is tall and vice versa. If someone is generous then alice is not strong or brave and vice versa. Everyone who is both old and not quiet is old and vice versa. If someone is funny then someone is either patient or not creative and vice versa. Everyone who is happy or not quiet is both curious and not humble. Everyone who is either happy or not happy is both not rich and not quiet and vice versa. Everyone who is not wise is either strong or not brave. Alice is not wise or humble. Someone is either not generous or generous. Fred is not humble. Susan is tall or not wise. Fred is either not happy or not kind. Fred is both curious and generous. John is rich or kind. Susan is quiet or calm. | John is tall. | entailment | (![X]:(~kind(X)=>(~curious(X)|generous(X))))&
(![X]:((rich(X)&generous(X))=>(tall(X)<~>happy(X))))&
(![X]:((~kind(X)&brave(X))=>~old(X)))&
(![X]:((~old(X)|calm(X))<=>(brave(X)<~>generous(X))))&
(((~kind(paul)&tall(paul)))<=>(?[X]:((strong(X)|~rich(X)))))&
((?[X]:((~funny(X)<~>creative(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~old(X)&rich(X))))<=>(~happy(alice)))&
(![X]:((rich(X)&happy(X))=>(~creative(X)|~rich(X))))&
((brave(susan))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((~calm(X)|curious(X))<=>tall(X)))&
((?[X]:(generous(X)))<=>((~strong(alice)|brave(alice))))&
(![X]:((old(X)&~quiet(X))<=>old(X)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((happy(X)|~quiet(X))=>(curious(X)&~humble(X))))&
(![X]:((happy(X)<~>~happy(X))<=>(~rich(X)&~quiet(X))))&
(![X]:(~wise(X)=>(strong(X)<~>~brave(X))))&
((~wise(alice)|humble(alice)))&
(?[X]:((~generous(X)<~>generous(X))))&
(~humble(fred))&
((tall(susan)|~wise(susan)))&
((~happy(fred)<~>~kind(fred)))&
((curious(fred)&generous(fred)))&
((rich(john)|kind(john)))&
((quiet(susan)|calm(susan))) | tall(john) | [
"p9",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3850819510408384756479758
% SZS output start Proof for 3850819510408384756479758
10. ! [X0] : ((curious(X0) | ~calm(X0)) <=> tall(X0)) [input p9]
14. ! [X0] : ((~quiet(X0) | happy(X0)) => (~humble(X0) & curious(X0))) [input p13]
15. ! [X0] : ((happy(X0) <~> ~happy(X0)) <=> (~quiet(X0) & ~rich(X0))) [input p14]
25. ~tall(john) [input hypothesis]
37. ! [X0] : ((~humble(X0) & curious(X0)) | (quiet(X0) & ~happy(X0))) [ennf transformation 14]
59. ! [X0] : (((curious(X0) | ~calm(X0)) | ~tall(X0)) & (tall(X0) | (~curious(X0) & calm(X0)))) [nnf transformation 10]
60. ! [X0] : ((curious(X0) | ~calm(X0) | ~tall(X0)) & (tall(X0) | (~curious(X0) & calm(X0)))) [flattening 59]
73. ! [X0] : ((((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0))))) [nnf transformation 15]
74. ! [X0] : ((((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0))))) [flattening 73]
105. ~curious(X0) | tall(X0) [cnf transformation 60]
118. quiet(X0) | curious(X0) [cnf transformation 37]
123. ~quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 74]
124. ~quiet(X0) | happy(X0) | happy(X0) [cnf transformation 74]
140. ~tall(john) [cnf transformation 25]
143. ~quiet(X0) | ~happy(X0) [duplicate literal removal 123]
144. ~quiet(X0) | happy(X0) [duplicate literal removal 124]
256. ~quiet(X0) [subsumption resolution 143,144]
295. curious(X1) [resolution 118,256]
296. tall(X0) [resolution 295,105]
297. $false [resolution 296,140]
% SZS output end Proof for 3850819510408384756479758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is old or not happy. If someone is either not generous or old then someone is not patient or not happy. Everyone who is calm or not creative is strong and vice versa. If someone is both not wise and patient then mary is either generous or not humble. If someone is quiet or old then someone is both patient and not humble. Everyone who is both happy and patient is not generous or happy and vice versa. If susan is not rich then someone is not quiet. Everyone who is humble is both strong and not happy. If someone is kind then alice is either not kind or curious and vice versa. If alice is brave then mary is rich. Everyone who is not rich or curious is not patient or not old and vice versa. Everyone who is either wise or not old is either happy or kind. If alice is humble then alice is either not humble or not old and vice versa. If paul is not old then someone is either calm or not quiet. If someone is tall or not rich then lucy is not strong or not generous. Everyone who is both not rich and wise is not kind and vice versa. John is both not rich and not kind. Alice is both not happy and not patient. Someone is calm. Mary is both humble and not calm. Someone is not patient or not brave. Someone is brave or not patient. Lucy is either not kind or tall. | Alice is not kind. | neutral | ((funny(alice))=>(?[X]:((old(X)|~happy(X)))))&
((?[X]:((~generous(X)<~>old(X))))=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:((calm(X)|~creative(X))<=>strong(X)))&
((?[X]:((~wise(X)&patient(X))))=>((generous(mary)<~>~humble(mary))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:((happy(X)&patient(X))<=>(~generous(X)|happy(X))))&
((~rich(susan))=>(?[X]:(~quiet(X))))&
(![X]:(humble(X)=>(strong(X)&~happy(X))))&
((?[X]:(kind(X)))<=>((~kind(alice)<~>curious(alice))))&
((brave(alice))=>(rich(mary)))&
(![X]:((~rich(X)|curious(X))<=>(~patient(X)|~old(X))))&
(![X]:((wise(X)<~>~old(X))=>(happy(X)<~>kind(X))))&
((humble(alice))<=>((~humble(alice)<~>~old(alice))))&
((~old(paul))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((tall(X)|~rich(X))))=>((~strong(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&wise(X))<=>~kind(X)))&
((~rich(john)&~kind(john)))&
((~happy(alice)&~patient(alice)))&
(?[X]:(calm(X)))&
((humble(mary)&~calm(mary)))&
(?[X]:((~patient(X)|~brave(X))))&
(?[X]:((brave(X)|~patient(X))))&
((~kind(lucy)<~>tall(lucy))) | ~kind(alice) | []
| null | 0 |
If someone is not rich then someone is both not tall and patient and vice versa. If someone is tall then someone is either not brave or happy and vice versa. Everyone who is both not quiet and rich is not funny or old and vice versa. If someone is both not generous and not strong then fred is both not happy and kind. Everyone who is not curious is not old or patient and vice versa. Everyone who is wise or creative is generous or not strong. If alice is strong then someone is not patient. Everyone who is both not curious and not happy is either not calm or not funny and vice versa. If susan is kind or calm then john is either not calm or old and vice versa. Everyone who is both not rich and not calm is either humble or not tall. Everyone who is tall or not happy is not creative and vice versa. Everyone who is tall is not creative and vice versa. If mary is not calm or happy then someone is creative or not quiet. If someone is both not generous and strong then someone is curious or generous and vice versa. Everyone who is both quiet and not wise is generous or not brave and vice versa. Everyone who is both not quiet and calm is either humble or brave. Paul is not curious or patient. Someone is creative. Alice is rich. Someone is either not generous or not patient. Fred is not curious. Someone is not curious or not patient. Paul is not tall or not curious. | Susan is not patient. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~tall(X)&patient(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~quiet(X)&rich(X))<=>(~funny(X)|old(X))))&
((?[X]:((~generous(X)&~strong(X))))=>((~happy(fred)&kind(fred))))&
(![X]:(~curious(X)<=>(~old(X)|patient(X))))&
(![X]:((wise(X)|creative(X))=>(generous(X)|~strong(X))))&
((strong(alice))=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)&~happy(X))<=>(~calm(X)<~>~funny(X))))&
(((kind(susan)|calm(susan)))<=>((~calm(john)<~>old(john))))&
(![X]:((~rich(X)&~calm(X))=>(humble(X)<~>~tall(X))))&
(![X]:((tall(X)|~happy(X))<=>~creative(X)))&
(![X]:(tall(X)<=>~creative(X)))&
(((~calm(mary)|happy(mary)))=>(?[X]:((creative(X)|~quiet(X)))))&
((?[X]:((~generous(X)&strong(X))))<=>(?[X]:((curious(X)|generous(X)))))&
(![X]:((quiet(X)&~wise(X))<=>(generous(X)|~brave(X))))&
(![X]:((~quiet(X)&calm(X))=>(humble(X)<~>brave(X))))&
((~curious(paul)|patient(paul)))&
(?[X]:(creative(X)))&
(rich(alice))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~curious(fred))&
(?[X]:((~curious(X)|~patient(X))))&
((~tall(paul)|~curious(paul))) | ~patient(susan) | []
| null | 0 |
Everyone who is either not brave or brave is either patient or quiet.
Everyone who is both not humble and patient is happy or kind and vice versa.
If fred is not old or not creative then someone is both not calm and not patient and vice versa.
Everyone who is both not curious and not creative is quiet or curious.
If someone is either rich or old then paul is either humble or funny and vice versa.
If mary is funny or not kind then alice is both wise and brave.
Everyone who is patient is not calm and vice versa.
Everyone who is brave or not strong is rich or quiet.
Everyone who is either not rich or not brave is both happy and not strong.
Everyone who is both strong and kind is old and vice versa.
Everyone who is generous or not funny is both creative and not kind and vice versa.
Everyone who is both not generous and not kind is not kind or not old.
Everyone who is humble or tall is patient and vice versa.
If john is calm then mary is not creative and vice versa.
Everyone who is not funny or wise is both rich and not kind and vice versa.
If lucy is not creative or patient then someone is both funny and quiet and vice versa.
Someone is either not curious or not calm.
Fred is old or not kind.
John is either not generous or tall.
John is patient.
Someone is not quiet.
Susan is either patient or not funny.
Someone is not happy or wise.
Someone is not rich. | Mary is not quiet. | neutral | (![X]:((~brave(X)<~>brave(X))=>(patient(X)<~>quiet(X))))&
(![X]:((~humble(X)&patient(X))<=>(happy(X)|kind(X))))&
(((~old(fred)|~creative(fred)))<=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~curious(X)&~creative(X))=>(quiet(X)|curious(X))))&
((?[X]:((rich(X)<~>old(X))))<=>((humble(paul)<~>funny(paul))))&
(((funny(mary)|~kind(mary)))=>((wise(alice)&brave(alice))))&
(![X]:(patient(X)<=>~calm(X)))&
(![X]:((brave(X)|~strong(X))=>(rich(X)|quiet(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(happy(X)&~strong(X))))&
(![X]:((strong(X)&kind(X))<=>old(X)))&
(![X]:((generous(X)|~funny(X))<=>(creative(X)&~kind(X))))&
(![X]:((~generous(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:((humble(X)|tall(X))<=>patient(X)))&
((calm(john))<=>(~creative(mary)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)&~kind(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)&quiet(X)))))&
(?[X]:((~curious(X)<~>~calm(X))))&
((old(fred)|~kind(fred)))&
((~generous(john)<~>tall(john)))&
(patient(john))&
(?[X]:(~quiet(X)))&
((patient(susan)<~>~funny(susan)))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:(~rich(X))) | ~quiet(mary) | []
| null | 0 |
Everyone who is both rich and brave is both not rich and wise. If someone is both not funny and not patient then someone is not quiet or happy. If mary is not curious then someone is either not brave or not old and vice versa. Everyone who is either not rich or funny is not funny or tall. Everyone who is happy is both not kind and quiet. If someone is not generous then mary is either wise or old. Everyone who is either old or not curious is both curious and not curious. If someone is either strong or brave then someone is kind and vice versa. If someone is generous then someone is not curious. Everyone who is not rich or calm is not creative. Everyone who is quiet is not calm and vice versa. Everyone who is not brave or not strong is calm or not quiet. Everyone who is either rich or not generous is both creative and curious and vice versa. Everyone who is either brave or funny is calm or not calm. If someone is not calm then paul is patient and vice versa. Everyone who is either funny or rich is brave or not happy. Someone is either not patient or not humble. Someone is kind or old. Someone is curious or not funny. Mary is happy or not funny. John is either not happy or not funny. Someone is both not old and strong. Someone is creative or not quiet. | Mary is brave. | neutral | (![X]:((rich(X)&brave(X))=>(~rich(X)&wise(X))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
((~curious(mary))<=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(~funny(X)|tall(X))))&
(![X]:(happy(X)=>(~kind(X)&quiet(X))))&
((?[X]:(~generous(X)))=>((wise(mary)<~>old(mary))))&
(![X]:((old(X)<~>~curious(X))=>(curious(X)&~curious(X))))&
((?[X]:((strong(X)<~>brave(X))))<=>(?[X]:(kind(X))))&
((?[X]:(generous(X)))=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)|calm(X))=>~creative(X)))&
(![X]:(quiet(X)<=>~calm(X)))&
(![X]:((~brave(X)|~strong(X))=>(calm(X)|~quiet(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(creative(X)&curious(X))))&
(![X]:((brave(X)<~>funny(X))=>(calm(X)|~calm(X))))&
((?[X]:(~calm(X)))<=>(patient(paul)))&
(![X]:((funny(X)<~>rich(X))=>(brave(X)|~happy(X))))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((curious(X)|~funny(X))))&
((happy(mary)|~funny(mary)))&
((~happy(john)<~>~funny(john)))&
(?[X]:((~old(X)&strong(X))))&
(?[X]:((creative(X)|~quiet(X)))) | brave(mary) | []
| null | 0 |
Everyone who is both creative and not creative is not kind or not generous and vice versa.
Everyone who is both quiet and creative is either quiet or not old.
If someone is tall or not generous then someone is funny or not rich and vice versa.
If someone is either funny or not generous then susan is either creative or not quiet and vice versa.
Everyone who is not funny is creative or not happy.
If someone is not funny or not quiet then mary is tall or humble and vice versa.
Everyone who is both not quiet and not calm is brave and vice versa.
If susan is either not kind or old then alice is strong.
Everyone who is both strong and not calm is either not strong or not old and vice versa.
If someone is either not curious or not tall then someone is not calm or not tall.
If mary is either creative or happy then fred is both old and not brave and vice versa.
If someone is either not calm or not kind then someone is patient or not tall and vice versa.
Everyone who is not curious is both rich and not quiet.
If mary is both happy and quiet then someone is both not tall and not patient.
If john is either rich or happy then susan is both not humble and wise and vice versa.
John is not funny or creative.
Lucy is either old or not curious.
Fred is either not curious or not quiet.
John is not patient or generous.
Someone is tall or not strong.
Someone is not funny.
Someone is either not old or tall. | Susan is not patient. | neutral | (![X]:((creative(X)&~creative(X))<=>(~kind(X)|~generous(X))))&
(![X]:((quiet(X)&creative(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((tall(X)|~generous(X))))<=>(?[X]:((funny(X)|~rich(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>((creative(susan)<~>~quiet(susan))))&
(![X]:(~funny(X)=>(creative(X)|~happy(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>((tall(mary)|humble(mary))))&
(![X]:((~quiet(X)&~calm(X))<=>brave(X)))&
(((~kind(susan)<~>old(susan)))=>(strong(alice)))&
(![X]:((strong(X)&~calm(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:((~calm(X)|~tall(X)))))&
(((creative(mary)<~>happy(mary)))<=>((old(fred)&~brave(fred))))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:(~curious(X)=>(rich(X)&~quiet(X))))&
(((happy(mary)&quiet(mary)))=>(?[X]:((~tall(X)&~patient(X)))))&
(((rich(john)<~>happy(john)))<=>((~humble(susan)&wise(susan))))&
((~funny(john)|creative(john)))&
((old(lucy)<~>~curious(lucy)))&
((~curious(fred)<~>~quiet(fred)))&
((~patient(john)|generous(john)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~old(X)<~>tall(X)))) | ~patient(susan) | []
| null | 0 |
If alice is either not strong or kind then lucy is strong.
Everyone who is both not rich and not calm is not kind or calm and vice versa.
Everyone who is curious is generous or not curious and vice versa.
If paul is both not kind and generous then someone is generous and vice versa.
If someone is strong or wise then someone is not kind or rich and vice versa.
Everyone who is either not quiet or not kind is either not humble or brave and vice versa.
If someone is patient then someone is not funny and vice versa.
Everyone who is both patient and not quiet is either patient or not humble.
If someone is either not kind or tall then someone is either calm or not creative.
If someone is both curious and wise then lucy is either not patient or generous.
Everyone who is not happy is either not old or strong and vice versa.
If paul is either brave or not tall then fred is both not humble and kind and vice versa.
Everyone who is not kind is not calm and vice versa.
Everyone who is either not happy or funny is not generous and vice versa.
If john is either not old or not happy then someone is both not wise and quiet.
If susan is kind or happy then susan is both not generous and funny.
Lucy is either creative or not old.
Someone is either not strong or rich.
Fred is not quiet or tall.
John is old.
Lucy is not quiet or not brave. | Paul is strong. | neutral | (((~strong(alice)<~>kind(alice)))=>(strong(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(~kind(X)|calm(X))))&
(![X]:(curious(X)<=>(generous(X)|~curious(X))))&
(((~kind(paul)&generous(paul)))<=>(?[X]:(generous(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~humble(X)<~>brave(X))))&
((?[X]:(patient(X)))<=>(?[X]:(~funny(X))))&
(![X]:((patient(X)&~quiet(X))=>(patient(X)<~>~humble(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:((calm(X)<~>~creative(X)))))&
((?[X]:((curious(X)&wise(X))))=>((~patient(lucy)<~>generous(lucy))))&
(![X]:(~happy(X)<=>(~old(X)<~>strong(X))))&
(((brave(paul)<~>~tall(paul)))<=>((~humble(fred)&kind(fred))))&
(![X]:(~kind(X)<=>~calm(X)))&
(![X]:((~happy(X)<~>funny(X))<=>~generous(X)))&
(((~old(john)<~>~happy(john)))=>(?[X]:((~wise(X)&quiet(X)))))&
(((kind(susan)|happy(susan)))=>((~generous(susan)&funny(susan))))&
((creative(lucy)<~>~old(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
((~quiet(fred)|tall(fred)))&
(old(john))&
((~quiet(lucy)|~brave(lucy))) | strong(paul) | []
| null | 0 |
If someone is not kind or humble then someone is both not wise and not quiet and vice versa.
Everyone who is quiet is not wise and vice versa.
Everyone who is quiet or creative is not strong and vice versa.
If someone is not funny then someone is either not patient or calm.
If someone is either not curious or patient then someone is not quiet.
If lucy is not funny then someone is quiet and vice versa.
If someone is not calm or rich then someone is both not patient and funny.
If someone is both humble and patient then alice is either not kind or generous.
If someone is both not old and funny then someone is both not kind and calm.
Everyone who is not humble is both calm and not creative.
Everyone who is either brave or humble is not wise or humble and vice versa.
Everyone who is either calm or not creative is either strong or funny and vice versa.
Everyone who is either calm or wise is both generous and funny and vice versa.
Everyone who is old is both strong and not rich and vice versa.
Everyone who is both not brave and kind is either not rich or creative and vice versa.
Everyone who is both not old and funny is not strong and vice versa.
Mary is not wise or happy.
Someone is both not creative and kind.
Someone is both not humble and not patient.
Someone is both not patient and strong.
Fred is quiet or not brave. | Lucy is not old. | contradiction | ((?[X]:((~kind(X)|humble(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((quiet(X)|creative(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)<~>calm(X)))))&
((?[X]:((~curious(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
((~funny(lucy))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((humble(X)&patient(X))))=>((~kind(alice)<~>generous(alice))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:(~humble(X)=>(calm(X)&~creative(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)|humble(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)<~>funny(X))))&
(![X]:((calm(X)<~>wise(X))<=>(generous(X)&funny(X))))&
(![X]:(old(X)<=>(strong(X)&~rich(X))))&
(![X]:((~brave(X)&kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)&funny(X))<=>~strong(X)))&
((~wise(mary)|happy(mary)))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~patient(X)&strong(X))))&
((quiet(fred)|~brave(fred))) | ~old(lucy) | [
"p0",
"p1",
"p2",
"p5",
"p8",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3671191918161167300813149
% SZS output start Proof for 3671191918161167300813149
1. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p0]
2. ! [X0] : (quiet(X0) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((creative(X0) | quiet(X0)) <=> ~strong(X0)) [input p2]
6. ~funny(lucy) <=> ? [X0] : quiet(X0) [input p5]
9. ? [X0] : (funny(X0) & ~old(X0)) => ? [X0] : (calm(X0) & ~kind(X0)) [input p8]
14. ! [X0] : (old(X0) <=> (~rich(X0) & strong(X0))) [input p13]
16. ! [X0] : ((funny(X0) & ~old(X0)) <=> ~strong(X0)) [input p15]
22. ~old(lucy) [input hypothesis]
23. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 1]
27. ? [X0] : (funny(X0) & ~old(X0)) => ? [X1] : (calm(X1) & ~kind(X1)) [rectify 9]
33. ? [X1] : (calm(X1) & ~kind(X1)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 27]
35. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (~humble(X0) & kind(X0))) [nnf transformation 23]
36. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (~humble(X3) & kind(X3))) [rectify 35]
37. ? [X0] : (humble(X0) | ~kind(X0)) => (humble(sK0) | ~kind(sK0)) [choice axiom]
38. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK1) & ~wise(sK1)) [choice axiom]
39. ((humble(sK0) | ~kind(sK0)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK1) & ~wise(sK1)) | ! [X3] : (~humble(X3) & kind(X3))) [skolemisation 36,38,37]
40. ! [X0] : ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))) [nnf transformation 2]
41. ! [X0] : (((creative(X0) | quiet(X0)) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : ((creative(X0) | quiet(X0) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 41]
51. (~funny(lucy) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | funny(lucy)) [nnf transformation 6]
52. (~funny(lucy) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | funny(lucy)) [rectify 51]
53. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
54. (~funny(lucy) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | funny(lucy)) [skolemisation 52,53]
59. ? [X0] : (calm(X0) & ~kind(X0)) | ! [X1] : (~funny(X1) | old(X1)) [rectify 33]
60. ? [X0] : (calm(X0) & ~kind(X0)) => (calm(sK6) & ~kind(sK6)) [choice axiom]
61. (calm(sK6) & ~kind(sK6)) | ! [X1] : (~funny(X1) | old(X1)) [skolemisation 59,60]
67. ! [X0] : ((old(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | ~old(X0))) [nnf transformation 14]
68. ! [X0] : ((old(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | ~old(X0))) [flattening 67]
71. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | old(X0)))) [nnf transformation 16]
72. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | old(X0))) [flattening 71]
79. ~wise(sK1) | kind(X3) [cnf transformation 39]
81. ~quiet(sK1) | kind(X3) [cnf transformation 39]
85. quiet(X0) | wise(X0) [cnf transformation 40]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 42]
93. quiet(sK4) | funny(lucy) [cnf transformation 54]
101. ~kind(sK6) | ~funny(X1) | old(X1) [cnf transformation 61]
125. ~old(X0) | strong(X0) [cnf transformation 68]
136. funny(X0) | strong(X0) [cnf transformation 72]
144. ~old(lucy) [cnf transformation 22]
148. 1 <=> ! [X1] : (quiet(X1) | wise(X1)) [avatar definition]
149. quiet(X1) | wise(X1) <- (1) [avatar component clause 148]
163. 5 <=> quiet(sK1) [avatar definition]
165. ~quiet(sK1) <- (~5) [avatar component clause 163]
168. 6 <=> ! [X3] : kind(X3) [avatar definition]
169. kind(X3) <- (6) [avatar component clause 168]
170. 6 | ~5 [avatar split clause 81,163,168]
172. 7 <=> wise(sK1) [avatar definition]
176. 6 | ~7 [avatar split clause 79,172,168]
177. 1 [avatar split clause 85,148]
204. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
205. ~quiet(X0) <- (14) [avatar component clause 204]
207. 15 <=> funny(lucy) [avatar definition]
208. funny(lucy) <- (15) [avatar component clause 207]
212. 16 <=> quiet(sK4) [avatar definition]
214. quiet(sK4) <- (16) [avatar component clause 212]
215. 15 | 16 [avatar split clause 93,212,207]
248. 24 <=> ! [X1] : (~funny(X1) | old(X1)) [avatar definition]
249. ~funny(X1) | old(X1) <- (24) [avatar component clause 248]
256. 26 <=> kind(sK6) [avatar definition]
258. ~kind(sK6) <- (~26) [avatar component clause 256]
259. 24 | ~26 [avatar split clause 101,256,248]
289. wise(sK1) <- (1, ~5) [resolution 149,165]
294. 7 | ~1 | 5 [avatar split clause 289,163,148,172]
296. old(X0) | strong(X0) <- (24) [resolution 249,136]
297. strong(X0) <- (24) [subsumption resolution 296,125]
303. ~quiet(X1) <- (24) [resolution 297,86]
304. 14 | ~24 [avatar split clause 303,248,204]
305. $false <- (14, 16) [resolution 205,214]
307. ~14 | ~16 [avatar contradiction clause 305]
308. old(lucy) <- (15, 24) [resolution 208,249]
309. $false <- (15, 24) [subsumption resolution 308,144]
310. ~15 | ~24 [avatar contradiction clause 309]
311. $false <- (6, ~26) [subsumption resolution 258,169]
312. ~6 | 26 [avatar contradiction clause 311]
313. $false [avatar sat refutation 170,176,177,215,259,294,304,307,310,312]
% SZS output end Proof for 3671191918161167300813149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either calm or not kind then someone is both not generous and humble.
Everyone who is both not creative and strong is not brave and vice versa.
If someone is both not creative and not strong then someone is not quiet and vice versa.
Everyone who is tall is either not kind or tall and vice versa.
If someone is creative or old then someone is not curious and vice versa.
Everyone who is calm or not kind is either not rich or not happy.
If mary is quiet then paul is either not funny or not strong and vice versa.
Everyone who is both creative and calm is not happy or not creative and vice versa.
Everyone who is strong or not generous is both calm and not calm.
If someone is not humble then john is both old and tall.
Everyone who is patient or not brave is not strong.
If paul is either curious or wise then someone is both humble and calm.
Everyone who is not wise is either not old or not curious and vice versa.
Everyone who is wise is either not happy or not creative.
Everyone who is calm is not old or generous.
Someone is either not funny or curious.
Someone is both calm and not old.
Alice is either not funny or not creative.
Susan is either not rich or calm.
Lucy is either not rich or patient. | Alice is not rich. | neutral | (((calm(lucy)<~>~kind(lucy)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~creative(X)&strong(X))<=>~brave(X)))&
((?[X]:((~creative(X)&~strong(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(tall(X)<=>(~kind(X)<~>tall(X))))&
((?[X]:((creative(X)|old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((calm(X)|~kind(X))=>(~rich(X)<~>~happy(X))))&
((quiet(mary))<=>((~funny(paul)<~>~strong(paul))))&
(![X]:((creative(X)&calm(X))<=>(~happy(X)|~creative(X))))&
(![X]:((strong(X)|~generous(X))=>(calm(X)&~calm(X))))&
((?[X]:(~humble(X)))=>((old(john)&tall(john))))&
(![X]:((patient(X)|~brave(X))=>~strong(X)))&
(((curious(paul)<~>wise(paul)))=>(?[X]:((humble(X)&calm(X)))))&
(![X]:(~wise(X)<=>(~old(X)<~>~curious(X))))&
(![X]:(wise(X)=>(~happy(X)<~>~creative(X))))&
(![X]:(calm(X)=>(~old(X)|generous(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(?[X]:((calm(X)&~old(X))))&
((~funny(alice)<~>~creative(alice)))&
((~rich(susan)<~>calm(susan)))&
((~rich(lucy)<~>patient(lucy))) | ~rich(alice) | []
| null | 0 |
Everyone who is not quiet or quiet is creative.
Everyone who is not generous or not old is kind or humble.
If susan is either tall or happy then alice is either not patient or humble.
If alice is both not kind and not generous then paul is either humble or wise and vice versa.
Everyone who is tall or generous is not happy.
Everyone who is quiet or not patient is not humble and vice versa.
Everyone who is humble is not quiet and vice versa.
Everyone who is not curious is not tall or patient and vice versa.
If paul is either not brave or not creative then susan is either not old or strong and vice versa.
Everyone who is either curious or not curious is not old.
Everyone who is not strong is both not wise and not strong and vice versa.
Everyone who is not kind is not generous and vice versa.
Everyone who is humble is both happy and not old and vice versa.
If lucy is not curious or not humble then susan is not rich.
Everyone who is both old and not humble is both tall and rich.
If someone is not rich or happy then someone is curious and vice versa.
Mary is strong or calm.
John is either strong or curious.
Someone is not generous.
Alice is wise or not strong.
Mary is both not patient and funny.
Mary is both strong and not brave. | Mary is not old. | entailment | (![X]:((~quiet(X)|quiet(X))=>creative(X)))&
(![X]:((~generous(X)|~old(X))=>(kind(X)|humble(X))))&
(((tall(susan)<~>happy(susan)))=>((~patient(alice)<~>humble(alice))))&
(((~kind(alice)&~generous(alice)))<=>((humble(paul)<~>wise(paul))))&
(![X]:((tall(X)|generous(X))=>~happy(X)))&
(![X]:((quiet(X)|~patient(X))<=>~humble(X)))&
(![X]:(humble(X)<=>~quiet(X)))&
(![X]:(~curious(X)<=>(~tall(X)|patient(X))))&
(((~brave(paul)<~>~creative(paul)))<=>((~old(susan)<~>strong(susan))))&
(![X]:((curious(X)<~>~curious(X))=>~old(X)))&
(![X]:(~strong(X)<=>(~wise(X)&~strong(X))))&
(![X]:(~kind(X)<=>~generous(X)))&
(![X]:(humble(X)<=>(happy(X)&~old(X))))&
(((~curious(lucy)|~humble(lucy)))=>(~rich(susan)))&
(![X]:((old(X)&~humble(X))=>(tall(X)&rich(X))))&
((?[X]:((~rich(X)|happy(X))))<=>(?[X]:(curious(X))))&
((strong(mary)|calm(mary)))&
((strong(john)<~>curious(john)))&
(?[X]:(~generous(X)))&
((wise(alice)|~strong(alice)))&
((~patient(mary)&funny(mary)))&
((strong(mary)&~brave(mary))) | ~old(mary) | [
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 4847587742820718126679009
% SZS output start Proof for 4847587742820718126679009
10. ! [X0] : ((curious(X0) <~> ~curious(X0)) => ~old(X0)) [input p9]
23. old(mary) [input hypothesis]
32. ! [X0] : (~old(X0) | (curious(X0) <=> ~curious(X0))) [ennf transformation 10]
45. ! [X0] : (~old(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 32]
91. ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
92. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 45]
115. old(mary) [cnf transformation 23]
116. ~old(X0) | ~curious(X0) [duplicate literal removal 91]
117. ~old(X0) | curious(X0) [duplicate literal removal 92]
181. ~old(X0) [subsumption resolution 116,117]
240. $false [subsumption resolution 115,181]
% SZS output end Proof for 4847587742820718126679009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not old or not rich and vice versa.
Everyone who is either not rich or not kind is either not brave or not funny and vice versa.
Everyone who is not kind or not funny is old or funny and vice versa.
If someone is funny then someone is either curious or not kind.
Everyone who is not strong or not funny is either not creative or tall and vice versa.
Everyone who is not tall or patient is both tall and not calm and vice versa.
Everyone who is either not strong or old is either not tall or kind and vice versa.
If john is both strong and not patient then lucy is either not tall or not kind.
Everyone who is not old is both tall and curious and vice versa.
If someone is not creative then someone is funny or rich and vice versa.
Everyone who is both not strong and not rich is either not wise or not funny.
Everyone who is not strong is both old and not patient and vice versa.
If susan is either not strong or quiet then alice is not tall or wise and vice versa.
Everyone who is either kind or not creative is generous or kind.
Everyone who is either wise or not brave is either calm or not calm.
If susan is calm then someone is either not patient or not kind.
Alice is not happy.
Someone is both not quiet and brave.
John is both creative and not curious.
Someone is either old or generous.
Someone is tall.
John is not rich.
Someone is not brave. | Susan is strong. | entailment | (![X]:(~rich(X)<=>(~old(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)|~funny(X))<=>(old(X)|funny(X))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((~tall(X)|patient(X))<=>(tall(X)&~calm(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~tall(X)<~>kind(X))))&
(((strong(john)&~patient(john)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~old(X)<=>(tall(X)&curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~strong(X)&~rich(X))=>(~wise(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(old(X)&~patient(X))))&
(((~strong(susan)<~>quiet(susan)))<=>((~tall(alice)|wise(alice))))&
(![X]:((kind(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((wise(X)<~>~brave(X))=>(calm(X)<~>~calm(X))))&
((calm(susan))=>(?[X]:((~patient(X)<~>~kind(X)))))&
(~happy(alice))&
(?[X]:((~quiet(X)&brave(X))))&
((creative(john)&~curious(john)))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:(tall(X)))&
(~rich(john))&
(?[X]:(~brave(X))) | strong(susan) | [
"p0",
"p5",
"p6",
"p11",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 5174925064475106176212814
% SZS output start Proof for 5174925064475106176212814
1. ! [X0] : (~rich(X0) <=> (~old(X0) <~> ~rich(X0))) [input p0]
6. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (~calm(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~strong(X0) <~> old(X0)) <=> (~tall(X0) <~> kind(X0))) [input p6]
12. ! [X0] : (~strong(X0) <=> (~patient(X0) & old(X0))) [input p11]
16. calm(susan) => ? [X0] : (~patient(X0) <~> ~kind(X0)) [input p15]
24. ~strong(susan) [input hypothesis]
36. ? [X0] : (~patient(X0) <~> ~kind(X0)) | ~calm(susan) [ennf transformation 16]
37. ! [X0] : ((~rich(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | rich(X0))) [nnf transformation 1]
47. ! [X0] : (((patient(X0) | ~tall(X0)) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | (~patient(X0) & tall(X0)))) [nnf transformation 6]
48. ! [X0] : ((patient(X0) | ~tall(X0) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | (~patient(X0) & tall(X0)))) [flattening 47]
49. ! [X0] : ((((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0))))) [nnf transformation 7]
59. ! [X0] : ((~strong(X0) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | strong(X0))) [nnf transformation 12]
60. ! [X0] : ((~strong(X0) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | strong(X0))) [flattening 59]
65. ? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~calm(susan) [nnf transformation 36]
66. ? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) => ((kind(sK3) | patient(sK3)) & (~kind(sK3) | ~patient(sK3))) [choice axiom]
67. ((kind(sK3) | patient(sK3)) & (~kind(sK3) | ~patient(sK3))) | ~calm(susan) [skolemisation 65,66]
78. rich(X0) | old(X0) | rich(X0) [cnf transformation 37]
79. ~rich(X0) | ~rich(X0) | old(X0) [cnf transformation 37]
101. tall(X0) | tall(X0) [cnf transformation 48]
105. patient(X0) | ~tall(X0) | calm(X0) | ~tall(X0) [cnf transformation 48]
107. kind(X0) | ~tall(X0) | ~strong(X0) | ~old(X0) [cnf transformation 49]
113. ~old(X0) | strong(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 49]
125. ~patient(X0) | strong(X0) [cnf transformation 60]
126. ~strong(X0) | patient(X0) | ~old(X0) [cnf transformation 60]
139. ~kind(sK3) | ~patient(sK3) | ~calm(susan) [cnf transformation 67]
140. kind(sK3) | patient(sK3) | ~calm(susan) [cnf transformation 67]
150. ~strong(susan) [cnf transformation 24]
152. tall(X0) [duplicate literal removal 101]
153. ~tall(X0) | patient(X0) | calm(X0) [duplicate literal removal 105]
156. rich(X0) | old(X0) [duplicate literal removal 78]
157. ~rich(X0) | old(X0) [duplicate literal removal 79]
158. old(X0) [subsumption resolution 156,157]
172. strong(X0) | ~tall(X0) | ~kind(X0) [subsumption resolution 113,158]
173. ~kind(X0) | strong(X0) [subsumption resolution 172,152]
174. kind(X0) | ~strong(X0) | ~old(X0) [subsumption resolution 107,152]
175. ~strong(X0) | kind(X0) [subsumption resolution 174,158]
213. ~strong(X0) | patient(X0) [subsumption resolution 126,158]
219. 13 <=> strong(susan) [avatar definition]
220. ~strong(susan) <- (~13) [avatar component clause 219]
233. 15 <=> calm(susan) [avatar definition]
235. ~calm(susan) <- (~15) [avatar component clause 233]
237. 16 <=> patient(sK3) [avatar definition]
238. ~patient(sK3) <- (~16) [avatar component clause 237]
239. patient(sK3) <- (16) [avatar component clause 237]
241. 17 <=> kind(sK3) [avatar definition]
242. ~kind(sK3) <- (~17) [avatar component clause 241]
243. kind(sK3) <- (17) [avatar component clause 241]
244. ~15 | 16 | 17 [avatar split clause 140,241,237,233]
245. ~15 | ~16 | ~17 [avatar split clause 139,241,237,233]
247. ~13 [avatar split clause 150,219]
273. calm(X0) | patient(X0) [resolution 153,152]
368. patient(susan) <- (~15) [resolution 273,235]
371. strong(susan) <- (~15) [resolution 368,125]
373. $false <- (~13, ~15) [subsumption resolution 371,220]
374. 13 | 15 [avatar contradiction clause 373]
377. strong(sK3) <- (16) [resolution 239,125]
381. kind(sK3) <- (16) [resolution 377,175]
382. $false <- (16, ~17) [subsumption resolution 381,242]
383. ~16 | 17 [avatar contradiction clause 382]
385. strong(sK3) <- (17) [resolution 243,173]
400. patient(sK3) <- (17) [resolution 385,213]
402. $false <- (~16, 17) [subsumption resolution 400,238]
403. 16 | ~17 [avatar contradiction clause 402]
404. $false [avatar sat refutation 244,245,247,374,383,403]
% SZS output end Proof for 5174925064475106176212814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not patient is both brave and not curious and vice versa.
Everyone who is patient or funny is rich and vice versa.
Everyone who is not happy or calm is not funny or not kind.
Everyone who is creative or quiet is calm or not quiet.
If someone is generous or calm then paul is strong or not strong and vice versa.
If susan is both generous and not calm then paul is not generous.
If susan is both wise and not patient then lucy is not rich.
Everyone who is not tall or old is either not funny or not curious and vice versa.
Everyone who is both not rich and not generous is both not kind and patient and vice versa.
Everyone who is brave is not humble or not kind and vice versa.
Everyone who is not tall or humble is not rich or not funny and vice versa.
Everyone who is not brave or not wise is old and vice versa.
Everyone who is not humble is not quiet.
If fred is happy then someone is brave or happy and vice versa.
Everyone who is both not old and old is not calm or not curious.
If fred is both patient and not old then someone is both calm and not creative.
Someone is not old.
Someone is both quiet and not funny.
Mary is rich.
Paul is both creative and not strong.
Someone is generous or calm.
Someone is both tall and quiet. | Susan is not old. | neutral | (![X]:((~brave(X)&~patient(X))<=>(brave(X)&~curious(X))))&
(![X]:((patient(X)|funny(X))<=>rich(X)))&
(![X]:((~happy(X)|calm(X))=>(~funny(X)|~kind(X))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)|~quiet(X))))&
((?[X]:((generous(X)|calm(X))))<=>((strong(paul)|~strong(paul))))&
(((generous(susan)&~calm(susan)))=>(~generous(paul)))&
(((wise(susan)&~patient(susan)))=>(~rich(lucy)))&
(![X]:((~tall(X)|old(X))<=>(~funny(X)<~>~curious(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~kind(X)&patient(X))))&
(![X]:(brave(X)<=>(~humble(X)|~kind(X))))&
(![X]:((~tall(X)|humble(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~brave(X)|~wise(X))<=>old(X)))&
(![X]:(~humble(X)=>~quiet(X)))&
((happy(fred))<=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~old(X)&old(X))=>(~calm(X)|~curious(X))))&
(((patient(fred)&~old(fred)))=>(?[X]:((calm(X)&~creative(X)))))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)&~funny(X))))&
(rich(mary))&
((creative(paul)&~strong(paul)))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:((tall(X)&quiet(X)))) | ~old(susan) | []
| null | 0 |
If mary is not wise or kind then someone is either happy or not patient and vice versa.
Everyone who is either patient or kind is both calm and not curious.
Everyone who is happy or not kind is not rich.
Everyone who is curious or brave is both calm and brave.
If someone is not calm or not old then fred is not happy.
If john is either not old or wise then someone is either not calm or not quiet.
Everyone who is not humble is both not humble and humble and vice versa.
Everyone who is either not rich or creative is both patient and funny.
If susan is both not calm and not patient then someone is either old or not curious and vice versa.
If someone is generous then susan is funny.
If lucy is both not tall and creative then someone is strong or tall.
If someone is either not kind or humble then someone is both old and quiet and vice versa.
If john is either funny or curious then alice is not rich and vice versa.
Everyone who is calm or not old is both not strong and strong and vice versa.
Everyone who is not generous is not tall or quiet and vice versa.
If someone is either curious or not kind then lucy is quiet or funny.
Paul is patient or not calm.
Someone is not rich.
Someone is not curious.
Paul is brave or not curious.
Alice is both not funny and wise.
Lucy is tall or happy.
Someone is creative or not funny.
Mary is either brave or not tall. | Susan is not brave. | entailment | (((~wise(mary)|kind(mary)))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((patient(X)<~>kind(X))=>(calm(X)&~curious(X))))&
(![X]:((happy(X)|~kind(X))=>~rich(X)))&
(![X]:((curious(X)|brave(X))=>(calm(X)&brave(X))))&
((?[X]:((~calm(X)|~old(X))))=>(~happy(fred)))&
(((~old(john)<~>wise(john)))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(patient(X)&funny(X))))&
(((~calm(susan)&~patient(susan)))<=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:(generous(X)))=>(funny(susan)))&
(((~tall(lucy)&creative(lucy)))=>(?[X]:((strong(X)|tall(X)))))&
((?[X]:((~kind(X)<~>humble(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(((funny(john)<~>curious(john)))<=>(~rich(alice)))&
(![X]:((calm(X)|~old(X))<=>(~strong(X)&strong(X))))&
(![X]:(~generous(X)<=>(~tall(X)|quiet(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>((quiet(lucy)|funny(lucy))))&
((patient(paul)|~calm(paul)))&
(?[X]:(~rich(X)))&
(?[X]:(~curious(X)))&
((brave(paul)|~curious(paul)))&
((~funny(alice)&wise(alice)))&
((tall(lucy)|happy(lucy)))&
(?[X]:((creative(X)|~funny(X))))&
((brave(mary)<~>~tall(mary))) | ~brave(susan) | [
"p3",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8378909390343916212640966
% SZS output start Proof for 8378909390343916212640966
4. ! [X0] : ((brave(X0) | curious(X0)) => (brave(X0) & calm(X0))) [input p3]
14. ! [X0] : ((~old(X0) | calm(X0)) <=> (strong(X0) & ~strong(X0))) [input p13]
25. brave(susan) [input hypothesis]
30. ! [X0] : ((brave(X0) & calm(X0)) | (~brave(X0) & ~curious(X0))) [ennf transformation 4]
66. ! [X0] : (((~old(X0) | calm(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (old(X0) & ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : ((~old(X0) | calm(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (old(X0) & ~calm(X0)))) [flattening 66]
89. ~brave(X0) | calm(X0) [cnf transformation 30]
123. ~strong(X0) | ~calm(X0) [cnf transformation 67]
125. strong(X0) | ~calm(X0) [cnf transformation 67]
141. brave(susan) [cnf transformation 25]
299. ~calm(X0) [subsumption resolution 123,125]
349. calm(susan) [resolution 89,141]
350. $false [subsumption resolution 349,299]
% SZS output end Proof for 8378909390343916212640966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and old is wise.
Everyone who is happy or not strong is not funny or wise and vice versa.
If someone is both happy and not strong then someone is not rich or not brave and vice versa.
Everyone who is either not tall or curious is either kind or patient and vice versa.
Everyone who is both not curious and not funny is not calm or patient and vice versa.
Everyone who is happy or wise is both not old and brave.
If paul is both not strong and curious then mary is generous.
Everyone who is not happy or old is tall and vice versa.
If someone is both not kind and not patient then john is both humble and not wise and vice versa.
If someone is either not funny or not kind then someone is either not brave or not tall.
If someone is both curious and old then susan is both not funny and not wise and vice versa.
If someone is not quiet or not calm then susan is either patient or humble.
Everyone who is both rich and not humble is not creative or brave and vice versa.
Everyone who is either not kind or curious is either funny or quiet.
Everyone who is not calm is either creative or not calm.
Everyone who is humble or not quiet is either brave or not kind and vice versa.
Someone is not generous or happy.
Someone is not funny.
Fred is both strong and patient.
Someone is patient.
Alice is happy or strong.
Someone is both not funny and not calm.
Someone is both patient and kind.
Someone is not kind or tall. | Fred is tall. | contradiction | (![X]:((~calm(X)&old(X))=>wise(X)))&
(![X]:((happy(X)|~strong(X))<=>(~funny(X)|wise(X))))&
((?[X]:((happy(X)&~strong(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~tall(X)<~>curious(X))<=>(kind(X)<~>patient(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~calm(X)|patient(X))))&
(![X]:((happy(X)|wise(X))=>(~old(X)&brave(X))))&
(((~strong(paul)&curious(paul)))=>(generous(mary)))&
(![X]:((~happy(X)|old(X))<=>tall(X)))&
((?[X]:((~kind(X)&~patient(X))))<=>((humble(john)&~wise(john))))&
((?[X]:((~funny(X)<~>~kind(X))))=>(?[X]:((~brave(X)<~>~tall(X)))))&
((?[X]:((curious(X)&old(X))))<=>((~funny(susan)&~wise(susan))))&
((?[X]:((~quiet(X)|~calm(X))))=>((patient(susan)<~>humble(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~creative(X)|brave(X))))&
(![X]:((~kind(X)<~>curious(X))=>(funny(X)<~>quiet(X))))&
(![X]:(~calm(X)=>(creative(X)<~>~calm(X))))&
(![X]:((humble(X)|~quiet(X))<=>(brave(X)<~>~kind(X))))&
(?[X]:((~generous(X)|happy(X))))&
(?[X]:(~funny(X)))&
((strong(fred)&patient(fred)))&
(?[X]:(patient(X)))&
((happy(alice)|strong(alice)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:((~kind(X)|tall(X)))) | tall(fred) | [
"p1",
"p4",
"p5",
"p7",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4470641336378289627995583
% SZS output start Proof for 4470641336378289627995583
2. ! [X0] : ((~strong(X0) | happy(X0)) <=> (wise(X0) | ~funny(X0))) [input p1]
5. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (patient(X0) | ~calm(X0))) [input p4]
6. ! [X0] : ((wise(X0) | happy(X0)) => (brave(X0) & ~old(X0))) [input p5]
8. ! [X0] : ((old(X0) | ~happy(X0)) <=> tall(X0)) [input p7]
19. patient(fred) & strong(fred) [input p18]
25. tall(fred) [input hypothesis]
30. ! [X0] : ((brave(X0) & ~old(X0)) | (~wise(X0) & ~happy(X0))) [ennf transformation 6]
37. ! [X0] : (((~strong(X0) | happy(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (strong(X0) & ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : ((~strong(X0) | happy(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | (strong(X0) & ~happy(X0)))) [flattening 37]
45. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 5]
46. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | funny(X0) | curious(X0))) [flattening 45]
47. ! [X0] : (((old(X0) | ~happy(X0)) | ~tall(X0)) & (tall(X0) | (~old(X0) & happy(X0)))) [nnf transformation 8]
48. ! [X0] : ((old(X0) | ~happy(X0) | ~tall(X0)) & (tall(X0) | (~old(X0) & happy(X0)))) [flattening 47]
85. ~strong(X0) | happy(X0) | funny(X0) [cnf transformation 38]
104. ~patient(X0) | ~funny(X0) [cnf transformation 46]
105. ~happy(X0) | ~old(X0) [cnf transformation 30]
112. old(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 48]
148. strong(fred) [cnf transformation 19]
149. patient(fred) [cnf transformation 19]
157. tall(fred) [cnf transformation 25]
202. ~tall(X0) | ~happy(X0) [subsumption resolution 112,105]
320. ~funny(fred) [resolution 104,149]
337. ~happy(fred) [resolution 202,157]
343. happy(fred) | funny(fred) [resolution 85,148]
344. funny(fred) [subsumption resolution 343,337]
345. $false [subsumption resolution 344,320]
% SZS output end Proof for 4470641336378289627995583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not brave is both rich and not funny.
Everyone who is either tall or creative is not patient.
Everyone who is brave is calm or strong.
Everyone who is both not old and not kind is either not creative or calm and vice versa.
If susan is strong then someone is both brave and not kind and vice versa.
If someone is both quiet and generous then alice is both patient and strong and vice versa.
If someone is wise then susan is both generous and not generous and vice versa.
Everyone who is either not tall or strong is either rich or funny and vice versa.
Everyone who is both not curious and not generous is not curious or not wise and vice versa.
If someone is not quiet then mary is either strong or rich.
If alice is brave then paul is either not kind or tall and vice versa.
Everyone who is both rich and not old is both tall and generous and vice versa.
Everyone who is either not old or not patient is wise or not happy.
Everyone who is happy is not generous and vice versa.
Everyone who is not quiet is either not happy or not calm.
John is either not creative or creative.
Fred is old.
Paul is either quiet or happy.
Someone is both happy and brave.
Someone is wise or not calm.
Someone is not rich or brave. | John is wise. | contradiction | (![X]:((~quiet(X)|~brave(X))=>(rich(X)&~funny(X))))&
(![X]:((tall(X)<~>creative(X))=>~patient(X)))&
(![X]:(brave(X)=>(calm(X)|strong(X))))&
(![X]:((~old(X)&~kind(X))<=>(~creative(X)<~>calm(X))))&
((strong(susan))<=>(?[X]:((brave(X)&~kind(X)))))&
((?[X]:((quiet(X)&generous(X))))<=>((patient(alice)&strong(alice))))&
((?[X]:(wise(X)))<=>((generous(susan)&~generous(susan))))&
(![X]:((~tall(X)<~>strong(X))<=>(rich(X)<~>funny(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~curious(X)|~wise(X))))&
((?[X]:(~quiet(X)))=>((strong(mary)<~>rich(mary))))&
((brave(alice))<=>((~kind(paul)<~>tall(paul))))&
(![X]:((rich(X)&~old(X))<=>(tall(X)&generous(X))))&
(![X]:((~old(X)<~>~patient(X))=>(wise(X)|~happy(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:(~quiet(X)=>(~happy(X)<~>~calm(X))))&
((~creative(john)<~>creative(john)))&
(old(fred))&
((quiet(paul)<~>happy(paul)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((~rich(X)|brave(X)))) | wise(john) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 422439560807765746665876
% SZS output start Proof for 422439560807765746665876
7. ? [X0] : wise(X0) <=> (~generous(susan) & generous(susan)) [input p6]
22. wise(john) [input hypothesis]
43. (? [X0] : wise(X0) | (generous(susan) | ~generous(susan))) & ((~generous(susan) & generous(susan)) | ! [X0] : ~wise(X0)) [nnf transformation 7]
44. (? [X0] : wise(X0) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X0] : ~wise(X0)) [flattening 43]
45. (? [X0] : wise(X0) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X1] : ~wise(X1)) [rectify 44]
46. ? [X0] : wise(X0) => wise(sK2) [choice axiom]
47. (wise(sK2) | generous(susan) | ~generous(susan)) & ((~generous(susan) & generous(susan)) | ! [X1] : ~wise(X1)) [skolemisation 45,46]
86. generous(susan) | ~wise(X1) [cnf transformation 47]
87. ~generous(susan) | ~wise(X1) [cnf transformation 47]
127. wise(john) [cnf transformation 22]
170. 10 <=> ! [X1] : ~wise(X1) [avatar definition]
171. ~wise(X1) <- (10) [avatar component clause 170]
173. 11 <=> generous(susan) [avatar definition]
176. 10 | ~11 [avatar split clause 87,173,170]
177. 10 | 11 [avatar split clause 86,173,170]
227. $false <- (10) [resolution 171,127]
228. ~10 [avatar contradiction clause 227]
229. $false [avatar sat refutation 176,177,228]
% SZS output end Proof for 422439560807765746665876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or patient is not patient and vice versa. Everyone who is either not rich or not funny is old. If alice is not old then someone is both rich and not funny and vice versa. Everyone who is brave or calm is not funny or not quiet and vice versa. Everyone who is calm is either wise or happy and vice versa. Everyone who is either not rich or rich is both strong and not patient and vice versa. Everyone who is both happy and strong is either not kind or kind and vice versa. If someone is not rich or generous then someone is either calm or patient and vice versa. If paul is tall then someone is either funny or brave. If fred is either old or not quiet then someone is either not happy or not kind and vice versa. Everyone who is both creative and not generous is patient and vice versa. If susan is kind or not patient then someone is rich. Everyone who is either wise or quiet is both creative and humble and vice versa. Everyone who is not calm or old is not curious or curious and vice versa. If someone is humble then someone is either funny or kind. If someone is not generous then someone is either old or wise and vice versa. Someone is either not generous or calm. Someone is brave or not happy. Someone is both not tall and not creative. John is wise or curious. Someone is not rich or not generous. Lucy is either happy or curious. John is calm or not generous. | Paul is old. | entailment | (![X]:((~wise(X)<~>patient(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>~funny(X))=>old(X)))&
((~old(alice))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((brave(X)|calm(X))<=>(~funny(X)|~quiet(X))))&
(![X]:(calm(X)<=>(wise(X)<~>happy(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(strong(X)&~patient(X))))&
(![X]:((happy(X)&strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((~rich(X)|generous(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
((tall(paul))=>(?[X]:((funny(X)<~>brave(X)))))&
(((old(fred)<~>~quiet(fred)))<=>(?[X]:((~happy(X)<~>~kind(X)))))&
(![X]:((creative(X)&~generous(X))<=>patient(X)))&
(((kind(susan)|~patient(susan)))=>(?[X]:(rich(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(creative(X)&humble(X))))&
(![X]:((~calm(X)|old(X))<=>(~curious(X)|curious(X))))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)<~>kind(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((old(X)<~>wise(X)))))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((wise(john)|curious(john)))&
(?[X]:((~rich(X)|~generous(X))))&
((happy(lucy)<~>curious(lucy)))&
((calm(john)|~generous(john))) | old(paul) | [
"p0",
"p4",
"p6",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 379137368942913833787907
% SZS output start Proof for 379137368942913833787907
1. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> ~patient(X0)) [input p0]
5. ! [X0] : (calm(X0) <=> (wise(X0) <~> happy(X0))) [input p4]
7. ! [X0] : ((strong(X0) & happy(X0)) <=> (~kind(X0) <~> kind(X0))) [input p6]
14. ! [X0] : ((old(X0) | ~calm(X0)) <=> (curious(X0) | ~curious(X0))) [input p13]
24. ~old(paul) [input hypothesis]
33. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | patient(X0)) & (~patient(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 1]
41. ! [X0] : ((calm(X0) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ~calm(X0))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~strong(X0) | ~happy(X0)))) [nnf transformation 7]
45. ! [X0] : (((strong(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~strong(X0) | ~happy(X0))) [flattening 44]
61. ! [X0] : (((old(X0) | ~calm(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (~old(X0) & calm(X0)))) [nnf transformation 14]
62. ! [X0] : ((old(X0) | ~calm(X0) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | (~old(X0) & calm(X0)))) [flattening 61]
83. ~patient(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 33]
84. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 33]
98. calm(X0) | wise(X0) | ~happy(X0) [cnf transformation 41]
107. happy(X0) | kind(X0) | kind(X0) [cnf transformation 45]
108. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 45]
138. old(X0) | ~calm(X0) | curious(X0) [cnf transformation 62]
139. old(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 62]
155. ~old(paul) [cnf transformation 24]
156. happy(X0) | kind(X0) [duplicate literal removal 107]
157. ~kind(X0) | happy(X0) [duplicate literal removal 108]
164. ~patient(X0) | ~wise(X0) [duplicate literal removal 83]
165. ~wise(X0) | patient(X0) [duplicate literal removal 84]
166. ~wise(X0) [subsumption resolution 164,165]
185. ~happy(X0) | calm(X0) [subsumption resolution 98,166]
189. happy(X0) [subsumption resolution 156,157]
245. ~calm(X0) | old(X0) [subsumption resolution 138,139]
318. calm(X0) [resolution 185,189]
324. old(X0) [resolution 245,318]
328. $false [resolution 324,155]
% SZS output end Proof for 379137368942913833787907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not curious then someone is strong or curious.
If lucy is both not curious and generous then alice is strong or rich and vice versa.
Everyone who is either wise or not strong is either calm or not calm.
If lucy is humble or not wise then susan is not funny or strong.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
If someone is either quiet or not tall then someone is both not creative and not curious and vice versa.
If someone is either wise or not old then someone is either not tall or not happy and vice versa.
Everyone who is not brave or not old is both kind and not generous.
Everyone who is brave or happy is both humble and strong and vice versa.
Everyone who is both not generous and tall is both not patient and brave.
If someone is either quiet or not tall then fred is not old and vice versa.
Someone is kind or brave.
Someone is not happy or not brave.
Someone is funny.
Someone is either not brave or kind.
Paul is either not curious or tall. | Mary is not quiet. | contradiction | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|curious(X)))))&
(((~curious(lucy)&generous(lucy)))<=>((strong(alice)|rich(alice))))&
(![X]:((wise(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(((humble(lucy)|~wise(lucy)))=>((~funny(susan)|strong(susan))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((brave(X)|happy(X))<=>(humble(X)&strong(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~curious(paul)<~>tall(paul))) | ~quiet(mary) | [
"p6",
"p8",
"p9",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 9196386426713113550774510
% SZS output start Proof for 9196386426713113550774510
7. ! [X0] : (patient(X0) <=> strong(X0)) [input p6]
9. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~brave(X0)) [input p8]
10. ! [X0] : (quiet(X0) <=> (strong(X0) | kind(X0))) [input p9]
14. ! [X0] : ((happy(X0) | brave(X0)) <=> (strong(X0) & humble(X0))) [input p13]
22. ~quiet(mary) [input hypothesis]
45. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 7]
47. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 9]
48. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~patient(X0) | creative(X0))) [flattening 47]
49. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | ~quiet(X0))) [nnf transformation 10]
50. ! [X0] : ((quiet(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | ~quiet(X0))) [flattening 49]
61. ! [X0] : (((happy(X0) | brave(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 14]
62. ! [X0] : ((happy(X0) | brave(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 61]
95. ~patient(X0) | strong(X0) [cnf transformation 45]
101. patient(X0) | brave(X0) [cnf transformation 48]
104. ~strong(X0) | quiet(X0) [cnf transformation 50]
125. ~brave(X0) | strong(X0) [cnf transformation 62]
141. ~quiet(mary) [cnf transformation 22]
208. 15 <=> quiet(mary) [avatar definition]
210. ~quiet(mary) <- (~15) [avatar component clause 208]
310. ~15 [avatar split clause 141,208]
313. brave(X0) | strong(X0) [resolution 101,95]
314. strong(X0) [subsumption resolution 313,125]
320. quiet(X0) [resolution 104,314]
334. $false <- (~15) [resolution 320,210]
339. 15 [avatar contradiction clause 334]
340. $false [avatar sat refutation 310,339]
% SZS output end Proof for 9196386426713113550774510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall is not funny. If someone is both rich and not old then fred is both not creative and not patient and vice versa. Everyone who is either curious or tall is not happy and vice versa. If john is not strong or not kind then fred is both not happy and humble. Everyone who is not humble is either wise or rich. If alice is both generous and humble then someone is wise or not humble. If fred is kind or wise then someone is either patient or not humble. If john is calm or not strong then alice is both patient and quiet and vice versa. Everyone who is not creative or not rich is not generous or not brave and vice versa. Everyone who is either humble or not tall is curious and vice versa. Everyone who is either funny or not wise is both not old and humble and vice versa. If fred is creative or not rich then fred is generous and vice versa. If someone is rich or not brave then paul is not old or wise. Everyone who is both not curious and rich is either strong or quiet and vice versa. Everyone who is both brave and not patient is either not rich or funny and vice versa. If someone is both not wise and not strong then alice is either not patient or kind. Paul is both funny and not wise. Alice is both wise and not quiet. Mary is strong. Lucy is both old and not generous. Someone is not creative or funny. Someone is brave or quiet. | Paul is not rich. | contradiction | (![X]:((~creative(X)|tall(X))=>~funny(X)))&
((?[X]:((rich(X)&~old(X))))<=>((~creative(fred)&~patient(fred))))&
(![X]:((curious(X)<~>tall(X))<=>~happy(X)))&
(((~strong(john)|~kind(john)))=>((~happy(fred)&humble(fred))))&
(![X]:(~humble(X)=>(wise(X)<~>rich(X))))&
(((generous(alice)&humble(alice)))=>(?[X]:((wise(X)|~humble(X)))))&
(((kind(fred)|wise(fred)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(((calm(john)|~strong(john)))<=>((patient(alice)&quiet(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(~generous(X)|~brave(X))))&
(![X]:((humble(X)<~>~tall(X))<=>curious(X)))&
(![X]:((funny(X)<~>~wise(X))<=>(~old(X)&humble(X))))&
(((creative(fred)|~rich(fred)))<=>(generous(fred)))&
((?[X]:((rich(X)|~brave(X))))=>((~old(paul)|wise(paul))))&
(![X]:((~curious(X)&rich(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((brave(X)&~patient(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~patient(alice)<~>kind(alice))))&
((funny(paul)&~wise(paul)))&
((wise(alice)&~quiet(alice)))&
(strong(mary))&
((old(lucy)&~generous(lucy)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((brave(X)|quiet(X)))) | ~rich(paul) | [
"p4",
"p8",
"p10",
"p11",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 68638107732272556036643
% SZS output start Proof for 68638107732272556036643
5. ! [X0] : (~humble(X0) => (wise(X0) <~> rich(X0))) [input p4]
9. ! [X0] : ((~rich(X0) | ~creative(X0)) <=> (~brave(X0) | ~generous(X0))) [input p8]
11. ! [X0] : ((funny(X0) <~> ~wise(X0)) <=> (humble(X0) & ~old(X0))) [input p10]
12. (~rich(fred) | creative(fred)) <=> generous(fred) [input p11]
13. ? [X0] : (~brave(X0) | rich(X0)) => (wise(paul) | ~old(paul)) [input p12]
17. ~wise(paul) & funny(paul) [input p16]
23. ~rich(paul) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> rich(X0)) | humble(X0)) [ennf transformation 5]
32. (wise(paul) | ~old(paul)) | ! [X0] : (brave(X0) & ~rich(X0)) [ennf transformation 13]
33. wise(paul) | ~old(paul) | ! [X0] : (brave(X0) & ~rich(X0)) [flattening 32]
41. ! [X0] : (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | humble(X0)) [nnf transformation 28]
49. ! [X0] : (((~rich(X0) | ~creative(X0)) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | (rich(X0) & creative(X0)))) [nnf transformation 9]
50. ! [X0] : ((~rich(X0) | ~creative(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | (rich(X0) & creative(X0)))) [flattening 49]
52. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [nnf transformation 11]
53. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [flattening 52]
54. ((~rich(fred) | creative(fred)) | ~generous(fred)) & (generous(fred) | (rich(fred) & ~creative(fred))) [nnf transformation 12]
55. (~rich(fred) | creative(fred) | ~generous(fred)) & (generous(fred) | (rich(fred) & ~creative(fred))) [flattening 54]
77. wise(X0) | rich(X0) | humble(X0) [cnf transformation 41]
90. ~brave(X0) | ~generous(X0) | rich(X0) [cnf transformation 50]
102. ~humble(X0) | ~funny(X0) | wise(X0) | old(X0) [cnf transformation 53]
104. generous(fred) | rich(fred) [cnf transformation 55]
106. wise(paul) | ~old(paul) | ~rich(X0) [cnf transformation 33]
107. wise(paul) | ~old(paul) | brave(X0) [cnf transformation 33]
122. funny(paul) [cnf transformation 17]
123. ~wise(paul) [cnf transformation 17]
131. ~rich(paul) [cnf transformation 23]
230. 21 <=> generous(fred) [avatar definition]
231. generous(fred) <- (21) [avatar component clause 230]
234. 22 <=> rich(fred) [avatar definition]
235. rich(fred) <- (22) [avatar component clause 234]
238. 22 | 21 [avatar split clause 104,230,234]
241. 23 <=> ! [X0] : brave(X0) [avatar definition]
242. brave(X0) <- (23) [avatar component clause 241]
244. 24 <=> old(paul) [avatar definition]
248. 25 <=> wise(paul) [avatar definition]
249. ~wise(paul) <- (~25) [avatar component clause 248]
251. 23 | ~24 | 25 [avatar split clause 107,248,244,241]
253. 26 <=> ! [X0] : ~rich(X0) [avatar definition]
254. ~rich(X0) <- (26) [avatar component clause 253]
255. 26 | ~24 | 25 [avatar split clause 106,248,244,253]
265. ~25 [avatar split clause 123,248]
288. rich(paul) | humble(paul) <- (~25) [resolution 77,249]
291. humble(paul) <- (~25) [subsumption resolution 288,131]
467. ~funny(paul) | wise(paul) | old(paul) <- (~25) [resolution 102,291]
479. wise(paul) | old(paul) <- (~25) [subsumption resolution 467,122]
480. old(paul) <- (~25) [subsumption resolution 479,249]
483. 24 | 25 [avatar split clause 480,248,244]
484. ~generous(X0) | rich(X0) <- (23) [resolution 242,90]
486. ~generous(X0) <- (23, 26) [subsumption resolution 484,254]
497. $false <- (22, 26) [subsumption resolution 235,254]
498. ~22 | ~26 [avatar contradiction clause 497]
502. $false <- (21, 23, 26) [subsumption resolution 231,486]
503. ~21 | ~23 | ~26 [avatar contradiction clause 502]
504. $false [avatar sat refutation 238,251,255,265,483,498,503]
% SZS output end Proof for 68638107732272556036643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not tall is either not strong or not wise.
If lucy is both not brave and creative then someone is wise and vice versa.
Everyone who is quiet is not funny.
If someone is either kind or brave then someone is happy.
Everyone who is both not quiet and not happy is tall and vice versa.
Everyone who is either not quiet or kind is both calm and not brave.
Everyone who is humble is either not patient or strong.
If lucy is not rich or not tall then lucy is patient.
Everyone who is old or not calm is not brave or rich.
Everyone who is both kind and wise is both patient and wise and vice versa.
Everyone who is not creative is not creative or not brave and vice versa.
Everyone who is not kind or curious is quiet or not wise and vice versa.
Everyone who is humble or not creative is both not happy and funny.
If someone is both not rich and not calm then someone is both not tall and not kind.
Everyone who is rich is either not calm or rich and vice versa.
If someone is strong or not curious then someone is not old or not creative and vice versa.
Someone is not wise or rich.
Susan is either not kind or rich.
Someone is both not old and calm.
Someone is not curious.
Paul is patient.
Someone is either brave or humble.
Someone is either calm or not generous. | Paul is not happy. | neutral | (![X]:((~happy(X)|~tall(X))=>(~strong(X)<~>~wise(X))))&
(((~brave(lucy)&creative(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(quiet(X)=>~funny(X)))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:(happy(X))))&
(![X]:((~quiet(X)&~happy(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>kind(X))=>(calm(X)&~brave(X))))&
(![X]:(humble(X)=>(~patient(X)<~>strong(X))))&
(((~rich(lucy)|~tall(lucy)))=>(patient(lucy)))&
(![X]:((old(X)|~calm(X))=>(~brave(X)|rich(X))))&
(![X]:((kind(X)&wise(X))<=>(patient(X)&wise(X))))&
(![X]:(~creative(X)<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|curious(X))<=>(quiet(X)|~wise(X))))&
(![X]:((humble(X)|~creative(X))=>(~happy(X)&funny(X))))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(rich(X)<=>(~calm(X)<~>rich(X))))&
((?[X]:((strong(X)|~curious(X))))<=>(?[X]:((~old(X)|~creative(X)))))&
(?[X]:((~wise(X)|rich(X))))&
((~kind(susan)<~>rich(susan)))&
(?[X]:((~old(X)&calm(X))))&
(?[X]:(~curious(X)))&
(patient(paul))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((calm(X)<~>~generous(X)))) | ~happy(paul) | []
| null | 0 |
If someone is either not calm or patient then john is either not creative or calm. Everyone who is both rich and not funny is either not brave or kind and vice versa. If someone is not patient or not old then someone is strong or humble and vice versa. Everyone who is not brave or quiet is creative or not humble and vice versa. Everyone who is not curious is not funny or not happy and vice versa. Everyone who is both not happy and not quiet is rich and vice versa. If lucy is creative or not calm then john is either not kind or funny and vice versa. If lucy is both not creative and patient then someone is not brave and vice versa. Everyone who is either not funny or patient is happy and vice versa. Everyone who is wise or not generous is creative or not strong. Everyone who is both kind and not humble is either not patient or not funny. If someone is either not strong or not funny then someone is curious and vice versa. If fred is either not strong or kind then paul is brave and vice versa. If paul is both patient and not curious then alice is both funny and not happy. Everyone who is calm or humble is not rich and vice versa. Everyone who is either wise or not wise is both old and not strong and vice versa. Fred is not wise. Paul is patient or not calm. John is not kind. Susan is not tall. Someone is both not generous and not calm. Paul is not quiet. Lucy is both not tall and wise. Alice is brave or curious. | Fred is not strong. | entailment | ((?[X]:((~calm(X)<~>patient(X))))=>((~creative(john)<~>calm(john))))&
(![X]:((rich(X)&~funny(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~brave(X)|quiet(X))<=>(creative(X)|~humble(X))))&
(![X]:(~curious(X)<=>(~funny(X)|~happy(X))))&
(![X]:((~happy(X)&~quiet(X))<=>rich(X)))&
(((creative(lucy)|~calm(lucy)))<=>((~kind(john)<~>funny(john))))&
(((~creative(lucy)&patient(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)<~>patient(X))<=>happy(X)))&
(![X]:((wise(X)|~generous(X))=>(creative(X)|~strong(X))))&
(![X]:((kind(X)&~humble(X))=>(~patient(X)<~>~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>(?[X]:(curious(X))))&
(((~strong(fred)<~>kind(fred)))<=>(brave(paul)))&
(((patient(paul)&~curious(paul)))=>((funny(alice)&~happy(alice))))&
(![X]:((calm(X)|humble(X))<=>~rich(X)))&
(![X]:((wise(X)<~>~wise(X))<=>(old(X)&~strong(X))))&
(~wise(fred))&
((patient(paul)|~calm(paul)))&
(~kind(john))&
(~tall(susan))&
(?[X]:((~generous(X)&~calm(X))))&
(~quiet(paul))&
((~tall(lucy)&wise(lucy)))&
((brave(alice)|curious(alice))) | ~strong(fred) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2077253876840386157477937
% SZS output start Proof for 2077253876840386157477937
16. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~strong(X0) & old(X0))) [input p15]
25. strong(fred) [input hypothesis]
68. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (strong(X0) | ~old(X0))) & ((~strong(X0) & old(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 16]
69. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | strong(X0) | ~old(X0)) & ((~strong(X0) & old(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [flattening 68]
128. ~strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 69]
129. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 69]
140. strong(fred) [cnf transformation 25]
143. ~strong(X0) | ~wise(X0) [duplicate literal removal 128]
144. ~strong(X0) | wise(X0) [duplicate literal removal 129]
176. 8 <=> ! [X1] : ~strong(X1) [avatar definition]
177. ~strong(X1) <- (8) [avatar component clause 176]
261. 27 <=> strong(fred) [avatar definition]
263. strong(fred) <- (27) [avatar component clause 261]
290. ~strong(X0) [subsumption resolution 143,144]
291. 8 [avatar split clause 290,176]
309. 27 [avatar split clause 140,261]
320. $false <- (8, 27) [resolution 263,177]
321. ~8 | ~27 [avatar contradiction clause 320]
322. $false [avatar sat refutation 291,309,321]
% SZS output end Proof for 2077253876840386157477937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or humble is either not wise or not happy and vice versa. If someone is not tall then paul is either old or not calm and vice versa. Everyone who is not humble is not quiet and vice versa. Everyone who is not quiet is both not brave and quiet and vice versa. Everyone who is either not wise or strong is not wise and vice versa. If someone is either creative or strong then paul is either not wise or not strong and vice versa. Everyone who is either not curious or not happy is not rich and vice versa. Everyone who is brave is not kind or not wise. If lucy is either not happy or wise then lucy is either quiet or not humble. Everyone who is not humble is either brave or curious and vice versa. If someone is not wise or not tall then someone is either not humble or kind and vice versa. If alice is not wise then paul is not happy or not generous and vice versa. Everyone who is both humble and not calm is not happy or rich. If john is both creative and not calm then someone is not quiet or not calm. Everyone who is both quiet and curious is either not wise or not brave and vice versa. If someone is either not funny or creative then someone is not brave or strong. Paul is both not patient and humble. Someone is both not wise and curious. Fred is funny. Someone is kind or quiet. | Alice is creative. | contradiction | (![X]:((happy(X)|humble(X))<=>(~wise(X)<~>~happy(X))))&
((?[X]:(~tall(X)))<=>((old(paul)<~>~calm(paul))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:(~quiet(X)<=>(~brave(X)&quiet(X))))&
(![X]:((~wise(X)<~>strong(X))<=>~wise(X)))&
((?[X]:((creative(X)<~>strong(X))))<=>((~wise(paul)<~>~strong(paul))))&
(![X]:((~curious(X)<~>~happy(X))<=>~rich(X)))&
(![X]:(brave(X)=>(~kind(X)|~wise(X))))&
(((~happy(lucy)<~>wise(lucy)))=>((quiet(lucy)<~>~humble(lucy))))&
(![X]:(~humble(X)<=>(brave(X)<~>curious(X))))&
((?[X]:((~wise(X)|~tall(X))))<=>(?[X]:((~humble(X)<~>kind(X)))))&
((~wise(alice))<=>((~happy(paul)|~generous(paul))))&
(![X]:((humble(X)&~calm(X))=>(~happy(X)|rich(X))))&
(((creative(john)&~calm(john)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~wise(X)<~>~brave(X))))&
((?[X]:((~funny(X)<~>creative(X))))=>(?[X]:((~brave(X)|strong(X)))))&
((~patient(paul)&humble(paul)))&
(?[X]:((~wise(X)&curious(X))))&
(funny(fred))&
(?[X]:((kind(X)|quiet(X)))) | creative(alice) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7008937230310067568657536
% SZS output start Proof for 7008937230310067568657536
3. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p2]
4. ! [X0] : (~quiet(X0) <=> (quiet(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((~wise(X0) <~> strong(X0)) <=> ~wise(X0)) [input p4]
6. ? [X0] : (creative(X0) <~> strong(X0)) <=> (~wise(paul) <~> ~strong(paul)) [input p5]
10. ! [X0] : (~humble(X0) <=> (brave(X0) <~> curious(X0))) [input p9]
15. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~wise(X0) <~> ~brave(X0))) [input p14]
21. creative(alice) [input hypothesis]
41. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 3]
42. ! [X0] : ((~quiet(X0) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | quiet(X0))) [nnf transformation 4]
43. ! [X0] : ((~quiet(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | quiet(X0))) [flattening 42]
44. ! [X0] : ((((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | wise(X0)) & (~wise(X0) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0))))) [nnf transformation 5]
45. (? [X0] : ((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) & (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X0] : ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0)))) [nnf transformation 6]
46. (? [X0] : ((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) & (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X1] : ((creative(X1) | ~strong(X1)) & (strong(X1) | ~creative(X1)))) [rectify 45]
47. ? [X0] : ((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) => ((~strong(sK1) | ~creative(sK1)) & (strong(sK1) | creative(sK1))) [choice axiom]
48. (((~strong(sK1) | ~creative(sK1)) & (strong(sK1) | creative(sK1))) | ((~wise(paul) | strong(paul)) & (~strong(paul) | wise(paul)))) & (((strong(paul) | wise(paul)) & (~strong(paul) | ~wise(paul))) | ! [X1] : ((creative(X1) | ~strong(X1)) & (strong(X1) | ~creative(X1)))) [skolemisation 46,47]
51. ! [X0] : ((~humble(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | humble(X0))) [nnf transformation 10]
61. ! [X0] : (((curious(X0) & quiet(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 15]
62. ! [X0] : (((curious(X0) & quiet(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 61]
81. ~quiet(X0) | humble(X0) [cnf transformation 41]
84. quiet(X0) | quiet(X0) [cnf transformation 43]
85. ~quiet(X0) | ~quiet(X0) | brave(X0) [cnf transformation 43]
87. ~wise(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 44]
89. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 44]
92. strong(paul) | wise(paul) | strong(X1) | ~creative(X1) [cnf transformation 48]
107. ~brave(X0) | curious(X0) | ~humble(X0) [cnf transformation 51]
120. ~brave(X0) | ~wise(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 62]
133. creative(alice) [cnf transformation 21]
134. ~wise(X0) | ~strong(X0) [duplicate literal removal 87]
135. ~strong(X0) | wise(X0) [duplicate literal removal 89]
136. quiet(X0) [duplicate literal removal 84]
137. ~quiet(X0) | brave(X0) [duplicate literal removal 85]
159. ~strong(X0) [subsumption resolution 134,135]
163. 5 <=> wise(paul) [avatar definition]
164. wise(paul) <- (5) [avatar component clause 163]
171. wise(paul) | strong(X1) | ~creative(X1) [subsumption resolution 92,159]
172. wise(paul) | ~creative(X1) [subsumption resolution 171,159]
174. 7 <=> ! [X1] : ~creative(X1) [avatar definition]
175. ~creative(X1) <- (7) [avatar component clause 174]
176. 7 | 5 [avatar split clause 172,163,174]
237. ~curious(X0) | ~wise(X0) | ~brave(X0) [subsumption resolution 120,136]
252. humble(X0) [resolution 81,136]
257. brave(X0) [resolution 137,136]
277. curious(X0) | ~humble(X0) [resolution 107,257]
278. curious(X0) [subsumption resolution 277,252]
291. ~wise(X0) | ~brave(X0) [resolution 237,278]
293. ~wise(X0) [subsumption resolution 291,257]
294. $false <- (5) [resolution 293,164]
296. ~5 [avatar contradiction clause 294]
297. $false <- (7) [resolution 175,133]
300. ~7 [avatar contradiction clause 297]
301. $false [avatar sat refutation 176,296,300]
% SZS output end Proof for 7008937230310067568657536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy or not happy then someone is brave. Everyone who is not wise or strong is not rich. Everyone who is not old or brave is quiet or not quiet. Everyone who is not kind is not curious or not quiet and vice versa. If someone is tall then someone is both not old and kind. If fred is both not strong and not funny then someone is both not patient and old. Everyone who is either kind or not strong is either tall or strong and vice versa. Everyone who is either not strong or brave is not tall. Everyone who is not generous is both not brave and generous and vice versa. If someone is not calm then susan is either not curious or not creative and vice versa. Everyone who is both not strong and not quiet is both humble and happy and vice versa. If alice is either calm or happy then mary is curious. If mary is patient then mary is kind and vice versa. If alice is old or not curious then mary is both not brave and calm and vice versa. If someone is not kind or strong then lucy is patient or not kind and vice versa. Someone is funny or old. Alice is both curious and not humble. Susan is both generous and happy. Paul is tall or wise. Someone is either generous or strong. Fred is not kind or not generous. Someone is strong or quiet. | Alice is not humble. | entailment | (((happy(john)|~happy(john)))=>(?[X]:(brave(X))))&
(![X]:((~wise(X)|strong(X))=>~rich(X)))&
(![X]:((~old(X)|brave(X))=>(quiet(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(((calm(alice)<~>happy(alice)))=>(curious(mary)))&
((patient(mary))<=>(kind(mary)))&
(((old(alice)|~curious(alice)))<=>((~brave(mary)&calm(mary))))&
((?[X]:((~kind(X)|strong(X))))<=>((patient(lucy)|~kind(lucy))))&
(?[X]:((funny(X)|old(X))))&
((curious(alice)&~humble(alice)))&
((generous(susan)&happy(susan)))&
((tall(paul)|wise(paul)))&
(?[X]:((generous(X)<~>strong(X))))&
((~kind(fred)|~generous(fred)))&
(?[X]:((strong(X)|quiet(X)))) | ~humble(alice) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 753298964624578285882662
% SZS output start Proof for 753298964624578285882662
17. ~humble(alice) & curious(alice) [input p16]
23. humble(alice) [input hypothesis]
110. ~humble(alice) [cnf transformation 17]
117. humble(alice) [cnf transformation 23]
251. $false [subsumption resolution 117,110]
% SZS output end Proof for 753298964624578285882662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If fred is brave or not brave then someone is tall or not rich and vice versa.
Everyone who is both not curious and patient is both patient and curious and vice versa.
If paul is not happy or not curious then someone is either not funny or strong.
Everyone who is either not creative or not generous is not strong or generous.
Everyone who is either brave or not wise is not kind or funny.
Everyone who is strong or funny is either not curious or not happy and vice versa.
If someone is wise then susan is funny or generous and vice versa.
Everyone who is either not creative or humble is not strong or curious.
If paul is both not calm and not patient then someone is not rich and vice versa.
If someone is either brave or not happy then fred is not funny or not happy and vice versa.
Everyone who is not generous or not strong is either not calm or curious.
If alice is not generous or quiet then susan is either not rich or not brave and vice versa.
If alice is both not patient and kind then someone is both not happy and not quiet and vice versa.
Everyone who is both not generous and funny is either not quiet or not humble.
If john is both not wise and curious then someone is both not quiet and not happy and vice versa.
Everyone who is not generous is either not generous or patient.
Fred is not creative.
Someone is either not quiet or patient.
John is creative.
Mary is both not curious and quiet.
Alice is either tall or not rich.
Alice is both calm and humble.
Someone is not humble or curious. | John is not strong. | neutral | (((brave(fred)|~brave(fred)))<=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:(~generous(X)=>(~generous(X)<~>patient(X))))&
(~creative(fred))&
(?[X]:((~quiet(X)<~>patient(X))))&
(creative(john))&
((~curious(mary)&quiet(mary)))&
((tall(alice)<~>~rich(alice)))&
((calm(alice)&humble(alice)))&
(?[X]:((~humble(X)|curious(X)))) | ~strong(john) | []
| null | 0 |
If someone is wise then someone is creative.
If mary is wise then paul is both brave and tall.
If alice is patient or not humble then lucy is not brave and vice versa.
Everyone who is not creative or not wise is either kind or rich.
If someone is quiet or funny then someone is either humble or not brave.
Everyone who is either not rich or humble is both not tall and not curious.
Everyone who is brave is not old.
Everyone who is wise or not rich is both rich and generous.
Everyone who is either not wise or funny is kind.
Everyone who is funny or wise is humble.
Everyone who is either calm or happy is not curious or not creative.
If someone is not tall then someone is happy or kind and vice versa.
Everyone who is both not funny and patient is both not old and not kind and vice versa.
If someone is not humble or not creative then paul is wise.
Everyone who is either strong or not happy is both strong and humble.
Someone is not tall.
Someone is either creative or old.
Someone is happy or not patient.
Mary is not patient or curious.
Someone is either generous or patient.
Fred is either not creative or funny.
John is not old or not curious.
Someone is not kind or not strong. | Fred is not tall. | entailment | ((?[X]:(wise(X)))=>(?[X]:(creative(X))))&
((wise(mary))=>((brave(paul)&tall(paul))))&
(((patient(alice)|~humble(alice)))<=>(~brave(lucy)))&
(![X]:((~creative(X)|~wise(X))=>(kind(X)<~>rich(X))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>humble(X))=>(~tall(X)&~curious(X))))&
(![X]:(brave(X)=>~old(X)))&
(![X]:((wise(X)|~rich(X))=>(rich(X)&generous(X))))&
(![X]:((~wise(X)<~>funny(X))=>kind(X)))&
(![X]:((funny(X)|wise(X))=>humble(X)))&
(![X]:((calm(X)<~>happy(X))=>(~curious(X)|~creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((happy(X)|kind(X)))))&
(![X]:((~funny(X)&patient(X))<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)|~creative(X))))=>(wise(paul)))&
(![X]:((strong(X)<~>~happy(X))=>(strong(X)&humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((creative(X)<~>old(X))))&
(?[X]:((happy(X)|~patient(X))))&
((~patient(mary)|curious(mary)))&
(?[X]:((generous(X)<~>patient(X))))&
((~creative(fred)<~>funny(fred)))&
((~old(john)|~curious(john)))&
(?[X]:((~kind(X)|~strong(X)))) | ~tall(fred) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 8722835614337542487340713
% SZS output start Proof for 8722835614337542487340713
4. ! [X0] : ((~wise(X0) | ~creative(X0)) => (kind(X0) <~> rich(X0))) [input p3]
6. ! [X0] : ((~rich(X0) <~> humble(X0)) => (~curious(X0) & ~tall(X0))) [input p5]
8. ! [X0] : ((~rich(X0) | wise(X0)) => (generous(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~wise(X0) <~> funny(X0)) => kind(X0)) [input p8]
10. ! [X0] : ((wise(X0) | funny(X0)) => humble(X0)) [input p9]
24. tall(fred) [input hypothesis]
31. ! [X0] : ((kind(X0) <~> rich(X0)) | (wise(X0) & creative(X0))) [ennf transformation 4]
33. ! [X0] : ((~curious(X0) & ~tall(X0)) | (~rich(X0) <=> humble(X0))) [ennf transformation 6]
35. ! [X0] : ((generous(X0) & rich(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 8]
36. ! [X0] : (kind(X0) | (~wise(X0) <=> funny(X0))) [ennf transformation 9]
37. ! [X0] : (humble(X0) | (~wise(X0) & ~funny(X0))) [ennf transformation 10]
47. ! [X0] : (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (wise(X0) & creative(X0))) [nnf transformation 31]
52. ! [X0] : ((~curious(X0) & ~tall(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) [nnf transformation 33]
53. ! [X0] : (kind(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0)))) [nnf transformation 36]
85. ~rich(X0) | ~kind(X0) | wise(X0) [cnf transformation 47]
89. ~rich(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 52]
94. rich(X0) | rich(X0) [cnf transformation 35]
97. funny(X0) | kind(X0) | wise(X0) [cnf transformation 53]
99. ~funny(X0) | humble(X0) [cnf transformation 37]
100. ~wise(X0) | humble(X0) [cnf transformation 37]
127. tall(fred) [cnf transformation 24]
129. rich(X0) [duplicate literal removal 94]
259. 30 <=> funny(fred) [avatar definition]
260. funny(fred) <- (30) [avatar component clause 259]
261. ~funny(fred) <- (~30) [avatar component clause 259]
296. ~kind(X2) | wise(X2) [resolution 85,129]
301. ~humble(X2) | ~tall(X2) [resolution 89,129]
314. 35 <=> wise(fred) [avatar definition]
316. wise(fred) <- (35) [avatar component clause 314]
322. humble(fred) <- (30) [resolution 260,99]
323. ~tall(fred) <- (30) [resolution 322,301]
324. $false <- (30) [subsumption resolution 323,127]
325. ~30 [avatar contradiction clause 324]
326. kind(fred) | wise(fred) <- (~30) [resolution 261,97]
329. humble(fred) <- (35) [resolution 316,100]
331. ~tall(fred) <- (35) [resolution 329,301]
332. $false <- (35) [subsumption resolution 331,127]
333. ~35 [avatar contradiction clause 332]
334. wise(fred) <- (~30) [subsumption resolution 326,296]
335. 35 | 30 [avatar split clause 334,259,314]
336. $false [avatar sat refutation 325,333,335]
% SZS output end Proof for 8722835614337542487340713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and kind then susan is rich or quiet.
Everyone who is either rich or not funny is either rich or creative.
Everyone who is strong is either not patient or calm and vice versa.
Everyone who is both kind and generous is both generous and not curious.
Everyone who is both quiet and funny is both not creative and not quiet.
Everyone who is either not curious or rich is curious and vice versa.
Everyone who is calm is both not strong and not curious and vice versa.
If lucy is brave then john is both not strong and not curious and vice versa.
Everyone who is creative or not tall is either not curious or not funny and vice versa.
Everyone who is both curious and not rich is wise.
If fred is old then someone is both strong and not humble and vice versa.
Everyone who is not generous is wise or humble and vice versa.
If someone is both calm and humble then someone is both not old and not brave.
If someone is old or quiet then someone is not rich.
Everyone who is both wise and not rich is both not brave and humble and vice versa.
Everyone who is both calm and not brave is either not patient or not strong and vice versa.
Lucy is both happy and not tall.
Someone is not curious.
Someone is either not brave or calm.
John is either wise or brave.
Someone is generous or not patient.
John is tall or patient.
Someone is not funny. | Fred is humble. | contradiction | (((~brave(mary)&kind(mary)))=>((rich(susan)|quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(rich(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)&~curious(X))))&
(![X]:((quiet(X)&funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)<~>rich(X))<=>curious(X)))&
(![X]:(calm(X)<=>(~strong(X)&~curious(X))))&
((brave(lucy))<=>((~strong(john)&~curious(john))))&
(![X]:((creative(X)|~tall(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((curious(X)&~rich(X))=>wise(X)))&
((old(fred))<=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:(~generous(X)<=>(wise(X)|humble(X))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((calm(X)&~brave(X))<=>(~patient(X)<~>~strong(X))))&
((happy(lucy)&~tall(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((wise(john)<~>brave(john)))&
(?[X]:((generous(X)|~patient(X))))&
((tall(john)|patient(john)))&
(?[X]:(~funny(X))) | humble(fred) | [
"p2",
"p6",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4948670990554578142323648
% SZS output start Proof for 4948670990554578142323648
3. ! [X0] : (strong(X0) <=> (~patient(X0) <~> calm(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> (~curious(X0) & ~strong(X0))) [input p6]
13. ? [X0] : (humble(X0) & calm(X0)) => ? [X0] : (~brave(X0) & ~old(X0)) [input p12]
16. ! [X0] : ((~brave(X0) & calm(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p15]
24. humble(fred) [input hypothesis]
25. ? [X0] : (humble(X0) & calm(X0)) => ? [X1] : (~brave(X1) & ~old(X1)) [rectify 13]
37. ? [X1] : (~brave(X1) & ~old(X1)) | ! [X0] : (~humble(X0) | ~calm(X0)) [ennf transformation 25]
40. ! [X0] : ((strong(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ~strong(X0))) [nnf transformation 3]
42. ! [X0] : ((calm(X0) | (curious(X0) | strong(X0))) & ((~curious(X0) & ~strong(X0)) | ~calm(X0))) [nnf transformation 7]
43. ! [X0] : ((calm(X0) | curious(X0) | strong(X0)) & ((~curious(X0) & ~strong(X0)) | ~calm(X0))) [flattening 42]
52. ? [X0] : (~brave(X0) & ~old(X0)) | ! [X1] : (~humble(X1) | ~calm(X1)) [rectify 37]
53. ? [X0] : (~brave(X0) & ~old(X0)) => (~brave(sK1) & ~old(sK1)) [choice axiom]
54. (~brave(sK1) & ~old(sK1)) | ! [X1] : (~humble(X1) | ~calm(X1)) [skolemisation 52,53]
60. ! [X0] : (((~brave(X0) & calm(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | (brave(X0) | ~calm(X0)))) [nnf transformation 16]
61. ! [X0] : (((~brave(X0) & calm(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | brave(X0) | ~calm(X0))) [flattening 60]
76. ~patient(X0) | calm(X0) | ~strong(X0) [cnf transformation 40]
78. calm(X0) | strong(X0) | patient(X0) [cnf transformation 40]
79. ~calm(X0) | ~patient(X0) | strong(X0) [cnf transformation 40]
84. ~calm(X0) | ~strong(X0) [cnf transformation 43]
103. ~brave(sK1) | ~humble(X1) | ~calm(X1) [cnf transformation 54]
110. strong(X0) | patient(X0) | brave(X0) | ~calm(X0) [cnf transformation 61]
111. calm(X0) | ~strong(X0) | patient(X0) [cnf transformation 61]
112. calm(X0) | ~patient(X0) | strong(X0) [cnf transformation 61]
124. humble(fred) [cnf transformation 24]
164. 8 <=> ! [X1] : (~humble(X1) | ~calm(X1)) [avatar definition]
165. ~humble(X1) | ~calm(X1) <- (8) [avatar component clause 164]
167. 9 <=> brave(sK1) [avatar definition]
169. ~brave(sK1) <- (~9) [avatar component clause 167]
170. 8 | ~9 [avatar split clause 103,167,164]
178. calm(X0) | strong(X0) [subsumption resolution 112,78]
179. calm(X0) | ~strong(X0) [subsumption resolution 111,76]
180. calm(X0) [subsumption resolution 179,178]
181. patient(X0) | strong(X0) | brave(X0) [subsumption resolution 110,180]
211. ~strong(X0) [resolution 84,180]
225. ~patient(X1) | strong(X1) | strong(X1) [resolution 79,178]
227. ~patient(X1) | strong(X1) [duplicate literal removal 225]
229. ~patient(X1) [subsumption resolution 227,211]
251. strong(X1) | brave(X1) [resolution 181,229]
255. brave(X1) [subsumption resolution 251,211]
273. $false <- (~9) [resolution 255,169]
274. 9 [avatar contradiction clause 273]
276. ~humble(X1) <- (8) [subsumption resolution 165,180]
277. $false <- (8) [resolution 276,124]
278. ~8 [avatar contradiction clause 277]
279. $false [avatar sat refutation 170,274,278]
% SZS output end Proof for 4948670990554578142323648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or humble is calm or kind.
If someone is both not creative and not calm then someone is generous.
Everyone who is either not strong or funny is not creative or humble and vice versa.
Everyone who is both not strong and funny is either not strong or not patient.
Everyone who is either not rich or not wise is either calm or not curious and vice versa.
If someone is not calm or not strong then lucy is both calm and not creative and vice versa.
Everyone who is curious or patient is both funny and old.
Everyone who is both not humble and not calm is both not quiet and humble and vice versa.
Everyone who is tall or not humble is not quiet and vice versa.
Everyone who is either kind or quiet is either not rich or strong and vice versa.
Everyone who is humble is both kind and not wise and vice versa.
If someone is either not calm or not creative then john is both creative and not curious and vice versa.
Everyone who is both quiet and curious is not happy or not kind and vice versa.
Everyone who is not rich is either tall or rich.
Everyone who is either not calm or generous is either not humble or happy and vice versa.
Everyone who is both wise and not tall is not strong or not happy and vice versa.
Someone is not happy or not funny.
Someone is happy.
Someone is either generous or creative.
Someone is creative. | Lucy is not patient. | entailment | (![X]:((brave(X)|humble(X))=>(calm(X)|kind(X))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~creative(X)|humble(X))))&
(![X]:((~strong(X)&funny(X))=>(~strong(X)<~>~patient(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(calm(X)<~>~curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>((calm(lucy)&~creative(lucy))))&
(![X]:((curious(X)|patient(X))=>(funny(X)&old(X))))&
(![X]:((~humble(X)&~calm(X))<=>(~quiet(X)&humble(X))))&
(![X]:((tall(X)|~humble(X))<=>~quiet(X)))&
(![X]:((kind(X)<~>quiet(X))<=>(~rich(X)<~>strong(X))))&
(![X]:(humble(X)<=>(kind(X)&~wise(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>((creative(john)&~curious(john))))&
(![X]:((quiet(X)&curious(X))<=>(~happy(X)|~kind(X))))&
(![X]:(~rich(X)=>(tall(X)<~>rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((wise(X)&~tall(X))<=>(~strong(X)|~happy(X))))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:(happy(X)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(creative(X))) | ~patient(lucy) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3502529065790426860246690
% SZS output start Proof for 3502529065790426860246690
3. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) | ~creative(X0))) [input p2]
6. ? [X0] : (~strong(X0) | ~calm(X0)) <=> (~creative(lucy) & calm(lucy)) [input p5]
7. ! [X0] : ((patient(X0) | curious(X0)) => (old(X0) & funny(X0))) [input p6]
8. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> (humble(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((~humble(X0) | tall(X0)) <=> ~quiet(X0)) [input p8]
10. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> (~rich(X0) <~> strong(X0))) [input p9]
11. ! [X0] : (humble(X0) <=> (~wise(X0) & kind(X0))) [input p10]
13. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~kind(X0) | ~happy(X0))) [input p12]
14. ! [X0] : (~rich(X0) => (tall(X0) <~> rich(X0))) [input p13]
16. ! [X0] : ((~tall(X0) & wise(X0)) <=> (~happy(X0) | ~strong(X0))) [input p15]
21. patient(lucy) [input hypothesis]
23. ! [X0] : ((patient(X0) | curious(X0)) => funny(X0)) [pure predicate removal 7]
30. ! [X0] : (funny(X0) | (~patient(X0) & ~curious(X0))) [ennf transformation 23]
31. ! [X0] : ((tall(X0) <~> rich(X0)) | rich(X0)) [ennf transformation 14]
35. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) & creative(X0))) & ((humble(X0) | ~creative(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 3]
36. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) & creative(X0))) & (humble(X0) | ~creative(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 35]
39. (? [X0] : (~strong(X0) | ~calm(X0)) | (creative(lucy) | ~calm(lucy))) & ((~creative(lucy) & calm(lucy)) | ! [X0] : (strong(X0) & calm(X0))) [nnf transformation 6]
40. (? [X0] : (~strong(X0) | ~calm(X0)) | creative(lucy) | ~calm(lucy)) & ((~creative(lucy) & calm(lucy)) | ! [X0] : (strong(X0) & calm(X0))) [flattening 39]
41. (? [X0] : (~strong(X0) | ~calm(X0)) | creative(lucy) | ~calm(lucy)) & ((~creative(lucy) & calm(lucy)) | ! [X1] : (strong(X1) & calm(X1))) [rectify 40]
42. ? [X0] : (~strong(X0) | ~calm(X0)) => (~strong(sK1) | ~calm(sK1)) [choice axiom]
43. ((~strong(sK1) | ~calm(sK1)) | creative(lucy) | ~calm(lucy)) & ((~creative(lucy) & calm(lucy)) | ! [X1] : (strong(X1) & calm(X1))) [skolemisation 41,42]
44. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~humble(X0) | quiet(X0))) & ((humble(X0) & ~quiet(X0)) | (calm(X0) | humble(X0)))) [nnf transformation 8]
45. ! [X0] : (((~calm(X0) & ~humble(X0)) | ~humble(X0) | quiet(X0)) & ((humble(X0) & ~quiet(X0)) | calm(X0) | humble(X0))) [flattening 44]
46. ! [X0] : (((~humble(X0) | tall(X0)) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~tall(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | tall(X0) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~tall(X0)))) [flattening 46]
48. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 10]
49. ! [X0] : ((humble(X0) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ~humble(X0))) [nnf transformation 11]
50. ! [X0] : ((humble(X0) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~humble(X0))) [flattening 49]
56. ! [X0] : (((curious(X0) & quiet(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 13]
57. ! [X0] : (((curious(X0) & quiet(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~curious(X0) | ~quiet(X0))) [flattening 56]
58. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | rich(X0)) [nnf transformation 31]
60. ! [X0] : (((~tall(X0) & wise(X0)) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 16]
61. ! [X0] : (((~tall(X0) & wise(X0)) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | tall(X0) | ~wise(X0))) [flattening 60]
74. ~funny(X0) | ~creative(X0) | ~strong(X0) | humble(X0) [cnf transformation 36]
89. calm(lucy) | calm(X1) [cnf transformation 43]
93. ~strong(sK1) | ~calm(sK1) | creative(lucy) | ~calm(lucy) [cnf transformation 43]
95. ~patient(X0) | funny(X0) [cnf transformation 30]
97. humble(X0) | calm(X0) | humble(X0) [cnf transformation 45]
98. ~humble(X0) | ~humble(X0) | quiet(X0) [cnf transformation 45]
100. ~tall(X0) | ~quiet(X0) [cnf transformation 47]
101. ~quiet(X0) | humble(X0) [cnf transformation 47]
103. ~rich(X0) | strong(X0) | quiet(X0) | ~kind(X0) [cnf transformation 48]
105. ~strong(X0) | rich(X0) | quiet(X0) | ~kind(X0) [cnf transformation 48]
110. ~quiet(X0) | ~kind(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 48]
111. ~humble(X0) | kind(X0) [cnf transformation 50]
112. ~wise(X0) | ~humble(X0) [cnf transformation 50]
122. quiet(X0) | kind(X0) [cnf transformation 57]
125. rich(X0) | tall(X0) | rich(X0) [cnf transformation 58]
136. wise(X0) | strong(X0) [cnf transformation 61]
138. ~tall(X0) | strong(X0) [cnf transformation 61]
145. patient(lucy) [cnf transformation 21]
146. tall(X0) | rich(X0) [duplicate literal removal 125]
147. calm(X0) | humble(X0) [duplicate literal removal 97]
148. ~humble(X0) | quiet(X0) [duplicate literal removal 98]
159. 3 <=> calm(lucy) [avatar definition]
161. ~calm(lucy) <- (~3) [avatar component clause 159]
163. 4 <=> creative(lucy) [avatar definition]
167. 5 <=> calm(sK1) [avatar definition]
169. ~calm(sK1) <- (~5) [avatar component clause 167]
171. 6 <=> strong(sK1) [avatar definition]
172. strong(sK1) <- (6) [avatar component clause 171]
173. ~strong(sK1) <- (~6) [avatar component clause 171]
174. ~3 | 4 | ~5 | ~6 [avatar split clause 93,171,167,163,159]
176. 7 <=> ! [X1] : strong(X1) [avatar definition]
177. strong(X1) <- (7) [avatar component clause 176]
180. 8 <=> ! [X1] : calm(X1) [avatar definition]
181. calm(X1) <- (8) [avatar component clause 180]
184. 8 | 3 [avatar split clause 89,159,180]
236. funny(lucy) [resolution 95,145]
239. kind(X0) | humble(X0) [resolution 122,101]
240. kind(X0) [subsumption resolution 239,111]
246. ~humble(X0) | strong(X0) [resolution 136,112]
248. rich(X1) | strong(X1) [resolution 146,138]
249. ~quiet(X2) | rich(X2) [resolution 146,100]
342. ~creative(lucy) | ~strong(lucy) | humble(lucy) [resolution 74,236]
406. strong(X0) | quiet(X0) | ~kind(X0) | strong(X0) [resolution 103,248]
409. strong(X0) | quiet(X0) | ~kind(X0) [duplicate literal removal 406]
410. quiet(X0) | strong(X0) [subsumption resolution 409,240]
766. 59 <=> humble(lucy) [avatar definition]
768. humble(lucy) <- (59) [avatar component clause 766]
770. 60 <=> strong(lucy) [avatar definition]
771. strong(lucy) <- (60) [avatar component clause 770]
772. ~strong(lucy) <- (~60) [avatar component clause 770]
773. 59 | ~60 | ~4 [avatar split clause 342,163,770,766]
775. $false <- (7, ~60) [subsumption resolution 772,177]
776. ~7 | 60 [avatar contradiction clause 775]
781. $false <- (~6, 7) [resolution 177,173]
788. 6 | ~7 [avatar contradiction clause 781]
806. humble(sK1) <- (~5) [resolution 169,147]
816. quiet(sK1) <- (~5) [resolution 806,148]
848. quiet(lucy) <- (59) [resolution 768,148]
953. ~kind(sK1) | ~rich(sK1) | ~strong(sK1) <- (~5) [resolution 816,110]
954. rich(sK1) <- (~5) [resolution 816,249]
957. ~rich(sK1) | ~strong(sK1) <- (~5) [subsumption resolution 953,240]
958. ~rich(sK1) <- (~5, 6) [subsumption resolution 957,172]
959. $false <- (~5, 6) [subsumption resolution 954,958]
960. 5 | ~6 [avatar contradiction clause 959]
993. $false <- (~3, 8) [subsumption resolution 161,181]
994. 3 | ~8 [avatar contradiction clause 993]
996. rich(X0) | quiet(X0) | ~kind(X0) <- (7) [resolution 177,105]
999. rich(X0) | quiet(X0) <- (7) [subsumption resolution 996,240]
1000. rich(X0) <- (7) [subsumption resolution 999,249]
1111. strong(X0) | humble(X0) [resolution 410,101]
1127. ~kind(lucy) | ~rich(lucy) | ~strong(lucy) <- (59) [resolution 848,110]
1131. ~rich(lucy) | ~strong(lucy) <- (59) [subsumption resolution 1127,240]
1132. ~strong(lucy) <- (7, 59) [subsumption resolution 1131,1000]
1133. $false <- (7, 59, 60) [subsumption resolution 1132,771]
1134. ~7 | ~59 | ~60 [avatar contradiction clause 1133]
1137. strong(X0) [subsumption resolution 1111,246]
1138. 7 [avatar split clause 1137,176]
1172. $false [avatar sat refutation 174,184,773,776,788,960,994,1134,1138]
% SZS output end Proof for 3502529065790426860246690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and creative is either not humble or not old and vice versa.
If someone is either tall or not strong then lucy is not creative and vice versa.
Everyone who is happy or patient is not humble.
If fred is either curious or calm then someone is both strong and creative and vice versa.
Everyone who is either tall or brave is tall or patient and vice versa.
Everyone who is not old or brave is happy and vice versa.
Everyone who is brave or not wise is humble.
Everyone who is either not old or kind is both generous and not kind.
Everyone who is creative is both humble and patient.
Everyone who is funny or happy is both creative and not strong.
Everyone who is not quiet or not funny is old and vice versa.
If someone is either patient or old then john is both humble and not quiet and vice versa.
If fred is not humble or not rich then someone is both funny and not creative.
Everyone who is humble is strong and vice versa.
If someone is patient or calm then alice is both rich and not brave.
Alice is either not rich or curious.
Lucy is both not curious and not tall.
Paul is not happy or not brave.
John is not brave or strong.
Fred is not curious or tall. | Lucy is brave. | contradiction | (![X]:((brave(X)&creative(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~strong(X))))<=>(~creative(lucy)))&
(![X]:((happy(X)|patient(X))=>~humble(X)))&
(((curious(fred)<~>calm(fred)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(tall(X)|patient(X))))&
(![X]:((~old(X)|brave(X))<=>happy(X)))&
(![X]:((brave(X)|~wise(X))=>humble(X)))&
(![X]:((~old(X)<~>kind(X))=>(generous(X)&~kind(X))))&
(![X]:(creative(X)=>(humble(X)&patient(X))))&
(![X]:((funny(X)|happy(X))=>(creative(X)&~strong(X))))&
(![X]:((~quiet(X)|~funny(X))<=>old(X)))&
((?[X]:((patient(X)<~>old(X))))<=>((humble(john)&~quiet(john))))&
(((~humble(fred)|~rich(fred)))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:(humble(X)<=>strong(X)))&
((?[X]:((patient(X)|calm(X))))=>((rich(alice)&~brave(alice))))&
((~rich(alice)<~>curious(alice)))&
((~curious(lucy)&~tall(lucy)))&
((~happy(paul)|~brave(paul)))&
((~brave(john)|strong(john)))&
((~curious(fred)|tall(fred))) | brave(lucy) | [
"p2",
"p5",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 6020986616697914544395639
% SZS output start Proof for 6020986616697914544395639
3. ! [X0] : ((patient(X0) | happy(X0)) => ~humble(X0)) [input p2]
6. ! [X0] : ((brave(X0) | ~old(X0)) <=> happy(X0)) [input p5]
7. ! [X0] : ((~wise(X0) | brave(X0)) => humble(X0)) [input p6]
21. brave(lucy) [input hypothesis]
22. ! [X0] : ((brave(X0) | ~old(X0)) => happy(X0)) [unused predicate definition removal 6]
24. ! [X0] : (brave(X0) => humble(X0)) [pure predicate removal 7]
25. ! [X0] : (~humble(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 3]
26. ! [X0] : (happy(X0) | (~brave(X0) & old(X0))) [ennf transformation 22]
27. ! [X0] : (humble(X0) | ~brave(X0)) [ennf transformation 24]
67. ~happy(X0) | ~humble(X0) [cnf transformation 25]
82. ~brave(X0) | happy(X0) [cnf transformation 26]
83. ~brave(X0) | humble(X0) [cnf transformation 27]
118. brave(lucy) [cnf transformation 21]
260. happy(lucy) [resolution 82,118]
261. ~humble(lucy) [resolution 260,67]
262. humble(lucy) [resolution 83,118]
263. $false [subsumption resolution 262,261]
% SZS output end Proof for 6020986616697914544395639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and patient is both not creative and not happy.
Everyone who is tall or not generous is curious and vice versa.
Everyone who is not strong or not wise is old.
If paul is both curious and not patient then fred is strong.
Everyone who is either funny or quiet is old or not tall and vice versa.
Everyone who is both tall and not happy is both not humble and not happy and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is not calm or kind is strong and vice versa.
Everyone who is not funny is both humble and not wise and vice versa.
Everyone who is not kind or generous is old or not old.
Everyone who is patient or tall is not strong and vice versa.
If fred is both not creative and not quiet then susan is either not kind or wise and vice versa.
If someone is either not humble or not tall then someone is either not creative or funny.
Everyone who is humble is not wise and vice versa.
Everyone who is patient or generous is rich or not creative.
Everyone who is quiet or funny is either quiet or not quiet.
Someone is both not kind and funny.
Alice is not patient.
John is curious or wise.
Mary is either not brave or not happy.
Someone is either not kind or not patient.
Fred is both brave and not calm.
Mary is tall. | Mary is not quiet. | entailment | (![X]:((curious(X)&patient(X))=>(~creative(X)&~happy(X))))&
(![X]:((tall(X)|~generous(X))<=>curious(X)))&
(![X]:((~strong(X)|~wise(X))=>old(X)))&
(((curious(paul)&~patient(paul)))=>(strong(fred)))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)|~tall(X))))&
(![X]:((tall(X)&~happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:((~calm(X)|kind(X))<=>strong(X)))&
(![X]:(~funny(X)<=>(humble(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(old(X)|~old(X))))&
(![X]:((patient(X)|tall(X))<=>~strong(X)))&
(((~creative(fred)&~quiet(fred)))<=>((~kind(susan)<~>wise(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((patient(X)|generous(X))=>(rich(X)|~creative(X))))&
(![X]:((quiet(X)|funny(X))=>(quiet(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&funny(X))))&
(~patient(alice))&
((curious(john)|wise(john)))&
((~brave(mary)<~>~happy(mary)))&
(?[X]:((~kind(X)<~>~patient(X))))&
((brave(fred)&~calm(fred)))&
(tall(mary)) | ~quiet(mary) | [
"p2",
"p4",
"p6",
"p8",
"p10",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 6703206460614573896341026
% SZS output start Proof for 6703206460614573896341026
3. ! [X0] : ((~wise(X0) | ~strong(X0)) => old(X0)) [input p2]
5. ! [X0] : ((funny(X0) <~> quiet(X0)) <=> (~tall(X0) | old(X0))) [input p4]
7. ! [X0] : (funny(X0) <=> (old(X0) | ~calm(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> (~wise(X0) & humble(X0))) [input p8]
11. ! [X0] : ((tall(X0) | patient(X0)) <=> ~strong(X0)) [input p10]
23. tall(mary) [input p22]
24. quiet(mary) [input hypothesis]
29. ! [X0] : (old(X0) | (wise(X0) & strong(X0))) [ennf transformation 3]
38. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [flattening 38]
42. ! [X0] : ((funny(X0) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ~funny(X0))) [nnf transformation 7]
43. ! [X0] : ((funny(X0) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~funny(X0))) [flattening 42]
46. ! [X0] : ((~funny(X0) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | funny(X0))) [nnf transformation 9]
47. ! [X0] : ((~funny(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | funny(X0))) [flattening 46]
48. ! [X0] : (((tall(X0) | patient(X0)) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~patient(X0)))) [nnf transformation 11]
49. ! [X0] : ((tall(X0) | patient(X0) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~patient(X0)))) [flattening 48]
69. old(X0) | strong(X0) [cnf transformation 29]
70. old(X0) | wise(X0) [cnf transformation 29]
76. ~quiet(X0) | ~funny(X0) | ~old(X0) [cnf transformation 39]
84. ~old(X0) | funny(X0) [cnf transformation 43]
89. ~wise(X0) | funny(X0) [cnf transformation 47]
94. ~strong(X0) | ~tall(X0) [cnf transformation 49]
122. tall(mary) [cnf transformation 23]
123. quiet(mary) [cnf transformation 24]
210. funny(X0) | wise(X0) [resolution 84,70]
212. funny(X0) [subsumption resolution 210,89]
238. ~funny(mary) | ~old(mary) [resolution 76,123]
240. ~old(mary) [subsumption resolution 238,212]
245. strong(mary) [resolution 240,69]
252. ~tall(mary) [resolution 245,94]
254. $false [subsumption resolution 252,122]
% SZS output end Proof for 6703206460614573896341026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either rich or not old then someone is both generous and not creative. If someone is both happy and creative then someone is humble and vice versa. Everyone who is not happy is both not creative and not happy and vice versa. If someone is either not humble or not kind then paul is either not kind or humble and vice versa. Everyone who is both calm and not kind is either not funny or calm and vice versa. If paul is either happy or not patient then john is either not quiet or not patient and vice versa. If someone is not patient or not calm then fred is both not rich and old and vice versa. Everyone who is not patient is both not curious and not old. If someone is not tall then someone is either not rich or not quiet and vice versa. Everyone who is not funny is patient or not generous. Everyone who is either humble or generous is both not humble and wise and vice versa. Everyone who is patient is either wise or quiet and vice versa. Everyone who is not rich or not quiet is not tall or not funny. Everyone who is both not funny and not happy is patient or not tall and vice versa. Everyone who is brave is not humble and vice versa. If alice is funny or not calm then paul is either old or kind. Someone is either not creative or not quiet. Lucy is not calm. Someone is rich or not tall. Someone is not brave. Paul is both not happy and wise. Mary is both not calm and creative. Someone is either not patient or patient. Alice is both rich and funny. | Paul is old. | contradiction | ((?[X]:((rich(X)<~>~old(X))))=>(?[X]:((generous(X)&~creative(X)))))&
((?[X]:((happy(X)&creative(X))))<=>(?[X]:(humble(X))))&
(![X]:(~happy(X)<=>(~creative(X)&~happy(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((~kind(paul)<~>humble(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)<~>calm(X))))&
(((happy(paul)<~>~patient(paul)))<=>((~quiet(john)<~>~patient(john))))&
((?[X]:((~patient(X)|~calm(X))))<=>((~rich(fred)&old(fred))))&
(![X]:(~patient(X)=>(~curious(X)&~old(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>(patient(X)|~generous(X))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
(![X]:(patient(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)|~funny(X))))&
(![X]:((~funny(X)&~happy(X))<=>(patient(X)|~tall(X))))&
(![X]:(brave(X)<=>~humble(X)))&
(((funny(alice)|~calm(alice)))=>((old(paul)<~>kind(paul))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~calm(lucy))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:(~brave(X)))&
((~happy(paul)&wise(paul)))&
((~calm(mary)&creative(mary)))&
(?[X]:((~patient(X)<~>patient(X))))&
((rich(alice)&funny(alice))) | old(paul) | [
"p4",
"p7",
"p13",
"p15",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 88254121198644095187430
% SZS output start Proof for 88254121198644095187430
5. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~funny(X0) <~> calm(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (~old(X0) & ~curious(X0))) [input p7]
14. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> (~tall(X0) | patient(X0))) [input p13]
16. (~calm(alice) | funny(alice)) => (old(paul) <~> kind(paul)) [input p15]
24. funny(alice) & rich(alice) [input p23]
25. old(paul) [input hypothesis]
30. ! [X0] : (~patient(X0) => ~old(X0)) [pure predicate removal 8]
32. ! [X0] : (~old(X0) | patient(X0)) [ennf transformation 30]
38. (old(paul) <~> kind(paul)) | (calm(alice) & ~funny(alice)) [ennf transformation 16]
54. ! [X0] : (((~kind(X0) & calm(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (kind(X0) | ~calm(X0)))) [nnf transformation 5]
55. ! [X0] : (((~kind(X0) & calm(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | kind(X0) | ~calm(X0))) [flattening 54]
70. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & ((~tall(X0) | patient(X0)) | (happy(X0) | funny(X0)))) [nnf transformation 14]
71. ! [X0] : (((~happy(X0) & ~funny(X0)) | (tall(X0) & ~patient(X0))) & (~tall(X0) | patient(X0) | happy(X0) | funny(X0))) [flattening 70]
72. ((~kind(paul) | ~old(paul)) & (kind(paul) | old(paul))) | (calm(alice) & ~funny(alice)) [nnf transformation 38]
102. ~calm(X0) | funny(X0) | kind(X0) | ~calm(X0) [cnf transformation 55]
103. calm(X0) | calm(X0) | funny(X0) [cnf transformation 55]
120. ~old(X0) | patient(X0) [cnf transformation 32]
139. ~patient(X0) | ~funny(X0) [cnf transformation 71]
146. ~kind(paul) | ~old(paul) | ~funny(alice) [cnf transformation 72]
160. funny(alice) [cnf transformation 24]
161. old(paul) [cnf transformation 25]
164. ~calm(X0) | funny(X0) | kind(X0) [duplicate literal removal 102]
165. funny(X0) | calm(X0) [duplicate literal removal 103]
210. 11 <=> kind(paul) [avatar definition]
212. ~kind(paul) <- (~11) [avatar component clause 210]
235. funny(X0) | kind(X0) [subsumption resolution 164,165]
249. 19 <=> patient(paul) [avatar definition]
251. patient(paul) <- (19) [avatar component clause 249]
317. 33 <=> old(paul) [avatar definition]
318. old(paul) <- (33) [avatar component clause 317]
322. 34 <=> funny(alice) [avatar definition]
325. ~34 | ~33 | ~11 [avatar split clause 146,210,317,322]
348. 34 [avatar split clause 160,322]
349. 33 [avatar split clause 161,317]
367. patient(paul) <- (33) [resolution 120,318]
370. 19 | ~33 [avatar split clause 367,317,249]
371. ~funny(paul) <- (19) [resolution 139,251]
385. kind(paul) <- (19) [resolution 235,371]
386. $false <- (~11, 19) [subsumption resolution 385,212]
387. 11 | ~19 [avatar contradiction clause 386]
388. $false [avatar sat refutation 325,348,349,370,387]
% SZS output end Proof for 88254121198644095187430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and curious is either not brave or old and vice versa.
If someone is not calm then someone is not tall or wise and vice versa.
If john is rich then john is either brave or not quiet.
Everyone who is either not kind or not wise is either wise or not quiet and vice versa.
Everyone who is both not patient and not wise is not funny or rich.
Everyone who is both not curious and not calm is not creative and vice versa.
Everyone who is either not calm or not happy is not patient.
If paul is not kind or curious then someone is brave or not kind and vice versa.
If alice is not tall then someone is brave.
Everyone who is rich or calm is both not funny and not tall.
Everyone who is not quiet is patient.
If susan is both not wise and brave then fred is strong or wise.
If susan is both not generous and quiet then someone is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Everyone who is either happy or tall is either not quiet or not tall.
Mary is patient.
Someone is both brave and kind.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative.
Fred is kind. | John is creative. | neutral | (![X]:((~tall(X)&curious(X))<=>(~brave(X)<~>old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)|wise(X)))))&
((rich(john))=>((brave(john)<~>~quiet(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~patient(X)&~wise(X))=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>~creative(X)))&
(![X]:((~calm(X)<~>~happy(X))=>~patient(X)))&
(((~kind(paul)|curious(paul)))<=>(?[X]:((brave(X)|~kind(X)))))&
((~tall(alice))=>(?[X]:(brave(X))))&
(![X]:((rich(X)|calm(X))=>(~funny(X)&~tall(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(((~wise(susan)&brave(susan)))=>((strong(fred)|wise(fred))))&
(((~generous(susan)&quiet(susan)))=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
(![X]:((happy(X)<~>tall(X))=>(~quiet(X)<~>~tall(X))))&
(patient(mary))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john)))&
(kind(fred)) | creative(john) | []
| null | 0 |
Everyone who is not kind or not happy is not brave or not funny and vice versa. Everyone who is creative is both tall and not generous. If john is brave then lucy is humble. If someone is funny then john is either not rich or happy. Everyone who is strong or old is old or creative. Everyone who is not quiet or happy is both not happy and generous. Everyone who is old is either generous or quiet and vice versa. Everyone who is calm or not happy is not wise. Everyone who is either not old or humble is both not creative and calm and vice versa. If alice is rich or wise then someone is both rich and creative and vice versa. Everyone who is not calm is either tall or rich and vice versa. If fred is both brave and not calm then mary is tall. If mary is either curious or happy then someone is both not patient and not creative and vice versa. Everyone who is tall or not quiet is both quiet and not funny and vice versa. If lucy is happy then someone is not old and vice versa. Everyone who is both not brave and not rich is both not generous and not tall. Fred is either strong or tall. Someone is not curious or not wise. Someone is old or quiet. Someone is either humble or old. Someone is either old or not curious. Someone is either not strong or tall. | Fred is creative. | neutral | (![X]:((~kind(X)|~happy(X))<=>(~brave(X)|~funny(X))))&
(![X]:(creative(X)=>(tall(X)&~generous(X))))&
((brave(john))=>(humble(lucy)))&
((?[X]:(funny(X)))=>((~rich(john)<~>happy(john))))&
(![X]:((strong(X)|old(X))=>(old(X)|creative(X))))&
(![X]:((~quiet(X)|happy(X))=>(~happy(X)&generous(X))))&
(![X]:(old(X)<=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)|~happy(X))=>~wise(X)))&
(![X]:((~old(X)<~>humble(X))<=>(~creative(X)&calm(X))))&
(((rich(alice)|wise(alice)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~calm(X)<=>(tall(X)<~>rich(X))))&
(((brave(fred)&~calm(fred)))=>(tall(mary)))&
(((curious(mary)<~>happy(mary)))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((tall(X)|~quiet(X))<=>(quiet(X)&~funny(X))))&
((happy(lucy))<=>(?[X]:(~old(X))))&
(![X]:((~brave(X)&~rich(X))=>(~generous(X)&~tall(X))))&
((strong(fred)<~>tall(fred)))&
(?[X]:((~curious(X)|~wise(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~strong(X)<~>tall(X)))) | creative(fred) | []
| null | 0 |
If someone is either not generous or calm then susan is both not rich and rich and vice versa.
If paul is either humble or not happy then someone is not old and vice versa.
Everyone who is not funny or creative is rich or wise.
If someone is either not happy or not humble then someone is both funny and not wise and vice versa.
Everyone who is both not quiet and creative is funny or curious.
Everyone who is brave or wise is both generous and not brave and vice versa.
If john is not funny or kind then paul is both wise and creative.
Everyone who is creative is not generous and vice versa.
If mary is both strong and not funny then someone is either not wise or not humble.
Everyone who is either not brave or not humble is both not brave and creative.
If john is both not happy and creative then paul is both not funny and not calm.
Everyone who is either not humble or not patient is both wise and not humble.
If paul is generous or strong then paul is not patient or not kind and vice versa.
If someone is both not rich and not funny then john is not kind.
If someone is not wise or not old then someone is both happy and not tall and vice versa.
If susan is patient or not tall then susan is either quiet or kind and vice versa.
Susan is either rich or not tall.
Fred is funny.
Someone is humble or not humble.
Paul is wise.
Fred is tall or not wise.
Susan is not patient.
Fred is not generous.
Someone is strong. | John is not kind. | entailment | ((?[X]:((~generous(X)<~>calm(X))))<=>((~rich(susan)&rich(susan))))&
(((humble(paul)<~>~happy(paul)))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)|creative(X))=>(rich(X)|wise(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|curious(X))))&
(![X]:((brave(X)|wise(X))<=>(generous(X)&~brave(X))))&
(((~funny(john)|kind(john)))=>((wise(paul)&creative(paul))))&
(![X]:(creative(X)<=>~generous(X)))&
(((strong(mary)&~funny(mary)))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~brave(X)<~>~humble(X))=>(~brave(X)&creative(X))))&
(((~happy(john)&creative(john)))=>((~funny(paul)&~calm(paul))))&
(![X]:((~humble(X)<~>~patient(X))=>(wise(X)&~humble(X))))&
(((generous(paul)|strong(paul)))<=>((~patient(paul)|~kind(paul))))&
((?[X]:((~rich(X)&~funny(X))))=>(~kind(john)))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(((patient(susan)|~tall(susan)))<=>((quiet(susan)<~>kind(susan))))&
((rich(susan)<~>~tall(susan)))&
(funny(fred))&
(?[X]:((humble(X)|~humble(X))))&
(wise(paul))&
((tall(fred)|~wise(fred)))&
(~patient(susan))&
(~generous(fred))&
(?[X]:(strong(X))) | ~kind(john) | [
"p5",
"p6",
"p7",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3097610622520567367476837
% SZS output start Proof for 3097610622520567367476837
6. ! [X0] : ((wise(X0) | brave(X0)) <=> (~brave(X0) & generous(X0))) [input p5]
7. (kind(john) | ~funny(john)) => (creative(paul) & wise(paul)) [input p6]
8. ! [X0] : (creative(X0) <=> ~generous(X0)) [input p7]
20. wise(paul) [input p19]
25. kind(john) [input hypothesis]
31. (creative(paul) & wise(paul)) | (~kind(john) & funny(john)) [ennf transformation 7]
53. ! [X0] : (((wise(X0) | brave(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 6]
54. ! [X0] : ((wise(X0) | brave(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 53]
55. ! [X0] : ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))) [nnf transformation 8]
94. ~wise(X0) | generous(X0) [cnf transformation 54]
101. creative(paul) | ~kind(john) [cnf transformation 31]
102. ~creative(X0) | ~generous(X0) [cnf transformation 55]
136. wise(paul) [cnf transformation 20]
141. kind(john) [cnf transformation 25]
211. 15 <=> kind(john) [avatar definition]
215. 16 <=> creative(paul) [avatar definition]
217. creative(paul) <- (16) [avatar component clause 215]
218. ~15 | 16 [avatar split clause 101,215,211]
225. 18 <=> wise(paul) [avatar definition]
227. wise(paul) <- (18) [avatar component clause 225]
272. 28 <=> generous(paul) [avatar definition]
342. 18 [avatar split clause 136,225]
353. 15 [avatar split clause 141,211]
362. generous(paul) <- (18) [resolution 94,227]
364. ~generous(paul) <- (16) [resolution 102,217]
367. ~28 | ~16 [avatar split clause 364,215,272]
368. 28 | ~18 [avatar split clause 362,225,272]
369. $false [avatar sat refutation 218,342,353,367,368]
% SZS output end Proof for 3097610622520567367476837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and not generous is happy or wise.
If someone is either not old or wise then lucy is happy or humble and vice versa.
Everyone who is either not tall or not patient is both kind and happy and vice versa.
If john is not curious then someone is not old or not calm and vice versa.
If fred is not quiet then someone is not strong or funny and vice versa.
Everyone who is both not strong and happy is not creative and vice versa.
Everyone who is either not generous or not old is not generous or funny.
If someone is kind then someone is both not humble and rich and vice versa.
Everyone who is not kind is either not happy or not calm and vice versa.
Everyone who is not funny or funny is not wise or not quiet and vice versa.
If someone is calm then fred is happy.
Everyone who is not creative is quiet or patient.
If someone is either not rich or not curious then someone is rich.
If someone is either not curious or old then john is not kind or not patient and vice versa.
Everyone who is both not happy and not patient is not kind and vice versa.
If fred is tall or wise then someone is both not rich and generous and vice versa.
Fred is either not wise or kind.
Paul is not tall.
Fred is creative or old.
Mary is calm or not funny.
Someone is both not curious and funny.
Someone is not kind or not old.
Paul is old.
Mary is both not humble and not creative. | Fred is wise. | entailment | (![X]:((~tall(X)&~generous(X))=>(happy(X)|wise(X))))&
((?[X]:((~old(X)<~>wise(X))))<=>((happy(lucy)|humble(lucy))))&
(![X]:((~tall(X)<~>~patient(X))<=>(kind(X)&happy(X))))&
((~curious(john))<=>(?[X]:((~old(X)|~calm(X)))))&
((~quiet(fred))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~strong(X)&happy(X))<=>~creative(X)))&
(![X]:((~generous(X)<~>~old(X))=>(~generous(X)|funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(~kind(X)<=>(~happy(X)<~>~calm(X))))&
(![X]:((~funny(X)|funny(X))<=>(~wise(X)|~quiet(X))))&
((?[X]:(calm(X)))=>(happy(fred)))&
(![X]:(~creative(X)=>(quiet(X)|patient(X))))&
((?[X]:((~rich(X)<~>~curious(X))))=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>((~kind(john)|~patient(john))))&
(![X]:((~happy(X)&~patient(X))<=>~kind(X)))&
(((tall(fred)|wise(fred)))<=>(?[X]:((~rich(X)&generous(X)))))&
((~wise(fred)<~>kind(fred)))&
(~tall(paul))&
((creative(fred)|old(fred)))&
((calm(mary)|~funny(mary)))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((~kind(X)|~old(X))))&
(old(paul))&
((~humble(mary)&~creative(mary))) | wise(fred) | [
"p8",
"p10",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 898469453901814221968904
% SZS output start Proof for 898469453901814221968904
9. ! [X0] : (~kind(X0) <=> (~happy(X0) <~> ~calm(X0))) [input p8]
11. ? [X0] : calm(X0) => happy(fred) [input p10]
15. ! [X0] : ((~patient(X0) & ~happy(X0)) <=> ~kind(X0)) [input p14]
17. ~wise(fred) <~> kind(fred) [input p16]
25. ~wise(fred) [input hypothesis]
32. happy(fred) | ! [X0] : ~calm(X0) [ennf transformation 11]
59. ! [X0] : ((~kind(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0)))) & (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | kind(X0))) [nnf transformation 9]
71. ! [X0] : (((~patient(X0) & ~happy(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) | happy(X0)))) [nnf transformation 15]
72. ! [X0] : (((~patient(X0) & ~happy(X0)) | kind(X0)) & (~kind(X0) | patient(X0) | happy(X0))) [flattening 71]
78. (~kind(fred) | wise(fred)) & (kind(fred) | ~wise(fred)) [nnf transformation 17]
111. calm(X0) | happy(X0) | kind(X0) [cnf transformation 59]
118. happy(fred) | ~calm(X0) [cnf transformation 32]
129. ~happy(X0) | kind(X0) [cnf transformation 72]
137. ~kind(fred) | wise(fred) [cnf transformation 78]
147. ~wise(fred) [cnf transformation 25]
242. 22 <=> ! [X0] : ~calm(X0) [avatar definition]
243. ~calm(X0) <- (22) [avatar component clause 242]
245. 23 <=> happy(fred) [avatar definition]
247. happy(fred) <- (23) [avatar component clause 245]
248. 22 | 23 [avatar split clause 118,245,242]
297. 35 <=> wise(fred) [avatar definition]
314. 38 <=> kind(fred) [avatar definition]
316. ~kind(fred) <- (~38) [avatar component clause 314]
317. 35 | ~38 [avatar split clause 137,314,297]
346. ~35 [avatar split clause 147,297]
374. happy(X1) | kind(X1) <- (22) [resolution 111,243]
376. kind(X1) <- (22) [subsumption resolution 374,129]
377. $false <- (22, ~38) [resolution 376,316]
380. ~22 | 38 [avatar contradiction clause 377]
383. kind(fred) <- (23) [resolution 247,129]
384. $false <- (23, ~38) [subsumption resolution 383,316]
385. ~23 | 38 [avatar contradiction clause 384]
386. $false [avatar sat refutation 248,317,346,380,385]
% SZS output end Proof for 898469453901814221968904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and curious is either not funny or old and vice versa.
Everyone who is both happy and not generous is either strong or tall.
Everyone who is either kind or not humble is both not creative and creative and vice versa.
Everyone who is both humble and creative is both tall and kind and vice versa.
If john is either not brave or not kind then alice is quiet.
Everyone who is either kind or patient is creative or kind.
If someone is generous or not generous then lucy is not strong.
If paul is both curious and not brave then someone is either not humble or not strong and vice versa.
Everyone who is humble is not generous or not strong.
Everyone who is either not humble or not generous is not tall or not happy and vice versa.
If someone is either not old or not tall then lucy is either not calm or creative and vice versa.
Everyone who is not creative is not old or generous.
Everyone who is happy or rich is patient.
If someone is both brave and creative then lucy is either not tall or creative and vice versa.
Everyone who is brave or not quiet is both strong and tall.
If someone is either tall or brave then someone is tall and vice versa.
Someone is old.
Paul is either not quiet or old.
John is both not generous and not curious.
Someone is tall or brave.
Someone is not humble or quiet.
Someone is either not kind or strong.
Fred is not generous.
Someone is generous or not curious. | John is not funny. | contradiction | (![X]:((brave(X)&curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((happy(X)&~generous(X))=>(strong(X)<~>tall(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~creative(X)&creative(X))))&
(![X]:((humble(X)&creative(X))<=>(tall(X)&kind(X))))&
(((~brave(john)<~>~kind(john)))=>(quiet(alice)))&
(![X]:((kind(X)<~>patient(X))=>(creative(X)|kind(X))))&
((?[X]:((generous(X)|~generous(X))))=>(~strong(lucy)))&
(((curious(paul)&~brave(paul)))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~generous(X)|~strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((~old(X)<~>~tall(X))))<=>((~calm(lucy)<~>creative(lucy))))&
(![X]:(~creative(X)=>(~old(X)|generous(X))))&
(![X]:((happy(X)|rich(X))=>patient(X)))&
((?[X]:((brave(X)&creative(X))))<=>((~tall(lucy)<~>creative(lucy))))&
(![X]:((brave(X)|~quiet(X))=>(strong(X)&tall(X))))&
((?[X]:((tall(X)<~>brave(X))))<=>(?[X]:(tall(X))))&
(?[X]:(old(X)))&
((~quiet(paul)<~>old(paul)))&
((~generous(john)&~curious(john)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
(~generous(fred))&
(?[X]:((generous(X)|~curious(X)))) | ~funny(john) | [
"p0",
"p2",
"p3",
"p9",
"p11",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7169024647553865819811909
% SZS output start Proof for 7169024647553865819811909
1. ! [X0] : ((curious(X0) & brave(X0)) <=> (~funny(X0) <~> old(X0))) [input p0]
3. ! [X0] : ((kind(X0) <~> ~humble(X0)) <=> (creative(X0) & ~creative(X0))) [input p2]
4. ! [X0] : ((creative(X0) & humble(X0)) <=> (kind(X0) & tall(X0))) [input p3]
10. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (~happy(X0) | ~tall(X0))) [input p9]
12. ! [X0] : (~creative(X0) => (generous(X0) | ~old(X0))) [input p11]
19. ~curious(john) & ~generous(john) [input p18]
25. ~funny(john) [input hypothesis]
36. ! [X0] : ((generous(X0) | ~old(X0)) | creative(X0)) [ennf transformation 12]
37. ! [X0] : (generous(X0) | ~old(X0) | creative(X0)) [flattening 36]
40. ! [X0] : (((curious(X0) & brave(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~curious(X0) | ~brave(X0)))) [nnf transformation 1]
41. ! [X0] : (((curious(X0) & brave(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~curious(X0) | ~brave(X0))) [flattening 40]
43. ! [X0] : ((((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) | creative(X0))) & ((creative(X0) & ~creative(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))))) [nnf transformation 3]
44. ! [X0] : ((((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | ~creative(X0) | creative(X0)) & ((creative(X0) & ~creative(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))))) [flattening 43]
45. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 4]
46. ! [X0] : (((creative(X0) & humble(X0)) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | ~creative(X0) | ~humble(X0))) [flattening 45]
54. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 10]
55. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [flattening 54]
85. old(X0) | curious(X0) | funny(X0) [cnf transformation 41]
89. ~creative(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 44]
90. ~creative(X0) | kind(X0) | humble(X0) [cnf transformation 44]
91. ~humble(X0) | creative(X0) | ~kind(X0) [cnf transformation 44]
92. creative(X0) | kind(X0) | humble(X0) [cnf transformation 44]
96. kind(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 46]
97. humble(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 46]
116. humble(X0) | generous(X0) | tall(X0) [cnf transformation 55]
126. ~old(X0) | generous(X0) | creative(X0) [cnf transformation 37]
145. ~generous(john) [cnf transformation 19]
146. ~curious(john) [cnf transformation 19]
153. ~funny(john) [cnf transformation 25]
155. humble(X0) | kind(X0) [subsumption resolution 90,92]
156. ~humble(X0) | ~kind(X0) [subsumption resolution 89,91]
157. ~kind(X0) | ~tall(X0) [subsumption resolution 97,156]
158. ~creative(X0) | ~humble(X0) [subsumption resolution 96,156]
408. generous(X4) | tall(X4) | ~kind(X4) [resolution 116,156]
413. ~kind(X4) | generous(X4) [subsumption resolution 408,157]
425. creative(X0) | generous(X0) | curious(X0) | funny(X0) [resolution 126,85]
617. ~humble(X1) | curious(X1) | funny(X1) | generous(X1) [resolution 425,158]
649. curious(X2) | funny(X2) | generous(X2) | kind(X2) [resolution 617,155]
662. generous(X2) | funny(X2) | curious(X2) [subsumption resolution 649,413]
688. funny(john) | curious(john) [resolution 662,145]
693. curious(john) [subsumption resolution 688,153]
694. $false [subsumption resolution 693,146]
% SZS output end Proof for 7169024647553865819811909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both kind and old then alice is not rich or not kind. Everyone who is brave is either old or not rich. If alice is both not calm and quiet then someone is both brave and not brave and vice versa. If someone is either not kind or not happy then alice is old. Everyone who is both happy and not old is not kind. Everyone who is both not funny and rich is generous or not kind. Everyone who is either not strong or not patient is humble or rich. If lucy is not brave or not strong then mary is both not old and not calm. Everyone who is not kind or not creative is either curious or wise. Everyone who is not rich is both creative and not creative. Everyone who is either creative or old is not rich or creative and vice versa. Everyone who is not funny or not generous is not tall and vice versa. If fred is tall then someone is happy or not rich. Everyone who is both not patient and rich is not happy and vice versa. Susan is not creative or tall. Lucy is humble. Someone is either not quiet or not creative. Lucy is humble or not old. Someone is funny or happy. Someone is either not tall or not kind. Susan is either wise or not patient. | Fred is tall. | contradiction | (((kind(mary)&old(mary)))=>((~rich(alice)|~kind(alice))))&
(![X]:(brave(X)=>(old(X)<~>~rich(X))))&
(((~calm(alice)&quiet(alice)))<=>(?[X]:((brave(X)&~brave(X)))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(old(alice)))&
(![X]:((happy(X)&~old(X))=>~kind(X)))&
(![X]:((~funny(X)&rich(X))=>(generous(X)|~kind(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)|rich(X))))&
(((~brave(lucy)|~strong(lucy)))=>((~old(mary)&~calm(mary))))&
(![X]:((~kind(X)|~creative(X))=>(curious(X)<~>wise(X))))&
(![X]:(~rich(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)<~>old(X))<=>(~rich(X)|creative(X))))&
(![X]:((~funny(X)|~generous(X))<=>~tall(X)))&
((tall(fred))=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~patient(X)&rich(X))<=>~happy(X)))&
((~creative(susan)|tall(susan)))&
(humble(lucy))&
(?[X]:((~quiet(X)<~>~creative(X))))&
((humble(lucy)|~old(lucy)))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:((~tall(X)<~>~kind(X))))&
((wise(susan)<~>~patient(susan))) | tall(fred) | [
"p3",
"p4",
"p9",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 7439580520845554952178406
% SZS output start Proof for 7439580520845554952178406
4. ? [X0] : (~kind(X0) <~> ~happy(X0)) => old(alice) [input p3]
5. ! [X0] : ((~old(X0) & happy(X0)) => ~kind(X0)) [input p4]
10. ! [X0] : (~rich(X0) => (~creative(X0) & creative(X0))) [input p9]
11. ! [X0] : ((creative(X0) <~> old(X0)) <=> (creative(X0) | ~rich(X0))) [input p10]
13. tall(fred) => ? [X0] : (~rich(X0) | happy(X0)) [input p12]
22. tall(fred) [input hypothesis]
30. old(alice) | ! [X0] : (~kind(X0) <=> ~happy(X0)) [ennf transformation 4]
31. ! [X0] : (~kind(X0) | (old(X0) | ~happy(X0))) [ennf transformation 5]
32. ! [X0] : (~kind(X0) | old(X0) | ~happy(X0)) [flattening 31]
37. ! [X0] : ((~creative(X0) & creative(X0)) | rich(X0)) [ennf transformation 10]
38. ? [X0] : (~rich(X0) | happy(X0)) | ~tall(fred) [ennf transformation 13]
45. old(alice) | ! [X0] : ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0))) [nnf transformation 30]
47. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [nnf transformation 11]
48. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [flattening 47]
51. ? [X0] : (~rich(X0) | happy(X0)) => (~rich(sK1) | happy(sK1)) [choice axiom]
52. (~rich(sK1) | happy(sK1)) | ~tall(fred) [skolemisation 38,51]
71. old(alice) | ~happy(X0) | kind(X0) [cnf transformation 45]
73. ~happy(X0) | old(X0) | ~kind(X0) [cnf transformation 32]
81. creative(X0) | rich(X0) [cnf transformation 37]
82. ~creative(X0) | rich(X0) [cnf transformation 37]
84. creative(X0) | ~rich(X0) | creative(X0) | ~old(X0) [cnf transformation 48]
88. ~old(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
92. ~rich(sK1) | happy(sK1) | ~tall(fred) [cnf transformation 52]
104. tall(fred) [cnf transformation 22]
105. creative(X0) | ~rich(X0) | ~old(X0) [duplicate literal removal 84]
106. ~creative(X0) | ~old(X0) [duplicate literal removal 88]
142. 9 <=> old(alice) [avatar definition]
144. old(alice) <- (9) [avatar component clause 142]
147. 10 <=> ! [X0] : (~happy(X0) | kind(X0)) [avatar definition]
148. ~happy(X0) | kind(X0) <- (10) [avatar component clause 147]
149. 10 | 9 [avatar split clause 71,142,147]
160. rich(X0) [subsumption resolution 81,82]
161. creative(X0) | ~old(X0) [subsumption resolution 105,160]
162. ~old(X0) [subsumption resolution 161,106]
163. happy(sK1) | ~tall(fred) [subsumption resolution 92,160]
165. 13 <=> tall(fred) [avatar definition]
169. 14 <=> happy(sK1) [avatar definition]
171. happy(sK1) <- (14) [avatar component clause 169]
172. ~13 | 14 [avatar split clause 163,169,165]
222. 13 [avatar split clause 104,165]
223. $false <- (9) [subsumption resolution 144,162]
224. ~9 [avatar contradiction clause 223]
229. kind(sK1) <- (10, 14) [resolution 148,171]
233. old(sK1) | ~kind(sK1) <- (14) [resolution 73,171]
234. ~kind(sK1) <- (14) [subsumption resolution 233,162]
235. $false <- (10, 14) [subsumption resolution 234,229]
236. ~10 | ~14 [avatar contradiction clause 235]
237. $false [avatar sat refutation 149,172,222,224,236]
% SZS output end Proof for 7439580520845554952178406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or funny is not funny and vice versa.
Everyone who is calm or not old is patient or not rich.
Everyone who is either not rich or funny is quiet or old and vice versa.
If mary is not rich then someone is not wise or not kind and vice versa.
If someone is not strong or humble then john is wise.
If alice is rich or generous then someone 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.
If someone is both quiet and not tall then someone is not generous and vice versa.
Alice is either quiet or not old.
Someone is patient.
Someone is old.
Someone is both generous and not patient.
Someone is either quiet or not humble.
Mary is not strong.
John is either old or not tall.
Alice is either creative or kind. | Lucy is brave. | neutral | (![X]:((~creative(X)|funny(X))<=>~funny(X)))&
(![X]:((calm(X)|~old(X))=>(patient(X)|~rich(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(quiet(X)|old(X))))&
((~rich(mary))<=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((~strong(X)|humble(X))))=>(wise(john)))&
(((rich(alice)|generous(alice)))<=>(?[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]:((quiet(X)&~tall(X))))<=>(?[X]:(~generous(X))))&
((quiet(alice)<~>~old(alice)))&
(?[X]:(patient(X)))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(~strong(mary))&
((old(john)<~>~tall(john)))&
((creative(alice)<~>kind(alice))) | brave(lucy) | []
| null | 0 |
If someone is not happy or not wise then alice is not quiet or not brave and vice versa. Everyone who is curious or strong is either not generous or old and vice versa. Everyone who is both funny and not happy is not humble or not curious and vice versa. Everyone who is both not brave and calm is not tall or curious. If alice is both old and not humble then mary is either rich or not tall. If someone is wise or quiet then mary is either not funny or tall and vice versa. If john is either not strong or not brave then someone is generous or brave and vice versa. Everyone who is not strong or not happy is old or patient and vice versa. If mary is not patient then alice is old and vice versa. If someone is kind or not calm then fred is either not generous or not patient and vice versa. If someone is both not brave and not old then john is not tall or brave. If someone is both old and strong then paul is either not funny or not old and vice versa. Everyone who is rich or not old is not wise. If fred is both happy and patient then fred is not quiet or patient. Everyone who is not creative or creative is both not brave and old and vice versa. Everyone who is both not humble and not creative is brave and vice versa. Fred is both not funny and quiet. Susan is either old or not funny. Paul is quiet. Someone is not brave. Someone is strong or quiet. Someone is old. Someone is not creative or rich. | Paul is not old. | contradiction | ((?[X]:((~happy(X)|~wise(X))))<=>((~quiet(alice)|~brave(alice))))&
(![X]:((curious(X)|strong(X))<=>(~generous(X)<~>old(X))))&
(![X]:((funny(X)&~happy(X))<=>(~humble(X)|~curious(X))))&
(![X]:((~brave(X)&calm(X))=>(~tall(X)|curious(X))))&
(((old(alice)&~humble(alice)))=>((rich(mary)<~>~tall(mary))))&
((?[X]:((wise(X)|quiet(X))))<=>((~funny(mary)<~>tall(mary))))&
(((~strong(john)<~>~brave(john)))<=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~strong(X)|~happy(X))<=>(old(X)|patient(X))))&
((~patient(mary))<=>(old(alice)))&
((?[X]:((kind(X)|~calm(X))))<=>((~generous(fred)<~>~patient(fred))))&
((?[X]:((~brave(X)&~old(X))))=>((~tall(john)|brave(john))))&
((?[X]:((old(X)&strong(X))))<=>((~funny(paul)<~>~old(paul))))&
(![X]:((rich(X)|~old(X))=>~wise(X)))&
(((happy(fred)&patient(fred)))=>((~quiet(fred)|patient(fred))))&
(![X]:((~creative(X)|creative(X))<=>(~brave(X)&old(X))))&
(![X]:((~humble(X)&~creative(X))<=>brave(X)))&
((~funny(fred)&quiet(fred)))&
((old(susan)<~>~funny(susan)))&
(quiet(paul))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|rich(X)))) | ~old(paul) | [
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 15879645725463550604918
% SZS output start Proof for 15879645725463550604918
15. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (old(X0) & ~brave(X0))) [input p14]
24. ~old(paul) [input hypothesis]
63. ! [X0] : (((creative(X0) | ~creative(X0)) | (~old(X0) | brave(X0))) & ((old(X0) & ~brave(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 15]
64. ! [X0] : ((creative(X0) | ~creative(X0) | ~old(X0) | brave(X0)) & ((old(X0) & ~brave(X0)) | (~creative(X0) & creative(X0)))) [flattening 63]
130. old(X0) | creative(X0) [cnf transformation 64]
131. old(X0) | ~creative(X0) [cnf transformation 64]
145. ~old(paul) [cnf transformation 24]
309. old(X0) [subsumption resolution 130,131]
331. $false [subsumption resolution 145,309]
% SZS output end Proof for 15879645725463550604918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and old then someone is either not humble or quiet and vice versa. Everyone who is not quiet is both not tall and rich and vice versa. Everyone who is not rich or not kind is either not calm or quiet and vice versa. Everyone who is generous is not happy or humble. Everyone who is kind or not strong is both not patient and humble and vice versa. Everyone who is wise is curious or generous. Everyone who is both rich and kind is both not curious and curious. Everyone who is both humble and not strong is not patient and vice versa. If fred is either old or kind then someone is both not calm and curious and vice versa. If john is humble or not creative then mary is not strong and vice versa. Everyone who is not calm is not happy or not tall and vice versa. Everyone who is brave is both not strong and brave. Everyone who is both not tall and generous is both not old and funny. If someone is both not curious and not happy then paul is both creative and not curious and vice versa. If someone is funny then someone is either not curious or quiet. If susan is both calm and kind then fred is not curious or old and vice versa. John is both brave and not funny. Someone is wise. Someone is either not wise or wise. Someone is humble or kind. Susan is not quiet. Someone is not generous or not curious. Lucy is either kind or not old. | John is calm. | contradiction | (((generous(susan)&old(susan)))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)&rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:(generous(X)=>(~happy(X)|humble(X))))&
(![X]:((kind(X)|~strong(X))<=>(~patient(X)&humble(X))))&
(![X]:(wise(X)=>(curious(X)|generous(X))))&
(![X]:((rich(X)&kind(X))=>(~curious(X)&curious(X))))&
(![X]:((humble(X)&~strong(X))<=>~patient(X)))&
(((old(fred)<~>kind(fred)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((humble(john)|~creative(john)))<=>(~strong(mary)))&
(![X]:(~calm(X)<=>(~happy(X)|~tall(X))))&
(![X]:(brave(X)=>(~strong(X)&brave(X))))&
(![X]:((~tall(X)&generous(X))=>(~old(X)&funny(X))))&
((?[X]:((~curious(X)&~happy(X))))<=>((creative(paul)&~curious(paul))))&
((?[X]:(funny(X)))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((calm(susan)&kind(susan)))<=>((~curious(fred)|old(fred))))&
((brave(john)&~funny(john)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((humble(X)|kind(X))))&
(~quiet(susan))&
(?[X]:((~generous(X)|~curious(X))))&
((kind(lucy)<~>~old(lucy))) | calm(john) | [
"p0",
"p1",
"p4",
"p10",
"p11",
"p12",
"p16",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 809289610691576428949591
% SZS output start Proof for 809289610691576428949591
1. (old(susan) & generous(susan)) <=> ? [X0] : (~humble(X0) <~> quiet(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> (rich(X0) & ~tall(X0))) [input p1]
5. ! [X0] : ((~strong(X0) | kind(X0)) <=> (humble(X0) & ~patient(X0))) [input p4]
11. ! [X0] : (~calm(X0) <=> (~tall(X0) | ~happy(X0))) [input p10]
12. ! [X0] : (brave(X0) => (brave(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~tall(X0)) => (funny(X0) & ~old(X0))) [input p12]
17. ~funny(john) & brave(john) [input p16]
21. ~quiet(susan) [input p20]
24. calm(john) [input hypothesis]
32. ! [X0] : ((brave(X0) & ~strong(X0)) | ~brave(X0)) [ennf transformation 12]
33. ! [X0] : ((funny(X0) & ~old(X0)) | (~generous(X0) | tall(X0))) [ennf transformation 13]
34. ! [X0] : ((funny(X0) & ~old(X0)) | ~generous(X0) | tall(X0)) [flattening 33]
36. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X0] : ((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (~old(susan) | ~generous(susan))) [nnf transformation 1]
37. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X0] : ((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | ~old(susan) | ~generous(susan)) [flattening 36]
38. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (? [X1] : ((~quiet(X1) | humble(X1)) & (quiet(X1) | ~humble(X1))) | ~old(susan) | ~generous(susan)) [rectify 37]
39. ? [X1] : ((~quiet(X1) | humble(X1)) & (quiet(X1) | ~humble(X1))) => ((~quiet(sK0) | humble(sK0)) & (quiet(sK0) | ~humble(sK0))) [choice axiom]
40. ((old(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) & (((~quiet(sK0) | humble(sK0)) & (quiet(sK0) | ~humble(sK0))) | ~old(susan) | ~generous(susan)) [skolemisation 38,39]
41. ! [X0] : ((~quiet(X0) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | quiet(X0))) [nnf transformation 2]
42. ! [X0] : ((~quiet(X0) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | quiet(X0))) [flattening 41]
45. ! [X0] : (((~strong(X0) | kind(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (strong(X0) & ~kind(X0)))) [nnf transformation 5]
46. ! [X0] : ((~strong(X0) | kind(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | (strong(X0) & ~kind(X0)))) [flattening 45]
55. ! [X0] : ((~calm(X0) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | calm(X0))) [nnf transformation 11]
56. ! [X0] : ((~calm(X0) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | calm(X0))) [flattening 55]
81. generous(susan) | ~humble(X0) | ~quiet(X0) [cnf transformation 40]
83. old(susan) | ~humble(X0) | ~quiet(X0) [cnf transformation 40]
84. ~tall(X0) | quiet(X0) [cnf transformation 42]
97. strong(X0) | humble(X0) [cnf transformation 46]
116. ~calm(X0) | tall(X0) [cnf transformation 56]
117. ~brave(X0) | ~strong(X0) [cnf transformation 32]
119. ~old(X0) | ~generous(X0) | tall(X0) [cnf transformation 34]
132. brave(john) [cnf transformation 17]
138. ~quiet(susan) [cnf transformation 21]
142. calm(john) [cnf transformation 24]
144. 1 <=> ! [X0] : (~humble(X0) | ~quiet(X0)) [avatar definition]
145. ~quiet(X0) | ~humble(X0) <- (1) [avatar component clause 144]
147. 2 <=> old(susan) [avatar definition]
149. old(susan) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 83,147,144]
156. 4 <=> generous(susan) [avatar definition]
158. generous(susan) <- (4) [avatar component clause 156]
159. 1 | 4 [avatar split clause 81,156,144]
204. 13 <=> humble(john) [avatar definition]
206. humble(john) <- (13) [avatar component clause 204]
292. tall(john) [resolution 116,142]
293. ~strong(john) [resolution 117,132]
294. quiet(john) [resolution 292,84]
297. humble(john) [resolution 293,97]
298. 13 [avatar split clause 297,204]
335. ~generous(susan) | tall(susan) <- (2) [resolution 119,149]
336. tall(susan) <- (2, 4) [subsumption resolution 335,158]
337. quiet(susan) <- (2, 4) [resolution 336,84]
338. $false <- (2, 4) [subsumption resolution 337,138]
339. ~2 | ~4 [avatar contradiction clause 338]
340. ~humble(john) <- (1) [resolution 145,294]
342. $false <- (1, 13) [subsumption resolution 340,206]
343. ~1 | ~13 [avatar contradiction clause 342]
345. $false [avatar sat refutation 150,159,298,339,343]
% SZS output end Proof for 809289610691576428949591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.