premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is not wise then susan is not kind and vice versa.
Everyone who is not humble is either generous or not calm.
If someone is either creative or not funny then someone is either not calm or old.
Everyone who is not rich is either curious or wise and vice versa.
If john is either creative or not tall then paul is kind.
If paul is not tall or wise then susan is not tall and vice versa.
Everyone who is not tall is either not patient or kind.
Everyone who is happy is funny and vice versa.
If someone is both funny and happy then someone is rich.
Everyone who is either not tall or kind is both not calm and humble.
If john is not rich or brave then fred is calm and vice versa.
Everyone who is both not wise and kind is tall and vice versa.
If lucy is both not funny and not calm then susan is rich or not tall.
If someone is not funny or happy then someone is both kind and old.
If susan is both tall and humble then paul is not humble and vice versa.
Everyone who is not patient is patient.
Alice is either not curious or rich.
Someone is both strong and not old.
Someone is both patient and not happy.
Someone is old.
Lucy is either not tall or not rich.
Paul is both creative and old. | Lucy is not rich. | contradiction | ((?[X]:(~wise(X)))<=>(~kind(susan)))&
(![X]:(~humble(X)=>(generous(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>~funny(X))))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~rich(X)<=>(curious(X)<~>wise(X))))&
(((creative(john)<~>~tall(john)))=>(kind(paul)))&
(((~tall(paul)|wise(paul)))<=>(~tall(susan)))&
(![X]:(~tall(X)=>(~patient(X)<~>kind(X))))&
(![X]:(happy(X)<=>funny(X)))&
((?[X]:((funny(X)&happy(X))))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)<~>kind(X))=>(~calm(X)&humble(X))))&
(((~rich(john)|brave(john)))<=>(calm(fred)))&
(![X]:((~wise(X)&kind(X))<=>tall(X)))&
(((~funny(lucy)&~calm(lucy)))=>((rich(susan)|~tall(susan))))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:((kind(X)&old(X)))))&
(((tall(susan)&humble(susan)))<=>(~humble(paul)))&
(![X]:(~patient(X)=>patient(X)))&
((~curious(alice)<~>rich(alice)))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:((patient(X)&~happy(X))))&
(?[X]:(old(X)))&
((~tall(lucy)<~>~rich(lucy)))&
((creative(paul)&old(paul))) | ~rich(lucy) | [
"p0",
"p6",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7252662431838376754609632
% SZS output start Proof for 7252662431838376754609632
1. ? [X0] : ~wise(X0) <=> ~kind(susan) [input p0]
7. ! [X0] : (~tall(X0) => (~patient(X0) <~> kind(X0))) [input p6]
12. ! [X0] : ((kind(X0) & ~wise(X0)) <=> tall(X0)) [input p11]
16. ! [X0] : (~patient(X0) => patient(X0)) [input p15]
21. ~tall(lucy) <~> ~rich(lucy) [input p20]
23. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((~patient(X0) <~> kind(X0)) | tall(X0)) [ennf transformation 7]
39. ! [X0] : (patient(X0) | patient(X0)) [ennf transformation 16]
40. (? [X0] : ~wise(X0) | kind(susan)) & (~kind(susan) | ! [X0] : wise(X0)) [nnf transformation 1]
41. (? [X0] : ~wise(X0) | kind(susan)) & (~kind(susan) | ! [X1] : wise(X1)) [rectify 40]
42. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
43. (~wise(sK0) | kind(susan)) & (~kind(susan) | ! [X1] : wise(X1)) [skolemisation 41,42]
53. ! [X0] : (((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | tall(X0)) [nnf transformation 32]
60. ! [X0] : (((kind(X0) & ~wise(X0)) | ~tall(X0)) & (tall(X0) | (~kind(X0) | wise(X0)))) [nnf transformation 12]
61. ! [X0] : (((kind(X0) & ~wise(X0)) | ~tall(X0)) & (tall(X0) | ~kind(X0) | wise(X0))) [flattening 60]
74. (rich(lucy) | tall(lucy)) & (~rich(lucy) | ~tall(lucy)) [nnf transformation 21]
75. ~kind(susan) | wise(X1) [cnf transformation 43]
92. ~patient(X0) | kind(X0) | tall(X0) [cnf transformation 53]
104. ~tall(X0) | ~wise(X0) [cnf transformation 61]
105. ~tall(X0) | kind(X0) [cnf transformation 61]
114. patient(X0) | patient(X0) [cnf transformation 39]
122. rich(lucy) | tall(lucy) [cnf transformation 74]
125. ~rich(lucy) [cnf transformation 23]
126. patient(X0) [duplicate literal removal 114]
128. 1 <=> kind(susan) [avatar definition]
129. ~kind(susan) <- (~1) [avatar component clause 128]
137. 3 <=> ! [X1] : wise(X1) [avatar definition]
138. wise(X1) <- (3) [avatar component clause 137]
139. 3 | ~1 [avatar split clause 75,128,137]
264. 30 <=> tall(lucy) [avatar definition]
266. tall(lucy) <- (30) [avatar component clause 264]
268. 31 <=> rich(lucy) [avatar definition]
271. 30 | 31 [avatar split clause 122,268,264]
273. ~31 [avatar split clause 125,268]
280. ~wise(lucy) <- (30) [resolution 104,266]
310. kind(X0) | tall(X0) [resolution 92,126]
311. kind(X0) [subsumption resolution 310,105]
315. $false <- (~1) [resolution 311,129]
317. 1 [avatar contradiction clause 315]
319. $false <- (3, 30) [resolution 138,280]
324. ~3 | ~30 [avatar contradiction clause 319]
326. $false [avatar sat refutation 139,271,273,317,324]
% SZS output end Proof for 7252662431838376754609632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either happy or not happy then fred is strong.
Everyone who is not creative or not strong is both curious and not patient.
If lucy is strong or not funny then susan is curious or wise and vice versa.
Everyone who is either curious or kind is both strong and funny and vice versa.
Everyone who is curious is both rich and funny.
Everyone who is not humble or not quiet is not tall.
Everyone who is not quiet or creative is either tall or funny and vice versa.
Everyone who is both humble and not quiet is either generous or wise and vice versa.
Everyone who is both not quiet and wise is either not generous or rich.
If someone is both curious and patient then someone is not creative and vice versa.
If someone is not patient or not creative then alice is either not patient or not funny and vice versa.
If someone is creative then someone is humble or patient and vice versa.
Everyone who is calm or not patient is creative or tall and vice versa.
If lucy is not strong then someone is both not tall and not brave and vice versa.
If someone is both creative and not kind then someone is not quiet or tall.
If someone is not strong or not generous then susan is patient and vice versa.
John is curious.
Susan is tall.
Someone is patient.
Someone is not wise or not creative.
Someone is either generous or strong.
John is not humble.
Someone is either rich or not humble. | Susan is funny. | contradiction | (((happy(susan)<~>~happy(susan)))=>(strong(fred)))&
(![X]:((~creative(X)|~strong(X))=>(curious(X)&~patient(X))))&
(((strong(lucy)|~funny(lucy)))<=>((curious(susan)|wise(susan))))&
(![X]:((curious(X)<~>kind(X))<=>(strong(X)&funny(X))))&
(![X]:(curious(X)=>(rich(X)&funny(X))))&
(![X]:((~humble(X)|~quiet(X))=>~tall(X)))&
(![X]:((~quiet(X)|creative(X))<=>(tall(X)<~>funny(X))))&
(![X]:((humble(X)&~quiet(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~quiet(X)&wise(X))=>(~generous(X)<~>rich(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>((~patient(alice)<~>~funny(alice))))&
((?[X]:(creative(X)))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((calm(X)|~patient(X))<=>(creative(X)|tall(X))))&
((~strong(lucy))<=>(?[X]:((~tall(X)&~brave(X)))))&
((?[X]:((creative(X)&~kind(X))))=>(?[X]:((~quiet(X)|tall(X)))))&
((?[X]:((~strong(X)|~generous(X))))<=>(patient(susan)))&
(curious(john))&
(tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|~creative(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(~humble(john))&
(?[X]:((rich(X)<~>~humble(X)))) | funny(susan) | [
"p1",
"p6",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1049644594838038228774832
% SZS output start Proof for 1049644594838038228774832
2. ! [X0] : ((~strong(X0) | ~creative(X0)) => (~patient(X0) & curious(X0))) [input p1]
7. ! [X0] : ((creative(X0) | ~quiet(X0)) <=> (tall(X0) <~> funny(X0))) [input p6]
16. ? [X0] : (~generous(X0) | ~strong(X0)) <=> patient(susan) [input p15]
18. tall(susan) [input p17]
21. ? [X0] : (generous(X0) <~> strong(X0)) [input p20]
24. funny(susan) [input hypothesis]
29. ! [X0] : ((~patient(X0) & curious(X0)) | (strong(X0) & creative(X0))) [ennf transformation 2]
40. ! [X0] : (((creative(X0) | ~quiet(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~creative(X0) & quiet(X0)))) [nnf transformation 7]
41. ! [X0] : ((creative(X0) | ~quiet(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~creative(X0) & quiet(X0)))) [flattening 40]
68. (? [X0] : (~generous(X0) | ~strong(X0)) | ~patient(susan)) & (patient(susan) | ! [X0] : (generous(X0) & strong(X0))) [nnf transformation 16]
69. (? [X0] : (~generous(X0) | ~strong(X0)) | ~patient(susan)) & (patient(susan) | ! [X1] : (generous(X1) & strong(X1))) [rectify 68]
70. ? [X0] : (~generous(X0) | ~strong(X0)) => (~generous(sK7) | ~strong(sK7)) [choice axiom]
71. ((~generous(sK7) | ~strong(sK7)) | ~patient(susan)) & (patient(susan) | ! [X1] : (generous(X1) & strong(X1))) [skolemisation 69,70]
76. ? [X0] : ((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) [nnf transformation 21]
77. ? [X0] : ((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) => ((~strong(sK10) | ~generous(sK10)) & (strong(sK10) | generous(sK10))) [choice axiom]
78. (~strong(sK10) | ~generous(sK10)) & (strong(sK10) | generous(sK10)) [skolemisation 76,77]
86. ~patient(X0) | creative(X0) [cnf transformation 29]
105. ~tall(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 41]
136. patient(susan) | strong(X1) [cnf transformation 71]
137. patient(susan) | generous(X1) [cnf transformation 71]
140. tall(susan) [cnf transformation 18]
144. ~strong(sK10) | ~generous(sK10) [cnf transformation 78]
148. funny(susan) [cnf transformation 24]
283. 28 <=> patient(susan) [avatar definition]
284. patient(susan) <- (28) [avatar component clause 283]
296. 31 <=> ! [X1] : generous(X1) [avatar definition]
297. generous(X1) <- (31) [avatar component clause 296]
298. 31 | 28 [avatar split clause 137,283,296]
300. 32 <=> ! [X1] : strong(X1) [avatar definition]
301. strong(X1) <- (32) [avatar component clause 300]
302. 32 | 28 [avatar split clause 136,283,300]
313. 35 <=> generous(sK10) [avatar definition]
315. ~generous(sK10) <- (~35) [avatar component clause 313]
317. 36 <=> strong(sK10) [avatar definition]
319. ~strong(sK10) <- (~36) [avatar component clause 317]
320. ~35 | ~36 [avatar split clause 144,317,313]
342. creative(susan) <- (28) [resolution 86,284]
390. ~funny(susan) | ~creative(susan) [resolution 105,140]
392. ~creative(susan) [subsumption resolution 390,148]
393. $false <- (28) [subsumption resolution 392,342]
394. ~28 [avatar contradiction clause 393]
398. $false <- (32, ~36) [resolution 301,319]
399. ~32 | 36 [avatar contradiction clause 398]
401. $false <- (31, ~35) [subsumption resolution 315,297]
402. ~31 | 35 [avatar contradiction clause 401]
403. $false [avatar sat refutation 298,302,320,394,399,402]
% SZS output end Proof for 1049644594838038228774832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or tall is both calm and not quiet and vice versa. If someone is either not rich or not funny then someone is not old. If someone is kind then someone is both not rich and kind and vice versa. If someone is both not funny and generous then john is creative or not strong. Everyone who is calm or not patient is tall or strong and vice versa. If someone is strong or curious then someone is not quiet. If someone is humble then someone is not funny or calm and vice versa. Everyone who is both tall and not strong is either not generous or patient and vice versa. Everyone who is not funny is not wise or funny. If someone is not patient then lucy is either brave or not generous. Everyone who is kind or not curious is calm or not rich and vice versa. If susan is either not funny or brave then john is both quiet and not tall. Everyone who is either curious or humble is quiet. Everyone who is not patient or quiet is not kind. Everyone who is both old and funny is either not curious or not wise and vice versa. Everyone who is either humble or strong is quiet or curious and vice versa. Someone is rich. Susan is either kind or not brave. Someone is either not funny or not creative. Someone is both tall and calm. Alice is either not rich or patient. Lucy is not strong or not curious. Someone is either not calm or curious. | Alice is not tall. | contradiction | (![X]:((~tall(X)<~>tall(X))<=>(calm(X)&~quiet(X))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:(~old(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((~funny(X)&generous(X))))=>((creative(john)|~strong(john))))&
(![X]:((calm(X)|~patient(X))<=>(tall(X)|strong(X))))&
((?[X]:((strong(X)|curious(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~funny(X)|calm(X)))))&
(![X]:((tall(X)&~strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~funny(X)=>(~wise(X)|funny(X))))&
((?[X]:(~patient(X)))=>((brave(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)|~curious(X))<=>(calm(X)|~rich(X))))&
(((~funny(susan)<~>brave(susan)))=>((quiet(john)&~tall(john))))&
(![X]:((curious(X)<~>humble(X))=>quiet(X)))&
(![X]:((~patient(X)|quiet(X))=>~kind(X)))&
(![X]:((old(X)&funny(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:((humble(X)<~>strong(X))<=>(quiet(X)|curious(X))))&
(?[X]:(rich(X)))&
((kind(susan)<~>~brave(susan)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((tall(X)&calm(X))))&
((~rich(alice)<~>patient(alice)))&
((~strong(lucy)|~curious(lucy)))&
(?[X]:((~calm(X)<~>curious(X)))) | ~tall(alice) | [
"p0",
"p4",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2307817528391751519502375
% SZS output start Proof for 2307817528391751519502375
1. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (~quiet(X0) & calm(X0))) [input p0]
5. ! [X0] : ((~patient(X0) | calm(X0)) <=> (strong(X0) | tall(X0))) [input p4]
13. ! [X0] : ((curious(X0) <~> humble(X0)) => quiet(X0)) [input p12]
16. ! [X0] : ((humble(X0) <~> strong(X0)) <=> (curious(X0) | quiet(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
37. ! [X0] : (quiet(X0) | (curious(X0) <=> humble(X0))) [ennf transformation 13]
39. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 1]
40. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [flattening 39]
50. ! [X0] : (((~patient(X0) | calm(X0)) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 5]
51. ! [X0] : ((~patient(X0) | calm(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | (patient(X0) & ~calm(X0)))) [flattening 50]
66. ! [X0] : (quiet(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 37]
69. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [nnf transformation 16]
70. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [flattening 69]
83. calm(X0) | tall(X0) | tall(X0) [cnf transformation 40]
84. calm(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 40]
85. ~quiet(X0) | tall(X0) | tall(X0) [cnf transformation 40]
86. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 40]
95. strong(X0) | tall(X0) | ~calm(X0) [cnf transformation 51]
121. quiet(X0) | humble(X0) | ~curious(X0) [cnf transformation 66]
122. quiet(X0) | curious(X0) | ~humble(X0) [cnf transformation 66]
132. curious(X0) | quiet(X0) | humble(X0) | ~strong(X0) [cnf transformation 70]
136. ~strong(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 70]
149. ~tall(alice) [cnf transformation 24]
151. calm(X0) | tall(X0) [duplicate literal removal 83]
152. ~tall(X0) | calm(X0) [duplicate literal removal 84]
153. ~quiet(X0) | tall(X0) [duplicate literal removal 85]
154. ~quiet(X0) | ~tall(X0) [duplicate literal removal 86]
155. ~quiet(X0) [subsumption resolution 153,154]
156. calm(X0) [subsumption resolution 151,152]
202. strong(X0) | tall(X0) [subsumption resolution 95,156]
238. ~humble(X0) | curious(X0) [subsumption resolution 122,155]
239. ~curious(X0) | humble(X0) [subsumption resolution 121,155]
242. ~curious(X0) | ~strong(X0) [subsumption resolution 136,239]
243. curious(X0) | humble(X0) | ~strong(X0) [subsumption resolution 132,155]
244. ~strong(X0) | humble(X0) [subsumption resolution 243,239]
292. humble(X0) | tall(X0) [resolution 244,202]
386. curious(X0) | tall(X0) [resolution 292,238]
400. tall(X2) | ~strong(X2) [resolution 386,242]
404. tall(X2) [subsumption resolution 400,202]
415. $false [resolution 404,149]
% SZS output end Proof for 2307817528391751519502375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and quiet is calm and vice versa.
Everyone who is kind is kind or not creative and vice versa.
Everyone who is both not funny and not tall is humble or not patient.
If lucy is not tall or not patient then someone is not happy or humble.
Everyone who is both not funny and humble is both not happy and strong.
Everyone who is not calm or not kind is humble or wise.
Everyone who is generous is kind or not strong and vice versa.
If paul is not happy then someone is funny or curious and vice versa.
Everyone who is calm or tall is either not generous or not tall.
Everyone who is not quiet or humble is not rich and vice versa.
Everyone who is not generous is either wise or creative and vice versa.
If someone is either not generous or patient then fred is not creative or generous.
If paul is both not rich and patient then someone is either generous or creative and vice versa.
Everyone who is not creative is either generous or not calm.
If someone is either funny or not happy then someone is humble.
If someone is either not rich or not old then susan is either rich or not rich and vice versa.
Someone is strong or not patient.
Paul is not humble.
Alice is either not tall or humble.
Someone is not curious or not patient.
Lucy is rich.
Paul is both curious and rich.
Lucy is old or not calm.
Someone is strong or generous. | Lucy is not tall. | entailment | (![X]:((happy(X)&quiet(X))<=>calm(X)))&
(![X]:(kind(X)<=>(kind(X)|~creative(X))))&
(![X]:((~funny(X)&~tall(X))=>(humble(X)|~patient(X))))&
(((~tall(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((~funny(X)&humble(X))=>(~happy(X)&strong(X))))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)|wise(X))))&
(![X]:(generous(X)<=>(kind(X)|~strong(X))))&
((~happy(paul))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((calm(X)|tall(X))=>(~generous(X)<~>~tall(X))))&
(![X]:((~quiet(X)|humble(X))<=>~rich(X)))&
(![X]:(~generous(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>((~creative(fred)|generous(fred))))&
(((~rich(paul)&patient(paul)))<=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~creative(X)=>(generous(X)<~>~calm(X))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((rich(susan)<~>~rich(susan))))&
(?[X]:((strong(X)|~patient(X))))&
(~humble(paul))&
((~tall(alice)<~>humble(alice)))&
(?[X]:((~curious(X)|~patient(X))))&
(rich(lucy))&
((curious(paul)&rich(paul)))&
((old(lucy)|~calm(lucy)))&
(?[X]:((strong(X)|generous(X)))) | ~tall(lucy) | [
"p1",
"p6",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 85459719655171729317206
% SZS output start Proof for 85459719655171729317206
2. ! [X0] : (kind(X0) <=> (~creative(X0) | kind(X0))) [input p1]
7. ! [X0] : (generous(X0) <=> (~strong(X0) | kind(X0))) [input p6]
9. ! [X0] : ((tall(X0) | calm(X0)) => (~generous(X0) <~> ~tall(X0))) [input p8]
13. (patient(paul) & ~rich(paul)) <=> ? [X0] : (generous(X0) <~> creative(X0)) [input p12]
22. rich(paul) & curious(paul) [input p21]
25. tall(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) <~> ~tall(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 9]
41. ! [X0] : ((kind(X0) | (creative(X0) & ~kind(X0))) & ((~creative(X0) | kind(X0)) | ~kind(X0))) [nnf transformation 2]
42. ! [X0] : ((kind(X0) | (creative(X0) & ~kind(X0))) & (~creative(X0) | kind(X0) | ~kind(X0))) [flattening 41]
45. ! [X0] : ((generous(X0) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | ~generous(X0))) [nnf transformation 7]
46. ! [X0] : ((generous(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | ~generous(X0))) [flattening 45]
51. ! [X0] : (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~tall(X0) & ~calm(X0))) [nnf transformation 34]
56. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X0] : ((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | (~patient(paul) | rich(paul))) [nnf transformation 13]
57. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X0] : ((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | ~patient(paul) | rich(paul)) [flattening 56]
58. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) | ~patient(paul) | rich(paul)) [rectify 57]
59. ? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) => ((~creative(sK2) | ~generous(sK2)) & (creative(sK2) | generous(sK2))) [choice axiom]
60. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(sK2) | ~generous(sK2)) & (creative(sK2) | generous(sK2))) | ~patient(paul) | rich(paul)) [skolemisation 58,59]
82. creative(X0) | kind(X0) [cnf transformation 42]
91. ~kind(X0) | generous(X0) [cnf transformation 46]
97. ~tall(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 51]
112. ~rich(paul) | generous(X0) | ~creative(X0) [cnf transformation 60]
134. rich(paul) [cnf transformation 22]
137. tall(lucy) [cnf transformation 25]
142. ~generous(X0) | ~tall(X0) [duplicate literal removal 97]
157. 4 <=> tall(lucy) [avatar definition]
159. tall(lucy) <- (4) [avatar component clause 157]
199. 14 <=> ! [X0] : (generous(X0) | ~creative(X0)) [avatar definition]
200. ~creative(X0) | generous(X0) <- (14) [avatar component clause 199]
211. 17 <=> rich(paul) [avatar definition]
214. 14 | ~17 [avatar split clause 112,211,199]
282. 17 [avatar split clause 134,211]
292. 4 [avatar split clause 137,157]
306. generous(X0) | kind(X0) <- (14) [resolution 200,82]
308. generous(X0) <- (14) [subsumption resolution 306,91]
313. ~tall(X2) <- (14) [resolution 308,142]
344. $false <- (4, 14) [resolution 313,159]
345. ~4 | ~14 [avatar contradiction clause 344]
346. $false [avatar sat refutation 214,282,292,345]
% SZS output end Proof for 85459719655171729317206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not generous is both not wise and brave and vice versa.
Everyone who is both tall and quiet is both patient and calm and vice versa.
If lucy is not creative or not old then someone is both curious and not calm and vice versa.
Everyone who is both tall and not patient is tall and vice versa.
Everyone who is not patient or generous is both old and not generous.
If someone is both happy and quiet then someone is not calm.
Everyone who is both old and wise is either rich or patient and vice versa.
If someone is either quiet or patient then someone is not quiet or not strong and vice versa.
If someone is either wise or funny then paul is either not funny or not happy and vice versa.
Everyone who is either creative or generous is either not kind or not quiet and vice versa.
If mary is funny then someone is either creative or not curious and vice versa.
Everyone who is patient is generous or not happy and vice versa.
Everyone who is either happy or rich is not wise and vice versa.
Everyone who is both not wise and not old is both quiet and happy and vice versa.
Everyone who is generous or quiet is tall and vice versa.
Everyone who is either not creative or funny is quiet or not happy.
Fred is not curious.
Someone is not happy or not generous.
Someone is not kind or not brave.
Someone is happy or humble.
Someone is tall or curious.
Someone is either not funny or rich. | Paul is not kind. | neutral | (![X]:((wise(X)&~generous(X))<=>(~wise(X)&brave(X))))&
(![X]:((tall(X)&quiet(X))<=>(patient(X)&calm(X))))&
(((~creative(lucy)|~old(lucy)))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((tall(X)&~patient(X))<=>tall(X)))&
(![X]:((~patient(X)|generous(X))=>(old(X)&~generous(X))))&
((?[X]:((happy(X)&quiet(X))))=>(?[X]:(~calm(X))))&
(![X]:((old(X)&wise(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)|~strong(X)))))&
((?[X]:((wise(X)<~>funny(X))))<=>((~funny(paul)<~>~happy(paul))))&
(![X]:((creative(X)<~>generous(X))<=>(~kind(X)<~>~quiet(X))))&
((funny(mary))<=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(patient(X)<=>(generous(X)|~happy(X))))&
(![X]:((happy(X)<~>rich(X))<=>~wise(X)))&
(![X]:((~wise(X)&~old(X))<=>(quiet(X)&happy(X))))&
(![X]:((generous(X)|quiet(X))<=>tall(X)))&
(![X]:((~creative(X)<~>funny(X))=>(quiet(X)|~happy(X))))&
(~curious(fred))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:((happy(X)|humble(X))))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((~funny(X)<~>rich(X)))) | ~kind(paul) | [] | null | 0 |
If someone is wise or old then mary is not humble.
If paul is not kind or curious then susan is not rich or not old.
Everyone who is not kind is either not kind or calm.
Everyone who is patient is either not rich or old and vice versa.
If someone is rich then paul is kind and vice versa.
If someone is calm or old then lucy is wise or quiet and vice versa.
Everyone who is either humble or not strong is both quiet and funny and vice versa.
Everyone who is not calm is both not calm and quiet and vice versa.
Everyone who is either wise or humble is either not quiet or not funny and vice versa.
Everyone who is either brave or not old is both wise and old.
Everyone who is both brave and generous is both quiet and brave and vice versa.
Everyone who is kind or not curious is calm.
If susan is kind then someone is funny or not generous and vice versa.
If lucy is both not generous and humble then someone is both wise and not kind.
If susan is either rich or not old then alice is both not creative and strong and vice versa.
If someone is either wise or humble then mary is either not curious or creative.
Alice is patient or not funny.
Someone is humble or funny.
Someone is kind.
Someone is rich or not calm.
Someone is both humble and wise.
Someone is both not wise and funny. | Alice is strong. | neutral | ((?[X]:((wise(X)|old(X))))=>(~humble(mary)))&
(((~kind(paul)|curious(paul)))=>((~rich(susan)|~old(susan))))&
(![X]:(~kind(X)=>(~kind(X)<~>calm(X))))&
(![X]:(patient(X)<=>(~rich(X)<~>old(X))))&
((?[X]:(rich(X)))<=>(kind(paul)))&
((?[X]:((calm(X)|old(X))))<=>((wise(lucy)|quiet(lucy))))&
(![X]:((humble(X)<~>~strong(X))<=>(quiet(X)&funny(X))))&
(![X]:(~calm(X)<=>(~calm(X)&quiet(X))))&
(![X]:((wise(X)<~>humble(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((brave(X)<~>~old(X))=>(wise(X)&old(X))))&
(![X]:((brave(X)&generous(X))<=>(quiet(X)&brave(X))))&
(![X]:((kind(X)|~curious(X))=>calm(X)))&
((kind(susan))<=>(?[X]:((funny(X)|~generous(X)))))&
(((~generous(lucy)&humble(lucy)))=>(?[X]:((wise(X)&~kind(X)))))&
(((rich(susan)<~>~old(susan)))<=>((~creative(alice)&strong(alice))))&
((?[X]:((wise(X)<~>humble(X))))=>((~curious(mary)<~>creative(mary))))&
((patient(alice)|~funny(alice)))&
(?[X]:((humble(X)|funny(X))))&
(?[X]:(kind(X)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((~wise(X)&funny(X)))) | strong(alice) | [] | null | 0 |
Everyone who is both tall and generous is creative or quiet and vice versa.
If someone is either not brave or not curious then mary is both not funny and happy and vice versa.
If lucy is either brave or humble then someone is both strong and not curious and vice versa.
If susan is both not tall and not curious then lucy is kind and vice versa.
If lucy is either calm or not patient then someone is both not generous and wise and vice versa.
Everyone who is kind or generous is both not calm and funny.
If someone is wise then someone is not strong and vice versa.
Everyone who is either kind or old is not humble or strong.
Everyone who is humble is both not kind and brave and vice versa.
If someone is both not wise and generous then john is either not old or not happy.
If lucy is rich then someone is both not curious and happy and vice versa.
Everyone who is calm is either wise or not funny.
Everyone who is both not patient and not wise is not tall or patient and vice versa.
Everyone who is both not rich and not tall is either not generous or not quiet.
Everyone who is quiet is not strong.
Everyone who is kind is not patient and vice versa.
Mary is happy.
Someone is both not brave and quiet.
Paul is not old or not kind.
Someone is either patient or not calm.
Someone is old or humble.
Someone is not calm or not brave.
Alice is not calm. | Alice is happy. | neutral | (![X]:((tall(X)&generous(X))<=>(creative(X)|quiet(X))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((~funny(mary)&happy(mary))))&
(((brave(lucy)<~>humble(lucy)))<=>(?[X]:((strong(X)&~curious(X)))))&
(((~tall(susan)&~curious(susan)))<=>(kind(lucy)))&
(((calm(lucy)<~>~patient(lucy)))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((kind(X)|generous(X))=>(~calm(X)&funny(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~strong(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|strong(X))))&
(![X]:(humble(X)<=>(~kind(X)&brave(X))))&
((?[X]:((~wise(X)&generous(X))))=>((~old(john)<~>~happy(john))))&
((rich(lucy))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(calm(X)=>(wise(X)<~>~funny(X))))&
(![X]:((~patient(X)&~wise(X))<=>(~tall(X)|patient(X))))&
(![X]:((~rich(X)&~tall(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:(kind(X)<=>~patient(X)))&
(happy(mary))&
(?[X]:((~brave(X)&quiet(X))))&
((~old(paul)|~kind(paul)))&
(?[X]:((patient(X)<~>~calm(X))))&
(?[X]:((old(X)|humble(X))))&
(?[X]:((~calm(X)|~brave(X))))&
(~calm(alice)) | happy(alice) | [] | null | 0 |
Everyone who is not generous or not curious is not strong or not kind and vice versa.
Everyone who is not generous is not creative or not rich and vice versa.
If paul is kind then fred is not curious or not humble and vice versa.
If someone is both not calm and not funny then paul is not curious or not funny and vice versa.
Everyone who is both not generous and quiet is not wise or not happy and vice versa.
If someone is brave or not kind then someone is both not humble and patient and vice versa.
If lucy is not generous or not rich then paul is both not creative and humble.
Everyone who is not wise is either quiet or not happy and vice versa.
If paul is either creative or tall then alice is either not patient or not kind and vice versa.
If someone is both brave and not generous then mary is either strong or not funny.
If someone is both wise and strong then someone is either not creative or not humble.
Everyone who is not old or not wise is generous and vice versa.
If someone is both not wise and wise then someone is either not wise or happy and vice versa.
If someone is either not quiet or brave then someone is both not kind and happy and vice versa.
If someone is both curious and not generous then alice is brave and vice versa.
If fred is not happy then someone is not tall and vice versa.
John is not wise or not curious.
Someone is both old and not funny.
Mary is tall.
John is rich or not old.
Someone is not funny. | Lucy is not wise. | contradiction | (![X]:((~generous(X)|~curious(X))<=>(~strong(X)|~kind(X))))&
(![X]:(~generous(X)<=>(~creative(X)|~rich(X))))&
((kind(paul))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~happy(X))))&
(((creative(paul)<~>tall(paul)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:((brave(X)&~generous(X))))=>((strong(mary)<~>~funny(mary))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~old(X)|~wise(X))<=>generous(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:((curious(X)&~generous(X))))<=>(brave(alice)))&
((~happy(fred))<=>(?[X]:(~tall(X))))&
((~wise(john)|~curious(john)))&
(?[X]:((old(X)&~funny(X))))&
(tall(mary))&
((rich(john)|~old(john)))&
(?[X]:(~funny(X))) | ~wise(lucy) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 824075999072511323547343
% SZS output start Proof for 824075999072511323547343
5. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~happy(X0) | ~wise(X0))) [input p4]
12. ! [X0] : ((~wise(X0) | ~old(X0)) <=> generous(X0)) [input p11]
22. ~wise(lucy) [input hypothesis]
41. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 5]
42. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~quiet(X0) | generous(X0))) [flattening 41]
55. ! [X0] : (((~wise(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [nnf transformation 12]
56. ! [X0] : ((~wise(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [flattening 55]
95. ~generous(X0) | wise(X0) [cnf transformation 42]
125. generous(X0) | wise(X0) [cnf transformation 56]
150. ~wise(lucy) [cnf transformation 22]
288. wise(X0) [subsumption resolution 125,95]
322. $false [subsumption resolution 150,288]
% SZS output end Proof for 824075999072511323547343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not wise and generous then mary is both rich and curious and vice versa. If susan is kind then alice is both not generous and not tall. If paul is funny or generous then someone is old or not calm. Everyone who is not funny is generous. Everyone who is not creative or not quiet is both humble and not humble and vice versa. If someone is either funny or kind then someone is both not calm and not rich. Everyone who is calm or generous is both calm and not tall and vice versa. If someone is not quiet then someone is either not kind or not wise and vice versa. If susan is either strong or not old then susan is strong and vice versa. If john is either not strong or funny then susan is funny or kind. If susan is either not brave or funny then john is either not old or not calm. If someone is not curious then someone is either not creative or humble and vice versa. If someone is kind or wise then someone is not strong or not kind. Everyone who is kind or rich is both quiet and patient. If someone is not kind then fred is not strong. Paul is not humble or not happy. Paul is both not rich and not brave. Fred is not rich or not generous. Someone is either not patient or wise. Alice is either not rich or strong. Someone is both funny and not rich. Someone is both rich and wise. Alice is not tall or calm. | Susan is not quiet. | contradiction | (((~wise(john)&generous(john)))<=>((rich(mary)&curious(mary))))&
((kind(susan))=>((~generous(alice)&~tall(alice))))&
(((funny(paul)|generous(paul)))=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(~funny(X)=>generous(X)))&
(![X]:((~creative(X)|~quiet(X))<=>(humble(X)&~humble(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:((~calm(X)&~rich(X)))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~kind(X)<~>~wise(X)))))&
(((strong(susan)<~>~old(susan)))<=>(strong(susan)))&
(((~strong(john)<~>funny(john)))=>((funny(susan)|kind(susan))))&
(((~brave(susan)<~>funny(susan)))=>((~old(john)<~>~calm(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
((?[X]:((kind(X)|wise(X))))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((kind(X)|rich(X))=>(quiet(X)&patient(X))))&
((?[X]:(~kind(X)))=>(~strong(fred)))&
((~humble(paul)|~happy(paul)))&
((~rich(paul)&~brave(paul)))&
((~rich(fred)|~generous(fred)))&
(?[X]:((~patient(X)<~>wise(X))))&
((~rich(alice)<~>strong(alice)))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((rich(X)&wise(X))))&
((~tall(alice)|calm(alice))) | ~quiet(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6403128376814057143245454
% SZS output start Proof for 6403128376814057143245454
5. ! [X0] : ((~quiet(X0) | ~creative(X0)) <=> (~humble(X0) & humble(X0))) [input p4]
24. ~quiet(susan) [input hypothesis]
44. ! [X0] : (((~quiet(X0) | ~creative(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (quiet(X0) & creative(X0)))) [nnf transformation 5]
45. ! [X0] : ((~quiet(X0) | ~creative(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (quiet(X0) & creative(X0)))) [flattening 44]
86. humble(X0) | quiet(X0) [cnf transformation 45]
88. ~humble(X0) | quiet(X0) [cnf transformation 45]
136. ~quiet(susan) [cnf transformation 24]
191. quiet(X0) [subsumption resolution 86,88]
326. $false [subsumption resolution 136,191]
% SZS output end Proof for 6403128376814057143245454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or happy is not generous or old.
Everyone who is either funny or strong is happy.
Everyone who is strong is either quiet or wise.
Everyone who is either not wise or calm is both kind and brave and vice versa.
Everyone who is kind or not creative is both kind and not wise.
Everyone who is creative or not happy is both patient and curious and vice versa.
Everyone who is either not tall or funny is both generous and not old.
If someone is not quiet then someone is either not brave or quiet and vice versa.
If mary is both not patient and brave then someone is both not strong and not creative and vice versa.
Everyone who is both not strong and quiet is not calm or quiet.
If someone is either not curious or not creative then john is calm and vice versa.
Everyone who is both not tall and not curious is not brave and vice versa.
If susan is both calm and not calm then paul is both not creative and not brave.
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
Paul is either calm or not generous.
Susan is either calm or not generous.
Susan is strong or humble.
Someone is both kind and generous.
Someone is wise or not generous.
Paul is both not quiet and not tall. | Mary is not strong. | entailment | (![X]:((~old(X)|happy(X))=>(~generous(X)|old(X))))&
(![X]:((funny(X)<~>strong(X))=>happy(X)))&
(![X]:(strong(X)=>(quiet(X)<~>wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(kind(X)&brave(X))))&
(![X]:((kind(X)|~creative(X))=>(kind(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~tall(X)<~>funny(X))=>(generous(X)&~old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((~patient(mary)&brave(mary)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((~strong(X)&quiet(X))=>(~calm(X)|quiet(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(calm(john)))&
(![X]:((~tall(X)&~curious(X))<=>~brave(X)))&
(((calm(susan)&~calm(susan)))=>((~creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
((calm(paul)<~>~generous(paul)))&
((calm(susan)<~>~generous(susan)))&
((strong(susan)|humble(susan)))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~quiet(paul)&~tall(paul))) | ~strong(mary) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5683621173723932305327160
% SZS output start Proof for 5683621173723932305327160
3. ! [X0] : (strong(X0) => (quiet(X0) <~> wise(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | kind(X0)) => (~wise(X0) & kind(X0))) [input p4]
6. ! [X0] : ((~happy(X0) | creative(X0)) <=> (curious(X0) & patient(X0))) [input p5]
8. ? [X0] : ~quiet(X0) <=> ? [X0] : (~brave(X0) <~> quiet(X0)) [input p7]
9. (brave(mary) & ~patient(mary)) <=> ? [X0] : (~creative(X0) & ~strong(X0)) [input p8]
12. ! [X0] : ((~curious(X0) & ~tall(X0)) <=> ~brave(X0)) [input p11]
14. ! [X0] : ((rich(X0) & ~quiet(X0)) <=> (~brave(X0) | brave(X0))) [input p13]
23. strong(mary) [input hypothesis]
24. ? [X0] : ~quiet(X0) <=> ? [X1] : (~brave(X1) <~> quiet(X1)) [rectify 8]
28. ! [X0] : ((quiet(X0) <~> wise(X0)) | ~strong(X0)) [ennf transformation 3]
29. ! [X0] : ((~wise(X0) & kind(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 5]
37. ! [X0] : (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~strong(X0)) [nnf transformation 28]
40. ! [X0] : (((~happy(X0) | creative(X0)) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | (happy(X0) & ~creative(X0)))) [nnf transformation 6]
41. ! [X0] : ((~happy(X0) | creative(X0) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | (happy(X0) & ~creative(X0)))) [flattening 40]
43. (? [X0] : ~quiet(X0) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X1] : ((~quiet(X1) | brave(X1)) & (quiet(X1) | ~brave(X1))) | ! [X0] : quiet(X0)) [nnf transformation 24]
44. (? [X0] : ~quiet(X0) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) | ! [X3] : quiet(X3)) [rectify 43]
45. ? [X0] : ~quiet(X0) => ~quiet(sK0) [choice axiom]
46. ? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) => ((~quiet(sK1) | brave(sK1)) & (quiet(sK1) | ~brave(sK1))) [choice axiom]
47. (~quiet(sK0) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (((~quiet(sK1) | brave(sK1)) & (quiet(sK1) | ~brave(sK1))) | ! [X3] : quiet(X3)) [skolemisation 44,46,45]
48. ((brave(mary) & ~patient(mary)) | ! [X0] : (creative(X0) | strong(X0))) & (? [X0] : (~creative(X0) & ~strong(X0)) | (~brave(mary) | patient(mary))) [nnf transformation 9]
49. ((brave(mary) & ~patient(mary)) | ! [X0] : (creative(X0) | strong(X0))) & (? [X0] : (~creative(X0) & ~strong(X0)) | ~brave(mary) | patient(mary)) [flattening 48]
50. ((brave(mary) & ~patient(mary)) | ! [X0] : (creative(X0) | strong(X0))) & (? [X1] : (~creative(X1) & ~strong(X1)) | ~brave(mary) | patient(mary)) [rectify 49]
51. ? [X1] : (~creative(X1) & ~strong(X1)) => (~creative(sK2) & ~strong(sK2)) [choice axiom]
52. ((brave(mary) & ~patient(mary)) | ! [X0] : (creative(X0) | strong(X0))) & ((~creative(sK2) & ~strong(sK2)) | ~brave(mary) | patient(mary)) [skolemisation 50,51]
57. ! [X0] : (((~curious(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | (curious(X0) | tall(X0)))) [nnf transformation 12]
58. ! [X0] : (((~curious(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | curious(X0) | tall(X0))) [flattening 57]
59. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (~rich(X0) | quiet(X0)))) [nnf transformation 14]
60. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~rich(X0) | quiet(X0))) [flattening 59]
74. ~strong(X0) | quiet(X0) | wise(X0) [cnf transformation 37]
83. creative(X0) | kind(X0) [cnf transformation 29]
84. ~kind(X0) | ~wise(X0) [cnf transformation 29]
86. ~creative(X0) | patient(X0) [cnf transformation 41]
88. ~creative(X0) | curious(X0) [cnf transformation 41]
95. quiet(sK1) | ~brave(sK1) | quiet(X3) [cnf transformation 47]
101. ~patient(mary) | creative(X0) | strong(X0) [cnf transformation 52]
110. ~curious(X0) | brave(X0) [cnf transformation 58]
114. ~quiet(X0) | ~brave(X0) [cnf transformation 60]
115. ~quiet(X0) | brave(X0) [cnf transformation 60]
134. strong(mary) [cnf transformation 23]
149. 4 <=> ! [X3] : quiet(X3) [avatar definition]
150. quiet(X3) <- (4) [avatar component clause 149]
152. 5 <=> brave(sK1) [avatar definition]
153. ~brave(sK1) <- (~5) [avatar component clause 152]
156. 6 <=> quiet(sK1) [avatar definition]
157. quiet(sK1) <- (6) [avatar component clause 156]
160. 4 | ~5 | 6 [avatar split clause 95,156,152,149]
162. 7 <=> ! [X0] : (creative(X0) | strong(X0)) [avatar definition]
163. creative(X0) | strong(X0) <- (7) [avatar component clause 162]
170. 9 <=> patient(mary) [avatar definition]
172. ~patient(mary) <- (~9) [avatar component clause 170]
173. 7 | ~9 [avatar split clause 101,170,162]
205. ~quiet(X0) [subsumption resolution 114,115]
248. patient(X0) | kind(X0) [resolution 86,83]
249. curious(X0) | kind(X0) [resolution 88,83]
257. brave(X0) | kind(X0) [resolution 249,110]
288. kind(mary) <- (~9) [resolution 172,248]
292. quiet(mary) | wise(mary) [resolution 74,134]
293. wise(mary) [subsumption resolution 292,205]
298. ~wise(mary) <- (~9) [resolution 288,84]
299. $false <- (~9) [subsumption resolution 298,293]
300. 9 [avatar contradiction clause 299]
304. curious(X0) | strong(X0) <- (7) [resolution 163,88]
317. 30 <=> wise(sK1) [avatar definition]
325. $false <- (6) [subsumption resolution 157,205]
326. ~6 [avatar contradiction clause 325]
327. $false <- (4) [subsumption resolution 150,205]
328. ~4 [avatar contradiction clause 327]
512. brave(X2) | strong(X2) <- (7) [resolution 304,110]
582. kind(sK1) <- (~5) [resolution 257,153]
592. strong(sK1) <- (~5, 7) [resolution 512,153]
632. ~wise(sK1) <- (~5) [resolution 582,84]
633. quiet(sK1) | wise(sK1) <- (~5, 7) [resolution 592,74]
635. wise(sK1) <- (~5, 7) [subsumption resolution 633,205]
638. 30 | 5 | ~7 [avatar split clause 635,162,152,317]
639. ~30 | 5 [avatar split clause 632,152,317]
642. $false [avatar sat refutation 160,173,300,326,328,638,639]
% SZS output end Proof for 5683621173723932305327160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is not quiet or not old.
If mary is either not rich or not calm then someone is strong or not calm and vice versa.
Everyone who is both funny and not brave is funny and vice versa.
If someone is not generous then john is not tall or creative and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is both rich and quiet is both creative and calm.
Everyone who is either quiet or not humble is both not curious and not happy.
If someone is not rich or not humble then someone is both generous and not curious and vice versa.
Everyone who is not creative or not curious is not happy or kind.
If someone is both patient and not brave then fred is both not brave and not happy.
Everyone who is both not funny and happy is both not rich and not tall.
If someone is not humble then someone is patient and vice versa.
Everyone who is not patient is quiet and vice versa.
Everyone who is both not generous and calm is both not tall and not brave and vice versa.
Everyone who is kind is curious or not tall and vice versa.
Everyone who is either brave or quiet is not strong and vice versa.
John is calm or rich.
Susan is either not happy or rich.
Someone is both not humble and patient.
Someone is both not quiet and generous.
Fred is both patient and old.
Susan is not patient or not quiet.
John is calm.
Someone is either rich or not wise. | John is not creative. | neutral | (![X]:((~strong(X)|~generous(X))=>(~quiet(X)|~old(X))))&
(((~rich(mary)<~>~calm(mary)))<=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((funny(X)&~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((~tall(john)|creative(john))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((rich(X)&quiet(X))=>(creative(X)&calm(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(~curious(X)&~happy(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((~creative(X)|~curious(X))=>(~happy(X)|kind(X))))&
((?[X]:((patient(X)&~brave(X))))=>((~brave(fred)&~happy(fred))))&
(![X]:((~funny(X)&happy(X))=>(~rich(X)&~tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(patient(X))))&
(![X]:(~patient(X)<=>quiet(X)))&
(![X]:((~generous(X)&calm(X))<=>(~tall(X)&~brave(X))))&
(![X]:(kind(X)<=>(curious(X)|~tall(X))))&
(![X]:((brave(X)<~>quiet(X))<=>~strong(X)))&
((calm(john)|rich(john)))&
((~happy(susan)<~>rich(susan)))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:((~quiet(X)&generous(X))))&
((patient(fred)&old(fred)))&
((~patient(susan)|~quiet(susan)))&
(calm(john))&
(?[X]:((rich(X)<~>~wise(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is both curious and not curious is brave or not strong and vice versa.
If alice is either not humble or brave then someone is either curious or not humble and vice versa.
Everyone who is creative or patient is both not old and not happy.
If someone is kind then john is not tall and vice versa.
If lucy is both kind and not kind then someone is either generous or curious.
If alice is not patient or not brave then fred is not strong or not generous and vice versa.
If someone is both not kind and not old then someone is curious and vice versa.
Everyone who is humble or not patient is either not quiet or old.
Everyone who is wise or not rich is either not happy or not creative.
If someone is old or generous then someone is not generous and vice versa.
If someone is calm then someone is both not brave and creative and vice versa.
If someone is either curious or not brave then someone is both not funny and not old.
If someone is both not tall and calm then someone is generous or brave and vice versa.
If someone is not generous then someone is not tall or not curious and vice versa.
Everyone who is either quiet or funny is either not tall or happy and vice versa.
Everyone who is either kind or generous is tall and vice versa.
Mary is either tall or not funny.
Susan is not tall or not old.
Someone is not tall or not creative.
Alice is funny.
Someone is calm or creative.
John is either patient or generous.
Someone is not funny or wise.
Fred is kind. | Susan is brave. | contradiction | (![X]:((curious(X)&~curious(X))<=>(brave(X)|~strong(X))))&
(((~humble(alice)<~>brave(alice)))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(![X]:((creative(X)|patient(X))=>(~old(X)&~happy(X))))&
((?[X]:(kind(X)))<=>(~tall(john)))&
(((kind(lucy)&~kind(lucy)))=>(?[X]:((generous(X)<~>curious(X)))))&
(((~patient(alice)|~brave(alice)))<=>((~strong(fred)|~generous(fred))))&
((?[X]:((~kind(X)&~old(X))))<=>(?[X]:(curious(X))))&
(![X]:((humble(X)|~patient(X))=>(~quiet(X)<~>old(X))))&
(![X]:((wise(X)|~rich(X))=>(~happy(X)<~>~creative(X))))&
((?[X]:((old(X)|generous(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)&creative(X)))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((~tall(X)&calm(X))))<=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((quiet(X)<~>funny(X))<=>(~tall(X)<~>happy(X))))&
(![X]:((kind(X)<~>generous(X))<=>tall(X)))&
((tall(mary)<~>~funny(mary)))&
((~tall(susan)|~old(susan)))&
(?[X]:((~tall(X)|~creative(X))))&
(funny(alice))&
(?[X]:((calm(X)|creative(X))))&
((patient(john)<~>generous(john)))&
(?[X]:((~funny(X)|wise(X))))&
(kind(fred)) | brave(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 9102341115806524074612324
% SZS output start Proof for 9102341115806524074612324
1. ! [X0] : ((~curious(X0) & curious(X0)) <=> (~strong(X0) | brave(X0))) [input p0]
25. brave(susan) [input hypothesis]
39. ! [X0] : (((~curious(X0) & curious(X0)) | (strong(X0) & ~brave(X0))) & ((~strong(X0) | brave(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 1]
40. ! [X0] : (((~curious(X0) & curious(X0)) | (strong(X0) & ~brave(X0))) & (~strong(X0) | brave(X0) | curious(X0) | ~curious(X0))) [flattening 39]
96. curious(X0) | ~brave(X0) [cnf transformation 40]
98. ~curious(X0) | ~brave(X0) [cnf transformation 40]
169. brave(susan) [cnf transformation 25]
171. ~brave(X0) [subsumption resolution 96,98]
384. $false [subsumption resolution 169,171]
% SZS output end Proof for 9102341115806524074612324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not rich then someone is rich and vice versa. Everyone who is not happy or happy is not kind and vice versa. Everyone who is both creative and not curious is either kind or humble. Everyone who is strong is both not wise and curious. If john is both wise and generous then someone is happy. If someone is both quiet and rich then someone is creative and vice versa. If fred is either humble or calm then someone is either kind or happy and vice versa. Everyone who is both not kind and not rich is both not creative and generous and vice versa. Everyone who is either wise or not happy is not wise. Everyone who is strong is not quiet. Everyone who is both not funny and not wise is funny or not funny and vice versa. If someone is either not kind or not happy then someone is either not wise or wise. Everyone who is not quiet or happy is not tall and vice versa. If someone is both strong and calm then someone is generous or not strong. If someone is either not creative or not old then someone is either humble or wise. Alice is either not calm or creative. Fred is patient or not rich. Someone is either calm or not wise. Paul is both not curious and not quiet. Fred is not wise. | Paul is generous. | entailment | ((?[X]:((creative(X)&~rich(X))))<=>(?[X]:(rich(X))))&
(![X]:((~happy(X)|happy(X))<=>~kind(X)))&
(![X]:((creative(X)&~curious(X))=>(kind(X)<~>humble(X))))&
(![X]:(strong(X)=>(~wise(X)&curious(X))))&
(((wise(john)&generous(john)))=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:(creative(X))))&
(((humble(fred)<~>calm(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~creative(X)&generous(X))))&
(![X]:((wise(X)<~>~happy(X))=>~wise(X)))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((~funny(X)&~wise(X))<=>(funny(X)|~funny(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((~quiet(X)|happy(X))<=>~tall(X)))&
((?[X]:((strong(X)&calm(X))))=>(?[X]:((generous(X)|~strong(X)))))&
((?[X]:((~creative(X)<~>~old(X))))=>(?[X]:((humble(X)<~>wise(X)))))&
((~calm(alice)<~>creative(alice)))&
((patient(fred)|~rich(fred)))&
(?[X]:((calm(X)<~>~wise(X))))&
((~curious(paul)&~quiet(paul)))&
(~wise(fred)) | generous(paul) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 9152547372321525889206061
% SZS output start Proof for 9152547372321525889206061
1. ? [X0] : (~rich(X0) & creative(X0)) <=> ? [X0] : rich(X0) [input p0]
2. ! [X0] : ((happy(X0) | ~happy(X0)) <=> ~kind(X0)) [input p1]
8. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (generous(X0) & ~creative(X0))) [input p7]
21. ~generous(paul) [input hypothesis]
22. ? [X0] : (~rich(X0) & creative(X0)) <=> ? [X1] : rich(X1) [rectify 1]
38. (? [X0] : (~rich(X0) & creative(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (rich(X0) | ~creative(X0))) [nnf transformation 22]
39. (? [X0] : (~rich(X0) & creative(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (rich(X3) | ~creative(X3))) [rectify 38]
40. ? [X0] : (~rich(X0) & creative(X0)) => (~rich(sK0) & creative(sK0)) [choice axiom]
41. ? [X2] : rich(X2) => rich(sK1) [choice axiom]
42. ((~rich(sK0) & creative(sK0)) | ! [X1] : ~rich(X1)) & (rich(sK1) | ! [X3] : (rich(X3) | ~creative(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((happy(X0) | ~happy(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) & happy(X0)))) [nnf transformation 2]
44. ! [X0] : ((happy(X0) | ~happy(X0) | kind(X0)) & (~kind(X0) | (~happy(X0) & happy(X0)))) [flattening 43]
57. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 8]
58. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | rich(X0) | kind(X0))) [flattening 57]
75. creative(sK0) | ~rich(X1) [cnf transformation 42]
76. ~rich(sK0) | ~rich(X1) [cnf transformation 42]
77. ~kind(X0) | happy(X0) [cnf transformation 44]
78. ~kind(X0) | ~happy(X0) [cnf transformation 44]
94. ~creative(X0) | rich(X0) | kind(X0) [cnf transformation 58]
95. generous(X0) | rich(X0) | kind(X0) [cnf transformation 58]
120. ~generous(paul) [cnf transformation 21]
125. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
126. ~rich(X1) <- (1) [avatar component clause 125]
128. 2 <=> rich(sK0) [avatar definition]
130. ~rich(sK0) <- (~2) [avatar component clause 128]
131. 1 | ~2 [avatar split clause 76,128,125]
133. 3 <=> creative(sK0) [avatar definition]
135. creative(sK0) <- (3) [avatar component clause 133]
136. 1 | 3 [avatar split clause 75,133,125]
138. 4 <=> ! [X3] : (rich(X3) | ~creative(X3)) [avatar definition]
139. ~creative(X3) | rich(X3) <- (4) [avatar component clause 138]
145. ~kind(X0) [subsumption resolution 77,78]
204. generous(X0) | rich(X0) [subsumption resolution 95,145]
205. ~creative(X0) | rich(X0) [subsumption resolution 94,145]
206. 4 [avatar split clause 205,138]
235. rich(sK0) <- (3, 4) [resolution 139,135]
236. $false <- (~2, 3, 4) [subsumption resolution 235,130]
237. 2 | ~3 | ~4 [avatar contradiction clause 236]
241. rich(paul) [resolution 204,120]
243. $false <- (1) [subsumption resolution 241,126]
244. ~1 [avatar contradiction clause 243]
247. $false [avatar sat refutation 131,136,206,237,244]
% SZS output end Proof for 9152547372321525889206061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is both quiet and not tall.
Everyone who is not curious is not kind or creative.
Everyone who is not curious or rich is either not curious or humble.
Everyone who is happy is not happy.
Everyone who is calm or tall is either funny or not humble and vice versa.
If someone is either not happy or not generous then fred is creative and vice versa.
Everyone who is not humble or not happy is either kind or not old.
If someone is rich or not strong then someone is not funny and vice versa.
Everyone who is quiet or not creative is either not calm or humble and vice versa.
If john is happy or kind then someone is either happy or not strong.
Everyone who is either kind or not happy is both generous and wise and vice versa.
Everyone who is both not quiet and not old is both strong and not curious and vice versa.
If fred is humble or tall then someone is both happy and not generous.
Everyone who is either not strong or not tall is happy or curious.
Everyone who is funny or not happy is funny or creative and vice versa.
If fred is both generous and wise then paul is either not creative or patient.
Someone is old.
Alice is both not creative and old.
Someone is happy or not patient.
Someone is both brave and not wise.
Lucy is either tall or funny.
Alice is brave or humble. | Paul is funny. | neutral | ((?[X]:(generous(X)))=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:(~curious(X)=>(~kind(X)|creative(X))))&
(![X]:((~curious(X)|rich(X))=>(~curious(X)<~>humble(X))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((calm(X)|tall(X))<=>(funny(X)<~>~humble(X))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>(creative(fred)))&
(![X]:((~humble(X)|~happy(X))=>(kind(X)<~>~old(X))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)<~>humble(X))))&
(((happy(john)|kind(john)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(strong(X)&~curious(X))))&
(((humble(fred)|tall(fred)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))<=>(funny(X)|creative(X))))&
(((generous(fred)&wise(fred)))=>((~creative(paul)<~>patient(paul))))&
(?[X]:(old(X)))&
((~creative(alice)&old(alice)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((brave(X)&~wise(X))))&
((tall(lucy)<~>funny(lucy)))&
((brave(alice)|humble(alice))) | funny(paul) | [] | null | 0 |
Everyone who is happy or funny is either not calm or rich and vice versa. Everyone who is either not calm or not strong is either not rich or kind and vice versa. Everyone who is either quiet or not humble is either not rich or not patient and vice versa. If someone is either calm or tall then paul is old or not funny and vice versa. Everyone who is wise is either generous or not quiet. If john is not brave then susan is not funny or tall. If lucy is patient or not brave then someone is not funny or not patient. Everyone who is both not wise and not funny is not wise. If someone is either not tall or not kind then someone is either humble or not kind and vice versa. If someone is both not brave and not generous then paul is brave or not strong. Everyone who is strong or creative is either patient or not brave. If paul is either not happy or not rich then paul is either creative or humble and vice versa. Everyone who is either not wise or wise is both not happy and rich and vice versa. If someone is either calm or not funny then john is not humble or not tall and vice versa. Everyone who is not kind or quiet is both strong and patient and vice versa. Everyone who is both funny and calm is tall or not funny. Paul is brave or creative. Lucy is not happy. Fred is patient. Lucy is either not strong or humble. Fred is generous. John is either not patient or not brave. Someone is not rich or patient. John is curious or old. | Fred is not rich. | contradiction | (![X]:((happy(X)|funny(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~rich(X)<~>kind(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~rich(X)<~>~patient(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>((old(paul)|~funny(paul))))&
(![X]:(wise(X)=>(generous(X)<~>~quiet(X))))&
((~brave(john))=>((~funny(susan)|tall(susan))))&
(((patient(lucy)|~brave(lucy)))=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~wise(X)&~funny(X))=>~wise(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((~brave(X)&~generous(X))))=>((brave(paul)|~strong(paul))))&
(![X]:((strong(X)|creative(X))=>(patient(X)<~>~brave(X))))&
(((~happy(paul)<~>~rich(paul)))<=>((creative(paul)<~>humble(paul))))&
(![X]:((~wise(X)<~>wise(X))<=>(~happy(X)&rich(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~humble(john)|~tall(john))))&
(![X]:((~kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((funny(X)&calm(X))=>(tall(X)|~funny(X))))&
((brave(paul)|creative(paul)))&
(~happy(lucy))&
(patient(fred))&
((~strong(lucy)<~>humble(lucy)))&
(generous(fred))&
((~patient(john)<~>~brave(john)))&
(?[X]:((~rich(X)|patient(X))))&
((curious(john)|old(john))) | ~rich(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4846505508897814439660569
% SZS output start Proof for 4846505508897814439660569
13. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) & ~happy(X0))) [input p12]
25. ~rich(fred) [input hypothesis]
58. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 58]
128. rich(X0) | wise(X0) | wise(X0) [cnf transformation 59]
129. rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 59]
153. ~rich(fred) [cnf transformation 25]
157. rich(X0) | wise(X0) [duplicate literal removal 128]
158. rich(X0) | ~wise(X0) [duplicate literal removal 129]
290. rich(X0) [subsumption resolution 157,158]
338. $false [subsumption resolution 153,290]
% SZS output end Proof for 4846505508897814439660569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not funny is both generous and not funny and vice versa. Everyone who is either strong or not tall is rich. Everyone who is not creative is not funny or not generous. Everyone who is both not funny and not quiet is not calm and vice versa. If someone is both not wise and rich then someone is either old or not creative. If someone is humble then paul is not kind or humble. Everyone who is either not patient or kind is not tall. If alice is both strong and not quiet then someone is quiet or not wise and vice versa. Everyone who is not rich is calm or funny and vice versa. Everyone who is curious is either not happy or humble. Everyone who is tall or quiet is both not patient and not strong. Everyone who is either not rich or funny is not happy and vice versa. If someone is calm then someone is not creative. Everyone who is patient or rich is old or tall and vice versa. If someone is either not creative or not humble then someone is both not brave and old and vice versa. Everyone who is not rich or generous is both not creative and rich. Alice is both curious and kind. Mary is brave. Someone is not happy or curious. Someone is both not curious and not old. Someone is not funny. Someone is either creative or not patient. | Paul is not generous. | contradiction | (![X]:((patient(X)|~funny(X))<=>(generous(X)&~funny(X))))&
(![X]:((strong(X)<~>~tall(X))=>rich(X)))&
(![X]:(~creative(X)=>(~funny(X)|~generous(X))))&
(![X]:((~funny(X)&~quiet(X))<=>~calm(X)))&
((?[X]:((~wise(X)&rich(X))))=>(?[X]:((old(X)<~>~creative(X)))))&
((?[X]:(humble(X)))=>((~kind(paul)|humble(paul))))&
(![X]:((~patient(X)<~>kind(X))=>~tall(X)))&
(((strong(alice)&~quiet(alice)))<=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:(~rich(X)<=>(calm(X)|funny(X))))&
(![X]:(curious(X)=>(~happy(X)<~>humble(X))))&
(![X]:((tall(X)|quiet(X))=>(~patient(X)&~strong(X))))&
(![X]:((~rich(X)<~>funny(X))<=>~happy(X)))&
((?[X]:(calm(X)))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)|rich(X))<=>(old(X)|tall(X))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&rich(X))))&
((curious(alice)&kind(alice)))&
(brave(mary))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>~patient(X)))) | ~generous(paul) | [
"p0",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5657175677227914155688886
% SZS output start Proof for 5657175677227914155688886
1. ! [X0] : ((~funny(X0) | patient(X0)) <=> (~funny(X0) & generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> ~calm(X0)) [input p3]
9. ! [X0] : (~rich(X0) <=> (funny(X0) | calm(X0))) [input p8]
16. ! [X0] : ((generous(X0) | ~rich(X0)) => (rich(X0) & ~creative(X0))) [input p15]
23. ~generous(paul) [input hypothesis]
37. ! [X0] : ((rich(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 16]
38. ! [X0] : (((~funny(X0) | patient(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (funny(X0) & ~patient(X0)))) [nnf transformation 1]
39. ! [X0] : ((~funny(X0) | patient(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (funny(X0) & ~patient(X0)))) [flattening 38]
41. ! [X0] : (((~quiet(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
42. ! [X0] : (((~quiet(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | quiet(X0) | funny(X0))) [flattening 41]
53. ! [X0] : ((~rich(X0) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | rich(X0))) [nnf transformation 9]
54. ! [X0] : ((~rich(X0) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | rich(X0))) [flattening 53]
77. generous(X0) | funny(X0) [cnf transformation 39]
85. ~funny(X0) | calm(X0) [cnf transformation 42]
98. ~calm(X0) | ~rich(X0) [cnf transformation 54]
123. rich(X0) | rich(X0) [cnf transformation 37]
134. ~generous(paul) [cnf transformation 23]
135. rich(X0) [duplicate literal removal 123]
253. funny(paul) [resolution 77,134]
255. calm(paul) [resolution 85,253]
256. ~rich(paul) [resolution 98,255]
257. $false [subsumption resolution 256,135]
% SZS output end Proof for 5657175677227914155688886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not tall then someone is either not humble or rich and vice versa.
Everyone who is both kind and not calm is not wise.
Everyone who is either old or not brave is wise or not rich.
Everyone who is both not old and curious is either curious or creative.
Everyone who is not generous is either funny or not rich and vice versa.
If someone is strong or not funny then alice is either funny or not creative and vice versa.
Everyone who is not old is both not tall and kind.
If someone is either not funny or generous then someone is not calm or not quiet and vice versa.
If someone is either not calm or not creative then someone is both not happy and not generous and vice versa.
Everyone who is generous is either not quiet or tall and vice versa.
If someone is not tall then someone is tall or happy and vice versa.
Everyone who is either not generous or rich is tall.
If fred is wise or old then someone is not brave.
Everyone who is both wise and not rich is funny.
If mary is both humble and rich then someone is not old.
Everyone who is either wise or not creative is both not curious and happy and vice versa.
Susan is either not happy or not generous.
Someone is either curious or not rich.
Someone is both patient and tall.
Alice is either tall or not humble.
Fred is generous or not funny.
Lucy is quiet or not calm.
Someone is both not happy and not generous. | Mary is humble. | neutral | ((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((kind(X)&~calm(X))=>~wise(X)))&
(![X]:((old(X)<~>~brave(X))=>(wise(X)|~rich(X))))&
(![X]:((~old(X)&curious(X))=>(curious(X)<~>creative(X))))&
(![X]:(~generous(X)<=>(funny(X)<~>~rich(X))))&
((?[X]:((strong(X)|~funny(X))))<=>((funny(alice)<~>~creative(alice))))&
(![X]:(~old(X)=>(~tall(X)&kind(X))))&
((?[X]:((~funny(X)<~>generous(X))))<=>(?[X]:((~calm(X)|~quiet(X)))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:(generous(X)<=>(~quiet(X)<~>tall(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((~generous(X)<~>rich(X))=>tall(X)))&
(((wise(fred)|old(fred)))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)&~rich(X))=>funny(X)))&
(((humble(mary)&rich(mary)))=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~creative(X))<=>(~curious(X)&happy(X))))&
((~happy(susan)<~>~generous(susan)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((patient(X)&tall(X))))&
((tall(alice)<~>~humble(alice)))&
((generous(fred)|~funny(fred)))&
((quiet(lucy)|~calm(lucy)))&
(?[X]:((~happy(X)&~generous(X)))) | humble(mary) | [] | null | 0 |
Everyone who is either not rich or quiet is not strong or wise and vice versa. If someone is either not quiet or kind then paul is both not quiet and not kind. Everyone who is not brave or not patient is not patient. Everyone who is not kind is both not patient and quiet and vice versa. If someone is not funny or not tall then alice is humble or creative and vice versa. Everyone who is either not quiet or not calm is either not calm or patient and vice versa. Everyone who is either happy or humble is both not brave and kind. If susan is not patient then susan is tall or not quiet and vice versa. If someone is both strong and not strong then alice is either not calm or not quiet. If alice is not calm or not rich then someone is either happy or not tall and vice versa. Everyone who is quiet or not tall is not patient or brave and vice versa. If alice is either not rich or not strong then mary is both not tall and not kind and vice versa. Everyone who is either not creative or not wise is both not patient and not creative. If lucy is both not rich and humble then fred is not old. Everyone who is brave or not funny is tall. Everyone who is kind is not rich and vice versa. Someone is not wise or wise. Susan is generous or strong. Someone is humble. Paul is either not tall or not kind. Someone is both brave and quiet. Someone is not old. Fred is either kind or not funny. | Lucy is rich. | entailment | (![X]:((~rich(X)<~>quiet(X))<=>(~strong(X)|wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((~brave(X)|~patient(X))=>~patient(X)))&
(![X]:(~kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>((humble(alice)|creative(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~calm(X)<~>patient(X))))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)&kind(X))))&
((~patient(susan))<=>((tall(susan)|~quiet(susan))))&
((?[X]:((strong(X)&~strong(X))))=>((~calm(alice)<~>~quiet(alice))))&
(((~calm(alice)|~rich(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((quiet(X)|~tall(X))<=>(~patient(X)|brave(X))))&
(((~rich(alice)<~>~strong(alice)))<=>((~tall(mary)&~kind(mary))))&
(![X]:((~creative(X)<~>~wise(X))=>(~patient(X)&~creative(X))))&
(((~rich(lucy)&humble(lucy)))=>(~old(fred)))&
(![X]:((brave(X)|~funny(X))=>tall(X)))&
(![X]:(kind(X)<=>~rich(X)))&
(?[X]:((~wise(X)|wise(X))))&
((generous(susan)|strong(susan)))&
(?[X]:(humble(X)))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:(~old(X)))&
((kind(fred)<~>~funny(fred))) | rich(lucy) | [
"p1",
"p2",
"p5",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 260209530221421798842438
% SZS output start Proof for 260209530221421798842438
2. ? [X0] : (~quiet(X0) <~> kind(X0)) => (~kind(paul) & ~quiet(paul)) [input p1]
3. ! [X0] : ((~patient(X0) | ~brave(X0)) => ~patient(X0)) [input p2]
6. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~calm(X0) <~> patient(X0))) [input p5]
11. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (brave(X0) | ~patient(X0))) [input p10]
15. ! [X0] : ((~funny(X0) | brave(X0)) => tall(X0)) [input p14]
16. ! [X0] : (kind(X0) <=> ~rich(X0)) [input p15]
24. ~rich(lucy) [input hypothesis]
28. (~kind(paul) & ~quiet(paul)) | ! [X0] : (~quiet(X0) <=> kind(X0)) [ennf transformation 2]
29. ! [X0] : (~patient(X0) | (patient(X0) & brave(X0))) [ennf transformation 3]
33. ! [X0] : (tall(X0) | (funny(X0) & ~brave(X0))) [ennf transformation 15]
36. (~kind(paul) & ~quiet(paul)) | ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 28]
44. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 6]
54. ! [X0] : (((~tall(X0) | quiet(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : ((~tall(X0) | quiet(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | (tall(X0) & ~quiet(X0)))) [flattening 54]
59. ! [X0] : ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0))) [nnf transformation 16]
75. ~quiet(paul) | ~quiet(X0) | ~kind(X0) [cnf transformation 36]
78. ~patient(X0) | brave(X0) [cnf transformation 29]
87. patient(X0) | ~calm(X0) | ~calm(X0) | quiet(X0) [cnf transformation 44]
93. calm(X0) | quiet(X0) | patient(X0) | calm(X0) [cnf transformation 44]
113. ~tall(X0) | quiet(X0) | ~brave(X0) [cnf transformation 55]
124. ~brave(X0) | tall(X0) [cnf transformation 33]
127. kind(X0) | rich(X0) [cnf transformation 59]
136. ~rich(lucy) [cnf transformation 24]
138. patient(X0) | ~calm(X0) | quiet(X0) [duplicate literal removal 87]
141. calm(X0) | quiet(X0) | patient(X0) [duplicate literal removal 93]
143. 1 <=> ! [X0] : (~quiet(X0) | ~kind(X0)) [avatar definition]
144. ~kind(X0) | ~quiet(X0) <- (1) [avatar component clause 143]
155. 4 <=> quiet(paul) [avatar definition]
157. ~quiet(paul) <- (~4) [avatar component clause 155]
158. 1 | ~4 [avatar split clause 75,155,143]
188. patient(X0) | quiet(X0) [subsumption resolution 138,141]
279. ~quiet(X1) | rich(X1) <- (1) [resolution 144,127]
284. brave(X2) | quiet(X2) [resolution 188,78]
356. tall(X0) | quiet(X0) [resolution 284,124]
378. quiet(X0) | quiet(X0) | ~brave(X0) [resolution 356,113]
382. quiet(X0) | ~brave(X0) [duplicate literal removal 378]
383. quiet(X0) [subsumption resolution 382,284]
384. $false <- (~4) [resolution 383,157]
385. rich(X0) <- (1) [resolution 383,279]
387. 4 [avatar contradiction clause 384]
394. $false <- (1) [resolution 385,136]
397. ~1 [avatar contradiction clause 394]
398. $false [avatar sat refutation 158,387,397]
% SZS output end Proof for 260209530221421798842438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not kind then someone is strong or not quiet. Everyone who is either humble or not calm is not curious. Everyone who is both kind and creative is either wise or not kind. Everyone who is either curious or not rich is either not patient or creative. If alice is both creative and calm then someone is either not calm or not happy. Everyone who is generous or not tall is both not wise and patient and vice versa. Everyone who is either wise or humble is either rich or old. Everyone who is not brave or not old is either not brave or humble. Everyone who is not funny or not patient is happy and vice versa. Everyone who is either not old or not brave is either kind or not calm and vice versa. Everyone who is both strong and rich is not happy. If john is brave or not humble then john is patient or brave and vice versa. Everyone who is both funny and happy is not wise or tall and vice versa. Everyone who is happy or not quiet is not rich. Everyone who is either not brave or creative is either calm or curious and vice versa. If someone is either not brave or calm then lucy is either generous or not calm. Someone is either not humble or not strong. John is brave or humble. Someone is humble or not happy. Alice is both not kind and not humble. Someone is not brave or calm. Someone is either not patient or creative. | John is not old. | neutral | ((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~curious(X)))&
(![X]:((kind(X)&creative(X))=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)<~>~rich(X))=>(~patient(X)<~>creative(X))))&
(((creative(alice)&calm(alice)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((generous(X)|~tall(X))<=>(~wise(X)&patient(X))))&
(![X]:((wise(X)<~>humble(X))=>(rich(X)<~>old(X))))&
(![X]:((~brave(X)|~old(X))=>(~brave(X)<~>humble(X))))&
(![X]:((~funny(X)|~patient(X))<=>happy(X)))&
(![X]:((~old(X)<~>~brave(X))<=>(kind(X)<~>~calm(X))))&
(![X]:((strong(X)&rich(X))=>~happy(X)))&
(((brave(john)|~humble(john)))<=>((patient(john)|brave(john))))&
(![X]:((funny(X)&happy(X))<=>(~wise(X)|tall(X))))&
(![X]:((happy(X)|~quiet(X))=>~rich(X)))&
(![X]:((~brave(X)<~>creative(X))<=>(calm(X)<~>curious(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>((generous(lucy)<~>~calm(lucy))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((brave(john)|humble(john)))&
(?[X]:((humble(X)|~happy(X))))&
((~kind(alice)&~humble(alice)))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:((~patient(X)<~>creative(X)))) | ~old(john) | [] | null | 0 |
Everyone who is generous is either happy or tall. Everyone who is brave or old is either not curious or creative and vice versa. Everyone who is not funny or not wise is both not rich and not wise and vice versa. If someone is either not rich or not old then mary is both funny and not creative and vice versa. If john is both not kind and wise then someone is either happy or not humble. Everyone who is not generous is both generous and patient and vice versa. If john is not calm or not funny then mary is patient and vice versa. If susan is both kind and not rich then someone is either wise or calm and vice versa. If someone is not humble then susan is not patient and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is not generous or wise is not wise or not patient and vice versa. If someone is not creative then someone is both quiet and patient. Everyone who is both happy and calm is either humble or calm. If someone is either not funny or quiet then someone is creative or not wise. Everyone who is creative is not tall or not rich. Someone is both not happy and not kind. Fred is either not creative or not strong. Alice is either creative or not kind. Fred is either strong or not old. | Mary is not curious. | entailment | (![X]:(generous(X)=>(happy(X)<~>tall(X))))&
(![X]:((brave(X)|old(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~funny(X)|~wise(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((funny(mary)&~creative(mary))))&
(((~kind(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~generous(X)<=>(generous(X)&patient(X))))&
(((~calm(john)|~funny(john)))<=>(patient(mary)))&
(((kind(susan)&~rich(susan)))<=>(?[X]:((wise(X)<~>calm(X)))))&
((?[X]:(~humble(X)))<=>(~patient(susan)))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((~generous(X)|wise(X))<=>(~wise(X)|~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((happy(X)&calm(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~funny(X)<~>quiet(X))))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
(?[X]:((~happy(X)&~kind(X))))&
((~creative(fred)<~>~strong(fred)))&
((creative(alice)<~>~kind(alice)))&
((strong(fred)<~>~old(fred))) | ~curious(mary) | [
"p2",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 142498286863787528815807
% SZS output start Proof for 142498286863787528815807
3. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (~wise(X0) & ~rich(X0))) [input p2]
6. ! [X0] : (~generous(X0) <=> (patient(X0) & generous(X0))) [input p5]
10. ! [X0] : (~curious(X0) <=> funny(X0)) [input p9]
11. ! [X0] : ((wise(X0) | ~generous(X0)) <=> (~patient(X0) | ~wise(X0))) [input p10]
20. curious(mary) [input hypothesis]
35. ! [X0] : (((~wise(X0) | ~funny(X0)) | (wise(X0) | rich(X0))) & ((~wise(X0) & ~rich(X0)) | (wise(X0) & funny(X0)))) [nnf transformation 3]
36. ! [X0] : ((~wise(X0) | ~funny(X0) | wise(X0) | rich(X0)) & ((~wise(X0) & ~rich(X0)) | (wise(X0) & funny(X0)))) [flattening 35]
45. ! [X0] : ((~generous(X0) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | generous(X0))) [nnf transformation 6]
46. ! [X0] : ((~generous(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | generous(X0))) [flattening 45]
58. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 10]
59. ! [X0] : (((wise(X0) | ~generous(X0)) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | (~wise(X0) & generous(X0)))) [nnf transformation 11]
60. ! [X0] : ((wise(X0) | ~generous(X0) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | (~wise(X0) & generous(X0)))) [flattening 59]
84. ~wise(X0) | funny(X0) [cnf transformation 36]
95. generous(X0) | generous(X0) [cnf transformation 46]
110. ~funny(X0) | ~curious(X0) [cnf transformation 58]
113. wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 60]
130. curious(mary) [cnf transformation 20]
133. wise(X0) | ~generous(X0) [duplicate literal removal 113]
134. generous(X0) [duplicate literal removal 95]
239. wise(X0) [subsumption resolution 133,134]
255. funny(X0) [resolution 84,239]
261. ~curious(X1) [resolution 110,255]
263. $false [resolution 261,130]
% SZS output end Proof for 142498286863787528815807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or rich is either not patient or not humble and vice versa.
Everyone who is either not patient or strong is happy and vice versa.
Everyone who is both generous and quiet is not brave or not rich.
Everyone who is not kind or old is tall.
If someone is either not quiet or not strong then someone is both happy and not happy and vice versa.
If lucy is creative or curious then someone is both not generous and happy and vice versa.
Everyone who is both creative and rich is not rich or creative and vice versa.
If someone is not creative or not old then fred is funny.
Everyone who is both calm and funny is either not funny or creative and vice versa.
If someone is curious or humble then lucy is brave or not wise and vice versa.
Everyone who is quiet or not humble is either kind or calm.
If susan is either old or not patient then fred is either quiet or not funny and vice versa.
Everyone who is either old or not humble is not quiet or quiet.
Everyone who is humble is both calm and tall and vice versa.
If someone is quiet then susan is not strong or not happy and vice versa.
If alice is strong then mary is either not patient or not quiet.
Susan is not rich or funny.
Susan is either funny or not quiet.
Someone is either rich or not generous.
Mary is either strong or not patient.
Someone is both generous and funny.
Someone is both happy and not humble.
Someone is both humble and kind. | Susan is not strong. | contradiction | (![X]:((tall(X)|rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>strong(X))<=>happy(X)))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)|~rich(X))))&
(![X]:((~kind(X)|old(X))=>tall(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~happy(X)))))&
(((creative(lucy)|curious(lucy)))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((creative(X)&rich(X))<=>(~rich(X)|creative(X))))&
((?[X]:((~creative(X)|~old(X))))=>(funny(fred)))&
(![X]:((calm(X)&funny(X))<=>(~funny(X)<~>creative(X))))&
((?[X]:((curious(X)|humble(X))))<=>((brave(lucy)|~wise(lucy))))&
(![X]:((quiet(X)|~humble(X))=>(kind(X)<~>calm(X))))&
(((old(susan)<~>~patient(susan)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|quiet(X))))&
(![X]:(humble(X)<=>(calm(X)&tall(X))))&
((?[X]:(quiet(X)))<=>((~strong(susan)|~happy(susan))))&
((strong(alice))=>((~patient(mary)<~>~quiet(mary))))&
((~rich(susan)|funny(susan)))&
((funny(susan)<~>~quiet(susan)))&
(?[X]:((rich(X)<~>~generous(X))))&
((strong(mary)<~>~patient(mary)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:((humble(X)&kind(X)))) | ~strong(susan) | [
"p4",
"p6",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7896365645840674471769115
% SZS output start Proof for 7896365645840674471769115
5. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X0] : (~happy(X0) & happy(X0)) [input p4]
7. ! [X0] : ((rich(X0) & creative(X0)) <=> (creative(X0) | ~rich(X0))) [input p6]
17. funny(susan) | ~rich(susan) [input p16]
18. funny(susan) <~> ~quiet(susan) [input p17]
24. ~strong(susan) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X1] : (~happy(X1) & happy(X1)) [rectify 5]
37. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) [nnf transformation 25]
38. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X2] : (~happy(X2) & happy(X2)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [rectify 37]
39. ? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) => ((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) [choice axiom]
40. ? [X2] : (~happy(X2) & happy(X2)) => (~happy(sK1) & happy(sK1)) [choice axiom]
41. (((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) | ! [X1] : (happy(X1) | ~happy(X1))) & ((~happy(sK1) & happy(sK1)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [skolemisation 38,40,39]
47. ! [X0] : (((rich(X0) & creative(X0)) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 7]
48. ! [X0] : (((rich(X0) & creative(X0)) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ~rich(X0) | ~creative(X0))) [flattening 47]
67. (quiet(susan) | ~funny(susan)) & (~quiet(susan) | funny(susan)) [nnf transformation 18]
92. happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
94. ~happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
105. rich(X0) | rich(X0) [cnf transformation 48]
141. funny(susan) | ~rich(susan) [cnf transformation 17]
143. quiet(susan) | ~funny(susan) [cnf transformation 67]
154. ~strong(susan) [cnf transformation 24]
158. rich(X0) [duplicate literal removal 105]
160. 1 <=> ! [X3] : (~quiet(X3) | strong(X3)) [avatar definition]
161. ~quiet(X3) | strong(X3) <- (1) [avatar component clause 160]
163. 2 <=> happy(sK1) [avatar definition]
166. 1 | ~2 [avatar split clause 94,163,160]
171. 1 | 2 [avatar split clause 92,163,160]
266. 23 <=> strong(susan) [avatar definition]
267. ~strong(susan) <- (~23) [avatar component clause 266]
288. funny(susan) [subsumption resolution 141,158]
289. quiet(susan) [subsumption resolution 143,288]
297. ~23 [avatar split clause 154,266]
307. strong(susan) <- (1) [resolution 161,289]
308. $false <- (1, ~23) [subsumption resolution 307,267]
309. ~1 | 23 [avatar contradiction clause 308]
310. $false [avatar sat refutation 166,171,297,309]
% SZS output end Proof for 7896365645840674471769115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and humble is tall and vice versa. If someone is both generous and not calm then someone is either wise or not quiet and vice versa. If someone is wise or not happy then john is both humble and not curious and vice versa. Everyone who is either not calm or not strong is either not brave or not rich and vice versa. Everyone who is either curious or strong is either happy or not generous and vice versa. If fred is either not creative or humble then someone is patient and vice versa. Everyone who is happy or not generous is either wise or old and vice versa. If someone is either not strong or generous then someone is either not creative or not quiet and vice versa. Everyone who is both not tall and not calm is either not patient or not brave and vice versa. If someone is both calm and humble then someone is both humble and creative and vice versa. Everyone who is either not calm or not tall is not humble. If lucy is brave then someone is not happy or not kind. Everyone who is not funny is either not generous or not strong. If mary is both not funny and tall then lucy is either rich or not brave and vice versa. If alice is either not rich or funny then fred is not strong or creative and vice versa. John is strong or tall. Someone is wise or not kind. Someone is not creative. Lucy is both humble and rich. John is both not kind and not happy. Someone is either happy or wise. Lucy is either not rich or not happy. John is either not generous or not tall. | John is not generous. | entailment | (![X]:((~creative(X)&humble(X))<=>tall(X)))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
((?[X]:((wise(X)|~happy(X))))<=>((humble(john)&~curious(john))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((curious(X)<~>strong(X))<=>(happy(X)<~>~generous(X))))&
(((~creative(fred)<~>humble(fred)))<=>(?[X]:(patient(X))))&
(![X]:((happy(X)|~generous(X))<=>(wise(X)<~>old(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:((calm(X)&humble(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(![X]:((~calm(X)<~>~tall(X))=>~humble(X)))&
((brave(lucy))=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:(~funny(X)=>(~generous(X)<~>~strong(X))))&
(((~funny(mary)&tall(mary)))<=>((rich(lucy)<~>~brave(lucy))))&
(((~rich(alice)<~>funny(alice)))<=>((~strong(fred)|creative(fred))))&
((strong(john)|tall(john)))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:(~creative(X)))&
((humble(lucy)&rich(lucy)))&
((~kind(john)&~happy(john)))&
(?[X]:((happy(X)<~>wise(X))))&
((~rich(lucy)<~>~happy(lucy)))&
((~generous(john)<~>~tall(john))) | ~generous(john) | [
"p2",
"p4",
"p15",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2765422961574484290656475
% SZS output start Proof for 2765422961574484290656475
3. ? [X0] : (~happy(X0) | wise(X0)) <=> (~curious(john) & humble(john)) [input p2]
5. ! [X0] : ((curious(X0) <~> strong(X0)) <=> (happy(X0) <~> ~generous(X0))) [input p4]
16. tall(john) | strong(john) [input p15]
20. ~happy(john) & ~kind(john) [input p19]
23. ~generous(john) <~> ~tall(john) [input p22]
24. generous(john) [input hypothesis]
30. ~happy(john) [pure predicate removal 20]
40. (? [X0] : (~happy(X0) | wise(X0)) | (curious(john) | ~humble(john))) & ((~curious(john) & humble(john)) | ! [X0] : (happy(X0) & ~wise(X0))) [nnf transformation 3]
41. (? [X0] : (~happy(X0) | wise(X0)) | curious(john) | ~humble(john)) & ((~curious(john) & humble(john)) | ! [X0] : (happy(X0) & ~wise(X0))) [flattening 40]
42. (? [X0] : (~happy(X0) | wise(X0)) | curious(john) | ~humble(john)) & ((~curious(john) & humble(john)) | ! [X1] : (happy(X1) & ~wise(X1))) [rectify 41]
43. ? [X0] : (~happy(X0) | wise(X0)) => (~happy(sK2) | wise(sK2)) [choice axiom]
44. ((~happy(sK2) | wise(sK2)) | curious(john) | ~humble(john)) & ((~curious(john) & humble(john)) | ! [X1] : (happy(X1) & ~wise(X1))) [skolemisation 42,43]
46. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) & (((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [nnf transformation 5]
77. (tall(john) | generous(john)) & (~tall(john) | ~generous(john)) [nnf transformation 23]
90. ~curious(john) | happy(X1) [cnf transformation 44]
101. ~strong(X0) | happy(X0) | curious(X0) | ~generous(X0) [cnf transformation 46]
152. tall(john) | strong(john) [cnf transformation 16]
156. ~happy(john) [cnf transformation 30]
161. ~tall(john) | ~generous(john) [cnf transformation 77]
163. generous(john) [cnf transformation 24]
200. 9 <=> curious(john) [avatar definition]
201. ~curious(john) <- (~9) [avatar component clause 200]
213. 12 <=> ! [X1] : happy(X1) [avatar definition]
214. happy(X1) <- (12) [avatar component clause 213]
215. 12 | ~9 [avatar split clause 90,200,213]
345. 39 <=> strong(john) [avatar definition]
347. strong(john) <- (39) [avatar component clause 345]
349. 40 <=> tall(john) [avatar definition]
352. 39 | 40 [avatar split clause 152,349,345]
371. 44 <=> generous(john) [avatar definition]
373. generous(john) <- (44) [avatar component clause 371]
375. ~44 | ~40 [avatar split clause 161,349,371]
376. 44 [avatar split clause 163,371]
385. $false <- (12) [resolution 214,156]
390. ~12 [avatar contradiction clause 385]
586. happy(john) | curious(john) | ~generous(john) <- (39) [resolution 101,347]
589. curious(john) | ~generous(john) <- (39) [subsumption resolution 586,156]
590. ~generous(john) <- (~9, 39) [subsumption resolution 589,201]
591. $false <- (~9, 39, 44) [subsumption resolution 590,373]
592. 9 | ~39 | ~44 [avatar contradiction clause 591]
593. $false [avatar sat refutation 215,352,375,376,390,592]
% SZS output end Proof for 2765422961574484290656475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and kind is not quiet or generous and vice versa.
Everyone who is creative or not rich is not calm or tall.
Everyone who is not happy is generous and vice versa.
Everyone who is not patient is both not kind and calm.
If someone is either kind or not quiet then someone is either happy or not strong and vice versa.
If someone is both quiet and not old then alice is tall or not brave.
Everyone who is either not brave or brave is both humble and not wise.
Everyone who is either quiet or not wise is either not funny or not old and vice versa.
Everyone who is either strong or not old is funny and vice versa.
Everyone who is both curious and not rich is calm or patient.
Everyone who is either not happy or tall is not happy or generous.
Everyone who is not kind is either tall or not happy and vice versa.
Everyone who is not happy or funny is either not generous or not strong.
Everyone who is either not wise or not creative is not generous or rich and vice versa.
If someone is not generous or not wise then alice is not curious.
If mary is both patient and creative then someone is either not patient or not strong.
Susan is either not curious or generous.
Someone is not quiet or wise.
Someone is not strong.
Someone is not strong or humble.
John is generous or happy. | Mary is funny. | contradiction | (![X]:((~tall(X)&kind(X))<=>(~quiet(X)|generous(X))))&
(![X]:((creative(X)|~rich(X))=>(~calm(X)|tall(X))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:(~patient(X)=>(~kind(X)&calm(X))))&
((?[X]:((kind(X)<~>~quiet(X))))<=>(?[X]:((happy(X)<~>~strong(X)))))&
((?[X]:((quiet(X)&~old(X))))=>((tall(alice)|~brave(alice))))&
(![X]:((~brave(X)<~>brave(X))=>(humble(X)&~wise(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(~funny(X)<~>~old(X))))&
(![X]:((strong(X)<~>~old(X))<=>funny(X)))&
(![X]:((curious(X)&~rich(X))=>(calm(X)|patient(X))))&
(![X]:((~happy(X)<~>tall(X))=>(~happy(X)|generous(X))))&
(![X]:(~kind(X)<=>(tall(X)<~>~happy(X))))&
(![X]:((~happy(X)|funny(X))=>(~generous(X)<~>~strong(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(~generous(X)|rich(X))))&
((?[X]:((~generous(X)|~wise(X))))=>(~curious(alice)))&
(((patient(mary)&creative(mary)))=>(?[X]:((~patient(X)<~>~strong(X)))))&
((~curious(susan)<~>generous(susan)))&
(?[X]:((~quiet(X)|wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~strong(X)|humble(X))))&
((generous(john)|happy(john))) | funny(mary) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2234818666029124111584945
% SZS output start Proof for 2234818666029124111584945
1. ! [X0] : ((kind(X0) & ~tall(X0)) <=> (generous(X0) | ~quiet(X0))) [input p0]
3. ! [X0] : (~happy(X0) <=> generous(X0)) [input p2]
7. ! [X0] : ((~brave(X0) <~> brave(X0)) => (~wise(X0) & humble(X0))) [input p6]
8. ! [X0] : ((quiet(X0) <~> ~wise(X0)) <=> (~funny(X0) <~> ~old(X0))) [input p7]
9. ! [X0] : ((strong(X0) <~> ~old(X0)) <=> funny(X0)) [input p8]
11. ! [X0] : ((~happy(X0) <~> tall(X0)) => (generous(X0) | ~happy(X0))) [input p10]
12. ! [X0] : (~kind(X0) <=> (tall(X0) <~> ~happy(X0))) [input p11]
13. ! [X0] : ((funny(X0) | ~happy(X0)) => (~generous(X0) <~> ~strong(X0))) [input p12]
22. funny(mary) [input hypothesis]
24. ! [X0] : ((~brave(X0) <~> brave(X0)) => ~wise(X0)) [pure predicate removal 7]
31. ! [X0] : (~wise(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 24]
34. ! [X0] : ((generous(X0) | ~happy(X0)) | (~happy(X0) <=> tall(X0))) [ennf transformation 11]
35. ! [X0] : (generous(X0) | ~happy(X0) | (~happy(X0) <=> tall(X0))) [flattening 34]
36. ! [X0] : ((~generous(X0) <~> ~strong(X0)) | (~funny(X0) & happy(X0))) [ennf transformation 13]
40. ! [X0] : (((kind(X0) & ~tall(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~kind(X0) | tall(X0)))) [nnf transformation 1]
41. ! [X0] : (((kind(X0) & ~tall(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~kind(X0) | tall(X0))) [flattening 40]
42. ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))) [nnf transformation 3]
48. ! [X0] : (~wise(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 31]
49. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [nnf transformation 8]
50. ! [X0] : ((((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~funny(X0)) & (funny(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0))))) [nnf transformation 9]
51. ! [X0] : (generous(X0) | ~happy(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) [nnf transformation 35]
52. ! [X0] : ((~kind(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | kind(X0))) [nnf transformation 12]
53. ! [X0] : (((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~funny(X0) & happy(X0))) [nnf transformation 36]
64. ~quiet(X0) | generous(X0) | ~kind(X0) | tall(X0) [cnf transformation 41]
66. ~generous(X0) | ~tall(X0) [cnf transformation 41]
68. ~generous(X0) | kind(X0) [cnf transformation 41]
71. happy(X0) | generous(X0) [cnf transformation 42]
72. ~happy(X0) | ~generous(X0) [cnf transformation 42]
84. ~wise(X0) | brave(X0) | brave(X0) [cnf transformation 48]
85. ~wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 48]
87. ~old(X0) | ~funny(X0) | quiet(X0) | wise(X0) [cnf transformation 49]
95. funny(X0) | strong(X0) | old(X0) [cnf transformation 50]
97. ~funny(X0) | ~strong(X0) | old(X0) [cnf transformation 50]
100. generous(X0) | ~happy(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 51]
101. ~happy(X0) | tall(X0) | kind(X0) [cnf transformation 52]
102. happy(X0) | ~tall(X0) | kind(X0) [cnf transformation 52]
104. ~kind(X0) | tall(X0) | happy(X0) [cnf transformation 52]
108. ~funny(X0) | generous(X0) | strong(X0) [cnf transformation 53]
124. funny(mary) [cnf transformation 22]
125. generous(X0) | ~happy(X0) | ~tall(X0) [duplicate literal removal 100]
126. ~wise(X0) | brave(X0) [duplicate literal removal 84]
127. ~wise(X0) | ~brave(X0) [duplicate literal removal 85]
175. ~wise(X0) [subsumption resolution 126,127]
179. ~funny(X0) | ~old(X0) | quiet(X0) [subsumption resolution 87,175]
180. ~happy(X0) | ~tall(X0) [subsumption resolution 125,72]
181. ~tall(X0) | kind(X0) [subsumption resolution 102,180]
182. ~happy(X0) | kind(X0) [subsumption resolution 101,181]
226. ~tall(X0) | generous(X0) [resolution 180,71]
227. ~tall(X0) [subsumption resolution 226,66]
228. kind(X0) | generous(X0) [resolution 182,71]
229. kind(X0) [subsumption resolution 228,68]
240. 17 <=> old(mary) [avatar definition]
241. old(mary) <- (17) [avatar component clause 240]
248. ~strong(mary) | old(mary) [resolution 97,124]
253. tall(X0) | happy(X0) [resolution 104,229]
257. happy(X0) [subsumption resolution 253,227]
261. ~generous(X2) [resolution 257,72]
273. generous(X0) | strong(X0) | strong(X0) | old(X0) [resolution 108,95]
274. generous(X0) | strong(X0) | old(X0) [duplicate literal removal 273]
278. old(X0) | strong(X0) [subsumption resolution 274,261]
279. old(mary) [subsumption resolution 248,278]
280. 17 [avatar split clause 279,240]
300. ~old(mary) | quiet(mary) [resolution 179,124]
304. quiet(mary) <- (17) [subsumption resolution 300,241]
321. generous(mary) | ~kind(mary) | tall(mary) <- (17) [resolution 64,304]
326. ~kind(mary) | tall(mary) <- (17) [subsumption resolution 321,261]
327. tall(mary) <- (17) [subsumption resolution 326,229]
328. $false <- (17) [subsumption resolution 327,227]
329. ~17 [avatar contradiction clause 328]
330. $false [avatar sat refutation 280,329]
% SZS output end Proof for 2234818666029124111584945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both not rich and not humble and vice versa.
If someone is not old then someone is both curious and calm.
If someone is either not generous or not brave then someone is not brave or creative.
If alice is both strong and brave then lucy is either kind or generous.
Everyone who is not strong is either not patient or not happy.
If someone is either generous or creative then mary is patient.
Everyone who is either calm or not happy is strong or patient and vice versa.
If someone is both not brave and calm then someone is not curious or quiet.
If fred is either not wise or not rich then someone is both not rich and not old.
Everyone who is either humble or rich is both not funny and funny.
Everyone who is not quiet is both not old and not quiet and vice versa.
If susan is either brave or not funny then someone is not humble or not quiet and vice versa.
Everyone who is both not brave and not strong is both funny and not curious and vice versa.
If someone is either creative or not happy then someone is either not funny or not calm.
Everyone who is not rich or not wise is not quiet and vice versa.
Everyone who is not brave is either creative or not generous and vice versa.
Mary is not strong.
Mary is not strong or kind.
Someone is either wise or curious.
John is either not brave or rich.
Alice is either quiet or happy.
Someone is curious or not humble.
Alice is both not funny and not calm.
Someone is happy or old. | Mary is not happy. | entailment | (![X]:(~calm(X)<=>(~rich(X)&~humble(X))))&
((?[X]:(~old(X)))=>(?[X]:((curious(X)&calm(X)))))&
((?[X]:((~generous(X)<~>~brave(X))))=>(?[X]:((~brave(X)|creative(X)))))&
(((strong(alice)&brave(alice)))=>((kind(lucy)<~>generous(lucy))))&
(![X]:(~strong(X)=>(~patient(X)<~>~happy(X))))&
((?[X]:((generous(X)<~>creative(X))))=>(patient(mary)))&
(![X]:((calm(X)<~>~happy(X))<=>(strong(X)|patient(X))))&
((?[X]:((~brave(X)&calm(X))))=>(?[X]:((~curious(X)|quiet(X)))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((humble(X)<~>rich(X))=>(~funny(X)&funny(X))))&
(![X]:(~quiet(X)<=>(~old(X)&~quiet(X))))&
(((brave(susan)<~>~funny(susan)))<=>(?[X]:((~humble(X)|~quiet(X)))))&
(![X]:((~brave(X)&~strong(X))<=>(funny(X)&~curious(X))))&
((?[X]:((creative(X)<~>~happy(X))))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:((~rich(X)|~wise(X))<=>~quiet(X)))&
(![X]:(~brave(X)<=>(creative(X)<~>~generous(X))))&
(~strong(mary))&
((~strong(mary)|kind(mary)))&
(?[X]:((wise(X)<~>curious(X))))&
((~brave(john)<~>rich(john)))&
((quiet(alice)<~>happy(alice)))&
(?[X]:((curious(X)|~humble(X))))&
((~funny(alice)&~calm(alice)))&
(?[X]:((happy(X)|old(X)))) | ~happy(mary) | [
"p0",
"p4",
"p5",
"p6",
"p12",
"p14",
"p15",
"p16",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2567699856638262585506409
% SZS output start Proof for 2567699856638262585506409
1. ! [X0] : (~calm(X0) <=> (~humble(X0) & ~rich(X0))) [input p0]
5. ! [X0] : (~strong(X0) => (~patient(X0) <~> ~happy(X0))) [input p4]
6. ? [X0] : (generous(X0) <~> creative(X0)) => patient(mary) [input p5]
7. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (patient(X0) | strong(X0))) [input p6]
13. ! [X0] : ((~strong(X0) & ~brave(X0)) <=> (~curious(X0) & funny(X0))) [input p12]
15. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> ~quiet(X0)) [input p14]
16. ! [X0] : (~brave(X0) <=> (creative(X0) <~> ~generous(X0))) [input p15]
17. ~strong(mary) [input p16]
21. quiet(alice) <~> happy(alice) [input p20]
23. ~calm(alice) & ~funny(alice) [input p22]
25. happy(mary) [input hypothesis]
34. ! [X0] : ((~patient(X0) <~> ~happy(X0)) | strong(X0)) [ennf transformation 5]
35. patient(mary) | ! [X0] : (generous(X0) <=> creative(X0)) [ennf transformation 6]
40. ! [X0] : ((~calm(X0) | (humble(X0) | rich(X0))) & ((~humble(X0) & ~rich(X0)) | calm(X0))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) | humble(X0) | rich(X0)) & ((~humble(X0) & ~rich(X0)) | calm(X0))) [flattening 40]
50. ! [X0] : (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | strong(X0)) [nnf transformation 34]
51. patient(mary) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0))) [nnf transformation 35]
52. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 7]
53. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [flattening 52]
67. ! [X0] : (((~strong(X0) & ~brave(X0)) | (curious(X0) | ~funny(X0))) & ((~curious(X0) & funny(X0)) | (strong(X0) | brave(X0)))) [nnf transformation 13]
68. ! [X0] : (((~strong(X0) & ~brave(X0)) | curious(X0) | ~funny(X0)) & ((~curious(X0) & funny(X0)) | strong(X0) | brave(X0))) [flattening 67]
73. ! [X0] : (((~wise(X0) | ~rich(X0)) | quiet(X0)) & (~quiet(X0) | (wise(X0) & rich(X0)))) [nnf transformation 15]
74. ! [X0] : ((~wise(X0) | ~rich(X0) | quiet(X0)) & (~quiet(X0) | (wise(X0) & rich(X0)))) [flattening 73]
75. ! [X0] : ((~brave(X0) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | brave(X0))) [nnf transformation 16]
80. (~happy(alice) | ~quiet(alice)) & (happy(alice) | quiet(alice)) [nnf transformation 21]
85. ~rich(X0) | calm(X0) [cnf transformation 41]
94. ~happy(X0) | ~patient(X0) | strong(X0) [cnf transformation 50]
96. patient(mary) | creative(X0) | ~generous(X0) [cnf transformation 51]
97. patient(mary) | generous(X0) | ~creative(X0) [cnf transformation 51]
100. ~happy(X0) | calm(X0) | ~strong(X0) [cnf transformation 53]
122. funny(X0) | strong(X0) | brave(X0) [cnf transformation 68]
130. ~quiet(X0) | rich(X0) [cnf transformation 74]
135. ~creative(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 75]
136. ~brave(X0) | creative(X0) | generous(X0) [cnf transformation 75]
137. ~strong(mary) [cnf transformation 17]
143. happy(alice) | quiet(alice) [cnf transformation 80]
146. ~funny(alice) [cnf transformation 23]
147. ~calm(alice) [cnf transformation 23]
149. happy(mary) [cnf transformation 25]
180. 8 <=> strong(alice) [avatar definition]
184. 9 <=> brave(alice) [avatar definition]
185. brave(alice) <- (9) [avatar component clause 184]
198. 12 <=> ! [X0] : (generous(X0) | ~creative(X0)) [avatar definition]
199. ~creative(X0) | generous(X0) <- (12) [avatar component clause 198]
201. 13 <=> patient(mary) [avatar definition]
204. 12 | 13 [avatar split clause 97,201,198]
206. 14 <=> ! [X0] : (creative(X0) | ~generous(X0)) [avatar definition]
207. ~generous(X0) | creative(X0) <- (14) [avatar component clause 206]
208. 14 | 13 [avatar split clause 96,201,206]
311. 36 <=> quiet(alice) [avatar definition]
312. quiet(alice) <- (36) [avatar component clause 311]
315. 37 <=> happy(alice) [avatar definition]
316. happy(alice) <- (37) [avatar component clause 315]
319. 36 | 37 [avatar split clause 143,315,311]
338. rich(alice) <- (36) [resolution 130,312]
340. calm(alice) <- (36) [resolution 338,85]
341. $false <- (36) [subsumption resolution 340,147]
342. ~36 [avatar contradiction clause 341]
347. ~patient(mary) | strong(mary) [resolution 94,149]
363. ~patient(mary) [subsumption resolution 347,137]
364. ~13 [avatar split clause 363,201]
370. calm(alice) | ~strong(alice) <- (37) [resolution 100,316]
384. strong(alice) | brave(alice) [resolution 122,146]
389. 9 | 8 [avatar split clause 384,180,184]
391. ~strong(alice) <- (37) [subsumption resolution 370,147]
392. ~8 | ~37 [avatar split clause 391,315,180]
450. creative(alice) | generous(alice) <- (9) [resolution 136,185]
452. creative(alice) <- (9, 14) [subsumption resolution 450,207]
454. ~generous(alice) | ~brave(alice) <- (9, 14) [resolution 452,135]
456. generous(alice) <- (9, 12, 14) [resolution 452,199]
457. ~generous(alice) <- (9, 14) [subsumption resolution 454,185]
458. $false <- (9, 12, 14) [subsumption resolution 456,457]
459. ~9 | ~12 | ~14 [avatar contradiction clause 458]
460. $false [avatar sat refutation 204,208,319,342,364,389,392,459]
% SZS output end Proof for 2567699856638262585506409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not creative then alice is either not creative or not quiet and vice versa.
Everyone who is either not tall or brave is both not quiet and not rich.
If john is both old and not calm then someone is either kind or not curious and vice versa.
Everyone who is not funny or not curious is calm and vice versa.
Everyone who is both tall and humble is either calm or not tall and vice versa.
Everyone who is not brave or not humble is both curious and not strong and vice versa.
If lucy is not tall then paul is funny and vice versa.
If john is both not strong and patient then john is either not rich or patient.
If someone is either not happy or not calm then someone is not funny or not wise.
If susan is either not brave or not strong then mary is both not wise and wise and vice versa.
Everyone who is both generous and brave is either not brave or not calm and vice versa.
If someone is either patient or not curious then someone is both not tall and wise and vice versa.
Everyone who is not kind is either rich or not calm and vice versa.
Everyone who is not creative is both not curious and not old and vice versa.
If someone is quiet then john is not creative.
If john is patient then paul is not kind or not calm and vice versa.
Susan is both not calm and not rich.
Alice is both generous and patient.
Alice is not quiet or not calm.
Someone is either not old or generous.
Someone is not strong.
John is calm.
John is both quiet and patient.
Someone is old. | Susan is not humble. | entailment | ((?[X]:((~humble(X)|~creative(X))))<=>((~creative(alice)<~>~quiet(alice))))&
(![X]:((~tall(X)<~>brave(X))=>(~quiet(X)&~rich(X))))&
(((old(john)&~calm(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)|~curious(X))<=>calm(X)))&
(![X]:((tall(X)&humble(X))<=>(calm(X)<~>~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(curious(X)&~strong(X))))&
((~tall(lucy))<=>(funny(paul)))&
(((~strong(john)&patient(john)))=>((~rich(john)<~>patient(john))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(((~brave(susan)<~>~strong(susan)))<=>((~wise(mary)&wise(mary))))&
(![X]:((generous(X)&brave(X))<=>(~brave(X)<~>~calm(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:(~kind(X)<=>(rich(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>(~curious(X)&~old(X))))&
((?[X]:(quiet(X)))=>(~creative(john)))&
((patient(john))<=>((~kind(paul)|~calm(paul))))&
((~calm(susan)&~rich(susan)))&
((generous(alice)&patient(alice)))&
((~quiet(alice)|~calm(alice)))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:(~strong(X)))&
(calm(john))&
((quiet(john)&patient(john)))&
(?[X]:(old(X))) | ~humble(susan) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8947278053357822341738207
% SZS output start Proof for 8947278053357822341738207
5. ! [X0] : ((humble(X0) & tall(X0)) <=> (calm(X0) <~> ~tall(X0))) [input p4]
17. ~rich(susan) & ~calm(susan) [input p16]
25. humble(susan) [input hypothesis]
45. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | (~humble(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((humble(X0) & tall(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | ~humble(X0) | ~tall(X0))) [flattening 45]
95. ~tall(X0) | calm(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 46]
98. tall(X0) | calm(X0) | tall(X0) [cnf transformation 46]
141. ~calm(susan) [cnf transformation 17]
153. humble(susan) [cnf transformation 25]
157. ~tall(X0) | calm(X0) | ~humble(X0) [duplicate literal removal 95]
158. calm(X0) | tall(X0) [duplicate literal removal 98]
215. ~humble(X0) | calm(X0) [subsumption resolution 157,158]
359. calm(susan) [resolution 215,153]
362. $false [subsumption resolution 359,141]
% SZS output end Proof for 8947278053357822341738207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and rich is not old. If lucy is either not strong or brave then fred is both not happy and rich and vice versa. If lucy is either tall or old then someone is not brave and vice versa. If fred is either not calm or not wise then lucy is both not curious and not strong. Everyone who is either creative or not brave is funny and vice versa. 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. Mary is either not brave or funny. Someone is not wise or brave. Someone is happy or patient. Someone is not happy or not generous. Mary is either not brave or tall. Susan is both not rich and calm. Someone is both wise and quiet. Someone is both rich and not brave. | Mary is not creative. | contradiction | (![X]:((strong(X)&rich(X))=>~old(X)))&
(((~strong(lucy)<~>brave(lucy)))<=>((~happy(fred)&rich(fred))))&
(((tall(lucy)<~>old(lucy)))<=>(?[X]:(~brave(X))))&
(((~calm(fred)<~>~wise(fred)))=>((~curious(lucy)&~strong(lucy))))&
(![X]:((creative(X)<~>~brave(X))<=>funny(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))))&
((~brave(mary)<~>funny(mary)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((~happy(X)|~generous(X))))&
((~brave(mary)<~>tall(mary)))&
((~rich(susan)&calm(susan)))&
(?[X]:((wise(X)&quiet(X))))&
(?[X]:((rich(X)&~brave(X)))) | ~creative(mary) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 303571072886437240208889
% SZS output start Proof for 303571072886437240208889
5. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> funny(X0)) [input p4]
17. ~brave(mary) <~> funny(mary) [input p16]
25. ~creative(mary) [input hypothesis]
44. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ~funny(X0)) & (funny(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 5]
69. (~funny(mary) | brave(mary)) & (funny(mary) | ~brave(mary)) [nnf transformation 17]
97. funny(X0) | creative(X0) | brave(X0) [cnf transformation 44]
98. ~funny(X0) | creative(X0) | ~brave(X0) [cnf transformation 44]
143. funny(mary) | ~brave(mary) [cnf transformation 69]
144. ~funny(mary) | brave(mary) [cnf transformation 69]
156. ~creative(mary) [cnf transformation 25]
287. 28 <=> brave(mary) [avatar definition]
288. ~brave(mary) <- (~28) [avatar component clause 287]
289. brave(mary) <- (28) [avatar component clause 287]
291. 29 <=> funny(mary) [avatar definition]
292. funny(mary) <- (29) [avatar component clause 291]
293. ~funny(mary) <- (~29) [avatar component clause 291]
294. 28 | ~29 [avatar split clause 144,291,287]
295. ~28 | 29 [avatar split clause 143,291,287]
334. creative(mary) | brave(mary) <- (~29) [resolution 97,293]
336. brave(mary) <- (~29) [subsumption resolution 334,156]
337. $false <- (~28, ~29) [subsumption resolution 336,288]
338. 28 | 29 [avatar contradiction clause 337]
342. creative(mary) | ~brave(mary) <- (29) [resolution 98,292]
353. ~brave(mary) <- (29) [subsumption resolution 342,156]
354. $false <- (28, 29) [subsumption resolution 353,289]
355. ~28 | ~29 [avatar contradiction clause 354]
356. $false [avatar sat refutation 294,295,338,355]
% SZS output end Proof for 303571072886437240208889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and wise is both patient and kind. Everyone who is both not wise and not happy is wise and vice versa. Everyone who is old or not tall is either quiet or patient. Everyone who is not rich or not happy is curious and vice versa. Everyone who is not strong is not tall or strong. Everyone who is not curious or happy is not humble or old. Everyone who is not tall is both not rich and kind and vice versa. Everyone who is not strong is either wise or strong. If someone is either quiet or old then someone is not kind or not curious. If mary is either wise or not kind then someone is tall and vice versa. If paul is not humble then lucy is not wise. Everyone who is rich or not tall is both not strong and not rich and vice versa. Everyone who is either not happy or wise is not curious or not patient and vice versa. Everyone who is not calm is not quiet or generous. Everyone who is either generous or not quiet is either not old or patient and vice versa. If someone is either humble or not creative then someone is either kind or rich and vice versa. Someone is not humble or not old. Someone is not quiet. Mary is tall or not humble. Someone is quiet. Someone is not creative or not rich. | Paul is not kind. | entailment | (![X]:((old(X)&wise(X))=>(patient(X)&kind(X))))&
(![X]:((~wise(X)&~happy(X))<=>wise(X)))&
(![X]:((old(X)|~tall(X))=>(quiet(X)<~>patient(X))))&
(![X]:((~rich(X)|~happy(X))<=>curious(X)))&
(![X]:(~strong(X)=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)|happy(X))=>(~humble(X)|old(X))))&
(![X]:(~tall(X)<=>(~rich(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>strong(X))))&
((?[X]:((quiet(X)<~>old(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(((wise(mary)<~>~kind(mary)))<=>(?[X]:(tall(X))))&
((~humble(paul))=>(~wise(lucy)))&
(![X]:((rich(X)|~tall(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(~curious(X)|~patient(X))))&
(![X]:(~calm(X)=>(~quiet(X)|generous(X))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~old(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((kind(X)<~>rich(X)))))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:(~quiet(X)))&
((tall(mary)|~humble(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)|~rich(X)))) | ~kind(paul) | [
"p1",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 677584239626814660549625
% SZS output start Proof for 677584239626814660549625
2. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : (~tall(X0) <=> (kind(X0) & ~rich(X0))) [input p6]
8. ! [X0] : (~strong(X0) => (wise(X0) <~> strong(X0))) [input p7]
12. ! [X0] : ((~tall(X0) | rich(X0)) <=> (~rich(X0) & ~strong(X0))) [input p11]
22. kind(paul) [input hypothesis]
33. ! [X0] : ((wise(X0) <~> strong(X0)) | strong(X0)) [ennf transformation 8]
36. ! [X0] : (((~happy(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) | wise(X0)))) [nnf transformation 2]
37. ! [X0] : (((~happy(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | happy(X0) | wise(X0))) [flattening 36]
41. ! [X0] : ((~tall(X0) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | tall(X0))) [nnf transformation 7]
42. ! [X0] : ((~tall(X0) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | tall(X0))) [flattening 41]
43. ! [X0] : (((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | strong(X0)) [nnf transformation 33]
52. ! [X0] : (((~tall(X0) | rich(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [nnf transformation 12]
53. ! [X0] : ((~tall(X0) | rich(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [flattening 52]
73. ~wise(X0) | ~wise(X0) [cnf transformation 37]
87. ~tall(X0) | ~kind(X0) | rich(X0) [cnf transformation 42]
88. strong(X0) | wise(X0) | strong(X0) [cnf transformation 43]
98. ~strong(X0) | tall(X0) [cnf transformation 53]
99. ~rich(X0) | ~rich(X0) [cnf transformation 53]
129. kind(paul) [cnf transformation 22]
130. ~rich(X0) [duplicate literal removal 99]
132. strong(X0) | wise(X0) [duplicate literal removal 88]
135. ~wise(X0) [duplicate literal removal 73]
139. strong(X0) [subsumption resolution 132,135]
171. tall(X0) [subsumption resolution 98,139]
181. 8 <=> ! [X1] : ~kind(X1) [avatar definition]
182. ~kind(X1) <- (8) [avatar component clause 181]
224. ~kind(X1) | rich(X1) [resolution 87,171]
225. ~kind(X1) [subsumption resolution 224,130]
226. 8 [avatar split clause 225,181]
227. $false <- (8) [resolution 182,129]
230. ~8 [avatar contradiction clause 227]
231. $false [avatar sat refutation 226,230]
% SZS output end Proof for 677584239626814660549625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or funny is generous and vice versa.
Everyone who is both creative and kind is not creative or not happy and vice versa.
If susan is not humble or not generous then someone is both funny and not patient.
Everyone who is either strong or brave is funny and vice versa.
If fred is kind then john is either funny or calm.
If someone is both funny and not rich then someone is either old or not strong and vice versa.
Everyone who is either not funny or creative is not happy or kind.
Everyone who is both brave and strong is both not old and not strong and vice versa.
Everyone who is either not curious or not calm is either not kind or not funny.
If someone is both creative and not calm then fred is old.
Everyone who is not quiet or not generous is both calm and not old.
If someone is not humble or not strong then someone is not happy and vice versa.
If alice is happy then someone is both not rich and not quiet.
Everyone who is creative or brave is wise or not brave.
Fred is not rich.
Fred is calm or tall.
Susan is either curious or not generous.
Susan is either humble or not humble. | Fred is calm. | neutral | (![X]:((~creative(X)<~>funny(X))<=>generous(X)))&
(![X]:((creative(X)&kind(X))<=>(~creative(X)|~happy(X))))&
(((~humble(susan)|~generous(susan)))=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:((strong(X)<~>brave(X))<=>funny(X)))&
((kind(fred))=>((funny(john)<~>calm(john))))&
((?[X]:((funny(X)&~rich(X))))<=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((~funny(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~old(X)&~strong(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>(old(fred)))&
(![X]:((~quiet(X)|~generous(X))=>(calm(X)&~old(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:(~happy(X))))&
((happy(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>(wise(X)|~brave(X))))&
(~rich(fred))&
((calm(fred)|tall(fred)))&
((curious(susan)<~>~generous(susan)))&
((humble(susan)<~>~humble(susan))) | calm(fred) | [] | null | 0 |
If someone is both not tall and kind then lucy is old and vice versa. If mary is curious then fred is either patient or humble. Everyone who is happy is either not curious or quiet and vice versa. Everyone who is both creative and not wise is both calm and not brave and vice versa. Everyone who is either not patient or happy is humble and vice versa. Everyone who is either happy or creative is either old or not wise and vice versa. Everyone who is rich is brave or patient and vice versa. If fred is both not wise and old then someone is either not tall or generous. Everyone who is brave or not curious is either curious or not quiet and vice versa. If someone is either not brave or not curious then someone is both curious and not old. Everyone who is calm is not funny or not old. If someone is rich or curious then lucy is patient and vice versa. Everyone who is both kind and not rich is either not happy or tall and vice versa. Everyone who is kind is not wise or happy and vice versa. Everyone who is not creative is strong and vice versa. If john is quiet or funny then susan is both generous and not funny. Someone is not tall. Someone is not humble. Someone is either funny or humble. Fred is either not curious or generous. Susan is not calm or curious. Mary is either not old or wise. Someone is either not creative or not wise. Someone is old. | Lucy is not rich. | contradiction | ((?[X]:((~tall(X)&kind(X))))<=>(old(lucy)))&
((curious(mary))=>((patient(fred)<~>humble(fred))))&
(![X]:(happy(X)<=>(~curious(X)<~>quiet(X))))&
(![X]:((creative(X)&~wise(X))<=>(calm(X)&~brave(X))))&
(![X]:((~patient(X)<~>happy(X))<=>humble(X)))&
(![X]:((happy(X)<~>creative(X))<=>(old(X)<~>~wise(X))))&
(![X]:(rich(X)<=>(brave(X)|patient(X))))&
(((~wise(fred)&old(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:((brave(X)|~curious(X))<=>(curious(X)<~>~quiet(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:(calm(X)=>(~funny(X)|~old(X))))&
((?[X]:((rich(X)|curious(X))))<=>(patient(lucy)))&
(![X]:((kind(X)&~rich(X))<=>(~happy(X)<~>tall(X))))&
(![X]:(kind(X)<=>(~wise(X)|happy(X))))&
(![X]:(~creative(X)<=>strong(X)))&
(((quiet(john)|funny(john)))=>((generous(susan)&~funny(susan))))&
(?[X]:(~tall(X)))&
(?[X]:(~humble(X)))&
(?[X]:((funny(X)<~>humble(X))))&
((~curious(fred)<~>generous(fred)))&
((~calm(susan)|curious(susan)))&
((~old(mary)<~>wise(mary)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:(old(X))) | ~rich(lucy) | [
"p2",
"p6",
"p8",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3730691645328032146234326
% SZS output start Proof for 3730691645328032146234326
3. ! [X0] : (happy(X0) <=> (~curious(X0) <~> quiet(X0))) [input p2]
7. ! [X0] : (rich(X0) <=> (patient(X0) | brave(X0))) [input p6]
9. ! [X0] : ((~curious(X0) | brave(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p8]
12. ? [X0] : (curious(X0) | rich(X0)) <=> patient(lucy) [input p11]
13. ! [X0] : ((~rich(X0) & kind(X0)) <=> (~happy(X0) <~> tall(X0))) [input p12]
14. ! [X0] : (kind(X0) <=> (happy(X0) | ~wise(X0))) [input p13]
17. ? [X0] : ~tall(X0) [input p16]
25. ~rich(lucy) [input hypothesis]
39. ! [X0] : ((happy(X0) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) & (((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 3]
44. ! [X0] : ((rich(X0) | (~patient(X0) & ~brave(X0))) & ((patient(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 7]
45. ! [X0] : ((rich(X0) | (~patient(X0) & ~brave(X0))) & (patient(X0) | brave(X0) | ~rich(X0))) [flattening 44]
49. ! [X0] : (((~curious(X0) | brave(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~brave(X0)))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | brave(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~brave(X0)))) [flattening 49]
55. (? [X0] : (curious(X0) | rich(X0)) | ~patient(lucy)) & (patient(lucy) | ! [X0] : (~curious(X0) & ~rich(X0))) [nnf transformation 12]
56. (? [X0] : (curious(X0) | rich(X0)) | ~patient(lucy)) & (patient(lucy) | ! [X1] : (~curious(X1) & ~rich(X1))) [rectify 55]
57. ? [X0] : (curious(X0) | rich(X0)) => (curious(sK3) | rich(sK3)) [choice axiom]
58. ((curious(sK3) | rich(sK3)) | ~patient(lucy)) & (patient(lucy) | ! [X1] : (~curious(X1) & ~rich(X1))) [skolemisation 56,57]
59. ! [X0] : (((~rich(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (rich(X0) | ~kind(X0)))) [nnf transformation 13]
60. ! [X0] : (((~rich(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | rich(X0) | ~kind(X0))) [flattening 59]
61. ! [X0] : ((kind(X0) | (~happy(X0) & wise(X0))) & ((happy(X0) | ~wise(X0)) | ~kind(X0))) [nnf transformation 14]
62. ! [X0] : ((kind(X0) | (~happy(X0) & wise(X0))) & (happy(X0) | ~wise(X0) | ~kind(X0))) [flattening 61]
64. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
65. ~tall(sK4) [skolemisation 17,64]
85. quiet(X0) | happy(X0) | curious(X0) [cnf transformation 39]
105. ~patient(X0) | rich(X0) [cnf transformation 45]
109. ~quiet(X0) | curious(X0) | curious(X0) [cnf transformation 50]
119. patient(lucy) | ~rich(X1) [cnf transformation 58]
120. patient(lucy) | ~curious(X1) [cnf transformation 58]
122. ~happy(X0) | tall(X0) | rich(X0) | ~kind(X0) [cnf transformation 60]
130. ~happy(X0) | kind(X0) [cnf transformation 62]
137. ~tall(sK4) [cnf transformation 65]
149. ~rich(lucy) [cnf transformation 25]
150. ~quiet(X0) | curious(X0) [duplicate literal removal 109]
221. 16 <=> patient(lucy) [avatar definition]
222. patient(lucy) <- (16) [avatar component clause 221]
234. 19 <=> ! [X1] : ~curious(X1) [avatar definition]
235. ~curious(X1) <- (19) [avatar component clause 234]
236. 19 | 16 [avatar split clause 120,221,234]
238. 20 <=> ! [X1] : ~rich(X1) [avatar definition]
239. ~rich(X1) <- (20) [avatar component clause 238]
240. 20 | 16 [avatar split clause 119,221,238]
310. rich(lucy) <- (16) [resolution 105,222]
311. $false <- (16) [subsumption resolution 310,149]
312. ~16 [avatar contradiction clause 311]
322. happy(X1) | curious(X1) | curious(X1) [resolution 85,150]
323. happy(X1) | curious(X1) [duplicate literal removal 322]
326. happy(X1) <- (19) [subsumption resolution 323,235]
334. kind(X1) <- (19) [resolution 326,130]
461. tall(X2) | rich(X2) | ~kind(X2) <- (19) [resolution 122,326]
468. tall(X2) | ~kind(X2) <- (19, 20) [subsumption resolution 461,239]
469. tall(X2) <- (19, 20) [subsumption resolution 468,334]
474. $false <- (19, 20) [resolution 469,137]
477. ~19 | ~20 [avatar contradiction clause 474]
478. $false [avatar sat refutation 236,240,312,477]
% SZS output end Proof for 3730691645328032146234326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or funny then mary is either not quiet or not wise and vice versa. Everyone who is either not strong or not tall is curious. If someone is not wise then someone is either not kind or quiet. Everyone who is both not patient and not humble is quiet. Everyone who is not kind is rich. Everyone who is either not patient or not strong is either not wise or not curious and vice versa. If paul is both calm and not creative then lucy is either not funny or not creative and vice versa. Everyone who is either tall or not quiet is funny or kind. Everyone who is tall or not curious is tall and vice versa. Everyone who is creative or not tall is old. Everyone who is both not tall and not calm is either not brave or not strong. Everyone who is humble or not calm is either not humble or not tall and vice versa. Everyone who is quiet or not strong is both happy and not happy and vice versa. Everyone who is both quiet and not kind is both not happy and calm and vice versa. If fred is not rich then lucy is old or creative and vice versa. Everyone who is either creative or not wise is both not funny and not wise. Someone is rich or not humble. Someone is either not old or curious. Fred is not generous. Someone is either quiet or not happy. Paul is either old or not creative. Mary is not curious. | Mary is strong. | entailment | ((?[X]:((old(X)|funny(X))))<=>((~quiet(mary)<~>~wise(mary))))&
(![X]:((~strong(X)<~>~tall(X))=>curious(X)))&
((?[X]:(~wise(X)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((~patient(X)&~humble(X))=>quiet(X)))&
(![X]:(~kind(X)=>rich(X)))&
(![X]:((~patient(X)<~>~strong(X))<=>(~wise(X)<~>~curious(X))))&
(((calm(paul)&~creative(paul)))<=>((~funny(lucy)<~>~creative(lucy))))&
(![X]:((tall(X)<~>~quiet(X))=>(funny(X)|kind(X))))&
(![X]:((tall(X)|~curious(X))<=>tall(X)))&
(![X]:((creative(X)|~tall(X))=>old(X)))&
(![X]:((~tall(X)&~calm(X))=>(~brave(X)<~>~strong(X))))&
(![X]:((humble(X)|~calm(X))<=>(~humble(X)<~>~tall(X))))&
(![X]:((quiet(X)|~strong(X))<=>(happy(X)&~happy(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~happy(X)&calm(X))))&
((~rich(fred))<=>((old(lucy)|creative(lucy))))&
(![X]:((creative(X)<~>~wise(X))=>(~funny(X)&~wise(X))))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:((~old(X)<~>curious(X))))&
(~generous(fred))&
(?[X]:((quiet(X)<~>~happy(X))))&
((old(paul)<~>~creative(paul)))&
(~curious(mary)) | strong(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9181472983498977210583932
% SZS output start Proof for 9181472983498977210583932
13. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~happy(X0) & happy(X0))) [input p12]
23. ~strong(mary) [input hypothesis]
55. ! [X0] : (((~strong(X0) | quiet(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 13]
56. ! [X0] : ((~strong(X0) | quiet(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 55]
113. happy(X0) | strong(X0) [cnf transformation 56]
115. ~happy(X0) | strong(X0) [cnf transformation 56]
136. ~strong(mary) [cnf transformation 23]
203. strong(X0) [subsumption resolution 113,115]
243. $false [subsumption resolution 136,203]
% SZS output end Proof for 9181472983498977210583932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is both tall and not kind.
If someone is both not funny and old then someone is not calm or not rich and vice versa.
Everyone who is both not calm and funny is rich or generous.
If someone is both not wise and not curious then lucy is not wise or not strong and vice versa.
If mary is patient then susan is both humble and not calm and vice versa.
If paul is not strong then someone is either kind or tall and vice versa.
Everyone who is tall is not old and vice versa.
Everyone who is both not creative and humble is tall and vice versa.
If someone is not patient then someone is either creative or tall and vice versa.
If someone is both calm and generous then someone is either generous or strong.
Everyone who is either not patient or wise is calm and vice versa.
Everyone who is not calm is not strong.
Everyone who is not happy or patient is either curious or not generous and vice versa.
Everyone who is not creative is curious or not old.
Everyone who is not generous or not brave is both not happy and not kind.
If someone is either humble or generous then someone is both kind and not wise and vice versa.
Mary is old or not quiet.
Paul is either happy or curious.
Someone is either humble or not kind.
Paul is either not generous or old.
Someone is not brave or not strong.
Mary is both not old and not patient. | Paul is not kind. | entailment | (![X]:((wise(X)|~strong(X))=>(tall(X)&~kind(X))))&
((?[X]:((~funny(X)&old(X))))<=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~calm(X)&funny(X))=>(rich(X)|generous(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>((~wise(lucy)|~strong(lucy))))&
((patient(mary))<=>((humble(susan)&~calm(susan))))&
((~strong(paul))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:(tall(X)<=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>tall(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((calm(X)&generous(X))))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>wise(X))<=>calm(X)))&
(![X]:(~calm(X)=>~strong(X)))&
(![X]:((~happy(X)|patient(X))<=>(curious(X)<~>~generous(X))))&
(![X]:(~creative(X)=>(curious(X)|~old(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~kind(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
((old(mary)|~quiet(mary)))&
((happy(paul)<~>curious(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~generous(paul)<~>old(paul)))&
(?[X]:((~brave(X)|~strong(X))))&
((~old(mary)&~patient(mary))) | ~kind(paul) | [
"p0",
"p5",
"p6",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1969923929709974425404995
% SZS output start Proof for 1969923929709974425404995
1. ! [X0] : ((~strong(X0) | wise(X0)) => (~kind(X0) & tall(X0))) [input p0]
6. ~strong(paul) <=> ? [X0] : (kind(X0) <~> tall(X0)) [input p5]
7. ! [X0] : (tall(X0) <=> ~old(X0)) [input p6]
15. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~kind(X0) & ~happy(X0))) [input p14]
20. ~generous(paul) <~> old(paul) [input p19]
23. kind(paul) [input hypothesis]
29. ! [X0] : ((~kind(X0) & tall(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 1]
36. ! [X0] : ((~kind(X0) & ~happy(X0)) | (brave(X0) & generous(X0))) [ennf transformation 15]
49. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X0] : ((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | strong(paul)) [nnf transformation 6]
50. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) | strong(paul)) [rectify 49]
51. ? [X1] : ((~tall(X1) | ~kind(X1)) & (tall(X1) | kind(X1))) => ((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) [choice axiom]
52. (~strong(paul) | ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) & (((~tall(sK3) | ~kind(sK3)) & (tall(sK3) | kind(sK3))) | strong(paul)) [skolemisation 50,51]
53. ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 7]
77. (~old(paul) | generous(paul)) & (old(paul) | ~generous(paul)) [nnf transformation 20]
83. ~kind(X0) | strong(X0) [cnf transformation 29]
100. ~strong(paul) | tall(X0) | ~kind(X0) [cnf transformation 52]
102. ~old(X0) | ~tall(X0) [cnf transformation 53]
127. ~kind(X0) | generous(X0) [cnf transformation 36]
139. old(paul) | ~generous(paul) [cnf transformation 77]
144. kind(paul) [cnf transformation 23]
218. 17 <=> strong(paul) [avatar definition]
223. 18 <=> ! [X0] : (tall(X0) | ~kind(X0)) [avatar definition]
224. ~kind(X0) | tall(X0) <- (18) [avatar component clause 223]
225. 18 | ~17 [avatar split clause 100,218,223]
329. 41 <=> generous(paul) [avatar definition]
333. 42 <=> old(paul) [avatar definition]
334. old(paul) <- (42) [avatar component clause 333]
337. ~41 | 42 [avatar split clause 139,333,329]
359. strong(paul) [resolution 83,144]
362. 17 [avatar split clause 359,218]
380. generous(paul) [resolution 127,144]
383. 41 [avatar split clause 380,329]
384. ~tall(paul) <- (42) [resolution 334,102]
398. tall(paul) <- (18) [resolution 224,144]
400. $false <- (18, 42) [subsumption resolution 398,384]
401. ~18 | ~42 [avatar contradiction clause 400]
402. $false [avatar sat refutation 225,337,362,383,401]
% SZS output end Proof for 1969923929709974425404995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not rich is both not tall and not old.
Everyone who is not quiet is not curious or humble and vice versa.
Everyone who is either patient or not patient is both rich and wise and vice versa.
Everyone who is either not strong or not rich is not kind or not funny and vice versa.
If someone is quiet then someone is either patient or not wise and vice versa.
Everyone who is both wise and calm is either old or not patient and vice versa.
If fred is either quiet or happy then lucy is both humble and creative.
If someone is either strong or rich then someone is not funny and vice versa.
If someone is not humble then someone is not quiet.
Everyone who is brave or wise is both old and not funny and vice versa.
Everyone who is both not old and wise is both wise and quiet.
Everyone who is curious is wise.
Everyone who is both tall and funny is either not strong or not humble.
If someone is either not patient or wise then fred is either not strong or wise.
If paul is either not generous or rich then fred is generous and vice versa.
If paul is both kind and strong then someone is either not brave or brave.
Someone is both tall and rich.
Susan is not curious.
Mary is both not funny and creative.
Susan is either brave or not strong.
Someone is not strong or not generous.
Someone is not funny.
Someone is both not calm and not patient.
Mary is not strong. | Susan is not calm. | entailment | (![X]:((generous(X)&~rich(X))=>(~tall(X)&~old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|humble(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(rich(X)&wise(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~kind(X)|~funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((patient(X)<~>~wise(X)))))&
(![X]:((wise(X)&calm(X))<=>(old(X)<~>~patient(X))))&
(((quiet(fred)<~>happy(fred)))=>((humble(lucy)&creative(lucy))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:(~funny(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|wise(X))<=>(old(X)&~funny(X))))&
(![X]:((~old(X)&wise(X))=>(wise(X)&quiet(X))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((tall(X)&funny(X))=>(~strong(X)<~>~humble(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>((~strong(fred)<~>wise(fred))))&
(((~generous(paul)<~>rich(paul)))<=>(generous(fred)))&
(((kind(paul)&strong(paul)))=>(?[X]:((~brave(X)<~>brave(X)))))&
(?[X]:((tall(X)&rich(X))))&
(~curious(susan))&
((~funny(mary)&creative(mary)))&
((brave(susan)<~>~strong(susan)))&
(?[X]:((~strong(X)|~generous(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(~strong(mary)) | ~calm(susan) | [
"p2",
"p3",
"p5",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6303359759926624519327778
% SZS output start Proof for 6303359759926624519327778
3. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (wise(X0) & rich(X0))) [input p2]
4. ! [X0] : ((~strong(X0) <~> ~rich(X0)) <=> (~funny(X0) | ~kind(X0))) [input p3]
6. ! [X0] : ((calm(X0) & wise(X0)) <=> (old(X0) <~> ~patient(X0))) [input p5]
10. ! [X0] : ((wise(X0) | brave(X0)) <=> (~funny(X0) & old(X0))) [input p9]
14. ? [X0] : (~patient(X0) <~> wise(X0)) => (~strong(fred) <~> wise(fred)) [input p13]
25. calm(susan) [input hypothesis]
40. (~strong(fred) <~> wise(fred)) | ! [X0] : (~patient(X0) <=> wise(X0)) [ennf transformation 14]
45. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~wise(X0) | ~rich(X0))) & ((wise(X0) & rich(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 3]
46. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~wise(X0) | ~rich(X0)) & ((wise(X0) & rich(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 45]
47. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [nnf transformation 4]
48. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [flattening 47]
54. ! [X0] : (((calm(X0) & wise(X0)) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~calm(X0) | ~wise(X0)))) [nnf transformation 6]
55. ! [X0] : (((calm(X0) & wise(X0)) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ~calm(X0) | ~wise(X0))) [flattening 54]
65. ! [X0] : (((wise(X0) | brave(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 10]
66. ! [X0] : ((wise(X0) | brave(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 65]
68. ((~wise(fred) | strong(fred)) & (wise(fred) | ~strong(fred))) | ! [X0] : ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))) [nnf transformation 40]
87. rich(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
88. rich(X0) | patient(X0) | patient(X0) [cnf transformation 46]
89. wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
90. wise(X0) | patient(X0) | patient(X0) [cnf transformation 46]
96. ~rich(X0) | ~strong(X0) | funny(X0) [cnf transformation 48]
104. patient(X0) | ~old(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 55]
117. old(X0) | ~wise(X0) [cnf transformation 66]
119. ~funny(X0) | ~wise(X0) [cnf transformation 66]
129. ~wise(fred) | strong(fred) | ~patient(X0) | ~wise(X0) [cnf transformation 68]
147. calm(susan) [cnf transformation 25]
148. rich(X0) | ~patient(X0) [duplicate literal removal 87]
149. patient(X0) | rich(X0) [duplicate literal removal 88]
150. wise(X0) | ~patient(X0) [duplicate literal removal 89]
151. wise(X0) | patient(X0) [duplicate literal removal 90]
152. wise(X0) [subsumption resolution 150,151]
153. rich(X0) [subsumption resolution 148,149]
154. ~strong(X0) | funny(X0) [subsumption resolution 96,153]
159. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (1) [avatar component clause 159]
175. ~calm(X0) | ~old(X0) | patient(X0) [subsumption resolution 104,152]
217. ~funny(X0) [subsumption resolution 119,152]
218. old(X0) [subsumption resolution 117,152]
219. strong(fred) | ~patient(X0) | ~wise(X0) [subsumption resolution 129,152]
220. strong(fred) | ~patient(X0) [subsumption resolution 219,152]
222. 14 <=> strong(fred) [avatar definition]
224. strong(fred) <- (14) [avatar component clause 222]
225. 1 | 14 [avatar split clause 220,222,159]
261. funny(fred) <- (14) [resolution 154,224]
262. $false <- (14) [subsumption resolution 261,217]
263. ~14 [avatar contradiction clause 262]
268. ~old(susan) | patient(susan) [resolution 175,147]
271. patient(susan) [subsumption resolution 268,218]
272. $false <- (1) [subsumption resolution 271,160]
273. ~1 [avatar contradiction clause 272]
274. $false [avatar sat refutation 225,263,273]
% SZS output end Proof for 6303359759926624519327778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not old or wise.
Everyone who is either funny or not happy is either not happy or not rich and vice versa.
Everyone who is strong is either not old or funny.
Everyone who is both not happy and not tall is either not generous or not calm and vice versa.
If someone is not old then paul is not tall.
Everyone who is both not quiet and not curious is both humble and curious and vice versa.
Everyone who is not patient is both humble and brave and vice versa.
Everyone who is old or not strong is generous and vice versa.
Everyone who is either calm or curious is generous.
Everyone who is not kind or strong is patient or not kind.
Everyone who is either not humble or humble is both not curious and not creative.
Everyone who is generous is not wise and vice versa.
Everyone who is both rich and brave is both happy and not wise and vice versa.
If someone is both not creative and happy then mary is both not brave and generous.
If lucy is either not happy or rich then paul is either generous or calm.
If someone is both wise and kind then mary is not creative or not happy.
Paul is both happy and not brave.
Someone is both not rich and brave.
Lucy is not happy.
Someone is strong.
Someone is rich.
Fred is either not brave or not old.
Someone is both strong and not kind. | Paul is wise. | entailment | (![X]:(~tall(X)=>(~old(X)|wise(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(strong(X)=>(~old(X)<~>funny(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~generous(X)<~>~calm(X))))&
((?[X]:(~old(X)))=>(~tall(paul)))&
(![X]:((~quiet(X)&~curious(X))<=>(humble(X)&curious(X))))&
(![X]:(~patient(X)<=>(humble(X)&brave(X))))&
(![X]:((old(X)|~strong(X))<=>generous(X)))&
(![X]:((calm(X)<~>curious(X))=>generous(X)))&
(![X]:((~kind(X)|strong(X))=>(patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>humble(X))=>(~curious(X)&~creative(X))))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:((rich(X)&brave(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~creative(X)&happy(X))))=>((~brave(mary)&generous(mary))))&
(((~happy(lucy)<~>rich(lucy)))=>((generous(paul)<~>calm(paul))))&
((?[X]:((wise(X)&kind(X))))=>((~creative(mary)|~happy(mary))))&
((happy(paul)&~brave(paul)))&
(?[X]:((~rich(X)&brave(X))))&
(~happy(lucy))&
(?[X]:(strong(X)))&
(?[X]:(rich(X)))&
((~brave(fred)<~>~old(fred)))&
(?[X]:((strong(X)&~kind(X)))) | wise(paul) | [
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8422722032316906040366513
% SZS output start Proof for 8422722032316906040366513
13. ! [X0] : ((brave(X0) & rich(X0)) <=> (~wise(X0) & happy(X0))) [input p12]
17. ~brave(paul) & happy(paul) [input p16]
24. ~wise(paul) [input hypothesis]
51. ! [X0] : (((brave(X0) & rich(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~brave(X0) | ~rich(X0)))) [nnf transformation 13]
52. ! [X0] : (((brave(X0) & rich(X0)) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ~brave(X0) | ~rich(X0))) [flattening 51]
102. ~happy(X0) | wise(X0) | brave(X0) [cnf transformation 52]
110. happy(paul) [cnf transformation 17]
111. ~brave(paul) [cnf transformation 17]
121. ~wise(paul) [cnf transformation 24]
296. wise(paul) | brave(paul) [resolution 102,110]
297. brave(paul) [subsumption resolution 296,121]
298. $false [subsumption resolution 297,111]
% SZS output end Proof for 8422722032316906040366513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not funny is either rich or tall and vice versa.
Everyone who is both not creative and happy is either kind or not old and vice versa.
Everyone who is happy is either not rich or not patient and vice versa.
If someone is both curious and not wise then john is either not old or not rich and vice versa.
If alice is both wise and not rich then someone is both not patient and happy.
Everyone who is both not humble and patient is not quiet or not strong and vice versa.
If lucy is not patient then someone is not humble and vice versa.
Everyone who is either tall or not kind is brave.
If alice is not quiet then someone is not funny or old.
If someone is both old and humble then mary is not creative and vice versa.
Everyone who is not generous or not happy is not calm or not funny.
Everyone who is happy or not wise is happy or quiet and vice versa.
Everyone who is either happy or creative is not curious.
Everyone who is both not tall and creative is either calm or not happy.
If lucy is both old and not curious then someone is tall or not strong.
If someone is both curious and not generous then john is both not funny and happy.
Someone is not old.
Fred is either not humble or not strong.
John is both kind and not humble.
Someone is not generous or brave.
Someone is either not curious or not old.
Someone is both not funny and not calm.
Someone is not humble.
Mary is both not tall and not strong. | Mary is humble. | contradiction | (![X]:((~strong(X)&~funny(X))<=>(rich(X)<~>tall(X))))&
(![X]:((~creative(X)&happy(X))<=>(kind(X)<~>~old(X))))&
(![X]:(happy(X)<=>(~rich(X)<~>~patient(X))))&
((?[X]:((curious(X)&~wise(X))))<=>((~old(john)<~>~rich(john))))&
(((wise(alice)&~rich(alice)))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:((~humble(X)&patient(X))<=>(~quiet(X)|~strong(X))))&
((~patient(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((tall(X)<~>~kind(X))=>brave(X)))&
((~quiet(alice))=>(?[X]:((~funny(X)|old(X)))))&
((?[X]:((old(X)&humble(X))))<=>(~creative(mary)))&
(![X]:((~generous(X)|~happy(X))=>(~calm(X)|~funny(X))))&
(![X]:((happy(X)|~wise(X))<=>(happy(X)|quiet(X))))&
(![X]:((happy(X)<~>creative(X))=>~curious(X)))&
(![X]:((~tall(X)&creative(X))=>(calm(X)<~>~happy(X))))&
(((old(lucy)&~curious(lucy)))=>(?[X]:((tall(X)|~strong(X)))))&
((?[X]:((curious(X)&~generous(X))))=>((~funny(john)&happy(john))))&
(?[X]:(~old(X)))&
((~humble(fred)<~>~strong(fred)))&
((kind(john)&~humble(john)))&
(?[X]:((~generous(X)|brave(X))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:(~humble(X)))&
((~tall(mary)&~strong(mary))) | humble(mary) | [
"p5",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6621619707520516975504292
% SZS output start Proof for 6621619707520516975504292
6. ! [X0] : ((patient(X0) & ~humble(X0)) <=> (~strong(X0) | ~quiet(X0))) [input p5]
24. ~strong(mary) & ~tall(mary) [input p23]
25. humble(mary) [input hypothesis]
51. ! [X0] : (((patient(X0) & ~humble(X0)) | (strong(X0) & quiet(X0))) & ((~strong(X0) | ~quiet(X0)) | (~patient(X0) | humble(X0)))) [nnf transformation 6]
52. ! [X0] : (((patient(X0) & ~humble(X0)) | (strong(X0) & quiet(X0))) & (~strong(X0) | ~quiet(X0) | ~patient(X0) | humble(X0))) [flattening 51]
105. ~humble(X0) | strong(X0) [cnf transformation 52]
135. ~strong(mary) [cnf transformation 24]
136. humble(mary) [cnf transformation 25]
255. strong(mary) [resolution 105,136]
257. $false [subsumption resolution 255,135]
% SZS output end Proof for 6621619707520516975504292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not calm is calm and vice versa.
Everyone who is calm is either not brave or brave and vice versa.
If paul is both not kind and not rich then someone is both calm and curious.
If paul is either not creative or not humble then mary is both not kind and brave and vice versa.
Everyone who is wise is both not happy and tall.
If alice is either old or rich then susan is not patient or strong.
Everyone who is rich or quiet is not rich or not humble.
Everyone who is not humble or not rich is either wise or not brave.
If lucy is either curious or calm then someone is either not brave or not humble.
If susan is either not patient or rich then someone is both not calm and not happy and vice versa.
Everyone who is either not happy or rich is not generous or not quiet and vice versa.
Everyone who is either wise or not brave is either rich or strong and vice versa.
If someone is not curious then mary is calm and vice versa.
Everyone who is either not quiet or wise is both wise and not kind and vice versa.
If someone is both not old and humble then lucy is not strong or rich.
If susan is humble or strong then susan is tall or not generous.
Lucy is either not humble or not wise.
Someone is not curious or not old.
Someone is not strong or not humble.
Someone is not old.
Someone is brave or happy.
Someone is either curious or not happy.
Alice is not old or not kind.
Someone is not rich or kind. | Lucy is not generous. | contradiction | (![X]:((generous(X)<~>~calm(X))<=>calm(X)))&
(![X]:(calm(X)<=>(~brave(X)<~>brave(X))))&
(((~kind(paul)&~rich(paul)))=>(?[X]:((calm(X)&curious(X)))))&
(((~creative(paul)<~>~humble(paul)))<=>((~kind(mary)&brave(mary))))&
(![X]:(wise(X)=>(~happy(X)&tall(X))))&
(((old(alice)<~>rich(alice)))=>((~patient(susan)|strong(susan))))&
(![X]:((rich(X)|quiet(X))=>(~rich(X)|~humble(X))))&
(![X]:((~humble(X)|~rich(X))=>(wise(X)<~>~brave(X))))&
(((curious(lucy)<~>calm(lucy)))=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((~patient(susan)<~>rich(susan)))<=>(?[X]:((~calm(X)&~happy(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(rich(X)<~>strong(X))))&
((?[X]:(~curious(X)))<=>(calm(mary)))&
(![X]:((~quiet(X)<~>wise(X))<=>(wise(X)&~kind(X))))&
((?[X]:((~old(X)&humble(X))))=>((~strong(lucy)|rich(lucy))))&
(((humble(susan)|strong(susan)))=>((tall(susan)|~generous(susan))))&
((~humble(lucy)<~>~wise(lucy)))&
(?[X]:((~curious(X)|~old(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)|happy(X))))&
(?[X]:((curious(X)<~>~happy(X))))&
((~old(alice)|~kind(alice)))&
(?[X]:((~rich(X)|kind(X)))) | ~generous(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3919999135315745404618736
% SZS output start Proof for 3919999135315745404618736
1. ! [X0] : ((generous(X0) <~> ~calm(X0)) <=> calm(X0)) [input p0]
25. ~generous(lucy) [input hypothesis]
39. ! [X0] : ((((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | ~calm(X0)) & (calm(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))))) [nnf transformation 1]
78. calm(X0) | generous(X0) | calm(X0) [cnf transformation 39]
79. ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 39]
145. ~generous(lucy) [cnf transformation 25]
151. calm(X0) | generous(X0) [duplicate literal removal 78]
152. ~calm(X0) | generous(X0) [duplicate literal removal 79]
153. generous(X0) [subsumption resolution 151,152]
316. $false [subsumption resolution 145,153]
% SZS output end Proof for 3919999135315745404618736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either happy or creative then alice is both not kind and patient and vice versa.
If someone is tall then alice is either not happy or not funny.
Everyone who is either not brave or calm is humble or quiet.
If someone is funny or not funny then someone is curious and vice versa.
If someone is not curious or happy then someone is both not quiet and not curious.
If lucy is either brave or creative then someone is not tall or rich and vice versa.
If someone is not wise then mary is generous or not funny and vice versa.
If lucy is not calm or not funny then alice is both calm and not tall and vice versa.
If someone is both strong and not quiet then someone is both not tall and not happy and vice versa.
If someone is not humble then someone is both not old and not rich.
If paul is quiet then someone is either creative or not kind and vice versa.
Everyone who is not rich or wise is generous and vice versa.
If someone is not wise then john is rich.
Everyone who is both rich and not strong is creative.
Everyone who is either not wise or not generous is not happy and vice versa.
Everyone who is both brave and not funny is wise and vice versa.
Lucy is not curious or wise.
Lucy is either not calm or curious.
Susan is tall.
Susan is both wise and not old.
Paul is both not patient and not rich.
Paul is both brave and not tall.
Susan is not wise or calm.
Someone is not old. | Alice is calm. | entailment | (((happy(fred)<~>creative(fred)))<=>((~kind(alice)&patient(alice))))&
((?[X]:(tall(X)))=>((~happy(alice)<~>~funny(alice))))&
(![X]:((~brave(X)<~>calm(X))=>(humble(X)|quiet(X))))&
((?[X]:((funny(X)|~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~curious(X)|happy(X))))=>(?[X]:((~quiet(X)&~curious(X)))))&
(((brave(lucy)<~>creative(lucy)))<=>(?[X]:((~tall(X)|rich(X)))))&
((?[X]:(~wise(X)))<=>((generous(mary)|~funny(mary))))&
(((~calm(lucy)|~funny(lucy)))<=>((calm(alice)&~tall(alice))))&
((?[X]:((strong(X)&~quiet(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&~rich(X)))))&
((quiet(paul))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~rich(X)|wise(X))<=>generous(X)))&
((?[X]:(~wise(X)))=>(rich(john)))&
(![X]:((rich(X)&~strong(X))=>creative(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>~happy(X)))&
(![X]:((brave(X)&~funny(X))<=>wise(X)))&
((~curious(lucy)|wise(lucy)))&
((~calm(lucy)<~>curious(lucy)))&
(tall(susan))&
((wise(susan)&~old(susan)))&
((~patient(paul)&~rich(paul)))&
((brave(paul)&~tall(paul)))&
((~wise(susan)|calm(susan)))&
(?[X]:(~old(X))) | calm(alice) | [
"p7",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7936294835111022519473481
% SZS output start Proof for 7936294835111022519473481
8. (~funny(lucy) | ~calm(lucy)) <=> (~tall(alice) & calm(alice)) [input p7]
16. ! [X0] : ((~funny(X0) & brave(X0)) <=> wise(X0)) [input p15]
17. wise(lucy) | ~curious(lucy) [input p16]
18. ~calm(lucy) <~> curious(lucy) [input p17]
25. ~calm(alice) [input hypothesis]
60. ((~funny(lucy) | ~calm(lucy)) | (tall(alice) | ~calm(alice))) & ((~tall(alice) & calm(alice)) | (funny(lucy) & calm(lucy))) [nnf transformation 8]
61. (~funny(lucy) | ~calm(lucy) | tall(alice) | ~calm(alice)) & ((~tall(alice) & calm(alice)) | (funny(lucy) & calm(lucy))) [flattening 60]
74. ! [X0] : (((~funny(X0) & brave(X0)) | ~wise(X0)) & (wise(X0) | (funny(X0) | ~brave(X0)))) [nnf transformation 16]
75. ! [X0] : (((~funny(X0) & brave(X0)) | ~wise(X0)) & (wise(X0) | funny(X0) | ~brave(X0))) [flattening 74]
76. (~curious(lucy) | calm(lucy)) & (curious(lucy) | ~calm(lucy)) [nnf transformation 18]
101. calm(alice) | calm(lucy) [cnf transformation 61]
102. calm(alice) | funny(lucy) [cnf transformation 61]
125. ~wise(X0) | ~funny(X0) [cnf transformation 75]
126. wise(lucy) | ~curious(lucy) [cnf transformation 17]
127. curious(lucy) | ~calm(lucy) [cnf transformation 76]
136. ~calm(alice) [cnf transformation 25]
249. 25 <=> calm(alice) [avatar definition]
257. 27 <=> calm(lucy) [avatar definition]
261. 28 <=> funny(lucy) [avatar definition]
262. funny(lucy) <- (28) [avatar component clause 261]
267. 28 | 25 [avatar split clause 102,249,261]
268. 27 | 25 [avatar split clause 101,249,257]
325. 41 <=> curious(lucy) [avatar definition]
329. 42 <=> wise(lucy) [avatar definition]
331. wise(lucy) <- (42) [avatar component clause 329]
332. ~41 | 42 [avatar split clause 126,329,325]
334. ~27 | 41 [avatar split clause 127,325,257]
336. ~25 [avatar split clause 136,249]
350. ~funny(lucy) <- (42) [resolution 125,331]
352. $false <- (28, 42) [subsumption resolution 350,262]
353. ~28 | ~42 [avatar contradiction clause 352]
354. $false [avatar sat refutation 267,268,332,334,336,353]
% SZS output end Proof for 7936294835111022519473481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or humble then alice is both funny and humble. Everyone who is either not brave or not kind is not creative or quiet and vice versa. Everyone who is creative is either not brave or curious. Everyone who is generous or patient is not patient or not kind and vice versa. Everyone who is both wise and not quiet is not brave or not quiet. Everyone who is either not curious or not rich is either kind or not generous and vice versa. Everyone who is either not calm or funny is both not happy and tall. Everyone who is not strong is both patient and old. Everyone who is either not wise or humble is both not old and humble and vice versa. Everyone who is both not rich and not kind is both wise and happy and vice versa. If susan is both old and tall then lucy is both not brave and brave and vice versa. Everyone who is either not old or patient is not old or not creative and vice versa. If someone is either curious or not wise then mary is both not old and not kind and vice versa. Everyone who is both not humble and old is wise or kind. Everyone who is either not kind or strong is both not wise and calm and vice versa. Everyone who is generous is both patient and funny. John is either humble or happy. Someone is not creative. Someone is happy. Mary is not creative or not brave. Someone is creative or not rich. Someone is quiet. Paul is not calm or not tall. Someone is both calm and curious. | Mary is kind. | contradiction | ((?[X]:((~old(X)<~>humble(X))))=>((funny(alice)&humble(alice))))&
(![X]:((~brave(X)<~>~kind(X))<=>(~creative(X)|quiet(X))))&
(![X]:(creative(X)=>(~brave(X)<~>curious(X))))&
(![X]:((generous(X)|patient(X))<=>(~patient(X)|~kind(X))))&
(![X]:((wise(X)&~quiet(X))=>(~brave(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~rich(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>funny(X))=>(~happy(X)&tall(X))))&
(![X]:(~strong(X)=>(patient(X)&old(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(~old(X)&humble(X))))&
(![X]:((~rich(X)&~kind(X))<=>(wise(X)&happy(X))))&
(((old(susan)&tall(susan)))<=>((~brave(lucy)&brave(lucy))))&
(![X]:((~old(X)<~>patient(X))<=>(~old(X)|~creative(X))))&
((?[X]:((curious(X)<~>~wise(X))))<=>((~old(mary)&~kind(mary))))&
(![X]:((~humble(X)&old(X))=>(wise(X)|kind(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(~wise(X)&calm(X))))&
(![X]:(generous(X)=>(patient(X)&funny(X))))&
((humble(john)<~>happy(john)))&
(?[X]:(~creative(X)))&
(?[X]:(happy(X)))&
((~creative(mary)|~brave(mary)))&
(?[X]:((creative(X)|~rich(X))))&
(?[X]:(quiet(X)))&
((~calm(paul)|~tall(paul)))&
(?[X]:((calm(X)&curious(X)))) | kind(mary) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1490880504976251542815846
% SZS output start Proof for 1490880504976251542815846
4. ! [X0] : ((patient(X0) | generous(X0)) <=> (~kind(X0) | ~patient(X0))) [input p3]
16. ! [X0] : (generous(X0) => (funny(X0) & patient(X0))) [input p15]
25. kind(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) & patient(X0)) | ~generous(X0)) [ennf transformation 16]
39. ! [X0] : (((patient(X0) | generous(X0)) | (kind(X0) & patient(X0))) & ((~kind(X0) | ~patient(X0)) | (~patient(X0) & ~generous(X0)))) [nnf transformation 4]
40. ! [X0] : ((patient(X0) | generous(X0) | (kind(X0) & patient(X0))) & (~kind(X0) | ~patient(X0) | (~patient(X0) & ~generous(X0)))) [flattening 39]
82. ~kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 40]
83. patient(X0) | generous(X0) | patient(X0) [cnf transformation 40]
133. patient(X0) | ~generous(X0) [cnf transformation 34]
145. kind(mary) [cnf transformation 25]
150. ~patient(X0) | ~kind(X0) [duplicate literal removal 82]
151. patient(X0) | generous(X0) [duplicate literal removal 83]
190. 9 <=> kind(mary) [avatar definition]
192. kind(mary) <- (9) [avatar component clause 190]
213. patient(X0) [subsumption resolution 133,151]
251. 9 [avatar split clause 145,190]
253. ~kind(X0) [resolution 150,213]
254. $false <- (9) [resolution 253,192]
255. ~9 [avatar contradiction clause 254]
256. $false [avatar sat refutation 251,255]
% SZS output end Proof for 1490880504976251542815846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and patient is either not calm or not wise and vice versa.
Everyone who is generous or wise is either calm or not rich.
If someone is not kind or not happy then mary is strong or not happy and vice versa.
Everyone who is either not humble or curious is not old or brave and vice versa.
Everyone who is both not rich and not wise is both brave and not wise.
Everyone who is not brave or rich is both strong and old.
If someone is both old and not humble then lucy is both not happy and not tall.
If paul is rich or not patient then susan is not generous or brave.
Everyone who is not calm is not patient.
Everyone who is both brave and funny is either rich or not tall and vice versa.
If someone is both not rich and strong then john is tall.
Everyone who is either not wise or not tall is rich.
Everyone who is both creative and not rich is both not tall and not funny and vice versa.
Everyone who is either not calm or humble is either calm or quiet and vice versa.
Everyone who is either tall or funny is rich or kind and vice versa.
If someone is not strong or not rich then john is either not wise or happy and vice versa.
Someone is either not happy or quiet.
Mary is both not curious and not old.
Lucy is either kind or happy.
Susan is either brave or not funny.
Fred is old or not humble.
Alice is either not patient or tall.
John is not old.
John is quiet. | Mary is not happy. | entailment | (![X]:((rich(X)&patient(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((generous(X)|wise(X))=>(calm(X)<~>~rich(X))))&
((?[X]:((~kind(X)|~happy(X))))<=>((strong(mary)|~happy(mary))))&
(![X]:((~humble(X)<~>curious(X))<=>(~old(X)|brave(X))))&
(![X]:((~rich(X)&~wise(X))=>(brave(X)&~wise(X))))&
(![X]:((~brave(X)|rich(X))=>(strong(X)&old(X))))&
((?[X]:((old(X)&~humble(X))))=>((~happy(lucy)&~tall(lucy))))&
(((rich(paul)|~patient(paul)))=>((~generous(susan)|brave(susan))))&
(![X]:(~calm(X)=>~patient(X)))&
(![X]:((brave(X)&funny(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((~rich(X)&strong(X))))=>(tall(john)))&
(![X]:((~wise(X)<~>~tall(X))=>rich(X)))&
(![X]:((creative(X)&~rich(X))<=>(~tall(X)&~funny(X))))&
(![X]:((~calm(X)<~>humble(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((tall(X)<~>funny(X))<=>(rich(X)|kind(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((~wise(john)<~>happy(john))))&
(?[X]:((~happy(X)<~>quiet(X))))&
((~curious(mary)&~old(mary)))&
((kind(lucy)<~>happy(lucy)))&
((brave(susan)<~>~funny(susan)))&
((old(fred)|~humble(fred)))&
((~patient(alice)<~>tall(alice)))&
(~old(john))&
(quiet(john)) | ~happy(mary) | [
"p0",
"p1",
"p2",
"p5",
"p9",
"p10",
"p11",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6743832314038708952972033
% SZS output start Proof for 6743832314038708952972033
1. ! [X0] : ((patient(X0) & rich(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p0]
2. ! [X0] : ((wise(X0) | generous(X0)) => (calm(X0) <~> ~rich(X0))) [input p1]
3. ? [X0] : (~happy(X0) | ~kind(X0)) <=> (~happy(mary) | strong(mary)) [input p2]
6. ! [X0] : ((rich(X0) | ~brave(X0)) => (old(X0) & strong(X0))) [input p5]
10. ! [X0] : ((funny(X0) & brave(X0)) <=> (rich(X0) <~> ~tall(X0))) [input p9]
11. ? [X0] : (strong(X0) & ~rich(X0)) => tall(john) [input p10]
12. ! [X0] : ((~wise(X0) <~> ~tall(X0)) => rich(X0)) [input p11]
15. ! [X0] : ((tall(X0) <~> funny(X0)) <=> (kind(X0) | rich(X0))) [input p14]
18. ~old(mary) & ~curious(mary) [input p17]
19. kind(lucy) <~> happy(lucy) [input p18]
25. happy(mary) [input hypothesis]
26. ! [X0] : (wise(X0) => (calm(X0) <~> ~rich(X0))) [pure predicate removal 2]
28. ! [X0] : ((calm(X0) <~> ~rich(X0)) | ~wise(X0)) [ennf transformation 26]
31. ! [X0] : ((old(X0) & strong(X0)) | (~rich(X0) & brave(X0))) [ennf transformation 6]
34. tall(john) | ! [X0] : (~strong(X0) | rich(X0)) [ennf transformation 11]
35. ! [X0] : (rich(X0) | (~wise(X0) <=> ~tall(X0))) [ennf transformation 12]
36. ! [X0] : (((patient(X0) & rich(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~patient(X0) | ~rich(X0)))) [nnf transformation 1]
37. ! [X0] : (((patient(X0) & rich(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ~patient(X0) | ~rich(X0))) [flattening 36]
38. ! [X0] : (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ~wise(X0)) [nnf transformation 28]
39. (? [X0] : (~happy(X0) | ~kind(X0)) | (happy(mary) & ~strong(mary))) & ((~happy(mary) | strong(mary)) | ! [X0] : (happy(X0) & kind(X0))) [nnf transformation 3]
40. (? [X0] : (~happy(X0) | ~kind(X0)) | (happy(mary) & ~strong(mary))) & (~happy(mary) | strong(mary) | ! [X0] : (happy(X0) & kind(X0))) [flattening 39]
41. (? [X0] : (~happy(X0) | ~kind(X0)) | (happy(mary) & ~strong(mary))) & (~happy(mary) | strong(mary) | ! [X1] : (happy(X1) & kind(X1))) [rectify 40]
42. ? [X0] : (~happy(X0) | ~kind(X0)) => (~happy(sK0) | ~kind(sK0)) [choice axiom]
43. ((~happy(sK0) | ~kind(sK0)) | (happy(mary) & ~strong(mary))) & (~happy(mary) | strong(mary) | ! [X1] : (happy(X1) & kind(X1))) [skolemisation 41,42]
46. ! [X0] : (((funny(X0) & brave(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | (~funny(X0) | ~brave(X0)))) [nnf transformation 10]
47. ! [X0] : (((funny(X0) & brave(X0)) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) & (((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ~funny(X0) | ~brave(X0))) [flattening 46]
48. ! [X0] : (rich(X0) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) [nnf transformation 35]
52. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 15]
53. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [flattening 52]
61. (~happy(lucy) | ~kind(lucy)) & (happy(lucy) | kind(lucy)) [nnf transformation 19]
66. rich(X0) | ~wise(X0) | calm(X0) [cnf transformation 37]
71. rich(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 38]
72. ~happy(mary) | strong(mary) | kind(X1) [cnf transformation 43]
73. ~happy(mary) | strong(mary) | happy(X1) [cnf transformation 43]
87. ~rich(X0) | old(X0) [cnf transformation 31]
95. funny(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 47]
97. tall(john) | ~strong(X0) | rich(X0) [cnf transformation 34]
98. rich(X0) | ~tall(X0) | wise(X0) [cnf transformation 48]
116. ~funny(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 53]
127. ~old(mary) [cnf transformation 18]
129. ~happy(lucy) | ~kind(lucy) [cnf transformation 61]
137. happy(mary) [cnf transformation 25]
142. ~wise(X0) | rich(X0) [subsumption resolution 71,66]
145. 1 <=> happy(mary) [avatar definition]
158. 4 <=> strong(mary) [avatar definition]
159. strong(mary) <- (4) [avatar component clause 158]
163. 5 <=> ! [X1] : happy(X1) [avatar definition]
164. happy(X1) <- (5) [avatar component clause 163]
165. 5 | 4 | ~1 [avatar split clause 73,145,158,163]
167. 6 <=> ! [X1] : kind(X1) [avatar definition]
168. kind(X1) <- (6) [avatar component clause 167]
169. 6 | 4 | ~1 [avatar split clause 72,145,158,167]
180. 9 <=> happy(lucy) [avatar definition]
182. ~happy(lucy) <- (~9) [avatar component clause 180]
187. 10 <=> ! [X0] : (~strong(X0) | rich(X0)) [avatar definition]
188. ~strong(X0) | rich(X0) <- (10) [avatar component clause 187]
190. 11 <=> tall(john) [avatar definition]
192. tall(john) <- (11) [avatar component clause 190]
193. 10 | 11 [avatar split clause 97,190,187]
194. rich(X0) | ~tall(X0) [subsumption resolution 98,142]
198. ~tall(X0) | ~rich(X0) [subsumption resolution 116,95]
199. ~tall(X0) [subsumption resolution 198,194]
238. 19 <=> kind(lucy) [avatar definition]
240. ~kind(lucy) <- (~19) [avatar component clause 238]
241. ~19 | ~9 [avatar split clause 129,180,238]
263. 1 [avatar split clause 137,145]
270. rich(mary) <- (4, 10) [resolution 188,159]
272. old(mary) <- (4, 10) [resolution 270,87]
274. $false <- (4, 10) [subsumption resolution 272,127]
275. ~4 | ~10 [avatar contradiction clause 274]
282. $false <- (11) [subsumption resolution 192,199]
283. ~11 [avatar contradiction clause 282]
284. $false <- (6, ~19) [resolution 168,240]
285. ~6 | 19 [avatar contradiction clause 284]
286. $false <- (5, ~9) [subsumption resolution 182,164]
287. ~5 | 9 [avatar contradiction clause 286]
288. $false [avatar sat refutation 165,169,193,241,263,275,283,285,287]
% SZS output end Proof for 6743832314038708952972033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is either wise or creative.
If alice is not brave or not kind then someone is not old or calm.
Everyone who is not kind is wise or not brave.
If mary is either not strong or not humble then mary is not generous or creative.
Everyone who is both not patient and old is not humble.
Everyone who is both brave and not quiet is calm and vice versa.
Everyone who is quiet or not curious is rich.
If someone is either wise or calm then someone is both not funny and not happy.
Everyone who is not humble is either calm or brave and vice versa.
Everyone who is not calm or calm is not strong or not wise.
Everyone who is both rich and happy is both not happy and not kind.
If john is both not brave and not strong then mary is both not rich and quiet.
If mary is not patient or not generous then someone is both not calm and not funny.
Everyone who is either humble or patient is not calm or patient and vice versa.
Everyone who is either not wise or not patient is both not humble and not tall and vice versa.
If someone is either not curious or calm then john is both not creative and calm.
Someone is curious.
Someone is either generous or old.
Mary is both not patient and not happy.
Fred is not funny or curious.
Someone is not generous.
Fred is either generous or not brave.
Someone is either not happy or brave.
Someone is either kind or not happy. | Alice is not curious. | contradiction | (![X]:(humble(X)=>(wise(X)<~>creative(X))))&
(((~brave(alice)|~kind(alice)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:(~kind(X)=>(wise(X)|~brave(X))))&
(((~strong(mary)<~>~humble(mary)))=>((~generous(mary)|creative(mary))))&
(![X]:((~patient(X)&old(X))=>~humble(X)))&
(![X]:((brave(X)&~quiet(X))<=>calm(X)))&
(![X]:((quiet(X)|~curious(X))=>rich(X)))&
((?[X]:((wise(X)<~>calm(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(~humble(X)<=>(calm(X)<~>brave(X))))&
(![X]:((~calm(X)|calm(X))=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&happy(X))=>(~happy(X)&~kind(X))))&
(((~brave(john)&~strong(john)))=>((~rich(mary)&quiet(mary))))&
(((~patient(mary)|~generous(mary)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((humble(X)<~>patient(X))<=>(~calm(X)|patient(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~humble(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))=>((~creative(john)&calm(john))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>old(X))))&
((~patient(mary)&~happy(mary)))&
((~funny(fred)|curious(fred)))&
(?[X]:(~generous(X)))&
((generous(fred)<~>~brave(fred)))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | ~curious(alice) | [
"p5",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 512752619205733966919911
% SZS output start Proof for 512752619205733966919911
6. ! [X0] : ((~quiet(X0) & brave(X0)) <=> calm(X0)) [input p5]
9. ! [X0] : (~humble(X0) <=> (calm(X0) <~> brave(X0))) [input p8]
14. ! [X0] : ((humble(X0) <~> patient(X0)) <=> (patient(X0) | ~calm(X0))) [input p13]
16. ? [X0] : (~curious(X0) <~> calm(X0)) => (calm(john) & ~creative(john)) [input p15]
25. ~curious(alice) [input hypothesis]
47. (calm(john) & ~creative(john)) | ! [X0] : (~curious(X0) <=> calm(X0)) [ennf transformation 16]
52. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | ~brave(X0)))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | ~brave(X0))) [flattening 52]
58. ! [X0] : ((~humble(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | humble(X0))) [nnf transformation 9]
61. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [flattening 61]
65. (calm(john) & ~creative(john)) | ! [X0] : ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0))) [nnf transformation 47]
89. brave(X0) | ~calm(X0) [cnf transformation 53]
96. ~brave(X0) | ~calm(X0) | humble(X0) [cnf transformation 58]
107. patient(X0) | ~calm(X0) | patient(X0) | ~humble(X0) [cnf transformation 62]
112. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 62]
121. calm(john) | calm(X0) | curious(X0) [cnf transformation 65]
135. ~curious(alice) [cnf transformation 25]
136. patient(X0) | ~calm(X0) | ~humble(X0) [duplicate literal removal 107]
137. ~patient(X0) | ~humble(X0) [duplicate literal removal 112]
187. ~calm(X0) | humble(X0) [subsumption resolution 96,89]
219. ~calm(X0) | ~humble(X0) [subsumption resolution 136,137]
220. ~calm(X0) [subsumption resolution 219,187]
223. calm(X0) | curious(X0) [subsumption resolution 121,220]
224. curious(X0) [subsumption resolution 223,220]
266. $false [subsumption resolution 135,224]
% SZS output end Proof for 512752619205733966919911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and old then lucy is both not curious and not kind.
If someone is old or brave then fred is not patient and vice versa.
Everyone who is either brave or not generous is quiet or old.
Everyone who is not patient or humble is not tall and vice versa.
If someone is not happy then mary is not happy.
Everyone who is generous or rich is either curious or not funny.
Everyone who is both not happy and happy is quiet or not curious and vice versa.
If alice is not wise or not rich then susan is either calm or not quiet and vice versa.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
If lucy is both calm and tall then someone is not generous and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
If someone is creative or humble then lucy is not calm.
Fred is not calm.
Someone is either not creative or not curious.
Someone is not kind or not creative.
John is curious.
Someone is both wise and happy.
Alice is either tall or funny. | Mary is generous. | entailment | (((~rich(lucy)&old(lucy)))=>((~curious(lucy)&~kind(lucy))))&
((?[X]:((old(X)|brave(X))))<=>(~patient(fred)))&
(![X]:((brave(X)<~>~generous(X))=>(quiet(X)|old(X))))&
(![X]:((~patient(X)|humble(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(~happy(mary)))&
(![X]:((generous(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))<=>(quiet(X)|~curious(X))))&
(((~wise(alice)|~rich(alice)))<=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
((?[X]:((creative(X)|humble(X))))=>(~calm(lucy)))&
(~calm(fred))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(curious(john))&
(?[X]:((wise(X)&happy(X))))&
((tall(alice)<~>funny(alice))) | generous(mary) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8461479184382551600822318
% SZS output start Proof for 8461479184382551600822318
2. ? [X0] : (brave(X0) | old(X0)) <=> ~patient(fred) [input p1]
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (old(X0) | quiet(X0))) [input p2]
4. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~tall(X0)) [input p3]
7. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~curious(X0) | quiet(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p9]
12. (tall(lucy) & calm(lucy)) <=> ? [X0] : ~generous(X0) [input p11]
13. ! [X0] : (kind(X0) => patient(X0)) [input p12]
15. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p14]
16. ? [X0] : (humble(X0) | creative(X0)) => ~calm(lucy) [input p15]
23. ~generous(mary) [input hypothesis]
26. ! [X0] : ((old(X0) | quiet(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
27. ! [X0] : (old(X0) | quiet(X0) | (brave(X0) <=> ~generous(X0))) [flattening 26]
32. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 13]
35. ~calm(lucy) | ! [X0] : (~humble(X0) & ~creative(X0)) [ennf transformation 16]
36. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (~brave(X0) & ~old(X0))) [nnf transformation 2]
37. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [rectify 36]
38. ? [X0] : (brave(X0) | old(X0)) => (brave(sK0) | old(sK0)) [choice axiom]
39. ((brave(sK0) | old(sK0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [skolemisation 37,38]
40. ! [X0] : (old(X0) | quiet(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 27]
41. ! [X0] : (((humble(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [flattening 41]
44. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 7]
45. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~happy(X0) | happy(X0))) [flattening 44]
49. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 10]
52. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (~tall(lucy) | ~calm(lucy))) [nnf transformation 12]
53. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~tall(lucy) | ~calm(lucy)) [flattening 52]
54. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~tall(lucy) | ~calm(lucy)) [rectify 53]
55. ? [X1] : ~generous(X1) => ~generous(sK1) [choice axiom]
56. ((tall(lucy) & calm(lucy)) | ! [X0] : generous(X0)) & (~generous(sK1) | ~tall(lucy) | ~calm(lucy)) [skolemisation 54,55]
57. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 15]
68. ~patient(fred) | ~old(X1) [cnf transformation 39]
69. ~patient(fred) | ~brave(X1) [cnf transformation 39]
72. quiet(X0) | old(X0) | brave(X0) | generous(X0) [cnf transformation 40]
73. ~tall(X0) | patient(X0) [cnf transformation 42]
75. ~patient(X0) | humble(X0) | tall(X0) [cnf transformation 42]
82. ~happy(X0) | ~quiet(X0) [cnf transformation 45]
84. ~quiet(X0) | happy(X0) [cnf transformation 45]
96. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
97. ~generous(X0) | ~tall(X0) | quiet(X0) [cnf transformation 49]
105. calm(lucy) | generous(X0) [cnf transformation 56]
107. ~kind(X0) | patient(X0) [cnf transformation 32]
110. ~generous(X0) | kind(X0) [cnf transformation 57]
112. ~calm(lucy) | ~humble(X0) [cnf transformation 35]
122. ~generous(mary) [cnf transformation 23]
142. 5 <=> patient(fred) [avatar definition]
143. ~patient(fred) <- (~5) [avatar component clause 142]
155. 8 <=> ! [X1] : ~brave(X1) [avatar definition]
156. ~brave(X1) <- (8) [avatar component clause 155]
157. 8 | ~5 [avatar split clause 69,142,155]
159. 9 <=> ! [X1] : ~old(X1) [avatar definition]
160. ~old(X1) <- (9) [avatar component clause 159]
161. 9 | ~5 [avatar split clause 68,142,159]
171. ~quiet(X0) [subsumption resolution 82,84]
190. ~tall(X0) | ~generous(X0) [subsumption resolution 97,171]
191. tall(X0) | generous(X0) [subsumption resolution 96,171]
193. 15 <=> ! [X0] : generous(X0) [avatar definition]
194. generous(X0) <- (15) [avatar component clause 193]
201. 17 <=> calm(lucy) [avatar definition]
204. 15 | 17 [avatar split clause 105,201,193]
220. 21 <=> ! [X0] : ~humble(X0) [avatar definition]
221. ~humble(X0) <- (21) [avatar component clause 220]
222. 21 | ~17 [avatar split clause 112,201,220]
247. $false <- (15) [resolution 194,122]
248. ~15 [avatar contradiction clause 247]
258. generous(X2) | patient(X2) [resolution 191,73]
261. patient(X0) | kind(X0) [resolution 258,110]
266. patient(X0) [subsumption resolution 261,107]
267. $false <- (~5) [resolution 266,143]
268. humble(X0) | tall(X0) [resolution 266,75]
269. 5 [avatar contradiction clause 267]
270. tall(X0) <- (21) [subsumption resolution 268,221]
273. ~generous(X0) <- (21) [resolution 270,190]
291. old(X1) | brave(X1) | generous(X1) [resolution 72,171]
296. brave(X1) | generous(X1) <- (9) [subsumption resolution 291,160]
297. generous(X1) <- (8, 9) [subsumption resolution 296,156]
298. $false <- (8, 9, 21) [subsumption resolution 297,273]
299. ~8 | ~9 | ~21 [avatar contradiction clause 298]
300. $false [avatar sat refutation 157,161,204,222,248,269,299]
% SZS output end Proof for 8461479184382551600822318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not wise is both not generous and quiet. If john is not calm or rich then someone is not patient. If mary is not happy then someone is kind or quiet and vice versa. If someone is calm then someone is not wise. Everyone who is not calm or not creative is funny or not funny and vice versa. If someone is both not quiet and not funny then someone is both wise and not old. Everyone who is both patient and strong is either not tall or not happy. Everyone who is generous is not strong or creative and vice versa. Everyone who is not brave is not curious or not creative. Everyone who is both tall and not generous is not wise and vice versa. Everyone who is either quiet or calm is both not happy and not patient. If someone is tall or not creative then someone is both not wise and not curious and vice versa. Everyone who is humble or not tall is not patient. Everyone who is both not quiet and funny is old and vice versa. Everyone who is kind is either strong or kind and vice versa. Everyone who is not calm or not tall is either old or not quiet. Someone is not quiet. Someone is either not humble or not curious. Mary is not humble or not brave. | John is not kind. | neutral | (![X]:((humble(X)<~>~wise(X))=>(~generous(X)&quiet(X))))&
(((~calm(john)|rich(john)))=>(?[X]:(~patient(X))))&
((~happy(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
((?[X]:(calm(X)))=>(?[X]:(~wise(X))))&
(![X]:((~calm(X)|~creative(X))<=>(funny(X)|~funny(X))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((patient(X)&strong(X))=>(~tall(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(~strong(X)|creative(X))))&
(![X]:(~brave(X)=>(~curious(X)|~creative(X))))&
(![X]:((tall(X)&~generous(X))<=>~wise(X)))&
(![X]:((quiet(X)<~>calm(X))=>(~happy(X)&~patient(X))))&
((?[X]:((tall(X)|~creative(X))))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((humble(X)|~tall(X))=>~patient(X)))&
(![X]:((~quiet(X)&funny(X))<=>old(X)))&
(![X]:(kind(X)<=>(strong(X)<~>kind(X))))&
(![X]:((~calm(X)|~tall(X))=>(old(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~humble(X)<~>~curious(X))))&
((~humble(mary)|~brave(mary))) | ~kind(john) | [] | null | 0 |
If someone is either not curious or not funny then someone is not creative and vice versa.
If fred is not creative then mary is either curious or not happy and vice versa.
Everyone who is humble is both not generous and kind.
Everyone who is not humble is either generous or tall and vice versa.
Everyone who is either not creative or not old is either not funny or not generous.
If lucy is either not wise or not creative then someone is both curious and not creative and vice versa.
Everyone who is either not funny or generous is both not patient and not creative.
If mary is not happy then someone is both funny and wise and vice versa.
If lucy is either not humble or not brave then lucy is either not quiet or tall and vice versa.
If someone is not patient then someone is humble or not patient.
If someone is not wise then someone is either not generous or old.
Everyone who is calm is quiet.
Everyone who is curious is either not generous or strong.
If someone is both not brave and calm then someone is both not curious and curious.
Everyone who is either not happy or tall is either not funny or generous and vice versa.
If fred is not patient or not old then someone is either tall or humble and vice versa.
Someone is both not wise and strong.
Someone is both not tall and brave.
Susan is not brave.
Someone is both humble and not generous.
Alice is both humble and not curious.
Susan is both creative and not kind.
Lucy is either happy or strong. | Fred is not patient. | neutral | ((?[X]:((~curious(X)<~>~funny(X))))<=>(?[X]:(~creative(X))))&
((~creative(fred))<=>((curious(mary)<~>~happy(mary))))&
(![X]:(humble(X)=>(~generous(X)&kind(X))))&
(![X]:(~humble(X)<=>(generous(X)<~>tall(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~funny(X)<~>~generous(X))))&
(((~wise(lucy)<~>~creative(lucy)))<=>(?[X]:((curious(X)&~creative(X)))))&
(![X]:((~funny(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
((~happy(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(((~humble(lucy)<~>~brave(lucy)))<=>((~quiet(lucy)<~>tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:(calm(X)=>quiet(X)))&
(![X]:(curious(X)=>(~generous(X)<~>strong(X))))&
((?[X]:((~brave(X)&calm(X))))=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(~funny(X)<~>generous(X))))&
(((~patient(fred)|~old(fred)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((~tall(X)&brave(X))))&
(~brave(susan))&
(?[X]:((humble(X)&~generous(X))))&
((humble(alice)&~curious(alice)))&
((creative(susan)&~kind(susan)))&
((happy(lucy)<~>strong(lucy))) | ~patient(fred) | [] | null | 0 |
If paul is not curious then lucy is not strong.
If someone is either not curious or not happy then paul is both not tall and tall and vice versa.
If alice is not funny or not quiet then mary is either happy or brave and vice versa.
If someone is creative then paul is both not old and kind and vice versa.
Everyone who is brave is either not creative or brave and vice versa.
Everyone who is both not brave and not kind is not funny.
Everyone who is either not tall or not brave is strong or not creative.
If alice is quiet or funny then someone is either not quiet or quiet and vice versa.
Everyone who is both creative and funny is calm.
Everyone who is humble or quiet is both not creative and not rich.
If someone is either old or not creative then someone is either strong or not tall and vice versa.
Everyone who is either tall or not quiet is either humble or generous and vice versa.
Everyone who is both not humble and old is both not quiet and curious and vice versa.
Everyone who is not brave is not happy.
Fred is not happy or not wise.
Someone is both not strong and not curious.
Someone is not quiet or rich.
John is both not kind and patient.
Lucy is not creative or tall.
Someone is either kind or not happy.
Someone is either old or not brave.
Paul is either happy or not humble. | Paul is not creative. | contradiction | ((~curious(paul))=>(~strong(lucy)))&
((?[X]:((~curious(X)<~>~happy(X))))<=>((~tall(paul)&tall(paul))))&
(((~funny(alice)|~quiet(alice)))<=>((happy(mary)<~>brave(mary))))&
((?[X]:(creative(X)))<=>((~old(paul)&kind(paul))))&
(![X]:(brave(X)<=>(~creative(X)<~>brave(X))))&
(![X]:((~brave(X)&~kind(X))=>~funny(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
((~happy(fred)|~wise(fred)))&
(?[X]:((~strong(X)&~curious(X))))&
(?[X]:((~quiet(X)|rich(X))))&
((~kind(john)&patient(john)))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul))) | ~creative(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1456915369662874196606088
% SZS output start Proof for 1456915369662874196606088
5. ! [X0] : (brave(X0) <=> (~creative(X0) <~> brave(X0))) [input p4]
23. ~creative(paul) [input hypothesis]
47. ! [X0] : ((brave(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ~brave(X0))) [nnf transformation 5]
90. ~brave(X0) | creative(X0) | ~brave(X0) [cnf transformation 47]
91. brave(X0) | brave(X0) | creative(X0) [cnf transformation 47]
138. ~creative(paul) [cnf transformation 23]
141. ~brave(X0) | creative(X0) [duplicate literal removal 90]
142. brave(X0) | creative(X0) [duplicate literal removal 91]
206. creative(X0) [subsumption resolution 141,142]
278. $false [subsumption resolution 138,206]
% SZS output end Proof for 1456915369662874196606088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or wise is funny or generous and vice versa.
Everyone who is generous or kind is curious.
Everyone who is either not old or not generous is either not patient or generous.
If someone is rich then lucy is not rich or not generous.
Everyone who is either not kind or not patient is both not generous and wise and vice versa.
If mary is not funny or strong then paul is not curious.
If someone is both not funny and not brave then mary is not funny and vice versa.
If susan is either not old or not tall then someone is both brave and not calm and vice versa.
If mary is both not curious and not wise then someone is generous and vice versa.
Everyone who is not happy is both not patient and not generous and vice versa.
Everyone who is either happy or not calm is both kind and curious.
If paul is quiet then someone is either creative or humble.
Everyone who is not creative is not calm and vice versa.
Everyone who is calm or not tall is both funny and wise.
If someone is quiet then susan is both not creative and patient and vice versa.
Someone is brave or calm.
Someone is curious or kind.
Someone is strong.
Someone is kind.
Lucy is not generous or quiet.
Someone is not curious or generous. | Susan is old. | contradiction | (![X]:((~patient(X)<~>wise(X))<=>(funny(X)|generous(X))))&
(![X]:((generous(X)|kind(X))=>curious(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~patient(X)<~>generous(X))))&
((?[X]:(rich(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~generous(X)&wise(X))))&
(((~funny(mary)|strong(mary)))=>(~curious(paul)))&
((?[X]:((~funny(X)&~brave(X))))<=>(~funny(mary)))&
(((~old(susan)<~>~tall(susan)))<=>(?[X]:((brave(X)&~calm(X)))))&
(((~curious(mary)&~wise(mary)))<=>(?[X]:(generous(X))))&
(![X]:(~happy(X)<=>(~patient(X)&~generous(X))))&
(![X]:((happy(X)<~>~calm(X))=>(kind(X)&curious(X))))&
((quiet(paul))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:(~creative(X)<=>~calm(X)))&
(![X]:((calm(X)|~tall(X))=>(funny(X)&wise(X))))&
((?[X]:(quiet(X)))<=>((~creative(susan)&patient(susan))))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
((~generous(lucy)|quiet(lucy)))&
(?[X]:((~curious(X)|generous(X)))) | old(susan) | [
"p0",
"p1",
"p2",
"p4",
"p7",
"p8",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 438392241724535328930078
% SZS output start Proof for 438392241724535328930078
1. ! [X0] : ((~patient(X0) <~> wise(X0)) <=> (generous(X0) | funny(X0))) [input p0]
2. ! [X0] : ((kind(X0) | generous(X0)) => curious(X0)) [input p1]
3. ! [X0] : ((~old(X0) <~> ~generous(X0)) => (~patient(X0) <~> generous(X0))) [input p2]
5. ! [X0] : ((~kind(X0) <~> ~patient(X0)) <=> (wise(X0) & ~generous(X0))) [input p4]
8. (~old(susan) <~> ~tall(susan)) <=> ? [X0] : (~calm(X0) & brave(X0)) [input p7]
9. (~wise(mary) & ~curious(mary)) <=> ? [X0] : generous(X0) [input p8]
10. ! [X0] : (~happy(X0) <=> (~generous(X0) & ~patient(X0))) [input p9]
11. ! [X0] : ((happy(X0) <~> ~calm(X0)) => (curious(X0) & kind(X0))) [input p10]
14. ! [X0] : ((~tall(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p13]
16. ? [X0] : (calm(X0) | brave(X0)) [input p15]
22. old(susan) [input hypothesis]
24. ! [X0] : (curious(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 2]
25. ! [X0] : ((~patient(X0) <~> generous(X0)) | (~old(X0) <=> ~generous(X0))) [ennf transformation 3]
27. ! [X0] : ((curious(X0) & kind(X0)) | (happy(X0) <=> ~calm(X0))) [ennf transformation 11]
29. ! [X0] : ((wise(X0) & funny(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 14]
30. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [nnf transformation 1]
31. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [flattening 30]
32. ! [X0] : (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0)))) [nnf transformation 25]
33. ! [X0] : ((((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~wise(X0) | generous(X0))) & ((wise(X0) & ~generous(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))))) [nnf transformation 5]
34. ! [X0] : ((((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~wise(X0) | generous(X0)) & ((wise(X0) & ~generous(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))))) [flattening 33]
39. (((tall(susan) | old(susan)) & (~tall(susan) | ~old(susan))) | ! [X0] : (calm(X0) | ~brave(X0))) & (? [X0] : (~calm(X0) & brave(X0)) | ((~old(susan) | tall(susan)) & (~tall(susan) | old(susan)))) [nnf transformation 8]
40. (((tall(susan) | old(susan)) & (~tall(susan) | ~old(susan))) | ! [X0] : (calm(X0) | ~brave(X0))) & (? [X1] : (~calm(X1) & brave(X1)) | ((~old(susan) | tall(susan)) & (~tall(susan) | old(susan)))) [rectify 39]
41. ? [X1] : (~calm(X1) & brave(X1)) => (~calm(sK1) & brave(sK1)) [choice axiom]
42. (((tall(susan) | old(susan)) & (~tall(susan) | ~old(susan))) | ! [X0] : (calm(X0) | ~brave(X0))) & ((~calm(sK1) & brave(sK1)) | ((~old(susan) | tall(susan)) & (~tall(susan) | old(susan)))) [skolemisation 40,41]
43. ((~wise(mary) & ~curious(mary)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (wise(mary) | curious(mary))) [nnf transformation 9]
44. ((~wise(mary) & ~curious(mary)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | wise(mary) | curious(mary)) [flattening 43]
45. ((~wise(mary) & ~curious(mary)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | wise(mary) | curious(mary)) [rectify 44]
46. ? [X1] : generous(X1) => generous(sK2) [choice axiom]
47. ((~wise(mary) & ~curious(mary)) | ! [X0] : ~generous(X0)) & (generous(sK2) | wise(mary) | curious(mary)) [skolemisation 45,46]
48. ! [X0] : ((~happy(X0) | (generous(X0) | patient(X0))) & ((~generous(X0) & ~patient(X0)) | happy(X0))) [nnf transformation 10]
49. ! [X0] : ((~happy(X0) | generous(X0) | patient(X0)) & ((~generous(X0) & ~patient(X0)) | happy(X0))) [flattening 48]
50. ! [X0] : ((curious(X0) & kind(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 27]
60. ? [X0] : (calm(X0) | brave(X0)) => (calm(sK5) | brave(sK5)) [choice axiom]
61. calm(sK5) | brave(sK5) [skolemisation 16,60]
74. ~funny(X0) | patient(X0) | ~wise(X0) [cnf transformation 31]
76. ~generous(X0) | curious(X0) [cnf transformation 24]
77. ~kind(X0) | curious(X0) [cnf transformation 24]
79. generous(X0) | ~patient(X0) | ~old(X0) | generous(X0) [cnf transformation 32]
84. ~patient(X0) | wise(X0) | kind(X0) [cnf transformation 34]
86. ~kind(X0) | ~patient(X0) | ~wise(X0) | generous(X0) [cnf transformation 34]
97. ~tall(susan) | ~old(susan) | calm(X0) | ~brave(X0) [cnf transformation 42]
100. ~curious(mary) | ~generous(X0) [cnf transformation 47]
101. ~wise(mary) | ~generous(X0) [cnf transformation 47]
102. ~patient(X0) | happy(X0) [cnf transformation 49]
104. ~happy(X0) | generous(X0) | patient(X0) [cnf transformation 49]
105. ~happy(X0) | ~calm(X0) | kind(X0) [cnf transformation 50]
108. happy(X0) | curious(X0) | calm(X0) [cnf transformation 50]
113. ~calm(X0) | funny(X0) [cnf transformation 29]
114. tall(X0) | funny(X0) [cnf transformation 29]
115. ~calm(X0) | wise(X0) [cnf transformation 29]
116. tall(X0) | wise(X0) [cnf transformation 29]
120. calm(sK5) | brave(sK5) [cnf transformation 61]
126. old(susan) [cnf transformation 22]
127. ~old(X0) | ~patient(X0) | generous(X0) [duplicate literal removal 79]
159. 7 <=> ! [X0] : (calm(X0) | ~brave(X0)) [avatar definition]
160. ~brave(X0) | calm(X0) <- (7) [avatar component clause 159]
162. 8 <=> old(susan) [avatar definition]
164. old(susan) <- (8) [avatar component clause 162]
166. 9 <=> tall(susan) [avatar definition]
167. ~tall(susan) <- (~9) [avatar component clause 166]
170. 7 | ~8 | ~9 [avatar split clause 97,166,162,159]
184. 12 <=> ! [X0] : ~generous(X0) [avatar definition]
185. ~generous(X0) <- (12) [avatar component clause 184]
187. 13 <=> wise(mary) [avatar definition]
189. ~wise(mary) <- (~13) [avatar component clause 187]
190. 12 | ~13 [avatar split clause 101,187,184]
192. 14 <=> curious(mary) [avatar definition]
194. ~curious(mary) <- (~14) [avatar component clause 192]
195. 12 | ~14 [avatar split clause 100,192,184]
220. 20 <=> patient(susan) [avatar definition]
221. patient(susan) <- (20) [avatar component clause 220]
234. 23 <=> brave(sK5) [avatar definition]
236. brave(sK5) <- (23) [avatar component clause 234]
238. 24 <=> calm(sK5) [avatar definition]
240. calm(sK5) <- (24) [avatar component clause 238]
241. 23 | 24 [avatar split clause 120,238,234]
261. 8 [avatar split clause 126,162]
264. calm(sK5) <- (7, 23) [resolution 160,236]
265. 24 | ~7 | ~23 [avatar split clause 264,234,159,238]
266. wise(susan) <- (~9) [resolution 167,116]
267. funny(susan) <- (~9) [resolution 167,114]
269. patient(susan) | ~wise(susan) <- (~9) [resolution 74,267]
306. curious(X2) | calm(X2) | generous(X2) | patient(X2) [resolution 108,104]
309. ~patient(susan) | generous(susan) <- (8) [resolution 127,164]
310. generous(susan) <- (8, 20) [subsumption resolution 309,221]
311. $false <- (8, 12, 20) [subsumption resolution 310,185]
312. ~8 | ~12 | ~20 [avatar contradiction clause 311]
313. calm(X2) | curious(X2) | patient(X2) [subsumption resolution 306,76]
346. patient(susan) <- (~9) [subsumption resolution 269,266]
347. 20 | 9 [avatar split clause 346,166,220]
350. wise(sK5) <- (24) [resolution 240,115]
351. funny(sK5) <- (24) [resolution 240,113]
401. 42 <=> patient(sK5) [avatar definition]
402. ~patient(sK5) <- (~42) [avatar component clause 401]
403. patient(sK5) <- (42) [avatar component clause 401]
405. 43 <=> kind(sK5) [avatar definition]
407. kind(sK5) <- (43) [avatar component clause 405]
409. patient(sK5) | ~wise(sK5) <- (24) [resolution 351,74]
422. curious(X0) | patient(X0) | wise(X0) [resolution 313,115]
442. happy(sK5) <- (42) [resolution 403,102]
496. 53 <=> patient(mary) [avatar definition]
498. patient(mary) <- (53) [avatar component clause 496]
538. wise(mary) | kind(mary) <- (53) [resolution 498,84]
540. kind(mary) <- (~13, 53) [subsumption resolution 538,189]
543. patient(mary) | wise(mary) <- (~14) [resolution 422,194]
558. ~calm(sK5) | kind(sK5) <- (42) [resolution 442,105]
561. kind(sK5) <- (24, 42) [subsumption resolution 558,240]
562. 43 | ~24 | ~42 [avatar split clause 561,401,238,405]
563. ~patient(sK5) | ~wise(sK5) | generous(sK5) <- (43) [resolution 407,86]
671. curious(mary) <- (~13, 53) [resolution 540,77]
672. $false <- (~13, ~14, 53) [subsumption resolution 671,194]
673. 13 | 14 | ~53 [avatar contradiction clause 672]
675. patient(mary) <- (~13, ~14) [subsumption resolution 543,189]
676. 53 | 13 | 14 [avatar split clause 675,192,187,496]
813. ~patient(sK5) | generous(sK5) <- (24, 43) [subsumption resolution 563,350]
814. ~patient(sK5) <- (12, 24, 43) [subsumption resolution 813,185]
815. ~42 | ~12 | ~24 | ~43 [avatar split clause 814,405,238,184,401]
816. ~wise(sK5) <- (24, ~42) [subsumption resolution 409,402]
817. $false <- (24, ~42) [subsumption resolution 816,350]
818. ~24 | 42 [avatar contradiction clause 817]
819. $false [avatar sat refutation 170,190,195,241,261,265,312,347,562,673,676,815,818]
% SZS output end Proof for 438392241724535328930078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not kind then someone is funny or not quiet. If alice is humble then someone is either not curious or not happy and vice versa. Everyone who is both not generous and not patient is either not happy or generous. If mary is either not funny or not generous then someone is quiet and vice versa. Everyone who is either generous or not strong is quiet. If someone is either rich or calm then someone is not happy. If lucy is not tall then someone is rich or brave. Everyone who is humble or strong is both not quiet and not tall. If someone is not kind or old then paul is either creative or generous and vice versa. Everyone who is tall is quiet or patient and vice versa. Everyone who is either old or rich is either quiet or not quiet. Everyone who is not kind or humble is either calm or funny and vice versa. If someone is not generous or tall then john is either kind or not creative and vice versa. If susan is both tall and rich then someone is old or not funny. If susan is not patient then someone is both tall and not strong. If fred is either not rich or funny then someone is quiet or not funny. Someone is patient or curious. Fred is either not old or brave. John is both not creative and not rich. Mary is both not old and strong. Someone is both tall and not quiet. Paul is either humble or not old. Someone is both not patient and not brave. Fred is calm. | Mary is tall. | contradiction | ((?[X]:((~rich(X)|~kind(X))))=>(?[X]:((funny(X)|~quiet(X)))))&
((humble(alice))<=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:((~generous(X)&~patient(X))=>(~happy(X)<~>generous(X))))&
(((~funny(mary)<~>~generous(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)<~>~strong(X))=>quiet(X)))&
((?[X]:((rich(X)<~>calm(X))))=>(?[X]:(~happy(X))))&
((~tall(lucy))=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((humble(X)|strong(X))=>(~quiet(X)&~tall(X))))&
((?[X]:((~kind(X)|old(X))))<=>((creative(paul)<~>generous(paul))))&
(![X]:(tall(X)<=>(quiet(X)|patient(X))))&
(![X]:((old(X)<~>rich(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((~kind(X)|humble(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~generous(X)|tall(X))))<=>((kind(john)<~>~creative(john))))&
(((tall(susan)&rich(susan)))=>(?[X]:((old(X)|~funny(X)))))&
((~patient(susan))=>(?[X]:((tall(X)&~strong(X)))))&
(((~rich(fred)<~>funny(fred)))=>(?[X]:((quiet(X)|~funny(X)))))&
(?[X]:((patient(X)|curious(X))))&
((~old(fred)<~>brave(fred)))&
((~creative(john)&~rich(john)))&
((~old(mary)&strong(mary)))&
(?[X]:((tall(X)&~quiet(X))))&
((humble(paul)<~>~old(paul)))&
(?[X]:((~patient(X)&~brave(X))))&
(calm(fred)) | tall(mary) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3314541020587074242938258
% SZS output start Proof for 3314541020587074242938258
8. ! [X0] : ((strong(X0) | humble(X0)) => (~tall(X0) & ~quiet(X0))) [input p7]
20. strong(mary) & ~old(mary) [input p19]
25. tall(mary) [input hypothesis]
34. ! [X0] : ((~tall(X0) & ~quiet(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 8]
107. ~tall(X0) | ~strong(X0) [cnf transformation 34]
144. strong(mary) [cnf transformation 20]
152. tall(mary) [cnf transformation 25]
373. ~strong(mary) [resolution 107,152]
375. $false [subsumption resolution 373,144]
% SZS output end Proof for 3314541020587074242938258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or funny then mary is not brave.
Everyone who is not strong or not rich is both wise and not funny and vice versa.
If someone is old or not patient then paul is kind.
Everyone who is both brave and quiet is not funny and vice versa.
If someone is either not creative or humble then alice is both not kind and not strong and vice versa.
If susan is generous or not humble then fred is either curious or not strong.
Everyone who is both not funny and not curious is both strong and not creative and vice versa.
If paul is not old or creative then lucy is not funny and vice versa.
If susan is not happy or calm then someone is not brave.
If someone is both calm and rich then fred is rich or kind and vice versa.
Everyone who is not tall is both calm and brave.
Everyone who is humble or not humble is both generous and not humble.
Everyone who is either not happy or not rich is either not curious or strong.
If susan is not rich or tall then alice is both brave and not patient and vice versa.
If someone is not kind then fred is not rich.
If someone is not old then someone is generous or not kind.
John is both quiet and rich.
Someone is strong or not tall.
Someone is both not old and rich.
Alice is either not generous or tall.
Someone is tall.
Someone is not brave. | John is generous. | entailment | (((~happy(alice)|funny(alice)))=>(~brave(mary)))&
(![X]:((~strong(X)|~rich(X))<=>(wise(X)&~funny(X))))&
((?[X]:((old(X)|~patient(X))))=>(kind(paul)))&
(![X]:((brave(X)&quiet(X))<=>~funny(X)))&
((?[X]:((~creative(X)<~>humble(X))))<=>((~kind(alice)&~strong(alice))))&
(((generous(susan)|~humble(susan)))=>((curious(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&~curious(X))<=>(strong(X)&~creative(X))))&
(((~old(paul)|creative(paul)))<=>(~funny(lucy)))&
(((~happy(susan)|calm(susan)))=>(?[X]:(~brave(X))))&
((?[X]:((calm(X)&rich(X))))<=>((rich(fred)|kind(fred))))&
(![X]:(~tall(X)=>(calm(X)&brave(X))))&
(![X]:((humble(X)|~humble(X))=>(generous(X)&~humble(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~curious(X)<~>strong(X))))&
(((~rich(susan)|tall(susan)))<=>((brave(alice)&~patient(alice))))&
((?[X]:(~kind(X)))=>(~rich(fred)))&
((?[X]:(~old(X)))=>(?[X]:((generous(X)|~kind(X)))))&
((quiet(john)&rich(john)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~old(X)&rich(X))))&
((~generous(alice)<~>tall(alice)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X))) | generous(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8670882870251962797289595
% SZS output start Proof for 8670882870251962797289595
12. ! [X0] : ((~humble(X0) | humble(X0)) => (~humble(X0) & generous(X0))) [input p11]
23. ~generous(john) [input hypothesis]
30. ! [X0] : ((~humble(X0) & generous(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 12]
109. generous(X0) | humble(X0) [cnf transformation 30]
110. ~humble(X0) | ~humble(X0) [cnf transformation 30]
132. ~generous(john) [cnf transformation 23]
133. ~humble(X0) [duplicate literal removal 110]
263. generous(X0) [subsumption resolution 109,133]
303. $false [subsumption resolution 132,263]
% SZS output end Proof for 8670882870251962797289595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and curious is both brave and not generous and vice versa. Everyone who is either not generous or tall is either not tall or not creative. If someone is either strong or happy then someone is not tall or not creative and vice versa. Everyone who is not calm is both wise and patient and vice versa. If susan is either strong or not curious then someone is either wise or not humble. Everyone who is both patient and old is both not strong and rich. Everyone who is both not generous and tall is both not quiet and calm. If someone is not brave then fred is not generous or not quiet. If someone is old or not patient then susan is either kind or not humble and vice versa. If someone is generous then someone is both not humble and not old and vice versa. Everyone who is not curious or not strong is both not calm and not wise. Everyone who is patient or strong is generous. Everyone who is not generous is either not funny or not humble. If susan is quiet then someone is both strong and not old and vice versa. Everyone who is not old or quiet is either brave or not strong and vice versa. Everyone who is rich is either quiet or strong and vice versa. John is not humble or calm. Someone is not funny. Someone is old or not happy. Susan is either not calm or happy. Mary is both humble and strong. Someone is either not brave or calm. Fred is both not kind and happy. | John is not strong. | contradiction | (![X]:((~strong(X)&curious(X))<=>(brave(X)&~generous(X))))&
(![X]:((~generous(X)<~>tall(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:(~calm(X)<=>(wise(X)&patient(X))))&
(((strong(susan)<~>~curious(susan)))=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((patient(X)&old(X))=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)&tall(X))=>(~quiet(X)&calm(X))))&
((?[X]:(~brave(X)))=>((~generous(fred)|~quiet(fred))))&
((?[X]:((old(X)|~patient(X))))<=>((kind(susan)<~>~humble(susan))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~curious(X)|~strong(X))=>(~calm(X)&~wise(X))))&
(![X]:((patient(X)|strong(X))=>generous(X)))&
(![X]:(~generous(X)=>(~funny(X)<~>~humble(X))))&
((quiet(susan))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((~old(X)|quiet(X))<=>(brave(X)<~>~strong(X))))&
(![X]:(rich(X)<=>(quiet(X)<~>strong(X))))&
((~humble(john)|calm(john)))&
(?[X]:(~funny(X)))&
(?[X]:((old(X)|~happy(X))))&
((~calm(susan)<~>happy(susan)))&
((humble(mary)&strong(mary)))&
(?[X]:((~brave(X)<~>calm(X))))&
((~kind(fred)&happy(fred))) | ~strong(john) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1931929604270913057122898
% SZS output start Proof for 1931929604270913057122898
4. ! [X0] : (~calm(X0) <=> (patient(X0) & wise(X0))) [input p3]
11. ! [X0] : ((~strong(X0) | ~curious(X0)) => (~wise(X0) & ~calm(X0))) [input p10]
24. ~strong(john) [input hypothesis]
36. ! [X0] : ((~wise(X0) & ~calm(X0)) | (strong(X0) & curious(X0))) [ennf transformation 11]
48. ! [X0] : ((~calm(X0) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | calm(X0))) [nnf transformation 4]
49. ! [X0] : ((~calm(X0) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | calm(X0))) [flattening 48]
92. wise(X0) | calm(X0) [cnf transformation 49]
114. ~calm(X0) | strong(X0) [cnf transformation 36]
116. ~wise(X0) | strong(X0) [cnf transformation 36]
143. ~strong(john) [cnf transformation 24]
325. strong(X0) | calm(X0) [resolution 116,92]
326. strong(X0) [subsumption resolution 325,114]
327. $false [resolution 326,143]
% SZS output end Proof for 1931929604270913057122898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is happy then someone is old or not rich and vice versa. If someone is not brave then susan is not quiet. Everyone who is not rich is either not humble or not patient. If fred is both generous and happy then fred is generous and vice versa. Everyone who is old is not tall. If someone is both not curious and not quiet then someone is both calm and humble. Everyone who is either not generous or not kind is either humble or not patient. If alice is both strong and not wise then susan is either not curious or quiet and vice versa. Everyone who is either not humble or quiet is not funny or not wise and vice versa. Everyone who is both not humble and tall is both not humble and happy. Everyone who is either not rich or not calm is either not kind or not strong. If susan is old or humble then susan is not calm or calm. Everyone who is humble or not kind is brave and vice versa. Everyone who is both creative and not patient is not humble or not happy and vice versa. Everyone who is either happy or not patient is either creative or old. If alice is either creative or quiet then fred is patient and vice versa. Alice is both not kind and generous. Someone is both not happy and not kind. John is both strong and patient. Susan is not happy or wise. Someone is creative. Someone is not old. Susan is both not funny and not happy. Someone is both creative and humble. | John is creative. | entailment | ((happy(susan))<=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:(~brave(X)))=>(~quiet(susan)))&
(![X]:(~rich(X)=>(~humble(X)<~>~patient(X))))&
(((generous(fred)&happy(fred)))<=>(generous(fred)))&
(![X]:(old(X)=>~tall(X)))&
((?[X]:((~curious(X)&~quiet(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~generous(X)<~>~kind(X))=>(humble(X)<~>~patient(X))))&
(((strong(alice)&~wise(alice)))<=>((~curious(susan)<~>quiet(susan))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~funny(X)|~wise(X))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)&happy(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~kind(X)<~>~strong(X))))&
(((old(susan)|humble(susan)))=>((~calm(susan)|calm(susan))))&
(![X]:((humble(X)|~kind(X))<=>brave(X)))&
(![X]:((creative(X)&~patient(X))<=>(~humble(X)|~happy(X))))&
(![X]:((happy(X)<~>~patient(X))=>(creative(X)<~>old(X))))&
(((creative(alice)<~>quiet(alice)))<=>(patient(fred)))&
((~kind(alice)&generous(alice)))&
(?[X]:((~happy(X)&~kind(X))))&
((strong(john)&patient(john)))&
((~happy(susan)|wise(susan)))&
(?[X]:(creative(X)))&
(?[X]:(~old(X)))&
((~funny(susan)&~happy(susan)))&
(?[X]:((creative(X)&humble(X)))) | creative(john) | [
"p0",
"p13",
"p14",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 461027796885002597855079
% SZS output start Proof for 461027796885002597855079
1. happy(susan) <=> ? [X0] : (~rich(X0) | old(X0)) [input p0]
14. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~happy(X0) | ~humble(X0))) [input p13]
15. ! [X0] : ((happy(X0) <~> ~patient(X0)) => (creative(X0) <~> old(X0))) [input p14]
19. patient(john) & strong(john) [input p18]
23. ~happy(susan) & ~funny(susan) [input p22]
25. ~creative(john) [input hypothesis]
39. ! [X0] : ((creative(X0) <~> old(X0)) | (happy(X0) <=> ~patient(X0))) [ennf transformation 15]
40. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & (? [X0] : (~rich(X0) | old(X0)) | ~happy(susan)) [nnf transformation 1]
41. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & (? [X1] : (~rich(X1) | old(X1)) | ~happy(susan)) [rectify 40]
42. ? [X1] : (~rich(X1) | old(X1)) => (~rich(sK0) | old(sK0)) [choice axiom]
43. (happy(susan) | ! [X0] : (rich(X0) & ~old(X0))) & ((~rich(sK0) | old(sK0)) | ~happy(susan)) [skolemisation 41,42]
56. ! [X0] : (((~patient(X0) & creative(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 14]
57. ! [X0] : (((~patient(X0) & creative(X0)) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | patient(X0) | ~creative(X0))) [flattening 56]
58. ! [X0] : (((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) [nnf transformation 39]
69. happy(susan) | ~old(X0) [cnf transformation 43]
104. creative(X0) | happy(X0) [cnf transformation 57]
107. old(X0) | creative(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 58]
120. patient(john) [cnf transformation 19]
125. ~happy(susan) [cnf transformation 23]
128. ~creative(john) [cnf transformation 25]
133. 2 <=> happy(susan) [avatar definition]
138. 3 <=> ! [X0] : ~old(X0) [avatar definition]
139. ~old(X0) <- (3) [avatar component clause 138]
140. 3 | 2 [avatar split clause 69,133,138]
201. ~patient(X0) | creative(X0) | old(X0) [subsumption resolution 107,104]
223. ~2 [avatar split clause 125,133]
288. creative(john) | old(john) [resolution 201,120]
290. old(john) [subsumption resolution 288,128]
291. $false <- (3) [subsumption resolution 290,139]
292. ~3 [avatar contradiction clause 291]
293. $false [avatar sat refutation 140,223,292]
% SZS output end Proof for 461027796885002597855079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is curious or not tall.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is either not happy or happy is curious and vice versa.
Everyone who is brave is generous and vice versa.
If fred is calm or creative then someone is both not tall and generous and vice versa.
Everyone who is both strong and happy is both creative and calm and vice versa.
If someone is both not old and not rich then someone is not patient or humble and vice versa.
Everyone who is either strong or not funny is not tall.
If someone is tall or funny then paul is either not happy or funny.
If mary is both generous and not old then paul is either not generous or creative and vice versa.
Everyone who is tall is either old or not tall.
Everyone who is either calm or not brave is not strong and vice versa.
Everyone who is both not funny and not creative is either quiet or calm.
If someone is wise then fred is either wise or not strong and vice versa.
Everyone who is both humble and funny is not calm and vice versa.
If someone is kind or not creative then someone is not patient or tall and vice versa.
Someone is both not wise and humble.
Mary is both not brave and funny.
John is funny.
John is both not rich and kind.
Someone is happy.
Someone is not creative or patient.
Someone is both funny and not humble. | Paul is not curious. | contradiction | (![X]:(~funny(X)=>(curious(X)|~tall(X))))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>happy(X))<=>curious(X)))&
(![X]:(brave(X)<=>generous(X)))&
(((calm(fred)|creative(fred)))<=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((strong(X)&happy(X))<=>(creative(X)&calm(X))))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~patient(X)|humble(X)))))&
(![X]:((strong(X)<~>~funny(X))=>~tall(X)))&
((?[X]:((tall(X)|funny(X))))=>((~happy(paul)<~>funny(paul))))&
(((generous(mary)&~old(mary)))<=>((~generous(paul)<~>creative(paul))))&
(![X]:(tall(X)=>(old(X)<~>~tall(X))))&
(![X]:((calm(X)<~>~brave(X))<=>~strong(X)))&
(![X]:((~funny(X)&~creative(X))=>(quiet(X)<~>calm(X))))&
((?[X]:(wise(X)))<=>((wise(fred)<~>~strong(fred))))&
(![X]:((humble(X)&funny(X))<=>~calm(X)))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~patient(X)|tall(X)))))&
(?[X]:((~wise(X)&humble(X))))&
((~brave(mary)&funny(mary)))&
(funny(john))&
((~rich(john)&kind(john)))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)|patient(X))))&
(?[X]:((funny(X)&~humble(X)))) | ~curious(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 744193564281161815650504
% SZS output start Proof for 744193564281161815650504
3. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> curious(X0)) [input p2]
24. ~curious(paul) [input hypothesis]
36. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~curious(X0)) & (curious(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 3]
80. curious(X0) | happy(X0) | happy(X0) [cnf transformation 36]
81. curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 36]
142. ~curious(paul) [cnf transformation 24]
144. curious(X0) | happy(X0) [duplicate literal removal 80]
145. curious(X0) | ~happy(X0) [duplicate literal removal 81]
146. curious(X0) [subsumption resolution 144,145]
296. $false [subsumption resolution 142,146]
% SZS output end Proof for 744193564281161815650504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or humble is not quiet.
Everyone who is either not brave or wise is both not generous and not humble and vice versa.
Everyone who is either strong or funny is both humble and not funny.
Everyone who is both not patient and happy is either not patient or not tall.
If someone is either funny or not patient then someone is not patient or brave.
Everyone who is strong or happy is either generous or not curious.
If alice is patient then mary is happy or not kind and vice versa.
If john is curious or not strong then someone is happy.
Everyone who is both kind and strong is either kind or not brave and vice versa.
If lucy is quiet then someone is either creative or rich.
Everyone who is kind is both humble and happy and vice versa.
Everyone who is quiet is happy.
Everyone who is not old is not wise or brave.
Everyone who is either old or brave is either not quiet or not old and vice versa.
Everyone who is old or tall is either not happy or curious and vice versa.
Everyone who is either not creative or not calm is wise.
Someone is not generous.
Someone is not strong or not rich.
Someone is happy.
Someone is wise or not kind.
Fred is quiet or not calm.
Someone is either not tall or patient.
Someone is not old. | Mary is happy. | entailment | (![X]:((creative(X)<~>humble(X))=>~quiet(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~generous(X)&~humble(X))))&
(![X]:((strong(X)<~>funny(X))=>(humble(X)&~funny(X))))&
(![X]:((~patient(X)&happy(X))=>(~patient(X)<~>~tall(X))))&
((?[X]:((funny(X)<~>~patient(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((strong(X)|happy(X))=>(generous(X)<~>~curious(X))))&
((patient(alice))<=>((happy(mary)|~kind(mary))))&
(((curious(john)|~strong(john)))=>(?[X]:(happy(X))))&
(![X]:((kind(X)&strong(X))<=>(kind(X)<~>~brave(X))))&
((quiet(lucy))=>(?[X]:((creative(X)<~>rich(X)))))&
(![X]:(kind(X)<=>(humble(X)&happy(X))))&
(![X]:(quiet(X)=>happy(X)))&
(![X]:(~old(X)=>(~wise(X)|brave(X))))&
(![X]:((old(X)<~>brave(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((old(X)|tall(X))<=>(~happy(X)<~>curious(X))))&
(![X]:((~creative(X)<~>~calm(X))=>wise(X)))&
(?[X]:(~generous(X)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)|~kind(X))))&
((quiet(fred)|~calm(fred)))&
(?[X]:((~tall(X)<~>patient(X))))&
(?[X]:(~old(X))) | happy(mary) | [
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3781468254370136491333600
% SZS output start Proof for 3781468254370136491333600
9. ! [X0] : ((strong(X0) & kind(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p8]
11. ! [X0] : (kind(X0) <=> (happy(X0) & humble(X0))) [input p10]
12. ! [X0] : (quiet(X0) => happy(X0)) [input p11]
14. ! [X0] : ((old(X0) <~> brave(X0)) <=> (~quiet(X0) <~> ~old(X0))) [input p13]
24. ~happy(mary) [input hypothesis]
34. ! [X0] : (happy(X0) | ~quiet(X0)) [ennf transformation 12]
52. ! [X0] : (((strong(X0) & kind(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~strong(X0) | ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : (((strong(X0) & kind(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~strong(X0) | ~kind(X0))) [flattening 52]
57. ! [X0] : ((kind(X0) | (~happy(X0) | ~humble(X0))) & ((happy(X0) & humble(X0)) | ~kind(X0))) [nnf transformation 11]
58. ! [X0] : ((kind(X0) | ~happy(X0) | ~humble(X0)) & ((happy(X0) & humble(X0)) | ~kind(X0))) [flattening 57]
59. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 14]
104. kind(X0) | kind(X0) | brave(X0) [cnf transformation 53]
110. ~kind(X0) | happy(X0) [cnf transformation 58]
112. ~quiet(X0) | happy(X0) [cnf transformation 34]
117. old(X0) | quiet(X0) | old(X0) | ~brave(X0) [cnf transformation 59]
120. ~brave(X0) | ~old(X0) | ~old(X0) | quiet(X0) [cnf transformation 59]
138. ~happy(mary) [cnf transformation 24]
140. old(X0) | quiet(X0) | ~brave(X0) [duplicate literal removal 117]
142. ~brave(X0) | ~old(X0) | quiet(X0) [duplicate literal removal 120]
144. kind(X0) | brave(X0) [duplicate literal removal 104]
164. 5 <=> kind(mary) [avatar definition]
165. ~kind(mary) <- (~5) [avatar component clause 164]
166. kind(mary) <- (5) [avatar component clause 164]
173. 7 <=> happy(mary) [avatar definition]
175. ~happy(mary) <- (~7) [avatar component clause 173]
207. ~brave(X0) | quiet(X0) [subsumption resolution 140,142]
246. ~7 [avatar split clause 138,173]
248. happy(mary) <- (5) [resolution 110,166]
249. $false <- (5, ~7) [subsumption resolution 248,175]
250. ~5 | 7 [avatar contradiction clause 249]
254. brave(mary) <- (~5) [resolution 144,165]
257. quiet(mary) <- (~5) [resolution 207,254]
262. happy(mary) <- (~5) [resolution 257,112]
263. $false <- (~5, ~7) [subsumption resolution 262,175]
264. 5 | 7 [avatar contradiction clause 263]
265. $false [avatar sat refutation 246,250,264]
% SZS output end Proof for 3781468254370136491333600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not patient is old or generous and vice versa.
If lucy is either not old or not happy then paul is either calm or tall and vice versa.
If someone is not calm or quiet then someone is either not curious or not quiet and vice versa.
Everyone who is generous or quiet is not humble.
Everyone who is not strong is both humble and calm and vice versa.
If paul is both not calm and brave then lucy is kind and vice versa.
If paul is tall or not funny then mary is tall or brave.
Everyone who is curious or not creative is not rich.
Everyone who is either not happy or wise is happy and vice versa.
Everyone who is both not happy and quiet is not quiet or not humble and vice versa.
If fred is both not tall and generous then someone is patient or wise and vice versa.
If alice is curious or not generous then paul is both not tall and strong.
If alice is not generous then alice is either not creative or tall and vice versa.
Everyone who is either rich or old is quiet.
If mary is not brave then someone is not wise.
Everyone who is either not tall or not kind is not brave or quiet.
Mary is not generous or generous.
Someone is wise.
Someone is either not humble or not wise.
John is quiet.
Lucy is calm or strong.
Someone is not strong or not creative.
Paul is not generous. | Paul is not quiet. | contradiction | (![X]:((~humble(X)|~patient(X))<=>(old(X)|generous(X))))&
(((~old(lucy)<~>~happy(lucy)))<=>((calm(paul)<~>tall(paul))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((generous(X)|quiet(X))=>~humble(X)))&
(![X]:(~strong(X)<=>(humble(X)&calm(X))))&
(((~calm(paul)&brave(paul)))<=>(kind(lucy)))&
(((tall(paul)|~funny(paul)))=>((tall(mary)|brave(mary))))&
(![X]:((curious(X)|~creative(X))=>~rich(X)))&
(![X]:((~happy(X)<~>wise(X))<=>happy(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~quiet(X)|~humble(X))))&
(((~tall(fred)&generous(fred)))<=>(?[X]:((patient(X)|wise(X)))))&
(((curious(alice)|~generous(alice)))=>((~tall(paul)&strong(paul))))&
((~generous(alice))<=>((~creative(alice)<~>tall(alice))))&
(![X]:((rich(X)<~>old(X))=>quiet(X)))&
((~brave(mary))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(~brave(X)|quiet(X))))&
((~generous(mary)|generous(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(quiet(john))&
((calm(lucy)|strong(lucy)))&
(?[X]:((~strong(X)|~creative(X))))&
(~generous(paul)) | ~quiet(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4366212959492757859699095
% SZS output start Proof for 4366212959492757859699095
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p9]
24. ~quiet(paul) [input hypothesis]
49. ! [X0] : (((quiet(X0) & ~happy(X0)) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
50. ! [X0] : (((quiet(X0) & ~happy(X0)) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0) | happy(X0))) [flattening 49]
104. quiet(X0) | quiet(X0) [cnf transformation 50]
132. ~quiet(paul) [cnf transformation 24]
134. quiet(X0) [duplicate literal removal 104]
258. $false [subsumption resolution 132,134]
% SZS output end Proof for 4366212959492757859699095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and rich is not creative and vice versa. If susan is brave then john is not kind or wise. Everyone who is both humble and not calm is calm and vice versa. Everyone who is either not wise or not old is not old or not funny and vice versa. Everyone who is not old is quiet and vice versa. If someone is either old or not funny then someone is either not calm or happy and vice versa. Everyone who is brave is not rich or not curious and vice versa. Everyone who is either happy or humble is either strong or tall and vice versa. Everyone who is both curious and not humble is either funny or patient and vice versa. Everyone who is not patient or not happy is not old and vice versa. Everyone who is either not creative or happy is not funny or not rich and vice versa. If paul is creative or not patient then mary is humble and vice versa. If alice is not happy then alice is not calm or generous and vice versa. If someone is humble then someone is either not old or tall and vice versa. Everyone who is both kind and not tall is not kind or funny. Everyone who is both creative and not quiet is both not generous and not quiet and vice versa. Fred is either curious or funny. Fred is either not humble or not tall. Someone is either not kind or happy. Susan is curious. Someone is either humble or not curious. Someone is either not creative or wise. Mary is kind or not tall. | Fred is wise. | entailment | (![X]:((quiet(X)&rich(X))<=>~creative(X)))&
((brave(susan))=>((~kind(john)|wise(john))))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~old(X)|~funny(X))))&
(![X]:(~old(X)<=>quiet(X)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(brave(X)<=>(~rich(X)|~curious(X))))&
(![X]:((happy(X)<~>humble(X))<=>(strong(X)<~>tall(X))))&
(![X]:((curious(X)&~humble(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~patient(X)|~happy(X))<=>~old(X)))&
(![X]:((~creative(X)<~>happy(X))<=>(~funny(X)|~rich(X))))&
(((creative(paul)|~patient(paul)))<=>(humble(mary)))&
((~happy(alice))<=>((~calm(alice)|generous(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:((kind(X)&~tall(X))=>(~kind(X)|funny(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~generous(X)&~quiet(X))))&
((curious(fred)<~>funny(fred)))&
((~humble(fred)<~>~tall(fred)))&
(?[X]:((~kind(X)<~>happy(X))))&
(curious(susan))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
((kind(mary)|~tall(mary))) | wise(fred) | [
"p2",
"p3",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9145178593990557826619098
% SZS output start Proof for 9145178593990557826619098
3. ! [X0] : ((~calm(X0) & humble(X0)) <=> calm(X0)) [input p2]
4. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> (~funny(X0) | ~old(X0))) [input p3]
14. ? [X0] : humble(X0) <=> ? [X0] : (~old(X0) <~> tall(X0)) [input p13]
18. ~humble(fred) <~> ~tall(fred) [input p17]
24. ~wise(fred) [input hypothesis]
26. ? [X0] : humble(X0) <=> ? [X1] : (~old(X1) <~> tall(X1)) [rectify 14]
35. ! [X0] : (((~calm(X0) & humble(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | ~humble(X0)))) [nnf transformation 3]
36. ! [X0] : (((~calm(X0) & humble(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | ~humble(X0))) [flattening 35]
37. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 4]
38. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [flattening 37]
56. (? [X0] : humble(X0) | ! [X1] : ((~old(X1) | ~tall(X1)) & (tall(X1) | old(X1)))) & (? [X1] : ((~tall(X1) | old(X1)) & (tall(X1) | ~old(X1))) | ! [X0] : ~humble(X0)) [nnf transformation 26]
57. (? [X0] : humble(X0) | ! [X1] : ((~old(X1) | ~tall(X1)) & (tall(X1) | old(X1)))) & (? [X2] : ((~tall(X2) | old(X2)) & (tall(X2) | ~old(X2))) | ! [X3] : ~humble(X3)) [rectify 56]
58. ? [X0] : humble(X0) => humble(sK2) [choice axiom]
59. ? [X2] : ((~tall(X2) | old(X2)) & (tall(X2) | ~old(X2))) => ((~tall(sK3) | old(sK3)) & (tall(sK3) | ~old(sK3))) [choice axiom]
60. (humble(sK2) | ! [X1] : ((~old(X1) | ~tall(X1)) & (tall(X1) | old(X1)))) & (((~tall(sK3) | old(sK3)) & (tall(sK3) | ~old(sK3))) | ! [X3] : ~humble(X3)) [skolemisation 57,59,58]
64. (tall(fred) | humble(fred)) & (~tall(fred) | ~humble(fred)) [nnf transformation 18]
78. calm(X0) | calm(X0) | ~humble(X0) [cnf transformation 36]
80. ~calm(X0) | ~calm(X0) [cnf transformation 36]
85. old(X0) | wise(X0) | old(X0) [cnf transformation 38]
131. humble(sK2) | ~old(X1) | ~tall(X1) [cnf transformation 60]
140. tall(fred) | humble(fred) [cnf transformation 64]
149. ~wise(fred) [cnf transformation 24]
152. old(X0) | wise(X0) [duplicate literal removal 85]
153. calm(X0) | ~humble(X0) [duplicate literal removal 78]
154. ~calm(X0) [duplicate literal removal 80]
168. ~humble(X0) [subsumption resolution 153,154]
220. ~tall(X1) | ~old(X1) [subsumption resolution 131,168]
233. tall(fred) [subsumption resolution 140,168]
280. ~old(fred) [resolution 220,233]
283. wise(fred) [resolution 280,152]
285. $false [subsumption resolution 283,149]
% SZS output end Proof for 9145178593990557826619098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not rich and vice versa. Everyone who is both not quiet and not calm is either not funny or kind and vice versa. Everyone who is not tall or not creative is creative or not kind. If someone is curious then someone is not creative and vice versa. Everyone who is either not kind or creative is not old. If mary is humble then john is not creative. Everyone who is kind is both not brave and quiet and vice versa. Everyone who is not tall or humble is both generous and not calm. Everyone who is not humble is brave. If someone is both not strong and tall then fred is not quiet or not generous. Everyone who is not wise is not strong. Everyone who is both not wise and strong is both brave and curious and vice versa. Everyone who is both not wise and brave is either wise or happy and vice versa. Everyone who is not brave is either generous or not calm and vice versa. If someone is either calm or not rich then john is either rich or strong. If lucy is rich or not strong then someone is both not patient and calm and vice versa. Someone is either happy or patient. Someone is either quiet or calm. Someone is patient. John is both strong and not old. Someone is wise. Fred is both humble and not calm. Alice is both not humble and not curious. | Alice is not happy. | contradiction | (![X]:(humble(X)<=>~rich(X)))&
(![X]:((~quiet(X)&~calm(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~tall(X)|~creative(X))=>(creative(X)|~kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>creative(X))=>~old(X)))&
((humble(mary))=>(~creative(john)))&
(![X]:(kind(X)<=>(~brave(X)&quiet(X))))&
(![X]:((~tall(X)|humble(X))=>(generous(X)&~calm(X))))&
(![X]:(~humble(X)=>brave(X)))&
((?[X]:((~strong(X)&tall(X))))=>((~quiet(fred)|~generous(fred))))&
(![X]:(~wise(X)=>~strong(X)))&
(![X]:((~wise(X)&strong(X))<=>(brave(X)&curious(X))))&
(![X]:((~wise(X)&brave(X))<=>(wise(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(generous(X)<~>~calm(X))))&
((?[X]:((calm(X)<~>~rich(X))))=>((rich(john)<~>strong(john))))&
(((rich(lucy)|~strong(lucy)))<=>(?[X]:((~patient(X)&calm(X)))))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((quiet(X)<~>calm(X))))&
(?[X]:(patient(X)))&
((strong(john)&~old(john)))&
(?[X]:(wise(X)))&
((humble(fred)&~calm(fred)))&
((~humble(alice)&~curious(alice))) | ~happy(alice) | [
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6113543682037915352846625
% SZS output start Proof for 6113543682037915352846625
9. ! [X0] : (~humble(X0) => brave(X0)) [input p8]
13. ! [X0] : ((brave(X0) & ~wise(X0)) <=> (wise(X0) <~> happy(X0))) [input p12]
23. ~curious(alice) & ~humble(alice) [input p22]
24. ~happy(alice) [input hypothesis]
32. ! [X0] : (brave(X0) | humble(X0)) [ennf transformation 9]
49. ! [X0] : (((brave(X0) & ~wise(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (~brave(X0) | wise(X0)))) [nnf transformation 13]
50. ! [X0] : (((brave(X0) & ~wise(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ~brave(X0) | wise(X0))) [flattening 49]
88. brave(X0) | humble(X0) [cnf transformation 32]
95. happy(X0) | wise(X0) | ~brave(X0) | wise(X0) [cnf transformation 50]
97. ~wise(X0) | happy(X0) | ~wise(X0) [cnf transformation 50]
123. ~humble(alice) [cnf transformation 23]
125. ~happy(alice) [cnf transformation 24]
126. happy(X0) | wise(X0) | ~brave(X0) [duplicate literal removal 95]
127. ~wise(X0) | happy(X0) [duplicate literal removal 97]
166. ~brave(X0) | happy(X0) [subsumption resolution 126,127]
243. happy(X0) | humble(X0) [resolution 166,88]
384. humble(alice) [resolution 243,125]
386. $false [subsumption resolution 384,123]
% SZS output end Proof for 6113543682037915352846625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or kind is tall.
If john is kind then alice is either not brave or not patient.
Everyone who is wise or not wise is rich.
Everyone who is both rich and not kind is both funny and strong and vice versa.
If someone is either tall or generous then someone is both not old and not wise.
Everyone who is not old or not calm is not tall or creative.
Everyone who is either not kind or not rich is either not creative or curious and vice versa.
Everyone who is both patient and not kind is both not curious and not happy.
Everyone who is not patient is not funny or kind and vice versa.
If someone is both not quiet and rich then mary is either not happy or not brave.
Everyone who is both not humble and strong is both kind and not quiet and vice versa.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
If someone is not humble or happy then paul is both not tall and not generous and vice versa.
Everyone who is calm or generous is either rich or patient and vice versa.
Mary is both not humble and not brave.
Someone is both tall and brave.
Someone is both not funny and not wise.
Someone is either tall or happy.
Someone is generous or not curious.
John is patient.
Someone is not rich or not wise. | John is strong. | entailment | (![X]:((~funny(X)|kind(X))=>tall(X)))&
((kind(john))=>((~brave(alice)<~>~patient(alice))))&
(![X]:((wise(X)|~wise(X))=>rich(X)))&
(![X]:((rich(X)&~kind(X))<=>(funny(X)&strong(X))))&
((?[X]:((tall(X)<~>generous(X))))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~old(X)|~calm(X))=>(~tall(X)|creative(X))))&
(![X]:((~kind(X)<~>~rich(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((patient(X)&~kind(X))=>(~curious(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~funny(X)|kind(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((~happy(mary)<~>~brave(mary))))&
(![X]:((~humble(X)&strong(X))<=>(kind(X)&~quiet(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
((?[X]:((~humble(X)|happy(X))))<=>((~tall(paul)&~generous(paul))))&
(![X]:((calm(X)|generous(X))<=>(rich(X)<~>patient(X))))&
((~humble(mary)&~brave(mary)))&
(?[X]:((tall(X)&brave(X))))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((tall(X)<~>happy(X))))&
(?[X]:((generous(X)|~curious(X))))&
(patient(john))&
(?[X]:((~rich(X)|~wise(X)))) | strong(john) | [
"p2",
"p3",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 12576197351059699697718
% SZS output start Proof for 12576197351059699697718
3. ! [X0] : ((~wise(X0) | wise(X0)) => rich(X0)) [input p2]
4. ! [X0] : ((~kind(X0) & rich(X0)) <=> (strong(X0) & funny(X0))) [input p3]
9. ! [X0] : (~patient(X0) <=> (kind(X0) | ~funny(X0))) [input p8]
22. patient(john) [input p21]
24. ~strong(john) [input hypothesis]
28. ! [X0] : (rich(X0) | (wise(X0) & ~wise(X0))) [ennf transformation 3]
38. ! [X0] : (((~kind(X0) & rich(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 4]
39. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | kind(X0) | ~rich(X0))) [flattening 38]
45. ! [X0] : ((~patient(X0) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | patient(X0))) [nnf transformation 9]
46. ! [X0] : ((~patient(X0) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | patient(X0))) [flattening 45]
76. rich(X0) | ~wise(X0) [cnf transformation 28]
77. rich(X0) | wise(X0) [cnf transformation 28]
79. strong(X0) | kind(X0) | ~rich(X0) [cnf transformation 39]
100. ~patient(X0) | ~kind(X0) [cnf transformation 46]
136. patient(john) [cnf transformation 22]
138. ~strong(john) [cnf transformation 24]
140. 1 <=> kind(john) [avatar definition]
153. rich(X0) [subsumption resolution 76,77]
154. strong(X0) | kind(X0) [subsumption resolution 79,153]
271. ~kind(john) [resolution 100,136]
273. kind(john) [resolution 154,138]
276. 1 [avatar split clause 273,140]
277. ~1 [avatar split clause 271,140]
278. $false [avatar sat refutation 276,277]
% SZS output end Proof for 12576197351059699697718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not 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. | Lucy is not strong. | 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)))) | ~strong(lucy) | [
"p1",
"p3",
"p10",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4866255856162848737976463
% SZS output start Proof for 4866255856162848737976463
2. ! [X0] : ((rich(X0) <~> ~brave(X0)) => (patient(X0) & ~quiet(X0))) [input p1]
4. ! [X0] : (~strong(X0) <=> (~brave(X0) | old(X0))) [input p3]
11. ! [X0] : ((patient(X0) <~> ~humble(X0)) <=> (~humble(X0) & ~strong(X0))) [input p10]
14. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) | curious(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | rich(X0)) => humble(X0)) [input p14]
17. ~funny(lucy) & wise(lucy) [input p16]
24. strong(lucy) [input hypothesis]
30. ! [X0] : ((rich(X0) <~> ~brave(X0)) => patient(X0)) [pure predicate removal 2]
32. ! [X0] : (patient(X0) | (rich(X0) <=> ~brave(X0))) [ennf transformation 30]
41. ! [X0] : (humble(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 15]
44. ! [X0] : (patient(X0) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) [nnf transformation 32]
45. ! [X0] : ((~strong(X0) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | strong(X0))) [nnf transformation 4]
46. ! [X0] : ((~strong(X0) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | strong(X0))) [flattening 45]
51. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [nnf transformation 11]
52. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [flattening 51]
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]
71. ~brave(X0) | patient(X0) | ~rich(X0) [cnf transformation 44]
76. ~strong(X0) | brave(X0) [cnf transformation 46]
91. ~humble(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 52]
97. funny(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 54]
98. ~curious(X0) | ~curious(X0) [cnf transformation 54]
102. ~rich(X0) | humble(X0) [cnf transformation 41]
106. ~funny(lucy) [cnf transformation 17]
115. strong(lucy) [cnf transformation 24]
116. funny(X0) | curious(X0) | rich(X0) [duplicate literal removal 97]
117. ~curious(X0) [duplicate literal removal 98]
118. ~humble(X0) | ~patient(X0) [duplicate literal removal 91]
159. funny(X0) | rich(X0) [subsumption resolution 116,117]
199. brave(lucy) [resolution 76,115]
208. rich(lucy) [resolution 159,106]
211. humble(lucy) [resolution 208,102]
215. patient(lucy) | ~rich(lucy) [resolution 71,199]
218. patient(lucy) [subsumption resolution 215,208]
233. ~patient(lucy) [resolution 211,118]
234. $false [subsumption resolution 233,218]
% SZS output end Proof for 4866255856162848737976463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not rich and not humble then lucy is either wise or patient and vice versa.
Everyone who is tall or not humble is not generous.
Everyone who is either not generous or old is both not kind and patient.
Everyone who is both not patient and not quiet is funny or not strong and vice versa.
Everyone who is both patient and not quiet is tall or kind.
Everyone who is either not happy or wise is both wise and brave.
If lucy is either not strong or not curious then someone is not humble or not kind and vice versa.
If someone is generous then someone is either not kind or wise.
If someone is either not funny or funny then paul is not funny or curious and vice versa.
Everyone who is either quiet or not kind is old or not kind and vice versa.
Everyone who is either quiet or not wise is both humble and not curious and vice versa.
Everyone who is not humble or not creative is either not strong or creative and vice versa.
Everyone who is either not quiet or calm is not curious or quiet.
Everyone who is both tall and happy is both creative and tall and vice versa.
Everyone who is not humble or patient is both tall and not quiet.
Everyone who is humble is happy or quiet.
Someone is either brave or not funny.
Someone is both not calm and strong.
Fred is not wise.
Someone is not generous or not rich.
Alice is either kind or not kind.
John is generous.
Someone is either not calm or strong.
Someone is not creative or not kind. | Fred is not humble. | contradiction | (((~rich(mary)&~humble(mary)))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((tall(X)|~humble(X))=>~generous(X)))&
(![X]:((~generous(X)<~>old(X))=>(~kind(X)&patient(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~quiet(X))=>(tall(X)|kind(X))))&
(![X]:((~happy(X)<~>wise(X))=>(wise(X)&brave(X))))&
(((~strong(lucy)<~>~curious(lucy)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~kind(X)<~>wise(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~funny(paul)|curious(paul))))&
(![X]:((quiet(X)<~>~kind(X))<=>(old(X)|~kind(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(humble(X)&~curious(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~curious(X)|quiet(X))))&
(![X]:((tall(X)&happy(X))<=>(creative(X)&tall(X))))&
(![X]:((~humble(X)|patient(X))=>(tall(X)&~quiet(X))))&
(![X]:(humble(X)=>(happy(X)|quiet(X))))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((~calm(X)&strong(X))))&
(~wise(fred))&
(?[X]:((~generous(X)|~rich(X))))&
((kind(alice)<~>~kind(alice)))&
(generous(john))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((~creative(X)|~kind(X)))) | ~humble(fred) | [
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6229526607289212659630603
% SZS output start Proof for 6229526607289212659630603
11. ! [X0] : ((quiet(X0) <~> ~wise(X0)) <=> (~curious(X0) & humble(X0))) [input p10]
15. ! [X0] : ((patient(X0) | ~humble(X0)) => (~quiet(X0) & tall(X0))) [input p14]
19. ~wise(fred) [input p18]
25. ~humble(fred) [input hypothesis]
35. ! [X0] : ((~quiet(X0) & tall(X0)) | (~patient(X0) & humble(X0))) [ennf transformation 15]
59. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [nnf transformation 11]
60. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [flattening 59]
122. quiet(X0) | humble(X0) | wise(X0) [cnf transformation 60]
141. ~quiet(X0) | humble(X0) [cnf transformation 35]
148. ~wise(fred) [cnf transformation 19]
156. ~humble(fred) [cnf transformation 25]
296. humble(X4) | wise(X4) | humble(X4) [resolution 122,141]
298. wise(X4) | humble(X4) [duplicate literal removal 296]
300. humble(fred) [resolution 298,148]
302. $false [subsumption resolution 300,156]
% SZS output end Proof for 6229526607289212659630603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not patient is both creative and not old.
Everyone who is both strong and wise is either not creative or not kind and vice versa.
If someone is both curious and strong then susan is not curious and vice versa.
Everyone who is both old and generous is either funny or rich.
Everyone who is either not kind or tall is not creative.
If someone is not curious then someone is both kind and not rich and vice versa.
Everyone who is wise or not creative is not patient and vice versa.
Everyone who is either quiet or brave is not calm.
Everyone who is both not funny and not generous is either not creative or tall and vice versa.
Everyone who is creative or not happy is not funny or happy.
If someone is wise or funny then susan is either curious or not generous.
Everyone who is humble is either humble or not strong.
If someone is both not kind and not funny then someone is not old or generous.
If someone is generous or not generous then someone is not old or old.
Everyone who is both old and not old is either tall or happy and vice versa.
John is rich.
Mary is happy.
Mary is either quiet or not funny.
Susan is not creative or brave.
Fred is either not creative or happy.
Alice is calm or not creative.
Paul is both not funny and not patient.
Someone is quiet or humble. | Mary is not creative. | contradiction | (![X]:((~funny(X)|~patient(X))=>(creative(X)&~old(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((curious(X)&strong(X))))<=>(~curious(susan)))&
(![X]:((old(X)&generous(X))=>(funny(X)<~>rich(X))))&
(![X]:((~kind(X)<~>tall(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((wise(X)|~creative(X))<=>~patient(X)))&
(![X]:((quiet(X)<~>brave(X))=>~calm(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((creative(X)|~happy(X))=>(~funny(X)|happy(X))))&
((?[X]:((wise(X)|funny(X))))=>((curious(susan)<~>~generous(susan))))&
(![X]:(humble(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~kind(X)&~funny(X))))=>(?[X]:((~old(X)|generous(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((~old(X)|old(X)))))&
(![X]:((old(X)&~old(X))<=>(tall(X)<~>happy(X))))&
(rich(john))&
(happy(mary))&
((quiet(mary)<~>~funny(mary)))&
((~creative(susan)|brave(susan)))&
((~creative(fred)<~>happy(fred)))&
((calm(alice)|~creative(alice)))&
((~funny(paul)&~patient(paul)))&
(?[X]:((quiet(X)|humble(X)))) | ~creative(mary) | [
"p0",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 414419265180981108259613
% SZS output start Proof for 414419265180981108259613
1. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~old(X0) & creative(X0))) [input p0]
7. ! [X0] : ((~creative(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
24. ~creative(mary) [input hypothesis]
28. ! [X0] : ((~old(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 1]
52. ! [X0] : (((~creative(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [nnf transformation 7]
53. ! [X0] : ((~creative(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [flattening 52]
72. creative(X0) | patient(X0) [cnf transformation 28]
92. ~patient(X0) | creative(X0) [cnf transformation 53]
130. ~creative(mary) [cnf transformation 24]
174. creative(X0) [subsumption resolution 92,72]
228. $false [subsumption resolution 130,174]
% SZS output end Proof for 414419265180981108259613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not rich is not happy. If someone is either not patient or not generous then someone is calm. Everyone who is generous or rich is happy and vice versa. Everyone who is calm or not generous is both not wise and old and vice versa. If john is either curious or not quiet then someone is tall or not happy and vice versa. Everyone who is either tall or not generous is tall or rich and vice versa. Everyone who is curious is both not creative and not funny and vice versa. Everyone who is not brave is both tall and calm and vice versa. Everyone who is both not creative and kind is both not strong and happy and vice versa. Everyone who is both not creative and curious is both not tall and happy. Everyone who is either tall or not generous is both wise and tall. Everyone who is either not happy or not wise is both rich and funny and vice versa. Everyone who is curious or not kind is happy and vice versa. Everyone who is not humble or not brave is not generous and vice versa. If lucy is both not calm and not brave then alice is either calm or humble. If john is both not strong and not calm then mary is not happy or not brave. Mary is either not generous or not kind. Someone is tall. Mary is either happy or not tall. Paul is not happy or generous. Someone is rich or quiet. John is either not old or kind. | Paul is wise. | entailment | (![X]:((quiet(X)|~rich(X))=>~happy(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(calm(X))))&
(![X]:((generous(X)|rich(X))<=>happy(X)))&
(![X]:((calm(X)|~generous(X))<=>(~wise(X)&old(X))))&
(((curious(john)<~>~quiet(john)))<=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((tall(X)<~>~generous(X))<=>(tall(X)|rich(X))))&
(![X]:(curious(X)<=>(~creative(X)&~funny(X))))&
(![X]:(~brave(X)<=>(tall(X)&calm(X))))&
(![X]:((~creative(X)&kind(X))<=>(~strong(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))=>(~tall(X)&happy(X))))&
(![X]:((tall(X)<~>~generous(X))=>(wise(X)&tall(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>(rich(X)&funny(X))))&
(![X]:((curious(X)|~kind(X))<=>happy(X)))&
(![X]:((~humble(X)|~brave(X))<=>~generous(X)))&
(((~calm(lucy)&~brave(lucy)))=>((calm(alice)<~>humble(alice))))&
(((~strong(john)&~calm(john)))=>((~happy(mary)|~brave(mary))))&
((~generous(mary)<~>~kind(mary)))&
(?[X]:(tall(X)))&
((happy(mary)<~>~tall(mary)))&
((~happy(paul)|generous(paul)))&
(?[X]:((rich(X)|quiet(X))))&
((~old(john)<~>kind(john))) | wise(paul) | [
"p0",
"p2",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9050066337977307696980434
% SZS output start Proof for 9050066337977307696980434
1. ! [X0] : ((~rich(X0) | quiet(X0)) => ~happy(X0)) [input p0]
3. ! [X0] : ((rich(X0) | generous(X0)) <=> happy(X0)) [input p2]
6. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (rich(X0) | tall(X0))) [input p5]
11. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (tall(X0) & wise(X0))) [input p10]
23. ~wise(paul) [input hypothesis]
25. ! [X0] : (~happy(X0) | (rich(X0) & ~quiet(X0))) [ennf transformation 1]
29. ! [X0] : ((tall(X0) & wise(X0)) | (tall(X0) <=> ~generous(X0))) [ennf transformation 11]
38. ! [X0] : (((rich(X0) | generous(X0)) | ~happy(X0)) & (happy(X0) | (~rich(X0) & ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : ((rich(X0) | generous(X0) | ~happy(X0)) & (happy(X0) | (~rich(X0) & ~generous(X0)))) [flattening 38]
46. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 6]
47. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 46]
54. ! [X0] : ((tall(X0) & wise(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 29]
70. ~happy(X0) | rich(X0) [cnf transformation 25]
73. ~generous(X0) | happy(X0) [cnf transformation 39]
90. ~generous(X0) | tall(X0) | ~rich(X0) [cnf transformation 47]
91. generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 47]
105. wise(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 54]
108. tall(X0) | tall(X0) | generous(X0) [cnf transformation 54]
133. ~wise(paul) [cnf transformation 23]
134. tall(X0) | generous(X0) [duplicate literal removal 108]
136. ~tall(X0) | generous(X0) [duplicate literal removal 91]
150. 4 <=> ! [X0] : happy(X0) [avatar definition]
151. happy(X0) <- (4) [avatar component clause 150]
180. generous(X0) [subsumption resolution 134,136]
181. ~tall(X0) | wise(X0) [subsumption resolution 105,180]
226. happy(X0) [resolution 73,180]
227. 4 [avatar split clause 226,150]
230. rich(X0) <- (4) [resolution 151,70]
253. tall(X1) | ~rich(X1) [resolution 90,180]
254. tall(X1) <- (4) [subsumption resolution 253,230]
273. wise(X1) <- (4) [resolution 254,181]
283. $false <- (4) [resolution 273,133]
287. ~4 [avatar contradiction clause 283]
288. $false [avatar sat refutation 227,287]
% SZS output end Proof for 9050066337977307696980434
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich then john is creative.
Everyone who is calm or brave is not calm and vice versa.
If susan is not quiet then susan is either not funny or strong and vice versa.
Everyone who is rich or not wise is either patient or not wise.
If someone is either not funny or quiet then mary is curious or brave.
Everyone who is either not quiet or brave is patient or not happy and vice versa.
If lucy is either not humble or calm then someone is not humble and vice versa.
Everyone who is not humble is generous and vice versa.
Everyone who is either curious or tall is not humble or quiet.
If someone is not patient or generous then someone is both not tall and tall.
Everyone who is both curious and not humble is either happy or wise and vice versa.
Everyone who is both not curious and not generous is either not creative or not kind.
Everyone who is either not patient or not calm is humble and vice versa.
If someone is not strong or calm then john is happy or not old and vice versa.
If someone is wise or curious then john is old.
Someone is brave or humble.
Someone is brave or old.
John is creative.
Someone is both strong and not rich.
Someone is either not funny or not strong. | Lucy is kind. | neutral | ((?[X]:((strong(X)|~rich(X))))=>(creative(john)))&
(![X]:((calm(X)|brave(X))<=>~calm(X)))&
((~quiet(susan))<=>((~funny(susan)<~>strong(susan))))&
(![X]:((rich(X)|~wise(X))=>(patient(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>quiet(X))))=>((curious(mary)|brave(mary))))&
(![X]:((~quiet(X)<~>brave(X))<=>(patient(X)|~happy(X))))&
(((~humble(lucy)<~>calm(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>generous(X)))&
(![X]:((curious(X)<~>tall(X))=>(~humble(X)|quiet(X))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((curious(X)&~humble(X))<=>(happy(X)<~>wise(X))))&
(![X]:((~curious(X)&~generous(X))=>(~creative(X)<~>~kind(X))))&
(![X]:((~patient(X)<~>~calm(X))<=>humble(X)))&
((?[X]:((~strong(X)|calm(X))))<=>((happy(john)|~old(john))))&
((?[X]:((wise(X)|curious(X))))=>(old(john)))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:((brave(X)|old(X))))&
(creative(john))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:((~funny(X)<~>~strong(X)))) | kind(lucy) | [] | null | 0 |
Everyone who is brave or humble is humble or patient and vice versa.
Everyone who is not old or happy is both not creative and kind and vice versa.
Everyone who is either humble or not curious is either not happy or strong.
If someone is not funny then someone is quiet or funny and vice versa.
Everyone who is both strong and patient is either tall or not creative.
If someone is not patient then someone is either tall or old.
If mary is not calm then susan is either not strong or creative and vice versa.
Everyone who is both humble and not funny is not strong.
Everyone who is both quiet and old is both not old and creative and vice versa.
Everyone who is quiet is not generous or calm and vice versa.
Everyone who is both not rich and not quiet is not quiet and vice versa.
If someone is both not generous and tall then paul is not calm or not tall.
Everyone who is both not generous and calm is strong.
Everyone who is not brave is either humble or kind and vice versa.
If someone is either patient or strong then alice is either not generous or not calm.
Lucy is strong or not patient.
Someone is strong or not humble.
Fred is both brave and not calm.
John is both curious and not kind.
John is not quiet.
Someone is generous.
Paul is not brave or not tall.
Fred is both not generous and not calm. | Paul is not brave. | neutral | (![X]:((brave(X)|humble(X))<=>(humble(X)|patient(X))))&
(![X]:((~old(X)|happy(X))<=>(~creative(X)&kind(X))))&
(![X]:((humble(X)<~>~curious(X))=>(~happy(X)<~>strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((quiet(X)|funny(X)))))&
(![X]:((strong(X)&patient(X))=>(tall(X)<~>~creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((tall(X)<~>old(X)))))&
((~calm(mary))<=>((~strong(susan)<~>creative(susan))))&
(![X]:((humble(X)&~funny(X))=>~strong(X)))&
(![X]:((quiet(X)&old(X))<=>(~old(X)&creative(X))))&
(![X]:(quiet(X)<=>(~generous(X)|calm(X))))&
(![X]:((~rich(X)&~quiet(X))<=>~quiet(X)))&
((?[X]:((~generous(X)&tall(X))))=>((~calm(paul)|~tall(paul))))&
(![X]:((~generous(X)&calm(X))=>strong(X)))&
(![X]:(~brave(X)<=>(humble(X)<~>kind(X))))&
((?[X]:((patient(X)<~>strong(X))))=>((~generous(alice)<~>~calm(alice))))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((strong(X)|~humble(X))))&
((brave(fred)&~calm(fred)))&
((curious(john)&~kind(john)))&
(~quiet(john))&
(?[X]:(generous(X)))&
((~brave(paul)|~tall(paul)))&
((~generous(fred)&~calm(fred))) | ~brave(paul) | [] | null | 0 |
Everyone who is generous or not funny is either creative or not rich and vice versa.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Mary is both happy and brave.
Mary is not quiet or patient.
John is either kind or funny.
Lucy is either old or not old.
Susan is not kind.
Someone is not funny or curious. | Paul is quiet. | entailment | (![X]:((generous(X)|~funny(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
((happy(mary)&brave(mary)))&
((~quiet(mary)|patient(mary)))&
((kind(john)<~>funny(john)))&
((old(lucy)<~>~old(lucy)))&
(~kind(susan))&
(?[X]:((~funny(X)|curious(X)))) | quiet(paul) | [
"p0",
"p7",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4190620110435566953250402
% SZS output start Proof for 4190620110435566953250402
1. ! [X0] : ((~funny(X0) | generous(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p0]
8. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p7]
9. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p8]
10. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p9]
11. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p10]
12. ! [X0] : (creative(X0) <=> (patient(X0) | kind(X0))) [input p11]
14. ? [X0] : rich(X0) => kind(paul) [input p13]
15. ! [X0] : (~happy(X0) <=> rich(X0)) [input p14]
22. ~quiet(paul) [input hypothesis]
29. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 8]
30. kind(paul) | ! [X0] : ~rich(X0) [ennf transformation 14]
31. ! [X0] : (((~funny(X0) | generous(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (funny(X0) & ~generous(X0)))) [nnf transformation 1]
32. ! [X0] : ((~funny(X0) | generous(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (funny(X0) & ~generous(X0)))) [flattening 31]
45. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 9]
46. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 45]
47. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 10]
48. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 47]
49. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 11]
50. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ~creative(X0))) [nnf transformation 12]
51. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ~creative(X0))) [flattening 50]
52. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 15]
55. ~rich(X0) | creative(X0) | ~generous(X0) [cnf transformation 32]
58. ~creative(X0) | rich(X0) | funny(X0) [cnf transformation 32]
80. ~rich(X0) | quiet(X0) [cnf transformation 29]
82. ~funny(X0) | ~rich(X0) [cnf transformation 46]
83. ~funny(X0) | rich(X0) [cnf transformation 46]
86. ~quiet(X0) | generous(X0) [cnf transformation 48]
90. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 49]
91. ~happy(lucy) | ~creative(fred) | ~rich(fred) [cnf transformation 49]
93. ~kind(X0) | creative(X0) [cnf transformation 51]
95. kind(paul) | ~rich(X0) [cnf transformation 30]
96. happy(X0) | rich(X0) [cnf transformation 52]
106. ~quiet(paul) [cnf transformation 22]
145. 9 <=> creative(paul) [avatar definition]
146. creative(paul) <- (9) [avatar component clause 145]
157. 12 <=> happy(lucy) [avatar definition]
159. ~happy(lucy) <- (~12) [avatar component clause 157]
173. ~funny(X0) [subsumption resolution 82,83]
175. 15 <=> rich(fred) [avatar definition]
176. rich(fred) <- (15) [avatar component clause 175]
179. 16 <=> creative(fred) [avatar definition]
180. creative(fred) <- (16) [avatar component clause 179]
181. ~creative(fred) <- (~16) [avatar component clause 179]
182. ~15 | ~16 | ~12 [avatar split clause 91,157,179,175]
183. 16 | 15 | ~12 [avatar split clause 90,157,175,179]
187. 17 <=> ! [X0] : ~rich(X0) [avatar definition]
188. ~rich(X0) <- (17) [avatar component clause 187]
190. 18 <=> kind(paul) [avatar definition]
192. kind(paul) <- (18) [avatar component clause 190]
193. 17 | 18 [avatar split clause 95,190,187]
210. rich(lucy) <- (~12) [resolution 96,159]
213. $false <- (~12, 17) [subsumption resolution 210,188]
214. 12 | ~17 [avatar contradiction clause 213]
216. quiet(fred) <- (15) [resolution 176,80]
217. creative(paul) <- (18) [resolution 192,93]
219. 9 | ~18 [avatar split clause 217,190,145]
224. creative(fred) | ~generous(fred) <- (15) [resolution 55,176]
226. ~generous(fred) <- (15, ~16) [subsumption resolution 224,181]
236. generous(fred) <- (15) [resolution 216,86]
238. $false <- (15, ~16) [subsumption resolution 236,226]
239. ~15 | 16 [avatar contradiction clause 238]
261. 26 <=> rich(paul) [avatar definition]
263. rich(paul) <- (26) [avatar component clause 261]
267. rich(paul) | funny(paul) <- (9) [resolution 58,146]
268. rich(fred) | funny(fred) <- (16) [resolution 58,180]
271. rich(paul) <- (9) [subsumption resolution 267,173]
272. 26 | ~9 [avatar split clause 271,145,261]
276. rich(fred) <- (16) [subsumption resolution 268,173]
277. 15 | ~16 [avatar split clause 276,179,175]
307. quiet(paul) <- (26) [resolution 263,80]
308. $false <- (26) [subsumption resolution 307,106]
309. ~26 [avatar contradiction clause 308]
310. $false [avatar sat refutation 182,183,193,214,219,239,272,277,309]
% SZS output end Proof for 4190620110435566953250402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not curious or not tall. Everyone who is not happy is both quiet and calm. If alice is both not creative and not curious then someone is not calm and vice versa. If someone is either funny or not humble then someone is wise or not humble and vice versa. If alice is both not strong and tall then alice is not calm and vice versa. If someone is not strong then someone is either not kind or not quiet and vice versa. Everyone who is both quiet and not tall is both calm and not strong and vice versa. Everyone who is strong or not patient is happy. Everyone who is both old and generous is strong or curious. If susan is both curious and patient then john is both wise and not generous and vice versa. If someone is both not patient and not tall then someone is patient and vice versa. If susan is not brave or not strong then someone is both not patient and kind and vice versa. Everyone who is either happy or not tall is not curious. Everyone who is both patient and not tall is not kind or not rich. Everyone who is not strong or rich is both not kind and generous. Everyone who is rich or not wise is either not calm or kind and vice versa. Someone is either creative or happy. Mary is either happy or brave. Lucy is either not calm or not happy. Someone is either not rich or not calm. Lucy is both not quiet and not calm. Someone is not tall or brave. Someone is both funny and generous. Someone is funny. | Alice is calm. | neutral | (![X]:(strong(X)=>(~curious(X)|~tall(X))))&
(![X]:(~happy(X)=>(quiet(X)&calm(X))))&
(((~creative(alice)&~curious(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((wise(X)|~humble(X)))))&
(((~strong(alice)&tall(alice)))<=>(~calm(alice)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~tall(X))<=>(calm(X)&~strong(X))))&
(![X]:((strong(X)|~patient(X))=>happy(X)))&
(![X]:((old(X)&generous(X))=>(strong(X)|curious(X))))&
(((curious(susan)&patient(susan)))<=>((wise(john)&~generous(john))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:(patient(X))))&
(((~brave(susan)|~strong(susan)))<=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:((happy(X)<~>~tall(X))=>~curious(X)))&
(![X]:((patient(X)&~tall(X))=>(~kind(X)|~rich(X))))&
(![X]:((~strong(X)|rich(X))=>(~kind(X)&generous(X))))&
(![X]:((rich(X)|~wise(X))<=>(~calm(X)<~>kind(X))))&
(?[X]:((creative(X)<~>happy(X))))&
((happy(mary)<~>brave(mary)))&
((~calm(lucy)<~>~happy(lucy)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~quiet(lucy)&~calm(lucy)))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:((funny(X)&generous(X))))&
(?[X]:(funny(X))) | calm(alice) | [] | null | 0 |
If someone is not happy or not brave then susan is both calm and not rich.
If someone is either not funny or funny then paul is either not calm or not tall and vice versa.
If someone is both generous and not generous then someone is kind and vice versa.
Everyone who is not funny is not calm or not generous and vice versa.
If alice is both patient and not generous then someone is wise.
If susan is tall then someone is not brave or not happy and vice versa.
If someone is either not calm or not brave then someone is both generous and not curious.
Everyone who is both rich and funny is not happy and vice versa.
Everyone who is both kind and creative is quiet and vice versa.
Everyone who is happy or old is both not funny and humble.
If lucy is either not generous or generous then someone is not funny or generous and vice versa.
Everyone who is tall or creative is either kind or not humble and vice versa.
Everyone who is not quiet is either not strong or funny and vice versa.
If someone is not brave or humble then someone is either not brave or not generous.
Everyone who is not strong or wise is either old or not rich.
If someone is both not old and not wise then someone is both not strong and curious.
Someone is not strong.
Someone is either patient or brave.
Someone is both not generous and humble.
John is both not quiet and not funny. | John is brave. | entailment | ((?[X]:((~happy(X)|~brave(X))))=>((calm(susan)&~rich(susan))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~calm(paul)<~>~tall(paul))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:(kind(X))))&
(![X]:(~funny(X)<=>(~calm(X)|~generous(X))))&
(((patient(alice)&~generous(alice)))=>(?[X]:(wise(X))))&
((tall(susan))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((rich(X)&funny(X))<=>~happy(X)))&
(![X]:((kind(X)&creative(X))<=>quiet(X)))&
(![X]:((happy(X)|old(X))=>(~funny(X)&humble(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((tall(X)|creative(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>funny(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(old(X)<~>~rich(X))))&
((?[X]:((~old(X)&~wise(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(?[X]:(~strong(X)))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:((~generous(X)&humble(X))))&
((~quiet(john)&~funny(john))) | brave(john) | [
"p0",
"p2",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3523022479007131334901256
% SZS output start Proof for 3523022479007131334901256
1. ? [X0] : (~brave(X0) | ~happy(X0)) => (~rich(susan) & calm(susan)) [input p0]
3. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X0] : kind(X0) [input p2]
6. tall(susan) <=> ? [X0] : (~happy(X0) | ~brave(X0)) [input p5]
8. ! [X0] : ((funny(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
10. ! [X0] : ((old(X0) | happy(X0)) => (humble(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((creative(X0) | tall(X0)) <=> (kind(X0) <~> ~humble(X0))) [input p11]
21. ~brave(john) [input hypothesis]
22. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X1] : kind(X1) [rectify 3]
26. (~rich(susan) & calm(susan)) | ! [X0] : (brave(X0) & happy(X0)) [ennf transformation 1]
30. ! [X0] : ((humble(X0) & ~funny(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 10]
38. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (generous(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (generous(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK1) & generous(sK1)) [choice axiom]
41. ? [X2] : kind(X2) => kind(sK2) [choice axiom]
42. ((~generous(sK1) & generous(sK1)) | ! [X1] : ~kind(X1)) & (kind(sK2) | ! [X3] : (generous(X3) | ~generous(X3))) [skolemisation 39,41,40]
47. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & (? [X0] : (~happy(X0) | ~brave(X0)) | ~tall(susan)) [nnf transformation 6]
48. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & (? [X1] : (~happy(X1) | ~brave(X1)) | ~tall(susan)) [rectify 47]
49. ? [X1] : (~happy(X1) | ~brave(X1)) => (~happy(sK4) | ~brave(sK4)) [choice axiom]
50. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & ((~happy(sK4) | ~brave(sK4)) | ~tall(susan)) [skolemisation 48,49]
55. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (~funny(X0) | ~rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | ~funny(X0) | ~rich(X0))) [flattening 55]
63. ! [X0] : (((creative(X0) | tall(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) & ~tall(X0)))) [nnf transformation 12]
64. ! [X0] : ((creative(X0) | tall(X0) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) & ~tall(X0)))) [flattening 63]
84. ~rich(susan) | brave(X0) [cnf transformation 26]
94. generous(sK1) | ~kind(X1) [cnf transformation 42]
95. ~generous(sK1) | ~kind(X1) [cnf transformation 42]
101. tall(susan) | brave(X0) [cnf transformation 50]
108. rich(X0) | happy(X0) [cnf transformation 56]
115. ~happy(X0) | humble(X0) [cnf transformation 30]
123. ~humble(X0) | kind(X0) | ~tall(X0) [cnf transformation 64]
150. ~brave(john) [cnf transformation 21]
158. 1 <=> ! [X0] : brave(X0) [avatar definition]
159. brave(X0) <- (1) [avatar component clause 158]
161. 2 <=> rich(susan) [avatar definition]
163. ~rich(susan) <- (~2) [avatar component clause 161]
164. 1 | ~2 [avatar split clause 84,161,158]
194. 9 <=> ! [X1] : ~kind(X1) [avatar definition]
195. ~kind(X1) <- (9) [avatar component clause 194]
197. 10 <=> generous(sK1) [avatar definition]
200. 9 | ~10 [avatar split clause 95,197,194]
201. 9 | 10 [avatar split clause 94,197,194]
216. 14 <=> tall(susan) [avatar definition]
220. 1 | 14 [avatar split clause 101,216,158]
286. happy(susan) <- (~2) [resolution 108,163]
291. humble(susan) <- (~2) [resolution 115,286]
307. kind(susan) | ~tall(susan) <- (~2) [resolution 123,291]
310. ~tall(susan) <- (~2, 9) [subsumption resolution 307,195]
314. ~14 | 2 | ~9 [avatar split clause 310,194,161,216]
316. $false <- (1) [resolution 159,150]
321. ~1 [avatar contradiction clause 316]
322. $false [avatar sat refutation 164,200,201,220,314,321]
% SZS output end Proof for 3523022479007131334901256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not tall or old.
If someone is both old and not tall then someone is both calm and curious and vice versa.
If john is not wise then lucy is both not happy and calm.
Everyone who is either not wise or brave is patient.
If someone is not funny or not quiet then john is wise or not creative and vice versa.
Everyone who is both calm and not patient is not funny and vice versa.
Everyone who is not rich is not old and vice versa.
Everyone who is quiet or brave is either strong or wise and vice versa.
If alice is either rich or not tall then alice is both strong and quiet.
If lucy is either not tall or quiet then someone is not tall or generous and vice versa.
If fred is both old and quiet then alice is not kind or not humble and vice versa.
If susan is tall then someone is not creative.
Everyone who is not happy is both brave and quiet and vice versa.
If someone is happy or tall then alice is both not kind and not brave.
Everyone who is not wise is both wise and rich.
If alice is either not patient or brave then someone is either not creative or brave.
John is not tall or quiet.
Lucy is not quiet.
Paul is both not tall and not brave.
Someone is not generous.
Someone is kind.
Someone is not strong.
Lucy is either not wise or not rich.
Someone is both tall and old. | Alice is happy. | entailment | (![X]:(old(X)=>(~tall(X)|old(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:((calm(X)&curious(X)))))&
((~wise(john))=>((~happy(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>brave(X))=>patient(X)))&
((?[X]:((~funny(X)|~quiet(X))))<=>((wise(john)|~creative(john))))&
(![X]:((calm(X)&~patient(X))<=>~funny(X)))&
(![X]:(~rich(X)<=>~old(X)))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)<~>wise(X))))&
(((rich(alice)<~>~tall(alice)))=>((strong(alice)&quiet(alice))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((old(fred)&quiet(fred)))<=>((~kind(alice)|~humble(alice))))&
((tall(susan))=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)<=>(brave(X)&quiet(X))))&
((?[X]:((happy(X)|tall(X))))=>((~kind(alice)&~brave(alice))))&
(![X]:(~wise(X)=>(wise(X)&rich(X))))&
(((~patient(alice)<~>brave(alice)))=>(?[X]:((~creative(X)<~>brave(X)))))&
((~tall(john)|quiet(john)))&
(~quiet(lucy))&
((~tall(paul)&~brave(paul)))&
(?[X]:(~generous(X)))&
(?[X]:(kind(X)))&
(?[X]:(~strong(X)))&
((~wise(lucy)<~>~rich(lucy)))&
(?[X]:((tall(X)&old(X)))) | happy(alice) | [
"p12",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2756988196866383933199680
% SZS output start Proof for 2756988196866383933199680
13. ! [X0] : (~happy(X0) <=> (quiet(X0) & brave(X0))) [input p12]
14. ? [X0] : (tall(X0) | happy(X0)) => (~brave(alice) & ~kind(alice)) [input p13]
24. ? [X0] : (old(X0) & tall(X0)) [input p23]
25. ~happy(alice) [input hypothesis]
27. ! [X0] : (~happy(X0) => (quiet(X0) & brave(X0))) [unused predicate definition removal 13]
34. ! [X0] : ((quiet(X0) & brave(X0)) | happy(X0)) [ennf transformation 27]
35. (~brave(alice) & ~kind(alice)) | ! [X0] : (~tall(X0) & ~happy(X0)) [ennf transformation 14]
73. ? [X0] : (old(X0) & tall(X0)) => (old(sK9) & tall(sK9)) [choice axiom]
74. old(sK9) & tall(sK9) [skolemisation 24,73]
115. brave(X0) | happy(X0) [cnf transformation 34]
120. ~brave(alice) | ~tall(X0) [cnf transformation 35]
136. tall(sK9) [cnf transformation 74]
138. ~happy(alice) [cnf transformation 25]
281. 31 <=> ! [X0] : ~tall(X0) [avatar definition]
282. ~tall(X0) <- (31) [avatar component clause 281]
284. 32 <=> brave(alice) [avatar definition]
286. ~brave(alice) <- (~32) [avatar component clause 284]
287. 31 | ~32 [avatar split clause 120,284,281]
326. happy(alice) <- (~32) [resolution 115,286]
328. $false <- (~32) [subsumption resolution 326,138]
329. 32 [avatar contradiction clause 328]
330. $false <- (31) [resolution 282,136]
333. ~31 [avatar contradiction clause 330]
334. $false [avatar sat refutation 287,329,333]
% SZS output end Proof for 2756988196866383933199680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is either happy or rich.
Everyone who is both brave and not strong is not calm or curious and vice versa.
If lucy is humble or generous then someone is not generous or creative.
If john is both not rich and kind then someone is both strong and not kind and vice versa.
If someone is not calm then paul is either wise or not rich and vice versa.
Everyone who is not patient or old is either patient or strong and vice versa.
If someone is either not old or generous then alice is curious and vice versa.
Everyone who is not rich or generous is either kind or not kind.
Everyone who is either humble or not brave is not brave or patient and vice versa.
If lucy is old or happy then someone is rich and vice versa.
If mary is not generous then lucy is either not rich or kind and vice versa.
Everyone who is either not quiet or calm is not wise.
Everyone who is either generous or not strong is either not kind or kind and vice versa.
If someone is either happy or not patient then someone is tall or funny.
Everyone who is not wise or not curious is generous and vice versa.
Everyone who is both not humble and not creative is both tall and not brave and vice versa.
Mary is either not wise or not generous.
Someone is strong or not wise.
Mary is either quiet or patient.
Someone is either not creative or old.
Someone is calm.
Someone is either not funny or not old.
Someone is not generous. | John is not tall. | neutral | (![X]:((~old(X)<~>old(X))=>(happy(X)<~>rich(X))))&
(![X]:((brave(X)&~strong(X))<=>(~calm(X)|curious(X))))&
(((humble(lucy)|generous(lucy)))=>(?[X]:((~generous(X)|creative(X)))))&
(((~rich(john)&kind(john)))<=>(?[X]:((strong(X)&~kind(X)))))&
((?[X]:(~calm(X)))<=>((wise(paul)<~>~rich(paul))))&
(![X]:((~patient(X)|old(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((~old(X)<~>generous(X))))<=>(curious(alice)))&
(![X]:((~rich(X)|generous(X))=>(kind(X)<~>~kind(X))))&
(![X]:((humble(X)<~>~brave(X))<=>(~brave(X)|patient(X))))&
(((old(lucy)|happy(lucy)))<=>(?[X]:(rich(X))))&
((~generous(mary))<=>((~rich(lucy)<~>kind(lucy))))&
(![X]:((~quiet(X)<~>calm(X))=>~wise(X)))&
(![X]:((generous(X)<~>~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>generous(X)))&
(![X]:((~humble(X)&~creative(X))<=>(tall(X)&~brave(X))))&
((~wise(mary)<~>~generous(mary)))&
(?[X]:((strong(X)|~wise(X))))&
((quiet(mary)<~>patient(mary)))&
(?[X]:((~creative(X)<~>old(X))))&
(?[X]:(calm(X)))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:(~generous(X))) | ~tall(john) | [] | null | 0 |
If someone is either funny or not quiet then paul is rich and vice versa. Everyone who is either not calm or not quiet is both not strong and not rich and vice versa. If mary is creative or not strong then susan is both not kind and kind and vice versa. If mary is both not rich and not old then alice is both not tall and tall. Everyone who is both not old and not generous is both old and not creative and vice versa. Everyone who is brave is wise and vice versa. Everyone who is both not calm and not funny is curious or calm. If paul is not happy then susan is either not strong or generous. Everyone who is either not patient or not creative is both not happy and not generous and vice versa. Everyone who is both generous and not strong is both rich and not brave and vice versa. If alice is both not rich and not brave then someone is either not wise or not patient and vice versa. Everyone who is wise or kind is old or kind and vice versa. Everyone who is old or not strong is brave or not humble. Everyone who is either not happy or not wise is not curious and vice versa. If someone is generous then fred is both old and calm and vice versa. Everyone who is not wise is not happy. John is not happy or wise. Someone is either not wise or not rich. Paul is brave. Lucy is not brave. Someone is either wise or curious. Lucy is both tall and humble. Someone is not rich or wise. | John is quiet. | neutral | ((?[X]:((funny(X)<~>~quiet(X))))<=>(rich(paul)))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~strong(X)&~rich(X))))&
(((creative(mary)|~strong(mary)))<=>((~kind(susan)&kind(susan))))&
(((~rich(mary)&~old(mary)))=>((~tall(alice)&tall(alice))))&
(![X]:((~old(X)&~generous(X))<=>(old(X)&~creative(X))))&
(![X]:(brave(X)<=>wise(X)))&
(![X]:((~calm(X)&~funny(X))=>(curious(X)|calm(X))))&
((~happy(paul))=>((~strong(susan)<~>generous(susan))))&
(![X]:((~patient(X)<~>~creative(X))<=>(~happy(X)&~generous(X))))&
(![X]:((generous(X)&~strong(X))<=>(rich(X)&~brave(X))))&
(((~rich(alice)&~brave(alice)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:((wise(X)|kind(X))<=>(old(X)|kind(X))))&
(![X]:((old(X)|~strong(X))=>(brave(X)|~humble(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>~curious(X)))&
((?[X]:(generous(X)))<=>((old(fred)&calm(fred))))&
(![X]:(~wise(X)=>~happy(X)))&
((~happy(john)|wise(john)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(brave(paul))&
(~brave(lucy))&
(?[X]:((wise(X)<~>curious(X))))&
((tall(lucy)&humble(lucy)))&
(?[X]:((~rich(X)|wise(X)))) | quiet(john) | [] | null | 0 |
Everyone who is both not patient and funny is not curious. Everyone who is quiet is both not humble and not creative. Everyone who is not humble is both happy and not humble. Everyone who is either kind or creative is not quiet or not brave. Everyone who is not tall or not kind is not old and vice versa. If someone is either not funny or not brave then someone is both rich and not strong and vice versa. Everyone who is not happy is both not wise and humble and vice versa. If paul is not patient or brave then someone is quiet and vice versa. Everyone who is calm or not humble is not happy or not curious and vice versa. Everyone who is not old or not quiet is not brave and vice versa. Everyone who is old is patient and vice versa. Everyone who is not humble is brave and vice versa. If someone is either not calm or happy then someone is not old or not wise. Everyone who is not kind is not humble and vice versa. If someone is both not brave and not old then someone is both not tall and not generous and vice versa. Everyone who is both not curious and tall is not quiet or not patient and vice versa. Susan is calm or not wise. John is not generous or tall. Someone is both tall and wise. | Susan is curious. | contradiction | (![X]:((~patient(X)&funny(X))=>~curious(X)))&
(![X]:(quiet(X)=>(~humble(X)&~creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~humble(X))))&
(![X]:((kind(X)<~>creative(X))=>(~quiet(X)|~brave(X))))&
(![X]:((~tall(X)|~kind(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>~brave(X))))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:(~happy(X)<=>(~wise(X)&humble(X))))&
(((~patient(paul)|brave(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((calm(susan)|~wise(susan)))&
((~generous(john)|tall(john)))&
(?[X]:((tall(X)&wise(X)))) | curious(susan) | [
"p1",
"p2",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5402054286453801217427463
% SZS output start Proof for 5402054286453801217427463
2. ! [X0] : (quiet(X0) => (~creative(X0) & ~humble(X0))) [input p1]
3. ! [X0] : (~humble(X0) => (~humble(X0) & happy(X0))) [input p2]
9. ! [X0] : ((~humble(X0) | calm(X0)) <=> (~curious(X0) | ~happy(X0))) [input p8]
16. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p15]
20. curious(susan) [input hypothesis]
26. ! [X0] : ((~creative(X0) & ~humble(X0)) | ~quiet(X0)) [ennf transformation 2]
27. ! [X0] : ((~humble(X0) & happy(X0)) | humble(X0)) [ennf transformation 3]
46. ! [X0] : (((~humble(X0) | calm(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (humble(X0) & ~calm(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | calm(X0) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | (humble(X0) & ~calm(X0)))) [flattening 46]
62. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 16]
63. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~tall(X0) | curious(X0))) [flattening 62]
67. ~humble(X0) | ~quiet(X0) [cnf transformation 26]
69. happy(X0) | humble(X0) [cnf transformation 27]
89. ~curious(X0) | ~happy(X0) | humble(X0) [cnf transformation 47]
108. ~curious(X0) | quiet(X0) [cnf transformation 63]
116. curious(susan) [cnf transformation 20]
168. ~curious(X0) | humble(X0) [subsumption resolution 89,69]
242. quiet(susan) [resolution 108,116]
262. humble(susan) [resolution 168,116]
288. ~quiet(susan) [resolution 262,67]
289. $false [subsumption resolution 288,242]
% SZS output end Proof for 5402054286453801217427463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not brave and not quiet then john is either curious or not old and vice versa. If someone is humble then susan is both calm and strong and vice versa. If paul is quiet or not old then mary is old and vice versa. If someone is either not brave or calm then mary is either not happy or brave and vice versa. Everyone who is not brave is kind and vice versa. If john is humble or not patient then someone is either not generous or not curious and vice versa. If lucy is not funny or wise then lucy is either not wise or tall. If someone is happy then someone is not strong. Everyone who is rich or not tall is both curious and not creative and vice versa. Everyone who is not humble or not strong is strong and vice versa. If someone is happy or kind then someone is either not curious or funny and vice versa. Everyone who is generous is either happy or not tall and vice versa. Everyone who is not old or curious is brave and vice versa. Everyone who is both not wise and creative is not tall or not funny and vice versa. Everyone who is either not curious or wise is not wise and vice versa. Someone is creative. Susan is either tall or calm. Lucy is both not brave and kind. Paul is either brave or not tall. Fred is old or calm. Susan is not kind or strong. Susan is old or not curious. | Paul is not happy. | entailment | (((~brave(paul)&~quiet(paul)))<=>((curious(john)<~>~old(john))))&
((?[X]:(humble(X)))<=>((calm(susan)&strong(susan))))&
(((quiet(paul)|~old(paul)))<=>(old(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((~happy(mary)<~>brave(mary))))&
(![X]:(~brave(X)<=>kind(X)))&
(((humble(john)|~patient(john)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~funny(lucy)|wise(lucy)))=>((~wise(lucy)<~>tall(lucy))))&
((?[X]:(happy(X)))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~humble(X)|~strong(X))<=>strong(X)))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
(![X]:((~old(X)|curious(X))<=>brave(X)))&
(![X]:((~wise(X)&creative(X))<=>(~tall(X)|~funny(X))))&
(![X]:((~curious(X)<~>wise(X))<=>~wise(X)))&
(?[X]:(creative(X)))&
((tall(susan)<~>calm(susan)))&
((~brave(lucy)&kind(lucy)))&
((brave(paul)<~>~tall(paul)))&
((old(fred)|calm(fred)))&
((~kind(susan)|strong(susan)))&
((old(susan)|~curious(susan))) | ~happy(paul) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5773185830048998544357558
% SZS output start Proof for 5773185830048998544357558
8. ? [X0] : happy(X0) => ? [X0] : ~strong(X0) [input p7]
10. ! [X0] : ((~strong(X0) | ~humble(X0)) <=> strong(X0)) [input p9]
23. happy(paul) [input hypothesis]
24. ? [X0] : happy(X0) => ? [X1] : ~strong(X1) [rectify 8]
27. ? [X1] : ~strong(X1) | ! [X0] : ~happy(X0) [ennf transformation 24]
48. ? [X0] : ~strong(X0) | ! [X1] : ~happy(X1) [rectify 27]
49. ? [X0] : ~strong(X0) => ~strong(sK3) [choice axiom]
50. ~strong(sK3) | ! [X1] : ~happy(X1) [skolemisation 48,49]
53. ! [X0] : (((~strong(X0) | ~humble(X0)) | ~strong(X0)) & (strong(X0) | (strong(X0) & humble(X0)))) [nnf transformation 10]
54. ! [X0] : ((~strong(X0) | ~humble(X0) | ~strong(X0)) & (strong(X0) | (strong(X0) & humble(X0)))) [flattening 53]
102. ~strong(sK3) | ~happy(X1) [cnf transformation 50]
109. strong(X0) | strong(X0) [cnf transformation 54]
143. happy(paul) [cnf transformation 23]
146. strong(X0) [duplicate literal removal 109]
274. 26 <=> ! [X1] : ~happy(X1) [avatar definition]
275. ~happy(X1) <- (26) [avatar component clause 274]
277. 27 <=> strong(sK3) [avatar definition]
279. ~strong(sK3) <- (~27) [avatar component clause 277]
280. 26 | ~27 [avatar split clause 102,277,274]
328. $false <- (~27) [subsumption resolution 279,146]
329. 27 [avatar contradiction clause 328]
335. $false <- (26) [resolution 275,143]
336. ~26 [avatar contradiction clause 335]
337. $false [avatar sat refutation 280,329,336]
% SZS output end Proof for 5773185830048998544357558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and funny is happy. Everyone who is not calm is brave or wise and vice versa. If paul is kind then someone is curious. Everyone who is both not kind and kind is either patient or not calm and vice versa. Everyone who is not happy is not rich or not quiet. Everyone who is creative or not wise is not strong or humble and vice versa. Everyone who is not rich or not curious is kind or not happy. Everyone who is both not happy and not rich is either strong or not curious. Everyone who is humble is either not rich or not humble and vice versa. If john is both tall and not humble then fred is either kind or calm and vice versa. If lucy is either generous or not brave then someone is both humble and not curious. If someone is not humble or not rich then susan is patient and vice versa. If fred is brave or funny then mary is either humble or funny and vice versa. If someone is humble then mary is both rich and kind and vice versa. If someone is either not happy or not brave then someone is both not quiet and happy and vice versa. If someone is either kind or tall then alice is not funny. John is quiet or humble. Lucy is not brave or not generous. Someone is both curious and calm. Someone is both brave and not quiet. Alice is both quiet and curious. Someone is both happy and not brave. Someone is both strong and not curious. Someone is creative or generous. | Paul is humble. | contradiction | (![X]:((~creative(X)&funny(X))=>happy(X)))&
(![X]:(~calm(X)<=>(brave(X)|wise(X))))&
((kind(paul))=>(?[X]:(curious(X))))&
(![X]:((~kind(X)&kind(X))<=>(patient(X)<~>~calm(X))))&
(![X]:(~happy(X)=>(~rich(X)|~quiet(X))))&
(![X]:((creative(X)|~wise(X))<=>(~strong(X)|humble(X))))&
(![X]:((~rich(X)|~curious(X))=>(kind(X)|~happy(X))))&
(![X]:((~happy(X)&~rich(X))=>(strong(X)<~>~curious(X))))&
(![X]:(humble(X)<=>(~rich(X)<~>~humble(X))))&
(((tall(john)&~humble(john)))<=>((kind(fred)<~>calm(fred))))&
(((generous(lucy)<~>~brave(lucy)))=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(patient(susan)))&
(((brave(fred)|funny(fred)))<=>((humble(mary)<~>funny(mary))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
((quiet(john)|humble(john)))&
((~brave(lucy)|~generous(lucy)))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:((brave(X)&~quiet(X))))&
((quiet(alice)&curious(alice)))&
(?[X]:((happy(X)&~brave(X))))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((creative(X)|generous(X)))) | humble(paul) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 241474787239007193188092
% SZS output start Proof for 241474787239007193188092
9. ! [X0] : (humble(X0) <=> (~rich(X0) <~> ~humble(X0))) [input p8]
14. ? [X0] : humble(X0) <=> (kind(mary) & rich(mary)) [input p13]
25. humble(paul) [input hypothesis]
47. ! [X0] : ((humble(X0) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) & (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | ~humble(X0))) [nnf transformation 9]
59. (? [X0] : humble(X0) | (~kind(mary) | ~rich(mary))) & ((kind(mary) & rich(mary)) | ! [X0] : ~humble(X0)) [nnf transformation 14]
60. (? [X0] : humble(X0) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X0] : ~humble(X0)) [flattening 59]
61. (? [X0] : humble(X0) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X1] : ~humble(X1)) [rectify 60]
62. ? [X0] : humble(X0) => humble(sK3) [choice axiom]
63. (humble(sK3) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X1] : ~humble(X1)) [skolemisation 61,62]
100. ~humble(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 47]
103. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 47]
123. rich(mary) | ~humble(X1) [cnf transformation 63]
147. humble(paul) [cnf transformation 25]
148. ~humble(X0) | ~rich(X0) [duplicate literal removal 100]
149. humble(X0) | ~rich(X0) [duplicate literal removal 103]
161. ~rich(X0) [subsumption resolution 148,149]
228. 15 <=> ! [X1] : ~humble(X1) [avatar definition]
229. ~humble(X1) <- (15) [avatar component clause 228]
235. ~humble(X1) [subsumption resolution 123,161]
236. 15 [avatar split clause 235,228]
297. $false <- (15) [resolution 229,147]
298. ~15 [avatar contradiction clause 297]
299. $false [avatar sat refutation 236,298]
% SZS output end Proof for 241474787239007193188092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both humble and not creative.
If someone is rich then lucy is rich.
Everyone who is both funny and not old is either patient or not happy.
Everyone who is either generous or not humble is not brave and vice versa.
Everyone who is both not calm and strong is either brave or quiet and vice versa.
If someone is not funny then someone is not old or patient and vice versa.
Everyone who is both quiet and not wise is either not quiet or not kind and vice versa.
If someone is either not creative or curious then alice is both not rich and rich.
Everyone who is either tall or not rich is both not patient and not funny and vice versa.
If someone is either not tall or creative then someone is either kind or tall and vice versa.
Everyone who is either not happy or brave is both not brave and not rich and vice versa.
Everyone who is either quiet or kind is tall.
Everyone who is not humble is either happy or not creative and vice versa.
Everyone who is strong or kind is both not strong and not funny.
Everyone who is not old is either not tall or not old and vice versa.
If someone is both not funny and not strong then susan is rich and vice versa.
Someone is not happy or creative.
Someone is happy.
Someone is not strong or not old.
Someone is both not patient and not funny.
Lucy is either not wise or creative.
Fred is not brave or not funny.
Someone is old.
Paul is not calm. | Fred is not brave. | entailment | (![X]:(~happy(X)=>(humble(X)&~creative(X))))&
((?[X]:(rich(X)))=>(rich(lucy)))&
(![X]:((funny(X)&~old(X))=>(patient(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~humble(X))<=>~brave(X)))&
(![X]:((~calm(X)&strong(X))<=>(brave(X)<~>quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((quiet(X)&~wise(X))<=>(~quiet(X)<~>~kind(X))))&
((?[X]:((~creative(X)<~>curious(X))))=>((~rich(alice)&rich(alice))))&
(![X]:((tall(X)<~>~rich(X))<=>(~patient(X)&~funny(X))))&
((?[X]:((~tall(X)<~>creative(X))))<=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~brave(X)&~rich(X))))&
(![X]:((quiet(X)<~>kind(X))=>tall(X)))&
(![X]:(~humble(X)<=>(happy(X)<~>~creative(X))))&
(![X]:((strong(X)|kind(X))=>(~strong(X)&~funny(X))))&
(![X]:(~old(X)<=>(~tall(X)<~>~old(X))))&
((?[X]:((~funny(X)&~strong(X))))<=>(rich(susan)))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:(happy(X)))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((~patient(X)&~funny(X))))&
((~wise(lucy)<~>creative(lucy)))&
((~brave(fred)|~funny(fred)))&
(?[X]:(old(X)))&
(~calm(paul)) | ~brave(fred) | [
"p0",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3482454196406515359125591
% SZS output start Proof for 3482454196406515359125591
1. ! [X0] : (~happy(X0) => (~creative(X0) & humble(X0))) [input p0]
11. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (~rich(X0) & ~brave(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> (happy(X0) <~> ~creative(X0))) [input p12]
25. brave(fred) [input hypothesis]
28. ! [X0] : ((~creative(X0) & humble(X0)) | happy(X0)) [ennf transformation 1]
54. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (rich(X0) | brave(X0))) & ((~rich(X0) & ~brave(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 11]
55. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | rich(X0) | brave(X0)) & ((~rich(X0) & ~brave(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 54]
57. ! [X0] : ((~humble(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | humble(X0))) [nnf transformation 13]
74. humble(X0) | happy(X0) [cnf transformation 28]
75. ~creative(X0) | happy(X0) [cnf transformation 28]
117. ~brave(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 55]
127. ~humble(X0) | happy(X0) | creative(X0) [cnf transformation 57]
149. brave(fred) [cnf transformation 25]
153. ~brave(X0) | ~happy(X0) [duplicate literal removal 117]
240. happy(X0) | creative(X0) [subsumption resolution 127,74]
241. happy(X0) [subsumption resolution 240,75]
268. 24 <=> brave(fred) [avatar definition]
269. brave(fred) <- (24) [avatar component clause 268]
276. 24 [avatar split clause 149,268]
290. ~happy(fred) <- (24) [resolution 153,269]
291. $false <- (24) [subsumption resolution 290,241]
292. ~24 [avatar contradiction clause 291]
293. $false [avatar sat refutation 276,292]
% SZS output end Proof for 3482454196406515359125591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and humble is not funny and vice versa.
Everyone who is either not strong or old is either not kind or patient.
If someone is not strong then susan is both not quiet and not generous.
If mary is generous or not brave then susan is not rich or not curious.
Everyone who is either rich or not kind is patient.
If someone is both humble and not generous then mary is strong and vice versa.
If lucy is not strong then someone is not happy or not wise.
Everyone who is both rich and not generous is either tall or not strong and vice versa.
Everyone who is both not old and not rich is not happy or not strong.
If mary is funny or tall then lucy is funny or not tall and vice versa.
Everyone who is curious or not humble is not kind and vice versa.
Everyone who is both wise and kind is not wise.
Everyone who is either not rich or generous is not tall and vice versa.
If john is both brave and generous then susan is not funny.
Everyone who is both not humble and not strong is kind and vice versa.
If john is either tall or not funny then someone is old.
Someone is either not generous or not creative.
John is patient or not curious.
Someone is either not strong or wise.
Someone is kind or not strong.
Lucy is not humble or creative.
Paul is both rich and creative.
Someone is both not kind and not generous.
Someone is strong or not rich. | Susan is not kind. | entailment | (![X]:((brave(X)&humble(X))<=>~funny(X)))&
(![X]:((~strong(X)<~>old(X))=>(~kind(X)<~>patient(X))))&
((?[X]:(~strong(X)))=>((~quiet(susan)&~generous(susan))))&
(((generous(mary)|~brave(mary)))=>((~rich(susan)|~curious(susan))))&
(![X]:((rich(X)<~>~kind(X))=>patient(X)))&
((?[X]:((humble(X)&~generous(X))))<=>(strong(mary)))&
((~strong(lucy))=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:((rich(X)&~generous(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((~old(X)&~rich(X))=>(~happy(X)|~strong(X))))&
(((funny(mary)|tall(mary)))<=>((funny(lucy)|~tall(lucy))))&
(![X]:((curious(X)|~humble(X))<=>~kind(X)))&
(![X]:((wise(X)&kind(X))=>~wise(X)))&
(![X]:((~rich(X)<~>generous(X))<=>~tall(X)))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
((patient(john)|~curious(john)))&
(?[X]:((~strong(X)<~>wise(X))))&
(?[X]:((kind(X)|~strong(X))))&
((~humble(lucy)|creative(lucy)))&
((rich(paul)&creative(paul)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((strong(X)|~rich(X)))) | ~kind(susan) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7696664709909184178131905
% SZS output start Proof for 7696664709909184178131905
11. ! [X0] : ((~humble(X0) | curious(X0)) <=> ~kind(X0)) [input p10]
15. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> kind(X0)) [input p14]
25. kind(susan) [input hypothesis]
51. ! [X0] : (((~humble(X0) | curious(X0)) | kind(X0)) & (~kind(X0) | (humble(X0) & ~curious(X0)))) [nnf transformation 11]
52. ! [X0] : ((~humble(X0) | curious(X0) | kind(X0)) & (~kind(X0) | (humble(X0) & ~curious(X0)))) [flattening 51]
54. ! [X0] : (((~strong(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | (strong(X0) | humble(X0)))) [nnf transformation 15]
55. ! [X0] : (((~strong(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | strong(X0) | humble(X0))) [flattening 54]
97. ~kind(X0) | humble(X0) [cnf transformation 52]
106. ~humble(X0) | ~kind(X0) [cnf transformation 55]
122. kind(susan) [cnf transformation 25]
201. ~kind(X0) [subsumption resolution 106,97]
265. $false [subsumption resolution 122,201]
% SZS output end Proof for 7696664709909184178131905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not tall or not kind then susan is both brave and curious.
Everyone who is either not wise or not humble is not generous or not old and vice versa.
Everyone who is either curious or not strong is either funny or not calm.
If someone is both generous and happy then susan is both funny and not creative.
Everyone who is humble is wise or happy and vice versa.
If someone is both old and quiet then mary is either strong or humble and vice versa.
Everyone who is either not curious or happy is either not calm or tall and vice versa.
Everyone who is happy is quiet or humble and vice versa.
Everyone who is not brave or calm is both strong and wise.
If lucy is either wise or strong then paul is either not happy or not tall.
If someone is quiet then someone is both not old and not happy and vice versa.
If someone is either not rich or not wise then susan is not curious and vice versa.
Everyone who is curious or not old is either creative or not quiet and vice versa.
Everyone who is rich or not happy is both wise and not calm and vice versa.
If alice is rich or not funny then someone is strong and vice versa.
Everyone who is tall or strong is not generous.
Paul is both happy and not strong.
Fred is either old or kind.
Someone is not patient.
Lucy is either not tall or not funny.
Someone is strong or not patient.
Alice is either not happy or patient. | Alice is not rich. | neutral | (((~tall(fred)<~>~kind(fred)))=>((brave(susan)&curious(susan))))&
(![X]:((~wise(X)<~>~humble(X))<=>(~generous(X)|~old(X))))&
(![X]:((curious(X)<~>~strong(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((generous(X)&happy(X))))=>((funny(susan)&~creative(susan))))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
((?[X]:((old(X)&quiet(X))))<=>((strong(mary)<~>humble(mary))))&
(![X]:((~curious(X)<~>happy(X))<=>(~calm(X)<~>tall(X))))&
(![X]:(happy(X)<=>(quiet(X)|humble(X))))&
(![X]:((~brave(X)|calm(X))=>(strong(X)&wise(X))))&
(((wise(lucy)<~>strong(lucy)))=>((~happy(paul)<~>~tall(paul))))&
((?[X]:(quiet(X)))<=>(?[X]:((~old(X)&~happy(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~curious(susan)))&
(![X]:((curious(X)|~old(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:((rich(X)|~happy(X))<=>(wise(X)&~calm(X))))&
(((rich(alice)|~funny(alice)))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)|strong(X))=>~generous(X)))&
((happy(paul)&~strong(paul)))&
((old(fred)<~>kind(fred)))&
(?[X]:(~patient(X)))&
((~tall(lucy)<~>~funny(lucy)))&
(?[X]:((strong(X)|~patient(X))))&
((~happy(alice)<~>patient(alice))) | ~rich(alice) | [] | null | 0 |
If someone is not calm then lucy is both tall and old. If paul is kind or old then someone is happy or generous. Everyone who is not happy or humble is not wise or funny and vice versa. Everyone who is either not old or kind is either not calm or generous and vice versa. If fred is both not quiet and rich then mary is both tall and creative. Everyone who is creative is calm and vice versa. Everyone who is happy or quiet is patient or old. Everyone who is either tall or strong is both not brave and funny and vice versa. Everyone who is both not curious and brave is both creative and not humble. If someone is not strong then someone is strong. If someone is both curious and old then someone is not curious or not happy. Everyone who is both rich and not wise is both patient and not brave. Everyone who is both not curious and not humble is either calm or not funny and vice versa. Everyone who is not curious is both patient and generous. If alice is both brave and not rich then alice is either kind or tall and vice versa. If mary is both not calm and old then someone is either patient or not humble and vice versa. John is kind or not creative. John is tall. Someone is both not funny and not strong. John is not happy or humble. Someone is both not funny and not calm. Someone is either brave or happy. Alice is both not creative and kind. Someone is rich. | Lucy is kind. | neutral | ((?[X]:(~calm(X)))=>((tall(lucy)&old(lucy))))&
(((kind(paul)|old(paul)))=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~happy(X)|humble(X))<=>(~wise(X)|funny(X))))&
(![X]:((~old(X)<~>kind(X))<=>(~calm(X)<~>generous(X))))&
(((~quiet(fred)&rich(fred)))=>((tall(mary)&creative(mary))))&
(![X]:(creative(X)<=>calm(X)))&
(![X]:((happy(X)|quiet(X))=>(patient(X)|old(X))))&
(![X]:((tall(X)<~>strong(X))<=>(~brave(X)&funny(X))))&
(![X]:((~curious(X)&brave(X))=>(creative(X)&~humble(X))))&
((?[X]:(~strong(X)))=>(?[X]:(strong(X))))&
((?[X]:((curious(X)&old(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((rich(X)&~wise(X))=>(patient(X)&~brave(X))))&
(![X]:((~curious(X)&~humble(X))<=>(calm(X)<~>~funny(X))))&
(![X]:(~curious(X)=>(patient(X)&generous(X))))&
(((brave(alice)&~rich(alice)))<=>((kind(alice)<~>tall(alice))))&
(((~calm(mary)&old(mary)))<=>(?[X]:((patient(X)<~>~humble(X)))))&
((kind(john)|~creative(john)))&
(tall(john))&
(?[X]:((~funny(X)&~strong(X))))&
((~happy(john)|humble(john)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((~creative(alice)&kind(alice)))&
(?[X]:(rich(X))) | kind(lucy) | [] | null | 0 |
If mary is not brave then lucy is either happy or curious and vice versa. If someone is both not kind and rich then john is either humble or not old. If paul is not tall then someone is curious or not quiet and vice versa. Everyone who is either humble or old is not brave and vice versa. Everyone who is either calm or not calm is both generous and not quiet and vice versa. If alice is humble or creative then someone is both generous and curious. If john is generous or old then lucy is old or not strong. If paul is both not calm and not old then paul is both brave and not calm. If someone is either not kind or not tall then alice is both not kind and strong and vice versa. If someone is both kind and old then someone is both generous and not kind and vice versa. If paul is both creative and funny then someone is both funny and not patient. Everyone who is not curious is both not tall and not curious. If someone is either happy or patient then someone is both not humble and not quiet and vice versa. If someone is not kind then someone is either brave or curious and vice versa. Someone is both generous and not quiet. Lucy is not strong or generous. Someone is both funny and generous. Someone is either not old or not happy. Someone is both not rich and patient. Someone is not funny or wise. Lucy is both calm and not quiet. | Lucy is generous. | entailment | ((~brave(mary))<=>((happy(lucy)<~>curious(lucy))))&
((?[X]:((~kind(X)&rich(X))))=>((humble(john)<~>~old(john))))&
((~tall(paul))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((humble(X)<~>old(X))<=>~brave(X)))&
(![X]:((calm(X)<~>~calm(X))<=>(generous(X)&~quiet(X))))&
(((humble(alice)|creative(alice)))=>(?[X]:((generous(X)&curious(X)))))&
(((generous(john)|old(john)))=>((old(lucy)|~strong(lucy))))&
(((~calm(paul)&~old(paul)))=>((brave(paul)&~calm(paul))))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~kind(alice)&strong(alice))))&
((?[X]:((kind(X)&old(X))))<=>(?[X]:((generous(X)&~kind(X)))))&
(((creative(paul)&funny(paul)))=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(~curious(X)=>(~tall(X)&~curious(X))))&
((?[X]:((happy(X)<~>patient(X))))<=>(?[X]:((~humble(X)&~quiet(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)<~>curious(X)))))&
(?[X]:((generous(X)&~quiet(X))))&
((~strong(lucy)|generous(lucy)))&
(?[X]:((funny(X)&generous(X))))&
(?[X]:((~old(X)<~>~happy(X))))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:((~funny(X)|wise(X))))&
((calm(lucy)&~quiet(lucy))) | generous(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2394659862463350418211245
% SZS output start Proof for 2394659862463350418211245
5. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (~quiet(X0) & generous(X0))) [input p4]
22. ~generous(lucy) [input hypothesis]
44. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 5]
45. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [flattening 44]
88. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
89. generous(X0) | calm(X0) | calm(X0) [cnf transformation 45]
131. ~generous(lucy) [cnf transformation 22]
132. generous(X0) | ~calm(X0) [duplicate literal removal 88]
133. generous(X0) | calm(X0) [duplicate literal removal 89]
174. generous(X0) [subsumption resolution 132,133]
322. $false [subsumption resolution 131,174]
% SZS output end Proof for 2394659862463350418211245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not curious is not humble and vice versa.
If susan is not brave or not generous then alice is both not tall and calm.
Everyone who is both patient and brave is patient or not humble and vice versa.
If someone is either happy or quiet then lucy is both not curious and not humble and vice versa.
Everyone who is both kind and not wise is generous or not tall and vice versa.
Everyone who is not funny is both not curious and tall.
If fred is either creative or wise then susan is both not old and curious.
If paul is both not old and not funny then lucy is not creative.
If someone is either not patient or wise then paul is curious or not calm and vice versa.
If someone is either not calm or generous then someone is either not generous or creative.
Everyone who is either patient or rich is happy or not old.
If lucy is not kind or not patient then someone is not happy or not strong.
If fred is not quiet or not patient then paul is either not patient or not quiet and vice versa.
Everyone who is tall is strong.
Everyone who is not calm is not tall or calm and vice versa.
Susan is either generous or rich.
Alice is generous or calm.
Someone is either patient or tall.
Lucy is not wise or not funny.
Someone is either not quiet or not wise.
Someone is not old or tall.
Susan is creative or wise. | Susan is generous. | entailment | (![X]:((~old(X)|~curious(X))<=>~humble(X)))&
(((~brave(susan)|~generous(susan)))=>((~tall(alice)&calm(alice))))&
(![X]:((patient(X)&brave(X))<=>(patient(X)|~humble(X))))&
((?[X]:((happy(X)<~>quiet(X))))<=>((~curious(lucy)&~humble(lucy))))&
(![X]:((kind(X)&~wise(X))<=>(generous(X)|~tall(X))))&
(![X]:(~funny(X)=>(~curious(X)&tall(X))))&
(((creative(fred)<~>wise(fred)))=>((~old(susan)&curious(susan))))&
(((~old(paul)&~funny(paul)))=>(~creative(lucy)))&
((?[X]:((~patient(X)<~>wise(X))))<=>((curious(paul)|~calm(paul))))&
((?[X]:((~calm(X)<~>generous(X))))=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:((patient(X)<~>rich(X))=>(happy(X)|~old(X))))&
(((~kind(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~quiet(fred)|~patient(fred)))<=>((~patient(paul)<~>~quiet(paul))))&
(![X]:(tall(X)=>strong(X)))&
(![X]:(~calm(X)<=>(~tall(X)|calm(X))))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|calm(alice)))&
(?[X]:((patient(X)<~>tall(X))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((~old(X)|tall(X))))&
((creative(susan)|wise(susan))) | generous(susan) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9223296139732784784982597
% SZS output start Proof for 9223296139732784784982597
2. (~generous(susan) | ~brave(susan)) => (calm(alice) & ~tall(alice)) [input p1]
15. ! [X0] : (~calm(X0) <=> (calm(X0) | ~tall(X0))) [input p14]
23. ~generous(susan) [input hypothesis]
25. (calm(alice) & ~tall(alice)) | (generous(susan) & brave(susan)) [ennf transformation 2]
61. ! [X0] : ((~calm(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | calm(X0))) [nnf transformation 15]
62. ! [X0] : ((~calm(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | calm(X0))) [flattening 61]
78. calm(alice) | generous(susan) [cnf transformation 25]
125. ~calm(X0) | ~calm(X0) [cnf transformation 62]
136. ~generous(susan) [cnf transformation 23]
138. ~calm(X0) [duplicate literal removal 125]
140. 1 <=> generous(susan) [avatar definition]
144. 2 <=> calm(alice) [avatar definition]
146. calm(alice) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 78,144,140]
346. ~1 [avatar split clause 136,140]
347. $false <- (2) [subsumption resolution 146,138]
348. ~2 [avatar contradiction clause 347]
349. $false [avatar sat refutation 147,346,348]
% SZS output end Proof for 9223296139732784784982597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not old is strong or quiet. If someone is either strong or not wise then mary is creative. Everyone who is both funny and strong is curious or not rich and vice versa. If alice is wise then someone is rich or not quiet. Everyone who is either kind or not old is either curious or not wise and vice versa. Everyone who is not calm or wise is either quiet or calm and vice versa. Everyone who is both not humble and not kind is either not wise or strong and vice versa. If someone is either not curious or quiet then someone is calm or not brave. Everyone who is both not creative and not curious is happy or not old and vice versa. Everyone who is not patient or not wise is not strong. If someone is either not funny or not old then john is not old or tall. Everyone who is either not generous or generous is both not tall and not brave and vice versa. Everyone who is tall is rich or quiet and vice versa. Everyone who is both kind and tall is not humble or patient. If someone is both not quiet and not curious then paul is either tall or not brave and vice versa. Someone is either not tall or not strong. Someone is strong. Lucy is calm or quiet. Alice is generous or not wise. Someone is old or generous. | Mary is not curious. | entailment | (![X]:((strong(X)&~old(X))=>(strong(X)|quiet(X))))&
((?[X]:((strong(X)<~>~wise(X))))=>(creative(mary)))&
(![X]:((funny(X)&strong(X))<=>(curious(X)|~rich(X))))&
((wise(alice))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((kind(X)<~>~old(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|wise(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~wise(X)<~>strong(X))))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~curious(X))<=>(happy(X)|~old(X))))&
(![X]:((~patient(X)|~wise(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>((~old(john)|tall(john))))&
(![X]:((~generous(X)<~>generous(X))<=>(~tall(X)&~brave(X))))&
(![X]:(tall(X)<=>(rich(X)|quiet(X))))&
(![X]:((kind(X)&tall(X))=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((tall(paul)<~>~brave(paul))))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:(strong(X)))&
((calm(lucy)|quiet(lucy)))&
((generous(alice)|~wise(alice)))&
(?[X]:((old(X)|generous(X)))) | ~curious(mary) | [
"p1",
"p2",
"p4",
"p6",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 310516290102352243967163
% SZS output start Proof for 310516290102352243967163
2. ? [X0] : (strong(X0) <~> ~wise(X0)) => creative(mary) [input p1]
3. ! [X0] : ((strong(X0) & funny(X0)) <=> (~rich(X0) | curious(X0))) [input p2]
5. ! [X0] : ((kind(X0) <~> ~old(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p4]
7. ! [X0] : ((~kind(X0) & ~humble(X0)) <=> (~wise(X0) <~> strong(X0))) [input p6]
9. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (~old(X0) | happy(X0))) [input p8]
10. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~strong(X0)) [input p9]
12. ! [X0] : ((~generous(X0) <~> generous(X0)) <=> (~brave(X0) & ~tall(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (quiet(X0) | rich(X0))) [input p12]
21. curious(mary) [input hypothesis]
23. ! [X0] : (~wise(X0) => ~strong(X0)) [pure predicate removal 10]
27. creative(mary) | ! [X0] : (strong(X0) <=> ~wise(X0)) [ennf transformation 2]
30. ! [X0] : (~strong(X0) | wise(X0)) [ennf transformation 23]
33. creative(mary) | ! [X0] : ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0))) [nnf transformation 27]
34. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 3]
35. ! [X0] : (((strong(X0) & funny(X0)) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ~strong(X0) | ~funny(X0))) [flattening 34]
38. ! [X0] : ((((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0))))) [nnf transformation 5]
41. ! [X0] : (((~kind(X0) & ~humble(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | (kind(X0) | humble(X0)))) [nnf transformation 7]
42. ! [X0] : (((~kind(X0) & ~humble(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | kind(X0) | humble(X0))) [flattening 41]
47. ! [X0] : (((~curious(X0) & ~creative(X0)) | (old(X0) & ~happy(X0))) & ((~old(X0) | happy(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 9]
48. ! [X0] : (((~curious(X0) & ~creative(X0)) | (old(X0) & ~happy(X0))) & (~old(X0) | happy(X0) | curious(X0) | creative(X0))) [flattening 47]
50. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [nnf transformation 12]
51. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [flattening 50]
52. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 13]
53. ! [X0] : ((tall(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~tall(X0))) [flattening 52]
66. creative(mary) | ~wise(X0) | ~strong(X0) [cnf transformation 33]
71. ~curious(X0) | strong(X0) [cnf transformation 35]
72. rich(X0) | strong(X0) [cnf transformation 35]
78. ~curious(X0) | kind(X0) | ~wise(X0) | ~old(X0) [cnf transformation 38]
93. ~kind(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 42]
98. ~creative(X0) | old(X0) [cnf transformation 48]
101. ~strong(X0) | wise(X0) [cnf transformation 30]
104. ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 51]
105. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 51]
111. tall(X0) | ~rich(X0) [cnf transformation 53]
125. curious(mary) [cnf transformation 21]
126. ~tall(X0) | generous(X0) [duplicate literal removal 104]
127. ~generous(X0) | ~tall(X0) [duplicate literal removal 105]
136. 2 <=> creative(mary) [avatar definition]
138. creative(mary) <- (2) [avatar component clause 136]
141. 3 <=> ! [X0] : (~wise(X0) | ~strong(X0)) [avatar definition]
142. ~wise(X0) | ~strong(X0) <- (3) [avatar component clause 141]
143. 3 | 2 [avatar split clause 66,136,141]
190. ~tall(X0) [subsumption resolution 126,127]
192. ~rich(X0) [subsumption resolution 111,190]
212. strong(mary) [resolution 71,125]
213. strong(X0) [resolution 72,192]
214. old(mary) <- (2) [resolution 98,138]
216. wise(X0) [resolution 101,213]
243. kind(mary) | ~wise(mary) | ~old(mary) [resolution 78,125]
244. kind(mary) | ~old(mary) [subsumption resolution 243,216]
245. kind(mary) <- (2) [subsumption resolution 244,214]
248. ~wise(mary) | ~strong(mary) <- (2) [resolution 245,93]
250. ~strong(mary) <- (2) [subsumption resolution 248,216]
251. $false <- (2) [subsumption resolution 250,212]
252. ~2 [avatar contradiction clause 251]
254. ~strong(X0) <- (3) [subsumption resolution 142,216]
255. $false <- (3) [subsumption resolution 254,213]
256. ~3 [avatar contradiction clause 255]
257. $false [avatar sat refutation 143,252,256]
% SZS output end Proof for 310516290102352243967163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and not brave then someone is happy.
Everyone who is generous is both not happy and not old and vice versa.
Everyone who is not brave or not kind is not creative or not curious.
If someone is both funny and not patient then john is both generous and strong.
If someone is creative then john is either tall or not humble.
If someone is both not old and curious then fred is both not wise and not tall and vice versa.
Everyone who is either not happy or not curious is generous or patient and vice versa.
Everyone who is either not kind or not humble is humble or not happy.
Everyone who is both strong and happy is both wise and not brave.
Everyone who is not calm is either not happy or kind and vice versa.
Everyone who is both tall and creative is kind or not humble.
Everyone who is either happy or not calm is quiet or not humble and vice versa.
If alice is not happy then john is either not wise or strong and vice versa.
If john is both quiet and not strong then alice is patient.
Everyone who is both quiet and not old is either not calm or not happy.
If someone is tall or not old then someone is either not patient or humble and vice versa.
Paul is tall.
Someone is not calm or strong.
Someone is not tall.
John is both wise and not strong.
Someone is both not brave and calm.
Someone is both not quiet and brave.
Someone is happy or not quiet. | Fred is wise. | neutral | (((~kind(john)&~brave(john)))=>(?[X]:(happy(X))))&
(![X]:(generous(X)<=>(~happy(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~creative(X)|~curious(X))))&
((?[X]:((funny(X)&~patient(X))))=>((generous(john)&strong(john))))&
((?[X]:(creative(X)))=>((tall(john)<~>~humble(john))))&
((?[X]:((~old(X)&curious(X))))<=>((~wise(fred)&~tall(fred))))&
(![X]:((~happy(X)<~>~curious(X))<=>(generous(X)|patient(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(humble(X)|~happy(X))))&
(![X]:((strong(X)&happy(X))=>(wise(X)&~brave(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>kind(X))))&
(![X]:((tall(X)&creative(X))=>(kind(X)|~humble(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(quiet(X)|~humble(X))))&
((~happy(alice))<=>((~wise(john)<~>strong(john))))&
(((quiet(john)&~strong(john)))=>(patient(alice)))&
(![X]:((quiet(X)&~old(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(tall(paul))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:(~tall(X)))&
((wise(john)&~strong(john)))&
(?[X]:((~brave(X)&calm(X))))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((happy(X)|~quiet(X)))) | wise(fred) | [] | null | 0 |
If someone is wise then someone is tall or curious. If someone is not quiet or not brave then someone is happy and vice versa. Everyone who is either not wise or not creative is curious or not humble and vice versa. If someone is either generous or not happy then someone is kind. Everyone who is either curious or patient is curious and vice versa. Everyone who is curious is not happy. Everyone who is either rich or not old is kind or not curious. Everyone who is not creative or kind is kind and vice versa. Everyone who is either kind or happy is both happy and not patient and vice versa. If fred is old or not funny then lucy is either not curious or not quiet and vice versa. If someone is not wise then lucy is not curious or calm and vice versa. Everyone who is both not calm and patient is both not happy and curious. If lucy is both not generous and calm then someone is both wise and generous. If someone is either not generous or funny then someone is funny and vice versa. Everyone who is curious is either not humble or not rich. Everyone who is not creative is wise or tall and vice versa. Susan is not wise or not calm. Someone is creative or not curious. Lucy is either not wise or tall. Susan is both not patient and not generous. Fred is both not brave and strong. Someone is either not funny or not strong. | Susan is not curious. | entailment | ((?[X]:(wise(X)))=>(?[X]:((tall(X)|curious(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(curious(X)|~humble(X))))&
((?[X]:((generous(X)<~>~happy(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>patient(X))<=>curious(X)))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((rich(X)<~>~old(X))=>(kind(X)|~curious(X))))&
(![X]:((~creative(X)|kind(X))<=>kind(X)))&
(![X]:((kind(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(((old(fred)|~funny(fred)))<=>((~curious(lucy)<~>~quiet(lucy))))&
((?[X]:(~wise(X)))<=>((~curious(lucy)|calm(lucy))))&
(![X]:((~calm(X)&patient(X))=>(~happy(X)&curious(X))))&
(((~generous(lucy)&calm(lucy)))=>(?[X]:((wise(X)&generous(X)))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:(funny(X))))&
(![X]:(curious(X)=>(~humble(X)<~>~rich(X))))&
(![X]:(~creative(X)<=>(wise(X)|tall(X))))&
((~wise(susan)|~calm(susan)))&
(?[X]:((creative(X)|~curious(X))))&
((~wise(lucy)<~>tall(lucy)))&
((~patient(susan)&~generous(susan)))&
((~brave(fred)&strong(fred)))&
(?[X]:((~funny(X)<~>~strong(X)))) | ~curious(susan) | [
"p3",
"p4",
"p5",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2356497288646654940297978
% SZS output start Proof for 2356497288646654940297978
4. ? [X0] : (generous(X0) <~> ~happy(X0)) => ? [X0] : kind(X0) [input p3]
5. ! [X0] : ((curious(X0) <~> patient(X0)) <=> curious(X0)) [input p4]
6. ! [X0] : (curious(X0) => ~happy(X0)) [input p5]
9. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (~patient(X0) & happy(X0))) [input p8]
20. ~generous(susan) & ~patient(susan) [input p19]
23. curious(susan) [input hypothesis]
26. ? [X0] : (generous(X0) <~> ~happy(X0)) => ? [X1] : kind(X1) [rectify 4]
29. ? [X1] : kind(X1) | ! [X0] : (generous(X0) <=> ~happy(X0)) [ennf transformation 26]
30. ! [X0] : (~happy(X0) | ~curious(X0)) [ennf transformation 6]
48. ? [X1] : kind(X1) | ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 29]
49. ? [X0] : kind(X0) | ! [X1] : ((generous(X1) | happy(X1)) & (~happy(X1) | ~generous(X1))) [rectify 48]
50. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
51. kind(sK3) | ! [X1] : ((generous(X1) | happy(X1)) & (~happy(X1) | ~generous(X1))) [skolemisation 49,50]
52. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 5]
56. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 9]
57. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 56]
92. kind(sK3) | generous(X1) | happy(X1) [cnf transformation 51]
94. curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 52]
96. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
97. ~happy(X0) | ~curious(X0) [cnf transformation 30]
103. happy(X0) | happy(X0) | ~kind(X0) [cnf transformation 57]
108. ~happy(X0) | ~kind(X0) | patient(X0) | ~happy(X0) [cnf transformation 57]
136. ~generous(susan) [cnf transformation 20]
141. curious(susan) [cnf transformation 23]
142. happy(X0) | ~kind(X0) [duplicate literal removal 103]
143. ~happy(X0) | ~kind(X0) | patient(X0) [duplicate literal removal 108]
144. curious(X0) | ~patient(X0) [duplicate literal removal 94]
145. ~patient(X0) | ~curious(X0) [duplicate literal removal 96]
183. 10 <=> ! [X1] : (generous(X1) | happy(X1)) [avatar definition]
184. generous(X1) | happy(X1) <- (10) [avatar component clause 183]
186. 11 <=> kind(sK3) [avatar definition]
188. kind(sK3) <- (11) [avatar component clause 186]
189. 10 | 11 [avatar split clause 92,186,183]
194. ~patient(X0) [subsumption resolution 144,145]
195. ~happy(X0) | ~kind(X0) [subsumption resolution 143,194]
196. ~kind(X0) [subsumption resolution 142,195]
310. $false <- (11) [subsumption resolution 188,196]
311. ~11 [avatar contradiction clause 310]
319. happy(susan) <- (10) [resolution 184,136]
322. ~curious(susan) <- (10) [resolution 319,97]
323. $false <- (10) [subsumption resolution 322,141]
324. ~10 [avatar contradiction clause 323]
325. $false [avatar sat refutation 189,311,324]
% SZS output end Proof for 2356497288646654940297978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and old then alice is not tall and vice versa. If someone is not funny or curious then john is not happy or not tall. Everyone who is funny or not calm is not kind or not calm. If someone is not brave then lucy is either kind or strong and vice versa. If someone is not rich or not calm then alice is both not creative and calm and vice versa. Everyone who is not calm is happy and vice versa. If paul is both old and calm then someone is either quiet or not tall. If someone is calm or strong then susan is either creative or not happy. If someone is not humble or not wise then susan is either not kind or humble. If someone is both strong and not happy then mary is strong and vice versa. If mary is either not brave or rich then someone is kind or curious and vice versa. Everyone who is generous is kind and vice versa. If susan is either not brave or not kind then someone is not kind. Everyone who is not strong or not rich is both not rich and not calm and vice versa. If someone is strong then someone is both not rich and not wise. Everyone who is old is either funny or rich. Paul is not rich. Fred is not humble. Lucy is both not humble and tall. Paul is generous or not wise. Someone is either not kind or rich. Someone is either not funny or not creative. Someone is not brave or not generous. Lucy is either calm or not patient. | Alice is strong. | entailment | ((?[X]:((~kind(X)&old(X))))<=>(~tall(alice)))&
((?[X]:((~funny(X)|curious(X))))=>((~happy(john)|~tall(john))))&
(![X]:((funny(X)|~calm(X))=>(~kind(X)|~calm(X))))&
((?[X]:(~brave(X)))<=>((kind(lucy)<~>strong(lucy))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~creative(alice)&calm(alice))))&
(![X]:(~calm(X)<=>happy(X)))&
(((old(paul)&calm(paul)))=>(?[X]:((quiet(X)<~>~tall(X)))))&
((?[X]:((calm(X)|strong(X))))=>((creative(susan)<~>~happy(susan))))&
((?[X]:((~humble(X)|~wise(X))))=>((~kind(susan)<~>humble(susan))))&
((?[X]:((strong(X)&~happy(X))))<=>(strong(mary)))&
(((~brave(mary)<~>rich(mary)))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(generous(X)<=>kind(X)))&
(((~brave(susan)<~>~kind(susan)))=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~rich(X)&~calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:(old(X)=>(funny(X)<~>rich(X))))&
(~rich(paul))&
(~humble(fred))&
((~humble(lucy)&tall(lucy)))&
((generous(paul)|~wise(paul)))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((calm(lucy)<~>~patient(lucy))) | strong(alice) | [
"p4",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7598297530853029293162540
% SZS output start Proof for 7598297530853029293162540
5. ? [X0] : (~calm(X0) | ~rich(X0)) <=> (calm(alice) & ~creative(alice)) [input p4]
14. ! [X0] : ((~rich(X0) | ~strong(X0)) <=> (~calm(X0) & ~rich(X0))) [input p13]
17. ~rich(paul) [input p16]
25. ~strong(alice) [input hypothesis]
46. (? [X0] : (~calm(X0) | ~rich(X0)) | (~calm(alice) | creative(alice))) & ((calm(alice) & ~creative(alice)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 5]
47. (? [X0] : (~calm(X0) | ~rich(X0)) | ~calm(alice) | creative(alice)) & ((calm(alice) & ~creative(alice)) | ! [X0] : (calm(X0) & rich(X0))) [flattening 46]
48. (? [X0] : (~calm(X0) | ~rich(X0)) | ~calm(alice) | creative(alice)) & ((calm(alice) & ~creative(alice)) | ! [X1] : (calm(X1) & rich(X1))) [rectify 47]
49. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK2) | ~rich(sK2)) [choice axiom]
50. ((~calm(sK2) | ~rich(sK2)) | ~calm(alice) | creative(alice)) & ((calm(alice) & ~creative(alice)) | ! [X1] : (calm(X1) & rich(X1))) [skolemisation 48,49]
69. ! [X0] : (((~rich(X0) | ~strong(X0)) | (calm(X0) | rich(X0))) & ((~calm(X0) & ~rich(X0)) | (rich(X0) & strong(X0)))) [nnf transformation 14]
70. ! [X0] : ((~rich(X0) | ~strong(X0) | calm(X0) | rich(X0)) & ((~calm(X0) & ~rich(X0)) | (rich(X0) & strong(X0)))) [flattening 69]
97. calm(alice) | rich(X1) [cnf transformation 50]
127. ~calm(X0) | strong(X0) [cnf transformation 70]
134. ~rich(paul) [cnf transformation 17]
146. ~strong(alice) [cnf transformation 25]
205. 14 <=> calm(alice) [avatar definition]
206. calm(alice) <- (14) [avatar component clause 205]
222. 18 <=> ! [X1] : rich(X1) [avatar definition]
223. rich(X1) <- (18) [avatar component clause 222]
224. 18 | 14 [avatar split clause 97,205,222]
402. $false <- (18) [resolution 223,134]
403. ~18 [avatar contradiction clause 402]
413. strong(alice) <- (14) [resolution 206,127]
415. $false <- (14) [subsumption resolution 413,146]
416. ~14 [avatar contradiction clause 415]
417. $false [avatar sat refutation 224,403,416]
% SZS output end Proof for 7598297530853029293162540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not curious is not happy.
If someone is either humble or not curious then someone is not strong.
If mary is both not curious and old then someone is both not curious and humble and vice versa.
Everyone who is both not patient and not generous is both not wise and brave.
Everyone who is either tall or funny is both humble and not wise and vice versa.
Everyone who is wise is calm or not calm.
Everyone who is happy or old is calm or humble and vice versa.
Everyone who is not humble is not strong or not brave.
Everyone who is either not kind or not quiet is either not rich or humble.
Everyone who is either not humble or curious is both not rich and patient.
Everyone who is not calm is not kind.
If someone is either not calm or not curious then john is not rich or not humble and vice versa.
If someone is creative or calm then alice is both not kind and not humble.
Everyone who is rich is patient or not humble.
Everyone who is not generous or not humble is both not curious and not strong and vice versa.
Everyone who is both not patient and brave is both calm and not happy and vice versa.
Someone is either not curious or not kind.
John is both not curious and not old.
Someone is generous.
Someone is both not calm and funny.
Someone is either not calm or not generous.
Fred is curious.
Someone is happy or not brave.
Alice is not curious or not patient. | Alice is humble. | neutral | (![X]:((~funny(X)&~curious(X))=>~happy(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:(~strong(X))))&
(((~curious(mary)&old(mary)))<=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((~patient(X)&~generous(X))=>(~wise(X)&brave(X))))&
(![X]:((tall(X)<~>funny(X))<=>(humble(X)&~wise(X))))&
(![X]:(wise(X)=>(calm(X)|~calm(X))))&
(![X]:((happy(X)|old(X))<=>(calm(X)|humble(X))))&
(![X]:(~humble(X)=>(~strong(X)|~brave(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:((~humble(X)<~>curious(X))=>(~rich(X)&patient(X))))&
(![X]:(~calm(X)=>~kind(X)))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~rich(john)|~humble(john))))&
((?[X]:((creative(X)|calm(X))))=>((~kind(alice)&~humble(alice))))&
(![X]:(rich(X)=>(patient(X)|~humble(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~curious(X)&~strong(X))))&
(![X]:((~patient(X)&brave(X))<=>(calm(X)&~happy(X))))&
(?[X]:((~curious(X)<~>~kind(X))))&
((~curious(john)&~old(john)))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:((~calm(X)<~>~generous(X))))&
(curious(fred))&
(?[X]:((happy(X)|~brave(X))))&
((~curious(alice)|~patient(alice))) | humble(alice) | [] | null | 0 |
If someone is either not happy or not brave then someone is either not wise or humble and vice versa.
If someone is both not wise and not generous then fred is calm or not old.
If paul is creative or not brave then alice is either curious or not funny.
Everyone who is not humble or not tall is both not old and quiet and vice versa.
Everyone who is not brave is either calm or not curious and vice versa.
If someone is both patient and kind then john is either funny or rich.
Everyone who is tall is patient.
Everyone who is not kind or quiet is both humble and patient and vice versa.
Everyone who is either old or not strong is both not creative and quiet.
Everyone who is either not curious or not funny is either not funny or patient and vice versa.
Everyone who is not curious or brave is quiet or tall and vice versa.
If someone is old or calm then mary is not creative.
Everyone who is tall is either rich or not funny and vice versa.
If john is both not tall and generous then paul is rich or not strong and vice versa.
If someone is not kind then someone is both strong and creative and vice versa.
If paul is either humble or not calm then mary is both humble and tall.
Fred is both strong and humble.
Fred is either not happy or calm.
Susan is not quiet or not curious.
Someone is not brave.
Someone is either tall or humble.
Mary is quiet.
Someone is generous or not kind. | Susan is not generous. | neutral | ((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
((?[X]:((~wise(X)&~generous(X))))=>((calm(fred)|~old(fred))))&
(((creative(paul)|~brave(paul)))=>((curious(alice)<~>~funny(alice))))&
(![X]:((~humble(X)|~tall(X))<=>(~old(X)&quiet(X))))&
(![X]:(~brave(X)<=>(calm(X)<~>~curious(X))))&
((?[X]:((patient(X)&kind(X))))=>((funny(john)<~>rich(john))))&
(![X]:(tall(X)=>patient(X)))&
(![X]:((~kind(X)|quiet(X))<=>(humble(X)&patient(X))))&
(![X]:((old(X)<~>~strong(X))=>(~creative(X)&quiet(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((~curious(X)|brave(X))<=>(quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>(~creative(mary)))&
(![X]:(tall(X)<=>(rich(X)<~>~funny(X))))&
(((~tall(john)&generous(john)))<=>((rich(paul)|~strong(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((strong(X)&creative(X)))))&
(((humble(paul)<~>~calm(paul)))=>((humble(mary)&tall(mary))))&
((strong(fred)&humble(fred)))&
((~happy(fred)<~>calm(fred)))&
((~quiet(susan)|~curious(susan)))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)<~>humble(X))))&
(quiet(mary))&
(?[X]:((generous(X)|~kind(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
If someone is both happy and calm then alice is either not brave or curious and vice versa.
If someone is either not brave or generous then fred is quiet and vice versa.
If someone is both curious and not funny then someone is wise.
If someone is both not tall and not patient then someone is both quiet and not creative.
If someone is not brave or not curious then paul is old and vice versa.
Lucy is wise or not humble.
Alice is not brave.
Susan is both not humble and quiet.
Someone is not kind.
Susan is both tall and not kind.
John is both kind and wise.
Someone is either kind or not quiet.
John is both brave and not patient. | Susan is curious. | entailment | (![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:(wise(X))))&
((?[X]:((~tall(X)&~patient(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
((?[X]:((~brave(X)|~curious(X))))<=>(old(paul)))&
((wise(lucy)|~humble(lucy)))&
(~brave(alice))&
((~humble(susan)&quiet(susan)))&
(?[X]:(~kind(X)))&
((tall(susan)&~kind(susan)))&
((kind(john)&wise(john)))&
(?[X]:((kind(X)<~>~quiet(X))))&
((brave(john)&~patient(john))) | curious(susan) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1582693285288750167411905
% SZS output start Proof for 1582693285288750167411905
4. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p3]
8. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p7]
25. ~curious(susan) [input hypothesis]
26. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 8]
39. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 26]
49. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 4]
53. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 39]
54. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK0) & quiet(sK0)) [choice axiom]
55. (patient(sK0) & quiet(sK0)) | ! [X1] : curious(X1) [skolemisation 53,54]
89. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 49]
93. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 49]
106. quiet(sK0) | curious(X1) [cnf transformation 55]
107. patient(sK0) | curious(X1) [cnf transformation 55]
140. ~curious(susan) [cnf transformation 25]
141. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 89]
143. ~calm(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 93]
146. ~quiet(X0) | ~patient(X0) [subsumption resolution 141,143]
148. 1 <=> ! [X1] : curious(X1) [avatar definition]
149. curious(X1) <- (1) [avatar component clause 148]
151. 2 <=> patient(sK0) [avatar definition]
153. patient(sK0) <- (2) [avatar component clause 151]
154. 1 | 2 [avatar split clause 107,151,148]
156. 3 <=> quiet(sK0) [avatar definition]
158. quiet(sK0) <- (3) [avatar component clause 156]
159. 1 | 3 [avatar split clause 106,156,148]
279. ~patient(sK0) <- (3) [resolution 146,158]
280. $false <- (2, 3) [subsumption resolution 279,153]
281. ~2 | ~3 [avatar contradiction clause 280]
282. $false <- (1) [resolution 149,140]
285. ~1 [avatar contradiction clause 282]
286. $false [avatar sat refutation 154,159,281,285]
% SZS output end Proof for 1582693285288750167411905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both patient and not brave then susan is kind or strong and vice versa.
Everyone who is either patient or not strong is not creative and vice versa.
If john is not creative then alice is both not patient and old.
If someone is both kind and not creative then someone is both old and quiet and vice versa.
If fred is kind then john is both quiet and not patient and vice versa.
If alice is both patient and not calm then alice is rich or creative.
Everyone who is either kind or not happy is either brave or not patient and vice versa.
If alice is both brave and quiet then alice is tall.
Everyone who is either not tall or not generous is not patient or patient and vice versa.
Everyone who is both tall and wise is not strong or wise.
Everyone who is both happy and tall is strong or not patient and vice versa.
Everyone who is either tall or not happy is either strong or rich.
Everyone who is either rich or kind is not rich and vice versa.
If someone is both not old and curious then lucy is humble or patient and vice versa.
If someone is both not brave and wise then someone is both quiet and calm and vice versa.
Everyone who is both creative and not happy is either tall or humble and vice versa.
Someone is old.
Alice is not curious.
Mary is not happy.
Someone is calm.
Someone is either not humble or strong.
Someone is not curious.
Someone is both not wise and not calm. | John is not tall. | contradiction | (((patient(alice)&~brave(alice)))<=>((kind(susan)|strong(susan))))&
(![X]:((patient(X)<~>~strong(X))<=>~creative(X)))&
((~creative(john))=>((~patient(alice)&old(alice))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:((old(X)&quiet(X)))))&
((kind(fred))<=>((quiet(john)&~patient(john))))&
(((patient(alice)&~calm(alice)))=>((rich(alice)|creative(alice))))&
(![X]:((kind(X)<~>~happy(X))<=>(brave(X)<~>~patient(X))))&
(((brave(alice)&quiet(alice)))=>(tall(alice)))&
(![X]:((~tall(X)<~>~generous(X))<=>(~patient(X)|patient(X))))&
(![X]:((tall(X)&wise(X))=>(~strong(X)|wise(X))))&
(![X]:((happy(X)&tall(X))<=>(strong(X)|~patient(X))))&
(![X]:((tall(X)<~>~happy(X))=>(strong(X)<~>rich(X))))&
(![X]:((rich(X)<~>kind(X))<=>~rich(X)))&
((?[X]:((~old(X)&curious(X))))<=>((humble(lucy)|patient(lucy))))&
((?[X]:((~brave(X)&wise(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(![X]:((creative(X)&~happy(X))<=>(tall(X)<~>humble(X))))&
(?[X]:(old(X)))&
(~curious(alice))&
(~happy(mary))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)&~calm(X)))) | ~tall(john) | [
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7825868303022973276293903
% SZS output start Proof for 7825868303022973276293903
5. kind(fred) <=> (~patient(john) & quiet(john)) [input p4]
11. ! [X0] : ((tall(X0) & happy(X0)) <=> (~patient(X0) | strong(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> kind(X0)) <=> ~rich(X0)) [input p12]
24. ~tall(john) [input hypothesis]
43. (kind(fred) | (patient(john) | ~quiet(john))) & ((~patient(john) & quiet(john)) | ~kind(fred)) [nnf transformation 5]
44. (kind(fred) | patient(john) | ~quiet(john)) & ((~patient(john) & quiet(john)) | ~kind(fred)) [flattening 43]
48. ! [X0] : (((tall(X0) & happy(X0)) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | (~tall(X0) | ~happy(X0)))) [nnf transformation 11]
49. ! [X0] : (((tall(X0) & happy(X0)) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ~tall(X0) | ~happy(X0))) [flattening 48]
51. ! [X0] : ((((~kind(X0) | ~rich(X0)) & (kind(X0) | rich(X0))) | rich(X0)) & (~rich(X0) | ((rich(X0) | ~kind(X0)) & (kind(X0) | ~rich(X0))))) [nnf transformation 13]
91. ~patient(john) | ~kind(fred) [cnf transformation 44]
114. tall(X0) | patient(X0) [cnf transformation 49]
119. ~rich(X0) | kind(X0) | ~rich(X0) [cnf transformation 51]
121. kind(X0) | rich(X0) | rich(X0) [cnf transformation 51]
147. ~tall(john) [cnf transformation 24]
148. ~rich(X0) | kind(X0) [duplicate literal removal 119]
149. kind(X0) | rich(X0) [duplicate literal removal 121]
212. 14 <=> patient(john) [avatar definition]
213. ~patient(john) <- (~14) [avatar component clause 212]
216. 15 <=> kind(fred) [avatar definition]
217. ~kind(fred) <- (~15) [avatar component clause 216]
220. ~15 | ~14 [avatar split clause 91,212,216]
249. kind(X0) [subsumption resolution 148,149]
310. $false <- (~15) [subsumption resolution 217,249]
311. 15 [avatar contradiction clause 310]
316. patient(john) [resolution 114,147]
317. $false <- (~14) [subsumption resolution 316,213]
318. 14 [avatar contradiction clause 317]
319. $false [avatar sat refutation 220,311,318]
% SZS output end Proof for 7825868303022973276293903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then fred is not generous or not brave and vice versa.
Everyone who is not strong is both not rich and not old and vice versa.
If someone is not generous or not quiet then someone is both not creative and not funny and vice versa.
Everyone who is not generous is both generous and not quiet and vice versa.
Everyone who is both kind and humble is not creative and vice versa.
If lucy is either not curious or not old then fred is patient or not strong.
Everyone who is happy is either patient or curious and vice versa.
Everyone who is both creative and not humble is either wise or kind and vice versa.
Everyone who is calm or not curious is not patient.
Everyone who is both wise and happy is funny or not happy.
Everyone who is both humble and not happy is curious or not calm and vice versa.
If someone is not creative or patient then someone is either not funny or rich and vice versa.
Everyone who is wise or not strong is both not strong and kind.
If someone is both not brave and tall then someone is not happy and vice versa.
If someone is not happy or not tall then fred is either tall or not rich and vice versa.
If john is both not wise and curious then someone is rich or not calm and vice versa.
Paul is either wise or patient.
Someone is either tall or not funny.
Someone is either creative or kind.
Mary is either humble or tall.
Someone is both not curious and not strong.
Someone is creative.
Someone is both rich and not wise. | Lucy is not creative. | neutral | ((?[X]:(~kind(X)))<=>((~generous(fred)|~brave(fred))))&
(![X]:(~strong(X)<=>(~rich(X)&~old(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:(~generous(X)<=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)&humble(X))<=>~creative(X)))&
(((~curious(lucy)<~>~old(lucy)))=>((patient(fred)|~strong(fred))))&
(![X]:(happy(X)<=>(patient(X)<~>curious(X))))&
(![X]:((creative(X)&~humble(X))<=>(wise(X)<~>kind(X))))&
(![X]:((calm(X)|~curious(X))=>~patient(X)))&
(![X]:((wise(X)&happy(X))=>(funny(X)|~happy(X))))&
(![X]:((humble(X)&~happy(X))<=>(curious(X)|~calm(X))))&
((?[X]:((~creative(X)|patient(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((wise(X)|~strong(X))=>(~strong(X)&kind(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~happy(X)|~tall(X))))<=>((tall(fred)<~>~rich(fred))))&
(((~wise(john)&curious(john)))<=>(?[X]:((rich(X)|~calm(X)))))&
((wise(paul)<~>patient(paul)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((humble(mary)<~>tall(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:(creative(X)))&
(?[X]:((rich(X)&~wise(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both not happy and not humble is either not creative or not rich.
If someone is not creative then someone is both wise and calm.
If someone is both not creative and not funny then john is old.
Everyone who is both not strong and not patient is both not kind and not funny.
Everyone who is not rich is not kind or strong.
If someone is not happy then fred is humble or creative.
Everyone who is not humble or happy is both kind and patient.
Everyone who is not kind is not wise or not quiet.
If john is not old then someone is brave and vice versa.
Everyone who is either not quiet or old is not wise.
If alice is both humble and not kind then paul is not patient and vice versa.
If paul is not quiet or kind then someone is either creative or not strong and vice versa.
Everyone who is either kind or patient is kind and vice versa.
If someone is patient then john is not old.
If someone is rich or curious then someone is not calm.
Everyone who is not brave or not strong is either rich or not curious.
Alice is not old or kind.
Alice is both not strong and quiet.
Someone is either kind or not brave.
Lucy is both old and wise.
Someone is either rich or not brave.
Someone is calm.
Someone is either kind or calm. | Fred is creative. | neutral | (![X]:((~happy(X)&~humble(X))=>(~creative(X)<~>~rich(X))))&
((?[X]:(~creative(X)))=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:((~creative(X)&~funny(X))))=>(old(john)))&
(![X]:((~strong(X)&~patient(X))=>(~kind(X)&~funny(X))))&
(![X]:(~rich(X)=>(~kind(X)|strong(X))))&
((?[X]:(~happy(X)))=>((humble(fred)|creative(fred))))&
(![X]:((~humble(X)|happy(X))=>(kind(X)&patient(X))))&
(![X]:(~kind(X)=>(~wise(X)|~quiet(X))))&
((~old(john))<=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>old(X))=>~wise(X)))&
(((humble(alice)&~kind(alice)))<=>(~patient(paul)))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>patient(X))<=>kind(X)))&
((?[X]:(patient(X)))=>(~old(john)))&
((?[X]:((rich(X)|curious(X))))=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((~old(alice)|kind(alice)))&
((~strong(alice)&quiet(alice)))&
(?[X]:((kind(X)<~>~brave(X))))&
((old(lucy)&wise(lucy)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>calm(X)))) | creative(fred) | [] | null | 0 |
Everyone who is not humble or not creative is rich or wise and vice versa.
Everyone who is calm or not wise is both not patient and not calm and vice versa.
If paul is creative or brave then someone is not humble and vice versa.
Everyone who is both brave and tall is not rich.
Everyone who is either generous or not rich is both not kind and not humble and vice versa.
If someone is both strong and not old then john is quiet and vice versa.
Everyone who is both curious and not brave is quiet or tall.
If someone is not tall then lucy is either brave or tall.
Everyone who is happy or not old is both not happy and not funny.
Everyone who is not wise is generous.
If someone is humble then alice is kind.
Everyone who is strong is not wise or happy and vice versa.
Everyone who is either humble or not strong is both not humble and funny and vice versa.
Everyone who is both wise and not tall is not old or not generous.
Everyone who is either not creative or humble is generous or not strong and vice versa.
If john is either calm or not strong then someone is either wise or old.
Susan is not strong or not curious.
Mary is not strong.
Someone is either not happy or not old.
Someone is not tall or brave.
Someone is either patient or not generous.
Someone is either not calm or happy.
Someone is not funny. | Paul is not creative. | entailment | (![X]:((~humble(X)|~creative(X))<=>(rich(X)|wise(X))))&
(![X]:((calm(X)|~wise(X))<=>(~patient(X)&~calm(X))))&
(((creative(paul)|brave(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&tall(X))=>~rich(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((strong(X)&~old(X))))<=>(quiet(john)))&
(![X]:((curious(X)&~brave(X))=>(quiet(X)|tall(X))))&
((?[X]:(~tall(X)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((happy(X)|~old(X))=>(~happy(X)&~funny(X))))&
(![X]:(~wise(X)=>generous(X)))&
((?[X]:(humble(X)))=>(kind(alice)))&
(![X]:(strong(X)<=>(~wise(X)|happy(X))))&
(![X]:((humble(X)<~>~strong(X))<=>(~humble(X)&funny(X))))&
(![X]:((wise(X)&~tall(X))=>(~old(X)|~generous(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)|~strong(X))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((wise(X)<~>old(X)))))&
((~strong(susan)|~curious(susan)))&
(~strong(mary))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:(~funny(X))) | ~creative(paul) | [
"p0",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3277763485702719713211008
% SZS output start Proof for 3277763485702719713211008
1. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (wise(X0) | rich(X0))) [input p0]
9. ! [X0] : ((~old(X0) | happy(X0)) => (~funny(X0) & ~happy(X0))) [input p8]
10. ! [X0] : (~wise(X0) => generous(X0)) [input p9]
12. ! [X0] : (strong(X0) <=> (happy(X0) | ~wise(X0))) [input p11]
13. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> (funny(X0) & ~humble(X0))) [input p12]
15. ! [X0] : ((~creative(X0) <~> humble(X0)) <=> (~strong(X0) | generous(X0))) [input p14]
24. creative(paul) [input hypothesis]
30. ! [X0] : ((~funny(X0) & ~happy(X0)) | (old(X0) & ~happy(X0))) [ennf transformation 9]
31. ! [X0] : (generous(X0) | wise(X0)) [ennf transformation 10]
36. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~wise(X0) & ~rich(X0))) & ((wise(X0) | rich(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~humble(X0) | (~wise(X0) & ~rich(X0))) & (wise(X0) | rich(X0) | (creative(X0) & humble(X0)))) [flattening 36]
52. ! [X0] : ((strong(X0) | (~happy(X0) & wise(X0))) & ((happy(X0) | ~wise(X0)) | ~strong(X0))) [nnf transformation 12]
53. ! [X0] : ((strong(X0) | (~happy(X0) & wise(X0))) & (happy(X0) | ~wise(X0) | ~strong(X0))) [flattening 52]
54. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 13]
55. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [flattening 54]
56. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [flattening 56]
77. ~wise(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 37]
98. ~happy(X0) | ~happy(X0) [cnf transformation 30]
102. generous(X0) | wise(X0) [cnf transformation 31]
104. happy(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 53]
105. strong(X0) | wise(X0) [cnf transformation 53]
107. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 55]
116. ~generous(X0) | ~creative(X0) | humble(X0) [cnf transformation 57]
117. ~creative(X0) | humble(X0) | strong(X0) [cnf transformation 57]
133. creative(paul) [cnf transformation 24]
134. ~strong(X0) | ~humble(X0) [duplicate literal removal 107]
136. ~happy(X0) [duplicate literal removal 98]
143. 2 <=> creative(paul) [avatar definition]
145. creative(paul) <- (2) [avatar component clause 143]
196. ~strong(X0) | ~wise(X0) [subsumption resolution 104,136]
235. 2 [avatar split clause 133,143]
242. ~humble(X0) | wise(X0) [resolution 134,105]
270. ~creative(X0) | humble(X0) | wise(X0) [resolution 116,102]
357. humble(paul) | strong(paul) <- (2) [resolution 117,145]
426. 40 <=> strong(paul) [avatar definition]
428. strong(paul) <- (40) [avatar component clause 426]
430. 41 <=> humble(paul) [avatar definition]
431. ~humble(paul) <- (~41) [avatar component clause 430]
432. humble(paul) <- (41) [avatar component clause 430]
433. 40 | 41 | ~2 [avatar split clause 357,143,430,426]
467. ~wise(paul) <- (40) [resolution 428,196]
536. humble(paul) | wise(paul) <- (2) [resolution 270,145]
537. wise(paul) <- (2, ~41) [subsumption resolution 536,431]
538. $false <- (2, 40, ~41) [subsumption resolution 537,467]
539. ~2 | ~40 | 41 [avatar contradiction clause 538]
540. wise(paul) <- (2) [subsumption resolution 536,242]
607. ~humble(paul) | ~creative(paul) <- (2) [resolution 540,77]
609. ~creative(paul) <- (2, 41) [subsumption resolution 607,432]
610. $false <- (2, 41) [subsumption resolution 609,145]
611. ~2 | ~41 [avatar contradiction clause 610]
612. $false [avatar sat refutation 235,433,539,611]
% SZS output end Proof for 3277763485702719713211008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is patient.
Everyone who is brave is not tall or not humble and vice versa.
If someone is not happy or happy then lucy is quiet and vice versa.
Everyone who is both not patient and not strong is both not quiet and strong and vice versa.
Everyone who is both not funny and not calm is not kind or not generous and vice versa.
If someone is either not brave or not humble then paul is both not creative and generous.
Everyone who is happy or creative is either not old or wise and vice versa.
Everyone who is either not calm or not humble is not happy.
If lucy is either creative or not tall then alice is either curious or brave and vice versa.
If someone is both curious and tall then fred is not quiet or not generous and vice versa.
Everyone who is not kind is either not brave or not humble.
If paul is both not humble and not funny then lucy is not creative and vice versa.
Everyone who is humble or not rich is either not brave or creative and vice versa.
Everyone who is happy is patient or kind and vice versa.
Everyone who is calm is either happy or wise and vice versa.
If mary is both not wise and not curious then someone is either strong or not quiet and vice versa.
Someone is either not calm or not brave.
Someone is both not quiet and humble.
Susan is not creative or not calm.
Someone is either calm or funny.
Someone is quiet.
Mary is not quiet or not kind.
Paul is either creative or tall. | Lucy is creative. | neutral | (![X]:(~calm(X)=>patient(X)))&
(![X]:(brave(X)<=>(~tall(X)|~humble(X))))&
((?[X]:((~happy(X)|happy(X))))<=>(quiet(lucy)))&
(![X]:((~patient(X)&~strong(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~kind(X)|~generous(X))))&
((?[X]:((~brave(X)<~>~humble(X))))=>((~creative(paul)&generous(paul))))&
(![X]:((happy(X)|creative(X))<=>(~old(X)<~>wise(X))))&
(![X]:((~calm(X)<~>~humble(X))=>~happy(X)))&
(((creative(lucy)<~>~tall(lucy)))<=>((curious(alice)<~>brave(alice))))&
((?[X]:((curious(X)&tall(X))))<=>((~quiet(fred)|~generous(fred))))&
(![X]:(~kind(X)=>(~brave(X)<~>~humble(X))))&
(((~humble(paul)&~funny(paul)))<=>(~creative(lucy)))&
(![X]:((humble(X)|~rich(X))<=>(~brave(X)<~>creative(X))))&
(![X]:(happy(X)<=>(patient(X)|kind(X))))&
(![X]:(calm(X)<=>(happy(X)<~>wise(X))))&
(((~wise(mary)&~curious(mary)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
(?[X]:((~calm(X)<~>~brave(X))))&
(?[X]:((~quiet(X)&humble(X))))&
((~creative(susan)|~calm(susan)))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
((~quiet(mary)|~kind(mary)))&
((creative(paul)<~>tall(paul))) | creative(lucy) | [] | null | 0 |
Everyone who is either calm or not old is both brave and not tall and vice versa. If someone is both not old and not quiet then paul is not kind. Everyone who is not tall or not quiet is either not strong or not old. Everyone who is both happy and not creative is not brave or brave and vice versa. Everyone who is not quiet is not funny or creative and vice versa. If someone is either curious or not kind then john is not generous. Everyone who is both creative and kind is both wise and not generous. If someone is either humble or wise then someone is either quiet or not calm. Everyone who is both not curious and quiet is happy and vice versa. If someone is either not wise or not calm then someone is both tall and not happy. If someone is both funny and not tall then lucy is not wise. Everyone who is not quiet is either not tall or not old and vice versa. Everyone who is either calm or not calm is either not generous or brave and vice versa. If john is both old and not kind then someone is rich or curious. Everyone who is tall is not patient or not rich. If someone is generous then someone is patient. Mary is curious or tall. Someone is both strong and kind. Someone is not old or not strong. Someone is both humble and not patient. Susan is quiet. Someone is not humble. | John is not creative. | entailment | (![X]:((calm(X)<~>~old(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~old(X)&~quiet(X))))=>(~kind(paul)))&
(![X]:((~tall(X)|~quiet(X))=>(~strong(X)<~>~old(X))))&
(![X]:((happy(X)&~creative(X))<=>(~brave(X)|brave(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|creative(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>(~generous(john)))&
(![X]:((creative(X)&kind(X))=>(wise(X)&~generous(X))))&
((?[X]:((humble(X)<~>wise(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~curious(X)&quiet(X))<=>happy(X)))&
((?[X]:((~wise(X)<~>~calm(X))))=>(?[X]:((tall(X)&~happy(X)))))&
((?[X]:((funny(X)&~tall(X))))=>(~wise(lucy)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~old(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(~generous(X)<~>brave(X))))&
(((old(john)&~kind(john)))=>(?[X]:((rich(X)|curious(X)))))&
(![X]:(tall(X)=>(~patient(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
((curious(mary)|tall(mary)))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((humble(X)&~patient(X))))&
(quiet(susan))&
(?[X]:(~humble(X))) | ~creative(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 373143218358103114193310
% SZS output start Proof for 373143218358103114193310
4. ! [X0] : ((~creative(X0) & happy(X0)) <=> (brave(X0) | ~brave(X0))) [input p3]
23. creative(john) [input hypothesis]
43. ! [X0] : (((~creative(X0) & happy(X0)) | (~brave(X0) & brave(X0))) & ((brave(X0) | ~brave(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 4]
44. ! [X0] : (((~creative(X0) & happy(X0)) | (~brave(X0) & brave(X0))) & (brave(X0) | ~brave(X0) | creative(X0) | ~happy(X0))) [flattening 43]
87. ~creative(X0) | brave(X0) [cnf transformation 44]
88. ~creative(X0) | ~brave(X0) [cnf transformation 44]
131. creative(john) [cnf transformation 23]
144. ~creative(X0) [subsumption resolution 87,88]
225. $false [subsumption resolution 131,144]
% SZS output end Proof for 373143218358103114193310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or quiet then john is creative or tall and vice versa.
Everyone who is either calm or not humble is wise and vice versa.
If someone is not tall then someone is not happy and vice versa.
Everyone who is happy or not tall is rich or not quiet and vice versa.
Everyone who is either not old or not wise is not calm and vice versa.
If someone is happy then john is both not creative and humble and vice versa.
Everyone who is either not old or kind is not wise and vice versa.
If lucy is both old and not tall then someone is not humble.
If john is either not curious or not generous then someone is either not funny or not happy and vice versa.
If paul is both not happy and not brave then someone is either tall or patient and vice versa.
If someone is both not creative and patient then john is kind or not curious.
Everyone who is either funny or not quiet is calm or not funny and vice versa.
If someone is both generous and not rich then mary is either strong or not curious and vice versa.
Everyone who is either not creative or not humble is both humble and generous.
Everyone who is not tall is either not old or brave and vice versa.
Everyone who is not wise or not quiet is both not tall and quiet.
Alice is rich.
Someone is old.
Someone is both not strong and not wise.
Susan is not kind.
Fred is not rich.
John is both not patient and old.
Someone is either rich or not curious. | Lucy is not generous. | neutral | ((?[X]:((~curious(X)<~>quiet(X))))<=>((creative(john)|tall(john))))&
(![X]:((calm(X)<~>~humble(X))<=>wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(~happy(X))))&
(![X]:((happy(X)|~tall(X))<=>(rich(X)|~quiet(X))))&
(![X]:((~old(X)<~>~wise(X))<=>~calm(X)))&
((?[X]:(happy(X)))<=>((~creative(john)&humble(john))))&
(![X]:((~old(X)<~>kind(X))<=>~wise(X)))&
(((old(lucy)&~tall(lucy)))=>(?[X]:(~humble(X))))&
(((~curious(john)<~>~generous(john)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~happy(paul)&~brave(paul)))<=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:((~creative(X)&patient(X))))=>((kind(john)|~curious(john))))&
(![X]:((funny(X)<~>~quiet(X))<=>(calm(X)|~funny(X))))&
((?[X]:((generous(X)&~rich(X))))<=>((strong(mary)<~>~curious(mary))))&
(![X]:((~creative(X)<~>~humble(X))=>(humble(X)&generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>(~tall(X)&quiet(X))))&
(rich(alice))&
(?[X]:(old(X)))&
(?[X]:((~strong(X)&~wise(X))))&
(~kind(susan))&
(~rich(fred))&
((~patient(john)&old(john)))&
(?[X]:((rich(X)<~>~curious(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is not funny or not quiet is strong or not generous and vice versa. Everyone who is either not happy or not creative is either strong or brave. If fred is either not humble or curious then susan is not curious or not creative and vice versa. Everyone who is either not generous or humble is not tall or not humble. If mary is both not creative and not old then john is patient and vice versa. Everyone who is brave is not curious. If susan is either curious or creative then lucy is not generous and vice versa. If mary is not old or strong then paul is either not patient or generous and vice versa. Everyone who is not rich or rich is strong. If paul is not creative or not tall then someone is either not generous or brave and vice versa. If fred is both strong and not creative then someone is either happy or calm and vice versa. Everyone who is quiet or old is not calm or not old and vice versa. If someone is patient then john is kind or not happy and vice versa. Everyone who is either not strong or not creative is not curious or not funny and vice versa. If lucy is both not rich and humble then fred is either happy or creative and vice versa. Everyone who is both not generous and not kind is generous or not curious and vice versa. Someone is either not humble or humble. Someone is not old or not humble. Fred is both wise and tall. Alice is both wise and patient. Someone is not strong or not old. Someone is curious or not funny. Susan is not patient. | John is not wise. | neutral | (![X]:((~funny(X)|~quiet(X))<=>(strong(X)|~generous(X))))&
(![X]:((~happy(X)<~>~creative(X))=>(strong(X)<~>brave(X))))&
(((~humble(fred)<~>curious(fred)))<=>((~curious(susan)|~creative(susan))))&
(![X]:((~generous(X)<~>humble(X))=>(~tall(X)|~humble(X))))&
(((~creative(mary)&~old(mary)))<=>(patient(john)))&
(![X]:(brave(X)=>~curious(X)))&
(((curious(susan)<~>creative(susan)))<=>(~generous(lucy)))&
(((~old(mary)|strong(mary)))<=>((~patient(paul)<~>generous(paul))))&
(![X]:((~rich(X)|rich(X))=>strong(X)))&
(((~creative(paul)|~tall(paul)))<=>(?[X]:((~generous(X)<~>brave(X)))))&
(((strong(fred)&~creative(fred)))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((quiet(X)|old(X))<=>(~calm(X)|~old(X))))&
((?[X]:(patient(X)))<=>((kind(john)|~happy(john))))&
(![X]:((~strong(X)<~>~creative(X))<=>(~curious(X)|~funny(X))))&
(((~rich(lucy)&humble(lucy)))<=>((happy(fred)<~>creative(fred))))&
(![X]:((~generous(X)&~kind(X))<=>(generous(X)|~curious(X))))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~old(X)|~humble(X))))&
((wise(fred)&tall(fred)))&
((wise(alice)&patient(alice)))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((curious(X)|~funny(X))))&
(~patient(susan)) | ~wise(john) | [] | null | 0 |
Everyone who is both not kind and not old is either not creative or calm.
If alice is both not happy and strong then someone is both not funny and generous and vice versa.
If mary is either not quiet or patient then someone is either strong or tall.
Everyone who is patient is either not happy or not strong.
If mary is creative or not kind then lucy is calm or strong.
Everyone who is either strong or not creative is both not calm and not kind and vice versa.
If paul is both not patient and not wise then someone is either not happy or not curious and vice versa.
Everyone who is both quiet and tall is generous and vice versa.
Everyone who is both not brave and not strong is not creative or not curious.
If someone is either kind or not kind then fred is creative and vice versa.
Everyone who is both not curious and funny is either tall or not curious and vice versa.
If alice is old or happy then john is humble and vice versa.
Everyone who is quiet or creative is brave or kind.
Everyone who is either humble or not funny is either quiet or not humble.
If someone is either humble or brave then alice is both funny and not humble and vice versa.
If lucy is either not quiet or kind then susan is both humble and brave.
John is either not funny or not creative.
Someone is funny.
Someone is humble.
Alice is both old and generous.
Mary is both funny and not tall.
Susan is both not generous and curious.
Someone is either not creative or generous.
Fred is both kind and not quiet. | Alice is brave. | entailment | (![X]:((~kind(X)&~old(X))=>(~creative(X)<~>calm(X))))&
(((~happy(alice)&strong(alice)))<=>(?[X]:((~funny(X)&generous(X)))))&
(((~quiet(mary)<~>patient(mary)))=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:(patient(X)=>(~happy(X)<~>~strong(X))))&
(((creative(mary)|~kind(mary)))=>((calm(lucy)|strong(lucy))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)&~kind(X))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:((quiet(X)&tall(X))<=>generous(X)))&
(![X]:((~brave(X)&~strong(X))=>(~creative(X)|~curious(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>(creative(fred)))&
(![X]:((~curious(X)&funny(X))<=>(tall(X)<~>~curious(X))))&
(((old(alice)|happy(alice)))<=>(humble(john)))&
(![X]:((quiet(X)|creative(X))=>(brave(X)|kind(X))))&
(![X]:((humble(X)<~>~funny(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((humble(X)<~>brave(X))))<=>((funny(alice)&~humble(alice))))&
(((~quiet(lucy)<~>kind(lucy)))=>((humble(susan)&brave(susan))))&
((~funny(john)<~>~creative(john)))&
(?[X]:(funny(X)))&
(?[X]:(humble(X)))&
((old(alice)&generous(alice)))&
((funny(mary)&~tall(mary)))&
((~generous(susan)&curious(susan)))&
(?[X]:((~creative(X)<~>generous(X))))&
((kind(fred)&~quiet(fred))) | brave(alice) | [
"p7",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3484720706807128922756655
% SZS output start Proof for 3484720706807128922756655
8. ! [X0] : ((tall(X0) & quiet(X0)) <=> generous(X0)) [input p7]
11. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p10]
14. ! [X0] : ((humble(X0) <~> ~funny(X0)) => (quiet(X0) <~> ~humble(X0))) [input p13]
15. ? [X0] : (humble(X0) <~> brave(X0)) <=> (~humble(alice) & funny(alice)) [input p14]
20. generous(alice) & old(alice) [input p19]
25. ~brave(alice) [input hypothesis]
36. ! [X0] : ((quiet(X0) <~> ~humble(X0)) | (humble(X0) <=> ~funny(X0))) [ennf transformation 14]
55. ! [X0] : (((tall(X0) & quiet(X0)) | ~generous(X0)) & (generous(X0) | (~tall(X0) | ~quiet(X0)))) [nnf transformation 8]
56. ! [X0] : (((tall(X0) & quiet(X0)) | ~generous(X0)) & (generous(X0) | ~tall(X0) | ~quiet(X0))) [flattening 55]
61. ! [X0] : (((funny(X0) & ~curious(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (~funny(X0) | curious(X0)))) [nnf transformation 11]
62. ! [X0] : (((funny(X0) & ~curious(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | ~funny(X0) | curious(X0))) [flattening 61]
65. ! [X0] : (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) [nnf transformation 36]
66. (? [X0] : ((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (humble(alice) | ~funny(alice))) & ((~humble(alice) & funny(alice)) | ! [X0] : ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) [nnf transformation 15]
67. (? [X0] : ((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X0] : ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) [flattening 66]
68. (? [X0] : ((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) [rectify 67]
69. ? [X0] : ((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) => ((~brave(sK4) | ~humble(sK4)) & (brave(sK4) | humble(sK4))) [choice axiom]
70. (((~brave(sK4) | ~humble(sK4)) & (brave(sK4) | humble(sK4))) | humble(alice) | ~funny(alice)) & ((~humble(alice) & funny(alice)) | ! [X1] : ((humble(X1) | ~brave(X1)) & (brave(X1) | ~humble(X1)))) [skolemisation 68,69]
107. ~generous(X0) | quiet(X0) [cnf transformation 56]
108. ~generous(X0) | tall(X0) [cnf transformation 56]
115. curious(X0) | ~tall(X0) | ~funny(X0) | curious(X0) [cnf transformation 62]
116. ~curious(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 62]
128. humble(X0) | ~quiet(X0) | humble(X0) | funny(X0) [cnf transformation 65]
129. funny(alice) | brave(X1) | ~humble(X1) [cnf transformation 70]
144. generous(alice) [cnf transformation 20]
153. ~brave(alice) [cnf transformation 25]
155. ~quiet(X0) | humble(X0) | funny(X0) [duplicate literal removal 128]
156. curious(X0) | ~tall(X0) | ~funny(X0) [duplicate literal removal 115]
157. ~curious(X0) | ~tall(X0) [duplicate literal removal 116]
261. ~tall(X0) | ~funny(X0) [subsumption resolution 156,157]
274. 25 <=> funny(alice) [avatar definition]
276. ~funny(alice) <- (~25) [avatar component clause 274]
278. 26 <=> humble(alice) [avatar definition]
280. humble(alice) <- (26) [avatar component clause 278]
296. 30 <=> ! [X1] : (brave(X1) | ~humble(X1)) [avatar definition]
297. ~humble(X1) | brave(X1) <- (30) [avatar component clause 296]
300. 30 | 25 [avatar split clause 129,274,296]
342. quiet(alice) [resolution 107,144]
344. tall(alice) [resolution 108,144]
348. ~funny(alice) [resolution 261,344]
352. ~25 [avatar split clause 348,274]
440. humble(alice) | funny(alice) [resolution 155,342]
446. humble(alice) <- (~25) [subsumption resolution 440,276]
447. 26 | 25 [avatar split clause 446,274,278]
449. brave(alice) <- (26, 30) [resolution 280,297]
450. $false <- (26, 30) [subsumption resolution 449,153]
451. ~26 | ~30 [avatar contradiction clause 450]
452. $false [avatar sat refutation 300,352,447,451]
% SZS output end Proof for 3484720706807128922756655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not funny then someone is both not kind and quiet and vice versa.
Everyone who is either funny or not rich is not tall or quiet.
If alice is both not humble and not curious then someone is either not tall or not happy and vice versa.
If mary is strong or brave then someone is not brave.
Everyone who is generous is either happy or not quiet and vice versa.
If someone is both generous and strong then alice is not patient.
If paul is not quiet then paul is tall and vice versa.
Everyone who is either rich or not generous is both not patient and generous.
Everyone who is both not happy and kind is calm and vice versa.
If john is either patient or not humble then fred is creative or quiet and vice versa.
Everyone who is not rich or not tall is both not patient and tall.
If susan is happy then someone is both not brave and humble.
Everyone who is not quiet or not happy is either brave or tall and vice versa.
Everyone who is either not funny or not wise is not quiet or not kind and vice versa.
If someone is not kind or not old then john is not quiet or old.
Everyone who is both not old and not patient is not tall.
Someone is either old or not happy.
Alice is both not generous and not patient.
Mary is quiet.
Susan is wise or not strong.
Alice is brave or strong.
Someone is curious or old.
Someone is not calm.
Someone is brave. | John is tall. | entailment | ((~funny(lucy))<=>(?[X]:((~kind(X)&quiet(X)))))&
(![X]:((funny(X)<~>~rich(X))=>(~tall(X)|quiet(X))))&
(((~humble(alice)&~curious(alice)))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(((strong(mary)|brave(mary)))=>(?[X]:(~brave(X))))&
(![X]:(generous(X)<=>(happy(X)<~>~quiet(X))))&
((?[X]:((generous(X)&strong(X))))=>(~patient(alice)))&
((~quiet(paul))<=>(tall(paul)))&
(![X]:((rich(X)<~>~generous(X))=>(~patient(X)&generous(X))))&
(![X]:((~happy(X)&kind(X))<=>calm(X)))&
(((patient(john)<~>~humble(john)))<=>((creative(fred)|quiet(fred))))&
(![X]:((~rich(X)|~tall(X))=>(~patient(X)&tall(X))))&
((happy(susan))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~quiet(X)|~kind(X))))&
((?[X]:((~kind(X)|~old(X))))=>((~quiet(john)|old(john))))&
(![X]:((~old(X)&~patient(X))=>~tall(X)))&
(?[X]:((old(X)<~>~happy(X))))&
((~generous(alice)&~patient(alice)))&
(quiet(mary))&
((wise(susan)|~strong(susan)))&
((brave(alice)|strong(alice)))&
(?[X]:((curious(X)|old(X))))&
(?[X]:(~calm(X)))&
(?[X]:(brave(X))) | tall(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7275250958128762020685393
% SZS output start Proof for 7275250958128762020685393
11. ! [X0] : ((~tall(X0) | ~rich(X0)) => (tall(X0) & ~patient(X0))) [input p10]
25. ~tall(john) [input hypothesis]
34. ! [X0] : ((tall(X0) & ~patient(X0)) | (tall(X0) & rich(X0))) [ennf transformation 11]
106. tall(X0) | tall(X0) [cnf transformation 34]
134. ~tall(john) [cnf transformation 25]
135. tall(X0) [duplicate literal removal 106]
309. $false [subsumption resolution 134,135]
% SZS output end Proof for 7275250958128762020685393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not wise then someone is creative.
Everyone who is humble or strong is happy.
Everyone who is either humble or old is either kind or strong and vice versa.
If john is both tall and happy then someone is happy and vice versa.
If someone is either generous or not rich then someone is kind or calm.
Everyone who is both not wise and old is either tall or not calm.
If someone is either creative or funny then someone is both not humble and strong and vice versa.
If fred is humble or not tall then lucy is patient or not calm.
Everyone who is either not generous or tall is either not rich or old and vice versa.
Everyone who is not generous or curious is either not wise or not quiet and vice versa.
If someone is old or not funny then someone is not creative or not patient.
If susan is not patient or not tall then someone is either wise or not humble and vice versa.
Everyone who is either not brave or not quiet is not generous.
Everyone who is generous is either funny or not humble and vice versa.
Everyone who is generous is creative.
If lucy is both not humble and not generous then someone is either not old or curious and vice versa.
Someone is either not patient or not rich.
Paul is either brave or curious.
Someone is funny.
Someone is both not creative and not kind.
Someone is both patient and humble.
John is either funny or not old.
Susan is not creative or calm.
Someone is not happy or calm. | John is not tall. | contradiction | ((~wise(fred))=>(?[X]:(creative(X))))&
(![X]:((humble(X)|strong(X))=>happy(X)))&
(![X]:((humble(X)<~>old(X))<=>(kind(X)<~>strong(X))))&
(((tall(john)&happy(john)))<=>(?[X]:(happy(X))))&
((?[X]:((generous(X)<~>~rich(X))))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~wise(X)&old(X))=>(tall(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>funny(X))))<=>(?[X]:((~humble(X)&strong(X)))))&
(((humble(fred)|~tall(fred)))=>((patient(lucy)|~calm(lucy))))&
(![X]:((~generous(X)<~>tall(X))<=>(~rich(X)<~>old(X))))&
(![X]:((~generous(X)|curious(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((old(X)|~funny(X))))=>(?[X]:((~creative(X)|~patient(X)))))&
(((~patient(susan)|~tall(susan)))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((~brave(X)<~>~quiet(X))=>~generous(X)))&
(![X]:(generous(X)<=>(funny(X)<~>~humble(X))))&
(![X]:(generous(X)=>creative(X)))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(?[X]:((~patient(X)<~>~rich(X))))&
((brave(paul)<~>curious(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((patient(X)&humble(X))))&
((funny(john)<~>~old(john)))&
((~creative(susan)|calm(susan)))&
(?[X]:((~happy(X)|calm(X)))) | ~tall(john) | [
"p1",
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3068062732122863107304989
% SZS output start Proof for 3068062732122863107304989
2. ! [X0] : ((strong(X0) | humble(X0)) => happy(X0)) [input p1]
4. (happy(john) & tall(john)) <=> ? [X0] : happy(X0) [input p3]
21. ? [X0] : (humble(X0) & patient(X0)) [input p20]
25. ~tall(john) [input hypothesis]
30. ! [X0] : (happy(X0) | (~strong(X0) & ~humble(X0))) [ennf transformation 2]
42. ((happy(john) & tall(john)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (~happy(john) | ~tall(john))) [nnf transformation 4]
43. ((happy(john) & tall(john)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~happy(john) | ~tall(john)) [flattening 42]
44. ((happy(john) & tall(john)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~happy(john) | ~tall(john)) [rectify 43]
45. ? [X1] : happy(X1) => happy(sK1) [choice axiom]
46. ((happy(john) & tall(john)) | ! [X0] : ~happy(X0)) & (happy(sK1) | ~happy(john) | ~tall(john)) [skolemisation 44,45]
83. ? [X0] : (humble(X0) & patient(X0)) => (humble(sK11) & patient(sK11)) [choice axiom]
84. humble(sK11) & patient(sK11) [skolemisation 21,83]
89. ~humble(X0) | happy(X0) [cnf transformation 30]
100. tall(john) | ~happy(X0) [cnf transformation 46]
157. humble(sK11) [cnf transformation 84]
162. ~tall(john) [cnf transformation 25]
173. 3 <=> ! [X0] : ~happy(X0) [avatar definition]
174. ~happy(X0) <- (3) [avatar component clause 173]
181. 5 <=> tall(john) [avatar definition]
184. 3 | 5 [avatar split clause 100,181,173]
375. ~5 [avatar split clause 162,181]
376. happy(sK11) [resolution 89,157]
377. $false <- (3) [subsumption resolution 376,174]
378. ~3 [avatar contradiction clause 377]
379. $false [avatar sat refutation 184,375,378]
% SZS output end Proof for 3068062732122863107304989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not old and not happy then someone is either not rich or not creative. Everyone who is not old or patient is not funny. If someone is both funny and brave then someone is not generous. If someone is either not strong or not quiet then lucy is humble or not tall and vice versa. If someone is quiet then someone is not rich. Everyone who is curious is tall or not rich and vice versa. If someone is either not tall or humble then someone is not humble. If fred is either not tall or not brave then susan is strong or not patient. If fred is creative or not curious then mary is not generous. If someone is both creative and not humble then alice is either generous or not tall. Everyone who is not rich is both not kind and wise. If john is funny then fred is both not tall and old and vice versa. Everyone who is happy or old is quiet or not old. If mary is patient then paul is not funny or quiet. Everyone who is both strong and not happy is either calm or not happy. If someone is both not creative and not patient then someone is not creative and vice versa. Someone is either not strong or tall. Someone is either not kind or funny. Susan is either humble or funny. Lucy is not strong or not calm. Someone is tall or old. Someone is both brave and not tall. John is both not generous and wise. Someone is generous or not quiet. | John is generous. | contradiction | (((~old(mary)&~happy(mary)))=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((~old(X)|patient(X))=>~funny(X)))&
((?[X]:((funny(X)&brave(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>((humble(lucy)|~tall(lucy))))&
((?[X]:(quiet(X)))=>(?[X]:(~rich(X))))&
(![X]:(curious(X)<=>(tall(X)|~rich(X))))&
((?[X]:((~tall(X)<~>humble(X))))=>(?[X]:(~humble(X))))&
(((~tall(fred)<~>~brave(fred)))=>((strong(susan)|~patient(susan))))&
(((creative(fred)|~curious(fred)))=>(~generous(mary)))&
((?[X]:((creative(X)&~humble(X))))=>((generous(alice)<~>~tall(alice))))&
(![X]:(~rich(X)=>(~kind(X)&wise(X))))&
((funny(john))<=>((~tall(fred)&old(fred))))&
(![X]:((happy(X)|old(X))=>(quiet(X)|~old(X))))&
((patient(mary))=>((~funny(paul)|quiet(paul))))&
(![X]:((strong(X)&~happy(X))=>(calm(X)<~>~happy(X))))&
((?[X]:((~creative(X)&~patient(X))))<=>(?[X]:(~creative(X))))&
(?[X]:((~strong(X)<~>tall(X))))&
(?[X]:((~kind(X)<~>funny(X))))&
((humble(susan)<~>funny(susan)))&
((~strong(lucy)|~calm(lucy)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((brave(X)&~tall(X))))&
((~generous(john)&wise(john)))&
(?[X]:((generous(X)|~quiet(X)))) | generous(john) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8088516584352870720199088
% SZS output start Proof for 8088516584352870720199088
23. wise(john) & ~generous(john) [input p22]
25. generous(john) [input hypothesis]
32. ~generous(john) [pure predicate removal 23]
136. ~generous(john) [cnf transformation 32]
138. generous(john) [cnf transformation 25]
362. $false [subsumption resolution 138,136]
% SZS output end Proof for 8088516584352870720199088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not calm or happy then fred is not old or wise and vice versa.
Everyone who is both happy and not generous is either creative or not tall and vice versa.
Everyone who is generous is both quiet and curious and vice versa.
If someone is either funny or not tall then mary is not humble or not kind.
If lucy is either calm or not kind then alice is not curious or brave.
Everyone who is both generous and tall is not curious and vice versa.
Everyone who is both humble and calm is both tall and not strong and vice versa.
Everyone who is funny is both not kind and not curious and vice versa.
If someone is not tall then susan is not wise or brave.
If fred is both generous and not curious then alice is generous or not kind.
If fred is not rich then someone is not old and vice versa.
Everyone who is either not creative or happy is both not rich and curious and vice versa.
If paul is quiet or not calm then john is generous and vice versa.
Everyone who is humble or not curious is either not patient or not rich and vice versa.
Everyone who is either quiet or not happy is both curious and not brave and vice versa.
Everyone who is not brave is old.
Someone is either not brave or not humble.
Someone is creative.
Mary is kind.
Mary is not calm or old.
Someone is both not strong and not kind.
Someone is either not creative or not tall.
Someone is wise or not strong.
Lucy is either calm or not curious. | Mary is not brave. | neutral | (((~calm(fred)<~>happy(fred)))<=>((~old(fred)|wise(fred))))&
(![X]:((happy(X)&~generous(X))<=>(creative(X)<~>~tall(X))))&
(![X]:(generous(X)<=>(quiet(X)&curious(X))))&
((?[X]:((funny(X)<~>~tall(X))))=>((~humble(mary)|~kind(mary))))&
(((calm(lucy)<~>~kind(lucy)))=>((~curious(alice)|brave(alice))))&
(![X]:((generous(X)&tall(X))<=>~curious(X)))&
(![X]:((humble(X)&calm(X))<=>(tall(X)&~strong(X))))&
(![X]:(funny(X)<=>(~kind(X)&~curious(X))))&
((?[X]:(~tall(X)))=>((~wise(susan)|brave(susan))))&
(((generous(fred)&~curious(fred)))=>((generous(alice)|~kind(alice))))&
((~rich(fred))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~rich(X)&curious(X))))&
(((quiet(paul)|~calm(paul)))<=>(generous(john)))&
(![X]:((humble(X)|~curious(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~happy(X))<=>(curious(X)&~brave(X))))&
(![X]:(~brave(X)=>old(X)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:(creative(X)))&
(kind(mary))&
((~calm(mary)|old(mary)))&
(?[X]:((~strong(X)&~kind(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((wise(X)|~strong(X))))&
((calm(lucy)<~>~curious(lucy))) | ~brave(mary) | [] | null | 0 |
Everyone who is both happy and not quiet is either quiet or not creative and vice versa.
If someone is either generous or not old then mary is not humble or curious.
Everyone who is rich or not quiet is kind or creative.
Everyone who is not curious or creative is wise.
If someone is both strong and not happy then someone is either quiet or not humble and vice versa.
If mary is either not curious or not wise then someone is either funny or quiet and vice versa.
Everyone who is not patient is either tall or brave and vice versa.
Everyone who is either not rich or generous is both not generous and not wise.
Everyone who is calm is both strong and kind.
Everyone who is kind or funny is not wise and vice versa.
Everyone who is not creative or patient is either happy or old and vice versa.
If john is kind or not wise then someone is either brave or not humble.
If someone is both rich and not happy then susan is both old and calm and vice versa.
If mary is either not strong or brave then someone is not brave or not strong.
Everyone who is either curious or funny is both not calm and humble.
Everyone who is either tall or not patient is either not brave or calm.
Someone is either creative or not kind.
Paul is not brave or not wise.
Someone is both not creative and wise.
John is both not strong and humble.
Mary is both not humble and not funny.
John is not tall.
Susan is both curious and generous.
Fred is not kind. | Mary is brave. | contradiction | (![X]:((happy(X)&~quiet(X))<=>(quiet(X)<~>~creative(X))))&
((?[X]:((generous(X)<~>~old(X))))=>((~humble(mary)|curious(mary))))&
(![X]:((rich(X)|~quiet(X))=>(kind(X)|creative(X))))&
(![X]:((~curious(X)|creative(X))=>wise(X)))&
((?[X]:((strong(X)&~happy(X))))<=>(?[X]:((quiet(X)<~>~humble(X)))))&
(((~curious(mary)<~>~wise(mary)))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:(~patient(X)<=>(tall(X)<~>brave(X))))&
(![X]:((~rich(X)<~>generous(X))=>(~generous(X)&~wise(X))))&
(![X]:(calm(X)=>(strong(X)&kind(X))))&
(![X]:((kind(X)|funny(X))<=>~wise(X)))&
(![X]:((~creative(X)|patient(X))<=>(happy(X)<~>old(X))))&
(((kind(john)|~wise(john)))=>(?[X]:((brave(X)<~>~humble(X)))))&
((?[X]:((rich(X)&~happy(X))))<=>((old(susan)&calm(susan))))&
(((~strong(mary)<~>brave(mary)))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((curious(X)<~>funny(X))=>(~calm(X)&humble(X))))&
(![X]:((tall(X)<~>~patient(X))=>(~brave(X)<~>calm(X))))&
(?[X]:((creative(X)<~>~kind(X))))&
((~brave(paul)|~wise(paul)))&
(?[X]:((~creative(X)&wise(X))))&
((~strong(john)&humble(john)))&
((~humble(mary)&~funny(mary)))&
(~tall(john))&
((curious(susan)&generous(susan)))&
(~kind(fred)) | brave(mary) | [
"p3",
"p6",
"p8",
"p9",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8818951027837718055123634
% SZS output start Proof for 8818951027837718055123634
4. ! [X0] : ((creative(X0) | ~curious(X0)) => wise(X0)) [input p3]
7. ! [X0] : (~patient(X0) <=> (tall(X0) <~> brave(X0))) [input p6]
9. ! [X0] : (calm(X0) => (kind(X0) & strong(X0))) [input p8]
10. ! [X0] : ((funny(X0) | kind(X0)) <=> ~wise(X0)) [input p9]
15. ! [X0] : ((curious(X0) <~> funny(X0)) => (humble(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> ~patient(X0)) => (~brave(X0) <~> calm(X0))) [input p15]
21. ~funny(mary) & ~humble(mary) [input p20]
25. brave(mary) [input hypothesis]
31. ! [X0] : (wise(X0) | (~creative(X0) & curious(X0))) [ennf transformation 4]
33. ! [X0] : ((kind(X0) & strong(X0)) | ~calm(X0)) [ennf transformation 9]
36. ! [X0] : ((humble(X0) & ~calm(X0)) | (curious(X0) <=> funny(X0))) [ennf transformation 15]
37. ! [X0] : ((~brave(X0) <~> calm(X0)) | (tall(X0) <=> ~patient(X0))) [ennf transformation 16]
50. ! [X0] : ((~patient(X0) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0)))) & (((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | patient(X0))) [nnf transformation 7]
52. ! [X0] : (((funny(X0) | kind(X0)) | wise(X0)) & (~wise(X0) | (~funny(X0) & ~kind(X0)))) [nnf transformation 10]
53. ! [X0] : ((funny(X0) | kind(X0) | wise(X0)) & (~wise(X0) | (~funny(X0) & ~kind(X0)))) [flattening 52]
67. ! [X0] : ((humble(X0) & ~calm(X0)) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0)))) [nnf transformation 36]
68. ! [X0] : (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) [nnf transformation 37]
84. wise(X0) | curious(X0) [cnf transformation 31]
101. ~brave(X0) | ~tall(X0) | patient(X0) [cnf transformation 50]
102. ~tall(X0) | brave(X0) | ~patient(X0) [cnf transformation 50]
103. ~brave(X0) | tall(X0) | ~patient(X0) [cnf transformation 50]
109. ~calm(X0) | kind(X0) [cnf transformation 33]
110. ~wise(X0) | ~kind(X0) [cnf transformation 53]
131. ~curious(X0) | funny(X0) | humble(X0) [cnf transformation 67]
133. calm(X0) | ~brave(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 68]
134. calm(X0) | ~brave(X0) | tall(X0) | patient(X0) [cnf transformation 68]
144. ~humble(mary) [cnf transformation 21]
145. ~funny(mary) [cnf transformation 21]
150. brave(mary) [cnf transformation 25]
159. 2 <=> humble(mary) [avatar definition]
161. ~humble(mary) <- (~2) [avatar component clause 159]
163. 3 <=> curious(mary) [avatar definition]
164. ~curious(mary) <- (~3) [avatar component clause 163]
165. curious(mary) <- (3) [avatar component clause 163]
206. 13 <=> wise(mary) [avatar definition]
207. wise(mary) <- (13) [avatar component clause 206]
208. ~wise(mary) <- (~13) [avatar component clause 206]
276. 26 <=> brave(mary) [avatar definition]
277. brave(mary) <- (26) [avatar component clause 276]
293. ~brave(X0) | calm(X0) | tall(X0) [subsumption resolution 134,103]
294. ~tall(X0) | ~patient(X0) | calm(X0) [subsumption resolution 133,102]
314. ~2 [avatar split clause 144,159]
315. 26 [avatar split clause 150,276]
319. ~kind(mary) <- (13) [resolution 110,207]
411. ~tall(mary) | patient(mary) <- (26) [resolution 101,277]
415. 48 <=> patient(mary) [avatar definition]
417. patient(mary) <- (48) [avatar component clause 415]
419. 49 <=> tall(mary) [avatar definition]
420. tall(mary) <- (49) [avatar component clause 419]
421. ~tall(mary) <- (~49) [avatar component clause 419]
422. 48 | ~49 | ~26 [avatar split clause 411,276,419,415]
474. funny(mary) | humble(mary) <- (3) [resolution 131,165]
484. humble(mary) <- (3) [subsumption resolution 474,145]
485. $false <- (~2, 3) [subsumption resolution 484,161]
486. 2 | ~3 [avatar contradiction clause 485]
520. calm(mary) | tall(mary) <- (26) [resolution 293,277]
523. calm(mary) <- (26, ~49) [subsumption resolution 520,421]
542. kind(mary) <- (26, ~49) [resolution 523,109]
544. $false <- (13, 26, ~49) [subsumption resolution 542,319]
545. ~13 | ~26 | 49 [avatar contradiction clause 544]
549. 60 <=> calm(mary) [avatar definition]
551. calm(mary) <- (60) [avatar component clause 549]
565. ~patient(mary) | calm(mary) <- (49) [resolution 420,294]
567. calm(mary) <- (48, 49) [subsumption resolution 565,417]
568. 60 | ~48 | ~49 [avatar split clause 567,419,415,549]
571. kind(mary) <- (60) [resolution 551,109]
573. $false <- (13, 60) [subsumption resolution 571,319]
574. ~13 | ~60 [avatar contradiction clause 573]
578. curious(mary) <- (~13) [resolution 208,84]
579. $false <- (~3, ~13) [subsumption resolution 578,164]
580. 3 | 13 [avatar contradiction clause 579]
581. $false [avatar sat refutation 314,315,422,486,545,568,574,580]
% SZS output end Proof for 8818951027837718055123634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and old is both not wise and curious.
Everyone who is not wise is rich or kind.
Everyone who is not wise or not rich is old or not funny and vice versa.
If someone is both not quiet and wise then someone is not rich.
Everyone who is both not generous and not happy is both not happy and tall and vice versa.
Everyone who is not happy is not curious or not happy and vice versa.
If fred is not wise then mary is not humble or not creative and vice versa.
Everyone who is rich or not humble is strong.
If john is kind then someone is wise or not brave.
If paul is not quiet then mary is calm or funny and vice versa.
Everyone who is tall is generous or not wise and vice versa.
Everyone who is patient or strong is both tall and not strong and vice versa.
Everyone who is old or generous is not humble and vice versa.
Everyone who is creative or not rich is not calm.
Everyone who is generous is both not kind and not wise.
If fred is both not generous and not calm then someone is old or happy.
Paul is not generous or curious.
Lucy is not creative or brave.
Alice is not calm.
Someone is both kind and wise. | Lucy is not humble. | contradiction | (![X]:((calm(X)&old(X))=>(~wise(X)&curious(X))))&
(![X]:(~wise(X)=>(rich(X)|kind(X))))&
(![X]:((~wise(X)|~rich(X))<=>(old(X)|~funny(X))))&
((?[X]:((~quiet(X)&wise(X))))=>(?[X]:(~rich(X))))&
(![X]:((~generous(X)&~happy(X))<=>(~happy(X)&tall(X))))&
(![X]:(~happy(X)<=>(~curious(X)|~happy(X))))&
((~wise(fred))<=>((~humble(mary)|~creative(mary))))&
(![X]:((rich(X)|~humble(X))=>strong(X)))&
((kind(john))=>(?[X]:((wise(X)|~brave(X)))))&
((~quiet(paul))<=>((calm(mary)|funny(mary))))&
(![X]:(tall(X)<=>(generous(X)|~wise(X))))&
(![X]:((patient(X)|strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((old(X)|generous(X))<=>~humble(X)))&
(![X]:((creative(X)|~rich(X))=>~calm(X)))&
(![X]:(generous(X)=>(~kind(X)&~wise(X))))&
(((~generous(fred)&~calm(fred)))=>(?[X]:((old(X)|happy(X)))))&
((~generous(paul)|curious(paul)))&
((~creative(lucy)|brave(lucy)))&
(~calm(alice))&
(?[X]:((kind(X)&wise(X)))) | ~humble(lucy) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2595443206882720577466846
% SZS output start Proof for 2595443206882720577466846
8. ! [X0] : ((~humble(X0) | rich(X0)) => strong(X0)) [input p7]
12. ! [X0] : ((strong(X0) | patient(X0)) <=> (~strong(X0) & tall(X0))) [input p11]
21. ~humble(lucy) [input hypothesis]
28. ! [X0] : (strong(X0) | (humble(X0) & ~rich(X0))) [ennf transformation 8]
51. ! [X0] : (((strong(X0) | patient(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (~strong(X0) & ~patient(X0)))) [nnf transformation 12]
52. ! [X0] : ((strong(X0) | patient(X0) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | (~strong(X0) & ~patient(X0)))) [flattening 51]
78. strong(X0) | humble(X0) [cnf transformation 28]
89. ~strong(X0) | ~strong(X0) [cnf transformation 52]
104. ~humble(lucy) [cnf transformation 21]
105. ~strong(X0) [duplicate literal removal 89]
193. humble(X0) [resolution 78,105]
195. $false [resolution 193,104]
% SZS output end Proof for 2595443206882720577466846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not curious is both not brave and happy. Everyone who is curious is both not happy and tall. Everyone who is generous is both generous and brave. If mary is humble or not quiet then alice is either old or not humble. Everyone who is not wise is both not rich and not humble. Everyone who is not creative is both brave and patient and vice versa. Everyone who is both generous and happy is both not happy and kind. If alice is not quiet then someone is humble. Everyone who is rich or strong is happy. If susan is both brave and not funny then alice is both not creative and not rich. Everyone who is either not old or creative is wise and vice versa. If someone is either funny or generous then alice is not quiet or not creative and vice versa. If someone is both humble and not wise then someone is both not patient and happy and vice versa. If someone is either not creative or not generous then someone is wise and vice versa. If alice is both strong and curious then susan is calm or not rich and vice versa. Everyone who is both not rich and not curious is both calm and rich and vice versa. Alice is generous. Susan is not happy or humble. Fred is either strong or generous. Someone is not generous or not strong. Someone is both not kind and calm. Someone is either not quiet or brave. Paul is either old or not quiet. Someone is generous. | Susan is not generous. | entailment | (![X]:((rich(X)&~curious(X))=>(~brave(X)&happy(X))))&
(![X]:(curious(X)=>(~happy(X)&tall(X))))&
(![X]:(generous(X)=>(generous(X)&brave(X))))&
(((humble(mary)|~quiet(mary)))=>((old(alice)<~>~humble(alice))))&
(![X]:(~wise(X)=>(~rich(X)&~humble(X))))&
(![X]:(~creative(X)<=>(brave(X)&patient(X))))&
(![X]:((generous(X)&happy(X))=>(~happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:(humble(X))))&
(![X]:((rich(X)|strong(X))=>happy(X)))&
(((brave(susan)&~funny(susan)))=>((~creative(alice)&~rich(alice))))&
(![X]:((~old(X)<~>creative(X))<=>wise(X)))&
((?[X]:((funny(X)<~>generous(X))))<=>((~quiet(alice)|~creative(alice))))&
((?[X]:((humble(X)&~wise(X))))<=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((~creative(X)<~>~generous(X))))<=>(?[X]:(wise(X))))&
(((strong(alice)&curious(alice)))<=>((calm(susan)|~rich(susan))))&
(![X]:((~rich(X)&~curious(X))<=>(calm(X)&rich(X))))&
(generous(alice))&
((~happy(susan)|humble(susan)))&
((strong(fred)<~>generous(fred)))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((old(paul)<~>~quiet(paul)))&
(?[X]:(generous(X))) | ~generous(susan) | [
"p6",
"p8",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7517290927000174920670331
% SZS output start Proof for 7517290927000174920670331
7. ! [X0] : ((happy(X0) & generous(X0)) => (kind(X0) & ~happy(X0))) [input p6]
9. ! [X0] : ((strong(X0) | rich(X0)) => happy(X0)) [input p8]
15. (curious(alice) & strong(alice)) <=> (~rich(susan) | calm(susan)) [input p14]
17. generous(alice) [input p16]
25. generous(susan) [input hypothesis]
35. ! [X0] : ((kind(X0) & ~happy(X0)) | (~happy(X0) | ~generous(X0))) [ennf transformation 7]
36. ! [X0] : ((kind(X0) & ~happy(X0)) | ~happy(X0) | ~generous(X0)) [flattening 35]
38. ! [X0] : (happy(X0) | (~strong(X0) & ~rich(X0))) [ennf transformation 9]
62. ((curious(alice) & strong(alice)) | (rich(susan) & ~calm(susan))) & ((~rich(susan) | calm(susan)) | (~curious(alice) | ~strong(alice))) [nnf transformation 15]
63. ((curious(alice) & strong(alice)) | (rich(susan) & ~calm(susan))) & (~rich(susan) | calm(susan) | ~curious(alice) | ~strong(alice)) [flattening 62]
91. ~happy(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 36]
94. ~rich(X0) | happy(X0) [cnf transformation 38]
95. ~strong(X0) | happy(X0) [cnf transformation 38]
118. strong(alice) | rich(susan) [cnf transformation 63]
125. generous(alice) [cnf transformation 17]
137. generous(susan) [cnf transformation 25]
140. ~generous(X0) | ~happy(X0) [duplicate literal removal 91]
247. 24 <=> rich(susan) [avatar definition]
249. rich(susan) <- (24) [avatar component clause 247]
261. 27 <=> strong(alice) [avatar definition]
263. strong(alice) <- (27) [avatar component clause 261]
264. 24 | 27 [avatar split clause 118,261,247]
268. 28 <=> happy(susan) [avatar definition]
269. happy(susan) <- (28) [avatar component clause 268]
270. ~happy(susan) <- (~28) [avatar component clause 268]
323. happy(susan) <- (24) [resolution 94,249]
324. $false <- (24, ~28) [subsumption resolution 323,270]
325. ~24 | 28 [avatar contradiction clause 324]
327. happy(alice) <- (27) [resolution 95,263]
344. ~happy(alice) [resolution 140,125]
346. ~happy(susan) [resolution 140,137]
347. $false <- (27) [subsumption resolution 344,327]
348. ~27 [avatar contradiction clause 347]
349. $false <- (28) [subsumption resolution 346,269]
350. ~28 [avatar contradiction clause 349]
351. $false [avatar sat refutation 264,325,348,350]
% SZS output end Proof for 7517290927000174920670331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not kind is patient.
If someone is either patient or not happy then someone is both not wise and humble and vice versa.
Everyone who is brave or strong is funny.
If someone is both creative and humble then someone is both generous and not generous.
If someone is brave or not funny then paul is both tall and not rich.
If someone is both not curious and not brave then john is wise.
If someone is both wise and calm then john is not patient or not quiet and vice versa.
Everyone who is not strong is either wise or not wise and vice versa.
If alice is both generous and calm then someone is patient or not tall.
If alice is not generous then paul is either not wise or kind.
Everyone who is both not wise and not old is humble or not old and vice versa.
If alice is both rich and wise then someone is wise or curious and vice versa.
If someone is tall then someone is both rich and not wise and vice versa.
If someone is either brave or strong then someone is either funny or creative.
Everyone who is either brave or not generous is either generous or funny and vice versa.
If lucy is either brave or not quiet then paul is either not happy or not funny.
Mary is either kind or quiet.
Someone is not rich.
Someone is tall.
Mary is both not creative and not happy.
Someone is both not humble and not kind.
Someone is not old.
Fred is not calm or humble. | Alice is strong. | contradiction | (![X]:((patient(X)|~kind(X))=>patient(X)))&
((?[X]:((patient(X)<~>~happy(X))))<=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((brave(X)|strong(X))=>funny(X)))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:((generous(X)&~generous(X)))))&
((?[X]:((brave(X)|~funny(X))))=>((tall(paul)&~rich(paul))))&
((?[X]:((~curious(X)&~brave(X))))=>(wise(john)))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(john)|~quiet(john))))&
(![X]:(~strong(X)<=>(wise(X)<~>~wise(X))))&
(((generous(alice)&calm(alice)))=>(?[X]:((patient(X)|~tall(X)))))&
((~generous(alice))=>((~wise(paul)<~>kind(paul))))&
(![X]:((~wise(X)&~old(X))<=>(humble(X)|~old(X))))&
(((rich(alice)&wise(alice)))<=>(?[X]:((wise(X)|curious(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((brave(X)<~>~generous(X))<=>(generous(X)<~>funny(X))))&
(((brave(lucy)<~>~quiet(lucy)))=>((~happy(paul)<~>~funny(paul))))&
((kind(mary)<~>quiet(mary)))&
(?[X]:(~rich(X)))&
(?[X]:(tall(X)))&
((~creative(mary)&~happy(mary)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:(~old(X)))&
((~calm(fred)|humble(fred))) | strong(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7209381632483943061863565
% SZS output start Proof for 7209381632483943061863565
8. ! [X0] : (~strong(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
24. strong(alice) [input hypothesis]
52. ! [X0] : ((~strong(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | strong(X0))) [nnf transformation 8]
107. ~strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 52]
108. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 52]
151. strong(alice) [cnf transformation 24]
156. ~strong(X0) | ~wise(X0) [duplicate literal removal 107]
157. ~strong(X0) | wise(X0) [duplicate literal removal 108]
248. ~strong(X0) [subsumption resolution 156,157]
383. $false [subsumption resolution 151,248]
% SZS output end Proof for 7209381632483943061863565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not old is strong.
Everyone who is both not generous and brave is both not happy and happy.
Everyone who is creative or not old is both not generous and rich and vice versa.
If fred is humble then lucy is either curious or generous and vice versa.
If someone is either curious or not strong then someone is either strong or not curious.
Everyone who is brave or wise is both humble and patient.
Everyone who is rich or kind is old and vice versa.
Everyone who is not creative or not quiet is either not wise or brave and vice versa.
Everyone who is not creative is happy or not calm and vice versa.
If john is creative or strong then someone is happy.
If lucy is both not calm and not humble then someone is not happy and vice versa.
If someone is either creative or wise then someone is either not funny or curious.
Everyone who is either not patient or humble is either strong or not wise and vice versa.
Everyone who is not happy or not funny is either funny or kind.
Everyone who is both not old and not wise is humble and vice versa.
Everyone who is tall or patient is either not old or happy.
Susan is funny.
Paul is either brave or not happy.
Someone is not tall.
Someone is either not tall or happy.
Susan is both tall and kind.
Someone is either not kind or not wise.
Alice is kind.
Paul is both not calm and not quiet. | Susan is not brave. | entailment | (![X]:((~kind(X)<~>~old(X))=>strong(X)))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)&happy(X))))&
(![X]:((creative(X)|~old(X))<=>(~generous(X)&rich(X))))&
((humble(fred))<=>((curious(lucy)<~>generous(lucy))))&
((?[X]:((curious(X)<~>~strong(X))))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((brave(X)|wise(X))=>(humble(X)&patient(X))))&
(![X]:((rich(X)|kind(X))<=>old(X)))&
(![X]:((~creative(X)|~quiet(X))<=>(~wise(X)<~>brave(X))))&
(![X]:(~creative(X)<=>(happy(X)|~calm(X))))&
(((creative(john)|strong(john)))=>(?[X]:(happy(X))))&
(((~calm(lucy)&~humble(lucy)))<=>(?[X]:(~happy(X))))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(strong(X)<~>~wise(X))))&
(![X]:((~happy(X)|~funny(X))=>(funny(X)<~>kind(X))))&
(![X]:((~old(X)&~wise(X))<=>humble(X)))&
(![X]:((tall(X)|patient(X))=>(~old(X)<~>happy(X))))&
(funny(susan))&
((brave(paul)<~>~happy(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((~tall(X)<~>happy(X))))&
((tall(susan)&kind(susan)))&
(?[X]:((~kind(X)<~>~wise(X))))&
(kind(alice))&
((~calm(paul)&~quiet(paul))) | ~brave(susan) | [
"p2",
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8437245020920599103322608
% SZS output start Proof for 8437245020920599103322608
3. ! [X0] : ((~old(X0) | creative(X0)) <=> (rich(X0) & ~generous(X0))) [input p2]
6. ! [X0] : ((wise(X0) | brave(X0)) => (patient(X0) & humble(X0))) [input p5]
7. ! [X0] : ((kind(X0) | rich(X0)) <=> old(X0)) [input p6]
15. ! [X0] : ((~wise(X0) & ~old(X0)) <=> humble(X0)) [input p14]
25. brave(susan) [input hypothesis]
32. ! [X0] : ((patient(X0) & humble(X0)) | (~wise(X0) & ~brave(X0))) [ennf transformation 6]
38. ! [X0] : (((~old(X0) | creative(X0)) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | (old(X0) & ~creative(X0)))) [nnf transformation 3]
39. ! [X0] : ((~old(X0) | creative(X0) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | (old(X0) & ~creative(X0)))) [flattening 38]
45. ! [X0] : (((kind(X0) | rich(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) & ~rich(X0)))) [nnf transformation 7]
46. ! [X0] : ((kind(X0) | rich(X0) | ~old(X0)) & (old(X0) | (~kind(X0) & ~rich(X0)))) [flattening 45]
64. ! [X0] : (((~wise(X0) & ~old(X0)) | ~humble(X0)) & (humble(X0) | (wise(X0) | old(X0)))) [nnf transformation 15]
65. ! [X0] : (((~wise(X0) & ~old(X0)) | ~humble(X0)) & (humble(X0) | wise(X0) | old(X0))) [flattening 64]
83. rich(X0) | old(X0) [cnf transformation 39]
93. ~brave(X0) | humble(X0) [cnf transformation 32]
97. old(X0) | ~rich(X0) [cnf transformation 46]
131. ~old(X0) | ~humble(X0) [cnf transformation 65]
150. brave(susan) [cnf transformation 25]
188. old(X0) [subsumption resolution 97,83]
245. ~humble(X0) [subsumption resolution 131,188]
268. humble(susan) [resolution 93,150]
269. $false [subsumption resolution 268,245]
% SZS output end Proof for 8437245020920599103322608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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