premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is quiet is not tall or not happy.
Everyone who is not strong is both not brave and calm.
Everyone who is both not creative and curious is both happy and not happy.
Everyone who is humble or wise is both not patient and wise.
Everyone who is both not strong and creative is either not curious or not rich.
Everyone who is not kind is either funny or old.
If someone is either not tall or not brave then someone is either tall or generous and vice versa.
Everyone who is either not curious or not rich is either generous or not calm.
If alice is rich then someone is old.
Everyone who is creative or humble is generous and vice versa.
If john is rich then someone is not calm or not curious.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is not brave or brave is not brave or not happy and vice versa.
Lucy is wise.
Mary is not rich or not calm.
Someone is not happy or kind.
Susan is calm.
Alice is both brave and creative.
Alice is generous.
Paul is wise or happy.
Someone is both strong and not wise. | Paul is wise. | entailment | (![X]:(quiet(X)=>(~tall(X)|~happy(X))))&
(![X]:(~strong(X)=>(~brave(X)&calm(X))))&
(![X]:((~creative(X)&curious(X))=>(happy(X)&~happy(X))))&
(![X]:((humble(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((~strong(X)&creative(X))=>(~curious(X)<~>~rich(X))))&
(![X]:(~kind(X)=>(funny(X)<~>old(X))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(generous(X)<~>~calm(X))))&
((rich(alice))=>(?[X]:(old(X))))&
(![X]:((creative(X)|humble(X))<=>generous(X)))&
((rich(john))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:((~brave(X)|brave(X))<=>(~brave(X)|~happy(X))))&
(wise(lucy))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~happy(X)|kind(X))))&
(calm(susan))&
((brave(alice)&creative(alice)))&
(generous(alice))&
((wise(paul)|happy(paul)))&
(?[X]:((strong(X)&~wise(X)))) | wise(paul) | [
"p11",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 230180982651457868362234
% SZS output start Proof for 230180982651457868362234
12. ? [X0] : (happy(X0) | ~strong(X0)) <=> (~creative(alice) & old(alice)) [input p11]
21. creative(alice) & brave(alice) [input p20]
23. happy(paul) | wise(paul) [input p22]
25. ~wise(paul) [input hypothesis]
55. (? [X0] : (happy(X0) | ~strong(X0)) | (creative(alice) | ~old(alice))) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [nnf transformation 12]
56. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X0] : (~happy(X0) & strong(X0))) [flattening 55]
57. (? [X0] : (happy(X0) | ~strong(X0)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [rectify 56]
58. ? [X0] : (happy(X0) | ~strong(X0)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
59. ((happy(sK4) | ~strong(sK4)) | creative(alice) | ~old(alice)) & ((~creative(alice) & old(alice)) | ! [X1] : (~happy(X1) & strong(X1))) [skolemisation 57,58]
106. ~creative(alice) | ~happy(X1) [cnf transformation 59]
129. creative(alice) [cnf transformation 21]
131. happy(paul) | wise(paul) [cnf transformation 23]
134. ~wise(paul) [cnf transformation 25]
202. 15 <=> creative(alice) [avatar definition]
215. 18 <=> ! [X1] : ~happy(X1) [avatar definition]
216. ~happy(X1) <- (18) [avatar component clause 215]
217. 18 | ~15 [avatar split clause 106,202,215]
254. 15 [avatar split clause 129,202]
256. 27 <=> wise(paul) [avatar definition]
260. 28 <=> happy(paul) [avatar definition]
262. happy(paul) <- (28) [avatar component clause 260]
263. 27 | 28 [avatar split clause 131,260,256]
264. ~27 [avatar split clause 134,256]
265. $false <- (18, 28) [resolution 262,216]
266. ~18 | ~28 [avatar contradiction clause 265]
267. $false [avatar sat refutation 217,254,263,264,266]
% SZS output end Proof for 230180982651457868362234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not curious and not generous then someone is quiet or brave and vice versa.
If someone is either not calm or strong then paul is not quiet and vice versa.
Everyone who is not curious is both calm and old and vice versa.
Everyone who is not generous or not humble is both not patient and not kind and vice versa.
If someone is either not old or funny then someone is either not kind or not happy.
Everyone who is not old is either kind or funny and vice versa.
Everyone who is either not creative or brave is both quiet and creative.
If susan is strong then alice is both generous and not funny.
Everyone who is not old is both patient and not generous and vice versa.
If someone is both patient and not old then someone is both calm and patient.
If paul is funny then lucy is either not kind or calm and vice versa.
Everyone who is generous is either not happy or rich and vice versa.
Everyone who is humble is not brave and vice versa.
If mary is either creative or not curious then alice is either funny or tall.
Everyone who is either patient or not strong is not brave or not tall and vice versa.
If someone is either not strong or not humble then fred is tall.
Lucy is either not calm or tall.
Someone is not calm.
John is quiet.
Paul is both not quiet and not rich.
Someone is strong.
Paul is either wise or not patient.
Someone is calm.
Susan is not generous. | Fred is not old. | contradiction | ((?[X]:((~curious(X)&~generous(X))))<=>(?[X]:((quiet(X)|brave(X)))))&
((?[X]:((~calm(X)<~>strong(X))))<=>(~quiet(paul)))&
(![X]:(~curious(X)<=>(calm(X)&old(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~patient(X)&~kind(X))))&
((?[X]:((~old(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:(~old(X)<=>(kind(X)<~>funny(X))))&
(![X]:((~creative(X)<~>brave(X))=>(quiet(X)&creative(X))))&
((strong(susan))=>((generous(alice)&~funny(alice))))&
(![X]:(~old(X)<=>(patient(X)&~generous(X))))&
((?[X]:((patient(X)&~old(X))))=>(?[X]:((calm(X)&patient(X)))))&
((funny(paul))<=>((~kind(lucy)<~>calm(lucy))))&
(![X]:(generous(X)<=>(~happy(X)<~>rich(X))))&
(![X]:(humble(X)<=>~brave(X)))&
(((creative(mary)<~>~curious(mary)))=>((funny(alice)<~>tall(alice))))&
(![X]:((patient(X)<~>~strong(X))<=>(~brave(X)|~tall(X))))&
((?[X]:((~strong(X)<~>~humble(X))))=>(tall(fred)))&
((~calm(lucy)<~>tall(lucy)))&
(?[X]:(~calm(X)))&
(quiet(john))&
((~quiet(paul)&~rich(paul)))&
(?[X]:(strong(X)))&
((wise(paul)<~>~patient(paul)))&
(?[X]:(calm(X)))&
(~generous(susan)) | ~old(fred) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7715650759454356644102862
% SZS output start Proof for 7715650759454356644102862
4. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> (~kind(X0) & ~patient(X0))) [input p3]
9. ! [X0] : (~old(X0) <=> (~generous(X0) & patient(X0))) [input p8]
25. ~old(fred) [input hypothesis]
46. ! [X0] : (((~humble(X0) | ~generous(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (humble(X0) & generous(X0)))) [nnf transformation 4]
47. ! [X0] : ((~humble(X0) | ~generous(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (humble(X0) & generous(X0)))) [flattening 46]
54. ! [X0] : ((~old(X0) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | old(X0))) [nnf transformation 9]
55. ! [X0] : ((~old(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | old(X0))) [flattening 54]
86. ~patient(X0) | generous(X0) [cnf transformation 47]
105. patient(X0) | old(X0) [cnf transformation 55]
106. ~generous(X0) | old(X0) [cnf transformation 55]
143. ~old(fred) [cnf transformation 25]
231. 20 <=> ! [X1] : old(X1) [avatar definition]
232. old(X1) <- (20) [avatar component clause 231]
305. $false <- (20) [resolution 232,143]
306. ~20 [avatar contradiction clause 305]
319. old(X1) | generous(X1) [resolution 105,86]
320. old(X1) [subsumption resolution 319,106]
321. 20 [avatar split clause 320,231]
322. $false [avatar sat refutation 306,321]
% SZS output end Proof for 7715650759454356644102862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not creative then paul is happy or not humble. Everyone who is not rich or not calm is both wise and not tall and vice versa. Everyone who is either creative or wise is both brave and not creative and vice versa. Everyone who is either generous or not rich is either quiet or rich and vice versa. Everyone who is not calm is either quiet or not patient. Everyone who is not creative is strong or rich. Everyone who is not old or generous is both happy and quiet. If mary is rich or patient then lucy is both curious and wise. Everyone who is both not kind and rich is both not curious and funny. If someone is both old and not calm then someone is creative. Everyone who is both not curious and happy is both calm and not humble. Everyone who is creative is generous and vice versa. If alice is not funny then someone is not calm. If paul is either not patient or not tall then someone is both not generous and not rich. Everyone who is not rich is rich or brave and vice versa. Everyone who is not brave is both curious and tall. Someone is both not generous and not tall. Someone is strong or not generous. Paul is either not wise or not generous. Paul is both wise and not kind. Someone is either not kind or tall. Mary is both curious and quiet. | Mary is generous. | contradiction | ((~creative(mary))=>((happy(paul)|~humble(paul))))&
(![X]:((~rich(X)|~calm(X))<=>(wise(X)&~tall(X))))&
(![X]:((creative(X)<~>wise(X))<=>(brave(X)&~creative(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(quiet(X)<~>rich(X))))&
(![X]:(~calm(X)=>(quiet(X)<~>~patient(X))))&
(![X]:(~creative(X)=>(strong(X)|rich(X))))&
(![X]:((~old(X)|generous(X))=>(happy(X)&quiet(X))))&
(((rich(mary)|patient(mary)))=>((curious(lucy)&wise(lucy))))&
(![X]:((~kind(X)&rich(X))=>(~curious(X)&funny(X))))&
((?[X]:((old(X)&~calm(X))))=>(?[X]:(creative(X))))&
(![X]:((~curious(X)&happy(X))=>(calm(X)&~humble(X))))&
(![X]:(creative(X)<=>generous(X)))&
((~funny(alice))=>(?[X]:(~calm(X))))&
(((~patient(paul)<~>~tall(paul)))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:(~rich(X)<=>(rich(X)|brave(X))))&
(![X]:(~brave(X)=>(curious(X)&tall(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~wise(paul)<~>~generous(paul)))&
((wise(paul)&~kind(paul)))&
(?[X]:((~kind(X)<~>tall(X))))&
((curious(mary)&quiet(mary))) | generous(mary) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 831754701374386972148827
% SZS output start Proof for 831754701374386972148827
4. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> rich(X0))) [input p3]
7. ! [X0] : ((generous(X0) | ~old(X0)) => (quiet(X0) & happy(X0))) [input p6]
23. generous(mary) [input hypothesis]
32. ! [X0] : ((quiet(X0) & happy(X0)) | (~generous(X0) & old(X0))) [ennf transformation 7]
45. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 4]
74. rich(X0) | quiet(X0) | generous(X0) | rich(X0) [cnf transformation 45]
75. ~rich(X0) | ~quiet(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 45]
78. ~rich(X0) | generous(X0) | quiet(X0) | ~rich(X0) [cnf transformation 45]
79. rich(X0) | ~generous(X0) | rich(X0) | ~quiet(X0) [cnf transformation 45]
86. quiet(X0) | ~generous(X0) [cnf transformation 32]
115. generous(mary) [cnf transformation 23]
118. rich(X0) | quiet(X0) | generous(X0) [duplicate literal removal 74]
119. ~rich(X0) | ~quiet(X0) | ~generous(X0) [duplicate literal removal 75]
120. ~rich(X0) | generous(X0) | quiet(X0) [duplicate literal removal 78]
121. rich(X0) | ~generous(X0) | ~quiet(X0) [duplicate literal removal 79]
124. ~quiet(X0) | ~generous(X0) [subsumption resolution 119,121]
125. quiet(X0) | generous(X0) [subsumption resolution 118,120]
126. quiet(X0) [subsumption resolution 86,125]
202. ~generous(X0) [resolution 124,126]
203. $false [resolution 202,115]
% SZS output end Proof for 831754701374386972148827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old then someone is happy or creative and vice versa.
If someone is generous then john is both quiet and not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
If lucy is quiet or tall then susan is humble or not patient.
If john is either not calm or not strong then someone is not creative or not humble and vice versa.
If lucy is not curious then fred is both not patient and curious.
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
If someone is strong then john is generous or quiet and vice versa.
Everyone who is either patient or not brave is not tall or old.
Everyone who is either not tall or generous is not quiet and vice versa.
Someone is brave.
Someone is kind or patient.
Alice is both not brave and old.
Mary is not strong or rich.
Someone is not curious or not kind.
Fred is both wise and brave.
Lucy is rich.
Alice is quiet or patient. | Alice is not tall. | entailment | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((happy(X)|creative(X)))))&
((?[X]:(generous(X)))<=>((quiet(john)&~rich(john))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(((quiet(lucy)|tall(lucy)))=>((humble(susan)|~patient(susan))))&
(((~calm(john)<~>~strong(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
((~curious(lucy))=>((~patient(fred)&curious(fred))))&
(![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
((?[X]:(strong(X)))<=>((generous(john)|quiet(john))))&
(![X]:((patient(X)<~>~brave(X))=>(~tall(X)|old(X))))&
(![X]:((~tall(X)<~>generous(X))<=>~quiet(X)))&
(?[X]:(brave(X)))&
(?[X]:((kind(X)|patient(X))))&
((~brave(alice)&old(alice)))&
((~strong(mary)|rich(mary)))&
(?[X]:((~curious(X)|~kind(X))))&
((wise(fred)&brave(fred)))&
(rich(lucy))&
((quiet(alice)|patient(alice))) | ~tall(alice) | [
"p1",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2040064462210840190737270
% SZS output start Proof for 2040064462210840190737270
2. ? [X0] : generous(X0) <=> (~rich(john) & quiet(john)) [input p1]
9. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (quiet(X0) | strong(X0))) [input p8]
16. ! [X0] : ((~tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p15]
25. tall(alice) [input hypothesis]
40. (? [X0] : generous(X0) | (rich(john) | ~quiet(john))) & ((~rich(john) & quiet(john)) | ! [X0] : ~generous(X0)) [nnf transformation 2]
41. (? [X0] : generous(X0) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X0] : ~generous(X0)) [flattening 40]
42. (? [X0] : generous(X0) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X1] : ~generous(X1)) [rectify 41]
43. ? [X0] : generous(X0) => generous(sK2) [choice axiom]
44. (generous(sK2) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X1] : ~generous(X1)) [skolemisation 42,43]
53. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 9]
54. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | wise(X0) | quiet(X0))) [flattening 53]
66. ! [X0] : ((((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | quiet(X0)) & (~quiet(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0))))) [nnf transformation 16]
77. quiet(john) | ~generous(X1) [cnf transformation 44]
105. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
133. generous(X0) | ~tall(X0) | quiet(X0) [cnf transformation 66]
145. tall(alice) [cnf transformation 25]
147. ~quiet(X0) [duplicate literal removal 105]
181. 9 <=> quiet(john) [avatar definition]
182. quiet(john) <- (9) [avatar component clause 181]
194. 12 <=> ! [X1] : ~generous(X1) [avatar definition]
195. ~generous(X1) <- (12) [avatar component clause 194]
197. 12 | 9 [avatar split clause 77,181,194]
306. ~tall(X0) | generous(X0) [subsumption resolution 133,147]
335. $false <- (9) [subsumption resolution 182,147]
336. ~9 [avatar contradiction clause 335]
349. generous(alice) [resolution 306,145]
350. $false <- (12) [subsumption resolution 349,195]
351. ~12 [avatar contradiction clause 350]
352. $false [avatar sat refutation 197,336,351]
% SZS output end Proof for 2040064462210840190737270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and brave is not kind or not calm.
Everyone who is humble or happy is not wise or old.
If someone is either tall or strong then lucy is rich.
If someone is happy or kind then lucy is not wise or not curious.
Everyone who is tall or not patient is either patient or not wise and vice versa.
If susan is not rich or not calm then john is curious or not patient.
Everyone who is kind is both not kind and funny and vice versa.
If someone is either calm or not patient then someone is funny or happy.
Everyone who is both not patient and generous is not humble or not tall and vice versa.
If mary is not calm then someone is humble and vice versa.
If susan is not kind or old then paul is both not rich and creative and vice versa.
Everyone who is either not funny or not kind is either kind or not patient.
Everyone who is curious is not wise and vice versa.
If lucy is both not calm and not old then lucy is either not strong or not quiet.
Everyone who is generous or patient is not kind or not creative.
If fred is either not generous or not quiet then paul is creative or not funny and vice versa.
Someone is either generous or old.
Susan is either not calm or calm.
Someone is both patient and brave.
Lucy is not strong or tall.
Susan is not creative or not quiet.
Fred is wise or curious.
Someone is kind or calm. | Lucy is not calm. | neutral | (![X]:((~curious(X)&brave(X))=>(~kind(X)|~calm(X))))&
(![X]:((humble(X)|happy(X))=>(~wise(X)|old(X))))&
((?[X]:((tall(X)<~>strong(X))))=>(rich(lucy)))&
((?[X]:((happy(X)|kind(X))))=>((~wise(lucy)|~curious(lucy))))&
(![X]:((tall(X)|~patient(X))<=>(patient(X)<~>~wise(X))))&
(((~rich(susan)|~calm(susan)))=>((curious(john)|~patient(john))))&
(![X]:(kind(X)<=>(~kind(X)&funny(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~patient(X)&generous(X))<=>(~humble(X)|~tall(X))))&
((~calm(mary))<=>(?[X]:(humble(X))))&
(((~kind(susan)|old(susan)))<=>((~rich(paul)&creative(paul))))&
(![X]:((~funny(X)<~>~kind(X))=>(kind(X)<~>~patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(((~calm(lucy)&~old(lucy)))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((generous(X)|patient(X))=>(~kind(X)|~creative(X))))&
(((~generous(fred)<~>~quiet(fred)))<=>((creative(paul)|~funny(paul))))&
(?[X]:((generous(X)<~>old(X))))&
((~calm(susan)<~>calm(susan)))&
(?[X]:((patient(X)&brave(X))))&
((~strong(lucy)|tall(lucy)))&
((~creative(susan)|~quiet(susan)))&
((wise(fred)|curious(fred)))&
(?[X]:((kind(X)|calm(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not patient is either humble or not rich.
Everyone who is not old or strong is either quiet or calm.
Everyone who is either not curious or generous is not patient.
If someone is either not kind or happy then lucy is either patient or generous.
Everyone who is curious or not creative is not kind or kind and vice versa.
Everyone who is either not funny or not wise is either funny or not wise.
If alice is not happy or kind then someone is both quiet and not funny.
If fred is either not tall or not funny then someone is calm and vice versa.
Everyone who is not patient is brave.
Everyone who is wise or quiet is not rich or strong.
If paul is brave then someone is happy and vice versa.
Everyone who is calm is both kind and patient.
Everyone who is old or kind is either wise or funny and vice versa.
If john is either rich or not generous then someone is funny and vice versa.
If fred is either brave or not old then someone is either curious or creative and vice versa.
If paul is patient then susan is not wise or calm and vice versa.
Susan is either funny or quiet.
Susan is not tall.
Lucy is strong or generous.
Someone is patient.
Someone is calm or brave.
Someone is both not brave and happy. | Susan is not quiet. | contradiction | (![X]:(~patient(X)=>(humble(X)<~>~rich(X))))&
(![X]:((~old(X)|strong(X))=>(quiet(X)<~>calm(X))))&
(![X]:((~curious(X)<~>generous(X))=>~patient(X)))&
((?[X]:((~kind(X)<~>happy(X))))=>((patient(lucy)<~>generous(lucy))))&
(![X]:((curious(X)|~creative(X))<=>(~kind(X)|kind(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(funny(X)<~>~wise(X))))&
(((~happy(alice)|kind(alice)))=>(?[X]:((quiet(X)&~funny(X)))))&
(((~tall(fred)<~>~funny(fred)))<=>(?[X]:(calm(X))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|kind(X))<=>(wise(X)<~>funny(X))))&
(((rich(john)<~>~generous(john)))<=>(?[X]:(funny(X))))&
(((brave(fred)<~>~old(fred)))<=>(?[X]:((curious(X)<~>creative(X)))))&
((patient(paul))<=>((~wise(susan)|calm(susan))))&
((funny(susan)<~>quiet(susan)))&
(~tall(susan))&
((strong(lucy)|generous(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((~brave(X)&happy(X)))) | ~quiet(susan) | [
"p1",
"p5",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8159833585290179773491250
% SZS output start Proof for 8159833585290179773491250
2. ! [X0] : ((strong(X0) | ~old(X0)) => (quiet(X0) <~> calm(X0))) [input p1]
6. ! [X0] : ((~funny(X0) <~> ~wise(X0)) => (funny(X0) <~> ~wise(X0))) [input p5]
8. (~tall(fred) <~> ~funny(fred)) <=> ? [X0] : calm(X0) [input p7]
12. ! [X0] : (calm(X0) => (patient(X0) & kind(X0))) [input p11]
13. ! [X0] : ((kind(X0) | old(X0)) <=> (wise(X0) <~> funny(X0))) [input p12]
23. ~quiet(susan) [input hypothesis]
25. ! [X0] : ((quiet(X0) <~> calm(X0)) | (~strong(X0) & old(X0))) [ennf transformation 2]
28. ! [X0] : ((funny(X0) <~> ~wise(X0)) | (~funny(X0) <=> ~wise(X0))) [ennf transformation 6]
33. ! [X0] : ((patient(X0) & kind(X0)) | ~calm(X0)) [ennf transformation 12]
35. ! [X0] : (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~strong(X0) & old(X0))) [nnf transformation 25]
40. ! [X0] : (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) [nnf transformation 28]
43. (((funny(fred) | tall(fred)) & (~funny(fred) | ~tall(fred))) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ((~tall(fred) | funny(fred)) & (~funny(fred) | tall(fred)))) [nnf transformation 8]
44. (((funny(fred) | tall(fred)) & (~funny(fred) | ~tall(fred))) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ((~tall(fred) | funny(fred)) & (~funny(fred) | tall(fred)))) [rectify 43]
45. ? [X1] : calm(X1) => calm(sK1) [choice axiom]
46. (((funny(fred) | tall(fred)) & (~funny(fred) | ~tall(fred))) | ! [X0] : ~calm(X0)) & (calm(sK1) | ((~tall(fred) | funny(fred)) & (~funny(fred) | tall(fred)))) [skolemisation 44,45]
51. ! [X0] : (((kind(X0) | old(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~kind(X0) & ~old(X0)))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) | old(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~kind(X0) & ~old(X0)))) [flattening 51]
72. calm(X0) | quiet(X0) | old(X0) [cnf transformation 35]
86. ~wise(X0) | funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 40]
89. wise(X0) | ~funny(X0) | ~funny(X0) | wise(X0) [cnf transformation 40]
94. calm(sK1) | ~funny(fred) | tall(fred) [cnf transformation 46]
95. calm(sK1) | ~tall(fred) | funny(fred) [cnf transformation 46]
96. ~funny(fred) | ~tall(fred) | ~calm(X0) [cnf transformation 46]
97. funny(fred) | tall(fred) | ~calm(X0) [cnf transformation 46]
103. ~calm(X0) | kind(X0) [cnf transformation 33]
105. funny(X0) | wise(X0) | ~old(X0) [cnf transformation 52]
106. funny(X0) | wise(X0) | ~kind(X0) [cnf transformation 52]
107. ~funny(X0) | ~wise(X0) | ~old(X0) [cnf transformation 52]
108. ~funny(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 52]
134. ~quiet(susan) [cnf transformation 23]
135. ~wise(X0) | funny(X0) [duplicate literal removal 86]
136. ~funny(X0) | wise(X0) [duplicate literal removal 89]
177. 9 <=> ! [X0] : ~calm(X0) [avatar definition]
178. ~calm(X0) <- (9) [avatar component clause 177]
180. 10 <=> tall(fred) [avatar definition]
184. 11 <=> funny(fred) [avatar definition]
187. 9 | 10 | 11 [avatar split clause 97,184,180,177]
188. 9 | ~10 | ~11 [avatar split clause 96,184,180,177]
190. 12 <=> calm(sK1) [avatar definition]
192. calm(sK1) <- (12) [avatar component clause 190]
193. 11 | ~10 | 12 [avatar split clause 95,190,180,184]
194. 10 | ~11 | 12 [avatar split clause 94,190,184,180]
208. ~wise(X0) | ~kind(X0) [subsumption resolution 108,135]
209. ~wise(X0) | ~old(X0) [subsumption resolution 107,135]
210. wise(X0) | ~kind(X0) [subsumption resolution 106,136]
211. ~kind(X0) [subsumption resolution 210,208]
212. wise(X0) | ~old(X0) [subsumption resolution 105,136]
213. ~old(X0) [subsumption resolution 212,209]
276. 28 <=> quiet(susan) [avatar definition]
278. ~quiet(susan) <- (~28) [avatar component clause 276]
295. ~28 [avatar split clause 134,276]
306. kind(sK1) <- (12) [resolution 103,192]
309. $false <- (12) [subsumption resolution 306,211]
310. ~12 [avatar contradiction clause 309]
327. quiet(X1) | old(X1) <- (9) [resolution 72,178]
332. quiet(X1) <- (9) [subsumption resolution 327,213]
333. $false <- (9, ~28) [resolution 332,278]
334. ~9 | 28 [avatar contradiction clause 333]
335. $false [avatar sat refutation 187,188,193,194,295,310,334]
% SZS output end Proof for 8159833585290179773491250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not tall and vice versa. Everyone who is not wise or humble is not kind. If alice is both wise and not patient then someone is not rich and vice versa. If alice is either wise or calm then lucy is both not calm and patient. Everyone who is both rich and calm is not tall and vice versa. Everyone who is either creative or curious is either generous or wise. Everyone who is either generous or not patient is not generous. If someone is brave or not brave then susan is both not wise and strong. Everyone who is either humble or rich is both quiet and not quiet and vice versa. If someone is either wise or humble then susan is creative and vice versa. If fred is tall then alice is not humble and vice versa. If john is not strong then someone is either not calm or patient and vice versa. If someone is both calm and not old then mary is not kind and vice versa. If susan is both quiet and not happy then mary is either creative or not generous and vice versa. Everyone who is either not kind or quiet is not generous. Everyone who is not strong or generous is both not kind and funny and vice versa. Someone is both brave and happy. Someone is not rich. Mary is either not generous or kind. Someone is either not quiet or generous. Fred is humble. Someone is patient or old. Someone is both not kind and humble. | John is not patient. | neutral | (![X]:(creative(X)<=>~tall(X)))&
(![X]:((~wise(X)|humble(X))=>~kind(X)))&
(((wise(alice)&~patient(alice)))<=>(?[X]:(~rich(X))))&
(((wise(alice)<~>calm(alice)))=>((~calm(lucy)&patient(lucy))))&
(![X]:((rich(X)&calm(X))<=>~tall(X)))&
(![X]:((creative(X)<~>curious(X))=>(generous(X)<~>wise(X))))&
(![X]:((generous(X)<~>~patient(X))=>~generous(X)))&
((?[X]:((brave(X)|~brave(X))))=>((~wise(susan)&strong(susan))))&
(![X]:((humble(X)<~>rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(creative(susan)))&
((tall(fred))<=>(~humble(alice)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(~kind(mary)))&
(((quiet(susan)&~happy(susan)))<=>((creative(mary)<~>~generous(mary))))&
(![X]:((~kind(X)<~>quiet(X))=>~generous(X)))&
(![X]:((~strong(X)|generous(X))<=>(~kind(X)&funny(X))))&
(?[X]:((brave(X)&happy(X))))&
(?[X]:(~rich(X)))&
((~generous(mary)<~>kind(mary)))&
(?[X]:((~quiet(X)<~>generous(X))))&
(humble(fred))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~kind(X)&humble(X)))) | ~patient(john) | [] | null | 0 |
Everyone who is both not funny and not brave is either patient or not tall.
Everyone who is either curious or not wise is both strong and not rich.
Everyone who is humble or not generous is humble and vice versa.
If someone is both generous and not quiet then lucy is both humble and brave and vice versa.
If someone is not quiet or calm then someone is not funny or rich.
Everyone who is not strong is both generous and funny.
If someone is quiet then someone is not old and vice versa.
If someone is both quiet and generous then mary is not happy and vice versa.
Everyone who is either not quiet or rich is either curious or creative and vice versa.
If alice is not curious or not calm then fred is rich or creative and vice versa.
If john is not generous or strong then someone is quiet.
If mary is not generous then someone is either brave or humble.
If someone is either tall or old then someone is either not quiet or brave and vice versa.
Everyone who is not generous or old is not happy.
If someone is both quiet and not rich then someone is either patient or happy.
Everyone who is not rich or not happy is not rich and vice versa.
Someone is either generous or curious.
Someone is both not patient and not quiet.
Mary is either patient or creative.
Alice is not brave or generous.
Fred is both not patient and not quiet.
John is both wise and not strong.
Someone is kind or not tall.
Susan is generous or not humble. | Fred is quiet. | contradiction | (![X]:((~funny(X)&~brave(X))=>(patient(X)<~>~tall(X))))&
(![X]:((curious(X)<~>~wise(X))=>(strong(X)&~rich(X))))&
(![X]:((humble(X)|~generous(X))<=>humble(X)))&
((?[X]:((generous(X)&~quiet(X))))<=>((humble(lucy)&brave(lucy))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:(~strong(X)=>(generous(X)&funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(~old(X))))&
((?[X]:((quiet(X)&generous(X))))<=>(~happy(mary)))&
(![X]:((~quiet(X)<~>rich(X))<=>(curious(X)<~>creative(X))))&
(((~curious(alice)|~calm(alice)))<=>((rich(fred)|creative(fred))))&
(((~generous(john)|strong(john)))=>(?[X]:(quiet(X))))&
((~generous(mary))=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:((~generous(X)|old(X))=>~happy(X)))&
((?[X]:((quiet(X)&~rich(X))))=>(?[X]:((patient(X)<~>happy(X)))))&
(![X]:((~rich(X)|~happy(X))<=>~rich(X)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
((patient(mary)<~>creative(mary)))&
((~brave(alice)|generous(alice)))&
((~patient(fred)&~quiet(fred)))&
((wise(john)&~strong(john)))&
(?[X]:((kind(X)|~tall(X))))&
((generous(susan)|~humble(susan))) | quiet(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 180746187980734614413450
% SZS output start Proof for 180746187980734614413450
21. ~quiet(fred) & ~patient(fred) [input p20]
25. quiet(fred) [input hypothesis]
147. ~quiet(fred) [cnf transformation 21]
151. quiet(fred) [cnf transformation 25]
353. $false [subsumption resolution 151,147]
% SZS output end Proof for 180746187980734614413450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not quiet then someone is not strong and vice versa.
Everyone who is either brave or quiet is creative or brave and vice versa.
If susan is not creative then fred is both not curious and quiet and vice versa.
Everyone who is both not quiet and not rich is both not humble and quiet and vice versa.
If mary is calm then someone is either strong or patient and vice versa.
Everyone who is either calm or quiet is not humble or generous.
Everyone who is both not patient and quiet is either not funny or not quiet.
If someone is happy then someone is happy or not old and vice versa.
If someone is humble then someone is either curious or calm.
Everyone who is not wise is brave.
Everyone who is both calm and not creative is quiet or not wise and vice versa.
If lucy is not happy then mary is not funny and vice versa.
If someone is wise or not humble then fred is funny or tall and vice versa.
If someone is not brave or not creative then someone is brave and vice versa.
Everyone who is both not funny and not strong is both generous and happy.
If mary is either not kind or quiet then mary is creative and vice versa.
Mary is happy or rich.
Someone is not quiet or not humble.
Lucy is either old or not kind.
Paul is both happy and not curious.
John is wise or old.
Lucy is not old.
John is either creative or calm.
John is either not quiet or calm. | John is not brave. | contradiction | ((?[X]:((~humble(X)|~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(creative(X)|brave(X))))&
((~creative(susan))<=>((~curious(fred)&quiet(fred))))&
(![X]:((~quiet(X)&~rich(X))<=>(~humble(X)&quiet(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((calm(X)<~>quiet(X))=>(~humble(X)|generous(X))))&
(![X]:((~patient(X)&quiet(X))=>(~funny(X)<~>~quiet(X))))&
((?[X]:(happy(X)))<=>(?[X]:((happy(X)|~old(X)))))&
((?[X]:(humble(X)))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:(~wise(X)=>brave(X)))&
(![X]:((calm(X)&~creative(X))<=>(quiet(X)|~wise(X))))&
((~happy(lucy))<=>(~funny(mary)))&
((?[X]:((wise(X)|~humble(X))))<=>((funny(fred)|tall(fred))))&
((?[X]:((~brave(X)|~creative(X))))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)&~strong(X))=>(generous(X)&happy(X))))&
(((~kind(mary)<~>quiet(mary)))<=>(creative(mary)))&
((happy(mary)|rich(mary)))&
(?[X]:((~quiet(X)|~humble(X))))&
((old(lucy)<~>~kind(lucy)))&
((happy(paul)&~curious(paul)))&
((wise(john)|old(john)))&
(~old(lucy))&
((creative(john)<~>calm(john)))&
((~quiet(john)<~>calm(john))) | ~brave(john) | [
"p1",
"p10",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 124863888220208857352690
% SZS output start Proof for 124863888220208857352690
2. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (brave(X0) | creative(X0))) [input p1]
11. ! [X0] : ((~creative(X0) & calm(X0)) <=> (~wise(X0) | quiet(X0))) [input p10]
23. creative(john) <~> calm(john) [input p22]
24. ~quiet(john) <~> calm(john) [input p23]
25. ~brave(john) [input hypothesis]
43. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 2]
44. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [flattening 43]
63. ! [X0] : (((~creative(X0) & calm(X0)) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | (creative(X0) | ~calm(X0)))) [nnf transformation 11]
64. ! [X0] : (((~creative(X0) & calm(X0)) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | creative(X0) | ~calm(X0))) [flattening 63]
80. (~calm(john) | ~creative(john)) & (calm(john) | creative(john)) [nnf transformation 23]
81. (~calm(john) | quiet(john)) & (calm(john) | ~quiet(john)) [nnf transformation 24]
86. brave(X0) | creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 44]
87. ~creative(X0) | brave(X0) | quiet(X0) [cnf transformation 44]
90. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
113. ~creative(X0) | ~quiet(X0) [cnf transformation 64]
137. calm(john) | creative(john) [cnf transformation 80]
140. ~calm(john) | quiet(john) [cnf transformation 81]
141. ~brave(john) [cnf transformation 25]
145. brave(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 86]
146. ~brave(X0) | ~quiet(X0) [duplicate literal removal 90]
171. ~quiet(X0) | creative(X0) [subsumption resolution 145,146]
243. ~quiet(X0) [subsumption resolution 113,171]
344. 44 <=> creative(john) [avatar definition]
345. creative(john) <- (44) [avatar component clause 344]
348. 45 <=> calm(john) [avatar definition]
352. 44 | 45 [avatar split clause 137,348,344]
353. ~calm(john) [subsumption resolution 140,243]
354. ~45 [avatar split clause 353,348]
363. brave(john) | quiet(john) <- (44) [resolution 87,345]
366. quiet(john) <- (44) [subsumption resolution 363,141]
367. $false <- (44) [subsumption resolution 366,243]
368. ~44 [avatar contradiction clause 367]
369. $false [avatar sat refutation 352,354,368]
% SZS output end Proof for 124863888220208857352690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not kind is happy and vice versa.
If alice is not strong or old then john is both not brave and not wise and vice versa.
If someone is not old then susan is not curious or funny.
Everyone who is both curious and not happy is either not calm or not strong and vice versa.
If paul is kind then mary is humble and vice versa.
Everyone who is both funny and not kind is either not rich or creative and vice versa.
Everyone who is not curious is strong or funny and vice versa.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
If someone is strong or not funny then someone is not happy or not brave and vice versa.
Everyone who is either curious or not funny is either kind or not brave and vice versa.
Everyone who is both patient and not old is both not patient and funny and vice versa.
Everyone who is both not happy and not generous is either not creative or not funny.
If john is not brave or old then fred is rich and vice versa.
Everyone who is strong is either not patient or not strong and vice versa.
Everyone who is not rich is either not calm or not brave.
Someone is either calm or rich.
Someone is not old.
Someone is strong.
Someone is quiet or not strong.
John is either humble or not wise.
Fred is both old and not patient.
Paul is not wise or not kind. | Mary is calm. | entailment | (![X]:((tall(X)&~kind(X))<=>happy(X)))&
(((~strong(alice)|old(alice)))<=>((~brave(john)&~wise(john))))&
((?[X]:(~old(X)))=>((~curious(susan)|funny(susan))))&
(![X]:((curious(X)&~happy(X))<=>(~calm(X)<~>~strong(X))))&
((kind(paul))<=>(humble(mary)))&
(![X]:((funny(X)&~kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:(~curious(X)<=>(strong(X)|funny(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)|~strong(X))))&
((humble(john)<~>~wise(john)))&
((old(fred)&~patient(fred)))&
((~wise(paul)|~kind(paul))) | calm(mary) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2348145480385051064103223
% SZS output start Proof for 2348145480385051064103223
1. ! [X0] : ((~kind(X0) & tall(X0)) <=> happy(X0)) [input p0]
4. ! [X0] : ((~happy(X0) & curious(X0)) <=> (~calm(X0) <~> ~strong(X0))) [input p3]
7. ! [X0] : (~curious(X0) <=> (funny(X0) | strong(X0))) [input p6]
8. ! [X0] : ((strong(X0) | ~curious(X0)) <=> wise(X0)) [input p7]
9. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p8]
11. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : ((~old(X0) & patient(X0)) <=> (funny(X0) & ~patient(X0))) [input p11]
15. ! [X0] : (strong(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p14]
24. ~calm(mary) [input hypothesis]
31. ! [X0] : (((~kind(X0) & tall(X0)) | ~happy(X0)) & (happy(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 1]
32. ! [X0] : (((~kind(X0) & tall(X0)) | ~happy(X0)) & (happy(X0) | kind(X0) | ~tall(X0))) [flattening 31]
35. ! [X0] : (((~happy(X0) & curious(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (happy(X0) | ~curious(X0)))) [nnf transformation 4]
36. ! [X0] : (((~happy(X0) & curious(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | happy(X0) | ~curious(X0))) [flattening 35]
40. ! [X0] : ((~curious(X0) | (~funny(X0) & ~strong(X0))) & ((funny(X0) | strong(X0)) | curious(X0))) [nnf transformation 7]
41. ! [X0] : ((~curious(X0) | (~funny(X0) & ~strong(X0))) & (funny(X0) | strong(X0) | curious(X0))) [flattening 40]
42. ! [X0] : (((strong(X0) | ~curious(X0)) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [nnf transformation 8]
43. ! [X0] : ((strong(X0) | ~curious(X0) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [flattening 42]
44. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 9]
45. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 44]
51. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 11]
52. ! [X0] : (((~old(X0) & patient(X0)) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | (old(X0) | ~patient(X0)))) [nnf transformation 12]
53. ! [X0] : (((~old(X0) & patient(X0)) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | old(X0) | ~patient(X0))) [flattening 52]
56. ! [X0] : ((strong(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~strong(X0))) [nnf transformation 15]
68. ~happy(X0) | ~kind(X0) [cnf transformation 32]
76. ~curious(X0) | calm(X0) | happy(X0) | strong(X0) [cnf transformation 36]
77. ~strong(X0) | curious(X0) | calm(X0) [cnf transformation 36]
79. ~strong(X0) | ~happy(X0) | calm(X0) [cnf transformation 36]
89. funny(X0) | strong(X0) | curious(X0) [cnf transformation 41]
90. ~curious(X0) | ~strong(X0) [cnf transformation 41]
91. ~funny(X0) | ~curious(X0) [cnf transformation 41]
92. curious(X0) | wise(X0) [cnf transformation 43]
93. ~strong(X0) | wise(X0) [cnf transformation 43]
94. strong(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 43]
96. ~brave(X0) | ~brave(X0) [cnf transformation 45]
109. ~funny(X0) | curious(X0) | kind(X0) | brave(X0) [cnf transformation 51]
111. funny(X0) | ~curious(X0) | kind(X0) | brave(X0) [cnf transformation 51]
114. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 53]
119. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 56]
122. strong(X0) | ~patient(X0) | strong(X0) [cnf transformation 56]
134. ~calm(mary) [cnf transformation 24]
135. ~strong(X0) | ~patient(X0) [duplicate literal removal 119]
136. ~patient(X0) | strong(X0) [duplicate literal removal 122]
138. ~funny(X0) | patient(X0) [duplicate literal removal 114]
140. ~brave(X0) [duplicate literal removal 96]
184. ~curious(X0) | ~wise(X0) [subsumption resolution 94,90]
200. funny(X0) | ~curious(X0) | kind(X0) [subsumption resolution 111,140]
201. ~curious(X0) | kind(X0) [subsumption resolution 200,91]
202. ~funny(X0) | curious(X0) | kind(X0) [subsumption resolution 109,140]
203. ~funny(X0) | kind(X0) [subsumption resolution 202,91]
216. ~patient(X0) [subsumption resolution 135,136]
297. strong(X0) | curious(X0) | kind(X0) [resolution 89,203]
298. strong(X1) | curious(X1) | patient(X1) [resolution 89,138]
305. strong(X0) | kind(X0) [subsumption resolution 297,201]
306. curious(X1) | strong(X1) [subsumption resolution 298,216]
357. calm(X0) | happy(X0) | strong(X0) | wise(X0) [resolution 76,92]
359. calm(X0) | happy(X0) | wise(X0) [subsumption resolution 357,93]
398. kind(X0) | ~happy(X0) | calm(X0) [resolution 305,79]
401. ~happy(X0) | calm(X0) [subsumption resolution 398,68]
407. ~wise(X2) | strong(X2) [resolution 306,184]
416. happy(mary) | wise(mary) [resolution 359,134]
423. 35 <=> wise(mary) [avatar definition]
425. wise(mary) <- (35) [avatar component clause 423]
427. 36 <=> happy(mary) [avatar definition]
429. happy(mary) <- (36) [avatar component clause 427]
430. 35 | 36 [avatar split clause 416,427,423]
449. calm(mary) <- (36) [resolution 401,429]
450. $false <- (36) [subsumption resolution 449,134]
451. ~36 [avatar contradiction clause 450]
465. strong(mary) <- (35) [resolution 407,425]
476. 40 <=> curious(mary) [avatar definition]
478. curious(mary) <- (40) [avatar component clause 476]
526. curious(mary) | calm(mary) <- (35) [resolution 465,77]
536. ~strong(mary) <- (40) [resolution 478,90]
539. $false <- (35, 40) [subsumption resolution 536,465]
540. ~35 | ~40 [avatar contradiction clause 539]
541. curious(mary) <- (35) [subsumption resolution 526,134]
542. 40 | ~35 [avatar split clause 541,423,476]
543. $false [avatar sat refutation 430,451,540,542]
% SZS output end Proof for 2348145480385051064103223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both patient and rich then someone is either not generous or old.
If someone is not quiet then someone is both funny and not funny and vice versa.
If someone is either happy or not calm then mary is either wise or happy and vice versa.
Everyone who is not quiet or strong is either generous or not tall and vice versa.
Everyone who is patient is not tall.
If paul is not wise then someone is quiet or happy and vice versa.
Everyone who is rich or humble is either curious or not wise.
Everyone who is either not quiet or not kind is not calm or happy.
Everyone who is both rich and creative is not humble or generous and vice versa.
If someone is not humble or calm then someone is not quiet.
Everyone who is happy or not tall is either patient or not rich and vice versa.
If fred is not rich then someone is not calm and vice versa.
Everyone who is either not kind or not generous is not wise or quiet and vice versa.
Everyone who is either calm or creative is both rich and calm.
If someone is not generous then john is not old and vice versa.
Someone is happy or not generous.
Fred is kind.
Someone is curious or happy.
Someone is wise or tall.
Someone is tall.
Fred is strong or not old. | Paul is creative. | contradiction | (((patient(lucy)&rich(lucy)))=>(?[X]:((~generous(X)<~>old(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((funny(X)&~funny(X)))))&
((?[X]:((happy(X)<~>~calm(X))))<=>((wise(mary)<~>happy(mary))))&
(![X]:((~quiet(X)|strong(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(patient(X)=>~tall(X)))&
((~wise(paul))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((rich(X)|humble(X))=>(curious(X)<~>~wise(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~calm(X)|happy(X))))&
(![X]:((rich(X)&creative(X))<=>(~humble(X)|generous(X))))&
((?[X]:((~humble(X)|calm(X))))=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)|~tall(X))<=>(patient(X)<~>~rich(X))))&
((~rich(fred))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~wise(X)|quiet(X))))&
(![X]:((calm(X)<~>creative(X))=>(rich(X)&calm(X))))&
((?[X]:(~generous(X)))<=>(~old(john)))&
(?[X]:((happy(X)|~generous(X))))&
(kind(fred))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:(tall(X)))&
((strong(fred)|~old(fred))) | creative(paul) | [
"p1",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5757507847168073637913184
% SZS output start Proof for 5757507847168073637913184
2. ? [X0] : ~quiet(X0) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p1]
10. ? [X0] : (calm(X0) | ~humble(X0)) => ? [X0] : ~quiet(X0) [input p9]
14. ! [X0] : ((calm(X0) <~> creative(X0)) => (calm(X0) & rich(X0))) [input p13]
22. creative(paul) [input hypothesis]
23. ? [X0] : ~quiet(X0) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 2]
24. ? [X0] : (calm(X0) | ~humble(X0)) => ? [X1] : ~quiet(X1) [rectify 10]
31. ? [X1] : ~quiet(X1) | ! [X0] : (~calm(X0) & humble(X0)) [ennf transformation 24]
32. ! [X0] : ((calm(X0) & rich(X0)) | (calm(X0) <=> creative(X0))) [ennf transformation 14]
36. (? [X0] : ~quiet(X0) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : quiet(X0)) [nnf transformation 23]
37. (? [X0] : ~quiet(X0) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : quiet(X3)) [rectify 36]
38. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
39. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK2) & funny(sK2)) [choice axiom]
40. (~quiet(sK1) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK2) & funny(sK2)) | ! [X3] : quiet(X3)) [skolemisation 37,39,38]
55. ? [X0] : ~quiet(X0) | ! [X1] : (~calm(X1) & humble(X1)) [rectify 31]
56. ? [X0] : ~quiet(X0) => ~quiet(sK5) [choice axiom]
57. ~quiet(sK5) | ! [X1] : (~calm(X1) & humble(X1)) [skolemisation 55,56]
66. ! [X0] : ((calm(X0) & rich(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) [nnf transformation 32]
81. funny(sK2) | quiet(X3) [cnf transformation 40]
82. ~funny(sK2) | quiet(X3) [cnf transformation 40]
114. ~quiet(sK5) | ~calm(X1) [cnf transformation 57]
132. calm(X0) | calm(X0) | ~creative(X0) [cnf transformation 66]
141. creative(paul) [cnf transformation 22]
142. ~creative(X0) | calm(X0) [duplicate literal removal 132]
162. 5 <=> ! [X3] : quiet(X3) [avatar definition]
163. quiet(X3) <- (5) [avatar component clause 162]
165. 6 <=> funny(sK2) [avatar definition]
168. 5 | ~6 [avatar split clause 82,165,162]
169. 5 | 6 [avatar split clause 81,165,162]
222. 18 <=> ! [X1] : ~calm(X1) [avatar definition]
223. ~calm(X1) <- (18) [avatar component clause 222]
225. 19 <=> quiet(sK5) [avatar definition]
227. ~quiet(sK5) <- (~19) [avatar component clause 225]
228. 18 | ~19 [avatar split clause 114,225,222]
301. $false <- (5, ~19) [resolution 227,163]
302. ~5 | 19 [avatar contradiction clause 301]
304. calm(paul) [resolution 142,141]
306. $false <- (18) [subsumption resolution 304,223]
307. ~18 [avatar contradiction clause 306]
308. $false [avatar sat refutation 168,169,228,302,307]
% SZS output end Proof for 5757507847168073637913184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not kind or humble.
Everyone who is happy is either curious or not strong and vice versa.
If someone is rich or not happy then someone is either tall or quiet.
Everyone who is humble or not wise is generous and vice versa.
If someone is not generous then someone is both strong and not funny.
Everyone who is either not funny or old is either not funny or not tall.
Everyone who is either not brave or patient is curious and vice versa.
If fred is creative or strong then someone is either happy or kind.
If someone is either not strong or funny then someone is not patient or brave.
Everyone who is not kind is either kind or quiet and vice versa.
If someone is either happy or not happy then someone is calm or quiet and vice versa.
Everyone who is either not humble or not calm is not funny.
Everyone who is either old or calm is not strong.
Everyone who is generous is both funny and calm and vice versa.
Everyone who is both not tall and not humble is both not calm and not creative and vice versa.
Everyone who is happy is either strong or creative and vice versa.
Someone is not quiet or quiet.
Susan is kind or tall.
Someone is either not old or not brave.
Fred is patient or curious.
Someone is either tall or funny.
Paul is either wise or not brave.
Lucy is both not happy and not humble.
Fred is either not brave or not funny. | Lucy is not wise. | contradiction | (![X]:(funny(X)=>(~kind(X)|humble(X))))&
(![X]:(happy(X)<=>(curious(X)<~>~strong(X))))&
((?[X]:((rich(X)|~happy(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:((humble(X)|~wise(X))<=>generous(X)))&
((?[X]:(~generous(X)))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~funny(X)<~>old(X))=>(~funny(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>curious(X)))&
(((creative(fred)|strong(fred)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>quiet(X))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>~funny(X)))&
(![X]:((old(X)<~>calm(X))=>~strong(X)))&
(![X]:(generous(X)<=>(funny(X)&calm(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~calm(X)&~creative(X))))&
(![X]:(happy(X)<=>(strong(X)<~>creative(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((kind(susan)|tall(susan)))&
(?[X]:((~old(X)<~>~brave(X))))&
((patient(fred)|curious(fred)))&
(?[X]:((tall(X)<~>funny(X))))&
((wise(paul)<~>~brave(paul)))&
((~happy(lucy)&~humble(lucy)))&
((~brave(fred)<~>~funny(fred))) | ~wise(lucy) | [
"p3",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3881876935036007033116991
% SZS output start Proof for 3881876935036007033116991
4. ! [X0] : ((~wise(X0) | humble(X0)) <=> generous(X0)) [input p3]
12. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => ~funny(X0)) [input p11]
14. ! [X0] : (generous(X0) <=> (calm(X0) & funny(X0))) [input p13]
23. ~humble(lucy) & ~happy(lucy) [input p22]
25. ~wise(lucy) [input hypothesis]
38. ! [X0] : (~funny(X0) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 12]
45. ! [X0] : (((~wise(X0) | humble(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & ~humble(X0)))) [nnf transformation 4]
46. ! [X0] : ((~wise(X0) | humble(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & ~humble(X0)))) [flattening 45]
65. ! [X0] : (~funny(X0) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 38]
67. ! [X0] : ((generous(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~generous(X0))) [nnf transformation 14]
68. ! [X0] : ((generous(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~generous(X0))) [flattening 67]
90. generous(X0) | wise(X0) [cnf transformation 46]
118. ~calm(X0) | ~funny(X0) | humble(X0) [cnf transformation 65]
122. ~generous(X0) | funny(X0) [cnf transformation 68]
123. ~generous(X0) | calm(X0) [cnf transformation 68]
143. ~humble(lucy) [cnf transformation 23]
146. ~wise(lucy) [cnf transformation 25]
278. wise(X0) | funny(X0) [resolution 122,90]
280. calm(X0) | wise(X0) [resolution 123,90]
324. ~funny(X0) | humble(X0) | wise(X0) [resolution 118,280]
333. wise(X0) | humble(X0) [subsumption resolution 324,278]
480. humble(lucy) [resolution 333,146]
482. $false [subsumption resolution 480,143]
% SZS output end Proof for 3881876935036007033116991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or generous then mary is not quiet or not humble. Everyone who is both wise and not happy is either old or not creative and vice versa. Everyone who is not quiet or not happy is both calm and creative. Everyone who is both patient and not generous is both quiet and not generous and vice versa. Everyone who is curious or not wise is not wise or not rich and vice versa. Everyone who is either not quiet or not happy is either not happy or brave. If lucy is both not rich and not patient then fred is both not tall and not old and vice versa. Everyone who is both creative and not rich is both not happy and rich and vice versa. Everyone who is not generous is generous. Everyone who is not wise or funny is not happy. Everyone who is either not patient or wise is either not brave or not strong. If someone is either rich or not curious then lucy is both happy and tall and vice versa. Everyone who is tall is both happy and not calm. Everyone who is either not patient or not humble is either strong or happy and vice versa. Everyone who is both curious and generous is either not happy or brave. Everyone who is either not generous or not strong is funny or not generous. Lucy is either tall or not quiet. Someone is brave. Someone is not old. Someone is either kind or calm. John is either not tall or old. Someone is calm or not curious. | John is not quiet. | neutral | ((?[X]:((~patient(X)|generous(X))))=>((~quiet(mary)|~humble(mary))))&
(![X]:((wise(X)&~happy(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~happy(X))=>(calm(X)&creative(X))))&
(![X]:((patient(X)&~generous(X))<=>(quiet(X)&~generous(X))))&
(![X]:((curious(X)|~wise(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(((~rich(lucy)&~patient(lucy)))<=>((~tall(fred)&~old(fred))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:((~wise(X)|funny(X))=>~happy(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~brave(X)<~>~strong(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((happy(lucy)&tall(lucy))))&
(![X]:(tall(X)=>(happy(X)&~calm(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(strong(X)<~>happy(X))))&
(![X]:((curious(X)&generous(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(funny(X)|~generous(X))))&
((tall(lucy)<~>~quiet(lucy)))&
(?[X]:(brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((kind(X)<~>calm(X))))&
((~tall(john)<~>old(john)))&
(?[X]:((calm(X)|~curious(X)))) | ~quiet(john) | [] | null | 0 |
If someone is not creative then someone is both not kind and curious.
If someone is both quiet and not quiet then someone is both old and creative and vice versa.
If mary is either not strong or creative then someone is either kind or brave and vice versa.
If mary is not creative or not curious then someone is both not strong and not kind.
Everyone who is not creative is both not quiet and tall and vice versa.
Everyone who is either creative or not kind is both not humble and not rich.
Everyone who is either brave or not wise is not brave.
Everyone who is not creative is either not calm or creative.
Everyone who is both not strong and not kind is not funny or not wise.
Everyone who is both not creative and rich is either creative or not quiet and vice versa.
Everyone who is not tall is not tall or calm.
If someone is kind then paul is calm or wise.
Everyone who is both old and strong is either not curious or curious.
Everyone who is either not brave or curious is both not old and not happy and vice versa.
Paul is not strong or kind.
Someone is either kind or not funny.
John is not old. | Paul is not strong. | neutral | ((?[X]:(~creative(X)))=>(?[X]:((~kind(X)&curious(X)))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((old(X)&creative(X)))))&
(((~strong(mary)<~>creative(mary)))<=>(?[X]:((kind(X)<~>brave(X)))))&
(((~creative(mary)|~curious(mary)))=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:(~creative(X)<=>(~quiet(X)&tall(X))))&
(![X]:((creative(X)<~>~kind(X))=>(~humble(X)&~rich(X))))&
(![X]:((brave(X)<~>~wise(X))=>~brave(X)))&
(![X]:(~creative(X)=>(~calm(X)<~>creative(X))))&
(![X]:((~strong(X)&~kind(X))=>(~funny(X)|~wise(X))))&
(![X]:((~creative(X)&rich(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:(~tall(X)=>(~tall(X)|calm(X))))&
((?[X]:(kind(X)))=>((calm(paul)|wise(paul))))&
(![X]:((old(X)&strong(X))=>(~curious(X)<~>curious(X))))&
(![X]:((~brave(X)<~>curious(X))<=>(~old(X)&~happy(X))))&
((~strong(paul)|kind(paul)))&
(?[X]:((kind(X)<~>~funny(X))))&
(~old(john)) | ~strong(paul) | [] | null | 0 |
Everyone who is generous is not kind or tall.
If someone is brave or creative then someone is both not funny and not happy.
If alice is both not curious and strong then someone is not generous.
Everyone who is both not happy and not wise is not old and vice versa.
If someone is calm then paul is not strong or wise and vice versa.
Everyone who is both happy and not quiet is wise and vice versa.
If someone is either humble or not generous then someone is wise.
If fred is either creative or not calm then john is both brave and not kind.
If someone is not generous then someone is either creative or not creative and vice versa.
Everyone who is both calm and not kind is either humble or rich.
Everyone who is not kind or curious is not calm or not rich.
If someone is both not tall and not kind then someone is either brave or not happy.
Everyone who is not curious or not kind is not happy.
If someone is not brave then alice is brave and vice versa.
Everyone who is not old or happy is either not kind or not brave and vice versa.
If susan is not humble then someone is tall.
Alice is either brave or strong.
Susan is either not wise or not curious.
Susan is either humble or old.
Paul is both not patient and not tall.
Fred is not calm.
Someone is either rich or not tall.
Someone is not kind.
Someone is old. | Susan is wise. | contradiction | (![X]:(generous(X)=>(~kind(X)|tall(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(((~curious(alice)&strong(alice)))=>(?[X]:(~generous(X))))&
(![X]:((~happy(X)&~wise(X))<=>~old(X)))&
((?[X]:(calm(X)))<=>((~strong(paul)|wise(paul))))&
(![X]:((happy(X)&~quiet(X))<=>wise(X)))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:(wise(X))))&
(((creative(fred)<~>~calm(fred)))=>((brave(john)&~kind(john))))&
((?[X]:(~generous(X)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
(![X]:((calm(X)&~kind(X))=>(humble(X)<~>rich(X))))&
(![X]:((~kind(X)|curious(X))=>(~calm(X)|~rich(X))))&
((?[X]:((~tall(X)&~kind(X))))=>(?[X]:((brave(X)<~>~happy(X)))))&
(![X]:((~curious(X)|~kind(X))=>~happy(X)))&
((?[X]:(~brave(X)))<=>(brave(alice)))&
(![X]:((~old(X)|happy(X))<=>(~kind(X)<~>~brave(X))))&
((~humble(susan))=>(?[X]:(tall(X))))&
((brave(alice)<~>strong(alice)))&
((~wise(susan)<~>~curious(susan)))&
((humble(susan)<~>old(susan)))&
((~patient(paul)&~tall(paul)))&
(~calm(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:(old(X))) | wise(susan) | [
"p5",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7569237370244722942865628
% SZS output start Proof for 7569237370244722942865628
6. ! [X0] : ((~quiet(X0) & happy(X0)) <=> wise(X0)) [input p5]
13. ! [X0] : ((~kind(X0) | ~curious(X0)) => ~happy(X0)) [input p12]
18. ~wise(susan) <~> ~curious(susan) [input p17]
25. wise(susan) [input hypothesis]
44. ! [X0] : (~happy(X0) | (kind(X0) & curious(X0))) [ennf transformation 13]
58. ! [X0] : (((~quiet(X0) & happy(X0)) | ~wise(X0)) & (wise(X0) | (quiet(X0) | ~happy(X0)))) [nnf transformation 6]
59. ! [X0] : (((~quiet(X0) & happy(X0)) | ~wise(X0)) & (wise(X0) | quiet(X0) | ~happy(X0))) [flattening 58]
84. (curious(susan) | wise(susan)) & (~curious(susan) | ~wise(susan)) [nnf transformation 18]
104. ~wise(X0) | happy(X0) [cnf transformation 59]
122. ~happy(X0) | curious(X0) [cnf transformation 44]
135. ~curious(susan) | ~wise(susan) [cnf transformation 84]
145. wise(susan) [cnf transformation 25]
272. 28 <=> wise(susan) [avatar definition]
274. wise(susan) <- (28) [avatar component clause 272]
276. 29 <=> curious(susan) [avatar definition]
277. ~curious(susan) <- (~29) [avatar component clause 276]
280. ~28 | ~29 [avatar split clause 135,276,272]
298. 28 [avatar split clause 145,272]
305. happy(susan) <- (28) [resolution 104,274]
309. curious(susan) <- (28) [resolution 122,305]
310. $false <- (28, ~29) [subsumption resolution 309,277]
311. ~28 | 29 [avatar contradiction clause 310]
312. $false [avatar sat refutation 280,298,311]
% SZS output end Proof for 7569237370244722942865628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then lucy is either calm or humble and vice versa.
Everyone who is either not curious or quiet is old and vice versa.
Everyone who is not curious or kind is not wise or not creative and vice versa.
Everyone who is not patient is not wise and vice versa.
Everyone who is either not tall or strong is tall or not patient and vice versa.
Everyone who is happy is both not humble and humble and vice versa.
Everyone who is strong is patient or not happy.
If mary is kind then alice is generous and vice versa.
If john is kind or not calm then someone is either generous or curious and vice versa.
If lucy is strong then susan is not funny or kind.
If lucy is not generous or old then someone is not old or old and vice versa.
If alice is either not old or rich then alice is either not humble or not patient and vice versa.
If someone is wise or not tall then someone is tall.
Everyone who is both wise and not patient is not patient and vice versa.
Everyone who is both brave and funny is not strong or not funny and vice versa.
Everyone who is generous is old or brave.
Someone is brave or wise.
Someone is either patient or humble.
Someone is not humble or generous.
Susan is either not strong or not tall.
Susan is not humble.
John is not strong or not quiet.
Someone is either wise or rich. | Susan is kind. | entailment | ((?[X]:(old(X)))<=>((calm(lucy)<~>humble(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>old(X)))&
(![X]:((~curious(X)|kind(X))<=>(~wise(X)|~creative(X))))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~tall(X)<~>strong(X))<=>(tall(X)|~patient(X))))&
(![X]:(happy(X)<=>(~humble(X)&humble(X))))&
(![X]:(strong(X)=>(patient(X)|~happy(X))))&
((kind(mary))<=>(generous(alice)))&
(((kind(john)|~calm(john)))<=>(?[X]:((generous(X)<~>curious(X)))))&
((strong(lucy))=>((~funny(susan)|kind(susan))))&
(((~generous(lucy)|old(lucy)))<=>(?[X]:((~old(X)|old(X)))))&
(((~old(alice)<~>rich(alice)))<=>((~humble(alice)<~>~patient(alice))))&
((?[X]:((wise(X)|~tall(X))))=>(?[X]:(tall(X))))&
(![X]:((wise(X)&~patient(X))<=>~patient(X)))&
(![X]:((brave(X)&funny(X))<=>(~strong(X)|~funny(X))))&
(![X]:(generous(X)=>(old(X)|brave(X))))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~humble(X)|generous(X))))&
((~strong(susan)<~>~tall(susan)))&
(~humble(susan))&
((~strong(john)|~quiet(john)))&
(?[X]:((wise(X)<~>rich(X)))) | kind(susan) | [
"p3",
"p4",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8199213545664328118934164
% SZS output start Proof for 8199213545664328118934164
4. ! [X0] : (~patient(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~patient(X0) | tall(X0))) [input p4]
10. strong(lucy) => (kind(susan) | ~funny(susan)) [input p9]
14. ! [X0] : ((~patient(X0) & wise(X0)) <=> ~patient(X0)) [input p13]
15. ! [X0] : ((funny(X0) & brave(X0)) <=> (~funny(X0) | ~strong(X0))) [input p14]
24. ~kind(susan) [input hypothesis]
31. (kind(susan) | ~funny(susan)) | ~strong(lucy) [ennf transformation 10]
32. kind(susan) | ~funny(susan) | ~strong(lucy) [flattening 31]
43. ! [X0] : ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))) [nnf transformation 4]
44. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (patient(X0) & ~tall(X0))) & ((~patient(X0) | tall(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (patient(X0) & ~tall(X0))) & (~patient(X0) | tall(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 44]
61. ! [X0] : (((~patient(X0) & wise(X0)) | patient(X0)) & (~patient(X0) | (patient(X0) | ~wise(X0)))) [nnf transformation 14]
62. ! [X0] : (((~patient(X0) & wise(X0)) | patient(X0)) & (~patient(X0) | patient(X0) | ~wise(X0))) [flattening 61]
63. ! [X0] : (((funny(X0) & brave(X0)) | (funny(X0) & strong(X0))) & ((~funny(X0) | ~strong(X0)) | (~funny(X0) | ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : (((funny(X0) & brave(X0)) | (funny(X0) & strong(X0))) & (~funny(X0) | ~strong(X0) | ~funny(X0) | ~brave(X0))) [flattening 63]
88. ~wise(X0) | patient(X0) [cnf transformation 43]
90. ~patient(X0) | tall(X0) | strong(X0) | tall(X0) [cnf transformation 45]
92. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 45]
106. kind(susan) | ~funny(susan) | ~strong(lucy) [cnf transformation 32]
122. wise(X0) | patient(X0) [cnf transformation 62]
128. funny(X0) | funny(X0) [cnf transformation 64]
140. ~kind(susan) [cnf transformation 24]
142. funny(X0) [duplicate literal removal 128]
143. ~patient(X0) | tall(X0) | strong(X0) [duplicate literal removal 90]
144. ~tall(X0) | strong(X0) [duplicate literal removal 92]
164. ~patient(X0) | strong(X0) [subsumption resolution 143,144]
204. 13 <=> strong(lucy) [avatar definition]
206. ~strong(lucy) <- (~13) [avatar component clause 204]
208. 14 <=> funny(susan) [avatar definition]
210. ~funny(susan) <- (~14) [avatar component clause 208]
212. 15 <=> kind(susan) [avatar definition]
215. ~13 | ~14 | 15 [avatar split clause 106,212,208,204]
265. patient(X0) [subsumption resolution 122,88]
307. ~15 [avatar split clause 140,212]
308. $false <- (~14) [subsumption resolution 210,142]
309. 14 [avatar contradiction clause 308]
314. strong(X0) [resolution 164,265]
315. $false <- (~13) [resolution 314,206]
318. 13 [avatar contradiction clause 315]
319. $false [avatar sat refutation 215,307,309,318]
% SZS output end Proof for 8199213545664328118934164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or generous then alice is funny.
If someone is not funny then someone is rich or funny.
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.
Someone is not brave.
John is not patient.
Lucy is both not curious and funny.
Susan is either not happy or not strong.
Someone is not happy or creative.
Fred is both happy and not funny.
Susan is tall. | Paul is rich. | neutral | ((?[X]:((humble(X)|generous(X))))=>(funny(alice)))&
((?[X]:(~funny(X)))=>(?[X]:((rich(X)|funny(X)))))&
(![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]:(~brave(X)))&
(~patient(john))&
((~curious(lucy)&funny(lucy)))&
((~happy(susan)<~>~strong(susan)))&
(?[X]:((~happy(X)|creative(X))))&
((happy(fred)&~funny(fred)))&
(tall(susan)) | rich(paul) | [] | null | 0 |
Everyone who is not calm is either humble or not quiet and vice versa.
If someone is either not quiet or humble then john is patient and vice versa.
If paul is either not funny or wise then someone is not curious and vice versa.
Everyone who is both not calm and generous is not strong and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Someone is funny.
Someone is either strong or tall.
John is both funny and not wise.
Someone is calm or not quiet. | Fred is not creative. | neutral | (![X]:(~calm(X)<=>(humble(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(patient(john)))&
(((~funny(paul)<~>wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&generous(X))<=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)<~>tall(X))))&
((funny(john)&~wise(john)))&
(?[X]:((calm(X)|~quiet(X)))) | ~creative(fred) | [] | null | 0 |
Everyone who is either wise or not old is either not old or not strong and vice versa.
If someone is both not old and creative then someone is brave.
If someone is either not strong or tall then mary is not funny and vice versa.
If someone is both not funny and not patient then someone is brave.
Everyone who is either not brave or old is not strong.
If someone is not strong then someone is patient or not happy.
If someone is curious then someone is old.
If paul is not happy then fred is both happy and not humble and vice versa.
If mary is not brave then john is not curious.
Everyone who is either generous or not happy is not humble.
Everyone who is not curious is both kind and strong.
If someone is both patient and not rich then someone is either old or strong and vice versa.
Everyone who is both not brave and wise is both quiet and creative and vice versa.
If susan is patient then susan is not happy or not curious and vice versa.
Everyone who is tall is not strong and vice versa.
Everyone who is not funny is tall and vice versa.
Someone is quiet.
Someone is calm or not wise.
John is not patient.
John is either not wise or curious.
Alice is curious.
Someone is both wise and not old.
Someone is not old. | Paul is not quiet. | neutral | (![X]:((wise(X)<~>~old(X))<=>(~old(X)<~>~strong(X))))&
((?[X]:((~old(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~strong(X)<~>tall(X))))<=>(~funny(mary)))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:(brave(X))))&
(![X]:((~brave(X)<~>old(X))=>~strong(X)))&
((?[X]:(~strong(X)))=>(?[X]:((patient(X)|~happy(X)))))&
((?[X]:(curious(X)))=>(?[X]:(old(X))))&
((~happy(paul))<=>((happy(fred)&~humble(fred))))&
((~brave(mary))=>(~curious(john)))&
(![X]:((generous(X)<~>~happy(X))=>~humble(X)))&
(![X]:(~curious(X)=>(kind(X)&strong(X))))&
((?[X]:((patient(X)&~rich(X))))<=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((~brave(X)&wise(X))<=>(quiet(X)&creative(X))))&
((patient(susan))<=>((~happy(susan)|~curious(susan))))&
(![X]:(tall(X)<=>~strong(X)))&
(![X]:(~funny(X)<=>tall(X)))&
(?[X]:(quiet(X)))&
(?[X]:((calm(X)|~wise(X))))&
(~patient(john))&
((~wise(john)<~>curious(john)))&
(curious(alice))&
(?[X]:((wise(X)&~old(X))))&
(?[X]:(~old(X))) | ~quiet(paul) | [] | null | 0 |
If someone is either calm or kind then john is both not kind and not creative and vice versa.
Everyone who is not quiet is not tall.
If someone is either not calm or calm then someone is calm.
If susan is both kind and not quiet then someone is not creative and vice versa.
Everyone who is not happy is either not calm or not quiet and vice versa.
Everyone who is generous is both patient and not creative and vice versa.
If alice is both not brave and brave then fred is both calm and not generous.
Everyone who is either not creative or tall is both not kind and not patient and vice versa.
If someone is curious or creative then someone is not creative and vice versa.
If john is generous or curious then alice is funny and vice versa.
If paul is not strong or creative then mary is not creative and vice versa.
Everyone who is both wise and not funny is not tall.
If someone is both kind and not wise then someone is both not brave and funny.
Everyone who is brave is not tall and vice versa.
Everyone who is calm is either tall or not kind and vice versa.
If someone is both not quiet and generous then lucy is both not rich and not funny and vice versa.
Lucy is either not generous or kind.
Someone is not quiet.
Someone is either kind or generous.
Someone is not strong or brave.
Someone is both curious and strong.
John is old.
Someone is not happy.
Paul is not humble. | Susan is quiet. | contradiction | ((?[X]:((calm(X)<~>kind(X))))<=>((~kind(john)&~creative(john))))&
(![X]:(~quiet(X)=>~tall(X)))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:(calm(X))))&
(((kind(susan)&~quiet(susan)))<=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)<=>(~calm(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(patient(X)&~creative(X))))&
(((~brave(alice)&brave(alice)))=>((calm(fred)&~generous(fred))))&
(![X]:((~creative(X)<~>tall(X))<=>(~kind(X)&~patient(X))))&
((?[X]:((curious(X)|creative(X))))<=>(?[X]:(~creative(X))))&
(((generous(john)|curious(john)))<=>(funny(alice)))&
(((~strong(paul)|creative(paul)))<=>(~creative(mary)))&
(![X]:((wise(X)&~funny(X))=>~tall(X)))&
((?[X]:((kind(X)&~wise(X))))=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:(brave(X)<=>~tall(X)))&
(![X]:(calm(X)<=>(tall(X)<~>~kind(X))))&
((?[X]:((~quiet(X)&generous(X))))<=>((~rich(lucy)&~funny(lucy))))&
((~generous(lucy)<~>kind(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((~strong(X)|brave(X))))&
(?[X]:((curious(X)&strong(X))))&
(old(john))&
(?[X]:(~happy(X)))&
(~humble(paul)) | quiet(susan) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7532727314468726828221985
% SZS output start Proof for 7532727314468726828221985
4. (~quiet(susan) & kind(susan)) <=> ? [X0] : ~creative(X0) [input p3]
9. ? [X0] : (creative(X0) | curious(X0)) <=> ? [X0] : ~creative(X0) [input p8]
25. quiet(susan) [input hypothesis]
27. ? [X0] : (creative(X0) | curious(X0)) <=> ? [X1] : ~creative(X1) [rectify 9]
49. ((~quiet(susan) & kind(susan)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (quiet(susan) | ~kind(susan))) [nnf transformation 4]
50. ((~quiet(susan) & kind(susan)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | quiet(susan) | ~kind(susan)) [flattening 49]
51. ((~quiet(susan) & kind(susan)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | quiet(susan) | ~kind(susan)) [rectify 50]
52. ? [X1] : ~creative(X1) => ~creative(sK2) [choice axiom]
53. ((~quiet(susan) & kind(susan)) | ! [X0] : creative(X0)) & (~creative(sK2) | quiet(susan) | ~kind(susan)) [skolemisation 51,52]
59. (? [X0] : (creative(X0) | curious(X0)) | ! [X1] : creative(X1)) & (? [X1] : ~creative(X1) | ! [X0] : (~creative(X0) & ~curious(X0))) [nnf transformation 27]
60. (? [X0] : (creative(X0) | curious(X0)) | ! [X1] : creative(X1)) & (? [X2] : ~creative(X2) | ! [X3] : (~creative(X3) & ~curious(X3))) [rectify 59]
61. ? [X0] : (creative(X0) | curious(X0)) => (creative(sK3) | curious(sK3)) [choice axiom]
62. ? [X2] : ~creative(X2) => ~creative(sK4) [choice axiom]
63. ((creative(sK3) | curious(sK3)) | ! [X1] : creative(X1)) & (~creative(sK4) | ! [X3] : (~creative(X3) & ~curious(X3))) [skolemisation 60,62,61]
101. ~quiet(susan) | creative(X0) [cnf transformation 53]
116. ~creative(sK4) | ~creative(X3) [cnf transformation 63]
146. quiet(susan) [cnf transformation 25]
190. 10 <=> ! [X0] : creative(X0) [avatar definition]
191. creative(X0) <- (10) [avatar component clause 190]
193. 11 <=> quiet(susan) [avatar definition]
196. 10 | ~11 [avatar split clause 101,193,190]
217. 16 <=> ! [X3] : ~creative(X3) [avatar definition]
218. ~creative(X3) <- (16) [avatar component clause 217]
220. 17 <=> creative(sK4) [avatar definition]
222. ~creative(sK4) <- (~17) [avatar component clause 220]
223. 16 | ~17 [avatar split clause 116,220,217]
323. 11 [avatar split clause 146,193]
326. $false <- (10, ~17) [resolution 222,191]
327. ~10 | 17 [avatar contradiction clause 326]
328. $false <- (10, 16) [subsumption resolution 218,191]
329. ~10 | ~16 [avatar contradiction clause 328]
330. $false [avatar sat refutation 196,223,323,327,329]
% SZS output end Proof for 7532727314468726828221985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or happy then susan is both kind and not brave and vice versa.
If someone is both not curious and not quiet then lucy is both creative and funny and vice versa.
Everyone who is either not happy or brave is both strong and not creative and vice versa.
If someone is both curious and kind then someone is not humble or not happy and vice versa.
Everyone who is not rich or not wise is quiet or creative and vice versa.
If fred is either happy or not old then fred is not funny or patient and vice versa.
Everyone who is wise is not old or rich.
Everyone who is not funny is both not quiet and patient and vice versa.
Everyone who is either creative or not tall is not calm or generous.
Everyone who is old is not funny and vice versa.
Everyone who is patient is not quiet or not rich.
Everyone who is humble or strong is both not quiet and not curious.
If paul is rich then someone is brave.
If someone is both not rich and curious then someone is either generous or not curious and vice versa.
Everyone who is both not patient and calm is both creative and not happy.
Everyone who is both not brave and strong is either strong or generous.
Someone is strong.
Fred is not brave.
Someone is both not humble and calm.
Someone is both creative and not old.
Susan is not quiet.
Someone is curious or not funny.
Susan is kind or rich.
Someone is not patient. | Paul is calm. | neutral | ((?[X]:((creative(X)<~>happy(X))))<=>((kind(susan)&~brave(susan))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((creative(lucy)&funny(lucy))))&
(![X]:((~happy(X)<~>brave(X))<=>(strong(X)&~creative(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(quiet(X)|creative(X))))&
(((happy(fred)<~>~old(fred)))<=>((~funny(fred)|patient(fred))))&
(![X]:(wise(X)=>(~old(X)|rich(X))))&
(![X]:(~funny(X)<=>(~quiet(X)&patient(X))))&
(![X]:((creative(X)<~>~tall(X))=>(~calm(X)|generous(X))))&
(![X]:(old(X)<=>~funny(X)))&
(![X]:(patient(X)=>(~quiet(X)|~rich(X))))&
(![X]:((humble(X)|strong(X))=>(~quiet(X)&~curious(X))))&
((rich(paul))=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((~patient(X)&calm(X))=>(creative(X)&~happy(X))))&
(![X]:((~brave(X)&strong(X))=>(strong(X)<~>generous(X))))&
(?[X]:(strong(X)))&
(~brave(fred))&
(?[X]:((~humble(X)&calm(X))))&
(?[X]:((creative(X)&~old(X))))&
(~quiet(susan))&
(?[X]:((curious(X)|~funny(X))))&
((kind(susan)|rich(susan)))&
(?[X]:(~patient(X))) | calm(paul) | [] | null | 0 |
Everyone who is calm or not old is either not strong or not generous and vice versa.
If someone is wise then lucy is tall.
If alice is both patient and happy then fred is not generous.
If john is both not kind and happy then someone is brave or calm and vice versa.
If lucy is not generous or humble then someone is not strong or not humble.
Everyone who is both generous and not creative is not generous.
Everyone who is tall or kind is both generous and not patient and vice versa.
If susan is either not funny or not calm then someone is either quiet or not old and vice versa.
If someone is both not tall and not kind then john is both humble and not happy.
If someone is both not generous and not creative then someone is both strong and brave.
Everyone who is both creative and kind is generous.
Everyone who is not creative or wise is either not calm or rich and vice versa.
Everyone who is not curious or tall is both not happy and old and vice versa.
If mary is both calm and not tall then someone is not tall.
Everyone who is either generous or not old is either kind or not curious.
Everyone who is not tall or not humble is both patient and strong.
Alice is not happy.
Someone is not funny or not kind.
Someone is not wise.
Mary is not humble or quiet.
Someone is not kind or tall.
Someone is either quiet or creative.
Someone is not happy. | Susan is generous. | entailment | (![X]:((calm(X)|~old(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:(wise(X)))=>(tall(lucy)))&
(((patient(alice)&happy(alice)))=>(~generous(fred)))&
(((~kind(john)&happy(john)))<=>(?[X]:((brave(X)|calm(X)))))&
(((~generous(lucy)|humble(lucy)))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((generous(X)&~creative(X))=>~generous(X)))&
(![X]:((tall(X)|kind(X))<=>(generous(X)&~patient(X))))&
(((~funny(susan)<~>~calm(susan)))<=>(?[X]:((quiet(X)<~>~old(X)))))&
((?[X]:((~tall(X)&~kind(X))))=>((humble(john)&~happy(john))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((creative(X)&kind(X))=>generous(X)))&
(![X]:((~creative(X)|wise(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~curious(X)|tall(X))<=>(~happy(X)&old(X))))&
(((calm(mary)&~tall(mary)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~old(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~tall(X)|~humble(X))=>(patient(X)&strong(X))))&
(~happy(alice))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:(~wise(X)))&
((~humble(mary)|quiet(mary)))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:(~happy(X))) | generous(susan) | [
"p0",
"p3",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8939465542350512637311773
% SZS output start Proof for 8939465542350512637311773
1. ! [X0] : ((~old(X0) | calm(X0)) <=> (~strong(X0) <~> ~generous(X0))) [input p0]
4. (happy(john) & ~kind(john)) <=> ? [X0] : (calm(X0) | brave(X0)) [input p3]
7. ! [X0] : ((kind(X0) | tall(X0)) <=> (~patient(X0) & generous(X0))) [input p6]
9. ? [X0] : (~kind(X0) & ~tall(X0)) => (~happy(john) & humble(john)) [input p8]
13. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (old(X0) & ~happy(X0))) [input p12]
15. ! [X0] : ((generous(X0) <~> ~old(X0)) => (kind(X0) <~> ~curious(X0))) [input p14]
16. ! [X0] : ((~humble(X0) | ~tall(X0)) => (strong(X0) & patient(X0))) [input p15]
24. ~generous(susan) [input hypothesis]
32. (~happy(john) & humble(john)) | ! [X0] : (kind(X0) | tall(X0)) [ennf transformation 9]
38. ! [X0] : ((kind(X0) <~> ~curious(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 15]
39. ! [X0] : ((strong(X0) & patient(X0)) | (humble(X0) & tall(X0))) [ennf transformation 16]
40. ! [X0] : (((~old(X0) | calm(X0)) | ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) & (((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | (old(X0) & ~calm(X0)))) [nnf transformation 1]
41. ! [X0] : ((~old(X0) | calm(X0) | ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) & (((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | (old(X0) & ~calm(X0)))) [flattening 40]
42. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | (~happy(john) | kind(john))) [nnf transformation 4]
43. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | ~happy(john) | kind(john)) [flattening 42]
44. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X1] : (calm(X1) | brave(X1)) | ~happy(john) | kind(john)) [rectify 43]
45. ? [X1] : (calm(X1) | brave(X1)) => (calm(sK0) | brave(sK0)) [choice axiom]
46. ((happy(john) & ~kind(john)) | ! [X0] : (~calm(X0) & ~brave(X0))) & ((calm(sK0) | brave(sK0)) | ~happy(john) | kind(john)) [skolemisation 44,45]
49. ! [X0] : (((kind(X0) | tall(X0)) | (patient(X0) | ~generous(X0))) & ((~patient(X0) & generous(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : ((kind(X0) | tall(X0) | patient(X0) | ~generous(X0)) & ((~patient(X0) & generous(X0)) | (~kind(X0) & ~tall(X0)))) [flattening 49]
60. ! [X0] : (((tall(X0) | ~curious(X0)) | (~old(X0) | happy(X0))) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 13]
61. ! [X0] : ((tall(X0) | ~curious(X0) | ~old(X0) | happy(X0)) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [flattening 60]
64. ! [X0] : (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 38]
81. ~strong(X0) | calm(X0) | ~old(X0) | generous(X0) [cnf transformation 41]
88. happy(john) | ~calm(X0) [cnf transformation 46]
92. ~tall(X0) | generous(X0) [cnf transformation 50]
93. ~kind(X0) | generous(X0) [cnf transformation 50]
106. ~happy(john) | kind(X0) | tall(X0) [cnf transformation 32]
118. curious(X0) | old(X0) [cnf transformation 61]
123. ~curious(X0) | kind(X0) | generous(X0) | old(X0) [cnf transformation 64]
128. tall(X0) | strong(X0) [cnf transformation 39]
138. ~generous(susan) [cnf transformation 24]
162. 6 <=> ! [X0] : ~calm(X0) [avatar definition]
163. ~calm(X0) <- (6) [avatar component clause 162]
165. 7 <=> happy(john) [avatar definition]
168. 6 | 7 [avatar split clause 88,165,162]
237. 22 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
238. kind(X0) | tall(X0) <- (22) [avatar component clause 237]
239. 22 | ~7 [avatar split clause 106,165,237]
275. kind(X0) | generous(X0) | old(X0) [subsumption resolution 123,118]
276. generous(X0) | old(X0) [subsumption resolution 275,93]
329. generous(X1) | strong(X1) [resolution 128,92]
342. tall(X1) | generous(X1) <- (22) [resolution 238,93]
347. generous(X1) <- (22) [subsumption resolution 342,92]
356. old(susan) [resolution 276,138]
373. $false <- (22) [resolution 347,138]
377. ~22 [avatar contradiction clause 373]
449. strong(susan) [resolution 329,138]
467. calm(susan) | ~old(susan) | generous(susan) [resolution 449,81]
472. ~old(susan) | generous(susan) <- (6) [subsumption resolution 467,163]
473. generous(susan) <- (6) [subsumption resolution 472,356]
474. $false <- (6) [subsumption resolution 473,138]
475. ~6 [avatar contradiction clause 474]
480. $false [avatar sat refutation 168,239,377,475]
% SZS output end Proof for 8939465542350512637311773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not humble is both not quiet and calm and vice versa.
If someone is both brave and calm then mary is patient or not generous and vice versa.
Everyone who is not old or not humble is not tall or happy and vice versa.
Everyone who is both curious and quiet is not brave.
Everyone who is not old is both not tall and not happy.
If someone is brave or not creative then susan is both brave and not kind and vice versa.
Everyone who is not calm or not humble is not tall and vice versa.
Everyone who is not funny or kind is either not patient or humble and vice versa.
If someone is either not patient or not creative then someone is humble and vice versa.
Everyone who is either not curious or curious is rich and vice versa.
Everyone who is either happy or not creative is both not brave and funny and vice versa.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
If fred is calm or not calm then alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is both not strong and not patient.
Mary is both brave and not calm.
Someone is either not generous or humble.
Fred is either creative or old.
Someone is not tall. | Fred is not brave. | neutral | (![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
(((calm(fred)|~calm(fred)))=>(~tall(alice)))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
((creative(fred)<~>old(fred)))&
(?[X]:(~tall(X))) | ~brave(fred) | [] | null | 0 |
Everyone who is rich or not curious is either not wise or quiet and vice versa.
Everyone who is either not generous or brave is both not curious and wise and vice versa.
Everyone who is both wise and not generous is humble or wise.
Everyone who is either curious or not rich is either quiet or happy and vice versa.
If john is both not humble and not tall then someone is kind.
Everyone who is both calm and not funny is happy or not generous and vice versa.
Everyone who is both not old and creative is both kind and not funny.
Everyone who is not generous or creative is calm or not creative.
If someone is either not humble or not rich then someone is happy or funny and vice versa.
If someone is quiet then someone is both not quiet and kind.
Everyone who is humble or creative is both not quiet and not tall and vice versa.
If someone is not old or happy then paul is rich.
Everyone who is both not rich and humble is either strong or calm.
If someone is either happy or curious then alice is kind or creative.
Everyone who is both tall and not calm is happy.
Everyone who is both not brave and funny is generous or patient.
Susan is patient.
Someone is both brave and not funny.
Alice is quiet or tall.
Alice is kind.
Someone is both not funny and brave.
Someone is either happy or not tall.
Someone is either patient or not quiet.
Someone is wise or patient. | John is humble. | neutral | (![X]:((rich(X)|~curious(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((~generous(X)<~>brave(X))<=>(~curious(X)&wise(X))))&
(![X]:((wise(X)&~generous(X))=>(humble(X)|wise(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(quiet(X)<~>happy(X))))&
(((~humble(john)&~tall(john)))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&~funny(X))<=>(happy(X)|~generous(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)&~funny(X))))&
(![X]:((~generous(X)|creative(X))=>(calm(X)|~creative(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)|creative(X))<=>(~quiet(X)&~tall(X))))&
((?[X]:((~old(X)|happy(X))))=>(rich(paul)))&
(![X]:((~rich(X)&humble(X))=>(strong(X)<~>calm(X))))&
((?[X]:((happy(X)<~>curious(X))))=>((kind(alice)|creative(alice))))&
(![X]:((tall(X)&~calm(X))=>happy(X)))&
(![X]:((~brave(X)&funny(X))=>(generous(X)|patient(X))))&
(patient(susan))&
(?[X]:((brave(X)&~funny(X))))&
((quiet(alice)|tall(alice)))&
(kind(alice))&
(?[X]:((~funny(X)&brave(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((wise(X)|patient(X)))) | humble(john) | [] | null | 0 |
Everyone who is either patient or brave is not humble and vice versa.
If susan is either creative or not creative then someone is tall and vice versa.
If mary is creative or not creative then john is curious or not patient.
Everyone who is either curious or not calm is both generous and humble.
If someone is both creative and wise then someone is both not happy and generous and vice versa.
If alice is old then lucy is not quiet or rich and vice versa.
If someone is either humble or strong then someone is not humble or funny.
Everyone who is both patient and not old is either not strong or curious and vice versa.
Everyone who is both not old and calm is not wise or not rich and vice versa.
If someone is both patient and strong then someone is not curious or rich.
Everyone who is either happy or brave is humble and vice versa.
Everyone who is not patient is both not strong and not kind and vice versa.
If someone is creative or not patient then paul is both not strong and not generous.
Everyone who is not kind or not humble is not creative or not calm and vice versa.
If fred is both not strong and not old then someone is brave.
Everyone who is either not kind or patient is strong or generous.
Lucy is either tall or old.
Lucy is old or not creative.
Lucy is either strong or quiet.
Fred is either not curious or quiet.
Fred is not curious or not kind. | Lucy is rich. | entailment | (![X]:((patient(X)<~>brave(X))<=>~humble(X)))&
(((creative(susan)<~>~creative(susan)))<=>(?[X]:(tall(X))))&
(((creative(mary)|~creative(mary)))=>((curious(john)|~patient(john))))&
(![X]:((curious(X)<~>~calm(X))=>(generous(X)&humble(X))))&
((?[X]:((creative(X)&wise(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
((old(alice))<=>((~quiet(lucy)|rich(lucy))))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((patient(X)&~old(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((~old(X)&calm(X))<=>(~wise(X)|~rich(X))))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:((happy(X)<~>brave(X))<=>humble(X)))&
(![X]:(~patient(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((creative(X)|~patient(X))))=>((~strong(paul)&~generous(paul))))&
(![X]:((~kind(X)|~humble(X))<=>(~creative(X)|~calm(X))))&
(((~strong(fred)&~old(fred)))=>(?[X]:(brave(X))))&
(![X]:((~kind(X)<~>patient(X))=>(strong(X)|generous(X))))&
((tall(lucy)<~>old(lucy)))&
((old(lucy)|~creative(lucy)))&
((strong(lucy)<~>quiet(lucy)))&
((~curious(fred)<~>quiet(fred)))&
((~curious(fred)|~kind(fred))) | rich(lucy) | [
"p0",
"p3",
"p4",
"p7",
"p8",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1122480556279931032177459
% SZS output start Proof for 1122480556279931032177459
1. ! [X0] : ((patient(X0) <~> brave(X0)) <=> ~humble(X0)) [input p0]
4. ! [X0] : ((curious(X0) <~> ~calm(X0)) => (humble(X0) & generous(X0))) [input p3]
5. ? [X0] : (wise(X0) & creative(X0)) <=> ? [X0] : (generous(X0) & ~happy(X0)) [input p4]
8. ! [X0] : ((~old(X0) & patient(X0)) <=> (~strong(X0) <~> curious(X0))) [input p7]
9. ! [X0] : ((calm(X0) & ~old(X0)) <=> (~rich(X0) | ~wise(X0))) [input p8]
11. ! [X0] : ((happy(X0) <~> brave(X0)) <=> humble(X0)) [input p10]
12. ! [X0] : (~patient(X0) <=> (~kind(X0) & ~strong(X0))) [input p11]
13. ? [X0] : (~patient(X0) | creative(X0)) => (~generous(paul) & ~strong(paul)) [input p12]
14. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (~calm(X0) | ~creative(X0))) [input p13]
16. ! [X0] : ((~kind(X0) <~> patient(X0)) => (generous(X0) | strong(X0))) [input p15]
22. ~rich(lucy) [input hypothesis]
23. ? [X0] : (wise(X0) & creative(X0)) <=> ? [X1] : (generous(X1) & ~happy(X1)) [rectify 5]
29. ! [X0] : ((humble(X0) & generous(X0)) | (curious(X0) <=> ~calm(X0))) [ennf transformation 4]
31. (~generous(paul) & ~strong(paul)) | ! [X0] : (patient(X0) & ~creative(X0)) [ennf transformation 13]
34. ! [X0] : ((generous(X0) | strong(X0)) | (~kind(X0) <=> patient(X0))) [ennf transformation 16]
35. ! [X0] : (generous(X0) | strong(X0) | (~kind(X0) <=> patient(X0))) [flattening 34]
36. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | humble(X0)) & (~humble(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 1]
41. ! [X0] : ((humble(X0) & generous(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) [nnf transformation 29]
42. (? [X0] : (wise(X0) & creative(X0)) | ! [X1] : (~generous(X1) | happy(X1))) & (? [X1] : (generous(X1) & ~happy(X1)) | ! [X0] : (~wise(X0) | ~creative(X0))) [nnf transformation 23]
43. (? [X0] : (wise(X0) & creative(X0)) | ! [X1] : (~generous(X1) | happy(X1))) & (? [X2] : (generous(X2) & ~happy(X2)) | ! [X3] : (~wise(X3) | ~creative(X3))) [rectify 42]
44. ? [X0] : (wise(X0) & creative(X0)) => (wise(sK1) & creative(sK1)) [choice axiom]
45. ? [X2] : (generous(X2) & ~happy(X2)) => (generous(sK2) & ~happy(sK2)) [choice axiom]
46. ((wise(sK1) & creative(sK1)) | ! [X1] : (~generous(X1) | happy(X1))) & ((generous(sK2) & ~happy(sK2)) | ! [X3] : (~wise(X3) | ~creative(X3))) [skolemisation 43,45,44]
49. ! [X0] : (((~old(X0) & patient(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (old(X0) | ~patient(X0)))) [nnf transformation 8]
50. ! [X0] : (((~old(X0) & patient(X0)) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | old(X0) | ~patient(X0))) [flattening 49]
51. ! [X0] : (((calm(X0) & ~old(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (~calm(X0) | old(X0)))) [nnf transformation 9]
52. ! [X0] : (((calm(X0) & ~old(X0)) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | ~calm(X0) | old(X0))) [flattening 51]
56. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~humble(X0)) & (humble(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 11]
57. ! [X0] : ((~patient(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | patient(X0))) [nnf transformation 12]
58. ! [X0] : ((~patient(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | patient(X0))) [flattening 57]
59. ! [X0] : (((~humble(X0) | ~kind(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 14]
60. ! [X0] : ((~humble(X0) | ~kind(X0) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | (humble(X0) & kind(X0)))) [flattening 59]
63. ! [X0] : (generous(X0) | strong(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) [nnf transformation 35]
67. ~humble(X0) | brave(X0) | ~patient(X0) [cnf transformation 36]
70. ~brave(X0) | ~patient(X0) | humble(X0) [cnf transformation 36]
77. ~calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 41]
79. ~calm(X0) | humble(X0) | ~curious(X0) [cnf transformation 41]
83. creative(sK1) | ~generous(X1) | happy(X1) [cnf transformation 46]
88. ~strong(X0) | curious(X0) | old(X0) | ~patient(X0) [cnf transformation 50]
96. ~old(X0) | rich(X0) [cnf transformation 52]
98. rich(X0) | calm(X0) [cnf transformation 52]
100. ~happy(X0) | brave(X0) | humble(X0) [cnf transformation 56]
103. ~happy(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 56]
105. ~kind(X0) | patient(X0) [cnf transformation 58]
106. ~patient(X0) | kind(X0) | strong(X0) [cnf transformation 58]
107. ~strong(paul) | ~creative(X0) [cnf transformation 31]
108. ~strong(paul) | patient(X0) [cnf transformation 31]
109. ~generous(paul) | ~creative(X0) [cnf transformation 31]
110. ~generous(paul) | patient(X0) [cnf transformation 31]
113. ~kind(X0) | ~humble(X0) | creative(X0) [cnf transformation 60]
116. generous(X0) | strong(X0) | patient(X0) | kind(X0) [cnf transformation 63]
117. generous(X0) | strong(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 63]
126. ~rich(lucy) [cnf transformation 22]
154. 6 <=> ! [X1] : (~generous(X1) | happy(X1)) [avatar definition]
155. ~generous(X1) | happy(X1) <- (6) [avatar component clause 154]
162. 8 <=> creative(sK1) [avatar definition]
164. creative(sK1) <- (8) [avatar component clause 162]
165. 6 | 8 [avatar split clause 83,162,154]
180. 12 <=> rich(lucy) [avatar definition]
182. ~rich(lucy) <- (~12) [avatar component clause 180]
207. 18 <=> ! [X0] : patient(X0) [avatar definition]
208. patient(X0) <- (18) [avatar component clause 207]
210. 19 <=> generous(paul) [avatar definition]
213. 18 | ~19 [avatar split clause 110,210,207]
215. 20 <=> ! [X0] : ~creative(X0) [avatar definition]
216. ~creative(X0) <- (20) [avatar component clause 215]
217. 20 | ~19 [avatar split clause 109,210,215]
219. 21 <=> strong(paul) [avatar definition]
221. ~strong(paul) <- (~21) [avatar component clause 219]
222. 18 | ~21 [avatar split clause 108,219,207]
223. 20 | ~21 [avatar split clause 107,219,215]
237. ~kind(X0) | strong(X0) | generous(X0) [subsumption resolution 117,105]
238. generous(X0) | strong(X0) | kind(X0) [subsumption resolution 116,106]
239. strong(X0) | generous(X0) [subsumption resolution 238,237]
245. 26 <=> old(lucy) [avatar definition]
246. old(lucy) <- (26) [avatar component clause 245]
256. 28 <=> strong(lucy) [avatar definition]
257. strong(lucy) <- (28) [avatar component clause 256]
258. ~strong(lucy) <- (~28) [avatar component clause 256]
276. ~12 [avatar split clause 126,180]
277. calm(lucy) <- (~12) [resolution 98,182]
280. generous(paul) <- (~21) [resolution 239,221]
281. generous(lucy) <- (~28) [resolution 239,258]
285. 19 | 21 [avatar split clause 280,219,210]
289. happy(lucy) <- (6, ~28) [resolution 281,155]
295. generous(lucy) | ~curious(lucy) <- (~12) [resolution 77,277]
297. humble(lucy) | ~curious(lucy) <- (~12) [resolution 79,277]
299. 32 <=> curious(lucy) [avatar definition]
301. ~curious(lucy) <- (~32) [avatar component clause 299]
303. 33 <=> humble(lucy) [avatar definition]
305. humble(lucy) <- (33) [avatar component clause 303]
306. ~32 | 33 | 12 [avatar split clause 297,180,303,299]
331. brave(lucy) | humble(lucy) <- (6, ~28) [resolution 100,289]
333. 36 <=> brave(lucy) [avatar definition]
335. brave(lucy) <- (36) [avatar component clause 333]
336. 33 | 36 | ~6 | 28 [avatar split clause 331,256,154,333,303]
338. ~patient(lucy) | humble(lucy) <- (36) [resolution 335,70]
339. humble(lucy) <- (18, 36) [subsumption resolution 338,208]
340. 33 | ~18 | ~36 [avatar split clause 339,333,207,303]
341. $false <- (8, 20) [subsumption resolution 164,216]
342. ~8 | ~20 [avatar contradiction clause 341]
365. kind(X0) | strong(X0) <- (18) [resolution 106,208]
372. ~humble(X0) | creative(X0) | strong(X0) <- (18) [resolution 113,365]
373. ~humble(X0) | strong(X0) <- (18, 20) [subsumption resolution 372,216]
382. curious(lucy) | old(lucy) | ~patient(lucy) <- (28) [resolution 88,257]
387. old(lucy) | ~patient(lucy) <- (28, ~32) [subsumption resolution 382,301]
397. old(lucy) <- (18, 28, ~32) [subsumption resolution 387,208]
398. 26 | ~18 | ~28 | 32 [avatar split clause 397,299,256,207,245]
407. rich(lucy) <- (26) [resolution 246,96]
409. $false <- (~12, 26) [subsumption resolution 407,182]
410. 12 | ~26 [avatar contradiction clause 409]
439. strong(lucy) <- (18, 20, 33) [resolution 305,373]
442. brave(lucy) | ~patient(lucy) <- (33) [resolution 305,67]
449. 41 <=> happy(lucy) [avatar definition]
451. happy(lucy) <- (41) [avatar component clause 449]
453. 28 | ~18 | ~20 | ~33 [avatar split clause 439,303,215,207,256]
455. 42 <=> generous(lucy) [avatar definition]
457. generous(lucy) <- (42) [avatar component clause 455]
458. ~32 | 42 | 12 [avatar split clause 295,180,455,299]
459. brave(lucy) <- (18, 33) [subsumption resolution 442,208]
460. 36 | ~18 | ~33 [avatar split clause 459,303,207,333]
486. happy(lucy) <- (6, 42) [resolution 457,155]
487. 41 | ~6 | ~42 [avatar split clause 486,455,154,449]
492. ~brave(lucy) | ~humble(lucy) <- (41) [resolution 451,103]
494. ~humble(lucy) <- (36, 41) [subsumption resolution 492,335]
495. $false <- (33, 36, 41) [subsumption resolution 494,305]
496. ~33 | ~36 | ~41 [avatar contradiction clause 495]
497. $false [avatar sat refutation 165,213,217,222,223,276,285,306,336,340,342,398,410,453,458,460,487,496]
% SZS output end Proof for 1122480556279931032177459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not rich then alice is not quiet.
Everyone who is not quiet is not generous.
Everyone who is not calm or not curious is both wise and not wise.
If mary is either not rich or curious then someone is either brave or happy.
Everyone who is either not brave or curious is both strong and kind.
Everyone who is not curious is both quiet and tall and vice versa.
If john is both brave and calm then someone is generous or not brave.
Everyone who is not patient or not creative is both not curious and kind and vice versa.
If paul is patient then someone is both strong and not quiet.
Everyone who is either rich or not tall is either generous or not rich and vice versa.
If mary is not wise then someone is either not rich or wise.
If someone is not humble then someone is both not tall and not rich and vice versa.
Everyone who is not quiet or generous is brave or humble and vice versa.
Everyone who is funny or generous is either strong or old.
Everyone who is either not humble or funny is kind or curious and vice versa.
Everyone who is either not tall or not humble is brave or creative and vice versa.
Mary is not quiet or not curious.
Lucy is either curious or not brave.
Susan is either creative or kind.
Susan is both funny and not quiet.
Someone is not tall or not generous. | Mary is not tall. | entailment | ((~rich(john))=>(~quiet(alice)))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((~calm(X)|~curious(X))=>(wise(X)&~wise(X))))&
(((~rich(mary)<~>curious(mary)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(strong(X)&kind(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
(((brave(john)&calm(john)))=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~curious(X)&kind(X))))&
((patient(paul))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~rich(X))))&
((~wise(mary))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(brave(X)|humble(X))))&
(![X]:((funny(X)|generous(X))=>(strong(X)<~>old(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(kind(X)|curious(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(brave(X)|creative(X))))&
((~quiet(mary)|~curious(mary)))&
((curious(lucy)<~>~brave(lucy)))&
((creative(susan)<~>kind(susan)))&
((funny(susan)&~quiet(susan)))&
(?[X]:((~tall(X)|~generous(X)))) | ~tall(mary) | [
"p1",
"p2",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2420102143473636191739643
% SZS output start Proof for 2420102143473636191739643
2. ! [X0] : (~quiet(X0) => ~generous(X0)) [input p1]
3. ! [X0] : ((~curious(X0) | ~calm(X0)) => (~wise(X0) & wise(X0))) [input p2]
10. ! [X0] : ((rich(X0) <~> ~tall(X0)) <=> (generous(X0) <~> ~rich(X0))) [input p9]
17. ~curious(mary) | ~quiet(mary) [input p16]
22. tall(mary) [input hypothesis]
25. ! [X0] : (~generous(X0) | quiet(X0)) [ennf transformation 2]
26. ! [X0] : ((~wise(X0) & wise(X0)) | (curious(X0) & calm(X0))) [ennf transformation 3]
46. ! [X0] : ((((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))))) [nnf transformation 10]
67. ~generous(X0) | quiet(X0) [cnf transformation 25]
69. wise(X0) | curious(X0) [cnf transformation 26]
71. ~wise(X0) | curious(X0) [cnf transformation 26]
91. ~rich(X0) | generous(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 46]
96. ~tall(X0) | rich(X0) | generous(X0) | rich(X0) [cnf transformation 46]
124. ~curious(mary) | ~quiet(mary) [cnf transformation 17]
132. tall(mary) [cnf transformation 22]
133. ~rich(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 91]
135. ~tall(X0) | rich(X0) | generous(X0) [duplicate literal removal 96]
146. curious(X0) [subsumption resolution 69,71]
186. ~tall(X0) | generous(X0) [subsumption resolution 133,135]
226. ~quiet(mary) [subsumption resolution 124,146]
233. generous(mary) [resolution 186,132]
236. quiet(mary) [resolution 233,67]
237. $false [subsumption resolution 236,226]
% SZS output end Proof for 2420102143473636191739643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not calm then someone is wise.
If someone is either quiet or old then fred is either calm or quiet.
If mary is not curious or quiet then alice is not tall or wise.
If paul is both rich and quiet then lucy is not strong and vice versa.
Everyone who is both brave and not humble is either not old or not funny and vice versa.
Everyone who is both rich and not kind is not wise or happy.
If alice is tall then someone is both not old and not tall and vice versa.
If paul is either quiet or not generous then someone is both generous and wise and vice versa.
If someone is not tall or quiet then someone is generous.
Everyone who is not patient or not wise is quiet and vice versa.
Everyone who is creative is kind or tall.
If lucy is curious then john is not calm.
If someone is not kind or humble then john is happy or kind.
Everyone who is either brave or not generous is tall or old.
If mary is either not happy or not curious then someone is not calm or not wise and vice versa.
If john is not generous then someone is tall or generous and vice versa.
Lucy is not tall.
Alice is both creative and happy.
Susan is either generous or not patient.
John is not generous or not old.
Someone is both patient and not calm.
Someone is either not patient or not rich.
Lucy is both wise and not humble.
Someone is calm. | John is generous. | contradiction | (((~funny(mary)|~calm(mary)))=>(?[X]:(wise(X))))&
((?[X]:((quiet(X)<~>old(X))))=>((calm(fred)<~>quiet(fred))))&
(((~curious(mary)|quiet(mary)))=>((~tall(alice)|wise(alice))))&
(((rich(paul)&quiet(paul)))<=>(~strong(lucy)))&
(![X]:((brave(X)&~humble(X))<=>(~old(X)<~>~funny(X))))&
(![X]:((rich(X)&~kind(X))=>(~wise(X)|happy(X))))&
((tall(alice))<=>(?[X]:((~old(X)&~tall(X)))))&
(((quiet(paul)<~>~generous(paul)))<=>(?[X]:((generous(X)&wise(X)))))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:(generous(X))))&
(![X]:((~patient(X)|~wise(X))<=>quiet(X)))&
(![X]:(creative(X)=>(kind(X)|tall(X))))&
((curious(lucy))=>(~calm(john)))&
((?[X]:((~kind(X)|humble(X))))=>((happy(john)|kind(john))))&
(![X]:((brave(X)<~>~generous(X))=>(tall(X)|old(X))))&
(((~happy(mary)<~>~curious(mary)))<=>(?[X]:((~calm(X)|~wise(X)))))&
((~generous(john))<=>(?[X]:((tall(X)|generous(X)))))&
(~tall(lucy))&
((creative(alice)&happy(alice)))&
((generous(susan)<~>~patient(susan)))&
((~generous(john)|~old(john)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
((wise(lucy)&~humble(lucy)))&
(?[X]:(calm(X))) | generous(john) | [
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5494098671415980103371993
% SZS output start Proof for 5494098671415980103371993
9. ? [X0] : (quiet(X0) | ~tall(X0)) => ? [X0] : generous(X0) [input p8]
16. ~generous(john) <=> ? [X0] : (generous(X0) | tall(X0)) [input p15]
25. generous(john) [input hypothesis]
26. ? [X0] : (quiet(X0) | ~tall(X0)) => ? [X1] : generous(X1) [rectify 9]
35. ? [X1] : generous(X1) | ! [X0] : (~quiet(X0) & tall(X0)) [ennf transformation 26]
54. ? [X0] : generous(X0) | ! [X1] : (~quiet(X1) & tall(X1)) [rectify 35]
55. ? [X0] : generous(X0) => generous(sK3) [choice axiom]
56. generous(sK3) | ! [X1] : (~quiet(X1) & tall(X1)) [skolemisation 54,55]
64. (~generous(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & (? [X0] : (generous(X0) | tall(X0)) | generous(john)) [nnf transformation 16]
65. (~generous(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & (? [X1] : (generous(X1) | tall(X1)) | generous(john)) [rectify 64]
66. ? [X1] : (generous(X1) | tall(X1)) => (generous(sK5) | tall(sK5)) [choice axiom]
67. (~generous(john) | ! [X0] : (~generous(X0) & ~tall(X0))) & ((generous(sK5) | tall(sK5)) | generous(john)) [skolemisation 65,66]
102. generous(sK3) | tall(X1) [cnf transformation 56]
117. ~generous(john) | ~tall(X0) [cnf transformation 67]
118. ~generous(john) | ~generous(X0) [cnf transformation 67]
131. generous(john) [cnf transformation 25]
236. 23 <=> generous(sK3) [avatar definition]
238. generous(sK3) <- (23) [avatar component clause 236]
241. 24 <=> ! [X1] : tall(X1) [avatar definition]
242. tall(X1) <- (24) [avatar component clause 241]
243. 24 | 23 [avatar split clause 102,236,241]
278. 32 <=> ! [X0] : ~generous(X0) [avatar definition]
279. ~generous(X0) <- (32) [avatar component clause 278]
281. 33 <=> generous(john) [avatar definition]
284. 32 | ~33 [avatar split clause 118,281,278]
286. 34 <=> ! [X0] : ~tall(X0) [avatar definition]
287. ~tall(X0) <- (34) [avatar component clause 286]
288. 34 | ~33 [avatar split clause 117,281,286]
323. 33 [avatar split clause 131,281]
324. $false <- (23, 32) [subsumption resolution 238,279]
325. ~23 | ~32 [avatar contradiction clause 324]
328. $false <- (24, 34) [subsumption resolution 242,287]
329. ~24 | ~34 [avatar contradiction clause 328]
331. $false [avatar sat refutation 243,284,288,323,325,329]
% SZS output end Proof for 5494098671415980103371993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not creative is both strong and humble and vice versa. Everyone who is brave or not wise is quiet or kind. If someone is not kind or not humble then lucy is curious or not old and vice versa. If someone is both generous and not creative then someone is not old. If someone is rich then alice is both humble and strong and vice versa. If someone is brave then someone is either not generous or brave. Everyone who is old is either not quiet or tall. Everyone who is funny is both generous and not brave. If someone is both not strong and strong then someone is creative. Everyone who is either humble or not humble is not funny and vice versa. If susan is not humble or funny then john is either patient or brave. Everyone who is brave or not kind is happy. Everyone who is not strong or not funny is both old and patient. Everyone who is happy is both generous and not creative. Everyone who is not patient or funny is both not funny and wise. Everyone who is not patient or quiet is curious or tall and vice versa. Alice is rich. Paul is not rich. Someone is either generous or patient. Someone is happy or old. Someone is either calm or funny. | Paul is old. | entailment | (![X]:((~brave(X)|~creative(X))<=>(strong(X)&humble(X))))&
(![X]:((brave(X)|~wise(X))=>(quiet(X)|kind(X))))&
((?[X]:((~kind(X)|~humble(X))))<=>((curious(lucy)|~old(lucy))))&
((?[X]:((generous(X)&~creative(X))))=>(?[X]:(~old(X))))&
((?[X]:(rich(X)))<=>((humble(alice)&strong(alice))))&
((?[X]:(brave(X)))=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:(old(X)=>(~quiet(X)<~>tall(X))))&
(![X]:(funny(X)=>(generous(X)&~brave(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:(creative(X))))&
(![X]:((humble(X)<~>~humble(X))<=>~funny(X)))&
(((~humble(susan)|funny(susan)))=>((patient(john)<~>brave(john))))&
(![X]:((brave(X)|~kind(X))=>happy(X)))&
(![X]:((~strong(X)|~funny(X))=>(old(X)&patient(X))))&
(![X]:(happy(X)=>(generous(X)&~creative(X))))&
(![X]:((~patient(X)|funny(X))=>(~funny(X)&wise(X))))&
(![X]:((~patient(X)|quiet(X))<=>(curious(X)|tall(X))))&
(rich(alice))&
(~rich(paul))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((calm(X)<~>funny(X)))) | old(paul) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7720552250546244543544519
% SZS output start Proof for 7720552250546244543544519
10. ! [X0] : ((humble(X0) <~> ~humble(X0)) <=> ~funny(X0)) [input p9]
13. ! [X0] : ((~funny(X0) | ~strong(X0)) => (patient(X0) & old(X0))) [input p12]
22. ~old(paul) [input hypothesis]
37. ! [X0] : ((patient(X0) & old(X0)) | (funny(X0) & strong(X0))) [ennf transformation 13]
63. ! [X0] : ((((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | funny(X0)) & (~funny(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0))))) [nnf transformation 10]
96. ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 63]
97. ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 63]
107. old(X0) | funny(X0) [cnf transformation 37]
125. ~old(paul) [cnf transformation 22]
127. ~funny(X0) | ~humble(X0) [duplicate literal removal 96]
128. ~funny(X0) | humble(X0) [duplicate literal removal 97]
194. ~funny(X0) [subsumption resolution 127,128]
210. old(X0) [subsumption resolution 107,194]
215. $false [subsumption resolution 125,210]
% SZS output end Proof for 7720552250546244543544519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not curious and vice versa.
If susan is not tall then someone is tall or not old and vice versa.
If john is not curious or not creative then someone is either generous or tall and vice versa.
Everyone who is patient or not rich is not brave or not curious and vice versa.
If someone is calm or wise then someone is either brave or curious.
Everyone who is strong or not creative is not creative or curious and vice versa.
Everyone who is both humble and tall is wise and vice versa.
If paul is both not kind and quiet then someone is old or not quiet.
Everyone who is either quiet or patient is curious or rich.
Everyone who is not brave is calm or not brave.
Everyone who is not happy is not tall or not brave.
Everyone who is not patient or not generous is both not calm and not patient and vice versa.
If someone is both happy and not patient then mary is tall.
Everyone who is patient is either not brave or curious and vice versa.
Everyone who is not curious is either generous or not humble.
If alice is not calm or not creative then susan is not funny or not old and vice versa.
Paul is not creative.
Paul is either not quiet or not strong.
Someone is happy or wise.
Someone is not strong or not kind.
Alice is not calm or kind.
Fred is either quiet or creative.
Someone is strong. | Paul is not rich. | entailment | (![X]:(~generous(X)<=>~curious(X)))&
((~tall(susan))<=>(?[X]:((tall(X)|~old(X)))))&
(((~curious(john)|~creative(john)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((patient(X)|~rich(X))<=>(~brave(X)|~curious(X))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((strong(X)|~creative(X))<=>(~creative(X)|curious(X))))&
(![X]:((humble(X)&tall(X))<=>wise(X)))&
(((~kind(paul)&quiet(paul)))=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>patient(X))=>(curious(X)|rich(X))))&
(![X]:(~brave(X)=>(calm(X)|~brave(X))))&
(![X]:(~happy(X)=>(~tall(X)|~brave(X))))&
(![X]:((~patient(X)|~generous(X))<=>(~calm(X)&~patient(X))))&
((?[X]:((happy(X)&~patient(X))))=>(tall(mary)))&
(![X]:(patient(X)<=>(~brave(X)<~>curious(X))))&
(![X]:(~curious(X)=>(generous(X)<~>~humble(X))))&
(((~calm(alice)|~creative(alice)))<=>((~funny(susan)|~old(susan))))&
(~creative(paul))&
((~quiet(paul)<~>~strong(paul)))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~strong(X)|~kind(X))))&
((~calm(alice)|kind(alice)))&
((quiet(fred)<~>creative(fred)))&
(?[X]:(strong(X))) | ~rich(paul) | [
"p0",
"p3",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4674238452360612543836571
% SZS output start Proof for 4674238452360612543836571
1. ! [X0] : (~generous(X0) <=> ~curious(X0)) [input p0]
4. ! [X0] : ((~rich(X0) | patient(X0)) <=> (~curious(X0) | ~brave(X0))) [input p3]
12. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~patient(X0) & ~calm(X0))) [input p11]
14. ! [X0] : (patient(X0) <=> (~brave(X0) <~> curious(X0))) [input p13]
24. rich(paul) [input hypothesis]
37. ! [X0] : ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))) [nnf transformation 1]
47. ! [X0] : (((~rich(X0) | patient(X0)) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | (rich(X0) & ~patient(X0)))) [nnf transformation 4]
48. ! [X0] : ((~rich(X0) | patient(X0) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | (rich(X0) & ~patient(X0)))) [flattening 47]
60. ! [X0] : (((~generous(X0) | ~patient(X0)) | (patient(X0) | calm(X0))) & ((~patient(X0) & ~calm(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 12]
61. ! [X0] : ((~generous(X0) | ~patient(X0) | patient(X0) | calm(X0)) & ((~patient(X0) & ~calm(X0)) | (generous(X0) & patient(X0)))) [flattening 60]
62. ! [X0] : ((patient(X0) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0)))) & (((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | ~patient(X0))) [nnf transformation 14]
75. ~generous(X0) | curious(X0) [cnf transformation 37]
85. ~brave(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 48]
87. ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 48]
88. ~rich(X0) | patient(X0) | curious(X0) [cnf transformation 48]
108. ~patient(X0) | generous(X0) [cnf transformation 61]
112. ~curious(X0) | brave(X0) | ~patient(X0) [cnf transformation 62]
114. patient(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 62]
130. rich(paul) [cnf transformation 24]
224. ~brave(X0) | ~curious(X0) [subsumption resolution 114,85]
225. ~patient(X0) | ~curious(X0) [subsumption resolution 112,85]
306. patient(paul) | brave(paul) [resolution 87,130]
308. 34 <=> brave(paul) [avatar definition]
310. brave(paul) <- (34) [avatar component clause 308]
312. 35 <=> patient(paul) [avatar definition]
314. patient(paul) <- (35) [avatar component clause 312]
315. 34 | 35 [avatar split clause 306,312,308]
316. patient(paul) | curious(paul) [resolution 88,130]
318. 36 <=> curious(paul) [avatar definition]
319. ~curious(paul) <- (~36) [avatar component clause 318]
321. 36 | 35 [avatar split clause 316,312,318]
325. ~curious(paul) <- (34) [resolution 310,224]
328. ~36 | ~34 [avatar split clause 325,308,318]
341. ~curious(paul) <- (35) [resolution 314,225]
342. generous(paul) <- (35) [resolution 314,108]
343. ~36 | ~35 [avatar split clause 341,312,318]
382. curious(paul) <- (35) [resolution 342,75]
383. $false <- (35, ~36) [subsumption resolution 382,319]
384. ~35 | 36 [avatar contradiction clause 383]
385. $false [avatar sat refutation 315,321,328,343,384]
% SZS output end Proof for 4674238452360612543836571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not kind and not curious then john is either quiet or wise.
Everyone who is wise is patient.
If fred is both generous and not happy then someone is not humble or humble and vice versa.
If someone is not generous then someone is both not tall and not brave and vice versa.
If susan is wise then alice is patient or not calm and vice versa.
Everyone who is both not happy and not tall is both strong and not generous.
If mary is either calm or creative then someone is either happy or humble and vice versa.
Everyone who is both curious and quiet is both tall and kind and vice versa.
If mary is both not humble and curious then someone is not rich.
If john is old then susan is either happy or rich.
Everyone who is rich is both not curious and not humble and vice versa.
If someone is either brave or humble then someone is creative.
Everyone who is both not strong and not generous is not brave.
Everyone who is both not wise and old is calm or old.
If someone is not funny then mary is brave and vice versa.
Everyone who is quiet is curious.
Susan is generous.
Someone is either happy or tall.
Alice is both not brave and not kind.
John is both calm and generous.
Someone is either not kind or not creative.
Mary is old. | Mary is rich. | neutral | (((~kind(alice)&~curious(alice)))=>((quiet(john)<~>wise(john))))&
(![X]:(wise(X)=>patient(X)))&
(((generous(fred)&~happy(fred)))<=>(?[X]:((~humble(X)|humble(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~tall(X)&~brave(X)))))&
((wise(susan))<=>((patient(alice)|~calm(alice))))&
(![X]:((~happy(X)&~tall(X))=>(strong(X)&~generous(X))))&
(((calm(mary)<~>creative(mary)))<=>(?[X]:((happy(X)<~>humble(X)))))&
(![X]:((curious(X)&quiet(X))<=>(tall(X)&kind(X))))&
(((~humble(mary)&curious(mary)))=>(?[X]:(~rich(X))))&
((old(john))=>((happy(susan)<~>rich(susan))))&
(![X]:(rich(X)<=>(~curious(X)&~humble(X))))&
((?[X]:((brave(X)<~>humble(X))))=>(?[X]:(creative(X))))&
(![X]:((~strong(X)&~generous(X))=>~brave(X)))&
(![X]:((~wise(X)&old(X))=>(calm(X)|old(X))))&
((?[X]:(~funny(X)))<=>(brave(mary)))&
(![X]:(quiet(X)=>curious(X)))&
(generous(susan))&
(?[X]:((happy(X)<~>tall(X))))&
((~brave(alice)&~kind(alice)))&
((calm(john)&generous(john)))&
(?[X]:((~kind(X)<~>~creative(X))))&
(old(mary)) | rich(mary) | [] | null | 0 |
Everyone who is either brave or not creative is tall or not wise and vice versa.
Everyone who is not happy is either patient or kind and vice versa.
If someone is wise then paul is both not patient and wise and vice versa.
If alice is both not kind and not funny then someone is not creative or funny and vice versa.
Everyone who is both not kind and tall is both generous and not tall and vice versa.
Everyone who is both not generous and rich is either strong or not creative.
If mary is either old or not patient then someone is both curious and not funny and vice versa.
If alice is not happy then alice is creative or humble and vice versa.
If someone is not quiet then mary is both not creative and patient and vice versa.
If someone is funny then someone is quiet or not rich.
Everyone who is both quiet and not strong is either kind or not tall and vice versa.
If someone is not creative then someone is either not brave or not tall.
If alice is not brave then paul is both not brave and not wise and vice versa.
If fred is not quiet or happy then someone is tall.
Everyone who is strong is old.
If paul is both not funny and not tall then john is not strong or not generous.
Someone is either tall or old.
Paul is both happy and not quiet.
Mary is either kind or humble.
Someone is both not quiet and old.
Someone is either not calm or not patient.
John is both not humble and not calm.
Someone is creative.
Someone is not patient or generous. | Mary is kind. | neutral | (![X]:((brave(X)<~>~creative(X))<=>(tall(X)|~wise(X))))&
(![X]:(~happy(X)<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))<=>((~patient(paul)&wise(paul))))&
(((~kind(alice)&~funny(alice)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((~kind(X)&tall(X))<=>(generous(X)&~tall(X))))&
(![X]:((~generous(X)&rich(X))=>(strong(X)<~>~creative(X))))&
(((old(mary)<~>~patient(mary)))<=>(?[X]:((curious(X)&~funny(X)))))&
((~happy(alice))<=>((creative(alice)|humble(alice))))&
((?[X]:(~quiet(X)))<=>((~creative(mary)&patient(mary))))&
((?[X]:(funny(X)))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((quiet(X)&~strong(X))<=>(kind(X)<~>~tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~brave(X)<~>~tall(X)))))&
((~brave(alice))<=>((~brave(paul)&~wise(paul))))&
(((~quiet(fred)|happy(fred)))=>(?[X]:(tall(X))))&
(![X]:(strong(X)=>old(X)))&
(((~funny(paul)&~tall(paul)))=>((~strong(john)|~generous(john))))&
(?[X]:((tall(X)<~>old(X))))&
((happy(paul)&~quiet(paul)))&
((kind(mary)<~>humble(mary)))&
(?[X]:((~quiet(X)&old(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
((~humble(john)&~calm(john)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|generous(X)))) | kind(mary) | [] | null | 0 |
If someone is happy then john is either funny or wise and vice versa.
Everyone who is tall or not generous is kind and vice versa.
If paul is brave or not old then someone is not curious or not creative.
Everyone who is not kind is either not kind or not old.
Everyone who is both not quiet and humble is both patient and not patient and vice versa.
Everyone who is not strong is both generous and not calm and vice versa.
Everyone who is patient or not patient is strong.
If john is rich or strong then someone is not funny and vice versa.
Everyone who is both calm and generous is both funny and old and vice versa.
Everyone who is humble is both patient and not rich.
If lucy is not old then mary is both patient and generous.
If someone is not humble or not rich then john is quiet.
Everyone who is not funny or not brave is either not wise or not kind.
If someone is both rich and wise then someone is quiet or not strong and vice versa.
Everyone who is not brave is not wise or kind and vice versa.
If someone is strong then someone is either not generous or not patient and vice versa.
Paul is not happy.
Susan is either humble or not funny.
Someone is either quiet or patient.
Mary is not calm.
Someone is not kind or curious.
Susan is brave.
Someone is not happy or not old.
Someone is not old or creative. | Mary is wise. | contradiction | ((?[X]:(happy(X)))<=>((funny(john)<~>wise(john))))&
(![X]:((tall(X)|~generous(X))<=>kind(X)))&
(((brave(paul)|~old(paul)))=>(?[X]:((~curious(X)|~creative(X)))))&
(![X]:(~kind(X)=>(~kind(X)<~>~old(X))))&
(![X]:((~quiet(X)&humble(X))<=>(patient(X)&~patient(X))))&
(![X]:(~strong(X)<=>(generous(X)&~calm(X))))&
(![X]:((patient(X)|~patient(X))=>strong(X)))&
(((rich(john)|strong(john)))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&generous(X))<=>(funny(X)&old(X))))&
(![X]:(humble(X)=>(patient(X)&~rich(X))))&
((~old(lucy))=>((patient(mary)&generous(mary))))&
((?[X]:((~humble(X)|~rich(X))))=>(quiet(john)))&
(![X]:((~funny(X)|~brave(X))=>(~wise(X)<~>~kind(X))))&
((?[X]:((rich(X)&wise(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:(~brave(X)<=>(~wise(X)|kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
(~happy(paul))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((quiet(X)<~>patient(X))))&
(~calm(mary))&
(?[X]:((~kind(X)|curious(X))))&
(brave(susan))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~old(X)|creative(X)))) | wise(mary) | [
"p1",
"p5",
"p6",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5952604870493836264173489
% SZS output start Proof for 5952604870493836264173489
2. ! [X0] : ((~generous(X0) | tall(X0)) <=> kind(X0)) [input p1]
6. ! [X0] : (~strong(X0) <=> (~calm(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | patient(X0)) => strong(X0)) [input p6]
13. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~wise(X0) <~> ~kind(X0))) [input p12]
15. ! [X0] : (~brave(X0) <=> (kind(X0) | ~wise(X0))) [input p14]
20. ~calm(mary) [input p19]
25. wise(mary) [input hypothesis]
30. ! [X0] : (strong(X0) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
34. ! [X0] : ((~wise(X0) <~> ~kind(X0)) | (brave(X0) & funny(X0))) [ennf transformation 13]
39. ! [X0] : (((~generous(X0) | tall(X0)) | ~kind(X0)) & (kind(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 2]
40. ! [X0] : ((~generous(X0) | tall(X0) | ~kind(X0)) & (kind(X0) | (generous(X0) & ~tall(X0)))) [flattening 39]
46. ! [X0] : ((~strong(X0) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | strong(X0))) [nnf transformation 6]
47. ! [X0] : ((~strong(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | strong(X0))) [flattening 46]
55. ! [X0] : (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (brave(X0) & funny(X0))) [nnf transformation 34]
61. ! [X0] : ((~brave(X0) | (~kind(X0) & wise(X0))) & ((kind(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 15]
62. ! [X0] : ((~brave(X0) | (~kind(X0) & wise(X0))) & (kind(X0) | ~wise(X0) | brave(X0))) [flattening 61]
83. kind(X0) | generous(X0) [cnf transformation 40]
95. ~strong(X0) | calm(X0) | ~generous(X0) [cnf transformation 47]
96. strong(X0) | ~patient(X0) [cnf transformation 30]
97. strong(X0) | patient(X0) [cnf transformation 30]
112. ~kind(X0) | ~wise(X0) | brave(X0) [cnf transformation 55]
120. kind(X0) | ~wise(X0) | brave(X0) [cnf transformation 62]
122. ~brave(X0) | ~kind(X0) [cnf transformation 62]
132. ~calm(mary) [cnf transformation 20]
137. wise(mary) [cnf transformation 25]
177. strong(X0) [subsumption resolution 96,97]
184. 10 <=> generous(mary) [avatar definition]
186. generous(mary) <- (10) [avatar component clause 184]
227. ~wise(X0) | brave(X0) [subsumption resolution 120,112]
308. brave(mary) [resolution 227,137]
322. ~kind(mary) [resolution 308,122]
328. ~generous(X2) | calm(X2) [resolution 95,177]
329. generous(mary) [resolution 322,83]
330. 10 [avatar split clause 329,184]
358. calm(mary) <- (10) [resolution 328,186]
363. $false <- (10) [subsumption resolution 358,132]
364. ~10 [avatar contradiction clause 363]
365. $false [avatar sat refutation 330,364]
% SZS output end Proof for 5952604870493836264173489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is generous or tall then paul is both creative and not tall. If someone is both not brave and not tall then john is either rich or not kind. Everyone who is both not wise and old is both kind and not old. If alice is either patient or funny then fred is both calm and tall. Everyone who is either not calm or not happy is not generous or brave and vice versa. If someone is both rich and not generous then someone is both not kind and not tall and vice versa. If someone is rich or tall then john is curious. Everyone who is creative or not creative is creative or generous and vice versa. Everyone who is generous or tall is wise. If someone is rich or not creative then someone is not calm and vice versa. Everyone who is both not rich and not patient is not quiet or wise and vice versa. Everyone who is not funny or brave is not kind or strong and vice versa. Everyone who is both not patient and rich is not brave or generous and vice versa. Everyone who is rich or not generous is either tall or patient and vice versa. Everyone who is wise or not rich is not curious or not happy and vice versa. If someone is funny or not old then someone is patient and vice versa. Someone is quiet. Someone is both not funny and quiet. Fred is patient or not strong. Someone is either rich or generous. Paul is both calm and not old. Alice is both brave and not old. Paul is not curious. | Mary is not generous. | entailment | (((generous(mary)|tall(mary)))=>((creative(paul)&~tall(paul))))&
((?[X]:((~brave(X)&~tall(X))))=>((rich(john)<~>~kind(john))))&
(![X]:((~wise(X)&old(X))=>(kind(X)&~old(X))))&
(((patient(alice)<~>funny(alice)))=>((calm(fred)&tall(fred))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~generous(X)|brave(X))))&
((?[X]:((rich(X)&~generous(X))))<=>(?[X]:((~kind(X)&~tall(X)))))&
((?[X]:((rich(X)|tall(X))))=>(curious(john)))&
(![X]:((creative(X)|~creative(X))<=>(creative(X)|generous(X))))&
(![X]:((generous(X)|tall(X))=>wise(X)))&
((?[X]:((rich(X)|~creative(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~rich(X)&~patient(X))<=>(~quiet(X)|wise(X))))&
(![X]:((~funny(X)|brave(X))<=>(~kind(X)|strong(X))))&
(![X]:((~patient(X)&rich(X))<=>(~brave(X)|generous(X))))&
(![X]:((rich(X)|~generous(X))<=>(tall(X)<~>patient(X))))&
(![X]:((wise(X)|~rich(X))<=>(~curious(X)|~happy(X))))&
((?[X]:((funny(X)|~old(X))))<=>(?[X]:(patient(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~funny(X)&quiet(X))))&
((patient(fred)|~strong(fred)))&
(?[X]:((rich(X)<~>generous(X))))&
((calm(paul)&~old(paul)))&
((brave(alice)&~old(alice)))&
(~curious(paul)) | ~generous(mary) | [
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 532257562690902831522577
% SZS output start Proof for 532257562690902831522577
9. ! [X0] : ((tall(X0) | generous(X0)) => wise(X0)) [input p8]
11. ! [X0] : ((~patient(X0) & ~rich(X0)) <=> (wise(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (generous(X0) | ~brave(X0))) [input p12]
24. generous(mary) [input hypothesis]
34. ! [X0] : (wise(X0) | (~tall(X0) & ~generous(X0))) [ennf transformation 9]
51. ! [X0] : (((~patient(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | (patient(X0) | rich(X0)))) [nnf transformation 11]
52. ! [X0] : (((~patient(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | patient(X0) | rich(X0))) [flattening 51]
55. ! [X0] : (((rich(X0) & ~patient(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 13]
56. ! [X0] : (((rich(X0) & ~patient(X0)) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | ~rich(X0) | patient(X0))) [flattening 55]
101. ~generous(X0) | wise(X0) [cnf transformation 34]
108. ~wise(X0) | ~rich(X0) [cnf transformation 52]
119. ~generous(X0) | rich(X0) [cnf transformation 56]
144. generous(mary) [cnf transformation 24]
158. 3 <=> generous(mary) [avatar definition]
159. generous(mary) <- (3) [avatar component clause 158]
298. 3 [avatar split clause 144,158]
299. wise(mary) <- (3) [resolution 101,159]
301. ~rich(mary) <- (3) [resolution 108,299]
308. rich(mary) <- (3) [resolution 119,159]
309. $false <- (3) [subsumption resolution 308,301]
310. ~3 [avatar contradiction clause 309]
311. $false [avatar sat refutation 298,310]
% SZS output end Proof for 532257562690902831522577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and old is both old and not kind and vice versa.
Everyone who is both quiet and patient is either not generous or happy.
Everyone who is either not patient or not curious is both curious and not generous.
Everyone who is not happy or happy is funny and vice versa.
If someone is both not creative and not curious then someone is both not humble and creative.
If paul is both not kind and not strong then lucy is either not brave or rich and vice versa.
Everyone who is humble is calm.
If someone is calm or not wise then alice is not quiet or brave.
Everyone who is both generous and quiet is either rich or not rich.
Everyone who is both happy and quiet is not happy or not funny and vice versa.
If mary is both patient and tall then someone is not generous and vice versa.
If mary is old then lucy is both humble and tall and vice versa.
Everyone who is either humble or not brave is both not patient and curious and vice versa.
Everyone who is either not humble or not rich is both rich and not rich and vice versa.
Everyone who is not funny is not calm.
Everyone who is not wise is either patient or tall.
Someone is kind or wise.
Paul is funny.
Someone is strong.
Someone is not rich.
Lucy is happy.
Someone is both funny and not curious.
Someone is both rich and not old. | Paul is not quiet. | entailment | (![X]:((kind(X)&old(X))<=>(old(X)&~kind(X))))&
(![X]:((quiet(X)&patient(X))=>(~generous(X)<~>happy(X))))&
(![X]:((~patient(X)<~>~curious(X))=>(curious(X)&~generous(X))))&
(![X]:((~happy(X)|happy(X))<=>funny(X)))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(((~kind(paul)&~strong(paul)))<=>((~brave(lucy)<~>rich(lucy))))&
(![X]:(humble(X)=>calm(X)))&
((?[X]:((calm(X)|~wise(X))))=>((~quiet(alice)|brave(alice))))&
(![X]:((generous(X)&quiet(X))=>(rich(X)<~>~rich(X))))&
(![X]:((happy(X)&quiet(X))<=>(~happy(X)|~funny(X))))&
(((patient(mary)&tall(mary)))<=>(?[X]:(~generous(X))))&
((old(mary))<=>((humble(lucy)&tall(lucy))))&
(![X]:((humble(X)<~>~brave(X))<=>(~patient(X)&curious(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(rich(X)&~rich(X))))&
(![X]:(~funny(X)=>~calm(X)))&
(![X]:(~wise(X)=>(patient(X)<~>tall(X))))&
(?[X]:((kind(X)|wise(X))))&
(funny(paul))&
(?[X]:(strong(X)))&
(?[X]:(~rich(X)))&
(happy(lucy))&
(?[X]:((funny(X)&~curious(X))))&
(?[X]:((rich(X)&~old(X)))) | ~quiet(paul) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8844890114314808939860103
% SZS output start Proof for 8844890114314808939860103
4. ! [X0] : ((happy(X0) | ~happy(X0)) <=> funny(X0)) [input p3]
10. ! [X0] : ((quiet(X0) & happy(X0)) <=> (~funny(X0) | ~happy(X0))) [input p9]
24. quiet(paul) [input hypothesis]
43. ! [X0] : (((happy(X0) | ~happy(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) & happy(X0)))) [nnf transformation 4]
44. ! [X0] : ((happy(X0) | ~happy(X0) | ~funny(X0)) & (funny(X0) | (~happy(X0) & happy(X0)))) [flattening 43]
48. ! [X0] : (((quiet(X0) & happy(X0)) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | (~quiet(X0) | ~happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((quiet(X0) & happy(X0)) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | ~quiet(X0) | ~happy(X0))) [flattening 48]
79. funny(X0) | happy(X0) [cnf transformation 44]
80. funny(X0) | ~happy(X0) [cnf transformation 44]
92. ~funny(X0) | ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 49]
93. happy(X0) | happy(X0) [cnf transformation 49]
124. quiet(paul) [cnf transformation 24]
129. ~funny(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 92]
130. happy(X0) [duplicate literal removal 93]
135. funny(X0) [subsumption resolution 79,80]
170. ~happy(X0) | ~quiet(X0) [subsumption resolution 129,135]
171. ~quiet(X0) [subsumption resolution 170,130]
200. $false [subsumption resolution 124,171]
% SZS output end Proof for 8844890114314808939860103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both not quiet and generous.
Everyone who is either calm or not creative is not brave or generous.
If someone is both humble and not quiet then lucy is either old or not funny and vice versa.
Everyone who is not calm is not strong.
If someone is not rich or curious then alice is not patient or tall.
Everyone who is 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.
If alice is both rich and kind then someone is not rich and vice versa.
If someone is not wise or wise then fred is not generous and vice versa.
If alice is not kind then fred is not rich.
If someone is either wise or old then someone is either rich or not curious.
Everyone who is humble or funny is strong and vice versa.
If fred is wise or tall then someone is both not happy and not wise and vice versa.
Everyone who is not quiet is not tall.
Paul is not rich.
Someone is not rich or not patient.
Fred is either not wise or not generous.
Someone is both not tall and rich.
Someone is quiet or kind.
John is both wise and not rich. | Fred is curious. | neutral | (![X]:(~old(X)=>(~quiet(X)&generous(X))))&
(![X]:((calm(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:((humble(X)&~quiet(X))))<=>((old(lucy)<~>~funny(lucy))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((~rich(X)|curious(X))))=>((~patient(alice)|tall(alice))))&
(![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)&kind(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((~wise(X)|wise(X))))<=>(~generous(fred)))&
((~kind(alice))=>(~rich(fred)))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((humble(X)|funny(X))<=>strong(X)))&
(((wise(fred)|tall(fred)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:(~quiet(X)=>~tall(X)))&
(~rich(paul))&
(?[X]:((~rich(X)|~patient(X))))&
((~wise(fred)<~>~generous(fred)))&
(?[X]:((~tall(X)&rich(X))))&
(?[X]:((quiet(X)|kind(X))))&
((wise(john)&~rich(john))) | curious(fred) | [] | null | 0 |
If lucy is not tall then lucy is either not humble or calm and vice versa.
Everyone who is patient is not creative or not patient and vice versa.
Everyone who is either not happy or kind is kind and vice versa.
If someone is either happy or not old then someone is either not old or not brave and vice versa.
Everyone who is both not rich and tall is both kind and not quiet.
Everyone who is both wise and not happy is either curious or creative.
Everyone who is either rich or not happy is either not old or brave.
If someone is not wise then lucy is either kind or curious and vice versa.
If someone is both not funny and not happy then someone is not curious or quiet and vice versa.
Everyone who is not happy or not calm is not quiet and vice versa.
Everyone who is either funny or not old is both not tall and not quiet and vice versa.
If someone is either old or wise then alice is both wise and creative.
Everyone who is both strong and not brave is not strong and vice versa.
Everyone who is either not generous or calm is not generous and vice versa.
If someone is both rich and generous then lucy is not rich.
Everyone who is both not rich and not old is wise or humble.
Someone is not strong or not creative.
John is not rich.
Lucy is not generous.
Susan is both curious and not humble.
Someone is either humble or kind. | Susan is wise. | entailment | ((~tall(lucy))<=>((~humble(lucy)<~>calm(lucy))))&
(![X]:(patient(X)<=>(~creative(X)|~patient(X))))&
(![X]:((~happy(X)<~>kind(X))<=>kind(X)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:((~rich(X)&tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((wise(X)&~happy(X))=>(curious(X)<~>creative(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~old(X)<~>brave(X))))&
((?[X]:(~wise(X)))<=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~old(X))<=>(~tall(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>((wise(alice)&creative(alice))))&
(![X]:((strong(X)&~brave(X))<=>~strong(X)))&
(![X]:((~generous(X)<~>calm(X))<=>~generous(X)))&
((?[X]:((rich(X)&generous(X))))=>(~rich(lucy)))&
(![X]:((~rich(X)&~old(X))=>(wise(X)|humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(~rich(john))&
(~generous(lucy))&
((curious(susan)&~humble(susan)))&
(?[X]:((humble(X)<~>kind(X)))) | wise(susan) | [
"p1",
"p2",
"p6",
"p11",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8199401770604387838370329
% SZS output start Proof for 8199401770604387838370329
2. ! [X0] : (patient(X0) <=> (~patient(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> kind(X0)) [input p2]
7. ! [X0] : ((rich(X0) <~> ~happy(X0)) => (~old(X0) <~> brave(X0))) [input p6]
12. ? [X0] : (old(X0) <~> wise(X0)) => (creative(alice) & wise(alice)) [input p11]
13. ! [X0] : ((~brave(X0) & strong(X0)) <=> ~strong(X0)) [input p12]
16. ! [X0] : ((~old(X0) & ~rich(X0)) => (humble(X0) | wise(X0))) [input p15]
20. ~humble(susan) & curious(susan) [input p19]
22. ~wise(susan) [input hypothesis]
29. ! [X0] : ((~old(X0) <~> brave(X0)) | (rich(X0) <=> ~happy(X0))) [ennf transformation 7]
30. (creative(alice) & wise(alice)) | ! [X0] : (old(X0) <=> wise(X0)) [ennf transformation 12]
32. ! [X0] : ((humble(X0) | wise(X0)) | (old(X0) | rich(X0))) [ennf transformation 16]
33. ! [X0] : (humble(X0) | wise(X0) | old(X0) | rich(X0)) [flattening 32]
35. ! [X0] : ((patient(X0) | (patient(X0) & creative(X0))) & ((~patient(X0) | ~creative(X0)) | ~patient(X0))) [nnf transformation 2]
36. ! [X0] : ((patient(X0) | (patient(X0) & creative(X0))) & (~patient(X0) | ~creative(X0) | ~patient(X0))) [flattening 35]
37. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~kind(X0)) & (kind(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 3]
44. ! [X0] : (((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) [nnf transformation 29]
58. (creative(alice) & wise(alice)) | ! [X0] : ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))) [nnf transformation 30]
59. ! [X0] : (((~brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (brave(X0) | ~strong(X0)))) [nnf transformation 13]
60. ! [X0] : (((~brave(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | brave(X0) | ~strong(X0))) [flattening 59]
71. ~patient(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 36]
73. patient(X0) | patient(X0) [cnf transformation 36]
74. kind(X0) | kind(X0) | happy(X0) [cnf transformation 37]
77. ~kind(X0) | happy(X0) | ~kind(X0) [cnf transformation 37]
92. ~brave(X0) | old(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 44]
114. creative(alice) | wise(X0) | ~old(X0) [cnf transformation 58]
116. ~strong(X0) | brave(X0) | ~strong(X0) [cnf transformation 60]
117. strong(X0) | strong(X0) [cnf transformation 60]
124. humble(X0) | wise(X0) | old(X0) | rich(X0) [cnf transformation 33]
129. ~humble(susan) [cnf transformation 20]
132. ~wise(susan) [cnf transformation 22]
135. ~strong(X0) | brave(X0) [duplicate literal removal 116]
136. strong(X0) [duplicate literal removal 117]
137. kind(X0) | happy(X0) [duplicate literal removal 74]
138. ~kind(X0) | happy(X0) [duplicate literal removal 77]
139. ~patient(X0) | ~creative(X0) [duplicate literal removal 71]
140. patient(X0) [duplicate literal removal 73]
157. ~creative(X0) [subsumption resolution 139,140]
158. happy(X0) [subsumption resolution 137,138]
188. ~rich(X0) | old(X0) | ~brave(X0) [subsumption resolution 92,158]
216. ~old(X0) | wise(X0) [subsumption resolution 114,157]
217. brave(X0) [subsumption resolution 135,136]
226. wise(X0) | humble(X0) | rich(X0) [subsumption resolution 124,216]
261. humble(susan) | rich(susan) [resolution 226,132]
264. rich(susan) [subsumption resolution 261,129]
275. old(susan) | ~brave(susan) [resolution 264,188]
276. old(susan) [subsumption resolution 275,217]
294. wise(susan) [resolution 276,216]
304. $false [subsumption resolution 294,132]
% SZS output end Proof for 8199401770604387838370329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm then fred is either not happy or not quiet.
If someone is not calm or patient then someone is both calm and not wise and vice versa.
Everyone who is either humble or tall is quiet or not brave and vice versa.
If mary is either not quiet or kind then paul is not tall or not patient.
If paul is both happy and not generous then someone is not funny or not rich.
Everyone who is both humble and not creative is either brave or not kind.
Everyone who is not brave or old is both not generous and brave and vice versa.
Everyone who is humble is either quiet or not tall.
Everyone who is not strong or kind is not creative or old and vice versa.
Everyone who is both not rich and rich is funny and vice versa.
Everyone who is either not creative or old is both not tall and funny and vice versa.
Everyone who is both quiet and not quiet is either tall or not brave and vice versa.
Everyone who is not curious or kind is wise.
Everyone who is not kind or happy is either rich or old and vice versa.
Everyone who is either old or not calm is patient or not curious.
If someone is either humble or not tall then lucy is both calm and not tall.
Alice is creative or wise.
Someone is not brave or not creative.
Someone is old.
John is not funny.
Someone is either not curious or not quiet.
Someone is both curious and calm.
Lucy is not wise. | Fred is not quiet. | entailment | (((rich(fred)<~>calm(fred)))=>((~happy(fred)<~>~quiet(fred))))&
((?[X]:((~calm(X)|patient(X))))<=>(?[X]:((calm(X)&~wise(X)))))&
(![X]:((humble(X)<~>tall(X))<=>(quiet(X)|~brave(X))))&
(((~quiet(mary)<~>kind(mary)))=>((~tall(paul)|~patient(paul))))&
(((happy(paul)&~generous(paul)))=>(?[X]:((~funny(X)|~rich(X)))))&
(![X]:((humble(X)&~creative(X))=>(brave(X)<~>~kind(X))))&
(![X]:((~brave(X)|old(X))<=>(~generous(X)&brave(X))))&
(![X]:(humble(X)=>(quiet(X)<~>~tall(X))))&
(![X]:((~strong(X)|kind(X))<=>(~creative(X)|old(X))))&
(![X]:((~rich(X)&rich(X))<=>funny(X)))&
(![X]:((~creative(X)<~>old(X))<=>(~tall(X)&funny(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~curious(X)|kind(X))=>wise(X)))&
(![X]:((~kind(X)|happy(X))<=>(rich(X)<~>old(X))))&
(![X]:((old(X)<~>~calm(X))=>(patient(X)|~curious(X))))&
((?[X]:((humble(X)<~>~tall(X))))=>((calm(lucy)&~tall(lucy))))&
((creative(alice)|wise(alice)))&
(?[X]:((~brave(X)|~creative(X))))&
(?[X]:(old(X)))&
(~funny(john))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((curious(X)&calm(X))))&
(~wise(lucy)) | ~quiet(fred) | [
"p2",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3122224465865865704395863
% SZS output start Proof for 3122224465865865704395863
3. ! [X0] : ((humble(X0) <~> tall(X0)) <=> (~brave(X0) | quiet(X0))) [input p2]
7. ! [X0] : ((old(X0) | ~brave(X0)) <=> (brave(X0) & ~generous(X0))) [input p6]
8. ! [X0] : (humble(X0) => (quiet(X0) <~> ~tall(X0))) [input p7]
12. ! [X0] : ((~quiet(X0) & quiet(X0)) <=> (tall(X0) <~> ~brave(X0))) [input p11]
24. quiet(fred) [input hypothesis]
33. ! [X0] : ((quiet(X0) <~> ~tall(X0)) | ~humble(X0)) [ennf transformation 8]
44. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [flattening 44]
50. ! [X0] : (((old(X0) | ~brave(X0)) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | (~old(X0) & brave(X0)))) [nnf transformation 7]
51. ! [X0] : ((old(X0) | ~brave(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | (~old(X0) & brave(X0)))) [flattening 50]
52. ! [X0] : (((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ~humble(X0)) [nnf transformation 33]
59. ! [X0] : (((~quiet(X0) & quiet(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | (quiet(X0) | ~quiet(X0)))) [nnf transformation 12]
60. ! [X0] : (((~quiet(X0) & quiet(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | quiet(X0) | ~quiet(X0))) [flattening 59]
85. ~quiet(X0) | humble(X0) | tall(X0) [cnf transformation 45]
87. ~tall(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 45]
96. brave(X0) | brave(X0) [cnf transformation 51]
100. tall(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 52]
116. quiet(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 60]
118. ~quiet(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 60]
143. quiet(fred) [cnf transformation 24]
144. brave(X0) [duplicate literal removal 96]
159. 4 <=> quiet(fred) [avatar definition]
161. quiet(fred) <- (4) [avatar component clause 159]
231. ~humble(X0) | ~quiet(X0) [subsumption resolution 100,87]
236. ~tall(X0) | ~quiet(X0) [subsumption resolution 118,144]
237. quiet(X0) | ~tall(X0) [subsumption resolution 116,144]
238. ~tall(X0) [subsumption resolution 237,236]
268. 4 [avatar split clause 143,159]
285. humble(fred) | tall(fred) <- (4) [resolution 85,161]
286. humble(fred) <- (4) [subsumption resolution 285,238]
287. ~quiet(fred) <- (4) [resolution 286,231]
288. $false <- (4) [subsumption resolution 287,161]
289. ~4 [avatar contradiction clause 288]
290. $false [avatar sat refutation 268,289]
% SZS output end Proof for 3122224465865865704395863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or creative is either generous or old and vice versa. Everyone who is strong or wise is either not brave or quiet and vice versa. Everyone who is kind or happy is not strong. Everyone who is not strong is both wise and not kind and vice versa. Everyone who is both brave and patient is not curious and vice versa. If someone is both kind and rich then mary is both not patient and happy. Everyone who is funny is either not happy or patient and vice versa. If someone is either patient or wise then fred is both not funny and not curious. Everyone who is both not brave and quiet is generous or funny. Everyone who is both rich and happy is patient or quiet and vice versa. Everyone who is not old is both not generous and not calm and vice versa. Everyone who is both wise and curious is not patient. If mary is both not curious and not humble then someone is both not tall and kind and vice versa. If someone is both patient and humble then someone is creative. If lucy is both not humble and quiet then alice is not old or rich. If john is either curious or not strong then lucy is either not generous or calm and vice versa. Someone is not humble. Susan is creative. Someone is either not happy or generous. Fred is both tall and humble. Someone is both brave and not humble. Alice is both old and creative. Mary is humble. | Mary is patient. | neutral | (![X]:((~wise(X)|creative(X))<=>(generous(X)<~>old(X))))&
(![X]:((strong(X)|wise(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:((kind(X)|happy(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(wise(X)&~kind(X))))&
(![X]:((brave(X)&patient(X))<=>~curious(X)))&
((?[X]:((kind(X)&rich(X))))=>((~patient(mary)&happy(mary))))&
(![X]:(funny(X)<=>(~happy(X)<~>patient(X))))&
((?[X]:((patient(X)<~>wise(X))))=>((~funny(fred)&~curious(fred))))&
(![X]:((~brave(X)&quiet(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)&happy(X))<=>(patient(X)|quiet(X))))&
(![X]:(~old(X)<=>(~generous(X)&~calm(X))))&
(![X]:((wise(X)&curious(X))=>~patient(X)))&
(((~curious(mary)&~humble(mary)))<=>(?[X]:((~tall(X)&kind(X)))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:(creative(X))))&
(((~humble(lucy)&quiet(lucy)))=>((~old(alice)|rich(alice))))&
(((curious(john)<~>~strong(john)))<=>((~generous(lucy)<~>calm(lucy))))&
(?[X]:(~humble(X)))&
(creative(susan))&
(?[X]:((~happy(X)<~>generous(X))))&
((tall(fred)&humble(fred)))&
(?[X]:((brave(X)&~humble(X))))&
((old(alice)&creative(alice)))&
(humble(mary)) | patient(mary) | [] | null | 0 |
Everyone who is not humble or not generous is tall or generous.
If john is funny then someone is not tall or not strong.
If someone is not creative then fred is not curious and vice versa.
If fred is both not funny and not tall then paul is both not kind and kind and vice versa.
Everyone who is not humble or not patient is humble or rich.
Everyone who is both patient and not quiet is not creative or curious.
Everyone who is both generous and strong is both not humble and not strong.
If someone is funny then someone is both not old and not curious.
Everyone who is either not humble or humble is not happy and vice versa.
If john is either not tall or generous then someone is strong and vice versa.
If paul is both happy and brave then alice is either patient or happy and vice versa.
Everyone who is both not funny and generous is happy.
Everyone who is either not humble or not old is happy or not humble and vice versa.
Everyone who is not brave is either not strong or curious and vice versa.
Everyone who is not quiet or wise is not old.
If fred is not calm then mary is happy and vice versa.
Mary is not curious or not quiet.
Someone is rich.
Someone is either not creative or not generous.
John is not wise or not happy.
Someone is both not curious and humble.
Someone is either not rich or not calm.
Someone is both not funny and brave. | Paul is not wise. | entailment | (![X]:((~humble(X)|~generous(X))=>(tall(X)|generous(X))))&
((funny(john))=>(?[X]:((~tall(X)|~strong(X)))))&
((?[X]:(~creative(X)))<=>(~curious(fred)))&
(((~funny(fred)&~tall(fred)))<=>((~kind(paul)&kind(paul))))&
(![X]:((~humble(X)|~patient(X))=>(humble(X)|rich(X))))&
(![X]:((patient(X)&~quiet(X))=>(~creative(X)|curious(X))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((~humble(X)<~>humble(X))<=>~happy(X)))&
(((~tall(john)<~>generous(john)))<=>(?[X]:(strong(X))))&
(((happy(paul)&brave(paul)))<=>((patient(alice)<~>happy(alice))))&
(![X]:((~funny(X)&generous(X))=>happy(X)))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~humble(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~quiet(X)|wise(X))=>~old(X)))&
((~calm(fred))<=>(happy(mary)))&
((~curious(mary)|~quiet(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)<~>~generous(X))))&
((~wise(john)|~happy(john)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~funny(X)&brave(X)))) | ~wise(paul) | [
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8250975170561103611251834
% SZS output start Proof for 8250975170561103611251834
9. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~happy(X0)) [input p8]
13. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (~humble(X0) | happy(X0))) [input p12]
15. ! [X0] : ((wise(X0) | ~quiet(X0)) => ~old(X0)) [input p14]
24. wise(paul) [input hypothesis]
38. ! [X0] : (~old(X0) | (~wise(X0) & quiet(X0))) [ennf transformation 15]
50. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0)) & (~happy(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 9]
57. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 13]
58. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 57]
89. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 50]
90. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 50]
105. ~humble(X0) | happy(X0) | ~humble(X0) | old(X0) [cnf transformation 58]
109. old(X0) | humble(X0) | humble(X0) [cnf transformation 58]
115. ~old(X0) | ~wise(X0) [cnf transformation 38]
129. wise(paul) [cnf transformation 24]
130. ~humble(X0) | happy(X0) | old(X0) [duplicate literal removal 105]
131. old(X0) | humble(X0) [duplicate literal removal 109]
132. ~happy(X0) | humble(X0) [duplicate literal removal 89]
133. ~happy(X0) | ~humble(X0) [duplicate literal removal 90]
190. ~happy(X0) [subsumption resolution 132,133]
225. ~humble(X0) | old(X0) [subsumption resolution 130,190]
226. old(X0) [subsumption resolution 225,131]
227. ~wise(X0) [subsumption resolution 115,226]
251. $false [subsumption resolution 129,227]
% SZS output end Proof for 8250975170561103611251834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient then paul is calm or not kind and vice versa. If mary is rich then susan is tall or not calm. Everyone who is not funny is either not tall or rich and vice versa. Everyone who is not creative or not funny is not curious and vice versa. Everyone who is either brave or not curious is either not tall or rich and vice versa. If someone is strong then mary is both not strong and calm. If alice is not happy or wise then mary is both not tall and not humble. If someone is humble then someone is either creative or not creative. If someone is both not old and not generous then someone is not patient or quiet. If someone is not creative or not rich then alice is quiet or not rich. If someone is both kind and not old then susan is not calm and vice versa. If someone is not brave or happy then someone is not quiet. If alice is patient then someone is not brave or tall. If fred is calm then someone is not curious or funny. If someone is both creative and tall then alice is wise. Everyone who is brave or not brave is both old and kind and vice versa. Someone is either not old or not generous. Someone is not tall or patient. Someone is rich. Alice is both strong and calm. John is not creative or quiet. Someone is both not curious and kind. Fred is brave. Paul is brave. | Paul is funny. | entailment | ((~patient(fred))<=>((calm(paul)|~kind(paul))))&
((rich(mary))=>((tall(susan)|~calm(susan))))&
(![X]:(~funny(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((~creative(X)|~funny(X))<=>~curious(X)))&
(![X]:((brave(X)<~>~curious(X))<=>(~tall(X)<~>rich(X))))&
((?[X]:(strong(X)))=>((~strong(mary)&calm(mary))))&
(((~happy(alice)|wise(alice)))=>((~tall(mary)&~humble(mary))))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>~creative(X)))))&
((?[X]:((~old(X)&~generous(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
((?[X]:((~creative(X)|~rich(X))))=>((quiet(alice)|~rich(alice))))&
((?[X]:((kind(X)&~old(X))))<=>(~calm(susan)))&
((?[X]:((~brave(X)|happy(X))))=>(?[X]:(~quiet(X))))&
((patient(alice))=>(?[X]:((~brave(X)|tall(X)))))&
((calm(fred))=>(?[X]:((~curious(X)|funny(X)))))&
((?[X]:((creative(X)&tall(X))))=>(wise(alice)))&
(![X]:((brave(X)|~brave(X))<=>(old(X)&kind(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:(rich(X)))&
((strong(alice)&calm(alice)))&
((~creative(john)|quiet(john)))&
(?[X]:((~curious(X)&kind(X))))&
(brave(fred))&
(brave(paul)) | funny(paul) | [
"p2",
"p3",
"p4",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1485380837391932894178508
% SZS output start Proof for 1485380837391932894178508
3. ! [X0] : (~funny(X0) <=> (~tall(X0) <~> rich(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> ~curious(X0)) [input p3]
5. ! [X0] : ((brave(X0) <~> ~curious(X0)) <=> (~tall(X0) <~> rich(X0))) [input p4]
24. brave(paul) [input p23]
25. ~funny(paul) [input hypothesis]
44. ! [X0] : ((~funny(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | funny(X0))) [nnf transformation 3]
45. ! [X0] : (((~funny(X0) | ~creative(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & creative(X0)))) [nnf transformation 4]
46. ! [X0] : ((~funny(X0) | ~creative(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & creative(X0)))) [flattening 45]
47. ! [X0] : ((((curious(X0) | ~brave(X0)) & (~curious(X0) | brave(X0))) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))))) [nnf transformation 5]
77. ~tall(X0) | rich(X0) | funny(X0) [cnf transformation 44]
78. ~rich(X0) | tall(X0) | funny(X0) [cnf transformation 44]
82. ~curious(X0) | funny(X0) [cnf transformation 46]
90. ~brave(X0) | curious(X0) | rich(X0) | tall(X0) [cnf transformation 47]
91. ~brave(X0) | curious(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 47]
122. brave(paul) [cnf transformation 24]
123. ~funny(paul) [cnf transformation 25]
309. 39 <=> rich(paul) [avatar definition]
310. ~rich(paul) <- (~39) [avatar component clause 309]
311. rich(paul) <- (39) [avatar component clause 309]
313. 40 <=> curious(paul) [avatar definition]
314. curious(paul) <- (40) [avatar component clause 313]
315. ~curious(paul) <- (~40) [avatar component clause 313]
317. 41 <=> tall(paul) [avatar definition]
318. tall(paul) <- (41) [avatar component clause 317]
319. ~tall(paul) <- (~41) [avatar component clause 317]
341. curious(paul) | rich(paul) | tall(paul) [resolution 90,122]
360. curious(paul) | ~tall(paul) | ~rich(paul) [resolution 91,122]
372. tall(paul) | funny(paul) <- (39) [resolution 311,78]
373. funny(paul) <- (39, ~41) [subsumption resolution 372,319]
374. $false <- (39, ~41) [subsumption resolution 373,123]
375. ~39 | 41 [avatar contradiction clause 374]
378. funny(paul) <- (40) [resolution 314,82]
380. $false <- (40) [subsumption resolution 378,123]
381. ~40 [avatar contradiction clause 380]
382. curious(paul) | tall(paul) <- (~39) [subsumption resolution 341,310]
383. 41 | 40 | 39 [avatar split clause 382,309,313,317]
385. rich(paul) | funny(paul) <- (41) [resolution 318,77]
389. rich(paul) <- (41) [subsumption resolution 385,123]
390. 39 | ~41 [avatar split clause 389,317,309]
391. ~tall(paul) | ~rich(paul) <- (~40) [subsumption resolution 360,315]
392. ~rich(paul) <- (~40, 41) [subsumption resolution 391,318]
393. ~39 | 40 | ~41 [avatar split clause 392,317,313,309]
394. $false [avatar sat refutation 375,381,383,390,393]
% SZS output end Proof for 1485380837391932894178508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both quiet and creative then someone is both not funny and not happy.
Everyone who is brave or curious is patient or not funny.
Everyone who is either not old or creative is either quiet or kind and vice versa.
Everyone who is curious is not quiet or not tall and vice versa.
If mary is calm then someone is either not funny or not tall.
Everyone who is either kind or funny is both curious and patient and vice versa.
Everyone who is not quiet or not curious is kind or not curious and vice versa.
Everyone who is either tall or curious is both not curious and not patient.
Everyone who is calm is creative and vice versa.
If mary is both patient and humble then someone is generous or old and vice versa.
Everyone who is either kind or tall is not brave and vice versa.
If someone is both not kind and not calm then someone is not happy and vice versa.
Everyone who is both funny and strong is both generous and not strong and vice versa.
If susan is either calm or not strong then john is either not tall or not rich and vice versa.
If mary is either not funny or funny then alice is both patient and not strong.
If paul is not curious or tall then susan is not calm and vice versa.
Someone is not funny.
Lucy is not quiet or not brave.
Someone is either not quiet or old.
Fred is both not kind and not funny.
John is quiet or not happy.
Someone is not generous.
Mary is strong or old.
Someone is not old or not strong. | John is not happy. | neutral | (((quiet(mary)&creative(mary)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((brave(X)|curious(X))=>(patient(X)|~funny(X))))&
(![X]:((~old(X)<~>creative(X))<=>(quiet(X)<~>kind(X))))&
(![X]:(curious(X)<=>(~quiet(X)|~tall(X))))&
((calm(mary))=>(?[X]:((~funny(X)<~>~tall(X)))))&
(![X]:((kind(X)<~>funny(X))<=>(curious(X)&patient(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(kind(X)|~curious(X))))&
(![X]:((tall(X)<~>curious(X))=>(~curious(X)&~patient(X))))&
(![X]:(calm(X)<=>creative(X)))&
(((patient(mary)&humble(mary)))<=>(?[X]:((generous(X)|old(X)))))&
(![X]:((kind(X)<~>tall(X))<=>~brave(X)))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:(~happy(X))))&
(![X]:((funny(X)&strong(X))<=>(generous(X)&~strong(X))))&
(((calm(susan)<~>~strong(susan)))<=>((~tall(john)<~>~rich(john))))&
(((~funny(mary)<~>funny(mary)))=>((patient(alice)&~strong(alice))))&
(((~curious(paul)|tall(paul)))<=>(~calm(susan)))&
(?[X]:(~funny(X)))&
((~quiet(lucy)|~brave(lucy)))&
(?[X]:((~quiet(X)<~>old(X))))&
((~kind(fred)&~funny(fred)))&
((quiet(john)|~happy(john)))&
(?[X]:(~generous(X)))&
((strong(mary)|old(mary)))&
(?[X]:((~old(X)|~strong(X)))) | ~happy(john) | [] | null | 0 |
If someone is not creative then someone is not kind.
If susan is rich then someone is either funny or brave.
If mary is both strong and not happy then mary is not rich and vice versa.
If someone is either not brave or not strong then someone is not humble and vice versa.
Everyone who is not calm or not patient is either quiet or not curious.
Everyone who is old is not calm and vice versa.
Everyone who is patient is not happy and vice versa.
If mary is humble or old then alice is not kind or not generous and vice versa.
If paul is brave or not funny then someone is not rich or not strong and vice versa.
If someone is wise or funny then someone is either not funny or rich and vice versa.
Everyone who is either creative or not brave is calm or not rich and vice versa.
Everyone who is either strong or not curious is either brave or not rich and vice versa.
If someone is not generous or old then susan is not happy and vice versa.
If someone is old or tall then lucy is not happy or not wise and vice versa.
Everyone who is old is either quiet or brave.
Everyone who is old is either patient or brave.
Someone is both creative and happy.
Someone is either humble or not generous.
John is either calm or wise.
Fred is either old or not funny.
Susan is both patient and calm.
Someone is both curious and tall.
Someone is patient or old.
Someone is not wise or not tall. | Paul is not kind. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~kind(X))))&
((rich(susan))=>(?[X]:((funny(X)<~>brave(X)))))&
(((strong(mary)&~happy(mary)))<=>(~rich(mary)))&
((?[X]:((~brave(X)<~>~strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~calm(X)|~patient(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(old(X)<=>~calm(X)))&
(![X]:(patient(X)<=>~happy(X)))&
(((humble(mary)|old(mary)))<=>((~kind(alice)|~generous(alice))))&
(((brave(paul)|~funny(paul)))<=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((wise(X)|funny(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>(calm(X)|~rich(X))))&
(![X]:((strong(X)<~>~curious(X))<=>(brave(X)<~>~rich(X))))&
((?[X]:((~generous(X)|old(X))))<=>(~happy(susan)))&
((?[X]:((old(X)|tall(X))))<=>((~happy(lucy)|~wise(lucy))))&
(![X]:(old(X)=>(quiet(X)<~>brave(X))))&
(![X]:(old(X)=>(patient(X)<~>brave(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((humble(X)<~>~generous(X))))&
((calm(john)<~>wise(john)))&
((old(fred)<~>~funny(fred)))&
((patient(susan)&calm(susan)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~wise(X)|~tall(X)))) | ~kind(paul) | [] | null | 0 |
If someone is curious or not creative then fred is both not strong and brave and vice versa. If lucy is both rich and funny then paul is not humble or not generous. If lucy is both not calm and creative then john is not humble or not wise and vice versa. Everyone who is creative is not tall or not rich. If someone is patient or not creative then someone is not kind and vice versa. Everyone who is either not brave or not funny is not brave and vice versa. Everyone who is not creative is kind or calm. Everyone who is both not tall and not brave is not happy. Everyone who is either not creative or not funny is calm or funny. If someone is either creative or not tall then john is both funny and not rich. Everyone who is either not wise or humble is not generous or wise and vice versa. Everyone who is either not tall or quiet is rich and vice versa. Everyone who is both happy and quiet is both not humble and not generous and vice versa. Everyone who is not calm or not humble is either kind or not generous. Everyone who is funny or not creative is not old and vice versa. Everyone who is either not generous or old is both creative and funny and vice versa. Fred is both quiet and calm. Someone is creative or happy. John is both not creative and calm. Someone is not wise or funny. Someone is either funny or generous. Fred is not strong. Someone is both generous and not calm. Someone is both not strong and not calm. | John is not humble. | contradiction | ((?[X]:((curious(X)|~creative(X))))<=>((~strong(fred)&brave(fred))))&
(((rich(lucy)&funny(lucy)))=>((~humble(paul)|~generous(paul))))&
(((~calm(lucy)&creative(lucy)))<=>((~humble(john)|~wise(john))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~funny(X))<=>~brave(X)))&
(![X]:(~creative(X)=>(kind(X)|calm(X))))&
(![X]:((~tall(X)&~brave(X))=>~happy(X)))&
(![X]:((~creative(X)<~>~funny(X))=>(calm(X)|funny(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>((funny(john)&~rich(john))))&
(![X]:((~wise(X)<~>humble(X))<=>(~generous(X)|wise(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>rich(X)))&
(![X]:((happy(X)&quiet(X))<=>(~humble(X)&~generous(X))))&
(![X]:((~calm(X)|~humble(X))=>(kind(X)<~>~generous(X))))&
(![X]:((funny(X)|~creative(X))<=>~old(X)))&
(![X]:((~generous(X)<~>old(X))<=>(creative(X)&funny(X))))&
((quiet(fred)&calm(fred)))&
(?[X]:((creative(X)|happy(X))))&
((~creative(john)&calm(john)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((funny(X)<~>generous(X))))&
(~strong(fred))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~strong(X)&~calm(X)))) | ~humble(john) | [
"p5",
"p10",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6330674842743072161712085
% SZS output start Proof for 6330674842743072161712085
6. ! [X0] : ((~brave(X0) <~> ~funny(X0)) <=> ~brave(X0)) [input p5]
11. ! [X0] : ((~wise(X0) <~> humble(X0)) <=> (wise(X0) | ~generous(X0))) [input p10]
15. ! [X0] : ((~creative(X0) | funny(X0)) <=> ~old(X0)) [input p14]
16. ! [X0] : ((~generous(X0) <~> old(X0)) <=> (funny(X0) & creative(X0))) [input p15]
19. calm(john) & ~creative(john) [input p18]
25. ~humble(john) [input hypothesis]
53. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [nnf transformation 6]
56. ! [X0] : ((((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))))) [nnf transformation 11]
57. ! [X0] : ((((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))))) [flattening 56]
62. ! [X0] : (((~creative(X0) | funny(X0)) | old(X0)) & (~old(X0) | (creative(X0) & ~funny(X0)))) [nnf transformation 15]
63. ! [X0] : ((~creative(X0) | funny(X0) | old(X0)) & (~old(X0) | (creative(X0) & ~funny(X0)))) [flattening 62]
64. ! [X0] : ((((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))))) [nnf transformation 16]
65. ! [X0] : ((((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))))) [flattening 64]
93. ~brave(X0) | ~brave(X0) | funny(X0) [cnf transformation 53]
95. funny(X0) | brave(X0) | brave(X0) [cnf transformation 53]
104. wise(X0) | ~generous(X0) | humble(X0) | wise(X0) [cnf transformation 57]
107. humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 57]
120. ~old(X0) | ~funny(X0) [cnf transformation 63]
123. creative(X0) | old(X0) | generous(X0) [cnf transformation 65]
132. ~creative(john) [cnf transformation 19]
142. ~humble(john) [cnf transformation 25]
143. wise(X0) | ~generous(X0) | humble(X0) [duplicate literal removal 104]
144. ~wise(X0) | humble(X0) [duplicate literal removal 107]
146. ~brave(X0) | funny(X0) [duplicate literal removal 93]
147. funny(X0) | brave(X0) [duplicate literal removal 95]
202. 13 <=> humble(john) [avatar definition]
203. ~humble(john) <- (~13) [avatar component clause 202]
234. funny(X0) [subsumption resolution 146,147]
247. ~generous(X0) | humble(X0) [subsumption resolution 143,144]
251. ~old(X0) [subsumption resolution 120,234]
254. generous(X0) | creative(X0) [subsumption resolution 123,251]
266. ~13 [avatar split clause 142,202]
275. humble(X1) | creative(X1) [resolution 254,247]
276. creative(john) <- (~13) [resolution 275,203]
277. $false <- (~13) [subsumption resolution 276,132]
278. 13 [avatar contradiction clause 277]
279. $false [avatar sat refutation 266,278]
% SZS output end Proof for 6330674842743072161712085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is both quiet and not strong and vice versa.
Everyone who is strong is either not rich or not happy.
Everyone who is strong or not humble is not patient.
Everyone who is strong is not creative or humble and vice versa.
Everyone who is not strong or happy is both funny and not patient.
If someone is not quiet then mary is curious.
If mary is either not generous or patient then someone is not strong and vice versa.
If someone is not strong then someone is not quiet.
If someone is either not tall or not creative then john is both not curious and not kind.
Everyone who is both strong and not rich is both not generous and funny and vice versa.
If john is not generous then susan is both old and quiet.
If someone is quiet or not quiet then someone is either wise or not wise and vice versa.
Everyone who is either happy or not kind is both not humble and not brave and vice versa.
Everyone who is both not happy and not brave is either happy or not generous and vice versa.
Everyone who is wise or generous is either patient or old.
Everyone who is not wise or curious is both quiet and not brave.
Mary is both rich and quiet.
Someone is happy.
Someone is not creative.
Lucy is not kind or funny.
Someone is both not rich and wise.
Someone is not funny. | Lucy is not strong. | contradiction | (![X]:((~brave(X)<~>~strong(X))<=>(quiet(X)&~strong(X))))&
(![X]:(strong(X)=>(~rich(X)<~>~happy(X))))&
(![X]:((strong(X)|~humble(X))=>~patient(X)))&
(![X]:(strong(X)<=>(~creative(X)|humble(X))))&
(![X]:((~strong(X)|happy(X))=>(funny(X)&~patient(X))))&
((?[X]:(~quiet(X)))=>(curious(mary)))&
(((~generous(mary)<~>patient(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~curious(john)&~kind(john))))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)&funny(X))))&
((~generous(john))=>((old(susan)&quiet(susan))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>~kind(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((wise(X)|generous(X))=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)|curious(X))=>(quiet(X)&~brave(X))))&
((rich(mary)&quiet(mary)))&
(?[X]:(happy(X)))&
(?[X]:(~creative(X)))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~rich(X)&wise(X))))&
(?[X]:(~funny(X))) | ~strong(lucy) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5668376350475868051679132
% SZS output start Proof for 5668376350475868051679132
1. ! [X0] : ((~brave(X0) <~> ~strong(X0)) <=> (~strong(X0) & quiet(X0))) [input p0]
3. ! [X0] : ((~humble(X0) | strong(X0)) => ~patient(X0)) [input p2]
5. ! [X0] : ((happy(X0) | ~strong(X0)) => (~patient(X0) & funny(X0))) [input p4]
6. ? [X0] : ~quiet(X0) => curious(mary) [input p5]
7. (~generous(mary) <~> patient(mary)) <=> ? [X0] : ~strong(X0) [input p6]
8. ? [X0] : ~strong(X0) => ? [X0] : ~quiet(X0) [input p7]
10. ! [X0] : ((~rich(X0) & strong(X0)) <=> (funny(X0) & ~generous(X0))) [input p9]
16. ! [X0] : ((curious(X0) | ~wise(X0)) => (~brave(X0) & quiet(X0))) [input p15]
23. ~strong(lucy) [input hypothesis]
24. ? [X0] : ~strong(X0) => ? [X1] : ~quiet(X1) [rectify 8]
27. ! [X0] : (~patient(X0) | (humble(X0) & ~strong(X0))) [ennf transformation 3]
28. ! [X0] : ((~patient(X0) & funny(X0)) | (~happy(X0) & strong(X0))) [ennf transformation 5]
29. curious(mary) | ! [X0] : quiet(X0) [ennf transformation 6]
30. ? [X1] : ~quiet(X1) | ! [X0] : strong(X0) [ennf transformation 24]
34. ! [X0] : ((~brave(X0) & quiet(X0)) | (~curious(X0) & wise(X0))) [ennf transformation 16]
35. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [nnf transformation 1]
36. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [flattening 35]
40. (((~patient(mary) | generous(mary)) & (patient(mary) | ~generous(mary))) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ((~generous(mary) | ~patient(mary)) & (patient(mary) | generous(mary)))) [nnf transformation 7]
41. (((~patient(mary) | generous(mary)) & (patient(mary) | ~generous(mary))) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ((~generous(mary) | ~patient(mary)) & (patient(mary) | generous(mary)))) [rectify 40]
42. ? [X1] : ~strong(X1) => ~strong(sK0) [choice axiom]
43. (((~patient(mary) | generous(mary)) & (patient(mary) | ~generous(mary))) | ! [X0] : strong(X0)) & (~strong(sK0) | ((~generous(mary) | ~patient(mary)) & (patient(mary) | generous(mary)))) [skolemisation 41,42]
44. ? [X0] : ~quiet(X0) | ! [X1] : strong(X1) [rectify 30]
45. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
46. ~quiet(sK1) | ! [X1] : strong(X1) [skolemisation 44,45]
48. ! [X0] : (((~rich(X0) & strong(X0)) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | (rich(X0) | ~strong(X0)))) [nnf transformation 10]
49. ! [X0] : (((~rich(X0) & strong(X0)) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | rich(X0) | ~strong(X0))) [flattening 48]
70. ~strong(X0) | ~strong(X0) | brave(X0) [cnf transformation 36]
76. ~patient(X0) | ~strong(X0) [cnf transformation 27]
81. funny(X0) | strong(X0) [cnf transformation 28]
83. ~patient(X0) | strong(X0) [cnf transformation 28]
85. curious(mary) | quiet(X0) [cnf transformation 29]
88. patient(mary) | ~generous(mary) | strong(X0) [cnf transformation 43]
90. ~quiet(sK1) | strong(X1) [cnf transformation 46]
97. strong(X0) | ~funny(X0) | generous(X0) [cnf transformation 49]
126. ~curious(X0) | ~brave(X0) [cnf transformation 34]
135. ~strong(lucy) [cnf transformation 23]
140. ~strong(X0) | brave(X0) [duplicate literal removal 70]
142. ~patient(X0) [subsumption resolution 83,76]
144. 1 <=> ! [X0] : quiet(X0) [avatar definition]
145. quiet(X0) <- (1) [avatar component clause 144]
147. 2 <=> curious(mary) [avatar definition]
149. curious(mary) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 85,147,144]
151. ~generous(mary) | strong(X0) [subsumption resolution 88,142]
153. 3 <=> ! [X0] : strong(X0) [avatar definition]
154. strong(X0) <- (3) [avatar component clause 153]
156. 4 <=> generous(mary) [avatar definition]
158. ~generous(mary) <- (~4) [avatar component clause 156]
159. 3 | ~4 [avatar split clause 151,156,153]
167. 6 <=> quiet(sK1) [avatar definition]
169. ~quiet(sK1) <- (~6) [avatar component clause 167]
170. 3 | ~6 [avatar split clause 90,167,153]
189. generous(X0) | strong(X0) [subsumption resolution 97,81]
221. ~brave(mary) <- (2) [resolution 126,149]
225. strong(mary) <- (~4) [resolution 189,158]
227. brave(mary) <- (~4) [resolution 225,140]
228. $false <- (2, ~4) [subsumption resolution 227,221]
229. ~2 | 4 [avatar contradiction clause 228]
230. $false <- (1, ~6) [resolution 145,169]
231. ~1 | 6 [avatar contradiction clause 230]
234. $false <- (3) [resolution 154,135]
238. ~3 [avatar contradiction clause 234]
239. $false [avatar sat refutation 150,159,170,229,231,238]
% SZS output end Proof for 5668376350475868051679132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or strong is not rich.
If someone is both curious and not generous then someone is either not strong or calm.
If someone is both strong and wise then someone is both curious and not funny.
Everyone who is either not kind or happy is creative or not wise and vice versa.
If susan is quiet then someone is both not funny and not patient.
If someone is not strong then alice is either not calm or wise and vice versa.
If someone is both not calm and happy then someone is either strong or quiet and vice versa.
Everyone who is not generous is not calm or not strong and vice versa.
If someone is generous then someone is not funny or not happy and vice versa.
If paul is old or not brave then susan is calm and vice versa.
If lucy is quiet or not humble then paul is either not wise or not quiet.
If mary is funny or tall then someone is not funny and vice versa.
Everyone who is either not wise or wise is not calm or rich and vice versa.
Everyone who is both patient and generous is generous or humble.
Everyone who is either not calm or wise is wise and vice versa.
If fred is both not patient and patient then alice is either creative or not wise and vice versa.
Mary is old.
Fred is quiet or not calm.
Paul is generous or rich.
Paul is not rich or not curious.
Someone is either not kind or creative. | Alice is not kind. | neutral | (![X]:((calm(X)<~>strong(X))=>~rich(X)))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~kind(X)<~>happy(X))<=>(creative(X)|~wise(X))))&
((quiet(susan))=>(?[X]:((~funny(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((~calm(alice)<~>wise(alice))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(((old(paul)|~brave(paul)))<=>(calm(susan)))&
(((quiet(lucy)|~humble(lucy)))=>((~wise(paul)<~>~quiet(paul))))&
(((funny(mary)|tall(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~calm(X)|rich(X))))&
(![X]:((patient(X)&generous(X))=>(generous(X)|humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>wise(X)))&
(((~patient(fred)&patient(fred)))<=>((creative(alice)<~>~wise(alice))))&
(old(mary))&
((quiet(fred)|~calm(fred)))&
((generous(paul)|rich(paul)))&
((~rich(paul)|~curious(paul)))&
(?[X]:((~kind(X)<~>creative(X)))) | ~kind(alice) | [] | null | 0 |
Everyone who is both strong and not tall is generous. If fred is either not generous or quiet then lucy is not strong. Everyone who is either not creative or humble is either quiet or not patient and vice versa. If someone is either strong or not curious then john is not strong and vice versa. If someone is not kind or not patient then lucy is both not rich and tall. If someone is either not tall or not creative then someone is not curious. Everyone who is both kind and not calm is not funny or brave and vice versa. Everyone who is not happy is not rich. If susan is not wise then paul is brave and vice versa. Everyone who is both wise and brave is either not funny or happy. Everyone who is happy is both creative and not tall and vice versa. Everyone who is both not creative and wise is either brave or calm and vice versa. If mary is both not old and not wise then someone is tall and vice versa. Everyone who is patient is either not creative or old and vice versa. Everyone who is not strong or not quiet is rich or patient and vice versa. Everyone who is humble or quiet is both generous and old. Someone is not brave. Someone is either not creative or not tall. Someone is not humble or kind. Lucy is not funny. Paul is not rich or not generous. Someone is humble. Susan is not humble. Someone is generous or curious. | John is not tall. | entailment | (![X]:((strong(X)&~tall(X))=>generous(X)))&
(((~generous(fred)<~>quiet(fred)))=>(~strong(lucy)))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)<~>~patient(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(~strong(john)))&
((?[X]:((~kind(X)|~patient(X))))=>((~rich(lucy)&tall(lucy))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)&~calm(X))<=>(~funny(X)|brave(X))))&
(![X]:(~happy(X)=>~rich(X)))&
((~wise(susan))<=>(brave(paul)))&
(![X]:((wise(X)&brave(X))=>(~funny(X)<~>happy(X))))&
(![X]:(happy(X)<=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)&wise(X))<=>(brave(X)<~>calm(X))))&
(((~old(mary)&~wise(mary)))<=>(?[X]:(tall(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(rich(X)|patient(X))))&
(![X]:((humble(X)|quiet(X))=>(generous(X)&old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:((~humble(X)|kind(X))))&
(~funny(lucy))&
((~rich(paul)|~generous(paul)))&
(?[X]:(humble(X)))&
(~humble(susan))&
(?[X]:((generous(X)|curious(X)))) | ~tall(john) | [
"p2",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7719999240226537717808615
% SZS output start Proof for 7719999240226537717808615
3. ! [X0] : ((~creative(X0) <~> humble(X0)) <=> (quiet(X0) <~> ~patient(X0))) [input p2]
13. (~wise(mary) & ~old(mary)) <=> ? [X0] : tall(X0) [input p12]
14. ! [X0] : (patient(X0) <=> (~creative(X0) <~> old(X0))) [input p13]
16. ! [X0] : ((quiet(X0) | humble(X0)) => (old(X0) & generous(X0))) [input p15]
25. tall(john) [input hypothesis]
35. ! [X0] : ((old(X0) & generous(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 16]
37. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [nnf transformation 3]
54. ((~wise(mary) & ~old(mary)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (wise(mary) | old(mary))) [nnf transformation 13]
55. ((~wise(mary) & ~old(mary)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | wise(mary) | old(mary)) [flattening 54]
56. ((~wise(mary) & ~old(mary)) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | wise(mary) | old(mary)) [rectify 55]
57. ? [X1] : tall(X1) => tall(sK2) [choice axiom]
58. ((~wise(mary) & ~old(mary)) | ! [X0] : ~tall(X0)) & (tall(sK2) | wise(mary) | old(mary)) [skolemisation 56,57]
59. ! [X0] : ((patient(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) & (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ~patient(X0))) [nnf transformation 14]
76. ~patient(X0) | quiet(X0) | humble(X0) | creative(X0) [cnf transformation 37]
81. ~creative(X0) | humble(X0) | quiet(X0) | patient(X0) [cnf transformation 37]
114. ~old(mary) | ~tall(X0) [cnf transformation 58]
116. ~patient(X0) | ~creative(X0) | old(X0) [cnf transformation 59]
118. old(X0) | patient(X0) | creative(X0) [cnf transformation 59]
126. ~humble(X0) | old(X0) [cnf transformation 35]
127. ~quiet(X0) | old(X0) [cnf transformation 35]
137. tall(john) [cnf transformation 25]
219. 18 <=> ! [X0] : ~tall(X0) [avatar definition]
220. ~tall(X0) <- (18) [avatar component clause 219]
227. 20 <=> old(mary) [avatar definition]
229. ~old(mary) <- (~20) [avatar component clause 227]
230. 18 | ~20 [avatar split clause 114,227,219]
275. $false <- (18) [resolution 220,137]
276. ~18 [avatar contradiction clause 275]
310. patient(mary) | creative(mary) <- (~20) [resolution 118,229]
314. 34 <=> creative(mary) [avatar definition]
316. creative(mary) <- (34) [avatar component clause 314]
318. 35 <=> patient(mary) [avatar definition]
319. ~patient(mary) <- (~35) [avatar component clause 318]
320. patient(mary) <- (35) [avatar component clause 318]
321. 34 | 35 | 20 [avatar split clause 310,227,318,314]
340. ~creative(mary) | old(mary) <- (35) [resolution 320,116]
358. 40 <=> quiet(mary) [avatar definition]
359. quiet(mary) <- (40) [avatar component clause 358]
360. ~quiet(mary) <- (~40) [avatar component clause 358]
366. quiet(mary) | humble(mary) | creative(mary) <- (35) [resolution 76,320]
416. 45 <=> humble(mary) [avatar definition]
418. humble(mary) <- (45) [avatar component clause 416]
492. ~creative(mary) <- (~20, 35) [subsumption resolution 340,229]
493. ~34 | 20 | ~35 [avatar split clause 492,318,227,314]
498. 34 | 45 | 40 | ~35 [avatar split clause 366,318,358,416,314]
549. old(mary) <- (40) [resolution 359,127]
551. $false <- (~20, 40) [subsumption resolution 549,229]
552. 20 | ~40 [avatar contradiction clause 551]
553. humble(mary) | quiet(mary) | patient(mary) <- (34) [resolution 316,81]
559. humble(mary) | patient(mary) <- (34, ~40) [subsumption resolution 553,360]
560. humble(mary) <- (34, ~35, ~40) [subsumption resolution 559,319]
561. 45 | ~34 | 35 | 40 [avatar split clause 560,358,318,314,416]
584. old(mary) <- (45) [resolution 418,126]
586. $false <- (~20, 45) [subsumption resolution 584,229]
587. 20 | ~45 [avatar contradiction clause 586]
588. $false [avatar sat refutation 230,276,321,493,498,552,561,587]
% SZS output end Proof for 7719999240226537717808615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is kind and vice versa.
If paul is not strong or funny then susan is not rich or not tall and vice versa.
If someone is both not happy and generous then susan is not calm or patient and vice versa.
Everyone who is rich or creative is both not strong and not wise.
Everyone who is not happy is both not generous and not brave and vice versa.
Everyone who is either not kind or not tall is creative or not patient.
If someone is either generous or not funny then john is either creative or happy.
If someone is either rich or strong then john is both funny and old.
Everyone who is either happy or not kind is either not old or creative and vice versa.
If someone is old or not tall then alice is either tall or not happy.
Everyone who is both creative and kind is curious and vice versa.
Everyone who is both quiet and funny is both not happy and wise and vice versa.
Everyone who is not creative or happy is both not strong and not rich and vice versa.
If someone is happy or old then alice is both generous and quiet.
Everyone who is either calm or not funny is both not generous and not quiet.
If someone is both kind and not creative then someone is both funny and not humble and vice versa.
Someone is either not humble or generous.
Lucy is both not creative and old.
Someone is both happy and humble.
Someone is either not creative or not patient.
Fred is strong or patient.
Someone is old or not strong.
Fred is not happy.
Lucy is kind or patient. | Susan is not strong. | entailment | (![X]:(~quiet(X)<=>kind(X)))&
(((~strong(paul)|funny(paul)))<=>((~rich(susan)|~tall(susan))))&
((?[X]:((~happy(X)&generous(X))))<=>((~calm(susan)|patient(susan))))&
(![X]:((rich(X)|creative(X))=>(~strong(X)&~wise(X))))&
(![X]:(~happy(X)<=>(~generous(X)&~brave(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(creative(X)|~patient(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>((creative(john)<~>happy(john))))&
((?[X]:((rich(X)<~>strong(X))))=>((funny(john)&old(john))))&
(![X]:((happy(X)<~>~kind(X))<=>(~old(X)<~>creative(X))))&
((?[X]:((old(X)|~tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((creative(X)&kind(X))<=>curious(X)))&
(![X]:((quiet(X)&funny(X))<=>(~happy(X)&wise(X))))&
(![X]:((~creative(X)|happy(X))<=>(~strong(X)&~rich(X))))&
((?[X]:((happy(X)|old(X))))=>((generous(alice)&quiet(alice))))&
(![X]:((calm(X)<~>~funny(X))=>(~generous(X)&~quiet(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:((funny(X)&~humble(X)))))&
(?[X]:((~humble(X)<~>generous(X))))&
((~creative(lucy)&old(lucy)))&
(?[X]:((happy(X)&humble(X))))&
(?[X]:((~creative(X)<~>~patient(X))))&
((strong(fred)|patient(fred)))&
(?[X]:((old(X)|~strong(X))))&
(~happy(fred))&
((kind(lucy)|patient(lucy))) | ~strong(susan) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5506008038885651939921874
% SZS output start Proof for 5506008038885651939921874
4. ! [X0] : ((creative(X0) | rich(X0)) => (~wise(X0) & ~strong(X0))) [input p3]
13. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~rich(X0) & ~strong(X0))) [input p12]
25. strong(susan) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~strong(X0)) | (~creative(X0) & ~rich(X0))) [ennf transformation 4]
52. ! [X0] : (((happy(X0) | ~creative(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 13]
53. ! [X0] : ((happy(X0) | ~creative(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [flattening 52]
82. ~strong(X0) | ~creative(X0) [cnf transformation 27]
114. ~strong(X0) | creative(X0) [cnf transformation 53]
143. strong(susan) [cnf transformation 25]
209. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
210. ~strong(X0) <- (14) [avatar component clause 209]
248. ~strong(X0) [subsumption resolution 114,82]
249. 14 [avatar split clause 248,209]
341. $false <- (14) [resolution 210,143]
342. ~14 [avatar contradiction clause 341]
343. $false [avatar sat refutation 249,342]
% SZS output end Proof for 5506008038885651939921874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is not happy or not calm and vice versa.
Everyone who is not creative or not wise is both not old and happy and vice versa.
Everyone who is either not strong or generous is not patient.
If someone is patient or calm then someone is old.
Everyone who is calm or strong is kind and vice versa.
If someone is either not strong or tall then someone is either not funny or brave and vice versa.
If susan is kind or tall then susan is not strong and vice versa.
If someone is both calm and kind then someone is both not generous and not curious and vice versa.
Everyone who is not humble or strong is both quiet and not calm.
Everyone who is not strong is brave or not old.
Everyone who is not strong or happy is not quiet and vice versa.
If someone is not happy or strong then someone is both creative and not tall and vice versa.
If someone is both not funny and creative then someone is both wise and tall and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is both rich and patient is wise or curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not humble.
Fred is not calm.
Someone is either not wise or curious.
Someone is either calm or not rich.
Alice is both quiet and not brave.
Someone is both not funny and not brave.
Someone is calm.
Someone is either wise or humble.
Susan is both not rich and tall. | Susan is not patient. | entailment | ((brave(mary))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~creative(X)|~wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~strong(X)<~>generous(X))=>~patient(X)))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(((kind(susan)|tall(susan)))<=>(~strong(susan)))&
((?[X]:((calm(X)&kind(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((~humble(X)|strong(X))=>(quiet(X)&~calm(X))))&
(![X]:(~strong(X)=>(brave(X)|~old(X))))&
(![X]:((~strong(X)|happy(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:((rich(X)&patient(X))<=>(wise(X)|curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>(funny(X)<~>~humble(X))))&
(~calm(fred))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((quiet(alice)&~brave(alice)))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
((~rich(susan)&tall(susan))) | ~patient(susan) | [
"p4",
"p6",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3969063626337065602929584
% SZS output start Proof for 3969063626337065602929584
5. ! [X0] : ((strong(X0) | calm(X0)) <=> kind(X0)) [input p4]
7. (tall(susan) | kind(susan)) <=> ~strong(susan) [input p6]
9. ! [X0] : ((strong(X0) | ~humble(X0)) => (~calm(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((happy(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p10]
14. ! [X0] : (~patient(X0) <=> (funny(X0) & humble(X0))) [input p13]
16. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) => (funny(X0) <~> ~humble(X0))) [input p15]
25. patient(susan) [input hypothesis]
33. ! [X0] : ((~calm(X0) & quiet(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 9]
36. ! [X0] : ((funny(X0) <~> ~humble(X0)) | (~quiet(X0) <=> ~humble(X0))) [ennf transformation 16]
47. ! [X0] : (((strong(X0) | calm(X0)) | ~kind(X0)) & (kind(X0) | (~strong(X0) & ~calm(X0)))) [nnf transformation 5]
48. ! [X0] : ((strong(X0) | calm(X0) | ~kind(X0)) & (kind(X0) | (~strong(X0) & ~calm(X0)))) [flattening 47]
54. ((tall(susan) | kind(susan)) | strong(susan)) & (~strong(susan) | (~tall(susan) & ~kind(susan))) [nnf transformation 7]
55. (tall(susan) | kind(susan) | strong(susan)) & (~strong(susan) | (~tall(susan) & ~kind(susan))) [flattening 54]
61. ! [X0] : (((happy(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & strong(X0)))) [nnf transformation 11]
62. ! [X0] : ((happy(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & strong(X0)))) [flattening 61]
73. ! [X0] : ((~patient(X0) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | patient(X0))) [nnf transformation 14]
74. ! [X0] : ((~patient(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | patient(X0))) [flattening 73]
77. ! [X0] : (((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0)))) [nnf transformation 36]
104. ~strong(X0) | kind(X0) [cnf transformation 48]
114. ~strong(susan) | ~kind(susan) [cnf transformation 55]
121. quiet(X0) | humble(X0) [cnf transformation 33]
126. ~quiet(X0) | strong(X0) [cnf transformation 62]
140. ~humble(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 74]
146. ~humble(X0) | funny(X0) | ~humble(X0) | quiet(X0) [cnf transformation 77]
164. patient(susan) [cnf transformation 25]
165. ~humble(X0) | funny(X0) | quiet(X0) [duplicate literal removal 146]
247. 19 <=> strong(susan) [avatar definition]
249. ~strong(susan) <- (~19) [avatar component clause 247]
251. ~strong(susan) [subsumption resolution 114,104]
252. ~19 [avatar split clause 251,247]
332. quiet(X0) | funny(X0) [subsumption resolution 165,121]
372. humble(X0) | strong(X0) [resolution 126,121]
406. funny(X1) | strong(X1) [resolution 332,126]
558. strong(X0) | ~funny(X0) | ~patient(X0) [resolution 372,140]
559. ~patient(X0) | strong(X0) [subsumption resolution 558,406]
622. strong(susan) [resolution 559,164]
629. $false <- (~19) [subsumption resolution 622,249]
630. 19 [avatar contradiction clause 629]
633. $false [avatar sat refutation 252,630]
% SZS output end Proof for 3969063626337065602929584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not wise is curious or rich. Everyone who is either kind or not humble is not funny or tall and vice versa. Everyone who is either strong or not calm is both not wise and quiet. Everyone who is not creative or patient is calm or funny. If someone is old then paul is either not rich or curious and vice versa. Everyone who is both not kind and not creative is not strong. Everyone who is both not creative and creative is curious or not quiet and vice versa. If paul is either happy or not patient then someone is both not wise and curious. If someone is both not creative and not happy then alice is not tall or patient. If someone is either not rich or not funny then paul is patient or not wise. If fred is not patient or old then someone is old and vice versa. Everyone who is not quiet is either not curious or not patient and vice versa. If someone is both old and not curious then someone is not old and vice versa. Everyone who is not strong is wise or not patient and vice versa. Everyone who is both kind and not strong is not generous and vice versa. Someone is either generous or not wise. Someone is kind. Someone is either creative or not humble. Someone is kind or not curious. Someone is both old and not humble. Alice is either kind or brave. Someone is humble or not strong. | Alice is not generous. | neutral | (![X]:((rich(X)|~wise(X))=>(curious(X)|rich(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~funny(X)|tall(X))))&
(![X]:((strong(X)<~>~calm(X))=>(~wise(X)&quiet(X))))&
(![X]:((~creative(X)|patient(X))=>(calm(X)|funny(X))))&
((?[X]:(old(X)))<=>((~rich(paul)<~>curious(paul))))&
(![X]:((~kind(X)&~creative(X))=>~strong(X)))&
(![X]:((~creative(X)&creative(X))<=>(curious(X)|~quiet(X))))&
(((happy(paul)<~>~patient(paul)))=>(?[X]:((~wise(X)&curious(X)))))&
((?[X]:((~creative(X)&~happy(X))))=>((~tall(alice)|patient(alice))))&
((?[X]:((~rich(X)<~>~funny(X))))=>((patient(paul)|~wise(paul))))&
(((~patient(fred)|old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((kind(X)&~strong(X))<=>~generous(X)))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((old(X)&~humble(X))))&
((kind(alice)<~>brave(alice)))&
(?[X]:((humble(X)|~strong(X)))) | ~generous(alice) | [] | null | 0 |
Everyone who is not patient or wise is both old and not rich. Everyone who is not humble or quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Someone is funny or not calm. Someone is funny. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Alice is not calm. | Alice is not creative. | neutral | (![X]:((~patient(X)|wise(X))=>(old(X)&~rich(X))))&
(![X]:((~humble(X)|quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | ~creative(alice) | [] | null | 0 |
Everyone who is strong or quiet is humble. Everyone who is both creative and not kind is not patient or not funny and vice versa. Everyone who is either humble or tall is either not humble or humble and vice versa. If alice is not humble then someone is either not humble or wise and vice versa. Everyone who is old is both kind and wise. Everyone who is either kind or creative is not brave or quiet and vice versa. Everyone who is either not quiet or old is not old and vice versa. If paul is either not old or not humble then someone is kind. Everyone who is rich or not rich is rich or funny. If alice is brave or rich then someone is generous or funny. Everyone who is wise is happy. Everyone who is humble or not brave is not strong or calm and vice versa. If susan is both kind and not kind then someone is generous and vice versa. Everyone who is not calm is not quiet and vice versa. If someone is not humble or humble then fred is both brave and not quiet. If someone is both kind and not wise then john is kind or curious. Fred is not happy. Susan is quiet or not curious. Lucy is either not rich or brave. Someone is both not rich and not creative. Someone is old or not strong. Someone is both not curious and patient. Someone is either patient or quiet. Someone is not wise. | Fred is not quiet. | entailment | (![X]:((strong(X)|quiet(X))=>humble(X)))&
(![X]:((creative(X)&~kind(X))<=>(~patient(X)|~funny(X))))&
(![X]:((humble(X)<~>tall(X))<=>(~humble(X)<~>humble(X))))&
((~humble(alice))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:(old(X)=>(kind(X)&wise(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|quiet(X))))&
(![X]:((~quiet(X)<~>old(X))<=>~old(X)))&
(((~old(paul)<~>~humble(paul)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)|~rich(X))=>(rich(X)|funny(X))))&
(((brave(alice)|rich(alice)))=>(?[X]:((generous(X)|funny(X)))))&
(![X]:(wise(X)=>happy(X)))&
(![X]:((humble(X)|~brave(X))<=>(~strong(X)|calm(X))))&
(((kind(susan)&~kind(susan)))<=>(?[X]:(generous(X))))&
(![X]:(~calm(X)<=>~quiet(X)))&
((?[X]:((~humble(X)|humble(X))))=>((brave(fred)&~quiet(fred))))&
((?[X]:((kind(X)&~wise(X))))=>((kind(john)|curious(john))))&
(~happy(fred))&
((quiet(susan)|~curious(susan)))&
((~rich(lucy)<~>brave(lucy)))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:((old(X)|~strong(X))))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:(~wise(X))) | ~quiet(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3423858158034519659684978
% SZS output start Proof for 3423858158034519659684978
7. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> ~old(X0)) [input p6]
25. quiet(fred) [input hypothesis]
45. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | old(X0)) & (~old(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 7]
99. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 45]
100. old(X0) | ~quiet(X0) | old(X0) [cnf transformation 45]
135. quiet(fred) [cnf transformation 25]
137. ~old(X0) | ~quiet(X0) [duplicate literal removal 99]
138. old(X0) | ~quiet(X0) [duplicate literal removal 100]
169. ~quiet(X0) [subsumption resolution 137,138]
259. $false [subsumption resolution 135,169]
% SZS output end Proof for 3423858158034519659684978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or creative is not quiet and vice versa.
If someone is both brave and rich then john is old.
If alice is both patient and kind then john is either not old or not quiet.
If mary is not wise or not patient then susan is old or brave.
If alice is funny or not curious then someone is not wise and vice versa.
Everyone who is both generous and not tall is patient and vice versa.
Everyone who is not humble is not creative or not brave.
If someone is brave then alice is not strong or strong.
If mary is not happy or not curious then someone is either brave or humble.
Everyone who is tall is not tall or not kind and vice versa.
Everyone who is either not patient or not quiet is not humble or not calm and vice versa.
Everyone who is quiet is either curious or calm.
If john is not kind or funny then someone is not generous or not calm.
Everyone who is either brave or not funny is both not creative and not brave and vice versa.
Everyone who is either not kind or not brave is not calm.
If someone is not strong then someone is not brave or calm.
Someone is creative.
Someone is either creative or calm.
Paul is kind or strong.
Fred is generous or not strong.
Mary is not humble or not curious.
John is either happy or not rich.
Someone is not generous or strong.
Mary is tall or curious. | Susan is not generous. | neutral | (![X]:((~generous(X)|creative(X))<=>~quiet(X)))&
((?[X]:((brave(X)&rich(X))))=>(old(john)))&
(((patient(alice)&kind(alice)))=>((~old(john)<~>~quiet(john))))&
(((~wise(mary)|~patient(mary)))=>((old(susan)|brave(susan))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:(~wise(X))))&
(![X]:((generous(X)&~tall(X))<=>patient(X)))&
(![X]:(~humble(X)=>(~creative(X)|~brave(X))))&
((?[X]:(brave(X)))=>((~strong(alice)|strong(alice))))&
(((~happy(mary)|~curious(mary)))=>(?[X]:((brave(X)<~>humble(X)))))&
(![X]:(tall(X)<=>(~tall(X)|~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:(quiet(X)=>(curious(X)<~>calm(X))))&
(((~kind(john)|funny(john)))=>(?[X]:((~generous(X)|~calm(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~kind(X)<~>~brave(X))=>~calm(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~brave(X)|calm(X)))))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)<~>calm(X))))&
((kind(paul)|strong(paul)))&
((generous(fred)|~strong(fred)))&
((~humble(mary)|~curious(mary)))&
((happy(john)<~>~rich(john)))&
(?[X]:((~generous(X)|strong(X))))&
((tall(mary)|curious(mary))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not curious or wise is strong and vice versa.
Everyone who is both funny and not quiet is not old and vice versa.
If someone is both not old and not curious then someone is either not calm or not quiet and vice versa.
Everyone who is both wise and happy is patient or not creative and vice versa.
If someone is both tall and strong then someone is not generous.
If someone is not old or brave then someone is generous and vice versa.
If alice is calm or wise then someone is both quiet and not creative and vice versa.
If someone is patient then mary is both creative and strong.
If mary is both old and tall then paul is either not rich or not tall and vice versa.
Everyone who is not wise is either old or not funny and vice versa.
If alice is both not quiet and not brave then alice is rich or brave.
If paul is both quiet and not generous then mary is both not strong and not wise.
Everyone who is funny is both not quiet and not curious.
Everyone who is either funny or curious is brave and vice versa.
Everyone who is not old or not tall is not rich or not humble.
Everyone who is either not wise or humble is either not humble or not brave and vice versa.
Someone is happy or not patient.
Fred is either creative or wise.
John is humble or not creative.
Fred is either not rich or not patient.
Alice is not happy. | Fred is not generous. | entailment | (![X]:((~curious(X)<~>wise(X))<=>strong(X)))&
(![X]:((funny(X)&~quiet(X))<=>~old(X)))&
((?[X]:((~old(X)&~curious(X))))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:((wise(X)&happy(X))<=>(patient(X)|~creative(X))))&
((?[X]:((tall(X)&strong(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:(generous(X))))&
(((calm(alice)|wise(alice)))<=>(?[X]:((quiet(X)&~creative(X)))))&
((?[X]:(patient(X)))=>((creative(mary)&strong(mary))))&
(((old(mary)&tall(mary)))<=>((~rich(paul)<~>~tall(paul))))&
(![X]:(~wise(X)<=>(old(X)<~>~funny(X))))&
(((~quiet(alice)&~brave(alice)))=>((rich(alice)|brave(alice))))&
(((quiet(paul)&~generous(paul)))=>((~strong(mary)&~wise(mary))))&
(![X]:(funny(X)=>(~quiet(X)&~curious(X))))&
(![X]:((funny(X)<~>curious(X))<=>brave(X)))&
(![X]:((~old(X)|~tall(X))=>(~rich(X)|~humble(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(~humble(X)<~>~brave(X))))&
(?[X]:((happy(X)|~patient(X))))&
((creative(fred)<~>wise(fred)))&
((humble(john)|~creative(john)))&
((~rich(fred)<~>~patient(fred)))&
(~happy(alice)) | ~generous(fred) | [
"p1",
"p5",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4707381563608957919550990
% SZS output start Proof for 4707381563608957919550990
2. ! [X0] : ((~quiet(X0) & funny(X0)) <=> ~old(X0)) [input p1]
6. ? [X0] : (brave(X0) | ~old(X0)) <=> ? [X0] : generous(X0) [input p5]
10. ! [X0] : (~wise(X0) <=> (old(X0) <~> ~funny(X0))) [input p9]
13. ! [X0] : (funny(X0) => (~curious(X0) & ~quiet(X0))) [input p12]
14. ! [X0] : ((funny(X0) <~> curious(X0)) <=> brave(X0)) [input p13]
16. ! [X0] : ((~wise(X0) <~> humble(X0)) <=> (~humble(X0) <~> ~brave(X0))) [input p15]
22. generous(fred) [input hypothesis]
25. ? [X0] : (brave(X0) | ~old(X0)) <=> ? [X1] : generous(X1) [rectify 6]
32. ! [X0] : ((~curious(X0) & ~quiet(X0)) | ~funny(X0)) [ennf transformation 13]
36. ! [X0] : (((~quiet(X0) & funny(X0)) | old(X0)) & (~old(X0) | (quiet(X0) | ~funny(X0)))) [nnf transformation 2]
37. ! [X0] : (((~quiet(X0) & funny(X0)) | old(X0)) & (~old(X0) | quiet(X0) | ~funny(X0))) [flattening 36]
48. (? [X0] : (brave(X0) | ~old(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (~brave(X0) & old(X0))) [nnf transformation 25]
49. (? [X0] : (brave(X0) | ~old(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (~brave(X3) & old(X3))) [rectify 48]
50. ? [X0] : (brave(X0) | ~old(X0)) => (brave(sK3) | ~old(sK3)) [choice axiom]
51. ? [X2] : generous(X2) => generous(sK4) [choice axiom]
52. ((brave(sK3) | ~old(sK3)) | ! [X1] : ~generous(X1)) & (generous(sK4) | ! [X3] : (~brave(X3) & old(X3))) [skolemisation 49,51,50]
60. ! [X0] : ((~wise(X0) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) & (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | wise(X0))) [nnf transformation 10]
61. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~brave(X0)) & (brave(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))))) [nnf transformation 16]
71. ~old(X0) | quiet(X0) | ~funny(X0) [cnf transformation 37]
72. old(X0) | funny(X0) [cnf transformation 37]
88. brave(sK3) | ~old(sK3) | ~generous(X1) [cnf transformation 52]
102. ~funny(X0) | old(X0) | wise(X0) [cnf transformation 60]
103. funny(X0) | ~old(X0) | wise(X0) [cnf transformation 60]
109. ~quiet(X0) | ~funny(X0) [cnf transformation 32]
110. ~funny(X0) | ~curious(X0) [cnf transformation 32]
111. brave(X0) | curious(X0) | ~funny(X0) [cnf transformation 61]
118. ~brave(X0) | ~humble(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 62]
121. humble(X0) | ~wise(X0) | ~brave(X0) | humble(X0) [cnf transformation 62]
132. generous(fred) [cnf transformation 22]
133. ~brave(X0) | ~humble(X0) | ~wise(X0) [duplicate literal removal 118]
135. humble(X0) | ~wise(X0) | ~brave(X0) [duplicate literal removal 121]
178. 10 <=> ! [X1] : ~generous(X1) [avatar definition]
179. ~generous(X1) <- (10) [avatar component clause 178]
181. 11 <=> old(sK3) [avatar definition]
183. ~old(sK3) <- (~11) [avatar component clause 181]
185. 12 <=> brave(sK3) [avatar definition]
187. brave(sK3) <- (12) [avatar component clause 185]
188. 10 | ~11 | 12 [avatar split clause 88,185,181,178]
260. funny(X0) | wise(X0) [subsumption resolution 103,72]
261. old(X0) | wise(X0) [subsumption resolution 102,72]
290. ~funny(X0) | brave(X0) [subsumption resolution 111,110]
292. ~brave(X0) | ~wise(X0) [subsumption resolution 133,135]
322. funny(sK3) <- (~11) [resolution 72,183]
351. brave(sK3) <- (~11) [resolution 290,322]
353. 12 | 11 [avatar split clause 351,181,185]
355. ~wise(sK3) <- (12) [resolution 292,187]
394. quiet(X0) | ~funny(X0) | wise(X0) [resolution 71,261]
399. ~funny(X0) | wise(X0) [subsumption resolution 394,109]
400. wise(X0) [subsumption resolution 399,260]
404. $false <- (12) [resolution 400,355]
405. ~12 [avatar contradiction clause 404]
407. $false <- (10) [resolution 179,132]
410. ~10 [avatar contradiction clause 407]
411. $false [avatar sat refutation 188,353,405,410]
% SZS output end Proof for 4707381563608957919550990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is kind.
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
If fred is curious or not kind then lucy is both old and quiet.
Everyone who is strong or not happy is not rich or not quiet.
Everyone who is calm is not strong.
Everyone who is brave is either happy or old and vice versa.
Everyone who is generous is kind and vice versa.
Someone is either not rich or humble.
Lucy is quiet.
Paul is kind or not creative.
Mary is either quiet or not funny.
Someone is not funny.
Mary is quiet.
Someone is either not humble or not patient. | Paul is not happy. | entailment | (![X]:(~wise(X)=>kind(X)))&
(((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
(((curious(fred)|~kind(fred)))=>((old(lucy)&quiet(lucy))))&
(![X]:((strong(X)|~happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:(brave(X)<=>(happy(X)<~>old(X))))&
(![X]:(generous(X)<=>kind(X)))&
(?[X]:((~rich(X)<~>humble(X))))&
(quiet(lucy))&
((kind(paul)|~creative(paul)))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:(~funny(X)))&
(quiet(mary))&
(?[X]:((~humble(X)<~>~patient(X)))) | ~happy(paul) | [
"p0",
"p4",
"p6",
"p7",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8106856763594842066927809
% SZS output start Proof for 8106856763594842066927809
1. ! [X0] : (~wise(X0) => kind(X0)) [input p0]
5. ! [X0] : ((~calm(X0) | ~quiet(X0)) => (~wise(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (~old(X0) & ~kind(X0))) [input p6]
8. ! [X0] : (strong(X0) <=> (~generous(X0) | ~creative(X0))) [input p7]
14. ! [X0] : (calm(X0) => ~strong(X0)) [input p13]
15. ! [X0] : (brave(X0) <=> (happy(X0) <~> old(X0))) [input p14]
19. ~creative(paul) | kind(paul) [input p18]
24. happy(paul) [input hypothesis]
26. ! [X0] : (kind(X0) | wise(X0)) [ennf transformation 1]
30. ! [X0] : ((~wise(X0) & ~creative(X0)) | (calm(X0) & quiet(X0))) [ennf transformation 5]
36. ! [X0] : (~strong(X0) | ~calm(X0)) [ennf transformation 14]
41. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 7]
42. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 41]
43. ! [X0] : ((strong(X0) | (generous(X0) & creative(X0))) & ((~generous(X0) | ~creative(X0)) | ~strong(X0))) [nnf transformation 8]
44. ! [X0] : ((strong(X0) | (generous(X0) & creative(X0))) & (~generous(X0) | ~creative(X0) | ~strong(X0))) [flattening 43]
51. ! [X0] : ((brave(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ~brave(X0))) [nnf transformation 15]
62. kind(X0) | wise(X0) [cnf transformation 26]
78. ~wise(X0) | calm(X0) [cnf transformation 30]
86. ~brave(X0) | ~kind(X0) | old(X0) [cnf transformation 42]
87. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 42]
92. creative(X0) | strong(X0) [cnf transformation 44]
112. ~calm(X0) | ~strong(X0) [cnf transformation 36]
114. ~old(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 51]
115. brave(X0) | old(X0) | ~happy(X0) [cnf transformation 51]
122. ~creative(paul) | kind(paul) [cnf transformation 19]
129. happy(paul) [cnf transformation 24]
130. ~old(X0) | brave(X0) [duplicate literal removal 87]
222. ~happy(X0) | brave(X0) [subsumption resolution 115,130]
223. ~happy(X0) | ~old(X0) [subsumption resolution 114,130]
236. 21 <=> kind(paul) [avatar definition]
237. ~kind(paul) <- (~21) [avatar component clause 236]
240. 22 <=> creative(paul) [avatar definition]
242. ~creative(paul) <- (~22) [avatar component clause 240]
243. 21 | ~22 [avatar split clause 122,240,236]
265. strong(paul) <- (~22) [resolution 92,242]
272. brave(paul) [resolution 222,129]
274. ~old(paul) [resolution 223,129]
279. ~kind(paul) | old(paul) [resolution 86,272]
281. ~kind(paul) [subsumption resolution 279,274]
282. ~21 [avatar split clause 281,236]
301. wise(paul) <- (~21) [resolution 237,62]
302. calm(paul) <- (~21) [resolution 301,78]
306. ~strong(paul) <- (~21) [resolution 302,112]
307. $false <- (~21, ~22) [subsumption resolution 306,265]
308. 21 | 22 [avatar contradiction clause 307]
309. $false [avatar sat refutation 243,282,308]
% SZS output end Proof for 8106856763594842066927809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not quiet then susan is either not kind or not wise and vice versa.
Everyone who is both creative and humble is both not quiet and not funny.
Everyone who is both curious and not curious is brave or not old.
Everyone who is not strong is both kind and generous.
If someone is both funny and not strong then lucy is either not kind or tall.
If someone is quiet then mary is both funny and not calm.
Everyone who is calm or not patient is either not calm or funny.
Everyone who is both not curious and not kind is both not kind and not tall and vice versa.
If someone is either rich or not calm then someone is funny or rich and vice versa.
If someone is either quiet or wise then someone is either brave or kind.
Everyone who is not humble or funny is either not patient or not humble and vice versa.
Everyone who is not generous is either not kind or calm.
Everyone who is both quiet and not patient is not strong or not kind and vice versa.
If alice is wise or brave then someone is tall or not generous.
If someone is both not tall and not curious then someone is old or not kind and vice versa.
If someone is rich or old then susan is not brave or old and vice versa.
Paul is both calm and not strong.
Someone is calm or not creative.
Someone is either patient or not curious.
Susan is both calm and not creative.
Someone is not old.
Susan is either not humble or not kind.
Fred is either generous or not tall.
Susan is either not brave or curious. | Susan is strong. | entailment | ((?[X]:((~curious(X)&~quiet(X))))<=>((~kind(susan)<~>~wise(susan))))&
(![X]:((creative(X)&humble(X))=>(~quiet(X)&~funny(X))))&
(![X]:((curious(X)&~curious(X))=>(brave(X)|~old(X))))&
(![X]:(~strong(X)=>(kind(X)&generous(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~kind(lucy)<~>tall(lucy))))&
((?[X]:(quiet(X)))=>((funny(mary)&~calm(mary))))&
(![X]:((calm(X)|~patient(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~curious(X)&~kind(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((~humble(X)|funny(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>calm(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~strong(X)|~kind(X))))&
(((wise(alice)|brave(alice)))=>(?[X]:((tall(X)|~generous(X)))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((rich(X)|old(X))))<=>((~brave(susan)|old(susan))))&
((calm(paul)&~strong(paul)))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:((patient(X)<~>~curious(X))))&
((calm(susan)&~creative(susan)))&
(?[X]:(~old(X)))&
((~humble(susan)<~>~kind(susan)))&
((generous(fred)<~>~tall(fred)))&
((~brave(susan)<~>curious(susan))) | strong(susan) | [
"p3",
"p10",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8883266986240810032581778
% SZS output start Proof for 8883266986240810032581778
4. ! [X0] : (~strong(X0) => (generous(X0) & kind(X0))) [input p3]
11. ! [X0] : ((funny(X0) | ~humble(X0)) <=> (~patient(X0) <~> ~humble(X0))) [input p10]
13. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~kind(X0) | ~strong(X0))) [input p12]
22. ~humble(susan) <~> ~kind(susan) [input p21]
25. ~strong(susan) [input hypothesis]
34. ! [X0] : ((generous(X0) & kind(X0)) | strong(X0)) [ennf transformation 4]
58. ! [X0] : (((funny(X0) | ~humble(X0)) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0)))) & (((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | (~funny(X0) & humble(X0)))) [nnf transformation 11]
59. ! [X0] : ((funny(X0) | ~humble(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0)))) & (((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | (~funny(X0) & humble(X0)))) [flattening 58]
61. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | (patient(X0) | ~quiet(X0)))) [nnf transformation 13]
62. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | patient(X0) | ~quiet(X0))) [flattening 61]
80. (kind(susan) | humble(susan)) & (~kind(susan) | ~humble(susan)) [nnf transformation 22]
90. strong(X0) | kind(X0) [cnf transformation 34]
116. humble(X0) | patient(X0) | humble(X0) [cnf transformation 59]
125. ~patient(X0) | strong(X0) [cnf transformation 62]
144. ~kind(susan) | ~humble(susan) [cnf transformation 80]
150. ~strong(susan) [cnf transformation 25]
151. patient(X0) | humble(X0) [duplicate literal removal 116]
159. 2 <=> kind(susan) [avatar definition]
336. 41 <=> humble(susan) [avatar definition]
340. ~41 | ~2 [avatar split clause 144,159,336]
358. kind(susan) [resolution 90,150]
372. strong(X1) | humble(X1) [resolution 151,125]
447. humble(susan) [resolution 372,150]
456. 2 [avatar split clause 358,159]
457. 41 [avatar split clause 447,336]
458. $false [avatar sat refutation 340,456,457]
% SZS output end Proof for 8883266986240810032581778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not calm is not happy or not wise.
Everyone who is not humble is rich and vice versa.
If alice is rich then susan is wise or not quiet.
If alice is both not funny and quiet then someone is either funny or wise.
If susan is not wise then mary is kind and vice versa.
Everyone who is both not wise and calm is not old and vice versa.
If someone is either humble or not patient then someone is both happy and not calm and vice versa.
If john is either curious or calm then someone is quiet or old.
Everyone who is both strong and curious is not humble.
If paul is either rich or not humble then someone is curious.
If mary is not creative or not generous then john is curious.
Everyone who is not strong or happy is either not tall or rich and vice versa.
If john is not rich then lucy is both not generous and brave and vice versa.
Everyone who is either kind or humble is both not creative and kind.
Everyone who is both curious and not calm is either calm or kind.
Paul is both old and not quiet.
John is either not brave or quiet.
Paul is either not strong or not calm.
Someone is either not old or not generous.
John is either not humble or old.
Mary is either not patient or kind.
Someone is not funny. | Susan is not happy. | neutral | (![X]:((funny(X)|~calm(X))=>(~happy(X)|~wise(X))))&
(![X]:(~humble(X)<=>rich(X)))&
((rich(alice))=>((wise(susan)|~quiet(susan))))&
(((~funny(alice)&quiet(alice)))=>(?[X]:((funny(X)<~>wise(X)))))&
((~wise(susan))<=>(kind(mary)))&
(![X]:((~wise(X)&calm(X))<=>~old(X)))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(((curious(john)<~>calm(john)))=>(?[X]:((quiet(X)|old(X)))))&
(![X]:((strong(X)&curious(X))=>~humble(X)))&
(((rich(paul)<~>~humble(paul)))=>(?[X]:(curious(X))))&
(((~creative(mary)|~generous(mary)))=>(curious(john)))&
(![X]:((~strong(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
((~rich(john))<=>((~generous(lucy)&brave(lucy))))&
(![X]:((kind(X)<~>humble(X))=>(~creative(X)&kind(X))))&
(![X]:((curious(X)&~calm(X))=>(calm(X)<~>kind(X))))&
((old(paul)&~quiet(paul)))&
((~brave(john)<~>quiet(john)))&
((~strong(paul)<~>~calm(paul)))&
(?[X]:((~old(X)<~>~generous(X))))&
((~humble(john)<~>old(john)))&
((~patient(mary)<~>kind(mary)))&
(?[X]:(~funny(X))) | ~happy(susan) | [] | null | 0 |
Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. If someone is creative then someone is not curious or not kind and vice versa. Everyone who is both not generous and not strong is either not humble or not rich. Alice is brave or strong. Alice is not quiet or not rich. Someone is rich. Paul is curious or not patient. Paul is either old or quiet. Someone is both not old and kind. Paul is not old or calm. | Paul is patient. | entailment | (![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((~generous(X)&~strong(X))=>(~humble(X)<~>~rich(X))))&
((brave(alice)|strong(alice)))&
((~quiet(alice)|~rich(alice)))&
(?[X]:(rich(X)))&
((curious(paul)|~patient(paul)))&
((old(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&kind(X))))&
((~old(paul)|calm(paul))) | patient(paul) | [
"p5",
"p11",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5606878472520667692241737
% SZS output start Proof for 5606878472520667692241737
6. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p5]
12. ! [X0] : (calm(X0) <=> patient(X0)) [input p11]
20. old(paul) <~> quiet(paul) [input p19]
22. calm(paul) | ~old(paul) [input p21]
23. ~patient(paul) [input hypothesis]
26. ! [X0] : (calm(X0) => patient(X0)) [unused predicate definition removal 12]
38. ! [X0] : (patient(X0) | ~calm(X0)) [ennf transformation 26]
48. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 48]
63. (~quiet(paul) | ~old(paul)) & (quiet(paul) | old(paul)) [nnf transformation 20]
77. ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
93. ~calm(X0) | patient(X0) [cnf transformation 38]
103. quiet(paul) | old(paul) [cnf transformation 63]
107. calm(paul) | ~old(paul) [cnf transformation 22]
108. ~patient(paul) [cnf transformation 23]
109. ~quiet(X0) [duplicate literal removal 77]
136. 7 <=> calm(paul) [avatar definition]
138. calm(paul) <- (7) [avatar component clause 136]
195. 20 <=> patient(paul) [avatar definition]
197. ~patient(paul) <- (~20) [avatar component clause 195]
199. old(paul) [subsumption resolution 103,109]
200. calm(paul) [subsumption resolution 107,199]
201. 7 [avatar split clause 200,136]
202. ~20 [avatar split clause 108,195]
207. patient(paul) <- (7) [resolution 93,138]
208. $false <- (7, ~20) [subsumption resolution 207,197]
209. ~7 | 20 [avatar contradiction clause 208]
210. $false [avatar sat refutation 201,202,209]
% SZS output end Proof for 5606878472520667692241737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not patient and calm then fred is not humble.
If susan is not curious or quiet then someone is patient or strong.
Everyone who is not wise is not generous or not old.
Everyone who is kind or strong is both not wise and patient and vice versa.
Everyone who is either strong or wise is tall or not humble.
Everyone who is humble is brave or rich and vice versa.
Everyone who is kind is both not humble and creative and vice versa.
Everyone who is curious or creative is either happy or not strong and vice versa.
If someone is not generous or humble then paul is both happy and not patient.
If someone is not strong or not funny then mary is either not kind or not old and vice versa.
If someone is either not kind or not quiet then someone is both humble and not wise.
Everyone who is either humble or not rich is both not tall and rich and vice versa.
Everyone who is either not quiet or funny is both not strong and patient.
Everyone who is wise is either calm or patient.
If someone is not quiet then someone is either quiet or not funny.
Everyone who is both funny and quiet is both not patient and rich.
John is either curious or wise.
Lucy is both not tall and rich.
Someone is calm or not rich.
Someone is either not curious or not brave.
Someone is wise.
Mary is either not humble or tall.
Someone is not kind.
Someone is both calm and not happy. | Lucy is rich. | entailment | (((~patient(paul)&calm(paul)))=>(~humble(fred)))&
(((~curious(susan)|quiet(susan)))=>(?[X]:((patient(X)|strong(X)))))&
(![X]:(~wise(X)=>(~generous(X)|~old(X))))&
(![X]:((kind(X)|strong(X))<=>(~wise(X)&patient(X))))&
(![X]:((strong(X)<~>wise(X))=>(tall(X)|~humble(X))))&
(![X]:(humble(X)<=>(brave(X)|rich(X))))&
(![X]:(kind(X)<=>(~humble(X)&creative(X))))&
(![X]:((curious(X)|creative(X))<=>(happy(X)<~>~strong(X))))&
((?[X]:((~generous(X)|humble(X))))=>((happy(paul)&~patient(paul))))&
((?[X]:((~strong(X)|~funny(X))))<=>((~kind(mary)<~>~old(mary))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((~quiet(X)<~>funny(X))=>(~strong(X)&patient(X))))&
(![X]:(wise(X)=>(calm(X)<~>patient(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((funny(X)&quiet(X))=>(~patient(X)&rich(X))))&
((curious(john)<~>wise(john)))&
((~tall(lucy)&rich(lucy)))&
(?[X]:((calm(X)|~rich(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:(wise(X)))&
((~humble(mary)<~>tall(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((calm(X)&~happy(X)))) | rich(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2396153050436502031266656
% SZS output start Proof for 2396153050436502031266656
18. rich(lucy) & ~tall(lucy) [input p17]
25. ~rich(lucy) [input hypothesis]
138. rich(lucy) [cnf transformation 18]
148. ~rich(lucy) [cnf transformation 25]
290. $false [subsumption resolution 148,138]
% SZS output end Proof for 2396153050436502031266656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not brave is not quiet or not old and vice versa.
If lucy is either not strong or quiet then someone is either brave or not generous.
Everyone who is not creative or not strong is quiet and vice versa.
Everyone who is either not brave or strong is not calm.
If someone is either not kind or not patient then someone is either not strong or not patient.
Everyone who is not old or brave is either not tall or not strong and vice versa.
If fred is rich then someone is not quiet or brave.
Everyone who is either kind or not brave is both not quiet and wise and vice versa.
If fred is both funny and tall then someone is both not funny and not kind.
Everyone who is creative is both not strong and wise and vice versa.
Everyone who is either not tall or not happy is not patient or not rich and vice versa.
Everyone who is humble is either not calm or not creative.
Everyone who is not curious is not calm.
If fred is not calm then someone is either calm or not brave and vice versa.
Everyone who is either not rich or kind is both not funny and quiet.
Someone is not old or strong.
Someone is not strong.
Lucy is not creative.
Alice is either not strong or not curious.
Lucy is either not happy or funny.
Someone is rich.
Alice is both calm and humble. | Fred is calm. | contradiction | (![X]:((~wise(X)&~brave(X))<=>(~quiet(X)|~old(X))))&
(((~strong(lucy)<~>quiet(lucy)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~creative(X)|~strong(X))<=>quiet(X)))&
(![X]:((~brave(X)<~>strong(X))=>~calm(X)))&
((?[X]:((~kind(X)<~>~patient(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((~old(X)|brave(X))<=>(~tall(X)<~>~strong(X))))&
((rich(fred))=>(?[X]:((~quiet(X)|brave(X)))))&
(![X]:((kind(X)<~>~brave(X))<=>(~quiet(X)&wise(X))))&
(((funny(fred)&tall(fred)))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:(creative(X)<=>(~strong(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(~patient(X)|~rich(X))))&
(![X]:(humble(X)=>(~calm(X)<~>~creative(X))))&
(![X]:(~curious(X)=>~calm(X)))&
((~calm(fred))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>kind(X))=>(~funny(X)&quiet(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(~strong(X)))&
(~creative(lucy))&
((~strong(alice)<~>~curious(alice)))&
((~happy(lucy)<~>funny(lucy)))&
(?[X]:(rich(X)))&
((calm(alice)&humble(alice))) | calm(fred) | [
"p3",
"p12",
"p13",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 865141273163364241901199
% SZS output start Proof for 865141273163364241901199
4. ! [X0] : ((~brave(X0) <~> strong(X0)) => ~calm(X0)) [input p3]
13. ! [X0] : (~curious(X0) => ~calm(X0)) [input p12]
14. ~calm(fred) <=> ? [X0] : (calm(X0) <~> ~brave(X0)) [input p13]
19. ~strong(alice) <~> ~curious(alice) [input p18]
22. humble(alice) & calm(alice) [input p21]
23. calm(fred) [input hypothesis]
26. ! [X0] : (~calm(X0) | (~brave(X0) <=> strong(X0))) [ennf transformation 4]
32. ! [X0] : (~calm(X0) | curious(X0)) [ennf transformation 13]
41. ! [X0] : (~calm(X0) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0)))) [nnf transformation 26]
59. (~calm(fred) | ! [X0] : ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (? [X0] : ((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | calm(fred)) [nnf transformation 14]
60. (~calm(fred) | ! [X0] : ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (? [X1] : ((brave(X1) | ~calm(X1)) & (~brave(X1) | calm(X1))) | calm(fred)) [rectify 59]
61. ? [X1] : ((brave(X1) | ~calm(X1)) & (~brave(X1) | calm(X1))) => ((brave(sK4) | ~calm(sK4)) & (~brave(sK4) | calm(sK4))) [choice axiom]
62. (~calm(fred) | ! [X0] : ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(sK4) | ~calm(sK4)) & (~brave(sK4) | calm(sK4))) | calm(fred)) [skolemisation 60,61]
68. (curious(alice) | strong(alice)) & (~curious(alice) | ~strong(alice)) [nnf transformation 19]
84. ~calm(X0) | strong(X0) | brave(X0) [cnf transformation 41]
116. ~calm(X0) | curious(X0) [cnf transformation 32]
119. ~calm(fred) | ~brave(X0) | ~calm(X0) [cnf transformation 62]
128. ~curious(alice) | ~strong(alice) [cnf transformation 68]
133. calm(alice) [cnf transformation 22]
135. calm(fred) [cnf transformation 23]
210. 17 <=> calm(fred) [avatar definition]
215. 18 <=> ! [X0] : (~brave(X0) | ~calm(X0)) [avatar definition]
216. ~calm(X0) | ~brave(X0) <- (18) [avatar component clause 215]
217. 18 | ~17 [avatar split clause 119,210,215]
238. 23 <=> strong(alice) [avatar definition]
239. ~strong(alice) <- (~23) [avatar component clause 238]
242. 24 <=> curious(alice) [avatar definition]
246. ~23 | ~24 [avatar split clause 128,242,238]
257. 17 [avatar split clause 135,210]
268. curious(alice) [resolution 116,133]
272. 24 [avatar split clause 268,242]
275. ~brave(alice) <- (18) [resolution 216,133]
279. strong(alice) | brave(alice) [resolution 84,133]
283. brave(alice) <- (~23) [subsumption resolution 279,239]
284. $false <- (18, ~23) [subsumption resolution 283,275]
285. ~18 | 23 [avatar contradiction clause 284]
287. $false [avatar sat refutation 217,246,257,272,285]
% SZS output end Proof for 865141273163364241901199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and old then alice is not rich or not kind. Everyone who is brave is either old or not rich. If alice is both not calm and quiet then someone is both brave and not brave and vice versa. If someone is either not kind or not happy then alice is old. Everyone who is both happy and not old is not kind. Everyone who is both not funny and rich is generous or not kind. Everyone who is either not strong or not patient is humble or rich. If lucy is not brave or not strong then mary is both not old and not calm. Everyone who is not kind or not creative is either curious or wise. Everyone who is not rich is both creative and not creative. Everyone who is either creative or old is not rich or creative and vice versa. Everyone who is not funny or not generous is not tall and vice versa. If fred is tall then someone is happy or not rich. Everyone who is both not patient and rich is not happy and vice versa. Susan is not creative or tall. Lucy is humble. Someone is either not quiet or not creative. Lucy is humble or not old. Someone is funny or happy. Someone is either not tall or not kind. Susan is either wise or not patient. | Susan is not creative. | neutral | (((kind(mary)&old(mary)))=>((~rich(alice)|~kind(alice))))&
(![X]:(brave(X)=>(old(X)<~>~rich(X))))&
(((~calm(alice)&quiet(alice)))<=>(?[X]:((brave(X)&~brave(X)))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(old(alice)))&
(![X]:((happy(X)&~old(X))=>~kind(X)))&
(![X]:((~funny(X)&rich(X))=>(generous(X)|~kind(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)|rich(X))))&
(((~brave(lucy)|~strong(lucy)))=>((~old(mary)&~calm(mary))))&
(![X]:((~kind(X)|~creative(X))=>(curious(X)<~>wise(X))))&
(![X]:(~rich(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)<~>old(X))<=>(~rich(X)|creative(X))))&
(![X]:((~funny(X)|~generous(X))<=>~tall(X)))&
((tall(fred))=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~patient(X)&rich(X))<=>~happy(X)))&
((~creative(susan)|tall(susan)))&
(humble(lucy))&
(?[X]:((~quiet(X)<~>~creative(X))))&
((humble(lucy)|~old(lucy)))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:((~tall(X)<~>~kind(X))))&
((wise(susan)<~>~patient(susan))) | ~creative(susan) | [] | null | 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either quiet or not kind is quiet or kind. If alice is not patient then mary is either creative or not brave. Everyone who is both tall and strong is both brave and generous and vice versa. Everyone who is funny or not wise is both tall and rich and vice versa. Everyone who is happy or not patient is patient. Everyone who is tall is both strong and humble and vice versa. If someone is either happy or brave then someone is not patient and vice versa. If someone is not kind then someone is brave or not creative. If lucy is brave or old then someone is either not strong or patient and vice versa. If alice is both not brave and humble then alice is either quiet or calm. If someone is either happy or not creative then someone is either not humble or patient. If paul is curious then susan is either not humble or old and vice versa. Everyone who is both rich and not creative is either not happy or curious. Everyone who is rich is not curious or creative. Someone is not rich or calm. Lucy is funny. Someone is either not old or brave. Someone is not creative or happy. Someone is creative or patient. John is either happy or not wise. Alice is either not kind or humble. Someone is either tall or not wise. | Alice is creative. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:((creative(X)|patient(X))))&
((happy(john)<~>~wise(john)))&
((~kind(alice)<~>humble(alice)))&
(?[X]:((tall(X)<~>~wise(X)))) | creative(alice) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1312997020483090111996631
% SZS output start Proof for 1312997020483090111996631
2. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (wise(X0) <~> ~funny(X0))) [input p1]
5. ! [X0] : ((strong(X0) & tall(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | happy(X0)) => patient(X0)) [input p6]
8. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p7]
9. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X0] : ~patient(X0) [input p8]
15. ! [X0] : ((~creative(X0) & rich(X0)) => (~happy(X0) <~> curious(X0))) [input p14]
16. ! [X0] : (rich(X0) => (creative(X0) | ~curious(X0))) [input p15]
23. ~kind(alice) <~> humble(alice) [input p22]
25. ~creative(alice) [input hypothesis]
26. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
32. ! [X0] : (patient(X0) | (patient(X0) & ~happy(X0))) [ennf transformation 7]
37. ! [X0] : ((~happy(X0) <~> curious(X0)) | (creative(X0) | ~rich(X0))) [ennf transformation 15]
38. ! [X0] : ((~happy(X0) <~> curious(X0)) | creative(X0) | ~rich(X0)) [flattening 37]
39. ! [X0] : ((creative(X0) | ~curious(X0)) | ~rich(X0)) [ennf transformation 16]
40. ! [X0] : (creative(X0) | ~curious(X0) | ~rich(X0)) [flattening 39]
43. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 2]
44. ! [X0] : ((~funny(X0) | ~kind(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) & (((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (funny(X0) & kind(X0)))) [flattening 43]
47. ! [X0] : (((strong(X0) & tall(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 5]
48. ! [X0] : (((strong(X0) & tall(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~strong(X0) | ~tall(X0))) [flattening 47]
49. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
50. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 49]
51. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 8]
52. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 51]
53. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 26]
54. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [rectify 53]
55. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) [choice axiom]
56. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
57. (((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [skolemisation 54,56,55]
72. ! [X0] : (((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | creative(X0) | ~rich(X0)) [nnf transformation 38]
83. (~humble(alice) | kind(alice)) & (humble(alice) | ~kind(alice)) [nnf transformation 23]
96. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 44]
97. ~funny(X0) | ~kind(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 44]
103. ~strong(X0) | brave(X0) | ~tall(X0) [cnf transformation 48]
107. ~funny(X0) | tall(X0) [cnf transformation 50]
108. wise(X0) | tall(X0) [cnf transformation 50]
110. rich(X0) | wise(X0) [cnf transformation 50]
113. patient(X0) | patient(X0) [cnf transformation 32]
114. ~tall(X0) | strong(X0) [cnf transformation 52]
115. ~tall(X0) | humble(X0) [cnf transformation 52]
118. ~patient(sK1) | happy(X3) | ~brave(X3) [cnf transformation 57]
138. ~rich(X0) | ~happy(X0) | creative(X0) | curious(X0) [cnf transformation 72]
140. ~curious(X0) | creative(X0) | ~rich(X0) [cnf transformation 40]
150. ~humble(alice) | kind(alice) [cnf transformation 83]
153. ~creative(alice) [cnf transformation 25]
154. patient(X0) [duplicate literal removal 113]
156. ~wise(X0) | funny(X0) [duplicate literal removal 96]
157. ~wise(X0) | ~kind(X0) | ~funny(X0) [duplicate literal removal 97]
172. ~brave(X3) | happy(X3) [subsumption resolution 118,154]
212. 12 <=> humble(alice) [avatar definition]
214. ~humble(alice) <- (~12) [avatar component clause 212]
294. 29 <=> kind(alice) [avatar definition]
296. kind(alice) <- (29) [avatar component clause 294]
297. 29 | ~12 [avatar split clause 150,212,294]
318. funny(X0) | tall(X0) [resolution 156,108]
320. tall(X0) [subsumption resolution 318,107]
323. humble(X0) [resolution 320,115]
324. strong(X1) [resolution 320,114]
380. $false <- (~12) [resolution 323,214]
384. 12 [avatar contradiction clause 380]
390. brave(X1) | ~tall(X1) [resolution 324,103]
392. brave(X1) [subsumption resolution 390,320]
418. ~happy(X0) | creative(X0) | curious(X0) | wise(X0) [resolution 138,110]
556. happy(X0) [resolution 392,172]
601. 55 <=> wise(alice) [avatar definition]
602. ~wise(alice) <- (~55) [avatar component clause 601]
603. wise(alice) <- (55) [avatar component clause 601]
609. curious(X0) | creative(X0) | wise(X0) [resolution 556,418]
619. ~kind(alice) | ~funny(alice) <- (55) [resolution 603,157]
620. funny(alice) <- (55) [resolution 603,156]
621. ~funny(alice) <- (29, 55) [subsumption resolution 619,296]
622. $false <- (29, 55) [subsumption resolution 620,621]
623. ~29 | ~55 [avatar contradiction clause 622]
660. creative(X1) | wise(X1) | creative(X1) | ~rich(X1) [resolution 609,140]
662. creative(X1) | wise(X1) | ~rich(X1) [duplicate literal removal 660]
673. creative(X1) | wise(X1) [subsumption resolution 662,110]
689. wise(alice) [resolution 673,153]
692. $false <- (~55) [subsumption resolution 689,602]
693. 55 [avatar contradiction clause 692]
694. $false [avatar sat refutation 297,384,623,693]
% SZS output end Proof for 1312997020483090111996631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either humble or tall then someone is calm.
Everyone who is creative or calm is kind and vice versa.
Everyone who is either not funny or kind is quiet.
Everyone who is either not generous or not wise is both humble and strong.
Everyone who is happy is not kind.
Everyone who is quiet or happy is both not happy and happy and vice versa.
If someone is not tall or not humble then someone is either not calm or brave and vice versa.
Everyone who is generous or not brave is both not wise and not brave and vice versa.
If someone is both creative and quiet then someone is either humble or rich and vice versa.
If alice is both not happy and not funny then someone is happy and vice versa.
If someone is calm or not patient then lucy is either not brave or not strong and vice versa.
If mary is both calm and wise then alice is both not quiet and brave.
If someone is either humble or not generous then someone is not calm or happy.
If someone is not happy or wise then someone is either humble or generous.
Everyone who is patient or strong is not happy and vice versa.
If someone is kind or creative then fred is not old and vice versa.
Someone is quiet or not tall.
Someone is not happy or not quiet.
Someone is both patient and not happy.
Fred is either kind or not calm.
Someone is not old.
Someone is wise. | Mary is not brave. | neutral | (((humble(john)<~>tall(john)))=>(?[X]:(calm(X))))&
(![X]:((creative(X)|calm(X))<=>kind(X)))&
(![X]:((~funny(X)<~>kind(X))=>quiet(X)))&
(![X]:((~generous(X)<~>~wise(X))=>(humble(X)&strong(X))))&
(![X]:(happy(X)=>~kind(X)))&
(![X]:((quiet(X)|happy(X))<=>(~happy(X)&happy(X))))&
((?[X]:((~tall(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((generous(X)|~brave(X))<=>(~wise(X)&~brave(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:((humble(X)<~>rich(X)))))&
(((~happy(alice)&~funny(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((~brave(lucy)<~>~strong(lucy))))&
(((calm(mary)&wise(mary)))=>((~quiet(alice)&brave(alice))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((~calm(X)|happy(X)))))&
((?[X]:((~happy(X)|wise(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((patient(X)|strong(X))<=>~happy(X)))&
((?[X]:((kind(X)|creative(X))))<=>(~old(fred)))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>~calm(fred)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X))) | ~brave(mary) | [] | null | 0 |
If paul is strong then someone is brave.
If john is both creative and not calm then someone is both not wise and not patient and vice versa.
If someone is tall or creative then someone is not generous and vice versa.
Everyone who is strong or kind is both funny and not strong and vice versa.
If fred is funny or curious then alice is not strong or kind and vice versa.
If someone is humble then someone is either not tall or strong and vice versa.
If someone is brave or tall then alice is both not rich and calm.
If someone is both wise and not patient then someone is not rich or not calm and vice versa.
Everyone who is not curious or not happy is curious and vice versa.
Everyone who is either not generous or not wise is funny.
Everyone who is wise or not calm is either not quiet or generous and vice versa.
Everyone who is not tall is strong and vice versa.
Everyone who is not humble or not old is funny or curious.
If susan is either not quiet or not patient then someone is either rich or creative and vice versa.
Mary is quiet or not calm.
Alice is funny or not tall.
Someone is not kind.
Someone is either not funny or generous.
Mary is kind or not brave.
Someone is both not kind and not brave.
Lucy is wise or not tall.
Someone is both not strong and not old. | Alice is not funny. | contradiction | ((strong(paul))=>(?[X]:(brave(X))))&
(((creative(john)&~calm(john)))<=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:((tall(X)|creative(X))))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)|kind(X))<=>(funny(X)&~strong(X))))&
(((funny(fred)|curious(fred)))<=>((~strong(alice)|kind(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
((?[X]:((brave(X)|tall(X))))=>((~rich(alice)&calm(alice))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~curious(X)|~happy(X))<=>curious(X)))&
(![X]:((~generous(X)<~>~wise(X))=>funny(X)))&
(![X]:((wise(X)|~calm(X))<=>(~quiet(X)<~>generous(X))))&
(![X]:(~tall(X)<=>strong(X)))&
(![X]:((~humble(X)|~old(X))=>(funny(X)|curious(X))))&
(((~quiet(susan)<~>~patient(susan)))<=>(?[X]:((rich(X)<~>creative(X)))))&
((quiet(mary)|~calm(mary)))&
((funny(alice)|~tall(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)<~>generous(X))))&
((kind(mary)|~brave(mary)))&
(?[X]:((~kind(X)&~brave(X))))&
((wise(lucy)|~tall(lucy)))&
(?[X]:((~strong(X)&~old(X)))) | ~funny(alice) | [
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2305637797952604536237988
% SZS output start Proof for 2305637797952604536237988
4. ! [X0] : ((kind(X0) | strong(X0)) <=> (~strong(X0) & funny(X0))) [input p3]
12. ! [X0] : (~tall(X0) <=> strong(X0)) [input p11]
16. ~tall(alice) | funny(alice) [input p15]
23. ~funny(alice) [input hypothesis]
44. ! [X0] : (((kind(X0) | strong(X0)) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | (~kind(X0) & ~strong(X0)))) [nnf transformation 4]
45. ! [X0] : ((kind(X0) | strong(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | (~kind(X0) & ~strong(X0)))) [flattening 44]
63. ! [X0] : ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))) [nnf transformation 12]
87. ~strong(X0) | ~strong(X0) [cnf transformation 45]
118. strong(X0) | tall(X0) [cnf transformation 63]
131. ~tall(alice) | funny(alice) [cnf transformation 16]
141. ~funny(alice) [cnf transformation 23]
144. ~strong(X0) [duplicate literal removal 87]
219. 17 <=> ! [X1] : tall(X1) [avatar definition]
220. tall(X1) <- (17) [avatar component clause 219]
280. tall(X0) [subsumption resolution 118,144]
281. 17 [avatar split clause 280,219]
322. 39 <=> funny(alice) [avatar definition]
326. 40 <=> tall(alice) [avatar definition]
328. ~tall(alice) <- (~40) [avatar component clause 326]
329. 39 | ~40 [avatar split clause 131,326,322]
358. ~39 [avatar split clause 141,322]
367. $false <- (17, ~40) [resolution 328,220]
368. ~17 | 40 [avatar contradiction clause 367]
369. $false [avatar sat refutation 281,329,358,368]
% SZS output end Proof for 2305637797952604536237988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not funny or not strong then someone is not calm and vice versa. If someone is both generous and not quiet then john is not humble or funny and vice versa. If someone is kind then lucy is both not patient and creative and vice versa. Everyone who is either not brave or not creative is both not generous and not rich and vice versa. Everyone who is creative or wise is generous and vice versa. Everyone who is old is not calm and vice versa. If someone is both patient and kind then mary is both not calm and not funny and vice versa. Everyone who is not wise or old is not patient and vice versa. Everyone who is both not tall and humble is both quiet and creative. Everyone who is brave is either not calm or not tall. If someone is not curious then fred is brave or funny and vice versa. If someone is rich or strong then john is curious. Everyone who is not humble is either not rich or tall and vice versa. If someone is either creative or not humble then alice is both not generous and creative and vice versa. If someone is not tall then someone is either not curious or not wise. If alice is funny then fred is not tall. John is both not kind and not patient. Susan is not humble or generous. Someone is strong or patient. John is not tall. Someone is either not creative or rich. Someone is not funny or not happy. | Lucy is humble. | neutral | (((~funny(alice)|~strong(alice)))<=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)&~quiet(X))))<=>((~humble(john)|funny(john))))&
((?[X]:(kind(X)))<=>((~patient(lucy)&creative(lucy))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~generous(X)&~rich(X))))&
(![X]:((creative(X)|wise(X))<=>generous(X)))&
(![X]:(old(X)<=>~calm(X)))&
((?[X]:((patient(X)&kind(X))))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~wise(X)|old(X))<=>~patient(X)))&
(![X]:((~tall(X)&humble(X))=>(quiet(X)&creative(X))))&
(![X]:(brave(X)=>(~calm(X)<~>~tall(X))))&
((?[X]:(~curious(X)))<=>((brave(fred)|funny(fred))))&
((?[X]:((rich(X)|strong(X))))=>(curious(john)))&
(![X]:(~humble(X)<=>(~rich(X)<~>tall(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>((~generous(alice)&creative(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
((funny(alice))=>(~tall(fred)))&
((~kind(john)&~patient(john)))&
((~humble(susan)|generous(susan)))&
(?[X]:((strong(X)|patient(X))))&
(~tall(john))&
(?[X]:((~creative(X)<~>rich(X))))&
(?[X]:((~funny(X)|~happy(X)))) | humble(lucy) | [] | null | 0 |
Everyone who is both not funny and calm is both humble and not humble and vice versa. Everyone who is either not brave or kind is both not wise and not strong and vice versa. If john is not wise or not quiet then someone is wise and vice versa. If someone is both not wise and generous then lucy is old. If john is either not old or strong then lucy is both wise and calm. If someone is not tall or tall then someone is happy or humble and vice versa. Everyone who is both not wise and creative is either curious or rich and vice versa. Everyone who is either not tall or quiet is either not tall or not wise and vice versa. Everyone who is both funny and not rich is either not funny or rich and vice versa. Everyone who is creative or funny is not quiet or not happy. Everyone who is tall is both not strong and quiet and vice versa. If susan is quiet then someone is calm and vice versa. If someone is both not kind and curious then someone is either generous or not curious. If someone is not rich then paul is either creative or not patient. Everyone who is either not happy or generous is curious or strong. Everyone who is both not patient and generous is not creative. John is funny or strong. Lucy is either old or funny. Someone is either not brave or not funny. Someone is both not patient and happy. Someone is brave or not strong. Fred is wise. Alice is not kind or wise. | Lucy is not creative. | neutral | (![X]:((~funny(X)&calm(X))<=>(humble(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~wise(X)&~strong(X))))&
(((~wise(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
((?[X]:((~wise(X)&generous(X))))=>(old(lucy)))&
(((~old(john)<~>strong(john)))=>((wise(lucy)&calm(lucy))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~wise(X)&creative(X))<=>(curious(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>~wise(X))))&
(![X]:((funny(X)&~rich(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((creative(X)|funny(X))=>(~quiet(X)|~happy(X))))&
(![X]:(tall(X)<=>(~strong(X)&quiet(X))))&
((quiet(susan))<=>(?[X]:(calm(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:(~rich(X)))=>((creative(paul)<~>~patient(paul))))&
(![X]:((~happy(X)<~>generous(X))=>(curious(X)|strong(X))))&
(![X]:((~patient(X)&generous(X))=>~creative(X)))&
((funny(john)|strong(john)))&
((old(lucy)<~>funny(lucy)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((brave(X)|~strong(X))))&
(wise(fred))&
((~kind(alice)|wise(alice))) | ~creative(lucy) | [] | null | 0 |
Everyone who is not funny is either kind or calm and vice versa.
Everyone who is happy is not wise or not strong and vice versa.
Everyone who is either old or not patient is both funny and kind.
If someone is not brave then john is wise.
Everyone who is kind is both not rich and funny and vice versa.
If someone is kind or not wise then someone is calm and vice versa.
Everyone who is brave is not strong or humble.
Everyone who is either strong or not calm is either rich or funny.
Everyone who is not generous is not strong or creative.
Everyone who is both not kind and not wise is brave or not rich and vice versa.
If paul is either strong or old then paul is either not rich or humble and vice versa.
Everyone who is not brave or not funny is not humble.
If paul is not humble then susan is either kind or funny and vice versa.
If susan is not tall then mary is either quiet or not creative.
Everyone who is both not wise and strong is both patient and calm and vice versa.
Everyone who is not patient is either not tall or generous and vice versa.
Someone is not generous.
Someone is not strong.
Paul is either not brave or kind.
John is either funny or rich.
Someone is not kind or quiet.
Fred is either patient or curious.
Lucy is both old and calm. | John is not funny. | entailment | (![X]:(~funny(X)<=>(kind(X)<~>calm(X))))&
(![X]:(happy(X)<=>(~wise(X)|~strong(X))))&
(![X]:((old(X)<~>~patient(X))=>(funny(X)&kind(X))))&
((?[X]:(~brave(X)))=>(wise(john)))&
(![X]:(kind(X)<=>(~rich(X)&funny(X))))&
((?[X]:((kind(X)|~wise(X))))<=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>(~strong(X)|humble(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>funny(X))))&
(![X]:(~generous(X)=>(~strong(X)|creative(X))))&
(![X]:((~kind(X)&~wise(X))<=>(brave(X)|~rich(X))))&
(((strong(paul)<~>old(paul)))<=>((~rich(paul)<~>humble(paul))))&
(![X]:((~brave(X)|~funny(X))=>~humble(X)))&
((~humble(paul))<=>((kind(susan)<~>funny(susan))))&
((~tall(susan))=>((quiet(mary)<~>~creative(mary))))&
(![X]:((~wise(X)&strong(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(~tall(X)<~>generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~strong(X)))&
((~brave(paul)<~>kind(paul)))&
((funny(john)<~>rich(john)))&
(?[X]:((~kind(X)|quiet(X))))&
((patient(fred)<~>curious(fred)))&
((old(lucy)&calm(lucy))) | ~funny(john) | [
"p3",
"p9",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8349236261478967540505706
% SZS output start Proof for 8349236261478967540505706
4. ? [X0] : ~brave(X0) => wise(john) [input p3]
10. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~rich(X0) | brave(X0))) [input p9]
19. ~brave(paul) <~> kind(paul) [input p18]
20. funny(john) <~> rich(john) [input p19]
24. funny(john) [input hypothesis]
27. wise(john) | ! [X0] : brave(X0) [ennf transformation 4]
45. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (wise(X0) | kind(X0)))) [nnf transformation 10]
46. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | wise(X0) | kind(X0))) [flattening 45]
57. (~kind(paul) | brave(paul)) & (kind(paul) | ~brave(paul)) [nnf transformation 19]
58. (~rich(john) | ~funny(john)) & (rich(john) | funny(john)) [nnf transformation 20]
70. wise(john) | brave(X0) [cnf transformation 27]
84. ~brave(X0) | ~kind(X0) [cnf transformation 46]
87. ~wise(X0) | rich(X0) [cnf transformation 46]
114. kind(paul) | ~brave(paul) [cnf transformation 57]
115. ~kind(paul) | brave(paul) [cnf transformation 57]
117. ~rich(john) | ~funny(john) [cnf transformation 58]
123. funny(john) [cnf transformation 24]
125. 1 <=> ! [X0] : brave(X0) [avatar definition]
126. brave(X0) <- (1) [avatar component clause 125]
128. 2 <=> wise(john) [avatar definition]
130. wise(john) <- (2) [avatar component clause 128]
131. 1 | 2 [avatar split clause 70,128,125]
210. ~kind(paul) [subsumption resolution 115,84]
211. ~brave(paul) [subsumption resolution 114,210]
213. 18 <=> funny(john) [avatar definition]
217. 19 <=> rich(john) [avatar definition]
219. ~rich(john) <- (~19) [avatar component clause 217]
220. ~18 | ~19 [avatar split clause 117,217,213]
241. 18 [avatar split clause 123,213]
246. rich(john) <- (2) [resolution 87,130]
247. $false <- (2, ~19) [subsumption resolution 246,219]
248. ~2 | 19 [avatar contradiction clause 247]
249. $false <- (1) [resolution 126,211]
252. ~1 [avatar contradiction clause 249]
253. $false [avatar sat refutation 131,220,241,248,252]
% SZS output end Proof for 8349236261478967540505706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is generous. If someone is both not happy and not funny then fred is both kind and rich and vice versa. Everyone who is both not quiet and not old is not rich or rich. If someone is not quiet or old then someone is both not generous and brave. Everyone who is both not kind and not calm is both funny and not creative. If fred is either creative or not old then someone is either not funny or not creative and vice versa. If john is both calm and funny then lucy is either generous or not quiet. Everyone who is brave is strong and vice versa. Everyone who is either kind or not generous is kind and vice versa. If alice is both curious and creative then john is quiet and vice versa. Everyone who is both not curious and wise is not patient. Everyone who is either not humble or not calm is old. If lucy is both rich and generous then someone is humble or happy. Everyone who is both not funny and not happy is rich. Everyone who is not funny or happy is generous. If someone is not old then john is both not rich and patient and vice versa. Someone is curious. Someone is not generous or not calm. John is not wise. Someone is either not funny or brave. Fred is both not old and not curious. Mary is either not rich or rich. Someone is either funny or not patient. | Fred is creative. | neutral | (![X]:(humble(X)=>generous(X)))&
((?[X]:((~happy(X)&~funny(X))))<=>((kind(fred)&rich(fred))))&
(![X]:((~quiet(X)&~old(X))=>(~rich(X)|rich(X))))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)&~creative(X))))&
(((creative(fred)<~>~old(fred)))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
(((calm(john)&funny(john)))=>((generous(lucy)<~>~quiet(lucy))))&
(![X]:(brave(X)<=>strong(X)))&
(![X]:((kind(X)<~>~generous(X))<=>kind(X)))&
(((curious(alice)&creative(alice)))<=>(quiet(john)))&
(![X]:((~curious(X)&wise(X))=>~patient(X)))&
(![X]:((~humble(X)<~>~calm(X))=>old(X)))&
(((rich(lucy)&generous(lucy)))=>(?[X]:((humble(X)|happy(X)))))&
(![X]:((~funny(X)&~happy(X))=>rich(X)))&
(![X]:((~funny(X)|happy(X))=>generous(X)))&
((?[X]:(~old(X)))<=>((~rich(john)&patient(john))))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|~calm(X))))&
(~wise(john))&
(?[X]:((~funny(X)<~>brave(X))))&
((~old(fred)&~curious(fred)))&
((~rich(mary)<~>rich(mary)))&
(?[X]:((funny(X)<~>~patient(X)))) | creative(fred) | [] | null | 0 |
Everyone who is either brave or not calm is quiet or not rich and vice versa.
If someone is not calm or strong then someone is curious or not brave and vice versa.
Everyone who is quiet is both patient and not funny and vice versa.
Everyone who is both not calm and kind is not funny or not patient and vice versa.
Everyone who is not quiet or strong is either not calm or not old and vice versa.
If someone is either brave or not brave then lucy is both not kind and strong.
If fred is both humble and not old then mary is either wise or tall.
If fred is either not happy or not quiet then someone is both not quiet and patient.
If someone is both happy and generous then someone is strong and vice versa.
If someone is both not patient and not happy then paul is both not strong and not creative.
Everyone who is either wise or brave is both not kind and wise.
Everyone who is both not curious and creative is either not funny or calm and vice versa.
If someone is either not kind or not strong then lucy is both not calm and old and vice versa.
Everyone who is tall or not wise is both not curious and brave.
If alice is both quiet and humble then lucy is curious and vice versa.
Someone is either not curious or old.
Someone is not rich.
Paul is not generous or not strong.
Lucy is not generous or not happy.
Fred is either curious or calm. | Lucy is funny. | entailment | (![X]:((brave(X)<~>~calm(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(patient(X)&~funny(X))))&
(![X]:((~calm(X)&kind(X))<=>(~funny(X)|~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((brave(X)<~>~brave(X))))=>((~kind(lucy)&strong(lucy))))&
(((humble(fred)&~old(fred)))=>((wise(mary)<~>tall(mary))))&
(((~happy(fred)<~>~quiet(fred)))=>(?[X]:((~quiet(X)&patient(X)))))&
((?[X]:((happy(X)&generous(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~patient(X)&~happy(X))))=>((~strong(paul)&~creative(paul))))&
(![X]:((wise(X)<~>brave(X))=>(~kind(X)&wise(X))))&
(![X]:((~curious(X)&creative(X))<=>(~funny(X)<~>calm(X))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>((~calm(lucy)&old(lucy))))&
(![X]:((tall(X)|~wise(X))=>(~curious(X)&brave(X))))&
(((quiet(alice)&humble(alice)))<=>(curious(lucy)))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:(~rich(X)))&
((~generous(paul)|~strong(paul)))&
((~generous(lucy)|~happy(lucy)))&
((curious(fred)<~>calm(fred))) | funny(lucy) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6512335487203787259589782
% SZS output start Proof for 6512335487203787259589782
4. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (~patient(X0) | ~funny(X0))) [input p3]
6. ? [X0] : (brave(X0) <~> ~brave(X0)) => (strong(lucy) & ~kind(lucy)) [input p5]
21. ~funny(lucy) [input hypothesis]
24. (strong(lucy) & ~kind(lucy)) | ! [X0] : (brave(X0) <=> ~brave(X0)) [ennf transformation 6]
40. ! [X0] : (((kind(X0) & ~calm(X0)) | (patient(X0) & funny(X0))) & ((~patient(X0) | ~funny(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 4]
41. ! [X0] : (((kind(X0) & ~calm(X0)) | (patient(X0) & funny(X0))) & (~patient(X0) | ~funny(X0) | ~kind(X0) | calm(X0))) [flattening 40]
44. (strong(lucy) & ~kind(lucy)) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))) [nnf transformation 24]
86. kind(X0) | funny(X0) [cnf transformation 41]
94. ~kind(lucy) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
95. ~kind(lucy) | brave(X0) | brave(X0) [cnf transformation 44]
139. ~funny(lucy) [cnf transformation 21]
141. ~kind(lucy) | ~brave(X0) [duplicate literal removal 94]
142. ~kind(lucy) | brave(X0) [duplicate literal removal 95]
146. 1 <=> ! [X1] : brave(X1) [avatar definition]
147. brave(X1) <- (1) [avatar component clause 146]
183. 10 <=> ! [X0] : ~brave(X0) [avatar definition]
184. ~brave(X0) <- (10) [avatar component clause 183]
187. 11 <=> kind(lucy) [avatar definition]
189. ~kind(lucy) <- (~11) [avatar component clause 187]
190. 1 | ~11 [avatar split clause 142,187,146]
191. 10 | ~11 [avatar split clause 141,187,183]
344. funny(lucy) <- (~11) [resolution 86,189]
345. $false <- (~11) [subsumption resolution 344,139]
346. 11 [avatar contradiction clause 345]
347. $false <- (1, 10) [subsumption resolution 147,184]
348. ~1 | ~10 [avatar contradiction clause 347]
349. $false [avatar sat refutation 190,191,346,348]
% SZS output end Proof for 6512335487203787259589782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not curious is either not wise or quiet and vice versa.
Everyone who is either not generous or brave is both not curious and wise and vice versa.
Everyone who is both wise and not generous is humble or wise.
Everyone who is either curious or not rich is either quiet or happy and vice versa.
If john is both not humble and not tall then someone is kind.
Everyone who is both calm and not funny is happy or not generous and vice versa.
Everyone who is both not old and creative is both kind and not funny.
Everyone who is not generous or creative is calm or not creative.
If someone is either not humble or not rich then someone is happy or funny and vice versa.
If someone is quiet then someone is both not quiet and kind.
Everyone who is humble or creative is both not quiet and not tall and vice versa.
If someone is not old or happy then paul is rich.
Everyone who is both not rich and humble is either strong or calm.
If someone is either happy or curious then alice is kind or creative.
Everyone who is both tall and not calm is happy.
Everyone who is both not brave and funny is generous or patient.
Susan is patient.
Someone is both brave and not funny.
Alice is quiet or tall.
Alice is kind.
Someone is both not funny and brave.
Someone is either happy or not tall.
Someone is either patient or not quiet.
Someone is wise or patient. | John is not humble. | neutral | (![X]:((rich(X)|~curious(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((~generous(X)<~>brave(X))<=>(~curious(X)&wise(X))))&
(![X]:((wise(X)&~generous(X))=>(humble(X)|wise(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(quiet(X)<~>happy(X))))&
(((~humble(john)&~tall(john)))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&~funny(X))<=>(happy(X)|~generous(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)&~funny(X))))&
(![X]:((~generous(X)|creative(X))=>(calm(X)|~creative(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)|creative(X))<=>(~quiet(X)&~tall(X))))&
((?[X]:((~old(X)|happy(X))))=>(rich(paul)))&
(![X]:((~rich(X)&humble(X))=>(strong(X)<~>calm(X))))&
((?[X]:((happy(X)<~>curious(X))))=>((kind(alice)|creative(alice))))&
(![X]:((tall(X)&~calm(X))=>happy(X)))&
(![X]:((~brave(X)&funny(X))=>(generous(X)|patient(X))))&
(patient(susan))&
(?[X]:((brave(X)&~funny(X))))&
((quiet(alice)|tall(alice)))&
(kind(alice))&
(?[X]:((~funny(X)&brave(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((wise(X)|patient(X)))) | ~humble(john) | [] | null | 0 |
If fred is both not calm and curious then fred is both not tall and not generous.
Everyone who is tall or not wise is both quiet and not happy.
If paul is both not creative and generous then someone is curious or not rich.
Everyone who is not calm or not wise is not happy or patient.
Everyone who is both happy and not wise is either not curious or not patient and vice versa.
If fred is not funny then paul is both not funny and quiet.
Everyone who is both not patient and wise is either not rich or humble and vice versa.
Everyone who is strong or tall is either not strong or happy and vice versa.
Everyone who is not patient is both generous and strong.
Everyone who is either kind or brave is both not rich and not funny and vice versa.
Everyone who is either not wise or rich is not happy.
If someone is both tall and strong then someone is generous or tall and vice versa.
If someone is both not quiet and humble then alice is not strong or not patient.
Everyone who is both creative and tall is either old or not old.
Everyone who is not rich is either not calm or kind and vice versa.
Everyone who is strong or not funny is quiet or not tall and vice versa.
Someone is not brave or not quiet.
Fred is not quiet or generous.
Someone is both quiet and curious.
Someone is not strong or quiet.
Susan is not rich or patient.
Someone is both strong and not kind.
Someone is either quiet or not quiet. | Paul is happy. | entailment | (((~calm(fred)&curious(fred)))=>((~tall(fred)&~generous(fred))))&
(![X]:((tall(X)|~wise(X))=>(quiet(X)&~happy(X))))&
(((~creative(paul)&generous(paul)))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((~calm(X)|~wise(X))=>(~happy(X)|patient(X))))&
(![X]:((happy(X)&~wise(X))<=>(~curious(X)<~>~patient(X))))&
((~funny(fred))=>((~funny(paul)&quiet(paul))))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((strong(X)|tall(X))<=>(~strong(X)<~>happy(X))))&
(![X]:(~patient(X)=>(generous(X)&strong(X))))&
(![X]:((kind(X)<~>brave(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~wise(X)<~>rich(X))=>~happy(X)))&
((?[X]:((tall(X)&strong(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((~quiet(X)&humble(X))))=>((~strong(alice)|~patient(alice))))&
(![X]:((creative(X)&tall(X))=>(old(X)<~>~old(X))))&
(![X]:(~rich(X)<=>(~calm(X)<~>kind(X))))&
(![X]:((strong(X)|~funny(X))<=>(quiet(X)|~tall(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((~quiet(fred)|generous(fred)))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((~strong(X)|quiet(X))))&
((~rich(susan)|patient(susan)))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | happy(paul) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6324339645751117437981351
% SZS output start Proof for 6324339645751117437981351
2. ! [X0] : ((~wise(X0) | tall(X0)) => (~happy(X0) & quiet(X0))) [input p1]
8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~strong(X0) <~> happy(X0))) [input p7]
12. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X0] : (tall(X0) | generous(X0)) [input p11]
24. ~happy(paul) [input hypothesis]
25. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X1] : (tall(X1) | generous(X1)) [rectify 12]
28. ! [X0] : ((~happy(X0) & quiet(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 2]
46. ! [X0] : (((tall(X0) | strong(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | strong(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [flattening 46]
51. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X1] : (tall(X1) | generous(X1)) | ! [X0] : (~strong(X0) | ~tall(X0))) [nnf transformation 25]
52. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X2] : (tall(X2) | generous(X2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [rectify 51]
53. ? [X0] : (strong(X0) & tall(X0)) => (strong(sK1) & tall(sK1)) [choice axiom]
54. ? [X2] : (tall(X2) | generous(X2)) => (tall(sK2) | generous(sK2)) [choice axiom]
55. ((strong(sK1) & tall(sK1)) | ! [X1] : (~tall(X1) & ~generous(X1))) & ((tall(sK2) | generous(sK2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [skolemisation 52,54,53]
75. ~happy(X0) | ~tall(X0) [cnf transformation 28]
94. happy(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 47]
95. happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 47]
98. tall(X0) | strong(X0) | happy(X0) | strong(X0) [cnf transformation 47]
112. tall(sK1) | ~tall(X1) [cnf transformation 55]
114. strong(sK1) | ~tall(X1) [cnf transformation 55]
136. ~happy(paul) [cnf transformation 24]
137. ~strong(X0) | happy(X0) [duplicate literal removal 94]
138. strong(X0) | tall(X0) | happy(X0) [duplicate literal removal 98]
188. ~strong(X0) | ~tall(X0) [subsumption resolution 95,75]
191. 12 <=> ! [X1] : ~tall(X1) [avatar definition]
192. ~tall(X1) <- (12) [avatar component clause 191]
194. 13 <=> strong(sK1) [avatar definition]
196. strong(sK1) <- (13) [avatar component clause 194]
197. 12 | 13 [avatar split clause 114,194,191]
203. 15 <=> tall(sK1) [avatar definition]
206. 12 | 15 [avatar split clause 112,203,191]
265. ~tall(sK1) <- (13) [resolution 188,196]
269. ~15 | ~13 [avatar split clause 265,194,203]
365. tall(X1) | happy(X1) | happy(X1) [resolution 138,137]
367. tall(X1) | happy(X1) [duplicate literal removal 365]
369. happy(X1) <- (12) [subsumption resolution 367,192]
373. $false <- (12) [resolution 369,136]
377. ~12 [avatar contradiction clause 373]
378. $false [avatar sat refutation 197,206,269,377]
% SZS output end Proof for 6324339645751117437981351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not kind is either wise or creative and vice versa.
If john is both rich and not wise then someone is both brave and not curious and vice versa.
If someone is either tall or patient then alice is either not calm or not quiet.
If someone is either creative or not patient then susan is either funny or kind and vice versa.
If someone is humble or not wise then lucy is both old and patient.
Everyone who is not curious is not brave or not tall.
Everyone who is not kind or brave is calm or not funny and vice versa.
Everyone who is both not generous and humble is happy.
If alice is either creative or kind then someone is either not happy or happy and vice versa.
Everyone who is both not curious and not kind is either brave or generous.
Everyone who is both not funny and brave is not funny or not curious.
Everyone who is not wise or not tall is both not humble and not old.
Everyone who is funny is both rich and not quiet and vice versa.
If alice is either tall or not rich then someone is wise or not quiet.
Everyone who is creative or brave is patient.
Everyone who is tall is both kind and quiet.
Someone is not rich or old.
Someone is either not kind or kind.
Someone is both not funny and not old.
Someone is both generous and funny.
Someone is wise or not rich.
Lucy is not strong.
John is old or curious.
Paul is not quiet. | Paul is not old. | entailment | (![X]:((calm(X)<~>~kind(X))<=>(wise(X)<~>creative(X))))&
(((rich(john)&~wise(john)))<=>(?[X]:((brave(X)&~curious(X)))))&
((?[X]:((tall(X)<~>patient(X))))=>((~calm(alice)<~>~quiet(alice))))&
((?[X]:((creative(X)<~>~patient(X))))<=>((funny(susan)<~>kind(susan))))&
((?[X]:((humble(X)|~wise(X))))=>((old(lucy)&patient(lucy))))&
(![X]:(~curious(X)=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)|brave(X))<=>(calm(X)|~funny(X))))&
(![X]:((~generous(X)&humble(X))=>happy(X)))&
(((creative(alice)<~>kind(alice)))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((~curious(X)&~kind(X))=>(brave(X)<~>generous(X))))&
(![X]:((~funny(X)&brave(X))=>(~funny(X)|~curious(X))))&
(![X]:((~wise(X)|~tall(X))=>(~humble(X)&~old(X))))&
(![X]:(funny(X)<=>(rich(X)&~quiet(X))))&
(((tall(alice)<~>~rich(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>patient(X)))&
(![X]:(tall(X)=>(kind(X)&quiet(X))))&
(?[X]:((~rich(X)|old(X))))&
(?[X]:((~kind(X)<~>kind(X))))&
(?[X]:((~funny(X)&~old(X))))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((wise(X)|~rich(X))))&
(~strong(lucy))&
((old(john)|curious(john)))&
(~quiet(paul)) | ~old(paul) | [
"p11",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4663584418896578764473373
% SZS output start Proof for 4663584418896578764473373
12. ! [X0] : ((~tall(X0) | ~wise(X0)) => (~old(X0) & ~humble(X0))) [input p11]
16. ! [X0] : (tall(X0) => (quiet(X0) & kind(X0))) [input p15]
24. ~quiet(paul) [input p23]
25. old(paul) [input hypothesis]
29. ! [X0] : ((~tall(X0) | ~wise(X0)) => ~old(X0)) [pure predicate removal 12]
38. ! [X0] : (~old(X0) | (tall(X0) & wise(X0))) [ennf transformation 29]
41. ! [X0] : ((quiet(X0) & kind(X0)) | ~tall(X0)) [ennf transformation 16]
119. ~old(X0) | tall(X0) [cnf transformation 38]
128. ~tall(X0) | quiet(X0) [cnf transformation 41]
138. ~quiet(paul) [cnf transformation 24]
139. old(paul) [cnf transformation 25]
298. tall(paul) [resolution 119,139]
306. quiet(paul) [resolution 128,298]
308. $false [subsumption resolution 306,138]
% SZS output end Proof for 4663584418896578764473373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or humble is not brave and vice versa. If someone is either strong or old then someone is not curious or kind and vice versa. If someone is brave then someone is both not calm and not brave. If fred is both not strong and not humble then someone is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. If lucy is curious or kind then mary is not brave and vice versa. Someone is happy or rich. Someone is generous. Susan is kind or not kind. Someone is either calm or not kind. Someone is both not kind and not generous. Someone is not quiet or not patient. Someone is rich or calm. | Susan is tall. | contradiction | (![X]:((~humble(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:((~curious(X)|kind(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(((~strong(fred)&~humble(fred)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X)))) | tall(susan) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6817610475840607976926448
% SZS output start Proof for 6817610475840607976926448
1. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~brave(X0)) [input p0]
5. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p4]
8. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p7]
9. ! [X0] : (old(X0) => brave(X0)) [input p8]
11. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~happy(X0) | old(X0))) [input p10]
22. tall(susan) [input hypothesis]
34. ! [X0] : (brave(X0) | ~old(X0)) [ennf transformation 9]
35. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | brave(X0)) & (~brave(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 1]
47. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 5]
49. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0) | tall(X0))) [flattening 49]
51. ! [X0] : (((~curious(X0) | ~calm(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 11]
52. ! [X0] : ((~curious(X0) | ~calm(X0) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | (curious(X0) & calm(X0)))) [flattening 51]
75. ~brave(X0) | humble(X0) | humble(X0) [cnf transformation 35]
76. ~brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 35]
90. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 47]
92. kind(X0) | kind(X0) | happy(X0) [cnf transformation 47]
97. ~tall(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 50]
101. brave(X0) | ~old(X0) [cnf transformation 34]
102. ~happy(X0) | old(X0) | calm(X0) [cnf transformation 52]
122. tall(susan) [cnf transformation 22]
123. happy(X0) | ~kind(X0) [duplicate literal removal 90]
124. happy(X0) | kind(X0) [duplicate literal removal 92]
125. ~brave(X0) | humble(X0) [duplicate literal removal 75]
126. ~brave(X0) | ~humble(X0) [duplicate literal removal 76]
127. ~brave(X0) [subsumption resolution 125,126]
176. happy(X0) [subsumption resolution 123,124]
178. ~tall(X0) | ~calm(X0) [subsumption resolution 97,176]
180. ~old(X0) [subsumption resolution 101,127]
184. old(X0) | calm(X0) [subsumption resolution 102,176]
185. calm(X0) [subsumption resolution 184,180]
226. ~calm(susan) [resolution 178,122]
227. $false [subsumption resolution 226,185]
% SZS output end Proof for 6817610475840607976926448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and strong is both not happy and not kind.
If someone is either kind or not tall then mary is not tall.
If someone is not strong then someone is not tall.
Everyone who is either generous or not calm is both rich and quiet.
Everyone who is not quiet is either not humble or wise.
If someone is tall then someone is happy and vice versa.
If someone is both not creative and not patient then someone is curious or old.
If susan is either not kind or not calm then alice is either not happy or strong.
If mary is tall or not tall then paul is not wise and vice versa.
Everyone who is either patient or generous is not curious or not funny and vice versa.
If someone is either not old or not happy then john is either kind or funny and vice versa.
Everyone who is either not humble or not patient is either rich or not rich and vice versa.
Everyone who is not old or not tall is both rich and kind.
Everyone who is humble or wise is strong.
Everyone who is wise is creative or not generous and vice versa.
Everyone who is not old is either happy or calm and vice versa.
Paul is both not happy and not patient.
John is not funny.
Mary is tall or brave.
Fred is not curious.
Someone is not strong or not funny.
Mary is either not generous or funny.
Someone is creative or happy.
Alice is either curious or strong. | Paul is not tall. | contradiction | (![X]:((quiet(X)&strong(X))=>(~happy(X)&~kind(X))))&
((?[X]:((kind(X)<~>~tall(X))))=>(~tall(mary)))&
((?[X]:(~strong(X)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~calm(X))=>(rich(X)&quiet(X))))&
(![X]:(~quiet(X)=>(~humble(X)<~>wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((curious(X)|old(X)))))&
(((~kind(susan)<~>~calm(susan)))=>((~happy(alice)<~>strong(alice))))&
(((tall(mary)|~tall(mary)))<=>(~wise(paul)))&
(![X]:((patient(X)<~>generous(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((~old(X)<~>~happy(X))))<=>((kind(john)<~>funny(john))))&
(![X]:((~humble(X)<~>~patient(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((~old(X)|~tall(X))=>(rich(X)&kind(X))))&
(![X]:((humble(X)|wise(X))=>strong(X)))&
(![X]:(wise(X)<=>(creative(X)|~generous(X))))&
(![X]:(~old(X)<=>(happy(X)<~>calm(X))))&
((~happy(paul)&~patient(paul)))&
(~funny(john))&
((tall(mary)|brave(mary)))&
(~curious(fred))&
(?[X]:((~strong(X)|~funny(X))))&
((~generous(mary)<~>funny(mary)))&
(?[X]:((creative(X)|happy(X))))&
((curious(alice)<~>strong(alice))) | ~tall(paul) | [
"p0",
"p4",
"p8",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3803700135316229243113217
% SZS output start Proof for 3803700135316229243113217
1. ! [X0] : ((strong(X0) & quiet(X0)) => (~kind(X0) & ~happy(X0))) [input p0]
5. ! [X0] : (~quiet(X0) => (~humble(X0) <~> wise(X0))) [input p4]
9. (~tall(mary) | tall(mary)) <=> ~wise(paul) [input p8]
12. ! [X0] : ((~humble(X0) <~> ~patient(X0)) <=> (rich(X0) <~> ~rich(X0))) [input p11]
13. ! [X0] : ((~tall(X0) | ~old(X0)) => (kind(X0) & rich(X0))) [input p12]
14. ! [X0] : ((wise(X0) | humble(X0)) => strong(X0)) [input p13]
17. ~patient(paul) & ~happy(paul) [input p16]
25. ~tall(paul) [input hypothesis]
30. ! [X0] : ((~kind(X0) & ~happy(X0)) | (~strong(X0) | ~quiet(X0))) [ennf transformation 1]
31. ! [X0] : ((~kind(X0) & ~happy(X0)) | ~strong(X0) | ~quiet(X0)) [flattening 30]
35. ! [X0] : ((~humble(X0) <~> wise(X0)) | quiet(X0)) [ennf transformation 5]
38. ! [X0] : ((kind(X0) & rich(X0)) | (tall(X0) & old(X0))) [ennf transformation 13]
39. ! [X0] : (strong(X0) | (~wise(X0) & ~humble(X0))) [ennf transformation 14]
45. ! [X0] : (((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 35]
55. ((~tall(mary) | tall(mary)) | wise(paul)) & (~wise(paul) | (tall(mary) & ~tall(mary))) [nnf transformation 9]
56. (~tall(mary) | tall(mary) | wise(paul)) & (~wise(paul) | (tall(mary) & ~tall(mary))) [flattening 55]
63. ! [X0] : ((((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) & (((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0))))) [nnf transformation 12]
74. ~kind(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 31]
82. ~humble(X0) | wise(X0) | quiet(X0) [cnf transformation 45]
91. ~wise(paul) | ~tall(mary) [cnf transformation 56]
92. ~wise(paul) | tall(mary) [cnf transformation 56]
114. patient(X0) | humble(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
115. patient(X0) | humble(X0) | rich(X0) | rich(X0) [cnf transformation 63]
119. kind(X0) | tall(X0) [cnf transformation 38]
120. ~humble(X0) | strong(X0) [cnf transformation 39]
130. ~patient(paul) [cnf transformation 17]
139. ~tall(paul) [cnf transformation 25]
142. patient(X0) | humble(X0) | ~rich(X0) [duplicate literal removal 114]
143. patient(X0) | humble(X0) | rich(X0) [duplicate literal removal 115]
145. 1 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
146. tall(X0) | kind(X0) <- (1) [avatar component clause 145]
148. 2 <=> tall(mary) [avatar definition]
213. 17 <=> wise(paul) [avatar definition]
215. ~wise(paul) <- (~17) [avatar component clause 213]
216. 2 | ~17 [avatar split clause 92,213,148]
217. ~2 | ~17 [avatar split clause 91,213,148]
248. patient(X0) | humble(X0) [subsumption resolution 142,143]
250. 1 [avatar split clause 119,145]
295. kind(paul) <- (1) [resolution 146,139]
299. humble(paul) [resolution 248,130]
305. strong(paul) [resolution 299,120]
318. ~strong(paul) | ~quiet(paul) <- (1) [resolution 74,295]
321. ~quiet(paul) <- (1) [subsumption resolution 318,305]
367. wise(paul) | quiet(paul) [resolution 82,299]
368. quiet(paul) <- (~17) [subsumption resolution 367,215]
369. $false <- (1, ~17) [subsumption resolution 368,321]
370. ~1 | 17 [avatar contradiction clause 369]
371. $false [avatar sat refutation 216,217,250,370]
% SZS output end Proof for 3803700135316229243113217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both quiet and not old then susan is kind or not wise and vice versa.
If someone is either not funny or not generous then someone is not tall and vice versa.
Everyone who is both curious and funny is not wise.
If paul is either not brave or happy then lucy is not wise or not creative.
Everyone who is strong is not calm.
If someone is either curious or old then susan is generous or not wise.
Everyone who is both kind and patient is strong or not generous and vice versa.
If someone is funny then someone is either strong or brave.
If paul is both not old and not happy then susan is either wise or not humble.
Everyone who is calm or quiet is both not patient and not funny and vice versa.
Everyone who is not happy is generous and vice versa.
Everyone who is calm is not rich.
Everyone who is either not quiet or strong is strong and vice versa.
If someone is either not humble or not brave then susan is happy and vice versa.
If someone is not generous then someone is creative and vice versa.
If someone is both tall and not funny then alice is curious or not brave.
Someone is humble or not rich.
Lucy is not funny.
Someone is both not old and quiet.
Mary is either creative or quiet.
Someone is either kind or calm.
Paul is either not humble or calm.
Fred is old or not brave.
Mary is wise. | Susan is not creative. | entailment | (((quiet(mary)&~old(mary)))<=>((kind(susan)|~wise(susan))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)&funny(X))=>~wise(X)))&
(((~brave(paul)<~>happy(paul)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:(strong(X)=>~calm(X)))&
((?[X]:((curious(X)<~>old(X))))=>((generous(susan)|~wise(susan))))&
(![X]:((kind(X)&patient(X))<=>(strong(X)|~generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~old(paul)&~happy(paul)))=>((wise(susan)<~>~humble(susan))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:(calm(X)=>~rich(X)))&
(![X]:((~quiet(X)<~>strong(X))<=>strong(X)))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(happy(susan)))&
((?[X]:(~generous(X)))<=>(?[X]:(creative(X))))&
((?[X]:((tall(X)&~funny(X))))=>((curious(alice)|~brave(alice))))&
(?[X]:((humble(X)|~rich(X))))&
(~funny(lucy))&
(?[X]:((~old(X)&quiet(X))))&
((creative(mary)<~>quiet(mary)))&
(?[X]:((kind(X)<~>calm(X))))&
((~humble(paul)<~>calm(paul)))&
((old(fred)|~brave(fred)))&
(wise(mary)) | ~creative(susan) | [
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5832851637867452436234181
% SZS output start Proof for 5832851637867452436234181
7. ! [X0] : ((patient(X0) & kind(X0)) <=> (~generous(X0) | strong(X0))) [input p6]
10. ! [X0] : ((quiet(X0) | calm(X0)) <=> (~funny(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~quiet(X0) <~> strong(X0)) <=> strong(X0)) [input p12]
15. ? [X0] : ~generous(X0) <=> ? [X0] : creative(X0) [input p14]
25. creative(susan) [input hypothesis]
28. ? [X0] : ~generous(X0) <=> ? [X1] : creative(X1) [rectify 15]
52. ! [X0] : (((patient(X0) & kind(X0)) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | (~patient(X0) | ~kind(X0)))) [nnf transformation 7]
53. ! [X0] : (((patient(X0) & kind(X0)) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | ~patient(X0) | ~kind(X0))) [flattening 52]
59. ! [X0] : (((quiet(X0) | calm(X0)) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 10]
60. ! [X0] : ((quiet(X0) | calm(X0) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 59]
62. ! [X0] : ((((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~strong(X0)) & (strong(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0))))) [nnf transformation 13]
67. (? [X0] : ~generous(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : generous(X0)) [nnf transformation 28]
68. (? [X0] : ~generous(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : generous(X3)) [rectify 67]
69. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
70. ? [X2] : creative(X2) => creative(sK5) [choice axiom]
71. (~generous(sK4) | ! [X1] : ~creative(X1)) & (creative(sK5) | ! [X3] : generous(X3)) [skolemisation 68,70,69]
98. patient(X0) | generous(X0) [cnf transformation 53]
104. ~patient(X0) | ~quiet(X0) [cnf transformation 60]
110. strong(X0) | strong(X0) | quiet(X0) [cnf transformation 62]
113. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 62]
119. ~generous(sK4) | ~creative(X1) [cnf transformation 71]
132. creative(susan) [cnf transformation 25]
133. strong(X0) | quiet(X0) [duplicate literal removal 110]
134. ~strong(X0) | quiet(X0) [duplicate literal removal 113]
234. quiet(X0) [subsumption resolution 133,134]
258. 28 <=> ! [X1] : ~creative(X1) [avatar definition]
259. ~creative(X1) <- (28) [avatar component clause 258]
261. 29 <=> generous(sK4) [avatar definition]
263. ~generous(sK4) <- (~29) [avatar component clause 261]
264. 28 | ~29 [avatar split clause 119,261,258]
266. 30 <=> ! [X3] : generous(X3) [avatar definition]
267. generous(X3) <- (30) [avatar component clause 266]
315. $false <- (~29, 30) [subsumption resolution 263,267]
316. 29 | ~30 [avatar contradiction clause 315]
322. $false <- (28) [resolution 259,132]
323. ~28 [avatar contradiction clause 322]
330. ~quiet(X0) | generous(X0) [resolution 104,98]
333. generous(X0) [subsumption resolution 330,234]
334. 30 [avatar split clause 333,266]
335. $false [avatar sat refutation 264,316,323,334]
% SZS output end Proof for 5832851637867452436234181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not wise is curious or happy and vice versa. Everyone who is not tall is wise or quiet. Everyone who is both not creative and not quiet is not strong or old and vice versa. If someone is both not old and kind then someone is both not funny and funny. If someone is either calm or kind then someone is curious and vice versa. Everyone who is either brave or not strong is tall. Everyone who is brave or wise is both strong and not strong and vice versa. If mary is both not creative and not funny then someone is kind or funny. Everyone who is either curious or strong is both strong and creative and vice versa. If someone is either not generous or not happy then someone is either curious or quiet and vice versa. If someone is humble then alice is both not generous and not calm and vice versa. If someone is not calm then fred is either brave or humble and vice versa. Everyone who is not patient or creative is both creative and not generous and vice versa. Everyone who is quiet is either not strong or brave and vice versa. Everyone who is not wise or not tall is not curious and vice versa. Everyone who is funny is quiet or creative and vice versa. Susan is both creative and not rich. Lucy is tall. Alice is not kind. Someone is either calm or not patient. | Mary is brave. | contradiction | (![X]:((tall(X)<~>~wise(X))<=>(curious(X)|happy(X))))&
(![X]:(~tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|old(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)<~>~strong(X))=>tall(X)))&
(![X]:((brave(X)|wise(X))<=>(strong(X)&~strong(X))))&
(((~creative(mary)&~funny(mary)))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(strong(X)&creative(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:(humble(X)))<=>((~generous(alice)&~calm(alice))))&
((?[X]:(~calm(X)))<=>((brave(fred)<~>humble(fred))))&
(![X]:((~patient(X)|creative(X))<=>(creative(X)&~generous(X))))&
(![X]:(quiet(X)<=>(~strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~tall(X))<=>~curious(X)))&
(![X]:(funny(X)<=>(quiet(X)|creative(X))))&
((creative(susan)&~rich(susan)))&
(tall(lucy))&
(~kind(alice))&
(?[X]:((calm(X)<~>~patient(X)))) | brave(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4862034851928514862227836
% SZS output start Proof for 4862034851928514862227836
7. ! [X0] : ((wise(X0) | brave(X0)) <=> (~strong(X0) & strong(X0))) [input p6]
21. brave(mary) [input hypothesis]
45. ! [X0] : (((wise(X0) | brave(X0)) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 7]
46. ! [X0] : ((wise(X0) | brave(X0) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 45]
95. strong(X0) | ~brave(X0) [cnf transformation 46]
97. ~strong(X0) | ~brave(X0) [cnf transformation 46]
142. brave(mary) [cnf transformation 21]
180. ~brave(X0) [subsumption resolution 95,97]
286. $false [subsumption resolution 142,180]
% SZS output end Proof for 4862034851928514862227836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind. | John is calm. | neutral | ((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice))) | calm(john) | [] | null | 0 |
Everyone who is both not patient and generous is either generous or strong. If fred is either funny or not calm then someone is not rich and vice versa. If someone is not patient or not tall then john is either not curious or kind. If susan is tall then someone is not strong and vice versa. Everyone who is both not generous and creative is not calm. If someone is not old or quiet then someone is not kind and vice versa. Everyone who is not quiet is not generous and vice versa. If someone is generous then fred is both kind and not kind and vice versa. Everyone who is either calm or tall is kind and vice versa. Everyone who is not old is not creative. Everyone who is either happy or quiet is not old and vice versa. If someone is curious then someone is creative or not funny and vice versa. Everyone who is wise is funny and vice versa. If someone is not humble then john is both funny and tall and vice versa. Everyone who is old is both not rich and not happy. Everyone who is not curious is not old. Someone is happy or not strong. Fred is strong. Fred is not rich. Someone is either brave or not quiet. Lucy is either funny or rich. Someone is not wise or funny. John is not quiet or not humble. | John is rich. | neutral | (![X]:((~patient(X)&generous(X))=>(generous(X)<~>strong(X))))&
(((funny(fred)<~>~calm(fred)))<=>(?[X]:(~rich(X))))&
((?[X]:((~patient(X)|~tall(X))))=>((~curious(john)<~>kind(john))))&
((tall(susan))<=>(?[X]:(~strong(X))))&
(![X]:((~generous(X)&creative(X))=>~calm(X)))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:(~kind(X))))&
(![X]:(~quiet(X)<=>~generous(X)))&
((?[X]:(generous(X)))<=>((kind(fred)&~kind(fred))))&
(![X]:((calm(X)<~>tall(X))<=>kind(X)))&
(![X]:(~old(X)=>~creative(X)))&
(![X]:((happy(X)<~>quiet(X))<=>~old(X)))&
((?[X]:(curious(X)))<=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:(wise(X)<=>funny(X)))&
((?[X]:(~humble(X)))<=>((funny(john)&tall(john))))&
(![X]:(old(X)=>(~rich(X)&~happy(X))))&
(![X]:(~curious(X)=>~old(X)))&
(?[X]:((happy(X)|~strong(X))))&
(strong(fred))&
(~rich(fred))&
(?[X]:((brave(X)<~>~quiet(X))))&
((funny(lucy)<~>rich(lucy)))&
(?[X]:((~wise(X)|funny(X))))&
((~quiet(john)|~humble(john))) | rich(john) | [] | null | 0 |
If someone is both brave and curious then someone is tall. If alice is generous or not kind then lucy is wise and vice versa. Everyone who is either not brave or funny is wise and vice versa. If paul is either happy or not humble then someone is both not generous and creative. Everyone who is brave or kind is wise. If someone is both not happy and not humble then someone is not brave or humble and vice versa. Everyone who is brave or strong is not brave and vice versa. Everyone who is both rich and not tall is either tall or not tall. If someone is not funny or not strong then someone is humble or not quiet. Everyone who is either not strong or strong is either creative or not humble. If someone is funny then alice is either not rich or not happy and vice versa. If alice is rich then mary is curious and vice versa. Everyone who is both quiet and curious is not calm or calm. Everyone who is not generous or funny is not creative. If john is either tall or quiet then john is generous and vice versa. Everyone who is not calm or calm is either not kind or humble. Someone is not happy. Lucy is both wise and not brave. Someone is either rich or not rich. Someone is funny. Alice is funny. Someone is either curious or creative. Someone is not patient. | Alice is not creative. | entailment | ((?[X]:((brave(X)&curious(X))))=>(?[X]:(tall(X))))&
(((generous(alice)|~kind(alice)))<=>(wise(lucy)))&
(![X]:((~brave(X)<~>funny(X))<=>wise(X)))&
(((happy(paul)<~>~humble(paul)))=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:((brave(X)|kind(X))=>wise(X)))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((brave(X)|strong(X))<=>~brave(X)))&
(![X]:((rich(X)&~tall(X))=>(tall(X)<~>~tall(X))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>((~rich(alice)<~>~happy(alice))))&
((rich(alice))<=>(curious(mary)))&
(![X]:((quiet(X)&curious(X))=>(~calm(X)|calm(X))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(((tall(john)<~>quiet(john)))<=>(generous(john)))&
(![X]:((~calm(X)|calm(X))=>(~kind(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((wise(lucy)&~brave(lucy)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
(funny(alice))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:(~patient(X))) | ~creative(alice) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5178131247808698731307191
% SZS output start Proof for 5178131247808698731307191
14. ! [X0] : ((funny(X0) | ~generous(X0)) => ~creative(X0)) [input p13]
21. funny(alice) [input p20]
24. creative(alice) [input hypothesis]
38. ! [X0] : (~creative(X0) | (~funny(X0) & generous(X0))) [ennf transformation 14]
116. ~creative(X0) | ~funny(X0) [cnf transformation 38]
131. funny(alice) [cnf transformation 21]
134. creative(alice) [cnf transformation 24]
290. ~funny(alice) [resolution 116,134]
291. $false [subsumption resolution 290,131]
% SZS output end Proof for 5178131247808698731307191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and funny is either not curious or generous. Everyone who is not generous or not old is creative. Everyone who is funny is either not creative or tall and vice versa. If alice is either not happy or not generous then paul is calm and vice versa. Everyone who is not funny is not generous. Everyone who is not quiet is patient or quiet. If susan is either not kind or not generous then paul is not curious. Everyone who is either not calm or creative is either rich or not rich and vice versa. If someone is patient then someone is not strong or not rich. Everyone who is not rich is not tall. If someone is not kind or not strong then someone is either calm or rich and vice versa. Everyone who is both not rich and not patient is strong and vice versa. Everyone who is creative or patient is not rich and vice versa. If lucy is either not tall or not old then mary is both not wise and strong. Everyone who is not quiet or old is not creative. If someone is both curious and old then john is either not patient or not wise. Fred is funny. Someone is either old or not tall. Someone is tall or not tall. Fred is rich or generous. Susan is both not kind and funny. Someone is brave. Lucy is not kind. Alice is creative or not kind. | Paul is generous. | contradiction | (![X]:((~tall(X)&funny(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~generous(X)|~old(X))=>creative(X)))&
(![X]:(funny(X)<=>(~creative(X)<~>tall(X))))&
(((~happy(alice)<~>~generous(alice)))<=>(calm(paul)))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:(~quiet(X)=>(patient(X)|quiet(X))))&
(((~kind(susan)<~>~generous(susan)))=>(~curious(paul)))&
(![X]:((~calm(X)<~>creative(X))<=>(rich(X)<~>~rich(X))))&
((?[X]:(patient(X)))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:(~rich(X)=>~tall(X)))&
((?[X]:((~kind(X)|~strong(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~rich(X)&~patient(X))<=>strong(X)))&
(![X]:((creative(X)|patient(X))<=>~rich(X)))&
(((~tall(lucy)<~>~old(lucy)))=>((~wise(mary)&strong(mary))))&
(![X]:((~quiet(X)|old(X))=>~creative(X)))&
((?[X]:((curious(X)&old(X))))=>((~patient(john)<~>~wise(john))))&
(funny(fred))&
(?[X]:((old(X)<~>~tall(X))))&
(?[X]:((tall(X)|~tall(X))))&
((rich(fred)|generous(fred)))&
((~kind(susan)&funny(susan)))&
(?[X]:(brave(X)))&
(~kind(lucy))&
((creative(alice)|~kind(alice))) | generous(paul) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3192620031687894786329059
% SZS output start Proof for 3192620031687894786329059
1. ! [X0] : ((funny(X0) & ~tall(X0)) => (~curious(X0) <~> generous(X0))) [input p0]
2. ! [X0] : ((~old(X0) | ~generous(X0)) => creative(X0)) [input p1]
3. ! [X0] : (funny(X0) <=> (~creative(X0) <~> tall(X0))) [input p2]
5. ! [X0] : (~funny(X0) => ~generous(X0)) [input p4]
7. (~kind(susan) <~> ~generous(susan)) => ~curious(paul) [input p6]
10. ! [X0] : (~rich(X0) => ~tall(X0)) [input p9]
13. ! [X0] : ((patient(X0) | creative(X0)) <=> ~rich(X0)) [input p12]
21. funny(susan) & ~kind(susan) [input p20]
25. generous(paul) [input hypothesis]
31. ! [X0] : ((~curious(X0) <~> generous(X0)) | (~funny(X0) | tall(X0))) [ennf transformation 1]
32. ! [X0] : ((~curious(X0) <~> generous(X0)) | ~funny(X0) | tall(X0)) [flattening 31]
33. ! [X0] : (creative(X0) | (old(X0) & generous(X0))) [ennf transformation 2]
34. ! [X0] : (~generous(X0) | funny(X0)) [ennf transformation 5]
35. ~curious(paul) | (~kind(susan) <=> ~generous(susan)) [ennf transformation 7]
37. ! [X0] : (~tall(X0) | rich(X0)) [ennf transformation 10]
41. ! [X0] : (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ~funny(X0) | tall(X0)) [nnf transformation 32]
42. ! [X0] : ((funny(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ~funny(X0))) [nnf transformation 3]
44. ~curious(paul) | ((~kind(susan) | generous(susan)) & (~generous(susan) | kind(susan))) [nnf transformation 35]
56. ! [X0] : (((patient(X0) | creative(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((patient(X0) | creative(X0) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [flattening 56]
66. ~generous(X0) | curious(X0) | ~funny(X0) | tall(X0) [cnf transformation 41]
67. creative(X0) | generous(X0) [cnf transformation 33]
69. ~creative(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
70. ~funny(X0) | creative(X0) | ~tall(X0) [cnf transformation 42]
77. ~generous(X0) | funny(X0) [cnf transformation 34]
78. ~curious(paul) | ~generous(susan) | kind(susan) [cnf transformation 44]
89. ~tall(X0) | rich(X0) [cnf transformation 37]
99. ~rich(X0) | ~creative(X0) [cnf transformation 57]
114. ~kind(susan) [cnf transformation 21]
115. funny(susan) [cnf transformation 21]
118. generous(paul) [cnf transformation 25]
140. 4 <=> generous(susan) [avatar definition]
144. 5 <=> kind(susan) [avatar definition]
148. 6 <=> curious(paul) [avatar definition]
152. 5 | ~4 | ~6 [avatar split clause 78,148,140,144]
253. ~5 [avatar split clause 114,144]
263. funny(paul) [resolution 77,118]
279. ~funny(X1) | tall(X1) | generous(X1) [resolution 69,67]
291. creative(susan) | ~tall(susan) [resolution 70,115]
292. creative(paul) | ~tall(paul) [resolution 70,263]
295. 33 <=> tall(susan) [avatar definition]
296. tall(susan) <- (33) [avatar component clause 295]
299. 34 <=> creative(susan) [avatar definition]
301. creative(susan) <- (34) [avatar component clause 299]
302. ~33 | 34 [avatar split clause 291,299,295]
304. 35 <=> tall(paul) [avatar definition]
305. tall(paul) <- (35) [avatar component clause 304]
308. 36 <=> creative(paul) [avatar definition]
310. creative(paul) <- (36) [avatar component clause 308]
311. ~35 | 36 [avatar split clause 292,308,304]
360. curious(paul) | ~funny(paul) | tall(paul) [resolution 66,118]
362. curious(paul) | tall(paul) [subsumption resolution 360,263]
386. tall(susan) | generous(susan) [resolution 279,115]
399. rich(susan) <- (33) [resolution 296,89]
410. ~creative(susan) <- (33) [resolution 399,99]
411. $false <- (33, 34) [subsumption resolution 410,301]
412. ~33 | ~34 [avatar contradiction clause 411]
413. 4 | 33 [avatar split clause 386,295,140]
414. 35 | 6 [avatar split clause 362,148,304]
424. rich(paul) <- (35) [resolution 305,89]
443. ~creative(paul) <- (35) [resolution 424,99]
444. $false <- (35, 36) [subsumption resolution 443,310]
445. ~35 | ~36 [avatar contradiction clause 444]
446. $false [avatar sat refutation 152,253,302,311,412,413,414,445]
% SZS output end Proof for 3192620031687894786329059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not generous is either not calm or not generous. Everyone who is quiet is wise. If someone is both not happy and quiet then someone is both funny and wise and vice versa. If john is calm then someone is wise or tall and vice versa. If someone is curious or not creative then paul is not humble or not funny and vice versa. Everyone who is quiet or generous is either not funny or brave. If john is not old or creative then alice is both creative and not curious. If mary is not tall or not brave then someone is both patient and quiet. Everyone who is curious or calm is either brave or not quiet and vice versa. Everyone who is not brave is not generous. Everyone who is old is either not happy or old and vice versa. If someone is funny then someone is both not creative and creative. If someone is not happy or not calm then someone is strong or curious and vice versa. If lucy is happy or not patient then mary is either creative or curious. Everyone who is wise is both not calm and not creative and vice versa. Lucy is funny or calm. Alice is either tall or patient. Someone is humble or not calm. Alice is not brave or quiet. Fred is patient. Fred is funny or not old. | Fred is quiet. | contradiction | (![X]:((patient(X)&~generous(X))=>(~calm(X)<~>~generous(X))))&
(![X]:(quiet(X)=>wise(X)))&
((?[X]:((~happy(X)&quiet(X))))<=>(?[X]:((funny(X)&wise(X)))))&
((calm(john))<=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((curious(X)|~creative(X))))<=>((~humble(paul)|~funny(paul))))&
(![X]:((quiet(X)|generous(X))=>(~funny(X)<~>brave(X))))&
(((~old(john)|creative(john)))=>((creative(alice)&~curious(alice))))&
(((~tall(mary)|~brave(mary)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:((curious(X)|calm(X))<=>(brave(X)<~>~quiet(X))))&
(![X]:(~brave(X)=>~generous(X)))&
(![X]:(old(X)<=>(~happy(X)<~>old(X))))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((strong(X)|curious(X)))))&
(((happy(lucy)|~patient(lucy)))=>((creative(mary)<~>curious(mary))))&
(![X]:(wise(X)<=>(~calm(X)&~creative(X))))&
((funny(lucy)|calm(lucy)))&
((tall(alice)<~>patient(alice)))&
(?[X]:((humble(X)|~calm(X))))&
((~brave(alice)|quiet(alice)))&
(patient(fred))&
((funny(fred)|~old(fred))) | quiet(fred) | [
"p0",
"p1",
"p5",
"p9",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5486205175091618814931339
% SZS output start Proof for 5486205175091618814931339
1. ! [X0] : ((~generous(X0) & patient(X0)) => (~calm(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : (quiet(X0) => wise(X0)) [input p1]
6. ! [X0] : ((generous(X0) | quiet(X0)) => (~funny(X0) <~> brave(X0))) [input p5]
10. ! [X0] : (~brave(X0) => ~generous(X0)) [input p9]
12. ? [X0] : funny(X0) => ? [X0] : (creative(X0) & ~creative(X0)) [input p11]
15. ! [X0] : (wise(X0) <=> (~creative(X0) & ~calm(X0))) [input p14]
20. patient(fred) [input p19]
22. quiet(fred) [input hypothesis]
24. ? [X0] : funny(X0) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 12]
26. ! [X0] : ((~calm(X0) <~> ~generous(X0)) | (generous(X0) | ~patient(X0))) [ennf transformation 1]
27. ! [X0] : ((~calm(X0) <~> ~generous(X0)) | generous(X0) | ~patient(X0)) [flattening 26]
28. ! [X0] : (wise(X0) | ~quiet(X0)) [ennf transformation 2]
29. ! [X0] : ((~funny(X0) <~> brave(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 6]
32. ! [X0] : (~generous(X0) | brave(X0)) [ennf transformation 10]
33. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : ~funny(X0) [ennf transformation 24]
35. ! [X0] : (((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | generous(X0) | ~patient(X0)) [nnf transformation 27]
50. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~generous(X0) & ~quiet(X0))) [nnf transformation 29]
56. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : ~funny(X1) [rectify 33]
57. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK5) & ~creative(sK5)) [choice axiom]
58. (creative(sK5) & ~creative(sK5)) | ! [X1] : ~funny(X1) [skolemisation 56,57]
65. ! [X0] : ((wise(X0) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | ~wise(X0))) [nnf transformation 15]
66. ! [X0] : ((wise(X0) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | ~wise(X0))) [flattening 65]
71. generous(X0) | calm(X0) | generous(X0) | ~patient(X0) [cnf transformation 35]
72. ~quiet(X0) | wise(X0) [cnf transformation 28]
86. ~brave(X0) | funny(X0) | ~quiet(X0) [cnf transformation 50]
102. ~generous(X0) | brave(X0) [cnf transformation 32]
107. ~creative(sK5) | ~funny(X1) [cnf transformation 58]
108. creative(sK5) | ~funny(X1) [cnf transformation 58]
117. ~wise(X0) | ~calm(X0) [cnf transformation 66]
125. patient(fred) [cnf transformation 20]
127. quiet(fred) [cnf transformation 22]
130. ~patient(X0) | calm(X0) | generous(X0) [duplicate literal removal 71]
246. 26 <=> ! [X1] : ~funny(X1) [avatar definition]
247. ~funny(X1) <- (26) [avatar component clause 246]
249. 27 <=> creative(sK5) [avatar definition]
252. 26 | 27 [avatar split clause 108,249,246]
253. 26 | ~27 [avatar split clause 107,249,246]
359. wise(fred) [resolution 72,127]
362. ~calm(fred) [resolution 117,359]
411. calm(fred) | generous(fred) [resolution 130,125]
412. generous(fred) [subsumption resolution 411,362]
432. brave(fred) [resolution 412,102]
437. funny(fred) | ~quiet(fred) [resolution 432,86]
443. ~quiet(fred) <- (26) [subsumption resolution 437,247]
444. $false <- (26) [subsumption resolution 443,127]
445. ~26 [avatar contradiction clause 444]
446. $false [avatar sat refutation 252,253,445]
% SZS output end Proof for 5486205175091618814931339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or generous is both not tall and not happy and vice versa. Everyone who is both not calm and creative is not creative and vice versa. Everyone who is not strong or not creative is both strong and kind and vice versa. If mary is patient or not humble then mary is both not tall and humble. Everyone who is quiet is not rich or not patient. If someone is either not old or tall then alice is both funny and not quiet. Everyone who is both wise and humble is both not strong and not quiet. Everyone who is either rich or old is happy or not tall and vice versa. Everyone who is not funny or patient is either quiet or rich and vice versa. Everyone who is not funny or happy is either not old or not patient. If fred is either not calm or kind then john is either rich or not brave and vice versa. Everyone who is both patient and generous is both not brave and not curious and vice versa. Everyone who is either not brave or not quiet is both not brave and funny and vice versa. If someone is either curious or tall then john is either not wise or generous and vice versa. If john is not kind or creative then someone is both curious and quiet. Someone is either patient or quiet. Someone is brave. Mary is generous or rich. Alice is brave. | Alice is rich. | contradiction | (![X]:((~strong(X)<~>generous(X))<=>(~tall(X)&~happy(X))))&
(![X]:((~calm(X)&creative(X))<=>~creative(X)))&
(![X]:((~strong(X)|~creative(X))<=>(strong(X)&kind(X))))&
(((patient(mary)|~humble(mary)))=>((~tall(mary)&humble(mary))))&
(![X]:(quiet(X)=>(~rich(X)|~patient(X))))&
((?[X]:((~old(X)<~>tall(X))))=>((funny(alice)&~quiet(alice))))&
(![X]:((wise(X)&humble(X))=>(~strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))<=>(happy(X)|~tall(X))))&
(![X]:((~funny(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~funny(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(((~calm(fred)<~>kind(fred)))<=>((rich(john)<~>~brave(john))))&
(![X]:((patient(X)&generous(X))<=>(~brave(X)&~curious(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~brave(X)&funny(X))))&
((?[X]:((curious(X)<~>tall(X))))<=>((~wise(john)<~>generous(john))))&
(((~kind(john)|creative(john)))=>(?[X]:((curious(X)&quiet(X)))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:(brave(X)))&
((generous(mary)|rich(mary)))&
(brave(alice)) | rich(alice) | [
"p4",
"p5",
"p7",
"p9",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 69478442322847152388107
% SZS output start Proof for 69478442322847152388107
5. ! [X0] : (quiet(X0) => (~patient(X0) | ~rich(X0))) [input p4]
6. ? [X0] : (~old(X0) <~> tall(X0)) => (~quiet(alice) & funny(alice)) [input p5]
8. ! [X0] : ((rich(X0) <~> old(X0)) <=> (~tall(X0) | happy(X0))) [input p7]
10. ! [X0] : ((happy(X0) | ~funny(X0)) => (~old(X0) <~> ~patient(X0))) [input p9]
13. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) <=> (funny(X0) & ~brave(X0))) [input p12]
19. brave(alice) [input p18]
20. rich(alice) [input hypothesis]
22. ! [X0] : ((~patient(X0) | ~rich(X0)) | ~quiet(X0)) [ennf transformation 5]
23. ! [X0] : (~patient(X0) | ~rich(X0) | ~quiet(X0)) [flattening 22]
24. (~quiet(alice) & funny(alice)) | ! [X0] : (~old(X0) <=> tall(X0)) [ennf transformation 6]
27. ! [X0] : ((~old(X0) <~> ~patient(X0)) | (~happy(X0) & funny(X0))) [ennf transformation 10]
35. (~quiet(alice) & funny(alice)) | ! [X0] : ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))) [nnf transformation 24]
36. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [nnf transformation 8]
37. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [flattening 36]
40. ! [X0] : (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~happy(X0) & funny(X0))) [nnf transformation 27]
44. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [nnf transformation 13]
45. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [flattening 44]
75. ~rich(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 23]
78. ~quiet(alice) | tall(X0) | old(X0) [cnf transformation 35]
79. ~quiet(alice) | ~old(X0) | ~tall(X0) [cnf transformation 35]
82. ~rich(X0) | happy(X0) | old(X0) | ~tall(X0) [cnf transformation 37]
87. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 37]
97. ~happy(X0) | old(X0) | patient(X0) [cnf transformation 40]
111. ~brave(X0) | ~brave(X0) | quiet(X0) [cnf transformation 45]
132. brave(alice) [cnf transformation 19]
133. rich(alice) [cnf transformation 20]
134. ~brave(X0) | quiet(X0) [duplicate literal removal 111]
153. 3 <=> ! [X0] : (~old(X0) | ~tall(X0)) [avatar definition]
154. ~old(X0) | ~tall(X0) <- (3) [avatar component clause 153]
156. 4 <=> quiet(alice) [avatar definition]
157. quiet(alice) <- (4) [avatar component clause 156]
159. 3 | ~4 [avatar split clause 79,156,153]
161. 5 <=> ! [X0] : (tall(X0) | old(X0)) [avatar definition]
162. old(X0) | tall(X0) <- (5) [avatar component clause 161]
163. 5 | ~4 [avatar split clause 78,156,161]
244. quiet(alice) [resolution 134,132]
248. 4 [avatar split clause 244,156]
251. ~patient(alice) | ~quiet(alice) [resolution 75,133]
252. ~patient(alice) <- (4) [subsumption resolution 251,157]
257. ~rich(X1) | tall(X1) | tall(X1) <- (5) [resolution 87,162]
258. ~rich(X1) | tall(X1) <- (5) [duplicate literal removal 257]
260. tall(alice) <- (5) [resolution 258,133]
349. happy(alice) | old(alice) | ~tall(alice) [resolution 82,133]
352. happy(alice) | old(alice) <- (5) [subsumption resolution 349,260]
354. 28 <=> old(alice) [avatar definition]
355. ~old(alice) <- (~28) [avatar component clause 354]
356. old(alice) <- (28) [avatar component clause 354]
358. 29 <=> happy(alice) [avatar definition]
360. happy(alice) <- (29) [avatar component clause 358]
361. 28 | 29 | ~5 [avatar split clause 352,161,358,354]
377. ~tall(alice) <- (3, 28) [resolution 356,154]
380. $false <- (3, 5, 28) [subsumption resolution 377,260]
381. ~3 | ~5 | ~28 [avatar contradiction clause 380]
400. old(alice) | patient(alice) <- (29) [resolution 360,97]
404. patient(alice) <- (~28, 29) [subsumption resolution 400,355]
405. $false <- (4, ~28, 29) [subsumption resolution 404,252]
406. ~4 | 28 | ~29 [avatar contradiction clause 405]
407. $false [avatar sat refutation 159,163,248,361,381,406]
% SZS output end Proof for 69478442322847152388107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not creative is not calm or not patient. If someone is both calm and not creative then someone is not kind and vice versa. Everyone who is kind is both kind and not old. If someone is both not old and tall then someone is either brave or humble and vice versa. If alice is both funny and not brave then fred is not strong or not rich. Everyone who is either calm or quiet is not generous or quiet and vice versa. Everyone who is not wise or not quiet is both not brave and wise and vice versa. Everyone who is kind or quiet is not quiet or tall. Everyone who is quiet is both not creative and not calm and vice versa. If alice is not kind then alice is both not kind and calm and vice versa. Everyone who is both not happy and not patient is either not kind or not humble and vice versa. Everyone who is generous or kind is creative and vice versa. Everyone who is either not funny or not generous is not wise or funny. If paul is either strong or brave then someone is both brave and quiet and vice versa. If someone is both rich and not calm then someone is either curious or funny and vice versa. Everyone who is either humble or patient is either not funny or curious. Lucy is both brave and not happy. Susan is both humble and curious. Someone is not generous. Fred is calm or not humble. Someone is calm or not generous. Fred is both not generous and not funny. Someone is both quiet and rich. | Alice is not kind. | neutral | (![X]:((rich(X)<~>~creative(X))=>(~calm(X)|~patient(X))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:(kind(X)=>(kind(X)&~old(X))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(alice)&~brave(alice)))=>((~strong(fred)|~rich(fred))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((brave(lucy)&~happy(lucy)))&
((humble(susan)&curious(susan)))&
(?[X]:(~generous(X)))&
((calm(fred)|~humble(fred)))&
(?[X]:((calm(X)|~generous(X))))&
((~generous(fred)&~funny(fred)))&
(?[X]:((quiet(X)&rich(X)))) | ~kind(alice) | [] | null | 0 |
If someone is both calm and curious then someone is either humble or not old and vice versa.
If someone is creative or not curious then mary is not generous and vice versa.
If someone is both generous and not humble then someone is not happy.
Everyone who is not creative is not calm or not tall.
Everyone who is either wise or generous is not wise or not calm and vice versa.
Everyone who is not wise or creative is both not happy and not rich.
Everyone who is either generous or not curious is not calm.
If fred is either not rich or old then paul is either not calm or not kind.
Everyone who is humble is curious or tall and vice versa.
Everyone who is strong is not curious and vice versa.
If john is both not funny and funny then someone is generous.
Everyone who is not wise or funny is not brave or humble and vice versa.
Everyone who is both curious and not patient is either not funny or not rich.
Everyone who is both creative and kind is not patient and vice versa.
If fred is not humble then someone is either not kind or not rich and vice versa.
If mary is either curious or humble then someone is not generous or not happy and vice versa.
Paul is both curious and not generous.
Someone is wise.
Lucy is both rich and generous.
Susan is generous.
Paul is patient or not wise.
Someone is either curious or not generous.
Mary is wise or not quiet.
Susan is both brave and wise. | Mary is wise. | entailment | ((?[X]:((calm(X)&curious(X))))<=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:((creative(X)|~curious(X))))<=>(~generous(mary)))&
((?[X]:((generous(X)&~humble(X))))=>(?[X]:(~happy(X))))&
(![X]:(~creative(X)=>(~calm(X)|~tall(X))))&
(![X]:((wise(X)<~>generous(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~rich(X))))&
(![X]:((generous(X)<~>~curious(X))=>~calm(X)))&
(((~rich(fred)<~>old(fred)))=>((~calm(paul)<~>~kind(paul))))&
(![X]:(humble(X)<=>(curious(X)|tall(X))))&
(![X]:(strong(X)<=>~curious(X)))&
(((~funny(john)&funny(john)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~patient(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)&kind(X))<=>~patient(X)))&
((~humble(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~generous(X)|~happy(X)))))&
((curious(paul)&~generous(paul)))&
(?[X]:(wise(X)))&
((rich(lucy)&generous(lucy)))&
(generous(susan))&
((patient(paul)|~wise(paul)))&
(?[X]:((curious(X)<~>~generous(X))))&
((wise(mary)|~quiet(mary)))&
((brave(susan)&wise(susan))) | wise(mary) | [
"p1",
"p4",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1139000563363364170244073
% SZS output start Proof for 1139000563363364170244073
2. ? [X0] : (~curious(X0) | creative(X0)) <=> ~generous(mary) [input p1]
5. ! [X0] : ((wise(X0) <~> generous(X0)) <=> (~calm(X0) | ~wise(X0))) [input p4]
9. ! [X0] : (humble(X0) <=> (tall(X0) | curious(X0))) [input p8]
16. (curious(mary) <~> humble(mary)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p15]
17. ~generous(paul) & curious(paul) [input p16]
25. ~wise(mary) [input hypothesis]
47. (? [X0] : (~curious(X0) | creative(X0)) | generous(mary)) & (~generous(mary) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 2]
48. (? [X0] : (~curious(X0) | creative(X0)) | generous(mary)) & (~generous(mary) | ! [X1] : (curious(X1) & ~creative(X1))) [rectify 47]
49. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK2) | creative(sK2)) [choice axiom]
50. ((~curious(sK2) | creative(sK2)) | generous(mary)) & (~generous(mary) | ! [X1] : (curious(X1) & ~creative(X1))) [skolemisation 48,49]
54. ! [X0] : ((((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0))))) [nnf transformation 5]
55. ! [X0] : ((((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0))))) [flattening 54]
58. ! [X0] : ((humble(X0) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | ~humble(X0))) [nnf transformation 9]
59. ! [X0] : ((humble(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | ~humble(X0))) [flattening 58]
69. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & (? [X0] : (~happy(X0) | ~generous(X0)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [nnf transformation 16]
70. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [rectify 69]
71. ? [X1] : (~happy(X1) | ~generous(X1)) => (~happy(sK6) | ~generous(sK6)) [choice axiom]
72. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & ((~happy(sK6) | ~generous(sK6)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [skolemisation 70,71]
85. ~generous(mary) | curious(X1) [cnf transformation 50]
91. generous(X0) | wise(X0) | wise(X0) [cnf transformation 55]
106. ~curious(X0) | humble(X0) [cnf transformation 59]
124. ~humble(mary) | ~curious(mary) | generous(X0) [cnf transformation 72]
127. ~generous(paul) [cnf transformation 17]
137. ~wise(mary) [cnf transformation 25]
139. wise(X0) | generous(X0) [duplicate literal removal 91]
172. 8 <=> generous(mary) [avatar definition]
173. ~generous(mary) <- (~8) [avatar component clause 172]
185. 11 <=> ! [X1] : curious(X1) [avatar definition]
186. curious(X1) <- (11) [avatar component clause 185]
187. 11 | ~8 [avatar split clause 85,172,185]
250. 25 <=> curious(mary) [avatar definition]
252. ~curious(mary) <- (~25) [avatar component clause 250]
254. ~curious(mary) | generous(X0) [subsumption resolution 124,106]
256. 26 <=> ! [X0] : generous(X0) [avatar definition]
257. generous(X0) <- (26) [avatar component clause 256]
258. 26 | ~25 [avatar split clause 254,250,256]
302. $false <- (11, ~25) [resolution 252,186]
303. ~11 | 25 [avatar contradiction clause 302]
304. $false <- (26) [resolution 257,127]
305. ~26 [avatar contradiction clause 304]
316. generous(mary) [resolution 139,137]
318. $false <- (~8) [subsumption resolution 316,173]
319. 8 [avatar contradiction clause 318]
322. $false [avatar sat refutation 187,258,303,305,319]
% SZS output end Proof for 1139000563363364170244073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not creative or happy then someone is both creative and not patient. Everyone who is not calm is kind. If someone is both not patient and quiet then someone is both patient and not funny and vice versa. If fred is not patient then someone is not curious. If paul is not old or old then lucy is not wise and vice versa. If mary is curious or quiet then someone is brave or not brave. Everyone who is rich is both not quiet and not patient. Everyone who is not calm or strong is both creative and funny and vice versa. If someone is both not creative and creative then someone is either not funny or not tall. If mary is generous then someone is either quiet or wise and vice versa. Everyone who is calm is not rich or strong and vice versa. Everyone who is not creative is not curious and vice versa. Everyone who is not strong or not humble is both strong and not calm. Everyone who is either not strong or not old is both not rich and not patient and vice versa. Everyone who is old is not kind or not brave. Everyone who is not old is old or rich. Alice is tall or not tall. Someone is not kind. Someone is funny or not old. Someone is not strong or calm. Lucy is either brave or not humble. Someone is either not strong or calm. Someone is either not rich or humble. Someone is both not tall and not patient. | Lucy is not kind. | entailment | (((~creative(mary)<~>happy(mary)))=>(?[X]:((creative(X)&~patient(X)))))&
(![X]:(~calm(X)=>kind(X)))&
((?[X]:((~patient(X)&quiet(X))))<=>(?[X]:((patient(X)&~funny(X)))))&
((~patient(fred))=>(?[X]:(~curious(X))))&
(((~old(paul)|old(paul)))<=>(~wise(lucy)))&
(((curious(mary)|quiet(mary)))=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:(rich(X)=>(~quiet(X)&~patient(X))))&
(![X]:((~calm(X)|strong(X))<=>(creative(X)&funny(X))))&
((?[X]:((~creative(X)&creative(X))))=>(?[X]:((~funny(X)<~>~tall(X)))))&
((generous(mary))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:(calm(X)<=>(~rich(X)|strong(X))))&
(![X]:(~creative(X)<=>~curious(X)))&
(![X]:((~strong(X)|~humble(X))=>(strong(X)&~calm(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(~rich(X)&~patient(X))))&
(![X]:(old(X)=>(~kind(X)|~brave(X))))&
(![X]:(~old(X)=>(old(X)|rich(X))))&
((tall(alice)|~tall(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)|~old(X))))&
(?[X]:((~strong(X)|calm(X))))&
((brave(lucy)<~>~humble(lucy)))&
(?[X]:((~strong(X)<~>calm(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~tall(X)&~patient(X)))) | ~kind(lucy) | [
"p10",
"p12",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1074666178672748514146846
% SZS output start Proof for 1074666178672748514146846
11. ! [X0] : (calm(X0) <=> (strong(X0) | ~rich(X0))) [input p10]
13. ! [X0] : ((~humble(X0) | ~strong(X0)) => (~calm(X0) & strong(X0))) [input p12]
14. ! [X0] : ((~strong(X0) <~> ~old(X0)) <=> (~patient(X0) & ~rich(X0))) [input p13]
15. ! [X0] : (old(X0) => (~brave(X0) | ~kind(X0))) [input p14]
16. ! [X0] : (~old(X0) => (rich(X0) | old(X0))) [input p15]
21. brave(lucy) <~> ~humble(lucy) [input p20]
25. kind(lucy) [input hypothesis]
34. ! [X0] : ((~calm(X0) & strong(X0)) | (humble(X0) & strong(X0))) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) | ~kind(X0)) | ~old(X0)) [ennf transformation 15]
36. ! [X0] : (~brave(X0) | ~kind(X0) | ~old(X0)) [flattening 35]
37. ! [X0] : ((rich(X0) | old(X0)) | old(X0)) [ennf transformation 16]
38. ! [X0] : (rich(X0) | old(X0) | old(X0)) [flattening 37]
63. ! [X0] : ((calm(X0) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | ~calm(X0))) [nnf transformation 11]
64. ! [X0] : ((calm(X0) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ~calm(X0))) [flattening 63]
66. ! [X0] : ((((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (patient(X0) | rich(X0))) & ((~patient(X0) & ~rich(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0))))) [nnf transformation 14]
67. ! [X0] : ((((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | patient(X0) | rich(X0)) & ((~patient(X0) & ~rich(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0))))) [flattening 66]
74. (humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy)) [nnf transformation 21]
113. ~strong(X0) | calm(X0) [cnf transformation 64]
116. strong(X0) | strong(X0) [cnf transformation 34]
119. ~calm(X0) | humble(X0) [cnf transformation 34]
121. ~rich(X0) | ~strong(X0) | old(X0) [cnf transformation 67]
126. ~brave(X0) | ~kind(X0) | ~old(X0) [cnf transformation 36]
127. rich(X0) | old(X0) | old(X0) [cnf transformation 38]
132. ~humble(lucy) | brave(lucy) [cnf transformation 74]
140. kind(lucy) [cnf transformation 25]
141. rich(X0) | old(X0) [duplicate literal removal 127]
142. strong(X0) [duplicate literal removal 116]
232. ~rich(X0) | old(X0) [subsumption resolution 121,142]
233. old(X0) [subsumption resolution 141,232]
236. 20 <=> brave(lucy) [avatar definition]
237. brave(lucy) <- (20) [avatar component clause 236]
240. 21 <=> humble(lucy) [avatar definition]
241. ~humble(lucy) <- (~21) [avatar component clause 240]
244. 20 | ~21 [avatar split clause 132,240,236]
261. calm(X0) [resolution 113,142]
275. humble(X0) [resolution 119,261]
279. $false <- (~21) [resolution 275,241]
282. 21 [avatar contradiction clause 279]
291. ~kind(lucy) | ~old(lucy) <- (20) [resolution 126,237]
292. ~old(lucy) <- (20) [subsumption resolution 291,140]
293. $false <- (20) [subsumption resolution 292,233]
294. ~20 [avatar contradiction clause 293]
295. $false [avatar sat refutation 244,282,294]
% SZS output end Proof for 1074666178672748514146846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is creative.
If mary is either strong or not quiet then lucy is either wise or curious and vice versa.
Everyone who is either wise or brave is not wise or not strong and vice versa.
If someone is either quiet or creative then john is either rich or not curious and vice versa.
Everyone who is not rich or brave is both calm and not calm.
If lucy is either not brave or not creative then someone is old or happy.
If lucy is both brave and not curious then someone is not happy and vice versa.
Everyone who is either not strong or patient is not rich and vice versa.
Everyone who is either not humble or not creative is either not generous or not happy and vice versa.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Someone is funny or happy.
Paul is either happy or not rich.
Someone is both not brave and generous.
Someone is happy.
Paul is kind. | John is not tall. | entailment | (![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((funny(X)|happy(X))))&
((happy(paul)<~>~rich(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(happy(X)))&
(kind(paul)) | ~tall(john) | [
"p0",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2542032325507898097682202
% SZS output start Proof for 2542032325507898097682202
1. ! [X0] : ((~tall(X0) <~> ~creative(X0)) => creative(X0)) [input p0]
5. ! [X0] : ((brave(X0) | ~rich(X0)) => (~calm(X0) & calm(X0))) [input p4]
12. ! [X0] : ((~brave(X0) | kind(X0)) <=> ~creative(X0)) [input p11]
22. tall(john) [input hypothesis]
24. ! [X0] : (creative(X0) | (~tall(X0) <=> ~creative(X0))) [ennf transformation 1]
25. ! [X0] : ((~calm(X0) & calm(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 5]
31. ! [X0] : (creative(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) [nnf transformation 24]
49. ! [X0] : (((~brave(X0) | kind(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) & ~kind(X0)))) [nnf transformation 12]
50. ! [X0] : ((~brave(X0) | kind(X0) | creative(X0)) & (~creative(X0) | (brave(X0) & ~kind(X0)))) [flattening 49]
67. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 31]
91. calm(X0) | ~brave(X0) [cnf transformation 25]
93. ~calm(X0) | ~brave(X0) [cnf transformation 25]
113. ~creative(X0) | brave(X0) [cnf transformation 50]
140. tall(john) [cnf transformation 22]
143. ~tall(X0) | creative(X0) [duplicate literal removal 67]
199. ~brave(X0) [subsumption resolution 91,93]
209. ~creative(X0) [subsumption resolution 113,199]
251. creative(john) [resolution 143,140]
252. $false [subsumption resolution 251,209]
% SZS output end Proof for 2542032325507898097682202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or humble then susan is both creative and tall and vice versa. Everyone who is either not funny or calm is not funny. Everyone who is both curious and not brave is either not funny or not strong and vice versa. Everyone who is not calm or not generous is either not strong or not patient. If someone is either not old or not curious then someone is both not kind and not curious. Everyone who is either not happy or creative is either not kind or not generous. Everyone who is both tall and not calm is tall or rich. Everyone who is either wise or creative is either not kind or not generous and vice versa. Everyone who is generous is both brave and old and vice versa. If someone is either tall or not curious then someone is either strong or humble. Everyone who is either not kind or not funny is funny and vice versa. Everyone who is not quiet or not brave is both not wise and creative. Everyone who is not quiet is not generous or not brave and vice versa. Everyone who is both strong and humble is not strong or humble and vice versa. If someone is funny then alice is either strong or creative and vice versa. John is both generous and strong. Someone is old. Someone is funny. Someone is not quiet or not kind. Fred is happy or not old. | Fred is calm. | contradiction | (((~patient(susan)|humble(susan)))<=>((creative(susan)&tall(susan))))&
(![X]:((~funny(X)<~>calm(X))=>~funny(X)))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
((generous(john)&strong(john)))&
(?[X]:(old(X)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(fred)|~old(fred))) | calm(fred) | [
"p1",
"p2",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8388207599482094147797872
% SZS output start Proof for 8388207599482094147797872
2. ! [X0] : ((~funny(X0) <~> calm(X0)) => ~funny(X0)) [input p1]
3. ! [X0] : ((~brave(X0) & curious(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p2]
8. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (~kind(X0) <~> ~generous(X0))) [input p7]
9. ! [X0] : (generous(X0) <=> (old(X0) & brave(X0))) [input p8]
11. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p10]
12. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p11]
14. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p13]
21. calm(fred) [input hypothesis]
25. ! [X0] : (~funny(X0) | (~funny(X0) <=> calm(X0))) [ennf transformation 2]
30. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 12]
33. ! [X0] : (~funny(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) [nnf transformation 25]
34. ! [X0] : (((~brave(X0) & curious(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (brave(X0) | ~curious(X0)))) [nnf transformation 3]
35. ! [X0] : (((~brave(X0) & curious(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | brave(X0) | ~curious(X0))) [flattening 34]
42. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 8]
43. ! [X0] : ((generous(X0) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ~generous(X0))) [nnf transformation 9]
44. ! [X0] : ((generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ~generous(X0))) [flattening 43]
49. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 11]
52. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 14]
53. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
70. ~funny(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 33]
75. ~strong(X0) | ~brave(X0) | funny(X0) [cnf transformation 35]
92. ~creative(X0) | kind(X0) | wise(X0) | generous(X0) [cnf transformation 42]
97. ~generous(X0) | brave(X0) [cnf transformation 44]
105. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 49]
106. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
109. ~wise(X0) | brave(X0) [cnf transformation 30]
111. brave(X0) | creative(X0) [cnf transformation 30]
117. strong(X0) | ~humble(X0) [cnf transformation 53]
118. strong(X0) | humble(X0) [cnf transformation 53]
130. calm(fred) [cnf transformation 21]
133. funny(X0) | ~kind(X0) [duplicate literal removal 105]
134. ~kind(X0) | ~funny(X0) [duplicate literal removal 106]
135. ~calm(X0) | ~funny(X0) [duplicate literal removal 70]
193. ~kind(X0) [subsumption resolution 133,134]
195. strong(X0) [subsumption resolution 117,118]
224. ~funny(fred) [resolution 135,130]
236. ~brave(X1) | funny(X1) [resolution 75,195]
244. funny(X0) | creative(X0) [resolution 236,111]
293. creative(fred) [resolution 244,224]
316. 23 <=> generous(fred) [avatar definition]
318. generous(fred) <- (23) [avatar component clause 316]
320. 24 <=> wise(fred) [avatar definition]
322. wise(fred) <- (24) [avatar component clause 320]
377. kind(fred) | wise(fred) | generous(fred) [resolution 293,92]
393. wise(fred) | generous(fred) [subsumption resolution 377,193]
394. 23 | 24 [avatar split clause 393,320,316]
402. brave(fred) <- (24) [resolution 322,109]
405. funny(fred) <- (24) [resolution 402,236]
408. $false <- (24) [subsumption resolution 405,224]
409. ~24 [avatar contradiction clause 408]
416. brave(fred) <- (23) [resolution 318,97]
421. funny(fred) <- (23) [resolution 416,236]
424. $false <- (23) [subsumption resolution 421,224]
425. ~23 [avatar contradiction clause 424]
426. $false [avatar sat refutation 394,409,425]
% SZS output end Proof for 8388207599482094147797872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not quiet is creative and vice versa.
If someone is either wise or not strong then someone is either quiet or kind.
If someone is either not curious or wise then fred is both quiet and creative and vice versa.
If someone is both not curious and not happy then john is either not brave or not wise and vice versa.
Everyone who is not creative or old is rich or not generous.
If lucy is old or tall then someone is not funny and vice versa.
Everyone who is either quiet or wise is not quiet or strong.
If fred is wise then someone is kind and vice versa.
Everyone who is both not brave and tall is either tall or brave and vice versa.
Everyone who is either happy or humble is not quiet.
Everyone who is rich or not old is either not happy or quiet and vice versa.
Everyone who is both not generous and not creative is not curious.
Everyone who is not old or rich is tall or brave and vice versa.
Everyone who is either not rich or curious is either not strong or not calm.
Everyone who is old is funny or curious.
If lucy is either humble or creative then someone is both happy and not curious and vice versa.
Someone is either funny or not creative.
Mary is either strong or quiet.
Alice is both strong and creative.
Mary is either not patient or funny.
Someone is quiet.
Susan is not brave or old.
John is both generous and strong.
Someone is brave. | John is not creative. | entailment | (![X]:((~happy(X)<~>~quiet(X))<=>creative(X)))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((quiet(X)<~>kind(X)))))&
((?[X]:((~curious(X)<~>wise(X))))<=>((quiet(fred)&creative(fred))))&
((?[X]:((~curious(X)&~happy(X))))<=>((~brave(john)<~>~wise(john))))&
(![X]:((~creative(X)|old(X))=>(rich(X)|~generous(X))))&
(((old(lucy)|tall(lucy)))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>wise(X))=>(~quiet(X)|strong(X))))&
((wise(fred))<=>(?[X]:(kind(X))))&
(![X]:((~brave(X)&tall(X))<=>(tall(X)<~>brave(X))))&
(![X]:((happy(X)<~>humble(X))=>~quiet(X)))&
(![X]:((rich(X)|~old(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:((~generous(X)&~creative(X))=>~curious(X)))&
(![X]:((~old(X)|rich(X))<=>(tall(X)|brave(X))))&
(![X]:((~rich(X)<~>curious(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(old(X)=>(funny(X)|curious(X))))&
(((humble(lucy)<~>creative(lucy)))<=>(?[X]:((happy(X)&~curious(X)))))&
(?[X]:((funny(X)<~>~creative(X))))&
((strong(mary)<~>quiet(mary)))&
((strong(alice)&creative(alice)))&
((~patient(mary)<~>funny(mary)))&
(?[X]:(quiet(X)))&
((~brave(susan)|old(susan)))&
((generous(john)&strong(john)))&
(?[X]:(brave(X))) | ~creative(john) | [
"p0",
"p4",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4045819871396192020617955
% SZS output start Proof for 4045819871396192020617955
1. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> creative(X0)) [input p0]
5. ! [X0] : ((old(X0) | ~creative(X0)) => (~generous(X0) | rich(X0))) [input p4]
11. ! [X0] : ((~old(X0) | rich(X0)) <=> (~happy(X0) <~> quiet(X0))) [input p10]
23. strong(john) & generous(john) [input p22]
25. creative(john) [input hypothesis]
28. ! [X0] : ((~generous(X0) | rich(X0)) | (~old(X0) & creative(X0))) [ennf transformation 5]
29. ! [X0] : (~generous(X0) | rich(X0) | (~old(X0) & creative(X0))) [flattening 28]
38. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ~creative(X0)) & (creative(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 1]
65. ! [X0] : (((~old(X0) | rich(X0)) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | (old(X0) & ~rich(X0)))) [nnf transformation 11]
66. ! [X0] : ((~old(X0) | rich(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | (old(X0) & ~rich(X0)))) [flattening 65]
85. ~creative(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 38]
86. ~creative(X0) | happy(X0) | quiet(X0) [cnf transformation 38]
104. ~generous(X0) | rich(X0) | ~old(X0) [cnf transformation 29]
120. ~rich(X0) | ~happy(X0) | quiet(X0) [cnf transformation 66]
121. ~happy(X0) | quiet(X0) | old(X0) [cnf transformation 66]
122. ~rich(X0) | happy(X0) | ~quiet(X0) [cnf transformation 66]
123. ~quiet(X0) | happy(X0) | old(X0) [cnf transformation 66]
152. generous(john) [cnf transformation 23]
155. creative(john) [cnf transformation 25]
358. ~happy(john) | ~quiet(john) [resolution 85,155]
370. 42 <=> quiet(john) [avatar definition]
371. quiet(john) <- (42) [avatar component clause 370]
372. ~quiet(john) <- (~42) [avatar component clause 370]
374. 43 <=> happy(john) [avatar definition]
375. happy(john) <- (43) [avatar component clause 374]
376. ~happy(john) <- (~43) [avatar component clause 374]
377. ~42 | ~43 [avatar split clause 358,374,370]
380. happy(john) | quiet(john) [resolution 86,155]
389. rich(john) | ~old(john) [resolution 104,152]
391. 44 <=> old(john) [avatar definition]
393. ~old(john) <- (~44) [avatar component clause 391]
395. 45 <=> rich(john) [avatar definition]
397. rich(john) <- (45) [avatar component clause 395]
398. ~44 | 45 [avatar split clause 389,395,391]
408. happy(john) | old(john) <- (42) [resolution 123,371]
412. old(john) <- (42, ~43) [subsumption resolution 408,376]
413. $false <- (42, ~43, ~44) [subsumption resolution 412,393]
414. ~42 | 43 | 44 [avatar contradiction clause 413]
416. 42 | 43 [avatar split clause 380,374,370]
434. quiet(john) | old(john) <- (43) [resolution 375,121]
437. old(john) <- (~42, 43) [subsumption resolution 434,372]
440. 44 | 42 | ~43 [avatar split clause 437,374,370,391]
463. happy(john) | ~quiet(john) <- (45) [resolution 397,122]
464. ~happy(john) | quiet(john) <- (45) [resolution 397,120]
469. 42 | ~43 | ~45 [avatar split clause 464,395,374,370]
470. ~42 | 43 | ~45 [avatar split clause 463,395,374,370]
480. $false [avatar sat refutation 377,398,414,416,440,469,470]
% SZS output end Proof for 4045819871396192020617955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not generous is either not kind or happy. If lucy is not happy or not patient then paul is calm or tall. If lucy is both happy and tall then alice is calm and vice versa. Everyone who is both not strong and rich is both not strong and not funny and vice versa. If susan is either tall or not quiet then someone is either brave or not creative. If someone is both tall and not calm then john is not rich or not strong and vice versa. Everyone who is generous or brave is both not humble and patient. If susan is not generous then paul is wise. Everyone who is not quiet or old is both brave and not patient. If susan is either kind or calm then fred is either not patient or rich and vice versa. If john is not creative or brave then alice is creative. Everyone who is not old is either generous or quiet. If susan is not curious then someone is not rich. Everyone who is tall is not quiet and vice versa. If paul is both rich and wise then alice is either patient or curious. Everyone who is not funny or not tall is not brave or not rich and vice versa. John is either not curious or creative. Mary is either not curious or brave. Mary is either strong or not creative. Someone is humble. Someone is not tall or tall. Someone is not happy or not humble. Someone is happy. Someone is either not curious or wise. | Mary is generous. | contradiction | (![X]:((~funny(X)&~generous(X))=>(~kind(X)<~>happy(X))))&
(((~happy(lucy)|~patient(lucy)))=>((calm(paul)|tall(paul))))&
(((happy(lucy)&tall(lucy)))<=>(calm(alice)))&
(![X]:((~strong(X)&rich(X))<=>(~strong(X)&~funny(X))))&
(((tall(susan)<~>~quiet(susan)))=>(?[X]:((brave(X)<~>~creative(X)))))&
((?[X]:((tall(X)&~calm(X))))<=>((~rich(john)|~strong(john))))&
(![X]:((generous(X)|brave(X))=>(~humble(X)&patient(X))))&
((~generous(susan))=>(wise(paul)))&
(![X]:((~quiet(X)|old(X))=>(brave(X)&~patient(X))))&
(((kind(susan)<~>calm(susan)))<=>((~patient(fred)<~>rich(fred))))&
(((~creative(john)|brave(john)))=>(creative(alice)))&
(![X]:(~old(X)=>(generous(X)<~>quiet(X))))&
((~curious(susan))=>(?[X]:(~rich(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
(((rich(paul)&wise(paul)))=>((patient(alice)<~>curious(alice))))&
(![X]:((~funny(X)|~tall(X))<=>(~brave(X)|~rich(X))))&
((~curious(john)<~>creative(john)))&
((~curious(mary)<~>brave(mary)))&
((strong(mary)<~>~creative(mary)))&
(?[X]:(humble(X)))&
(?[X]:((~tall(X)|tall(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:(happy(X)))&
(?[X]:((~curious(X)<~>wise(X)))) | generous(mary) | [
"p6",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2679451815731102142510367
% SZS output start Proof for 2679451815731102142510367
7. ! [X0] : ((brave(X0) | generous(X0)) => (patient(X0) & ~humble(X0))) [input p6]
9. ! [X0] : ((old(X0) | ~quiet(X0)) => (~patient(X0) & brave(X0))) [input p8]
12. ! [X0] : (~old(X0) => (generous(X0) <~> quiet(X0))) [input p11]
14. ! [X0] : (tall(X0) <=> ~quiet(X0)) [input p13]
25. generous(mary) [input hypothesis]
31. ! [X0] : ((patient(X0) & ~humble(X0)) | (~brave(X0) & ~generous(X0))) [ennf transformation 7]
33. ! [X0] : ((~patient(X0) & brave(X0)) | (~old(X0) & quiet(X0))) [ennf transformation 9]
35. ! [X0] : ((generous(X0) <~> quiet(X0)) | old(X0)) [ennf transformation 12]
53. ! [X0] : (((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | old(X0)) [nnf transformation 35]
56. ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))) [nnf transformation 14]
96. ~generous(X0) | patient(X0) [cnf transformation 31]
97. ~brave(X0) | patient(X0) [cnf transformation 31]
99. brave(X0) | quiet(X0) [cnf transformation 33]
101. ~patient(X0) | quiet(X0) [cnf transformation 33]
102. ~old(X0) | ~patient(X0) [cnf transformation 33]
114. ~quiet(X0) | ~generous(X0) | old(X0) [cnf transformation 53]
116. ~quiet(X0) | ~tall(X0) [cnf transformation 56]
117. quiet(X0) | tall(X0) [cnf transformation 56]
136. generous(mary) [cnf transformation 25]
327. patient(mary) [resolution 96,136]
329. quiet(X0) | patient(X0) [resolution 99,97]
333. quiet(X0) [subsumption resolution 329,101]
336. ~tall(X0) [resolution 116,333]
379. ~generous(X0) | old(X0) | tall(X0) [resolution 114,117]
381. ~generous(X0) | old(X0) [subsumption resolution 379,336]
383. old(mary) [resolution 381,136]
386. ~patient(mary) [resolution 383,102]
388. $false [subsumption resolution 386,327]
% SZS output end Proof for 2679451815731102142510367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both wise and not curious then mary is either brave or not tall and vice versa. Everyone who is both happy and kind is both not rich and not curious and vice versa. Everyone who is either not funny or not wise is either not old or strong and vice versa. If someone is both not creative and kind then susan is not rich. Everyone who is both not funny and not calm is both wise and not happy and vice versa. If susan is not calm then lucy is not patient. Everyone who is both curious and not creative is calm and vice versa. Everyone who is not funny or not humble is either quiet or calm. Everyone who is brave is not brave or calm and vice versa. Everyone who is either not creative or not happy is old or patient. If lucy is not happy or happy then mary is both not tall and patient and vice versa. If someone is quiet or not old then someone is quiet. Everyone who is either kind or creative is both not curious and not calm. If john is both humble and not patient then fred is either not humble or patient and vice versa. Everyone who is not funny is both not humble and not strong. Lucy is generous. Mary is both not happy and brave. Someone is not kind. Lucy is both not funny and not old. Lucy is either strong or tall. Someone is both patient and wise. Susan is both calm and not funny. Someone is strong. | Susan is quiet. | contradiction | (((wise(lucy)&~curious(lucy)))<=>((brave(mary)<~>~tall(mary))))&
(![X]:((happy(X)&kind(X))<=>(~rich(X)&~curious(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~old(X)<~>strong(X))))&
((?[X]:((~creative(X)&kind(X))))=>(~rich(susan)))&
(![X]:((~funny(X)&~calm(X))<=>(wise(X)&~happy(X))))&
((~calm(susan))=>(~patient(lucy)))&
(![X]:((curious(X)&~creative(X))<=>calm(X)))&
(![X]:((~funny(X)|~humble(X))=>(quiet(X)<~>calm(X))))&
(![X]:(brave(X)<=>(~brave(X)|calm(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(old(X)|patient(X))))&
(((~happy(lucy)|happy(lucy)))<=>((~tall(mary)&patient(mary))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:(quiet(X))))&
(![X]:((kind(X)<~>creative(X))=>(~curious(X)&~calm(X))))&
(((humble(john)&~patient(john)))<=>((~humble(fred)<~>patient(fred))))&
(![X]:(~funny(X)=>(~humble(X)&~strong(X))))&
(generous(lucy))&
((~happy(mary)&brave(mary)))&
(?[X]:(~kind(X)))&
((~funny(lucy)&~old(lucy)))&
((strong(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)&wise(X))))&
((calm(susan)&~funny(susan)))&
(?[X]:(strong(X))) | quiet(susan) | [
"p7",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7195593479598927259124511
% SZS output start Proof for 7195593479598927259124511
8. ! [X0] : ((~humble(X0) | ~funny(X0)) => (quiet(X0) <~> calm(X0))) [input p7]
9. ! [X0] : (brave(X0) <=> (calm(X0) | ~brave(X0))) [input p8]
22. ~funny(susan) & calm(susan) [input p21]
24. quiet(susan) [input hypothesis]
29. ! [X0] : ((quiet(X0) <~> calm(X0)) | (humble(X0) & funny(X0))) [ennf transformation 8]
44. ! [X0] : (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (humble(X0) & funny(X0))) [nnf transformation 29]
45. ! [X0] : ((brave(X0) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | ~brave(X0))) [nnf transformation 9]
46. ! [X0] : ((brave(X0) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | ~brave(X0))) [flattening 45]
92. ~quiet(X0) | ~calm(X0) | funny(X0) [cnf transformation 44]
94. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 46]
95. brave(X0) | brave(X0) [cnf transformation 46]
128. ~funny(susan) [cnf transformation 22]
130. quiet(susan) [cnf transformation 24]
131. calm(X0) | ~brave(X0) [duplicate literal removal 94]
132. brave(X0) [duplicate literal removal 95]
172. calm(X0) [subsumption resolution 131,132]
258. ~calm(susan) | funny(susan) [resolution 92,130]
263. funny(susan) [subsumption resolution 258,172]
264. $false [subsumption resolution 263,128]
% SZS output end Proof for 7195593479598927259124511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not generous or not wise then mary is both funny and not old and vice versa.
If lucy is both calm and curious then someone is either not old or not curious and vice versa.
Everyone who is both tall and not generous is rich or curious.
Everyone who is either not generous or not strong is not generous and vice versa.
Everyone who is rich is not curious or humble and vice versa.
If susan is not kind or not humble then alice is not strong and vice versa.
If alice is both not curious and not tall then alice is either not tall or not funny and vice versa.
Everyone who is either not humble or not wise is funny or curious.
Everyone who is brave or not brave is both happy and funny.
Everyone who is both not curious and not funny is not calm.
Everyone who is both not generous and generous is either not tall or not strong and vice versa.
If mary is either humble or creative then susan is not generous or creative and vice versa.
If lucy is not wise then susan is wise and vice versa.
Everyone who is both old and not wise is rich or not kind and vice versa.
If someone is calm or not creative then someone is both brave and patient and vice versa.
If paul is not kind then someone is both not old and kind and vice versa.
Mary is both not kind and old.
John is wise.
Someone is wise.
Mary is either happy or not happy.
Alice is either creative or not brave.
Someone is both old and not creative.
Someone is tall or not wise.
John is both strong and brave. | Lucy is not kind. | contradiction | (((~generous(paul)<~>~wise(paul)))<=>((funny(mary)&~old(mary))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((~old(X)<~>~curious(X)))))&
(![X]:((tall(X)&~generous(X))=>(rich(X)|curious(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>~generous(X)))&
(![X]:(rich(X)<=>(~curious(X)|humble(X))))&
(((~kind(susan)|~humble(susan)))<=>(~strong(alice)))&
(((~curious(alice)&~tall(alice)))<=>((~tall(alice)<~>~funny(alice))))&
(![X]:((~humble(X)<~>~wise(X))=>(funny(X)|curious(X))))&
(![X]:((brave(X)|~brave(X))=>(happy(X)&funny(X))))&
(![X]:((~curious(X)&~funny(X))=>~calm(X)))&
(![X]:((~generous(X)&generous(X))<=>(~tall(X)<~>~strong(X))))&
(((humble(mary)<~>creative(mary)))<=>((~generous(susan)|creative(susan))))&
((~wise(lucy))<=>(wise(susan)))&
(![X]:((old(X)&~wise(X))<=>(rich(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((~kind(paul))<=>(?[X]:((~old(X)&kind(X)))))&
((~kind(mary)&old(mary)))&
(wise(john))&
(?[X]:(wise(X)))&
((happy(mary)<~>~happy(mary)))&
((creative(alice)<~>~brave(alice)))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(john)&brave(john))) | ~kind(lucy) | [
"p3",
"p4",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7148050679924546494674662
% SZS output start Proof for 7148050679924546494674662
4. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> ~generous(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> (humble(X0) | ~curious(X0))) [input p4]
6. (~humble(susan) | ~kind(susan)) <=> ~strong(alice) [input p5]
13. ~wise(lucy) <=> wise(susan) [input p12]
14. ! [X0] : ((~wise(X0) & old(X0)) <=> (~kind(X0) | rich(X0))) [input p13]
25. ~kind(lucy) [input hypothesis]
41. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | generous(X0)) & (~generous(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 4]
42. ! [X0] : ((rich(X0) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | ~rich(X0))) [nnf transformation 5]
43. ! [X0] : ((rich(X0) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | ~rich(X0))) [flattening 42]
44. ((~humble(susan) | ~kind(susan)) | strong(alice)) & (~strong(alice) | (humble(susan) & kind(susan))) [nnf transformation 6]
45. (~humble(susan) | ~kind(susan) | strong(alice)) & (~strong(alice) | (humble(susan) & kind(susan))) [flattening 44]
53. (~wise(lucy) | ~wise(susan)) & (wise(susan) | wise(lucy)) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) & old(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 14]
55. ! [X0] : (((~wise(X0) & old(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | wise(X0) | ~old(X0))) [flattening 54]
87. ~generous(X0) | ~generous(X0) | strong(X0) [cnf transformation 41]
89. strong(X0) | generous(X0) | generous(X0) [cnf transformation 41]
92. ~humble(X0) | rich(X0) [cnf transformation 43]
94. ~strong(alice) | humble(susan) [cnf transformation 45]
121. wise(susan) | wise(lucy) [cnf transformation 53]
126. ~rich(X0) | ~wise(X0) [cnf transformation 55]
127. ~wise(X0) | kind(X0) [cnf transformation 55]
149. ~kind(lucy) [cnf transformation 25]
152. ~generous(X0) | strong(X0) [duplicate literal removal 87]
153. strong(X0) | generous(X0) [duplicate literal removal 89]
204. strong(X0) [subsumption resolution 152,153]
205. humble(susan) [subsumption resolution 94,204]
251. 18 <=> wise(susan) [avatar definition]
255. 19 <=> wise(lucy) [avatar definition]
256. wise(lucy) <- (19) [avatar component clause 255]
259. 19 | 18 [avatar split clause 121,251,255]
340. rich(susan) [resolution 92,205]
347. ~wise(susan) [resolution 126,340]
350. ~18 [avatar split clause 347,251]
353. kind(lucy) <- (19) [resolution 127,256]
354. $false <- (19) [subsumption resolution 353,149]
355. ~19 [avatar contradiction clause 354]
356. $false [avatar sat refutation 259,350,355]
% SZS output end Proof for 7148050679924546494674662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not calm is either not rich or not calm.
Everyone who is both not patient and not funny is either not tall or not happy.
If someone is both happy and not patient then lucy is either not quiet or brave and vice versa.
Everyone who is generous is generous or quiet and vice versa.
If paul is both not old and old then someone is not calm or humble and vice versa.
Everyone who is rich or not patient is either old or not patient and vice versa.
Everyone who is both quiet and not quiet is both not kind and not funny.
Everyone who is funny is both not tall and humble.
If mary is generous then lucy is both strong and not creative.
If fred is not tall then someone is not old and vice versa.
If fred is both not brave and not generous then alice is both happy and not tall and vice versa.
Everyone who is both kind and calm is not tall or not rich and vice versa.
Everyone who is not old or not kind is patient.
If john is not brave then someone is tall or not kind.
Fred is both quiet and not wise.
Someone is not happy or not patient.
Alice is not wise or not creative.
John is either brave or not happy.
Paul is kind or not strong. | John is not generous. | neutral | (![X]:((~funny(X)|~calm(X))=>(~rich(X)<~>~calm(X))))&
(![X]:((~patient(X)&~funny(X))=>(~tall(X)<~>~happy(X))))&
((?[X]:((happy(X)&~patient(X))))<=>((~quiet(lucy)<~>brave(lucy))))&
(![X]:(generous(X)<=>(generous(X)|quiet(X))))&
(((~old(paul)&old(paul)))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((rich(X)|~patient(X))<=>(old(X)<~>~patient(X))))&
(![X]:((quiet(X)&~quiet(X))=>(~kind(X)&~funny(X))))&
(![X]:(funny(X)=>(~tall(X)&humble(X))))&
((generous(mary))=>((strong(lucy)&~creative(lucy))))&
((~tall(fred))<=>(?[X]:(~old(X))))&
(((~brave(fred)&~generous(fred)))<=>((happy(alice)&~tall(alice))))&
(![X]:((kind(X)&calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((~old(X)|~kind(X))=>patient(X)))&
((~brave(john))=>(?[X]:((tall(X)|~kind(X)))))&
((quiet(fred)&~wise(fred)))&
(?[X]:((~happy(X)|~patient(X))))&
((~wise(alice)|~creative(alice)))&
((brave(john)<~>~happy(john)))&
((kind(paul)|~strong(paul))) | ~generous(john) | [] | null | 0 |
Everyone who is either curious or not tall is either not strong or curious and vice versa. Everyone who is either happy or not creative is creative. Everyone who is both not humble and not generous is not curious and vice versa. If someone is happy then someone is humble or not tall. Everyone who is both not kind and kind is either not wise or quiet. If someone is both calm and not happy then someone is quiet and vice versa. Everyone who is not funny or not wise is both not generous and wise. Everyone who is not humble or humble is funny or not generous and vice versa. If someone is patient then someone is either wise or happy. Everyone who is both not generous and not brave is funny or creative. Everyone who is both kind and not strong is either not tall or not quiet. If someone is tall then fred is either funny or not happy. Everyone who is not funny is both not humble and old. If someone is either brave or generous then lucy is both old and kind and vice versa. If someone is humble or brave then someone is not rich. If someone is not funny then lucy is brave. Someone is not funny. Paul is not funny. Someone is tall. Someone is both generous and not quiet. Someone is curious. Someone is both not brave and not humble. | Paul is not curious. | entailment | (![X]:((curious(X)<~>~tall(X))<=>(~strong(X)<~>curious(X))))&
(![X]:((happy(X)<~>~creative(X))=>creative(X)))&
(![X]:((~humble(X)&~generous(X))<=>~curious(X)))&
((?[X]:(happy(X)))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~kind(X)&kind(X))=>(~wise(X)<~>quiet(X))))&
((?[X]:((calm(X)&~happy(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~wise(X))=>(~generous(X)&wise(X))))&
(![X]:((~humble(X)|humble(X))<=>(funny(X)|~generous(X))))&
((?[X]:(patient(X)))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~generous(X)&~brave(X))=>(funny(X)|creative(X))))&
(![X]:((kind(X)&~strong(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:(tall(X)))=>((funny(fred)<~>~happy(fred))))&
(![X]:(~funny(X)=>(~humble(X)&old(X))))&
((?[X]:((brave(X)<~>generous(X))))<=>((old(lucy)&kind(lucy))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(?[X]:(~funny(X)))&
(~funny(paul))&
(?[X]:(tall(X)))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)&~humble(X)))) | ~curious(paul) | [
"p2",
"p6",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8563356621234311799659392
% SZS output start Proof for 8563356621234311799659392
3. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> ~curious(X0)) [input p2]
7. ! [X0] : ((~wise(X0) | ~funny(X0)) => (wise(X0) & ~generous(X0))) [input p6]
13. ! [X0] : (~funny(X0) => (old(X0) & ~humble(X0))) [input p12]
18. ~funny(paul) [input p17]
23. curious(paul) [input hypothesis]
34. ! [X0] : ((wise(X0) & ~generous(X0)) | (wise(X0) & funny(X0))) [ennf transformation 7]
40. ! [X0] : ((old(X0) & ~humble(X0)) | funny(X0)) [ennf transformation 13]
44. ! [X0] : (((~generous(X0) & ~humble(X0)) | curious(X0)) & (~curious(X0) | (generous(X0) | humble(X0)))) [nnf transformation 3]
45. ! [X0] : (((~generous(X0) & ~humble(X0)) | curious(X0)) & (~curious(X0) | generous(X0) | humble(X0))) [flattening 44]
84. ~curious(X0) | generous(X0) | humble(X0) [cnf transformation 45]
93. ~generous(X0) | funny(X0) [cnf transformation 34]
106. ~humble(X0) | funny(X0) [cnf transformation 40]
116. ~funny(paul) [cnf transformation 18]
123. curious(paul) [cnf transformation 23]
229. generous(paul) | humble(paul) [resolution 84,123]
241. 22 <=> humble(paul) [avatar definition]
243. humble(paul) <- (22) [avatar component clause 241]
245. 23 <=> generous(paul) [avatar definition]
247. generous(paul) <- (23) [avatar component clause 245]
248. 22 | 23 [avatar split clause 229,245,241]
252. funny(paul) <- (22) [resolution 243,106]
254. $false <- (22) [subsumption resolution 252,116]
255. ~22 [avatar contradiction clause 254]
267. funny(paul) <- (23) [resolution 247,93]
269. $false <- (23) [subsumption resolution 267,116]
270. ~23 [avatar contradiction clause 269]
271. $false [avatar sat refutation 248,255,270]
% SZS output end Proof for 8563356621234311799659392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous or not brave then someone is patient.
If someone is not funny then someone is both wise and not brave.
Everyone who is not curious is funny and vice versa.
Everyone who is both generous and kind is both not wise and not old and vice versa.
If mary is either tall or quiet then someone is both not old and not quiet.
Everyone who is either curious or not curious is not old or kind and vice versa.
Everyone who is not brave or curious is not curious and vice versa.
If someone is curious or humble then john is creative.
If someone is either not kind or not happy then alice is both funny and not humble and vice versa.
Everyone who is both generous and not generous is generous.
Everyone who is both brave and not patient is either wise or not quiet.
Everyone who is either tall or patient is both not quiet and not creative.
Everyone who is either not funny or not kind is curious or not patient and vice versa.
If someone is either creative or brave then someone is wise or kind.
Everyone who is both creative and strong is patient or old and vice versa.
If someone is quiet or not strong then fred is both quiet and not strong and vice versa.
Someone is not calm or tall.
Paul is either curious or not rich.
Someone is both calm and not brave.
Paul is not tall or creative.
Alice is both not calm and kind.
Someone is either tall or not strong.
Someone is either not creative or kind. | Paul is brave. | contradiction | (((~generous(alice)|~brave(alice)))=>(?[X]:(patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(?[X]:((~calm(X)|tall(X))))&
((curious(paul)<~>~rich(paul)))&
(?[X]:((calm(X)&~brave(X))))&
((~tall(paul)|creative(paul)))&
((~calm(alice)&kind(alice)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~creative(X)<~>kind(X)))) | brave(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4196080010197203122191949
% SZS output start Proof for 4196080010197203122191949
7. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p6]
24. brave(paul) [input hypothesis]
50. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 7]
51. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 50]
104. ~curious(X0) | ~curious(X0) [cnf transformation 51]
105. curious(X0) | ~brave(X0) | curious(X0) [cnf transformation 51]
151. brave(paul) [cnf transformation 24]
153. ~curious(X0) [duplicate literal removal 104]
154. ~brave(X0) | curious(X0) [duplicate literal removal 105]
328. curious(paul) [resolution 154,151]
329. $false [subsumption resolution 328,153]
% SZS output end Proof for 4196080010197203122191949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not humble then someone is not brave or curious and vice versa.
If someone is creative then susan is either strong or calm and vice versa.
If someone is both not calm and rich then someone is not strong.
If alice is either rich or not humble then susan is not strong or not generous and vice versa.
If mary is both generous and kind then mary is happy or not calm.
If fred is creative then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Paul is both humble and not curious.
Fred is either not rich or humble.
Someone is both wise and not rich.
Fred is either patient or quiet. | Susan is humble. | neutral | (((patient(lucy)|~humble(lucy)))<=>(?[X]:((~brave(X)|curious(X)))))&
((?[X]:(creative(X)))<=>((strong(susan)<~>calm(susan))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:(~strong(X))))&
(((rich(alice)<~>~humble(alice)))<=>((~strong(susan)|~generous(susan))))&
(((generous(mary)&kind(mary)))=>((happy(mary)|~calm(mary))))&
((creative(fred))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
((humble(paul)&~curious(paul)))&
((~rich(fred)<~>humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
((patient(fred)<~>quiet(fred))) | humble(susan) | [] | null | 0 |
If someone is not creative then alice is either brave or not strong and vice versa.
Everyone who is rich is either quiet or strong.
Everyone who is humble or not calm is both not humble and brave and vice versa.
Everyone who is both not wise and wise is wise or not funny.
If mary is either not curious or quiet then someone is tall or brave.
If paul is not kind or not funny then alice is kind.
If susan is either not calm or not funny then someone is both creative and wise and vice versa.
If someone is not calm or rich then fred is both rich and patient and vice versa.
If alice is creative then someone is creative or old and vice versa.
Everyone who is either generous or not humble is either not curious or not humble.
If susan is either funny or not funny then someone is wise or strong.
If someone is both not creative and creative then lucy is either not strong or not brave.
Everyone who is not wise is old.
If mary is not quiet then paul is not wise.
Everyone who is wise is not brave.
If someone is either not funny or not happy then someone is both tall and not creative.
Someone is either not wise or strong.
Someone is either old or kind.
John is funny or creative.
Lucy is not old.
Someone is either not generous or not old.
Someone is not kind or generous.
Someone is curious or not happy. | Susan is funny. | neutral | ((?[X]:(~creative(X)))<=>((brave(alice)<~>~strong(alice))))&
(![X]:(rich(X)=>(quiet(X)<~>strong(X))))&
(![X]:((humble(X)|~calm(X))<=>(~humble(X)&brave(X))))&
(![X]:((~wise(X)&wise(X))=>(wise(X)|~funny(X))))&
(((~curious(mary)<~>quiet(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(((~kind(paul)|~funny(paul)))=>(kind(alice)))&
(((~calm(susan)<~>~funny(susan)))<=>(?[X]:((creative(X)&wise(X)))))&
((?[X]:((~calm(X)|rich(X))))<=>((rich(fred)&patient(fred))))&
((creative(alice))<=>(?[X]:((creative(X)|old(X)))))&
(![X]:((generous(X)<~>~humble(X))=>(~curious(X)<~>~humble(X))))&
(((funny(susan)<~>~funny(susan)))=>(?[X]:((wise(X)|strong(X)))))&
((?[X]:((~creative(X)&creative(X))))=>((~strong(lucy)<~>~brave(lucy))))&
(![X]:(~wise(X)=>old(X)))&
((~quiet(mary))=>(~wise(paul)))&
(![X]:(wise(X)=>~brave(X)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&~creative(X)))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((old(X)<~>kind(X))))&
((funny(john)|creative(john)))&
(~old(lucy))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:((~kind(X)|generous(X))))&
(?[X]:((curious(X)|~happy(X)))) | funny(susan) | [] | null | 0 |
Everyone who is either not tall or not patient is both old and creative. If someone is happy then someone is both creative and not creative and vice versa. If someone is not creative or not funny then fred is not creative. Everyone who is both not rich and old is not happy. Everyone who is either funny or brave is either not kind or rich and vice versa. Everyone who is either old or happy is not strong or not old and vice versa. If paul is kind or not brave then someone is both not funny and not tall. If alice is either strong or not funny then someone is either curious or not brave. Everyone who is both not happy and not calm is both not kind and not old. Everyone who is not calm or not curious is curious or not brave. Everyone who is both not old and not strong is not tall and vice versa. Everyone who is humble or brave is not funny or old and vice versa. Everyone who is rich or generous is funny and vice versa. Everyone who is not creative is calm or not tall. If susan is generous or not curious then someone is both not strong and generous and vice versa. Someone is not humble. Someone is not creative. Someone is rich. Someone is kind or not brave. Susan is strong or not funny. Someone is either not generous or not brave. | Alice is not curious. | neutral | (![X]:((~tall(X)<~>~patient(X))=>(old(X)&creative(X))))&
((?[X]:(happy(X)))<=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:((~creative(X)|~funny(X))))=>(~creative(fred)))&
(![X]:((~rich(X)&old(X))=>~happy(X)))&
(![X]:((funny(X)<~>brave(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)<~>happy(X))<=>(~strong(X)|~old(X))))&
(((kind(paul)|~brave(paul)))=>(?[X]:((~funny(X)&~tall(X)))))&
(((strong(alice)<~>~funny(alice)))=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~kind(X)&~old(X))))&
(![X]:((~calm(X)|~curious(X))=>(curious(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))<=>~tall(X)))&
(![X]:((humble(X)|brave(X))<=>(~funny(X)|old(X))))&
(![X]:((rich(X)|generous(X))<=>funny(X)))&
(![X]:(~creative(X)=>(calm(X)|~tall(X))))&
(((generous(susan)|~curious(susan)))<=>(?[X]:((~strong(X)&generous(X)))))&
(?[X]:(~humble(X)))&
(?[X]:(~creative(X)))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|~brave(X))))&
((strong(susan)|~funny(susan)))&
(?[X]:((~generous(X)<~>~brave(X)))) | ~curious(alice) | [] | null | 0 |
Everyone who is not strong or strong is both not curious and not happy and vice versa. If someone is either funny or generous then someone is both not calm and not patient. Everyone who is both not curious and not wise is not happy. If paul is both funny and not kind then someone is either tall or not creative and vice versa. Everyone who is not patient is both not humble and rich. If someone is not old then mary is not wise and vice versa. Everyone who is either patient or strong is not wise. Everyone who is both quiet and curious is not creative and vice versa. If lucy is either not old or not generous then mary is both wise and calm and vice versa. If fred is brave then someone is either tall or quiet and vice versa. If someone is not calm then susan is both not brave and not patient and vice versa. Everyone who is either humble or not happy is rich or not funny. Everyone who is not tall or not quiet is not old or generous. If alice is both not happy and not funny then someone is generous. If lucy is not old then someone is patient and vice versa. John is funny. Someone is either not tall or funny. Someone is patient. Someone is either calm or humble. Lucy is not kind or quiet. | Paul is not patient. | neutral | (![X]:((~strong(X)|strong(X))<=>(~curious(X)&~happy(X))))&
((?[X]:((funny(X)<~>generous(X))))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~curious(X)&~wise(X))=>~happy(X)))&
(((funny(paul)&~kind(paul)))<=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:(~patient(X)=>(~humble(X)&rich(X))))&
((?[X]:(~old(X)))<=>(~wise(mary)))&
(![X]:((patient(X)<~>strong(X))=>~wise(X)))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(((~happy(alice)&~funny(alice)))=>(?[X]:(generous(X))))&
((~old(lucy))<=>(?[X]:(patient(X))))&
(funny(john))&
(?[X]:((~tall(X)<~>funny(X))))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)<~>humble(X))))&
((~kind(lucy)|quiet(lucy))) | ~patient(paul) | [] | null | 0 |
If someone is either not patient or patient then someone is either not creative or not funny. Everyone who is either not quiet or quiet is either funny or patient. Everyone who is either not generous or not curious is creative and vice versa. Everyone who is generous is both rich and generous. If someone is not curious or not generous then paul is both calm and not creative and vice versa. If fred is either patient or not humble then someone is rich or wise and vice versa. Everyone who is both wise and not calm is not brave or curious and vice versa. If lucy is either not happy or not rich then someone is both not wise and not generous. If someone is both not kind and not patient then john is not strong or not brave and vice versa. Everyone who is rich is not quiet or old and vice versa. If someone is both not patient and funny then lucy is not rich or not brave. Everyone who is calm or not brave is not kind or not rich and vice versa. Everyone who is old is either not creative or kind. Everyone who is either not patient or not calm is creative or patient. Everyone who is either not calm or not generous is both patient and tall and vice versa. If someone is calm then someone is both old and happy. Someone is both not calm and funny. Susan is either quiet or happy. Mary is not creative. Someone is funny. Mary is quiet or curious. Lucy is curious. Someone is either not patient or generous. John is patient. | Paul is not tall. | contradiction | ((?[X]:((~patient(X)<~>patient(X))))=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>(funny(X)<~>patient(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>creative(X)))&
(![X]:(generous(X)=>(rich(X)&generous(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((calm(paul)&~creative(paul))))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((wise(X)&~calm(X))<=>(~brave(X)|curious(X))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(![X]:(rich(X)<=>(~quiet(X)|old(X))))&
((?[X]:((~patient(X)&funny(X))))=>((~rich(lucy)|~brave(lucy))))&
(![X]:((calm(X)|~brave(X))<=>(~kind(X)|~rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>kind(X))))&
(![X]:((~patient(X)<~>~calm(X))=>(creative(X)|patient(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(patient(X)&tall(X))))&
((?[X]:(calm(X)))=>(?[X]:((old(X)&happy(X)))))&
(?[X]:((~calm(X)&funny(X))))&
((quiet(susan)<~>happy(susan)))&
(~creative(mary))&
(?[X]:(funny(X)))&
((quiet(mary)|curious(mary)))&
(curious(lucy))&
(?[X]:((~patient(X)<~>generous(X))))&
(patient(john)) | ~tall(paul) | [
"p2",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6998028340987868492722620
% SZS output start Proof for 6998028340987868492722620
3. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> creative(X0)) [input p2]
5. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (~creative(paul) & calm(paul)) [input p4]
7. ! [X0] : ((~calm(X0) & wise(X0)) <=> (curious(X0) | ~brave(X0))) [input p6]
15. ! [X0] : ((~calm(X0) <~> ~generous(X0)) <=> (tall(X0) & patient(X0))) [input p14]
25. ~tall(paul) [input hypothesis]
43. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~creative(X0)) & (creative(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 3]
44. (? [X0] : (~generous(X0) | ~curious(X0)) | (creative(paul) | ~calm(paul))) & ((~creative(paul) & calm(paul)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 5]
45. (? [X0] : (~generous(X0) | ~curious(X0)) | creative(paul) | ~calm(paul)) & ((~creative(paul) & calm(paul)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 44]
46. (? [X0] : (~generous(X0) | ~curious(X0)) | creative(paul) | ~calm(paul)) & ((~creative(paul) & calm(paul)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 45]
47. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK1) | ~curious(sK1)) [choice axiom]
48. ((~generous(sK1) | ~curious(sK1)) | creative(paul) | ~calm(paul)) & ((~creative(paul) & calm(paul)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 46,47]
53. ! [X0] : (((~calm(X0) & wise(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 7]
54. ! [X0] : (((~calm(X0) & wise(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | calm(X0) | ~wise(X0))) [flattening 53]
69. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [nnf transformation 15]
70. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [flattening 69]
91. ~generous(X0) | creative(X0) | curious(X0) [cnf transformation 43]
97. calm(paul) | generous(X1) [cnf transformation 48]
98. ~creative(paul) | curious(X1) [cnf transformation 48]
111. ~calm(X0) | ~curious(X0) [cnf transformation 54]
135. ~generous(X0) | tall(X0) | calm(X0) [cnf transformation 70]
136. ~calm(X0) | tall(X0) | generous(X0) [cnf transformation 70]
152. ~tall(paul) [cnf transformation 25]
183. 5 <=> calm(paul) [avatar definition]
184. calm(paul) <- (5) [avatar component clause 183]
185. ~calm(paul) <- (~5) [avatar component clause 183]
187. 6 <=> creative(paul) [avatar definition]
188. ~creative(paul) <- (~6) [avatar component clause 187]
200. 9 <=> ! [X1] : generous(X1) [avatar definition]
201. generous(X1) <- (9) [avatar component clause 200]
204. 10 <=> ! [X1] : curious(X1) [avatar definition]
205. curious(X1) <- (10) [avatar component clause 204]
206. 10 | ~6 [avatar split clause 98,187,204]
207. 9 | 5 [avatar split clause 97,183,200]
354. ~curious(paul) <- (5) [resolution 111,184]
355. $false <- (5, 10) [subsumption resolution 354,205]
356. ~5 | ~10 [avatar contradiction clause 355]
449. 48 <=> generous(paul) [avatar definition]
450. ~generous(paul) <- (~48) [avatar component clause 449]
451. generous(paul) <- (48) [avatar component clause 449]
458. creative(paul) | curious(paul) <- (48) [resolution 451,91]
460. curious(paul) <- (~6, 48) [subsumption resolution 458,188]
461. $false <- (5, ~6, 48) [subsumption resolution 460,354]
462. ~5 | 6 | ~48 [avatar contradiction clause 461]
473. tall(paul) | generous(paul) <- (5) [resolution 136,184]
474. generous(paul) <- (5) [subsumption resolution 473,152]
475. $false <- (5, ~48) [subsumption resolution 474,450]
476. ~5 | 48 [avatar contradiction clause 475]
477. tall(X0) | calm(X0) <- (9) [resolution 201,135]
515. calm(paul) <- (9) [resolution 477,152]
519. $false <- (~5, 9) [subsumption resolution 515,185]
520. 5 | ~9 [avatar contradiction clause 519]
521. $false [avatar sat refutation 206,207,356,462,476,520]
% SZS output end Proof for 6998028340987868492722620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or patient then lucy is either calm or not rich and vice versa. Everyone who is curious or not kind is not old. Everyone who is funny is both old and not quiet. If someone is both tall and generous then alice is either not kind or happy. Everyone who is not happy or not rich is old or happy. Everyone who is either humble or generous is tall. Everyone who is not patient is old and vice versa. If susan is not brave then mary is both not happy and not quiet. Everyone who is not generous or generous is both not old and not wise. Everyone who is either creative or not funny is kind. Everyone who is both kind and not calm is either not wise or curious. If someone is either not calm or kind then someone is either not funny or not wise. Everyone who is humble or not strong is either not rich or creative. Everyone who is old or not kind is either wise or strong and vice versa. If someone is either not tall or not old then fred is happy. Someone is creative or not brave. Someone is either not humble or not old. Susan is happy or not patient. Someone is either funny or kind. Alice is not quiet or not rich. Alice is both not humble and not strong. | Fred is not curious. | neutral | ((?[X]:((wise(X)<~>patient(X))))<=>((calm(lucy)<~>~rich(lucy))))&
(![X]:((curious(X)|~kind(X))=>~old(X)))&
(![X]:(funny(X)=>(old(X)&~quiet(X))))&
((?[X]:((tall(X)&generous(X))))=>((~kind(alice)<~>happy(alice))))&
(![X]:((~happy(X)|~rich(X))=>(old(X)|happy(X))))&
(![X]:((humble(X)<~>generous(X))=>tall(X)))&
(![X]:(~patient(X)<=>old(X)))&
((~brave(susan))=>((~happy(mary)&~quiet(mary))))&
(![X]:((~generous(X)|generous(X))=>(~old(X)&~wise(X))))&
(![X]:((creative(X)<~>~funny(X))=>kind(X)))&
(![X]:((kind(X)&~calm(X))=>(~wise(X)<~>curious(X))))&
((?[X]:((~calm(X)<~>kind(X))))=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((humble(X)|~strong(X))=>(~rich(X)<~>creative(X))))&
(![X]:((old(X)|~kind(X))<=>(wise(X)<~>strong(X))))&
((?[X]:((~tall(X)<~>~old(X))))=>(happy(fred)))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
((happy(susan)|~patient(susan)))&
(?[X]:((funny(X)<~>kind(X))))&
((~quiet(alice)|~rich(alice)))&
((~humble(alice)&~strong(alice))) | ~curious(fred) | [] | null | 0 |
If someone is quiet or not curious then someone is not patient and vice versa.
If paul is not curious or not tall then someone is either not generous or not calm.
Everyone who is either not quiet or curious is quiet and vice versa.
Everyone who is kind or not curious is not funny or not generous and vice versa.
Everyone who is not rich or not brave is both not curious and not old and vice versa.
If someone is generous or not old then someone is either generous or not quiet and vice versa.
Everyone who is not wise is not generous and vice versa.
If mary is either not old or not patient then someone is not old.
Everyone who is both not brave and happy is both happy and not kind.
Everyone who is tall is not patient and vice versa.
If paul is happy then someone is either patient or not happy.
Everyone who is quiet is either creative or quiet.
If someone is not calm then susan is old or curious and vice versa.
Everyone who is either not creative or not quiet is not brave.
Fred is not wise.
Someone is funny.
Someone is either patient or not old.
Someone is not creative or not strong.
Fred is old. | Mary is not brave. | contradiction | ((?[X]:((quiet(X)|~curious(X))))<=>(?[X]:(~patient(X))))&
(((~curious(paul)|~tall(paul)))=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((~quiet(X)<~>curious(X))<=>quiet(X)))&
(![X]:((kind(X)|~curious(X))<=>(~funny(X)|~generous(X))))&
(![X]:((~rich(X)|~brave(X))<=>(~curious(X)&~old(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:(~wise(X)<=>~generous(X)))&
(((~old(mary)<~>~patient(mary)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)&happy(X))=>(happy(X)&~kind(X))))&
(![X]:(tall(X)<=>~patient(X)))&
((happy(paul))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
((?[X]:(~calm(X)))<=>((old(susan)|curious(susan))))&
(![X]:((~creative(X)<~>~quiet(X))=>~brave(X)))&
(~wise(fred))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)<~>~old(X))))&
(?[X]:((~creative(X)|~strong(X))))&
(old(fred)) | ~brave(mary) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7224549377081006830438518
% SZS output start Proof for 7224549377081006830438518
3. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> quiet(X0)) [input p2]
5. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> (~old(X0) & ~curious(X0))) [input p4]
20. ~brave(mary) [input hypothesis]
43. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 3]
46. ! [X0] : (((~brave(X0) | ~rich(X0)) | (old(X0) | curious(X0))) & ((~old(X0) & ~curious(X0)) | (brave(X0) & rich(X0)))) [nnf transformation 5]
47. ! [X0] : ((~brave(X0) | ~rich(X0) | old(X0) | curious(X0)) & ((~old(X0) & ~curious(X0)) | (brave(X0) & rich(X0)))) [flattening 46]
78. quiet(X0) | curious(X0) | quiet(X0) [cnf transformation 43]
80. curious(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 43]
87. ~curious(X0) | brave(X0) [cnf transformation 47]
117. ~brave(mary) [cnf transformation 20]
119. quiet(X0) | curious(X0) [duplicate literal removal 78]
120. curious(X0) | ~quiet(X0) [duplicate literal removal 80]
134. 4 <=> ! [X3] : curious(X3) [avatar definition]
135. curious(X3) <- (4) [avatar component clause 134]
165. curious(X0) [subsumption resolution 119,120]
166. 4 [avatar split clause 165,134]
267. brave(X0) <- (4) [resolution 87,135]
269. $false <- (4) [resolution 267,117]
270. ~4 [avatar contradiction clause 269]
271. $false [avatar sat refutation 166,270]
% SZS output end Proof for 7224549377081006830438518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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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