premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both not patient and brave is either creative or curious. If someone is not creative then susan is humble. Everyone who is quiet or not strong is either not tall or calm. Everyone who is tall or kind is generous and vice versa. Everyone who is both not tall and not quiet is brave. If john is not humble or patient then someone is rich or not generous. If someone is not humble then someone is not old and vice versa. If someone is both calm and not wise then alice is not wise or creative. Everyone who is both not patient and not humble is either not curious or calm. If mary is patient or wise then lucy is both not calm and quiet. Everyone who is kind or humble is both not creative and kind. Everyone who is either quiet or brave is either not tall or humble and vice versa. Everyone who is either humble or kind is brave and vice versa. Everyone who is wise or quiet is not rich or strong. If paul is brave then someone is happy and vice versa. Everyone who is calm is both kind and patient. Someone is not funny. Lucy is both generous and not kind. Someone is both not kind and old. Lucy is either curious or calm. Susan is either calm or quiet. Mary is not funny or not wise. Someone is either not wise or not happy. Susan is not humble. | John is not calm. | entailment | (![X]:((~patient(X)&brave(X))=>(creative(X)<~>curious(X))))&
((?[X]:(~creative(X)))=>(humble(susan)))&
(![X]:((quiet(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:((tall(X)|kind(X))<=>generous(X)))&
(![X]:((~tall(X)&~quiet(X))=>brave(X)))&
(((~humble(john)|patient(john)))=>(?[X]:((rich(X)|~generous(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((calm(X)&~wise(X))))=>((~wise(alice)|creative(alice))))&
(![X]:((~patient(X)&~humble(X))=>(~curious(X)<~>calm(X))))&
(((patient(mary)|wise(mary)))=>((~calm(lucy)&quiet(lucy))))&
(![X]:((kind(X)|humble(X))=>(~creative(X)&kind(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(?[X]:(~funny(X)))&
((generous(lucy)&~kind(lucy)))&
(?[X]:((~kind(X)&old(X))))&
((curious(lucy)<~>calm(lucy)))&
((calm(susan)<~>quiet(susan)))&
((~funny(mary)|~wise(mary)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(~humble(susan)) | ~calm(john) | [
"p1",
"p10",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4228406115664719742332674
% SZS output start Proof for 4228406115664719742332674
2. ? [X0] : ~creative(X0) => humble(susan) [input p1]
11. ! [X0] : ((humble(X0) | kind(X0)) => (kind(X0) & ~creative(X0))) [input p10]
16. ! [X0] : (calm(X0) => (patient(X0) & kind(X0))) [input p15]
24. ~humble(susan) [input p23]
25. calm(john) [input hypothesis]
35. humble(susan) | ! [X0] : creative(X0) [ennf transformation 2]
46. ! [X0] : ((kind(X0) & ~creative(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 11]
47. ! [X0] : ((patient(X0) & kind(X0)) | ~calm(X0)) [ennf transformation 16]
71. humble(susan) | creative(X0) [cnf transformation 35]
85. ~kind(X0) | ~creative(X0) [cnf transformation 46]
103. ~calm(X0) | kind(X0) [cnf transformation 47]
115. ~humble(susan) [cnf transformation 24]
116. calm(john) [cnf transformation 25]
118. 1 <=> ! [X0] : creative(X0) [avatar definition]
119. creative(X0) <- (1) [avatar component clause 118]
121. 2 <=> humble(susan) [avatar definition]
124. 1 | 2 [avatar split clause 71,121,118]
217. ~2 [avatar split clause 115,121]
218. kind(john) [resolution 103,116]
223. ~creative(john) [resolution 218,85]
224. $false <- (1) [subsumption resolution 223,119]
225. ~1 [avatar contradiction clause 224]
226. $false [avatar sat refutation 124,217,225]
% SZS output end Proof for 4228406115664719742332674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is either kind or not rich and vice versa.
Everyone who is not old or humble is both brave and not tall and vice versa.
Everyone who is not old is not happy and vice versa.
If someone is either not kind or strong then someone is either humble or not happy.
Everyone who is not humble is both not wise and not generous and vice versa.
If someone is either funny or patient then lucy is creative.
If someone is funny or not strong then paul is generous or not creative and vice versa.
If someone is tall or not generous then someone is not strong.
Everyone who is tall is not wise or not happy.
If alice is rich or not humble then fred is either kind or not brave.
If paul is both not curious and not rich then paul is either creative or rich and vice versa.
If lucy is not generous or old then someone is calm.
Everyone who is kind or not humble is both not happy and patient and vice versa.
Everyone who is not calm or rich is not rich or not humble.
Everyone who is happy or not humble is not old or not tall.
John is either rich or not quiet.
Someone is either patient or quiet.
Someone is not strong.
Someone is wise. | Alice is brave. | entailment | (![X]:((~funny(X)&~calm(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((~old(X)|humble(X))<=>(brave(X)&~tall(X))))&
(![X]:(~old(X)<=>~happy(X)))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:(~humble(X)<=>(~wise(X)&~generous(X))))&
((?[X]:((funny(X)<~>patient(X))))=>(creative(lucy)))&
((?[X]:((funny(X)|~strong(X))))<=>((generous(paul)|~creative(paul))))&
((?[X]:((tall(X)|~generous(X))))=>(?[X]:(~strong(X))))&
(![X]:(tall(X)=>(~wise(X)|~happy(X))))&
(((rich(alice)|~humble(alice)))=>((kind(fred)<~>~brave(fred))))&
(((~curious(paul)&~rich(paul)))<=>((creative(paul)<~>rich(paul))))&
(((~generous(lucy)|old(lucy)))=>(?[X]:(calm(X))))&
(![X]:((kind(X)|~humble(X))<=>(~happy(X)&patient(X))))&
(![X]:((~calm(X)|rich(X))=>(~rich(X)|~humble(X))))&
(![X]:((happy(X)|~humble(X))=>(~old(X)|~tall(X))))&
((rich(john)<~>~quiet(john)))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:(wise(X))) | brave(alice) | [
"p1",
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6174898841971495932975255
% SZS output start Proof for 6174898841971495932975255
2. ! [X0] : ((humble(X0) | ~old(X0)) <=> (~tall(X0) & brave(X0))) [input p1]
3. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p2]
13. ! [X0] : ((~humble(X0) | kind(X0)) <=> (patient(X0) & ~happy(X0))) [input p12]
20. ~brave(alice) [input hypothesis]
36. ! [X0] : (((humble(X0) | ~old(X0)) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 2]
37. ! [X0] : ((humble(X0) | ~old(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | (~humble(X0) & old(X0)))) [flattening 36]
38. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 3]
59. ! [X0] : (((~humble(X0) | kind(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (humble(X0) & ~kind(X0)))) [nnf transformation 13]
60. ! [X0] : ((~humble(X0) | kind(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | (humble(X0) & ~kind(X0)))) [flattening 59]
75. brave(X0) | old(X0) [cnf transformation 37]
76. ~humble(X0) | brave(X0) [cnf transformation 37]
81. ~old(X0) | happy(X0) [cnf transformation 38]
111. ~happy(X0) | humble(X0) [cnf transformation 60]
125. ~brave(alice) [cnf transformation 20]
198. 17 <=> humble(alice) [avatar definition]
200. humble(alice) <- (17) [avatar component clause 198]
267. old(alice) [resolution 75,125]
269. happy(alice) [resolution 81,267]
277. humble(alice) [resolution 111,269]
278. 17 [avatar split clause 277,198]
279. brave(alice) <- (17) [resolution 200,76]
280. $false <- (17) [subsumption resolution 279,125]
281. ~17 [avatar contradiction clause 280]
282. $false [avatar sat refutation 278,281]
% SZS output end Proof for 6174898841971495932975255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not wise is both not creative and strong. Everyone who is both not rich and brave is not creative and vice versa. Everyone who is rich is not generous or not humble. Everyone who is both creative and not happy is either quiet or not quiet. Everyone who is not brave is not happy. If someone is both not wise and happy then susan is funny and vice versa. Everyone who is humble is not happy and vice versa. If mary is patient or curious then mary is not brave and vice versa. Everyone who is calm is not kind or wise. Everyone who is both kind and not patient is not old and vice versa. If paul is not happy then someone is either not strong or not creative. Everyone who is strong or old is both not brave and not old and vice versa. If lucy is not humble then someone is not generous or not patient. If someone is both tall and funny then someone is either not patient or not quiet and vice versa. Everyone who is both calm and not rich is either not tall or not old. If someone is old then someone is quiet and vice versa. Someone is either quiet or generous. Mary is calm or kind. Someone is both not calm and happy. Lucy is either not kind or not creative. Susan is either wise or not humble. Someone is kind or not rich. Mary is either not kind or rich. | Susan is funny. | contradiction | (![X]:((kind(X)&~wise(X))=>(~creative(X)&strong(X))))&
(![X]:((~rich(X)&brave(X))<=>~creative(X)))&
(![X]:(rich(X)=>(~generous(X)|~humble(X))))&
(![X]:((creative(X)&~happy(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:(~brave(X)=>~happy(X)))&
((?[X]:((~wise(X)&happy(X))))<=>(funny(susan)))&
(![X]:(humble(X)<=>~happy(X)))&
(((patient(mary)|curious(mary)))<=>(~brave(mary)))&
(![X]:(calm(X)=>(~kind(X)|wise(X))))&
(![X]:((kind(X)&~patient(X))<=>~old(X)))&
((~happy(paul))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((strong(X)|old(X))<=>(~brave(X)&~old(X))))&
((~humble(lucy))=>(?[X]:((~generous(X)|~patient(X)))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((calm(X)&~rich(X))=>(~tall(X)<~>~old(X))))&
((?[X]:(old(X)))<=>(?[X]:(quiet(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((calm(mary)|kind(mary)))&
(?[X]:((~calm(X)&happy(X))))&
((~kind(lucy)<~>~creative(lucy)))&
((wise(susan)<~>~humble(susan)))&
(?[X]:((kind(X)|~rich(X))))&
((~kind(mary)<~>rich(mary))) | funny(susan) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6842158423664236053950393
% SZS output start Proof for 6842158423664236053950393
1. ! [X0] : ((~wise(X0) & kind(X0)) => (strong(X0) & ~creative(X0))) [input p0]
5. ! [X0] : (~brave(X0) => ~happy(X0)) [input p4]
6. ? [X0] : (happy(X0) & ~wise(X0)) <=> funny(susan) [input p5]
10. ! [X0] : ((~patient(X0) & kind(X0)) <=> ~old(X0)) [input p9]
12. ! [X0] : ((old(X0) | strong(X0)) <=> (~old(X0) & ~brave(X0))) [input p11]
24. funny(susan) [input hypothesis]
27. ! [X0] : ((strong(X0) & ~creative(X0)) | (wise(X0) | ~kind(X0))) [ennf transformation 1]
28. ! [X0] : ((strong(X0) & ~creative(X0)) | wise(X0) | ~kind(X0)) [flattening 27]
33. ! [X0] : (~happy(X0) | brave(X0)) [ennf transformation 5]
43. (? [X0] : (happy(X0) & ~wise(X0)) | ~funny(susan)) & (funny(susan) | ! [X0] : (~happy(X0) | wise(X0))) [nnf transformation 6]
44. (? [X0] : (happy(X0) & ~wise(X0)) | ~funny(susan)) & (funny(susan) | ! [X1] : (~happy(X1) | wise(X1))) [rectify 43]
45. ? [X0] : (happy(X0) & ~wise(X0)) => (happy(sK0) & ~wise(sK0)) [choice axiom]
46. ((happy(sK0) & ~wise(sK0)) | ~funny(susan)) & (funny(susan) | ! [X1] : (~happy(X1) | wise(X1))) [skolemisation 44,45]
50. ! [X0] : (((~patient(X0) & kind(X0)) | old(X0)) & (~old(X0) | (patient(X0) | ~kind(X0)))) [nnf transformation 10]
51. ! [X0] : (((~patient(X0) & kind(X0)) | old(X0)) & (~old(X0) | patient(X0) | ~kind(X0))) [flattening 50]
55. ! [X0] : (((old(X0) | strong(X0)) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 12]
56. ! [X0] : ((old(X0) | strong(X0) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0)))) [flattening 55]
81. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 28]
88. ~happy(X0) | brave(X0) [cnf transformation 33]
90. ~wise(sK0) | ~funny(susan) [cnf transformation 46]
91. happy(sK0) | ~funny(susan) [cnf transformation 46]
99. old(X0) | kind(X0) [cnf transformation 51]
103. ~brave(X0) | ~strong(X0) [cnf transformation 56]
106. ~old(X0) | ~old(X0) [cnf transformation 56]
131. funny(susan) [cnf transformation 24]
132. ~old(X0) [duplicate literal removal 106]
135. 1 <=> funny(susan) [avatar definition]
139. 2 <=> happy(sK0) [avatar definition]
141. happy(sK0) <- (2) [avatar component clause 139]
142. ~1 | 2 [avatar split clause 91,139,135]
144. 3 <=> wise(sK0) [avatar definition]
146. ~wise(sK0) <- (~3) [avatar component clause 144]
147. ~1 | ~3 [avatar split clause 90,144,135]
272. 1 [avatar split clause 131,135]
275. brave(sK0) <- (2) [resolution 88,141]
282. kind(X0) [resolution 99,132]
286. ~strong(sK0) <- (2) [resolution 103,275]
292. strong(X0) | wise(X0) [resolution 81,282]
371. wise(sK0) <- (2) [resolution 292,286]
375. $false <- (2, ~3) [subsumption resolution 371,146]
376. ~2 | 3 [avatar contradiction clause 375]
377. $false [avatar sat refutation 142,147,272,376]
% SZS output end Proof for 6842158423664236053950393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong is either patient or not happy.
Everyone who is either generous or strong is old and vice versa.
Everyone who is both not creative and humble is both generous and funny.
If someone is strong or not humble then someone is both not quiet and strong and vice versa.
If someone is brave or not humble then someone is not tall or not funny.
Everyone who is both not creative and not kind is not funny or not curious and vice versa.
Everyone who is not quiet is both not curious and not kind and vice versa.
If someone is rich then someone is quiet and vice versa.
If fred is rich then someone is not curious or not happy and vice versa.
If someone is both rich and not funny then susan is both not strong and not brave.
If paul is either not wise or not happy then alice is either calm or funny and vice versa.
Everyone who is calm is not patient and vice versa.
If someone is not rich then someone is both not brave and not wise.
Everyone who is either not tall or not happy is either kind or creative.
Everyone who is patient is either not humble or not funny.
If susan is either creative or not wise then someone is either not brave or not old and vice versa.
Susan is both not happy and not creative.
John is brave.
Someone is either not generous or not strong.
Someone is either funny or not rich.
Mary is both funny and generous.
Mary is either humble or not brave.
Mary is either not funny or tall.
Paul is generous. | Mary is tall. | entailment | (![X]:((tall(X)|~strong(X))=>(patient(X)<~>~happy(X))))&
(![X]:((generous(X)<~>strong(X))<=>old(X)))&
(![X]:((~creative(X)&humble(X))=>(generous(X)&funny(X))))&
((?[X]:((strong(X)|~humble(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(~funny(X)|~curious(X))))&
(![X]:(~quiet(X)<=>(~curious(X)&~kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:(quiet(X))))&
((rich(fred))<=>(?[X]:((~curious(X)|~happy(X)))))&
((?[X]:((rich(X)&~funny(X))))=>((~strong(susan)&~brave(susan))))&
(((~wise(paul)<~>~happy(paul)))<=>((calm(alice)<~>funny(alice))))&
(![X]:(calm(X)<=>~patient(X)))&
((?[X]:(~rich(X)))=>(?[X]:((~brave(X)&~wise(X)))))&
(![X]:((~tall(X)<~>~happy(X))=>(kind(X)<~>creative(X))))&
(![X]:(patient(X)=>(~humble(X)<~>~funny(X))))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
((~happy(susan)&~creative(susan)))&
(brave(john))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
((funny(mary)&generous(mary)))&
((humble(mary)<~>~brave(mary)))&
((~funny(mary)<~>tall(mary)))&
(generous(paul)) | tall(mary) | [
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8522789898323482518726031
% SZS output start Proof for 8522789898323482518726031
21. generous(mary) & funny(mary) [input p20]
23. ~funny(mary) <~> tall(mary) [input p22]
25. ~tall(mary) [input hypothesis]
79. (~tall(mary) | funny(mary)) & (tall(mary) | ~funny(mary)) [nnf transformation 23]
145. funny(mary) [cnf transformation 21]
149. tall(mary) | ~funny(mary) [cnf transformation 79]
152. ~tall(mary) [cnf transformation 25]
345. tall(mary) [subsumption resolution 149,145]
346. $false [subsumption resolution 152,345]
% SZS output end Proof for 8522789898323482518726031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or creative is either calm or not creative and vice versa.
Everyone who is either happy or old is either not kind or not brave.
If paul is rich or not brave then someone is both not kind and not happy.
Everyone who is either generous or not generous is both not strong and not patient and vice versa.
If paul is either not generous or not calm then alice is both not creative and kind.
If john is either not funny or tall then someone is tall and vice versa.
Everyone who is humble is generous and vice versa.
Everyone who is either curious or old is both quiet and not funny and vice versa.
Everyone who is either quiet or patient is either funny or quiet.
If paul is both happy and kind then someone is either creative or patient and vice versa.
If fred is not brave or not creative then someone is either not strong or not kind.
If susan is happy then paul is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Someone is either tall or not rich.
John is quiet.
Lucy is both happy and humble.
Mary is both not patient and generous.
Someone is patient or not strong.
Someone is both not kind and not curious.
Lucy is wise or humble. | Paul is not old. | entailment | (![X]:((calm(X)|creative(X))<=>(calm(X)<~>~creative(X))))&
(![X]:((happy(X)<~>old(X))=>(~kind(X)<~>~brave(X))))&
(((rich(paul)|~brave(paul)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~strong(X)&~patient(X))))&
(((~generous(paul)<~>~calm(paul)))=>((~creative(alice)&kind(alice))))&
(((~funny(john)<~>tall(john)))<=>(?[X]:(tall(X))))&
(![X]:(humble(X)<=>generous(X)))&
(![X]:((curious(X)<~>old(X))<=>(quiet(X)&~funny(X))))&
(![X]:((quiet(X)<~>patient(X))=>(funny(X)<~>quiet(X))))&
(((happy(paul)&kind(paul)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(((~brave(fred)|~creative(fred)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
((happy(susan))<=>((~happy(paul)|~kind(paul))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
(quiet(john))&
((happy(lucy)&humble(lucy)))&
((~patient(mary)&generous(mary)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((~kind(X)&~curious(X))))&
((wise(lucy)|humble(lucy))) | ~old(paul) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6110303454161248824480057
% SZS output start Proof for 6110303454161248824480057
1. ! [X0] : ((creative(X0) | calm(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p0]
4. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> (~patient(X0) & ~strong(X0))) [input p3]
5. (~generous(paul) <~> ~calm(paul)) => (kind(alice) & ~creative(alice)) [input p4]
7. ! [X0] : (humble(X0) <=> generous(X0)) [input p6]
10. (kind(paul) & happy(paul)) <=> ? [X0] : (creative(X0) <~> patient(X0)) [input p9]
14. ! [X0] : ((kind(X0) <~> humble(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p13]
23. old(paul) [input hypothesis]
27. (kind(alice) & ~creative(alice)) | (~generous(paul) <=> ~calm(paul)) [ennf transformation 5]
31. ! [X0] : (((creative(X0) | calm(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (~creative(X0) & ~calm(X0)))) [nnf transformation 1]
32. ! [X0] : ((creative(X0) | calm(X0) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (~creative(X0) & ~calm(X0)))) [flattening 31]
36. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 4]
37. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [flattening 36]
38. (kind(alice) & ~creative(alice)) | ((~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul))) [nnf transformation 27]
43. ! [X0] : ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0))) [nnf transformation 7]
47. ((kind(paul) & happy(paul)) | ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (? [X0] : ((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (~kind(paul) | ~happy(paul))) [nnf transformation 10]
48. ((kind(paul) & happy(paul)) | ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (? [X0] : ((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | ~kind(paul) | ~happy(paul)) [flattening 47]
49. ((kind(paul) & happy(paul)) | ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (? [X1] : ((~patient(X1) | ~creative(X1)) & (patient(X1) | creative(X1))) | ~kind(paul) | ~happy(paul)) [rectify 48]
50. ? [X1] : ((~patient(X1) | ~creative(X1)) & (patient(X1) | creative(X1))) => ((~patient(sK2) | ~creative(sK2)) & (patient(sK2) | creative(sK2))) [choice axiom]
51. ((kind(paul) & happy(paul)) | ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(sK2) | ~creative(sK2)) & (patient(sK2) | creative(sK2))) | ~kind(paul) | ~happy(paul)) [skolemisation 49,50]
62. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [nnf transformation 14]
72. ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 32]
73. creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 32]
76. creative(X0) | calm(X0) | calm(X0) | creative(X0) [cnf transformation 32]
87. ~patient(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 37]
88. ~patient(X0) | generous(X0) | generous(X0) [cnf transformation 37]
91. ~creative(alice) | ~calm(paul) | generous(paul) [cnf transformation 38]
100. ~generous(X0) | humble(X0) [cnf transformation 43]
115. kind(paul) | patient(X0) | ~creative(X0) [cnf transformation 51]
136. ~humble(X0) | ~kind(X0) | ~old(X0) | patient(X0) [cnf transformation 62]
151. old(paul) [cnf transformation 23]
156. ~patient(X0) | ~generous(X0) [duplicate literal removal 87]
157. ~patient(X0) | generous(X0) [duplicate literal removal 88]
158. ~creative(X0) | calm(X0) [duplicate literal removal 72]
159. creative(X0) | ~calm(X0) [duplicate literal removal 73]
160. creative(X0) | calm(X0) [duplicate literal removal 76]
161. creative(X0) [subsumption resolution 159,160]
162. calm(X0) [subsumption resolution 158,161]
183. ~patient(X0) [subsumption resolution 156,157]
187. 5 <=> generous(paul) [avatar definition]
189. generous(paul) <- (5) [avatar component clause 187]
195. ~calm(paul) | generous(paul) [subsumption resolution 91,161]
196. generous(paul) [subsumption resolution 195,162]
197. 5 [avatar split clause 196,187]
218. kind(paul) | ~creative(X0) [subsumption resolution 115,183]
219. kind(paul) [subsumption resolution 218,161]
261. ~humble(X0) | ~kind(X0) | ~old(X0) [subsumption resolution 136,183]
418. humble(paul) <- (5) [resolution 189,100]
421. ~kind(paul) | ~old(paul) <- (5) [resolution 418,261]
423. ~old(paul) <- (5) [subsumption resolution 421,219]
424. $false <- (5) [subsumption resolution 423,151]
425. ~5 [avatar contradiction clause 424]
426. $false [avatar sat refutation 197,425]
% SZS output end Proof for 6110303454161248824480057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is patient and vice versa.
Everyone who is either not tall or not kind is not funny or humble.
Everyone who is rich is both wise and not curious and vice versa.
If someone is rich or tall then someone is either not creative or not tall and vice versa.
Everyone who is either happy or not patient is not happy or creative and vice versa.
If john is funny then someone is either not rich or rich and vice versa.
If fred is not brave then john is calm or wise and vice versa.
If lucy is patient or calm then paul is either quiet or calm.
If someone is not quiet or creative then alice is not humble.
Everyone who is either humble or kind is either not calm or not rich.
Everyone who is either not strong or curious is not creative and vice versa.
Everyone who is rich is either old or tall and vice versa.
Everyone who is either not happy or not quiet is not humble or funny and vice versa.
Everyone who is not curious or generous is generous or wise.
Everyone who is either creative or not quiet is not tall.
Everyone who is not quiet is either not creative or brave.
Lucy is old or not humble.
Someone is either not brave or patient.
Someone is either not humble or wise.
Someone is both not happy and not tall.
Someone is happy.
Someone is calm.
Susan is either humble or not patient.
Someone is humble. | John is tall. | neutral | (![X]:(humble(X)<=>patient(X)))&
(![X]:((~tall(X)<~>~kind(X))=>(~funny(X)|humble(X))))&
(![X]:(rich(X)<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|tall(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((happy(X)<~>~patient(X))<=>(~happy(X)|creative(X))))&
((funny(john))<=>(?[X]:((~rich(X)<~>rich(X)))))&
((~brave(fred))<=>((calm(john)|wise(john))))&
(((patient(lucy)|calm(lucy)))=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~quiet(X)|creative(X))))=>(~humble(alice)))&
(![X]:((humble(X)<~>kind(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(old(X)<~>tall(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(~humble(X)|funny(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)|wise(X))))&
(![X]:((creative(X)<~>~quiet(X))=>~tall(X)))&
(![X]:(~quiet(X)=>(~creative(X)<~>brave(X))))&
((old(lucy)|~humble(lucy)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((~happy(X)&~tall(X))))&
(?[X]:(happy(X)))&
(?[X]:(calm(X)))&
((humble(susan)<~>~patient(susan)))&
(?[X]:(humble(X))) | tall(john) | [] | null | 0 |
Everyone who is brave or kind is either wise or not old and vice versa.
Everyone who is either not happy or not calm is both not patient and calm and vice versa.
If someone is patient or tall then someone is either not curious or kind and vice versa.
If john is quiet or not strong then someone is not rich.
If someone is either funny or not calm then alice is not calm or not wise and vice versa.
Everyone who is both brave and calm is curious and vice versa.
If mary is either funny or not creative then someone is both humble and not creative.
Everyone who is brave is not strong or not rich and vice versa.
Everyone who is both strong and quiet is humble or not humble.
Everyone who is funny or not generous is not kind and vice versa.
If paul is old or happy then someone is either strong or brave and vice versa.
If paul is either old or rich then someone is curious or humble and vice versa.
If mary is happy then someone is either tall or not quiet.
If paul is happy then someone is both not calm and funny and vice versa.
Everyone who is kind is not creative or generous.
Everyone who is not patient is wise or quiet and vice versa.
Alice is happy.
Someone is happy.
Paul is funny or patient.
Paul is tall.
Susan is either funny or brave. | Alice is strong. | neutral | (![X]:((brave(X)|kind(X))<=>(wise(X)<~>~old(X))))&
(![X]:((~happy(X)<~>~calm(X))<=>(~patient(X)&calm(X))))&
((?[X]:((patient(X)|tall(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(((quiet(john)|~strong(john)))=>(?[X]:(~rich(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>((~calm(alice)|~wise(alice))))&
(![X]:((brave(X)&calm(X))<=>curious(X)))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:(brave(X)<=>(~strong(X)|~rich(X))))&
(![X]:((strong(X)&quiet(X))=>(humble(X)|~humble(X))))&
(![X]:((funny(X)|~generous(X))<=>~kind(X)))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(happy(alice))&
(?[X]:(happy(X)))&
((funny(paul)|patient(paul)))&
(tall(paul))&
((funny(susan)<~>brave(susan))) | strong(alice) | [] | null | 0 |
If mary is not brave then mary is either tall or kind and vice versa.
Everyone who is not old is kind or old and vice versa.
Everyone who is quiet or happy is either patient or old and vice versa.
If fred is either tall or humble then susan is kind or brave and vice versa.
Everyone who is both not rich and quiet is either strong or not curious and vice versa.
If lucy is funny then paul is tall.
If someone is generous then lucy is both not generous and brave.
Everyone who is either old or kind is happy and vice versa.
Everyone who is either curious or not rich is either brave or not wise and vice versa.
If fred is not humble or not patient then someone is not curious or not tall.
Everyone who is both quiet and tall is either calm or quiet and vice versa.
Everyone who is either funny or strong is either not patient or humble.
If someone is not curious then lucy is both quiet and wise and vice versa.
If someone is both not rich and not strong then someone is either happy or not kind.
Everyone who is both happy and not old is not patient or calm.
Everyone who is both not brave and not generous is either not curious or happy.
Susan is not kind or not old.
Someone is both rich and not curious.
Someone is brave.
Someone is creative or generous.
Paul is either funny or not wise. | Fred is brave. | neutral | ((~brave(mary))<=>((tall(mary)<~>kind(mary))))&
(![X]:(~old(X)<=>(kind(X)|old(X))))&
(![X]:((quiet(X)|happy(X))<=>(patient(X)<~>old(X))))&
(((tall(fred)<~>humble(fred)))<=>((kind(susan)|brave(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(strong(X)<~>~curious(X))))&
((funny(lucy))=>(tall(paul)))&
((?[X]:(generous(X)))=>((~generous(lucy)&brave(lucy))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(brave(X)<~>~wise(X))))&
(((~humble(fred)|~patient(fred)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((quiet(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((funny(X)<~>strong(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)&wise(lucy))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((happy(X)&~old(X))=>(~patient(X)|calm(X))))&
(![X]:((~brave(X)&~generous(X))=>(~curious(X)<~>happy(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)|generous(X))))&
((funny(paul)<~>~wise(paul))) | brave(fred) | [] | null | 0 |
Everyone who is either creative or tall is creative and vice versa.
Everyone who is either not old or kind is brave.
If mary is not quiet or not patient then lucy is not kind or not happy.
If someone is not old then someone is happy or tall.
Everyone who is not funny or not calm is either tall or not kind.
If lucy is either brave or not brave then someone is not old and vice versa.
If someone is not strong then someone is both happy and not creative.
Everyone who is either kind or humble is either funny or humble.
Everyone who is happy is both wise and not quiet and vice versa.
Everyone who is either brave or not humble is not old or funny and vice versa.
Everyone who is either generous or not patient is not happy and vice versa.
Everyone who is both not happy and patient is happy or quiet.
Everyone who is either creative or not strong is either not strong or patient.
If someone is kind then fred is both strong and not rich.
Everyone who is creative is not patient and vice versa.
If someone is either not creative or calm then someone is either funny or kind.
Someone is either not wise or old.
Alice is either wise or not humble.
Mary is both not humble and not curious.
Someone is either not rich or brave.
Someone is generous.
Mary is not curious or not creative.
Someone is not generous or happy. | Mary is humble. | contradiction | (![X]:((creative(X)<~>tall(X))<=>creative(X)))&
(![X]:((~old(X)<~>kind(X))=>brave(X)))&
(((~quiet(mary)|~patient(mary)))=>((~kind(lucy)|~happy(lucy))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|tall(X)))))&
(![X]:((~funny(X)|~calm(X))=>(tall(X)<~>~kind(X))))&
(((brave(lucy)<~>~brave(lucy)))<=>(?[X]:(~old(X))))&
((?[X]:(~strong(X)))=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((kind(X)<~>humble(X))=>(funny(X)<~>humble(X))))&
(![X]:(happy(X)<=>(wise(X)&~quiet(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~old(X)|funny(X))))&
(![X]:((generous(X)<~>~patient(X))<=>~happy(X)))&
(![X]:((~happy(X)&patient(X))=>(happy(X)|quiet(X))))&
(![X]:((creative(X)<~>~strong(X))=>(~strong(X)<~>patient(X))))&
((?[X]:(kind(X)))=>((strong(fred)&~rich(fred))))&
(![X]:(creative(X)<=>~patient(X)))&
((?[X]:((~creative(X)<~>calm(X))))=>(?[X]:((funny(X)<~>kind(X)))))&
(?[X]:((~wise(X)<~>old(X))))&
((wise(alice)<~>~humble(alice)))&
((~humble(mary)&~curious(mary)))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(generous(X)))&
((~curious(mary)|~creative(mary)))&
(?[X]:((~generous(X)|happy(X)))) | humble(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 201097189050146992849197
% SZS output start Proof for 201097189050146992849197
19. ~curious(mary) & ~humble(mary) [input p18]
24. humble(mary) [input hypothesis]
28. ~humble(mary) [pure predicate removal 19]
131. ~humble(mary) [cnf transformation 28]
136. humble(mary) [cnf transformation 24]
273. $false [subsumption resolution 136,131]
% SZS output end Proof for 201097189050146992849197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not curious then someone is either creative or not rich and vice versa. Everyone who is either funny or quiet is not wise or kind and vice versa. If fred is both not old and generous then lucy is both patient and quiet and vice versa. If alice is either not funny or not wise then paul is both not wise and not kind. Everyone who is generous or not old is rich and vice versa. If susan is either not patient or not rich then someone is both not rich and creative and vice versa. If someone is not generous then lucy is not old. Everyone who is kind or generous is not kind. Everyone who is either calm or patient is not wise. Everyone who is either curious or humble is either quiet or not generous and vice versa. If someone is both rich and not old then someone is happy or patient. Everyone who is funny or old is both not funny and kind and vice versa. If mary is both not creative and tall then someone is either humble or happy. Everyone who is not rich is both not strong and creative and vice versa. If lucy is either not curious or not brave then someone is either curious or quiet and vice versa. If someone is not humble then someone is both creative and quiet and vice versa. Someone is either not calm or not old. John is either patient or not calm. Someone is both calm and tall. Someone is strong. Lucy is not strong or not brave. Susan is not generous. Susan is either not curious or wise. Alice is either calm or not patient. | Paul is funny. | contradiction | ((?[X]:((quiet(X)|~curious(X))))<=>(?[X]:((creative(X)<~>~rich(X)))))&
(![X]:((funny(X)<~>quiet(X))<=>(~wise(X)|kind(X))))&
(((~old(fred)&generous(fred)))<=>((patient(lucy)&quiet(lucy))))&
(((~funny(alice)<~>~wise(alice)))=>((~wise(paul)&~kind(paul))))&
(![X]:((generous(X)|~old(X))<=>rich(X)))&
(((~patient(susan)<~>~rich(susan)))<=>(?[X]:((~rich(X)&creative(X)))))&
((?[X]:(~generous(X)))=>(~old(lucy)))&
(![X]:((kind(X)|generous(X))=>~kind(X)))&
(![X]:((calm(X)<~>patient(X))=>~wise(X)))&
(![X]:((curious(X)<~>humble(X))<=>(quiet(X)<~>~generous(X))))&
((?[X]:((rich(X)&~old(X))))=>(?[X]:((happy(X)|patient(X)))))&
(![X]:((funny(X)|old(X))<=>(~funny(X)&kind(X))))&
(((~creative(mary)&tall(mary)))=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:(~rich(X)<=>(~strong(X)&creative(X))))&
(((~curious(lucy)<~>~brave(lucy)))<=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)&quiet(X)))))&
(?[X]:((~calm(X)<~>~old(X))))&
((patient(john)<~>~calm(john)))&
(?[X]:((calm(X)&tall(X))))&
(?[X]:(strong(X)))&
((~strong(lucy)|~brave(lucy)))&
(~generous(susan))&
((~curious(susan)<~>wise(susan)))&
((calm(alice)<~>~patient(alice))) | funny(paul) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4588726506912317625679270
% SZS output start Proof for 4588726506912317625679270
8. ! [X0] : ((generous(X0) | kind(X0)) => ~kind(X0)) [input p7]
12. ! [X0] : ((old(X0) | funny(X0)) <=> (kind(X0) & ~funny(X0))) [input p11]
25. funny(paul) [input hypothesis]
31. ! [X0] : (~kind(X0) | (~generous(X0) & ~kind(X0))) [ennf transformation 8]
57. ! [X0] : (((old(X0) | funny(X0)) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [nnf transformation 12]
58. ! [X0] : ((old(X0) | funny(X0) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [flattening 57]
113. ~kind(X0) | ~kind(X0) [cnf transformation 31]
128. kind(X0) | ~funny(X0) [cnf transformation 58]
160. funny(paul) [cnf transformation 25]
163. ~kind(X0) [duplicate literal removal 113]
285. ~funny(X0) [subsumption resolution 128,163]
392. $false [subsumption resolution 160,285]
% SZS output end Proof for 4588726506912317625679270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is kind. Everyone who is both kind and quiet is not strong. Everyone who is tall is both strong and not curious. Everyone who is either not tall or not curious is either not brave or not funny. Everyone who is either not patient or calm is brave or not rich and vice versa. If someone is both curious and not tall then someone is rich or not kind and vice versa. Everyone who is both wise and not old is either not happy or not calm and vice versa. If alice is either not rich or calm then paul is funny and vice versa. Everyone who is rich is not quiet and vice versa. If alice is either not quiet or not tall then someone is either not funny or not happy and vice versa. If someone is both not curious and old then john is not old or creative. If susan is patient or brave then mary is not kind. Everyone who is either brave or not funny is either tall or not tall and vice versa. Everyone who is either funny or strong is either not kind or not creative. Everyone who is not calm is not kind or not humble. If someone is either not brave or creative then someone is either not quiet or not creative. Someone is old. Someone is not happy. Someone is either not rich or not old. Someone is not curious. Fred is kind. Paul is either kind or brave. Someone is kind. | Alice is not strong. | entailment | (![X]:(humble(X)=>kind(X)))&
(![X]:((kind(X)&quiet(X))=>~strong(X)))&
(![X]:(tall(X)=>(strong(X)&~curious(X))))&
(![X]:((~tall(X)<~>~curious(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(brave(X)|~rich(X))))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((wise(X)&~old(X))<=>(~happy(X)<~>~calm(X))))&
(((~rich(alice)<~>calm(alice)))<=>(funny(paul)))&
(![X]:(rich(X)<=>~quiet(X)))&
(((~quiet(alice)<~>~tall(alice)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
((?[X]:((~curious(X)&old(X))))=>((~old(john)|creative(john))))&
(((patient(susan)|brave(susan)))=>(~kind(mary)))&
(![X]:((brave(X)<~>~funny(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((funny(X)<~>strong(X))=>(~kind(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(~kind(X)|~humble(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(?[X]:(old(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(kind(fred))&
((kind(paul)<~>brave(paul)))&
(?[X]:(kind(X))) | ~strong(alice) | [
"p1",
"p2",
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4563995652755257902883190
% SZS output start Proof for 4563995652755257902883190
2. ! [X0] : ((quiet(X0) & kind(X0)) => ~strong(X0)) [input p1]
3. ! [X0] : (tall(X0) => (~curious(X0) & strong(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> ~curious(X0)) => (~brave(X0) <~> ~funny(X0))) [input p3]
6. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X0] : (~kind(X0) | rich(X0)) [input p5]
9. ! [X0] : (rich(X0) <=> ~quiet(X0)) [input p8]
13. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
24. strong(alice) [input hypothesis]
25. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X1] : (~kind(X1) | rich(X1)) [rectify 6]
29. ! [X0] : (~strong(X0) | (~quiet(X0) | ~kind(X0))) [ennf transformation 2]
30. ! [X0] : (~strong(X0) | ~quiet(X0) | ~kind(X0)) [flattening 29]
31. ! [X0] : ((~curious(X0) & strong(X0)) | ~tall(X0)) [ennf transformation 3]
32. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (~tall(X0) <=> ~curious(X0))) [ennf transformation 4]
38. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 32]
41. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X1] : (~kind(X1) | rich(X1)) | ! [X0] : (tall(X0) | ~curious(X0))) [nnf transformation 25]
42. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X2] : (~kind(X2) | rich(X2)) | ! [X3] : (tall(X3) | ~curious(X3))) [rectify 41]
43. ? [X0] : (~tall(X0) & curious(X0)) => (~tall(sK0) & curious(sK0)) [choice axiom]
44. ? [X2] : (~kind(X2) | rich(X2)) => (~kind(sK1) | rich(sK1)) [choice axiom]
45. ((~tall(sK0) & curious(sK0)) | ! [X1] : (kind(X1) & ~rich(X1))) & ((~kind(sK1) | rich(sK1)) | ! [X3] : (tall(X3) | ~curious(X3))) [skolemisation 42,44,43]
49. ! [X0] : ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))) [nnf transformation 9]
54. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 13]
72. ~strong(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 30]
74. ~curious(X0) | ~tall(X0) [cnf transformation 31]
75. ~funny(X0) | ~brave(X0) | ~curious(X0) | tall(X0) [cnf transformation 38]
76. ~funny(X0) | ~brave(X0) | ~tall(X0) | curious(X0) [cnf transformation 38]
77. funny(X0) | brave(X0) | ~curious(X0) | tall(X0) [cnf transformation 38]
78. funny(X0) | brave(X0) | ~tall(X0) | curious(X0) [cnf transformation 38]
86. curious(sK0) | ~rich(X1) [cnf transformation 45]
87. curious(sK0) | kind(X1) [cnf transformation 45]
101. rich(X0) | quiet(X0) [cnf transformation 49]
117. ~funny(X0) | brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
118. ~funny(X0) | brave(X0) | tall(X0) | tall(X0) [cnf transformation 54]
119. funny(X0) | ~brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
120. funny(X0) | ~brave(X0) | tall(X0) | tall(X0) [cnf transformation 54]
138. strong(alice) [cnf transformation 24]
139. ~funny(X0) | brave(X0) | ~tall(X0) [duplicate literal removal 117]
140. ~funny(X0) | brave(X0) | tall(X0) [duplicate literal removal 118]
141. funny(X0) | ~brave(X0) | ~tall(X0) [duplicate literal removal 119]
142. ~brave(X0) | funny(X0) | tall(X0) [duplicate literal removal 120]
143. ~tall(X0) | brave(X0) | funny(X0) [subsumption resolution 78,74]
144. ~curious(X0) | brave(X0) | funny(X0) [subsumption resolution 77,143]
145. ~funny(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 76,74]
146. ~funny(X0) | ~brave(X0) | ~curious(X0) [subsumption resolution 75,145]
148. 1 <=> ! [X1] : kind(X1) [avatar definition]
149. kind(X1) <- (1) [avatar component clause 148]
156. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
157. ~rich(X1) <- (3) [avatar component clause 156]
160. 4 <=> curious(sK0) [avatar definition]
162. curious(sK0) <- (4) [avatar component clause 160]
163. 1 | 4 [avatar split clause 87,160,148]
164. 3 | 4 [avatar split clause 86,160,156]
183. 9 <=> rich(alice) [avatar definition]
184. ~rich(alice) <- (~9) [avatar component clause 183]
185. rich(alice) <- (9) [avatar component clause 183]
198. 12 <=> quiet(alice) [avatar definition]
199. ~quiet(alice) <- (~12) [avatar component clause 198]
250. ~tall(X0) | funny(X0) [subsumption resolution 141,143]
251. ~funny(X0) | ~tall(X0) [subsumption resolution 139,145]
252. ~tall(X0) [subsumption resolution 251,250]
293. quiet(alice) <- (~9) [resolution 101,184]
295. $false <- (~9, ~12) [subsumption resolution 293,199]
296. 9 | 12 [avatar contradiction clause 295]
300. ~quiet(alice) | ~kind(alice) [resolution 72,138]
370. brave(sK0) | funny(sK0) <- (4) [resolution 144,162]
372. 42 <=> funny(sK0) [avatar definition]
374. funny(sK0) <- (42) [avatar component clause 372]
376. 43 <=> brave(sK0) [avatar definition]
378. brave(sK0) <- (43) [avatar component clause 376]
379. 42 | 43 | ~4 [avatar split clause 370,160,376,372]
380. funny(sK0) | tall(sK0) <- (43) [resolution 378,142]
381. funny(sK0) <- (43) [subsumption resolution 380,252]
382. 42 | ~43 [avatar split clause 381,376,372]
384. brave(sK0) | tall(sK0) <- (42) [resolution 374,140]
386. ~brave(sK0) | ~curious(sK0) <- (42) [resolution 146,374]
396. $false <- (3, 9) [resolution 157,185]
401. ~3 | ~9 [avatar contradiction clause 396]
402. brave(sK0) <- (42) [subsumption resolution 384,252]
403. 43 | ~42 [avatar split clause 402,372,376]
406. ~4 | ~43 | ~42 [avatar split clause 386,372,376,160]
407. ~quiet(alice) <- (1) [subsumption resolution 300,149]
408. ~12 | ~1 [avatar split clause 407,148,198]
411. $false [avatar sat refutation 163,164,296,379,382,401,403,406,408]
% SZS output end Proof for 4563995652755257902883190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is tall or funny is old or patient and vice versa.
If someone is both happy and not creative then fred is not old.
Everyone who is not humble or creative is either not old or creative.
Everyone who is not calm is both not patient and tall and vice versa.
If paul is not curious then someone is both quiet and not quiet.
Everyone who is not curious or not patient is either generous or wise and vice versa.
Everyone who is both not rich and curious is old.
If paul is either not brave or not rich then someone is either not strong or brave.
Everyone who is either not curious or humble is funny or not curious and vice versa.
Everyone who is not tall or rich is either old or rich.
Everyone who is either funny or not happy is either not kind or rich.
Everyone who is not humble or not tall is either not generous or not funny.
Everyone who is either brave or tall is funny or generous.
If someone is both calm and not wise then susan is not strong or not wise and vice versa.
If someone is either creative or tall then someone is not patient and vice versa.
Everyone who is kind or not quiet is not curious or creative.
Fred is either creative or strong.
Susan is both not funny and old.
Someone is not creative or humble.
Someone is not quiet.
Someone is both brave and not generous.
Someone is not funny or funny.
Someone is not happy or not curious. | Susan is not old. | contradiction | (![X]:((tall(X)|funny(X))<=>(old(X)|patient(X))))&
((?[X]:((happy(X)&~creative(X))))=>(~old(fred)))&
(![X]:((~humble(X)|creative(X))=>(~old(X)<~>creative(X))))&
(![X]:(~calm(X)<=>(~patient(X)&tall(X))))&
((~curious(paul))=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~curious(X)|~patient(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~rich(X)&curious(X))=>old(X)))&
(((~brave(paul)<~>~rich(paul)))=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((~curious(X)<~>humble(X))<=>(funny(X)|~curious(X))))&
(![X]:((~tall(X)|rich(X))=>(old(X)<~>rich(X))))&
(![X]:((funny(X)<~>~happy(X))=>(~kind(X)<~>rich(X))))&
(![X]:((~humble(X)|~tall(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((brave(X)<~>tall(X))=>(funny(X)|generous(X))))&
((?[X]:((calm(X)&~wise(X))))<=>((~strong(susan)|~wise(susan))))&
((?[X]:((creative(X)<~>tall(X))))<=>(?[X]:(~patient(X))))&
(![X]:((kind(X)|~quiet(X))=>(~curious(X)|creative(X))))&
((creative(fred)<~>strong(fred)))&
((~funny(susan)&old(susan)))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((~happy(X)|~curious(X)))) | ~old(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 273142227341054963462817
% SZS output start Proof for 273142227341054963462817
18. old(susan) & ~funny(susan) [input p17]
24. ~old(susan) [input hypothesis]
137. old(susan) [cnf transformation 18]
144. ~old(susan) [cnf transformation 24]
266. $false [subsumption resolution 144,137]
% SZS output end Proof for 273142227341054963462817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative then someone is brave and vice versa.
If someone is both not brave and curious then alice is either happy or old and vice versa.
If someone is either not strong or not kind then alice is not old.
Everyone who is both humble and not humble is wise and vice versa.
If someone is old then someone is either kind or happy.
Everyone who is both kind and humble is not old.
If paul is both wise and not wise then lucy is either not humble or not wise.
If lucy is both rich and funny then someone is not curious and vice versa.
If someone is rich or not tall then alice is either curious or not happy.
Everyone who is either quiet or not rich is wise or not old.
Everyone who is both kind and not happy is rich and vice versa.
Everyone who is kind is either calm or patient and vice versa.
Everyone who is either rich or not brave is both strong and not quiet and vice versa.
Everyone who is both humble and not calm is not tall and vice versa.
If someone is curious then lucy is wise or not funny.
Everyone who is both old and tall is funny.
John is not brave.
Lucy is both not quiet and not wise.
Fred is brave or not curious.
Someone is both kind and generous.
Someone is humble.
Someone is either not rich or not funny.
Fred is either not curious or kind.
Lucy is not curious. | Alice is happy. | contradiction | (((patient(mary)|~creative(mary)))<=>(?[X]:(brave(X))))&
((?[X]:((~brave(X)&curious(X))))<=>((happy(alice)<~>old(alice))))&
((?[X]:((~strong(X)<~>~kind(X))))=>(~old(alice)))&
(![X]:((humble(X)&~humble(X))<=>wise(X)))&
((?[X]:(old(X)))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((kind(X)&humble(X))=>~old(X)))&
(((wise(paul)&~wise(paul)))=>((~humble(lucy)<~>~wise(lucy))))&
(((rich(lucy)&funny(lucy)))<=>(?[X]:(~curious(X))))&
((?[X]:((rich(X)|~tall(X))))=>((curious(alice)<~>~happy(alice))))&
(![X]:((quiet(X)<~>~rich(X))=>(wise(X)|~old(X))))&
(![X]:((kind(X)&~happy(X))<=>rich(X)))&
(![X]:(kind(X)<=>(calm(X)<~>patient(X))))&
(![X]:((rich(X)<~>~brave(X))<=>(strong(X)&~quiet(X))))&
(![X]:((humble(X)&~calm(X))<=>~tall(X)))&
((?[X]:(curious(X)))=>((wise(lucy)|~funny(lucy))))&
(![X]:((old(X)&tall(X))=>funny(X)))&
(~brave(john))&
((~quiet(lucy)&~wise(lucy)))&
((brave(fred)|~curious(fred)))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:(humble(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((~curious(fred)<~>kind(fred)))&
(~curious(lucy)) | happy(alice) | [
"p3",
"p7",
"p8",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5199447778779203643569855
% SZS output start Proof for 5199447778779203643569855
4. ! [X0] : ((~humble(X0) & humble(X0)) <=> wise(X0)) [input p3]
8. (funny(lucy) & rich(lucy)) <=> ? [X0] : ~curious(X0) [input p7]
9. ? [X0] : (~tall(X0) | rich(X0)) => (curious(alice) <~> ~happy(alice)) [input p8]
15. ? [X0] : curious(X0) => (~funny(lucy) | wise(lucy)) [input p14]
24. ~curious(lucy) [input p23]
25. happy(alice) [input hypothesis]
34. (curious(alice) <~> ~happy(alice)) | ! [X0] : (tall(X0) & ~rich(X0)) [ennf transformation 9]
37. (~funny(lucy) | wise(lucy)) | ! [X0] : ~curious(X0) [ennf transformation 15]
38. ~funny(lucy) | wise(lucy) | ! [X0] : ~curious(X0) [flattening 37]
51. ! [X0] : (((~humble(X0) & humble(X0)) | ~wise(X0)) & (wise(X0) | (humble(X0) | ~humble(X0)))) [nnf transformation 4]
52. ! [X0] : (((~humble(X0) & humble(X0)) | ~wise(X0)) & (wise(X0) | humble(X0) | ~humble(X0))) [flattening 51]
58. ((funny(lucy) & rich(lucy)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(lucy) | ~rich(lucy))) [nnf transformation 8]
59. ((funny(lucy) & rich(lucy)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~funny(lucy) | ~rich(lucy)) [flattening 58]
60. ((funny(lucy) & rich(lucy)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~funny(lucy) | ~rich(lucy)) [rectify 59]
61. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
62. ((funny(lucy) & rich(lucy)) | ! [X0] : curious(X0)) & (~curious(sK3) | ~funny(lucy) | ~rich(lucy)) [skolemisation 60,61]
63. ((happy(alice) | ~curious(alice)) & (~happy(alice) | curious(alice))) | ! [X0] : (tall(X0) & ~rich(X0)) [nnf transformation 34]
92. humble(X0) | ~wise(X0) [cnf transformation 52]
93. ~humble(X0) | ~wise(X0) [cnf transformation 52]
100. rich(lucy) | curious(X0) [cnf transformation 62]
101. funny(lucy) | curious(X0) [cnf transformation 62]
102. ~happy(alice) | curious(alice) | ~rich(X0) [cnf transformation 63]
124. ~funny(lucy) | wise(lucy) | ~curious(X0) [cnf transformation 38]
136. ~curious(lucy) [cnf transformation 24]
137. happy(alice) [cnf transformation 25]
161. 6 <=> happy(alice) [avatar definition]
189. ~wise(X0) [subsumption resolution 92,93]
204. 15 <=> ! [X0] : curious(X0) [avatar definition]
205. curious(X0) <- (15) [avatar component clause 204]
207. 16 <=> funny(lucy) [avatar definition]
210. 15 | 16 [avatar split clause 101,207,204]
212. 17 <=> rich(lucy) [avatar definition]
214. rich(lucy) <- (17) [avatar component clause 212]
215. 15 | 17 [avatar split clause 100,212,204]
225. 20 <=> curious(alice) [avatar definition]
226. curious(alice) <- (20) [avatar component clause 225]
230. 21 <=> ! [X0] : ~rich(X0) [avatar definition]
231. ~rich(X0) <- (21) [avatar component clause 230]
234. 21 | 20 | ~6 [avatar split clause 102,161,225,230]
237. ~funny(lucy) | ~curious(X0) [subsumption resolution 124,189]
239. 22 <=> ! [X0] : ~curious(X0) [avatar definition]
240. ~curious(X0) <- (22) [avatar component clause 239]
241. 22 | ~16 [avatar split clause 237,207,239]
267. 6 [avatar split clause 137,161]
268. $false <- (15) [resolution 205,136]
269. ~15 [avatar contradiction clause 268]
271. $false <- (20, 22) [resolution 240,226]
272. ~20 | ~22 [avatar contradiction clause 271]
276. $false <- (17, 21) [resolution 231,214]
277. ~17 | ~21 [avatar contradiction clause 276]
278. $false [avatar sat refutation 210,215,234,241,267,269,272,277]
% SZS output end Proof for 5199447778779203643569855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not funny then someone is either patient or not brave and vice versa. Everyone who is humble or not wise is quiet. Everyone who is either strong or not funny is not generous or not old and vice versa. Everyone who is both calm and not patient is rich. Everyone who is not old is either calm or not generous and vice versa. Everyone who is not happy is creative. If someone is calm then someone is not rich or kind. Everyone who is both not patient and creative is both not old and creative and vice versa. If someone is both humble and quiet then someone is not funny or tall and vice versa. Everyone who is either not strong or happy is not funny or not rich. Everyone who is quiet or creative is both tall and not humble. If john is both not quiet and not happy then mary is both old and quiet. Everyone who is both not happy and not strong is both strong and not rich. Everyone who is either not happy or kind is both brave and rich. Everyone who is both not tall and calm is both humble and not brave. Everyone who is either old or rich is not wise or not quiet. Lucy is not old. Fred is either not happy or kind. Paul is both not kind and not calm. Someone is not tall or not patient. Paul is both not brave and happy. Someone is either patient or not calm. | Fred is calm. | contradiction | (((creative(mary)|~funny(mary)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((strong(X)<~>~funny(X))<=>(~generous(X)|~old(X))))&
(![X]:((calm(X)&~patient(X))=>rich(X)))&
(![X]:(~old(X)<=>(calm(X)<~>~generous(X))))&
(![X]:(~happy(X)=>creative(X)))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)|creative(X))=>(tall(X)&~humble(X))))&
(((~quiet(john)&~happy(john)))=>((old(mary)&quiet(mary))))&
(![X]:((~happy(X)&~strong(X))=>(strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
(![X]:((~tall(X)&calm(X))=>(humble(X)&~brave(X))))&
(![X]:((old(X)<~>rich(X))=>(~wise(X)|~quiet(X))))&
(~old(lucy))&
((~happy(fred)<~>kind(fred)))&
((~kind(paul)&~calm(paul)))&
(?[X]:((~tall(X)|~patient(X))))&
((~brave(paul)&happy(paul)))&
(?[X]:((patient(X)<~>~calm(X)))) | calm(fred) | [
"p1",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8455649143745803079226158
% SZS output start Proof for 8455649143745803079226158
2. ! [X0] : ((~wise(X0) | humble(X0)) => quiet(X0)) [input p1]
9. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X0] : (tall(X0) | ~funny(X0)) [input p8]
11. ! [X0] : ((creative(X0) | quiet(X0)) => (~humble(X0) & tall(X0))) [input p10]
15. ! [X0] : ((calm(X0) & ~tall(X0)) => (~brave(X0) & humble(X0))) [input p14]
23. calm(fred) [input hypothesis]
25. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X1] : (tall(X1) | ~funny(X1)) [rectify 9]
26. ! [X0] : (quiet(X0) | (wise(X0) & ~humble(X0))) [ennf transformation 2]
33. ! [X0] : ((~humble(X0) & tall(X0)) | (~creative(X0) & ~quiet(X0))) [ennf transformation 11]
39. ! [X0] : ((~brave(X0) & humble(X0)) | (~calm(X0) | tall(X0))) [ennf transformation 15]
40. ! [X0] : ((~brave(X0) & humble(X0)) | ~calm(X0) | tall(X0)) [flattening 39]
56. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X1] : (tall(X1) | ~funny(X1)) | ! [X0] : (~quiet(X0) | ~humble(X0))) [nnf transformation 25]
57. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X2] : (tall(X2) | ~funny(X2)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [rectify 56]
58. ? [X0] : (quiet(X0) & humble(X0)) => (quiet(sK2) & humble(sK2)) [choice axiom]
59. ? [X2] : (tall(X2) | ~funny(X2)) => (tall(sK3) | ~funny(sK3)) [choice axiom]
60. ((quiet(sK2) & humble(sK2)) | ! [X1] : (~tall(X1) & funny(X1))) & ((tall(sK3) | ~funny(sK3)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [skolemisation 57,59,58]
76. ~humble(X0) | quiet(X0) [cnf transformation 26]
97. humble(sK2) | ~tall(X1) [cnf transformation 60]
104. ~humble(X0) | ~quiet(X0) [cnf transformation 33]
114. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 40]
128. calm(fred) [cnf transformation 23]
171. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
172. ~tall(X1) <- (10) [avatar component clause 171]
183. 13 <=> humble(sK2) [avatar definition]
185. humble(sK2) <- (13) [avatar component clause 183]
186. 10 | 13 [avatar split clause 97,183,171]
190. 14 <=> ! [X3] : ~humble(X3) [avatar definition]
191. ~humble(X3) <- (14) [avatar component clause 190]
201. ~humble(X0) [subsumption resolution 104,76]
202. 14 [avatar split clause 201,190]
252. $false <- (13, 14) [subsumption resolution 185,191]
253. ~13 | ~14 [avatar contradiction clause 252]
342. humble(fred) | tall(fred) [resolution 114,128]
343. tall(fred) <- (14) [subsumption resolution 342,191]
344. $false <- (10, 14) [subsumption resolution 343,172]
345. ~10 | ~14 [avatar contradiction clause 344]
346. $false [avatar sat refutation 186,202,253,345]
% SZS output end Proof for 8455649143745803079226158
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not curious is both creative and happy and vice versa. If fred is not calm or wise then someone is not patient or curious. If paul is not curious then someone is not funny or not brave and vice versa. Everyone who is both not old and generous is not brave. Everyone who is not brave is either not funny or not curious. If paul is kind then lucy is either not humble or not quiet. Everyone who is both happy and not curious is not humble or creative. Everyone who is either not tall or funny is not kind. If someone is both not old and happy then someone is both not brave and not wise. Everyone who is not tall is not brave. Everyone who is both not creative and not kind is both not kind and not happy. Everyone who is both not strong and not happy is either kind or old and vice versa. If someone is either not tall or not kind then fred is patient or not patient and vice versa. Everyone who is quiet is both curious and tall and vice versa. Everyone who is either patient or not old is old or funny. Everyone who is either not humble or not tall is both generous and funny. John is not patient. Paul is both tall and generous. Susan is both quiet and not kind. Someone is not strong. Lucy is both curious and not quiet. Someone is curious or not patient. John is not funny or kind. Mary is funny or calm. | Lucy is kind. | contradiction | (![X]:((generous(X)&~curious(X))<=>(creative(X)&happy(X))))&
(((~calm(fred)|wise(fred)))=>(?[X]:((~patient(X)|curious(X)))))&
((~curious(paul))<=>(?[X]:((~funny(X)|~brave(X)))))&
(![X]:((~old(X)&generous(X))=>~brave(X)))&
(![X]:(~brave(X)=>(~funny(X)<~>~curious(X))))&
((kind(paul))=>((~humble(lucy)<~>~quiet(lucy))))&
(![X]:((happy(X)&~curious(X))=>(~humble(X)|creative(X))))&
(![X]:((~tall(X)<~>funny(X))=>~kind(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((~brave(X)&~wise(X)))))&
(![X]:(~tall(X)=>~brave(X)))&
(![X]:((~creative(X)&~kind(X))=>(~kind(X)&~happy(X))))&
(![X]:((~strong(X)&~happy(X))<=>(kind(X)<~>old(X))))&
((?[X]:((~tall(X)<~>~kind(X))))<=>((patient(fred)|~patient(fred))))&
(![X]:(quiet(X)<=>(curious(X)&tall(X))))&
(![X]:((patient(X)<~>~old(X))=>(old(X)|funny(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(generous(X)&funny(X))))&
(~patient(john))&
((tall(paul)&generous(paul)))&
((quiet(susan)&~kind(susan)))&
(?[X]:(~strong(X)))&
((curious(lucy)&~quiet(lucy)))&
(?[X]:((curious(X)|~patient(X))))&
((~funny(john)|kind(john)))&
((funny(mary)|calm(mary))) | kind(lucy) | [
"p4",
"p7",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6505566365914641715173711
% SZS output start Proof for 6505566365914641715173711
5. ! [X0] : (~brave(X0) => (~funny(X0) <~> ~curious(X0))) [input p4]
8. ! [X0] : ((~tall(X0) <~> funny(X0)) => ~kind(X0)) [input p7]
10. ! [X0] : (~tall(X0) => ~brave(X0)) [input p9]
14. ! [X0] : (quiet(X0) <=> (tall(X0) & curious(X0))) [input p13]
21. ~quiet(lucy) & curious(lucy) [input p20]
25. kind(lucy) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~curious(X0)) | brave(X0)) [ennf transformation 5]
37. ! [X0] : (~kind(X0) | (~tall(X0) <=> funny(X0))) [ennf transformation 8]
39. ! [X0] : (~brave(X0) | tall(X0)) [ennf transformation 10]
51. ! [X0] : (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | brave(X0)) [nnf transformation 33]
53. ! [X0] : (~kind(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) [nnf transformation 37]
64. ! [X0] : ((quiet(X0) | (~tall(X0) | ~curious(X0))) & ((tall(X0) & curious(X0)) | ~quiet(X0))) [nnf transformation 14]
65. ! [X0] : ((quiet(X0) | ~tall(X0) | ~curious(X0)) & ((tall(X0) & curious(X0)) | ~quiet(X0))) [flattening 64]
80. ~funny(X0) | ~curious(X0) | brave(X0) [cnf transformation 51]
85. ~kind(X0) | funny(X0) | tall(X0) [cnf transformation 53]
88. ~brave(X0) | tall(X0) [cnf transformation 39]
105. ~tall(X0) | quiet(X0) | ~curious(X0) [cnf transformation 65]
118. curious(lucy) [cnf transformation 21]
119. ~quiet(lucy) [cnf transformation 21]
122. kind(lucy) [cnf transformation 25]
154. 8 <=> quiet(lucy) [avatar definition]
155. ~quiet(lucy) <- (~8) [avatar component clause 154]
183. ~8 [avatar split clause 119,154]
222. funny(lucy) | tall(lucy) [resolution 85,122]
224. 20 <=> tall(lucy) [avatar definition]
225. ~tall(lucy) <- (~20) [avatar component clause 224]
226. tall(lucy) <- (20) [avatar component clause 224]
228. 21 <=> funny(lucy) [avatar definition]
230. funny(lucy) <- (21) [avatar component clause 228]
231. 20 | 21 [avatar split clause 222,228,224]
250. quiet(lucy) | ~curious(lucy) <- (20) [resolution 105,226]
253. ~curious(lucy) <- (~8, 20) [subsumption resolution 250,155]
254. $false <- (~8, 20) [subsumption resolution 253,118]
255. 8 | ~20 [avatar contradiction clause 254]
286. ~curious(lucy) | brave(lucy) <- (21) [resolution 230,80]
287. brave(lucy) <- (21) [subsumption resolution 286,118]
383. tall(lucy) <- (21) [resolution 287,88]
385. $false <- (~20, 21) [subsumption resolution 383,225]
386. 20 | ~21 [avatar contradiction clause 385]
387. $false [avatar sat refutation 183,231,255,386]
% SZS output end Proof for 6505566365914641715173711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is both strong and curious then someone is old and vice versa.
Everyone who is either rich or not humble is either not kind or not wise.
If someone is either not wise or wise then susan is not strong.
If someone is both curious and not funny then someone is both funny and not old.
Everyone who is humble is either not brave or not generous and vice versa.
If someone is creative then alice is either not funny or not kind and vice versa.
If someone is either funny or not patient then paul is both generous and wise and vice versa.
Everyone who is both not rich and quiet is not patient or old and vice versa.
If paul is calm or old then someone is tall.
Everyone who is not rich or patient is humble and vice versa.
Everyone who is not funny or quiet is old.
Everyone who is either humble or not generous is not wise and vice versa.
If someone is both not funny and not strong then john is brave and vice versa.
If someone is either tall or not rich then someone is not quiet.
If alice is tall or strong then someone is tall.
Someone is calm or curious.
Someone is both tall and not wise.
Mary is either not humble or wise.
Mary is curious or not patient.
Fred is happy. | Alice is tall. | entailment | (((strong(john)&curious(john)))<=>(?[X]:(old(X))))&
(![X]:((rich(X)<~>~humble(X))=>(~kind(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>(~strong(susan)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:((funny(X)&~old(X)))))&
(![X]:(humble(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(creative(X)))<=>((~funny(alice)<~>~kind(alice))))&
((?[X]:((funny(X)<~>~patient(X))))<=>((generous(paul)&wise(paul))))&
(![X]:((~rich(X)&quiet(X))<=>(~patient(X)|old(X))))&
(((calm(paul)|old(paul)))=>(?[X]:(tall(X))))&
(![X]:((~rich(X)|patient(X))<=>humble(X)))&
(![X]:((~funny(X)|quiet(X))=>old(X)))&
(![X]:((humble(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((~funny(X)&~strong(X))))<=>(brave(john)))&
((?[X]:((tall(X)<~>~rich(X))))=>(?[X]:(~quiet(X))))&
(((tall(alice)|strong(alice)))=>(?[X]:(tall(X))))&
(?[X]:((calm(X)|curious(X))))&
(?[X]:((tall(X)&~wise(X))))&
((~humble(mary)<~>wise(mary)))&
((curious(mary)|~patient(mary)))&
(happy(fred)) | tall(alice) | [
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7067431883315910496730646
% SZS output start Proof for 7067431883315910496730646
7. ? [X0] : (funny(X0) <~> ~patient(X0)) <=> (wise(paul) & generous(paul)) [input p6]
8. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (old(X0) | ~patient(X0))) [input p7]
10. ! [X0] : ((patient(X0) | ~rich(X0)) <=> humble(X0)) [input p9]
11. ! [X0] : ((quiet(X0) | ~funny(X0)) => old(X0)) [input p10]
12. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p11]
14. ? [X0] : (tall(X0) <~> ~rich(X0)) => ? [X0] : ~quiet(X0) [input p13]
21. ~tall(alice) [input hypothesis]
23. ? [X0] : (tall(X0) <~> ~rich(X0)) => ? [X1] : ~quiet(X1) [rectify 14]
29. ! [X0] : (old(X0) | (~quiet(X0) & funny(X0))) [ennf transformation 11]
30. ? [X1] : ~quiet(X1) | ! [X0] : (tall(X0) <=> ~rich(X0)) [ennf transformation 23]
47. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~wise(paul) | ~generous(paul))) & ((wise(paul) & generous(paul)) | ! [X0] : ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) [nnf transformation 7]
48. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X0] : ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) [flattening 47]
49. (? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) [rectify 48]
50. ? [X0] : ((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) => ((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) [choice axiom]
51. (((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) | ~wise(paul) | ~generous(paul)) & ((wise(paul) & generous(paul)) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) [skolemisation 49,50]
52. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 8]
53. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~quiet(X0) | rich(X0))) [flattening 52]
56. ! [X0] : (((patient(X0) | ~rich(X0)) | ~humble(X0)) & (humble(X0) | (~patient(X0) & rich(X0)))) [nnf transformation 10]
57. ! [X0] : ((patient(X0) | ~rich(X0) | ~humble(X0)) & (humble(X0) | (~patient(X0) & rich(X0)))) [flattening 56]
58. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | wise(X0)) & (~wise(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 12]
63. ? [X1] : ~quiet(X1) | ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))) [nnf transformation 30]
64. ? [X0] : ~quiet(X0) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1))) [rectify 63]
65. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
66. ~quiet(sK6) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1))) [skolemisation 64,65]
93. generous(paul) | ~patient(X1) | ~funny(X1) [cnf transformation 51]
95. wise(paul) | ~patient(X1) | ~funny(X1) [cnf transformation 51]
101. ~rich(X0) | ~old(X0) [cnf transformation 53]
102. quiet(X0) | patient(X0) [cnf transformation 53]
103. ~old(X0) | quiet(X0) [cnf transformation 53]
106. humble(X0) | rich(X0) [cnf transformation 57]
107. ~patient(X0) | humble(X0) [cnf transformation 57]
109. funny(X0) | old(X0) [cnf transformation 29]
110. ~quiet(X0) | old(X0) [cnf transformation 29]
111. ~generous(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 58]
119. ~quiet(sK6) | tall(X1) | rich(X1) [cnf transformation 66]
128. ~tall(alice) [cnf transformation 21]
194. 15 <=> generous(paul) [avatar definition]
195. generous(paul) <- (15) [avatar component clause 194]
198. 16 <=> wise(paul) [avatar definition]
216. 20 <=> ! [X1] : (~patient(X1) | ~funny(X1)) [avatar definition]
217. ~patient(X1) | ~funny(X1) <- (20) [avatar component clause 216]
218. 20 | 16 [avatar split clause 95,198,216]
220. 20 | 15 [avatar split clause 93,194,216]
222. 21 <=> old(paul) [avatar definition]
254. 28 <=> ! [X1] : (tall(X1) | rich(X1)) [avatar definition]
255. tall(X1) | rich(X1) <- (28) [avatar component clause 254]
257. 29 <=> quiet(sK6) [avatar definition]
259. ~quiet(sK6) <- (~29) [avatar component clause 257]
260. 28 | ~29 [avatar split clause 119,257,254]
275. 33 <=> tall(alice) [avatar definition]
277. ~tall(alice) <- (~33) [avatar component clause 275]
307. ~33 [avatar split clause 128,275]
320. patient(X0) | old(X0) [resolution 110,102]
327. 40 <=> humble(paul) [avatar definition]
328. humble(paul) <- (40) [avatar component clause 327]
329. ~humble(paul) <- (~40) [avatar component clause 327]
356. rich(paul) <- (~40) [resolution 329,106]
439. ~old(paul) <- (~40) [resolution 356,101]
443. humble(X0) | old(X0) [resolution 320,107]
469. old(paul) <- (~40) [resolution 443,329]
476. 21 | 40 [avatar split clause 469,327,222]
477. ~21 | 40 [avatar split clause 439,327,222]
511. ~funny(X1) | old(X1) <- (20) [resolution 217,320]
512. old(X1) <- (20) [subsumption resolution 511,109]
528. quiet(X0) <- (20) [resolution 512,103]
592. $false <- (20, ~29) [resolution 528,259]
593. ~20 | 29 [avatar contradiction clause 592]
600. ~wise(paul) | ~humble(paul) <- (15) [resolution 195,111]
606. ~wise(paul) <- (15, 40) [subsumption resolution 600,328]
607. ~16 | ~15 | ~40 [avatar split clause 606,327,194,198]
623. ~funny(X1) | old(X1) <- (20) [resolution 217,320]
625. old(X1) <- (20) [subsumption resolution 623,109]
631. rich(alice) <- (28, ~33) [resolution 255,277]
655. ~old(alice) <- (28, ~33) [resolution 631,101]
657. $false <- (20, 28, ~33) [subsumption resolution 655,625]
658. ~20 | ~28 | 33 [avatar contradiction clause 657]
659. $false [avatar sat refutation 218,220,260,307,476,477,593,607,658]
% SZS output end Proof for 7067431883315910496730646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is not generous and vice versa. Everyone who is not generous or not funny is funny. Everyone who is old is not creative and vice versa. If someone is either not creative or creative then alice is either rich or kind and vice versa. Everyone who is both not rich and not happy is strong. If fred is kind or patient then susan is both wise and not generous. Everyone who is tall is both not rich and not humble. Everyone who is both not humble and strong is not wise or creative. If lucy is both kind and not tall then john is curious and vice versa. If fred is quiet then someone is either curious or wise. Everyone who is both not brave and not happy is creative or quiet. If someone is both not tall and not wise then someone is not humble or creative and vice versa. Everyone who is both kind and not curious is not old or rich and vice versa. Everyone who is both strong and not tall is not calm. Everyone who is both not humble and not quiet is not kind. If mary is either happy or not calm then someone is either brave or not rich. Paul is either not strong or not funny. Paul is either not strong or rich. Lucy is either not brave or quiet. Someone is either old or rich. Mary is either creative or not calm. Someone is either not funny or not happy. Mary is not wise. Someone is rich or kind. | Mary is not funny. | contradiction | (![X]:((quiet(X)&~funny(X))<=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:(old(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
(![X]:((~humble(X)&~quiet(X))=>~kind(X)))&
(((happy(mary)<~>~calm(mary)))=>(?[X]:((brave(X)<~>~rich(X)))))&
((~strong(paul)<~>~funny(paul)))&
((~strong(paul)<~>rich(paul)))&
((~brave(lucy)<~>quiet(lucy)))&
(?[X]:((old(X)<~>rich(X))))&
((creative(mary)<~>~calm(mary)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(~wise(mary))&
(?[X]:((rich(X)|kind(X)))) | ~funny(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1244227842215690682581837
% SZS output start Proof for 1244227842215690682581837
2. ! [X0] : ((~funny(X0) | ~generous(X0)) => funny(X0)) [input p1]
25. ~funny(mary) [input hypothesis]
28. ! [X0] : (funny(X0) | (funny(X0) & generous(X0))) [ennf transformation 2]
81. funny(X0) | funny(X0) [cnf transformation 28]
134. ~funny(mary) [cnf transformation 25]
139. funny(X0) [duplicate literal removal 81]
278. $false [subsumption resolution 134,139]
% SZS output end Proof for 1244227842215690682581837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not creative is both not funny and not rich and vice versa.
Everyone who is not brave or generous is old or happy.
Everyone who is both generous and not kind is either not tall or generous.
If alice is curious or not quiet then mary is either not calm or creative and vice versa.
If lucy is both not curious and not tall then someone is both tall and kind.
If someone is kind or not calm then someone is strong or humble and vice versa.
Everyone who is generous is both not brave and not creative.
Everyone who is both not wise and not calm is both not rich and calm.
If susan is both humble and not generous then mary is both generous and not happy.
If alice is either quiet or not happy then someone is not tall and vice versa.
Everyone who is both not happy and not humble is both not wise and happy and vice versa.
If someone is both not creative and not old then fred is not old or happy and vice versa.
Everyone who is calm or kind is both not wise and humble.
Everyone who is both not kind and calm is not brave or patient and vice versa.
Everyone who is calm or brave is both wise and old.
If john is not patient then someone is both not calm and old and vice versa.
Lucy is both not happy and not curious.
Lucy is not brave or not curious.
Someone is both strong and not tall.
Mary is either not brave or quiet.
Paul is not quiet or tall.
Fred is either not wise or creative. | Mary is generous. | contradiction | (![X]:((tall(X)&~creative(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~brave(X)|generous(X))=>(old(X)|happy(X))))&
(![X]:((generous(X)&~kind(X))=>(~tall(X)<~>generous(X))))&
(((curious(alice)|~quiet(alice)))<=>((~calm(mary)<~>creative(mary))))&
(((~curious(lucy)&~tall(lucy)))=>(?[X]:((tall(X)&kind(X)))))&
((?[X]:((kind(X)|~calm(X))))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
(![X]:((~wise(X)&~calm(X))=>(~rich(X)&calm(X))))&
(((humble(susan)&~generous(susan)))=>((generous(mary)&~happy(mary))))&
(((quiet(alice)<~>~happy(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&~humble(X))<=>(~wise(X)&happy(X))))&
((?[X]:((~creative(X)&~old(X))))<=>((~old(fred)|happy(fred))))&
(![X]:((calm(X)|kind(X))=>(~wise(X)&humble(X))))&
(![X]:((~kind(X)&calm(X))<=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|brave(X))=>(wise(X)&old(X))))&
((~patient(john))<=>(?[X]:((~calm(X)&old(X)))))&
((~happy(lucy)&~curious(lucy)))&
((~brave(lucy)|~curious(lucy)))&
(?[X]:((strong(X)&~tall(X))))&
((~brave(mary)<~>quiet(mary)))&
((~quiet(paul)|tall(paul)))&
((~wise(fred)<~>creative(fred))) | generous(mary) | [
"p6",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4154493762939245588125746
% SZS output start Proof for 4154493762939245588125746
7. ! [X0] : (generous(X0) => (~creative(X0) & ~brave(X0))) [input p6]
8. ! [X0] : ((~calm(X0) & ~wise(X0)) => (calm(X0) & ~rich(X0))) [input p7]
13. ! [X0] : ((kind(X0) | calm(X0)) => (humble(X0) & ~wise(X0))) [input p12]
14. ! [X0] : ((calm(X0) & ~kind(X0)) <=> (patient(X0) | ~brave(X0))) [input p13]
15. ! [X0] : ((brave(X0) | calm(X0)) => (old(X0) & wise(X0))) [input p14]
23. generous(mary) [input hypothesis]
31. ! [X0] : ((~creative(X0) & ~brave(X0)) | ~generous(X0)) [ennf transformation 7]
32. ! [X0] : ((calm(X0) & ~rich(X0)) | (calm(X0) | wise(X0))) [ennf transformation 8]
33. ! [X0] : ((calm(X0) & ~rich(X0)) | calm(X0) | wise(X0)) [flattening 32]
36. ! [X0] : ((humble(X0) & ~wise(X0)) | (~kind(X0) & ~calm(X0))) [ennf transformation 13]
37. ! [X0] : ((old(X0) & wise(X0)) | (~brave(X0) & ~calm(X0))) [ennf transformation 15]
61. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~calm(X0) | kind(X0)))) [nnf transformation 14]
62. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~calm(X0) | kind(X0))) [flattening 61]
91. ~generous(X0) | ~brave(X0) [cnf transformation 31]
94. calm(X0) | calm(X0) | wise(X0) [cnf transformation 33]
110. ~wise(X0) | ~calm(X0) [cnf transformation 36]
117. calm(X0) | brave(X0) [cnf transformation 62]
119. wise(X0) | ~calm(X0) [cnf transformation 37]
136. generous(mary) [cnf transformation 23]
139. calm(X0) | wise(X0) [duplicate literal removal 94]
227. 20 <=> generous(mary) [avatar definition]
229. generous(mary) <- (20) [avatar component clause 227]
270. wise(X0) [subsumption resolution 119,139]
315. 20 [avatar split clause 136,227]
316. ~brave(mary) <- (20) [resolution 91,229]
318. ~calm(X0) [resolution 110,270]
324. brave(X0) [resolution 117,318]
330. $false <- (20) [subsumption resolution 316,324]
331. ~20 [avatar contradiction clause 330]
332. $false [avatar sat refutation 315,331]
% SZS output end Proof for 4154493762939245588125746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient or not creative then someone is not happy and vice versa.
Everyone who is both not tall and not wise is not generous or kind.
If someone is funny then john is either calm or not happy.
Everyone who is rich or humble is wise.
If someone is either not rich or creative then mary is curious.
If paul is brave then someone is not happy or curious.
Everyone who is old or not patient is both not rich and not creative.
If mary is rich then alice is either funny or not tall.
Everyone who is humble is not happy or not old and vice versa.
Everyone who is old is both not happy and not creative.
If someone is both tall and funny then alice is not humble or not tall and vice versa.
If someone is either not strong or not curious then someone is not wise and vice versa.
If susan is either not old or creative then someone is either not tall or not kind.
If someone is creative then fred is not wise or funny.
Everyone who is both not happy and not humble is not quiet or tall.
Everyone who is tall is not quiet or quiet.
John is old or kind.
Alice is strong or not patient.
Someone is curious or quiet.
Mary is old or not strong.
Someone is not generous or funny.
Someone is either quiet or rich.
Someone is not brave or strong.
Someone is not funny. | John is wise. | entailment | (((patient(john)|~creative(john)))<=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)&~wise(X))=>(~generous(X)|kind(X))))&
((?[X]:(funny(X)))=>((calm(john)<~>~happy(john))))&
(![X]:((rich(X)|humble(X))=>wise(X)))&
((?[X]:((~rich(X)<~>creative(X))))=>(curious(mary)))&
((brave(paul))=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:((old(X)|~patient(X))=>(~rich(X)&~creative(X))))&
((rich(mary))=>((funny(alice)<~>~tall(alice))))&
(![X]:(humble(X)<=>(~happy(X)|~old(X))))&
(![X]:(old(X)=>(~happy(X)&~creative(X))))&
((?[X]:((tall(X)&funny(X))))<=>((~humble(alice)|~tall(alice))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>(?[X]:(~wise(X))))&
(((~old(susan)<~>creative(susan)))=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(creative(X)))=>((~wise(fred)|funny(fred))))&
(![X]:((~happy(X)&~humble(X))=>(~quiet(X)|tall(X))))&
(![X]:(tall(X)=>(~quiet(X)|quiet(X))))&
((old(john)|kind(john)))&
((strong(alice)|~patient(alice)))&
(?[X]:((curious(X)|quiet(X))))&
((old(mary)|~strong(mary)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((quiet(X)<~>rich(X))))&
(?[X]:((~brave(X)|strong(X))))&
(?[X]:(~funny(X))) | wise(john) | [
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3146810604747369513719541
% SZS output start Proof for 3146810604747369513719541
4. ! [X0] : ((humble(X0) | rich(X0)) => wise(X0)) [input p3]
9. ! [X0] : (humble(X0) <=> (~old(X0) | ~happy(X0))) [input p8]
10. ! [X0] : (old(X0) => (~creative(X0) & ~happy(X0))) [input p9]
25. ~wise(john) [input hypothesis]
32. ! [X0] : (wise(X0) | (~humble(X0) & ~rich(X0))) [ennf transformation 4]
36. ! [X0] : ((~creative(X0) & ~happy(X0)) | ~old(X0)) [ennf transformation 10]
52. ! [X0] : ((humble(X0) | (old(X0) & happy(X0))) & ((~old(X0) | ~happy(X0)) | ~humble(X0))) [nnf transformation 9]
53. ! [X0] : ((humble(X0) | (old(X0) & happy(X0))) & (~old(X0) | ~happy(X0) | ~humble(X0))) [flattening 52]
80. ~humble(X0) | wise(X0) [cnf transformation 32]
90. humble(X0) | happy(X0) [cnf transformation 53]
91. old(X0) | humble(X0) [cnf transformation 53]
92. ~old(X0) | ~happy(X0) [cnf transformation 36]
117. ~wise(john) [cnf transformation 25]
196. 18 <=> ! [X1] : wise(X1) [avatar definition]
197. wise(X1) <- (18) [avatar component clause 196]
296. $false <- (18) [resolution 197,117]
297. ~18 [avatar contradiction clause 296]
308. ~happy(X0) | humble(X0) [resolution 92,91]
309. humble(X0) [subsumption resolution 308,90]
313. wise(X0) [resolution 309,80]
314. 18 [avatar split clause 313,196]
315. $false [avatar sat refutation 297,314]
% SZS output end Proof for 3146810604747369513719541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or old is both not brave and creative. Everyone who is both not calm and strong is happy or not quiet and vice versa. Everyone who is not brave is either not calm or happy. Everyone who is both not calm and calm is either not funny or curious. If someone is kind or not tall then paul is rich or not tall. Everyone who is both strong and not calm is both not humble and happy. Everyone who is either not brave or generous is not rich or not brave and vice versa. Everyone who is either wise or happy is either not humble or not strong and vice versa. If lucy is not wise then mary is not strong and vice versa. If someone is not strong then alice is both strong and happy. Everyone who is not humble or not tall is not happy and vice versa. Everyone who is both old and kind is either patient or old and vice versa. If someone is both patient and not calm then john is not humble and vice versa. If lucy is either not humble or not creative then fred is either quiet or not kind. If someone is both rich and not old then someone is calm or strong and vice versa. Alice is not kind. Paul is either rich or humble. Fred is kind or strong. Someone is both calm and not patient. Paul is not humble. Someone is funny or not wise. Someone is brave or funny. | John is wise. | contradiction | (![X]:((funny(X)|old(X))=>(~brave(X)&creative(X))))&
(![X]:((~calm(X)&strong(X))<=>(happy(X)|~quiet(X))))&
(![X]:(~brave(X)=>(~calm(X)<~>happy(X))))&
(![X]:((~calm(X)&calm(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((kind(X)|~tall(X))))=>((rich(paul)|~tall(paul))))&
(![X]:((strong(X)&~calm(X))=>(~humble(X)&happy(X))))&
(![X]:((~brave(X)<~>generous(X))<=>(~rich(X)|~brave(X))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)<~>~strong(X))))&
((~wise(lucy))<=>(~strong(mary)))&
((?[X]:(~strong(X)))=>((strong(alice)&happy(alice))))&
(![X]:((~humble(X)|~tall(X))<=>~happy(X)))&
(![X]:((old(X)&kind(X))<=>(patient(X)<~>old(X))))&
((?[X]:((patient(X)&~calm(X))))<=>(~humble(john)))&
(((~humble(lucy)<~>~creative(lucy)))=>((quiet(fred)<~>~kind(fred))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(~kind(alice))&
((rich(paul)<~>humble(paul)))&
((kind(fred)|strong(fred)))&
(?[X]:((calm(X)&~patient(X))))&
(~humble(paul))&
(?[X]:((funny(X)|~wise(X))))&
(?[X]:((brave(X)|funny(X)))) | wise(john) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 322731635712979110972148
% SZS output start Proof for 322731635712979110972148
1. ! [X0] : ((old(X0) | funny(X0)) => (creative(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (~quiet(X0) | happy(X0))) [input p1]
3. ! [X0] : (~brave(X0) => (~calm(X0) <~> happy(X0))) [input p2]
6. ! [X0] : ((~calm(X0) & strong(X0)) => (happy(X0) & ~humble(X0))) [input p5]
8. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p7]
10. ? [X0] : ~strong(X0) => (happy(alice) & strong(alice)) [input p9]
11. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((kind(X0) & old(X0)) <=> (patient(X0) <~> old(X0))) [input p11]
13. ? [X0] : (~calm(X0) & patient(X0)) <=> ~humble(john) [input p12]
23. wise(john) [input hypothesis]
25. ! [X0] : ((creative(X0) & ~brave(X0)) | (~old(X0) & ~funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~calm(X0) <~> happy(X0)) | brave(X0)) [ennf transformation 3]
31. ! [X0] : ((happy(X0) & ~humble(X0)) | (calm(X0) | ~strong(X0))) [ennf transformation 6]
32. ! [X0] : ((happy(X0) & ~humble(X0)) | calm(X0) | ~strong(X0)) [flattening 31]
33. (happy(alice) & strong(alice)) | ! [X0] : strong(X0) [ennf transformation 10]
35. ! [X0] : (((strong(X0) & ~calm(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (~strong(X0) | calm(X0)))) [nnf transformation 2]
36. ! [X0] : (((strong(X0) & ~calm(X0)) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | ~strong(X0) | calm(X0))) [flattening 35]
37. ! [X0] : (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | brave(X0)) [nnf transformation 26]
41. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 8]
43. ! [X0] : (((~tall(X0) | ~humble(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) & humble(X0)))) [nnf transformation 11]
44. ! [X0] : ((~tall(X0) | ~humble(X0) | happy(X0)) & (~happy(X0) | (tall(X0) & humble(X0)))) [flattening 43]
45. ! [X0] : (((kind(X0) & old(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 12]
46. ! [X0] : (((kind(X0) & old(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~kind(X0) | ~old(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) & patient(X0)) | humble(john)) & (~humble(john) | ! [X0] : (calm(X0) | ~patient(X0))) [nnf transformation 13]
48. (? [X0] : (~calm(X0) & patient(X0)) | humble(john)) & (~humble(john) | ! [X1] : (calm(X1) | ~patient(X1))) [rectify 47]
49. ? [X0] : (~calm(X0) & patient(X0)) => (~calm(sK0) & patient(sK0)) [choice axiom]
50. ((~calm(sK0) & patient(sK0)) | humble(john)) & (~humble(john) | ! [X1] : (calm(X1) | ~patient(X1))) [skolemisation 48,49]
65. ~brave(X0) | ~old(X0) [cnf transformation 25]
69. ~happy(X0) | ~calm(X0) [cnf transformation 36]
73. happy(X0) | ~calm(X0) | brave(X0) [cnf transformation 37]
74. ~happy(X0) | calm(X0) | brave(X0) [cnf transformation 37]
79. ~humble(X0) | calm(X0) | ~strong(X0) [cnf transformation 32]
80. ~strong(X0) | calm(X0) | happy(X0) [cnf transformation 32]
87. ~wise(X0) | ~humble(X0) | happy(X0) | ~strong(X0) [cnf transformation 41]
97. strong(alice) | strong(X0) [cnf transformation 33]
98. happy(alice) | strong(X0) [cnf transformation 33]
99. ~happy(X0) | humble(X0) [cnf transformation 44]
104. old(X0) | old(X0) | ~patient(X0) [cnf transformation 46]
109. patient(sK0) | humble(john) [cnf transformation 50]
129. wise(john) [cnf transformation 23]
131. ~patient(X0) | old(X0) [duplicate literal removal 104]
134. ~happy(X0) | brave(X0) [subsumption resolution 74,69]
135. ~calm(X0) | brave(X0) [subsumption resolution 73,134]
168. 7 <=> ! [X0] : strong(X0) [avatar definition]
169. strong(X0) <- (7) [avatar component clause 168]
171. 8 <=> happy(alice) [avatar definition]
173. happy(alice) <- (8) [avatar component clause 171]
174. 7 | 8 [avatar split clause 98,171,168]
176. 9 <=> strong(alice) [avatar definition]
178. strong(alice) <- (9) [avatar component clause 176]
179. 7 | 9 [avatar split clause 97,176,168]
182. 10 <=> humble(john) [avatar definition]
191. 12 <=> patient(sK0) [avatar definition]
193. patient(sK0) <- (12) [avatar component clause 191]
194. 10 | 12 [avatar split clause 109,191,182]
295. old(sK0) <- (12) [resolution 131,193]
314. happy(X0) | calm(X0) <- (7) [resolution 80,169]
360. ~humble(john) | happy(john) | ~strong(john) [resolution 87,129]
362. calm(X0) | brave(X0) <- (7) [resolution 314,134]
364. humble(X2) | calm(X2) <- (7) [resolution 314,99]
368. brave(X0) <- (7) [subsumption resolution 362,135]
380. ~old(X1) <- (7) [resolution 368,65]
395. calm(X3) | calm(X3) | ~strong(X3) <- (7) [resolution 364,79]
399. calm(X3) | ~strong(X3) <- (7) [duplicate literal removal 395]
401. calm(X3) <- (7) [subsumption resolution 399,169]
402. $false <- (7, 12) [resolution 380,295]
403. ~7 | ~12 [avatar contradiction clause 402]
404. ~humble(john) | happy(john) <- (7) [subsumption resolution 360,169]
406. 37 <=> happy(john) [avatar definition]
408. happy(john) <- (37) [avatar component clause 406]
409. 37 | ~10 | ~7 [avatar split clause 404,168,182,406]
418. ~calm(john) <- (37) [resolution 408,69]
419. $false <- (7, 37) [subsumption resolution 418,401]
420. ~7 | ~37 [avatar contradiction clause 419]
461. humble(alice) <- (8) [resolution 173,99]
463. ~calm(alice) <- (8) [resolution 173,69]
484. calm(alice) | ~strong(alice) <- (8) [resolution 461,79]
486. ~strong(alice) <- (8) [subsumption resolution 484,463]
487. $false <- (8, 9) [subsumption resolution 486,178]
488. ~8 | ~9 [avatar contradiction clause 487]
489. $false [avatar sat refutation 174,179,194,403,409,420,488]
% SZS output end Proof for 322731635712979110972148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is tall.
If someone is both not curious and curious then someone is not curious.
If alice is wise then alice is creative and vice versa.
Everyone who is creative is either funny or not patient.
Everyone who is both not generous and not happy is strong or tall and vice versa.
If someone is not tall or not calm then lucy is either kind or curious.
If someone is either not quiet or not wise then fred is old or calm.
Everyone who is curious is either brave or not rich and vice versa.
Everyone who is quiet is not kind and vice versa.
Everyone who is either not rich or generous is wise or quiet and vice versa.
Everyone who is both not brave and strong is either not curious or not quiet.
Everyone who is both kind and not patient is brave or happy and vice versa.
If alice is not strong or patient then someone is either not quiet or not patient and vice versa.
If fred is not strong or kind then paul is either old or not patient.
Everyone who is not quiet is not tall or old.
Everyone who is both wise and tall is both quiet and generous and vice versa.
Someone is both not patient and not humble.
Alice is either not strong or happy.
Someone is either not calm or calm.
Susan is both not humble and not funny.
Fred is not curious or curious.
Someone is both old and brave.
Lucy is both strong and not creative.
Mary is both creative and not calm. | Lucy is wise. | entailment | ((?[X]:(~happy(X)))=>(tall(fred)))&
((?[X]:((~curious(X)&curious(X))))=>(?[X]:(~curious(X))))&
((wise(alice))<=>(creative(alice)))&
(![X]:(creative(X)=>(funny(X)<~>~patient(X))))&
(![X]:((~generous(X)&~happy(X))<=>(strong(X)|tall(X))))&
((?[X]:((~tall(X)|~calm(X))))=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~quiet(X)<~>~wise(X))))=>((old(fred)|calm(fred))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(![X]:((wise(X)&tall(X))<=>(quiet(X)&generous(X))))&
(?[X]:((~patient(X)&~humble(X))))&
((~strong(alice)<~>happy(alice)))&
(?[X]:((~calm(X)<~>calm(X))))&
((~humble(susan)&~funny(susan)))&
((~curious(fred)|curious(fred)))&
(?[X]:((old(X)&brave(X))))&
((strong(lucy)&~creative(lucy)))&
((creative(mary)&~calm(mary))) | wise(lucy) | [
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p15",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 481894826480070949129007
% SZS output start Proof for 481894826480070949129007
5. ! [X0] : ((~happy(X0) & ~generous(X0)) <=> (tall(X0) | strong(X0))) [input p4]
6. ? [X0] : (~calm(X0) | ~tall(X0)) => (kind(lucy) <~> curious(lucy)) [input p5]
8. ! [X0] : (curious(X0) <=> (brave(X0) <~> ~rich(X0))) [input p7]
9. ! [X0] : (quiet(X0) <=> ~kind(X0)) [input p8]
10. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> (quiet(X0) | wise(X0))) [input p9]
11. ! [X0] : ((strong(X0) & ~brave(X0)) => (~curious(X0) <~> ~quiet(X0))) [input p10]
12. ! [X0] : ((~patient(X0) & kind(X0)) <=> (happy(X0) | brave(X0))) [input p11]
16. ! [X0] : ((tall(X0) & wise(X0)) <=> (generous(X0) & quiet(X0))) [input p15]
23. ~creative(lucy) & strong(lucy) [input p22]
24. ~calm(mary) & creative(mary) [input p23]
25. ~wise(lucy) [input hypothesis]
32. (kind(lucy) <~> curious(lucy)) | ! [X0] : (calm(X0) & tall(X0)) [ennf transformation 6]
35. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) | (~strong(X0) | brave(X0))) [ennf transformation 11]
36. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) | ~strong(X0) | brave(X0)) [flattening 35]
45. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~tall(X0) & ~strong(X0))) & ((tall(X0) | strong(X0)) | (happy(X0) | generous(X0)))) [nnf transformation 5]
46. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~tall(X0) & ~strong(X0))) & (tall(X0) | strong(X0) | happy(X0) | generous(X0))) [flattening 45]
47. ((~curious(lucy) | ~kind(lucy)) & (curious(lucy) | kind(lucy))) | ! [X0] : (calm(X0) & tall(X0)) [nnf transformation 32]
49. ! [X0] : ((curious(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ~curious(X0))) [nnf transformation 8]
50. ! [X0] : ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))) [nnf transformation 9]
51. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [flattening 51]
53. ! [X0] : (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | ~strong(X0) | brave(X0)) [nnf transformation 36]
54. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | (patient(X0) | ~kind(X0)))) [nnf transformation 12]
55. ! [X0] : (((~patient(X0) & kind(X0)) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | patient(X0) | ~kind(X0))) [flattening 54]
62. ! [X0] : (((tall(X0) & wise(X0)) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 16]
63. ! [X0] : (((tall(X0) & wise(X0)) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ~tall(X0) | ~wise(X0))) [flattening 62]
79. ~strong(X0) | ~generous(X0) [cnf transformation 46]
80. ~generous(X0) | ~tall(X0) [cnf transformation 46]
86. ~curious(lucy) | ~kind(lucy) | calm(X0) [cnf transformation 47]
91. ~rich(X0) | curious(X0) | ~brave(X0) [cnf transformation 49]
92. rich(X0) | brave(X0) | curious(X0) [cnf transformation 49]
93. ~quiet(X0) | ~kind(X0) [cnf transformation 50]
94. quiet(X0) | kind(X0) [cnf transformation 50]
95. rich(X0) | wise(X0) | generous(X0) | quiet(X0) [cnf transformation 52]
98. ~rich(X0) | generous(X0) | ~quiet(X0) [cnf transformation 52]
101. ~quiet(X0) | ~curious(X0) | ~strong(X0) | brave(X0) [cnf transformation 53]
102. ~strong(X0) | curious(X0) | quiet(X0) | brave(X0) [cnf transformation 53]
104. ~brave(X0) | kind(X0) [cnf transformation 55]
122. tall(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 63]
132. strong(lucy) [cnf transformation 23]
135. ~calm(mary) [cnf transformation 24]
136. ~wise(lucy) [cnf transformation 25]
156. 5 <=> ! [X0] : calm(X0) [avatar definition]
157. calm(X0) <- (5) [avatar component clause 156]
159. 6 <=> kind(lucy) [avatar definition]
160. kind(lucy) <- (6) [avatar component clause 159]
163. 7 <=> curious(lucy) [avatar definition]
166. 5 | ~6 | ~7 [avatar split clause 86,163,159,156]
237. ~quiet(X0) | ~generous(X0) [subsumption resolution 122,80]
242. ~generous(lucy) [resolution 79,132]
266. generous(X0) | ~quiet(X0) | brave(X0) | curious(X0) [resolution 98,92]
267. ~quiet(X0) | brave(X0) | curious(X0) [subsumption resolution 266,237]
290. ~brave(X2) | generous(X2) | quiet(X2) | curious(X2) | wise(X2) [resolution 95,91]
299. ~curious(X0) | ~strong(X0) | brave(X0) | kind(X0) [resolution 101,94]
313. ~strong(X0) | ~curious(X0) | kind(X0) [subsumption resolution 299,104]
343. curious(lucy) | quiet(lucy) | brave(lucy) [resolution 102,132]
347. 35 <=> brave(lucy) [avatar definition]
349. brave(lucy) <- (35) [avatar component clause 347]
351. 36 <=> quiet(lucy) [avatar definition]
353. quiet(lucy) <- (36) [avatar component clause 351]
356. curious(lucy) | brave(lucy) [subsumption resolution 343,267]
357. 35 | 7 [avatar split clause 356,163,347]
405. brave(X0) | curious(X0) | kind(X0) [resolution 267,94]
407. curious(X0) | kind(X0) [subsumption resolution 405,104]
420. ~curious(lucy) | kind(lucy) [resolution 313,132]
428. kind(lucy) [subsumption resolution 420,407]
429. 6 [avatar split clause 428,159]
444. generous(lucy) | quiet(lucy) | curious(lucy) | wise(lucy) <- (35) [resolution 290,349]
459. quiet(lucy) | curious(lucy) | wise(lucy) <- (35) [subsumption resolution 444,242]
467. ~kind(lucy) <- (36) [resolution 353,93]
468. $false <- (6, 36) [subsumption resolution 467,160]
469. ~6 | ~36 [avatar contradiction clause 468]
470. quiet(lucy) | curious(lucy) <- (35) [subsumption resolution 459,136]
471. 7 | 36 | ~35 [avatar split clause 470,347,351,163]
477. $false <- (5) [resolution 157,135]
478. ~5 [avatar contradiction clause 477]
479. $false [avatar sat refutation 166,357,429,469,471,478]
% SZS output end Proof for 481894826480070949129007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then fred is both not generous and not rich and vice versa.
Everyone who is rich is either generous or not happy and vice versa.
If fred is both not old and not strong then john is tall or not kind.
If someone is both humble and not happy then alice is both kind and wise.
If lucy is rich then fred is calm or not happy and vice versa.
If fred is not kind then mary is either not curious or funny and vice versa.
If someone is both quiet and creative then paul is both not quiet and old and vice versa.
Everyone who is both generous and not old is both not patient and brave and vice versa.
If someone is not old then someone is both wise and tall.
If susan is either old or not generous then susan is not strong or not happy and vice versa.
Everyone who is both old and happy is not patient.
If someone is both creative and funny then fred is not rich or tall and vice versa.
Everyone who is both patient and not curious is tall.
Everyone who is both happy and not curious is both generous and brave.
Everyone who is both calm and old is patient.
Everyone who is not happy or patient is both not quiet and not humble.
Someone is both not curious and quiet.
Mary is not patient.
Someone is not brave or curious.
Someone is either not curious or patient.
John is both not tall and not funny.
Susan is either not wise or strong.
Mary is both old and not curious.
Paul is generous. | Mary is brave. | contradiction | ((?[X]:(~strong(X)))<=>((~generous(fred)&~rich(fred))))&
(![X]:(rich(X)<=>(generous(X)<~>~happy(X))))&
(((~old(fred)&~strong(fred)))=>((tall(john)|~kind(john))))&
((?[X]:((humble(X)&~happy(X))))=>((kind(alice)&wise(alice))))&
((rich(lucy))<=>((calm(fred)|~happy(fred))))&
((~kind(fred))<=>((~curious(mary)<~>funny(mary))))&
((?[X]:((quiet(X)&creative(X))))<=>((~quiet(paul)&old(paul))))&
(![X]:((generous(X)&~old(X))<=>(~patient(X)&brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((wise(X)&tall(X)))))&
(((old(susan)<~>~generous(susan)))<=>((~strong(susan)|~happy(susan))))&
(![X]:((old(X)&happy(X))=>~patient(X)))&
((?[X]:((creative(X)&funny(X))))<=>((~rich(fred)|tall(fred))))&
(![X]:((patient(X)&~curious(X))=>tall(X)))&
(![X]:((happy(X)&~curious(X))=>(generous(X)&brave(X))))&
(![X]:((calm(X)&old(X))=>patient(X)))&
(![X]:((~happy(X)|patient(X))=>(~quiet(X)&~humble(X))))&
(?[X]:((~curious(X)&quiet(X))))&
(~patient(mary))&
(?[X]:((~brave(X)|curious(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((~tall(john)&~funny(john)))&
((~wise(susan)<~>strong(susan)))&
((old(mary)&~curious(mary)))&
(generous(paul)) | brave(mary) | [
"p7",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4172002997957641527854684
% SZS output start Proof for 4172002997957641527854684
8. ! [X0] : ((~old(X0) & generous(X0)) <=> (brave(X0) & ~patient(X0))) [input p7]
18. ~patient(mary) [input p17]
23. ~curious(mary) & old(mary) [input p22]
25. brave(mary) [input hypothesis]
55. ! [X0] : (((~old(X0) & generous(X0)) | (~brave(X0) | patient(X0))) & ((brave(X0) & ~patient(X0)) | (old(X0) | ~generous(X0)))) [nnf transformation 8]
56. ! [X0] : (((~old(X0) & generous(X0)) | ~brave(X0) | patient(X0)) & ((brave(X0) & ~patient(X0)) | old(X0) | ~generous(X0))) [flattening 55]
97. ~brave(X0) | ~old(X0) | patient(X0) [cnf transformation 56]
120. ~patient(mary) [cnf transformation 18]
128. old(mary) [cnf transformation 23]
131. brave(mary) [cnf transformation 25]
358. ~old(mary) | patient(mary) [resolution 97,131]
360. patient(mary) [subsumption resolution 358,128]
361. $false [subsumption resolution 360,120]
% SZS output end Proof for 4172002997957641527854684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich is old or strong and vice versa.
If someone is calm or not calm then someone is generous and vice versa.
If lucy is either kind or not kind then lucy is creative.
If fred is calm or not old then someone is either not tall or not old and vice versa.
Everyone who is either old or not funny is humble and vice versa.
Everyone who is funny or not funny is either creative or tall.
Everyone who is either tall or not wise is both not rich and curious and vice versa.
Everyone who is not funny or humble is both strong and wise and vice versa.
Everyone who is both not calm and not funny is not curious or calm and vice versa.
If someone is not old then fred is not kind.
If mary is not tall or tall then someone is patient and vice versa.
Everyone who is both tall and not curious is rich or not creative.
Everyone who is quiet is not old and vice versa.
If susan is both not kind and not patient then lucy is either not happy or not kind and vice versa.
If paul is both strong and old then mary is not patient.
If lucy is creative then someone is either not patient or rich.
Someone is either generous or not old.
Lucy is both happy and not old.
Fred is both not kind and curious.
Someone is either not tall or not happy.
Someone is not quiet or not curious.
Someone is tall.
Paul is old.
Someone is not tall. | Paul is not old. | contradiction | (![X]:(~rich(X)<=>(old(X)|strong(X))))&
((?[X]:((calm(X)|~calm(X))))<=>(?[X]:(generous(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(creative(lucy)))&
(((calm(fred)|~old(fred)))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((old(X)<~>~funny(X))<=>humble(X)))&
(![X]:((funny(X)|~funny(X))=>(creative(X)<~>tall(X))))&
(![X]:((tall(X)<~>~wise(X))<=>(~rich(X)&curious(X))))&
(![X]:((~funny(X)|humble(X))<=>(strong(X)&wise(X))))&
(![X]:((~calm(X)&~funny(X))<=>(~curious(X)|calm(X))))&
((?[X]:(~old(X)))=>(~kind(fred)))&
(((~tall(mary)|tall(mary)))<=>(?[X]:(patient(X))))&
(![X]:((tall(X)&~curious(X))=>(rich(X)|~creative(X))))&
(![X]:(quiet(X)<=>~old(X)))&
(((~kind(susan)&~patient(susan)))<=>((~happy(lucy)<~>~kind(lucy))))&
(((strong(paul)&old(paul)))=>(~patient(mary)))&
((creative(lucy))=>(?[X]:((~patient(X)<~>rich(X)))))&
(?[X]:((generous(X)<~>~old(X))))&
((happy(lucy)&~old(lucy)))&
((~kind(fred)&curious(fred)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:(tall(X)))&
(old(paul))&
(?[X]:(~tall(X))) | ~old(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1343312693303694075526901
% SZS output start Proof for 1343312693303694075526901
23. old(paul) [input p22]
25. ~old(paul) [input hypothesis]
143. old(paul) [cnf transformation 23]
145. ~old(paul) [cnf transformation 25]
244. 20 <=> old(paul) [avatar definition]
293. 20 [avatar split clause 143,244]
294. ~20 [avatar split clause 145,244]
295. $false [avatar sat refutation 293,294]
% SZS output end Proof for 1343312693303694075526901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or tall then someone is not wise or curious.
Everyone who is either not wise or patient is strong and vice versa.
If someone is not tall then alice is either creative or not old and vice versa.
If someone is not creative then susan is both not kind and rich.
If someone is not tall or not curious then someone is not kind or funny.
If someone is not generous or happy then fred is funny.
Everyone who is strong or calm is both happy and old.
Everyone who is old is strong and vice versa.
Everyone who is both not brave and not curious is both strong and happy and vice versa.
Everyone who is both not humble and tall is both not kind and not humble.
Everyone who is not strong is patient or not curious.
Everyone who is not calm or not curious is both not humble and brave.
Everyone who is old is both not rich and not tall.
Everyone who is either old or not generous is either tall or curious and vice versa.
If someone is either not happy or old then lucy is either not generous or patient.
Everyone who is wise or not brave is either patient or quiet and vice versa.
Someone is both kind and not generous.
Someone is either generous or rich.
Someone is either generous or brave.
John is either not funny or happy. | Fred is quiet. | entailment | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>strong(X)))&
((?[X]:(~tall(X)))<=>((creative(alice)<~>~old(alice))))&
((?[X]:(~creative(X)))=>((~kind(susan)&rich(susan))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((~generous(X)|happy(X))))=>(funny(fred)))&
(![X]:((strong(X)|calm(X))=>(happy(X)&old(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)&happy(X))))&
(![X]:((~humble(X)&tall(X))=>(~kind(X)&~humble(X))))&
(![X]:(~strong(X)=>(patient(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~humble(X)&brave(X))))&
(![X]:(old(X)=>(~rich(X)&~tall(X))))&
(![X]:((old(X)<~>~generous(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>old(X))))=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((wise(X)|~brave(X))<=>(patient(X)<~>quiet(X))))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((~funny(john)<~>happy(john))) | quiet(fred) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 283171316539532325355501
% SZS output start Proof for 283171316539532325355501
2. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> strong(X0)) [input p1]
7. ! [X0] : ((calm(X0) | strong(X0)) => (old(X0) & happy(X0))) [input p6]
8. ! [X0] : (old(X0) <=> strong(X0)) [input p7]
9. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (happy(X0) & strong(X0))) [input p8]
12. ! [X0] : ((~curious(X0) | ~calm(X0)) => (brave(X0) & ~humble(X0))) [input p11]
16. ! [X0] : ((~brave(X0) | wise(X0)) <=> (patient(X0) <~> quiet(X0))) [input p15]
21. ~quiet(fred) [input hypothesis]
28. ! [X0] : ((old(X0) & happy(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 7]
33. ! [X0] : ((brave(X0) & ~humble(X0)) | (curious(X0) & calm(X0))) [ennf transformation 12]
39. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 2]
47. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 8]
48. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((~curious(X0) & ~brave(X0)) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | curious(X0) | brave(X0))) [flattening 48]
52. ! [X0] : (((~brave(X0) | wise(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 16]
53. ! [X0] : ((~brave(X0) | wise(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [flattening 52]
65. patient(X0) | strong(X0) | wise(X0) [cnf transformation 39]
66. ~patient(X0) | ~wise(X0) | strong(X0) [cnf transformation 39]
79. ~strong(X0) | happy(X0) [cnf transformation 28]
82. ~calm(X0) | old(X0) [cnf transformation 28]
83. ~old(X0) | strong(X0) [cnf transformation 47]
87. ~brave(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
88. ~curious(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
94. brave(X0) | calm(X0) [cnf transformation 33]
95. brave(X0) | curious(X0) [cnf transformation 33]
110. ~wise(X0) | patient(X0) | quiet(X0) [cnf transformation 53]
114. ~brave(X0) | wise(X0) | quiet(X0) | ~patient(X0) [cnf transformation 53]
124. ~quiet(fred) [cnf transformation 21]
198. ~curious(X0) | ~strong(X0) [subsumption resolution 88,79]
199. ~brave(X0) | ~strong(X0) [subsumption resolution 87,79]
268. ~strong(X0) | curious(X0) [resolution 199,95]
271. ~strong(X0) [subsumption resolution 268,198]
295. 28 <=> brave(fred) [avatar definition]
296. ~brave(fred) <- (~28) [avatar component clause 295]
297. brave(fred) <- (28) [avatar component clause 295]
299. 29 <=> patient(fred) [avatar definition]
300. ~patient(fred) <- (~29) [avatar component clause 299]
301. patient(fred) <- (29) [avatar component clause 299]
417. wise(fred) | quiet(fred) | ~patient(fred) <- (28) [resolution 114,297]
432. wise(fred) | ~patient(fred) <- (28) [subsumption resolution 417,124]
434. 46 <=> wise(fred) [avatar definition]
436. wise(fred) <- (46) [avatar component clause 434]
437. ~29 | 46 | ~28 [avatar split clause 432,295,434,299]
438. strong(fred) | wise(fred) <- (~29) [resolution 300,65]
439. wise(fred) <- (~29) [subsumption resolution 438,271]
440. 46 | 29 [avatar split clause 439,299,434]
466. patient(fred) | quiet(fred) <- (46) [resolution 436,110]
471. patient(fred) <- (46) [subsumption resolution 466,124]
472. 29 | ~46 [avatar split clause 471,434,299]
475. ~wise(fred) | strong(fred) <- (29) [resolution 301,66]
479. ~wise(fred) <- (29) [subsumption resolution 475,271]
480. ~46 | ~29 [avatar split clause 479,299,434]
484. calm(fred) <- (~28) [resolution 296,94]
514. old(fred) <- (~28) [resolution 484,82]
537. strong(fred) <- (~28) [resolution 514,83]
540. $false <- (~28) [subsumption resolution 537,271]
541. 28 [avatar contradiction clause 540]
542. $false [avatar sat refutation 437,440,472,480,541]
% SZS output end Proof for 283171316539532325355501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either not wise or funny and vice versa. Everyone who is brave or patient is both kind and rich. If fred is not generous or funny then someone is not patient or not creative and vice versa. Everyone who is brave or creative is curious or rich. Everyone who is quiet or not rich is not calm and vice versa. If someone is either not happy or not wise then someone is wise and vice versa. Everyone who is both not wise and rich is either generous or brave and vice versa. If susan is either strong or happy then paul is either patient or not tall and vice versa. Everyone who is brave is either tall or not brave and vice versa. Everyone who is either not humble or not old is both tall and old and vice versa. Everyone who is both patient and calm is humble or not happy. If someone is not creative then susan is not rich or happy. Everyone who is either patient or not wise is rich. If someone is both not curious and not kind then someone is patient and vice versa. If alice is not tall or not wise then someone is both not creative and tall. Someone is both not calm and quiet. John is either not patient or wise. Someone is patient. Paul is either not funny or not tall. Alice is calm or not creative. Someone is not kind. | Susan is not happy. | neutral | (![X]:(funny(X)<=>(~wise(X)<~>funny(X))))&
(![X]:((brave(X)|patient(X))=>(kind(X)&rich(X))))&
(((~generous(fred)|funny(fred)))<=>(?[X]:((~patient(X)|~creative(X)))))&
(![X]:((brave(X)|creative(X))=>(curious(X)|rich(X))))&
(![X]:((quiet(X)|~rich(X))<=>~calm(X)))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:(wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(((~tall(alice)|~wise(alice)))=>(?[X]:((~creative(X)&tall(X)))))&
(?[X]:((~calm(X)&quiet(X))))&
((~patient(john)<~>wise(john)))&
(?[X]:(patient(X)))&
((~funny(paul)<~>~tall(paul)))&
((calm(alice)|~creative(alice)))&
(?[X]:(~kind(X))) | ~happy(susan) | [] | null | 0 |
Everyone who is both not creative and creative is happy and vice versa. If alice is humble then someone is both not wise and strong and vice versa. Everyone who is not quiet is not calm. Everyone who is both brave and curious is not tall or not rich and vice versa. If paul is either not funny or not calm then someone is not quiet or not creative and vice versa. Everyone who is either not strong or tall is both not kind and generous. If someone is patient then mary is either humble or calm. Everyone who is both not tall and patient is either not old or not brave and vice versa. Everyone who is both not humble and brave is both not brave and not rich. Everyone who is tall is both old and not brave and vice versa. Everyone who is not generous is curious or not happy. If someone is kind then fred is both not kind and not rich. Everyone who is both not calm and not patient is either funny or generous. Everyone who is wise is either strong or not tall. Everyone who is either strong or calm is not happy. Everyone who is both quiet and brave is not creative and vice versa. Someone is quiet or old. Lucy is quiet. Mary is either kind or curious. Fred is either not quiet or not tall. Someone is either not curious or not wise. Someone is rich. Someone is strong or not funny. | Mary is curious. | entailment | (![X]:((~creative(X)&creative(X))<=>happy(X)))&
((humble(alice))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:(~quiet(X)=>~calm(X)))&
(![X]:((brave(X)&curious(X))<=>(~tall(X)|~rich(X))))&
(((~funny(paul)<~>~calm(paul)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(~kind(X)&generous(X))))&
((?[X]:(patient(X)))=>((humble(mary)<~>calm(mary))))&
(![X]:((~tall(X)&patient(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((~humble(X)&brave(X))=>(~brave(X)&~rich(X))))&
(![X]:(tall(X)<=>(old(X)&~brave(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((?[X]:(kind(X)))=>((~kind(fred)&~rich(fred))))&
(![X]:((~calm(X)&~patient(X))=>(funny(X)<~>generous(X))))&
(![X]:(wise(X)=>(strong(X)<~>~tall(X))))&
(![X]:((strong(X)<~>calm(X))=>~happy(X)))&
(![X]:((quiet(X)&brave(X))<=>~creative(X)))&
(?[X]:((quiet(X)|old(X))))&
(quiet(lucy))&
((kind(mary)<~>curious(mary)))&
((~quiet(fred)<~>~tall(fred)))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:(rich(X)))&
(?[X]:((strong(X)|~funny(X)))) | curious(mary) | [
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6013754968897505305174380
% SZS output start Proof for 6013754968897505305174380
4. ! [X0] : ((curious(X0) & brave(X0)) <=> (~rich(X0) | ~tall(X0))) [input p3]
8. ! [X0] : ((patient(X0) & ~tall(X0)) <=> (~old(X0) <~> ~brave(X0))) [input p7]
10. ! [X0] : (tall(X0) <=> (~brave(X0) & old(X0))) [input p9]
24. ~curious(mary) [input hypothesis]
44. ! [X0] : (((curious(X0) & brave(X0)) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 4]
45. ! [X0] : (((curious(X0) & brave(X0)) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ~curious(X0) | ~brave(X0))) [flattening 44]
52. ! [X0] : (((patient(X0) & ~tall(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (~patient(X0) | tall(X0)))) [nnf transformation 8]
53. ! [X0] : (((patient(X0) & ~tall(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | ~patient(X0) | tall(X0))) [flattening 52]
54. ! [X0] : ((tall(X0) | (brave(X0) | ~old(X0))) & ((~brave(X0) & old(X0)) | ~tall(X0))) [nnf transformation 10]
55. ! [X0] : ((tall(X0) | brave(X0) | ~old(X0)) & ((~brave(X0) & old(X0)) | ~tall(X0))) [flattening 54]
78. tall(X0) | brave(X0) [cnf transformation 45]
80. tall(X0) | curious(X0) [cnf transformation 45]
97. ~tall(X0) | ~old(X0) | brave(X0) [cnf transformation 53]
102. ~tall(X0) | old(X0) [cnf transformation 55]
103. ~tall(X0) | ~brave(X0) [cnf transformation 55]
127. ~curious(mary) [cnf transformation 24]
188. ~old(X0) | brave(X0) [subsumption resolution 97,78]
217. 20 <=> curious(mary) [avatar definition]
219. ~curious(mary) <- (~20) [avatar component clause 217]
251. ~20 [avatar split clause 127,217]
257. old(X1) | brave(X1) [resolution 102,78]
258. brave(X1) [subsumption resolution 257,188]
259. ~brave(X0) | curious(X0) [resolution 103,80]
261. curious(X0) [subsumption resolution 259,258]
262. $false <- (~20) [resolution 261,219]
263. 20 [avatar contradiction clause 262]
264. $false [avatar sat refutation 251,263]
% SZS output end Proof for 6013754968897505305174380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not creative is happy and vice versa.
If someone is not happy then someone is funny and vice versa.
Everyone who is both wise and curious is strong or creative.
If john is not brave then mary is happy or rich.
If paul is either not patient or brave then fred is humble or not tall and vice versa.
Everyone who is tall or not kind is both happy and tall and vice versa.
Everyone who is either calm or not curious is brave or happy and vice versa.
If someone is either patient or kind then someone is not happy or not funny and vice versa.
Everyone who is both not brave and kind is not wise or not tall and vice versa.
Everyone who is not funny is either kind or not rich and vice versa.
Everyone who is rich is not creative or not happy.
If mary is both funny and calm then someone is not curious and vice versa.
Everyone who is funny is not patient or not rich and vice versa.
If someone is not strong then someone is both wise and not calm and vice versa.
Everyone who is either not generous or not old is not brave or wise and vice versa.
Paul is both strong and patient.
Lucy is either brave or not calm.
Someone is either curious or not brave.
Someone is generous or not rich.
Someone is not generous.
Susan is either tall or not humble. | Paul is humble. | neutral | (![X]:((strong(X)|~creative(X))<=>happy(X)))&
((?[X]:(~happy(X)))<=>(?[X]:(funny(X))))&
(![X]:((wise(X)&curious(X))=>(strong(X)|creative(X))))&
((~brave(john))=>((happy(mary)|rich(mary))))&
(((~patient(paul)<~>brave(paul)))<=>((humble(fred)|~tall(fred))))&
(![X]:((tall(X)|~kind(X))<=>(happy(X)&tall(X))))&
(![X]:((calm(X)<~>~curious(X))<=>(brave(X)|happy(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~brave(X)&kind(X))<=>(~wise(X)|~tall(X))))&
(![X]:(~funny(X)<=>(kind(X)<~>~rich(X))))&
(![X]:(rich(X)=>(~creative(X)|~happy(X))))&
(((funny(mary)&calm(mary)))<=>(?[X]:(~curious(X))))&
(![X]:(funny(X)<=>(~patient(X)|~rich(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((~generous(X)<~>~old(X))<=>(~brave(X)|wise(X))))&
((strong(paul)&patient(paul)))&
((brave(lucy)<~>~calm(lucy)))&
(?[X]:((curious(X)<~>~brave(X))))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:(~generous(X)))&
((tall(susan)<~>~humble(susan))) | humble(paul) | [] | null | 0 |
Everyone who is not creative or creative is either not curious or quiet.
Everyone who is strong is not strong or not curious.
Everyone who is both kind and curious is patient and vice versa.
Everyone who is both kind and not humble is creative.
If lucy is not funny then someone is not old and vice versa.
Everyone who is either funny or brave is not brave and vice versa.
If alice is rich or not rich then john is old.
Everyone who is either happy or not strong is either creative or rich.
Everyone who is not old or patient is not quiet or not humble and vice versa.
If susan is either not old or happy then lucy is calm or creative.
If someone is not strong or not kind then someone is not patient and vice versa.
If alice is old or not old then susan is not humble or not funny.
Everyone who is both not patient and not curious is both not patient and generous and vice versa.
If someone is not curious or rich then someone is both wise and tall and vice versa.
If someone is not tall or not calm then lucy is patient and vice versa.
Someone is either not curious or curious.
Paul is kind or curious.
Someone is not generous or rich.
Lucy is either quiet or not kind.
Someone is brave.
Susan is funny or wise. | Alice is funny. | entailment | (![X]:((~creative(X)|creative(X))=>(~curious(X)<~>quiet(X))))&
(![X]:(strong(X)=>(~strong(X)|~curious(X))))&
(![X]:((kind(X)&curious(X))<=>patient(X)))&
(![X]:((kind(X)&~humble(X))=>creative(X)))&
((~funny(lucy))<=>(?[X]:(~old(X))))&
(![X]:((funny(X)<~>brave(X))<=>~brave(X)))&
(((rich(alice)|~rich(alice)))=>(old(john)))&
(![X]:((happy(X)<~>~strong(X))=>(creative(X)<~>rich(X))))&
(![X]:((~old(X)|patient(X))<=>(~quiet(X)|~humble(X))))&
(((~old(susan)<~>happy(susan)))=>((calm(lucy)|creative(lucy))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:(~patient(X))))&
(((old(alice)|~old(alice)))=>((~humble(susan)|~funny(susan))))&
(![X]:((~patient(X)&~curious(X))<=>(~patient(X)&generous(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((wise(X)&tall(X)))))&
((?[X]:((~tall(X)|~calm(X))))<=>(patient(lucy)))&
(?[X]:((~curious(X)<~>curious(X))))&
((kind(paul)|curious(paul)))&
(?[X]:((~generous(X)|rich(X))))&
((quiet(lucy)<~>~kind(lucy)))&
(?[X]:(brave(X)))&
((funny(susan)|wise(susan))) | funny(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 996543985464551431564867
% SZS output start Proof for 996543985464551431564867
6. ! [X0] : ((funny(X0) <~> brave(X0)) <=> ~brave(X0)) [input p5]
22. ~funny(alice) [input hypothesis]
43. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | brave(X0)) & (~brave(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 6]
84. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 43]
85. brave(X0) | funny(X0) | brave(X0) [cnf transformation 43]
124. ~funny(alice) [cnf transformation 22]
125. ~brave(X0) | funny(X0) [duplicate literal removal 84]
126. brave(X0) | funny(X0) [duplicate literal removal 85]
143. funny(X0) [subsumption resolution 125,126]
288. $false [subsumption resolution 124,143]
% SZS output end Proof for 996543985464551431564867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is either not rich or brave.
Everyone who is tall is both creative and funny and vice versa.
If paul is both calm and not rich then paul is both not strong and not happy.
Everyone who is both happy and not brave is not humble or humble and vice versa.
Everyone who is old or not brave is not quiet or not strong.
Everyone who is not kind or not happy is curious or not wise.
Everyone who is both not funny and rich is not patient.
Everyone who is both kind and not patient is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
If someone is both kind and not rich then someone is not curious.
Everyone who is rich or not tall is either tall or calm.
If someone is either not strong or not rich then paul is both not humble and not rich.
Everyone who is kind or funny is not rich or happy.
Everyone who is both funny and not old is not tall or not quiet and vice versa.
Everyone who is old is not quiet or not generous.
Someone is quiet or creative.
Lucy is wise.
Lucy is not kind.
Paul is not brave.
Lucy is both funny and not brave.
Fred is tall.
Someone is both tall and old.
Alice is strong. | Paul is old. | neutral | ((?[X]:(~strong(X)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:(tall(X)<=>(creative(X)&funny(X))))&
(((calm(paul)&~rich(paul)))=>((~strong(paul)&~happy(paul))))&
(![X]:((happy(X)&~brave(X))<=>(~humble(X)|humble(X))))&
(![X]:((old(X)|~brave(X))=>(~quiet(X)|~strong(X))))&
(![X]:((~kind(X)|~happy(X))=>(curious(X)|~wise(X))))&
(![X]:((~funny(X)&rich(X))=>~patient(X)))&
(![X]:((kind(X)&~patient(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>((~humble(paul)&~rich(paul))))&
(![X]:((kind(X)|funny(X))=>(~rich(X)|happy(X))))&
(![X]:((funny(X)&~old(X))<=>(~tall(X)|~quiet(X))))&
(![X]:(old(X)=>(~quiet(X)|~generous(X))))&
(?[X]:((quiet(X)|creative(X))))&
(wise(lucy))&
(~kind(lucy))&
(~brave(paul))&
((funny(lucy)&~brave(lucy)))&
(tall(fred))&
(?[X]:((tall(X)&old(X))))&
(strong(alice)) | old(paul) | [] | null | 0 |
If someone is not happy then fred is strong. If susan is both calm and happy then mary is both old and patient. Everyone who is not generous or calm is not kind. Everyone who is not creative is patient or not curious and vice versa. If lucy is not curious or happy then someone is generous. Everyone who is either not strong or curious is not strong. If someone is either not generous or not tall then someone is not happy and vice versa. Everyone who is creative is happy or not happy. If someone is calm or wise then someone is either strong or kind and vice versa. If lucy is both not tall and not generous then someone is both rich and tall and vice versa. Everyone who is wise or not kind is both not funny and not wise and vice versa. If someone is quiet or humble then susan is creative or not generous and vice versa. Everyone who is either not kind or not wise is not curious or creative and vice versa. Everyone who is either not patient or strong is either not strong or strong and vice versa. Everyone who is either not humble or not generous is not quiet or humble and vice versa. Everyone who is not patient is creative. Someone is either not strong or old. Paul is patient. Someone is not happy. Paul is both brave and rich. John is either creative or tall. Someone is brave or tall. Paul is not humble. | John is strong. | entailment | ((?[X]:(~happy(X)))=>(strong(fred)))&
(((calm(susan)&happy(susan)))=>((old(mary)&patient(mary))))&
(![X]:((~generous(X)|calm(X))=>~kind(X)))&
(![X]:(~creative(X)<=>(patient(X)|~curious(X))))&
(((~curious(lucy)|happy(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>curious(X))=>~strong(X)))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(?[X]:(~happy(X))))&
(![X]:(creative(X)=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|wise(X))))<=>(?[X]:((strong(X)<~>kind(X)))))&
(((~tall(lucy)&~generous(lucy)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:((wise(X)|~kind(X))<=>(~funny(X)&~wise(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((creative(susan)|~generous(susan))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~curious(X)|creative(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~quiet(X)|humble(X))))&
(![X]:(~patient(X)=>creative(X)))&
(?[X]:((~strong(X)<~>old(X))))&
(patient(paul))&
(?[X]:(~happy(X)))&
((brave(paul)&rich(paul)))&
((creative(john)<~>tall(john)))&
(?[X]:((brave(X)|tall(X))))&
(~humble(paul)) | strong(john) | [
"p2",
"p5",
"p8",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5560031453919712876420081
% SZS output start Proof for 5560031453919712876420081
3. ! [X0] : ((calm(X0) | ~generous(X0)) => ~kind(X0)) [input p2]
6. ! [X0] : ((~strong(X0) <~> curious(X0)) => ~strong(X0)) [input p5]
9. ? [X0] : (wise(X0) | calm(X0)) <=> ? [X0] : (strong(X0) <~> kind(X0)) [input p8]
11. ! [X0] : ((~kind(X0) | wise(X0)) <=> (~wise(X0) & ~funny(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> ~wise(X0)) <=> (creative(X0) | ~curious(X0))) [input p12]
14. ! [X0] : ((~patient(X0) <~> strong(X0)) <=> (~strong(X0) <~> strong(X0))) [input p13]
16. ! [X0] : (~patient(X0) => creative(X0)) [input p15]
24. ~strong(john) [input hypothesis]
26. ? [X0] : (wise(X0) | calm(X0)) <=> ? [X1] : (strong(X1) <~> kind(X1)) [rectify 9]
32. ! [X0] : (~kind(X0) | (~calm(X0) & generous(X0))) [ennf transformation 3]
34. ! [X0] : (~strong(X0) | (~strong(X0) <=> curious(X0))) [ennf transformation 6]
37. ! [X0] : (creative(X0) | patient(X0)) [ennf transformation 16]
42. ! [X0] : (~strong(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) [nnf transformation 34]
48. (? [X0] : (wise(X0) | calm(X0)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (? [X1] : ((~kind(X1) | ~strong(X1)) & (kind(X1) | strong(X1))) | ! [X0] : (~wise(X0) & ~calm(X0))) [nnf transformation 26]
49. (? [X0] : (wise(X0) | calm(X0)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (? [X2] : ((~kind(X2) | ~strong(X2)) & (kind(X2) | strong(X2))) | ! [X3] : (~wise(X3) & ~calm(X3))) [rectify 48]
50. ? [X0] : (wise(X0) | calm(X0)) => (wise(sK3) | calm(sK3)) [choice axiom]
51. ? [X2] : ((~kind(X2) | ~strong(X2)) & (kind(X2) | strong(X2))) => ((~kind(sK4) | ~strong(sK4)) & (kind(sK4) | strong(sK4))) [choice axiom]
52. ((wise(sK3) | calm(sK3)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (((~kind(sK4) | ~strong(sK4)) & (kind(sK4) | strong(sK4))) | ! [X3] : (~wise(X3) & ~calm(X3))) [skolemisation 49,51,50]
58. ! [X0] : (((~kind(X0) | wise(X0)) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [nnf transformation 11]
59. ! [X0] : ((~kind(X0) | wise(X0) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [flattening 58]
65. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [nnf transformation 13]
66. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [flattening 65]
67. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [nnf transformation 14]
80. ~kind(X0) | ~calm(X0) [cnf transformation 32]
87. ~strong(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 42]
98. wise(sK3) | calm(sK3) | strong(X1) | ~kind(X1) [cnf transformation 52]
105. ~wise(X0) | ~wise(X0) [cnf transformation 59]
106. ~wise(X0) | kind(X0) [cnf transformation 59]
116. wise(X0) | kind(X0) | curious(X0) [cnf transformation 66]
117. wise(X0) | kind(X0) | ~creative(X0) [cnf transformation 66]
122. strong(X0) | ~patient(X0) | strong(X0) | strong(X0) [cnf transformation 67]
132. creative(X0) | patient(X0) [cnf transformation 37]
141. ~strong(john) [cnf transformation 24]
148. ~patient(X0) | strong(X0) [duplicate literal removal 122]
152. ~wise(X0) [duplicate literal removal 105]
154. ~curious(X0) | ~strong(X0) [duplicate literal removal 87]
218. 15 <=> ! [X1] : (strong(X1) | ~kind(X1)) [avatar definition]
219. ~kind(X1) | strong(X1) <- (15) [avatar component clause 218]
221. 16 <=> calm(sK3) [avatar definition]
223. calm(sK3) <- (16) [avatar component clause 221]
225. 17 <=> wise(sK3) [avatar definition]
227. wise(sK3) <- (17) [avatar component clause 225]
228. 15 | 16 | 17 [avatar split clause 98,225,221,218]
230. 18 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
231. ~strong(X1) | kind(X1) <- (18) [avatar component clause 230]
234. 19 <=> ! [X3] : ~wise(X3) [avatar definition]
235. ~wise(X3) <- (19) [avatar component clause 234]
274. 19 [avatar split clause 152,234]
301. ~creative(X0) | kind(X0) [subsumption resolution 117,106]
302. curious(X0) | kind(X0) [subsumption resolution 116,106]
317. 36 <=> creative(john) [avatar definition]
318. creative(john) <- (36) [avatar component clause 317]
319. ~creative(john) <- (~36) [avatar component clause 317]
338. kind(john) <- (36) [resolution 301,318]
339. kind(X0) | patient(X0) [resolution 301,132]
342. kind(X0) | ~strong(X0) [resolution 302,154]
343. 18 [avatar split clause 342,230]
391. ~calm(X1) | patient(X1) [resolution 339,80]
398. patient(sK3) <- (16) [resolution 391,223]
403. strong(sK3) <- (16) [resolution 398,148]
408. kind(sK3) <- (16, 18) [resolution 403,231]
415. ~calm(sK3) <- (16, 18) [resolution 408,80]
418. $false <- (16, 18) [subsumption resolution 415,223]
419. ~16 | ~18 [avatar contradiction clause 418]
423. strong(john) <- (15, 36) [resolution 219,338]
426. $false <- (15, 36) [subsumption resolution 423,141]
427. ~15 | ~36 [avatar contradiction clause 426]
430. $false <- (17, 19) [subsumption resolution 227,235]
431. ~17 | ~19 [avatar contradiction clause 430]
434. patient(john) <- (~36) [resolution 319,132]
441. strong(john) <- (~36) [resolution 434,148]
442. $false <- (~36) [subsumption resolution 441,141]
443. 36 [avatar contradiction clause 442]
444. $false [avatar sat refutation 228,274,343,419,427,431,443]
% SZS output end Proof for 5560031453919712876420081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not creative is not curious.
Everyone who is both brave and not funny is strong or not old and vice versa.
If someone is either generous or not kind then someone is not wise or curious and vice versa.
Everyone who is both tall and not funny is not calm and vice versa.
Everyone who is kind is either strong or not kind.
Everyone who is either old or strong is funny and vice versa.
If alice is funny then someone is not calm or not old.
If someone is both not generous and not old then someone is both happy and generous.
Everyone who is rich or brave is not rich.
Everyone who is either kind or not creative is both not generous and rich and vice versa.
If someone is both not tall and humble then someone is generous and vice versa.
If someone is not curious then john is both generous and old and vice versa.
If mary is both creative and not wise then lucy is not happy.
Everyone who is humble is either not old or not generous and vice versa.
Everyone who is creative or strong is tall.
Alice is patient.
Someone is creative.
Paul is either kind or funny.
Someone is either curious or calm.
Alice is old or not quiet. | John is not humble. | contradiction | (![X]:((kind(X)&~creative(X))=>~curious(X)))&
(![X]:((brave(X)&~funny(X))<=>(strong(X)|~old(X))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((tall(X)&~funny(X))<=>~calm(X)))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
(![X]:((old(X)<~>strong(X))<=>funny(X)))&
((funny(alice))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((rich(X)|brave(X))=>~rich(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(~generous(X)&rich(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:(~curious(X)))<=>((generous(john)&old(john))))&
(((creative(mary)&~wise(mary)))=>(~happy(lucy)))&
(![X]:(humble(X)<=>(~old(X)<~>~generous(X))))&
(![X]:((creative(X)|strong(X))=>tall(X)))&
(patient(alice))&
(?[X]:(creative(X)))&
((kind(paul)<~>funny(paul)))&
(?[X]:((curious(X)<~>calm(X))))&
((old(alice)|~quiet(alice))) | ~humble(john) | [
"p4",
"p7",
"p8",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 926358611551240731790027
% SZS output start Proof for 926358611551240731790027
5. ! [X0] : (kind(X0) => (strong(X0) <~> ~kind(X0))) [input p4]
8. ? [X0] : (~old(X0) & ~generous(X0)) => ? [X0] : (generous(X0) & happy(X0)) [input p7]
9. ! [X0] : ((brave(X0) | rich(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (rich(X0) & ~generous(X0))) [input p9]
11. ? [X0] : (humble(X0) & ~tall(X0)) <=> ? [X0] : generous(X0) [input p10]
14. ! [X0] : (humble(X0) <=> (~old(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : ((strong(X0) | creative(X0)) => tall(X0)) [input p14]
21. ~humble(john) [input hypothesis]
23. ? [X0] : (~old(X0) & ~generous(X0)) => ? [X1] : (generous(X1) & happy(X1)) [rectify 8]
24. ? [X0] : (humble(X0) & ~tall(X0)) <=> ? [X1] : generous(X1) [rectify 11]
29. ! [X0] : ((strong(X0) <~> ~kind(X0)) | ~kind(X0)) [ennf transformation 5]
31. ? [X1] : (generous(X1) & happy(X1)) | ! [X0] : (old(X0) | generous(X0)) [ennf transformation 23]
32. ! [X0] : (~rich(X0) | (~brave(X0) & ~rich(X0))) [ennf transformation 9]
35. ! [X0] : (tall(X0) | (~strong(X0) & ~creative(X0))) [ennf transformation 15]
45. ! [X0] : (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~kind(X0)) [nnf transformation 29]
49. ? [X0] : (generous(X0) & happy(X0)) | ! [X1] : (old(X1) | generous(X1)) [rectify 31]
50. ? [X0] : (generous(X0) & happy(X0)) => (generous(sK3) & happy(sK3)) [choice axiom]
51. (generous(sK3) & happy(sK3)) | ! [X1] : (old(X1) | generous(X1)) [skolemisation 49,50]
52. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 10]
53. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [flattening 52]
54. (? [X0] : (humble(X0) & ~tall(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (~humble(X0) | tall(X0))) [nnf transformation 24]
55. (? [X0] : (humble(X0) & ~tall(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (~humble(X3) | tall(X3))) [rectify 54]
56. ? [X0] : (humble(X0) & ~tall(X0)) => (humble(sK4) & ~tall(sK4)) [choice axiom]
57. ? [X2] : generous(X2) => generous(sK5) [choice axiom]
58. ((humble(sK4) & ~tall(sK4)) | ! [X1] : ~generous(X1)) & (generous(sK5) | ! [X3] : (~humble(X3) | tall(X3))) [skolemisation 55,57,56]
64. ! [X0] : ((humble(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0)))) & (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | ~humble(X0))) [nnf transformation 14]
86. ~kind(X0) | strong(X0) | ~kind(X0) [cnf transformation 45]
94. generous(sK3) | old(X1) | generous(X1) [cnf transformation 51]
95. ~rich(X0) | ~rich(X0) [cnf transformation 32]
100. rich(X0) | kind(X0) | creative(X0) [cnf transformation 53]
104. ~tall(sK4) | ~generous(X1) [cnf transformation 58]
113. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 64]
114. ~creative(X0) | tall(X0) [cnf transformation 35]
115. ~strong(X0) | tall(X0) [cnf transformation 35]
121. ~humble(john) [cnf transformation 21]
122. ~rich(X0) [duplicate literal removal 95]
123. ~kind(X0) | strong(X0) [duplicate literal removal 86]
173. 12 <=> ! [X1] : (old(X1) | generous(X1)) [avatar definition]
174. generous(X1) | old(X1) <- (12) [avatar component clause 173]
176. 13 <=> generous(sK3) [avatar definition]
178. generous(sK3) <- (13) [avatar component clause 176]
179. 12 | 13 [avatar split clause 94,176,173]
185. creative(X0) | kind(X0) [subsumption resolution 100,122]
188. 15 <=> ! [X1] : ~generous(X1) [avatar definition]
189. ~generous(X1) <- (15) [avatar component clause 188]
196. 17 <=> tall(sK4) [avatar definition]
198. ~tall(sK4) <- (~17) [avatar component clause 196]
199. 15 | ~17 [avatar split clause 104,196,188]
270. tall(X0) | kind(X0) [resolution 185,114]
324. $false <- (13, 15) [resolution 189,178]
327. ~13 | ~15 [avatar contradiction clause 324]
328. old(X1) <- (12, 15) [subsumption resolution 174,189]
340. humble(X0) | generous(X0) <- (12, 15) [resolution 113,328]
343. humble(X0) <- (12, 15) [subsumption resolution 340,189]
344. $false <- (12, 15) [resolution 343,121]
350. ~12 | ~15 [avatar contradiction clause 344]
423. kind(sK4) <- (~17) [resolution 270,198]
439. strong(sK4) <- (~17) [resolution 423,123]
450. tall(sK4) <- (~17) [resolution 439,115]
455. $false <- (~17) [subsumption resolution 450,198]
456. 17 [avatar contradiction clause 455]
457. $false [avatar sat refutation 179,199,327,350,456]
% SZS output end Proof for 926358611551240731790027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not kind is either not funny or not brave and vice versa.
Everyone who is strong is old and vice versa.
If someone is not strong then someone is calm.
Everyone who is both not tall and wise is either not quiet or tall and vice versa.
Everyone who is patient or not rich is not patient and vice versa.
Everyone who is either calm or not funny is not brave or generous and vice versa.
Everyone who is wise is not strong or brave and vice versa.
Everyone who is both not creative and not wise is either not kind or rich and vice versa.
Everyone who is not old or not calm is creative or not humble and vice versa.
If paul is old or generous then mary is both not old and not calm and vice versa.
Everyone who is both not rich and creative is strong and vice versa.
Everyone who is both not generous and creative is quiet or brave.
Everyone who is old or tall is happy and vice versa.
If someone is both not wise and not strong then fred is curious and vice versa.
Susan is not tall or not patient.
Alice is curious.
Someone is funny or generous.
Paul is either not funny or not happy. | Alice is kind. | entailment | (![X]:((~old(X)&~kind(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:(strong(X)<=>old(X)))&
((?[X]:(~strong(X)))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)&wise(X))<=>(~quiet(X)<~>tall(X))))&
(![X]:((patient(X)|~rich(X))<=>~patient(X)))&
(![X]:((calm(X)<~>~funny(X))<=>(~brave(X)|generous(X))))&
(![X]:(wise(X)<=>(~strong(X)|brave(X))))&
(![X]:((~creative(X)&~wise(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~old(X)|~calm(X))<=>(creative(X)|~humble(X))))&
(((old(paul)|generous(paul)))<=>((~old(mary)&~calm(mary))))&
(![X]:((~rich(X)&creative(X))<=>strong(X)))&
(![X]:((~generous(X)&creative(X))=>(quiet(X)|brave(X))))&
(![X]:((old(X)|tall(X))<=>happy(X)))&
((?[X]:((~wise(X)&~strong(X))))<=>(curious(fred)))&
((~tall(susan)|~patient(susan)))&
(curious(alice))&
(?[X]:((funny(X)|generous(X))))&
((~funny(paul)<~>~happy(paul))) | kind(alice) | [
"p4",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7703696139583877205221210
% SZS output start Proof for 7703696139583877205221210
5. ! [X0] : ((~rich(X0) | patient(X0)) <=> ~patient(X0)) [input p4]
7. ! [X0] : (wise(X0) <=> (brave(X0) | ~strong(X0))) [input p6]
8. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> (~kind(X0) <~> rich(X0))) [input p7]
11. ! [X0] : ((creative(X0) & ~rich(X0)) <=> strong(X0)) [input p10]
19. ~kind(alice) [input hypothesis]
32. ! [X0] : (((~rich(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (rich(X0) & ~patient(X0)))) [nnf transformation 5]
33. ! [X0] : ((~rich(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (rich(X0) & ~patient(X0)))) [flattening 32]
36. ! [X0] : ((wise(X0) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | ~wise(X0))) [nnf transformation 7]
37. ! [X0] : ((wise(X0) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | ~wise(X0))) [flattening 36]
38. ! [X0] : (((~wise(X0) & ~creative(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) | creative(X0)))) [nnf transformation 8]
39. ! [X0] : (((~wise(X0) & ~creative(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | wise(X0) | creative(X0))) [flattening 38]
44. ! [X0] : (((creative(X0) & ~rich(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | rich(X0)))) [nnf transformation 11]
45. ! [X0] : (((creative(X0) & ~rich(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | rich(X0))) [flattening 44]
70. ~patient(X0) | ~patient(X0) [cnf transformation 33]
72. ~rich(X0) | patient(X0) | patient(X0) [cnf transformation 33]
80. wise(X0) | strong(X0) [cnf transformation 37]
84. ~creative(X0) | rich(X0) | kind(X0) [cnf transformation 39]
86. ~wise(X0) | rich(X0) | kind(X0) [cnf transformation 39]
99. ~strong(X0) | creative(X0) [cnf transformation 45]
112. ~kind(alice) [cnf transformation 19]
113. ~patient(X0) [duplicate literal removal 70]
114. ~rich(X0) | patient(X0) [duplicate literal removal 72]
270. rich(X0) | kind(X0) | strong(X0) [resolution 86,80]
355. kind(X2) | strong(X2) | patient(X2) [resolution 270,114]
359. strong(X2) | kind(X2) [subsumption resolution 355,113]
387. creative(X0) | kind(X0) [resolution 359,99]
406. kind(X4) | rich(X4) | kind(X4) [resolution 387,84]
407. rich(X4) | kind(X4) [duplicate literal removal 406]
508. kind(X2) | patient(X2) [resolution 407,114]
514. kind(X2) [subsumption resolution 508,113]
519. $false [resolution 514,112]
% SZS output end Proof for 7703696139583877205221210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either tall or patient then alice is kind or not strong.
Everyone who is not old is either tall or not rich and vice versa.
Everyone who is not funny or happy is both happy and not quiet and vice versa.
Everyone who is either not curious or not wise is both calm and kind and vice versa.
If fred is both generous and humble then someone is not old or tall.
Everyone who is wise is both curious and wise.
Everyone who is both not funny and not generous is not happy.
If john is curious or not funny then someone is not strong or calm and vice versa.
Everyone who is either not strong or patient is either not rich or wise.
If mary is not generous then susan is not kind or not old and vice versa.
If someone is happy or creative then fred is either patient or curious and vice versa.
Everyone who is both not happy and rich is either not quiet or not funny.
Everyone who is not curious is either quiet or not wise and vice versa.
If someone is either calm or not patient then john is rich or not wise.
Everyone who is curious is both not happy and not quiet.
Everyone who is not happy is happy.
John is not kind.
Someone is not creative.
Lucy is calm.
Lucy is not funny or not kind.
Lucy is happy.
Someone is not humble.
Someone is happy or quiet. | Susan is not wise. | entailment | (((tall(paul)<~>patient(paul)))=>((kind(alice)|~strong(alice))))&
(![X]:(~old(X)<=>(tall(X)<~>~rich(X))))&
(![X]:((~funny(X)|happy(X))<=>(happy(X)&~quiet(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>(calm(X)&kind(X))))&
(((generous(fred)&humble(fred)))=>(?[X]:((~old(X)|tall(X)))))&
(![X]:(wise(X)=>(curious(X)&wise(X))))&
(![X]:((~funny(X)&~generous(X))=>~happy(X)))&
(((curious(john)|~funny(john)))<=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~strong(X)<~>patient(X))=>(~rich(X)<~>wise(X))))&
((~generous(mary))<=>((~kind(susan)|~old(susan))))&
((?[X]:((happy(X)|creative(X))))<=>((patient(fred)<~>curious(fred))))&
(![X]:((~happy(X)&rich(X))=>(~quiet(X)<~>~funny(X))))&
(![X]:(~curious(X)<=>(quiet(X)<~>~wise(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>((rich(john)|~wise(john))))&
(![X]:(curious(X)=>(~happy(X)&~quiet(X))))&
(![X]:(~happy(X)=>happy(X)))&
(~kind(john))&
(?[X]:(~creative(X)))&
(calm(lucy))&
((~funny(lucy)|~kind(lucy)))&
(happy(lucy))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)|quiet(X)))) | ~wise(susan) | [
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5206563700168861340731841
% SZS output start Proof for 5206563700168861340731841
6. ! [X0] : (wise(X0) => (wise(X0) & curious(X0))) [input p5]
15. ! [X0] : (curious(X0) => (~quiet(X0) & ~happy(X0))) [input p14]
16. ! [X0] : (~happy(X0) => happy(X0)) [input p15]
24. wise(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 6]
37. ! [X0] : ((~quiet(X0) & ~happy(X0)) | ~curious(X0)) [ennf transformation 15]
38. ! [X0] : (happy(X0) | happy(X0)) [ennf transformation 16]
81. ~wise(X0) | curious(X0) [cnf transformation 29]
109. ~curious(X0) | ~happy(X0) [cnf transformation 37]
111. happy(X0) | happy(X0) [cnf transformation 38]
118. wise(susan) [cnf transformation 24]
119. happy(X0) [duplicate literal removal 111]
238. curious(susan) [resolution 81,118]
245. ~happy(susan) [resolution 238,109]
246. $false [subsumption resolution 245,119]
% SZS output end Proof for 5206563700168861340731841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not humble then someone is old or not strong and vice versa.
Everyone who is tall is both strong and calm.
Everyone who is generous or not calm is tall or not wise and vice versa.
If someone is not old or patient then susan is not calm or not old.
Everyone who is not curious is strong or not humble.
Everyone who is both happy and not kind is not quiet.
If lucy is funny or not humble then someone is humble or brave.
Everyone who is not quiet or not old is not generous or rich and vice versa.
Everyone who is both curious and not strong is not tall and vice versa.
If lucy is quiet or not generous then mary is curious or not patient.
If fred is both funny and not patient then someone is not brave or creative and vice versa.
Everyone who is both not strong and not brave is both calm and funny and vice versa.
If mary is both not calm and not brave then susan is brave and vice versa.
If someone is both happy and wise then someone is generous and vice versa.
Everyone who is calm or quiet is not curious or not strong and vice versa.
Everyone who is humble is brave or patient.
Someone is wise.
Lucy is either curious or not curious.
Mary is creative or calm.
Someone is both not wise and not tall.
Paul is either kind or brave.
Mary is both not humble and curious.
Someone is either curious or quiet.
Fred is generous. | Susan is not brave. | entailment | ((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:(tall(X)=>(strong(X)&calm(X))))&
(![X]:((generous(X)|~calm(X))<=>(tall(X)|~wise(X))))&
((?[X]:((~old(X)|patient(X))))=>((~calm(susan)|~old(susan))))&
(![X]:(~curious(X)=>(strong(X)|~humble(X))))&
(![X]:((happy(X)&~kind(X))=>~quiet(X)))&
(((funny(lucy)|~humble(lucy)))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:((~quiet(X)|~old(X))<=>(~generous(X)|rich(X))))&
(![X]:((curious(X)&~strong(X))<=>~tall(X)))&
(((quiet(lucy)|~generous(lucy)))=>((curious(mary)|~patient(mary))))&
(((funny(fred)&~patient(fred)))<=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:((~strong(X)&~brave(X))<=>(calm(X)&funny(X))))&
(((~calm(mary)&~brave(mary)))<=>(brave(susan)))&
((?[X]:((happy(X)&wise(X))))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)|quiet(X))<=>(~curious(X)|~strong(X))))&
(![X]:(humble(X)=>(brave(X)|patient(X))))&
(?[X]:(wise(X)))&
((curious(lucy)<~>~curious(lucy)))&
((creative(mary)|calm(mary)))&
(?[X]:((~wise(X)&~tall(X))))&
((kind(paul)<~>brave(paul)))&
((~humble(mary)&curious(mary)))&
(?[X]:((curious(X)<~>quiet(X))))&
(generous(fred)) | ~brave(susan) | [
"p1",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5462722552874749138293834
% SZS output start Proof for 5462722552874749138293834
2. ! [X0] : (tall(X0) => (calm(X0) & strong(X0))) [input p1]
9. ! [X0] : ((~strong(X0) & curious(X0)) <=> ~tall(X0)) [input p8]
12. ! [X0] : ((~brave(X0) & ~strong(X0)) <=> (funny(X0) & calm(X0))) [input p11]
13. (~brave(mary) & ~calm(mary)) <=> brave(susan) [input p12]
25. brave(susan) [input hypothesis]
28. ! [X0] : ((calm(X0) & strong(X0)) | ~tall(X0)) [ennf transformation 2]
51. ! [X0] : (((~strong(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | (strong(X0) | ~curious(X0)))) [nnf transformation 9]
52. ! [X0] : (((~strong(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | strong(X0) | ~curious(X0))) [flattening 51]
58. ! [X0] : (((~brave(X0) & ~strong(X0)) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | (brave(X0) | strong(X0)))) [nnf transformation 12]
59. ! [X0] : (((~brave(X0) & ~strong(X0)) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | brave(X0) | strong(X0))) [flattening 58]
60. ((~brave(mary) & ~calm(mary)) | ~brave(susan)) & (brave(susan) | (brave(mary) | calm(mary))) [nnf transformation 13]
61. ((~brave(mary) & ~calm(mary)) | ~brave(susan)) & (brave(susan) | brave(mary) | calm(mary)) [flattening 60]
84. ~tall(X0) | calm(X0) [cnf transformation 28]
101. ~strong(X0) | tall(X0) [cnf transformation 52]
109. brave(X0) | calm(X0) | strong(X0) [cnf transformation 59]
114. ~calm(mary) | ~brave(susan) [cnf transformation 61]
115. ~brave(mary) | ~brave(susan) [cnf transformation 61]
137. brave(susan) [cnf transformation 25]
250. 26 <=> brave(susan) [avatar definition]
254. 27 <=> brave(mary) [avatar definition]
256. ~brave(mary) <- (~27) [avatar component clause 254]
257. ~26 | ~27 [avatar split clause 115,254,250]
259. 28 <=> calm(mary) [avatar definition]
261. ~calm(mary) <- (~28) [avatar component clause 259]
262. ~26 | ~28 [avatar split clause 114,259,250]
311. 26 [avatar split clause 137,250]
423. calm(mary) | strong(mary) <- (~27) [resolution 109,256]
434. strong(mary) <- (~27, ~28) [subsumption resolution 423,261]
495. tall(mary) <- (~27, ~28) [resolution 434,101]
536. calm(mary) <- (~27, ~28) [resolution 495,84]
538. $false <- (~27, ~28) [subsumption resolution 536,261]
539. 27 | 28 [avatar contradiction clause 538]
540. $false [avatar sat refutation 257,262,311,539]
% SZS output end Proof for 5462722552874749138293834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both curious and generous then mary is either not curious or old and vice versa.
If fred is both not happy and kind then susan is not creative.
If fred is patient then someone is happy.
Everyone who is either not brave or quiet is either tall or curious and vice versa.
If fred is not happy or not strong then someone is both not curious and not kind and vice versa.
Everyone who is not kind or not tall is not strong or not creative.
Everyone who is quiet is both brave and creative and vice versa.
Everyone who is not funny or strong is not brave or patient.
If someone is both not funny and not happy then fred is not calm.
If someone is not patient or brave then alice is both creative and strong and vice versa.
If lucy is creative or not generous then mary is not calm and vice versa.
If alice is humble or not old then someone is both not tall and not old.
Everyone who is rich or not calm is not patient and vice versa.
Everyone who is both humble and not happy is both not old and calm.
If lucy is both wise and not generous then someone is rich or strong.
If someone is either not strong or not happy then paul is both not strong and not creative.
Someone is either happy or not humble.
Someone is both funny and not happy.
Alice is either not humble or creative.
Mary is either not strong or wise.
Someone is not kind.
Someone is either brave or funny.
Someone is either not funny or generous. | Alice is humble. | neutral | ((?[X]:((curious(X)&generous(X))))<=>((~curious(mary)<~>old(mary))))&
(((~happy(fred)&kind(fred)))=>(~creative(susan)))&
((patient(fred))=>(?[X]:(happy(X))))&
(![X]:((~brave(X)<~>quiet(X))<=>(tall(X)<~>curious(X))))&
(((~happy(fred)|~strong(fred)))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((~kind(X)|~tall(X))=>(~strong(X)|~creative(X))))&
(![X]:(quiet(X)<=>(brave(X)&creative(X))))&
(![X]:((~funny(X)|strong(X))=>(~brave(X)|patient(X))))&
((?[X]:((~funny(X)&~happy(X))))=>(~calm(fred)))&
((?[X]:((~patient(X)|brave(X))))<=>((creative(alice)&strong(alice))))&
(((creative(lucy)|~generous(lucy)))<=>(~calm(mary)))&
(((humble(alice)|~old(alice)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((rich(X)|~calm(X))<=>~patient(X)))&
(![X]:((humble(X)&~happy(X))=>(~old(X)&calm(X))))&
(((wise(lucy)&~generous(lucy)))=>(?[X]:((rich(X)|strong(X)))))&
((?[X]:((~strong(X)<~>~happy(X))))=>((~strong(paul)&~creative(paul))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((funny(X)&~happy(X))))&
((~humble(alice)<~>creative(alice)))&
((~strong(mary)<~>wise(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((~funny(X)<~>generous(X)))) | humble(alice) | [] | null | 0 |
Everyone who is not brave is both rich and quiet and vice versa. Everyone who is not old or tall is not curious and vice versa. If alice is either not kind or not humble then susan is quiet or not patient. If someone is kind or old then fred is brave. Everyone who is not generous or not old is both not brave and brave. Everyone who is not kind is either not tall or not funny and vice versa. Everyone who is both not wise and not old is both not humble and not kind. Everyone who is not brave or not funny is not calm. If someone is not generous or not kind then lucy is not funny and vice versa. If paul is not patient or humble then someone is patient or not funny and vice versa. Everyone who is both happy and not wise is both rich and happy. Everyone who is both not curious and not creative is generous. If paul is either brave or not quiet then susan is not rich or not strong and vice versa. Everyone who is either creative or not happy is not tall or wise and vice versa. If susan is not wise then someone is not strong or not patient. If someone is either not old or not quiet then someone is both funny and not curious and vice versa. Someone is either calm or not kind. Someone is either curious or old. Alice is both quiet and old. Paul is either calm or not funny. Someone is both rich and kind. Paul is old. John is not happy or not calm. Mary is either not tall or generous. | Paul is old. | entailment | (![X]:(~brave(X)<=>(rich(X)&quiet(X))))&
(![X]:((~old(X)|tall(X))<=>~curious(X)))&
(((~kind(alice)<~>~humble(alice)))=>((quiet(susan)|~patient(susan))))&
((?[X]:((kind(X)|old(X))))=>(brave(fred)))&
(![X]:((~generous(X)|~old(X))=>(~brave(X)&brave(X))))&
(![X]:(~kind(X)<=>(~tall(X)<~>~funny(X))))&
(![X]:((~wise(X)&~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)|~funny(X))=>~calm(X)))&
((?[X]:((~generous(X)|~kind(X))))<=>(~funny(lucy)))&
(((~patient(paul)|humble(paul)))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>generous(X)))&
(((brave(paul)<~>~quiet(paul)))<=>((~rich(susan)|~strong(susan))))&
(![X]:((creative(X)<~>~happy(X))<=>(~tall(X)|wise(X))))&
((~wise(susan))=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((curious(X)<~>old(X))))&
((quiet(alice)&old(alice)))&
((calm(paul)<~>~funny(paul)))&
(?[X]:((rich(X)&kind(X))))&
(old(paul))&
((~happy(john)|~calm(john)))&
((~tall(mary)<~>generous(mary))) | old(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3441743102909221867342445
% SZS output start Proof for 3441743102909221867342445
5. ! [X0] : ((~old(X0) | ~generous(X0)) => (brave(X0) & ~brave(X0))) [input p4]
25. ~old(paul) [input hypothesis]
30. ! [X0] : ((brave(X0) & ~brave(X0)) | (old(X0) & generous(X0))) [ennf transformation 5]
86. ~brave(X0) | old(X0) [cnf transformation 30]
88. brave(X0) | old(X0) [cnf transformation 30]
140. ~old(paul) [cnf transformation 25]
171. old(X0) [subsumption resolution 86,88]
305. $false [subsumption resolution 140,171]
% SZS output end Proof for 3441743102909221867342445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either quiet or not generous and vice versa. Everyone who is both creative and not tall is either not funny or not strong. Everyone who is either wise or patient is patient and vice versa. Everyone who is happy or not quiet is both generous and not old and vice versa. If susan is both wise and rich then lucy is either tall or not brave and vice versa. If someone is generous or wise then someone is not calm and vice versa. Everyone who is either strong or not kind is both not curious and strong. If fred is either patient or not wise then susan is either not curious or tall. If paul is strong or not rich then someone is not patient. Everyone who is either not calm or quiet is both curious and kind and vice versa. Everyone who is not quiet is kind and vice versa. Everyone who is both rich and creative is both curious and not old and vice versa. If susan is not quiet or calm then someone is both old and tall and vice versa. If someone is both not funny and not calm then someone is funny. If someone is generous or tall then someone is wise or not funny. Susan is not humble. Susan is kind or not humble. Paul is either not funny or rich. Lucy is either not humble or happy. Someone is either not wise or not humble. | Lucy is strong. | entailment | (![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(funny(X))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((wise(X)|~funny(X)))))&
(~humble(susan))&
((kind(susan)|~humble(susan)))&
((~funny(paul)<~>rich(paul)))&
((~humble(lucy)<~>happy(lucy)))&
(?[X]:((~wise(X)<~>~humble(X)))) | strong(lucy) | [
"p0",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2928694568500904462540903
% SZS output start Proof for 2928694568500904462540903
1. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p0]
7. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (strong(X0) & ~curious(X0))) [input p6]
11. ! [X0] : (~quiet(X0) <=> kind(X0)) [input p10]
21. ~strong(lucy) [input hypothesis]
27. ! [X0] : ((strong(X0) & ~curious(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 7]
32. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 1]
44. ! [X0] : ((strong(X0) & ~curious(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 27]
50. ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 11]
69. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 32]
72. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 32]
96. strong(X0) | strong(X0) | kind(X0) [cnf transformation 44]
110. ~quiet(X0) | ~kind(X0) [cnf transformation 50]
131. ~strong(lucy) [cnf transformation 21]
132. kind(X0) | strong(X0) [duplicate literal removal 96]
135. ~generous(X0) | quiet(X0) [duplicate literal removal 69]
136. generous(X0) | quiet(X0) [duplicate literal removal 72]
137. quiet(X0) [subsumption resolution 135,136]
208. ~kind(X0) [subsumption resolution 110,137]
266. strong(X0) [resolution 132,208]
267. $false [resolution 266,131]
% SZS output end Proof for 2928694568500904462540903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not calm then someone is not happy. Everyone who is both not patient and not happy is either not quiet or not tall and vice versa. If someone is either not brave or not calm then fred is both kind and humble. If john is patient or not funny then lucy is both not wise and not happy and vice versa. Everyone who is both quiet and not funny is tall and vice versa. Everyone who is not tall is not old or not kind and vice versa. Everyone who is quiet is both brave and funny and vice versa. If someone is both calm and creative then mary is both not tall and not humble and vice versa. If alice is either rich or not old then someone is not rich and vice versa. Everyone who is not kind or not brave is old and vice versa. Everyone who is both strong and not rich is either rich or not generous and vice versa. If susan is generous or not old then alice is humble and vice versa. Everyone who is either strong or calm is both not patient and calm and vice versa. Everyone who is kind or quiet is either not brave or rich and vice versa. Everyone who is old or rich is either quiet or rich and vice versa. Everyone who is not happy is patient. Someone is either rich or not wise. Someone is both funny and not creative. Someone is not wise. Mary is not funny. Alice is calm or not rich. Fred is both curious and not patient. | John is generous. | contradiction | ((~calm(susan))=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)&~happy(X))<=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~brave(X)<~>~calm(X))))=>((kind(fred)&humble(fred))))&
(((patient(john)|~funny(john)))<=>((~wise(lucy)&~happy(lucy))))&
(![X]:((quiet(X)&~funny(X))<=>tall(X)))&
(![X]:(~tall(X)<=>(~old(X)|~kind(X))))&
(![X]:(quiet(X)<=>(brave(X)&funny(X))))&
((?[X]:((calm(X)&creative(X))))<=>((~tall(mary)&~humble(mary))))&
(((rich(alice)<~>~old(alice)))<=>(?[X]:(~rich(X))))&
(![X]:((~kind(X)|~brave(X))<=>old(X)))&
(![X]:((strong(X)&~rich(X))<=>(rich(X)<~>~generous(X))))&
(((generous(susan)|~old(susan)))<=>(humble(alice)))&
(![X]:((strong(X)<~>calm(X))<=>(~patient(X)&calm(X))))&
(![X]:((kind(X)|quiet(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((old(X)|rich(X))<=>(quiet(X)<~>rich(X))))&
(![X]:(~happy(X)=>patient(X)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:(~wise(X)))&
(~funny(mary))&
((calm(alice)|~rich(alice)))&
((curious(fred)&~patient(fred))) | generous(john) | [
"p6",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1022740988029392707472057
% SZS output start Proof for 1022740988029392707472057
7. ! [X0] : (quiet(X0) <=> (funny(X0) & brave(X0))) [input p6]
10. ! [X0] : ((~brave(X0) | ~kind(X0)) <=> old(X0)) [input p9]
11. ! [X0] : ((~rich(X0) & strong(X0)) <=> (rich(X0) <~> ~generous(X0))) [input p10]
14. ! [X0] : ((quiet(X0) | kind(X0)) <=> (~brave(X0) <~> rich(X0))) [input p13]
15. ! [X0] : ((rich(X0) | old(X0)) <=> (quiet(X0) <~> rich(X0))) [input p14]
23. generous(john) [input hypothesis]
39. ! [X0] : ((quiet(X0) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ~quiet(X0))) [nnf transformation 7]
40. ! [X0] : ((quiet(X0) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ~quiet(X0))) [flattening 39]
50. ! [X0] : (((~brave(X0) | ~kind(X0)) | ~old(X0)) & (old(X0) | (brave(X0) & kind(X0)))) [nnf transformation 10]
51. ! [X0] : ((~brave(X0) | ~kind(X0) | ~old(X0)) & (old(X0) | (brave(X0) & kind(X0)))) [flattening 50]
52. ! [X0] : (((~rich(X0) & strong(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 11]
53. ! [X0] : (((~rich(X0) & strong(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | rich(X0) | ~strong(X0))) [flattening 52]
58. ! [X0] : (((quiet(X0) | kind(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 14]
59. ! [X0] : ((quiet(X0) | kind(X0) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~quiet(X0) & ~kind(X0)))) [flattening 58]
60. ! [X0] : (((rich(X0) | old(X0)) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (~rich(X0) & ~old(X0)))) [nnf transformation 15]
61. ! [X0] : ((rich(X0) | old(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (~rich(X0) & ~old(X0)))) [flattening 60]
91. ~quiet(X0) | brave(X0) [cnf transformation 40]
102. old(X0) | kind(X0) [cnf transformation 51]
103. old(X0) | brave(X0) [cnf transformation 51]
109. ~rich(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 53]
120. ~kind(X0) | ~brave(X0) | rich(X0) [cnf transformation 59]
121. rich(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 59]
126. rich(X0) | quiet(X0) | ~old(X0) [cnf transformation 61]
129. ~rich(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 61]
141. generous(john) [cnf transformation 23]
142. ~rich(X0) | ~quiet(X0) [duplicate literal removal 129]
147. ~generous(X0) | ~rich(X0) [duplicate literal removal 109]
255. ~quiet(X0) | rich(X0) [subsumption resolution 121,91]
256. ~quiet(X0) [subsumption resolution 142,255]
257. ~old(X0) | rich(X0) [subsumption resolution 126,256]
279. ~rich(john) [resolution 147,141]
297. rich(X0) | brave(X0) [resolution 257,103]
298. rich(X1) | kind(X1) [resolution 257,102]
307. brave(john) [resolution 297,279]
343. kind(john) [resolution 298,279]
351. ~brave(john) | rich(john) [resolution 343,120]
352. rich(john) [subsumption resolution 351,307]
353. $false [subsumption resolution 352,279]
% SZS output end Proof for 1022740988029392707472057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not strong then someone is either not happy or old. Everyone who is either funny or not old is either not kind or not creative and vice versa. Everyone who is both not curious and not brave is either not kind or not creative. If lucy is creative or calm then someone is either quiet or not funny and vice versa. Everyone who is either quiet or rich is both kind and not quiet. Everyone who is either not old or not kind is either not curious or not patient and vice versa. Everyone who is creative is either not wise or not brave. Everyone who is not rich or not kind is not strong or not rich. If mary is curious or kind then fred is not curious or not humble and vice versa. If someone is both not calm and not funny then paul is not curious or not funny and vice versa. Everyone who is both not generous and quiet is not wise or not happy and vice versa. If someone is brave or not kind then someone is both not humble and patient and vice versa. If lucy is not generous or not rich then paul is both not creative and humble. Everyone who is not wise is either quiet or not happy and vice versa. If paul is either creative or tall then alice is either not patient or not kind and vice versa. If someone is both brave and not generous then mary is either strong or not funny. Mary is both not patient and strong. Someone is either not creative or not humble. Someone is old. Mary is tall. Lucy is either patient or not wise. Someone is either happy or not quiet. Lucy is old. Lucy is strong. | Lucy is generous. | neutral | ((?[X]:((calm(X)|~strong(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((funny(X)<~>~old(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~curious(X)&~brave(X))=>(~kind(X)<~>~creative(X))))&
(((creative(lucy)|calm(lucy)))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((quiet(X)<~>rich(X))=>(kind(X)&~quiet(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:(creative(X)=>(~wise(X)<~>~brave(X))))&
(![X]:((~rich(X)|~kind(X))=>(~strong(X)|~rich(X))))&
(((curious(mary)|kind(mary)))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~happy(X))))&
(((creative(paul)<~>tall(paul)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:((brave(X)&~generous(X))))=>((strong(mary)<~>~funny(mary))))&
((~patient(mary)&strong(mary)))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:(old(X)))&
(tall(mary))&
((patient(lucy)<~>~wise(lucy)))&
(?[X]:((happy(X)<~>~quiet(X))))&
(old(lucy))&
(strong(lucy)) | generous(lucy) | [] | null | 0 |
Everyone who is not tall or quiet is not calm or happy and vice versa. Everyone who is not strong is either not funny or strong and vice versa. Everyone who is not kind is kind. If someone is humble or rich then someone is both not humble and strong. If fred is either not creative or not curious then someone is either not brave or not patient and vice versa. If lucy is not quiet or kind then alice is not funny or not quiet. If someone is brave then mary is not brave and vice versa. If fred is not generous then someone is patient and vice versa. If mary is not old then someone is not quiet and vice versa. Everyone who is either not curious or not funny is not rich. Everyone who is either not brave or not calm is not generous. Everyone who is either kind or not creative is both not patient and not curious and vice versa. If someone is not patient or not rich then paul is not funny or not wise. Everyone who is either not wise or brave is not wise or not curious and vice versa. Everyone who is both not quiet and curious is both not strong and not kind. If someone is either not funny or not rich then someone is not rich or tall. Mary is not tall. Someone is both generous and old. Paul is both not tall and not quiet. Someone is both strong and brave. Someone is strong. Paul is both not funny and not humble. Mary is either generous or not happy. | Paul is not humble. | entailment | (![X]:((~tall(X)|quiet(X))<=>(~calm(X)|happy(X))))&
(![X]:(~strong(X)<=>(~funny(X)<~>strong(X))))&
(![X]:(~kind(X)=>kind(X)))&
((?[X]:((humble(X)|rich(X))))=>(?[X]:((~humble(X)&strong(X)))))&
(((~creative(fred)<~>~curious(fred)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(((~quiet(lucy)|kind(lucy)))=>((~funny(alice)|~quiet(alice))))&
((?[X]:(brave(X)))<=>(~brave(mary)))&
((~generous(fred))<=>(?[X]:(patient(X))))&
((~old(mary))<=>(?[X]:(~quiet(X))))&
(![X]:((~curious(X)<~>~funny(X))=>~rich(X)))&
(![X]:((~brave(X)<~>~calm(X))=>~generous(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(~patient(X)&~curious(X))))&
((?[X]:((~patient(X)|~rich(X))))=>((~funny(paul)|~wise(paul))))&
(![X]:((~wise(X)<~>brave(X))<=>(~wise(X)|~curious(X))))&
(![X]:((~quiet(X)&curious(X))=>(~strong(X)&~kind(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((~rich(X)|tall(X)))))&
(~tall(mary))&
(?[X]:((generous(X)&old(X))))&
((~tall(paul)&~quiet(paul)))&
(?[X]:((strong(X)&brave(X))))&
(?[X]:(strong(X)))&
((~funny(paul)&~humble(paul)))&
((generous(mary)<~>~happy(mary))) | ~humble(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3220292764715505607546397
% SZS output start Proof for 3220292764715505607546397
22. ~humble(paul) & ~funny(paul) [input p21]
24. humble(paul) [input hypothesis]
137. ~humble(paul) [cnf transformation 22]
140. humble(paul) [cnf transformation 24]
260. $false [subsumption resolution 140,137]
% SZS output end Proof for 3220292764715505607546397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and kind is either not old or brave.
Everyone who is not generous is calm and vice versa.
Everyone who is either not generous or not rich is not kind and vice versa.
If paul is either generous or patient then someone is not tall or not generous and vice versa.
If someone is strong then mary is either curious or not calm.
Everyone who is not brave is not happy or not funny.
Everyone who is not wise or brave is calm and vice versa.
If someone is not generous then susan is both kind and patient.
If someone is happy or generous then fred is creative.
If mary is either not wise or brave then someone is both not brave and not tall and vice versa.
Everyone who is not old or curious is either humble or generous.
Everyone who is both not calm and humble is either not wise or calm.
If fred is both strong and creative then fred is not curious or humble.
If lucy is either not tall or not humble then mary is both happy and not wise and vice versa.
Everyone who is either curious or quiet is either wise or calm.
If fred is not creative or calm then lucy is both not happy and not strong and vice versa.
Someone is both not brave and patient.
Someone is rich.
Someone is strong or not strong.
Someone is not funny.
Fred is not calm.
John is rich or not humble.
John is either kind or humble.
Someone is either not old or not wise. | Susan is kind. | entailment | (![X]:((wise(X)&kind(X))=>(~old(X)<~>brave(X))))&
(![X]:(~generous(X)<=>calm(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>~kind(X)))&
(((generous(paul)<~>patient(paul)))<=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:(strong(X)))=>((curious(mary)<~>~calm(mary))))&
(![X]:(~brave(X)=>(~happy(X)|~funny(X))))&
(![X]:((~wise(X)|brave(X))<=>calm(X)))&
((?[X]:(~generous(X)))=>((kind(susan)&patient(susan))))&
((?[X]:((happy(X)|generous(X))))=>(creative(fred)))&
(((~wise(mary)<~>brave(mary)))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((~old(X)|curious(X))=>(humble(X)<~>generous(X))))&
(![X]:((~calm(X)&humble(X))=>(~wise(X)<~>calm(X))))&
(((strong(fred)&creative(fred)))=>((~curious(fred)|humble(fred))))&
(((~tall(lucy)<~>~humble(lucy)))<=>((happy(mary)&~wise(mary))))&
(![X]:((curious(X)<~>quiet(X))=>(wise(X)<~>calm(X))))&
(((~creative(fred)|calm(fred)))<=>((~happy(lucy)&~strong(lucy))))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(~calm(fred))&
((rich(john)|~humble(john)))&
((kind(john)<~>humble(john)))&
(?[X]:((~old(X)<~>~wise(X)))) | kind(susan) | [
"p1",
"p3",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8675779520783065566153653
% SZS output start Proof for 8675779520783065566153653
2. ! [X0] : (~generous(X0) <=> calm(X0)) [input p1]
4. (generous(paul) <~> patient(paul)) <=> ? [X0] : (~generous(X0) | ~tall(X0)) [input p3]
7. ! [X0] : ((brave(X0) | ~wise(X0)) <=> calm(X0)) [input p6]
8. ? [X0] : ~generous(X0) => (patient(susan) & kind(susan)) [input p7]
10. (~wise(mary) <~> brave(mary)) <=> ? [X0] : (~tall(X0) & ~brave(X0)) [input p9]
12. ! [X0] : ((humble(X0) & ~calm(X0)) => (~wise(X0) <~> calm(X0))) [input p11]
14. (~tall(lucy) <~> ~humble(lucy)) <=> (~wise(mary) & happy(mary)) [input p13]
25. ~kind(susan) [input hypothesis]
31. (patient(susan) & kind(susan)) | ! [X0] : generous(X0) [ennf transformation 8]
34. ! [X0] : ((~wise(X0) <~> calm(X0)) | (~humble(X0) | calm(X0))) [ennf transformation 12]
35. ! [X0] : ((~wise(X0) <~> calm(X0)) | ~humble(X0) | calm(X0)) [flattening 34]
40. ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))) [nnf transformation 2]
42. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X0] : (~generous(X0) | ~tall(X0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [nnf transformation 4]
43. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & (? [X1] : (~generous(X1) | ~tall(X1)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [rectify 42]
44. ? [X1] : (~generous(X1) | ~tall(X1)) => (~generous(sK0) | ~tall(sK0)) [choice axiom]
45. (((~patient(paul) | ~generous(paul)) & (patient(paul) | generous(paul))) | ! [X0] : (generous(X0) & tall(X0))) & ((~generous(sK0) | ~tall(sK0)) | ((generous(paul) | ~patient(paul)) & (patient(paul) | ~generous(paul)))) [skolemisation 43,44]
47. ! [X0] : (((brave(X0) | ~wise(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 7]
48. ! [X0] : ((brave(X0) | ~wise(X0) | ~calm(X0)) & (calm(X0) | (~brave(X0) & wise(X0)))) [flattening 47]
49. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X0] : (~tall(X0) & ~brave(X0)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [nnf transformation 10]
50. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & (? [X1] : (~tall(X1) & ~brave(X1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [rectify 49]
51. ? [X1] : (~tall(X1) & ~brave(X1)) => (~tall(sK1) & ~brave(sK1)) [choice axiom]
52. (((~brave(mary) | wise(mary)) & (brave(mary) | ~wise(mary))) | ! [X0] : (tall(X0) | brave(X0))) & ((~tall(sK1) & ~brave(sK1)) | ((~wise(mary) | ~brave(mary)) & (brave(mary) | wise(mary)))) [skolemisation 50,51]
54. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~humble(X0) | calm(X0)) [nnf transformation 35]
55. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | (wise(mary) | ~happy(mary))) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [nnf transformation 14]
56. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | wise(mary) | ~happy(mary)) & ((~wise(mary) & happy(mary)) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [flattening 55]
73. ~calm(X0) | ~generous(X0) [cnf transformation 40]
78. ~generous(sK0) | ~tall(sK0) | patient(paul) | ~generous(paul) [cnf transformation 45]
82. ~patient(paul) | ~generous(paul) | tall(X0) [cnf transformation 45]
86. calm(X0) | wise(X0) [cnf transformation 48]
87. ~brave(X0) | calm(X0) [cnf transformation 48]
89. kind(susan) | generous(X0) [cnf transformation 31]
97. brave(mary) | ~wise(mary) | tall(X0) | brave(X0) [cnf transformation 52]
103. calm(X0) | ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 54]
109. ~wise(mary) | ~tall(lucy) | humble(lucy) [cnf transformation 56]
131. ~kind(susan) [cnf transformation 25]
132. calm(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 103]
134. 1 <=> ! [X0] : generous(X0) [avatar definition]
135. generous(X0) <- (1) [avatar component clause 134]
137. 2 <=> generous(paul) [avatar definition]
139. ~generous(paul) <- (~2) [avatar component clause 137]
141. 3 <=> patient(paul) [avatar definition]
146. 4 <=> ! [X0] : tall(X0) [avatar definition]
147. tall(X0) <- (4) [avatar component clause 146]
148. 4 | ~2 | ~3 [avatar split clause 82,141,137,146]
152. 5 <=> tall(sK0) [avatar definition]
154. ~tall(sK0) <- (~5) [avatar component clause 152]
156. 6 <=> generous(sK0) [avatar definition]
158. ~generous(sK0) <- (~6) [avatar component clause 156]
160. ~2 | 3 | ~5 | ~6 [avatar split clause 78,156,152,141,137]
169. 9 <=> calm(mary) [avatar definition]
170. ~calm(mary) <- (~9) [avatar component clause 169]
171. calm(mary) <- (9) [avatar component clause 169]
180. 11 <=> kind(susan) [avatar definition]
183. 1 | 11 [avatar split clause 89,180,134]
197. 15 <=> ! [X0] : (tall(X0) | brave(X0)) [avatar definition]
198. tall(X0) | brave(X0) <- (15) [avatar component clause 197]
200. 16 <=> wise(mary) [avatar definition]
201. ~wise(mary) <- (~16) [avatar component clause 200]
204. 17 <=> brave(mary) [avatar definition]
205. brave(mary) <- (17) [avatar component clause 204]
208. 15 | ~16 | 17 [avatar split clause 97,204,200,197]
221. ~humble(X0) | calm(X0) [subsumption resolution 132,86]
240. 24 <=> tall(lucy) [avatar definition]
241. ~tall(lucy) <- (~24) [avatar component clause 240]
244. 25 <=> humble(lucy) [avatar definition]
246. humble(lucy) <- (25) [avatar component clause 244]
249. 25 | ~24 | ~16 [avatar split clause 109,200,240,244]
296. ~11 [avatar split clause 131,180]
299. $false <- (1, ~2) [subsumption resolution 139,135]
300. ~1 | 2 [avatar contradiction clause 299]
301. $false <- (1, ~6) [subsumption resolution 158,135]
302. ~1 | 6 [avatar contradiction clause 301]
308. wise(mary) <- (~9) [resolution 86,170]
311. $false <- (~9, ~16) [subsumption resolution 308,201]
312. 9 | 16 [avatar contradiction clause 311]
314. ~generous(mary) <- (9) [resolution 171,73]
315. $false <- (1, 9) [subsumption resolution 314,135]
316. ~1 | ~9 [avatar contradiction clause 315]
326. calm(mary) <- (17) [resolution 205,87]
327. $false <- (~9, 17) [subsumption resolution 326,170]
328. 9 | ~17 [avatar contradiction clause 327]
329. brave(sK0) <- (~5, 15) [resolution 198,154]
332. calm(sK0) <- (~5, 15) [resolution 329,87]
347. ~generous(sK0) <- (~5, 15) [resolution 332,73]
348. $false <- (1, ~5, 15) [subsumption resolution 347,135]
349. ~1 | 5 | ~15 [avatar contradiction clause 348]
350. $false <- (4, ~24) [resolution 147,241]
351. ~4 | 24 [avatar contradiction clause 350]
352. calm(lucy) <- (25) [resolution 246,221]
356. ~generous(lucy) <- (25) [resolution 352,73]
358. $false <- (1, 25) [subsumption resolution 356,135]
359. ~1 | ~25 [avatar contradiction clause 358]
360. $false [avatar sat refutation 148,160,183,208,249,296,300,302,312,316,328,349,351,359]
% SZS output end Proof for 8675779520783065566153653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If alice is quiet then fred is either creative or patient.
Everyone who is either rich or generous is either not brave or humble and vice versa.
If someone is both not old and happy then susan is not curious and vice versa.
Everyone who is both not kind and funny is not patient.
If alice is both not kind and rich then susan is either quiet or creative and vice versa.
If alice is brave then susan is not curious.
Everyone who is both not wise and not happy is both not curious and curious and vice versa.
Everyone who is not patient is kind and vice versa.
If mary is kind or not quiet then someone is both creative and humble.
Everyone who is both rich and brave is both funny and not curious and vice versa.
Everyone who is either curious or not curious is both not generous and not happy and vice versa.
If lucy is generous or not rich then paul is either not humble or strong.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise 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.
Someone is creative or not quiet.
Lucy is old.
Someone is either curious or funny.
Lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet.
Susan is both brave and strong.
Paul is not calm. | John is wise. | entailment | ((quiet(alice))=>((creative(fred)<~>patient(fred))))&
(![X]:((rich(X)<~>generous(X))<=>(~brave(X)<~>humble(X))))&
((?[X]:((~old(X)&happy(X))))<=>(~curious(susan)))&
(![X]:((~kind(X)&funny(X))=>~patient(X)))&
(((~kind(alice)&rich(alice)))<=>((quiet(susan)<~>creative(susan))))&
((brave(alice))=>(~curious(susan)))&
(![X]:((~wise(X)&~happy(X))<=>(~curious(X)&curious(X))))&
(![X]:(~patient(X)<=>kind(X)))&
(((kind(mary)|~quiet(mary)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((rich(X)&brave(X))<=>(funny(X)&~curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~generous(X)&~happy(X))))&
(((generous(lucy)|~rich(lucy)))=>((~humble(paul)<~>strong(paul))))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(?[X]:((creative(X)|~quiet(X))))&
(old(lucy))&
(?[X]:((curious(X)<~>funny(X))))&
((~rich(lucy)|~brave(lucy)))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred)))&
((brave(susan)&strong(susan)))&
(~calm(paul)) | wise(john) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5188558296464967030643009
% SZS output start Proof for 5188558296464967030643009
7. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> (curious(X0) & ~curious(X0))) [input p6]
11. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~happy(X0) & ~generous(X0))) [input p10]
25. ~wise(john) [input hypothesis]
42. ! [X0] : (((~happy(X0) & ~wise(X0)) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | (happy(X0) | wise(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & ~wise(X0)) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | happy(X0) | wise(X0))) [flattening 42]
49. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (happy(X0) | generous(X0))) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 11]
50. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | happy(X0) | generous(X0)) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 49]
95. ~curious(X0) | happy(X0) | wise(X0) [cnf transformation 43]
96. curious(X0) | happy(X0) | wise(X0) [cnf transformation 43]
111. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 50]
112. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 50]
149. ~wise(john) [cnf transformation 25]
152. ~happy(X0) | ~curious(X0) [duplicate literal removal 111]
153. ~happy(X0) | curious(X0) [duplicate literal removal 112]
213. wise(X0) | happy(X0) [subsumption resolution 95,96]
234. ~happy(X0) [subsumption resolution 152,153]
366. happy(john) [resolution 213,149]
367. $false [subsumption resolution 366,234]
% SZS output end Proof for 5188558296464967030643009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or calm is rich or not quiet.
If paul is both happy and calm then mary is not tall or happy and vice versa.
If mary is not funny or old then paul is both not kind and patient.
If john is not calm or not strong then someone is either calm or humble.
If someone is creative or calm then susan is either not happy or not humble and vice versa.
If john is both not wise and happy then someone is patient and vice versa.
Everyone who is both humble and not strong is both happy and kind.
Everyone who is both not happy and not funny is funny and vice versa.
If alice is wise then someone is both quiet and creative.
Everyone who is both calm and generous is not funny or not strong and vice versa.
If someone is kind then someone is either strong or not happy.
If someone is not generous or creative then someone is both creative and not kind.
Everyone who is not strong or brave is rich or tall and vice versa.
If lucy is patient then someone is either not patient or calm.
If paul is both funny and not brave then lucy is not old or creative and vice versa.
Fred is both not funny and not quiet.
Susan is both tall and not brave.
Someone is not patient or quiet.
Susan is either not creative or not patient.
Someone is not tall.
John is not rich or curious.
Someone is creative or not humble. | Lucy is not humble. | neutral | (![X]:((rich(X)|calm(X))=>(rich(X)|~quiet(X))))&
(((happy(paul)&calm(paul)))<=>((~tall(mary)|happy(mary))))&
(((~funny(mary)|old(mary)))=>((~kind(paul)&patient(paul))))&
(((~calm(john)|~strong(john)))=>(?[X]:((calm(X)<~>humble(X)))))&
((?[X]:((creative(X)|calm(X))))<=>((~happy(susan)<~>~humble(susan))))&
(((~wise(john)&happy(john)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~strong(X))=>(happy(X)&kind(X))))&
(![X]:((~happy(X)&~funny(X))<=>funny(X)))&
((wise(alice))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((calm(X)&generous(X))<=>(~funny(X)|~strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)<~>~happy(X)))))&
((?[X]:((~generous(X)|creative(X))))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>(rich(X)|tall(X))))&
((patient(lucy))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((funny(paul)&~brave(paul)))<=>((~old(lucy)|creative(lucy))))&
((~funny(fred)&~quiet(fred)))&
((tall(susan)&~brave(susan)))&
(?[X]:((~patient(X)|quiet(X))))&
((~creative(susan)<~>~patient(susan)))&
(?[X]:(~tall(X)))&
((~rich(john)|curious(john)))&
(?[X]:((creative(X)|~humble(X)))) | ~humble(lucy) | [] | null | 0 |
If alice is both not generous and rich then someone is not patient and vice versa. Everyone who is funny or generous is not funny and vice versa. Everyone who is both not tall and happy is kind. Everyone who is either not calm or humble is not generous or calm. If someone is either happy or not calm then someone is either not happy or happy. If alice is both strong and not tall then susan is not wise or not generous and vice versa. Everyone who is not generous or not kind is both not wise and strong. Everyone who is both not tall and not patient is both not kind and funny. If someone is kind or quiet then alice is either not quiet or quiet. If fred is old or not kind then someone is not brave or creative. Everyone who is not generous is either not strong or patient. If alice is both rich and not curious then john is tall or not happy. Everyone who is curious is wise or not creative. If susan is funny then someone is not creative or not tall and vice versa. Everyone who is both not old and not rich is both not wise and funny and vice versa. If john is brave or humble then someone is not happy or not calm. Mary is kind or not curious. Someone is both not curious and not funny. Lucy is both generous and not funny. Someone is kind or not happy. Alice is curious or not funny. Someone is either curious or creative. | Fred is not calm. | neutral | (((~generous(alice)&rich(alice)))<=>(?[X]:(~patient(X))))&
(![X]:((funny(X)|generous(X))<=>~funny(X)))&
(![X]:((~tall(X)&happy(X))=>kind(X)))&
(![X]:((~calm(X)<~>humble(X))=>(~generous(X)|calm(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(((strong(alice)&~tall(alice)))<=>((~wise(susan)|~generous(susan))))&
(![X]:((~generous(X)|~kind(X))=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&~patient(X))=>(~kind(X)&funny(X))))&
((?[X]:((kind(X)|quiet(X))))=>((~quiet(alice)<~>quiet(alice))))&
(((old(fred)|~kind(fred)))=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:(~generous(X)=>(~strong(X)<~>patient(X))))&
(((rich(alice)&~curious(alice)))=>((tall(john)|~happy(john))))&
(![X]:(curious(X)=>(wise(X)|~creative(X))))&
((funny(susan))<=>(?[X]:((~creative(X)|~tall(X)))))&
(![X]:((~old(X)&~rich(X))<=>(~wise(X)&funny(X))))&
(((brave(john)|humble(john)))=>(?[X]:((~happy(X)|~calm(X)))))&
((kind(mary)|~curious(mary)))&
(?[X]:((~curious(X)&~funny(X))))&
((generous(lucy)&~funny(lucy)))&
(?[X]:((kind(X)|~happy(X))))&
((curious(alice)|~funny(alice)))&
(?[X]:((curious(X)<~>creative(X)))) | ~calm(fred) | [] | null | 0 |
If someone is either tall or calm then john is either patient or quiet and vice versa. If someone is not happy or not tall then alice is either strong or curious. If john is not strong then someone is wise or kind and vice versa. Everyone who is creative is both calm and not generous. Everyone who is kind is either not kind or brave. Everyone who is either not strong or patient is not calm. If paul is either rich or curious then someone is happy or strong and vice versa. Everyone who is not wise or funny is not happy and vice versa. If mary is both kind and funny then someone is not strong or not brave and vice versa. Everyone who is both old and humble is wise. If someone is not strong then someone is not brave or strong. Everyone who is not generous or not kind is creative. If someone is rich or not rich then someone is both not funny and curious. Everyone who is happy or funny is rich and vice versa. Everyone who is both not generous and rich is both not strong and patient and vice versa. If someone is both humble and not patient then paul is curious or not curious and vice versa. John is kind. Someone is wise. Someone is both generous and not curious. Fred is both quiet and not patient. Mary is brave. Someone is humble. Paul is not kind. Someone is not wise or generous. | Paul is curious. | neutral | ((?[X]:((tall(X)<~>calm(X))))<=>((patient(john)<~>quiet(john))))&
((?[X]:((~happy(X)|~tall(X))))=>((strong(alice)<~>curious(alice))))&
((~strong(john))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:(creative(X)=>(calm(X)&~generous(X))))&
(![X]:(kind(X)=>(~kind(X)<~>brave(X))))&
(![X]:((~strong(X)<~>patient(X))=>~calm(X)))&
(((rich(paul)<~>curious(paul)))<=>(?[X]:((happy(X)|strong(X)))))&
(![X]:((~wise(X)|funny(X))<=>~happy(X)))&
(((kind(mary)&funny(mary)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((old(X)&humble(X))=>wise(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:((~generous(X)|~kind(X))=>creative(X)))&
((?[X]:((rich(X)|~rich(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:((happy(X)|funny(X))<=>rich(X)))&
(![X]:((~generous(X)&rich(X))<=>(~strong(X)&patient(X))))&
((?[X]:((humble(X)&~patient(X))))<=>((curious(paul)|~curious(paul))))&
(kind(john))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)&~curious(X))))&
((quiet(fred)&~patient(fred)))&
(brave(mary))&
(?[X]:(humble(X)))&
(~kind(paul))&
(?[X]:((~wise(X)|generous(X)))) | curious(paul) | [] | null | 0 |
Everyone who is kind or not strong is strong and vice versa. Everyone who is brave or funny is both not funny and patient. If someone is creative or not humble then someone is not old and vice versa. If someone is either kind or not tall then someone is either kind or not rich and vice versa. Everyone who is wise or not happy is either wise or not generous. If someone is old or not brave then john is both wise and not patient and vice versa. If someone is either patient or not creative then mary is both not generous and not calm. If susan is both strong and not funny then mary is rich and vice versa. If someone is rich then paul is not brave and vice versa. If fred is not wise then susan is both not old and not funny. Everyone who is not happy or not brave is either calm or not curious. If someone is humble or patient then someone is not funny or not kind and vice versa. Everyone who is generous is either brave or creative. Everyone who is either old or not rich is either not brave or strong and vice versa. Everyone who is both quiet and not generous is not old or patient. Everyone who is either not funny or not calm is either wise or generous and vice versa. Someone is both patient and calm. Someone is not funny. Someone is both tall and curious. John is not old or calm. Mary is not strong or not wise. John is humble. Susan is brave. | John is rich. | entailment | (![X]:((kind(X)|~strong(X))<=>strong(X)))&
(![X]:((brave(X)|funny(X))=>(~funny(X)&patient(X))))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:(~old(X))))&
((?[X]:((kind(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((wise(X)|~happy(X))=>(wise(X)<~>~generous(X))))&
((?[X]:((old(X)|~brave(X))))<=>((wise(john)&~patient(john))))&
((?[X]:((patient(X)<~>~creative(X))))=>((~generous(mary)&~calm(mary))))&
(((strong(susan)&~funny(susan)))<=>(rich(mary)))&
((?[X]:(rich(X)))<=>(~brave(paul)))&
((~wise(fred))=>((~old(susan)&~funny(susan))))&
(![X]:((~happy(X)|~brave(X))=>(calm(X)<~>~curious(X))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(generous(X)=>(brave(X)<~>creative(X))))&
(![X]:((old(X)<~>~rich(X))<=>(~brave(X)<~>strong(X))))&
(![X]:((quiet(X)&~generous(X))=>(~old(X)|patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(wise(X)<~>generous(X))))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:(~funny(X)))&
(?[X]:((tall(X)&curious(X))))&
((~old(john)|calm(john)))&
((~strong(mary)|~wise(mary)))&
(humble(john))&
(brave(susan)) | rich(john) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2537812159117074316761561
% SZS output start Proof for 2537812159117074316761561
1. ! [X0] : ((~strong(X0) | kind(X0)) <=> strong(X0)) [input p0]
2. ! [X0] : ((funny(X0) | brave(X0)) => (patient(X0) & ~funny(X0))) [input p1]
5. ! [X0] : ((~happy(X0) | wise(X0)) => (wise(X0) <~> ~generous(X0))) [input p4]
6. ? [X0] : (~brave(X0) | old(X0)) <=> (~patient(john) & wise(john)) [input p5]
8. (~funny(susan) & strong(susan)) <=> rich(mary) [input p7]
9. ? [X0] : rich(X0) <=> ~brave(paul) [input p8]
14. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (~brave(X0) <~> strong(X0))) [input p13]
16. ! [X0] : ((~funny(X0) <~> ~calm(X0)) <=> (wise(X0) <~> generous(X0))) [input p15]
20. calm(john) | ~old(john) [input p19]
24. ~rich(john) [input hypothesis]
30. ! [X0] : (wise(X0) => (wise(X0) <~> ~generous(X0))) [pure predicate removal 5]
31. ! [X0] : ((patient(X0) & ~funny(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 2]
32. ! [X0] : ((wise(X0) <~> ~generous(X0)) | ~wise(X0)) [ennf transformation 30]
37. ! [X0] : (((~strong(X0) | kind(X0)) | ~strong(X0)) & (strong(X0) | (strong(X0) & ~kind(X0)))) [nnf transformation 1]
38. ! [X0] : ((~strong(X0) | kind(X0) | ~strong(X0)) & (strong(X0) | (strong(X0) & ~kind(X0)))) [flattening 37]
49. ! [X0] : (((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | ~wise(X0)) [nnf transformation 32]
50. (? [X0] : (~brave(X0) | old(X0)) | (patient(john) | ~wise(john))) & ((~patient(john) & wise(john)) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 6]
51. (? [X0] : (~brave(X0) | old(X0)) | patient(john) | ~wise(john)) & ((~patient(john) & wise(john)) | ! [X0] : (brave(X0) & ~old(X0))) [flattening 50]
52. (? [X0] : (~brave(X0) | old(X0)) | patient(john) | ~wise(john)) & ((~patient(john) & wise(john)) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 51]
53. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK4) | old(sK4)) [choice axiom]
54. ((~brave(sK4) | old(sK4)) | patient(john) | ~wise(john)) & ((~patient(john) & wise(john)) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 52,53]
56. ((~funny(susan) & strong(susan)) | ~rich(mary)) & (rich(mary) | (funny(susan) | ~strong(susan))) [nnf transformation 8]
57. ((~funny(susan) & strong(susan)) | ~rich(mary)) & (rich(mary) | funny(susan) | ~strong(susan)) [flattening 56]
58. (? [X0] : rich(X0) | brave(paul)) & (~brave(paul) | ! [X0] : ~rich(X0)) [nnf transformation 9]
59. (? [X0] : rich(X0) | brave(paul)) & (~brave(paul) | ! [X1] : ~rich(X1)) [rectify 58]
60. ? [X0] : rich(X0) => rich(sK5) [choice axiom]
61. (rich(sK5) | brave(paul)) & (~brave(paul) | ! [X1] : ~rich(X1)) [skolemisation 59,60]
69. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0)))) & (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 14]
70. ! [X0] : ((((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))))) [nnf transformation 16]
78. strong(X0) | strong(X0) [cnf transformation 38]
81. ~funny(X0) | ~funny(X0) [cnf transformation 31]
82. ~brave(X0) | patient(X0) [cnf transformation 31]
96. generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 49]
98. wise(john) | brave(X1) [cnf transformation 54]
100. ~patient(john) | brave(X1) [cnf transformation 54]
106. rich(mary) | funny(susan) | ~strong(susan) [cnf transformation 57]
109. ~brave(paul) | ~rich(X1) [cnf transformation 61]
124. ~strong(X0) | brave(X0) | old(X0) | rich(X0) [cnf transformation 69]
131. ~generous(X0) | ~wise(X0) | ~calm(X0) | funny(X0) [cnf transformation 70]
142. calm(john) | ~old(john) [cnf transformation 20]
146. ~rich(john) [cnf transformation 24]
147. ~wise(X0) | generous(X0) [duplicate literal removal 96]
148. ~funny(X0) [duplicate literal removal 81]
149. strong(X0) [duplicate literal removal 78]
212. 15 <=> wise(john) [avatar definition]
213. wise(john) <- (15) [avatar component clause 212]
216. 16 <=> patient(john) [avatar definition]
217. ~patient(john) <- (~16) [avatar component clause 216]
229. 19 <=> ! [X1] : brave(X1) [avatar definition]
230. brave(X1) <- (19) [avatar component clause 229]
231. 19 | ~16 [avatar split clause 100,216,229]
236. 19 | 15 [avatar split clause 98,212,229]
256. rich(mary) | ~strong(susan) [subsumption resolution 106,148]
257. rich(mary) [subsumption resolution 256,149]
259. 25 <=> brave(paul) [avatar definition]
260. ~brave(paul) <- (~25) [avatar component clause 259]
268. 27 <=> ! [X1] : ~rich(X1) [avatar definition]
269. ~rich(X1) <- (27) [avatar component clause 268]
270. 27 | ~25 [avatar split clause 109,259,268]
296. rich(X0) | old(X0) | brave(X0) [subsumption resolution 124,149]
299. ~generous(X0) | ~wise(X0) | ~calm(X0) [subsumption resolution 131,148]
300. ~calm(X0) | ~wise(X0) [subsumption resolution 299,147]
304. 33 <=> old(john) [avatar definition]
308. 34 <=> calm(john) [avatar definition]
310. calm(john) <- (34) [avatar component clause 308]
311. ~33 | 34 [avatar split clause 142,308,304]
351. 40 <=> brave(john) [avatar definition]
353. brave(john) <- (40) [avatar component clause 351]
356. $false <- (19, ~25) [resolution 230,260]
358. ~19 | 25 [avatar contradiction clause 356]
360. $false <- (27) [resolution 269,257]
365. ~27 [avatar contradiction clause 360]
382. old(john) | brave(john) [resolution 296,146]
423. ~wise(john) <- (34) [resolution 310,300]
425. $false <- (15, 34) [subsumption resolution 423,213]
426. ~15 | ~34 [avatar contradiction clause 425]
427. 40 | 33 [avatar split clause 382,304,351]
443. patient(john) <- (40) [resolution 353,82]
444. $false <- (~16, 40) [subsumption resolution 443,217]
445. 16 | ~40 [avatar contradiction clause 444]
446. $false [avatar sat refutation 231,236,270,311,358,365,426,427,445]
% SZS output end Proof for 2537812159117074316761561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is kind and vice versa. Everyone who is both not rich and not strong is quiet and vice versa. If susan is not curious then paul is not generous or not wise. Everyone who is not creative is not tall and vice versa. Everyone who is either not humble or tall is not strong or not happy. Everyone who is creative or quiet is either calm or brave. If lucy is either not quiet or not funny then someone is both not quiet and not old and vice versa. Everyone who is not wise is either not curious or old and vice versa. Everyone who is patient is either quiet or not strong and vice versa. Everyone who is either not patient or brave is creative or not generous and vice versa. Everyone who is either not patient or not tall is creative and vice versa. Everyone who is either tall or brave is not rich and vice versa. If someone is rich then someone is either humble or not creative and vice versa. Everyone who is either not kind or not calm is kind and vice versa. If fred is patient then someone is either humble or tall. Everyone who is either rich or not calm is calm or strong and vice versa. Fred is either happy or not tall. Someone is either happy or old. Someone is either kind or not curious. Paul is both curious and old. | Lucy is brave. | entailment | (![X]:(rich(X)<=>kind(X)))&
(![X]:((~rich(X)&~strong(X))<=>quiet(X)))&
((~curious(susan))=>((~generous(paul)|~wise(paul))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~humble(X)<~>tall(X))=>(~strong(X)|~happy(X))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)<~>brave(X))))&
(((~quiet(lucy)<~>~funny(lucy)))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:(~wise(X)<=>(~curious(X)<~>old(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)<~>brave(X))<=>(creative(X)|~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>brave(X))<=>~rich(X)))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>kind(X)))&
((patient(fred))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>(calm(X)|strong(X))))&
((happy(fred)<~>~tall(fred)))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((kind(X)<~>~curious(X))))&
((curious(paul)&old(paul))) | brave(lucy) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6767488315724989323512206
% SZS output start Proof for 6767488315724989323512206
2. ! [X0] : ((~strong(X0) & ~rich(X0)) <=> quiet(X0)) [input p1]
4. ! [X0] : (~creative(X0) <=> ~tall(X0)) [input p3]
6. ! [X0] : ((quiet(X0) | creative(X0)) => (calm(X0) <~> brave(X0))) [input p5]
9. ! [X0] : (patient(X0) <=> (quiet(X0) <~> ~strong(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : ((tall(X0) <~> brave(X0)) <=> ~rich(X0)) [input p11]
14. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> kind(X0)) [input p13]
16. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (strong(X0) | calm(X0))) [input p15]
21. ~brave(lucy) [input hypothesis]
28. ! [X0] : ((calm(X0) <~> brave(X0)) | (~quiet(X0) & ~creative(X0))) [ennf transformation 6]
32. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) | rich(X0)))) [nnf transformation 2]
33. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | strong(X0) | rich(X0))) [flattening 32]
34. ! [X0] : ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))) [nnf transformation 4]
36. ! [X0] : (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~quiet(X0) & ~creative(X0))) [nnf transformation 28]
42. ! [X0] : ((patient(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | ~patient(X0))) [nnf transformation 9]
45. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~creative(X0)) & (creative(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 11]
46. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | rich(X0)) & (~rich(X0) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 12]
52. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~kind(X0)) & (kind(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 14]
56. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & ((strong(X0) | calm(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 16]
57. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & (strong(X0) | calm(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [flattening 56]
68. ~quiet(X0) | ~rich(X0) [cnf transformation 33]
71. ~tall(X0) | creative(X0) [cnf transformation 34]
72. ~creative(X0) | tall(X0) [cnf transformation 34]
75. ~creative(X0) | calm(X0) | brave(X0) [cnf transformation 36]
90. patient(X0) | quiet(X0) | strong(X0) [cnf transformation 42]
98. creative(X0) | ~patient(X0) | tall(X0) [cnf transformation 45]
99. ~tall(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 45]
103. brave(X0) | tall(X0) | rich(X0) [cnf transformation 46]
109. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 52]
111. ~calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 52]
116. strong(X0) | calm(X0) | rich(X0) | calm(X0) [cnf transformation 57]
120. calm(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 57]
129. ~brave(lucy) [cnf transformation 21]
130. strong(X0) | calm(X0) | rich(X0) [duplicate literal removal 116]
132. kind(X0) | ~calm(X0) [duplicate literal removal 109]
133. ~calm(X0) | ~kind(X0) [duplicate literal removal 111]
174. ~patient(X0) | ~tall(X0) [subsumption resolution 99,71]
175. ~patient(X0) | tall(X0) [subsumption resolution 98,72]
176. ~patient(X0) [subsumption resolution 175,174]
190. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
191. ~rich(X3) <- (12) [avatar component clause 190]
202. ~calm(X0) [subsumption resolution 132,133]
203. ~strong(X0) | ~rich(X0) [subsumption resolution 120,202]
204. strong(X0) | rich(X0) [subsumption resolution 130,202]
259. quiet(X3) | strong(X3) [resolution 90,176]
262. strong(X2) | ~rich(X2) [resolution 259,68]
266. strong(X2) [subsumption resolution 262,204]
268. ~rich(X0) [resolution 266,203]
269. 12 [avatar split clause 268,190]
284. tall(lucy) | rich(lucy) [resolution 103,129]
291. tall(lucy) <- (12) [subsumption resolution 284,191]
295. creative(lucy) <- (12) [resolution 291,71]
299. calm(lucy) | brave(lucy) <- (12) [resolution 295,75]
301. brave(lucy) <- (12) [subsumption resolution 299,202]
302. $false <- (12) [subsumption resolution 301,129]
303. ~12 [avatar contradiction clause 302]
304. $false [avatar sat refutation 269,303]
% SZS output end Proof for 6767488315724989323512206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old or not tall then paul is wise or curious.
Everyone who is not humble is either not tall or creative and vice versa.
Everyone who is either not humble or wise is either not kind or not funny.
Everyone who is strong or generous is both not tall and not strong.
Everyone who is both not patient and humble is generous and vice versa.
If someone is either brave or not old then lucy is either rich or not tall and vice versa.
If mary is brave then paul is either humble or funny.
Everyone who is curious is not funny and vice versa.
If someone is tall or funny then someone is not funny or quiet and vice versa.
Everyone who is not old or not creative is either tall or not calm and vice versa.
Everyone who is not generous is not happy.
Everyone who is not old is not curious.
Everyone who is either not happy or strong is not tall.
If someone is both not old and happy then someone is funny.
If someone is not happy then someone is generous.
Everyone who is either old or not wise is not humble.
Someone is brave.
Lucy is not old or not rich.
Paul is not funny.
John is not old.
Someone is either rich or not patient.
Lucy is not happy.
John is rich or kind.
Paul is either not quiet or not tall. | Lucy is tall. | contradiction | (((old(lucy)|~tall(lucy)))=>((wise(paul)|curious(paul))))&
(![X]:(~humble(X)<=>(~tall(X)<~>creative(X))))&
(![X]:((~humble(X)<~>wise(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((strong(X)|generous(X))=>(~tall(X)&~strong(X))))&
(![X]:((~patient(X)&humble(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~old(X))))<=>((rich(lucy)<~>~tall(lucy))))&
((brave(mary))=>((humble(paul)<~>funny(paul))))&
(![X]:(curious(X)<=>~funny(X)))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~old(X)|~creative(X))<=>(tall(X)<~>~calm(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:(~old(X)=>~curious(X)))&
(![X]:((~happy(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((old(X)<~>~wise(X))=>~humble(X)))&
(?[X]:(brave(X)))&
((~old(lucy)|~rich(lucy)))&
(~funny(paul))&
(~old(john))&
(?[X]:((rich(X)<~>~patient(X))))&
(~happy(lucy))&
((rich(john)|kind(john)))&
((~quiet(paul)<~>~tall(paul))) | tall(lucy) | [
"p3",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5155935310536164202610284
% SZS output start Proof for 5155935310536164202610284
4. ! [X0] : ((generous(X0) | strong(X0)) => (~strong(X0) & ~tall(X0))) [input p3]
13. ! [X0] : ((~happy(X0) <~> strong(X0)) => ~tall(X0)) [input p12]
22. ~happy(lucy) [input p21]
25. tall(lucy) [input hypothesis]
32. ! [X0] : ((~strong(X0) & ~tall(X0)) | (~generous(X0) & ~strong(X0))) [ennf transformation 4]
36. ! [X0] : (~tall(X0) | (~happy(X0) <=> strong(X0))) [ennf transformation 13]
57. ! [X0] : (~tall(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) [nnf transformation 36]
83. ~strong(X0) | ~strong(X0) [cnf transformation 32]
112. ~tall(X0) | strong(X0) | happy(X0) [cnf transformation 57]
124. ~happy(lucy) [cnf transformation 22]
128. tall(lucy) [cnf transformation 25]
129. ~strong(X0) [duplicate literal removal 83]
131. 1 <=> tall(lucy) [avatar definition]
133. tall(lucy) <- (1) [avatar component clause 131]
220. ~tall(X0) | happy(X0) [subsumption resolution 112,129]
268. 1 [avatar split clause 128,131]
286. happy(lucy) <- (1) [resolution 220,133]
288. $false <- (1) [subsumption resolution 286,124]
289. ~1 [avatar contradiction clause 288]
290. $false [avatar sat refutation 268,289]
% SZS output end Proof for 5155935310536164202610284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or patient then someone is not creative or not patient and vice versa. Everyone who is not calm is not wise or not patient. Everyone who is either not creative or humble is patient. If john is both not funny and not creative then fred is either not patient or generous and vice versa. Everyone who is either not quiet or not calm is either patient or strong and vice versa. Everyone who is either quiet or not quiet is brave or strong and vice versa. If alice is brave then someone is not kind or funny. Everyone who is generous is both not calm and not strong and vice versa. Everyone who is either not wise or calm is curious. If alice is both brave and calm then someone is old. If fred is both funny and not patient then susan is both not humble and calm. If someone is both not generous and not calm then paul is generous or strong. Everyone who is both not curious and not brave is not creative or kind and vice versa. If fred is both generous and rich then someone is both not tall and not creative and vice versa. If someone is wise then alice is not brave or not curious and vice versa. Everyone who is not generous or not brave is both not strong and not generous. Susan is humble or quiet. Someone is either humble or wise. Paul is either not calm or not quiet. Fred is not rich or not curious. John is not kind or creative. John is either not happy or funny. Someone is not quiet or not generous. | Alice is not curious. | neutral | ((?[X]:((~old(X)|patient(X))))<=>(?[X]:((~creative(X)|~patient(X)))))&
(![X]:(~calm(X)=>(~wise(X)|~patient(X))))&
(![X]:((~creative(X)<~>humble(X))=>patient(X)))&
(((~funny(john)&~creative(john)))<=>((~patient(fred)<~>generous(fred))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(patient(X)<~>strong(X))))&
(![X]:((quiet(X)<~>~quiet(X))<=>(brave(X)|strong(X))))&
((brave(alice))=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:(generous(X)<=>(~calm(X)&~strong(X))))&
(![X]:((~wise(X)<~>calm(X))=>curious(X)))&
(((brave(alice)&calm(alice)))=>(?[X]:(old(X))))&
(((funny(fred)&~patient(fred)))=>((~humble(susan)&calm(susan))))&
((?[X]:((~generous(X)&~calm(X))))=>((generous(paul)|strong(paul))))&
(![X]:((~curious(X)&~brave(X))<=>(~creative(X)|kind(X))))&
(((generous(fred)&rich(fred)))<=>(?[X]:((~tall(X)&~creative(X)))))&
((?[X]:(wise(X)))<=>((~brave(alice)|~curious(alice))))&
(![X]:((~generous(X)|~brave(X))=>(~strong(X)&~generous(X))))&
((humble(susan)|quiet(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
((~calm(paul)<~>~quiet(paul)))&
((~rich(fred)|~curious(fred)))&
((~kind(john)|creative(john)))&
((~happy(john)<~>funny(john)))&
(?[X]:((~quiet(X)|~generous(X)))) | ~curious(alice) | [] | null | 0 |
Everyone who is both wise and not patient is either not funny or not strong.
If paul is patient then someone is kind or tall.
If john is curious then paul is both humble and quiet.
Everyone who is either not tall or not happy is either kind or generous and vice versa.
If someone is brave or not kind then someone is either not tall or not quiet and vice versa.
Everyone who is both old and not patient is not old or not creative and vice versa.
Everyone who is either not creative or not tall is calm.
If someone is both not wise and calm then fred is curious or not tall and vice versa.
If mary is both not rich and tall then mary is both not generous and not funny and vice versa.
Everyone who is either funny or not generous is strong.
Everyone who is humble is either creative or not curious.
Everyone who is both tall and patient is both old and creative.
Everyone who is both rich and brave is not humble and vice versa.
If someone is not quiet then paul is either not humble or not quiet.
Everyone who is not strong is curious or kind and vice versa.
If someone is not kind or not calm then john is both not creative and rich.
Fred is not creative.
Paul is not wise.
Fred is both rich and strong.
Fred is old or creative.
Someone is brave or curious.
Someone is not quiet.
Someone is calm. | Fred is strong. | entailment | (![X]:((wise(X)&~patient(X))=>(~funny(X)<~>~strong(X))))&
((patient(paul))=>(?[X]:((kind(X)|tall(X)))))&
((curious(john))=>((humble(paul)&quiet(paul))))&
(![X]:((~tall(X)<~>~happy(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((old(X)&~patient(X))<=>(~old(X)|~creative(X))))&
(![X]:((~creative(X)<~>~tall(X))=>calm(X)))&
((?[X]:((~wise(X)&calm(X))))<=>((curious(fred)|~tall(fred))))&
(((~rich(mary)&tall(mary)))<=>((~generous(mary)&~funny(mary))))&
(![X]:((funny(X)<~>~generous(X))=>strong(X)))&
(![X]:(humble(X)=>(creative(X)<~>~curious(X))))&
(![X]:((tall(X)&patient(X))=>(old(X)&creative(X))))&
(![X]:((rich(X)&brave(X))<=>~humble(X)))&
((?[X]:(~quiet(X)))=>((~humble(paul)<~>~quiet(paul))))&
(![X]:(~strong(X)<=>(curious(X)|kind(X))))&
((?[X]:((~kind(X)|~calm(X))))=>((~creative(john)&rich(john))))&
(~creative(fred))&
(~wise(paul))&
((rich(fred)&strong(fred)))&
((old(fred)|creative(fred)))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X))) | strong(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6042254722941392211430536
% SZS output start Proof for 6042254722941392211430536
19. strong(fred) & rich(fred) [input p18]
24. ~strong(fred) [input hypothesis]
125. strong(fred) [cnf transformation 19]
130. ~strong(fred) [cnf transformation 24]
268. $false [subsumption resolution 130,125]
% SZS output end Proof for 6042254722941392211430536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or brave then fred is calm.
If fred is brave then john is old or not happy and vice versa.
If someone is kind or not generous then alice is either funny or not quiet.
If mary is creative or old then someone is either creative or not generous and vice versa.
Everyone who is not kind is funny or not funny.
If someone is brave then someone is not happy or generous and vice versa.
If someone is strong then fred is curious and vice versa.
Everyone who is patient or kind is either not quiet or wise and vice versa.
Everyone who is wise is either old or wise.
Everyone who is both not strong and not funny is both not quiet and not wise and vice versa.
Everyone who is both not old and quiet is curious.
If paul is generous or not brave then lucy is both generous and happy and vice versa.
Everyone who is tall or creative is both kind and not funny.
Everyone who is happy is either not calm or rich and vice versa.
Everyone who is both not brave and not generous is either not patient or tall.
Everyone who is not humble or tall is not tall.
Someone is either not curious or creative.
Someone is not funny or not humble.
Paul is both not kind and quiet.
Lucy is both happy and rich.
Someone is both not funny and not kind.
Alice is calm.
John is either patient or funny. | John is happy. | neutral | ((?[X]:((~creative(X)|brave(X))))=>(calm(fred)))&
((brave(fred))<=>((old(john)|~happy(john))))&
((?[X]:((kind(X)|~generous(X))))=>((funny(alice)<~>~quiet(alice))))&
(((creative(mary)|old(mary)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~kind(X)=>(funny(X)|~funny(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~happy(X)|generous(X)))))&
((?[X]:(strong(X)))<=>(curious(fred)))&
(![X]:((patient(X)|kind(X))<=>(~quiet(X)<~>wise(X))))&
(![X]:(wise(X)=>(old(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))<=>(~quiet(X)&~wise(X))))&
(![X]:((~old(X)&quiet(X))=>curious(X)))&
(((generous(paul)|~brave(paul)))<=>((generous(lucy)&happy(lucy))))&
(![X]:((tall(X)|creative(X))=>(kind(X)&~funny(X))))&
(![X]:(happy(X)<=>(~calm(X)<~>rich(X))))&
(![X]:((~brave(X)&~generous(X))=>(~patient(X)<~>tall(X))))&
(![X]:((~humble(X)|tall(X))=>~tall(X)))&
(?[X]:((~curious(X)<~>creative(X))))&
(?[X]:((~funny(X)|~humble(X))))&
((~kind(paul)&quiet(paul)))&
((happy(lucy)&rich(lucy)))&
(?[X]:((~funny(X)&~kind(X))))&
(calm(alice))&
((patient(john)<~>funny(john))) | happy(john) | [] | null | 0 |
If someone is brave or wise then lucy is either calm or quiet and vice versa.
Everyone who is not strong or happy is either not kind or kind and vice versa.
Everyone who is either not brave or not tall is patient and vice versa.
Everyone who is not rich is quiet and vice versa.
Everyone who is strong or old is not happy.
Everyone who is not quiet or wise is generous or brave and vice versa.
If fred is old then someone is either not patient or not strong and vice versa.
If someone is not curious then someone is not happy and vice versa.
If someone is either not humble or not curious then someone is humble or not humble and vice versa.
If someone is creative then fred is calm or not calm and vice versa.
Everyone who is either happy or calm is both kind and not patient.
If paul is creative then someone is either not calm or not generous and vice versa.
Everyone who is either not old or not quiet is not curious or not quiet and vice versa.
Everyone who is both funny and not old is either creative or humble.
If someone is not generous or curious then fred is either happy or not funny.
Everyone who is curious is strong or quiet and vice versa.
Someone is humble.
Mary is both calm and not curious.
Someone is either not wise or not humble.
Alice is tall or not strong.
Someone is either not wise or not generous. | Paul is calm. | neutral | ((?[X]:((brave(X)|wise(X))))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>patient(X)))&
(![X]:(~rich(X)<=>quiet(X)))&
(![X]:((strong(X)|old(X))=>~happy(X)))&
(![X]:((~quiet(X)|wise(X))<=>(generous(X)|brave(X))))&
((old(fred))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:(~happy(X))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:(creative(X)))<=>((calm(fred)|~calm(fred))))&
(![X]:((happy(X)<~>calm(X))=>(kind(X)&~patient(X))))&
((creative(paul))<=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((funny(X)&~old(X))=>(creative(X)<~>humble(X))))&
((?[X]:((~generous(X)|curious(X))))=>((happy(fred)<~>~funny(fred))))&
(![X]:(curious(X)<=>(strong(X)|quiet(X))))&
(?[X]:(humble(X)))&
((calm(mary)&~curious(mary)))&
(?[X]:((~wise(X)<~>~humble(X))))&
((tall(alice)|~strong(alice)))&
(?[X]:((~wise(X)<~>~generous(X)))) | calm(paul) | [] | null | 0 |
If mary is both curious and not curious then mary is not creative.
Everyone who is both calm and kind is either not quiet or old.
If alice is both not humble and not patient then someone is patient or not strong and vice versa.
If someone is both strong and not funny then lucy is both not humble and kind.
If someone is funny or not curious then mary is both old and curious.
If mary is either quiet or not funny then fred is calm.
If paul is both curious and not funny then paul is funny and vice versa.
If someone is both not wise and tall then paul is not funny and vice versa.
If someone is either not wise or quiet then someone is kind or patient.
If alice is both not curious and not strong then someone is either not old or patient and vice versa.
If susan is not generous then someone is either patient or not humble and vice versa.
If paul is not humble or curious then someone is not generous or happy.
Everyone who is not happy or not old is both not wise and not calm and vice versa.
Everyone who is brave is funny and vice versa.
Everyone who is both not calm and old is not calm or humble and vice versa.
Everyone who is curious or not tall is both not brave and not strong and vice versa.
Fred is both creative and old.
Alice is calm.
Someone is quiet or not humble.
Mary is not happy.
Lucy is generous.
Alice is not kind.
Someone is either brave or old.
Fred is both funny and not kind. | Mary is not funny. | entailment | (((curious(mary)&~curious(mary)))=>(~creative(mary)))&
(![X]:((calm(X)&kind(X))=>(~quiet(X)<~>old(X))))&
(((~humble(alice)&~patient(alice)))<=>(?[X]:((patient(X)|~strong(X)))))&
((?[X]:((strong(X)&~funny(X))))=>((~humble(lucy)&kind(lucy))))&
((?[X]:((funny(X)|~curious(X))))=>((old(mary)&curious(mary))))&
(((quiet(mary)<~>~funny(mary)))=>(calm(fred)))&
(((curious(paul)&~funny(paul)))<=>(funny(paul)))&
((?[X]:((~wise(X)&tall(X))))<=>(~funny(paul)))&
((?[X]:((~wise(X)<~>quiet(X))))=>(?[X]:((kind(X)|patient(X)))))&
(((~curious(alice)&~strong(alice)))<=>(?[X]:((~old(X)<~>patient(X)))))&
((~generous(susan))<=>(?[X]:((patient(X)<~>~humble(X)))))&
(((~humble(paul)|curious(paul)))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~happy(X)|~old(X))<=>(~wise(X)&~calm(X))))&
(![X]:(brave(X)<=>funny(X)))&
(![X]:((~calm(X)&old(X))<=>(~calm(X)|humble(X))))&
(![X]:((curious(X)|~tall(X))<=>(~brave(X)&~strong(X))))&
((creative(fred)&old(fred)))&
(calm(alice))&
(?[X]:((quiet(X)|~humble(X))))&
(~happy(mary))&
(generous(lucy))&
(~kind(alice))&
(?[X]:((brave(X)<~>old(X))))&
((funny(fred)&~kind(fred))) | ~funny(mary) | [
"p4",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 10553339513284554222303
% SZS output start Proof for 10553339513284554222303
5. ? [X0] : (~curious(X0) | funny(X0)) => (curious(mary) & old(mary)) [input p4]
14. ! [X0] : (brave(X0) <=> funny(X0)) [input p13]
16. ! [X0] : ((~tall(X0) | curious(X0)) <=> (~strong(X0) & ~brave(X0))) [input p15]
24. ~kind(fred) & funny(fred) [input p23]
25. funny(mary) [input hypothesis]
32. (curious(mary) & old(mary)) | ! [X0] : (curious(X0) & ~funny(X0)) [ennf transformation 5]
66. ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))) [nnf transformation 14]
69. ! [X0] : (((~tall(X0) | curious(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (tall(X0) & ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : ((~tall(X0) | curious(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (tall(X0) & ~curious(X0)))) [flattening 69]
88. curious(mary) | ~funny(X0) [cnf transformation 32]
118. ~funny(X0) | brave(X0) [cnf transformation 66]
124. ~brave(X0) | ~curious(X0) [cnf transformation 70]
138. funny(fred) [cnf transformation 24]
140. funny(mary) [cnf transformation 25]
187. 11 <=> curious(mary) [avatar definition]
189. curious(mary) <- (11) [avatar component clause 187]
192. 12 <=> ! [X0] : ~funny(X0) [avatar definition]
193. ~funny(X0) <- (12) [avatar component clause 192]
194. 12 | 11 [avatar split clause 88,187,192]
202. 14 <=> funny(mary) [avatar definition]
204. funny(mary) <- (14) [avatar component clause 202]
308. 14 [avatar split clause 140,202]
316. $false <- (12) [resolution 193,138]
317. ~12 [avatar contradiction clause 316]
323. brave(mary) <- (14) [resolution 118,204]
327. ~curious(mary) <- (14) [resolution 124,323]
328. $false <- (11, 14) [subsumption resolution 327,189]
329. ~11 | ~14 [avatar contradiction clause 328]
330. $false [avatar sat refutation 194,308,317,329]
% SZS output end Proof for 10553339513284554222303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not kind is not humble and vice versa.
If mary is not humble then someone is both creative and not creative.
If susan is quiet or not kind then lucy is not tall or not rich and vice versa.
Everyone who is either not creative or old is wise and vice versa.
Everyone who is creative is either not humble or not tall.
If susan is both not calm and quiet then john is both tall and not old.
If alice is kind or not patient then someone is happy or not happy.
Everyone who is either not curious or creative is either generous or brave.
If someone is not old then someone is both not calm and curious and vice versa.
Everyone who is both old and happy is generous or not old and vice versa.
Everyone who is funny or brave is not quiet or not funny and vice versa.
Everyone who is either not tall or not strong is either not old or calm.
Everyone who is funny is old.
Everyone who is both patient and not generous is either not happy or old.
If lucy is either not brave or not happy then fred is calm.
If susan is rich then someone is either not funny or not strong.
Lucy is happy.
Someone is both humble and not tall.
Someone is not old or happy.
Susan is kind.
Mary is old.
John is both not quiet and not tall.
Paul is not happy or not rich. | Mary is not humble. | contradiction | (![X]:((rich(X)<~>~kind(X))<=>~humble(X)))&
((~humble(mary))=>(?[X]:((creative(X)&~creative(X)))))&
(((quiet(susan)|~kind(susan)))<=>((~tall(lucy)|~rich(lucy))))&
(![X]:((~creative(X)<~>old(X))<=>wise(X)))&
(![X]:(creative(X)=>(~humble(X)<~>~tall(X))))&
(((~calm(susan)&quiet(susan)))=>((tall(john)&~old(john))))&
(((kind(alice)|~patient(alice)))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(generous(X)<~>brave(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:((old(X)&happy(X))<=>(generous(X)|~old(X))))&
(![X]:((funny(X)|brave(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~old(X)<~>calm(X))))&
(![X]:(funny(X)=>old(X)))&
(![X]:((patient(X)&~generous(X))=>(~happy(X)<~>old(X))))&
(((~brave(lucy)<~>~happy(lucy)))=>(calm(fred)))&
((rich(susan))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(happy(lucy))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((~old(X)|happy(X))))&
(kind(susan))&
(old(mary))&
((~quiet(john)&~tall(john)))&
((~happy(paul)|~rich(paul))) | ~humble(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 556076379599969296089023
% SZS output start Proof for 556076379599969296089023
2. ~humble(mary) => ? [X0] : (~creative(X0) & creative(X0)) [input p1]
24. ~humble(mary) [input hypothesis]
26. ? [X0] : (~creative(X0) & creative(X0)) | humble(mary) [ennf transformation 2]
39. ? [X0] : (~creative(X0) & creative(X0)) => (~creative(sK0) & creative(sK0)) [choice axiom]
40. (~creative(sK0) & creative(sK0)) | humble(mary) [skolemisation 26,39]
70. creative(sK0) | humble(mary) [cnf transformation 40]
71. ~creative(sK0) | humble(mary) [cnf transformation 40]
118. ~humble(mary) [cnf transformation 24]
124. 1 <=> humble(mary) [avatar definition]
128. 2 <=> creative(sK0) [avatar definition]
131. 1 | ~2 [avatar split clause 71,128,124]
132. 1 | 2 [avatar split clause 70,128,124]
234. ~1 [avatar split clause 118,124]
235. $false [avatar sat refutation 131,132,234]
% SZS output end Proof for 556076379599969296089023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or creative is creative or generous.
Everyone who is not brave or brave is curious.
Everyone who is not wise or not old is not generous or humble and vice versa.
If susan is rich or generous then someone is either creative or calm and vice versa.
If mary is either funny or curious then alice is not creative or not patient and vice versa.
If susan is either not humble or calm then alice is either not brave or rich.
Everyone who is either not humble or not patient is happy.
If someone is either calm or not quiet then someone is either not wise or funny.
If someone is patient or brave then someone is not funny or calm and vice versa.
Everyone who is both not brave and tall is old and vice versa.
If someone is both rich and humble then susan is both patient and not happy.
Everyone who is quiet or not calm is both kind and not funny.
If someone is not patient then someone is not curious and vice versa.
Everyone who is either not tall or happy is both not brave and generous.
Everyone who is either patient or funny is either not calm or brave and vice versa.
Everyone who is generous or not kind is kind or not brave.
Someone is not creative or not old.
Paul is either old or not kind.
Someone is brave.
Someone is creative or not curious.
Susan is not creative.
Susan is both quiet and not happy.
Someone is calm. | Susan is funny. | contradiction | (![X]:((~curious(X)<~>creative(X))=>(creative(X)|generous(X))))&
(![X]:((~brave(X)|brave(X))=>curious(X)))&
(![X]:((~wise(X)|~old(X))<=>(~generous(X)|humble(X))))&
(((rich(susan)|generous(susan)))<=>(?[X]:((creative(X)<~>calm(X)))))&
(((funny(mary)<~>curious(mary)))<=>((~creative(alice)|~patient(alice))))&
(((~humble(susan)<~>calm(susan)))=>((~brave(alice)<~>rich(alice))))&
(![X]:((~humble(X)<~>~patient(X))=>happy(X)))&
((?[X]:((calm(X)<~>~quiet(X))))=>(?[X]:((~wise(X)<~>funny(X)))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~funny(X)|calm(X)))))&
(![X]:((~brave(X)&tall(X))<=>old(X)))&
((?[X]:((rich(X)&humble(X))))=>((patient(susan)&~happy(susan))))&
(![X]:((quiet(X)|~calm(X))=>(kind(X)&~funny(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(~curious(X))))&
(![X]:((~tall(X)<~>happy(X))=>(~brave(X)&generous(X))))&
(![X]:((patient(X)<~>funny(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((generous(X)|~kind(X))=>(kind(X)|~brave(X))))&
(?[X]:((~creative(X)|~old(X))))&
((old(paul)<~>~kind(paul)))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)|~curious(X))))&
(~creative(susan))&
((quiet(susan)&~happy(susan)))&
(?[X]:(calm(X))) | funny(susan) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1185007916606276607837299
% SZS output start Proof for 1185007916606276607837299
12. ! [X0] : ((~calm(X0) | quiet(X0)) => (~funny(X0) & kind(X0))) [input p11]
22. ~happy(susan) & quiet(susan) [input p21]
24. funny(susan) [input hypothesis]
35. ! [X0] : ((~funny(X0) & kind(X0)) | (calm(X0) & ~quiet(X0))) [ennf transformation 12]
119. ~quiet(X0) | ~funny(X0) [cnf transformation 35]
143. quiet(susan) [cnf transformation 22]
146. funny(susan) [cnf transformation 24]
311. ~funny(susan) [resolution 119,143]
312. $false [subsumption resolution 311,146]
% SZS output end Proof for 1185007916606276607837299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is not generous and vice versa. Everyone who is either not kind or not brave is either kind or not funny and vice versa. Everyone who is either funny or not strong is both funny and quiet. Everyone who is not curious or patient is not strong and vice versa. If someone is either not kind or funny then someone is both not tall and not calm. Everyone who is brave or not strong is either not quiet or funny and vice versa. If john is either not creative or not rich then someone is not calm and vice versa. If lucy is both not funny and curious then susan is either not old or strong. If someone is both not wise and happy then alice is both tall and not creative and vice versa. Everyone who is not humble is not curious. If someone is either kind or not strong then susan is either not calm or not wise. If susan is not calm then someone is not creative or not rich. Everyone who is either generous or not brave is either calm or not strong and vice versa. Everyone who is funny or not wise is both rich and creative. Everyone who is strong is not creative. If lucy is both strong and not kind then someone is not quiet and vice versa. Someone is either not wise or not old. Mary is both kind and not rich. Fred is not rich or not brave. Susan is not curious. Fred is not quiet. Alice is creative or happy. Someone is calm or tall. Alice is both tall and not kind. | Mary is not kind. | contradiction | (![X]:(~humble(X)<=>~generous(X)))&
(![X]:((~kind(X)<~>~brave(X))<=>(kind(X)<~>~funny(X))))&
(![X]:((funny(X)<~>~strong(X))=>(funny(X)&quiet(X))))&
(![X]:((~curious(X)|patient(X))<=>~strong(X)))&
((?[X]:((~kind(X)<~>funny(X))))=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:((brave(X)|~strong(X))<=>(~quiet(X)<~>funny(X))))&
(((~creative(john)<~>~rich(john)))<=>(?[X]:(~calm(X))))&
(((~funny(lucy)&curious(lucy)))=>((~old(susan)<~>strong(susan))))&
((?[X]:((~wise(X)&happy(X))))<=>((tall(alice)&~creative(alice))))&
(![X]:(~humble(X)=>~curious(X)))&
((?[X]:((kind(X)<~>~strong(X))))=>((~calm(susan)<~>~wise(susan))))&
((~calm(susan))=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:((generous(X)<~>~brave(X))<=>(calm(X)<~>~strong(X))))&
(![X]:((funny(X)|~wise(X))=>(rich(X)&creative(X))))&
(![X]:(strong(X)=>~creative(X)))&
(((strong(lucy)&~kind(lucy)))<=>(?[X]:(~quiet(X))))&
(?[X]:((~wise(X)<~>~old(X))))&
((kind(mary)&~rich(mary)))&
((~rich(fred)|~brave(fred)))&
(~curious(susan))&
(~quiet(fred))&
((creative(alice)|happy(alice)))&
(?[X]:((calm(X)|tall(X))))&
((tall(alice)&~kind(alice))) | ~kind(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7888098795512236750537749
% SZS output start Proof for 7888098795512236750537749
18. ~rich(mary) & kind(mary) [input p17]
25. ~kind(mary) [input hypothesis]
132. kind(mary) [cnf transformation 18]
141. ~kind(mary) [cnf transformation 25]
310. $false [subsumption resolution 141,132]
% SZS output end Proof for 7888098795512236750537749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or humble is both strong and tall and vice versa. Everyone who is both not strong and not patient is not funny and vice versa. If john is not curious then lucy is not creative and vice versa. Everyone who is either not tall or not rich is both strong and not kind. Everyone who is not humble or not quiet is not happy and vice versa. If someone is not tall or quiet then someone is not calm. If john is happy then fred is either calm or not kind. If lucy is not curious or not funny then someone is either not quiet or not strong. If susan is either happy or not old then susan is both not tall and not old and vice versa. Everyone who is not curious or not brave is not generous and vice versa. Everyone who is either not funny or not generous is either not tall or not wise. Everyone who is not curious is either not rich or not patient and vice versa. If someone is not curious or not creative then someone is either strong or rich and vice versa. Everyone who is not brave or not humble is brave or curious and vice versa. Everyone who is not funny is humble or patient and vice versa. If someone is both not happy and not curious then someone is both not generous and patient and vice versa. Fred is either creative or not quiet. Fred is strong or not quiet. Someone is either not tall or not funny. Someone is not humble or patient. Someone is both tall and not calm. Someone is either happy or not old. Someone is wise or quiet. | Susan is not rich. | entailment | (![X]:((~kind(X)<~>humble(X))<=>(strong(X)&tall(X))))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
((~curious(john))<=>(~creative(lucy)))&
(![X]:((~tall(X)<~>~rich(X))=>(strong(X)&~kind(X))))&
(![X]:((~humble(X)|~quiet(X))<=>~happy(X)))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:(~calm(X))))&
((happy(john))=>((calm(fred)<~>~kind(fred))))&
(((~curious(lucy)|~funny(lucy)))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(((happy(susan)<~>~old(susan)))<=>((~tall(susan)&~old(susan))))&
(![X]:((~curious(X)|~brave(X))<=>~generous(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(~curious(X)<=>(~rich(X)<~>~patient(X))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:((strong(X)<~>rich(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(brave(X)|curious(X))))&
(![X]:(~funny(X)<=>(humble(X)|patient(X))))&
((?[X]:((~happy(X)&~curious(X))))<=>(?[X]:((~generous(X)&patient(X)))))&
((creative(fred)<~>~quiet(fred)))&
((strong(fred)|~quiet(fred)))&
(?[X]:((~tall(X)<~>~funny(X))))&
(?[X]:((~humble(X)|patient(X))))&
(?[X]:((tall(X)&~calm(X))))&
(?[X]:((happy(X)<~>~old(X))))&
(?[X]:((wise(X)|quiet(X)))) | ~rich(susan) | [
"p1",
"p4",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 565806066178135619511609
% SZS output start Proof for 565806066178135619511609
2. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> ~funny(X0)) [input p1]
5. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> ~happy(X0)) [input p4]
12. ! [X0] : (~curious(X0) <=> (~rich(X0) <~> ~patient(X0))) [input p11]
14. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (curious(X0) | brave(X0))) [input p13]
15. ! [X0] : (~funny(X0) <=> (patient(X0) | humble(X0))) [input p14]
16. ? [X0] : (~curious(X0) & ~happy(X0)) <=> ? [X0] : (patient(X0) & ~generous(X0)) [input p15]
24. rich(susan) [input hypothesis]
27. ? [X0] : (~curious(X0) & ~happy(X0)) <=> ? [X1] : (patient(X1) & ~generous(X1)) [rectify 16]
35. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) | strong(X0)))) [nnf transformation 2]
36. ! [X0] : (((~patient(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | patient(X0) | strong(X0))) [flattening 35]
39. ! [X0] : (((~quiet(X0) | ~humble(X0)) | happy(X0)) & (~happy(X0) | (quiet(X0) & humble(X0)))) [nnf transformation 5]
40. ! [X0] : ((~quiet(X0) | ~humble(X0) | happy(X0)) & (~happy(X0) | (quiet(X0) & humble(X0)))) [flattening 39]
53. ! [X0] : ((~curious(X0) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0)))) & (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | curious(X0))) [nnf transformation 12]
59. ! [X0] : (((~humble(X0) | ~brave(X0)) | (~curious(X0) & ~brave(X0))) & ((curious(X0) | brave(X0)) | (humble(X0) & brave(X0)))) [nnf transformation 14]
60. ! [X0] : ((~humble(X0) | ~brave(X0) | (~curious(X0) & ~brave(X0))) & (curious(X0) | brave(X0) | (humble(X0) & brave(X0)))) [flattening 59]
61. ! [X0] : ((~funny(X0) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | funny(X0))) [nnf transformation 15]
62. ! [X0] : ((~funny(X0) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | funny(X0))) [flattening 61]
63. (? [X0] : (~curious(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X1] : (patient(X1) & ~generous(X1)) | ! [X0] : (curious(X0) | happy(X0))) [nnf transformation 27]
64. (? [X0] : (~curious(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X2] : (patient(X2) & ~generous(X2)) | ! [X3] : (curious(X3) | happy(X3))) [rectify 63]
65. ? [X0] : (~curious(X0) & ~happy(X0)) => (~curious(sK4) & ~happy(sK4)) [choice axiom]
66. ? [X2] : (patient(X2) & ~generous(X2)) => (patient(sK5) & ~generous(sK5)) [choice axiom]
67. ((~curious(sK4) & ~happy(sK4)) | ! [X1] : (~patient(X1) | generous(X1))) & ((patient(sK5) & ~generous(sK5)) | ! [X3] : (curious(X3) | happy(X3))) [skolemisation 64,66,65]
89. ~patient(X0) | funny(X0) [cnf transformation 36]
96. ~happy(X0) | humble(X0) [cnf transformation 40]
123. ~rich(X0) | ~curious(X0) | patient(X0) [cnf transformation 53]
130. curious(X0) | brave(X0) | brave(X0) [cnf transformation 60]
132. ~humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
136. ~funny(X0) | ~patient(X0) [cnf transformation 62]
138. patient(sK5) | curious(X3) | happy(X3) [cnf transformation 67]
152. rich(susan) [cnf transformation 24]
153. brave(X0) | curious(X0) [duplicate literal removal 130]
154. ~brave(X0) | ~humble(X0) [duplicate literal removal 132]
258. 23 <=> ! [X3] : curious(X3) [avatar definition]
259. curious(X3) <- (23) [avatar component clause 258]
263. ~patient(X0) [subsumption resolution 136,89]
265. happy(X3) | curious(X3) [subsumption resolution 138,263]
313. ~humble(X0) | curious(X0) [resolution 154,153]
317. curious(X1) | humble(X1) [resolution 265,96]
321. curious(X1) [subsumption resolution 317,313]
322. 23 [avatar split clause 321,258]
450. ~curious(susan) | patient(susan) [resolution 123,152]
454. patient(susan) <- (23) [subsumption resolution 450,259]
455. $false <- (23) [subsumption resolution 454,263]
456. ~23 [avatar contradiction clause 455]
463. $false [avatar sat refutation 322,456]
% SZS output end Proof for 565806066178135619511609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or curious is not kind or not humble. Everyone who is not quiet or brave is not wise and vice versa. If fred is humble then someone is both strong and old and vice versa. Everyone who is not curious is creative or not curious. Everyone who is either funny or not old is either not brave or humble and vice versa. Everyone who is both not old and not calm is either not curious or not strong. If someone is both not old and happy then alice is not funny or not tall and vice versa. If someone is either not humble or not wise then someone is funny and vice versa. If someone is both not humble and not quiet then someone is either not creative or funny and vice versa. If alice is both not creative and not strong then mary is old or strong. Everyone who is not old is not wise and vice versa. If someone is wise then someone is both not creative and not strong and vice versa. If someone is either not rich or not curious then someone is wise or not curious and vice versa. Everyone who is not happy or not humble is both not strong and not creative and vice versa. If mary is both old and not funny then alice is not strong or not kind and vice versa. If someone is not patient then alice is not tall or not wise and vice versa. Susan is both rich and brave. Fred is tall or kind. Someone is tall. Someone is not brave. Fred is either strong or patient. Someone is patient. Someone is either calm or not strong. Someone is either rich or humble. | Fred is curious. | neutral | (![X]:((~calm(X)<~>curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~quiet(X)|brave(X))<=>~wise(X)))&
((humble(fred))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:(~curious(X)=>(creative(X)|~curious(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)&~calm(X))=>(~curious(X)<~>~strong(X))))&
((?[X]:((~old(X)&happy(X))))<=>((~funny(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
(((~creative(alice)&~strong(alice)))=>((old(mary)|strong(mary))))&
(![X]:(~old(X)<=>~wise(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~creative(X)&~strong(X)))))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((~happy(X)|~humble(X))<=>(~strong(X)&~creative(X))))&
(((old(mary)&~funny(mary)))<=>((~strong(alice)|~kind(alice))))&
((?[X]:(~patient(X)))<=>((~tall(alice)|~wise(alice))))&
((rich(susan)&brave(susan)))&
((tall(fred)|kind(fred)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X)))&
((strong(fred)<~>patient(fred)))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)<~>~strong(X))))&
(?[X]:((rich(X)<~>humble(X)))) | curious(fred) | [] | null | 0 |
If paul is curious then someone is either tall or funny.
If susan is not quiet then fred is either not brave or not calm.
Everyone who is calm or rich is humble and vice versa.
Everyone who is not brave or calm is both not happy and funny.
Everyone who is both not generous and funny is happy or brave and vice versa.
If fred is not creative or quiet then someone is patient and vice versa.
Everyone who is generous is either not patient or rich and vice versa.
Everyone who is happy is not funny or not brave.
Everyone who is not humble is both not calm and happy and vice versa.
Everyone who is either not funny or curious is both not patient and strong and vice versa.
Everyone who is not brave is creative.
If someone is not rich then someone is both funny and not rich.
If someone is both not wise and happy then alice is either quiet or not patient and vice versa.
Everyone who is both quiet and generous is not humble or generous.
Everyone who is not kind is either strong or brave and vice versa.
Everyone who is not wise or not happy is both not wise and calm and vice versa.
Susan is either creative or not creative.
Alice is either kind or not humble.
Someone is not generous.
Someone is both creative and generous. | Alice is not kind. | contradiction | ((curious(paul))=>(?[X]:((tall(X)<~>funny(X)))))&
((~quiet(susan))=>((~brave(fred)<~>~calm(fred))))&
(![X]:((calm(X)|rich(X))<=>humble(X)))&
(![X]:((~brave(X)|calm(X))=>(~happy(X)&funny(X))))&
(![X]:((~generous(X)&funny(X))<=>(happy(X)|brave(X))))&
(((~creative(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>rich(X))))&
(![X]:(happy(X)=>(~funny(X)|~brave(X))))&
(![X]:(~humble(X)<=>(~calm(X)&happy(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~patient(X)&strong(X))))&
(![X]:(~brave(X)=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~wise(X)&happy(X))))<=>((quiet(alice)<~>~patient(alice))))&
(![X]:((quiet(X)&generous(X))=>(~humble(X)|generous(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~wise(X)&calm(X))))&
((creative(susan)<~>~creative(susan)))&
((kind(alice)<~>~humble(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((creative(X)&generous(X)))) | ~kind(alice) | [
"p3",
"p4",
"p7",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7759161205583975599313877
% SZS output start Proof for 7759161205583975599313877
4. ! [X0] : ((calm(X0) | ~brave(X0)) => (funny(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (brave(X0) | happy(X0))) [input p4]
8. ! [X0] : (happy(X0) => (~brave(X0) | ~funny(X0))) [input p7]
9. ! [X0] : (~humble(X0) <=> (happy(X0) & ~calm(X0))) [input p8]
18. kind(alice) <~> ~humble(alice) [input p17]
21. ~kind(alice) [input hypothesis]
25. ! [X0] : ((funny(X0) & ~happy(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 4]
26. ! [X0] : ((~brave(X0) | ~funny(X0)) | ~happy(X0)) [ennf transformation 8]
27. ! [X0] : (~brave(X0) | ~funny(X0) | ~happy(X0)) [flattening 26]
38. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~funny(X0) | generous(X0))) [flattening 38]
46. ! [X0] : ((~humble(X0) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | humble(X0))) [flattening 46]
61. (humble(alice) | ~kind(alice)) & (~humble(alice) | kind(alice)) [nnf transformation 18]
73. ~happy(X0) | brave(X0) [cnf transformation 25]
75. funny(X0) | brave(X0) [cnf transformation 25]
81. funny(X0) | ~brave(X0) [cnf transformation 39]
89. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 27]
91. happy(X0) | humble(X0) [cnf transformation 47]
120. ~humble(alice) | kind(alice) [cnf transformation 61]
125. ~kind(alice) [cnf transformation 21]
154. funny(X0) [subsumption resolution 81,75]
175. ~brave(X0) | ~happy(X0) [subsumption resolution 89,154]
176. ~happy(X0) [subsumption resolution 175,73]
177. humble(X0) [subsumption resolution 91,176]
209. kind(alice) [subsumption resolution 120,177]
210. $false [subsumption resolution 125,209]
% SZS output end Proof for 7759161205583975599313877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not kind is both generous and not kind and vice versa.
Everyone who is not humble is not patient or kind.
If someone is either happy or not happy then someone is either tall or curious.
If fred is both not tall and not humble then someone is both not brave and rich.
If someone is not quiet then someone is either not rich or rich.
Everyone who is tall is not creative or not funny.
Everyone who is both old and not humble is both not funny and not calm and vice versa.
Everyone who is not strong or wise is not funny and vice versa.
Everyone who is not old or not wise is both not curious and rich.
Everyone who is either funny or not tall is both not strong and brave.
If someone is curious or not curious then someone is humble or not generous.
If alice is not patient or not generous then lucy is funny.
Everyone who is both not quiet and not old is both not creative and not calm.
If someone is old then lucy is either tall or humble and vice versa.
If someone is not kind then john is both calm and creative and vice versa.
If fred is kind then someone is funny.
Mary is either not rich or not quiet.
John is both not calm and not generous.
Someone is both not funny and tall.
Mary is both wise and tall.
Fred is either not tall or not happy.
Lucy is either patient or not brave.
Someone is either not strong or generous. | John is not patient. | contradiction | (![X]:((~patient(X)<~>~kind(X))<=>(generous(X)&~kind(X))))&
(![X]:(~humble(X)=>(~patient(X)|kind(X))))&
((?[X]:((happy(X)<~>~happy(X))))=>(?[X]:((tall(X)<~>curious(X)))))&
(((~tall(fred)&~humble(fred)))=>(?[X]:((~brave(X)&rich(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:(tall(X)=>(~creative(X)|~funny(X))))&
(![X]:((old(X)&~humble(X))<=>(~funny(X)&~calm(X))))&
(![X]:((~strong(X)|wise(X))<=>~funny(X)))&
(![X]:((~old(X)|~wise(X))=>(~curious(X)&rich(X))))&
(![X]:((funny(X)<~>~tall(X))=>(~strong(X)&brave(X))))&
((?[X]:((curious(X)|~curious(X))))=>(?[X]:((humble(X)|~generous(X)))))&
(((~patient(alice)|~generous(alice)))=>(funny(lucy)))&
(![X]:((~quiet(X)&~old(X))=>(~creative(X)&~calm(X))))&
((?[X]:(old(X)))<=>((tall(lucy)<~>humble(lucy))))&
((?[X]:(~kind(X)))<=>((calm(john)&creative(john))))&
((kind(fred))=>(?[X]:(funny(X))))&
((~rich(mary)<~>~quiet(mary)))&
((~calm(john)&~generous(john)))&
(?[X]:((~funny(X)&tall(X))))&
((wise(mary)&tall(mary)))&
((~tall(fred)<~>~happy(fred)))&
((patient(lucy)<~>~brave(lucy)))&
(?[X]:((~strong(X)<~>generous(X)))) | ~patient(john) | [
"p0",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1147310793730511239890205
% SZS output start Proof for 1147310793730511239890205
1. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> (~kind(X0) & generous(X0))) [input p0]
15. ? [X0] : ~kind(X0) <=> (creative(john) & calm(john)) [input p14]
18. ~generous(john) & ~calm(john) [input p17]
24. ~patient(john) [input hypothesis]
43. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 1]
44. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [flattening 43]
67. (? [X0] : ~kind(X0) | (~creative(john) | ~calm(john))) & ((creative(john) & calm(john)) | ! [X0] : kind(X0)) [nnf transformation 15]
68. (? [X0] : ~kind(X0) | ~creative(john) | ~calm(john)) & ((creative(john) & calm(john)) | ! [X0] : kind(X0)) [flattening 67]
69. (? [X0] : ~kind(X0) | ~creative(john) | ~calm(john)) & ((creative(john) & calm(john)) | ! [X1] : kind(X1)) [rectify 68]
70. ? [X0] : ~kind(X0) => ~kind(sK5) [choice axiom]
71. (~kind(sK5) | ~creative(john) | ~calm(john)) & ((creative(john) & calm(john)) | ! [X1] : kind(X1)) [skolemisation 69,70]
84. ~kind(X0) | ~kind(X0) | patient(X0) [cnf transformation 44]
123. calm(john) | kind(X1) [cnf transformation 71]
129. ~calm(john) [cnf transformation 18]
141. ~patient(john) [cnf transformation 24]
146. ~kind(X0) | patient(X0) [duplicate literal removal 84]
235. 20 <=> calm(john) [avatar definition]
248. 23 <=> ! [X1] : kind(X1) [avatar definition]
249. kind(X1) <- (23) [avatar component clause 248]
251. 23 | 20 [avatar split clause 123,235,248]
271. ~20 [avatar split clause 129,235]
307. patient(X0) <- (23) [resolution 146,249]
308. $false <- (23) [resolution 307,141]
311. ~23 [avatar contradiction clause 308]
312. $false [avatar sat refutation 251,271,311]
% SZS output end Proof for 1147310793730511239890205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is quiet or not creative and vice versa.
Everyone who is not humble is both funny and rich.
If someone is either humble or not curious then alice is both not humble and not curious and vice versa.
If someone is both not humble and not kind then john is not old or rich and vice versa.
Everyone who is rich is wise or not patient.
Everyone who is either patient or not patient is not generous or not wise and vice versa.
If susan is both not generous and not calm then fred is both rich and not wise.
Everyone who is not wise is rich or old and vice versa.
If lucy is not humble or not rich then someone is not quiet and vice versa.
Everyone who is both not rich and not kind is happy or rich and vice versa.
If someone is either not patient or old then lucy is not strong or humble.
If paul is not calm or brave then someone is both not old and not rich and vice versa.
Everyone who is brave or not wise is humble and vice versa.
Everyone who is not quiet or humble is both creative and not tall.
Everyone who is either not creative or generous is humble or not generous and vice versa.
Everyone who is either not funny or not quiet is either not old or curious.
Someone is not wise or calm.
Someone is either funny or not humble.
Mary is kind.
Someone is both happy and not patient.
Someone is creative or funny. | Fred is brave. | neutral | (![X]:(calm(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)=>(funny(X)&rich(X))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((~humble(alice)&~curious(alice))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~old(john)|rich(john))))&
(![X]:(rich(X)=>(wise(X)|~patient(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~generous(X)|~wise(X))))&
(((~generous(susan)&~calm(susan)))=>((rich(fred)&~wise(fred))))&
(![X]:(~wise(X)<=>(rich(X)|old(X))))&
(((~humble(lucy)|~rich(lucy)))<=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)&~kind(X))<=>(happy(X)|rich(X))))&
((?[X]:((~patient(X)<~>old(X))))=>((~strong(lucy)|humble(lucy))))&
(((~calm(paul)|brave(paul)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((brave(X)|~wise(X))<=>humble(X)))&
(![X]:((~quiet(X)|humble(X))=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(humble(X)|~generous(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(~old(X)<~>curious(X))))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(kind(mary))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((creative(X)|funny(X)))) | brave(fred) | [] | null | 0 |
Everyone who is either creative or calm is brave. If someone is either not patient or not funny then fred is both wise and strong. Everyone who is wise or not humble is not happy and vice versa. Everyone who is funny or not old is either generous or not patient and vice versa. If someone is funny then paul is wise and vice versa. If alice is both rich and tall then paul is either not calm or brave and vice versa. Everyone who is brave or not calm is both funny and not funny. If fred is both wise and not curious then someone is humble or not strong. Everyone who is either patient or not happy is not creative or generous and vice versa. If someone is not quiet then john is curious and vice versa. Everyone who is humble or patient is calm or not patient. If mary is curious then someone is not calm or not quiet and vice versa. If paul is either not quiet or kind then mary is either strong or not kind and vice versa. If someone is either not funny or not tall then someone is both happy and not kind. Everyone who is not kind or old is not calm. If someone is either not strong or creative then fred is not kind. Someone is brave or not brave. Paul is both creative and not curious. Someone is strong or happy. Someone is either not funny or not rich. Lucy is not brave or quiet. | Paul is calm. | entailment | (![X]:((creative(X)<~>calm(X))=>brave(X)))&
((?[X]:((~patient(X)<~>~funny(X))))=>((wise(fred)&strong(fred))))&
(![X]:((wise(X)|~humble(X))<=>~happy(X)))&
(![X]:((funny(X)|~old(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:(funny(X)))<=>(wise(paul)))&
(((rich(alice)&tall(alice)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((brave(X)|~calm(X))=>(funny(X)&~funny(X))))&
(((wise(fred)&~curious(fred)))=>(?[X]:((humble(X)|~strong(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>(~creative(X)|generous(X))))&
((?[X]:(~quiet(X)))<=>(curious(john)))&
(![X]:((humble(X)|patient(X))=>(calm(X)|~patient(X))))&
((curious(mary))<=>(?[X]:((~calm(X)|~quiet(X)))))&
(((~quiet(paul)<~>kind(paul)))<=>((strong(mary)<~>~kind(mary))))&
((?[X]:((~funny(X)<~>~tall(X))))=>(?[X]:((happy(X)&~kind(X)))))&
(![X]:((~kind(X)|old(X))=>~calm(X)))&
((?[X]:((~strong(X)<~>creative(X))))=>(~kind(fred)))&
(?[X]:((brave(X)|~brave(X))))&
((creative(paul)&~curious(paul)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((~funny(X)<~>~rich(X))))&
((~brave(lucy)|quiet(lucy))) | calm(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4750084513662312103514346
% SZS output start Proof for 4750084513662312103514346
7. ! [X0] : ((~calm(X0) | brave(X0)) => (~funny(X0) & funny(X0))) [input p6]
22. ~calm(paul) [input hypothesis]
26. ! [X0] : ((~funny(X0) & funny(X0)) | (calm(X0) & ~brave(X0))) [ennf transformation 7]
95. funny(X0) | calm(X0) [cnf transformation 26]
97. ~funny(X0) | calm(X0) [cnf transformation 26]
135. ~calm(paul) [cnf transformation 22]
190. calm(X0) [subsumption resolution 95,97]
294. $false [subsumption resolution 135,190]
% SZS output end Proof for 4750084513662312103514346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not wise then lucy is wise or not happy and vice versa.
Everyone who is patient is either generous or not creative.
Everyone who is calm or not quiet is both brave and not humble.
If fred is either not calm or funny then lucy is not brave.
Everyone who is both not creative and not old is either not old or quiet.
If someone is both not wise and generous then someone is tall or generous.
If someone is either generous or not humble then susan is not strong and vice versa.
Everyone who is not generous is old or not quiet and vice versa.
Everyone who is not strong or not generous is either not brave or calm and vice versa.
Everyone who is calm is rich or humble and vice versa.
Everyone who is kind is not kind or not quiet and vice versa.
If lucy is not tall then someone is both not brave and rich.
Everyone who is both curious and humble is humble.
If fred is calm or generous then someone is either not funny or wise and vice versa.
If someone is not humble or happy then someone is not strong and vice versa.
If lucy is either not brave or creative then alice is either not wise or creative and vice versa.
Someone is not wise.
Lucy is both not funny and not wise.
Someone is not humble or strong.
Fred is not funny or not patient.
Susan is not patient. | Alice is rich. | entailment | ((?[X]:((calm(X)<~>~wise(X))))<=>((wise(lucy)|~happy(lucy))))&
(![X]:(patient(X)=>(generous(X)<~>~creative(X))))&
(![X]:((calm(X)|~quiet(X))=>(brave(X)&~humble(X))))&
(((~calm(fred)<~>funny(fred)))=>(~brave(lucy)))&
(![X]:((~creative(X)&~old(X))=>(~old(X)<~>quiet(X))))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((tall(X)|generous(X)))))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~strong(susan)))&
(![X]:(~generous(X)<=>(old(X)|~quiet(X))))&
(![X]:((~strong(X)|~generous(X))<=>(~brave(X)<~>calm(X))))&
(![X]:(calm(X)<=>(rich(X)|humble(X))))&
(![X]:(kind(X)<=>(~kind(X)|~quiet(X))))&
((~tall(lucy))=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((curious(X)&humble(X))=>humble(X)))&
(((calm(fred)|generous(fred)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:(~strong(X))))&
(((~brave(lucy)<~>creative(lucy)))<=>((~wise(alice)<~>creative(alice))))&
(?[X]:(~wise(X)))&
((~funny(lucy)&~wise(lucy)))&
(?[X]:((~humble(X)|strong(X))))&
((~funny(fred)|~patient(fred)))&
(~patient(susan)) | rich(alice) | [
"p2",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4740103840619194151571318
% SZS output start Proof for 4740103840619194151571318
3. ! [X0] : ((~quiet(X0) | calm(X0)) => (~humble(X0) & brave(X0))) [input p2]
8. ! [X0] : (~generous(X0) <=> (~quiet(X0) | old(X0))) [input p7]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (~brave(X0) <~> calm(X0))) [input p8]
10. ! [X0] : (calm(X0) <=> (humble(X0) | rich(X0))) [input p9]
11. ! [X0] : (kind(X0) <=> (~quiet(X0) | ~kind(X0))) [input p10]
22. ~rich(alice) [input hypothesis]
31. ! [X0] : ((~humble(X0) & brave(X0)) | (quiet(X0) & ~calm(X0))) [ennf transformation 3]
46. ! [X0] : ((~generous(X0) | (quiet(X0) & ~old(X0))) & ((~quiet(X0) | old(X0)) | generous(X0))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | (quiet(X0) & ~old(X0))) & (~quiet(X0) | old(X0) | generous(X0))) [flattening 46]
48. ! [X0] : (((~generous(X0) | ~strong(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | (generous(X0) & strong(X0)))) [nnf transformation 9]
49. ! [X0] : ((~generous(X0) | ~strong(X0) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | (generous(X0) & strong(X0)))) [flattening 48]
50. ! [X0] : ((calm(X0) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | ~calm(X0))) [nnf transformation 10]
51. ! [X0] : ((calm(X0) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ~calm(X0))) [flattening 50]
52. ! [X0] : ((kind(X0) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 11]
53. ! [X0] : ((kind(X0) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | ~kind(X0))) [flattening 52]
76. brave(X0) | quiet(X0) [cnf transformation 31]
77. ~humble(X0) | ~calm(X0) [cnf transformation 31]
89. ~generous(X0) | quiet(X0) [cnf transformation 47]
91. ~brave(X0) | calm(X0) | generous(X0) [cnf transformation 49]
96. humble(X0) | rich(X0) | ~calm(X0) [cnf transformation 51]
98. calm(X0) | ~humble(X0) [cnf transformation 51]
99. ~quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 53]
100. kind(X0) | kind(X0) [cnf transformation 53]
123. ~rich(alice) [cnf transformation 22]
124. ~quiet(X0) | ~kind(X0) [duplicate literal removal 99]
125. kind(X0) [duplicate literal removal 100]
193. ~humble(X0) [subsumption resolution 98,77]
194. ~calm(X0) | rich(X0) [subsumption resolution 96,193]
195. ~quiet(X0) [subsumption resolution 124,125]
262. calm(X0) | generous(X0) | quiet(X0) [resolution 91,76]
264. generous(X0) | calm(X0) [subsumption resolution 262,195]
279. calm(X0) | quiet(X0) [resolution 264,89]
280. calm(X0) [subsumption resolution 279,195]
284. rich(X0) [resolution 280,194]
294. $false [resolution 284,123]
% SZS output end Proof for 4740103840619194151571318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy or not kind then someone is not brave.
If someone is not wise or not kind then alice is either not tall or not generous and vice versa.
Everyone who is quiet or brave is strong or wise and vice versa.
If someone is either generous or not funny then someone is either not generous or not happy.
Everyone who is not calm is not generous or rich and vice versa.
Everyone who is not rich is both strong and not brave.
Everyone who is both not happy and not kind is happy or funny.
Everyone who is rich or not generous is both patient and not curious and vice versa.
If someone is both not patient and not wise then mary is quiet or not brave and vice versa.
Everyone who is both not old and happy is not happy or wise and vice versa.
Everyone who is either generous or happy is both not calm and not happy and vice versa.
Everyone who is either rich or creative is not happy and vice versa.
Everyone who is both quiet and patient is both calm and tall.
Everyone who is generous or happy is not tall or brave.
If someone is creative then someone is either not calm or not funny.
Everyone who is either not old or not tall is not patient or wise.
Alice is curious.
Someone is creative.
Someone is not humble or not curious.
Someone is strong or not curious.
Someone is either happy or creative.
Someone is rich or strong. | John is not curious. | neutral | (((happy(john)|~kind(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~wise(X)|~kind(X))))<=>((~tall(alice)<~>~generous(alice))))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)|wise(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~calm(X)<=>(~generous(X)|rich(X))))&
(![X]:(~rich(X)=>(strong(X)&~brave(X))))&
(![X]:((~happy(X)&~kind(X))=>(happy(X)|funny(X))))&
(![X]:((rich(X)|~generous(X))<=>(patient(X)&~curious(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((quiet(mary)|~brave(mary))))&
(![X]:((~old(X)&happy(X))<=>(~happy(X)|wise(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)<~>creative(X))<=>~happy(X)))&
(![X]:((quiet(X)&patient(X))=>(calm(X)&tall(X))))&
(![X]:((generous(X)|happy(X))=>(~tall(X)|brave(X))))&
((?[X]:(creative(X)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((~old(X)<~>~tall(X))=>(~patient(X)|wise(X))))&
(curious(alice))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((rich(X)|strong(X)))) | ~curious(john) | [] | null | 0 |
If john is either wise or not funny then mary is not creative and vice versa.
Everyone who is either calm or not rich is not old.
If someone is both not funny and not patient then someone is not kind or tall.
If someone is either funny or wise then someone is either not kind or not strong.
Everyone who is curious is not funny or tall and vice versa.
Everyone who is curious or not calm is both wise and creative.
If alice is not generous then someone is not humble or not strong and vice versa.
Everyone who is either old or patient is both not humble and happy.
Everyone who is not generous or funny is both curious and not tall and vice versa.
Everyone who is not creative or not wise is not rich or not kind and vice versa.
If paul is either brave or not wise then someone is both not rich and tall and vice versa.
If someone is either not brave or calm then someone is patient or humble and vice versa.
Everyone who is both not strong and curious is either happy or not creative.
Everyone who is creative or quiet is either not calm or quiet.
Everyone who is not calm or not old is wise or not creative.
Everyone who is generous or quiet is not quiet or calm.
Someone is either not calm or strong.
Someone is either tall or funny.
Lucy is quiet.
Someone is both patient and creative.
Alice is either not curious or old.
Someone is either not humble or not brave.
Someone is both creative and not old.
Someone is not funny or not creative. | Lucy is wise. | entailment | (((wise(john)<~>~funny(john)))<=>(~creative(mary)))&
(![X]:((calm(X)<~>~rich(X))=>~old(X)))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((funny(X)<~>wise(X))))=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:(curious(X)<=>(~funny(X)|tall(X))))&
(![X]:((curious(X)|~calm(X))=>(wise(X)&creative(X))))&
((~generous(alice))<=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((old(X)<~>patient(X))=>(~humble(X)&happy(X))))&
(![X]:((~generous(X)|funny(X))<=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)|~wise(X))<=>(~rich(X)|~kind(X))))&
(((brave(paul)<~>~wise(paul)))<=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~strong(X)&curious(X))=>(happy(X)<~>~creative(X))))&
(![X]:((creative(X)|quiet(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)|~creative(X))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)|calm(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(quiet(lucy))&
(?[X]:((patient(X)&creative(X))))&
((~curious(alice)<~>old(alice)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~funny(X)|~creative(X)))) | wise(lucy) | [
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6619642715354458844983088
% SZS output start Proof for 6619642715354458844983088
5. ! [X0] : (curious(X0) <=> (tall(X0) | ~funny(X0))) [input p4]
6. ! [X0] : ((~calm(X0) | curious(X0)) => (creative(X0) & wise(X0))) [input p5]
9. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~tall(X0) & curious(X0))) [input p8]
25. ~wise(lucy) [input hypothesis]
32. ! [X0] : ((creative(X0) & wise(X0)) | (calm(X0) & ~curious(X0))) [ennf transformation 6]
50. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ~curious(X0))) [nnf transformation 5]
51. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~curious(X0))) [flattening 50]
57. ! [X0] : (((funny(X0) | ~generous(X0)) | (tall(X0) | ~curious(X0))) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 9]
58. ! [X0] : ((funny(X0) | ~generous(X0) | tall(X0) | ~curious(X0)) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [flattening 57]
100. curious(X0) | funny(X0) [cnf transformation 51]
102. ~curious(X0) | wise(X0) [cnf transformation 32]
114. curious(X0) | ~funny(X0) [cnf transformation 58]
158. ~wise(lucy) [cnf transformation 25]
229. curious(X0) [subsumption resolution 114,100]
331. wise(X1) [resolution 102,229]
332. $false [resolution 331,158]
% SZS output end Proof for 6619642715354458844983088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not wise then someone is both wise and not humble.
Everyone who is both curious and humble is either strong or not calm.
If someone is not strong then someone is either calm or tall and vice versa.
Everyone who is both rich and not old is either not generous or patient and vice versa.
If mary is both humble and not wise then someone is quiet and vice versa.
Everyone who is quiet or calm is not brave.
If mary is both not creative and not curious then lucy is happy or not creative and vice versa.
If paul is both not wise and funny then susan is not old and vice versa.
Everyone who is wise or rich is both quiet and not brave and vice versa.
If paul is not tall or tall then someone is not rich or not strong.
If someone is not strong or not tall then susan is both not brave and rich.
Everyone who is both humble and quiet is both creative and not old and vice versa.
If someone is both wise and brave then someone is rich.
If fred is both not old and not strong then someone is generous or humble.
If someone is both curious and not funny then paul is either not rich or not tall and vice versa.
Everyone who is not tall or tall is not tall or not strong.
Fred is either not brave or not curious.
Someone is humble or not quiet.
Mary is not funny or not tall.
Fred is patient.
John is both not generous and old.
Fred is not patient or tall.
Fred is patient or old. | John is patient. | entailment | ((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:((wise(X)&~humble(X)))))&
(![X]:((curious(X)&humble(X))=>(strong(X)<~>~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((rich(X)&~old(X))<=>(~generous(X)<~>patient(X))))&
(((humble(mary)&~wise(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)|calm(X))=>~brave(X)))&
(((~creative(mary)&~curious(mary)))<=>((happy(lucy)|~creative(lucy))))&
(((~wise(paul)&funny(paul)))<=>(~old(susan)))&
(![X]:((wise(X)|rich(X))<=>(quiet(X)&~brave(X))))&
(((~tall(paul)|tall(paul)))=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((~strong(X)|~tall(X))))=>((~brave(susan)&rich(susan))))&
(![X]:((humble(X)&quiet(X))<=>(creative(X)&~old(X))))&
((?[X]:((wise(X)&brave(X))))=>(?[X]:(rich(X))))&
(((~old(fred)&~strong(fred)))=>(?[X]:((generous(X)|humble(X)))))&
((?[X]:((curious(X)&~funny(X))))<=>((~rich(paul)<~>~tall(paul))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)|~strong(X))))&
((~brave(fred)<~>~curious(fred)))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|~tall(mary)))&
(patient(fred))&
((~generous(john)&old(john)))&
((~patient(fred)|tall(fred)))&
((patient(fred)|old(fred))) | patient(john) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4622036758971292275962762
% SZS output start Proof for 4622036758971292275962762
4. ! [X0] : ((~old(X0) & rich(X0)) <=> (~generous(X0) <~> patient(X0))) [input p3]
21. old(john) & ~generous(john) [input p20]
24. ~patient(john) [input hypothesis]
49. ! [X0] : (((~old(X0) & rich(X0)) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0)))) & (((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 4]
50. ! [X0] : (((~old(X0) & rich(X0)) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0)))) & (((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | old(X0) | ~rich(X0))) [flattening 49]
92. ~old(X0) | patient(X0) | generous(X0) [cnf transformation 50]
137. ~generous(john) [cnf transformation 21]
138. old(john) [cnf transformation 21]
141. ~patient(john) [cnf transformation 24]
368. patient(john) | generous(john) [resolution 92,138]
370. generous(john) [subsumption resolution 368,141]
371. $false [subsumption resolution 370,137]
% SZS output end Proof for 4622036758971292275962762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious is not kind or not humble.
Everyone who is not quiet or brave is not wise and vice versa.
If fred is humble then someone is both strong and old and vice versa.
Everyone who is not curious is creative or not curious.
Everyone who is either funny or not old is either not brave or humble and vice versa.
Everyone who is both not old and not calm is either not curious or not strong.
If someone is both not old and happy then alice is not funny or not tall and vice versa.
If someone is either not humble or not wise then someone is funny and vice versa.
If someone is both not humble and not quiet then someone is either not creative or funny and vice versa.
If alice is both not creative and not strong then mary is old or strong.
Everyone who is not old is not wise and vice versa.
If someone is wise then someone is both not creative and not strong and vice versa.
If someone is either not rich or not curious then someone is wise or not curious and vice versa.
Everyone who is not happy or not humble is both not strong and not creative and vice versa.
If mary is both old and not funny then alice is not strong or not kind and vice versa.
If someone is not patient then alice is not tall or not wise and vice versa.
Susan is both rich and brave.
Fred is tall or kind.
Someone is tall.
Someone is not brave.
John is either tall or calm.
Someone is patient or not kind.
Someone is humble or not old.
Alice is either funny or strong. | Susan is not creative. | neutral | (![X]:((~calm(X)<~>curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~quiet(X)|brave(X))<=>~wise(X)))&
((humble(fred))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:(~curious(X)=>(creative(X)|~curious(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)&~calm(X))=>(~curious(X)<~>~strong(X))))&
((?[X]:((~old(X)&happy(X))))<=>((~funny(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
(((~creative(alice)&~strong(alice)))=>((old(mary)|strong(mary))))&
(![X]:(~old(X)<=>~wise(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~creative(X)&~strong(X)))))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((~happy(X)|~humble(X))<=>(~strong(X)&~creative(X))))&
(((old(mary)&~funny(mary)))<=>((~strong(alice)|~kind(alice))))&
((?[X]:(~patient(X)))<=>((~tall(alice)|~wise(alice))))&
((rich(susan)&brave(susan)))&
((tall(fred)|kind(fred)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X)))&
((tall(john)<~>calm(john)))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:((humble(X)|~old(X))))&
((funny(alice)<~>strong(alice))) | ~creative(susan) | [] | null | 0 |
Everyone who is wise or strong is either not kind or happy and vice versa. If susan is curious or tall then someone is creative or strong and vice versa. If john is both not calm and not strong then susan is not curious. Everyone who is both rich and creative is not wise. Everyone who is not generous or not kind is either wise or not strong and vice versa. Everyone who is tall or not strong is not kind or not strong. Everyone who is either not tall or strong is not creative or not brave and vice versa. Everyone who is not humble is both tall and calm and vice versa. If someone is brave or not old then someone is either wise or not brave and vice versa. Everyone who is either not patient or not brave is both not kind and not rich and vice versa. Everyone who is not wise or creative is both not calm and strong. If someone is either patient or funny then john is quiet or not generous. Everyone who is both not kind and generous is not strong or not old and vice versa. Everyone who is both curious and not kind is either not wise or not happy and vice versa. Everyone who is both generous and not curious is either brave or patient and vice versa. If fred is not tall then fred is not rich or old and vice versa. Someone is quiet. Someone is either not old or not patient. Lucy is both old and not kind. Lucy is either not kind or not calm. Susan is either not generous or not tall. Someone is kind. Someone is generous or not brave. | Fred is not funny. | neutral | (![X]:((wise(X)|strong(X))<=>(~kind(X)<~>happy(X))))&
(((curious(susan)|tall(susan)))<=>(?[X]:((creative(X)|strong(X)))))&
(((~calm(john)&~strong(john)))=>(~curious(susan)))&
(![X]:((rich(X)&creative(X))=>~wise(X)))&
(![X]:((~generous(X)|~kind(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~humble(X)<=>(tall(X)&calm(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((quiet(john)|~generous(john))))&
(![X]:((~kind(X)&generous(X))<=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&~kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((generous(X)&~curious(X))<=>(brave(X)<~>patient(X))))&
((~tall(fred))<=>((~rich(fred)|old(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~patient(X))))&
((old(lucy)&~kind(lucy)))&
((~kind(lucy)<~>~calm(lucy)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)|~brave(X)))) | ~funny(fred) | [] | null | 0 |
If paul is both strong and quiet then someone is either tall or not curious.
Everyone who is both generous and curious is both curious and happy and vice versa.
If fred is either curious or happy then someone is either quiet or not curious and vice versa.
If someone is either quiet or creative then someone is either kind or humble and vice versa.
Everyone who is not rich or rich is either funny or not wise.
If mary is not calm or not quiet then someone is both old and rich.
Everyone who is either calm or not creative is either not wise or not humble.
If paul is kind or creative then fred is tall.
Everyone who is not rich is brave and vice versa.
If someone is patient then someone is generous or creative.
Everyone who is funny is not happy and vice versa.
Everyone who is not rich or not generous is either not happy or rich.
Everyone who is rich or not rich is both curious and rich.
Everyone who is kind is funny.
Everyone who is not quiet is brave or patient.
If someone is not curious or generous then someone is not strong or wise.
Paul is tall.
John is either old or not funny.
Someone is patient.
Someone is both not humble and not brave.
Someone is either not patient or curious.
Someone is either not rich or not calm. | Fred is wise. | contradiction | (((strong(paul)&quiet(paul)))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:((generous(X)&curious(X))<=>(curious(X)&happy(X))))&
(((curious(fred)<~>happy(fred)))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((~rich(X)|rich(X))=>(funny(X)<~>~wise(X))))&
(((~calm(mary)|~quiet(mary)))=>(?[X]:((old(X)&rich(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(~wise(X)<~>~humble(X))))&
(((kind(paul)|creative(paul)))=>(tall(fred)))&
(![X]:(~rich(X)<=>brave(X)))&
((?[X]:(patient(X)))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:(funny(X)<=>~happy(X)))&
(![X]:((~rich(X)|~generous(X))=>(~happy(X)<~>rich(X))))&
(![X]:((rich(X)|~rich(X))=>(curious(X)&rich(X))))&
(![X]:(kind(X)=>funny(X)))&
(![X]:(~quiet(X)=>(brave(X)|patient(X))))&
((?[X]:((~curious(X)|generous(X))))=>(?[X]:((~strong(X)|wise(X)))))&
(tall(paul))&
((old(john)<~>~funny(john)))&
(?[X]:(patient(X)))&
(?[X]:((~humble(X)&~brave(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((~rich(X)<~>~calm(X)))) | wise(fred) | [
"p1",
"p4",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7257740309502008855644900
% SZS output start Proof for 7257740309502008855644900
2. ! [X0] : ((curious(X0) & generous(X0)) <=> (happy(X0) & curious(X0))) [input p1]
5. ! [X0] : ((rich(X0) | ~rich(X0)) => (funny(X0) <~> ~wise(X0))) [input p4]
11. ! [X0] : (funny(X0) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((~generous(X0) | ~rich(X0)) => (~happy(X0) <~> rich(X0))) [input p11]
13. ! [X0] : ((~rich(X0) | rich(X0)) => (rich(X0) & curious(X0))) [input p12]
23. wise(fred) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> ~wise(X0)) | (~rich(X0) & rich(X0))) [ennf transformation 5]
35. ! [X0] : ((~happy(X0) <~> rich(X0)) | (generous(X0) & rich(X0))) [ennf transformation 12]
36. ! [X0] : ((rich(X0) & curious(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 13]
40. ! [X0] : (((curious(X0) & generous(X0)) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | (~curious(X0) | ~generous(X0)))) [nnf transformation 2]
41. ! [X0] : (((curious(X0) & generous(X0)) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | ~curious(X0) | ~generous(X0))) [flattening 40]
51. ! [X0] : (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~rich(X0) & rich(X0))) [nnf transformation 31]
59. ! [X0] : ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))) [nnf transformation 11]
60. ! [X0] : (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (generous(X0) & rich(X0))) [nnf transformation 35]
73. ~generous(X0) | ~curious(X0) | happy(X0) [cnf transformation 41]
92. ~wise(X0) | funny(X0) | rich(X0) [cnf transformation 51]
93. ~wise(X0) | funny(X0) | ~rich(X0) [cnf transformation 51]
107. ~funny(X0) | ~happy(X0) [cnf transformation 59]
112. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 60]
113. curious(X0) | ~rich(X0) [cnf transformation 36]
116. rich(X0) | rich(X0) [cnf transformation 36]
128. wise(fred) [cnf transformation 23]
129. rich(X0) [duplicate literal removal 116]
139. 3 <=> happy(fred) [avatar definition]
141. ~happy(fred) <- (~3) [avatar component clause 139]
198. ~wise(X0) | funny(X0) [subsumption resolution 92,93]
231. curious(X0) [subsumption resolution 113,129]
257. funny(fred) [resolution 198,128]
260. ~happy(fred) [resolution 257,107]
277. happy(X0) | generous(X0) [resolution 112,129]
278. generous(fred) <- (~3) [resolution 277,141]
286. ~curious(fred) | happy(fred) <- (~3) [resolution 278,73]
287. happy(fred) <- (~3) [subsumption resolution 286,231]
288. $false <- (~3) [subsumption resolution 287,141]
289. 3 [avatar contradiction clause 288]
290. ~3 [avatar split clause 260,139]
293. $false [avatar sat refutation 289,290]
% SZS output end Proof for 7257740309502008855644900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is both not creative and tall and vice versa.
If mary is both rich and wise then someone is not kind or brave.
Everyone who is either not strong or creative is either quiet or not strong.
If someone is not humble or not happy then someone is not quiet.
If susan is both not curious and not brave then someone is both happy and not wise.
Everyone who is either not wise or not calm is quiet or curious and vice versa.
Everyone who is either tall or not happy is not rich and vice versa.
Everyone who is not generous or brave is both generous and not kind.
Everyone who is either not creative or not brave is either not creative or strong and vice versa.
Everyone who is both patient and curious is strong or not wise and vice versa.
Everyone who is either humble or not old is either not generous or happy and vice versa.
Everyone who is either not humble or calm is happy.
If alice is both not old and not tall then someone is happy and vice versa.
If someone is either not brave or patient then mary is generous.
If john is not strong or not brave then someone is humble.
If alice is either wise or tall then john is either not creative or not humble and vice versa.
Mary is tall.
Someone is either funny or not brave.
Someone is either old or not old.
Someone is quiet or not patient.
Someone is either creative or not funny.
Mary is generous or happy. | John is not generous. | contradiction | (![X]:(humble(X)<=>(~creative(X)&tall(X))))&
(((rich(mary)&wise(mary)))=>(?[X]:((~kind(X)|brave(X)))))&
(![X]:((~strong(X)<~>creative(X))=>(quiet(X)<~>~strong(X))))&
((?[X]:((~humble(X)|~happy(X))))=>(?[X]:(~quiet(X))))&
(((~curious(susan)&~brave(susan)))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(quiet(X)|curious(X))))&
(![X]:((tall(X)<~>~happy(X))<=>~rich(X)))&
(![X]:((~generous(X)|brave(X))=>(generous(X)&~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~creative(X)<~>strong(X))))&
(![X]:((patient(X)&curious(X))<=>(strong(X)|~wise(X))))&
(![X]:((humble(X)<~>~old(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~humble(X)<~>calm(X))=>happy(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>(generous(mary)))&
(((~strong(john)|~brave(john)))=>(?[X]:(humble(X))))&
(((wise(alice)<~>tall(alice)))<=>((~creative(john)<~>~humble(john))))&
(tall(mary))&
(?[X]:((funny(X)<~>~brave(X))))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((creative(X)<~>~funny(X))))&
((generous(mary)|happy(mary))) | ~generous(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1725424544746512161922113
% SZS output start Proof for 1725424544746512161922113
8. ! [X0] : ((brave(X0) | ~generous(X0)) => (~kind(X0) & generous(X0))) [input p7]
23. ~generous(john) [input hypothesis]
27. ! [X0] : ((brave(X0) | ~generous(X0)) => generous(X0)) [pure predicate removal 8]
33. ! [X0] : (generous(X0) | (~brave(X0) & generous(X0))) [ennf transformation 27]
89. generous(X0) | generous(X0) [cnf transformation 33]
138. ~generous(john) [cnf transformation 23]
143. generous(X0) [duplicate literal removal 89]
265. $false [subsumption resolution 138,143]
% SZS output end Proof for 1725424544746512161922113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and tall then fred is calm or not wise.
If someone is either not calm or not funny then someone is both calm and not humble and vice versa.
Everyone who is not wise is strong or happy.
Everyone who is not tall or not creative is both not rich and strong and vice versa.
Everyone who is either not old or creative is both not kind and not curious and vice versa.
If john is either not quiet or not happy then fred is both not strong and not wise.
Everyone who is both curious and not humble 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 both not happy and humble then someone is not rich or curious and vice versa.
Someone is either not tall or not calm.
Paul is old.
Someone is not brave or not humble.
Mary is quiet or old.
Mary is creative or rich.
Someone is humble. | Lucy is tall. | entailment | (((~kind(john)&tall(john)))=>((calm(fred)|~wise(fred))))&
((?[X]:((~calm(X)<~>~funny(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~wise(X)=>(strong(X)|happy(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(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]:((~happy(X)&humble(X))))<=>(?[X]:((~rich(X)|curious(X)))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X))) | tall(lucy) | [
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7040004345997741849645384
% SZS output start Proof for 7040004345997741849645384
4. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (strong(X0) & ~rich(X0))) [input p3]
8. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p7]
16. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X0] : (curious(X0) | ~rich(X0)) [input p15]
23. ~tall(lucy) [input hypothesis]
25. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X1] : (curious(X1) | ~rich(X1)) [rectify 16]
44. ! [X0] : (((~creative(X0) | ~tall(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (creative(X0) & tall(X0)))) [nnf transformation 4]
45. ! [X0] : ((~creative(X0) | ~tall(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (creative(X0) & tall(X0)))) [flattening 44]
50. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 8]
61. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X1] : (curious(X1) | ~rich(X1)) | ! [X0] : (~humble(X0) | happy(X0))) [nnf transformation 25]
62. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X2] : (curious(X2) | ~rich(X2)) | ! [X3] : (~humble(X3) | happy(X3))) [rectify 61]
63. ? [X0] : (humble(X0) & ~happy(X0)) => (humble(sK3) & ~happy(sK3)) [choice axiom]
64. ? [X2] : (curious(X2) | ~rich(X2)) => (curious(sK4) | ~rich(sK4)) [choice axiom]
65. ((humble(sK3) & ~happy(sK3)) | ! [X1] : (~curious(X1) & rich(X1))) & ((curious(sK4) | ~rich(sK4)) | ! [X3] : (~humble(X3) | happy(X3))) [skolemisation 62,64,63]
81. ~rich(X0) | tall(X0) [cnf transformation 45]
99. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 50]
101. kind(X0) | kind(X0) | happy(X0) [cnf transformation 50]
122. ~happy(sK3) | rich(X1) [cnf transformation 65]
133. ~tall(lucy) [cnf transformation 23]
134. happy(X0) | ~kind(X0) [duplicate literal removal 99]
135. kind(X0) | happy(X0) [duplicate literal removal 101]
200. happy(X0) [subsumption resolution 134,135]
255. 25 <=> ! [X1] : rich(X1) [avatar definition]
256. rich(X1) <- (25) [avatar component clause 255]
260. rich(X1) [subsumption resolution 122,200]
261. 25 [avatar split clause 260,255]
284. tall(X0) <- (25) [resolution 81,256]
285. $false <- (25) [resolution 284,133]
286. ~25 [avatar contradiction clause 285]
287. $false [avatar sat refutation 261,286]
% SZS output end Proof for 7040004345997741849645384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not old or curious then someone is wise and vice versa.
If someone is patient or not tall then someone is either not strong or not kind and vice versa.
Everyone who is not generous or not humble is not kind or not creative.
Everyone who is creative or not curious is both patient and not old.
If alice is not calm then mary is calm.
Everyone who is old or not humble is not curious and vice versa.
If mary is either generous or creative then paul is both not happy and not wise.
Everyone who is both rich and curious is not generous and vice versa.
Everyone who is not patient or calm is wise or not generous.
If someone is both not rich and not kind then someone is both funny and not wise.
Everyone who is not calm is either curious or not strong and vice versa.
Everyone who is either not calm or not generous is not brave or not rich and vice versa.
If lucy is not old then someone is not kind and vice versa.
Everyone who is either happy or not humble is not happy and vice versa.
Everyone who is not humble or tall is either not brave or quiet.
Mary is either tall or not generous.
Someone is not happy.
Someone is not old.
Alice is not funny or not humble.
Lucy is not brave. | Mary is not generous. | contradiction | (((~old(alice)<~>curious(alice)))<=>(?[X]:(wise(X))))&
((?[X]:((patient(X)|~tall(X))))<=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~generous(X)|~humble(X))=>(~kind(X)|~creative(X))))&
(![X]:((creative(X)|~curious(X))=>(patient(X)&~old(X))))&
((~calm(alice))=>(calm(mary)))&
(![X]:((old(X)|~humble(X))<=>~curious(X)))&
(((generous(mary)<~>creative(mary)))=>((~happy(paul)&~wise(paul))))&
(![X]:((rich(X)&curious(X))<=>~generous(X)))&
(![X]:((~patient(X)|calm(X))=>(wise(X)|~generous(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:(~calm(X)<=>(curious(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~happy(X)))&
(![X]:((~humble(X)|tall(X))=>(~brave(X)<~>quiet(X))))&
((tall(mary)<~>~generous(mary)))&
(?[X]:(~happy(X)))&
(?[X]:(~old(X)))&
((~funny(alice)|~humble(alice)))&
(~brave(lucy)) | ~generous(mary) | [
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 869452490446869331120356
% SZS output start Proof for 869452490446869331120356
6. ! [X0] : ((~humble(X0) | old(X0)) <=> ~curious(X0)) [input p5]
8. ! [X0] : ((curious(X0) & rich(X0)) <=> ~generous(X0)) [input p7]
14. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> ~happy(X0)) [input p13]
21. ~generous(mary) [input hypothesis]
42. ! [X0] : (((~humble(X0) | old(X0)) | curious(X0)) & (~curious(X0) | (humble(X0) & ~old(X0)))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | old(X0) | curious(X0)) & (~curious(X0) | (humble(X0) & ~old(X0)))) [flattening 42]
45. ! [X0] : (((curious(X0) & rich(X0)) | generous(X0)) & (~generous(X0) | (~curious(X0) | ~rich(X0)))) [nnf transformation 8]
46. ! [X0] : (((curious(X0) & rich(X0)) | generous(X0)) & (~generous(X0) | ~curious(X0) | ~rich(X0))) [flattening 45]
57. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 14]
82. ~curious(X0) | humble(X0) [cnf transformation 43]
90. generous(X0) | curious(X0) [cnf transformation 46]
107. ~happy(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 57]
109. ~humble(X0) | happy(X0) | happy(X0) [cnf transformation 57]
121. ~generous(mary) [cnf transformation 21]
122. ~happy(X0) | ~humble(X0) [duplicate literal removal 107]
123. ~humble(X0) | happy(X0) [duplicate literal removal 109]
193. 16 <=> generous(mary) [avatar definition]
194. ~generous(mary) <- (~16) [avatar component clause 193]
224. ~humble(X0) [subsumption resolution 122,123]
233. ~16 [avatar split clause 121,193]
234. curious(mary) <- (~16) [resolution 90,194]
235. humble(mary) <- (~16) [resolution 234,82]
236. $false <- (~16) [subsumption resolution 235,224]
237. 16 [avatar contradiction clause 236]
238. $false [avatar sat refutation 233,237]
% SZS output end Proof for 869452490446869331120356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not wise and not patient then someone is not old or not rich and vice versa.
Everyone who is either brave or not patient is either happy or funny and vice versa.
Everyone who is brave or not curious is both patient and generous.
Everyone who is both not tall and tall is happy or not calm and vice versa.
Everyone who is either calm or old is both not curious and funny and vice versa.
If paul is not strong then someone is either not quiet or funny and vice versa.
If alice is either calm or happy then mary is both tall and strong and vice versa.
If someone is not rich or brave then alice is not patient or not humble.
Everyone who is rich is both kind and not humble and vice versa.
If paul is wise or kind then alice is both funny and not generous and vice versa.
If fred is not generous then someone is not rich or not old and vice versa.
If alice is both brave and not curious then alice is both brave and not creative.
If someone is not rich then someone is either funny or not rich.
If paul is strong then john is humble and vice versa.
If someone is patient then someone is either creative or not patient and vice versa.
Everyone who is strong or not calm is generous.
Lucy is both quiet and strong.
Someone is not strong or rich.
Paul is not creative or not quiet.
Someone is wise or curious.
Paul is either creative or funny.
John is not tall or not rich.
Alice is patient or not old.
Paul is both not patient and not brave. | Alice is patient. | entailment | (((~wise(susan)&~patient(susan)))<=>(?[X]:((~old(X)|~rich(X)))))&
(![X]:((brave(X)<~>~patient(X))<=>(happy(X)<~>funny(X))))&
(![X]:((brave(X)|~curious(X))=>(patient(X)&generous(X))))&
(![X]:((~tall(X)&tall(X))<=>(happy(X)|~calm(X))))&
(![X]:((calm(X)<~>old(X))<=>(~curious(X)&funny(X))))&
((~strong(paul))<=>(?[X]:((~quiet(X)<~>funny(X)))))&
(((calm(alice)<~>happy(alice)))<=>((tall(mary)&strong(mary))))&
((?[X]:((~rich(X)|brave(X))))=>((~patient(alice)|~humble(alice))))&
(![X]:(rich(X)<=>(kind(X)&~humble(X))))&
(((wise(paul)|kind(paul)))<=>((funny(alice)&~generous(alice))))&
((~generous(fred))<=>(?[X]:((~rich(X)|~old(X)))))&
(((brave(alice)&~curious(alice)))=>((brave(alice)&~creative(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)<~>~rich(X)))))&
((strong(paul))<=>(humble(john)))&
((?[X]:(patient(X)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((strong(X)|~calm(X))=>generous(X)))&
((quiet(lucy)&strong(lucy)))&
(?[X]:((~strong(X)|rich(X))))&
((~creative(paul)|~quiet(paul)))&
(?[X]:((wise(X)|curious(X))))&
((creative(paul)<~>funny(paul)))&
((~tall(john)|~rich(john)))&
((patient(alice)|~old(alice)))&
((~patient(paul)&~brave(paul))) | patient(alice) | [
"p2",
"p3",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4952776610602896040689369
% SZS output start Proof for 4952776610602896040689369
3. ! [X0] : ((~curious(X0) | brave(X0)) => (generous(X0) & patient(X0))) [input p2]
4. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | happy(X0))) [input p3]
5. ! [X0] : ((calm(X0) <~> old(X0)) <=> (funny(X0) & ~curious(X0))) [input p4]
23. ~old(alice) | patient(alice) [input p22]
25. ~patient(alice) [input hypothesis]
28. ! [X0] : ((generous(X0) & patient(X0)) | (curious(X0) & ~brave(X0))) [ennf transformation 3]
41. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 4]
42. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | ~tall(X0) | tall(X0))) [flattening 41]
43. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [flattening 43]
88. curious(X0) | patient(X0) [cnf transformation 28]
93. ~tall(X0) | calm(X0) [cnf transformation 42]
95. calm(X0) | tall(X0) [cnf transformation 42]
96. ~curious(X0) | old(X0) | ~calm(X0) [cnf transformation 44]
145. ~old(alice) | patient(alice) [cnf transformation 23]
148. ~patient(alice) [cnf transformation 25]
176. calm(X0) [subsumption resolution 93,95]
180. ~curious(X0) | old(X0) [subsumption resolution 96,176]
211. 13 <=> patient(alice) [avatar definition]
213. ~patient(alice) <- (~13) [avatar component clause 211]
353. 43 <=> old(alice) [avatar definition]
355. ~old(alice) <- (~43) [avatar component clause 353]
356. 13 | ~43 [avatar split clause 145,353,211]
357. ~13 [avatar split clause 148,211]
369. old(X0) | patient(X0) [resolution 180,88]
412. patient(alice) <- (~43) [resolution 369,355]
414. $false <- (~13, ~43) [subsumption resolution 412,213]
415. 13 | 43 [avatar contradiction clause 414]
418. $false [avatar sat refutation 356,357,415]
% SZS output end Proof for 4952776610602896040689369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is old or not rich then someone is not patient and vice versa. Everyone who is both not generous and tall is both not funny and humble and vice versa. Everyone who is either not old or patient is not generous and vice versa. Everyone who is both not brave and not patient is either not patient or not wise and vice versa. Everyone who is either calm or funny is both not kind and not happy and vice versa. Everyone who is either not funny or happy is generous or rich and vice versa. If paul is patient or not happy then someone is either quiet or not rich. If someone is both not kind and generous then fred is humble or not quiet. Everyone who is either not tall or happy is quiet and vice versa. Everyone who is both not quiet and not generous is both not generous and funny. Everyone who is both wise and tall is either curious or generous. If someone is either generous or funny then someone is both kind and not strong and vice versa. If someone is both not strong and old then paul is both not generous and curious. Everyone who is not quiet is either patient or calm. Everyone who is funny is brave and vice versa. Everyone who is not humble or happy is either not patient or not wise. John is either curious or not kind. John is both wise and not curious. Someone is both happy and tall. Someone is not old. Someone is both not generous and not rich. Someone is curious. Someone is not rich or quiet. Someone is not curious. | Paul is humble. | neutral | ((?[X]:((old(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~generous(X)&tall(X))<=>(~funny(X)&humble(X))))&
(![X]:((~old(X)<~>patient(X))<=>~generous(X)))&
(![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>~wise(X))))&
(![X]:((calm(X)<~>funny(X))<=>(~kind(X)&~happy(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(generous(X)|rich(X))))&
(((patient(paul)|~happy(paul)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&generous(X))))=>((humble(fred)|~quiet(fred))))&
(![X]:((~tall(X)<~>happy(X))<=>quiet(X)))&
(![X]:((~quiet(X)&~generous(X))=>(~generous(X)&funny(X))))&
(![X]:((wise(X)&tall(X))=>(curious(X)<~>generous(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((~strong(X)&old(X))))=>((~generous(paul)&curious(paul))))&
(![X]:(~quiet(X)=>(patient(X)<~>calm(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~humble(X)|happy(X))=>(~patient(X)<~>~wise(X))))&
((curious(john)<~>~kind(john)))&
((wise(john)&~curious(john)))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:(~curious(X))) | humble(paul) | [] | null | 0 |
Everyone who is calm or old is both brave and not happy and vice versa. Everyone who is both not calm and old is either strong or not strong and vice versa. If john is either not curious or not wise then someone is both generous and old and vice versa. Everyone who is either patient or not quiet is not calm or curious. If john is either wise or brave then alice is either generous or humble and vice versa. Everyone who is not rich or funny is not happy and vice versa. Everyone who is not rich or strong is old. If someone is either not happy or strong then john is both not wise and brave. If someone is both wise and not wise then someone is not patient and vice versa. If john is either not generous or not happy then lucy is both not rich and generous. Everyone who is either quiet or brave is either tall or wise and vice versa. If someone is not tall then someone is strong or not brave. Everyone who is either old or not curious is both old and calm. If paul is tall then lucy is both not wise and generous and vice versa. Everyone who is either tall or not old is either happy or not creative and vice versa. If someone is either not patient or not generous then someone is not old or not quiet and vice versa. Alice is either not strong or generous. John is both not tall and quiet. Someone is both not tall and not strong. Susan is kind. Paul is funny. Lucy is both tall and strong. Lucy is not calm. Someone is rich. | Alice is calm. | contradiction | (![X]:((calm(X)|old(X))<=>(brave(X)&~happy(X))))&
(![X]:((~calm(X)&old(X))<=>(strong(X)<~>~strong(X))))&
(((~curious(john)<~>~wise(john)))<=>(?[X]:((generous(X)&old(X)))))&
(![X]:((patient(X)<~>~quiet(X))=>(~calm(X)|curious(X))))&
(((wise(john)<~>brave(john)))<=>((generous(alice)<~>humble(alice))))&
(![X]:((~rich(X)|funny(X))<=>~happy(X)))&
(![X]:((~rich(X)|strong(X))=>old(X)))&
((?[X]:((~happy(X)<~>strong(X))))=>((~wise(john)&brave(john))))&
((?[X]:((wise(X)&~wise(X))))<=>(?[X]:(~patient(X))))&
(((~generous(john)<~>~happy(john)))=>((~rich(lucy)&generous(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(tall(X)<~>wise(X))))&
((?[X]:(~tall(X)))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((old(X)<~>~curious(X))=>(old(X)&calm(X))))&
((tall(paul))<=>((~wise(lucy)&generous(lucy))))&
(![X]:((tall(X)<~>~old(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(?[X]:((~old(X)|~quiet(X)))))&
((~strong(alice)<~>generous(alice)))&
((~tall(john)&quiet(john)))&
(?[X]:((~tall(X)&~strong(X))))&
(kind(susan))&
(funny(paul))&
((tall(lucy)&strong(lucy)))&
(~calm(lucy))&
(?[X]:(rich(X))) | calm(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 425411123306931918080973
% SZS output start Proof for 425411123306931918080973
2. ! [X0] : ((old(X0) & ~calm(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p1]
25. calm(alice) [input hypothesis]
39. ! [X0] : (((old(X0) & ~calm(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~old(X0) | calm(X0)))) [nnf transformation 2]
40. ! [X0] : (((old(X0) & ~calm(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~old(X0) | calm(X0))) [flattening 39]
81. ~calm(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
82. ~calm(X0) | strong(X0) | strong(X0) [cnf transformation 40]
158. calm(alice) [cnf transformation 25]
160. ~calm(X0) | ~strong(X0) [duplicate literal removal 81]
161. ~calm(X0) | strong(X0) [duplicate literal removal 82]
165. ~calm(X0) [subsumption resolution 160,161]
306. $false [subsumption resolution 158,165]
% SZS output end Proof for 425411123306931918080973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not strong is not curious or humble.
Everyone who is both calm and rich is not curious.
Everyone who is not quiet or not tall is generous or not rich and vice versa.
If alice is either generous or not wise then someone is not strong or not curious and vice versa.
If susan is either not creative or funny then john is not generous or not humble and vice versa.
Everyone who is both not funny and not creative is either strong or curious and vice versa.
Everyone who is both not creative and not brave is old or not humble.
Everyone who is either kind or humble is either creative or not happy.
If john is tall then lucy is either not creative or not humble.
If someone is either humble or not brave then lucy is not strong or not quiet.
If someone is either not creative or not happy then alice is either calm or old.
If lucy is both humble and not strong then susan is not humble or quiet.
Everyone who is either not curious or not quiet is not patient.
Everyone who is either not brave or funny is not rich or creative.
Everyone who is not quiet is both not quiet and not happy.
Everyone who is both not creative and not quiet is patient or not strong and vice versa.
John is both not brave and not curious.
John is calm or quiet.
Someone is not quiet or happy.
Someone is happy.
Mary is either calm or curious.
Someone is both brave and not humble.
Someone is curious or creative.
Someone is not humble or creative. | Susan is not creative. | neutral | (![X]:((generous(X)<~>~strong(X))=>(~curious(X)|humble(X))))&
(![X]:((calm(X)&rich(X))=>~curious(X)))&
(![X]:((~quiet(X)|~tall(X))<=>(generous(X)|~rich(X))))&
(((generous(alice)<~>~wise(alice)))<=>(?[X]:((~strong(X)|~curious(X)))))&
(((~creative(susan)<~>funny(susan)))<=>((~generous(john)|~humble(john))))&
(![X]:((~funny(X)&~creative(X))<=>(strong(X)<~>curious(X))))&
(![X]:((~creative(X)&~brave(X))=>(old(X)|~humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(creative(X)<~>~happy(X))))&
((tall(john))=>((~creative(lucy)<~>~humble(lucy))))&
((?[X]:((humble(X)<~>~brave(X))))=>((~strong(lucy)|~quiet(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>((calm(alice)<~>old(alice))))&
(((humble(lucy)&~strong(lucy)))=>((~humble(susan)|quiet(susan))))&
(![X]:((~curious(X)<~>~quiet(X))=>~patient(X)))&
(![X]:((~brave(X)<~>funny(X))=>(~rich(X)|creative(X))))&
(![X]:(~quiet(X)=>(~quiet(X)&~happy(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(patient(X)|~strong(X))))&
((~brave(john)&~curious(john)))&
((calm(john)|quiet(john)))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:(happy(X)))&
((calm(mary)<~>curious(mary)))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~humble(X)|creative(X)))) | ~creative(susan) | [] | null | 0 |
Everyone who is either curious or not rich is either not creative or not humble. Everyone who is patient or not humble is both kind and funny. Everyone who is either quiet or not happy is tall. If someone is kind or not creative then mary is both funny and happy and vice versa. If someone is tall or creative then lucy is creative and vice versa. If someone is either humble or not strong then someone is patient and vice versa. Everyone who is wise or humble is creative and vice versa. Everyone who is not creative or kind is both not curious and happy. If alice is either not brave or not calm then john is strong and vice versa. If susan is both not calm and not creative then alice is both happy and wise and vice versa. Everyone who is not strong or not kind is both not happy and tall. If someone is not patient or not calm then someone is not quiet and vice versa. Everyone who is either not tall or not brave is both rich and not creative and vice versa. Everyone who is calm is both wise and not tall and vice versa. If mary is not calm or humble then someone is not patient. If someone is not funny then alice is either not humble or quiet. Someone is both not curious and not brave. Someone is not brave or strong. Susan is curious. Someone is both not creative and not curious. Someone is curious or not generous. Someone is both not old and not humble. | Alice is not calm. | entailment | (![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&tall(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~tall(X)<~>~brave(X))<=>(rich(X)&~creative(X))))&
(![X]:(calm(X)<=>(wise(X)&~tall(X))))&
(((~calm(mary)|humble(mary)))=>(?[X]:(~patient(X))))&
((?[X]:(~funny(X)))=>((~humble(alice)<~>quiet(alice))))&
(?[X]:((~curious(X)&~brave(X))))&
(?[X]:((~brave(X)|strong(X))))&
(curious(susan))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~old(X)&~humble(X)))) | ~calm(alice) | [
"p7",
"p9",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6242803791735134334562744
% SZS output start Proof for 6242803791735134334562744
8. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p7]
10. (~creative(susan) & ~calm(susan)) <=> (wise(alice) & happy(alice)) [input p9]
11. ! [X0] : ((~kind(X0) | ~strong(X0)) => (tall(X0) & ~happy(X0))) [input p10]
14. ! [X0] : (calm(X0) <=> (~tall(X0) & wise(X0))) [input p13]
19. curious(susan) [input p18]
23. calm(alice) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 8]
32. ! [X0] : ((tall(X0) & ~happy(X0)) | (kind(X0) & strong(X0))) [ennf transformation 11]
54. ((~creative(susan) & ~calm(susan)) | (~wise(alice) | ~happy(alice))) & ((wise(alice) & happy(alice)) | (creative(susan) | calm(susan))) [nnf transformation 10]
55. ((~creative(susan) & ~calm(susan)) | ~wise(alice) | ~happy(alice)) & ((wise(alice) & happy(alice)) | creative(susan) | calm(susan)) [flattening 54]
63. ! [X0] : ((calm(X0) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | ~calm(X0))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | ~calm(X0))) [flattening 63]
101. ~curious(X0) | creative(X0) [cnf transformation 31]
104. ~kind(X0) | happy(X0) [cnf transformation 31]
112. ~creative(susan) | ~wise(alice) | ~happy(alice) [cnf transformation 55]
116. tall(X0) | kind(X0) [cnf transformation 32]
126. ~calm(X0) | wise(X0) [cnf transformation 64]
127. ~calm(X0) | ~tall(X0) [cnf transformation 64]
136. curious(susan) [cnf transformation 19]
140. calm(alice) [cnf transformation 23]
223. 20 <=> calm(alice) [avatar definition]
225. calm(alice) <- (20) [avatar component clause 223]
231. 21 <=> happy(alice) [avatar definition]
233. ~happy(alice) <- (~21) [avatar component clause 231]
235. 22 <=> wise(alice) [avatar definition]
239. 23 <=> creative(susan) [avatar definition]
242. ~21 | ~22 | ~23 [avatar split clause 112,239,235,231]
310. 20 [avatar split clause 140,223]
318. creative(susan) [resolution 101,136]
321. 23 [avatar split clause 318,239]
336. wise(alice) <- (20) [resolution 126,225]
337. ~tall(alice) <- (20) [resolution 127,225]
338. kind(alice) <- (20) [resolution 337,116]
365. 22 | ~20 [avatar split clause 336,223,235]
440. happy(alice) <- (20) [resolution 338,104]
442. $false <- (20, ~21) [subsumption resolution 440,233]
443. ~20 | 21 [avatar contradiction clause 442]
444. $false [avatar sat refutation 242,310,321,365,443]
% SZS output end Proof for 6242803791735134334562744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and not humble then someone is old or rich. Everyone who is funny or creative is not tall or not brave. Everyone who is either not calm or rich is patient. Everyone who is both funny and not rich is not kind or not rich. If someone is not wise or funny then someone is humble and vice versa. Everyone who is creative is both quiet and not funny. Everyone who is creative is generous or not happy and vice versa. Everyone who is not happy is creative or strong and vice versa. If lucy is not creative or patient then someone is either funny or rich and vice versa. Everyone who is both not strong and humble is both not generous and funny and vice versa. If someone is both not rich and creative then paul is patient or not strong. Everyone who is either not wise or not old is both not generous and not old. Everyone who is either humble or not old is both not brave and strong. If someone is both not strong and not rich then susan is both generous and quiet. Everyone who is strong is both patient and strong and vice versa. Everyone who is both tall and humble is not tall and vice versa. Someone is either not calm or old. Someone is not calm or not old. Someone is old or not old. Paul is not strong. Someone is not kind or not curious. Someone is calm. Someone is not patient. | Lucy is not humble. | entailment | ((?[X]:((kind(X)&~humble(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((funny(X)|creative(X))=>(~tall(X)|~brave(X))))&
(![X]:((~calm(X)<~>rich(X))=>patient(X)))&
(![X]:((funny(X)&~rich(X))=>(~kind(X)|~rich(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:(humble(X))))&
(![X]:(creative(X)=>(quiet(X)&~funny(X))))&
(![X]:(creative(X)<=>(generous(X)|~happy(X))))&
(![X]:(~happy(X)<=>(creative(X)|strong(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)<~>rich(X)))))&
(![X]:((~strong(X)&humble(X))<=>(~generous(X)&funny(X))))&
((?[X]:((~rich(X)&creative(X))))=>((patient(paul)|~strong(paul))))&
(![X]:((~wise(X)<~>~old(X))=>(~generous(X)&~old(X))))&
(![X]:((humble(X)<~>~old(X))=>(~brave(X)&strong(X))))&
((?[X]:((~strong(X)&~rich(X))))=>((generous(susan)&quiet(susan))))&
(![X]:(strong(X)<=>(patient(X)&strong(X))))&
(![X]:((tall(X)&humble(X))<=>~tall(X)))&
(?[X]:((~calm(X)<~>old(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((old(X)|~old(X))))&
(~strong(paul))&
(?[X]:((~kind(X)|~curious(X))))&
(?[X]:(calm(X)))&
(?[X]:(~patient(X))) | ~humble(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2751126862281841660830308
% SZS output start Proof for 2751126862281841660830308
16. ! [X0] : ((humble(X0) & tall(X0)) <=> ~tall(X0)) [input p15]
24. humble(lucy) [input hypothesis]
62. ! [X0] : (((humble(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) | ~tall(X0)))) [nnf transformation 16]
63. ! [X0] : (((humble(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | ~humble(X0) | ~tall(X0))) [flattening 62]
108. ~tall(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 63]
109. tall(X0) | tall(X0) [cnf transformation 63]
118. humble(lucy) [cnf transformation 24]
119. ~tall(X0) | ~humble(X0) [duplicate literal removal 108]
120. tall(X0) [duplicate literal removal 109]
123. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
124. ~humble(X1) <- (1) [avatar component clause 123]
194. ~humble(X0) [subsumption resolution 119,120]
195. 1 [avatar split clause 194,123]
216. $false <- (1) [resolution 124,118]
217. ~1 [avatar contradiction clause 216]
218. $false [avatar sat refutation 195,217]
% SZS output end Proof for 2751126862281841660830308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong then susan is both not curious and not strong.
Everyone who is not generous is either patient or not generous and vice versa.
If someone is not curious then lucy is both not kind and not creative and vice versa.
If someone is both patient and strong then mary is not tall.
If paul is humble then alice is not patient or wise.
If someone is both not happy and wise then alice is strong or not strong.
Everyone who is both not humble and patient is not creative and vice versa.
Everyone who is both not tall and generous is either not curious or not humble and vice versa.
Everyone who is either old or not curious is both not funny and creative and vice versa.
If mary is not humble or patient then fred is tall or old and vice versa.
If fred is kind then someone is both creative and brave and vice versa.
Everyone who is not creative or not calm is either funny or brave.
If someone is either not rich or rich then alice is not calm.
If paul is not funny or rich then susan is old and vice versa.
If fred is patient or creative then alice is strong.
Everyone who is not happy is both funny and not curious.
Paul is kind or brave.
John is both not calm and not quiet.
Someone is either patient or calm.
Someone is either not patient or generous.
Someone is not old.
Paul is not old or brave.
Someone is funny. | John is not strong. | contradiction | ((?[X]:((~wise(X)|~strong(X))))=>((~curious(susan)&~strong(susan))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
((?[X]:(~curious(X)))<=>((~kind(lucy)&~creative(lucy))))&
((?[X]:((patient(X)&strong(X))))=>(~tall(mary)))&
((humble(paul))=>((~patient(alice)|wise(alice))))&
((?[X]:((~happy(X)&wise(X))))=>((strong(alice)|~strong(alice))))&
(![X]:((~humble(X)&patient(X))<=>~creative(X)))&
(![X]:((~tall(X)&generous(X))<=>(~curious(X)<~>~humble(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~funny(X)&creative(X))))&
(((~humble(mary)|patient(mary)))<=>((tall(fred)|old(fred))))&
((kind(fred))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:((~creative(X)|~calm(X))=>(funny(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>(~calm(alice)))&
(((~funny(paul)|rich(paul)))<=>(old(susan)))&
(((patient(fred)|creative(fred)))=>(strong(alice)))&
(![X]:(~happy(X)=>(funny(X)&~curious(X))))&
((kind(paul)|brave(paul)))&
((~calm(john)&~quiet(john)))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:(~old(X)))&
((~old(paul)|brave(paul)))&
(?[X]:(funny(X))) | ~strong(john) | [
"p0",
"p1",
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2995375432934032449681916
% SZS output start Proof for 2995375432934032449681916
1. ? [X0] : (~strong(X0) | ~wise(X0)) => (~strong(susan) & ~curious(susan)) [input p0]
2. ! [X0] : (~generous(X0) <=> (patient(X0) <~> ~generous(X0))) [input p1]
3. ? [X0] : ~curious(X0) <=> (~creative(lucy) & ~kind(lucy)) [input p2]
7. ! [X0] : ((patient(X0) & ~humble(X0)) <=> ~creative(X0)) [input p6]
24. ~strong(john) [input hypothesis]
28. ? [X0] : ~strong(X0) => (~strong(susan) & ~curious(susan)) [pure predicate removal 1]
30. (~strong(susan) & ~curious(susan)) | ! [X0] : strong(X0) [ennf transformation 28]
35. ! [X0] : ((~generous(X0) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | generous(X0))) [nnf transformation 2]
36. (? [X0] : ~curious(X0) | (creative(lucy) | kind(lucy))) & ((~creative(lucy) & ~kind(lucy)) | ! [X0] : curious(X0)) [nnf transformation 3]
37. (? [X0] : ~curious(X0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X0] : curious(X0)) [flattening 36]
38. (? [X0] : ~curious(X0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X1] : curious(X1)) [rectify 37]
39. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
40. (~curious(sK0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X1] : curious(X1)) [skolemisation 38,39]
41. ! [X0] : (((patient(X0) & ~humble(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) | humble(X0)))) [nnf transformation 7]
42. ! [X0] : (((patient(X0) & ~humble(X0)) | creative(X0)) & (~creative(X0) | ~patient(X0) | humble(X0))) [flattening 41]
67. ~curious(susan) | strong(X0) [cnf transformation 30]
70. generous(X0) | ~patient(X0) | generous(X0) [cnf transformation 35]
71. ~generous(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 35]
74. ~creative(lucy) | curious(X1) [cnf transformation 40]
79. patient(X0) | creative(X0) [cnf transformation 42]
119. ~strong(john) [cnf transformation 24]
122. generous(X0) | ~patient(X0) [duplicate literal removal 70]
123. ~generous(X0) | ~patient(X0) [duplicate literal removal 71]
125. 1 <=> ! [X0] : strong(X0) [avatar definition]
126. strong(X0) <- (1) [avatar component clause 125]
133. 3 <=> curious(susan) [avatar definition]
135. ~curious(susan) <- (~3) [avatar component clause 133]
136. 1 | ~3 [avatar split clause 67,133,125]
137. ~patient(X0) [subsumption resolution 122,123]
143. 5 <=> creative(lucy) [avatar definition]
144. ~creative(lucy) <- (~5) [avatar component clause 143]
152. 7 <=> ! [X1] : curious(X1) [avatar definition]
153. curious(X1) <- (7) [avatar component clause 152]
154. 7 | ~5 [avatar split clause 74,143,152]
156. creative(X0) [subsumption resolution 79,137]
234. $false <- (~5) [subsumption resolution 144,156]
235. 5 [avatar contradiction clause 234]
236. $false <- (~3, 7) [resolution 153,135]
239. 3 | ~7 [avatar contradiction clause 236]
240. $false <- (1) [resolution 126,119]
243. ~1 [avatar contradiction clause 240]
244. $false [avatar sat refutation 136,154,235,239,243]
% SZS output end Proof for 2995375432934032449681916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not old and vice versa.
If paul is not creative then someone is either old or wise and vice versa.
Everyone who is both not happy and not patient is either old or not happy and vice versa.
If mary is either not brave or brave then lucy is not funny.
If someone is either generous or old then someone is either creative or wise and vice versa.
Everyone who is not kind or not curious is either not generous or not happy.
Everyone who is not old or funny is not calm and vice versa.
If someone is both rich and not curious then someone is either not kind or brave and vice versa.
If someone is humble then someone is funny.
If alice is kind then alice is either creative or kind and vice versa.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
Alice is not kind or not strong.
Mary is wise or not curious.
Someone is both curious and humble.
Lucy is not creative.
Lucy is either not generous or humble.
Fred is either creative or not wise.
Someone is either not quiet or patient. | Lucy is calm. | entailment | (![X]:(brave(X)<=>~old(X)))&
((~creative(paul))<=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~brave(mary)<~>brave(mary)))=>(~funny(lucy)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|funny(X))<=>~calm(X)))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((kind(alice))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
((~kind(alice)|~strong(alice)))&
((wise(mary)|~curious(mary)))&
(?[X]:((curious(X)&humble(X))))&
(~creative(lucy))&
((~generous(lucy)<~>humble(lucy)))&
((creative(fred)<~>~wise(fred)))&
(?[X]:((~quiet(X)<~>patient(X)))) | calm(lucy) | [
"p2",
"p3",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6619892791449349982763954
% SZS output start Proof for 6619892791449349982763954
3. ! [X0] : ((~patient(X0) & ~happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p2]
4. (~brave(mary) <~> brave(mary)) => ~funny(lucy) [input p3]
14. ! [X0] : ((generous(X0) | creative(X0)) <=> (happy(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (~calm(X0) <~> funny(X0))) [input p14]
16. ! [X0] : ((curious(X0) | generous(X0)) => patient(X0)) [input p15]
24. ~calm(lucy) [input hypothesis]
28. ~funny(lucy) | (~brave(mary) <=> brave(mary)) [ennf transformation 4]
33. ! [X0] : (patient(X0) | (~curious(X0) & ~generous(X0))) [ennf transformation 16]
39. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (patient(X0) | happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | patient(X0) | happy(X0))) [flattening 39]
41. ~funny(lucy) | ((~brave(mary) | ~brave(mary)) & (brave(mary) | brave(mary))) [nnf transformation 28]
68. ! [X0] : (((generous(X0) | creative(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [nnf transformation 14]
69. ! [X0] : ((generous(X0) | creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [flattening 68]
70. ! [X0] : (((generous(X0) & ~rich(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (~generous(X0) | rich(X0)))) [nnf transformation 15]
71. ! [X0] : (((generous(X0) & ~rich(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~generous(X0) | rich(X0))) [flattening 70]
87. ~happy(X0) | ~happy(X0) | ~old(X0) [cnf transformation 40]
90. ~patient(X0) | old(X0) | happy(X0) [cnf transformation 40]
91. ~funny(lucy) | brave(mary) | brave(mary) [cnf transformation 41]
92. ~funny(lucy) | ~brave(mary) | ~brave(mary) [cnf transformation 41]
127. ~old(X0) | happy(X0) | ~generous(X0) [cnf transformation 69]
129. old(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 69]
136. calm(X0) | funny(X0) | generous(X0) [cnf transformation 71]
138. ~generous(X0) | patient(X0) [cnf transformation 33]
151. ~calm(lucy) [cnf transformation 24]
154. ~funny(lucy) | brave(mary) [duplicate literal removal 91]
155. ~funny(lucy) | ~brave(mary) [duplicate literal removal 92]
157. ~happy(X0) | ~old(X0) [duplicate literal removal 87]
182. 6 <=> brave(mary) [avatar definition]
186. 7 <=> funny(lucy) [avatar definition]
188. ~funny(lucy) <- (~7) [avatar component clause 186]
189. ~6 | ~7 [avatar split clause 155,186,182]
190. 6 | ~7 [avatar split clause 154,186,182]
312. ~generous(X0) | ~happy(X0) [subsumption resolution 129,157]
314. ~generous(X0) | ~old(X0) [subsumption resolution 127,312]
333. 38 <=> generous(lucy) [avatar definition]
335. generous(lucy) <- (38) [avatar component clause 333]
511. funny(lucy) | generous(lucy) [resolution 136,151]
514. generous(lucy) <- (~7) [subsumption resolution 511,188]
517. 38 | 7 [avatar split clause 514,186,333]
520. ~old(lucy) <- (38) [resolution 335,314]
521. ~happy(lucy) <- (38) [resolution 335,312]
522. patient(lucy) <- (38) [resolution 335,138]
528. 63 <=> happy(lucy) [avatar definition]
530. ~happy(lucy) <- (~63) [avatar component clause 528]
537. ~63 | ~38 [avatar split clause 521,333,528]
559. old(lucy) | happy(lucy) <- (38) [resolution 522,90]
561. happy(lucy) <- (38) [subsumption resolution 559,520]
562. $false <- (38, ~63) [subsumption resolution 561,530]
563. ~38 | 63 [avatar contradiction clause 562]
564. $false [avatar sat refutation 189,190,517,537,563]
% SZS output end Proof for 6619892791449349982763954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not brave is both calm and not wise. Everyone who is not brave is either not kind or brave. Everyone who is both not wise and brave is both not humble and not funny. If someone is not happy then alice is funny or not curious and vice versa. Everyone who is either funny or kind is either old or funny. If someone is funny or not generous then someone is both not tall and not quiet. Everyone who is either rich or creative is not strong. If someone is not happy or not curious then john is not humble. If someone is not rich then someone is either tall or not wise. Everyone who is either happy or curious is creative and vice versa. Everyone who is both not creative and humble is both not old and curious and vice versa. If someone is not happy or not kind then john is both generous and not quiet. Everyone who is not wise is not patient or happy. Everyone who is curious or not strong is either not old or wise. Everyone who is wise or not wise is both not curious and not wise. Everyone who is not strong is not quiet or not rich and vice versa. Lucy is not happy or not kind. Someone is funny or not happy. Someone is tall. Paul is either rich or not happy. Someone is either not creative or humble. Someone is either creative or not rich. Paul is both calm and generous. | Lucy is kind. | contradiction | (![X]:((~quiet(X)|~brave(X))=>(calm(X)&~wise(X))))&
(![X]:(~brave(X)=>(~kind(X)<~>brave(X))))&
(![X]:((~wise(X)&brave(X))=>(~humble(X)&~funny(X))))&
((?[X]:(~happy(X)))<=>((funny(alice)|~curious(alice))))&
(![X]:((funny(X)<~>kind(X))=>(old(X)<~>funny(X))))&
((?[X]:((funny(X)|~generous(X))))=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:((rich(X)<~>creative(X))=>~strong(X)))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~rich(X))))&
((~happy(lucy)|~kind(lucy)))&
(?[X]:((funny(X)|~happy(X))))&
(?[X]:(tall(X)))&
((rich(paul)<~>~happy(paul)))&
(?[X]:((~creative(X)<~>humble(X))))&
(?[X]:((creative(X)<~>~rich(X))))&
((calm(paul)&generous(paul))) | kind(lucy) | [
"p1",
"p2",
"p4",
"p6",
"p9",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6257730321669440257620248
% SZS output start Proof for 6257730321669440257620248
2. ! [X0] : (~brave(X0) => (~kind(X0) <~> brave(X0))) [input p1]
3. ! [X0] : ((brave(X0) & ~wise(X0)) => (~funny(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((funny(X0) <~> kind(X0)) => (old(X0) <~> funny(X0))) [input p4]
7. ! [X0] : ((rich(X0) <~> creative(X0)) => ~strong(X0)) [input p6]
10. ! [X0] : ((happy(X0) <~> curious(X0)) <=> creative(X0)) [input p9]
14. ! [X0] : ((~strong(X0) | curious(X0)) => (~old(X0) <~> wise(X0))) [input p13]
15. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p14]
16. ! [X0] : (~strong(X0) <=> (~rich(X0) | ~quiet(X0))) [input p15]
17. ~kind(lucy) | ~happy(lucy) [input p16]
24. kind(lucy) [input hypothesis]
34. ! [X0] : ((~kind(X0) <~> brave(X0)) | brave(X0)) [ennf transformation 2]
35. ! [X0] : ((~funny(X0) & ~humble(X0)) | (~brave(X0) | wise(X0))) [ennf transformation 3]
36. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~brave(X0) | wise(X0)) [flattening 35]
37. ! [X0] : ((old(X0) <~> funny(X0)) | (funny(X0) <=> kind(X0))) [ennf transformation 5]
39. ! [X0] : (~strong(X0) | (rich(X0) <=> creative(X0))) [ennf transformation 7]
43. ! [X0] : ((~old(X0) <~> wise(X0)) | (strong(X0) & ~curious(X0))) [ennf transformation 14]
44. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 15]
45. ! [X0] : (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | brave(X0)) [nnf transformation 34]
51. ! [X0] : (((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0)))) [nnf transformation 37]
55. ! [X0] : (~strong(X0) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) [nnf transformation 39]
60. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | ~creative(X0)) & (creative(X0) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [nnf transformation 10]
63. ! [X0] : (((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (strong(X0) & ~curious(X0))) [nnf transformation 43]
64. ! [X0] : ((~strong(X0) | (rich(X0) & quiet(X0))) & ((~rich(X0) | ~quiet(X0)) | strong(X0))) [nnf transformation 16]
65. ! [X0] : ((~strong(X0) | (rich(X0) & quiet(X0))) & (~rich(X0) | ~quiet(X0) | strong(X0))) [flattening 64]
79. brave(X0) | ~kind(X0) | brave(X0) [cnf transformation 45]
82. ~funny(X0) | ~brave(X0) | wise(X0) [cnf transformation 36]
87. funny(X0) | old(X0) | funny(X0) | ~kind(X0) [cnf transformation 51]
92. ~strong(X0) | creative(X0) | ~rich(X0) [cnf transformation 55]
100. ~creative(X0) | happy(X0) | curious(X0) [cnf transformation 60]
109. ~old(X0) | wise(X0) | strong(X0) [cnf transformation 63]
113. ~curious(X0) | wise(X0) [cnf transformation 44]
114. ~wise(X0) | ~wise(X0) [cnf transformation 44]
118. ~strong(X0) | rich(X0) [cnf transformation 65]
119. ~kind(lucy) | ~happy(lucy) [cnf transformation 17]
128. kind(lucy) [cnf transformation 24]
129. ~wise(X0) [duplicate literal removal 114]
130. ~kind(X0) | old(X0) | funny(X0) [duplicate literal removal 87]
132. ~kind(X0) | brave(X0) [duplicate literal removal 79]
195. ~curious(X0) [subsumption resolution 113,129]
197. 15 <=> happy(lucy) [avatar definition]
199. ~happy(lucy) <- (~15) [avatar component clause 197]
201. 16 <=> kind(lucy) [avatar definition]
202. kind(lucy) <- (16) [avatar component clause 201]
204. ~15 | ~16 [avatar split clause 119,201,197]
244. 16 [avatar split clause 128,201]
245. brave(lucy) <- (16) [resolution 132,202]
246. old(lucy) | funny(lucy) <- (16) [resolution 130,202]
248. 25 <=> funny(lucy) [avatar definition]
250. funny(lucy) <- (25) [avatar component clause 248]
252. 26 <=> old(lucy) [avatar definition]
254. old(lucy) <- (26) [avatar component clause 252]
255. 25 | 26 | ~16 [avatar split clause 246,201,252,248]
256. ~brave(lucy) | wise(lucy) <- (25) [resolution 250,82]
257. wise(lucy) <- (16, 25) [subsumption resolution 256,245]
258. $false <- (16, 25) [subsumption resolution 257,129]
259. ~16 | ~25 [avatar contradiction clause 258]
261. wise(lucy) | strong(lucy) <- (26) [resolution 254,109]
264. strong(lucy) <- (26) [subsumption resolution 261,129]
266. 27 <=> creative(lucy) [avatar definition]
268. creative(lucy) <- (27) [avatar component clause 266]
275. creative(lucy) | ~rich(lucy) <- (26) [resolution 264,92]
276. rich(lucy) <- (26) [resolution 264,118]
279. 29 <=> rich(lucy) [avatar definition]
283. ~29 | 27 | ~26 [avatar split clause 275,252,266,279]
284. 29 | ~26 [avatar split clause 276,252,279]
287. happy(lucy) | curious(lucy) <- (27) [resolution 268,100]
288. curious(lucy) <- (~15, 27) [subsumption resolution 287,199]
289. $false <- (~15, 27) [subsumption resolution 288,195]
290. 15 | ~27 [avatar contradiction clause 289]
291. $false [avatar sat refutation 204,244,255,259,283,284,290]
% SZS output end Proof for 6257730321669440257620248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and happy then someone is not kind.
Everyone who is wise is either not humble or not kind.
If someone is tall then lucy is humble or not brave.
Everyone who is not patient or brave is patient or not old and vice versa.
Everyone who is strong or kind is both wise and not tall and vice versa.
Everyone who is not brave is both not tall and not brave and vice versa.
If someone is quiet then mary is not calm or not kind.
If someone is both not patient and not calm then someone is not calm or humble.
Everyone who is patient is both not creative and humble and vice versa.
Everyone who is either wise or not calm is both not old and rich.
Everyone who is happy or creative is both not creative and not patient and vice versa.
Everyone who is not strong or humble is either tall or not kind and vice versa.
Everyone who is tall is generous or humble.
If mary is either calm or not old then someone is not patient and vice versa.
If susan is quiet then someone is not funny.
Everyone who is quiet is not humble.
Mary is both not brave and not rich.
Someone is either not curious or calm.
Someone is humble or not kind.
Someone is either generous or rich.
Paul is either curious or not patient.
John is not creative.
Someone is either not patient or generous. | Paul is not creative. | entailment | ((?[X]:((~rich(X)&happy(X))))=>(?[X]:(~kind(X))))&
(![X]:(wise(X)=>(~humble(X)<~>~kind(X))))&
((?[X]:(tall(X)))=>((humble(lucy)|~brave(lucy))))&
(![X]:((~patient(X)|brave(X))<=>(patient(X)|~old(X))))&
(![X]:((strong(X)|kind(X))<=>(wise(X)&~tall(X))))&
(![X]:(~brave(X)<=>(~tall(X)&~brave(X))))&
((?[X]:(quiet(X)))=>((~calm(mary)|~kind(mary))))&
((?[X]:((~patient(X)&~calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:(patient(X)<=>(~creative(X)&humble(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~old(X)&rich(X))))&
(![X]:((happy(X)|creative(X))<=>(~creative(X)&~patient(X))))&
(![X]:((~strong(X)|humble(X))<=>(tall(X)<~>~kind(X))))&
(![X]:(tall(X)=>(generous(X)|humble(X))))&
(((calm(mary)<~>~old(mary)))<=>(?[X]:(~patient(X))))&
((quiet(susan))=>(?[X]:(~funny(X))))&
(![X]:(quiet(X)=>~humble(X)))&
((~brave(mary)&~rich(mary)))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((humble(X)|~kind(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((curious(paul)<~>~patient(paul)))&
(~creative(john))&
(?[X]:((~patient(X)<~>generous(X)))) | ~creative(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6443103566613998216521932
% SZS output start Proof for 6443103566613998216521932
11. ! [X0] : ((creative(X0) | happy(X0)) <=> (~patient(X0) & ~creative(X0))) [input p10]
24. creative(paul) [input hypothesis]
54. ! [X0] : (((creative(X0) | happy(X0)) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | (~creative(X0) & ~happy(X0)))) [nnf transformation 11]
55. ! [X0] : ((creative(X0) | happy(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | (~creative(X0) & ~happy(X0)))) [flattening 54]
99. ~creative(X0) | ~creative(X0) [cnf transformation 55]
126. creative(paul) [cnf transformation 24]
127. ~creative(X0) [duplicate literal removal 99]
231. $false [subsumption resolution 126,127]
% SZS output end Proof for 6443103566613998216521932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or old is both funny and creative. Everyone who is curious or tall is happy and vice versa. Everyone who is both not old and patient is generous and vice versa. Everyone who is rich or patient is not patient or not strong and vice versa. Everyone who is either funny or happy is not patient. Everyone who is brave or not patient is not tall or funny and vice versa. Everyone who is either not strong or not wise is not funny. If paul is either humble or not creative then someone is brave. Everyone who is both not happy and happy is quiet or creative. Everyone who is not humble or rich is not tall. Everyone who is quiet or not happy is not generous. Everyone who is not generous or not funny is not rich or kind and vice versa. Everyone who is quiet is calm. Everyone who is either not happy or tall is either tall or not happy and vice versa. If someone is not humble or not strong then someone is either calm or quiet and vice versa. Everyone who is both not creative and not humble is not brave. Someone is calm or quiet. Alice is not old. Someone is rich or humble. John is either not tall or not generous. Alice is both not happy and brave. Someone is curious or old. Someone is either not wise or not rich. Someone is not tall or strong. | Alice is not funny. | contradiction | (![X]:((~old(X)|old(X))=>(funny(X)&creative(X))))&
(![X]:((curious(X)|tall(X))<=>happy(X)))&
(![X]:((~old(X)&patient(X))<=>generous(X)))&
(![X]:((rich(X)|patient(X))<=>(~patient(X)|~strong(X))))&
(![X]:((funny(X)<~>happy(X))=>~patient(X)))&
(![X]:((brave(X)|~patient(X))<=>(~tall(X)|funny(X))))&
(![X]:((~strong(X)<~>~wise(X))=>~funny(X)))&
(((humble(paul)<~>~creative(paul)))=>(?[X]:(brave(X))))&
(![X]:((~happy(X)&happy(X))=>(quiet(X)|creative(X))))&
(![X]:((~humble(X)|rich(X))=>~tall(X)))&
(![X]:((quiet(X)|~happy(X))=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))<=>(~rich(X)|kind(X))))&
(![X]:(quiet(X)=>calm(X)))&
(![X]:((~happy(X)<~>tall(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((~creative(X)&~humble(X))=>~brave(X)))&
(?[X]:((calm(X)|quiet(X))))&
(~old(alice))&
(?[X]:((rich(X)|humble(X))))&
((~tall(john)<~>~generous(john)))&
((~happy(alice)&brave(alice)))&
(?[X]:((curious(X)|old(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:((~tall(X)|strong(X)))) | ~funny(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8364516096513095402983267
% SZS output start Proof for 8364516096513095402983267
1. ! [X0] : ((old(X0) | ~old(X0)) => (creative(X0) & funny(X0))) [input p0]
25. ~funny(alice) [input hypothesis]
27. ! [X0] : ((creative(X0) & funny(X0)) | (~old(X0) & old(X0))) [ennf transformation 1]
71. funny(X0) | old(X0) [cnf transformation 27]
72. funny(X0) | ~old(X0) [cnf transformation 27]
131. ~funny(alice) [cnf transformation 25]
143. funny(X0) [subsumption resolution 71,72]
242. $false [subsumption resolution 131,143]
% SZS output end Proof for 8364516096513095402983267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or brave is humble and vice versa. Everyone who is either not old or tall is both not quiet and wise and vice versa. Everyone who is both not brave and curious is either brave or wise. Everyone who is both rich and not generous is not curious and vice versa. If john is calm then someone is creative or not happy. If susan is funny then paul is quiet or not tall. Everyone who is not calm is happy or not creative and vice versa. Everyone who is either funny or generous is patient. Everyone who is not curious is both brave and not kind. Everyone who is both not wise and not humble is patient or rich and vice versa. If someone is not wise or brave then john is both strong and patient and vice versa. Everyone who is either not happy or wise is both not old and not humble. If someone is either tall or calm then lucy is happy and vice versa. If lucy is not wise then paul is not funny or not old and vice versa. Everyone who is not old is not tall or wise. Someone is both not happy and creative. Someone is either not strong or rich. Mary is either not humble or rich. Someone is generous or tall. Someone is not calm. | Mary is not funny. | entailment | (![X]:((funny(X)|brave(X))<=>humble(X)))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~brave(X)&curious(X))=>(brave(X)<~>wise(X))))&
(![X]:((rich(X)&~generous(X))<=>~curious(X)))&
((calm(john))=>(?[X]:((creative(X)|~happy(X)))))&
((funny(susan))=>((quiet(paul)|~tall(paul))))&
(![X]:(~calm(X)<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>patient(X)))&
(![X]:(~curious(X)=>(brave(X)&~kind(X))))&
(![X]:((~wise(X)&~humble(X))<=>(patient(X)|rich(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((strong(john)&patient(john))))&
(![X]:((~happy(X)<~>wise(X))=>(~old(X)&~humble(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(happy(lucy)))&
((~wise(lucy))<=>((~funny(paul)|~old(paul))))&
(![X]:(~old(X)=>(~tall(X)|wise(X))))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((~humble(mary)<~>rich(mary)))&
(?[X]:((generous(X)|tall(X))))&
(?[X]:(~calm(X))) | ~funny(mary) | [
"p0",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 222160596088412443238412
% SZS output start Proof for 222160596088412443238412
1. ! [X0] : ((brave(X0) | funny(X0)) <=> humble(X0)) [input p0]
10. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (rich(X0) | patient(X0))) [input p9]
18. ~humble(mary) <~> rich(mary) [input p17]
21. funny(mary) [input hypothesis]
33. ! [X0] : (((brave(X0) | funny(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((brave(X0) | funny(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [flattening 33]
45. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 10]
46. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | humble(X0) | wise(X0))) [flattening 45]
64. (~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary)) [nnf transformation 18]
69. ~funny(X0) | humble(X0) [cnf transformation 34]
95. ~humble(X0) | ~rich(X0) [cnf transformation 46]
117. rich(mary) | ~humble(mary) [cnf transformation 64]
118. ~rich(mary) | humble(mary) [cnf transformation 64]
121. funny(mary) [cnf transformation 21]
224. ~rich(mary) [subsumption resolution 118,95]
225. ~humble(mary) [subsumption resolution 117,224]
235. humble(mary) [resolution 69,121]
236. $false [subsumption resolution 235,225]
% SZS output end Proof for 222160596088412443238412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not brave and quiet. If someone is both not humble and not calm then lucy is either quiet or not wise and vice versa. Everyone who is both rich and not humble is wise and vice versa. If someone is not brave then lucy is both not old and not creative. Everyone who is not quiet or not generous is not brave or tall. If paul is not strong then mary is not curious or brave. If someone is both not quiet and curious then someone is both tall and not humble. If fred is kind then someone is generous or strong and vice versa. Everyone who is humble or not generous is both patient and creative and vice versa. Everyone who is kind or quiet is both not generous and not patient and vice versa. If someone is either brave or creative then mary is not old or not rich and vice versa. If someone is both not brave and not kind then someone is either not strong or quiet. Everyone who is funny is either funny or not strong. Everyone who is both funny and calm is both not old and not calm and vice versa. Paul is not creative or not old. Fred is either not humble or old. Lucy is either happy or calm. Fred is not humble or wise. Someone is either wise or calm. Someone is either calm or not curious. | Fred is not kind. | entailment | (![X]:(~curious(X)=>(~brave(X)&quiet(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>((quiet(lucy)<~>~wise(lucy))))&
(![X]:((rich(X)&~humble(X))<=>wise(X)))&
((?[X]:(~brave(X)))=>((~old(lucy)&~creative(lucy))))&
(![X]:((~quiet(X)|~generous(X))=>(~brave(X)|tall(X))))&
((~strong(paul))=>((~curious(mary)|brave(mary))))&
((?[X]:((~quiet(X)&curious(X))))=>(?[X]:((tall(X)&~humble(X)))))&
((kind(fred))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((humble(X)|~generous(X))<=>(patient(X)&creative(X))))&
(![X]:((kind(X)|quiet(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((brave(X)<~>creative(X))))<=>((~old(mary)|~rich(mary))))&
((?[X]:((~brave(X)&~kind(X))))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:(funny(X)=>(funny(X)<~>~strong(X))))&
(![X]:((funny(X)&calm(X))<=>(~old(X)&~calm(X))))&
((~creative(paul)|~old(paul)))&
((~humble(fred)<~>old(fred)))&
((happy(lucy)<~>calm(lucy)))&
((~humble(fred)|wise(fred)))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:((calm(X)<~>~curious(X)))) | ~kind(fred) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8640383885102664224948608
% SZS output start Proof for 8640383885102664224948608
9. ! [X0] : ((~generous(X0) | humble(X0)) <=> (creative(X0) & patient(X0))) [input p8]
10. ! [X0] : ((quiet(X0) | kind(X0)) <=> (~patient(X0) & ~generous(X0))) [input p9]
21. kind(fred) [input hypothesis]
46. ! [X0] : (((~generous(X0) | humble(X0)) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | (generous(X0) & ~humble(X0)))) [nnf transformation 9]
47. ! [X0] : ((~generous(X0) | humble(X0) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | (generous(X0) & ~humble(X0)))) [flattening 46]
48. ! [X0] : (((quiet(X0) | kind(X0)) | (patient(X0) | generous(X0))) & ((~patient(X0) & ~generous(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((quiet(X0) | kind(X0) | patient(X0) | generous(X0)) & ((~patient(X0) & ~generous(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 48]
89. patient(X0) | generous(X0) [cnf transformation 47]
93. ~kind(X0) | ~generous(X0) [cnf transformation 49]
95. ~patient(X0) | ~kind(X0) [cnf transformation 49]
122. kind(fred) [cnf transformation 21]
190. 15 <=> kind(fred) [avatar definition]
192. kind(fred) <- (15) [avatar component clause 190]
299. 15 [avatar split clause 122,190]
310. ~kind(X0) | generous(X0) [resolution 95,89]
311. ~kind(X0) [subsumption resolution 310,93]
312. $false <- (15) [resolution 311,192]
313. ~15 [avatar contradiction clause 312]
314. $false [avatar sat refutation 299,313]
% SZS output end Proof for 8640383885102664224948608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not old is humble or brave. If john is both kind and not patient then fred is strong and vice versa. Everyone who is either not quiet or patient is either not old or not brave. Everyone who is not tall or not brave is either curious or not kind. Everyone who is not quiet is calm or not brave. Everyone who is strong is both not happy and humble. Everyone who is both not funny and humble is old or not tall and vice versa. If someone is not curious then alice is both not old and wise and vice versa. Everyone who is both tall and not calm is either not tall or not brave and vice versa. If susan is either not rich or brave then mary is not calm or calm and vice versa. Everyone who is not curious or tall is both strong and not generous and vice versa. Everyone who is either not strong or not generous is both not quiet and tall. If lucy is humble or patient then fred is either happy or funny and vice versa. If someone is not calm or generous then someone is both happy and old and vice versa. If lucy is rich or tall then susan is both calm and not funny. Susan is calm or not humble. Someone is either wise or humble. Someone is not quiet. Paul is both not tall and not happy. Someone is not creative. Someone is not patient. Someone is not funny. | Alice is not generous. | neutral | (![X]:((strong(X)|~old(X))=>(humble(X)|brave(X))))&
(((kind(john)&~patient(john)))<=>(strong(fred)))&
(![X]:((~quiet(X)<~>patient(X))=>(~old(X)<~>~brave(X))))&
(![X]:((~tall(X)|~brave(X))=>(curious(X)<~>~kind(X))))&
(![X]:(~quiet(X)=>(calm(X)|~brave(X))))&
(![X]:(strong(X)=>(~happy(X)&humble(X))))&
(![X]:((~funny(X)&humble(X))<=>(old(X)|~tall(X))))&
((?[X]:(~curious(X)))<=>((~old(alice)&wise(alice))))&
(![X]:((tall(X)&~calm(X))<=>(~tall(X)<~>~brave(X))))&
(((~rich(susan)<~>brave(susan)))<=>((~calm(mary)|calm(mary))))&
(![X]:((~curious(X)|tall(X))<=>(strong(X)&~generous(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(~quiet(X)&tall(X))))&
(((humble(lucy)|patient(lucy)))<=>((happy(fred)<~>funny(fred))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:((happy(X)&old(X)))))&
(((rich(lucy)|tall(lucy)))=>((calm(susan)&~funny(susan))))&
((calm(susan)|~humble(susan)))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:(~quiet(X)))&
((~tall(paul)&~happy(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(~patient(X)))&
(?[X]:(~funny(X))) | ~generous(alice) | [] | null | 0 |
Everyone who is not funny or not generous is both quiet and not kind.
If someone is brave then someone is not curious or wise and vice versa.
Everyone who is either creative or quiet is curious.
If someone is not quiet or not humble then paul is both not humble and not creative.
Everyone who is either not kind or old is both calm and not generous.
Everyone who is funny is both tall and humble.
If someone is both not curious and not old then someone is not calm.
Everyone who is either not brave or not kind is not old.
Everyone who is not wise is not happy and vice versa.
Everyone who is either quiet or strong is not strong.
If mary is either not patient or wise then mary is creative.
Everyone who is either not old or not patient is both strong and not wise.
Everyone who is humble is both happy and not calm.
If susan is either old or not creative then lucy is not rich or humble.
Everyone who is happy is not funny or not generous.
If fred is not tall then susan is either not quiet or not strong.
Paul is rich or strong.
Mary is not humble.
John is either old or not generous.
Alice is either strong or wise.
Someone is either wise or funny.
John is generous.
Mary is not strong. | Paul is not curious. | contradiction | (![X]:((~funny(X)|~generous(X))=>(quiet(X)&~kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((creative(X)<~>quiet(X))=>curious(X)))&
((?[X]:((~quiet(X)|~humble(X))))=>((~humble(paul)&~creative(paul))))&
(![X]:((~kind(X)<~>old(X))=>(calm(X)&~generous(X))))&
(![X]:(funny(X)=>(tall(X)&humble(X))))&
((?[X]:((~curious(X)&~old(X))))=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)<~>~kind(X))=>~old(X)))&
(![X]:(~wise(X)<=>~happy(X)))&
(![X]:((quiet(X)<~>strong(X))=>~strong(X)))&
(((~patient(mary)<~>wise(mary)))=>(creative(mary)))&
(![X]:((~old(X)<~>~patient(X))=>(strong(X)&~wise(X))))&
(![X]:(humble(X)=>(happy(X)&~calm(X))))&
(((old(susan)<~>~creative(susan)))=>((~rich(lucy)|humble(lucy))))&
(![X]:(happy(X)=>(~funny(X)|~generous(X))))&
((~tall(fred))=>((~quiet(susan)<~>~strong(susan))))&
((rich(paul)|strong(paul)))&
(~humble(mary))&
((old(john)<~>~generous(john)))&
((strong(alice)<~>wise(alice)))&
(?[X]:((wise(X)<~>funny(X))))&
(generous(john))&
(~strong(mary)) | ~curious(paul) | [
"p0",
"p2",
"p3",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8257319119439191967234598
% SZS output start Proof for 8257319119439191967234598
1. ! [X0] : ((~generous(X0) | ~funny(X0)) => (~kind(X0) & quiet(X0))) [input p0]
3. ! [X0] : ((creative(X0) <~> quiet(X0)) => curious(X0)) [input p2]
4. ? [X0] : (~humble(X0) | ~quiet(X0)) => (~creative(paul) & ~humble(paul)) [input p3]
6. ! [X0] : (funny(X0) => (humble(X0) & tall(X0))) [input p5]
18. ~humble(mary) [input p17]
24. ~curious(paul) [input hypothesis]
27. ! [X0] : (funny(X0) => humble(X0)) [pure predicate removal 6]
29. ! [X0] : ((~kind(X0) & quiet(X0)) | (generous(X0) & funny(X0))) [ennf transformation 1]
30. ! [X0] : (curious(X0) | (creative(X0) <=> quiet(X0))) [ennf transformation 3]
31. (~creative(paul) & ~humble(paul)) | ! [X0] : (humble(X0) & quiet(X0)) [ennf transformation 4]
33. ! [X0] : (humble(X0) | ~funny(X0)) [ennf transformation 27]
49. ! [X0] : (curious(X0) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 30]
65. quiet(X0) | funny(X0) [cnf transformation 29]
73. ~quiet(X0) | creative(X0) | curious(X0) [cnf transformation 49]
75. ~humble(paul) | humble(X0) [cnf transformation 31]
77. ~creative(paul) | humble(X0) [cnf transformation 31]
82. ~funny(X0) | humble(X0) [cnf transformation 33]
102. ~humble(mary) [cnf transformation 18]
111. ~curious(paul) [cnf transformation 24]
138. 7 <=> ! [X0] : humble(X0) [avatar definition]
139. humble(X0) <- (7) [avatar component clause 138]
141. 8 <=> creative(paul) [avatar definition]
143. ~creative(paul) <- (~8) [avatar component clause 141]
144. 7 | ~8 [avatar split clause 77,141,138]
150. 10 <=> humble(paul) [avatar definition]
153. 7 | ~10 [avatar split clause 75,150,138]
245. creative(X1) | curious(X1) | funny(X1) [resolution 73,65]
314. curious(paul) | funny(paul) <- (~8) [resolution 245,143]
317. funny(paul) <- (~8) [subsumption resolution 314,111]
328. humble(paul) <- (~8) [resolution 317,82]
331. 10 | 8 [avatar split clause 328,141,150]
334. $false <- (7) [resolution 139,102]
337. ~7 [avatar contradiction clause 334]
338. $false [avatar sat refutation 144,153,331,337]
% SZS output end Proof for 8257319119439191967234598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not quiet then mary is either happy or brave and vice versa. If someone is creative then paul is both not old and kind and vice versa. Everyone who is brave is either not creative or brave and vice versa. Everyone who is both not brave and not kind is not funny. Everyone who is either not tall or not brave is strong or not creative. If alice is quiet or funny then someone is either not quiet or quiet and vice versa. Everyone who is both creative and funny is calm. Everyone who is humble or quiet is both not creative and not rich. If someone is either old or not creative then someone is either strong or not tall and vice versa. Everyone who is either tall or not quiet is either humble or generous and vice versa. Everyone who is both not humble and old is both not quiet and curious and vice versa. Everyone who is not brave is not happy. If susan is both happy and not wise then someone is both not strong and not curious. Everyone who is either not quiet or rich is wise or patient and vice versa. Lucy is not creative or tall. Someone is either kind or not happy. Someone is either old or not brave. Paul is either happy or not humble. Someone is either not wise or happy. Someone is not tall or not generous. Paul is both not rich and not generous. | Lucy is creative. | entailment | ((?[X]:((~funny(X)|~quiet(X))))<=>((happy(mary)<~>brave(mary))))&
((?[X]:(creative(X)))<=>((~old(paul)&kind(paul))))&
(![X]:(brave(X)<=>(~creative(X)<~>brave(X))))&
(![X]:((~brave(X)&~kind(X))=>~funny(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(((happy(susan)&~wise(susan)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~quiet(X)<~>rich(X))<=>(wise(X)|patient(X))))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul)))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((~tall(X)|~generous(X))))&
((~rich(paul)&~generous(paul))) | creative(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7851287691295806787777211
% SZS output start Proof for 7851287691295806787777211
3. ! [X0] : (brave(X0) <=> (~creative(X0) <~> brave(X0))) [input p2]
22. ~creative(lucy) [input hypothesis]
42. ! [X0] : ((brave(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ~brave(X0))) [nnf transformation 3]
83. ~brave(X0) | creative(X0) | ~brave(X0) [cnf transformation 42]
84. brave(X0) | brave(X0) | creative(X0) [cnf transformation 42]
140. ~creative(lucy) [cnf transformation 22]
143. ~brave(X0) | creative(X0) [duplicate literal removal 83]
144. brave(X0) | creative(X0) [duplicate literal removal 84]
191. creative(X0) [subsumption resolution 143,144]
308. $false [subsumption resolution 140,191]
% SZS output end Proof for 7851287691295806787777211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble is either not wise or tall.
If mary is either not old or kind then someone is not old or generous and vice versa.
Everyone who is both old and not brave is not curious and vice versa.
Everyone who is both not old and creative is creative or tall.
Everyone who is not wise is not brave or quiet and vice versa.
If alice is both creative and not happy then alice is either not patient or not humble.
Everyone who is either brave or not tall is either generous or quiet and vice versa.
Everyone who is either calm or not curious is funny or not humble.
Everyone who is patient or strong is either funny or strong.
Everyone who is both not funny and not curious is either funny or wise and vice versa.
Everyone who is creative or not quiet is curious and vice versa.
Everyone who is not humble or quiet is both not strong and not creative.
Everyone who is either not brave or creative is humble.
If fred is either old or not funny then someone is either creative or not curious.
If john is either tall or kind then someone is either not happy or old.
If alice is either not humble or not strong then someone is either funny or not generous and vice versa.
Someone is not quiet.
Susan is either wise or not creative.
Someone is wise.
John is calm.
Lucy is either not curious or not generous.
Someone is both not rich and not humble.
Alice is either wise or not rich.
Susan is not quiet. | Susan is humble. | entailment | (![X]:((~creative(X)|~humble(X))=>(~wise(X)<~>tall(X))))&
(((~old(mary)<~>kind(mary)))<=>(?[X]:((~old(X)|generous(X)))))&
(![X]:((old(X)&~brave(X))<=>~curious(X)))&
(![X]:((~old(X)&creative(X))=>(creative(X)|tall(X))))&
(![X]:(~wise(X)<=>(~brave(X)|quiet(X))))&
(((creative(alice)&~happy(alice)))=>((~patient(alice)<~>~humble(alice))))&
(![X]:((brave(X)<~>~tall(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)<~>~curious(X))=>(funny(X)|~humble(X))))&
(![X]:((patient(X)|strong(X))=>(funny(X)<~>strong(X))))&
(![X]:((~funny(X)&~curious(X))<=>(funny(X)<~>wise(X))))&
(![X]:((creative(X)|~quiet(X))<=>curious(X)))&
(![X]:((~humble(X)|quiet(X))=>(~strong(X)&~creative(X))))&
(![X]:((~brave(X)<~>creative(X))=>humble(X)))&
(((old(fred)<~>~funny(fred)))=>(?[X]:((creative(X)<~>~curious(X)))))&
(((tall(john)<~>kind(john)))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~humble(alice)<~>~strong(alice)))<=>(?[X]:((funny(X)<~>~generous(X)))))&
(?[X]:(~quiet(X)))&
((wise(susan)<~>~creative(susan)))&
(?[X]:(wise(X)))&
(calm(john))&
((~curious(lucy)<~>~generous(lucy)))&
(?[X]:((~rich(X)&~humble(X))))&
((wise(alice)<~>~rich(alice)))&
(~quiet(susan)) | humble(susan) | [
"p4",
"p11",
"p12",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3037301001503264657716078
% SZS output start Proof for 3037301001503264657716078
5. ! [X0] : (~wise(X0) <=> (quiet(X0) | ~brave(X0))) [input p4]
12. ! [X0] : ((quiet(X0) | ~humble(X0)) => (~creative(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~brave(X0) <~> creative(X0)) => humble(X0)) [input p12]
18. wise(susan) <~> ~creative(susan) [input p17]
24. ~quiet(susan) [input p23]
25. ~humble(susan) [input hypothesis]
34. ! [X0] : ((~creative(X0) & ~strong(X0)) | (~quiet(X0) & humble(X0))) [ennf transformation 12]
35. ! [X0] : (humble(X0) | (~brave(X0) <=> creative(X0))) [ennf transformation 13]
45. ! [X0] : ((~wise(X0) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | wise(X0))) [nnf transformation 5]
46. ! [X0] : ((~wise(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | wise(X0))) [flattening 45]
55. ! [X0] : (humble(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) [nnf transformation 35]
68. (creative(susan) | ~wise(susan)) & (~creative(susan) | wise(susan)) [nnf transformation 18]
89. ~brave(X0) | quiet(X0) | wise(X0) [cnf transformation 46]
119. ~creative(X0) | humble(X0) [cnf transformation 34]
121. humble(X0) | creative(X0) | brave(X0) [cnf transformation 55]
141. creative(susan) | ~wise(susan) [cnf transformation 68]
150. ~quiet(susan) [cnf transformation 24]
151. ~humble(susan) [cnf transformation 25]
202. brave(X0) | humble(X0) [subsumption resolution 121,119]
270. 24 <=> wise(susan) [avatar definition]
272. ~wise(susan) <- (~24) [avatar component clause 270]
274. 25 <=> creative(susan) [avatar definition]
276. creative(susan) <- (25) [avatar component clause 274]
277. ~24 | 25 [avatar split clause 141,274,270]
415. 43 <=> brave(susan) [avatar definition]
416. ~brave(susan) <- (~43) [avatar component clause 415]
417. brave(susan) <- (43) [avatar component clause 415]
496. quiet(susan) | wise(susan) <- (43) [resolution 417,89]
501. wise(susan) <- (43) [subsumption resolution 496,150]
502. $false <- (~24, 43) [subsumption resolution 501,272]
503. 24 | ~43 [avatar contradiction clause 502]
504. humble(susan) <- (~43) [resolution 416,202]
505. $false <- (~43) [subsumption resolution 504,151]
506. 43 [avatar contradiction clause 505]
516. humble(susan) <- (25) [resolution 276,119]
518. $false <- (25) [subsumption resolution 516,151]
519. ~25 [avatar contradiction clause 518]
520. $false [avatar sat refutation 277,503,506,519]
% SZS output end Proof for 3037301001503264657716078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either rich or tall then mary is both curious and kind and vice versa.
If someone is not curious then lucy is creative.
Everyone who is both funny and rich is both strong and generous and vice versa.
Everyone who is both tall and not wise is calm or wise and vice versa.
If fred is either not old or not rich then lucy is both wise and brave.
Everyone who is both not kind and wise is either humble or not strong.
Everyone who is not creative is either not creative or curious and vice versa.
If someone is strong then someone is either not old or not patient and vice versa.
Everyone who is either quiet or not quiet is creative or not creative and vice versa.
If someone is not patient then someone is old or rich.
If someone is not happy then someone is either not kind or funny.
Everyone who is both not kind and not rich is not patient or patient and vice versa.
Everyone who is both not humble and kind is either not curious or strong and vice versa.
If someone is either wise or not strong then lucy is not tall.
If susan is both not tall and strong then someone is both not calm and not strong and vice versa.
Someone is both tall and not old.
Someone is not humble.
Paul is both not kind and not patient.
Susan is either strong or kind.
Mary is quiet.
Fred is not funny. | Paul is not happy. | neutral | (((rich(paul)<~>tall(paul)))<=>((curious(mary)&kind(mary))))&
((?[X]:(~curious(X)))=>(creative(lucy)))&
(![X]:((funny(X)&rich(X))<=>(strong(X)&generous(X))))&
(![X]:((tall(X)&~wise(X))<=>(calm(X)|wise(X))))&
(((~old(fred)<~>~rich(fred)))=>((wise(lucy)&brave(lucy))))&
(![X]:((~kind(X)&wise(X))=>(humble(X)<~>~strong(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>curious(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>~quiet(X))<=>(creative(X)|~creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)|rich(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)&kind(X))<=>(~curious(X)<~>strong(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(~tall(lucy)))&
(((~tall(susan)&strong(susan)))<=>(?[X]:((~calm(X)&~strong(X)))))&
(?[X]:((tall(X)&~old(X))))&
(?[X]:(~humble(X)))&
((~kind(paul)&~patient(paul)))&
((strong(susan)<~>kind(susan)))&
(quiet(mary))&
(~funny(fred)) | ~happy(paul) | [] | null | 0 |
Everyone who is either not old or old is not kind and vice versa. If someone is either not generous or not brave then someone is either not generous or strong and vice versa. Everyone who is creative is either patient or wise. If someone is either strong or not calm then lucy is either not old or not quiet. If someone is not curious then alice is strong. Everyone who is not rich or brave is not quiet. Everyone who is both not funny and generous is curious or happy. If someone is happy or not patient then someone is old or not rich and vice versa. Everyone who is not creative is not wise. Everyone who is both brave and creative is not strong. If someone is either not funny or not happy then fred is both wise and not tall. If someone is creative then john is quiet. If someone is generous or not rich then someone is either not generous or wise. Everyone who is both generous and quiet is strong. If someone is either not funny or tall then john is both generous and kind. Paul is both happy and tall. Someone is not creative. Someone is not old. Lucy is not old or curious. Someone is either not creative or not wise. Someone is not funny or not patient. Someone is not patient. | Lucy is kind. | contradiction | (![X]:((~old(X)<~>old(X))<=>~kind(X)))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(creative(X)=>(patient(X)<~>wise(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~old(lucy)<~>~quiet(lucy))))&
((?[X]:(~curious(X)))=>(strong(alice)))&
(![X]:((~rich(X)|brave(X))=>~quiet(X)))&
(![X]:((~funny(X)&generous(X))=>(curious(X)|happy(X))))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:(~creative(X)=>~wise(X)))&
(![X]:((brave(X)&creative(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~happy(X))))=>((wise(fred)&~tall(fred))))&
((?[X]:(creative(X)))=>(quiet(john)))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((generous(X)&quiet(X))=>strong(X)))&
((?[X]:((~funny(X)<~>tall(X))))=>((generous(john)&kind(john))))&
((happy(paul)&tall(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(~old(X)))&
((~old(lucy)|curious(lucy)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | kind(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 626636026140362045505127
% SZS output start Proof for 626636026140362045505127
1. ! [X0] : ((~old(X0) <~> old(X0)) <=> ~kind(X0)) [input p0]
23. kind(lucy) [input hypothesis]
27. ! [X0] : ((~old(X0) <~> old(X0)) => ~kind(X0)) [unused predicate definition removal 1]
31. ! [X0] : (~kind(X0) | (~old(X0) <=> old(X0))) [ennf transformation 27]
44. ! [X0] : (~kind(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 31]
74. ~kind(X0) | old(X0) | old(X0) [cnf transformation 44]
75. ~kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 44]
120. kind(lucy) [cnf transformation 23]
121. ~kind(X0) | old(X0) [duplicate literal removal 74]
122. ~kind(X0) | ~old(X0) [duplicate literal removal 75]
123. ~kind(X0) [subsumption resolution 121,122]
264. $false [subsumption resolution 120,123]
% SZS output end Proof for 626636026140362045505127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or calm is both not happy and humble. Everyone who is both generous and not calm is either tall or not tall. If someone is both not kind and not generous then fred is both creative and quiet. If someone is either rich or not patient then alice is either not brave or not humble and vice versa. If someone is not strong then john is both happy and kind. If john is brave or not quiet then someone is humble or not calm. If mary is kind or humble then someone is either happy or wise. If lucy is not generous or strong then someone is both creative and curious. If alice is both not funny and not curious then susan is generous or not quiet. Everyone who is brave or not creative is kind. Everyone who is not calm is either generous or not quiet and vice versa. Everyone who is not calm or brave is not curious and vice versa. Everyone who is both strong and not happy is brave and vice versa. If someone is both funny and not quiet then someone is either not rich or not old and vice versa. If someone is both not tall and not creative then mary is not wise and vice versa. Everyone who is either not calm or quiet is patient. Someone is either wise or not funny. Someone is rich or not rich. John is not calm or old. Someone is both strong and not tall. John is generous or creative. Someone is brave. Someone is both creative and rich. Paul is either brave or calm. | John is not kind. | contradiction | (![X]:((~wise(X)|calm(X))=>(~happy(X)&humble(X))))&
(![X]:((generous(X)&~calm(X))=>(tall(X)<~>~tall(X))))&
((?[X]:((~kind(X)&~generous(X))))=>((creative(fred)&quiet(fred))))&
((?[X]:((rich(X)<~>~patient(X))))<=>((~brave(alice)<~>~humble(alice))))&
((?[X]:(~strong(X)))=>((happy(john)&kind(john))))&
(((brave(john)|~quiet(john)))=>(?[X]:((humble(X)|~calm(X)))))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(![X]:((brave(X)|~creative(X))=>kind(X)))&
(![X]:(~calm(X)<=>(generous(X)<~>~quiet(X))))&
(![X]:((~calm(X)|brave(X))<=>~curious(X)))&
(![X]:((strong(X)&~happy(X))<=>brave(X)))&
((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((~tall(X)&~creative(X))))<=>(~wise(mary)))&
(![X]:((~calm(X)<~>quiet(X))=>patient(X)))&
(?[X]:((wise(X)<~>~funny(X))))&
(?[X]:((rich(X)|~rich(X))))&
((~calm(john)|old(john)))&
(?[X]:((strong(X)&~tall(X))))&
((generous(john)|creative(john)))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&rich(X))))&
((brave(paul)<~>calm(paul))) | ~kind(john) | [
"p0",
"p4",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1535298500944561090446482
% SZS output start Proof for 1535298500944561090446482
1. ! [X0] : ((calm(X0) | ~wise(X0)) => (humble(X0) & ~happy(X0))) [input p0]
5. ? [X0] : ~strong(X0) => (kind(john) & happy(john)) [input p4]
8. (strong(lucy) | ~generous(lucy)) => ? [X0] : (curious(X0) & creative(X0)) [input p7]
12. ! [X0] : ((brave(X0) | ~calm(X0)) <=> ~curious(X0)) [input p11]
13. ! [X0] : ((~happy(X0) & strong(X0)) <=> brave(X0)) [input p12]
25. ~kind(john) [input hypothesis]
27. ! [X0] : ((brave(X0) | ~calm(X0)) => ~curious(X0)) [unused predicate definition removal 12]
28. ! [X0] : ((humble(X0) & ~happy(X0)) | (~calm(X0) & wise(X0))) [ennf transformation 1]
32. (kind(john) & happy(john)) | ! [X0] : strong(X0) [ennf transformation 5]
35. ? [X0] : (curious(X0) & creative(X0)) | (~strong(lucy) & generous(lucy)) [ennf transformation 8]
39. ! [X0] : (~curious(X0) | (~brave(X0) & calm(X0))) [ennf transformation 27]
51. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK3) & creative(sK3)) [choice axiom]
52. (curious(sK3) & creative(sK3)) | (~strong(lucy) & generous(lucy)) [skolemisation 35,51]
54. ! [X0] : (((~happy(X0) & strong(X0)) | ~brave(X0)) & (brave(X0) | (happy(X0) | ~strong(X0)))) [nnf transformation 13]
55. ! [X0] : (((~happy(X0) & strong(X0)) | ~brave(X0)) & (brave(X0) | happy(X0) | ~strong(X0))) [flattening 54]
79. ~happy(X0) | ~calm(X0) [cnf transformation 28]
95. kind(john) | strong(X0) [cnf transformation 32]
105. curious(sK3) | ~strong(lucy) [cnf transformation 52]
113. ~curious(X0) | calm(X0) [cnf transformation 39]
114. ~curious(X0) | ~brave(X0) [cnf transformation 39]
115. ~strong(X0) | happy(X0) | brave(X0) [cnf transformation 55]
141. ~kind(john) [cnf transformation 25]
186. 10 <=> ! [X0] : strong(X0) [avatar definition]
187. strong(X0) <- (10) [avatar component clause 186]
189. 11 <=> kind(john) [avatar definition]
192. 10 | 11 [avatar split clause 95,189,186]
223. 17 <=> strong(lucy) [avatar definition]
225. ~strong(lucy) <- (~17) [avatar component clause 223]
227. 18 <=> curious(sK3) [avatar definition]
229. curious(sK3) <- (18) [avatar component clause 227]
230. ~17 | 18 [avatar split clause 105,227,223]
346. ~11 [avatar split clause 141,189]
347. $false <- (10, ~17) [resolution 225,187]
348. ~10 | 17 [avatar contradiction clause 347]
355. calm(sK3) <- (18) [resolution 113,229]
356. ~brave(sK3) <- (18) [resolution 114,229]
404. brave(X0) | happy(X0) <- (10) [resolution 115,187]
437. happy(sK3) <- (10, 18) [resolution 404,356]
446. ~calm(sK3) <- (10, 18) [resolution 437,79]
448. $false <- (10, 18) [subsumption resolution 446,355]
449. ~10 | ~18 [avatar contradiction clause 448]
450. $false [avatar sat refutation 192,230,346,348,449]
% SZS output end Proof for 1535298500944561090446482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or patient is happy or curious. Everyone who is not rich or old is brave or not generous and vice versa. Everyone who is either not tall or not funny is either funny or humble. If someone is wise then alice is kind and vice versa. If paul is either not wise or not kind then someone is either not happy or not creative. Everyone who is either curious or not funny is wise and vice versa. If alice is not happy then someone is not happy or happy. Everyone who is happy or humble is not wise and vice versa. If lucy is not calm then susan is strong and vice versa. Everyone who is happy is rich or not humble and vice versa. Everyone who is either not brave or happy is calm. Everyone who is quiet or tall is both not kind and not patient and vice versa. Everyone who is not curious or patient is strong or not quiet. Everyone who is not humble or curious is either not calm or curious and vice versa. If lucy is either calm or not kind then someone is both not generous and humble. Everyone who is both not creative and strong is not brave and vice versa. Someone is rich. Someone is patient or happy. Someone is calm or not kind. Paul is creative or strong. Paul is either old or funny. Someone is both not calm and not rich. Alice is not strong. Someone is humble or not kind. | Susan is not curious. | neutral | (![X]:((quiet(X)<~>patient(X))=>(happy(X)|curious(X))))&
(![X]:((~rich(X)|old(X))<=>(brave(X)|~generous(X))))&
(![X]:((~tall(X)<~>~funny(X))=>(funny(X)<~>humble(X))))&
((?[X]:(wise(X)))<=>(kind(alice)))&
(((~wise(paul)<~>~kind(paul)))=>(?[X]:((~happy(X)<~>~creative(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>wise(X)))&
((~happy(alice))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((happy(X)|humble(X))<=>~wise(X)))&
((~calm(lucy))<=>(strong(susan)))&
(![X]:(happy(X)<=>(rich(X)|~humble(X))))&
(![X]:((~brave(X)<~>happy(X))=>calm(X)))&
(![X]:((quiet(X)|tall(X))<=>(~kind(X)&~patient(X))))&
(![X]:((~curious(X)|patient(X))=>(strong(X)|~quiet(X))))&
(![X]:((~humble(X)|curious(X))<=>(~calm(X)<~>curious(X))))&
(((calm(lucy)<~>~kind(lucy)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~creative(X)&strong(X))<=>~brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((calm(X)|~kind(X))))&
((creative(paul)|strong(paul)))&
((old(paul)<~>funny(paul)))&
(?[X]:((~calm(X)&~rich(X))))&
(~strong(alice))&
(?[X]:((humble(X)|~kind(X)))) | ~curious(susan) | [] | null | 0 |
If someone is both not funny and not kind then someone is not humble or not quiet.
If john is not funny then fred is either not generous or generous.
Everyone who is either not brave or not tall is either not brave or kind.
Everyone who is not tall is both funny and not tall and vice versa.
Everyone who is not old is kind or tall and vice versa.
If mary is not humble then someone is kind.
Everyone who is either calm or not patient is either old or funny.
Everyone who is brave is not tall and vice versa.
If mary is humble then john is either wise or not happy.
Everyone who is not kind or not tall is either humble or not patient and vice versa.
Everyone who is both quiet and not happy is happy or curious and vice versa.
Everyone who is calm is both curious and wise.
Everyone who is either tall or not creative is both quiet and rich.
Everyone who is either not strong or generous is both not generous and not humble.
Everyone who is both happy and not strong is both kind and calm and vice versa.
If someone is happy or not funny then someone is both calm and quiet and vice versa.
Someone is either quiet or old.
Susan is not strong.
Someone is either creative or not funny.
Someone is not kind.
John is curious.
Paul is either calm or creative.
Someone is not tall.
Mary is creative. | Mary is happy. | contradiction | ((?[X]:((~funny(X)&~kind(X))))=>(?[X]:((~humble(X)|~quiet(X)))))&
((~funny(john))=>((~generous(fred)<~>generous(fred))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)<~>kind(X))))&
(![X]:(~tall(X)<=>(funny(X)&~tall(X))))&
(![X]:(~old(X)<=>(kind(X)|tall(X))))&
((~humble(mary))=>(?[X]:(kind(X))))&
(![X]:((calm(X)<~>~patient(X))=>(old(X)<~>funny(X))))&
(![X]:(brave(X)<=>~tall(X)))&
((humble(mary))=>((wise(john)<~>~happy(john))))&
(![X]:((~kind(X)|~tall(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((quiet(X)&~happy(X))<=>(happy(X)|curious(X))))&
(![X]:(calm(X)=>(curious(X)&wise(X))))&
(![X]:((tall(X)<~>~creative(X))=>(quiet(X)&rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>(~generous(X)&~humble(X))))&
(![X]:((happy(X)&~strong(X))<=>(kind(X)&calm(X))))&
((?[X]:((happy(X)|~funny(X))))<=>(?[X]:((calm(X)&quiet(X)))))&
(?[X]:((quiet(X)<~>old(X))))&
(~strong(susan))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:(~kind(X)))&
(curious(john))&
((calm(paul)<~>creative(paul)))&
(?[X]:(~tall(X)))&
(creative(mary)) | happy(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2289185619867602597860582
% SZS output start Proof for 2289185619867602597860582
11. ! [X0] : ((~happy(X0) & quiet(X0)) <=> (curious(X0) | happy(X0))) [input p10]
25. happy(mary) [input hypothesis]
54. ! [X0] : (((~happy(X0) & quiet(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (happy(X0) | ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : (((~happy(X0) & quiet(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | happy(X0) | ~quiet(X0))) [flattening 54]
107. ~happy(X0) | ~happy(X0) [cnf transformation 55]
137. happy(mary) [cnf transformation 25]
140. ~happy(X0) [duplicate literal removal 107]
228. $false [subsumption resolution 137,140]
% SZS output end Proof for 2289185619867602597860582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not wise and not funny is not old. Everyone who is either not kind or creative is not curious and vice versa. If paul is both not strong and quiet then someone is old or not brave. Everyone who is tall or happy is either not generous or not curious. Everyone who is either not creative or not curious is generous or wise. Everyone who is both kind and not old is wise or not curious. Everyone who is both funny and curious is not generous or quiet. Everyone who is both not rich and old is not wise or old. Everyone who is either not tall or not curious is brave and vice versa. Everyone who is quiet or patient is either tall or not quiet and vice versa. Everyone who is either not generous or wise is tall or not brave. If someone is strong then alice is funny or not quiet. If john is either not curious or quiet then someone is both funny and not kind. Everyone who is both wise and patient is not wise and vice versa. If susan is both not wise and not rich then someone is old and vice versa. Everyone who is both not wise and quiet is quiet and vice versa. John is both not old and not patient. Someone is not creative or humble. Someone is creative or not curious. Someone is strong. Alice is creative. Someone is either not humble or calm. | Alice is not patient. | entailment | (![X]:((~wise(X)&~funny(X))=>~old(X)))&
(![X]:((~kind(X)<~>creative(X))<=>~curious(X)))&
(((~strong(paul)&quiet(paul)))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((tall(X)|happy(X))=>(~generous(X)<~>~curious(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(generous(X)|wise(X))))&
(![X]:((kind(X)&~old(X))=>(wise(X)|~curious(X))))&
(![X]:((funny(X)&curious(X))=>(~generous(X)|quiet(X))))&
(![X]:((~rich(X)&old(X))=>(~wise(X)|old(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))<=>(tall(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>wise(X))=>(tall(X)|~brave(X))))&
((?[X]:(strong(X)))=>((funny(alice)|~quiet(alice))))&
(((~curious(john)<~>quiet(john)))=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((wise(X)&patient(X))<=>~wise(X)))&
(((~wise(susan)&~rich(susan)))<=>(?[X]:(old(X))))&
(![X]:((~wise(X)&quiet(X))<=>quiet(X)))&
((~old(john)&~patient(john)))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:(strong(X)))&
(creative(alice))&
(?[X]:((~humble(X)<~>calm(X)))) | ~patient(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 236693608838447475491948
% SZS output start Proof for 236693608838447475491948
14. ! [X0] : ((patient(X0) & wise(X0)) <=> ~wise(X0)) [input p13]
23. patient(alice) [input hypothesis]
57. ! [X0] : (((patient(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) | ~wise(X0)))) [nnf transformation 14]
58. ! [X0] : (((patient(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | ~patient(X0) | ~wise(X0))) [flattening 57]
103. ~wise(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 58]
104. wise(X0) | wise(X0) [cnf transformation 58]
120. patient(alice) [cnf transformation 23]
121. ~wise(X0) | ~patient(X0) [duplicate literal removal 103]
122. wise(X0) [duplicate literal removal 104]
174. ~patient(X0) [subsumption resolution 121,122]
214. $false [subsumption resolution 120,174]
% SZS output end Proof for 236693608838447475491948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not tall is both not brave and not happy.
Everyone who is not happy is both brave and not humble and vice versa.
Everyone who is not rich or humble is kind or generous and vice versa.
Everyone who is brave or not old is both not wise and curious.
If someone is not patient or not wise then lucy is wise and vice versa.
Everyone who is both not creative and patient is both not humble and happy.
If someone is either not generous or tall then someone is either not happy or generous and vice versa.
If someone is both generous and humble then lucy is both kind and generous and vice versa.
Everyone who is not quiet or creative is not happy or funny.
Everyone who is not creative is funny or not humble and vice versa.
If someone is happy or brave then someone is both not generous and funny.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
If susan is generous then susan is happy and vice versa.
If someone is both kind and not humble then fred is either not funny or creative.
Someone is not generous or rich.
Someone is both old and not happy.
Paul is both not generous and not kind.
Someone is both not old and quiet.
Alice is both old and wise.
Susan is not quiet. | Lucy is not generous. | neutral | (![X]:((~curious(X)|~tall(X))=>(~brave(X)&~happy(X))))&
(![X]:(~happy(X)<=>(brave(X)&~humble(X))))&
(![X]:((~rich(X)|humble(X))<=>(kind(X)|generous(X))))&
(![X]:((brave(X)|~old(X))=>(~wise(X)&curious(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>(wise(lucy)))&
(![X]:((~creative(X)&patient(X))=>(~humble(X)&happy(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((generous(X)&humble(X))))<=>((kind(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|creative(X))=>(~happy(X)|funny(X))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(?[X]:((~generous(X)|rich(X))))&
(?[X]:((old(X)&~happy(X))))&
((~generous(paul)&~kind(paul)))&
(?[X]:((~old(X)&quiet(X))))&
((old(alice)&wise(alice)))&
(~quiet(susan)) | ~generous(lucy) | [] | null | 0 |
Everyone who is not patient or not quiet is kind. Everyone who is both not tall and not funny is quiet or rich. Everyone who is not patient or brave is either not generous or not wise. If someone is brave or curious then alice is not funny or curious and vice versa. If someone is not happy or happy then someone is both not kind and rich and vice versa. If someone is either kind or humble then someone is not quiet and vice versa. If susan is both brave and generous then someone is both not old and not patient. Everyone who is not calm or rich is happy or not quiet and vice versa. Everyone who is brave or not calm is either not happy or generous and vice versa. Everyone who is humble or not brave is quiet and vice versa. Everyone who is either creative or wise is either not tall or tall. Everyone who is both not tall and happy is not tall or old and vice versa. Everyone who is either not calm or happy is rich or strong and vice versa. Everyone who is brave or strong is tall. If someone is tall then someone is either not creative or curious and vice versa. Lucy is not calm. Someone is both kind and not strong. Someone is patient or kind. John is curious. Someone is either kind or not generous. Lucy is not quiet. Someone is happy. | Alice is not creative. | neutral | (![X]:((~patient(X)|~quiet(X))=>kind(X)))&
(![X]:((~tall(X)&~funny(X))=>(quiet(X)|rich(X))))&
(![X]:((~patient(X)|brave(X))=>(~generous(X)<~>~wise(X))))&
((?[X]:((brave(X)|curious(X))))<=>((~funny(alice)|curious(alice))))&
((?[X]:((~happy(X)|happy(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:(~quiet(X))))&
(((brave(susan)&generous(susan)))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:((~calm(X)|rich(X))<=>(happy(X)|~quiet(X))))&
(![X]:((brave(X)|~calm(X))<=>(~happy(X)<~>generous(X))))&
(![X]:((humble(X)|~brave(X))<=>quiet(X)))&
(![X]:((creative(X)<~>wise(X))=>(~tall(X)<~>tall(X))))&
(![X]:((~tall(X)&happy(X))<=>(~tall(X)|old(X))))&
(![X]:((~calm(X)<~>happy(X))<=>(rich(X)|strong(X))))&
(![X]:((brave(X)|strong(X))=>tall(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(~calm(lucy))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:((patient(X)|kind(X))))&
(curious(john))&
(?[X]:((kind(X)<~>~generous(X))))&
(~quiet(lucy))&
(?[X]:(happy(X))) | ~creative(alice) | [] | null | 0 |
Everyone who is both not old and funny is rich and vice versa.
Everyone who is both strong and quiet is old.
If paul is not kind or not strong then mary is either humble or curious.
Everyone who is not wise is not generous or not kind and vice versa.
Everyone who is quiet is either not funny or not wise.
Everyone who is brave is not wise.
Everyone who is not humble is both not happy and wise.
Everyone who is brave is not rich and vice versa.
If someone is either not rich or old then susan is strong or quiet and vice versa.
If someone is both quiet and not humble then someone is not humble or kind.
Everyone who is both patient and strong is generous or not creative.
If paul is not humble or wise then susan is both wise and not wise and vice versa.
Everyone who is not rich is both kind and not brave.
If someone is generous or not generous then someone is both strong and not kind.
If someone is kind or not strong then lucy is either not generous or not patient.
Everyone who is quiet is quiet or not quiet.
Mary is both humble and quiet.
Someone is not kind or not curious.
Alice is either strong or generous.
Susan is tall or not creative.
John is both not curious and kind.
Someone is not quiet.
Someone is creative. | Susan is not strong. | entailment | (![X]:((~old(X)&funny(X))<=>rich(X)))&
(![X]:((strong(X)&quiet(X))=>old(X)))&
(((~kind(paul)|~strong(paul)))=>((humble(mary)<~>curious(mary))))&
(![X]:(~wise(X)<=>(~generous(X)|~kind(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~wise(X))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:(~humble(X)=>(~happy(X)&wise(X))))&
(![X]:(brave(X)<=>~rich(X)))&
((?[X]:((~rich(X)<~>old(X))))<=>((strong(susan)|quiet(susan))))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((patient(X)&strong(X))=>(generous(X)|~creative(X))))&
(((~humble(paul)|wise(paul)))<=>((wise(susan)&~wise(susan))))&
(![X]:(~rich(X)=>(kind(X)&~brave(X))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((strong(X)&~kind(X)))))&
((?[X]:((kind(X)|~strong(X))))=>((~generous(lucy)<~>~patient(lucy))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((humble(mary)&quiet(mary)))&
(?[X]:((~kind(X)|~curious(X))))&
((strong(alice)<~>generous(alice)))&
((tall(susan)|~creative(susan)))&
((~curious(john)&kind(john)))&
(?[X]:(~quiet(X)))&
(?[X]:(creative(X))) | ~strong(susan) | [
"p0",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4550956390930608400593476
% SZS output start Proof for 4550956390930608400593476
1. ! [X0] : ((funny(X0) & ~old(X0)) <=> rich(X0)) [input p0]
8. ! [X0] : (brave(X0) <=> ~rich(X0)) [input p7]
9. ? [X0] : (~rich(X0) <~> old(X0)) <=> (quiet(susan) | strong(susan)) [input p8]
13. ! [X0] : (~rich(X0) => (~brave(X0) & kind(X0))) [input p12]
24. strong(susan) [input hypothesis]
27. ! [X0] : (~rich(X0) => brave(X0)) [unused predicate definition removal 8]
36. ! [X0] : (brave(X0) | rich(X0)) [ennf transformation 27]
40. ! [X0] : ((~brave(X0) & kind(X0)) | rich(X0)) [ennf transformation 13]
45. ! [X0] : (((funny(X0) & ~old(X0)) | ~rich(X0)) & (rich(X0) | (~funny(X0) | old(X0)))) [nnf transformation 1]
46. ! [X0] : (((funny(X0) & ~old(X0)) | ~rich(X0)) & (rich(X0) | ~funny(X0) | old(X0))) [flattening 45]
51. (? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~quiet(susan) & ~strong(susan))) & ((quiet(susan) | strong(susan)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) [nnf transformation 9]
52. (? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~quiet(susan) & ~strong(susan))) & (quiet(susan) | strong(susan) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) [flattening 51]
53. (? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~quiet(susan) & ~strong(susan))) & (quiet(susan) | strong(susan) | ! [X1] : ((~rich(X1) | ~old(X1)) & (old(X1) | rich(X1)))) [rectify 52]
54. ? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) => ((~old(sK0) | rich(sK0)) & (old(sK0) | ~rich(sK0))) [choice axiom]
55. (((~old(sK0) | rich(sK0)) & (old(sK0) | ~rich(sK0))) | (~quiet(susan) & ~strong(susan))) & (quiet(susan) | strong(susan) | ! [X1] : ((~rich(X1) | ~old(X1)) & (old(X1) | rich(X1)))) [skolemisation 53,54]
73. ~old(X0) | ~rich(X0) [cnf transformation 46]
87. brave(X0) | rich(X0) [cnf transformation 36]
90. old(sK0) | ~rich(sK0) | ~strong(susan) [cnf transformation 55]
102. ~brave(X0) | rich(X0) [cnf transformation 40]
121. strong(susan) [cnf transformation 24]
155. 7 <=> strong(susan) [avatar definition]
161. 8 <=> rich(sK0) [avatar definition]
163. ~rich(sK0) <- (~8) [avatar component clause 161]
165. ~rich(sK0) | ~strong(susan) [subsumption resolution 90,73]
166. ~7 | ~8 [avatar split clause 165,161,155]
199. rich(X0) [subsumption resolution 102,87]
256. 7 [avatar split clause 121,155]
259. $false <- (~8) [subsumption resolution 163,199]
260. 8 [avatar contradiction clause 259]
261. $false [avatar sat refutation 166,256,260]
% SZS output end Proof for 4550956390930608400593476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not curious or creative then mary is both not patient and not old.
Everyone who is either calm or happy is wise or kind and vice versa.
Everyone who is not brave is either not strong or not humble and vice versa.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
If someone is quiet or not kind then someone is either not humble or not patient and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Everyone who is either curious or kind is not old and vice versa.
If mary is both not happy and not humble then fred is both calm and not strong.
Someone is either not quiet or not generous.
Fred is both not wise and not kind.
Mary is strong.
Someone is either not rich or not brave.
Paul is both not old and not quiet.
Alice is humble or not tall.
Fred is not patient.
Lucy is not curious or patient. | Paul is humble. | entailment | (((~curious(fred)|creative(fred)))=>((~patient(mary)&~old(mary))))&
(![X]:((calm(X)<~>happy(X))<=>(wise(X)|kind(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~humble(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(((~happy(mary)&~humble(mary)))=>((calm(fred)&~strong(fred))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((~wise(fred)&~kind(fred)))&
(strong(mary))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~old(paul)&~quiet(paul)))&
((humble(alice)|~tall(alice)))&
(~patient(fred))&
((~curious(lucy)|patient(lucy))) | humble(paul) | [
"p7",
"p9",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2808436432544044933827958
% SZS output start Proof for 2808436432544044933827958
8. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p7]
10. ! [X0] : ((~kind(X0) & patient(X0)) <=> (~generous(X0) | kind(X0))) [input p9]
11. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (curious(X0) <~> ~humble(X0))) [input p10]
15. ! [X0] : ((curious(X0) <~> kind(X0)) <=> ~old(X0)) [input p14]
21. ~quiet(paul) & ~old(paul) [input p20]
25. ~humble(paul) [input hypothesis]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 8]
56. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (kind(X0) | ~patient(X0)))) [nnf transformation 10]
57. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | kind(X0) | ~patient(X0))) [flattening 56]
58. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (creative(X0) | kind(X0)))) [nnf transformation 11]
59. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | creative(X0) | kind(X0))) [flattening 58]
67. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | old(X0)) & (~old(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 15]
106. ~creative(X0) | ~creative(X0) [cnf transformation 31]
112. ~kind(X0) | ~kind(X0) [cnf transformation 57]
115. humble(X0) | ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 59]
136. kind(X0) | curious(X0) | old(X0) [cnf transformation 67]
147. ~old(paul) [cnf transformation 21]
152. ~humble(paul) [cnf transformation 25]
154. ~kind(X0) [duplicate literal removal 112]
155. ~creative(X0) [duplicate literal removal 106]
280. humble(X0) | ~curious(X0) | kind(X0) [subsumption resolution 115,155]
281. ~curious(X0) | humble(X0) [subsumption resolution 280,154]
301. old(X0) | curious(X0) [subsumption resolution 136,154]
386. curious(paul) [resolution 301,147]
391. humble(paul) [resolution 386,281]
392. $false [subsumption resolution 391,152]
% SZS output end Proof for 2808436432544044933827958
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or not calm is both not quiet and quiet.
Everyone who is either strong or not happy is both not brave and not creative and vice versa.
If someone is both calm and not tall then someone is not patient or quiet and vice versa.
Everyone who is either happy or not quiet is not generous or happy and vice versa.
If someone is not quiet then someone is brave or not curious and vice versa.
If susan is not calm or strong then john is calm and vice versa.
If someone is either not brave or not kind then someone is both not brave and not generous.
Everyone who is kind is patient or not brave.
If paul is either not tall or not old then someone is kind and vice versa.
If fred is quiet then fred is both kind and humble.
If mary is not tall then someone is humble and vice versa.
If john is creative or curious then someone is not tall.
Everyone who is not wise or not happy is curious.
Everyone who is either not tall or humble is not old or curious.
If someone is wise then paul is either not old or funny.
Everyone who is not kind or not brave is both not strong and not wise and vice versa.
Someone is either brave or rich.
Lucy is either not brave or funny.
Someone is both not old and patient.
Susan is not wise or strong.
Fred is not strong or funny.
Fred is not quiet.
Someone is either not wise or strong. | Fred is quiet. | contradiction | (![X]:((~wise(X)|~calm(X))=>(~quiet(X)&quiet(X))))&
(![X]:((strong(X)<~>~happy(X))<=>(~brave(X)&~creative(X))))&
((?[X]:((calm(X)&~tall(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~generous(X)|happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((brave(X)|~curious(X)))))&
(((~calm(susan)|strong(susan)))<=>(calm(john)))&
((?[X]:((~brave(X)<~>~kind(X))))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:(kind(X)=>(patient(X)|~brave(X))))&
(((~tall(paul)<~>~old(paul)))<=>(?[X]:(kind(X))))&
((quiet(fred))=>((kind(fred)&humble(fred))))&
((~tall(mary))<=>(?[X]:(humble(X))))&
(((creative(john)|curious(john)))=>(?[X]:(~tall(X))))&
(![X]:((~wise(X)|~happy(X))=>curious(X)))&
(![X]:((~tall(X)<~>humble(X))=>(~old(X)|curious(X))))&
((?[X]:(wise(X)))=>((~old(paul)<~>funny(paul))))&
(![X]:((~kind(X)|~brave(X))<=>(~strong(X)&~wise(X))))&
(?[X]:((brave(X)<~>rich(X))))&
((~brave(lucy)<~>funny(lucy)))&
(?[X]:((~old(X)&patient(X))))&
((~wise(susan)|strong(susan)))&
((~strong(fred)|funny(fred)))&
(~quiet(fred))&
(?[X]:((~wise(X)<~>strong(X)))) | quiet(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8328842708225135868448876
% SZS output start Proof for 8328842708225135868448876
22. ~quiet(fred) [input p21]
24. quiet(fred) [input hypothesis]
142. ~quiet(fred) [cnf transformation 22]
145. quiet(fred) [cnf transformation 24]
240. 21 <=> quiet(fred) [avatar definition]
301. ~21 [avatar split clause 142,240]
303. 21 [avatar split clause 145,240]
304. $false [avatar sat refutation 301,303]
% SZS output end Proof for 8328842708225135868448876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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