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 either not brave or not wise is both happy and not patient and vice versa. Everyone who is not happy or not tall is both rich and not strong and vice versa. If someone is both kind and not brave then someone is not funny or old and vice versa. Everyone who is not generous or not happy is both happy and not rich. Everyone who is both not strong and old is brave or patient. If alice is either rich or old then john is either patient or not wise and vice versa. If someone is quiet then alice is either funny or not quiet. Everyone who is either not patient or humble is not wise or funny and vice versa. Everyone who is strong is not funny. If mary is both funny and not creative then lucy is both not wise and curious. If alice is not tall then someone is both funny and not humble and vice versa. If susan is either not generous or brave then someone is patient. Everyone who is both patient and not humble is not brave or calm and vice versa. If someone is generous or quiet then someone is not creative or humble and vice versa. Everyone who is brave or not curious is humble or rich. Someone is either curious or funny. Paul is kind or humble. Paul is both quiet and not generous. | Susan is funny. | entailment | (![X]:((~brave(X)<~>~wise(X))<=>(happy(X)&~patient(X))))&
(![X]:((~happy(X)|~tall(X))<=>(rich(X)&~strong(X))))&
((?[X]:((kind(X)&~brave(X))))<=>(?[X]:((~funny(X)|old(X)))))&
(![X]:((~generous(X)|~happy(X))=>(happy(X)&~rich(X))))&
(![X]:((~strong(X)&old(X))=>(brave(X)|patient(X))))&
(((rich(alice)<~>old(alice)))<=>((patient(john)<~>~wise(john))))&
((?[X]:(quiet(X)))=>((funny(alice)<~>~quiet(alice))))&
(![X]:((~patient(X)<~>humble(X))<=>(~wise(X)|funny(X))))&
(![X]:(strong(X)=>~funny(X)))&
(((funny(mary)&~creative(mary)))=>((~wise(lucy)&curious(lucy))))&
((~tall(alice))<=>(?[X]:((funny(X)&~humble(X)))))&
(((~generous(susan)<~>brave(susan)))=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~humble(X))<=>(~brave(X)|calm(X))))&
((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((brave(X)|~curious(X))=>(humble(X)|rich(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((kind(paul)|humble(paul)))&
((quiet(paul)&~generous(paul))) | funny(susan) | [
"p0",
"p2",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2484843024123037155224317
% SZS output start Proof for 2484843024123037155224317
1. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~patient(X0) & happy(X0))) [input p0]
3. ? [X0] : (~brave(X0) & kind(X0)) <=> ? [X0] : (old(X0) | ~funny(X0)) [input p2]
8. ! [X0] : ((~patient(X0) <~> humble(X0)) <=> (funny(X0) | ~wise(X0))) [input p7]
13. ! [X0] : ((~humble(X0) & patient(X0)) <=> (calm(X0) | ~brave(X0))) [input p12]
19. ~funny(susan) [input hypothesis]
20. ? [X0] : (~brave(X0) & kind(X0)) <=> ? [X1] : (old(X1) | ~funny(X1)) [rectify 3]
32. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 1]
33. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 32]
36. (? [X0] : (~brave(X0) & kind(X0)) | ! [X1] : (~old(X1) & funny(X1))) & (? [X1] : (old(X1) | ~funny(X1)) | ! [X0] : (brave(X0) | ~kind(X0))) [nnf transformation 20]
37. (? [X0] : (~brave(X0) & kind(X0)) | ! [X1] : (~old(X1) & funny(X1))) & (? [X2] : (old(X2) | ~funny(X2)) | ! [X3] : (brave(X3) | ~kind(X3))) [rectify 36]
38. ? [X0] : (~brave(X0) & kind(X0)) => (~brave(sK0) & kind(sK0)) [choice axiom]
39. ? [X2] : (old(X2) | ~funny(X2)) => (old(sK1) | ~funny(sK1)) [choice axiom]
40. ((~brave(sK0) & kind(sK0)) | ! [X1] : (~old(X1) & funny(X1))) & ((old(sK1) | ~funny(sK1)) | ! [X3] : (brave(X3) | ~kind(X3))) [skolemisation 37,39,38]
43. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [nnf transformation 8]
44. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [flattening 43]
52. ! [X0] : (((~humble(X0) & patient(X0)) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | (humble(X0) | ~patient(X0)))) [nnf transformation 13]
53. ! [X0] : (((~humble(X0) & patient(X0)) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | humble(X0) | ~patient(X0))) [flattening 52]
64. ~patient(X0) | ~wise(X0) | brave(X0) [cnf transformation 33]
76. ~brave(sK0) | funny(X1) [cnf transformation 40]
95. ~patient(X0) | humble(X0) | wise(X0) [cnf transformation 44]
108. patient(X0) | brave(X0) [cnf transformation 53]
110. ~humble(X0) | brave(X0) [cnf transformation 53]
123. ~funny(susan) [cnf transformation 19]
129. 2 <=> brave(sK0) [avatar definition]
131. ~brave(sK0) <- (~2) [avatar component clause 129]
134. 3 <=> ! [X1] : funny(X1) [avatar definition]
135. funny(X1) <- (3) [avatar component clause 134]
136. 3 | ~2 [avatar split clause 76,129,134]
301. ~wise(X0) | brave(X0) | brave(X0) [resolution 64,108]
302. ~wise(X0) | brave(X0) [duplicate literal removal 301]
305. humble(X0) | wise(X0) | brave(X0) [resolution 95,108]
306. wise(X0) | brave(X0) [subsumption resolution 305,110]
307. brave(X0) [subsumption resolution 306,302]
308. $false <- (~2) [resolution 307,131]
310. 2 [avatar contradiction clause 308]
316. $false <- (3) [resolution 135,123]
321. ~3 [avatar contradiction clause 316]
324. $false [avatar sat refutation 136,310,321]
% SZS output end Proof for 2484843024123037155224317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not rich is tall or not old.
Everyone who is either humble or quiet is not generous and vice versa.
If fred is tall then alice is not humble or funny and vice versa.
If someone is either calm or happy then mary is not funny or not old and vice versa.
If someone is not wise or generous then susan is not old and vice versa.
If someone is humble or patient then john is funny.
Everyone who is not funny is tall and vice versa.
Everyone who is both not humble and wise is either not creative or not brave and vice versa.
Everyone who is either not strong or humble is quiet.
If someone is both rich and funny then alice is not curious or not creative.
Everyone who is either kind or wise is not tall or calm.
Everyone who is both not tall and not brave is not creative.
Everyone who is funny or curious is both not tall and happy.
Everyone who is not quiet is both not creative and not brave.
If alice is both quiet and not humble then someone is quiet.
Everyone who is both curious and not kind is both not kind and brave and vice versa.
Someone is happy.
Mary is not happy or funny.
Fred is either not creative or tall.
Susan is rich or quiet.
Lucy is both not curious and happy.
Someone is brave or quiet.
Alice is not tall or not strong. | Fred is not generous. | neutral | (![X]:((~curious(X)|~rich(X))=>(tall(X)|~old(X))))&
(![X]:((humble(X)<~>quiet(X))<=>~generous(X)))&
((tall(fred))<=>((~humble(alice)|funny(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~funny(mary)|~old(mary))))&
((?[X]:((~wise(X)|generous(X))))<=>(~old(susan)))&
((?[X]:((humble(X)|patient(X))))=>(funny(john)))&
(![X]:(~funny(X)<=>tall(X)))&
(![X]:((~humble(X)&wise(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:((~strong(X)<~>humble(X))=>quiet(X)))&
((?[X]:((rich(X)&funny(X))))=>((~curious(alice)|~creative(alice))))&
(![X]:((kind(X)<~>wise(X))=>(~tall(X)|calm(X))))&
(![X]:((~tall(X)&~brave(X))=>~creative(X)))&
(![X]:((funny(X)|curious(X))=>(~tall(X)&happy(X))))&
(![X]:(~quiet(X)=>(~creative(X)&~brave(X))))&
(((quiet(alice)&~humble(alice)))=>(?[X]:(quiet(X))))&
(![X]:((curious(X)&~kind(X))<=>(~kind(X)&brave(X))))&
(?[X]:(happy(X)))&
((~happy(mary)|funny(mary)))&
((~creative(fred)<~>tall(fred)))&
((rich(susan)|quiet(susan)))&
((~curious(lucy)&happy(lucy)))&
(?[X]:((brave(X)|quiet(X))))&
((~tall(alice)|~strong(alice))) | ~generous(fred) | [] | null | 0 |
If someone is both wise and not kind then john is generous.
Everyone who is patient or strong is both humble and not kind and vice versa.
If someone is funny then someone is not strong and vice versa.
Everyone who is either not happy or happy is both not tall and strong and vice versa.
Everyone who is not quiet is either not kind or calm.
Everyone who is both curious and creative is not quiet or not rich.
If someone is quiet or wise then someone is both not tall and humble.
Everyone who is not creative is not wise or not humble and vice versa.
If paul is curious then fred is wise or old.
If john is humble or quiet then john is either not rich or not old.
Everyone who is generous or not happy is not calm and vice versa.
If someone is old or not quiet then someone is both happy and funny.
Everyone who is both not humble and funny is both not patient and funny.
Everyone who is not quiet or old is funny or creative and vice versa.
If mary is not curious then someone is both kind and not tall.
Someone is funny or not generous.
Someone is wise or not creative.
Lucy is rich.
Paul is not generous or curious. | Lucy is not old. | entailment | ((?[X]:((wise(X)&~kind(X))))=>(generous(john)))&
(![X]:((patient(X)|strong(X))<=>(humble(X)&~kind(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~tall(X)&strong(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>calm(X))))&
(![X]:((curious(X)&creative(X))=>(~quiet(X)|~rich(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:(~creative(X)<=>(~wise(X)|~humble(X))))&
((curious(paul))=>((wise(fred)|old(fred))))&
(((humble(john)|quiet(john)))=>((~rich(john)<~>~old(john))))&
(![X]:((generous(X)|~happy(X))<=>~calm(X)))&
((?[X]:((old(X)|~quiet(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~humble(X)&funny(X))=>(~patient(X)&funny(X))))&
(![X]:((~quiet(X)|old(X))<=>(funny(X)|creative(X))))&
((~curious(mary))=>(?[X]:((kind(X)&~tall(X)))))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((wise(X)|~creative(X))))&
(rich(lucy))&
((~generous(paul)|curious(paul))) | ~old(lucy) | [
"p2",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 855279299704256083480889
% SZS output start Proof for 855279299704256083480889
3. ? [X0] : funny(X0) <=> ? [X0] : ~strong(X0) [input p2]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> (strong(X0) & ~tall(X0))) [input p3]
12. ? [X0] : (~quiet(X0) | old(X0)) => ? [X0] : (funny(X0) & happy(X0)) [input p11]
20. old(lucy) [input hypothesis]
21. ? [X0] : funny(X0) <=> ? [X1] : ~strong(X1) [rectify 3]
23. ? [X0] : (~quiet(X0) | old(X0)) => ? [X1] : (funny(X1) & happy(X1)) [rectify 12]
32. ? [X1] : (funny(X1) & happy(X1)) | ! [X0] : (quiet(X0) & ~old(X0)) [ennf transformation 23]
38. (? [X0] : funny(X0) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ~funny(X0)) [nnf transformation 21]
39. (? [X0] : funny(X0) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ~funny(X3)) [rectify 38]
40. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
41. ? [X2] : ~strong(X2) => ~strong(sK1) [choice axiom]
42. (funny(sK0) | ! [X1] : strong(X1)) & (~strong(sK1) | ! [X3] : ~funny(X3)) [skolemisation 39,41,40]
43. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~strong(X0) | tall(X0))) & ((strong(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~strong(X0) | tall(X0)) & ((strong(X0) & ~tall(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [flattening 43]
54. ? [X0] : (funny(X0) & happy(X0)) | ! [X1] : (quiet(X1) & ~old(X1)) [rectify 32]
55. ? [X0] : (funny(X0) & happy(X0)) => (funny(sK3) & happy(sK3)) [choice axiom]
56. (funny(sK3) & happy(sK3)) | ! [X1] : (quiet(X1) & ~old(X1)) [skolemisation 54,55]
71. ~strong(sK1) | ~funny(X3) [cnf transformation 42]
75. strong(X0) | happy(X0) | happy(X0) [cnf transformation 44]
76. strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 44]
99. funny(sK3) | ~old(X1) [cnf transformation 56]
113. old(lucy) [cnf transformation 20]
116. strong(X0) | happy(X0) [duplicate literal removal 75]
117. strong(X0) | ~happy(X0) [duplicate literal removal 76]
127. 3 <=> ! [X1] : strong(X1) [avatar definition]
128. strong(X1) <- (3) [avatar component clause 127]
135. 5 <=> ! [X3] : ~funny(X3) [avatar definition]
136. ~funny(X3) <- (5) [avatar component clause 135]
138. 6 <=> strong(sK1) [avatar definition]
140. ~strong(sK1) <- (~6) [avatar component clause 138]
141. 5 | ~6 [avatar split clause 71,138,135]
142. strong(X0) [subsumption resolution 116,117]
143. 3 [avatar split clause 142,127]
194. 18 <=> funny(sK3) [avatar definition]
196. funny(sK3) <- (18) [avatar component clause 194]
199. 19 <=> ! [X1] : ~old(X1) [avatar definition]
200. ~old(X1) <- (19) [avatar component clause 199]
201. 19 | 18 [avatar split clause 99,194,199]
233. $false <- (3, ~6) [resolution 140,128]
234. ~3 | 6 [avatar contradiction clause 233]
235. $false <- (19) [resolution 200,113]
236. ~19 [avatar contradiction clause 235]
237. $false <- (5, 18) [subsumption resolution 196,136]
238. ~5 | ~18 [avatar contradiction clause 237]
239. $false [avatar sat refutation 141,143,201,234,236,238]
% SZS output end Proof for 855279299704256083480889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or funny is either not calm or patient and vice versa. If someone is patient then someone is strong. If someone is kind then mary is either rich or curious and vice versa. If susan is not rich or not quiet then someone is not generous or generous and vice versa. Everyone who is patient is not wise and vice versa. If someone is wise then fred is both strong and rich. Everyone who is both not strong and not curious is patient and vice versa. If susan is not calm then susan is not rich or old and vice versa. If alice is not wise or not quiet then someone is old. If fred is quiet or not wise then paul is either creative or not tall and vice versa. Everyone who is both rich and strong is both not quiet and generous. If susan is either not happy or old then alice is not old or curious. If john is both not brave and not strong then someone is brave. Everyone who is not rich is either not humble or not creative. Everyone who is both not quiet and not happy is both not tall and quiet and vice versa. If someone is calm then paul is both not rich and rich. John is both not happy and not patient. Susan is both not strong and not creative. Someone is both brave and not curious. Alice is not curious. Someone is both not curious and happy. Susan is either kind or tall. Someone is either not funny or funny. Someone is both not creative and happy. | Fred is not strong. | contradiction | (![X]:((strong(X)<~>funny(X))<=>(~calm(X)<~>patient(X))))&
((?[X]:(patient(X)))=>(?[X]:(strong(X))))&
((?[X]:(kind(X)))<=>((rich(mary)<~>curious(mary))))&
(((~rich(susan)|~quiet(susan)))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:(patient(X)<=>~wise(X)))&
((?[X]:(wise(X)))=>((strong(fred)&rich(fred))))&
(![X]:((~strong(X)&~curious(X))<=>patient(X)))&
((~calm(susan))<=>((~rich(susan)|old(susan))))&
(((~wise(alice)|~quiet(alice)))=>(?[X]:(old(X))))&
(((quiet(fred)|~wise(fred)))<=>((creative(paul)<~>~tall(paul))))&
(![X]:((rich(X)&strong(X))=>(~quiet(X)&generous(X))))&
(((~happy(susan)<~>old(susan)))=>((~old(alice)|curious(alice))))&
(((~brave(john)&~strong(john)))=>(?[X]:(brave(X))))&
(![X]:(~rich(X)=>(~humble(X)<~>~creative(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:(calm(X)))=>((~rich(paul)&rich(paul))))&
((~happy(john)&~patient(john)))&
((~strong(susan)&~creative(susan)))&
(?[X]:((brave(X)&~curious(X))))&
(~curious(alice))&
(?[X]:((~curious(X)&happy(X))))&
((kind(susan)<~>tall(susan)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:((~creative(X)&happy(X)))) | ~strong(fred) | [
"p4",
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 877577135241303899663605
% SZS output start Proof for 877577135241303899663605
5. ! [X0] : (patient(X0) <=> ~wise(X0)) [input p4]
6. ? [X0] : wise(X0) => (rich(fred) & strong(fred)) [input p5]
17. ~patient(john) & ~happy(john) [input p16]
25. ~strong(fred) [input hypothesis]
30. (rich(fred) & strong(fred)) | ! [X0] : ~wise(X0) [ennf transformation 6]
51. ! [X0] : ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0))) [nnf transformation 5]
92. wise(X0) | patient(X0) [cnf transformation 51]
93. strong(fred) | ~wise(X0) [cnf transformation 30]
122. ~patient(john) [cnf transformation 17]
135. ~strong(fred) [cnf transformation 25]
182. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
183. ~wise(X0) <- (11) [avatar component clause 182]
190. 13 <=> strong(fred) [avatar definition]
193. 11 | 13 [avatar split clause 93,190,182]
275. ~13 [avatar split clause 135,190]
277. patient(X1) <- (11) [resolution 92,183]
279. $false <- (11) [resolution 277,122]
281. ~11 [avatar contradiction clause 279]
282. $false [avatar sat refutation 193,275,281]
% SZS output end Proof for 877577135241303899663605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative. Everyone who is old or humble is creative. Everyone who is old or patient is both not old and not strong. Everyone who is not strong or not happy is both not happy and kind. Everyone who is not kind or generous is calm and vice versa. If john is both not quiet and tall then someone is tall or humble and vice versa. Everyone who is curious or quiet is both funny and rich. Everyone who is not patient is both not old and funny and vice versa. Everyone who is not curious or calm is both not humble and kind and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Everyone who is quiet is both humble and not creative and vice versa. If paul is not creative or not strong then someone is strong and vice versa. John is not patient or humble. John is brave or not funny. Someone is not old. Lucy is both not old and not rich. Someone is brave. Lucy is patient or calm. | John is not humble. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
(![X]:((old(X)|patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
((~patient(john)|humble(john)))&
((brave(john)|~funny(john)))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy)))&
(?[X]:(brave(X)))&
((patient(lucy)|calm(lucy))) | ~humble(john) | [
"p0",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5491016329423642630559112
% SZS output start Proof for 5491016329423642630559112
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p2]
7. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p6]
9. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p8]
23. humble(john) [input hypothesis]
24. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 3]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 7]
32. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 24]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 9]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 42]
66. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 32]
71. ~old(X0) | ~old(X0) [cnf transformation 26]
87. ~curious(X0) | funny(X0) [cnf transformation 28]
94. ~humble(X0) | curious(X0) [cnf transformation 43]
131. humble(john) [cnf transformation 23]
132. ~old(X0) [duplicate literal removal 71]
165. 7 <=> humble(john) [avatar definition]
166. humble(john) <- (7) [avatar component clause 165]
188. 12 <=> funny(john) [avatar definition]
190. funny(john) <- (12) [avatar component clause 188]
256. 7 [avatar split clause 131,165]
266. curious(john) <- (7) [resolution 94,166]
268. funny(john) <- (7) [resolution 266,87]
271. 12 | ~7 [avatar split clause 268,165,188]
291. ~curious(john) | old(john) <- (12) [resolution 66,190]
294. old(john) <- (7, 12) [subsumption resolution 291,266]
295. $false <- (7, 12) [subsumption resolution 294,132]
296. ~7 | ~12 [avatar contradiction clause 295]
299. $false [avatar sat refutation 256,271,296]
% SZS output end Proof for 5491016329423642630559112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not creative or funny then someone is either not brave or tall.
If someone is wise or patient then someone is both funny and rich.
Everyone who is both strong and creative is brave or not happy and vice versa.
Everyone who is both not funny and funny is not tall and vice versa.
Everyone who is not tall is quiet or not humble.
If mary is not tall then someone is not rich or not brave and vice versa.
If john is either calm or not strong then someone is not wise or quiet.
If someone is not curious or not wise then someone is curious or not creative.
Everyone who is quiet is either creative or quiet.
Everyone who is either rich or not humble is not patient and vice versa.
Everyone who is either strong or not brave is creative and vice versa.
Everyone who is either strong or humble is either generous or calm and vice versa.
Everyone who is either not happy or not curious is either brave or strong.
If someone is curious then paul is not happy or generous.
Everyone who is either creative or not kind is humble and vice versa.
Everyone who is not curious or not kind is both not tall and rich.
Someone is both humble and not patient.
Alice is either humble or quiet.
Someone is either not happy or generous.
Lucy is not quiet or creative.
Someone is creative.
Someone is either not curious or generous. | John is not generous. | neutral | (((~creative(susan)<~>funny(susan)))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)|~happy(X))))&
(![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~curious(X)|~kind(X))=>(~tall(X)&rich(X))))&
(?[X]:((humble(X)&~patient(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is quiet or not patient is both not quiet and curious. If mary is curious or not tall then mary is quiet and vice versa. If john is not humble then someone is both not tall and funny. Everyone who is both not funny and not old is both not strong and happy and vice versa. Everyone who is not patient is both not tall and not calm and vice versa. Everyone who is either not quiet or not calm is either not creative or rich and vice versa. Everyone who is either patient or rich is not curious or quiet. Everyone who is both old and calm is happy or not old. Everyone who is both brave and happy is either not brave or generous. Everyone who is both not curious and not old is curious and vice versa. Everyone who is not generous is not creative and vice versa. Everyone who is patient is not strong or rich. Everyone who is calm is both humble and not patient and vice versa. If someone is calm then someone is funny. If someone is brave or generous then someone is both not patient and not calm. Someone is wise or not curious. Someone is either wise or not kind. Someone is both not humble and not strong. Alice is either not generous or generous. Someone is creative or wise. | John is wise. | neutral | (![X]:((quiet(X)|~patient(X))=>(~quiet(X)&curious(X))))&
(((curious(mary)|~tall(mary)))<=>(quiet(mary)))&
((~humble(john))=>(?[X]:((~tall(X)&funny(X)))))&
(![X]:((~funny(X)&~old(X))<=>(~strong(X)&happy(X))))&
(![X]:(~patient(X)<=>(~tall(X)&~calm(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((patient(X)<~>rich(X))=>(~curious(X)|quiet(X))))&
(![X]:((old(X)&calm(X))=>(happy(X)|~old(X))))&
(![X]:((brave(X)&happy(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&~old(X))<=>curious(X)))&
(![X]:(~generous(X)<=>~creative(X)))&
(![X]:(patient(X)=>(~strong(X)|rich(X))))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
((?[X]:(calm(X)))=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)&~calm(X)))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~generous(alice)<~>generous(alice)))&
(?[X]:((creative(X)|wise(X)))) | wise(john) | [] | null | 0 |
Everyone who is both generous and funny is humble. If lucy is brave then someone is strong or not old. Everyone who is brave is not brave or not funny and vice versa. Everyone who is wise is either patient or not patient and vice versa. If paul is both not brave and wise then john is either patient or not funny and vice versa. If someone is funny then paul is not rich or not tall. If someone is either happy or creative then fred is not patient or not curious. If someone is happy then someone is either not quiet or rich. Everyone who is both patient and kind is not kind or tall. If someone is kind then lucy is strong and vice versa. Everyone who is curious is old. Everyone who is either funny or calm is quiet or funny. If paul is creative or not generous then someone is either not rich or not humble and vice versa. Everyone who is either not happy or not patient is quiet. If someone is humble or quiet then mary is brave. Everyone who is both patient and creative is both not tall and strong. Someone is calm. Paul is both not tall and not calm. Lucy is quiet. Someone is both not curious and not funny. John is not patient or calm. John is either calm or not humble. Alice is strong or not wise. Someone is quiet. | Mary is funny. | contradiction | (![X]:((generous(X)&funny(X))=>humble(X)))&
((brave(lucy))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:(brave(X)<=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)<=>(patient(X)<~>~patient(X))))&
(((~brave(paul)&wise(paul)))<=>((patient(john)<~>~funny(john))))&
((?[X]:(funny(X)))=>((~rich(paul)|~tall(paul))))&
((?[X]:((happy(X)<~>creative(X))))=>((~patient(fred)|~curious(fred))))&
((?[X]:(happy(X)))=>(?[X]:((~quiet(X)<~>rich(X)))))&
(![X]:((patient(X)&kind(X))=>(~kind(X)|tall(X))))&
((?[X]:(kind(X)))<=>(strong(lucy)))&
(![X]:(curious(X)=>old(X)))&
(![X]:((funny(X)<~>calm(X))=>(quiet(X)|funny(X))))&
(((creative(paul)|~generous(paul)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~happy(X)<~>~patient(X))=>quiet(X)))&
((?[X]:((humble(X)|quiet(X))))=>(brave(mary)))&
(![X]:((patient(X)&creative(X))=>(~tall(X)&strong(X))))&
(?[X]:(calm(X)))&
((~tall(paul)&~calm(paul)))&
(quiet(lucy))&
(?[X]:((~curious(X)&~funny(X))))&
((~patient(john)|calm(john)))&
((calm(john)<~>~humble(john)))&
((strong(alice)|~wise(alice)))&
(?[X]:(quiet(X))) | funny(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3986274214423304456851586
% SZS output start Proof for 3986274214423304456851586
3. ! [X0] : (brave(X0) <=> (~funny(X0) | ~brave(X0))) [input p2]
25. funny(mary) [input hypothesis]
44. ! [X0] : ((brave(X0) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | ~brave(X0))) [nnf transformation 3]
45. ! [X0] : ((brave(X0) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | ~brave(X0))) [flattening 44]
72. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 45]
73. brave(X0) | brave(X0) [cnf transformation 45]
115. funny(mary) [cnf transformation 25]
120. ~funny(X0) | ~brave(X0) [duplicate literal removal 72]
121. brave(X0) [duplicate literal removal 73]
122. ~funny(X0) [subsumption resolution 120,121]
184. $false [subsumption resolution 115,122]
% SZS output end Proof for 3986274214423304456851586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either brave or not generous then fred is kind or not wise and vice versa. If someone is wise then someone is patient. If mary is either generous or not brave then someone is not quiet. If alice is both wise and not quiet then someone is generous and vice versa. Everyone who is kind or quiet is both quiet and funny. Everyone who is both funny and strong is not calm and vice versa. Everyone who is both calm and not wise is both quiet and patient and vice versa. If susan is not curious then someone is both brave and kind. If someone is not quiet or curious then fred is either patient or not curious. If someone is both not wise and tall then someone is either humble or quiet. Everyone who is not curious or not brave is not generous and vice versa. Everyone who is both not quiet and not funny is both not strong and kind. Everyone who is either not generous or wise is both patient and not curious and vice versa. If someone is either tall or generous then someone is both not humble and wise and vice versa. Everyone who is rich is not wise or not tall. If mary is both not old and generous then someone is both tall and strong and vice versa. Mary is both not old and happy. Fred is not patient or not creative. Someone is brave. Someone is not patient or not strong. Susan is happy. Alice is both strong and not calm. Someone is rich or kind. Fred is both not quiet and creative. | Alice is generous. | contradiction | (((brave(paul)<~>~generous(paul)))<=>((kind(fred)|~wise(fred))))&
((?[X]:(wise(X)))=>(?[X]:(patient(X))))&
(((generous(mary)<~>~brave(mary)))=>(?[X]:(~quiet(X))))&
(((wise(alice)&~quiet(alice)))<=>(?[X]:(generous(X))))&
(![X]:((kind(X)|quiet(X))=>(quiet(X)&funny(X))))&
(![X]:((funny(X)&strong(X))<=>~calm(X)))&
(![X]:((calm(X)&~wise(X))<=>(quiet(X)&patient(X))))&
((~curious(susan))=>(?[X]:((brave(X)&kind(X)))))&
((?[X]:((~quiet(X)|curious(X))))=>((patient(fred)<~>~curious(fred))))&
((?[X]:((~wise(X)&tall(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
(![X]:((~curious(X)|~brave(X))<=>~generous(X)))&
(![X]:((~quiet(X)&~funny(X))=>(~strong(X)&kind(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(patient(X)&~curious(X))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:(rich(X)=>(~wise(X)|~tall(X))))&
(((~old(mary)&generous(mary)))<=>(?[X]:((tall(X)&strong(X)))))&
((~old(mary)&happy(mary)))&
((~patient(fred)|~creative(fred)))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)|~strong(X))))&
(happy(susan))&
((strong(alice)&~calm(alice)))&
(?[X]:((rich(X)|kind(X))))&
((~quiet(fred)&creative(fred))) | generous(alice) | [
"p3",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8639729787254056724358179
% SZS output start Proof for 8639729787254056724358179
4. (~quiet(alice) & wise(alice)) <=> ? [X0] : generous(X0) [input p3]
11. ! [X0] : ((~brave(X0) | ~curious(X0)) <=> ~generous(X0)) [input p10]
13. ! [X0] : ((~generous(X0) <~> wise(X0)) <=> (~curious(X0) & patient(X0))) [input p12]
25. generous(alice) [input hypothesis]
49. ((~quiet(alice) & wise(alice)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (quiet(alice) | ~wise(alice))) [nnf transformation 4]
50. ((~quiet(alice) & wise(alice)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | quiet(alice) | ~wise(alice)) [flattening 49]
51. ((~quiet(alice) & wise(alice)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | quiet(alice) | ~wise(alice)) [rectify 50]
52. ? [X1] : generous(X1) => generous(sK2) [choice axiom]
53. ((~quiet(alice) & wise(alice)) | ! [X0] : ~generous(X0)) & (generous(sK2) | quiet(alice) | ~wise(alice)) [skolemisation 51,52]
65. ! [X0] : (((~brave(X0) | ~curious(X0)) | generous(X0)) & (~generous(X0) | (brave(X0) & curious(X0)))) [nnf transformation 11]
66. ! [X0] : ((~brave(X0) | ~curious(X0) | generous(X0)) & (~generous(X0) | (brave(X0) & curious(X0)))) [flattening 65]
67. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [nnf transformation 13]
68. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [flattening 67]
95. wise(alice) | ~generous(X0) [cnf transformation 53]
116. ~generous(X0) | curious(X0) [cnf transformation 66]
124. ~curious(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 68]
147. generous(alice) [cnf transformation 25]
193. 10 <=> ! [X0] : ~generous(X0) [avatar definition]
194. ~generous(X0) <- (10) [avatar component clause 193]
201. 12 <=> wise(alice) [avatar definition]
203. wise(alice) <- (12) [avatar component clause 201]
204. 10 | 12 [avatar split clause 95,201,193]
258. ~wise(X0) | ~generous(X0) [subsumption resolution 124,116]
334. $false <- (10) [resolution 194,147]
335. ~10 [avatar contradiction clause 334]
344. ~generous(alice) <- (12) [resolution 258,203]
346. $false <- (12) [subsumption resolution 344,147]
347. ~12 [avatar contradiction clause 346]
348. $false [avatar sat refutation 204,335,347]
% SZS output end Proof for 8639729787254056724358179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and not funny is either not happy or wise and vice versa.
If alice is both not strong and kind then paul is either patient or kind.
Everyone who is strong is both not humble and tall and vice versa.
Everyone who is either not humble or patient is not kind and vice versa.
If john is either strong or not old then john is either patient or creative and vice versa.
Everyone who is brave is generous or not rich.
Everyone who is either happy or curious is either not brave or creative.
If fred is either humble or wise then someone is both rich and not wise and vice versa.
If someone is both not brave and calm then paul is either not tall or not happy and vice versa.
Everyone who is either rich or calm is both happy and not wise.
Everyone who is tall or quiet is either not happy or tall and vice versa.
Everyone who is both wise and funny is generous or brave and vice versa.
Everyone who is either not strong or not rich is either not happy or not patient and vice versa.
Everyone who is either not calm or curious is not patient.
If alice is not humble or not brave then someone is not strong.
If someone is humble or generous then someone is either not old or not humble and vice versa.
John is either funny or not brave.
Alice is both not old and not brave.
Someone is either not kind or generous.
Susan is either not calm or not wise.
Susan is patient or calm.
Someone is wise or not humble.
Paul is strong or curious. | Paul is not rich. | neutral | (![X]:((~humble(X)&~funny(X))<=>(~happy(X)<~>wise(X))))&
(((~strong(alice)&kind(alice)))=>((patient(paul)<~>kind(paul))))&
(![X]:(strong(X)<=>(~humble(X)&tall(X))))&
(![X]:((~humble(X)<~>patient(X))<=>~kind(X)))&
(((strong(john)<~>~old(john)))<=>((patient(john)<~>creative(john))))&
(![X]:(brave(X)=>(generous(X)|~rich(X))))&
(![X]:((happy(X)<~>curious(X))=>(~brave(X)<~>creative(X))))&
(((humble(fred)<~>wise(fred)))<=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((~brave(X)&calm(X))))<=>((~tall(paul)<~>~happy(paul))))&
(![X]:((rich(X)<~>calm(X))=>(happy(X)&~wise(X))))&
(![X]:((tall(X)|quiet(X))<=>(~happy(X)<~>tall(X))))&
(![X]:((wise(X)&funny(X))<=>(generous(X)|brave(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~happy(X)<~>~patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>~patient(X)))&
(((~humble(alice)|~brave(alice)))=>(?[X]:(~strong(X))))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((~old(X)<~>~humble(X)))))&
((funny(john)<~>~brave(john)))&
((~old(alice)&~brave(alice)))&
(?[X]:((~kind(X)<~>generous(X))))&
((~calm(susan)<~>~wise(susan)))&
((patient(susan)|calm(susan)))&
(?[X]:((wise(X)|~humble(X))))&
((strong(paul)|curious(paul))) | ~rich(paul) | [] | null | 0 |
Everyone who is calm or not rich is either creative or happy.
If fred is either not happy or not patient then mary is funny and vice versa.
If john is strong then john is both not generous and rich.
If someone is both not rich and strong then someone is both not calm and strong and vice versa.
If someone is happy or not curious then someone is either not quiet or old.
Everyone who is either happy or patient is both tall and old.
If someone is not happy or funny then john is brave or not quiet and vice versa.
Everyone who is not quiet is either not strong or brave and vice versa.
Everyone who is patient or not curious is not calm.
If someone is either not generous or patient then someone is either not curious or tall.
Everyone who is funny or happy is not tall.
Everyone who is rich or not tall is curious or not brave and vice versa.
Everyone who is patient is either not creative or calm and vice versa.
Everyone who is not brave is not old.
If someone is both patient and strong then mary is both not patient and humble.
Everyone who is both not rich and happy is both quiet and not humble and vice versa.
John is either funny or not humble.
Someone is either quiet or creative.
Someone is creative.
Someone is quiet or calm.
Lucy is both rich and patient.
Someone is generous.
Paul is not quiet.
Someone is not quiet or calm. | Paul is old. | neutral | (![X]:((calm(X)|~rich(X))=>(creative(X)<~>happy(X))))&
(((~happy(fred)<~>~patient(fred)))<=>(funny(mary)))&
((strong(john))=>((~generous(john)&rich(john))))&
((?[X]:((~rich(X)&strong(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
((?[X]:((happy(X)|~curious(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((happy(X)<~>patient(X))=>(tall(X)&old(X))))&
((?[X]:((~happy(X)|funny(X))))<=>((brave(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>brave(X))))&
(![X]:((patient(X)|~curious(X))=>~calm(X)))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((funny(X)|happy(X))=>~tall(X)))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)|~brave(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>calm(X))))&
(![X]:(~brave(X)=>~old(X)))&
((?[X]:((patient(X)&strong(X))))=>((~patient(mary)&humble(mary))))&
(![X]:((~rich(X)&happy(X))<=>(quiet(X)&~humble(X))))&
((funny(john)<~>~humble(john)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)|calm(X))))&
((rich(lucy)&patient(lucy)))&
(?[X]:(generous(X)))&
(~quiet(paul))&
(?[X]:((~quiet(X)|calm(X)))) | old(paul) | [] | null | 0 |
If someone is not curious or not generous then john is not tall or not quiet and vice versa.
Everyone who is either not kind or not funny is curious or wise and vice versa.
If someone is not creative then someone is both kind and wise and vice versa.
If fred is both not kind and not rich then someone is not curious and vice versa.
Everyone who is rich or not wise is not brave and vice versa.
Everyone who is not creative or old is both wise and not kind.
Everyone who is both not calm and creative is not quiet or generous and vice versa.
Everyone who is both wise and patient is brave or not happy and vice versa.
If fred is brave or not rich then someone is tall and vice versa.
If someone is generous or happy then lucy is not creative or not generous.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
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 not kind. | neutral | ((?[X]:((~curious(X)|~generous(X))))<=>((~tall(john)|~quiet(john))))&
(![X]:((~kind(X)<~>~funny(X))<=>(curious(X)|wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~kind(fred)&~rich(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~wise(X))<=>~brave(X)))&
(![X]:((~creative(X)|old(X))=>(wise(X)&~kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((wise(X)&patient(X))<=>(brave(X)|~happy(X))))&
(((brave(fred)|~rich(fred)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)|happy(X))))=>((~creative(lucy)|~generous(lucy))))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![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)))) | ~kind(paul) | [] | null | 0 |
If susan is either not happy or creative then lucy is not tall or not wise and vice versa.
If mary is either not funny or humble then susan is not patient or funny and vice versa.
If someone is either not calm or kind then someone is either rich or not funny and vice versa.
Everyone who is both not strong and not generous is happy.
Everyone who is either not wise or strong is funny or not patient and vice versa.
If someone is happy then someone is either not curious or not patient and vice versa.
If alice is not creative then someone is generous.
If someone is not patient or not quiet then paul is strong or not patient.
Everyone who is either patient or not quiet is both creative and not generous and vice versa.
Everyone who is not curious is either tall or not generous.
Everyone who is not tall is happy or curious and vice versa.
If mary is either not humble or strong then john is tall.
Everyone who is not rich or wise is rich and vice versa.
If alice is not old then someone is not patient.
If paul is strong or not curious then john is rich or old.
If someone is both rich and quiet then someone is wise.
Susan is not kind.
Susan is tall or humble.
Paul is calm or quiet.
John is creative or not brave.
Paul is not creative or not curious.
John is either not generous or not strong.
Lucy is creative.
Someone is either quiet or tall. | John is not humble. | neutral | (((~happy(susan)<~>creative(susan)))<=>((~tall(lucy)|~wise(lucy))))&
(((~funny(mary)<~>humble(mary)))<=>((~patient(susan)|funny(susan))))&
((?[X]:((~calm(X)<~>kind(X))))<=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~strong(X)&~generous(X))=>happy(X)))&
(![X]:((~wise(X)<~>strong(X))<=>(funny(X)|~patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
((~creative(alice))=>(?[X]:(generous(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>((strong(paul)|~patient(paul))))&
(![X]:((patient(X)<~>~quiet(X))<=>(creative(X)&~generous(X))))&
(![X]:(~curious(X)=>(tall(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(happy(X)|curious(X))))&
(((~humble(mary)<~>strong(mary)))=>(tall(john)))&
(![X]:((~rich(X)|wise(X))<=>rich(X)))&
((~old(alice))=>(?[X]:(~patient(X))))&
(((strong(paul)|~curious(paul)))=>((rich(john)|old(john))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:(wise(X))))&
(~kind(susan))&
((tall(susan)|humble(susan)))&
((calm(paul)|quiet(paul)))&
((creative(john)|~brave(john)))&
((~creative(paul)|~curious(paul)))&
((~generous(john)<~>~strong(john)))&
(creative(lucy))&
(?[X]:((quiet(X)<~>tall(X)))) | ~humble(john) | [] | null | 0 |
Everyone who is either not rich or not creative is both not patient and calm and vice versa. Everyone who is not strong or not happy is brave and vice versa. Everyone who is curious or tall is creative and vice versa. Everyone who is either creative or funny is both not calm and patient and vice versa. Everyone who is not brave or kind is not generous. Everyone who is not creative is not brave or not kind and vice versa. Everyone who is either not quiet or calm is either not kind or not tall. Everyone who is both tall and brave is both not creative and not old and vice versa. Everyone who is either not funny or patient is either not tall or creative and vice versa. If alice is funny then someone is kind or curious. If john is not happy then paul is both not quiet and brave. If someone is quiet or not curious then mary is not brave and vice versa. If mary is both not wise and funny then someone is strong or generous and vice versa. If paul is not strong or kind then fred is not tall or generous and vice versa. Everyone who is both not rich and humble is not brave or not curious. Everyone who is not brave or not wise is quiet or wise. John is not creative. Alice is either patient or not curious. Someone is not rich or strong. Someone is both calm and strong. Alice is not wise. Someone is not tall or creative. Lucy is both curious and funny. Fred is both wise and not quiet. | Alice is not funny. | entailment | (![X]:((~rich(X)<~>~creative(X))<=>(~patient(X)&calm(X))))&
(![X]:((~strong(X)|~happy(X))<=>brave(X)))&
(![X]:((curious(X)|tall(X))<=>creative(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~calm(X)&patient(X))))&
(![X]:((~brave(X)|kind(X))=>~generous(X)))&
(![X]:(~creative(X)<=>(~brave(X)|~kind(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~kind(X)<~>~tall(X))))&
(![X]:((tall(X)&brave(X))<=>(~creative(X)&~old(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(~tall(X)<~>creative(X))))&
((funny(alice))=>(?[X]:((kind(X)|curious(X)))))&
((~happy(john))=>((~quiet(paul)&brave(paul))))&
((?[X]:((quiet(X)|~curious(X))))<=>(~brave(mary)))&
(((~wise(mary)&funny(mary)))<=>(?[X]:((strong(X)|generous(X)))))&
(((~strong(paul)|kind(paul)))<=>((~tall(fred)|generous(fred))))&
(![X]:((~rich(X)&humble(X))=>(~brave(X)|~curious(X))))&
(![X]:((~brave(X)|~wise(X))=>(quiet(X)|wise(X))))&
(~creative(john))&
((patient(alice)<~>~curious(alice)))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((calm(X)&strong(X))))&
(~wise(alice))&
(?[X]:((~tall(X)|creative(X))))&
((curious(lucy)&funny(lucy)))&
((wise(fred)&~quiet(fred))) | ~funny(alice) | [
"p2",
"p3",
"p5",
"p6",
"p8",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8711843198573061371176804
% SZS output start Proof for 8711843198573061371176804
3. ! [X0] : ((tall(X0) | curious(X0)) <=> creative(X0)) [input p2]
4. ! [X0] : ((creative(X0) <~> funny(X0)) <=> (patient(X0) & ~calm(X0))) [input p3]
6. ! [X0] : (~creative(X0) <=> (~kind(X0) | ~brave(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) <~> calm(X0)) => (~kind(X0) <~> ~tall(X0))) [input p6]
9. ! [X0] : ((~funny(X0) <~> patient(X0)) <=> (~tall(X0) <~> creative(X0))) [input p8]
16. ! [X0] : ((~wise(X0) | ~brave(X0)) => (wise(X0) | quiet(X0))) [input p15]
18. patient(alice) <~> ~curious(alice) [input p17]
21. ~wise(alice) [input p20]
25. funny(alice) [input hypothesis]
28. ! [X0] : ((~kind(X0) <~> ~tall(X0)) | (~quiet(X0) <=> calm(X0))) [ennf transformation 7]
31. ! [X0] : ((wise(X0) | quiet(X0)) | (wise(X0) & brave(X0))) [ennf transformation 16]
32. ! [X0] : (wise(X0) | quiet(X0) | (wise(X0) & brave(X0))) [flattening 31]
37. ! [X0] : (((tall(X0) | curious(X0)) | ~creative(X0)) & (creative(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 3]
38. ! [X0] : ((tall(X0) | curious(X0) | ~creative(X0)) & (creative(X0) | (~tall(X0) & ~curious(X0)))) [flattening 37]
39. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 4]
40. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [flattening 39]
41. ! [X0] : ((~creative(X0) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | creative(X0))) [nnf transformation 6]
42. ! [X0] : ((~creative(X0) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | creative(X0))) [flattening 41]
43. ! [X0] : (((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) [nnf transformation 28]
46. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [nnf transformation 9]
60. (curious(alice) | ~patient(alice)) & (~curious(alice) | patient(alice)) [nnf transformation 18]
76. ~curious(X0) | creative(X0) [cnf transformation 38]
77. ~tall(X0) | creative(X0) [cnf transformation 38]
78. ~creative(X0) | curious(X0) | tall(X0) [cnf transformation 38]
82. ~funny(X0) | creative(X0) | patient(X0) [cnf transformation 40]
84. ~funny(X0) | ~creative(X0) | ~patient(X0) | calm(X0) [cnf transformation 40]
89. ~creative(X0) | kind(X0) [cnf transformation 42]
91. ~quiet(X0) | ~kind(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 43]
101. ~funny(X0) | tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 46]
103. patient(X0) | ~funny(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 46]
122. wise(X0) | quiet(X0) | wise(X0) [cnf transformation 32]
124. ~curious(alice) | patient(alice) [cnf transformation 60]
125. curious(alice) | ~patient(alice) [cnf transformation 60]
129. ~wise(alice) [cnf transformation 21]
135. funny(alice) [cnf transformation 25]
136. wise(X0) | quiet(X0) [duplicate literal removal 122]
142. ~funny(X0) | patient(X0) | ~tall(X0) [subsumption resolution 103,77]
144. 1 <=> funny(alice) [avatar definition]
145. funny(alice) <- (1) [avatar component clause 144]
239. 22 <=> patient(alice) [avatar definition]
240. patient(alice) <- (22) [avatar component clause 239]
241. ~patient(alice) <- (~22) [avatar component clause 239]
243. 23 <=> curious(alice) [avatar definition]
244. ~curious(alice) <- (~23) [avatar component clause 243]
245. curious(alice) <- (23) [avatar component clause 243]
246. ~22 | 23 [avatar split clause 125,243,239]
247. 22 | ~23 [avatar split clause 124,243,239]
257. 1 [avatar split clause 135,144]
269. quiet(alice) [resolution 136,129]
331. 36 <=> calm(alice) [avatar definition]
332. calm(alice) <- (36) [avatar component clause 331]
335. 37 <=> creative(alice) [avatar definition]
337. creative(alice) <- (37) [avatar component clause 335]
360. creative(alice) | patient(alice) <- (1) [resolution 82,145]
369. 22 | 37 | ~1 [avatar split clause 360,144,335,239]
378. creative(alice) <- (23) [resolution 245,76]
381. 37 | ~23 [avatar split clause 378,243,335]
383. curious(alice) | tall(alice) <- (37) [resolution 337,78]
385. kind(alice) <- (37) [resolution 337,89]
439. patient(alice) | ~tall(alice) <- (1) [resolution 142,145]
473. ~creative(alice) | ~patient(alice) | calm(alice) <- (1) [resolution 84,145]
477. ~patient(alice) | calm(alice) <- (1, 37) [subsumption resolution 473,337]
478. calm(alice) <- (1, 22, 37) [subsumption resolution 477,240]
481. 36 | ~1 | ~22 | ~37 [avatar split clause 478,335,239,144,331]
496. ~kind(alice) | ~tall(alice) | ~calm(alice) [resolution 91,269]
498. ~tall(alice) | ~calm(alice) <- (37) [subsumption resolution 496,385]
499. ~tall(alice) <- (36, 37) [subsumption resolution 498,332]
518. tall(alice) | ~creative(alice) | ~patient(alice) <- (1) [resolution 101,145]
520. ~creative(alice) | ~patient(alice) <- (1, 36, 37) [subsumption resolution 518,499]
521. ~patient(alice) <- (1, 36, 37) [subsumption resolution 520,337]
524. ~22 | ~1 | ~36 | ~37 [avatar split clause 521,335,331,144,239]
530. tall(alice) <- (~23, 37) [subsumption resolution 383,244]
531. ~tall(alice) <- (1, ~22) [subsumption resolution 439,241]
532. $false <- (1, ~22, ~23, 37) [subsumption resolution 531,530]
533. ~1 | 22 | 23 | ~37 [avatar contradiction clause 532]
536. $false [avatar sat refutation 246,247,257,369,381,481,524,533]
% SZS output end Proof for 8711843198573061371176804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both tall and generous then someone is both not kind and not patient and vice versa.
Everyone who is not quiet is both not brave and calm.
Everyone who is both not calm and funny is both not tall and generous and vice versa.
If someone is tall or not old then john is kind.
Everyone who is tall is both not strong and wise.
If alice is rich or not old then someone is either calm or not generous and vice versa.
If fred is not curious or old then mary is not wise or tall.
Everyone who is not funny is both not rich and not quiet and vice versa.
If john is creative then john is not old or kind and vice versa.
If someone is creative then alice is not quiet and vice versa.
Everyone who is either not rich or quiet is not creative or funny.
Everyone who is not funny is not quiet or not generous and vice versa.
Everyone who is either not calm or not quiet is patient and vice versa.
Everyone who is rich is either not strong or not tall and vice versa.
Everyone who is both happy and curious is either not tall or not happy and vice versa.
Everyone who is not tall or not humble is old or not funny.
Alice is wise or happy.
Paul is either not wise or not humble.
Lucy is either not strong or not curious.
Someone is not kind or not quiet.
Lucy is old.
Someone is strong.
Fred is both kind and not brave.
Paul is not patient. | Paul is strong. | contradiction | (((tall(john)&generous(john)))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(~tall(X)&generous(X))))&
((?[X]:((tall(X)|~old(X))))=>(kind(john)))&
(![X]:(tall(X)=>(~strong(X)&wise(X))))&
(((rich(alice)|~old(alice)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(((~curious(fred)|old(fred)))=>((~wise(mary)|tall(mary))))&
(![X]:(~funny(X)<=>(~rich(X)&~quiet(X))))&
((creative(john))<=>((~old(john)|kind(john))))&
((?[X]:(creative(X)))<=>(~quiet(alice)))&
(![X]:((~rich(X)<~>quiet(X))=>(~creative(X)|funny(X))))&
(![X]:(~funny(X)<=>(~quiet(X)|~generous(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>patient(X)))&
(![X]:(rich(X)<=>(~strong(X)<~>~tall(X))))&
(![X]:((happy(X)&curious(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~tall(X)|~humble(X))=>(old(X)|~funny(X))))&
((wise(alice)|happy(alice)))&
((~wise(paul)<~>~humble(paul)))&
((~strong(lucy)<~>~curious(lucy)))&
(?[X]:((~kind(X)|~quiet(X))))&
(old(lucy))&
(?[X]:(strong(X)))&
((kind(fred)&~brave(fred)))&
(~patient(paul)) | strong(paul) | [
"p1",
"p2",
"p4",
"p7",
"p11",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5637175793847177603631079
% SZS output start Proof for 5637175793847177603631079
2. ! [X0] : (~quiet(X0) => (calm(X0) & ~brave(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (generous(X0) & ~tall(X0))) [input p2]
5. ! [X0] : (tall(X0) => (wise(X0) & ~strong(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~quiet(X0) & ~rich(X0))) [input p7]
12. ! [X0] : (~funny(X0) <=> (~generous(X0) | ~quiet(X0))) [input p11]
13. ! [X0] : ((~calm(X0) <~> ~quiet(X0)) <=> patient(X0)) [input p12]
24. ~patient(paul) [input p23]
25. strong(paul) [input hypothesis]
26. ! [X0] : (~quiet(X0) => calm(X0)) [pure predicate removal 2]
28. ! [X0] : (calm(X0) | quiet(X0)) [ennf transformation 26]
30. ! [X0] : ((wise(X0) & ~strong(X0)) | ~tall(X0)) [ennf transformation 5]
42. ! [X0] : (((funny(X0) & ~calm(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 3]
43. ! [X0] : (((funny(X0) & ~calm(X0)) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~funny(X0) | calm(X0))) [flattening 42]
49. ! [X0] : ((~funny(X0) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | funny(X0))) [nnf transformation 8]
50. ! [X0] : ((~funny(X0) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | funny(X0))) [flattening 49]
58. ! [X0] : ((~funny(X0) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | funny(X0))) [nnf transformation 12]
59. ! [X0] : ((~funny(X0) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | funny(X0))) [flattening 58]
60. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | ~patient(X0)) & (patient(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [nnf transformation 13]
74. calm(X0) | quiet(X0) [cnf transformation 28]
77. ~calm(X0) | ~generous(X0) | tall(X0) [cnf transformation 43]
81. ~strong(X0) | ~tall(X0) [cnf transformation 30]
92. ~quiet(X0) | funny(X0) [cnf transformation 50]
103. ~funny(X0) | generous(X0) [cnf transformation 59]
104. patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 60]
105. patient(X0) | ~calm(X0) | quiet(X0) [cnf transformation 60]
129. ~patient(paul) [cnf transformation 24]
130. strong(paul) [cnf transformation 25]
239. quiet(X0) | patient(X0) [subsumption resolution 105,74]
240. calm(X0) | patient(X0) [subsumption resolution 104,74]
284. ~tall(paul) [resolution 81,130]
298. funny(X0) | patient(X0) [resolution 239,92]
312. ~generous(X0) | tall(X0) | patient(X0) [resolution 77,240]
425. patient(X4) | generous(X4) [resolution 298,103]
448. patient(X0) | tall(X0) [subsumption resolution 312,425]
479. tall(paul) [resolution 448,129]
482. $false [subsumption resolution 479,284]
% SZS output end Proof for 5637175793847177603631079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not strong or not kind then someone is either tall or not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
If someone is not old or happy then lucy is either not creative or not wise and vice versa.
Everyone who is either funny or tall is strong.
Alice is either not curious or brave.
John is either not quiet or not creative.
Alice is either creative or not wise.
Someone is either not calm or not wise.
Someone is both not curious and brave.
Someone is either kind or not kind.
Lucy is brave. | John is kind. | contradiction | (((~strong(john)|~kind(john)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
((?[X]:((~old(X)|happy(X))))<=>((~creative(lucy)<~>~wise(lucy))))&
(![X]:((funny(X)<~>tall(X))=>strong(X)))&
((~curious(alice)<~>brave(alice)))&
((~quiet(john)<~>~creative(john)))&
((creative(alice)<~>~wise(alice)))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(brave(lucy)) | kind(john) | [
"p1",
"p2",
"p3",
"p6",
"p8",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2411647002323144096415105
% SZS output start Proof for 2411647002323144096415105
2. ! [X0] : ((~patient(X0) | ~calm(X0)) => (wise(X0) | ~kind(X0))) [input p1]
3. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (tall(X0) | ~wise(X0))) [input p2]
4. ! [X0] : (~kind(X0) <=> (old(X0) | happy(X0))) [input p3]
7. ! [X0] : ((wise(X0) | curious(X0)) => (calm(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p8]
14. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (~quiet(X0) & happy(X0))) [input p13]
18. ~quiet(john) <~> ~creative(john) [input p17]
24. kind(john) [input hypothesis]
26. ! [X0] : ((wise(X0) | ~kind(X0)) | (patient(X0) & calm(X0))) [ennf transformation 2]
27. ! [X0] : (wise(X0) | ~kind(X0) | (patient(X0) & calm(X0))) [flattening 26]
30. ! [X0] : ((calm(X0) <~> humble(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 7]
38. ! [X0] : (((humble(X0) | ~wise(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 3]
39. ! [X0] : ((humble(X0) | ~wise(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | (~humble(X0) & wise(X0)))) [flattening 38]
40. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | kind(X0))) [nnf transformation 4]
41. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | kind(X0))) [flattening 40]
48. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 30]
54. ! [X0] : (((creative(X0) | ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 9]
55. ! [X0] : ((creative(X0) | ~old(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [flattening 54]
61. ! [X0] : (((~calm(X0) & ~creative(X0)) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 14]
62. ! [X0] : (((~calm(X0) & ~creative(X0)) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | calm(X0) | creative(X0))) [flattening 61]
69. (creative(john) | quiet(john)) & (~creative(john) | ~quiet(john)) [nnf transformation 18]
83. ~kind(X0) | wise(X0) | calm(X0) [cnf transformation 27]
86. ~humble(X0) | ~wise(X0) | tall(X0) [cnf transformation 39]
91. ~old(X0) | ~kind(X0) [cnf transformation 41]
101. ~wise(X0) | calm(X0) | humble(X0) [cnf transformation 48]
108. ~calm(X0) | old(X0) [cnf transformation 55]
109. ~creative(X0) | ~calm(X0) [cnf transformation 55]
111. ~creative(X0) | ~tall(X0) [cnf transformation 55]
128. ~quiet(X0) | calm(X0) | creative(X0) [cnf transformation 62]
142. creative(john) | quiet(john) [cnf transformation 69]
152. kind(john) [cnf transformation 24]
156. 1 <=> kind(john) [avatar definition]
158. kind(john) <- (1) [avatar component clause 156]
235. 17 <=> humble(john) [avatar definition]
236. humble(john) <- (17) [avatar component clause 235]
240. 18 <=> creative(john) [avatar definition]
241. ~creative(john) <- (~18) [avatar component clause 240]
242. creative(john) <- (18) [avatar component clause 240]
248. 20 <=> tall(john) [avatar definition]
249. ~tall(john) <- (~20) [avatar component clause 248]
291. 29 <=> quiet(john) [avatar definition]
293. quiet(john) <- (29) [avatar component clause 291]
294. 29 | 18 [avatar split clause 142,240,291]
316. 1 [avatar split clause 152,156]
320. ~calm(john) <- (18) [resolution 109,242]
321. ~tall(john) <- (18) [resolution 111,242]
322. ~20 | ~18 [avatar split clause 321,240,248]
325. wise(john) | calm(john) <- (1) [resolution 83,158]
327. wise(john) <- (1, 18) [subsumption resolution 325,320]
362. calm(john) | humble(john) <- (1, 18) [resolution 101,327]
369. humble(john) <- (1, 18) [subsumption resolution 362,320]
370. 17 | ~1 | ~18 [avatar split clause 369,240,156,235]
373. ~wise(john) | tall(john) <- (17) [resolution 236,86]
374. tall(john) <- (1, 17, 18) [subsumption resolution 373,327]
375. $false <- (1, 17, 18, ~20) [subsumption resolution 374,249]
376. ~1 | ~17 | ~18 | 20 [avatar contradiction clause 375]
429. calm(john) | creative(john) <- (29) [resolution 128,293]
435. calm(john) <- (~18, 29) [subsumption resolution 429,241]
445. old(john) <- (~18, 29) [resolution 435,108]
457. ~kind(john) <- (~18, 29) [resolution 445,91]
458. $false <- (1, ~18, 29) [subsumption resolution 457,158]
459. ~1 | 18 | ~29 [avatar contradiction clause 458]
460. $false [avatar sat refutation 294,316,322,370,376,459]
% SZS output end Proof for 2411647002323144096415105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not humble or not happy then fred is not brave or not funny. If fred is quiet then john is either rich or not generous. If john is generous then someone is old or not rich. Everyone who is both quiet and curious is not patient and vice versa. Everyone who is not funny or happy is not generous. If someone is quiet or not humble then someone is funny and vice versa. Everyone who is happy or not curious is not brave or creative and vice versa. Everyone who is both wise and creative is both not rich and curious and vice versa. Everyone who is either brave or not quiet is generous and vice versa. Everyone who is not wise or not curious is both tall and not quiet and vice versa. Everyone who is both not humble and kind is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Everyone who is either not generous or patient is curious and vice versa. Everyone who is both calm and quiet is both not patient and not brave and vice versa. Susan is either tall or not brave. Paul is kind or not humble. Alice is both humble and not strong. Someone is curious. Someone is both calm and not funny. Someone is creative. | Fred is humble. | entailment | (((~humble(lucy)<~>~happy(lucy)))=>((~brave(fred)|~funny(fred))))&
((quiet(fred))=>((rich(john)<~>~generous(john))))&
((generous(john))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>~patient(X)))&
(![X]:((~funny(X)|happy(X))=>~generous(X)))&
((?[X]:((quiet(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)|~curious(X))<=>(~brave(X)|creative(X))))&
(![X]:((wise(X)&creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((~wise(X)|~curious(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~old(X))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>patient(X))<=>curious(X)))&
(![X]:((calm(X)&quiet(X))<=>(~patient(X)&~brave(X))))&
((tall(susan)<~>~brave(susan)))&
((kind(paul)|~humble(paul)))&
((humble(alice)&~strong(alice)))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:(creative(X))) | humble(fred) | [
"p3",
"p4",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2076624804397100201346641
% SZS output start Proof for 2076624804397100201346641
4. ! [X0] : ((curious(X0) & quiet(X0)) <=> ~patient(X0)) [input p3]
5. ! [X0] : ((happy(X0) | ~funny(X0)) => ~generous(X0)) [input p4]
7. ! [X0] : ((~curious(X0) | happy(X0)) <=> (creative(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((brave(X0) <~> ~quiet(X0)) <=> generous(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> (~quiet(X0) & tall(X0))) [input p9]
11. ! [X0] : ((kind(X0) & ~humble(X0)) <=> (~old(X0) | patient(X0))) [input p10]
12. ! [X0] : ((strong(X0) | quiet(X0)) <=> (~humble(X0) <~> ~brave(X0))) [input p11]
13. ! [X0] : (tall(X0) <=> (rich(X0) <~> ~old(X0))) [input p12]
14. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p13]
15. ! [X0] : ((~generous(X0) <~> patient(X0)) <=> curious(X0)) [input p14]
23. ~humble(fred) [input hypothesis]
29. ! [X0] : (~generous(X0) | (~happy(X0) & funny(X0))) [ennf transformation 5]
30. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 14]
35. ! [X0] : (((curious(X0) & quiet(X0)) | patient(X0)) & (~patient(X0) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 4]
36. ! [X0] : (((curious(X0) & quiet(X0)) | patient(X0)) & (~patient(X0) | ~curious(X0) | ~quiet(X0))) [flattening 35]
42. ! [X0] : (((~curious(X0) | happy(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (curious(X0) & ~happy(X0)))) [nnf transformation 7]
43. ! [X0] : ((~curious(X0) | happy(X0) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | (curious(X0) & ~happy(X0)))) [flattening 42]
46. ! [X0] : ((((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ~generous(X0)) & (generous(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))))) [nnf transformation 9]
47. ! [X0] : (((~curious(X0) | ~wise(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (curious(X0) & wise(X0)))) [nnf transformation 10]
48. ! [X0] : ((~curious(X0) | ~wise(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (curious(X0) & wise(X0)))) [flattening 47]
49. ! [X0] : (((kind(X0) & ~humble(X0)) | (old(X0) & ~patient(X0))) & ((~old(X0) | patient(X0)) | (~kind(X0) | humble(X0)))) [nnf transformation 11]
50. ! [X0] : (((kind(X0) & ~humble(X0)) | (old(X0) & ~patient(X0))) & (~old(X0) | patient(X0) | ~kind(X0) | humble(X0))) [flattening 49]
51. ! [X0] : (((strong(X0) | quiet(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (~strong(X0) & ~quiet(X0)))) [nnf transformation 12]
52. ! [X0] : ((strong(X0) | quiet(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (~strong(X0) & ~quiet(X0)))) [flattening 51]
53. ! [X0] : ((tall(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0))) [nnf transformation 13]
54. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 30]
55. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | ~curious(X0)) & (curious(X0) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [nnf transformation 15]
70. ~patient(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 36]
71. patient(X0) | quiet(X0) [cnf transformation 36]
72. patient(X0) | curious(X0) [cnf transformation 36]
74. ~generous(X0) | ~happy(X0) [cnf transformation 29]
80. ~curious(X0) | happy(X0) | brave(X0) [cnf transformation 43]
86. ~quiet(X0) | generous(X0) | ~brave(X0) [cnf transformation 46]
89. ~generous(X0) | ~brave(X0) | quiet(X0) [cnf transformation 46]
91. tall(X0) | curious(X0) [cnf transformation 48]
98. ~patient(X0) | kind(X0) [cnf transformation 50]
99. kind(X0) | old(X0) [cnf transformation 50]
102. ~quiet(X0) | humble(X0) | brave(X0) [cnf transformation 52]
106. ~tall(X0) | rich(X0) | ~old(X0) [cnf transformation 53]
107. ~tall(X0) | ~rich(X0) | old(X0) [cnf transformation 53]
110. ~kind(X0) | ~old(X0) | ~rich(X0) [cnf transformation 54]
111. rich(X0) | old(X0) | ~kind(X0) [cnf transformation 54]
114. patient(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 55]
115. ~patient(X0) | generous(X0) | ~curious(X0) [cnf transformation 55]
129. ~humble(fred) [cnf transformation 23]
139. 3 <=> brave(fred) [avatar definition]
140. brave(fred) <- (3) [avatar component clause 139]
141. ~brave(fred) <- (~3) [avatar component clause 139]
195. old(X0) | rich(X0) [subsumption resolution 111,99]
196. ~generous(X0) | patient(X0) [subsumption resolution 114,72]
222. kind(X0) | curious(X0) [resolution 98,72]
354. rich(X0) | ~old(X0) | curious(X0) [resolution 106,91]
357. curious(X0) | rich(X0) [subsumption resolution 354,195]
359. ~rich(X0) | old(X0) | curious(X0) [resolution 107,91]
362. curious(X0) | old(X0) [subsumption resolution 359,357]
375. ~old(X0) | ~rich(X0) | curious(X0) [resolution 110,222]
377. ~old(X0) | curious(X0) [subsumption resolution 375,357]
378. curious(X0) [subsumption resolution 377,362]
381. brave(X2) | happy(X2) [resolution 378,80]
388. generous(X1) | ~curious(X1) | quiet(X1) [resolution 115,71]
389. generous(X1) | quiet(X1) [subsumption resolution 388,378]
534. quiet(X0) | ~brave(X0) | quiet(X0) [resolution 389,89]
538. ~happy(X4) | quiet(X4) [resolution 389,74]
540. ~brave(X0) | quiet(X0) [duplicate literal removal 534]
713. happy(X0) | quiet(X0) [resolution 381,540]
723. quiet(X0) [subsumption resolution 713,538]
738. brave(X0) | humble(X0) [resolution 723,102]
740. ~brave(X2) | generous(X2) [resolution 723,86]
780. generous(fred) <- (3) [resolution 740,140]
784. patient(fred) <- (3) [resolution 780,196]
791. ~curious(fred) | ~quiet(fred) <- (3) [resolution 784,70]
794. ~quiet(fred) <- (3) [subsumption resolution 791,378]
795. $false <- (3) [subsumption resolution 794,723]
796. ~3 [avatar contradiction clause 795]
797. humble(fred) <- (~3) [resolution 141,738]
799. $false <- (~3) [subsumption resolution 797,129]
800. 3 [avatar contradiction clause 799]
801. $false [avatar sat refutation 796,800]
% SZS output end Proof for 2076624804397100201346641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is old and vice versa.
Everyone who is not brave is funny and vice versa.
If susan is both humble and patient then someone is not rich.
Everyone who is humble or not creative is both not brave and tall and vice versa.
If someone is tall then mary is either calm or strong.
Everyone who is curious is happy and vice versa.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is kind or old is brave or not quiet and vice versa.
Everyone who is not kind or calm is not brave or not funny.
Everyone who is wise is not humble.
Everyone who is humble or wise is both not generous and not creative.
Everyone who is humble is rich or brave and vice versa.
If someone is brave then lucy is not patient or not generous and vice versa.
If someone is not quiet or calm then someone is not happy and vice versa.
If alice is either wise or not generous then someone is both not brave and old and vice versa.
Someone is either not tall or rich.
Someone is strong or rich.
Someone is not quiet or quiet.
John is either not calm or happy.
Fred is both tall and not patient.
Someone is not humble.
Susan is not rich or creative. | Mary is not quiet. | entailment | (![X]:(happy(X)<=>old(X)))&
(![X]:(~brave(X)<=>funny(X)))&
(((humble(susan)&patient(susan)))=>(?[X]:(~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((~calm(john)<~>happy(john)))&
((tall(fred)&~patient(fred)))&
(?[X]:(~humble(X)))&
((~rich(susan)|creative(susan))) | ~quiet(mary) | [
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2698812808335052193538071
% SZS output start Proof for 2698812808335052193538071
4. ! [X0] : ((~creative(X0) | humble(X0)) <=> (tall(X0) & ~brave(X0))) [input p3]
7. ! [X0] : ((~kind(X0) & brave(X0)) <=> quiet(X0)) [input p6]
12. ! [X0] : (humble(X0) <=> (brave(X0) | rich(X0))) [input p11]
23. quiet(mary) [input hypothesis]
36. ! [X0] : (((~creative(X0) | humble(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : ((~creative(X0) | humble(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [flattening 36]
39. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 7]
40. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 12]
44. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0))) [flattening 43]
74. ~humble(X0) | ~brave(X0) [cnf transformation 37]
82. ~quiet(X0) | brave(X0) [cnf transformation 40]
97. humble(X0) | ~brave(X0) [cnf transformation 44]
120. quiet(mary) [cnf transformation 23]
147. ~brave(X0) [subsumption resolution 97,74]
239. brave(mary) [resolution 82,120]
240. $false [subsumption resolution 239,147]
% SZS output end Proof for 2698812808335052193538071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is either humble or not curious.
If someone is not calm or not patient then lucy is both not humble and wise and vice versa.
Everyone who is either not patient or not quiet is quiet.
Everyone who is not creative or creative is both not quiet and kind and vice versa.
Everyone who is not creative is generous or not humble and vice versa.
If someone is not curious then lucy is either quiet or not old and vice versa.
If fred is not generous then someone is generous or humble.
Everyone who is brave or not rich is either happy or funny.
Everyone who is not rich or generous is not brave or not old and vice versa.
Everyone who is either not generous or old is not funny or not quiet and vice versa.
If paul is both not humble and humble then someone is not strong or not happy.
Everyone who is either not curious or funny is either not kind or tall and vice versa.
If someone is generous then someone is both tall and rich.
If someone is both kind and generous then fred is not curious or not generous.
If mary is not rich then john is wise.
If mary is not rich then someone is funny or not wise.
Someone is either brave or wise.
Fred is not tall or not generous.
Someone is both happy and not quiet.
Someone is either not brave or rich.
John is wise.
Someone is either not humble or brave. | Lucy is kind. | entailment | ((?[X]:(generous(X)))=>(?[X]:((humble(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~patient(X))))<=>((~humble(lucy)&wise(lucy))))&
(![X]:((~patient(X)<~>~quiet(X))=>quiet(X)))&
(![X]:((~creative(X)|creative(X))<=>(~quiet(X)&kind(X))))&
(![X]:(~creative(X)<=>(generous(X)|~humble(X))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)<~>~old(lucy))))&
((~generous(fred))=>(?[X]:((generous(X)|humble(X)))))&
(![X]:((brave(X)|~rich(X))=>(happy(X)<~>funny(X))))&
(![X]:((~rich(X)|generous(X))<=>(~brave(X)|~old(X))))&
(![X]:((~generous(X)<~>old(X))<=>(~funny(X)|~quiet(X))))&
(((~humble(paul)&humble(paul)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((~curious(X)<~>funny(X))<=>(~kind(X)<~>tall(X))))&
((?[X]:(generous(X)))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((kind(X)&generous(X))))=>((~curious(fred)|~generous(fred))))&
((~rich(mary))=>(wise(john)))&
((~rich(mary))=>(?[X]:((funny(X)|~wise(X)))))&
(?[X]:((brave(X)<~>wise(X))))&
((~tall(fred)|~generous(fred)))&
(?[X]:((happy(X)&~quiet(X))))&
(?[X]:((~brave(X)<~>rich(X))))&
(wise(john))&
(?[X]:((~humble(X)<~>brave(X)))) | kind(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9104634475930222387252580
% SZS output start Proof for 9104634475930222387252580
4. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (kind(X0) & ~quiet(X0))) [input p3]
23. ~kind(lucy) [input hypothesis]
46. ! [X0] : (((creative(X0) | ~creative(X0)) | (~kind(X0) | quiet(X0))) & ((kind(X0) & ~quiet(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 4]
47. ! [X0] : ((creative(X0) | ~creative(X0) | ~kind(X0) | quiet(X0)) & ((kind(X0) & ~quiet(X0)) | (~creative(X0) & creative(X0)))) [flattening 46]
89. kind(X0) | creative(X0) [cnf transformation 47]
90. kind(X0) | ~creative(X0) [cnf transformation 47]
137. ~kind(lucy) [cnf transformation 23]
179. kind(X0) [subsumption resolution 89,90]
285. $false [subsumption resolution 137,179]
% SZS output end Proof for 9104634475930222387252580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is both not happy and strong then susan is either not humble or generous. Everyone who is both not rich and rich is quiet and vice versa. Everyone who is not tall or generous is calm and vice versa. If paul is either not patient or not funny then someone is both rich and generous and vice versa. If someone is not curious or humble then john is wise. Everyone who is curious is not happy. If susan is humble or not wise then alice is old and vice versa. If someone is humble then john is either generous or not old and vice versa. Everyone who is not tall is wise or old. Everyone who is both not brave and curious is quiet or not humble and vice versa. If someone is creative or not tall then someone is both not patient and rich. If fred is not tall or kind then someone is either not brave or not kind and vice versa. If paul is not humble or not curious then paul is either brave or tall. Everyone who is curious is not quiet and vice versa. Everyone who is not brave is both humble and not strong. If someone is either not happy or not strong then someone is rich or strong. Someone is either curious or rich. Mary is rich. Someone is happy or not strong. Paul is strong or curious. Alice is both rich and wise. Someone is either not kind or not generous. Paul is kind. | Lucy is quiet. | contradiction | (((~happy(lucy)&strong(lucy)))=>((~humble(susan)<~>generous(susan))))&
(![X]:((~rich(X)&rich(X))<=>quiet(X)))&
(![X]:((~tall(X)|generous(X))<=>calm(X)))&
(((~patient(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&generous(X)))))&
((?[X]:((~curious(X)|humble(X))))=>(wise(john)))&
(![X]:(curious(X)=>~happy(X)))&
(((humble(susan)|~wise(susan)))<=>(old(alice)))&
((?[X]:(humble(X)))<=>((generous(john)<~>~old(john))))&
(![X]:(~tall(X)=>(wise(X)|old(X))))&
(![X]:((~brave(X)&curious(X))<=>(quiet(X)|~humble(X))))&
((?[X]:((creative(X)|~tall(X))))=>(?[X]:((~patient(X)&rich(X)))))&
(((~tall(fred)|kind(fred)))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((~humble(paul)|~curious(paul)))=>((brave(paul)<~>tall(paul))))&
(![X]:(curious(X)<=>~quiet(X)))&
(![X]:(~brave(X)=>(humble(X)&~strong(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(?[X]:((rich(X)|strong(X)))))&
(?[X]:((curious(X)<~>rich(X))))&
(rich(mary))&
(?[X]:((happy(X)|~strong(X))))&
((strong(paul)|curious(paul)))&
((rich(alice)&wise(alice)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(kind(paul)) | quiet(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 277799295563037988209488
% SZS output start Proof for 277799295563037988209488
2. ! [X0] : ((rich(X0) & ~rich(X0)) <=> quiet(X0)) [input p1]
24. quiet(lucy) [input hypothesis]
39. ! [X0] : (((rich(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~rich(X0) | rich(X0)))) [nnf transformation 2]
40. ! [X0] : (((rich(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | ~rich(X0) | rich(X0))) [flattening 39]
78. ~rich(X0) | ~quiet(X0) [cnf transformation 40]
79. rich(X0) | ~quiet(X0) [cnf transformation 40]
130. quiet(lucy) [cnf transformation 24]
149. ~quiet(X0) [subsumption resolution 78,79]
329. $false [subsumption resolution 130,149]
% SZS output end Proof for 277799295563037988209488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If fred is old or quiet then someone is either not creative or not old and vice versa.
If paul is either rich or not curious then someone is both creative and not wise.
If john is not old or not creative then mary is not funny or happy and vice versa.
Everyone who is rich or curious is either not wise or creative and vice versa.
Everyone who is not brave or tall is both happy and not happy.
Everyone who is strong or not calm is strong or not generous.
Everyone who is both not kind and rich is not patient or not rich and vice versa.
Everyone who is not quiet is not funny and vice versa.
Everyone who is not curious or brave is not curious or rich.
If someone is both not tall and calm then john is both creative and not happy and vice versa.
Everyone who is funny or not old is not patient or brave and vice versa.
If someone is not humble or curious then lucy is not creative.
Everyone who is both not humble and patient is not funny or not curious and vice versa.
If someone is either not creative or old then someone is wise or not patient and vice versa.
Everyone who is either quiet or not tall is wise and vice versa.
Someone is not funny.
Someone is not quiet.
Someone is not happy or funny.
Someone is curious or not old.
Mary is both old and calm.
Lucy is either not funny or quiet.
Someone is not calm. | Lucy is not creative. | entailment | (((old(fred)|quiet(fred)))<=>(?[X]:((~creative(X)<~>~old(X)))))&
(((rich(paul)<~>~curious(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(((~old(john)|~creative(john)))<=>((~funny(mary)|happy(mary))))&
(![X]:((rich(X)|curious(X))<=>(~wise(X)<~>creative(X))))&
(![X]:((~brave(X)|tall(X))=>(happy(X)&~happy(X))))&
(![X]:((strong(X)|~calm(X))=>(strong(X)|~generous(X))))&
(![X]:((~kind(X)&rich(X))<=>(~patient(X)|~rich(X))))&
(![X]:(~quiet(X)<=>~funny(X)))&
(![X]:((~curious(X)|brave(X))=>(~curious(X)|rich(X))))&
((?[X]:((~tall(X)&calm(X))))<=>((creative(john)&~happy(john))))&
(![X]:((funny(X)|~old(X))<=>(~patient(X)|brave(X))))&
((?[X]:((~humble(X)|curious(X))))=>(~creative(lucy)))&
(![X]:((~humble(X)&patient(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>wise(X)))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)|funny(X))))&
(?[X]:((curious(X)|~old(X))))&
((old(mary)&calm(mary)))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:(~calm(X))) | ~creative(lucy) | [
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 491899549125125078938040
% SZS output start Proof for 491899549125125078938040
12. ? [X0] : (curious(X0) | ~humble(X0)) => ~creative(lucy) [input p11]
13. ! [X0] : ((patient(X0) & ~humble(X0)) <=> (~curious(X0) | ~funny(X0))) [input p12]
16. ? [X0] : ~funny(X0) [input p15]
23. creative(lucy) [input hypothesis]
30. ~creative(lucy) | ! [X0] : (~curious(X0) & humble(X0)) [ennf transformation 12]
53. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~patient(X0) | humble(X0)))) [nnf transformation 13]
54. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~patient(X0) | humble(X0))) [flattening 53]
61. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
62. ~funny(sK5) [skolemisation 16,61]
113. ~creative(lucy) | humble(X0) [cnf transformation 30]
116. ~humble(X0) | funny(X0) [cnf transformation 54]
130. ~funny(sK5) [cnf transformation 62]
139. creative(lucy) [cnf transformation 23]
234. 19 <=> creative(lucy) [avatar definition]
239. 20 <=> ! [X0] : humble(X0) [avatar definition]
240. humble(X0) <- (20) [avatar component clause 239]
241. 20 | ~19 [avatar split clause 113,234,239]
296. 19 [avatar split clause 139,234]
303. funny(X0) <- (20) [resolution 116,240]
304. $false <- (20) [resolution 303,130]
308. ~20 [avatar contradiction clause 304]
309. $false [avatar sat refutation 241,296,308]
% SZS output end Proof for 491899549125125078938040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or strong is either not creative or happy and vice versa.
Everyone who is both not generous and not rich is either calm or not funny.
Everyone who is both not happy and happy is strong.
Everyone who is either patient or curious is either not happy or generous and vice versa.
Everyone who is both quiet and patient is either tall or not old and vice versa.
If someone is kind then susan is either not humble or strong and vice versa.
If paul is either quiet or funny then someone is both strong and not curious.
If someone is either patient or not wise then someone is either strong or happy and vice versa.
Everyone who is old is either not brave or kind.
Everyone who is not kind is not quiet or curious and vice versa.
Everyone who is not calm is either not happy or strong and vice versa.
Everyone who is not creative or rich is both not patient and old and vice versa.
Everyone who is either kind or not kind is not kind and vice versa.
If someone is both patient and creative then someone is either brave or rich.
Everyone who is either calm or not creative is not curious.
If mary is happy then someone is either tall or not quiet.
Someone is both old and not patient.
Someone is either humble or tall.
Someone is both patient and not kind.
Mary is not creative.
Paul is either not kind or calm.
Someone is patient or not kind.
Lucy is quiet. | Mary is not quiet. | entailment | (![X]:((~tall(X)<~>strong(X))<=>(~creative(X)<~>happy(X))))&
(![X]:((~generous(X)&~rich(X))=>(calm(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))=>strong(X)))&
(![X]:((patient(X)<~>curious(X))<=>(~happy(X)<~>generous(X))))&
(![X]:((quiet(X)&patient(X))<=>(tall(X)<~>~old(X))))&
((?[X]:(kind(X)))<=>((~humble(susan)<~>strong(susan))))&
(((quiet(paul)<~>funny(paul)))=>(?[X]:((strong(X)&~curious(X)))))&
((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(old(X)=>(~brave(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(~quiet(X)|curious(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>strong(X))))&
(![X]:((~creative(X)|rich(X))<=>(~patient(X)&old(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~kind(X)))&
((?[X]:((patient(X)&creative(X))))=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:((calm(X)<~>~creative(X))=>~curious(X)))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((patient(X)&~kind(X))))&
(~creative(mary))&
((~kind(paul)<~>calm(paul)))&
(?[X]:((patient(X)|~kind(X))))&
(quiet(lucy)) | ~quiet(mary) | [
"p0",
"p4",
"p9",
"p10",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8434973119183125509356571
% SZS output start Proof for 8434973119183125509356571
1. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~creative(X0) <~> happy(X0))) [input p0]
5. ! [X0] : ((patient(X0) & quiet(X0)) <=> (tall(X0) <~> ~old(X0))) [input p4]
10. ! [X0] : (~kind(X0) <=> (curious(X0) | ~quiet(X0))) [input p9]
11. ! [X0] : (~calm(X0) <=> (~happy(X0) <~> strong(X0))) [input p10]
12. ! [X0] : ((rich(X0) | ~creative(X0)) <=> (old(X0) & ~patient(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p12]
15. ! [X0] : ((calm(X0) <~> ~creative(X0)) => ~curious(X0)) [input p14]
20. ~creative(mary) [input p19]
24. quiet(mary) [input hypothesis]
34. ! [X0] : (~curious(X0) | (calm(X0) <=> ~creative(X0))) [ennf transformation 15]
36. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 1]
39. ! [X0] : (((patient(X0) & quiet(X0)) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | (~patient(X0) | ~quiet(X0)))) [nnf transformation 5]
40. ! [X0] : (((patient(X0) & quiet(X0)) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | ~patient(X0) | ~quiet(X0))) [flattening 39]
54. ! [X0] : ((~kind(X0) | (~curious(X0) & quiet(X0))) & ((curious(X0) | ~quiet(X0)) | kind(X0))) [nnf transformation 10]
55. ! [X0] : ((~kind(X0) | (~curious(X0) & quiet(X0))) & (curious(X0) | ~quiet(X0) | kind(X0))) [flattening 54]
56. ! [X0] : ((~calm(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | calm(X0))) [nnf transformation 11]
57. ! [X0] : (((rich(X0) | ~creative(X0)) | (~old(X0) | patient(X0))) & ((old(X0) & ~patient(X0)) | (~rich(X0) & creative(X0)))) [nnf transformation 12]
58. ! [X0] : ((rich(X0) | ~creative(X0) | ~old(X0) | patient(X0)) & ((old(X0) & ~patient(X0)) | (~rich(X0) & creative(X0)))) [flattening 57]
59. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | kind(X0)) & (~kind(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 13]
64. ! [X0] : (~curious(X0) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) [nnf transformation 34]
80. ~happy(X0) | creative(X0) | strong(X0) | tall(X0) [cnf transformation 36]
84. ~strong(X0) | tall(X0) | happy(X0) | creative(X0) [cnf transformation 36]
101. ~old(X0) | patient(X0) | ~tall(X0) [cnf transformation 40]
121. ~quiet(X0) | curious(X0) | kind(X0) [cnf transformation 55]
126. ~calm(X0) | strong(X0) | happy(X0) [cnf transformation 56]
127. ~calm(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 56]
128. ~patient(X0) | creative(X0) [cnf transformation 58]
130. old(X0) | creative(X0) [cnf transformation 58]
133. ~kind(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 59]
140. ~curious(X0) | calm(X0) | creative(X0) [cnf transformation 64]
149. ~creative(mary) [cnf transformation 20]
154. quiet(mary) [cnf transformation 24]
155. ~kind(X0) [duplicate literal removal 133]
174. 4 <=> ! [X1] : ~kind(X1) [avatar definition]
175. ~kind(X1) <- (4) [avatar component clause 174]
234. 4 [avatar split clause 155,174]
251. 20 <=> happy(mary) [avatar definition]
252. happy(mary) <- (20) [avatar component clause 251]
253. ~happy(mary) <- (~20) [avatar component clause 251]
312. patient(X1) | ~tall(X1) | creative(X1) [resolution 101,130]
313. ~tall(X1) | creative(X1) [subsumption resolution 312,128]
342. curious(mary) | kind(mary) [resolution 121,154]
344. curious(mary) <- (4) [subsumption resolution 342,175]
361. calm(mary) | creative(mary) <- (4) [resolution 140,344]
364. calm(mary) <- (4) [subsumption resolution 361,149]
405. ~happy(mary) | ~strong(mary) <- (4) [resolution 364,127]
406. strong(mary) | happy(mary) <- (4) [resolution 364,126]
407. strong(mary) <- (4, ~20) [subsumption resolution 406,253]
670. tall(mary) | happy(mary) | creative(mary) <- (4, ~20) [resolution 407,84]
672. tall(mary) | creative(mary) <- (4, ~20) [subsumption resolution 670,253]
673. tall(mary) <- (4, ~20) [subsumption resolution 672,149]
703. creative(mary) <- (4, ~20) [resolution 673,313]
704. $false <- (4, ~20) [subsumption resolution 703,149]
705. ~4 | 20 [avatar contradiction clause 704]
708. 64 <=> strong(mary) [avatar definition]
709. ~strong(mary) <- (~64) [avatar component clause 708]
716. ~64 | ~20 | ~4 [avatar split clause 405,174,251,708]
722. creative(mary) | strong(mary) | tall(mary) <- (20) [resolution 252,80]
724. strong(mary) | tall(mary) <- (20) [subsumption resolution 722,149]
725. tall(mary) <- (20, ~64) [subsumption resolution 724,709]
728. creative(mary) <- (20, ~64) [resolution 725,313]
729. $false <- (20, ~64) [subsumption resolution 728,149]
730. ~20 | 64 [avatar contradiction clause 729]
731. $false [avatar sat refutation 234,705,716,730]
% SZS output end Proof for 8434973119183125509356571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is both curious and creative. If alice is either not strong or not curious then someone is funny or not old and vice versa. If paul is both funny and not quiet then someone is either not happy or not funny and vice versa. If john is rich or kind then alice is both happy and not old. If someone is not funny or not strong then mary is not kind or kind and vice versa. If john is both not humble and not patient then susan is not curious or curious and vice versa. If alice is not generous then someone is both not curious and patient. Everyone who is kind is either not curious or not old and vice versa. If someone is not old then mary is not strong or kind and vice versa. Everyone who is not strong is either kind or not kind. Everyone who is not brave or not funny is either old or not kind and vice versa. Everyone who is quiet or not old is not happy or not creative. Everyone who is both not generous and not old is both not patient and not funny. If fred is not patient then someone is creative or happy. If someone is both not generous and wise then mary is either curious or brave and vice versa. Everyone who is creative is both rich and not rich and vice versa. Someone is not quiet or not brave. Someone is both not old and not funny. Susan is not calm or not strong. Someone is not patient or not strong. Lucy is not creative or curious. Susan is rich or kind. | Lucy is brave. | neutral | (![X]:(humble(X)=>(curious(X)&creative(X))))&
(((~strong(alice)<~>~curious(alice)))<=>(?[X]:((funny(X)|~old(X)))))&
(((funny(paul)&~quiet(paul)))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
(((rich(john)|kind(john)))=>((happy(alice)&~old(alice))))&
((?[X]:((~funny(X)|~strong(X))))<=>((~kind(mary)|kind(mary))))&
(((~humble(john)&~patient(john)))<=>((~curious(susan)|curious(susan))))&
((~generous(alice))=>(?[X]:((~curious(X)&patient(X)))))&
(![X]:(kind(X)<=>(~curious(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>((~strong(mary)|kind(mary))))&
(![X]:(~strong(X)=>(kind(X)<~>~kind(X))))&
(![X]:((~brave(X)|~funny(X))<=>(old(X)<~>~kind(X))))&
(![X]:((quiet(X)|~old(X))=>(~happy(X)|~creative(X))))&
(![X]:((~generous(X)&~old(X))=>(~patient(X)&~funny(X))))&
((~patient(fred))=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:((~generous(X)&wise(X))))<=>((curious(mary)<~>brave(mary))))&
(![X]:(creative(X)<=>(rich(X)&~rich(X))))&
(?[X]:((~quiet(X)|~brave(X))))&
(?[X]:((~old(X)&~funny(X))))&
((~calm(susan)|~strong(susan)))&
(?[X]:((~patient(X)|~strong(X))))&
((~creative(lucy)|curious(lucy)))&
((rich(susan)|kind(susan))) | brave(lucy) | [] | null | 0 |
If alice is either wise or creative then fred is both not strong and not happy and vice versa.
If alice is not quiet or rich then someone is both calm and not old and vice versa.
Everyone who is both patient and creative is both curious and not patient.
If someone is both tall and patient then someone is either not strong or not old and vice versa.
If someone is both not brave and brave then someone is both quiet and not generous.
Everyone who is not funny or rich is humble or happy.
Everyone who is not old or old is both not brave and calm.
If lucy is not wise then someone is not wise or curious.
Everyone who is either creative or not calm is rich and vice versa.
Everyone who is creative is either not rich or generous.
If lucy is either not quiet or not rich then susan is not happy or not wise.
Everyone who is both wise and not wise is either not generous or rich and vice versa.
If paul is either not curious or not strong then someone is either not strong or not wise and vice versa.
Everyone who is not tall is both strong and not calm.
Everyone who is either not brave or not humble is either patient or not tall.
If someone is curious or strong then someone is not brave and vice versa.
Someone is either not humble or happy.
Alice is either not generous or not old.
Someone is wise.
John is not rich or not tall.
Lucy is both not humble and not wise.
Someone is either not curious or happy.
Fred is not brave or rich. | John is rich. | contradiction | (((wise(alice)<~>creative(alice)))<=>((~strong(fred)&~happy(fred))))&
(((~quiet(alice)|rich(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((patient(X)&creative(X))=>(curious(X)&~patient(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((~strong(X)<~>~old(X)))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:((quiet(X)&~generous(X)))))&
(![X]:((~funny(X)|rich(X))=>(humble(X)|happy(X))))&
(![X]:((~old(X)|old(X))=>(~brave(X)&calm(X))))&
((~wise(lucy))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((creative(X)<~>~calm(X))<=>rich(X)))&
(![X]:(creative(X)=>(~rich(X)<~>generous(X))))&
(((~quiet(lucy)<~>~rich(lucy)))=>((~happy(susan)|~wise(susan))))&
(![X]:((wise(X)&~wise(X))<=>(~generous(X)<~>rich(X))))&
(((~curious(paul)<~>~strong(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:(~tall(X)=>(strong(X)&~calm(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~brave(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
((~generous(alice)<~>~old(alice)))&
(?[X]:(wise(X)))&
((~rich(john)|~tall(john)))&
((~humble(lucy)&~wise(lucy)))&
(?[X]:((~curious(X)<~>happy(X))))&
((~brave(fred)|rich(fred))) | rich(john) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 27617344965619530565040
% SZS output start Proof for 27617344965619530565040
7. ! [X0] : ((old(X0) | ~old(X0)) => (calm(X0) & ~brave(X0))) [input p6]
14. ! [X0] : (~tall(X0) => (~calm(X0) & strong(X0))) [input p13]
20. ~tall(john) | ~rich(john) [input p19]
24. rich(john) [input hypothesis]
34. ! [X0] : ((calm(X0) & ~brave(X0)) | (~old(X0) & old(X0))) [ennf transformation 7]
39. ! [X0] : ((~calm(X0) & strong(X0)) | tall(X0)) [ennf transformation 14]
106. calm(X0) | old(X0) [cnf transformation 34]
107. calm(X0) | ~old(X0) [cnf transformation 34]
132. ~calm(X0) | tall(X0) [cnf transformation 39]
145. ~tall(john) | ~rich(john) [cnf transformation 20]
151. rich(john) [cnf transformation 24]
230. calm(X0) [subsumption resolution 106,107]
298. tall(X0) [subsumption resolution 132,230]
331. ~rich(john) [subsumption resolution 145,298]
343. $false [subsumption resolution 151,331]
% SZS output end Proof for 27617344965619530565040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is not funny.
If someone is not humble or humble then alice is not patient or not old.
If susan is either not tall or happy then someone is tall and vice versa.
Everyone who is both calm and funny is both happy and not curious and vice versa.
Everyone who is not funny is either humble or not wise and vice versa.
If fred is not kind then someone is curious or not patient and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
Everyone who is both not creative and rich is both not creative and not strong.
If lucy is either not humble or generous then someone is either kind or generous and vice versa.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Everyone who is not quiet or not rich is both not happy and not patient.
Everyone who is not old or not wise is either rich or not tall and vice versa.
If someone is both brave and tall then someone is both not wise and not creative and vice versa.
Everyone who is curious is not happy and vice versa.
Everyone who is both not generous and quiet is not generous or not kind.
Fred is humble.
Fred is not generous.
Someone is not creative or not funny.
Someone is both not brave and not kind.
Someone is not humble.
Fred is either calm or creative.
Alice is not patient.
Someone is either funny or not happy. | Alice is tall. | neutral | (![X]:((curious(X)<~>kind(X))=>~funny(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~patient(alice)|~old(alice))))&
(((~tall(susan)<~>happy(susan)))<=>(?[X]:(tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
((~kind(fred))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
(![X]:((~creative(X)&rich(X))=>(~creative(X)&~strong(X))))&
(((~humble(lucy)<~>generous(lucy)))<=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(humble(fred))&
(~generous(fred))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:(~humble(X)))&
((calm(fred)<~>creative(fred)))&
(~patient(alice))&
(?[X]:((funny(X)<~>~happy(X)))) | tall(alice) | [] | null | 0 |
If lucy is quiet then someone is not humble or not funny and vice versa. If fred is curious or generous then someone is either not creative or not wise. If paul is wise or kind then someone is humble or old and vice versa. Everyone who is not wise or generous is both not strong and quiet and vice versa. Everyone who is both kind and humble is either humble or not old and vice versa. If someone is either kind or old then mary is tall or not kind. Everyone who is not calm or not happy is both strong and not tall. Everyone who is calm is curious or strong. If alice is both not humble and brave then someone is both not happy and calm. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is funny or wise is happy. Everyone who is both patient and rich is not funny and vice versa. If lucy is not humble or happy then susan is either not wise or happy and vice versa. If someone is not brave or brave then lucy is either not quiet or curious. Everyone who is either old or wise is both not creative and not funny and vice versa. Everyone who is either not quiet or curious is kind and vice versa. Paul is either not humble or not old. Someone is funny or not rich. Lucy is not creative or not funny. Paul is not kind. Someone is kind. John is either curious or not brave. Someone is both curious and not calm. Someone is calm or not calm. | Lucy is not wise. | contradiction | ((quiet(lucy))<=>(?[X]:((~humble(X)|~funny(X)))))&
(((curious(fred)|generous(fred)))=>(?[X]:((~creative(X)<~>~wise(X)))))&
(((wise(paul)|kind(paul)))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>kind(X)))&
((~humble(paul)<~>~old(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((calm(X)|~calm(X)))) | ~wise(lucy) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6981207520059139732704175
% SZS output start Proof for 6981207520059139732704175
4. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~tall(X0) & strong(X0))) [input p6]
8. ! [X0] : (calm(X0) => (strong(X0) | curious(X0))) [input p7]
10. ! [X0] : (patient(X0) <=> (~quiet(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((rich(X0) & patient(X0)) <=> ~funny(X0)) [input p11]
14. ? [X0] : (brave(X0) | ~brave(X0)) => (~quiet(lucy) <~> curious(lucy)) [input p13]
15. ! [X0] : ((old(X0) <~> wise(X0)) <=> (~funny(X0) & ~creative(X0))) [input p14]
16. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> kind(X0)) [input p15]
25. ~wise(lucy) [input hypothesis]
29. ! [X0] : ((~tall(X0) & strong(X0)) | (happy(X0) & calm(X0))) [ennf transformation 7]
30. ! [X0] : ((strong(X0) | curious(X0)) | ~calm(X0)) [ennf transformation 8]
31. ! [X0] : (strong(X0) | curious(X0) | ~calm(X0)) [flattening 30]
35. (~quiet(lucy) <~> curious(lucy)) | ! [X0] : (~brave(X0) & brave(X0)) [ennf transformation 14]
48. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 4]
49. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 48]
50. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
51. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ~humble(X0) | ~kind(X0))) [flattening 50]
55. ! [X0] : ((patient(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~patient(X0))) [nnf transformation 10]
56. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | ~patient(X0)))) [nnf transformation 12]
57. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | ~patient(X0))) [flattening 56]
60. ((~curious(lucy) | quiet(lucy)) & (curious(lucy) | ~quiet(lucy))) | ! [X0] : (~brave(X0) & brave(X0)) [nnf transformation 35]
61. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [flattening 61]
63. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | ~kind(X0)) & (kind(X0) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 16]
85. ~strong(X0) | wise(X0) [cnf transformation 49]
91. old(X0) | ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 51]
95. humble(X0) | humble(X0) | old(X0) [cnf transformation 51]
98. calm(X0) | strong(X0) [cnf transformation 29]
102. strong(X0) | curious(X0) | ~calm(X0) [cnf transformation 31]
105. ~patient(X0) | ~quiet(X0) | strong(X0) [cnf transformation 55]
112. patient(X0) | funny(X0) [cnf transformation 57]
122. ~curious(lucy) | quiet(lucy) | brave(X0) [cnf transformation 60]
123. ~curious(lucy) | quiet(lucy) | ~brave(X0) [cnf transformation 60]
126. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 62]
131. ~curious(X0) | ~quiet(X0) | kind(X0) [cnf transformation 63]
145. ~wise(lucy) [cnf transformation 25]
146. old(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 91]
147. old(X0) | humble(X0) [duplicate literal removal 95]
152. 2 <=> quiet(lucy) [avatar definition]
154. quiet(lucy) <- (2) [avatar component clause 152]
215. ~kind(X0) | old(X0) [subsumption resolution 146,147]
228. strong(X0) | curious(X0) [subsumption resolution 102,98]
270. 27 <=> ! [X0] : ~brave(X0) [avatar definition]
271. ~brave(X0) <- (27) [avatar component clause 270]
273. 28 <=> curious(lucy) [avatar definition]
274. curious(lucy) <- (28) [avatar component clause 273]
276. 27 | 2 | ~28 [avatar split clause 123,273,152,270]
278. 29 <=> ! [X0] : brave(X0) [avatar definition]
279. brave(X0) <- (29) [avatar component clause 278]
280. 29 | 2 | ~28 [avatar split clause 122,273,152,278]
298. 33 <=> funny(lucy) [avatar definition]
300. ~funny(lucy) <- (~33) [avatar component clause 298]
345. wise(X1) | curious(X1) [resolution 228,85]
348. ~quiet(X0) | strong(X0) | funny(X0) [resolution 105,112]
354. curious(lucy) [resolution 345,145]
448. ~quiet(lucy) | kind(lucy) <- (28) [resolution 131,274]
449. kind(lucy) <- (2, 28) [subsumption resolution 448,154]
516. old(lucy) <- (2, 28) [resolution 449,215]
525. strong(lucy) | funny(lucy) <- (2) [resolution 348,154]
526. strong(lucy) <- (2, ~33) [subsumption resolution 525,300]
540. wise(lucy) | ~funny(lucy) <- (2, 28) [resolution 516,126]
548. wise(lucy) <- (2, ~33) [resolution 526,85]
550. $false <- (2, ~33) [subsumption resolution 548,145]
551. ~2 | 33 [avatar contradiction clause 550]
552. ~funny(lucy) <- (2, 28) [subsumption resolution 540,145]
553. ~33 | ~2 | ~28 [avatar split clause 552,273,152,298]
564. 28 [avatar split clause 354,273]
565. $false <- (27, 29) [subsumption resolution 271,279]
566. ~27 | ~29 [avatar contradiction clause 565]
567. $false [avatar sat refutation 276,280,551,553,564,566]
% SZS output end Proof for 6981207520059139732704175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not humble and not wise is not generous and vice versa. If susan is rich or humble then lucy is both funny and not strong and vice versa. Everyone who is not tall is either not humble or kind. Everyone who is both creative and not rich is either creative or funny and vice versa. Everyone who is quiet or happy is both patient and rich. Everyone who is not generous is either not tall or not funny and vice versa. If someone is not calm then someone is not funny and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Someone is both patient and not kind. Someone is either happy or curious. | John is not happy. | neutral | (![X]:((~humble(X)&~wise(X))<=>~generous(X)))&
(((rich(susan)|humble(susan)))<=>((funny(lucy)&~strong(lucy))))&
(![X]:(~tall(X)=>(~humble(X)<~>kind(X))))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)<~>funny(X))))&
(![X]:((quiet(X)|happy(X))=>(patient(X)&rich(X))))&
(![X]:(~generous(X)<=>(~tall(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((happy(X)<~>curious(X)))) | ~happy(john) | [] | null | 0 |
If paul is not happy or strong then someone is not old.
Everyone who is both kind and wise is both happy and rich and vice versa.
Everyone who is old is not creative and vice versa.
Everyone who is either patient or happy is curious.
If fred is not strong or old then paul is calm.
Everyone who is either old or not rich is both not patient and generous.
Everyone who is either old or not generous is either rich or not old.
Everyone who is either not quiet or generous is not old or not patient.
Everyone who is both wise and kind is either not brave or funny.
If someone is either funny or not old then alice is both not quiet and not brave.
Everyone who is either humble or not old is both brave and not brave and vice versa.
If someone is creative then lucy is rich or not quiet.
Everyone who is both not funny and quiet is either not curious or not kind.
Everyone who is old or wise is both not old and humble and vice versa.
Everyone who is both funny and not patient is calm.
If alice is humble or not funny then fred is generous or funny and vice versa.
Alice is strong or not calm.
Someone is either tall or creative.
Alice is either not curious or not humble.
Someone is both not happy and wise.
Someone is either wise or not kind.
Someone is creative. | Lucy is not wise. | contradiction | (((~happy(paul)|strong(paul)))=>(?[X]:(~old(X))))&
(![X]:((kind(X)&wise(X))<=>(happy(X)&rich(X))))&
(![X]:(old(X)<=>~creative(X)))&
(![X]:((patient(X)<~>happy(X))=>curious(X)))&
(((~strong(fred)|old(fred)))=>(calm(paul)))&
(![X]:((old(X)<~>~rich(X))=>(~patient(X)&generous(X))))&
(![X]:((old(X)<~>~generous(X))=>(rich(X)<~>~old(X))))&
(![X]:((~quiet(X)<~>generous(X))=>(~old(X)|~patient(X))))&
(![X]:((wise(X)&kind(X))=>(~brave(X)<~>funny(X))))&
((?[X]:((funny(X)<~>~old(X))))=>((~quiet(alice)&~brave(alice))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&~brave(X))))&
((?[X]:(creative(X)))=>((rich(lucy)|~quiet(lucy))))&
(![X]:((~funny(X)&quiet(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((old(X)|wise(X))<=>(~old(X)&humble(X))))&
(![X]:((funny(X)&~patient(X))=>calm(X)))&
(((humble(alice)|~funny(alice)))<=>((generous(fred)|funny(fred))))&
((strong(alice)|~calm(alice)))&
(?[X]:((tall(X)<~>creative(X))))&
((~curious(alice)<~>~humble(alice)))&
(?[X]:((~happy(X)&wise(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:(creative(X))) | ~wise(lucy) | [
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7571426003577842509583934
% SZS output start Proof for 7571426003577842509583934
11. ! [X0] : ((humble(X0) <~> ~old(X0)) <=> (~brave(X0) & brave(X0))) [input p10]
14. ! [X0] : ((wise(X0) | old(X0)) <=> (humble(X0) & ~old(X0))) [input p13]
23. ~wise(lucy) [input hypothesis]
51. ! [X0] : ((((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))))) [nnf transformation 11]
52. ! [X0] : ((((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))))) [flattening 51]
54. ! [X0] : (((wise(X0) | old(X0)) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 14]
55. ! [X0] : ((wise(X0) | old(X0) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | (~wise(X0) & ~old(X0)))) [flattening 54]
97. brave(X0) | ~old(X0) | ~humble(X0) [cnf transformation 52]
98. brave(X0) | humble(X0) | old(X0) [cnf transformation 52]
99. ~brave(X0) | ~old(X0) | ~humble(X0) [cnf transformation 52]
100. ~brave(X0) | humble(X0) | old(X0) [cnf transformation 52]
106. ~old(X0) | ~old(X0) [cnf transformation 55]
110. wise(X0) | old(X0) | ~humble(X0) | old(X0) [cnf transformation 55]
126. ~wise(lucy) [cnf transformation 23]
127. ~old(X0) [duplicate literal removal 106]
128. wise(X0) | old(X0) | ~humble(X0) [duplicate literal removal 110]
179. humble(X0) | old(X0) [subsumption resolution 98,100]
180. ~humble(X0) | ~old(X0) [subsumption resolution 97,99]
193. ~humble(X0) | wise(X0) [subsumption resolution 128,180]
250. wise(X0) | old(X0) [resolution 193,179]
252. wise(X0) [subsumption resolution 250,127]
255. $false [resolution 252,126]
% SZS output end Proof for 7571426003577842509583934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is either rich or funny and vice versa.
If someone is either not old or not quiet then lucy is not generous or funny.
If someone is not kind or not tall then lucy is not kind or calm.
If someone is either rich or brave then paul is not generous.
Everyone who is strong or old is both calm and not patient.
Everyone who is either creative or old is happy.
Everyone who is generous or not wise is not creative or strong and vice versa.
If someone is not strong then fred is not creative.
If paul is both not tall and quiet then someone is quiet or not wise and vice versa.
Everyone who is either humble or not wise is both not funny and wise and vice versa.
Everyone who is either not strong or not tall is either funny or not patient.
Everyone who is either calm or not generous is both calm and not old and vice versa.
Everyone who is funny is not creative.
If john is happy then someone is both funny and not calm.
Everyone who is not curious is both brave and generous and vice versa.
Everyone who is not generous is not tall or humble and vice versa.
Mary is generous or curious.
John is tall.
Someone is kind or not wise.
Paul is brave.
John is both not patient and rich.
Alice is either wise or not strong.
Fred is either not creative or not kind.
Paul is not humble or tall. | Mary is not wise. | contradiction | ((?[X]:(generous(X)))<=>(?[X]:((rich(X)<~>funny(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~generous(lucy)|funny(lucy))))&
((?[X]:((~kind(X)|~tall(X))))=>((~kind(lucy)|calm(lucy))))&
((?[X]:((rich(X)<~>brave(X))))=>(~generous(paul)))&
(![X]:((strong(X)|old(X))=>(calm(X)&~patient(X))))&
(![X]:((creative(X)<~>old(X))=>happy(X)))&
(![X]:((generous(X)|~wise(X))<=>(~creative(X)|strong(X))))&
((?[X]:(~strong(X)))=>(~creative(fred)))&
(((~tall(paul)&quiet(paul)))<=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((humble(X)<~>~wise(X))<=>(~funny(X)&wise(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(funny(X)<~>~patient(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(funny(X)=>~creative(X)))&
((happy(john))=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:(~curious(X)<=>(brave(X)&generous(X))))&
(![X]:(~generous(X)<=>(~tall(X)|humble(X))))&
((generous(mary)|curious(mary)))&
(tall(john))&
(?[X]:((kind(X)|~wise(X))))&
(brave(paul))&
((~patient(john)&rich(john)))&
((wise(alice)<~>~strong(alice)))&
((~creative(fred)<~>~kind(fred)))&
((~humble(paul)|tall(paul))) | ~wise(mary) | [
"p6",
"p8",
"p9",
"p12",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4349969079512299614360413
% SZS output start Proof for 4349969079512299614360413
7. ! [X0] : ((~wise(X0) | generous(X0)) <=> (strong(X0) | ~creative(X0))) [input p6]
9. (quiet(paul) & ~tall(paul)) <=> ? [X0] : (~wise(X0) | quiet(X0)) [input p8]
10. ! [X0] : ((humble(X0) <~> ~wise(X0)) <=> (wise(X0) & ~funny(X0))) [input p9]
13. ! [X0] : (funny(X0) => ~creative(X0)) [input p12]
16. ! [X0] : (~generous(X0) <=> (humble(X0) | ~tall(X0))) [input p15]
24. tall(paul) | ~humble(paul) [input p23]
25. ~wise(mary) [input hypothesis]
37. ! [X0] : (~creative(X0) | ~funny(X0)) [ennf transformation 13]
49. ! [X0] : (((~wise(X0) | generous(X0)) | (~strong(X0) & creative(X0))) & ((strong(X0) | ~creative(X0)) | (wise(X0) & ~generous(X0)))) [nnf transformation 7]
50. ! [X0] : ((~wise(X0) | generous(X0) | (~strong(X0) & creative(X0))) & (strong(X0) | ~creative(X0) | (wise(X0) & ~generous(X0)))) [flattening 49]
51. ((quiet(paul) & ~tall(paul)) | ! [X0] : (wise(X0) & ~quiet(X0))) & (? [X0] : (~wise(X0) | quiet(X0)) | (~quiet(paul) | tall(paul))) [nnf transformation 9]
52. ((quiet(paul) & ~tall(paul)) | ! [X0] : (wise(X0) & ~quiet(X0))) & (? [X0] : (~wise(X0) | quiet(X0)) | ~quiet(paul) | tall(paul)) [flattening 51]
53. ((quiet(paul) & ~tall(paul)) | ! [X0] : (wise(X0) & ~quiet(X0))) & (? [X1] : (~wise(X1) | quiet(X1)) | ~quiet(paul) | tall(paul)) [rectify 52]
54. ? [X1] : (~wise(X1) | quiet(X1)) => (~wise(sK2) | quiet(sK2)) [choice axiom]
55. ((quiet(paul) & ~tall(paul)) | ! [X0] : (wise(X0) & ~quiet(X0))) & ((~wise(sK2) | quiet(sK2)) | ~quiet(paul) | tall(paul)) [skolemisation 53,54]
56. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [nnf transformation 10]
57. ! [X0] : ((((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))))) [flattening 56]
63. ! [X0] : ((~generous(X0) | (~humble(X0) & tall(X0))) & ((humble(X0) | ~tall(X0)) | generous(X0))) [nnf transformation 16]
64. ! [X0] : ((~generous(X0) | (~humble(X0) & tall(X0))) & (humble(X0) | ~tall(X0) | generous(X0))) [flattening 63]
87. ~wise(X0) | generous(X0) | creative(X0) [cnf transformation 50]
92. ~tall(paul) | wise(X0) [cnf transformation 55]
98. wise(X0) | humble(X0) | wise(X0) [cnf transformation 57]
99. ~wise(X0) | humble(X0) | ~wise(X0) | funny(X0) [cnf transformation 57]
111. ~creative(X0) | ~funny(X0) [cnf transformation 37]
116. ~generous(X0) | tall(X0) [cnf transformation 64]
128. tall(paul) | ~humble(paul) [cnf transformation 24]
129. ~wise(mary) [cnf transformation 25]
132. humble(X0) | wise(X0) [duplicate literal removal 98]
133. ~wise(X0) | humble(X0) | funny(X0) [duplicate literal removal 99]
195. 16 <=> generous(paul) [avatar definition]
196. generous(paul) <- (16) [avatar component clause 195]
212. 20 <=> ! [X0] : wise(X0) [avatar definition]
213. wise(X0) <- (20) [avatar component clause 212]
224. 23 <=> tall(paul) [avatar definition]
227. 20 | ~23 [avatar split clause 92,224,212]
290. 36 <=> humble(paul) [avatar definition]
292. ~humble(paul) <- (~36) [avatar component clause 290]
293. ~36 | 23 [avatar split clause 128,224,290]
302. wise(paul) <- (~36) [resolution 132,292]
319. generous(paul) | creative(paul) <- (~36) [resolution 87,302]
345. 43 <=> creative(paul) [avatar definition]
347. creative(paul) <- (43) [avatar component clause 345]
348. 43 | 16 | 36 [avatar split clause 319,290,195,345]
350. tall(paul) <- (16) [resolution 196,116]
353. 23 | ~16 [avatar split clause 350,195,224]
355. $false <- (20) [resolution 213,129]
362. ~20 [avatar contradiction clause 355]
368. ~funny(paul) <- (43) [resolution 347,111]
398. humble(paul) | funny(paul) <- (~36) [resolution 133,302]
409. funny(paul) <- (~36) [subsumption resolution 398,292]
410. $false <- (~36, 43) [subsumption resolution 409,368]
411. 36 | ~43 [avatar contradiction clause 410]
417. $false [avatar sat refutation 227,293,348,353,362,411]
% SZS output end Proof for 4349969079512299614360413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both not tall and generous. Everyone who is not kind is not generous or strong and vice versa. Everyone who is both not calm and not creative is not humble and vice versa. Everyone who is wise or not tall is not funny and vice versa. Everyone who is not patient is tall or creative and vice versa. Everyone who is not quiet is not old or curious and vice versa. If someone is either funny or creative then mary is both generous and quiet. If someone is both not old and not creative then someone is either happy or old. If mary is happy or generous then someone is not wise or not creative and vice versa. Everyone who is either happy or not brave is both creative and old and vice versa. Everyone who is both not funny and strong is both old and not brave. Everyone who is brave is both brave and strong and vice versa. If someone is brave then mary is both strong and kind. If john is either calm or not wise then fred is both not humble and calm. Everyone who is calm or wise is not patient or rich and vice versa. Everyone who is wise or not humble is either brave or happy and vice versa. Someone is both not generous and not calm. John is either not happy or not brave. John is both not creative and not kind. Fred is wise or not patient. Someone is either not curious or not patient. Paul is either not calm or not curious. Someone is either not curious or not kind. Someone is both kind and old. | John is humble. | contradiction | (![X]:(~strong(X)=>(~tall(X)&generous(X))))&
(![X]:(~kind(X)<=>(~generous(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~humble(X)))&
(![X]:((wise(X)|~tall(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(tall(X)|creative(X))))&
(![X]:(~quiet(X)<=>(~old(X)|curious(X))))&
((?[X]:((funny(X)<~>creative(X))))=>((generous(mary)&quiet(mary))))&
((?[X]:((~old(X)&~creative(X))))=>(?[X]:((happy(X)<~>old(X)))))&
(((happy(mary)|generous(mary)))<=>(?[X]:((~wise(X)|~creative(X)))))&
(![X]:((happy(X)<~>~brave(X))<=>(creative(X)&old(X))))&
(![X]:((~funny(X)&strong(X))=>(old(X)&~brave(X))))&
(![X]:(brave(X)<=>(brave(X)&strong(X))))&
((?[X]:(brave(X)))=>((strong(mary)&kind(mary))))&
(((calm(john)<~>~wise(john)))=>((~humble(fred)&calm(fred))))&
(![X]:((calm(X)|wise(X))<=>(~patient(X)|rich(X))))&
(![X]:((wise(X)|~humble(X))<=>(brave(X)<~>happy(X))))&
(?[X]:((~generous(X)&~calm(X))))&
((~happy(john)<~>~brave(john)))&
((~creative(john)&~kind(john)))&
((wise(fred)|~patient(fred)))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~calm(paul)<~>~curious(paul)))&
(?[X]:((~curious(X)<~>~kind(X))))&
(?[X]:((kind(X)&old(X)))) | humble(john) | [
"p1",
"p2",
"p12",
"p13",
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8167928401882647539328212
% SZS output start Proof for 8167928401882647539328212
2. ! [X0] : (~kind(X0) <=> (strong(X0) | ~generous(X0))) [input p1]
3. ! [X0] : ((~creative(X0) & ~calm(X0)) <=> ~humble(X0)) [input p2]
13. ? [X0] : brave(X0) => (kind(mary) & strong(mary)) [input p12]
14. (calm(john) <~> ~wise(john)) => (calm(fred) & ~humble(fred)) [input p13]
16. ! [X0] : ((~humble(X0) | wise(X0)) <=> (brave(X0) <~> happy(X0))) [input p15]
18. ~happy(john) <~> ~brave(john) [input p17]
19. ~kind(john) & ~creative(john) [input p18]
25. humble(john) [input hypothesis]
34. (kind(mary) & strong(mary)) | ! [X0] : ~brave(X0) [ennf transformation 13]
35. (calm(fred) & ~humble(fred)) | (calm(john) <=> ~wise(john)) [ennf transformation 14]
36. ! [X0] : ((~kind(X0) | (~strong(X0) & generous(X0))) & ((strong(X0) | ~generous(X0)) | kind(X0))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | (~strong(X0) & generous(X0))) & (strong(X0) | ~generous(X0) | kind(X0))) [flattening 36]
38. ! [X0] : (((~creative(X0) & ~calm(X0)) | humble(X0)) & (~humble(X0) | (creative(X0) | calm(X0)))) [nnf transformation 3]
39. ! [X0] : (((~creative(X0) & ~calm(X0)) | humble(X0)) & (~humble(X0) | creative(X0) | calm(X0))) [flattening 38]
58. (calm(fred) & ~humble(fred)) | ((calm(john) | wise(john)) & (~wise(john) | ~calm(john))) [nnf transformation 35]
61. ! [X0] : (((~humble(X0) | wise(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (humble(X0) & ~wise(X0)))) [nnf transformation 16]
62. ! [X0] : ((~humble(X0) | wise(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (humble(X0) & ~wise(X0)))) [flattening 61]
65. (brave(john) | happy(john)) & (~brave(john) | ~happy(john)) [nnf transformation 18]
79. ~kind(X0) | ~strong(X0) [cnf transformation 37]
80. ~humble(X0) | creative(X0) | calm(X0) [cnf transformation 39]
81. ~calm(X0) | humble(X0) [cnf transformation 39]
112. strong(mary) | ~brave(X0) [cnf transformation 34]
113. kind(mary) | ~brave(X0) [cnf transformation 34]
114. ~humble(fred) | ~wise(john) | ~calm(john) [cnf transformation 58]
116. calm(fred) | ~wise(john) | ~calm(john) [cnf transformation 58]
127. ~happy(X0) | wise(X0) | brave(X0) | ~humble(X0) [cnf transformation 62]
131. brave(john) | happy(john) [cnf transformation 65]
132. ~creative(john) [cnf transformation 19]
143. humble(john) [cnf transformation 25]
199. 13 <=> ! [X0] : ~brave(X0) [avatar definition]
200. ~brave(X0) <- (13) [avatar component clause 199]
202. 14 <=> kind(mary) [avatar definition]
204. kind(mary) <- (14) [avatar component clause 202]
205. 13 | 14 [avatar split clause 113,202,199]
207. 15 <=> strong(mary) [avatar definition]
210. 13 | 15 [avatar split clause 112,207,199]
212. 16 <=> wise(john) [avatar definition]
216. 17 <=> calm(john) [avatar definition]
220. 18 <=> calm(fred) [avatar definition]
222. calm(fred) <- (18) [avatar component clause 220]
224. ~17 | ~16 | 18 [avatar split clause 116,220,212,216]
226. 19 <=> humble(fred) [avatar definition]
228. ~humble(fred) <- (~19) [avatar component clause 226]
230. ~17 | ~16 | ~19 [avatar split clause 114,226,212,216]
232. 20 <=> happy(john) [avatar definition]
234. happy(john) <- (20) [avatar component clause 232]
236. 21 <=> brave(john) [avatar definition]
237. ~brave(john) <- (~21) [avatar component clause 236]
238. brave(john) <- (21) [avatar component clause 236]
239. 20 | 21 [avatar split clause 131,236,232]
291. creative(john) | calm(john) [resolution 80,143]
293. calm(john) [subsumption resolution 291,132]
296. 17 [avatar split clause 293,216]
450. wise(john) | brave(john) | ~humble(john) <- (20) [resolution 127,234]
456. wise(john) | ~humble(john) <- (20, ~21) [subsumption resolution 450,237]
457. wise(john) <- (20, ~21) [subsumption resolution 456,143]
458. 16 | ~20 | 21 [avatar split clause 457,236,232,212]
466. $false <- (13, 21) [subsumption resolution 238,200]
467. ~13 | ~21 [avatar contradiction clause 466]
478. ~strong(mary) <- (14) [resolution 204,79]
482. ~15 | ~14 [avatar split clause 478,202,207]
487. humble(fred) <- (18) [resolution 222,81]
488. $false <- (18, ~19) [subsumption resolution 487,228]
489. ~18 | 19 [avatar contradiction clause 488]
490. $false [avatar sat refutation 205,210,224,230,239,296,458,467,482,489]
% SZS output end Proof for 8167928401882647539328212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is patient or not brave and vice versa.
If fred is brave or not kind then paul is wise and vice versa.
If someone is either old or not generous then someone is both not humble and old and vice versa.
Everyone who is both not brave and not patient is either not curious or not humble and vice versa.
If someone is both creative and not strong then someone is either brave or curious.
If someone is both not creative and happy then someone is both not rich and creative.
Everyone who is rich or not tall is quiet or not generous.
If alice is both tall and quiet then susan is not kind or calm and vice versa.
If someone is not patient or creative then someone is both generous and not quiet.
Everyone who is wise or creative is both wise and not patient.
Everyone who is not calm is both not strong and not curious.
If someone is both generous and not old then someone is not kind.
Everyone who is either brave or patient is not strong and vice versa.
Everyone who is both old and creative is happy or rich and vice versa.
Everyone who is either not creative or not tall is either kind or strong.
If someone is not humble or not rich then lucy is not quiet and vice versa.
Lucy is both patient and not brave.
Fred is both patient and not generous.
Mary is both not generous and not funny.
Someone is either not strong or not calm.
Someone is either not happy or old.
Alice is both not happy and not curious.
Alice is either generous or not quiet.
Someone is either brave or not old. | Lucy is not curious. | entailment | (![X]:(~humble(X)<=>(patient(X)|~brave(X))))&
(((brave(fred)|~kind(fred)))<=>(wise(paul)))&
((?[X]:((old(X)<~>~generous(X))))<=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((~brave(X)&~patient(X))<=>(~curious(X)<~>~humble(X))))&
((?[X]:((creative(X)&~strong(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
((?[X]:((~creative(X)&happy(X))))=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((rich(X)|~tall(X))=>(quiet(X)|~generous(X))))&
(((tall(alice)&quiet(alice)))<=>((~kind(susan)|calm(susan))))&
((?[X]:((~patient(X)|creative(X))))=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((wise(X)|creative(X))=>(wise(X)&~patient(X))))&
(![X]:(~calm(X)=>(~strong(X)&~curious(X))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:(~kind(X))))&
(![X]:((brave(X)<~>patient(X))<=>~strong(X)))&
(![X]:((old(X)&creative(X))<=>(happy(X)|rich(X))))&
(![X]:((~creative(X)<~>~tall(X))=>(kind(X)<~>strong(X))))&
((?[X]:((~humble(X)|~rich(X))))<=>(~quiet(lucy)))&
((patient(lucy)&~brave(lucy)))&
((patient(fred)&~generous(fred)))&
((~generous(mary)&~funny(mary)))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:((~happy(X)<~>old(X))))&
((~happy(alice)&~curious(alice)))&
((generous(alice)<~>~quiet(alice)))&
(?[X]:((brave(X)<~>~old(X)))) | ~curious(lucy) | [
"p0",
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4740857092162603082126157
% SZS output start Proof for 4740857092162603082126157
1. ! [X0] : (~humble(X0) <=> (~brave(X0) | patient(X0))) [input p0]
4. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (~curious(X0) <~> ~humble(X0))) [input p3]
17. ~brave(lucy) & patient(lucy) [input p16]
25. curious(lucy) [input hypothesis]
41. ! [X0] : ((~humble(X0) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | humble(X0))) [nnf transformation 1]
42. ! [X0] : ((~humble(X0) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | humble(X0))) [flattening 41]
50. ! [X0] : (((~patient(X0) & ~brave(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | (patient(X0) | brave(X0)))) [nnf transformation 4]
51. ! [X0] : (((~patient(X0) & ~brave(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | patient(X0) | brave(X0))) [flattening 50]
86. ~patient(X0) | ~humble(X0) [cnf transformation 42]
102. ~patient(X0) | ~curious(X0) | humble(X0) [cnf transformation 51]
141. patient(lucy) [cnf transformation 17]
156. curious(lucy) [cnf transformation 25]
203. ~curious(X0) | ~patient(X0) [subsumption resolution 102,86]
333. ~patient(lucy) [resolution 203,156]
334. $false [subsumption resolution 333,141]
% SZS output end Proof for 4740857092162603082126157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not creative is not strong or rich and vice versa.
If someone is either brave or humble then mary is either not rich or not patient.
If fred is not strong or tall then susan is curious or kind.
Everyone who is either not calm or not humble is creative or not humble and vice versa.
Everyone who is both not wise and generous is both not happy and happy and vice versa.
If lucy is either not strong or not wise then someone is either not funny or not brave.
If mary is both not happy and not calm then someone is both calm and tall.
Everyone who is either not strong or not calm is both not generous and not kind and vice versa.
Everyone who is kind is not kind or old and vice versa.
If susan is either creative or not happy then fred is both not brave and tall.
Everyone who is not wise or not patient is funny.
Everyone who is not calm is both funny and not patient and vice versa.
Everyone who is either generous or creative is old or not curious and vice versa.
If someone is either not creative or not strong then someone is not brave or not old.
If someone is not strong then someone is not creative or not kind.
If someone is either not wise or kind then fred is funny or not brave and vice versa.
Someone is old or not rich.
John is brave or not calm.
Paul is either rich or not tall.
Someone is both kind and rich.
Susan is not tall or not generous.
Someone is both not humble and creative.
Mary is funny or not funny. | Paul is humble. | neutral | (![X]:((calm(X)&~creative(X))<=>(~strong(X)|rich(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((~rich(mary)<~>~patient(mary))))&
(((~strong(fred)|tall(fred)))=>((curious(susan)|kind(susan))))&
(![X]:((~calm(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
(![X]:((~wise(X)&generous(X))<=>(~happy(X)&happy(X))))&
(((~strong(lucy)<~>~wise(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((~happy(mary)&~calm(mary)))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~generous(X)&~kind(X))))&
(![X]:(kind(X)<=>(~kind(X)|old(X))))&
(((creative(susan)<~>~happy(susan)))=>((~brave(fred)&tall(fred))))&
(![X]:((~wise(X)|~patient(X))=>funny(X)))&
(![X]:(~calm(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)<~>creative(X))<=>(old(X)|~curious(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~kind(X)))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((funny(fred)|~brave(fred))))&
(?[X]:((old(X)|~rich(X))))&
((brave(john)|~calm(john)))&
((rich(paul)<~>~tall(paul)))&
(?[X]:((kind(X)&rich(X))))&
((~tall(susan)|~generous(susan)))&
(?[X]:((~humble(X)&creative(X))))&
((funny(mary)|~funny(mary))) | humble(paul) | [] | null | 0 |
Everyone who is not humble is either not funny or brave and vice versa.
Everyone who is funny or happy is both not wise and calm and vice versa.
If lucy is not creative then susan is not curious or kind and vice versa.
Everyone who is both patient and rich is patient or not old.
Everyone who is either wise or calm is both kind and not kind.
If john is either tall or not generous then john is either not kind or curious.
If someone is not quiet then paul is both not brave and wise and vice versa.
If someone is either not quiet or patient then someone is patient and vice versa.
If someone is either not patient or not funny then someone is creative and vice versa.
If susan is wise or not creative then fred is either not quiet or funny.
Everyone who is either not creative or strong is kind and vice versa.
Everyone who is both not calm and calm is humble and vice versa.
If someone is both kind and not curious then someone is both not curious and kind and vice versa.
If someone is curious or not wise then someone is either rich or not creative.
If someone is both patient and generous then someone is either tall or not quiet and vice versa.
If susan is either tall or not tall then someone is not funny or generous.
Someone is not calm.
Someone is both kind and tall.
Fred is strong or not creative.
Someone is patient or humble.
Lucy is either not brave or generous.
Someone is both not patient and curious.
Fred is either not creative or not quiet. | John is humble. | contradiction | (![X]:(~humble(X)<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)|happy(X))<=>(~wise(X)&calm(X))))&
((~creative(lucy))<=>((~curious(susan)|kind(susan))))&
(![X]:((patient(X)&rich(X))=>(patient(X)|~old(X))))&
(![X]:((wise(X)<~>calm(X))=>(kind(X)&~kind(X))))&
(((tall(john)<~>~generous(john)))=>((~kind(john)<~>curious(john))))&
((?[X]:(~quiet(X)))<=>((~brave(paul)&wise(paul))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:(creative(X))))&
(((wise(susan)|~creative(susan)))=>((~quiet(fred)<~>funny(fred))))&
(![X]:((~creative(X)<~>strong(X))<=>kind(X)))&
(![X]:((~calm(X)&calm(X))<=>humble(X)))&
((?[X]:((kind(X)&~curious(X))))<=>(?[X]:((~curious(X)&kind(X)))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
(((tall(susan)<~>~tall(susan)))=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:(~calm(X)))&
(?[X]:((kind(X)&tall(X))))&
((strong(fred)|~creative(fred)))&
(?[X]:((patient(X)|humble(X))))&
((~brave(lucy)<~>generous(lucy)))&
(?[X]:((~patient(X)&curious(X))))&
((~creative(fred)<~>~quiet(fred))) | humble(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4652284199598953262778134
% SZS output start Proof for 4652284199598953262778134
12. ! [X0] : ((calm(X0) & ~calm(X0)) <=> humble(X0)) [input p11]
24. humble(john) [input hypothesis]
60. ! [X0] : (((calm(X0) & ~calm(X0)) | ~humble(X0)) & (humble(X0) | (~calm(X0) | calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((calm(X0) & ~calm(X0)) | ~humble(X0)) & (humble(X0) | ~calm(X0) | calm(X0))) [flattening 60]
129. ~calm(X0) | ~humble(X0) [cnf transformation 61]
130. calm(X0) | ~humble(X0) [cnf transformation 61]
158. humble(john) [cnf transformation 24]
286. ~humble(X0) [subsumption resolution 129,130]
395. $false [subsumption resolution 158,286]
% SZS output end Proof for 4652284199598953262778134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and curious is either patient or not calm and vice versa. If paul is both not wise and not brave then someone is kind or not creative and vice versa. Everyone who is both calm and patient is not calm or funny. If someone is both old and not curious then someone is either not funny or not rich and vice versa. If someone is not happy or not wise then alice is both tall and generous. Everyone who is not wise or quiet is both not tall and not wise and vice versa. Everyone who is both curious and brave is both curious and not creative and vice versa. Everyone who is not generous is both not happy and not calm and vice versa. Everyone who is patient is not brave or not old and vice versa. Everyone who is kind is curious. If fred is not patient or brave then susan is both not rich and rich. If fred is both not rich and tall then someone is both quiet and not strong and vice versa. If someone is not tall or not creative then someone is not generous and vice versa. Everyone who is either humble or not kind is either happy or tall and vice versa. Everyone who is both not quiet and not strong is both not kind and not patient. If lucy is both creative and strong then john is not brave or not funny and vice versa. Someone is kind. Fred is both generous and not quiet. Lucy is both humble and brave. Someone is not funny or rich. Fred is either not kind or funny. Someone is not happy or funny. Fred is both not old and not humble. | Alice is quiet. | contradiction | (![X]:((~curious(X)&curious(X))<=>(patient(X)<~>~calm(X))))&
(((~wise(paul)&~brave(paul)))<=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)|funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((tall(alice)&generous(alice))))&
(![X]:((~wise(X)|quiet(X))<=>(~tall(X)&~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(curious(X)&~creative(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~calm(X))))&
(![X]:(patient(X)<=>(~brave(X)|~old(X))))&
(![X]:(kind(X)=>curious(X)))&
(((~patient(fred)|brave(fred)))=>((~rich(susan)&rich(susan))))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(happy(X)<~>tall(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&strong(lucy)))<=>((~brave(john)|~funny(john))))&
(?[X]:(kind(X)))&
((generous(fred)&~quiet(fred)))&
((humble(lucy)&brave(lucy)))&
(?[X]:((~funny(X)|rich(X))))&
((~kind(fred)<~>funny(fred)))&
(?[X]:((~happy(X)|funny(X))))&
((~old(fred)&~humble(fred))) | quiet(alice) | [
"p1",
"p4",
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8997923833731341659702809
% SZS output start Proof for 8997923833731341659702809
2. (~brave(paul) & ~wise(paul)) <=> ? [X0] : (~creative(X0) | kind(X0)) [input p1]
5. ? [X0] : (~wise(X0) | ~happy(X0)) => (generous(alice) & tall(alice)) [input p4]
6. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~wise(X0) & ~tall(X0))) [input p5]
17. ? [X0] : kind(X0) [input p16]
24. quiet(alice) [input hypothesis]
29. (generous(alice) & tall(alice)) | ! [X0] : (wise(X0) & happy(X0)) [ennf transformation 5]
36. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | (brave(paul) | wise(paul))) [nnf transformation 2]
37. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | brave(paul) | wise(paul)) [flattening 36]
38. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X1] : (~creative(X1) | kind(X1)) | brave(paul) | wise(paul)) [rectify 37]
39. ? [X1] : (~creative(X1) | kind(X1)) => (~creative(sK0) | kind(sK0)) [choice axiom]
40. ((~brave(paul) & ~wise(paul)) | ! [X0] : (creative(X0) & ~kind(X0))) & ((~creative(sK0) | kind(sK0)) | brave(paul) | wise(paul)) [skolemisation 38,39]
46. ! [X0] : (((quiet(X0) | ~wise(X0)) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 6]
47. ! [X0] : ((quiet(X0) | ~wise(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | (~quiet(X0) & wise(X0)))) [flattening 46]
67. ? [X0] : kind(X0) => kind(sK6) [choice axiom]
68. kind(sK6) [skolemisation 17,67]
81. ~wise(paul) | ~kind(X0) [cnf transformation 40]
93. tall(alice) | wise(X0) [cnf transformation 29]
97. ~quiet(X0) | ~tall(X0) [cnf transformation 47]
138. kind(sK6) [cnf transformation 68]
149. quiet(alice) [cnf transformation 24]
162. 3 <=> ! [X0] : ~kind(X0) [avatar definition]
163. ~kind(X0) <- (3) [avatar component clause 162]
166. 4 <=> wise(paul) [avatar definition]
168. ~wise(paul) <- (~4) [avatar component clause 166]
170. 3 | ~4 [avatar split clause 81,166,162]
212. 14 <=> ! [X0] : wise(X0) [avatar definition]
213. wise(X0) <- (14) [avatar component clause 212]
224. 17 <=> tall(alice) [avatar definition]
226. tall(alice) <- (17) [avatar component clause 224]
227. 14 | 17 [avatar split clause 93,224,212]
338. $false <- (~4, 14) [subsumption resolution 168,213]
339. 4 | ~14 [avatar contradiction clause 338]
340. $false <- (3) [resolution 163,138]
341. ~3 [avatar contradiction clause 340]
347. ~tall(alice) [resolution 97,149]
348. $false <- (17) [subsumption resolution 347,226]
349. ~17 [avatar contradiction clause 348]
350. $false [avatar sat refutation 170,227,339,341,349]
% SZS output end Proof for 8997923833731341659702809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not wise then fred is old or humble and vice versa. Everyone who is either not rich or not curious is both creative and strong. If lucy is happy or brave then john is both not rich and calm and vice versa. If alice is either not old or old then john is either strong or quiet. Everyone who is either rich or strong is not patient or quiet and vice versa. Everyone who is not creative or brave is both not rich and not calm and vice versa. If mary is both not humble and quiet then susan is both creative and not quiet. Everyone who is either not old or brave is either not brave or kind and vice versa. Everyone who is either not kind or kind is calm or not brave and vice versa. Everyone who is not humble or not quiet is either not patient or generous and vice versa. Everyone who is either not generous or strong is not brave or kind and vice versa. If mary is happy or not happy then alice is not creative. If john is calm then susan is either rich or not humble. Everyone who is either happy or not humble is both not strong and brave. If mary is not strong or not old then susan is rich or not wise and vice versa. Fred is either not brave or not funny. Someone is rich or wise. Someone is not kind or funny. Someone is not generous. Someone is strong or not creative. Someone is either not tall or not calm. Someone is either brave or humble. Someone is either kind or not happy. | John is not rich. | contradiction | (((~calm(susan)&~wise(susan)))<=>((old(fred)|humble(fred))))&
(![X]:((~rich(X)<~>~curious(X))=>(creative(X)&strong(X))))&
(((happy(lucy)|brave(lucy)))<=>((~rich(john)&calm(john))))&
(((~old(alice)<~>old(alice)))=>((strong(john)<~>quiet(john))))&
(![X]:((rich(X)<~>strong(X))<=>(~patient(X)|quiet(X))))&
(![X]:((~creative(X)|brave(X))<=>(~rich(X)&~calm(X))))&
(((~humble(mary)&quiet(mary)))=>((creative(susan)&~quiet(susan))))&
(![X]:((~old(X)<~>brave(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(calm(X)|~brave(X))))&
(![X]:((~humble(X)|~quiet(X))<=>(~patient(X)<~>generous(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|kind(X))))&
(((happy(mary)|~happy(mary)))=>(~creative(alice)))&
((calm(john))=>((rich(susan)<~>~humble(susan))))&
(![X]:((happy(X)<~>~humble(X))=>(~strong(X)&brave(X))))&
(((~strong(mary)|~old(mary)))<=>((rich(susan)|~wise(susan))))&
((~brave(fred)<~>~funny(fred)))&
(?[X]:((rich(X)|wise(X))))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | ~rich(john) | [
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8541213169977898654112403
% SZS output start Proof for 8541213169977898654112403
4. (~old(alice) <~> old(alice)) => (strong(john) <~> quiet(john)) [input p3]
5. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (quiet(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((brave(X0) | ~creative(X0)) <=> (~calm(X0) & ~rich(X0))) [input p5]
9. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (~brave(X0) | calm(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> (~patient(X0) <~> generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> strong(X0)) <=> (kind(X0) | ~brave(X0))) [input p10]
24. ~rich(john) [input hypothesis]
26. (strong(john) <~> quiet(john)) | (~old(alice) <=> old(alice)) [ennf transformation 4]
37. ((~quiet(john) | ~strong(john)) & (quiet(john) | strong(john))) | ((~old(alice) | ~old(alice)) & (old(alice) | old(alice))) [nnf transformation 26]
38. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (~quiet(X0) & patient(X0))) & ((quiet(X0) | ~patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (~quiet(X0) & patient(X0))) & (quiet(X0) | ~patient(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [flattening 38]
40. ! [X0] : (((brave(X0) | ~creative(X0)) | (calm(X0) | rich(X0))) & ((~calm(X0) & ~rich(X0)) | (~brave(X0) & creative(X0)))) [nnf transformation 6]
41. ! [X0] : ((brave(X0) | ~creative(X0) | calm(X0) | rich(X0)) & ((~calm(X0) & ~rich(X0)) | (~brave(X0) & creative(X0)))) [flattening 40]
43. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 9]
44. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 43]
45. ! [X0] : (((~quiet(X0) | ~humble(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) & (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (quiet(X0) & humble(X0)))) [nnf transformation 10]
46. ! [X0] : ((~quiet(X0) | ~humble(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) & (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (quiet(X0) & humble(X0)))) [flattening 45]
47. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [nnf transformation 11]
48. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [flattening 47]
87. ~quiet(john) | ~strong(john) | old(alice) | old(alice) [cnf transformation 37]
88. ~quiet(john) | ~strong(john) | ~old(alice) | ~old(alice) [cnf transformation 37]
90. ~patient(X0) | quiet(X0) | rich(X0) | ~strong(X0) [cnf transformation 39]
91. patient(X0) | rich(X0) | strong(X0) [cnf transformation 39]
92. ~quiet(X0) | rich(X0) | strong(X0) [cnf transformation 39]
98. ~brave(X0) | ~calm(X0) [cnf transformation 41]
110. ~brave(X0) | calm(X0) | kind(X0) | kind(X0) [cnf transformation 44]
111. ~brave(X0) | calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44]
117. ~patient(X0) | generous(X0) | quiet(X0) [cnf transformation 46]
119. ~generous(X0) | patient(X0) | quiet(X0) [cnf transformation 46]
124. strong(X0) | ~generous(X0) | brave(X0) [cnf transformation 48]
126. ~strong(X0) | generous(X0) | brave(X0) [cnf transformation 48]
152. ~rich(john) [cnf transformation 24]
153. ~brave(X0) | calm(X0) | kind(X0) [duplicate literal removal 110]
154. ~brave(X0) | calm(X0) | ~kind(X0) [duplicate literal removal 111]
161. ~quiet(john) | ~strong(john) | old(alice) [duplicate literal removal 87]
162. ~quiet(john) | ~strong(john) | ~old(alice) [duplicate literal removal 88]
185. 5 <=> rich(john) [avatar definition]
186. ~rich(john) <- (~5) [avatar component clause 185]
206. 9 <=> old(alice) [avatar definition]
210. 10 <=> strong(john) [avatar definition]
211. strong(john) <- (10) [avatar component clause 210]
212. ~strong(john) <- (~10) [avatar component clause 210]
214. 11 <=> quiet(john) [avatar definition]
216. ~quiet(john) <- (~11) [avatar component clause 214]
217. ~9 | ~10 | ~11 [avatar split clause 162,214,210,206]
218. 9 | ~10 | ~11 [avatar split clause 161,214,210,206]
241. ~kind(X0) | ~brave(X0) [subsumption resolution 154,98]
242. ~brave(X0) | kind(X0) [subsumption resolution 153,98]
243. ~brave(X0) [subsumption resolution 242,241]
244. ~strong(X0) | generous(X0) [subsumption resolution 126,243]
245. ~generous(X0) | strong(X0) [subsumption resolution 124,243]
329. ~5 [avatar split clause 152,185]
333. generous(john) <- (10) [resolution 244,211]
354. generous(X0) | quiet(X0) | rich(X0) | strong(X0) [resolution 117,91]
355. quiet(X0) | rich(X0) | strong(X0) [subsumption resolution 354,245]
356. strong(X0) | rich(X0) [subsumption resolution 355,92]
366. 35 <=> patient(john) [avatar definition]
368. patient(john) <- (35) [avatar component clause 366]
374. patient(john) | quiet(john) <- (10) [resolution 119,333]
409. quiet(john) | rich(john) | ~strong(john) <- (35) [resolution 90,368]
411. rich(john) | ~strong(john) <- (~11, 35) [subsumption resolution 409,216]
412. ~strong(john) <- (~5, ~11, 35) [subsumption resolution 411,186]
413. $false <- (~5, 10, ~11, 35) [subsumption resolution 412,211]
414. 5 | ~10 | 11 | ~35 [avatar contradiction clause 413]
415. patient(john) <- (10, ~11) [subsumption resolution 374,216]
416. 35 | ~10 | 11 [avatar split clause 415,214,210,366]
417. rich(john) <- (~10) [resolution 212,356]
418. $false <- (~5, ~10) [subsumption resolution 417,186]
419. 5 | 10 [avatar contradiction clause 418]
420. $false [avatar sat refutation 217,218,329,414,416,419]
% SZS output end Proof for 8541213169977898654112403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not quiet is either not brave or kind.
If mary is either wise or not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Everyone who is either not wise or not calm is either not curious or wise.
Everyone who is tall is both strong and not happy.
Everyone who is not humble or old is not rich and vice versa.
Everyone who is both strong and not rich is either not generous or creative and vice versa.
Everyone who is either not brave or patient is both rich and not kind and vice versa.
If someone is either humble or rich then lucy is quiet or not funny.
If someone is either kind or not kind then alice is quiet or not happy.
Everyone who is kind is either not quiet or happy.
If alice is quiet then john is either not old or not generous and vice versa.
Everyone who is not generous is quiet or wise and vice versa.
If lucy is either not kind or not happy then someone is not wise.
Everyone who is both not generous and not strong is calm or kind and vice versa.
Everyone who is not rich is either generous or quiet and vice versa.
Someone is either brave or not strong.
Susan is both not funny and not kind.
Susan is not old.
Someone is either not generous or generous.
Someone is either happy or humble.
Fred is either tall or not old.
Someone is wise or not brave.
Paul is either not happy or not tall. | Lucy is not tall. | neutral | (![X]:((~tall(X)|~quiet(X))=>(~brave(X)<~>kind(X))))&
(((wise(mary)<~>~old(mary)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(![X]:((~wise(X)<~>~calm(X))=>(~curious(X)<~>wise(X))))&
(![X]:(tall(X)=>(strong(X)&~happy(X))))&
(![X]:((~humble(X)|old(X))<=>~rich(X)))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(rich(X)&~kind(X))))&
((?[X]:((humble(X)<~>rich(X))))=>((quiet(lucy)|~funny(lucy))))&
((?[X]:((kind(X)<~>~kind(X))))=>((quiet(alice)|~happy(alice))))&
(![X]:(kind(X)=>(~quiet(X)<~>happy(X))))&
((quiet(alice))<=>((~old(john)<~>~generous(john))))&
(![X]:(~generous(X)<=>(quiet(X)|wise(X))))&
(((~kind(lucy)<~>~happy(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>(calm(X)|kind(X))))&
(![X]:(~rich(X)<=>(generous(X)<~>quiet(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
((~funny(susan)&~kind(susan)))&
(~old(susan))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((tall(fred)<~>~old(fred)))&
(?[X]:((wise(X)|~brave(X))))&
((~happy(paul)<~>~tall(paul))) | ~tall(lucy) | [] | null | 0 |
If fred is either not kind or not happy then someone is tall or not strong and vice versa.
If mary is both calm and funny then paul is humble and vice versa.
Everyone who is both patient and not generous is curious.
If alice is both happy and not strong then someone is both not generous and not tall.
If john is both not tall and not happy then someone is not patient or old and vice versa.
Everyone who is either not kind or not strong is not curious or quiet.
If someone is quiet then someone is both tall and funny and vice versa.
Everyone who is not curious or not rich is both not calm and not rich and vice versa.
If fred is either not rich or not calm then someone is both not wise and not patient.
If someone is generous then fred is generous or patient.
Everyone who is both brave and wise is both patient and strong.
Everyone who is not creative is either not generous or not rich.
If someone is patient then paul is not generous and vice versa.
If susan is both old and strong then fred is both not rich and not calm and vice versa.
Everyone who is creative is either not creative or old.
If paul is either old or tall then someone is either wise or not rich.
Paul is both rich and not patient.
Someone is both not wise and brave.
Someone is strong.
Someone is both quiet and not kind.
Someone is either not wise or tall.
Alice is not strong or not quiet.
Someone is not wise.
Someone is both not tall and not strong. | Paul is old. | neutral | (((~kind(fred)<~>~happy(fred)))<=>(?[X]:((tall(X)|~strong(X)))))&
(((calm(mary)&funny(mary)))<=>(humble(paul)))&
(![X]:((patient(X)&~generous(X))=>curious(X)))&
(((happy(alice)&~strong(alice)))=>(?[X]:((~generous(X)&~tall(X)))))&
(((~tall(john)&~happy(john)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((~kind(X)<~>~strong(X))=>(~curious(X)|quiet(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~curious(X)|~rich(X))<=>(~calm(X)&~rich(X))))&
(((~rich(fred)<~>~calm(fred)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(generous(X)))=>((generous(fred)|patient(fred))))&
(![X]:((brave(X)&wise(X))=>(patient(X)&strong(X))))&
(![X]:(~creative(X)=>(~generous(X)<~>~rich(X))))&
((?[X]:(patient(X)))<=>(~generous(paul)))&
(((old(susan)&strong(susan)))<=>((~rich(fred)&~calm(fred))))&
(![X]:(creative(X)=>(~creative(X)<~>old(X))))&
(((old(paul)<~>tall(paul)))=>(?[X]:((wise(X)<~>~rich(X)))))&
((rich(paul)&~patient(paul)))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~wise(X)<~>tall(X))))&
((~strong(alice)|~quiet(alice)))&
(?[X]:(~wise(X)))&
(?[X]:((~tall(X)&~strong(X)))) | old(paul) | [] | null | 0 |
Everyone who is not calm or calm is either curious or not generous.
Everyone who is both creative and strong is not kind.
Everyone who is both not wise and not strong is either not wise or patient and vice versa.
Everyone who is not kind or not rich is either quiet or not brave.
Everyone who is curious is generous or not rich.
If mary is either kind or curious then someone is either funny or not funny.
Everyone who is both not wise and old is not kind or not brave and vice versa.
Everyone who is either tall or not quiet is not strong.
If someone is calm then paul is both not rich and generous and vice versa.
If someone is not wise or not strong then john is both patient and tall.
Everyone who is calm or kind is creative or wise and vice versa.
If susan is both not creative and not old then paul is either not strong or wise.
If someone is either strong or not kind then someone is not quiet or not humble.
Everyone who is both old and curious is both not brave and not generous and vice versa.
If lucy is both strong and happy then alice is not tall or quiet and vice versa.
If someone is either not rich or not funny then alice is quiet or humble and vice versa.
Fred is both not old and not curious.
Someone is either not curious or generous.
Alice is either not patient or old.
Paul is old or not tall.
Susan is either old or humble.
Someone is either not funny or rich. | Paul is not wise. | contradiction | (![X]:((~calm(X)|calm(X))=>(curious(X)<~>~generous(X))))&
(![X]:((creative(X)&strong(X))=>~kind(X)))&
(![X]:((~wise(X)&~strong(X))<=>(~wise(X)<~>patient(X))))&
(![X]:((~kind(X)|~rich(X))=>(quiet(X)<~>~brave(X))))&
(![X]:(curious(X)=>(generous(X)|~rich(X))))&
(((kind(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((~wise(X)&old(X))<=>(~kind(X)|~brave(X))))&
(![X]:((tall(X)<~>~quiet(X))=>~strong(X)))&
((?[X]:(calm(X)))<=>((~rich(paul)&generous(paul))))&
((?[X]:((~wise(X)|~strong(X))))=>((patient(john)&tall(john))))&
(![X]:((calm(X)|kind(X))<=>(creative(X)|wise(X))))&
(((~creative(susan)&~old(susan)))=>((~strong(paul)<~>wise(paul))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)&~generous(X))))&
(((strong(lucy)&happy(lucy)))<=>((~tall(alice)|quiet(alice))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>((quiet(alice)|humble(alice))))&
((~old(fred)&~curious(fred)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~patient(alice)<~>old(alice)))&
((old(paul)|~tall(paul)))&
((old(susan)<~>humble(susan)))&
(?[X]:((~funny(X)<~>rich(X)))) | ~wise(paul) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8441994887800448029465802
% SZS output start Proof for 8441994887800448029465802
1. ! [X0] : ((calm(X0) | ~calm(X0)) => (curious(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : ((strong(X0) & creative(X0)) => ~kind(X0)) [input p1]
3. ! [X0] : ((~strong(X0) & ~wise(X0)) <=> (~wise(X0) <~> patient(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | ~kind(X0)) => (quiet(X0) <~> ~brave(X0))) [input p3]
7. ! [X0] : ((old(X0) & ~wise(X0)) <=> (~brave(X0) | ~kind(X0))) [input p6]
8. ! [X0] : ((tall(X0) <~> ~quiet(X0)) => ~strong(X0)) [input p7]
10. ? [X0] : (~strong(X0) | ~wise(X0)) => (tall(john) & patient(john)) [input p9]
11. ! [X0] : ((kind(X0) | calm(X0)) <=> (wise(X0) | creative(X0))) [input p10]
14. ! [X0] : ((curious(X0) & old(X0)) <=> (~generous(X0) & ~brave(X0))) [input p13]
23. ~wise(paul) [input hypothesis]
25. ! [X0] : ((curious(X0) <~> ~generous(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 1]
26. ! [X0] : (~kind(X0) | (~strong(X0) | ~creative(X0))) [ennf transformation 2]
27. ! [X0] : (~kind(X0) | ~strong(X0) | ~creative(X0)) [flattening 26]
28. ! [X0] : ((quiet(X0) <~> ~brave(X0)) | (rich(X0) & kind(X0))) [ennf transformation 4]
32. ! [X0] : (~strong(X0) | (tall(X0) <=> ~quiet(X0))) [ennf transformation 8]
33. (tall(john) & patient(john)) | ! [X0] : (strong(X0) & wise(X0)) [ennf transformation 10]
37. ! [X0] : (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~calm(X0) & calm(X0))) [nnf transformation 25]
38. ! [X0] : (((~strong(X0) & ~wise(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (strong(X0) | wise(X0)))) [nnf transformation 3]
39. ! [X0] : (((~strong(X0) & ~wise(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | strong(X0) | wise(X0))) [flattening 38]
40. ! [X0] : (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (rich(X0) & kind(X0))) [nnf transformation 28]
44. ! [X0] : (((old(X0) & ~wise(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 7]
45. ! [X0] : (((old(X0) & ~wise(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~old(X0) | wise(X0))) [flattening 44]
46. ! [X0] : (~strong(X0) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 32]
52. ! [X0] : (((kind(X0) | calm(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~kind(X0) & ~calm(X0)))) [nnf transformation 11]
53. ! [X0] : ((kind(X0) | calm(X0) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | (~kind(X0) & ~calm(X0)))) [flattening 52]
59. ! [X0] : (((curious(X0) & old(X0)) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 14]
60. ! [X0] : (((curious(X0) & old(X0)) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | ~curious(X0) | ~old(X0))) [flattening 59]
76. ~generous(X0) | curious(X0) | calm(X0) [cnf transformation 37]
77. ~generous(X0) | curious(X0) | ~calm(X0) [cnf transformation 37]
78. generous(X0) | ~curious(X0) | calm(X0) [cnf transformation 37]
79. ~curious(X0) | generous(X0) | ~calm(X0) [cnf transformation 37]
80. ~kind(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 27]
82. ~patient(X0) | wise(X0) | strong(X0) | wise(X0) [cnf transformation 39]
84. ~wise(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 39]
87. ~brave(X0) | quiet(X0) | kind(X0) [cnf transformation 40]
99. old(X0) | kind(X0) [cnf transformation 45]
101. ~tall(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 46]
106. patient(john) | wise(X0) [cnf transformation 33]
108. tall(john) | wise(X0) [cnf transformation 33]
111. ~kind(X0) | creative(X0) | wise(X0) [cnf transformation 53]
119. ~generous(X0) | ~curious(X0) | ~old(X0) [cnf transformation 60]
121. curious(X0) | generous(X0) | brave(X0) [cnf transformation 60]
144. ~wise(paul) [cnf transformation 23]
145. ~patient(X0) | wise(X0) | strong(X0) [duplicate literal removal 82]
146. ~patient(X0) | ~wise(X0) [duplicate literal removal 84]
147. ~curious(X0) | generous(X0) [subsumption resolution 78,79]
148. ~generous(X0) | curious(X0) [subsumption resolution 76,77]
149. ~patient(X0) | strong(X0) [subsumption resolution 145,146]
172. 6 <=> tall(john) [avatar definition]
174. tall(john) <- (6) [avatar component clause 172]
177. 7 <=> ! [X0] : wise(X0) [avatar definition]
178. wise(X0) <- (7) [avatar component clause 177]
179. 7 | 6 [avatar split clause 108,172,177]
181. 8 <=> patient(john) [avatar definition]
183. patient(john) <- (8) [avatar component clause 181]
185. 7 | 8 [avatar split clause 106,181,177]
199. 12 <=> wise(paul) [avatar definition]
201. ~wise(paul) <- (~12) [avatar component clause 199]
220. brave(X0) | generous(X0) [subsumption resolution 121,147]
221. ~old(X0) | ~curious(X0) [subsumption resolution 119,147]
302. ~12 [avatar split clause 144,199]
303. $false <- (7, ~12) [resolution 201,178]
304. ~7 | 12 [avatar contradiction clause 303]
309. ~wise(john) <- (8) [resolution 146,183]
311. strong(john) <- (8) [resolution 149,183]
315. ~curious(X1) | kind(X1) [resolution 221,99]
326. quiet(X0) | kind(X0) | generous(X0) [resolution 87,220]
360. ~quiet(john) | ~strong(john) <- (6) [resolution 101,174]
407. 40 <=> generous(john) [avatar definition]
408. ~generous(john) <- (~40) [avatar component clause 407]
409. generous(john) <- (40) [avatar component clause 407]
411. 41 <=> kind(john) [avatar definition]
412. ~kind(john) <- (~41) [avatar component clause 411]
413. kind(john) <- (41) [avatar component clause 411]
448. curious(john) <- (40) [resolution 409,148]
453. kind(john) <- (40) [resolution 448,315]
457. 41 | ~40 [avatar split clause 453,407,411]
458. creative(john) | wise(john) <- (41) [resolution 413,111]
459. ~strong(john) | ~creative(john) <- (41) [resolution 413,80]
460. creative(john) <- (8, 41) [subsumption resolution 458,309]
464. ~strong(john) <- (8, 41) [subsumption resolution 459,460]
493. $false <- (8, 41) [subsumption resolution 311,464]
494. ~8 | ~41 [avatar contradiction clause 493]
509. ~quiet(john) <- (6, 8) [subsumption resolution 360,311]
542. kind(john) | generous(john) <- (6, 8) [resolution 509,326]
544. generous(john) <- (6, 8, ~41) [subsumption resolution 542,412]
545. $false <- (6, 8, ~40, ~41) [subsumption resolution 544,408]
546. ~6 | ~8 | 40 | 41 [avatar contradiction clause 545]
547. $false [avatar sat refutation 179,185,302,304,457,494,546]
% SZS output end Proof for 8441994887800448029465802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is creative and vice versa.
If someone is happy then john is curious.
Everyone who is not tall is either creative or tall and vice versa.
Everyone who is humble or wise is not calm.
Everyone who is not strong is either old or not creative and vice versa.
If someone is curious then alice is rich or not calm.
Everyone who is both not creative and not tall is either not creative or not humble and vice versa.
Everyone who is both brave and not curious is not calm and vice versa.
Everyone who is patient is wise.
If someone is both funny and not creative then someone is either not brave or tall and vice versa.
Everyone who is both quiet and not brave is either not brave or not tall.
Everyone who is funny or not brave is tall and vice versa.
Everyone who is either old or humble is not brave and vice versa.
If someone is either tall or patient then fred is not patient and vice versa.
If lucy is either not funny or not quiet then alice is either quiet or tall.
Someone is not wise or brave.
Alice is not quiet or not rich.
Lucy is either not quiet or not kind.
Paul is both quiet and kind.
Someone is not curious.
Susan is either not quiet or funny. | Paul is patient. | neutral | (![X]:(rich(X)<=>creative(X)))&
((?[X]:(happy(X)))=>(curious(john)))&
(![X]:(~tall(X)<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)|wise(X))=>~calm(X)))&
(![X]:(~strong(X)<=>(old(X)<~>~creative(X))))&
((?[X]:(curious(X)))=>((rich(alice)|~calm(alice))))&
(![X]:((~creative(X)&~tall(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:((brave(X)&~curious(X))<=>~calm(X)))&
(![X]:(patient(X)=>wise(X)))&
((?[X]:((funny(X)&~creative(X))))<=>(?[X]:((~brave(X)<~>tall(X)))))&
(![X]:((quiet(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(![X]:((funny(X)|~brave(X))<=>tall(X)))&
(![X]:((old(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((tall(X)<~>patient(X))))<=>(~patient(fred)))&
(((~funny(lucy)<~>~quiet(lucy)))=>((quiet(alice)<~>tall(alice))))&
(?[X]:((~wise(X)|brave(X))))&
((~quiet(alice)|~rich(alice)))&
((~quiet(lucy)<~>~kind(lucy)))&
((quiet(paul)&kind(paul)))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>funny(susan))) | patient(paul) | [] | null | 0 |
Everyone who is not curious or not strong is either curious or quiet.
If alice is not wise then someone is brave or wise and vice versa.
Everyone who is not happy or curious is curious.
Everyone who is both generous and patient is not calm or not happy and vice versa.
Everyone who is quiet or not wise is either not generous or not calm.
Everyone who is not old or strong is both not generous and curious and vice versa.
If someone is both not creative and not old then someone is either not patient or rich and vice versa.
If fred is not rich then someone is kind and vice versa.
Everyone who is not curious is both not curious and brave.
Everyone who is not humble is wise.
If someone is either not humble or not calm then lucy is either not generous or not old and vice versa.
Everyone who is either rich or calm is curious.
If someone is old or generous then someone is either old or not curious.
Everyone who is not happy is both quiet and brave.
Everyone who is both not creative and happy is either quiet or old.
Everyone who is either humble or not patient is both not patient and funny and vice versa.
Someone is rich.
Alice is calm.
Someone is both not kind and old.
Fred is not brave.
Fred is not wise or not old.
Susan is either funny or patient.
Someone is either calm or funny.
John is either funny or patient. | John is wise. | entailment | (![X]:((~curious(X)|~strong(X))=>(curious(X)<~>quiet(X))))&
((~wise(alice))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:((~happy(X)|curious(X))=>curious(X)))&
(![X]:((generous(X)&patient(X))<=>(~calm(X)|~happy(X))))&
(![X]:((quiet(X)|~wise(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((~old(X)|strong(X))<=>(~generous(X)&curious(X))))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((~rich(fred))<=>(?[X]:(kind(X))))&
(![X]:(~curious(X)=>(~curious(X)&brave(X))))&
(![X]:(~humble(X)=>wise(X)))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((~generous(lucy)<~>~old(lucy))))&
(![X]:((rich(X)<~>calm(X))=>curious(X)))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:(~happy(X)=>(quiet(X)&brave(X))))&
(![X]:((~creative(X)&happy(X))=>(quiet(X)<~>old(X))))&
(![X]:((humble(X)<~>~patient(X))<=>(~patient(X)&funny(X))))&
(?[X]:(rich(X)))&
(calm(alice))&
(?[X]:((~kind(X)&old(X))))&
(~brave(fred))&
((~wise(fred)|~old(fred)))&
((funny(susan)<~>patient(susan)))&
(?[X]:((calm(X)<~>funny(X))))&
((funny(john)<~>patient(john))) | wise(john) | [
"p9",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8121430958379549064208795
% SZS output start Proof for 8121430958379549064208795
10. ! [X0] : (~humble(X0) => wise(X0)) [input p9]
16. ! [X0] : ((humble(X0) <~> ~patient(X0)) <=> (funny(X0) & ~patient(X0))) [input p15]
24. funny(john) <~> patient(john) [input p23]
25. ~wise(john) [input hypothesis]
32. ! [X0] : (wise(X0) | humble(X0)) [ennf transformation 10]
67. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [nnf transformation 16]
68. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [flattening 67]
77. (~patient(john) | ~funny(john)) & (patient(john) | funny(john)) [nnf transformation 24]
111. humble(X0) | wise(X0) [cnf transformation 32]
130. ~patient(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 68]
135. patient(X0) | ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 68]
146. patient(john) | funny(john) [cnf transformation 77]
148. ~wise(john) [cnf transformation 25]
149. ~humble(X0) | ~patient(X0) [duplicate literal removal 130]
150. ~funny(X0) | ~humble(X0) | patient(X0) [duplicate literal removal 135]
302. 32 <=> funny(john) [avatar definition]
303. funny(john) <- (32) [avatar component clause 302]
306. 33 <=> patient(john) [avatar definition]
307. patient(john) <- (33) [avatar component clause 306]
308. ~patient(john) <- (~33) [avatar component clause 306]
310. 32 | 33 [avatar split clause 146,306,302]
329. ~patient(X0) | wise(X0) [resolution 149,111]
383. ~humble(john) | patient(john) <- (32) [resolution 150,303]
392. ~humble(john) <- (32, ~33) [subsumption resolution 383,308]
539. wise(john) <- (32, ~33) [resolution 392,111]
540. $false <- (32, ~33) [subsumption resolution 539,148]
541. ~32 | 33 [avatar contradiction clause 540]
543. wise(john) <- (33) [resolution 307,329]
544. $false <- (33) [subsumption resolution 543,148]
545. ~33 [avatar contradiction clause 544]
546. $false [avatar sat refutation 310,541,545]
% SZS output end Proof for 8121430958379549064208795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or tall then fred is both tall and not generous and vice versa.
Everyone who is not strong or wise is both curious and strong and vice versa.
If john is either wise or strong then someone is either not rich or not happy.
Everyone who is not happy is either happy or not humble and vice versa.
Everyone who is tall or wise is not old or not strong.
Everyone who is either not brave or humble is either old or not creative.
If someone is both not patient and old then someone is not rich.
Everyone who is both tall and not rich is both tall and creative.
If someone is kind or brave then someone is both not strong and kind and vice versa.
Everyone who is either funny or patient is both wise and generous.
Everyone who is wise or not rich is either curious or happy and vice versa.
If lucy is both not strong and not funny then paul is both happy and not happy and vice versa.
Everyone who is tall or calm is either rich or not tall.
Everyone who is not rich or not happy is either strong or kind and vice versa.
Everyone who is either happy or not funny is both not humble and not rich.
If someone is both not kind and not wise then someone is both not old and creative and vice versa.
Susan is tall.
Someone is either not funny or not tall.
Someone is wise. | Lucy is humble. | contradiction | ((?[X]:((patient(X)<~>tall(X))))<=>((tall(fred)&~generous(fred))))&
(![X]:((~strong(X)|wise(X))<=>(curious(X)&strong(X))))&
(((wise(john)<~>strong(john)))=>(?[X]:((~rich(X)<~>~happy(X)))))&
(![X]:(~happy(X)<=>(happy(X)<~>~humble(X))))&
(![X]:((tall(X)|wise(X))=>(~old(X)|~strong(X))))&
(![X]:((~brave(X)<~>humble(X))=>(old(X)<~>~creative(X))))&
((?[X]:((~patient(X)&old(X))))=>(?[X]:(~rich(X))))&
(![X]:((tall(X)&~rich(X))=>(tall(X)&creative(X))))&
((?[X]:((kind(X)|brave(X))))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((funny(X)<~>patient(X))=>(wise(X)&generous(X))))&
(![X]:((wise(X)|~rich(X))<=>(curious(X)<~>happy(X))))&
(((~strong(lucy)&~funny(lucy)))<=>((happy(paul)&~happy(paul))))&
(![X]:((tall(X)|calm(X))=>(rich(X)<~>~tall(X))))&
(![X]:((~rich(X)|~happy(X))<=>(strong(X)<~>kind(X))))&
(![X]:((happy(X)<~>~funny(X))=>(~humble(X)&~rich(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>(?[X]:((~old(X)&creative(X)))))&
(tall(susan))&
(?[X]:((~funny(X)<~>~tall(X))))&
(?[X]:(wise(X))) | humble(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8312779300571828860558883
% SZS output start Proof for 8312779300571828860558883
4. ! [X0] : (~happy(X0) <=> (happy(X0) <~> ~humble(X0))) [input p3]
20. humble(lucy) [input hypothesis]
45. ! [X0] : ((~happy(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) & (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | happy(X0))) [nnf transformation 4]
89. ~humble(X0) | happy(X0) | happy(X0) [cnf transformation 45]
91. ~happy(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 45]
141. humble(lucy) [cnf transformation 20]
143. ~humble(X0) | happy(X0) [duplicate literal removal 89]
144. ~happy(X0) | ~humble(X0) [duplicate literal removal 91]
191. ~humble(X0) [subsumption resolution 143,144]
261. $false [subsumption resolution 141,191]
% SZS output end Proof for 8312779300571828860558883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is quiet or rich then someone is not strong or strong.
Everyone who is not humble is patient or tall.
Everyone who is not rich is not generous and vice versa.
If someone is not quiet then someone is not calm or not creative and vice versa.
Everyone who is both patient and generous is funny and vice versa.
Everyone who is either not happy or generous is humble or tall.
Everyone who is happy or brave is both not tall and strong and vice versa.
Everyone who is curious or creative is either curious or patient and vice versa.
If someone is happy then someone is not kind and vice versa.
If someone is both generous and not curious then paul is both funny and wise.
Everyone who is quiet or not rich is rich.
Everyone who is patient or old is kind or wise.
If john is both tall and not curious then someone is either creative or humble and vice versa.
Everyone who is not tall or not creative is either happy or generous and vice versa.
Everyone who is not kind is not brave and vice versa.
Everyone who is kind is curious or old.
Lucy is either not kind or not quiet.
Someone is both quiet and not wise.
John is not happy or generous.
Mary is wise or not patient.
John is not quiet.
Someone is both brave and kind.
Mary is not humble or not quiet. | Paul is not brave. | contradiction | (((quiet(mary)|rich(mary)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:(~humble(X)=>(patient(X)|tall(X))))&
(![X]:(~rich(X)<=>~generous(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((patient(X)&generous(X))<=>funny(X)))&
(![X]:((~happy(X)<~>generous(X))=>(humble(X)|tall(X))))&
(![X]:((happy(X)|brave(X))<=>(~tall(X)&strong(X))))&
(![X]:((curious(X)|creative(X))<=>(curious(X)<~>patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~kind(X))))&
((?[X]:((generous(X)&~curious(X))))=>((funny(paul)&wise(paul))))&
(![X]:((quiet(X)|~rich(X))=>rich(X)))&
(![X]:((patient(X)|old(X))=>(kind(X)|wise(X))))&
(((tall(john)&~curious(john)))<=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:((~tall(X)|~creative(X))<=>(happy(X)<~>generous(X))))&
(![X]:(~kind(X)<=>~brave(X)))&
(![X]:(kind(X)=>(curious(X)|old(X))))&
((~kind(lucy)<~>~quiet(lucy)))&
(?[X]:((quiet(X)&~wise(X))))&
((~happy(john)|generous(john)))&
((wise(mary)|~patient(mary)))&
(~quiet(john))&
(?[X]:((brave(X)&kind(X))))&
((~humble(mary)|~quiet(mary))) | ~brave(paul) | [
"p2",
"p6",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2499167218840964506389177
% SZS output start Proof for 2499167218840964506389177
3. ! [X0] : (~rich(X0) <=> ~generous(X0)) [input p2]
7. ! [X0] : ((brave(X0) | happy(X0)) <=> (strong(X0) & ~tall(X0))) [input p6]
9. ? [X0] : happy(X0) <=> ? [X0] : ~kind(X0) [input p8]
11. ! [X0] : ((~rich(X0) | quiet(X0)) => rich(X0)) [input p10]
14. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (happy(X0) <~> generous(X0))) [input p13]
15. ! [X0] : (~kind(X0) <=> ~brave(X0)) [input p14]
24. ~brave(paul) [input hypothesis]
26. ? [X0] : happy(X0) <=> ? [X1] : ~kind(X1) [rectify 9]
35. ! [X0] : (rich(X0) | (rich(X0) & ~quiet(X0))) [ennf transformation 11]
42. ! [X0] : ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))) [nnf transformation 3]
49. ! [X0] : (((brave(X0) | happy(X0)) | (~strong(X0) | tall(X0))) & ((strong(X0) & ~tall(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 7]
50. ! [X0] : ((brave(X0) | happy(X0) | ~strong(X0) | tall(X0)) & ((strong(X0) & ~tall(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 49]
53. (? [X0] : happy(X0) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : ~happy(X0)) [nnf transformation 26]
54. (? [X0] : happy(X0) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : ~happy(X3)) [rectify 53]
55. ? [X0] : happy(X0) => happy(sK3) [choice axiom]
56. ? [X2] : ~kind(X2) => ~kind(sK4) [choice axiom]
57. (happy(sK3) | ! [X1] : kind(X1)) & (~kind(sK4) | ! [X3] : ~happy(X3)) [skolemisation 54,56,55]
63. ! [X0] : (((~creative(X0) | ~tall(X0)) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (creative(X0) & tall(X0)))) [nnf transformation 14]
64. ! [X0] : ((~creative(X0) | ~tall(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (creative(X0) & tall(X0)))) [flattening 63]
65. ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0))) [nnf transformation 15]
75. ~rich(X0) | generous(X0) [cnf transformation 42]
83. ~happy(X0) | ~tall(X0) [cnf transformation 50]
95. happy(sK3) | kind(X1) [cnf transformation 57]
99. rich(X0) | rich(X0) [cnf transformation 35]
110. ~generous(X0) | ~happy(X0) | tall(X0) [cnf transformation 64]
115. ~kind(X0) | brave(X0) [cnf transformation 65]
127. ~brave(paul) [cnf transformation 24]
128. rich(X0) [duplicate literal removal 99]
156. 7 <=> ! [X1] : kind(X1) [avatar definition]
157. kind(X1) <- (7) [avatar component clause 156]
159. 8 <=> happy(sK3) [avatar definition]
161. happy(sK3) <- (8) [avatar component clause 159]
162. 7 | 8 [avatar split clause 95,159,156]
213. ~happy(X0) | ~generous(X0) [subsumption resolution 110,83]
245. generous(X0) [resolution 75,128]
263. ~generous(sK3) <- (8) [resolution 213,161]
264. $false <- (8) [subsumption resolution 263,245]
265. ~8 [avatar contradiction clause 264]
266. brave(X0) <- (7) [resolution 157,115]
302. $false <- (7) [resolution 266,127]
306. ~7 [avatar contradiction clause 302]
307. $false [avatar sat refutation 162,265,306]
% SZS output end Proof for 2499167218840964506389177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or kind is either not calm or not generous. If paul is not patient or not old then mary is not tall or not happy and vice versa. Everyone who is both not happy and generous is not wise and vice versa. Everyone who is funny is calm or humble and vice versa. If lucy is both not tall and generous then someone is not wise and vice versa. Everyone who is both not quiet and not brave is either creative or curious. Everyone who is both not curious and not brave is either not quiet or old and vice versa. If mary is either not happy or not rich then someone is either funny or not happy. Everyone who is quiet is both old and not humble. Everyone who is both creative and funny is brave or calm and vice versa. Everyone who is either not kind or rich is funny and vice versa. Everyone who is either brave or not quiet is not happy. Everyone who is not strong is either happy or funny and vice versa. If alice is creative then someone is not creative and vice versa. If mary is both not curious and not happy then paul is both funny and happy and vice versa. If alice is either not happy or kind then someone is both strong and not creative. Someone is either not calm or not generous. John is either wise or not humble. Mary is either not tall or wise. Lucy is either not generous or not curious. Someone is both not patient and curious. Someone is both calm and happy. Alice is not humble or humble. Alice is both not funny and not quiet. | Alice is not old. | entailment | (![X]:((~happy(X)<~>kind(X))=>(~calm(X)<~>~generous(X))))&
(((~patient(paul)|~old(paul)))<=>((~tall(mary)|~happy(mary))))&
(![X]:((~happy(X)&generous(X))<=>~wise(X)))&
(![X]:(funny(X)<=>(calm(X)|humble(X))))&
(((~tall(lucy)&generous(lucy)))<=>(?[X]:(~wise(X))))&
(![X]:((~quiet(X)&~brave(X))=>(creative(X)<~>curious(X))))&
(![X]:((~curious(X)&~brave(X))<=>(~quiet(X)<~>old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(![X]:((~kind(X)<~>rich(X))<=>funny(X)))&
(![X]:((brave(X)<~>~quiet(X))=>~happy(X)))&
(![X]:(~strong(X)<=>(happy(X)<~>funny(X))))&
((creative(alice))<=>(?[X]:(~creative(X))))&
(((~curious(mary)&~happy(mary)))<=>((funny(paul)&happy(paul))))&
(((~happy(alice)<~>kind(alice)))=>(?[X]:((strong(X)&~creative(X)))))&
(?[X]:((~calm(X)<~>~generous(X))))&
((wise(john)<~>~humble(john)))&
((~tall(mary)<~>wise(mary)))&
((~generous(lucy)<~>~curious(lucy)))&
(?[X]:((~patient(X)&curious(X))))&
(?[X]:((calm(X)&happy(X))))&
((~humble(alice)|humble(alice)))&
((~funny(alice)&~quiet(alice))) | ~old(alice) | [
"p5",
"p6",
"p9",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2573013882720192678377241
% SZS output start Proof for 2573013882720192678377241
6. ! [X0] : ((~brave(X0) & ~quiet(X0)) => (creative(X0) <~> curious(X0))) [input p5]
7. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~quiet(X0) <~> old(X0))) [input p6]
10. ! [X0] : ((funny(X0) & creative(X0)) <=> (calm(X0) | brave(X0))) [input p9]
14. creative(alice) <=> ? [X0] : ~creative(X0) [input p13]
24. ~quiet(alice) & ~funny(alice) [input p23]
25. old(alice) [input hypothesis]
28. ! [X0] : ((creative(X0) <~> curious(X0)) | (brave(X0) | quiet(X0))) [ennf transformation 6]
29. ! [X0] : ((creative(X0) <~> curious(X0)) | brave(X0) | quiet(X0)) [flattening 28]
47. ! [X0] : (((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | brave(X0) | quiet(X0)) [nnf transformation 29]
48. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (brave(X0) | curious(X0)))) [nnf transformation 7]
49. ! [X0] : (((~brave(X0) & ~curious(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | brave(X0) | curious(X0))) [flattening 48]
53. ! [X0] : (((funny(X0) & creative(X0)) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | (~funny(X0) | ~creative(X0)))) [nnf transformation 10]
54. ! [X0] : (((funny(X0) & creative(X0)) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | ~funny(X0) | ~creative(X0))) [flattening 53]
58. (creative(alice) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~creative(alice)) [nnf transformation 14]
59. (creative(alice) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~creative(alice)) [rectify 58]
60. ? [X1] : ~creative(X1) => ~creative(sK2) [choice axiom]
61. (creative(alice) | ! [X0] : creative(X0)) & (~creative(sK2) | ~creative(alice)) [skolemisation 59,60]
95. ~curious(X0) | ~creative(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
97. ~old(X0) | quiet(X0) | brave(X0) | curious(X0) [cnf transformation 49]
111. ~brave(X0) | funny(X0) [cnf transformation 54]
122. creative(alice) | creative(X0) [cnf transformation 61]
144. ~funny(alice) [cnf transformation 24]
145. ~quiet(alice) [cnf transformation 24]
146. old(alice) [cnf transformation 25]
202. 12 <=> ! [X0] : creative(X0) [avatar definition]
203. creative(X0) <- (12) [avatar component clause 202]
205. 13 <=> creative(alice) [avatar definition]
206. ~creative(alice) <- (~13) [avatar component clause 205]
208. 12 | 13 [avatar split clause 122,205,202]
500. quiet(alice) | brave(alice) | curious(alice) [resolution 97,146]
503. brave(alice) | curious(alice) [subsumption resolution 500,145]
505. 56 <=> curious(alice) [avatar definition]
507. curious(alice) <- (56) [avatar component clause 505]
509. 57 <=> brave(alice) [avatar definition]
511. brave(alice) <- (57) [avatar component clause 509]
512. 56 | 57 [avatar split clause 503,509,505]
525. ~creative(alice) | brave(alice) | quiet(alice) <- (56) [resolution 507,95]
531. ~creative(alice) | brave(alice) <- (56) [subsumption resolution 525,145]
532. 57 | ~13 | ~56 [avatar split clause 531,505,205,509]
552. $false <- (12, ~13) [resolution 206,203]
553. ~12 | 13 [avatar contradiction clause 552]
607. funny(alice) <- (57) [resolution 511,111]
609. $false <- (57) [subsumption resolution 607,144]
610. ~57 [avatar contradiction clause 609]
611. $false [avatar sat refutation 208,512,532,553,610]
% SZS output end Proof for 2573013882720192678377241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not strong and vice versa.
If john is happy then someone is humble or not funny and vice versa.
If paul is brave then fred is not creative or not old.
If someone is both brave and not generous then someone is either tall or not creative.
Everyone who is either not rich or kind is both kind and humble and vice versa.
Everyone who is both kind and wise is brave or not quiet.
Everyone who is not curious or curious is not quiet and vice versa.
Everyone who is wise or happy is old or calm.
Everyone who is happy is not creative or not happy and vice versa.
Everyone who is either not patient or creative is both calm and funny.
If someone is both not strong and creative then someone is either rich or not creative and vice versa.
Everyone who is either strong or calm is not tall and vice versa.
If lucy is not creative or not happy then someone is calm and vice versa.
Everyone who is creative or tall is funny and vice versa.
If someone is patient or not tall then someone is wise.
Everyone who is kind is either tall or not quiet and vice versa.
Someone is happy.
Someone is funny.
Someone is either not humble or generous.
Mary is not happy or tall.
Lucy is either not rich or not tall.
Someone is wise or happy.
Mary is either not creative or not funny. | John is rich. | entailment | (![X]:(~patient(X)<=>~strong(X)))&
((happy(john))<=>(?[X]:((humble(X)|~funny(X)))))&
((brave(paul))=>((~creative(fred)|~old(fred))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>(kind(X)&humble(X))))&
(![X]:((kind(X)&wise(X))=>(brave(X)|~quiet(X))))&
(![X]:((~curious(X)|curious(X))<=>~quiet(X)))&
(![X]:((wise(X)|happy(X))=>(old(X)|calm(X))))&
(![X]:(happy(X)<=>(~creative(X)|~happy(X))))&
(![X]:((~patient(X)<~>creative(X))=>(calm(X)&funny(X))))&
((?[X]:((~strong(X)&creative(X))))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>calm(X))<=>~tall(X)))&
(((~creative(lucy)|~happy(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((creative(X)|tall(X))<=>funny(X)))&
((?[X]:((patient(X)|~tall(X))))=>(?[X]:(wise(X))))&
(![X]:(kind(X)<=>(tall(X)<~>~quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:(funny(X)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~happy(mary)|tall(mary)))&
((~rich(lucy)<~>~tall(lucy)))&
(?[X]:((wise(X)|happy(X))))&
((~creative(mary)<~>~funny(mary))) | rich(john) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4513748847471919295524471
% SZS output start Proof for 4513748847471919295524471
9. ! [X0] : (happy(X0) <=> (~happy(X0) | ~creative(X0))) [input p8]
11. ? [X0] : (creative(X0) & ~strong(X0)) <=> ? [X0] : (rich(X0) <~> ~creative(X0)) [input p10]
24. ~rich(john) [input hypothesis]
26. ? [X0] : (creative(X0) & ~strong(X0)) <=> ? [X1] : (rich(X1) <~> ~creative(X1)) [rectify 11]
50. ! [X0] : ((happy(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | ~happy(X0))) [nnf transformation 9]
51. ! [X0] : ((happy(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~happy(X0))) [flattening 50]
53. (? [X0] : (creative(X0) & ~strong(X0)) | ! [X1] : ((rich(X1) | creative(X1)) & (~creative(X1) | ~rich(X1)))) & (? [X1] : ((creative(X1) | ~rich(X1)) & (~creative(X1) | rich(X1))) | ! [X0] : (~creative(X0) | strong(X0))) [nnf transformation 26]
54. (? [X0] : (creative(X0) & ~strong(X0)) | ! [X1] : ((rich(X1) | creative(X1)) & (~creative(X1) | ~rich(X1)))) & (? [X2] : ((creative(X2) | ~rich(X2)) & (~creative(X2) | rich(X2))) | ! [X3] : (~creative(X3) | strong(X3))) [rectify 53]
55. ? [X0] : (creative(X0) & ~strong(X0)) => (creative(sK2) & ~strong(sK2)) [choice axiom]
56. ? [X2] : ((creative(X2) | ~rich(X2)) & (~creative(X2) | rich(X2))) => ((creative(sK3) | ~rich(sK3)) & (~creative(sK3) | rich(sK3))) [choice axiom]
57. ((creative(sK2) & ~strong(sK2)) | ! [X1] : ((rich(X1) | creative(X1)) & (~creative(X1) | ~rich(X1)))) & (((creative(sK3) | ~rich(sK3)) & (~creative(sK3) | rich(sK3))) | ! [X3] : (~creative(X3) | strong(X3))) [skolemisation 54,56,55]
101. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 51]
103. happy(X0) | happy(X0) [cnf transformation 51]
113. creative(sK2) | rich(X1) | creative(X1) [cnf transformation 57]
140. ~rich(john) [cnf transformation 24]
141. ~happy(X0) | ~creative(X0) [duplicate literal removal 101]
142. happy(X0) [duplicate literal removal 103]
193. ~creative(X0) [subsumption resolution 141,142]
196. rich(X1) | creative(X1) [subsumption resolution 113,193]
197. rich(X1) [subsumption resolution 196,193]
227. $false [subsumption resolution 140,197]
% SZS output end Proof for 4513748847471919295524471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall is both not rich and kind.
Everyone who is rich is both old and not generous and vice versa.
Everyone who is not old or kind is either patient or not rich.
Everyone who is not strong or not kind is both not strong and quiet and vice versa.
Everyone who is kind is patient.
If lucy is calm or not happy then alice is not strong or rich.
Everyone who is not wise or patient is funny and vice versa.
If someone is old then paul is either not generous or not strong and vice versa.
Everyone who is either happy or not brave is creative.
Everyone who is not funny is brave or not old.
Everyone who is not kind or not wise is both creative and quiet and vice versa.
If someone is not calm or happy then fred is not humble or not quiet and vice versa.
Everyone who is not tall is generous or not quiet.
If someone is both generous and happy then someone is calm and vice versa.
If someone is either creative or happy then john is creative or not creative.
If john is not tall then lucy is either happy or not rich.
Someone is humble.
Someone is either not humble or not brave.
Someone is strong or not patient.
Susan is tall or not rich.
Alice is not strong.
Paul is not funny or not rich.
Someone is not strong or kind. | Alice is not rich. | entailment | (![X]:((kind(X)|tall(X))=>(~rich(X)&kind(X))))&
(![X]:(rich(X)<=>(old(X)&~generous(X))))&
(![X]:((~old(X)|kind(X))=>(patient(X)<~>~rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>(~strong(X)&quiet(X))))&
(![X]:(kind(X)=>patient(X)))&
(((calm(lucy)|~happy(lucy)))=>((~strong(alice)|rich(alice))))&
(![X]:((~wise(X)|patient(X))<=>funny(X)))&
((?[X]:(old(X)))<=>((~generous(paul)<~>~strong(paul))))&
(![X]:((happy(X)<~>~brave(X))=>creative(X)))&
(![X]:(~funny(X)=>(brave(X)|~old(X))))&
(![X]:((~kind(X)|~wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((~calm(X)|happy(X))))<=>((~humble(fred)|~quiet(fred))))&
(![X]:(~tall(X)=>(generous(X)|~quiet(X))))&
((?[X]:((generous(X)&happy(X))))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)<~>happy(X))))=>((creative(john)|~creative(john))))&
((~tall(john))=>((happy(lucy)<~>~rich(lucy))))&
(?[X]:(humble(X)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((strong(X)|~patient(X))))&
((tall(susan)|~rich(susan)))&
(~strong(alice))&
((~funny(paul)|~rich(paul)))&
(?[X]:((~strong(X)|kind(X)))) | ~rich(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 698856822187431687757081
% SZS output start Proof for 698856822187431687757081
1. ! [X0] : ((tall(X0) | kind(X0)) => (kind(X0) & ~rich(X0))) [input p0]
2. ! [X0] : (rich(X0) <=> (~generous(X0) & old(X0))) [input p1]
3. ! [X0] : ((kind(X0) | ~old(X0)) => (patient(X0) <~> ~rich(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : (kind(X0) => patient(X0)) [input p4]
13. ! [X0] : (~tall(X0) => (~quiet(X0) | generous(X0))) [input p12]
24. rich(alice) [input hypothesis]
26. ! [X0] : ((kind(X0) & ~rich(X0)) | (~tall(X0) & ~kind(X0))) [ennf transformation 1]
27. ! [X0] : ((patient(X0) <~> ~rich(X0)) | (~kind(X0) & old(X0))) [ennf transformation 3]
28. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 5]
34. ! [X0] : ((~quiet(X0) | generous(X0)) | tall(X0)) [ennf transformation 13]
35. ! [X0] : (~quiet(X0) | generous(X0) | tall(X0)) [flattening 34]
39. ! [X0] : ((rich(X0) | (generous(X0) | ~old(X0))) & ((~generous(X0) & old(X0)) | ~rich(X0))) [nnf transformation 2]
40. ! [X0] : ((rich(X0) | generous(X0) | ~old(X0)) & ((~generous(X0) & old(X0)) | ~rich(X0))) [flattening 39]
41. ! [X0] : (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (~kind(X0) & old(X0))) [nnf transformation 27]
42. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 4]
43. ! [X0] : ((~kind(X0) | ~strong(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (kind(X0) & strong(X0)))) [flattening 42]
74. ~rich(X0) | ~kind(X0) [cnf transformation 26]
75. ~rich(X0) | ~tall(X0) [cnf transformation 26]
79. ~generous(X0) | ~rich(X0) [cnf transformation 40]
84. rich(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 41]
88. quiet(X0) | kind(X0) [cnf transformation 43]
90. patient(X0) | ~kind(X0) [cnf transformation 28]
112. ~quiet(X0) | generous(X0) | tall(X0) [cnf transformation 35]
128. rich(alice) [cnf transformation 24]
129. ~patient(X0) | ~kind(X0) [subsumption resolution 84,74]
131. ~kind(X0) [subsumption resolution 90,129]
141. 3 <=> rich(alice) [avatar definition]
143. rich(alice) <- (3) [avatar component clause 141]
257. 3 [avatar split clause 128,141]
310. generous(X0) | tall(X0) | kind(X0) [resolution 112,88]
313. generous(X0) | tall(X0) [subsumption resolution 310,131]
324. tall(X0) | ~rich(X0) [resolution 313,79]
325. ~rich(X0) [subsumption resolution 324,75]
337. $false <- (3) [resolution 325,143]
340. ~3 [avatar contradiction clause 337]
341. $false [avatar sat refutation 257,340]
% SZS output end Proof for 698856822187431687757081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or rich is either happy or humble.
Everyone who is either generous or not brave is either not calm or not rich and vice versa.
If someone is brave then someone is either generous or not humble.
Everyone who is funny is funny or not calm and vice versa.
Everyone who is not kind is not brave and vice versa.
Everyone who is quiet or not kind is generous and vice versa.
If someone is either not generous or happy then someone is either calm or not calm and vice versa.
If lucy is either generous or not old then paul is not tall.
If fred is either creative or not rich then someone is not strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
If john is either not generous or generous then someone is either not old or not calm.
Everyone who is either brave or not funny is either calm or not brave and vice versa.
Everyone who is brave is not patient or not calm.
Someone is both curious and not tall.
Lucy is generous or not funny.
Someone is not quiet or not rich.
Someone is strong.
Someone is not old or tall.
Someone is not rich.
Someone is not kind or brave.
Paul is both old and not wise. | Paul is not creative. | entailment | (![X]:((quiet(X)<~>rich(X))=>(happy(X)<~>humble(X))))&
(![X]:((generous(X)<~>~brave(X))<=>(~calm(X)<~>~rich(X))))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:(funny(X)<=>(funny(X)|~calm(X))))&
(![X]:(~kind(X)<=>~brave(X)))&
(![X]:((quiet(X)|~kind(X))<=>generous(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
(((generous(lucy)<~>~old(lucy)))=>(~tall(paul)))&
(((creative(fred)<~>~rich(fred)))<=>(?[X]:(~strong(X))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(brave(X)=>(~patient(X)|~calm(X))))&
(?[X]:((curious(X)&~tall(X))))&
((generous(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)|brave(X))))&
((old(paul)&~wise(paul))) | ~creative(paul) | [
"p3",
"p11",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2080700483949571109286700
% SZS output start Proof for 2080700483949571109286700
4. ! [X0] : (funny(X0) <=> (~calm(X0) | funny(X0))) [input p3]
12. ! [X0] : (old(X0) => (~creative(X0) <~> ~calm(X0))) [input p11]
15. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p14]
24. ~wise(paul) & old(paul) [input p23]
25. creative(paul) [input hypothesis]
35. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | ~old(X0)) [ennf transformation 12]
43. ! [X0] : ((funny(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ~funny(X0))) [nnf transformation 4]
44. ! [X0] : ((funny(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~funny(X0))) [flattening 43]
64. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~old(X0)) [nnf transformation 35]
70. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 15]
99. funny(X0) | calm(X0) [cnf transformation 44]
127. ~creative(X0) | ~calm(X0) | ~old(X0) [cnf transformation 64]
137. ~brave(X0) | calm(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 70]
140. brave(X0) | ~calm(X0) | brave(X0) | funny(X0) [cnf transformation 70]
142. ~funny(X0) | brave(X0) | calm(X0) | brave(X0) [cnf transformation 70]
143. funny(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 70]
153. old(paul) [cnf transformation 24]
155. creative(paul) [cnf transformation 25]
156. ~brave(X0) | calm(X0) | ~funny(X0) [duplicate literal removal 137]
157. brave(X0) | ~calm(X0) | funny(X0) [duplicate literal removal 140]
158. ~funny(X0) | brave(X0) | calm(X0) [duplicate literal removal 142]
159. funny(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 143]
182. 4 <=> ! [X1] : calm(X1) [avatar definition]
183. calm(X1) <- (4) [avatar component clause 182]
282. ~brave(X0) | funny(X0) [subsumption resolution 159,99]
283. calm(X0) | brave(X0) [subsumption resolution 158,99]
284. brave(X0) | funny(X0) [subsumption resolution 157,99]
285. funny(X0) [subsumption resolution 284,282]
286. ~brave(X0) | calm(X0) [subsumption resolution 156,285]
287. calm(X0) [subsumption resolution 286,283]
288. 4 [avatar split clause 287,182]
324. ~calm(paul) | ~old(paul) [resolution 127,155]
325. ~old(paul) <- (4) [subsumption resolution 324,183]
326. $false <- (4) [subsumption resolution 325,153]
327. ~4 [avatar contradiction clause 326]
328. $false [avatar sat refutation 288,327]
% SZS output end Proof for 2080700483949571109286700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not creative then someone is either not calm or patient.
Everyone who is not old is not kind or not tall.
Everyone who is both not quiet and not funny is funny or wise and vice versa.
Everyone who is either happy or not quiet is either not funny or creative.
Everyone who is either quiet or not creative is calm or not funny.
Everyone who is either strong or funny is both rich and brave.
If alice is either curious or not curious then someone is tall and vice versa.
Everyone who is both curious and not calm is not creative or not strong and vice versa.
If someone is either patient or generous then someone is strong or kind and vice versa.
If someone is tall or rich then someone is both not curious and not kind.
Everyone who is brave or generous is not happy and vice versa.
Everyone who is curious is calm or not creative.
If fred is rich then someone is brave or not generous.
If someone is either kind or creative then john is either not kind or not funny.
If paul is not old then someone is either curious or not old.
Lucy is both patient and humble.
Mary is either not calm or not curious.
Someone is not creative.
Someone is happy. | Paul is humble. | neutral | ((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:(~old(X)=>(~kind(X)|~tall(X))))&
(![X]:((~quiet(X)&~funny(X))<=>(funny(X)|wise(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(~funny(X)<~>creative(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(calm(X)|~funny(X))))&
(![X]:((strong(X)<~>funny(X))=>(rich(X)&brave(X))))&
(((curious(alice)<~>~curious(alice)))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)&~calm(X))<=>(~creative(X)|~strong(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((tall(X)|rich(X))))=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((brave(X)|generous(X))<=>~happy(X)))&
(![X]:(curious(X)=>(calm(X)|~creative(X))))&
((rich(fred))=>(?[X]:((brave(X)|~generous(X)))))&
((?[X]:((kind(X)<~>creative(X))))=>((~kind(john)<~>~funny(john))))&
((~old(paul))=>(?[X]:((curious(X)<~>~old(X)))))&
((patient(lucy)&humble(lucy)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:(~creative(X)))&
(?[X]:(happy(X))) | humble(paul) | [] | null | 0 |
Everyone who is wise or patient is both kind and not kind and vice versa.
If someone is not kind then someone is strong or curious and vice versa.
Everyone who is curious is either patient or humble.
Everyone who is either not happy or not curious is not humble and vice versa.
Everyone who is either strong or humble is either brave or curious.
If susan is both not tall and not brave then fred is not funny or strong and vice versa.
If lucy is creative then lucy is funny and vice versa.
Everyone who is rich or not wise is not kind and vice versa.
Everyone who is generous is either rich or not tall.
If lucy is both wise and quiet then someone is wise.
Everyone who is not rich is either strong or not patient.
Everyone who is not curious or not patient is either old or not happy.
Everyone who is creative is both strong and not calm.
If someone is kind or not happy then paul is not patient or rich.
If someone is both rich and brave then someone is tall.
If someone is both brave and generous then john is generous and vice versa.
Fred is kind or not patient.
Fred is not strong.
Susan is both not brave and curious.
Lucy is wise or quiet.
Someone is both not generous and not patient.
Paul is either not humble or not funny.
Someone is strong. | Fred is not funny. | neutral | (![X]:((wise(X)|patient(X))<=>(kind(X)&~kind(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((strong(X)|curious(X)))))&
(![X]:(curious(X)=>(patient(X)<~>humble(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>~humble(X)))&
(![X]:((strong(X)<~>humble(X))=>(brave(X)<~>curious(X))))&
(((~tall(susan)&~brave(susan)))<=>((~funny(fred)|strong(fred))))&
((creative(lucy))<=>(funny(lucy)))&
(![X]:((rich(X)|~wise(X))<=>~kind(X)))&
(![X]:(generous(X)=>(rich(X)<~>~tall(X))))&
(((wise(lucy)&quiet(lucy)))=>(?[X]:(wise(X))))&
(![X]:(~rich(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~curious(X)|~patient(X))=>(old(X)<~>~happy(X))))&
(![X]:(creative(X)=>(strong(X)&~calm(X))))&
((?[X]:((kind(X)|~happy(X))))=>((~patient(paul)|rich(paul))))&
((?[X]:((rich(X)&brave(X))))=>(?[X]:(tall(X))))&
((?[X]:((brave(X)&generous(X))))<=>(generous(john)))&
((kind(fred)|~patient(fred)))&
(~strong(fred))&
((~brave(susan)&curious(susan)))&
((wise(lucy)|quiet(lucy)))&
(?[X]:((~generous(X)&~patient(X))))&
((~humble(paul)<~>~funny(paul)))&
(?[X]:(strong(X))) | ~funny(fred) | [] | null | 0 |
If someone is both humble and not curious then someone is generous or brave and vice versa.
If lucy is both generous and happy then someone is not generous or funny.
If paul is generous or not humble then paul is both not curious and patient and vice versa.
If lucy is both not calm and calm then someone is both wise and not generous.
If someone is not kind or not strong then paul is not creative.
Everyone who is not creative or not old is both not humble and not creative and vice versa.
If someone is patient or kind then lucy is both curious and not quiet and vice versa.
If fred is either funny or calm then lucy is either not rich or curious and vice versa.
If someone is both not happy and creative then mary is not funny or not creative and vice versa.
Everyone who is not strong or not curious is either curious or humble.
If someone is both not generous and happy then someone is patient.
If someone is either not calm or generous then someone is both not humble and patient and vice versa.
If susan is both not kind and not tall then paul is rich and vice versa.
Everyone who is quiet is both not generous and tall.
If someone is either not old or happy then someone is calm or patient and vice versa.
If someone is either not old or wise then lucy is creative and vice versa.
Mary is kind.
Susan is not tall or not creative.
Someone is either curious or not strong.
Someone is wise.
Someone is either not rich or not generous.
Lucy is both rich and not old.
Someone is both not old and not quiet. | Fred is strong. | entailment | ((?[X]:((humble(X)&~curious(X))))<=>(?[X]:((generous(X)|brave(X)))))&
(((generous(lucy)&happy(lucy)))=>(?[X]:((~generous(X)|funny(X)))))&
(((generous(paul)|~humble(paul)))<=>((~curious(paul)&patient(paul))))&
(((~calm(lucy)&calm(lucy)))=>(?[X]:((wise(X)&~generous(X)))))&
((?[X]:((~kind(X)|~strong(X))))=>(~creative(paul)))&
(![X]:((~creative(X)|~old(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((patient(X)|kind(X))))<=>((curious(lucy)&~quiet(lucy))))&
(((funny(fred)<~>calm(fred)))<=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((~happy(X)&creative(X))))<=>((~funny(mary)|~creative(mary))))&
(![X]:((~strong(X)|~curious(X))=>(curious(X)<~>humble(X))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:(patient(X))))&
((?[X]:((~calm(X)<~>generous(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~kind(susan)&~tall(susan)))<=>(rich(paul)))&
(![X]:(quiet(X)=>(~generous(X)&tall(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))<=>(creative(lucy)))&
(kind(mary))&
((~tall(susan)|~creative(susan)))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>~generous(X))))&
((rich(lucy)&~old(lucy)))&
(?[X]:((~old(X)&~quiet(X)))) | strong(fred) | [
"p2",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6553332107658181384852762
% SZS output start Proof for 6553332107658181384852762
3. (~humble(paul) | generous(paul)) <=> (patient(paul) & ~curious(paul)) [input p2]
5. ? [X0] : (~strong(X0) | ~kind(X0)) => ~creative(paul) [input p4]
6. ! [X0] : ((~old(X0) | ~creative(X0)) <=> (~creative(X0) & ~humble(X0))) [input p5]
10. ! [X0] : ((~curious(X0) | ~strong(X0)) => (curious(X0) <~> humble(X0))) [input p9]
24. ~strong(fred) [input hypothesis]
33. ~creative(paul) | ! [X0] : (strong(X0) & kind(X0)) [ennf transformation 5]
34. ! [X0] : ((curious(X0) <~> humble(X0)) | (curious(X0) & strong(X0))) [ennf transformation 10]
44. ((~humble(paul) | generous(paul)) | (~patient(paul) | curious(paul))) & ((patient(paul) & ~curious(paul)) | (humble(paul) & ~generous(paul))) [nnf transformation 3]
45. (~humble(paul) | generous(paul) | ~patient(paul) | curious(paul)) & ((patient(paul) & ~curious(paul)) | (humble(paul) & ~generous(paul))) [flattening 44]
48. ! [X0] : (((~old(X0) | ~creative(X0)) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | (old(X0) & creative(X0)))) [nnf transformation 6]
49. ! [X0] : ((~old(X0) | ~creative(X0) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | (old(X0) & creative(X0)))) [flattening 48]
61. ! [X0] : (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (curious(X0) & strong(X0))) [nnf transformation 34]
98. ~curious(paul) | humble(paul) [cnf transformation 45]
105. ~creative(paul) | strong(X0) [cnf transformation 33]
106. ~humble(X0) | creative(X0) [cnf transformation 49]
130. humble(X0) | curious(X0) | curious(X0) [cnf transformation 61]
166. ~strong(fred) [cnf transformation 24]
167. curious(X0) | humble(X0) [duplicate literal removal 130]
216. 12 <=> curious(paul) [avatar definition]
217. ~curious(paul) <- (~12) [avatar component clause 216]
228. 15 <=> humble(paul) [avatar definition]
229. humble(paul) <- (15) [avatar component clause 228]
230. ~humble(paul) <- (~15) [avatar component clause 228]
234. 15 | ~12 [avatar split clause 98,216,228]
237. 16 <=> ! [X0] : strong(X0) [avatar definition]
238. strong(X0) <- (16) [avatar component clause 237]
240. 17 <=> creative(paul) [avatar definition]
243. 16 | ~17 [avatar split clause 105,240,237]
464. creative(paul) <- (15) [resolution 106,229]
467. 17 | ~15 [avatar split clause 464,228,240]
468. $false <- (16) [resolution 238,166]
471. ~16 [avatar contradiction clause 468]
481. humble(paul) <- (~12) [resolution 167,217]
483. $false <- (~12, ~15) [subsumption resolution 481,230]
484. 12 | 15 [avatar contradiction clause 483]
485. $false [avatar sat refutation 234,243,467,471,484]
% SZS output end Proof for 6553332107658181384852762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Paul is not humble. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~humble(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7329547201543101904918918
% SZS output start Proof for 7329547201543101904918918
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p1]
3. ? [X0] : ~old(X0) <=> ~calm(susan) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) => ~curious(X0)) [input p3]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
7. ? [X0] : (~creative(X0) <~> happy(X0)) <=> (~generous(mary) & ~tall(mary)) [input p6]
8. ? [X0] : brave(X0) <=> (~rich(fred) & kind(fred)) [input p7]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> old(X0)) => (humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (~strong(X0) => brave(X0)) [input p11]
15. ! [X0] : ((patient(X0) & curious(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p14]
21. ~humble(paul) [input hypothesis]
22. ! [X0] : (~curious(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> generous(X0)) | (~creative(X0) <=> old(X0))) [ennf transformation 10]
24. ! [X0] : (brave(X0) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
30. ! [X0] : (((~humble(X0) | ~curious(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | ~curious(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [flattening 30]
32. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X0] : old(X0)) [nnf transformation 3]
33. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [rectify 32]
34. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
35. (~old(sK0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [skolemisation 33,34]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
40. (? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (generous(mary) | tall(mary))) & ((~generous(mary) & ~tall(mary)) | ! [X0] : ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) [nnf transformation 7]
41. (? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | generous(mary) | tall(mary)) & ((~generous(mary) & ~tall(mary)) | ! [X0] : ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) [flattening 40]
42. (? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | generous(mary) | tall(mary)) & ((~generous(mary) & ~tall(mary)) | ! [X1] : ((~creative(X1) | ~happy(X1)) & (happy(X1) | creative(X1)))) [rectify 41]
43. ? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) => ((~happy(sK1) | creative(sK1)) & (happy(sK1) | ~creative(sK1))) [choice axiom]
44. (((~happy(sK1) | creative(sK1)) & (happy(sK1) | ~creative(sK1))) | generous(mary) | tall(mary)) & ((~generous(mary) & ~tall(mary)) | ! [X1] : ((~creative(X1) | ~happy(X1)) & (happy(X1) | creative(X1)))) [skolemisation 42,43]
45. (? [X0] : brave(X0) | (rich(fred) | ~kind(fred))) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
46. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
49. (brave(sK2) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 23]
56. ! [X0] : (((patient(X0) & curious(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | (~patient(X0) | ~curious(X0)))) [nnf transformation 15]
57. ! [X0] : (((patient(X0) & curious(X0)) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ~patient(X0) | ~curious(X0))) [flattening 56]
66. brave(X0) | generous(X0) | rich(X0) [cnf transformation 29]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
68. brave(X0) | calm(X0) | rich(X0) [cnf transformation 29]
70. ~creative(X0) | ~calm(X0) | curious(X0) [cnf transformation 31]
71. ~creative(X0) | ~calm(X0) | humble(X0) [cnf transformation 31]
76. ~calm(susan) | old(X1) [cnf transformation 35]
77. ~old(sK0) | calm(susan) [cnf transformation 35]
78. ~strong(X0) | ~curious(X0) [cnf transformation 22]
79. ~curious(X0) | creative(X0) [cnf transformation 22]
80. old(X0) | humble(X0) | brave(X0) | rich(X0) [cnf transformation 37]
83. ~old(X0) | ~rich(X0) | brave(X0) [cnf transformation 37]
85. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
93. ~generous(mary) | happy(X1) | creative(X1) [cnf transformation 44]
97. kind(fred) | ~brave(X1) [cnf transformation 49]
98. ~rich(fred) | ~brave(X1) [cnf transformation 49]
99. brave(sK2) | rich(fred) | ~kind(fred) [cnf transformation 49]
100. ~old(X0) | brave(X0) | funny(X0) [cnf transformation 51]
101. ~funny(X0) | old(X0) [cnf transformation 51]
102. ~brave(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~generous(X0) | old(X0) | creative(X0) [cnf transformation 52]
113. strong(X0) | brave(X0) [cnf transformation 24]
121. ~happy(X0) | curious(X0) | humble(X0) [cnf transformation 57]
132. ~humble(paul) [cnf transformation 21]
134. 1 <=> calm(susan) [avatar definition]
138. 2 <=> old(sK0) [avatar definition]
140. ~old(sK0) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 77,138,134]
143. 3 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (3) [avatar component clause 143]
145. 3 | ~1 [avatar split clause 76,134,143]
151. 5 <=> generous(mary) [avatar definition]
152. ~generous(mary) <- (~5) [avatar component clause 151]
169. 9 <=> ! [X1] : (happy(X1) | creative(X1)) [avatar definition]
170. happy(X1) | creative(X1) <- (9) [avatar component clause 169]
171. 9 | ~5 [avatar split clause 93,151,169]
175. 10 <=> kind(fred) [avatar definition]
179. 11 <=> rich(fred) [avatar definition]
183. 12 <=> brave(sK2) [avatar definition]
185. brave(sK2) <- (12) [avatar component clause 183]
186. ~10 | 11 | 12 [avatar split clause 99,183,179,175]
188. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (13) [avatar component clause 188]
190. 13 | ~11 [avatar split clause 98,179,188]
191. 13 | 10 [avatar split clause 97,175,188]
201. 16 <=> funny(paul) [avatar definition]
202. ~funny(paul) <- (~16) [avatar component clause 201]
203. funny(paul) <- (16) [avatar component clause 201]
205. 17 <=> calm(paul) [avatar definition]
207. calm(paul) <- (17) [avatar component clause 205]
272. old(sK2) <- (12) [resolution 102,185]
273. ~curious(X0) | brave(X0) [resolution 113,78]
287. ~rich(sK2) | generous(sK2) <- (12) [resolution 67,185]
291. ~rich(sK2) <- (12) [subsumption resolution 287,87]
349. rich(sK2) | ~brave(sK2) <- (12) [resolution 85,272]
355. ~brave(sK2) <- (12) [subsumption resolution 349,291]
356. $false <- (12) [subsumption resolution 355,185]
357. ~12 [avatar contradiction clause 356]
372. rich(X0) | calm(X0) <- (13) [resolution 189,68]
373. rich(X1) | generous(X1) <- (13) [resolution 189,66]
419. humble(sK0) | brave(sK0) | rich(sK0) <- (~2) [resolution 80,140]
420. humble(X0) | brave(X0) | rich(X0) | brave(X0) | funny(X0) [resolution 80,100]
425. humble(X0) | brave(X0) | rich(X0) | funny(X0) [duplicate literal removal 420]
426. humble(sK0) | rich(sK0) <- (~2, 13) [subsumption resolution 419,189]
428. 40 <=> rich(sK0) [avatar definition]
429. ~rich(sK0) <- (~40) [avatar component clause 428]
430. rich(sK0) <- (40) [avatar component clause 428]
432. 41 <=> humble(sK0) [avatar definition]
434. humble(sK0) <- (41) [avatar component clause 432]
435. 40 | 41 | 2 | ~13 [avatar split clause 426,188,138,432,428]
436. humble(X0) | rich(X0) | funny(X0) <- (13) [subsumption resolution 425,189]
437. funny(X0) | humble(X0) <- (13) [subsumption resolution 436,88]
453. 44 <=> curious(sK0) [avatar definition]
455. curious(sK0) <- (44) [avatar component clause 453]
513. 50 <=> creative(sK0) [avatar definition]
515. creative(sK0) <- (50) [avatar component clause 513]
517. 51 <=> generous(sK0) [avatar definition]
518. generous(sK0) <- (51) [avatar component clause 517]
519. ~generous(sK0) <- (~51) [avatar component clause 517]
595. generous(sK0) <- (13, ~40) [resolution 373,429]
598. $false <- (13, ~40, ~51) [subsumption resolution 595,519]
599. ~13 | 40 | 51 [avatar contradiction clause 598]
606. funny(sK0) <- (40) [resolution 430,88]
608. humble(paul) <- (13, ~16) [resolution 437,202]
611. $false <- (13, ~16) [subsumption resolution 608,132]
612. ~13 | 16 [avatar contradiction clause 611]
614. old(paul) <- (16) [resolution 203,101]
619. ~rich(paul) | brave(paul) <- (16) [resolution 614,83]
626. 61 <=> creative(paul) [avatar definition]
627. creative(paul) <- (61) [avatar component clause 626]
628. ~creative(paul) <- (~61) [avatar component clause 626]
630. ~rich(paul) <- (13, 16) [subsumption resolution 619,189]
714. creative(X4) | curious(X4) | humble(X4) <- (9) [resolution 170,121]
716. creative(X4) | humble(X4) <- (9) [subsumption resolution 714,79]
734. ~calm(sK0) | curious(sK0) <- (50) [resolution 515,70]
736. 67 <=> calm(sK0) [avatar definition]
739. 44 | ~67 | ~50 [avatar split clause 734,513,736,453]
761. old(sK0) <- (40) [resolution 606,101]
764. 2 | ~40 [avatar split clause 761,428,138]
779. humble(paul) <- (9, ~61) [resolution 628,716]
783. $false <- (9, ~61) [subsumption resolution 779,132]
784. ~9 | 61 [avatar contradiction clause 783]
845. ~calm(paul) | humble(paul) <- (61) [resolution 627,71]
855. calm(paul) <- (13, 16) [resolution 630,372]
885. humble(paul) <- (17, 61) [subsumption resolution 845,207]
886. $false <- (17, 61) [subsumption resolution 885,132]
887. ~17 | ~61 [avatar contradiction clause 886]
892. 17 | ~13 | ~16 [avatar split clause 855,201,188,205]
918. calm(sK0) <- (13, ~40) [resolution 429,372]
921. 67 | ~13 | 40 [avatar split clause 918,428,188,736]
924. ~generous(sK0) | old(sK0) | creative(sK0) <- (41) [resolution 434,105]
935. brave(sK0) <- (44) [resolution 455,273]
937. $false <- (13, 44) [subsumption resolution 935,189]
938. ~13 | ~44 [avatar contradiction clause 937]
942. old(sK0) | creative(sK0) <- (41, 51) [subsumption resolution 924,518]
943. 50 | 2 | ~41 | ~51 [avatar split clause 942,517,432,138,513]
948. ~rich(X4) | brave(X4) <- (3) [resolution 144,83]
951. ~rich(X4) <- (3, 13) [subsumption resolution 948,189]
957. generous(X0) <- (3, 13) [resolution 951,373]
983. $false <- (3, ~5, 13) [resolution 957,152]
984. ~3 | 5 | ~13 [avatar contradiction clause 983]
985. $false [avatar sat refutation 141,145,171,186,190,191,357,435,599,612,739,764,784,887,892,921,938,943,984]
% SZS output end Proof for 7329547201543101904918918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and generous is either wise or not funny. Everyone who is funny or quiet is not creative. If susan is not old then someone is brave or not brave and vice versa. If someone is patient or not old then lucy is not generous and vice versa. If someone is either wise or humble then mary is both not generous and not old and vice versa. Everyone who is both not generous and generous is both patient and not calm and vice versa. Everyone who is creative is old. If paul is curious then someone is generous. Everyone who is not old is curious or not kind and vice versa. If someone is curious or not generous then someone is both humble and rich and vice versa. If someone is both not tall and tall then someone is strong or funny. If someone is either wise or not quiet then susan is not old or not creative and vice versa. Everyone who is both not happy and not curious is both funny and not calm and vice versa. If someone is not funny then paul is not tall or not curious and vice versa. If someone is funny then paul is not kind or curious and vice versa. Everyone who is brave or not kind is either not wise or not quiet and vice versa. Paul is both curious and not calm. Lucy is either tall or not kind. Someone is both not rich and not kind. Susan is humble. Someone is both not rich and tall. Someone is either kind or not happy. Susan is both not generous and quiet. Someone is not funny. | Paul is kind. | neutral | (![X]:((~happy(X)&generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((funny(X)|quiet(X))=>~creative(X)))&
((~old(susan))<=>(?[X]:((brave(X)|~brave(X)))))&
((?[X]:((patient(X)|~old(X))))<=>(~generous(lucy)))&
((?[X]:((wise(X)<~>humble(X))))<=>((~generous(mary)&~old(mary))))&
(![X]:((~generous(X)&generous(X))<=>(patient(X)&~calm(X))))&
(![X]:(creative(X)=>old(X)))&
((curious(paul))=>(?[X]:(generous(X))))&
(![X]:(~old(X)<=>(curious(X)|~kind(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((strong(X)|funny(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~old(susan)|~creative(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((?[X]:(~funny(X)))<=>((~tall(paul)|~curious(paul))))&
((?[X]:(funny(X)))<=>((~kind(paul)|curious(paul))))&
(![X]:((brave(X)|~kind(X))<=>(~wise(X)<~>~quiet(X))))&
((curious(paul)&~calm(paul)))&
((tall(lucy)<~>~kind(lucy)))&
(?[X]:((~rich(X)&~kind(X))))&
(humble(susan))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((kind(X)<~>~happy(X))))&
((~generous(susan)&quiet(susan)))&
(?[X]:(~funny(X))) | kind(paul) | [] | null | 0 |
Everyone who is curious or not tall is either tall or creative and vice versa.
Everyone who is either humble or not strong is not kind.
If someone is not funny or wise then someone is either generous or not strong and vice versa.
Everyone who is not kind or kind is either not old or kind and vice versa.
Everyone who is brave is both patient and not rich.
If fred is happy or not wise then someone is either not rich or wise.
If someone is calm then alice is brave or rich.
Everyone who is either not brave or strong is not generous or patient.
If someone is not happy then someone is creative and vice versa.
Everyone who is both not strong and not quiet is not generous and vice versa.
If someone is not curious or not strong then fred is either generous or not funny and vice versa.
If someone is either not funny or not brave then paul is not happy and vice versa.
Everyone who is either brave or not creative is not rich or humble and vice versa.
If alice is not humble or patient then someone is not happy or not funny and vice versa.
If someone is either wise or not brave then lucy is either funny or not creative and vice versa.
Everyone who is both not strong and not generous is either calm or not happy.
Lucy is wise or not wise.
Someone is rich or creative.
Alice is rich.
Someone is rich.
Someone is patient.
Fred is tall or not strong.
Fred is brave or funny. | Alice is not kind. | neutral | (![X]:((curious(X)|~tall(X))<=>(tall(X)<~>creative(X))))&
(![X]:((humble(X)<~>~strong(X))=>~kind(X)))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~kind(X)|kind(X))<=>(~old(X)<~>kind(X))))&
(![X]:(brave(X)=>(patient(X)&~rich(X))))&
(((happy(fred)|~wise(fred)))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(calm(X)))=>((brave(alice)|rich(alice))))&
(![X]:((~brave(X)<~>strong(X))=>(~generous(X)|patient(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(creative(X))))&
(![X]:((~strong(X)&~quiet(X))<=>~generous(X)))&
((?[X]:((~curious(X)|~strong(X))))<=>((generous(fred)<~>~funny(fred))))&
((?[X]:((~funny(X)<~>~brave(X))))<=>(~happy(paul)))&
(![X]:((brave(X)<~>~creative(X))<=>(~rich(X)|humble(X))))&
(((~humble(alice)|patient(alice)))<=>(?[X]:((~happy(X)|~funny(X)))))&
((?[X]:((wise(X)<~>~brave(X))))<=>((funny(lucy)<~>~creative(lucy))))&
(![X]:((~strong(X)&~generous(X))=>(calm(X)<~>~happy(X))))&
((wise(lucy)|~wise(lucy)))&
(?[X]:((rich(X)|creative(X))))&
(rich(alice))&
(?[X]:(rich(X)))&
(?[X]:(patient(X)))&
((tall(fred)|~strong(fred)))&
((brave(fred)|funny(fred))) | ~kind(alice) | [] | null | 0 |
Everyone who is quiet or curious is brave or strong and vice versa. Everyone who is strong is either not rich or rich and vice versa. Everyone who is not happy or rich is either old or rich and vice versa. Everyone who is rich is not generous. If susan is not strong then lucy is either not rich or not wise. If someone is wise then john is both not patient and not calm and vice versa. If someone is both curious and not curious then lucy is not rich and vice versa. Everyone who is not tall or rich is both not tall and humble and vice versa. Everyone who is calm is either not wise or tall. If lucy is either not strong or wise then someone is curious or calm. If someone is patient then paul is either tall or generous and vice versa. Everyone who is both kind and not patient is not wise and vice versa. If mary is either quiet or brave then someone is both not happy and calm. Everyone who is either quiet or rich is not rich and vice versa. Everyone who is either patient or not happy is either happy or generous and vice versa. Everyone who is not quiet is wise or not curious. Paul is both not rich and tall. Susan is old. Susan is either tall or not generous. Someone is both not kind and brave. Someone is both not curious and not brave. Someone is both not kind and not funny. Alice is either not rich or not creative. Mary is not rich or not wise. | Paul is not generous. | entailment | (![X]:((quiet(X)|curious(X))<=>(brave(X)|strong(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>rich(X))))&
(![X]:((~happy(X)|rich(X))<=>(old(X)<~>rich(X))))&
(![X]:(rich(X)=>~generous(X)))&
((~strong(susan))=>((~rich(lucy)<~>~wise(lucy))))&
((?[X]:(wise(X)))<=>((~patient(john)&~calm(john))))&
((?[X]:((curious(X)&~curious(X))))<=>(~rich(lucy)))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)&humble(X))))&
(![X]:(calm(X)=>(~wise(X)<~>tall(X))))&
(((~strong(lucy)<~>wise(lucy)))=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:(patient(X)))<=>((tall(paul)<~>generous(paul))))&
(![X]:((kind(X)&~patient(X))<=>~wise(X)))&
(((quiet(mary)<~>brave(mary)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~rich(X)))&
(![X]:((patient(X)<~>~happy(X))<=>(happy(X)<~>generous(X))))&
(![X]:(~quiet(X)=>(wise(X)|~curious(X))))&
((~rich(paul)&tall(paul)))&
(old(susan))&
((tall(susan)<~>~generous(susan)))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~curious(X)&~brave(X))))&
(?[X]:((~kind(X)&~funny(X))))&
((~rich(alice)<~>~creative(alice)))&
((~rich(mary)|~wise(mary))) | ~generous(paul) | [
"p3",
"p6",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5089091297303193074904768
% SZS output start Proof for 5089091297303193074904768
4. ! [X0] : (rich(X0) => ~generous(X0)) [input p3]
7. ? [X0] : (~curious(X0) & curious(X0)) <=> ~rich(lucy) [input p6]
11. ? [X0] : patient(X0) <=> (tall(paul) <~> generous(paul)) [input p10]
15. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (happy(X0) <~> generous(X0))) [input p14]
17. tall(paul) & ~rich(paul) [input p16]
25. generous(paul) [input hypothesis]
27. ! [X0] : (~generous(X0) | ~rich(X0)) [ennf transformation 4]
45. (? [X0] : (~curious(X0) & curious(X0)) | rich(lucy)) & (~rich(lucy) | ! [X0] : (curious(X0) | ~curious(X0))) [nnf transformation 7]
46. (? [X0] : (~curious(X0) & curious(X0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (curious(X1) | ~curious(X1))) [rectify 45]
47. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK1) & curious(sK1)) [choice axiom]
48. ((~curious(sK1) & curious(sK1)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (curious(X1) | ~curious(X1))) [skolemisation 46,47]
55. (? [X0] : patient(X0) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X0] : ~patient(X0)) [nnf transformation 11]
56. (? [X0] : patient(X0) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X1] : ~patient(X1)) [rectify 55]
57. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
58. (patient(sK3) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X1] : ~patient(X1)) [skolemisation 56,57]
65. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 15]
88. ~generous(X0) | ~rich(X0) [cnf transformation 27]
95. curious(sK1) | rich(lucy) [cnf transformation 48]
96. ~curious(sK1) | rich(lucy) [cnf transformation 48]
107. ~generous(paul) | ~tall(paul) | ~patient(X1) [cnf transformation 58]
122. generous(X0) | happy(X0) | patient(X0) | happy(X0) [cnf transformation 65]
125. ~happy(X0) | patient(X0) | generous(X0) | ~happy(X0) [cnf transformation 65]
131. tall(paul) [cnf transformation 17]
143. generous(paul) [cnf transformation 25]
144. generous(X0) | happy(X0) | patient(X0) [duplicate literal removal 122]
146. ~happy(X0) | patient(X0) | generous(X0) [duplicate literal removal 125]
174. 5 <=> rich(lucy) [avatar definition]
176. rich(lucy) <- (5) [avatar component clause 174]
178. 6 <=> curious(sK1) [avatar definition]
181. 5 | ~6 [avatar split clause 96,178,174]
182. 5 | 6 [avatar split clause 95,178,174]
198. 10 <=> generous(paul) [avatar definition]
202. 11 <=> tall(paul) [avatar definition]
212. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
213. ~patient(X1) <- (13) [avatar component clause 212]
214. 13 | ~11 | ~10 [avatar split clause 107,198,202,212]
238. patient(X0) | generous(X0) [subsumption resolution 144,146]
239. 11 [avatar split clause 131,202]
269. 10 [avatar split clause 143,198]
288. generous(X2) <- (13) [resolution 238,213]
290. ~rich(X0) <- (13) [resolution 288,88]
293. $false <- (5, 13) [resolution 290,176]
297. ~5 | ~13 [avatar contradiction clause 293]
298. $false [avatar sat refutation 181,182,214,239,269,297]
% SZS output end Proof for 5089091297303193074904768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not brave or not funny.
Everyone who is either quiet or tall is curious.
Everyone who is both brave and funny is both not creative and strong and vice versa.
If john is both tall and not kind then someone is both not rich and wise and vice versa.
Everyone who is old is both brave and humble and vice versa.
If mary is not curious or wise then someone is not curious and vice versa.
Everyone who is either not humble or patient is strong.
Everyone who is both funny and not old is both not humble and not brave and vice versa.
Everyone who is calm is not strong.
If lucy is quiet then paul is both not curious and quiet.
Everyone who is either not quiet or not curious is not happy and vice versa.
If paul is both creative and not kind then someone is either patient or not calm.
Everyone who is both not kind and not curious is either not curious or patient and vice versa.
If someone is not rich or not patient then alice is rich and vice versa.
If john is rich then someone is calm or not calm and vice versa.
Everyone who is happy or not curious is not calm and vice versa.
Susan is not generous or not quiet.
Someone is either not curious or calm.
Someone is curious or patient.
Someone is either wise or brave.
Susan is either tall or not strong.
Someone is not curious or calm.
Paul is not humble or happy. | Susan is tall. | neutral | (![X]:(generous(X)=>(~brave(X)|~funny(X))))&
(![X]:((quiet(X)<~>tall(X))=>curious(X)))&
(![X]:((brave(X)&funny(X))<=>(~creative(X)&strong(X))))&
(((tall(john)&~kind(john)))<=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:(old(X)<=>(brave(X)&humble(X))))&
(((~curious(mary)|wise(mary)))<=>(?[X]:(~curious(X))))&
(![X]:((~humble(X)<~>patient(X))=>strong(X)))&
(![X]:((funny(X)&~old(X))<=>(~humble(X)&~brave(X))))&
(![X]:(calm(X)=>~strong(X)))&
((quiet(lucy))=>((~curious(paul)&quiet(paul))))&
(![X]:((~quiet(X)<~>~curious(X))<=>~happy(X)))&
(((creative(paul)&~kind(paul)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~kind(X)&~curious(X))<=>(~curious(X)<~>patient(X))))&
((?[X]:((~rich(X)|~patient(X))))<=>(rich(alice)))&
((rich(john))<=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((happy(X)|~curious(X))<=>~calm(X)))&
((~generous(susan)|~quiet(susan)))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((wise(X)<~>brave(X))))&
((tall(susan)<~>~strong(susan)))&
(?[X]:((~curious(X)|calm(X))))&
((~humble(paul)|happy(paul))) | tall(susan) | [] | null | 0 |
Everyone who is not happy is either not happy or tall and vice versa. If someone is creative then john is either not humble or not brave and vice versa. If alice is either not patient or not happy then someone is patient and vice versa. If lucy is either not strong or old then someone is not calm or not quiet. Everyone who is not patient is not tall or not calm and vice versa. Everyone who is both patient and kind is either not rich or brave and vice versa. Everyone who is both wise and not old is both quiet and not quiet. If alice is not funny or strong then paul is generous. Everyone who is either curious or not curious is not calm or curious and vice versa. Everyone who is not creative or wise is brave or not calm and vice versa. If lucy is either not curious or strong then someone is not strong and vice versa. If someone is humble or not old then someone is either not brave or not happy. Everyone who is kind or funny is either not rich or quiet. If alice is either happy or tall then fred is creative or strong and vice versa. If lucy is not rich then fred is either humble or not funny and vice versa. If fred is not humble or not strong then mary is not calm or humble. Lucy is either old or strong. Someone is both not old and not funny. Someone is not old or wise. Someone is both happy and not quiet. Someone is not generous or funny. Someone is not wise or not old. Mary is either creative or wise. | John is funny. | neutral | (![X]:(~happy(X)<=>(~happy(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((~humble(john)<~>~brave(john))))&
(((~patient(alice)<~>~happy(alice)))<=>(?[X]:(patient(X))))&
(((~strong(lucy)<~>old(lucy)))=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:(~patient(X)<=>(~tall(X)|~calm(X))))&
(![X]:((patient(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((wise(X)&~old(X))=>(quiet(X)&~quiet(X))))&
(((~funny(alice)|strong(alice)))=>(generous(paul)))&
(![X]:((curious(X)<~>~curious(X))<=>(~calm(X)|curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(brave(X)|~calm(X))))&
(((~curious(lucy)<~>strong(lucy)))<=>(?[X]:(~strong(X))))&
((?[X]:((humble(X)|~old(X))))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((kind(X)|funny(X))=>(~rich(X)<~>quiet(X))))&
(((happy(alice)<~>tall(alice)))<=>((creative(fred)|strong(fred))))&
((~rich(lucy))<=>((humble(fred)<~>~funny(fred))))&
(((~humble(fred)|~strong(fred)))=>((~calm(mary)|humble(mary))))&
((old(lucy)<~>strong(lucy)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((happy(X)&~quiet(X))))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((~wise(X)|~old(X))))&
((creative(mary)<~>wise(mary))) | funny(john) | [] | null | 0 |
Everyone who is either curious or calm is either not old or old and vice versa.
If someone is both not strong and not kind then mary is both not funny and not wise.
If someone is happy then susan is not brave.
If mary is either not tall or not quiet then lucy is not creative and vice versa.
Everyone who is not quiet or not calm is calm and vice versa.
Everyone who is both not rich and not wise is not rich and vice versa.
Everyone who is generous or rich is either old or not patient and vice versa.
Everyone who is either not brave or not curious is not kind.
Everyone who is either patient or curious is not quiet or not happy.
Everyone who is not creative is curious and vice versa.
Everyone who is rich is both happy and not tall and vice versa.
Everyone who is not happy or not brave is not quiet.
If someone is not calm or brave then someone is not quiet.
Everyone who is both generous and funny is both tall and not funny and vice versa.
If someone is not tall or not happy then someone is not strong or brave.
If someone is either not rich or rich then someone is either calm or not creative and vice versa.
John is both not quiet and brave.
Someone is either kind or not kind.
Susan is creative.
Someone is calm or rich.
Susan is both not rich and not quiet.
Someone is both calm and funny. | John is kind. | contradiction | (![X]:((curious(X)<~>calm(X))<=>(~old(X)<~>old(X))))&
((?[X]:((~strong(X)&~kind(X))))=>((~funny(mary)&~wise(mary))))&
((?[X]:(happy(X)))=>(~brave(susan)))&
(((~tall(mary)<~>~quiet(mary)))<=>(~creative(lucy)))&
(![X]:((~quiet(X)|~calm(X))<=>calm(X)))&
(![X]:((~rich(X)&~wise(X))<=>~rich(X)))&
(![X]:((generous(X)|rich(X))<=>(old(X)<~>~patient(X))))&
(![X]:((~brave(X)<~>~curious(X))=>~kind(X)))&
(![X]:((patient(X)<~>curious(X))=>(~quiet(X)|~happy(X))))&
(![X]:(~creative(X)<=>curious(X)))&
(![X]:(rich(X)<=>(happy(X)&~tall(X))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)&funny(X))<=>(tall(X)&~funny(X))))&
((?[X]:((~tall(X)|~happy(X))))=>(?[X]:((~strong(X)|brave(X)))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((calm(X)<~>~creative(X)))))&
((~quiet(john)&brave(john)))&
(?[X]:((kind(X)<~>~kind(X))))&
(creative(susan))&
(?[X]:((calm(X)|rich(X))))&
((~rich(susan)&~quiet(susan)))&
(?[X]:((calm(X)&funny(X)))) | kind(john) | [
"p0",
"p4",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6498777421283658910567949
% SZS output start Proof for 6498777421283658910567949
1. ! [X0] : ((curious(X0) <~> calm(X0)) <=> (~old(X0) <~> old(X0))) [input p0]
5. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> calm(X0)) [input p4]
8. ! [X0] : ((~brave(X0) <~> ~curious(X0)) => ~kind(X0)) [input p7]
17. brave(john) & ~quiet(john) [input p16]
23. kind(john) [input hypothesis]
29. ! [X0] : (~kind(X0) | (~brave(X0) <=> ~curious(X0))) [ennf transformation 8]
35. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [nnf transformation 1]
37. ! [X0] : (((~calm(X0) | ~quiet(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) & quiet(X0)))) [nnf transformation 5]
38. ! [X0] : ((~calm(X0) | ~quiet(X0) | ~calm(X0)) & (calm(X0) | (calm(X0) & quiet(X0)))) [flattening 37]
43. ! [X0] : (~kind(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) [nnf transformation 29]
74. ~calm(X0) | ~curious(X0) | old(X0) | old(X0) [cnf transformation 35]
75. ~calm(X0) | ~curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 35]
84. calm(X0) | calm(X0) [cnf transformation 38]
96. ~brave(X0) | ~kind(X0) | curious(X0) [cnf transformation 43]
123. brave(john) [cnf transformation 17]
132. kind(john) [cnf transformation 23]
139. calm(X0) [duplicate literal removal 84]
143. ~calm(X0) | ~curious(X0) | old(X0) [duplicate literal removal 74]
144. ~calm(X0) | ~curious(X0) | ~old(X0) [duplicate literal removal 75]
145. ~calm(X0) | ~curious(X0) [subsumption resolution 143,144]
226. ~curious(X0) [resolution 145,139]
229. ~kind(john) | curious(john) [resolution 96,123]
230. curious(john) [subsumption resolution 229,132]
231. $false [subsumption resolution 230,226]
% SZS output end Proof for 6498777421283658910567949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is both not generous and not happy and vice versa. If someone is either tall or happy then someone is either not strong or not creative. Everyone who is either creative or not brave is humble or not creative and vice versa. Everyone who is either not humble or curious is either generous or not curious and vice versa. Everyone who is funny or not calm is wise and vice versa. If fred is either not quiet or kind then someone is not rich or not curious and vice versa. If someone is not humble or not creative then someone is old and vice versa. If mary is either not calm or quiet then someone is tall or not funny and vice versa. Everyone who is both patient and not brave is either not creative or calm and vice versa. Everyone who is either not humble or generous is both not curious and funny and vice versa. Everyone who is both old and not calm is curious. If someone is rich or creative then mary is both patient and curious and vice versa. Everyone who is not tall is not wise or funny and vice versa. Everyone who is not creative is not brave and vice versa. Everyone who is curious is not humble. If lucy is tall or not strong then lucy is not tall. Alice is not calm. Mary is either generous or not rich. Someone is not curious. Someone is either calm or not old. Someone is either not humble or brave. Someone is both not curious and happy. | Lucy is old. | neutral | (![X]:((happy(X)<~>~curious(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((tall(X)<~>happy(X))))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>(humble(X)|~creative(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)<~>~curious(X))))&
(![X]:((funny(X)|~calm(X))<=>wise(X)))&
(((~quiet(fred)<~>kind(fred)))<=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:(old(X))))&
(((~calm(mary)<~>quiet(mary)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>calm(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(~curious(X)&funny(X))))&
(![X]:((old(X)&~calm(X))=>curious(X)))&
((?[X]:((rich(X)|creative(X))))<=>((patient(mary)&curious(mary))))&
(![X]:(~tall(X)<=>(~wise(X)|funny(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:(curious(X)=>~humble(X)))&
(((tall(lucy)|~strong(lucy)))=>(~tall(lucy)))&
(~calm(alice))&
((generous(mary)<~>~rich(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((~curious(X)&happy(X)))) | old(lucy) | [] | null | 0 |
If mary is not strong or strong then lucy is both not brave and not tall and vice versa.
Everyone who is not patient or brave is quiet and vice versa.
Everyone who is both humble and rich is both not generous and not calm and vice versa.
Everyone who is either brave or not calm is brave.
Everyone who is either not humble or not calm is both wise and humble.
Everyone who is either not humble or not old is kind or calm and vice versa.
Everyone who is not rich or not happy is quiet and vice versa.
If someone is either not old or not brave then someone is both rich and not curious.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | Alice is not brave. | entailment | (((~strong(mary)|strong(mary)))<=>((~brave(lucy)&~tall(lucy))))&
(![X]:((~patient(X)|brave(X))<=>quiet(X)))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&~calm(X))))&
(![X]:((brave(X)<~>~calm(X))=>brave(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(kind(X)|calm(X))))&
(![X]:((~rich(X)|~happy(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | ~brave(alice) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8210842114950882771881413
% SZS output start Proof for 8210842114950882771881413
2. ! [X0] : ((brave(X0) | ~patient(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : ((rich(X0) & humble(X0)) <=> (~calm(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((brave(X0) <~> ~calm(X0)) => brave(X0)) [input p3]
5. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => (humble(X0) & wise(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> quiet(X0)) [input p6]
8. ? [X0] : (~old(X0) <~> ~brave(X0)) => ? [X0] : (~curious(X0) & rich(X0)) [input p7]
13. ? [X0] : old(X0) => ? [X0] : (~quiet(X0) & ~calm(X0)) [input p12]
15. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> happy(X0)) [input p14]
25. brave(alice) [input hypothesis]
26. ? [X0] : (~old(X0) <~> ~brave(X0)) => ? [X1] : (~curious(X1) & rich(X1)) [rectify 8]
28. ? [X0] : old(X0) => ? [X1] : (~quiet(X1) & ~calm(X1)) [rectify 13]
29. ! [X0] : (brave(X0) | (brave(X0) <=> ~calm(X0))) [ennf transformation 4]
30. ! [X0] : ((humble(X0) & wise(X0)) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 5]
31. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : (~old(X0) <=> ~brave(X0)) [ennf transformation 26]
33. ? [X1] : (~quiet(X1) & ~calm(X1)) | ! [X0] : ~old(X0) [ennf transformation 28]
38. ! [X0] : (((brave(X0) | ~patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~patient(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [flattening 38]
40. ! [X0] : (((rich(X0) & humble(X0)) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((rich(X0) & humble(X0)) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~rich(X0) | ~humble(X0))) [flattening 40]
42. ! [X0] : (brave(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) [nnf transformation 29]
43. ! [X0] : ((humble(X0) & wise(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 30]
46. ! [X0] : (((~happy(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [nnf transformation 7]
47. ! [X0] : ((~happy(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [flattening 46]
48. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))) [nnf transformation 31]
49. ? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1))) [rectify 48]
50. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK0) & rich(sK0)) [choice axiom]
51. (~curious(sK0) & rich(sK0)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1))) [skolemisation 49,50]
67. ? [X0] : (~quiet(X0) & ~calm(X0)) | ! [X1] : ~old(X1) [rectify 33]
68. ? [X0] : (~quiet(X0) & ~calm(X0)) => (~quiet(sK5) & ~calm(sK5)) [choice axiom]
69. (~quiet(sK5) & ~calm(sK5)) | ! [X1] : ~old(X1) [skolemisation 67,68]
70. ! [X0] : (((~rich(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [nnf transformation 15]
71. ! [X0] : ((~rich(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [flattening 70]
85. ~brave(X0) | quiet(X0) [cnf transformation 39]
88. ~calm(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 41]
92. brave(X0) | brave(X0) | calm(X0) [cnf transformation 42]
95. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 43]
103. rich(X0) | quiet(X0) [cnf transformation 47]
105. ~happy(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 47]
106. rich(sK0) | ~brave(X1) | old(X1) [cnf transformation 51]
126. ~calm(sK5) | ~old(X1) [cnf transformation 69]
127. ~quiet(sK5) | ~old(X1) [cnf transformation 69]
129. happy(X0) | calm(X0) [cnf transformation 71]
143. brave(alice) [cnf transformation 25]
144. ~calm(X0) | humble(X0) [duplicate literal removal 95]
145. calm(X0) | brave(X0) [duplicate literal removal 92]
173. 6 <=> ! [X1] : (~brave(X1) | old(X1)) [avatar definition]
174. ~brave(X1) | old(X1) <- (6) [avatar component clause 173]
177. 7 <=> rich(sK0) [avatar definition]
179. rich(sK0) <- (7) [avatar component clause 177]
181. 6 | 7 [avatar split clause 106,177,173]
241. 21 <=> ! [X1] : ~old(X1) [avatar definition]
242. ~old(X1) <- (21) [avatar component clause 241]
244. 22 <=> quiet(sK5) [avatar definition]
247. 21 | ~22 [avatar split clause 127,244,241]
249. 23 <=> calm(sK5) [avatar definition]
251. ~calm(sK5) <- (~23) [avatar component clause 249]
252. 21 | ~23 [avatar split clause 126,249,241]
313. brave(sK5) <- (~23) [resolution 145,251]
314. humble(X0) | brave(X0) [resolution 145,144]
315. quiet(sK5) <- (~23) [resolution 313,85]
318. 22 | 23 [avatar split clause 315,249,244]
319. old(alice) <- (6) [resolution 174,143]
321. $false <- (6, 21) [subsumption resolution 319,242]
322. ~6 | ~21 [avatar contradiction clause 321]
328. ~rich(X0) | ~humble(X0) | brave(X0) [resolution 88,145]
330. ~rich(X0) | brave(X0) [subsumption resolution 328,314]
349. brave(X0) | quiet(X0) [resolution 330,103]
351. quiet(X0) [subsumption resolution 349,85]
360. ~rich(X1) | ~quiet(X1) | calm(X1) [resolution 105,129]
363. ~rich(X1) | calm(X1) [subsumption resolution 360,351]
389. calm(sK0) <- (7) [resolution 363,179]
394. ~rich(sK0) | ~humble(sK0) <- (7) [resolution 389,88]
395. humble(sK0) <- (7) [resolution 389,144]
396. ~humble(sK0) <- (7) [subsumption resolution 394,179]
397. $false <- (7) [subsumption resolution 395,396]
398. ~7 [avatar contradiction clause 397]
399. $false [avatar sat refutation 181,247,252,318,322,398]
% SZS output end Proof for 8210842114950882771881413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and calm then alice is generous or brave.
Everyone who is both wise and not patient is kind or tall and vice versa.
Everyone who is strong or funny is not patient or not quiet.
Everyone who is either funny or not humble is either not generous or not tall.
Everyone who is rich or not old is both not happy and tall.
Everyone who is funny is not kind or quiet and vice versa.
If susan is not rich or creative then fred is kind or old.
If someone is creative or not kind then someone is not old or humble and vice versa.
Everyone who is creative is strong or not tall and vice versa.
If lucy is humble then someone is not wise.
If someone is not rich then john is both brave and not curious and vice versa.
Everyone who is both not old and not curious is not wise.
Everyone who is either not brave or brave is both not happy and calm.
Everyone who is quiet is patient and vice versa.
If someone is not rich or not curious then someone is not calm.
Everyone who is not strong is either kind or not generous.
Someone is both not generous and old.
Someone is rich or not creative.
Lucy is curious or not funny.
Someone is curious or wise.
Someone is not calm or curious. | Fred is not tall. | contradiction | ((?[X]:((~generous(X)&calm(X))))=>((generous(alice)|brave(alice))))&
(![X]:((wise(X)&~patient(X))<=>(kind(X)|tall(X))))&
(![X]:((strong(X)|funny(X))=>(~patient(X)|~quiet(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~generous(X)<~>~tall(X))))&
(![X]:((rich(X)|~old(X))=>(~happy(X)&tall(X))))&
(![X]:(funny(X)<=>(~kind(X)|quiet(X))))&
(((~rich(susan)|creative(susan)))=>((kind(fred)|old(fred))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((~old(X)|humble(X)))))&
(![X]:(creative(X)<=>(strong(X)|~tall(X))))&
((humble(lucy))=>(?[X]:(~wise(X))))&
((?[X]:(~rich(X)))<=>((brave(john)&~curious(john))))&
(![X]:((~old(X)&~curious(X))=>~wise(X)))&
(![X]:((~brave(X)<~>brave(X))=>(~happy(X)&calm(X))))&
(![X]:(quiet(X)<=>patient(X)))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:(~calm(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~generous(X))))&
(?[X]:((~generous(X)&old(X))))&
(?[X]:((rich(X)|~creative(X))))&
((curious(lucy)|~funny(lucy)))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~calm(X)|curious(X)))) | ~tall(fred) | [
"p4",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3070776449687923209832928
% SZS output start Proof for 3070776449687923209832928
5. ! [X0] : ((~old(X0) | rich(X0)) => (tall(X0) & ~happy(X0))) [input p4]
13. ! [X0] : ((~brave(X0) <~> brave(X0)) => (calm(X0) & ~happy(X0))) [input p12]
15. ? [X0] : (~curious(X0) | ~rich(X0)) => ? [X0] : ~calm(X0) [input p14]
22. ~tall(fred) [input hypothesis]
24. ? [X0] : (~curious(X0) | ~rich(X0)) => ? [X1] : ~calm(X1) [rectify 15]
25. ! [X0] : ((~old(X0) | rich(X0)) => tall(X0)) [pure predicate removal 5]
26. ! [X0] : ((~brave(X0) <~> brave(X0)) => calm(X0)) [pure predicate removal 13]
32. ! [X0] : (tall(X0) | (old(X0) & ~rich(X0))) [ennf transformation 25]
38. ! [X0] : (calm(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 26]
39. ? [X1] : ~calm(X1) | ! [X0] : (curious(X0) & rich(X0)) [ennf transformation 24]
60. ! [X0] : (calm(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 38]
62. ? [X0] : ~calm(X0) | ! [X1] : (curious(X1) & rich(X1)) [rectify 39]
63. ? [X0] : ~calm(X0) => ~calm(sK4) [choice axiom]
64. ~calm(sK4) | ! [X1] : (curious(X1) & rich(X1)) [skolemisation 62,63]
86. ~rich(X0) | tall(X0) [cnf transformation 32]
105. calm(X0) | brave(X0) | brave(X0) [cnf transformation 60]
106. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
109. ~calm(sK4) | rich(X1) [cnf transformation 64]
119. ~tall(fred) [cnf transformation 22]
120. calm(X0) | brave(X0) [duplicate literal removal 105]
121. calm(X0) | ~brave(X0) [duplicate literal removal 106]
207. 21 <=> ! [X1] : rich(X1) [avatar definition]
208. rich(X1) <- (21) [avatar component clause 207]
211. calm(X0) [subsumption resolution 120,121]
213. rich(X1) [subsumption resolution 109,211]
214. 21 [avatar split clause 213,207]
226. tall(X0) <- (21) [resolution 86,208]
227. $false <- (21) [resolution 226,119]
230. ~21 [avatar contradiction clause 227]
231. $false [avatar sat refutation 214,230]
% SZS output end Proof for 3070776449687923209832928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not patient is both not patient and old.
If someone is either calm or quiet then someone is both not old and happy.
Everyone who is wise or tall is humble and vice versa.
If someone is not tall then someone is old or calm and vice versa.
If someone is either generous or happy then someone is either strong or creative.
Everyone who is not old is kind or not rich and vice versa.
Everyone who is either not creative or not funny is both strong and patient.
Everyone who is patient is not rich and vice versa.
Everyone who is both kind and not generous is tall or not patient.
If alice is either quiet or brave then someone is both wise and not kind.
If paul is either not humble or funny then mary is either not tall or not curious.
If john is brave then someone is curious or strong.
Everyone who is both happy and humble is rich.
If someone is both not creative and old then someone is both not happy and wise.
If mary is wise then someone is both generous and not brave and vice versa.
Everyone who is either not wise or rich is either not generous or not wise and vice versa.
Someone is strong.
Susan is either calm or not old.
Alice is not quiet.
Someone is both strong and not creative.
Someone is not old or wise. | John is generous. | contradiction | (![X]:((generous(X)|~patient(X))=>(~patient(X)&old(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((wise(X)|tall(X))<=>humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((old(X)|calm(X)))))&
((?[X]:((generous(X)<~>happy(X))))=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:(~old(X)<=>(kind(X)|~rich(X))))&
(![X]:((~creative(X)<~>~funny(X))=>(strong(X)&patient(X))))&
(![X]:(patient(X)<=>~rich(X)))&
(![X]:((kind(X)&~generous(X))=>(tall(X)|~patient(X))))&
(((quiet(alice)<~>brave(alice)))=>(?[X]:((wise(X)&~kind(X)))))&
(((~humble(paul)<~>funny(paul)))=>((~tall(mary)<~>~curious(mary))))&
((brave(john))=>(?[X]:((curious(X)|strong(X)))))&
(![X]:((happy(X)&humble(X))=>rich(X)))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((~happy(X)&wise(X)))))&
((wise(mary))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((~wise(X)<~>rich(X))<=>(~generous(X)<~>~wise(X))))&
(?[X]:(strong(X)))&
((calm(susan)<~>~old(susan)))&
(~quiet(alice))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((~old(X)|wise(X)))) | generous(john) | [
"p0",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2922736644484406590970801
% SZS output start Proof for 2922736644484406590970801
1. ! [X0] : ((~patient(X0) | generous(X0)) => (old(X0) & ~patient(X0))) [input p0]
8. ! [X0] : (patient(X0) <=> ~rich(X0)) [input p7]
16. ! [X0] : ((~wise(X0) <~> rich(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p15]
22. generous(john) [input hypothesis]
27. ! [X0] : ((old(X0) & ~patient(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 1]
57. ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 8]
71. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [nnf transformation 16]
79. ~patient(X0) | ~generous(X0) [cnf transformation 27]
104. ~rich(X0) | ~patient(X0) [cnf transformation 57]
105. rich(X0) | patient(X0) [cnf transformation 57]
123. ~wise(X0) | ~generous(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 71]
124. wise(X0) | generous(X0) | rich(X0) | wise(X0) [cnf transformation 71]
126. rich(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 71]
129. ~rich(X0) | wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 71]
137. generous(john) [cnf transformation 22]
138. ~wise(X0) | ~generous(X0) | ~rich(X0) [duplicate literal removal 123]
139. wise(X0) | generous(X0) | rich(X0) [duplicate literal removal 124]
140. rich(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 126]
141. ~rich(X0) | wise(X0) | ~generous(X0) [duplicate literal removal 129]
287. rich(X0) | generous(X0) [subsumption resolution 139,140]
288. ~rich(X0) | ~generous(X0) [subsumption resolution 138,141]
333. generous(X0) | ~patient(X0) [resolution 287,104]
334. ~patient(X0) [subsumption resolution 333,79]
354. ~generous(X1) | patient(X1) [resolution 288,105]
358. ~generous(X1) [subsumption resolution 354,334]
435. $false [resolution 358,137]
% SZS output end Proof for 2922736644484406590970801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or generous is not funny or not kind.
Everyone who is patient or brave is quiet or curious.
Everyone who is not curious is generous or not generous and vice versa.
If lucy is either not tall or not patient then someone is not humble and vice versa.
Everyone who is both not patient and not happy is not creative and vice versa.
Everyone who is both not creative and tall is both wise and happy.
Everyone who is not calm is either humble or calm.
If someone is brave or not wise then someone is not kind or quiet.
If susan is happy then susan is not brave and vice versa.
If someone is either not creative or not patient then john is generous or brave and vice versa.
Everyone who is kind or not creative is both tall and not tall.
Everyone who is happy is either not generous or patient and vice versa.
Everyone who is both humble and not wise is happy and vice versa.
Everyone who is not happy is both not brave and old.
Everyone who is either not humble or not happy is strong or tall and vice versa.
If someone is not calm or humble then someone is kind or not funny.
Fred is wise.
Someone is happy.
Fred is funny.
Alice is tall or strong.
Paul is either creative or funny.
Someone is calm or generous.
Alice is both not happy and calm. | John is not generous. | neutral | (![X]:((kind(X)|generous(X))=>(~funny(X)|~kind(X))))&
(![X]:((patient(X)|brave(X))=>(quiet(X)|curious(X))))&
(![X]:(~curious(X)<=>(generous(X)|~generous(X))))&
(((~tall(lucy)<~>~patient(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~happy(X))<=>~creative(X)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&happy(X))))&
(![X]:(~calm(X)=>(humble(X)<~>calm(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((~kind(X)|quiet(X)))))&
((happy(susan))<=>(~brave(susan)))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(john)|brave(john))))&
(![X]:((kind(X)|~creative(X))=>(tall(X)&~tall(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>patient(X))))&
(![X]:((humble(X)&~wise(X))<=>happy(X)))&
(![X]:(~happy(X)=>(~brave(X)&old(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(strong(X)|tall(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((kind(X)|~funny(X)))))&
(wise(fred))&
(?[X]:(happy(X)))&
(funny(fred))&
((tall(alice)|strong(alice)))&
((creative(paul)<~>funny(paul)))&
(?[X]:((calm(X)|generous(X))))&
((~happy(alice)&calm(alice))) | ~generous(john) | [] | null | 0 |
Everyone who is not calm or generous is old.
Everyone who is old is not brave or old.
If paul is both not old and patient then someone is patient and vice versa.
Everyone who is both not rich and quiet is either kind or not generous and vice versa.
If someone is both tall and not wise then john is not strong.
Everyone who is either not quiet or funny is not old and vice versa.
Everyone who is old or not funny is either not curious or not creative.
Everyone who is not generous or not brave is not old.
If paul is generous or not funny then alice is both old and kind and vice versa.
Everyone who is either not funny or patient is brave or not tall and vice versa.
Everyone who is tall or not tall is not curious or humble and vice versa.
If paul is either rich or happy then someone is not funny or brave.
Everyone who is not curious is both quiet and not happy.
If someone is both funny and not old then someone is not quiet or not wise.
If someone is both not humble and not wise then susan is not strong and vice versa.
If someone is humble then someone is not generous or creative.
Someone is either not humble or not happy.
Someone is happy or curious.
Someone is not kind or not quiet.
Someone is either curious or humble.
Fred is either calm or humble.
Fred is wise.
Someone is not old or not wise. | Alice is kind. | neutral | (![X]:((~calm(X)|generous(X))=>old(X)))&
(![X]:(old(X)=>(~brave(X)|old(X))))&
(((~old(paul)&patient(paul)))<=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&quiet(X))<=>(kind(X)<~>~generous(X))))&
((?[X]:((tall(X)&~wise(X))))=>(~strong(john)))&
(![X]:((~quiet(X)<~>funny(X))<=>~old(X)))&
(![X]:((old(X)|~funny(X))=>(~curious(X)<~>~creative(X))))&
(![X]:((~generous(X)|~brave(X))=>~old(X)))&
(((generous(paul)|~funny(paul)))<=>((old(alice)&kind(alice))))&
(![X]:((~funny(X)<~>patient(X))<=>(brave(X)|~tall(X))))&
(![X]:((tall(X)|~tall(X))<=>(~curious(X)|humble(X))))&
(((rich(paul)<~>happy(paul)))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:(~curious(X)=>(quiet(X)&~happy(X))))&
((?[X]:((funny(X)&~old(X))))=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((~humble(X)&~wise(X))))<=>(~strong(susan)))&
((?[X]:(humble(X)))=>(?[X]:((~generous(X)|creative(X)))))&
(?[X]:((~humble(X)<~>~happy(X))))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~kind(X)|~quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((calm(fred)<~>humble(fred)))&
(wise(fred))&
(?[X]:((~old(X)|~wise(X)))) | kind(alice) | [] | null | 0 |
Everyone who is happy or brave is either not generous or rich.
Everyone who is both brave and not humble is both not rich and kind.
Everyone who is either not strong or humble is brave or not kind.
Everyone who is not strong is not creative.
Everyone who is either patient or brave is either patient or not kind and vice versa.
If mary is generous then someone is tall or strong.
Everyone who is not calm is not humble and vice versa.
If alice is not generous or not happy then someone is old.
If fred is curious or not humble then john is either strong or not generous and vice versa.
Everyone who is both happy and humble is both calm and not curious and vice versa.
Everyone who is brave or kind is either not funny or generous.
If someone is both not humble and humble then someone is humble or not tall and vice versa.
If someone is both not quiet and curious then someone is either calm or quiet and vice versa.
Everyone who is both old and curious is not brave or patient and vice versa.
If john is strong then someone is creative or not quiet and vice versa.
Everyone who is either not curious or not wise is not generous and vice versa.
Someone is both quiet and kind.
Mary is either creative or brave.
Someone is either not tall or not quiet.
Someone is both not patient and not funny.
Someone is either not wise or generous. | Alice is happy. | neutral | (![X]:((happy(X)|brave(X))=>(~generous(X)<~>rich(X))))&
(![X]:((brave(X)&~humble(X))=>(~rich(X)&kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)|~kind(X))))&
(![X]:(~strong(X)=>~creative(X)))&
(![X]:((patient(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
((generous(mary))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
(((~generous(alice)|~happy(alice)))=>(?[X]:(old(X))))&
(((curious(fred)|~humble(fred)))<=>((strong(john)<~>~generous(john))))&
(![X]:((happy(X)&humble(X))<=>(calm(X)&~curious(X))))&
(![X]:((brave(X)|kind(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((~humble(X)&humble(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)|patient(X))))&
((strong(john))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)&kind(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((~wise(X)<~>generous(X)))) | happy(alice) | [] | null | 0 |
Everyone who is both not brave and not quiet is not funny or creative.
Everyone who is either brave or not rich is not kind or creative and vice versa.
Everyone who is happy is either not curious or not wise.
If someone is not patient then mary is either strong or not funny.
Everyone who is not happy or not tall is humble or curious and vice versa.
Everyone who is creative or kind is both wise and old.
If someone is either not wise or strong then fred is either not tall or not strong.
Everyone who is calm or not tall is brave or creative.
If lucy is not tall then someone is either not generous or quiet and vice versa.
Everyone who is both calm and brave is both not calm and not curious and vice versa.
If someone is either not happy or not rich then someone is not old or wise and vice versa.
Everyone who is both humble and not kind is both old and not creative and vice versa.
Everyone who is either not generous or not tall is both brave and not brave.
Everyone who is either brave or not kind is strong and vice versa.
Everyone who is not patient or happy is quiet or creative and vice versa.
If susan is not old or not creative then someone is either not humble or not kind and vice versa.
Someone is both humble and not kind.
Someone is not funny or creative.
Alice is both happy and not calm.
Someone is not happy.
Alice is brave or quiet.
Mary is either generous or not curious.
Someone is calm.
Someone is humble. | Alice is rich. | entailment | (![X]:((~brave(X)&~quiet(X))=>(~funny(X)|creative(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(~kind(X)|creative(X))))&
(![X]:(happy(X)=>(~curious(X)<~>~wise(X))))&
((?[X]:(~patient(X)))=>((strong(mary)<~>~funny(mary))))&
(![X]:((~happy(X)|~tall(X))<=>(humble(X)|curious(X))))&
(![X]:((creative(X)|kind(X))=>(wise(X)&old(X))))&
((?[X]:((~wise(X)<~>strong(X))))=>((~tall(fred)<~>~strong(fred))))&
(![X]:((calm(X)|~tall(X))=>(brave(X)|creative(X))))&
((~tall(lucy))<=>(?[X]:((~generous(X)<~>quiet(X)))))&
(![X]:((calm(X)&brave(X))<=>(~calm(X)&~curious(X))))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((humble(X)&~kind(X))<=>(old(X)&~creative(X))))&
(![X]:((~generous(X)<~>~tall(X))=>(brave(X)&~brave(X))))&
(![X]:((brave(X)<~>~kind(X))<=>strong(X)))&
(![X]:((~patient(X)|happy(X))<=>(quiet(X)|creative(X))))&
(((~old(susan)|~creative(susan)))<=>(?[X]:((~humble(X)<~>~kind(X)))))&
(?[X]:((humble(X)&~kind(X))))&
(?[X]:((~funny(X)|creative(X))))&
((happy(alice)&~calm(alice)))&
(?[X]:(~happy(X)))&
((brave(alice)|quiet(alice)))&
((generous(mary)<~>~curious(mary)))&
(?[X]:(calm(X)))&
(?[X]:(humble(X))) | rich(alice) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p9",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5833213885869503317417408
% SZS output start Proof for 5833213885869503317417408
2. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (creative(X0) | ~kind(X0))) [input p1]
3. ! [X0] : (happy(X0) => (~curious(X0) <~> ~wise(X0))) [input p2]
5. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (curious(X0) | humble(X0))) [input p4]
6. ! [X0] : ((kind(X0) | creative(X0)) => (old(X0) & wise(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | calm(X0)) => (creative(X0) | brave(X0))) [input p7]
10. ! [X0] : ((brave(X0) & calm(X0)) <=> (~curious(X0) & ~calm(X0))) [input p9]
12. ! [X0] : ((~kind(X0) & humble(X0)) <=> (~creative(X0) & old(X0))) [input p11]
19. ~calm(alice) & happy(alice) [input p18]
25. ~rich(alice) [input hypothesis]
29. ! [X0] : ((~curious(X0) <~> ~wise(X0)) | ~happy(X0)) [ennf transformation 3]
31. ! [X0] : ((old(X0) & wise(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 6]
33. ! [X0] : ((creative(X0) | brave(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 8]
34. ! [X0] : (creative(X0) | brave(X0) | (tall(X0) & ~calm(X0))) [flattening 33]
36. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (~creative(X0) & kind(X0))) & ((creative(X0) | ~kind(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 2]
37. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (~creative(X0) & kind(X0))) & (creative(X0) | ~kind(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [flattening 36]
38. ! [X0] : (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | ~happy(X0)) [nnf transformation 29]
40. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 5]
41. ! [X0] : ((~tall(X0) | ~happy(X0) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | (tall(X0) & happy(X0)))) [flattening 40]
47. ! [X0] : (((brave(X0) & calm(X0)) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | (~brave(X0) | ~calm(X0)))) [nnf transformation 10]
48. ! [X0] : (((brave(X0) & calm(X0)) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ~brave(X0) | ~calm(X0))) [flattening 47]
54. ! [X0] : (((~kind(X0) & humble(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (kind(X0) | ~humble(X0)))) [nnf transformation 12]
55. ! [X0] : (((~kind(X0) & humble(X0)) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | kind(X0) | ~humble(X0))) [flattening 54]
81. ~brave(X0) | rich(X0) | kind(X0) [cnf transformation 37]
82. ~creative(X0) | ~brave(X0) | rich(X0) [cnf transformation 37]
83. ~wise(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 38]
90. ~tall(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 41]
91. ~creative(X0) | wise(X0) [cnf transformation 31]
94. ~kind(X0) | old(X0) [cnf transformation 31]
99. ~calm(X0) | brave(X0) | creative(X0) [cnf transformation 34]
100. tall(X0) | brave(X0) | creative(X0) [cnf transformation 34]
105. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 48]
107. calm(X0) | curious(X0) | calm(X0) [cnf transformation 48]
118. ~kind(X0) | creative(X0) | ~old(X0) [cnf transformation 55]
140. happy(alice) [cnf transformation 19]
141. ~calm(alice) [cnf transformation 19]
148. ~rich(alice) [cnf transformation 25]
149. ~calm(X0) | ~brave(X0) [duplicate literal removal 105]
150. calm(X0) | curious(X0) [duplicate literal removal 107]
238. ~kind(X0) | creative(X0) [subsumption resolution 118,94]
282. 29 <=> brave(alice) [avatar definition]
283. ~brave(alice) <- (~29) [avatar component clause 282]
284. brave(alice) <- (29) [avatar component clause 282]
301. curious(alice) [resolution 150,141]
302. ~brave(X0) | curious(X0) [resolution 150,149]
308. rich(alice) | kind(alice) <- (29) [resolution 81,284]
309. kind(alice) <- (29) [subsumption resolution 308,148]
310. creative(alice) <- (29) [resolution 309,238]
313. ~brave(alice) | rich(alice) <- (29) [resolution 310,82]
316. rich(alice) <- (29) [subsumption resolution 313,284]
317. $false <- (29) [subsumption resolution 316,148]
318. ~29 [avatar contradiction clause 317]
399. brave(X0) | creative(X0) | curious(X0) [resolution 99,150]
401. curious(X0) | creative(X0) [subsumption resolution 399,302]
403. brave(X0) | creative(X0) | ~happy(X0) | ~curious(X0) [resolution 100,90]
415. ~happy(X0) | creative(X0) | brave(X0) [subsumption resolution 403,401]
589. creative(alice) | brave(alice) [resolution 415,140]
591. creative(alice) <- (~29) [subsumption resolution 589,283]
648. wise(alice) <- (~29) [resolution 591,91]
704. ~curious(alice) | ~happy(alice) <- (~29) [resolution 648,83]
705. ~happy(alice) <- (~29) [subsumption resolution 704,301]
706. $false <- (~29) [subsumption resolution 705,140]
707. 29 [avatar contradiction clause 706]
708. $false [avatar sat refutation 318,707]
% SZS output end Proof for 5833213885869503317417408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is kind. Everyone who is both not calm and calm is either not rich or not patient. Everyone who is both not quiet and not rich is both generous and curious. If someone is both kind and not old then someone is tall or creative. Everyone who is either creative or tall is either funny or not happy. If lucy is both not generous and not creative then alice is both not wise and tall and vice versa. If someone is both not old and not funny then someone is not funny and vice versa. Everyone who is both not patient and generous is curious and vice versa. If susan is humble then someone is either not generous or not curious. If someone is brave or funny then someone is both not old and not happy and vice versa. Everyone who is either not creative or rich is both not calm and patient. If someone is either not generous or not curious then someone is not creative and vice versa. Everyone who is both not brave and not kind is strong. If someone is both quiet and happy then lucy is both humble and not quiet. Everyone who is either not rich or not wise is either generous or not generous. Someone is calm. Alice is either creative or not wise. Susan is either generous or not kind. Someone is creative or generous. Susan is generous or old. Fred is both calm and not curious. Susan is not funny or not humble. Fred is both happy and creative. | Fred is not tall. | neutral | (![X]:(quiet(X)=>kind(X)))&
(![X]:((~calm(X)&calm(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~rich(X))=>(generous(X)&curious(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((creative(X)<~>tall(X))=>(funny(X)<~>~happy(X))))&
(((~generous(lucy)&~creative(lucy)))<=>((~wise(alice)&tall(alice))))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&generous(X))<=>curious(X)))&
((humble(susan))=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((brave(X)|funny(X))))<=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~calm(X)&patient(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~brave(X)&~kind(X))=>strong(X)))&
((?[X]:((quiet(X)&happy(X))))=>((humble(lucy)&~quiet(lucy))))&
(![X]:((~rich(X)<~>~wise(X))=>(generous(X)<~>~generous(X))))&
(?[X]:(calm(X)))&
((creative(alice)<~>~wise(alice)))&
((generous(susan)<~>~kind(susan)))&
(?[X]:((creative(X)|generous(X))))&
((generous(susan)|old(susan)))&
((calm(fred)&~curious(fred)))&
((~funny(susan)|~humble(susan)))&
((happy(fred)&creative(fred))) | ~tall(fred) | [] | null | 0 |
Everyone who is not calm or calm is funny. Everyone who is either brave or not brave is either not funny or not wise. If someone is calm then someone is not kind. If someone is humble or curious then fred is kind and vice versa. Everyone who is both creative and not patient is both generous and not rich. Everyone who is both not old and quiet is both humble and not happy and vice versa. Everyone who is not funny or calm is both not kind and humble and vice versa. Everyone who is not patient is both old and calm. Everyone who is either not brave or quiet is either rich or strong and vice versa. Everyone who is not creative is strong. If fred is both not generous and curious then someone is either not wise or not kind. Everyone who is both not generous and not old is either not humble or not funny and vice versa. Everyone who is not strong or not generous is not happy and vice versa. Everyone who is either not happy or brave is either not happy or not strong. If lucy is both generous and funny then someone is not humble and vice versa. Everyone who is not tall is curious or quiet. Paul is not generous or not strong. Alice is not quiet. Someone is both not brave and tall. Fred is either not tall or quiet. Someone is happy or strong. Someone is creative or not funny. Someone is not calm or generous. Someone is not patient or not rich. | Fred is not tall. | neutral | (![X]:((~calm(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)<~>~brave(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:(calm(X)))=>(?[X]:(~kind(X))))&
((?[X]:((humble(X)|curious(X))))<=>(kind(fred)))&
(![X]:((creative(X)&~patient(X))=>(generous(X)&~rich(X))))&
(![X]:((~old(X)&quiet(X))<=>(humble(X)&~happy(X))))&
(![X]:((~funny(X)|calm(X))<=>(~kind(X)&humble(X))))&
(![X]:(~patient(X)=>(old(X)&calm(X))))&
(![X]:((~brave(X)<~>quiet(X))<=>(rich(X)<~>strong(X))))&
(![X]:(~creative(X)=>strong(X)))&
(((~generous(fred)&curious(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~generous(X)&~old(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~strong(X)|~generous(X))<=>~happy(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~happy(X)<~>~strong(X))))&
(((generous(lucy)&funny(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)=>(curious(X)|quiet(X))))&
((~generous(paul)|~strong(paul)))&
(~quiet(alice))&
(?[X]:((~brave(X)&tall(X))))&
((~tall(fred)<~>quiet(fred)))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((~calm(X)|generous(X))))&
(?[X]:((~patient(X)|~rich(X)))) | ~tall(fred) | [] | null | 0 |
Everyone who is either generous or wise is both not creative and calm. Everyone who is funny is both humble and not humble and vice versa. If john is not happy or patient then mary is not creative and vice versa. If mary is both not brave and not kind then someone is rich or not strong and vice versa. If someone is rich or not strong then someone is not humble and vice versa. Everyone who is patient or generous is creative. Everyone who is not kind or not brave is humble. If someone is both wise and funny then someone is not old or not strong. Everyone who is quiet or not brave is creative or not calm. Everyone who is not calm or rich is not tall or generous. If someone is not happy then someone is both not generous and creative and vice versa. Everyone who is funny is not brave and vice versa. Everyone who is both patient and tall is either not wise or curious and vice versa. Everyone who is both kind and curious is either old or calm and vice versa. Everyone who is both kind and not kind is either not quiet or strong and vice versa. Susan is not strong or not funny. Someone is not rich or rich. Someone is either not wise or not humble. Mary is curious. Mary is not funny. Someone is either not funny or not old. | Mary is not creative. | neutral | (![X]:((generous(X)<~>wise(X))=>(~creative(X)&calm(X))))&
(![X]:(funny(X)<=>(humble(X)&~humble(X))))&
(((~happy(john)|patient(john)))<=>(~creative(mary)))&
(((~brave(mary)&~kind(mary)))<=>(?[X]:((rich(X)|~strong(X)))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((patient(X)|generous(X))=>creative(X)))&
(![X]:((~kind(X)|~brave(X))=>humble(X)))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((quiet(X)|~brave(X))=>(creative(X)|~calm(X))))&
(![X]:((~calm(X)|rich(X))=>(~tall(X)|generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:(funny(X)<=>~brave(X)))&
(![X]:((patient(X)&tall(X))<=>(~wise(X)<~>curious(X))))&
(![X]:((kind(X)&curious(X))<=>(old(X)<~>calm(X))))&
(![X]:((kind(X)&~kind(X))<=>(~quiet(X)<~>strong(X))))&
((~strong(susan)|~funny(susan)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(curious(mary))&
(~funny(mary))&
(?[X]:((~funny(X)<~>~old(X)))) | ~creative(mary) | [] | null | 0 |
If someone is both not brave and not calm then susan is not old.
If someone is either not quiet or not curious then someone is both funny and not funny and vice versa.
If someone is either not calm or not brave then lucy is both not wise and kind.
Everyone who is brave is both generous and not wise and vice versa.
If someone is not patient then someone is not patient or not quiet.
If alice is tall then paul is not creative or not quiet.
Everyone who is quiet or kind is not patient and vice versa.
If john is not happy or not wise then someone is both quiet and not curious and vice versa.
If someone is old then someone is creative and vice versa.
Everyone who is funny is not kind or not creative and vice versa.
If mary is either not strong or not patient then someone is strong and vice versa.
If someone is not wise or not calm then john is not curious or not calm and vice versa.
Everyone who is funny is not calm or humble and vice versa.
Everyone who is kind or not rich is either quiet or happy.
Everyone who is both wise and not creative is not generous or not calm and vice versa.
Everyone who is not tall or creative is humble.
Someone is either kind or not calm.
John is both generous and not creative.
Mary is either not happy or not quiet.
Alice is not old or not creative.
Someone is quiet or humble.
Fred is not rich.
Lucy is both funny and not tall.
Someone is either not wise or not humble. | Susan is old. | contradiction | ((?[X]:((~brave(X)&~calm(X))))=>(~old(susan)))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))=>((~wise(lucy)&kind(lucy))))&
(![X]:(brave(X)<=>(generous(X)&~wise(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~patient(X)|~quiet(X)))))&
((tall(alice))=>((~creative(paul)|~quiet(paul))))&
(![X]:((quiet(X)|kind(X))<=>~patient(X)))&
(((~happy(john)|~wise(john)))<=>(?[X]:((quiet(X)&~curious(X)))))&
((?[X]:(old(X)))<=>(?[X]:(creative(X))))&
(![X]:(funny(X)<=>(~kind(X)|~creative(X))))&
(((~strong(mary)<~>~patient(mary)))<=>(?[X]:(strong(X))))&
((?[X]:((~wise(X)|~calm(X))))<=>((~curious(john)|~calm(john))))&
(![X]:(funny(X)<=>(~calm(X)|humble(X))))&
(![X]:((kind(X)|~rich(X))=>(quiet(X)<~>happy(X))))&
(![X]:((wise(X)&~creative(X))<=>(~generous(X)|~calm(X))))&
(![X]:((~tall(X)|creative(X))=>humble(X)))&
(?[X]:((kind(X)<~>~calm(X))))&
((generous(john)&~creative(john)))&
((~happy(mary)<~>~quiet(mary)))&
((~old(alice)|~creative(alice)))&
(?[X]:((quiet(X)|humble(X))))&
(~rich(fred))&
((funny(lucy)&~tall(lucy)))&
(?[X]:((~wise(X)<~>~humble(X)))) | old(susan) | [
"p0",
"p1",
"p3",
"p7",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6480396992019360824976250
% SZS output start Proof for 6480396992019360824976250
1. ? [X0] : (~calm(X0) & ~brave(X0)) => ~old(susan) [input p0]
2. ? [X0] : (~quiet(X0) <~> ~curious(X0)) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p1]
4. ! [X0] : (brave(X0) <=> (~wise(X0) & generous(X0))) [input p3]
8. (~wise(john) | ~happy(john)) <=> ? [X0] : (~curious(X0) & quiet(X0)) [input p7]
15. ! [X0] : ((~creative(X0) & wise(X0)) <=> (~calm(X0) | ~generous(X0))) [input p14]
18. ~creative(john) & generous(john) [input p17]
25. old(susan) [input hypothesis]
26. ? [X0] : (~quiet(X0) <~> ~curious(X0)) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 2]
29. ~old(susan) | ! [X0] : (calm(X0) | brave(X0)) [ennf transformation 1]
36. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 26]
37. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : ((~quiet(X3) | curious(X3)) & (~curious(X3) | quiet(X3)))) [rectify 36]
38. ? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) => ((curious(sK0) | quiet(sK0)) & (~curious(sK0) | ~quiet(sK0))) [choice axiom]
39. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK1) & funny(sK1)) [choice axiom]
40. (((curious(sK0) | quiet(sK0)) & (~curious(sK0) | ~quiet(sK0))) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK1) & funny(sK1)) | ! [X3] : ((~quiet(X3) | curious(X3)) & (~curious(X3) | quiet(X3)))) [skolemisation 37,39,38]
42. ! [X0] : ((brave(X0) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ~brave(X0))) [nnf transformation 4]
43. ! [X0] : ((brave(X0) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ~brave(X0))) [flattening 42]
49. ((~wise(john) | ~happy(john)) | ! [X0] : (curious(X0) | ~quiet(X0))) & (? [X0] : (~curious(X0) & quiet(X0)) | (wise(john) & happy(john))) [nnf transformation 8]
50. (~wise(john) | ~happy(john) | ! [X0] : (curious(X0) | ~quiet(X0))) & (? [X0] : (~curious(X0) & quiet(X0)) | (wise(john) & happy(john))) [flattening 49]
51. (~wise(john) | ~happy(john) | ! [X0] : (curious(X0) | ~quiet(X0))) & (? [X1] : (~curious(X1) & quiet(X1)) | (wise(john) & happy(john))) [rectify 50]
52. ? [X1] : (~curious(X1) & quiet(X1)) => (~curious(sK3) & quiet(sK3)) [choice axiom]
53. (~wise(john) | ~happy(john) | ! [X0] : (curious(X0) | ~quiet(X0))) & ((~curious(sK3) & quiet(sK3)) | (wise(john) & happy(john))) [skolemisation 51,52]
73. ! [X0] : (((~creative(X0) & wise(X0)) | (calm(X0) & generous(X0))) & ((~calm(X0) | ~generous(X0)) | (creative(X0) | ~wise(X0)))) [nnf transformation 15]
74. ! [X0] : (((~creative(X0) & wise(X0)) | (calm(X0) & generous(X0))) & (~calm(X0) | ~generous(X0) | creative(X0) | ~wise(X0))) [flattening 73]
84. ~old(susan) | calm(X0) | brave(X0) [cnf transformation 29]
86. funny(sK1) | ~quiet(X3) | curious(X3) [cnf transformation 40]
88. ~funny(sK1) | ~quiet(X3) | curious(X3) [cnf transformation 40]
96. ~wise(X0) | ~brave(X0) [cnf transformation 43]
104. quiet(sK3) | wise(john) [cnf transformation 53]
106. ~curious(sK3) | wise(john) [cnf transformation 53]
128. ~generous(X0) | ~calm(X0) | creative(X0) | ~wise(X0) [cnf transformation 74]
130. wise(X0) | calm(X0) [cnf transformation 74]
137. generous(john) [cnf transformation 18]
138. ~creative(john) [cnf transformation 18]
148. old(susan) [cnf transformation 25]
150. 1 <=> ! [X0] : (calm(X0) | brave(X0)) [avatar definition]
151. calm(X0) | brave(X0) <- (1) [avatar component clause 150]
153. 2 <=> old(susan) [avatar definition]
156. 1 | ~2 [avatar split clause 84,153,150]
158. 3 <=> ! [X3] : (~quiet(X3) | curious(X3)) [avatar definition]
159. ~quiet(X3) | curious(X3) <- (3) [avatar component clause 158]
161. 4 <=> funny(sK1) [avatar definition]
164. 3 | ~4 [avatar split clause 88,161,158]
169. 3 | 4 [avatar split clause 86,161,158]
219. 17 <=> wise(john) [avatar definition]
220. wise(john) <- (17) [avatar component clause 219]
224. 18 <=> curious(sK3) [avatar definition]
226. ~curious(sK3) <- (~18) [avatar component clause 224]
227. 17 | ~18 [avatar split clause 106,224,219]
230. 19 <=> quiet(sK3) [avatar definition]
232. quiet(sK3) <- (19) [avatar component clause 230]
233. 17 | 19 [avatar split clause 104,230,219]
289. 32 <=> ! [X1] : calm(X1) [avatar definition]
290. calm(X1) <- (32) [avatar component clause 289]
344. 2 [avatar split clause 148,153]
359. calm(X0) | ~brave(X0) [resolution 130,96]
363. calm(X0) <- (1) [subsumption resolution 359,151]
364. 32 | ~1 [avatar split clause 363,150,289]
435. curious(sK3) <- (3, 19) [resolution 232,159]
436. $false <- (3, ~18, 19) [subsumption resolution 435,226]
437. ~3 | 18 | ~19 [avatar contradiction clause 436]
473. ~calm(john) | creative(john) | ~wise(john) [resolution 128,137]
477. creative(john) | ~wise(john) <- (32) [subsumption resolution 473,290]
478. ~wise(john) <- (32) [subsumption resolution 477,138]
479. $false <- (17, 32) [subsumption resolution 478,220]
480. ~17 | ~32 [avatar contradiction clause 479]
481. $false [avatar sat refutation 156,164,169,227,233,344,364,437,480]
% SZS output end Proof for 6480396992019360824976250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is happy or creative then someone is either not calm or humble.
Everyone who is both wise and kind is happy.
Everyone who is either not funny or rich is both old and rich and vice versa.
Everyone who is both not kind and kind is either not wise or humble and vice versa.
If someone is not brave or brave then alice is either kind or rich.
Everyone who is old or happy is funny.
Everyone who is not funny or not creative is both not patient and old.
Everyone who is both not old and not curious is not humble.
If someone is both not funny and humble then john is either not rich or calm.
Everyone who is both not generous and quiet is not wise or not creative and vice versa.
If susan is either old or brave then john is not calm or patient and vice versa.
Everyone who is either not brave or not rich is patient or not quiet and vice versa.
Everyone who is not wise or strong is generous and vice versa.
Everyone who is rich is both funny and tall and vice versa.
Everyone who is patient or not rich is not creative and vice versa.
Everyone who is not patient or not tall is either not tall or tall and vice versa.
John is both wise and creative.
Someone is both creative and rich.
Alice is either not quiet or humble.
Someone is both generous and curious.
Someone is kind or funny.
Fred is curious.
Someone is not happy.
Alice is either not creative or calm. | Alice is patient. | contradiction | (((happy(lucy)|creative(lucy)))=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:((wise(X)&kind(X))=>happy(X)))&
(![X]:((~funny(X)<~>rich(X))<=>(old(X)&rich(X))))&
(![X]:((~kind(X)&kind(X))<=>(~wise(X)<~>humble(X))))&
((?[X]:((~brave(X)|brave(X))))=>((kind(alice)<~>rich(alice))))&
(![X]:((old(X)|happy(X))=>funny(X)))&
(![X]:((~funny(X)|~creative(X))=>(~patient(X)&old(X))))&
(![X]:((~old(X)&~curious(X))=>~humble(X)))&
((?[X]:((~funny(X)&humble(X))))=>((~rich(john)<~>calm(john))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~creative(X))))&
(((old(susan)<~>brave(susan)))<=>((~calm(john)|patient(john))))&
(![X]:((~brave(X)<~>~rich(X))<=>(patient(X)|~quiet(X))))&
(![X]:((~wise(X)|strong(X))<=>generous(X)))&
(![X]:(rich(X)<=>(funny(X)&tall(X))))&
(![X]:((patient(X)|~rich(X))<=>~creative(X)))&
(![X]:((~patient(X)|~tall(X))<=>(~tall(X)<~>tall(X))))&
((wise(john)&creative(john)))&
(?[X]:((creative(X)&rich(X))))&
((~quiet(alice)<~>humble(alice)))&
(?[X]:((generous(X)&curious(X))))&
(?[X]:((kind(X)|funny(X))))&
(curious(fred))&
(?[X]:(~happy(X)))&
((~creative(alice)<~>calm(alice))) | patient(alice) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3233738491715683730777162
% SZS output start Proof for 3233738491715683730777162
7. ! [X0] : ((~creative(X0) | ~funny(X0)) => (old(X0) & ~patient(X0))) [input p6]
15. ! [X0] : ((~rich(X0) | patient(X0)) <=> ~creative(X0)) [input p14]
25. patient(alice) [input hypothesis]
34. ! [X0] : ((old(X0) & ~patient(X0)) | (creative(X0) & funny(X0))) [ennf transformation 7]
55. ! [X0] : (((~rich(X0) | patient(X0)) | creative(X0)) & (~creative(X0) | (rich(X0) & ~patient(X0)))) [nnf transformation 15]
56. ! [X0] : ((~rich(X0) | patient(X0) | creative(X0)) & (~creative(X0) | (rich(X0) & ~patient(X0)))) [flattening 55]
93. ~patient(X0) | creative(X0) [cnf transformation 34]
121. ~creative(X0) | ~patient(X0) [cnf transformation 56]
141. patient(alice) [cnf transformation 25]
215. ~patient(X0) [subsumption resolution 121,93]
236. $false [subsumption resolution 141,215]
% SZS output end Proof for 3233738491715683730777162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then lucy is not curious or not creative. Everyone who is either not tall or not kind is not funny or creative and vice versa. Everyone who is not quiet or creative is strong. Everyone who is not happy or happy is patient or not generous and vice versa. Everyone who is not funny is not calm and vice versa. Everyone who is either not kind or not creative is old or calm. If mary is both not brave and quiet then someone is either old or not happy. Everyone who is not brave is not kind or strong. If someone is either generous or not tall then someone is curious or not patient. Everyone who is funny or not calm is both not brave and curious and vice versa. If susan is rich then someone is old or kind. If fred is both not old and rich then someone is both not kind and wise and vice versa. If someone is not curious then someone is creative or rich and vice versa. Everyone who is not rich or not curious is tall. If susan is either wise or generous then lucy is either not funny or tall and vice versa. Everyone who is not patient or not humble is either creative or tall and vice versa. John is curious or patient. Mary is strong or quiet. Someone is both not calm and not kind. Someone is either creative or kind. Someone is both curious and kind. John is either kind or not kind. | Fred is creative. | contradiction | ((?[X]:(quiet(X)))=>((~curious(lucy)|~creative(lucy))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~funny(X)|creative(X))))&
(![X]:((~quiet(X)|creative(X))=>strong(X)))&
(![X]:((~happy(X)|happy(X))<=>(patient(X)|~generous(X))))&
(![X]:(~funny(X)<=>~calm(X)))&
(![X]:((~kind(X)<~>~creative(X))=>(old(X)|calm(X))))&
(((~brave(mary)&quiet(mary)))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:(~brave(X)=>(~kind(X)|strong(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~brave(X)&curious(X))))&
((rich(susan))=>(?[X]:((old(X)|kind(X)))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
((curious(john)|patient(john)))&
((strong(mary)|quiet(mary)))&
(?[X]:((~calm(X)&~kind(X))))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:((curious(X)&kind(X))))&
((kind(john)<~>~kind(john))) | creative(fred) | [
"p4",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5908032839658604745986154
% SZS output start Proof for 5908032839658604745986154
5. ! [X0] : (~funny(X0) <=> ~calm(X0)) [input p4]
10. ! [X0] : ((~calm(X0) | funny(X0)) <=> (curious(X0) & ~brave(X0))) [input p9]
13. ? [X0] : ~curious(X0) <=> ? [X0] : (rich(X0) | creative(X0)) [input p12]
23. creative(fred) [input hypothesis]
25. ? [X0] : ~curious(X0) <=> ? [X1] : (rich(X1) | creative(X1)) [rectify 13]
40. ! [X0] : ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))) [nnf transformation 5]
46. ! [X0] : (((~calm(X0) | funny(X0)) | (~curious(X0) | brave(X0))) & ((curious(X0) & ~brave(X0)) | (calm(X0) & ~funny(X0)))) [nnf transformation 10]
47. ! [X0] : ((~calm(X0) | funny(X0) | ~curious(X0) | brave(X0)) & ((curious(X0) & ~brave(X0)) | (calm(X0) & ~funny(X0)))) [flattening 46]
55. (? [X0] : ~curious(X0) | ! [X1] : (~rich(X1) & ~creative(X1))) & (? [X1] : (rich(X1) | creative(X1)) | ! [X0] : curious(X0)) [nnf transformation 25]
56. (? [X0] : ~curious(X0) | ! [X1] : (~rich(X1) & ~creative(X1))) & (? [X2] : (rich(X2) | creative(X2)) | ! [X3] : curious(X3)) [rectify 55]
57. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
58. ? [X2] : (rich(X2) | creative(X2)) => (rich(sK4) | creative(sK4)) [choice axiom]
59. (~curious(sK3) | ! [X1] : (~rich(X1) & ~creative(X1))) & ((rich(sK4) | creative(sK4)) | ! [X3] : curious(X3)) [skolemisation 56,58,57]
81. ~calm(X0) | funny(X0) [cnf transformation 40]
89. ~funny(X0) | curious(X0) [cnf transformation 47]
90. calm(X0) | curious(X0) [cnf transformation 47]
98. ~curious(sK3) | ~creative(X1) [cnf transformation 59]
125. creative(fred) [cnf transformation 23]
183. 14 <=> curious(sK3) [avatar definition]
185. ~curious(sK3) <- (~14) [avatar component clause 183]
188. 15 <=> ! [X1] : ~creative(X1) [avatar definition]
189. ~creative(X1) <- (15) [avatar component clause 188]
190. 15 | ~14 [avatar split clause 98,183,188]
192. 16 <=> ! [X3] : curious(X3) [avatar definition]
193. curious(X3) <- (16) [avatar component clause 192]
246. $false <- (~14, 16) [subsumption resolution 185,193]
247. 14 | ~16 [avatar contradiction clause 246]
248. $false <- (15) [resolution 189,125]
249. ~15 [avatar contradiction clause 248]
251. curious(X0) | funny(X0) [resolution 90,81]
252. curious(X0) [subsumption resolution 251,89]
253. 16 [avatar split clause 252,192]
254. $false [avatar sat refutation 190,247,249,253]
% SZS output end Proof for 5908032839658604745986154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or not kind then alice is kind or brave.
Everyone who is rich is not rich.
If someone is funny then someone is funny or not generous.
Everyone who is either happy or kind is not funny and vice versa.
Everyone who is quiet is both generous and wise and vice versa.
If alice is both quiet and creative then someone is not tall and vice versa.
Everyone who is not tall or humble is humble or not generous.
Everyone who is not quiet is tall or rich and vice versa.
Everyone who is not strong is not old or not calm.
If someone is old or not rich then someone is either kind or quiet.
Everyone who is humble is curious and vice versa.
If someone is not brave or old then someone is curious and vice versa.
If lucy is calm then mary is not rich and vice versa.
If someone is both happy and strong then mary is not rich.
If mary is either not old or not rich then someone is both rich and not generous and vice versa.
Everyone who is generous is quiet and vice versa.
Lucy is both wise and kind.
Someone is both brave and not quiet.
Susan is not funny or not tall.
Fred is tall or not quiet.
John is patient.
Susan is happy.
Alice is both not funny and old.
Someone is not humble or rich. | Alice is old. | entailment | ((?[X]:((~patient(X)<~>~kind(X))))=>((kind(alice)|brave(alice))))&
(![X]:(rich(X)=>~rich(X)))&
((?[X]:(funny(X)))=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((happy(X)<~>kind(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(generous(X)&wise(X))))&
(((quiet(alice)&creative(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|humble(X))=>(humble(X)|~generous(X))))&
(![X]:(~quiet(X)<=>(tall(X)|rich(X))))&
(![X]:(~strong(X)=>(~old(X)|~calm(X))))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:(humble(X)<=>curious(X)))&
((?[X]:((~brave(X)|old(X))))<=>(?[X]:(curious(X))))&
((calm(lucy))<=>(~rich(mary)))&
((?[X]:((happy(X)&strong(X))))=>(~rich(mary)))&
(((~old(mary)<~>~rich(mary)))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(generous(X)<=>quiet(X)))&
((wise(lucy)&kind(lucy)))&
(?[X]:((brave(X)&~quiet(X))))&
((~funny(susan)|~tall(susan)))&
((tall(fred)|~quiet(fred)))&
(patient(john))&
(happy(susan))&
((~funny(alice)&old(alice)))&
(?[X]:((~humble(X)|rich(X)))) | old(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6061321642665063305680672
% SZS output start Proof for 6061321642665063305680672
23. old(alice) & ~funny(alice) [input p22]
25. ~old(alice) [input hypothesis]
122. old(alice) [cnf transformation 23]
124. ~old(alice) [cnf transformation 25]
236. $false [subsumption resolution 124,122]
% SZS output end Proof for 6061321642665063305680672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or tall is both not humble and not brave. Everyone who is either not wise or not tall is not curious or old. Everyone who is either tall or not strong is both humble and old and vice versa. Everyone who is not funny is either happy or not kind. Everyone who is both not patient and not strong is either strong or kind and vice versa. Everyone who is both not humble and not quiet is either kind or not tall and vice versa. If susan is either strong or rich then someone is either creative or not curious. Everyone who is kind is either strong or not patient and vice versa. Everyone who is both not strong and not happy is either not calm or strong. Everyone who is kind or not curious is funny or not curious and vice versa. If alice is both kind and not creative then john is tall and vice versa. If paul is either old or not curious then susan is either strong or not strong and vice versa. If mary is patient or quiet then someone is either not calm or rich and vice versa. If someone is creative or curious then john is both not old and happy. If mary is not rich then someone is not humble or not happy and vice versa. If alice is both quiet and not rich then someone is both calm and tall and vice versa. Lucy is both not patient and not calm. Fred is both not old and funny. Susan is not humble. Susan is both kind and old. Someone is curious. Someone is both quiet and generous. Someone is not happy. Someone is both not brave and creative. | John is happy. | entailment | (![X]:((~patient(X)|tall(X))=>(~humble(X)&~brave(X))))&
(![X]:((~wise(X)<~>~tall(X))=>(~curious(X)|old(X))))&
(![X]:((tall(X)<~>~strong(X))<=>(humble(X)&old(X))))&
(![X]:(~funny(X)=>(happy(X)<~>~kind(X))))&
(![X]:((~patient(X)&~strong(X))<=>(strong(X)<~>kind(X))))&
(![X]:((~humble(X)&~quiet(X))<=>(kind(X)<~>~tall(X))))&
(((strong(susan)<~>rich(susan)))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(kind(X)<=>(strong(X)<~>~patient(X))))&
(![X]:((~strong(X)&~happy(X))=>(~calm(X)<~>strong(X))))&
(![X]:((kind(X)|~curious(X))<=>(funny(X)|~curious(X))))&
(((kind(alice)&~creative(alice)))<=>(tall(john)))&
(((old(paul)<~>~curious(paul)))<=>((strong(susan)<~>~strong(susan))))&
(((patient(mary)|quiet(mary)))<=>(?[X]:((~calm(X)<~>rich(X)))))&
((?[X]:((creative(X)|curious(X))))=>((~old(john)&happy(john))))&
((~rich(mary))<=>(?[X]:((~humble(X)|~happy(X)))))&
(((quiet(alice)&~rich(alice)))<=>(?[X]:((calm(X)&tall(X)))))&
((~patient(lucy)&~calm(lucy)))&
((~old(fred)&funny(fred)))&
(~humble(susan))&
((kind(susan)&old(susan)))&
(?[X]:(curious(X)))&
(?[X]:((quiet(X)&generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~brave(X)&creative(X)))) | happy(john) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2721669206347484341943322
% SZS output start Proof for 2721669206347484341943322
14. ? [X0] : (curious(X0) | creative(X0)) => (happy(john) & ~old(john)) [input p13]
21. ? [X0] : curious(X0) [input p20]
25. ~happy(john) [input hypothesis]
36. (happy(john) & ~old(john)) | ! [X0] : (~curious(X0) & ~creative(X0)) [ennf transformation 14]
69. ? [X0] : curious(X0) => curious(sK4) [choice axiom]
70. curious(sK4) [skolemisation 21,69]
135. happy(john) | ~curious(X0) [cnf transformation 36]
150. curious(sK4) [cnf transformation 70]
154. ~happy(john) [cnf transformation 25]
244. 16 <=> ! [X0] : ~curious(X0) [avatar definition]
245. ~curious(X0) <- (16) [avatar component clause 244]
247. 17 <=> happy(john) [avatar definition]
250. 16 | 17 [avatar split clause 135,247,244]
305. ~17 [avatar split clause 154,247]
306. $false <- (16) [resolution 245,150]
307. ~16 [avatar contradiction clause 306]
308. $false [avatar sat refutation 250,305,307]
% SZS output end Proof for 2721669206347484341943322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not creative or not happy then mary is not funny.
Everyone who is not wise is both not calm and not funny.
If alice is both not strong and curious then john is either brave or patient and vice versa.
Everyone who is both not old and not strong is both old and not kind and vice versa.
If alice is calm or creative then someone is humble.
If someone is creative or generous then lucy is not humble or funny and vice versa.
Everyone who is not humble or not brave is both not patient and generous and vice versa.
If fred is both not generous and tall then someone is not brave or not funny and vice versa.
If john is either creative or wise then someone is either humble or curious.
If someone is wise then someone is funny or patient and vice versa.
Everyone who is not creative is both not generous and tall and vice versa.
If lucy is either not calm or not tall then john is either not kind or funny.
Everyone who is not quiet is both not funny and rich and vice versa.
If someone is not funny then someone is patient or generous.
Everyone who is not old or quiet is both patient and not wise and vice versa.
If someone is both not rich and not patient then alice is not generous.
Someone is either not kind or not old.
Someone is both not tall and happy.
Someone is not strong or strong.
Someone is humble.
Someone is patient or not quiet.
Mary is either brave or creative.
Susan is both not wise and not funny.
Someone is either not quiet or calm. | Lucy is not patient. | entailment | (((~creative(john)<~>~happy(john)))=>(~funny(mary)))&
(![X]:(~wise(X)=>(~calm(X)&~funny(X))))&
(((~strong(alice)&curious(alice)))<=>((brave(john)<~>patient(john))))&
(![X]:((~old(X)&~strong(X))<=>(old(X)&~kind(X))))&
(((calm(alice)|creative(alice)))=>(?[X]:(humble(X))))&
((?[X]:((creative(X)|generous(X))))<=>((~humble(lucy)|funny(lucy))))&
(![X]:((~humble(X)|~brave(X))<=>(~patient(X)&generous(X))))&
(((~generous(fred)&tall(fred)))<=>(?[X]:((~brave(X)|~funny(X)))))&
(((creative(john)<~>wise(john)))=>(?[X]:((humble(X)<~>curious(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:(~creative(X)<=>(~generous(X)&tall(X))))&
(((~calm(lucy)<~>~tall(lucy)))=>((~kind(john)<~>funny(john))))&
(![X]:(~quiet(X)<=>(~funny(X)&rich(X))))&
((?[X]:(~funny(X)))=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~old(X)|quiet(X))<=>(patient(X)&~wise(X))))&
((?[X]:((~rich(X)&~patient(X))))=>(~generous(alice)))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|~quiet(X))))&
((brave(mary)<~>creative(mary)))&
((~wise(susan)&~funny(susan)))&
(?[X]:((~quiet(X)<~>calm(X)))) | ~patient(lucy) | [
"p1",
"p5",
"p6",
"p10",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8088811359643908908203391
% SZS output start Proof for 8088811359643908908203391
2. ! [X0] : (~wise(X0) => (~funny(X0) & ~calm(X0))) [input p1]
6. ? [X0] : (generous(X0) | creative(X0)) <=> (funny(lucy) | ~humble(lucy)) [input p5]
7. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> (generous(X0) & ~patient(X0))) [input p6]
11. ! [X0] : (~creative(X0) <=> (tall(X0) & ~generous(X0))) [input p10]
13. ! [X0] : (~quiet(X0) <=> (rich(X0) & ~funny(X0))) [input p12]
15. ! [X0] : ((quiet(X0) | ~old(X0)) <=> (~wise(X0) & patient(X0))) [input p14]
18. ? [X0] : (happy(X0) & ~tall(X0)) [input p17]
25. patient(lucy) [input hypothesis]
29. ! [X0] : ((~funny(X0) & ~calm(X0)) | wise(X0)) [ennf transformation 2]
42. (? [X0] : (generous(X0) | creative(X0)) | (~funny(lucy) & humble(lucy))) & ((funny(lucy) | ~humble(lucy)) | ! [X0] : (~generous(X0) & ~creative(X0))) [nnf transformation 6]
43. (? [X0] : (generous(X0) | creative(X0)) | (~funny(lucy) & humble(lucy))) & (funny(lucy) | ~humble(lucy) | ! [X0] : (~generous(X0) & ~creative(X0))) [flattening 42]
44. (? [X0] : (generous(X0) | creative(X0)) | (~funny(lucy) & humble(lucy))) & (funny(lucy) | ~humble(lucy) | ! [X1] : (~generous(X1) & ~creative(X1))) [rectify 43]
45. ? [X0] : (generous(X0) | creative(X0)) => (generous(sK1) | creative(sK1)) [choice axiom]
46. ((generous(sK1) | creative(sK1)) | (~funny(lucy) & humble(lucy))) & (funny(lucy) | ~humble(lucy) | ! [X1] : (~generous(X1) & ~creative(X1))) [skolemisation 44,45]
47. ! [X0] : (((~brave(X0) | ~humble(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [nnf transformation 7]
48. ! [X0] : ((~brave(X0) | ~humble(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [flattening 47]
62. ! [X0] : ((~creative(X0) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | creative(X0))) [nnf transformation 11]
63. ! [X0] : ((~creative(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | creative(X0))) [flattening 62]
65. ! [X0] : ((~quiet(X0) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | quiet(X0))) [nnf transformation 13]
66. ! [X0] : ((~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | quiet(X0))) [flattening 65]
70. ! [X0] : (((quiet(X0) | ~old(X0)) | (wise(X0) | ~patient(X0))) & ((~wise(X0) & patient(X0)) | (~quiet(X0) & old(X0)))) [nnf transformation 15]
71. ! [X0] : ((quiet(X0) | ~old(X0) | wise(X0) | ~patient(X0)) & ((~wise(X0) & patient(X0)) | (~quiet(X0) & old(X0)))) [flattening 70]
75. ? [X0] : (happy(X0) & ~tall(X0)) => (happy(sK8) & ~tall(sK8)) [choice axiom]
76. happy(sK8) & ~tall(sK8) [skolemisation 18,75]
90. ~funny(X0) | wise(X0) [cnf transformation 29]
103. funny(lucy) | ~humble(lucy) | ~creative(X1) [cnf transformation 46]
107. ~patient(X0) | humble(X0) [cnf transformation 48]
125. tall(X0) | creative(X0) [cnf transformation 63]
131. ~funny(X0) | quiet(X0) [cnf transformation 66]
138. ~quiet(X0) | ~wise(X0) [cnf transformation 71]
143. ~tall(sK8) [cnf transformation 76]
154. patient(lucy) [cnf transformation 25]
208. 11 <=> funny(lucy) [avatar definition]
209. funny(lucy) <- (11) [avatar component clause 208]
221. 14 <=> humble(lucy) [avatar definition]
230. 16 <=> ! [X1] : ~creative(X1) [avatar definition]
231. ~creative(X1) <- (16) [avatar component clause 230]
232. 16 | ~14 | 11 [avatar split clause 103,208,221,230]
368. humble(lucy) [resolution 107,154]
372. 14 [avatar split clause 368,221]
373. wise(lucy) <- (11) [resolution 209,90]
382. creative(sK8) [resolution 125,143]
385. quiet(lucy) <- (11) [resolution 131,209]
396. ~wise(lucy) <- (11) [resolution 138,385]
399. $false <- (11) [subsumption resolution 396,373]
400. ~11 [avatar contradiction clause 399]
405. $false <- (16) [resolution 231,382]
408. ~16 [avatar contradiction clause 405]
410. $false [avatar sat refutation 232,372,400,408]
% SZS output end Proof for 8088811359643908908203391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not calm is funny and vice versa. If someone is not calm or kind then someone is old. Everyone who is either calm or not wise is both not calm and kind and vice versa. If someone is generous then alice is both curious and rich and vice versa. If someone is both not brave and kind then someone is not curious or not generous and vice versa. If someone is not kind or strong then someone is both not old and not creative. Everyone who is calm is patient or not happy. Everyone who is patient is not wise or not old and vice versa. Everyone who is either not rich or rich is not patient or strong and vice versa. Everyone who is either creative or curious is humble or not quiet. If someone is either humble or not kind then alice is not wise or wise and vice versa. Everyone who is both funny and rich is either not quiet or not patient and vice versa. Everyone who is tall or not generous is not calm or creative. Everyone who is not strong is not quiet and vice versa. If someone is either generous or not humble then susan is not old and vice versa. Everyone who is either happy or funny is curious or happy and vice versa. Someone is both happy and patient. Someone is either wise or not brave. Someone is both tall and not funny. Susan is not generous or happy. Someone is either not patient or not humble. Someone is both patient and kind. Paul is both old and tall. Someone is both not funny and brave. | Susan is funny. | neutral | (![X]:((~humble(X)&~calm(X))<=>funny(X)))&
((?[X]:((~calm(X)|kind(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~calm(X)&kind(X))))&
((?[X]:(generous(X)))<=>((curious(alice)&rich(alice))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:((~kind(X)|strong(X))))=>(?[X]:((~old(X)&~creative(X)))))&
(![X]:(calm(X)=>(patient(X)|~happy(X))))&
(![X]:(patient(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~patient(X)|strong(X))))&
(![X]:((creative(X)<~>curious(X))=>(humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((tall(X)&~funny(X))))&
((~generous(susan)|happy(susan)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((patient(X)&kind(X))))&
((old(paul)&tall(paul)))&
(?[X]:((~funny(X)&brave(X)))) | funny(susan) | [] | null | 0 |
If susan is either not calm or not kind then someone is not generous and vice versa.
Everyone who is either quiet or not brave is not old or not calm and vice versa.
Everyone who is not rich or not calm is both not humble and happy.
If fred is kind then susan is both not calm and not patient.
If john is both patient and calm then someone is both wise and brave and vice versa.
Everyone who is tall is either not creative or kind and vice versa.
If someone is both not kind and not creative then someone is either not calm or not wise.
If john is both generous and not generous then mary is tall or rich.
Everyone who is wise is both happy and not generous and vice versa.
If someone is either not rich or not strong then someone is either not wise or calm and vice versa.
If someone is either not quiet or not strong then fred is either rich or old.
Everyone who is not rich or not happy is either not old or not kind.
If john is either generous or strong then john is creative and vice versa.
Everyone who is not wise or not generous is not calm or brave.
If alice is strong then someone is either not calm or wise and vice versa.
Everyone who is kind or brave is both not tall and not generous and vice versa.
Mary is both not calm and not old.
Fred is quiet.
Alice is either strong or creative.
John is either not calm or not wise.
Someone is not rich.
Mary is not quiet or not curious.
Fred is both not creative and not strong. | Alice is tall. | neutral | (((~calm(susan)<~>~kind(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~old(X)|~calm(X))))&
(![X]:((~rich(X)|~calm(X))=>(~humble(X)&happy(X))))&
((kind(fred))=>((~calm(susan)&~patient(susan))))&
(((patient(john)&calm(john)))<=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(tall(X)<=>(~creative(X)<~>kind(X))))&
((?[X]:((~kind(X)&~creative(X))))=>(?[X]:((~calm(X)<~>~wise(X)))))&
(((generous(john)&~generous(john)))=>((tall(mary)|rich(mary))))&
(![X]:(wise(X)<=>(happy(X)&~generous(X))))&
((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:((~wise(X)<~>calm(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))=>((rich(fred)<~>old(fred))))&
(![X]:((~rich(X)|~happy(X))=>(~old(X)<~>~kind(X))))&
(((generous(john)<~>strong(john)))<=>(creative(john)))&
(![X]:((~wise(X)|~generous(X))=>(~calm(X)|brave(X))))&
((strong(alice))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((kind(X)|brave(X))<=>(~tall(X)&~generous(X))))&
((~calm(mary)&~old(mary)))&
(quiet(fred))&
((strong(alice)<~>creative(alice)))&
((~calm(john)<~>~wise(john)))&
(?[X]:(~rich(X)))&
((~quiet(mary)|~curious(mary)))&
((~creative(fred)&~strong(fred))) | tall(alice) | [] | null | 0 |
If lucy is old or not generous then paul is either funny or not quiet.
Everyone who is not funny is patient or tall.
Everyone who is either not creative or not quiet is either rich or not brave and vice versa.
If someone is generous then someone is both not creative and old.
Everyone who is generous or not funny is either not calm or not humble and vice versa.
Everyone who is happy or brave is both not creative and not rich and vice versa.
Everyone who is happy is not funny or kind.
Everyone who is both not brave and generous is strong or not rich.
If alice is both brave and quiet then someone is not humble or not happy and vice versa.
Everyone who is both not rich and not kind is both not happy and calm.
Everyone who is not patient is both quiet and not creative and vice versa.
Everyone who is both not wise and not curious is not happy or not rich.
If someone is happy then someone is either not curious or not generous and vice versa.
If someone is both not curious and humble then someone is both not kind and wise.
If someone is quiet or rich then someone is either happy or kind.
If fred is both not patient and not happy then someone is either not strong or tall.
John is wise.
Someone is either not quiet or quiet.
Someone is either not rich or not calm.
Someone is either generous or wise. | Paul is not brave. | contradiction | (((old(lucy)|~generous(lucy)))=>((funny(paul)<~>~quiet(paul))))&
(![X]:(~funny(X)=>(patient(X)|tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(rich(X)<~>~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((generous(X)|~funny(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((happy(X)|brave(X))<=>(~creative(X)&~rich(X))))&
(![X]:(happy(X)=>(~funny(X)|kind(X))))&
(![X]:((~brave(X)&generous(X))=>(strong(X)|~rich(X))))&
(((brave(alice)&quiet(alice)))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~rich(X)&~kind(X))=>(~happy(X)&calm(X))))&
(![X]:(~patient(X)<=>(quiet(X)&~creative(X))))&
(![X]:((~wise(X)&~curious(X))=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:((happy(X)<~>kind(X)))))&
(((~patient(fred)&~happy(fred)))=>(?[X]:((~strong(X)<~>tall(X)))))&
(wise(john))&
(?[X]:((~quiet(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>wise(X)))) | ~brave(paul) | [
"p2",
"p5",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7399393683113325936175330
% SZS output start Proof for 7399393683113325936175330
3. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p2]
6. ! [X0] : ((brave(X0) | happy(X0)) <=> (~rich(X0) & ~creative(X0))) [input p5]
9. (quiet(alice) & brave(alice)) <=> ? [X0] : (~happy(X0) | ~humble(X0)) [input p8]
10. ! [X0] : ((~kind(X0) & ~rich(X0)) => (calm(X0) & ~happy(X0))) [input p9]
15. ? [X0] : (rich(X0) | quiet(X0)) => ? [X0] : (happy(X0) <~> kind(X0)) [input p14]
21. ~brave(paul) [input hypothesis]
25. ? [X0] : (rich(X0) | quiet(X0)) => ? [X1] : (happy(X1) <~> kind(X1)) [rectify 15]
35. ! [X0] : ((calm(X0) & ~happy(X0)) | (kind(X0) | rich(X0))) [ennf transformation 10]
36. ! [X0] : ((calm(X0) & ~happy(X0)) | kind(X0) | rich(X0)) [flattening 35]
42. ? [X1] : (happy(X1) <~> kind(X1)) | ! [X0] : (~rich(X0) & ~quiet(X0)) [ennf transformation 25]
46. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 3]
52. ! [X0] : (((brave(X0) | happy(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 6]
53. ! [X0] : ((brave(X0) | happy(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 52]
54. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X0] : (~happy(X0) | ~humble(X0)) | (~quiet(alice) | ~brave(alice))) [nnf transformation 9]
55. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X0] : (~happy(X0) | ~humble(X0)) | ~quiet(alice) | ~brave(alice)) [flattening 54]
56. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X1] : (~happy(X1) | ~humble(X1)) | ~quiet(alice) | ~brave(alice)) [rectify 55]
57. ? [X1] : (~happy(X1) | ~humble(X1)) => (~happy(sK1) | ~humble(sK1)) [choice axiom]
58. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & ((~happy(sK1) | ~humble(sK1)) | ~quiet(alice) | ~brave(alice)) [skolemisation 56,57]
67. ? [X1] : ((~kind(X1) | ~happy(X1)) & (kind(X1) | happy(X1))) | ! [X0] : (~rich(X0) & ~quiet(X0)) [nnf transformation 42]
68. ? [X0] : ((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | ! [X1] : (~rich(X1) & ~quiet(X1)) [rectify 67]
69. ? [X0] : ((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) => ((~kind(sK5) | ~happy(sK5)) & (kind(sK5) | happy(sK5))) [choice axiom]
70. ((~kind(sK5) | ~happy(sK5)) & (kind(sK5) | happy(sK5))) | ! [X1] : (~rich(X1) & ~quiet(X1)) [skolemisation 68,69]
88. ~brave(X0) | rich(X0) | ~quiet(X0) | creative(X0) [cnf transformation 46]
95. brave(X0) | creative(X0) | rich(X0) | quiet(X0) [cnf transformation 46]
104. ~happy(X0) | ~creative(X0) [cnf transformation 53]
105. ~brave(X0) | ~creative(X0) [cnf transformation 53]
106. ~happy(X0) | ~rich(X0) [cnf transformation 53]
107. ~brave(X0) | ~rich(X0) [cnf transformation 53]
113. brave(alice) | happy(X0) [cnf transformation 58]
115. quiet(alice) | happy(X0) [cnf transformation 58]
116. ~happy(X0) | kind(X0) | rich(X0) [cnf transformation 36]
128. ~kind(sK5) | ~happy(sK5) | ~quiet(X1) [cnf transformation 70]
129. ~kind(sK5) | ~happy(sK5) | ~rich(X1) [cnf transformation 70]
139. ~brave(paul) [cnf transformation 21]
175. 8 <=> ! [X0] : happy(X0) [avatar definition]
176. happy(X0) <- (8) [avatar component clause 175]
178. 9 <=> quiet(alice) [avatar definition]
181. 8 | 9 [avatar split clause 115,178,175]
187. 11 <=> brave(alice) [avatar definition]
189. brave(alice) <- (11) [avatar component clause 187]
190. 8 | 11 [avatar split clause 113,187,175]
201. ~happy(X0) | kind(X0) [subsumption resolution 116,106]
240. ~happy(sK5) | ~rich(X1) [subsumption resolution 129,201]
242. 23 <=> ! [X1] : ~rich(X1) [avatar definition]
243. ~rich(X1) <- (23) [avatar component clause 242]
245. 24 <=> happy(sK5) [avatar definition]
247. ~happy(sK5) <- (~24) [avatar component clause 245]
248. 23 | ~24 [avatar split clause 240,245,242]
249. ~happy(sK5) | ~quiet(X1) [subsumption resolution 128,201]
251. 25 <=> ! [X1] : ~quiet(X1) [avatar definition]
252. ~quiet(X1) <- (25) [avatar component clause 251]
253. 25 | ~24 [avatar split clause 249,245,251]
313. $false <- (8, ~24) [subsumption resolution 247,176]
314. ~8 | 24 [avatar contradiction clause 313]
318. ~creative(alice) <- (11) [resolution 105,189]
320. ~rich(alice) <- (11) [resolution 107,189]
351. rich(alice) | ~quiet(alice) | creative(alice) <- (11) [resolution 88,189]
352. ~quiet(alice) | creative(alice) <- (11) [subsumption resolution 351,320]
356. ~quiet(alice) <- (11) [subsumption resolution 352,318]
357. ~9 | ~11 [avatar split clause 356,187,178]
362. ~creative(X3) <- (8) [resolution 176,104]
373. creative(paul) | rich(paul) | quiet(paul) [resolution 95,139]
383. rich(paul) | quiet(paul) <- (8) [subsumption resolution 373,362]
384. quiet(paul) <- (8, 23) [subsumption resolution 383,243]
387. $false <- (8, 23, 25) [subsumption resolution 384,252]
388. ~8 | ~23 | ~25 [avatar contradiction clause 387]
393. $false [avatar sat refutation 181,190,248,253,314,357,388]
% SZS output end Proof for 7399393683113325936175330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is 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 generous. | 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))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not creative or not rich is generous and vice versa. Everyone who is either not rich or strong is both happy and not creative. If paul is both curious and not wise then someone is happy and vice versa. If fred is either not rich or not creative then someone is either patient or strong and vice versa. If mary is tall or not wise then someone is kind or creative and vice versa. If someone is either brave or patient then someone is creative and vice versa. Everyone who is calm is happy or not patient. If lucy is tall then someone is both patient and quiet. If someone is creative or humble then someone is either tall or kind and vice versa. If someone is not happy then mary is either humble or tall. Everyone who is either not happy or not humble is either not funny or not strong. Everyone who is either rich or tall is both generous and calm. Everyone who is either not patient or not creative is not patient. If someone is either tall or calm then someone is both kind and old and vice versa. Everyone who is generous or curious is either not brave or old and vice versa. Everyone who is both strong and not creative is not happy or happy and vice versa. Someone is tall or not calm. Lucy is not brave or not patient. Mary is not curious. Someone is not wise or not strong. Someone is both not patient and not humble. Mary is not curious or calm. | Lucy is not creative. | entailment | (![X]:((~creative(X)<~>~rich(X))<=>generous(X)))&
(![X]:((~rich(X)<~>strong(X))=>(happy(X)&~creative(X))))&
(((curious(paul)&~wise(paul)))<=>(?[X]:(happy(X))))&
(((~rich(fred)<~>~creative(fred)))<=>(?[X]:((patient(X)<~>strong(X)))))&
(((tall(mary)|~wise(mary)))<=>(?[X]:((kind(X)|creative(X)))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:(creative(X))))&
(![X]:(calm(X)=>(happy(X)|~patient(X))))&
((tall(lucy))=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((creative(X)|humble(X))))<=>(?[X]:((tall(X)<~>kind(X)))))&
((?[X]:(~happy(X)))=>((humble(mary)<~>tall(mary))))&
(![X]:((~happy(X)<~>~humble(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((rich(X)<~>tall(X))=>(generous(X)&calm(X))))&
(![X]:((~patient(X)<~>~creative(X))=>~patient(X)))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((generous(X)|curious(X))<=>(~brave(X)<~>old(X))))&
(![X]:((strong(X)&~creative(X))<=>(~happy(X)|happy(X))))&
(?[X]:((tall(X)|~calm(X))))&
((~brave(lucy)|~patient(lucy)))&
(~curious(mary))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~patient(X)&~humble(X))))&
((~curious(mary)|calm(mary))) | ~creative(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5794068376887367431994597
% SZS output start Proof for 5794068376887367431994597
16. ! [X0] : ((~creative(X0) & strong(X0)) <=> (happy(X0) | ~happy(X0))) [input p15]
23. creative(lucy) [input hypothesis]
75. ! [X0] : (((~creative(X0) & strong(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 16]
76. ! [X0] : (((~creative(X0) & strong(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | creative(X0) | ~strong(X0))) [flattening 75]
145. ~creative(X0) | happy(X0) [cnf transformation 76]
146. ~creative(X0) | ~happy(X0) [cnf transformation 76]
154. creative(lucy) [cnf transformation 23]
205. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
206. ~creative(X0) <- (11) [avatar component clause 205]
332. ~creative(X0) [subsumption resolution 145,146]
333. 11 [avatar split clause 332,205]
355. $false <- (11) [resolution 206,154]
356. ~11 [avatar contradiction clause 355]
357. $false [avatar sat refutation 333,356]
% SZS output end Proof for 5794068376887367431994597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and rich then lucy is either rich or humble.
If someone is humble or brave then someone is kind.
If someone is both generous and not creative then paul is either quiet or not brave.
If someone is both not rich and rich then mary is rich and vice versa.
If susan is wise or not old then someone is either creative or not generous and vice versa.
Everyone who is not wise is not humble and vice versa.
If fred is not creative then mary is either generous or quiet and vice versa.
Everyone who is not curious is calm and vice versa.
If lucy is either not tall or not kind then someone is strong or kind.
If someone is tall or curious then paul is both not quiet and humble.
If someone is either not happy or happy then someone is not calm or not humble.
Everyone who is calm is not curious or not generous.
If someone is funny or curious then someone is both not rich and rich and vice versa.
If someone is kind then fred is both quiet and not humble and vice versa.
Everyone who is not wise is patient or not patient and vice versa.
If someone is strong then someone is both not funny and not old.
Alice is humble or not generous.
Fred is either not generous or generous.
John is both not curious and kind.
Susan is not brave.
Someone is both not curious and happy.
Someone is both not tall and not funny.
Paul is either not quiet or not generous. | Lucy is tall. | contradiction | (((~rich(lucy)&rich(lucy)))=>((rich(lucy)<~>humble(lucy))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~creative(X))))=>((quiet(paul)<~>~brave(paul))))&
((?[X]:((~rich(X)&rich(X))))<=>(rich(mary)))&
(((wise(susan)|~old(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~wise(X)<=>~humble(X)))&
((~creative(fred))<=>((generous(mary)<~>quiet(mary))))&
(![X]:(~curious(X)<=>calm(X)))&
(((~tall(lucy)<~>~kind(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((~happy(X)<~>happy(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(calm(X)=>(~curious(X)|~generous(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:(kind(X)))<=>((quiet(fred)&~humble(fred))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~funny(X)&~old(X)))))&
((humble(alice)|~generous(alice)))&
((~generous(fred)<~>generous(fred)))&
((~curious(john)&kind(john)))&
(~brave(susan))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((~tall(X)&~funny(X))))&
((~quiet(paul)<~>~generous(paul))) | tall(lucy) | [
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2146001194077642394419483
% SZS output start Proof for 2146001194077642394419483
6. ! [X0] : (~wise(X0) <=> ~humble(X0)) [input p5]
10. ? [X0] : (curious(X0) | tall(X0)) => (humble(paul) & ~quiet(paul)) [input p9]
15. ! [X0] : (~wise(X0) <=> (~patient(X0) | patient(X0))) [input p14]
24. tall(lucy) [input hypothesis]
34. (humble(paul) & ~quiet(paul)) | ! [X0] : (~curious(X0) & ~tall(X0)) [ennf transformation 10]
53. ! [X0] : ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))) [nnf transformation 6]
73. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | wise(X0))) [nnf transformation 15]
74. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | wise(X0))) [flattening 73]
99. ~humble(X0) | wise(X0) [cnf transformation 53]
111. humble(paul) | ~tall(X0) [cnf transformation 34]
125. ~wise(X0) | ~patient(X0) [cnf transformation 74]
126. ~wise(X0) | patient(X0) [cnf transformation 74]
141. tall(lucy) [cnf transformation 24]
230. 19 <=> tall(lucy) [avatar definition]
231. tall(lucy) <- (19) [avatar component clause 230]
247. 23 <=> humble(paul) [avatar definition]
249. humble(paul) <- (23) [avatar component clause 247]
252. 24 <=> ! [X0] : ~tall(X0) [avatar definition]
253. ~tall(X0) <- (24) [avatar component clause 252]
254. 24 | 23 [avatar split clause 111,247,252]
302. ~wise(X0) [subsumption resolution 125,126]
331. 19 [avatar split clause 141,230]
332. $false <- (19, 24) [subsumption resolution 231,253]
333. ~19 | ~24 [avatar contradiction clause 332]
334. wise(paul) <- (23) [resolution 99,249]
335. $false <- (23) [subsumption resolution 334,302]
336. ~23 [avatar contradiction clause 335]
337. $false [avatar sat refutation 254,331,333,336]
% SZS output end Proof for 2146001194077642394419483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm then susan is rich or wise. Everyone who is generous is either not humble or not old. Everyone who is either not patient or not wise is brave or not calm and vice versa. Everyone who is either not quiet or generous is not happy and vice versa. Everyone who is both not kind and curious is both brave and not calm and vice versa. If paul is both tall and rich then susan is either not old or humble. If mary is brave or not funny then fred is not tall and vice versa. If alice is generous or quiet then mary is not quiet and vice versa. Everyone who is either wise or happy is not tall or happy and vice versa. If lucy is not quiet or not tall then susan is not rich. Everyone who is both not generous and tall is both happy and not funny. Everyone who is curious or brave is curious or not patient. If paul is curious or not calm then someone is both not wise and not rich and vice versa. If paul is both not calm and not kind then paul is both not tall and generous and vice versa. Everyone who is creative or brave is not tall or not quiet. Everyone who is both not rich and old is either happy or calm and vice versa. Fred is not generous or wise. Someone is not generous. Mary is either not funny or funny. Fred is not rich. Someone is either wise or funny. Someone is both not calm and generous. Mary is either not patient or curious. | Fred is not generous. | neutral | ((~calm(john))=>((rich(susan)|wise(susan))))&
(![X]:(generous(X)=>(~humble(X)<~>~old(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(brave(X)|~calm(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>~happy(X)))&
(![X]:((~kind(X)&curious(X))<=>(brave(X)&~calm(X))))&
(((tall(paul)&rich(paul)))=>((~old(susan)<~>humble(susan))))&
(((brave(mary)|~funny(mary)))<=>(~tall(fred)))&
(((generous(alice)|quiet(alice)))<=>(~quiet(mary)))&
(![X]:((wise(X)<~>happy(X))<=>(~tall(X)|happy(X))))&
(((~quiet(lucy)|~tall(lucy)))=>(~rich(susan)))&
(![X]:((~generous(X)&tall(X))=>(happy(X)&~funny(X))))&
(![X]:((curious(X)|brave(X))=>(curious(X)|~patient(X))))&
(((curious(paul)|~calm(paul)))<=>(?[X]:((~wise(X)&~rich(X)))))&
(((~calm(paul)&~kind(paul)))<=>((~tall(paul)&generous(paul))))&
(![X]:((creative(X)|brave(X))=>(~tall(X)|~quiet(X))))&
(![X]:((~rich(X)&old(X))<=>(happy(X)<~>calm(X))))&
((~generous(fred)|wise(fred)))&
(?[X]:(~generous(X)))&
((~funny(mary)<~>funny(mary)))&
(~rich(fred))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((~calm(X)&generous(X))))&
((~patient(mary)<~>curious(mary))) | ~generous(fred) | [] | null | 0 |
Everyone who is both not curious and kind is wise. Everyone who is both not creative and patient is both not generous and not creative and vice versa. Everyone who is not calm is both not creative and wise and vice versa. If paul is both not creative and generous then someone is brave and vice versa. If alice is both not strong and strong then alice is creative or not funny and vice versa. If fred is creative or not rich then someone is funny or not patient and vice versa. Everyone who is both not wise and not old is old or funny and vice versa. Everyone who is either tall or not curious is either not funny or not brave and vice versa. If someone is wise or not wise then paul is not generous and vice versa. If someone is wise then alice is both happy and not generous. If someone is not tall or not wise then paul is humble or not strong. If someone is old then someone is not curious and vice versa. Everyone who is either not calm or rich is funny. Everyone who is not humble is either not rich or not kind. Everyone who is rich is either not brave or not curious. Everyone who is not strong is not old and vice versa. Someone is not humble or rich. Fred is either not creative or not funny. Someone is both not old and tall. Mary is both not calm and not generous. Someone is either not happy or humble. Susan is not old. | Paul is not brave. | entailment | (![X]:((~curious(X)&kind(X))=>wise(X)))&
(![X]:((~creative(X)&patient(X))<=>(~generous(X)&~creative(X))))&
(![X]:(~calm(X)<=>(~creative(X)&wise(X))))&
(((~creative(paul)&generous(paul)))<=>(?[X]:(brave(X))))&
(((~strong(alice)&strong(alice)))<=>((creative(alice)|~funny(alice))))&
(((creative(fred)|~rich(fred)))<=>(?[X]:((funny(X)|~patient(X)))))&
(![X]:((~wise(X)&~old(X))<=>(old(X)|funny(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(~funny(X)<~>~brave(X))))&
((?[X]:((wise(X)|~wise(X))))<=>(~generous(paul)))&
((?[X]:(wise(X)))=>((happy(alice)&~generous(alice))))&
((?[X]:((~tall(X)|~wise(X))))=>((humble(paul)|~strong(paul))))&
((?[X]:(old(X)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)<~>rich(X))=>funny(X)))&
(![X]:(~humble(X)=>(~rich(X)<~>~kind(X))))&
(![X]:(rich(X)=>(~brave(X)<~>~curious(X))))&
(![X]:(~strong(X)<=>~old(X)))&
(?[X]:((~humble(X)|rich(X))))&
((~creative(fred)<~>~funny(fred)))&
(?[X]:((~old(X)&tall(X))))&
((~calm(mary)&~generous(mary)))&
(?[X]:((~happy(X)<~>humble(X))))&
(~old(susan)) | ~brave(paul) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 404503665703153553895482
% SZS output start Proof for 404503665703153553895482
4. (generous(paul) & ~creative(paul)) <=> ? [X0] : brave(X0) [input p3]
9. ? [X0] : (~wise(X0) | wise(X0)) <=> ~generous(paul) [input p8]
23. brave(paul) [input hypothesis]
37. ((generous(paul) & ~creative(paul)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~generous(paul) | creative(paul))) [nnf transformation 4]
38. ((generous(paul) & ~creative(paul)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~generous(paul) | creative(paul)) [flattening 37]
39. ((generous(paul) & ~creative(paul)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~generous(paul) | creative(paul)) [rectify 38]
40. ? [X1] : brave(X1) => brave(sK0) [choice axiom]
41. ((generous(paul) & ~creative(paul)) | ! [X0] : ~brave(X0)) & (brave(sK0) | ~generous(paul) | creative(paul)) [skolemisation 39,40]
52. (? [X0] : (~wise(X0) | wise(X0)) | generous(paul)) & (~generous(paul) | ! [X0] : (wise(X0) & ~wise(X0))) [nnf transformation 9]
53. (? [X0] : (~wise(X0) | wise(X0)) | generous(paul)) & (~generous(paul) | ! [X1] : (wise(X1) & ~wise(X1))) [rectify 52]
54. ? [X0] : (~wise(X0) | wise(X0)) => (~wise(sK2) | wise(sK2)) [choice axiom]
55. ((~wise(sK2) | wise(sK2)) | generous(paul)) & (~generous(paul) | ! [X1] : (wise(X1) & ~wise(X1))) [skolemisation 53,54]
83. generous(paul) | ~brave(X0) [cnf transformation 41]
106. ~generous(paul) | ~wise(X1) [cnf transformation 55]
107. ~generous(paul) | wise(X1) [cnf transformation 55]
133. brave(paul) [cnf transformation 23]
137. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
138. ~brave(X0) <- (1) [avatar component clause 137]
140. 2 <=> generous(paul) [avatar definition]
143. 1 | 2 [avatar split clause 83,140,137]
198. 14 <=> ! [X1] : wise(X1) [avatar definition]
199. wise(X1) <- (14) [avatar component clause 198]
200. 14 | ~2 [avatar split clause 107,140,198]
202. 15 <=> ! [X1] : ~wise(X1) [avatar definition]
203. ~wise(X1) <- (15) [avatar component clause 202]
204. 15 | ~2 [avatar split clause 106,140,202]
256. $false <- (14, 15) [subsumption resolution 199,203]
257. ~14 | ~15 [avatar contradiction clause 256]
258. $false <- (1) [resolution 138,133]
259. ~1 [avatar contradiction clause 258]
260. $false [avatar sat refutation 143,200,204,257,259]
% SZS output end Proof for 404503665703153553895482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not quiet is not curious or not humble. Everyone who is not rich or curious is either patient or quiet and vice versa. If mary is either curious or not curious then paul is kind or brave and vice versa. If someone is generous or not tall then someone is both creative and curious and vice versa. If someone is either not kind or not creative then someone is not humble or old. Everyone who is not curious is either quiet or kind and vice versa. Everyone who is kind is not calm or not rich. Everyone who is both not quiet and not generous is kind or curious and vice versa. Everyone who is both not brave and patient is either humble or funny and vice versa. Everyone who is not funny or curious is either tall or not tall. Everyone who is not rich is both not brave and calm and vice versa. Everyone who is either tall or patient is either not rich or strong. Everyone who is both tall and strong is either not patient or not strong. If someone is both not generous and humble then paul is not quiet or not funny and vice versa. Everyone who is both happy and not strong is either strong or not curious and vice versa. Everyone who is not curious or not rich is both not creative and patient. Someone is not funny or brave. Susan is both brave and wise. Mary is not happy. Someone is patient. Someone is either patient or not curious. Someone is not generous or not curious. John is not strong or not curious. | Susan is not strong. | neutral | (![X]:((curious(X)<~>~quiet(X))=>(~curious(X)|~humble(X))))&
(![X]:((~rich(X)|curious(X))<=>(patient(X)<~>quiet(X))))&
(((curious(mary)<~>~curious(mary)))<=>((kind(paul)|brave(paul))))&
((?[X]:((generous(X)|~tall(X))))<=>(?[X]:((creative(X)&curious(X)))))&
((?[X]:((~kind(X)<~>~creative(X))))=>(?[X]:((~humble(X)|old(X)))))&
(![X]:(~curious(X)<=>(quiet(X)<~>kind(X))))&
(![X]:(kind(X)=>(~calm(X)|~rich(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(kind(X)|curious(X))))&
(![X]:((~brave(X)&patient(X))<=>(humble(X)<~>funny(X))))&
(![X]:((~funny(X)|curious(X))=>(tall(X)<~>~tall(X))))&
(![X]:(~rich(X)<=>(~brave(X)&calm(X))))&
(![X]:((tall(X)<~>patient(X))=>(~rich(X)<~>strong(X))))&
(![X]:((tall(X)&strong(X))=>(~patient(X)<~>~strong(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((~quiet(paul)|~funny(paul))))&
(![X]:((happy(X)&~strong(X))<=>(strong(X)<~>~curious(X))))&
(![X]:((~curious(X)|~rich(X))=>(~creative(X)&patient(X))))&
(?[X]:((~funny(X)|brave(X))))&
((brave(susan)&wise(susan)))&
(~happy(mary))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)<~>~curious(X))))&
(?[X]:((~generous(X)|~curious(X))))&
((~strong(john)|~curious(john))) | ~strong(susan) | [] | null | 0 |
Everyone who is not strong is humble or wise and vice versa.
Everyone who is happy or humble is either not happy or not strong and vice versa.
If susan is both not humble and old then someone is either curious or brave.
Everyone who is both kind and not curious is either not happy or not rich and vice versa.
Everyone who is kind or curious is humble and vice versa.
Everyone who is both not calm and quiet is either not rich or brave and vice versa.
Everyone who is happy or wise is either rich or not strong and vice versa.
Everyone who is not patient is either old or happy.
Everyone who is either quiet or not tall is not quiet or patient and vice versa.
Everyone who is either quiet or not humble is either not generous or not strong and vice versa.
If someone is patient then mary is brave or not tall and vice versa.
If alice is not old then someone is not rich or not wise.
If lucy is creative or old then someone is not patient and vice versa.
Everyone who is creative is both patient and happy and vice versa.
If someone is both wise and not generous then someone is both not wise and generous and vice versa.
If someone is creative then fred is both curious and calm.
Fred is either not old or happy.
Paul is both not happy and not tall.
John is either not creative or quiet.
Someone is either strong or not rich.
John is both generous and not quiet.
Lucy is either funny or not generous.
Someone is both humble and happy. | John is not wise. | contradiction | (![X]:(~strong(X)<=>(humble(X)|wise(X))))&
(![X]:((happy(X)|humble(X))<=>(~happy(X)<~>~strong(X))))&
(((~humble(susan)&old(susan)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((kind(X)|curious(X))<=>humble(X)))&
(![X]:((~calm(X)&quiet(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((happy(X)|wise(X))<=>(rich(X)<~>~strong(X))))&
(![X]:(~patient(X)=>(old(X)<~>happy(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>(~quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:(patient(X)))<=>((brave(mary)|~tall(mary))))&
((~old(alice))=>(?[X]:((~rich(X)|~wise(X)))))&
(((creative(lucy)|old(lucy)))<=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(patient(X)&happy(X))))&
((?[X]:((wise(X)&~generous(X))))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:(creative(X)))=>((curious(fred)&calm(fred))))&
((~old(fred)<~>happy(fred)))&
((~happy(paul)&~tall(paul)))&
((~creative(john)<~>quiet(john)))&
(?[X]:((strong(X)<~>~rich(X))))&
((generous(john)&~quiet(john)))&
((funny(lucy)<~>~generous(lucy)))&
(?[X]:((humble(X)&happy(X)))) | ~wise(john) | [
"p0",
"p1",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5020219063253812599128027
% SZS output start Proof for 5020219063253812599128027
1. ! [X0] : (~strong(X0) <=> (wise(X0) | humble(X0))) [input p0]
2. ! [X0] : ((humble(X0) | happy(X0)) <=> (~happy(X0) <~> ~strong(X0))) [input p1]
10. ! [X0] : ((quiet(X0) <~> ~humble(X0)) <=> (~generous(X0) <~> ~strong(X0))) [input p9]
21. ~quiet(john) & generous(john) [input p20]
24. ~wise(john) [input hypothesis]
31. ! [X0] : ((~strong(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | strong(X0))) [nnf transformation 1]
32. ! [X0] : ((~strong(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | strong(X0))) [flattening 31]
33. ! [X0] : (((humble(X0) | happy(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0)))) [nnf transformation 2]
34. ! [X0] : ((humble(X0) | happy(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0)))) [flattening 33]
49. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0)))) & (((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [nnf transformation 10]
77. wise(X0) | humble(X0) | strong(X0) [cnf transformation 32]
78. ~humble(X0) | ~strong(X0) [cnf transformation 32]
80. ~strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 34]
84. humble(X0) | happy(X0) | ~strong(X0) | happy(X0) [cnf transformation 34]
122. ~humble(X0) | quiet(X0) | ~generous(X0) | strong(X0) [cnf transformation 49]
149. generous(john) [cnf transformation 21]
150. ~quiet(john) [cnf transformation 21]
155. ~wise(john) [cnf transformation 24]
158. ~strong(X0) | ~happy(X0) [duplicate literal removal 80]
159. humble(X0) | happy(X0) | ~strong(X0) [duplicate literal removal 84]
160. ~strong(X0) | happy(X0) [subsumption resolution 159,78]
162. ~strong(X0) [subsumption resolution 158,160]
186. ~generous(X0) | quiet(X0) | ~humble(X0) [subsumption resolution 122,162]
279. 25 <=> quiet(john) [avatar definition]
281. ~quiet(john) <- (~25) [avatar component clause 279]
285. ~25 [avatar split clause 150,279]
309. humble(john) | strong(john) [resolution 77,155]
312. humble(john) [subsumption resolution 309,162]
439. quiet(john) | ~humble(john) [resolution 186,149]
441. ~humble(john) <- (~25) [subsumption resolution 439,281]
442. $false <- (~25) [subsumption resolution 441,312]
443. 25 [avatar contradiction clause 442]
445. $false [avatar sat refutation 285,443]
% SZS output end Proof for 5020219063253812599128027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or tall is not old or not kind. Everyone who is not creative is not happy. If someone is patient then mary is both brave and wise and vice versa. If someone is both old and curious then someone is not creative and vice versa. Everyone who is either not happy or happy is wise or not strong. If someone is either not curious or not patient then john is not creative or wise and vice versa. Everyone who is either not happy or quiet is either not brave or not funny. If paul is not humble or tall then mary is both calm and tall and vice versa. Everyone who is either not old or curious is not brave. Everyone who is not generous or happy is both calm and happy and vice versa. Everyone who is not kind or not calm is either not generous or happy. Everyone who is rich is both patient and not tall and vice versa. Everyone who is both not patient and not creative is both not creative and happy and vice versa. Everyone who is both not rich and not wise is both humble and not patient and vice versa. If paul is either not old or humble then someone is strong or not calm. Everyone who is either not wise or curious is either old or not humble. Someone is not humble or not tall. Mary is both not curious and not old. Mary is either kind or not generous. John is not kind or not calm. Mary is tall or funny. Lucy is both not strong and calm. Alice is either kind or happy. Paul is wise. | Lucy is patient. | contradiction | (![X]:((~old(X)|tall(X))=>(~old(X)|~kind(X))))&
(![X]:(~creative(X)=>~happy(X)))&
((?[X]:(patient(X)))<=>((brave(mary)&wise(mary))))&
((?[X]:((old(X)&curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)<~>happy(X))=>(wise(X)|~strong(X))))&
((?[X]:((~curious(X)<~>~patient(X))))<=>((~creative(john)|wise(john))))&
(![X]:((~happy(X)<~>quiet(X))=>(~brave(X)<~>~funny(X))))&
(((~humble(paul)|tall(paul)))<=>((calm(mary)&tall(mary))))&
(![X]:((~old(X)<~>curious(X))=>~brave(X)))&
(![X]:((~generous(X)|happy(X))<=>(calm(X)&happy(X))))&
(![X]:((~kind(X)|~calm(X))=>(~generous(X)<~>happy(X))))&
(![X]:(rich(X)<=>(patient(X)&~tall(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~creative(X)&happy(X))))&
(![X]:((~rich(X)&~wise(X))<=>(humble(X)&~patient(X))))&
(((~old(paul)<~>humble(paul)))=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((~wise(X)<~>curious(X))=>(old(X)<~>~humble(X))))&
(?[X]:((~humble(X)|~tall(X))))&
((~curious(mary)&~old(mary)))&
((kind(mary)<~>~generous(mary)))&
((~kind(john)|~calm(john)))&
((tall(mary)|funny(mary)))&
((~strong(lucy)&calm(lucy)))&
((kind(alice)<~>happy(alice)))&
(wise(paul)) | patient(lucy) | [
"p2",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4977922602569826548431880
% SZS output start Proof for 4977922602569826548431880
3. ? [X0] : patient(X0) <=> (wise(mary) & brave(mary)) [input p2]
9. ! [X0] : ((~old(X0) <~> curious(X0)) => ~brave(X0)) [input p8]
18. ~old(mary) & ~curious(mary) [input p17]
25. patient(lucy) [input hypothesis]
33. ! [X0] : (~brave(X0) | (~old(X0) <=> curious(X0))) [ennf transformation 9]
37. (? [X0] : patient(X0) | (~wise(mary) | ~brave(mary))) & ((wise(mary) & brave(mary)) | ! [X0] : ~patient(X0)) [nnf transformation 3]
38. (? [X0] : patient(X0) | ~wise(mary) | ~brave(mary)) & ((wise(mary) & brave(mary)) | ! [X0] : ~patient(X0)) [flattening 37]
39. (? [X0] : patient(X0) | ~wise(mary) | ~brave(mary)) & ((wise(mary) & brave(mary)) | ! [X1] : ~patient(X1)) [rectify 38]
40. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
41. (patient(sK0) | ~wise(mary) | ~brave(mary)) & ((wise(mary) & brave(mary)) | ! [X1] : ~patient(X1)) [skolemisation 39,40]
56. ! [X0] : (~brave(X0) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) [nnf transformation 33]
77. brave(mary) | ~patient(X1) [cnf transformation 41]
100. ~brave(X0) | curious(X0) | old(X0) [cnf transformation 56]
129. ~curious(mary) [cnf transformation 18]
130. ~old(mary) [cnf transformation 18]
140. patient(lucy) [cnf transformation 25]
144. 1 <=> brave(mary) [avatar definition]
145. brave(mary) <- (1) [avatar component clause 144]
157. 4 <=> ! [X1] : ~patient(X1) [avatar definition]
158. ~patient(X1) <- (4) [avatar component clause 157]
160. 4 | 1 [avatar split clause 77,144,157]
277. $false <- (4) [resolution 158,140]
278. ~4 [avatar contradiction clause 277]
300. curious(mary) | old(mary) <- (1) [resolution 100,145]
301. old(mary) <- (1) [subsumption resolution 300,129]
302. $false <- (1) [subsumption resolution 301,130]
303. ~1 [avatar contradiction clause 302]
304. $false [avatar sat refutation 160,278,303]
% SZS output end Proof for 4977922602569826548431880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not quiet is either not old or patient and vice versa.
If paul is not calm or not generous then paul is both happy and old and vice versa.
If someone is not calm or not tall then susan is not curious.
If paul is not creative or not quiet then someone is kind or not quiet.
If fred is happy then someone is happy and vice versa.
Everyone who is both not patient and creative is both calm and not old.
If mary is humble then lucy is patient or rich and vice versa.
If someone is either not old or not kind then someone is funny and vice versa.
If someone is not old or not funny then mary is both kind and rich and vice versa.
Everyone who is either not brave or old is not wise or quiet and vice versa.
Everyone who is either generous or kind is both not rich and not brave.
Everyone who is both not calm and creative is not funny.
If someone is humble or tall then someone is creative.
Everyone who is not patient is either not quiet or creative and vice versa.
If alice is tall or wise then susan is creative or not strong.
Everyone who is both tall and not strong is strong and vice versa.
Someone is either not patient or generous.
John is not curious or not old.
Someone is either tall or not generous.
Susan is either patient or rich.
Susan is both not kind and not patient.
Paul is both not brave and not quiet.
Alice is both generous and not curious. | Susan is generous. | contradiction | (![X]:((strong(X)&~quiet(X))<=>(~old(X)<~>patient(X))))&
(((~calm(paul)|~generous(paul)))<=>((happy(paul)&old(paul))))&
((?[X]:((~calm(X)|~tall(X))))=>(~curious(susan)))&
(((~creative(paul)|~quiet(paul)))=>(?[X]:((kind(X)|~quiet(X)))))&
((happy(fred))<=>(?[X]:(happy(X))))&
(![X]:((~patient(X)&creative(X))=>(calm(X)&~old(X))))&
((humble(mary))<=>((patient(lucy)|rich(lucy))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~old(X)|~funny(X))))<=>((kind(mary)&rich(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(~wise(X)|quiet(X))))&
(![X]:((generous(X)<~>kind(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)&creative(X))=>~funny(X)))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>creative(X))))&
(((tall(alice)|wise(alice)))=>((creative(susan)|~strong(susan))))&
(![X]:((tall(X)&~strong(X))<=>strong(X)))&
(?[X]:((~patient(X)<~>generous(X))))&
((~curious(john)|~old(john)))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(susan)<~>rich(susan)))&
((~kind(susan)&~patient(susan)))&
((~brave(paul)&~quiet(paul)))&
((generous(alice)&~curious(alice))) | generous(susan) | [
"p10",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2215230904397019971667395
% SZS output start Proof for 2215230904397019971667395
11. ! [X0] : ((generous(X0) <~> kind(X0)) => (~brave(X0) & ~rich(X0))) [input p10]
20. patient(susan) <~> rich(susan) [input p19]
21. ~patient(susan) & ~kind(susan) [input p20]
24. generous(susan) [input hypothesis]
33. ! [X0] : ((~brave(X0) & ~rich(X0)) | (generous(X0) <=> kind(X0))) [ennf transformation 11]
63. ! [X0] : ((~brave(X0) & ~rich(X0)) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) [nnf transformation 33]
76. (~rich(susan) | ~patient(susan)) & (rich(susan) | patient(susan)) [nnf transformation 20]
112. ~rich(X0) | kind(X0) | ~generous(X0) [cnf transformation 63]
132. rich(susan) | patient(susan) [cnf transformation 76]
134. ~kind(susan) [cnf transformation 21]
135. ~patient(susan) [cnf transformation 21]
139. generous(susan) [cnf transformation 24]
314. 38 <=> patient(susan) [avatar definition]
318. 39 <=> rich(susan) [avatar definition]
319. rich(susan) <- (39) [avatar component clause 318]
322. 38 | 39 [avatar split clause 132,318,314]
323. ~38 [avatar split clause 135,314]
436. kind(susan) | ~generous(susan) <- (39) [resolution 112,319]
437. ~generous(susan) <- (39) [subsumption resolution 436,134]
438. $false <- (39) [subsumption resolution 437,139]
439. ~39 [avatar contradiction clause 438]
440. $false [avatar sat refutation 322,323,439]
% SZS output end Proof for 2215230904397019971667395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either tall or not tall then john is both curious and not happy. If alice is not creative or kind then someone is both not curious and curious and vice versa. If someone is both generous and strong then someone is brave or not happy and vice versa. Everyone who is old or not strong is not patient or not wise and vice versa. If john is patient or not rich then fred is either patient or rich and vice versa. Everyone who is funny or generous is quiet or old. If mary is either strong or not creative then john is both not creative and tall. Everyone who is not happy is not funny and vice versa. If someone is not calm or quiet then paul is either not tall or not old and vice versa. Everyone who is either not curious or not old is creative. Everyone who is not brave is brave. Everyone who is not creative or not kind is old or quiet and vice versa. If susan is both not funny and tall then someone is not quiet. If paul is not rich or not generous then fred is either quiet or not funny and vice versa. Everyone who is both not happy and not patient is either strong or not kind. If mary is funny or strong then paul is rich or not patient. Alice is not rich. Someone is quiet. Someone is both patient and not humble. Someone is calm or not kind. Someone is both not creative and tall. Someone is both curious and wise. Lucy is either humble or happy. | Mary is not brave. | contradiction | (((tall(paul)<~>~tall(paul)))=>((curious(john)&~happy(john))))&
(((~creative(alice)|kind(alice)))<=>(?[X]:((~curious(X)&curious(X)))))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((old(X)|~strong(X))<=>(~patient(X)|~wise(X))))&
(((patient(john)|~rich(john)))<=>((patient(fred)<~>rich(fred))))&
(![X]:((funny(X)|generous(X))=>(quiet(X)|old(X))))&
(((strong(mary)<~>~creative(mary)))=>((~creative(john)&tall(john))))&
(![X]:(~happy(X)<=>~funny(X)))&
((?[X]:((~calm(X)|quiet(X))))<=>((~tall(paul)<~>~old(paul))))&
(![X]:((~curious(X)<~>~old(X))=>creative(X)))&
(![X]:(~brave(X)=>brave(X)))&
(![X]:((~creative(X)|~kind(X))<=>(old(X)|quiet(X))))&
(((~funny(susan)&tall(susan)))=>(?[X]:(~quiet(X))))&
(((~rich(paul)|~generous(paul)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((~happy(X)&~patient(X))=>(strong(X)<~>~kind(X))))&
(((funny(mary)|strong(mary)))=>((rich(paul)|~patient(paul))))&
(~rich(alice))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)&~humble(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((curious(X)&wise(X))))&
((humble(lucy)<~>happy(lucy))) | ~brave(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6536494969974173175963122
% SZS output start Proof for 6536494969974173175963122
11. ! [X0] : (~brave(X0) => brave(X0)) [input p10]
24. ~brave(mary) [input hypothesis]
31. ! [X0] : (brave(X0) | brave(X0)) [ennf transformation 11]
118. brave(X0) | brave(X0) [cnf transformation 31]
145. ~brave(mary) [cnf transformation 24]
146. brave(X0) [duplicate literal removal 118]
343. $false [subsumption resolution 145,146]
% SZS output end Proof for 6536494969974173175963122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or humble then someone is either not happy or creative. If someone is both not brave and not happy then mary is old and vice versa. If susan is not creative or funny then susan is not kind or not old. Everyone who is both not kind and not old is not curious or not patient. Everyone who is either not brave or not wise is happy and vice versa. If someone is either not old or patient then someone is both funny and curious and vice versa. Everyone who is not old is funny or calm and vice versa. Everyone who is funny is not happy or happy and vice versa. If fred is not brave or not patient then fred is both not old and brave. If someone is both not strong and not rich then mary is both not patient and not wise and vice versa. If someone is not rich then mary is generous or brave. Everyone who is not kind is calm and vice versa. Everyone who is not creative is not rich or calm. Everyone who is either not kind or quiet is both not creative and not happy and vice versa. Everyone who is both calm and kind is either old or not tall and vice versa. If someone is quiet or wise then susan is both wise and not old. Someone is both not strong and brave. Fred is either not humble or not curious. Susan is quiet. Someone is both creative and brave. Someone is both not humble and not strong. Mary is not strong or not kind. | Susan is not funny. | contradiction | ((?[X]:((generous(X)|humble(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>(old(mary)))&
(((~creative(susan)|funny(susan)))=>((~kind(susan)|~old(susan))))&
(![X]:((~kind(X)&~old(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~old(X)<=>(funny(X)|calm(X))))&
(![X]:(funny(X)<=>(~happy(X)|happy(X))))&
(((~brave(fred)|~patient(fred)))=>((~old(fred)&brave(fred))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:(~rich(X)))=>((generous(mary)|brave(mary))))&
(![X]:(~kind(X)<=>calm(X)))&
(![X]:(~creative(X)=>(~rich(X)|calm(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((quiet(X)|wise(X))))=>((wise(susan)&~old(susan))))&
(?[X]:((~strong(X)&brave(X))))&
((~humble(fred)<~>~curious(fred)))&
(quiet(susan))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~strong(mary)|~kind(mary))) | ~funny(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3241863111511840516639963
% SZS output start Proof for 3241863111511840516639963
8. ! [X0] : (funny(X0) <=> (happy(X0) | ~happy(X0))) [input p7]
23. ~funny(susan) [input hypothesis]
53. ! [X0] : ((funny(X0) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ~funny(X0))) [nnf transformation 8]
54. ! [X0] : ((funny(X0) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ~funny(X0))) [flattening 53]
96. funny(X0) | happy(X0) [cnf transformation 54]
97. funny(X0) | ~happy(X0) [cnf transformation 54]
136. ~funny(susan) [cnf transformation 23]
223. funny(X0) [subsumption resolution 96,97]
309. $false [subsumption resolution 136,223]
% SZS output end Proof for 3241863111511840516639963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not old and humble and vice versa.
Everyone who is both calm and rich is quiet.
If someone is either not brave or tall then someone is not wise.
Everyone who is both not funny and humble is brave.
Everyone who is both not quiet and quiet is funny or humble and vice versa.
Everyone who is either not calm or not curious is both not wise and curious and vice versa.
If someone is generous then someone is brave and vice versa.
If someone is happy then someone is either not tall or strong.
Everyone who is not creative is both humble and not creative and vice versa.
Everyone who is not quiet is both curious and not quiet.
If someone is both not creative and strong then fred is calm and vice versa.
Everyone who is not brave or not creative is either generous or not strong.
Everyone who is both not happy and kind is both quiet and not calm and vice versa.
Everyone who is quiet or old is not quiet or patient and vice versa.
Everyone who is kind is either not rich or not generous and vice versa.
Paul is not happy.
Susan is not strong or not happy.
Fred is tall.
Someone is not quiet.
John is either not brave or not kind.
Someone is both not generous and not brave.
Someone is either not rich or funny. | Paul is rich. | neutral | (![X]:(kind(X)<=>(~old(X)&humble(X))))&
(![X]:((calm(X)&rich(X))=>quiet(X)))&
((?[X]:((~brave(X)<~>tall(X))))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)&humble(X))=>brave(X)))&
(![X]:((~quiet(X)&quiet(X))<=>(funny(X)|humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(~wise(X)&curious(X))))&
((?[X]:(generous(X)))<=>(?[X]:(brave(X))))&
((?[X]:(happy(X)))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:(~creative(X)<=>(humble(X)&~creative(X))))&
(![X]:(~quiet(X)=>(curious(X)&~quiet(X))))&
((?[X]:((~creative(X)&strong(X))))<=>(calm(fred)))&
(![X]:((~brave(X)|~creative(X))=>(generous(X)<~>~strong(X))))&
(![X]:((~happy(X)&kind(X))<=>(quiet(X)&~calm(X))))&
(![X]:((quiet(X)|old(X))<=>(~quiet(X)|patient(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>~generous(X))))&
(~happy(paul))&
((~strong(susan)|~happy(susan)))&
(tall(fred))&
(?[X]:(~quiet(X)))&
((~brave(john)<~>~kind(john)))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((~rich(X)<~>funny(X)))) | rich(paul) | [] | null | 0 |
If mary is either generous or not calm then john is both not creative and patient and vice versa.
Everyone who is both happy and not strong is calm and vice versa.
If someone is not rich or not patient then susan is old and vice versa.
Everyone who is both generous and not creative is both old and rich.
Everyone who is either not creative or not quiet is funny.
Everyone who is happy is not wise or not brave.
If susan is either wise or not happy then mary is wise.
If someone is not creative or not quiet then someone is creative or calm and vice versa.
If alice is not funny or not brave then someone is not generous and vice versa.
Everyone who is not tall or tall is not curious and vice versa.
If lucy is both not creative and not calm then someone is both funny and not happy and vice versa.
Everyone who is both not calm and creative is not wise and vice versa.
Everyone who is both not happy and calm is either not humble or not kind.
If someone is either funny or not humble then someone is not old and vice versa.
Everyone who is either not patient or patient is not creative and vice versa.
Everyone who is either not patient or creative is not kind or not curious and vice versa.
John is either not calm or curious.
Fred is not old.
Paul is both not creative and not curious.
Someone is either strong or wise.
Someone is either not humble or not creative.
Paul is either not humble or not funny.
Someone is either not quiet or not rich. | Lucy is quiet. | neutral | (((generous(mary)<~>~calm(mary)))<=>((~creative(john)&patient(john))))&
(![X]:((happy(X)&~strong(X))<=>calm(X)))&
((?[X]:((~rich(X)|~patient(X))))<=>(old(susan)))&
(![X]:((generous(X)&~creative(X))=>(old(X)&rich(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>funny(X)))&
(![X]:(happy(X)=>(~wise(X)|~brave(X))))&
(((wise(susan)<~>~happy(susan)))=>(wise(mary)))&
((?[X]:((~creative(X)|~quiet(X))))<=>(?[X]:((creative(X)|calm(X)))))&
(((~funny(alice)|~brave(alice)))<=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)|tall(X))<=>~curious(X)))&
(((~creative(lucy)&~calm(lucy)))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((~calm(X)&creative(X))<=>~wise(X)))&
(![X]:((~happy(X)&calm(X))=>(~humble(X)<~>~kind(X))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:(~old(X))))&
(![X]:((~patient(X)<~>patient(X))<=>~creative(X)))&
(![X]:((~patient(X)<~>creative(X))<=>(~kind(X)|~curious(X))))&
((~calm(john)<~>curious(john)))&
(~old(fred))&
((~creative(paul)&~curious(paul)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~humble(X)<~>~creative(X))))&
((~humble(paul)<~>~funny(paul)))&
(?[X]:((~quiet(X)<~>~rich(X)))) | quiet(lucy) | [] | null | 0 |
If someone is not curious or happy then mary is not funny or not quiet and vice versa. Everyone who is not quiet is creative or happy and vice versa. Everyone who is brave or not creative is not humble and vice versa. Everyone who is both patient and not happy is calm or not funny. Everyone who is brave is either quiet or not kind. Everyone who is not humble or rich is either not generous or not creative. If alice is both not old and not happy then someone is calm and vice versa. Everyone who is both not brave and creative is both generous and rich. Everyone who is not patient is not wise and vice versa. Everyone who is generous or wise is not patient or curious and vice versa. If someone is either happy or not quiet then paul is either not curious or creative and vice versa. If susan is both creative and not kind then alice is not kind or tall. Everyone who is both rich and curious is either not kind or rich and vice versa. Everyone who is either not curious or happy is both not humble and not creative and vice versa. Everyone who is both brave and not generous is both funny and kind. Someone is either not rich or happy. Someone is generous. Someone is quiet or happy. Someone is generous or old. Someone is calm or generous. | Alice is not generous. | contradiction | ((?[X]:((~curious(X)|happy(X))))<=>((~funny(mary)|~quiet(mary))))&
(![X]:(~quiet(X)<=>(creative(X)|happy(X))))&
(![X]:((brave(X)|~creative(X))<=>~humble(X)))&
(![X]:((patient(X)&~happy(X))=>(calm(X)|~funny(X))))&
(![X]:(brave(X)=>(quiet(X)<~>~kind(X))))&
(![X]:((~humble(X)|rich(X))=>(~generous(X)<~>~creative(X))))&
(((~old(alice)&~happy(alice)))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)&creative(X))=>(generous(X)&rich(X))))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((generous(X)|wise(X))<=>(~patient(X)|curious(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((~curious(paul)<~>creative(paul))))&
(((creative(susan)&~kind(susan)))=>((~kind(alice)|tall(alice))))&
(![X]:((rich(X)&curious(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(~humble(X)&~creative(X))))&
(![X]:((brave(X)&~generous(X))=>(funny(X)&kind(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)|happy(X))))&
(?[X]:((generous(X)|old(X))))&
(?[X]:((calm(X)|generous(X)))) | ~generous(alice) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2835293992375983083496534
% SZS output start Proof for 2835293992375983083496534
2. ! [X0] : (~quiet(X0) <=> (happy(X0) | creative(X0))) [input p1]
3. ! [X0] : ((~creative(X0) | brave(X0)) <=> ~humble(X0)) [input p2]
5. ! [X0] : (brave(X0) => (quiet(X0) <~> ~kind(X0))) [input p4]
6. ! [X0] : ((rich(X0) | ~humble(X0)) => (~generous(X0) <~> ~creative(X0))) [input p5]
8. ! [X0] : ((creative(X0) & ~brave(X0)) => (rich(X0) & generous(X0))) [input p7]
15. ! [X0] : ((~generous(X0) & brave(X0)) => (kind(X0) & funny(X0))) [input p14]
21. ~generous(alice) [input hypothesis]
25. ! [X0] : ((quiet(X0) <~> ~kind(X0)) | ~brave(X0)) [ennf transformation 5]
26. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | (~rich(X0) & humble(X0))) [ennf transformation 6]
27. ! [X0] : ((rich(X0) & generous(X0)) | (~creative(X0) | brave(X0))) [ennf transformation 8]
28. ! [X0] : ((rich(X0) & generous(X0)) | ~creative(X0) | brave(X0)) [flattening 27]
29. ! [X0] : ((kind(X0) & funny(X0)) | (generous(X0) | ~brave(X0))) [ennf transformation 15]
30. ! [X0] : ((kind(X0) & funny(X0)) | generous(X0) | ~brave(X0)) [flattening 29]
36. ! [X0] : ((~quiet(X0) | (~happy(X0) & ~creative(X0))) & ((happy(X0) | creative(X0)) | quiet(X0))) [nnf transformation 2]
37. ! [X0] : ((~quiet(X0) | (~happy(X0) & ~creative(X0))) & (happy(X0) | creative(X0) | quiet(X0))) [flattening 36]
38. ! [X0] : (((~creative(X0) | brave(X0)) | humble(X0)) & (~humble(X0) | (creative(X0) & ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : ((~creative(X0) | brave(X0) | humble(X0)) & (~humble(X0) | (creative(X0) & ~brave(X0)))) [flattening 38]
40. ! [X0] : (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~brave(X0)) [nnf transformation 25]
41. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~rich(X0) & humble(X0))) [nnf transformation 26]
74. ~creative(X0) | ~quiet(X0) [cnf transformation 37]
77. ~humble(X0) | creative(X0) [cnf transformation 39]
80. ~kind(X0) | quiet(X0) | ~brave(X0) [cnf transformation 40]
84. creative(X0) | generous(X0) | humble(X0) [cnf transformation 41]
89. generous(X0) | ~creative(X0) | brave(X0) [cnf transformation 28]
118. kind(X0) | generous(X0) | ~brave(X0) [cnf transformation 30]
125. ~generous(alice) [cnf transformation 21]
154. generous(X0) | creative(X0) [subsumption resolution 84,77]
173. generous(X0) | brave(X0) [subsumption resolution 89,154]
208. generous(X0) | kind(X0) [subsumption resolution 118,173]
252. creative(alice) [resolution 154,125]
253. ~quiet(alice) [resolution 252,74]
254. brave(alice) [resolution 173,125]
257. kind(alice) [resolution 208,125]
289. quiet(alice) | ~brave(alice) [resolution 80,257]
299. ~brave(alice) [subsumption resolution 289,253]
300. $false [subsumption resolution 299,254]
% SZS output end Proof for 2835293992375983083496534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not happy is brave or kind.
Everyone who is either old or not happy is not patient or curious.
Everyone who is either curious or rich is either not brave or strong.
If someone is not creative then someone is not rich or funny.
If someone is both wise and happy then paul is either curious or not curious and vice versa.
Everyone who is both not kind and humble is either not quiet or old and vice versa.
If someone is creative then someone is not strong.
If someone is either not old or patient then someone is not old or strong and vice versa.
Everyone who is strong or not curious is both not wise and not generous.
If paul is not happy or not patient then someone is both tall and not kind and vice versa.
Everyone who is not kind or happy is both not old and not tall and vice versa.
Everyone who is both not humble and not quiet is creative or not strong.
If someone is not humble or not brave then someone is either not creative or not strong.
If john is either not funny or not wise then someone is both humble and calm.
If alice is either wise or not kind then susan is both not happy and curious.
If susan is kind or tall then someone is either not brave or funny.
Paul is either not creative or rich.
Someone is both wise and funny.
Someone is either not happy or patient.
Someone is calm or not kind.
Susan is both curious and not wise.
Someone is both not wise and humble.
Lucy is strong.
Someone is not humble or patient. | Paul is patient. | entailment | (![X]:((~curious(X)&~happy(X))=>(brave(X)|kind(X))))&
(![X]:((old(X)<~>~happy(X))=>(~patient(X)|curious(X))))&
(![X]:((curious(X)<~>rich(X))=>(~brave(X)<~>strong(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~rich(X)|funny(X)))))&
((?[X]:((wise(X)&happy(X))))<=>((curious(paul)<~>~curious(paul))))&
(![X]:((~kind(X)&humble(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:(creative(X)))=>(?[X]:(~strong(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(![X]:((strong(X)|~curious(X))=>(~wise(X)&~generous(X))))&
(((~happy(paul)|~patient(paul)))<=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((~kind(X)|happy(X))<=>(~old(X)&~tall(X))))&
(![X]:((~humble(X)&~quiet(X))=>(creative(X)|~strong(X))))&
((?[X]:((~humble(X)|~brave(X))))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((~funny(john)<~>~wise(john)))=>(?[X]:((humble(X)&calm(X)))))&
(((wise(alice)<~>~kind(alice)))=>((~happy(susan)&curious(susan))))&
(((kind(susan)|tall(susan)))=>(?[X]:((~brave(X)<~>funny(X)))))&
((~creative(paul)<~>rich(paul)))&
(?[X]:((wise(X)&funny(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((calm(X)|~kind(X))))&
((curious(susan)&~wise(susan)))&
(?[X]:((~wise(X)&humble(X))))&
(strong(lucy))&
(?[X]:((~humble(X)|patient(X)))) | patient(paul) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 392494255256458414291446
% SZS output start Proof for 392494255256458414291446
10. (~patient(paul) | ~happy(paul)) <=> ? [X0] : (~kind(X0) & tall(X0)) [input p9]
11. ! [X0] : ((happy(X0) | ~kind(X0)) <=> (~tall(X0) & ~old(X0))) [input p10]
25. ~patient(paul) [input hypothesis]
66. ((~patient(paul) | ~happy(paul)) | ! [X0] : (kind(X0) | ~tall(X0))) & (? [X0] : (~kind(X0) & tall(X0)) | (patient(paul) & happy(paul))) [nnf transformation 10]
67. (~patient(paul) | ~happy(paul) | ! [X0] : (kind(X0) | ~tall(X0))) & (? [X0] : (~kind(X0) & tall(X0)) | (patient(paul) & happy(paul))) [flattening 66]
68. (~patient(paul) | ~happy(paul) | ! [X0] : (kind(X0) | ~tall(X0))) & (? [X1] : (~kind(X1) & tall(X1)) | (patient(paul) & happy(paul))) [rectify 67]
69. ? [X1] : (~kind(X1) & tall(X1)) => (~kind(sK5) & tall(sK5)) [choice axiom]
70. (~patient(paul) | ~happy(paul) | ! [X0] : (kind(X0) | ~tall(X0))) & ((~kind(sK5) & tall(sK5)) | (patient(paul) & happy(paul))) [skolemisation 68,69]
71. ! [X0] : (((happy(X0) | ~kind(X0)) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | (~happy(X0) & kind(X0)))) [nnf transformation 11]
72. ! [X0] : ((happy(X0) | ~kind(X0) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | (~happy(X0) & kind(X0)))) [flattening 71]
124. tall(sK5) | patient(paul) [cnf transformation 70]
126. ~kind(sK5) | patient(paul) [cnf transformation 70]
130. ~tall(X0) | kind(X0) [cnf transformation 72]
160. ~patient(paul) [cnf transformation 25]
236. 17 <=> ! [X0] : (kind(X0) | ~tall(X0)) [avatar definition]
237. ~tall(X0) | kind(X0) <- (17) [avatar component clause 236]
243. 19 <=> patient(paul) [avatar definition]
248. 20 <=> kind(sK5) [avatar definition]
250. ~kind(sK5) <- (~20) [avatar component clause 248]
251. 19 | ~20 [avatar split clause 126,248,243]
254. 21 <=> tall(sK5) [avatar definition]
256. tall(sK5) <- (21) [avatar component clause 254]
257. 19 | 21 [avatar split clause 124,254,243]
259. 17 [avatar split clause 130,236]
362. ~19 [avatar split clause 160,243]
368. kind(sK5) <- (17, 21) [resolution 237,256]
369. $false <- (17, ~20, 21) [subsumption resolution 368,250]
370. ~17 | 20 | ~21 [avatar contradiction clause 369]
371. $false [avatar sat refutation 251,257,259,362,370]
% SZS output end Proof for 392494255256458414291446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or generous is both rich and brave.
Everyone who is not quiet is funny or strong.
Everyone who is not patient is not old and vice versa.
If someone is funny then mary is not quiet.
Everyone who is either happy or patient is either not wise or kind and vice versa.
Everyone who is funny or not curious is not wise.
If someone is both patient and brave then lucy is not brave or not curious and vice versa.
If someone is not old then fred is either wise or rich and vice versa.
If someone is either not tall or not happy then someone is both not humble and brave and vice versa.
Everyone who is not old or not strong is either not tall or wise and vice versa.
If fred is not kind or not happy then john is both not wise and not strong.
If mary is humble or not creative then paul is not tall.
Everyone who is both quiet and not humble is tall or not curious and vice versa.
Everyone who is either not patient or humble is not generous or not brave and vice versa.
If someone is not kind then someone is curious or humble.
If someone is either funny or not generous then someone is both not curious and not brave and vice versa.
Someone is not old.
Paul is either not kind or not calm.
Someone is both tall and brave.
Fred is either old or not rich.
Someone is not wise.
Lucy is not generous or rich.
Someone is humble.
Lucy is both calm and not tall. | Lucy is curious. | neutral | (![X]:((kind(X)|generous(X))=>(rich(X)&brave(X))))&
(![X]:(~quiet(X)=>(funny(X)|strong(X))))&
(![X]:(~patient(X)<=>~old(X)))&
((?[X]:(funny(X)))=>(~quiet(mary)))&
(![X]:((happy(X)<~>patient(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((funny(X)|~curious(X))=>~wise(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~brave(lucy)|~curious(lucy))))&
((?[X]:(~old(X)))<=>((wise(fred)<~>rich(fred))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~tall(X)<~>wise(X))))&
(((~kind(fred)|~happy(fred)))=>((~wise(john)&~strong(john))))&
(((humble(mary)|~creative(mary)))=>(~tall(paul)))&
(![X]:((quiet(X)&~humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(?[X]:(~old(X)))&
((~kind(paul)<~>~calm(paul)))&
(?[X]:((tall(X)&brave(X))))&
((old(fred)<~>~rich(fred)))&
(?[X]:(~wise(X)))&
((~generous(lucy)|rich(lucy)))&
(?[X]:(humble(X)))&
((calm(lucy)&~tall(lucy))) | curious(lucy) | [] | null | 0 |
If someone is quiet then someone is both strong and not wise and vice versa. If fred is either quiet or not funny then someone is either humble or not humble. Everyone who is both creative and strong is both quiet and calm. If fred is not generous then someone is both strong and calm. If mary is not old then lucy is either not humble or calm. Everyone who is either not tall or humble is wise. Everyone who is funny or strong is not quiet and vice versa. If someone is not old or kind then someone is both wise and not brave and vice versa. Everyone who is both rich and quiet is rich or quiet and vice versa. Everyone who is either calm or not brave is either not old or kind. If someone is either funny or not strong then someone is not strong and vice versa. If someone is brave or humble then susan is rich and vice versa. Everyone who is not funny is either wise or humble and vice versa. If fred is either wise or curious then someone is either funny or not quiet. If lucy is not tall then susan is either not wise or not tall. If someone is either happy or patient then fred is funny and vice versa. Someone is curious or not calm. Alice is not wise. Alice is either patient or not curious. Someone is both not kind and not creative. Mary is generous. John is either not generous or funny. Paul is not funny. Alice is both patient and strong. | Alice is not creative. | entailment | ((?[X]:(quiet(X)))<=>(?[X]:((strong(X)&~wise(X)))))&
(((quiet(fred)<~>~funny(fred)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((creative(X)&strong(X))=>(quiet(X)&calm(X))))&
((~generous(fred))=>(?[X]:((strong(X)&calm(X)))))&
((~old(mary))=>((~humble(lucy)<~>calm(lucy))))&
(![X]:((~tall(X)<~>humble(X))=>wise(X)))&
(![X]:((funny(X)|strong(X))<=>~quiet(X)))&
((?[X]:((~old(X)|kind(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((rich(X)&quiet(X))<=>(rich(X)|quiet(X))))&
(![X]:((calm(X)<~>~brave(X))=>(~old(X)<~>kind(X))))&
((?[X]:((funny(X)<~>~strong(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((brave(X)|humble(X))))<=>(rich(susan)))&
(![X]:(~funny(X)<=>(wise(X)<~>humble(X))))&
(((wise(fred)<~>curious(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
((~tall(lucy))=>((~wise(susan)<~>~tall(susan))))&
((?[X]:((happy(X)<~>patient(X))))<=>(funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice)))&
(?[X]:((~kind(X)&~creative(X))))&
(generous(mary))&
((~generous(john)<~>funny(john)))&
(~funny(paul))&
((patient(alice)&strong(alice))) | ~creative(alice) | [
"p2",
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5010570957312935322456972
% SZS output start Proof for 5010570957312935322456972
3. ! [X0] : ((strong(X0) & creative(X0)) => (calm(X0) & quiet(X0))) [input p2]
7. ! [X0] : ((strong(X0) | funny(X0)) <=> ~quiet(X0)) [input p6]
24. strong(alice) & patient(alice) [input p23]
25. creative(alice) [input hypothesis]
30. ! [X0] : ((calm(X0) & quiet(X0)) | (~strong(X0) | ~creative(X0))) [ennf transformation 3]
31. ! [X0] : ((calm(X0) & quiet(X0)) | ~strong(X0) | ~creative(X0)) [flattening 30]
50. ! [X0] : (((strong(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & ~funny(X0)))) [nnf transformation 7]
51. ! [X0] : ((strong(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & ~funny(X0)))) [flattening 50]
91. ~creative(X0) | ~strong(X0) | quiet(X0) [cnf transformation 31]
100. ~strong(X0) | ~quiet(X0) [cnf transformation 51]
148. strong(alice) [cnf transformation 24]
149. creative(alice) [cnf transformation 25]
370. ~quiet(alice) [resolution 100,148]
376. ~strong(alice) | quiet(alice) [resolution 91,149]
377. quiet(alice) [subsumption resolution 376,148]
378. $false [subsumption resolution 377,370]
% SZS output end Proof for 5010570957312935322456972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is not humble. Everyone who is either not creative or generous is either not patient or old. Everyone who is either not generous or quiet is not patient and vice versa. Everyone who is both not tall and not happy is either quiet or humble and vice versa. Everyone who is curious is either old or not patient and vice versa. Everyone who is funny is not funny or not creative and vice versa. If alice is either not curious or humble then lucy is either creative or not wise. If someone is either not brave or not curious then mary is curious or calm and vice versa. Everyone who is both happy and not happy is calm or quiet and vice versa. If someone is rich or patient then someone is kind. Everyone who is tall is creative or rich. If someone is not creative or tall then someone is funny or happy and vice versa. Everyone who is either not old or not brave is both not calm and not tall. Everyone who is either calm or creative is generous or rich and vice versa. Fred is either not patient or not strong. Someone is both funny and not generous. Someone is either humble or not patient. | Fred is not old. | entailment | (![X]:((~creative(X)&curious(X))=>~humble(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~patient(X)<~>old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>~patient(X)))&
(![X]:((~tall(X)&~happy(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(curious(X)<=>(old(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~funny(X)|~creative(X))))&
(((~curious(alice)<~>humble(alice)))=>((creative(lucy)<~>~wise(lucy))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((happy(X)&~happy(X))<=>(calm(X)|quiet(X))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(kind(X))))&
(![X]:(tall(X)=>(creative(X)|rich(X))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
(![X]:((calm(X)<~>creative(X))<=>(generous(X)|rich(X))))&
((~patient(fred)<~>~strong(fred)))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~old(fred) | [
"p1",
"p2",
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 811141817632741536351548
% SZS output start Proof for 811141817632741536351548
2. ! [X0] : ((~creative(X0) <~> generous(X0)) => (~patient(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> ~patient(X0)) [input p2]
6. ! [X0] : (funny(X0) <=> (~creative(X0) | ~funny(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & happy(X0)) <=> (quiet(X0) | calm(X0))) [input p8]
14. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (rich(X0) | generous(X0))) [input p13]
18. old(fred) [input hypothesis]
24. ! [X0] : ((~patient(X0) <~> old(X0)) | (~creative(X0) <=> generous(X0))) [ennf transformation 2]
29. ! [X0] : (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 24]
30. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | patient(X0)) & (~patient(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 3]
34. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 6]
35. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~funny(X0))) [flattening 34]
42. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | happy(X0) | ~happy(X0))) [flattening 42]
50. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & ((rich(X0) | generous(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 14]
51. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & (rich(X0) | generous(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 50]
61. ~old(X0) | patient(X0) | generous(X0) | creative(X0) [cnf transformation 29]
63. ~patient(X0) | quiet(X0) | generous(X0) [cnf transformation 30]
77. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 35]
78. funny(X0) | funny(X0) [cnf transformation 35]
91. happy(X0) | ~calm(X0) [cnf transformation 43]
92. happy(X0) | ~quiet(X0) [cnf transformation 43]
93. ~calm(X0) | ~happy(X0) [cnf transformation 43]
94. ~happy(X0) | ~quiet(X0) [cnf transformation 43]
106. creative(X0) | calm(X0) | ~generous(X0) [cnf transformation 51]
116. old(fred) [cnf transformation 18]
117. ~creative(X0) | ~funny(X0) [duplicate literal removal 77]
118. funny(X0) [duplicate literal removal 78]
119. ~creative(X0) [subsumption resolution 117,118]
164. ~quiet(X0) [subsumption resolution 92,94]
165. ~calm(X0) [subsumption resolution 91,93]
169. calm(X0) | ~generous(X0) [subsumption resolution 106,119]
170. ~generous(X0) [subsumption resolution 169,165]
172. 10 <=> patient(fred) [avatar definition]
173. ~patient(fred) <- (~10) [avatar component clause 172]
174. patient(fred) <- (10) [avatar component clause 172]
193. quiet(fred) | generous(fred) <- (10) [resolution 63,174]
194. generous(fred) <- (10) [subsumption resolution 193,164]
195. $false <- (10) [subsumption resolution 194,170]
196. ~10 [avatar contradiction clause 195]
214. patient(fred) | generous(fred) | creative(fred) [resolution 61,116]
217. generous(fred) | creative(fred) <- (~10) [subsumption resolution 214,173]
218. creative(fred) <- (~10) [subsumption resolution 217,170]
219. $false <- (~10) [subsumption resolution 218,119]
220. 10 [avatar contradiction clause 219]
223. $false [avatar sat refutation 196,220]
% SZS output end Proof for 811141817632741536351548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is humble and vice versa.
Everyone who is either not happy or not quiet is not happy or not humble.
If someone is not wise then paul is both tall and not patient and vice versa.
Everyone who is either wise or not humble is either calm or generous and vice versa.
If fred is not calm or not quiet then john is both not rich and quiet and vice versa.
Everyone who is not funny or rich is either funny or happy and vice versa.
If paul is not quiet or humble then alice is both generous and not funny.
If someone is either funny or patient then alice is not quiet or rich.
Everyone who is not curious is either wise or not old and vice versa.
If someone is either not patient or not tall then someone is either tall or not kind.
Everyone who is not patient or not generous is either old or not generous.
Everyone who is generous or curious is either not wise or not rich and vice versa.
If someone is old or not wise then susan is not old or humble.
If fred is rich or not rich then alice is old.
If paul is strong or generous then someone is not humble or quiet.
If someone is not calm then john is not calm and vice versa.
Fred is humble or funny.
Someone is funny or not happy.
Someone is both not wise and not brave.
Someone is both not humble and tall.
Susan is not patient or calm.
Someone is both generous and not rich.
Someone is both brave and curious.
Someone is not strong or not humble. | John is happy. | entailment | (![X]:(~calm(X)<=>humble(X)))&
(![X]:((~happy(X)<~>~quiet(X))=>(~happy(X)|~humble(X))))&
((?[X]:(~wise(X)))<=>((tall(paul)&~patient(paul))))&
(![X]:((wise(X)<~>~humble(X))<=>(calm(X)<~>generous(X))))&
(((~calm(fred)|~quiet(fred)))<=>((~rich(john)&quiet(john))))&
(![X]:((~funny(X)|rich(X))<=>(funny(X)<~>happy(X))))&
(((~quiet(paul)|humble(paul)))=>((generous(alice)&~funny(alice))))&
((?[X]:((funny(X)<~>patient(X))))=>((~quiet(alice)|rich(alice))))&
(![X]:(~curious(X)<=>(wise(X)<~>~old(X))))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~generous(X))=>(old(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))<=>(~wise(X)<~>~rich(X))))&
((?[X]:((old(X)|~wise(X))))=>((~old(susan)|humble(susan))))&
(((rich(fred)|~rich(fred)))=>(old(alice)))&
(((strong(paul)|generous(paul)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:(~calm(X)))<=>(~calm(john)))&
((humble(fred)|funny(fred)))&
(?[X]:((funny(X)|~happy(X))))&
(?[X]:((~wise(X)&~brave(X))))&
(?[X]:((~humble(X)&tall(X))))&
((~patient(susan)|calm(susan)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~strong(X)|~humble(X)))) | happy(john) | [
"p0",
"p3",
"p5",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4685977927289085876479708
% SZS output start Proof for 4685977927289085876479708
1. ! [X0] : (~calm(X0) <=> humble(X0)) [input p0]
4. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> (calm(X0) <~> generous(X0))) [input p3]
6. ! [X0] : ((rich(X0) | ~funny(X0)) <=> (funny(X0) <~> happy(X0))) [input p5]
9. ! [X0] : (~curious(X0) <=> (wise(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((~generous(X0) | ~patient(X0)) => (old(X0) <~> ~generous(X0))) [input p10]
12. ! [X0] : ((curious(X0) | generous(X0)) <=> (~wise(X0) <~> ~rich(X0))) [input p11]
25. ~happy(john) [input hypothesis]
35. ! [X0] : ((old(X0) <~> ~generous(X0)) | (generous(X0) & patient(X0))) [ennf transformation 11]
40. ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))) [nnf transformation 1]
47. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 4]
50. ! [X0] : (((rich(X0) | ~funny(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~rich(X0) & funny(X0)))) [nnf transformation 6]
51. ! [X0] : ((rich(X0) | ~funny(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~rich(X0) & funny(X0)))) [flattening 50]
53. ! [X0] : ((~curious(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | curious(X0))) [nnf transformation 9]
58. ! [X0] : (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (generous(X0) & patient(X0))) [nnf transformation 35]
59. ! [X0] : (((curious(X0) | generous(X0)) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0)))) & (((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | (~curious(X0) & ~generous(X0)))) [nnf transformation 12]
60. ! [X0] : ((curious(X0) | generous(X0) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0)))) & (((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | (~curious(X0) & ~generous(X0)))) [flattening 59]
77. humble(X0) | calm(X0) [cnf transformation 40]
78. ~humble(X0) | ~calm(X0) [cnf transformation 40]
84. generous(X0) | calm(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 47]
87. ~generous(X0) | ~calm(X0) | wise(X0) | humble(X0) [cnf transformation 47]
89. ~humble(X0) | wise(X0) | calm(X0) | ~generous(X0) [cnf transformation 47]
90. humble(X0) | ~wise(X0) | generous(X0) | ~calm(X0) [cnf transformation 47]
97. happy(X0) | funny(X0) | funny(X0) [cnf transformation 51]
101. rich(X0) | ~funny(X0) | happy(X0) | ~funny(X0) [cnf transformation 51]
112. ~curious(X0) | wise(X0) | old(X0) [cnf transformation 53]
120. generous(X0) | ~old(X0) | generous(X0) [cnf transformation 58]
121. ~rich(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 60]
122. ~curious(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 60]
125. curious(X0) | generous(X0) | ~rich(X0) | wise(X0) [cnf transformation 60]
145. ~happy(john) [cnf transformation 25]
146. ~old(X0) | generous(X0) [duplicate literal removal 120]
147. funny(X0) | happy(X0) [duplicate literal removal 97]
148. ~funny(X0) | rich(X0) | happy(X0) [duplicate literal removal 101]
168. ~wise(X0) | humble(X0) | generous(X0) [subsumption resolution 90,77]
169. ~generous(X0) | wise(X0) | ~humble(X0) [subsumption resolution 89,78]
170. ~generous(X0) | wise(X0) | humble(X0) [subsumption resolution 87,77]
171. ~generous(X0) | wise(X0) [subsumption resolution 170,169]
172. generous(X0) | ~humble(X0) | ~wise(X0) [subsumption resolution 84,78]
173. ~wise(X0) | generous(X0) [subsumption resolution 172,168]
175. 5 <=> rich(john) [avatar definition]
176. ~rich(john) <- (~5) [avatar component clause 175]
177. rich(john) <- (5) [avatar component clause 175]
249. ~rich(X0) | generous(X0) | curious(X0) [subsumption resolution 125,173]
250. ~rich(X0) | ~generous(X0) [subsumption resolution 121,171]
405. rich(X0) | happy(X0) | happy(X0) [resolution 148,147]
406. rich(X0) | happy(X0) [duplicate literal removal 405]
433. happy(john) <- (~5) [resolution 406,176]
437. $false <- (~5) [subsumption resolution 433,145]
438. 5 [avatar contradiction clause 437]
439. generous(john) | curious(john) <- (5) [resolution 177,249]
441. ~generous(john) <- (5) [resolution 177,250]
443. 46 <=> curious(john) [avatar definition]
445. curious(john) <- (46) [avatar component clause 443]
447. 47 <=> generous(john) [avatar definition]
448. ~generous(john) <- (~47) [avatar component clause 447]
450. 46 | 47 | ~5 [avatar split clause 439,175,447,443]
451. ~47 | ~5 [avatar split clause 441,175,447]
461. ~wise(john) | ~rich(john) <- (46) [resolution 445,122]
462. wise(john) | old(john) <- (46) [resolution 445,112]
463. ~wise(john) <- (5, 46) [subsumption resolution 461,177]
464. old(john) <- (5, 46) [subsumption resolution 462,463]
493. generous(john) <- (5, 46) [resolution 464,146]
494. $false <- (5, 46, ~47) [subsumption resolution 493,448]
495. ~5 | ~46 | 47 [avatar contradiction clause 494]
496. $false [avatar sat refutation 438,450,451,495]
% SZS output end Proof for 4685977927289085876479708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not calm or calm is both rich and old.
If alice is not humble or not patient then lucy is curious or not brave and vice versa.
If someone is both old and not patient then fred is tall or not quiet.
Everyone who is humble is tall.
Everyone who is strong is both rich and tall.
Everyone who is not curious is either generous or not happy.
If john is either kind or happy then lucy is either old or not brave and vice versa.
Everyone who is kind or not calm is either not funny or not humble.
Everyone who is both not happy and not tall is both not calm and wise and vice versa.
If someone is either not strong or not creative then mary is either tall or not wise.
Everyone who is not curious is tall and vice versa.
If paul is both tall and calm then someone is quiet and vice versa.
If susan is either not happy or tall then someone is curious and vice versa.
Everyone who is brave is both not brave and not humble.
Everyone who is both not generous and old is both not old and not quiet.
If someone is either old or wise then fred is quiet or kind and vice versa.
Someone is either generous or not strong.
Someone is not curious.
Someone is not humble.
Susan is not calm or not old.
Mary is both not creative and kind.
Paul is generous or not curious. | Lucy is generous. | entailment | (![X]:((~calm(X)|calm(X))=>(rich(X)&old(X))))&
(((~humble(alice)|~patient(alice)))<=>((curious(lucy)|~brave(lucy))))&
((?[X]:((old(X)&~patient(X))))=>((tall(fred)|~quiet(fred))))&
(![X]:(humble(X)=>tall(X)))&
(![X]:(strong(X)=>(rich(X)&tall(X))))&
(![X]:(~curious(X)=>(generous(X)<~>~happy(X))))&
(((kind(john)<~>happy(john)))<=>((old(lucy)<~>~brave(lucy))))&
(![X]:((kind(X)|~calm(X))=>(~funny(X)<~>~humble(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~calm(X)&wise(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>((tall(mary)<~>~wise(mary))))&
(![X]:(~curious(X)<=>tall(X)))&
(((tall(paul)&calm(paul)))<=>(?[X]:(quiet(X))))&
(((~happy(susan)<~>tall(susan)))<=>(?[X]:(curious(X))))&
(![X]:(brave(X)=>(~brave(X)&~humble(X))))&
(![X]:((~generous(X)&old(X))=>(~old(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))<=>((quiet(fred)|kind(fred))))&
(?[X]:((generous(X)<~>~strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:(~humble(X)))&
((~calm(susan)|~old(susan)))&
((~creative(mary)&kind(mary)))&
((generous(paul)|~curious(paul))) | generous(lucy) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 461737901225527630491485
% SZS output start Proof for 461737901225527630491485
1. ! [X0] : ((calm(X0) | ~calm(X0)) => (old(X0) & rich(X0))) [input p0]
15. ! [X0] : ((old(X0) & ~generous(X0)) => (~quiet(X0) & ~old(X0))) [input p14]
23. ~generous(lucy) [input hypothesis]
24. ! [X0] : ((calm(X0) | ~calm(X0)) => old(X0)) [pure predicate removal 1]
26. ! [X0] : (old(X0) | (~calm(X0) & calm(X0))) [ennf transformation 24]
35. ! [X0] : ((~quiet(X0) & ~old(X0)) | (~old(X0) | generous(X0))) [ennf transformation 15]
36. ! [X0] : ((~quiet(X0) & ~old(X0)) | ~old(X0) | generous(X0)) [flattening 35]
67. old(X0) | calm(X0) [cnf transformation 26]
68. old(X0) | ~calm(X0) [cnf transformation 26]
109. ~old(X0) | ~old(X0) | generous(X0) [cnf transformation 36]
125. ~generous(lucy) [cnf transformation 23]
126. ~old(X0) | generous(X0) [duplicate literal removal 109]
128. old(X0) [subsumption resolution 67,68]
234. generous(X0) [subsumption resolution 126,128]
254. $false [subsumption resolution 125,234]
% SZS output end Proof for 461737901225527630491485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or wise is not old or not patient and vice versa.
Everyone who is not tall or not rich is not patient.
If someone is either curious or calm then someone is tall.
If someone is strong then someone is either curious or funny and vice versa.
Everyone who is both not funny and not calm is not humble or wise.
If someone is curious or not rich then someone is rich.
Everyone who is either not calm or not rich is either patient or not strong.
If john is either calm or humble then mary is either not wise or happy and vice versa.
Everyone who is not quiet or old is wise or calm.
If john is brave then mary is both humble and creative and vice versa.
If someone is either tall or not tall then someone is either humble or not tall.
Everyone who is not curious is either not old or humble and vice versa.
Everyone who is not generous or funny is either funny or not tall.
If susan is rich or brave then someone is either not strong or wise and vice versa.
Everyone who is either quiet or not tall is not calm or not quiet.
Everyone who is not old or happy is strong or not curious and vice versa.
Someone is either not wise or generous.
Someone is not rich.
Someone is not generous or not strong.
Someone is not patient.
Someone is not generous.
Susan is both not brave and not curious.
Someone is wise. | Susan is old. | neutral | (![X]:((~humble(X)|wise(X))<=>(~old(X)|~patient(X))))&
(![X]:((~tall(X)|~rich(X))=>~patient(X)))&
((?[X]:((curious(X)<~>calm(X))))=>(?[X]:(tall(X))))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~funny(X)&~calm(X))=>(~humble(X)|wise(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:(rich(X))))&
(![X]:((~calm(X)<~>~rich(X))=>(patient(X)<~>~strong(X))))&
(((calm(john)<~>humble(john)))<=>((~wise(mary)<~>happy(mary))))&
(![X]:((~quiet(X)|old(X))=>(wise(X)|calm(X))))&
((brave(john))<=>((humble(mary)&creative(mary))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:(~curious(X)<=>(~old(X)<~>humble(X))))&
(![X]:((~generous(X)|funny(X))=>(funny(X)<~>~tall(X))))&
(((rich(susan)|brave(susan)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~old(X)|happy(X))<=>(strong(X)|~curious(X))))&
(?[X]:((~wise(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~generous(X)))&
((~brave(susan)&~curious(susan)))&
(?[X]:(wise(X))) | old(susan) | [] | null | 0 |
If paul is both curious and patient then someone is both quiet and generous. Everyone who is brave is not creative or kind and vice versa. If susan is either old or happy then lucy is not curious or curious and vice versa. Everyone who is old or not funny is both not creative and not humble and vice versa. Everyone who is either not creative or not old is happy. Everyone who is both not strong and not patient is not funny and vice versa. Everyone who is either not generous or not happy is not quiet or curious. Everyone who is strong is not strong or not quiet and vice versa. Everyone who is not creative or not quiet is either humble or not funny. Everyone who is not humble or happy is creative. If alice is not creative or not generous then someone is not old and vice versa. Everyone who is brave is humble or brave and vice versa. Everyone who is both not tall and not happy is either not rich or not curious and vice versa. Everyone who is not happy is both not humble and quiet and vice versa. If john is not tall then someone is not brave or not kind and vice versa. Everyone who is old is not happy and vice versa. Susan is not quiet or quiet. Lucy is either happy or not brave. John is either not happy or happy. Paul is not quiet or creative. Someone is not old or kind. Fred is both rich and humble. | Fred is not patient. | neutral | (((curious(paul)&patient(paul)))=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:(brave(X)<=>(~creative(X)|kind(X))))&
(((old(susan)<~>happy(susan)))<=>((~curious(lucy)|curious(lucy))))&
(![X]:((old(X)|~funny(X))<=>(~creative(X)&~humble(X))))&
(![X]:((~creative(X)<~>~old(X))=>happy(X)))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(~quiet(X)|curious(X))))&
(![X]:(strong(X)<=>(~strong(X)|~quiet(X))))&
(![X]:((~creative(X)|~quiet(X))=>(humble(X)<~>~funny(X))))&
(![X]:((~humble(X)|happy(X))=>creative(X)))&
(((~creative(alice)|~generous(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>(humble(X)|brave(X))))&
(![X]:((~tall(X)&~happy(X))<=>(~rich(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(~humble(X)&quiet(X))))&
((~tall(john))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(old(X)<=>~happy(X)))&
((~quiet(susan)|quiet(susan)))&
((happy(lucy)<~>~brave(lucy)))&
((~happy(john)<~>happy(john)))&
((~quiet(paul)|creative(paul)))&
(?[X]:((~old(X)|kind(X))))&
((rich(fred)&humble(fred))) | ~patient(fred) | [] | null | 0 |
Everyone who is both happy and not humble is either not creative or not humble and vice versa.
Everyone who is happy is either funny or wise and vice versa.
Everyone who is not old is generous.
If paul is both not happy and not calm then someone is both tall and not happy.
Everyone who is old or not funny is either rich or happy and vice versa.
If fred is tall or old then someone is either quiet or not quiet.
Everyone who is either not wise or happy is not brave and vice versa.
If susan is not quiet then someone is either old or strong.
If someone is either tall or generous then alice is both not humble and not tall.
Everyone who is generous or not tall is kind and vice versa.
Everyone who is either not patient or not funny is both not tall and patient and vice versa.
If someone is either rich or patient then someone is either happy or not funny and vice versa.
Everyone who is not creative or old is both wise and funny.
If someone is funny or tall then lucy is both not tall and old.
Everyone who is both not calm and kind is tall.
Everyone who is both rich and not wise is not creative.
Someone is happy or not old.
John is humble.
Fred is generous or not quiet.
Someone is either generous or not kind. | John is generous. | entailment | (![X]:((happy(X)&~humble(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(happy(X)<=>(funny(X)<~>wise(X))))&
(![X]:(~old(X)=>generous(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((old(X)|~funny(X))<=>(rich(X)<~>happy(X))))&
(((tall(fred)|old(fred)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~brave(X)))&
((~quiet(susan))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((~humble(alice)&~tall(alice))))&
(![X]:((generous(X)|~tall(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~creative(X)|old(X))=>(wise(X)&funny(X))))&
((?[X]:((funny(X)|tall(X))))=>((~tall(lucy)&old(lucy))))&
(![X]:((~calm(X)&kind(X))=>tall(X)))&
(![X]:((rich(X)&~wise(X))=>~creative(X)))&
(?[X]:((happy(X)|~old(X))))&
(humble(john))&
((generous(fred)|~quiet(fred)))&
(?[X]:((generous(X)<~>~kind(X)))) | generous(john) | [
"p2",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7384668067083945043522562
% SZS output start Proof for 7384668067083945043522562
3. ! [X0] : (~old(X0) => generous(X0)) [input p2]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (patient(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~creative(X0)) => (funny(X0) & wise(X0))) [input p12]
14. ? [X0] : (tall(X0) | funny(X0)) => (old(lucy) & ~tall(lucy)) [input p13]
21. ~generous(john) [input hypothesis]
25. ! [X0] : (generous(X0) | old(X0)) [ennf transformation 3]
29. ! [X0] : ((funny(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 13]
30. (old(lucy) & ~tall(lucy)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 14]
47. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
48. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 47]
69. generous(X0) | old(X0) [cnf transformation 25]
91. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 48]
93. ~funny(X0) | ~patient(X0) | ~patient(X0) | tall(X0) [cnf transformation 48]
106. ~old(X0) | funny(X0) [cnf transformation 29]
107. ~tall(lucy) | ~funny(X0) [cnf transformation 30]
109. old(lucy) | ~funny(X0) [cnf transformation 30]
117. ~generous(john) [cnf transformation 21]
118. ~funny(X0) | patient(X0) [duplicate literal removal 91]
119. ~patient(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 93]
195. 17 <=> old(lucy) [avatar definition]
197. old(lucy) <- (17) [avatar component clause 195]
200. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
201. ~funny(X0) <- (18) [avatar component clause 200]
202. 18 | 17 [avatar split clause 109,195,200]
204. 19 <=> tall(lucy) [avatar definition]
206. ~tall(lucy) <- (~19) [avatar component clause 204]
208. 18 | ~19 [avatar split clause 107,204,200]
237. old(john) [resolution 69,117]
245. funny(lucy) <- (17) [resolution 106,197]
246. funny(john) [resolution 106,237]
250. patient(lucy) <- (17) [resolution 245,118]
318. ~funny(lucy) | tall(lucy) <- (17) [resolution 119,250]
321. tall(lucy) <- (17) [subsumption resolution 318,245]
322. $false <- (17, ~19) [subsumption resolution 321,206]
323. ~17 | 19 [avatar contradiction clause 322]
331. $false <- (18) [resolution 201,246]
334. ~18 [avatar contradiction clause 331]
335. $false [avatar sat refutation 202,208,323,334]
% SZS output end Proof for 7384668067083945043522562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is not wise then fred is either not curious or funny.
If alice is not quiet then someone is happy and vice versa.
Everyone who is not wise or generous is either not rich or not old.
If someone is quiet then paul is happy and vice versa.
Everyone who is not humble is both not happy and not curious and vice versa.
If someone is both not rich and not quiet then someone is not creative or patient and vice versa.
If someone is wise or humble then john is tall and vice versa.
If someone is quiet or not rich then someone is either not tall or not calm.
If lucy is either happy or not kind then john is either not funny or funny.
If mary is both tall and not old then mary is patient or rich and vice versa.
If someone is either not tall or kind then someone is either creative or kind.
If john is both kind and old then john is both brave and not generous.
Everyone who is either calm or generous is either curious or generous and vice versa.
Everyone who is either generous or tall is not tall and vice versa.
If mary is not quiet then lucy is either not funny or happy.
Everyone who is curious or not old is either not calm or rich and vice versa.
Mary is calm or strong.
Someone is both not patient and funny.
Someone is not strong or not old.
Alice is either wise or patient. | Fred is patient. | contradiction | ((~wise(susan))=>((~curious(fred)<~>funny(fred))))&
((~quiet(alice))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|generous(X))=>(~rich(X)<~>~old(X))))&
((?[X]:(quiet(X)))<=>(happy(paul)))&
(![X]:(~humble(X)<=>(~happy(X)&~curious(X))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(tall(john)))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((happy(lucy)<~>~kind(lucy)))=>((~funny(john)<~>funny(john))))&
(((tall(mary)&~old(mary)))<=>((patient(mary)|rich(mary))))&
((?[X]:((~tall(X)<~>kind(X))))=>(?[X]:((creative(X)<~>kind(X)))))&
(((kind(john)&old(john)))=>((brave(john)&~generous(john))))&
(![X]:((calm(X)<~>generous(X))<=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>tall(X))<=>~tall(X)))&
((~quiet(mary))=>((~funny(lucy)<~>happy(lucy))))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)<~>rich(X))))&
((calm(mary)|strong(mary)))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((~strong(X)|~old(X))))&
((wise(alice)<~>patient(alice))) | patient(fred) | [
"p2",
"p5",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8123012059152114903914559
% SZS output start Proof for 8123012059152114903914559
3. ! [X0] : ((generous(X0) | ~wise(X0)) => (~rich(X0) <~> ~old(X0))) [input p2]
6. ? [X0] : (~quiet(X0) & ~rich(X0)) <=> ? [X0] : (patient(X0) | ~creative(X0)) [input p5]
13. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (curious(X0) <~> generous(X0))) [input p12]
14. ! [X0] : ((generous(X0) <~> tall(X0)) <=> ~tall(X0)) [input p13]
16. ! [X0] : ((~old(X0) | curious(X0)) <=> (~calm(X0) <~> rich(X0))) [input p15]
21. patient(fred) [input hypothesis]
22. ? [X0] : (~quiet(X0) & ~rich(X0)) <=> ? [X1] : (patient(X1) | ~creative(X1)) [rectify 6]
27. ! [X0] : ((~rich(X0) <~> ~old(X0)) | (~generous(X0) & wise(X0))) [ennf transformation 3]
39. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~generous(X0) & wise(X0))) [nnf transformation 27]
46. (? [X0] : (~quiet(X0) & ~rich(X0)) | ! [X1] : (~patient(X1) & creative(X1))) & (? [X1] : (patient(X1) | ~creative(X1)) | ! [X0] : (quiet(X0) | rich(X0))) [nnf transformation 22]
47. (? [X0] : (~quiet(X0) & ~rich(X0)) | ! [X1] : (~patient(X1) & creative(X1))) & (? [X2] : (patient(X2) | ~creative(X2)) | ! [X3] : (quiet(X3) | rich(X3))) [rectify 46]
48. ? [X0] : (~quiet(X0) & ~rich(X0)) => (~quiet(sK2) & ~rich(sK2)) [choice axiom]
49. ? [X2] : (patient(X2) | ~creative(X2)) => (patient(sK3) | ~creative(sK3)) [choice axiom]
50. ((~quiet(sK2) & ~rich(sK2)) | ! [X1] : (~patient(X1) & creative(X1))) & ((patient(sK3) | ~creative(sK3)) | ! [X3] : (quiet(X3) | rich(X3))) [skolemisation 47,49,48]
66. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 14]
69. ! [X0] : (((~old(X0) | curious(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : ((~old(X0) | curious(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [flattening 69]
83. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 39]
91. ~rich(sK2) | ~patient(X1) [cnf transformation 50]
115. generous(X0) | curious(X0) | generous(X0) | ~calm(X0) [cnf transformation 66]
118. ~generous(X0) | ~curious(X0) | calm(X0) | ~generous(X0) [cnf transformation 66]
119. generous(X0) | calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 66]
122. ~generous(X0) | ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 66]
124. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 67]
125. tall(X0) | generous(X0) | tall(X0) [cnf transformation 67]
129. rich(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 70]
133. ~old(X0) | curious(X0) | rich(X0) | calm(X0) [cnf transformation 70]
141. patient(fred) [cnf transformation 21]
142. ~tall(X0) | generous(X0) [duplicate literal removal 124]
143. tall(X0) | generous(X0) [duplicate literal removal 125]
144. generous(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 115]
145. ~generous(X0) | ~curious(X0) | calm(X0) [duplicate literal removal 118]
146. ~curious(X0) | calm(X0) | generous(X0) [duplicate literal removal 119]
147. ~calm(X0) | ~generous(X0) | curious(X0) [duplicate literal removal 122]
189. 10 <=> ! [X1] : ~patient(X1) [avatar definition]
190. ~patient(X1) <- (10) [avatar component clause 189]
201. 13 <=> rich(sK2) [avatar definition]
203. ~rich(sK2) <- (~13) [avatar component clause 201]
204. 10 | ~13 [avatar split clause 91,201,189]
240. 22 <=> ! [X1] : rich(X1) [avatar definition]
241. rich(X1) <- (22) [avatar component clause 240]
306. ~curious(X0) | calm(X0) [subsumption resolution 145,146]
307. ~calm(X0) | curious(X0) [subsumption resolution 144,147]
308. generous(X0) [subsumption resolution 142,143]
323. ~old(X0) | rich(X0) | calm(X0) [subsumption resolution 133,306]
324. ~calm(X0) | rich(X0) [subsumption resolution 129,307]
355. $false <- (~13, 22) [subsumption resolution 203,241]
356. 13 | ~22 [avatar contradiction clause 355]
361. $false <- (10) [resolution 190,141]
362. ~10 [avatar contradiction clause 361]
416. old(X0) | rich(X0) [resolution 83,308]
427. rich(X0) | calm(X0) | rich(X0) [resolution 323,416]
432. rich(X0) | calm(X0) [duplicate literal removal 427]
433. rich(X0) [subsumption resolution 432,324]
434. 22 [avatar split clause 433,240]
438. $false [avatar sat refutation 204,356,362,434]
% SZS output end Proof for 8123012059152114903914559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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