premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both happy and creative is both not strong and not tall. If someone is not kind then paul is not wise. If john is tall or wise then someone is both not funny and strong. If fred is both not tall and creative then lucy is both humble and brave. Everyone who is strong is old. Everyone who is not rich is either rich or funny and vice versa. Everyone who is both not patient and not generous is either wise or not old. Everyone who is creative is not happy and vice versa. If someone is kind then someone is not old or not happy. Everyone who is either not quiet or humble is either rich or tall. Everyone who is not old or patient is quiet or not strong. Everyone who is either patient or not strong is both patient and not strong and vice versa. Everyone who is either not curious or curious is not humble and vice versa. Everyone who is not strong is both wise and creative. If john is either strong or calm then lucy is both rich and wise and vice versa. Everyone who is both not old and curious is curious or creative. Paul is creative. Mary is both brave and not kind. Lucy is either patient or not brave. Someone is tall. Someone is both curious and not rich. Someone is both strong and old. Someone is calm or generous. Paul is not funny or tall. | Paul is generous. | entailment | (![X]:((happy(X)&creative(X))=>(~strong(X)&~tall(X))))&
((?[X]:(~kind(X)))=>(~wise(paul)))&
(((tall(john)|wise(john)))=>(?[X]:((~funny(X)&strong(X)))))&
(((~tall(fred)&creative(fred)))=>((humble(lucy)&brave(lucy))))&
(![X]:(strong(X)=>old(X)))&
(![X]:(~rich(X)<=>(rich(X)<~>funny(X))))&
(![X]:((~patient(X)&~generous(X))=>(wise(X)<~>~old(X))))&
(![X]:(creative(X)<=>~happy(X)))&
((?[X]:(kind(X)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:((~quiet(X)<~>humble(X))=>(rich(X)<~>tall(X))))&
(![X]:((~old(X)|patient(X))=>(quiet(X)|~strong(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(patient(X)&~strong(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~humble(X)))&
(![X]:(~strong(X)=>(wise(X)&creative(X))))&
(((strong(john)<~>calm(john)))<=>((rich(lucy)&wise(lucy))))&
(![X]:((~old(X)&curious(X))=>(curious(X)|creative(X))))&
(creative(paul))&
((brave(mary)&~kind(mary)))&
((patient(lucy)<~>~brave(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((strong(X)&old(X))))&
(?[X]:((calm(X)|generous(X))))&
((~funny(paul)|tall(paul))) | generous(paul) | [
"p1",
"p4",
"p6",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 14869865139111199203360
% SZS output start Proof for 14869865139111199203360
2. ? [X0] : ~kind(X0) => ~wise(paul) [input p1]
5. ! [X0] : (strong(X0) => old(X0)) [input p4]
7. ! [X0] : ((~generous(X0) & ~patient(X0)) => (wise(X0) <~> ~old(X0))) [input p6]
12. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (~strong(X0) & patient(X0))) [input p11]
18. ~kind(mary) & brave(mary) [input p17]
25. ~generous(paul) [input hypothesis]
29. ~wise(paul) | ! [X0] : kind(X0) [ennf transformation 2]
33. ! [X0] : (old(X0) | ~strong(X0)) [ennf transformation 5]
34. ! [X0] : ((wise(X0) <~> ~old(X0)) | (generous(X0) | patient(X0))) [ennf transformation 7]
35. ! [X0] : ((wise(X0) <~> ~old(X0)) | generous(X0) | patient(X0)) [flattening 34]
46. ! [X0] : (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | generous(X0) | patient(X0)) [nnf transformation 35]
52. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 12]
53. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 52]
68. ~wise(paul) | kind(X0) [cnf transformation 29]
75. ~strong(X0) | old(X0) [cnf transformation 33]
80. ~old(X0) | wise(X0) | generous(X0) | patient(X0) [cnf transformation 46]
92. patient(X0) | patient(X0) | strong(X0) [cnf transformation 53]
93. ~strong(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 53]
96. strong(X0) | ~patient(X0) | strong(X0) | ~patient(X0) [cnf transformation 53]
112. ~kind(mary) [cnf transformation 18]
122. ~generous(paul) [cnf transformation 25]
125. patient(X0) | strong(X0) [duplicate literal removal 92]
126. ~strong(X0) | ~patient(X0) [duplicate literal removal 93]
127. ~patient(X0) | strong(X0) [duplicate literal removal 96]
131. 1 <=> ! [X0] : kind(X0) [avatar definition]
132. kind(X0) <- (1) [avatar component clause 131]
134. 2 <=> wise(paul) [avatar definition]
137. 1 | ~2 [avatar split clause 68,134,131]
189. ~patient(X0) [subsumption resolution 126,127]
190. strong(X0) [subsumption resolution 125,189]
222. old(X0) [resolution 75,190]
232. wise(X0) | generous(X0) | patient(X0) [resolution 80,222]
243. generous(X0) | wise(X0) [subsumption resolution 232,189]
245. wise(paul) [resolution 243,122]
248. 2 [avatar split clause 245,134]
249. $false <- (1) [resolution 132,112]
250. ~1 [avatar contradiction clause 249]
251. $false [avatar sat refutation 137,248,250]
% SZS output end Proof for 14869865139111199203360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and generous is not tall or not humble and vice versa.
If paul is both not kind and not strong then paul is rich or not rich.
If mary is not kind or creative then someone is not brave or not quiet and vice versa.
Everyone who is not generous is either not generous or tall.
Everyone who is either brave or humble is not kind or strong and vice versa.
Everyone who is not calm or kind is not brave.
If john is either curious or strong then paul is either not creative or calm and vice versa.
If lucy is both brave and strong then fred is not generous and vice versa.
Everyone who is either happy or tall is humble and vice versa.
If susan is either kind or not wise then someone is not calm.
Everyone who is rich or wise is generous.
If susan is happy or not creative then someone is both not tall and not quiet.
If fred is either humble or creative then someone is either not calm or not rich and vice versa.
If someone is both happy and not wise then john is both not wise and funny and vice versa.
Everyone who is both not strong and creative is both not strong and happy.
Everyone who is either not curious or calm is not wise and vice versa.
Lucy is not calm.
Fred is tall.
John is not rich or wise.
Lucy is either not funny or not wise.
Someone is generous.
Someone is either strong or brave. | Lucy is not creative. | neutral | (![X]:((~generous(X)&generous(X))<=>(~tall(X)|~humble(X))))&
(((~kind(paul)&~strong(paul)))=>((rich(paul)|~rich(paul))))&
(((~kind(mary)|creative(mary)))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:(~generous(X)=>(~generous(X)<~>tall(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~kind(X)|strong(X))))&
(![X]:((~calm(X)|kind(X))=>~brave(X)))&
(((curious(john)<~>strong(john)))<=>((~creative(paul)<~>calm(paul))))&
(((brave(lucy)&strong(lucy)))<=>(~generous(fred)))&
(![X]:((happy(X)<~>tall(X))<=>humble(X)))&
(((kind(susan)<~>~wise(susan)))=>(?[X]:(~calm(X))))&
(![X]:((rich(X)|wise(X))=>generous(X)))&
(((happy(susan)|~creative(susan)))=>(?[X]:((~tall(X)&~quiet(X)))))&
(((humble(fred)<~>creative(fred)))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:((happy(X)&~wise(X))))<=>((~wise(john)&funny(john))))&
(![X]:((~strong(X)&creative(X))=>(~strong(X)&happy(X))))&
(![X]:((~curious(X)<~>calm(X))<=>~wise(X)))&
(~calm(lucy))&
(tall(fred))&
((~rich(john)|wise(john)))&
((~funny(lucy)<~>~wise(lucy)))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>brave(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is either not happy or wise is both not creative and humble.
If someone is either not funny or not old then someone is kind or rich and vice versa.
Everyone who is not strong is either not wise or calm.
If someone is curious then mary is both not old and generous and vice versa.
Everyone who is not curious is both not generous and not old and vice versa.
Everyone who is not kind or wise is funny.
Everyone who is either brave or rich is tall.
Everyone who is not old is both not generous and not calm.
If susan is either old or not strong then fred is strong or funny.
If paul is not generous then john is not kind and vice versa.
If someone is either not brave or wise then mary is both not old and generous.
If alice is humble or patient then paul is not generous and vice versa.
If someone is not kind then someone is happy.
If someone is either rich or tall then someone is not quiet or humble.
Everyone who is both generous and happy is either brave or tall and vice versa.
Everyone who is both not happy and curious is either not calm or happy and vice versa.
Someone is either humble or not wise.
Paul is not kind or patient.
Someone is quiet.
Paul is not curious.
Fred is either generous or strong. | John is not calm. | entailment | (![X]:((~happy(X)<~>wise(X))=>(~creative(X)&humble(X))))&
((?[X]:((~funny(X)<~>~old(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:(~strong(X)=>(~wise(X)<~>calm(X))))&
((?[X]:(curious(X)))<=>((~old(mary)&generous(mary))))&
(![X]:(~curious(X)<=>(~generous(X)&~old(X))))&
(![X]:((~kind(X)|wise(X))=>funny(X)))&
(![X]:((brave(X)<~>rich(X))=>tall(X)))&
(![X]:(~old(X)=>(~generous(X)&~calm(X))))&
(((old(susan)<~>~strong(susan)))=>((strong(fred)|funny(fred))))&
((~generous(paul))<=>(~kind(john)))&
((?[X]:((~brave(X)<~>wise(X))))=>((~old(mary)&generous(mary))))&
(((humble(alice)|patient(alice)))<=>(~generous(paul)))&
((?[X]:(~kind(X)))=>(?[X]:(happy(X))))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
((~kind(paul)|patient(paul)))&
(?[X]:(quiet(X)))&
(~curious(paul))&
((generous(fred)<~>strong(fred))) | ~calm(john) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5149700396125093224822452
% SZS output start Proof for 5149700396125093224822452
4. ? [X0] : curious(X0) <=> (generous(mary) & ~old(mary)) [input p3]
5. ! [X0] : (~curious(X0) <=> (~old(X0) & ~generous(X0))) [input p4]
8. ! [X0] : (~old(X0) => (~calm(X0) & ~generous(X0))) [input p7]
22. calm(john) [input hypothesis]
31. ! [X0] : ((~calm(X0) & ~generous(X0)) | old(X0)) [ennf transformation 8]
44. (? [X0] : curious(X0) | (~generous(mary) | old(mary))) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [nnf transformation 4]
45. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [flattening 44]
46. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [rectify 45]
47. ? [X0] : curious(X0) => curious(sK2) [choice axiom]
48. (curious(sK2) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [skolemisation 46,47]
49. ! [X0] : ((~curious(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | curious(X0))) [nnf transformation 5]
50. ! [X0] : ((~curious(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | curious(X0))) [flattening 49]
84. ~old(mary) | ~curious(X1) [cnf transformation 48]
85. generous(mary) | ~curious(X1) [cnf transformation 48]
88. ~old(X0) | curious(X0) [cnf transformation 50]
94. ~generous(X0) | old(X0) [cnf transformation 31]
95. ~calm(X0) | old(X0) [cnf transformation 31]
129. calm(john) [cnf transformation 22]
167. 9 <=> old(mary) [avatar definition]
168. ~old(mary) <- (~9) [avatar component clause 167]
171. 10 <=> generous(mary) [avatar definition]
172. generous(mary) <- (10) [avatar component clause 171]
180. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
181. ~curious(X1) <- (12) [avatar component clause 180]
182. 12 | 10 [avatar split clause 85,171,180]
183. 12 | ~9 [avatar split clause 84,167,180]
291. old(mary) <- (10) [resolution 94,172]
292. $false <- (~9, 10) [subsumption resolution 291,168]
293. 9 | ~10 [avatar contradiction clause 292]
296. old(john) [resolution 95,129]
298. curious(john) [resolution 296,88]
299. $false <- (12) [subsumption resolution 298,181]
300. ~12 [avatar contradiction clause 299]
301. $false [avatar sat refutation 182,183,293,300]
% SZS output end Proof for 5149700396125093224822452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not tall then fred is not humble or not generous and vice versa. If someone is old then paul is rich and vice versa. Everyone who is either not wise or not patient is both humble and not rich and vice versa. Everyone who is either not rich or not patient is not calm and vice versa. Everyone who is not quiet is either not quiet or not patient. Everyone who is both not wise and kind is either rich or funny and vice versa. Everyone who is tall or quiet is not rich and vice versa. Everyone who is either funny or tall is either kind or not rich. Everyone who is tall or not wise is either not funny or not happy. Everyone who is either strong or not strong is happy or not wise and vice versa. If lucy is not rich or not calm then someone is either old or not strong. If fred is old then someone is not old or happy and vice versa. If lucy is not old then fred is either not kind or not creative. If someone is not quiet then someone is calm and vice versa. If paul is both curious and not funny then someone is humble and vice versa. If alice is either wise or not creative then paul is not creative or creative. John is either patient or creative. Paul is both strong and not generous. Someone is not funny or not rich. Someone is both funny and not patient. John is not wise. | Lucy is not quiet. | neutral | ((?[X]:((creative(X)<~>~tall(X))))<=>((~humble(fred)|~generous(fred))))&
((?[X]:(old(X)))<=>(rich(paul)))&
(![X]:((~wise(X)<~>~patient(X))<=>(humble(X)&~rich(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>~calm(X)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))<=>(rich(X)<~>funny(X))))&
(![X]:((tall(X)|quiet(X))<=>~rich(X)))&
(![X]:((funny(X)<~>tall(X))=>(kind(X)<~>~rich(X))))&
(![X]:((tall(X)|~wise(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(happy(X)|~wise(X))))&
(((~rich(lucy)|~calm(lucy)))=>(?[X]:((old(X)<~>~strong(X)))))&
((old(fred))<=>(?[X]:((~old(X)|happy(X)))))&
((~old(lucy))=>((~kind(fred)<~>~creative(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(((curious(paul)&~funny(paul)))<=>(?[X]:(humble(X))))&
(((wise(alice)<~>~creative(alice)))=>((~creative(paul)|creative(paul))))&
((patient(john)<~>creative(john)))&
((strong(paul)&~generous(paul)))&
(?[X]:((~funny(X)|~rich(X))))&
(?[X]:((funny(X)&~patient(X))))&
(~wise(john)) | ~quiet(lucy) | [] | null | 0 |
If alice is both creative and tall then someone is funny and vice versa. If someone is both not curious and not tall then someone is either curious or not old and vice versa. Everyone who is not tall or not brave is both kind and curious. Everyone who is tall or happy is not brave or humble. If alice is not patient then mary is either not creative or brave and vice versa. Everyone who is not strong or not wise is both calm and not humble and vice versa. Everyone who is both not funny and patient is either wise or not wise and vice versa. Everyone who is both generous and brave is either wise or not calm. Everyone who is rich or not patient is old. Everyone who is either funny or patient is humble. If susan is both brave and tall then someone is wise. If fred is humble then mary is either funny or rich. If alice is both not curious and not wise then someone is not generous or not quiet. Everyone who is creative is not happy and vice versa. Everyone who is not wise or not happy is happy. Everyone who is not brave is both not brave and not generous and vice versa. Someone is quiet. John is creative or brave. Paul is not old. Fred is not funny or wise. Someone is either brave or not quiet. Lucy is quiet or humble. | Susan is not wise. | contradiction | (((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(![X]:((~funny(X)&patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((generous(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:((rich(X)|~patient(X))=>old(X)))&
(![X]:((funny(X)<~>patient(X))=>humble(X)))&
(((brave(susan)&tall(susan)))=>(?[X]:(wise(X))))&
((humble(fred))=>((funny(mary)<~>rich(mary))))&
(((~curious(alice)&~wise(alice)))=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:(creative(X)<=>~happy(X)))&
(![X]:((~wise(X)|~happy(X))=>happy(X)))&
(![X]:(~brave(X)<=>(~brave(X)&~generous(X))))&
(?[X]:(quiet(X)))&
((creative(john)|brave(john)))&
(~old(paul))&
((~funny(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~quiet(X))))&
((quiet(lucy)|humble(lucy))) | ~wise(susan) | [
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3420489383466425852972488
% SZS output start Proof for 3420489383466425852972488
6. ! [X0] : ((~wise(X0) | ~strong(X0)) <=> (~humble(X0) & calm(X0))) [input p5]
7. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p6]
10. ! [X0] : ((funny(X0) <~> patient(X0)) => humble(X0)) [input p9]
23. ~wise(susan) [input hypothesis]
32. ! [X0] : (humble(X0) | (funny(X0) <=> patient(X0))) [ennf transformation 10]
50. ! [X0] : (((~wise(X0) | ~strong(X0)) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | (wise(X0) & strong(X0)))) [nnf transformation 6]
51. ! [X0] : ((~wise(X0) | ~strong(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | (wise(X0) & strong(X0)))) [flattening 50]
52. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~patient(X0) | funny(X0)))) [nnf transformation 7]
53. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~patient(X0) | funny(X0))) [flattening 52]
55. ! [X0] : (humble(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) [nnf transformation 32]
89. ~humble(X0) | wise(X0) [cnf transformation 51]
93. ~funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 53]
94. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 53]
95. patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 53]
96. patient(X0) | wise(X0) | wise(X0) [cnf transformation 53]
102. humble(X0) | funny(X0) | ~patient(X0) [cnf transformation 55]
121. ~wise(susan) [cnf transformation 23]
123. ~funny(X0) | ~wise(X0) [duplicate literal removal 93]
124. ~funny(X0) | wise(X0) [duplicate literal removal 94]
125. patient(X0) | ~wise(X0) [duplicate literal removal 95]
126. wise(X0) | patient(X0) [duplicate literal removal 96]
128. 1 <=> ! [X0] : ~funny(X0) [avatar definition]
129. ~funny(X0) <- (1) [avatar component clause 128]
193. patient(X0) [subsumption resolution 125,126]
194. ~funny(X0) [subsumption resolution 123,124]
195. 1 [avatar split clause 194,128]
198. humble(X0) | funny(X0) [subsumption resolution 102,193]
287. funny(X0) | wise(X0) [resolution 198,89]
291. wise(X0) <- (1) [subsumption resolution 287,129]
320. $false <- (1) [resolution 291,121]
321. ~1 [avatar contradiction clause 320]
322. $false [avatar sat refutation 195,321]
% SZS output end Proof for 3420489383466425852972488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not creative is either creative or calm and vice versa.
If someone is not wise or not kind then someone is either not creative or calm and vice versa.
Everyone who is either not quiet or not strong is both not curious and not brave.
Everyone who is quiet or not generous is not rich or funny and vice versa.
If someone is both not strong and kind then susan is brave.
Everyone who is either not old or not happy is either kind or not calm.
If someone is both kind and creative then someone is either calm or creative.
If lucy is both calm and not funny then john is not quiet or kind and vice versa.
Everyone who is either creative or not wise is either not quiet or not rich.
If alice is not kind then john is both not calm and not humble and vice versa.
If someone is both not curious and wise then lucy is not curious.
If mary is both not funny and calm then paul is not kind or wise and vice versa.
Everyone who is calm or not generous is either brave or not patient.
If john is not brave or patient then someone is not curious and vice versa.
If susan is either rich or not strong then paul is both generous and not calm and vice versa.
If someone is not wise then lucy is both rich and funny and vice versa.
Paul is rich or not old.
Paul is not wise or not old.
Someone is old or not curious.
Susan is wise or tall.
Someone is both not humble and not quiet.
John is both rich and quiet.
Someone is both not kind and curious.
Someone is both not quiet and not generous. | Paul is wise. | neutral | (![X]:((~funny(X)|~creative(X))<=>(creative(X)<~>calm(X))))&
((?[X]:((~wise(X)|~kind(X))))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(![X]:((~quiet(X)<~>~strong(X))=>(~curious(X)&~brave(X))))&
(![X]:((quiet(X)|~generous(X))<=>(~rich(X)|funny(X))))&
((?[X]:((~strong(X)&kind(X))))=>(brave(susan)))&
(![X]:((~old(X)<~>~happy(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((kind(X)&creative(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
(((calm(lucy)&~funny(lucy)))<=>((~quiet(john)|kind(john))))&
(![X]:((creative(X)<~>~wise(X))=>(~quiet(X)<~>~rich(X))))&
((~kind(alice))<=>((~calm(john)&~humble(john))))&
((?[X]:((~curious(X)&wise(X))))=>(~curious(lucy)))&
(((~funny(mary)&calm(mary)))<=>((~kind(paul)|wise(paul))))&
(![X]:((calm(X)|~generous(X))=>(brave(X)<~>~patient(X))))&
(((~brave(john)|patient(john)))<=>(?[X]:(~curious(X))))&
(((rich(susan)<~>~strong(susan)))<=>((generous(paul)&~calm(paul))))&
((?[X]:(~wise(X)))<=>((rich(lucy)&funny(lucy))))&
((rich(paul)|~old(paul)))&
((~wise(paul)|~old(paul)))&
(?[X]:((old(X)|~curious(X))))&
((wise(susan)|tall(susan)))&
(?[X]:((~humble(X)&~quiet(X))))&
((rich(john)&quiet(john)))&
(?[X]:((~kind(X)&curious(X))))&
(?[X]:((~quiet(X)&~generous(X)))) | wise(paul) | [] | null | 0 |
Everyone who is both curious and not curious is both not rich and brave. If john is not old then someone is both rich and not funny and vice versa. If susan is either not wise or funny then someone is either not strong or generous and vice versa. Everyone who is not kind is either not strong or not calm and vice versa. Everyone who is not calm is humble. Everyone who is both not patient and patient is not tall and vice versa. Everyone who is patient or happy is happy and vice versa. If paul is strong or quiet then someone is brave. Everyone who is both creative and not strong is both kind and creative. Everyone who is both generous and not strong is both not rich and kind. Everyone who is curious is not creative. Everyone who is not brave is both strong and not kind and vice versa. If mary is not old then someone is both calm and not funny and vice versa. Everyone who is either strong or curious is both not old and not tall and vice versa. Everyone who is either not humble or patient is either calm or not quiet and vice versa. Everyone who is either not brave or not humble is creative. Alice is not rich or not kind. Someone is both humble and not rich. Someone is both curious and brave. Someone is not patient. Someone is tall or not patient. Paul is either happy or rich. Mary is calm. | Susan is not generous. | neutral | (![X]:((curious(X)&~curious(X))=>(~rich(X)&brave(X))))&
((~old(john))<=>(?[X]:((rich(X)&~funny(X)))))&
(((~wise(susan)<~>funny(susan)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(~kind(X)<=>(~strong(X)<~>~calm(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((~patient(X)&patient(X))<=>~tall(X)))&
(![X]:((patient(X)|happy(X))<=>happy(X)))&
(((strong(paul)|quiet(paul)))=>(?[X]:(brave(X))))&
(![X]:((creative(X)&~strong(X))=>(kind(X)&creative(X))))&
(![X]:((generous(X)&~strong(X))=>(~rich(X)&kind(X))))&
(![X]:(curious(X)=>~creative(X)))&
(![X]:(~brave(X)<=>(strong(X)&~kind(X))))&
((~old(mary))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:((strong(X)<~>curious(X))<=>(~old(X)&~tall(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~humble(X))=>creative(X)))&
((~rich(alice)|~kind(alice)))&
(?[X]:((humble(X)&~rich(X))))&
(?[X]:((curious(X)&brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|~patient(X))))&
((happy(paul)<~>rich(paul)))&
(calm(mary)) | ~generous(susan) | [] | null | 0 |
Everyone who is humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not calm.
Everyone who is either generous or calm is rich and vice versa.
If someone is either creative or strong then mary is not brave.
Everyone who is both humble and happy is either not kind or funny and vice versa.
Everyone who is not quiet is not brave or not rich and vice versa.
Everyone who is old is generous or not old and vice versa.
Everyone who is not rich is both strong and quiet.
Everyone who is both not rich and not tall is both patient and happy.
Everyone who is quiet or not funny is curious or generous.
If someone is humble or not kind then someone is not brave or not old and vice versa.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
If someone is not quiet then someone is strong and vice versa.
If someone is either not brave or curious then someone is both happy and not creative.
If john is both tall and not patient then someone is either not funny or not generous.
If someone is wise or not wise then someone is happy or not kind.
Susan is either not quiet or not funny.
Someone is not happy or not humble.
Someone is kind or not patient.
Fred is both patient and not tall.
Someone is not tall.
Alice is not funny or creative.
Someone is not happy or old.
Fred is old. | Mary is not creative. | entailment | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~calm(X)))&
(![X]:((generous(X)<~>calm(X))<=>rich(X)))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(((tall(john)&~patient(john)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((happy(X)|~kind(X)))))&
((~quiet(susan)<~>~funny(susan)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((kind(X)|~patient(X))))&
((patient(fred)&~tall(fred)))&
(?[X]:(~tall(X)))&
((~funny(alice)|creative(alice)))&
(?[X]:((~happy(X)|old(X))))&
(old(fred)) | ~creative(mary) | [
"p0",
"p3",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3235728904134376387720966
% SZS output start Proof for 3235728904134376387720966
1. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~strong(X0)) [input p0]
4. ? [X0] : (creative(X0) <~> strong(X0)) => ~brave(mary) [input p3]
6. ! [X0] : (~quiet(X0) <=> (~rich(X0) | ~brave(X0))) [input p5]
13. ? [X0] : ~quiet(X0) <=> ? [X0] : strong(X0) [input p12]
25. creative(mary) [input hypothesis]
27. ? [X0] : ~quiet(X0) <=> ? [X1] : strong(X1) [rectify 13]
31. ~brave(mary) | ! [X0] : (creative(X0) <=> strong(X0)) [ennf transformation 4]
41. ! [X0] : (((~humble(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 1]
42. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [flattening 41]
45. ~brave(mary) | ! [X0] : ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))) [nnf transformation 31]
48. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | quiet(X0))) [flattening 48]
62. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : quiet(X0)) [nnf transformation 27]
63. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : quiet(X3)) [rectify 62]
64. ? [X0] : ~quiet(X0) => ~quiet(sK3) [choice axiom]
65. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
66. (~quiet(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : quiet(X3)) [skolemisation 63,65,64]
86. ~strong(X0) | ~humble(X0) [cnf transformation 42]
87. ~strong(X0) | humble(X0) [cnf transformation 42]
95. ~brave(mary) | strong(X0) | ~creative(X0) [cnf transformation 45]
104. ~quiet(X0) | brave(X0) [cnf transformation 49]
125. strong(sK4) | quiet(X3) [cnf transformation 66]
145. creative(mary) [cnf transformation 25]
149. ~strong(X0) [subsumption resolution 86,87]
150. ~brave(mary) | ~creative(X0) [subsumption resolution 95,149]
152. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
153. ~creative(X0) <- (1) [avatar component clause 152]
155. 2 <=> brave(mary) [avatar definition]
157. ~brave(mary) <- (~2) [avatar component clause 155]
158. 1 | ~2 [avatar split clause 150,155,152]
162. 3 <=> ! [X1] : brave(X1) [avatar definition]
163. brave(X1) <- (3) [avatar component clause 162]
211. quiet(X3) [subsumption resolution 125,149]
288. brave(X0) [resolution 104,211]
289. 3 [avatar split clause 288,162]
290. $false <- (~2, 3) [resolution 163,157]
293. 2 | ~3 [avatar contradiction clause 290]
294. $false <- (1) [resolution 153,145]
295. ~1 [avatar contradiction clause 294]
296. $false [avatar sat refutation 158,289,293,295]
% SZS output end Proof for 3235728904134376387720966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and humble is quiet or humble and vice versa.
Everyone who is either funny or humble is either not funny or patient and vice versa.
Everyone who is both curious and patient is not patient or not quiet and vice versa.
Everyone who is either strong or not creative is tall or not tall.
If someone is not brave then someone is not curious or strong.
Everyone who is either not humble or quiet is old.
If mary is both not happy and curious then someone is either not tall or patient.
If paul is both calm and not humble then someone is both quiet and wise and vice versa.
If lucy is strong then alice is not brave and vice versa.
Everyone who is not humble is either wise or not creative.
If lucy is either not generous or not quiet then someone is not quiet or wise and vice versa.
If susan is either not quiet or wise then lucy is either generous or not rich and vice versa.
Everyone who is old is both not humble and not calm and vice versa.
Everyone who is not old is both brave and not wise.
If alice is either not tall or kind then someone is happy and vice versa.
If someone is both quiet and not brave then fred is not tall.
Someone is not tall or not funny.
Fred is humble or strong.
Mary is either not strong or not wise.
Mary is funny.
Someone is strong or not creative. | Lucy is quiet. | contradiction | (![X]:((kind(X)&humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((curious(X)&patient(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((strong(X)<~>~creative(X))=>(tall(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~humble(X)<~>quiet(X))=>old(X)))&
(((~happy(mary)&curious(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((calm(paul)&~humble(paul)))<=>(?[X]:((quiet(X)&wise(X)))))&
((strong(lucy))<=>(~brave(alice)))&
(![X]:(~humble(X)=>(wise(X)<~>~creative(X))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(((~quiet(susan)<~>wise(susan)))<=>((generous(lucy)<~>~rich(lucy))))&
(![X]:(old(X)<=>(~humble(X)&~calm(X))))&
(![X]:(~old(X)=>(brave(X)&~wise(X))))&
(((~tall(alice)<~>kind(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)&~brave(X))))=>(~tall(fred)))&
(?[X]:((~tall(X)|~funny(X))))&
((humble(fred)|strong(fred)))&
((~strong(mary)<~>~wise(mary)))&
(funny(mary))&
(?[X]:((strong(X)|~creative(X)))) | quiet(lucy) | [
"p0",
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 9126266135843178662763119
% SZS output start Proof for 9126266135843178662763119
1. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) | quiet(X0))) [input p0]
2. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (~funny(X0) <~> patient(X0))) [input p1]
3. ! [X0] : ((patient(X0) & curious(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p2]
22. quiet(lucy) [input hypothesis]
35. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 1]
36. ! [X0] : (((humble(X0) & kind(X0)) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | ~humble(X0) | ~kind(X0))) [flattening 35]
37. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 2]
38. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 3]
39. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | ~patient(X0) | ~curious(X0))) [flattening 38]
72. ~quiet(X0) | humble(X0) [cnf transformation 36]
77. ~patient(X0) | funny(X0) | funny(X0) | ~humble(X0) [cnf transformation 37]
81. ~humble(X0) | ~funny(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 37]
85. patient(X0) | patient(X0) [cnf transformation 39]
131. quiet(lucy) [cnf transformation 22]
133. patient(X0) [duplicate literal removal 85]
135. ~patient(X0) | funny(X0) | ~humble(X0) [duplicate literal removal 77]
137. ~humble(X0) | ~funny(X0) | ~patient(X0) [duplicate literal removal 81]
138. ~patient(X0) | ~humble(X0) [subsumption resolution 135,137]
210. 16 <=> quiet(lucy) [avatar definition]
212. quiet(lucy) <- (16) [avatar component clause 210]
314. 16 [avatar split clause 131,210]
317. humble(lucy) <- (16) [resolution 72,212]
329. ~humble(X1) [resolution 138,133]
331. $false <- (16) [resolution 329,317]
336. ~16 [avatar contradiction clause 331]
338. $false [avatar sat refutation 314,336]
% SZS output end Proof for 9126266135843178662763119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet then someone is either not funny or curious.
If mary is not strong or tall then someone is not old or not calm and vice versa.
Everyone who is curious or funny is not creative or not funny and vice versa.
If someone is either patient or wise then someone is either creative or not curious and vice versa.
Everyone who is either quiet or not quiet is not funny and vice versa.
Everyone who is both quiet and not old is either not funny or tall and vice versa.
If someone is either brave or wise then alice is both funny and not calm and vice versa.
Everyone who is not brave or not strong is not tall or not curious.
Everyone who is strong or not kind is not patient and vice versa.
If susan is both not quiet and not calm then someone is calm.
Everyone who is not wise is old.
If someone is either kind or curious then someone is not curious or generous.
If alice is both not funny and not strong then someone is either generous or not rich.
If someone is generous or rich then someone is both curious and not generous.
Everyone who is not strong is either creative or funny and vice versa.
Everyone who is not generous is both curious and not old and vice versa.
Lucy is either tall or not curious.
Paul is not wise or not humble.
Someone is not generous or calm.
Mary is curious or not strong.
Someone is not humble or funny.
Mary is not old or calm. | Susan is not curious. | contradiction | ((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((~strong(mary)|tall(mary)))<=>(?[X]:((~old(X)|~calm(X)))))&
(![X]:((curious(X)|funny(X))<=>(~creative(X)|~funny(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:((quiet(X)<~>~quiet(X))<=>~funny(X)))&
(![X]:((quiet(X)&~old(X))<=>(~funny(X)<~>tall(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((funny(alice)&~calm(alice))))&
(![X]:((~brave(X)|~strong(X))=>(~tall(X)|~curious(X))))&
(![X]:((strong(X)|~kind(X))<=>~patient(X)))&
(((~quiet(susan)&~calm(susan)))=>(?[X]:(calm(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((kind(X)<~>curious(X))))=>(?[X]:((~curious(X)|generous(X)))))&
(((~funny(alice)&~strong(alice)))=>(?[X]:((generous(X)<~>~rich(X)))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:(~strong(X)<=>(creative(X)<~>funny(X))))&
(![X]:(~generous(X)<=>(curious(X)&~old(X))))&
((tall(lucy)<~>~curious(lucy)))&
((~wise(paul)|~humble(paul)))&
(?[X]:((~generous(X)|calm(X))))&
((curious(mary)|~strong(mary)))&
(?[X]:((~humble(X)|funny(X))))&
((~old(mary)|calm(mary))) | ~curious(susan) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7547658009590961557688943
% SZS output start Proof for 7547658009590961557688943
3. ! [X0] : ((funny(X0) | curious(X0)) <=> (~funny(X0) | ~creative(X0))) [input p2]
5. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) <=> ~funny(X0)) [input p4]
23. ~curious(susan) [input hypothesis]
49. ! [X0] : (((funny(X0) | curious(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~funny(X0) & ~curious(X0)))) [nnf transformation 3]
50. ! [X0] : ((funny(X0) | curious(X0) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | (~funny(X0) & ~curious(X0)))) [flattening 49]
56. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | funny(X0)) & (~funny(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [nnf transformation 5]
95. funny(X0) | curious(X0) | funny(X0) [cnf transformation 50]
104. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
105. ~funny(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
147. ~curious(susan) [cnf transformation 23]
148. ~funny(X0) | ~quiet(X0) [duplicate literal removal 104]
149. ~funny(X0) | quiet(X0) [duplicate literal removal 105]
151. curious(X0) | funny(X0) [duplicate literal removal 95]
232. ~funny(X0) [subsumption resolution 148,149]
368. funny(susan) [resolution 151,147]
373. $false [subsumption resolution 368,232]
% SZS output end Proof for 7547658009590961557688943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or kind is not humble or brave and vice versa. Everyone who is not happy is generous and vice versa. If someone is not quiet then someone is quiet and vice versa. If someone is either not funny or not humble then someone is both not tall and quiet and vice versa. Everyone who is either not happy or not patient is either wise or not kind. If someone is wise then someone is either patient or not strong and vice versa. Everyone who is either not patient or strong is either not strong or strong and vice versa. Everyone who is either not humble or not generous is not quiet or humble and vice versa. Everyone who is not patient is creative. If alice is patient then someone is both brave and rich. Everyone who is not creative is both tall and funny. If someone is tall or funny then someone is both not wise and not rich. If mary is either strong or humble then someone is both quiet and not strong and vice versa. Everyone who is both patient and brave is both old and not kind and vice versa. If susan is rich or not rich then someone is not brave or tall. Paul is humble or not humble. Fred is not creative. Paul is both creative and not quiet. Someone is both not humble and kind. Lucy is both not funny and patient. Someone is not happy. Someone is either not rich or brave. Fred is quiet. | Fred is patient. | entailment | (![X]:((~patient(X)<~>kind(X))<=>(~humble(X)|brave(X))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:(quiet(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:((~happy(X)<~>~patient(X))=>(wise(X)<~>~kind(X))))&
((?[X]:(wise(X)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((~patient(X)<~>strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~quiet(X)|humble(X))))&
(![X]:(~patient(X)=>creative(X)))&
((patient(alice))=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(~creative(X)=>(tall(X)&funny(X))))&
((?[X]:((tall(X)|funny(X))))=>(?[X]:((~wise(X)&~rich(X)))))&
(((strong(mary)<~>humble(mary)))<=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((patient(X)&brave(X))<=>(old(X)&~kind(X))))&
(((rich(susan)|~rich(susan)))=>(?[X]:((~brave(X)|tall(X)))))&
((humble(paul)|~humble(paul)))&
(~creative(fred))&
((creative(paul)&~quiet(paul)))&
(?[X]:((~humble(X)&kind(X))))&
((~funny(lucy)&patient(lucy)))&
(?[X]:(~happy(X)))&
(?[X]:((~rich(X)<~>brave(X))))&
(quiet(fred)) | patient(fred) | [
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5154114453696521831308000
% SZS output start Proof for 5154114453696521831308000
9. ! [X0] : (~patient(X0) => creative(X0)) [input p8]
17. ~creative(fred) [input p16]
24. ~patient(fred) [input hypothesis]
30. ! [X0] : (creative(X0) | patient(X0)) [ennf transformation 9]
115. creative(X0) | patient(X0) [cnf transformation 30]
137. ~creative(fred) [cnf transformation 17]
148. ~patient(fred) [cnf transformation 24]
319. patient(fred) [resolution 115,137]
320. $false [subsumption resolution 319,148]
% SZS output end Proof for 5154114453696521831308000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is curious and vice versa.
Everyone who is either generous or not old is either tall or calm and vice versa.
If someone is creative then alice is generous or strong.
If john is either humble or funny then paul is both not rich and not calm.
If someone is both not patient and not happy then susan is generous or not funny.
Everyone who is not strong is both not happy and not calm and vice versa.
Everyone who is both not happy and not strong is both not creative and patient.
If lucy is both not funny and not happy then paul is humble or rich and vice versa.
If mary is not brave then susan is both not funny and not strong and vice versa.
If someone is generous or kind then lucy is curious and vice versa.
Everyone who is both not generous and wise is wise or kind and vice versa.
Everyone who is creative is both happy and humble and vice versa.
If someone is either not creative or kind then someone is either kind or not brave and vice versa.
Everyone who is both curious and wise is not rich.
If someone is humble then lucy is both happy and not brave.
Everyone who is either not rich or kind is both brave and not humble.
Fred is rich.
Alice is not tall or not kind.
Someone is not old or kind.
Fred is not curious or old.
Someone is either brave or wise.
Paul is not tall or brave.
Fred is creative or not quiet.
Someone is either not curious or not kind. | John is not generous. | neutral | (![X]:(~happy(X)<=>curious(X)))&
(![X]:((generous(X)<~>~old(X))<=>(tall(X)<~>calm(X))))&
((?[X]:(creative(X)))=>((generous(alice)|strong(alice))))&
(((humble(john)<~>funny(john)))=>((~rich(paul)&~calm(paul))))&
((?[X]:((~patient(X)&~happy(X))))=>((generous(susan)|~funny(susan))))&
(![X]:(~strong(X)<=>(~happy(X)&~calm(X))))&
(![X]:((~happy(X)&~strong(X))=>(~creative(X)&patient(X))))&
(((~funny(lucy)&~happy(lucy)))<=>((humble(paul)|rich(paul))))&
((~brave(mary))<=>((~funny(susan)&~strong(susan))))&
((?[X]:((generous(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~generous(X)&wise(X))<=>(wise(X)|kind(X))))&
(![X]:(creative(X)<=>(happy(X)&humble(X))))&
((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((curious(X)&wise(X))=>~rich(X)))&
((?[X]:(humble(X)))=>((happy(lucy)&~brave(lucy))))&
(![X]:((~rich(X)<~>kind(X))=>(brave(X)&~humble(X))))&
(rich(fred))&
((~tall(alice)|~kind(alice)))&
(?[X]:((~old(X)|kind(X))))&
((~curious(fred)|old(fred)))&
(?[X]:((brave(X)<~>wise(X))))&
((~tall(paul)|brave(paul)))&
((creative(fred)|~quiet(fred)))&
(?[X]:((~curious(X)<~>~kind(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both creative and not old is both curious and wise.
Everyone who is both old and humble is not calm or kind and vice versa.
Everyone who is not curious or not creative is not brave or happy.
If someone is either patient or wise then someone is either not kind or kind and vice versa.
If alice is not old then paul is either not tall or not curious and vice versa.
Everyone who is either not old or not tall is either not patient or generous and vice versa.
Everyone who is either patient or not generous is both not strong and not quiet and vice versa.
Everyone who is either rich or not kind is both not patient and not rich.
If someone is generous or creative then someone is both quiet and not brave and vice versa.
If someone is not generous or not tall then someone is both kind and not creative.
Everyone who is not old is both not patient and not generous and vice versa.
Everyone who is either not patient or not curious is not quiet or tall.
Everyone who is either not calm or rich is kind.
If paul is both tall and quiet then lucy is either funny or not creative and vice versa.
Everyone who is not calm is both not rich and tall and vice versa.
Everyone who is not brave is not generous.
Lucy is either quiet or not patient.
Someone is generous or not creative.
Someone is patient.
Mary is either not quiet or not creative.
Someone is both creative and humble.
Someone is both old and calm.
Susan is not funny or not patient.
Mary is not brave. | Mary is rich. | contradiction | (![X]:((creative(X)&~old(X))=>(curious(X)&wise(X))))&
(![X]:((old(X)&humble(X))<=>(~calm(X)|kind(X))))&
(![X]:((~curious(X)|~creative(X))=>(~brave(X)|happy(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((~old(alice))<=>((~tall(paul)<~>~curious(paul))))&
(![X]:((~old(X)<~>~tall(X))<=>(~patient(X)<~>generous(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>~kind(X))=>(~patient(X)&~rich(X))))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((quiet(X)&~brave(X)))))&
((?[X]:((~generous(X)|~tall(X))))=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:(~old(X)<=>(~patient(X)&~generous(X))))&
(![X]:((~patient(X)<~>~curious(X))=>(~quiet(X)|tall(X))))&
(![X]:((~calm(X)<~>rich(X))=>kind(X)))&
(((tall(paul)&quiet(paul)))<=>((funny(lucy)<~>~creative(lucy))))&
(![X]:(~calm(X)<=>(~rich(X)&tall(X))))&
(![X]:(~brave(X)=>~generous(X)))&
((quiet(lucy)<~>~patient(lucy)))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:(patient(X)))&
((~quiet(mary)<~>~creative(mary)))&
(?[X]:((creative(X)&humble(X))))&
(?[X]:((old(X)&calm(X))))&
((~funny(susan)|~patient(susan)))&
(~brave(mary)) | rich(mary) | [
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2626847898590688283780526
% SZS output start Proof for 2626847898590688283780526
8. ! [X0] : ((rich(X0) <~> ~kind(X0)) => (~rich(X0) & ~patient(X0))) [input p7]
13. ! [X0] : ((~calm(X0) <~> rich(X0)) => kind(X0)) [input p12]
15. ! [X0] : (~calm(X0) <=> (tall(X0) & ~rich(X0))) [input p14]
25. rich(mary) [input hypothesis]
32. ! [X0] : ((~rich(X0) & ~patient(X0)) | (rich(X0) <=> ~kind(X0))) [ennf transformation 8]
36. ! [X0] : (kind(X0) | (~calm(X0) <=> rich(X0))) [ennf transformation 13]
49. ! [X0] : ((~rich(X0) & ~patient(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) [nnf transformation 32]
61. ! [X0] : (kind(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) [nnf transformation 36]
64. ! [X0] : ((~calm(X0) | (~tall(X0) | rich(X0))) & ((tall(X0) & ~rich(X0)) | calm(X0))) [nnf transformation 15]
65. ! [X0] : ((~calm(X0) | ~tall(X0) | rich(X0)) & ((tall(X0) & ~rich(X0)) | calm(X0))) [flattening 64]
111. ~rich(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 49]
128. kind(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 61]
135. ~rich(X0) | calm(X0) [cnf transformation 65]
151. rich(mary) [cnf transformation 25]
152. ~rich(X0) | ~kind(X0) [duplicate literal removal 111]
239. ~calm(X0) | ~rich(X0) [subsumption resolution 128,152]
259. ~rich(X0) [subsumption resolution 135,239]
298. $false [subsumption resolution 151,259]
% SZS output end Proof for 2626847898590688283780526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not curious is not creative and vice versa. Everyone who is curious or quiet is both kind and wise. Everyone who is not creative or creative is funny or not kind. If someone is either wise or old then someone is both not old and generous and vice versa. Everyone who is old or rich is not tall and vice versa. If john is both not tall and happy then someone is either tall or not kind. Everyone who is not quiet is both not brave and not kind. Everyone who is either kind or creative is both strong and not generous and vice versa. If someone is either rich or not calm then alice is quiet or patient and vice versa. If someone is old then someone is both not brave and patient and vice versa. Everyone who is rich is not quiet or rich. Everyone who is both patient and not old is quiet or not generous and vice versa. Everyone who is both not creative and not calm is either not funny or kind. If paul is either humble or calm then someone is creative and vice versa. Everyone who is not strong is either not happy or not creative and vice versa. Everyone who is either not calm or not funny is not strong and vice versa. Fred is both curious and rich. Lucy is both not creative and patient. Alice is both wise and not rich. Someone is not patient. Someone is rich or old. Susan is both not calm and strong. Alice is both not old and not generous. Fred is wise or not old. | Susan is not patient. | neutral | (![X]:((strong(X)&~curious(X))<=>~creative(X)))&
(![X]:((curious(X)|quiet(X))=>(kind(X)&wise(X))))&
(![X]:((~creative(X)|creative(X))=>(funny(X)|~kind(X))))&
((?[X]:((wise(X)<~>old(X))))<=>(?[X]:((~old(X)&generous(X)))))&
(![X]:((old(X)|rich(X))<=>~tall(X)))&
(((~tall(john)&happy(john)))=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&~kind(X))))&
(![X]:((kind(X)<~>creative(X))<=>(strong(X)&~generous(X))))&
((?[X]:((rich(X)<~>~calm(X))))<=>((quiet(alice)|patient(alice))))&
((?[X]:(old(X)))<=>(?[X]:((~brave(X)&patient(X)))))&
(![X]:(rich(X)=>(~quiet(X)|rich(X))))&
(![X]:((patient(X)&~old(X))<=>(quiet(X)|~generous(X))))&
(![X]:((~creative(X)&~calm(X))=>(~funny(X)<~>kind(X))))&
(((humble(paul)<~>calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:(~strong(X)<=>(~happy(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>~funny(X))<=>~strong(X)))&
((curious(fred)&rich(fred)))&
((~creative(lucy)&patient(lucy)))&
((wise(alice)&~rich(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|old(X))))&
((~calm(susan)&strong(susan)))&
((~old(alice)&~generous(alice)))&
((wise(fred)|~old(fred))) | ~patient(susan) | [] | null | 0 |
Everyone who is both not funny and creative is not patient. If alice is both not generous and strong then someone is either wise or not brave and vice versa. If paul is not creative or not generous then john is both not old and not curious and vice versa. Everyone who is not happy is not funny and vice versa. Everyone who is either not tall or patient is both not funny and rich and vice versa. Everyone who is both strong and not wise is not happy and vice versa. Everyone who is either strong or happy is tall. Everyone who is not rich is both curious and humble and vice versa. If someone is old or not patient then someone is tall and vice versa. Everyone who is not happy is happy or not quiet and vice versa. Everyone who is either not happy or brave is both not happy and not old. If someone is not rich or wise then someone is not strong or not generous and vice versa. If someone is curious then john is both not calm and not humble. Everyone who is kind is not old or not funny. Everyone who is calm or patient is not brave or funny. Everyone who is both creative and kind is old and vice versa. Lucy is not quiet or not rich. Fred is either not humble or not brave. Someone is not creative. Alice is either humble or not tall. Susan is both old and kind. Someone is either not funny or not generous. | Susan is not curious. | contradiction | (![X]:((~funny(X)&creative(X))=>~patient(X)))&
(((~generous(alice)&strong(alice)))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(((~creative(paul)|~generous(paul)))<=>((~old(john)&~curious(john))))&
(![X]:(~happy(X)<=>~funny(X)))&
(![X]:((~tall(X)<~>patient(X))<=>(~funny(X)&rich(X))))&
(![X]:((strong(X)&~wise(X))<=>~happy(X)))&
(![X]:((strong(X)<~>happy(X))=>tall(X)))&
(![X]:(~rich(X)<=>(curious(X)&humble(X))))&
((?[X]:((old(X)|~patient(X))))<=>(?[X]:(tall(X))))&
(![X]:(~happy(X)<=>(happy(X)|~quiet(X))))&
(![X]:((~happy(X)<~>brave(X))=>(~happy(X)&~old(X))))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
((?[X]:(curious(X)))=>((~calm(john)&~humble(john))))&
(![X]:(kind(X)=>(~old(X)|~funny(X))))&
(![X]:((calm(X)|patient(X))=>(~brave(X)|funny(X))))&
(![X]:((creative(X)&kind(X))<=>old(X)))&
((~quiet(lucy)|~rich(lucy)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:(~creative(X)))&
((humble(alice)<~>~tall(alice)))&
((old(susan)&kind(susan)))&
(?[X]:((~funny(X)<~>~generous(X)))) | ~curious(susan) | [
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3478284485269829897302296
% SZS output start Proof for 3478284485269829897302296
5. ! [X0] : ((~tall(X0) <~> patient(X0)) <=> (rich(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((~wise(X0) & strong(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : ((strong(X0) <~> happy(X0)) => tall(X0)) [input p6]
8. ! [X0] : (~rich(X0) <=> (humble(X0) & curious(X0))) [input p7]
10. ! [X0] : (~happy(X0) <=> (~quiet(X0) | happy(X0))) [input p9]
11. ! [X0] : ((~happy(X0) <~> brave(X0)) => (~old(X0) & ~happy(X0))) [input p10]
14. ! [X0] : (kind(X0) => (~funny(X0) | ~old(X0))) [input p13]
15. ! [X0] : ((patient(X0) | calm(X0)) => (funny(X0) | ~brave(X0))) [input p14]
21. kind(susan) & old(susan) [input p20]
23. ~curious(susan) [input hypothesis]
26. ! [X0] : (patient(X0) => (funny(X0) | ~brave(X0))) [pure predicate removal 15]
30. ! [X0] : (tall(X0) | (strong(X0) <=> happy(X0))) [ennf transformation 7]
31. ! [X0] : ((~old(X0) & ~happy(X0)) | (~happy(X0) <=> brave(X0))) [ennf transformation 11]
33. ! [X0] : ((~funny(X0) | ~old(X0)) | ~kind(X0)) [ennf transformation 14]
34. ! [X0] : (~funny(X0) | ~old(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : ((funny(X0) | ~brave(X0)) | ~patient(X0)) [ennf transformation 26]
36. ! [X0] : (funny(X0) | ~brave(X0) | ~patient(X0)) [flattening 35]
45. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [flattening 45]
47. ! [X0] : (((~wise(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | (wise(X0) | ~strong(X0)))) [nnf transformation 6]
48. ! [X0] : (((~wise(X0) & strong(X0)) | happy(X0)) & (~happy(X0) | wise(X0) | ~strong(X0))) [flattening 47]
49. ! [X0] : (tall(X0) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) [nnf transformation 30]
50. ! [X0] : ((~rich(X0) | (~humble(X0) | ~curious(X0))) & ((humble(X0) & curious(X0)) | rich(X0))) [nnf transformation 8]
51. ! [X0] : ((~rich(X0) | ~humble(X0) | ~curious(X0)) & ((humble(X0) & curious(X0)) | rich(X0))) [flattening 50]
57. ! [X0] : ((~happy(X0) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | happy(X0))) [nnf transformation 10]
58. ! [X0] : ((~happy(X0) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | happy(X0))) [flattening 57]
59. ! [X0] : ((~old(X0) & ~happy(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) [nnf transformation 31]
92. ~rich(X0) | ~tall(X0) | patient(X0) | funny(X0) [cnf transformation 46]
95. happy(X0) | strong(X0) [cnf transformation 48]
97. tall(X0) | happy(X0) | ~strong(X0) [cnf transformation 49]
98. tall(X0) | strong(X0) | ~happy(X0) [cnf transformation 49]
99. rich(X0) | curious(X0) [cnf transformation 51]
106. ~happy(X0) | ~happy(X0) [cnf transformation 58]
110. ~old(X0) | brave(X0) | happy(X0) [cnf transformation 59]
117. ~kind(X0) | ~old(X0) | ~funny(X0) [cnf transformation 34]
118. ~brave(X0) | funny(X0) | ~patient(X0) [cnf transformation 36]
128. old(susan) [cnf transformation 21]
129. kind(susan) [cnf transformation 21]
132. ~curious(susan) [cnf transformation 23]
135. ~happy(X0) [duplicate literal removal 106]
185. tall(X0) | strong(X0) [subsumption resolution 98,95]
186. tall(X0) | happy(X0) [subsumption resolution 97,185]
212. ~old(X0) | brave(X0) [subsumption resolution 110,135]
301. brave(susan) [resolution 212,128]
377. ~old(susan) | ~funny(susan) [resolution 117,129]
378. ~funny(susan) [subsumption resolution 377,128]
379. funny(susan) | ~patient(susan) [resolution 118,301]
380. ~patient(susan) [subsumption resolution 379,378]
383. ~tall(X1) | patient(X1) | funny(X1) | curious(X1) [resolution 92,99]
408. patient(X0) | funny(X0) | curious(X0) | happy(X0) [resolution 383,186]
413. curious(X0) | funny(X0) | patient(X0) [subsumption resolution 408,135]
440. funny(susan) | patient(susan) [resolution 413,132]
450. patient(susan) [subsumption resolution 440,378]
451. $false [subsumption resolution 450,380]
% SZS output end Proof for 3478284485269829897302296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or humble is tall.
If someone is either funny or not kind then john is not generous and vice versa.
Everyone who is either calm or creative is either humble or not curious.
If someone is happy or not strong then someone is curious or not brave.
Everyone who is both calm and not creative is both rich and happy.
If paul is not old then mary is quiet and vice versa.
If someone is not patient then someone is either not funny or calm.
Everyone who is either not kind or calm is generous.
Everyone who is not happy is both old and kind and vice versa.
If someone is not calm or wise then someone is not tall or not patient.
If someone is not curious or not humble then paul is either not tall or not funny.
If someone is wise or kind then someone is not curious.
Everyone who is either calm or creative is both generous and not patient and vice versa.
Everyone who is quiet or generous is either not quiet or not tall and vice versa.
Everyone who is not funny or not calm is either not creative or calm and vice versa.
Everyone who is not strong is creative or not tall and vice versa.
Paul is either not funny or not creative.
Someone is wise or not curious.
Paul is either not funny or funny.
Someone is either not tall or old.
Someone is both kind and not happy.
Paul is either brave or quiet.
Mary is either not happy or not quiet.
Someone is not humble or not happy. | Paul is creative. | neutral | (![X]:((calm(X)|humble(X))=>tall(X)))&
((?[X]:((funny(X)<~>~kind(X))))<=>(~generous(john)))&
(![X]:((calm(X)<~>creative(X))=>(humble(X)<~>~curious(X))))&
((?[X]:((happy(X)|~strong(X))))=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:((calm(X)&~creative(X))=>(rich(X)&happy(X))))&
((~old(paul))<=>(quiet(mary)))&
((?[X]:(~patient(X)))=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((~kind(X)<~>calm(X))=>generous(X)))&
(![X]:(~happy(X)<=>(old(X)&kind(X))))&
((?[X]:((~calm(X)|wise(X))))=>(?[X]:((~tall(X)|~patient(X)))))&
((?[X]:((~curious(X)|~humble(X))))=>((~tall(paul)<~>~funny(paul))))&
((?[X]:((wise(X)|kind(X))))=>(?[X]:(~curious(X))))&
(![X]:((calm(X)<~>creative(X))<=>(generous(X)&~patient(X))))&
(![X]:((quiet(X)|generous(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~funny(X)|~calm(X))<=>(~creative(X)<~>calm(X))))&
(![X]:(~strong(X)<=>(creative(X)|~tall(X))))&
((~funny(paul)<~>~creative(paul)))&
(?[X]:((wise(X)|~curious(X))))&
((~funny(paul)<~>funny(paul)))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((kind(X)&~happy(X))))&
((brave(paul)<~>quiet(paul)))&
((~happy(mary)<~>~quiet(mary)))&
(?[X]:((~humble(X)|~happy(X)))) | creative(paul) | [] | null | 0 |
Everyone who is both strong and not creative is generous or not quiet. If someone is funny or not generous then john is both strong and not creative. If susan is calm then someone is not humble and vice versa. Everyone who is either not rich or not old is old or kind. Everyone who is not generous is happy or generous and vice versa. If someone is either not wise or not generous then someone is either not strong or not quiet. Everyone who is humble or tall is tall or funny and vice versa. Everyone who is either not brave or rich is not rich or patient and vice versa. Everyone who is wise or not patient is both curious and humble. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Someone is either tall or creative. Someone is both not calm and not humble. Someone is not curious or happy. Fred is either not happy or not rich. Someone is not happy or happy. Someone is either brave or kind. | Susan is not strong. | neutral | (![X]:((strong(X)&~creative(X))=>(generous(X)|~quiet(X))))&
((?[X]:((funny(X)|~generous(X))))=>((strong(john)&~creative(john))))&
((calm(susan))<=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))<=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(?[X]:((tall(X)<~>creative(X))))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~curious(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa.
If someone is both funny and not tall then someone is funny or happy.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Someone is both rich and old.
Alice is not happy or old.
Someone is either generous or brave.
Someone is curious or quiet.
John is both humble and not patient.
Someone is not generous. | Alice is patient. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(?[X]:((rich(X)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(?[X]:(~generous(X))) | patient(alice) | [
"p5",
"p8",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3371374462579090181694362
% SZS output start Proof for 3371374462579090181694362
6. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p5]
9. (happy(alice) <~> calm(alice)) => (quiet(susan) & ~quiet(susan)) [input p8]
11. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p10]
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
16. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p15]
23. patient(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 6]
32. (quiet(susan) & ~quiet(susan)) | (happy(alice) <=> calm(alice)) [ennf transformation 9]
33. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 11]
47. (quiet(susan) & ~quiet(susan)) | ((happy(alice) | ~calm(alice)) & (calm(alice) | ~happy(alice))) [nnf transformation 32]
52. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 12]
53. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 52]
65. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 16]
91. ~happy(X0) | ~kind(X0) [cnf transformation 30]
101. ~quiet(susan) | happy(alice) | ~calm(alice) [cnf transformation 47]
103. quiet(susan) | happy(alice) | ~calm(alice) [cnf transformation 47]
109. ~patient(X0) | old(X0) [cnf transformation 33]
112. kind(X0) | kind(X0) [cnf transformation 53]
128. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 65]
135. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 65]
145. patient(alice) [cnf transformation 23]
146. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 128]
149. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 135]
150. kind(X0) [duplicate literal removal 112]
202. 11 <=> calm(alice) [avatar definition]
206. 12 <=> happy(alice) [avatar definition]
208. happy(alice) <- (12) [avatar component clause 206]
210. 13 <=> quiet(susan) [avatar definition]
213. ~11 | 12 | 13 [avatar split clause 103,210,206,202]
215. ~11 | 12 | ~13 [avatar split clause 101,210,206,202]
277. ~old(X0) | calm(X0) [subsumption resolution 146,149]
279. 26 <=> old(alice) [avatar definition]
281. old(alice) <- (26) [avatar component clause 279]
292. old(alice) [resolution 109,145]
293. 26 [avatar split clause 292,279]
298. calm(alice) <- (26) [resolution 277,281]
302. 11 | ~26 [avatar split clause 298,279,202]
305. ~kind(alice) <- (12) [resolution 208,91]
306. $false <- (12) [subsumption resolution 305,150]
307. ~12 [avatar contradiction clause 306]
308. $false [avatar sat refutation 213,215,293,302,307]
% SZS output end Proof for 3371374462579090181694362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not humble or patient.
Everyone who is not funny or not happy is either not kind or quiet and vice versa.
Everyone who is both brave and not calm is both not curious and not creative.
Everyone who is both rich and not kind is both generous and quiet and vice versa.
If someone is rich then someone is not patient.
Everyone who is old is either not funny or quiet.
If paul is not happy then fred is both not creative and not funny and vice versa.
Everyone who is either not old or tall is either not generous or happy and vice versa.
Everyone who is not quiet is either not wise or wise and vice versa.
Everyone who is either not tall or not humble is wise or not happy and vice versa.
If fred is both quiet and tall then someone is either tall or not creative and vice versa.
If someone is not funny then someone is rich.
Everyone who is either not curious or not old is funny or not brave.
If mary is quiet or not generous then alice is either humble or quiet and vice versa.
If someone is both humble and not humble then someone is either tall or not creative and vice versa.
Everyone who is both not generous and old is either not quiet or not creative and vice versa.
Susan is either not old or not generous.
Someone is not curious.
Alice is patient.
Someone is either creative or not kind.
Someone is both not happy and not creative.
Alice is not brave.
Alice is old.
Someone is patient or not happy. | Fred is tall. | neutral | (![X]:(~creative(X)=>(~humble(X)|patient(X))))&
(![X]:((~funny(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)&~calm(X))=>(~curious(X)&~creative(X))))&
(![X]:((rich(X)&~kind(X))<=>(generous(X)&quiet(X))))&
((?[X]:(rich(X)))=>(?[X]:(~patient(X))))&
(![X]:(old(X)=>(~funny(X)<~>quiet(X))))&
((~happy(paul))<=>((~creative(fred)&~funny(fred))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>happy(X))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>wise(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(wise(X)|~happy(X))))&
(((quiet(fred)&tall(fred)))<=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:(~funny(X)))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)<~>~old(X))=>(funny(X)|~brave(X))))&
(((quiet(mary)|~generous(mary)))<=>((humble(alice)<~>quiet(alice))))&
((?[X]:((humble(X)&~humble(X))))<=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((~generous(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
((~old(susan)<~>~generous(susan)))&
(?[X]:(~curious(X)))&
(patient(alice))&
(?[X]:((creative(X)<~>~kind(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(~brave(alice))&
(old(alice))&
(?[X]:((patient(X)|~happy(X)))) | tall(fred) | [] | null | 0 |
Everyone who is strong is not humble or funny.
Everyone who is both creative and strong is curious and vice versa.
Everyone who is either wise or not old is generous or not patient and vice versa.
If alice is not quiet then paul is either not rich or happy and vice versa.
Everyone who is not humble is either not generous or not patient and vice versa.
If someone is either not strong or tall then someone is not generous and vice versa.
Everyone who is not tall or not strong is both rich and not strong and vice versa.
Everyone who is brave or generous is either tall or not old and vice versa.
Everyone who is either brave or curious is both kind and not happy.
If someone is both curious and brave then someone is both tall and not generous and vice versa.
If paul is funny or kind then someone is not kind or not curious.
Everyone who is humble is not rich and vice versa.
Everyone who is not rich is either not wise or happy.
If lucy is not quiet then fred is either not generous or tall.
If someone is not patient then someone is not wise.
Everyone who is not quiet is generous and vice versa.
Someone is not strong.
Someone is not happy or not kind.
John is funny or not brave.
Someone is not old.
Fred is not calm.
Someone is funny.
Mary is patient or not tall.
Susan is both kind and not creative. | Mary is not humble. | neutral | (![X]:(strong(X)=>(~humble(X)|funny(X))))&
(![X]:((creative(X)&strong(X))<=>curious(X)))&
(![X]:((wise(X)<~>~old(X))<=>(generous(X)|~patient(X))))&
((~quiet(alice))<=>((~rich(paul)<~>happy(paul))))&
(![X]:(~humble(X)<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)|~strong(X))<=>(rich(X)&~strong(X))))&
(![X]:((brave(X)|generous(X))<=>(tall(X)<~>~old(X))))&
(![X]:((brave(X)<~>curious(X))=>(kind(X)&~happy(X))))&
((?[X]:((curious(X)&brave(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(((funny(paul)|kind(paul)))=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:(humble(X)<=>~rich(X)))&
(![X]:(~rich(X)=>(~wise(X)<~>happy(X))))&
((~quiet(lucy))=>((~generous(fred)<~>tall(fred))))&
((?[X]:(~patient(X)))=>(?[X]:(~wise(X))))&
(![X]:(~quiet(X)<=>generous(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)|~kind(X))))&
((funny(john)|~brave(john)))&
(?[X]:(~old(X)))&
(~calm(fred))&
(?[X]:(funny(X)))&
((patient(mary)|~tall(mary)))&
((kind(susan)&~creative(susan))) | ~humble(mary) | [] | null | 0 |
Everyone who is rich or old is both not humble and not wise. Everyone who is either not patient or not happy is either calm or not rich. If someone is not strong or not rich then john is not curious or not creative. If paul is both wise and happy then someone is either not tall or generous and vice versa. If someone is both strong and not rich then alice is both not strong and not calm and vice versa. Everyone who is either patient or not patient is both quiet and strong. If john is either not creative or not tall then fred is either not funny or not happy and vice versa. If mary is both not quiet and not creative then susan is funny or not curious. Everyone who is both not patient and not funny is not funny or generous and vice versa. If someone is both not funny and not generous then mary is both calm and humble. If paul is tall then someone is not rich. If someone is not humble or not wise then fred is both creative and not curious and vice versa. Everyone who is not generous or kind is both not wise and not calm and vice versa. Everyone who is either not wise or curious is curious or rich and vice versa. If someone is either wise or humble then someone is either not old or not happy and vice versa. Everyone who is either not strong or not happy is not tall and vice versa. Fred is calm. Someone is either old or not happy. Someone is either funny or kind. Alice is either rich or not happy. Someone is either kind or not generous. John is tall. Lucy is rich or not patient. | John is kind. | neutral | (![X]:((rich(X)|old(X))=>(~humble(X)&~wise(X))))&
(![X]:((~patient(X)<~>~happy(X))=>(calm(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~rich(X))))=>((~curious(john)|~creative(john))))&
(((wise(paul)&happy(paul)))<=>(?[X]:((~tall(X)<~>generous(X)))))&
((?[X]:((strong(X)&~rich(X))))<=>((~strong(alice)&~calm(alice))))&
(![X]:((patient(X)<~>~patient(X))=>(quiet(X)&strong(X))))&
(((~creative(john)<~>~tall(john)))<=>((~funny(fred)<~>~happy(fred))))&
(((~quiet(mary)&~creative(mary)))=>((funny(susan)|~curious(susan))))&
(![X]:((~patient(X)&~funny(X))<=>(~funny(X)|generous(X))))&
((?[X]:((~funny(X)&~generous(X))))=>((calm(mary)&humble(mary))))&
((tall(paul))=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))<=>((creative(fred)&~curious(fred))))&
(![X]:((~generous(X)|kind(X))<=>(~wise(X)&~calm(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(curious(X)|rich(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(?[X]:((~old(X)<~>~happy(X)))))&
(![X]:((~strong(X)<~>~happy(X))<=>~tall(X)))&
(calm(fred))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((funny(X)<~>kind(X))))&
((rich(alice)<~>~happy(alice)))&
(?[X]:((kind(X)<~>~generous(X))))&
(tall(john))&
((rich(lucy)|~patient(lucy))) | kind(john) | [] | null | 0 |
If someone is either quiet or not strong then someone is old or not wise and vice versa.
Everyone who is not happy is either not wise or not curious.
Everyone who is funny is both not old and humble and vice versa.
Everyone who is strong is either patient or not rich and vice versa.
Everyone who is either not old or not funny is not rich or wise and vice versa.
If someone is old or rich then mary is not generous or not kind.
If lucy is creative then alice is not strong.
Everyone who is strong or not patient is not rich or curious and vice versa.
Everyone who is old or not tall is happy or funny and vice versa.
If someone is both not quiet and quiet then mary is both curious and not funny.
Everyone who is both not calm and creative is either not wise or rich.
If someone is both not humble and not generous then someone is not strong or not tall and vice versa.
If someone is not humble then someone is either creative or not patient and vice versa.
If someone is either rich or not rich then john is both not strong and funny.
Everyone who is quiet is either not happy or kind and vice versa.
Alice is either not humble or strong.
John is not curious or generous.
Someone is curious or not humble.
Someone is both not quiet and not kind.
Someone is either funny or not humble.
Someone is both happy and curious.
Someone is both creative and brave.
Paul is either calm or not old. | John is not tall. | entailment | ((?[X]:((quiet(X)<~>~strong(X))))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:(~happy(X)=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)<=>(~old(X)&humble(X))))&
(![X]:(strong(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~rich(X)|wise(X))))&
((?[X]:((old(X)|rich(X))))=>((~generous(mary)|~kind(mary))))&
((creative(lucy))=>(~strong(alice)))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)|curious(X))))&
(![X]:((old(X)|~tall(X))<=>(happy(X)|funny(X))))&
((?[X]:((~quiet(X)&quiet(X))))=>((curious(mary)&~funny(mary))))&
(![X]:((~calm(X)&creative(X))=>(~wise(X)<~>rich(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((?[X]:((rich(X)<~>~rich(X))))=>((~strong(john)&funny(john))))&
(![X]:(quiet(X)<=>(~happy(X)<~>kind(X))))&
((~humble(alice)<~>strong(alice)))&
((~curious(john)|generous(john)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((creative(X)&brave(X))))&
((calm(paul)<~>~old(paul))) | ~tall(john) | [
"p2",
"p3",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7106371006194320269920877
% SZS output start Proof for 7106371006194320269920877
3. ! [X0] : (funny(X0) <=> (humble(X0) & ~old(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> (patient(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((~patient(X0) | strong(X0)) <=> (curious(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | old(X0)) <=> (funny(X0) | happy(X0))) [input p8]
14. ? [X0] : (rich(X0) <~> ~rich(X0)) => (funny(john) & ~strong(john)) [input p13]
24. tall(john) [input hypothesis]
36. (funny(john) & ~strong(john)) | ! [X0] : (rich(X0) <=> ~rich(X0)) [ennf transformation 14]
43. ! [X0] : ((funny(X0) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [nnf transformation 3]
44. ! [X0] : ((funny(X0) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [flattening 43]
45. ! [X0] : ((strong(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 4]
48. ! [X0] : (((~patient(X0) | strong(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (patient(X0) & ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : ((~patient(X0) | strong(X0) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | (patient(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((~tall(X0) | old(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (tall(X0) & ~old(X0)))) [nnf transformation 9]
51. ! [X0] : ((~tall(X0) | old(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (tall(X0) & ~old(X0)))) [flattening 50]
63. (funny(john) & ~strong(john)) | ! [X0] : ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))) [nnf transformation 36]
86. ~funny(X0) | ~old(X0) [cnf transformation 44]
92. strong(X0) | patient(X0) | rich(X0) [cnf transformation 45]
104. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 49]
109. ~tall(X0) | old(X0) | ~funny(X0) [cnf transformation 51]
124. ~strong(john) | rich(X0) | rich(X0) [cnf transformation 63]
125. funny(john) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
144. tall(john) [cnf transformation 24]
146. ~strong(john) | rich(X0) [duplicate literal removal 124]
147. funny(john) | ~rich(X0) [duplicate literal removal 125]
186. 9 <=> ! [X0] : ~rich(X0) [avatar definition]
187. ~rich(X0) <- (9) [avatar component clause 186]
207. rich(X0) | strong(X0) [subsumption resolution 104,92]
208. ~tall(X0) | ~funny(X0) [subsumption resolution 109,86]
219. 16 <=> ! [X1] : strong(X1) [avatar definition]
220. strong(X1) <- (16) [avatar component clause 219]
266. 27 <=> ! [X0] : rich(X0) [avatar definition]
267. rich(X0) <- (27) [avatar component clause 266]
269. 28 <=> funny(john) [avatar definition]
271. funny(john) <- (28) [avatar component clause 269]
273. 9 | 28 [avatar split clause 147,269,186]
275. 29 <=> strong(john) [avatar definition]
277. ~strong(john) <- (~29) [avatar component clause 275]
278. 27 | ~29 [avatar split clause 146,275,266]
323. $false <- (9, 27) [subsumption resolution 187,267]
324. ~9 | ~27 [avatar contradiction clause 323]
327. strong(X0) <- (9) [resolution 207,187]
328. 16 | ~9 [avatar split clause 327,186,219]
330. $false <- (16, ~29) [resolution 220,277]
335. ~16 | 29 [avatar contradiction clause 330]
337. ~funny(john) [resolution 208,144]
338. $false <- (28) [subsumption resolution 337,271]
339. ~28 [avatar contradiction clause 338]
340. $false [avatar sat refutation 273,278,324,328,335,339]
% SZS output end Proof for 7106371006194320269920877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and kind.
Everyone who is either creative or not creative is both patient and not curious.
If paul is both rich and not brave then mary is both not old and generous and vice versa.
Everyone who is brave is humble or calm.
If fred is both quiet and patient then someone is both creative and calm and vice versa.
Everyone who is wise or not kind is either rich or not brave and vice versa.
Everyone who is either not brave or brave is happy or not brave and vice versa.
Everyone who is calm is not tall or not generous and vice versa.
Everyone who is either brave or not humble is not creative.
If paul is both not quiet and quiet then someone is not humble and vice versa.
If mary is patient then fred is not quiet or not calm.
If someone is creative then someone is not rich and vice versa.
Everyone who is not rich or old is not happy or curious and vice versa.
If fred is not kind or not calm then fred is either rich or not calm.
Everyone who is not calm or not kind is not kind and vice versa.
Everyone who is not curious is rich or calm.
Someone is either not humble or generous.
Lucy is either not curious or generous.
Fred is both not strong and not funny.
Someone is happy or creative.
Fred is not curious or curious.
John is both not strong and not kind.
Paul is not happy or not patient. | John is creative. | contradiction | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&kind(X))))&
(![X]:((creative(X)<~>~creative(X))=>(patient(X)&~curious(X))))&
(((rich(paul)&~brave(paul)))<=>((~old(mary)&generous(mary))))&
(![X]:(brave(X)=>(humble(X)|calm(X))))&
(((quiet(fred)&patient(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((wise(X)|~kind(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(happy(X)|~brave(X))))&
(![X]:(calm(X)<=>(~tall(X)|~generous(X))))&
(![X]:((brave(X)<~>~humble(X))=>~creative(X)))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((patient(mary))=>((~quiet(fred)|~calm(fred))))&
((?[X]:(creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|old(X))<=>(~happy(X)|curious(X))))&
(((~kind(fred)|~calm(fred)))=>((rich(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~kind(X))<=>~kind(X)))&
(![X]:(~curious(X)=>(rich(X)|calm(X))))&
(?[X]:((~humble(X)<~>generous(X))))&
((~curious(lucy)<~>generous(lucy)))&
((~strong(fred)&~funny(fred)))&
(?[X]:((happy(X)|creative(X))))&
((~curious(fred)|curious(fred)))&
((~strong(john)&~kind(john)))&
((~happy(paul)|~patient(paul))) | creative(john) | [
"p1",
"p4",
"p5",
"p8",
"p9",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5374134076328187705292826
% SZS output start Proof for 5374134076328187705292826
2. ! [X0] : ((creative(X0) <~> ~creative(X0)) => (~curious(X0) & patient(X0))) [input p1]
5. (patient(fred) & quiet(fred)) <=> ? [X0] : (calm(X0) & creative(X0)) [input p4]
6. ! [X0] : ((~kind(X0) | wise(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p5]
9. ! [X0] : ((brave(X0) <~> ~humble(X0)) => ~creative(X0)) [input p8]
10. (quiet(paul) & ~quiet(paul)) <=> ? [X0] : ~humble(X0) [input p9]
11. patient(mary) => (~calm(fred) | ~quiet(fred)) [input p10]
14. (~calm(fred) | ~kind(fred)) => (rich(fred) <~> ~calm(fred)) [input p13]
15. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> ~kind(X0)) [input p14]
16. ! [X0] : (~curious(X0) => (calm(X0) | rich(X0))) [input p15]
24. creative(john) [input hypothesis]
30. ! [X0] : ((~curious(X0) & patient(X0)) | (creative(X0) <=> ~creative(X0))) [ennf transformation 2]
33. ! [X0] : (~creative(X0) | (brave(X0) <=> ~humble(X0))) [ennf transformation 9]
34. (~calm(fred) | ~quiet(fred)) | ~patient(mary) [ennf transformation 11]
35. ~calm(fred) | ~quiet(fred) | ~patient(mary) [flattening 34]
36. (rich(fred) <~> ~calm(fred)) | (calm(fred) & kind(fred)) [ennf transformation 14]
37. ! [X0] : ((calm(X0) | rich(X0)) | curious(X0)) [ennf transformation 16]
38. ! [X0] : (calm(X0) | rich(X0) | curious(X0)) [flattening 37]
40. ! [X0] : ((~curious(X0) & patient(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) [nnf transformation 30]
43. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X0] : (calm(X0) & creative(X0)) | (~patient(fred) | ~quiet(fred))) [nnf transformation 5]
44. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X0] : (calm(X0) & creative(X0)) | ~patient(fred) | ~quiet(fred)) [flattening 43]
45. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & (? [X1] : (calm(X1) & creative(X1)) | ~patient(fred) | ~quiet(fred)) [rectify 44]
46. ? [X1] : (calm(X1) & creative(X1)) => (calm(sK0) & creative(sK0)) [choice axiom]
47. ((patient(fred) & quiet(fred)) | ! [X0] : (~calm(X0) | ~creative(X0))) & ((calm(sK0) & creative(sK0)) | ~patient(fred) | ~quiet(fred)) [skolemisation 45,46]
48. ! [X0] : (((~kind(X0) | wise(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (kind(X0) & ~wise(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | wise(X0) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (kind(X0) & ~wise(X0)))) [flattening 48]
54. ! [X0] : (~creative(X0) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 33]
55. ((quiet(paul) & ~quiet(paul)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (~quiet(paul) | quiet(paul))) [nnf transformation 10]
56. ((quiet(paul) & ~quiet(paul)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ~quiet(paul) | quiet(paul)) [flattening 55]
57. ((quiet(paul) & ~quiet(paul)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ~quiet(paul) | quiet(paul)) [rectify 56]
58. ? [X1] : ~humble(X1) => ~humble(sK1) [choice axiom]
59. ((quiet(paul) & ~quiet(paul)) | ! [X0] : humble(X0)) & (~humble(sK1) | ~quiet(paul) | quiet(paul)) [skolemisation 57,58]
67. ((calm(fred) | ~rich(fred)) & (~calm(fred) | rich(fred))) | (calm(fred) & kind(fred)) [nnf transformation 36]
68. ! [X0] : (((~kind(X0) | ~calm(X0)) | kind(X0)) & (~kind(X0) | (kind(X0) & calm(X0)))) [nnf transformation 15]
69. ! [X0] : ((~kind(X0) | ~calm(X0) | kind(X0)) & (~kind(X0) | (kind(X0) & calm(X0)))) [flattening 68]
80. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
81. patient(X0) | creative(X0) | creative(X0) [cnf transformation 40]
82. ~curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
83. ~curious(X0) | creative(X0) | creative(X0) [cnf transformation 40]
91. quiet(fred) | ~calm(X0) | ~creative(X0) [cnf transformation 47]
96. ~rich(X0) | brave(X0) | kind(X0) [cnf transformation 49]
108. ~humble(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 54]
111. ~quiet(paul) | humble(X0) [cnf transformation 59]
112. quiet(paul) | humble(X0) [cnf transformation 59]
113. ~calm(fred) | ~quiet(fred) | ~patient(mary) [cnf transformation 35]
123. calm(fred) | ~rich(fred) | calm(fred) [cnf transformation 67]
124. ~kind(X0) | calm(X0) [cnf transformation 69]
127. calm(X0) | rich(X0) | curious(X0) [cnf transformation 38]
136. creative(john) [cnf transformation 24]
137. calm(fred) | ~rich(fred) [duplicate literal removal 123]
142. patient(X0) | ~creative(X0) [duplicate literal removal 80]
143. patient(X0) | creative(X0) [duplicate literal removal 81]
144. ~curious(X0) | ~creative(X0) [duplicate literal removal 82]
145. ~curious(X0) | creative(X0) [duplicate literal removal 83]
146. ~curious(X0) [subsumption resolution 144,145]
147. patient(X0) [subsumption resolution 142,143]
169. 5 <=> ! [X0] : (~calm(X0) | ~creative(X0)) [avatar definition]
170. ~creative(X0) | ~calm(X0) <- (5) [avatar component clause 169]
172. 6 <=> quiet(fred) [avatar definition]
175. 5 | 6 [avatar split clause 91,172,169]
189. 9 <=> ! [X0] : humble(X0) [avatar definition]
190. humble(X0) <- (9) [avatar component clause 189]
192. 10 <=> quiet(paul) [avatar definition]
195. 9 | 10 [avatar split clause 112,192,189]
196. 9 | ~10 [avatar split clause 111,192,189]
197. ~calm(fred) | ~quiet(fred) [subsumption resolution 113,147]
199. 11 <=> calm(fred) [avatar definition]
201. ~calm(fred) <- (~11) [avatar component clause 199]
202. ~6 | ~11 [avatar split clause 197,199,172]
212. 14 <=> ! [X3] : ~creative(X3) [avatar definition]
213. ~creative(X3) <- (14) [avatar component clause 212]
222. 16 <=> rich(fred) [avatar definition]
224. ~rich(fred) <- (~16) [avatar component clause 222]
225. ~16 | 11 [avatar split clause 137,199,222]
232. rich(X0) | calm(X0) [subsumption resolution 127,146]
266. calm(fred) <- (~16) [resolution 232,224]
267. $false <- (~11, ~16) [subsumption resolution 266,201]
268. 11 | 16 [avatar contradiction clause 267]
302. brave(X0) | kind(X0) | calm(X0) [resolution 96,232]
306. brave(X0) | calm(X0) [subsumption resolution 302,124]
327. ~brave(X0) | ~creative(X0) <- (9) [resolution 108,190]
357. ~creative(X0) | calm(X0) <- (9) [resolution 327,306]
358. ~creative(X0) <- (5, 9) [subsumption resolution 357,170]
359. 14 | ~5 | ~9 [avatar split clause 358,189,169,212]
360. $false <- (14) [resolution 213,136]
363. ~14 [avatar contradiction clause 360]
364. $false [avatar sat refutation 175,195,196,202,225,268,359,363]
% SZS output end Proof for 5374134076328187705292826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and tall is quiet and vice versa.
If fred is both brave and not brave then someone is both not quiet and generous and vice versa.
Everyone who is both happy and patient is either funny or generous and vice versa.
Everyone who is both quiet and not funny is both tall and quiet and vice versa.
If mary is brave or not tall then fred is both wise and not tall.
If someone is both not happy and funny then fred is not generous.
Everyone who is both wise and not rich is not rich.
Everyone who is wise or not happy is curious or kind.
If someone is either not patient or quiet then someone is not calm or creative and vice versa.
Everyone who is not wise or patient is either not patient or rich.
Everyone who is either not kind or not old is either not rich or quiet.
Everyone who is both old and not tall is not humble or not quiet and vice versa.
Everyone who is both not rich and calm is both not wise and not creative and vice versa.
If susan is both not rich and wise then someone is both tall and quiet and vice versa.
Everyone who is both happy and not strong is either creative or not generous and vice versa.
If someone is both curious and funny then alice is rich.
Someone is wise.
Susan is not calm or not old.
Fred is either not brave or not strong.
Fred is either creative or not brave.
Susan is not patient or not wise.
Someone is either tall or not rich.
Lucy is brave or not brave. | Susan is not kind. | neutral | (![X]:((~rich(X)&tall(X))<=>quiet(X)))&
(((brave(fred)&~brave(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((happy(X)&patient(X))<=>(funny(X)<~>generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(tall(X)&quiet(X))))&
(((brave(mary)|~tall(mary)))=>((wise(fred)&~tall(fred))))&
((?[X]:((~happy(X)&funny(X))))=>(~generous(fred)))&
(![X]:((wise(X)&~rich(X))=>~rich(X)))&
(![X]:((wise(X)|~happy(X))=>(curious(X)|kind(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((~wise(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&~creative(X))))&
(((~rich(susan)&wise(susan)))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:((curious(X)&funny(X))))=>(rich(alice)))&
(?[X]:(wise(X)))&
((~calm(susan)|~old(susan)))&
((~brave(fred)<~>~strong(fred)))&
((creative(fred)<~>~brave(fred)))&
((~patient(susan)|~wise(susan)))&
(?[X]:((tall(X)<~>~rich(X))))&
((brave(lucy)|~brave(lucy))) | ~kind(susan) | [] | null | 0 |
If alice is not rich or not quiet then fred is generous or strong and vice versa.
If mary is not brave or not patient then lucy is both not calm and not funny and vice versa.
If susan is both patient and calm then someone is both old and curious and vice versa.
Everyone who is both not strong and creative is not humble or patient and vice versa.
If john is both creative and not calm then lucy is either calm or not rich and vice versa.
If someone is happy or not curious then alice is tall.
If susan is not happy then someone is strong or generous and vice versa.
If john is generous then someone is both curious and not brave and vice versa.
If john is either not happy or kind then someone is both not kind and not brave.
If someone is strong then someone is either not quiet or not brave and vice versa.
If someone is both tall and creative then paul is both not funny and brave and vice versa.
Everyone who is creative or tall is both not curious and brave and vice versa.
Everyone who is not funny is both not old and not curious and vice versa.
If lucy is humble then mary is curious or old and vice versa.
If lucy is both not generous and not tall then susan is not kind or humble.
Everyone who is not rich or tall is both calm and not creative.
Mary is both not funny and not happy.
Someone is either curious or patient.
Someone is humble or brave.
Someone is not kind or humble.
Someone is kind or quiet.
Someone is either kind or strong.
Fred is kind.
Lucy is kind or patient. | Lucy is tall. | contradiction | (((~rich(alice)|~quiet(alice)))<=>((generous(fred)|strong(fred))))&
(((~brave(mary)|~patient(mary)))<=>((~calm(lucy)&~funny(lucy))))&
(((patient(susan)&calm(susan)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~strong(X)&creative(X))<=>(~humble(X)|patient(X))))&
(((creative(john)&~calm(john)))<=>((calm(lucy)<~>~rich(lucy))))&
((?[X]:((happy(X)|~curious(X))))=>(tall(alice)))&
((~happy(susan))<=>(?[X]:((strong(X)|generous(X)))))&
((generous(john))<=>(?[X]:((curious(X)&~brave(X)))))&
(((~happy(john)<~>kind(john)))=>(?[X]:((~kind(X)&~brave(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~funny(paul)&brave(paul))))&
(![X]:((creative(X)|tall(X))<=>(~curious(X)&brave(X))))&
(![X]:(~funny(X)<=>(~old(X)&~curious(X))))&
((humble(lucy))<=>((curious(mary)|old(mary))))&
(((~generous(lucy)&~tall(lucy)))=>((~kind(susan)|humble(susan))))&
(![X]:((~rich(X)|tall(X))=>(calm(X)&~creative(X))))&
((~funny(mary)&~happy(mary)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((kind(X)<~>strong(X))))&
(kind(fred))&
((kind(lucy)|patient(lucy))) | tall(lucy) | [
"p1",
"p3",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2425920601223453854661177
% SZS output start Proof for 2425920601223453854661177
2. (~patient(mary) | ~brave(mary)) <=> (~funny(lucy) & ~calm(lucy)) [input p1]
4. ! [X0] : ((creative(X0) & ~strong(X0)) <=> (patient(X0) | ~humble(X0))) [input p3]
12. ! [X0] : ((tall(X0) | creative(X0)) <=> (brave(X0) & ~curious(X0))) [input p11]
13. ! [X0] : (~funny(X0) <=> (~curious(X0) & ~old(X0))) [input p12]
14. humble(lucy) <=> (old(mary) | curious(mary)) [input p13]
16. ! [X0] : ((tall(X0) | ~rich(X0)) => (~creative(X0) & calm(X0))) [input p15]
17. ~happy(mary) & ~funny(mary) [input p16]
25. tall(lucy) [input hypothesis]
31. ! [X0] : ((~creative(X0) & calm(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 16]
34. ((~patient(mary) | ~brave(mary)) | (funny(lucy) | calm(lucy))) & ((~funny(lucy) & ~calm(lucy)) | (patient(mary) & brave(mary))) [nnf transformation 2]
35. (~patient(mary) | ~brave(mary) | funny(lucy) | calm(lucy)) & ((~funny(lucy) & ~calm(lucy)) | (patient(mary) & brave(mary))) [flattening 34]
41. ! [X0] : (((creative(X0) & ~strong(X0)) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | (~creative(X0) | strong(X0)))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) & ~strong(X0)) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ~creative(X0) | strong(X0))) [flattening 41]
66. ! [X0] : (((tall(X0) | creative(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 12]
67. ! [X0] : ((tall(X0) | creative(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 66]
68. ! [X0] : ((~funny(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | funny(X0))) [nnf transformation 13]
69. ! [X0] : ((~funny(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | funny(X0))) [flattening 68]
70. (humble(lucy) | (~old(mary) & ~curious(mary))) & ((old(mary) | curious(mary)) | ~humble(lucy)) [nnf transformation 14]
71. (humble(lucy) | (~old(mary) & ~curious(mary))) & (old(mary) | curious(mary) | ~humble(lucy)) [flattening 70]
89. ~calm(lucy) | patient(mary) [cnf transformation 35]
100. humble(X0) | creative(X0) [cnf transformation 42]
101. ~patient(X0) | creative(X0) [cnf transformation 42]
128. ~creative(X0) | ~curious(X0) [cnf transformation 67]
133. ~old(X0) | funny(X0) [cnf transformation 69]
136. old(mary) | curious(mary) | ~humble(lucy) [cnf transformation 71]
141. ~tall(X0) | calm(X0) [cnf transformation 31]
143. ~creative(X0) | ~tall(X0) [cnf transformation 31]
144. ~funny(mary) [cnf transformation 17]
155. tall(lucy) [cnf transformation 25]
177. 5 <=> calm(lucy) [avatar definition]
189. 8 <=> patient(mary) [avatar definition]
190. patient(mary) <- (8) [avatar component clause 189]
195. 8 | ~5 [avatar split clause 89,177,189]
350. 42 <=> ! [X1] : (~creative(X1) | ~tall(X1)) [avatar definition]
351. ~tall(X1) | ~creative(X1) <- (42) [avatar component clause 350]
355. 43 <=> old(mary) [avatar definition]
356. old(mary) <- (43) [avatar component clause 355]
359. 44 <=> humble(lucy) [avatar definition]
360. ~humble(lucy) <- (~44) [avatar component clause 359]
364. 45 <=> curious(mary) [avatar definition]
368. ~44 | 45 | 43 [avatar split clause 136,355,364,359]
374. 47 <=> tall(lucy) [avatar definition]
376. tall(lucy) <- (47) [avatar component clause 374]
386. 42 [avatar split clause 143,350]
443. 47 [avatar split clause 155,374]
447. creative(lucy) <- (~44) [resolution 100,360]
448. creative(mary) <- (8) [resolution 101,190]
450. ~curious(mary) <- (8) [resolution 128,448]
460. calm(lucy) <- (47) [resolution 141,376]
465. 5 | ~47 [avatar split clause 460,374,177]
479. ~creative(lucy) <- (42, 47) [resolution 351,376]
480. $false <- (42, ~44, 47) [subsumption resolution 479,447]
481. ~42 | 44 | ~47 [avatar contradiction clause 480]
482. funny(mary) <- (43) [resolution 356,133]
483. $false <- (43) [subsumption resolution 482,144]
484. ~43 [avatar contradiction clause 483]
485. ~45 | ~8 [avatar split clause 450,189,364]
486. $false [avatar sat refutation 195,368,386,443,465,481,484,485]
% SZS output end Proof for 2425920601223453854661177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or kind is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Everyone who is curious is not curious or not happy and vice versa.
Everyone who is both not generous and calm is both strong and not happy and vice versa.
Everyone who is either not kind or generous is either happy or not funny and vice versa.
Everyone who is tall or not old is not funny or not creative and vice versa.
If fred is not patient or quiet then someone is not brave.
Everyone who is either tall or not happy is quiet or not humble and vice versa.
If susan is either funny or not wise then someone is either not funny or not calm.
Everyone who is not happy is humble and vice versa.
Fred is not old or happy.
Susan is not kind.
Alice is patient or old.
Someone is not brave.
Someone is not calm.
Someone is either not creative or not kind.
Fred is either strong or old.
Someone is brave or not wise. | Alice is not humble. | contradiction | (![X]:((~patient(X)<~>kind(X))=>(~generous(X)<~>quiet(X))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~curious(X)|~happy(X))))&
(![X]:((~generous(X)&calm(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~funny(X)|~creative(X))))&
(((~patient(fred)|quiet(fred)))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(quiet(X)|~humble(X))))&
(((funny(susan)<~>~wise(susan)))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~happy(X)<=>humble(X)))&
((~old(fred)|happy(fred)))&
(~kind(susan))&
((patient(alice)|old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(fred)<~>old(fred)))&
(?[X]:((brave(X)|~wise(X)))) | ~humble(alice) | [
"p1",
"p7",
"p8",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4921850262170633991794989
% SZS output start Proof for 4921850262170633991794989
2. ~happy(alice) <=> ? [X0] : (curious(X0) <~> ~brave(X0)) [input p1]
8. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : (curious(X0) <=> (~happy(X0) | ~curious(X0))) [input p8]
16. ! [X0] : (~happy(X0) <=> humble(X0)) [input p15]
24. ? [X0] : (~wise(X0) | brave(X0)) [input p23]
25. ~humble(alice) [input hypothesis]
33. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (? [X0] : ((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | happy(alice)) [nnf transformation 2]
34. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (? [X1] : ((brave(X1) | ~curious(X1)) & (~brave(X1) | curious(X1))) | happy(alice)) [rectify 33]
35. ? [X1] : ((brave(X1) | ~curious(X1)) & (~brave(X1) | curious(X1))) => ((brave(sK0) | ~curious(sK0)) & (~brave(sK0) | curious(sK0))) [choice axiom]
36. (~happy(alice) | ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(sK0) | ~curious(sK0)) & (~brave(sK0) | curious(sK0))) | happy(alice)) [skolemisation 34,35]
52. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 8]
53. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~curious(X0))) [flattening 53]
67. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 16]
76. ? [X0] : (~wise(X0) | brave(X0)) => (~wise(sK10) | brave(sK10)) [choice axiom]
77. ~wise(sK10) | brave(sK10) [skolemisation 24,76]
84. ~happy(alice) | ~brave(X0) | ~curious(X0) [cnf transformation 36]
109. wise(X0) | wise(X0) | wise(X0) [cnf transformation 52]
111. curious(X0) | curious(X0) [cnf transformation 54]
141. humble(X0) | happy(X0) [cnf transformation 67]
152. ~wise(sK10) | brave(sK10) [cnf transformation 77]
153. ~humble(alice) [cnf transformation 25]
155. curious(X0) [duplicate literal removal 111]
159. wise(X0) [duplicate literal removal 109]
166. 2 <=> happy(alice) [avatar definition]
171. 3 <=> ! [X0] : (~brave(X0) | ~curious(X0)) [avatar definition]
172. ~brave(X0) | ~curious(X0) <- (3) [avatar component clause 171]
173. 3 | ~2 [avatar split clause 84,166,171]
193. 8 <=> ! [X1] : curious(X1) [avatar definition]
194. curious(X1) <- (8) [avatar component clause 193]
239. 8 [avatar split clause 155,193]
304. brave(sK10) [subsumption resolution 152,159]
314. happy(alice) [resolution 141,153]
317. 2 [avatar split clause 314,166]
318. ~brave(X0) <- (3, 8) [subsumption resolution 172,194]
320. $false <- (3, 8) [resolution 318,304]
321. ~3 | ~8 [avatar contradiction clause 320]
323. $false [avatar sat refutation 173,239,317,321]
% SZS output end Proof for 4921850262170633991794989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either old or not tall then someone is both patient and not happy.
If someone is not wise or not quiet then john is both calm and creative and vice versa.
Everyone who is both not humble and happy is both not happy and brave.
If mary is not brave then someone is either not happy or strong and vice versa.
Everyone who is brave or not brave is strong and vice versa.
Everyone who is either wise or strong is either rich or humble and vice versa.
Everyone who is both not kind and not old is not patient and vice versa.
If fred is not strong or calm then john is not curious or rich and vice versa.
If susan is either strong or old then john is patient and vice versa.
Everyone who is both generous and not calm is funny or tall.
Everyone who is both calm and strong is not patient and vice versa.
If someone is tall then fred is generous or brave.
Everyone who is either not wise or not brave is either not wise or not generous and vice versa.
If someone is quiet then someone is not strong or generous.
If someone is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
Someone is creative.
Someone is brave or not creative.
Someone is both calm and not kind.
Fred is either patient or not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm. | John is not creative. | neutral | (((old(alice)<~>~tall(alice)))=>(?[X]:((patient(X)&~happy(X)))))&
((?[X]:((~wise(X)|~quiet(X))))<=>((calm(john)&creative(john))))&
(![X]:((~humble(X)&happy(X))=>(~happy(X)&brave(X))))&
((~brave(mary))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((brave(X)|~brave(X))<=>strong(X)))&
(![X]:((wise(X)<~>strong(X))<=>(rich(X)<~>humble(X))))&
(![X]:((~kind(X)&~old(X))<=>~patient(X)))&
(((~strong(fred)|calm(fred)))<=>((~curious(john)|rich(john))))&
(((strong(susan)<~>old(susan)))<=>(patient(john)))&
(![X]:((generous(X)&~calm(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&strong(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>((generous(fred)|brave(fred))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(?[X]:(creative(X)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:((calm(X)&~kind(X))))&
((patient(fred)<~>~creative(fred)))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is either humble or calm is not brave and vice versa. If someone is not tall then mary is either calm or not rich and vice versa. Everyone who is generous or not kind is happy or not tall. Everyone who is funny or not generous is both not happy and patient. Everyone who is either kind or not funny is either not calm or strong and vice versa. If someone is both creative and kind then someone is either not wise or not creative. Everyone who is not rich or not old is both old and quiet and vice versa. Everyone who is both not rich and not generous is both not tall and curious and vice versa. If john is either not strong or not generous then someone is rich or happy. Everyone who is both patient and not curious is not strong and vice versa. Everyone who is kind or not curious is calm or funny and vice versa. Everyone who is humble is both not brave and old. If someone is both not tall and not rich then someone is both not wise and not old. If susan is either not happy or kind then susan is generous and vice versa. Everyone who is both wise and humble is either generous or brave and vice versa. Everyone who is either not generous or brave is old. Someone is either not humble or not strong. Fred is both not curious and funny. John is old. Someone is not strong or not curious. Someone is either generous or wise. Lucy is both not happy and not tall. | Fred is not old. | contradiction | (![X]:((humble(X)<~>calm(X))<=>~brave(X)))&
((?[X]:(~tall(X)))<=>((calm(mary)<~>~rich(mary))))&
(![X]:((generous(X)|~kind(X))=>(happy(X)|~tall(X))))&
(![X]:((funny(X)|~generous(X))=>(~happy(X)&patient(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~calm(X)<~>strong(X))))&
((?[X]:((creative(X)&kind(X))))=>(?[X]:((~wise(X)<~>~creative(X)))))&
(![X]:((~rich(X)|~old(X))<=>(old(X)&quiet(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~tall(X)&curious(X))))&
(((~strong(john)<~>~generous(john)))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((patient(X)&~curious(X))<=>~strong(X)))&
(![X]:((kind(X)|~curious(X))<=>(calm(X)|funny(X))))&
(![X]:(humble(X)=>(~brave(X)&old(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((~wise(X)&~old(X)))))&
(((~happy(susan)<~>kind(susan)))<=>(generous(susan)))&
(![X]:((wise(X)&humble(X))<=>(generous(X)<~>brave(X))))&
(![X]:((~generous(X)<~>brave(X))=>old(X)))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~curious(fred)&funny(fred)))&
(old(john))&
(?[X]:((~strong(X)|~curious(X))))&
(?[X]:((generous(X)<~>wise(X))))&
((~happy(lucy)&~tall(lucy))) | ~old(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8542081467077425575461885
% SZS output start Proof for 8542081467077425575461885
7. ! [X0] : ((~old(X0) | ~rich(X0)) <=> (quiet(X0) & old(X0))) [input p6]
23. ~old(fred) [input hypothesis]
44. ! [X0] : (((~old(X0) | ~rich(X0)) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | (old(X0) & rich(X0)))) [nnf transformation 7]
45. ! [X0] : ((~old(X0) | ~rich(X0) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | (old(X0) & rich(X0)))) [flattening 44]
95. old(X0) | old(X0) [cnf transformation 45]
138. ~old(fred) [cnf transformation 23]
139. old(X0) [duplicate literal removal 95]
232. $false [subsumption resolution 138,139]
% SZS output end Proof for 8542081467077425575461885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not patient then someone is either not creative or quiet and vice versa. If john is both not generous and wise then fred is either not creative or not generous and vice versa. Everyone who is not strong or not brave is either not quiet or happy and vice versa. Everyone who is both patient and not old is either rich or humble and vice versa. Everyone who is patient or happy is strong or not curious and vice versa. If someone is either kind or wise then someone is curious and vice versa. Everyone who is either not humble or not creative is both not happy and kind and vice versa. Everyone who is not kind or tall is not old or rich and vice versa. Everyone who is both not calm and not quiet is both not humble and not kind and vice versa. Everyone who is both not brave and tall is not quiet or wise and vice versa. If someone is either not quiet or not humble then alice is either wise or patient and vice versa. Everyone who is either not curious or not happy is both funny and patient. If someone is both not curious and creative then mary is either rich or old. If someone is both not wise and old then someone is tall or quiet and vice versa. Everyone who is not patient is tall or humble. Everyone who is both not old and quiet is not old. Someone is not calm. Someone is not happy. Alice is not funny. Someone is tall. Lucy is either old or not tall. Lucy is either not humble or not tall. Someone is not brave or not wise. | Mary is not curious. | neutral | ((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((~generous(john)&wise(john)))<=>((~creative(fred)<~>~generous(fred))))&
(![X]:((~strong(X)|~brave(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((patient(X)&~old(X))<=>(rich(X)<~>humble(X))))&
(![X]:((patient(X)|happy(X))<=>(strong(X)|~curious(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((~humble(X)<~>~creative(X))<=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|tall(X))<=>(~old(X)|rich(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)&tall(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>((wise(alice)<~>patient(alice))))&
(![X]:((~curious(X)<~>~happy(X))=>(funny(X)&patient(X))))&
((?[X]:((~curious(X)&creative(X))))=>((rich(mary)<~>old(mary))))&
((?[X]:((~wise(X)&old(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:(~patient(X)=>(tall(X)|humble(X))))&
(![X]:((~old(X)&quiet(X))=>~old(X)))&
(?[X]:(~calm(X)))&
(?[X]:(~happy(X)))&
(~funny(alice))&
(?[X]:(tall(X)))&
((old(lucy)<~>~tall(lucy)))&
((~humble(lucy)<~>~tall(lucy)))&
(?[X]:((~brave(X)|~wise(X)))) | ~curious(mary) | [] | null | 0 |
If someone is both rich and happy then someone is not brave and vice versa. If someone is either creative or brave then lucy is both not quiet and tall and vice versa. If someone is calm or not tall then john is both brave and tall and vice versa. Everyone who is rich or not old is both not curious and not wise and vice versa. Everyone who is both not kind and not strong is either kind or not funny. Everyone who is not happy is brave. Everyone who is happy is not humble and vice versa. Everyone who is both not wise and generous is not calm. Everyone who is brave or rich is not patient or happy and vice versa. If someone is kind then paul is both not funny and not strong and vice versa. If lucy is calm or kind then someone is old or creative. Everyone who is strong or kind is not kind or not generous and vice versa. Everyone who is not wise is either not curious or not creative. Everyone who is both not curious and wise is not wise or not funny and vice versa. If someone is quiet or not kind then lucy is not generous or not wise and vice versa. Everyone who is either not strong or not patient is either not wise or not humble. Someone is either strong or calm. Mary is humble. Someone is both curious and not rich. Someone is both happy and curious. John is happy. Someone is not humble. Mary is creative or funny. | Paul is happy. | neutral | ((?[X]:((rich(X)&happy(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~quiet(lucy)&tall(lucy))))&
((?[X]:((calm(X)|~tall(X))))<=>((brave(john)&tall(john))))&
(![X]:((rich(X)|~old(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~kind(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((~wise(X)&generous(X))=>~calm(X)))&
(![X]:((brave(X)|rich(X))<=>(~patient(X)|happy(X))))&
((?[X]:(kind(X)))<=>((~funny(paul)&~strong(paul))))&
(((calm(lucy)|kind(lucy)))=>(?[X]:((old(X)|creative(X)))))&
(![X]:((strong(X)|kind(X))<=>(~kind(X)|~generous(X))))&
(![X]:(~wise(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((~curious(X)&wise(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~generous(lucy)|~wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))=>(~wise(X)<~>~humble(X))))&
(?[X]:((strong(X)<~>calm(X))))&
(humble(mary))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((happy(X)&curious(X))))&
(happy(john))&
(?[X]:(~humble(X)))&
((creative(mary)|funny(mary))) | happy(paul) | [] | null | 0 |
If someone is both kind and old then mary is either tall or happy.
If lucy is both calm and not calm then mary is both tall and not rich and vice versa.
Everyone who is not quiet or creative is either not tall or not patient.
If someone is both not creative and brave then fred is strong.
Everyone who is not quiet is both patient and humble.
If susan is both patient and humble then someone is not calm and vice versa.
Everyone who is not strong or not quiet is tall and vice versa.
Everyone who is both not funny and brave is either quiet or not creative and vice versa.
If mary is either kind or not strong then someone is creative or brave and vice versa.
Everyone who is quiet or not curious is either creative or not curious.
Everyone who is not calm is either not tall or generous and vice versa.
Everyone who is both old and not rich is not strong or not happy.
If lucy is both not kind and not patient then john is both not quiet and not kind.
If fred is not wise then paul is not strong.
If john is humble or not old then someone is creative.
Everyone who is both not patient and not calm is calm or not calm.
Someone is not kind.
Someone is wise or not quiet.
Someone is not wise.
Paul is wise.
John is both not humble and not curious.
Susan is patient. | Fred is quiet. | entailment | ((?[X]:((kind(X)&old(X))))=>((tall(mary)<~>happy(mary))))&
(((calm(lucy)&~calm(lucy)))<=>((tall(mary)&~rich(mary))))&
(![X]:((~quiet(X)|creative(X))=>(~tall(X)<~>~patient(X))))&
((?[X]:((~creative(X)&brave(X))))=>(strong(fred)))&
(![X]:(~quiet(X)=>(patient(X)&humble(X))))&
(((patient(susan)&humble(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)|~quiet(X))<=>tall(X)))&
(![X]:((~funny(X)&brave(X))<=>(quiet(X)<~>~creative(X))))&
(((kind(mary)<~>~strong(mary)))<=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((quiet(X)|~curious(X))=>(creative(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(~tall(X)<~>generous(X))))&
(![X]:((old(X)&~rich(X))=>(~strong(X)|~happy(X))))&
(((~kind(lucy)&~patient(lucy)))=>((~quiet(john)&~kind(john))))&
((~wise(fred))=>(~strong(paul)))&
(((humble(john)|~old(john)))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:(~wise(X)))&
(wise(paul))&
((~humble(john)&~curious(john)))&
(patient(susan)) | quiet(fred) | [
"p2",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8128785853281369304990310
% SZS output start Proof for 8128785853281369304990310
3. ! [X0] : ((creative(X0) | ~quiet(X0)) => (~tall(X0) <~> ~patient(X0))) [input p2]
5. ! [X0] : (~quiet(X0) => (humble(X0) & patient(X0))) [input p4]
7. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> tall(X0)) [input p6]
23. ~quiet(fred) [input hypothesis]
25. ! [X0] : ((~tall(X0) <~> ~patient(X0)) | (~creative(X0) & quiet(X0))) [ennf transformation 3]
27. ! [X0] : ((humble(X0) & patient(X0)) | quiet(X0)) [ennf transformation 5]
40. ! [X0] : (((patient(X0) | tall(X0)) & (~patient(X0) | ~tall(X0))) | (~creative(X0) & quiet(X0))) [nnf transformation 25]
46. ! [X0] : (((~quiet(X0) | ~strong(X0)) | ~tall(X0)) & (tall(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 7]
47. ! [X0] : ((~quiet(X0) | ~strong(X0) | ~tall(X0)) & (tall(X0) | (quiet(X0) & strong(X0)))) [flattening 46]
70. ~patient(X0) | ~tall(X0) | quiet(X0) [cnf transformation 40]
75. patient(X0) | quiet(X0) [cnf transformation 27]
81. quiet(X0) | tall(X0) [cnf transformation 47]
117. ~quiet(fred) [cnf transformation 23]
259. ~tall(X0) | quiet(X0) | quiet(X0) [resolution 70,75]
260. ~tall(X0) | quiet(X0) [duplicate literal removal 259]
261. quiet(X0) [subsumption resolution 260,81]
264. $false [resolution 261,117]
% SZS output end Proof for 8128785853281369304990310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or kind is both not patient and not creative.
Everyone who is not rich or quiet is calm or tall.
Everyone who is both happy and not old is both wise and funny and vice versa.
If someone is either not quiet or kind then someone is either not calm or brave.
Everyone who is both not funny and strong is either tall or quiet and vice versa.
If john is creative then someone is both kind and strong.
Everyone who is not tall or not wise is either tall or curious and vice versa.
If someone is both not humble and happy then someone is strong.
If someone is either not curious or kind then john is both not rich and not happy.
If someone is not generous or not patient then someone is either not humble or not funny.
Everyone who is generous or not curious is not calm.
If someone is both funny and not calm then someone is either patient or not happy.
Everyone who is both not kind and wise is brave or wise and vice versa.
If someone is rich then someone is both not kind and not happy and vice versa.
Everyone who is curious is happy.
Everyone who is calm is either brave or calm and vice versa.
Someone is both not creative and not happy.
Someone is both not brave and not kind.
Someone is both strong and funny.
Fred is either creative or not strong.
Lucy is not curious.
Mary is old.
Paul is both not curious and not patient.
Lucy is both not wise and not brave. | John is not brave. | entailment | (![X]:((~quiet(X)|kind(X))=>(~patient(X)&~creative(X))))&
(![X]:((~rich(X)|quiet(X))=>(calm(X)|tall(X))))&
(![X]:((happy(X)&~old(X))<=>(wise(X)&funny(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((~funny(X)&strong(X))<=>(tall(X)<~>quiet(X))))&
((creative(john))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~tall(X)|~wise(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~humble(X)&happy(X))))=>(?[X]:(strong(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>((~rich(john)&~happy(john))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:((~humble(X)<~>~funny(X)))))&
(![X]:((generous(X)|~curious(X))=>~calm(X)))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:((~kind(X)&wise(X))<=>(brave(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(curious(X)=>happy(X)))&
(![X]:(calm(X)<=>(brave(X)<~>calm(X))))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((strong(X)&funny(X))))&
((creative(fred)<~>~strong(fred)))&
(~curious(lucy))&
(old(mary))&
((~curious(paul)&~patient(paul)))&
((~wise(lucy)&~brave(lucy))) | ~brave(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 536213790167653196525680
% SZS output start Proof for 536213790167653196525680
16. ! [X0] : (calm(X0) <=> (brave(X0) <~> calm(X0))) [input p15]
25. brave(john) [input hypothesis]
73. ! [X0] : ((calm(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ~calm(X0))) [nnf transformation 16]
132. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 73]
133. calm(X0) | calm(X0) | ~brave(X0) [cnf transformation 73]
149. brave(john) [cnf transformation 25]
150. ~calm(X0) | ~brave(X0) [duplicate literal removal 132]
151. calm(X0) | ~brave(X0) [duplicate literal removal 133]
264. ~brave(X0) [subsumption resolution 150,151]
275. $false [subsumption resolution 149,264]
% SZS output end Proof for 536213790167653196525680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or not creative is curious or funny. Everyone who is both happy and calm is both not brave and not tall. Everyone who is strong is both calm and generous. Everyone who is both calm and tall is not generous. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Everyone who is both happy and funny is not brave and vice versa. Everyone who is both wise and not wise is both not brave and not calm and vice versa. If paul is either wise or curious then someone is not humble or not kind. If someone is either not happy or not humble then someone is either not humble or not curious and vice versa. Everyone who is not curious or not tall is kind and vice versa. If lucy is both not happy and funny then alice is not kind and vice versa. Everyone who is not strong is calm. Everyone who is both rich and strong is either kind or not quiet. Everyone who is either kind or happy is not wise. Alice is not happy. Someone is not kind. Someone is either not calm or strong. Someone is not creative. Someone is old or humble. Lucy is either curious or not funny. Someone is both strong and patient. | Paul is not calm. | contradiction | (![X]:((~patient(X)|~creative(X))=>(curious(X)|funny(X))))&
(![X]:((happy(X)&calm(X))=>(~brave(X)&~tall(X))))&
(![X]:(strong(X)=>(calm(X)&generous(X))))&
(![X]:((calm(X)&tall(X))=>~generous(X)))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(~happy(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)|humble(X))))&
((curious(lucy)<~>~funny(lucy)))&
(?[X]:((strong(X)&patient(X)))) | ~calm(paul) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5204337558754911910270664
% SZS output start Proof for 5204337558754911910270664
3. ! [X0] : (strong(X0) => (generous(X0) & calm(X0))) [input p2]
13. ! [X0] : (~strong(X0) => calm(X0)) [input p12]
23. ~calm(paul) [input hypothesis]
33. ! [X0] : ((generous(X0) & calm(X0)) | ~strong(X0)) [ennf transformation 3]
38. ! [X0] : (calm(X0) | strong(X0)) [ennf transformation 13]
75. calm(X0) | ~strong(X0) [cnf transformation 33]
107. calm(X0) | strong(X0) [cnf transformation 38]
118. ~calm(paul) [cnf transformation 23]
214. calm(X0) [subsumption resolution 107,75]
222. $false [subsumption resolution 118,214]
% SZS output end Proof for 5204337558754911910270664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and wise is either not wise or not humble.
Everyone who is both not humble and not happy is funny or not calm.
Everyone who is not rich is either patient or humble and vice versa.
Everyone who is old is quiet and vice versa.
Everyone who is either not creative or calm is both tall and not wise and vice versa.
Everyone who is kind or old is not wise or calm and vice versa.
Everyone who is both not humble and strong is not creative or not generous.
Everyone who is rich or kind is rich or patient.
Everyone who is not humble is humble or calm.
Everyone who is not funny or strong is either patient or quiet and vice versa.
If alice is curious or humble then mary is wise or quiet and vice versa.
Everyone who is both tall and not brave is not creative or happy.
If someone is not calm or not quiet then fred is both not curious and curious and vice versa.
Everyone who is not patient is wise and vice versa.
If lucy is patient then someone is strong or not kind and vice versa.
Everyone who is either not creative or calm is either not rich or not creative and vice versa.
John is quiet or calm.
Someone is rich or kind.
John is both generous and not curious.
Someone is either not brave or happy.
Susan is humble or brave. | Susan is not creative. | neutral | (![X]:((~rich(X)&wise(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((~humble(X)&~happy(X))=>(funny(X)|~calm(X))))&
(![X]:(~rich(X)<=>(patient(X)<~>humble(X))))&
(![X]:(old(X)<=>quiet(X)))&
(![X]:((~creative(X)<~>calm(X))<=>(tall(X)&~wise(X))))&
(![X]:((kind(X)|old(X))<=>(~wise(X)|calm(X))))&
(![X]:((~humble(X)&strong(X))=>(~creative(X)|~generous(X))))&
(![X]:((rich(X)|kind(X))=>(rich(X)|patient(X))))&
(![X]:(~humble(X)=>(humble(X)|calm(X))))&
(![X]:((~funny(X)|strong(X))<=>(patient(X)<~>quiet(X))))&
(((curious(alice)|humble(alice)))<=>((wise(mary)|quiet(mary))))&
(![X]:((tall(X)&~brave(X))=>(~creative(X)|happy(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~curious(fred)&curious(fred))))&
(![X]:(~patient(X)<=>wise(X)))&
((patient(lucy))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(~rich(X)<~>~creative(X))))&
((quiet(john)|calm(john)))&
(?[X]:((rich(X)|kind(X))))&
((generous(john)&~curious(john)))&
(?[X]:((~brave(X)<~>happy(X))))&
((humble(susan)|brave(susan))) | ~creative(susan) | [] | null | 0 |
Everyone who is not kind is happy or not rich.
If someone is tall or not creative then paul is not tall or brave and vice versa.
If alice is either not patient or curious then someone is either calm or rich and vice versa.
Everyone who is either not patient or creative is either not old or wise.
Everyone who is either not kind or brave is brave and vice versa.
Everyone who is either calm or not old is not funny.
If fred is both patient and tall then john is old or calm and vice versa.
Everyone who is rich is wise or old and vice versa.
Everyone who is both humble and not generous is not patient and vice versa.
If someone is creative or generous then lucy is not humble or funny.
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.
Someone is either not quiet or not happy.
Fred is kind or not funny.
Someone is either not curious or generous.
Paul is humble or creative.
Someone is generous or creative.
Paul is both not old and humble.
Susan is either not generous or not tall.
Someone is either not generous or not tall. | Susan is not brave. | contradiction | (![X]:(~kind(X)=>(happy(X)|~rich(X))))&
((?[X]:((tall(X)|~creative(X))))<=>((~tall(paul)|brave(paul))))&
(((~patient(alice)<~>curious(alice)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~old(X)<~>wise(X))))&
(![X]:((~kind(X)<~>brave(X))<=>brave(X)))&
(![X]:((calm(X)<~>~old(X))=>~funny(X)))&
(((patient(fred)&tall(fred)))<=>((old(john)|calm(john))))&
(![X]:(rich(X)<=>(wise(X)|old(X))))&
(![X]:((humble(X)&~generous(X))<=>~patient(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)<~>~happy(X))))&
((kind(fred)|~funny(fred)))&
(?[X]:((~curious(X)<~>generous(X))))&
((humble(paul)|creative(paul)))&
(?[X]:((generous(X)|creative(X))))&
((~old(paul)&humble(paul)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:((~generous(X)<~>~tall(X)))) | ~brave(susan) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 819798509066684979114558
% SZS output start Proof for 819798509066684979114558
9. ! [X0] : ((~generous(X0) & humble(X0)) <=> ~patient(X0)) [input p8]
11. ! [X0] : ((~brave(X0) | ~humble(X0)) <=> (generous(X0) & ~patient(X0))) [input p10]
25. ~brave(susan) [input hypothesis]
51. ! [X0] : (((~generous(X0) & humble(X0)) | patient(X0)) & (~patient(X0) | (generous(X0) | ~humble(X0)))) [nnf transformation 9]
52. ! [X0] : (((~generous(X0) & humble(X0)) | patient(X0)) & (~patient(X0) | generous(X0) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((~brave(X0) | ~humble(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [nnf transformation 11]
54. ! [X0] : ((~brave(X0) | ~humble(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (brave(X0) & humble(X0)))) [flattening 53]
116. ~generous(X0) | patient(X0) [cnf transformation 52]
120. ~patient(X0) | brave(X0) [cnf transformation 54]
122. generous(X0) | brave(X0) [cnf transformation 54]
156. ~brave(susan) [cnf transformation 25]
259. 22 <=> ! [X0] : brave(X0) [avatar definition]
260. brave(X0) <- (22) [avatar component clause 259]
396. brave(X0) | patient(X0) [resolution 122,116]
400. brave(X0) [subsumption resolution 396,120]
401. 22 [avatar split clause 400,259]
403. $false <- (22) [resolution 260,156]
406. ~22 [avatar contradiction clause 403]
407. $false [avatar sat refutation 401,406]
% SZS output end Proof for 819798509066684979114558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then susan is not creative or curious.
If someone is not quiet then fred is either not wise or not generous and vice versa.
If someone is both not brave and brave then someone is calm.
If alice is humble or curious then john is either not kind or not calm and vice versa.
Everyone who is happy is humble.
If someone is not creative then susan is tall.
If susan is not kind then john is not humble or rich.
If someone is not kind or not curious then paul is either funny or strong and vice versa.
Everyone who is brave is either not tall or creative and vice versa.
Everyone who is not old or not rich is not brave.
Everyone who is patient or not old is both calm and creative and vice versa.
Everyone who is kind or funny is either not wise or happy and vice versa.
Everyone who is calm is either not funny or not generous and vice versa.
Everyone who is funny or rich is either strong or not kind.
Everyone who is not funny or funny is not curious and vice versa.
Everyone who is either wise or humble is tall or happy and vice versa.
Paul is either not wise or not brave.
Mary is not funny.
Someone is either old or happy.
Lucy is either not humble or wise.
Fred is both generous and patient.
Fred is happy.
Someone is not funny. | Fred is not generous. | contradiction | ((?[X]:(generous(X)))=>((~creative(susan)|curious(susan))))&
((?[X]:(~quiet(X)))<=>((~wise(fred)<~>~generous(fred))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(calm(X))))&
(((humble(alice)|curious(alice)))<=>((~kind(john)<~>~calm(john))))&
(![X]:(happy(X)=>humble(X)))&
((?[X]:(~creative(X)))=>(tall(susan)))&
((~kind(susan))=>((~humble(john)|rich(john))))&
((?[X]:((~kind(X)|~curious(X))))<=>((funny(paul)<~>strong(paul))))&
(![X]:(brave(X)<=>(~tall(X)<~>creative(X))))&
(![X]:((~old(X)|~rich(X))=>~brave(X)))&
(![X]:((patient(X)|~old(X))<=>(calm(X)&creative(X))))&
(![X]:((kind(X)|funny(X))<=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~funny(X)<~>~generous(X))))&
(![X]:((funny(X)|rich(X))=>(strong(X)<~>~kind(X))))&
(![X]:((~funny(X)|funny(X))<=>~curious(X)))&
(![X]:((wise(X)<~>humble(X))<=>(tall(X)|happy(X))))&
((~wise(paul)<~>~brave(paul)))&
(~funny(mary))&
(?[X]:((old(X)<~>happy(X))))&
((~humble(lucy)<~>wise(lucy)))&
((generous(fred)&patient(fred)))&
(happy(fred))&
(?[X]:(~funny(X))) | ~generous(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4189794348411836809536080
% SZS output start Proof for 4189794348411836809536080
21. patient(fred) & generous(fred) [input p20]
24. ~generous(fred) [input hypothesis]
128. generous(fred) [cnf transformation 21]
132. ~generous(fred) [cnf transformation 24]
146. 4 <=> generous(fred) [avatar definition]
268. 4 [avatar split clause 128,146]
269. ~4 [avatar split clause 132,146]
270. $false [avatar sat refutation 268,269]
% SZS output end Proof for 4189794348411836809536080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or patient is both not wise and happy and vice versa.
If mary is both creative and not patient then someone is either creative or not patient and vice versa.
If mary is not calm then susan is kind and vice versa.
Everyone who is not kind or not calm is both brave and not old.
If someone is either brave or strong then someone is brave.
If susan is either rich or old then someone is both happy and patient.
If someone is both not calm and tall then someone is not patient.
If someone is both calm and tall then someone is both not curious and humble.
Everyone who is not generous or humble is either humble or not wise and vice versa.
If john is not brave then someone is not old.
Everyone who is both strong and kind is not strong and vice versa.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
If someone is both not happy and strong then someone is generous or not patient.
Everyone who is not patient is both wise and not patient.
Someone is either quiet or wise.
Lucy is both not funny and not wise.
Someone is either not brave or not tall.
Someone is quiet. | John is tall. | contradiction | (![X]:((~patient(X)<~>patient(X))<=>(~wise(X)&happy(X))))&
(((creative(mary)&~patient(mary)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((~calm(mary))<=>(kind(susan)))&
(![X]:((~kind(X)|~calm(X))=>(brave(X)&~old(X))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:(brave(X))))&
(((rich(susan)<~>old(susan)))=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:((~calm(X)&tall(X))))=>(?[X]:(~patient(X))))&
((?[X]:((calm(X)&tall(X))))=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((~generous(X)|humble(X))<=>(humble(X)<~>~wise(X))))&
((~brave(john))=>(?[X]:(~old(X))))&
(![X]:((strong(X)&kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((?[X]:((~happy(X)&strong(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:(~patient(X)=>(wise(X)&~patient(X))))&
(?[X]:((quiet(X)<~>wise(X))))&
((~funny(lucy)&~wise(lucy)))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:(quiet(X))) | tall(john) | [
"p0",
"p6",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2779870269868551392371210
% SZS output start Proof for 2779870269868551392371210
1. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> (happy(X0) & ~wise(X0))) [input p0]
7. ? [X0] : (tall(X0) & ~calm(X0)) => ? [X0] : ~patient(X0) [input p6]
8. ? [X0] : (tall(X0) & calm(X0)) => ? [X0] : (humble(X0) & ~curious(X0)) [input p7]
11. ! [X0] : ((kind(X0) & strong(X0)) <=> ~strong(X0)) [input p10]
12. ! [X0] : ((~kind(X0) | generous(X0)) => curious(X0)) [input p11]
13. ? [X0] : (~patient(X0) <~> kind(X0)) => ? [X0] : (~happy(X0) | wise(X0)) [input p12]
20. tall(john) [input hypothesis]
22. ? [X0] : (tall(X0) & ~calm(X0)) => ? [X1] : ~patient(X1) [rectify 7]
23. ? [X0] : (tall(X0) & calm(X0)) => ? [X1] : (humble(X1) & ~curious(X1)) [rectify 8]
24. ? [X0] : (~patient(X0) <~> kind(X0)) => ? [X1] : (~happy(X1) | wise(X1)) [rectify 13]
30. ? [X1] : ~patient(X1) | ! [X0] : (~tall(X0) | calm(X0)) [ennf transformation 22]
31. ? [X1] : (humble(X1) & ~curious(X1)) | ! [X0] : (~tall(X0) | ~calm(X0)) [ennf transformation 23]
33. ! [X0] : (curious(X0) | (kind(X0) & ~generous(X0))) [ennf transformation 12]
34. ? [X1] : (~happy(X1) | wise(X1)) | ! [X0] : (~patient(X0) <=> kind(X0)) [ennf transformation 24]
37. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (~happy(X0) | wise(X0))) & ((happy(X0) & ~wise(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ~happy(X0) | wise(X0)) & ((happy(X0) & ~wise(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [flattening 37]
52. ? [X0] : ~patient(X0) | ! [X1] : (~tall(X1) | calm(X1)) [rectify 30]
53. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
54. ~patient(sK3) | ! [X1] : (~tall(X1) | calm(X1)) [skolemisation 52,53]
55. ? [X0] : (humble(X0) & ~curious(X0)) | ! [X1] : (~tall(X1) | ~calm(X1)) [rectify 31]
56. ? [X0] : (humble(X0) & ~curious(X0)) => (humble(sK4) & ~curious(sK4)) [choice axiom]
57. (humble(sK4) & ~curious(sK4)) | ! [X1] : (~tall(X1) | ~calm(X1)) [skolemisation 55,56]
62. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | ~strong(X0)))) [nnf transformation 11]
63. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | ~strong(X0))) [flattening 62]
64. ? [X1] : (~happy(X1) | wise(X1)) | ! [X0] : ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))) [nnf transformation 34]
65. ? [X0] : (~happy(X0) | wise(X0)) | ! [X1] : ((~patient(X1) | ~kind(X1)) & (kind(X1) | patient(X1))) [rectify 64]
66. ? [X0] : (~happy(X0) | wise(X0)) => (~happy(sK6) | wise(sK6)) [choice axiom]
67. (~happy(sK6) | wise(sK6)) | ! [X1] : ((~patient(X1) | ~kind(X1)) & (kind(X1) | patient(X1))) [skolemisation 65,66]
79. ~wise(X0) | patient(X0) | patient(X0) [cnf transformation 38]
80. ~wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 38]
81. happy(X0) | patient(X0) | patient(X0) [cnf transformation 38]
82. happy(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 38]
103. ~patient(sK3) | ~tall(X1) | calm(X1) [cnf transformation 54]
104. ~curious(sK4) | ~tall(X1) | ~calm(X1) [cnf transformation 57]
113. ~strong(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 63]
114. strong(X0) | strong(X0) [cnf transformation 63]
117. curious(X0) | kind(X0) [cnf transformation 33]
118. ~happy(sK6) | wise(sK6) | kind(X1) | patient(X1) [cnf transformation 67]
129. tall(john) [cnf transformation 20]
130. ~strong(X0) | ~kind(X0) [duplicate literal removal 113]
131. strong(X0) [duplicate literal removal 114]
134. ~wise(X0) | patient(X0) [duplicate literal removal 79]
135. ~wise(X0) | ~patient(X0) [duplicate literal removal 80]
136. happy(X0) | patient(X0) [duplicate literal removal 81]
137. happy(X0) | ~patient(X0) [duplicate literal removal 82]
138. happy(X0) [subsumption resolution 136,137]
139. ~wise(X0) [subsumption resolution 134,135]
205. 15 <=> ! [X1] : (~tall(X1) | calm(X1)) [avatar definition]
206. ~tall(X1) | calm(X1) <- (15) [avatar component clause 205]
208. 16 <=> patient(sK3) [avatar definition]
210. ~patient(sK3) <- (~16) [avatar component clause 208]
211. 15 | ~16 [avatar split clause 103,208,205]
213. 17 <=> ! [X1] : (~tall(X1) | ~calm(X1)) [avatar definition]
214. ~tall(X1) | ~calm(X1) <- (17) [avatar component clause 213]
221. 19 <=> curious(sK4) [avatar definition]
223. ~curious(sK4) <- (~19) [avatar component clause 221]
224. 17 | ~19 [avatar split clause 104,221,213]
236. ~kind(X0) [subsumption resolution 130,131]
237. curious(X0) [subsumption resolution 117,236]
238. wise(sK6) | kind(X1) | patient(X1) [subsumption resolution 118,138]
239. kind(X1) | patient(X1) [subsumption resolution 238,139]
240. patient(X1) [subsumption resolution 239,236]
252. $false <- (~16) [subsumption resolution 210,240]
253. 16 [avatar contradiction clause 252]
260. ~tall(X1) <- (15, 17) [subsumption resolution 206,214]
262. $false <- (15, 17) [resolution 260,129]
263. ~15 | ~17 [avatar contradiction clause 262]
264. $false <- (~19) [subsumption resolution 223,237]
265. 19 [avatar contradiction clause 264]
268. $false [avatar sat refutation 211,224,253,263,265]
% SZS output end Proof for 2779870269868551392371210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either not tall or old and vice versa. If someone is either curious or not creative then someone is not funny. Everyone who is not quiet is not curious or not funny. Everyone who is both creative and humble is either not kind or not tall. If someone is not curious or creative then susan is both not creative and not quiet and vice versa. If fred is both not strong and patient then alice is not calm or not strong. If lucy is humble or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. Paul is creative. | Paul is not old. | contradiction | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:(~funny(X))))&
(![X]:(~quiet(X)=>(~curious(X)|~funny(X))))&
(![X]:((creative(X)&humble(X))=>(~kind(X)<~>~tall(X))))&
((?[X]:((~curious(X)|creative(X))))<=>((~creative(susan)&~quiet(susan))))&
(((~strong(fred)&patient(fred)))=>((~calm(alice)|~strong(alice))))&
(((humble(lucy)|~old(lucy)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul)) | ~old(paul) | [
"p8",
"p14",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 595538603366149082569973
% SZS output start Proof for 595538603366149082569973
9. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~strong(X0) & wise(X0))) [input p8]
15. ! [X0] : ((old(X0) <~> funny(X0)) => (creative(X0) <~> wise(X0))) [input p14]
17. funny(paul) [input p16]
23. creative(paul) [input p22]
24. ~old(paul) [input hypothesis]
42. ! [X0] : ((creative(X0) <~> wise(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 15]
59. ! [X0] : (((~wise(X0) | kind(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 9]
60. ! [X0] : ((~wise(X0) | kind(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [flattening 59]
68. ! [X0] : (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 42]
112. wise(X0) | wise(X0) [cnf transformation 60]
130. ~wise(X0) | ~creative(X0) | old(X0) | ~funny(X0) [cnf transformation 68]
134. funny(paul) [cnf transformation 17]
141. creative(paul) [cnf transformation 23]
142. ~old(paul) [cnf transformation 24]
144. wise(X0) [duplicate literal removal 112]
263. ~funny(X0) | old(X0) | ~creative(X0) [subsumption resolution 130,144]
401. old(paul) | ~creative(paul) [resolution 263,134]
402. ~creative(paul) [subsumption resolution 401,142]
403. $false [subsumption resolution 402,141]
% SZS output end Proof for 595538603366149082569973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or kind is either not patient or generous and vice versa.
Everyone who is not humble is curious or creative and vice versa.
If mary is both not wise and generous then susan is not kind.
Everyone who is not wise or kind is not humble and vice versa.
Everyone who is either curious or not generous is not tall.
Everyone who is both wise and not happy is not funny.
Everyone who is both patient and not funny is either not funny or strong.
If john is both patient and not patient then someone is wise and vice versa.
Everyone who is brave is not quiet or not patient.
Everyone who is strong or creative is both not old and happy.
Everyone who is both brave and not wise is either brave or funny and vice versa.
Everyone who is both quiet and not generous is generous or calm.
Everyone who is both humble and old is both rich and brave and vice versa.
If someone is not kind or not patient then lucy is either not rich or curious.
If alice is not funny or generous then lucy is both not creative and generous and vice versa.
Someone is either kind or humble.
Someone is not wise.
Someone is not generous.
Paul is either patient or funny.
Alice is not kind.
Someone is not happy or humble.
Someone is not funny. | Paul is not patient. | contradiction | (![X]:((patient(X)|kind(X))<=>(~patient(X)<~>generous(X))))&
(![X]:(~humble(X)<=>(curious(X)|creative(X))))&
(((~wise(mary)&generous(mary)))=>(~kind(susan)))&
(![X]:((~wise(X)|kind(X))<=>~humble(X)))&
(![X]:((curious(X)<~>~generous(X))=>~tall(X)))&
(![X]:((wise(X)&~happy(X))=>~funny(X)))&
(![X]:((patient(X)&~funny(X))=>(~funny(X)<~>strong(X))))&
(((patient(john)&~patient(john)))<=>(?[X]:(wise(X))))&
(![X]:(brave(X)=>(~quiet(X)|~patient(X))))&
(![X]:((strong(X)|creative(X))=>(~old(X)&happy(X))))&
(![X]:((brave(X)&~wise(X))<=>(brave(X)<~>funny(X))))&
(![X]:((quiet(X)&~generous(X))=>(generous(X)|calm(X))))&
(![X]:((humble(X)&old(X))<=>(rich(X)&brave(X))))&
((?[X]:((~kind(X)|~patient(X))))=>((~rich(lucy)<~>curious(lucy))))&
(((~funny(alice)|generous(alice)))<=>((~creative(lucy)&generous(lucy))))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~generous(X)))&
((patient(paul)<~>funny(paul)))&
(~kind(alice))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:(~funny(X))) | ~patient(paul) | [
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7871840636220417520632119
% SZS output start Proof for 7871840636220417520632119
8. (~patient(john) & patient(john)) <=> ? [X0] : wise(X0) [input p7]
11. ! [X0] : ((~wise(X0) & brave(X0)) <=> (brave(X0) <~> funny(X0))) [input p10]
19. patient(paul) <~> funny(paul) [input p18]
23. ~patient(paul) [input hypothesis]
42. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (patient(john) | ~patient(john))) [nnf transformation 8]
43. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | patient(john) | ~patient(john)) [flattening 42]
44. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | patient(john) | ~patient(john)) [rectify 43]
45. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
46. ((~patient(john) & patient(john)) | ! [X0] : ~wise(X0)) & (wise(sK0) | patient(john) | ~patient(john)) [skolemisation 44,45]
47. ! [X0] : (((~wise(X0) & brave(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (wise(X0) | ~brave(X0)))) [nnf transformation 11]
48. ! [X0] : (((~wise(X0) & brave(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | wise(X0) | ~brave(X0))) [flattening 47]
61. (~funny(paul) | ~patient(paul)) & (funny(paul) | patient(paul)) [nnf transformation 19]
83. patient(john) | ~wise(X0) [cnf transformation 46]
84. ~patient(john) | ~wise(X0) [cnf transformation 46]
90. ~funny(X0) | ~brave(X0) | wise(X0) | ~brave(X0) [cnf transformation 48]
92. brave(X0) | brave(X0) | ~funny(X0) [cnf transformation 48]
112. funny(paul) | patient(paul) [cnf transformation 61]
117. ~patient(paul) [cnf transformation 23]
118. ~funny(X0) | ~brave(X0) | wise(X0) [duplicate literal removal 90]
119. ~funny(X0) | brave(X0) [duplicate literal removal 92]
137. 4 <=> ! [X0] : ~wise(X0) [avatar definition]
138. ~wise(X0) <- (4) [avatar component clause 137]
140. 5 <=> patient(john) [avatar definition]
143. 4 | ~5 [avatar split clause 84,140,137]
144. 4 | 5 [avatar split clause 83,140,137]
145. ~funny(X0) | wise(X0) [subsumption resolution 118,119]
195. 16 <=> patient(paul) [avatar definition]
199. 17 <=> funny(paul) [avatar definition]
200. funny(paul) <- (17) [avatar component clause 199]
203. 16 | 17 [avatar split clause 112,199,195]
213. ~16 [avatar split clause 117,195]
215. wise(paul) <- (17) [resolution 145,200]
216. $false <- (4, 17) [subsumption resolution 215,138]
217. ~4 | ~17 [avatar contradiction clause 216]
218. $false [avatar sat refutation 143,144,203,213,217]
% SZS output end Proof for 7871840636220417520632119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both curious and patient then lucy is tall or not wise and vice versa.
Everyone who is either not curious or not creative is both not curious and curious.
Everyone who is both patient and old is both not wise and funny.
If mary is both kind and quiet then paul is not old or not creative.
Everyone who is either curious or not rich is patient.
Everyone who is either not funny or not happy is both old and kind and vice versa.
Everyone who is either not kind or not happy is either kind or funny and vice versa.
If john is both curious and not calm then someone is quiet and vice versa.
Everyone who is both curious and calm is either curious or not funny and vice versa.
Everyone who is either not rich or strong is not humble.
If someone is both wise and not brave then john is both not brave and not humble and vice versa.
If paul is not brave or not humble then someone is not creative or wise.
Everyone who is not curious is either not funny or quiet.
If john is not creative then alice is either not curious or not calm and vice versa.
Everyone who is not wise is wise or not rich.
Someone is either strong or calm.
Susan is either not curious or not quiet.
Paul is both calm and brave.
Susan is not kind.
Mary is both not calm and creative.
Someone is both not calm and not strong.
Someone is either not brave or not kind.
Someone is both not old and not happy. | Mary is curious. | entailment | (((curious(alice)&patient(alice)))<=>((tall(lucy)|~wise(lucy))))&
(![X]:((~curious(X)<~>~creative(X))=>(~curious(X)&curious(X))))&
(![X]:((patient(X)&old(X))=>(~wise(X)&funny(X))))&
(((kind(mary)&quiet(mary)))=>((~old(paul)|~creative(paul))))&
(![X]:((curious(X)<~>~rich(X))=>patient(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(old(X)&kind(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>(kind(X)<~>funny(X))))&
(((curious(john)&~calm(john)))<=>(?[X]:(quiet(X))))&
(![X]:((curious(X)&calm(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~rich(X)<~>strong(X))=>~humble(X)))&
((?[X]:((wise(X)&~brave(X))))<=>((~brave(john)&~humble(john))))&
(((~brave(paul)|~humble(paul)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:(~curious(X)=>(~funny(X)<~>quiet(X))))&
((~creative(john))<=>((~curious(alice)<~>~calm(alice))))&
(![X]:(~wise(X)=>(wise(X)|~rich(X))))&
(?[X]:((strong(X)<~>calm(X))))&
((~curious(susan)<~>~quiet(susan)))&
((calm(paul)&brave(paul)))&
(~kind(susan))&
((~calm(mary)&creative(mary)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((~brave(X)<~>~kind(X))))&
(?[X]:((~old(X)&~happy(X)))) | curious(mary) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4719104573356127006243190
% SZS output start Proof for 4719104573356127006243190
2. ! [X0] : ((~curious(X0) <~> ~creative(X0)) => (curious(X0) & ~curious(X0))) [input p1]
20. creative(mary) & ~calm(mary) [input p19]
24. ~curious(mary) [input hypothesis]
25. ! [X0] : ((curious(X0) & ~curious(X0)) | (~curious(X0) <=> ~creative(X0))) [ennf transformation 2]
38. ! [X0] : ((curious(X0) & ~curious(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) [nnf transformation 25]
78. curious(X0) | ~creative(X0) | curious(X0) [cnf transformation 38]
131. creative(mary) [cnf transformation 20]
138. ~curious(mary) [cnf transformation 24]
147. ~creative(X0) | curious(X0) [duplicate literal removal 78]
292. curious(mary) [resolution 147,131]
293. $false [subsumption resolution 292,138]
% SZS output end Proof for 4719104573356127006243190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not quiet then someone is both tall and not creative and vice versa.
Everyone who is creative or not creative is both not curious and not funny.
Everyone who is happy is wise.
Everyone who is rich or not funny is happy or generous.
Everyone who is not tall is either not old or not calm and vice versa.
If susan is both wise and patient then someone is creative or brave and vice versa.
If susan is either happy or creative then susan is both not curious and old.
Everyone who is both generous and humble is both not brave and old.
If someone is generous or not calm then someone is either not calm or not tall and vice versa.
Everyone who is generous is both generous and wise.
Everyone who is either humble or not generous is either not happy or not curious and vice versa.
Everyone who is either not humble or not strong is generous and vice versa.
If mary is curious then lucy is not calm or not generous and vice versa.
Everyone who is patient or not wise is not quiet or creative.
Everyone who is either rich or not happy is both not old and not happy and vice versa.
If susan is either brave or curious then someone is strong or not calm.
Someone is not humble.
Paul is not calm.
Someone is both not strong and quiet.
John is both calm and quiet.
Someone is both not rich and not happy.
Paul is generous or creative.
Someone is not creative. | Paul is creative. | neutral | ((~quiet(fred))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((creative(X)|~creative(X))=>(~curious(X)&~funny(X))))&
(![X]:(happy(X)=>wise(X)))&
(![X]:((rich(X)|~funny(X))=>(happy(X)|generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>~calm(X))))&
(((wise(susan)&patient(susan)))<=>(?[X]:((creative(X)|brave(X)))))&
(((happy(susan)<~>creative(susan)))=>((~curious(susan)&old(susan))))&
(![X]:((generous(X)&humble(X))=>(~brave(X)&old(X))))&
((?[X]:((generous(X)|~calm(X))))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:(generous(X)=>(generous(X)&wise(X))))&
(![X]:((humble(X)<~>~generous(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>generous(X)))&
((curious(mary))<=>((~calm(lucy)|~generous(lucy))))&
(![X]:((patient(X)|~wise(X))=>(~quiet(X)|creative(X))))&
(![X]:((rich(X)<~>~happy(X))<=>(~old(X)&~happy(X))))&
(((brave(susan)<~>curious(susan)))=>(?[X]:((strong(X)|~calm(X)))))&
(?[X]:(~humble(X)))&
(~calm(paul))&
(?[X]:((~strong(X)&quiet(X))))&
((calm(john)&quiet(john)))&
(?[X]:((~rich(X)&~happy(X))))&
((generous(paul)|creative(paul)))&
(?[X]:(~creative(X))) | creative(paul) | [] | null | 0 |
Everyone who is either not rich or not creative is both humble and not tall and vice versa. Everyone who is tall or not old is both not curious and not strong. Everyone who is both creative and strong is not patient or not creative. If someone is generous then alice is either happy or funny and vice versa. If fred is not calm or funny then mary is both not creative and not kind and vice versa. Everyone who is both kind and not rich is not generous or quiet and vice versa. If someone is either not strong or creative then john is creative or not wise. Everyone who is either tall or not brave is both not tall and not rich. Everyone who is either old or patient is calm or not calm and vice versa. If someone is either wise or not calm then alice is happy and vice versa. Everyone who is wise is both brave and quiet. If someone is humble or patient then alice is either not calm or brave. Everyone who is funny is either curious or not happy. If lucy is both not rich and rich then paul is both not patient and quiet and vice versa. Everyone who is either not calm or calm is either kind or not rich. If mary is rich then someone is either curious or not kind and vice versa. Paul is not funny. Paul is not tall or curious. Someone is both not tall and rich. Alice is not funny or not kind. Someone is kind. Fred is not humble. Susan is funny. Someone is either not quiet or not strong. | Alice is not quiet. | entailment | (![X]:((~rich(X)<~>~creative(X))<=>(humble(X)&~tall(X))))&
(![X]:((tall(X)|~old(X))=>(~curious(X)&~strong(X))))&
(![X]:((creative(X)&strong(X))=>(~patient(X)|~creative(X))))&
((?[X]:(generous(X)))<=>((happy(alice)<~>funny(alice))))&
(((~calm(fred)|funny(fred)))<=>((~creative(mary)&~kind(mary))))&
(![X]:((kind(X)&~rich(X))<=>(~generous(X)|quiet(X))))&
((?[X]:((~strong(X)<~>creative(X))))=>((creative(john)|~wise(john))))&
(![X]:((tall(X)<~>~brave(X))=>(~tall(X)&~rich(X))))&
(![X]:((old(X)<~>patient(X))<=>(calm(X)|~calm(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(happy(alice)))&
(![X]:(wise(X)=>(brave(X)&quiet(X))))&
((?[X]:((humble(X)|patient(X))))=>((~calm(alice)<~>brave(alice))))&
(![X]:(funny(X)=>(curious(X)<~>~happy(X))))&
(((~rich(lucy)&rich(lucy)))<=>((~patient(paul)&quiet(paul))))&
(![X]:((~calm(X)<~>calm(X))=>(kind(X)<~>~rich(X))))&
((rich(mary))<=>(?[X]:((curious(X)<~>~kind(X)))))&
(~funny(paul))&
((~tall(paul)|curious(paul)))&
(?[X]:((~tall(X)&rich(X))))&
((~funny(alice)|~kind(alice)))&
(?[X]:(kind(X)))&
(~humble(fred))&
(funny(susan))&
(?[X]:((~quiet(X)<~>~strong(X)))) | ~quiet(alice) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2801019602544436514107940
% SZS output start Proof for 2801019602544436514107940
6. ! [X0] : ((~rich(X0) & kind(X0)) <=> (quiet(X0) | ~generous(X0))) [input p5]
15. ! [X0] : ((~calm(X0) <~> calm(X0)) => (kind(X0) <~> ~rich(X0))) [input p14]
25. quiet(alice) [input hypothesis]
35. ! [X0] : ((kind(X0) <~> ~rich(X0)) | (~calm(X0) <=> calm(X0))) [ennf transformation 15]
44. ! [X0] : (((~rich(X0) & kind(X0)) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | (rich(X0) | ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : (((~rich(X0) & kind(X0)) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | rich(X0) | ~kind(X0))) [flattening 44]
58. ! [X0] : (((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) [nnf transformation 35]
92. ~quiet(X0) | kind(X0) [cnf transformation 45]
94. ~quiet(X0) | ~rich(X0) [cnf transformation 45]
125. rich(X0) | ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 58]
126. rich(X0) | ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 58]
141. quiet(alice) [cnf transformation 25]
144. rich(X0) | ~kind(X0) | calm(X0) [duplicate literal removal 125]
145. rich(X0) | ~kind(X0) | ~calm(X0) [duplicate literal removal 126]
256. ~kind(X0) | rich(X0) [subsumption resolution 144,145]
282. 29 <=> kind(alice) [avatar definition]
283. kind(alice) <- (29) [avatar component clause 282]
298. kind(alice) [resolution 92,141]
300. 29 [avatar split clause 298,282]
303. ~rich(alice) [resolution 94,141]
307. rich(alice) <- (29) [resolution 256,283]
311. $false <- (29) [subsumption resolution 307,303]
312. ~29 [avatar contradiction clause 311]
315. $false [avatar sat refutation 300,312]
% SZS output end Proof for 2801019602544436514107940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and strong then alice is both not patient and brave and vice versa. Everyone who is old is funny and vice versa. If john is funny then lucy is not generous or not humble and vice versa. Everyone who is both not generous and not curious is both happy and not patient and vice versa. Everyone who is brave or not happy is both kind and not calm. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. If someone is not funny then lucy is brave. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Fred is either patient or calm. Lucy is not quiet. Lucy is not quiet or not strong. Someone is not curious or happy. Paul is either creative or patient. | Mary is not humble. | entailment | ((?[X]:((~happy(X)&strong(X))))<=>((~patient(alice)&brave(alice))))&
(![X]:(old(X)<=>funny(X)))&
((funny(john))<=>((~generous(lucy)|~humble(lucy))))&
(![X]:((~generous(X)&~curious(X))<=>(happy(X)&~patient(X))))&
(![X]:((brave(X)|~happy(X))=>(kind(X)&~calm(X))))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
((patient(fred)<~>calm(fred)))&
(~quiet(lucy))&
((~quiet(lucy)|~strong(lucy)))&
(?[X]:((~curious(X)|happy(X))))&
((creative(paul)<~>patient(paul))) | ~humble(mary) | [
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5572890442474663992199150
% SZS output start Proof for 5572890442474663992199150
7. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : (~rich(X0) <=> (calm(X0) & ~calm(X0))) [input p8]
10. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~rich(X0) [input p9]
22. humble(mary) [input hypothesis]
23. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~rich(X1) [rectify 10]
24. ! [X0] : (~rich(X0) => (calm(X0) & ~calm(X0))) [unused predicate definition removal 9]
32. ! [X0] : ((calm(X0) & ~calm(X0)) | rich(X0)) [ennf transformation 24]
33. ? [X1] : ~rich(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 23]
48. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 7]
50. ? [X0] : ~rich(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 33]
51. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
52. ~rich(sK1) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 50,51]
85. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 48]
87. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48]
92. calm(X0) | rich(X0) [cnf transformation 32]
93. ~rich(sK1) | ~humble(X1) [cnf transformation 52]
120. humble(mary) [cnf transformation 22]
121. curious(X0) | ~calm(X0) [duplicate literal removal 85]
122. ~calm(X0) | ~curious(X0) [duplicate literal removal 87]
161. ~calm(X0) [subsumption resolution 121,122]
162. rich(X0) [subsumption resolution 92,161]
164. ~humble(X1) [subsumption resolution 93,162]
244. $false [subsumption resolution 120,164]
% SZS output end Proof for 5572890442474663992199150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not funny and not brave then mary is not tall.
Everyone who is both strong and humble is patient.
Everyone who is not patient or not quiet is either not kind or happy.
If alice is not kind then someone is tall and vice versa.
Everyone who is quiet or curious is not old.
If mary is both not curious and strong then someone is both quiet and generous and vice versa.
Everyone who is not kind or funny is both not patient and brave and vice versa.
Everyone who is both not kind and generous is either not rich or not strong.
If john is rich then lucy is not rich and vice versa.
Everyone who is both kind and funny is not funny and vice versa.
Everyone who is either kind or quiet is both not happy and generous.
If someone is generous or not brave then susan is either generous or not old and vice versa.
Everyone who is not creative is both not curious and wise.
If someone is not strong or not calm then john is both funny and kind.
If mary is both not happy and old then alice is both brave and not funny and vice versa.
Everyone who is either not kind or not old is patient or old and vice versa.
Lucy is not calm or not humble.
Someone is either calm or patient.
Mary is not kind.
Alice is either not rich or not generous.
Fred is either patient or calm. | Alice is not happy. | entailment | (((~funny(john)&~brave(john)))=>(~tall(mary)))&
(![X]:((strong(X)&humble(X))=>patient(X)))&
(![X]:((~patient(X)|~quiet(X))=>(~kind(X)<~>happy(X))))&
((~kind(alice))<=>(?[X]:(tall(X))))&
(![X]:((quiet(X)|curious(X))=>~old(X)))&
(((~curious(mary)&strong(mary)))<=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:((~kind(X)|funny(X))<=>(~patient(X)&brave(X))))&
(![X]:((~kind(X)&generous(X))=>(~rich(X)<~>~strong(X))))&
((rich(john))<=>(~rich(lucy)))&
(![X]:((kind(X)&funny(X))<=>~funny(X)))&
(![X]:((kind(X)<~>quiet(X))=>(~happy(X)&generous(X))))&
((?[X]:((generous(X)|~brave(X))))<=>((generous(susan)<~>~old(susan))))&
(![X]:(~creative(X)=>(~curious(X)&wise(X))))&
((?[X]:((~strong(X)|~calm(X))))=>((funny(john)&kind(john))))&
(((~happy(mary)&old(mary)))<=>((brave(alice)&~funny(alice))))&
(![X]:((~kind(X)<~>~old(X))<=>(patient(X)|old(X))))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((calm(X)<~>patient(X))))&
(~kind(mary))&
((~rich(alice)<~>~generous(alice)))&
((patient(fred)<~>calm(fred))) | ~happy(alice) | [
"p2",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3691911334086668580941726
% SZS output start Proof for 3691911334086668580941726
3. ! [X0] : ((~quiet(X0) | ~patient(X0)) => (~kind(X0) <~> happy(X0))) [input p2]
7. ! [X0] : ((funny(X0) | ~kind(X0)) <=> (brave(X0) & ~patient(X0))) [input p6]
10. ! [X0] : ((funny(X0) & kind(X0)) <=> ~funny(X0)) [input p9]
22. happy(alice) [input hypothesis]
29. ! [X0] : ((~kind(X0) <~> happy(X0)) | (quiet(X0) & patient(X0))) [ennf transformation 3]
35. ! [X0] : (((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | (quiet(X0) & patient(X0))) [nnf transformation 29]
45. ! [X0] : (((funny(X0) | ~kind(X0)) | (~brave(X0) | patient(X0))) & ((brave(X0) & ~patient(X0)) | (~funny(X0) & kind(X0)))) [nnf transformation 7]
46. ! [X0] : ((funny(X0) | ~kind(X0) | ~brave(X0) | patient(X0)) & ((brave(X0) & ~patient(X0)) | (~funny(X0) & kind(X0)))) [flattening 45]
49. ! [X0] : (((funny(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) | ~kind(X0)))) [nnf transformation 10]
50. ! [X0] : (((funny(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | ~funny(X0) | ~kind(X0))) [flattening 49]
68. ~happy(X0) | kind(X0) | patient(X0) [cnf transformation 35]
79. ~patient(X0) | ~funny(X0) [cnf transformation 46]
87. ~funny(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 50]
89. funny(X0) | funny(X0) [cnf transformation 50]
121. happy(alice) [cnf transformation 22]
124. ~funny(X0) | ~kind(X0) [duplicate literal removal 87]
125. funny(X0) [duplicate literal removal 89]
185. ~kind(X0) [subsumption resolution 124,125]
260. kind(alice) | patient(alice) [resolution 68,121]
261. patient(alice) [subsumption resolution 260,185]
262. ~funny(alice) [resolution 261,79]
264. $false [subsumption resolution 262,125]
% SZS output end Proof for 3691911334086668580941726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and wise is not wise.
Everyone who is either not old or wise is both old and not funny and vice versa.
Everyone who is both not old and not wise is both generous and brave.
If alice is either not patient or kind then someone is either not brave or not happy and vice versa.
If someone is either not quiet or quiet then fred is both not patient and not funny.
Everyone who is kind or rich is quiet.
If lucy is quiet or not creative then john is wise or happy and vice versa.
If john is both not generous and not rich then someone is both not old and patient.
Everyone who is either rich or not strong is not generous.
Everyone who is not calm or rich is not brave.
If alice is both funny and happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
If mary is both patient and rich then someone is not patient or happy.
If john is not strong or brave then someone is not tall or not generous.
Susan is not wise or humble.
Lucy is both not rich and not curious.
Susan is both rich and strong.
Mary is not funny.
Someone is both curious and kind.
Someone is either humble or kind. | Mary is not curious. | entailment | (![X]:((curious(X)&wise(X))=>~wise(X)))&
(![X]:((~old(X)<~>wise(X))<=>(old(X)&~funny(X))))&
(![X]:((~old(X)&~wise(X))=>(generous(X)&brave(X))))&
(((~patient(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((~quiet(X)<~>quiet(X))))=>((~patient(fred)&~funny(fred))))&
(![X]:((kind(X)|rich(X))=>quiet(X)))&
(((quiet(lucy)|~creative(lucy)))<=>((wise(john)|happy(john))))&
(((~generous(john)&~rich(john)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((rich(X)<~>~strong(X))=>~generous(X)))&
(![X]:((~calm(X)|rich(X))=>~brave(X)))&
(((funny(alice)&happy(alice)))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
(((patient(mary)&rich(mary)))=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(john)|brave(john)))=>(?[X]:((~tall(X)|~generous(X)))))&
((~wise(susan)|humble(susan)))&
((~rich(lucy)&~curious(lucy)))&
((rich(susan)&strong(susan)))&
(~funny(mary))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:((humble(X)<~>kind(X)))) | ~curious(mary) | [
"p0",
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5463188357163810137461719
% SZS output start Proof for 5463188357163810137461719
1. ! [X0] : ((wise(X0) & curious(X0)) => ~wise(X0)) [input p0]
2. ! [X0] : ((~old(X0) <~> wise(X0)) <=> (~funny(X0) & old(X0))) [input p1]
20. ~funny(mary) [input p19]
23. curious(mary) [input hypothesis]
25. ! [X0] : (~wise(X0) | (~wise(X0) | ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (~wise(X0) | ~wise(X0) | ~curious(X0)) [flattening 25]
39. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [flattening 39]
68. ~wise(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 26]
69. old(X0) | wise(X0) | old(X0) [cnf transformation 40]
73. wise(X0) | ~old(X0) | funny(X0) | ~old(X0) [cnf transformation 40]
123. ~funny(mary) [cnf transformation 20]
128. curious(mary) [cnf transformation 23]
135. old(X0) | wise(X0) [duplicate literal removal 69]
136. ~old(X0) | wise(X0) | funny(X0) [duplicate literal removal 73]
137. ~wise(X0) | ~curious(X0) [duplicate literal removal 68]
382. wise(X0) | funny(X0) | wise(X0) [resolution 136,135]
383. funny(X0) | wise(X0) [duplicate literal removal 382]
391. wise(mary) [resolution 383,123]
398. ~curious(mary) [resolution 391,137]
399. $false [subsumption resolution 398,128]
% SZS output end Proof for 5463188357163810137461719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not generous.
Everyone who is wise is not happy and vice versa.
Everyone who is not quiet is not generous or wise.
Everyone who is strong is both creative and calm.
Everyone who is strong is strong or not patient.
If john is brave or not funny then someone is quiet or not quiet.
If john is not calm then alice is not kind or old.
Everyone who is both tall and old is both not tall and generous and vice versa.
Everyone who is generous is calm or not wise and vice versa.
If lucy is both not funny and strong then someone is not old.
If alice is either not kind or not happy then john is generous.
If alice is either happy or calm then lucy is either quiet or strong and vice versa.
If someone is creative then lucy is happy.
Everyone who is both not funny and happy is funny or humble.
Everyone who is either not patient or not funny is curious or not tall and vice versa.
If paul is curious then someone is either not creative or not brave and vice versa.
Paul is not happy.
John is not wise or not creative.
Mary is old.
Lucy is either not tall or not creative.
Someone is either curious or not generous.
Alice is both not humble and not calm.
Susan is wise. | John is not quiet. | neutral | (![X]:(funny(X)=>~generous(X)))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:(~quiet(X)=>(~generous(X)|wise(X))))&
(![X]:(strong(X)=>(creative(X)&calm(X))))&
(![X]:(strong(X)=>(strong(X)|~patient(X))))&
(((brave(john)|~funny(john)))=>(?[X]:((quiet(X)|~quiet(X)))))&
((~calm(john))=>((~kind(alice)|old(alice))))&
(![X]:((tall(X)&old(X))<=>(~tall(X)&generous(X))))&
(![X]:(generous(X)<=>(calm(X)|~wise(X))))&
(((~funny(lucy)&strong(lucy)))=>(?[X]:(~old(X))))&
(((~kind(alice)<~>~happy(alice)))=>(generous(john)))&
(((happy(alice)<~>calm(alice)))<=>((quiet(lucy)<~>strong(lucy))))&
((?[X]:(creative(X)))=>(happy(lucy)))&
(![X]:((~funny(X)&happy(X))=>(funny(X)|humble(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(curious(X)|~tall(X))))&
((curious(paul))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(~happy(paul))&
((~wise(john)|~creative(john)))&
(old(mary))&
((~tall(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)<~>~generous(X))))&
((~humble(alice)&~calm(alice)))&
(wise(susan)) | ~quiet(john) | [] | null | 0 |
Everyone who is both not calm and humble is both not wise and quiet and vice versa.
If someone is not wise or not old then fred is either creative or not brave and vice versa.
If alice is not calm or not happy then john is patient.
Everyone who is not generous is quiet or not kind and vice versa.
If someone is happy then someone is either kind or funny and vice versa.
Everyone who is not curious is either not curious or funny and vice versa.
Everyone who is not happy is curious and vice versa.
If fred is patient or quiet then someone is both not generous and tall.
Everyone who is not curious or not funny is either not old or not quiet.
If someone is either calm or not brave then someone is both not calm and not brave and vice versa.
Everyone who is both quiet and not kind is both not creative and kind.
If someone is not tall then someone is both not strong and kind.
If lucy is calm or not quiet then alice is both calm and curious and vice versa.
Everyone who is not kind or strong is either not humble or patient and vice versa.
If someone is not rich then alice is calm.
Everyone who is either quiet or not calm is not humble or wise.
Lucy is not happy or not tall.
Someone is quiet.
Someone is not old or not generous.
Someone is either not wise or curious.
Lucy is rich or kind.
Someone is strong.
Someone is either old or not curious.
Lucy is not kind or tall. | Lucy is patient. | neutral | (![X]:((~calm(X)&humble(X))<=>(~wise(X)&quiet(X))))&
((?[X]:((~wise(X)|~old(X))))<=>((creative(fred)<~>~brave(fred))))&
(((~calm(alice)|~happy(alice)))=>(patient(john)))&
(![X]:(~generous(X)<=>(quiet(X)|~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:(~curious(X)<=>(~curious(X)<~>funny(X))))&
(![X]:(~happy(X)<=>curious(X)))&
(((patient(fred)|quiet(fred)))=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)|~funny(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((quiet(X)&~kind(X))=>(~creative(X)&kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((calm(lucy)|~quiet(lucy)))<=>((calm(alice)&curious(alice))))&
(![X]:((~kind(X)|strong(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:(~rich(X)))=>(calm(alice)))&
(![X]:((quiet(X)<~>~calm(X))=>(~humble(X)|wise(X))))&
((~happy(lucy)|~tall(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)|~generous(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
((rich(lucy)|kind(lucy)))&
(?[X]:(strong(X)))&
(?[X]:((old(X)<~>~curious(X))))&
((~kind(lucy)|tall(lucy))) | patient(lucy) | [] | null | 0 |
If alice is curious or generous then paul is not rich or not wise and vice versa. Everyone who is either not old or generous is both not old and not quiet and vice versa. Everyone who is both rich and not curious is curious and vice versa. If paul is both not happy and rich then someone is either generous or not rich. Everyone who is old is wise and vice versa. Everyone who is not funny or generous is both not happy and not creative. Everyone who is not tall or patient is either not strong or strong and vice versa. Everyone who is either funny or not funny is either not patient or happy and vice versa. Everyone who is not calm or not generous is not happy or creative and vice versa. If mary is generous then someone is not brave or not patient and vice versa. Everyone who is either not wise or not happy is kind or patient and vice versa. Everyone who is either not tall or not calm is not rich. Everyone who is both rich and not patient is tall or curious. If someone is brave or strong then someone is either not tall or happy and vice versa. Someone is either not funny or not generous. John is happy. Susan is not humble. | Mary is humble. | neutral | (((curious(alice)|generous(alice)))<=>((~rich(paul)|~wise(paul))))&
(![X]:((~old(X)<~>generous(X))<=>(~old(X)&~quiet(X))))&
(![X]:((rich(X)&~curious(X))<=>curious(X)))&
(((~happy(paul)&rich(paul)))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((~funny(X)|generous(X))=>(~happy(X)&~creative(X))))&
(![X]:((~tall(X)|patient(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((funny(X)<~>~funny(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~happy(X)|creative(X))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(happy(john))&
(~humble(susan)) | humble(mary) | [] | null | 0 |
Everyone who is either not patient or not curious is both not creative and rich. Everyone who is not brave or curious is both strong and not strong and vice versa. If someone is not wise or not patient then someone is both generous and not kind. Everyone who is curious or not curious is either not creative or not kind and vice versa. Everyone who is creative is old or patient. Everyone who is either generous or kind is brave. Everyone who is both creative and tall is not calm and vice versa. Everyone who is either creative or not happy is both not creative and not patient and vice versa. Everyone who is old is not strong or kind and vice versa. Everyone who is either not quiet or not funny is both not strong and rich. Everyone who is both quiet and not happy is not quiet. Everyone who is either not calm or not rich is calm and vice versa. If paul is both tall and not funny then paul is both kind and not funny and vice versa. Someone is not curious. Someone is either rich or not happy. Someone is not creative. Someone is both strong and brave. | Paul is not strong. | neutral | (![X]:((~patient(X)<~>~curious(X))=>(~creative(X)&rich(X))))&
(![X]:((~brave(X)|curious(X))<=>(strong(X)&~strong(X))))&
((?[X]:((~wise(X)|~patient(X))))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((curious(X)|~curious(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:(creative(X)=>(old(X)|patient(X))))&
(![X]:((generous(X)<~>kind(X))=>brave(X)))&
(![X]:((creative(X)&tall(X))<=>~calm(X)))&
(![X]:((creative(X)<~>~happy(X))<=>(~creative(X)&~patient(X))))&
(![X]:(old(X)<=>(~strong(X)|kind(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~strong(X)&rich(X))))&
(![X]:((quiet(X)&~happy(X))=>~quiet(X)))&
(![X]:((~calm(X)<~>~rich(X))<=>calm(X)))&
(((tall(paul)&~funny(paul)))<=>((kind(paul)&~funny(paul))))&
(?[X]:(~curious(X)))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)&brave(X)))) | ~strong(paul) | [] | null | 0 |
If someone is both not creative and generous then someone is both wise and not kind and vice versa.
Everyone who is quiet or not funny is both generous and not old and vice versa.
If john is rich then mary is either not brave or not wise.
If alice is not calm or funny then susan is happy or creative.
If paul is either not old or not wise then someone is both funny and not strong and vice versa.
Everyone who is either quiet or not generous is not wise and vice versa.
Everyone who is both not kind and generous is generous and vice versa.
Everyone who is rich or curious is either not brave or quiet and vice versa.
If mary is not generous then someone is not strong and vice versa.
Everyone who is both calm and not patient is either not strong or not happy and vice versa.
Everyone who is not strong or tall is either quiet or funny.
If mary is not curious then mary is strong.
If someone is either not happy or not creative then someone is patient or not wise and vice versa.
If lucy is both not old and not happy then john is either not humble or tall and vice versa.
Everyone who is calm or not tall is either not generous or humble and vice versa.
Everyone who is not kind is both creative and not generous.
Someone is strong.
Fred is not quiet or brave.
Someone is tall.
Someone is not tall or not wise.
Alice is tall or curious. | Mary is wise. | contradiction | ((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((quiet(X)|~funny(X))<=>(generous(X)&~old(X))))&
((rich(john))=>((~brave(mary)<~>~wise(mary))))&
(((~calm(alice)|funny(alice)))=>((happy(susan)|creative(susan))))&
(((~old(paul)<~>~wise(paul)))<=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((quiet(X)<~>~generous(X))<=>~wise(X)))&
(![X]:((~kind(X)&generous(X))<=>generous(X)))&
(![X]:((rich(X)|curious(X))<=>(~brave(X)<~>quiet(X))))&
((~generous(mary))<=>(?[X]:(~strong(X))))&
(![X]:((calm(X)&~patient(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~strong(X)|tall(X))=>(quiet(X)<~>funny(X))))&
((~curious(mary))=>(strong(mary)))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~old(lucy)&~happy(lucy)))<=>((~humble(john)<~>tall(john))))&
(![X]:((calm(X)|~tall(X))<=>(~generous(X)<~>humble(X))))&
(![X]:(~kind(X)=>(creative(X)&~generous(X))))&
(?[X]:(strong(X)))&
((~quiet(fred)|brave(fred)))&
(?[X]:(tall(X)))&
(?[X]:((~tall(X)|~wise(X))))&
((tall(alice)|curious(alice))) | wise(mary) | [
"p1",
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3351851837422202198543684
% SZS output start Proof for 3351851837422202198543684
2. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (~old(X0) & generous(X0))) [input p1]
6. ! [X0] : ((quiet(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p5]
7. ! [X0] : ((generous(X0) & ~kind(X0)) <=> generous(X0)) [input p6]
16. ! [X0] : (~kind(X0) => (~generous(X0) & creative(X0))) [input p15]
22. wise(mary) [input hypothesis]
30. ! [X0] : ((~generous(X0) & creative(X0)) | kind(X0)) [ennf transformation 16]
36. ! [X0] : (((~funny(X0) | quiet(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~funny(X0) | quiet(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (funny(X0) & ~quiet(X0)))) [flattening 36]
43. ! [X0] : ((((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))))) [nnf transformation 6]
44. ! [X0] : (((generous(X0) & ~kind(X0)) | ~generous(X0)) & (generous(X0) | (~generous(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((generous(X0) & ~kind(X0)) | ~generous(X0)) & (generous(X0) | ~generous(X0) | kind(X0))) [flattening 44]
74. ~quiet(X0) | generous(X0) [cnf transformation 37]
90. ~wise(X0) | quiet(X0) | generous(X0) [cnf transformation 43]
94. ~kind(X0) | ~generous(X0) [cnf transformation 45]
134. ~generous(X0) | kind(X0) [cnf transformation 30]
140. wise(mary) [cnf transformation 22]
176. 9 <=> wise(mary) [avatar definition]
178. wise(mary) <- (9) [avatar component clause 176]
224. ~wise(X0) | generous(X0) [subsumption resolution 90,74]
304. ~generous(X0) [subsumption resolution 134,94]
332. 9 [avatar split clause 140,176]
343. generous(mary) <- (9) [resolution 224,178]
344. $false <- (9) [subsumption resolution 343,304]
345. ~9 [avatar contradiction clause 344]
346. $false [avatar sat refutation 332,345]
% SZS output end Proof for 3351851837422202198543684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or strong is not wise or patient and vice versa.
Everyone who is tall or not calm is either not rich or generous and vice versa.
If alice is either creative or rich then someone is funny.
Everyone who is both kind and not strong is tall.
If lucy is brave then susan is humble or not curious.
If someone is both old and strong then fred is not funny or kind and vice versa.
If someone is either not tall or brave then someone is both rich and creative and vice versa.
Everyone who is both not generous and humble is either not generous or not old and vice versa.
Everyone who is not humble or not happy is either old or wise.
Everyone who is not wise is either not calm or curious and vice versa.
If fred is tall or not happy then someone is not happy or wise and vice versa.
If someone is either calm or not brave then someone is patient.
If someone is quiet or not wise then someone is both not calm and not happy.
Everyone who is either tall or not generous is patient or wise.
Everyone who is either wise or not strong is not wise and vice versa.
If someone is either not creative or rich then someone is either quiet or not rich and vice versa.
Lucy is not old or not humble.
Someone is both not patient and not happy.
Someone is either not patient or wise.
Someone is not old.
Someone is not quiet or old.
Someone is either kind or funny.
Alice is not calm.
Someone is creative or not old. | Lucy is not old. | entailment | (![X]:((~generous(X)<~>strong(X))<=>(~wise(X)|patient(X))))&
(![X]:((tall(X)|~calm(X))<=>(~rich(X)<~>generous(X))))&
(((creative(alice)<~>rich(alice)))=>(?[X]:(funny(X))))&
(![X]:((kind(X)&~strong(X))=>tall(X)))&
((brave(lucy))=>((humble(susan)|~curious(susan))))&
((?[X]:((old(X)&strong(X))))<=>((~funny(fred)|kind(fred))))&
((?[X]:((~tall(X)<~>brave(X))))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((~generous(X)&humble(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((~humble(X)|~happy(X))=>(old(X)<~>wise(X))))&
(![X]:(~wise(X)<=>(~calm(X)<~>curious(X))))&
(((tall(fred)|~happy(fred)))<=>(?[X]:((~happy(X)|wise(X)))))&
((?[X]:((calm(X)<~>~brave(X))))=>(?[X]:(patient(X))))&
((?[X]:((quiet(X)|~wise(X))))=>(?[X]:((~calm(X)&~happy(X)))))&
(![X]:((tall(X)<~>~generous(X))=>(patient(X)|wise(X))))&
(![X]:((wise(X)<~>~strong(X))<=>~wise(X)))&
((?[X]:((~creative(X)<~>rich(X))))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((~old(lucy)|~humble(lucy)))&
(?[X]:((~patient(X)&~happy(X))))&
(?[X]:((~patient(X)<~>wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((kind(X)<~>funny(X))))&
(~calm(alice))&
(?[X]:((creative(X)|~old(X)))) | ~old(lucy) | [
"p0",
"p7",
"p8",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2657590779566721942392588
% SZS output start Proof for 2657590779566721942392588
1. ! [X0] : ((~generous(X0) <~> strong(X0)) <=> (patient(X0) | ~wise(X0))) [input p0]
8. ! [X0] : ((humble(X0) & ~generous(X0)) <=> (~generous(X0) <~> ~old(X0))) [input p7]
9. ! [X0] : ((~happy(X0) | ~humble(X0)) => (old(X0) <~> wise(X0))) [input p8]
15. ! [X0] : ((wise(X0) <~> ~strong(X0)) <=> ~wise(X0)) [input p14]
17. ~humble(lucy) | ~old(lucy) [input p16]
25. old(lucy) [input hypothesis]
35. ! [X0] : ((old(X0) <~> wise(X0)) | (happy(X0) & humble(X0))) [ennf transformation 9]
40. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~patient(X0) & wise(X0))) & ((patient(X0) | ~wise(X0)) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~patient(X0) & wise(X0))) & (patient(X0) | ~wise(X0) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [flattening 40]
57. ! [X0] : (((humble(X0) & ~generous(X0)) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) & (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | (~humble(X0) | generous(X0)))) [nnf transformation 8]
58. ! [X0] : (((humble(X0) & ~generous(X0)) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) & (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ~humble(X0) | generous(X0))) [flattening 57]
59. ! [X0] : (((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (happy(X0) & humble(X0))) [nnf transformation 35]
74. ! [X0] : ((((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | wise(X0)) & (~wise(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))))) [nnf transformation 15]
96. ~generous(X0) | strong(X0) | wise(X0) [cnf transformation 41]
122. old(X0) | generous(X0) | ~humble(X0) | generous(X0) [cnf transformation 58]
124. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 58]
125. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 58]
129. ~old(X0) | ~wise(X0) | humble(X0) [cnf transformation 59]
147. ~wise(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 74]
149. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 74]
159. ~humble(lucy) | ~old(lucy) [cnf transformation 17]
170. old(lucy) [cnf transformation 25]
171. ~wise(X0) | ~strong(X0) [duplicate literal removal 147]
172. ~strong(X0) | wise(X0) [duplicate literal removal 149]
173. old(X0) | generous(X0) | ~humble(X0) [duplicate literal removal 122]
174. ~generous(X0) | old(X0) [duplicate literal removal 124]
257. ~humble(X0) | old(X0) [subsumption resolution 173,174]
315. ~strong(X0) [subsumption resolution 171,172]
349. ~humble(lucy) [subsumption resolution 159,257]
412. humble(lucy) | generous(lucy) [resolution 125,170]
415. generous(lucy) [subsumption resolution 412,349]
437. strong(lucy) | wise(lucy) [resolution 415,96]
448. wise(lucy) [subsumption resolution 437,315]
467. ~wise(lucy) | humble(lucy) [resolution 129,170]
470. humble(lucy) [subsumption resolution 467,448]
471. $false [subsumption resolution 470,349]
% SZS output end Proof for 2657590779566721942392588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is funny then lucy is either not creative or humble and vice versa.
If mary is either calm or not generous then someone is curious and vice versa.
If mary is both curious and not kind then someone is both wise and not kind and vice versa.
If paul is either not quiet or wise then someone is both rich and not quiet and vice versa.
Everyone who is not old or tall is both happy and not calm and vice versa.
Everyone who is either old or not kind is both kind and patient.
Everyone who is strong is either not funny or not curious.
Everyone who is not calm or not rich is not tall and vice versa.
If someone is both not old and tall then someone is not humble and vice versa.
If alice is not quiet then someone is patient or wise and vice versa.
If lucy is either not brave or not old then someone is not tall.
If someone is both funny and quiet then fred is not kind or not calm.
Everyone who is both not quiet and not rich is not wise.
If someone is quiet or brave then mary is happy or rich.
If mary is not wise or not curious then someone is not creative.
Everyone who is not funny or old is both quiet and creative.
Fred is either not calm or not creative.
Someone is not patient.
Someone is rich.
Mary is not kind or not happy.
Someone is both kind and funny. | Mary is tall. | contradiction | ((?[X]:(funny(X)))<=>((~creative(lucy)<~>humble(lucy))))&
(((calm(mary)<~>~generous(mary)))<=>(?[X]:(curious(X))))&
(((curious(mary)&~kind(mary)))<=>(?[X]:((wise(X)&~kind(X)))))&
(((~quiet(paul)<~>wise(paul)))<=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((~old(X)|tall(X))<=>(happy(X)&~calm(X))))&
(![X]:((old(X)<~>~kind(X))=>(kind(X)&patient(X))))&
(![X]:(strong(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~calm(X)|~rich(X))<=>~tall(X)))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>(?[X]:((patient(X)|wise(X)))))&
(((~brave(lucy)<~>~old(lucy)))=>(?[X]:(~tall(X))))&
((?[X]:((funny(X)&quiet(X))))=>((~kind(fred)|~calm(fred))))&
(![X]:((~quiet(X)&~rich(X))=>~wise(X)))&
((?[X]:((quiet(X)|brave(X))))=>((happy(mary)|rich(mary))))&
(((~wise(mary)|~curious(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|old(X))=>(quiet(X)&creative(X))))&
((~calm(fred)<~>~creative(fred)))&
(?[X]:(~patient(X)))&
(?[X]:(rich(X)))&
((~kind(mary)|~happy(mary)))&
(?[X]:((kind(X)&funny(X)))) | tall(mary) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3148282299428363100675371
% SZS output start Proof for 3148282299428363100675371
5. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~calm(X0) & happy(X0))) [input p4]
8. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> ~tall(X0)) [input p7]
22. tall(mary) [input hypothesis]
52. ! [X0] : (((tall(X0) | ~old(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 5]
53. ! [X0] : ((tall(X0) | ~old(X0) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [flattening 52]
55. ! [X0] : (((~rich(X0) | ~calm(X0)) | tall(X0)) & (~tall(X0) | (rich(X0) & calm(X0)))) [nnf transformation 8]
56. ! [X0] : ((~rich(X0) | ~calm(X0) | tall(X0)) & (~tall(X0) | (rich(X0) & calm(X0)))) [flattening 55]
99. ~calm(X0) | ~tall(X0) [cnf transformation 53]
105. ~tall(X0) | calm(X0) [cnf transformation 56]
133. tall(mary) [cnf transformation 22]
222. ~tall(X0) [subsumption resolution 105,99]
290. $false [subsumption resolution 133,222]
% SZS output end Proof for 3148282299428363100675371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is patient or funny and vice versa. 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. If paul is either strong or generous then someone is patient and vice versa. Someone is either old or happy. 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. Alice is either not patient or calm. Lucy is calm. | Paul is not quiet. | entailment | (![X]:(wise(X)<=>(patient(X)|funny(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))))&
(((strong(paul)<~>generous(paul)))<=>(?[X]:(patient(X))))&
(?[X]:((old(X)<~>happy(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~patient(alice)<~>calm(alice)))&
(calm(lucy)) | ~quiet(paul) | [
"p1",
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4450933489490854821621336
% SZS output start Proof for 4450933489490854821621336
2. ! [X0] : ((creative(X0) & strong(X0)) <=> (~happy(X0) | brave(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p2]
5. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p4]
8. ! [X0] : (quiet(X0) => (creative(X0) <~> quiet(X0))) [input p7]
25. quiet(paul) [input hypothesis]
31. ! [X0] : ((creative(X0) <~> quiet(X0)) | ~quiet(X0)) [ennf transformation 8]
38. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (~creative(X0) | ~strong(X0)))) [nnf transformation 2]
39. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ~creative(X0) | ~strong(X0))) [flattening 38]
40. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 40]
42. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 5]
43. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 42]
44. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK0) | ~rich(sK0)) [choice axiom]
45. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK0) | ~rich(sK0)) | tall(mary)) [skolemisation 43,44]
52. ! [X0] : (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~quiet(X0)) [nnf transformation 31]
81. ~brave(X0) | creative(X0) [cnf transformation 39]
84. ~funny(X0) | tall(X0) [cnf transformation 41]
85. tall(X0) | funny(X0) [cnf transformation 41]
89. ~tall(mary) | brave(X0) [cnf transformation 45]
95. ~quiet(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 52]
142. quiet(paul) [cnf transformation 25]
143. ~quiet(X0) | ~creative(X0) [duplicate literal removal 95]
144. tall(X0) [subsumption resolution 84,85]
145. brave(X0) [subsumption resolution 89,144]
275. creative(X0) [resolution 81,145]
285. ~creative(paul) [resolution 143,142]
287. $false [subsumption resolution 285,275]
% SZS output end Proof for 4450933489490854821621336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both funny and not curious then mary is strong and vice versa.
If someone is either not happy or not creative then someone is patient or not wise and vice versa.
If lucy is both not old and not happy then john is either not humble or tall and vice versa.
Everyone who is calm or not tall is either not generous or humble and vice versa.
Everyone who is not kind is both creative and not generous.
If someone is both strong and humble then lucy is either not funny or creative and vice versa.
If lucy is both brave and humble then someone is both not quiet and not strong.
If paul is both curious and not brave then paul is both not brave and tall and vice versa.
Everyone who is either not curious or funny is not calm or not old and vice versa.
Everyone who is either not rich or humble is either tall or not creative.
If someone is both not funny and calm then susan is either old or not quiet.
Everyone who is not old or not generous is brave or calm.
If john is not generous or not tall then fred is both calm and curious and vice versa.
If someone is both not humble and not patient then someone is generous.
Everyone who is tall is either not generous or not patient and vice versa.
If someone is curious or brave then fred is both creative and not creative.
Someone is both not kind and tall.
Fred is both not curious and generous.
Alice is not humble.
Someone is both calm and not humble.
Paul is not old or not wise.
Someone is not wise or not quiet. | Lucy is not brave. | entailment | (((funny(alice)&~curious(alice)))<=>(strong(mary)))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~old(lucy)&~happy(lucy)))<=>((~humble(john)<~>tall(john))))&
(![X]:((calm(X)|~tall(X))<=>(~generous(X)<~>humble(X))))&
(![X]:(~kind(X)=>(creative(X)&~generous(X))))&
((?[X]:((strong(X)&humble(X))))<=>((~funny(lucy)<~>creative(lucy))))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((~quiet(X)&~strong(X)))))&
(((curious(paul)&~brave(paul)))<=>((~brave(paul)&tall(paul))))&
(![X]:((~curious(X)<~>funny(X))<=>(~calm(X)|~old(X))))&
(![X]:((~rich(X)<~>humble(X))=>(tall(X)<~>~creative(X))))&
((?[X]:((~funny(X)&calm(X))))=>((old(susan)<~>~quiet(susan))))&
(![X]:((~old(X)|~generous(X))=>(brave(X)|calm(X))))&
(((~generous(john)|~tall(john)))<=>((calm(fred)&curious(fred))))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:(generous(X))))&
(![X]:(tall(X)<=>(~generous(X)<~>~patient(X))))&
((?[X]:((curious(X)|brave(X))))=>((creative(fred)&~creative(fred))))&
(?[X]:((~kind(X)&tall(X))))&
((~curious(fred)&generous(fred)))&
(~humble(alice))&
(?[X]:((calm(X)&~humble(X))))&
((~old(paul)|~wise(paul)))&
(?[X]:((~wise(X)|~quiet(X)))) | ~brave(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8415484057520159202242969
% SZS output start Proof for 8415484057520159202242969
16. ? [X0] : (brave(X0) | curious(X0)) => (~creative(fred) & creative(fred)) [input p15]
23. brave(lucy) [input hypothesis]
34. (~creative(fred) & creative(fred)) | ! [X0] : (~brave(X0) & ~curious(X0)) [ennf transformation 16]
130. creative(fred) | ~brave(X0) [cnf transformation 34]
132. ~creative(fred) | ~brave(X0) [cnf transformation 34]
142. brave(lucy) [cnf transformation 23]
240. 21 <=> brave(lucy) [avatar definition]
241. brave(lucy) <- (21) [avatar component clause 240]
310. 36 <=> ! [X0] : ~brave(X0) [avatar definition]
311. ~brave(X0) <- (36) [avatar component clause 310]
313. 37 <=> creative(fred) [avatar definition]
316. 36 | ~37 [avatar split clause 132,313,310]
321. 36 | 37 [avatar split clause 130,313,310]
342. 21 [avatar split clause 142,240]
343. $false <- (21, 36) [subsumption resolution 241,311]
344. ~21 | ~36 [avatar contradiction clause 343]
345. $false [avatar sat refutation 316,321,342,344]
% SZS output end Proof for 8415484057520159202242969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then fred is not generous or not rich and vice versa. If mary is generous then someone is both quiet and tall. Everyone who is calm or quiet is both not patient and creative and vice versa. Everyone who is not calm is not creative or not happy. Everyone who is not happy or not curious is both calm and not rich. Everyone who is both not curious and not old is either not calm or not funny and vice versa. Everyone who is either tall or not tall is either not brave or not quiet and vice versa. If someone is old or quiet then fred is rich or curious and vice versa. Everyone who is curious is either rich or humble and vice versa. Everyone who is both brave and tall is not tall or not curious. Everyone who is humble is either old or not patient and vice versa. Everyone who is not wise or not funny is either not humble or not brave and vice versa. If john is either not humble or not generous then alice is tall. If paul is both not generous and not funny then john is either creative or not brave. Someone is not wise or curious. Alice is creative. Paul is strong. Someone is not tall or kind. Someone is kind or tall. Someone is tall. | Fred is creative. | neutral | ((?[X]:(old(X)))<=>((~generous(fred)|~rich(fred))))&
((generous(mary))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(![X]:(~calm(X)=>(~creative(X)|~happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&~old(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(?[X]:((~wise(X)|curious(X))))&
(creative(alice))&
(strong(paul))&
(?[X]:((~tall(X)|kind(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:(tall(X))) | creative(fred) | [] | null | 0 |
If someone is either not quiet or not humble then someone is either not wise or funny. If someone is quiet or not patient then paul is curious and vice versa. Everyone who is not creative is either not generous or funny and vice versa. If someone is both curious and rich then someone is both patient and not tall and vice versa. Everyone who is not curious is old and vice versa. Everyone who is either not old or not happy is strong. If someone is either not creative or not strong then fred is both generous and creative and vice versa. If paul is both curious and not humble then lucy is not funny. Everyone who is either humble or tall is not brave or not tall and vice versa. Everyone who is patient or calm is old or brave. Everyone who is not curious or not generous is either not generous or not happy. If someone is rich then someone is both not patient and not rich. Everyone who is either not humble or kind is both strong and old. Everyone who is not happy is either not patient or not calm and vice versa. If mary is either not tall or not wise then john is not humble or kind and vice versa. If paul is kind then someone is brave or calm and vice versa. Alice is both not creative and not brave. Someone is happy. Lucy is either not wise or brave. Someone is quiet or not tall. Paul is not kind or rich. Alice is either not humble or not rich. Susan is wise or kind. Someone is creative. | Paul is not brave. | entailment | ((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((~wise(X)<~>funny(X)))))&
((?[X]:((quiet(X)|~patient(X))))<=>(curious(paul)))&
(![X]:(~creative(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:(~curious(X)<=>old(X)))&
(![X]:((~old(X)<~>~happy(X))=>strong(X)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(fred)&creative(fred))))&
(((curious(paul)&~humble(paul)))=>(~funny(lucy)))&
(![X]:((humble(X)<~>tall(X))<=>(~brave(X)|~tall(X))))&
(![X]:((patient(X)|calm(X))=>(old(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>(~generous(X)<~>~happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((~humble(X)<~>kind(X))=>(strong(X)&old(X))))&
(![X]:(~happy(X)<=>(~patient(X)<~>~calm(X))))&
(((~tall(mary)<~>~wise(mary)))<=>((~humble(john)|kind(john))))&
((kind(paul))<=>(?[X]:((brave(X)|calm(X)))))&
((~creative(alice)&~brave(alice)))&
(?[X]:(happy(X)))&
((~wise(lucy)<~>brave(lucy)))&
(?[X]:((quiet(X)|~tall(X))))&
((~kind(paul)|rich(paul)))&
((~humble(alice)<~>~rich(alice)))&
((wise(susan)|kind(susan)))&
(?[X]:(creative(X))) | ~brave(paul) | [
"p1",
"p4",
"p8",
"p11",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5989450781779927290513147
% SZS output start Proof for 5989450781779927290513147
2. ? [X0] : (~patient(X0) | quiet(X0)) <=> curious(paul) [input p1]
5. ! [X0] : (~curious(X0) <=> old(X0)) [input p4]
9. ! [X0] : ((humble(X0) <~> tall(X0)) <=> (~tall(X0) | ~brave(X0))) [input p8]
12. ? [X0] : rich(X0) => ? [X0] : (~rich(X0) & ~patient(X0)) [input p11]
13. ! [X0] : ((~humble(X0) <~> kind(X0)) => (old(X0) & strong(X0))) [input p12]
16. kind(paul) <=> ? [X0] : (calm(X0) | brave(X0)) [input p15]
21. rich(paul) | ~kind(paul) [input p20]
25. brave(paul) [input hypothesis]
28. ? [X0] : rich(X0) => ? [X1] : (~rich(X1) & ~patient(X1)) [rectify 12]
36. ? [X1] : (~rich(X1) & ~patient(X1)) | ! [X0] : ~rich(X0) [ennf transformation 28]
37. ! [X0] : ((old(X0) & strong(X0)) | (~humble(X0) <=> kind(X0))) [ennf transformation 13]
42. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X0] : (patient(X0) & ~quiet(X0))) [nnf transformation 2]
43. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [rectify 42]
44. ? [X0] : (~patient(X0) | quiet(X0)) => (~patient(sK1) | quiet(sK1)) [choice axiom]
45. ((~patient(sK1) | quiet(sK1)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [skolemisation 43,44]
52. ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0))) [nnf transformation 5]
59. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 9]
60. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [flattening 59]
62. ? [X0] : (~rich(X0) & ~patient(X0)) | ! [X1] : ~rich(X1) [rectify 36]
63. ? [X0] : (~rich(X0) & ~patient(X0)) => (~rich(sK5) & ~patient(sK5)) [choice axiom]
64. (~rich(sK5) & ~patient(sK5)) | ! [X1] : ~rich(X1) [skolemisation 62,63]
65. ! [X0] : ((old(X0) & strong(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) [nnf transformation 37]
69. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | ~kind(paul)) [nnf transformation 16]
70. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X1] : (calm(X1) | brave(X1)) | ~kind(paul)) [rectify 69]
71. ? [X1] : (calm(X1) | brave(X1)) => (calm(sK6) | brave(sK6)) [choice axiom]
72. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & ((calm(sK6) | brave(sK6)) | ~kind(paul)) [skolemisation 70,71]
86. curious(paul) | patient(X1) [cnf transformation 45]
97. ~old(X0) | ~curious(X0) [cnf transformation 52]
108. ~tall(X0) | ~brave(X0) | humble(X0) | ~tall(X0) [cnf transformation 60]
110. tall(X0) | humble(X0) | tall(X0) [cnf transformation 60]
119. ~patient(sK5) | ~rich(X1) [cnf transformation 64]
124. ~kind(X0) | ~humble(X0) | old(X0) [cnf transformation 65]
136. kind(paul) | ~brave(X0) [cnf transformation 72]
144. rich(paul) | ~kind(paul) [cnf transformation 21]
149. brave(paul) [cnf transformation 25]
151. ~tall(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 108]
152. tall(X0) | humble(X0) [duplicate literal removal 110]
172. 5 <=> curious(paul) [avatar definition]
173. curious(paul) <- (5) [avatar component clause 172]
185. 8 <=> ! [X1] : patient(X1) [avatar definition]
186. patient(X1) <- (8) [avatar component clause 185]
187. 8 | 5 [avatar split clause 86,172,185]
247. 22 <=> humble(paul) [avatar definition]
249. humble(paul) <- (22) [avatar component clause 247]
255. ~brave(X0) | humble(X0) [subsumption resolution 151,152]
257. 24 <=> ! [X1] : ~rich(X1) [avatar definition]
258. ~rich(X1) <- (24) [avatar component clause 257]
265. 26 <=> patient(sK5) [avatar definition]
267. ~patient(sK5) <- (~26) [avatar component clause 265]
268. 24 | ~26 [avatar split clause 119,265,257]
295. 32 <=> kind(paul) [avatar definition]
297. kind(paul) <- (32) [avatar component clause 295]
300. 33 <=> ! [X0] : ~brave(X0) [avatar definition]
301. ~brave(X0) <- (33) [avatar component clause 300]
302. 33 | 32 [avatar split clause 136,295,300]
332. 40 <=> rich(paul) [avatar definition]
334. rich(paul) <- (40) [avatar component clause 332]
335. ~32 | 40 [avatar split clause 144,332,295]
355. $false <- (33) [resolution 301,149]
356. ~33 [avatar contradiction clause 355]
364. $false <- (8, ~26) [resolution 186,267]
366. ~8 | 26 [avatar contradiction clause 364]
372. humble(paul) [resolution 255,149]
374. 22 [avatar split clause 372,247]
442. $false <- (24, 40) [resolution 258,334]
445. ~24 | ~40 [avatar contradiction clause 442]
465. ~humble(paul) | old(paul) <- (32) [resolution 124,297]
469. old(paul) <- (22, 32) [subsumption resolution 465,249]
471. ~curious(paul) <- (22, 32) [resolution 469,97]
472. $false <- (5, 22, 32) [subsumption resolution 471,173]
473. ~5 | ~22 | ~32 [avatar contradiction clause 472]
474. $false [avatar sat refutation 187,268,302,335,356,366,374,445,473]
% SZS output end Proof for 5989450781779927290513147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is either patient or not old.
If someone is not kind then someone is either generous or not curious.
If susan is either not funny or not rich then someone is either not happy or not strong.
If someone is happy or not creative then someone is both quiet and generous and vice versa.
If mary is not creative then fred is either funny or not old and vice versa.
Everyone who is not tall or not brave is not patient and vice versa.
Everyone who is not patient is strong.
If someone is both tall and not generous then someone is not rich and vice versa.
If mary is either humble or calm then someone is both old and curious.
Everyone who is quiet is both not rich and curious.
Everyone who is tall or happy is either patient or funny.
Everyone who is strong is creative or tall.
Everyone who is not creative is either not patient or not happy and vice versa.
Everyone who is not kind or rich is happy and vice versa.
If someone is either not strong or kind then lucy is both brave and strong.
Everyone who is not old or happy is both not creative and kind and vice versa.
John is either not strong or tall.
Someone is both humble and not creative.
Susan is not old.
Someone is quiet or funny.
Someone is rich.
Someone is patient or rich.
Someone is rich or brave.
Someone is wise or not creative. | Susan is funny. | entailment | (![X]:(patient(X)=>(patient(X)<~>~old(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((~funny(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
((?[X]:((happy(X)|~creative(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
((~creative(mary))<=>((funny(fred)<~>~old(fred))))&
(![X]:((~tall(X)|~brave(X))<=>~patient(X)))&
(![X]:(~patient(X)=>strong(X)))&
((?[X]:((tall(X)&~generous(X))))<=>(?[X]:(~rich(X))))&
(((humble(mary)<~>calm(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:(quiet(X)=>(~rich(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(patient(X)<~>funny(X))))&
(![X]:(strong(X)=>(creative(X)|tall(X))))&
(![X]:(~creative(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((~kind(X)|rich(X))<=>happy(X)))&
((?[X]:((~strong(X)<~>kind(X))))=>((brave(lucy)&strong(lucy))))&
(![X]:((~old(X)|happy(X))<=>(~creative(X)&kind(X))))&
((~strong(john)<~>tall(john)))&
(?[X]:((humble(X)&~creative(X))))&
(~old(susan))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((rich(X)|brave(X))))&
(?[X]:((wise(X)|~creative(X)))) | funny(susan) | [
"p0",
"p10",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4021190718833487593267689
% SZS output start Proof for 4021190718833487593267689
1. ! [X0] : (patient(X0) => (patient(X0) <~> ~old(X0))) [input p0]
11. ! [X0] : ((happy(X0) | tall(X0)) => (patient(X0) <~> funny(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> (~patient(X0) <~> ~happy(X0))) [input p12]
14. ! [X0] : ((rich(X0) | ~kind(X0)) <=> happy(X0)) [input p13]
16. ! [X0] : ((happy(X0) | ~old(X0)) <=> (kind(X0) & ~creative(X0))) [input p15]
19. ~old(susan) [input p18]
25. ~funny(susan) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~old(X0)) | ~patient(X0)) [ennf transformation 1]
36. ! [X0] : ((patient(X0) <~> funny(X0)) | (~happy(X0) & ~tall(X0))) [ennf transformation 11]
40. ! [X0] : (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~patient(X0)) [nnf transformation 30]
64. ! [X0] : (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (~happy(X0) & ~tall(X0))) [nnf transformation 36]
65. ! [X0] : ((~creative(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | creative(X0))) [nnf transformation 13]
66. ! [X0] : (((rich(X0) | ~kind(X0)) | ~happy(X0)) & (happy(X0) | (~rich(X0) & kind(X0)))) [nnf transformation 14]
67. ! [X0] : ((rich(X0) | ~kind(X0) | ~happy(X0)) & (happy(X0) | (~rich(X0) & kind(X0)))) [flattening 66]
69. ! [X0] : (((happy(X0) | ~old(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 16]
70. ! [X0] : ((happy(X0) | ~old(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [flattening 69]
83. old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 40]
113. ~happy(X0) | patient(X0) | funny(X0) [cnf transformation 64]
117. ~happy(X0) | ~patient(X0) | creative(X0) [cnf transformation 65]
118. creative(X0) | patient(X0) | happy(X0) [cnf transformation 65]
121. happy(X0) | kind(X0) [cnf transformation 67]
122. ~rich(X0) | happy(X0) [cnf transformation 67]
123. ~happy(X0) | ~kind(X0) | rich(X0) [cnf transformation 67]
128. ~creative(X0) | old(X0) [cnf transformation 70]
131. kind(X0) | ~happy(X0) [cnf transformation 70]
137. ~old(susan) [cnf transformation 19]
142. ~funny(susan) [cnf transformation 25]
143. ~patient(X0) | old(X0) [duplicate literal removal 83]
145. 1 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (1) [avatar component clause 145]
158. 4 <=> rich(susan) [avatar definition]
159. ~rich(susan) <- (~4) [avatar component clause 158]
160. rich(susan) <- (4) [avatar component clause 158]
162. 5 <=> funny(susan) [avatar definition]
164. ~funny(susan) <- (~5) [avatar component clause 162]
284. kind(X0) [subsumption resolution 131,121]
285. 1 [avatar split clause 284,145]
323. ~5 [avatar split clause 142,162]
467. patient(X1) | happy(X1) | old(X1) [resolution 118,128]
471. happy(X1) | old(X1) [subsumption resolution 467,143]
554. old(X0) | ~kind(X0) | rich(X0) [resolution 471,123]
562. rich(X0) | old(X0) <- (1) [subsumption resolution 554,146]
662. old(susan) <- (1, ~4) [resolution 562,159]
667. $false <- (1, ~4) [subsumption resolution 662,137]
668. ~1 | 4 [avatar contradiction clause 667]
669. happy(susan) <- (4) [resolution 160,122]
671. ~patient(susan) | creative(susan) <- (4) [resolution 669,117]
673. patient(susan) | funny(susan) <- (4) [resolution 669,113]
675. 63 <=> creative(susan) [avatar definition]
677. creative(susan) <- (63) [avatar component clause 675]
679. 64 <=> patient(susan) [avatar definition]
682. 63 | ~64 | ~4 [avatar split clause 671,158,679,675]
683. patient(susan) <- (4, ~5) [subsumption resolution 673,164]
684. 64 | ~4 | 5 [avatar split clause 683,162,158,679]
688. old(susan) <- (63) [resolution 677,128]
691. $false <- (63) [subsumption resolution 688,137]
692. ~63 [avatar contradiction clause 691]
693. $false [avatar sat refutation 285,323,668,682,684,692]
% SZS output end Proof for 4021190718833487593267689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or calm is both not calm and not generous.
If someone is not wise then susan is old or patient.
Everyone who is rich or creative is not brave and vice versa.
Everyone who is either not wise or wise is not tall or wise.
If someone is either quiet or strong then someone is not wise or not patient and vice versa.
If someone is either not generous or not strong then someone is both patient and not funny and vice versa.
If someone is either not generous or rich then fred is not funny or not curious.
Everyone who is not creative is not quiet or not old and vice versa.
Everyone who is both quiet and strong is either generous or not calm and vice versa.
If susan is both calm and not wise then fred is kind.
If someone is either not kind or not old then fred is either not wise or kind.
If paul is not old or not happy then john is both not happy and happy and vice versa.
If someone is either generous or rich then susan is both old and not patient and vice versa.
Everyone who is wise or not humble is not humble.
Everyone who is not creative is both rich and calm and vice versa.
If lucy is either not funny or patient then susan is both not curious and not calm.
Someone is kind or not creative.
Someone is either not old or quiet.
Someone is wise or not patient.
Someone is happy or not humble.
Someone is either not funny or calm.
Someone is either not calm or happy.
Someone is either quiet or rich. | Fred is not quiet. | contradiction | (![X]:((~quiet(X)|calm(X))=>(~calm(X)&~generous(X))))&
((?[X]:(~wise(X)))=>((old(susan)|patient(susan))))&
(![X]:((rich(X)|creative(X))<=>~brave(X)))&
(![X]:((~wise(X)<~>wise(X))=>(~tall(X)|wise(X))))&
((?[X]:((quiet(X)<~>strong(X))))<=>(?[X]:((~wise(X)|~patient(X)))))&
((?[X]:((~generous(X)<~>~strong(X))))<=>(?[X]:((patient(X)&~funny(X)))))&
((?[X]:((~generous(X)<~>rich(X))))=>((~funny(fred)|~curious(fred))))&
(![X]:(~creative(X)<=>(~quiet(X)|~old(X))))&
(![X]:((quiet(X)&strong(X))<=>(generous(X)<~>~calm(X))))&
(((calm(susan)&~wise(susan)))=>(kind(fred)))&
((?[X]:((~kind(X)<~>~old(X))))=>((~wise(fred)<~>kind(fred))))&
(((~old(paul)|~happy(paul)))<=>((~happy(john)&happy(john))))&
((?[X]:((generous(X)<~>rich(X))))<=>((old(susan)&~patient(susan))))&
(![X]:((wise(X)|~humble(X))=>~humble(X)))&
(![X]:(~creative(X)<=>(rich(X)&calm(X))))&
(((~funny(lucy)<~>patient(lucy)))=>((~curious(susan)&~calm(susan))))&
(?[X]:((kind(X)|~creative(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:((quiet(X)<~>rich(X)))) | ~quiet(fred) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2788672120316013965703424
% SZS output start Proof for 2788672120316013965703424
1. ! [X0] : ((calm(X0) | ~quiet(X0)) => (~generous(X0) & ~calm(X0))) [input p0]
9. ! [X0] : ((strong(X0) & quiet(X0)) <=> (generous(X0) <~> ~calm(X0))) [input p8]
24. ~quiet(fred) [input hypothesis]
30. ! [X0] : ((~generous(X0) & ~calm(X0)) | (~calm(X0) & quiet(X0))) [ennf transformation 1]
50. ! [X0] : (((strong(X0) & quiet(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (~strong(X0) | ~quiet(X0)))) [nnf transformation 9]
51. ! [X0] : (((strong(X0) & quiet(X0)) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) & (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | ~strong(X0) | ~quiet(X0))) [flattening 50]
82. ~calm(X0) | ~calm(X0) [cnf transformation 30]
83. ~generous(X0) | quiet(X0) [cnf transformation 30]
104. quiet(X0) | generous(X0) | calm(X0) [cnf transformation 51]
141. ~quiet(fred) [cnf transformation 24]
142. ~calm(X0) [duplicate literal removal 82]
218. quiet(X0) | generous(X0) [subsumption resolution 104,142]
219. quiet(X0) [subsumption resolution 218,83]
300. $false [subsumption resolution 141,219]
% SZS output end Proof for 2788672120316013965703424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not rich or calm.
Everyone who is not old or funny is either not happy or not creative.
If paul is not old then john is wise.
Everyone who is both not kind and not wise is tall and vice versa.
Everyone who is curious or not strong is both strong and not curious.
Everyone who is either not curious or not creative is either humble or not funny.
Everyone who is both brave and not happy is both calm and curious.
Everyone who is not kind or not tall is both patient and not brave and vice versa.
Everyone who is not kind or rich is either not generous or strong and vice versa.
If someone is rich then someone is not kind.
Everyone who is either brave or rich is not rich or humble.
Everyone who is not creative is not quiet or quiet and vice versa.
Everyone who is not kind is both patient and curious and vice versa.
If fred is not calm or not kind then someone is not calm or old.
Everyone who is creative is either wise or not happy and vice versa.
Someone is curious or patient.
Susan is calm or not old.
Someone is either not rich or not old.
Paul is patient.
Susan is not tall or not creative. | John is not funny. | neutral | (![X]:(strong(X)=>(~rich(X)<~>calm(X))))&
(![X]:((~old(X)|funny(X))=>(~happy(X)<~>~creative(X))))&
((~old(paul))=>(wise(john)))&
(![X]:((~kind(X)&~wise(X))<=>tall(X)))&
(![X]:((curious(X)|~strong(X))=>(strong(X)&~curious(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(humble(X)<~>~funny(X))))&
(![X]:((brave(X)&~happy(X))=>(calm(X)&curious(X))))&
(![X]:((~kind(X)|~tall(X))<=>(patient(X)&~brave(X))))&
(![X]:((~kind(X)|rich(X))<=>(~generous(X)<~>strong(X))))&
((?[X]:(rich(X)))=>(?[X]:(~kind(X))))&
(![X]:((brave(X)<~>rich(X))=>(~rich(X)|humble(X))))&
(![X]:(~creative(X)<=>(~quiet(X)|quiet(X))))&
(![X]:(~kind(X)<=>(patient(X)&curious(X))))&
(((~calm(fred)|~kind(fred)))=>(?[X]:((~calm(X)|old(X)))))&
(![X]:(creative(X)<=>(wise(X)<~>~happy(X))))&
(?[X]:((curious(X)|patient(X))))&
((calm(susan)|~old(susan)))&
(?[X]:((~rich(X)<~>~old(X))))&
(patient(paul))&
((~tall(susan)|~creative(susan))) | ~funny(john) | [] | null | 0 |
If someone is not patient then mary is calm.
If paul is creative or rich then lucy is not kind.
Everyone who is quiet is either curious or kind and vice versa.
If paul is quiet or humble then someone is not kind or brave.
Everyone who is either not curious or not kind is either not funny or old and vice versa.
If someone is patient or not old then fred is either tall or kind.
If john is either not quiet or not generous then paul is calm or not calm.
If paul is not kind then someone is either not brave or wise and vice versa.
Everyone who is either patient or curious is rich or not patient.
If fred is not calm or patient then someone is not funny.
Everyone who is both not calm and not funny is not rich and vice versa.
If john is both not generous and quiet then someone is not kind or kind and vice versa.
Everyone who is brave or not strong is either not curious or creative.
Everyone who is either generous or not humble is either brave or not kind.
Everyone who is tall or not happy is tall and vice versa.
If john is both brave and humble then fred is not old and vice versa.
Susan is humble or old.
Someone is old or happy.
Someone is both strong and not creative.
Someone is tall or not rich.
Someone is kind or not kind.
Mary is both patient and not curious.
Susan is either funny or not old.
Someone is both not old and brave. | Mary is rich. | entailment | ((?[X]:(~patient(X)))=>(calm(mary)))&
(((creative(paul)|rich(paul)))=>(~kind(lucy)))&
(![X]:(quiet(X)<=>(curious(X)<~>kind(X))))&
(((quiet(paul)|humble(paul)))=>(?[X]:((~kind(X)|brave(X)))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~funny(X)<~>old(X))))&
((?[X]:((patient(X)|~old(X))))=>((tall(fred)<~>kind(fred))))&
(((~quiet(john)<~>~generous(john)))=>((calm(paul)|~calm(paul))))&
((~kind(paul))<=>(?[X]:((~brave(X)<~>wise(X)))))&
(![X]:((patient(X)<~>curious(X))=>(rich(X)|~patient(X))))&
(((~calm(fred)|patient(fred)))=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)&~funny(X))<=>~rich(X)))&
(((~generous(john)&quiet(john)))<=>(?[X]:((~kind(X)|kind(X)))))&
(![X]:((brave(X)|~strong(X))=>(~curious(X)<~>creative(X))))&
(![X]:((generous(X)<~>~humble(X))=>(brave(X)<~>~kind(X))))&
(![X]:((tall(X)|~happy(X))<=>tall(X)))&
(((brave(john)&humble(john)))<=>(~old(fred)))&
((humble(susan)|old(susan)))&
(?[X]:((old(X)|happy(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((kind(X)|~kind(X))))&
((patient(mary)&~curious(mary)))&
((funny(susan)<~>~old(susan)))&
(?[X]:((~old(X)&brave(X)))) | rich(mary) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4311594082751260300432375
% SZS output start Proof for 4311594082751260300432375
9. ! [X0] : ((patient(X0) <~> curious(X0)) => (~patient(X0) | rich(X0))) [input p8]
22. ~curious(mary) & patient(mary) [input p21]
25. ~rich(mary) [input hypothesis]
34. ! [X0] : ((~patient(X0) | rich(X0)) | (patient(X0) <=> curious(X0))) [ennf transformation 9]
35. ! [X0] : (~patient(X0) | rich(X0) | (patient(X0) <=> curious(X0))) [flattening 34]
49. ! [X0] : (~patient(X0) | rich(X0) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) [nnf transformation 35]
103. ~patient(X0) | rich(X0) | curious(X0) | ~patient(X0) [cnf transformation 49]
132. patient(mary) [cnf transformation 22]
133. ~curious(mary) [cnf transformation 22]
138. ~rich(mary) [cnf transformation 25]
139. ~patient(X0) | rich(X0) | curious(X0) [duplicate literal removal 103]
348. rich(mary) | curious(mary) [resolution 139,132]
350. curious(mary) [subsumption resolution 348,138]
351. $false [subsumption resolution 350,133]
% SZS output end Proof for 4311594082751260300432375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not humble then someone is wise or not patient and vice versa. Everyone who is both strong and generous is both humble and not creative and vice versa. Everyone who is either not kind or not brave is not creative. If someone is not curious then mary is not calm or not generous and vice versa. Everyone who is either not old or curious is both curious and not tall. Everyone who is both not creative and strong is humble or not tall. Everyone who is both strong and not funny is happy or not calm and vice versa. If someone is rich then someone is both happy and not brave and vice versa. Everyone who is either not old or not generous is not creative and vice versa. Everyone who is both not creative and not humble is tall and vice versa. Everyone who is both rich and not humble is either not humble or curious. If someone is both strong and old then someone is brave or not happy and vice versa. If paul is not tall then john is rich or not funny and vice versa. If someone is old or not happy then john is not curious or kind. Everyone who is not kind is not generous or creative. Everyone who is old or not calm is quiet or not tall. Someone is not old or not curious. John is brave or happy. John is calm or not happy. Alice is not strong or not rich. Someone is not old or not kind. | Mary is calm. | entailment | ((?[X]:((tall(X)&~humble(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((strong(X)&generous(X))<=>(humble(X)&~creative(X))))&
(![X]:((~kind(X)<~>~brave(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>((~calm(mary)|~generous(mary))))&
(![X]:((~old(X)<~>curious(X))=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)&strong(X))=>(humble(X)|~tall(X))))&
(![X]:((strong(X)&~funny(X))<=>(happy(X)|~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~creative(X)&~humble(X))<=>tall(X)))&
(![X]:((rich(X)&~humble(X))=>(~humble(X)<~>curious(X))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
((~tall(paul))<=>((rich(john)|~funny(john))))&
((?[X]:((old(X)|~happy(X))))=>((~curious(john)|kind(john))))&
(![X]:(~kind(X)=>(~generous(X)|creative(X))))&
(![X]:((old(X)|~calm(X))=>(quiet(X)|~tall(X))))&
(?[X]:((~old(X)|~curious(X))))&
((brave(john)|happy(john)))&
((calm(john)|~happy(john)))&
((~strong(alice)|~rich(alice)))&
(?[X]:((~old(X)|~kind(X)))) | calm(mary) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 713542194150803714316262
% SZS output start Proof for 713542194150803714316262
2. ! [X0] : ((generous(X0) & strong(X0)) <=> (~creative(X0) & humble(X0))) [input p1]
4. ? [X0] : ~curious(X0) <=> (~generous(mary) | ~calm(mary)) [input p3]
5. ! [X0] : ((~old(X0) <~> curious(X0)) => (~tall(X0) & curious(X0))) [input p4]
6. ! [X0] : ((strong(X0) & ~creative(X0)) => (~tall(X0) | humble(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & strong(X0)) <=> (~calm(X0) | happy(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> tall(X0)) [input p9]
12. ? [X0] : (old(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | brave(X0)) [input p11]
22. ~calm(mary) [input hypothesis]
25. ? [X0] : (old(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | brave(X1)) [rectify 12]
28. ! [X0] : ((~tall(X0) & curious(X0)) | (~old(X0) <=> curious(X0))) [ennf transformation 5]
29. ! [X0] : ((~tall(X0) | humble(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 6]
30. ! [X0] : (~tall(X0) | humble(X0) | ~strong(X0) | creative(X0)) [flattening 29]
42. ! [X0] : (((generous(X0) & strong(X0)) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | (~generous(X0) | ~strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((generous(X0) & strong(X0)) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | ~generous(X0) | ~strong(X0))) [flattening 42]
45. (? [X0] : ~curious(X0) | (generous(mary) & calm(mary))) & ((~generous(mary) | ~calm(mary)) | ! [X0] : curious(X0)) [nnf transformation 4]
46. (? [X0] : ~curious(X0) | (generous(mary) & calm(mary))) & (~generous(mary) | ~calm(mary) | ! [X0] : curious(X0)) [flattening 45]
47. (? [X0] : ~curious(X0) | (generous(mary) & calm(mary))) & (~generous(mary) | ~calm(mary) | ! [X1] : curious(X1)) [rectify 46]
48. ? [X0] : ~curious(X0) => ~curious(sK2) [choice axiom]
49. (~curious(sK2) | (generous(mary) & calm(mary))) & (~generous(mary) | ~calm(mary) | ! [X1] : curious(X1)) [skolemisation 47,48]
50. ! [X0] : ((~tall(X0) & curious(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) [nnf transformation 28]
51. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | (funny(X0) | ~strong(X0)))) [nnf transformation 7]
52. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | funny(X0) | ~strong(X0))) [flattening 51]
58. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | creative(X0)) & (~creative(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 9]
59. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) | creative(X0)))) [nnf transformation 10]
60. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | humble(X0) | creative(X0))) [flattening 59]
62. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X1] : (~happy(X1) | brave(X1)) | ! [X0] : (~old(X0) | ~strong(X0))) [nnf transformation 25]
63. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X2] : (~happy(X2) | brave(X2)) | ! [X3] : (~old(X3) | ~strong(X3))) [rectify 62]
64. ? [X0] : (old(X0) & strong(X0)) => (old(sK5) & strong(sK5)) [choice axiom]
65. ? [X2] : (~happy(X2) | brave(X2)) => (~happy(sK6) | brave(sK6)) [choice axiom]
66. ((old(sK5) & strong(sK5)) | ! [X1] : (happy(X1) & ~brave(X1))) & ((~happy(sK6) | brave(sK6)) | ! [X3] : (~old(X3) | ~strong(X3))) [skolemisation 63,65,64]
78. ~generous(X0) | humble(X0) | ~strong(X0) [cnf transformation 43]
79. ~creative(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 43]
81. ~humble(X0) | creative(X0) | generous(X0) [cnf transformation 43]
85. ~curious(sK2) | calm(mary) [cnf transformation 49]
87. curious(X0) | curious(X0) | old(X0) [cnf transformation 50]
91. ~strong(X0) | humble(X0) | ~tall(X0) | creative(X0) [cnf transformation 30]
93. ~happy(X0) | strong(X0) [cnf transformation 52]
101. ~old(X0) | ~creative(X0) | generous(X0) [cnf transformation 58]
102. ~old(X0) | ~generous(X0) | creative(X0) [cnf transformation 58]
104. creative(X0) | humble(X0) | tall(X0) [cnf transformation 60]
109. ~happy(sK6) | brave(sK6) | ~old(X3) | ~strong(X3) [cnf transformation 66]
110. strong(sK5) | ~brave(X1) [cnf transformation 66]
111. strong(sK5) | happy(X1) [cnf transformation 66]
112. old(sK5) | ~brave(X1) [cnf transformation 66]
113. old(sK5) | happy(X1) [cnf transformation 66]
125. ~calm(mary) [cnf transformation 22]
127. old(X0) | curious(X0) [duplicate literal removal 87]
163. 9 <=> curious(sK2) [avatar definition]
165. ~curious(sK2) <- (~9) [avatar component clause 163]
168. 10 <=> calm(mary) [avatar definition]
171. 10 | ~9 [avatar split clause 85,163,168]
173. 11 <=> ! [X1] : curious(X1) [avatar definition]
174. curious(X1) <- (11) [avatar component clause 173]
198. 17 <=> ! [X1] : happy(X1) [avatar definition]
199. happy(X1) <- (17) [avatar component clause 198]
201. 18 <=> old(sK5) [avatar definition]
203. old(sK5) <- (18) [avatar component clause 201]
204. 17 | 18 [avatar split clause 113,201,198]
206. 19 <=> ! [X1] : ~brave(X1) [avatar definition]
207. ~brave(X1) <- (19) [avatar component clause 206]
208. 19 | 18 [avatar split clause 112,201,206]
210. 20 <=> strong(sK5) [avatar definition]
212. strong(sK5) <- (20) [avatar component clause 210]
213. 17 | 20 [avatar split clause 111,210,198]
214. 19 | 20 [avatar split clause 110,210,206]
216. 21 <=> ! [X3] : (~old(X3) | ~strong(X3)) [avatar definition]
217. ~old(X3) | ~strong(X3) <- (21) [avatar component clause 216]
219. 22 <=> brave(sK6) [avatar definition]
221. brave(sK6) <- (22) [avatar component clause 219]
223. 23 <=> happy(sK6) [avatar definition]
225. ~happy(sK6) <- (~23) [avatar component clause 223]
226. 21 | 22 | ~23 [avatar split clause 109,223,219,216]
252. 29 <=> ! [X0] : ~old(X0) [avatar definition]
253. ~old(X0) <- (29) [avatar component clause 252]
296. ~10 [avatar split clause 125,168]
302. $false <- (17, ~23) [resolution 225,199]
303. ~17 | 23 [avatar contradiction clause 302]
323. 41 <=> tall(sK5) [avatar definition]
324. tall(sK5) <- (41) [avatar component clause 323]
330. 42 <=> generous(sK5) [avatar definition]
331. ~generous(sK5) <- (~42) [avatar component clause 330]
332. generous(sK5) <- (42) [avatar component clause 330]
334. 43 <=> creative(sK5) [avatar definition]
335. creative(sK5) <- (43) [avatar component clause 334]
336. ~creative(sK5) <- (~43) [avatar component clause 334]
352. humble(sK5) | tall(sK5) <- (~43) [resolution 104,336]
363. 46 <=> humble(sK5) [avatar definition]
365. humble(sK5) <- (46) [avatar component clause 363]
366. 41 | 46 | 43 [avatar split clause 352,334,363,323]
397. humble(sK5) | ~tall(sK5) | creative(sK5) <- (20) [resolution 91,212]
400. humble(sK5) | creative(sK5) <- (20, 41) [subsumption resolution 397,324]
423. 43 | 46 | ~20 | ~41 [avatar split clause 400,323,210,363,334]
426. humble(sK5) | ~strong(sK5) <- (42) [resolution 332,78]
427. humble(sK5) <- (20, 42) [subsumption resolution 426,212]
428. 46 | ~20 | ~42 [avatar split clause 427,330,210,363]
435. strong(X1) <- (17) [resolution 199,93]
441. $false <- (19, 22) [resolution 221,207]
443. ~19 | ~22 [avatar contradiction clause 441]
453. ~old(X3) <- (17, 21) [subsumption resolution 217,435]
454. 29 | ~17 | ~21 [avatar split clause 453,216,198,252]
458. curious(X1) <- (29) [resolution 253,127]
459. 11 | ~29 [avatar split clause 458,252,173]
461. $false <- (~9, 11) [resolution 174,165]
464. 9 | ~11 [avatar contradiction clause 461]
468. ~generous(sK5) | creative(sK5) <- (18) [resolution 203,102]
469. ~creative(sK5) | generous(sK5) <- (18) [resolution 203,101]
480. ~generous(sK5) | ~strong(sK5) <- (43) [resolution 335,79]
482. ~strong(sK5) <- (42, 43) [subsumption resolution 480,332]
483. $false <- (20, 42, 43) [subsumption resolution 482,212]
484. ~20 | ~42 | ~43 [avatar contradiction clause 483]
487. 42 | ~43 | ~18 [avatar split clause 469,201,334,330]
488. 43 | ~42 | ~18 [avatar split clause 468,201,330,334]
510. creative(sK5) | generous(sK5) <- (46) [resolution 365,81]
513. generous(sK5) <- (~43, 46) [subsumption resolution 510,336]
514. $false <- (~42, ~43, 46) [subsumption resolution 513,331]
515. 42 | 43 | ~46 [avatar contradiction clause 514]
517. $false [avatar sat refutation 171,204,208,213,214,226,296,303,366,423,428,443,454,459,464,484,487,488,515]
% SZS output end Proof for 713542194150803714316262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and rich then lucy is either curious or not patient.
If lucy is patient or tall then someone is either not funny or not patient and vice versa.
If susan is generous or old then paul is not old and vice versa.
If someone is both not brave and curious then someone is not funny and vice versa.
Everyone who is either not humble or not strong is both calm and patient and vice versa.
Everyone who is both not creative and strong is both not calm and not humble.
Everyone who is either brave or not happy is both not patient and not funny and vice versa.
Everyone who is patient is both not humble and not calm.
If someone is humble then lucy is not rich or not generous.
Everyone who is both brave and wise is either kind or not curious and vice versa.
If someone is either curious or kind then john is both calm and not creative.
Everyone who is either not strong or not humble is both not calm and humble and vice versa.
If someone is happy or not quiet then someone is patient or kind and vice versa.
Everyone who is not rich is both not wise and humble.
If john is not curious or happy then someone is both humble and generous and vice versa.
Paul is either rich or not generous.
Alice is either curious or not tall.
Susan is not old.
Susan is either creative or not quiet.
Someone is both patient and rich.
Someone is not patient or tall. | Lucy is not calm. | neutral | ((?[X]:((wise(X)&rich(X))))=>((curious(lucy)<~>~patient(lucy))))&
(((patient(lucy)|tall(lucy)))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(((generous(susan)|old(susan)))<=>(~old(paul)))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(calm(X)&patient(X))))&
(![X]:((~creative(X)&strong(X))=>(~calm(X)&~humble(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)=>(~humble(X)&~calm(X))))&
((?[X]:(humble(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((brave(X)&wise(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((calm(john)&~creative(john))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)|~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:(~rich(X)=>(~wise(X)&humble(X))))&
(((~curious(john)|happy(john)))<=>(?[X]:((humble(X)&generous(X)))))&
((rich(paul)<~>~generous(paul)))&
((curious(alice)<~>~tall(alice)))&
(~old(susan))&
((creative(susan)<~>~quiet(susan)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((~patient(X)|tall(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is either curious or kind is not curious.
Everyone who is creative or old is not calm and vice versa.
Everyone who is not creative is not tall or funny and vice versa.
Everyone who is either not humble or not kind is not patient.
If someone is not happy then mary is not happy or not wise.
If someone is both curious and not rich then susan is either funny or not kind.
If someone is not curious or not creative then someone is both not wise and calm and vice versa.
Everyone who is either curious or not wise is both not calm and rich.
Everyone who is brave is not creative and vice versa.
If someone is either not curious or generous then mary is either kind or creative and vice versa.
Everyone who is not creative or not calm is not generous or not rich and vice versa.
Everyone who is happy is both curious and funny.
Everyone who is both not creative and not old is both calm and humble and vice versa.
Everyone who is brave or happy is humble or not wise.
If fred is not rich or not humble then someone is either quiet or rich and vice versa.
Lucy is either tall or curious.
Someone is not tall.
Susan is strong or funny.
Lucy is either not quiet or not tall.
Paul is rich.
Someone is either not old or rich. | Fred is tall. | neutral | (![X]:((curious(X)<~>kind(X))=>~curious(X)))&
(![X]:((creative(X)|old(X))<=>~calm(X)))&
(![X]:(~creative(X)<=>(~tall(X)|funny(X))))&
(![X]:((~humble(X)<~>~kind(X))=>~patient(X)))&
((?[X]:(~happy(X)))=>((~happy(mary)|~wise(mary))))&
((?[X]:((curious(X)&~rich(X))))=>((funny(susan)<~>~kind(susan))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((curious(X)<~>~wise(X))=>(~calm(X)&rich(X))))&
(![X]:(brave(X)<=>~creative(X)))&
((?[X]:((~curious(X)<~>generous(X))))<=>((kind(mary)<~>creative(mary))))&
(![X]:((~creative(X)|~calm(X))<=>(~generous(X)|~rich(X))))&
(![X]:(happy(X)=>(curious(X)&funny(X))))&
(![X]:((~creative(X)&~old(X))<=>(calm(X)&humble(X))))&
(![X]:((brave(X)|happy(X))=>(humble(X)|~wise(X))))&
(((~rich(fred)|~humble(fred)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(~tall(X)))&
((strong(susan)|funny(susan)))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(paul))&
(?[X]:((~old(X)<~>rich(X)))) | tall(fred) | [] | null | 0 |
If mary is both brave and not wise then alice is either not creative or not humble and vice versa.
If mary is not kind then someone is not generous or not rich and vice versa.
If fred is both rich and brave then someone is both not wise and not quiet.
If someone is strong then someone is both not strong and humble and vice versa.
If someone is either not happy or not calm then lucy is not humble.
Everyone who is both not brave and humble is either tall or kind and vice versa.
Everyone who is either kind or not funny is curious or tall and vice versa.
Everyone who is both not tall and old is not kind or curious.
If someone is either funny or not wise then someone is rich.
Everyone who is either not brave or patient is both generous and kind.
Everyone who is both not patient and not generous is not kind or not patient.
If someone is either funny or not rich then someone is old and vice versa.
Everyone who is both not wise and curious is not funny or not humble and vice versa.
Everyone who is not humble is not humble or not wise and vice versa.
Everyone who is patient is creative and vice versa.
If mary is not tall or not funny then someone is quiet or tall and vice versa.
Someone is not happy.
Paul is both not wise and not happy.
Fred is calm.
Mary is rich or happy.
Fred is not old.
Someone is both happy and rich.
Someone is both not happy and old.
Paul is either rich or not patient. | Fred is rich. | neutral | (((brave(mary)&~wise(mary)))<=>((~creative(alice)<~>~humble(alice))))&
((~kind(mary))<=>(?[X]:((~generous(X)|~rich(X)))))&
(((rich(fred)&brave(fred)))=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&humble(X)))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(~humble(lucy)))&
(![X]:((~brave(X)&humble(X))<=>(tall(X)<~>kind(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(curious(X)|tall(X))))&
(![X]:((~tall(X)&old(X))=>(~kind(X)|curious(X))))&
((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>patient(X))=>(generous(X)&kind(X))))&
(![X]:((~patient(X)&~generous(X))=>(~kind(X)|~patient(X))))&
((?[X]:((funny(X)<~>~rich(X))))<=>(?[X]:(old(X))))&
(![X]:((~wise(X)&curious(X))<=>(~funny(X)|~humble(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~wise(X))))&
(![X]:(patient(X)<=>creative(X)))&
(((~tall(mary)|~funny(mary)))<=>(?[X]:((quiet(X)|tall(X)))))&
(?[X]:(~happy(X)))&
((~wise(paul)&~happy(paul)))&
(calm(fred))&
((rich(mary)|happy(mary)))&
(~old(fred))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:((~happy(X)&old(X))))&
((rich(paul)<~>~patient(paul))) | rich(fred) | [] | null | 0 |
If someone is either quiet or patient then susan is quiet and vice versa.
If susan is wise then susan is either funny or not old and vice versa.
If alice is both not curious and strong then mary is calm or tall and vice versa.
If alice is quiet then someone is both not rich and not funny.
If fred is either not generous or not strong then someone is both quiet and not brave and vice versa.
If someone is not creative then alice is either not creative or brave and vice versa.
Everyone who is either kind or not patient is both curious and funny and vice versa.
Everyone who is either old or curious is calm and vice versa.
Everyone who is patient or not happy is tall or kind.
If someone is not strong or not rich then someone is either happy or not rich.
If fred is either calm or curious then lucy is both kind and not calm and vice versa.
If someone is either happy or creative then susan is not old or not kind.
If mary is not funny or calm then someone is not patient or wise.
If someone is both happy and not generous then susan is both rich and not calm.
Everyone who is not old or not calm is old.
Everyone who is not old is either patient or kind and vice versa.
Someone is either patient or strong.
Someone is not curious or old.
Someone is funny.
Susan is either humble or funny.
Someone is either not quiet or curious.
Fred is both creative and not humble.
Lucy is kind or wise. | Susan is calm. | contradiction | ((?[X]:((quiet(X)<~>patient(X))))<=>(quiet(susan)))&
((wise(susan))<=>((funny(susan)<~>~old(susan))))&
(((~curious(alice)&strong(alice)))<=>((calm(mary)|tall(mary))))&
((quiet(alice))=>(?[X]:((~rich(X)&~funny(X)))))&
(((~generous(fred)<~>~strong(fred)))<=>(?[X]:((quiet(X)&~brave(X)))))&
((?[X]:(~creative(X)))<=>((~creative(alice)<~>brave(alice))))&
(![X]:((kind(X)<~>~patient(X))<=>(curious(X)&funny(X))))&
(![X]:((old(X)<~>curious(X))<=>calm(X)))&
(![X]:((patient(X)|~happy(X))=>(tall(X)|kind(X))))&
((?[X]:((~strong(X)|~rich(X))))=>(?[X]:((happy(X)<~>~rich(X)))))&
(((calm(fred)<~>curious(fred)))<=>((kind(lucy)&~calm(lucy))))&
((?[X]:((happy(X)<~>creative(X))))=>((~old(susan)|~kind(susan))))&
(((~funny(mary)|calm(mary)))=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((happy(X)&~generous(X))))=>((rich(susan)&~calm(susan))))&
(![X]:((~old(X)|~calm(X))=>old(X)))&
(![X]:(~old(X)<=>(patient(X)<~>kind(X))))&
(?[X]:((patient(X)<~>strong(X))))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:(funny(X)))&
((humble(susan)<~>funny(susan)))&
(?[X]:((~quiet(X)<~>curious(X))))&
((creative(fred)&~humble(fred)))&
((kind(lucy)|wise(lucy))) | calm(susan) | [
"p6",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2555905324385702341525900
% SZS output start Proof for 2555905324385702341525900
7. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> (funny(X0) & curious(X0))) [input p6]
8. ! [X0] : ((old(X0) <~> curious(X0)) <=> calm(X0)) [input p7]
15. ! [X0] : ((~calm(X0) | ~old(X0)) => old(X0)) [input p14]
16. ! [X0] : (~old(X0) <=> (patient(X0) <~> kind(X0))) [input p15]
24. calm(susan) [input hypothesis]
34. ! [X0] : (old(X0) | (calm(X0) & old(X0))) [ennf transformation 15]
52. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (~funny(X0) | ~curious(X0))) & ((funny(X0) & curious(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 7]
53. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | ~funny(X0) | ~curious(X0)) & ((funny(X0) & curious(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [flattening 52]
54. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ~calm(X0)) & (calm(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 8]
64. ! [X0] : ((~old(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | old(X0))) [nnf transformation 16]
101. ~kind(X0) | ~patient(X0) | curious(X0) [cnf transformation 53]
102. kind(X0) | curious(X0) | patient(X0) [cnf transformation 53]
110. ~calm(X0) | ~old(X0) | ~curious(X0) [cnf transformation 54]
129. old(X0) | old(X0) [cnf transformation 34]
133. ~old(X0) | kind(X0) | ~patient(X0) [cnf transformation 64]
134. ~old(X0) | patient(X0) | ~kind(X0) [cnf transformation 64]
146. calm(susan) [cnf transformation 24]
147. old(X0) [duplicate literal removal 129]
309. 34 <=> kind(susan) [avatar definition]
310. kind(susan) <- (34) [avatar component clause 309]
311. ~kind(susan) <- (~34) [avatar component clause 309]
335. 40 <=> calm(susan) [avatar definition]
336. calm(susan) <- (40) [avatar component clause 335]
344. ~kind(X0) | patient(X0) [subsumption resolution 134,147]
345. ~patient(X0) | kind(X0) [subsumption resolution 133,147]
377. 40 [avatar split clause 146,335]
394. curious(susan) | patient(susan) <- (~34) [resolution 102,311]
396. curious(X1) | patient(X1) | patient(X1) [resolution 102,344]
397. curious(X1) | patient(X1) [duplicate literal removal 396]
400. 48 <=> patient(susan) [avatar definition]
402. patient(susan) <- (48) [avatar component clause 400]
404. 49 <=> curious(susan) [avatar definition]
406. curious(susan) <- (49) [avatar component clause 404]
407. 48 | 49 | 34 [avatar split clause 394,309,404,400]
408. ~patient(susan) | curious(susan) <- (34) [resolution 310,101]
410. curious(susan) <- (34) [subsumption resolution 408,397]
411. 49 | ~34 [avatar split clause 410,309,404]
414. kind(susan) <- (48) [resolution 402,345]
416. $false <- (~34, 48) [subsumption resolution 414,311]
417. 34 | ~48 [avatar contradiction clause 416]
448. ~old(susan) | ~curious(susan) <- (40) [resolution 110,336]
453. ~curious(susan) <- (40) [subsumption resolution 448,147]
454. $false <- (40, 49) [subsumption resolution 453,406]
455. ~40 | ~49 [avatar contradiction clause 454]
456. $false [avatar sat refutation 377,407,411,417,455]
% SZS output end Proof for 2555905324385702341525900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is creative or happy and vice versa. Everyone who is both not curious and humble is quiet or wise. Everyone who is both old and not funny is either funny or not creative and vice versa. Everyone who is either not humble or not brave is both creative and patient. Everyone who is either humble or brave is not kind or not rich and vice versa. Everyone who is not strong or generous is not brave and vice versa. Everyone who is either funny or not tall is creative or strong and vice versa. If someone is either not wise or not old then john is humble or kind. If someone is both rich and quiet then mary is quiet and vice versa. If susan is both calm and not calm then someone is both patient and not happy and vice versa. Everyone who is both not quiet and not curious is either not patient or not funny and vice versa. Everyone who is not brave is not kind or funny. Everyone who is not old is wise or not happy. Everyone who is both not wise and not kind is both not old and wise and vice versa. Everyone who is both not generous and calm is both not patient and not creative. If fred is either curious or quiet then someone is either not rich or humble and vice versa. Someone is both not happy and not quiet. John is not brave. Paul is creative or kind. Mary is not tall. Someone is not old. Someone is both creative and not patient. Someone is both creative and not curious. | Mary is quiet. | entailment | (![X]:(kind(X)<=>(creative(X)|happy(X))))&
(![X]:((~curious(X)&humble(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)&~funny(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(creative(X)&patient(X))))&
(![X]:((humble(X)<~>brave(X))<=>(~kind(X)|~rich(X))))&
(![X]:((~strong(X)|generous(X))<=>~brave(X)))&
(![X]:((funny(X)<~>~tall(X))<=>(creative(X)|strong(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>((humble(john)|kind(john))))&
((?[X]:((rich(X)&quiet(X))))<=>(quiet(mary)))&
(((calm(susan)&~calm(susan)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:((~quiet(X)&~curious(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:(~brave(X)=>(~kind(X)|funny(X))))&
(![X]:(~old(X)=>(wise(X)|~happy(X))))&
(![X]:((~wise(X)&~kind(X))<=>(~old(X)&wise(X))))&
(![X]:((~generous(X)&calm(X))=>(~patient(X)&~creative(X))))&
(((curious(fred)<~>quiet(fred)))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(?[X]:((~happy(X)&~quiet(X))))&
(~brave(john))&
((creative(paul)|kind(paul)))&
(~tall(mary))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)&~patient(X))))&
(?[X]:((creative(X)&~curious(X)))) | quiet(mary) | [
"p0",
"p2",
"p3",
"p4",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2384929240159880350695349
% SZS output start Proof for 2384929240159880350695349
1. ! [X0] : (kind(X0) <=> (happy(X0) | creative(X0))) [input p0]
3. ! [X0] : ((~funny(X0) & old(X0)) <=> (funny(X0) <~> ~creative(X0))) [input p2]
4. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => (patient(X0) & creative(X0))) [input p3]
5. ! [X0] : ((humble(X0) <~> brave(X0)) <=> (~rich(X0) | ~kind(X0))) [input p4]
9. ? [X0] : (quiet(X0) & rich(X0)) <=> quiet(mary) [input p8]
10. (~calm(susan) & calm(susan)) <=> ? [X0] : (~happy(X0) & patient(X0)) [input p9]
11. ! [X0] : ((~curious(X0) & ~quiet(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : (~brave(X0) => (funny(X0) | ~kind(X0))) [input p11]
13. ! [X0] : (~old(X0) => (~happy(X0) | wise(X0))) [input p12]
14. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> (wise(X0) & ~old(X0))) [input p13]
23. ? [X0] : (~curious(X0) & creative(X0)) [input p22]
24. ~quiet(mary) [input hypothesis]
27. ! [X0] : ((patient(X0) & creative(X0)) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 4]
30. ! [X0] : ((funny(X0) | ~kind(X0)) | brave(X0)) [ennf transformation 12]
31. ! [X0] : (funny(X0) | ~kind(X0) | brave(X0)) [flattening 30]
32. ! [X0] : ((~happy(X0) | wise(X0)) | old(X0)) [ennf transformation 13]
33. ! [X0] : (~happy(X0) | wise(X0) | old(X0)) [flattening 32]
36. ! [X0] : ((kind(X0) | (~happy(X0) & ~creative(X0))) & ((happy(X0) | creative(X0)) | ~kind(X0))) [nnf transformation 1]
37. ! [X0] : ((kind(X0) | (~happy(X0) & ~creative(X0))) & (happy(X0) | creative(X0) | ~kind(X0))) [flattening 36]
38. ! [X0] : (((~funny(X0) & old(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (funny(X0) | ~old(X0)))) [nnf transformation 3]
39. ! [X0] : (((~funny(X0) & old(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | funny(X0) | ~old(X0))) [flattening 38]
40. ! [X0] : ((patient(X0) & creative(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 27]
41. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [flattening 41]
48. (? [X0] : (quiet(X0) & rich(X0)) | ~quiet(mary)) & (quiet(mary) | ! [X0] : (~quiet(X0) | ~rich(X0))) [nnf transformation 9]
49. (? [X0] : (quiet(X0) & rich(X0)) | ~quiet(mary)) & (quiet(mary) | ! [X1] : (~quiet(X1) | ~rich(X1))) [rectify 48]
50. ? [X0] : (quiet(X0) & rich(X0)) => (quiet(sK0) & rich(sK0)) [choice axiom]
51. ((quiet(sK0) & rich(sK0)) | ~quiet(mary)) & (quiet(mary) | ! [X1] : (~quiet(X1) | ~rich(X1))) [skolemisation 49,50]
52. ((~calm(susan) & calm(susan)) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X0] : (~happy(X0) & patient(X0)) | (calm(susan) | ~calm(susan))) [nnf transformation 10]
53. ((~calm(susan) & calm(susan)) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X0] : (~happy(X0) & patient(X0)) | calm(susan) | ~calm(susan)) [flattening 52]
54. ((~calm(susan) & calm(susan)) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X1] : (~happy(X1) & patient(X1)) | calm(susan) | ~calm(susan)) [rectify 53]
55. ? [X1] : (~happy(X1) & patient(X1)) => (~happy(sK1) & patient(sK1)) [choice axiom]
56. ((~calm(susan) & calm(susan)) | ! [X0] : (happy(X0) | ~patient(X0))) & ((~happy(sK1) & patient(sK1)) | calm(susan) | ~calm(susan)) [skolemisation 54,55]
57. ! [X0] : (((~curious(X0) & ~quiet(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (curious(X0) | quiet(X0)))) [nnf transformation 11]
58. ! [X0] : (((~curious(X0) & ~quiet(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | curious(X0) | quiet(X0))) [flattening 57]
59. ! [X0] : (((~kind(X0) & ~wise(X0)) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | (kind(X0) | wise(X0)))) [nnf transformation 14]
60. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | kind(X0) | wise(X0))) [flattening 59]
71. ? [X0] : (~curious(X0) & creative(X0)) => (~curious(sK6) & creative(sK6)) [choice axiom]
72. ~curious(sK6) & creative(sK6) [skolemisation 23,71]
74. ~creative(X0) | kind(X0) [cnf transformation 37]
77. ~creative(X0) | funny(X0) | funny(X0) | ~old(X0) [cnf transformation 39]
81. ~funny(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 39]
85. ~brave(X0) | patient(X0) | humble(X0) [cnf transformation 40]
92. ~brave(X0) | ~humble(X0) | rich(X0) [cnf transformation 42]
104. quiet(mary) | ~quiet(X1) | ~rich(X1) [cnf transformation 51]
109. calm(susan) | happy(X0) | ~patient(X0) [cnf transformation 56]
110. ~calm(susan) | happy(X0) | ~patient(X0) [cnf transformation 56]
112. patient(X0) | funny(X0) | curious(X0) | quiet(X0) [cnf transformation 58]
117. ~kind(X0) | funny(X0) | brave(X0) [cnf transformation 31]
118. ~happy(X0) | wise(X0) | old(X0) [cnf transformation 33]
121. ~wise(X0) | ~wise(X0) | old(X0) [cnf transformation 60]
141. creative(sK6) [cnf transformation 72]
142. ~curious(sK6) [cnf transformation 72]
143. ~quiet(mary) [cnf transformation 24]
145. ~wise(X0) | old(X0) [duplicate literal removal 121]
146. ~creative(X0) | funny(X0) | ~old(X0) [duplicate literal removal 77]
147. ~funny(X0) | ~creative(X0) [duplicate literal removal 81]
148. ~old(X0) | ~creative(X0) [subsumption resolution 146,147]
152. 1 <=> ! [X0] : (~wise(X0) | old(X0)) [avatar definition]
153. ~wise(X0) | old(X0) <- (1) [avatar component clause 152]
168. 5 <=> quiet(mary) [avatar definition]
182. 8 <=> ! [X1] : (~quiet(X1) | ~rich(X1)) [avatar definition]
183. ~rich(X1) | ~quiet(X1) <- (8) [avatar component clause 182]
184. 8 | 5 [avatar split clause 104,168,182]
186. 9 <=> ! [X0] : (happy(X0) | ~patient(X0)) [avatar definition]
187. ~patient(X0) | happy(X0) <- (9) [avatar component clause 186]
189. 10 <=> calm(susan) [avatar definition]
192. 9 | ~10 [avatar split clause 110,189,186]
193. 9 | 10 [avatar split clause 109,189,186]
194. 1 [avatar split clause 145,152]
226. ~5 [avatar split clause 143,168]
228. kind(sK6) [resolution 74,141]
319. funny(sK6) | brave(sK6) [resolution 117,228]
349. 31 <=> brave(sK6) [avatar definition]
351. brave(sK6) <- (31) [avatar component clause 349]
353. 32 <=> funny(sK6) [avatar definition]
355. funny(sK6) <- (32) [avatar component clause 353]
356. 31 | 32 [avatar split clause 319,353,349]
485. funny(X3) | curious(X3) | quiet(X3) | happy(X3) <- (9) [resolution 112,187]
531. 52 <=> rich(sK6) [avatar definition]
533. rich(sK6) <- (52) [avatar component clause 531]
535. 53 <=> humble(sK6) [avatar definition]
540. 54 <=> patient(sK6) [avatar definition]
542. patient(sK6) <- (54) [avatar component clause 540]
574. ~creative(X2) | quiet(X2) | happy(X2) | curious(X2) <- (9) [resolution 485,147]
579. ~creative(sK6) <- (32) [resolution 355,147]
581. 60 <=> quiet(sK6) [avatar definition]
582. quiet(sK6) <- (60) [avatar component clause 581]
585. $false <- (32) [subsumption resolution 579,141]
586. ~32 [avatar contradiction clause 585]
587. ~humble(sK6) | rich(sK6) <- (31) [resolution 351,92]
589. patient(sK6) | humble(sK6) <- (31) [resolution 351,85]
596. 61 <=> happy(sK6) [avatar definition]
598. happy(sK6) <- (61) [avatar component clause 596]
643. quiet(sK6) | happy(sK6) | curious(sK6) <- (9) [resolution 574,141]
678. ~quiet(sK6) <- (8, 52) [resolution 533,183]
679. $false <- (8, 52, 60) [subsumption resolution 678,582]
680. ~8 | ~52 | ~60 [avatar contradiction clause 679]
681. 52 | ~53 | ~31 [avatar split clause 587,349,535,531]
682. 53 | 54 | ~31 [avatar split clause 589,349,540,535]
688. happy(sK6) <- (9, 54) [resolution 542,187]
692. 61 | ~9 | ~54 [avatar split clause 688,540,186,596]
695. quiet(sK6) | happy(sK6) <- (9) [subsumption resolution 643,142]
696. 61 | 60 | ~9 [avatar split clause 695,186,581,596]
699. wise(sK6) | old(sK6) <- (61) [resolution 598,118]
701. old(sK6) <- (1, 61) [subsumption resolution 699,153]
834. ~creative(sK6) <- (1, 61) [resolution 701,148]
835. $false <- (1, 61) [subsumption resolution 834,141]
836. ~1 | ~61 [avatar contradiction clause 835]
837. $false [avatar sat refutation 184,192,193,194,226,356,586,680,681,682,692,696,836]
% SZS output end Proof for 2384929240159880350695349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and not curious is not humble or quiet.
If someone is either kind or strong then fred is both not kind and funny and vice versa.
Everyone who is either not brave or not rich is quiet or strong and vice versa.
If someone is both not wise and not curious then alice is wise and vice versa.
Everyone who is calm or generous is either old or calm and vice versa.
If fred is either not happy or not curious then someone is quiet.
Everyone who is either rich or not wise is not patient or funny and vice versa.
If mary is either not brave or not funny then someone is wise and vice versa.
If lucy is generous then someone is generous.
If alice is not quiet then susan is both not old and creative and vice versa.
If someone is either old or not wise then someone is both not generous and not calm and vice versa.
Everyone who is funny is rich or generous.
Everyone who is both old and not patient is not old and vice versa.
Everyone who is either brave or strong is not happy.
If fred is both happy and not happy then someone is not creative.
If paul is not happy then someone is both strong and creative and vice versa.
Alice is either strong or brave.
Fred is both quiet and not rich.
Alice is old or happy.
Fred is not creative.
Lucy is not rich or curious.
Someone is either old or not patient.
Fred is quiet or tall. | Mary is not generous. | contradiction | (![X]:((~tall(X)&~curious(X))=>(~humble(X)|quiet(X))))&
((?[X]:((kind(X)<~>strong(X))))<=>((~kind(fred)&funny(fred))))&
(![X]:((~brave(X)<~>~rich(X))<=>(quiet(X)|strong(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>(wise(alice)))&
(![X]:((calm(X)|generous(X))<=>(old(X)<~>calm(X))))&
(((~happy(fred)<~>~curious(fred)))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(~patient(X)|funny(X))))&
(((~brave(mary)<~>~funny(mary)))<=>(?[X]:(wise(X))))&
((generous(lucy))=>(?[X]:(generous(X))))&
((~quiet(alice))<=>((~old(susan)&creative(susan))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:(funny(X)=>(rich(X)|generous(X))))&
(![X]:((old(X)&~patient(X))<=>~old(X)))&
(![X]:((brave(X)<~>strong(X))=>~happy(X)))&
(((happy(fred)&~happy(fred)))=>(?[X]:(~creative(X))))&
((~happy(paul))<=>(?[X]:((strong(X)&creative(X)))))&
((strong(alice)<~>brave(alice)))&
((quiet(fred)&~rich(fred)))&
((old(alice)|happy(alice)))&
(~creative(fred))&
((~rich(lucy)|curious(lucy)))&
(?[X]:((old(X)<~>~patient(X))))&
((quiet(fred)|tall(fred))) | ~generous(mary) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4689176473186564109650741
% SZS output start Proof for 4689176473186564109650741
5. ! [X0] : ((generous(X0) | calm(X0)) <=> (old(X0) <~> calm(X0))) [input p4]
13. ! [X0] : ((~patient(X0) & old(X0)) <=> ~old(X0)) [input p12]
24. ~generous(mary) [input hypothesis]
46. ! [X0] : (((generous(X0) | calm(X0)) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (~generous(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((generous(X0) | calm(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (~generous(X0) & ~calm(X0)))) [flattening 46]
66. ! [X0] : (((~patient(X0) & old(X0)) | old(X0)) & (~old(X0) | (patient(X0) | ~old(X0)))) [nnf transformation 13]
67. ! [X0] : (((~patient(X0) & old(X0)) | old(X0)) & (~old(X0) | patient(X0) | ~old(X0))) [flattening 66]
96. ~calm(X0) | ~old(X0) | ~calm(X0) [cnf transformation 47]
98. generous(X0) | calm(X0) | calm(X0) | ~old(X0) [cnf transformation 47]
124. old(X0) | old(X0) [cnf transformation 67]
141. ~generous(mary) [cnf transformation 24]
143. old(X0) [duplicate literal removal 124]
144. ~old(X0) | ~calm(X0) [duplicate literal removal 96]
145. ~old(X0) | calm(X0) | generous(X0) [duplicate literal removal 98]
330. ~calm(X0) [resolution 144,143]
399. calm(X0) | generous(X0) [resolution 145,143]
400. generous(X0) [subsumption resolution 399,330]
404. $false [resolution 400,141]
% SZS output end Proof for 4689176473186564109650741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and happy is either not funny or brave and vice versa.
Everyone who is curious or humble is either not brave or patient and vice versa.
If someone is not calm then someone is not generous and vice versa.
If mary is funny or not strong then lucy is not happy and vice versa.
Everyone who is not calm or not happy is not old or not kind and vice versa.
If fred is brave then john is not old or brave.
Everyone who is not kind is either not funny or kind and vice versa.
Everyone who is not funny or old is both happy and brave and vice versa.
If someone is both not rich and not happy then someone is either old or humble and vice versa.
Everyone who is either patient or not kind is wise or rich and vice versa.
Everyone who is either not funny or creative is not curious or not wise.
If someone is generous or humble then someone is not happy.
If someone is calm or tall then alice is not brave.
If john is patient or old then someone is either not quiet or brave.
Everyone who is both funny and wise is not old.
If someone is both not strong and happy then someone is either not tall or generous and vice versa.
Paul is both not quiet and not calm.
Someone is either not humble or rich.
Someone is either not patient or curious.
Mary is either not quiet or happy.
Someone is either not old or creative. | Fred is kind. | neutral | (![X]:((~patient(X)&happy(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((curious(X)|humble(X))<=>(~brave(X)<~>patient(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~generous(X))))&
(((funny(mary)|~strong(mary)))<=>(~happy(lucy)))&
(![X]:((~calm(X)|~happy(X))<=>(~old(X)|~kind(X))))&
((brave(fred))=>((~old(john)|brave(john))))&
(![X]:(~kind(X)<=>(~funny(X)<~>kind(X))))&
(![X]:((~funny(X)|old(X))<=>(happy(X)&brave(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~kind(X))<=>(wise(X)|rich(X))))&
(![X]:((~funny(X)<~>creative(X))=>(~curious(X)|~wise(X))))&
((?[X]:((generous(X)|humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:((calm(X)|tall(X))))=>(~brave(alice)))&
(((patient(john)|old(john)))=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:((funny(X)&wise(X))=>~old(X)))&
((?[X]:((~strong(X)&happy(X))))<=>(?[X]:((~tall(X)<~>generous(X)))))&
((~quiet(paul)&~calm(paul)))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
((~quiet(mary)<~>happy(mary)))&
(?[X]:((~old(X)<~>creative(X)))) | kind(fred) | [] | null | 0 |
Everyone who is both curious and not rich is both not humble and wise and vice versa.
If john is tall then someone is not calm or strong and vice versa.
If someone is both creative and patient then someone is either not patient or wise and vice versa.
If john is both generous and brave then someone is both not wise and strong.
If someone is not funny then someone is both not calm and not quiet and vice versa.
If someone is not funny then fred is strong.
Everyone who is not tall or not brave is not happy or not brave.
If someone is both happy and funny then someone is either not strong or not creative.
If mary is not brave or strong then susan is not brave and vice versa.
Everyone who is not humble is either not wise or not tall.
Everyone who is both curious and quiet is both not brave and not humble and vice versa.
Everyone who is calm is both not humble and not patient and vice versa.
Everyone who is both curious and not creative is quiet or curious and vice versa.
Everyone who is either not creative or generous is either not strong or patient and vice versa.
If lucy is not patient or not generous then someone is both not old and calm.
Everyone who is humble is both tall and not kind and vice versa.
Fred is calm or not calm.
Paul is both not brave and not generous.
John is patient or tall.
Fred is not quiet.
Someone is both happy and creative.
Paul is either not humble or old.
Susan is not quiet.
Alice is either rich or not patient. | Fred is not strong. | contradiction | (![X]:((curious(X)&~rich(X))<=>(~humble(X)&wise(X))))&
((tall(john))<=>(?[X]:((~calm(X)|strong(X)))))&
((?[X]:((creative(X)&patient(X))))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(((generous(john)&brave(john)))=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~calm(X)&~quiet(X)))))&
((?[X]:(~funny(X)))=>(strong(fred)))&
(![X]:((~tall(X)|~brave(X))=>(~happy(X)|~brave(X))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(((~brave(mary)|strong(mary)))<=>(~brave(susan)))&
(![X]:(~humble(X)=>(~wise(X)<~>~tall(X))))&
(![X]:((curious(X)&quiet(X))<=>(~brave(X)&~humble(X))))&
(![X]:(calm(X)<=>(~humble(X)&~patient(X))))&
(![X]:((curious(X)&~creative(X))<=>(quiet(X)|curious(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~strong(X)<~>patient(X))))&
(((~patient(lucy)|~generous(lucy)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:(humble(X)<=>(tall(X)&~kind(X))))&
((calm(fred)|~calm(fred)))&
((~brave(paul)&~generous(paul)))&
((patient(john)|tall(john)))&
(~quiet(fred))&
(?[X]:((happy(X)&creative(X))))&
((~humble(paul)<~>old(paul)))&
(~quiet(susan))&
((rich(alice)<~>~patient(alice))) | ~strong(fred) | [
"p2",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6067630580795700257606827
% SZS output start Proof for 6067630580795700257606827
3. ? [X0] : (patient(X0) & creative(X0)) <=> ? [X0] : (~patient(X0) <~> wise(X0)) [input p2]
5. ? [X0] : ~funny(X0) <=> ? [X0] : (~quiet(X0) & ~calm(X0)) [input p4]
6. ? [X0] : ~funny(X0) => strong(fred) [input p5]
7. ! [X0] : ((~brave(X0) | ~tall(X0)) => (~brave(X0) | ~happy(X0))) [input p6]
10. ! [X0] : (~humble(X0) => (~wise(X0) <~> ~tall(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & curious(X0)) <=> (~humble(X0) & ~brave(X0))) [input p10]
12. ! [X0] : (calm(X0) <=> (~patient(X0) & ~humble(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & curious(X0)) <=> (curious(X0) | quiet(X0))) [input p12]
21. ? [X0] : (creative(X0) & happy(X0)) [input p20]
25. ~strong(fred) [input hypothesis]
26. ? [X0] : (patient(X0) & creative(X0)) <=> ? [X1] : (~patient(X1) <~> wise(X1)) [rectify 3]
27. ? [X0] : ~funny(X0) <=> ? [X1] : (~quiet(X1) & ~calm(X1)) [rectify 5]
31. strong(fred) | ! [X0] : funny(X0) [ennf transformation 6]
32. ! [X0] : ((~brave(X0) | ~happy(X0)) | (brave(X0) & tall(X0))) [ennf transformation 7]
33. ! [X0] : (~brave(X0) | ~happy(X0) | (brave(X0) & tall(X0))) [flattening 32]
35. ! [X0] : ((~wise(X0) <~> ~tall(X0)) | humble(X0)) [ennf transformation 10]
43. (? [X0] : (patient(X0) & creative(X0)) | ! [X1] : ((~patient(X1) | ~wise(X1)) & (wise(X1) | patient(X1)))) & (? [X1] : ((~wise(X1) | patient(X1)) & (wise(X1) | ~patient(X1))) | ! [X0] : (~patient(X0) | ~creative(X0))) [nnf transformation 26]
44. (? [X0] : (patient(X0) & creative(X0)) | ! [X1] : ((~patient(X1) | ~wise(X1)) & (wise(X1) | patient(X1)))) & (? [X2] : ((~wise(X2) | patient(X2)) & (wise(X2) | ~patient(X2))) | ! [X3] : (~patient(X3) | ~creative(X3))) [rectify 43]
45. ? [X0] : (patient(X0) & creative(X0)) => (patient(sK1) & creative(sK1)) [choice axiom]
46. ? [X2] : ((~wise(X2) | patient(X2)) & (wise(X2) | ~patient(X2))) => ((~wise(sK2) | patient(sK2)) & (wise(sK2) | ~patient(sK2))) [choice axiom]
47. ((patient(sK1) & creative(sK1)) | ! [X1] : ((~patient(X1) | ~wise(X1)) & (wise(X1) | patient(X1)))) & (((~wise(sK2) | patient(sK2)) & (wise(sK2) | ~patient(sK2))) | ! [X3] : (~patient(X3) | ~creative(X3))) [skolemisation 44,46,45]
50. (? [X0] : ~funny(X0) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X1] : (~quiet(X1) & ~calm(X1)) | ! [X0] : funny(X0)) [nnf transformation 27]
51. (? [X0] : ~funny(X0) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X2] : (~quiet(X2) & ~calm(X2)) | ! [X3] : funny(X3)) [rectify 50]
52. ? [X0] : ~funny(X0) => ~funny(sK4) [choice axiom]
53. ? [X2] : (~quiet(X2) & ~calm(X2)) => (~quiet(sK5) & ~calm(sK5)) [choice axiom]
54. (~funny(sK4) | ! [X1] : (quiet(X1) | calm(X1))) & ((~quiet(sK5) & ~calm(sK5)) | ! [X3] : funny(X3)) [skolemisation 51,53,52]
61. ! [X0] : (((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | humble(X0)) [nnf transformation 35]
62. ! [X0] : (((quiet(X0) & curious(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (~quiet(X0) | ~curious(X0)))) [nnf transformation 11]
63. ! [X0] : (((quiet(X0) & curious(X0)) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | ~quiet(X0) | ~curious(X0))) [flattening 62]
64. ! [X0] : ((calm(X0) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ~calm(X0))) [nnf transformation 12]
65. ! [X0] : ((calm(X0) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ~calm(X0))) [flattening 64]
66. ! [X0] : (((~creative(X0) & curious(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (creative(X0) | ~curious(X0)))) [nnf transformation 13]
67. ! [X0] : (((~creative(X0) & curious(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | creative(X0) | ~curious(X0))) [flattening 66]
73. ? [X0] : (creative(X0) & happy(X0)) => (creative(sK8) & happy(sK8)) [choice axiom]
74. creative(sK8) & happy(sK8) [skolemisation 21,73]
86. creative(sK1) | wise(X1) | patient(X1) [cnf transformation 47]
88. patient(sK1) | wise(X1) | patient(X1) [cnf transformation 47]
94. ~funny(sK4) | quiet(X1) | calm(X1) [cnf transformation 54]
95. strong(fred) | funny(X0) [cnf transformation 31]
96. ~happy(X0) | ~brave(X0) | tall(X0) [cnf transformation 33]
103. ~tall(X0) | ~wise(X0) | humble(X0) [cnf transformation 61]
106. ~quiet(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 63]
107. brave(X0) | humble(X0) | curious(X0) [cnf transformation 63]
109. ~calm(X0) | ~humble(X0) [cnf transformation 65]
110. ~patient(X0) | ~calm(X0) [cnf transformation 65]
113. ~quiet(X0) | curious(X0) [cnf transformation 67]
115. ~quiet(X0) | ~creative(X0) [cnf transformation 67]
116. ~creative(X0) | ~curious(X0) [cnf transformation 67]
137. happy(sK8) [cnf transformation 74]
138. creative(sK8) [cnf transformation 74]
144. ~strong(fred) [cnf transformation 25]
170. 7 <=> patient(sK1) [avatar definition]
172. patient(sK1) <- (7) [avatar component clause 170]
175. 8 <=> ! [X1] : (wise(X1) | patient(X1)) [avatar definition]
176. patient(X1) | wise(X1) <- (8) [avatar component clause 175]
177. 8 | 7 [avatar split clause 88,170,175]
179. 9 <=> creative(sK1) [avatar definition]
181. creative(sK1) <- (9) [avatar component clause 179]
183. 8 | 9 [avatar split clause 86,179,175]
216. 17 <=> ! [X1] : (quiet(X1) | calm(X1)) [avatar definition]
217. quiet(X1) | calm(X1) <- (17) [avatar component clause 216]
219. 18 <=> funny(sK4) [avatar definition]
221. ~funny(sK4) <- (~18) [avatar component clause 219]
222. 17 | ~18 [avatar split clause 94,219,216]
224. 19 <=> ! [X3] : funny(X3) [avatar definition]
225. funny(X3) <- (19) [avatar component clause 224]
237. 22 <=> strong(fred) [avatar definition]
240. 19 | 22 [avatar split clause 95,237,224]
314. ~22 [avatar split clause 144,237]
315. $false <- (~18, 19) [subsumption resolution 221,225]
316. 18 | ~19 [avatar contradiction clause 315]
318. ~curious(sK8) [resolution 116,138]
326. ~calm(sK1) <- (7) [resolution 172,110]
330. ~creative(X0) | calm(X0) <- (17) [resolution 217,115]
331. calm(X1) | curious(X1) <- (17) [resolution 217,113]
337. ~brave(sK8) | tall(sK8) [resolution 96,137]
339. 38 <=> tall(sK8) [avatar definition]
341. tall(sK8) <- (38) [avatar component clause 339]
343. 39 <=> brave(sK8) [avatar definition]
345. ~brave(sK8) <- (~39) [avatar component clause 343]
346. 38 | ~39 [avatar split clause 337,343,339]
359. calm(sK8) <- (17) [resolution 330,138]
360. calm(sK1) <- (9, 17) [resolution 330,181]
361. $false <- (7, 9, 17) [subsumption resolution 360,326]
362. ~7 | ~9 | ~17 [avatar contradiction clause 361]
366. ~calm(X1) | wise(X1) <- (8) [resolution 176,110]
397. ~humble(X0) | ~curious(X0) | calm(X0) <- (17) [resolution 106,217]
398. ~humble(X0) | calm(X0) <- (17) [subsumption resolution 397,331]
399. ~humble(X0) <- (17) [subsumption resolution 398,109]
404. humble(sK8) | curious(sK8) <- (~39) [resolution 107,345]
409. curious(sK8) <- (17, ~39) [subsumption resolution 404,399]
410. $false <- (17, ~39) [subsumption resolution 409,318]
411. ~17 | 39 [avatar contradiction clause 410]
412. ~wise(sK8) | humble(sK8) <- (38) [resolution 341,103]
413. ~wise(sK8) <- (17, 38) [subsumption resolution 412,399]
532. wise(sK8) <- (8, 17) [resolution 366,359]
533. $false <- (8, 17, 38) [subsumption resolution 532,413]
534. ~8 | ~17 | ~38 [avatar contradiction clause 533]
535. $false [avatar sat refutation 177,183,222,240,314,316,346,362,411,534]
% SZS output end Proof for 6067630580795700257606827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or funny is both not strong and not quiet and vice versa.
Everyone who is patient or not brave is wise or not kind and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
Everyone who is generous or not generous is not tall.
Everyone who is not quiet is creative.
Everyone who is strong is either not kind or creative and vice versa.
If someone is both not quiet and strong then paul is not wise or calm and vice versa.
If susan is not funny or patient then susan is happy or rich and vice versa.
Everyone who is either not wise or old is not creative or creative and vice versa.
Everyone who is both patient and strong is patient and vice versa.
Everyone who is generous is not strong or rich and vice versa.
If someone is both not calm and not old then susan is not strong or not curious and vice versa.
Everyone who is both not kind and old is both creative and not calm.
If susan is either patient or curious then alice is either not humble or not strong and vice versa.
If paul is not rich then susan is both happy and not tall and vice versa.
If someone is both not calm and old then someone is either not humble or funny and vice versa.
Someone is not generous.
Someone is funny or not patient.
Mary is not creative.
Someone is rich or not quiet.
Someone is rich or not brave.
Alice is both quiet and not generous.
Someone is not happy or strong.
Lucy is not calm or old. | Paul is calm. | contradiction | (![X]:((kind(X)|funny(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((patient(X)|~brave(X))<=>(wise(X)|~kind(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
(![X]:((generous(X)|~generous(X))=>~tall(X)))&
(![X]:(~quiet(X)=>creative(X)))&
(![X]:(strong(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~quiet(X)&strong(X))))<=>((~wise(paul)|calm(paul))))&
(((~funny(susan)|patient(susan)))<=>((happy(susan)|rich(susan))))&
(![X]:((~wise(X)<~>old(X))<=>(~creative(X)|creative(X))))&
(![X]:((patient(X)&strong(X))<=>patient(X)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~calm(X)&~old(X))))<=>((~strong(susan)|~curious(susan))))&
(![X]:((~kind(X)&old(X))=>(creative(X)&~calm(X))))&
(((patient(susan)<~>curious(susan)))<=>((~humble(alice)<~>~strong(alice))))&
((~rich(paul))<=>((happy(susan)&~tall(susan))))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)|~patient(X))))&
(~creative(mary))&
(?[X]:((rich(X)|~quiet(X))))&
(?[X]:((rich(X)|~brave(X))))&
((quiet(alice)&~generous(alice)))&
(?[X]:((~happy(X)|strong(X))))&
((~calm(lucy)|old(lucy))) | calm(paul) | [
"p0",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4588223230421062295816487
% SZS output start Proof for 4588223230421062295816487
1. ! [X0] : ((funny(X0) | kind(X0)) <=> (~quiet(X0) & ~strong(X0))) [input p0]
5. ! [X0] : (~quiet(X0) => creative(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (~kind(X0) <~> creative(X0))) [input p5]
7. ? [X0] : (strong(X0) & ~quiet(X0)) <=> (calm(paul) | ~wise(paul)) [input p6]
25. calm(paul) [input hypothesis]
29. ! [X0] : (creative(X0) | quiet(X0)) [ennf transformation 5]
32. ! [X0] : (((funny(X0) | kind(X0)) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | (~funny(X0) & ~kind(X0)))) [nnf transformation 1]
33. ! [X0] : ((funny(X0) | kind(X0) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | (~funny(X0) & ~kind(X0)))) [flattening 32]
37. ! [X0] : ((strong(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~strong(X0))) [nnf transformation 6]
38. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & ((calm(paul) | ~wise(paul)) | ! [X0] : (~strong(X0) | quiet(X0))) [nnf transformation 7]
39. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X0] : (~strong(X0) | quiet(X0))) [flattening 38]
40. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X1] : (~strong(X1) | quiet(X1))) [rectify 39]
41. ? [X0] : (strong(X0) & ~quiet(X0)) => (strong(sK0) & ~quiet(sK0)) [choice axiom]
42. ((strong(sK0) & ~quiet(sK0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X1] : (~strong(X1) | quiet(X1))) [skolemisation 40,41]
74. ~strong(X0) | ~kind(X0) [cnf transformation 33]
89. creative(X0) | quiet(X0) [cnf transformation 29]
91. ~creative(X0) | kind(X0) | ~strong(X0) [cnf transformation 37]
93. strong(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 37]
96. ~quiet(sK0) | ~calm(paul) [cnf transformation 42]
98. strong(sK0) | ~calm(paul) [cnf transformation 42]
148. calm(paul) [cnf transformation 25]
150. ~creative(X0) | ~kind(X0) [subsumption resolution 93,74]
151. ~creative(X0) | ~strong(X0) [subsumption resolution 91,150]
153. 1 <=> calm(paul) [avatar definition]
157. 2 <=> strong(sK0) [avatar definition]
159. strong(sK0) <- (2) [avatar component clause 157]
160. ~1 | 2 [avatar split clause 98,157,153]
167. 4 <=> quiet(sK0) [avatar definition]
169. ~quiet(sK0) <- (~4) [avatar component clause 167]
170. ~1 | ~4 [avatar split clause 96,167,153]
173. 5 <=> ! [X1] : (~strong(X1) | quiet(X1)) [avatar definition]
174. ~strong(X1) | quiet(X1) <- (5) [avatar component clause 173]
321. 1 [avatar split clause 148,153]
342. ~strong(X0) | quiet(X0) [resolution 151,89]
343. 5 [avatar split clause 342,173]
344. quiet(sK0) <- (2, 5) [resolution 174,159]
347. $false <- (2, ~4, 5) [subsumption resolution 344,169]
348. ~2 | 4 | ~5 [avatar contradiction clause 347]
349. $false [avatar sat refutation 160,170,321,343,348]
% SZS output end Proof for 4588223230421062295816487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or funny then someone is old or patient and vice versa.
Everyone who is either not creative or not kind is rich or not patient and vice versa.
If someone is not funny then someone is both wise and not humble.
If someone is strong then alice is not rich.
If someone is tall or not patient then someone is both not patient and creative and vice versa.
Everyone who is not creative is both not funny and not quiet.
If someone is not creative then someone is not tall or old.
If alice is both strong and not old then someone is either not tall or tall and vice versa.
Everyone who is quiet or not tall is calm.
Everyone who is both wise and happy is both not happy and not old.
Everyone who is calm or not generous is not calm.
If someone is either funny or happy then someone is not humble or tall.
Everyone who is either happy or not curious is both not rich and not strong.
If someone is creative then someone is strong and vice versa.
If mary is both not curious and funny then someone is either brave or not curious and vice versa.
Someone is both generous and not calm.
Someone is either not kind or calm.
John is not kind or not calm.
Fred is both humble and not generous.
Paul is both wise and not rich.
Someone is either not quiet or not old.
Paul is not patient. | Paul is happy. | contradiction | ((?[X]:((rich(X)|funny(X))))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:((~creative(X)<~>~kind(X))<=>(rich(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
((?[X]:((tall(X)|~patient(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:(~creative(X)=>(~funny(X)&~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)|old(X)))))&
(((strong(alice)&~old(alice)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((quiet(X)|~tall(X))=>calm(X)))&
(![X]:((wise(X)&happy(X))=>(~happy(X)&~old(X))))&
(![X]:((calm(X)|~generous(X))=>~calm(X)))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((happy(X)<~>~curious(X))=>(~rich(X)&~strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:(strong(X))))&
(((~curious(mary)&funny(mary)))<=>(?[X]:((brave(X)<~>~curious(X)))))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~kind(X)<~>calm(X))))&
((~kind(john)|~calm(john)))&
((humble(fred)&~generous(fred)))&
((wise(paul)&~rich(paul)))&
(?[X]:((~quiet(X)<~>~old(X))))&
(~patient(paul)) | happy(paul) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4859170152786757155793364
% SZS output start Proof for 4859170152786757155793364
10. ! [X0] : ((happy(X0) & wise(X0)) => (~old(X0) & ~happy(X0))) [input p9]
20. ~rich(paul) & wise(paul) [input p19]
23. happy(paul) [input hypothesis]
35. ! [X0] : ((~old(X0) & ~happy(X0)) | (~happy(X0) | ~wise(X0))) [ennf transformation 10]
36. ! [X0] : ((~old(X0) & ~happy(X0)) | ~happy(X0) | ~wise(X0)) [flattening 35]
115. ~happy(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 36]
140. wise(paul) [cnf transformation 20]
145. happy(paul) [cnf transformation 23]
147. ~happy(X0) | ~wise(X0) [duplicate literal removal 115]
352. ~wise(paul) [resolution 147,145]
353. $false [subsumption resolution 352,140]
% SZS output end Proof for 4859170152786757155793364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is curious or not humble. Everyone who is either not strong or not quiet is both calm and not generous and vice versa. If someone is either not funny or patient then someone is not patient or generous. If lucy is either quiet or kind then someone is generous or not old and vice versa. If mary is both not generous and humble then someone is both not funny and not rich and vice versa. Everyone who is not brave is quiet and vice versa. If someone is either old or not patient then john is not patient. If susan is wise then someone is wise or not creative and vice versa. Everyone who is either not kind or not curious is either rich or not curious and vice versa. If someone is either quiet or curious then lucy is either not strong or quiet. Everyone who is either not wise or old is either not brave or not calm and vice versa. Everyone who is both strong and not calm is not brave and vice versa. If someone is patient or not strong then fred is not calm and vice versa. Everyone who is either creative or happy is both kind and not happy. If someone is not kind or not old then someone is either not tall or not rich and vice versa. Everyone who is not creative or not patient is both not generous and not patient and vice versa. Someone is not happy. Someone is wise or not rich. Someone is either humble or calm. John is both humble and brave. Alice is quiet or curious. Paul is patient. Lucy is either funny or not kind. Someone is either not funny or calm. | John is tall. | neutral | (![X]:(calm(X)=>(curious(X)|~humble(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(calm(X)&~generous(X))))&
((?[X]:((~funny(X)<~>patient(X))))=>(?[X]:((~patient(X)|generous(X)))))&
(((quiet(lucy)<~>kind(lucy)))<=>(?[X]:((generous(X)|~old(X)))))&
(((~generous(mary)&humble(mary)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:(~brave(X)<=>quiet(X)))&
((?[X]:((old(X)<~>~patient(X))))=>(~patient(john)))&
((wise(susan))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~kind(X)<~>~curious(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((~strong(lucy)<~>quiet(lucy))))&
(![X]:((~wise(X)<~>old(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((strong(X)&~calm(X))<=>~brave(X)))&
((?[X]:((patient(X)|~strong(X))))<=>(~calm(fred)))&
(![X]:((creative(X)<~>happy(X))=>(kind(X)&~happy(X))))&
((?[X]:((~kind(X)|~old(X))))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(~generous(X)&~patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((humble(X)<~>calm(X))))&
((humble(john)&brave(john)))&
((quiet(alice)|curious(alice)))&
(patient(paul))&
((funny(lucy)<~>~kind(lucy)))&
(?[X]:((~funny(X)<~>calm(X)))) | tall(john) | [] | null | 0 |
Everyone who is both not rich and not brave is either wise or creative and vice versa.
If someone is both funny and not patient then someone is either not happy or kind and vice versa.
If someone is both kind and quiet then someone is patient.
Everyone who is either kind or strong is either not funny or kind.
Everyone who is either not calm or creative is creative or wise.
If mary is both not curious and old then someone is both not quiet and calm.
If paul is not rich or not happy then someone is rich or not old and vice versa.
Everyone who is curious or not quiet is both calm and curious and vice versa.
Everyone who is not brave or creative is not curious or generous.
Everyone who is both old and calm is both not funny and not tall and vice versa.
If someone is both not curious and strong then someone is both quiet and wise.
If paul is both rich and humble then mary is either happy or patient and vice versa.
If someone is not old or kind then fred is funny and vice versa.
Everyone who is not creative is not wise.
If someone is either not happy or not humble then lucy is not tall and vice versa.
Everyone who is either happy or not kind is funny and vice versa.
Someone is calm or wise.
Someone is not quiet.
Someone is rich or not humble.
Mary is both generous and creative.
Someone is brave or humble.
Someone is generous.
Someone is both not curious and not kind.
Mary is not rich or calm. | Lucy is patient. | neutral | (![X]:((~rich(X)&~brave(X))<=>(wise(X)<~>creative(X))))&
((?[X]:((funny(X)&~patient(X))))<=>(?[X]:((~happy(X)<~>kind(X)))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>strong(X))=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)<~>creative(X))=>(creative(X)|wise(X))))&
(((~curious(mary)&old(mary)))=>(?[X]:((~quiet(X)&calm(X)))))&
(((~rich(paul)|~happy(paul)))<=>(?[X]:((rich(X)|~old(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(calm(X)&curious(X))))&
(![X]:((~brave(X)|creative(X))=>(~curious(X)|generous(X))))&
(![X]:((old(X)&calm(X))<=>(~funny(X)&~tall(X))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((quiet(X)&wise(X)))))&
(((rich(paul)&humble(paul)))<=>((happy(mary)<~>patient(mary))))&
((?[X]:((~old(X)|kind(X))))<=>(funny(fred)))&
(![X]:(~creative(X)=>~wise(X)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(~tall(lucy)))&
(![X]:((happy(X)<~>~kind(X))<=>funny(X)))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~humble(X))))&
((generous(mary)&creative(mary)))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((~curious(X)&~kind(X))))&
((~rich(mary)|calm(mary))) | patient(lucy) | [] | null | 0 |
If someone is both not quiet and not kind then someone is either not curious or kind. Everyone who is old is either not humble or not brave and vice versa. Everyone who is creative or not kind is either not humble or creative and vice versa. Everyone who is calm is either not tall or happy and vice versa. If someone is either kind or happy then someone is funny. If mary is either not tall or not kind then alice is not strong or wise. Everyone who is not curious or not rich is either rich or not happy and vice versa. Everyone who is humble or not wise is either calm or wise and vice versa. If mary is either patient or not curious then john is either kind or strong and vice versa. If alice is either not brave or curious then alice is not calm. If john is either not generous or quiet then mary is not tall or not old and vice versa. Everyone who is both not quiet and not wise is happy. If paul is happy then someone is either calm or not generous. Everyone who is either calm or kind is either not tall or not old and vice versa. If john is either tall or not patient then someone is both quiet and not brave. Everyone who is kind or not brave is not brave or not calm and vice versa. Lucy is either calm or curious. Paul is not tall or generous. Paul is happy or patient. Someone is old. Someone is not tall or calm. Someone is both funny and not old. Someone is not rich. Alice is not creative or tall. | Mary is not happy. | neutral | ((?[X]:((~quiet(X)&~kind(X))))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(old(X)<=>(~humble(X)<~>~brave(X))))&
(![X]:((creative(X)|~kind(X))<=>(~humble(X)<~>creative(X))))&
(![X]:(calm(X)<=>(~tall(X)<~>happy(X))))&
((?[X]:((kind(X)<~>happy(X))))=>(?[X]:(funny(X))))&
(((~tall(mary)<~>~kind(mary)))=>((~strong(alice)|wise(alice))))&
(![X]:((~curious(X)|~rich(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(calm(X)<~>wise(X))))&
(((patient(mary)<~>~curious(mary)))<=>((kind(john)<~>strong(john))))&
(((~brave(alice)<~>curious(alice)))=>(~calm(alice)))&
(((~generous(john)<~>quiet(john)))<=>((~tall(mary)|~old(mary))))&
(![X]:((~quiet(X)&~wise(X))=>happy(X)))&
((happy(paul))=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>kind(X))<=>(~tall(X)<~>~old(X))))&
(((tall(john)<~>~patient(john)))=>(?[X]:((quiet(X)&~brave(X)))))&
(![X]:((kind(X)|~brave(X))<=>(~brave(X)|~calm(X))))&
((calm(lucy)<~>curious(lucy)))&
((~tall(paul)|generous(paul)))&
((happy(paul)|patient(paul)))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)|calm(X))))&
(?[X]:((funny(X)&~old(X))))&
(?[X]:(~rich(X)))&
((~creative(alice)|tall(alice))) | ~happy(mary) | [] | null | 0 |
If paul is not generous or not quiet then someone is either brave or curious and vice versa.
Everyone who is wise is both not kind and kind.
If someone is either not happy or strong then someone is not patient.
If lucy is not wise or not calm then someone is brave.
If susan is both creative and brave then someone is not curious.
If lucy is either quiet or brave then someone is both generous and quiet and vice versa.
If someone is patient or not brave then lucy is both calm and not kind.
If someone is not generous then someone is both not old and not wise.
If someone is not generous or creative then fred is humble and vice versa.
Everyone who is wise is calm and vice versa.
If someone is generous or not old then fred is either rich or not kind and vice versa.
If someone is either strong or wise then someone is either not creative or not patient and vice versa.
If someone is not strong or kind then someone is not calm and vice versa.
If someone is either tall or not rich then fred is not wise or not happy and vice versa.
If lucy is calm then paul is both not creative and not happy and vice versa.
If john is both happy and not creative then someone is brave or not tall.
Someone is either not calm or kind.
Someone is old.
Someone is old or calm.
Someone is curious or strong.
Someone is old or not humble.
Paul is not humble.
Fred is not tall. | Fred is calm. | contradiction | (((~generous(paul)|~quiet(paul)))<=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:(wise(X)=>(~kind(X)&kind(X))))&
((?[X]:((~happy(X)<~>strong(X))))=>(?[X]:(~patient(X))))&
(((~wise(lucy)|~calm(lucy)))=>(?[X]:(brave(X))))&
(((creative(susan)&brave(susan)))=>(?[X]:(~curious(X))))&
(((quiet(lucy)<~>brave(lucy)))<=>(?[X]:((generous(X)&quiet(X)))))&
((?[X]:((patient(X)|~brave(X))))=>((calm(lucy)&~kind(lucy))))&
((?[X]:(~generous(X)))=>(?[X]:((~old(X)&~wise(X)))))&
((?[X]:((~generous(X)|creative(X))))<=>(humble(fred)))&
(![X]:(wise(X)<=>calm(X)))&
((?[X]:((generous(X)|~old(X))))<=>((rich(fred)<~>~kind(fred))))&
((?[X]:((strong(X)<~>wise(X))))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
((?[X]:((~strong(X)|kind(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((tall(X)<~>~rich(X))))<=>((~wise(fred)|~happy(fred))))&
((calm(lucy))<=>((~creative(paul)&~happy(paul))))&
(((happy(john)&~creative(john)))=>(?[X]:((brave(X)|~tall(X)))))&
(?[X]:((~calm(X)<~>kind(X))))&
(?[X]:(old(X)))&
(?[X]:((old(X)|calm(X))))&
(?[X]:((curious(X)|strong(X))))&
(?[X]:((old(X)|~humble(X))))&
(~humble(paul))&
(~tall(fred)) | calm(fred) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3354985946970286748178519
% SZS output start Proof for 3354985946970286748178519
2. ! [X0] : (wise(X0) => (kind(X0) & ~kind(X0))) [input p1]
10. ! [X0] : (wise(X0) <=> calm(X0)) [input p9]
24. calm(fred) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~kind(X0)) | ~wise(X0)) [ennf transformation 2]
62. ! [X0] : ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))) [nnf transformation 10]
103. ~kind(X0) | ~wise(X0) [cnf transformation 29]
104. kind(X0) | ~wise(X0) [cnf transformation 29]
126. wise(X0) | ~calm(X0) [cnf transformation 62]
162. calm(fred) [cnf transformation 24]
191. ~wise(X0) [subsumption resolution 103,104]
293. ~calm(X0) [subsumption resolution 126,191]
426. $false [subsumption resolution 162,293]
% SZS output end Proof for 3354985946970286748178519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is calm then someone is not quiet.
If someone is either wise or not happy then someone is either not humble or not quiet.
If someone is either old or creative then someone is quiet.
Everyone who is either not humble or patient is either tall or creative and vice versa.
Everyone who is humble or brave is not tall or not humble.
Everyone who is either not humble or not strong is either patient or generous and vice versa.
Everyone who is not patient is both not happy and creative.
Everyone who is not calm or not strong is both not strong and strong and vice versa.
Everyone who is both not happy and not funny is either not brave or not rich and vice versa.
If someone is happy or not strong then fred is either not quiet or calm.
Everyone who is both wise and not quiet is not funny or not quiet and vice versa.
If someone is calm or not old then susan is either funny or happy and vice versa.
If fred is funny then susan is both not kind and not humble.
Everyone who is strong is both not humble and wise and vice versa.
Everyone who is happy or old is calm.
Everyone who is brave is either not strong or tall and vice versa.
Someone is not strong or old.
Lucy is not humble.
Someone is both patient and brave.
Someone is not tall or not rich.
Someone is either not kind or humble.
John is happy.
Someone is either not generous or not brave. | Fred is not wise. | contradiction | ((calm(mary))=>(?[X]:(~quiet(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
((?[X]:((old(X)<~>creative(X))))=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(tall(X)<~>creative(X))))&
(![X]:((humble(X)|brave(X))=>(~tall(X)|~humble(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(patient(X)<~>generous(X))))&
(![X]:(~patient(X)=>(~happy(X)&creative(X))))&
(![X]:((~calm(X)|~strong(X))<=>(~strong(X)&strong(X))))&
(![X]:((~happy(X)&~funny(X))<=>(~brave(X)<~>~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((~quiet(fred)<~>calm(fred))))&
(![X]:((wise(X)&~quiet(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((calm(X)|~old(X))))<=>((funny(susan)<~>happy(susan))))&
((funny(fred))=>((~kind(susan)&~humble(susan))))&
(![X]:(strong(X)<=>(~humble(X)&wise(X))))&
(![X]:((happy(X)|old(X))=>calm(X)))&
(![X]:(brave(X)<=>(~strong(X)<~>tall(X))))&
(?[X]:((~strong(X)|old(X))))&
(~humble(lucy))&
(?[X]:((patient(X)&brave(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((~kind(X)<~>humble(X))))&
(happy(john))&
(?[X]:((~generous(X)<~>~brave(X)))) | ~wise(fred) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6124359201338612753637175
% SZS output start Proof for 6124359201338612753637175
8. ! [X0] : ((~strong(X0) | ~calm(X0)) <=> (strong(X0) & ~strong(X0))) [input p7]
14. ! [X0] : (strong(X0) <=> (wise(X0) & ~humble(X0))) [input p13]
24. ~wise(fred) [input hypothesis]
48. ! [X0] : (((~strong(X0) | ~calm(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (strong(X0) & calm(X0)))) [nnf transformation 8]
49. ! [X0] : ((~strong(X0) | ~calm(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (strong(X0) & calm(X0)))) [flattening 48]
59. ! [X0] : ((strong(X0) | (~wise(X0) | humble(X0))) & ((wise(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 14]
60. ! [X0] : ((strong(X0) | ~wise(X0) | humble(X0)) & ((wise(X0) & ~humble(X0)) | ~strong(X0))) [flattening 59]
104. strong(X0) | strong(X0) [cnf transformation 49]
130. wise(X0) | ~strong(X0) [cnf transformation 60]
148. ~wise(fred) [cnf transformation 24]
149. strong(X0) [duplicate literal removal 104]
232. wise(X0) [subsumption resolution 130,149]
257. $false [subsumption resolution 148,232]
% SZS output end Proof for 6124359201338612753637175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm or humble then susan is either not kind or wise.
Everyone who is happy or not humble is creative and vice versa.
If someone is rich then someone is either not patient or not kind.
Everyone who is both quiet and not tall is either not calm or not humble.
If someone is both not brave and tall then someone is either brave or not rich and vice versa.
Everyone who is humble is either calm or rich.
Everyone who is not calm is either not funny or patient and vice versa.
Everyone who is either not funny or not calm is not tall or curious and vice versa.
If someone is rich then alice is not happy or strong.
If someone is old then someone is either wise or not generous and vice versa.
If someone is not quiet or not calm then someone is not calm or happy and vice versa.
Everyone who is either not brave or calm is old or not curious and vice versa.
If someone is not strong then alice is strong or calm and vice versa.
Everyone who is calm or not old is tall.
Everyone who is both rich and humble is not wise or curious.
If alice is either humble or tall then someone is either calm or quiet.
Someone is generous.
Lucy is not creative.
Lucy is generous or not strong.
Paul is either kind or happy.
Mary is either not curious or not kind.
Susan is both rich and not humble.
Someone is both not curious and old.
Lucy is calm. | Lucy is not happy. | entailment | (((calm(fred)|humble(fred)))=>((~kind(susan)<~>wise(susan))))&
(![X]:((happy(X)|~humble(X))<=>creative(X)))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)<~>~kind(X)))))&
(![X]:((quiet(X)&~tall(X))=>(~calm(X)<~>~humble(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(humble(X)=>(calm(X)<~>rich(X))))&
(![X]:(~calm(X)<=>(~funny(X)<~>patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~tall(X)|curious(X))))&
((?[X]:(rich(X)))=>((~happy(alice)|strong(alice))))&
((?[X]:(old(X)))<=>(?[X]:((wise(X)<~>~generous(X)))))&
((?[X]:((~quiet(X)|~calm(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(old(X)|~curious(X))))&
((?[X]:(~strong(X)))<=>((strong(alice)|calm(alice))))&
(![X]:((calm(X)|~old(X))=>tall(X)))&
(![X]:((rich(X)&humble(X))=>(~wise(X)|curious(X))))&
(((humble(alice)<~>tall(alice)))=>(?[X]:((calm(X)<~>quiet(X)))))&
(?[X]:(generous(X)))&
(~creative(lucy))&
((generous(lucy)|~strong(lucy)))&
((kind(paul)<~>happy(paul)))&
((~curious(mary)<~>~kind(mary)))&
((rich(susan)&~humble(susan)))&
(?[X]:((~curious(X)&old(X))))&
(calm(lucy)) | ~happy(lucy) | [
"p1",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 66218096917658930585251
% SZS output start Proof for 66218096917658930585251
2. ! [X0] : ((~humble(X0) | happy(X0)) <=> creative(X0)) [input p1]
18. ~creative(lucy) [input p17]
25. happy(lucy) [input hypothesis]
30. ! [X0] : ((~humble(X0) | happy(X0)) => creative(X0)) [unused predicate definition removal 2]
32. ! [X0] : (creative(X0) | (humble(X0) & ~happy(X0))) [ennf transformation 30]
88. ~happy(X0) | creative(X0) [cnf transformation 32]
138. ~creative(lucy) [cnf transformation 18]
149. happy(lucy) [cnf transformation 25]
342. creative(lucy) [resolution 88,149]
343. $false [subsumption resolution 342,138]
% SZS output end Proof for 66218096917658930585251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then john is both creative and patient and vice versa.
Everyone who is either not quiet or brave is both happy and creative and vice versa.
Everyone who is not calm is not funny or quiet.
If someone is not humble then someone is either brave or not quiet.
Everyone who is both not old and not generous is both not curious and rich.
Everyone who is not kind is happy or kind.
Everyone who is tall or kind is both curious and not generous.
If someone is either rich or generous then susan is both strong and not creative and vice versa.
If alice is either funny or not calm then mary is brave and vice versa.
Everyone who is not wise is not happy or generous and vice versa.
Everyone who is both not strong and brave is creative and vice versa.
If fred is both not happy and not rich then someone is curious or not patient and vice versa.
Everyone who is patient or not patient is not calm or funny and vice versa.
If fred is not kind or patient then someone is either humble or calm.
If alice is rich or not rich then someone is not quiet or happy.
Everyone who is either funny or not kind is not happy or humble.
Someone is either strong or not kind.
Someone is either generous or patient.
Someone is generous.
Someone is either not strong or calm.
Mary is either rich or not brave.
Mary is not patient or funny.
Susan is both curious and not quiet.
Lucy is both happy and calm. | John is not strong. | entailment | ((?[X]:(old(X)))<=>((creative(john)&patient(john))))&
(![X]:((~quiet(X)<~>brave(X))<=>(happy(X)&creative(X))))&
(![X]:(~calm(X)=>(~funny(X)|quiet(X))))&
((?[X]:(~humble(X)))=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((~old(X)&~generous(X))=>(~curious(X)&rich(X))))&
(![X]:(~kind(X)=>(happy(X)|kind(X))))&
(![X]:((tall(X)|kind(X))=>(curious(X)&~generous(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>((strong(susan)&~creative(susan))))&
(((funny(alice)<~>~calm(alice)))<=>(brave(mary)))&
(![X]:(~wise(X)<=>(~happy(X)|generous(X))))&
(![X]:((~strong(X)&brave(X))<=>creative(X)))&
(((~happy(fred)&~rich(fred)))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((patient(X)|~patient(X))<=>(~calm(X)|funny(X))))&
(((~kind(fred)|patient(fred)))=>(?[X]:((humble(X)<~>calm(X)))))&
(((rich(alice)|~rich(alice)))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((funny(X)<~>~kind(X))=>(~happy(X)|humble(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:(generous(X)))&
(?[X]:((~strong(X)<~>calm(X))))&
((rich(mary)<~>~brave(mary)))&
((~patient(mary)|funny(mary)))&
((curious(susan)&~quiet(susan)))&
((happy(lucy)&calm(lucy))) | ~strong(john) | [
"p0",
"p4",
"p5",
"p6",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2824404425398842837109088
% SZS output start Proof for 2824404425398842837109088
1. ? [X0] : old(X0) <=> (patient(john) & creative(john)) [input p0]
5. ! [X0] : ((~generous(X0) & ~old(X0)) => (rich(X0) & ~curious(X0))) [input p4]
6. ! [X0] : (~kind(X0) => (kind(X0) | happy(X0))) [input p5]
7. ! [X0] : ((kind(X0) | tall(X0)) => (~generous(X0) & curious(X0))) [input p6]
11. ! [X0] : ((brave(X0) & ~strong(X0)) <=> creative(X0)) [input p10]
12. (~rich(fred) & ~happy(fred)) <=> ? [X0] : (~patient(X0) | curious(X0)) [input p11]
23. ~quiet(susan) & curious(susan) [input p22]
25. strong(john) [input hypothesis]
27. ! [X0] : (kind(X0) => (~generous(X0) & curious(X0))) [pure predicate removal 7]
31. ! [X0] : ((rich(X0) & ~curious(X0)) | (generous(X0) | old(X0))) [ennf transformation 5]
32. ! [X0] : ((rich(X0) & ~curious(X0)) | generous(X0) | old(X0)) [flattening 31]
33. ! [X0] : ((kind(X0) | happy(X0)) | kind(X0)) [ennf transformation 6]
34. ! [X0] : (kind(X0) | happy(X0) | kind(X0)) [flattening 33]
35. ! [X0] : ((~generous(X0) & curious(X0)) | ~kind(X0)) [ennf transformation 27]
40. (? [X0] : old(X0) | (~patient(john) | ~creative(john))) & ((patient(john) & creative(john)) | ! [X0] : ~old(X0)) [nnf transformation 1]
41. (? [X0] : old(X0) | ~patient(john) | ~creative(john)) & ((patient(john) & creative(john)) | ! [X0] : ~old(X0)) [flattening 40]
42. (? [X0] : old(X0) | ~patient(john) | ~creative(john)) & ((patient(john) & creative(john)) | ! [X1] : ~old(X1)) [rectify 41]
43. ? [X0] : old(X0) => old(sK0) [choice axiom]
44. (old(sK0) | ~patient(john) | ~creative(john)) & ((patient(john) & creative(john)) | ! [X1] : ~old(X1)) [skolemisation 42,43]
57. ! [X0] : (((brave(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | (~brave(X0) | strong(X0)))) [nnf transformation 11]
58. ! [X0] : (((brave(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | ~brave(X0) | strong(X0))) [flattening 57]
59. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X0] : (~patient(X0) | curious(X0)) | (rich(fred) | happy(fred))) [nnf transformation 12]
60. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X0] : (~patient(X0) | curious(X0)) | rich(fred) | happy(fred)) [flattening 59]
61. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & (? [X1] : (~patient(X1) | curious(X1)) | rich(fred) | happy(fred)) [rectify 60]
62. ? [X1] : (~patient(X1) | curious(X1)) => (~patient(sK3) | curious(sK3)) [choice axiom]
63. ((~rich(fred) & ~happy(fred)) | ! [X0] : (patient(X0) & ~curious(X0))) & ((~patient(sK3) | curious(sK3)) | rich(fred) | happy(fred)) [skolemisation 61,62]
84. creative(john) | ~old(X1) [cnf transformation 44]
97. rich(X0) | generous(X0) | old(X0) [cnf transformation 32]
98. kind(X0) | happy(X0) | kind(X0) [cnf transformation 34]
100. ~kind(X0) | ~generous(X0) [cnf transformation 35]
112. ~strong(X0) | ~creative(X0) [cnf transformation 58]
115. ~happy(fred) | ~curious(X0) [cnf transformation 63]
117. ~rich(fred) | ~curious(X0) [cnf transformation 63]
141. curious(susan) [cnf transformation 23]
145. strong(john) [cnf transformation 25]
146. kind(X0) | happy(X0) [duplicate literal removal 98]
148. 1 <=> creative(john) [avatar definition]
161. 4 <=> ! [X1] : ~old(X1) [avatar definition]
162. ~old(X1) <- (4) [avatar component clause 161]
164. 4 | 1 [avatar split clause 84,148,161]
226. 18 <=> rich(fred) [avatar definition]
228. ~rich(fred) <- (~18) [avatar component clause 226]
231. 19 <=> ! [X0] : ~curious(X0) [avatar definition]
232. ~curious(X0) <- (19) [avatar component clause 231]
233. 19 | ~18 [avatar split clause 117,226,231]
235. 20 <=> happy(fred) [avatar definition]
237. ~happy(fred) <- (~20) [avatar component clause 235]
239. 19 | ~20 [avatar split clause 115,235,231]
330. ~creative(john) [resolution 112,145]
332. ~1 [avatar split clause 330,148]
334. ~generous(X0) | happy(X0) [resolution 146,100]
357. $false <- (19) [resolution 232,141]
358. ~19 [avatar contradiction clause 357]
390. generous(fred) | old(fred) <- (~18) [resolution 97,228]
391. generous(fred) <- (4, ~18) [subsumption resolution 390,162]
453. happy(fred) <- (4, ~18) [resolution 334,391]
457. $false <- (4, ~18, ~20) [subsumption resolution 453,237]
458. ~4 | 18 | 20 [avatar contradiction clause 457]
459. $false [avatar sat refutation 164,233,239,332,358,458]
% SZS output end Proof for 2824404425398842837109088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not tall or strong then someone is not old or curious.
Everyone who is both not generous and not tall is both not quiet and wise and vice versa.
Everyone who is not creative or not funny is creative or not quiet.
Everyone who is calm is both old and creative and vice versa.
Everyone who is either calm or patient is curious and vice versa.
Everyone who is creative is either tall or not rich.
Everyone who is either not humble or not happy is both generous and calm.
Everyone who is either not wise or patient is either not curious or rich.
Everyone who is funny is brave and vice versa.
Everyone who is not creative or not funny is not tall or wise and vice versa.
Everyone who is not happy is both old and tall and vice versa.
Everyone who is either not kind or not old is not quiet.
Everyone who is both not rich and not humble is either not curious or wise.
Everyone who is curious is not patient.
Everyone who is either quiet or old is not happy and vice versa.
Everyone who is both not generous and kind is not strong.
Susan is humble or not old.
Lucy is not calm or quiet.
Lucy is either kind or not brave.
Someone is both happy and strong.
Lucy is both not old and not tall.
Someone is not tall or happy.
John is not calm or not creative.
Someone is not happy. | Lucy is generous. | neutral | (((~tall(lucy)|strong(lucy)))=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((~generous(X)&~tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~creative(X)|~funny(X))=>(creative(X)|~quiet(X))))&
(![X]:(calm(X)<=>(old(X)&creative(X))))&
(![X]:((calm(X)<~>patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(generous(X)&calm(X))))&
(![X]:((~wise(X)<~>patient(X))=>(~curious(X)<~>rich(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~creative(X)|~funny(X))<=>(~tall(X)|wise(X))))&
(![X]:(~happy(X)<=>(old(X)&tall(X))))&
(![X]:((~kind(X)<~>~old(X))=>~quiet(X)))&
(![X]:((~rich(X)&~humble(X))=>(~curious(X)<~>wise(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((quiet(X)<~>old(X))<=>~happy(X)))&
(![X]:((~generous(X)&kind(X))=>~strong(X)))&
((humble(susan)|~old(susan)))&
((~calm(lucy)|quiet(lucy)))&
((kind(lucy)<~>~brave(lucy)))&
(?[X]:((happy(X)&strong(X))))&
((~old(lucy)&~tall(lucy)))&
(?[X]:((~tall(X)|happy(X))))&
((~calm(john)|~creative(john)))&
(?[X]:(~happy(X))) | generous(lucy) | [] | null | 0 |
If someone is either funny or not wise then paul is humble and vice versa. Everyone who is either not kind or funny is both old and not old. Everyone who is both not kind and curious is both not wise and old. If mary is both patient and kind then someone is wise or funny and vice versa. If susan is both not brave and not curious then someone is not quiet. Everyone who is not brave or not strong is either tall or strong and vice versa. If mary is both quiet and kind then alice is both not old and happy. If someone is not rich or not generous then alice is not happy. If someone is either not tall or humble then mary is calm and vice versa. Everyone who is generous or not brave is either not old or not generous. Everyone who is not old is either quiet or not happy and vice versa. If someone is either funny or not humble then someone is either not tall or old. If someone is both tall and humble then lucy is not happy or not calm and vice versa. If susan is both not kind and humble then someone is both not old and not patient and vice versa. If someone is either not calm or old then alice is both not rich and not patient and vice versa. If fred is humble then someone is not strong or old and vice versa. Someone is either old or not brave. Someone is old or not curious. Someone is both old and humble. Mary is either not kind or not calm. Someone is generous. Someone is not funny. Someone is not humble. | Mary is not kind. | contradiction | ((?[X]:((funny(X)<~>~wise(X))))<=>(humble(paul)))&
(![X]:((~kind(X)<~>funny(X))=>(old(X)&~old(X))))&
(![X]:((~kind(X)&curious(X))=>(~wise(X)&old(X))))&
(((patient(mary)&kind(mary)))<=>(?[X]:((wise(X)|funny(X)))))&
(((~brave(susan)&~curious(susan)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)|~strong(X))<=>(tall(X)<~>strong(X))))&
(((quiet(mary)&kind(mary)))=>((~old(alice)&happy(alice))))&
((?[X]:((~rich(X)|~generous(X))))=>(~happy(alice)))&
((?[X]:((~tall(X)<~>humble(X))))<=>(calm(mary)))&
(![X]:((generous(X)|~brave(X))=>(~old(X)<~>~generous(X))))&
(![X]:(~old(X)<=>(quiet(X)<~>~happy(X))))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((tall(X)&humble(X))))<=>((~happy(lucy)|~calm(lucy))))&
(((~kind(susan)&humble(susan)))<=>(?[X]:((~old(X)&~patient(X)))))&
((?[X]:((~calm(X)<~>old(X))))<=>((~rich(alice)&~patient(alice))))&
((humble(fred))<=>(?[X]:((~strong(X)|old(X)))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((old(X)|~curious(X))))&
(?[X]:((old(X)&humble(X))))&
((~kind(mary)<~>~calm(mary)))&
(?[X]:(generous(X)))&
(?[X]:(~funny(X)))&
(?[X]:(~humble(X))) | ~kind(mary) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2114035821656854397822511
% SZS output start Proof for 2114035821656854397822511
2. ! [X0] : ((~kind(X0) <~> funny(X0)) => (~old(X0) & old(X0))) [input p1]
4. (kind(mary) & patient(mary)) <=> ? [X0] : (funny(X0) | wise(X0)) [input p3]
24. ~kind(mary) [input hypothesis]
26. ! [X0] : ((~old(X0) & old(X0)) | (~kind(X0) <=> funny(X0))) [ennf transformation 2]
40. ! [X0] : ((~old(X0) & old(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) [nnf transformation 26]
41. ((kind(mary) & patient(mary)) | ! [X0] : (~funny(X0) & ~wise(X0))) & (? [X0] : (funny(X0) | wise(X0)) | (~kind(mary) | ~patient(mary))) [nnf transformation 4]
42. ((kind(mary) & patient(mary)) | ! [X0] : (~funny(X0) & ~wise(X0))) & (? [X0] : (funny(X0) | wise(X0)) | ~kind(mary) | ~patient(mary)) [flattening 41]
43. ((kind(mary) & patient(mary)) | ! [X0] : (~funny(X0) & ~wise(X0))) & (? [X1] : (funny(X1) | wise(X1)) | ~kind(mary) | ~patient(mary)) [rectify 42]
44. ? [X1] : (funny(X1) | wise(X1)) => (funny(sK1) | wise(sK1)) [choice axiom]
45. ((kind(mary) & patient(mary)) | ! [X0] : (~funny(X0) & ~wise(X0))) & ((funny(sK1) | wise(sK1)) | ~kind(mary) | ~patient(mary)) [skolemisation 43,44]
97. old(X0) | funny(X0) | kind(X0) [cnf transformation 40]
99. ~old(X0) | funny(X0) | kind(X0) [cnf transformation 40]
107. kind(mary) | ~funny(X0) [cnf transformation 45]
163. ~kind(mary) [cnf transformation 24]
190. kind(X0) | funny(X0) [subsumption resolution 97,99]
192. 6 <=> ! [X0] : ~funny(X0) [avatar definition]
193. ~funny(X0) <- (6) [avatar component clause 192]
195. 7 <=> kind(mary) [avatar definition]
196. ~kind(mary) <- (~7) [avatar component clause 195]
198. 6 | 7 [avatar split clause 107,195,192]
407. ~7 [avatar split clause 163,195]
414. funny(mary) <- (~7) [resolution 190,196]
416. $false <- (6, ~7) [subsumption resolution 414,193]
417. ~6 | 7 [avatar contradiction clause 416]
418. $false [avatar sat refutation 198,407,417]
% SZS output end Proof for 2114035821656854397822511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous then mary is both happy and strong.
If someone is either patient or rich then someone is calm or happy and vice versa.
Everyone who is not happy or calm is either humble or wise and vice versa.
Everyone who is not happy is not old or not quiet and vice versa.
Everyone who is kind or not curious is happy or not funny and vice versa.
If mary is brave then mary is wise or not tall and vice versa.
If someone is both tall and not funny then paul is both patient and calm and vice versa.
If someone is not curious or not generous then alice is both brave and happy.
If susan is either not funny or not strong then fred is both not funny and funny and vice versa.
If lucy is humble or not old then someone is funny and vice versa.
Everyone who is funny or not quiet is both not patient and rich and vice versa.
Everyone who is rich is either humble or funny and vice versa.
Everyone who is generous or not humble is both not brave and not old.
Everyone who is either not funny or not old is patient or not strong and vice versa.
If someone is quiet or funny then someone is both not brave and creative and vice versa.
Lucy is either kind or not quiet.
Paul is generous or quiet.
Someone is not wise or rich.
John is curious.
Mary is both patient and brave.
Someone is creative or not wise.
Someone is both quiet and brave. | John is tall. | neutral | ((?[X]:(~generous(X)))=>((happy(mary)&strong(mary))))&
((?[X]:((patient(X)<~>rich(X))))<=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~happy(X)|calm(X))<=>(humble(X)<~>wise(X))))&
(![X]:(~happy(X)<=>(~old(X)|~quiet(X))))&
(![X]:((kind(X)|~curious(X))<=>(happy(X)|~funny(X))))&
((brave(mary))<=>((wise(mary)|~tall(mary))))&
((?[X]:((tall(X)&~funny(X))))<=>((patient(paul)&calm(paul))))&
((?[X]:((~curious(X)|~generous(X))))=>((brave(alice)&happy(alice))))&
(((~funny(susan)<~>~strong(susan)))<=>((~funny(fred)&funny(fred))))&
(((humble(lucy)|~old(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~patient(X)&rich(X))))&
(![X]:(rich(X)<=>(humble(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))=>(~brave(X)&~old(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(patient(X)|~strong(X))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
((kind(lucy)<~>~quiet(lucy)))&
((generous(paul)|quiet(paul)))&
(?[X]:((~wise(X)|rich(X))))&
(curious(john))&
((patient(mary)&brave(mary)))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((quiet(X)&brave(X)))) | tall(john) | [] | null | 0 |
If someone is both tall and not old then mary is either calm or not curious. If alice is not calm or not quiet then someone is either not calm or not happy. If mary is both tall and kind then john is either not humble or curious. Everyone who is not creative is either not funny or not tall and vice versa. Everyone who is either not creative or curious is either not creative or not funny. Everyone who is both not patient and not funny is both not humble and generous and vice versa. Everyone who is not happy or kind is either tall or humble. Everyone who is not rich or wise is either not patient or calm and vice versa. Everyone who is either patient or brave is either not happy or strong and vice versa. If someone is either not tall or curious then someone is either quiet or not humble and vice versa. Everyone who is strong is not quiet and vice versa. If alice is calm then fred is either not strong or tall and vice versa. Everyone who is either not creative or not happy is not patient and vice versa. Everyone who is either creative or not tall is both not old and not strong. Everyone who is not generous or kind is both old and kind and vice versa. Someone is either not wise or humble. Someone is either tall or not generous. Lucy is not rich. Alice is not rich. Someone is not wise. | John is creative. | neutral | ((?[X]:((tall(X)&~old(X))))=>((calm(mary)<~>~curious(mary))))&
(((~calm(alice)|~quiet(alice)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(((tall(mary)&kind(mary)))=>((~humble(john)<~>curious(john))))&
(![X]:(~creative(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>curious(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~humble(X)&generous(X))))&
(![X]:((~happy(X)|kind(X))=>(tall(X)<~>humble(X))))&
(![X]:((~rich(X)|wise(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((patient(X)<~>brave(X))<=>(~happy(X)<~>strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((quiet(X)<~>~humble(X)))))&
(![X]:(strong(X)<=>~quiet(X)))&
((calm(alice))<=>((~strong(fred)<~>tall(fred))))&
(![X]:((~creative(X)<~>~happy(X))<=>~patient(X)))&
(![X]:((creative(X)<~>~tall(X))=>(~old(X)&~strong(X))))&
(![X]:((~generous(X)|kind(X))<=>(old(X)&kind(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
(~rich(lucy))&
(~rich(alice))&
(?[X]:(~wise(X))) | creative(john) | [] | null | 0 |
Everyone who is both tall and funny is not funny.
If alice is either not humble or rich then someone is not wise.
Everyone who is both not tall and not calm is both not creative and kind and vice versa.
If paul is calm or not patient then john is not brave.
Everyone who is either curious or generous is patient and vice versa.
Everyone who is calm is either not rich or not creative and vice versa.
Everyone who is either creative or brave is not creative or not wise and vice versa.
Everyone who is either kind or not old is both not strong and quiet.
If mary is tall then paul is quiet or not patient.
If mary is not old then susan is either not curious or wise and vice versa.
Everyone who is wise or strong is both patient and strong.
Everyone who is both generous and not kind is not rich or not kind and vice versa.
Everyone who is either not happy or not tall is either kind or generous and vice versa.
If someone is either not brave or happy then fred is not creative or strong.
Everyone who is creative is funny or calm and vice versa.
Everyone who is either rich or humble is not quiet or not brave.
Someone is not calm.
Susan is patient.
Alice is creative.
Paul is both not rich and not curious.
Alice is not rich.
Mary is not quiet.
Paul is both not wise and not calm.
Someone is both not wise and not funny. | Susan is brave. | entailment | (![X]:((tall(X)&funny(X))=>~funny(X)))&
(((~humble(alice)<~>rich(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>(~creative(X)&kind(X))))&
(((calm(paul)|~patient(paul)))=>(~brave(john)))&
(![X]:((curious(X)<~>generous(X))<=>patient(X)))&
(![X]:(calm(X)<=>(~rich(X)<~>~creative(X))))&
(![X]:((creative(X)<~>brave(X))<=>(~creative(X)|~wise(X))))&
(![X]:((kind(X)<~>~old(X))=>(~strong(X)&quiet(X))))&
((tall(mary))=>((quiet(paul)|~patient(paul))))&
((~old(mary))<=>((~curious(susan)<~>wise(susan))))&
(![X]:((wise(X)|strong(X))=>(patient(X)&strong(X))))&
(![X]:((generous(X)&~kind(X))<=>(~rich(X)|~kind(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>((~creative(fred)|strong(fred))))&
(![X]:(creative(X)<=>(funny(X)|calm(X))))&
(![X]:((rich(X)<~>humble(X))=>(~quiet(X)|~brave(X))))&
(?[X]:(~calm(X)))&
(patient(susan))&
(creative(alice))&
((~rich(paul)&~curious(paul)))&
(~rich(alice))&
(~quiet(mary))&
((~wise(paul)&~calm(paul)))&
(?[X]:((~wise(X)&~funny(X)))) | brave(susan) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p7",
"p9",
"p11",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8691628729439504662354078
% SZS output start Proof for 8691628729439504662354078
1. ! [X0] : ((funny(X0) & tall(X0)) => ~funny(X0)) [input p0]
3. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> (kind(X0) & ~creative(X0))) [input p2]
5. ! [X0] : ((curious(X0) <~> generous(X0)) <=> patient(X0)) [input p4]
6. ! [X0] : (calm(X0) <=> (~rich(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : ((creative(X0) <~> brave(X0)) <=> (~wise(X0) | ~creative(X0))) [input p6]
8. ! [X0] : ((kind(X0) <~> ~old(X0)) => (quiet(X0) & ~strong(X0))) [input p7]
10. ~old(mary) <=> (~curious(susan) <~> wise(susan)) [input p9]
12. ! [X0] : ((~kind(X0) & generous(X0)) <=> (~kind(X0) | ~rich(X0))) [input p11]
15. ! [X0] : (creative(X0) <=> (calm(X0) | funny(X0))) [input p14]
18. patient(susan) [input p17]
22. ~quiet(mary) [input p21]
25. ~brave(susan) [input hypothesis]
26. ! [X0] : (~funny(X0) | (~funny(X0) | ~tall(X0))) [ennf transformation 1]
27. ! [X0] : (~funny(X0) | ~funny(X0) | ~tall(X0)) [flattening 26]
30. ! [X0] : ((quiet(X0) & ~strong(X0)) | (kind(X0) <=> ~old(X0))) [ennf transformation 8]
41. ! [X0] : (((~calm(X0) & ~tall(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (calm(X0) | tall(X0)))) [nnf transformation 3]
42. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | calm(X0) | tall(X0))) [flattening 41]
43. ! [X0] : ((((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ~patient(X0)) & (patient(X0) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0))))) [nnf transformation 5]
44. ! [X0] : ((calm(X0) | ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0)))) & (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | ~calm(X0))) [nnf transformation 6]
45. ! [X0] : ((((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (wise(X0) & creative(X0))) & ((~wise(X0) | ~creative(X0)) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (wise(X0) & creative(X0))) & (~wise(X0) | ~creative(X0) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))))) [flattening 45]
47. ! [X0] : ((quiet(X0) & ~strong(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) [nnf transformation 30]
48. (~old(mary) | ((~curious(susan) | ~wise(susan)) & (wise(susan) | curious(susan)))) & (((~wise(susan) | curious(susan)) & (wise(susan) | ~curious(susan))) | old(mary)) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & generous(X0)) | (kind(X0) & rich(X0))) & ((~kind(X0) | ~rich(X0)) | (kind(X0) | ~generous(X0)))) [nnf transformation 12]
50. ! [X0] : (((~kind(X0) & generous(X0)) | (kind(X0) & rich(X0))) & (~kind(X0) | ~rich(X0) | kind(X0) | ~generous(X0))) [flattening 49]
53. ! [X0] : ((creative(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | ~creative(X0))) [nnf transformation 15]
54. ! [X0] : ((creative(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | ~creative(X0))) [flattening 53]
60. ~funny(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 27]
63. ~creative(X0) | calm(X0) | tall(X0) [cnf transformation 42]
72. ~generous(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 43]
73. ~creative(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 44]
76. ~rich(X0) | calm(X0) | creative(X0) [cnf transformation 44]
77. ~wise(X0) | ~creative(X0) | brave(X0) | ~creative(X0) [cnf transformation 46]
79. brave(X0) | creative(X0) | creative(X0) [cnf transformation 46]
86. quiet(X0) | kind(X0) | old(X0) [cnf transformation 47]
90. ~old(mary) | wise(susan) | curious(susan) [cnf transformation 48]
98. generous(X0) | kind(X0) [cnf transformation 50]
99. ~kind(X0) | rich(X0) [cnf transformation 50]
111. ~creative(X0) | funny(X0) | calm(X0) [cnf transformation 54]
113. ~calm(X0) | creative(X0) [cnf transformation 54]
117. patient(susan) [cnf transformation 18]
122. ~quiet(mary) [cnf transformation 22]
127. ~brave(susan) [cnf transformation 25]
128. ~wise(X0) | ~creative(X0) | brave(X0) [duplicate literal removal 77]
129. brave(X0) | creative(X0) [duplicate literal removal 79]
130. ~funny(X0) | ~tall(X0) [duplicate literal removal 60]
159. ~wise(X0) | brave(X0) [subsumption resolution 128,129]
161. 7 <=> tall(mary) [avatar definition]
162. tall(mary) <- (7) [avatar component clause 161]
163. ~tall(mary) <- (~7) [avatar component clause 161]
170. 9 <=> wise(susan) [avatar definition]
171. wise(susan) <- (9) [avatar component clause 170]
174. 10 <=> curious(susan) [avatar definition]
175. curious(susan) <- (10) [avatar component clause 174]
178. 11 <=> old(mary) [avatar definition]
180. ~old(mary) <- (~11) [avatar component clause 178]
182. 10 | 9 | ~11 [avatar split clause 90,178,170,174]
207. creative(susan) [resolution 129,127]
210. calm(susan) | tall(susan) [resolution 63,207]
222. 18 <=> tall(susan) [avatar definition]
224. tall(susan) <- (18) [avatar component clause 222]
226. 19 <=> calm(susan) [avatar definition]
229. 18 | 19 [avatar split clause 210,226,222]
247. ~curious(X0) | ~patient(X0) | kind(X0) [resolution 72,98]
251. ~rich(susan) | ~calm(susan) [resolution 73,207]
254. 22 <=> rich(susan) [avatar definition]
257. ~19 | ~22 [avatar split clause 251,254,226]
295. kind(mary) | old(mary) [resolution 86,122]
296. kind(mary) <- (~11) [subsumption resolution 295,180]
299. rich(mary) <- (~11) [resolution 296,99]
301. funny(susan) | calm(susan) [resolution 111,207]
302. calm(mary) | creative(mary) <- (~11) [resolution 299,76]
303. creative(mary) <- (~11) [subsumption resolution 302,113]
304. funny(mary) | calm(mary) <- (~11) [resolution 303,111]
306. ~rich(mary) | ~calm(mary) <- (~11) [resolution 303,73]
307. calm(mary) | tall(mary) <- (~11) [resolution 303,63]
309. 26 <=> calm(mary) [avatar definition]
313. 27 <=> funny(mary) [avatar definition]
315. funny(mary) <- (27) [avatar component clause 313]
316. 26 | 27 | 11 [avatar split clause 304,178,313,309]
317. ~calm(mary) <- (~11) [subsumption resolution 306,299]
318. ~26 | 11 [avatar split clause 317,178,309]
319. calm(mary) <- (~7, ~11) [subsumption resolution 307,163]
320. 26 | 7 | 11 [avatar split clause 319,178,161,309]
434. ~patient(susan) | kind(susan) <- (10) [resolution 247,175]
438. kind(susan) <- (10) [subsumption resolution 434,117]
441. rich(susan) <- (10) [resolution 438,99]
445. 36 <=> funny(susan) [avatar definition]
447. funny(susan) <- (36) [avatar component clause 445]
448. 19 | 36 [avatar split clause 301,445,226]
449. 22 | ~10 [avatar split clause 441,174,254]
450. brave(susan) <- (9) [resolution 171,159]
453. $false <- (9) [subsumption resolution 450,127]
454. ~9 [avatar contradiction clause 453]
529. ~tall(mary) <- (27) [resolution 315,130]
531. $false <- (7, 27) [subsumption resolution 529,162]
532. ~7 | ~27 [avatar contradiction clause 531]
599. ~tall(susan) <- (36) [resolution 447,130]
601. $false <- (18, 36) [subsumption resolution 599,224]
602. ~18 | ~36 [avatar contradiction clause 601]
603. $false [avatar sat refutation 182,229,257,316,318,320,448,449,454,532,602]
% SZS output end Proof for 8691628729439504662354078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or happy is tall and vice versa. Everyone who is either not patient or not tall is old or happy. Everyone who is wise is funny or not kind. If someone is old then someone is not generous and vice versa. Everyone who is creative or not strong is both strong and curious. If lucy is either not strong or not creative then someone is both not happy and not patient and vice versa. If someone is either quiet or not wise then someone is kind and vice versa. Everyone who is either generous or old is not humble or not wise and vice versa. Everyone who is either patient or curious is either not generous or humble. If fred is not happy then someone is wise or not calm. Everyone who is not patient is not happy and vice versa. Everyone who is both tall and not creative is not generous or not humble and vice versa. If susan is both happy and not strong then someone is either not old or curious and vice versa. Everyone who is either not generous or humble is either not happy or not creative and vice versa. If fred is both not rich and not old then lucy is either not calm or not humble and vice versa. Everyone who is not wise is both calm and old and vice versa. Someone is not humble. Someone is quiet. Fred is either not happy or not quiet. Mary is either not curious or not strong. Susan is not funny. Someone is funny. Alice is both not curious and humble. Susan is brave. | Fred is not quiet. | neutral | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(old(X)|happy(X))))&
(![X]:(wise(X)=>(funny(X)|~kind(X))))&
((?[X]:(old(X)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~strong(X))=>(strong(X)&curious(X))))&
(((~strong(lucy)<~>~creative(lucy)))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
(![X]:((patient(X)<~>curious(X))=>(~generous(X)<~>humble(X))))&
((~happy(fred))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((tall(X)&~creative(X))<=>(~generous(X)|~humble(X))))&
(((happy(susan)&~strong(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~happy(X)<~>~creative(X))))&
(((~rich(fred)&~old(fred)))<=>((~calm(lucy)<~>~humble(lucy))))&
(![X]:(~wise(X)<=>(calm(X)&old(X))))&
(?[X]:(~humble(X)))&
(?[X]:(quiet(X)))&
((~happy(fred)<~>~quiet(fred)))&
((~curious(mary)<~>~strong(mary)))&
(~funny(susan))&
(?[X]:(funny(X)))&
((~curious(alice)&humble(alice)))&
(brave(susan)) | ~quiet(fred) | [] | null | 0 |
Everyone who is either not curious or patient is either funny or not curious and vice versa.
Everyone who is either tall or not calm is both not curious and not humble.
If paul is either not patient or patient then mary is not patient and vice versa.
If fred is not creative or not strong then someone is either brave or not curious and vice versa.
If lucy is both patient and not kind then someone is either kind or not funny.
If fred is both not calm and creative then mary is brave or wise.
If someone is either not funny or not kind then someone is not humble and vice versa.
Everyone who is not humble is not quiet or not strong and vice versa.
If someone is patient or humble then john is either quiet or patient and vice versa.
If alice is old or not brave then lucy is both not quiet and not brave and vice versa.
Everyone who is both rich and creative is both not generous and strong and vice versa.
Everyone who is creative is both not happy and not creative and vice versa.
Everyone who is not brave or not happy is old.
Everyone who is either wise or curious is either quiet or not old and vice versa.
If alice is both curious and not patient then susan is both not generous and patient.
Someone is both not wise and not creative.
Mary is either not curious or not quiet.
John is curious or not old.
Someone is not wise.
Susan is tall or not happy.
Alice is patient.
Someone is not generous or curious.
Someone is both not patient and generous. | Lucy is happy. | entailment | (![X]:((~curious(X)<~>patient(X))<=>(funny(X)<~>~curious(X))))&
(![X]:((tall(X)<~>~calm(X))=>(~curious(X)&~humble(X))))&
(((~patient(paul)<~>patient(paul)))<=>(~patient(mary)))&
(((~creative(fred)|~strong(fred)))<=>(?[X]:((brave(X)<~>~curious(X)))))&
(((patient(lucy)&~kind(lucy)))=>(?[X]:((kind(X)<~>~funny(X)))))&
(((~calm(fred)&creative(fred)))=>((brave(mary)|wise(mary))))&
((?[X]:((~funny(X)<~>~kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~strong(X))))&
((?[X]:((patient(X)|humble(X))))<=>((quiet(john)<~>patient(john))))&
(((old(alice)|~brave(alice)))<=>((~quiet(lucy)&~brave(lucy))))&
(![X]:((rich(X)&creative(X))<=>(~generous(X)&strong(X))))&
(![X]:(creative(X)<=>(~happy(X)&~creative(X))))&
(![X]:((~brave(X)|~happy(X))=>old(X)))&
(![X]:((wise(X)<~>curious(X))<=>(quiet(X)<~>~old(X))))&
(((curious(alice)&~patient(alice)))=>((~generous(susan)&patient(susan))))&
(?[X]:((~wise(X)&~creative(X))))&
((~curious(mary)<~>~quiet(mary)))&
((curious(john)|~old(john)))&
(?[X]:(~wise(X)))&
((tall(susan)|~happy(susan)))&
(patient(alice))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((~patient(X)&generous(X)))) | happy(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 843533378869670707336391
% SZS output start Proof for 843533378869670707336391
12. ! [X0] : (creative(X0) <=> (~creative(X0) & ~happy(X0))) [input p11]
24. ~happy(lucy) [input hypothesis]
60. ! [X0] : ((creative(X0) | (creative(X0) | happy(X0))) & ((~creative(X0) & ~happy(X0)) | ~creative(X0))) [nnf transformation 12]
61. ! [X0] : ((creative(X0) | creative(X0) | happy(X0)) & ((~creative(X0) & ~happy(X0)) | ~creative(X0))) [flattening 60]
120. ~creative(X0) | ~creative(X0) [cnf transformation 61]
121. creative(X0) | creative(X0) | happy(X0) [cnf transformation 61]
145. ~happy(lucy) [cnf transformation 24]
146. ~creative(X0) [duplicate literal removal 120]
147. happy(X0) | creative(X0) [duplicate literal removal 121]
360. creative(lucy) [resolution 147,145]
362. $false [subsumption resolution 360,146]
% SZS output end Proof for 843533378869670707336391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is quiet. If someone is either tall or not creative then someone is both not curious and brave. If someone is either kind or not curious then lucy is both patient and quiet and vice versa. Everyone who is both not wise and calm is both not happy and not curious and vice versa. If someone is either creative or rich then susan is both not tall and not wise. Everyone who is either humble or not creative is both not creative and not happy and vice versa. If paul is both tall and not tall then someone is happy. Everyone who is patient is brave and vice versa. If susan is both not funny and not quiet then paul is both curious and humble. If someone is both strong and not strong then paul is brave or humble. Everyone who is generous or not humble is patient. Everyone who is either calm or strong is both old and not wise. Everyone who is not tall is either calm or quiet. Everyone who is either not funny or happy is not kind or happy. If someone is both not creative and not rich then susan is both not rich and not curious. Everyone who is both tall and calm is not humble. Fred is not strong or not wise. Someone is both not calm and wise. Someone is either not curious or not strong. Someone is either not rich or not tall. Mary is rich or calm. Someone is quiet. Mary is not brave. Paul is both strong and patient. | Mary is happy. | entailment | ((?[X]:(generous(X)))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)<~>~creative(X))))=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:((kind(X)<~>~curious(X))))<=>((patient(lucy)&quiet(lucy))))&
(![X]:((~wise(X)&calm(X))<=>(~happy(X)&~curious(X))))&
((?[X]:((creative(X)<~>rich(X))))=>((~tall(susan)&~wise(susan))))&
(![X]:((humble(X)<~>~creative(X))<=>(~creative(X)&~happy(X))))&
(((tall(paul)&~tall(paul)))=>(?[X]:(happy(X))))&
(![X]:(patient(X)<=>brave(X)))&
(((~funny(susan)&~quiet(susan)))=>((curious(paul)&humble(paul))))&
((?[X]:((strong(X)&~strong(X))))=>((brave(paul)|humble(paul))))&
(![X]:((generous(X)|~humble(X))=>patient(X)))&
(![X]:((calm(X)<~>strong(X))=>(old(X)&~wise(X))))&
(![X]:(~tall(X)=>(calm(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>happy(X))=>(~kind(X)|happy(X))))&
((?[X]:((~creative(X)&~rich(X))))=>((~rich(susan)&~curious(susan))))&
(![X]:((tall(X)&calm(X))=>~humble(X)))&
((~strong(fred)|~wise(fred)))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((~curious(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
((rich(mary)|calm(mary)))&
(?[X]:(quiet(X)))&
(~brave(mary))&
((strong(paul)&patient(paul))) | happy(mary) | [
"p5",
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 79916202753024350186756
% SZS output start Proof for 79916202753024350186756
6. ! [X0] : ((humble(X0) <~> ~creative(X0)) <=> (~happy(X0) & ~creative(X0))) [input p5]
8. ! [X0] : (patient(X0) <=> brave(X0)) [input p7]
11. ! [X0] : ((~humble(X0) | generous(X0)) => patient(X0)) [input p10]
23. ~brave(mary) [input p22]
25. ~happy(mary) [input hypothesis]
29. ! [X0] : (~humble(X0) => patient(X0)) [pure predicate removal 11]
39. ! [X0] : (patient(X0) | humble(X0)) [ennf transformation 29]
59. ! [X0] : ((((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0))))) [nnf transformation 6]
60. ! [X0] : ((((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0))))) [flattening 59]
63. ! [X0] : ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))) [nnf transformation 8]
95. ~creative(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 60]
100. creative(X0) | ~humble(X0) | happy(X0) | creative(X0) [cnf transformation 60]
102. ~patient(X0) | brave(X0) [cnf transformation 63]
107. humble(X0) | patient(X0) [cnf transformation 39]
126. ~brave(mary) [cnf transformation 23]
129. ~happy(mary) [cnf transformation 25]
131. ~humble(X0) | ~creative(X0) [duplicate literal removal 95]
132. ~humble(X0) | creative(X0) | happy(X0) [duplicate literal removal 100]
271. ~creative(X0) | patient(X0) [resolution 131,107]
351. creative(X0) | happy(X0) | patient(X0) [resolution 132,107]
352. happy(X0) | patient(X0) [subsumption resolution 351,271]
353. patient(mary) [resolution 352,129]
359. brave(mary) [resolution 353,102]
360. $false [subsumption resolution 359,126]
% SZS output end Proof for 79916202753024350186756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is curious and vice versa.
If lucy is not quiet then someone is curious or quiet and vice versa.
Everyone who is either curious or patient is both not happy and creative and vice versa.
If someone is either calm or funny then someone is quiet or not humble and vice versa.
If lucy is calm then paul is wise.
Everyone who is not humble or not rich is not funny or funny.
If paul is quiet then someone is both tall and not happy.
Everyone who is old is both not wise and not quiet.
Everyone who is both not humble and curious is either creative or not creative and vice versa.
If lucy is either calm or not patient then someone is not old or not strong.
Everyone who is both creative and strong is both tall and not strong and vice versa.
Everyone who is either not generous or humble is both kind and not rich.
If someone is not curious or quiet then susan is either not rich or not calm.
Everyone who is not tall or old is both creative and funny.
Everyone who is both not tall and not curious is humble and vice versa.
Someone is both generous and not calm.
Someone is either not funny or not wise.
Someone is either generous or not curious.
Alice is not rich.
Mary is both old and calm.
Someone is both patient and generous.
Fred is not kind. | Lucy is not happy. | neutral | (![X]:(old(X)<=>curious(X)))&
((~quiet(lucy))<=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~happy(X)&creative(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
((calm(lucy))=>(wise(paul)))&
(![X]:((~humble(X)|~rich(X))=>(~funny(X)|funny(X))))&
((quiet(paul))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(old(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(creative(X)<~>~creative(X))))&
(((calm(lucy)<~>~patient(lucy)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)&strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(kind(X)&~rich(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((~tall(X)|old(X))=>(creative(X)&funny(X))))&
(![X]:((~tall(X)&~curious(X))<=>humble(X)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(~rich(alice))&
((old(mary)&calm(mary)))&
(?[X]:((patient(X)&generous(X))))&
(~kind(fred)) | ~happy(lucy) | [] | null | 0 |
Everyone who is rich or not happy is either not rich or not calm.
If fred is wise then someone is not strong.
If fred is either not strong or not tall then someone is either not wise or not strong.
Everyone who is either kind or not brave is either not curious or wise and vice versa.
If someone is either not tall or kind then someone is not strong and vice versa.
If someone is both generous and not tall then someone is either not calm or not curious.
If someone is both not happy and not strong then someone is not kind.
If fred is not generous or creative then fred is either not old or tall.
Everyone who is quiet is not brave or curious and vice versa.
Everyone who is not funny or creative is both not old and not curious and vice versa.
If someone is either not old or strong then someone is both not kind and not generous.
Everyone who is brave is both not funny and not brave and vice versa.
Everyone who is both not quiet and old is not kind or not patient.
Everyone who is creative or not brave is brave or not patient.
If someone is kind or tall then someone is both not tall and strong and vice versa.
If someone is either funny or kind then paul is either patient or generous.
Someone is both generous and calm.
Someone is wise or not creative.
Someone is both not tall and not calm.
Someone is not tall or kind.
Mary is kind.
Paul is not tall.
Alice is either not strong or not happy. | Fred is not quiet. | contradiction | (![X]:((rich(X)|~happy(X))=>(~rich(X)<~>~calm(X))))&
((wise(fred))=>(?[X]:(~strong(X))))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>~brave(X))<=>(~curious(X)<~>wise(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)&~tall(X))))=>(?[X]:((~calm(X)<~>~curious(X)))))&
((?[X]:((~happy(X)&~strong(X))))=>(?[X]:(~kind(X))))&
(((~generous(fred)|creative(fred)))=>((~old(fred)<~>tall(fred))))&
(![X]:(quiet(X)<=>(~brave(X)|curious(X))))&
(![X]:((~funny(X)|creative(X))<=>(~old(X)&~curious(X))))&
((?[X]:((~old(X)<~>strong(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(brave(X)<=>(~funny(X)&~brave(X))))&
(![X]:((~quiet(X)&old(X))=>(~kind(X)|~patient(X))))&
(![X]:((creative(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((funny(X)<~>kind(X))))=>((patient(paul)<~>generous(paul))))&
(?[X]:((generous(X)&calm(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:((~tall(X)|kind(X))))&
(kind(mary))&
(~tall(paul))&
((~strong(alice)<~>~happy(alice))) | ~quiet(fred) | [
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 164684119262683526586022
% SZS output start Proof for 164684119262683526586022
9. ! [X0] : (quiet(X0) <=> (curious(X0) | ~brave(X0))) [input p8]
12. ! [X0] : (brave(X0) <=> (~brave(X0) & ~funny(X0))) [input p11]
24. ~quiet(fred) [input hypothesis]
62. ! [X0] : ((quiet(X0) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | ~quiet(X0))) [nnf transformation 9]
63. ! [X0] : ((quiet(X0) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | ~quiet(X0))) [flattening 62]
70. ! [X0] : ((brave(X0) | (brave(X0) | funny(X0))) & ((~brave(X0) & ~funny(X0)) | ~brave(X0))) [nnf transformation 12]
71. ! [X0] : ((brave(X0) | brave(X0) | funny(X0)) & ((~brave(X0) & ~funny(X0)) | ~brave(X0))) [flattening 70]
116. quiet(X0) | brave(X0) [cnf transformation 63]
128. ~brave(X0) | ~brave(X0) [cnf transformation 71]
152. ~quiet(fred) [cnf transformation 24]
154. ~brave(X0) [duplicate literal removal 128]
339. brave(fred) [resolution 116,152]
340. $false [subsumption resolution 339,154]
% SZS output end Proof for 164684119262683526586022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or not creative is either old or happy.
If susan is not strong or not funny then mary is not quiet or happy.
Everyone who is both tall and not funny is either not happy or not strong.
If mary is both patient and not kind then someone is not happy or not generous and vice versa.
If mary is either calm or not tall then alice is either not curious or not quiet.
If john is either not calm or funny then paul is both not wise and not happy.
Everyone who is both happy and not quiet is not tall or kind.
If someone is either curious or not patient then susan is curious or not brave.
Everyone who is either quiet or not humble is either not wise or funny.
Everyone who is either quiet or not quiet is not wise or wise and vice versa.
If susan is not generous or quiet then paul is funny or not patient and vice versa.
Everyone who is both tall and not old is either not kind or not brave.
If fred is not curious then someone is both not strong and funny and vice versa.
Everyone who is both funny and happy is both humble and generous and vice versa.
Everyone who is both not patient and old is not strong or not generous.
Everyone who is not rich is either quiet or not rich.
Someone is calm or not calm.
Someone is both not curious and not generous.
Someone is not strong or rich.
Someone is both brave and patient.
John is funny or not funny.
Someone is not quiet.
Paul is not funny.
Someone is brave. | John is funny. | neutral | (![X]:((~tall(X)<~>~creative(X))=>(old(X)<~>happy(X))))&
(((~strong(susan)|~funny(susan)))=>((~quiet(mary)|happy(mary))))&
(![X]:((tall(X)&~funny(X))=>(~happy(X)<~>~strong(X))))&
(((patient(mary)&~kind(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(((calm(mary)<~>~tall(mary)))=>((~curious(alice)<~>~quiet(alice))))&
(((~calm(john)<~>funny(john)))=>((~wise(paul)&~happy(paul))))&
(![X]:((happy(X)&~quiet(X))=>(~tall(X)|kind(X))))&
((?[X]:((curious(X)<~>~patient(X))))=>((curious(susan)|~brave(susan))))&
(![X]:((quiet(X)<~>~humble(X))=>(~wise(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~wise(X)|wise(X))))&
(((~generous(susan)|quiet(susan)))<=>((funny(paul)|~patient(paul))))&
(![X]:((tall(X)&~old(X))=>(~kind(X)<~>~brave(X))))&
((~curious(fred))<=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:((funny(X)&happy(X))<=>(humble(X)&generous(X))))&
(![X]:((~patient(X)&old(X))=>(~strong(X)|~generous(X))))&
(![X]:(~rich(X)=>(quiet(X)<~>~rich(X))))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~curious(X)&~generous(X))))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:((brave(X)&patient(X))))&
((funny(john)|~funny(john)))&
(?[X]:(~quiet(X)))&
(~funny(paul))&
(?[X]:(brave(X))) | funny(john) | [] | null | 0 |
If someone is both not creative and rich then someone is old and vice versa.
Everyone who is both not creative and tall is either generous or quiet and vice versa.
If someone is both quiet and brave then susan is not wise and vice versa.
Everyone who is not wise is either not strong or not happy and vice versa.
Everyone who is either patient or not rich is happy.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
Everyone who is either patient or not kind is either calm or not wise.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Everyone who is not curious is kind.
If someone is patient or not wise then someone is either happy or strong and vice versa.
Everyone who is wise or creative is both rich and funny.
John is both creative and happy.
Someone is both not patient and not happy.
Someone is brave or generous.
Someone is both rich and not curious.
Someone is not old or not creative.
Someone is both not strong and patient.
Someone is not tall.
Someone is both tall and not calm. | Susan is patient. | neutral | ((?[X]:((~creative(X)&rich(X))))<=>(?[X]:(old(X))))&
(![X]:((~creative(X)&tall(X))<=>(generous(X)<~>quiet(X))))&
((?[X]:((quiet(X)&brave(X))))<=>(~wise(susan)))&
(![X]:(~wise(X)<=>(~strong(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~rich(X))=>happy(X)))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~kind(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
(![X]:(~curious(X)=>kind(X)))&
((?[X]:((patient(X)|~wise(X))))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)&funny(X))))&
((creative(john)&happy(john)))&
(?[X]:((~patient(X)&~happy(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:(~tall(X)))&
(?[X]:((tall(X)&~calm(X)))) | patient(susan) | [] | null | 0 |
If john is either not strong or curious then someone is strong or not strong and vice versa.
If fred is creative then lucy is either strong or not curious.
If susan is not old or kind then someone is not humble and vice versa.
Everyone who is not generous or patient is strong.
If someone is either patient or not funny then susan is either rich or creative and vice versa.
If fred is either creative or not calm then paul is both not wise and generous and vice versa.
Everyone who is either not quiet or wise is either not strong or kind.
Everyone who is not funny or brave is either generous or happy.
Everyone who is not happy is either not wise or not generous.
If someone is not generous or patient then susan is both not creative and not rich.
Everyone who is funny is not happy or rich.
Everyone who is strong or humble is not humble or not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
If fred is both kind and not humble then susan is funny and vice versa.
Lucy is kind.
Someone is not happy.
Someone is both not tall and not creative.
Lucy is curious or not tall.
Someone is either not humble or not rich.
Alice is not happy.
Alice is humble or kind.
Someone is both not funny and not curious. | Alice is rich. | contradiction | (((~strong(john)<~>curious(john)))<=>(?[X]:((strong(X)|~strong(X)))))&
((creative(fred))=>((strong(lucy)<~>~curious(lucy))))&
(((~old(susan)|kind(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|patient(X))=>strong(X)))&
((?[X]:((patient(X)<~>~funny(X))))<=>((rich(susan)<~>creative(susan))))&
(((creative(fred)<~>~calm(fred)))<=>((~wise(paul)&generous(paul))))&
(![X]:((~quiet(X)<~>wise(X))=>(~strong(X)<~>kind(X))))&
(![X]:((~funny(X)|brave(X))=>(generous(X)<~>happy(X))))&
(![X]:(~happy(X)=>(~wise(X)<~>~generous(X))))&
((?[X]:((~generous(X)|patient(X))))=>((~creative(susan)&~rich(susan))))&
(![X]:(funny(X)=>(~happy(X)|rich(X))))&
(![X]:((strong(X)|humble(X))=>(~humble(X)|~rich(X))))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(((kind(fred)&~humble(fred)))<=>(funny(susan)))&
(kind(lucy))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)&~creative(X))))&
((curious(lucy)|~tall(lucy)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(~happy(alice))&
((humble(alice)|kind(alice)))&
(?[X]:((~funny(X)&~curious(X)))) | rich(alice) | [
"p7",
"p8",
"p11",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 378005986366910249341996
% SZS output start Proof for 378005986366910249341996
8. ! [X0] : ((brave(X0) | ~funny(X0)) => (generous(X0) <~> happy(X0))) [input p7]
9. ! [X0] : (~happy(X0) => (~wise(X0) <~> ~generous(X0))) [input p8]
12. ! [X0] : ((humble(X0) | strong(X0)) => (~rich(X0) | ~humble(X0))) [input p11]
15. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p14]
22. ~happy(alice) [input p21]
25. rich(alice) [input hypothesis]
28. ! [X0] : (~funny(X0) => (generous(X0) <~> happy(X0))) [pure predicate removal 8]
32. ! [X0] : ((generous(X0) <~> happy(X0)) | funny(X0)) [ennf transformation 28]
33. ! [X0] : ((~wise(X0) <~> ~generous(X0)) | happy(X0)) [ennf transformation 9]
37. ! [X0] : ((~rich(X0) | ~humble(X0)) | (~humble(X0) & ~strong(X0))) [ennf transformation 12]
38. ! [X0] : (~rich(X0) | ~humble(X0) | (~humble(X0) & ~strong(X0))) [flattening 37]
59. ! [X0] : (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | funny(X0)) [nnf transformation 32]
60. ! [X0] : (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | happy(X0)) [nnf transformation 33]
64. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 15]
65. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 64]
108. happy(X0) | generous(X0) | funny(X0) [cnf transformation 59]
110. ~wise(X0) | ~generous(X0) | happy(X0) [cnf transformation 60]
118. ~rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38]
122. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 65]
124. wise(X0) | humble(X0) | wise(X0) [cnf transformation 65]
134. ~happy(alice) [cnf transformation 22]
138. rich(alice) [cnf transformation 25]
139. ~wise(X0) | ~funny(X0) [duplicate literal removal 122]
140. wise(X0) | humble(X0) [duplicate literal removal 124]
141. ~rich(X0) | ~humble(X0) [duplicate literal removal 118]
292. 32 <=> humble(alice) [avatar definition]
293. ~humble(alice) <- (~32) [avatar component clause 292]
302. ~humble(alice) [resolution 141,138]
305. ~32 [avatar split clause 302,292]
312. generous(alice) | funny(alice) [resolution 108,134]
323. 36 <=> funny(alice) [avatar definition]
325. funny(alice) <- (36) [avatar component clause 323]
327. 37 <=> generous(alice) [avatar definition]
329. generous(alice) <- (37) [avatar component clause 327]
330. 36 | 37 [avatar split clause 312,327,323]
345. 39 <=> wise(alice) [avatar definition]
346. ~wise(alice) <- (~39) [avatar component clause 345]
347. wise(alice) <- (39) [avatar component clause 345]
437. humble(alice) <- (~39) [resolution 346,140]
438. $false <- (~32, ~39) [subsumption resolution 437,293]
439. 32 | 39 [avatar contradiction clause 438]
441. ~generous(alice) | happy(alice) <- (39) [resolution 347,110]
442. ~funny(alice) <- (39) [resolution 347,139]
443. happy(alice) <- (37, 39) [subsumption resolution 441,329]
444. $false <- (37, 39) [subsumption resolution 443,134]
445. ~37 | ~39 [avatar contradiction clause 444]
446. $false <- (36, 39) [subsumption resolution 442,325]
447. ~36 | ~39 [avatar contradiction clause 446]
448. $false [avatar sat refutation 305,330,439,445,447]
% SZS output end Proof for 378005986366910249341996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and happy then someone is not strong.
If alice is either funny or curious then mary is curious.
Everyone who is brave or kind is strong or happy and vice versa.
Everyone who is not humble or not tall is either not generous or not creative and vice versa.
Everyone who is both wise and not funny is both curious and not old and vice versa.
If john is both wise and not happy then alice is not funny or old and vice versa.
Everyone who is both not curious and tall is both funny and old and vice versa.
If someone is either not quiet or not humble then someone is either kind or creative.
If mary is funny then someone is both creative and quiet and vice versa.
Everyone who is either not patient or rich is both kind and calm and vice versa.
If someone is either humble or not humble then someone is either not humble or not creative.
If lucy is both not curious and not patient then someone is not brave or not funny.
Everyone who is either not wise or wise is not generous and vice versa.
Everyone who is not tall is either not humble or kind and vice versa.
Everyone who is not quiet or brave is both not curious and not strong.
Everyone who is kind is either not tall or not kind and vice versa.
Someone is both not calm and not happy.
Someone is either not calm or not tall.
Someone is both not curious and brave.
Someone is both humble and brave.
Alice is both rich and not happy.
Someone is brave.
Paul is not curious. | Lucy is not rich. | neutral | ((?[X]:((tall(X)&happy(X))))=>(?[X]:(~strong(X))))&
(((funny(alice)<~>curious(alice)))=>(curious(mary)))&
(![X]:((brave(X)|kind(X))<=>(strong(X)|happy(X))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)&~old(X))))&
(((wise(john)&~happy(john)))<=>((~funny(alice)|old(alice))))&
(![X]:((~curious(X)&tall(X))<=>(funny(X)&old(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((kind(X)<~>creative(X)))))&
((funny(mary))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>(kind(X)&calm(X))))&
((?[X]:((humble(X)<~>~humble(X))))=>(?[X]:((~humble(X)<~>~creative(X)))))&
(((~curious(lucy)&~patient(lucy)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~generous(X)))&
(![X]:(~tall(X)<=>(~humble(X)<~>kind(X))))&
(![X]:((~quiet(X)|brave(X))=>(~curious(X)&~strong(X))))&
(![X]:(kind(X)<=>(~tall(X)<~>~kind(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((humble(X)&brave(X))))&
((rich(alice)&~happy(alice)))&
(?[X]:(brave(X)))&
(~curious(paul)) | ~rich(lucy) | [] | null | 0 |
If someone is either not old or not patient then lucy is creative or not happy. Everyone who is both funny and curious is rich or brave and vice versa. If paul is either tall or curious then alice is both not old and generous and vice versa. Everyone who is not brave or not tall is humble and vice versa. Everyone who is not curious is calm and vice versa. Everyone who is either wise or not generous is not generous. If someone is not funny then someone is either not strong or not generous. Everyone who is rich or not curious is either not humble or strong and vice versa. Everyone who is not quiet is not curious or not calm and vice versa. Everyone who is not generous or brave is both happy and kind and vice versa. Everyone who is either wise or curious is not happy and vice versa. If mary is both not wise and not creative then john is both funny and humble and vice versa. If fred is not old then susan is not humble. If someone is brave then someone is either generous or curious. If mary is not humble or not old then someone is both happy and not quiet and vice versa. If alice is rich or not quiet then someone is generous and vice versa. Someone is either wise or not old. Susan is patient. Mary is wise or not quiet. Alice is both funny and kind. Paul is happy or not funny. Someone is either quiet or not rich. Someone is both not wise and tall. Someone is either brave or not humble. | Paul is not humble. | neutral | ((?[X]:((~old(X)<~>~patient(X))))=>((creative(lucy)|~happy(lucy))))&
(![X]:((funny(X)&curious(X))<=>(rich(X)|brave(X))))&
(((tall(paul)<~>curious(paul)))<=>((~old(alice)&generous(alice))))&
(![X]:((~brave(X)|~tall(X))<=>humble(X)))&
(![X]:(~curious(X)<=>calm(X)))&
(![X]:((wise(X)<~>~generous(X))=>~generous(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~humble(X)<~>strong(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|~calm(X))))&
(![X]:((~generous(X)|brave(X))<=>(happy(X)&kind(X))))&
(![X]:((wise(X)<~>curious(X))<=>~happy(X)))&
(((~wise(mary)&~creative(mary)))<=>((funny(john)&humble(john))))&
((~old(fred))=>(~humble(susan)))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>curious(X)))))&
(((~humble(mary)|~old(mary)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((rich(alice)|~quiet(alice)))<=>(?[X]:(generous(X))))&
(?[X]:((wise(X)<~>~old(X))))&
(patient(susan))&
((wise(mary)|~quiet(mary)))&
((funny(alice)&kind(alice)))&
((happy(paul)|~funny(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((brave(X)<~>~humble(X)))) | ~humble(paul) | [] | null | 0 |
If someone is happy then john is either funny or wise and vice versa.
Everyone who is tall or not generous is kind and vice versa.
If paul is brave or not old then someone is not curious or not creative.
Everyone who is not kind is either not kind or not old.
Everyone who is both not quiet and humble is both patient and not patient and vice versa.
Everyone who is not strong is both generous and not calm and vice versa.
Everyone who is patient or not patient is strong.
If john is rich or strong then someone is not funny and vice versa.
Everyone who is both calm and generous is both funny and old and vice versa.
Everyone who is humble is both patient and not rich.
If lucy is not old then mary is both patient and generous.
If someone is not humble or not rich then john is quiet.
Everyone who is not funny or not brave is either not wise or not kind.
If someone is both rich and wise then someone is quiet or not strong and vice versa.
Everyone who is not brave is not wise or kind and vice versa.
If someone is strong then someone is either not generous or not patient and vice versa.
Paul is not happy.
Susan is either humble or not funny.
Someone is either quiet or patient.
Mary is not calm.
Someone is not kind or curious.
Susan is brave.
Someone is not happy or not old.
Someone is not old or creative. | Mary is wise. | contradiction | ((?[X]:(happy(X)))<=>((funny(john)<~>wise(john))))&
(![X]:((tall(X)|~generous(X))<=>kind(X)))&
(((brave(paul)|~old(paul)))=>(?[X]:((~curious(X)|~creative(X)))))&
(![X]:(~kind(X)=>(~kind(X)<~>~old(X))))&
(![X]:((~quiet(X)&humble(X))<=>(patient(X)&~patient(X))))&
(![X]:(~strong(X)<=>(generous(X)&~calm(X))))&
(![X]:((patient(X)|~patient(X))=>strong(X)))&
(((rich(john)|strong(john)))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&generous(X))<=>(funny(X)&old(X))))&
(![X]:(humble(X)=>(patient(X)&~rich(X))))&
((~old(lucy))=>((patient(mary)&generous(mary))))&
((?[X]:((~humble(X)|~rich(X))))=>(quiet(john)))&
(![X]:((~funny(X)|~brave(X))=>(~wise(X)<~>~kind(X))))&
((?[X]:((rich(X)&wise(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:(~brave(X)<=>(~wise(X)|kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
(~happy(paul))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((quiet(X)<~>patient(X))))&
(~calm(mary))&
(?[X]:((~kind(X)|curious(X))))&
(brave(susan))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~old(X)|creative(X)))) | wise(mary) | [
"p1",
"p5",
"p6",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5952604870493836264253082
% SZS output start Proof for 5952604870493836264253082
2. ! [X0] : ((~generous(X0) | tall(X0)) <=> kind(X0)) [input p1]
6. ! [X0] : (~strong(X0) <=> (~calm(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | patient(X0)) => strong(X0)) [input p6]
13. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~wise(X0) <~> ~kind(X0))) [input p12]
15. ! [X0] : (~brave(X0) <=> (kind(X0) | ~wise(X0))) [input p14]
20. ~calm(mary) [input p19]
25. wise(mary) [input hypothesis]
30. ! [X0] : (strong(X0) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
34. ! [X0] : ((~wise(X0) <~> ~kind(X0)) | (brave(X0) & funny(X0))) [ennf transformation 13]
39. ! [X0] : (((~generous(X0) | tall(X0)) | ~kind(X0)) & (kind(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 2]
40. ! [X0] : ((~generous(X0) | tall(X0) | ~kind(X0)) & (kind(X0) | (generous(X0) & ~tall(X0)))) [flattening 39]
46. ! [X0] : ((~strong(X0) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | strong(X0))) [nnf transformation 6]
47. ! [X0] : ((~strong(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | strong(X0))) [flattening 46]
55. ! [X0] : (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (brave(X0) & funny(X0))) [nnf transformation 34]
61. ! [X0] : ((~brave(X0) | (~kind(X0) & wise(X0))) & ((kind(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 15]
62. ! [X0] : ((~brave(X0) | (~kind(X0) & wise(X0))) & (kind(X0) | ~wise(X0) | brave(X0))) [flattening 61]
83. kind(X0) | generous(X0) [cnf transformation 40]
95. ~strong(X0) | calm(X0) | ~generous(X0) [cnf transformation 47]
96. strong(X0) | ~patient(X0) [cnf transformation 30]
97. strong(X0) | patient(X0) [cnf transformation 30]
112. ~kind(X0) | ~wise(X0) | brave(X0) [cnf transformation 55]
120. kind(X0) | ~wise(X0) | brave(X0) [cnf transformation 62]
122. ~brave(X0) | ~kind(X0) [cnf transformation 62]
132. ~calm(mary) [cnf transformation 20]
137. wise(mary) [cnf transformation 25]
177. strong(X0) [subsumption resolution 96,97]
184. 10 <=> generous(mary) [avatar definition]
186. generous(mary) <- (10) [avatar component clause 184]
227. ~wise(X0) | brave(X0) [subsumption resolution 120,112]
308. brave(mary) [resolution 227,137]
322. ~kind(mary) [resolution 308,122]
328. ~generous(X2) | calm(X2) [resolution 95,177]
329. generous(mary) [resolution 322,83]
330. 10 [avatar split clause 329,184]
358. calm(mary) <- (10) [resolution 328,186]
363. $false <- (10) [subsumption resolution 358,132]
364. ~10 [avatar contradiction clause 363]
365. $false [avatar sat refutation 330,364]
% SZS output end Proof for 5952604870493836264253082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or funny is not old or not tall and vice versa.
Everyone who is either funny or generous is not patient or tall and vice versa.
If paul is both not strong and not wise then mary is either not old or generous and vice versa.
Everyone who is either not old or strong is either patient or funny and vice versa.
Everyone who is patient or not old is both not strong and not humble.
If someone is both not quiet and humble then someone is not wise.
If susan is patient or generous then someone is both not brave and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is rich is either not brave or wise.
Paul is not rich or not patient.
Susan is either brave or not quiet.
Alice is not humble.
Someone is either not old or old.
Fred is old or not patient.
John is not kind or not quiet.
Paul is wise.
Someone is either not quiet or not strong. | Mary is not calm. | entailment | (![X]:((~calm(X)<~>funny(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)<~>generous(X))<=>(~patient(X)|tall(X))))&
(((~strong(paul)&~wise(paul)))<=>((~old(mary)<~>generous(mary))))&
(![X]:((~old(X)<~>strong(X))<=>(patient(X)<~>funny(X))))&
(![X]:((patient(X)|~old(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~quiet(X)&humble(X))))=>(?[X]:(~wise(X))))&
(((patient(susan)|generous(susan)))=>(?[X]:((~brave(X)&~quiet(X)))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((~rich(paul)|~patient(paul)))&
((brave(susan)<~>~quiet(susan)))&
(~humble(alice))&
(?[X]:((~old(X)<~>old(X))))&
((old(fred)|~patient(fred)))&
((~kind(john)|~quiet(john)))&
(wise(paul))&
(?[X]:((~quiet(X)<~>~strong(X)))) | ~calm(mary) | [
"p0",
"p1",
"p2",
"p9",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 497318623548869291552214
% SZS output start Proof for 497318623548869291552214
1. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~tall(X0) | ~old(X0))) [input p0]
2. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (tall(X0) | ~patient(X0))) [input p1]
3. (~wise(paul) & ~strong(paul)) <=> (~old(mary) <~> generous(mary)) [input p2]
10. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p10]
22. wise(paul) [input p21]
24. calm(mary) [input hypothesis]
32. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 10]
33. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (tall(X0) & old(X0))) & ((~tall(X0) | ~old(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 1]
34. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (tall(X0) & old(X0))) & (~tall(X0) | ~old(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [flattening 33]
35. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~tall(X0) & patient(X0))) & ((tall(X0) | ~patient(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 2]
36. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~tall(X0) & patient(X0))) & (tall(X0) | ~patient(X0) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 35]
37. ((~wise(paul) & ~strong(paul)) | ((~old(mary) | ~generous(mary)) & (generous(mary) | old(mary)))) & (((~generous(mary) | old(mary)) & (generous(mary) | ~old(mary))) | (wise(paul) | strong(paul))) [nnf transformation 3]
38. ((~wise(paul) & ~strong(paul)) | ((~old(mary) | ~generous(mary)) & (generous(mary) | old(mary)))) & (((~generous(mary) | old(mary)) & (generous(mary) | ~old(mary))) | wise(paul) | strong(paul)) [flattening 37]
50. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 50]
71. ~tall(X0) | ~old(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 34]
79. ~tall(X0) | funny(X0) | generous(X0) [cnf transformation 36]
80. ~generous(X0) | ~funny(X0) | patient(X0) [cnf transformation 36]
86. ~wise(paul) | generous(mary) | old(mary) [cnf transformation 38]
87. ~wise(paul) | ~old(mary) | ~generous(mary) [cnf transformation 38]
113. old(X0) | funny(X0) [cnf transformation 32]
114. ~patient(X0) | old(X0) [cnf transformation 32]
116. generous(X0) | tall(X0) [cnf transformation 51]
140. wise(paul) [cnf transformation 22]
143. calm(mary) [cnf transformation 24]
149. 1 <=> generous(mary) [avatar definition]
150. generous(mary) <- (1) [avatar component clause 149]
151. ~generous(mary) <- (~1) [avatar component clause 149]
153. 2 <=> old(mary) [avatar definition]
154. old(mary) <- (2) [avatar component clause 153]
155. ~old(mary) <- (~2) [avatar component clause 153]
157. 3 <=> wise(paul) [avatar definition]
160. ~1 | ~2 | ~3 [avatar split clause 87,157,153,149]
161. 2 | 1 | ~3 [avatar split clause 86,157,149,153]
278. 3 [avatar split clause 140,157]
289. tall(mary) <- (~1) [resolution 116,151]
301. funny(mary) | generous(mary) <- (~1) [resolution 79,289]
305. funny(mary) <- (~1) [subsumption resolution 301,151]
377. ~old(mary) | ~calm(mary) | ~funny(mary) <- (~1) [resolution 71,289]
380. ~calm(mary) | ~funny(mary) <- (~1, 2) [subsumption resolution 377,154]
381. ~funny(mary) <- (~1, 2) [subsumption resolution 380,143]
382. $false <- (~1, 2) [subsumption resolution 381,305]
383. 1 | ~2 [avatar contradiction clause 382]
389. 34 <=> funny(mary) [avatar definition]
395. ~funny(mary) | patient(mary) <- (1) [resolution 150,80]
399. 35 <=> patient(mary) [avatar definition]
401. patient(mary) <- (35) [avatar component clause 399]
402. 35 | ~34 | ~1 [avatar split clause 395,149,389,399]
403. funny(mary) <- (~2) [resolution 155,113]
412. 34 | 2 [avatar split clause 403,153,389]
464. old(mary) <- (35) [resolution 401,114]
465. $false <- (~2, 35) [subsumption resolution 464,155]
466. 2 | ~35 [avatar contradiction clause 465]
467. $false [avatar sat refutation 160,161,278,383,402,412,466]
% SZS output end Proof for 497318623548869291552214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then alice is creative or wise and vice versa.
Everyone who is not wise is humble and vice versa.
If lucy is both humble and not patient then someone is generous or not curious.
Everyone who is both not happy and not calm is both not wise and rich.
Everyone who is brave is creative or patient and vice versa.
If lucy is either not brave or generous then lucy is both curious and calm and vice versa.
Everyone who is not old or not generous is either funny or curious and vice versa.
If someone is either not tall or not wise then susan is tall or rich.
Everyone who is brave is tall and vice versa.
Everyone who is old is both tall and not old and vice versa.
If alice is either not calm or wise then someone is either not kind or kind.
Everyone who is quiet is kind.
Everyone who is not funny or generous is not happy or not strong and vice versa.
Everyone who is generous or curious is creative or not happy.
Everyone who is either kind or not kind is not curious and vice versa.
Lucy is either not humble or not strong.
Someone is either rich or strong.
Someone is either not strong or not creative.
Someone is either happy or not funny.
Mary is happy.
Mary is funny.
Mary is not calm. | Lucy is brave. | contradiction | ((?[X]:(~old(X)))<=>((creative(alice)|wise(alice))))&
(![X]:(~wise(X)<=>humble(X)))&
(((humble(lucy)&~patient(lucy)))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~wise(X)&rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
(((~brave(lucy)<~>generous(lucy)))<=>((curious(lucy)&calm(lucy))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)<~>curious(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>((tall(susan)|rich(susan))))&
(![X]:(brave(X)<=>tall(X)))&
(![X]:(old(X)<=>(tall(X)&~old(X))))&
(((~calm(alice)<~>wise(alice)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)|~strong(X))))&
(![X]:((generous(X)|curious(X))=>(creative(X)|~happy(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~curious(X)))&
((~humble(lucy)<~>~strong(lucy)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(happy(mary))&
(funny(mary))&
(~calm(mary)) | brave(lucy) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7798199737196345387766988
% SZS output start Proof for 7798199737196345387766988
9. ! [X0] : (brave(X0) <=> tall(X0)) [input p8]
10. ! [X0] : (old(X0) <=> (~old(X0) & tall(X0))) [input p9]
23. brave(lucy) [input hypothesis]
49. ! [X0] : ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0))) [nnf transformation 9]
50. ! [X0] : ((old(X0) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | ~old(X0))) [nnf transformation 10]
51. ! [X0] : ((old(X0) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | ~old(X0))) [flattening 50]
93. ~brave(X0) | tall(X0) [cnf transformation 49]
96. ~old(X0) | ~old(X0) [cnf transformation 51]
97. old(X0) | old(X0) | ~tall(X0) [cnf transformation 51]
123. brave(lucy) [cnf transformation 23]
126. ~old(X0) [duplicate literal removal 96]
127. ~tall(X0) | old(X0) [duplicate literal removal 97]
172. 11 <=> brave(lucy) [avatar definition]
174. brave(lucy) <- (11) [avatar component clause 172]
238. 11 [avatar split clause 123,172]
242. tall(lucy) <- (11) [resolution 93,174]
248. old(lucy) <- (11) [resolution 127,242]
251. $false <- (11) [subsumption resolution 248,126]
252. ~11 [avatar contradiction clause 251]
253. $false [avatar sat refutation 238,252]
% SZS output end Proof for 7798199737196345387766988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is brave or not curious and vice versa. If someone is not creative then lucy is not old or not brave and vice versa. Everyone who is tall or generous is both not quiet and kind. Everyone who is not funny or calm is not quiet. If paul is not quiet then susan is happy or not kind and vice versa. If lucy is either humble or not humble then alice is not generous and vice versa. Everyone who is either tall or not creative is both tall and not rich. If someone is either not rich or not tall then lucy is either not humble or rich. Everyone who is strong or calm is calm and vice versa. Everyone who is either not brave or not patient is both not humble and not strong. Everyone who is either generous or strong is not calm or quiet and vice versa. If someone is either strong or not wise then someone is not kind or curious and vice versa. If someone is both old and not tall then paul is not patient or not brave. If mary is both not strong and happy then lucy is either not old or calm. Everyone who is either not kind or not funny is both funny and not old. If someone is both not old and tall then someone is either curious or old and vice versa. Someone is both creative and generous. Lucy is not patient or not rich. Someone is not humble. Someone is either not strong or kind. John is curious. Alice is not wise or happy. Alice is both funny and patient. Someone is patient or not happy. | Lucy is quiet. | contradiction | (![X]:(patient(X)<=>(brave(X)|~curious(X))))&
((?[X]:(~creative(X)))<=>((~old(lucy)|~brave(lucy))))&
(![X]:((tall(X)|generous(X))=>(~quiet(X)&kind(X))))&
(![X]:((~funny(X)|calm(X))=>~quiet(X)))&
((~quiet(paul))<=>((happy(susan)|~kind(susan))))&
(((humble(lucy)<~>~humble(lucy)))<=>(~generous(alice)))&
(![X]:((tall(X)<~>~creative(X))=>(tall(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~tall(X))))=>((~humble(lucy)<~>rich(lucy))))&
(![X]:((strong(X)|calm(X))<=>calm(X)))&
(![X]:((~brave(X)<~>~patient(X))=>(~humble(X)&~strong(X))))&
(![X]:((generous(X)<~>strong(X))<=>(~calm(X)|quiet(X))))&
((?[X]:((strong(X)<~>~wise(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
((?[X]:((old(X)&~tall(X))))=>((~patient(paul)|~brave(paul))))&
(((~strong(mary)&happy(mary)))=>((~old(lucy)<~>calm(lucy))))&
(![X]:((~kind(X)<~>~funny(X))=>(funny(X)&~old(X))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((curious(X)<~>old(X)))))&
(?[X]:((creative(X)&generous(X))))&
((~patient(lucy)|~rich(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)<~>kind(X))))&
(curious(john))&
((~wise(alice)|happy(alice)))&
((funny(alice)&patient(alice)))&
(?[X]:((patient(X)|~happy(X)))) | quiet(lucy) | [
"p2",
"p3",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8829668234610977240143331
% SZS output start Proof for 8829668234610977240143331
3. ! [X0] : ((generous(X0) | tall(X0)) => (kind(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : ((calm(X0) | ~funny(X0)) => ~quiet(X0)) [input p3]
9. ! [X0] : ((calm(X0) | strong(X0)) <=> calm(X0)) [input p8]
11. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p10]
25. quiet(lucy) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~quiet(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 3]
29. ! [X0] : (~quiet(X0) | (~calm(X0) & funny(X0))) [ennf transformation 4]
50. ! [X0] : (((calm(X0) | strong(X0)) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((calm(X0) | strong(X0) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~strong(X0)))) [flattening 50]
53. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 11]
54. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 53]
83. ~quiet(X0) | ~generous(X0) [cnf transformation 28]
87. ~calm(X0) | ~quiet(X0) [cnf transformation 29]
103. ~strong(X0) | calm(X0) [cnf transformation 51]
113. strong(X0) | generous(X0) | ~quiet(X0) [cnf transformation 54]
146. quiet(lucy) [cnf transformation 25]
208. ~quiet(X0) | strong(X0) [subsumption resolution 113,83]
264. 25 <=> calm(lucy) [avatar definition]
265. calm(lucy) <- (25) [avatar component clause 264]
342. strong(lucy) [resolution 208,146]
343. calm(lucy) [resolution 342,103]
344. 25 [avatar split clause 343,264]
345. ~quiet(lucy) <- (25) [resolution 265,87]
346. $false <- (25) [subsumption resolution 345,146]
347. ~25 [avatar contradiction clause 346]
348. $false [avatar sat refutation 344,347]
% SZS output end Proof for 8829668234610977240143331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient then lucy is both not rich and kind.
If someone is not brave or tall then lucy is humble or not generous.
Everyone who is both not rich and not tall is not funny or old and vice versa.
If susan is both not funny and not humble then john is both happy and not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Mary is curious or not funny.
Someone is not quiet.
John is both wise and not patient.
Paul is either not creative or not kind.
Mary is both not patient and kind.
Someone is not happy or not generous.
Fred is both strong and humble. | Fred is happy. | contradiction | ((patient(lucy))=>((~rich(lucy)&kind(lucy))))&
((?[X]:((~brave(X)|tall(X))))=>((humble(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&~tall(X))<=>(~funny(X)|old(X))))&
(((~funny(susan)&~humble(susan)))<=>((happy(john)&~kind(john))))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
((curious(mary)|~funny(mary)))&
(?[X]:(~quiet(X)))&
((wise(john)&~patient(john)))&
((~creative(paul)<~>~kind(paul)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
((strong(fred)&humble(fred))) | happy(fred) | [
"p7",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 247269310310652883928276
% SZS output start Proof for 247269310310652883928276
8. ? [X0] : (generous(X0) | ~old(X0)) <=> (kind(paul) & brave(paul)) [input p7]
13. ! [X0] : ((~happy(X0) & generous(X0)) <=> (~funny(X0) | old(X0))) [input p12]
14. (~strong(fred) | old(fred)) <=> ? [X0] : (kind(X0) | happy(X0)) [input p13]
23. humble(fred) & strong(fred) [input p22]
24. happy(fred) [input hypothesis]
44. (? [X0] : (generous(X0) | ~old(X0)) | (~kind(paul) | ~brave(paul))) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [nnf transformation 8]
45. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [flattening 44]
46. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [rectify 45]
47. ? [X0] : (generous(X0) | ~old(X0)) => (generous(sK1) | ~old(sK1)) [choice axiom]
48. ((generous(sK1) | ~old(sK1)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [skolemisation 46,47]
61. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (happy(X0) | ~generous(X0)))) [nnf transformation 13]
62. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | happy(X0) | ~generous(X0))) [flattening 61]
63. ((~strong(fred) | old(fred)) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X0] : (kind(X0) | happy(X0)) | (strong(fred) & ~old(fred))) [nnf transformation 14]
64. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X0] : (kind(X0) | happy(X0)) | (strong(fred) & ~old(fred))) [flattening 63]
65. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X1] : (kind(X1) | happy(X1)) | (strong(fred) & ~old(fred))) [rectify 64]
66. ? [X1] : (kind(X1) | happy(X1)) => (kind(sK4) | happy(sK4)) [choice axiom]
67. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & ((kind(sK4) | happy(sK4)) | (strong(fred) & ~old(fred))) [skolemisation 65,66]
110. kind(paul) | old(X1) [cnf transformation 48]
111. kind(paul) | ~generous(X1) [cnf transformation 48]
128. ~old(X0) | generous(X0) [cnf transformation 62]
130. ~happy(X0) | ~old(X0) [cnf transformation 62]
135. ~strong(fred) | old(fred) | ~kind(X0) [cnf transformation 67]
156. strong(fred) [cnf transformation 23]
158. happy(fred) [cnf transformation 24]
226. 16 <=> kind(paul) [avatar definition]
227. kind(paul) <- (16) [avatar component clause 226]
239. 19 <=> ! [X1] : ~generous(X1) [avatar definition]
240. ~generous(X1) <- (19) [avatar component clause 239]
241. 19 | 16 [avatar split clause 111,226,239]
243. 20 <=> ! [X1] : old(X1) [avatar definition]
244. old(X1) <- (20) [avatar component clause 243]
245. 20 | 16 [avatar split clause 110,226,243]
309. 34 <=> ! [X0] : ~kind(X0) [avatar definition]
310. ~kind(X0) <- (34) [avatar component clause 309]
312. 35 <=> old(fred) [avatar definition]
316. 36 <=> strong(fred) [avatar definition]
319. 34 | 35 | ~36 [avatar split clause 135,316,312,309]
404. 36 [avatar split clause 156,316]
405. $false <- (16, 34) [subsumption resolution 227,310]
406. ~16 | ~34 [avatar contradiction clause 405]
446. ~old(fred) [resolution 130,158]
451. ~35 [avatar split clause 446,312]
453. generous(X0) <- (20) [resolution 244,128]
456. $false <- (19, 20) [subsumption resolution 453,240]
457. ~19 | ~20 [avatar contradiction clause 456]
460. $false [avatar sat refutation 241,245,319,404,406,451,457]
% SZS output end Proof for 247269310310652883928276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is both humble and quiet.
Everyone who is both not funny and not strong is not kind or not humble and vice versa.
If someone is either not rich or not strong then mary is either curious or calm.
Everyone who is either not humble or not calm is either not tall or quiet.
If someone is not old or not humble then someone is either calm or not kind.
Everyone who is both not brave and not wise is not kind and vice versa.
If someone is both wise and humble then someone is both old and calm and vice versa.
Everyone who is both not curious and rich is curious.
Everyone who is either not patient or not curious is either humble or not creative and vice versa.
Everyone who is either not patient or not wise is both wise and humble and vice versa.
If paul is either patient or not creative then susan is both tall and not creative and vice versa.
Everyone who is quiet is either patient or not creative and vice versa.
Everyone who is both not patient and generous is rich or strong and vice versa.
If susan is old or kind then alice is old.
If john is not humble then someone is both curious and patient.
Everyone who is both not kind and not old is both creative and not creative.
John is both not happy and funny.
Someone is brave.
Alice is either not creative or not quiet.
Mary is not wise.
Susan is strong or curious.
Someone is funny or not kind.
Someone is both funny and wise. | John is not creative. | entailment | (![X]:(funny(X)=>(humble(X)&quiet(X))))&
(![X]:((~funny(X)&~strong(X))<=>(~kind(X)|~humble(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((curious(mary)<~>calm(mary))))&
(![X]:((~humble(X)<~>~calm(X))=>(~tall(X)<~>quiet(X))))&
((?[X]:((~old(X)|~humble(X))))=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~brave(X)&~wise(X))<=>~kind(X)))&
((?[X]:((wise(X)&humble(X))))<=>(?[X]:((old(X)&calm(X)))))&
(![X]:((~curious(X)&rich(X))=>curious(X)))&
(![X]:((~patient(X)<~>~curious(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&humble(X))))&
(((patient(paul)<~>~creative(paul)))<=>((tall(susan)&~creative(susan))))&
(![X]:(quiet(X)<=>(patient(X)<~>~creative(X))))&
(![X]:((~patient(X)&generous(X))<=>(rich(X)|strong(X))))&
(((old(susan)|kind(susan)))=>(old(alice)))&
((~humble(john))=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((~kind(X)&~old(X))=>(creative(X)&~creative(X))))&
((~happy(john)&funny(john)))&
(?[X]:(brave(X)))&
((~creative(alice)<~>~quiet(alice)))&
(~wise(mary))&
((strong(susan)|curious(susan)))&
(?[X]:((funny(X)|~kind(X))))&
(?[X]:((funny(X)&wise(X)))) | ~creative(john) | [
"p0",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2771594535731155948431765
% SZS output start Proof for 2771594535731155948431765
1. ! [X0] : (funny(X0) => (quiet(X0) & humble(X0))) [input p0]
10. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (humble(X0) & wise(X0))) [input p9]
12. ! [X0] : (quiet(X0) <=> (patient(X0) <~> ~creative(X0))) [input p11]
17. funny(john) & ~happy(john) [input p16]
24. creative(john) [input hypothesis]
27. funny(john) [pure predicate removal 17]
28. ! [X0] : ((quiet(X0) & humble(X0)) | ~funny(X0)) [ennf transformation 1]
54. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 10]
55. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 54]
58. ! [X0] : ((quiet(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ~quiet(X0))) [nnf transformation 12]
70. ~funny(X0) | humble(X0) [cnf transformation 28]
71. ~funny(X0) | quiet(X0) [cnf transformation 28]
106. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 55]
109. ~wise(X0) | ~patient(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 55]
117. ~creative(X0) | patient(X0) | ~quiet(X0) [cnf transformation 58]
132. funny(john) [cnf transformation 27]
141. creative(john) [cnf transformation 24]
142. ~patient(X0) | wise(X0) [duplicate literal removal 106]
143. ~patient(X0) | ~wise(X0) | ~humble(X0) [duplicate literal removal 109]
244. 22 <=> humble(john) [avatar definition]
286. humble(john) [resolution 70,132]
288. quiet(john) [resolution 71,132]
328. 34 <=> wise(john) [avatar definition]
330. wise(john) <- (34) [avatar component clause 328]
336. patient(john) | ~quiet(john) [resolution 117,141]
338. patient(john) [subsumption resolution 336,288]
341. wise(john) [resolution 338,142]
344. 34 [avatar split clause 341,328]
399. ~wise(john) | ~humble(john) [resolution 143,338]
400. ~humble(john) <- (34) [subsumption resolution 399,330]
403. ~22 | ~34 [avatar split clause 400,328,244]
404. 22 [avatar split clause 286,244]
405. $false [avatar sat refutation 344,403,404]
% SZS output end Proof for 2771594535731155948431765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not tall then john is both calm and not happy and vice versa.
If someone is both humble and not wise then lucy is both rich and not calm.
Everyone who is both not tall and happy is not quiet and vice versa.
If susan is both not old and creative then john is humble or not old and vice versa.
Everyone who is either curious or wise is wise or not patient.
Everyone who is not creative or not humble is both humble and not patient.
If mary is both generous and funny then mary is humble or calm.
Everyone who is tall is either not calm or quiet and vice versa.
If fred is happy or not curious then someone is not old or tall and vice versa.
Everyone who is wise or not brave is both wise and not quiet and vice versa.
Everyone who is either patient or tall is curious or not curious.
If someone is happy then someone is both patient and creative.
Everyone who is both not brave and curious is not kind and vice versa.
If lucy is either not rich or brave then someone is not creative or strong and vice versa.
Everyone who is tall is not creative.
If fred is happy or wise then someone is either rich or not old.
Someone is either old or calm.
Mary is old or funny.
Someone is not wise.
Someone is not happy.
Susan is both not generous and not wise.
Paul is both not wise and not patient.
Someone is calm or not wise. | John is kind. | entailment | ((?[X]:((humble(X)&~tall(X))))<=>((calm(john)&~happy(john))))&
((?[X]:((humble(X)&~wise(X))))=>((rich(lucy)&~calm(lucy))))&
(![X]:((~tall(X)&happy(X))<=>~quiet(X)))&
(((~old(susan)&creative(susan)))<=>((humble(john)|~old(john))))&
(![X]:((curious(X)<~>wise(X))=>(wise(X)|~patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(humble(X)&~patient(X))))&
(((generous(mary)&funny(mary)))=>((humble(mary)|calm(mary))))&
(![X]:(tall(X)<=>(~calm(X)<~>quiet(X))))&
(((happy(fred)|~curious(fred)))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((wise(X)|~brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((patient(X)<~>tall(X))=>(curious(X)|~curious(X))))&
((?[X]:(happy(X)))=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((~brave(X)&curious(X))<=>~kind(X)))&
(((~rich(lucy)<~>brave(lucy)))<=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:(tall(X)=>~creative(X)))&
(((happy(fred)|wise(fred)))=>(?[X]:((rich(X)<~>~old(X)))))&
(?[X]:((old(X)<~>calm(X))))&
((old(mary)|funny(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(~happy(X)))&
((~generous(susan)&~wise(susan)))&
((~wise(paul)&~patient(paul)))&
(?[X]:((calm(X)|~wise(X)))) | kind(john) | [
"p0",
"p2",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 811007628673611607989460
% SZS output start Proof for 811007628673611607989460
1. ? [X0] : (~tall(X0) & humble(X0)) <=> (~happy(john) & calm(john)) [input p0]
3. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~quiet(X0)) [input p2]
6. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~patient(X0) & humble(X0))) [input p5]
10. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~quiet(X0) & wise(X0))) [input p9]
13. ! [X0] : ((curious(X0) & ~brave(X0)) <=> ~kind(X0)) [input p12]
24. ~kind(john) [input hypothesis]
26. ! [X0] : (~kind(X0) => (curious(X0) & ~brave(X0))) [unused predicate definition removal 13]
33. ! [X0] : ((~patient(X0) & humble(X0)) | (humble(X0) & creative(X0))) [ennf transformation 6]
37. ! [X0] : ((curious(X0) & ~brave(X0)) | kind(X0)) [ennf transformation 26]
40. (? [X0] : (~tall(X0) & humble(X0)) | (happy(john) | ~calm(john))) & ((~happy(john) & calm(john)) | ! [X0] : (tall(X0) | ~humble(X0))) [nnf transformation 1]
41. (? [X0] : (~tall(X0) & humble(X0)) | happy(john) | ~calm(john)) & ((~happy(john) & calm(john)) | ! [X0] : (tall(X0) | ~humble(X0))) [flattening 40]
42. (? [X0] : (~tall(X0) & humble(X0)) | happy(john) | ~calm(john)) & ((~happy(john) & calm(john)) | ! [X1] : (tall(X1) | ~humble(X1))) [rectify 41]
43. ? [X0] : (~tall(X0) & humble(X0)) => (~tall(sK0) & humble(sK0)) [choice axiom]
44. ((~tall(sK0) & humble(sK0)) | happy(john) | ~calm(john)) & ((~happy(john) & calm(john)) | ! [X1] : (tall(X1) | ~humble(X1))) [skolemisation 42,43]
45. ! [X0] : (((happy(X0) & ~tall(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 3]
46. ! [X0] : (((happy(X0) & ~tall(X0)) | quiet(X0)) & (~quiet(X0) | ~happy(X0) | tall(X0))) [flattening 45]
56. ! [X0] : (((~brave(X0) | wise(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (brave(X0) & ~wise(X0)))) [nnf transformation 10]
57. ! [X0] : ((~brave(X0) | wise(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (brave(X0) & ~wise(X0)))) [flattening 56]
79. ~happy(john) | tall(X1) | ~humble(X1) [cnf transformation 44]
85. ~tall(X0) | quiet(X0) [cnf transformation 46]
86. quiet(X0) | happy(X0) [cnf transformation 46]
95. humble(X0) | humble(X0) [cnf transformation 33]
107. brave(X0) | wise(X0) [cnf transformation 57]
108. ~quiet(X0) | ~wise(X0) [cnf transformation 57]
115. ~brave(X0) | kind(X0) [cnf transformation 37]
136. ~kind(john) [cnf transformation 24]
137. humble(X0) [duplicate literal removal 95]
144. 2 <=> happy(john) [avatar definition]
145. ~happy(john) <- (~2) [avatar component clause 144]
158. 5 <=> ! [X1] : (tall(X1) | ~humble(X1)) [avatar definition]
159. tall(X1) | ~humble(X1) <- (5) [avatar component clause 158]
160. 5 | ~2 [avatar split clause 79,144,158]
299. tall(X1) <- (5) [subsumption resolution 159,137]
310. quiet(X0) <- (5) [resolution 85,299]
311. ~wise(X0) <- (5) [resolution 108,310]
312. ~wise(X1) | happy(X1) [resolution 108,86]
316. kind(X0) | wise(X0) [resolution 115,107]
317. kind(X0) <- (5) [subsumption resolution 316,311]
319. $false <- (5) [resolution 317,136]
320. ~5 [avatar contradiction clause 319]
349. wise(john) [resolution 316,136]
351. happy(john) [resolution 349,312]
352. $false <- (~2) [subsumption resolution 351,145]
353. 2 [avatar contradiction clause 352]
354. $false [avatar sat refutation 160,320,353]
% SZS output end Proof for 811007628673611607989460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
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