premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If fred is not old then john is not patient or calm.
Everyone who is kind is not humble or not wise.
If someone is not generous then someone is not curious or not rich.
If lucy is generous then someone is not calm and vice versa.
If lucy is both not strong and wise then someone is either not funny or strong and vice versa.
Everyone who is both humble and not strong is patient or quiet and vice versa.
If lucy is not funny or curious then someone is either generous or not generous and vice versa.
Everyone who is old is either not humble or humble and vice versa.
If lucy is not patient then susan is either creative or humble and vice versa.
If someone is both not creative and quiet then someone is either not kind or not tall and vice versa.
Everyone who is either not generous or not curious is not tall or strong and vice versa.
Everyone who is both not wise and creative is both generous and not quiet and vice versa.
If alice is either not old or not strong then someone is either not patient or not funny and vice versa.
If someone is either patient or not kind then mary is wise and vice versa.
If someone is not generous or patient then mary is both patient and not quiet.
If someone is not tall or not old then lucy is not quiet or not wise.
Mary is both wise and not tall.
Someone is creative.
Someone is not calm or not kind.
Someone is either not funny or not strong.
Alice is both not quiet and generous.
Someone is either brave or humble.
Mary is either generous or rich.
Mary is patient. | Mary is not kind. | entailment | ((~old(fred))=>((~patient(john)|calm(john))))&
(![X]:(kind(X)=>(~humble(X)|~wise(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)|~rich(X)))))&
((generous(lucy))<=>(?[X]:(~calm(X))))&
(((~strong(lucy)&wise(lucy)))<=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((humble(X)&~strong(X))<=>(patient(X)|quiet(X))))&
(((~funny(lucy)|curious(lucy)))<=>(?[X]:((generous(X)<~>~generous(X)))))&
(![X]:(old(X)<=>(~humble(X)<~>humble(X))))&
((~patient(lucy))<=>((creative(susan)<~>humble(susan))))&
((?[X]:((~creative(X)&quiet(X))))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~tall(X)|strong(X))))&
(![X]:((~wise(X)&creative(X))<=>(generous(X)&~quiet(X))))&
(((~old(alice)<~>~strong(alice)))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(wise(mary)))&
((?[X]:((~generous(X)|patient(X))))=>((patient(mary)&~quiet(mary))))&
((?[X]:((~tall(X)|~old(X))))=>((~quiet(lucy)|~wise(lucy))))&
((wise(mary)&~tall(mary)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)|~kind(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
((~quiet(alice)&generous(alice)))&
(?[X]:((brave(X)<~>humble(X))))&
((generous(mary)<~>rich(mary)))&
(patient(mary)) | ~kind(mary) | [
"p1",
"p5",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 390707221404875218837353
% SZS output start Proof for 390707221404875218837353
2. ! [X0] : (kind(X0) => (~wise(X0) | ~humble(X0))) [input p1]
6. ! [X0] : ((~strong(X0) & humble(X0)) <=> (quiet(X0) | patient(X0))) [input p5]
17. ~tall(mary) & wise(mary) [input p16]
24. patient(mary) [input p23]
25. kind(mary) [input hypothesis]
30. ! [X0] : ((~wise(X0) | ~humble(X0)) | ~kind(X0)) [ennf transformation 2]
31. ! [X0] : (~wise(X0) | ~humble(X0) | ~kind(X0)) [flattening 30]
48. ! [X0] : (((~strong(X0) & humble(X0)) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 6]
49. ! [X0] : (((~strong(X0) & humble(X0)) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | strong(X0) | ~humble(X0))) [flattening 48]
86. ~wise(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 31]
97. ~patient(X0) | humble(X0) [cnf transformation 49]
149. wise(mary) [cnf transformation 17]
161. patient(mary) [cnf transformation 24]
162. kind(mary) [cnf transformation 25]
321. 34 <=> wise(mary) [avatar definition]
322. wise(mary) <- (34) [avatar component clause 321]
352. 41 <=> patient(mary) [avatar definition]
354. patient(mary) <- (41) [avatar component clause 352]
365. 34 [avatar split clause 149,321]
405. 41 [avatar split clause 161,352]
408. humble(mary) <- (41) [resolution 97,354]
430. ~humble(mary) | ~kind(mary) <- (34) [resolution 86,322]
440. ~kind(mary) <- (34, 41) [subsumption resolution 430,408]
441. $false <- (34, 41) [subsumption resolution 440,162]
442. ~34 | ~41 [avatar contradiction clause 441]
443. $false [avatar sat refutation 365,405,442]
% SZS output end Proof for 390707221404875218837353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not curious is strong. If someone is generous or tall then susan is generous. If paul is either not wise or not curious then john is creative or not curious. Everyone who is either not old or not strong is both quiet and not funny and vice versa. If alice is not quiet then paul is not creative. If someone is not humble or wise then someone is not quiet or not creative and vice versa. Everyone who is either not brave or not kind is either funny or not generous. Everyone who is not brave or patient is curious or kind. Everyone who is either not tall or not funny is both not old and generous and vice versa. Everyone who is not curious is both happy and wise. Everyone who is both quiet and funny is kind or not humble. If alice is both happy and strong then someone is quiet. Everyone who is rich or quiet is kind or not patient. Everyone who is generous is both curious and quiet. If alice is both creative and not kind then paul is either not happy or not humble and vice versa. Someone is wise or not quiet. Paul is either kind or patient. Alice is not funny. Alice is not brave or not funny. Someone is either creative or not creative. Someone is both wise and funny. | Susan is not tall. | contradiction | (![X]:((~strong(X)|~curious(X))=>strong(X)))&
((?[X]:((generous(X)|tall(X))))=>(generous(susan)))&
(((~wise(paul)<~>~curious(paul)))=>((creative(john)|~curious(john))))&
(![X]:((~old(X)<~>~strong(X))<=>(quiet(X)&~funny(X))))&
((~quiet(alice))=>(~creative(paul)))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~brave(X)|patient(X))=>(curious(X)|kind(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(~old(X)&generous(X))))&
(![X]:(~curious(X)=>(happy(X)&wise(X))))&
(![X]:((quiet(X)&funny(X))=>(kind(X)|~humble(X))))&
(((happy(alice)&strong(alice)))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)|quiet(X))=>(kind(X)|~patient(X))))&
(![X]:(generous(X)=>(curious(X)&quiet(X))))&
(((creative(alice)&~kind(alice)))<=>((~happy(paul)<~>~humble(paul))))&
(?[X]:((wise(X)|~quiet(X))))&
((kind(paul)<~>patient(paul)))&
(~funny(alice))&
((~brave(alice)|~funny(alice)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((wise(X)&funny(X)))) | ~tall(susan) | [
"p0",
"p1",
"p3",
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5047049819635904456894652
% SZS output start Proof for 5047049819635904456894652
1. ! [X0] : ((~curious(X0) | ~strong(X0)) => strong(X0)) [input p0]
2. ? [X0] : (tall(X0) | generous(X0)) => generous(susan) [input p1]
4. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~funny(X0) & quiet(X0))) [input p3]
9. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> (generous(X0) & ~old(X0))) [input p8]
14. ! [X0] : (generous(X0) => (quiet(X0) & curious(X0))) [input p13]
21. ? [X0] : (funny(X0) & wise(X0)) [input p20]
22. ~tall(susan) [input hypothesis]
25. ! [X0] : (strong(X0) | (curious(X0) & strong(X0))) [ennf transformation 1]
26. generous(susan) | ! [X0] : (~tall(X0) & ~generous(X0)) [ennf transformation 2]
40. ! [X0] : ((quiet(X0) & curious(X0)) | ~generous(X0)) [ennf transformation 14]
42. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 4]
43. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 42]
50. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~generous(X0) | old(X0))) & ((generous(X0) & ~old(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 9]
51. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~generous(X0) | old(X0)) & ((generous(X0) & ~old(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [flattening 50]
62. ? [X0] : (funny(X0) & wise(X0)) => (funny(sK5) & wise(sK5)) [choice axiom]
63. funny(sK5) & wise(sK5) [skolemisation 21,62]
64. strong(X0) | strong(X0) [cnf transformation 25]
67. generous(susan) | ~tall(X0) [cnf transformation 26]
72. ~funny(X0) | ~strong(X0) | old(X0) [cnf transformation 43]
74. ~strong(X0) | ~old(X0) | funny(X0) | ~quiet(X0) [cnf transformation 43]
87. ~old(X0) | ~funny(X0) | tall(X0) [cnf transformation 51]
92. funny(X0) | tall(X0) | ~generous(X0) | old(X0) [cnf transformation 51]
99. ~generous(X0) | quiet(X0) [cnf transformation 40]
114. funny(sK5) [cnf transformation 63]
115. ~tall(susan) [cnf transformation 22]
116. strong(X0) [duplicate literal removal 64]
118. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
119. ~tall(X0) <- (1) [avatar component clause 118]
121. 2 <=> generous(susan) [avatar definition]
123. generous(susan) <- (2) [avatar component clause 121]
124. 1 | 2 [avatar split clause 67,121,118]
147. ~quiet(X0) | funny(X0) | ~old(X0) [subsumption resolution 74,116]
148. ~funny(X0) | old(X0) [subsumption resolution 72,116]
191. ~generous(X0) | tall(X0) | old(X0) [subsumption resolution 92,148]
192. ~funny(X0) | tall(X0) [subsumption resolution 87,148]
249. quiet(susan) <- (2) [resolution 99,123]
252. tall(sK5) [resolution 192,114]
266. funny(susan) | ~old(susan) <- (2) [resolution 147,249]
269. 30 <=> old(susan) [avatar definition]
271. ~old(susan) <- (~30) [avatar component clause 269]
273. 31 <=> funny(susan) [avatar definition]
275. funny(susan) <- (31) [avatar component clause 273]
276. ~30 | 31 | ~2 [avatar split clause 266,121,273,269]
277. tall(susan) | old(susan) <- (2) [resolution 191,123]
278. old(susan) <- (2) [subsumption resolution 277,115]
279. $false <- (2, ~30) [subsumption resolution 278,271]
280. ~2 | 30 [avatar contradiction clause 279]
281. $false <- (1) [resolution 119,252]
282. ~1 [avatar contradiction clause 281]
313. tall(susan) <- (31) [resolution 275,192]
315. $false <- (31) [subsumption resolution 313,115]
316. ~31 [avatar contradiction clause 315]
317. $false [avatar sat refutation 124,276,280,282,316]
% SZS output end Proof for 5047049819635904456894652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not happy and not patient.
Everyone who is calm is curious.
If someone is old or creative then someone is both wise and not wise and vice versa.
If john is either not old or not curious then mary is both curious and strong and vice versa.
If someone is either rich or not curious then someone is either not patient or not humble and vice versa.
If lucy is both generous and calm then someone is not brave and vice versa.
Everyone who is both not creative and brave is quiet or not kind and vice versa.
If paul is brave then mary is either not rich or calm.
If someone is patient then john is not generous or not humble.
Everyone who is not quiet is tall or humble.
Everyone who is not curious is both not funny and not patient and vice versa.
If someone is either not kind or not strong then susan is not old or wise and vice versa.
If fred is either not happy or quiet then mary is either not humble or not funny.
Everyone who is both curious and creative is not funny.
If someone is both old and not old then someone is not humble or not kind.
Everyone who is either not quiet or quiet is either not old or strong and vice versa.
Lucy is either not quiet or generous.
Lucy is either old or not humble.
Someone is not creative.
Someone is either not tall or not wise.
Fred is not kind or not old.
Someone is brave.
Someone is calm. | Paul is creative. | contradiction | (![X]:((~calm(X)<~>calm(X))=>(~happy(X)&~patient(X))))&
(![X]:(calm(X)=>curious(X)))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(((~old(john)<~>~curious(john)))<=>((curious(mary)&strong(mary))))&
((?[X]:((rich(X)<~>~curious(X))))<=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((generous(lucy)&calm(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~creative(X)&brave(X))<=>(quiet(X)|~kind(X))))&
((brave(paul))=>((~rich(mary)<~>calm(mary))))&
((?[X]:(patient(X)))=>((~generous(john)|~humble(john))))&
(![X]:(~quiet(X)=>(tall(X)|humble(X))))&
(![X]:(~curious(X)<=>(~funny(X)&~patient(X))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>((~old(susan)|wise(susan))))&
(((~happy(fred)<~>quiet(fred)))=>((~humble(mary)<~>~funny(mary))))&
(![X]:((curious(X)&creative(X))=>~funny(X)))&
((?[X]:((old(X)&~old(X))))=>(?[X]:((~humble(X)|~kind(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~old(X)<~>strong(X))))&
((~quiet(lucy)<~>generous(lucy)))&
((old(lucy)<~>~humble(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)<~>~wise(X))))&
((~kind(fred)|~old(fred)))&
(?[X]:(brave(X)))&
(?[X]:(calm(X))) | creative(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1364552110984579988763560
% SZS output start Proof for 1364552110984579988763560
3. ? [X0] : (creative(X0) | old(X0)) <=> ? [X0] : (~wise(X0) & wise(X0)) [input p2]
24. creative(paul) [input hypothesis]
25. ? [X0] : (creative(X0) | old(X0)) <=> ? [X1] : (~wise(X1) & wise(X1)) [rectify 3]
40. (? [X0] : (creative(X0) | old(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~creative(X0) & ~old(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) | old(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X2] : (~wise(X2) & wise(X2)) | ! [X3] : (~creative(X3) & ~old(X3))) [rectify 40]
42. ? [X0] : (creative(X0) | old(X0)) => (creative(sK0) | old(sK0)) [choice axiom]
43. ? [X2] : (~wise(X2) & wise(X2)) => (~wise(sK1) & wise(sK1)) [choice axiom]
44. ((creative(sK0) | old(sK0)) | ! [X1] : (wise(X1) | ~wise(X1))) & ((~wise(sK1) & wise(sK1)) | ! [X3] : (~creative(X3) & ~old(X3))) [skolemisation 41,43,42]
89. wise(sK1) | ~creative(X3) [cnf transformation 44]
91. ~wise(sK1) | ~creative(X3) [cnf transformation 44]
152. creative(paul) [cnf transformation 24]
164. 1 <=> ! [X3] : ~creative(X3) [avatar definition]
165. ~creative(X3) <- (1) [avatar component clause 164]
167. 2 <=> wise(sK1) [avatar definition]
170. 1 | ~2 [avatar split clause 91,167,164]
175. 1 | 2 [avatar split clause 89,167,164]
343. $false <- (1) [resolution 165,152]
344. ~1 [avatar contradiction clause 343]
345. $false [avatar sat refutation 170,175,344]
% SZS output end Proof for 1364552110984579988763560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both creative and not happy then someone is both humble and not quiet and vice versa.
If susan is not brave then someone is both not wise and not tall and vice versa.
If lucy is either not generous or not old then someone is patient or not rich and vice versa.
Everyone who is not tall or quiet is not generous.
Everyone who is either humble or curious is both calm and patient and vice versa.
Everyone who is both not quiet and wise is brave.
Everyone who is not curious or not old is either not calm or not humble and vice versa.
Everyone who is strong or not calm is either not strong or quiet.
Everyone who is not curious is either not brave or not old.
If paul is generous or not happy then paul is not quiet or not curious.
Everyone who is either humble or not kind is not brave and vice versa.
If someone is either not creative or not tall then someone is both tall and kind and vice versa.
Everyone who is not kind is not kind or not humble.
If paul is not curious or not wise then someone is both not old and calm.
Everyone who is not kind is both kind and not curious.
Everyone who is either not calm or strong is not generous and vice versa.
John is both not rich and not wise.
Mary is happy or not tall.
Someone is either quiet or not happy.
Someone is both brave and patient.
Someone is either calm or strong.
Paul is either quiet or not quiet.
Someone is not old or strong.
Lucy is old. | Lucy is not strong. | contradiction | (((creative(john)&~happy(john)))<=>(?[X]:((humble(X)&~quiet(X)))))&
((~brave(susan))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~generous(lucy)<~>~old(lucy)))<=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((~tall(X)|quiet(X))=>~generous(X)))&
(![X]:((humble(X)<~>curious(X))<=>(calm(X)&patient(X))))&
(![X]:((~quiet(X)&wise(X))=>brave(X)))&
(![X]:((~curious(X)|~old(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((strong(X)|~calm(X))=>(~strong(X)<~>quiet(X))))&
(![X]:(~curious(X)=>(~brave(X)<~>~old(X))))&
(((generous(paul)|~happy(paul)))=>((~quiet(paul)|~curious(paul))))&
(![X]:((humble(X)<~>~kind(X))<=>~brave(X)))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((tall(X)&kind(X)))))&
(![X]:(~kind(X)=>(~kind(X)|~humble(X))))&
(((~curious(paul)|~wise(paul)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:(~kind(X)=>(kind(X)&~curious(X))))&
(![X]:((~calm(X)<~>strong(X))<=>~generous(X)))&
((~rich(john)&~wise(john)))&
((happy(mary)|~tall(mary)))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((quiet(paul)<~>~quiet(paul)))&
(?[X]:((~old(X)|strong(X))))&
(old(lucy)) | ~strong(lucy) | [
"p2",
"p4",
"p6",
"p8",
"p10",
"p14",
"p15",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5658402699230786431680812
% SZS output start Proof for 5658402699230786431680812
3. (~generous(lucy) <~> ~old(lucy)) <=> ? [X0] : (~rich(X0) | patient(X0)) [input p2]
5. ! [X0] : ((humble(X0) <~> curious(X0)) <=> (patient(X0) & calm(X0))) [input p4]
7. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (~calm(X0) <~> ~humble(X0))) [input p6]
9. ! [X0] : (~curious(X0) => (~brave(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((humble(X0) <~> ~kind(X0)) <=> ~brave(X0)) [input p10]
15. ! [X0] : (~kind(X0) => (~curious(X0) & kind(X0))) [input p14]
16. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> ~generous(X0)) [input p15]
20. ? [X0] : (patient(X0) & brave(X0)) [input p19]
24. old(lucy) [input p23]
25. ~strong(lucy) [input hypothesis]
31. ! [X0] : ((~brave(X0) <~> ~old(X0)) | curious(X0)) [ennf transformation 9]
37. ! [X0] : ((~curious(X0) & kind(X0)) | kind(X0)) [ennf transformation 15]
47. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & (? [X0] : (~rich(X0) | patient(X0)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [nnf transformation 3]
48. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & (? [X1] : (~rich(X1) | patient(X1)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [rectify 47]
49. ? [X1] : (~rich(X1) | patient(X1)) => (~rich(sK2) | patient(sK2)) [choice axiom]
50. (((old(lucy) | generous(lucy)) & (~old(lucy) | ~generous(lucy))) | ! [X0] : (rich(X0) & ~patient(X0))) & ((~rich(sK2) | patient(sK2)) | ((~generous(lucy) | old(lucy)) & (~old(lucy) | generous(lucy)))) [skolemisation 48,49]
51. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 5]
52. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [flattening 51]
53. ! [X0] : (((~old(X0) | ~curious(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (old(X0) & curious(X0)))) [nnf transformation 7]
54. ! [X0] : ((~old(X0) | ~curious(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) & (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (old(X0) & curious(X0)))) [flattening 53]
56. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | curious(X0)) [nnf transformation 31]
57. ! [X0] : ((((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | brave(X0)) & (~brave(X0) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0))))) [nnf transformation 11]
65. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | generous(X0)) & (~generous(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 16]
69. ? [X0] : (patient(X0) & brave(X0)) => (patient(sK7) & brave(sK7)) [choice axiom]
70. patient(sK7) & brave(sK7) [skolemisation 20,69]
86. ~old(lucy) | ~generous(lucy) | ~patient(X0) [cnf transformation 50]
92. ~humble(X0) | curious(X0) | calm(X0) [cnf transformation 52]
93. ~curious(X0) | humble(X0) | calm(X0) [cnf transformation 52]
103. ~old(X0) | ~curious(X0) | ~humble(X0) | calm(X0) [cnf transformation 54]
104. ~old(X0) | ~curious(X0) | ~calm(X0) | humble(X0) [cnf transformation 54]
109. ~old(X0) | ~brave(X0) | curious(X0) [cnf transformation 56]
113. ~kind(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 57]
115. ~kind(X0) | humble(X0) | brave(X0) [cnf transformation 57]
128. kind(X0) | kind(X0) [cnf transformation 37]
132. ~calm(X0) | strong(X0) | generous(X0) [cnf transformation 65]
140. patient(sK7) [cnf transformation 70]
146. old(lucy) [cnf transformation 24]
147. ~strong(lucy) [cnf transformation 25]
148. kind(X0) [duplicate literal removal 128]
195. 11 <=> generous(lucy) [avatar definition]
199. 12 <=> old(lucy) [avatar definition]
201. old(lucy) <- (12) [avatar component clause 199]
204. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
205. ~patient(X0) <- (13) [avatar component clause 204]
208. 13 | ~11 | ~12 [avatar split clause 86,199,195,204]
219. ~curious(X0) | ~old(X0) | humble(X0) [subsumption resolution 104,93]
220. ~old(X0) | ~humble(X0) | calm(X0) [subsumption resolution 103,92]
321. 12 [avatar split clause 146,199]
376. ~brave(lucy) | curious(lucy) <- (12) [resolution 109,201]
378. 43 <=> curious(lucy) [avatar definition]
380. curious(lucy) <- (43) [avatar component clause 378]
382. 44 <=> brave(lucy) [avatar definition]
383. brave(lucy) <- (44) [avatar component clause 382]
384. ~brave(lucy) <- (~44) [avatar component clause 382]
385. 43 | ~44 | ~12 [avatar split clause 376,199,382,378]
389. ~brave(X0) | ~humble(X0) [resolution 113,148]
394. brave(X0) | humble(X0) [resolution 115,148]
396. humble(lucy) <- (~44) [resolution 394,384]
449. ~old(lucy) | humble(lucy) <- (43) [resolution 219,380]
454. ~humble(lucy) | calm(lucy) <- (12) [resolution 220,201]
455. calm(lucy) <- (12, ~44) [subsumption resolution 454,396]
456. strong(lucy) | generous(lucy) <- (12, ~44) [resolution 455,132]
458. generous(lucy) <- (12, ~44) [subsumption resolution 456,147]
461. 11 | ~12 | 44 [avatar split clause 458,382,199,195]
471. 51 <=> humble(lucy) [avatar definition]
472. humble(lucy) <- (51) [avatar component clause 471]
475. humble(lucy) <- (12, 43) [subsumption resolution 449,201]
476. 51 | ~12 | ~43 [avatar split clause 475,378,199,471]
480. $false <- (13) [resolution 205,140]
483. ~13 [avatar contradiction clause 480]
485. ~humble(lucy) <- (44) [resolution 383,389]
486. $false <- (44, 51) [subsumption resolution 485,472]
487. ~44 | ~51 [avatar contradiction clause 486]
488. $false [avatar sat refutation 208,321,385,461,476,483,487]
% SZS output end Proof for 5658402699230786431680812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not humble is both not curious and humble.
Everyone who is wise or not kind is brave.
Everyone who is not calm is both generous and not wise and vice versa.
Everyone who is either old or calm is brave and vice versa.
Everyone who is either not quiet or generous is not curious or generous.
Everyone who is not humble or curious is both funny and calm and vice versa.
Everyone who is creative or not strong is both funny and generous.
Everyone who is not curious is not old and vice versa.
If john is not old then fred is either not humble or not happy.
If lucy is either generous or not funny then someone is quiet.
If lucy is rich then someone is both wise and not brave.
Everyone who is happy or not strong is either quiet or curious and vice versa.
If someone is creative then john is strong or generous and vice versa.
If fred is both curious and generous then someone is not quiet and vice versa.
Everyone who is both not wise and happy is either not kind or tall.
Everyone who is not wise or not happy is not curious or not rich and vice versa.
John is either happy or patient.
Someone is either not curious or not happy.
John is either not strong or creative.
Fred is humble or not calm.
Lucy is both happy and generous.
Someone is strong.
Someone is calm.
Lucy is both quiet and not wise. | John is not wise. | entailment | (![X]:((~quiet(X)|~humble(X))=>(~curious(X)&humble(X))))&
(![X]:((wise(X)|~kind(X))=>brave(X)))&
(![X]:(~calm(X)<=>(generous(X)&~wise(X))))&
(![X]:((old(X)<~>calm(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>generous(X))=>(~curious(X)|generous(X))))&
(![X]:((~humble(X)|curious(X))<=>(funny(X)&calm(X))))&
(![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
((happy(john)<~>patient(john)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((~strong(john)<~>creative(john)))&
((humble(fred)|~calm(fred)))&
((happy(lucy)&generous(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(calm(X)))&
((quiet(lucy)&~wise(lucy))) | ~wise(john) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6941291577522714240891399
% SZS output start Proof for 6941291577522714240891399
1. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (humble(X0) & ~curious(X0))) [input p0]
2. ! [X0] : ((~kind(X0) | wise(X0)) => brave(X0)) [input p1]
3. ! [X0] : (~calm(X0) <=> (~wise(X0) & generous(X0))) [input p2]
4. ! [X0] : ((old(X0) <~> calm(X0)) <=> brave(X0)) [input p3]
6. ! [X0] : ((curious(X0) | ~humble(X0)) <=> (calm(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~strong(X0) | creative(X0)) => (generous(X0) & funny(X0))) [input p6]
8. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p7]
12. ! [X0] : ((~strong(X0) | happy(X0)) <=> (quiet(X0) <~> curious(X0))) [input p11]
14. (generous(fred) & curious(fred)) <=> ? [X0] : ~quiet(X0) [input p13]
16. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~rich(X0) | ~curious(X0))) [input p15]
25. wise(john) [input hypothesis]
26. ! [X0] : ((humble(X0) & ~curious(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 1]
27. ! [X0] : (brave(X0) | (kind(X0) & ~wise(X0))) [ennf transformation 2]
30. ! [X0] : ((generous(X0) & funny(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 7]
36. ! [X0] : ((~calm(X0) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | calm(X0))) [nnf transformation 3]
37. ! [X0] : ((~calm(X0) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | calm(X0))) [flattening 36]
38. ! [X0] : ((((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ~brave(X0)) & (brave(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0))))) [nnf transformation 4]
40. ! [X0] : (((curious(X0) | ~humble(X0)) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | (~curious(X0) & humble(X0)))) [nnf transformation 6]
41. ! [X0] : ((curious(X0) | ~humble(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | (~curious(X0) & humble(X0)))) [flattening 40]
42. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 8]
49. ! [X0] : (((~strong(X0) | happy(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [nnf transformation 12]
50. ! [X0] : ((~strong(X0) | happy(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [flattening 49]
56. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~generous(fred) | ~curious(fred))) [nnf transformation 14]
57. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~generous(fred) | ~curious(fred)) [flattening 56]
58. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~generous(fred) | ~curious(fred)) [rectify 57]
59. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
60. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~generous(fred) | ~curious(fred)) [skolemisation 58,59]
62. ! [X0] : (((~happy(X0) | ~wise(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 16]
63. ! [X0] : ((~happy(X0) | ~wise(X0) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | (happy(X0) & wise(X0)))) [flattening 62]
73. ~curious(X0) | quiet(X0) [cnf transformation 26]
76. humble(X0) | humble(X0) [cnf transformation 26]
77. ~wise(X0) | brave(X0) [cnf transformation 27]
80. ~wise(X0) | calm(X0) [cnf transformation 37]
81. ~generous(X0) | wise(X0) | ~calm(X0) [cnf transformation 37]
85. ~old(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 38]
91. ~curious(X0) | calm(X0) [cnf transformation 41]
92. curious(X0) | ~humble(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 41]
94. strong(X0) | funny(X0) [cnf transformation 30]
98. ~curious(X0) | old(X0) [cnf transformation 42]
107. ~curious(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 50]
109. ~strong(X0) | happy(X0) | curious(X0) | ~quiet(X0) [cnf transformation 50]
115. curious(fred) | quiet(X0) [cnf transformation 60]
116. generous(fred) | quiet(X0) [cnf transformation 60]
121. ~happy(X0) | ~wise(X0) | curious(X0) [cnf transformation 63]
136. wise(john) [cnf transformation 25]
138. humble(X0) [duplicate literal removal 76]
139. ~funny(X0) | ~calm(X0) | curious(X0) [subsumption resolution 92,138]
142. 1 <=> old(john) [avatar definition]
144. old(john) <- (1) [avatar component clause 142]
179. ~happy(X0) | ~curious(X0) [subsumption resolution 107,73]
192. 11 <=> strong(john) [avatar definition]
193. strong(john) <- (11) [avatar component clause 192]
194. ~strong(john) <- (~11) [avatar component clause 192]
197. 12 <=> ! [X0] : quiet(X0) [avatar definition]
198. quiet(X0) <- (12) [avatar component clause 197]
200. 13 <=> generous(fred) [avatar definition]
202. generous(fred) <- (13) [avatar component clause 200]
203. 12 | 13 [avatar split clause 116,200,197]
205. 14 <=> curious(fred) [avatar definition]
207. curious(fred) <- (14) [avatar component clause 205]
208. 12 | 14 [avatar split clause 115,205,197]
214. ~happy(X0) | ~wise(X0) [subsumption resolution 121,179]
217. 16 <=> happy(john) [avatar definition]
218. happy(john) <- (16) [avatar component clause 217]
219. ~happy(john) <- (~16) [avatar component clause 217]
246. brave(john) [resolution 77,136]
248. calm(john) [resolution 80,136]
251. calm(fred) <- (14) [resolution 91,207]
253. funny(john) <- (~11) [resolution 94,194]
260. old(fred) <- (14) [resolution 98,207]
272. ~wise(john) <- (16) [resolution 214,218]
273. $false <- (16) [subsumption resolution 272,136]
274. ~16 [avatar contradiction clause 273]
277. wise(fred) | ~calm(fred) <- (13) [resolution 81,202]
280. wise(fred) <- (13, 14) [subsumption resolution 277,251]
294. brave(fred) <- (13, 14) [resolution 280,77]
311. ~calm(fred) | ~brave(fred) <- (14) [resolution 85,260]
313. ~brave(fred) <- (14) [subsumption resolution 311,251]
314. $false <- (13, 14) [subsumption resolution 313,294]
315. ~13 | ~14 [avatar contradiction clause 314]
327. ~calm(john) | curious(john) <- (~11) [resolution 139,253]
330. curious(john) <- (~11) [subsumption resolution 327,248]
400. old(john) <- (~11) [resolution 330,98]
406. 1 | 11 [avatar split clause 400,192,142]
407. happy(john) | curious(john) | ~quiet(john) <- (11) [resolution 193,109]
408. curious(john) | ~quiet(john) <- (11, ~16) [subsumption resolution 407,219]
409. curious(john) <- (11, 12, ~16) [subsumption resolution 408,198]
413. old(john) <- (11, 12, ~16) [resolution 409,98]
417. 1 | ~11 | ~12 | 16 [avatar split clause 413,217,197,192,142]
418. ~calm(john) | ~brave(john) <- (1) [resolution 144,85]
421. ~brave(john) <- (1) [subsumption resolution 418,248]
422. $false <- (1) [subsumption resolution 421,246]
423. ~1 [avatar contradiction clause 422]
424. $false [avatar sat refutation 203,208,274,315,406,417,423]
% SZS output end Proof for 6941291577522714240891399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and tall is both not funny and not generous.
If someone is tall then someone is both not humble and wise and vice versa.
Everyone who is either funny or not patient is quiet or creative.
Everyone who is not quiet is not tall and vice versa.
If someone is both quiet and not curious then someone is both creative and curious.
Everyone who is both not funny and creative is not curious and vice versa.
If someone is both not strong and not old then paul is either happy or not strong and vice versa.
Everyone who is both generous and strong is patient and vice versa.
If alice is not happy then someone is either happy or strong.
If someone is both not quiet and not tall then john is either patient or funny and vice versa.
Everyone who is either curious or not funny is both patient and not brave and vice versa.
If someone is not quiet then mary is strong and vice versa.
Everyone who is both funny and tall is calm or happy.
Everyone who is kind or old is both not humble and rich and vice versa.
If john is either old or not strong then paul is either patient or not happy.
Everyone who is both not creative and not strong is both not happy and old.
Alice is wise.
Someone is not brave or strong.
John is either not creative or not happy.
Lucy is both not humble and not tall.
Paul is quiet or not wise.
Mary is both not old and quiet. | John is not strong. | contradiction | (![X]:((quiet(X)&tall(X))=>(~funny(X)&~generous(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:((funny(X)<~>~patient(X))=>(quiet(X)|creative(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((quiet(X)&~curious(X))))=>(?[X]:((creative(X)&curious(X)))))&
(![X]:((~funny(X)&creative(X))<=>~curious(X)))&
((?[X]:((~strong(X)&~old(X))))<=>((happy(paul)<~>~strong(paul))))&
(![X]:((generous(X)&strong(X))<=>patient(X)))&
((~happy(alice))=>(?[X]:((happy(X)<~>strong(X)))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((patient(john)<~>funny(john))))&
(![X]:((curious(X)<~>~funny(X))<=>(patient(X)&~brave(X))))&
((?[X]:(~quiet(X)))<=>(strong(mary)))&
(![X]:((funny(X)&tall(X))=>(calm(X)|happy(X))))&
(![X]:((kind(X)|old(X))<=>(~humble(X)&rich(X))))&
(((old(john)<~>~strong(john)))=>((patient(paul)<~>~happy(paul))))&
(![X]:((~creative(X)&~strong(X))=>(~happy(X)&old(X))))&
(wise(alice))&
(?[X]:((~brave(X)|strong(X))))&
((~creative(john)<~>~happy(john)))&
((~humble(lucy)&~tall(lucy)))&
((quiet(paul)|~wise(paul)))&
((~old(mary)&quiet(mary))) | ~strong(john) | [
"p3",
"p5",
"p7",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2357696246892851185646214
% SZS output start Proof for 2357696246892851185646214
4. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p3]
6. ! [X0] : ((creative(X0) & ~funny(X0)) <=> ~curious(X0)) [input p5]
8. ! [X0] : ((strong(X0) & generous(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (~tall(X0) & ~quiet(X0)) <=> (patient(john) <~> funny(john)) [input p9]
11. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (~brave(X0) & patient(X0))) [input p10]
20. ~tall(lucy) & ~humble(lucy) [input p19]
23. ~strong(john) [input hypothesis]
42. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 4]
46. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | funny(X0)))) [nnf transformation 6]
47. ! [X0] : (((creative(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | funny(X0))) [flattening 46]
52. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) | ~generous(X0)))) [nnf transformation 8]
53. ! [X0] : (((strong(X0) & generous(X0)) | ~patient(X0)) & (patient(X0) | ~strong(X0) | ~generous(X0))) [flattening 52]
57. (? [X0] : (~tall(X0) & ~quiet(X0)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X0] : (tall(X0) | quiet(X0))) [nnf transformation 10]
58. (? [X0] : (~tall(X0) & ~quiet(X0)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X1] : (tall(X1) | quiet(X1))) [rectify 57]
59. ? [X0] : (~tall(X0) & ~quiet(X0)) => (~tall(sK5) & ~quiet(sK5)) [choice axiom]
60. ((~tall(sK5) & ~quiet(sK5)) | ((patient(john) | ~funny(john)) & (funny(john) | ~patient(john)))) & (((~funny(john) | ~patient(john)) & (funny(john) | patient(john))) | ! [X1] : (tall(X1) | quiet(X1))) [skolemisation 58,59]
61. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 11]
62. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 61]
80. ~tall(X0) | quiet(X0) [cnf transformation 42]
81. ~quiet(X0) | tall(X0) [cnf transformation 42]
85. ~funny(X0) | curious(X0) [cnf transformation 47]
95. ~patient(X0) | strong(X0) [cnf transformation 53]
98. funny(john) | patient(john) | tall(X1) | quiet(X1) [cnf transformation 60]
104. patient(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 62]
105. patient(X0) | curious(X0) | funny(X0) [cnf transformation 62]
128. ~tall(lucy) [cnf transformation 20]
132. ~strong(john) [cnf transformation 23]
207. 17 <=> funny(john) [avatar definition]
208. funny(john) <- (17) [avatar component clause 207]
211. 18 <=> patient(john) [avatar definition]
212. ~patient(john) <- (~18) [avatar component clause 211]
213. patient(john) <- (18) [avatar component clause 211]
228. 21 <=> ! [X1] : quiet(X1) [avatar definition]
229. quiet(X1) <- (21) [avatar component clause 228]
231. funny(john) | patient(john) | quiet(X1) [subsumption resolution 98,80]
232. 21 | 18 | 17 [avatar split clause 231,207,211,228]
235. curious(X0) | patient(X0) [subsumption resolution 105,85]
236. ~funny(X0) | patient(X0) [subsumption resolution 104,235]
248. 24 <=> strong(john) [avatar definition]
249. ~strong(john) <- (~24) [avatar component clause 248]
291. ~24 [avatar split clause 132,248]
296. tall(X0) <- (21) [resolution 81,229]
303. $false <- (21) [resolution 296,128]
305. ~21 [avatar contradiction clause 303]
316. patient(john) <- (17) [resolution 236,208]
317. $false <- (17, ~18) [subsumption resolution 316,212]
318. ~17 | 18 [avatar contradiction clause 317]
319. strong(john) <- (18) [resolution 213,95]
321. $false <- (18, ~24) [subsumption resolution 319,249]
322. ~18 | 24 [avatar contradiction clause 321]
323. $false [avatar sat refutation 232,291,305,318,322]
% SZS output end Proof for 2357696246892851185646214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is wise then fred is either kind or brave and vice versa.
Everyone who is either not calm or strong is both wise and not happy and vice versa.
Everyone who is creative is both creative and not strong and vice versa.
Everyone who is happy or curious is brave.
If mary is not curious then paul is not tall.
Everyone who is both not curious and not happy is either not curious or old.
Everyone who is happy is strong.
If susan is not funny then alice is tall and vice versa.
Everyone who is either not strong or curious is either old or calm and vice versa.
Everyone who is tall or generous is calm and vice versa.
Everyone who is either patient or not creative is not rich and vice versa.
If paul is funny or kind then someone is old or not curious.
Everyone who is not brave or not humble is either not happy or not humble.
Everyone who is either not strong or wise is both not kind and generous.
If someone is both funny and quiet then lucy is not rich.
Everyone who is not kind is either not happy or not old.
Paul is not old.
Alice is either not quiet or not funny.
Someone is both humble and not happy.
Susan is old.
Fred is strong or patient.
Alice is both not tall and old.
Paul is either not wise or calm. | Paul is tall. | contradiction | ((wise(lucy))<=>((kind(fred)<~>brave(fred))))&
(![X]:((~calm(X)<~>strong(X))<=>(wise(X)&~happy(X))))&
(![X]:(creative(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|curious(X))=>brave(X)))&
((~curious(mary))=>(~tall(paul)))&
(![X]:((~curious(X)&~happy(X))=>(~curious(X)<~>old(X))))&
(![X]:(happy(X)=>strong(X)))&
((~funny(susan))<=>(tall(alice)))&
(![X]:((~strong(X)<~>curious(X))<=>(old(X)<~>calm(X))))&
(![X]:((tall(X)|generous(X))<=>calm(X)))&
(![X]:((patient(X)<~>~creative(X))<=>~rich(X)))&
(((funny(paul)|kind(paul)))=>(?[X]:((old(X)|~curious(X)))))&
(![X]:((~brave(X)|~humble(X))=>(~happy(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>wise(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&quiet(X))))=>(~rich(lucy)))&
(![X]:(~kind(X)=>(~happy(X)<~>~old(X))))&
(~old(paul))&
((~quiet(alice)<~>~funny(alice)))&
(?[X]:((humble(X)&~happy(X))))&
(old(susan))&
((strong(fred)|patient(fred)))&
((~tall(alice)&old(alice)))&
((~wise(paul)<~>calm(paul))) | tall(paul) | [
"p1",
"p6",
"p9",
"p13",
"p15",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7393205512134638707257839
% SZS output start Proof for 7393205512134638707257839
2. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (~happy(X0) & wise(X0))) [input p1]
7. ! [X0] : (happy(X0) => strong(X0)) [input p6]
10. ! [X0] : ((generous(X0) | tall(X0)) <=> calm(X0)) [input p9]
14. ! [X0] : ((~strong(X0) <~> wise(X0)) => (generous(X0) & ~kind(X0))) [input p13]
16. ! [X0] : (~kind(X0) => (~happy(X0) <~> ~old(X0))) [input p15]
17. ~old(paul) [input p16]
23. ~wise(paul) <~> calm(paul) [input p22]
24. tall(paul) [input hypothesis]
30. ! [X0] : (strong(X0) | ~happy(X0)) [ennf transformation 7]
34. ! [X0] : ((generous(X0) & ~kind(X0)) | (~strong(X0) <=> wise(X0))) [ennf transformation 14]
36. ! [X0] : ((~happy(X0) <~> ~old(X0)) | kind(X0)) [ennf transformation 16]
38. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 38]
45. ! [X0] : (((generous(X0) | tall(X0)) | ~calm(X0)) & (calm(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 10]
46. ! [X0] : ((generous(X0) | tall(X0) | ~calm(X0)) & (calm(X0) | (~generous(X0) & ~tall(X0)))) [flattening 45]
51. ! [X0] : ((generous(X0) & ~kind(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) [nnf transformation 34]
52. ! [X0] : (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | kind(X0)) [nnf transformation 36]
56. (~calm(paul) | wise(paul)) & (calm(paul) | ~wise(paul)) [nnf transformation 23]
64. ~happy(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 39]
65. ~calm(X0) | strong(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
75. ~happy(X0) | strong(X0) [cnf transformation 30]
86. ~tall(X0) | calm(X0) [cnf transformation 46]
98. ~strong(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 51]
103. old(X0) | happy(X0) | kind(X0) [cnf transformation 52]
104. ~old(paul) [cnf transformation 17]
114. ~calm(paul) | wise(paul) [cnf transformation 56]
115. tall(paul) [cnf transformation 24]
139. 5 <=> tall(paul) [avatar definition]
140. tall(paul) <- (5) [avatar component clause 139]
154. 8 <=> kind(paul) [avatar definition]
200. 18 <=> wise(paul) [avatar definition]
202. wise(paul) <- (18) [avatar component clause 200]
204. 19 <=> calm(paul) [avatar definition]
205. calm(paul) <- (19) [avatar component clause 204]
207. 18 | ~19 [avatar split clause 114,204,200]
209. 5 [avatar split clause 115,139]
211. calm(paul) <- (5) [resolution 86,140]
214. 19 | ~5 [avatar split clause 211,139,204]
258. happy(paul) | kind(paul) [resolution 103,104]
262. 27 <=> happy(paul) [avatar definition]
264. happy(paul) <- (27) [avatar component clause 262]
265. 8 | 27 [avatar split clause 258,262,154]
273. strong(paul) | happy(paul) | ~wise(paul) <- (19) [resolution 65,205]
274. strong(paul) | happy(paul) <- (18, 19) [subsumption resolution 273,202]
275. strong(paul) <- (18, 19) [subsumption resolution 274,75]
304. ~kind(paul) | ~wise(paul) <- (18, 19) [resolution 275,98]
310. ~kind(paul) <- (18, 19) [subsumption resolution 304,202]
311. ~8 | ~18 | ~19 [avatar split clause 310,204,200,154]
312. ~calm(paul) | ~strong(paul) <- (27) [resolution 264,64]
316. ~strong(paul) <- (19, 27) [subsumption resolution 312,205]
317. $false <- (18, 19, 27) [subsumption resolution 316,275]
318. ~18 | ~19 | ~27 [avatar contradiction clause 317]
319. $false [avatar sat refutation 207,209,214,265,311,318]
% SZS output end Proof for 7393205512134638707257839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is strong then alice is both not rich and creative. If someone is either not calm or creative then someone is brave or calm. If someone is strong or not tall then someone is both not quiet and not humble and vice versa. If mary is humble then paul is either not curious or creative and vice versa. If alice is either not strong or not curious then someone is funny or not old and vice versa. If paul is both funny and not quiet then someone is either not happy or not funny and vice versa. If john is rich or kind then alice is both happy and not old. If someone is not funny or not strong then mary is not kind or kind and vice versa. If john is both not humble and not patient then susan is not curious or curious and vice versa. If alice is not generous then someone is both not curious and patient. Everyone who is kind is either not curious or not old and vice versa. If someone is not old then mary is not strong or kind and vice versa. Everyone who is not strong is either kind or not kind. Everyone who is not brave or not funny is either old or not kind and vice versa. Everyone who is quiet or not old is not happy or not creative. Everyone who is both not generous and not old is both not patient and not funny. John is either strong or not generous. Someone is both happy and strong. Someone is not old or not creative. Mary is brave. Someone is humble. Lucy is creative or not rich. Fred is both curious and not patient. Susan is both not humble and tall. | Mary is kind. | neutral | ((strong(fred))=>((~rich(alice)&creative(alice))))&
((?[X]:((~calm(X)<~>creative(X))))=>(?[X]:((brave(X)|calm(X)))))&
((?[X]:((strong(X)|~tall(X))))<=>(?[X]:((~quiet(X)&~humble(X)))))&
((humble(mary))<=>((~curious(paul)<~>creative(paul))))&
(((~strong(alice)<~>~curious(alice)))<=>(?[X]:((funny(X)|~old(X)))))&
(((funny(paul)&~quiet(paul)))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
(((rich(john)|kind(john)))=>((happy(alice)&~old(alice))))&
((?[X]:((~funny(X)|~strong(X))))<=>((~kind(mary)|kind(mary))))&
(((~humble(john)&~patient(john)))<=>((~curious(susan)|curious(susan))))&
((~generous(alice))=>(?[X]:((~curious(X)&patient(X)))))&
(![X]:(kind(X)<=>(~curious(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>((~strong(mary)|kind(mary))))&
(![X]:(~strong(X)=>(kind(X)<~>~kind(X))))&
(![X]:((~brave(X)|~funny(X))<=>(old(X)<~>~kind(X))))&
(![X]:((quiet(X)|~old(X))=>(~happy(X)|~creative(X))))&
(![X]:((~generous(X)&~old(X))=>(~patient(X)&~funny(X))))&
((strong(john)<~>~generous(john)))&
(?[X]:((happy(X)&strong(X))))&
(?[X]:((~old(X)|~creative(X))))&
(brave(mary))&
(?[X]:(humble(X)))&
((creative(lucy)|~rich(lucy)))&
((curious(fred)&~patient(fred)))&
((~humble(susan)&tall(susan))) | kind(mary) | [] | null | 0 |
Everyone who is brave or not humble is both not creative and not happy and vice versa.
If lucy is not tall then mary is not kind or not funny and vice versa.
Everyone who is either creative or not old is kind and vice versa.
If someone is either generous or not calm then paul is either tall or not kind and vice versa.
Everyone who is either not happy or not strong is both not creative and strong.
If mary is not kind then fred is not old and vice versa.
If fred is both not happy and quiet then lucy is either not strong or not quiet.
Everyone who is humble is both funny and rich and vice versa.
If paul is wise then mary is either tall or quiet.
If someone is wise then someone is not happy.
Everyone who is either strong or funny is not funny.
Everyone who is both not tall and not happy is not patient.
If john is not rich then fred is happy and vice versa.
If john is quiet or rich then lucy is brave or wise.
If susan is strong or not wise then lucy is both humble and not happy.
Everyone who is both not funny and not creative is both not strong and old and vice versa.
Alice is either not wise or quiet.
Someone is brave.
Alice is both kind and funny.
Someone is quiet or creative.
Someone is not calm or not humble.
Alice is strong or not patient.
Someone is not wise. | Mary is funny. | neutral | (![X]:((brave(X)|~humble(X))<=>(~creative(X)&~happy(X))))&
((~tall(lucy))<=>((~kind(mary)|~funny(mary))))&
(![X]:((creative(X)<~>~old(X))<=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((tall(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~strong(X))=>(~creative(X)&strong(X))))&
((~kind(mary))<=>(~old(fred)))&
(((~happy(fred)&quiet(fred)))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:(humble(X)<=>(funny(X)&rich(X))))&
((wise(paul))=>((tall(mary)<~>quiet(mary))))&
((?[X]:(wise(X)))=>(?[X]:(~happy(X))))&
(![X]:((strong(X)<~>funny(X))=>~funny(X)))&
(![X]:((~tall(X)&~happy(X))=>~patient(X)))&
((~rich(john))<=>(happy(fred)))&
(((quiet(john)|rich(john)))=>((brave(lucy)|wise(lucy))))&
(((strong(susan)|~wise(susan)))=>((humble(lucy)&~happy(lucy))))&
(![X]:((~funny(X)&~creative(X))<=>(~strong(X)&old(X))))&
((~wise(alice)<~>quiet(alice)))&
(?[X]:(brave(X)))&
((kind(alice)&funny(alice)))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~calm(X)|~humble(X))))&
((strong(alice)|~patient(alice)))&
(?[X]:(~wise(X))) | funny(mary) | [] | null | 0 |
Everyone who is not tall or not calm is generous or not curious and vice versa. Everyone who is either not curious or generous is either not happy or not funny. If lucy is rich then alice is funny. Everyone who is generous is not strong or rich and vice versa. If someone is not rich or not funny then mary is kind. Everyone who is quiet or not generous is not creative or happy and vice versa. Everyone who is not generous or not brave is happy and vice versa. If fred is both tall and not happy then mary is either not tall or not patient. If someone is not patient or not happy then mary is both not happy and not funny. Everyone who is either quiet or not tall is either not calm or funny. If fred is not rich then someone is funny. Everyone who is both quiet and wise is not brave. Everyone who is either not creative or kind is either rich or tall. Everyone who is humble or not quiet is not kind. Everyone who is not patient or not creative is both not patient and not kind and vice versa. Alice is calm. Someone is strong or not tall. Someone is calm. Someone is not patient or generous. John is calm or not old. Someone is either rich or tall. Lucy is happy or patient. Someone is not tall. | Fred is not patient. | contradiction | (![X]:((~tall(X)|~calm(X))<=>(generous(X)|~curious(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~happy(X)<~>~funny(X))))&
((rich(lucy))=>(funny(alice)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~rich(X)|~funny(X))))=>(kind(mary)))&
(![X]:((quiet(X)|~generous(X))<=>(~creative(X)|happy(X))))&
(![X]:((~generous(X)|~brave(X))<=>happy(X)))&
(((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(![X]:((~patient(X)|~creative(X))<=>(~patient(X)&~kind(X))))&
(calm(alice))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:(calm(X)))&
(?[X]:((~patient(X)|generous(X))))&
((calm(john)|~old(john)))&
(?[X]:((rich(X)<~>tall(X))))&
((happy(lucy)|patient(lucy)))&
(?[X]:(~tall(X))) | ~patient(fred) | [
"p4",
"p5",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 329530424618988170043667
% SZS output start Proof for 329530424618988170043667
5. ? [X0] : (~funny(X0) | ~rich(X0)) => kind(mary) [input p4]
6. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (happy(X0) | ~creative(X0))) [input p5]
9. ? [X0] : (~happy(X0) | ~patient(X0)) => (~funny(mary) & ~happy(mary)) [input p8]
14. ! [X0] : ((~quiet(X0) | humble(X0)) => ~kind(X0)) [input p13]
15. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~kind(X0) & ~patient(X0))) [input p14]
24. ~patient(fred) [input hypothesis]
26. ! [X0] : (~quiet(X0) => ~kind(X0)) [pure predicate removal 14]
30. kind(mary) | ! [X0] : (funny(X0) & rich(X0)) [ennf transformation 5]
33. (~funny(mary) & ~happy(mary)) | ! [X0] : (happy(X0) & patient(X0)) [ennf transformation 9]
37. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 26]
43. ! [X0] : (((~generous(X0) | quiet(X0)) | (~happy(X0) & creative(X0))) & ((happy(X0) | ~creative(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((~generous(X0) | quiet(X0) | (~happy(X0) & creative(X0))) & (happy(X0) | ~creative(X0) | (generous(X0) & ~quiet(X0)))) [flattening 43]
52. ! [X0] : (((~creative(X0) | ~patient(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 15]
53. ! [X0] : ((~creative(X0) | ~patient(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [flattening 52]
78. kind(mary) | funny(X0) [cnf transformation 30]
79. ~creative(X0) | happy(X0) | ~quiet(X0) [cnf transformation 44]
88. ~happy(mary) | patient(X0) [cnf transformation 33]
90. ~funny(mary) | patient(X0) [cnf transformation 33]
101. ~kind(X0) | quiet(X0) [cnf transformation 37]
103. ~patient(X0) | creative(X0) [cnf transformation 53]
104. ~kind(X0) | patient(X0) [cnf transformation 53]
115. ~patient(fred) [cnf transformation 24]
126. 3 <=> ! [X0] : funny(X0) [avatar definition]
127. funny(X0) <- (3) [avatar component clause 126]
129. 4 <=> kind(mary) [avatar definition]
131. kind(mary) <- (4) [avatar component clause 129]
132. 3 | 4 [avatar split clause 78,129,126]
150. 9 <=> patient(mary) [avatar definition]
152. patient(mary) <- (9) [avatar component clause 150]
159. 11 <=> funny(mary) [avatar definition]
161. ~funny(mary) <- (~11) [avatar component clause 159]
164. 12 <=> ! [X0] : patient(X0) [avatar definition]
165. patient(X0) <- (12) [avatar component clause 164]
166. 12 | ~11 [avatar split clause 90,159,164]
168. 13 <=> happy(mary) [avatar definition]
172. 12 | ~13 [avatar split clause 88,168,164]
223. patient(mary) <- (4) [resolution 104,131]
224. 9 | ~4 [avatar split clause 223,129,150]
225. $false <- (3, ~11) [resolution 127,161]
226. ~3 | 11 [avatar contradiction clause 225]
228. quiet(mary) <- (4) [resolution 131,101]
232. creative(mary) <- (9) [resolution 152,103]
263. happy(mary) | ~quiet(mary) <- (9) [resolution 79,232]
267. happy(mary) <- (4, 9) [subsumption resolution 263,228]
268. 13 | ~4 | ~9 [avatar split clause 267,150,129,168]
269. $false <- (12) [resolution 165,115]
273. ~12 [avatar contradiction clause 269]
274. $false [avatar sat refutation 132,166,172,224,226,268,273]
% SZS output end Proof for 329530424618988170043667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not tall is calm or not funny.
Everyone who is funny or brave is not kind or not happy and vice versa.
Everyone who is either not funny or not rich is both not quiet and curious.
If someone is not calm then someone is both not generous and old.
If someone is brave or strong then paul is either not calm or not quiet and vice versa.
Everyone who is either old or humble is both brave and not patient.
Everyone who is humble is not calm or wise.
Everyone who is brave is either not quiet or not creative and vice versa.
If john is either not creative or curious then someone is both not quiet and not rich.
If fred is both not funny and not humble then someone is both not curious and not humble and vice versa.
Everyone who is funny is both not strong and not generous and vice versa.
Everyone who is happy is either not strong or not old and vice versa.
Everyone who is both funny and not creative is curious and vice versa.
Everyone who is calm is funny or not calm and vice versa.
Everyone who is either not old or not humble is either not rich or brave.
Everyone who is either funny or rich is brave.
Fred is both tall and creative.
Fred is not quiet.
Alice is both not patient and not kind.
Someone is both old and not quiet.
Someone is either brave or not rich.
Someone is both rich and not tall.
Paul is not strong or not quiet.
Someone is either creative or happy. | Paul is not rich. | contradiction | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~quiet(X)&curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~generous(X)&old(X)))))&
((?[X]:((brave(X)|strong(X))))<=>((~calm(paul)<~>~quiet(paul))))&
(![X]:((old(X)<~>humble(X))=>(brave(X)&~patient(X))))&
(![X]:(humble(X)=>(~calm(X)|wise(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~creative(X))))&
(((~creative(john)<~>curious(john)))=>(?[X]:((~quiet(X)&~rich(X)))))&
(((~funny(fred)&~humble(fred)))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:(funny(X)<=>(~strong(X)&~generous(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~old(X))))&
(![X]:((funny(X)&~creative(X))<=>curious(X)))&
(![X]:(calm(X)<=>(funny(X)|~calm(X))))&
(![X]:((~old(X)<~>~humble(X))=>(~rich(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>brave(X)))&
((tall(fred)&creative(fred)))&
(~quiet(fred))&
((~patient(alice)&~kind(alice)))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((rich(X)&~tall(X))))&
((~strong(paul)|~quiet(paul)))&
(?[X]:((creative(X)<~>happy(X)))) | ~rich(paul) | [
"p2",
"p7",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8772831959343889109958148
% SZS output start Proof for 8772831959343889109958148
3. ! [X0] : ((~funny(X0) <~> ~rich(X0)) => (curious(X0) & ~quiet(X0))) [input p2]
8. ! [X0] : (brave(X0) <=> (~quiet(X0) <~> ~creative(X0))) [input p7]
13. ! [X0] : ((~creative(X0) & funny(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : (calm(X0) <=> (~calm(X0) | funny(X0))) [input p13]
16. ! [X0] : ((funny(X0) <~> rich(X0)) => brave(X0)) [input p15]
25. ~rich(paul) [input hypothesis]
32. ! [X0] : ((curious(X0) & ~quiet(X0)) | (~funny(X0) <=> ~rich(X0))) [ennf transformation 3]
37. ! [X0] : (brave(X0) | (funny(X0) <=> rich(X0))) [ennf transformation 16]
40. ! [X0] : ((curious(X0) & ~quiet(X0)) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) [nnf transformation 32]
49. ! [X0] : ((brave(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~brave(X0))) [nnf transformation 8]
61. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | ~funny(X0)))) [nnf transformation 13]
62. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | ~funny(X0))) [flattening 61]
63. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ~calm(X0))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~calm(X0))) [flattening 63]
66. ! [X0] : (brave(X0) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) [nnf transformation 37]
84. ~quiet(X0) | ~funny(X0) | rich(X0) [cnf transformation 40]
86. ~funny(X0) | curious(X0) | rich(X0) [cnf transformation 40]
98. ~brave(X0) | quiet(X0) | creative(X0) [cnf transformation 49]
118. ~creative(X0) | ~curious(X0) [cnf transformation 62]
119. ~calm(X0) | funny(X0) | ~calm(X0) [cnf transformation 64]
121. calm(X0) | calm(X0) [cnf transformation 64]
126. ~funny(X0) | rich(X0) | brave(X0) [cnf transformation 66]
141. ~rich(paul) [cnf transformation 25]
142. ~calm(X0) | funny(X0) [duplicate literal removal 119]
143. calm(X0) [duplicate literal removal 121]
146. 1 <=> ! [X1] : calm(X1) [avatar definition]
147. calm(X1) <- (1) [avatar component clause 146]
159. 4 <=> quiet(paul) [avatar definition]
160. ~quiet(paul) <- (~4) [avatar component clause 159]
161. quiet(paul) <- (4) [avatar component clause 159]
229. 1 [avatar split clause 143,146]
263. funny(X0) <- (1) [resolution 142,147]
279. ~funny(paul) | rich(paul) <- (4) [resolution 84,161]
280. rich(paul) <- (1, 4) [subsumption resolution 279,263]
281. $false <- (1, 4) [subsumption resolution 280,141]
282. ~1 | ~4 [avatar contradiction clause 281]
284. curious(X0) | rich(X0) <- (1) [resolution 86,263]
389. rich(X0) | brave(X0) <- (1) [resolution 126,263]
421. brave(paul) <- (1) [resolution 389,141]
494. quiet(paul) | creative(paul) <- (1) [resolution 421,98]
495. creative(paul) <- (1, ~4) [subsumption resolution 494,160]
512. ~curious(paul) <- (1, ~4) [resolution 495,118]
541. rich(paul) <- (1, ~4) [resolution 512,284]
542. $false <- (1, ~4) [subsumption resolution 541,141]
543. ~1 | 4 [avatar contradiction clause 542]
544. $false [avatar sat refutation 229,282,543]
% SZS output end Proof for 8772831959343889109958148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not creative then someone is curious and vice versa.
If fred is both strong and not patient then john is both creative and not curious and vice versa.
Everyone who is kind is either not strong or generous and vice versa.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
If mary is not brave or not quiet then lucy is wise or curious and vice versa.
Everyone who is both not happy and calm is either not brave or calm and vice versa.
Everyone who is both not old and rich is calm and vice versa.
If susan is rich then alice is both funny and quiet.
Everyone who is rich or not happy is not patient and vice versa.
Everyone who is brave or quiet is generous.
Everyone who is not tall is not kind or not humble and vice versa.
Everyone who is wise is not brave or not rich.
Everyone who is either not happy or calm is not curious or not old and vice versa.
If mary is either happy or curious then john is patient.
Everyone who is patient or not curious is not quiet or patient and vice versa.
Someone is calm.
Someone is not rich.
Mary is old.
Someone is quiet or humble.
Paul is not creative.
Paul is happy or creative.
Mary is funny.
Susan is either not calm or strong. | Paul is tall. | neutral | ((?[X]:((~old(X)&~creative(X))))<=>(?[X]:(curious(X))))&
(((strong(fred)&~patient(fred)))<=>((creative(john)&~curious(john))))&
(![X]:(kind(X)<=>(~strong(X)<~>generous(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
(![X]:((~happy(X)&calm(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((~old(X)&rich(X))<=>calm(X)))&
((rich(susan))=>((funny(alice)&quiet(alice))))&
(![X]:((rich(X)|~happy(X))<=>~patient(X)))&
(![X]:((brave(X)|quiet(X))=>generous(X)))&
(![X]:(~tall(X)<=>(~kind(X)|~humble(X))))&
(![X]:(wise(X)=>(~brave(X)|~rich(X))))&
(![X]:((~happy(X)<~>calm(X))<=>(~curious(X)|~old(X))))&
(((happy(mary)<~>curious(mary)))=>(patient(john)))&
(![X]:((patient(X)|~curious(X))<=>(~quiet(X)|patient(X))))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
(old(mary))&
(?[X]:((quiet(X)|humble(X))))&
(~creative(paul))&
((happy(paul)|creative(paul)))&
(funny(mary))&
((~calm(susan)<~>strong(susan))) | tall(paul) | [] | null | 0 |
Everyone who is rich is both not kind and happy.
Everyone who is tall is either generous or not brave.
If someone is both not calm and old then someone is either not wise or wise and vice versa.
Everyone who is either patient or curious is not generous and vice versa.
If lucy is not rich then susan is either patient or generous and vice versa.
If someone is not curious then someone is either not wise or quiet and vice versa.
Everyone who is not happy or wise is not wise or not tall.
If someone is either quiet or rich then john is either generous or quiet and vice versa.
Everyone who is not calm or old is not generous.
Everyone who is generous or not calm is happy and vice versa.
Everyone who is either happy or rich is either old or strong and vice versa.
Everyone who is generous is humble and vice versa.
Everyone who is either rich or not funny is patient or brave.
If susan is not funny or creative then mary is not happy or calm.
Everyone who is not quiet or not tall is both patient and generous.
Everyone who is either not humble or creative is either not patient or tall and vice versa.
John is both not funny and happy.
Lucy is either not funny or not rich.
Fred is not wise.
Someone is not funny.
Someone is happy or kind.
Lucy is old.
Alice is generous.
John is not curious. | Alice is not old. | entailment | (![X]:(rich(X)=>(~kind(X)&happy(X))))&
(![X]:(tall(X)=>(generous(X)<~>~brave(X))))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((patient(X)<~>curious(X))<=>~generous(X)))&
((~rich(lucy))<=>((patient(susan)<~>generous(susan))))&
((?[X]:(~curious(X)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((~happy(X)|wise(X))=>(~wise(X)|~tall(X))))&
((?[X]:((quiet(X)<~>rich(X))))<=>((generous(john)<~>quiet(john))))&
(![X]:((~calm(X)|old(X))=>~generous(X)))&
(![X]:((generous(X)|~calm(X))<=>happy(X)))&
(![X]:((happy(X)<~>rich(X))<=>(old(X)<~>strong(X))))&
(![X]:(generous(X)<=>humble(X)))&
(![X]:((rich(X)<~>~funny(X))=>(patient(X)|brave(X))))&
(((~funny(susan)|creative(susan)))=>((~happy(mary)|calm(mary))))&
(![X]:((~quiet(X)|~tall(X))=>(patient(X)&generous(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(~patient(X)<~>tall(X))))&
((~funny(john)&happy(john)))&
((~funny(lucy)<~>~rich(lucy)))&
(~wise(fred))&
(?[X]:(~funny(X)))&
(?[X]:((happy(X)|kind(X))))&
(old(lucy))&
(generous(alice))&
(~curious(john)) | ~old(alice) | [
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 639556332048989010802124
% SZS output start Proof for 639556332048989010802124
9. ! [X0] : ((old(X0) | ~calm(X0)) => ~generous(X0)) [input p8]
23. generous(alice) [input p22]
25. old(alice) [input hypothesis]
32. ! [X0] : (~generous(X0) | (~old(X0) & calm(X0))) [ennf transformation 9]
99. ~old(X0) | ~generous(X0) [cnf transformation 32]
137. generous(alice) [cnf transformation 23]
139. old(alice) [cnf transformation 25]
276. ~generous(alice) [resolution 99,139]
278. $false [subsumption resolution 276,137]
% SZS output end Proof for 639556332048989010802124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not humble is either tall or strong.
If someone is happy then alice is both wise and not wise.
Everyone who is both not brave and rich is both not rich and kind and vice versa.
Everyone who is either not quiet or tall is either not funny or not patient.
If john is both not old and old then someone is both old and funny.
Everyone who is not wise or tall is not wise.
If alice is both not strong and humble then someone is either not calm or not old and vice versa.
If alice is both kind and not tall then alice is brave or not happy and vice versa.
Everyone who is not brave is either humble or not funny and vice versa.
Everyone who is calm is both tall and not curious.
If fred is either not patient or humble then someone is not tall.
Everyone who is either creative or calm is not creative or happy.
Everyone who is funny is either tall or creative and vice versa.
If john is not creative then someone is happy and vice versa.
If paul is not happy or kind then someone is either tall or not brave.
John is tall or not old.
Someone is not strong.
Susan is not tall or not brave.
Someone is not rich.
Susan is old.
Someone is curious or not generous.
Someone is either humble or funny.
Mary is both not creative and curious. | Mary is not old. | entailment | (![X]:((kind(X)|~humble(X))=>(tall(X)<~>strong(X))))&
((?[X]:(happy(X)))=>((wise(alice)&~wise(alice))))&
(![X]:((~brave(X)&rich(X))<=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~funny(X)<~>~patient(X))))&
(((~old(john)&old(john)))=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~wise(X)|tall(X))=>~wise(X)))&
(((~strong(alice)&humble(alice)))<=>(?[X]:((~calm(X)<~>~old(X)))))&
(((kind(alice)&~tall(alice)))<=>((brave(alice)|~happy(alice))))&
(![X]:(~brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(calm(X)=>(tall(X)&~curious(X))))&
(((~patient(fred)<~>humble(fred)))=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>calm(X))=>(~creative(X)|happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>creative(X))))&
((~creative(john))<=>(?[X]:(happy(X))))&
(((~happy(paul)|kind(paul)))=>(?[X]:((tall(X)<~>~brave(X)))))&
((tall(john)|~old(john)))&
(?[X]:(~strong(X)))&
((~tall(susan)|~brave(susan)))&
(?[X]:(~rich(X)))&
(old(susan))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((humble(X)<~>funny(X))))&
((~creative(mary)&curious(mary))) | ~old(mary) | [
"p0",
"p1",
"p6",
"p7",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8069267652469533296391979
% SZS output start Proof for 8069267652469533296391979
1. ! [X0] : ((~humble(X0) | kind(X0)) => (tall(X0) <~> strong(X0))) [input p0]
2. ? [X0] : happy(X0) => (~wise(alice) & wise(alice)) [input p1]
7. (humble(alice) & ~strong(alice)) <=> ? [X0] : (~calm(X0) <~> ~old(X0)) [input p6]
8. (~tall(alice) & kind(alice)) <=> (~happy(alice) | brave(alice)) [input p7]
10. ! [X0] : (calm(X0) => (~curious(X0) & tall(X0))) [input p9]
23. curious(mary) & ~creative(mary) [input p22]
24. old(mary) [input hypothesis]
26. ! [X0] : ((tall(X0) <~> strong(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
27. (~wise(alice) & wise(alice)) | ! [X0] : ~happy(X0) [ennf transformation 2]
32. ! [X0] : ((~curious(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 10]
37. ! [X0] : (((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | (humble(X0) & ~kind(X0))) [nnf transformation 26]
43. ((humble(alice) & ~strong(alice)) | ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (? [X0] : ((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (~humble(alice) | strong(alice))) [nnf transformation 7]
44. ((humble(alice) & ~strong(alice)) | ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (? [X0] : ((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~humble(alice) | strong(alice)) [flattening 43]
45. ((humble(alice) & ~strong(alice)) | ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (? [X1] : ((old(X1) | calm(X1)) & (~old(X1) | ~calm(X1))) | ~humble(alice) | strong(alice)) [rectify 44]
46. ? [X1] : ((old(X1) | calm(X1)) & (~old(X1) | ~calm(X1))) => ((old(sK1) | calm(sK1)) & (~old(sK1) | ~calm(sK1))) [choice axiom]
47. ((humble(alice) & ~strong(alice)) | ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(sK1) | calm(sK1)) & (~old(sK1) | ~calm(sK1))) | ~humble(alice) | strong(alice)) [skolemisation 45,46]
48. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & ((~happy(alice) | brave(alice)) | (tall(alice) | ~kind(alice))) [nnf transformation 8]
49. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & (~happy(alice) | brave(alice) | tall(alice) | ~kind(alice)) [flattening 48]
70. ~kind(X0) | tall(X0) | strong(X0) [cnf transformation 37]
74. wise(alice) | ~happy(X0) [cnf transformation 27]
75. ~wise(alice) | ~happy(X0) [cnf transformation 27]
90. ~strong(alice) | ~old(X0) | calm(X0) [cnf transformation 47]
96. kind(alice) | happy(alice) [cnf transformation 49]
98. ~tall(alice) | happy(alice) [cnf transformation 49]
104. ~curious(X0) | ~calm(X0) [cnf transformation 32]
127. curious(mary) [cnf transformation 23]
128. old(mary) [cnf transformation 24]
133. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
134. ~happy(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(alice) [avatar definition]
139. 1 | ~2 [avatar split clause 75,136,133]
140. 1 | 2 [avatar split clause 74,136,133]
150. 5 <=> ! [X0] : (~old(X0) | calm(X0)) [avatar definition]
151. ~old(X0) | calm(X0) <- (5) [avatar component clause 150]
154. 6 <=> strong(alice) [avatar definition]
156. ~strong(alice) <- (~6) [avatar component clause 154]
158. 5 | ~6 [avatar split clause 90,154,150]
170. 9 <=> happy(alice) [avatar definition]
172. happy(alice) <- (9) [avatar component clause 170]
174. 10 <=> tall(alice) [avatar definition]
176. ~tall(alice) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 98,174,170]
184. 12 <=> kind(alice) [avatar definition]
186. kind(alice) <- (12) [avatar component clause 184]
187. 9 | 12 [avatar split clause 96,184,170]
262. $false <- (1, 9) [resolution 172,134]
263. ~1 | ~9 [avatar contradiction clause 262]
264. ~calm(mary) [resolution 104,127]
271. calm(mary) <- (5) [resolution 151,128]
272. $false <- (5) [subsumption resolution 271,264]
273. ~5 [avatar contradiction clause 272]
274. tall(alice) | strong(alice) <- (12) [resolution 70,186]
275. strong(alice) <- (~10, 12) [subsumption resolution 274,176]
276. $false <- (~6, ~10, 12) [subsumption resolution 275,156]
277. 6 | 10 | ~12 [avatar contradiction clause 276]
278. $false [avatar sat refutation 139,140,158,177,187,263,273,277]
% SZS output end Proof for 8069267652469533296391979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both quiet and not quiet then someone is either not strong or not patient and vice versa. Everyone who is both not curious and wise is either not quiet or not humble. Everyone who is happy or not rich is not calm or not wise and vice versa. If john is both not patient and not tall then someone is both not wise and brave. Everyone who is humble or not calm is old and vice versa. Everyone who is either old or not patient is both funny and not quiet. Everyone who is both rich and creative is humble. Everyone who is both rich and patient is both not quiet and not brave. If susan is quiet then someone is not rich or calm and vice versa. Everyone who is not humble or not strong is not rich or not brave. If susan is either not happy or funny then someone is not calm or humble and vice versa. If someone is rich then mary is both not rich and strong and vice versa. If someone is both tall and not funny then someone is either curious or not old. Everyone who is both curious and not happy is not humble. Everyone who is not patient or generous is not wise. Everyone who is old or generous is not creative or humble. John is rich. Someone is both not brave and tall. Mary is both not generous and not creative. Someone is funny or not humble. Someone is either not funny or calm. Fred is either not brave or tall. Fred is both brave and wise. Someone is either not strong or not old. | Fred is quiet. | contradiction | (((quiet(susan)&~quiet(susan)))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((~curious(X)&wise(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((happy(X)|~rich(X))<=>(~calm(X)|~wise(X))))&
(((~patient(john)&~tall(john)))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((humble(X)|~calm(X))<=>old(X)))&
(![X]:((old(X)<~>~patient(X))=>(funny(X)&~quiet(X))))&
(![X]:((rich(X)&creative(X))=>humble(X)))&
(![X]:((rich(X)&patient(X))=>(~quiet(X)&~brave(X))))&
((quiet(susan))<=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((~humble(X)|~strong(X))=>(~rich(X)|~brave(X))))&
(((~happy(susan)<~>funny(susan)))<=>(?[X]:((~calm(X)|humble(X)))))&
((?[X]:(rich(X)))<=>((~rich(mary)&strong(mary))))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((curious(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
(![X]:((old(X)|generous(X))=>(~creative(X)|humble(X))))&
(rich(john))&
(?[X]:((~brave(X)&tall(X))))&
((~generous(mary)&~creative(mary)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((~brave(fred)<~>tall(fred)))&
((brave(fred)&wise(fred)))&
(?[X]:((~strong(X)<~>~old(X)))) | quiet(fred) | [
"p2",
"p4",
"p5",
"p7",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5386771240406453697436697
% SZS output start Proof for 5386771240406453697436697
3. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~wise(X0) | ~calm(X0))) [input p2]
5. ! [X0] : ((~calm(X0) | humble(X0)) <=> old(X0)) [input p4]
6. ! [X0] : ((old(X0) <~> ~patient(X0)) => (~quiet(X0) & funny(X0))) [input p5]
8. ! [X0] : ((patient(X0) & rich(X0)) => (~brave(X0) & ~quiet(X0))) [input p7]
15. ! [X0] : ((generous(X0) | ~patient(X0)) => ~wise(X0)) [input p14]
23. wise(fred) & brave(fred) [input p22]
25. quiet(fred) [input hypothesis]
29. ! [X0] : (~patient(X0) => ~wise(X0)) [pure predicate removal 15]
37. ! [X0] : ((~quiet(X0) & funny(X0)) | (old(X0) <=> ~patient(X0))) [ennf transformation 6]
38. ! [X0] : ((~brave(X0) & ~quiet(X0)) | (~patient(X0) | ~rich(X0))) [ennf transformation 8]
39. ! [X0] : ((~brave(X0) & ~quiet(X0)) | ~patient(X0) | ~rich(X0)) [flattening 38]
45. ! [X0] : (~wise(X0) | patient(X0)) [ennf transformation 29]
52. ! [X0] : (((~rich(X0) | happy(X0)) | (wise(X0) & calm(X0))) & ((~wise(X0) | ~calm(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 3]
53. ! [X0] : ((~rich(X0) | happy(X0) | (wise(X0) & calm(X0))) & (~wise(X0) | ~calm(X0) | (rich(X0) & ~happy(X0)))) [flattening 52]
56. ! [X0] : (((~calm(X0) | humble(X0)) | ~old(X0)) & (old(X0) | (calm(X0) & ~humble(X0)))) [nnf transformation 5]
57. ! [X0] : ((~calm(X0) | humble(X0) | ~old(X0)) & (old(X0) | (calm(X0) & ~humble(X0)))) [flattening 56]
58. ! [X0] : ((~quiet(X0) & funny(X0)) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) [nnf transformation 37]
96. ~calm(X0) | ~wise(X0) | rich(X0) [cnf transformation 53]
102. old(X0) | calm(X0) [cnf transformation 57]
106. ~old(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 58]
109. ~brave(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 39]
127. ~wise(X0) | patient(X0) [cnf transformation 45]
136. brave(fred) [cnf transformation 23]
137. wise(fred) [cnf transformation 23]
140. quiet(fred) [cnf transformation 25]
269. 29 <=> brave(fred) [avatar definition]
271. brave(fred) <- (29) [avatar component clause 269]
278. 29 [avatar split clause 136,269]
296. patient(fred) [resolution 127,137]
393. ~patient(X0) | ~quiet(X0) | calm(X0) [resolution 106,102]
420. ~patient(fred) | ~rich(fred) <- (29) [resolution 109,271]
421. ~rich(fred) <- (29) [subsumption resolution 420,296]
451. 56 <=> calm(fred) [avatar definition]
453. calm(fred) <- (56) [avatar component clause 451]
463. ~quiet(fred) | calm(fred) [resolution 393,296]
465. calm(fred) [subsumption resolution 463,140]
466. 56 [avatar split clause 465,451]
470. ~wise(fred) | rich(fred) <- (56) [resolution 453,96]
472. rich(fred) <- (56) [subsumption resolution 470,137]
473. $false <- (29, 56) [subsumption resolution 472,421]
474. ~29 | ~56 [avatar contradiction clause 473]
476. $false [avatar sat refutation 278,466,474]
% SZS output end Proof for 5386771240406453697436697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not calm is not old or curious and vice versa.
If john is brave then john is either not kind or not curious and vice versa.
Everyone who is not creative is patient or brave and vice versa.
Everyone who is not quiet or strong is either curious or not calm.
Everyone who is either generous or kind is either not quiet or wise.
If someone is either not old or not quiet then susan is both not wise and not rich and vice versa.
Everyone who is either not wise or old is either not quiet or not brave and vice versa.
If paul is not rich or curious then someone is not creative.
If paul is generous then mary is both happy and not curious and vice versa.
Everyone who is both humble and creative is either rich or funny.
Everyone who is not humble is both not humble and humble and vice versa.
If someone is both old and not rich then susan is both brave and not strong.
If alice is either calm or rich then paul is generous or not creative and vice versa.
If someone is either humble or not kind then susan is tall.
Everyone who is not humble is brave or not curious and vice versa.
Everyone who is patient or calm is strong.
Someone is both happy and rich.
Mary is wise or not old.
Susan is either generous or not old.
Someone is either rich or not rich.
Someone is either not humble or not rich.
Alice is both not patient and not quiet.
John is not tall.
Someone is both funny and not creative. | Alice is calm. | entailment | (![X]:((old(X)|~calm(X))<=>(~old(X)|curious(X))))&
((brave(john))<=>((~kind(john)<~>~curious(john))))&
(![X]:(~creative(X)<=>(patient(X)|brave(X))))&
(![X]:((~quiet(X)|strong(X))=>(curious(X)<~>~calm(X))))&
(![X]:((generous(X)<~>kind(X))=>(~quiet(X)<~>wise(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>((~wise(susan)&~rich(susan))))&
(![X]:((~wise(X)<~>old(X))<=>(~quiet(X)<~>~brave(X))))&
(((~rich(paul)|curious(paul)))=>(?[X]:(~creative(X))))&
((generous(paul))<=>((happy(mary)&~curious(mary))))&
(![X]:((humble(X)&creative(X))=>(rich(X)<~>funny(X))))&
(![X]:(~humble(X)<=>(~humble(X)&humble(X))))&
((?[X]:((old(X)&~rich(X))))=>((brave(susan)&~strong(susan))))&
(((calm(alice)<~>rich(alice)))<=>((generous(paul)|~creative(paul))))&
((?[X]:((humble(X)<~>~kind(X))))=>(tall(susan)))&
(![X]:(~humble(X)<=>(brave(X)|~curious(X))))&
(![X]:((patient(X)|calm(X))=>strong(X)))&
(?[X]:((happy(X)&rich(X))))&
((wise(mary)|~old(mary)))&
((generous(susan)<~>~old(susan)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((~humble(X)<~>~rich(X))))&
((~patient(alice)&~quiet(alice)))&
(~tall(john))&
(?[X]:((funny(X)&~creative(X)))) | calm(alice) | [
"p3",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1582856973557777629348912
% SZS output start Proof for 1582856973557777629348912
4. ! [X0] : ((strong(X0) | ~quiet(X0)) => (curious(X0) <~> ~calm(X0))) [input p3]
11. ! [X0] : (~humble(X0) <=> (humble(X0) & ~humble(X0))) [input p10]
15. ! [X0] : (~humble(X0) <=> (~curious(X0) | brave(X0))) [input p14]
22. ~quiet(alice) & ~patient(alice) [input p21]
25. ~calm(alice) [input hypothesis]
26. ! [X0] : ((curious(X0) <~> ~calm(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 4]
39. ! [X0] : (((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | (~strong(X0) & quiet(X0))) [nnf transformation 26]
52. ! [X0] : ((~humble(X0) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | humble(X0))) [nnf transformation 11]
53. ! [X0] : ((~humble(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | humble(X0))) [flattening 52]
57. ! [X0] : ((~humble(X0) | (curious(X0) & ~brave(X0))) & ((~curious(X0) | brave(X0)) | humble(X0))) [nnf transformation 15]
58. ! [X0] : ((~humble(X0) | (curious(X0) & ~brave(X0))) & (~curious(X0) | brave(X0) | humble(X0))) [flattening 57]
83. ~curious(X0) | calm(X0) | quiet(X0) [cnf transformation 39]
111. humble(X0) | humble(X0) [cnf transformation 53]
125. ~humble(X0) | curious(X0) [cnf transformation 58]
138. ~quiet(alice) [cnf transformation 22]
142. ~calm(alice) [cnf transformation 25]
143. humble(X0) [duplicate literal removal 111]
238. 20 <=> calm(alice) [avatar definition]
240. ~calm(alice) <- (~20) [avatar component clause 238]
260. curious(X0) [subsumption resolution 125,143]
282. ~20 [avatar split clause 142,238]
301. quiet(X0) | calm(X0) [resolution 83,260]
302. calm(alice) [resolution 301,138]
304. $false <- (~20) [subsumption resolution 302,240]
305. 20 [avatar contradiction clause 304]
306. $false [avatar sat refutation 282,305]
% SZS output end Proof for 1582856973557777629348912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or strong is both not brave and not curious. Everyone who is humble is rich or not strong and vice versa. Everyone who is rich or generous is brave or not happy. If susan is either strong or rich then fred is tall. If someone is quiet or not quiet then someone is generous. Everyone who is either kind or not quiet is both not patient and not old and vice versa. Everyone who is happy is rich and vice versa. Everyone who is not humble or generous is happy or not quiet and vice versa. Everyone who is creative is both not strong and calm and vice versa. If lucy is either brave or not funny then fred is not humble or brave and vice versa. Everyone who is either generous or not happy is not humble. If alice is quiet then someone is not tall or not old. Everyone who is funny is quiet. If lucy is both not calm and not funny then fred is either not curious or not happy and vice versa. Everyone who is either wise or not tall is both tall and not calm. If someone is both not creative and not kind then lucy is either funny or generous. Someone is either not calm or old. Someone is both not wise and not old. Someone is not kind or generous. Paul is either kind or not humble. Susan is both not rich and humble. Someone is either not strong or not brave. Susan is not strong. | Paul is not happy. | entailment | (![X]:((calm(X)<~>strong(X))=>(~brave(X)&~curious(X))))&
(![X]:(humble(X)<=>(rich(X)|~strong(X))))&
(![X]:((rich(X)|generous(X))=>(brave(X)|~happy(X))))&
(((strong(susan)<~>rich(susan)))=>(tall(fred)))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:(generous(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(~patient(X)&~old(X))))&
(![X]:(happy(X)<=>rich(X)))&
(![X]:((~humble(X)|generous(X))<=>(happy(X)|~quiet(X))))&
(![X]:(creative(X)<=>(~strong(X)&calm(X))))&
(((brave(lucy)<~>~funny(lucy)))<=>((~humble(fred)|brave(fred))))&
(![X]:((generous(X)<~>~happy(X))=>~humble(X)))&
((quiet(alice))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(funny(X)=>quiet(X)))&
(((~calm(lucy)&~funny(lucy)))<=>((~curious(fred)<~>~happy(fred))))&
(![X]:((wise(X)<~>~tall(X))=>(tall(X)&~calm(X))))&
((?[X]:((~creative(X)&~kind(X))))=>((funny(lucy)<~>generous(lucy))))&
(?[X]:((~calm(X)<~>old(X))))&
(?[X]:((~wise(X)&~old(X))))&
(?[X]:((~kind(X)|generous(X))))&
((kind(paul)<~>~humble(paul)))&
((~rich(susan)&humble(susan)))&
(?[X]:((~strong(X)<~>~brave(X))))&
(~strong(susan)) | ~happy(paul) | [
"p1",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6592093617656225379587623
% SZS output start Proof for 6592093617656225379587623
2. ! [X0] : (humble(X0) <=> (~strong(X0) | rich(X0))) [input p1]
7. ! [X0] : (happy(X0) <=> rich(X0)) [input p6]
8. ! [X0] : ((generous(X0) | ~humble(X0)) <=> (~quiet(X0) | happy(X0))) [input p7]
11. ! [X0] : ((generous(X0) <~> ~happy(X0)) => ~humble(X0)) [input p10]
24. happy(paul) [input hypothesis]
33. ! [X0] : (~humble(X0) | (generous(X0) <=> ~happy(X0))) [ennf transformation 11]
39. ! [X0] : ((humble(X0) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 2]
40. ! [X0] : ((humble(X0) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ~humble(X0))) [flattening 39]
47. ! [X0] : ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))) [nnf transformation 7]
48. ! [X0] : (((generous(X0) | ~humble(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (~generous(X0) & humble(X0)))) [nnf transformation 8]
49. ! [X0] : ((generous(X0) | ~humble(X0) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | (~generous(X0) & humble(X0)))) [flattening 48]
52. ! [X0] : (~humble(X0) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) [nnf transformation 33]
75. ~rich(X0) | humble(X0) [cnf transformation 40]
89. ~happy(X0) | rich(X0) [cnf transformation 47]
93. generous(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 49]
103. ~humble(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 52]
131. happy(paul) [cnf transformation 24]
182. ~happy(X0) | ~humble(X0) [subsumption resolution 103,93]
247. 24 <=> humble(paul) [avatar definition]
249. humble(paul) <- (24) [avatar component clause 247]
266. rich(paul) [resolution 89,131]
268. humble(paul) [resolution 266,75]
271. 24 [avatar split clause 268,247]
277. ~humble(paul) [resolution 182,131]
278. $false <- (24) [subsumption resolution 277,249]
279. ~24 [avatar contradiction clause 278]
280. $false [avatar sat refutation 271,279]
% SZS output end Proof for 6592093617656225379587623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or not creative then someone is both brave and not humble.
Everyone who is happy is not rich or happy.
Everyone who is wise is not curious or not quiet and vice versa.
Everyone who is both not creative and not curious is both not curious and not tall and vice versa.
Everyone who is either not calm or not humble is either calm or not strong.
Everyone who is not happy or not patient is either not kind or not creative.
Everyone who is wise or generous is either brave or not kind and vice versa.
Everyone who is either not old or calm is either not brave or brave and vice versa.
Everyone who is either happy or not happy is both not rich and not strong and vice versa.
If someone is not calm or generous then someone is kind and vice versa.
If someone is not curious or curious then fred is curious or not wise and vice versa.
Everyone who is creative or patient is kind or not quiet and vice versa.
Everyone who is happy or not brave is both funny and calm.
If john is not patient or creative then fred is either strong or rich and vice versa.
Everyone who is not kind or not humble is not patient and vice versa.
Everyone who is either not old or not generous is both not calm and calm.
Paul is not tall.
Paul is both brave and patient.
Someone is both creative and quiet.
Someone is calm.
Paul is generous.
Paul is funny.
Someone is both not old and humble. | Paul is not curious. | contradiction | ((?[X]:((~generous(X)<~>~creative(X))))=>(?[X]:((brave(X)&~humble(X)))))&
(![X]:(happy(X)=>(~rich(X)|happy(X))))&
(![X]:(wise(X)<=>(~curious(X)|~quiet(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~curious(X)&~tall(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(calm(X)<~>~strong(X))))&
(![X]:((~happy(X)|~patient(X))=>(~kind(X)<~>~creative(X))))&
(![X]:((wise(X)|generous(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((~old(X)<~>calm(X))<=>(~brave(X)<~>brave(X))))&
(![X]:((happy(X)<~>~happy(X))<=>(~rich(X)&~strong(X))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~curious(X)|curious(X))))<=>((curious(fred)|~wise(fred))))&
(![X]:((creative(X)|patient(X))<=>(kind(X)|~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>(funny(X)&calm(X))))&
(((~patient(john)|creative(john)))<=>((strong(fred)<~>rich(fred))))&
(![X]:((~kind(X)|~humble(X))<=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~calm(X)&calm(X))))&
(~tall(paul))&
((brave(paul)&patient(paul)))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:(calm(X)))&
(generous(paul))&
(funny(paul))&
(?[X]:((~old(X)&humble(X)))) | ~curious(paul) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p11",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 705936551252898669510388
% SZS output start Proof for 705936551252898669510388
1. ? [X0] : (~generous(X0) <~> ~creative(X0)) => ? [X0] : (~humble(X0) & brave(X0)) [input p0]
3. ! [X0] : (wise(X0) <=> (~quiet(X0) | ~curious(X0))) [input p2]
4. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (~tall(X0) & ~curious(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | ~happy(X0)) => (~kind(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : ((generous(X0) | wise(X0)) <=> (brave(X0) <~> ~kind(X0))) [input p6]
12. ! [X0] : ((patient(X0) | creative(X0)) <=> (~quiet(X0) | kind(X0))) [input p11]
15. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> ~patient(X0)) [input p14]
17. ~tall(paul) [input p16]
21. generous(paul) [input p20]
24. ~curious(paul) [input hypothesis]
25. ? [X0] : (~generous(X0) <~> ~creative(X0)) => ? [X1] : (~humble(X1) & brave(X1)) [rectify 1]
29. ? [X1] : (~humble(X1) & brave(X1)) | ! [X0] : (~generous(X0) <=> ~creative(X0)) [ennf transformation 25]
33. ! [X0] : ((~kind(X0) <~> ~creative(X0)) | (patient(X0) & happy(X0))) [ennf transformation 6]
36. ? [X1] : (~humble(X1) & brave(X1)) | ! [X0] : ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))) [nnf transformation 29]
37. ? [X0] : (~humble(X0) & brave(X0)) | ! [X1] : ((~generous(X1) | creative(X1)) & (~creative(X1) | generous(X1))) [rectify 36]
38. ? [X0] : (~humble(X0) & brave(X0)) => (~humble(sK0) & brave(sK0)) [choice axiom]
39. (~humble(sK0) & brave(sK0)) | ! [X1] : ((~generous(X1) | creative(X1)) & (~creative(X1) | generous(X1))) [skolemisation 37,38]
40. ! [X0] : ((wise(X0) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | ~wise(X0))) [nnf transformation 3]
41. ! [X0] : ((wise(X0) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ~wise(X0))) [flattening 40]
42. ! [X0] : (((~curious(X0) & ~creative(X0)) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 4]
43. ! [X0] : (((~curious(X0) & ~creative(X0)) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | curious(X0) | creative(X0))) [flattening 42]
45. ! [X0] : (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | (patient(X0) & happy(X0))) [nnf transformation 33]
46. ! [X0] : (((generous(X0) | wise(X0)) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | (~generous(X0) & ~wise(X0)))) [nnf transformation 7]
47. ! [X0] : ((generous(X0) | wise(X0) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | (~generous(X0) & ~wise(X0)))) [flattening 46]
61. ! [X0] : (((patient(X0) | creative(X0)) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | (~patient(X0) & ~creative(X0)))) [nnf transformation 12]
62. ! [X0] : ((patient(X0) | creative(X0) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | (~patient(X0) & ~creative(X0)))) [flattening 61]
65. ! [X0] : (((~humble(X0) | ~kind(X0)) | patient(X0)) & (~patient(X0) | (humble(X0) & kind(X0)))) [nnf transformation 15]
66. ! [X0] : ((~humble(X0) | ~kind(X0) | patient(X0)) & (~patient(X0) | (humble(X0) & kind(X0)))) [flattening 65]
75. brave(sK0) | ~generous(X1) | creative(X1) [cnf transformation 39]
77. ~humble(sK0) | ~generous(X1) | creative(X1) [cnf transformation 39]
81. quiet(X0) | wise(X0) [cnf transformation 41]
84. ~creative(X0) | tall(X0) | curious(X0) [cnf transformation 43]
91. ~kind(X0) | ~creative(X0) | patient(X0) [cnf transformation 45]
93. kind(X0) | creative(X0) | patient(X0) [cnf transformation 45]
96. ~wise(X0) | ~brave(X0) | kind(X0) [cnf transformation 47]
121. ~quiet(X0) | kind(X0) | ~creative(X0) [cnf transformation 62]
123. patient(X0) | creative(X0) | ~kind(X0) [cnf transformation 62]
134. ~patient(X0) | humble(X0) [cnf transformation 66]
140. ~tall(paul) [cnf transformation 17]
146. generous(paul) [cnf transformation 21]
149. ~curious(paul) [cnf transformation 24]
161. 1 <=> ! [X1] : (~generous(X1) | creative(X1)) [avatar definition]
162. ~generous(X1) | creative(X1) <- (1) [avatar component clause 161]
164. 2 <=> humble(sK0) [avatar definition]
166. ~humble(sK0) <- (~2) [avatar component clause 164]
167. 1 | ~2 [avatar split clause 77,164,161]
173. 4 <=> brave(sK0) [avatar definition]
175. brave(sK0) <- (4) [avatar component clause 173]
176. 1 | 4 [avatar split clause 75,173,161]
220. ~kind(X0) | patient(X0) [subsumption resolution 123,91]
279. 20 <=> creative(paul) [avatar definition]
280. creative(paul) <- (20) [avatar component clause 279]
294. creative(X2) | patient(X2) | patient(X2) [resolution 93,220]
295. patient(X2) | creative(X2) [duplicate literal removal 294]
344. 28 <=> kind(sK0) [avatar definition]
345. ~kind(sK0) <- (~28) [avatar component clause 344]
346. kind(sK0) <- (28) [avatar component clause 344]
354. ~creative(X0) | kind(X0) | wise(X0) [resolution 121,81]
422. humble(X1) | creative(X1) [resolution 295,134]
569. creative(sK0) <- (~2) [resolution 422,166]
579. kind(sK0) | wise(sK0) <- (~2) [resolution 569,354]
582. 40 <=> wise(sK0) [avatar definition]
584. wise(sK0) <- (40) [avatar component clause 582]
585. 40 | 28 | 2 [avatar split clause 579,164,344,582]
595. creative(paul) <- (1) [resolution 162,146]
603. 20 | ~1 [avatar split clause 595,161,279]
609. tall(paul) | curious(paul) <- (20) [resolution 280,84]
610. curious(paul) <- (20) [subsumption resolution 609,140]
611. $false <- (20) [subsumption resolution 610,149]
612. ~20 [avatar contradiction clause 611]
613. creative(sK0) <- (~2) [resolution 166,422]
616. ~creative(sK0) | patient(sK0) <- (28) [resolution 346,91]
622. patient(sK0) <- (~2, 28) [subsumption resolution 616,613]
650. humble(sK0) <- (~2, 28) [resolution 622,134]
652. $false <- (~2, 28) [subsumption resolution 650,166]
653. 2 | ~28 [avatar contradiction clause 652]
697. ~brave(sK0) | kind(sK0) <- (40) [resolution 584,96]
698. kind(sK0) <- (4, 40) [subsumption resolution 697,175]
699. $false <- (4, ~28, 40) [subsumption resolution 698,345]
700. ~4 | 28 | ~40 [avatar contradiction clause 699]
701. $false [avatar sat refutation 167,176,585,603,612,653,700]
% SZS output end Proof for 705936551252898669510388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
If john is quiet or not tall then mary is either not wise or creative and vice versa.
Everyone who is both quiet and rich is generous or funny and vice versa.
If mary is both wise and rich then someone is both not quiet and brave and vice versa.
Everyone who is curious or funny is not rich.
If someone is either not old or wise then someone is both not humble and tall and vice versa.
If someone is both generous and not generous then paul is both creative and strong and vice versa.
Everyone who is rich is either not wise or not patient.
Everyone who is wise or curious is both curious and generous and vice versa.
Everyone who is not rich or generous is not generous or wise and vice versa.
If susan is either wise or not happy then someone is not humble.
If alice is patient or funny then lucy is patient or creative.
Everyone who is both not brave and not funny is curious or not curious and vice versa.
If someone is brave then john is both wise and not calm and vice versa.
If mary is humble then lucy is old or not calm.
If someone is either brave or not old then fred is either not calm or not strong.
If someone is either not wise or tall then someone is both patient and not calm and vice versa.
Someone is not tall.
Someone is creative.
Fred is either humble or rich.
Fred is either curious or not creative.
Someone is either not calm or generous. | Lucy is not calm. | neutral | (((quiet(john)|~tall(john)))<=>((~wise(mary)<~>creative(mary))))&
(![X]:((quiet(X)&rich(X))<=>(generous(X)|funny(X))))&
(((wise(mary)&rich(mary)))<=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((curious(X)|funny(X))=>~rich(X)))&
((?[X]:((~old(X)<~>wise(X))))<=>(?[X]:((~humble(X)&tall(X)))))&
((?[X]:((generous(X)&~generous(X))))<=>((creative(paul)&strong(paul))))&
(![X]:(rich(X)=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|curious(X))<=>(curious(X)&generous(X))))&
(![X]:((~rich(X)|generous(X))<=>(~generous(X)|wise(X))))&
(((wise(susan)<~>~happy(susan)))=>(?[X]:(~humble(X))))&
(((patient(alice)|funny(alice)))=>((patient(lucy)|creative(lucy))))&
(![X]:((~brave(X)&~funny(X))<=>(curious(X)|~curious(X))))&
((?[X]:(brave(X)))<=>((wise(john)&~calm(john))))&
((humble(mary))=>((old(lucy)|~calm(lucy))))&
((?[X]:((brave(X)<~>~old(X))))=>((~calm(fred)<~>~strong(fred))))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((patient(X)&~calm(X)))))&
(?[X]:(~tall(X)))&
(?[X]:(creative(X)))&
((humble(fred)<~>rich(fred)))&
((curious(fred)<~>~creative(fred)))&
(?[X]:((~calm(X)<~>generous(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is either not quiet or not creative is not wise or calm and vice versa. Everyone who is not kind or calm is old or strong and vice versa. Everyone who is both not wise and generous is either humble or not wise and vice versa. If someone is not generous then john is either happy or not humble and vice versa. Everyone who is both calm and not curious is both not happy and calm and vice versa. If someone is either kind or strong then mary is both tall and not rich. If john is patient or not humble then someone is kind and vice versa. Everyone who is either funny or tall is not brave or not generous. Everyone who is either creative or not generous is either not quiet or calm and vice versa. Everyone who is funny or not kind is either old or rich and vice versa. Everyone who is not tall or not generous is funny and vice versa. Everyone who is funny is both not kind and creative and vice versa. If someone is not calm or not patient then someone is either old or not happy. Everyone who is not brave is either not happy or not wise and vice versa. Everyone who is either not old or kind is both humble and not kind. Everyone who is not humble is either not funny or strong. Someone is either not creative or not quiet. Mary is tall. Paul is quiet. Someone is either funny or rich. John is either quiet or not humble. Someone is either not wise or not quiet. Alice is not old or humble. Alice is generous or brave. | Mary is rich. | contradiction | (![X]:((~quiet(X)<~>~creative(X))<=>(~wise(X)|calm(X))))&
(![X]:((~kind(X)|calm(X))<=>(old(X)|strong(X))))&
(![X]:((~wise(X)&generous(X))<=>(humble(X)<~>~wise(X))))&
((?[X]:(~generous(X)))<=>((happy(john)<~>~humble(john))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)&calm(X))))&
((?[X]:((kind(X)<~>strong(X))))=>((tall(mary)&~rich(mary))))&
(((patient(john)|~humble(john)))<=>(?[X]:(kind(X))))&
(![X]:((funny(X)<~>tall(X))=>(~brave(X)|~generous(X))))&
(![X]:((creative(X)<~>~generous(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((funny(X)|~kind(X))<=>(old(X)<~>rich(X))))&
(![X]:((~tall(X)|~generous(X))<=>funny(X)))&
(![X]:(funny(X)<=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)|~patient(X))))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~wise(X))))&
(![X]:((~old(X)<~>kind(X))=>(humble(X)&~kind(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>strong(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(tall(mary))&
(quiet(paul))&
(?[X]:((funny(X)<~>rich(X))))&
((quiet(john)<~>~humble(john)))&
(?[X]:((~wise(X)<~>~quiet(X))))&
((~old(alice)|humble(alice)))&
((generous(alice)|brave(alice))) | rich(mary) | [
"p1",
"p5",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2334449037804169286557898
% SZS output start Proof for 2334449037804169286557898
2. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (strong(X0) | old(X0))) [input p1]
6. ? [X0] : (kind(X0) <~> strong(X0)) => (~rich(mary) & tall(mary)) [input p5]
10. ! [X0] : ((~kind(X0) | funny(X0)) <=> (old(X0) <~> rich(X0))) [input p9]
12. ! [X0] : (funny(X0) <=> (creative(X0) & ~kind(X0))) [input p11]
15. ! [X0] : ((~old(X0) <~> kind(X0)) => (~kind(X0) & humble(X0))) [input p14]
25. rich(mary) [input hypothesis]
27. (~rich(mary) & tall(mary)) | ! [X0] : (kind(X0) <=> strong(X0)) [ennf transformation 6]
31. ! [X0] : ((~kind(X0) & humble(X0)) | (~old(X0) <=> kind(X0))) [ennf transformation 15]
35. ! [X0] : (((calm(X0) | ~kind(X0)) | (~strong(X0) & ~old(X0))) & ((strong(X0) | old(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 2]
36. ! [X0] : ((calm(X0) | ~kind(X0) | (~strong(X0) & ~old(X0))) & (strong(X0) | old(X0) | (~calm(X0) & kind(X0)))) [flattening 35]
45. (~rich(mary) & tall(mary)) | ! [X0] : ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))) [nnf transformation 27]
53. ! [X0] : (((~kind(X0) | funny(X0)) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (kind(X0) & ~funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((~kind(X0) | funny(X0) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (kind(X0) & ~funny(X0)))) [flattening 53]
57. ! [X0] : ((funny(X0) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | ~funny(X0))) [nnf transformation 12]
58. ! [X0] : ((funny(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | ~funny(X0))) [flattening 57]
64. ! [X0] : ((~kind(X0) & humble(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) [nnf transformation 31]
82. strong(X0) | old(X0) | kind(X0) [cnf transformation 36]
103. ~rich(mary) | kind(X0) | ~strong(X0) [cnf transformation 45]
120. ~rich(X0) | ~old(X0) | kind(X0) [cnf transformation 54]
122. ~rich(X0) | funny(X0) | old(X0) | ~kind(X0) [cnf transformation 54]
126. ~funny(X0) | ~kind(X0) [cnf transformation 58]
140. ~kind(X0) | ~old(X0) | ~kind(X0) [cnf transformation 64]
155. rich(mary) [cnf transformation 25]
156. ~old(X0) | ~kind(X0) [duplicate literal removal 140]
180. 5 <=> ! [X0] : (kind(X0) | ~strong(X0)) [avatar definition]
181. ~strong(X0) | kind(X0) <- (5) [avatar component clause 180]
183. 6 <=> rich(mary) [avatar definition]
184. rich(mary) <- (6) [avatar component clause 183]
186. 5 | ~6 [avatar split clause 103,183,180]
288. 6 [avatar split clause 155,183]
309. old(X0) | kind(X0) | kind(X0) <- (5) [resolution 82,181]
310. old(X0) | kind(X0) <- (5) [duplicate literal removal 309]
397. ~old(mary) | kind(mary) <- (6) [resolution 120,184]
400. ~old(mary) <- (6) [subsumption resolution 397,156]
621. funny(mary) | old(mary) | ~kind(mary) <- (6) [resolution 122,184]
624. funny(mary) | ~kind(mary) <- (6) [subsumption resolution 621,400]
625. ~kind(mary) <- (6) [subsumption resolution 624,126]
636. kind(mary) <- (5, 6) [resolution 310,400]
639. $false <- (5, 6) [subsumption resolution 636,625]
640. ~5 | ~6 [avatar contradiction clause 639]
641. $false [avatar sat refutation 186,288,640]
% SZS output end Proof for 2334449037804169286557898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not calm is not rich and vice versa. Everyone who is either not old or not happy is not kind or not brave. Everyone who is humble or not quiet is not wise and vice versa. If someone is either brave or not generous then paul is either rich or not tall. If john is old then someone is either not tall or not generous and vice versa. Everyone who is not creative is both not creative and rich. If fred is kind then paul is both rich and not wise. Everyone who is not humble is both not wise and not rich and vice versa. Everyone who is not brave is either not happy or quiet. If susan is either funny or not funny then lucy is either curious or happy and vice versa. If susan is quiet then alice is both tall and not wise and vice versa. Everyone who is rich or calm is not patient and vice versa. Everyone who is quiet is either quiet or not happy and vice versa. If mary is either not kind or not quiet then someone is quiet or not brave and vice versa. If someone is not rich then someone is both tall and humble. Everyone who is either not kind or curious is both not quiet and humble. Someone is both not kind and strong. Someone is either rich or not patient. Someone is either not calm or curious. Someone is not quiet. Someone is both rich and not generous. Someone is both not funny and tall. Mary is either strong or not kind. Someone is either funny or not humble. | Lucy is not tall. | neutral | (![X]:((~rich(X)<~>~calm(X))<=>~rich(X)))&
(![X]:((~old(X)<~>~happy(X))=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)|~quiet(X))<=>~wise(X)))&
((?[X]:((brave(X)<~>~generous(X))))=>((rich(paul)<~>~tall(paul))))&
((old(john))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:(~creative(X)=>(~creative(X)&rich(X))))&
((kind(fred))=>((rich(paul)&~wise(paul))))&
(![X]:(~humble(X)<=>(~wise(X)&~rich(X))))&
(![X]:(~brave(X)=>(~happy(X)<~>quiet(X))))&
(((funny(susan)<~>~funny(susan)))<=>((curious(lucy)<~>happy(lucy))))&
((quiet(susan))<=>((tall(alice)&~wise(alice))))&
(![X]:((rich(X)|calm(X))<=>~patient(X)))&
(![X]:(quiet(X)<=>(quiet(X)<~>~happy(X))))&
(((~kind(mary)<~>~quiet(mary)))<=>(?[X]:((quiet(X)|~brave(X)))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&humble(X)))))&
(![X]:((~kind(X)<~>curious(X))=>(~quiet(X)&humble(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:((~calm(X)<~>curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)&~generous(X))))&
(?[X]:((~funny(X)&tall(X))))&
((strong(mary)<~>~kind(mary)))&
(?[X]:((funny(X)<~>~humble(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is generous or not wise is either not humble or old.
Everyone who is both not rich and creative is either not tall or not humble and vice versa.
If susan is both not brave and not curious then someone is humble and vice versa.
If alice is either not creative or quiet then paul is both calm and humble.
Everyone who is not rich or not funny is either not kind or not old.
If john is not old or quiet then alice is either not happy or not calm and vice versa.
If someone is brave or not humble then someone is calm and vice versa.
If paul is both humble and calm then paul is not humble or rich.
Everyone who is kind is either humble or rich.
Everyone who is both tall and not humble is not patient or patient and vice versa.
Everyone who is either not humble or humble is both curious and calm and vice versa.
If fred is not happy or not curious then alice is generous or calm and vice versa.
Everyone who is both not calm and kind is both humble and not old.
If someone is funny then lucy is curious or not strong and vice versa.
Someone is not patient.
Someone is quiet or wise.
Someone is creative.
Someone is not patient or not wise.
Someone is not generous.
Someone is both not brave and not funny.
Mary is brave. | Susan is not creative. | contradiction | (![X]:((generous(X)|~wise(X))=>(~humble(X)<~>old(X))))&
(![X]:((~rich(X)&creative(X))<=>(~tall(X)<~>~humble(X))))&
(((~brave(susan)&~curious(susan)))<=>(?[X]:(humble(X))))&
(((~creative(alice)<~>quiet(alice)))=>((calm(paul)&humble(paul))))&
(![X]:((~rich(X)|~funny(X))=>(~kind(X)<~>~old(X))))&
(((~old(john)|quiet(john)))<=>((~happy(alice)<~>~calm(alice))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(((humble(paul)&calm(paul)))=>((~humble(paul)|rich(paul))))&
(![X]:(kind(X)=>(humble(X)<~>rich(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(curious(X)&calm(X))))&
(((~happy(fred)|~curious(fred)))<=>((generous(alice)|calm(alice))))&
(![X]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~brave(X)&~funny(X))))&
(brave(mary)) | ~creative(susan) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 382584116891684605776009
% SZS output start Proof for 382584116891684605776009
2. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p1]
10. ! [X0] : ((~humble(X0) & tall(X0)) <=> (patient(X0) | ~patient(X0))) [input p9]
22. ~creative(susan) [input hypothesis]
33. ! [X0] : (((creative(X0) & ~rich(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~creative(X0) | rich(X0)))) [nnf transformation 2]
34. ! [X0] : (((creative(X0) & ~rich(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ~creative(X0) | rich(X0))) [flattening 33]
50. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 10]
51. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0))) [flattening 50]
82. ~tall(X0) | creative(X0) | humble(X0) [cnf transformation 34]
107. tall(X0) | patient(X0) [cnf transformation 51]
108. ~patient(X0) | tall(X0) [cnf transformation 51]
109. ~humble(X0) | patient(X0) [cnf transformation 51]
110. ~patient(X0) | ~humble(X0) [cnf transformation 51]
134. ~creative(susan) [cnf transformation 22]
141. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
142. ~humble(X0) <- (1) [avatar component clause 141]
229. ~humble(X0) [subsumption resolution 109,110]
230. 1 [avatar split clause 229,141]
231. tall(X0) [subsumption resolution 107,108]
267. creative(X0) | humble(X0) [resolution 82,231]
268. creative(X0) <- (1) [subsumption resolution 267,142]
269. $false <- (1) [resolution 268,134]
272. ~1 [avatar contradiction clause 269]
273. $false [avatar sat refutation 230,272]
% SZS output end Proof for 382584116891684605776009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble or funny then someone is patient and vice versa.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
If someone is both not generous and not funny then someone is either generous or not funny.
If john is not calm then someone is either generous or happy.
Everyone who is both patient and not humble is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Everyone who is both not brave and generous is funny or not generous and vice versa.
Everyone who is both not wise and not tall is tall or not wise and vice versa.
Everyone who is both strong and not calm is not quiet.
Someone is not tall or old.
Someone is wise or not strong.
Fred is humble or wise.
Mary is not kind or not curious.
John is both not humble and old. | John is not old. | contradiction | (((humble(john)|funny(john)))<=>(?[X]:(patient(X))))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
((~calm(john))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)|~generous(X))))&
(![X]:((~wise(X)&~tall(X))<=>(tall(X)|~wise(X))))&
(![X]:((strong(X)&~calm(X))=>~quiet(X)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((wise(X)|~strong(X))))&
((humble(fred)|wise(fred)))&
((~kind(mary)|~curious(mary)))&
((~humble(john)&old(john))) | ~old(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6964472408731500725433711
% SZS output start Proof for 6964472408731500725433711
21. old(john) & ~humble(john) [input p20]
22. ~old(john) [input hypothesis]
128. old(john) [cnf transformation 21]
129. ~old(john) [cnf transformation 22]
244. $false [subsumption resolution 129,128]
% SZS output end Proof for 6964472408731500725433711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is curious or not funny and vice versa.
If lucy is both quiet and strong then someone is either funny or creative and vice versa.
Everyone who is either not old or not humble is either brave or not curious.
If alice is calm or not curious then someone is not kind or patient.
If john is funny then someone is not wise or brave.
Everyone who is both not patient and not humble is brave and vice versa.
Everyone who is quiet or patient is kind or not generous.
If someone is both patient and not strong then someone is kind.
If someone is quiet or not curious then fred is both not quiet and kind.
Everyone who is tall or not strong is either curious or not funny and vice versa.
If someone is kind or calm then someone is both tall and kind.
Everyone who is creative or kind is not patient.
Everyone who is both patient and happy is humble or rich and vice versa.
Everyone who is both not wise and not happy is curious or not patient.
Everyone who is wise or not brave is both not rich and old and vice versa.
Everyone who is quiet is both tall and not curious and vice versa.
John is either generous or not curious.
Susan is either strong or not rich.
Mary is both calm and not quiet.
Someone is strong or quiet.
Someone is both not wise and not happy.
Someone is strong.
Alice is funny.
Paul is patient. | Alice is creative. | entailment | (![X]:(~strong(X)<=>(curious(X)|~funny(X))))&
(((quiet(lucy)&strong(lucy)))<=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((~old(X)<~>~humble(X))=>(brave(X)<~>~curious(X))))&
(((calm(alice)|~curious(alice)))=>(?[X]:((~kind(X)|patient(X)))))&
((funny(john))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:((~patient(X)&~humble(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))=>(kind(X)|~generous(X))))&
((?[X]:((patient(X)&~strong(X))))=>(?[X]:(kind(X))))&
((?[X]:((quiet(X)|~curious(X))))=>((~quiet(fred)&kind(fred))))&
(![X]:((tall(X)|~strong(X))<=>(curious(X)<~>~funny(X))))&
((?[X]:((kind(X)|calm(X))))=>(?[X]:((tall(X)&kind(X)))))&
(![X]:((creative(X)|kind(X))=>~patient(X)))&
(![X]:((patient(X)&happy(X))<=>(humble(X)|rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(curious(X)|~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~rich(X)&old(X))))&
(![X]:(quiet(X)<=>(tall(X)&~curious(X))))&
((generous(john)<~>~curious(john)))&
((strong(susan)<~>~rich(susan)))&
((calm(mary)&~quiet(mary)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((~wise(X)&~happy(X))))&
(?[X]:(strong(X)))&
(funny(alice))&
(patient(paul)) | creative(alice) | [
"p0",
"p1",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5826116177682622317483281
% SZS output start Proof for 5826116177682622317483281
1. ! [X0] : (~strong(X0) <=> (~funny(X0) | curious(X0))) [input p0]
2. (strong(lucy) & quiet(lucy)) <=> ? [X0] : (funny(X0) <~> creative(X0)) [input p1]
10. ! [X0] : ((~strong(X0) | tall(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p9]
16. ! [X0] : (quiet(X0) <=> (~curious(X0) & tall(X0))) [input p15]
23. funny(alice) [input p22]
25. ~creative(alice) [input hypothesis]
39. ! [X0] : ((~strong(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | strong(X0))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | strong(X0))) [flattening 39]
41. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~strong(lucy) | ~quiet(lucy))) [nnf transformation 2]
42. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~strong(lucy) | ~quiet(lucy)) [flattening 41]
43. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X1] : ((~creative(X1) | ~funny(X1)) & (creative(X1) | funny(X1))) | ~strong(lucy) | ~quiet(lucy)) [rectify 42]
44. ? [X1] : ((~creative(X1) | ~funny(X1)) & (creative(X1) | funny(X1))) => ((~creative(sK0) | ~funny(sK0)) & (creative(sK0) | funny(sK0))) [choice axiom]
45. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(sK0) | ~funny(sK0)) & (creative(sK0) | funny(sK0))) | ~strong(lucy) | ~quiet(lucy)) [skolemisation 43,44]
56. ! [X0] : (((~strong(X0) | tall(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (strong(X0) & ~tall(X0)))) [nnf transformation 10]
57. ! [X0] : ((~strong(X0) | tall(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (strong(X0) & ~tall(X0)))) [flattening 56]
65. ! [X0] : ((quiet(X0) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((quiet(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [flattening 65]
77. ~strong(X0) | funny(X0) [cnf transformation 40]
80. quiet(lucy) | creative(X0) | ~funny(X0) [cnf transformation 45]
82. strong(lucy) | creative(X0) | ~funny(X0) [cnf transformation 45]
101. ~tall(X0) | curious(X0) | ~funny(X0) [cnf transformation 57]
124. ~quiet(X0) | tall(X0) [cnf transformation 66]
125. ~quiet(X0) | ~curious(X0) [cnf transformation 66]
137. funny(alice) [cnf transformation 23]
139. ~creative(alice) [cnf transformation 25]
144. 2 <=> strong(lucy) [avatar definition]
146. strong(lucy) <- (2) [avatar component clause 144]
149. 3 <=> ! [X0] : (creative(X0) | ~funny(X0)) [avatar definition]
150. ~funny(X0) | creative(X0) <- (3) [avatar component clause 149]
151. 3 | 2 [avatar split clause 82,144,149]
153. 4 <=> quiet(lucy) [avatar definition]
155. quiet(lucy) <- (4) [avatar component clause 153]
157. 3 | 4 [avatar split clause 80,153,149]
282. funny(lucy) <- (2) [resolution 77,146]
289. tall(lucy) <- (4) [resolution 124,155]
290. ~curious(lucy) <- (4) [resolution 125,155]
322. curious(lucy) | ~funny(lucy) <- (4) [resolution 101,289]
332. ~funny(lucy) <- (4) [subsumption resolution 322,290]
333. $false <- (2, 4) [subsumption resolution 332,282]
334. ~2 | ~4 [avatar contradiction clause 333]
336. creative(alice) <- (3) [resolution 150,137]
341. $false <- (3) [subsumption resolution 336,139]
342. ~3 [avatar contradiction clause 341]
347. $false [avatar sat refutation 151,157,334,342]
% SZS output end Proof for 5826116177682622317483281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either curious or tall and vice versa.
Everyone who is either not rich or not creative is either patient or not generous.
If fred is either not creative or creative then paul is both happy and strong and vice versa.
If john is rich or quiet then someone is both not strong and brave.
Everyone who is not creative is not calm or not generous.
Everyone who is not kind is either rich or old.
If lucy is wise then john is calm or not strong and vice versa.
Everyone who is not quiet is either wise or not rich and vice versa.
Everyone who is not tall or humble is both not old and not brave and vice versa.
If john is kind or patient then fred is both calm and kind.
If someone is both strong and not patient then someone is not creative or patient.
If susan is either humble or quiet then someone is both happy and not humble and vice versa.
If someone is humble then someone is either not rich or not kind and vice versa.
Everyone who is both not patient and curious is not calm or not generous and vice versa.
Everyone who is not brave is not old and vice versa.
If mary is either calm or not rich then someone is not funny or not kind.
Someone is either happy or not tall.
Lucy is patient or not old.
Someone is either not patient or not generous.
Someone is kind.
John is either brave or funny.
Someone is not patient or happy.
Lucy is not strong.
Mary is both not wise and tall. | Fred is not generous. | neutral | (![X]:(~patient(X)<=>(curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>~creative(X))=>(patient(X)<~>~generous(X))))&
(((~creative(fred)<~>creative(fred)))<=>((happy(paul)&strong(paul))))&
(((rich(john)|quiet(john)))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:(~creative(X)=>(~calm(X)|~generous(X))))&
(![X]:(~kind(X)=>(rich(X)<~>old(X))))&
((wise(lucy))<=>((calm(john)|~strong(john))))&
(![X]:(~quiet(X)<=>(wise(X)<~>~rich(X))))&
(![X]:((~tall(X)|humble(X))<=>(~old(X)&~brave(X))))&
(((kind(john)|patient(john)))=>((calm(fred)&kind(fred))))&
((?[X]:((strong(X)&~patient(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(((humble(susan)<~>quiet(susan)))<=>(?[X]:((happy(X)&~humble(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~patient(X)&curious(X))<=>(~calm(X)|~generous(X))))&
(![X]:(~brave(X)<=>~old(X)))&
(((calm(mary)<~>~rich(mary)))=>(?[X]:((~funny(X)|~kind(X)))))&
(?[X]:((happy(X)<~>~tall(X))))&
((patient(lucy)|~old(lucy)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
((brave(john)<~>funny(john)))&
(?[X]:((~patient(X)|happy(X))))&
(~strong(lucy))&
((~wise(mary)&tall(mary))) | ~generous(fred) | [] | null | 0 |
If john is either rich or funny then paul is either humble or happy.
If someone is not kind then someone is not rich or not curious and vice versa.
If john is both not strong and not patient then lucy is either not patient or not tall and vice versa.
If someone is wise then paul is rich or not calm.
Everyone who is both kind and not patient is not strong or patient and vice versa.
If someone is not calm then fred is not funny and vice versa.
Everyone who is either humble or calm is not quiet or rich.
If someone is kind or not patient then someone is not patient and vice versa.
If susan is either not wise or not brave then susan is both humble and not tall.
If paul is strong then alice is either tall or not strong and vice versa.
Everyone who is both not happy and kind is both not strong and not funny.
Everyone who is both brave and rich is not curious or not kind and vice versa.
If someone is either patient or not strong then someone is either not curious or not wise.
Everyone who is not creative or not old is not quiet or not brave.
Everyone who is kind is funny or not strong and vice versa.
Everyone who is both patient and not creative is patient or not old and vice versa.
Someone is rich or patient.
Fred is old or rich.
Lucy is not brave or creative.
Someone is both not humble and not calm.
Lucy is not kind.
Fred is not wise or not creative.
Alice is not wise or not kind. | Paul is rich. | neutral | (((rich(john)<~>funny(john)))=>((humble(paul)<~>happy(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((~rich(X)|~curious(X)))))&
(((~strong(john)&~patient(john)))<=>((~patient(lucy)<~>~tall(lucy))))&
((?[X]:(wise(X)))=>((rich(paul)|~calm(paul))))&
(![X]:((kind(X)&~patient(X))<=>(~strong(X)|patient(X))))&
((?[X]:(~calm(X)))<=>(~funny(fred)))&
(![X]:((humble(X)<~>calm(X))=>(~quiet(X)|rich(X))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:(~patient(X))))&
(((~wise(susan)<~>~brave(susan)))=>((humble(susan)&~tall(susan))))&
((strong(paul))<=>((tall(alice)<~>~strong(alice))))&
(![X]:((~happy(X)&kind(X))=>(~strong(X)&~funny(X))))&
(![X]:((brave(X)&rich(X))<=>(~curious(X)|~kind(X))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~creative(X)|~old(X))=>(~quiet(X)|~brave(X))))&
(![X]:(kind(X)<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~creative(X))<=>(patient(X)|~old(X))))&
(?[X]:((rich(X)|patient(X))))&
((old(fred)|rich(fred)))&
((~brave(lucy)|creative(lucy)))&
(?[X]:((~humble(X)&~calm(X))))&
(~kind(lucy))&
((~wise(fred)|~creative(fred)))&
((~wise(alice)|~kind(alice))) | rich(paul) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa.
Everyone who is calm is quiet and vice versa.
Everyone who is tall is either not happy or funny.
Everyone who is either brave or not patient is patient.
Everyone who is both quiet and not happy is either kind or not generous.
Everyone who is not brave is not creative and vice versa.
Everyone who is either not calm or happy is brave and vice versa.
If mary is not patient or not creative then someone is both not curious and not humble.
If alice is not brave or not funny then lucy is either not patient or curious.
Everyone who is creative or funny is both humble and strong and vice versa.
Everyone who is brave or not curious is both tall and not curious and vice versa.
If someone is calm then someone is both not curious and not calm.
If someone is both wise and generous then someone is either happy or not strong.
Everyone who is humble is either not patient or wise.
If someone is not kind then susan is both tall and not funny and vice versa.
Everyone who is either strong or not brave is kind.
Someone is generous or calm.
Alice is not creative or not generous.
Someone is either patient or generous.
Someone is either not funny or not old.
Alice is both not wise and not calm.
Alice is either not rich or not quiet.
Someone is both not kind and not humble. | Susan is not creative. | contradiction | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:((brave(X)<~>~patient(X))=>patient(X)))&
(![X]:((quiet(X)&~happy(X))=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
(?[X]:((generous(X)|calm(X))))&
((~creative(alice)|~generous(alice)))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
((~wise(alice)&~calm(alice)))&
((~rich(alice)<~>~quiet(alice)))&
(?[X]:((~kind(X)&~humble(X)))) | ~creative(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4845665488391704007747508
% SZS output start Proof for 4845665488391704007747508
1. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~happy(X0))) [input p0]
2. ! [X0] : (calm(X0) <=> quiet(X0)) [input p1]
3. ! [X0] : (tall(X0) => (~happy(X0) <~> funny(X0))) [input p2]
6. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p5]
7. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> brave(X0)) [input p6]
15. ? [X0] : ~kind(X0) <=> (~funny(susan) & tall(susan)) [input p14]
23. ? [X0] : (~humble(X0) & ~kind(X0)) [input p22]
24. ~creative(susan) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> funny(X0)) | ~tall(X0)) [ennf transformation 3]
37. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 37]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 2]
40. ! [X0] : (((~funny(X0) | happy(X0)) & (funny(X0) | ~happy(X0))) | ~tall(X0)) [nnf transformation 27]
43. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 6]
44. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 7]
60. (? [X0] : ~kind(X0) | (funny(susan) | ~tall(susan))) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [nnf transformation 15]
61. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [flattening 60]
62. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [rectify 61]
63. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
64. (~kind(sK3) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [skolemisation 62,63]
75. ? [X0] : (~humble(X0) & ~kind(X0)) => (~humble(sK7) & ~kind(sK7)) [choice axiom]
76. ~humble(sK7) & ~kind(sK7) [skolemisation 23,75]
78. ~quiet(X0) | happy(X0) [cnf transformation 38]
82. ~calm(X0) | quiet(X0) [cnf transformation 39]
84. ~tall(X0) | ~happy(X0) | funny(X0) [cnf transformation 40]
91. ~brave(X0) | creative(X0) [cnf transformation 43]
92. brave(X0) | happy(X0) | calm(X0) [cnf transformation 44]
120. tall(susan) | kind(X1) [cnf transformation 64]
121. ~funny(susan) | kind(X1) [cnf transformation 64]
135. ~kind(sK7) [cnf transformation 76]
137. ~creative(susan) [cnf transformation 24]
206. 15 <=> tall(susan) [avatar definition]
207. tall(susan) <- (15) [avatar component clause 206]
210. 16 <=> funny(susan) [avatar definition]
211. ~funny(susan) <- (~16) [avatar component clause 210]
219. 18 <=> ! [X1] : kind(X1) [avatar definition]
220. kind(X1) <- (18) [avatar component clause 219]
221. 18 | ~16 [avatar split clause 121,210,219]
222. 18 | 15 [avatar split clause 120,206,219]
271. ~happy(susan) | funny(susan) <- (15) [resolution 84,207]
274. ~happy(susan) <- (15, ~16) [subsumption resolution 271,211]
316. calm(X1) | happy(X1) | creative(X1) [resolution 92,91]
408. happy(X1) | creative(X1) | quiet(X1) [resolution 316,82]
412. creative(X1) | happy(X1) [subsumption resolution 408,78]
435. happy(susan) [resolution 412,137]
442. $false <- (15, ~16) [subsumption resolution 435,274]
443. ~15 | 16 [avatar contradiction clause 442]
445. $false <- (18) [resolution 220,135]
448. ~18 [avatar contradiction clause 445]
449. $false [avatar sat refutation 221,222,443,448]
% SZS output end Proof for 4845665488391704007747508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not brave is both rich and not happy.
If lucy is both not creative and curious then susan is not old and vice versa.
Everyone who is either not humble or not rich is generous or calm.
Everyone who is both not strong and funny is either wise or not rich.
If someone is both not kind and calm then alice is either not brave or creative.
If alice is creative then someone is both not wise and humble and vice versa.
If someone is not strong or strong then someone is tall.
Everyone who is tall or not quiet is both not calm and not funny and vice versa.
If john is curious or not wise then mary is either calm or happy.
Everyone who is either curious or creative is not funny or curious and vice versa.
If alice is not creative or not humble then someone is both happy and not old and vice versa.
If someone is either generous or not generous then someone is either calm or rich and vice versa.
Everyone who is both not creative and not wise is either curious or not tall.
Everyone who is both not curious and not generous is calm and vice versa.
Everyone who is curious or rich is either kind or brave.
Everyone who is both not kind and not generous is creative or rich and vice versa.
Someone is either creative or not generous.
Someone is not old.
Susan is both not rich and not patient.
Someone is both not patient and creative.
Someone is not tall or not strong.
Someone is either rich or old.
Susan is either strong or not happy.
Someone is either not patient or strong. | Alice is brave. | entailment | (![X]:((~humble(X)|~brave(X))=>(rich(X)&~happy(X))))&
(((~creative(lucy)&curious(lucy)))<=>(~old(susan)))&
(![X]:((~humble(X)<~>~rich(X))=>(generous(X)|calm(X))))&
(![X]:((~strong(X)&funny(X))=>(wise(X)<~>~rich(X))))&
((?[X]:((~kind(X)&calm(X))))=>((~brave(alice)<~>creative(alice))))&
((creative(alice))<=>(?[X]:((~wise(X)&humble(X)))))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:(tall(X))))&
(![X]:((tall(X)|~quiet(X))<=>(~calm(X)&~funny(X))))&
(((curious(john)|~wise(john)))=>((calm(mary)<~>happy(mary))))&
(![X]:((curious(X)<~>creative(X))<=>(~funny(X)|curious(X))))&
(((~creative(alice)|~humble(alice)))<=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~creative(X)&~wise(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~curious(X)&~generous(X))<=>calm(X)))&
(![X]:((curious(X)|rich(X))=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&~generous(X))<=>(creative(X)|rich(X))))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:(~old(X)))&
((~rich(susan)&~patient(susan)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:((rich(X)<~>old(X))))&
((strong(susan)<~>~happy(susan)))&
(?[X]:((~patient(X)<~>strong(X)))) | brave(alice) | [
"p0",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6142952444365318486353669
% SZS output start Proof for 6142952444365318486353669
1. ! [X0] : ((~brave(X0) | ~humble(X0)) => (~happy(X0) & rich(X0))) [input p0]
15. ! [X0] : ((rich(X0) | curious(X0)) => (kind(X0) <~> brave(X0))) [input p14]
16. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (rich(X0) | creative(X0))) [input p15]
25. ~brave(alice) [input hypothesis]
28. ! [X0] : ((~happy(X0) & rich(X0)) | (brave(X0) & humble(X0))) [ennf transformation 1]
38. ! [X0] : ((kind(X0) <~> brave(X0)) | (~rich(X0) & ~curious(X0))) [ennf transformation 15]
69. ! [X0] : (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (~rich(X0) & ~curious(X0))) [nnf transformation 38]
70. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 16]
71. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | generous(X0) | kind(X0))) [flattening 70]
89. rich(X0) | brave(X0) [cnf transformation 28]
140. brave(X0) | kind(X0) | ~rich(X0) [cnf transformation 69]
145. ~kind(X0) | ~rich(X0) [cnf transformation 71]
162. ~brave(alice) [cnf transformation 25]
190. 5 <=> brave(alice) [avatar definition]
191. ~brave(alice) <- (~5) [avatar component clause 190]
285. kind(X0) | brave(X0) [subsumption resolution 140,89]
327. ~5 [avatar split clause 162,190]
341. brave(X0) | ~rich(X0) [resolution 285,145]
343. brave(X0) [subsumption resolution 341,89]
360. $false <- (~5) [resolution 343,191]
361. 5 [avatar contradiction clause 360]
362. $false [avatar sat refutation 327,361]
% SZS output end Proof for 6142952444365318486353669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is quiet then mary is both calm and not generous and vice versa.
If someone is tall then fred is generous and vice versa.
Everyone who is calm is both not generous and curious and vice versa.
If fred is either kind or not kind then lucy is both not wise and not strong and vice versa.
Everyone who is strong or not calm is happy and vice versa.
Everyone who is not calm or not generous is either tall or generous and vice versa.
Everyone who is either not funny or not kind is either not happy or not kind.
If lucy is not patient then alice is either old or not funny and vice versa.
Everyone who is not patient is either strong or happy.
If paul is not humble then someone is both not humble and not calm.
If paul is either tall or not happy then lucy is either patient or funny and vice versa.
If someone is creative then someone is not tall and vice versa.
If someone is both not strong and humble then susan is both not curious and not wise and vice versa.
If someone is either strong or not happy then mary is rich or not generous and vice versa.
Everyone who is either strong or funny is humble.
Everyone who is humble is tall or not brave and vice versa.
Lucy is either tall or wise.
Someone is not happy or not humble.
Susan is curious or not wise.
Alice is not strong or not generous.
Someone is wise.
Mary is not happy or not generous.
Someone is either not old or tall.
John is old. | Lucy is not generous. | entailment | ((?[X]:(quiet(X)))<=>((calm(mary)&~generous(mary))))&
((?[X]:(tall(X)))<=>(generous(fred)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
(((kind(fred)<~>~kind(fred)))<=>((~wise(lucy)&~strong(lucy))))&
(![X]:((strong(X)|~calm(X))<=>happy(X)))&
(![X]:((~calm(X)|~generous(X))<=>(tall(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(~happy(X)<~>~kind(X))))&
((~patient(lucy))<=>((old(alice)<~>~funny(alice))))&
(![X]:(~patient(X)=>(strong(X)<~>happy(X))))&
((~humble(paul))=>(?[X]:((~humble(X)&~calm(X)))))&
(((tall(paul)<~>~happy(paul)))<=>((patient(lucy)<~>funny(lucy))))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~strong(X)&humble(X))))<=>((~curious(susan)&~wise(susan))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((rich(mary)|~generous(mary))))&
(![X]:((strong(X)<~>funny(X))=>humble(X)))&
(![X]:(humble(X)<=>(tall(X)|~brave(X))))&
((tall(lucy)<~>wise(lucy)))&
(?[X]:((~happy(X)|~humble(X))))&
((curious(susan)|~wise(susan)))&
((~strong(alice)|~generous(alice)))&
(?[X]:(wise(X)))&
((~happy(mary)|~generous(mary)))&
(?[X]:((~old(X)<~>tall(X))))&
(old(john)) | ~generous(lucy) | [
"p2",
"p3",
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6953400854195570656593176
% SZS output start Proof for 6953400854195570656593176
3. ! [X0] : (calm(X0) <=> (curious(X0) & ~generous(X0))) [input p2]
4. (kind(fred) <~> ~kind(fred)) <=> (~strong(lucy) & ~wise(lucy)) [input p3]
6. ! [X0] : ((~generous(X0) | ~calm(X0)) <=> (tall(X0) <~> generous(X0))) [input p5]
17. tall(lucy) <~> wise(lucy) [input p16]
25. generous(lucy) [input hypothesis]
40. ! [X0] : ((calm(X0) | (~curious(X0) | generous(X0))) & ((curious(X0) & ~generous(X0)) | ~calm(X0))) [nnf transformation 3]
41. ! [X0] : ((calm(X0) | ~curious(X0) | generous(X0)) & ((curious(X0) & ~generous(X0)) | ~calm(X0))) [flattening 40]
42. (((kind(fred) | ~kind(fred)) & (~kind(fred) | kind(fred))) | (strong(lucy) | wise(lucy))) & ((~strong(lucy) & ~wise(lucy)) | ((kind(fred) | kind(fred)) & (~kind(fred) | ~kind(fred)))) [nnf transformation 4]
43. (((kind(fred) | ~kind(fred)) & (~kind(fred) | kind(fred))) | strong(lucy) | wise(lucy)) & ((~strong(lucy) & ~wise(lucy)) | ((kind(fred) | kind(fred)) & (~kind(fred) | ~kind(fred)))) [flattening 42]
46. ! [X0] : (((~generous(X0) | ~calm(X0)) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | (generous(X0) & calm(X0)))) [nnf transformation 6]
47. ! [X0] : ((~generous(X0) | ~calm(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | (generous(X0) & calm(X0)))) [flattening 46]
72. (~wise(lucy) | ~tall(lucy)) & (wise(lucy) | tall(lucy)) [nnf transformation 17]
85. ~generous(X0) | ~calm(X0) [cnf transformation 41]
88. ~wise(lucy) | ~kind(fred) | ~kind(fred) [cnf transformation 43]
89. ~wise(lucy) | kind(fred) | kind(fred) [cnf transformation 43]
99. ~generous(X0) | ~tall(X0) | calm(X0) [cnf transformation 47]
140. wise(lucy) | tall(lucy) [cnf transformation 72]
150. generous(lucy) [cnf transformation 25]
155. ~wise(lucy) | ~kind(fred) [duplicate literal removal 88]
156. ~wise(lucy) | kind(fred) [duplicate literal removal 89]
191. 8 <=> kind(fred) [avatar definition]
201. 10 <=> wise(lucy) [avatar definition]
204. 8 | ~10 [avatar split clause 156,201,191]
205. ~8 | ~10 [avatar split clause 155,201,191]
206. ~tall(X0) | ~generous(X0) [subsumption resolution 99,85]
323. 34 <=> tall(lucy) [avatar definition]
324. tall(lucy) <- (34) [avatar component clause 323]
327. 34 | 10 [avatar split clause 140,201,323]
382. ~generous(lucy) <- (34) [resolution 206,324]
385. $false <- (34) [subsumption resolution 382,150]
386. ~34 [avatar contradiction clause 385]
387. $false [avatar sat refutation 204,205,327,386]
% SZS output end Proof for 6953400854195570656593176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny and not quiet then someone is old or not strong and vice versa. If mary is not curious then john is not funny or kind and vice versa. If someone is calm then lucy is either happy or strong. If alice is either not happy or not wise then someone is not creative. If mary is wise then paul is either not calm or not creative. Everyone who is either tall or not old is either not old or funny. Everyone who is both not humble and not generous is either quiet or not happy and vice versa. Everyone who is either strong or humble is strong or not old and vice versa. Everyone who is either not curious or quiet is not strong or brave. Everyone who is not rich or not old is either not strong or happy and vice versa. Everyone who is either creative or strong is either patient or tall and vice versa. If someone is either not happy or not tall then someone is not kind or patient and vice versa. If paul is either not brave or not curious then someone is not wise or patient and vice versa. Everyone who is either humble or not funny is patient or not happy. Everyone who is patient is either not old or not curious. Everyone who is not calm or not brave is either wise or not calm and vice versa. Someone is either generous or brave. Someone is not rich or not calm. Someone is humble or generous. Someone is both not brave and not funny. Someone is old or not strong. Mary is happy. John is curious. | Lucy is generous. | neutral | ((?[X]:((~funny(X)&~quiet(X))))<=>(?[X]:((old(X)|~strong(X)))))&
((~curious(mary))<=>((~funny(john)|kind(john))))&
((?[X]:(calm(X)))=>((happy(lucy)<~>strong(lucy))))&
(((~happy(alice)<~>~wise(alice)))=>(?[X]:(~creative(X))))&
((wise(mary))=>((~calm(paul)<~>~creative(paul))))&
(![X]:((tall(X)<~>~old(X))=>(~old(X)<~>funny(X))))&
(![X]:((~humble(X)&~generous(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((strong(X)<~>humble(X))<=>(strong(X)|~old(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(~strong(X)|brave(X))))&
(![X]:((~rich(X)|~old(X))<=>(~strong(X)<~>happy(X))))&
(![X]:((creative(X)<~>strong(X))<=>(patient(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>~tall(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
(((~brave(paul)<~>~curious(paul)))<=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(patient(X)|~happy(X))))&
(![X]:(patient(X)=>(~old(X)<~>~curious(X))))&
(![X]:((~calm(X)|~brave(X))<=>(wise(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:((old(X)|~strong(X))))&
(happy(mary))&
(curious(john)) | generous(lucy) | [] | null | 0 |
Everyone who is not rich or not generous is both brave and not old and vice versa.
Everyone who is not quiet is not tall or patient and vice versa.
Everyone who is both kind and not brave is both not quiet and calm.
If someone is either not happy or happy then fred is old and vice versa.
If john is calm then fred is strong or not happy and vice versa.
If someone is both not quiet and quiet then someone is either not funny or not curious.
Everyone who is both humble and not wise is patient or not happy and vice versa.
If someone is either not strong or funny then mary is both rich and not calm.
Everyone who is not curious or rich is not quiet or not calm and vice versa.
Everyone who is patient or funny is patient and vice versa.
If alice is not strong or not tall then someone is not old or not funny.
If someone is either funny or rich then john is curious or kind.
Everyone who is happy or not quiet is rich or not quiet and vice versa.
Everyone who is either tall or not wise is not old.
Everyone who is not old is strong.
Everyone who is brave is tall or not old and vice versa.
Someone is humble or not kind.
John is curious.
John is either humble or wise.
Someone is both generous and brave.
Susan is curious or rich.
Someone is not rich or patient.
Mary is not humble.
Someone is both humble and not calm. | Alice is not tall. | neutral | (![X]:((~rich(X)|~generous(X))<=>(brave(X)&~old(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|patient(X))))&
(![X]:((kind(X)&~brave(X))=>(~quiet(X)&calm(X))))&
((?[X]:((~happy(X)<~>happy(X))))<=>(old(fred)))&
((calm(john))<=>((strong(fred)|~happy(fred))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((humble(X)&~wise(X))<=>(patient(X)|~happy(X))))&
((?[X]:((~strong(X)<~>funny(X))))=>((rich(mary)&~calm(mary))))&
(![X]:((~curious(X)|rich(X))<=>(~quiet(X)|~calm(X))))&
(![X]:((patient(X)|funny(X))<=>patient(X)))&
(((~strong(alice)|~tall(alice)))=>(?[X]:((~old(X)|~funny(X)))))&
((?[X]:((funny(X)<~>rich(X))))=>((curious(john)|kind(john))))&
(![X]:((happy(X)|~quiet(X))<=>(rich(X)|~quiet(X))))&
(![X]:((tall(X)<~>~wise(X))=>~old(X)))&
(![X]:(~old(X)=>strong(X)))&
(![X]:(brave(X)<=>(tall(X)|~old(X))))&
(?[X]:((humble(X)|~kind(X))))&
(curious(john))&
((humble(john)<~>wise(john)))&
(?[X]:((generous(X)&brave(X))))&
((curious(susan)|rich(susan)))&
(?[X]:((~rich(X)|patient(X))))&
(~humble(mary))&
(?[X]:((humble(X)&~calm(X)))) | ~tall(alice) | [] | null | 0 |
Everyone who is both strong and not happy is kind or not wise and vice versa. If fred is either not funny or not rich then someone is not quiet or calm. Everyone who is both old and creative is old and vice versa. Everyone who is either patient or happy is not quiet or calm and vice versa. Everyone who is both not kind and not tall is not rich or not brave. Everyone who is both not tall and not wise is both wise and creative and vice versa. Everyone who is both not creative and not strong is either not old or kind. If someone is either humble or patient then susan is not tall and vice versa. Everyone who is either happy or not generous is humble or not rich. Everyone who is not creative is both not generous and not curious and vice versa. If lucy is not tall or not patient then john is not generous and vice versa. If susan is not curious then fred is both not happy and not generous and vice versa. If alice is either not kind or not funny then mary is humble and vice versa. Everyone who is either quiet or brave is either not calm or not old and vice versa. If mary is either not rich or tall then fred is not brave. Everyone who is not brave or calm is both not humble and not rich. Lucy is quiet or curious. Someone is either happy or patient. Someone is either not curious or not patient. Someone is creative. John is both not wise and curious. Mary is either wise or not quiet. Lucy is not old. Fred is curious or happy. | Susan is not generous. | neutral | (![X]:((strong(X)&~happy(X))<=>(kind(X)|~wise(X))))&
(((~funny(fred)<~>~rich(fred)))=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((old(X)&creative(X))<=>old(X)))&
(![X]:((patient(X)<~>happy(X))<=>(~quiet(X)|calm(X))))&
(![X]:((~kind(X)&~tall(X))=>(~rich(X)|~brave(X))))&
(![X]:((~tall(X)&~wise(X))<=>(wise(X)&creative(X))))&
(![X]:((~creative(X)&~strong(X))=>(~old(X)<~>kind(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>(~tall(susan)))&
(![X]:((happy(X)<~>~generous(X))=>(humble(X)|~rich(X))))&
(![X]:(~creative(X)<=>(~generous(X)&~curious(X))))&
(((~tall(lucy)|~patient(lucy)))<=>(~generous(john)))&
((~curious(susan))<=>((~happy(fred)&~generous(fred))))&
(((~kind(alice)<~>~funny(alice)))<=>(humble(mary)))&
(![X]:((quiet(X)<~>brave(X))<=>(~calm(X)<~>~old(X))))&
(((~rich(mary)<~>tall(mary)))=>(~brave(fred)))&
(![X]:((~brave(X)|calm(X))=>(~humble(X)&~rich(X))))&
((quiet(lucy)|curious(lucy)))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:(creative(X)))&
((~wise(john)&curious(john)))&
((wise(mary)<~>~quiet(mary)))&
(~old(lucy))&
((curious(fred)|happy(fred))) | ~generous(susan) | [] | null | 0 |
Everyone who is funny or brave is humble and vice versa. Everyone who is either not old or tall is both not quiet and wise and vice versa. Everyone who is both not brave and curious is either brave or wise. Everyone who is both rich and not generous is not curious and vice versa. If john is calm then someone is creative or not happy. If susan is funny then paul is quiet or not tall. Everyone who is not calm is happy or not creative and vice versa. Everyone who is either funny or generous is patient. Everyone who is not curious is both brave and not kind. Everyone who is both not wise and not humble is patient or rich and vice versa. If someone is not wise or brave then john is both strong and patient and vice versa. Everyone who is either not happy or wise is both not old and not humble. If someone is either tall or calm then lucy is happy and vice versa. If lucy is not wise then paul is not funny or not old and vice versa. Everyone who is not old is not tall or wise. Someone is both not happy and creative. Someone is either not strong or rich. Mary is either not humble or rich. Someone is generous or tall. Someone is not calm. | Susan is not rich. | entailment | (![X]:((funny(X)|brave(X))<=>humble(X)))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~brave(X)&curious(X))=>(brave(X)<~>wise(X))))&
(![X]:((rich(X)&~generous(X))<=>~curious(X)))&
((calm(john))=>(?[X]:((creative(X)|~happy(X)))))&
((funny(susan))=>((quiet(paul)|~tall(paul))))&
(![X]:(~calm(X)<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>patient(X)))&
(![X]:(~curious(X)=>(brave(X)&~kind(X))))&
(![X]:((~wise(X)&~humble(X))<=>(patient(X)|rich(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((strong(john)&patient(john))))&
(![X]:((~happy(X)<~>wise(X))=>(~old(X)&~humble(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(happy(lucy)))&
((~wise(lucy))<=>((~funny(paul)|~old(paul))))&
(![X]:(~old(X)=>(~tall(X)|wise(X))))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((~humble(mary)<~>rich(mary)))&
(?[X]:((generous(X)|tall(X))))&
(?[X]:(~calm(X))) | ~rich(susan) | [
"p0",
"p2",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3642117701947085367686851
% SZS output start Proof for 3642117701947085367686851
1. ! [X0] : ((brave(X0) | funny(X0)) <=> humble(X0)) [input p0]
3. ! [X0] : ((curious(X0) & ~brave(X0)) => (brave(X0) <~> wise(X0))) [input p2]
9. ! [X0] : (~curious(X0) => (~kind(X0) & brave(X0))) [input p8]
10. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (rich(X0) | patient(X0))) [input p9]
11. ? [X0] : (brave(X0) | ~wise(X0)) <=> (patient(john) & strong(john)) [input p10]
21. rich(susan) [input hypothesis]
22. ! [X0] : (~curious(X0) => brave(X0)) [pure predicate removal 9]
23. ! [X0] : ((brave(X0) <~> wise(X0)) | (~curious(X0) | brave(X0))) [ennf transformation 3]
24. ! [X0] : ((brave(X0) <~> wise(X0)) | ~curious(X0) | brave(X0)) [flattening 23]
29. ! [X0] : (brave(X0) | curious(X0)) [ennf transformation 22]
33. ! [X0] : (((brave(X0) | funny(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((brave(X0) | funny(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [flattening 33]
37. ! [X0] : (((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | ~curious(X0) | brave(X0)) [nnf transformation 24]
45. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 10]
46. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | humble(X0) | wise(X0))) [flattening 45]
47. (? [X0] : (brave(X0) | ~wise(X0)) | (~patient(john) | ~strong(john))) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [nnf transformation 11]
48. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [flattening 47]
49. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [rectify 48]
50. ? [X0] : (brave(X0) | ~wise(X0)) => (brave(sK1) | ~wise(sK1)) [choice axiom]
51. ((brave(sK1) | ~wise(sK1)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [skolemisation 49,50]
70. ~brave(X0) | humble(X0) [cnf transformation 34]
78. wise(X0) | brave(X0) | ~curious(X0) | brave(X0) [cnf transformation 37]
90. curious(X0) | brave(X0) [cnf transformation 29]
92. ~patient(X0) | ~wise(X0) [cnf transformation 46]
93. ~rich(X0) | ~wise(X0) [cnf transformation 46]
94. ~patient(X0) | ~humble(X0) [cnf transformation 46]
98. patient(john) | wise(X1) [cnf transformation 51]
121. rich(susan) [cnf transformation 21]
122. ~curious(X0) | brave(X0) | wise(X0) [duplicate literal removal 78]
154. 8 <=> patient(john) [avatar definition]
155. patient(john) <- (8) [avatar component clause 154]
171. 12 <=> ! [X1] : wise(X1) [avatar definition]
172. wise(X1) <- (12) [avatar component clause 171]
173. 12 | 8 [avatar split clause 98,154,171]
240. ~wise(susan) [resolution 93,121]
289. $false <- (12) [resolution 172,240]
290. ~12 [avatar contradiction clause 289]
293. ~humble(john) <- (8) [resolution 155,94]
294. ~wise(john) <- (8) [resolution 155,92]
373. brave(X0) | wise(X0) | brave(X0) [resolution 122,90]
377. wise(X0) | brave(X0) [duplicate literal removal 373]
426. brave(john) <- (8) [resolution 377,294]
444. humble(john) <- (8) [resolution 426,70]
445. $false <- (8) [subsumption resolution 444,293]
446. ~8 [avatar contradiction clause 445]
447. $false [avatar sat refutation 173,290,446]
% SZS output end Proof for 3642117701947085367686851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or quiet then someone is either humble or not tall and vice versa.
If someone is both old and not tall then alice is quiet.
Everyone who is not tall or tall is either not strong or strong and vice versa.
Everyone who is either not quiet or quiet is either not brave or not old.
If someone is either not generous or kind then someone is not kind.
If someone is either not rich or not calm then alice is both not happy and old.
Everyone who is not generous is not old and vice versa.
Everyone who is strong or old is not kind and vice versa.
Everyone who is quiet or not strong is not patient or rich and vice versa.
If alice is both tall and curious then someone is either happy or not tall and vice versa.
Everyone who is not wise or not humble is either rich or quiet and vice versa.
Everyone who is both generous and not brave is strong.
If susan is either not generous or not calm then susan is not creative or kind.
If someone is not kind then paul is both funny and calm.
Everyone who is both brave and not rich is either humble or not brave and vice versa.
Everyone who is both old and not strong is not brave and vice versa.
Fred is either curious or not humble.
John is not patient.
Fred is not generous or not funny.
Fred is not wise.
Someone is not tall or not happy.
Alice is either not creative or rich.
Susan is either funny or patient. | Alice is not tall. | neutral | ((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((humble(X)<~>~tall(X)))))&
((?[X]:((old(X)&~tall(X))))=>(quiet(alice)))&
(![X]:((~tall(X)|tall(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~brave(X)<~>~old(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:(~kind(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~happy(alice)&old(alice))))&
(![X]:(~generous(X)<=>~old(X)))&
(![X]:((strong(X)|old(X))<=>~kind(X)))&
(![X]:((quiet(X)|~strong(X))<=>(~patient(X)|rich(X))))&
(((tall(alice)&curious(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((generous(X)&~brave(X))=>strong(X)))&
(((~generous(susan)<~>~calm(susan)))=>((~creative(susan)|kind(susan))))&
((?[X]:(~kind(X)))=>((funny(paul)&calm(paul))))&
(![X]:((brave(X)&~rich(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((old(X)&~strong(X))<=>~brave(X)))&
((curious(fred)<~>~humble(fred)))&
(~patient(john))&
((~generous(fred)|~funny(fred)))&
(~wise(fred))&
(?[X]:((~tall(X)|~happy(X))))&
((~creative(alice)<~>rich(alice)))&
((funny(susan)<~>patient(susan))) | ~tall(alice) | [] | null | 0 |
If mary is both not creative and not rich then paul is creative or not calm and vice versa.
If alice is generous then someone is quiet and vice versa.
If someone is not curious or humble then someone is not brave and vice versa.
Everyone who is both brave and wise is either not generous or not creative.
Everyone who is both happy and generous is both quiet and curious and vice versa.
Everyone who is either not brave or not curious is both quiet and not generous.
Everyone who is either funny or not generous is either humble or strong and vice versa.
Everyone who is patient or not humble is both not old and not quiet and vice versa.
If someone is both strong and rich then someone is not quiet or old and vice versa.
If paul is strong then lucy is either quiet or not wise.
Everyone who is calm is happy and vice versa.
Everyone who is kind is not creative or not old and vice versa.
If someone is either not rich or wise then alice is either not strong or not funny.
If lucy is both kind and not creative then paul is either calm or wise and vice versa.
If paul is both not rich and patient then susan is either not creative or not wise.
Everyone who is calm or patient is both not old and quiet.
Susan is either not strong or wise.
Someone is both not brave and quiet.
Lucy is creative.
Someone is not quiet or not wise.
Someone is either not wise or old.
Fred is strong.
John is curious. | Paul is not rich. | neutral | (((~creative(mary)&~rich(mary)))<=>((creative(paul)|~calm(paul))))&
((generous(alice))<=>(?[X]:(quiet(X))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((brave(X)&wise(X))=>(~generous(X)<~>~creative(X))))&
(![X]:((happy(X)&generous(X))<=>(quiet(X)&curious(X))))&
(![X]:((~brave(X)<~>~curious(X))=>(quiet(X)&~generous(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(humble(X)<~>strong(X))))&
(![X]:((patient(X)|~humble(X))<=>(~old(X)&~quiet(X))))&
((?[X]:((strong(X)&rich(X))))<=>(?[X]:((~quiet(X)|old(X)))))&
((strong(paul))=>((quiet(lucy)<~>~wise(lucy))))&
(![X]:(calm(X)<=>happy(X)))&
(![X]:(kind(X)<=>(~creative(X)|~old(X))))&
((?[X]:((~rich(X)<~>wise(X))))=>((~strong(alice)<~>~funny(alice))))&
(((kind(lucy)&~creative(lucy)))<=>((calm(paul)<~>wise(paul))))&
(((~rich(paul)&patient(paul)))=>((~creative(susan)<~>~wise(susan))))&
(![X]:((calm(X)|patient(X))=>(~old(X)&quiet(X))))&
((~strong(susan)<~>wise(susan)))&
(?[X]:((~brave(X)&quiet(X))))&
(creative(lucy))&
(?[X]:((~quiet(X)|~wise(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(strong(fred))&
(curious(john)) | ~rich(paul) | [] | null | 0 |
Everyone who is both funny and not creative is both not quiet and not funny and vice versa. Everyone who is not kind is either not old or not brave and vice versa. Everyone who is happy or not patient is either not kind or not quiet. Everyone who is quiet or not funny is not creative. Everyone who is happy is kind and vice versa. Everyone who is not happy is not rich and vice versa. If someone is not rich or not old then someone is creative or not happy. If someone is not old or not patient then paul is wise. Everyone who is not creative is either not kind or quiet and vice versa. If someone is funny or not old then someone is either tall or happy. If someone is either not rich or wise then someone is not patient. Everyone who is calm is curious or generous. Everyone who is quiet or rich is either not wise or happy. Everyone who is calm is either funny or not curious and vice versa. Someone is not curious. Someone is brave or strong. Lucy is curious. Fred is calm. Susan is curious or not strong. John is not humble. | Paul is patient. | neutral | (![X]:((funny(X)&~creative(X))<=>(~quiet(X)&~funny(X))))&
(![X]:(~kind(X)<=>(~old(X)<~>~brave(X))))&
(![X]:((happy(X)|~patient(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:((quiet(X)|~funny(X))=>~creative(X)))&
(![X]:(happy(X)<=>kind(X)))&
(![X]:(~happy(X)<=>~rich(X)))&
((?[X]:((~rich(X)|~old(X))))=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~old(X)|~patient(X))))=>(wise(paul)))&
(![X]:(~creative(X)<=>(~kind(X)<~>quiet(X))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~patient(X))))&
(![X]:(calm(X)=>(curious(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)|strong(X))))&
(curious(lucy))&
(calm(fred))&
((curious(susan)|~strong(susan)))&
(~humble(john)) | patient(paul) | [] | null | 0 |
Everyone who is either humble or not kind is not brave or not funny and vice versa.
Everyone who is both not calm and not happy is not generous or not rich.
Everyone who is either funny or creative is kind or funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
Everyone who is not rich or kind is not calm.
Someone is either old or not tall.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative.
Someone is both not humble and not wise.
Someone is both rich and quiet.
Lucy is either not humble or humble.
Someone is either creative or not wise. | Mary is not calm. | contradiction | (![X]:((humble(X)<~>~kind(X))<=>(~brave(X)|~funny(X))))&
(![X]:((~calm(X)&~happy(X))=>(~generous(X)|~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(kind(X)|funny(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((rich(X)&quiet(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X)))) | ~calm(mary) | [
"p2",
"p7",
"p11",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2490655251141689616801670
% SZS output start Proof for 2490655251141689616801670
3. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (funny(X0) | kind(X0))) [input p2]
8. ! [X0] : ((humble(X0) & ~tall(X0)) <=> strong(X0)) [input p7]
12. ! [X0] : ((~rich(X0) | ~tall(X0)) => calm(X0)) [input p11]
14. ? [X0] : (~funny(X0) <~> strong(X0)) <=> (tall(mary) <~> ~calm(mary)) [input p13]
16. ! [X0] : ((kind(X0) | ~rich(X0)) => ~calm(X0)) [input p15]
20. rich(alice) <~> ~creative(alice) [input p19]
25. ~calm(mary) [input hypothesis]
30. ! [X0] : (calm(X0) | (rich(X0) & tall(X0))) [ennf transformation 12]
33. ! [X0] : (~calm(X0) | (~kind(X0) & rich(X0))) [ennf transformation 16]
36. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 36]
45. ! [X0] : (((humble(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | (~humble(X0) | tall(X0)))) [nnf transformation 8]
46. ! [X0] : (((humble(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | ~humble(X0) | tall(X0))) [flattening 45]
59. (? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X0] : ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0)))) [nnf transformation 14]
60. (? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X1] : ((~funny(X1) | ~strong(X1)) & (strong(X1) | funny(X1)))) [rectify 59]
61. ? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) => ((~strong(sK3) | funny(sK3)) & (strong(sK3) | ~funny(sK3))) [choice axiom]
62. (((~strong(sK3) | funny(sK3)) & (strong(sK3) | ~funny(sK3))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X1] : ((~funny(X1) | ~strong(X1)) & (strong(X1) | funny(X1)))) [skolemisation 60,61]
69. (creative(alice) | ~rich(alice)) & (~creative(alice) | rich(alice)) [nnf transformation 20]
85. funny(X0) | kind(X0) | funny(X0) | ~creative(X0) [cnf transformation 37]
89. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 37]
106. ~strong(X0) | ~tall(X0) [cnf transformation 46]
123. tall(X0) | calm(X0) [cnf transformation 30]
124. rich(X0) | calm(X0) [cnf transformation 30]
130. calm(mary) | ~tall(mary) | strong(X1) | funny(X1) [cnf transformation 62]
138. ~calm(X0) | rich(X0) [cnf transformation 33]
139. ~calm(X0) | ~kind(X0) [cnf transformation 33]
146. creative(alice) | ~rich(alice) [cnf transformation 69]
155. ~calm(mary) [cnf transformation 25]
158. funny(X0) | kind(X0) | ~creative(X0) [duplicate literal removal 85]
159. ~creative(X0) | ~funny(X0) [duplicate literal removal 89]
160. ~creative(X0) | kind(X0) [subsumption resolution 158,159]
258. 21 <=> calm(mary) [avatar definition]
276. calm(mary) | strong(X1) | funny(X1) [subsumption resolution 130,123]
278. 25 <=> ! [X1] : (strong(X1) | funny(X1)) [avatar definition]
279. strong(X1) | funny(X1) <- (25) [avatar component clause 278]
280. 25 | 21 [avatar split clause 276,258,278]
286. rich(X0) [subsumption resolution 138,124]
298. creative(alice) [subsumption resolution 146,286]
309. ~21 [avatar split clause 155,258]
321. ~funny(alice) [resolution 159,298]
322. kind(alice) [resolution 160,298]
325. ~tall(X2) | funny(X2) <- (25) [resolution 279,106]
420. 41 <=> tall(alice) [avatar definition]
421. ~tall(alice) <- (~41) [avatar component clause 420]
422. tall(alice) <- (41) [avatar component clause 420]
566. funny(alice) <- (25, 41) [resolution 422,325]
572. $false <- (25, 41) [subsumption resolution 566,321]
573. ~25 | ~41 [avatar contradiction clause 572]
588. calm(alice) <- (~41) [resolution 421,123]
716. ~kind(alice) <- (~41) [resolution 588,139]
717. $false <- (~41) [subsumption resolution 716,322]
718. 41 [avatar contradiction clause 717]
719. $false [avatar sat refutation 280,309,573,718]
% SZS output end Proof for 2490655251141689616801670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not happy.
If susan is either not patient or kind then someone is funny or not happy.
If susan is both patient and not generous then alice is not generous or not calm and vice versa.
If susan is humble then someone is either not strong or not tall.
If paul is not happy then someone is not funny and vice versa.
Everyone who is both not happy and funny is not curious.
Everyone who is either not brave or not kind is either wise or funny.
Everyone who is both not calm and generous is not humble or funny and vice versa.
Everyone who is both not old and not curious is both not tall and not calm.
If lucy is both not wise and not funny then mary is not brave or not tall and vice versa.
If someone is not patient then someone is either kind or wise.
Everyone who is not generous is either not rich or kind and vice versa.
Everyone who is old is both not funny and not curious and vice versa.
If someone is both not curious and not rich then paul is either wise or not curious.
If mary is not calm or not rich then fred is brave or not curious and vice versa.
If fred is not humble or calm then someone is not brave and vice versa.
Someone is both not rich and curious.
Susan is both not old and brave.
Someone is rich.
Fred is not curious or brave.
John is rich.
Alice is funny or not creative.
John is either not humble or strong.
Someone is not patient or not funny. | Paul is happy. | contradiction | (![X]:(~quiet(X)=>~happy(X)))&
(((~patient(susan)<~>kind(susan)))=>(?[X]:((funny(X)|~happy(X)))))&
(((patient(susan)&~generous(susan)))<=>((~generous(alice)|~calm(alice))))&
((humble(susan))=>(?[X]:((~strong(X)<~>~tall(X)))))&
((~happy(paul))<=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)&funny(X))=>~curious(X)))&
(![X]:((~brave(X)<~>~kind(X))=>(wise(X)<~>funny(X))))&
(![X]:((~calm(X)&generous(X))<=>(~humble(X)|funny(X))))&
(![X]:((~old(X)&~curious(X))=>(~tall(X)&~calm(X))))&
(((~wise(lucy)&~funny(lucy)))<=>((~brave(mary)|~tall(mary))))&
((?[X]:(~patient(X)))=>(?[X]:((kind(X)<~>wise(X)))))&
(![X]:(~generous(X)<=>(~rich(X)<~>kind(X))))&
(![X]:(old(X)<=>(~funny(X)&~curious(X))))&
((?[X]:((~curious(X)&~rich(X))))=>((wise(paul)<~>~curious(paul))))&
(((~calm(mary)|~rich(mary)))<=>((brave(fred)|~curious(fred))))&
(((~humble(fred)|calm(fred)))<=>(?[X]:(~brave(X))))&
(?[X]:((~rich(X)&curious(X))))&
((~old(susan)&brave(susan)))&
(?[X]:(rich(X)))&
((~curious(fred)|brave(fred)))&
(rich(john))&
((funny(alice)|~creative(alice)))&
((~humble(john)<~>strong(john)))&
(?[X]:((~patient(X)|~funny(X)))) | happy(paul) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4849119278646641482716663
% SZS output start Proof for 4849119278646641482716663
3. (~generous(susan) & patient(susan)) <=> (~calm(alice) | ~generous(alice)) [input p2]
5. ~happy(paul) <=> ? [X0] : ~funny(X0) [input p4]
8. ! [X0] : ((generous(X0) & ~calm(X0)) <=> (funny(X0) | ~humble(X0))) [input p7]
25. happy(paul) [input hypothesis]
41. ((~generous(susan) & patient(susan)) | (calm(alice) & generous(alice))) & ((~calm(alice) | ~generous(alice)) | (generous(susan) | ~patient(susan))) [nnf transformation 3]
42. ((~generous(susan) & patient(susan)) | (calm(alice) & generous(alice))) & (~calm(alice) | ~generous(alice) | generous(susan) | ~patient(susan)) [flattening 41]
46. (~happy(paul) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | happy(paul)) [nnf transformation 5]
47. (~happy(paul) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | happy(paul)) [rectify 46]
48. ? [X1] : ~funny(X1) => ~funny(sK2) [choice axiom]
49. (~happy(paul) | ! [X0] : funny(X0)) & (~funny(sK2) | happy(paul)) [skolemisation 47,48]
51. ! [X0] : (((generous(X0) & ~calm(X0)) | (~funny(X0) & humble(X0))) & ((funny(X0) | ~humble(X0)) | (~generous(X0) | calm(X0)))) [nnf transformation 8]
52. ! [X0] : (((generous(X0) & ~calm(X0)) | (~funny(X0) & humble(X0))) & (funny(X0) | ~humble(X0) | ~generous(X0) | calm(X0))) [flattening 51]
83. ~generous(susan) | calm(alice) [cnf transformation 42]
87. ~happy(paul) | funny(X0) [cnf transformation 49]
95. ~calm(X0) | ~funny(X0) [cnf transformation 52]
97. ~funny(X0) | generous(X0) [cnf transformation 52]
133. happy(paul) [cnf transformation 25]
153. 5 <=> calm(alice) [avatar definition]
155. calm(alice) <- (5) [avatar component clause 153]
157. 6 <=> generous(susan) [avatar definition]
159. ~generous(susan) <- (~6) [avatar component clause 157]
160. 5 | ~6 [avatar split clause 83,157,153]
184. 11 <=> ! [X0] : funny(X0) [avatar definition]
185. funny(X0) <- (11) [avatar component clause 184]
187. 12 <=> happy(paul) [avatar definition]
190. 11 | ~12 [avatar split clause 87,187,184]
301. 12 [avatar split clause 133,187]
314. ~funny(alice) <- (5) [resolution 155,95]
316. $false <- (5, 11) [subsumption resolution 314,185]
317. ~5 | ~11 [avatar contradiction clause 316]
318. generous(X0) <- (11) [resolution 97,185]
319. $false <- (~6, 11) [resolution 318,159]
320. 6 | ~11 [avatar contradiction clause 319]
321. $false [avatar sat refutation 160,190,301,317,320]
% SZS output end Proof for 4849119278646641482716663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or brave is not strong. Everyone who is both not funny and quiet is either generous or not humble. If someone is both generous and not strong then someone is generous or humble and vice versa. If alice is happy then someone is either patient or not old. Everyone who is not tall is both not humble and tall. Everyone who is not happy or brave is not humble and vice versa. Everyone who is either quiet or not patient is strong and vice versa. If someone is quiet then someone is kind. Everyone who is both not creative and quiet is not humble or not strong and vice versa. If paul is both happy and rich then someone is both not calm and curious and vice versa. If lucy is both patient and not strong then susan is not quiet and vice versa. If someone is either humble or not brave then mary is not quiet or quiet and vice versa. Everyone who is happy or not humble is either not tall or quiet. Everyone who is creative is either not happy or funny. If lucy is both not calm and not generous then lucy is not rich. Paul is quiet. Fred is both old and not humble. John is either wise or not funny. Alice is humble or rich. Someone is humble. Susan is both curious and humble. Paul is calm or humble. | Alice is curious. | neutral | (![X]:((~brave(X)<~>brave(X))=>~strong(X)))&
(![X]:((~funny(X)&quiet(X))=>(generous(X)<~>~humble(X))))&
((?[X]:((generous(X)&~strong(X))))<=>(?[X]:((generous(X)|humble(X)))))&
((happy(alice))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:(~tall(X)=>(~humble(X)&tall(X))))&
(![X]:((~happy(X)|brave(X))<=>~humble(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:(kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~humble(X)|~strong(X))))&
(((happy(paul)&rich(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((patient(lucy)&~strong(lucy)))<=>(~quiet(susan)))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~quiet(mary)|quiet(mary))))&
(![X]:((happy(X)|~humble(X))=>(~tall(X)<~>quiet(X))))&
(![X]:(creative(X)=>(~happy(X)<~>funny(X))))&
(((~calm(lucy)&~generous(lucy)))=>(~rich(lucy)))&
(quiet(paul))&
((old(fred)&~humble(fred)))&
((wise(john)<~>~funny(john)))&
((humble(alice)|rich(alice)))&
(?[X]:(humble(X)))&
((curious(susan)&humble(susan)))&
((calm(paul)|humble(paul))) | curious(alice) | [] | null | 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa.
If lucy is tall or not brave then mary is either funny or not brave and vice versa.
If someone is patient then someone is happy and vice versa.
If someone is both strong and old then susan is calm and vice versa.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Someone is not patient or tall.
Someone is either brave or calm.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny.
Alice is both not rich and not wise. | Fred is not calm. | entailment | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
(((tall(lucy)|~brave(lucy)))<=>((funny(mary)<~>~brave(mary))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice))) | ~calm(fred) | [
"p0",
"p2",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2702084022158628305262072
% SZS output start Proof for 2702084022158628305262072
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
3. ? [X0] : patient(X0) <=> ? [X0] : happy(X0) [input p2]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~calm(X0) | ~wise(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> tall(X0)) => (~quiet(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p12]
25. calm(fred) [input hypothesis]
26. ? [X0] : patient(X0) <=> ? [X1] : happy(X1) [rectify 3]
32. ! [X0] : ((~calm(X0) | ~wise(X0)) | quiet(X0)) [ennf transformation 10]
33. ! [X0] : (~calm(X0) | ~wise(X0) | quiet(X0)) [flattening 32]
34. ! [X0] : ((~quiet(X0) & ~rich(X0)) | (~wise(X0) <=> tall(X0))) [ennf transformation 11]
36. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 13]
39. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
40. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 39]
43. (? [X0] : patient(X0) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : ~patient(X0)) [nnf transformation 26]
44. (? [X0] : patient(X0) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : ~patient(X3)) [rectify 43]
45. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
46. ? [X2] : happy(X2) => happy(sK1) [choice axiom]
47. (patient(sK0) | ! [X1] : ~happy(X1)) & (happy(sK1) | ! [X3] : ~patient(X3)) [skolemisation 44,46,45]
54. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 54]
56. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) [nnf transformation 34]
57. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 36]
82. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 40]
84. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 40]
85. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 40]
93. happy(sK1) | ~patient(X3) [cnf transformation 47]
94. patient(sK0) | ~happy(X1) [cnf transformation 47]
114. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 55]
116. tall(X0) | patient(X0) | tall(X0) [cnf transformation 55]
119. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 33]
123. ~quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 56]
127. ~patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 57]
128. ~strong(X0) | wise(X0) | ~calm(X0) [cnf transformation 57]
152. calm(fred) [cnf transformation 25]
153. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 114]
154. tall(X0) | patient(X0) [duplicate literal removal 116]
159. ~patient(X0) | wise(X0) [duplicate literal removal 82]
160. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 85]
184. 5 <=> ! [X1] : ~happy(X1) [avatar definition]
185. ~happy(X1) <- (5) [avatar component clause 184]
187. 6 <=> patient(sK0) [avatar definition]
189. patient(sK0) <- (6) [avatar component clause 187]
190. 5 | 6 [avatar split clause 94,187,184]
192. 7 <=> ! [X3] : ~patient(X3) [avatar definition]
193. ~patient(X3) <- (7) [avatar component clause 192]
195. 8 <=> happy(sK1) [avatar definition]
197. happy(sK1) <- (8) [avatar component clause 195]
198. 7 | 8 [avatar split clause 93,195,192]
255. strong(X0) | patient(X0) [subsumption resolution 153,154]
270. ~patient(X0) | calm(X0) [subsumption resolution 127,84]
272. 24 <=> quiet(fred) [avatar definition]
274. quiet(fred) <- (24) [avatar component clause 272]
358. $false <- (5, 8) [subsumption resolution 197,185]
359. ~5 | ~8 [avatar contradiction clause 358]
360. calm(sK0) <- (6) [resolution 189,270]
361. wise(sK0) <- (6) [resolution 189,159]
387. ~wise(fred) | quiet(fred) [resolution 119,152]
402. 47 <=> wise(fred) [avatar definition]
404. wise(fred) <- (47) [avatar component clause 402]
406. 48 <=> tall(fred) [avatar definition]
407. ~tall(fred) <- (~48) [avatar component clause 406]
410. 24 | ~47 [avatar split clause 387,402,272]
417. wise(X0) | ~calm(X0) | patient(X0) [resolution 128,255]
427. ~calm(X0) | wise(X0) [subsumption resolution 417,159]
455. ~patient(sK0) | ~wise(sK0) <- (6) [resolution 160,360]
457. ~wise(sK0) <- (6) [subsumption resolution 455,189]
458. $false <- (6) [subsumption resolution 457,361]
459. ~6 [avatar contradiction clause 458]
497. wise(fred) [resolution 427,152]
502. 47 [avatar split clause 497,402]
503. ~wise(fred) | ~tall(fred) <- (24) [resolution 274,123]
505. ~tall(fred) <- (24, 47) [subsumption resolution 503,404]
506. ~48 | ~24 | ~47 [avatar split clause 505,402,272,406]
511. patient(fred) <- (~48) [resolution 407,154]
514. $false <- (7, ~48) [subsumption resolution 511,193]
515. ~7 | 48 [avatar contradiction clause 514]
518. $false [avatar sat refutation 190,198,359,410,459,502,506,515]
% SZS output end Proof for 2702084022158628305262072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not tall or not patient then john is both not kind and not humble and vice versa.
Everyone who is both not tall and patient is both strong and happy.
If someone is both not funny and not creative then alice is both not rich and humble and vice versa.
Everyone who is either patient or creative is either humble or not old.
If someone is strong then paul is not kind.
Everyone who is not rich is both not calm and happy and vice versa.
If someone is either not quiet or not curious then someone is either humble or not patient.
If john is either kind or creative then someone is either not creative or not generous.
Everyone who is happy is both not calm and not tall and vice versa.
If paul is both not wise and curious then susan is both rich and happy and vice versa.
If someone is not strong then someone is not tall or not wise.
Everyone who is not patient is rich or old.
Everyone who is either quiet or patient is not brave or patient.
If alice is both not patient and not strong then susan is generous or not calm and vice versa.
Everyone who is not happy or wise is old or calm.
Everyone who is not humble is funny.
Alice is not curious.
Someone is not old or generous.
Paul is not rich.
Someone is both not patient and not humble.
Someone is both not happy and quiet.
Someone is both brave and calm.
Someone is not calm.
Mary is wise or not quiet. | Paul is wise. | neutral | (((~tall(alice)|~patient(alice)))<=>((~kind(john)&~humble(john))))&
(![X]:((~tall(X)&patient(X))=>(strong(X)&happy(X))))&
((?[X]:((~funny(X)&~creative(X))))<=>((~rich(alice)&humble(alice))))&
(![X]:((patient(X)<~>creative(X))=>(humble(X)<~>~old(X))))&
((?[X]:(strong(X)))=>(~kind(paul)))&
(![X]:(~rich(X)<=>(~calm(X)&happy(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>~patient(X)))))&
(((kind(john)<~>creative(john)))=>(?[X]:((~creative(X)<~>~generous(X)))))&
(![X]:(happy(X)<=>(~calm(X)&~tall(X))))&
(((~wise(paul)&curious(paul)))<=>((rich(susan)&happy(susan))))&
((?[X]:(~strong(X)))=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(~patient(X)=>(rich(X)|old(X))))&
(![X]:((quiet(X)<~>patient(X))=>(~brave(X)|patient(X))))&
(((~patient(alice)&~strong(alice)))<=>((generous(susan)|~calm(susan))))&
(![X]:((~happy(X)|wise(X))=>(old(X)|calm(X))))&
(![X]:(~humble(X)=>funny(X)))&
(~curious(alice))&
(?[X]:((~old(X)|generous(X))))&
(~rich(paul))&
(?[X]:((~patient(X)&~humble(X))))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:(~calm(X)))&
((wise(mary)|~quiet(mary))) | wise(paul) | [] | null | 0 |
If someone is not generous or not creative then susan is either not tall or calm and vice versa. If alice is both generous and not strong then someone is not kind or generous. If mary is either not brave or rich then john is either kind or curious. If someone is happy or not strong then paul is calm or not calm. Everyone who is both tall and generous is not humble. Everyone who is not rich or humble is either patient or brave. Everyone who is not patient is creative and vice versa. Everyone who is creative is both not kind and not wise and vice versa. Everyone who is not strong is patient or not humble and vice versa. If alice is both generous and humble then susan is not patient. Everyone who is not tall is not happy and vice versa. Everyone who is either not happy or humble is either not generous or tall and vice versa. Everyone who is either old or not wise is either not brave or rich and vice versa. If someone is either calm or not creative then mary is either strong or not strong. Everyone who is calm or not curious is humble. Everyone who is not old or not calm is both kind and not funny. Paul is not quiet. Susan is both not patient and not wise. Someone is quiet. Susan is brave or curious. Someone is not quiet. Someone is not tall. Someone is humble. | Mary is happy. | contradiction | ((?[X]:((~generous(X)|~creative(X))))<=>((~tall(susan)<~>calm(susan))))&
(((generous(alice)&~strong(alice)))=>(?[X]:((~kind(X)|generous(X)))))&
(((~brave(mary)<~>rich(mary)))=>((kind(john)<~>curious(john))))&
((?[X]:((happy(X)|~strong(X))))=>((calm(paul)|~calm(paul))))&
(![X]:((tall(X)&generous(X))=>~humble(X)))&
(![X]:((~rich(X)|humble(X))=>(patient(X)<~>brave(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:(creative(X)<=>(~kind(X)&~wise(X))))&
(![X]:(~strong(X)<=>(patient(X)|~humble(X))))&
(((generous(alice)&humble(alice)))=>(~patient(susan)))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((~happy(X)<~>humble(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((calm(X)<~>~creative(X))))=>((strong(mary)<~>~strong(mary))))&
(![X]:((calm(X)|~curious(X))=>humble(X)))&
(![X]:((~old(X)|~calm(X))=>(kind(X)&~funny(X))))&
(~quiet(paul))&
((~patient(susan)&~wise(susan)))&
(?[X]:(quiet(X)))&
((brave(susan)|curious(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X))) | happy(mary) | [
"p0",
"p4",
"p6",
"p7",
"p10",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5038660526352196681634126
% SZS output start Proof for 5038660526352196681634126
1. ? [X0] : (~creative(X0) | ~generous(X0)) <=> (~tall(susan) <~> calm(susan)) [input p0]
5. ! [X0] : ((generous(X0) & tall(X0)) => ~humble(X0)) [input p4]
7. ! [X0] : (~patient(X0) <=> creative(X0)) [input p6]
8. ! [X0] : (creative(X0) <=> (~wise(X0) & ~kind(X0))) [input p7]
11. ! [X0] : (~tall(X0) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((~happy(X0) <~> humble(X0)) <=> (~generous(X0) <~> tall(X0))) [input p11]
15. ! [X0] : ((~curious(X0) | calm(X0)) => humble(X0)) [input p14]
16. ! [X0] : ((~calm(X0) | ~old(X0)) => (~funny(X0) & kind(X0))) [input p15]
18. ~wise(susan) & ~patient(susan) [input p17]
24. happy(mary) [input hypothesis]
25. ! [X0] : ((~calm(X0) | ~old(X0)) => kind(X0)) [pure predicate removal 16]
31. ! [X0] : (~humble(X0) | (~generous(X0) | ~tall(X0))) [ennf transformation 5]
32. ! [X0] : (~humble(X0) | ~generous(X0) | ~tall(X0)) [flattening 31]
37. ! [X0] : (humble(X0) | (curious(X0) & ~calm(X0))) [ennf transformation 15]
38. ! [X0] : (kind(X0) | (calm(X0) & old(X0))) [ennf transformation 25]
39. (? [X0] : (~creative(X0) | ~generous(X0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X0] : (creative(X0) & generous(X0))) [nnf transformation 1]
40. (? [X0] : (~creative(X0) | ~generous(X0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X1] : (creative(X1) & generous(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~generous(X0)) => (~creative(sK0) | ~generous(sK0)) [choice axiom]
42. ((~creative(sK0) | ~generous(sK0)) | ((~tall(susan) | ~calm(susan)) & (calm(susan) | tall(susan)))) & (((~calm(susan) | tall(susan)) & (calm(susan) | ~tall(susan))) | ! [X1] : (creative(X1) & generous(X1))) [skolemisation 40,41]
47. ! [X0] : ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))) [nnf transformation 7]
48. ! [X0] : ((creative(X0) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | ~creative(X0))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | ~creative(X0))) [flattening 48]
52. ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 11]
53. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [nnf transformation 12]
66. ~calm(susan) | tall(susan) | generous(X1) [cnf transformation 42]
77. ~humble(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 32]
82. patient(X0) | creative(X0) [cnf transformation 47]
84. ~kind(X0) | ~creative(X0) [cnf transformation 49]
91. ~happy(X0) | tall(X0) [cnf transformation 52]
92. ~tall(X0) | happy(X0) [cnf transformation 52]
96. ~tall(X0) | generous(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 53]
98. humble(X0) | ~happy(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 53]
99. ~humble(X0) | happy(X0) | tall(X0) | generous(X0) [cnf transformation 53]
113. ~calm(X0) | humble(X0) [cnf transformation 37]
116. kind(X0) | calm(X0) [cnf transformation 38]
118. ~patient(susan) [cnf transformation 18]
125. happy(mary) [cnf transformation 24]
127. 1 <=> calm(susan) [avatar definition]
128. calm(susan) <- (1) [avatar component clause 127]
131. 2 <=> tall(susan) [avatar definition]
132. tall(susan) <- (2) [avatar component clause 131]
149. 6 <=> ! [X1] : generous(X1) [avatar definition]
150. generous(X1) <- (6) [avatar component clause 149]
151. 6 | 2 | ~1 [avatar split clause 66,127,131,149]
196. 16 <=> patient(susan) [avatar definition]
198. ~patient(susan) <- (~16) [avatar component clause 196]
200. ~humble(X0) | tall(X0) | generous(X0) [subsumption resolution 99,91]
201. ~happy(X0) | ~generous(X0) | ~tall(X0) [subsumption resolution 98,77]
202. ~tall(X0) | ~generous(X0) [subsumption resolution 201,92]
203. ~humble(X0) | ~happy(X0) | generous(X0) [subsumption resolution 96,200]
205. ~16 [avatar split clause 118,196]
215. creative(susan) <- (~16) [resolution 82,198]
218. tall(mary) [resolution 91,125]
220. ~creative(X0) | calm(X0) [resolution 116,84]
221. ~generous(mary) [resolution 202,218]
227. calm(susan) <- (~16) [resolution 220,215]
230. 1 | 16 [avatar split clause 227,196,127]
231. humble(susan) <- (1) [resolution 128,113]
232. ~generous(susan) <- (2) [resolution 132,202]
233. happy(susan) <- (2) [resolution 132,92]
294. ~happy(susan) | generous(susan) <- (1) [resolution 203,231]
295. generous(susan) <- (1, 2) [subsumption resolution 294,233]
296. $false <- (1, 2) [subsumption resolution 295,232]
297. ~1 | ~2 [avatar contradiction clause 296]
310. $false <- (6) [resolution 150,221]
313. ~6 [avatar contradiction clause 310]
315. $false [avatar sat refutation 151,205,230,297,313]
% SZS output end Proof for 5038660526352196681634126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both happy and kind and vice versa. Everyone who is not happy is either not patient or not humble. If susan is either not kind or wise then someone is not curious or patient and vice versa. If paul is funny then john is not brave and vice versa. If someone is both not humble and not happy then someone is patient or not strong. If someone is either old or not curious then fred is not funny and vice versa. Everyone who is either not old or not generous is curious. Everyone who is not generous is quiet. If alice is both kind and not quiet then lucy is either not happy or patient. Everyone who is old is calm or not generous. Everyone who is either patient or not old is both rich and not strong and vice versa. If someone is not generous then someone is not curious or not patient. If someone is not happy then paul is not calm and vice versa. Everyone who is curious is both not brave and not happy. Everyone who is tall is either not happy or kind and vice versa. If fred is wise then lucy is either not old or curious. Alice is either not humble or not patient. Someone is strong. Someone is either not old or old. Lucy is both not quiet and generous. Someone is either funny or not curious. Fred is not tall or humble. Someone is either rich or not happy. Alice is both not funny and not quiet. | John is kind. | contradiction | (![X]:(~tall(X)<=>(happy(X)&kind(X))))&
(![X]:(~happy(X)=>(~patient(X)<~>~humble(X))))&
(((~kind(susan)<~>wise(susan)))<=>(?[X]:((~curious(X)|patient(X)))))&
((funny(paul))<=>(~brave(john)))&
((?[X]:((~humble(X)&~happy(X))))=>(?[X]:((patient(X)|~strong(X)))))&
((?[X]:((old(X)<~>~curious(X))))<=>(~funny(fred)))&
(![X]:((~old(X)<~>~generous(X))=>curious(X)))&
(![X]:(~generous(X)=>quiet(X)))&
(((kind(alice)&~quiet(alice)))=>((~happy(lucy)<~>patient(lucy))))&
(![X]:(old(X)=>(calm(X)|~generous(X))))&
(![X]:((patient(X)<~>~old(X))<=>(rich(X)&~strong(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)|~patient(X)))))&
((?[X]:(~happy(X)))<=>(~calm(paul)))&
(![X]:(curious(X)=>(~brave(X)&~happy(X))))&
(![X]:(tall(X)<=>(~happy(X)<~>kind(X))))&
((wise(fred))=>((~old(lucy)<~>curious(lucy))))&
((~humble(alice)<~>~patient(alice)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)<~>old(X))))&
((~quiet(lucy)&generous(lucy)))&
(?[X]:((funny(X)<~>~curious(X))))&
((~tall(fred)|humble(fred)))&
(?[X]:((rich(X)<~>~happy(X))))&
((~funny(alice)&~quiet(alice))) | kind(john) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7948970590728024878580108
% SZS output start Proof for 7948970590728024878580108
1. ! [X0] : (~tall(X0) <=> (kind(X0) & happy(X0))) [input p0]
15. ! [X0] : (tall(X0) <=> (~happy(X0) <~> kind(X0))) [input p14]
25. kind(john) [input hypothesis]
39. ! [X0] : ((~tall(X0) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | tall(X0))) [nnf transformation 1]
40. ! [X0] : ((~tall(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | tall(X0))) [flattening 39]
65. ! [X0] : ((tall(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~tall(X0))) [nnf transformation 15]
79. happy(X0) | tall(X0) [cnf transformation 40]
81. ~tall(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 40]
115. ~kind(X0) | happy(X0) | ~tall(X0) [cnf transformation 65]
117. tall(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 65]
134. kind(john) [cnf transformation 25]
250. ~happy(X0) | ~kind(X0) [subsumption resolution 117,81]
251. ~kind(X0) | happy(X0) [subsumption resolution 115,79]
252. ~kind(X0) [subsumption resolution 251,250]
308. $false [subsumption resolution 134,252]
% SZS output end Proof for 7948970590728024878580108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not wise is either tall or old.
If fred is not old or not happy then someone is either not calm or not strong and vice versa.
Everyone who is strong is either not old or humble.
Everyone who is not creative or not humble is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
If someone is rich then someone is both happy and funny and vice versa.
Fred is either tall or not wise.
Susan is not tall.
Lucy is either rich or not humble.
Someone is both not quiet and not wise.
Someone is not wise or patient. | Paul is generous. | contradiction | (![X]:((~calm(X)<~>~wise(X))=>(tall(X)<~>old(X))))&
(((~old(fred)|~happy(fred)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~wise(X)|patient(X)))) | generous(paul) | [
"p3",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3001533162555990640842242
% SZS output start Proof for 3001533162555990640842242
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
8. (tall(paul) | ~generous(paul)) <=> (~quiet(paul) | ~happy(paul)) [input p7]
9. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~quiet(X0) & happy(X0))) [input p10]
21. generous(paul) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
37. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 7]
38. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 37]
39. ((tall(paul) | ~generous(paul)) | (quiet(paul) & happy(paul))) & ((~quiet(paul) | ~happy(paul)) | (~tall(paul) & generous(paul))) [nnf transformation 8]
40. (tall(paul) | ~generous(paul) | (quiet(paul) & happy(paul))) & (~quiet(paul) | ~happy(paul) | (~tall(paul) & generous(paul))) [flattening 39]
41. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
42. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 41]
45. ! [X0] : ((funny(X0) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 11]
46. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [flattening 45]
76. ~tall(X0) | creative(X0) [cnf transformation 27]
82. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 38]
83. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 38]
91. tall(paul) | ~generous(paul) | quiet(paul) [cnf transformation 40]
93. funny(X0) | funny(X0) [cnf transformation 42]
99. ~quiet(X0) | ~funny(X0) [cnf transformation 46]
123. generous(paul) [cnf transformation 21]
125. funny(X0) [duplicate literal removal 93]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 82]
127. ~creative(X0) | strong(X0) [duplicate literal removal 83]
159. ~creative(X0) [subsumption resolution 126,127]
161. 7 <=> quiet(paul) [avatar definition]
163. quiet(paul) <- (7) [avatar component clause 161]
165. 8 <=> generous(paul) [avatar definition]
169. 9 <=> tall(paul) [avatar definition]
171. tall(paul) <- (9) [avatar component clause 169]
172. 7 | ~8 | 9 [avatar split clause 91,169,165,161]
182. ~quiet(X0) [subsumption resolution 99,125]
210. 8 [avatar split clause 123,165]
223. creative(paul) <- (9) [resolution 76,171]
224. $false <- (9) [subsumption resolution 223,159]
225. ~9 [avatar contradiction clause 224]
226. $false <- (7) [subsumption resolution 163,182]
227. ~7 [avatar contradiction clause 226]
228. $false [avatar sat refutation 172,210,225,227]
% SZS output end Proof for 3001533162555990640842242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If 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 not humble and happy and vice versa.
Everyone who is not funny is not rich or not old.
Everyone who is either creative or not tall is both strong and not old.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Fred is not generous or not quiet.
Someone is both patient and not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous. | Lucy is not creative. | entailment | (((old(alice)<~>~tall(alice)))=>(?[X]:((patient(X)&~happy(X)))))&
((?[X]:((~wise(X)|~quiet(X))))<=>((~humble(john)&happy(john))))&
(![X]:(~funny(X)=>(~rich(X)|~old(X))))&
(![X]:((creative(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
((~generous(fred)|~quiet(fred)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X)))) | ~creative(lucy) | [
"p2",
"p3",
"p5",
"p6",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6697207792751760226335131
% SZS output start Proof for 6697207792751760226335131
3. ! [X0] : (~funny(X0) => (~old(X0) | ~rich(X0))) [input p2]
4. ! [X0] : ((creative(X0) <~> ~tall(X0)) => (~old(X0) & strong(X0))) [input p3]
6. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (~humble(X0) & ~brave(X0))) [input p6]
11. ! [X0] : (~brave(X0) <=> (funny(X0) | ~wise(X0))) [input p10]
16. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p15]
20. ~rich(lucy) <~> humble(lucy) [input p19]
25. creative(lucy) [input hypothesis]
29. ! [X0] : ((~old(X0) | ~rich(X0)) | funny(X0)) [ennf transformation 3]
30. ! [X0] : (~old(X0) | ~rich(X0) | funny(X0)) [flattening 29]
31. ! [X0] : ((~old(X0) & strong(X0)) | (creative(X0) <=> ~tall(X0))) [ennf transformation 4]
34. ! [X0] : ((~humble(X0) & ~brave(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 7]
47. ! [X0] : ((~old(X0) & strong(X0)) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0)))) [nnf transformation 31]
49. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | ~humble(X0)))) [nnf transformation 6]
50. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | ~humble(X0))) [flattening 49]
51. ! [X0] : ((~humble(X0) & ~brave(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 34]
61. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 11]
62. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | brave(X0))) [flattening 61]
65. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 16]
70. (~humble(lucy) | rich(lucy)) & (humble(lucy) | ~rich(lucy)) [nnf transformation 20]
88. ~rich(X0) | ~old(X0) | funny(X0) [cnf transformation 30]
91. ~creative(X0) | ~tall(X0) | ~old(X0) [cnf transformation 47]
97. ~creative(X0) | humble(X0) | old(X0) [cnf transformation 50]
104. ~humble(X0) | brave(X0) | tall(X0) [cnf transformation 51]
124. ~brave(X0) | ~funny(X0) [cnf transformation 62]
132. ~old(X0) | humble(X0) [cnf transformation 65]
133. ~humble(X0) | old(X0) [cnf transformation 65]
139. ~humble(lucy) | rich(lucy) [cnf transformation 70]
147. creative(lucy) [cnf transformation 25]
264. 25 <=> rich(lucy) [avatar definition]
266. rich(lucy) <- (25) [avatar component clause 264]
268. 26 <=> humble(lucy) [avatar definition]
269. humble(lucy) <- (26) [avatar component clause 268]
271. 25 | ~26 [avatar split clause 139,268,264]
294. 30 <=> tall(lucy) [avatar definition]
296. ~tall(lucy) <- (~30) [avatar component clause 294]
298. ~tall(lucy) | ~old(lucy) [resolution 91,147]
303. humble(lucy) | old(lucy) [resolution 97,147]
310. humble(lucy) [subsumption resolution 303,132]
311. 26 [avatar split clause 310,268]
312. ~old(lucy) | funny(lucy) <- (25) [resolution 266,88]
314. 31 <=> funny(lucy) [avatar definition]
316. funny(lucy) <- (31) [avatar component clause 314]
318. 32 <=> old(lucy) [avatar definition]
319. old(lucy) <- (32) [avatar component clause 318]
321. 31 | ~32 | ~25 [avatar split clause 312,264,318,314]
322. old(lucy) <- (26) [resolution 269,133]
325. 32 | ~26 [avatar split clause 322,268,318]
334. brave(lucy) | tall(lucy) <- (26) [resolution 104,269]
336. brave(lucy) <- (26, ~30) [subsumption resolution 334,296]
339. ~funny(lucy) <- (26, ~30) [resolution 336,124]
341. $false <- (26, ~30, 31) [subsumption resolution 339,316]
342. ~26 | 30 | ~31 [avatar contradiction clause 341]
348. ~tall(lucy) <- (32) [subsumption resolution 298,319]
349. ~30 | ~32 [avatar split clause 348,318,294]
350. $false [avatar sat refutation 271,311,321,325,342,349]
% SZS output end Proof for 6697207792751760226335131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or wise is both not funny and old and vice versa.
Everyone who is both wise and rich is both happy and not curious.
Everyone who is strong is wise and vice versa.
Everyone who is both quiet and tall is either strong or not old and vice versa.
Everyone who is both old and quiet is both strong and not strong and vice versa.
If lucy is both not brave and not creative then someone is not old or not quiet and vice versa.
Everyone who is not generous or not curious is either happy or wise.
If alice is both tall and not creative then lucy is not curious.
If someone is wise then john is both brave and not curious and vice versa.
Everyone who is not rich is quiet or not funny.
If someone is not patient then someone is wise or kind and vice versa.
Everyone who is both not happy and calm is not creative.
Everyone who is either old or generous is brave or not patient and vice versa.
Everyone who is both creative and not rich is brave or kind.
If someone is both patient and not old then someone is not calm or humble.
Everyone who is not humble or not curious is both not patient and not tall.
Someone is both kind and not strong.
Someone is not wise or happy.
Someone is not rich or not humble.
Fred is either not wise or kind.
Susan is generous.
Someone is either not funny or kind.
Someone is both not tall and calm. | Alice is not wise. | entailment | (![X]:((~wise(X)<~>wise(X))<=>(~funny(X)&old(X))))&
(![X]:((wise(X)&rich(X))=>(happy(X)&~curious(X))))&
(![X]:(strong(X)<=>wise(X)))&
(![X]:((quiet(X)&tall(X))<=>(strong(X)<~>~old(X))))&
(![X]:((old(X)&quiet(X))<=>(strong(X)&~strong(X))))&
(((~brave(lucy)&~creative(lucy)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((~generous(X)|~curious(X))=>(happy(X)<~>wise(X))))&
(((tall(alice)&~creative(alice)))=>(~curious(lucy)))&
((?[X]:(wise(X)))<=>((brave(john)&~curious(john))))&
(![X]:(~rich(X)=>(quiet(X)|~funny(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((~happy(X)&calm(X))=>~creative(X)))&
(![X]:((old(X)<~>generous(X))<=>(brave(X)|~patient(X))))&
(![X]:((creative(X)&~rich(X))=>(brave(X)|kind(X))))&
((?[X]:((patient(X)&~old(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~patient(X)&~tall(X))))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~rich(X)|~humble(X))))&
((~wise(fred)<~>kind(fred)))&
(generous(susan))&
(?[X]:((~funny(X)<~>kind(X))))&
(?[X]:((~tall(X)&calm(X)))) | ~wise(alice) | [
"p0",
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3728963104130970032203546
% SZS output start Proof for 3728963104130970032203546
1. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (old(X0) & ~funny(X0))) [input p0]
3. ! [X0] : (strong(X0) <=> wise(X0)) [input p2]
4. ! [X0] : ((tall(X0) & quiet(X0)) <=> (strong(X0) <~> ~old(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & old(X0)) <=> (~strong(X0) & strong(X0))) [input p4]
24. wise(alice) [input hypothesis]
40. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 40]
42. ! [X0] : ((strong(X0) | ~wise(X0)) & (wise(X0) | ~strong(X0))) [nnf transformation 3]
43. ! [X0] : (((tall(X0) & quiet(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | (~tall(X0) | ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : (((tall(X0) & quiet(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~tall(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((quiet(X0) & old(X0)) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | (~quiet(X0) | ~old(X0)))) [nnf transformation 5]
46. ! [X0] : (((quiet(X0) & old(X0)) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | ~quiet(X0) | ~old(X0))) [flattening 45]
82. old(X0) | wise(X0) | wise(X0) [cnf transformation 41]
83. old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 41]
89. ~wise(X0) | strong(X0) [cnf transformation 42]
92. quiet(X0) | ~old(X0) | ~strong(X0) [cnf transformation 44]
97. ~strong(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 46]
141. wise(alice) [cnf transformation 24]
144. old(X0) | wise(X0) [duplicate literal removal 82]
145. old(X0) | ~wise(X0) [duplicate literal removal 83]
146. old(X0) [subsumption resolution 144,145]
149. quiet(X0) | ~strong(X0) [subsumption resolution 92,146]
151. ~strong(X0) | ~quiet(X0) [subsumption resolution 97,146]
152. ~strong(X0) [subsumption resolution 151,149]
249. strong(alice) [resolution 89,141]
252. $false [subsumption resolution 249,152]
% SZS output end Proof for 3728963104130970032203546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative then mary is not old.
If john is not rich or happy then fred is both curious and tall.
Everyone who is both not humble and not creative is tall or rich.
Everyone who is not tall is either not patient or rich.
If someone is either not brave or old then someone is either kind or not quiet and vice versa.
Everyone who is both strong and tall is wise or not funny.
Everyone who is both tall and not calm is humble.
If fred is both not rich and not patient then susan is both brave and happy.
If someone is both old and funny then someone is both not funny and funny and vice versa.
Everyone who is both not wise and strong is both not rich and not brave.
Everyone who is wise is not patient.
Everyone who is not patient is not strong or not generous.
If someone is both not curious and not funny then someone is both old and generous.
Everyone who is either brave or not rich is not creative and vice versa.
If someone is either not old or not patient then someone is both not kind and happy.
Everyone who is happy or not humble is humble or creative.
Paul is not patient.
Alice is either wise or not kind.
Someone is not old.
Someone is curious.
Someone is either happy or kind.
Someone is quiet or not happy.
Someone is curious or tall.
Someone is tall. | Mary is funny. | neutral | ((creative(mary))=>(~old(mary)))&
(((~rich(john)|happy(john)))=>((curious(fred)&tall(fred))))&
(![X]:((~humble(X)&~creative(X))=>(tall(X)|rich(X))))&
(![X]:(~tall(X)=>(~patient(X)<~>rich(X))))&
((?[X]:((~brave(X)<~>old(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((strong(X)&tall(X))=>(wise(X)|~funny(X))))&
(![X]:((tall(X)&~calm(X))=>humble(X)))&
(((~rich(fred)&~patient(fred)))=>((brave(susan)&happy(susan))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~wise(X)&strong(X))=>(~rich(X)&~brave(X))))&
(![X]:(wise(X)=>~patient(X)))&
(![X]:(~patient(X)=>(~strong(X)|~generous(X))))&
((?[X]:((~curious(X)&~funny(X))))=>(?[X]:((old(X)&generous(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>~creative(X)))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((happy(X)|~humble(X))=>(humble(X)|creative(X))))&
(~patient(paul))&
((wise(alice)<~>~kind(alice)))&
(?[X]:(~old(X)))&
(?[X]:(curious(X)))&
(?[X]:((happy(X)<~>kind(X))))&
(?[X]:((quiet(X)|~happy(X))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:(tall(X))) | funny(mary) | [] | null | 0 |
Everyone who is both patient and not wise is both not generous and not quiet and vice versa.
If someone is either old or rich then paul is not old or strong and vice versa.
Everyone who is old is patient and vice versa.
If someone is not strong or strong then someone is creative or happy.
Everyone who is not rich is either not quiet or creative.
If someone is not tall then someone is either humble or strong and vice versa.
If someone is generous or not curious then someone is either not old or wise and vice versa.
Everyone who is not curious is happy or strong.
If fred is not quiet then lucy is either not generous or funny.
Everyone who is both not brave and curious is either strong or not generous and vice versa.
If mary is not old then someone is both generous and brave.
If someone is rich then alice is both not tall and curious.
Everyone who is both tall and not rich is not wise or not rich and vice versa.
If paul is either wise or creative then someone is quiet and vice versa.
Everyone who is not brave or not humble is strong or not wise and vice versa.
If alice is either not curious or not kind then mary is happy or funny and vice versa.
Someone is not brave.
John is not brave or not creative.
Someone is either not creative or not quiet.
Paul is not quiet.
Susan is not generous.
Fred is either funny or curious.
Susan is rich. | Fred is happy. | neutral | (![X]:((patient(X)&~wise(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((old(X)<~>rich(X))))<=>((~old(paul)|strong(paul))))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:(~rich(X)=>(~quiet(X)<~>creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((humble(X)<~>strong(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~old(X)<~>wise(X)))))&
(![X]:(~curious(X)=>(happy(X)|strong(X))))&
((~quiet(fred))=>((~generous(lucy)<~>funny(lucy))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)<~>~generous(X))))&
((~old(mary))=>(?[X]:((generous(X)&brave(X)))))&
((?[X]:(rich(X)))=>((~tall(alice)&curious(alice))))&
(![X]:((tall(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(((wise(paul)<~>creative(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~humble(X))<=>(strong(X)|~wise(X))))&
(((~curious(alice)<~>~kind(alice)))<=>((happy(mary)|funny(mary))))&
(?[X]:(~brave(X)))&
((~brave(john)|~creative(john)))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~quiet(paul))&
(~generous(susan))&
((funny(fred)<~>curious(fred)))&
(rich(susan)) | happy(fred) | [] | null | 0 |
If someone is humble then someone is either patient or not funny and vice versa.
If someone is not happy then someone is both not patient and not funny and vice versa.
Everyone who is rich or not wise is either patient or generous.
Everyone who is either not funny or patient is kind or not brave and vice versa.
Everyone who is either not patient or not happy is tall and vice versa.
If someone is generous then someone is either calm or curious.
If someone is wise then mary is generous or tall and vice versa.
If fred is both not generous and happy then someone is strong and vice versa.
Everyone who is kind or strong is either curious or tall.
Everyone who is both not curious and not kind is kind and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is either tall or quiet is not strong and vice versa.
If lucy is calm or quiet then fred is not quiet or not calm and vice versa.
If john is not wise then someone is funny or rich.
Everyone who is either not rich or brave is not happy.
Everyone who is not wise is funny or not quiet.
John is generous.
Alice is either kind or not funny.
Someone is creative.
Someone is not humble or not creative.
Mary is both not humble and tall.
Mary is curious.
Alice is humble.
Someone is either not calm or not rich. | Fred is kind. | contradiction | ((?[X]:(humble(X)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:((rich(X)|~wise(X))=>(patient(X)<~>generous(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(kind(X)|~brave(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>tall(X)))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>curious(X)))))&
((?[X]:(wise(X)))<=>((generous(mary)|tall(mary))))&
(((~generous(fred)&happy(fred)))<=>(?[X]:(strong(X))))&
(![X]:((kind(X)|strong(X))=>(curious(X)<~>tall(X))))&
(![X]:((~curious(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((tall(X)<~>quiet(X))<=>~strong(X)))&
(((calm(lucy)|quiet(lucy)))<=>((~quiet(fred)|~calm(fred))))&
((~wise(john))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~rich(X)<~>brave(X))=>~happy(X)))&
(![X]:(~wise(X)=>(funny(X)|~quiet(X))))&
(generous(john))&
((kind(alice)<~>~funny(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~creative(X))))&
((~humble(mary)&tall(mary)))&
(curious(mary))&
(humble(alice))&
(?[X]:((~calm(X)<~>~rich(X)))) | kind(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9217356757015881489178778
% SZS output start Proof for 9217356757015881489178778
10. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> kind(X0)) [input p9]
25. kind(fred) [input hypothesis]
65. ! [X0] : (((~kind(X0) & ~curious(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | curious(X0)))) [nnf transformation 10]
66. ! [X0] : (((~kind(X0) & ~curious(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | curious(X0))) [flattening 65]
117. ~kind(X0) | ~kind(X0) [cnf transformation 66]
143. kind(fred) [cnf transformation 25]
145. ~kind(X0) [duplicate literal removal 117]
293. $false [subsumption resolution 143,145]
% SZS output end Proof for 9217356757015881489178778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not happy is either old or funny.
Everyone who is not calm or not quiet is both not brave and not curious.
Everyone who is both tall and kind is not quiet and vice versa.
If paul is not patient or not rich then mary is either not strong or not tall.
Everyone who is both funny and wise is both not funny and not curious and vice versa.
If fred is not happy or not generous then mary is not funny and vice versa.
If fred is not old then someone is curious or not happy.
Everyone who is both kind and not curious is both not happy and calm and vice versa.
If alice is generous then someone is brave.
Everyone who is wise is either humble or not creative.
If john is old or wise then john is not curious or not wise and vice versa.
Everyone who is both not rich and generous is tall or not creative.
If someone is both not funny and not curious then paul is wise or not kind.
If susan is either rich or generous then john is strong or not quiet.
If paul is both not creative and kind then fred is not calm or calm and vice versa.
Everyone who is both wise and not generous is not quiet and vice versa.
Alice is not generous.
Alice is brave.
Mary is both humble and not creative.
Someone is quiet.
John is not wise or not funny.
Someone is not generous or funny.
Mary is not rich.
Someone is both not wise and strong. | Susan is not wise. | neutral | (![X]:((~calm(X)&~happy(X))=>(old(X)<~>funny(X))))&
(![X]:((~calm(X)|~quiet(X))=>(~brave(X)&~curious(X))))&
(![X]:((tall(X)&kind(X))<=>~quiet(X)))&
(((~patient(paul)|~rich(paul)))=>((~strong(mary)<~>~tall(mary))))&
(![X]:((funny(X)&wise(X))<=>(~funny(X)&~curious(X))))&
(((~happy(fred)|~generous(fred)))<=>(~funny(mary)))&
((~old(fred))=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~happy(X)&calm(X))))&
((generous(alice))=>(?[X]:(brave(X))))&
(![X]:(wise(X)=>(humble(X)<~>~creative(X))))&
(((old(john)|wise(john)))<=>((~curious(john)|~wise(john))))&
(![X]:((~rich(X)&generous(X))=>(tall(X)|~creative(X))))&
((?[X]:((~funny(X)&~curious(X))))=>((wise(paul)|~kind(paul))))&
(((rich(susan)<~>generous(susan)))=>((strong(john)|~quiet(john))))&
(((~creative(paul)&kind(paul)))<=>((~calm(fred)|calm(fred))))&
(![X]:((wise(X)&~generous(X))<=>~quiet(X)))&
(~generous(alice))&
(brave(alice))&
((humble(mary)&~creative(mary)))&
(?[X]:(quiet(X)))&
((~wise(john)|~funny(john)))&
(?[X]:((~generous(X)|funny(X))))&
(~rich(mary))&
(?[X]:((~wise(X)&strong(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is either not rich or not generous is either not tall or creative.
Everyone who is both not brave and not rich is not humble and vice versa.
If someone is either kind or not calm then susan is either not patient or not quiet.
If john is either not old or strong then someone is quiet.
Everyone who is either not generous or not rich is both quiet and curious.
Everyone who is either not creative or not patient is happy or funny and vice versa.
If someone is both not old and brave then lucy is both not calm and not kind and vice versa.
If someone is either tall or not quiet then john is not tall or not old.
Everyone who is either humble or not curious is not wise or not quiet and vice versa.
Everyone who is rich or not kind is both funny and kind.
Everyone who is both not wise and wise is either not humble or not kind.
Everyone who is both kind and not curious is either patient or not generous.
Everyone who is both not wise and generous is both not strong and rich and vice versa.
Everyone who is not creative or brave is not strong.
Everyone who is both not kind and wise is not rich and vice versa.
If someone is either not curious or not quiet then fred is both not strong and not patient.
Someone is not funny or wise.
Someone is either humble or not tall.
Someone is rich or happy.
John is kind or creative.
Alice is either curious or brave.
John is either not strong or rich. | Alice is brave. | contradiction | (![X]:((~rich(X)<~>~generous(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>~humble(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>((~patient(susan)<~>~quiet(susan))))&
(((~old(john)<~>strong(john)))=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)<~>~rich(X))=>(quiet(X)&curious(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>(happy(X)|funny(X))))&
((?[X]:((~old(X)&brave(X))))<=>((~calm(lucy)&~kind(lucy))))&
((?[X]:((tall(X)<~>~quiet(X))))=>((~tall(john)|~old(john))))&
(![X]:((humble(X)<~>~curious(X))<=>(~wise(X)|~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(funny(X)&kind(X))))&
(![X]:((~wise(X)&wise(X))=>(~humble(X)<~>~kind(X))))&
(![X]:((kind(X)&~curious(X))=>(patient(X)<~>~generous(X))))&
(![X]:((~wise(X)&generous(X))<=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)|brave(X))=>~strong(X)))&
(![X]:((~kind(X)&wise(X))<=>~rich(X)))&
((?[X]:((~curious(X)<~>~quiet(X))))=>((~strong(fred)&~patient(fred))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((rich(X)|happy(X))))&
((kind(john)|creative(john)))&
((curious(alice)<~>brave(alice)))&
((~strong(john)<~>rich(john))) | brave(alice) | [
"p1",
"p4",
"p5",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2138022965525468447625262
% SZS output start Proof for 2138022965525468447625262
2. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> ~humble(X0)) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~rich(X0)) => (curious(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~creative(X0) <~> ~patient(X0)) <=> (funny(X0) | happy(X0))) [input p5]
9. ! [X0] : ((humble(X0) <~> ~curious(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((~kind(X0) | rich(X0)) => (kind(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~curious(X0) & kind(X0)) => (patient(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (rich(X0) & ~strong(X0))) [input p12]
14. ! [X0] : ((brave(X0) | ~creative(X0)) => ~strong(X0)) [input p13]
15. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~rich(X0)) [input p14]
21. curious(alice) <~> brave(alice) [input p20]
23. brave(alice) [input hypothesis]
27. ! [X0] : ((curious(X0) & quiet(X0)) | (~generous(X0) <=> ~rich(X0))) [ennf transformation 5]
30. ! [X0] : ((kind(X0) & funny(X0)) | (kind(X0) & ~rich(X0))) [ennf transformation 10]
33. ! [X0] : ((patient(X0) <~> ~generous(X0)) | (curious(X0) | ~kind(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) <~> ~generous(X0)) | curious(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : (~strong(X0) | (~brave(X0) & creative(X0))) [ennf transformation 14]
38. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) | brave(X0)))) [nnf transformation 2]
39. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | rich(X0) | brave(X0))) [flattening 38]
44. ! [X0] : ((curious(X0) & quiet(X0)) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) [nnf transformation 27]
45. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [nnf transformation 6]
46. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [flattening 45]
53. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [nnf transformation 9]
54. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [flattening 53]
56. ! [X0] : (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | curious(X0) | ~kind(X0)) [nnf transformation 34]
57. ! [X0] : (((generous(X0) & ~wise(X0)) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 13]
58. ! [X0] : (((generous(X0) & ~wise(X0)) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | ~generous(X0) | wise(X0))) [flattening 57]
59. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 15]
60. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | ~wise(X0) | kind(X0))) [flattening 59]
69. (~brave(alice) | ~curious(alice)) & (brave(alice) | curious(alice)) [nnf transformation 21]
77. ~rich(X0) | humble(X0) [cnf transformation 39]
86. ~rich(X0) | curious(X0) | generous(X0) [cnf transformation 44]
91. ~funny(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 46]
104. ~humble(X0) | curious(X0) | wise(X0) [cnf transformation 54]
106. ~rich(X0) | funny(X0) [cnf transformation 30]
109. kind(X0) | kind(X0) [cnf transformation 30]
112. ~generous(X0) | patient(X0) | curious(X0) | ~kind(X0) [cnf transformation 56]
116. ~wise(X0) | ~rich(X0) | strong(X0) [cnf transformation 58]
118. ~strong(X0) | creative(X0) [cnf transformation 35]
121. ~kind(X0) | rich(X0) [cnf transformation 60]
133. ~brave(alice) | ~curious(alice) [cnf transformation 69]
136. brave(alice) [cnf transformation 23]
137. kind(X0) [duplicate literal removal 109]
206. ~generous(X0) | patient(X0) | curious(X0) [subsumption resolution 112,137]
207. rich(X0) [subsumption resolution 121,137]
246. 24 <=> curious(alice) [avatar definition]
248. ~curious(alice) <- (~24) [avatar component clause 246]
250. 25 <=> brave(alice) [avatar definition]
253. ~24 | ~25 [avatar split clause 133,250,246]
257. 25 [avatar split clause 136,250]
262. humble(X0) [resolution 77,207]
263. funny(X0) [resolution 106,207]
278. curious(X0) | generous(X0) [resolution 86,207]
281. generous(alice) <- (~24) [resolution 278,248]
284. ~patient(X0) | ~creative(X0) [resolution 91,263]
291. wise(X0) | curious(X0) [resolution 104,262]
312. ~rich(X0) | strong(X0) | curious(X0) [resolution 116,291]
315. curious(X0) | strong(X0) [subsumption resolution 312,207]
323. patient(alice) | curious(alice) <- (~24) [resolution 206,281]
324. patient(alice) <- (~24) [subsumption resolution 323,248]
327. ~creative(alice) <- (~24) [resolution 324,284]
452. strong(alice) <- (~24) [resolution 315,248]
476. creative(alice) <- (~24) [resolution 452,118]
480. $false <- (~24) [subsumption resolution 476,327]
481. 24 [avatar contradiction clause 480]
482. $false [avatar sat refutation 253,257,481]
% SZS output end Proof for 2138022965525468447625262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or wise is both not creative and not quiet.
If someone is both not old and quiet then someone is either funny or not happy and vice versa.
Everyone who is either brave or not funny is either not patient or quiet and vice versa.
Everyone who is both happy and kind is not old or not humble and vice versa.
Everyone who is not kind or not creative is not strong or funny.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is both wise and humble is not strong or wise.
If john is both not creative and not rich then lucy is both not brave and happy.
Someone is either curious or not wise.
Someone is both strong and not generous.
Someone is not kind or not strong.
Someone is both not funny and wise.
Someone is tall or not tall.
Paul is either wise or not old.
Susan is both quiet and not creative. | Paul is curious. | neutral | (![X]:((~brave(X)<~>wise(X))=>(~creative(X)&~quiet(X))))&
((?[X]:((~old(X)&quiet(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:((happy(X)&kind(X))<=>(~old(X)|~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~strong(X)|funny(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(((~creative(john)&~rich(john)))=>((~brave(lucy)&happy(lucy))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((tall(X)|~tall(X))))&
((wise(paul)<~>~old(paul)))&
((quiet(susan)&~creative(susan))) | curious(paul) | [] | null | 0 |
Everyone who is either not tall or not calm is both brave and not strong and vice versa.
If someone is calm or not strong then someone is calm or patient and vice versa.
Everyone who is kind is either not rich or humble.
Everyone who is either not quiet or generous is both curious and not quiet.
If someone is kind then someone is generous and vice versa.
Everyone who is funny is curious.
If alice is both not brave and brave then someone is not brave.
If alice is not old then fred is wise and vice versa.
If someone is both curious and humble then someone is either generous or brave and vice versa.
If someone is either not generous or quiet then alice is brave or quiet and vice versa.
Everyone who is either not brave or humble is not old and vice versa.
Everyone who is either old or not rich is not quiet and vice versa.
Everyone who is either wise or quiet is happy.
If lucy is either not happy or not quiet then fred is tall.
Everyone who is both patient and not funny is both not happy and quiet.
If lucy is either creative or tall then someone is not patient or patient and vice versa.
Fred is both funny and strong.
Mary is both brave and calm.
Someone is wise or creative.
Someone is brave.
Susan is both curious and funny.
Mary is curious or not patient.
Someone is both strong and wise.
John is both not kind and patient. | Alice is not old. | neutral | (![X]:((~tall(X)<~>~calm(X))<=>(brave(X)&~strong(X))))&
((?[X]:((calm(X)|~strong(X))))<=>(?[X]:((calm(X)|patient(X)))))&
(![X]:(kind(X)=>(~rich(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>generous(X))=>(curious(X)&~quiet(X))))&
((?[X]:(kind(X)))<=>(?[X]:(generous(X))))&
(![X]:(funny(X)=>curious(X)))&
(((~brave(alice)&brave(alice)))=>(?[X]:(~brave(X))))&
((~old(alice))<=>(wise(fred)))&
((?[X]:((curious(X)&humble(X))))<=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((brave(alice)|quiet(alice))))&
(![X]:((~brave(X)<~>humble(X))<=>~old(X)))&
(![X]:((old(X)<~>~rich(X))<=>~quiet(X)))&
(![X]:((wise(X)<~>quiet(X))=>happy(X)))&
(((~happy(lucy)<~>~quiet(lucy)))=>(tall(fred)))&
(![X]:((patient(X)&~funny(X))=>(~happy(X)&quiet(X))))&
(((creative(lucy)<~>tall(lucy)))<=>(?[X]:((~patient(X)|patient(X)))))&
((funny(fred)&strong(fred)))&
((brave(mary)&calm(mary)))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:(brave(X)))&
((curious(susan)&funny(susan)))&
((curious(mary)|~patient(mary)))&
(?[X]:((strong(X)&wise(X))))&
((~kind(john)&patient(john))) | ~old(alice) | [] | null | 0 |
If susan is tall then someone is either happy or wise.
Everyone who is both generous and not rich is not creative.
If lucy is both not happy and not wise then john is both wise and not wise.
If paul is both not kind and creative then alice is strong.
Everyone who is both not rich and not quiet is curious and vice versa.
Everyone who is either happy or humble is brave.
If fred is both not rich and tall then someone is quiet or not patient and vice versa.
If someone is both not curious and not strong then someone is happy or not quiet.
Everyone who is not funny or generous is not kind and vice versa.
Everyone who is both not brave and wise is happy and vice versa.
If lucy is curious then john is patient or not old.
Everyone who is creative is either strong or not happy.
If lucy is creative or not funny then fred is either creative or not generous and vice versa.
Everyone who is not creative is rich and vice versa.
Everyone who is not rich is both not strong and not patient and vice versa.
If paul is quiet then someone is both not generous and quiet.
Someone is both not wise and not funny.
Someone is both brave and tall.
Mary is brave.
Paul is rich.
John is kind.
Someone is not funny or funny. | Lucy is creative. | contradiction | ((tall(susan))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:((generous(X)&~rich(X))=>~creative(X)))&
(((~happy(lucy)&~wise(lucy)))=>((wise(john)&~wise(john))))&
(((~kind(paul)&creative(paul)))=>(strong(alice)))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(?[X]:((~wise(X)&~funny(X))))&
(?[X]:((brave(X)&tall(X))))&
(brave(mary))&
(rich(paul))&
(kind(john))&
(?[X]:((~funny(X)|funny(X)))) | creative(lucy) | [
"p1",
"p6",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 504873744014475600879154
% SZS output start Proof for 504873744014475600879154
2. ! [X0] : ((~rich(X0) & generous(X0)) => ~creative(X0)) [input p1]
7. (tall(fred) & ~rich(fred)) <=> ? [X0] : (~patient(X0) | quiet(X0)) [input p6]
13. (~funny(lucy) | creative(lucy)) <=> (creative(fred) <~> ~generous(fred)) [input p12]
14. ! [X0] : (~creative(X0) <=> rich(X0)) [input p13]
15. ! [X0] : (~rich(X0) <=> (~patient(X0) & ~strong(X0))) [input p14]
23. creative(lucy) [input hypothesis]
29. ! [X0] : (~creative(X0) | (rich(X0) | ~generous(X0))) [ennf transformation 2]
30. ! [X0] : (~creative(X0) | rich(X0) | ~generous(X0)) [flattening 29]
45. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (~tall(fred) | rich(fred))) [nnf transformation 7]
46. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | ~tall(fred) | rich(fred)) [flattening 45]
47. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X1] : (~patient(X1) | quiet(X1)) | ~tall(fred) | rich(fred)) [rectify 46]
48. ? [X1] : (~patient(X1) | quiet(X1)) => (~patient(sK1) | quiet(sK1)) [choice axiom]
49. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & ((~patient(sK1) | quiet(sK1)) | ~tall(fred) | rich(fred)) [skolemisation 47,48]
56. ((~funny(lucy) | creative(lucy)) | ((creative(fred) | generous(fred)) & (~generous(fred) | ~creative(fred)))) & (((generous(fred) | ~creative(fred)) & (~generous(fred) | creative(fred))) | (funny(lucy) & ~creative(lucy))) [nnf transformation 13]
57. (~funny(lucy) | creative(lucy) | ((creative(fred) | generous(fred)) & (~generous(fred) | ~creative(fred)))) & (((generous(fred) | ~creative(fred)) & (~generous(fred) | creative(fred))) | (funny(lucy) & ~creative(lucy))) [flattening 56]
58. ! [X0] : ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))) [nnf transformation 14]
59. ! [X0] : ((~rich(X0) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [nnf transformation 15]
60. ! [X0] : ((~rich(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [flattening 59]
71. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 30]
81. ~rich(fred) | patient(X0) [cnf transformation 49]
94. generous(fred) | ~creative(fred) | ~creative(lucy) [cnf transformation 57]
98. creative(X0) | rich(X0) [cnf transformation 58]
99. ~creative(X0) | ~rich(X0) [cnf transformation 58]
101. ~patient(X0) | rich(X0) [cnf transformation 60]
113. creative(lucy) [cnf transformation 23]
156. 10 <=> ! [X0] : patient(X0) [avatar definition]
157. patient(X0) <- (10) [avatar component clause 156]
168. 13 <=> rich(fred) [avatar definition]
170. ~rich(fred) <- (~13) [avatar component clause 168]
171. 10 | ~13 [avatar split clause 81,168,156]
195. 19 <=> generous(fred) [avatar definition]
197. generous(fred) <- (19) [avatar component clause 195]
199. 20 <=> creative(fred) [avatar definition]
200. ~creative(fred) <- (~20) [avatar component clause 199]
203. 21 <=> creative(lucy) [avatar definition]
205. creative(lucy) <- (21) [avatar component clause 203]
213. ~21 | ~20 | 19 [avatar split clause 94,195,199,203]
230. 21 [avatar split clause 113,203]
238. rich(fred) <- (~20) [resolution 98,200]
241. 13 | 20 [avatar split clause 238,199,168]
244. ~rich(lucy) <- (21) [resolution 99,205]
246. rich(X0) <- (10) [resolution 101,157]
248. rich(X0) | ~generous(X0) | rich(X0) [resolution 71,98]
249. ~generous(X0) | rich(X0) [duplicate literal removal 248]
250. $false <- (10, 21) [resolution 246,244]
251. ~10 | ~21 [avatar contradiction clause 250]
315. rich(fred) <- (19) [resolution 249,197]
316. $false <- (~13, 19) [subsumption resolution 315,170]
317. 13 | ~19 [avatar contradiction clause 316]
318. $false [avatar sat refutation 171,213,230,241,251,317]
% SZS output end Proof for 504873744014475600879154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or curious is both not humble and tall.
Everyone who is not curious is both not wise and brave and vice versa.
If mary is generous then someone is both not kind and not happy and vice versa.
If someone is generous or not creative then paul is not funny or calm and vice versa.
If alice is both happy and not quiet then someone is curious and vice versa.
If someone is both not brave and curious then someone is not kind.
Everyone who is either curious or creative is tall or not creative and vice versa.
Everyone who is not tall or not kind is not strong or not old.
Everyone who is kind or not calm is both not kind and not funny and vice versa.
Everyone who is not wise is patient or calm and vice versa.
If mary is happy then someone is both not creative and not tall and vice versa.
If john is tall then someone is wise or strong.
If someone is strong or not creative then john is either not generous or not curious and vice versa.
Everyone who is either not creative or curious is generous or kind.
If fred is wise then someone is brave or not funny and vice versa.
Everyone who is either not wise or not generous is funny.
Someone is either funny or wise.
Someone is quiet.
Fred is either strong or not old.
Lucy is curious or not generous.
Someone is not funny.
Someone is both brave and not quiet.
Fred is tall. | Paul is not kind. | entailment | (![X]:((strong(X)|curious(X))=>(~humble(X)&tall(X))))&
(![X]:(~curious(X)<=>(~wise(X)&brave(X))))&
((generous(mary))<=>(?[X]:((~kind(X)&~happy(X)))))&
((?[X]:((generous(X)|~creative(X))))<=>((~funny(paul)|calm(paul))))&
(((happy(alice)&~quiet(alice)))<=>(?[X]:(curious(X))))&
((?[X]:((~brave(X)&curious(X))))=>(?[X]:(~kind(X))))&
(![X]:((curious(X)<~>creative(X))<=>(tall(X)|~creative(X))))&
(![X]:((~tall(X)|~kind(X))=>(~strong(X)|~old(X))))&
(![X]:((kind(X)|~calm(X))<=>(~kind(X)&~funny(X))))&
(![X]:(~wise(X)<=>(patient(X)|calm(X))))&
((happy(mary))<=>(?[X]:((~creative(X)&~tall(X)))))&
((tall(john))=>(?[X]:((wise(X)|strong(X)))))&
((?[X]:((strong(X)|~creative(X))))<=>((~generous(john)<~>~curious(john))))&
(![X]:((~creative(X)<~>curious(X))=>(generous(X)|kind(X))))&
((wise(fred))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>funny(X)))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:(quiet(X)))&
((strong(fred)<~>~old(fred)))&
((curious(lucy)|~generous(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((brave(X)&~quiet(X))))&
(tall(fred)) | ~kind(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 330359430673733086585786
% SZS output start Proof for 330359430673733086585786
9. ! [X0] : ((~calm(X0) | kind(X0)) <=> (~funny(X0) & ~kind(X0))) [input p8]
24. kind(paul) [input hypothesis]
56. ! [X0] : (((~calm(X0) | kind(X0)) | (funny(X0) | kind(X0))) & ((~funny(X0) & ~kind(X0)) | (calm(X0) & ~kind(X0)))) [nnf transformation 9]
57. ! [X0] : ((~calm(X0) | kind(X0) | funny(X0) | kind(X0)) & ((~funny(X0) & ~kind(X0)) | (calm(X0) & ~kind(X0)))) [flattening 56]
110. ~kind(X0) | ~kind(X0) [cnf transformation 57]
145. kind(paul) [cnf transformation 24]
146. ~kind(X0) [duplicate literal removal 110]
330. $false [subsumption resolution 145,146]
% SZS output end Proof for 330359430673733086585786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not curious then someone is either not patient or calm and vice versa.
Everyone who is not creative or not funny is either not tall or not curious.
Everyone who is humble or tall is both wise and not brave and vice versa.
If lucy is rich then alice is either not kind or quiet and vice versa.
If john is funny then fred is curious and vice versa.
If someone is both not wise and generous then someone is both generous and not humble.
Everyone who is not quiet or curious is both not calm and old.
Everyone who is either not kind or not calm is both humble and old and vice versa.
If paul is not humble or funny then someone is funny or not happy and vice versa.
Everyone who is rich or not tall is calm or humble.
Everyone who is calm or happy is both calm and not funny and vice versa.
Everyone who is old or not tall is not happy.
Everyone who is both not curious and not funny is not rich.
Everyone who is brave is tall or strong.
If alice is happy then fred is either tall or not curious and vice versa.
Paul is not generous or calm.
John is not old or not calm.
Someone is both happy and not patient.
John is curious.
John is not humble.
Alice is both generous and not brave. | Lucy is curious. | neutral | ((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:((~creative(X)|~funny(X))=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)|tall(X))<=>(wise(X)&~brave(X))))&
((rich(lucy))<=>((~kind(alice)<~>quiet(alice))))&
((funny(john))<=>(curious(fred)))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~quiet(X)|curious(X))=>(~calm(X)&old(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(humble(X)&old(X))))&
(((~humble(paul)|funny(paul)))<=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:((rich(X)|~tall(X))=>(calm(X)|humble(X))))&
(![X]:((calm(X)|happy(X))<=>(calm(X)&~funny(X))))&
(![X]:((old(X)|~tall(X))=>~happy(X)))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:(brave(X)=>(tall(X)|strong(X))))&
((happy(alice))<=>((tall(fred)<~>~curious(fred))))&
((~generous(paul)|calm(paul)))&
((~old(john)|~calm(john)))&
(?[X]:((happy(X)&~patient(X))))&
(curious(john))&
(~humble(john))&
((generous(alice)&~brave(alice))) | curious(lucy) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is rich is either creative or not calm and vice versa.
If someone is either curious or creative then susan is either calm or creative.
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.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich. | Lucy is not brave. | entailment | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(rich(X)<=>(creative(X)<~>~calm(X))))&
((?[X]:((curious(X)<~>creative(X))))=>((calm(susan)<~>creative(susan))))&
((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]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan))) | ~brave(lucy) | [
"p0",
"p2",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6212155879704338959499813
% SZS output start Proof for 6212155879704338959499813
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : (rich(X0) <=> (creative(X0) <~> ~calm(X0))) [input p2]
7. ! [X0] : ((~tall(X0) <~> ~calm(X0)) => ~rich(X0)) [input p6]
9. ! [X0] : (~creative(X0) => (happy(X0) & ~quiet(X0))) [input p8]
10. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X0] : (~tall(X0) <~> happy(X0)) [input p9]
13. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p13]
21. brave(lucy) [input hypothesis]
22. ? [X0] : (strong(X0) | brave(X0)) <=> ? [X1] : (~tall(X1) <~> happy(X1)) [rectify 10]
23. ! [X0] : ((creative(X0) <~> ~calm(X0)) => rich(X0)) [unused predicate definition removal 3]
25. ! [X0] : (rich(X0) | (creative(X0) <=> ~calm(X0))) [ennf transformation 23]
27. ! [X0] : (~rich(X0) | (~tall(X0) <=> ~calm(X0))) [ennf transformation 7]
30. ! [X0] : ((happy(X0) & ~quiet(X0)) | creative(X0)) [ennf transformation 9]
34. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 34]
36. ! [X0] : (rich(X0) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0)))) [nnf transformation 25]
44. ! [X0] : (~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) [nnf transformation 27]
45. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X1] : ((~happy(X1) | tall(X1)) & (happy(X1) | ~tall(X1))) | ! [X0] : (~strong(X0) & ~brave(X0))) [nnf transformation 22]
46. (? [X0] : (strong(X0) | brave(X0)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [rectify 45]
47. ? [X0] : (strong(X0) | brave(X0)) => (strong(sK1) | brave(sK1)) [choice axiom]
48. ? [X2] : ((~happy(X2) | tall(X2)) & (happy(X2) | ~tall(X2))) => ((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) [choice axiom]
49. ((strong(sK1) | brave(sK1)) | ! [X1] : ((~tall(X1) | ~happy(X1)) & (happy(X1) | tall(X1)))) & (((~happy(sK2) | tall(sK2)) & (happy(sK2) | ~tall(sK2))) | ! [X3] : (~strong(X3) & ~brave(X3))) [skolemisation 46,48,47]
51. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 13]
52. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 51]
53. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 14]
58. ~happy(X0) | ~curious(X0) [cnf transformation 35]
60. ~calm(X0) | rich(X0) | ~creative(X0) [cnf transformation 36]
75. ~calm(X0) | ~rich(X0) | tall(X0) [cnf transformation 44]
79. creative(X0) | happy(X0) [cnf transformation 30]
80. happy(sK2) | ~tall(sK2) | ~brave(X3) [cnf transformation 49]
90. curious(X0) | curious(X0) [cnf transformation 52]
96. tall(X0) | happy(X0) | calm(X0) [cnf transformation 53]
110. brave(lucy) [cnf transformation 21]
111. curious(X0) [duplicate literal removal 90]
174. 15 <=> tall(sK2) [avatar definition]
175. ~tall(sK2) <- (~15) [avatar component clause 174]
178. 16 <=> happy(sK2) [avatar definition]
179. happy(sK2) <- (16) [avatar component clause 178]
180. ~happy(sK2) <- (~16) [avatar component clause 178]
183. 17 <=> ! [X3] : ~brave(X3) [avatar definition]
184. ~brave(X3) <- (17) [avatar component clause 183]
187. 17 | ~15 | 16 [avatar split clause 80,178,174,183]
242. ~curious(sK2) <- (16) [resolution 179,58]
243. $false <- (16) [subsumption resolution 242,111]
244. ~16 [avatar contradiction clause 243]
246. 19 <=> calm(sK2) [avatar definition]
248. calm(sK2) <- (19) [avatar component clause 246]
250. 20 <=> rich(sK2) [avatar definition]
252. ~rich(sK2) <- (~20) [avatar component clause 250]
256. $false <- (17) [resolution 184,110]
259. ~17 [avatar contradiction clause 256]
263. happy(sK2) | calm(sK2) <- (~15) [resolution 175,96]
264. calm(sK2) <- (~15, ~16) [subsumption resolution 263,180]
267. 19 | 15 | 16 [avatar split clause 264,178,174,246]
269. ~rich(sK2) | tall(sK2) <- (19) [resolution 248,75]
270. rich(sK2) | ~creative(sK2) <- (19) [resolution 248,60]
271. ~creative(sK2) <- (19, ~20) [subsumption resolution 270,252]
272. happy(sK2) <- (19, ~20) [resolution 271,79]
273. $false <- (~16, 19, ~20) [subsumption resolution 272,180]
274. 16 | ~19 | 20 [avatar contradiction clause 273]
280. ~rich(sK2) <- (~15, 19) [subsumption resolution 269,175]
281. ~20 | 15 | ~19 [avatar split clause 280,246,174,250]
282. $false [avatar sat refutation 187,244,259,267,274,281]
% SZS output end Proof for 6212155879704338959499813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or rich is both not happy and funny. Everyone who is wise or generous is both tall and not strong and vice versa. If someone is not kind or happy then someone is not strong and vice versa. If someone is not strong then lucy is both not kind and brave and vice versa. If fred is not funny then lucy is both curious and not old and vice versa. Everyone who is patient or not curious is not old. If john is either not creative or creative then susan is both wise and old and vice versa. Everyone who is both not curious and not rich is both funny and quiet. If someone is either not funny or not kind then someone is both patient and not generous. If someone is not wise or tall then john is kind and vice versa. If fred is both not humble and not old then lucy is not calm and vice versa. Everyone who is not brave or calm is strong and vice versa. If fred is both not strong and not old then alice is not wise. If someone is humble or not quiet then alice is not generous. Everyone who is both tall and quiet is not calm. Everyone who is both kind and happy is both not funny and funny. Someone is either quiet or not rich. Lucy is tall. Someone is not humble. Someone is either not humble or wise. Alice is both kind and quiet. Someone is kind. Mary is old or happy. Paul is both not tall and happy. | Susan is tall. | entailment | (![X]:((humble(X)<~>rich(X))=>(~happy(X)&funny(X))))&
(![X]:((wise(X)|generous(X))<=>(tall(X)&~strong(X))))&
((?[X]:((~kind(X)|happy(X))))<=>(?[X]:(~strong(X))))&
((?[X]:(~strong(X)))<=>((~kind(lucy)&brave(lucy))))&
((~funny(fred))<=>((curious(lucy)&~old(lucy))))&
(![X]:((patient(X)|~curious(X))=>~old(X)))&
(((~creative(john)<~>creative(john)))<=>((wise(susan)&old(susan))))&
(![X]:((~curious(X)&~rich(X))=>(funny(X)&quiet(X))))&
((?[X]:((~funny(X)<~>~kind(X))))=>(?[X]:((patient(X)&~generous(X)))))&
((?[X]:((~wise(X)|tall(X))))<=>(kind(john)))&
(((~humble(fred)&~old(fred)))<=>(~calm(lucy)))&
(![X]:((~brave(X)|calm(X))<=>strong(X)))&
(((~strong(fred)&~old(fred)))=>(~wise(alice)))&
((?[X]:((humble(X)|~quiet(X))))=>(~generous(alice)))&
(![X]:((tall(X)&quiet(X))=>~calm(X)))&
(![X]:((kind(X)&happy(X))=>(~funny(X)&funny(X))))&
(?[X]:((quiet(X)<~>~rich(X))))&
(tall(lucy))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)<~>wise(X))))&
((kind(alice)&quiet(alice)))&
(?[X]:(kind(X)))&
((old(mary)|happy(mary)))&
((~tall(paul)&happy(paul))) | tall(susan) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9030471378589580629676200
% SZS output start Proof for 9030471378589580629676200
2. ! [X0] : ((generous(X0) | wise(X0)) <=> (~strong(X0) & tall(X0))) [input p1]
7. (~creative(john) <~> creative(john)) <=> (old(susan) & wise(susan)) [input p6]
25. ~tall(susan) [input hypothesis]
41. ! [X0] : (((generous(X0) | wise(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (~generous(X0) & ~wise(X0)))) [nnf transformation 2]
42. ! [X0] : ((generous(X0) | wise(X0) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | (~generous(X0) & ~wise(X0)))) [flattening 41]
55. (((~creative(john) | creative(john)) & (creative(john) | ~creative(john))) | (~old(susan) | ~wise(susan))) & ((old(susan) & wise(susan)) | ((~creative(john) | ~creative(john)) & (creative(john) | creative(john)))) [nnf transformation 7]
56. (((~creative(john) | creative(john)) & (creative(john) | ~creative(john))) | ~old(susan) | ~wise(susan)) & ((old(susan) & wise(susan)) | ((~creative(john) | ~creative(john)) & (creative(john) | creative(john)))) [flattening 55]
83. ~wise(X0) | tall(X0) [cnf transformation 42]
99. wise(susan) | creative(john) | creative(john) [cnf transformation 56]
100. wise(susan) | ~creative(john) | ~creative(john) [cnf transformation 56]
138. ~tall(susan) [cnf transformation 25]
139. wise(susan) | creative(john) [duplicate literal removal 99]
140. wise(susan) | ~creative(john) [duplicate literal removal 100]
198. 13 <=> creative(john) [avatar definition]
208. 15 <=> wise(susan) [avatar definition]
210. wise(susan) <- (15) [avatar component clause 208]
211. ~13 | 15 [avatar split clause 140,208,198]
212. 13 | 15 [avatar split clause 139,208,198]
309. tall(susan) <- (15) [resolution 83,210]
310. $false <- (15) [subsumption resolution 309,138]
311. ~15 [avatar contradiction clause 310]
312. $false [avatar sat refutation 211,212,311]
% SZS output end Proof for 9030471378589580629676200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not quiet then lucy is both not generous and old and vice versa. Everyone who is tall is not tall or not wise and vice versa. If alice is both quiet and not kind then lucy is not tall or not wise and vice versa. Everyone who is not wise is both not curious and not old and vice versa. Everyone who is not old is either not old or strong. Everyone who is not creative or humble is happy or not tall. If lucy is happy or not quiet then john is both not patient and happy. Everyone who is rich is either calm or curious and vice versa. If john is either not generous or not creative then lucy is both not creative and wise and vice versa. Everyone who is either not calm or not kind is curious and vice versa. If someone is either strong or calm then john is both humble and not humble and vice versa. If fred is not funny then someone is not generous. Everyone who is either not curious or funny is either brave or not tall. If john is not happy then someone is generous. Fred is either not strong or not creative. Someone is not creative or rich. Paul is either not generous or not calm. Fred is patient. Someone is either funny or not curious. | Lucy is not quiet. | neutral | ((~quiet(susan))<=>((~generous(lucy)&old(lucy))))&
(![X]:(tall(X)<=>(~tall(X)|~wise(X))))&
(((quiet(alice)&~kind(alice)))<=>((~tall(lucy)|~wise(lucy))))&
(![X]:(~wise(X)<=>(~curious(X)&~old(X))))&
(![X]:(~old(X)=>(~old(X)<~>strong(X))))&
(![X]:((~creative(X)|humble(X))=>(happy(X)|~tall(X))))&
(((happy(lucy)|~quiet(lucy)))=>((~patient(john)&happy(john))))&
(![X]:(rich(X)<=>(calm(X)<~>curious(X))))&
(((~generous(john)<~>~creative(john)))<=>((~creative(lucy)&wise(lucy))))&
(![X]:((~calm(X)<~>~kind(X))<=>curious(X)))&
((?[X]:((strong(X)<~>calm(X))))<=>((humble(john)&~humble(john))))&
((~funny(fred))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>funny(X))=>(brave(X)<~>~tall(X))))&
((~happy(john))=>(?[X]:(generous(X))))&
((~strong(fred)<~>~creative(fred)))&
(?[X]:((~creative(X)|rich(X))))&
((~generous(paul)<~>~calm(paul)))&
(patient(fred))&
(?[X]:((funny(X)<~>~curious(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is quiet or curious is both brave and not patient.
Everyone who is not happy is either not strong or not funny and vice versa.
Everyone who is kind or not rich is not strong and vice versa.
Everyone who is both curious and not curious is quiet or not funny.
If someone is not patient then mary is not patient and vice versa.
If john is strong then mary is generous or creative and vice versa.
If lucy is tall then paul is both not patient and brave and vice versa.
If someone is not creative then paul is both not curious and wise.
Everyone who is wise or not curious is both not rich and generous and vice versa.
If someone is either not kind or not patient then someone is either not funny or not calm and vice versa.
If fred is not tall or not humble then someone is creative or quiet and vice versa.
If lucy is not kind or happy then someone is both funny and brave and vice versa.
Everyone who is not happy is kind and vice versa.
If john is calm or not tall then someone is either not curious or not creative and vice versa.
Everyone who is either not wise or wise is not tall and vice versa.
If john is both not curious and not humble then john is tall or humble and vice versa.
Someone is either not patient or not curious.
Someone is not calm.
Lucy is kind.
Fred is either not kind or not quiet.
Lucy is either creative or patient.
Someone is humble.
Fred is both generous and quiet. | Fred is not strong. | entailment | (![X]:((quiet(X)|curious(X))=>(brave(X)&~patient(X))))&
(![X]:(~happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((kind(X)|~rich(X))<=>~strong(X)))&
(![X]:((curious(X)&~curious(X))=>(quiet(X)|~funny(X))))&
((?[X]:(~patient(X)))<=>(~patient(mary)))&
((strong(john))<=>((generous(mary)|creative(mary))))&
((tall(lucy))<=>((~patient(paul)&brave(paul))))&
((?[X]:(~creative(X)))=>((~curious(paul)&wise(paul))))&
(![X]:((wise(X)|~curious(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)<~>~patient(X))))<=>(?[X]:((~funny(X)<~>~calm(X)))))&
(((~tall(fred)|~humble(fred)))<=>(?[X]:((creative(X)|quiet(X)))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(~happy(X)<=>kind(X)))&
(((calm(john)|~tall(john)))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~tall(X)))&
(((~curious(john)&~humble(john)))<=>((tall(john)|humble(john))))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
((~kind(fred)<~>~quiet(fred)))&
((creative(lucy)<~>patient(lucy)))&
(?[X]:(humble(X)))&
((generous(fred)&quiet(fred))) | ~strong(fred) | [
"p0",
"p1",
"p11",
"p12",
"p18",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7315129975366846271497765
% SZS output start Proof for 7315129975366846271497765
1. ! [X0] : ((curious(X0) | quiet(X0)) => (~patient(X0) & brave(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p1]
12. (happy(lucy) | ~kind(lucy)) <=> ? [X0] : (brave(X0) & funny(X0)) [input p11]
13. ! [X0] : (~happy(X0) <=> kind(X0)) [input p12]
19. kind(lucy) [input p18]
20. ~kind(fred) <~> ~quiet(fred) [input p19]
23. quiet(fred) & generous(fred) [input p22]
24. strong(fred) [input hypothesis]
26. ! [X0] : ((~patient(X0) & brave(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 1]
30. ! [X0] : ((~happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | happy(X0))) [nnf transformation 2]
53. ((happy(lucy) | ~kind(lucy)) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [nnf transformation 12]
54. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [flattening 53]
55. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X1] : (brave(X1) & funny(X1)) | (~happy(lucy) & kind(lucy))) [rectify 54]
56. ? [X1] : (brave(X1) & funny(X1)) => (brave(sK4) & funny(sK4)) [choice axiom]
57. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & ((brave(sK4) & funny(sK4)) | (~happy(lucy) & kind(lucy))) [skolemisation 55,56]
58. ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 13]
72. (quiet(fred) | kind(fred)) & (~quiet(fred) | ~kind(fred)) [nnf transformation 20]
76. ~quiet(X0) | brave(X0) [cnf transformation 26]
83. ~strong(X0) | ~happy(X0) | funny(X0) [cnf transformation 30]
119. happy(lucy) | ~kind(lucy) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. kind(X0) | happy(X0) [cnf transformation 58]
121. ~kind(X0) | ~happy(X0) [cnf transformation 58]
140. kind(lucy) [cnf transformation 19]
141. ~quiet(fred) | ~kind(fred) [cnf transformation 72]
147. quiet(fred) [cnf transformation 23]
148. strong(fred) [cnf transformation 24]
272. 27 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition]
273. ~funny(X0) | ~brave(X0) <- (27) [avatar component clause 272]
275. 28 <=> kind(lucy) [avatar definition]
276. kind(lucy) <- (28) [avatar component clause 275]
279. 29 <=> happy(lucy) [avatar definition]
282. 27 | ~28 | 29 [avatar split clause 119,279,275,272]
335. 28 [avatar split clause 140,275]
337. 40 <=> kind(fred) [avatar definition]
338. ~kind(fred) <- (~40) [avatar component clause 337]
341. 41 <=> quiet(fred) [avatar definition]
343. quiet(fred) <- (41) [avatar component clause 341]
345. ~40 | ~41 [avatar split clause 141,341,337]
356. 41 [avatar split clause 147,341]
367. brave(fred) <- (41) [resolution 76,343]
380. happy(fred) <- (~40) [resolution 120,338]
383. ~happy(lucy) <- (28) [resolution 121,276]
417. ~happy(fred) | funny(fred) [resolution 83,148]
418. funny(fred) <- (~40) [subsumption resolution 417,380]
421. ~brave(fred) <- (27, ~40) [resolution 418,273]
422. $false <- (27, ~40, 41) [subsumption resolution 421,367]
423. ~27 | 40 | ~41 [avatar contradiction clause 422]
424. ~29 | ~28 [avatar split clause 383,275,279]
425. $false [avatar sat refutation 282,335,345,356,423,424]
% SZS output end Proof for 7315129975366846271497765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not wise then someone is both not generous and brave and vice versa.
If someone is tall or quiet then fred is both not old and tall.
Everyone who is not generous is both not funny and kind and vice versa.
Everyone who is both not funny and not quiet is curious or not funny and vice versa.
If someone is not tall or not old then someone is both patient and not tall.
If someone is creative or humble then fred is both not old and not patient and vice versa.
If susan is wise or calm then someone is strong.
Everyone who is generous is humble.
Everyone who is either not funny or not kind is either kind or not creative and vice versa.
If susan is not brave or rich then someone is either humble or not tall.
If someone is either not calm or humble then alice is both not strong and funny.
Everyone who is either not tall or humble is either patient or tall.
Everyone who is either curious or old is not generous or not old and vice versa.
If someone is both rich and not tall then someone is both quiet and rich.
Everyone who is calm is not brave or creative.
If someone is creative then susan is both not quiet and not tall and vice versa.
Someone is either not kind or not wise.
Alice is either not happy or strong.
Someone is not old.
Someone is both not curious and patient.
John is not calm or rich.
John is both not generous and not strong.
Someone is not generous or not rich.
Susan is either brave or creative. | Susan is not creative. | contradiction | ((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
((?[X]:((tall(X)|quiet(X))))=>((~old(fred)&tall(fred))))&
(![X]:(~generous(X)<=>(~funny(X)&kind(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(curious(X)|~funny(X))))&
((?[X]:((~tall(X)|~old(X))))=>(?[X]:((patient(X)&~tall(X)))))&
((?[X]:((creative(X)|humble(X))))<=>((~old(fred)&~patient(fred))))&
(((wise(susan)|calm(susan)))=>(?[X]:(strong(X))))&
(![X]:(generous(X)=>humble(X)))&
(![X]:((~funny(X)<~>~kind(X))<=>(kind(X)<~>~creative(X))))&
(((~brave(susan)|rich(susan)))=>(?[X]:((humble(X)<~>~tall(X)))))&
((?[X]:((~calm(X)<~>humble(X))))=>((~strong(alice)&funny(alice))))&
(![X]:((~tall(X)<~>humble(X))=>(patient(X)<~>tall(X))))&
(![X]:((curious(X)<~>old(X))<=>(~generous(X)|~old(X))))&
((?[X]:((rich(X)&~tall(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:(calm(X)=>(~brave(X)|creative(X))))&
((?[X]:(creative(X)))<=>((~quiet(susan)&~tall(susan))))&
(?[X]:((~kind(X)<~>~wise(X))))&
((~happy(alice)<~>strong(alice)))&
(?[X]:(~old(X)))&
(?[X]:((~curious(X)&patient(X))))&
((~calm(john)|rich(john)))&
((~generous(john)&~strong(john)))&
(?[X]:((~generous(X)|~rich(X))))&
((brave(susan)<~>creative(susan))) | ~creative(susan) | [
"p0",
"p2",
"p3",
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2298904746258877311914097
% SZS output start Proof for 2298904746258877311914097
1. ? [X0] : (~wise(X0) & funny(X0)) <=> ? [X0] : (brave(X0) & ~generous(X0)) [input p0]
3. ! [X0] : (~generous(X0) <=> (kind(X0) & ~funny(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> (~funny(X0) | curious(X0))) [input p3]
9. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> (kind(X0) <~> ~creative(X0))) [input p8]
13. ! [X0] : ((curious(X0) <~> old(X0)) <=> (~old(X0) | ~generous(X0))) [input p12]
24. brave(susan) <~> creative(susan) [input p23]
25. ~creative(susan) [input hypothesis]
26. ? [X0] : (~wise(X0) & funny(X0)) <=> ? [X1] : (brave(X1) & ~generous(X1)) [rectify 1]
39. (? [X0] : (~wise(X0) & funny(X0)) | ! [X1] : (~brave(X1) | generous(X1))) & (? [X1] : (brave(X1) & ~generous(X1)) | ! [X0] : (wise(X0) | ~funny(X0))) [nnf transformation 26]
40. (? [X0] : (~wise(X0) & funny(X0)) | ! [X1] : (~brave(X1) | generous(X1))) & (? [X2] : (brave(X2) & ~generous(X2)) | ! [X3] : (wise(X3) | ~funny(X3))) [rectify 39]
41. ? [X0] : (~wise(X0) & funny(X0)) => (~wise(sK0) & funny(sK0)) [choice axiom]
42. ? [X2] : (brave(X2) & ~generous(X2)) => (brave(sK1) & ~generous(sK1)) [choice axiom]
43. ((~wise(sK0) & funny(sK0)) | ! [X1] : (~brave(X1) | generous(X1))) & ((brave(sK1) & ~generous(sK1)) | ! [X3] : (wise(X3) | ~funny(X3))) [skolemisation 40,42,41]
44. ! [X0] : ((~generous(X0) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | generous(X0))) [nnf transformation 3]
45. ! [X0] : ((~generous(X0) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | generous(X0))) [flattening 44]
46. ! [X0] : (((~quiet(X0) & ~funny(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
47. ! [X0] : (((~quiet(X0) & ~funny(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | quiet(X0) | funny(X0))) [flattening 46]
58. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 9]
64. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 13]
65. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [flattening 64]
84. (~creative(susan) | ~brave(susan)) & (creative(susan) | brave(susan)) [nnf transformation 24]
87. funny(sK0) | ~brave(X1) | generous(X1) [cnf transformation 43]
93. ~funny(X0) | generous(X0) [cnf transformation 45]
97. ~curious(X0) | ~funny(X0) [cnf transformation 47]
115. creative(X0) | ~kind(X0) | ~kind(X0) | funny(X0) [cnf transformation 58]
120. kind(X0) | funny(X0) | kind(X0) | creative(X0) [cnf transformation 58]
134. ~old(X0) | ~generous(X0) | curious(X0) | ~old(X0) [cnf transformation 65]
136. old(X0) | curious(X0) | old(X0) [cnf transformation 65]
156. creative(susan) | brave(susan) [cnf transformation 84]
158. ~creative(susan) [cnf transformation 25]
159. ~old(X0) | ~generous(X0) | curious(X0) [duplicate literal removal 134]
160. curious(X0) | old(X0) [duplicate literal removal 136]
164. creative(X0) | ~kind(X0) | funny(X0) [duplicate literal removal 115]
166. kind(X0) | funny(X0) | creative(X0) [duplicate literal removal 120]
168. 1 <=> ! [X1] : (~brave(X1) | generous(X1)) [avatar definition]
169. ~brave(X1) | generous(X1) <- (1) [avatar component clause 168]
176. 3 <=> funny(sK0) [avatar definition]
178. funny(sK0) <- (3) [avatar component clause 176]
179. 1 | 3 [avatar split clause 87,176,168]
266. creative(X0) | funny(X0) [subsumption resolution 164,166]
282. 26 <=> brave(susan) [avatar definition]
284. brave(susan) <- (26) [avatar component clause 282]
306. ~generous(X0) | curious(X0) [subsumption resolution 159,160]
370. 44 <=> creative(susan) [avatar definition]
372. ~creative(susan) <- (~44) [avatar component clause 370]
374. 26 | 44 [avatar split clause 156,370,282]
375. ~44 [avatar split clause 158,370]
382. generous(sK0) <- (3) [resolution 93,178]
401. generous(susan) <- (1, 26) [resolution 169,284]
403. funny(susan) <- (~44) [resolution 266,372]
407. curious(sK0) <- (3) [resolution 306,382]
421. curious(susan) <- (1, 26) [resolution 401,306]
466. ~funny(sK0) <- (3) [resolution 407,97]
467. $false <- (3) [subsumption resolution 466,178]
468. ~3 [avatar contradiction clause 467]
476. ~funny(susan) <- (1, 26) [resolution 421,97]
477. $false <- (1, 26, ~44) [subsumption resolution 476,403]
478. ~1 | ~26 | 44 [avatar contradiction clause 477]
479. $false [avatar sat refutation 179,374,375,468,478]
% SZS output end Proof for 2298904746258877311914097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is tall is not tall.
If john is either humble or not strong then fred is either patient or calm and vice versa.
Everyone who is either not kind or not humble is not kind.
If mary is both rich and funny then someone is not quiet or funny.
If someone is kind then someone is both not wise and happy.
If someone is either wise or happy then john is both quiet and not humble.
Everyone who is both not humble and strong is not curious.
Everyone who is not tall is both rich and quiet and vice versa.
If someone is both not generous and not wise then someone is either not kind or not quiet and vice versa.
If someone is both not patient and not tall then alice is both quiet and not brave and vice versa.
If lucy is either not humble or not funny then someone is strong and vice versa.
If john is both not tall and not generous then someone is strong or not rich.
If someone is not calm then someone is rich or kind.
Paul is funny.
Someone is both not happy and not old.
Paul is not patient.
Paul is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall. | Mary is strong. | neutral | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(tall(X)=>~tall(X)))&
(((humble(john)<~>~strong(john)))<=>((patient(fred)<~>calm(fred))))&
(![X]:((~kind(X)<~>~humble(X))=>~kind(X)))&
(((rich(mary)&funny(mary)))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((wise(X)<~>happy(X))))=>((quiet(john)&~humble(john))))&
(![X]:((~humble(X)&strong(X))=>~curious(X)))&
(![X]:(~tall(X)<=>(rich(X)&quiet(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)&~brave(alice))))&
(((~humble(lucy)<~>~funny(lucy)))<=>(?[X]:(strong(X))))&
(((~tall(john)&~generous(john)))=>(?[X]:((strong(X)|~rich(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(funny(paul))&
(?[X]:((~happy(X)&~old(X))))&
(~patient(paul))&
((old(paul)|~humble(paul)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X)))) | strong(mary) | [] | null | 0 |
Everyone who is not strong or not old is either old or not calm and vice versa.
If someone is both curious and wise then someone is not creative or not generous.
Everyone who is either old or rich is not wise.
Everyone who is either wise or brave is both not wise and generous.
Everyone who is both not curious and not rich is wise.
If alice is rich then susan is quiet.
Everyone who is either humble or not strong is curious.
Everyone who is both not old and kind is wise and vice versa.
Everyone who is either calm or tall is not old or humble.
If susan is either not creative or funny then someone is either not kind or calm.
Everyone who is both not kind and not calm is both not kind and kind and vice versa.
Everyone who is either not curious or not rich is both not curious and humble.
Everyone who is strong is rich.
Everyone who is either strong or brave is either not funny or not kind and vice versa.
Everyone who is both not happy and not tall is brave or generous and vice versa.
If susan is brave then lucy is quiet or not humble and vice versa.
Fred is tall.
Susan is not patient.
Someone is not generous or not strong.
Someone is both not quiet and humble.
Someone is kind or not happy.
Someone is either not calm or quiet.
Someone is creative. | Susan is quiet. | neutral | (![X]:((~strong(X)|~old(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((old(X)<~>rich(X))=>~wise(X)))&
(![X]:((wise(X)<~>brave(X))=>(~wise(X)&generous(X))))&
(![X]:((~curious(X)&~rich(X))=>wise(X)))&
((rich(alice))=>(quiet(susan)))&
(![X]:((humble(X)<~>~strong(X))=>curious(X)))&
(![X]:((~old(X)&kind(X))<=>wise(X)))&
(![X]:((calm(X)<~>tall(X))=>(~old(X)|humble(X))))&
(((~creative(susan)<~>funny(susan)))=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~kind(X)&~calm(X))<=>(~kind(X)&kind(X))))&
(![X]:((~curious(X)<~>~rich(X))=>(~curious(X)&humble(X))))&
(![X]:(strong(X)=>rich(X)))&
(![X]:((strong(X)<~>brave(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:((~happy(X)&~tall(X))<=>(brave(X)|generous(X))))&
((brave(susan))<=>((quiet(lucy)|~humble(lucy))))&
(tall(fred))&
(~patient(susan))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(creative(X))) | quiet(susan) | [] | null | 0 |
If someone is not brave then john is either brave or not humble and vice versa.
Everyone who is old is not old.
If someone is not creative then mary is either calm or not kind.
Everyone who is patient or not happy is both happy and not brave.
Everyone who is happy is both not funny and not old.
If someone is both not tall and patient then someone is both not curious and not old.
Everyone who is both humble and not humble is either patient or not old and vice versa.
If alice is not calm or curious then john is kind or not brave.
If fred is tall or wise then someone is both funny and wise.
If someone is either wise or generous then someone is both not creative and not old and vice versa.
If someone is either not humble or patient then lucy is not tall and vice versa.
Everyone who is not generous is either kind or creative.
If fred is either kind or not tall then someone is both old and not funny and vice versa.
If someone is both happy and calm then someone is both brave and old.
If someone is not creative or not kind then alice is patient and vice versa.
Paul is either tall or not strong.
Susan is brave or not tall.
John is either curious or generous.
Mary is both rich and not strong.
John is strong or humble. | Alice is patient. | entailment | ((?[X]:(~brave(X)))<=>((brave(john)<~>~humble(john))))&
(![X]:(old(X)=>~old(X)))&
((?[X]:(~creative(X)))=>((calm(mary)<~>~kind(mary))))&
(![X]:((patient(X)|~happy(X))=>(happy(X)&~brave(X))))&
(![X]:(happy(X)=>(~funny(X)&~old(X))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((humble(X)&~humble(X))<=>(patient(X)<~>~old(X))))&
(((~calm(alice)|curious(alice)))=>((kind(john)|~brave(john))))&
(((tall(fred)|wise(fred)))=>(?[X]:((funny(X)&wise(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(~tall(lucy)))&
(![X]:(~generous(X)=>(kind(X)<~>creative(X))))&
(((kind(fred)<~>~tall(fred)))<=>(?[X]:((old(X)&~funny(X)))))&
((?[X]:((happy(X)&calm(X))))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~creative(X)|~kind(X))))<=>(patient(alice)))&
((tall(paul)<~>~strong(paul)))&
((brave(susan)|~tall(susan)))&
((curious(john)<~>generous(john)))&
((rich(mary)&~strong(mary)))&
((strong(john)|humble(john))) | patient(alice) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8871874184972055358488763
% SZS output start Proof for 8871874184972055358488763
2. ! [X0] : (old(X0) => ~old(X0)) [input p1]
7. ! [X0] : ((~humble(X0) & humble(X0)) <=> (patient(X0) <~> ~old(X0))) [input p6]
21. ~patient(alice) [input hypothesis]
26. ! [X0] : (~old(X0) | ~old(X0)) [ennf transformation 2]
44. ! [X0] : (((~humble(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (humble(X0) | ~humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((~humble(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | humble(X0) | ~humble(X0))) [flattening 44]
75. ~old(X0) | ~old(X0) [cnf transformation 26]
89. humble(X0) | patient(X0) | old(X0) [cnf transformation 45]
91. ~humble(X0) | patient(X0) | old(X0) [cnf transformation 45]
128. ~patient(alice) [cnf transformation 21]
130. ~old(X0) [duplicate literal removal 75]
172. ~humble(X0) | patient(X0) [subsumption resolution 91,130]
173. humble(X0) | patient(X0) [subsumption resolution 89,130]
174. patient(X0) [subsumption resolution 173,172]
300. $false [subsumption resolution 128,174]
% SZS output end Proof for 8871874184972055358488763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is calm or not humble.
Everyone who is either not wise or not calm is both kind and not generous.
If someone is rich or brave then someone is not happy.
If someone is both calm and brave then someone is wise.
If mary is not curious or not patient then someone is not brave or funny.
If lucy is both brave and not generous then someone is creative or not curious and vice versa.
Everyone who is not patient or not quiet is either not humble or wise and vice versa.
Everyone who is patient is both generous and strong and vice versa.
If mary is both not calm and rich then fred is funny or not wise.
If john is either strong or not curious then someone is not old or brave.
Everyone who is not strong or not creative is either not creative or quiet and vice versa.
Everyone who is either tall or not old is either calm or quiet.
Everyone who is either not funny or wise is both not old and not humble and vice versa.
If someone is quiet then paul is not humble and vice versa.
If paul is both not creative and calm then someone is both not curious and not quiet and vice versa.
Everyone who is not funny or not generous is generous or happy and vice versa.
Paul is both not creative and not strong.
John is tall.
Lucy is brave or patient.
Susan is either not calm or funny.
Someone is funny.
Someone is wise.
Someone is happy or old.
Alice is either not happy or not old. | Lucy is brave. | entailment | (![X]:((~quiet(X)|humble(X))=>(calm(X)|~humble(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(kind(X)&~generous(X))))&
((?[X]:((rich(X)|brave(X))))=>(?[X]:(~happy(X))))&
((?[X]:((calm(X)&brave(X))))=>(?[X]:(wise(X))))&
(((~curious(mary)|~patient(mary)))=>(?[X]:((~brave(X)|funny(X)))))&
(((brave(lucy)&~generous(lucy)))<=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(~humble(X)<~>wise(X))))&
(![X]:(patient(X)<=>(generous(X)&strong(X))))&
(((~calm(mary)&rich(mary)))=>((funny(fred)|~wise(fred))))&
(((strong(john)<~>~curious(john)))=>(?[X]:((~old(X)|brave(X)))))&
(![X]:((~strong(X)|~creative(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~old(X))=>(calm(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(~old(X)&~humble(X))))&
((?[X]:(quiet(X)))<=>(~humble(paul)))&
(((~creative(paul)&calm(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((~funny(X)|~generous(X))<=>(generous(X)|happy(X))))&
((~creative(paul)&~strong(paul)))&
(tall(john))&
((brave(lucy)|patient(lucy)))&
((~calm(susan)<~>funny(susan)))&
(?[X]:(funny(X)))&
(?[X]:(wise(X)))&
(?[X]:((happy(X)|old(X))))&
((~happy(alice)<~>~old(alice))) | brave(lucy) | [
"p0",
"p5",
"p10",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7982548920583804729296151
% SZS output start Proof for 7982548920583804729296151
1. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~humble(X0) | calm(X0))) [input p0]
6. (~generous(lucy) & brave(lucy)) <=> ? [X0] : (~curious(X0) | creative(X0)) [input p5]
11. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (~creative(X0) <~> quiet(X0))) [input p10]
14. ? [X0] : quiet(X0) <=> ~humble(paul) [input p13]
15. (calm(paul) & ~creative(paul)) <=> ? [X0] : (~quiet(X0) & ~curious(X0)) [input p14]
17. ~strong(paul) & ~creative(paul) [input p16]
25. ~brave(lucy) [input hypothesis]
31. ! [X0] : ((~humble(X0) | calm(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 1]
32. ! [X0] : (~humble(X0) | calm(X0) | (~humble(X0) & quiet(X0))) [flattening 31]
48. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X0] : (~curious(X0) | creative(X0)) | (generous(lucy) | ~brave(lucy))) [nnf transformation 6]
49. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X0] : (~curious(X0) | creative(X0)) | generous(lucy) | ~brave(lucy)) [flattening 48]
50. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X1] : (~curious(X1) | creative(X1)) | generous(lucy) | ~brave(lucy)) [rectify 49]
51. ? [X1] : (~curious(X1) | creative(X1)) => (~curious(sK3) | creative(sK3)) [choice axiom]
52. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & ((~curious(sK3) | creative(sK3)) | generous(lucy) | ~brave(lucy)) [skolemisation 50,51]
60. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 11]
61. ! [X0] : ((~creative(X0) | ~strong(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | (creative(X0) & strong(X0)))) [flattening 60]
65. (? [X0] : quiet(X0) | humble(paul)) & (~humble(paul) | ! [X0] : ~quiet(X0)) [nnf transformation 14]
66. (? [X0] : quiet(X0) | humble(paul)) & (~humble(paul) | ! [X1] : ~quiet(X1)) [rectify 65]
67. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
68. (quiet(sK5) | humble(paul)) & (~humble(paul) | ! [X1] : ~quiet(X1)) [skolemisation 66,67]
69. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X0] : (~quiet(X0) & ~curious(X0)) | (~calm(paul) | creative(paul))) [nnf transformation 15]
70. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X0] : (~quiet(X0) & ~curious(X0)) | ~calm(paul) | creative(paul)) [flattening 69]
71. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X1] : (~quiet(X1) & ~curious(X1)) | ~calm(paul) | creative(paul)) [rectify 70]
72. ? [X1] : (~quiet(X1) & ~curious(X1)) => (~quiet(sK6) & ~curious(sK6)) [choice axiom]
73. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & ((~quiet(sK6) & ~curious(sK6)) | ~calm(paul) | creative(paul)) [skolemisation 71,72]
85. ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 32]
93. brave(lucy) | ~creative(X0) [cnf transformation 52]
94. brave(lucy) | curious(X0) [cnf transformation 52]
111. ~quiet(X0) | creative(X0) | creative(X0) [cnf transformation 61]
125. quiet(sK5) | humble(paul) [cnf transformation 68]
126. ~curious(sK6) | ~calm(paul) | creative(paul) [cnf transformation 73]
134. ~creative(paul) [cnf transformation 17]
145. ~brave(lucy) [cnf transformation 25]
148. ~quiet(X0) | creative(X0) [duplicate literal removal 111]
150. ~humble(X0) | calm(X0) [duplicate literal removal 85]
186. 9 <=> ! [X0] : curious(X0) [avatar definition]
187. curious(X0) <- (9) [avatar component clause 186]
194. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
195. ~creative(X0) <- (11) [avatar component clause 194]
198. 12 <=> brave(lucy) [avatar definition]
201. 9 | 12 [avatar split clause 94,198,186]
202. 11 | 12 [avatar split clause 93,198,194]
231. 19 <=> humble(paul) [avatar definition]
233. humble(paul) <- (19) [avatar component clause 231]
235. 20 <=> quiet(sK5) [avatar definition]
237. quiet(sK5) <- (20) [avatar component clause 235]
238. 19 | 20 [avatar split clause 125,235,231]
247. 23 <=> calm(paul) [avatar definition]
252. 24 <=> creative(paul) [avatar definition]
262. 26 <=> curious(sK6) [avatar definition]
264. ~curious(sK6) <- (~26) [avatar component clause 262]
265. 24 | ~23 | ~26 [avatar split clause 126,262,247,252]
266. ~24 [avatar split clause 134,252]
301. ~12 [avatar split clause 145,198]
307. creative(sK5) <- (20) [resolution 148,237]
308. $false <- (11, 20) [subsumption resolution 307,195]
309. ~11 | ~20 [avatar contradiction clause 308]
310. calm(paul) <- (19) [resolution 150,233]
313. 23 | ~19 [avatar split clause 310,231,247]
314. $false <- (9, ~26) [subsumption resolution 264,187]
315. ~9 | 26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 201,202,238,265,266,301,309,313,315]
% SZS output end Proof for 7982548920583804729296151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is not humble. Everyone who is not kind or not tall is not patient or not calm. If john is both not creative and humble then lucy is curious and vice versa. Everyone who is both wise and old is happy. Everyone who is not creative is either not quiet or not old. Everyone who is both calm and brave is both not strong and funny. If fred is old or wise then someone is both not wise and not patient. If someone is not wise then john is creative and vice versa. Everyone who is both not creative and tall is both wise and not kind. If lucy is wise then someone is not patient or generous. If fred is both funny and not generous then lucy is both strong and not quiet and vice versa. If someone is either happy or not brave then someone is not humble and vice versa. Everyone who is either generous or not happy is either calm or not brave. If paul is both wise and tall then paul is both funny and not kind. Everyone who is quiet or old is not kind. Everyone who is either not generous or funny is either not creative or not kind and vice versa. Someone is either brave or curious. Someone is either curious or tall. Fred is not funny. Alice is not patient. Someone is either not brave or quiet. Alice is not wise or not quiet. Someone is calm. | Alice is quiet. | neutral | (![X]:(generous(X)=>~humble(X)))&
(![X]:((~kind(X)|~tall(X))=>(~patient(X)|~calm(X))))&
(((~creative(john)&humble(john)))<=>(curious(lucy)))&
(![X]:((wise(X)&old(X))=>happy(X)))&
(![X]:(~creative(X)=>(~quiet(X)<~>~old(X))))&
(![X]:((calm(X)&brave(X))=>(~strong(X)&funny(X))))&
(((old(fred)|wise(fred)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(~wise(X)))<=>(creative(john)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&~kind(X))))&
((wise(lucy))=>(?[X]:((~patient(X)|generous(X)))))&
(((funny(fred)&~generous(fred)))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:(~humble(X))))&
(![X]:((generous(X)<~>~happy(X))=>(calm(X)<~>~brave(X))))&
(((wise(paul)&tall(paul)))=>((funny(paul)&~kind(paul))))&
(![X]:((quiet(X)|old(X))=>~kind(X)))&
(![X]:((~generous(X)<~>funny(X))<=>(~creative(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(~funny(fred))&
(~patient(alice))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~wise(alice)|~quiet(alice)))&
(?[X]:(calm(X))) | quiet(alice) | [] | null | 0 |
Everyone who is not creative or tall is both old and not strong. Everyone who is not rich or not humble is both kind and not tall and vice versa. If fred is not old or not tall then someone is either tall or not rich. Everyone who is either rich or quiet is both kind and quiet. If someone is both not curious and calm then someone is curious or not generous. Everyone who is both kind and not rich is both rich and calm. Everyone who is either tall or not funny is brave or quiet and vice versa. Everyone who is both not old and not curious is both wise and patient and vice versa. If someone is either funny or not kind then mary is happy or not old and vice versa. If someone is tall then mary is not funny and vice versa. Everyone who is both generous and brave is either happy or not old and vice versa. If someone is patient or kind then alice is not creative. If someone is either not funny or not happy then alice is brave. Everyone who is both not patient and curious is curious or quiet. If susan is either funny or tall then alice is both patient and not rich and vice versa. Everyone who is not humble is not humble or not tall. Someone is both rich and not curious. Someone is not tall or brave. Someone is curious. Someone is either curious or wise. Someone is both not wise and not patient. Lucy is curious. Susan is not calm. John is both not kind and patient. | Alice is quiet. | entailment | (![X]:((~creative(X)|tall(X))=>(old(X)&~strong(X))))&
(![X]:((~rich(X)|~humble(X))<=>(kind(X)&~tall(X))))&
(((~old(fred)|~tall(fred)))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(kind(X)&quiet(X))))&
((?[X]:((~curious(X)&calm(X))))=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((kind(X)&~rich(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)|quiet(X))))&
(![X]:((~old(X)&~curious(X))<=>(wise(X)&patient(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((happy(mary)|~old(mary))))&
((?[X]:(tall(X)))<=>(~funny(mary)))&
(![X]:((generous(X)&brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((patient(X)|kind(X))))=>(~creative(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(brave(alice)))&
(![X]:((~patient(X)&curious(X))=>(curious(X)|quiet(X))))&
(((funny(susan)<~>tall(susan)))<=>((patient(alice)&~rich(alice))))&
(![X]:(~humble(X)=>(~humble(X)|~tall(X))))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((~wise(X)&~patient(X))))&
(curious(lucy))&
(~calm(susan))&
((~kind(john)&patient(john))) | quiet(alice) | [
"p1",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6506062548413753887515011
% SZS output start Proof for 6506062548413753887515011
2. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~tall(X0) & kind(X0))) [input p1]
4. ! [X0] : ((rich(X0) <~> quiet(X0)) => (quiet(X0) & kind(X0))) [input p3]
6. ! [X0] : ((~rich(X0) & kind(X0)) => (calm(X0) & rich(X0))) [input p5]
25. ~quiet(alice) [input hypothesis]
30. ! [X0] : ((quiet(X0) & kind(X0)) | (rich(X0) <=> quiet(X0))) [ennf transformation 4]
32. ! [X0] : ((calm(X0) & rich(X0)) | (rich(X0) | ~kind(X0))) [ennf transformation 6]
33. ! [X0] : ((calm(X0) & rich(X0)) | rich(X0) | ~kind(X0)) [flattening 32]
40. ! [X0] : (((~humble(X0) | ~rich(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | ~rich(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [flattening 40]
45. ! [X0] : ((quiet(X0) & kind(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) [nnf transformation 30]
80. kind(X0) | rich(X0) [cnf transformation 41]
91. quiet(X0) | quiet(X0) | ~rich(X0) [cnf transformation 45]
94. rich(X0) | rich(X0) | ~kind(X0) [cnf transformation 33]
144. ~quiet(alice) [cnf transformation 25]
145. rich(X0) | ~kind(X0) [duplicate literal removal 94]
146. ~rich(X0) | quiet(X0) [duplicate literal removal 91]
178. rich(X0) [subsumption resolution 145,80]
294. quiet(X0) [resolution 146,178]
306. $false [resolution 294,144]
% SZS output end Proof for 6506062548413753887515011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not tall is both not patient and not humble and vice versa. If john is both not old and tall then paul is funny or old and vice versa. Everyone who is not tall is either generous or not brave and vice versa. If alice is not kind then alice is either not rich or not creative. If someone is both curious and not happy then someone is not generous or patient and vice versa. Everyone who is patient or not creative is brave or not quiet. If someone is both calm and not humble then someone is tall or quiet. Everyone who is both quiet and not calm is not rich. Everyone who is either not patient or funny is not happy and vice versa. Everyone who is tall or curious is not rich or not strong. Everyone who is old is not tall or kind and vice versa. Everyone who is not rich is generous or not kind. Everyone who is both not quiet and humble is strong or funny. If lucy is both funny and generous then mary is not strong. If someone is either generous or happy then someone is both not calm and quiet. Everyone who is not quiet or not funny is brave or not creative. Someone is both humble and calm. Mary is either brave or generous. Someone is either not rich or not funny. Mary is either not generous or not kind. Alice is both not happy and not calm. Someone is not happy. Someone is not funny. Someone is both humble and kind. | Mary is generous. | neutral | (![X]:((~patient(X)|~tall(X))<=>(~patient(X)&~humble(X))))&
(((~old(john)&tall(john)))<=>((funny(paul)|old(paul))))&
(![X]:(~tall(X)<=>(generous(X)<~>~brave(X))))&
((~kind(alice))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((curious(X)&~happy(X))))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((patient(X)|~creative(X))=>(brave(X)|~quiet(X))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((quiet(X)&~calm(X))=>~rich(X)))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(![X]:((tall(X)|curious(X))=>(~rich(X)|~strong(X))))&
(![X]:(old(X)<=>(~tall(X)|kind(X))))&
(![X]:(~rich(X)=>(generous(X)|~kind(X))))&
(![X]:((~quiet(X)&humble(X))=>(strong(X)|funny(X))))&
(((funny(lucy)&generous(lucy)))=>(~strong(mary)))&
((?[X]:((generous(X)<~>happy(X))))=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((~quiet(X)|~funny(X))=>(brave(X)|~creative(X))))&
(?[X]:((humble(X)&calm(X))))&
((brave(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((~generous(mary)<~>~kind(mary)))&
((~happy(alice)&~calm(alice)))&
(?[X]:(~happy(X)))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)&kind(X)))) | generous(mary) | [] | null | 0 |
Everyone who is either not creative or not quiet is not tall or kind.
Everyone who is brave or not wise is not patient or funny.
Everyone who is both not funny and not happy is not funny.
Everyone who is not patient or not humble is both patient and not creative and vice versa.
If someone is not tall then someone is either not rich or rich and vice versa.
Everyone who is not kind or kind is not tall and vice versa.
If fred is either not curious or patient then john is not rich and vice versa.
Everyone who is either not creative or creative is both creative and curious and vice versa.
Everyone who is both strong and not curious is not patient or brave and vice versa.
If lucy is both not brave and rich then john is either quiet or not brave and vice versa.
Everyone who is both not quiet and tall is both not rich and generous.
Everyone who is both rich and humble is either not old or patient and vice versa.
If someone is patient or wise then lucy is either not old or not kind and vice versa.
If someone is either not calm or generous then someone is either old or creative.
Everyone who is either not funny or not creative is either not wise or quiet.
Everyone who is both not rich and not creative is both not calm and curious.
John is strong.
Someone is not tall or funny.
John is both not rich and calm.
Alice is both kind and old.
Someone is not funny or tall.
Mary is either not generous or calm.
Susan is brave or not generous. | John is not generous. | neutral | (![X]:((~creative(X)<~>~quiet(X))=>(~tall(X)|kind(X))))&
(![X]:((brave(X)|~wise(X))=>(~patient(X)|funny(X))))&
(![X]:((~funny(X)&~happy(X))=>~funny(X)))&
(![X]:((~patient(X)|~humble(X))<=>(patient(X)&~creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:((~kind(X)|kind(X))<=>~tall(X)))&
(((~curious(fred)<~>patient(fred)))<=>(~rich(john)))&
(![X]:((~creative(X)<~>creative(X))<=>(creative(X)&curious(X))))&
(![X]:((strong(X)&~curious(X))<=>(~patient(X)|brave(X))))&
(((~brave(lucy)&rich(lucy)))<=>((quiet(john)<~>~brave(john))))&
(![X]:((~quiet(X)&tall(X))=>(~rich(X)&generous(X))))&
(![X]:((rich(X)&humble(X))<=>(~old(X)<~>patient(X))))&
((?[X]:((patient(X)|wise(X))))<=>((~old(lucy)<~>~kind(lucy))))&
((?[X]:((~calm(X)<~>generous(X))))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~wise(X)<~>quiet(X))))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)&curious(X))))&
(strong(john))&
(?[X]:((~tall(X)|funny(X))))&
((~rich(john)&calm(john)))&
((kind(alice)&old(alice)))&
(?[X]:((~funny(X)|tall(X))))&
((~generous(mary)<~>calm(mary)))&
((brave(susan)|~generous(susan))) | ~generous(john) | [] | null | 0 |
If alice is either not quiet or not generous then fred is both not wise and not curious and vice versa. If alice is not rich then someone is either not humble or not curious and vice versa. Everyone who is both strong and not wise is either funny or happy and vice versa. If someone is both wise and happy then susan is not generous and vice versa. Everyone who is not curious is either not brave or not happy and vice versa. Everyone who is both humble and rich is either tall or funny. Everyone who is generous or curious is brave. Everyone who is either not quiet or not funny is calm or not generous. Everyone who is both quiet and generous is not old or not generous and vice versa. Everyone who is both not creative and not rich is either humble or kind. Everyone who is patient or not curious is either funny or not happy and vice versa. Everyone who is both not funny and not strong is funny. Everyone who is either curious or humble is old or not rich. If someone is funny or not creative then someone is not curious or not funny. If someone is not strong then someone is quiet or wise and vice versa. If susan is not wise or not funny then someone is both not wise and curious and vice versa. John is patient. Someone is not rich or not creative. Someone is not humble. John is not funny. Someone is both wise and not kind. Lucy is not wise. Paul is funny or not patient. | Susan is wise. | neutral | (((~quiet(alice)<~>~generous(alice)))<=>((~wise(fred)&~curious(fred))))&
((~rich(alice))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((strong(X)&~wise(X))<=>(funny(X)<~>happy(X))))&
((?[X]:((wise(X)&happy(X))))<=>(~generous(susan)))&
(![X]:(~curious(X)<=>(~brave(X)<~>~happy(X))))&
(![X]:((humble(X)&rich(X))=>(tall(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>brave(X)))&
(![X]:((~quiet(X)<~>~funny(X))=>(calm(X)|~generous(X))))&
(![X]:((quiet(X)&generous(X))<=>(~old(X)|~generous(X))))&
(![X]:((~creative(X)&~rich(X))=>(humble(X)<~>kind(X))))&
(![X]:((patient(X)|~curious(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((~funny(X)&~strong(X))=>funny(X)))&
(![X]:((curious(X)<~>humble(X))=>(old(X)|~rich(X))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:((~curious(X)|~funny(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((quiet(X)|wise(X)))))&
(((~wise(susan)|~funny(susan)))<=>(?[X]:((~wise(X)&curious(X)))))&
(patient(john))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(~humble(X)))&
(~funny(john))&
(?[X]:((wise(X)&~kind(X))))&
(~wise(lucy))&
((funny(paul)|~patient(paul))) | wise(susan) | [] | null | 0 |
If mary is not kind or not tall then mary is both not brave and funny and vice versa.
If someone is either strong or not happy then someone is not old and vice versa.
If someone is happy or not patient then fred is humble or funny.
If mary is either not creative or kind then someone is not strong and vice versa.
Everyone who is both not quiet and strong is not happy.
If someone is either not curious or brave then someone is not patient or not humble.
If someone is not calm or wise then john is both not wise and funny and vice versa.
If mary is brave or creative then lucy is not funny or calm.
Everyone who is funny is both not humble and funny and vice versa.
Everyone who is wise is either not generous or funny and vice versa.
Everyone who is both brave and happy is not rich or patient.
If someone is both not generous and not old then someone is both not quiet and not wise.
If mary is not calm or patient then someone is not happy or not patient and vice versa.
Everyone who is creative or not humble is generous or not wise and vice versa.
If alice is rich or not generous then mary is not brave.
If someone is quiet then someone is not humble.
Mary is both calm and not happy.
Susan is both old and brave.
Someone is patient.
Someone is not kind or old.
Alice is either not kind or old.
Someone is both patient and funny.
Mary is both humble and wise.
Paul is not humble or not patient. | Mary is creative. | contradiction | (((~kind(mary)|~tall(mary)))<=>((~brave(mary)&funny(mary))))&
((?[X]:((strong(X)<~>~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((happy(X)|~patient(X))))=>((humble(fred)|funny(fred))))&
(((~creative(mary)<~>kind(mary)))<=>(?[X]:(~strong(X))))&
(![X]:((~quiet(X)&strong(X))=>~happy(X)))&
((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((~patient(X)|~humble(X)))))&
((?[X]:((~calm(X)|wise(X))))<=>((~wise(john)&funny(john))))&
(((brave(mary)|creative(mary)))=>((~funny(lucy)|calm(lucy))))&
(![X]:(funny(X)<=>(~humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>funny(X))))&
(![X]:((brave(X)&happy(X))=>(~rich(X)|patient(X))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(((~calm(mary)|patient(mary)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((creative(X)|~humble(X))<=>(generous(X)|~wise(X))))&
(((rich(alice)|~generous(alice)))=>(~brave(mary)))&
((?[X]:(quiet(X)))=>(?[X]:(~humble(X))))&
((calm(mary)&~happy(mary)))&
((old(susan)&brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)|old(X))))&
((~kind(alice)<~>old(alice)))&
(?[X]:((patient(X)&funny(X))))&
((humble(mary)&wise(mary)))&
((~humble(paul)|~patient(paul))) | creative(mary) | [
"p8",
"p9",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1273600763398170142100061
% SZS output start Proof for 1273600763398170142100061
9. ! [X0] : (funny(X0) <=> (funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> (~generous(X0) <~> funny(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | creative(X0)) <=> (~wise(X0) | generous(X0))) [input p13]
23. wise(mary) & humble(mary) [input p22]
25. creative(mary) [input hypothesis]
62. ! [X0] : ((funny(X0) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [nnf transformation 9]
63. ! [X0] : ((funny(X0) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [flattening 62]
64. ! [X0] : ((wise(X0) | ((~generous(X0) | ~funny(X0)) & (funny(X0) | generous(X0)))) & (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | ~wise(X0))) [nnf transformation 10]
73. ! [X0] : (((~humble(X0) | creative(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (humble(X0) & ~creative(X0)))) [nnf transformation 14]
74. ! [X0] : ((~humble(X0) | creative(X0) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | (humble(X0) & ~creative(X0)))) [flattening 73]
110. ~humble(X0) | ~funny(X0) [cnf transformation 63]
113. ~generous(X0) | funny(X0) | ~wise(X0) [cnf transformation 64]
123. ~wise(X0) | generous(X0) | ~creative(X0) [cnf transformation 74]
139. humble(mary) [cnf transformation 23]
140. wise(mary) [cnf transformation 23]
142. creative(mary) [cnf transformation 25]
148. 2 <=> funny(mary) [avatar definition]
150. ~funny(mary) <- (~2) [avatar component clause 148]
209. 16 <=> creative(mary) [avatar definition]
211. creative(mary) <- (16) [avatar component clause 209]
351. 16 [avatar split clause 142,209]
352. ~funny(mary) [resolution 110,139]
357. ~2 [avatar split clause 352,148]
363. generous(mary) | ~creative(mary) [resolution 123,140]
364. generous(mary) <- (16) [subsumption resolution 363,211]
367. funny(mary) | ~wise(mary) <- (16) [resolution 364,113]
368. ~wise(mary) <- (~2, 16) [subsumption resolution 367,150]
369. $false <- (~2, 16) [subsumption resolution 368,140]
370. 2 | ~16 [avatar contradiction clause 369]
371. $false [avatar sat refutation 351,357,370]
% SZS output end Proof for 1273600763398170142100061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or kind is not tall. If paul is both not strong and generous then someone is either curious or not patient and vice versa. If john is either calm or generous then someone is quiet or tall and vice versa. If someone is both not calm and patient then paul is not tall. Everyone who is both not funny and creative is happy or not happy. If someone is either generous or not quiet then someone is either happy or humble and vice versa. If john is either quiet or not quiet then someone is not calm or not brave. Everyone who is both not creative and not old is tall. Everyone who is either creative or not rich is both quiet and not wise. Everyone who is either not wise or strong is either creative or patient. Everyone who is not brave is curious or old. If someone is both old and wise then lucy is either creative or not brave. If someone is calm then someone is happy or not wise and vice versa. Everyone who is not patient or strong is both quiet and not funny and vice versa. If someone is not tall then john is both not brave and not creative. Everyone who is not wise or rich is both funny and not curious. Lucy is either not brave or not wise. Someone is both old and funny. Someone is not strong or not quiet. John is both not tall and not brave. Someone is either not creative or curious. Fred is not creative. Someone is either strong or not old. Someone is not brave. | John is not strong. | entailment | (![X]:((tall(X)<~>kind(X))=>~tall(X)))&
(((~strong(paul)&generous(paul)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(((calm(john)<~>generous(john)))<=>(?[X]:((quiet(X)|tall(X)))))&
((?[X]:((~calm(X)&patient(X))))=>(~tall(paul)))&
(![X]:((~funny(X)&creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(?[X]:((happy(X)<~>humble(X)))))&
(((quiet(john)<~>~quiet(john)))=>(?[X]:((~calm(X)|~brave(X)))))&
(![X]:((~creative(X)&~old(X))=>tall(X)))&
(![X]:((creative(X)<~>~rich(X))=>(quiet(X)&~wise(X))))&
(![X]:((~wise(X)<~>strong(X))=>(creative(X)<~>patient(X))))&
(![X]:(~brave(X)=>(curious(X)|old(X))))&
((?[X]:((old(X)&wise(X))))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:((~patient(X)|strong(X))<=>(quiet(X)&~funny(X))))&
((?[X]:(~tall(X)))=>((~brave(john)&~creative(john))))&
(![X]:((~wise(X)|rich(X))=>(funny(X)&~curious(X))))&
((~brave(lucy)<~>~wise(lucy)))&
(?[X]:((old(X)&funny(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
((~tall(john)&~brave(john)))&
(?[X]:((~creative(X)<~>curious(X))))&
(~creative(fred))&
(?[X]:((strong(X)<~>~old(X))))&
(?[X]:(~brave(X))) | ~strong(john) | [
"p8",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6400371239204840069319102
% SZS output start Proof for 6400371239204840069319102
9. ! [X0] : ((creative(X0) <~> ~rich(X0)) => (~wise(X0) & quiet(X0))) [input p8]
14. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~funny(X0) & quiet(X0))) [input p13]
15. ? [X0] : ~tall(X0) => (~creative(john) & ~brave(john)) [input p14]
16. ! [X0] : ((rich(X0) | ~wise(X0)) => (~curious(X0) & funny(X0))) [input p15]
20. ~brave(john) & ~tall(john) [input p19]
25. strong(john) [input hypothesis]
35. ! [X0] : ((~wise(X0) & quiet(X0)) | (creative(X0) <=> ~rich(X0))) [ennf transformation 9]
40. (~creative(john) & ~brave(john)) | ! [X0] : tall(X0) [ennf transformation 15]
41. ! [X0] : ((~curious(X0) & funny(X0)) | (~rich(X0) & wise(X0))) [ennf transformation 16]
60. ! [X0] : ((~wise(X0) & quiet(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 35]
68. ! [X0] : (((strong(X0) | ~patient(X0)) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 14]
69. ! [X0] : ((strong(X0) | ~patient(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | (~strong(X0) & patient(X0)))) [flattening 68]
113. ~wise(X0) | creative(X0) | rich(X0) [cnf transformation 60]
127. ~funny(X0) | ~strong(X0) [cnf transformation 69]
130. ~creative(john) | tall(X0) [cnf transformation 40]
131. wise(X0) | funny(X0) [cnf transformation 41]
132. ~rich(X0) | funny(X0) [cnf transformation 41]
140. ~tall(john) [cnf transformation 20]
148. strong(john) [cnf transformation 25]
304. 35 <=> ! [X0] : tall(X0) [avatar definition]
305. tall(X0) <- (35) [avatar component clause 304]
307. 36 <=> creative(john) [avatar definition]
309. ~creative(john) <- (~36) [avatar component clause 307]
310. 35 | ~36 [avatar split clause 130,307,304]
385. creative(X0) | rich(X0) | funny(X0) [resolution 113,131]
387. creative(X0) | funny(X0) [subsumption resolution 385,132]
430. funny(john) <- (~36) [resolution 387,309]
450. ~strong(john) <- (~36) [resolution 430,127]
452. $false <- (~36) [subsumption resolution 450,148]
453. 36 [avatar contradiction clause 452]
456. $false <- (35) [resolution 305,140]
460. ~35 [avatar contradiction clause 456]
461. $false [avatar sat refutation 310,453,460]
% SZS output end Proof for 6400371239204840069319102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not happy is either wise or not old and vice versa. Everyone who is both not tall and generous is generous and vice versa. If someone is either not quiet or not patient then alice is not creative and vice versa. Everyone who is not generous is both not patient and not humble. Everyone who is both not funny and funny is both not patient and patient and vice versa. Everyone who is either quiet or not old is either not tall or rich. Everyone who is not quiet or generous is kind or not old and vice versa. Everyone who is both generous and not creative is rich or not funny and vice versa. If mary is both creative and not patient then someone is either not generous or patient and vice versa. Everyone who is both rich and not humble is not rich or not funny. Everyone who is wise is not strong and vice versa. If lucy is funny then fred is kind and vice versa. Everyone who is brave or happy is either happy or not humble and vice versa. If alice is not funny or humble then someone is either calm or not old. Everyone who is both old and rich is brave and vice versa. Alice is happy or curious. Someone is both calm and old. Someone is either strong or humble. Someone is not generous or not tall. Someone is either not brave or not quiet. Mary is both creative and generous. John is either rich or not calm. Mary is either not tall or not happy. | John is funny. | neutral | (![X]:((strong(X)&~happy(X))<=>(wise(X)<~>~old(X))))&
(![X]:((~tall(X)&generous(X))<=>generous(X)))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(~creative(alice)))&
(![X]:(~generous(X)=>(~patient(X)&~humble(X))))&
(![X]:((~funny(X)&funny(X))<=>(~patient(X)&patient(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~tall(X)<~>rich(X))))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)|~old(X))))&
(![X]:((generous(X)&~creative(X))<=>(rich(X)|~funny(X))))&
(((creative(mary)&~patient(mary)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(![X]:((rich(X)&~humble(X))=>(~rich(X)|~funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
((funny(lucy))<=>(kind(fred)))&
(![X]:((brave(X)|happy(X))<=>(happy(X)<~>~humble(X))))&
(((~funny(alice)|humble(alice)))=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:((old(X)&rich(X))<=>brave(X)))&
((happy(alice)|curious(alice)))&
(?[X]:((calm(X)&old(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((creative(mary)&generous(mary)))&
((rich(john)<~>~calm(john)))&
((~tall(mary)<~>~happy(mary))) | funny(john) | [] | null | 0 |
Everyone who is not tall or not brave is not old. Everyone who is both not brave and patient is not quiet and vice versa. Everyone who is both not tall and happy is both rich and tall. If someone is both not happy and old then someone is either humble or generous. If someone is curious or rich then someone is both rich and not generous and vice versa. If someone is either generous or wise then someone is curious. If someone is not curious then someone is not humble or old. If fred is both generous and not old then mary is brave or curious and vice versa. Everyone who is not old is either not happy or not wise and vice versa. If fred is both not calm and not old then someone is happy and vice versa. If john is either wise or happy then alice is old or strong. Everyone who is both not kind and not tall is not funny or brave. If mary is both kind and curious then alice is not wise or curious. Everyone who is either not patient or not brave is either not rich or not calm. If mary is both strong and creative then someone is both patient and not generous and vice versa. If fred is both creative and not quiet then someone is not old. Someone is not kind. Someone is humble or rich. Someone is not funny. Alice is not kind or tall. John is not funny or funny. Someone is humble or generous. Someone is wise or not quiet. Fred is brave or not calm. | Alice is wise. | neutral | (![X]:((~tall(X)|~brave(X))=>~old(X)))&
(![X]:((~brave(X)&patient(X))<=>~quiet(X)))&
(![X]:((~tall(X)&happy(X))=>(rich(X)&tall(X))))&
((?[X]:((~happy(X)&old(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((?[X]:((curious(X)|rich(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
((?[X]:((generous(X)<~>wise(X))))=>(?[X]:(curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~humble(X)|old(X)))))&
(((generous(fred)&~old(fred)))<=>((brave(mary)|curious(mary))))&
(![X]:(~old(X)<=>(~happy(X)<~>~wise(X))))&
(((~calm(fred)&~old(fred)))<=>(?[X]:(happy(X))))&
(((wise(john)<~>happy(john)))=>((old(alice)|strong(alice))))&
(![X]:((~kind(X)&~tall(X))=>(~funny(X)|brave(X))))&
(((kind(mary)&curious(mary)))=>((~wise(alice)|curious(alice))))&
(![X]:((~patient(X)<~>~brave(X))=>(~rich(X)<~>~calm(X))))&
(((strong(mary)&creative(mary)))<=>(?[X]:((patient(X)&~generous(X)))))&
(((creative(fred)&~quiet(fred)))=>(?[X]:(~old(X))))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:(~funny(X)))&
((~kind(alice)|tall(alice)))&
((~funny(john)|funny(john)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((wise(X)|~quiet(X))))&
((brave(fred)|~calm(fred))) | wise(alice) | [] | null | 0 |
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Everyone who is either not quiet or curious is kind and vice versa.
If someone is not quiet then someone is both not old and patient.
If paul is not calm then susan is not strong.
Everyone who is either not curious or not strong is both kind and not happy and vice versa.
Everyone who is both not kind and strong is wise or not rich and vice versa.
Everyone who is not happy or not funny is either curious or quiet.
If mary is both strong and not tall then someone is both strong and creative and vice versa.
Everyone who is either humble or tall is either old or rich.
Everyone who is either happy or not old is either old or not old.
Everyone who is either generous or wise is both humble and not happy.
If someone is funny or calm then someone is both rich and not patient.
Someone is not humble or old.
Fred is either wise or not funny.
John is creative.
Paul is not kind or not rich. | Paul is not strong. | neutral | (![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>kind(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((~old(X)&patient(X)))))&
((~calm(paul))=>(~strong(susan)))&
(![X]:((~curious(X)<~>~strong(X))<=>(kind(X)&~happy(X))))&
(![X]:((~kind(X)&strong(X))<=>(wise(X)|~rich(X))))&
(![X]:((~happy(X)|~funny(X))=>(curious(X)<~>quiet(X))))&
(((strong(mary)&~tall(mary)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((humble(X)<~>tall(X))=>(old(X)<~>rich(X))))&
(![X]:((happy(X)<~>~old(X))=>(old(X)<~>~old(X))))&
(![X]:((generous(X)<~>wise(X))=>(humble(X)&~happy(X))))&
((?[X]:((funny(X)|calm(X))))=>(?[X]:((rich(X)&~patient(X)))))&
(?[X]:((~humble(X)|old(X))))&
((wise(fred)<~>~funny(fred)))&
(creative(john))&
((~kind(paul)|~rich(paul))) | ~strong(paul) | [] | null | 0 |
Everyone who is either rich or not kind is not humble and vice versa.
If mary is not humble then someone is both creative and not creative.
If susan is quiet or not kind then lucy is not tall or not rich and vice versa.
Everyone who is either not creative or old is wise and vice versa.
Everyone who is creative is either not humble or not tall.
If susan is both not calm and quiet then john is both tall and not old.
If alice is kind or not patient then someone is happy or not happy.
Everyone who is either not curious or creative is either generous or brave.
If someone is not old then someone is both not calm and curious and vice versa.
Everyone who is both old and happy is generous or not old and vice versa.
Everyone who is funny or brave is not quiet or not funny and vice versa.
Everyone who is either not tall or not strong is either not old or calm.
Everyone who is funny is old.
Everyone who is both patient and not generous is either not happy or old.
If lucy is either not brave or not happy then fred is calm.
If susan is rich then someone is either not funny or not strong.
Lucy is happy.
Someone is both humble and not tall.
Someone is not old or happy.
Susan is kind.
Mary is old.
John is both not quiet and not tall.
Paul is not happy or not rich. | Fred is not old. | contradiction | (![X]:((rich(X)<~>~kind(X))<=>~humble(X)))&
((~humble(mary))=>(?[X]:((creative(X)&~creative(X)))))&
(((quiet(susan)|~kind(susan)))<=>((~tall(lucy)|~rich(lucy))))&
(![X]:((~creative(X)<~>old(X))<=>wise(X)))&
(![X]:(creative(X)=>(~humble(X)<~>~tall(X))))&
(((~calm(susan)&quiet(susan)))=>((tall(john)&~old(john))))&
(((kind(alice)|~patient(alice)))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(generous(X)<~>brave(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:((old(X)&happy(X))<=>(generous(X)|~old(X))))&
(![X]:((funny(X)|brave(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~old(X)<~>calm(X))))&
(![X]:(funny(X)=>old(X)))&
(![X]:((patient(X)&~generous(X))=>(~happy(X)<~>old(X))))&
(((~brave(lucy)<~>~happy(lucy)))=>(calm(fred)))&
((rich(susan))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(happy(lucy))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((~old(X)|happy(X))))&
(kind(susan))&
(old(mary))&
((~quiet(john)&~tall(john)))&
((~happy(paul)|~rich(paul))) | ~old(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5610257047998147782769229
% SZS output start Proof for 5610257047998147782769229
10. ! [X0] : ((happy(X0) & old(X0)) <=> (~old(X0) | generous(X0))) [input p9]
24. ~old(fred) [input hypothesis]
52. ! [X0] : (((happy(X0) & old(X0)) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 10]
53. ! [X0] : (((happy(X0) & old(X0)) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~happy(X0) | ~old(X0))) [flattening 52]
91. old(X0) | old(X0) [cnf transformation 53]
118. ~old(fred) [cnf transformation 24]
122. old(X0) [duplicate literal removal 91]
176. 12 <=> ! [X3] : old(X3) [avatar definition]
177. old(X3) <- (12) [avatar component clause 176]
188. 12 [avatar split clause 122,176]
236. $false <- (12) [resolution 177,118]
237. ~12 [avatar contradiction clause 236]
238. $false [avatar sat refutation 188,237]
% SZS output end Proof for 5610257047998147782769229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not tall or not brave then someone is not patient and vice versa.
Everyone who is tall or funny is both not creative and not wise.
If fred is either calm or kind then someone is not calm or not tall and vice versa.
Everyone who is both not patient and not strong is patient or not curious and vice versa.
If someone is not old then alice is not generous or not patient.
If susan is not quiet then lucy is either tall or happy and vice versa.
If someone is generous or not old then someone is either funny or not brave and vice versa.
If alice is not rich or tall then someone is not brave and vice versa.
Everyone who is either not old or not rich is both brave and not rich and vice versa.
Everyone who is both curious and not kind is both not calm and not happy and vice versa.
Everyone who is rich or curious is not tall or wise and vice versa.
If someone is happy or tall then alice is rich and vice versa.
If someone is both calm and old then someone is patient.
If mary is wise or happy then susan is funny and vice versa.
If someone is funny then john is either not humble or old and vice versa.
If lucy is either not humble or humble then alice is happy.
Alice is either brave or tall.
Alice is old or brave.
Someone is either patient or generous.
Susan is not strong or not rich.
Someone is not creative.
Someone is not quiet.
Someone is quiet or not strong.
Lucy is humble or not kind. | Fred is not kind. | contradiction | (((~tall(mary)<~>~brave(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((tall(X)|funny(X))=>(~creative(X)&~wise(X))))&
(((calm(fred)<~>kind(fred)))<=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:((~patient(X)&~strong(X))<=>(patient(X)|~curious(X))))&
((?[X]:(~old(X)))=>((~generous(alice)|~patient(alice))))&
((~quiet(susan))<=>((tall(lucy)<~>happy(lucy))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(((~rich(alice)|tall(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(brave(X)&~rich(X))))&
(![X]:((curious(X)&~kind(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)|curious(X))<=>(~tall(X)|wise(X))))&
((?[X]:((happy(X)|tall(X))))<=>(rich(alice)))&
((?[X]:((calm(X)&old(X))))=>(?[X]:(patient(X))))&
(((wise(mary)|happy(mary)))<=>(funny(susan)))&
((?[X]:(funny(X)))<=>((~humble(john)<~>old(john))))&
(((~humble(lucy)<~>humble(lucy)))=>(happy(alice)))&
((brave(alice)<~>tall(alice)))&
((old(alice)|brave(alice)))&
(?[X]:((patient(X)<~>generous(X))))&
((~strong(susan)|~rich(susan)))&
(?[X]:(~creative(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)|~strong(X))))&
((humble(lucy)|~kind(lucy))) | ~kind(fred) | [
"p1",
"p2",
"p3",
"p7",
"p8",
"p10",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7072127692074501231521368
% SZS output start Proof for 7072127692074501231521368
2. ! [X0] : ((funny(X0) | tall(X0)) => (~wise(X0) & ~creative(X0))) [input p1]
3. (calm(fred) <~> kind(fred)) <=> ? [X0] : (~tall(X0) | ~calm(X0)) [input p2]
4. ! [X0] : ((~strong(X0) & ~patient(X0)) <=> (~curious(X0) | patient(X0))) [input p3]
8. (tall(alice) | ~rich(alice)) <=> ? [X0] : ~brave(X0) [input p7]
9. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (~rich(X0) & brave(X0))) [input p8]
11. ! [X0] : ((curious(X0) | rich(X0)) <=> (wise(X0) | ~tall(X0))) [input p10]
12. ? [X0] : (tall(X0) | happy(X0)) <=> rich(alice) [input p11]
13. ? [X0] : (old(X0) & calm(X0)) => ? [X0] : patient(X0) [input p12]
16. (~humble(lucy) <~> humble(lucy)) => happy(alice) [input p15]
25. ~kind(fred) [input hypothesis]
27. ? [X0] : (old(X0) & calm(X0)) => ? [X1] : patient(X1) [rectify 13]
28. ! [X0] : ((funny(X0) | tall(X0)) => ~wise(X0)) [pure predicate removal 2]
30. ! [X0] : (~wise(X0) | (~funny(X0) & ~tall(X0))) [ennf transformation 28]
33. ? [X1] : patient(X1) | ! [X0] : (~old(X0) | ~calm(X0)) [ennf transformation 27]
34. happy(alice) | (~humble(lucy) <=> humble(lucy)) [ennf transformation 16]
39. (((~kind(fred) | ~calm(fred)) & (kind(fred) | calm(fred))) | ! [X0] : (tall(X0) & calm(X0))) & (? [X0] : (~tall(X0) | ~calm(X0)) | ((calm(fred) | ~kind(fred)) & (kind(fred) | ~calm(fred)))) [nnf transformation 3]
40. (((~kind(fred) | ~calm(fred)) & (kind(fred) | calm(fred))) | ! [X0] : (tall(X0) & calm(X0))) & (? [X1] : (~tall(X1) | ~calm(X1)) | ((calm(fred) | ~kind(fred)) & (kind(fred) | ~calm(fred)))) [rectify 39]
41. ? [X1] : (~tall(X1) | ~calm(X1)) => (~tall(sK1) | ~calm(sK1)) [choice axiom]
42. (((~kind(fred) | ~calm(fred)) & (kind(fred) | calm(fred))) | ! [X0] : (tall(X0) & calm(X0))) & ((~tall(sK1) | ~calm(sK1)) | ((calm(fred) | ~kind(fred)) & (kind(fred) | ~calm(fred)))) [skolemisation 40,41]
43. ! [X0] : (((~strong(X0) & ~patient(X0)) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | (strong(X0) | patient(X0)))) [nnf transformation 4]
44. ! [X0] : (((~strong(X0) & ~patient(X0)) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | strong(X0) | patient(X0))) [flattening 43]
51. ((tall(alice) | ~rich(alice)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~tall(alice) & rich(alice))) [nnf transformation 8]
52. (tall(alice) | ~rich(alice) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~tall(alice) & rich(alice))) [flattening 51]
53. (tall(alice) | ~rich(alice) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | (~tall(alice) & rich(alice))) [rectify 52]
54. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
55. (tall(alice) | ~rich(alice) | ! [X0] : brave(X0)) & (~brave(sK4) | (~tall(alice) & rich(alice))) [skolemisation 53,54]
56. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (rich(X0) | ~brave(X0))) & ((~rich(X0) & brave(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 9]
57. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | rich(X0) | ~brave(X0)) & ((~rich(X0) & brave(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 56]
60. ! [X0] : (((curious(X0) | rich(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 11]
61. ! [X0] : ((curious(X0) | rich(X0) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | (~curious(X0) & ~rich(X0)))) [flattening 60]
62. (? [X0] : (tall(X0) | happy(X0)) | ~rich(alice)) & (rich(alice) | ! [X0] : (~tall(X0) & ~happy(X0))) [nnf transformation 12]
63. (? [X0] : (tall(X0) | happy(X0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (~tall(X1) & ~happy(X1))) [rectify 62]
64. ? [X0] : (tall(X0) | happy(X0)) => (tall(sK5) | happy(sK5)) [choice axiom]
65. ((tall(sK5) | happy(sK5)) | ~rich(alice)) & (rich(alice) | ! [X1] : (~tall(X1) & ~happy(X1))) [skolemisation 63,64]
66. ? [X0] : patient(X0) | ! [X1] : (~old(X1) | ~calm(X1)) [rectify 33]
67. ? [X0] : patient(X0) => patient(sK6) [choice axiom]
68. patient(sK6) | ! [X1] : (~old(X1) | ~calm(X1)) [skolemisation 66,67]
75. happy(alice) | ((~humble(lucy) | ~humble(lucy)) & (humble(lucy) | humble(lucy))) [nnf transformation 34]
88. ~wise(X0) | ~tall(X0) [cnf transformation 30]
92. kind(fred) | calm(fred) | calm(X0) [cnf transformation 42]
97. ~patient(X0) | ~patient(X0) [cnf transformation 44]
114. tall(alice) | ~rich(alice) | brave(X0) [cnf transformation 55]
117. ~rich(X0) | ~rich(X0) | old(X0) [cnf transformation 57]
120. rich(X0) | old(X0) | rich(X0) | ~brave(X0) [cnf transformation 57]
125. wise(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 61]
129. rich(alice) | ~happy(X1) [cnf transformation 65]
132. patient(sK6) | ~old(X1) | ~calm(X1) [cnf transformation 68]
140. happy(alice) | humble(lucy) | humble(lucy) [cnf transformation 75]
141. happy(alice) | ~humble(lucy) | ~humble(lucy) [cnf transformation 75]
151. ~kind(fred) [cnf transformation 25]
152. happy(alice) | humble(lucy) [duplicate literal removal 140]
153. happy(alice) | ~humble(lucy) [duplicate literal removal 141]
154. ~rich(X0) | old(X0) [duplicate literal removal 117]
155. ~brave(X0) | old(X0) | rich(X0) [duplicate literal removal 120]
157. ~patient(X0) [duplicate literal removal 97]
181. 6 <=> calm(fred) [avatar definition]
182. calm(fred) <- (6) [avatar component clause 181]
185. 7 <=> kind(fred) [avatar definition]
190. 8 <=> ! [X0] : calm(X0) [avatar definition]
191. calm(X0) <- (8) [avatar component clause 190]
194. 8 | 6 | 7 [avatar split clause 92,185,181,190]
239. 18 <=> ! [X3] : old(X3) [avatar definition]
240. old(X3) <- (18) [avatar component clause 239]
257. 22 <=> ! [X0] : brave(X0) [avatar definition]
258. brave(X0) <- (22) [avatar component clause 257]
260. 23 <=> rich(alice) [avatar definition]
261. rich(alice) <- (23) [avatar component clause 260]
264. 24 <=> tall(alice) [avatar definition]
267. 22 | ~23 | 24 [avatar split clause 114,264,260,257]
275. ~rich(X0) | ~tall(X0) [subsumption resolution 125,88]
290. 29 <=> ! [X1] : ~happy(X1) [avatar definition]
291. ~happy(X1) <- (29) [avatar component clause 290]
292. 29 | 23 [avatar split clause 129,260,290]
293. ~old(X1) | ~calm(X1) [subsumption resolution 132,157]
329. 37 <=> humble(lucy) [avatar definition]
333. 38 <=> happy(alice) [avatar definition]
335. happy(alice) <- (38) [avatar component clause 333]
336. ~37 | 38 [avatar split clause 153,333,329]
337. 37 | 38 [avatar split clause 152,333,329]
373. ~7 [avatar split clause 151,185]
380. $false <- (29, 38) [resolution 335,291]
381. ~29 | ~38 [avatar contradiction clause 380]
386. ~tall(alice) <- (23) [resolution 275,261]
437. old(X0) | rich(X0) <- (22) [resolution 155,258]
440. old(X0) <- (22) [subsumption resolution 437,154]
441. 18 | ~22 [avatar split clause 440,257,239]
452. ~24 | ~23 [avatar split clause 386,260,264]
454. ~calm(X1) <- (18) [resolution 240,293]
471. $false <- (6, 18) [resolution 454,182]
476. ~6 | ~18 [avatar contradiction clause 471]
477. $false <- (8, 18) [subsumption resolution 191,454]
478. ~8 | ~18 [avatar contradiction clause 477]
479. $false [avatar sat refutation 194,267,292,336,337,373,381,441,452,476,478]
% SZS output end Proof for 7072127692074501231521368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is brave then someone is not happy or not calm and vice versa.
Everyone who is not creative or not wise is both not old and happy and vice versa.
Everyone who is either not strong or generous is not patient.
If someone is patient or calm then someone is old.
Everyone who is calm or strong is kind and vice versa.
If someone is either not strong or tall then someone is either not funny or brave and vice versa.
If susan is kind or tall then susan is not strong and vice versa.
If someone is both calm and kind then someone is both not generous and not curious and vice versa.
Everyone who is not humble or strong is both quiet and not calm.
Everyone who is not strong is brave or not old.
Everyone who is not strong or happy is not quiet and vice versa.
If someone is not happy or strong then someone is both creative and not tall and vice versa.
If someone is both not funny and creative then someone is both wise and tall and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is both rich and patient is wise or curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not humble.
Fred is not calm.
Someone is either not wise or curious.
Someone is either calm or not rich.
Alice is both quiet and not brave.
Someone is both not funny and not brave.
Someone is calm.
Someone is either wise or humble.
Susan is both not rich and tall. | Mary is generous. | neutral | ((brave(mary))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~creative(X)|~wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~strong(X)<~>generous(X))=>~patient(X)))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(((kind(susan)|tall(susan)))<=>(~strong(susan)))&
((?[X]:((calm(X)&kind(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((~humble(X)|strong(X))=>(quiet(X)&~calm(X))))&
(![X]:(~strong(X)=>(brave(X)|~old(X))))&
(![X]:((~strong(X)|happy(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:((rich(X)&patient(X))<=>(wise(X)|curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>(funny(X)<~>~humble(X))))&
(~calm(fred))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((quiet(alice)&~brave(alice)))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
((~rich(susan)&tall(susan))) | generous(mary) | [] | null | 0 |
Everyone who is either rich or funny is either not happy or not funny and vice versa.
Everyone who is either not happy or quiet is not kind or curious.
Everyone who is both not calm and not funny is rich or not old and vice versa.
If john is either not tall or not calm then someone is humble or funny and vice versa.
If mary is curious or creative then someone is humble and vice versa.
Everyone who is both not generous and not creative is tall or not generous.
Everyone who is not humble is not strong or not rich and vice versa.
If someone is both kind and not creative then someone is rich.
Everyone who is curious is either brave or not quiet.
If susan is both generous and not kind then lucy is funny or strong and vice versa.
If someone is both not tall and not calm then someone is both wise and quiet and vice versa.
Everyone who is happy is both calm and old.
Everyone who is either quiet or not happy is both not happy and not rich.
If someone is not happy or creative then fred is not funny or not rich.
Everyone who is both not kind and not tall is either creative or curious and vice versa.
If someone is not brave or not humble then someone is not happy and vice versa.
Lucy is not tall.
Mary is both not funny and not patient.
Lucy is either not tall or brave.
Someone is tall or not brave.
Someone is either not kind or not old.
Someone is either kind or not old. | Lucy is humble. | contradiction | (![X]:((rich(X)<~>funny(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(~kind(X)|curious(X))))&
(![X]:((~calm(X)&~funny(X))<=>(rich(X)|~old(X))))&
(((~tall(john)<~>~calm(john)))<=>(?[X]:((humble(X)|funny(X)))))&
(((curious(mary)|creative(mary)))<=>(?[X]:(humble(X))))&
(![X]:((~generous(X)&~creative(X))=>(tall(X)|~generous(X))))&
(![X]:(~humble(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((kind(X)&~creative(X))))=>(?[X]:(rich(X))))&
(![X]:(curious(X)=>(brave(X)<~>~quiet(X))))&
(((generous(susan)&~kind(susan)))<=>((funny(lucy)|strong(lucy))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((wise(X)&quiet(X)))))&
(![X]:(happy(X)=>(calm(X)&old(X))))&
(![X]:((quiet(X)<~>~happy(X))=>(~happy(X)&~rich(X))))&
((?[X]:((~happy(X)|creative(X))))=>((~funny(fred)|~rich(fred))))&
(![X]:((~kind(X)&~tall(X))<=>(creative(X)<~>curious(X))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:(~happy(X))))&
(~tall(lucy))&
((~funny(mary)&~patient(mary)))&
((~tall(lucy)<~>brave(lucy)))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((kind(X)<~>~old(X)))) | humble(lucy) | [
"p0",
"p2",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 340962486777813263597716
% SZS output start Proof for 340962486777813263597716
1. ! [X0] : ((rich(X0) <~> funny(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p0]
3. ! [X0] : ((~funny(X0) & ~calm(X0)) <=> (~old(X0) | rich(X0))) [input p2]
7. ! [X0] : (~humble(X0) <=> (~rich(X0) | ~strong(X0))) [input p6]
12. ! [X0] : (happy(X0) => (old(X0) & calm(X0))) [input p11]
23. humble(lucy) [input hypothesis]
34. ! [X0] : ((old(X0) & calm(X0)) | ~happy(X0)) [ennf transformation 12]
38. ! [X0] : ((((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0))))) [nnf transformation 1]
40. ! [X0] : (((~funny(X0) & ~calm(X0)) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | (funny(X0) | calm(X0)))) [nnf transformation 3]
41. ! [X0] : (((~funny(X0) & ~calm(X0)) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | funny(X0) | calm(X0))) [flattening 40]
51. ! [X0] : ((~humble(X0) | (rich(X0) & strong(X0))) & ((~rich(X0) | ~strong(X0)) | humble(X0))) [nnf transformation 7]
52. ! [X0] : ((~humble(X0) | (rich(X0) & strong(X0))) & (~rich(X0) | ~strong(X0) | humble(X0))) [flattening 51]
83. funny(X0) | happy(X0) | funny(X0) | ~rich(X0) [cnf transformation 38]
87. ~funny(X0) | ~rich(X0) | ~funny(X0) | happy(X0) [cnf transformation 38]
92. ~calm(X0) | ~rich(X0) [cnf transformation 41]
108. ~humble(X0) | rich(X0) [cnf transformation 52]
121. ~happy(X0) | calm(X0) [cnf transformation 34]
147. humble(lucy) [cnf transformation 23]
150. funny(X0) | happy(X0) | ~rich(X0) [duplicate literal removal 83]
152. ~funny(X0) | ~rich(X0) | happy(X0) [duplicate literal removal 87]
153. ~rich(X0) | happy(X0) [subsumption resolution 150,152]
316. rich(lucy) [resolution 108,147]
319. happy(lucy) [resolution 153,316]
336. calm(lucy) [resolution 319,121]
373. ~rich(lucy) [resolution 336,92]
374. $false [subsumption resolution 373,316]
% SZS output end Proof for 340962486777813263597716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not humble is either calm or not creative.
Everyone who is both not funny and not quiet is calm or funny and vice versa.
Everyone who is wise is not kind.
If someone is happy or calm then someone is both calm and old.
Everyone who is either not wise or funny is quiet or curious.
Everyone who is both not brave and not tall is both tall and not patient and vice versa.
Everyone who is both not humble and happy is not happy and vice versa.
If someone is either creative or not patient then someone is either not tall or funny.
If mary is quiet then someone is either not patient or not humble.
Everyone who is creative is not tall or not patient.
Everyone who is either not curious or creative is both generous and kind and vice versa.
If paul is both old and not brave then john is funny or kind and vice versa.
If someone is not humble or funny then someone is not funny or brave.
Everyone who is either wise or strong is curious or not generous and vice versa.
If someone is humble or old then mary is not happy or wise.
Someone is not humble or patient.
Someone is calm or creative.
Someone is brave or not quiet.
Paul is patient or not kind.
John is either wise or not strong.
Someone is tall or not curious.
Someone is not brave or curious. | Mary is not quiet. | neutral | (![X]:((~tall(X)&~humble(X))=>(calm(X)<~>~creative(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(calm(X)|funny(X))))&
(![X]:(wise(X)=>~kind(X)))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((calm(X)&old(X)))))&
(![X]:((~wise(X)<~>funny(X))=>(quiet(X)|curious(X))))&
(![X]:((~brave(X)&~tall(X))<=>(tall(X)&~patient(X))))&
(![X]:((~humble(X)&happy(X))<=>~happy(X)))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>funny(X)))))&
((quiet(mary))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(![X]:(creative(X)=>(~tall(X)|~patient(X))))&
(![X]:((~curious(X)<~>creative(X))<=>(generous(X)&kind(X))))&
(((old(paul)&~brave(paul)))<=>((funny(john)|kind(john))))&
((?[X]:((~humble(X)|funny(X))))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((wise(X)<~>strong(X))<=>(curious(X)|~generous(X))))&
((?[X]:((humble(X)|old(X))))=>((~happy(mary)|wise(mary))))&
(?[X]:((~humble(X)|patient(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((patient(paul)|~kind(paul)))&
((wise(john)<~>~strong(john)))&
(?[X]:((tall(X)|~curious(X))))&
(?[X]:((~brave(X)|curious(X)))) | ~quiet(mary) | [] | null | 0 |
Everyone who is not funny is both calm and not funny and vice versa.
If fred is not quiet or patient then john is creative and vice versa.
If john is not calm or not patient then mary is not happy or not old and vice versa.
If someone is either kind or humble then alice is creative and vice versa.
Everyone who is wise or calm is not humble or tall.
Everyone who is curious or strong is either funny or wise and vice versa.
Everyone who is calm or brave is both calm and not tall and vice versa.
Everyone who is either not generous or not funny is either not curious or not generous and vice versa.
If fred is either funny or creative then mary is tall and vice versa.
Everyone who is either old or strong is calm or not brave.
Everyone who is not funny is tall and vice versa.
If lucy is patient then someone is both not kind and not strong and vice versa.
Everyone who is not creative is either not calm or not tall and vice versa.
If fred is not patient or brave then susan is not brave or curious and vice versa.
If someone is either calm or generous then someone is generous.
If paul is both curious and happy then someone is curious and vice versa.
Someone is kind.
Lucy is humble.
Lucy is either not brave or quiet.
Alice is humble.
Alice is not calm.
Someone is not creative or kind.
Fred is not quiet or not humble.
Someone is either old or not old. | Alice is funny. | entailment | (![X]:(~funny(X)<=>(calm(X)&~funny(X))))&
(((~quiet(fred)|patient(fred)))<=>(creative(john)))&
(((~calm(john)|~patient(john)))<=>((~happy(mary)|~old(mary))))&
((?[X]:((kind(X)<~>humble(X))))<=>(creative(alice)))&
(![X]:((wise(X)|calm(X))=>(~humble(X)|tall(X))))&
(![X]:((curious(X)|strong(X))<=>(funny(X)<~>wise(X))))&
(![X]:((calm(X)|brave(X))<=>(calm(X)&~tall(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>(~curious(X)<~>~generous(X))))&
(((funny(fred)<~>creative(fred)))<=>(tall(mary)))&
(![X]:((old(X)<~>strong(X))=>(calm(X)|~brave(X))))&
(![X]:(~funny(X)<=>tall(X)))&
((patient(lucy))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:(~creative(X)<=>(~calm(X)<~>~tall(X))))&
(((~patient(fred)|brave(fred)))<=>((~brave(susan)|curious(susan))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:(generous(X))))&
(((curious(paul)&happy(paul)))<=>(?[X]:(curious(X))))&
(?[X]:(kind(X)))&
(humble(lucy))&
((~brave(lucy)<~>quiet(lucy)))&
(humble(alice))&
(~calm(alice))&
(?[X]:((~creative(X)|kind(X))))&
((~quiet(fred)|~humble(fred)))&
(?[X]:((old(X)<~>~old(X)))) | funny(alice) | [
"p0",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4093262690033194492747402
% SZS output start Proof for 4093262690033194492747402
1. ! [X0] : (~funny(X0) <=> (~funny(X0) & calm(X0))) [input p0]
21. ~calm(alice) [input p20]
25. ~funny(alice) [input hypothesis]
32. ! [X0] : ((~funny(X0) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | funny(X0))) [nnf transformation 1]
33. ! [X0] : ((~funny(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | funny(X0))) [flattening 32]
74. calm(X0) | funny(X0) [cnf transformation 33]
138. ~calm(alice) [cnf transformation 21]
143. ~funny(alice) [cnf transformation 25]
313. funny(alice) [resolution 74,138]
315. $false [subsumption resolution 313,143]
% SZS output end Proof for 4093262690033194492747402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not wise is both tall and patient.
If someone is both not wise and curious then susan is not calm or happy and vice versa.
If someone is either happy or not strong then mary is both not happy and not strong.
Everyone who is both not strong and not creative is either not wise or creative and vice versa.
If someone is not wise or calm then john is calm or not strong and vice versa.
Everyone who is not kind or happy is not old and vice versa.
Everyone who is either brave or not happy is not curious and vice versa.
Everyone who is both curious and not funny is not strong.
If someone is both old and not funny then lucy is quiet or curious and vice versa.
If paul is not brave then someone is not patient or not quiet and vice versa.
Everyone who is both not creative and funny is patient and vice versa.
Everyone who is either tall or curious is either not wise or humble.
If mary is not curious or curious then alice is either wise or not wise.
If someone is funny then fred is both not calm and creative.
If fred is happy or calm then fred is not patient and vice versa.
If someone is both not rich and funny then paul is not creative or kind.
Someone is either old or not old.
Someone is either curious or not generous.
Someone is either not tall or not patient.
Lucy is either not funny or humble.
Alice is either not funny or rich. | Lucy is not calm. | neutral | (![X]:((~old(X)|~wise(X))=>(tall(X)&patient(X))))&
((?[X]:((~wise(X)&curious(X))))<=>((~calm(susan)|happy(susan))))&
((?[X]:((happy(X)<~>~strong(X))))=>((~happy(mary)&~strong(mary))))&
(![X]:((~strong(X)&~creative(X))<=>(~wise(X)<~>creative(X))))&
((?[X]:((~wise(X)|calm(X))))<=>((calm(john)|~strong(john))))&
(![X]:((~kind(X)|happy(X))<=>~old(X)))&
(![X]:((brave(X)<~>~happy(X))<=>~curious(X)))&
(![X]:((curious(X)&~funny(X))=>~strong(X)))&
((?[X]:((old(X)&~funny(X))))<=>((quiet(lucy)|curious(lucy))))&
((~brave(paul))<=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:((~creative(X)&funny(X))<=>patient(X)))&
(![X]:((tall(X)<~>curious(X))=>(~wise(X)<~>humble(X))))&
(((~curious(mary)|curious(mary)))=>((wise(alice)<~>~wise(alice))))&
((?[X]:(funny(X)))=>((~calm(fred)&creative(fred))))&
(((happy(fred)|calm(fred)))<=>(~patient(fred)))&
((?[X]:((~rich(X)&funny(X))))=>((~creative(paul)|kind(paul))))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((curious(X)<~>~generous(X))))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~funny(lucy)<~>humble(lucy)))&
((~funny(alice)<~>rich(alice))) | ~calm(lucy) | [] | null | 0 |
If someone is not happy then mary is either not calm or not quiet and vice versa. If someone is either not strong or creative then susan is strong or not happy. If mary is brave then someone is either strong or happy and vice versa. Everyone who is either wise or not brave is not rich or not wise and vice versa. If someone is not wise then paul is not humble or generous. Everyone who is both not rich and not funny is both not quiet and generous. If mary is old or rich then someone is strong or not old. If alice is either generous or not tall then alice is both not brave and not creative and vice versa. If someone is not calm then john is patient. If someone is either not quiet or creative then someone is not humble and vice versa. If fred is happy or quiet then john is both not creative and strong. Everyone who is both strong and calm is either strong or kind and vice versa. If someone is calm then someone is either rich or not curious and vice versa. Everyone who is rich is either quiet or not funny. If someone is not happy or patient then someone is not strong or not humble. If susan is rich then fred is either not tall or not happy. Alice is both not strong and wise. Someone is both tall and rich. Someone is either not calm or not strong. Paul is both happy and not curious. Susan is either not generous or patient. Someone is not creative or kind. Paul is both generous and not humble. Someone is kind or not humble. | Paul is humble. | contradiction | ((?[X]:(~happy(X)))<=>((~calm(mary)<~>~quiet(mary))))&
((?[X]:((~strong(X)<~>creative(X))))=>((strong(susan)|~happy(susan))))&
((brave(mary))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((wise(X)<~>~brave(X))<=>(~rich(X)|~wise(X))))&
((?[X]:(~wise(X)))=>((~humble(paul)|generous(paul))))&
(![X]:((~rich(X)&~funny(X))=>(~quiet(X)&generous(X))))&
(((old(mary)|rich(mary)))=>(?[X]:((strong(X)|~old(X)))))&
(((generous(alice)<~>~tall(alice)))<=>((~brave(alice)&~creative(alice))))&
((?[X]:(~calm(X)))=>(patient(john)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(~humble(X))))&
(((happy(fred)|quiet(fred)))=>((~creative(john)&strong(john))))&
(![X]:((strong(X)&calm(X))<=>(strong(X)<~>kind(X))))&
((?[X]:(calm(X)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(rich(X)=>(quiet(X)<~>~funny(X))))&
((?[X]:((~happy(X)|patient(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
((rich(susan))=>((~tall(fred)<~>~happy(fred))))&
((~strong(alice)&wise(alice)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((happy(paul)&~curious(paul)))&
((~generous(susan)<~>patient(susan)))&
(?[X]:((~creative(X)|kind(X))))&
((generous(paul)&~humble(paul)))&
(?[X]:((kind(X)|~humble(X)))) | humble(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 626593115871482927958720
% SZS output start Proof for 626593115871482927958720
23. ~humble(paul) & generous(paul) [input p22]
25. humble(paul) [input hypothesis]
143. ~humble(paul) [cnf transformation 23]
145. humble(paul) [cnf transformation 25]
212. 15 <=> humble(paul) [avatar definition]
374. ~15 [avatar split clause 143,212]
385. 15 [avatar split clause 145,212]
386. $false [avatar sat refutation 374,385]
% SZS output end Proof for 626593115871482927958720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both patient and not strong then someone is funny.
If lucy is both not tall and patient then someone is old and vice versa.
Everyone who is not creative or strong is either quiet or old.
If someone is either strong or curious then john is not wise and vice versa.
If someone is either not strong or not quiet then fred is not calm.
If someone is both not quiet and generous then paul is both not calm and not generous.
Everyone who is both not curious and tall is both strong and not tall.
If susan is both not calm and quiet then john is both tall and not old.
If alice is kind or not patient then someone is happy or not happy.
Everyone who is either not curious or creative is either generous or brave.
If someone is not old then someone is both not calm and curious and vice versa.
Everyone who is both old and happy is generous or not old and vice versa.
Everyone who is funny or brave is not quiet or not funny and vice versa.
Everyone who is either not tall or not strong is either not old or calm.
Everyone who is funny is old.
Everyone who is both patient and not generous is either not happy or old.
Susan is quiet.
Someone is either not funny or not humble.
Susan is either not funny or tall.
Mary is both quiet and tall.
Mary is either not wise or not humble.
Paul is tall.
Someone is old. | Mary is not strong. | entailment | (((patient(mary)&~strong(mary)))=>(?[X]:(funny(X))))&
(((~tall(lucy)&patient(lucy)))<=>(?[X]:(old(X))))&
(![X]:((~creative(X)|strong(X))=>(quiet(X)<~>old(X))))&
((?[X]:((strong(X)<~>curious(X))))<=>(~wise(john)))&
((?[X]:((~strong(X)<~>~quiet(X))))=>(~calm(fred)))&
((?[X]:((~quiet(X)&generous(X))))=>((~calm(paul)&~generous(paul))))&
(![X]:((~curious(X)&tall(X))=>(strong(X)&~tall(X))))&
(((~calm(susan)&quiet(susan)))=>((tall(john)&~old(john))))&
(((kind(alice)|~patient(alice)))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(generous(X)<~>brave(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:((old(X)&happy(X))<=>(generous(X)|~old(X))))&
(![X]:((funny(X)|brave(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~old(X)<~>calm(X))))&
(![X]:(funny(X)=>old(X)))&
(![X]:((patient(X)&~generous(X))=>(~happy(X)<~>old(X))))&
(quiet(susan))&
(?[X]:((~funny(X)<~>~humble(X))))&
((~funny(susan)<~>tall(susan)))&
((quiet(mary)&tall(mary)))&
((~wise(mary)<~>~humble(mary)))&
(tall(paul))&
(?[X]:(old(X))) | ~strong(mary) | [
"p2",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8668052566602169887837892
% SZS output start Proof for 8668052566602169887837892
3. ! [X0] : ((strong(X0) | ~creative(X0)) => (quiet(X0) <~> old(X0))) [input p2]
12. ! [X0] : ((happy(X0) & old(X0)) <=> (~old(X0) | generous(X0))) [input p11]
20. tall(mary) & quiet(mary) [input p19]
24. strong(mary) [input hypothesis]
29. ! [X0] : ((quiet(X0) <~> old(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 3]
49. ! [X0] : (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (~strong(X0) & creative(X0))) [nnf transformation 29]
63. ! [X0] : (((happy(X0) & old(X0)) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 12]
64. ! [X0] : (((happy(X0) & old(X0)) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~happy(X0) | ~old(X0))) [flattening 63]
83. ~quiet(X0) | ~old(X0) | ~strong(X0) [cnf transformation 49]
106. old(X0) | old(X0) [cnf transformation 64]
125. quiet(mary) [cnf transformation 20]
131. strong(mary) [cnf transformation 24]
135. old(X0) [duplicate literal removal 106]
142. 2 <=> strong(mary) [avatar definition]
144. strong(mary) <- (2) [avatar component clause 142]
242. 25 <=> ! [X3] : old(X3) [avatar definition]
243. old(X3) <- (25) [avatar component clause 242]
254. 25 [avatar split clause 135,242]
290. 2 [avatar split clause 131,142]
316. ~old(mary) | ~strong(mary) [resolution 83,125]
319. ~strong(mary) <- (25) [subsumption resolution 316,243]
320. $false <- (2, 25) [subsumption resolution 319,144]
321. ~2 | ~25 [avatar contradiction clause 320]
323. $false [avatar sat refutation 254,290,321]
% SZS output end Proof for 8668052566602169887837892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not patient is patient.
Everyone who is old is either not brave or funny.
Everyone who is wise is wise or patient.
Everyone who is not funny or creative is not creative or not old.
Everyone who is funny or strong is strong and vice versa.
If alice is tall then mary is patient.
Everyone who is both not humble and not creative is humble.
Everyone who is creative is not funny.
Everyone who is either kind or wise is either generous or not calm.
If john is either not happy or not brave then someone is wise or tall.
If someone is both quiet and kind then someone is both patient and not old.
Everyone who is not kind is not humble or humble.
Everyone who is patient is not rich or old and vice versa.
If someone is not patient or curious then susan is creative.
Everyone who is creative or rich is quiet or not generous.
Everyone who is either not creative or not wise is happy or brave.
Someone is not calm.
Someone is both not generous and kind.
Alice is either not creative or not quiet.
Someone is both kind and not curious.
Lucy is either calm or patient.
Lucy is either quiet or patient.
Paul is curious or strong.
Someone is calm or creative. | Mary is wise. | neutral | (![X]:((generous(X)<~>~patient(X))=>patient(X)))&
(![X]:(old(X)=>(~brave(X)<~>funny(X))))&
(![X]:(wise(X)=>(wise(X)|patient(X))))&
(![X]:((~funny(X)|creative(X))=>(~creative(X)|~old(X))))&
(![X]:((funny(X)|strong(X))<=>strong(X)))&
((tall(alice))=>(patient(mary)))&
(![X]:((~humble(X)&~creative(X))=>humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((kind(X)<~>wise(X))=>(generous(X)<~>~calm(X))))&
(((~happy(john)<~>~brave(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:(~kind(X)=>(~humble(X)|humble(X))))&
(![X]:(patient(X)<=>(~rich(X)|old(X))))&
((?[X]:((~patient(X)|curious(X))))=>(creative(susan)))&
(![X]:((creative(X)|rich(X))=>(quiet(X)|~generous(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(happy(X)|brave(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)&kind(X))))&
((~creative(alice)<~>~quiet(alice)))&
(?[X]:((kind(X)&~curious(X))))&
((calm(lucy)<~>patient(lucy)))&
((quiet(lucy)<~>patient(lucy)))&
((curious(paul)|strong(paul)))&
(?[X]:((calm(X)|creative(X)))) | wise(mary) | [] | null | 0 |
If susan is not old or not wise then john is not humble and vice versa.
Everyone who is curious or generous is both happy and tall.
Everyone who is tall or strong is brave or not tall.
If someone is rich then mary is either strong or generous and vice versa.
If paul is both not kind and humble then someone is either not brave or not creative and vice versa.
If someone is both not generous and not humble then someone is old or not strong and vice versa.
Everyone who is tall is both strong and calm.
Everyone who is generous or not calm is tall or not wise and vice versa.
If someone is not old or patient then susan is not calm or not old.
Everyone who is not curious is strong or not humble.
Everyone who is both happy and not kind is not quiet.
If lucy is funny or not humble then someone is humble or brave.
Everyone who is not quiet or not old is not generous or rich and vice versa.
If lucy is quiet or not generous then mary is curious or not patient.
If fred is both funny and not patient then someone is not brave or creative and vice versa.
Someone is patient or tall.
Someone is both calm and funny.
Susan is either not humble or not patient.
Someone is humble. | Mary is not happy. | neutral | (((~old(susan)|~wise(susan)))<=>(~humble(john)))&
(![X]:((curious(X)|generous(X))=>(happy(X)&tall(X))))&
(![X]:((tall(X)|strong(X))=>(brave(X)|~tall(X))))&
((?[X]:(rich(X)))<=>((strong(mary)<~>generous(mary))))&
(((~kind(paul)&humble(paul)))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:(tall(X)=>(strong(X)&calm(X))))&
(![X]:((generous(X)|~calm(X))<=>(tall(X)|~wise(X))))&
((?[X]:((~old(X)|patient(X))))=>((~calm(susan)|~old(susan))))&
(![X]:(~curious(X)=>(strong(X)|~humble(X))))&
(![X]:((happy(X)&~kind(X))=>~quiet(X)))&
(((funny(lucy)|~humble(lucy)))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:((~quiet(X)|~old(X))<=>(~generous(X)|rich(X))))&
(((quiet(lucy)|~generous(lucy)))=>((curious(mary)|~patient(mary))))&
(((funny(fred)&~patient(fred)))<=>(?[X]:((~brave(X)|creative(X)))))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:((calm(X)&funny(X))))&
((~humble(susan)<~>~patient(susan)))&
(?[X]:(humble(X))) | ~happy(mary) | [] | null | 0 |
Everyone who is curious is both rich and old. Everyone who is not wise is old. If mary is not old or kind then john is either not wise or old and vice versa. If fred is both not wise and not strong then someone is either old or generous and vice versa. Everyone who is patient is not old. If alice is both tall and not tall then fred is both not curious and not creative and vice versa. If alice is either not quiet or old then susan is both kind and humble and vice versa. If someone is not calm or funny then lucy is not patient or not wise and vice versa. Everyone who is not creative is either wise or rich. Everyone who is either happy or old is not tall or not quiet. If alice is either not creative or happy then someone is not quiet and vice versa. Everyone who is both rich and not creative is tall or brave and vice versa. Everyone who is not generous or kind is either rich or not humble and vice versa. If fred is both not wise and not patient then someone is both not kind and quiet. Everyone who is patient is both not brave and happy. Everyone who is happy or rich is not curious or not strong and vice versa. John is either calm or not happy. Someone is either not calm or curious. Someone is not creative or not funny. Mary is both not generous and brave. Susan is either old or not tall. John is either not funny or wise. Someone is not quiet. John is not curious or rich. | Fred is not calm. | neutral | (![X]:(curious(X)=>(rich(X)&old(X))))&
(![X]:(~wise(X)=>old(X)))&
(((~old(mary)|kind(mary)))<=>((~wise(john)<~>old(john))))&
(((~wise(fred)&~strong(fred)))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(patient(X)=>~old(X)))&
(((tall(alice)&~tall(alice)))<=>((~curious(fred)&~creative(fred))))&
(((~quiet(alice)<~>old(alice)))<=>((kind(susan)&humble(susan))))&
((?[X]:((~calm(X)|funny(X))))<=>((~patient(lucy)|~wise(lucy))))&
(![X]:(~creative(X)=>(wise(X)<~>rich(X))))&
(![X]:((happy(X)<~>old(X))=>(~tall(X)|~quiet(X))))&
(((~creative(alice)<~>happy(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((rich(X)&~creative(X))<=>(tall(X)|brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(rich(X)<~>~humble(X))))&
(((~wise(fred)&~patient(fred)))=>(?[X]:((~kind(X)&quiet(X)))))&
(![X]:(patient(X)=>(~brave(X)&happy(X))))&
(![X]:((happy(X)|rich(X))<=>(~curious(X)|~strong(X))))&
((calm(john)<~>~happy(john)))&
(?[X]:((~calm(X)<~>curious(X))))&
(?[X]:((~creative(X)|~funny(X))))&
((~generous(mary)&brave(mary)))&
((old(susan)<~>~tall(susan)))&
((~funny(john)<~>wise(john)))&
(?[X]:(~quiet(X)))&
((~curious(john)|rich(john))) | ~calm(fred) | [] | null | 0 |
Everyone who is rich or patient is either curious or not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is either creative or brave is either rich or not happy and vice versa. Alice is either not patient or not old. John is not calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | Lucy is not brave. | neutral | (![X]:((rich(X)|patient(X))=>(curious(X)<~>~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~patient(alice)<~>~old(alice)))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | ~brave(lucy) | [] | null | 0 |
Everyone who is rich or old is old or happy.
Everyone who is strong or funny is either not kind or not curious.
If john is both not wise and generous then john is both wise and not curious.
Everyone who is funny is not quiet or creative and vice versa.
Everyone who is either funny or not creative is generous or kind.
Everyone who is either not strong or not old is calm.
Everyone who is rich or not calm is not patient.
If mary is strong or generous then paul is either rich or not kind.
Everyone who is not patient or not rich is both not wise and not quiet.
Everyone who is not tall or calm is either not creative or not wise and vice versa.
If someone is patient or not funny then someone is not patient.
Everyone who is strong is humble.
If someone is not happy or funny then mary is not tall.
Everyone who is quiet is either not tall or not curious.
If someone is either rich or not generous then someone is not patient or rich and vice versa.
If someone is not strong then susan is not tall or not funny.
Someone is patient or not funny.
Someone is either funny or not funny.
Someone is both not patient and not generous.
Someone is both strong and not wise.
Someone is not kind.
Someone is not patient.
Mary is not rich.
Someone is brave or not tall. | Susan is not tall. | neutral | (![X]:((rich(X)|old(X))=>(old(X)|happy(X))))&
(![X]:((strong(X)|funny(X))=>(~kind(X)<~>~curious(X))))&
(((~wise(john)&generous(john)))=>((wise(john)&~curious(john))))&
(![X]:(funny(X)<=>(~quiet(X)|creative(X))))&
(![X]:((funny(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((~strong(X)<~>~old(X))=>calm(X)))&
(![X]:((rich(X)|~calm(X))=>~patient(X)))&
(((strong(mary)|generous(mary)))=>((rich(paul)<~>~kind(paul))))&
(![X]:((~patient(X)|~rich(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~tall(X)|calm(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~patient(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~tall(mary)))&
(![X]:(quiet(X)=>(~tall(X)<~>~curious(X))))&
((?[X]:((rich(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|rich(X)))))&
((?[X]:(~strong(X)))=>((~tall(susan)|~funny(susan))))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((strong(X)&~wise(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~patient(X)))&
(~rich(mary))&
(?[X]:((brave(X)|~tall(X)))) | ~tall(susan) | [] | null | 0 |
Everyone who is not wise is either calm or funny and vice versa.
If mary is not kind then someone is both calm and old.
If someone is either not calm or not tall then someone is either tall or not rich.
Everyone who is old or not calm is either not brave or creative and vice versa.
Everyone who is either not wise or strong is kind or not brave.
Everyone who is both not patient and rich is old or not strong.
If someone is both not patient and not brave then someone is both not curious and brave and vice versa.
If someone is both not quiet and creative then fred is generous or tall and vice versa.
Everyone who is not wise or not old is either not creative or calm.
Everyone who is both not patient and not quiet is rich.
If someone is both not patient and curious then someone is happy and vice versa.
Everyone who is either not tall or kind is not funny.
Everyone who is both not calm and not patient is both not happy and not kind.
If fred is funny or humble then someone is either not creative or old and vice versa.
Everyone who is either generous or not tall is not old or not creative.
If alice is curious then paul is both rich and creative and vice versa.
Lucy is both funny and not quiet.
Someone is both rich and not old.
Someone is not funny.
Someone is both not humble and calm.
Someone is both generous and rich.
Someone is both tall and not brave.
Someone is generous.
Mary is creative or happy. | Alice is curious. | neutral | (![X]:(~wise(X)<=>(calm(X)<~>funny(X))))&
((~kind(mary))=>(?[X]:((calm(X)&old(X)))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((old(X)|~calm(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((~wise(X)<~>strong(X))=>(kind(X)|~brave(X))))&
(![X]:((~patient(X)&rich(X))=>(old(X)|~strong(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:((~quiet(X)&creative(X))))<=>((generous(fred)|tall(fred))))&
(![X]:((~wise(X)|~old(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~patient(X)&~quiet(X))=>rich(X)))&
((?[X]:((~patient(X)&curious(X))))<=>(?[X]:(happy(X))))&
(![X]:((~tall(X)<~>kind(X))=>~funny(X)))&
(![X]:((~calm(X)&~patient(X))=>(~happy(X)&~kind(X))))&
(((funny(fred)|humble(fred)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~old(X)|~creative(X))))&
((curious(alice))<=>((rich(paul)&creative(paul))))&
((funny(lucy)&~quiet(lucy)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&calm(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:(generous(X)))&
((creative(mary)|happy(mary))) | curious(alice) | [] | null | 0 |
If alice is not calm or humble then lucy is old or calm.
If paul is either not patient or not kind then someone is not curious.
Everyone who is strong is both not patient and happy and vice versa.
Everyone who is wise or not funny is curious.
If someone is either calm or old then john is both strong and happy and vice versa.
Everyone who is both not calm and not patient is funny or not strong.
If john is not kind then susan is not happy and vice versa.
Everyone who is both patient and curious is not kind or brave.
Everyone who is both funny and patient is strong.
Everyone who is not tall or quiet is either not humble or not rich.
If alice is not tall or brave then fred is both quiet and tall.
If fred is either not humble or creative then someone is either old or not happy.
If fred is not rich or not creative then someone is either not brave or calm.
Everyone who is both brave and not quiet is not generous or not strong.
If mary is both wise and not tall then someone is not rich or not generous.
Everyone who is either brave or creative is wise.
Paul is both patient and not tall.
Alice is not curious.
Someone is not curious or not calm.
Fred is not tall or not generous.
John is both tall and calm.
Someone is either kind or old.
Lucy is both rich and funny.
Someone is both not funny and curious. | John is calm. | entailment | (((~calm(alice)|humble(alice)))=>((old(lucy)|calm(lucy))))&
(((~patient(paul)<~>~kind(paul)))=>(?[X]:(~curious(X))))&
(![X]:(strong(X)<=>(~patient(X)&happy(X))))&
(![X]:((wise(X)|~funny(X))=>curious(X)))&
((?[X]:((calm(X)<~>old(X))))<=>((strong(john)&happy(john))))&
(![X]:((~calm(X)&~patient(X))=>(funny(X)|~strong(X))))&
((~kind(john))<=>(~happy(susan)))&
(![X]:((patient(X)&curious(X))=>(~kind(X)|brave(X))))&
(![X]:((funny(X)&patient(X))=>strong(X)))&
(![X]:((~tall(X)|quiet(X))=>(~humble(X)<~>~rich(X))))&
(((~tall(alice)|brave(alice)))=>((quiet(fred)&tall(fred))))&
(((~humble(fred)<~>creative(fred)))=>(?[X]:((old(X)<~>~happy(X)))))&
(((~rich(fred)|~creative(fred)))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((brave(X)&~quiet(X))=>(~generous(X)|~strong(X))))&
(((wise(mary)&~tall(mary)))=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((brave(X)<~>creative(X))=>wise(X)))&
((patient(paul)&~tall(paul)))&
(~curious(alice))&
(?[X]:((~curious(X)|~calm(X))))&
((~tall(fred)|~generous(fred)))&
((tall(john)&calm(john)))&
(?[X]:((kind(X)<~>old(X))))&
((rich(lucy)&funny(lucy)))&
(?[X]:((~funny(X)&curious(X)))) | calm(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6271965689827445766146647
% SZS output start Proof for 6271965689827445766146647
21. calm(john) & tall(john) [input p20]
25. ~calm(john) [input hypothesis]
113. calm(john) [cnf transformation 21]
120. ~calm(john) [cnf transformation 25]
271. $false [subsumption resolution 120,113]
% SZS output end Proof for 6271965689827445766146647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is rich then someone is both humble and not funny.
Everyone who is both old and not creative is either calm or not funny.
Everyone who is both generous and not happy is either not strong or not kind and vice versa.
Everyone who is both not kind and tall is both tall and generous and vice versa.
If susan is not patient or not brave then someone is patient.
Everyone who is not humble or not rich is not generous and vice versa.
If fred is not humble or not rich then someone is either not patient or wise.
Everyone who is not kind or not funny is not generous or not brave and vice versa.
If john is strong or not patient then john is either rich or not wise and vice versa.
Everyone who is both not kind and funny is both funny and not kind and vice versa.
If someone is happy then someone is either not creative or not curious and vice versa.
Everyone who is funny or not patient is both wise and not rich and vice versa.
Everyone who is not rich is strong or not quiet and vice versa.
If mary is not humble then susan is either wise or strong.
If john is either quiet or not old then john is either kind or not curious and vice versa.
If mary is either not tall or not rich then lucy is not creative.
John is creative.
Someone is both not old and creative.
Someone is not brave or not happy.
Someone is both quiet and not brave.
John is not quiet.
Mary is either wise or not kind. | Mary is old. | neutral | ((rich(mary))=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:((old(X)&~creative(X))=>(calm(X)<~>~funny(X))))&
(![X]:((generous(X)&~happy(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:((~kind(X)&tall(X))<=>(tall(X)&generous(X))))&
(((~patient(susan)|~brave(susan)))=>(?[X]:(patient(X))))&
(![X]:((~humble(X)|~rich(X))<=>~generous(X)))&
(((~humble(fred)|~rich(fred)))=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((~kind(X)|~funny(X))<=>(~generous(X)|~brave(X))))&
(((strong(john)|~patient(john)))<=>((rich(john)<~>~wise(john))))&
(![X]:((~kind(X)&funny(X))<=>(funny(X)&~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>(strong(X)|~quiet(X))))&
((~humble(mary))=>((wise(susan)<~>strong(susan))))&
(((quiet(john)<~>~old(john)))<=>((kind(john)<~>~curious(john))))&
(((~tall(mary)<~>~rich(mary)))=>(~creative(lucy)))&
(creative(john))&
(?[X]:((~old(X)&creative(X))))&
(?[X]:((~brave(X)|~happy(X))))&
(?[X]:((quiet(X)&~brave(X))))&
(~quiet(john))&
((wise(mary)<~>~kind(mary))) | old(mary) | [] | null | 0 |
Everyone who is not happy or patient is either not happy or not patient. If paul is either not old or curious then someone is not patient or curious and vice versa. Everyone who is not rich or not calm is not happy and vice versa. Everyone who is both tall and strong is both not strong and kind and vice versa. Everyone who is old or not tall is both not creative and not humble. Everyone who is both calm and rich is not funny or not brave and vice versa. If susan is curious or not strong then paul is both not tall and not brave and vice versa. If lucy is not curious or generous then paul is not strong or calm. If susan is brave or not patient then john is not funny or creative. If someone is not generous or not strong then fred is creative and vice versa. If paul is both rich and not quiet then someone is not curious. Everyone who is happy is both not kind and funny and vice versa. If john is both not rich and not creative then someone is patient or funny. If someone is both not quiet and not funny then alice is both not happy and tall and vice versa. Everyone who is either not happy or old is happy or not creative. Everyone who is not patient is both happy and creative. Lucy is not calm. Paul is brave. Someone is brave or humble. Someone is quiet or not brave. Someone is either quiet or not quiet. | Fred is not quiet. | neutral | (![X]:((~happy(X)|patient(X))=>(~happy(X)<~>~patient(X))))&
(((~old(paul)<~>curious(paul)))<=>(?[X]:((~patient(X)|curious(X)))))&
(![X]:((~rich(X)|~calm(X))<=>~happy(X)))&
(![X]:((tall(X)&strong(X))<=>(~strong(X)&kind(X))))&
(![X]:((old(X)|~tall(X))=>(~creative(X)&~humble(X))))&
(![X]:((calm(X)&rich(X))<=>(~funny(X)|~brave(X))))&
(((curious(susan)|~strong(susan)))<=>((~tall(paul)&~brave(paul))))&
(((~curious(lucy)|generous(lucy)))=>((~strong(paul)|calm(paul))))&
(((brave(susan)|~patient(susan)))=>((~funny(john)|creative(john))))&
((?[X]:((~generous(X)|~strong(X))))<=>(creative(fred)))&
(((rich(paul)&~quiet(paul)))=>(?[X]:(~curious(X))))&
(![X]:(happy(X)<=>(~kind(X)&funny(X))))&
(((~rich(john)&~creative(john)))=>(?[X]:((patient(X)|funny(X)))))&
((?[X]:((~quiet(X)&~funny(X))))<=>((~happy(alice)&tall(alice))))&
(![X]:((~happy(X)<~>old(X))=>(happy(X)|~creative(X))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(~calm(lucy))&
(brave(paul))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~quiet(fred) | [] | null | 0 |
Everyone who is old is either not wise or not patient.
Everyone who is not kind is either humble or patient.
Everyone who is both not creative and brave is rich.
Everyone who is generous is both happy and strong.
Everyone who is strong or quiet is both humble and not tall and vice versa.
If someone is either humble or not happy then paul is either not generous or wise and vice versa.
If someone is either calm or humble then susan is not happy and vice versa.
Everyone who is not wise is either curious or not humble and vice versa.
Everyone who is both not strong and not tall is brave or not kind and vice versa.
Everyone who is both not humble and tall is either old or happy and vice versa.
If someone is humble then someone is either funny or kind.
If john is funny then john is not kind or not calm and vice versa.
Everyone who is either not happy or old is happy and vice versa.
If mary is generous then alice is both generous and not quiet.
Everyone who is either not funny or not brave is both not funny and humble and vice versa.
If john is not humble or strong then someone is both not rich and creative.
Lucy is either not rich or not funny.
Someone is both creative and not happy.
Someone is not rich or not brave.
Someone is curious.
Someone is both humble and not calm.
Someone is funny.
Fred is both humble and not creative.
Someone is not funny. | Paul is not old. | contradiction | (![X]:(old(X)=>(~wise(X)<~>~patient(X))))&
(![X]:(~kind(X)=>(humble(X)<~>patient(X))))&
(![X]:((~creative(X)&brave(X))=>rich(X)))&
(![X]:(generous(X)=>(happy(X)&strong(X))))&
(![X]:((strong(X)|quiet(X))<=>(humble(X)&~tall(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~generous(paul)<~>wise(paul))))&
((?[X]:((calm(X)<~>humble(X))))<=>(~happy(susan)))&
(![X]:(~wise(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((~strong(X)&~tall(X))<=>(brave(X)|~kind(X))))&
(![X]:((~humble(X)&tall(X))<=>(old(X)<~>happy(X))))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)<~>kind(X)))))&
((funny(john))<=>((~kind(john)|~calm(john))))&
(![X]:((~happy(X)<~>old(X))<=>happy(X)))&
((generous(mary))=>((generous(alice)&~quiet(alice))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~funny(X)&humble(X))))&
(((~humble(john)|strong(john)))=>(?[X]:((~rich(X)&creative(X)))))&
((~rich(lucy)<~>~funny(lucy)))&
(?[X]:((creative(X)&~happy(X))))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:(funny(X)))&
((humble(fred)&~creative(fred)))&
(?[X]:(~funny(X))) | ~old(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2526654657986021909670732
% SZS output start Proof for 2526654657986021909670732
13. ! [X0] : ((~happy(X0) <~> old(X0)) <=> happy(X0)) [input p12]
25. ~old(paul) [input hypothesis]
58. ! [X0] : ((((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | ~happy(X0)) & (happy(X0) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0))))) [nnf transformation 13]
120. happy(X0) | old(X0) | happy(X0) [cnf transformation 58]
122. old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 58]
148. ~old(paul) [cnf transformation 25]
151. happy(X0) | old(X0) [duplicate literal removal 120]
152. old(X0) | ~happy(X0) [duplicate literal removal 122]
233. old(X0) [subsumption resolution 151,152]
287. $false [subsumption resolution 148,233]
% SZS output end Proof for 2526654657986021909670732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or patient is both not rich and quiet and vice versa.
If fred is wise then someone is both generous and strong.
If someone is both kind and not creative then someone is patient.
Everyone who is both not creative and not curious is creative and vice versa.
Everyone who is both not rich and wise is not humble or not kind.
Everyone who is both not calm and not old is not kind or not humble and vice versa.
If someone is happy or not wise then john is not tall or not brave and vice versa.
Everyone who is wise or generous is both not old and strong and vice versa.
Everyone who is both kind and tall is both kind and not tall.
Everyone who is curious is not patient.
Everyone who is both creative and not kind is not patient.
If someone is both rich and tall then mary is both not tall and tall and vice versa.
Everyone who is either not quiet or strong is either not curious or not tall.
Everyone who is not old or not wise is both humble and not rich.
If lucy is not tall then fred is either brave or strong and vice versa.
Everyone who is not old or not brave is either calm or not wise.
John is either brave or calm.
Someone is rich or tall.
Mary is either kind or not happy.
Alice is old or not wise.
Someone is not kind or not funny.
Someone is kind or happy. | John is tall. | contradiction | (![X]:((happy(X)<~>patient(X))<=>(~rich(X)&quiet(X))))&
((wise(fred))=>(?[X]:((generous(X)&strong(X)))))&
((?[X]:((kind(X)&~creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)&~curious(X))<=>creative(X)))&
(![X]:((~rich(X)&wise(X))=>(~humble(X)|~kind(X))))&
(![X]:((~calm(X)&~old(X))<=>(~kind(X)|~humble(X))))&
((?[X]:((happy(X)|~wise(X))))<=>((~tall(john)|~brave(john))))&
(![X]:((wise(X)|generous(X))<=>(~old(X)&strong(X))))&
(![X]:((kind(X)&tall(X))=>(kind(X)&~tall(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((creative(X)&~kind(X))=>~patient(X)))&
((?[X]:((rich(X)&tall(X))))<=>((~tall(mary)&tall(mary))))&
(![X]:((~quiet(X)<~>strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~old(X)|~wise(X))=>(humble(X)&~rich(X))))&
((~tall(lucy))<=>((brave(fred)<~>strong(fred))))&
(![X]:((~old(X)|~brave(X))=>(calm(X)<~>~wise(X))))&
((brave(john)<~>calm(john)))&
(?[X]:((rich(X)|tall(X))))&
((kind(mary)<~>~happy(mary)))&
((old(alice)|~wise(alice)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((kind(X)|happy(X)))) | tall(john) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4715501888722366297420590
% SZS output start Proof for 4715501888722366297420590
3. ? [X0] : (~creative(X0) & kind(X0)) => ? [X0] : patient(X0) [input p2]
4. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> creative(X0)) [input p3]
6. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (~humble(X0) | ~kind(X0))) [input p5]
7. ? [X0] : (~wise(X0) | happy(X0)) <=> (~brave(john) | ~tall(john)) [input p6]
10. ! [X0] : (curious(X0) => ~patient(X0)) [input p9]
17. brave(john) <~> calm(john) [input p16]
22. ? [X0] : (happy(X0) | kind(X0)) [input p21]
23. tall(john) [input hypothesis]
24. ? [X0] : (~creative(X0) & kind(X0)) => ? [X1] : patient(X1) [rectify 3]
27. ? [X1] : patient(X1) | ! [X0] : (creative(X0) | ~kind(X0)) [ennf transformation 24]
32. ! [X0] : (~patient(X0) | ~curious(X0)) [ennf transformation 10]
42. ? [X0] : patient(X0) | ! [X1] : (creative(X1) | ~kind(X1)) [rectify 27]
43. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
44. patient(sK1) | ! [X1] : (creative(X1) | ~kind(X1)) [skolemisation 42,43]
45. ! [X0] : (((~curious(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | creative(X0)))) [nnf transformation 4]
46. ! [X0] : (((~curious(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | creative(X0))) [flattening 45]
47. ! [X0] : (((~old(X0) & ~calm(X0)) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | (old(X0) | calm(X0)))) [nnf transformation 6]
48. ! [X0] : (((~old(X0) & ~calm(X0)) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | old(X0) | calm(X0))) [flattening 47]
49. (? [X0] : (~wise(X0) | happy(X0)) | (brave(john) & tall(john))) & ((~brave(john) | ~tall(john)) | ! [X0] : (wise(X0) & ~happy(X0))) [nnf transformation 7]
50. (? [X0] : (~wise(X0) | happy(X0)) | (brave(john) & tall(john))) & (~brave(john) | ~tall(john) | ! [X0] : (wise(X0) & ~happy(X0))) [flattening 49]
51. (? [X0] : (~wise(X0) | happy(X0)) | (brave(john) & tall(john))) & (~brave(john) | ~tall(john) | ! [X1] : (wise(X1) & ~happy(X1))) [rectify 50]
52. ? [X0] : (~wise(X0) | happy(X0)) => (~wise(sK2) | happy(sK2)) [choice axiom]
53. ((~wise(sK2) | happy(sK2)) | (brave(john) & tall(john))) & (~brave(john) | ~tall(john) | ! [X1] : (wise(X1) & ~happy(X1))) [skolemisation 51,52]
64. (~calm(john) | ~brave(john)) & (calm(john) | brave(john)) [nnf transformation 17]
68. ? [X0] : (happy(X0) | kind(X0)) => (happy(sK5) | kind(sK5)) [choice axiom]
69. happy(sK5) | kind(sK5) [skolemisation 22,68]
78. patient(sK1) | creative(X1) | ~kind(X1) [cnf transformation 44]
79. creative(X0) | curious(X0) | creative(X0) [cnf transformation 46]
80. ~creative(X0) | ~creative(X0) [cnf transformation 46]
84. ~calm(X0) | kind(X0) [cnf transformation 48]
88. ~brave(john) | ~tall(john) | ~happy(X1) [cnf transformation 53]
99. ~patient(X0) | ~curious(X0) [cnf transformation 32]
121. calm(john) | brave(john) [cnf transformation 64]
127. happy(sK5) | kind(sK5) [cnf transformation 69]
128. tall(john) [cnf transformation 23]
130. creative(X0) | curious(X0) [duplicate literal removal 79]
131. ~creative(X0) [duplicate literal removal 80]
147. 4 <=> ! [X1] : (creative(X1) | ~kind(X1)) [avatar definition]
148. creative(X1) | ~kind(X1) <- (4) [avatar component clause 147]
150. 5 <=> patient(sK1) [avatar definition]
152. patient(sK1) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 78,150,147]
154. curious(X0) [subsumption resolution 130,131]
156. 6 <=> brave(john) [avatar definition]
169. 9 <=> tall(john) [avatar definition]
178. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
179. ~happy(X1) <- (11) [avatar component clause 178]
180. 11 | ~9 | ~6 [avatar split clause 88,156,169,178]
181. ~patient(X0) [subsumption resolution 99,154]
212. 17 <=> calm(john) [avatar definition]
213. calm(john) <- (17) [avatar component clause 212]
216. 6 | 17 [avatar split clause 121,212,156]
238. 22 <=> kind(sK5) [avatar definition]
240. kind(sK5) <- (22) [avatar component clause 238]
242. 23 <=> happy(sK5) [avatar definition]
244. happy(sK5) <- (23) [avatar component clause 242]
245. 22 | 23 [avatar split clause 127,242,238]
246. 9 [avatar split clause 128,169]
247. ~kind(X1) <- (4) [subsumption resolution 148,131]
250. $false <- (4, 22) [resolution 247,240]
251. ~4 | ~22 [avatar contradiction clause 250]
252. $false <- (5) [subsumption resolution 152,181]
253. ~5 [avatar contradiction clause 252]
254. $false <- (11, 23) [subsumption resolution 244,179]
255. ~11 | ~23 [avatar contradiction clause 254]
256. ~kind(X1) <- (4) [subsumption resolution 148,131]
258. kind(john) <- (17) [resolution 84,213]
259. $false <- (4, 17) [subsumption resolution 258,256]
260. ~4 | ~17 [avatar contradiction clause 259]
261. $false [avatar sat refutation 153,180,216,245,246,251,253,255,260]
% SZS output end Proof for 4715501888722366297420590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not patient is generous.
If lucy is rich or quiet then someone is not brave and vice versa.
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.
If susan is wise or not rich then someone is both not kind and not brave.
Everyone who is not calm is not funny or not kind.
Everyone who is not old or rich is both not funny and not strong.
If john is brave or not wise then lucy is not tall.
If mary is both not creative and rich then someone is both not generous and calm and vice versa.
If mary is either kind or not happy then someone is not quiet or not calm.
Everyone who is not humble is not calm and vice versa.
Everyone who is both curious and wise is either happy or not generous.
Everyone who is both patient and not curious is either not old or strong and vice versa.
Everyone who is funny or wise is happy or funny.
John is either not old or not generous.
Alice is either not strong or not curious.
Someone is both wise and not calm.
Someone is either not generous or strong.
Someone is either strong or not old.
Fred is both not funny and humble.
Someone is either not happy or not wise.
Mary is rich. | Fred is not calm. | contradiction | (![X]:((~old(X)&~patient(X))=>generous(X)))&
(((rich(lucy)|quiet(lucy)))<=>(?[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)))&
(((wise(susan)|~rich(susan)))=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:(~calm(X)=>(~funny(X)|~kind(X))))&
(![X]:((~old(X)|rich(X))=>(~funny(X)&~strong(X))))&
(((brave(john)|~wise(john)))=>(~tall(lucy)))&
(((~creative(mary)&rich(mary)))<=>(?[X]:((~generous(X)&calm(X)))))&
(((kind(mary)<~>~happy(mary)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:(~humble(X)<=>~calm(X)))&
(![X]:((curious(X)&wise(X))=>(happy(X)<~>~generous(X))))&
(![X]:((patient(X)&~curious(X))<=>(~old(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>(happy(X)|funny(X))))&
((~old(john)<~>~generous(john)))&
((~strong(alice)<~>~curious(alice)))&
(?[X]:((wise(X)&~calm(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:((strong(X)<~>~old(X))))&
((~funny(fred)&humble(fred)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(rich(mary)) | ~calm(fred) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2131150452206691682669275
% SZS output start Proof for 2131150452206691682669275
12. ! [X0] : (~humble(X0) <=> ~calm(X0)) [input p11]
21. humble(fred) & ~funny(fred) [input p20]
24. ~calm(fred) [input hypothesis]
59. ! [X0] : ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0))) [nnf transformation 12]
110. ~humble(X0) | calm(X0) [cnf transformation 59]
132. humble(fred) [cnf transformation 21]
136. ~calm(fred) [cnf transformation 24]
303. calm(fred) [resolution 110,132]
305. $false [subsumption resolution 303,136]
% SZS output end Proof for 2131150452206691682669275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either patient or not humble then someone is both not kind and calm and vice versa. Everyone who is both rich and happy is both not patient and not strong. Everyone who is either not happy or brave is quiet and vice versa. Everyone who is happy or calm is either rich or humble. Everyone who is either kind or rich is strong. Everyone who is either funny or happy is either brave or funny and vice versa. Everyone who is both not happy and tall is not generous. If lucy is wise then john is either calm or not patient. If someone is both not happy and not creative then someone is rich or calm and vice versa. If lucy is either not tall or calm then someone is patient or not funny. Everyone who is either creative or strong is both not kind and not creative and vice versa. If someone is either generous or tall then lucy is either not wise or not tall. If someone is both not quiet and not patient then someone is not strong or happy and vice versa. If susan is either not patient or not happy then mary is kind and vice versa. If someone is both strong and not funny then susan is rich. Everyone who is creative or rich is both not humble and rich and vice versa. Alice is quiet. Someone is rich or not rich. Alice is either tall or wise. Fred is generous. Lucy is creative. John is either old or tall. Someone is not curious or not strong. Someone is old. | John is brave. | contradiction | (((patient(mary)<~>~humble(mary)))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((rich(X)&happy(X))=>(~patient(X)&~strong(X))))&
(![X]:((~happy(X)<~>brave(X))<=>quiet(X)))&
(![X]:((happy(X)|calm(X))=>(rich(X)<~>humble(X))))&
(![X]:((kind(X)<~>rich(X))=>strong(X)))&
(![X]:((funny(X)<~>happy(X))<=>(brave(X)<~>funny(X))))&
(![X]:((~happy(X)&tall(X))=>~generous(X)))&
((wise(lucy))=>((calm(john)<~>~patient(john))))&
((?[X]:((~happy(X)&~creative(X))))<=>(?[X]:((rich(X)|calm(X)))))&
(((~tall(lucy)<~>calm(lucy)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((creative(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
((?[X]:((generous(X)<~>tall(X))))=>((~wise(lucy)<~>~tall(lucy))))&
((?[X]:((~quiet(X)&~patient(X))))<=>(?[X]:((~strong(X)|happy(X)))))&
(((~patient(susan)<~>~happy(susan)))<=>(kind(mary)))&
((?[X]:((strong(X)&~funny(X))))=>(rich(susan)))&
(![X]:((creative(X)|rich(X))<=>(~humble(X)&rich(X))))&
(quiet(alice))&
(?[X]:((rich(X)|~rich(X))))&
((tall(alice)<~>wise(alice)))&
(generous(fred))&
(creative(lucy))&
((old(john)<~>tall(john)))&
(?[X]:((~curious(X)|~strong(X))))&
(?[X]:(old(X))) | brave(john) | [
"p2",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7550314109862931427439891
% SZS output start Proof for 7550314109862931427439891
3. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> quiet(X0)) [input p2]
6. ! [X0] : ((funny(X0) <~> happy(X0)) <=> (brave(X0) <~> funny(X0))) [input p5]
13. ? [X0] : (~patient(X0) & ~quiet(X0)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p12]
25. brave(john) [input hypothesis]
27. ? [X0] : (~patient(X0) & ~quiet(X0)) <=> ? [X1] : (happy(X1) | ~strong(X1)) [rectify 13]
43. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~quiet(X0)) & (quiet(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 3]
46. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [nnf transformation 6]
59. (? [X0] : (~patient(X0) & ~quiet(X0)) | ! [X1] : (~happy(X1) & strong(X1))) & (? [X1] : (happy(X1) | ~strong(X1)) | ! [X0] : (patient(X0) | quiet(X0))) [nnf transformation 27]
60. (? [X0] : (~patient(X0) & ~quiet(X0)) | ! [X1] : (~happy(X1) & strong(X1))) & (? [X2] : (happy(X2) | ~strong(X2)) | ! [X3] : (patient(X3) | quiet(X3))) [rectify 59]
61. ? [X0] : (~patient(X0) & ~quiet(X0)) => (~patient(sK4) & ~quiet(sK4)) [choice axiom]
62. ? [X2] : (happy(X2) | ~strong(X2)) => (happy(sK5) | ~strong(sK5)) [choice axiom]
63. ((~patient(sK4) & ~quiet(sK4)) | ! [X1] : (~happy(X1) & strong(X1))) & ((happy(sK5) | ~strong(sK5)) | ! [X3] : (patient(X3) | quiet(X3))) [skolemisation 60,62,61]
81. quiet(X0) | brave(X0) | happy(X0) [cnf transformation 43]
82. ~brave(X0) | ~happy(X0) | quiet(X0) [cnf transformation 43]
92. funny(X0) | brave(X0) | funny(X0) | ~happy(X0) [cnf transformation 46]
93. ~funny(X0) | ~brave(X0) | happy(X0) | ~funny(X0) [cnf transformation 46]
95. happy(X0) | funny(X0) | funny(X0) | ~brave(X0) [cnf transformation 46]
98. ~happy(X0) | ~funny(X0) | brave(X0) | ~funny(X0) [cnf transformation 46]
121. ~quiet(sK4) | ~happy(X1) [cnf transformation 63]
143. brave(john) [cnf transformation 25]
146. funny(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 92]
147. ~funny(X0) | ~brave(X0) | happy(X0) [duplicate literal removal 93]
148. happy(X0) | funny(X0) | ~brave(X0) [duplicate literal removal 95]
149. ~happy(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 98]
175. ~brave(X0) | happy(X0) [subsumption resolution 147,148]
176. ~happy(X0) | brave(X0) [subsumption resolution 146,149]
250. 22 <=> ! [X1] : ~happy(X1) [avatar definition]
251. ~happy(X1) <- (22) [avatar component clause 250]
262. 25 <=> quiet(sK4) [avatar definition]
264. ~quiet(sK4) <- (~25) [avatar component clause 262]
265. 22 | ~25 [avatar split clause 121,262,250]
327. happy(john) [resolution 175,143]
345. brave(sK4) | happy(sK4) <- (~25) [resolution 81,264]
346. brave(sK4) <- (~25) [subsumption resolution 345,176]
347. happy(sK4) <- (~25) [resolution 346,175]
349. ~happy(sK4) | quiet(sK4) <- (~25) [resolution 82,346]
351. quiet(sK4) <- (~25) [subsumption resolution 349,347]
352. $false <- (~25) [subsumption resolution 351,264]
353. 25 [avatar contradiction clause 352]
354. $false <- (22) [resolution 251,327]
355. ~22 [avatar contradiction clause 354]
356. $false [avatar sat refutation 265,353,355]
% SZS output end Proof for 7550314109862931427439891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or not old is wise and vice versa.
If someone is kind then alice is either quiet or not kind.
Everyone who is not old is not brave.
Everyone who is humble or not brave is both not happy and happy.
Everyone who is not brave or happy is not patient or strong and vice versa.
Everyone who is both old and calm is either kind or not patient and vice versa.
If someone is either not happy or quiet then someone is curious or funny.
Everyone who is both not curious and funny is both wise and not patient.
If alice is not wise or not old then someone is old and vice versa.
Everyone who is not generous is both funny and curious and vice versa.
Everyone who is both not rich and calm is generous or not rich.
Everyone who is not rich is both creative and not rich and vice versa.
Everyone who is happy is both not curious and kind.
If someone is humble then someone is both not patient and not funny.
If paul is not quiet or not kind then someone is happy and vice versa.
Everyone who is either calm or humble is old and vice versa.
Someone is funny or creative.
Susan is funny.
Someone is creative or rich. | Susan is not strong. | entailment | (![X]:((~patient(X)|~old(X))<=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~curious(X)&funny(X))=>(wise(X)&~patient(X))))&
(((~wise(alice)|~old(alice)))<=>(?[X]:(old(X))))&
(![X]:(~generous(X)<=>(funny(X)&curious(X))))&
(![X]:((~rich(X)&calm(X))=>(generous(X)|~rich(X))))&
(![X]:(~rich(X)<=>(creative(X)&~rich(X))))&
(![X]:(happy(X)=>(~curious(X)&kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~patient(X)&~funny(X)))))&
(((~quiet(paul)|~kind(paul)))<=>(?[X]:(happy(X))))&
(![X]:((calm(X)<~>humble(X))<=>old(X)))&
(?[X]:((funny(X)|creative(X))))&
(funny(susan))&
(?[X]:((creative(X)|rich(X)))) | ~strong(susan) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7412881826363978747898733
% SZS output start Proof for 7412881826363978747898733
3. ! [X0] : (~old(X0) => ~brave(X0)) [input p2]
4. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((happy(X0) | ~brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((calm(X0) & old(X0)) <=> (kind(X0) <~> ~patient(X0))) [input p5]
8. ! [X0] : ((funny(X0) & ~curious(X0)) => (~patient(X0) & wise(X0))) [input p7]
13. ! [X0] : (happy(X0) => (kind(X0) & ~curious(X0))) [input p12]
16. ! [X0] : ((calm(X0) <~> humble(X0)) <=> old(X0)) [input p15]
18. funny(susan) [input p17]
20. strong(susan) [input hypothesis]
25. ! [X0] : (~brave(X0) | old(X0)) [ennf transformation 3]
26. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 4]
28. ! [X0] : ((~patient(X0) & wise(X0)) | (~funny(X0) | curious(X0))) [ennf transformation 8]
29. ! [X0] : ((~patient(X0) & wise(X0)) | ~funny(X0) | curious(X0)) [flattening 28]
34. ! [X0] : ((kind(X0) & ~curious(X0)) | ~happy(X0)) [ennf transformation 13]
39. ! [X0] : (((happy(X0) | ~brave(X0)) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | (~happy(X0) & brave(X0)))) [nnf transformation 5]
40. ! [X0] : ((happy(X0) | ~brave(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | (~happy(X0) & brave(X0)))) [flattening 39]
41. ! [X0] : (((calm(X0) & old(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | (~calm(X0) | ~old(X0)))) [nnf transformation 6]
42. ! [X0] : (((calm(X0) & old(X0)) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) & (((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | ~calm(X0) | ~old(X0))) [flattening 41]
62. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ~old(X0)) & (old(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [nnf transformation 16]
72. ~brave(X0) | old(X0) [cnf transformation 25]
73. ~happy(X0) | ~humble(X0) [cnf transformation 26]
74. ~happy(X0) | brave(X0) [cnf transformation 26]
75. ~humble(X0) | happy(X0) [cnf transformation 26]
76. happy(X0) | brave(X0) [cnf transformation 26]
79. happy(X0) | ~brave(X0) | patient(X0) [cnf transformation 40]
80. happy(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 40]
81. ~calm(X0) | kind(X0) | ~patient(X0) | ~old(X0) [cnf transformation 42]
82. ~calm(X0) | ~kind(X0) | patient(X0) | ~old(X0) [cnf transformation 42]
90. ~funny(X0) | ~patient(X0) | curious(X0) [cnf transformation 29]
99. ~curious(X0) | ~happy(X0) [cnf transformation 34]
100. ~happy(X0) | kind(X0) [cnf transformation 34]
108. humble(X0) | calm(X0) | ~old(X0) [cnf transformation 62]
111. funny(susan) [cnf transformation 18]
113. strong(susan) [cnf transformation 20]
127. brave(X0) [subsumption resolution 74,76]
128. ~humble(X0) [subsumption resolution 73,75]
129. ~strong(X0) | happy(X0) [subsumption resolution 80,127]
130. happy(X0) | patient(X0) [subsumption resolution 79,127]
183. ~old(X0) | calm(X0) [subsumption resolution 108,128]
196. old(X0) [resolution 72,127]
204. happy(susan) [resolution 129,113]
209. kind(X0) | patient(X0) [resolution 130,100]
213. calm(X0) [resolution 183,196]
248. 20 <=> curious(susan) [avatar definition]
249. ~curious(susan) <- (~20) [avatar component clause 248]
250. curious(susan) <- (20) [avatar component clause 248]
265. ~happy(susan) <- (20) [resolution 250,99]
266. $false <- (20) [subsumption resolution 265,204]
267. ~20 [avatar contradiction clause 266]
268. ~patient(susan) | curious(susan) [resolution 90,111]
270. ~patient(susan) <- (~20) [subsumption resolution 268,249]
279. kind(X1) | ~patient(X1) | ~old(X1) [resolution 81,213]
283. kind(X1) | ~patient(X1) [subsumption resolution 279,196]
284. kind(X1) [subsumption resolution 283,209]
288. ~kind(X1) | patient(X1) | ~old(X1) [resolution 82,213]
292. patient(X1) | ~old(X1) [subsumption resolution 288,284]
293. patient(X1) [subsumption resolution 292,196]
305. $false <- (~20) [resolution 293,270]
308. 20 [avatar contradiction clause 305]
310. $false [avatar sat refutation 267,308]
% SZS output end Proof for 7412881826363978747898733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or wise then someone is both not quiet and creative.
Everyone who is old is either not brave or rich and vice versa.
If someone is either funny or tall then someone is strong and vice versa.
If someone is rich then susan is either not curious or old.
Everyone who is not rich is brave or not happy and vice versa.
Everyone who is not quiet is both not brave and humble and vice versa.
If someone is not kind then someone is quiet.
If someone is tall or strong then john is not rich.
Everyone who is humble or not quiet is both wise and not creative.
Everyone who is either not creative or patient is not generous.
Everyone who is brave is either not curious or not creative.
If someone is not strong or humble then someone is both not curious and wise.
If someone is funny or happy then john is either not rich or not calm.
Everyone who is not rich or quiet is happy and vice versa.
Everyone who is funny or patient is happy or not calm.
Everyone who is either not rich or wise is either tall or funny and vice versa.
Lucy is both not rich and not funny.
Paul is not tall or generous.
Someone is not generous.
Someone is not rich or kind.
Someone is either rich or not old.
Someone is either not funny or not rich.
Someone is both not patient and not brave. | John is not old. | entailment | ((?[X]:((curious(X)<~>wise(X))))=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:(old(X)<=>(~brave(X)<~>rich(X))))&
((?[X]:((funny(X)<~>tall(X))))<=>(?[X]:(strong(X))))&
((?[X]:(rich(X)))=>((~curious(susan)<~>old(susan))))&
(![X]:(~rich(X)<=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)<=>(~brave(X)&humble(X))))&
((?[X]:(~kind(X)))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)|strong(X))))=>(~rich(john)))&
(![X]:((humble(X)|~quiet(X))=>(wise(X)&~creative(X))))&
(![X]:((~creative(X)<~>patient(X))=>~generous(X)))&
(![X]:(brave(X)=>(~curious(X)<~>~creative(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((~curious(X)&wise(X)))))&
((?[X]:((funny(X)|happy(X))))=>((~rich(john)<~>~calm(john))))&
(![X]:((~rich(X)|quiet(X))<=>happy(X)))&
(![X]:((funny(X)|patient(X))=>(happy(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(tall(X)<~>funny(X))))&
((~rich(lucy)&~funny(lucy)))&
((~tall(paul)|generous(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((~funny(X)<~>~rich(X))))&
(?[X]:((~patient(X)&~brave(X)))) | ~old(john) | [
"p0",
"p1",
"p4",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4495158373953638457847161
% SZS output start Proof for 4495158373953638457847161
1. ? [X0] : (curious(X0) <~> wise(X0)) => ? [X0] : (creative(X0) & ~quiet(X0)) [input p0]
2. ! [X0] : (old(X0) <=> (~brave(X0) <~> rich(X0))) [input p1]
5. ! [X0] : (~rich(X0) <=> (~happy(X0) | brave(X0))) [input p4]
8. ? [X0] : (strong(X0) | tall(X0)) => ~rich(john) [input p7]
9. ! [X0] : ((~quiet(X0) | humble(X0)) => (~creative(X0) & wise(X0))) [input p8]
12. ? [X0] : (humble(X0) | ~strong(X0)) => ? [X0] : (wise(X0) & ~curious(X0)) [input p11]
14. ! [X0] : ((quiet(X0) | ~rich(X0)) <=> happy(X0)) [input p13]
24. old(john) [input hypothesis]
25. ? [X0] : (curious(X0) <~> wise(X0)) => ? [X1] : (creative(X1) & ~quiet(X1)) [rectify 1]
28. ? [X0] : (humble(X0) | ~strong(X0)) => ? [X1] : (wise(X1) & ~curious(X1)) [rectify 12]
31. ? [X1] : (creative(X1) & ~quiet(X1)) | ! [X0] : (curious(X0) <=> wise(X0)) [ennf transformation 25]
33. ~rich(john) | ! [X0] : (~strong(X0) & ~tall(X0)) [ennf transformation 8]
34. ! [X0] : ((~creative(X0) & wise(X0)) | (quiet(X0) & ~humble(X0))) [ennf transformation 9]
37. ? [X1] : (wise(X1) & ~curious(X1)) | ! [X0] : (~humble(X0) & strong(X0)) [ennf transformation 28]
41. ? [X1] : (creative(X1) & ~quiet(X1)) | ! [X0] : ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))) [nnf transformation 31]
42. ? [X0] : (creative(X0) & ~quiet(X0)) | ! [X1] : ((curious(X1) | ~wise(X1)) & (wise(X1) | ~curious(X1))) [rectify 41]
43. ? [X0] : (creative(X0) & ~quiet(X0)) => (creative(sK0) & ~quiet(sK0)) [choice axiom]
44. (creative(sK0) & ~quiet(sK0)) | ! [X1] : ((curious(X1) | ~wise(X1)) & (wise(X1) | ~curious(X1))) [skolemisation 42,43]
45. ! [X0] : ((old(X0) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ~old(X0))) [nnf transformation 2]
52. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | rich(X0))) [nnf transformation 5]
53. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | rich(X0))) [flattening 52]
58. ? [X0] : (wise(X0) & ~curious(X0)) | ! [X1] : (~humble(X1) & strong(X1)) [rectify 37]
59. ? [X0] : (wise(X0) & ~curious(X0)) => (wise(sK3) & ~curious(sK3)) [choice axiom]
60. (wise(sK3) & ~curious(sK3)) | ! [X1] : (~humble(X1) & strong(X1)) [skolemisation 58,59]
62. ! [X0] : (((quiet(X0) | ~rich(X0)) | ~happy(X0)) & (happy(X0) | (~quiet(X0) & rich(X0)))) [nnf transformation 14]
63. ! [X0] : ((quiet(X0) | ~rich(X0) | ~happy(X0)) & (happy(X0) | (~quiet(X0) & rich(X0)))) [flattening 62]
76. ~quiet(sK0) | curious(X1) | ~wise(X1) [cnf transformation 44]
78. creative(sK0) | curious(X1) | ~wise(X1) [cnf transformation 44]
79. ~brave(X0) | rich(X0) | ~old(X0) [cnf transformation 45]
89. ~happy(X0) | brave(X0) | rich(X0) [cnf transformation 53]
91. ~rich(X0) | happy(X0) [cnf transformation 53]
96. ~rich(john) | ~strong(X0) [cnf transformation 33]
100. ~creative(X0) | quiet(X0) [cnf transformation 34]
105. ~curious(sK3) | strong(X1) [cnf transformation 60]
107. wise(sK3) | strong(X1) [cnf transformation 60]
113. happy(X0) | rich(X0) [cnf transformation 63]
136. old(john) [cnf transformation 24]
138. 1 <=> ! [X1] : (curious(X1) | ~wise(X1)) [avatar definition]
139. ~wise(X1) | curious(X1) <- (1) [avatar component clause 138]
141. 2 <=> creative(sK0) [avatar definition]
143. creative(sK0) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 78,141,138]
150. 4 <=> quiet(sK0) [avatar definition]
153. 1 | ~4 [avatar split clause 76,150,138]
156. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
157. ~strong(X1) <- (5) [avatar component clause 156]
194. 14 <=> rich(john) [avatar definition]
196. ~rich(john) <- (~14) [avatar component clause 194]
197. 5 | ~14 [avatar split clause 96,194,156]
206. 17 <=> wise(sK3) [avatar definition]
208. wise(sK3) <- (17) [avatar component clause 206]
211. 18 <=> ! [X1] : strong(X1) [avatar definition]
212. strong(X1) <- (18) [avatar component clause 211]
213. 18 | 17 [avatar split clause 107,206,211]
215. 19 <=> curious(sK3) [avatar definition]
217. ~curious(sK3) <- (~19) [avatar component clause 215]
219. 18 | ~19 [avatar split clause 105,215,211]
235. happy(X0) [subsumption resolution 113,91]
274. quiet(sK0) <- (2) [resolution 100,143]
277. 4 | ~2 [avatar split clause 274,141,150]
280. curious(sK3) <- (1, 17) [resolution 139,208]
281. $false <- (1, 17, ~19) [subsumption resolution 280,217]
282. ~1 | ~17 | 19 [avatar contradiction clause 281]
319. rich(X0) | brave(X0) [resolution 89,235]
328. brave(john) <- (~14) [resolution 319,196]
381. rich(john) | ~old(john) <- (~14) [resolution 328,79]
393. ~old(john) <- (~14) [subsumption resolution 381,196]
394. $false <- (~14) [subsumption resolution 393,136]
395. 14 [avatar contradiction clause 394]
400. $false <- (5, 18) [subsumption resolution 157,212]
401. ~5 | ~18 [avatar contradiction clause 400]
402. $false [avatar sat refutation 144,153,197,213,219,277,282,395,401]
% SZS output end Proof for 4495158373953638457847161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
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If mary is not brave then someone is either not quiet or not patient.
If someone is not curious or not kind then someone is both not kind and not brave and vice versa.
Everyone who is not strong or generous is calm or generous and vice versa.
If john is both not quiet and funny then someone is either not kind or not tall and vice versa.
If lucy is both not humble and not old then someone is wise and vice versa.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Susan is both generous and not wise.
Someone is either tall or creative. | Alice is rich. | entailment | ((~brave(mary))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)|generous(X))))&
(((~quiet(john)&funny(john)))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~humble(lucy)&~old(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | rich(alice) | [
"p3",
"p4",
"p5",
"p7",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5086870185360375601420675
% SZS output start Proof for 5086870185360375601420675
4. (funny(john) & ~quiet(john)) <=> ? [X0] : (~kind(X0) <~> ~tall(X0)) [input p3]
5. (~old(lucy) & ~humble(lucy)) <=> ? [X0] : wise(X0) [input p4]
6. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p7]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
13. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p12]
14. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p13]
24. ~rich(alice) [input hypothesis]
27. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 13]
30. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 8]
32. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 14]
33. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 32]
46. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (~funny(john) | quiet(john))) [nnf transformation 4]
47. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ~funny(john) | quiet(john)) [flattening 46]
48. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) | ~funny(john) | quiet(john)) [rectify 47]
49. ? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) => ((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) [choice axiom]
50. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) | ~funny(john) | quiet(john)) [skolemisation 48,49]
51. ((~old(lucy) & ~humble(lucy)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (old(lucy) | humble(lucy))) [nnf transformation 5]
52. ((~old(lucy) & ~humble(lucy)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | old(lucy) | humble(lucy)) [flattening 51]
53. ((~old(lucy) & ~humble(lucy)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | old(lucy) | humble(lucy)) [rectify 52]
54. ? [X1] : wise(X1) => wise(sK4) [choice axiom]
55. ((~old(lucy) & ~humble(lucy)) | ! [X0] : ~wise(X0)) & (wise(sK4) | old(lucy) | humble(lucy)) [skolemisation 53,54]
56. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 6]
64. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 64]
66. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 27]
67. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 66]
68. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK6) & kind(sK6)) [choice axiom]
69. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK7) & wise(sK7)) [choice axiom]
70. ((generous(sK6) & kind(sK6)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK7) & wise(sK7)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 67,69,68]
103. funny(john) | ~tall(X0) | kind(X0) [cnf transformation 50]
105. wise(sK4) | old(lucy) | humble(lucy) [cnf transformation 55]
106. ~humble(lucy) | ~wise(X0) [cnf transformation 55]
107. ~old(lucy) | ~wise(X0) [cnf transformation 55]
108. ~happy(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
114. strong(X0) | happy(X0) [cnf transformation 30]
115. ~happy(X0) | strong(X0) [cnf transformation 30]
127. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
128. happy(X0) | happy(X0) [cnf transformation 65]
129. happy(X0) | kind(X0) [cnf transformation 65]
132. kind(sK6) | tall(X1) | ~wise(X1) [cnf transformation 70]
135. ~happy(X0) | wise(X0) | rich(X0) [cnf transformation 33]
154. ~rich(alice) [cnf transformation 24]
155. ~kind(X0) | ~happy(X0) [duplicate literal removal 127]
156. happy(X0) [duplicate literal removal 128]
207. 12 <=> funny(john) [avatar definition]
209. funny(john) <- (12) [avatar component clause 207]
212. 13 <=> ! [X0] : (~tall(X0) | kind(X0)) [avatar definition]
213. ~tall(X0) | kind(X0) <- (13) [avatar component clause 212]
214. 13 | 12 [avatar split clause 103,207,212]
232. 17 <=> ! [X0] : ~wise(X0) [avatar definition]
233. ~wise(X0) <- (17) [avatar component clause 232]
235. 18 <=> old(lucy) [avatar definition]
238. 17 | ~18 [avatar split clause 107,235,232]
240. 19 <=> humble(lucy) [avatar definition]
243. 17 | ~19 [avatar split clause 106,240,232]
245. 20 <=> wise(sK4) [avatar definition]
247. wise(sK4) <- (20) [avatar component clause 245]
248. 19 | 18 | 20 [avatar split clause 105,245,235,240]
249. strong(X0) [subsumption resolution 114,115]
263. ~kind(X0) [subsumption resolution 155,156]
265. 24 <=> ! [X1] : (tall(X1) | ~wise(X1)) [avatar definition]
266. ~wise(X1) | tall(X1) <- (24) [avatar component clause 265]
272. tall(X1) | ~wise(X1) [subsumption resolution 132,263]
273. 24 [avatar split clause 272,265]
274. rich(X0) | wise(X0) [subsumption resolution 135,156]
349. wise(alice) [resolution 274,154]
350. $false <- (17) [subsumption resolution 349,233]
351. ~17 [avatar contradiction clause 350]
353. tall(sK4) <- (20, 24) [resolution 247,266]
360. ~strong(X0) | ~funny(X0) | kind(X0) [resolution 108,129]
362. ~funny(X0) | kind(X0) [subsumption resolution 360,249]
363. ~funny(X0) [subsumption resolution 362,263]
367. $false <- (12) [resolution 363,209]
368. ~12 [avatar contradiction clause 367]
369. ~tall(X0) <- (13) [subsumption resolution 213,263]
374. $false <- (13, 20, 24) [resolution 369,353]
375. ~13 | ~20 | ~24 [avatar contradiction clause 374]
378. $false [avatar sat refutation 214,238,243,248,273,351,368,375]
% SZS output end Proof for 5086870185360375601420675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
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