premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either not curious or patient is humble or not generous and vice versa.
Everyone who is not kind or not funny is not wise and vice versa.
If someone is either not patient or quiet then someone is both brave and not wise and vice versa.
If someone is both not curious and not kind then fred is wise.
Everyone who is both not happy and calm is either not happy or quiet and vice versa.
Everyone who is both humble and not patient is rich.
Everyone who is either not funny or old is patient or brave.
If fred is either not funny or not quiet then mary is either generous or not humble and vice versa.
If john is either not humble or kind then fred is either not funny or rich.
Everyone who is calm or happy is strong.
Everyone who is either not rich or not curious is generous.
If lucy is old or not quiet then alice is not rich.
If lucy is both brave and kind then someone is both not old and creative and vice versa.
If someone is creative or patient then susan is not patient or generous.
Everyone who is calm is wise and vice versa.
Everyone who is tall or not funny is either funny or tall.
Lucy is generous.
Someone is old or not generous.
Mary is wise.
Someone is both not humble and happy.
Someone is not humble.
Someone is both brave and kind.
Someone is happy or funny.
Someone is funny or not funny. | Mary is generous. | neutral | (![X]:((~curious(X)<~>patient(X))<=>(humble(X)|~generous(X))))&
(![X]:((~kind(X)|~funny(X))<=>~wise(X)))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
((?[X]:((~curious(X)&~kind(X))))=>(wise(fred)))&
(![X]:((~happy(X)&calm(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:((humble(X)&~patient(X))=>rich(X)))&
(![X]:((~funny(X)<~>old(X))=>(patient(X)|brave(X))))&
(((~funny(fred)<~>~quiet(fred)))<=>((generous(mary)<~>~humble(mary))))&
(((~humble(john)<~>kind(john)))=>((~funny(fred)<~>rich(fred))))&
(![X]:((calm(X)|happy(X))=>strong(X)))&
(![X]:((~rich(X)<~>~curious(X))=>generous(X)))&
(((old(lucy)|~quiet(lucy)))=>(~rich(alice)))&
(((brave(lucy)&kind(lucy)))<=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(generous(lucy))&
(?[X]:((old(X)|~generous(X))))&
(wise(mary))&
(?[X]:((~humble(X)&happy(X))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((funny(X)|~funny(X)))) | generous(mary) | [] | null | 0 |
If someone is funny or not funny then lucy is both brave and generous. Everyone who is wise is old. Everyone who is either patient or not wise is both brave and not creative. If someone is not quiet or creative then lucy is tall or wise. Everyone who is both not generous and happy is not happy and vice versa. If someone is not strong or not tall then fred is either not kind or curious. Everyone who is either not rich or funny is strong. If someone is old then fred is happy or not generous. Everyone who is tall is either not generous or not brave and vice versa. If lucy is not quiet then lucy is both not generous and not brave and vice versa. If alice is both not tall and not calm then fred is humble and vice versa. Everyone who is tall or not wise is either patient or not old and vice versa. Everyone who is either not tall or not wise is not calm or not creative and vice versa. Everyone who is not curious or humble is not funny or wise and vice versa. Everyone who is not kind or not rich is both not curious and not tall and vice versa. Everyone who is creative or not wise is both not patient and generous and vice versa. Paul is both old and generous. Someone is not funny or not tall. Susan is not patient or creative. Alice is not creative or not tall. Someone is humble or not creative. | Alice is not rich. | neutral | ((?[X]:((funny(X)|~funny(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((patient(X)<~>~wise(X))=>(brave(X)&~creative(X))))&
((?[X]:((~quiet(X)|creative(X))))=>((tall(lucy)|wise(lucy))))&
(![X]:((~generous(X)&happy(X))<=>~happy(X)))&
((?[X]:((~strong(X)|~tall(X))))=>((~kind(fred)<~>curious(fred))))&
(![X]:((~rich(X)<~>funny(X))=>strong(X)))&
((?[X]:(old(X)))=>((happy(fred)|~generous(fred))))&
(![X]:(tall(X)<=>(~generous(X)<~>~brave(X))))&
((~quiet(lucy))<=>((~generous(lucy)&~brave(lucy))))&
(((~tall(alice)&~calm(alice)))<=>(humble(fred)))&
(![X]:((tall(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)|humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((~kind(X)|~rich(X))<=>(~curious(X)&~tall(X))))&
(![X]:((creative(X)|~wise(X))<=>(~patient(X)&generous(X))))&
((old(paul)&generous(paul)))&
(?[X]:((~funny(X)|~tall(X))))&
((~patient(susan)|creative(susan)))&
((~creative(alice)|~tall(alice)))&
(?[X]:((humble(X)|~creative(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is both not curious and not old is not generous.
If paul is rich or old then alice is either not brave or not kind and vice versa.
If someone is generous or not tall then fred is either calm or not strong and vice versa.
Everyone who is not wise or calm is wise and vice versa.
If someone is both brave and not strong then someone is either not happy or tall and vice versa.
Everyone who is either not brave or not patient is quiet.
Everyone who is wise is either not curious or tall and vice versa.
Everyone who is not wise is happy and vice versa.
Everyone who is happy is not quiet and vice versa.
If someone is brave or old then lucy is not old or wise and vice versa.
If john is funny or brave then mary is not happy or old and vice versa.
If someone is both not wise and not calm then alice is both not humble and not old.
If someone is either kind or patient then someone is not kind or tall.
If john is brave then paul is patient or quiet and vice versa.
If paul is either humble or brave then someone is either quiet or not happy and vice versa.
If someone is both not tall and tall then lucy is happy and vice versa.
Someone is either not tall or not strong.
Someone is wise or not generous.
Fred is either not wise or rich.
Someone is either not funny or not creative.
Paul is both creative and not tall.
John is either not quiet or rich.
Paul is humble or funny. | Paul is not quiet. | contradiction | (![X]:((~curious(X)&~old(X))=>~generous(X)))&
(((rich(paul)|old(paul)))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((generous(X)|~tall(X))))<=>((calm(fred)<~>~strong(fred))))&
(![X]:((~wise(X)|calm(X))<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&tall(X))))<=>(happy(lucy)))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~wise(fred)<~>rich(fred)))&
(?[X]:((~funny(X)<~>~creative(X))))&
((creative(paul)&~tall(paul)))&
((~quiet(john)<~>rich(john)))&
((humble(paul)|funny(paul))) | ~quiet(paul) | [
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7029864980088751371486694
% SZS output start Proof for 7029864980088751371486694
4. ! [X0] : ((calm(X0) | ~wise(X0)) <=> wise(X0)) [input p3]
8. ! [X0] : (~wise(X0) <=> happy(X0)) [input p7]
9. ! [X0] : (happy(X0) <=> ~quiet(X0)) [input p8]
24. ~quiet(paul) [input hypothesis]
38. ! [X0] : (((calm(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [nnf transformation 4]
39. ! [X0] : ((calm(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [flattening 38]
47. ! [X0] : ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))) [nnf transformation 9]
93. wise(X0) | wise(X0) [cnf transformation 39]
109. ~wise(X0) | ~happy(X0) [cnf transformation 47]
111. happy(X0) | quiet(X0) [cnf transformation 48]
150. ~quiet(paul) [cnf transformation 24]
151. wise(X0) [duplicate literal removal 93]
236. ~happy(X0) [subsumption resolution 109,151]
237. quiet(X0) [subsumption resolution 111,236]
332. $false [subsumption resolution 150,237]
% SZS output end Proof for 7029864980088751371486694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both tall and humble then someone is both not kind and creative and vice versa.
Everyone who is either not curious or curious is either not funny or calm.
Everyone who is either not humble or calm is not rich and vice versa.
Everyone who is not patient or not humble is either patient or not generous and vice versa.
If someone is strong or not tall then john is patient or old.
If someone is either not humble or strong then susan is either strong or calm.
If fred is not quiet or happy then john is old or not curious and vice versa.
Everyone who is either calm or not happy is both not creative and wise.
If someone is both kind and brave then susan is not funny.
If fred is both not curious and kind then alice is both not kind and not happy.
If someone is funny then lucy is brave and vice versa.
Everyone who is rich is both not rich and not creative and vice versa.
If someone is old or not kind then someone is not strong and vice versa.
Everyone who is both wise and not happy is both rich and kind.
Everyone who is either not creative or quiet is calm and vice versa.
If mary is not wise then mary is both not strong and not quiet.
John is either not old or tall.
Alice is either not brave or creative.
Someone is not wise.
Paul is either not calm or curious.
Someone is both kind and not wise.
Someone is generous.
Someone is both calm and not wise.
Someone is both brave and wise. | Susan is not humble. | entailment | (((tall(mary)&humble(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~curious(X)<~>curious(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~humble(X)<~>calm(X))<=>~rich(X)))&
(![X]:((~patient(X)|~humble(X))<=>(patient(X)<~>~generous(X))))&
((?[X]:((strong(X)|~tall(X))))=>((patient(john)|old(john))))&
((?[X]:((~humble(X)<~>strong(X))))=>((strong(susan)<~>calm(susan))))&
(((~quiet(fred)|happy(fred)))<=>((old(john)|~curious(john))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)&wise(X))))&
((?[X]:((kind(X)&brave(X))))=>(~funny(susan)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>calm(X)))&
((~wise(mary))=>((~strong(mary)&~quiet(mary))))&
((~old(john)<~>tall(john)))&
((~brave(alice)<~>creative(alice)))&
(?[X]:(~wise(X)))&
((~calm(paul)<~>curious(paul)))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((brave(X)&wise(X)))) | ~humble(susan) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p11",
"p13",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8474904269319672829878200
% SZS output start Proof for 8474904269319672829878200
1. (humble(mary) & tall(mary)) <=> ? [X0] : (creative(X0) & ~kind(X0)) [input p0]
2. ! [X0] : ((~curious(X0) <~> curious(X0)) => (~funny(X0) <~> calm(X0))) [input p1]
3. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> ~rich(X0)) [input p2]
8. ! [X0] : ((calm(X0) <~> ~happy(X0)) => (wise(X0) & ~creative(X0))) [input p7]
9. ? [X0] : (brave(X0) & kind(X0)) => ~funny(susan) [input p8]
12. ! [X0] : (rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p11]
14. ! [X0] : ((~happy(X0) & wise(X0)) => (kind(X0) & rich(X0))) [input p13]
15. ! [X0] : ((~creative(X0) <~> quiet(X0)) <=> calm(X0)) [input p14]
16. ~wise(mary) => (~quiet(mary) & ~strong(mary)) [input p15]
24. ? [X0] : (wise(X0) & brave(X0)) [input p23]
25. humble(susan) [input hypothesis]
27. ! [X0] : ((~funny(X0) <~> calm(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 2]
31. ! [X0] : ((wise(X0) & ~creative(X0)) | (calm(X0) <=> ~happy(X0))) [ennf transformation 8]
32. ~funny(susan) | ! [X0] : (~brave(X0) | ~kind(X0)) [ennf transformation 9]
35. ! [X0] : ((kind(X0) & rich(X0)) | (happy(X0) | ~wise(X0))) [ennf transformation 14]
36. ! [X0] : ((kind(X0) & rich(X0)) | happy(X0) | ~wise(X0)) [flattening 35]
37. (~quiet(mary) & ~strong(mary)) | wise(mary) [ennf transformation 16]
38. ((humble(mary) & tall(mary)) | ! [X0] : (~creative(X0) | kind(X0))) & (? [X0] : (creative(X0) & ~kind(X0)) | (~humble(mary) | ~tall(mary))) [nnf transformation 1]
39. ((humble(mary) & tall(mary)) | ! [X0] : (~creative(X0) | kind(X0))) & (? [X0] : (creative(X0) & ~kind(X0)) | ~humble(mary) | ~tall(mary)) [flattening 38]
40. ((humble(mary) & tall(mary)) | ! [X0] : (~creative(X0) | kind(X0))) & (? [X1] : (creative(X1) & ~kind(X1)) | ~humble(mary) | ~tall(mary)) [rectify 39]
41. ? [X1] : (creative(X1) & ~kind(X1)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
42. ((humble(mary) & tall(mary)) | ! [X0] : (~creative(X0) | kind(X0))) & ((creative(sK0) & ~kind(sK0)) | ~humble(mary) | ~tall(mary)) [skolemisation 40,41]
43. ! [X0] : (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 27]
44. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | rich(X0)) & (~rich(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 3]
50. ! [X0] : ((wise(X0) & ~creative(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) [nnf transformation 31]
55. ! [X0] : ((rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [nnf transformation 12]
56. ! [X0] : ((rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [flattening 55]
62. ! [X0] : ((((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | ~calm(X0)) & (calm(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0))))) [nnf transformation 15]
74. ? [X0] : (wise(X0) & brave(X0)) => (wise(sK8) & brave(sK8)) [choice axiom]
75. wise(sK8) & brave(sK8) [skolemisation 24,74]
79. humble(mary) | ~creative(X0) | kind(X0) [cnf transformation 42]
82. ~calm(X0) | funny(X0) | curious(X0) | curious(X0) [cnf transformation 43]
83. ~calm(X0) | funny(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
86. ~humble(X0) | calm(X0) | rich(X0) [cnf transformation 44]
104. ~happy(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 50]
108. ~funny(susan) | ~brave(X0) | ~kind(X0) [cnf transformation 32]
113. ~rich(X0) | ~rich(X0) [cnf transformation 56]
115. rich(X0) | creative(X0) | rich(X0) [cnf transformation 56]
119. rich(X0) | happy(X0) | ~wise(X0) [cnf transformation 36]
123. ~calm(X0) | ~creative(X0) | quiet(X0) [cnf transformation 62]
126. ~quiet(mary) | wise(mary) [cnf transformation 37]
139. brave(sK8) [cnf transformation 75]
141. humble(susan) [cnf transformation 25]
142. ~rich(X0) [duplicate literal removal 113]
143. rich(X0) | creative(X0) [duplicate literal removal 115]
148. ~calm(X0) | funny(X0) | curious(X0) [duplicate literal removal 82]
149. ~calm(X0) | funny(X0) | ~curious(X0) [duplicate literal removal 83]
151. 1 <=> ! [X0] : (~creative(X0) | kind(X0)) [avatar definition]
152. ~creative(X0) | kind(X0) <- (1) [avatar component clause 151]
154. 2 <=> humble(mary) [avatar definition]
156. humble(mary) <- (2) [avatar component clause 154]
157. 1 | 2 [avatar split clause 79,154,151]
173. ~calm(X0) | funny(X0) [subsumption resolution 148,149]
199. 12 <=> calm(susan) [avatar definition]
200. calm(susan) <- (12) [avatar component clause 199]
226. 17 <=> ! [X0] : (~brave(X0) | ~kind(X0)) [avatar definition]
227. ~brave(X0) | ~kind(X0) <- (17) [avatar component clause 226]
229. 18 <=> funny(susan) [avatar definition]
232. 17 | ~18 [avatar split clause 108,229,226]
277. 29 <=> ! [X3] : kind(X3) [avatar definition]
278. kind(X3) <- (29) [avatar component clause 277]
288. ~wise(X0) | happy(X0) [subsumption resolution 119,142]
290. 32 <=> wise(mary) [avatar definition]
292. wise(mary) <- (32) [avatar component clause 290]
294. 33 <=> quiet(mary) [avatar definition]
297. 32 | ~33 [avatar split clause 126,294,290]
330. creative(X1) [resolution 143,142]
341. calm(susan) | rich(susan) [resolution 86,141]
347. calm(susan) [subsumption resolution 341,142]
348. 12 [avatar split clause 347,199]
349. funny(susan) <- (12) [resolution 200,173]
352. 18 | ~12 [avatar split clause 349,199,229]
354. ~kind(sK8) <- (17) [resolution 227,139]
392. kind(X0) <- (1) [subsumption resolution 152,330]
393. 29 | ~1 [avatar split clause 392,151,277]
399. $false <- (17, 29) [resolution 278,354]
400. ~17 | ~29 [avatar contradiction clause 399]
406. calm(mary) | rich(mary) <- (2) [resolution 156,86]
407. calm(mary) <- (2) [subsumption resolution 406,142]
428. ~creative(mary) | quiet(mary) <- (2) [resolution 123,407]
433. quiet(mary) <- (2) [subsumption resolution 428,330]
440. 33 | ~2 [avatar split clause 433,154,294]
442. happy(mary) <- (32) [resolution 292,288]
448. 45 <=> happy(mary) [avatar definition]
450. happy(mary) <- (45) [avatar component clause 448]
452. 45 | ~32 [avatar split clause 442,290,448]
464. ~creative(mary) | ~calm(mary) <- (45) [resolution 450,104]
465. ~calm(mary) <- (45) [subsumption resolution 464,330]
466. $false <- (2, 45) [subsumption resolution 465,407]
467. ~2 | ~45 [avatar contradiction clause 466]
468. $false [avatar sat refutation 157,232,297,348,352,393,400,440,452,467]
% SZS output end Proof for 8474904269319672829878200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not brave then lucy is generous and vice versa.
Everyone who is tall or not calm is humble or not calm.
Everyone who is both calm and strong is either quiet or not patient and vice versa.
Everyone who is humble is either not happy or happy and vice versa.
Everyone who is strong or brave is not strong or not happy.
Everyone who is not quiet or not tall is brave or not tall.
If alice is either not wise or not rich then mary is both patient and not humble and vice versa.
Everyone who is either curious or wise is either not rich or not old and vice versa.
If someone is either not strong or humble then someone is either quiet or not patient and vice versa.
If john is not wise or not brave then fred is both patient and not happy.
If someone is not generous or not patient then someone is either not quiet or wise and vice versa.
If susan is either humble or not creative then alice is funny or rich.
If lucy is both happy and not tall then alice is generous.
Everyone who is either not curious or generous is curious or creative.
Everyone who is either not kind or not brave is not tall or not rich.
If someone is both tall and not humble then lucy is either kind or generous and vice versa.
Paul is either curious or not happy.
Susan is either calm or not tall.
Someone is both brave and not quiet.
Someone is curious.
Paul is wise.
John is wise or not brave.
Alice is not curious or wise.
John is either not patient or not tall. | Lucy is not humble. | contradiction | ((?[X]:((brave(X)<~>~brave(X))))<=>(generous(lucy)))&
(![X]:((tall(X)|~calm(X))=>(humble(X)|~calm(X))))&
(![X]:((calm(X)&strong(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:(humble(X)<=>(~happy(X)<~>happy(X))))&
(![X]:((strong(X)|brave(X))=>(~strong(X)|~happy(X))))&
(![X]:((~quiet(X)|~tall(X))=>(brave(X)|~tall(X))))&
(((~wise(alice)<~>~rich(alice)))<=>((patient(mary)&~humble(mary))))&
(![X]:((curious(X)<~>wise(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~strong(X)<~>humble(X))))<=>(?[X]:((quiet(X)<~>~patient(X)))))&
(((~wise(john)|~brave(john)))=>((patient(fred)&~happy(fred))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(((humble(susan)<~>~creative(susan)))=>((funny(alice)|rich(alice))))&
(((happy(lucy)&~tall(lucy)))=>(generous(alice)))&
(![X]:((~curious(X)<~>generous(X))=>(curious(X)|creative(X))))&
(![X]:((~kind(X)<~>~brave(X))=>(~tall(X)|~rich(X))))&
((?[X]:((tall(X)&~humble(X))))<=>((kind(lucy)<~>generous(lucy))))&
((curious(paul)<~>~happy(paul)))&
((calm(susan)<~>~tall(susan)))&
(?[X]:((brave(X)&~quiet(X))))&
(?[X]:(curious(X)))&
(wise(paul))&
((wise(john)|~brave(john)))&
((~curious(alice)|wise(alice)))&
((~patient(john)<~>~tall(john))) | ~humble(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8498578499464587995779964
% SZS output start Proof for 8498578499464587995779964
4. ! [X0] : (humble(X0) <=> (~happy(X0) <~> happy(X0))) [input p3]
25. ~humble(lucy) [input hypothesis]
47. ! [X0] : ((humble(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~humble(X0))) [nnf transformation 4]
87. humble(X0) | happy(X0) | happy(X0) [cnf transformation 47]
88. humble(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 47]
146. ~humble(lucy) [cnf transformation 25]
148. humble(X0) | happy(X0) [duplicate literal removal 87]
149. humble(X0) | ~happy(X0) [duplicate literal removal 88]
164. humble(X0) [subsumption resolution 148,149]
329. $false [subsumption resolution 146,164]
% SZS output end Proof for 8498578499464587995779964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and not rich then mary is both kind and not quiet.
If lucy is either humble or not funny then mary is both wise and not old and vice versa.
Everyone who is either curious or not kind is both not old and patient and vice versa.
Everyone who is wise or not curious is calm or not tall and vice versa.
If someone is either happy or wise then someone is humble or funny and vice versa.
Everyone who is not brave is old.
If lucy is either kind or not strong then someone is happy or not creative.
Everyone who is both not happy and not tall is both not tall and funny and vice versa.
If alice is either creative or not humble then someone is both not tall and not brave and vice versa.
Everyone who is both not calm and not humble is happy and vice versa.
If someone is funny then paul is both not happy and not humble and vice versa.
If someone is generous then someone is either not strong or not calm.
If john is either not kind or tall then someone is not curious.
Everyone who is generous is either calm or wise and vice versa.
Everyone who is both not creative and not tall is not creative and vice versa.
If someone is funny then paul is not humble or quiet.
Someone is not generous or curious.
Someone is not happy.
Someone is curious or happy.
Someone is either not humble or not generous.
Fred is not wise.
Fred is both brave and generous.
Mary is both not curious and not calm.
Fred is both patient and funny. | Paul is happy. | contradiction | ((?[X]:((brave(X)&~rich(X))))=>((kind(mary)&~quiet(mary))))&
(((humble(lucy)<~>~funny(lucy)))<=>((wise(mary)&~old(mary))))&
(![X]:((curious(X)<~>~kind(X))<=>(~old(X)&patient(X))))&
(![X]:((wise(X)|~curious(X))<=>(calm(X)|~tall(X))))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:((humble(X)|funny(X)))))&
(![X]:(~brave(X)=>old(X)))&
(((kind(lucy)<~>~strong(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((~happy(X)&~tall(X))<=>(~tall(X)&funny(X))))&
(((creative(alice)<~>~humble(alice)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~calm(X)&~humble(X))<=>happy(X)))&
((?[X]:(funny(X)))<=>((~happy(paul)&~humble(paul))))&
((?[X]:(generous(X)))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(((~kind(john)<~>tall(john)))=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(calm(X)<~>wise(X))))&
(![X]:((~creative(X)&~tall(X))<=>~creative(X)))&
((?[X]:(funny(X)))=>((~humble(paul)|quiet(paul))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(~wise(fred))&
((brave(fred)&generous(fred)))&
((~curious(mary)&~calm(mary)))&
((patient(fred)&funny(fred))) | happy(paul) | [
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 181066955955359128676107
% SZS output start Proof for 181066955955359128676107
11. ? [X0] : funny(X0) <=> (~humble(paul) & ~happy(paul)) [input p10]
24. funny(fred) & patient(fred) [input p23]
25. happy(paul) [input hypothesis]
56. (? [X0] : funny(X0) | (humble(paul) | happy(paul))) & ((~humble(paul) & ~happy(paul)) | ! [X0] : ~funny(X0)) [nnf transformation 11]
57. (? [X0] : funny(X0) | humble(paul) | happy(paul)) & ((~humble(paul) & ~happy(paul)) | ! [X0] : ~funny(X0)) [flattening 56]
58. (? [X0] : funny(X0) | humble(paul) | happy(paul)) & ((~humble(paul) & ~happy(paul)) | ! [X1] : ~funny(X1)) [rectify 57]
59. ? [X0] : funny(X0) => funny(sK4) [choice axiom]
60. (funny(sK4) | humble(paul) | happy(paul)) & ((~humble(paul) & ~happy(paul)) | ! [X1] : ~funny(X1)) [skolemisation 58,59]
118. ~happy(paul) | ~funny(X1) [cnf transformation 60]
143. funny(fred) [cnf transformation 24]
144. happy(paul) [cnf transformation 25]
168. 5 <=> ! [X1] : ~funny(X1) [avatar definition]
169. ~funny(X1) <- (5) [avatar component clause 168]
245. 22 <=> happy(paul) [avatar definition]
258. 5 | ~22 [avatar split clause 118,245,168]
314. 22 [avatar split clause 144,245]
315. $false <- (5) [resolution 169,143]
316. ~5 [avatar contradiction clause 315]
317. $false [avatar sat refutation 258,314,316]
% SZS output end Proof for 181066955955359128676107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and quiet then someone is both patient and brave.
If someone is calm or humble then someone is either curious or not funny and vice versa.
Everyone who is not creative is both not creative and not quiet and vice versa.
Everyone who is either rich or not rich is both rich and generous and vice versa.
If someone is strong then fred is both not old and patient.
Everyone who is calm or not funny is old and vice versa.
Everyone who is old or humble is both brave and not rich.
Everyone who is either funny or not humble is generous or not funny.
If fred is not humble or not old then john is either not curious or not wise.
Everyone who is either not wise or generous is both not tall and not creative and vice versa.
Everyone who is patient or not funny is both funny and not calm.
Everyone who is not brave or not curious is either not strong or not humble and vice versa.
Everyone who is funny or not happy is rich or not old and vice versa.
If john is not wise then someone is either not tall or creative.
If someone is both curious and generous then mary is either old or curious.
Fred is generous or not humble.
Someone is either not rich or brave.
Someone is not tall or not patient.
Mary is not happy or not wise.
Someone is both patient and rich. | Fred is strong. | entailment | ((?[X]:((curious(X)&quiet(X))))=>(?[X]:((patient(X)&brave(X)))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:((curious(X)<~>~funny(X)))))&
(![X]:(~creative(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
((?[X]:(strong(X)))=>((~old(fred)&patient(fred))))&
(![X]:((calm(X)|~funny(X))<=>old(X)))&
(![X]:((old(X)|humble(X))=>(brave(X)&~rich(X))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(X)|~funny(X))))&
(((~humble(fred)|~old(fred)))=>((~curious(john)<~>~wise(john))))&
(![X]:((~wise(X)<~>generous(X))<=>(~tall(X)&~creative(X))))&
(![X]:((patient(X)|~funny(X))=>(funny(X)&~calm(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((funny(X)|~happy(X))<=>(rich(X)|~old(X))))&
((~wise(john))=>(?[X]:((~tall(X)<~>creative(X)))))&
((?[X]:((curious(X)&generous(X))))=>((old(mary)<~>curious(mary))))&
((generous(fred)|~humble(fred)))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:((~tall(X)|~patient(X))))&
((~happy(mary)|~wise(mary)))&
(?[X]:((patient(X)&rich(X)))) | strong(fred) | [
"p1",
"p3",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3297205594865119175759211
% SZS output start Proof for 3297205594865119175759211
2. ? [X0] : (humble(X0) | calm(X0)) <=> ? [X0] : (curious(X0) <~> ~funny(X0)) [input p1]
4. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (generous(X0) & rich(X0))) [input p3]
6. ! [X0] : ((~funny(X0) | calm(X0)) <=> old(X0)) [input p5]
7. ! [X0] : ((humble(X0) | old(X0)) => (~rich(X0) & brave(X0))) [input p6]
11. ! [X0] : ((~funny(X0) | patient(X0)) => (~calm(X0) & funny(X0))) [input p10]
12. ! [X0] : ((~curious(X0) | ~brave(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p11]
21. ~strong(fred) [input hypothesis]
23. ? [X0] : (humble(X0) | calm(X0)) <=> ? [X1] : (curious(X1) <~> ~funny(X1)) [rectify 2]
26. ! [X0] : ((~rich(X0) & brave(X0)) | (~humble(X0) & ~old(X0))) [ennf transformation 7]
30. ! [X0] : ((~calm(X0) & funny(X0)) | (funny(X0) & ~patient(X0))) [ennf transformation 11]
36. (? [X0] : (humble(X0) | calm(X0)) | ! [X1] : ((curious(X1) | funny(X1)) & (~funny(X1) | ~curious(X1)))) & (? [X1] : ((funny(X1) | ~curious(X1)) & (~funny(X1) | curious(X1))) | ! [X0] : (~humble(X0) & ~calm(X0))) [nnf transformation 23]
37. (? [X0] : (humble(X0) | calm(X0)) | ! [X1] : ((curious(X1) | funny(X1)) & (~funny(X1) | ~curious(X1)))) & (? [X2] : ((funny(X2) | ~curious(X2)) & (~funny(X2) | curious(X2))) | ! [X3] : (~humble(X3) & ~calm(X3))) [rectify 36]
38. ? [X0] : (humble(X0) | calm(X0)) => (humble(sK1) | calm(sK1)) [choice axiom]
39. ? [X2] : ((funny(X2) | ~curious(X2)) & (~funny(X2) | curious(X2))) => ((funny(sK2) | ~curious(sK2)) & (~funny(sK2) | curious(sK2))) [choice axiom]
40. ((humble(sK1) | calm(sK1)) | ! [X1] : ((curious(X1) | funny(X1)) & (~funny(X1) | ~curious(X1)))) & (((funny(sK2) | ~curious(sK2)) & (~funny(sK2) | curious(sK2))) | ! [X3] : (~humble(X3) & ~calm(X3))) [skolemisation 37,39,38]
43. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 4]
44. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [flattening 43]
45. ! [X0] : (((~funny(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (funny(X0) & ~calm(X0)))) [nnf transformation 6]
46. ! [X0] : ((~funny(X0) | calm(X0) | ~old(X0)) & (old(X0) | (funny(X0) & ~calm(X0)))) [flattening 45]
51. ! [X0] : (((~curious(X0) | ~brave(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (curious(X0) & brave(X0)))) [nnf transformation 12]
52. ! [X0] : ((~curious(X0) | ~brave(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (curious(X0) & brave(X0)))) [flattening 51]
72. humble(sK1) | calm(sK1) | ~funny(X1) | ~curious(X1) [cnf transformation 40]
78. rich(X0) | rich(X0) | rich(X0) [cnf transformation 44]
85. ~calm(X0) | old(X0) [cnf transformation 46]
90. ~rich(X0) | ~old(X0) [cnf transformation 26]
91. ~rich(X0) | ~humble(X0) [cnf transformation 26]
105. funny(X0) | funny(X0) [cnf transformation 30]
111. strong(X0) | humble(X0) | curious(X0) [cnf transformation 52]
129. ~strong(fred) [cnf transformation 21]
130. funny(X0) [duplicate literal removal 105]
133. rich(X0) [duplicate literal removal 78]
155. 5 <=> calm(sK1) [avatar definition]
157. calm(sK1) <- (5) [avatar component clause 155]
159. 6 <=> humble(sK1) [avatar definition]
161. humble(sK1) <- (6) [avatar component clause 159]
164. 7 <=> ! [X1] : (~funny(X1) | ~curious(X1)) [avatar definition]
165. ~funny(X1) | ~curious(X1) <- (7) [avatar component clause 164]
166. 7 | 5 | 6 [avatar split clause 72,159,155,164]
168. 8 <=> ! [X3] : ~humble(X3) [avatar definition]
169. ~humble(X3) <- (8) [avatar component clause 168]
199. ~humble(X0) [subsumption resolution 91,133]
200. 8 [avatar split clause 199,168]
201. ~old(X0) [subsumption resolution 90,133]
238. 20 <=> ! [X0] : ~curious(X0) [avatar definition]
239. ~curious(X0) <- (20) [avatar component clause 238]
272. $false <- (6, 8) [subsumption resolution 161,169]
273. ~6 | ~8 [avatar contradiction clause 272]
280. humble(fred) | curious(fred) [resolution 111,129]
284. curious(fred) <- (8) [subsumption resolution 280,169]
285. $false <- (8, 20) [subsumption resolution 284,239]
286. ~8 | ~20 [avatar contradiction clause 285]
299. old(sK1) <- (5) [resolution 157,85]
300. $false <- (5) [subsumption resolution 299,201]
301. ~5 [avatar contradiction clause 300]
302. ~curious(X1) <- (7) [subsumption resolution 165,130]
303. 20 | ~7 [avatar split clause 302,164,238]
304. $false [avatar sat refutation 166,200,273,286,301,303]
% SZS output end Proof for 3297205594865119175759211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient then lucy is humble or not wise. Everyone who is not quiet is both not quiet and generous and vice versa. Everyone who is not funny is either not generous or not happy and vice versa. If someone is not kind or not curious then someone is both not wise and funny and vice versa. Everyone who is both not curious and not generous is brave and vice versa. Everyone who is both strong and old is either generous or not patient. Everyone who is either rich or wise is either not funny or not tall and vice versa. Everyone who is calm is generous or curious. Everyone who is either calm or not curious is both not wise and not calm. Everyone who is both not strong and patient is both not strong and not kind and vice versa. If someone is either funny or tall then someone is both not curious and not brave. If mary is not wise or happy then someone is both funny and not strong and vice versa. Everyone who is calm or not quiet is both not humble and wise and vice versa. If someone is patient then susan is either not patient or not kind and vice versa. If mary is not happy then mary is either not old or strong. If john is tall or creative then susan is either not wise or strong. Someone is not patient. Lucy is curious. Alice is happy or not happy. Someone is strong. Someone is both not patient and old. Someone is not brave. Someone is either patient or not creative. | Lucy is brave. | contradiction | ((?[X]:(~patient(X)))=>((humble(lucy)|~wise(lucy))))&
(![X]:(~quiet(X)<=>(~quiet(X)&generous(X))))&
(![X]:(~funny(X)<=>(~generous(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~curious(X)&~generous(X))<=>brave(X)))&
(![X]:((strong(X)&old(X))=>(generous(X)<~>~patient(X))))&
(![X]:((rich(X)<~>wise(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:(calm(X)=>(generous(X)|curious(X))))&
(![X]:((calm(X)<~>~curious(X))=>(~wise(X)&~calm(X))))&
(![X]:((~strong(X)&patient(X))<=>(~strong(X)&~kind(X))))&
((?[X]:((funny(X)<~>tall(X))))=>(?[X]:((~curious(X)&~brave(X)))))&
(((~wise(mary)|happy(mary)))<=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((calm(X)|~quiet(X))<=>(~humble(X)&wise(X))))&
((?[X]:(patient(X)))<=>((~patient(susan)<~>~kind(susan))))&
((~happy(mary))=>((~old(mary)<~>strong(mary))))&
(((tall(john)|creative(john)))=>((~wise(susan)<~>strong(susan))))&
(?[X]:(~patient(X)))&
(curious(lucy))&
((happy(alice)|~happy(alice)))&
(?[X]:(strong(X)))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((patient(X)<~>~creative(X)))) | brave(lucy) | [
"p4",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2094426442843014008886091
% SZS output start Proof for 2094426442843014008886091
5. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> brave(X0)) [input p4]
18. curious(lucy) [input p17]
24. brave(lucy) [input hypothesis]
45. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) | curious(X0)))) [nnf transformation 5]
46. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | generous(X0) | curious(X0))) [flattening 45]
94. ~brave(X0) | ~curious(X0) [cnf transformation 46]
140. curious(lucy) [cnf transformation 18]
148. brave(lucy) [cnf transformation 24]
293. ~curious(lucy) [resolution 94,148]
294. $false [subsumption resolution 293,140]
% SZS output end Proof for 2094426442843014008886091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or happy is both not tall and quiet and vice versa.
If someone is either not kind or not generous then fred is both happy and not creative.
If someone is either not brave or not funny then someone is either not curious or not strong and vice versa.
If someone is quiet then susan is both kind and not kind and vice versa.
Everyone who is not rich or not funny is not humble.
If someone is either calm or patient then someone is rich.
Everyone who is quiet is either tall or not rich and vice versa.
Everyone who is either not strong or calm is both strong and creative and vice versa.
If mary is both not brave and not old then someone is both not rich and quiet.
If mary is either not quiet or not curious then paul is not humble and vice versa.
Everyone who is both not wise and humble is brave and vice versa.
If alice is old or not brave then fred is either not curious or quiet.
If susan is either calm or not brave then someone is both kind and patient.
If someone is either not kind or calm then someone is both old and generous.
If fred is not humble then someone is not kind or not wise.
If alice is both not kind and not strong then lucy is both not wise and generous and vice versa.
John is curious or tall.
John is not generous.
Paul is both not quiet and old.
Someone is either old or curious.
Someone is either not happy or not kind. | Mary is not curious. | entailment | (![X]:((~humble(X)|happy(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~generous(X))))=>((happy(fred)&~creative(fred))))&
((?[X]:((~brave(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:(quiet(X)))<=>((kind(susan)&~kind(susan))))&
(![X]:((~rich(X)|~funny(X))=>~humble(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(rich(X))))&
(![X]:(quiet(X)<=>(tall(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>calm(X))<=>(strong(X)&creative(X))))&
(((~brave(mary)&~old(mary)))=>(?[X]:((~rich(X)&quiet(X)))))&
(((~quiet(mary)<~>~curious(mary)))<=>(~humble(paul)))&
(![X]:((~wise(X)&humble(X))<=>brave(X)))&
(((old(alice)|~brave(alice)))=>((~curious(fred)<~>quiet(fred))))&
(((calm(susan)<~>~brave(susan)))=>(?[X]:((kind(X)&patient(X)))))&
((?[X]:((~kind(X)<~>calm(X))))=>(?[X]:((old(X)&generous(X)))))&
((~humble(fred))=>(?[X]:((~kind(X)|~wise(X)))))&
(((~kind(alice)&~strong(alice)))<=>((~wise(lucy)&generous(lucy))))&
((curious(john)|tall(john)))&
(~generous(john))&
((~quiet(paul)&old(paul)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((~happy(X)<~>~kind(X)))) | ~curious(mary) | [
"p0",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 808253796646769592461683
% SZS output start Proof for 808253796646769592461683
1. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (quiet(X0) & ~tall(X0))) [input p0]
4. ? [X0] : quiet(X0) <=> (~kind(susan) & kind(susan)) [input p3]
10. (~quiet(mary) <~> ~curious(mary)) <=> ~humble(paul) [input p9]
22. curious(mary) [input hypothesis]
35. ! [X0] : (((happy(X0) | ~humble(X0)) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | (~happy(X0) & humble(X0)))) [nnf transformation 1]
36. ! [X0] : ((happy(X0) | ~humble(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | (~happy(X0) & humble(X0)))) [flattening 35]
43. (? [X0] : quiet(X0) | (kind(susan) | ~kind(susan))) & ((~kind(susan) & kind(susan)) | ! [X0] : ~quiet(X0)) [nnf transformation 4]
44. (? [X0] : quiet(X0) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X0] : ~quiet(X0)) [flattening 43]
45. (? [X0] : quiet(X0) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
47. (quiet(sK2) | kind(susan) | ~kind(susan)) & ((~kind(susan) & kind(susan)) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
57. (((curious(mary) | quiet(mary)) & (~curious(mary) | ~quiet(mary))) | humble(paul)) & (~humble(paul) | ((~quiet(mary) | curious(mary)) & (~curious(mary) | quiet(mary)))) [nnf transformation 10]
80. quiet(X0) | humble(X0) [cnf transformation 36]
95. kind(susan) | ~quiet(X1) [cnf transformation 47]
96. ~kind(susan) | ~quiet(X1) [cnf transformation 47]
114. ~humble(paul) | ~curious(mary) | quiet(mary) [cnf transformation 57]
146. curious(mary) [cnf transformation 22]
204. 13 <=> ! [X1] : ~quiet(X1) [avatar definition]
205. ~quiet(X1) <- (13) [avatar component clause 204]
207. 14 <=> kind(susan) [avatar definition]
210. 13 | ~14 [avatar split clause 96,207,204]
211. 13 | 14 [avatar split clause 95,207,204]
243. 22 <=> humble(paul) [avatar definition]
244. ~humble(paul) <- (~22) [avatar component clause 243]
247. 23 <=> quiet(mary) [avatar definition]
249. quiet(mary) <- (23) [avatar component clause 247]
251. 24 <=> curious(mary) [avatar definition]
257. 23 | ~24 | ~22 [avatar split clause 114,243,251,247]
378. 24 [avatar split clause 146,251]
379. humble(X0) <- (13) [resolution 80,205]
393. $false <- (13, ~22) [resolution 379,244]
394. ~13 | 22 [avatar contradiction clause 393]
395. $false <- (13, 23) [subsumption resolution 249,205]
396. ~13 | ~23 [avatar contradiction clause 395]
397. $false [avatar sat refutation 210,211,257,378,394,396]
% SZS output end Proof for 808253796646769592461683
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous is not patient or funny and vice versa. Everyone who is not brave is happy and vice versa. Everyone who is tall or strong is curious. Everyone who is either calm or not humble is either not wise or rich and vice versa. If someone is either tall or curious then lucy is humble and vice versa. Everyone who is both brave and not wise is both not generous and creative and vice versa. If someone is funny then lucy is either kind or not rich. Everyone who is either happy or not patient is curious or not wise. Everyone who is both creative and quiet is not calm or wise and vice versa. If john is humble or not tall then someone is not humble or generous and vice versa. Everyone who is either strong or not creative is either not calm or strong and vice versa. Everyone who is not brave is not humble. Everyone who is happy or not humble is both brave and generous and vice versa. If susan is wise then someone is both brave and tall. If mary is either not patient or tall then fred is curious or tall. Everyone who is either creative or not patient is not wise. Susan is either not rich or not kind. Paul is both old and not humble. Someone is both not kind and tall. Lucy is both tall and not patient. Susan is generous or not happy. Someone is patient or not calm. Paul is old or generous. | Paul is not wise. | contradiction | (![X]:((kind(X)<~>~generous(X))<=>(~patient(X)|funny(X))))&
(![X]:(~brave(X)<=>happy(X)))&
(![X]:((tall(X)|strong(X))=>curious(X)))&
(![X]:((calm(X)<~>~humble(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>(humble(lucy)))&
(![X]:((brave(X)&~wise(X))<=>(~generous(X)&creative(X))))&
((?[X]:(funny(X)))=>((kind(lucy)<~>~rich(lucy))))&
(![X]:((happy(X)<~>~patient(X))=>(curious(X)|~wise(X))))&
(![X]:((creative(X)&quiet(X))<=>(~calm(X)|wise(X))))&
(((humble(john)|~tall(john)))<=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>strong(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((happy(X)|~humble(X))<=>(brave(X)&generous(X))))&
((wise(susan))=>(?[X]:((brave(X)&tall(X)))))&
(((~patient(mary)<~>tall(mary)))=>((curious(fred)|tall(fred))))&
(![X]:((creative(X)<~>~patient(X))=>~wise(X)))&
((~rich(susan)<~>~kind(susan)))&
((old(paul)&~humble(paul)))&
(?[X]:((~kind(X)&tall(X))))&
((tall(lucy)&~patient(lucy)))&
((generous(susan)|~happy(susan)))&
(?[X]:((patient(X)|~calm(X))))&
((old(paul)|generous(paul))) | ~wise(paul) | [
"p5",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 102377647725558470880038
% SZS output start Proof for 102377647725558470880038
6. ! [X0] : ((~wise(X0) & brave(X0)) <=> (creative(X0) & ~generous(X0))) [input p5]
12. ! [X0] : (~brave(X0) => ~humble(X0)) [input p11]
13. ! [X0] : ((~humble(X0) | happy(X0)) <=> (generous(X0) & brave(X0))) [input p12]
18. ~humble(paul) & old(paul) [input p17]
24. ~wise(paul) [input hypothesis]
25. ~humble(paul) [pure predicate removal 18]
31. ! [X0] : (~humble(X0) | brave(X0)) [ennf transformation 12]
44. ! [X0] : (((~wise(X0) & brave(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 6]
45. ! [X0] : (((~wise(X0) & brave(X0)) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | wise(X0) | ~brave(X0))) [flattening 44]
56. ! [X0] : (((~humble(X0) | happy(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (humble(X0) & ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : ((~humble(X0) | happy(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (humble(X0) & ~happy(X0)))) [flattening 56]
89. ~brave(X0) | wise(X0) | ~generous(X0) [cnf transformation 45]
114. ~humble(X0) | brave(X0) [cnf transformation 31]
116. brave(X0) | humble(X0) [cnf transformation 57]
118. humble(X0) | generous(X0) [cnf transformation 57]
128. ~humble(paul) [cnf transformation 25]
135. ~wise(paul) [cnf transformation 24]
206. brave(X0) [subsumption resolution 116,114]
251. generous(paul) [resolution 118,128]
302. ~generous(X0) | wise(X0) [resolution 89,206]
304. wise(paul) [resolution 302,251]
306. $false [subsumption resolution 304,135]
% SZS output end Proof for 102377647725558470880038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not wise then someone is either tall or funny.
If susan is not quiet then fred is either not brave or not calm.
Everyone who is calm or rich is humble and vice versa.
Everyone who is not brave or calm is both not happy and funny.
Everyone who is both not generous and funny is happy or brave and vice versa.
If fred is not creative or quiet then someone is patient and vice versa.
Everyone who is generous is either not patient or rich and vice versa.
Everyone who is happy is not funny or not brave.
Everyone who is not humble is both not calm and happy and vice versa.
Everyone who is either not funny or curious is both not patient and strong and vice versa.
Everyone who is not brave is creative.
If someone is not rich then someone is both funny and not rich.
If someone is both not wise and happy then alice is either quiet or not patient and vice versa.
Everyone who is both quiet and generous is not humble or generous.
Everyone who is not kind is either strong or brave and vice versa.
Everyone who is not wise or not happy is both not wise and calm and vice versa.
Susan is either creative or not creative.
Alice is either kind or not humble.
Someone is not generous.
Someone is both creative and generous. | Alice is humble. | entailment | ((~wise(paul))=>(?[X]:((tall(X)<~>funny(X)))))&
((~quiet(susan))=>((~brave(fred)<~>~calm(fred))))&
(![X]:((calm(X)|rich(X))<=>humble(X)))&
(![X]:((~brave(X)|calm(X))=>(~happy(X)&funny(X))))&
(![X]:((~generous(X)&funny(X))<=>(happy(X)|brave(X))))&
(((~creative(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>rich(X))))&
(![X]:(happy(X)=>(~funny(X)|~brave(X))))&
(![X]:(~humble(X)<=>(~calm(X)&happy(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~patient(X)&strong(X))))&
(![X]:(~brave(X)=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~wise(X)&happy(X))))<=>((quiet(alice)<~>~patient(alice))))&
(![X]:((quiet(X)&generous(X))=>(~humble(X)|generous(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~wise(X)&calm(X))))&
((creative(susan)<~>~creative(susan)))&
((kind(alice)<~>~humble(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((creative(X)&generous(X)))) | humble(alice) | [
"p3",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8241761714061394517806382
% SZS output start Proof for 8241761714061394517806382
4. ! [X0] : ((calm(X0) | ~brave(X0)) => (funny(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (brave(X0) | happy(X0))) [input p4]
8. ! [X0] : (happy(X0) => (~brave(X0) | ~funny(X0))) [input p7]
9. ! [X0] : (~humble(X0) <=> (happy(X0) & ~calm(X0))) [input p8]
21. ~humble(alice) [input hypothesis]
25. ! [X0] : ((funny(X0) & ~happy(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 4]
26. ! [X0] : ((~brave(X0) | ~funny(X0)) | ~happy(X0)) [ennf transformation 8]
27. ! [X0] : (~brave(X0) | ~funny(X0) | ~happy(X0)) [flattening 26]
38. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((funny(X0) & ~generous(X0)) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~funny(X0) | generous(X0))) [flattening 38]
46. ! [X0] : ((~humble(X0) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | humble(X0))) [flattening 46]
73. ~happy(X0) | brave(X0) [cnf transformation 25]
75. funny(X0) | brave(X0) [cnf transformation 25]
81. funny(X0) | ~brave(X0) [cnf transformation 39]
89. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 27]
91. happy(X0) | humble(X0) [cnf transformation 47]
125. ~humble(alice) [cnf transformation 21]
154. funny(X0) [subsumption resolution 81,75]
175. ~brave(X0) | ~happy(X0) [subsumption resolution 89,154]
176. ~happy(X0) [subsumption resolution 175,73]
177. humble(X0) [subsumption resolution 91,176]
210. $false [subsumption resolution 125,177]
% SZS output end Proof for 8241761714061394517806382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not old then mary is generous and vice versa.
If mary is either not kind or quiet then someone is both brave and not old.
Everyone who is not quiet is not wise or not brave and vice versa.
If lucy is both generous and quiet then someone is either curious or kind and vice versa.
Everyone who is both not calm and happy is old.
If someone is tall or rich then alice is not generous.
Everyone who is both calm and creative is not calm or rich and vice versa.
If someone is not calm then someone is either strong or not funny and vice versa.
Everyone who is happy or quiet is either not brave or not strong and vice versa.
Everyone who is either not strong or not wise is both generous and patient.
Everyone who is both humble and tall is either tall or not creative.
If lucy is kind then mary is old and vice versa.
Everyone who is either tall or creative is not kind and vice versa.
Everyone who is happy or not creative is wise or generous and vice versa.
If someone is either tall or not tall then paul is both not old and not kind and vice versa.
Everyone who is either wise or not creative is either not curious or curious and vice versa.
Someone is not quiet or not rich.
Someone is either wise or not patient.
Someone is both generous and kind.
Someone is rich.
Someone is generous.
Someone is either rich or patient.
Someone is either curious or not calm.
Someone is both quiet and creative. | Alice is funny. | contradiction | ((?[X]:((happy(X)&~old(X))))<=>(generous(mary)))&
(((~kind(mary)<~>quiet(mary)))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:(~quiet(X)<=>(~wise(X)|~brave(X))))&
(((generous(lucy)&quiet(lucy)))<=>(?[X]:((curious(X)<~>kind(X)))))&
(![X]:((~calm(X)&happy(X))=>old(X)))&
((?[X]:((tall(X)|rich(X))))=>(~generous(alice)))&
(![X]:((calm(X)&creative(X))<=>(~calm(X)|rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
(![X]:((happy(X)|quiet(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(generous(X)&patient(X))))&
(![X]:((humble(X)&tall(X))=>(tall(X)<~>~creative(X))))&
((kind(lucy))<=>(old(mary)))&
(![X]:((tall(X)<~>creative(X))<=>~kind(X)))&
(![X]:((happy(X)|~creative(X))<=>(wise(X)|generous(X))))&
((?[X]:((tall(X)<~>~tall(X))))<=>((~old(paul)&~kind(paul))))&
(![X]:((wise(X)<~>~creative(X))<=>(~curious(X)<~>curious(X))))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:((wise(X)<~>~patient(X))))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:(rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:((quiet(X)&creative(X)))) | funny(alice) | [
"p5",
"p6",
"p7",
"p9",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7451534544892223057551353
% SZS output start Proof for 7451534544892223057551353
6. ? [X0] : (rich(X0) | tall(X0)) => ~generous(alice) [input p5]
7. ! [X0] : ((creative(X0) & calm(X0)) <=> (rich(X0) | ~calm(X0))) [input p6]
8. ? [X0] : ~calm(X0) <=> ? [X0] : (strong(X0) <~> ~funny(X0)) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~wise(X0)) => (patient(X0) & generous(X0))) [input p9]
14. ! [X0] : ((~creative(X0) | happy(X0)) <=> (generous(X0) | wise(X0))) [input p13]
16. ! [X0] : ((wise(X0) <~> ~creative(X0)) <=> (~curious(X0) <~> curious(X0))) [input p15]
20. ? [X0] : rich(X0) [input p19]
25. funny(alice) [input hypothesis]
26. ? [X0] : ~calm(X0) <=> ? [X1] : (strong(X1) <~> ~funny(X1)) [rectify 8]
31. ~generous(alice) | ! [X0] : (~rich(X0) & ~tall(X0)) [ennf transformation 6]
32. ! [X0] : ((patient(X0) & generous(X0)) | (~strong(X0) <=> ~wise(X0))) [ennf transformation 10]
47. ! [X0] : (((creative(X0) & calm(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~creative(X0) | ~calm(X0)))) [nnf transformation 7]
48. ! [X0] : (((creative(X0) & calm(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~creative(X0) | ~calm(X0))) [flattening 47]
49. (? [X0] : ~calm(X0) | ! [X1] : ((strong(X1) | funny(X1)) & (~funny(X1) | ~strong(X1)))) & (? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) | ! [X0] : calm(X0)) [nnf transformation 26]
50. (? [X0] : ~calm(X0) | ! [X1] : ((strong(X1) | funny(X1)) & (~funny(X1) | ~strong(X1)))) & (? [X2] : ((funny(X2) | ~strong(X2)) & (~funny(X2) | strong(X2))) | ! [X3] : calm(X3)) [rectify 49]
51. ? [X0] : ~calm(X0) => ~calm(sK3) [choice axiom]
52. ? [X2] : ((funny(X2) | ~strong(X2)) & (~funny(X2) | strong(X2))) => ((funny(sK4) | ~strong(sK4)) & (~funny(sK4) | strong(sK4))) [choice axiom]
53. (~calm(sK3) | ! [X1] : ((strong(X1) | funny(X1)) & (~funny(X1) | ~strong(X1)))) & (((funny(sK4) | ~strong(sK4)) & (~funny(sK4) | strong(sK4))) | ! [X3] : calm(X3)) [skolemisation 50,52,51]
56. ! [X0] : ((patient(X0) & generous(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) [nnf transformation 32]
59. ! [X0] : (((~creative(X0) | happy(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (creative(X0) & ~happy(X0)))) [nnf transformation 14]
60. ! [X0] : ((~creative(X0) | happy(X0) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | (creative(X0) & ~happy(X0)))) [flattening 59]
66. ! [X0] : ((((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ((wise(X0) | creative(X0)) & (~creative(X0) | ~wise(X0))))) [nnf transformation 16]
74. ? [X0] : rich(X0) => rich(sK9) [choice axiom]
75. rich(sK9) [skolemisation 20,74]
104. ~generous(alice) | ~rich(X0) [cnf transformation 31]
106. calm(X0) | calm(X0) [cnf transformation 48]
112. ~calm(sK3) | ~funny(X1) | ~strong(X1) [cnf transformation 53]
120. ~wise(X0) | generous(X0) | strong(X0) [cnf transformation 56]
131. creative(X0) | wise(X0) | generous(X0) [cnf transformation 60]
144. ~creative(X0) | wise(X0) | curious(X0) | curious(X0) [cnf transformation 66]
145. ~creative(X0) | wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 66]
153. rich(sK9) [cnf transformation 75]
161. funny(alice) [cnf transformation 25]
162. ~creative(X0) | wise(X0) | curious(X0) [duplicate literal removal 144]
163. ~creative(X0) | wise(X0) | ~curious(X0) [duplicate literal removal 145]
171. calm(X0) [duplicate literal removal 106]
239. 15 <=> ! [X0] : ~rich(X0) [avatar definition]
240. ~rich(X0) <- (15) [avatar component clause 239]
242. 16 <=> generous(alice) [avatar definition]
245. 15 | ~16 [avatar split clause 104,242,239]
252. ~funny(X1) | ~strong(X1) [subsumption resolution 112,171]
281. ~creative(X0) | wise(X0) [subsumption resolution 162,163]
330. ~strong(alice) [resolution 252,161]
469. wise(X2) | generous(X2) | wise(X2) [resolution 131,281]
471. wise(X2) | generous(X2) [duplicate literal removal 469]
513. generous(X1) | generous(X1) | strong(X1) [resolution 471,120]
516. strong(X1) | generous(X1) [duplicate literal removal 513]
602. generous(alice) [resolution 516,330]
608. 16 [avatar split clause 602,242]
610. $false <- (15) [resolution 240,153]
613. ~15 [avatar contradiction clause 610]
615. $false [avatar sat refutation 245,608,613]
% SZS output end Proof for 7451534544892223057551353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not kind or not rich then susan is strong and vice versa. Everyone who is either not brave or not curious is both quiet and generous. Everyone who is generous or happy is either not funny or strong and vice versa. If susan is both funny and not curious then fred is either not quiet or not patient and vice versa. Everyone who is both not brave and not humble is not creative or humble. If someone is not patient or not rich then someone is not creative or not kind and vice versa. If alice is not funny then someone is both not old and not calm and vice versa. If someone is either happy or funny then susan is both generous and not humble. If john is humble or not creative then fred is both not calm and funny. If someone is generous then john is not calm and vice versa. Everyone who is calm is either not calm or not wise and vice versa. Everyone who is either wise or not wise is both not curious and not funny and vice versa. If someone is either not rich or patient then mary is both not tall and not calm and vice versa. If paul is both not humble and humble then mary is either old or not creative. Everyone who is rich or humble is not generous. If lucy is not quiet then susan is either calm or not old. Susan is either not old or curious. Mary is both not humble and quiet. Someone is not funny. Fred is patient. Mary is either not brave or not tall. Someone is wise or happy. John is not kind or not rich. | John is not generous. | contradiction | (((~kind(john)<~>~rich(john)))<=>(strong(susan)))&
(![X]:((~brave(X)<~>~curious(X))=>(quiet(X)&generous(X))))&
(![X]:((generous(X)|happy(X))<=>(~funny(X)<~>strong(X))))&
(((funny(susan)&~curious(susan)))<=>((~quiet(fred)<~>~patient(fred))))&
(![X]:((~brave(X)&~humble(X))=>(~creative(X)|humble(X))))&
((?[X]:((~patient(X)|~rich(X))))<=>(?[X]:((~creative(X)|~kind(X)))))&
((~funny(alice))<=>(?[X]:((~old(X)&~calm(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>((generous(susan)&~humble(susan))))&
(((humble(john)|~creative(john)))=>((~calm(fred)&funny(fred))))&
((?[X]:(generous(X)))<=>(~calm(john)))&
(![X]:(calm(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(~curious(X)&~funny(X))))&
((?[X]:((~rich(X)<~>patient(X))))<=>((~tall(mary)&~calm(mary))))&
(((~humble(paul)&humble(paul)))=>((old(mary)<~>~creative(mary))))&
(![X]:((rich(X)|humble(X))=>~generous(X)))&
((~quiet(lucy))=>((calm(susan)<~>~old(susan))))&
((~old(susan)<~>curious(susan)))&
((~humble(mary)&quiet(mary)))&
(?[X]:(~funny(X)))&
(patient(fred))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((wise(X)|happy(X))))&
((~kind(john)|~rich(john))) | ~generous(john) | [
"p1",
"p4",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9044564815844172495770231
% SZS output start Proof for 9044564815844172495770231
2. ! [X0] : ((~brave(X0) <~> ~curious(X0)) => (generous(X0) & quiet(X0))) [input p1]
5. ! [X0] : ((~humble(X0) & ~brave(X0)) => (humble(X0) | ~creative(X0))) [input p4]
9. (~creative(john) | humble(john)) => (funny(fred) & ~calm(fred)) [input p8]
11. ! [X0] : (calm(X0) <=> (~calm(X0) <~> ~wise(X0))) [input p10]
12. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~funny(X0) & ~curious(X0))) [input p11]
24. ~generous(john) [input hypothesis]
26. ! [X0] : ((generous(X0) & quiet(X0)) | (~brave(X0) <=> ~curious(X0))) [ennf transformation 2]
27. ! [X0] : ((humble(X0) | ~creative(X0)) | (humble(X0) | brave(X0))) [ennf transformation 5]
28. ! [X0] : (humble(X0) | ~creative(X0) | humble(X0) | brave(X0)) [flattening 27]
30. (funny(fred) & ~calm(fred)) | (creative(john) & ~humble(john)) [ennf transformation 9]
36. ! [X0] : ((generous(X0) & quiet(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) [nnf transformation 26]
55. ! [X0] : ((calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ~calm(X0))) [nnf transformation 11]
56. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 12]
57. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [flattening 56]
78. ~brave(X0) | generous(X0) | curious(X0) [cnf transformation 36]
91. humble(X0) | ~creative(X0) | humble(X0) | brave(X0) [cnf transformation 28]
105. funny(fred) | ~humble(john) [cnf transformation 30]
106. funny(fred) | creative(john) [cnf transformation 30]
109. ~wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 55]
111. calm(X0) | ~wise(X0) | calm(X0) [cnf transformation 55]
114. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 57]
116. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 57]
141. ~generous(john) [cnf transformation 24]
143. ~curious(X0) | wise(X0) [duplicate literal removal 114]
145. ~funny(X0) | wise(X0) [duplicate literal removal 116]
146. ~wise(X0) | ~calm(X0) [duplicate literal removal 109]
147. ~wise(X0) | calm(X0) [duplicate literal removal 111]
148. ~creative(X0) | humble(X0) | brave(X0) [duplicate literal removal 91]
256. 24 <=> creative(john) [avatar definition]
258. creative(john) <- (24) [avatar component clause 256]
260. 25 <=> funny(fred) [avatar definition]
262. funny(fred) <- (25) [avatar component clause 260]
263. 24 | 25 [avatar split clause 106,260,256]
265. 26 <=> humble(john) [avatar definition]
267. ~humble(john) <- (~26) [avatar component clause 265]
268. ~26 | 25 [avatar split clause 105,260,265]
288. ~wise(X0) [subsumption resolution 146,147]
289. ~funny(X0) [subsumption resolution 145,288]
290. ~curious(X0) [subsumption resolution 143,288]
356. humble(john) | brave(john) <- (24) [resolution 148,258]
357. brave(john) <- (24, ~26) [subsumption resolution 356,267]
363. generous(john) | curious(john) <- (24, ~26) [resolution 357,78]
365. curious(john) <- (24, ~26) [subsumption resolution 363,141]
366. $false <- (24, ~26) [subsumption resolution 365,290]
367. ~24 | 26 [avatar contradiction clause 366]
369. $false <- (25) [subsumption resolution 262,289]
370. ~25 [avatar contradiction clause 369]
371. $false [avatar sat refutation 263,268,367,370]
% SZS output end Proof for 9044564815844172495770231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or old then someone is either not patient or happy.
Everyone who is both old and generous is creative or generous.
If someone is calm or brave then someone is wise and vice versa.
Everyone who is both not curious and wise is not quiet or not kind and vice versa.
If someone is strong or not creative then someone is not humble or not curious.
If someone is not funny or patient then someone is both not creative and not humble and vice versa.
Everyone who is either funny or strong is either not funny or not old.
Everyone who is not creative or curious is both wise and creative.
If someone is both curious and not quiet then someone is old.
If john is either not brave or not curious then someone is old or quiet and vice versa.
Everyone who is strong or not old is curious or not funny.
Everyone who is both tall and quiet is calm or not tall and vice versa.
If lucy is both patient and not wise then mary is either patient or old and vice versa.
Everyone who is both funny and not rich is not old.
Paul is either rich or not strong.
Someone is either strong or funny.
Mary is not old. | Lucy is quiet. | entailment | ((?[X]:((~funny(X)|old(X))))=>(?[X]:((~patient(X)<~>happy(X)))))&
(![X]:((old(X)&generous(X))=>(creative(X)|generous(X))))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:(wise(X))))&
(![X]:((~curious(X)&wise(X))<=>(~quiet(X)|~kind(X))))&
((?[X]:((strong(X)|~creative(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((funny(X)<~>strong(X))=>(~funny(X)<~>~old(X))))&
(![X]:((~creative(X)|curious(X))=>(wise(X)&creative(X))))&
((?[X]:((curious(X)&~quiet(X))))=>(?[X]:(old(X))))&
(((~brave(john)<~>~curious(john)))<=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((strong(X)|~old(X))=>(curious(X)|~funny(X))))&
(![X]:((tall(X)&quiet(X))<=>(calm(X)|~tall(X))))&
(((patient(lucy)&~wise(lucy)))<=>((patient(mary)<~>old(mary))))&
(![X]:((funny(X)&~rich(X))=>~old(X)))&
((rich(paul)<~>~strong(paul)))&
(?[X]:((strong(X)<~>funny(X))))&
(~old(mary)) | quiet(lucy) | [
"p3",
"p5",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8664945634658117573431665
% SZS output start Proof for 8664945634658117573431665
4. ! [X0] : ((wise(X0) & ~curious(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p3]
6. ? [X0] : (patient(X0) | ~funny(X0)) <=> ? [X0] : (~humble(X0) & ~creative(X0)) [input p5]
7. ! [X0] : ((funny(X0) <~> strong(X0)) => (~funny(X0) <~> ~old(X0))) [input p6]
8. ! [X0] : ((curious(X0) | ~creative(X0)) => (creative(X0) & wise(X0))) [input p7]
11. ! [X0] : ((~old(X0) | strong(X0)) => (~funny(X0) | curious(X0))) [input p10]
18. ~quiet(lucy) [input hypothesis]
22. ? [X0] : (patient(X0) | ~funny(X0)) <=> ? [X1] : (~humble(X1) & ~creative(X1)) [rectify 6]
28. ! [X0] : ((~funny(X0) <~> ~old(X0)) | (funny(X0) <=> strong(X0))) [ennf transformation 7]
29. ! [X0] : ((creative(X0) & wise(X0)) | (~curious(X0) & creative(X0))) [ennf transformation 8]
31. ! [X0] : ((~funny(X0) | curious(X0)) | (old(X0) & ~strong(X0))) [ennf transformation 11]
32. ! [X0] : (~funny(X0) | curious(X0) | (old(X0) & ~strong(X0))) [flattening 31]
44. ! [X0] : (((wise(X0) & ~curious(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (~wise(X0) | curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((wise(X0) & ~curious(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ~wise(X0) | curious(X0))) [flattening 44]
49. (? [X0] : (patient(X0) | ~funny(X0)) | ! [X1] : (humble(X1) | creative(X1))) & (? [X1] : (~humble(X1) & ~creative(X1)) | ! [X0] : (~patient(X0) & funny(X0))) [nnf transformation 22]
50. (? [X0] : (patient(X0) | ~funny(X0)) | ! [X1] : (humble(X1) | creative(X1))) & (? [X2] : (~humble(X2) & ~creative(X2)) | ! [X3] : (~patient(X3) & funny(X3))) [rectify 49]
51. ? [X0] : (patient(X0) | ~funny(X0)) => (patient(sK4) | ~funny(sK4)) [choice axiom]
52. ? [X2] : (~humble(X2) & ~creative(X2)) => (~humble(sK5) & ~creative(sK5)) [choice axiom]
53. ((patient(sK4) | ~funny(sK4)) | ! [X1] : (humble(X1) | creative(X1))) & ((~humble(sK5) & ~creative(sK5)) | ! [X3] : (~patient(X3) & funny(X3))) [skolemisation 50,52,51]
54. ! [X0] : (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0)))) [nnf transformation 28]
79. ~curious(X0) | quiet(X0) [cnf transformation 45]
85. ~creative(sK5) | funny(X3) [cnf transformation 53]
90. ~old(X0) | ~funny(X0) | strong(X0) | ~funny(X0) [cnf transformation 54]
96. creative(X0) | creative(X0) [cnf transformation 29]
105. ~strong(X0) | curious(X0) | ~funny(X0) [cnf transformation 32]
106. ~funny(X0) | curious(X0) | old(X0) [cnf transformation 32]
124. ~quiet(lucy) [cnf transformation 18]
127. creative(X0) [duplicate literal removal 96]
128. ~old(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 90]
143. 4 <=> ! [X1] : funny(X1) [avatar definition]
144. funny(X1) <- (4) [avatar component clause 143]
173. 11 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (11) [avatar component clause 173]
210. 20 <=> creative(sK5) [avatar definition]
212. ~creative(sK5) <- (~20) [avatar component clause 210]
214. 4 | ~20 [avatar split clause 85,210,143]
215. 11 [avatar split clause 127,173]
289. $false <- (11, ~20) [resolution 212,174]
290. ~11 | 20 [avatar contradiction clause 289]
305. curious(X0) | old(X0) <- (4) [resolution 106,144]
337. quiet(X3) | old(X3) <- (4) [resolution 305,79]
357. old(lucy) <- (4) [resolution 337,124]
359. ~funny(lucy) | strong(lucy) <- (4) [resolution 357,128]
361. strong(lucy) <- (4) [subsumption resolution 359,144]
366. curious(lucy) | ~funny(lucy) <- (4) [resolution 361,105]
367. curious(lucy) <- (4) [subsumption resolution 366,144]
375. quiet(lucy) <- (4) [resolution 367,79]
376. $false <- (4) [subsumption resolution 375,124]
377. ~4 [avatar contradiction clause 376]
378. $false [avatar sat refutation 214,215,290,377]
% SZS output end Proof for 8664945634658117573431665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and old then lucy is both not curious and not kind.
If someone is old or brave then fred is not patient and vice versa.
Everyone who is either brave or not generous is quiet or old.
Everyone who is not patient or humble is not tall and vice versa.
If someone is not happy then mary is not happy.
Everyone who is generous or rich is either curious or not funny.
Everyone who is both not happy and happy is quiet or not curious and vice versa.
If alice is not wise or not rich then susan is either calm or not quiet and vice versa.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
If lucy is both calm and tall then someone is not generous and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
If someone is creative or humble then lucy is not calm.
Fred is not calm.
Someone is either not creative or not curious.
Someone is not kind or not creative.
John is curious.
Someone is both wise and happy.
Alice is either tall or funny. | Mary is not humble. | contradiction | (((~rich(lucy)&old(lucy)))=>((~curious(lucy)&~kind(lucy))))&
((?[X]:((old(X)|brave(X))))<=>(~patient(fred)))&
(![X]:((brave(X)<~>~generous(X))=>(quiet(X)|old(X))))&
(![X]:((~patient(X)|humble(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(~happy(mary)))&
(![X]:((generous(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))<=>(quiet(X)|~curious(X))))&
(((~wise(alice)|~rich(alice)))<=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
((?[X]:((creative(X)|humble(X))))=>(~calm(lucy)))&
(~calm(fred))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(curious(john))&
(?[X]:((wise(X)&happy(X))))&
((tall(alice)<~>funny(alice))) | ~humble(mary) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 342766013894156685832477
% SZS output start Proof for 342766013894156685832477
2. ? [X0] : (brave(X0) | old(X0)) <=> ~patient(fred) [input p1]
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (old(X0) | quiet(X0))) [input p2]
4. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~tall(X0)) [input p3]
7. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~curious(X0) | quiet(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p9]
13. ! [X0] : (kind(X0) => patient(X0)) [input p12]
15. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p14]
23. ~humble(mary) [input hypothesis]
26. ! [X0] : ((old(X0) | quiet(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
27. ! [X0] : (old(X0) | quiet(X0) | (brave(X0) <=> ~generous(X0))) [flattening 26]
32. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 13]
36. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (~brave(X0) & ~old(X0))) [nnf transformation 2]
37. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [rectify 36]
38. ? [X0] : (brave(X0) | old(X0)) => (brave(sK0) | old(sK0)) [choice axiom]
39. ((brave(sK0) | old(sK0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [skolemisation 37,38]
40. ! [X0] : (old(X0) | quiet(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 27]
41. ! [X0] : (((humble(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [flattening 41]
44. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 7]
45. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~happy(X0) | happy(X0))) [flattening 44]
49. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 10]
57. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 15]
68. ~patient(fred) | ~old(X1) [cnf transformation 39]
69. ~patient(fred) | ~brave(X1) [cnf transformation 39]
72. quiet(X0) | old(X0) | brave(X0) | generous(X0) [cnf transformation 40]
73. ~tall(X0) | patient(X0) [cnf transformation 42]
75. ~patient(X0) | humble(X0) | tall(X0) [cnf transformation 42]
82. ~happy(X0) | ~quiet(X0) [cnf transformation 45]
84. ~quiet(X0) | happy(X0) [cnf transformation 45]
96. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
97. ~generous(X0) | ~tall(X0) | quiet(X0) [cnf transformation 49]
107. ~kind(X0) | patient(X0) [cnf transformation 32]
110. ~generous(X0) | kind(X0) [cnf transformation 57]
122. ~humble(mary) [cnf transformation 23]
142. 5 <=> patient(fred) [avatar definition]
143. ~patient(fred) <- (~5) [avatar component clause 142]
155. 8 <=> ! [X1] : ~brave(X1) [avatar definition]
156. ~brave(X1) <- (8) [avatar component clause 155]
157. 8 | ~5 [avatar split clause 69,142,155]
159. 9 <=> ! [X1] : ~old(X1) [avatar definition]
160. ~old(X1) <- (9) [avatar component clause 159]
161. 9 | ~5 [avatar split clause 68,142,159]
171. ~quiet(X0) [subsumption resolution 82,84]
190. ~tall(X0) | ~generous(X0) [subsumption resolution 97,171]
191. tall(X0) | generous(X0) [subsumption resolution 96,171]
193. 15 <=> ! [X0] : generous(X0) [avatar definition]
194. generous(X0) <- (15) [avatar component clause 193]
259. generous(X2) | patient(X2) [resolution 191,73]
262. patient(X0) | kind(X0) [resolution 259,110]
266. patient(X0) [subsumption resolution 262,107]
268. $false <- (~5) [resolution 266,143]
269. tall(X0) | humble(X0) [resolution 266,75]
270. 5 [avatar contradiction clause 268]
291. old(X1) | brave(X1) | generous(X1) [resolution 72,171]
296. brave(X1) | generous(X1) <- (9) [subsumption resolution 291,160]
297. generous(X1) <- (8, 9) [subsumption resolution 296,156]
300. 15 | ~8 | ~9 [avatar split clause 297,159,155,193]
331. humble(X0) | ~generous(X0) [resolution 269,190]
336. humble(X0) <- (15) [subsumption resolution 331,194]
337. $false <- (15) [resolution 336,122]
339. ~15 [avatar contradiction clause 337]
340. $false [avatar sat refutation 157,161,270,300,339]
% SZS output end Proof for 342766013894156685832477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not curious then alice is both strong and not brave and vice versa.
If someone is calm then john is either quiet or not humble and vice versa.
If mary is either funny or strong then alice is either not quiet or not patient and vice versa.
Everyone who is not curious is calm or happy.
Everyone who is not wise is generous.
Everyone who is both tall and not tall is both strong and creative and vice versa.
Everyone who is both not tall and not happy is both not generous and not creative and vice versa.
If someone is not brave then mary is either strong or rich.
Everyone who is both humble and not kind is either quiet or not funny.
Everyone who is not patient or generous is either generous or not creative and vice versa.
If fred is not patient or wise then someone is either curious or not tall.
If susan is either not brave or happy then someone is not funny or old and vice versa.
If someone is either curious or patient then someone is both curious and not patient.
Everyone who is quiet or not tall is either kind or calm.
If mary is rich or curious then someone is curious and vice versa.
Everyone who is old or not generous is creative or not curious.
Alice is both patient and not quiet.
Someone is generous or curious.
Someone is either kind or not patient.
Someone is both not generous and not curious.
Someone is both not patient and creative.
Someone is not humble or wise. | Alice is happy. | neutral | ((?[X]:((quiet(X)<~>~curious(X))))<=>((strong(alice)&~brave(alice))))&
((?[X]:(calm(X)))<=>((quiet(john)<~>~humble(john))))&
(((funny(mary)<~>strong(mary)))<=>((~quiet(alice)<~>~patient(alice))))&
(![X]:(~curious(X)=>(calm(X)|happy(X))))&
(![X]:(~wise(X)=>generous(X)))&
(![X]:((tall(X)&~tall(X))<=>(strong(X)&creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>(~generous(X)&~creative(X))))&
((?[X]:(~brave(X)))=>((strong(mary)<~>rich(mary))))&
(![X]:((humble(X)&~kind(X))=>(quiet(X)<~>~funny(X))))&
(![X]:((~patient(X)|generous(X))<=>(generous(X)<~>~creative(X))))&
(((~patient(fred)|wise(fred)))=>(?[X]:((curious(X)<~>~tall(X)))))&
(((~brave(susan)<~>happy(susan)))<=>(?[X]:((~funny(X)|old(X)))))&
((?[X]:((curious(X)<~>patient(X))))=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((quiet(X)|~tall(X))=>(kind(X)<~>calm(X))))&
(((rich(mary)|curious(mary)))<=>(?[X]:(curious(X))))&
(![X]:((old(X)|~generous(X))=>(creative(X)|~curious(X))))&
((patient(alice)&~quiet(alice)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~generous(X)&~curious(X))))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((~humble(X)|wise(X)))) | happy(alice) | [] | null | 0 |
Everyone who is either not happy or kind is creative and vice versa. If someone is curious then someone is both not kind and strong and vice versa. If someone is calm then john is not rich. Everyone who is either not patient or not curious is not brave and vice versa. If susan is not kind then mary is either not creative or humble. If mary is both wise and old then lucy is not humble. Everyone who is either creative or strong is strong and vice versa. Everyone who is either old or not funny is both not calm and funny. Everyone who is not creative is not calm. If someone is both not wise and not funny then someone is both not generous and brave and vice versa. If someone is either not patient or patient then alice is kind and vice versa. If someone is both not patient and not humble then someone is both rich and not creative. Everyone who is brave or not funny is either calm or not brave. If lucy is both not happy and old then someone is rich. Everyone who is rich or not calm is humble. Everyone who is not humble or not patient is humble or not wise and vice versa. Fred is both not quiet and not patient. Someone is humble or creative. Mary is patient or not tall. Someone is old. Someone is either quiet or creative. Someone is not strong or not kind. | Mary is not curious. | contradiction | (![X]:((~happy(X)<~>kind(X))<=>creative(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:(calm(X)))=>(~rich(john)))&
(![X]:((~patient(X)<~>~curious(X))<=>~brave(X)))&
((~kind(susan))=>((~creative(mary)<~>humble(mary))))&
(((wise(mary)&old(mary)))=>(~humble(lucy)))&
(![X]:((creative(X)<~>strong(X))<=>strong(X)))&
(![X]:((old(X)<~>~funny(X))=>(~calm(X)&funny(X))))&
(![X]:(~creative(X)=>~calm(X)))&
((?[X]:((~wise(X)&~funny(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
((?[X]:((~patient(X)<~>patient(X))))<=>(kind(alice)))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((brave(X)|~funny(X))=>(calm(X)<~>~brave(X))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:((~humble(X)|~patient(X))<=>(humble(X)|~wise(X))))&
((~quiet(fred)&~patient(fred)))&
(?[X]:((humble(X)|creative(X))))&
((patient(mary)|~tall(mary)))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:((~strong(X)|~kind(X)))) | ~curious(mary) | [
"p3",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4213087966945661166131016
% SZS output start Proof for 4213087966945661166131016
4. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p3]
7. ! [X0] : ((creative(X0) <~> strong(X0)) <=> strong(X0)) [input p6]
9. ! [X0] : (~creative(X0) => ~calm(X0)) [input p8]
13. ! [X0] : ((~funny(X0) | brave(X0)) => (calm(X0) <~> ~brave(X0))) [input p12]
15. ! [X0] : ((~calm(X0) | rich(X0)) => humble(X0)) [input p14]
16. ! [X0] : ((~patient(X0) | ~humble(X0)) <=> (~wise(X0) | humble(X0))) [input p15]
23. ~curious(mary) [input hypothesis]
33. ! [X0] : (~calm(X0) | creative(X0)) [ennf transformation 9]
35. ! [X0] : ((calm(X0) <~> ~brave(X0)) | (funny(X0) & ~brave(X0))) [ennf transformation 13]
38. ! [X0] : (humble(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 15]
45. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | brave(X0)) & (~brave(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ~strong(X0)) & (strong(X0) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 7]
61. ! [X0] : (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (funny(X0) & ~brave(X0))) [nnf transformation 35]
64. ! [X0] : (((~patient(X0) | ~humble(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (patient(X0) & humble(X0)))) [nnf transformation 16]
65. ! [X0] : ((~patient(X0) | ~humble(X0) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | (patient(X0) & humble(X0)))) [flattening 64]
86. brave(X0) | patient(X0) | curious(X0) [cnf transformation 45]
90. strong(X0) | strong(X0) | ~creative(X0) [cnf transformation 47]
93. ~strong(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 47]
98. ~calm(X0) | creative(X0) [cnf transformation 33]
109. ~brave(X0) | calm(X0) | ~brave(X0) [cnf transformation 61]
115. humble(X0) | calm(X0) [cnf transformation 38]
118. ~patient(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 65]
127. ~curious(mary) [cnf transformation 23]
129. ~humble(X0) | ~patient(X0) [duplicate literal removal 118]
130. ~brave(X0) | calm(X0) [duplicate literal removal 109]
134. strong(X0) | ~creative(X0) [duplicate literal removal 90]
135. ~strong(X0) | ~creative(X0) [duplicate literal removal 93]
158. 6 <=> ! [X0] : ~calm(X0) [avatar definition]
159. ~calm(X0) <- (6) [avatar component clause 158]
192. ~creative(X0) [subsumption resolution 134,135]
193. ~calm(X0) [subsumption resolution 98,192]
194. 6 [avatar split clause 193,158]
222. 20 <=> ! [X1] : ~patient(X1) [avatar definition]
223. ~patient(X1) <- (20) [avatar component clause 222]
273. ~patient(X0) | calm(X0) [resolution 129,115]
277. ~patient(X0) <- (6) [subsumption resolution 273,159]
278. 20 | ~6 [avatar split clause 277,158,222]
298. patient(X3) | curious(X3) | calm(X3) [resolution 86,130]
303. curious(X3) | calm(X3) <- (20) [subsumption resolution 298,223]
307. curious(X3) <- (6, 20) [subsumption resolution 303,159]
318. $false <- (6, 20) [resolution 307,127]
319. ~6 | ~20 [avatar contradiction clause 318]
320. $false [avatar sat refutation 194,278,319]
% SZS output end Proof for 4213087966945661166131016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not humble.
Everyone who is curious is not quiet or strong.
If someone is both old and not kind then fred is both funny and not funny.
If john is either not tall or not curious then someone is not happy and vice versa.
Everyone who is either creative or not tall is both tall and not calm.
Everyone who is either generous or calm is rich and vice versa.
If someone is either creative or strong then mary is not brave.
Everyone who is both humble and happy is either not kind or funny and vice versa.
Everyone who is not quiet is not brave or not rich and vice versa.
Everyone who is old is generous or not old and vice versa.
Everyone who is not rich is both strong and quiet.
Everyone who is both not rich and not tall is both patient and happy.
Everyone who is quiet or not funny is curious or generous.
If someone is humble or not kind then someone is not brave or not old and vice versa.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
John is either not funny or patient.
Someone is not humble.
Alice is quiet.
Alice is not happy or happy.
Someone is not rich or not curious. | Mary is not brave. | contradiction | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~humble(X)))&
(![X]:(curious(X)=>(~quiet(X)|strong(X))))&
((?[X]:((old(X)&~kind(X))))=>((funny(fred)&~funny(fred))))&
(((~tall(john)<~>~curious(john)))<=>(?[X]:(~happy(X))))&
(![X]:((creative(X)<~>~tall(X))=>(tall(X)&~calm(X))))&
(![X]:((generous(X)<~>calm(X))<=>rich(X)))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((~funny(john)<~>patient(john)))&
(?[X]:(~humble(X)))&
(quiet(alice))&
((~happy(alice)|happy(alice)))&
(?[X]:((~rich(X)|~curious(X)))) | ~brave(mary) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 598412704717572602151705
% SZS output start Proof for 598412704717572602151705
2. ! [X0] : ((~calm(X0) <~> ~kind(X0)) => ~humble(X0)) [input p1]
4. ? [X0] : (~kind(X0) & old(X0)) => (~funny(fred) & funny(fred)) [input p3]
7. ! [X0] : ((generous(X0) <~> calm(X0)) <=> rich(X0)) [input p6]
10. ! [X0] : (~quiet(X0) <=> (~rich(X0) | ~brave(X0))) [input p9]
11. ! [X0] : (old(X0) <=> (~old(X0) | generous(X0))) [input p10]
12. ! [X0] : (~rich(X0) => (quiet(X0) & strong(X0))) [input p11]
15. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : (~old(X0) | ~brave(X0)) [input p14]
22. ~brave(mary) [input hypothesis]
23. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : (~old(X1) | ~brave(X1)) [rectify 15]
24. ! [X0] : (~humble(X0) | (~calm(X0) <=> ~kind(X0))) [ennf transformation 2]
27. (~funny(fred) & funny(fred)) | ! [X0] : (kind(X0) | ~old(X0)) [ennf transformation 4]
30. ! [X0] : ((quiet(X0) & strong(X0)) | rich(X0)) [ennf transformation 12]
37. ! [X0] : (~humble(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) [nnf transformation 24]
43. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | ~rich(X0)) & (rich(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 7]
47. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 10]
48. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | quiet(X0))) [flattening 47]
49. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | ~old(X0))) [nnf transformation 11]
50. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~old(X0))) [flattening 49]
51. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X1] : (~old(X1) | ~brave(X1)) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 23]
52. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X2] : (~old(X2) | ~brave(X2)) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 51]
53. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK1) | humble(sK1)) [choice axiom]
54. ? [X2] : (~old(X2) | ~brave(X2)) => (~old(sK2) | ~brave(sK2)) [choice axiom]
55. ((~kind(sK1) | humble(sK1)) | ! [X1] : (old(X1) & brave(X1))) & ((~old(sK2) | ~brave(sK2)) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 52,54,53]
69. ~kind(X0) | ~humble(X0) | calm(X0) [cnf transformation 37]
72. funny(fred) | kind(X0) | ~old(X0) [cnf transformation 27]
73. ~funny(fred) | kind(X0) | ~old(X0) [cnf transformation 27]
85. ~rich(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 43]
96. ~quiet(X0) | rich(X0) [cnf transformation 48]
97. ~old(X0) | generous(X0) | ~old(X0) [cnf transformation 50]
99. old(X0) | old(X0) [cnf transformation 50]
101. quiet(X0) | rich(X0) [cnf transformation 30]
108. ~kind(sK1) | humble(sK1) | brave(X1) [cnf transformation 55]
122. ~brave(mary) [cnf transformation 22]
123. ~old(X0) | generous(X0) [duplicate literal removal 97]
124. old(X0) [duplicate literal removal 99]
129. 1 <=> ! [X0] : (kind(X0) | ~old(X0)) [avatar definition]
130. kind(X0) | ~old(X0) <- (1) [avatar component clause 129]
132. 2 <=> funny(fred) [avatar definition]
135. 1 | ~2 [avatar split clause 73,132,129]
136. 1 | 2 [avatar split clause 72,132,129]
161. 8 <=> brave(mary) [avatar definition]
163. ~brave(mary) <- (~8) [avatar component clause 161]
165. generous(X0) [subsumption resolution 123,124]
166. rich(X0) [subsumption resolution 101,96]
168. 9 <=> ! [X1] : brave(X1) [avatar definition]
169. brave(X1) <- (9) [avatar component clause 168]
171. 10 <=> humble(sK1) [avatar definition]
173. humble(sK1) <- (10) [avatar component clause 171]
175. 11 <=> kind(sK1) [avatar definition]
177. ~kind(sK1) <- (~11) [avatar component clause 175]
178. 9 | 10 | ~11 [avatar split clause 108,175,171,168]
181. 12 <=> ! [X3] : kind(X3) [avatar definition]
182. kind(X3) <- (12) [avatar component clause 181]
228. ~8 [avatar split clause 122,161]
229. kind(X0) <- (1) [subsumption resolution 130,124]
230. 12 | ~1 [avatar split clause 229,129,181]
233. $false <- (~11, 12) [resolution 182,177]
234. 11 | ~12 [avatar contradiction clause 233]
235. $false <- (~8, 9) [resolution 169,163]
236. 8 | ~9 [avatar contradiction clause 235]
240. ~humble(X0) | calm(X0) <- (12) [resolution 69,182]
241. calm(sK1) <- (10, 12) [resolution 240,173]
248. ~generous(X0) | ~calm(X0) [resolution 85,166]
249. ~calm(X0) [subsumption resolution 248,165]
251. $false <- (10, 12) [resolution 249,241]
252. ~10 | ~12 [avatar contradiction clause 251]
253. $false [avatar sat refutation 135,136,178,228,230,234,236,252]
% SZS output end Proof for 598412704717572602151705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not funny or not curious.
Everyone who is both tall and curious is not humble.
If someone is either curious or old then someone is both not humble and not happy.
Everyone who is curious or not kind is not wise or not tall.
Everyone who is both not patient and rich is both quiet and not generous.
Everyone who is funny or calm is not brave and vice versa.
Everyone who is not generous is kind or not kind and vice versa.
If alice is either not funny or not strong then someone is not strong or not curious.
Everyone who is either creative or not curious is strong and vice versa.
If john is both humble and rich then someone is both calm and brave.
If fred is funny or not creative then someone is kind or not wise and vice versa.
If someone is quiet then paul is not creative or not wise.
If someone is not brave or not funny then fred is both brave and not creative and vice versa.
If someone is quiet then someone is creative and vice versa.
Everyone who is both creative and not rich is both not happy and not wise and vice versa.
Lucy is either not happy or not strong.
Mary is humble.
Paul is strong or curious.
Someone is tall.
Susan is either not curious or funny. | Fred is not wise. | neutral | (![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((tall(X)&curious(X))=>~humble(X)))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((curious(X)|~kind(X))=>(~wise(X)|~tall(X))))&
(![X]:((~patient(X)&rich(X))=>(quiet(X)&~generous(X))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
(![X]:(~generous(X)<=>(kind(X)|~kind(X))))&
(((~funny(alice)<~>~strong(alice)))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((creative(X)<~>~curious(X))<=>strong(X)))&
(((humble(john)&rich(john)))=>(?[X]:((calm(X)&brave(X)))))&
(((funny(fred)|~creative(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:(quiet(X)))=>((~creative(paul)|~wise(paul))))&
((?[X]:((~brave(X)|~funny(X))))<=>((brave(fred)&~creative(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:(creative(X))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&~wise(X))))&
((~happy(lucy)<~>~strong(lucy)))&
(humble(mary))&
((strong(paul)|curious(paul)))&
(?[X]:(tall(X)))&
((~curious(susan)<~>funny(susan))) | ~wise(fred) | [] | null | 0 |
If lucy is strong or quiet then someone is not funny or curious.
If someone is not old then alice is both not calm and not happy and vice versa.
Everyone who is either generous or not generous is not tall or not quiet and vice versa.
Everyone who is not kind is rich or not kind and vice versa.
Everyone who is generous is either tall or not patient.
Everyone who is creative or not curious is not old or curious and vice versa.
If mary is either not brave or curious then john is both wise and not tall and vice versa.
Everyone who is strong is humble or not tall and vice versa.
Everyone who is either tall or not quiet is not kind.
If someone is quiet then someone is both not kind and quiet and vice versa.
If mary is either calm or creative then someone is either tall or kind and vice versa.
If someone is tall or not creative then john is not calm and vice versa.
Everyone who is either not happy or old is either wise or not happy.
Everyone who is kind or not funny is both not creative and not funny and vice versa.
If susan is funny or kind then susan is kind or not funny.
If someone is either not patient or old then susan is either tall or kind.
Mary is not happy or not tall.
Someone is strong or not quiet.
Someone is either generous or funny.
Someone is not kind or not rich.
Someone is both strong and patient.
Fred is curious or brave.
Alice is not patient or not humble.
Someone is not quiet or tall. | Alice is not calm. | entailment | (((strong(lucy)|quiet(lucy)))=>(?[X]:((~funny(X)|curious(X)))))&
((?[X]:(~old(X)))<=>((~calm(alice)&~happy(alice))))&
(![X]:((generous(X)<~>~generous(X))<=>(~tall(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(rich(X)|~kind(X))))&
(![X]:(generous(X)=>(tall(X)<~>~patient(X))))&
(![X]:((creative(X)|~curious(X))<=>(~old(X)|curious(X))))&
(((~brave(mary)<~>curious(mary)))<=>((wise(john)&~tall(john))))&
(![X]:(strong(X)<=>(humble(X)|~tall(X))))&
(![X]:((tall(X)<~>~quiet(X))=>~kind(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~kind(X)&quiet(X)))))&
(((calm(mary)<~>creative(mary)))<=>(?[X]:((tall(X)<~>kind(X)))))&
((?[X]:((tall(X)|~creative(X))))<=>(~calm(john)))&
(![X]:((~happy(X)<~>old(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)|~funny(X))<=>(~creative(X)&~funny(X))))&
(((funny(susan)|kind(susan)))=>((kind(susan)|~funny(susan))))&
((?[X]:((~patient(X)<~>old(X))))=>((tall(susan)<~>kind(susan))))&
((~happy(mary)|~tall(mary)))&
(?[X]:((strong(X)|~quiet(X))))&
(?[X]:((generous(X)<~>funny(X))))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((strong(X)&patient(X))))&
((curious(fred)|brave(fred)))&
((~patient(alice)|~humble(alice)))&
(?[X]:((~quiet(X)|tall(X)))) | ~calm(alice) | [
"p1",
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 252449656051442229162037
% SZS output start Proof for 252449656051442229162037
2. ? [X0] : ~old(X0) <=> (~happy(alice) & ~calm(alice)) [input p1]
6. ! [X0] : ((~curious(X0) | creative(X0)) <=> (curious(X0) | ~old(X0))) [input p5]
14. ! [X0] : ((~funny(X0) | kind(X0)) <=> (~funny(X0) & ~creative(X0))) [input p13]
15. (kind(susan) | funny(susan)) => (~funny(susan) | kind(susan)) [input p14]
25. calm(alice) [input hypothesis]
31. (~funny(susan) | kind(susan)) | (~kind(susan) & ~funny(susan)) [ennf transformation 15]
32. ~funny(susan) | kind(susan) | (~kind(susan) & ~funny(susan)) [flattening 31]
36. (? [X0] : ~old(X0) | (happy(alice) | calm(alice))) & ((~happy(alice) & ~calm(alice)) | ! [X0] : old(X0)) [nnf transformation 2]
37. (? [X0] : ~old(X0) | happy(alice) | calm(alice)) & ((~happy(alice) & ~calm(alice)) | ! [X0] : old(X0)) [flattening 36]
38. (? [X0] : ~old(X0) | happy(alice) | calm(alice)) & ((~happy(alice) & ~calm(alice)) | ! [X1] : old(X1)) [rectify 37]
39. ? [X0] : ~old(X0) => ~old(sK1) [choice axiom]
40. (~old(sK1) | happy(alice) | calm(alice)) & ((~happy(alice) & ~calm(alice)) | ! [X1] : old(X1)) [skolemisation 38,39]
46. ! [X0] : (((~curious(X0) | creative(X0)) | (~curious(X0) & old(X0))) & ((curious(X0) | ~old(X0)) | (curious(X0) & ~creative(X0)))) [nnf transformation 6]
47. ! [X0] : ((~curious(X0) | creative(X0) | (~curious(X0) & old(X0))) & (curious(X0) | ~old(X0) | (curious(X0) & ~creative(X0)))) [flattening 46]
67. ! [X0] : (((~funny(X0) | kind(X0)) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | (funny(X0) & ~kind(X0)))) [nnf transformation 14]
68. ! [X0] : ((~funny(X0) | kind(X0) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | (funny(X0) & ~kind(X0)))) [flattening 67]
83. ~calm(alice) | old(X1) [cnf transformation 40]
98. curious(X0) | ~old(X0) | curious(X0) [cnf transformation 47]
100. ~curious(X0) | creative(X0) | ~curious(X0) [cnf transformation 47]
131. ~creative(X0) | funny(X0) [cnf transformation 68]
132. ~kind(X0) | ~funny(X0) [cnf transformation 68]
135. ~funny(susan) | kind(susan) | ~funny(susan) [cnf transformation 32]
151. calm(alice) [cnf transformation 25]
152. ~funny(susan) | kind(susan) [duplicate literal removal 135]
155. ~old(X0) | curious(X0) [duplicate literal removal 98]
156. ~curious(X0) | creative(X0) [duplicate literal removal 100]
178. 5 <=> calm(alice) [avatar definition]
191. 8 <=> ! [X1] : old(X1) [avatar definition]
192. old(X1) <- (8) [avatar component clause 191]
194. 8 | ~5 [avatar split clause 83,178,191]
283. 27 <=> ! [X1] : creative(X1) [avatar definition]
284. creative(X1) <- (27) [avatar component clause 283]
290. ~funny(susan) [subsumption resolution 152,132]
356. 5 [avatar split clause 151,178]
358. curious(X0) <- (8) [resolution 155,192]
361. creative(X0) <- (8) [resolution 358,156]
363. 27 | ~8 [avatar split clause 361,191,283]
367. funny(X0) <- (27) [resolution 284,131]
377. $false <- (27) [resolution 367,290]
380. ~27 [avatar contradiction clause 377]
382. $false [avatar sat refutation 194,356,363,380]
% SZS output end Proof for 252449656051442229162037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or happy then john is either not tall or not generous and vice versa.
Everyone who is happy or old is not brave or not patient and vice versa.
Everyone who is humble or not quiet is patient and vice versa.
If susan is either funny or brave then lucy is either not wise or not brave and vice versa.
If paul is not curious or not patient then someone is not curious or not generous and vice versa.
If susan is either not patient or not happy then susan is both not patient and generous.
If someone is both not funny and kind then someone is both not funny and not rich.
Everyone who is not happy is curious and vice versa.
Everyone who is old is both old and kind and vice versa.
If mary is funny then someone is either not brave or not funny and vice versa.
Everyone who is not calm or not tall is old or tall and vice versa.
Everyone who is strong or funny is both happy and not creative and vice versa.
If mary is not happy or strong then mary is not rich or brave and vice versa.
If john is not rich then someone is not humble or rich.
Everyone who is both not kind and wise is both wise and not humble.
Everyone who is both not calm and rich is either patient or not patient.
Someone is tall.
Someone is rich or quiet.
Someone is not kind.
Someone is either not curious or not patient.
Someone is not old or patient.
Someone is not wise or funny.
Someone is not old or rich.
John is creative. | Paul is old. | neutral | ((?[X]:((curious(X)<~>happy(X))))<=>((~tall(john)<~>~generous(john))))&
(![X]:((happy(X)|old(X))<=>(~brave(X)|~patient(X))))&
(![X]:((humble(X)|~quiet(X))<=>patient(X)))&
(((funny(susan)<~>brave(susan)))<=>((~wise(lucy)<~>~brave(lucy))))&
(((~curious(paul)|~patient(paul)))<=>(?[X]:((~curious(X)|~generous(X)))))&
(((~patient(susan)<~>~happy(susan)))=>((~patient(susan)&generous(susan))))&
((?[X]:((~funny(X)&kind(X))))=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:(~happy(X)<=>curious(X)))&
(![X]:(old(X)<=>(old(X)&kind(X))))&
((funny(mary))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(old(X)|tall(X))))&
(![X]:((strong(X)|funny(X))<=>(happy(X)&~creative(X))))&
(((~happy(mary)|strong(mary)))<=>((~rich(mary)|brave(mary))))&
((~rich(john))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((~kind(X)&wise(X))=>(wise(X)&~humble(X))))&
(![X]:((~calm(X)&rich(X))=>(patient(X)<~>~patient(X))))&
(?[X]:(tall(X)))&
(?[X]:((rich(X)|quiet(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~old(X)|rich(X))))&
(creative(john)) | old(paul) | [] | null | 0 |
Everyone who is both wise and not funny is either not creative or not old. If someone is not rich or happy then alice is both kind and not patient and vice versa. If someone is either not funny or wise then john is happy or not rich and vice versa. If someone is old then someone is both not rich and not old. Everyone who is generous or not humble is either not kind or patient. If someone is both rich and not happy then mary is not creative or not rich. Everyone who is not rich or generous is both not creative and not generous. Everyone who is curious is not tall or not strong. If someone is both not creative and generous then someone is both not calm and tall and vice versa. Everyone who is quiet or humble is patient. Everyone who is quiet is old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Someone is both not kind and creative. John is either creative or patient. Someone is both tall and funny. Alice is calm. Susan is either not humble or not wise. | John is not happy. | entailment | (![X]:((wise(X)&~funny(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((kind(alice)&~patient(alice))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((happy(john)|~rich(john))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((generous(X)|~humble(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((~creative(mary)|~rich(mary))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&~generous(X))))&
(![X]:(curious(X)=>(~tall(X)|~strong(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((quiet(X)|humble(X))=>patient(X)))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(?[X]:((~kind(X)&creative(X))))&
((creative(john)<~>patient(john)))&
(?[X]:((tall(X)&funny(X))))&
(calm(alice))&
((~humble(susan)<~>~wise(susan))) | ~happy(john) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4280739085607670115314006
% SZS output start Proof for 4280739085607670115314006
2. ? [X0] : (happy(X0) | ~rich(X0)) <=> (~patient(alice) & kind(alice)) [input p1]
4. ? [X0] : old(X0) => ? [X0] : (~old(X0) & ~rich(X0)) [input p3]
7. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~creative(X0))) [input p6]
10. ! [X0] : ((humble(X0) | quiet(X0)) => patient(X0)) [input p9]
11. ! [X0] : (quiet(X0) => old(X0)) [input p10]
15. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~kind(X0))) [input p14]
22. happy(john) [input hypothesis]
23. ? [X0] : old(X0) => ? [X1] : (~old(X1) & ~rich(X1)) [rectify 4]
28. ? [X1] : (~old(X1) & ~rich(X1)) | ! [X0] : ~old(X0) [ennf transformation 23]
32. ! [X0] : ((~generous(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 7]
35. ! [X0] : (patient(X0) | (~humble(X0) & ~quiet(X0))) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~quiet(X0)) [ennf transformation 11]
42. (? [X0] : (happy(X0) | ~rich(X0)) | (patient(alice) | ~kind(alice))) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 2]
43. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 42]
44. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 43]
45. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
46. ((happy(sK0) | ~rich(sK0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 44,45]
52. ? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ~old(X1) [rectify 28]
53. ? [X0] : (~old(X0) & ~rich(X0)) => (~old(sK2) & ~rich(sK2)) [choice axiom]
54. (~old(sK2) & ~rich(sK2)) | ! [X1] : ~old(X1) [skolemisation 52,53]
66. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 15]
67. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | generous(X0))) [flattening 66]
77. kind(alice) | ~happy(X1) [cnf transformation 46]
78. ~patient(alice) | rich(X1) [cnf transformation 46]
87. ~rich(sK2) | ~old(X1) [cnf transformation 54]
97. ~generous(X0) | ~generous(X0) [cnf transformation 32]
103. ~quiet(X0) | patient(X0) [cnf transformation 35]
105. ~quiet(X0) | old(X0) [cnf transformation 36]
112. quiet(X0) | ~kind(X0) | generous(X0) [cnf transformation 67]
126. happy(john) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 97]
129. 1 <=> kind(alice) [avatar definition]
130. kind(alice) <- (1) [avatar component clause 129]
133. 2 <=> patient(alice) [avatar definition]
134. ~patient(alice) <- (~2) [avatar component clause 133]
146. 5 <=> ! [X1] : ~happy(X1) [avatar definition]
147. ~happy(X1) <- (5) [avatar component clause 146]
150. 6 <=> ! [X1] : rich(X1) [avatar definition]
151. rich(X1) <- (6) [avatar component clause 150]
152. 6 | ~2 [avatar split clause 78,133,150]
153. 5 | 1 [avatar split clause 77,129,146]
169. 10 <=> happy(john) [avatar definition]
170. happy(john) <- (10) [avatar component clause 169]
184. 13 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (13) [avatar component clause 184]
192. 15 <=> rich(sK2) [avatar definition]
194. ~rich(sK2) <- (~15) [avatar component clause 192]
195. 13 | ~15 [avatar split clause 87,192,184]
224. ~kind(X0) | quiet(X0) [subsumption resolution 112,127]
255. 10 [avatar split clause 126,169]
258. $false <- (5, 10) [resolution 170,147]
259. ~5 | ~10 [avatar contradiction clause 258]
260. $false <- (6, ~15) [resolution 194,151]
261. ~6 | 15 [avatar contradiction clause 260]
275. quiet(alice) <- (1) [resolution 224,130]
276. old(alice) <- (1) [resolution 275,105]
277. patient(alice) <- (1) [resolution 275,103]
278. $false <- (1, 13) [subsumption resolution 276,185]
279. ~1 | ~13 [avatar contradiction clause 278]
280. $false <- (1, ~2) [subsumption resolution 277,134]
281. ~1 | 2 [avatar contradiction clause 280]
282. $false [avatar sat refutation 152,153,195,255,259,261,279,281]
% SZS output end Proof for 4280739085607670115314006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not kind is not wise or calm and vice versa. Everyone who is both not wise and not happy is either wise or not rich. Everyone who is both not creative and not curious is humble or not creative and vice versa. If someone is both curious and happy then paul is either creative or not tall. Everyone who is either not old or patient is funny. If mary is either not funny or not happy then someone is either not funny or curious and vice versa. If mary is not old then someone is humble and vice versa. If someone is both funny and not generous then alice is either rich or funny. Everyone who is not rich or curious is tall or not rich and vice versa. Everyone who is either rich or old is not humble. Everyone who is tall or not creative is quiet. Everyone who is both generous and not patient is not calm or funny. Everyone who is either humble or strong is both creative and funny. Everyone who is not humble or not funny is both strong and not funny and vice versa. Everyone who is old is not strong or tall and vice versa. Lucy is not tall or not strong. Someone is either not kind or not generous. Someone is either generous or not funny. | Alice is patient. | neutral | (![X]:((creative(X)&~kind(X))<=>(~wise(X)|calm(X))))&
(![X]:((~wise(X)&~happy(X))=>(wise(X)<~>~rich(X))))&
(![X]:((~creative(X)&~curious(X))<=>(humble(X)|~creative(X))))&
((?[X]:((curious(X)&happy(X))))=>((creative(paul)<~>~tall(paul))))&
(![X]:((~old(X)<~>patient(X))=>funny(X)))&
(((~funny(mary)<~>~happy(mary)))<=>(?[X]:((~funny(X)<~>curious(X)))))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | patient(alice) | [] | null | 0 |
If paul is creative or strong then lucy is calm and vice versa. If someone is both not curious and creative then someone is both generous and not strong. Everyone who is not wise or tall is both creative and calm. If someone is both generous and creative then john is either calm or not wise and vice versa. If someone is kind then lucy is either not generous or not creative and vice versa. Everyone who is either kind or curious is either curious or not funny and vice versa. Everyone who is humble or happy is not rich or not generous and vice versa. Everyone who is generous or curious is not calm or tall. If someone is both funny and creative then someone is patient. Everyone who is not rich is not curious and vice versa. Everyone who is not funny is not happy or not creative and vice versa. If someone is not strong or patient then fred is not old or not funny and vice versa. Everyone who is both not happy and tall is not calm and vice versa. Everyone who is either quiet or not happy is not curious or patient. Everyone who is either tall or not creative is either wise or not kind and vice versa. If someone is strong or funny then john is not generous or calm and vice versa. Someone is not patient. Someone is both patient and not wise. Susan is not generous. Paul is either happy or not happy. Paul is not happy or tall. Someone is both not generous and not strong. Mary is funny or not creative. | John is generous. | contradiction | (((creative(paul)|strong(paul)))<=>(calm(lucy)))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((generous(X)&~strong(X)))))&
(![X]:((~wise(X)|tall(X))=>(creative(X)&calm(X))))&
((?[X]:((generous(X)&creative(X))))<=>((calm(john)<~>~wise(john))))&
((?[X]:(kind(X)))<=>((~generous(lucy)<~>~creative(lucy))))&
(![X]:((kind(X)<~>curious(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((humble(X)|happy(X))<=>(~rich(X)|~generous(X))))&
(![X]:((generous(X)|curious(X))=>(~calm(X)|tall(X))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(patient(X))))&
(![X]:(~rich(X)<=>~curious(X)))&
(![X]:(~funny(X)<=>(~happy(X)|~creative(X))))&
((?[X]:((~strong(X)|patient(X))))<=>((~old(fred)|~funny(fred))))&
(![X]:((~happy(X)&tall(X))<=>~calm(X)))&
(![X]:((quiet(X)<~>~happy(X))=>(~curious(X)|patient(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(wise(X)<~>~kind(X))))&
((?[X]:((strong(X)|funny(X))))<=>((~generous(john)|calm(john))))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)&~wise(X))))&
(~generous(susan))&
((happy(paul)<~>~happy(paul)))&
((~happy(paul)|tall(paul)))&
(?[X]:((~generous(X)&~strong(X))))&
((funny(mary)|~creative(mary))) | generous(john) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4058306311003929866312403
% SZS output start Proof for 4058306311003929866312403
3. ! [X0] : ((tall(X0) | ~wise(X0)) => (calm(X0) & creative(X0))) [input p2]
4. ? [X0] : (creative(X0) & generous(X0)) <=> (calm(john) <~> ~wise(john)) [input p3]
6. ! [X0] : ((kind(X0) <~> curious(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((curious(X0) | generous(X0)) => (tall(X0) | ~calm(X0))) [input p7]
11. ! [X0] : (~funny(X0) <=> (~creative(X0) | ~happy(X0))) [input p10]
13. ! [X0] : ((tall(X0) & ~happy(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (wise(X0) <~> ~kind(X0))) [input p14]
24. generous(john) [input hypothesis]
28. ! [X0] : ((calm(X0) & creative(X0)) | (~tall(X0) & wise(X0))) [ennf transformation 3]
29. ! [X0] : ((tall(X0) | ~calm(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 8]
30. ! [X0] : (tall(X0) | ~calm(X0) | (~curious(X0) & ~generous(X0))) [flattening 29]
39. (? [X0] : (creative(X0) & generous(X0)) | ((calm(john) | wise(john)) & (~wise(john) | ~calm(john)))) & (((wise(john) | ~calm(john)) & (~wise(john) | calm(john))) | ! [X0] : (~creative(X0) | ~generous(X0))) [nnf transformation 4]
40. (? [X0] : (creative(X0) & generous(X0)) | ((calm(john) | wise(john)) & (~wise(john) | ~calm(john)))) & (((wise(john) | ~calm(john)) & (~wise(john) | calm(john))) | ! [X1] : (~creative(X1) | ~generous(X1))) [rectify 39]
41. ? [X0] : (creative(X0) & generous(X0)) => (creative(sK1) & generous(sK1)) [choice axiom]
42. ((creative(sK1) & generous(sK1)) | ((calm(john) | wise(john)) & (~wise(john) | ~calm(john)))) & (((wise(john) | ~calm(john)) & (~wise(john) | calm(john))) | ! [X1] : (~creative(X1) | ~generous(X1))) [skolemisation 40,41]
47. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 6]
54. ! [X0] : ((~funny(X0) | (creative(X0) & happy(X0))) & ((~creative(X0) | ~happy(X0)) | funny(X0))) [nnf transformation 11]
55. ! [X0] : ((~funny(X0) | (creative(X0) & happy(X0))) & (~creative(X0) | ~happy(X0) | funny(X0))) [flattening 54]
61. ! [X0] : (((tall(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (~tall(X0) | happy(X0)))) [nnf transformation 13]
62. ! [X0] : (((tall(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | ~tall(X0) | happy(X0))) [flattening 61]
64. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0)))) & (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 15]
83. ~tall(X0) | creative(X0) [cnf transformation 28]
84. wise(X0) | calm(X0) [cnf transformation 28]
85. ~tall(X0) | calm(X0) [cnf transformation 28]
87. wise(john) | ~calm(john) | ~creative(X1) | ~generous(X1) [cnf transformation 42]
96. ~funny(X0) | curious(X0) | curious(X0) | ~kind(X0) [cnf transformation 47]
102. ~curious(X0) | ~kind(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 47]
108. ~generous(X0) | ~calm(X0) | tall(X0) [cnf transformation 30]
113. ~happy(X0) | ~creative(X0) | funny(X0) [cnf transformation 55]
120. ~calm(X0) | ~tall(X0) | happy(X0) [cnf transformation 62]
122. tall(X0) | calm(X0) [cnf transformation 62]
127. kind(X0) | ~wise(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 64]
147. generous(john) [cnf transformation 24]
148. ~funny(X0) | curious(X0) | ~kind(X0) [duplicate literal removal 96]
151. ~funny(X0) | ~kind(X0) | ~curious(X0) [duplicate literal removal 102]
185. 8 <=> wise(john) [avatar definition]
186. wise(john) <- (8) [avatar component clause 185]
198. wise(john) | ~creative(X1) | ~generous(X1) [subsumption resolution 87,84]
200. 11 <=> ! [X1] : (~creative(X1) | ~generous(X1)) [avatar definition]
201. ~generous(X1) | ~creative(X1) <- (11) [avatar component clause 200]
202. 11 | 8 [avatar split clause 198,185,200]
225. ~funny(X0) | ~kind(X0) [subsumption resolution 148,151]
260. calm(X0) [subsumption resolution 122,85]
261. ~tall(X0) | happy(X0) [subsumption resolution 120,260]
265. ~tall(X0) | ~wise(X0) | kind(X0) [subsumption resolution 127,83]
278. 26 <=> generous(john) [avatar definition]
280. generous(john) <- (26) [avatar component clause 278]
300. 26 [avatar split clause 147,278]
326. ~calm(john) | tall(john) <- (26) [resolution 108,280]
329. tall(john) <- (26) [subsumption resolution 326,260]
343. happy(john) <- (26) [resolution 329,261]
345. creative(john) <- (26) [resolution 329,83]
361. ~creative(john) | funny(john) <- (26) [resolution 343,113]
362. funny(john) <- (26) [subsumption resolution 361,345]
371. ~creative(john) <- (11, 26) [resolution 201,280]
372. $false <- (11, 26) [subsumption resolution 371,345]
373. ~11 | ~26 [avatar contradiction clause 372]
379. ~wise(john) | kind(john) <- (26) [resolution 265,329]
380. kind(john) <- (8, 26) [subsumption resolution 379,186]
562. ~kind(john) <- (26) [resolution 362,225]
566. $false <- (8, 26) [subsumption resolution 562,380]
567. ~8 | ~26 [avatar contradiction clause 566]
568. $false [avatar sat refutation 202,300,373,567]
% SZS output end Proof for 4058306311003929866312403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not generous or not strong is either not rich or tall and vice versa.
Everyone who is not wise or calm is both not wise and tall.
If someone is both calm and happy then someone is tall or strong.
Everyone who is patient is not old.
Everyone who is not tall is patient or humble.
If someone is tall then susan is humble and vice versa.
Everyone who is curious or humble is generous or funny and vice versa.
If someone is strong then someone is either humble or curious and vice versa.
If someone is both rich and not old then someone is not kind.
If someone is curious or not calm then paul is both not patient and old and vice versa.
If someone is old or not kind then someone is rich.
If lucy is both not rich and rich then someone is both not rich and humble.
Everyone who is both kind and strong is either humble or funny and vice versa.
Everyone who is strong or not humble is both not kind and not calm and vice versa.
If someone is humble then susan is both old and strong and vice versa.
Everyone who is both not creative and not patient is not generous or not patient.
Someone is either not calm or not quiet.
Someone is not strong.
Someone is not tall.
Someone is either not rich or rich.
Someone is either not brave or patient.
Fred is both not humble and creative.
Someone is not generous.
Someone is either not funny or not rich. | Susan is patient. | contradiction | (![X]:((~generous(X)<~>~strong(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|calm(X))=>(~wise(X)&tall(X))))&
((?[X]:((calm(X)&happy(X))))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:(patient(X)=>~old(X)))&
(![X]:(~tall(X)=>(patient(X)|humble(X))))&
((?[X]:(tall(X)))<=>(humble(susan)))&
(![X]:((curious(X)|humble(X))<=>(generous(X)|funny(X))))&
((?[X]:(strong(X)))<=>(?[X]:((humble(X)<~>curious(X)))))&
((?[X]:((rich(X)&~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~calm(X))))<=>((~patient(paul)&old(paul))))&
((?[X]:((old(X)|~kind(X))))=>(?[X]:(rich(X))))&
(((~rich(lucy)&rich(lucy)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((kind(X)&strong(X))<=>(humble(X)<~>funny(X))))&
(![X]:((strong(X)|~humble(X))<=>(~kind(X)&~calm(X))))&
((?[X]:(humble(X)))<=>((old(susan)&strong(susan))))&
(![X]:((~creative(X)&~patient(X))=>(~generous(X)|~patient(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
((~humble(fred)&creative(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~rich(X)))) | patient(susan) | [
"p3",
"p4",
"p5",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1311408944692583788768604
% SZS output start Proof for 1311408944692583788768604
4. ! [X0] : (patient(X0) => ~old(X0)) [input p3]
5. ! [X0] : (~tall(X0) => (humble(X0) | patient(X0))) [input p4]
6. ? [X0] : tall(X0) <=> humble(susan) [input p5]
10. ? [X0] : (~calm(X0) | curious(X0)) <=> (old(paul) & ~patient(paul)) [input p9]
14. ! [X0] : ((~humble(X0) | strong(X0)) <=> (~calm(X0) & ~kind(X0))) [input p13]
15. ? [X0] : humble(X0) <=> (strong(susan) & old(susan)) [input p14]
25. patient(susan) [input hypothesis]
34. ! [X0] : (~old(X0) | ~patient(X0)) [ennf transformation 4]
35. ! [X0] : ((humble(X0) | patient(X0)) | tall(X0)) [ennf transformation 5]
36. ! [X0] : (humble(X0) | patient(X0) | tall(X0)) [flattening 35]
42. (? [X0] : tall(X0) | ~humble(susan)) & (humble(susan) | ! [X0] : ~tall(X0)) [nnf transformation 6]
43. (? [X0] : tall(X0) | ~humble(susan)) & (humble(susan) | ! [X1] : ~tall(X1)) [rectify 42]
44. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
45. (tall(sK0) | ~humble(susan)) & (humble(susan) | ! [X1] : ~tall(X1)) [skolemisation 43,44]
56. (? [X0] : (~calm(X0) | curious(X0)) | (~old(paul) | patient(paul))) & ((old(paul) & ~patient(paul)) | ! [X0] : (calm(X0) & ~curious(X0))) [nnf transformation 10]
57. (? [X0] : (~calm(X0) | curious(X0)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X0] : (calm(X0) & ~curious(X0))) [flattening 56]
58. (? [X0] : (~calm(X0) | curious(X0)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X1] : (calm(X1) & ~curious(X1))) [rectify 57]
59. ? [X0] : (~calm(X0) | curious(X0)) => (~calm(sK4) | curious(sK4)) [choice axiom]
60. ((~calm(sK4) | curious(sK4)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X1] : (calm(X1) & ~curious(X1))) [skolemisation 58,59]
68. ! [X0] : (((~humble(X0) | strong(X0)) | (calm(X0) | kind(X0))) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [nnf transformation 14]
69. ! [X0] : ((~humble(X0) | strong(X0) | calm(X0) | kind(X0)) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [flattening 68]
70. (? [X0] : humble(X0) | (~strong(susan) | ~old(susan))) & ((strong(susan) & old(susan)) | ! [X0] : ~humble(X0)) [nnf transformation 15]
71. (? [X0] : humble(X0) | ~strong(susan) | ~old(susan)) & ((strong(susan) & old(susan)) | ! [X0] : ~humble(X0)) [flattening 70]
72. (? [X0] : humble(X0) | ~strong(susan) | ~old(susan)) & ((strong(susan) & old(susan)) | ! [X1] : ~humble(X1)) [rectify 71]
73. ? [X0] : humble(X0) => humble(sK7) [choice axiom]
74. (humble(sK7) | ~strong(susan) | ~old(susan)) & ((strong(susan) & old(susan)) | ! [X1] : ~humble(X1)) [skolemisation 72,73]
105. ~old(X0) | ~patient(X0) [cnf transformation 34]
106. humble(X0) | patient(X0) | tall(X0) [cnf transformation 36]
107. humble(susan) | ~tall(X1) [cnf transformation 45]
119. ~patient(paul) | calm(X1) [cnf transformation 60]
136. ~calm(X0) | humble(X0) [cnf transformation 69]
138. old(susan) | ~humble(X1) [cnf transformation 74]
153. patient(susan) [cnf transformation 25]
155. 1 <=> humble(susan) [avatar definition]
156. humble(susan) <- (1) [avatar component clause 155]
164. 3 <=> ! [X1] : ~tall(X1) [avatar definition]
165. ~tall(X1) <- (3) [avatar component clause 164]
166. 3 | 1 [avatar split clause 107,155,164]
215. 15 <=> ! [X1] : calm(X1) [avatar definition]
216. calm(X1) <- (15) [avatar component clause 215]
223. 17 <=> patient(paul) [avatar definition]
225. ~patient(paul) <- (~17) [avatar component clause 223]
226. 15 | ~17 [avatar split clause 119,223,215]
241. 21 <=> old(susan) [avatar definition]
242. old(susan) <- (21) [avatar component clause 241]
254. 24 <=> ! [X1] : ~humble(X1) [avatar definition]
255. ~humble(X1) <- (24) [avatar component clause 254]
257. 24 | 21 [avatar split clause 138,241,254]
297. ~patient(susan) <- (21) [resolution 105,242]
298. $false <- (21) [subsumption resolution 297,153]
299. ~21 [avatar contradiction clause 298]
310. patient(X1) | tall(X1) <- (24) [resolution 106,255]
313. patient(X1) <- (3, 24) [subsumption resolution 310,165]
327. $false <- (3, ~17, 24) [resolution 313,225]
330. ~3 | 17 | ~24 [avatar contradiction clause 327]
334. humble(X0) <- (15) [resolution 216,136]
341. $false <- (15, 24) [subsumption resolution 334,255]
342. ~15 | ~24 [avatar contradiction clause 341]
345. $false <- (1, 24) [subsumption resolution 156,255]
346. ~1 | ~24 [avatar contradiction clause 345]
347. $false [avatar sat refutation 166,226,257,299,330,342,346]
% SZS output end Proof for 1311408944692583788768604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not creative or not rich then someone is not creative or not funny and vice versa.
Everyone who is both humble and creative is generous and vice versa.
Everyone who is both quiet and funny is both not happy and tall.
Everyone who is both not tall and not strong is not creative.
Everyone who is not strong or rich is either generous or quiet.
Everyone who is not patient or not old is both calm and not happy.
If someone is not curious or not old then susan is old or not quiet.
If alice is both generous and not brave then susan is humble.
Everyone who is patient is brave or not patient and vice versa.
If someone is both not patient and not brave then someone is either old or not patient and vice versa.
If someone is both not kind and not quiet then someone is not creative.
If someone is both not creative and not funny then fred is not happy or not old.
If someone is either wise or tall then fred is not kind.
Everyone who is both not rich and creative is not wise or not kind.
Everyone who is either not calm or old is not wise and vice versa.
If someone is humble then someone is not wise or patient and vice versa.
Someone is not old.
Fred is rich.
Someone is not humble.
Someone is tall or not kind.
Someone is old or quiet. | Lucy is not brave. | contradiction | (((~creative(lucy)|~rich(lucy)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((humble(X)&creative(X))<=>generous(X)))&
(![X]:((quiet(X)&funny(X))=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~strong(X))=>~creative(X)))&
(![X]:((~strong(X)|rich(X))=>(generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|~old(X))=>(calm(X)&~happy(X))))&
((?[X]:((~curious(X)|~old(X))))=>((old(susan)|~quiet(susan))))&
(((generous(alice)&~brave(alice)))=>(humble(susan)))&
(![X]:(patient(X)<=>(brave(X)|~patient(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((old(X)<~>~patient(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~happy(fred)|~old(fred))))&
((?[X]:((wise(X)<~>tall(X))))=>(~kind(fred)))&
(![X]:((~rich(X)&creative(X))=>(~wise(X)|~kind(X))))&
(![X]:((~calm(X)<~>old(X))<=>~wise(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|patient(X)))))&
(?[X]:(~old(X)))&
(rich(fred))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((old(X)|quiet(X)))) | ~brave(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2876318016200581137327101
% SZS output start Proof for 2876318016200581137327101
9. ! [X0] : (patient(X0) <=> (~patient(X0) | brave(X0))) [input p8]
22. ~brave(lucy) [input hypothesis]
52. ! [X0] : ((patient(X0) | (patient(X0) & ~brave(X0))) & ((~patient(X0) | brave(X0)) | ~patient(X0))) [nnf transformation 9]
53. ! [X0] : ((patient(X0) | (patient(X0) & ~brave(X0))) & (~patient(X0) | brave(X0) | ~patient(X0))) [flattening 52]
91. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 53]
93. patient(X0) | patient(X0) [cnf transformation 53]
116. ~brave(lucy) [cnf transformation 22]
117. ~patient(X0) | brave(X0) [duplicate literal removal 91]
118. patient(X0) [duplicate literal removal 93]
170. brave(X0) [subsumption resolution 117,118]
205. $false [subsumption resolution 116,170]
% SZS output end Proof for 2876318016200581137327101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not kind then someone is not calm or creative and vice versa.
If someone is not funny or not strong then someone is tall or kind and vice versa.
Everyone who is both kind and not funny is not strong and vice versa.
Everyone who is both not generous and strong is creative.
Everyone who is both not brave and rich is both not rich and old and vice versa.
If someone is either patient or not kind then someone is not old or not brave and vice versa.
If john is not rich or not wise then someone is both humble and quiet and vice versa.
Everyone who is either kind or wise is either not calm or brave and vice versa.
Everyone who is not generous or calm is both not generous and not funny and vice versa.
If someone is not kind then lucy is both not patient and brave.
Everyone who is either old or generous is not old or not quiet.
If someone is kind or not humble then someone is either calm or kind and vice versa.
Everyone who is either not wise or wise is not quiet and vice versa.
Everyone who is either not brave or humble is quiet and vice versa.
Everyone who is both not humble and not strong is wise or not generous.
If paul is either not quiet or not strong then someone is happy and vice versa.
Alice is not patient or not brave.
Fred is not old.
Lucy is wise or happy.
Someone is either happy or quiet.
Someone is creative or not funny.
Someone is strong or tall.
Someone is either brave or quiet. | Fred is calm. | neutral | ((~kind(john))<=>(?[X]:((~calm(X)|creative(X)))))&
((?[X]:((~funny(X)|~strong(X))))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:((kind(X)&~funny(X))<=>~strong(X)))&
(![X]:((~generous(X)&strong(X))=>creative(X)))&
(![X]:((~brave(X)&rich(X))<=>(~rich(X)&old(X))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~rich(john)|~wise(john)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((kind(X)<~>wise(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((~generous(X)|calm(X))<=>(~generous(X)&~funny(X))))&
((?[X]:(~kind(X)))=>((~patient(lucy)&brave(lucy))))&
(![X]:((old(X)<~>generous(X))=>(~old(X)|~quiet(X))))&
((?[X]:((kind(X)|~humble(X))))<=>(?[X]:((calm(X)<~>kind(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~quiet(X)))&
(![X]:((~brave(X)<~>humble(X))<=>quiet(X)))&
(![X]:((~humble(X)&~strong(X))=>(wise(X)|~generous(X))))&
(((~quiet(paul)<~>~strong(paul)))<=>(?[X]:(happy(X))))&
((~patient(alice)|~brave(alice)))&
(~old(fred))&
((wise(lucy)|happy(lucy)))&
(?[X]:((happy(X)<~>quiet(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((brave(X)<~>quiet(X)))) | calm(fred) | [] | null | 0 |
Everyone who is tall is both old and not wise and vice versa. Everyone who is not old or brave is both calm and not funny and vice versa. Everyone who is not calm is either not strong or not happy and vice versa. If alice is not quiet then susan is not wise. If john is not kind then someone is patient and vice versa. Everyone who is either brave or not rich is either quiet or not old and vice versa. Everyone who is both not quiet and strong is both funny and not patient. Everyone who is both not brave and not generous is either patient or old and vice versa. Everyone who is wise or not strong is both not brave and wise. Everyone who is humble is either not happy or not generous. If susan is not quiet or not kind then mary is not humble and vice versa. Everyone who is not kind or brave is both not quiet and creative. If lucy is tall then someone is not happy or not quiet. If someone is both rich and tall then alice is both not funny and humble. Everyone who is old is both strong and brave. Everyone who is not old is either kind or happy and vice versa. Someone is either not patient or funny. Someone is both calm and kind. Someone is wise or not calm. Paul is not funny. Someone is not quiet. John is both rich and not old. Lucy is either not generous or humble. | Susan is kind. | entailment | (![X]:(tall(X)<=>(old(X)&~wise(X))))&
(![X]:((~old(X)|brave(X))<=>(calm(X)&~funny(X))))&
(![X]:(~calm(X)<=>(~strong(X)<~>~happy(X))))&
((~quiet(alice))=>(~wise(susan)))&
((~kind(john))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~quiet(X)&strong(X))=>(funny(X)&~patient(X))))&
(![X]:((~brave(X)&~generous(X))<=>(patient(X)<~>old(X))))&
(![X]:((wise(X)|~strong(X))=>(~brave(X)&wise(X))))&
(![X]:(humble(X)=>(~happy(X)<~>~generous(X))))&
(((~quiet(susan)|~kind(susan)))<=>(~humble(mary)))&
(![X]:((~kind(X)|brave(X))=>(~quiet(X)&creative(X))))&
((tall(lucy))=>(?[X]:((~happy(X)|~quiet(X)))))&
((?[X]:((rich(X)&tall(X))))=>((~funny(alice)&humble(alice))))&
(![X]:(old(X)=>(strong(X)&brave(X))))&
(![X]:(~old(X)<=>(kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:((wise(X)|~calm(X))))&
(~funny(paul))&
(?[X]:(~quiet(X)))&
((rich(john)&~old(john)))&
((~generous(lucy)<~>humble(lucy))) | kind(susan) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p8",
"p11",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1677689354986118963731215
% SZS output start Proof for 1677689354986118963731215
2. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~funny(X0) & calm(X0))) [input p1]
3. ! [X0] : (~calm(X0) <=> (~strong(X0) <~> ~happy(X0))) [input p2]
5. ~kind(john) <=> ? [X0] : patient(X0) [input p4]
6. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : ((strong(X0) & ~quiet(X0)) => (~patient(X0) & funny(X0))) [input p6]
8. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (patient(X0) <~> old(X0))) [input p7]
9. ! [X0] : ((~strong(X0) | wise(X0)) => (wise(X0) & ~brave(X0))) [input p8]
12. ! [X0] : ((brave(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p11]
15. ! [X0] : (old(X0) => (brave(X0) & strong(X0))) [input p14]
16. ! [X0] : (~old(X0) <=> (kind(X0) <~> happy(X0))) [input p15]
22. ~old(john) & rich(john) [input p21]
24. ~kind(susan) [input hypothesis]
26. ! [X0] : ((brave(X0) | ~kind(X0)) => ~quiet(X0)) [pure predicate removal 12]
30. ! [X0] : ((~patient(X0) & funny(X0)) | (~strong(X0) | quiet(X0))) [ennf transformation 7]
31. ! [X0] : ((~patient(X0) & funny(X0)) | ~strong(X0) | quiet(X0)) [flattening 30]
32. ! [X0] : ((wise(X0) & ~brave(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 9]
34. ! [X0] : (~quiet(X0) | (~brave(X0) & kind(X0))) [ennf transformation 26]
37. ! [X0] : ((brave(X0) & strong(X0)) | ~old(X0)) [ennf transformation 15]
38. ! [X0] : (((brave(X0) | ~old(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~old(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [flattening 38]
40. ! [X0] : ((~calm(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | calm(X0))) [nnf transformation 3]
41. (~kind(john) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | kind(john)) [nnf transformation 5]
42. (~kind(john) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | kind(john)) [rectify 41]
43. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
44. (~kind(john) | ! [X0] : ~patient(X0)) & (patient(sK0) | kind(john)) [skolemisation 42,43]
45. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 6]
46. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (generous(X0) | brave(X0)))) [nnf transformation 8]
47. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | generous(X0) | brave(X0))) [flattening 46]
53. ! [X0] : ((~old(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | old(X0))) [nnf transformation 16]
65. calm(X0) | old(X0) [cnf transformation 39]
67. ~funny(X0) | old(X0) [cnf transformation 39]
68. ~funny(X0) | ~brave(X0) [cnf transformation 39]
72. ~happy(X0) | ~calm(X0) | strong(X0) [cnf transformation 40]
76. ~kind(john) | ~patient(X0) [cnf transformation 44]
82. ~rich(X0) | brave(X0) | quiet(X0) | old(X0) [cnf transformation 45]
85. ~strong(X0) | funny(X0) | quiet(X0) [cnf transformation 31]
90. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 47]
93. ~brave(X0) | ~wise(X0) [cnf transformation 32]
96. strong(X0) | wise(X0) [cnf transformation 32]
102. ~quiet(X0) | kind(X0) [cnf transformation 34]
103. ~quiet(X0) | ~brave(X0) [cnf transformation 34]
108. ~old(X0) | brave(X0) [cnf transformation 37]
109. kind(X0) | happy(X0) | old(X0) [cnf transformation 53]
120. rich(john) [cnf transformation 22]
121. ~old(john) [cnf transformation 22]
124. ~kind(susan) [cnf transformation 24]
135. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
136. ~patient(X0) <- (3) [avatar component clause 135]
138. 4 <=> kind(john) [avatar definition]
140. ~kind(john) <- (~4) [avatar component clause 138]
141. 3 | ~4 [avatar split clause 76,138,135]
152. 7 <=> quiet(susan) [avatar definition]
153. quiet(susan) <- (7) [avatar component clause 152]
156. 8 <=> kind(susan) [avatar definition]
158. ~kind(susan) <- (~8) [avatar component clause 156]
217. ~8 [avatar split clause 124,156]
233. quiet(X0) | funny(X0) | wise(X0) [resolution 85,96]
234. happy(susan) | old(susan) <- (~8) [resolution 109,158]
236. 21 <=> old(susan) [avatar definition]
237. ~old(susan) <- (~21) [avatar component clause 236]
238. old(susan) <- (21) [avatar component clause 236]
240. 22 <=> happy(susan) [avatar definition]
242. happy(susan) <- (22) [avatar component clause 240]
243. 21 | 22 | 8 [avatar split clause 234,156,240,236]
259. brave(susan) <- (21) [resolution 238,108]
284. patient(susan) | ~old(susan) <- (21) [resolution 259,90]
288. ~old(susan) <- (3, 21) [subsumption resolution 284,136]
289. $false <- (3, 21) [subsumption resolution 288,238]
290. ~3 | ~21 [avatar contradiction clause 289]
296. 27 <=> strong(susan) [avatar definition]
298. strong(susan) <- (27) [avatar component clause 296]
300. 28 <=> calm(susan) [avatar definition]
302. ~calm(susan) <- (~28) [avatar component clause 300]
362. brave(john) | quiet(john) | old(john) [resolution 82,120]
363. brave(john) | quiet(john) [subsumption resolution 362,121]
365. 37 <=> quiet(john) [avatar definition]
367. quiet(john) <- (37) [avatar component clause 365]
369. 38 <=> brave(john) [avatar definition]
371. brave(john) <- (38) [avatar component clause 369]
372. 37 | 38 [avatar split clause 363,369,365]
374. ~calm(susan) | strong(susan) <- (22) [resolution 242,72]
414. kind(john) <- (37) [resolution 367,102]
416. $false <- (~4, 37) [subsumption resolution 414,140]
417. 4 | ~37 [avatar contradiction clause 416]
474. funny(X2) | wise(X2) | ~brave(X2) [resolution 233,103]
484. funny(X2) | ~brave(X2) [subsumption resolution 474,93]
485. ~brave(X2) [subsumption resolution 484,68]
530. funny(susan) | quiet(susan) <- (27) [resolution 298,85]
533. 53 <=> funny(susan) [avatar definition]
535. funny(susan) <- (53) [avatar component clause 533]
536. 7 | 53 | ~27 [avatar split clause 530,296,533,152]
540. $false <- (38) [resolution 485,371]
541. ~38 [avatar contradiction clause 540]
609. old(susan) <- (53) [resolution 535,67]
610. $false <- (~21, 53) [subsumption resolution 609,237]
611. 21 | ~53 [avatar contradiction clause 610]
612. 27 | ~28 | ~22 [avatar split clause 374,240,300,296]
615. old(susan) <- (~28) [resolution 302,65]
616. $false <- (~21, ~28) [subsumption resolution 615,237]
617. 21 | 28 [avatar contradiction clause 616]
621. kind(susan) <- (7) [resolution 153,102]
625. $false <- (7, ~8) [subsumption resolution 621,158]
626. ~7 | 8 [avatar contradiction clause 625]
627. $false [avatar sat refutation 141,217,243,290,372,417,536,541,611,612,617,626]
% SZS output end Proof for 1677689354986118963731215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or calm is not wise or not old. If someone is curious or brave then someone is not patient. Everyone who is not old is both not curious and not rich. Everyone who is not tall or tall is either not tall or generous. Everyone who is both strong and not wise is both not creative and brave and vice versa. If someone is humble then fred is happy or not kind. If john is curious then someone is patient or not calm and vice versa. If mary is curious then someone is both funny and generous. Everyone who is old is either wise or not patient and vice versa. If fred is strong or not calm then paul is not humble and vice versa. If john is either not kind or not generous then alice is either not quiet or creative. If someone is funny then someone is not quiet and vice versa. Everyone who is either quiet or not creative is not rich and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is not humble or humble is both not patient and not rich. If someone is either not humble or funny then fred is old and vice versa. Paul is calm. Someone is both generous and creative. Someone is both not old and humble. Someone is curious or not generous. Someone is both brave and not old. Fred is either not generous or rich. Someone is wise. Paul is not tall. | Alice is not rich. | entailment | (![X]:((creative(X)|calm(X))=>(~wise(X)|~old(X))))&
((?[X]:((curious(X)|brave(X))))=>(?[X]:(~patient(X))))&
(![X]:(~old(X)=>(~curious(X)&~rich(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:((strong(X)&~wise(X))<=>(~creative(X)&brave(X))))&
((?[X]:(humble(X)))=>((happy(fred)|~kind(fred))))&
((curious(john))<=>(?[X]:((patient(X)|~calm(X)))))&
((curious(mary))=>(?[X]:((funny(X)&generous(X)))))&
(![X]:(old(X)<=>(wise(X)<~>~patient(X))))&
(((strong(fred)|~calm(fred)))<=>(~humble(paul)))&
(((~kind(john)<~>~generous(john)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~humble(X)|humble(X))=>(~patient(X)&~rich(X))))&
((?[X]:((~humble(X)<~>funny(X))))<=>(old(fred)))&
(calm(paul))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((~old(X)&humble(X))))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((brave(X)&~old(X))))&
((~generous(fred)<~>rich(fred)))&
(?[X]:(wise(X)))&
(~tall(paul)) | ~rich(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3284188533364002168269522
% SZS output start Proof for 3284188533364002168269522
15. ! [X0] : ((humble(X0) | ~humble(X0)) => (~rich(X0) & ~patient(X0))) [input p14]
25. rich(alice) [input hypothesis]
36. ! [X0] : ((~rich(X0) & ~patient(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 15]
115. ~rich(X0) | humble(X0) [cnf transformation 36]
116. ~rich(X0) | ~humble(X0) [cnf transformation 36]
133. rich(alice) [cnf transformation 25]
234. ~rich(X0) [subsumption resolution 115,116]
269. $false [subsumption resolution 133,234]
% SZS output end Proof for 3284188533364002168269522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is wise or not old then fred is both quiet and not quiet and vice versa. Everyone who is either kind or generous is both not curious and not funny and vice versa. Everyone who is both not old and not quiet is either not old or not quiet and vice versa. Everyone who is generous is curious or old and vice versa. Everyone who is strong or not curious is either not kind or patient and vice versa. Everyone who is both funny and not patient is both old and not patient and vice versa. Everyone who is both quiet and not quiet is strong or calm and vice versa. If alice is happy then someone is both old and not quiet and vice versa. Everyone who is either rich or not curious is either not wise or not old and vice versa. Everyone who is either not patient or calm is either not tall or generous. Everyone who is both tall and not humble is both not patient and funny and vice versa. Everyone who is funny is not wise and vice versa. If fred is curious or brave then someone is either creative or not strong and vice versa. If mary is not wise or curious then fred is humble or not patient and vice versa. Everyone who is either funny or not brave is calm and vice versa. Fred is not kind or not curious. Someone is both generous and patient. Paul is humble. Someone is generous or not old. Mary is not brave. | Alice is humble. | neutral | (((wise(paul)|~old(paul)))<=>((quiet(fred)&~quiet(fred))))&
(![X]:((kind(X)<~>generous(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~old(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(curious(X)|old(X))))&
(![X]:((strong(X)|~curious(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((funny(X)&~patient(X))<=>(old(X)&~patient(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(strong(X)|calm(X))))&
((happy(alice))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~curious(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)&funny(X))))&
(![X]:(funny(X)<=>~wise(X)))&
(((curious(fred)|brave(fred)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~wise(mary)|curious(mary)))<=>((humble(fred)|~patient(fred))))&
(![X]:((funny(X)<~>~brave(X))<=>calm(X)))&
((~kind(fred)|~curious(fred)))&
(?[X]:((generous(X)&patient(X))))&
(humble(paul))&
(?[X]:((generous(X)|~old(X))))&
(~brave(mary)) | humble(alice) | [] | null | 0 |
If someone is either not tall or funny then mary is either brave or not curious and vice versa.
Everyone who is not curious or curious is both not humble and not funny and vice versa.
If someone is both happy and not calm then someone is calm or rich and vice versa.
Everyone who is either not brave or not happy is not old or not strong and vice versa.
Everyone who is both not wise and patient is either creative or not tall and vice versa.
If someone is not kind then john is both creative and kind.
If paul is not tall or not strong then fred is happy.
Everyone who is both not calm and not kind is either calm or quiet and vice versa.
Everyone who is either old or not tall is creative or humble and vice versa.
Everyone who is both wise and not kind is both wise and quiet.
Everyone who is not strong or calm is both not tall and tall.
If alice is not rich then someone is both not rich and not calm.
If someone is rich or strong then paul is not wise or not calm and vice versa.
If john is not tall then someone is not happy.
If someone is humble then someone is quiet or not creative and vice versa.
Everyone who is not calm or calm is not creative or curious.
Someone is rich or not tall.
Someone is either not curious or patient.
Alice is brave or strong.
Someone is either old or not happy.
Someone is generous or not brave. | Mary is quiet. | contradiction | ((?[X]:((~tall(X)<~>funny(X))))<=>((brave(mary)<~>~curious(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((happy(X)&~calm(X))))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~brave(X)<~>~happy(X))<=>(~old(X)|~strong(X))))&
(![X]:((~wise(X)&patient(X))<=>(creative(X)<~>~tall(X))))&
((?[X]:(~kind(X)))=>((creative(john)&kind(john))))&
(((~tall(paul)|~strong(paul)))=>(happy(fred)))&
(![X]:((~calm(X)&~kind(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(creative(X)|humble(X))))&
(![X]:((wise(X)&~kind(X))=>(wise(X)&quiet(X))))&
(![X]:((~strong(X)|calm(X))=>(~tall(X)&tall(X))))&
((~rich(alice))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((rich(X)|strong(X))))<=>((~wise(paul)|~calm(paul))))&
((~tall(john))=>(?[X]:(~happy(X))))&
((?[X]:(humble(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((brave(alice)|strong(alice)))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((generous(X)|~brave(X)))) | quiet(mary) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8998756635159519109888312
% SZS output start Proof for 8998756635159519109888312
2. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~funny(X0) & ~humble(X0))) [input p1]
15. ? [X0] : humble(X0) <=> ? [X0] : (~creative(X0) | quiet(X0)) [input p14]
22. quiet(mary) [input hypothesis]
24. ? [X0] : humble(X0) <=> ? [X1] : (~creative(X1) | quiet(X1)) [rectify 15]
39. ! [X0] : (((curious(X0) | ~curious(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 2]
40. ! [X0] : ((curious(X0) | ~curious(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~curious(X0) & curious(X0)))) [flattening 39]
63. (? [X0] : humble(X0) | ! [X1] : (creative(X1) & ~quiet(X1))) & (? [X1] : (~creative(X1) | quiet(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 24]
64. (? [X0] : humble(X0) | ! [X1] : (creative(X1) & ~quiet(X1))) & (? [X2] : (~creative(X2) | quiet(X2)) | ! [X3] : ~humble(X3)) [rectify 63]
65. ? [X0] : humble(X0) => humble(sK6) [choice axiom]
66. ? [X2] : (~creative(X2) | quiet(X2)) => (~creative(sK7) | quiet(sK7)) [choice axiom]
67. (humble(sK6) | ! [X1] : (creative(X1) & ~quiet(X1))) & ((~creative(sK7) | quiet(sK7)) | ! [X3] : ~humble(X3)) [skolemisation 64,66,65]
84. ~humble(X0) | curious(X0) [cnf transformation 40]
85. ~humble(X0) | ~curious(X0) [cnf transformation 40]
136. humble(sK6) | ~quiet(X1) [cnf transformation 67]
146. quiet(mary) [cnf transformation 22]
180. ~humble(X0) [subsumption resolution 84,85]
279. ~quiet(X1) [subsumption resolution 136,180]
303. $false [subsumption resolution 146,279]
% SZS output end Proof for 8998756635159519109888312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not humble or not kind and vice versa.
Everyone who is either not rich or curious is both not humble and not curious and vice versa.
If susan is wise or creative then lucy is either not tall or not patient and vice versa.
Everyone who is creative is either not kind or not patient and vice versa.
Everyone who is either not old or not kind is either rich or brave.
Everyone who is either not quiet or brave is not quiet or creative and vice versa.
If alice is rich then susan is either wise or generous.
Everyone who is calm or not patient is both rich and not happy and vice versa.
Everyone who is not calm is not wise or not humble.
Everyone who is not rich or rich is either not tall or brave and vice versa.
If mary is both not patient and curious then someone is brave or not old.
Everyone who is both funny and not creative is both not curious and not humble and vice versa.
Everyone who is not wise is either calm or not tall and vice versa.
If someone is brave or rich then fred is strong and vice versa.
Everyone who is either not rich or not patient is either patient or not calm and vice versa.
If someone is not patient then alice is humble or not humble and vice versa.
Paul is either curious or not brave.
Someone is not generous.
Someone is either not old or not wise.
Someone is happy or not old.
Someone is not wise or not humble.
Someone is either not kind or not brave.
Alice is tall or humble. | Lucy is not creative. | entailment | (![X]:(~happy(X)<=>(~humble(X)<~>~kind(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~humble(X)&~curious(X))))&
(((wise(susan)|creative(susan)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:(creative(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)<~>~kind(X))=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>brave(X))<=>(~quiet(X)|creative(X))))&
((rich(alice))=>((wise(susan)<~>generous(susan))))&
(![X]:((calm(X)|~patient(X))<=>(rich(X)&~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|rich(X))<=>(~tall(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((~rich(X)<~>~patient(X))<=>(patient(X)<~>~calm(X))))&
((?[X]:(~patient(X)))<=>((humble(alice)|~humble(alice))))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((tall(alice)|humble(alice))) | ~creative(lucy) | [
"p0",
"p1",
"p3",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6071836788482984236451319
% SZS output start Proof for 6071836788482984236451319
1. ! [X0] : (~happy(X0) <=> (~humble(X0) <~> ~kind(X0))) [input p0]
2. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> (~curious(X0) & ~humble(X0))) [input p1]
4. ! [X0] : (creative(X0) <=> (~kind(X0) <~> ~patient(X0))) [input p3]
8. ! [X0] : ((~patient(X0) | calm(X0)) <=> (~happy(X0) & rich(X0))) [input p7]
12. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~humble(X0) & ~curious(X0))) [input p11]
15. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (patient(X0) <~> ~calm(X0))) [input p14]
24. creative(lucy) [input hypothesis]
31. ! [X0] : ((~happy(X0) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0)))) & (((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | happy(X0))) [nnf transformation 1]
32. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 2]
33. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [flattening 32]
36. ! [X0] : ((creative(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 4]
41. ! [X0] : (((~patient(X0) | calm(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 8]
42. ! [X0] : ((~patient(X0) | calm(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [flattening 41]
47. ! [X0] : (((~creative(X0) & funny(X0)) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 12]
48. ! [X0] : (((~creative(X0) & funny(X0)) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | creative(X0) | ~funny(X0))) [flattening 47]
54. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) & (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 15]
73. ~kind(X0) | ~humble(X0) | happy(X0) [cnf transformation 31]
76. ~humble(X0) | ~happy(X0) | kind(X0) [cnf transformation 31]
80. ~curious(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 33]
89. ~patient(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 36]
90. ~creative(X0) | kind(X0) | patient(X0) [cnf transformation 36]
105. ~calm(X0) | rich(X0) [cnf transformation 42]
106. patient(X0) | rich(X0) [cnf transformation 42]
108. ~happy(X0) | patient(X0) [cnf transformation 42]
109. ~patient(X0) | calm(X0) | happy(X0) | ~rich(X0) [cnf transformation 42]
121. ~creative(X0) | humble(X0) | curious(X0) [cnf transformation 48]
130. ~calm(X0) | patient(X0) | ~rich(X0) | patient(X0) [cnf transformation 54]
131. calm(X0) | ~patient(X0) | ~patient(X0) | rich(X0) [cnf transformation 54]
133. ~patient(X0) | ~rich(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 54]
150. creative(lucy) [cnf transformation 24]
151. ~calm(X0) | patient(X0) | ~rich(X0) [duplicate literal removal 130]
152. calm(X0) | ~patient(X0) | rich(X0) [duplicate literal removal 131]
153. ~patient(X0) | ~rich(X0) | ~calm(X0) [duplicate literal removal 133]
157. ~curious(X0) | ~rich(X0) [duplicate literal removal 80]
160. 1 <=> patient(lucy) [avatar definition]
161. ~patient(lucy) <- (~1) [avatar component clause 160]
162. patient(lucy) <- (1) [avatar component clause 160]
232. ~calm(X0) | ~patient(X0) [subsumption resolution 153,105]
233. ~patient(X0) | rich(X0) [subsumption resolution 152,232]
234. rich(X0) [subsumption resolution 233,106]
235. ~calm(X0) | patient(X0) [subsumption resolution 151,234]
236. ~calm(X0) [subsumption resolution 235,232]
337. kind(lucy) | patient(lucy) [resolution 90,150]
339. kind(lucy) <- (~1) [subsumption resolution 337,161]
350. ~humble(lucy) | happy(lucy) <- (~1) [resolution 339,73]
352. 35 <=> humble(lucy) [avatar definition]
353. ~humble(lucy) <- (~35) [avatar component clause 352]
354. humble(lucy) <- (35) [avatar component clause 352]
356. 36 <=> happy(lucy) [avatar definition]
357. happy(lucy) <- (36) [avatar component clause 356]
358. ~happy(lucy) <- (~36) [avatar component clause 356]
360. 36 | ~35 | 1 [avatar split clause 350,160,352,356]
393. humble(lucy) | curious(lucy) [resolution 121,150]
394. curious(lucy) <- (~35) [subsumption resolution 393,353]
395. ~rich(lucy) <- (~35) [resolution 394,157]
396. $false <- (~35) [subsumption resolution 395,234]
397. 35 [avatar contradiction clause 396]
404. ~happy(lucy) | kind(lucy) <- (35) [resolution 354,76]
405. patient(lucy) <- (36) [resolution 357,108]
408. 1 | ~36 [avatar split clause 405,356,160]
411. ~kind(lucy) | ~creative(lucy) <- (1) [resolution 162,89]
415. ~kind(lucy) <- (1) [subsumption resolution 411,150]
416. ~happy(lucy) <- (1, 35) [subsumption resolution 404,415]
417. ~36 | ~1 | ~35 [avatar split clause 416,352,160,356]
463. calm(lucy) | happy(lucy) | ~rich(lucy) <- (1) [resolution 109,162]
465. happy(lucy) | ~rich(lucy) <- (1) [subsumption resolution 463,236]
466. ~rich(lucy) <- (1, ~36) [subsumption resolution 465,358]
467. $false <- (1, ~36) [subsumption resolution 466,234]
468. ~1 | 36 [avatar contradiction clause 467]
473. $false [avatar sat refutation 360,397,408,417,468]
% SZS output end Proof for 6071836788482984236451319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is strong and vice versa. Everyone who is either happy or not funny is tall or not quiet. If john is either kind or rich then someone is either not rich or kind. Everyone who is either not old or not strong is not happy or not brave and vice versa. Everyone who is either not creative or not kind is generous or calm and vice versa. If alice is either rich or happy then mary is both happy and not wise and vice versa. Everyone who is either calm or strong is humble or not old and vice versa. Everyone who is either brave or calm is either not humble or not strong and vice versa. Everyone who is not funny is both not calm and curious. If someone is quiet then someone is either humble or not strong and vice versa. If someone is brave or happy then someone is both funny and not curious and vice versa. If someone is either not patient or quiet then someone is not brave or not wise. If someone is both not creative and not tall then paul is tall or not patient and vice versa. Everyone who is not brave is both not patient and not rich. If susan is not kind or not calm then someone is both not patient and not happy and vice versa. If susan is either kind or strong then fred is either not calm or not humble and vice versa. Someone is quiet. Someone is either rich or creative. Lucy is either tall or generous. Alice is either not tall or quiet. John is brave. Someone is not creative or humble. Susan is either not old or rich. Lucy is either not rich or funny. | Alice is calm. | entailment | (![X]:(old(X)<=>strong(X)))&
(![X]:((happy(X)<~>~funny(X))=>(tall(X)|~quiet(X))))&
(((kind(john)<~>rich(john)))=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(~happy(X)|~brave(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(generous(X)|calm(X))))&
(((rich(alice)<~>happy(alice)))<=>((happy(mary)&~wise(mary))))&
(![X]:((calm(X)<~>strong(X))<=>(humble(X)|~old(X))))&
(![X]:((brave(X)<~>calm(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~funny(X)=>(~calm(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((brave(X)|happy(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>((tall(paul)|~patient(paul))))&
(![X]:(~brave(X)=>(~patient(X)&~rich(X))))&
(((~kind(susan)|~calm(susan)))<=>(?[X]:((~patient(X)&~happy(X)))))&
(((kind(susan)<~>strong(susan)))<=>((~calm(fred)<~>~humble(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((rich(X)<~>creative(X))))&
((tall(lucy)<~>generous(lucy)))&
((~tall(alice)<~>quiet(alice)))&
(brave(john))&
(?[X]:((~creative(X)|humble(X))))&
((~old(susan)<~>rich(susan)))&
((~rich(lucy)<~>funny(lucy))) | calm(alice) | [
"p0",
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8848809593155640071950447
% SZS output start Proof for 8848809593155640071950447
1. ! [X0] : (old(X0) <=> strong(X0)) [input p0]
4. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~brave(X0) | ~happy(X0))) [input p3]
7. ! [X0] : ((calm(X0) <~> strong(X0)) <=> (~old(X0) | humble(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p7]
25. ~calm(alice) [input hypothesis]
35. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 1]
40. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 4]
41. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 40]
46. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [flattening 46]
48. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 8]
85. ~old(X0) | strong(X0) [cnf transformation 35]
86. ~strong(X0) | old(X0) [cnf transformation 35]
96. ~strong(X0) | ~old(X0) | brave(X0) [cnf transformation 41]
98. strong(X0) | old(X0) | brave(X0) [cnf transformation 41]
112. ~old(X0) | humble(X0) | calm(X0) | ~strong(X0) [cnf transformation 47]
113. ~humble(X0) | calm(X0) | strong(X0) [cnf transformation 47]
114. strong(X0) | calm(X0) | old(X0) [cnf transformation 47]
117. ~strong(X0) | ~humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 48]
119. strong(X0) | humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 48]
171. ~calm(alice) [cnf transformation 25]
192. brave(X0) | old(X0) [subsumption resolution 98,86]
194. ~strong(X0) | brave(X0) [subsumption resolution 96,192]
218. calm(X0) | old(X0) [subsumption resolution 114,86]
219. ~strong(X0) | calm(X0) | humble(X0) [subsumption resolution 112,86]
224. ~brave(X0) | calm(X0) | humble(X0) [subsumption resolution 119,219]
225. ~humble(X0) | calm(X0) | ~brave(X0) [subsumption resolution 117,113]
226. ~brave(X0) | calm(X0) [subsumption resolution 225,224]
442. old(alice) [resolution 218,171]
503. strong(alice) [resolution 442,85]
730. brave(alice) [resolution 503,194]
857. calm(alice) [resolution 730,226]
858. $false [subsumption resolution 857,171]
% SZS output end Proof for 8848809593155640071950447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then someone is either old or creative. Everyone who is not rich is not generous. If someone is not wise then paul is both kind and happy and vice versa. If john is both tall and quiet then paul is not brave or calm. Everyone who is both not calm and not patient is strong or not curious and vice versa. If paul is both not calm and calm then susan is not old or creative and vice versa. If alice is creative then paul is old and vice versa. If someone is curious then mary is not wise or not creative. If paul is not old then mary is tall and vice versa. Everyone who is curious is both quiet and generous. If fred is not kind then someone is either not patient or not happy and vice versa. Everyone who is either not old or strong is not old and vice versa. Everyone who is not old is either wise or not patient. If lucy is both not humble and not calm then susan is either not wise or quiet. Everyone who is old is generous. Everyone who is not patient is either generous or happy and vice versa. Someone is not funny. Paul is rich or not funny. Paul is both not humble and rich. Paul is patient. Someone is not rich or generous. Susan is both not funny and happy. | Fred is brave. | neutral | ((?[X]:((kind(X)<~>old(X))))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:(~rich(X)=>~generous(X)))&
((?[X]:(~wise(X)))<=>((kind(paul)&happy(paul))))&
(((tall(john)&quiet(john)))=>((~brave(paul)|calm(paul))))&
(![X]:((~calm(X)&~patient(X))<=>(strong(X)|~curious(X))))&
(((~calm(paul)&calm(paul)))<=>((~old(susan)|creative(susan))))&
((creative(alice))<=>(old(paul)))&
((?[X]:(curious(X)))=>((~wise(mary)|~creative(mary))))&
((~old(paul))<=>(tall(mary)))&
(![X]:(curious(X)=>(quiet(X)&generous(X))))&
((~kind(fred))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((~old(X)<~>strong(X))<=>~old(X)))&
(![X]:(~old(X)=>(wise(X)<~>~patient(X))))&
(((~humble(lucy)&~calm(lucy)))=>((~wise(susan)<~>quiet(susan))))&
(![X]:(old(X)=>generous(X)))&
(![X]:(~patient(X)<=>(generous(X)<~>happy(X))))&
(?[X]:(~funny(X)))&
((rich(paul)|~funny(paul)))&
((~humble(paul)&rich(paul)))&
(patient(paul))&
(?[X]:((~rich(X)|generous(X))))&
((~funny(susan)&happy(susan))) | brave(fred) | [] | null | 0 |
If someone is strong or generous then someone is both funny and rich.
Everyone who is not brave is not calm or not creative and vice versa.
Everyone who is either not old or strong is not tall.
If someone is not kind or not humble then alice is both happy and not wise and vice versa.
If john is both not creative and happy then someone is happy and vice versa.
Everyone who is patient is not calm.
Everyone who is both not brave and funny is curious or rich and vice versa.
Everyone who is not strong is both not creative and curious.
If someone is either funny or patient then lucy is both generous and curious and vice versa.
Everyone who is both quiet and patient is not creative or humble and vice versa.
If someone is either not kind or not tall then alice is either not humble or not curious and vice versa.
Everyone who is both not quiet and patient is not quiet.
If someone is funny or curious then someone is not tall or happy.
If someone is both not happy and strong then susan is both not quiet and not patient and vice versa.
Everyone who is not patient is both not strong and calm.
If paul is not patient or happy then someone is either not happy or brave and vice versa.
Someone is generous or curious.
Paul is not brave or curious.
John is old or not calm.
Alice is curious or calm.
Someone is creative.
Fred is both not wise and not old. | Susan is not quiet. | neutral | ((?[X]:((strong(X)|generous(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:(~brave(X)<=>(~calm(X)|~creative(X))))&
(![X]:((~old(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~kind(X)|~humble(X))))<=>((happy(alice)&~wise(alice))))&
(((~creative(john)&happy(john)))<=>(?[X]:(happy(X))))&
(![X]:(patient(X)=>~calm(X)))&
(![X]:((~brave(X)&funny(X))<=>(curious(X)|rich(X))))&
(![X]:(~strong(X)=>(~creative(X)&curious(X))))&
((?[X]:((funny(X)<~>patient(X))))<=>((generous(lucy)&curious(lucy))))&
(![X]:((quiet(X)&patient(X))<=>(~creative(X)|humble(X))))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~humble(alice)<~>~curious(alice))))&
(![X]:((~quiet(X)&patient(X))=>~quiet(X)))&
((?[X]:((funny(X)|curious(X))))=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((~happy(X)&strong(X))))<=>((~quiet(susan)&~patient(susan))))&
(![X]:(~patient(X)=>(~strong(X)&calm(X))))&
(((~patient(paul)|happy(paul)))<=>(?[X]:((~happy(X)<~>brave(X)))))&
(?[X]:((generous(X)|curious(X))))&
((~brave(paul)|curious(paul)))&
((old(john)|~calm(john)))&
((curious(alice)|calm(alice)))&
(?[X]:(creative(X)))&
((~wise(fred)&~old(fred))) | ~quiet(susan) | [] | null | 0 |
Everyone who is creative is both creative and curious.
Everyone who is either strong or not funny is not quiet or not humble.
If someone is not quiet then alice is kind or calm and vice versa.
Everyone who is creative is either calm or creative and vice versa.
Everyone who is not calm is both old and wise.
If someone is not brave then someone is not old and vice versa.
If someone is not happy then someone is not wise or humble and vice versa.
Everyone who is both not tall and curious is not humble.
If someone is either not generous or happy then someone is wise or tall and vice versa.
Everyone who is either not quiet or not brave is both rich and humble.
If someone is both tall and kind then alice is not old.
Everyone who is not humble is either not funny or creative and vice versa.
Everyone who is curious or tall is not brave.
Everyone who is old is creative or not humble and vice versa.
Mary is not patient or not humble.
Someone is either not humble or generous.
Someone is both not tall and not patient.
Susan is generous.
Someone is humble or quiet.
Lucy is not strong or not humble.
Fred is not patient. | Fred is not creative. | entailment | (![X]:(creative(X)=>(creative(X)&curious(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~quiet(X)|~humble(X))))&
((?[X]:(~quiet(X)))<=>((kind(alice)|calm(alice))))&
(![X]:(creative(X)<=>(calm(X)<~>creative(X))))&
(![X]:(~calm(X)=>(old(X)&wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)&curious(X))=>~humble(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(rich(X)&humble(X))))&
((?[X]:((tall(X)&kind(X))))=>(~old(alice)))&
(![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((~patient(mary)|~humble(mary)))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(generous(susan))&
(?[X]:((humble(X)|quiet(X))))&
((~strong(lucy)|~humble(lucy)))&
(~patient(fred)) | ~creative(fred) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8281560330550530179755238
% SZS output start Proof for 8281560330550530179755238
1. ! [X0] : (creative(X0) => (curious(X0) & creative(X0))) [input p0]
4. ! [X0] : (creative(X0) <=> (calm(X0) <~> creative(X0))) [input p3]
5. ! [X0] : (~calm(X0) => (wise(X0) & old(X0))) [input p4]
6. ? [X0] : ~brave(X0) <=> ? [X0] : ~old(X0) [input p5]
13. ! [X0] : ((tall(X0) | curious(X0)) => ~brave(X0)) [input p12]
22. creative(fred) [input hypothesis]
23. ? [X0] : ~brave(X0) <=> ? [X1] : ~old(X1) [rectify 6]
30. ! [X0] : ((curious(X0) & creative(X0)) | ~creative(X0)) [ennf transformation 1]
33. ! [X0] : ((wise(X0) & old(X0)) | calm(X0)) [ennf transformation 5]
38. ! [X0] : (~brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 13]
45. ! [X0] : ((creative(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~creative(X0))) [nnf transformation 4]
46. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : brave(X0)) [nnf transformation 23]
47. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : brave(X3)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
49. ? [X2] : ~old(X2) => ~old(sK2) [choice axiom]
50. (~brave(sK1) | ! [X1] : old(X1)) & (~old(sK2) | ! [X3] : brave(X3)) [skolemisation 47,49,48]
73. ~creative(X0) | curious(X0) [cnf transformation 30]
80. ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 45]
81. creative(X0) | creative(X0) | ~calm(X0) [cnf transformation 45]
83. old(X0) | calm(X0) [cnf transformation 33]
85. ~old(sK2) | brave(X3) [cnf transformation 50]
104. ~brave(X0) | ~curious(X0) [cnf transformation 38]
115. creative(fred) [cnf transformation 22]
116. ~creative(X0) | ~calm(X0) [duplicate literal removal 80]
117. creative(X0) | ~calm(X0) [duplicate literal removal 81]
136. ~calm(X0) [subsumption resolution 116,117]
138. old(X0) [subsumption resolution 83,136]
139. brave(X3) [subsumption resolution 85,138]
178. ~curious(X0) [subsumption resolution 104,139]
205. curious(fred) [resolution 73,115]
206. $false [subsumption resolution 205,178]
% SZS output end Proof for 8281560330550530179755238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or creative then fred is either not curious or old and vice versa. If someone is either not kind or not rich then someone is not brave or not generous. Everyone who is both creative and not rich is both not patient and quiet and vice versa. Everyone who is not happy or not rich is not humble and vice versa. Everyone who is not funny or not quiet is either creative or not tall. Everyone who is tall is old and vice versa. Everyone who is not patient is quiet and vice versa. Everyone who is wise is old. If mary is quiet or not kind then someone is either funny or calm and vice versa. Everyone who is either not rich or creative is either old or happy and vice versa. If paul is both strong and tall then someone is not patient and vice versa. If mary is not kind or not patient then alice is both not funny and creative. Everyone who is not curious or not quiet is kind. If fred is both not funny and quiet then john is not curious. Everyone who is either not curious or generous is both not kind and not strong. If someone is either kind or wise then fred is generous and vice versa. John is calm or wise. Susan is not strong or not happy. Paul is both not curious and not creative. Susan is both not tall and not generous. Someone is not calm or not patient. Someone is either humble or curious. | Fred is not creative. | entailment | ((?[X]:((~kind(X)<~>creative(X))))<=>((~curious(fred)<~>old(fred))))&
((?[X]:((~kind(X)<~>~rich(X))))=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((creative(X)&~rich(X))<=>(~patient(X)&quiet(X))))&
(![X]:((~happy(X)|~rich(X))<=>~humble(X)))&
(![X]:((~funny(X)|~quiet(X))=>(creative(X)<~>~tall(X))))&
(![X]:(tall(X)<=>old(X)))&
(![X]:(~patient(X)<=>quiet(X)))&
(![X]:(wise(X)=>old(X)))&
(((quiet(mary)|~kind(mary)))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(old(X)<~>happy(X))))&
(((strong(paul)&tall(paul)))<=>(?[X]:(~patient(X))))&
(((~kind(mary)|~patient(mary)))=>((~funny(alice)&creative(alice))))&
(![X]:((~curious(X)|~quiet(X))=>kind(X)))&
(((~funny(fred)&quiet(fred)))=>(~curious(john)))&
(![X]:((~curious(X)<~>generous(X))=>(~kind(X)&~strong(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>(generous(fred)))&
((calm(john)|wise(john)))&
((~strong(susan)|~happy(susan)))&
((~curious(paul)&~creative(paul)))&
((~tall(susan)&~generous(susan)))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((humble(X)<~>curious(X)))) | ~creative(fred) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p7",
"p10",
"p12",
"p14",
"p15",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 559181332066455711381510
% SZS output start Proof for 559181332066455711381510
1. ? [X0] : (~kind(X0) <~> creative(X0)) <=> (~curious(fred) <~> old(fred)) [input p0]
3. ! [X0] : ((~rich(X0) & creative(X0)) <=> (quiet(X0) & ~patient(X0))) [input p2]
5. ! [X0] : ((~quiet(X0) | ~funny(X0)) => (creative(X0) <~> ~tall(X0))) [input p4]
6. ! [X0] : (tall(X0) <=> old(X0)) [input p5]
7. ! [X0] : (~patient(X0) <=> quiet(X0)) [input p6]
8. ! [X0] : (wise(X0) => old(X0)) [input p7]
11. (tall(paul) & strong(paul)) <=> ? [X0] : ~patient(X0) [input p10]
13. ! [X0] : ((~quiet(X0) | ~curious(X0)) => kind(X0)) [input p12]
15. ! [X0] : ((~curious(X0) <~> generous(X0)) => (~strong(X0) & ~kind(X0))) [input p14]
16. ? [X0] : (kind(X0) <~> wise(X0)) <=> generous(fred) [input p15]
19. ~creative(paul) & ~curious(paul) [input p18]
20. ~generous(susan) & ~tall(susan) [input p19]
23. creative(fred) [input hypothesis]
26. ! [X0] : ((creative(X0) <~> ~tall(X0)) | (quiet(X0) & funny(X0))) [ennf transformation 5]
27. ! [X0] : (old(X0) | ~wise(X0)) [ennf transformation 8]
29. ! [X0] : (kind(X0) | (quiet(X0) & curious(X0))) [ennf transformation 13]
32. ! [X0] : ((~strong(X0) & ~kind(X0)) | (~curious(X0) <=> generous(X0))) [ennf transformation 15]
33. (? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~curious(fred) | ~old(fred)) & (old(fred) | curious(fred)))) & (((~old(fred) | curious(fred)) & (old(fred) | ~curious(fred))) | ! [X0] : ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) [nnf transformation 1]
34. (? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~curious(fred) | ~old(fred)) & (old(fred) | curious(fred)))) & (((~old(fred) | curious(fred)) & (old(fred) | ~curious(fred))) | ! [X1] : ((~kind(X1) | ~creative(X1)) & (creative(X1) | kind(X1)))) [rectify 33]
35. ? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) => ((~creative(sK0) | kind(sK0)) & (creative(sK0) | ~kind(sK0))) [choice axiom]
36. (((~creative(sK0) | kind(sK0)) & (creative(sK0) | ~kind(sK0))) | ((~curious(fred) | ~old(fred)) & (old(fred) | curious(fred)))) & (((~old(fred) | curious(fred)) & (old(fred) | ~curious(fred))) | ! [X1] : ((~kind(X1) | ~creative(X1)) & (creative(X1) | kind(X1)))) [skolemisation 34,35]
37. ! [X0] : (((~rich(X0) & creative(X0)) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 3]
38. ! [X0] : (((~rich(X0) & creative(X0)) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | rich(X0) | ~creative(X0))) [flattening 37]
41. ! [X0] : (((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (quiet(X0) & funny(X0))) [nnf transformation 26]
42. ! [X0] : ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))) [nnf transformation 6]
43. ! [X0] : ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))) [nnf transformation 7]
50. ((tall(paul) & strong(paul)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (~tall(paul) | ~strong(paul))) [nnf transformation 11]
51. ((tall(paul) & strong(paul)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~tall(paul) | ~strong(paul)) [flattening 50]
52. ((tall(paul) & strong(paul)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~tall(paul) | ~strong(paul)) [rectify 51]
53. ? [X1] : ~patient(X1) => ~patient(sK2) [choice axiom]
54. ((tall(paul) & strong(paul)) | ! [X0] : patient(X0)) & (~patient(sK2) | ~tall(paul) | ~strong(paul)) [skolemisation 52,53]
55. ! [X0] : ((~strong(X0) & ~kind(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 32]
56. (? [X0] : ((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ~generous(fred)) & (generous(fred) | ! [X0] : ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0)))) [nnf transformation 16]
57. (? [X0] : ((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ~generous(fred)) & (generous(fred) | ! [X1] : ((kind(X1) | ~wise(X1)) & (wise(X1) | ~kind(X1)))) [rectify 56]
58. ? [X0] : ((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) => ((~wise(sK3) | ~kind(sK3)) & (wise(sK3) | kind(sK3))) [choice axiom]
59. (((~wise(sK3) | ~kind(sK3)) & (wise(sK3) | kind(sK3))) | ~generous(fred)) & (generous(fred) | ! [X1] : ((kind(X1) | ~wise(X1)) & (wise(X1) | ~kind(X1)))) [skolemisation 57,58]
68. ~old(fred) | curious(fred) | ~kind(X1) | ~creative(X1) [cnf transformation 36]
75. ~quiet(X0) | creative(X0) | patient(X0) [cnf transformation 38]
81. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 41]
83. ~creative(X0) | tall(X0) | quiet(X0) [cnf transformation 41]
84. ~tall(X0) | old(X0) [cnf transformation 42]
85. ~old(X0) | tall(X0) [cnf transformation 42]
86. quiet(X0) | patient(X0) [cnf transformation 43]
87. ~quiet(X0) | ~patient(X0) [cnf transformation 43]
88. ~wise(X0) | old(X0) [cnf transformation 27]
105. tall(paul) | patient(X0) [cnf transformation 54]
111. quiet(X0) | kind(X0) [cnf transformation 29]
114. ~generous(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 55]
117. generous(fred) | wise(X1) | ~kind(X1) [cnf transformation 59]
124. ~creative(paul) [cnf transformation 19]
125. ~tall(susan) [cnf transformation 20]
130. creative(fred) [cnf transformation 23]
132. 1 <=> old(fred) [avatar definition]
136. 2 <=> curious(fred) [avatar definition]
152. 5 <=> ! [X1] : (~kind(X1) | ~creative(X1)) [avatar definition]
153. ~creative(X1) | ~kind(X1) <- (5) [avatar component clause 152]
154. 5 | 2 | ~1 [avatar split clause 68,132,136,152]
190. 13 <=> ! [X0] : patient(X0) [avatar definition]
191. patient(X0) <- (13) [avatar component clause 190]
193. 14 <=> tall(paul) [avatar definition]
195. tall(paul) <- (14) [avatar component clause 193]
196. 13 | 14 [avatar split clause 105,193,190]
228. 21 <=> quiet(fred) [avatar definition]
229. quiet(fred) <- (21) [avatar component clause 228]
238. 23 <=> generous(fred) [avatar definition]
239. generous(fred) <- (23) [avatar component clause 238]
256. 27 <=> ! [X1] : (wise(X1) | ~kind(X1)) [avatar definition]
257. ~kind(X1) | wise(X1) <- (27) [avatar component clause 256]
258. 27 | 23 [avatar split clause 117,238,256]
309. ~patient(X0) | kind(X0) [resolution 111,87]
329. ~patient(fred) <- (21) [resolution 229,87]
331. creative(X1) | patient(X1) | patient(X1) [resolution 75,86]
333. patient(X1) | creative(X1) [duplicate literal removal 331]
353. ~kind(fred) <- (5) [resolution 153,130]
378. 41 <=> tall(fred) [avatar definition]
380. tall(fred) <- (41) [avatar component clause 378]
383. tall(fred) | quiet(fred) [resolution 83,130]
386. ~curious(fred) | ~kind(fred) <- (23) [resolution 114,239]
411. kind(X0) <- (13) [resolution 191,309]
413. $false <- (13, 21) [resolution 191,329]
416. ~13 | ~21 [avatar contradiction clause 413]
417. 21 | 41 [avatar split clause 383,378,228]
425. old(fred) <- (41) [resolution 380,84]
428. 1 | ~41 [avatar split clause 425,378,132]
432. $false <- (5, 13) [resolution 411,353]
433. ~5 | ~13 [avatar contradiction clause 432]
434. ~curious(fred) <- (13, 23) [subsumption resolution 386,411]
435. ~2 | ~13 | ~23 [avatar split clause 434,238,190,136]
436. wise(X1) <- (13, 27) [subsumption resolution 257,411]
451. old(X0) <- (13, 27) [resolution 436,88]
478. tall(X0) <- (13, 27) [resolution 451,85]
485. $false <- (13, 27) [resolution 478,125]
491. ~13 | ~27 [avatar contradiction clause 485]
504. creative(paul) | quiet(paul) <- (14) [resolution 195,81]
507. quiet(paul) <- (14) [subsumption resolution 504,124]
542. ~patient(paul) <- (14) [resolution 507,87]
637. creative(paul) <- (14) [resolution 542,333]
638. $false <- (14) [subsumption resolution 637,124]
639. ~14 [avatar contradiction clause 638]
640. $false [avatar sat refutation 154,196,258,416,417,428,433,435,491,639]
% SZS output end Proof for 559181332066455711381510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is both creative and not happy then fred is not strong and vice versa.
If someone is both humble and not quiet then john is either brave or 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. | Paul is creative. | neutral | (((creative(john)&~happy(john)))<=>(~strong(fred)))&
((?[X]:((humble(X)&~quiet(X))))<=>((brave(john)<~>~tall(john))))&
(((~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)) | creative(paul) | [] | null | 0 |
If mary is both not kind and not brave then someone is both rich and not funny and vice versa.
Everyone who is kind or not tall is not creative or brave and vice versa.
If alice is creative then mary is rich.
If alice is either patient or kind then someone is both kind and quiet.
Everyone who is both strong and creative is curious and vice versa.
If someone is not humble then someone is both humble and generous.
If john is quiet then someone is both not humble and happy and vice versa.
Everyone who is not creative or not patient is either not quiet or not funny.
If susan is not funny or humble then john is both strong and not quiet.
Everyone who is not calm is tall.
Everyone who is quiet or curious is both not kind and not humble.
Everyone who is not tall is both not creative and not brave and vice versa.
Everyone who is both happy and patient is both old and brave.
Everyone who is both not patient and brave is not rich or not brave and vice versa.
Everyone who is not brave or not wise is both not happy and strong.
Everyone who is creative is both not generous and not curious and vice versa.
John is tall.
Someone is wise.
Alice is both not generous and not humble.
Someone is both funny and not wise.
Someone is not calm.
Lucy is generous.
Someone is both not humble and not creative. | Mary is rich. | entailment | (((~kind(mary)&~brave(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((kind(X)|~tall(X))<=>(~creative(X)|brave(X))))&
((creative(alice))=>(rich(mary)))&
(((patient(alice)<~>kind(alice)))=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:((strong(X)&creative(X))<=>curious(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)&generous(X)))))&
((quiet(john))<=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:((~creative(X)|~patient(X))=>(~quiet(X)<~>~funny(X))))&
(((~funny(susan)|humble(susan)))=>((strong(john)&~quiet(john))))&
(![X]:(~calm(X)=>tall(X)))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))&
(![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))&
(![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~generous(X)&~curious(X))))&
(tall(john))&
(?[X]:(wise(X)))&
((~generous(alice)&~humble(alice)))&
(?[X]:((funny(X)&~wise(X))))&
(?[X]:(~calm(X)))&
(generous(lucy))&
(?[X]:((~humble(X)&~creative(X)))) | rich(mary) | [
"p2",
"p4",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2347367215947908264877231
% SZS output start Proof for 2347367215947908264877231
3. creative(alice) => rich(mary) [input p2]
5. ! [X0] : ((creative(X0) & strong(X0)) <=> curious(X0)) [input p4]
16. ! [X0] : (creative(X0) <=> (~curious(X0) & ~generous(X0))) [input p15]
19. ~humble(alice) & ~generous(alice) [input p18]
24. ~rich(mary) [input hypothesis]
27. rich(mary) | ~creative(alice) [ennf transformation 3]
47. ! [X0] : (((creative(X0) & strong(X0)) | ~curious(X0)) & (curious(X0) | (~creative(X0) | ~strong(X0)))) [nnf transformation 5]
48. ! [X0] : (((creative(X0) & strong(X0)) | ~curious(X0)) & (curious(X0) | ~creative(X0) | ~strong(X0))) [flattening 47]
61. ! [X0] : ((creative(X0) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | ~creative(X0))) [nnf transformation 16]
62. ! [X0] : ((creative(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | ~creative(X0))) [flattening 61]
79. rich(mary) | ~creative(alice) [cnf transformation 27]
86. ~curious(X0) | creative(X0) [cnf transformation 48]
120. creative(X0) | curious(X0) | generous(X0) [cnf transformation 62]
123. ~generous(alice) [cnf transformation 19]
131. ~rich(mary) [cnf transformation 24]
158. 6 <=> creative(alice) [avatar definition]
160. ~creative(alice) <- (~6) [avatar component clause 158]
162. 7 <=> rich(mary) [avatar definition]
165. ~6 | 7 [avatar split clause 79,162,158]
234. generous(X0) | creative(X0) [subsumption resolution 120,86]
236. ~7 [avatar split clause 131,162]
253. creative(alice) [resolution 234,123]
255. $false <- (~6) [subsumption resolution 253,160]
256. 6 [avatar contradiction clause 255]
257. $false [avatar sat refutation 165,236,256]
% SZS output end Proof for 2347367215947908264877231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and humble is wise and vice versa.
If john is not happy or happy then mary is both brave and not happy.
If lucy is not brave then someone is patient or not old.
If john is both not tall and patient then mary is either curious or not old and vice versa.
Everyone who is not calm is either not generous or not old.
Everyone who is strong is either not happy or not rich.
If someone is calm or not brave then someone is either humble or not calm and vice versa.
Everyone who is rich or not curious is either strong or not brave and vice versa.
Everyone who is curious is either rich or not wise and vice versa.
If susan is not funny then john is both not funny and curious.
Everyone who is either not brave or calm is not wise.
Everyone who is not old is not kind or wise.
If someone is not rich or kind then someone is either generous or humble.
If john is rich or not quiet then someone is old.
Everyone who is both not patient and quiet is not strong or funny.
If someone is both not tall and curious then someone is both generous and not rich and vice versa.
Mary is creative or not creative.
Someone is both not quiet and wise.
Someone is either kind or not brave.
Susan is humble or tall.
Someone is generous.
Susan is humble.
Someone is either quiet or not calm.
Someone is patient. | Susan is tall. | neutral | (![X]:((tall(X)&humble(X))<=>wise(X)))&
(((~happy(john)|happy(john)))=>((brave(mary)&~happy(mary))))&
((~brave(lucy))=>(?[X]:((patient(X)|~old(X)))))&
(((~tall(john)&patient(john)))<=>((curious(mary)<~>~old(mary))))&
(![X]:(~calm(X)=>(~generous(X)<~>~old(X))))&
(![X]:(strong(X)=>(~happy(X)<~>~rich(X))))&
((?[X]:((calm(X)|~brave(X))))<=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((rich(X)|~curious(X))<=>(strong(X)<~>~brave(X))))&
(![X]:(curious(X)<=>(rich(X)<~>~wise(X))))&
((~funny(susan))=>((~funny(john)&curious(john))))&
(![X]:((~brave(X)<~>calm(X))=>~wise(X)))&
(![X]:(~old(X)=>(~kind(X)|wise(X))))&
((?[X]:((~rich(X)|kind(X))))=>(?[X]:((generous(X)<~>humble(X)))))&
(((rich(john)|~quiet(john)))=>(?[X]:(old(X))))&
(![X]:((~patient(X)&quiet(X))=>(~strong(X)|funny(X))))&
((?[X]:((~tall(X)&curious(X))))<=>(?[X]:((generous(X)&~rich(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)&wise(X))))&
(?[X]:((kind(X)<~>~brave(X))))&
((humble(susan)|tall(susan)))&
(?[X]:(generous(X)))&
(humble(susan))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:(patient(X))) | tall(susan) | [] | null | 0 |
Everyone who is either curious or not calm is curious and vice versa. Everyone who is both funny and not calm is not wise or not curious and vice versa. Everyone who is calm or old is both not humble and quiet. Everyone who is both not rich and not wise is not creative. If someone is either not kind or not tall then paul is tall or generous and vice versa. Everyone who is rich or humble is not patient. Everyone who is either calm or not strong is not old. Everyone who is not brave or rich is happy or not kind and vice versa. If alice is either not wise or strong then someone is not quiet and vice versa. Everyone who is quiet is curious or strong. If someone is happy or not creative then someone is both not creative and funny. Everyone who is either old or not strong is not wise or quiet. Everyone who is calm or funny is funny or humble and vice versa. Everyone who is both not quiet and not old is either calm or not brave and vice versa. If mary is either not patient or strong then someone is either brave or humble and vice versa. If someone is either rich or tall then someone is not quiet or humble. Someone is not rich or not patient. John is both not old and not kind. Someone is either rich or curious. Paul is not brave or not patient. Alice is both calm and not creative. Someone is not brave. | Alice is brave. | contradiction | (![X]:((curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((funny(X)&~calm(X))<=>(~wise(X)|~curious(X))))&
(![X]:((calm(X)|old(X))=>(~humble(X)&quiet(X))))&
(![X]:((~rich(X)&~wise(X))=>~creative(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((tall(paul)|generous(paul))))&
(![X]:((rich(X)|humble(X))=>~patient(X)))&
(![X]:((calm(X)<~>~strong(X))=>~old(X)))&
(![X]:((~brave(X)|rich(X))<=>(happy(X)|~kind(X))))&
(((~wise(alice)<~>strong(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(curious(X)|strong(X))))&
((?[X]:((happy(X)|~creative(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(![X]:((old(X)<~>~strong(X))=>(~wise(X)|quiet(X))))&
(![X]:((calm(X)|funny(X))<=>(funny(X)|humble(X))))&
(![X]:((~quiet(X)&~old(X))<=>(calm(X)<~>~brave(X))))&
(((~patient(mary)<~>strong(mary)))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(?[X]:((~rich(X)|~patient(X))))&
((~old(john)&~kind(john)))&
(?[X]:((rich(X)<~>curious(X))))&
((~brave(paul)|~patient(paul)))&
((calm(alice)&~creative(alice)))&
(?[X]:(~brave(X))) | brave(alice) | [
"p0",
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5119999843990925948388507
% SZS output start Proof for 5119999843990925948388507
1. ! [X0] : ((curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p0]
3. ! [X0] : ((old(X0) | calm(X0)) => (quiet(X0) & ~humble(X0))) [input p2]
14. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p13]
23. brave(alice) [input hypothesis]
26. ! [X0] : ((quiet(X0) & ~humble(X0)) | (~old(X0) & ~calm(X0))) [ennf transformation 3]
37. ! [X0] : ((((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))))) [nnf transformation 1]
58. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 14]
59. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | old(X0) | quiet(X0))) [flattening 58]
76. curious(X0) | curious(X0) | calm(X0) [cnf transformation 37]
78. calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 37]
86. quiet(X0) | ~calm(X0) [cnf transformation 26]
120. ~quiet(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 59]
143. brave(alice) [cnf transformation 23]
144. curious(X0) | calm(X0) [duplicate literal removal 76]
145. calm(X0) | ~curious(X0) [duplicate literal removal 78]
146. calm(X0) [subsumption resolution 144,145]
149. quiet(X0) [subsumption resolution 86,146]
203. ~brave(X0) | ~calm(X0) [subsumption resolution 120,149]
204. ~brave(X0) [subsumption resolution 203,146]
224. $false [subsumption resolution 143,204]
% SZS output end Proof for 5119999843990925948388507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either tall or not curious then susan is both generous and kind.
Everyone who is not happy or kind is patient or wise.
If someone is not humble or patient then susan is not quiet.
Everyone who is curious is either not funny or not kind and vice versa.
Everyone who is not brave or tall is either old or patient and vice versa.
If mary is both not tall and tall then someone is not curious or not patient and vice versa.
Everyone who is both not old and not patient is not tall or not rich and vice versa.
Everyone who is either strong or not curious is both not kind and not old.
Everyone who is both not happy and strong is not generous or not wise and vice versa.
If paul is not happy then paul is not curious and vice versa.
If someone is either old or brave then paul is rich or not patient.
If susan is happy or not generous then alice is both generous and calm.
If alice is both happy and wise then mary is creative or curious and vice versa.
Everyone who is not brave is not kind or not happy and vice versa.
If someone is brave then someone is either not kind or kind.
If mary is both not rich and not old then fred is both quiet and not creative and vice versa.
Paul is either not generous or wise.
Someone is not calm.
Someone is quiet.
Someone is not strong.
Paul is both not old and calm.
Someone is both creative and not strong.
Alice is patient. | Susan is not wise. | contradiction | (((tall(susan)<~>~curious(susan)))=>((generous(susan)&kind(susan))))&
(![X]:((~happy(X)|kind(X))=>(patient(X)|wise(X))))&
((?[X]:((~humble(X)|patient(X))))=>(~quiet(susan)))&
(![X]:(curious(X)<=>(~funny(X)<~>~kind(X))))&
(![X]:((~brave(X)|tall(X))<=>(old(X)<~>patient(X))))&
(((~tall(mary)&tall(mary)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((~old(X)&~patient(X))<=>(~tall(X)|~rich(X))))&
(![X]:((strong(X)<~>~curious(X))=>(~kind(X)&~old(X))))&
(![X]:((~happy(X)&strong(X))<=>(~generous(X)|~wise(X))))&
((~happy(paul))<=>(~curious(paul)))&
((?[X]:((old(X)<~>brave(X))))=>((rich(paul)|~patient(paul))))&
(((happy(susan)|~generous(susan)))=>((generous(alice)&calm(alice))))&
(((happy(alice)&wise(alice)))<=>((creative(mary)|curious(mary))))&
(![X]:(~brave(X)<=>(~kind(X)|~happy(X))))&
((?[X]:(brave(X)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(((~rich(mary)&~old(mary)))<=>((quiet(fred)&~creative(fred))))&
((~generous(paul)<~>wise(paul)))&
(?[X]:(~calm(X)))&
(?[X]:(quiet(X)))&
(?[X]:(~strong(X)))&
((~old(paul)&calm(paul)))&
(?[X]:((creative(X)&~strong(X))))&
(patient(alice)) | ~wise(susan) | [
"p0",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 149881368216285818253979
% SZS output start Proof for 149881368216285818253979
1. (tall(susan) <~> ~curious(susan)) => (kind(susan) & generous(susan)) [input p0]
6. (tall(mary) & ~tall(mary)) <=> ? [X0] : (~patient(X0) | ~curious(X0)) [input p5]
7. ! [X0] : ((~patient(X0) & ~old(X0)) <=> (~rich(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((strong(X0) <~> ~curious(X0)) => (~old(X0) & ~kind(X0))) [input p7]
9. ! [X0] : ((strong(X0) & ~happy(X0)) <=> (~wise(X0) | ~generous(X0))) [input p8]
24. ~wise(susan) [input hypothesis]
27. (kind(susan) & generous(susan)) | (tall(susan) <=> ~curious(susan)) [ennf transformation 1]
31. ! [X0] : ((~old(X0) & ~kind(X0)) | (strong(X0) <=> ~curious(X0))) [ennf transformation 8]
36. (kind(susan) & generous(susan)) | ((tall(susan) | curious(susan)) & (~curious(susan) | ~tall(susan))) [nnf transformation 27]
40. ((tall(mary) & ~tall(mary)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | (~tall(mary) | tall(mary))) [nnf transformation 6]
41. ((tall(mary) & ~tall(mary)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | ~tall(mary) | tall(mary)) [flattening 40]
42. ((tall(mary) & ~tall(mary)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X1] : (~patient(X1) | ~curious(X1)) | ~tall(mary) | tall(mary)) [rectify 41]
43. ? [X1] : (~patient(X1) | ~curious(X1)) => (~patient(sK0) | ~curious(sK0)) [choice axiom]
44. ((tall(mary) & ~tall(mary)) | ! [X0] : (patient(X0) & curious(X0))) & ((~patient(sK0) | ~curious(sK0)) | ~tall(mary) | tall(mary)) [skolemisation 42,43]
45. ! [X0] : (((~patient(X0) & ~old(X0)) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | (patient(X0) | old(X0)))) [nnf transformation 7]
46. ! [X0] : (((~patient(X0) & ~old(X0)) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | patient(X0) | old(X0))) [flattening 45]
47. ! [X0] : ((~old(X0) & ~kind(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) [nnf transformation 31]
48. ! [X0] : (((strong(X0) & ~happy(X0)) | (wise(X0) & generous(X0))) & ((~wise(X0) | ~generous(X0)) | (~strong(X0) | happy(X0)))) [nnf transformation 9]
49. ! [X0] : (((strong(X0) & ~happy(X0)) | (wise(X0) & generous(X0))) & (~wise(X0) | ~generous(X0) | ~strong(X0) | happy(X0))) [flattening 48]
73. kind(susan) | ~curious(susan) | ~tall(susan) [cnf transformation 36]
89. ~tall(mary) | curious(X0) [cnf transformation 44]
90. ~tall(mary) | patient(X0) [cnf transformation 44]
91. tall(mary) | curious(X0) [cnf transformation 44]
92. tall(mary) | patient(X0) [cnf transformation 44]
96. ~patient(X0) | tall(X0) [cnf transformation 46]
98. ~strong(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 47]
106. strong(X0) | wise(X0) [cnf transformation 49]
139. ~wise(susan) [cnf transformation 24]
141. 1 <=> curious(susan) [avatar definition]
142. ~curious(susan) <- (~1) [avatar component clause 141]
145. 2 <=> tall(susan) [avatar definition]
146. ~tall(susan) <- (~2) [avatar component clause 145]
149. 3 <=> kind(susan) [avatar definition]
151. kind(susan) <- (3) [avatar component clause 149]
153. ~2 | ~1 | 3 [avatar split clause 73,149,141,145]
169. 7 <=> ! [X0] : patient(X0) [avatar definition]
170. patient(X0) <- (7) [avatar component clause 169]
172. 8 <=> tall(mary) [avatar definition]
175. 7 | 8 [avatar split clause 92,172,169]
177. 9 <=> ! [X0] : curious(X0) [avatar definition]
178. curious(X0) <- (9) [avatar component clause 177]
179. 9 | 8 [avatar split clause 91,172,177]
180. 7 | ~8 [avatar split clause 90,172,169]
181. 9 | ~8 [avatar split clause 89,172,177]
267. tall(X0) <- (7) [resolution 96,170]
270. $false <- (~2, 7) [resolution 267,146]
271. 2 | ~7 [avatar contradiction clause 270]
272. $false <- (~1, 9) [subsumption resolution 142,178]
273. 1 | ~9 [avatar contradiction clause 272]
304. ~curious(X0) | ~kind(X0) | wise(X0) [resolution 98,106]
306. ~kind(X0) | wise(X0) <- (9) [subsumption resolution 304,178]
308. wise(susan) <- (3, 9) [resolution 306,151]
309. $false <- (3, 9) [subsumption resolution 308,139]
310. ~3 | ~9 [avatar contradiction clause 309]
311. $false [avatar sat refutation 153,175,179,180,181,271,273,310]
% SZS output end Proof for 149881368216285818253979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not humble is creative or happy.
Everyone who is either not curious or not strong is curious or happy and vice versa.
If someone is both tall and not curious then lucy is both rich and curious and vice versa.
Everyone who is not calm or brave is both not quiet and generous and vice versa.
Everyone who is not strong or rich is creative.
If someone is not calm then someone is not humble.
Everyone who is creative is both not tall and old.
Everyone who is either not kind or not humble is both rich and not funny and vice versa.
Everyone who is either not curious or quiet is either funny or strong.
Everyone who is not patient or not happy is either not calm or not happy.
Everyone who is strong is not old.
If someone is either creative or not happy then lucy is not humble and vice versa.
If john is either strong or calm then fred is both calm and not rich and vice versa.
If fred is either calm or patient then someone is not rich or not strong.
If fred is not curious or not calm then someone is generous or not old.
If lucy is not curious or not humble then fred is not creative.
Susan is not creative or not humble.
Someone is either not creative or not funny.
Fred is both old and patient.
John is not calm.
Susan is brave.
Susan is not humble.
John is happy or patient. | Fred is not happy. | entailment | (![X]:((curious(X)<~>~humble(X))=>(creative(X)|happy(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(curious(X)|happy(X))))&
((?[X]:((tall(X)&~curious(X))))<=>((rich(lucy)&curious(lucy))))&
(![X]:((~calm(X)|brave(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:(creative(X)=>(~tall(X)&old(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(funny(X)<~>strong(X))))&
(![X]:((~patient(X)|~happy(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((creative(X)<~>~happy(X))))<=>(~humble(lucy)))&
(((strong(john)<~>calm(john)))<=>((calm(fred)&~rich(fred))))&
(((calm(fred)<~>patient(fred)))=>(?[X]:((~rich(X)|~strong(X)))))&
(((~curious(fred)|~calm(fred)))=>(?[X]:((generous(X)|~old(X)))))&
(((~curious(lucy)|~humble(lucy)))=>(~creative(fred)))&
((~creative(susan)|~humble(susan)))&
(?[X]:((~creative(X)<~>~funny(X))))&
((old(fred)&patient(fred)))&
(~calm(john))&
(brave(susan))&
(~humble(susan))&
((happy(john)|patient(john))) | ~happy(fred) | [
"p4",
"p10",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 975435185918911525549359
% SZS output start Proof for 975435185918911525549359
5. ! [X0] : ((rich(X0) | ~strong(X0)) => creative(X0)) [input p4]
11. ! [X0] : (strong(X0) => ~old(X0)) [input p10]
12. ? [X0] : (creative(X0) <~> ~happy(X0)) <=> ~humble(lucy) [input p11]
16. (~humble(lucy) | ~curious(lucy)) => ~creative(fred) [input p15]
19. patient(fred) & old(fred) [input p18]
24. happy(fred) [input hypothesis]
28. ! [X0] : (creative(X0) | (~rich(X0) & strong(X0))) [ennf transformation 5]
33. ! [X0] : (~old(X0) | ~strong(X0)) [ennf transformation 11]
36. ~creative(fred) | (humble(lucy) & curious(lucy)) [ennf transformation 16]
54. (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | humble(lucy)) & (~humble(lucy) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) [nnf transformation 12]
55. (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((creative(X1) | happy(X1)) & (~happy(X1) | ~creative(X1)))) [rectify 54]
56. ? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) => ((happy(sK2) | ~creative(sK2)) & (~happy(sK2) | creative(sK2))) [choice axiom]
57. (((happy(sK2) | ~creative(sK2)) & (~happy(sK2) | creative(sK2))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((creative(X1) | happy(X1)) & (~happy(X1) | ~creative(X1)))) [skolemisation 55,56]
85. strong(X0) | creative(X0) [cnf transformation 28]
104. ~old(X0) | ~strong(X0) [cnf transformation 33]
105. ~humble(lucy) | ~happy(X1) | ~creative(X1) [cnf transformation 57]
120. ~creative(fred) | humble(lucy) [cnf transformation 36]
124. old(fred) [cnf transformation 19]
130. happy(fred) [cnf transformation 24]
169. 8 <=> humble(lucy) [avatar definition]
187. 12 <=> ! [X1] : (~happy(X1) | ~creative(X1)) [avatar definition]
188. ~happy(X1) | ~creative(X1) <- (12) [avatar component clause 187]
189. 12 | ~8 [avatar split clause 105,169,187]
241. 23 <=> creative(fred) [avatar definition]
242. creative(fred) <- (23) [avatar component clause 241]
244. 8 | ~23 [avatar split clause 120,241,169]
283. ~strong(fred) [resolution 104,124]
285. creative(fred) [resolution 283,85]
288. 23 [avatar split clause 285,241]
302. ~creative(fred) <- (12) [resolution 188,130]
305. $false <- (12, 23) [subsumption resolution 302,242]
306. ~12 | ~23 [avatar contradiction clause 305]
309. $false [avatar sat refutation 189,244,288,306]
% SZS output end Proof for 975435185918911525549359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or old is funny and vice versa.
If lucy is wise then paul is rich and vice versa.
If john is not funny or not wise then fred is both brave and strong.
If lucy is rich or happy then someone is either kind or calm.
Everyone who is not strong or not patient is both strong and calm.
If fred is either tall or happy then someone is either not strong or not calm and vice versa.
Everyone who is humble or not wise is both not generous and funny.
If paul is not quiet or not kind then someone is either tall or wise and vice versa.
Everyone who is either not rich or not generous is both not generous and not kind.
Everyone who is either strong or kind is both not strong and not kind and vice versa.
If john is both not quiet and not rich then someone is tall and vice versa.
If paul is not rich then someone is not patient.
Everyone who is patient is not patient or not quiet.
Everyone who is either not generous or quiet is not curious or not tall and vice versa.
If alice is either not funny or happy then someone is both not kind and old.
Everyone who is either not old or not strong is either humble or not funny and vice versa.
Paul is both not brave and kind.
Susan is not creative or curious.
Someone is not creative or kind.
Alice is either not curious or not kind.
Lucy is not calm.
Someone is both not humble and not calm.
Someone is both not curious and not happy. | John is not quiet. | entailment | (![X]:((~patient(X)<~>old(X))<=>funny(X)))&
((wise(lucy))<=>(rich(paul)))&
(((~funny(john)|~wise(john)))=>((brave(fred)&strong(fred))))&
(((rich(lucy)|happy(lucy)))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((~strong(X)|~patient(X))=>(strong(X)&calm(X))))&
(((tall(fred)<~>happy(fred)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((humble(X)|~wise(X))=>(~generous(X)&funny(X))))&
(((~quiet(paul)|~kind(paul)))<=>(?[X]:((tall(X)<~>wise(X)))))&
(![X]:((~rich(X)<~>~generous(X))=>(~generous(X)&~kind(X))))&
(![X]:((strong(X)<~>kind(X))<=>(~strong(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))<=>(?[X]:(tall(X))))&
((~rich(paul))=>(?[X]:(~patient(X))))&
(![X]:(patient(X)=>(~patient(X)|~quiet(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~curious(X)|~tall(X))))&
(((~funny(alice)<~>happy(alice)))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(humble(X)<~>~funny(X))))&
((~brave(paul)&kind(paul)))&
((~creative(susan)|curious(susan)))&
(?[X]:((~creative(X)|kind(X))))&
((~curious(alice)<~>~kind(alice)))&
(~calm(lucy))&
(?[X]:((~humble(X)&~calm(X))))&
(?[X]:((~curious(X)&~happy(X)))) | ~quiet(john) | [
"p0",
"p4",
"p6",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 629524482512736249401972
% SZS output start Proof for 629524482512736249401972
1. ! [X0] : ((~patient(X0) <~> old(X0)) <=> funny(X0)) [input p0]
5. ! [X0] : ((~patient(X0) | ~strong(X0)) => (calm(X0) & strong(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | humble(X0)) => (funny(X0) & ~generous(X0))) [input p6]
11. (~rich(john) & ~quiet(john)) <=> ? [X0] : tall(X0) [input p10]
13. ! [X0] : (patient(X0) => (~quiet(X0) | ~patient(X0))) [input p12]
14. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> (~tall(X0) | ~curious(X0))) [input p13]
16. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (humble(X0) <~> ~funny(X0))) [input p15]
24. quiet(john) [input hypothesis]
29. ! [X0] : ((calm(X0) & strong(X0)) | (patient(X0) & strong(X0))) [ennf transformation 5]
30. ! [X0] : ((funny(X0) & ~generous(X0)) | (wise(X0) & ~humble(X0))) [ennf transformation 7]
33. ! [X0] : ((~quiet(X0) | ~patient(X0)) | ~patient(X0)) [ennf transformation 13]
34. ! [X0] : (~quiet(X0) | ~patient(X0) | ~patient(X0)) [flattening 33]
36. ! [X0] : ((((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ~funny(X0)) & (funny(X0) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))))) [nnf transformation 1]
53. ((~rich(john) & ~quiet(john)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (rich(john) | quiet(john))) [nnf transformation 11]
54. ((~rich(john) & ~quiet(john)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | rich(john) | quiet(john)) [flattening 53]
55. ((~rich(john) & ~quiet(john)) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | rich(john) | quiet(john)) [rectify 54]
56. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
57. ((~rich(john) & ~quiet(john)) | ! [X0] : ~tall(X0)) & (tall(sK3) | rich(john) | quiet(john)) [skolemisation 55,56]
60. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 14]
61. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [flattening 60]
65. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 16]
71. funny(X0) | old(X0) | patient(X0) [cnf transformation 36]
74. ~funny(X0) | patient(X0) | ~old(X0) [cnf transformation 36]
85. strong(X0) | strong(X0) [cnf transformation 29]
97. ~generous(X0) | ~humble(X0) [cnf transformation 30]
99. ~humble(X0) | funny(X0) [cnf transformation 30]
118. ~quiet(john) | ~tall(X0) [cnf transformation 57]
121. ~quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 34]
127. ~quiet(X0) | generous(X0) | tall(X0) [cnf transformation 61]
132. ~funny(X0) | humble(X0) | ~strong(X0) | old(X0) [cnf transformation 65]
137. ~strong(X0) | ~old(X0) | humble(X0) | funny(X0) [cnf transformation 65]
149. quiet(john) [cnf transformation 24]
150. ~quiet(X0) | ~patient(X0) [duplicate literal removal 121]
155. strong(X0) [duplicate literal removal 85]
176. 5 <=> funny(john) [avatar definition]
177. ~funny(john) <- (~5) [avatar component clause 176]
178. funny(john) <- (5) [avatar component clause 176]
259. 21 <=> ! [X0] : ~tall(X0) [avatar definition]
260. ~tall(X0) <- (21) [avatar component clause 259]
267. 23 <=> quiet(john) [avatar definition]
268. quiet(john) <- (23) [avatar component clause 267]
270. 21 | ~23 [avatar split clause 118,267,259]
299. ~old(X0) | humble(X0) | funny(X0) [subsumption resolution 137,155]
300. ~old(X0) | funny(X0) [subsumption resolution 299,99]
303. ~funny(X0) | humble(X0) | old(X0) [subsumption resolution 132,155]
305. 23 [avatar split clause 149,267]
326. ~patient(john) <- (23) [resolution 150,268]
342. patient(john) | ~old(john) <- (5) [resolution 74,178]
346. ~old(john) <- (5, 23) [subsumption resolution 342,326]
356. 32 <=> generous(john) [avatar definition]
358. generous(john) <- (32) [avatar component clause 356]
360. generous(john) | tall(john) <- (23) [resolution 127,268]
361. generous(john) <- (21, 23) [subsumption resolution 360,260]
362. 32 | ~21 | ~23 [avatar split clause 361,267,259,356]
368. ~humble(john) <- (32) [resolution 358,97]
373. humble(john) | old(john) <- (5) [resolution 303,178]
377. old(john) <- (5, 32) [subsumption resolution 373,368]
378. $false <- (5, 23, 32) [subsumption resolution 377,346]
379. ~5 | ~23 | ~32 [avatar contradiction clause 378]
380. old(john) | patient(john) <- (~5) [resolution 177,71]
381. old(john) <- (~5, 23) [subsumption resolution 380,326]
383. funny(john) <- (~5, 23) [resolution 381,300]
384. $false <- (~5, 23) [subsumption resolution 383,177]
385. 5 | ~23 [avatar contradiction clause 384]
386. $false [avatar sat refutation 270,305,362,379,385]
% SZS output end Proof for 629524482512736249401972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.045 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is creative or not humble.
Everyone who is humble is both creative and happy.
Everyone who is both not calm and generous is either old or not creative.
Everyone who is not old is both kind and not strong and vice versa.
Everyone who is not kind is not brave or not tall and vice versa.
Everyone who is both humble and not wise is either not calm or strong.
If fred is wise then fred is either generous or not patient.
If john is not old then someone is either curious or not wise.
If susan is either not curious or not tall then alice is not old or not curious.
If mary is both not generous and curious then mary is tall or not generous.
Everyone who is both not wise and old is either not calm or happy.
If someone is either strong or happy then lucy is either not humble or strong and vice versa.
Everyone who is not kind is both not curious and not rich and vice versa.
If someone is not brave then susan is either not kind or patient and vice versa.
Everyone who is not quiet or brave is both funny and not funny and vice versa.
If someone is both wise and old then john is both brave and patient.
Mary is not happy or not humble.
Susan is not strong or brave.
John is either old or rich.
Paul is either patient or strong.
Paul is tall or not humble.
John is not funny.
Someone is not patient. | Mary is old. | entailment | (![X]:(~brave(X)=>(creative(X)|~humble(X))))&
(![X]:(humble(X)=>(creative(X)&happy(X))))&
(![X]:((~calm(X)&generous(X))=>(old(X)<~>~creative(X))))&
(![X]:(~old(X)<=>(kind(X)&~strong(X))))&
(![X]:(~kind(X)<=>(~brave(X)|~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(~calm(X)<~>strong(X))))&
((wise(fred))=>((generous(fred)<~>~patient(fred))))&
((~old(john))=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~curious(susan)<~>~tall(susan)))=>((~old(alice)|~curious(alice))))&
(((~generous(mary)&curious(mary)))=>((tall(mary)|~generous(mary))))&
(![X]:((~wise(X)&old(X))=>(~calm(X)<~>happy(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>((~humble(lucy)<~>strong(lucy))))&
(![X]:(~kind(X)<=>(~curious(X)&~rich(X))))&
((?[X]:(~brave(X)))<=>((~kind(susan)<~>patient(susan))))&
(![X]:((~quiet(X)|brave(X))<=>(funny(X)&~funny(X))))&
((?[X]:((wise(X)&old(X))))=>((brave(john)&patient(john))))&
((~happy(mary)|~humble(mary)))&
((~strong(susan)|brave(susan)))&
((old(john)<~>rich(john)))&
((patient(paul)<~>strong(paul)))&
((tall(paul)|~humble(paul)))&
(~funny(john))&
(?[X]:(~patient(X))) | old(mary) | [
"p3",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3885224767312744499709278
% SZS output start Proof for 3885224767312744499709278
4. ! [X0] : (~old(X0) <=> (~strong(X0) & kind(X0))) [input p3]
5. ! [X0] : (~kind(X0) <=> (~tall(X0) | ~brave(X0))) [input p4]
15. ! [X0] : ((brave(X0) | ~quiet(X0)) <=> (~funny(X0) & funny(X0))) [input p14]
24. ~old(mary) [input hypothesis]
42. ! [X0] : ((~old(X0) | (strong(X0) | ~kind(X0))) & ((~strong(X0) & kind(X0)) | old(X0))) [nnf transformation 4]
43. ! [X0] : ((~old(X0) | strong(X0) | ~kind(X0)) & ((~strong(X0) & kind(X0)) | old(X0))) [flattening 42]
44. ! [X0] : ((~kind(X0) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | kind(X0))) [nnf transformation 5]
45. ! [X0] : ((~kind(X0) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | kind(X0))) [flattening 44]
63. ! [X0] : (((brave(X0) | ~quiet(X0)) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | (~brave(X0) & quiet(X0)))) [nnf transformation 15]
64. ! [X0] : ((brave(X0) | ~quiet(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | (~brave(X0) & quiet(X0)))) [flattening 63]
74. kind(X0) | old(X0) [cnf transformation 43]
78. ~kind(X0) | brave(X0) [cnf transformation 45]
107. funny(X0) | ~brave(X0) [cnf transformation 64]
109. ~funny(X0) | ~brave(X0) [cnf transformation 64]
122. ~old(mary) [cnf transformation 24]
218. ~brave(X0) [subsumption resolution 107,109]
259. brave(X0) | old(X0) [resolution 78,74]
260. old(X0) [subsumption resolution 259,218]
262. $false [resolution 260,122]
% SZS output end Proof for 3885224767312744499709278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not funny and not patient then someone is either tall or humble and vice versa.
Everyone who is not strong or not happy is either quiet or not happy.
Everyone who is both quiet and kind is both humble and not tall.
If john is either patient or not happy then someone is not brave.
If someone is not brave or patient then mary is either kind or not strong and vice versa.
If lucy is calm then someone is not happy.
If paul is either kind or not curious then susan is kind and vice versa.
If john is not old then someone is not funny.
If someone is not rich then someone is both tall and patient.
Everyone who is not old or not wise is kind.
If someone is old then someone is both rich and strong and vice versa.
Everyone who is either not tall or not wise is strong.
Everyone who is curious or quiet is tall and vice versa.
If fred is either not strong or not tall then someone is either humble or strong.
Everyone who is wise is either not funny or not curious.
Everyone who is either not humble or not generous is wise and vice versa.
Fred is both quiet and happy.
Someone is not strong.
Someone is both generous and old.
Someone is either happy or not quiet.
Someone is quiet.
Paul is either not old or funny.
John is either quiet or not tall.
Lucy is either funny or not humble. | Susan is kind. | neutral | (((~funny(fred)&~patient(fred)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:((~strong(X)|~happy(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((quiet(X)&kind(X))=>(humble(X)&~tall(X))))&
(((patient(john)<~>~happy(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)|patient(X))))<=>((kind(mary)<~>~strong(mary))))&
((calm(lucy))=>(?[X]:(~happy(X))))&
(((kind(paul)<~>~curious(paul)))<=>(kind(susan)))&
((~old(john))=>(?[X]:(~funny(X))))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)&patient(X)))))&
(![X]:((~old(X)|~wise(X))=>kind(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>strong(X)))&
(![X]:((curious(X)|quiet(X))<=>tall(X)))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((humble(X)<~>strong(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>wise(X)))&
((quiet(fred)&happy(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((generous(X)&old(X))))&
(?[X]:((happy(X)<~>~quiet(X))))&
(?[X]:(quiet(X)))&
((~old(paul)<~>funny(paul)))&
((quiet(john)<~>~tall(john)))&
((funny(lucy)<~>~humble(lucy))) | kind(susan) | [] | null | 0 |
Everyone who is either not creative or brave is both creative and not brave.
If fred is both humble and not patient then lucy is not funny or strong.
If john is not creative or not funny then lucy is both not tall and not brave and vice versa.
Everyone who is tall or generous is wise.
Everyone who is both rich and curious is either rich or happy.
Everyone who is not generous or not old is not wise and vice versa.
If susan is both not strong and not patient then someone is wise.
Everyone who is calm is either tall or kind and vice versa.
Everyone who is both not wise and not funny is either not calm or tall.
Everyone who is either patient or brave is funny and vice versa.
Everyone who is both not wise and strong is either rich or curious and vice versa.
If someone is not old or happy then alice is kind or curious.
If someone is both not wise and happy then someone is both rich and humble.
Everyone who is not patient is either not happy or rich and vice versa.
Everyone who is kind or old is either not tall or curious and vice versa.
Everyone who is brave is either not happy or not curious and vice versa.
Mary is both not kind and old.
Someone is not happy.
Alice is wise.
Alice is either not creative or not quiet.
Fred is not old.
Someone is not quiet or curious.
Lucy is strong.
Fred is strong or old. | Fred is not patient. | neutral | (![X]:((~creative(X)<~>brave(X))=>(creative(X)&~brave(X))))&
(((humble(fred)&~patient(fred)))=>((~funny(lucy)|strong(lucy))))&
(((~creative(john)|~funny(john)))<=>((~tall(lucy)&~brave(lucy))))&
(![X]:((tall(X)|generous(X))=>wise(X)))&
(![X]:((rich(X)&curious(X))=>(rich(X)<~>happy(X))))&
(![X]:((~generous(X)|~old(X))<=>~wise(X)))&
(((~strong(susan)&~patient(susan)))=>(?[X]:(wise(X))))&
(![X]:(calm(X)<=>(tall(X)<~>kind(X))))&
(![X]:((~wise(X)&~funny(X))=>(~calm(X)<~>tall(X))))&
(![X]:((patient(X)<~>brave(X))<=>funny(X)))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)<~>curious(X))))&
((?[X]:((~old(X)|happy(X))))=>((kind(alice)|curious(alice))))&
((?[X]:((~wise(X)&happy(X))))=>(?[X]:((rich(X)&humble(X)))))&
(![X]:(~patient(X)<=>(~happy(X)<~>rich(X))))&
(![X]:((kind(X)|old(X))<=>(~tall(X)<~>curious(X))))&
(![X]:(brave(X)<=>(~happy(X)<~>~curious(X))))&
((~kind(mary)&old(mary)))&
(?[X]:(~happy(X)))&
(wise(alice))&
((~creative(alice)<~>~quiet(alice)))&
(~old(fred))&
(?[X]:((~quiet(X)|curious(X))))&
(strong(lucy))&
((strong(fred)|old(fred))) | ~patient(fred) | [] | null | 0 |
If someone is funny or calm then paul is wise or quiet and vice versa.
Everyone who is both not tall and humble is quiet or not brave.
If someone is either old or kind then someone is either not patient or rich.
If susan is either not strong or not happy then someone is not brave or not patient and vice versa.
If mary is both happy and funny then someone is both not kind and creative and vice versa.
Everyone who is either calm or old is both not patient and patient and vice versa.
Everyone who is not wise is patient.
If alice is either patient or rich then someone is not curious and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not creative and curious is either not tall or not funny and vice versa.
If someone is rich then someone is both not kind and patient.
Everyone who is not old is both quiet and not wise.
Everyone who is both generous and not quiet is not patient and vice versa.
Everyone who is either tall or not creative is funny or not patient and vice versa.
If someone is either generous or tall then fred is not patient.
If someone is either not patient or curious then someone is both not curious and not calm and vice versa.
Mary is both strong and old.
Lucy is both not quiet and rich.
Susan is either humble or not wise.
Lucy is happy.
Someone is patient or wise.
Someone is creative.
Someone is not kind or strong.
John is brave. | Lucy is not old. | contradiction | ((?[X]:((funny(X)|calm(X))))<=>((wise(paul)|quiet(paul))))&
(![X]:((~tall(X)&humble(X))=>(quiet(X)|~brave(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(((~strong(susan)<~>~happy(susan)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((calm(X)<~>old(X))<=>(~patient(X)&patient(X))))&
(![X]:(~wise(X)=>patient(X)))&
(((patient(alice)<~>rich(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~creative(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:(~old(X)=>(quiet(X)&~wise(X))))&
(![X]:((generous(X)&~quiet(X))<=>~patient(X)))&
(![X]:((tall(X)<~>~creative(X))<=>(funny(X)|~patient(X))))&
((?[X]:((generous(X)<~>tall(X))))=>(~patient(fred)))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((~curious(X)&~calm(X)))))&
((strong(mary)&old(mary)))&
((~quiet(lucy)&rich(lucy)))&
((humble(susan)<~>~wise(susan)))&
(happy(lucy))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|strong(X))))&
(brave(john)) | ~old(lucy) | [
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7592064038226938586729402
% SZS output start Proof for 7592064038226938586729402
12. ! [X0] : (~old(X0) => (~wise(X0) & quiet(X0))) [input p11]
18. rich(lucy) & ~quiet(lucy) [input p17]
25. ~old(lucy) [input hypothesis]
36. ! [X0] : ((~wise(X0) & quiet(X0)) | old(X0)) [ennf transformation 12]
123. old(X0) | quiet(X0) [cnf transformation 36]
144. ~quiet(lucy) [cnf transformation 18]
153. ~old(lucy) [cnf transformation 25]
353. quiet(lucy) [resolution 123,153]
354. $false [subsumption resolution 353,144]
% SZS output end Proof for 7592064038226938586729402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then susan is not funny.
If mary is patient then someone is not calm and vice versa.
If john is either not happy or rich then someone is old or not strong and vice versa.
Everyone who is not quiet or not happy is both not funny and rich and vice versa.
Everyone who is either not quiet or calm is both kind and not brave and vice versa.
Everyone who is either old or not strong is both patient and not happy and vice versa.
Everyone who is both not curious and rich is not strong.
Everyone who is both not calm and not quiet is both calm and not creative.
Everyone who is both not calm and curious is not funny or not quiet and vice versa.
If someone is not creative or strong then fred is quiet or humble.
If mary is either humble or happy then someone is not happy or humble and vice versa.
Everyone who is either quiet or tall is either not tall or brave and vice versa.
Everyone who is not curious or not calm is both not quiet and old and vice versa.
Everyone who is quiet or not rich is both quiet and not wise.
If someone is calm or brave then someone is both not brave and humble.
Everyone who is either creative or not tall is both not rich and funny.
Lucy is creative.
Susan is either generous or not quiet.
Susan is not rich or old.
Mary is not kind or not tall.
Fred is both not rich and generous.
Mary is not rich.
Susan is humble or not humble. | Susan is not brave. | entailment | ((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&old(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
((?[X]:((calm(X)|brave(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((creative(X)<~>~tall(X))=>(~rich(X)&funny(X))))&
(creative(lucy))&
((generous(susan)<~>~quiet(susan)))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary)))&
((~rich(fred)&generous(fred)))&
(~rich(mary))&
((humble(susan)|~humble(susan))) | ~brave(susan) | [
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1987369337369216161898114
% SZS output start Proof for 1987369337369216161898114
8. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p7]
9. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p8]
12. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~tall(X0) <~> brave(X0))) [input p11]
24. brave(susan) [input hypothesis]
30. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 8]
31. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 30]
51. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 51]
57. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 12]
92. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 31]
96. ~calm(X0) | quiet(X0) [cnf transformation 52]
109. ~brave(X0) | tall(X0) | tall(X0) | ~quiet(X0) [cnf transformation 57]
114. ~tall(X0) | ~quiet(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 57]
139. brave(susan) [cnf transformation 24]
141. ~brave(X0) | tall(X0) | ~quiet(X0) [duplicate literal removal 109]
143. ~tall(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 114]
144. calm(X0) | quiet(X0) [duplicate literal removal 92]
194. quiet(X0) [subsumption resolution 96,144]
224. ~tall(X0) | ~brave(X0) [subsumption resolution 143,194]
225. ~brave(X0) | tall(X0) [subsumption resolution 141,194]
226. ~brave(X0) [subsumption resolution 225,224]
257. $false [subsumption resolution 139,226]
% SZS output end Proof for 1987369337369216161898114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then lucy is creative or strong and vice versa. Everyone who is generous or not strong is either curious or not wise and vice versa. Everyone who is not humble is either curious or not patient and vice versa. If someone is calm then john is not strong. If mary is both not wise and not tall then fred is either not funny or not rich. Everyone who is either not patient or calm is both rich and not happy and vice versa. Everyone who is generous or not patient is both humble and brave. If someone is kind then fred is both not brave and not calm and vice versa. If susan is creative then john is both not strong and patient and vice versa. Everyone who is both not happy and tall is both not tall and not creative. Everyone who is either not creative or happy is not rich or not tall. If someone is both quiet and not tall then fred is wise or creative. If alice is either not funny or not happy then paul is not funny or strong. If susan is creative or generous then someone is both not wise and brave and vice versa. Everyone who is either tall or not tall is either tall or generous and vice versa. Everyone who is not tall is either not old or humble and vice versa. Someone is both kind and happy. Someone is happy. Someone is brave. Someone is happy or not strong. Mary is not calm. Someone is either humble or patient. Mary is old or not tall. Susan is both not rich and not humble. | Susan is not patient. | contradiction | ((?[X]:(tall(X)))<=>((creative(lucy)|strong(lucy))))&
(![X]:((generous(X)|~strong(X))<=>(curious(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:(calm(X)))=>(~strong(john)))&
(((~wise(mary)&~tall(mary)))=>((~funny(fred)<~>~rich(fred))))&
(![X]:((~patient(X)<~>calm(X))<=>(rich(X)&~happy(X))))&
(![X]:((generous(X)|~patient(X))=>(humble(X)&brave(X))))&
((?[X]:(kind(X)))<=>((~brave(fred)&~calm(fred))))&
((creative(susan))<=>((~strong(john)&patient(john))))&
(![X]:((~happy(X)&tall(X))=>(~tall(X)&~creative(X))))&
(![X]:((~creative(X)<~>happy(X))=>(~rich(X)|~tall(X))))&
((?[X]:((quiet(X)&~tall(X))))=>((wise(fred)|creative(fred))))&
(((~funny(alice)<~>~happy(alice)))=>((~funny(paul)|strong(paul))))&
(((creative(susan)|generous(susan)))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((tall(X)<~>~tall(X))<=>(tall(X)<~>generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>humble(X))))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:(happy(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)|~strong(X))))&
(~calm(mary))&
(?[X]:((humble(X)<~>patient(X))))&
((old(mary)|~tall(mary)))&
((~rich(susan)&~humble(susan))) | ~patient(susan) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5734895336627173321744110
% SZS output start Proof for 5734895336627173321744110
7. ! [X0] : ((~patient(X0) | generous(X0)) => (brave(X0) & humble(X0))) [input p6]
24. ~humble(susan) & ~rich(susan) [input p23]
25. ~patient(susan) [input hypothesis]
30. ! [X0] : ((brave(X0) & humble(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 7]
98. patient(X0) | humble(X0) [cnf transformation 30]
140. ~humble(susan) [cnf transformation 24]
141. ~patient(susan) [cnf transformation 25]
286. humble(susan) [resolution 98,141]
288. $false [subsumption resolution 286,140]
% SZS output end Proof for 5734895336627173321744110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or generous then susan is both rich and not calm. If alice is either tall or creative then john is either kind or not brave and vice versa. Everyone who is both old and patient is creative or humble and vice versa. If susan is both strong and not happy then someone is both not strong and not brave. If someone is old then someone is either tall or not creative. If someone is not creative then paul is both not curious and generous. Everyone who is either old or calm is both not curious and funny and vice versa. Everyone who is both not funny and humble is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. If someone is both not old and not strong then susan is tall and vice versa. If alice is not humble or not tall then mary is either not kind or not humble. Everyone who is either patient or not strong is happy and vice versa. Everyone who is either not tall or not curious is brave and vice versa. John is both not tall and not strong. Susan is either not generous or not tall. Someone is not tall. Alice is either not tall or not wise. Lucy is not calm. | Susan is not curious. | contradiction | ((?[X]:((~funny(X)|generous(X))))=>((rich(susan)&~calm(susan))))&
(((tall(alice)<~>creative(alice)))<=>((kind(john)<~>~brave(john))))&
(![X]:((old(X)&patient(X))<=>(creative(X)|humble(X))))&
(((strong(susan)&~happy(susan)))=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:(old(X)))=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:(~creative(X)))=>((~curious(paul)&generous(paul))))&
(![X]:((old(X)<~>calm(X))<=>(~curious(X)&funny(X))))&
(![X]:((~funny(X)&humble(X))<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
(((~humble(alice)|~tall(alice)))=>((~kind(mary)<~>~humble(mary))))&
(![X]:((patient(X)<~>~strong(X))<=>happy(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>brave(X)))&
((~tall(john)&~strong(john)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(~tall(X)))&
((~tall(alice)<~>~wise(alice)))&
(~calm(lucy)) | ~curious(susan) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4146460785280562569687487
% SZS output start Proof for 4146460785280562569687487
1. ? [X0] : (generous(X0) | ~funny(X0)) => (~calm(susan) & rich(susan)) [input p0]
3. ! [X0] : ((patient(X0) & old(X0)) <=> (humble(X0) | creative(X0))) [input p2]
6. ? [X0] : ~creative(X0) => (generous(paul) & ~curious(paul)) [input p5]
7. ! [X0] : ((old(X0) <~> calm(X0)) <=> (funny(X0) & ~curious(X0))) [input p6]
8. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (wise(X0) | ~curious(X0))) [input p7]
11. ? [X0] : (~strong(X0) & ~old(X0)) <=> tall(susan) [input p10]
16. ~generous(susan) <~> ~tall(susan) [input p15]
20. ~curious(susan) [input hypothesis]
24. (~calm(susan) & rich(susan)) | ! [X0] : (~generous(X0) & funny(X0)) [ennf transformation 1]
28. (generous(paul) & ~curious(paul)) | ! [X0] : creative(X0) [ennf transformation 6]
33. ! [X0] : (((patient(X0) & old(X0)) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | (~patient(X0) | ~old(X0)))) [nnf transformation 3]
34. ! [X0] : (((patient(X0) & old(X0)) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | ~patient(X0) | ~old(X0))) [flattening 33]
41. ! [X0] : ((((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0))))) [nnf transformation 7]
42. ! [X0] : ((((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0))))) [flattening 41]
43. ! [X0] : (((humble(X0) & ~funny(X0)) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 8]
44. ! [X0] : (((humble(X0) & ~funny(X0)) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | ~humble(X0) | funny(X0))) [flattening 43]
50. (? [X0] : (~strong(X0) & ~old(X0)) | ~tall(susan)) & (tall(susan) | ! [X0] : (strong(X0) | old(X0))) [nnf transformation 11]
51. (? [X0] : (~strong(X0) & ~old(X0)) | ~tall(susan)) & (tall(susan) | ! [X1] : (strong(X1) | old(X1))) [rectify 50]
52. ? [X0] : (~strong(X0) & ~old(X0)) => (~strong(sK3) & ~old(sK3)) [choice axiom]
53. ((~strong(sK3) & ~old(sK3)) | ~tall(susan)) & (tall(susan) | ! [X1] : (strong(X1) | old(X1))) [skolemisation 51,52]
57. (tall(susan) | generous(susan)) & (~tall(susan) | ~generous(susan)) [nnf transformation 16]
64. ~calm(susan) | ~generous(X0) [cnf transformation 24]
74. ~creative(X0) | old(X0) [cnf transformation 34]
75. ~humble(X0) | old(X0) [cnf transformation 34]
83. generous(paul) | creative(X0) [cnf transformation 28]
86. ~old(X0) | calm(X0) | funny(X0) [cnf transformation 42]
91. ~funny(X0) | curious(X0) [cnf transformation 44]
93. curious(X0) | humble(X0) [cnf transformation 44]
101. ~old(sK3) | ~tall(susan) [cnf transformation 53]
116. tall(susan) | generous(susan) [cnf transformation 57]
121. ~curious(susan) [cnf transformation 20]
123. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
124. ~generous(X0) <- (1) [avatar component clause 123]
126. 2 <=> calm(susan) [avatar definition]
128. ~calm(susan) <- (~2) [avatar component clause 126]
129. 1 | ~2 [avatar split clause 64,126,123]
196. 16 <=> ! [X0] : creative(X0) [avatar definition]
197. creative(X0) <- (16) [avatar component clause 196]
199. 17 <=> generous(paul) [avatar definition]
201. generous(paul) <- (17) [avatar component clause 199]
202. 16 | 17 [avatar split clause 83,199,196]
235. 25 <=> tall(susan) [avatar definition]
244. 27 <=> old(sK3) [avatar definition]
246. ~old(sK3) <- (~27) [avatar component clause 244]
247. ~25 | ~27 [avatar split clause 101,244,235]
269. 32 <=> generous(susan) [avatar definition]
271. generous(susan) <- (32) [avatar component clause 269]
272. 32 | 25 [avatar split clause 116,235,269]
284. old(X0) <- (16) [resolution 74,197]
287. $false <- (16, ~27) [resolution 284,246]
288. ~16 | 27 [avatar contradiction clause 287]
294. humble(susan) [resolution 93,121]
298. old(susan) [resolution 294,75]
321. calm(susan) | funny(susan) [resolution 298,86]
322. funny(susan) <- (~2) [subsumption resolution 321,128]
424. curious(susan) <- (~2) [resolution 322,91]
425. $false <- (~2) [subsumption resolution 424,121]
426. 2 [avatar contradiction clause 425]
432. $false <- (1, 17) [resolution 124,201]
433. ~1 | ~17 [avatar contradiction clause 432]
434. $false <- (1, 32) [subsumption resolution 271,124]
435. ~1 | ~32 [avatar contradiction clause 434]
436. $false [avatar sat refutation 129,202,247,272,288,426,433,435]
% SZS output end Proof for 4146460785280562569687487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not calm is patient.
Everyone who is not brave is either not old or rich.
If someone is strong or not patient then alice is not wise.
Everyone who is rich or not rich is wise and vice versa.
Everyone who is kind is humble.
If someone is rich or not rich then lucy is not old.
Everyone who is both not brave and not kind is rich.
If susan is not brave then someone is curious.
Everyone who is either not wise or not curious is either curious or not quiet.
Everyone who is not rich is either quiet or tall and vice versa.
Everyone who is both quiet and not old is not tall.
Everyone who is both tall and not curious is tall or humble and vice versa.
Everyone who is both wise and happy is both not happy and not old.
Everyone who is calm or not generous is not calm.
If someone is either funny or happy then someone is not humble or tall.
Alice is either calm or creative.
Someone is either not rich or not strong.
John is either funny or brave.
Paul is wise or strong.
Mary is either old or creative.
Someone is either old or not kind.
Someone is either not happy or creative.
Mary is both rich and not calm. | John is not wise. | contradiction | (![X]:((~patient(X)<~>~calm(X))=>patient(X)))&
(![X]:(~brave(X)=>(~old(X)<~>rich(X))))&
((?[X]:((strong(X)|~patient(X))))=>(~wise(alice)))&
(![X]:((rich(X)|~rich(X))<=>wise(X)))&
(![X]:(kind(X)=>humble(X)))&
((?[X]:((rich(X)|~rich(X))))=>(~old(lucy)))&
(![X]:((~brave(X)&~kind(X))=>rich(X)))&
((~brave(susan))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)<~>~curious(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(~rich(X)<=>(quiet(X)<~>tall(X))))&
(![X]:((quiet(X)&~old(X))=>~tall(X)))&
(![X]:((tall(X)&~curious(X))<=>(tall(X)|humble(X))))&
(![X]:((wise(X)&happy(X))=>(~happy(X)&~old(X))))&
(![X]:((calm(X)|~generous(X))=>~calm(X)))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((~humble(X)|tall(X)))))&
((calm(alice)<~>creative(alice)))&
(?[X]:((~rich(X)<~>~strong(X))))&
((funny(john)<~>brave(john)))&
((wise(paul)|strong(paul)))&
((old(mary)<~>creative(mary)))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
((rich(mary)&~calm(mary))) | ~wise(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1726582852381279199671992
% SZS output start Proof for 1726582852381279199671992
4. ! [X0] : ((~rich(X0) | rich(X0)) <=> wise(X0)) [input p3]
24. ~wise(john) [input hypothesis]
44. ! [X0] : (((~rich(X0) | rich(X0)) | ~wise(X0)) & (wise(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 4]
45. ! [X0] : ((~rich(X0) | rich(X0) | ~wise(X0)) & (wise(X0) | (rich(X0) & ~rich(X0)))) [flattening 44]
74. wise(X0) | ~rich(X0) [cnf transformation 45]
75. wise(X0) | rich(X0) [cnf transformation 45]
116. ~wise(john) [cnf transformation 24]
134. wise(X0) [subsumption resolution 74,75]
201. $false [subsumption resolution 116,134]
% SZS output end Proof for 1726582852381279199671992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or calm then fred is both not curious and not old.
Everyone who is either not patient or not strong is either not generous or not curious.
If someone is not humble then someone is both not humble and not patient.
If john is both old and not tall then someone is not strong or generous.
If susan is tall or not tall then fred is tall or funny and vice versa.
If paul is either patient or rich then someone is not funny or not old and vice versa.
If someone is both humble and old then mary is both quiet and not brave.
Everyone who is either rich or quiet is both not quiet and patient and vice versa.
If john is not creative or not strong then alice is either not brave or brave and vice versa.
Everyone who is either not humble or not quiet is both not brave and kind and vice versa.
If paul is quiet then someone is either kind or not kind.
Everyone who is either kind or patient is both not rich and not funny.
Everyone who is either kind or quiet is not happy or not strong and vice versa.
Everyone who is either not curious or not creative is either wise or generous.
Everyone who is not curious is both not kind and not calm.
If someone is either not strong or rich then john is not happy or not rich.
Lucy is both not quiet and not brave.
Someone is either brave or quiet.
Someone is both not creative and kind.
Mary is not tall or rich.
Someone is not funny.
Someone is calm or not old.
Someone is funny or kind.
Fred is not wise or not old. | Paul is quiet. | entailment | (((patient(susan)|calm(susan)))=>((~curious(fred)&~old(fred))))&
(![X]:((~patient(X)<~>~strong(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~humble(X)&~patient(X)))))&
(((old(john)&~tall(john)))=>(?[X]:((~strong(X)|generous(X)))))&
(((tall(susan)|~tall(susan)))<=>((tall(fred)|funny(fred))))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)|~old(X)))))&
((?[X]:((humble(X)&old(X))))=>((quiet(mary)&~brave(mary))))&
(![X]:((rich(X)<~>quiet(X))<=>(~quiet(X)&patient(X))))&
(((~creative(john)|~strong(john)))<=>((~brave(alice)<~>brave(alice))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((quiet(paul))=>(?[X]:((kind(X)<~>~kind(X)))))&
(![X]:((kind(X)<~>patient(X))=>(~rich(X)&~funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(~happy(X)|~strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(wise(X)<~>generous(X))))&
(![X]:(~curious(X)=>(~kind(X)&~calm(X))))&
((?[X]:((~strong(X)<~>rich(X))))=>((~happy(john)|~rich(john))))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((~creative(X)&kind(X))))&
((~tall(mary)|rich(mary)))&
(?[X]:(~funny(X)))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:((funny(X)|kind(X))))&
((~wise(fred)|~old(fred))) | quiet(paul) | [
"p5",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6855620450127845388938732
% SZS output start Proof for 6855620450127845388938732
6. (patient(paul) <~> rich(paul)) <=> ? [X0] : (~old(X0) | ~funny(X0)) [input p5]
8. ! [X0] : ((rich(X0) <~> quiet(X0)) <=> (patient(X0) & ~quiet(X0))) [input p7]
21. ? [X0] : ~funny(X0) [input p20]
25. ~quiet(paul) [input hypothesis]
47. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & (? [X0] : (~old(X0) | ~funny(X0)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [nnf transformation 6]
48. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & (? [X1] : (~old(X1) | ~funny(X1)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [rectify 47]
49. ? [X1] : (~old(X1) | ~funny(X1)) => (~old(sK2) | ~funny(sK2)) [choice axiom]
50. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & ((~old(sK2) | ~funny(sK2)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [skolemisation 48,49]
51. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [flattening 51]
70. ? [X0] : ~funny(X0) => ~funny(sK6) [choice axiom]
71. ~funny(sK6) [skolemisation 21,70]
93. rich(paul) | patient(paul) | funny(X0) [cnf transformation 50]
95. ~rich(paul) | ~patient(paul) | funny(X0) [cnf transformation 50]
101. ~rich(X0) | quiet(X0) | patient(X0) [cnf transformation 52]
103. quiet(X0) | rich(X0) | ~patient(X0) | quiet(X0) [cnf transformation 52]
144. ~funny(sK6) [cnf transformation 71]
148. ~quiet(paul) [cnf transformation 25]
152. ~patient(X0) | rich(X0) | quiet(X0) [duplicate literal removal 103]
221. 16 <=> patient(paul) [avatar definition]
222. patient(paul) <- (16) [avatar component clause 221]
223. ~patient(paul) <- (~16) [avatar component clause 221]
225. 17 <=> rich(paul) [avatar definition]
226. rich(paul) <- (17) [avatar component clause 225]
227. ~rich(paul) <- (~17) [avatar component clause 225]
230. 18 <=> ! [X0] : funny(X0) [avatar definition]
231. funny(X0) <- (18) [avatar component clause 230]
232. 18 | ~16 | ~17 [avatar split clause 95,225,221,230]
234. 18 | 16 | 17 [avatar split clause 93,225,221,230]
408. rich(paul) | quiet(paul) <- (16) [resolution 152,222]
409. quiet(paul) <- (16, ~17) [subsumption resolution 408,227]
410. $false <- (16, ~17) [subsumption resolution 409,148]
411. ~16 | 17 [avatar contradiction clause 410]
413. quiet(paul) | patient(paul) <- (17) [resolution 226,101]
414. patient(paul) <- (17) [subsumption resolution 413,148]
415. $false <- (~16, 17) [subsumption resolution 414,223]
416. 16 | ~17 [avatar contradiction clause 415]
423. $false <- (18) [resolution 231,144]
427. ~18 [avatar contradiction clause 423]
428. $false [avatar sat refutation 232,234,411,416,427]
% SZS output end Proof for 6855620450127845388938732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or funny is both not brave and not strong and vice versa.
If someone is not kind or not quiet then someone is generous or humble and vice versa.
If lucy is not rich then someone is both not tall and wise.
If someone is both calm and not old then alice is not tall.
Everyone who is not funny is both not generous and brave and vice versa.
Everyone who is patient is both not tall and not wise and vice versa.
Everyone who is both not curious and not patient is tall or not wise and vice versa.
Everyone who is both not creative and not tall is tall or curious.
Everyone who is either happy or creative is either not calm or kind.
If john is either not funny or funny then someone is rich or happy and vice versa.
If mary is both happy and strong then someone is both not curious and not patient.
If mary is not old then someone is either rich or not tall.
Everyone who is both tall and rich is either generous or not brave and vice versa.
Everyone who is both strong and generous is not kind and vice versa.
Everyone who is either kind or not strong is patient and vice versa.
Everyone who is not quiet is not happy or patient and vice versa.
John is not quiet.
Fred is not quiet or not creative.
Lucy is either not generous or not strong.
Someone is either not old or strong.
Lucy is quiet or not patient.
Fred is both not calm and not funny.
Someone is both not creative and not patient. | John is not funny. | neutral | (![X]:((~old(X)<~>funny(X))<=>(~brave(X)&~strong(X))))&
((?[X]:((~kind(X)|~quiet(X))))<=>(?[X]:((generous(X)|humble(X)))))&
((~rich(lucy))=>(?[X]:((~tall(X)&wise(X)))))&
((?[X]:((calm(X)&~old(X))))=>(~tall(alice)))&
(![X]:(~funny(X)<=>(~generous(X)&brave(X))))&
(![X]:(patient(X)<=>(~tall(X)&~wise(X))))&
(![X]:((~curious(X)&~patient(X))<=>(tall(X)|~wise(X))))&
(![X]:((~creative(X)&~tall(X))=>(tall(X)|curious(X))))&
(![X]:((happy(X)<~>creative(X))=>(~calm(X)<~>kind(X))))&
(((~funny(john)<~>funny(john)))<=>(?[X]:((rich(X)|happy(X)))))&
(((happy(mary)&strong(mary)))=>(?[X]:((~curious(X)&~patient(X)))))&
((~old(mary))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:((tall(X)&rich(X))<=>(generous(X)<~>~brave(X))))&
(![X]:((strong(X)&generous(X))<=>~kind(X)))&
(![X]:((kind(X)<~>~strong(X))<=>patient(X)))&
(![X]:(~quiet(X)<=>(~happy(X)|patient(X))))&
(~quiet(john))&
((~quiet(fred)|~creative(fred)))&
((~generous(lucy)<~>~strong(lucy)))&
(?[X]:((~old(X)<~>strong(X))))&
((quiet(lucy)|~patient(lucy)))&
((~calm(fred)&~funny(fred)))&
(?[X]:((~creative(X)&~patient(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is funny is either not brave or rich. Everyone who is either not calm or generous is both patient and not curious and vice versa. Everyone who is both not rich and brave is not calm or generous. Everyone who is either not patient or wise is either happy or not creative. If fred is not curious then someone is both brave and not old and vice versa. Everyone who is strong or not funny is both not humble and not quiet and vice versa. Everyone who is both not kind and tall is both calm and not wise. Everyone who is not patient or not funny is both patient and not rich and vice versa. Everyone who is brave is creative or patient and vice versa. If fred is tall then someone is not funny or not calm and vice versa. Everyone who is either not strong or happy is not tall or calm. If fred is old or not brave then john is not strong or curious and vice versa. If susan is either not kind or tall then someone is not brave or patient. Everyone who is not quiet or humble is strong. If alice is both not humble and old then someone is not funny and vice versa. Everyone who is both not patient and strong is both generous and not strong. Someone is not rich or old. Fred is either old or generous. Someone is both not happy and not curious. Someone is rich. Susan is kind. Susan is generous or not curious. | John is not patient. | contradiction | (![X]:(funny(X)=>(~brave(X)<~>rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(((old(fred)|~brave(fred)))<=>((~strong(john)|curious(john))))&
(((~kind(susan)<~>tall(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(((~humble(alice)&old(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&strong(X))=>(generous(X)&~strong(X))))&
(?[X]:((~rich(X)|old(X))))&
((old(fred)<~>generous(fred)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(rich(X)))&
(kind(susan))&
((generous(susan)|~curious(susan))) | ~patient(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2382119763994099672866902
% SZS output start Proof for 2382119763994099672866902
8. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~rich(X0) & patient(X0))) [input p7]
23. ~patient(john) [input hypothesis]
46. ! [X0] : (((~funny(X0) | ~patient(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [nnf transformation 8]
47. ! [X0] : ((~funny(X0) | ~patient(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [flattening 46]
95. patient(X0) | patient(X0) [cnf transformation 47]
129. ~patient(john) [cnf transformation 23]
131. patient(X0) [duplicate literal removal 95]
226. $false [subsumption resolution 129,131]
% SZS output end Proof for 2382119763994099672866902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is tall or creative then someone is either not generous or not curious and vice versa. If john is both not patient and strong then paul is not funny or humble. Everyone who is funny or quiet is either not humble or not rich. If lucy is either funny or not humble then alice is either humble or not kind. If mary is both wise and not humble then someone is not rich and vice versa. If someone is not old then paul is strong. Everyone who is either rich or generous is either not tall or wise. If someone is not rich then someone is not creative or happy and vice versa. If susan is not wise then paul is rich and vice versa. If alice is both calm and not wise then someone is not wise or not humble. Everyone who is patient or creative is brave. Everyone who is not curious is both tall and wise. Everyone who is either not quiet or tall is not quiet or not old. Everyone who is both creative and wise is either creative or not generous and vice versa. Everyone who is generous or curious is both humble and not tall. Everyone who is not tall or humble is funny or humble and vice versa. Paul is not funny or not strong. Someone is not patient. John is rich or creative. John is quiet or old. Someone is either not rich or not calm. | Lucy is generous. | neutral | (((tall(alice)|creative(alice)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~patient(john)&strong(john)))=>((~funny(paul)|humble(paul))))&
(![X]:((funny(X)|quiet(X))=>(~humble(X)<~>~rich(X))))&
(((funny(lucy)<~>~humble(lucy)))=>((humble(alice)<~>~kind(alice))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~old(X)))=>(strong(paul)))&
(![X]:((rich(X)<~>generous(X))=>(~tall(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)|happy(X)))))&
((~wise(susan))<=>(rich(paul)))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((patient(X)|creative(X))=>brave(X)))&
(![X]:(~curious(X)=>(tall(X)&wise(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~tall(X)|humble(X))<=>(funny(X)|humble(X))))&
((~funny(paul)|~strong(paul)))&
(?[X]:(~patient(X)))&
((rich(john)|creative(john)))&
((quiet(john)|old(john)))&
(?[X]:((~rich(X)<~>~calm(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is tall is either not happy or curious and vice versa. Everyone who is either kind or old is both not curious and not calm and vice versa. If someone is not brave then someone is both calm and not brave and vice versa. If susan is both not happy and curious then susan is kind or humble and vice versa. Everyone who is both not generous and strong is calm. If someone is not kind then someone is both not generous and brave. Everyone who is wise or funny is both kind and not generous and vice versa. Everyone who is quiet is both not patient and not old. If fred is both not brave and not strong then alice is not patient and vice versa. If mary is either brave or patient then john is either old or creative and vice versa. If john is calm or kind then alice is both old and not happy. If someone is not brave then someone is funny and vice versa. If lucy is both happy and not wise then john is patient or not happy. Everyone who is not calm or old is either not quiet or happy and vice versa. If mary is either kind or curious then someone is strong. Everyone who is either patient or brave is both not wise and wise and vice versa. Someone is both not curious and old. Alice is not calm or happy. Someone is either not quiet or not generous. John is both rich and not kind. Someone is either wise or not wise. Fred is quiet. Susan is both not calm and quiet. Fred is calm. | Fred is wise. | contradiction | (![X]:(tall(X)<=>(~happy(X)<~>curious(X))))&
(![X]:((kind(X)<~>old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~happy(susan)&curious(susan)))<=>((kind(susan)|humble(susan))))&
(![X]:((~generous(X)&strong(X))=>calm(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((wise(X)|funny(X))<=>(kind(X)&~generous(X))))&
(![X]:(quiet(X)=>(~patient(X)&~old(X))))&
(((~brave(fred)&~strong(fred)))<=>(~patient(alice)))&
(((brave(mary)<~>patient(mary)))<=>((old(john)<~>creative(john))))&
(((calm(john)|kind(john)))=>((old(alice)&~happy(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:(funny(X))))&
(((happy(lucy)&~wise(lucy)))=>((patient(john)|~happy(john))))&
(![X]:((~calm(X)|old(X))<=>(~quiet(X)<~>happy(X))))&
(((kind(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(![X]:((patient(X)<~>brave(X))<=>(~wise(X)&wise(X))))&
(?[X]:((~curious(X)&old(X))))&
((~calm(alice)|happy(alice)))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((rich(john)&~kind(john)))&
(?[X]:((wise(X)<~>~wise(X))))&
(quiet(fred))&
((~calm(susan)&quiet(susan)))&
(calm(fred)) | wise(fred) | [
"p1",
"p6",
"p7",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 841297056950266448836960
% SZS output start Proof for 841297056950266448836960
2. ! [X0] : ((kind(X0) <~> old(X0)) <=> (~calm(X0) & ~curious(X0))) [input p1]
7. ! [X0] : ((funny(X0) | wise(X0)) <=> (~generous(X0) & kind(X0))) [input p6]
8. ! [X0] : (quiet(X0) => (~old(X0) & ~patient(X0))) [input p7]
22. quiet(fred) [input p21]
24. calm(fred) [input p23]
25. wise(fred) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~patient(X0)) | ~quiet(X0)) [ennf transformation 8]
38. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [flattening 38]
50. ! [X0] : (((funny(X0) | wise(X0)) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | (~funny(X0) & ~wise(X0)))) [nnf transformation 7]
51. ! [X0] : ((funny(X0) | wise(X0) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | (~funny(X0) & ~wise(X0)))) [flattening 50]
77. ~calm(X0) | old(X0) | ~kind(X0) [cnf transformation 39]
92. ~wise(X0) | kind(X0) [cnf transformation 51]
98. ~quiet(X0) | ~old(X0) [cnf transformation 33]
139. quiet(fred) [cnf transformation 22]
142. calm(fred) [cnf transformation 24]
143. wise(fred) [cnf transformation 25]
328. kind(fred) [resolution 92,143]
332. ~old(fred) [resolution 98,139]
356. old(fred) | ~kind(fred) [resolution 77,142]
358. ~kind(fred) [subsumption resolution 356,332]
359. $false [subsumption resolution 358,328]
% SZS output end Proof for 841297056950266448836960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is either not calm or patient.
If someone is funny then someone is strong or kind and vice versa.
Everyone who is either quiet or calm is either rich or not generous.
If someone is not tall then john is brave.
If someone is wise then someone is funny.
Everyone who is both curious and not tall is rich and vice versa.
If someone is not old or generous then someone is either patient or old and vice versa.
If fred is both not brave and happy then someone is brave and vice versa.
Everyone who is both not wise and strong is wise or rich and vice versa.
Everyone who is either curious or not rich is not happy.
Everyone who is not kind is both rich and not brave.
Everyone who is either not rich or not creative is creative.
Everyone who is generous or calm is not quiet.
If someone is curious or not generous then someone is either kind or not patient.
Everyone who is brave is curious.
Everyone who is not brave or generous is either not patient or not rich and vice versa.
Someone is creative or curious.
Lucy is tall.
Someone is both not funny and not tall.
Someone is both not strong and brave.
Paul is both not kind and old.
Someone is not kind or not brave.
Someone is either brave or not quiet. | Fred is not rich. | entailment | (![X]:(creative(X)=>(~calm(X)<~>patient(X))))&
((?[X]:(funny(X)))<=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((quiet(X)<~>calm(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(~tall(X)))=>(brave(john)))&
((?[X]:(wise(X)))=>(?[X]:(funny(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
(((~brave(fred)&happy(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~wise(X)&strong(X))<=>(wise(X)|rich(X))))&
(![X]:((curious(X)<~>~rich(X))=>~happy(X)))&
(![X]:(~kind(X)=>(rich(X)&~brave(X))))&
(![X]:((~rich(X)<~>~creative(X))=>creative(X)))&
(![X]:((generous(X)|calm(X))=>~quiet(X)))&
((?[X]:((curious(X)|~generous(X))))=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((~brave(X)|generous(X))<=>(~patient(X)<~>~rich(X))))&
(?[X]:((creative(X)|curious(X))))&
(tall(lucy))&
(?[X]:((~funny(X)&~tall(X))))&
(?[X]:((~strong(X)&brave(X))))&
((~kind(paul)&old(paul)))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:((brave(X)<~>~quiet(X)))) | ~rich(fred) | [
"p3",
"p5",
"p7",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2539335999198854863419879
% SZS output start Proof for 2539335999198854863419879
4. ? [X0] : ~tall(X0) => brave(john) [input p3]
6. ! [X0] : ((~tall(X0) & curious(X0)) <=> rich(X0)) [input p5]
8. (happy(fred) & ~brave(fred)) <=> ? [X0] : brave(X0) [input p7]
10. ! [X0] : ((curious(X0) <~> ~rich(X0)) => ~happy(X0)) [input p9]
19. ? [X0] : (~tall(X0) & ~funny(X0)) [input p18]
24. rich(fred) [input hypothesis]
31. brave(john) | ! [X0] : tall(X0) [ennf transformation 4]
33. ! [X0] : (~happy(X0) | (curious(X0) <=> ~rich(X0))) [ennf transformation 10]
49. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) | ~curious(X0)))) [nnf transformation 6]
50. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | tall(X0) | ~curious(X0))) [flattening 49]
56. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~happy(fred) | brave(fred))) [nnf transformation 8]
57. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~happy(fred) | brave(fred)) [flattening 56]
58. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~happy(fred) | brave(fred)) [rectify 57]
59. ? [X1] : brave(X1) => brave(sK5) [choice axiom]
60. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (brave(sK5) | ~happy(fred) | brave(fred)) [skolemisation 58,59]
63. ! [X0] : (~happy(X0) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 33]
73. ? [X0] : (~tall(X0) & ~funny(X0)) => (~tall(sK8) & ~funny(sK8)) [choice axiom]
74. ~tall(sK8) & ~funny(sK8) [skolemisation 19,73]
91. brave(john) | tall(X0) [cnf transformation 31]
94. ~rich(X0) | curious(X0) [cnf transformation 50]
104. happy(fred) | ~brave(X0) [cnf transformation 60]
110. ~happy(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 63]
132. ~tall(sK8) [cnf transformation 74]
140. rich(fred) [cnf transformation 24]
169. 7 <=> ! [X0] : tall(X0) [avatar definition]
170. tall(X0) <- (7) [avatar component clause 169]
172. 8 <=> brave(john) [avatar definition]
174. brave(john) <- (8) [avatar component clause 172]
175. 7 | 8 [avatar split clause 91,172,169]
219. 19 <=> ! [X0] : ~brave(X0) [avatar definition]
220. ~brave(X0) <- (19) [avatar component clause 219]
222. 20 <=> happy(fred) [avatar definition]
224. happy(fred) <- (20) [avatar component clause 222]
225. 19 | 20 [avatar split clause 104,222,219]
238. ~happy(X0) | ~rich(X0) [subsumption resolution 110,94]
279. $false <- (7) [resolution 170,132]
280. ~7 [avatar contradiction clause 279]
281. $false <- (8, 19) [subsumption resolution 174,220]
282. ~8 | ~19 [avatar contradiction clause 281]
298. ~rich(fred) <- (20) [resolution 238,224]
299. $false <- (20) [subsumption resolution 298,140]
300. ~20 [avatar contradiction clause 299]
301. $false [avatar sat refutation 175,225,280,282,300]
% SZS output end Proof for 2539335999198854863419879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not tall is not quiet or not rich. Everyone who is not calm is funny and vice versa. If someone is quiet or not calm then someone is not kind and vice versa. If someone is both generous and humble then someone is both not funny and brave and vice versa. If alice is either old or not strong then someone is tall. Everyone who is not strong or not rich is both brave and not brave and vice versa. If lucy is both not kind and not creative then susan is either not humble or creative and vice versa. Everyone who is quiet or not strong is rich. If mary is either brave or not brave then someone is not curious and vice versa. Everyone who is funny or patient is both patient and not funny and vice versa. If someone is either not wise or not old then alice is either patient or generous. If john is creative or not wise then someone is curious. If mary is brave then someone is both not calm and brave and vice versa. Everyone who is either not humble or funny is not old or not rich and vice versa. If someone is funny then someone is not tall or not old. John is either not wise or not rich. Someone is both not wise and not tall. Susan is both generous and not old. Fred is not generous or not old. Someone is humble or not old. Someone is happy. John is not tall. | Susan is not old. | entailment | (![X]:((calm(X)<~>~tall(X))=>(~quiet(X)|~rich(X))))&
(![X]:(~calm(X)<=>funny(X)))&
((?[X]:((quiet(X)|~calm(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((generous(X)&humble(X))))<=>(?[X]:((~funny(X)&brave(X)))))&
(((old(alice)<~>~strong(alice)))=>(?[X]:(tall(X))))&
(![X]:((~strong(X)|~rich(X))<=>(brave(X)&~brave(X))))&
(((~kind(lucy)&~creative(lucy)))<=>((~humble(susan)<~>creative(susan))))&
(![X]:((quiet(X)|~strong(X))=>rich(X)))&
(((brave(mary)<~>~brave(mary)))<=>(?[X]:(~curious(X))))&
(![X]:((funny(X)|patient(X))<=>(patient(X)&~funny(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>((patient(alice)<~>generous(alice))))&
(((creative(john)|~wise(john)))=>(?[X]:(curious(X))))&
((brave(mary))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(~old(X)|~rich(X))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)|~old(X)))))&
((~wise(john)<~>~rich(john)))&
(?[X]:((~wise(X)&~tall(X))))&
((generous(susan)&~old(susan)))&
((~generous(fred)|~old(fred)))&
(?[X]:((humble(X)|~old(X))))&
(?[X]:(happy(X)))&
(~tall(john)) | ~old(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2514350649456338842169022
% SZS output start Proof for 2514350649456338842169022
18. ~old(susan) & generous(susan) [input p17]
23. old(susan) [input hypothesis]
133. ~old(susan) [cnf transformation 18]
137. old(susan) [cnf transformation 23]
300. $false [subsumption resolution 137,133]
% SZS output end Proof for 2514350649456338842169022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or generous is quiet.
If lucy is patient then fred is either strong or calm.
Everyone who is both not calm and not humble is both not creative and not strong.
If lucy is not rich then paul is either tall or not happy and vice versa.
If someone is funny or kind then paul is both not kind and wise and vice versa.
Everyone who is creative or generous is old or calm.
Everyone who is either not happy or rich is either not creative or rich and vice versa.
Everyone who is both not quiet and not happy is not wise.
If fred is generous or not curious then susan is creative or not generous.
If fred is old or not creative then someone is creative or not wise and vice versa.
Everyone who is funny or not creative is not funny and vice versa.
Everyone who is not humble is both not brave and kind and vice versa.
Everyone who is not funny is quiet and vice versa.
If mary is both quiet and calm then fred is creative or not quiet and vice versa.
Everyone who is either not calm or generous is both not quiet and not creative.
If someone is rich then someone is both not funny and not happy and vice versa.
Someone is not happy or not humble.
John is wise or not calm.
John is either not patient or rich.
Someone is either not happy or not brave.
Someone is funny or not kind.
Someone is both brave and not patient.
Someone is either brave or not curious.
Fred is both not tall and rich. | Paul is not humble. | contradiction | (![X]:((quiet(X)<~>generous(X))=>quiet(X)))&
((patient(lucy))=>((strong(fred)<~>calm(fred))))&
(![X]:((~calm(X)&~humble(X))=>(~creative(X)&~strong(X))))&
((~rich(lucy))<=>((tall(paul)<~>~happy(paul))))&
((?[X]:((funny(X)|kind(X))))<=>((~kind(paul)&wise(paul))))&
(![X]:((creative(X)|generous(X))=>(old(X)|calm(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&~happy(X))=>~wise(X)))&
(((generous(fred)|~curious(fred)))=>((creative(susan)|~generous(susan))))&
(((old(fred)|~creative(fred)))<=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:((funny(X)|~creative(X))<=>~funny(X)))&
(![X]:(~humble(X)<=>(~brave(X)&kind(X))))&
(![X]:(~funny(X)<=>quiet(X)))&
(((quiet(mary)&calm(mary)))<=>((creative(fred)|~quiet(fred))))&
(![X]:((~calm(X)<~>generous(X))=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~funny(X)&~happy(X)))))&
(?[X]:((~happy(X)|~humble(X))))&
((wise(john)|~calm(john)))&
((~patient(john)<~>rich(john)))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((funny(X)|~kind(X))))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((brave(X)<~>~curious(X))))&
((~tall(fred)&rich(fred))) | ~humble(paul) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1884015136354414145257311
% SZS output start Proof for 1884015136354414145257311
5. ? [X0] : (kind(X0) | funny(X0)) <=> (wise(paul) & ~kind(paul)) [input p4]
12. ! [X0] : (~humble(X0) <=> (kind(X0) & ~brave(X0))) [input p11]
25. ~humble(paul) [input hypothesis]
41. (? [X0] : (kind(X0) | funny(X0)) | (~wise(paul) | kind(paul))) & ((wise(paul) & ~kind(paul)) | ! [X0] : (~kind(X0) & ~funny(X0))) [nnf transformation 5]
42. (? [X0] : (kind(X0) | funny(X0)) | ~wise(paul) | kind(paul)) & ((wise(paul) & ~kind(paul)) | ! [X0] : (~kind(X0) & ~funny(X0))) [flattening 41]
43. (? [X0] : (kind(X0) | funny(X0)) | ~wise(paul) | kind(paul)) & ((wise(paul) & ~kind(paul)) | ! [X1] : (~kind(X1) & ~funny(X1))) [rectify 42]
44. ? [X0] : (kind(X0) | funny(X0)) => (kind(sK0) | funny(sK0)) [choice axiom]
45. ((kind(sK0) | funny(sK0)) | ~wise(paul) | kind(paul)) & ((wise(paul) & ~kind(paul)) | ! [X1] : (~kind(X1) & ~funny(X1))) [skolemisation 43,44]
54. ! [X0] : ((~humble(X0) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | humble(X0))) [nnf transformation 12]
55. ! [X0] : ((~humble(X0) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | humble(X0))) [flattening 54]
89. ~kind(paul) | ~kind(X1) [cnf transformation 45]
114. kind(X0) | humble(X0) [cnf transformation 55]
143. ~humble(paul) [cnf transformation 25]
182. 7 <=> kind(paul) [avatar definition]
183. ~kind(paul) <- (~7) [avatar component clause 182]
184. kind(paul) <- (7) [avatar component clause 182]
199. 11 <=> ! [X1] : ~kind(X1) [avatar definition]
200. ~kind(X1) <- (11) [avatar component clause 199]
206. 11 | ~7 [avatar split clause 89,182,199]
354. humble(paul) <- (~7) [resolution 114,183]
356. $false <- (~7) [subsumption resolution 354,143]
357. 7 [avatar contradiction clause 356]
358. $false <- (7, 11) [subsumption resolution 184,200]
359. ~7 | ~11 [avatar contradiction clause 358]
360. $false [avatar sat refutation 206,357,359]
% SZS output end Proof for 1884015136354414145257311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not strong.
Everyone who is either not patient or not brave is not strong or tall and vice versa.
Everyone who is old is curious and vice versa.
If lucy is not quiet then someone is curious or quiet and vice versa.
Everyone who is either curious or patient is both not happy and creative and vice versa.
If someone is either calm or funny then someone is quiet or not humble and vice versa.
If lucy is calm then paul is wise.
Everyone who is not humble or not rich is not funny or funny.
If paul is quiet then someone is both tall and not happy.
Everyone who is old is both not wise and not quiet.
Everyone who is both not humble and curious is either creative or not creative and vice versa.
If lucy is either calm or not patient then someone is not old or not strong.
Everyone who is both creative and strong is both tall and not strong and vice versa.
Everyone who is either not generous or humble is both kind and not rich.
If someone is not curious or quiet then susan is either not rich or not calm.
Everyone who is not tall or old is both creative and funny.
Paul is not rich or calm.
Fred is not brave or kind.
Someone is not humble.
Alice is both not quiet and patient.
Someone is not tall or wise.
Alice is rich or patient. | Fred is funny. | entailment | (![X]:(~calm(X)=>~strong(X)))&
(![X]:((~patient(X)<~>~brave(X))<=>(~strong(X)|tall(X))))&
(![X]:(old(X)<=>curious(X)))&
((~quiet(lucy))<=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~happy(X)&creative(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
((calm(lucy))=>(wise(paul)))&
(![X]:((~humble(X)|~rich(X))=>(~funny(X)|funny(X))))&
((quiet(paul))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(old(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(creative(X)<~>~creative(X))))&
(((calm(lucy)<~>~patient(lucy)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)&strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(kind(X)&~rich(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((~tall(X)|old(X))=>(creative(X)&funny(X))))&
((~rich(paul)|calm(paul)))&
((~brave(fred)|kind(fred)))&
(?[X]:(~humble(X)))&
((~quiet(alice)&patient(alice)))&
(?[X]:((~tall(X)|wise(X))))&
((rich(alice)|patient(alice))) | funny(fred) | [
"p2",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4433847270047565795516075
% SZS output start Proof for 4433847270047565795516075
3. ! [X0] : (old(X0) <=> curious(X0)) [input p2]
11. ! [X0] : ((curious(X0) & ~humble(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p10]
13. ! [X0] : ((strong(X0) & creative(X0)) <=> (~strong(X0) & tall(X0))) [input p12]
16. ! [X0] : ((old(X0) | ~tall(X0)) => (funny(X0) & creative(X0))) [input p15]
23. ~funny(fred) [input hypothesis]
25. ! [X0] : (curious(X0) => old(X0)) [unused predicate definition removal 3]
29. ! [X0] : (old(X0) | ~curious(X0)) [ennf transformation 25]
38. ! [X0] : ((funny(X0) & creative(X0)) | (~old(X0) & tall(X0))) [ennf transformation 16]
54. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~curious(X0) | humble(X0)))) [nnf transformation 11]
55. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~curious(X0) | humble(X0))) [flattening 54]
59. ! [X0] : (((strong(X0) & creative(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 13]
60. ! [X0] : (((strong(X0) & creative(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | ~strong(X0) | ~creative(X0))) [flattening 59]
74. ~curious(X0) | old(X0) [cnf transformation 29]
101. curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 55]
102. curious(X0) | creative(X0) | creative(X0) [cnf transformation 55]
106. ~strong(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 60]
108. strong(X0) | strong(X0) | ~tall(X0) [cnf transformation 60]
116. ~old(X0) | creative(X0) [cnf transformation 38]
117. funny(X0) | tall(X0) [cnf transformation 38]
125. ~funny(fred) [cnf transformation 23]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 106]
127. ~tall(X0) | strong(X0) [duplicate literal removal 108]
130. curious(X0) | ~creative(X0) [duplicate literal removal 101]
131. curious(X0) | creative(X0) [duplicate literal removal 102]
207. curious(X0) [subsumption resolution 130,131]
252. old(X0) [resolution 74,207]
255. creative(X0) [resolution 116,252]
256. tall(fred) [resolution 117,125]
260. ~strong(X0) [resolution 255,126]
261. strong(fred) [resolution 127,256]
263. $false [subsumption resolution 261,260]
% SZS output end Proof for 4433847270047565795516075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then mary is kind or old and vice versa.
Everyone who is not old is both patient and not tall.
Everyone who is not happy is both wise and not funny.
Everyone who is brave is wise or patient and vice versa.
If someone is either humble or funny then someone is patient or not brave.
If susan is brave or not rich then someone is not brave or not kind.
Everyone who is not strong or funny is not wise or happy and vice versa.
Everyone who is either not patient or not quiet is either quiet or happy and vice versa.
If susan is either not generous or not humble then someone is not wise and vice versa.
If someone is both patient and not tall then someone is not strong and vice versa.
If someone is either not tall or curious then someone is not old or strong and vice versa.
If paul is brave or generous then alice is either not curious or not humble.
Everyone who is both brave and strong is either funny or not creative and vice versa.
Everyone who is creative or not quiet is both old and not creative and vice versa.
If someone is not curious then someone is generous and vice versa.
Someone is both brave and not patient.
Lucy is either not humble or generous.
Someone is either humble or quiet.
Someone is both wise and not happy.
Someone is brave.
Lucy is either generous or not tall.
Someone is not strong or not patient. | Paul is not brave. | contradiction | ((?[X]:(~kind(X)))<=>((kind(mary)|old(mary))))&
(![X]:(~old(X)=>(patient(X)&~tall(X))))&
(![X]:(~happy(X)=>(wise(X)&~funny(X))))&
(![X]:(brave(X)<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((brave(susan)|~rich(susan)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)|funny(X))<=>(~wise(X)|happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(quiet(X)<~>happy(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((brave(paul)|generous(paul)))=>((~curious(alice)<~>~humble(alice))))&
(![X]:((brave(X)&strong(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~quiet(X))<=>(old(X)&~creative(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(generous(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~humble(lucy)<~>generous(lucy)))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:(brave(X)))&
((generous(lucy)<~>~tall(lucy)))&
(?[X]:((~strong(X)|~patient(X)))) | ~brave(paul) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7424662584332555952516988
% SZS output start Proof for 7424662584332555952516988
3. ! [X0] : (~happy(X0) => (~funny(X0) & wise(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (patient(X0) | wise(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (quiet(X0) <~> happy(X0))) [input p7]
23. ~brave(paul) [input hypothesis]
30. ! [X0] : ((~funny(X0) & wise(X0)) | happy(X0)) [ennf transformation 3]
39. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ~brave(X0))) [nnf transformation 4]
40. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~brave(X0))) [flattening 39]
49. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 8]
92. wise(X0) | happy(X0) [cnf transformation 30]
95. ~wise(X0) | brave(X0) [cnf transformation 40]
96. ~patient(X0) | brave(X0) [cnf transformation 40]
106. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 49]
111. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 49]
154. ~brave(paul) [cnf transformation 23]
158. ~happy(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 106]
160. ~happy(X0) | patient(X0) | quiet(X0) [duplicate literal removal 111]
209. ~happy(X0) | patient(X0) [subsumption resolution 158,160]
299. 32 <=> brave(paul) [avatar definition]
301. ~brave(paul) <- (~32) [avatar component clause 299]
356. ~32 [avatar split clause 154,299]
371. brave(X0) | happy(X0) [resolution 95,92]
448. happy(paul) <- (~32) [resolution 371,301]
453. patient(paul) <- (~32) [resolution 448,209]
459. 49 <=> patient(paul) [avatar definition]
461. patient(paul) <- (49) [avatar component clause 459]
463. 49 | 32 [avatar split clause 453,299,459]
533. brave(paul) <- (49) [resolution 461,96]
534. $false <- (~32, 49) [subsumption resolution 533,301]
535. 32 | ~49 [avatar contradiction clause 534]
536. $false [avatar sat refutation 356,463,535]
% SZS output end Proof for 7424662584332555952516988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or strong is not generous or generous. If someone is either wise or not humble then fred is either not rich or not strong and vice versa. Everyone who is both humble and tall is either humble or not brave. Everyone who is generous is either not creative or not patient and vice versa. If john is not tall or not generous then someone is creative. If someone is both not old and rich then alice is not old or humble and vice versa. Everyone who is both brave and not creative is not brave or not rich and vice versa. If someone is both kind and happy then john is both curious and generous and vice versa. Everyone who is not calm or curious is not humble or not curious. If someone is either old or brave then someone is not rich or wise and vice versa. If someone is both old and not calm then someone is funny or kind and vice versa. Everyone who is both not patient and not brave is not humble or not rich and vice versa. If mary is funny then someone is both not curious and not creative. If fred is not calm then susan is quiet or curious and vice versa. Everyone who is either quiet or creative is both generous and not funny and vice versa. If someone is both not rich and not strong then someone is either not calm or tall and vice versa. Someone is either not patient or not humble. Susan is calm or brave. Someone is not old. Someone is wise. Alice is kind. | Fred is strong. | contradiction | (![X]:((~rich(X)|strong(X))=>(~generous(X)|generous(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>((~rich(fred)<~>~strong(fred))))&
(![X]:((humble(X)&tall(X))=>(humble(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~creative(X)<~>~patient(X))))&
(((~tall(john)|~generous(john)))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)&rich(X))))<=>((~old(alice)|humble(alice))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((kind(X)&happy(X))))<=>((curious(john)&generous(john))))&
(![X]:((~calm(X)|curious(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)<~>brave(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~patient(X)&~brave(X))<=>(~humble(X)|~rich(X))))&
((funny(mary))=>(?[X]:((~curious(X)&~creative(X)))))&
((~calm(fred))<=>((quiet(susan)|curious(susan))))&
(![X]:((quiet(X)<~>creative(X))<=>(generous(X)&~funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((~calm(X)<~>tall(X)))))&
(?[X]:((~patient(X)<~>~humble(X))))&
((calm(susan)|brave(susan)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X)))&
(kind(alice)) | strong(fred) | [
"p1",
"p6",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 418508314312158759774597
% SZS output start Proof for 418508314312158759774597
2. ? [X0] : (wise(X0) <~> ~humble(X0)) <=> (~rich(fred) <~> ~strong(fred)) [input p1]
7. ! [X0] : ((~creative(X0) & brave(X0)) <=> (~rich(X0) | ~brave(X0))) [input p6]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~rich(X0) | ~humble(X0))) [input p11]
20. ? [X0] : wise(X0) [input p19]
22. strong(fred) [input hypothesis]
34. (? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X0] : ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) [nnf transformation 2]
35. (? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X1] : ((wise(X1) | humble(X1)) & (~humble(X1) | ~wise(X1)))) [rectify 34]
36. ? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) => ((humble(sK0) | ~wise(sK0)) & (~humble(sK0) | wise(sK0))) [choice axiom]
37. (((humble(sK0) | ~wise(sK0)) & (~humble(sK0) | wise(sK0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X1] : ((wise(X1) | humble(X1)) & (~humble(X1) | ~wise(X1)))) [skolemisation 35,36]
47. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | (creative(X0) | ~brave(X0)))) [nnf transformation 7]
48. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | creative(X0) | ~brave(X0))) [flattening 47]
64. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
65. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | brave(X0) | patient(X0))) [flattening 64]
82. ? [X0] : wise(X0) => wise(sK13) [choice axiom]
83. wise(sK13) [skolemisation 20,82]
86. ~strong(fred) | ~rich(fred) | ~humble(X1) | ~wise(X1) [cnf transformation 37]
108. brave(X0) | brave(X0) [cnf transformation 48]
132. ~brave(X0) | humble(X0) [cnf transformation 65]
133. ~brave(X0) | rich(X0) [cnf transformation 65]
155. wise(sK13) [cnf transformation 83]
157. strong(fred) [cnf transformation 22]
160. brave(X0) [duplicate literal removal 108]
163. 1 <=> strong(fred) [avatar definition]
167. 2 <=> rich(fred) [avatar definition]
169. ~rich(fred) <- (~2) [avatar component clause 167]
187. 6 <=> ! [X1] : (~humble(X1) | ~wise(X1)) [avatar definition]
188. ~humble(X1) | ~wise(X1) <- (6) [avatar component clause 187]
191. 6 | ~2 | ~1 [avatar split clause 86,163,167,187]
252. 19 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (19) [avatar component clause 252]
261. 21 <=> ! [X1] : rich(X1) [avatar definition]
262. rich(X1) <- (21) [avatar component clause 261]
307. rich(X0) [subsumption resolution 133,160]
308. 21 [avatar split clause 307,261]
309. humble(X0) [subsumption resolution 132,160]
371. 1 [avatar split clause 157,163]
376. $false <- (~2, 21) [subsumption resolution 169,262]
377. 2 | ~21 [avatar contradiction clause 376]
378. ~wise(X1) <- (6) [subsumption resolution 188,309]
379. 19 | ~6 [avatar split clause 378,187,252]
380. $false <- (19) [resolution 253,155]
381. ~19 [avatar contradiction clause 380]
382. $false [avatar sat refutation 191,308,371,377,379,381]
% SZS output end Proof for 418508314312158759774597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
If someone is both not curious and old then mary is tall.
Everyone who is not happy is not patient and vice versa.
Everyone who is calm or curious is both calm and kind.
Everyone who is both not creative and not humble is old or tall.
Everyone who is both not kind and brave is creative or tall.
Alice is either funny or not humble.
Someone is not curious or strong.
Mary is not humble or kind.
Someone is generous.
Someone is both not wise and not generous.
John is old or quiet. | Mary is happy. | entailment | (![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
((?[X]:((~curious(X)&old(X))))=>(tall(mary)))&
(![X]:(~happy(X)<=>~patient(X)))&
(![X]:((calm(X)|curious(X))=>(calm(X)&kind(X))))&
(![X]:((~creative(X)&~humble(X))=>(old(X)|tall(X))))&
(![X]:((~kind(X)&brave(X))=>(creative(X)|tall(X))))&
((funny(alice)<~>~humble(alice)))&
(?[X]:((~curious(X)|strong(X))))&
((~humble(mary)|kind(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&~generous(X))))&
((old(john)|quiet(john))) | happy(mary) | [
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7142408626817580502791375
% SZS output start Proof for 7142408626817580502791375
6. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p5]
7. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p6]
9. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p8]
10. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X0] : (patient(X0) & ~kind(X0)) [input p9]
13. ! [X0] : (~happy(X0) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((curious(X0) | calm(X0)) => (kind(X0) & calm(X0))) [input p13]
23. ~happy(mary) [input hypothesis]
24. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X1] : (patient(X1) & ~kind(X1)) [rectify 10]
29. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 7]
35. ! [X0] : ((kind(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 14]
51. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 6]
52. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 9]
53. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 52]
54. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X1] : (patient(X1) & ~kind(X1)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) [nnf transformation 24]
55. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X2] : (patient(X2) & ~kind(X2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [rectify 54]
56. ? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) => ((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) [choice axiom]
57. ? [X2] : (patient(X2) & ~kind(X2)) => (patient(sK2) & ~kind(sK2)) [choice axiom]
58. (((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) | ! [X1] : (~patient(X1) | kind(X1))) & ((patient(sK2) & ~kind(sK2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [skolemisation 55,57,56]
59. ! [X0] : ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0))) [nnf transformation 13]
90. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 51]
93. creative(X0) | calm(X0) [cnf transformation 29]
99. ~creative(X0) | kind(X0) [cnf transformation 53]
100. ~creative(X0) | ~funny(X0) [cnf transformation 53]
101. ~kind(sK2) | creative(X3) | ~funny(X3) [cnf transformation 58]
102. ~kind(sK2) | funny(X3) | ~creative(X3) [cnf transformation 58]
109. ~patient(X0) | happy(X0) [cnf transformation 59]
113. ~calm(X0) | kind(X0) [cnf transformation 35]
124. ~happy(mary) [cnf transformation 23]
152. 6 <=> ! [X1] : kind(X1) [avatar definition]
153. kind(X1) <- (6) [avatar component clause 152]
171. 10 <=> ! [X3] : ~creative(X3) [avatar definition]
172. ~creative(X3) <- (10) [avatar component clause 171]
180. 12 <=> ! [X3] : ~funny(X3) [avatar definition]
181. ~funny(X3) <- (12) [avatar component clause 180]
183. ~kind(sK2) | ~creative(X3) [subsumption resolution 102,100]
185. 13 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~13) [avatar component clause 185]
188. 10 | ~13 [avatar split clause 183,185,171]
189. ~kind(sK2) | ~funny(X3) [subsumption resolution 101,100]
190. 12 | ~13 [avatar split clause 189,185,180]
228. kind(X0) | calm(X0) [resolution 99,93]
229. kind(X0) [subsumption resolution 228,113]
230. 6 [avatar split clause 229,152]
232. $false <- (6, ~13) [resolution 153,187]
233. ~6 | 13 [avatar contradiction clause 232]
235. calm(X0) <- (10) [resolution 172,93]
263. patient(X0) | funny(X0) <- (10) [resolution 90,235]
265. patient(X0) <- (10, 12) [subsumption resolution 263,181]
272. happy(X2) <- (10, 12) [resolution 265,109]
285. $false <- (10, 12) [resolution 272,124]
291. ~10 | ~12 [avatar contradiction clause 285]
292. $false [avatar sat refutation 188,190,230,233,291]
% SZS output end Proof for 7142408626817580502791375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is curious or wise then alice is both not old and funny and vice versa.
Everyone who is either not rich or not patient is either creative or humble.
If lucy is either curious or strong then someone is both not happy and not curious.
If someone is not happy then lucy is rich.
If susan is not happy then alice is not kind or not old and vice versa.
Everyone who is not calm or calm is not happy and vice versa.
Everyone who is not patient is not funny or not calm and vice versa.
Everyone who is not generous or not strong is funny or not wise and vice versa.
If susan is both not calm and wise then someone is not generous and vice versa.
If someone is not strong or creative then fred is either not wise or quiet.
If alice is kind or not humble then someone is both not brave and happy and vice versa.
Everyone who is patient or creative is either strong or not brave and vice versa.
If paul is both not quiet and not rich then someone is wise or not tall and vice versa.
If someone is both humble and not humble then john is both not rich and calm and vice versa.
Everyone who is not patient or not curious is both not humble and not curious.
If paul is calm or old then someone is both patient and not old.
John is patient or funny.
Someone is either not humble or not strong.
Mary is not quiet or happy.
Someone is not brave or happy.
Someone is curious.
Alice is kind or old.
Someone is both not funny and not brave. | Paul is wise. | contradiction | (((curious(paul)|wise(paul)))<=>((~old(alice)&funny(alice))))&
(![X]:((~rich(X)<~>~patient(X))=>(creative(X)<~>humble(X))))&
(((curious(lucy)<~>strong(lucy)))=>(?[X]:((~happy(X)&~curious(X)))))&
((?[X]:(~happy(X)))=>(rich(lucy)))&
((~happy(susan))<=>((~kind(alice)|~old(alice))))&
(![X]:((~calm(X)|calm(X))<=>~happy(X)))&
(![X]:(~patient(X)<=>(~funny(X)|~calm(X))))&
(![X]:((~generous(X)|~strong(X))<=>(funny(X)|~wise(X))))&
(((~calm(susan)&wise(susan)))<=>(?[X]:(~generous(X))))&
((?[X]:((~strong(X)|creative(X))))=>((~wise(fred)<~>quiet(fred))))&
(((kind(alice)|~humble(alice)))<=>(?[X]:((~brave(X)&happy(X)))))&
(![X]:((patient(X)|creative(X))<=>(strong(X)<~>~brave(X))))&
(((~quiet(paul)&~rich(paul)))<=>(?[X]:((wise(X)|~tall(X)))))&
((?[X]:((humble(X)&~humble(X))))<=>((~rich(john)&calm(john))))&
(![X]:((~patient(X)|~curious(X))=>(~humble(X)&~curious(X))))&
(((calm(paul)|old(paul)))=>(?[X]:((patient(X)&~old(X)))))&
((patient(john)|funny(john)))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~quiet(mary)|happy(mary)))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:(curious(X)))&
((kind(alice)|old(alice)))&
(?[X]:((~funny(X)&~brave(X)))) | wise(paul) | [
"p0",
"p5",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7557084608064610409735838
% SZS output start Proof for 7557084608064610409735838
1. (wise(paul) | curious(paul)) <=> (funny(alice) & ~old(alice)) [input p0]
6. ! [X0] : ((calm(X0) | ~calm(X0)) <=> ~happy(X0)) [input p5]
11. (~humble(alice) | kind(alice)) <=> ? [X0] : (happy(X0) & ~brave(X0)) [input p10]
22. old(alice) | kind(alice) [input p21]
24. wise(paul) [input hypothesis]
31. ((wise(paul) | curious(paul)) | (~funny(alice) | old(alice))) & ((funny(alice) & ~old(alice)) | (~wise(paul) & ~curious(paul))) [nnf transformation 1]
32. (wise(paul) | curious(paul) | ~funny(alice) | old(alice)) & ((funny(alice) & ~old(alice)) | (~wise(paul) & ~curious(paul))) [flattening 31]
39. ! [X0] : (((calm(X0) | ~calm(X0)) | happy(X0)) & (~happy(X0) | (~calm(X0) & calm(X0)))) [nnf transformation 6]
40. ! [X0] : ((calm(X0) | ~calm(X0) | happy(X0)) & (~happy(X0) | (~calm(X0) & calm(X0)))) [flattening 39]
51. ((~humble(alice) | kind(alice)) | ! [X0] : (~happy(X0) | brave(X0))) & (? [X0] : (happy(X0) & ~brave(X0)) | (humble(alice) & ~kind(alice))) [nnf transformation 11]
52. (~humble(alice) | kind(alice) | ! [X0] : (~happy(X0) | brave(X0))) & (? [X0] : (happy(X0) & ~brave(X0)) | (humble(alice) & ~kind(alice))) [flattening 51]
53. (~humble(alice) | kind(alice) | ! [X0] : (~happy(X0) | brave(X0))) & (? [X1] : (happy(X1) & ~brave(X1)) | (humble(alice) & ~kind(alice))) [rectify 52]
54. ? [X1] : (happy(X1) & ~brave(X1)) => (happy(sK2) & ~brave(sK2)) [choice axiom]
55. (~humble(alice) | kind(alice) | ! [X0] : (~happy(X0) | brave(X0))) & ((happy(sK2) & ~brave(sK2)) | (humble(alice) & ~kind(alice))) [skolemisation 53,54]
80. ~old(alice) | ~wise(paul) [cnf transformation 32]
96. ~happy(X0) | calm(X0) [cnf transformation 40]
97. ~happy(X0) | ~calm(X0) [cnf transformation 40]
115. happy(sK2) | ~kind(alice) [cnf transformation 55]
147. old(alice) | kind(alice) [cnf transformation 22]
150. wise(paul) [cnf transformation 24]
152. 1 <=> old(alice) [avatar definition]
164. 4 <=> wise(paul) [avatar definition]
170. ~4 | ~1 [avatar split clause 80,152,164]
206. 12 <=> kind(alice) [avatar definition]
211. ~happy(X0) [subsumption resolution 96,97]
249. ~kind(alice) [subsumption resolution 115,211]
250. ~12 [avatar split clause 249,206]
330. 12 | 1 [avatar split clause 147,152,206]
331. 4 [avatar split clause 150,164]
332. $false [avatar sat refutation 170,250,330,331]
% SZS output end Proof for 7557084608064610409735838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or brave is not funny.
Everyone who is both old and not patient is humble.
Everyone who is either patient or tall is both patient and not generous.
If someone is not kind then someone is either funny or not strong and vice versa.
Everyone who is not wise is rich and vice versa.
Everyone who is both curious and not wise is not quiet and vice versa.
Everyone who is strong is either not brave or not quiet and vice versa.
Everyone who is either not creative or curious is not quiet and vice versa.
Everyone who is wise or not wise is curious and vice versa.
Everyone who is not tall is patient or not happy and vice versa.
If fred is tall then paul is either curious or generous and vice versa.
If susan is not patient or not tall then lucy is not patient or not strong.
Everyone who is either not strong or kind is happy.
If someone is brave then susan is both patient and curious.
If mary is either not curious or tall then john is both not calm and generous and vice versa.
If someone is either generous or old then lucy is either not creative or funny.
Alice is calm.
Someone is both strong and not kind.
Someone is creative.
Someone is both not patient and not funny.
Paul is brave.
Someone is either brave or not tall.
Someone is both happy and curious. | Susan is not strong. | neutral | (![X]:((~curious(X)<~>brave(X))=>~funny(X)))&
(![X]:((old(X)&~patient(X))=>humble(X)))&
(![X]:((patient(X)<~>tall(X))=>(patient(X)&~generous(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>rich(X)))&
(![X]:((curious(X)&~wise(X))<=>~quiet(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>curious(X))<=>~quiet(X)))&
(![X]:((wise(X)|~wise(X))<=>curious(X)))&
(![X]:(~tall(X)<=>(patient(X)|~happy(X))))&
((tall(fred))<=>((curious(paul)<~>generous(paul))))&
(((~patient(susan)|~tall(susan)))=>((~patient(lucy)|~strong(lucy))))&
(![X]:((~strong(X)<~>kind(X))=>happy(X)))&
((?[X]:(brave(X)))=>((patient(susan)&curious(susan))))&
(((~curious(mary)<~>tall(mary)))<=>((~calm(john)&generous(john))))&
((?[X]:((generous(X)<~>old(X))))=>((~creative(lucy)<~>funny(lucy))))&
(calm(alice))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)&~funny(X))))&
(brave(paul))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:((happy(X)&curious(X)))) | ~strong(susan) | [] | null | 0 |
If someone is both not tall and not humble then paul is funny or not tall.
If someone is both not wise and brave then alice is either rich or generous and vice versa.
Everyone who is both not generous and not tall is either quiet or not generous and vice versa.
Everyone who is wise or tall is not brave and vice versa.
Everyone who is both tall and not rich is both kind and quiet and vice versa.
Everyone who is both not happy and strong is old and vice versa.
Everyone who is either brave or not brave is not creative or calm.
Everyone who is both not happy and not old is not curious and vice versa.
If someone is both tall and not patient then someone is either old or funny and vice versa.
Everyone who is both not creative and not happy is curious and vice versa.
If alice is not happy or curious then someone is not wise and vice versa.
If alice is both creative and not generous then someone is not kind or not brave and vice versa.
Everyone who is either old or generous is both calm and not rich.
Everyone who is funny is not quiet or rich and vice versa.
If mary is both not quiet and not strong then susan is both not humble and not happy.
Everyone who is either old or generous is not funny.
Lucy is patient or not happy.
Someone is not quiet or not patient.
Lucy is either funny or not wise.
Fred is both curious and not wise.
Someone is either not generous or not funny.
Someone is funny or generous.
Someone is kind.
Someone is not wise or old. | Paul is happy. | contradiction | ((?[X]:((~tall(X)&~humble(X))))=>((funny(paul)|~tall(paul))))&
((?[X]:((~wise(X)&brave(X))))<=>((rich(alice)<~>generous(alice))))&
(![X]:((~generous(X)&~tall(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((wise(X)|tall(X))<=>~brave(X)))&
(![X]:((tall(X)&~rich(X))<=>(kind(X)&quiet(X))))&
(![X]:((~happy(X)&strong(X))<=>old(X)))&
(![X]:((brave(X)<~>~brave(X))=>(~creative(X)|calm(X))))&
(![X]:((~happy(X)&~old(X))<=>~curious(X)))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~creative(X)&~happy(X))<=>curious(X)))&
(((~happy(alice)|curious(alice)))<=>(?[X]:(~wise(X))))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:((old(X)<~>generous(X))=>(calm(X)&~rich(X))))&
(![X]:(funny(X)<=>(~quiet(X)|rich(X))))&
(((~quiet(mary)&~strong(mary)))=>((~humble(susan)&~happy(susan))))&
(![X]:((old(X)<~>generous(X))=>~funny(X)))&
((patient(lucy)|~happy(lucy)))&
(?[X]:((~quiet(X)|~patient(X))))&
((funny(lucy)<~>~wise(lucy)))&
((curious(fred)&~wise(fred)))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:(kind(X)))&
(?[X]:((~wise(X)|old(X)))) | happy(paul) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7305527072775580014839570
% SZS output start Proof for 7305527072775580014839570
8. ! [X0] : ((~old(X0) & ~happy(X0)) <=> ~curious(X0)) [input p7]
10. ! [X0] : ((~happy(X0) & ~creative(X0)) <=> curious(X0)) [input p9]
25. happy(paul) [input hypothesis]
47. ! [X0] : (((~old(X0) & ~happy(X0)) | curious(X0)) & (~curious(X0) | (old(X0) | happy(X0)))) [nnf transformation 8]
48. ! [X0] : (((~old(X0) & ~happy(X0)) | curious(X0)) & (~curious(X0) | old(X0) | happy(X0))) [flattening 47]
54. ! [X0] : (((~happy(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | (happy(X0) | creative(X0)))) [nnf transformation 10]
55. ! [X0] : (((~happy(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | happy(X0) | creative(X0))) [flattening 54]
106. ~happy(X0) | curious(X0) [cnf transformation 48]
116. ~happy(X0) | ~curious(X0) [cnf transformation 55]
145. happy(paul) [cnf transformation 25]
217. ~happy(X0) [subsumption resolution 116,106]
313. $false [subsumption resolution 145,217]
% SZS output end Proof for 7305527072775580014839570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not brave or old then alice is not funny or happy and vice versa. Everyone who is either rich or not funny is not calm. If mary is either rich or brave then lucy is either not old or not quiet. Everyone who is both not kind and happy is both not tall and curious and vice versa. If alice is both not strong and old then someone is rich or humble and vice versa. Everyone who is kind or rich is both not old and kind. Everyone who is brave or not old is brave or not rich and vice versa. If alice is not kind then lucy is creative or not calm. If someone is either not creative or strong then someone is rich and vice versa. Everyone who is not old or rich is kind or curious and vice versa. Everyone who is either not kind or not old is both rich and not quiet. Everyone who is not wise or happy is rich or funny. If susan is either rich or not patient then fred is both not kind and brave. If paul is both not rich and not kind then paul is patient and vice versa. If someone is either not funny or not humble then susan is both not tall and tall. Everyone who is strong or curious is calm or not generous. Susan is not strong or tall. John is either not strong or curious. Fred is not patient or not brave. | Fred is not happy. | entailment | (((~brave(john)|old(john)))<=>((~funny(alice)|happy(alice))))&
(![X]:((rich(X)<~>~funny(X))=>~calm(X)))&
(((rich(mary)<~>brave(mary)))=>((~old(lucy)<~>~quiet(lucy))))&
(![X]:((~kind(X)&happy(X))<=>(~tall(X)&curious(X))))&
(((~strong(alice)&old(alice)))<=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((kind(X)|rich(X))=>(~old(X)&kind(X))))&
(![X]:((brave(X)|~old(X))<=>(brave(X)|~rich(X))))&
((~kind(alice))=>((creative(lucy)|~calm(lucy))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)|rich(X))<=>(kind(X)|curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(rich(X)|funny(X))))&
(((rich(susan)<~>~patient(susan)))=>((~kind(fred)&brave(fred))))&
(((~rich(paul)&~kind(paul)))<=>(patient(paul)))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~tall(susan)&tall(susan))))&
(![X]:((strong(X)|curious(X))=>(calm(X)|~generous(X))))&
((~strong(susan)|tall(susan)))&
((~strong(john)<~>curious(john)))&
((~patient(fred)|~brave(fred))) | ~happy(fred) | [
"p4",
"p5",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4233820138123852488544477
% SZS output start Proof for 4233820138123852488544477
5. (old(alice) & ~strong(alice)) <=> ? [X0] : (humble(X0) | rich(X0)) [input p4]
6. ! [X0] : ((rich(X0) | kind(X0)) => (kind(X0) & ~old(X0))) [input p5]
11. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (~quiet(X0) & rich(X0))) [input p10]
12. ! [X0] : ((happy(X0) | ~wise(X0)) => (funny(X0) | rich(X0))) [input p11]
15. ? [X0] : (~funny(X0) <~> ~humble(X0)) => (tall(susan) & ~tall(susan)) [input p14]
20. happy(fred) [input hypothesis]
25. ! [X0] : (happy(X0) => (funny(X0) | rich(X0))) [pure predicate removal 12]
27. ! [X0] : ((kind(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 6]
28. ! [X0] : ((~quiet(X0) & rich(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 11]
29. ! [X0] : ((funny(X0) | rich(X0)) | ~happy(X0)) [ennf transformation 25]
30. ! [X0] : (funny(X0) | rich(X0) | ~happy(X0)) [flattening 29]
32. (tall(susan) & ~tall(susan)) | ! [X0] : (~funny(X0) <=> ~humble(X0)) [ennf transformation 15]
38. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | (~old(alice) | strong(alice))) [nnf transformation 5]
39. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | ~old(alice) | strong(alice)) [flattening 38]
40. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X1] : (humble(X1) | rich(X1)) | ~old(alice) | strong(alice)) [rectify 39]
41. ? [X1] : (humble(X1) | rich(X1)) => (humble(sK0) | rich(sK0)) [choice axiom]
42. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & ((humble(sK0) | rich(sK0)) | ~old(alice) | strong(alice)) [skolemisation 40,41]
52. ! [X0] : ((~quiet(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 28]
56. (tall(susan) & ~tall(susan)) | ! [X0] : ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))) [nnf transformation 32]
73. old(alice) | ~rich(X0) [cnf transformation 42]
74. old(alice) | ~humble(X0) [cnf transformation 42]
75. ~kind(X0) | ~old(X0) [cnf transformation 27]
76. ~rich(X0) | ~old(X0) [cnf transformation 27]
91. rich(X0) | ~old(X0) | kind(X0) [cnf transformation 52]
95. ~happy(X0) | rich(X0) | funny(X0) [cnf transformation 30]
104. ~tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 56]
106. tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 56]
111. happy(fred) [cnf transformation 20]
153. 9 <=> ! [X0] : ~humble(X0) [avatar definition]
154. ~humble(X0) <- (9) [avatar component clause 153]
156. 10 <=> old(alice) [avatar definition]
158. old(alice) <- (10) [avatar component clause 156]
159. 9 | 10 [avatar split clause 74,156,153]
161. 11 <=> ! [X0] : ~rich(X0) [avatar definition]
162. ~rich(X0) <- (11) [avatar component clause 161]
163. 11 | 10 [avatar split clause 73,156,161]
207. rich(X0) | ~old(X0) [subsumption resolution 91,75]
208. ~old(X0) [subsumption resolution 207,76]
246. 27 <=> ! [X0] : (~funny(X0) | humble(X0)) [avatar definition]
247. ~funny(X0) | humble(X0) <- (27) [avatar component clause 246]
249. 28 <=> tall(susan) [avatar definition]
252. 27 | 28 [avatar split clause 106,249,246]
257. 27 | ~28 [avatar split clause 104,249,246]
281. $false <- (10) [subsumption resolution 158,208]
282. ~10 [avatar contradiction clause 281]
310. rich(fred) | funny(fred) [resolution 95,111]
311. funny(fred) <- (11) [subsumption resolution 310,162]
334. humble(fred) <- (11, 27) [resolution 311,247]
335. $false <- (9, 11, 27) [subsumption resolution 334,154]
336. ~9 | ~11 | ~27 [avatar contradiction clause 335]
337. $false [avatar sat refutation 159,163,252,257,282,336]
% SZS output end Proof for 4233820138123852488544477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both humble and wise then someone is not happy or strong and vice versa.
Everyone who is curious is tall or calm.
If someone is either not wise or funny then mary is both rich and kind.
If someone is either old or happy then someone is not rich or not wise.
Everyone who is not calm is both not quiet and not patient and vice versa.
Everyone who is not patient or curious is not happy or kind and vice versa.
Everyone who is not humble is generous or brave and vice versa.
Everyone who is creative is not quiet or humble.
Everyone who is both not calm and humble is either brave or curious and vice versa.
Everyone who is both humble and patient is not quiet or not tall and vice versa.
If someone is either not kind or not old then someone is either quiet or not wise.
If someone is both humble and not strong then someone is both old and not tall and vice versa.
Everyone who is not quiet is both funny and not old.
If fred is not rich then someone is both creative and old.
Everyone who is brave is both quiet and not strong and vice versa.
If someone is not strong then someone is either not kind or not tall.
Someone is either not quiet or creative.
Susan is happy or not wise.
Someone is both not rich and not tall.
Someone is either brave or not quiet.
Someone is both not quiet and not wise.
Fred is either not quiet or not wise.
Lucy is not funny or not strong.
Fred is either strong or calm. | Alice is curious. | contradiction | (((humble(alice)&wise(alice)))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:(curious(X)=>(tall(X)|calm(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>((rich(mary)&kind(mary))))&
((?[X]:((old(X)<~>happy(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~calm(X)<=>(~quiet(X)&~patient(X))))&
(![X]:((~patient(X)|curious(X))<=>(~happy(X)|kind(X))))&
(![X]:(~humble(X)<=>(generous(X)|brave(X))))&
(![X]:(creative(X)=>(~quiet(X)|humble(X))))&
(![X]:((~calm(X)&humble(X))<=>(brave(X)<~>curious(X))))&
(![X]:((humble(X)&patient(X))<=>(~quiet(X)|~tall(X))))&
((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:((quiet(X)<~>~wise(X)))))&
((?[X]:((humble(X)&~strong(X))))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:(~quiet(X)=>(funny(X)&~old(X))))&
((~rich(fred))=>(?[X]:((creative(X)&old(X)))))&
(![X]:(brave(X)<=>(quiet(X)&~strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((happy(susan)|~wise(susan)))&
(?[X]:((~rich(X)&~tall(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:((~quiet(X)&~wise(X))))&
((~quiet(fred)<~>~wise(fred)))&
((~funny(lucy)|~strong(lucy)))&
((strong(fred)<~>calm(fred))) | curious(alice) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2661987238884879427810516
% SZS output start Proof for 2661987238884879427810516
1. (wise(alice) & humble(alice)) <=> ? [X0] : (strong(X0) | ~happy(X0)) [input p0]
5. ! [X0] : (~calm(X0) <=> (~patient(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : (~humble(X0) <=> (brave(X0) | generous(X0))) [input p6]
9. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (brave(X0) <~> curious(X0))) [input p8]
10. ! [X0] : ((patient(X0) & humble(X0)) <=> (~tall(X0) | ~quiet(X0))) [input p9]
12. ? [X0] : (~strong(X0) & humble(X0)) <=> ? [X0] : (~tall(X0) & old(X0)) [input p11]
13. ! [X0] : (~quiet(X0) => (~old(X0) & funny(X0))) [input p12]
15. ! [X0] : (brave(X0) <=> (~strong(X0) & quiet(X0))) [input p14]
19. ? [X0] : (~tall(X0) & ~rich(X0)) [input p18]
25. curious(alice) [input hypothesis]
28. ? [X0] : (~strong(X0) & humble(X0)) <=> ? [X1] : (~tall(X1) & old(X1)) [rectify 12]
37. ! [X0] : ((~old(X0) & funny(X0)) | quiet(X0)) [ennf transformation 13]
40. ((wise(alice) & humble(alice)) | ! [X0] : (~strong(X0) & happy(X0))) & (? [X0] : (strong(X0) | ~happy(X0)) | (~wise(alice) | ~humble(alice))) [nnf transformation 1]
41. ((wise(alice) & humble(alice)) | ! [X0] : (~strong(X0) & happy(X0))) & (? [X0] : (strong(X0) | ~happy(X0)) | ~wise(alice) | ~humble(alice)) [flattening 40]
42. ((wise(alice) & humble(alice)) | ! [X0] : (~strong(X0) & happy(X0))) & (? [X1] : (strong(X1) | ~happy(X1)) | ~wise(alice) | ~humble(alice)) [rectify 41]
43. ? [X1] : (strong(X1) | ~happy(X1)) => (strong(sK0) | ~happy(sK0)) [choice axiom]
44. ((wise(alice) & humble(alice)) | ! [X0] : (~strong(X0) & happy(X0))) & ((strong(sK0) | ~happy(sK0)) | ~wise(alice) | ~humble(alice)) [skolemisation 42,43]
50. ! [X0] : ((~calm(X0) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | calm(X0))) [nnf transformation 5]
51. ! [X0] : ((~calm(X0) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | calm(X0))) [flattening 50]
54. ! [X0] : ((~humble(X0) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | humble(X0))) [nnf transformation 7]
55. ! [X0] : ((~humble(X0) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | humble(X0))) [flattening 54]
56. ! [X0] : (((humble(X0) & ~calm(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (~humble(X0) | calm(X0)))) [nnf transformation 9]
57. ! [X0] : (((humble(X0) & ~calm(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ~humble(X0) | calm(X0))) [flattening 56]
58. ! [X0] : (((patient(X0) & humble(X0)) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | (~patient(X0) | ~humble(X0)))) [nnf transformation 10]
59. ! [X0] : (((patient(X0) & humble(X0)) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ~patient(X0) | ~humble(X0))) [flattening 58]
64. (? [X0] : (~strong(X0) & humble(X0)) | ! [X1] : (tall(X1) | ~old(X1))) & (? [X1] : (~tall(X1) & old(X1)) | ! [X0] : (strong(X0) | ~humble(X0))) [nnf transformation 28]
65. (? [X0] : (~strong(X0) & humble(X0)) | ! [X1] : (tall(X1) | ~old(X1))) & (? [X2] : (~tall(X2) & old(X2)) | ! [X3] : (strong(X3) | ~humble(X3))) [rectify 64]
66. ? [X0] : (~strong(X0) & humble(X0)) => (~strong(sK3) & humble(sK3)) [choice axiom]
67. ? [X2] : (~tall(X2) & old(X2)) => (~tall(sK4) & old(sK4)) [choice axiom]
68. ((~strong(sK3) & humble(sK3)) | ! [X1] : (tall(X1) | ~old(X1))) & ((~tall(sK4) & old(sK4)) | ! [X3] : (strong(X3) | ~humble(X3))) [skolemisation 65,67,66]
71. ! [X0] : ((brave(X0) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | ~brave(X0))) [nnf transformation 15]
72. ! [X0] : ((brave(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | ~brave(X0))) [flattening 71]
80. ? [X0] : (~tall(X0) & ~rich(X0)) => (~tall(sK8) & ~rich(sK8)) [choice axiom]
81. ~tall(sK8) & ~rich(sK8) [skolemisation 19,80]
91. humble(alice) | ~strong(X0) [cnf transformation 44]
101. ~quiet(X0) | calm(X0) [cnf transformation 51]
102. ~patient(X0) | calm(X0) [cnf transformation 51]
110. ~brave(X0) | ~humble(X0) [cnf transformation 55]
115. ~calm(X0) | brave(X0) | ~curious(X0) [cnf transformation 57]
120. tall(X0) | humble(X0) [cnf transformation 59]
121. patient(X0) | quiet(X0) [cnf transformation 59]
127. old(sK4) | strong(X3) | ~humble(X3) [cnf transformation 68]
128. ~tall(sK4) | strong(X3) | ~humble(X3) [cnf transformation 68]
132. ~old(X0) | quiet(X0) [cnf transformation 37]
137. ~quiet(X0) | strong(X0) | brave(X0) [cnf transformation 72]
144. ~tall(sK8) [cnf transformation 81]
154. curious(alice) [cnf transformation 25]
156. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
157. ~strong(X0) <- (1) [avatar component clause 156]
168. 4 <=> humble(alice) [avatar definition]
171. 1 | 4 [avatar split clause 91,168,156]
250. 22 <=> ! [X3] : (strong(X3) | ~humble(X3)) [avatar definition]
251. ~humble(X3) | strong(X3) <- (22) [avatar component clause 250]
253. 23 <=> tall(sK4) [avatar definition]
255. ~tall(sK4) <- (~23) [avatar component clause 253]
256. 22 | ~23 [avatar split clause 128,253,250]
258. 24 <=> old(sK4) [avatar definition]
260. old(sK4) <- (24) [avatar component clause 258]
261. 22 | 24 [avatar split clause 127,258,250]
357. humble(sK8) [resolution 120,144]
359. quiet(X0) | calm(X0) [resolution 121,102]
360. calm(X0) [subsumption resolution 359,101]
383. humble(sK4) <- (~23) [resolution 255,120]
385. quiet(sK4) <- (24) [resolution 260,132]
411. ~curious(X1) | brave(X1) [resolution 115,360]
412. brave(alice) [resolution 411,154]
417. ~humble(alice) [resolution 412,110]
420. ~4 [avatar split clause 417,168]
428. strong(sK4) | brave(sK4) <- (24) [resolution 137,385]
431. brave(sK4) <- (1, 24) [subsumption resolution 428,157]
435. ~humble(sK4) <- (1, 24) [resolution 431,110]
436. $false <- (1, ~23, 24) [subsumption resolution 435,383]
437. ~1 | 23 | ~24 [avatar contradiction clause 436]
438. ~humble(X3) <- (1, 22) [subsumption resolution 251,157]
446. $false <- (1, 22) [resolution 438,357]
451. ~1 | ~22 [avatar contradiction clause 446]
456. $false [avatar sat refutation 171,256,261,420,437,451]
% SZS output end Proof for 2661987238884879427810516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both not generous and humble. If alice is either not calm or funny then someone is not calm or not funny and vice versa. Everyone who is not quiet or wise is both brave and old. If lucy is rich or tall then paul is not humble and vice versa. Everyone who is creative is not patient. Everyone who is strong is rich or not kind and vice versa. Everyone who is both not patient and generous is not brave or curious and vice versa. Everyone who is generous or funny is both not old and funny. If someone is either funny or brave then susan is curious or funny. If someone is funny then paul is both not brave and not rich and vice versa. Everyone who is either humble or curious is both not wise and patient and vice versa. If paul is both old and curious then someone is either creative or funny. Everyone who is generous is both not tall and not creative. If susan is either creative or not quiet then lucy is not tall or strong. Everyone who is either not happy or generous is either wise or not brave and vice versa. Everyone who is both calm and not curious is either old or not kind. Someone is either curious or not patient. Someone is humble. Fred is not happy. Susan is not generous or happy. Someone is either not quiet or patient. Someone is both funny and not strong. Fred is wise. Someone is not humble or kind. | Fred is not humble. | entailment | (![X]:(humble(X)=>(~generous(X)&humble(X))))&
(((~calm(alice)<~>funny(alice)))<=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((~quiet(X)|wise(X))=>(brave(X)&old(X))))&
(((rich(lucy)|tall(lucy)))<=>(~humble(paul)))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(strong(X)<=>(rich(X)|~kind(X))))&
(![X]:((~patient(X)&generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)&funny(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((curious(susan)|funny(susan))))&
((?[X]:(funny(X)))<=>((~brave(paul)&~rich(paul))))&
(![X]:((humble(X)<~>curious(X))<=>(~wise(X)&patient(X))))&
(((old(paul)&curious(paul)))=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:(generous(X)=>(~tall(X)&~creative(X))))&
(((creative(susan)<~>~quiet(susan)))=>((~tall(lucy)|strong(lucy))))&
(![X]:((~happy(X)<~>generous(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((calm(X)&~curious(X))=>(old(X)<~>~kind(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:(humble(X)))&
(~happy(fred))&
((~generous(susan)|happy(susan)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((funny(X)&~strong(X))))&
(wise(fred))&
(?[X]:((~humble(X)|kind(X)))) | ~humble(fred) | [
"p2",
"p6",
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8544566042527462336257189
% SZS output start Proof for 8544566042527462336257189
3. ! [X0] : ((wise(X0) | ~quiet(X0)) => (old(X0) & brave(X0))) [input p2]
7. ! [X0] : ((generous(X0) & ~patient(X0)) <=> (curious(X0) | ~brave(X0))) [input p6]
8. ! [X0] : ((funny(X0) | generous(X0)) => (funny(X0) & ~old(X0))) [input p7]
11. ! [X0] : ((humble(X0) <~> curious(X0)) <=> (patient(X0) & ~wise(X0))) [input p10]
23. wise(fred) [input p22]
25. humble(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & brave(X0)) | (~wise(X0) & quiet(X0))) [ennf transformation 3]
29. ! [X0] : ((funny(X0) & ~old(X0)) | (~funny(X0) & ~generous(X0))) [ennf transformation 8]
47. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (~generous(X0) | patient(X0)))) [nnf transformation 7]
48. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | ~generous(X0) | patient(X0))) [flattening 47]
55. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [flattening 55]
86. ~wise(X0) | old(X0) [cnf transformation 27]
98. ~curious(X0) | generous(X0) [cnf transformation 48]
99. ~old(X0) | ~generous(X0) [cnf transformation 29]
108. ~wise(X0) | curious(X0) | ~humble(X0) [cnf transformation 56]
139. wise(fred) [cnf transformation 23]
141. humble(fred) [cnf transformation 25]
291. old(fred) [resolution 86,139]
311. ~generous(fred) [resolution 99,291]
323. curious(fred) | ~humble(fred) [resolution 108,139]
324. curious(fred) [subsumption resolution 323,141]
326. generous(fred) [resolution 324,98]
328. $false [subsumption resolution 326,311]
% SZS output end Proof for 8544566042527462336257189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then alice is not funny or creative.
Everyone who is either generous or creative is either humble or old and vice versa.
Everyone who is either not generous or not old is not humble.
If lucy is not generous then paul is either not funny or not rich and vice versa.
Everyone who is both not old and not curious is not rich or generous and vice versa.
Everyone who is both not old and not curious is not kind or not quiet.
If fred is not brave or humble then alice is not wise or humble.
Everyone who is not rich or not quiet is not patient.
Everyone who is tall or quiet is curious and vice versa.
Everyone who is either not strong or not calm is not happy and vice versa.
Everyone who is not happy or calm is not calm or curious.
Everyone who is not funny or patient is both brave and creative.
Everyone who is both not tall and wise is kind or not creative and vice versa.
If john is both not old and not strong then paul is happy.
Everyone who is not happy or not kind is either happy or not brave and vice versa.
Everyone who is not humble is not kind and vice versa.
Susan is both humble and not old.
Someone is rich or calm.
Fred is not rich or tall.
John is not patient.
Someone is either not wise or old.
Someone is not patient.
Someone is quiet or not patient.
Someone is funny or wise. | Susan is funny. | entailment | ((?[X]:(~generous(X)))=>((~funny(alice)|creative(alice))))&
(![X]:((generous(X)<~>creative(X))<=>(humble(X)<~>old(X))))&
(![X]:((~generous(X)<~>~old(X))=>~humble(X)))&
((~generous(lucy))<=>((~funny(paul)<~>~rich(paul))))&
(![X]:((~old(X)&~curious(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~curious(X))=>(~kind(X)|~quiet(X))))&
(((~brave(fred)|humble(fred)))=>((~wise(alice)|humble(alice))))&
(![X]:((~rich(X)|~quiet(X))=>~patient(X)))&
(![X]:((tall(X)|quiet(X))<=>curious(X)))&
(![X]:((~strong(X)<~>~calm(X))<=>~happy(X)))&
(![X]:((~happy(X)|calm(X))=>(~calm(X)|curious(X))))&
(![X]:((~funny(X)|patient(X))=>(brave(X)&creative(X))))&
(![X]:((~tall(X)&wise(X))<=>(kind(X)|~creative(X))))&
(((~old(john)&~strong(john)))=>(happy(paul)))&
(![X]:((~happy(X)|~kind(X))<=>(happy(X)<~>~brave(X))))&
(![X]:(~humble(X)<=>~kind(X)))&
((humble(susan)&~old(susan)))&
(?[X]:((rich(X)|calm(X))))&
((~rich(fred)|tall(fred)))&
(~patient(john))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((funny(X)|wise(X)))) | funny(susan) | [
"p11",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2002081703227668313137089
% SZS output start Proof for 2002081703227668313137089
12. ! [X0] : ((patient(X0) | ~funny(X0)) => (creative(X0) & brave(X0))) [input p11]
15. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (happy(X0) <~> ~brave(X0))) [input p14]
16. ! [X0] : (~humble(X0) <=> ~kind(X0)) [input p15]
17. ~old(susan) & humble(susan) [input p16]
25. ~funny(susan) [input hypothesis]
28. ! [X0] : (~funny(X0) => (creative(X0) & brave(X0))) [pure predicate removal 12]
40. ! [X0] : ((creative(X0) & brave(X0)) | funny(X0)) [ennf transformation 28]
53. ! [X0] : (((~kind(X0) | ~happy(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [nnf transformation 15]
54. ! [X0] : ((~kind(X0) | ~happy(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [flattening 53]
55. ! [X0] : ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))) [nnf transformation 16]
95. brave(X0) | funny(X0) [cnf transformation 40]
103. ~brave(X0) | happy(X0) | happy(X0) [cnf transformation 54]
107. ~kind(X0) | ~happy(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 54]
110. ~humble(X0) | kind(X0) [cnf transformation 55]
111. humble(susan) [cnf transformation 17]
118. ~funny(susan) [cnf transformation 25]
119. ~brave(X0) | happy(X0) [duplicate literal removal 103]
120. ~happy(X0) | ~kind(X0) | ~brave(X0) [duplicate literal removal 107]
223. kind(susan) [resolution 110,111]
226. happy(X0) | funny(X0) [resolution 119,95]
241. ~kind(X1) | ~brave(X1) | funny(X1) [resolution 120,226]
242. ~kind(X1) | funny(X1) [subsumption resolution 241,95]
243. funny(susan) [resolution 242,223]
244. $false [subsumption resolution 243,118]
% SZS output end Proof for 2002081703227668313137089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both wise and not curious then mary is either brave or not tall and vice versa. Everyone who is both happy and kind is both not rich and not curious and vice versa. Everyone who is either not funny or not wise is either not old or strong and vice versa. If someone is both not creative and kind then susan is not rich. Everyone who is both not funny and not calm is both wise and not happy and vice versa. If susan is not calm then lucy is not patient. Everyone who is both curious and not creative is calm and vice versa. Everyone who is not funny or not humble is either quiet or calm. Everyone who is brave is not brave or calm and vice versa. Everyone who is either not creative or not happy is old or patient. If lucy is not happy or happy then mary is both not tall and patient and vice versa. If someone is quiet or not old then someone is quiet. Everyone who is either kind or creative is both not curious and not calm. If john is both humble and not patient then fred is either not humble or patient and vice versa. Everyone who is not funny is both not humble and not strong. Lucy is generous. Mary is both not happy and brave. Someone is not kind. Lucy is both not funny and not old. Lucy is either strong or tall. Someone is both patient and wise. Susan is both calm and not funny. Someone is strong. | Susan is not kind. | entailment | (((wise(lucy)&~curious(lucy)))<=>((brave(mary)<~>~tall(mary))))&
(![X]:((happy(X)&kind(X))<=>(~rich(X)&~curious(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~old(X)<~>strong(X))))&
((?[X]:((~creative(X)&kind(X))))=>(~rich(susan)))&
(![X]:((~funny(X)&~calm(X))<=>(wise(X)&~happy(X))))&
((~calm(susan))=>(~patient(lucy)))&
(![X]:((curious(X)&~creative(X))<=>calm(X)))&
(![X]:((~funny(X)|~humble(X))=>(quiet(X)<~>calm(X))))&
(![X]:(brave(X)<=>(~brave(X)|calm(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(old(X)|patient(X))))&
(((~happy(lucy)|happy(lucy)))<=>((~tall(mary)&patient(mary))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:(quiet(X))))&
(![X]:((kind(X)<~>creative(X))=>(~curious(X)&~calm(X))))&
(((humble(john)&~patient(john)))<=>((~humble(fred)<~>patient(fred))))&
(![X]:(~funny(X)=>(~humble(X)&~strong(X))))&
(generous(lucy))&
((~happy(mary)&brave(mary)))&
(?[X]:(~kind(X)))&
((~funny(lucy)&~old(lucy)))&
((strong(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)&wise(X))))&
((calm(susan)&~funny(susan)))&
(?[X]:(strong(X))) | ~kind(susan) | [
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 748839431759258499110066
% SZS output start Proof for 748839431759258499110066
7. ! [X0] : ((~creative(X0) & curious(X0)) <=> calm(X0)) [input p6]
9. ! [X0] : (brave(X0) <=> (calm(X0) | ~brave(X0))) [input p8]
13. ! [X0] : ((kind(X0) <~> creative(X0)) => (~calm(X0) & ~curious(X0))) [input p12]
24. kind(susan) [input hypothesis]
33. ! [X0] : ((~calm(X0) & ~curious(X0)) | (kind(X0) <=> creative(X0))) [ennf transformation 13]
42. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) | ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | creative(X0) | ~curious(X0))) [flattening 42]
45. ! [X0] : ((brave(X0) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | ~brave(X0))) [nnf transformation 9]
46. ! [X0] : ((brave(X0) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | ~brave(X0))) [flattening 45]
53. ! [X0] : ((~calm(X0) & ~curious(X0)) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) [nnf transformation 33]
89. ~calm(X0) | ~creative(X0) [cnf transformation 43]
94. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 46]
95. brave(X0) | brave(X0) [cnf transformation 46]
108. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 53]
130. kind(susan) [cnf transformation 24]
131. calm(X0) | ~brave(X0) [duplicate literal removal 94]
132. brave(X0) [duplicate literal removal 95]
156. 5 <=> ! [X0] : (~kind(X0) | creative(X0)) [avatar definition]
157. ~kind(X0) | creative(X0) <- (5) [avatar component clause 156]
172. calm(X0) [subsumption resolution 131,132]
197. creative(X0) | ~kind(X0) [subsumption resolution 108,172]
198. 5 [avatar split clause 197,156]
232. ~creative(X0) [resolution 89,172]
238. creative(susan) <- (5) [resolution 157,130]
239. $false <- (5) [subsumption resolution 238,232]
240. ~5 [avatar contradiction clause 239]
241. $false [avatar sat refutation 198,240]
% SZS output end Proof for 748839431759258499110066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is rich. Everyone who is both creative and funny is rich or tall and vice versa. Everyone who is either creative or old is old and vice versa. If someone is either not wise or not patient then john is not calm. Everyone who is old or calm is not tall or not happy and vice versa. Everyone who is happy is not humble or happy and vice versa. If fred is not happy or wise then mary is both humble and not patient and vice versa. If fred is wise or not brave then alice is happy and vice versa. Everyone who is not kind or not creative is both quiet and not brave. If mary is not kind or wise then paul is either not funny or not creative. Everyone who is either not brave or calm is not calm or not tall. If someone is not patient then someone is old or rich. If someone is both creative and not wise then someone is both not patient and not kind and vice versa. Everyone who is either funny or generous is either tall or not quiet and vice versa. If someone is not curious or not rich then mary is not strong and vice versa. Everyone who is both funny and tall is either happy or old and vice versa. Someone is kind. Susan is either curious or not humble. Someone is either calm or patient. Someone is either funny or brave. John is either wise or not generous. Someone is both funny and calm. | Susan is patient. | neutral | (![X]:(curious(X)=>rich(X)))&
(![X]:((creative(X)&funny(X))<=>(rich(X)|tall(X))))&
(![X]:((creative(X)<~>old(X))<=>old(X)))&
((?[X]:((~wise(X)<~>~patient(X))))=>(~calm(john)))&
(![X]:((old(X)|calm(X))<=>(~tall(X)|~happy(X))))&
(![X]:(happy(X)<=>(~humble(X)|happy(X))))&
(((~happy(fred)|wise(fred)))<=>((humble(mary)&~patient(mary))))&
(((wise(fred)|~brave(fred)))<=>(happy(alice)))&
(![X]:((~kind(X)|~creative(X))=>(quiet(X)&~brave(X))))&
(((~kind(mary)|wise(mary)))=>((~funny(paul)<~>~creative(paul))))&
(![X]:((~brave(X)<~>calm(X))=>(~calm(X)|~tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)|rich(X)))))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:((~patient(X)&~kind(X)))))&
(![X]:((funny(X)<~>generous(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~curious(X)|~rich(X))))<=>(~strong(mary)))&
(![X]:((funny(X)&tall(X))<=>(happy(X)<~>old(X))))&
(?[X]:(kind(X)))&
((curious(susan)<~>~humble(susan)))&
(?[X]:((calm(X)<~>patient(X))))&
(?[X]:((funny(X)<~>brave(X))))&
((wise(john)<~>~generous(john)))&
(?[X]:((funny(X)&calm(X)))) | patient(susan) | [] | null | 0 |
If someone is not wise then someone is not tall. Everyone who is quiet or patient is either not kind or not patient. Everyone who is either not wise or not generous is not rich or calm. Everyone who is both funny and kind is either wise or not rich and vice versa. If someone is both not curious and patient then fred is creative. Everyone who is brave is either humble or not patient. Everyone who is either old or not funny is not curious. Everyone who is both not rich and not wise is not kind and vice versa. If john is not calm then fred is either happy or not generous and vice versa. Everyone who is not funny is not calm or not kind and vice versa. Everyone who is rich is not creative. If someone is patient then someone is tall and vice versa. If john is both calm and not happy then paul is not creative or not strong. Everyone who is not generous or not old is both quiet and not quiet. If someone is not curious then someone is kind or not rich. If john is tall or brave then someone is both not quiet and not tall and vice versa. Alice is both curious and creative. Someone is either not humble or curious. Someone is not generous or quiet. Paul is either funny or not wise. Someone is not tall or humble. Fred is not curious or not calm. | John is tall. | contradiction | ((?[X]:(~wise(X)))=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)|patient(X))=>(~kind(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~generous(X))=>(~rich(X)|calm(X))))&
(![X]:((funny(X)&kind(X))<=>(wise(X)<~>~rich(X))))&
((?[X]:((~curious(X)&patient(X))))=>(creative(fred)))&
(![X]:(brave(X)=>(humble(X)<~>~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~rich(X)&~wise(X))<=>~kind(X)))&
((~calm(john))<=>((happy(fred)<~>~generous(fred))))&
(![X]:(~funny(X)<=>(~calm(X)|~kind(X))))&
(![X]:(rich(X)=>~creative(X)))&
((?[X]:(patient(X)))<=>(?[X]:(tall(X))))&
(((calm(john)&~happy(john)))=>((~creative(paul)|~strong(paul))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~rich(X)))))&
(((tall(john)|brave(john)))<=>(?[X]:((~quiet(X)&~tall(X)))))&
((curious(alice)&creative(alice)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~generous(X)|quiet(X))))&
((funny(paul)<~>~wise(paul)))&
(?[X]:((~tall(X)|humble(X))))&
((~curious(fred)|~calm(fred))) | tall(john) | [
"p1",
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4875657907216262536449338
% SZS output start Proof for 4875657907216262536449338
2. ! [X0] : ((patient(X0) | quiet(X0)) => (~kind(X0) <~> ~patient(X0))) [input p1]
4. ! [X0] : ((kind(X0) & funny(X0)) <=> (wise(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> ~kind(X0)) [input p7]
12. ? [X0] : patient(X0) <=> ? [X0] : tall(X0) [input p11]
23. tall(john) [input hypothesis]
25. ? [X0] : patient(X0) <=> ? [X1] : tall(X1) [rectify 12]
29. ! [X0] : ((~kind(X0) <~> ~patient(X0)) | (~patient(X0) & ~quiet(X0))) [ennf transformation 2]
41. ! [X0] : (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~patient(X0) & ~quiet(X0))) [nnf transformation 29]
43. ! [X0] : (((kind(X0) & funny(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) & (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~kind(X0) | ~funny(X0)))) [nnf transformation 4]
44. ! [X0] : (((kind(X0) & funny(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) & (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | ~kind(X0) | ~funny(X0))) [flattening 43]
47. ! [X0] : (((~wise(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | (wise(X0) | rich(X0)))) [nnf transformation 8]
48. ! [X0] : (((~wise(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | wise(X0) | rich(X0))) [flattening 47]
52. (? [X0] : patient(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : ~patient(X0)) [nnf transformation 25]
53. (? [X0] : patient(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : ~patient(X3)) [rectify 52]
54. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
55. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
56. (patient(sK1) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : ~patient(X3)) [skolemisation 53,55,54]
75. ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 41]
85. kind(X0) | wise(X0) | rich(X0) [cnf transformation 44]
91. ~kind(X0) | wise(X0) | rich(X0) [cnf transformation 48]
92. ~rich(X0) | kind(X0) [cnf transformation 48]
93. ~wise(X0) | kind(X0) [cnf transformation 48]
103. patient(sK1) | ~tall(X1) [cnf transformation 56]
123. tall(john) [cnf transformation 23]
124. ~kind(X0) | ~patient(X0) [duplicate literal removal 75]
141. rich(X0) | wise(X0) [subsumption resolution 91,85]
159. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
160. ~tall(X1) <- (8) [avatar component clause 159]
162. 9 <=> patient(sK1) [avatar definition]
164. patient(sK1) <- (9) [avatar component clause 162]
165. 8 | 9 [avatar split clause 103,162,159]
167. 10 <=> ! [X3] : ~patient(X3) [avatar definition]
168. ~patient(X3) <- (10) [avatar component clause 167]
180. 13 <=> tall(john) [avatar definition]
182. tall(john) <- (13) [avatar component clause 180]
239. 13 [avatar split clause 123,180]
242. $false <- (8, 13) [resolution 182,160]
243. ~8 | ~13 [avatar contradiction clause 242]
244. $false <- (9, 10) [subsumption resolution 164,168]
245. ~9 | ~10 [avatar contradiction clause 244]
250. wise(X0) | kind(X0) [resolution 141,92]
252. kind(X0) [subsumption resolution 250,93]
254. ~patient(X0) [resolution 252,124]
255. 10 [avatar split clause 254,167]
256. $false [avatar sat refutation 165,239,243,245,255]
% SZS output end Proof for 4875657907216262536449338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not wise is either curious or happy. Everyone who is strong or humble is either brave or not happy. Everyone who is either patient or curious is either creative or not curious. Everyone who is both patient and happy is not funny or not wise and vice versa. If lucy is kind then someone is either not wise or not calm. If someone is not generous or brave then someone is not tall or not calm. Everyone who is quiet or not generous is both calm and not old and vice versa. Everyone who is not brave is kind or not wise. Everyone who is happy or not rich is both not kind and not calm. Everyone who is brave or tall is both quiet and tall and vice versa. Everyone who is calm is both not humble and not wise. Everyone who is either happy or brave is curious and vice versa. If mary is rich then alice is either calm or curious. Everyone who is both not patient and strong is not strong. Everyone who is both not strong and funny is both not rich and old. Everyone who is either not quiet or old is both strong and not tall and vice versa. John is either humble or not curious. Someone is either not generous or rich. Someone is rich. Someone is both patient and rich. Someone is either funny or not wise. Someone is both happy and not humble. John is strong or not quiet. | Alice is rich. | entailment | (![X]:((~rich(X)&~wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((strong(X)|humble(X))=>(brave(X)<~>~happy(X))))&
(![X]:((patient(X)<~>curious(X))=>(creative(X)<~>~curious(X))))&
(![X]:((patient(X)&happy(X))<=>(~funny(X)|~wise(X))))&
((kind(lucy))=>(?[X]:((~wise(X)<~>~calm(X)))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(~brave(X)=>(kind(X)|~wise(X))))&
(![X]:((happy(X)|~rich(X))=>(~kind(X)&~calm(X))))&
(![X]:((brave(X)|tall(X))<=>(quiet(X)&tall(X))))&
(![X]:(calm(X)=>(~humble(X)&~wise(X))))&
(![X]:((happy(X)<~>brave(X))<=>curious(X)))&
((rich(mary))=>((calm(alice)<~>curious(alice))))&
(![X]:((~patient(X)&strong(X))=>~strong(X)))&
(![X]:((~strong(X)&funny(X))=>(~rich(X)&old(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(strong(X)&~tall(X))))&
((humble(john)<~>~curious(john)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((happy(X)&~humble(X))))&
((strong(john)|~quiet(john))) | rich(alice) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 221199744241215978453538
% SZS output start Proof for 221199744241215978453538
1. ! [X0] : ((~wise(X0) & ~rich(X0)) => (curious(X0) <~> happy(X0))) [input p0]
4. ! [X0] : ((happy(X0) & patient(X0)) <=> (~wise(X0) | ~funny(X0))) [input p3]
7. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (~old(X0) & calm(X0))) [input p6]
8. ! [X0] : (~brave(X0) => (~wise(X0) | kind(X0))) [input p7]
9. ! [X0] : ((~rich(X0) | happy(X0)) => (~calm(X0) & ~kind(X0))) [input p8]
10. ! [X0] : ((tall(X0) | brave(X0)) <=> (tall(X0) & quiet(X0))) [input p9]
12. ! [X0] : ((happy(X0) <~> brave(X0)) <=> curious(X0)) [input p11]
24. ~rich(alice) [input hypothesis]
26. ! [X0] : ((curious(X0) <~> happy(X0)) | (wise(X0) | rich(X0))) [ennf transformation 1]
27. ! [X0] : ((curious(X0) <~> happy(X0)) | wise(X0) | rich(X0)) [flattening 26]
32. ! [X0] : ((~wise(X0) | kind(X0)) | brave(X0)) [ennf transformation 8]
33. ! [X0] : (~wise(X0) | kind(X0) | brave(X0)) [flattening 32]
34. ! [X0] : ((~calm(X0) & ~kind(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 9]
41. ! [X0] : (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | wise(X0) | rich(X0)) [nnf transformation 27]
44. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & patient(X0)) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~happy(X0) | ~patient(X0))) [flattening 44]
52. ! [X0] : (((~generous(X0) | quiet(X0)) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 7]
53. ! [X0] : ((~generous(X0) | quiet(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | (generous(X0) & ~quiet(X0)))) [flattening 52]
54. ! [X0] : (((tall(X0) | brave(X0)) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 10]
55. ! [X0] : ((tall(X0) | brave(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 54]
56. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~curious(X0)) & (curious(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 12]
74. ~happy(X0) | ~curious(X0) | wise(X0) | rich(X0) [cnf transformation 41]
87. happy(X0) | wise(X0) [cnf transformation 45]
92. ~quiet(X0) | calm(X0) [cnf transformation 53]
97. ~wise(X0) | kind(X0) | brave(X0) [cnf transformation 33]
99. ~kind(X0) | rich(X0) [cnf transformation 34]
101. ~calm(X0) | rich(X0) [cnf transformation 34]
102. ~brave(X0) | quiet(X0) [cnf transformation 55]
109. ~happy(X0) | brave(X0) | curious(X0) [cnf transformation 56]
136. ~rich(alice) [cnf transformation 24]
236. brave(X0) | curious(X0) | wise(X0) [resolution 109,87]
300. ~curious(X1) | wise(X1) | rich(X1) | wise(X1) [resolution 74,87]
302. ~curious(X1) | wise(X1) | rich(X1) [duplicate literal removal 300]
339. quiet(X5) | wise(X5) | curious(X5) [resolution 236,102]
528. calm(X2) | curious(X2) | wise(X2) [resolution 339,92]
584. curious(X2) | wise(X2) | rich(X2) [resolution 528,101]
588. wise(X2) | rich(X2) [subsumption resolution 584,302]
622. rich(X0) | kind(X0) | brave(X0) [resolution 588,97]
625. brave(X0) | rich(X0) [subsumption resolution 622,99]
641. quiet(X5) | rich(X5) [resolution 625,102]
651. rich(X3) | calm(X3) [resolution 641,92]
655. rich(X3) [subsumption resolution 651,101]
661. $false [resolution 655,136]
% SZS output end Proof for 221199744241215978453538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not happy is patient and vice versa.
Everyone who is both brave and not calm is not strong.
If someone is both not humble and tall then someone is both not old and patient.
If mary is both not funny and old then someone is either not funny or humble.
Everyone who is not brave is not creative or not calm.
Everyone who is either not humble or not calm is not funny and vice versa.
Everyone who is both not patient and not old is both not quiet and not calm.
If someone is not generous or brave then someone is not happy and vice versa.
If someone is not wise then someone is not calm or not old.
If someone is not curious or wise then susan is either humble or not rich and vice versa.
Everyone who is happy is not calm.
If paul is both generous and not brave then mary is strong or patient.
Everyone who is both happy and quiet is both rich and calm and vice versa.
Everyone who is both not humble and not tall is both calm and happy and vice versa.
Everyone who is not tall or not old is both not happy and calm.
Everyone who is either not generous or generous is both not creative and humble.
Someone is funny or quiet.
Someone is either not humble or tall.
Mary is rich or creative.
Someone is both humble and not kind.
Susan is either generous or rich.
Someone is not brave or brave.
Paul is both calm and not curious. | Paul is humble. | entailment | (![X]:((strong(X)|~happy(X))<=>patient(X)))&
(![X]:((brave(X)&~calm(X))=>~strong(X)))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:((~old(X)&patient(X)))))&
(((~funny(mary)&old(mary)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:(~brave(X)=>(~creative(X)|~calm(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>~funny(X)))&
(![X]:((~patient(X)&~old(X))=>(~quiet(X)&~calm(X))))&
((?[X]:((~generous(X)|brave(X))))<=>(?[X]:(~happy(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~curious(X)|wise(X))))<=>((humble(susan)<~>~rich(susan))))&
(![X]:(happy(X)=>~calm(X)))&
(((generous(paul)&~brave(paul)))=>((strong(mary)|patient(mary))))&
(![X]:((happy(X)&quiet(X))<=>(rich(X)&calm(X))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&happy(X))))&
(![X]:((~tall(X)|~old(X))=>(~happy(X)&calm(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~creative(X)&humble(X))))&
(?[X]:((funny(X)|quiet(X))))&
(?[X]:((~humble(X)<~>tall(X))))&
((rich(mary)|creative(mary)))&
(?[X]:((humble(X)&~kind(X))))&
((generous(susan)<~>rich(susan)))&
(?[X]:((~brave(X)|brave(X))))&
((calm(paul)&~curious(paul))) | humble(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3655635555250111825706785
% SZS output start Proof for 3655635555250111825706785
16. ! [X0] : ((~generous(X0) <~> generous(X0)) => (humble(X0) & ~creative(X0))) [input p15]
24. ~humble(paul) [input hypothesis]
46. ! [X0] : ((humble(X0) & ~creative(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 16]
70. ! [X0] : ((humble(X0) & ~creative(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 46]
120. humble(X0) | generous(X0) | generous(X0) [cnf transformation 70]
121. humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 70]
132. ~humble(paul) [cnf transformation 24]
135. humble(X0) | generous(X0) [duplicate literal removal 120]
136. humble(X0) | ~generous(X0) [duplicate literal removal 121]
251. humble(X0) [subsumption resolution 135,136]
270. $false [subsumption resolution 132,251]
% SZS output end Proof for 3655635555250111825706785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is funny or not funny and vice versa.
If lucy is both not funny and curious then someone is tall or not strong and vice versa.
Everyone who is not happy is strong and vice versa.
Everyone who is either old or not tall is rich or patient.
Everyone who is generous or tall is not kind or not rich and vice versa.
Everyone who is not tall or kind is both kind and not quiet.
Everyone who is either not funny or not creative is both not creative and not rich.
If someone is wise then john is both wise and not kind.
If fred is generous or not old then someone is both rich and brave.
If someone is both not brave and not kind then someone is either not wise or not patient and vice versa.
Everyone who is not humble is either not creative or not patient.
If someone is both humble and not happy then someone is either not generous or not kind.
If someone is either not brave or old then lucy is funny or not rich and vice versa.
If fred is both not quiet and not wise then someone is either brave or not funny.
Everyone who is both not kind and strong is patient or not creative and vice versa.
Everyone who is either not humble or generous is both curious and not happy.
Someone is either not strong or not curious.
Fred is not wise or not kind.
Someone is not rich or happy.
Someone is not quiet or happy.
Alice is both generous and curious. | Fred is generous. | neutral | (![X]:(creative(X)<=>(funny(X)|~funny(X))))&
(((~funny(lucy)&curious(lucy)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((old(X)<~>~tall(X))=>(rich(X)|patient(X))))&
(![X]:((generous(X)|tall(X))<=>(~kind(X)|~rich(X))))&
(![X]:((~tall(X)|kind(X))=>(kind(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~creative(X)&~rich(X))))&
((?[X]:(wise(X)))=>((wise(john)&~kind(john))))&
(((generous(fred)|~old(fred)))=>(?[X]:((rich(X)&brave(X)))))&
((?[X]:((~brave(X)&~kind(X))))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(~humble(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((humble(X)&~happy(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
((?[X]:((~brave(X)<~>old(X))))<=>((funny(lucy)|~rich(lucy))))&
(((~quiet(fred)&~wise(fred)))=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((~kind(X)&strong(X))<=>(patient(X)|~creative(X))))&
(![X]:((~humble(X)<~>generous(X))=>(curious(X)&~happy(X))))&
(?[X]:((~strong(X)<~>~curious(X))))&
((~wise(fred)|~kind(fred)))&
(?[X]:((~rich(X)|happy(X))))&
(?[X]:((~quiet(X)|happy(X))))&
((generous(alice)&curious(alice))) | generous(fred) | [] | null | 0 |
Everyone who is not patient is either patient or tall.
Everyone who is either creative or not brave is both wise and not humble and vice versa.
If someone is not quiet then someone is either not strong or generous.
If someone is either not humble or funny then mary is not strong or tall and vice versa.
Everyone who is funny or creative is both not strong and tall.
Everyone who is not brave or not patient is not funny.
Everyone who is happy or not tall is either not generous or generous and vice versa.
Everyone who is happy or brave is rich and vice versa.
Everyone who is curious or kind is both not old and not curious.
If paul is either strong or humble then lucy is not rich or curious.
If paul is generous or not kind then susan is creative and vice versa.
If someone is calm or kind then someone is patient or old and vice versa.
Everyone who is quiet or not funny is either not calm or curious.
If alice is both curious and not old then someone is not strong or happy and vice versa.
Everyone who is rich is not quiet or funny.
Someone is not creative.
Lucy is old or rich.
Someone is either not curious or wise.
Susan is not quiet.
Someone is either patient or not strong. | Susan is not rich. | contradiction | (![X]:(~patient(X)=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(wise(X)&~humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((~strong(mary)|tall(mary))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(((curious(alice)&~old(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
(?[X]:(~creative(X)))&
((old(lucy)|rich(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~quiet(susan))&
(?[X]:((patient(X)<~>~strong(X)))) | ~rich(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 303607384284832973097343
% SZS output start Proof for 303607384284832973097343
2. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (~humble(X0) & wise(X0))) [input p1]
4. ? [X0] : (~humble(X0) <~> funny(X0)) <=> (tall(mary) | ~strong(mary)) [input p3]
5. ! [X0] : ((creative(X0) | funny(X0)) => (tall(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~brave(X0)) => ~funny(X0)) [input p5]
7. ! [X0] : ((~tall(X0) | happy(X0)) <=> (~generous(X0) <~> generous(X0))) [input p6]
8. ! [X0] : ((brave(X0) | happy(X0)) <=> rich(X0)) [input p7]
9. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p8]
14. (~old(alice) & curious(alice)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p13]
21. ~rich(susan) [input hypothesis]
26. ! [X0] : ((tall(X0) & ~strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 5]
27. ! [X0] : (~funny(X0) | (patient(X0) & brave(X0))) [ennf transformation 6]
28. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 9]
35. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 2]
36. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [flattening 35]
41. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & ((tall(mary) | ~strong(mary)) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 4]
42. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [flattening 41]
43. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [rectify 42]
44. ? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) => ((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) [choice axiom]
45. (((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [skolemisation 43,44]
46. ! [X0] : (((~tall(X0) | happy(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [nnf transformation 7]
47. ! [X0] : ((~tall(X0) | happy(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [flattening 46]
48. ! [X0] : (((brave(X0) | happy(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((brave(X0) | happy(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~happy(X0)))) [flattening 48]
59. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | (old(alice) | ~curious(alice))) [nnf transformation 14]
60. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | old(alice) | ~curious(alice)) [flattening 59]
61. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X1] : (happy(X1) | ~strong(X1)) | old(alice) | ~curious(alice)) [rectify 60]
62. ? [X1] : (happy(X1) | ~strong(X1)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
63. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & ((happy(sK4) | ~strong(sK4)) | old(alice) | ~curious(alice)) [skolemisation 61,62]
77. ~humble(X0) | creative(X0) | brave(X0) [cnf transformation 36]
82. tall(mary) | ~strong(mary) | funny(X1) | humble(X1) [cnf transformation 45]
89. ~strong(X0) | ~creative(X0) [cnf transformation 26]
92. ~funny(X0) | brave(X0) [cnf transformation 27]
98. ~tall(X0) | happy(X0) | generous(X0) | generous(X0) [cnf transformation 47]
99. ~tall(X0) | happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 47]
101. ~brave(X0) | rich(X0) [cnf transformation 49]
105. ~curious(X0) | ~curious(X0) [cnf transformation 28]
121. curious(alice) | strong(X0) [cnf transformation 63]
122. curious(alice) | ~happy(X0) [cnf transformation 63]
133. ~rich(susan) [cnf transformation 21]
134. ~curious(X0) [duplicate literal removal 105]
135. ~tall(X0) | happy(X0) | generous(X0) [duplicate literal removal 98]
136. ~generous(X0) | happy(X0) | ~tall(X0) [duplicate literal removal 99]
152. 4 <=> tall(mary) [avatar definition]
153. tall(mary) <- (4) [avatar component clause 152]
165. 7 <=> strong(mary) [avatar definition]
166. ~strong(mary) <- (~7) [avatar component clause 165]
176. 9 <=> ! [X1] : (funny(X1) | humble(X1)) [avatar definition]
177. funny(X1) | humble(X1) <- (9) [avatar component clause 176]
178. 9 | ~7 | 4 [avatar split clause 82,152,165,176]
179. ~tall(X0) | happy(X0) [subsumption resolution 135,136]
246. 24 <=> ! [X0] : ~happy(X0) [avatar definition]
247. ~happy(X0) <- (24) [avatar component clause 246]
254. 26 <=> ! [X0] : strong(X0) [avatar definition]
255. strong(X0) <- (26) [avatar component clause 254]
257. ~happy(X0) [subsumption resolution 122,134]
258. 24 [avatar split clause 257,246]
259. strong(X0) [subsumption resolution 121,134]
260. 26 [avatar split clause 259,254]
279. $false <- (~7, 26) [subsumption resolution 166,255]
280. 7 | ~26 [avatar contradiction clause 279]
285. ~creative(X0) <- (26) [resolution 89,255]
289. happy(mary) <- (4) [resolution 179,153]
291. $false <- (4, 24) [subsumption resolution 289,247]
292. ~4 | ~24 [avatar contradiction clause 291]
298. humble(X2) | brave(X2) <- (9) [resolution 177,92]
332. creative(X0) | brave(X0) | brave(X0) <- (9) [resolution 77,298]
334. creative(X0) | brave(X0) <- (9) [duplicate literal removal 332]
336. brave(X0) <- (9, 26) [subsumption resolution 334,285]
342. rich(X1) <- (9, 26) [resolution 336,101]
377. $false <- (9, 26) [resolution 342,133]
380. ~9 | ~26 [avatar contradiction clause 377]
381. $false [avatar sat refutation 178,258,260,280,292,380]
% SZS output end Proof for 303607384284832973097343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and wise then someone is not tall or wise.
Everyone who is either quiet or not curious is not kind.
If john is not happy then someone is both humble and not wise.
Everyone who is not old is either happy or not happy.
Everyone who is not quiet is either not happy or tall and vice versa.
Everyone who is both not tall and not patient is humble or curious and vice versa.
Everyone who is both not generous and not humble is not wise or not funny and vice versa.
If lucy is both not brave and wise then lucy is rich or funny.
Everyone who is either brave or not old is rich and vice versa.
If john is either patient or curious then someone is both rich and not quiet.
If lucy is both not rich and not humble then paul is either not kind or not humble and vice versa.
If john is both curious and not strong then someone is either not rich or old and vice versa.
Everyone who is both kind and not old is either generous or patient.
If someone is generous or brave then someone is old or not generous.
Everyone who is both humble and brave is not kind and vice versa.
Everyone who is wise is not patient and vice versa.
Someone is both not kind and happy.
Alice is calm.
Paul is either not brave or not kind.
Someone is both not calm and not curious.
Lucy is either not happy or tall.
John is not old.
Someone is not wise.
Paul is both not tall and calm. | John is kind. | contradiction | ((?[X]:((creative(X)&wise(X))))=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((quiet(X)<~>~curious(X))=>~kind(X)))&
((~happy(john))=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:(~old(X)=>(happy(X)<~>~happy(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>tall(X))))&
(![X]:((~tall(X)&~patient(X))<=>(humble(X)|curious(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~wise(X)|~funny(X))))&
(((~brave(lucy)&wise(lucy)))=>((rich(lucy)|funny(lucy))))&
(![X]:((brave(X)<~>~old(X))<=>rich(X)))&
(((patient(john)<~>curious(john)))=>(?[X]:((rich(X)&~quiet(X)))))&
(((~rich(lucy)&~humble(lucy)))<=>((~kind(paul)<~>~humble(paul))))&
(((curious(john)&~strong(john)))<=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((kind(X)&~old(X))=>(generous(X)<~>patient(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((humble(X)&brave(X))<=>~kind(X)))&
(![X]:(wise(X)<=>~patient(X)))&
(?[X]:((~kind(X)&happy(X))))&
(calm(alice))&
((~brave(paul)<~>~kind(paul)))&
(?[X]:((~calm(X)&~curious(X))))&
((~happy(lucy)<~>tall(lucy)))&
(~old(john))&
(?[X]:(~wise(X)))&
((~tall(paul)&calm(paul))) | kind(john) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p8",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2919269157608551396670129
% SZS output start Proof for 2919269157608551396670129
2. ! [X0] : ((quiet(X0) <~> ~curious(X0)) => ~kind(X0)) [input p1]
3. ~happy(john) => ? [X0] : (~wise(X0) & humble(X0)) [input p2]
5. ! [X0] : (~quiet(X0) <=> (~happy(X0) <~> tall(X0))) [input p4]
6. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (curious(X0) | humble(X0))) [input p5]
7. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (~funny(X0) | ~wise(X0))) [input p6]
9. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> rich(X0)) [input p8]
12. (~strong(john) & curious(john)) <=> ? [X0] : (~rich(X0) <~> old(X0)) [input p11]
15. ! [X0] : ((brave(X0) & humble(X0)) <=> ~kind(X0)) [input p14]
17. ? [X0] : (happy(X0) & ~kind(X0)) [input p16]
25. kind(john) [input hypothesis]
29. ! [X0] : (~kind(X0) | (quiet(X0) <=> ~curious(X0))) [ennf transformation 2]
30. ? [X0] : (~wise(X0) & humble(X0)) | happy(john) [ennf transformation 3]
38. ! [X0] : (~kind(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) [nnf transformation 29]
39. ? [X0] : (~wise(X0) & humble(X0)) => (~wise(sK0) & humble(sK0)) [choice axiom]
40. (~wise(sK0) & humble(sK0)) | happy(john) [skolemisation 30,39]
42. ! [X0] : ((~quiet(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | quiet(X0))) [nnf transformation 5]
43. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 6]
44. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | patient(X0) | tall(X0))) [flattening 43]
45. ! [X0] : (((~humble(X0) & ~generous(X0)) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 7]
46. ! [X0] : (((~humble(X0) & ~generous(X0)) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | humble(X0) | generous(X0))) [flattening 45]
47. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~rich(X0)) & (rich(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 9]
53. ((~strong(john) & curious(john)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (strong(john) | ~curious(john))) [nnf transformation 12]
54. ((~strong(john) & curious(john)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (? [X0] : ((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | strong(john) | ~curious(john)) [flattening 53]
55. ((~strong(john) & curious(john)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (? [X1] : ((~old(X1) | rich(X1)) & (old(X1) | ~rich(X1))) | strong(john) | ~curious(john)) [rectify 54]
56. ? [X1] : ((~old(X1) | rich(X1)) & (old(X1) | ~rich(X1))) => ((~old(sK2) | rich(sK2)) & (old(sK2) | ~rich(sK2))) [choice axiom]
57. ((~strong(john) & curious(john)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (((~old(sK2) | rich(sK2)) & (old(sK2) | ~rich(sK2))) | strong(john) | ~curious(john)) [skolemisation 55,56]
62. ! [X0] : (((brave(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | (~brave(X0) | ~humble(X0)))) [nnf transformation 15]
63. ! [X0] : (((brave(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | ~brave(X0) | ~humble(X0))) [flattening 62]
65. ? [X0] : (happy(X0) & ~kind(X0)) => (happy(sK4) & ~kind(sK4)) [choice axiom]
66. happy(sK4) & ~kind(sK4) [skolemisation 17,65]
73. ~kind(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 38]
75. humble(sK0) | happy(john) [cnf transformation 40]
76. ~wise(sK0) | happy(john) [cnf transformation 40]
79. ~happy(X0) | tall(X0) | quiet(X0) [cnf transformation 42]
85. ~curious(X0) | ~tall(X0) [cnf transformation 44]
91. ~humble(X0) | wise(X0) [cnf transformation 46]
94. ~brave(X0) | ~old(X0) | rich(X0) [cnf transformation 47]
97. ~rich(X0) | ~brave(X0) | old(X0) [cnf transformation 47]
110. curious(john) | old(X0) | rich(X0) [cnf transformation 57]
111. curious(john) | ~rich(X0) | ~old(X0) [cnf transformation 57]
120. brave(X0) | kind(X0) [cnf transformation 63]
123. ~kind(sK4) [cnf transformation 66]
136. kind(john) [cnf transformation 25]
138. 1 <=> happy(john) [avatar definition]
140. happy(john) <- (1) [avatar component clause 138]
142. 2 <=> wise(sK0) [avatar definition]
145. 1 | ~2 [avatar split clause 76,142,138]
147. 3 <=> humble(sK0) [avatar definition]
149. humble(sK0) <- (3) [avatar component clause 147]
150. 1 | 3 [avatar split clause 75,147,138]
170. 8 <=> curious(john) [avatar definition]
171. curious(john) <- (8) [avatar component clause 170]
211. 15 <=> ! [X0] : (~rich(X0) | ~old(X0)) [avatar definition]
212. ~rich(X0) | ~old(X0) <- (15) [avatar component clause 211]
219. 17 <=> ! [X0] : (old(X0) | rich(X0)) [avatar definition]
220. rich(X0) | old(X0) <- (17) [avatar component clause 219]
222. 15 | 8 [avatar split clause 111,170,211]
223. 17 | 8 [avatar split clause 110,170,219]
266. ~tall(john) <- (8) [resolution 85,171]
267. wise(sK0) <- (3) [resolution 91,149]
270. 2 | ~3 [avatar split clause 267,147,142]
285. ~curious(john) | ~quiet(john) [resolution 73,136]
287. ~quiet(john) <- (8) [subsumption resolution 285,171]
302. tall(john) | quiet(john) <- (1) [resolution 79,140]
312. quiet(john) <- (1, 8) [subsumption resolution 302,266]
313. $false <- (1, 8) [subsumption resolution 312,287]
314. ~1 | ~8 [avatar contradiction clause 313]
341. ~old(X0) | rich(X0) | kind(X0) [resolution 94,120]
342. rich(X0) | kind(X0) <- (17) [subsumption resolution 341,220]
353. ~brave(X1) | old(X1) | old(X1) <- (17) [resolution 97,220]
355. ~brave(X1) | old(X1) <- (17) [duplicate literal removal 353]
431. kind(X2) | ~old(X2) <- (15, 17) [resolution 342,212]
434. old(X0) | kind(X0) <- (17) [resolution 355,120]
435. kind(X0) <- (15, 17) [subsumption resolution 434,431]
436. $false <- (15, 17) [resolution 435,123]
442. ~15 | ~17 [avatar contradiction clause 436]
443. $false [avatar sat refutation 145,150,222,223,270,314,442]
% SZS output end Proof for 2919269157608551396670129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not funny then someone is kind or not tall.
Everyone who is either funny or rich is not quiet or not rich and vice versa.
If fred is either not quiet or not kind then someone is both not brave and brave and vice versa.
If susan is either not wise or not tall then mary is curious and vice versa.
Everyone who is calm or rich is not brave or not happy and vice versa.
Everyone who is both not old and not strong is happy or not tall and vice versa.
Everyone who is creative or not tall is either not kind or brave.
Everyone who is quiet or kind is not tall and vice versa.
If someone is happy or humble then someone is either not humble or not calm and vice versa.
Everyone who is not creative is strong or not generous and vice versa.
If john is curious then someone is both not curious and happy and vice versa.
Everyone who is not happy or not tall is both quiet and wise.
Everyone who is quiet is not patient or not old.
If someone is humble then lucy is funny or not quiet and vice versa.
Everyone who is not kind is either strong or creative.
If lucy is either curious or tall then someone is not happy and vice versa.
Someone is either not creative or not calm.
Fred is both calm and not creative.
Someone is either not brave or not tall.
Lucy is either not kind or humble.
Alice is either not kind or patient.
Mary is kind or wise. | Fred is happy. | contradiction | ((?[X]:((old(X)&~funny(X))))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:((funny(X)<~>rich(X))<=>(~quiet(X)|~rich(X))))&
(((~quiet(fred)<~>~kind(fred)))<=>(?[X]:((~brave(X)&brave(X)))))&
(((~wise(susan)<~>~tall(susan)))<=>(curious(mary)))&
(![X]:((calm(X)|rich(X))<=>(~brave(X)|~happy(X))))&
(![X]:((~old(X)&~strong(X))<=>(happy(X)|~tall(X))))&
(![X]:((creative(X)|~tall(X))=>(~kind(X)<~>brave(X))))&
(![X]:((quiet(X)|kind(X))<=>~tall(X)))&
((?[X]:((happy(X)|humble(X))))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(strong(X)|~generous(X))))&
((curious(john))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:((~happy(X)|~tall(X))=>(quiet(X)&wise(X))))&
(![X]:(quiet(X)=>(~patient(X)|~old(X))))&
((?[X]:(humble(X)))<=>((funny(lucy)|~quiet(lucy))))&
(![X]:(~kind(X)=>(strong(X)<~>creative(X))))&
(((curious(lucy)<~>tall(lucy)))<=>(?[X]:(~happy(X))))&
(?[X]:((~creative(X)<~>~calm(X))))&
((calm(fred)&~creative(fred)))&
(?[X]:((~brave(X)<~>~tall(X))))&
((~kind(lucy)<~>humble(lucy)))&
((~kind(alice)<~>patient(alice)))&
((kind(mary)|wise(mary))) | happy(fred) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 967635020853667218255762
% SZS output start Proof for 967635020853667218255762
3. (~quiet(fred) <~> ~kind(fred)) <=> ? [X0] : (brave(X0) & ~brave(X0)) [input p2]
5. ! [X0] : ((rich(X0) | calm(X0)) <=> (~happy(X0) | ~brave(X0))) [input p4]
6. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~tall(X0) | happy(X0))) [input p5]
7. ! [X0] : ((~tall(X0) | creative(X0)) => (~kind(X0) <~> brave(X0))) [input p6]
8. ! [X0] : ((kind(X0) | quiet(X0)) <=> ~tall(X0)) [input p7]
15. ! [X0] : (~kind(X0) => (strong(X0) <~> creative(X0))) [input p14]
18. ~creative(fred) & calm(fred) [input p17]
23. happy(fred) [input hypothesis]
27. ! [X0] : ((~kind(X0) <~> brave(X0)) | (tall(X0) & ~creative(X0))) [ennf transformation 7]
31. ! [X0] : ((strong(X0) <~> creative(X0)) | kind(X0)) [ennf transformation 15]
37. (((kind(fred) | quiet(fred)) & (~kind(fred) | ~quiet(fred))) | ! [X0] : (~brave(X0) | brave(X0))) & (? [X0] : (brave(X0) & ~brave(X0)) | ((~quiet(fred) | kind(fred)) & (~kind(fred) | quiet(fred)))) [nnf transformation 3]
38. (((kind(fred) | quiet(fred)) & (~kind(fred) | ~quiet(fred))) | ! [X0] : (~brave(X0) | brave(X0))) & (? [X1] : (brave(X1) & ~brave(X1)) | ((~quiet(fred) | kind(fred)) & (~kind(fred) | quiet(fred)))) [rectify 37]
39. ? [X1] : (brave(X1) & ~brave(X1)) => (brave(sK1) & ~brave(sK1)) [choice axiom]
40. (((kind(fred) | quiet(fred)) & (~kind(fred) | ~quiet(fred))) | ! [X0] : (~brave(X0) | brave(X0))) & ((brave(sK1) & ~brave(sK1)) | ((~quiet(fred) | kind(fred)) & (~kind(fred) | quiet(fred)))) [skolemisation 38,39]
42. ! [X0] : (((rich(X0) | calm(X0)) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 5]
43. ! [X0] : ((rich(X0) | calm(X0) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | (~rich(X0) & ~calm(X0)))) [flattening 42]
44. ! [X0] : (((~strong(X0) & ~old(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (strong(X0) | old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~strong(X0) & ~old(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | strong(X0) | old(X0))) [flattening 44]
46. ! [X0] : (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (tall(X0) & ~creative(X0))) [nnf transformation 27]
47. ! [X0] : (((kind(X0) | quiet(X0)) | tall(X0)) & (~tall(X0) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 8]
48. ! [X0] : ((kind(X0) | quiet(X0) | tall(X0)) & (~tall(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 47]
65. ! [X0] : (((~creative(X0) | ~strong(X0)) & (creative(X0) | strong(X0))) | kind(X0)) [nnf transformation 31]
85. ~brave(sK1) | ~kind(fred) | quiet(fred) [cnf transformation 40]
87. brave(sK1) | ~kind(fred) | quiet(fred) [cnf transformation 40]
95. ~happy(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 43]
102. ~strong(X0) | ~happy(X0) [cnf transformation 45]
105. ~kind(X0) | brave(X0) | tall(X0) [cnf transformation 46]
108. ~quiet(X0) | ~tall(X0) [cnf transformation 48]
131. creative(X0) | strong(X0) | kind(X0) [cnf transformation 65]
139. calm(fred) [cnf transformation 18]
140. ~creative(fred) [cnf transformation 18]
148. happy(fred) [cnf transformation 23]
165. 4 <=> kind(fred) [avatar definition]
166. ~kind(fred) <- (~4) [avatar component clause 165]
167. kind(fred) <- (4) [avatar component clause 165]
169. 5 <=> quiet(fred) [avatar definition]
170. quiet(fred) <- (5) [avatar component clause 169]
173. 6 <=> brave(sK1) [avatar definition]
177. 5 | ~4 | 6 [avatar split clause 87,173,165,169]
179. 5 | ~4 | ~6 [avatar split clause 85,173,165,169]
363. ~brave(fred) | ~calm(fred) [resolution 95,148]
367. ~brave(fred) [subsumption resolution 363,139]
460. strong(fred) | kind(fred) [resolution 131,140]
467. strong(fred) <- (~4) [subsumption resolution 460,166]
478. ~happy(fred) <- (~4) [resolution 467,102]
479. $false <- (~4) [subsumption resolution 478,148]
480. 4 [avatar contradiction clause 479]
486. brave(fred) | tall(fred) <- (4) [resolution 167,105]
487. tall(fred) <- (4) [subsumption resolution 486,367]
489. ~tall(fred) <- (5) [resolution 170,108]
490. $false <- (4, 5) [subsumption resolution 489,487]
491. ~4 | ~5 [avatar contradiction clause 490]
492. $false [avatar sat refutation 177,179,480,491]
% SZS output end Proof for 967635020853667218255762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is both tall and patient and vice versa.
If paul is either not rich or funny then someone is either kind or rich and vice versa.
Everyone who is both not curious and not wise is both curious and not rich and vice versa.
If someone is happy or not old then someone is both not happy and quiet and vice versa.
Everyone who is either generous or brave is strong and vice versa.
Everyone who is not curious or calm is old and vice versa.
Everyone who is not old is both not wise and not kind and vice versa.
Everyone who is both not strong and not rich is not wise and vice versa.
Everyone who is both not patient and tall is not curious.
If someone is not calm then susan is old or not rich and vice versa.
If someone is not humble or creative then someone is wise.
If fred is either not creative or humble then paul is not creative or generous and vice versa.
Everyone who is not quiet or not creative is not patient.
If fred is either not brave or curious then someone is either old or happy and vice versa.
Everyone who is both not curious and brave is both quiet and brave and vice versa.
Everyone who is patient or not rich is either strong or not calm.
Alice is not generous or funny.
Susan is kind or not calm.
Someone is curious.
Someone is either creative or humble.
Susan is either not brave or not happy.
Someone is either not strong or not generous.
Paul is either not humble or quiet.
Someone is tall. | Alice is not calm. | neutral | ((?[X]:(~wise(X)))<=>(?[X]:((tall(X)&patient(X)))))&
(((~rich(paul)<~>funny(paul)))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(curious(X)&~rich(X))))&
((?[X]:((happy(X)|~old(X))))<=>(?[X]:((~happy(X)&quiet(X)))))&
(![X]:((generous(X)<~>brave(X))<=>strong(X)))&
(![X]:((~curious(X)|calm(X))<=>old(X)))&
(![X]:(~old(X)<=>(~wise(X)&~kind(X))))&
(![X]:((~strong(X)&~rich(X))<=>~wise(X)))&
(![X]:((~patient(X)&tall(X))=>~curious(X)))&
((?[X]:(~calm(X)))<=>((old(susan)|~rich(susan))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:(wise(X))))&
(((~creative(fred)<~>humble(fred)))<=>((~creative(paul)|generous(paul))))&
(![X]:((~quiet(X)|~creative(X))=>~patient(X)))&
(((~brave(fred)<~>curious(fred)))<=>(?[X]:((old(X)<~>happy(X)))))&
(![X]:((~curious(X)&brave(X))<=>(quiet(X)&brave(X))))&
(![X]:((patient(X)|~rich(X))=>(strong(X)<~>~calm(X))))&
((~generous(alice)|funny(alice)))&
((kind(susan)|~calm(susan)))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)<~>humble(X))))&
((~brave(susan)<~>~happy(susan)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~humble(paul)<~>quiet(paul)))&
(?[X]:(tall(X))) | ~calm(alice) | [] | null | 0 |
Everyone who is either not curious or happy is generous or wise and vice versa.
Everyone who is not rich or not generous is not creative or not curious.
If someone is calm or kind then someone is patient or not calm and vice versa.
Everyone who is not tall is both not brave and humble.
If lucy is both funny and not tall then alice is not curious or not wise and vice versa.
Everyone who is either curious or not humble is both not strong and not curious and vice versa.
Everyone who is either not quiet or patient is either not wise or not creative and vice versa.
If someone is either humble or not kind then someone is either not calm or kind and vice versa.
Everyone who is not kind or not curious is creative and vice versa.
Everyone who is kind or not strong is not humble and vice versa.
Everyone who is not creative is either not happy or humble and vice versa.
Everyone who is either not creative or rich is tall or quiet.
If john is either old or kind then someone is either humble or not calm and vice versa.
Everyone who is both rich and not kind is both patient and old and vice versa.
Everyone who is not rich or brave is tall and vice versa.
Everyone who is either not funny or not calm is either not tall or not funny.
Paul is both tall and happy.
Alice is generous or creative.
Lucy is both patient and not funny.
Someone is either not quiet or not happy.
Fred is kind.
Someone is funny or creative.
Someone is not humble.
Lucy is not rich or not generous. | Lucy is not patient. | contradiction | (![X]:((~curious(X)<~>happy(X))<=>(generous(X)|wise(X))))&
(![X]:((~rich(X)|~generous(X))=>(~creative(X)|~curious(X))))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:(~tall(X)=>(~brave(X)&humble(X))))&
(((funny(lucy)&~tall(lucy)))<=>((~curious(alice)|~wise(alice))))&
(![X]:((curious(X)<~>~humble(X))<=>(~strong(X)&~curious(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~wise(X)<~>~creative(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((~kind(X)|~curious(X))<=>creative(X)))&
(![X]:((kind(X)|~strong(X))<=>~humble(X)))&
(![X]:(~creative(X)<=>(~happy(X)<~>humble(X))))&
(![X]:((~creative(X)<~>rich(X))=>(tall(X)|quiet(X))))&
(((old(john)<~>kind(john)))<=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((rich(X)&~kind(X))<=>(patient(X)&old(X))))&
(![X]:((~rich(X)|brave(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~calm(X))=>(~tall(X)<~>~funny(X))))&
((tall(paul)&happy(paul)))&
((generous(alice)|creative(alice)))&
((patient(lucy)&~funny(lucy)))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(kind(fred))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:(~humble(X)))&
((~rich(lucy)|~generous(lucy))) | ~patient(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 978936328234058199440731
% SZS output start Proof for 978936328234058199440731
19. ~funny(lucy) & patient(lucy) [input p18]
25. ~patient(lucy) [input hypothesis]
148. patient(lucy) [cnf transformation 19]
156. ~patient(lucy) [cnf transformation 25]
319. $false [subsumption resolution 156,148]
% SZS output end Proof for 978936328234058199440731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not old is kind or creative. Everyone who is humble or patient is not tall. If someone is not brave then someone is not tall or funny and vice versa. Everyone who is generous or not generous is both old and patient. If someone is calm then someone is not creative and vice versa. If mary is either curious or not wise then susan is not humble or not funny. If fred is tall then susan is either kind or not humble and vice versa. If fred is not tall then lucy is not wise or not strong. Everyone who is not humble or generous is not funny or not humble and vice versa. Everyone who is either not humble or not curious is calm. Everyone who is either funny or old is either calm or curious. Everyone who is both quiet and not old is both calm and patient. Everyone who is calm or rich is either not brave or not humble. Everyone who is either patient or not kind is both curious and old and vice versa. Everyone who is not calm or not patient is both not curious and not quiet and vice versa. Everyone who is not curious or not happy is not quiet and vice versa. Paul is curious or not rich. Mary is not brave or not old. Someone is not old or not brave. Someone is either old or generous. Alice is either not happy or brave. Someone is curious. Alice is either generous or not calm. Paul is not patient or not rich. | Susan is brave. | entailment | (![X]:((~strong(X)<~>~old(X))=>(kind(X)|creative(X))))&
(![X]:((humble(X)|patient(X))=>~tall(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)|funny(X)))))&
(![X]:((generous(X)|~generous(X))=>(old(X)&patient(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~creative(X))))&
(((curious(mary)<~>~wise(mary)))=>((~humble(susan)|~funny(susan))))&
((tall(fred))<=>((kind(susan)<~>~humble(susan))))&
((~tall(fred))=>((~wise(lucy)|~strong(lucy))))&
(![X]:((~humble(X)|generous(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~humble(X)<~>~curious(X))=>calm(X)))&
(![X]:((funny(X)<~>old(X))=>(calm(X)<~>curious(X))))&
(![X]:((quiet(X)&~old(X))=>(calm(X)&patient(X))))&
(![X]:((calm(X)|rich(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((patient(X)<~>~kind(X))<=>(curious(X)&old(X))))&
(![X]:((~calm(X)|~patient(X))<=>(~curious(X)&~quiet(X))))&
(![X]:((~curious(X)|~happy(X))<=>~quiet(X)))&
((curious(paul)|~rich(paul)))&
((~brave(mary)|~old(mary)))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((old(X)<~>generous(X))))&
((~happy(alice)<~>brave(alice)))&
(?[X]:(curious(X)))&
((generous(alice)<~>~calm(alice)))&
((~patient(paul)|~rich(paul))) | brave(susan) | [
"p1",
"p3",
"p6",
"p9",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7636605882290654979180629
% SZS output start Proof for 7636605882290654979180629
2. ! [X0] : ((patient(X0) | humble(X0)) => ~tall(X0)) [input p1]
4. ! [X0] : ((~generous(X0) | generous(X0)) => (patient(X0) & old(X0))) [input p3]
7. tall(fred) <=> (kind(susan) <~> ~humble(susan)) [input p6]
10. ! [X0] : ((~humble(X0) <~> ~curious(X0)) => calm(X0)) [input p9]
13. ! [X0] : ((rich(X0) | calm(X0)) => (~brave(X0) <~> ~humble(X0))) [input p12]
14. ! [X0] : ((patient(X0) <~> ~kind(X0)) <=> (old(X0) & curious(X0))) [input p13]
15. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (~quiet(X0) & ~curious(X0))) [input p14]
16. ! [X0] : ((~happy(X0) | ~curious(X0)) <=> ~quiet(X0)) [input p15]
25. ~brave(susan) [input hypothesis]
30. ! [X0] : (calm(X0) => (~brave(X0) <~> ~humble(X0))) [pure predicate removal 13]
33. ! [X0] : (~tall(X0) | (~patient(X0) & ~humble(X0))) [ennf transformation 2]
34. ! [X0] : ((patient(X0) & old(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 4]
39. ! [X0] : (calm(X0) | (~humble(X0) <=> ~curious(X0))) [ennf transformation 10]
43. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | ~calm(X0)) [ennf transformation 30]
56. (tall(fred) | ((kind(susan) | humble(susan)) & (~humble(susan) | ~kind(susan)))) & (((humble(susan) | ~kind(susan)) & (~humble(susan) | kind(susan))) | ~tall(fred)) [nnf transformation 7]
59. ! [X0] : (calm(X0) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) [nnf transformation 39]
61. ! [X0] : (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | ~calm(X0)) [nnf transformation 43]
62. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [nnf transformation 14]
63. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [flattening 62]
64. ! [X0] : (((~patient(X0) | ~calm(X0)) | (quiet(X0) | curious(X0))) & ((~quiet(X0) & ~curious(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 15]
65. ! [X0] : ((~patient(X0) | ~calm(X0) | quiet(X0) | curious(X0)) & ((~quiet(X0) & ~curious(X0)) | (patient(X0) & calm(X0)))) [flattening 64]
66. ! [X0] : (((~happy(X0) | ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (happy(X0) & curious(X0)))) [nnf transformation 16]
67. ! [X0] : ((~happy(X0) | ~curious(X0) | quiet(X0)) & (~quiet(X0) | (happy(X0) & curious(X0)))) [flattening 66]
80. ~tall(X0) | ~patient(X0) [cnf transformation 33]
84. old(X0) | ~generous(X0) [cnf transformation 34]
85. generous(X0) | old(X0) [cnf transformation 34]
86. patient(X0) | ~generous(X0) [cnf transformation 34]
87. generous(X0) | patient(X0) [cnf transformation 34]
94. tall(fred) | ~humble(susan) | ~kind(susan) [cnf transformation 56]
95. tall(fred) | kind(susan) | humble(susan) [cnf transformation 56]
102. ~humble(X0) | calm(X0) | curious(X0) [cnf transformation 59]
110. ~calm(X0) | brave(X0) | humble(X0) [cnf transformation 61]
111. curious(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 63]
116. kind(X0) | ~patient(X0) | ~old(X0) | ~curious(X0) [cnf transformation 63]
117. ~curious(X0) | calm(X0) [cnf transformation 65]
121. ~patient(X0) | ~calm(X0) | quiet(X0) | curious(X0) [cnf transformation 65]
122. ~quiet(X0) | curious(X0) [cnf transformation 67]
134. ~brave(susan) [cnf transformation 25]
159. patient(X0) [subsumption resolution 86,87]
160. old(X0) [subsumption resolution 84,85]
186. 13 <=> humble(susan) [avatar definition]
187. humble(susan) <- (13) [avatar component clause 186]
188. ~humble(susan) <- (~13) [avatar component clause 186]
196. 15 <=> kind(susan) [avatar definition]
197. ~kind(susan) <- (~15) [avatar component clause 196]
198. kind(susan) <- (15) [avatar component clause 196]
200. 16 <=> tall(fred) [avatar definition]
202. tall(fred) <- (16) [avatar component clause 200]
203. 13 | 15 | 16 [avatar split clause 95,200,196,186]
204. ~15 | ~13 | 16 [avatar split clause 94,200,186,196]
218. kind(X0) | ~old(X0) | ~curious(X0) [subsumption resolution 116,159]
219. ~curious(X0) | kind(X0) [subsumption resolution 218,160]
220. ~kind(X0) | curious(X0) [subsumption resolution 111,159]
221. ~calm(X0) | quiet(X0) | curious(X0) [subsumption resolution 121,159]
260. calm(susan) | curious(susan) <- (13) [resolution 102,187]
261. calm(susan) <- (13) [subsumption resolution 260,117]
318. quiet(susan) | curious(susan) <- (13) [resolution 221,261]
321. curious(susan) <- (13) [subsumption resolution 318,122]
343. kind(susan) <- (13) [resolution 321,219]
348. $false <- (13, ~15) [subsumption resolution 343,197]
349. ~13 | 15 [avatar contradiction clause 348]
350. curious(susan) <- (15) [resolution 198,220]
354. calm(susan) <- (15) [resolution 350,117]
380. brave(susan) | humble(susan) <- (15) [resolution 354,110]
382. humble(susan) <- (15) [subsumption resolution 380,134]
383. $false <- (~13, 15) [subsumption resolution 382,188]
384. 13 | ~15 [avatar contradiction clause 383]
385. ~patient(fred) <- (16) [resolution 202,80]
387. $false <- (16) [subsumption resolution 385,159]
388. ~16 [avatar contradiction clause 387]
389. $false [avatar sat refutation 203,204,349,384,388]
% SZS output end Proof for 7636605882290654979180629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is brave and vice versa.
Everyone who is not strong or patient is both not calm and rich and vice versa.
Everyone who is both not quiet and not happy is either calm or patient.
If someone is both not rich and not happy then someone is creative and vice versa.
If mary is kind or creative then fred is not brave and vice versa.
Everyone who is not kind is both not generous and not old.
If someone is either not brave or not wise then john is both tall and wise and vice versa.
If lucy is happy or kind then someone is both happy and rich.
Everyone who is not tall is both wise and not calm and vice versa.
If alice is both rich and kind then alice is not rich and vice versa.
If someone is both not curious and humble then someone is both patient and humble.
Everyone who is both quiet and not calm is not old or humble.
If someone is either not wise or generous then susan is both old and wise and vice versa.
If susan is wise then paul is both rich and strong and vice versa.
Everyone who is either curious or wise is not curious or not calm and vice versa.
If someone is either not calm or humble then susan is both generous and tall and vice versa.
Someone is both happy and tall.
Someone is either not patient or generous.
Fred is strong or brave.
Someone is old.
John is either not calm or not funny.
Mary is either wise or strong. | John is happy. | neutral | (![X]:(wise(X)<=>brave(X)))&
(![X]:((~strong(X)|patient(X))<=>(~calm(X)&rich(X))))&
(![X]:((~quiet(X)&~happy(X))=>(calm(X)<~>patient(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>(?[X]:(creative(X))))&
(((kind(mary)|creative(mary)))<=>(~brave(fred)))&
(![X]:(~kind(X)=>(~generous(X)&~old(X))))&
((?[X]:((~brave(X)<~>~wise(X))))<=>((tall(john)&wise(john))))&
(((happy(lucy)|kind(lucy)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(~tall(X)<=>(wise(X)&~calm(X))))&
(((rich(alice)&kind(alice)))<=>(~rich(alice)))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((patient(X)&humble(X)))))&
(![X]:((quiet(X)&~calm(X))=>(~old(X)|humble(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>((old(susan)&wise(susan))))&
((wise(susan))<=>((rich(paul)&strong(paul))))&
(![X]:((curious(X)<~>wise(X))<=>(~curious(X)|~calm(X))))&
((?[X]:((~calm(X)<~>humble(X))))<=>((generous(susan)&tall(susan))))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((strong(fred)|brave(fred)))&
(?[X]:(old(X)))&
((~calm(john)<~>~funny(john)))&
((wise(mary)<~>strong(mary))) | happy(john) | [] | null | 0 |
Everyone who is creative is both humble and brave. If someone is both not strong and old then susan is not creative. Everyone who is not strong or quiet is either curious or old. Everyone who is both old and generous is not kind or not rich and vice versa. If alice is tall then someone is either not generous or not rich and vice versa. If fred is both funny and not quiet then lucy is either not generous or not wise. Everyone who is not quiet or old is either not calm or not creative and vice versa. Everyone who is both not old and curious is not wise or not brave and vice versa. Everyone who is wise or patient is both not generous and patient and vice versa. If someone is both not happy and not old then fred is strong or not curious. Everyone who is tall or not generous is brave. Everyone who is both not brave and kind is quiet or humble. If someone is not curious or curious then someone is not rich or not curious. Everyone who is both generous and patient is not humble and vice versa. If someone is both quiet and not old then someone is not happy or not kind. Everyone who is not funny or not patient is both not rich and kind and vice versa. Someone is either not wise or not generous. Someone is either not creative or not curious. Someone is either not quiet or calm. Someone is either quiet or not rich. | Fred is not brave. | contradiction | (![X]:(creative(X)=>(humble(X)&brave(X))))&
((?[X]:((~strong(X)&old(X))))=>(~creative(susan)))&
(![X]:((~strong(X)|quiet(X))=>(curious(X)<~>old(X))))&
(![X]:((old(X)&generous(X))<=>(~kind(X)|~rich(X))))&
((tall(alice))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((funny(fred)&~quiet(fred)))=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:((~quiet(X)|old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~old(X)&curious(X))<=>(~wise(X)|~brave(X))))&
(![X]:((wise(X)|patient(X))<=>(~generous(X)&patient(X))))&
((?[X]:((~happy(X)&~old(X))))=>((strong(fred)|~curious(fred))))&
(![X]:((tall(X)|~generous(X))=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(~rich(X)&kind(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:((quiet(X)<~>~rich(X)))) | ~brave(fred) | [
"p3",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7871360545705985135109452
% SZS output start Proof for 7871360545705985135109452
4. ! [X0] : ((generous(X0) & old(X0)) <=> (~rich(X0) | ~kind(X0))) [input p3]
8. ! [X0] : ((curious(X0) & ~old(X0)) <=> (~brave(X0) | ~wise(X0))) [input p7]
9. ! [X0] : ((patient(X0) | wise(X0)) <=> (patient(X0) & ~generous(X0))) [input p8]
11. ! [X0] : ((~generous(X0) | tall(X0)) => brave(X0)) [input p10]
16. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (kind(X0) & ~rich(X0))) [input p15]
21. ~brave(fred) [input hypothesis]
33. ! [X0] : (brave(X0) | (generous(X0) & ~tall(X0))) [ennf transformation 11]
40. ! [X0] : (((generous(X0) & old(X0)) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | (~generous(X0) | ~old(X0)))) [nnf transformation 4]
41. ! [X0] : (((generous(X0) & old(X0)) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | ~generous(X0) | ~old(X0))) [flattening 40]
49. ! [X0] : (((curious(X0) & ~old(X0)) | (brave(X0) & wise(X0))) & ((~brave(X0) | ~wise(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 8]
50. ! [X0] : (((curious(X0) & ~old(X0)) | (brave(X0) & wise(X0))) & (~brave(X0) | ~wise(X0) | ~curious(X0) | old(X0))) [flattening 49]
51. ! [X0] : (((patient(X0) | wise(X0)) | (~patient(X0) | generous(X0))) & ((patient(X0) & ~generous(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 9]
52. ! [X0] : ((patient(X0) | wise(X0) | ~patient(X0) | generous(X0)) & ((patient(X0) & ~generous(X0)) | (~patient(X0) & ~wise(X0)))) [flattening 51]
56. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 16]
57. ! [X0] : ((~patient(X0) | ~funny(X0) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | (patient(X0) & funny(X0)))) [flattening 56]
76. rich(X0) | old(X0) [cnf transformation 41]
93. ~old(X0) | brave(X0) [cnf transformation 50]
97. ~patient(X0) | ~generous(X0) [cnf transformation 52]
102. generous(X0) | brave(X0) [cnf transformation 33]
108. ~rich(X0) | patient(X0) [cnf transformation 57]
120. ~brave(fred) [cnf transformation 21]
241. patient(X1) | old(X1) [resolution 108,76]
361. ~generous(X1) | old(X1) [resolution 241,97]
400. old(X0) | brave(X0) [resolution 361,102]
403. brave(X0) [subsumption resolution 400,93]
505. $false [resolution 403,120]
% SZS output end Proof for 7871360545705985135109452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not generous or not patient then susan is both not old and happy. Everyone who is funny or happy is both not wise and not humble. If john is both curious and not creative then someone is either creative or not kind. If john is not humble then someone is not creative or quiet. Everyone who is not wise is either not kind or not humble and vice versa. If lucy is both patient and not patient then someone is either tall or patient. Everyone who is tall or creative is either curious or funny. If someone is brave then someone is generous or not creative. Everyone who is either not generous or not humble is either kind or not tall. Everyone who is both old and not creative is both rich and generous and vice versa. Everyone who is not patient or not happy is funny. Everyone who is either not strong or happy is both old and calm. Everyone who is either not brave or tall is both rich and not patient. Everyone who is either strong or not curious is either funny or quiet and vice versa. Everyone who is both not curious and tall is quiet or not creative and vice versa. If someone is either not tall or old then paul is both wise and kind. Someone is rich or not humble. Alice is either not happy or wise. Alice is not patient. Someone is both patient and not quiet. Someone is not curious or creative. Someone is either strong or tall. | Susan is not strong. | neutral | (((~generous(mary)|~patient(mary)))=>((~old(susan)&happy(susan))))&
(![X]:((funny(X)|happy(X))=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
((~humble(john))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~humble(X))))&
(((patient(lucy)&~patient(lucy)))=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((tall(X)|creative(X))=>(curious(X)<~>funny(X))))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(kind(X)<~>~tall(X))))&
(![X]:((old(X)&~creative(X))<=>(rich(X)&generous(X))))&
(![X]:((~patient(X)|~happy(X))=>funny(X)))&
(![X]:((~strong(X)<~>happy(X))=>(old(X)&calm(X))))&
(![X]:((~brave(X)<~>tall(X))=>(rich(X)&~patient(X))))&
(![X]:((strong(X)<~>~curious(X))<=>(funny(X)<~>quiet(X))))&
(![X]:((~curious(X)&tall(X))<=>(quiet(X)|~creative(X))))&
((?[X]:((~tall(X)<~>old(X))))=>((wise(paul)&kind(paul))))&
(?[X]:((rich(X)|~humble(X))))&
((~happy(alice)<~>wise(alice)))&
(~patient(alice))&
(?[X]:((patient(X)&~quiet(X))))&
(?[X]:((~curious(X)|creative(X))))&
(?[X]:((strong(X)<~>tall(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is both creative and funny is both brave and not creative. Everyone who is both not rich and creative is both quiet and strong. Everyone who is patient is creative or not old. Everyone who is not kind is curious or not funny and vice versa. If someone is both not strong and strong then someone is funny or creative and vice versa. Everyone who is quiet is both not wise and generous and vice versa. If lucy is either not happy or not generous then someone is not tall or not generous and vice versa. If alice is not funny or not wise then someone is either creative or old. If alice is both happy and rich then someone is not humble or wise and vice versa. If someone is happy or curious then lucy is either not brave or wise. Everyone who is either tall or not rich is either not happy or not brave and vice versa. Everyone who is brave is either happy or not kind. If lucy is both not curious and not tall then alice is not strong and vice versa. Everyone who is both quiet and tall is either patient or rich and vice versa. Everyone who is kind is tall. Everyone who is either not kind or funny is old and vice versa. Lucy is either tall or happy. Alice is happy. John is not wise. Fred is either not brave or curious. Someone is both not happy and curious. Someone is either not happy or rich. Someone is not wise. | Alice is strong. | neutral | (![X]:((creative(X)&funny(X))=>(brave(X)&~creative(X))))&
(![X]:((~rich(X)&creative(X))=>(quiet(X)&strong(X))))&
(![X]:(patient(X)=>(creative(X)|~old(X))))&
(![X]:(~kind(X)<=>(curious(X)|~funny(X))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(![X]:(quiet(X)<=>(~wise(X)&generous(X))))&
(((~happy(lucy)<~>~generous(lucy)))<=>(?[X]:((~tall(X)|~generous(X)))))&
(((~funny(alice)|~wise(alice)))=>(?[X]:((creative(X)<~>old(X)))))&
(((happy(alice)&rich(alice)))<=>(?[X]:((~humble(X)|wise(X)))))&
((?[X]:((happy(X)|curious(X))))=>((~brave(lucy)<~>wise(lucy))))&
(![X]:((tall(X)<~>~rich(X))<=>(~happy(X)<~>~brave(X))))&
(![X]:(brave(X)=>(happy(X)<~>~kind(X))))&
(((~curious(lucy)&~tall(lucy)))<=>(~strong(alice)))&
(![X]:((quiet(X)&tall(X))<=>(patient(X)<~>rich(X))))&
(![X]:(kind(X)=>tall(X)))&
(![X]:((~kind(X)<~>funny(X))<=>old(X)))&
((tall(lucy)<~>happy(lucy)))&
(happy(alice))&
(~wise(john))&
((~brave(fred)<~>curious(fred)))&
(?[X]:((~happy(X)&curious(X))))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~wise(X))) | strong(alice) | [] | null | 0 |
If someone is tall or kind then alice is both not patient and not strong and vice versa. Everyone who is both not quiet and not curious is kind or curious and vice versa. If someone is old then fred is not humble and vice versa. Everyone who is tall is generous and vice versa. If someone is both curious and funny then someone is either curious or not humble and vice versa. If paul is both not wise and not kind then someone is not rich or not calm and vice versa. Everyone who is either not humble or not old is not generous. If alice is old or not calm then susan is both curious and not tall. Everyone who is old is strong or brave. Everyone who is not old is both patient and rich and vice versa. Everyone who is both not humble and not tall is wise or not tall. If alice is not happy then paul is both funny and calm. If mary is either not rich or patient then someone is both not happy and calm and vice versa. If lucy is not humble then alice is generous or not quiet. If someone is not calm or not quiet then someone is not brave or not strong. Everyone who is both not happy and strong is either happy or not quiet. Mary is quiet. Fred is either not patient or not funny. Someone is both happy and not kind. Paul is both not wise and brave. Someone is calm or not old. | Lucy is humble. | entailment | ((?[X]:((tall(X)|kind(X))))<=>((~patient(alice)&~strong(alice))))&
(![X]:((~quiet(X)&~curious(X))<=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>(~humble(fred)))&
(![X]:(tall(X)<=>generous(X)))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(((~wise(paul)&~kind(paul)))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~old(X))=>~generous(X)))&
(((old(alice)|~calm(alice)))=>((curious(susan)&~tall(susan))))&
(![X]:(old(X)=>(strong(X)|brave(X))))&
(![X]:(~old(X)<=>(patient(X)&rich(X))))&
(![X]:((~humble(X)&~tall(X))=>(wise(X)|~tall(X))))&
((~happy(alice))=>((funny(paul)&calm(paul))))&
(((~rich(mary)<~>patient(mary)))<=>(?[X]:((~happy(X)&calm(X)))))&
((~humble(lucy))=>((generous(alice)|~quiet(alice))))&
((?[X]:((~calm(X)|~quiet(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((~happy(X)&strong(X))=>(happy(X)<~>~quiet(X))))&
(quiet(mary))&
((~patient(fred)<~>~funny(fred)))&
(?[X]:((happy(X)&~kind(X))))&
((~wise(paul)&brave(paul)))&
(?[X]:((calm(X)|~old(X)))) | humble(lucy) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8738487261636976744635926
% SZS output start Proof for 8738487261636976744635926
2. ! [X0] : ((~curious(X0) & ~quiet(X0)) <=> (curious(X0) | kind(X0))) [input p1]
5. ? [X0] : (funny(X0) & curious(X0)) <=> ? [X0] : (curious(X0) <~> ~humble(X0)) [input p4]
22. ~humble(lucy) [input hypothesis]
23. ? [X0] : (funny(X0) & curious(X0)) <=> ? [X1] : (curious(X1) <~> ~humble(X1)) [rectify 5]
42. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (~curious(X0) & ~kind(X0))) & ((curious(X0) | kind(X0)) | (curious(X0) | quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (~curious(X0) & ~kind(X0))) & (curious(X0) | kind(X0) | curious(X0) | quiet(X0))) [flattening 42]
49. (? [X0] : (funny(X0) & curious(X0)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (? [X1] : ((humble(X1) | ~curious(X1)) & (~humble(X1) | curious(X1))) | ! [X0] : (~funny(X0) | ~curious(X0))) [nnf transformation 23]
50. (? [X0] : (funny(X0) & curious(X0)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (? [X2] : ((humble(X2) | ~curious(X2)) & (~humble(X2) | curious(X2))) | ! [X3] : (~funny(X3) | ~curious(X3))) [rectify 49]
51. ? [X0] : (funny(X0) & curious(X0)) => (funny(sK2) & curious(sK2)) [choice axiom]
52. ? [X2] : ((humble(X2) | ~curious(X2)) & (~humble(X2) | curious(X2))) => ((humble(sK3) | ~curious(sK3)) & (~humble(sK3) | curious(sK3))) [choice axiom]
53. ((funny(sK2) & curious(sK2)) | ! [X1] : ((curious(X1) | humble(X1)) & (~humble(X1) | ~curious(X1)))) & (((humble(sK3) | ~curious(sK3)) & (~humble(sK3) | curious(sK3))) | ! [X3] : (~funny(X3) | ~curious(X3))) [skolemisation 50,52,51]
84. ~curious(X0) | ~curious(X0) [cnf transformation 43]
92. curious(sK2) | curious(X1) | humble(X1) [cnf transformation 53]
132. ~humble(lucy) [cnf transformation 22]
135. ~curious(X0) [duplicate literal removal 84]
179. 10 <=> ! [X1] : humble(X1) [avatar definition]
180. humble(X1) <- (10) [avatar component clause 179]
186. curious(X1) | humble(X1) [subsumption resolution 92,135]
187. humble(X1) [subsumption resolution 186,135]
188. 10 [avatar split clause 187,179]
274. 29 <=> humble(lucy) [avatar definition]
275. ~humble(lucy) <- (~29) [avatar component clause 274]
319. ~29 [avatar split clause 132,274]
324. $false <- (10, ~29) [resolution 275,180]
325. ~10 | 29 [avatar contradiction clause 324]
326. $false [avatar sat refutation 188,319,325]
% SZS output end Proof for 8738487261636976744635926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not generous is both strong and not tall and vice versa.
If someone is both generous and happy then lucy is rich.
If mary is not creative or not curious then someone is either not curious or not creative.
Everyone who is both tall and not rich is both not quiet and happy and vice versa.
Everyone who is wise is patient and vice versa.
Everyone who is not tall is not rich.
If lucy is either not humble or not patient then someone is wise or not strong.
Everyone who is not kind or creative is either strong or curious.
If john is not strong then lucy is both not funny and not brave.
Everyone who is patient or old is funny and vice versa.
Everyone who is either creative or curious is rich and vice versa.
Everyone who is not calm is either not wise or funny and vice versa.
Everyone who is wise is both kind and patient.
Everyone who is not kind is happy.
If john is not brave or kind then lucy is either tall or rich and vice versa.
If mary is either funny or not kind then someone is not brave and vice versa.
John is both happy and creative.
Lucy is either strong or not humble.
Someone is kind.
Someone is not tall or generous.
Someone is both not wise and tall.
Someone is either happy or rich.
Someone is wise or patient.
Lucy is not strong or not calm. | Lucy is not strong. | neutral | (![X]:((generous(X)&~generous(X))<=>(strong(X)&~tall(X))))&
((?[X]:((generous(X)&happy(X))))=>(rich(lucy)))&
(((~creative(mary)|~curious(mary)))=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((tall(X)&~rich(X))<=>(~quiet(X)&happy(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:(~tall(X)=>~rich(X)))&
(((~humble(lucy)<~>~patient(lucy)))=>(?[X]:((wise(X)|~strong(X)))))&
(![X]:((~kind(X)|creative(X))=>(strong(X)<~>curious(X))))&
((~strong(john))=>((~funny(lucy)&~brave(lucy))))&
(![X]:((patient(X)|old(X))<=>funny(X)))&
(![X]:((creative(X)<~>curious(X))<=>rich(X)))&
(![X]:(~calm(X)<=>(~wise(X)<~>funny(X))))&
(![X]:(wise(X)=>(kind(X)&patient(X))))&
(![X]:(~kind(X)=>happy(X)))&
(((~brave(john)|kind(john)))<=>((tall(lucy)<~>rich(lucy))))&
(((funny(mary)<~>~kind(mary)))<=>(?[X]:(~brave(X))))&
((happy(john)&creative(john)))&
((strong(lucy)<~>~humble(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((wise(X)|patient(X))))&
((~strong(lucy)|~calm(lucy))) | ~strong(lucy) | [] | null | 0 |
Everyone who is wise or not funny is both tall and not happy and vice versa. Everyone who is both generous and humble is not generous and vice versa. Everyone who is both funny and patient is not old or not happy and vice versa. Everyone who is not happy is both not funny and not creative and vice versa. If someone is not creative or patient then someone is either brave or not patient. If susan is creative then someone is not tall or wise and vice versa. Everyone who is patient is either not funny or not strong. Everyone who is patient is either not funny or kind and vice versa. If someone is not humble then someone is both not brave and happy. If john is not curious then lucy is both wise and strong. Everyone who is either patient or not happy is generous or quiet and vice versa. Everyone who is either not strong or not humble is both not patient and not rich. If alice is rich then susan is either tall or not tall and vice versa. If someone is curious then lucy is not happy or not curious. If someone is either not funny or not rich then someone is not patient. If paul is wise then alice is quiet. Someone is tall or funny. John is either not rich or quiet. Mary is old or patient. Paul is either tall or not kind. Someone is either tall or not wise. | Alice is not kind. | contradiction | (![X]:((wise(X)|~funny(X))<=>(tall(X)&~happy(X))))&
(![X]:((generous(X)&humble(X))<=>~generous(X)))&
(![X]:((funny(X)&patient(X))<=>(~old(X)|~happy(X))))&
(![X]:(~happy(X)<=>(~funny(X)&~creative(X))))&
((?[X]:((~creative(X)|patient(X))))=>(?[X]:((brave(X)<~>~patient(X)))))&
((creative(susan))<=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:(patient(X)=>(~funny(X)<~>~strong(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~brave(X)&happy(X)))))&
((~curious(john))=>((wise(lucy)&strong(lucy))))&
(![X]:((patient(X)<~>~happy(X))<=>(generous(X)|quiet(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(~patient(X)&~rich(X))))&
((rich(alice))<=>((tall(susan)<~>~tall(susan))))&
((?[X]:(curious(X)))=>((~happy(lucy)|~curious(lucy))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:(~patient(X))))&
((wise(paul))=>(quiet(alice)))&
(?[X]:((tall(X)|funny(X))))&
((~rich(john)<~>quiet(john)))&
((old(mary)|patient(mary)))&
((tall(paul)<~>~kind(paul)))&
(?[X]:((tall(X)<~>~wise(X)))) | ~kind(alice) | [
"p0",
"p1",
"p2",
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 429566616638477711378535
% SZS output start Proof for 429566616638477711378535
1. ! [X0] : ((~funny(X0) | wise(X0)) <=> (~happy(X0) & tall(X0))) [input p0]
2. ! [X0] : ((humble(X0) & generous(X0)) <=> ~generous(X0)) [input p1]
3. ! [X0] : ((patient(X0) & funny(X0)) <=> (~happy(X0) | ~old(X0))) [input p2]
4. ! [X0] : (~happy(X0) <=> (~creative(X0) & ~funny(X0))) [input p3]
8. ! [X0] : (patient(X0) <=> (~funny(X0) <~> kind(X0))) [input p7]
11. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (quiet(X0) | generous(X0))) [input p10]
22. ~kind(alice) [input hypothesis]
35. ! [X0] : (((~funny(X0) | wise(X0)) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | (funny(X0) & ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((~funny(X0) | wise(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | (funny(X0) & ~wise(X0)))) [flattening 35]
37. ! [X0] : (((humble(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | (~humble(X0) | ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : (((humble(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | ~humble(X0) | ~generous(X0))) [flattening 37]
39. ! [X0] : (((patient(X0) & funny(X0)) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | (~patient(X0) | ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : (((patient(X0) & funny(X0)) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | ~patient(X0) | ~funny(X0))) [flattening 39]
41. ! [X0] : ((~happy(X0) | (creative(X0) | funny(X0))) & ((~creative(X0) & ~funny(X0)) | happy(X0))) [nnf transformation 4]
42. ! [X0] : ((~happy(X0) | creative(X0) | funny(X0)) & ((~creative(X0) & ~funny(X0)) | happy(X0))) [flattening 41]
52. ! [X0] : ((patient(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) & (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | ~patient(X0))) [nnf transformation 8]
56. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~quiet(X0) & ~generous(X0))) & ((quiet(X0) | generous(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 11]
57. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~quiet(X0) & ~generous(X0))) & (quiet(X0) | generous(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [flattening 56]
74. ~happy(X0) | funny(X0) [cnf transformation 36]
77. generous(X0) | generous(X0) [cnf transformation 38]
81. funny(X0) | happy(X0) [cnf transformation 40]
84. ~funny(X0) | happy(X0) [cnf transformation 42]
96. kind(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 52]
106. ~happy(X0) | patient(X0) | ~generous(X0) [cnf transformation 57]
130. ~kind(alice) [cnf transformation 22]
134. generous(X0) [duplicate literal removal 77]
136. funny(X0) [subsumption resolution 81,74]
138. happy(X0) [subsumption resolution 84,136]
180. ~patient(X0) | kind(X0) [subsumption resolution 96,136]
197. patient(X0) | ~generous(X0) [subsumption resolution 106,138]
198. patient(X0) [subsumption resolution 197,134]
264. kind(X1) [resolution 180,198]
266. $false [resolution 264,130]
% SZS output end Proof for 429566616638477711378535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not quiet or brave.
Everyone who is both generous and not generous is either not calm or curious.
Everyone who is brave or curious is wise or not strong.
Everyone who is funny or happy is either rich or tall and vice versa.
Everyone who is kind or not humble is not humble and vice versa.
Everyone who is either not happy or not rich is either brave or happy and vice versa.
If someone is both not wise and not strong then paul is both wise and tall and vice versa.
Everyone who is either brave or not creative is either not rich or not wise and vice versa.
Everyone who is either curious or old is creative and vice versa.
Everyone who is rich is either not kind or curious and vice versa.
Everyone who is either not wise or curious is either not happy or quiet and vice versa.
Everyone who is not quiet is quiet or not humble and vice versa.
Everyone who is either not tall or creative is either generous or quiet and vice versa.
If paul is both not generous and not wise then someone is both curious and creative and vice versa.
Everyone who is not creative or calm is not calm or humble and vice versa.
Everyone who is either humble or calm is not humble or kind.
Someone is either not patient or curious.
Paul is both strong and not quiet.
Fred is calm or not rich.
Someone is generous.
John is not strong or not creative.
Alice is patient or not rich.
Someone is either not kind or funny. | Fred is not old. | neutral | (![X]:(~calm(X)=>(~quiet(X)|brave(X))))&
(![X]:((generous(X)&~generous(X))=>(~calm(X)<~>curious(X))))&
(![X]:((brave(X)|curious(X))=>(wise(X)|~strong(X))))&
(![X]:((funny(X)|happy(X))<=>(rich(X)<~>tall(X))))&
(![X]:((kind(X)|~humble(X))<=>~humble(X)))&
(![X]:((~happy(X)<~>~rich(X))<=>(brave(X)<~>happy(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>((wise(paul)&tall(paul))))&
(![X]:((brave(X)<~>~creative(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((curious(X)<~>old(X))<=>creative(X)))&
(![X]:(rich(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:(~quiet(X)<=>(quiet(X)|~humble(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(generous(X)<~>quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)|humble(X))))&
(![X]:((humble(X)<~>calm(X))=>(~humble(X)|kind(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
((strong(paul)&~quiet(paul)))&
((calm(fred)|~rich(fred)))&
(?[X]:(generous(X)))&
((~strong(john)|~creative(john)))&
((patient(alice)|~rich(alice)))&
(?[X]:((~kind(X)<~>funny(X)))) | ~old(fred) | [] | null | 0 |
If john is either not kind or creative then someone is either not old or tall and vice versa.
If mary is not funny then someone is either not brave or not creative and vice versa.
If someone is either not rich or not tall then alice is not old or not wise and vice versa.
Everyone who is not funny or old is creative or not funny and vice versa.
Everyone who is both not humble and not wise is not curious or not brave.
Everyone who is happy or calm is not quiet.
Everyone who is not kind or not quiet is quiet and vice versa.
Everyone who is both not rich and strong is either not calm or not patient and vice versa.
If mary is patient or not old then susan is not curious or rich.
Everyone who is either not calm or quiet is either old or brave.
If mary is both kind and tall then paul is both patient and not happy.
Everyone who is either not patient or rich is not kind or not generous and vice versa.
Everyone who is both funny and not patient is both not brave and old and vice versa.
If john is either not generous or not wise then lucy is humble or not wise and vice versa.
If someone is kind then susan is either rich or not generous and vice versa.
Everyone who is not brave is either not strong or not rich and vice versa.
Paul is not generous.
Someone is either not curious or kind.
Alice is both not old and not patient.
Mary is either not patient or rich.
Paul is tall or old.
Lucy is not funny. | Susan is not strong. | entailment | (((~kind(john)<~>creative(john)))<=>(?[X]:((~old(X)<~>tall(X)))))&
((~funny(mary))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~old(alice)|~wise(alice))))&
(![X]:((~funny(X)|old(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)|~brave(X))))&
(![X]:((happy(X)|calm(X))=>~quiet(X)))&
(![X]:((~kind(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(mary)|~old(mary)))=>((~curious(susan)|rich(susan))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)<~>brave(X))))&
(((kind(mary)&tall(mary)))=>((patient(paul)&~happy(paul))))&
(![X]:((~patient(X)<~>rich(X))<=>(~kind(X)|~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~brave(X)&old(X))))&
(((~generous(john)<~>~wise(john)))<=>((humble(lucy)|~wise(lucy))))&
((?[X]:(kind(X)))<=>((rich(susan)<~>~generous(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~rich(X))))&
(~generous(paul))&
(?[X]:((~curious(X)<~>kind(X))))&
((~old(alice)&~patient(alice)))&
((~patient(mary)<~>rich(mary)))&
((tall(paul)|old(paul)))&
(~funny(lucy)) | ~strong(susan) | [
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8501378828978058233374366
% SZS output start Proof for 8501378828978058233374366
6. ! [X0] : ((calm(X0) | happy(X0)) => ~quiet(X0)) [input p5]
7. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> quiet(X0)) [input p6]
8. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p7]
12. ! [X0] : ((~patient(X0) <~> rich(X0)) <=> (~generous(X0) | ~kind(X0))) [input p11]
23. strong(susan) [input hypothesis]
25. ! [X0] : (calm(X0) => ~quiet(X0)) [pure predicate removal 6]
28. ! [X0] : (~quiet(X0) | ~calm(X0)) [ennf transformation 25]
49. ! [X0] : (((~quiet(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [nnf transformation 7]
50. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [flattening 49]
51. ! [X0] : (((strong(X0) & ~rich(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~strong(X0) | rich(X0)))) [nnf transformation 8]
52. ! [X0] : (((strong(X0) & ~rich(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | ~strong(X0) | rich(X0))) [flattening 51]
54. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [nnf transformation 12]
55. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [flattening 54]
92. ~quiet(X0) | ~calm(X0) [cnf transformation 28]
94. quiet(X0) | quiet(X0) [cnf transformation 50]
95. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 50]
97. ~strong(X0) | calm(X0) | patient(X0) | rich(X0) [cnf transformation 52]
98. ~patient(X0) | ~rich(X0) | calm(X0) [cnf transformation 52]
111. ~patient(X0) | rich(X0) | kind(X0) [cnf transformation 55]
113. ~rich(X0) | patient(X0) | kind(X0) [cnf transformation 55]
142. strong(susan) [cnf transformation 23]
143. quiet(X0) [duplicate literal removal 94]
144. ~quiet(X0) | ~kind(X0) [duplicate literal removal 95]
234. 20 <=> rich(susan) [avatar definition]
235. ~rich(susan) <- (~20) [avatar component clause 234]
236. rich(susan) <- (20) [avatar component clause 234]
289. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
290. ~kind(X1) <- (31) [avatar component clause 289]
319. ~calm(X0) [resolution 92,143]
320. ~kind(X0) [resolution 144,143]
321. 31 [avatar split clause 320,289]
352. calm(susan) | patient(susan) | rich(susan) [resolution 97,142]
355. patient(susan) | rich(susan) [subsumption resolution 352,319]
356. patient(susan) <- (~20) [subsumption resolution 355,235]
361. rich(susan) | kind(susan) <- (~20) [resolution 356,111]
365. kind(susan) <- (~20) [subsumption resolution 361,235]
366. $false <- (~20, 31) [subsumption resolution 365,290]
367. 20 | ~31 [avatar contradiction clause 366]
369. 39 <=> patient(susan) [avatar definition]
371. patient(susan) <- (39) [avatar component clause 369]
381. patient(susan) | kind(susan) <- (20) [resolution 236,113]
384. patient(susan) <- (20, 31) [subsumption resolution 381,290]
385. 39 | ~20 | ~31 [avatar split clause 384,289,234,369]
391. ~rich(susan) | calm(susan) <- (39) [resolution 371,98]
392. calm(susan) <- (20, 39) [subsumption resolution 391,236]
393. $false <- (20, 39) [subsumption resolution 392,319]
394. ~20 | ~39 [avatar contradiction clause 393]
395. $false [avatar sat refutation 321,367,385,394]
% SZS output end Proof for 8501378828978058233374366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and kind is either calm or tall. If paul is either quiet or not happy then fred is both not old and strong and vice versa. Everyone who is either rich or happy is quiet and vice versa. If someone is both not curious and creative then fred is not calm or not rich and vice versa. If john is not generous or not strong then fred is either not patient or funny. If fred is not wise or not patient then mary is wise. Everyone who is either old or not brave is kind or funny and vice versa. Everyone who is generous or not old is either not brave or not quiet. If susan is either strong or creative then john is generous or humble and vice versa. Everyone who is both not brave and not curious is not generous. If lucy is rich or not tall then fred is both not funny and not rich. 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. Someone is not funny or tall. Someone is either not funny or brave. Someone is both not old and quiet. Fred is both patient and curious. Someone is not kind or wise. Fred is kind or not brave. Someone is either tall or not strong. Someone is creative. | Fred is not brave. | neutral | (![X]:((happy(X)&kind(X))=>(calm(X)<~>tall(X))))&
(((quiet(paul)<~>~happy(paul)))<=>((~old(fred)&strong(fred))))&
(![X]:((rich(X)<~>happy(X))<=>quiet(X)))&
((?[X]:((~curious(X)&creative(X))))<=>((~calm(fred)|~rich(fred))))&
(((~generous(john)|~strong(john)))=>((~patient(fred)<~>funny(fred))))&
(((~wise(fred)|~patient(fred)))=>(wise(mary)))&
(![X]:((old(X)<~>~brave(X))<=>(kind(X)|funny(X))))&
(![X]:((generous(X)|~old(X))=>(~brave(X)<~>~quiet(X))))&
(((strong(susan)<~>creative(susan)))<=>((generous(john)|humble(john))))&
(![X]:((~brave(X)&~curious(X))=>~generous(X)))&
(((rich(lucy)|~tall(lucy)))=>((~funny(fred)&~rich(fred))))&
((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]:((~funny(X)|tall(X))))&
(?[X]:((~funny(X)<~>brave(X))))&
(?[X]:((~old(X)&quiet(X))))&
((patient(fred)&curious(fred)))&
(?[X]:((~kind(X)|wise(X))))&
((kind(fred)|~brave(fred)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:(creative(X))) | ~brave(fred) | [] | null | 0 |
If mary is either not patient or humble then someone is either not humble or rich and vice versa.
Everyone who is not kind or quiet is either not kind or tall.
Everyone who is not calm is quiet.
Everyone who is kind is not old.
Everyone who is not funny is not rich or not tall.
Everyone who is not rich or not happy is not calm or brave.
Everyone who is creative is funny or kind.
Everyone who is both not funny and tall is quiet or brave and vice versa.
Everyone who is both patient and kind is either not happy or not quiet.
Everyone who is creative or rich is not rich.
Everyone who is generous is both calm and not creative.
If someone is either not funny or not humble then susan is not patient.
Everyone who is either not funny or not old is calm or not kind.
If someone is not creative then john is both strong and not tall and vice versa.
Everyone who is patient or not calm is both not wise and old.
If john is funny or curious then lucy is either generous or tall.
Someone is either humble or curious.
John is calm.
Fred is wise or rich.
Someone is not tall or not quiet.
Susan is both curious and not rich. | Susan is tall. | entailment | (((~patient(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|~kind(X))))&
((?[X]:(~creative(X)))<=>((strong(john)&~tall(john))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>curious(X))))&
(calm(john))&
((wise(fred)|rich(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
((curious(susan)&~rich(susan))) | tall(susan) | [
"p2",
"p5",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7253105108131259492578876
% SZS output start Proof for 7253105108131259492578876
3. ! [X0] : (~calm(X0) => quiet(X0)) [input p2]
6. ! [X0] : ((~happy(X0) | ~rich(X0)) => (brave(X0) | ~calm(X0))) [input p5]
8. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (brave(X0) | quiet(X0))) [input p7]
10. ! [X0] : ((rich(X0) | creative(X0)) => ~rich(X0)) [input p9]
22. ~tall(susan) [input hypothesis]
24. ! [X0] : (quiet(X0) | calm(X0)) [ennf transformation 3]
28. ! [X0] : ((brave(X0) | ~calm(X0)) | (happy(X0) & rich(X0))) [ennf transformation 6]
29. ! [X0] : (brave(X0) | ~calm(X0) | (happy(X0) & rich(X0))) [flattening 28]
34. ! [X0] : (~rich(X0) | (~rich(X0) & ~creative(X0))) [ennf transformation 10]
46. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & ((brave(X0) | quiet(X0)) | (~tall(X0) | funny(X0)))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & (brave(X0) | quiet(X0) | ~tall(X0) | funny(X0))) [flattening 46]
74. calm(X0) | quiet(X0) [cnf transformation 24]
77. ~calm(X0) | brave(X0) | rich(X0) [cnf transformation 29]
83. ~quiet(X0) | tall(X0) [cnf transformation 47]
84. ~brave(X0) | tall(X0) [cnf transformation 47]
88. ~rich(X0) | ~rich(X0) [cnf transformation 34]
113. ~tall(susan) [cnf transformation 22]
114. ~rich(X0) [duplicate literal removal 88]
213. brave(X0) | rich(X0) | quiet(X0) [resolution 77,74]
216. brave(X0) | quiet(X0) [subsumption resolution 213,114]
270. quiet(X0) | tall(X0) [resolution 216,84]
272. tall(X0) [subsumption resolution 270,83]
274. $false [resolution 272,113]
% SZS output end Proof for 7253105108131259492578876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Alice is happy. | entailment | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | happy(alice) | [
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 413599286982828257814605
% SZS output start Proof for 413599286982828257814605
6. ! [X0] : ((brave(X0) | ~strong(X0)) <=> (~happy(X0) | ~humble(X0))) [input p5]
11. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p10]
12. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p11]
20. ~happy(alice) [input hypothesis]
25. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 11]
38. ! [X0] : (((brave(X0) | ~strong(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (~brave(X0) & strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((brave(X0) | ~strong(X0) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | (~brave(X0) & strong(X0)))) [flattening 38]
48. ! [X0] : ((strong(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [flattening 48]
81. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 39]
100. strong(X0) | brave(X0) [cnf transformation 25]
101. ~brave(X0) | strong(X0) [cnf transformation 25]
103. ~brave(X0) | ~strong(X0) [cnf transformation 49]
123. ~happy(alice) [cnf transformation 20]
205. strong(X0) [subsumption resolution 100,101]
207. ~brave(X0) [subsumption resolution 103,205]
237. brave(X0) | happy(X0) [resolution 81,205]
238. happy(X0) [subsumption resolution 237,207]
253. $false [resolution 238,123]
% SZS output end Proof for 413599286982828257814605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not creative or not curious and vice versa.
Everyone who is both strong and old is not happy.
If someone is happy then mary is funny or not humble and vice versa.
If susan is either not calm or creative then someone is both not rich and rich and vice versa.
Everyone who is either not creative or not brave is not quiet.
If someone is not generous then fred is either not brave or not humble and vice versa.
If someone is strong or kind then someone is either generous or not humble and vice versa.
Everyone who is both not humble and tall is curious or quiet and vice versa.
Everyone who is either not patient or not brave is rich and vice versa.
If susan is curious then alice is humble.
If someone is humble then someone is either not old or calm and vice versa.
Everyone who is not creative is both old and generous.
Everyone who is not funny is either not creative or not humble and vice versa.
Everyone who is either happy or not tall is both not happy and quiet and vice versa.
If someone is quiet or calm then fred is both not curious and quiet and vice versa.
If someone is not curious then someone is not funny or not brave.
Someone is either generous or not calm.
Someone is humble or funny.
Alice is not happy.
Mary is funny.
Someone is not humble or not old.
Someone is either not creative or not humble. | Susan is patient. | neutral | (![X]:((~tall(X)&~kind(X))<=>(~creative(X)|~curious(X))))&
(![X]:((strong(X)&old(X))=>~happy(X)))&
((?[X]:(happy(X)))<=>((funny(mary)|~humble(mary))))&
(((~calm(susan)<~>creative(susan)))<=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((~creative(X)<~>~brave(X))=>~quiet(X)))&
((?[X]:(~generous(X)))<=>((~brave(fred)<~>~humble(fred))))&
((?[X]:((strong(X)|kind(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~humble(X)&tall(X))<=>(curious(X)|quiet(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>rich(X)))&
((curious(susan))=>(humble(alice)))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:(~creative(X)=>(old(X)&generous(X))))&
(![X]:(~funny(X)<=>(~creative(X)<~>~humble(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(~happy(X)&quiet(X))))&
((?[X]:((quiet(X)|calm(X))))<=>((~curious(fred)&quiet(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|~brave(X)))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((humble(X)|funny(X))))&
(~happy(alice))&
(funny(mary))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~creative(X)<~>~humble(X)))) | patient(susan) | [] | null | 0 |
Everyone who is both rich and not funny is either not happy or not patient. Everyone who is either not humble or wise is both happy and not humble and vice versa. Everyone who is both not strong and old is both kind and not funny. If susan is not happy or not calm then someone is both not creative and funny. If someone is not funny or strong then someone is both brave and humble and vice versa. Everyone who is not rich is humble and vice versa. If someone is not happy or not kind then paul is humble or rich and vice versa. Everyone who is not generous or strong is calm or old. Everyone who is both not patient and patient is either not funny or not kind and vice versa. Everyone who is not humble is curious or not happy. If someone is both not tall and humble then someone is both curious and strong. If mary is not quiet then alice is both patient and creative. If susan is either generous or calm then someone is both not calm and strong. Everyone who is both curious and not brave is both rich and funny. If alice is strong then someone is both not calm and patient. Everyone who is both tall and old is either not tall or not patient. Someone is old. Alice is both tall and not kind. Alice is kind or not quiet. John is not kind. Someone is either tall or not humble. Someone is quiet or funny. Lucy is both not creative and not happy. Alice is not patient or not strong. | Paul is rich. | neutral | (![X]:((rich(X)&~funny(X))=>(~happy(X)<~>~patient(X))))&
(![X]:((~humble(X)<~>wise(X))<=>(happy(X)&~humble(X))))&
(![X]:((~strong(X)&old(X))=>(kind(X)&~funny(X))))&
(((~happy(susan)|~calm(susan)))=>(?[X]:((~creative(X)&funny(X)))))&
((?[X]:((~funny(X)|strong(X))))<=>(?[X]:((brave(X)&humble(X)))))&
(![X]:(~rich(X)<=>humble(X)))&
((?[X]:((~happy(X)|~kind(X))))<=>((humble(paul)|rich(paul))))&
(![X]:((~generous(X)|strong(X))=>(calm(X)|old(X))))&
(![X]:((~patient(X)&patient(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(~humble(X)=>(curious(X)|~happy(X))))&
((?[X]:((~tall(X)&humble(X))))=>(?[X]:((curious(X)&strong(X)))))&
((~quiet(mary))=>((patient(alice)&creative(alice))))&
(((generous(susan)<~>calm(susan)))=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:((curious(X)&~brave(X))=>(rich(X)&funny(X))))&
((strong(alice))=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((tall(X)&old(X))=>(~tall(X)<~>~patient(X))))&
(?[X]:(old(X)))&
((tall(alice)&~kind(alice)))&
((kind(alice)|~quiet(alice)))&
(~kind(john))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((quiet(X)|funny(X))))&
((~creative(lucy)&~happy(lucy)))&
((~patient(alice)|~strong(alice))) | rich(paul) | [] | null | 0 |
Everyone who is not patient is either not happy or humble.
If john is both not curious and not happy then mary is not humble or not kind and vice versa.
Everyone who is either not brave or not tall is not old or calm and vice versa.
Everyone who is not happy or not creative is strong or not humble.
Everyone who is both kind and old is both curious and generous and vice versa.
Everyone who is both not old and not curious is not funny and vice versa.
Everyone who is funny or happy is not brave or quiet and vice versa.
Everyone who is funny or not rich is either not quiet or wise.
Everyone who is either not creative or not patient is not creative and vice versa.
If alice is not curious then someone is not humble.
Everyone who is not brave is either humble or not kind.
If fred is either funny or not strong then someone is either tall or patient and vice versa.
Everyone who is quiet is brave.
Everyone who is either not creative or not kind is either not old or not kind.
If someone is either not brave or wise then someone is not patient and vice versa.
If someone is humble then susan is calm.
Fred is not creative or not strong.
Alice is either not humble or not old.
Someone is either not old or wise.
Mary is either quiet or not strong.
Someone is not kind or curious.
Lucy is humble or not humble.
Someone is not happy or not old.
Mary is rich. | John is curious. | contradiction | (![X]:(~patient(X)=>(~happy(X)<~>humble(X))))&
(((~curious(john)&~happy(john)))<=>((~humble(mary)|~kind(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>(~old(X)|calm(X))))&
(![X]:((~happy(X)|~creative(X))=>(strong(X)|~humble(X))))&
(![X]:((kind(X)&old(X))<=>(curious(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>~funny(X)))&
(![X]:((funny(X)|happy(X))<=>(~brave(X)|quiet(X))))&
(![X]:((funny(X)|~rich(X))=>(~quiet(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>~creative(X)))&
((~curious(alice))=>(?[X]:(~humble(X))))&
(![X]:(~brave(X)=>(humble(X)<~>~kind(X))))&
(((funny(fred)<~>~strong(fred)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:(quiet(X)=>brave(X)))&
(![X]:((~creative(X)<~>~kind(X))=>(~old(X)<~>~kind(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(humble(X)))=>(calm(susan)))&
((~creative(fred)|~strong(fred)))&
((~humble(alice)<~>~old(alice)))&
(?[X]:((~old(X)<~>wise(X))))&
((quiet(mary)<~>~strong(mary)))&
(?[X]:((~kind(X)|curious(X))))&
((humble(lucy)|~humble(lucy)))&
(?[X]:((~happy(X)|~old(X))))&
(rich(mary)) | curious(john) | [
"p5",
"p6",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 32770954872083234483320
% SZS output start Proof for 32770954872083234483320
6. ! [X0] : ((~curious(X0) & ~old(X0)) <=> ~funny(X0)) [input p5]
7. ! [X0] : ((happy(X0) | funny(X0)) <=> (quiet(X0) | ~brave(X0))) [input p6]
8. ! [X0] : ((~rich(X0) | funny(X0)) => (~quiet(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((~creative(X0) <~> ~patient(X0)) <=> ~creative(X0)) [input p8]
13. ! [X0] : (quiet(X0) => brave(X0)) [input p12]
15. ? [X0] : (~brave(X0) <~> wise(X0)) <=> ? [X0] : ~patient(X0) [input p14]
25. curious(john) [input hypothesis]
26. ? [X0] : (~brave(X0) <~> wise(X0)) <=> ? [X1] : ~patient(X1) [rectify 15]
27. ! [X0] : (funny(X0) => (~quiet(X0) <~> wise(X0))) [pure predicate removal 8]
32. ! [X0] : ((~quiet(X0) <~> wise(X0)) | ~funny(X0)) [ennf transformation 27]
35. ! [X0] : (brave(X0) | ~quiet(X0)) [ennf transformation 13]
45. ! [X0] : (((~curious(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | (curious(X0) | old(X0)))) [nnf transformation 6]
46. ! [X0] : (((~curious(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | curious(X0) | old(X0))) [flattening 45]
47. ! [X0] : (((happy(X0) | funny(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (~happy(X0) & ~funny(X0)))) [nnf transformation 7]
48. ! [X0] : ((happy(X0) | funny(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (~happy(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~funny(X0)) [nnf transformation 32]
50. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | creative(X0)) & (~creative(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [nnf transformation 9]
59. (? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) [nnf transformation 26]
60. (? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((~brave(X3) | ~wise(X3)) & (wise(X3) | brave(X3)))) [rectify 59]
61. ? [X0] : ((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) => ((~wise(sK2) | brave(sK2)) & (wise(sK2) | ~brave(sK2))) [choice axiom]
62. ? [X2] : ~patient(X2) => ~patient(sK3) [choice axiom]
63. (((~wise(sK2) | brave(sK2)) & (wise(sK2) | ~brave(sK2))) | ! [X1] : patient(X1)) & (~patient(sK3) | ! [X3] : ((~brave(X3) | ~wise(X3)) & (wise(X3) | brave(X3)))) [skolemisation 60,62,61]
94. ~curious(X0) | funny(X0) [cnf transformation 46]
95. ~funny(X0) | ~brave(X0) | quiet(X0) [cnf transformation 48]
99. ~quiet(X0) | wise(X0) | ~funny(X0) [cnf transformation 49]
100. ~wise(X0) | quiet(X0) | ~funny(X0) [cnf transformation 49]
102. ~creative(X0) | ~creative(X0) | patient(X0) [cnf transformation 50]
104. patient(X0) | creative(X0) | creative(X0) [cnf transformation 50]
116. ~quiet(X0) | brave(X0) [cnf transformation 35]
121. ~patient(sK3) | wise(X3) | brave(X3) [cnf transformation 63]
122. ~patient(sK3) | ~brave(X3) | ~wise(X3) [cnf transformation 63]
136. curious(john) [cnf transformation 25]
139. ~creative(X0) | patient(X0) [duplicate literal removal 102]
140. creative(X0) | patient(X0) [duplicate literal removal 104]
156. 4 <=> curious(john) [avatar definition]
157. curious(john) <- (4) [avatar component clause 156]
162. patient(X0) [subsumption resolution 139,140]
195. ~wise(X3) | ~brave(X3) [subsumption resolution 122,162]
196. wise(X3) | brave(X3) [subsumption resolution 121,162]
258. 4 [avatar split clause 136,156]
261. funny(john) <- (4) [resolution 94,157]
313. 29 <=> quiet(john) [avatar definition]
315. quiet(john) <- (29) [avatar component clause 313]
317. 30 <=> brave(john) [avatar definition]
318. brave(john) <- (30) [avatar component clause 317]
368. quiet(X0) | ~funny(X0) | brave(X0) [resolution 100,196]
369. ~funny(X0) | quiet(X0) [subsumption resolution 368,95]
371. quiet(john) <- (4) [resolution 369,261]
374. 29 | ~4 [avatar split clause 371,156,313]
402. wise(john) | ~funny(john) <- (29) [resolution 315,99]
404. brave(john) <- (29) [resolution 315,116]
405. wise(john) <- (4, 29) [subsumption resolution 402,261]
408. 30 | ~29 [avatar split clause 404,313,317]
429. ~brave(john) <- (4, 29) [resolution 405,195]
430. $false <- (4, 29, 30) [subsumption resolution 429,318]
431. ~4 | ~29 | ~30 [avatar contradiction clause 430]
432. $false [avatar sat refutation 258,374,408,431]
% SZS output end Proof for 32770954872083234483320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either tall or calm then alice is not curious and vice versa. Everyone who is not wise or not creative is either curious or not tall. Everyone who is either brave or not generous is not curious or rich. Everyone who is either not tall or not strong is generous or not generous and vice versa. Everyone who is both quiet and humble is old. If mary is calm then someone is not generous and vice versa. Everyone who is both not calm and strong is strong and vice versa. If fred is not patient or not curious then someone is both quiet and curious and vice versa. Everyone who is both kind and humble is both not brave and humble and vice versa. Everyone who is either not tall or rich is generous and vice versa. If fred is either not calm or curious then someone is rich or not funny. Everyone who is either not brave or not kind is not funny or quiet. If someone is not funny or kind then someone is rich and vice versa. If someone is funny then mary is either not wise or creative. Everyone who is either funny or not tall is either strong or patient. If lucy is either not wise or not funny then someone is both creative and not patient and vice versa. Someone is either not calm or humble. Someone is wise. Fred is both brave and not patient. Someone is both not curious and brave. Someone is either not calm or not quiet. Mary is both not calm and not humble. Someone is either not kind or calm. Someone is either happy or not patient. | Alice is not generous. | contradiction | (((tall(paul)<~>calm(paul)))<=>(~curious(alice)))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)<~>~tall(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)|rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(generous(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>old(X)))&
((calm(mary))<=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)&strong(X))<=>strong(X)))&
(((~patient(fred)|~curious(fred)))<=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((kind(X)&humble(X))<=>(~brave(X)&humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>generous(X)))&
(((~calm(fred)<~>curious(fred)))=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:(funny(X)))=>((~wise(mary)<~>creative(mary))))&
(![X]:((funny(X)<~>~tall(X))=>(strong(X)<~>patient(X))))&
(((~wise(lucy)<~>~funny(lucy)))<=>(?[X]:((creative(X)&~patient(X)))))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:(wise(X)))&
((brave(fred)&~patient(fred)))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((~calm(mary)&~humble(mary)))&
(?[X]:((~kind(X)<~>calm(X))))&
(?[X]:((happy(X)<~>~patient(X)))) | ~generous(alice) | [
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8662549476534944366973165
% SZS output start Proof for 8662549476534944366973165
6. calm(mary) <=> ? [X0] : ~generous(X0) [input p5]
22. ~humble(mary) & ~calm(mary) [input p21]
25. ~generous(alice) [input hypothesis]
41. (calm(mary) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~calm(mary)) [nnf transformation 6]
42. (calm(mary) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~calm(mary)) [rectify 41]
43. ? [X1] : ~generous(X1) => ~generous(sK0) [choice axiom]
44. (calm(mary) | ! [X0] : generous(X0)) & (~generous(sK0) | ~calm(mary)) [skolemisation 42,43]
103. calm(mary) | generous(X0) [cnf transformation 44]
148. ~calm(mary) [cnf transformation 22]
154. ~generous(alice) [cnf transformation 25]
174. 4 <=> ! [X0] : generous(X0) [avatar definition]
175. generous(X0) <- (4) [avatar component clause 174]
177. 5 <=> calm(mary) [avatar definition]
180. 4 | 5 [avatar split clause 103,177,174]
309. ~5 [avatar split clause 148,177]
330. $false <- (4) [resolution 175,154]
331. ~4 [avatar contradiction clause 330]
332. $false [avatar sat refutation 180,309,331]
% SZS output end Proof for 8662549476534944366973165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or wise is both happy and funny.
Everyone who is either not humble or not generous is not tall.
Everyone who is not brave or wise is both calm and not generous and vice versa.
Everyone who is both not tall and not funny is curious or not old and vice versa.
If john is either wise or not kind then susan is wise or patient.
Everyone who is not creative or happy is either funny or not creative and vice versa.
If susan is both brave and patient then someone is both not patient and not happy and vice versa.
If someone is happy then someone is both not quiet and rich and vice versa.
If fred is not wise then someone is either wise or not wise and vice versa.
Everyone who is not old or not calm is both wise and calm and vice versa.
If mary is both not creative and kind then fred is not rich or not tall.
Everyone who is humble or wise is both not tall and rich.
If mary is both wise and brave then john is both not funny and not happy.
Everyone who is both old and not creative is patient or not kind and vice versa.
Everyone who is both curious and not generous is happy or not kind.
Someone is not kind.
Someone is brave.
Someone is humble.
Alice is not tall or strong.
Someone is rich.
Lucy is either strong or happy. | Mary is old. | entailment | (![X]:((patient(X)|wise(X))=>(happy(X)&funny(X))))&
(![X]:((~humble(X)<~>~generous(X))=>~tall(X)))&
(![X]:((~brave(X)|wise(X))<=>(calm(X)&~generous(X))))&
(![X]:((~tall(X)&~funny(X))<=>(curious(X)|~old(X))))&
(((wise(john)<~>~kind(john)))=>((wise(susan)|patient(susan))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~creative(X))))&
(((brave(susan)&patient(susan)))<=>(?[X]:((~patient(X)&~happy(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((~wise(fred))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:((~old(X)|~calm(X))<=>(wise(X)&calm(X))))&
(((~creative(mary)&kind(mary)))=>((~rich(fred)|~tall(fred))))&
(![X]:((humble(X)|wise(X))=>(~tall(X)&rich(X))))&
(((wise(mary)&brave(mary)))=>((~funny(john)&~happy(john))))&
(![X]:((old(X)&~creative(X))<=>(patient(X)|~kind(X))))&
(![X]:((curious(X)&~generous(X))=>(happy(X)|~kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(brave(X)))&
(?[X]:(humble(X)))&
((~tall(alice)|strong(alice)))&
(?[X]:(rich(X)))&
((strong(lucy)<~>happy(lucy))) | old(mary) | [
"p0",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2966152918379259173805320
% SZS output start Proof for 2966152918379259173805320
1. ! [X0] : ((wise(X0) | patient(X0)) => (funny(X0) & happy(X0))) [input p0]
4. ! [X0] : ((~funny(X0) & ~tall(X0)) <=> (~old(X0) | curious(X0))) [input p3]
10. ! [X0] : ((~calm(X0) | ~old(X0)) <=> (calm(X0) & wise(X0))) [input p9]
22. ~old(mary) [input hypothesis]
24. ! [X0] : ((funny(X0) & happy(X0)) | (~wise(X0) & ~patient(X0))) [ennf transformation 1]
38. ! [X0] : (((~funny(X0) & ~tall(X0)) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | (funny(X0) | tall(X0)))) [nnf transformation 4]
39. ! [X0] : (((~funny(X0) & ~tall(X0)) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | funny(X0) | tall(X0))) [flattening 38]
57. ! [X0] : (((~calm(X0) | ~old(X0)) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | (calm(X0) & old(X0)))) [nnf transformation 10]
58. ! [X0] : ((~calm(X0) | ~old(X0) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | (calm(X0) & old(X0)))) [flattening 57]
73. ~wise(X0) | funny(X0) [cnf transformation 24]
85. ~funny(X0) | old(X0) [cnf transformation 39]
105. old(X0) | wise(X0) [cnf transformation 58]
130. ~old(mary) [cnf transformation 22]
228. 21 <=> wise(mary) [avatar definition]
229. wise(mary) <- (21) [avatar component clause 228]
280. wise(mary) [resolution 105,130]
281. 21 [avatar split clause 280,228]
283. funny(mary) <- (21) [resolution 229,73]
285. old(mary) <- (21) [resolution 283,85]
286. $false <- (21) [subsumption resolution 285,130]
287. ~21 [avatar contradiction clause 286]
288. $false [avatar sat refutation 281,287]
% SZS output end Proof for 2966152918379259173805320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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