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
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|---|---|---|---|---|---|---|---|
Everyone who is not curious is both not funny and not generous. Everyone who is not happy is not curious and vice versa. If susan is either not funny or humble then fred is generous or wise and vice versa. If someone is not tall then someone is not creative or wise. If susan is quiet or not brave then someone is not kind and vice versa. Everyone who is both not curious and kind is either not wise or creative and vice versa. Everyone who is not quiet is both calm and not humble. Everyone who is creative or strong is not tall and vice versa. If paul is either not happy or not tall then someone is not generous and vice versa. If someone is not curious then someone is not quiet and vice versa. Everyone who is both not wise and brave is either happy or patient. Everyone who is rich or not tall is both humble and funny. Everyone who is either kind or strong is both not kind and funny and vice versa. If susan is not calm or curious then someone is not patient or not old. Everyone who is generous is both not kind and not happy and vice versa. If someone is brave then someone is not funny or tall. John is both strong and not kind. Someone is both not creative and old. Someone is wise or not happy. Someone is either not calm or not rich. Someone is either not rich or brave. | Susan is happy. | entailment | (![X]:(~curious(X)=>(~funny(X)&~generous(X))))&
(![X]:(~happy(X)<=>~curious(X)))&
(((~funny(susan)<~>humble(susan)))<=>((generous(fred)|wise(fred))))&
((?[X]:(~tall(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(((quiet(susan)|~brave(susan)))<=>(?[X]:(~kind(X))))&
(![X]:((~curious(X)&kind(X))<=>(~wise(X)<~>creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~humble(X))))&
(![X]:((creative(X)|strong(X))<=>~tall(X)))&
(((~happy(paul)<~>~tall(paul)))<=>(?[X]:(~generous(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&brave(X))=>(happy(X)<~>patient(X))))&
(![X]:((rich(X)|~tall(X))=>(humble(X)&funny(X))))&
(![X]:((kind(X)<~>strong(X))<=>(~kind(X)&funny(X))))&
(((~calm(susan)|curious(susan)))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(generous(X)<=>(~kind(X)&~happy(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)|tall(X)))))&
((strong(john)&~kind(john)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((wise(X)|~happy(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~rich(X)<~>brave(X)))) | happy(susan) | [
"p0",
"p1",
"p7",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1259881205583668730794229
% SZS output start Proof for 1259881205583668730794229
1. ! [X0] : (~curious(X0) => (~generous(X0) & ~funny(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> ~curious(X0)) [input p1]
8. ! [X0] : ((strong(X0) | creative(X0)) <=> ~tall(X0)) [input p7]
12. ! [X0] : ((~tall(X0) | rich(X0)) => (funny(X0) & humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> strong(X0)) <=> (funny(X0) & ~kind(X0))) [input p12]
15. ! [X0] : (generous(X0) <=> (~happy(X0) & ~kind(X0))) [input p14]
22. ~happy(susan) [input hypothesis]
26. ! [X0] : ((~generous(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 1]
31. ! [X0] : ((funny(X0) & humble(X0)) | (tall(X0) & ~rich(X0))) [ennf transformation 12]
34. ! [X0] : ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))) [nnf transformation 2]
47. ! [X0] : (((strong(X0) | creative(X0)) | tall(X0)) & (~tall(X0) | (~strong(X0) & ~creative(X0)))) [nnf transformation 8]
48. ! [X0] : ((strong(X0) | creative(X0) | tall(X0)) & (~tall(X0) | (~strong(X0) & ~creative(X0)))) [flattening 47]
59. ! [X0] : ((((~strong(X0) | ~kind(X0)) & (strong(X0) | kind(X0))) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~strong(X0) | ~kind(X0)) & (strong(X0) | kind(X0))) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))))) [flattening 59]
63. ! [X0] : ((generous(X0) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | ~generous(X0))) [nnf transformation 15]
64. ! [X0] : ((generous(X0) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | ~generous(X0))) [flattening 63]
78. ~funny(X0) | curious(X0) [cnf transformation 26]
79. ~generous(X0) | curious(X0) [cnf transformation 26]
80. ~curious(X0) | happy(X0) [cnf transformation 34]
81. ~happy(X0) | curious(X0) [cnf transformation 34]
101. ~strong(X0) | ~tall(X0) [cnf transformation 48]
114. tall(X0) | funny(X0) [cnf transformation 31]
115. ~kind(X0) | strong(X0) | ~kind(X0) [cnf transformation 60]
125. kind(X0) | happy(X0) | generous(X0) [cnf transformation 64]
136. ~happy(susan) [cnf transformation 22]
137. ~kind(X0) | strong(X0) [duplicate literal removal 115]
219. 18 <=> ! [X3] : curious(X3) [avatar definition]
220. curious(X3) <- (18) [avatar component clause 219]
227. 20 <=> curious(susan) [avatar definition]
228. curious(susan) <- (20) [avatar component clause 227]
229. ~curious(susan) <- (~20) [avatar component clause 227]
289. happy(susan) <- (20) [resolution 80,228]
290. $false <- (20) [subsumption resolution 289,136]
291. ~20 [avatar contradiction clause 290]
370. strong(X1) | generous(X1) | happy(X1) [resolution 125,137]
407. ~tall(X1) | happy(X1) | generous(X1) [resolution 370,101]
452. happy(X0) | generous(X0) | funny(X0) [resolution 407,114]
499. generous(X1) | funny(X1) | curious(X1) [resolution 452,81]
502. funny(X1) | curious(X1) [subsumption resolution 499,79]
503. curious(X1) [subsumption resolution 502,78]
504. 18 [avatar split clause 503,219]
517. $false <- (18, ~20) [resolution 220,229]
520. ~18 | 20 [avatar contradiction clause 517]
521. $false [avatar sat refutation 291,504,520]
% SZS output end Proof for 1259881205583668730794229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not funny then someone is quiet or happy and vice versa.
Everyone who is not happy or funny is calm or old.
Everyone who is not humble is old or not strong and vice versa.
If john is creative then someone is both not funny and calm and vice versa.
If someone is funny then someone is both creative and not quiet and vice versa.
Everyone who is not rich is rich or not rich.
Everyone who is not brave or not strong is either not rich or funny.
Everyone who is tall or old is both humble and quiet and vice versa.
Everyone who is either not quiet or not calm is humble.
If someone is not kind or not generous then someone is both rich and patient and vice versa.
Everyone who is both old and creative is old or wise.
Everyone who is brave is both wise and creative and vice versa.
If someone is either not tall or not rich then someone is not old.
Everyone who is both humble and not strong is humble and vice versa.
Everyone who is not curious is either not kind or not strong.
If john is humble then susan is not funny or not calm and vice versa.
Paul is either not humble or not funny.
Lucy is patient.
Mary is not old.
Lucy is either tall or brave.
Someone is not wise.
Paul is either funny or not happy. | John is humble. | contradiction | ((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((~happy(X)|funny(X))=>(calm(X)|old(X))))&
(![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((creative(john))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~brave(X)|~strong(X))=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)|old(X))<=>(humble(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>humble(X)))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((old(X)&creative(X))=>(old(X)|wise(X))))&
(![X]:(brave(X)<=>(wise(X)&creative(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(~old(X))))&
(![X]:((humble(X)&~strong(X))<=>humble(X)))&
(![X]:(~curious(X)=>(~kind(X)<~>~strong(X))))&
((humble(john))<=>((~funny(susan)|~calm(susan))))&
((~humble(paul)<~>~funny(paul)))&
(patient(lucy))&
(~old(mary))&
((tall(lucy)<~>brave(lucy)))&
(?[X]:(~wise(X)))&
((funny(paul)<~>~happy(paul))) | humble(john) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3568577941345426248456702
% SZS output start Proof for 3568577941345426248456702
3. ! [X0] : (~humble(X0) <=> (~strong(X0) | old(X0))) [input p2]
14. ! [X0] : ((~strong(X0) & humble(X0)) <=> humble(X0)) [input p13]
23. humble(john) [input hypothesis]
43. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | humble(X0))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | humble(X0))) [flattening 43]
69. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) | ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | strong(X0) | ~humble(X0))) [flattening 69]
86. ~humble(X0) | strong(X0) [cnf transformation 44]
118. ~strong(X0) | ~humble(X0) [cnf transformation 70]
131. humble(john) [cnf transformation 23]
233. ~humble(X0) [subsumption resolution 118,86]
248. $false [subsumption resolution 131,233]
% SZS output end Proof for 3568577941345426248456702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or tall then paul is not patient and vice versa.
If mary is either not kind or not curious then fred is not rich or not creative.
Everyone who is old or not strong is both wise and generous.
If someone is both not quiet and not funny then someone is creative or not rich and vice versa.
If john is not creative or not rich then alice is either not quiet or not curious.
If someone is either not brave or not happy then lucy is both not humble and humble.
Everyone who is happy is humble or happy and vice versa.
Everyone who is rich is both not happy and generous.
If fred is not strong or happy then someone is not patient.
Everyone who is not creative is both humble and rich and vice versa.
If lucy is not happy or not creative then someone is either not brave or not old.
Everyone who is not generous or not brave is not happy or quiet.
If someone is not quiet then someone is both quiet and not wise and vice versa.
Everyone who is both quiet and not tall is either not patient or creative.
Everyone who is funny or creative is both kind and not brave.
If susan is both not creative and not humble then someone is either not quiet or wise and vice versa.
John is patient.
John is both tall and curious.
Someone is not funny.
Someone is patient or tall.
Paul is wise.
Someone is either humble or not tall.
Paul is both curious and not calm. | Paul is quiet. | contradiction | ((?[X]:((~calm(X)<~>tall(X))))<=>(~patient(paul)))&
(((~kind(mary)<~>~curious(mary)))=>((~rich(fred)|~creative(fred))))&
(![X]:((old(X)|~strong(X))=>(wise(X)&generous(X))))&
((?[X]:((~quiet(X)&~funny(X))))<=>(?[X]:((creative(X)|~rich(X)))))&
(((~creative(john)|~rich(john)))=>((~quiet(alice)<~>~curious(alice))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:(happy(X)<=>(humble(X)|happy(X))))&
(![X]:(rich(X)=>(~happy(X)&generous(X))))&
(((~strong(fred)|happy(fred)))=>(?[X]:(~patient(X))))&
(![X]:(~creative(X)<=>(humble(X)&rich(X))))&
(((~happy(lucy)|~creative(lucy)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)|quiet(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>creative(X))))&
(![X]:((funny(X)|creative(X))=>(kind(X)&~brave(X))))&
(((~creative(susan)&~humble(susan)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(patient(john))&
((tall(john)&curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)|tall(X))))&
(wise(paul))&
(?[X]:((humble(X)<~>~tall(X))))&
((curious(paul)&~calm(paul))) | quiet(paul) | [
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8564550910833352495557210
% SZS output start Proof for 8564550910833352495557210
10. ! [X0] : (~creative(X0) <=> (rich(X0) & humble(X0))) [input p9]
16. (~humble(susan) & ~creative(susan)) <=> ? [X0] : (~quiet(X0) <~> wise(X0)) [input p15]
21. wise(paul) [input p20]
24. quiet(paul) [input hypothesis]
61. ! [X0] : ((~creative(X0) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | creative(X0))) [nnf transformation 10]
62. ! [X0] : ((~creative(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | creative(X0))) [flattening 61]
72. ((~humble(susan) & ~creative(susan)) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (? [X0] : ((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | (humble(susan) | creative(susan))) [nnf transformation 16]
73. ((~humble(susan) & ~creative(susan)) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (? [X0] : ((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | humble(susan) | creative(susan)) [flattening 72]
74. ((~humble(susan) & ~creative(susan)) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (? [X1] : ((~wise(X1) | quiet(X1)) & (wise(X1) | ~quiet(X1))) | humble(susan) | creative(susan)) [rectify 73]
75. ? [X1] : ((~wise(X1) | quiet(X1)) & (wise(X1) | ~quiet(X1))) => ((~wise(sK7) | quiet(sK7)) & (wise(sK7) | ~quiet(sK7))) [choice axiom]
76. ((~humble(susan) & ~creative(susan)) | ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (((~wise(sK7) | quiet(sK7)) & (wise(sK7) | ~quiet(sK7))) | humble(susan) | creative(susan)) [skolemisation 74,75]
109. humble(X0) | creative(X0) [cnf transformation 62]
129. ~creative(susan) | ~quiet(X0) | ~wise(X0) [cnf transformation 76]
131. ~humble(susan) | ~quiet(X0) | ~wise(X0) [cnf transformation 76]
137. wise(paul) [cnf transformation 21]
142. quiet(paul) [cnf transformation 24]
298. 35 <=> ! [X0] : (~quiet(X0) | ~wise(X0)) [avatar definition]
299. ~quiet(X0) | ~wise(X0) <- (35) [avatar component clause 298]
301. 36 <=> humble(susan) [avatar definition]
303. ~humble(susan) <- (~36) [avatar component clause 301]
304. 35 | ~36 [avatar split clause 131,301,298]
310. 38 <=> creative(susan) [avatar definition]
312. ~creative(susan) <- (~38) [avatar component clause 310]
313. 35 | ~38 [avatar split clause 129,310,298]
343. creative(susan) <- (~36) [resolution 109,303]
346. $false <- (~36, ~38) [subsumption resolution 343,312]
347. 36 | 38 [avatar contradiction clause 346]
378. ~wise(paul) <- (35) [resolution 299,142]
381. $false <- (35) [subsumption resolution 378,137]
382. ~35 [avatar contradiction clause 381]
383. $false [avatar sat refutation 304,313,347,382]
% SZS output end Proof for 8564550910833352495557210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or happy is either rich or happy and vice versa.
Everyone who is funny is wise and vice versa.
Everyone who is not funny or not old is kind.
Everyone who is both humble and not tall is both calm and not tall and vice versa.
If someone is both not patient and not humble then someone is either patient or not happy.
If someone is not curious then someone is not funny and vice versa.
Everyone who is not calm or not patient is not strong.
If someone is both old and humble then someone is not humble and vice versa.
If paul is not brave then someone is both brave and kind.
If someone is both not humble and patient then someone is not creative and vice versa.
Everyone who is brave is either not creative or not tall.
If alice is either not strong or not creative then paul is not calm or not happy and vice versa.
Everyone who is either not funny or humble is not humble or not tall.
Everyone who is kind or old is not curious.
If someone is both humble and not brave then someone is both not quiet and curious and vice versa.
If someone is either old or not funny then someone is patient or not curious.
Alice is creative or rich.
Someone is strong.
Alice is not funny.
Someone is either curious or patient.
Someone is not humble.
Paul is not happy.
Lucy is brave or not curious.
Someone is both quiet and humble. | Alice is not strong. | neutral | (![X]:((tall(X)|happy(X))<=>(rich(X)<~>happy(X))))&
(![X]:(funny(X)<=>wise(X)))&
(![X]:((~funny(X)|~old(X))=>kind(X)))&
(![X]:((humble(X)&~tall(X))<=>(calm(X)&~tall(X))))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)|~patient(X))=>~strong(X)))&
((?[X]:((old(X)&humble(X))))<=>(?[X]:(~humble(X))))&
((~brave(paul))=>(?[X]:((brave(X)&kind(X)))))&
((?[X]:((~humble(X)&patient(X))))<=>(?[X]:(~creative(X))))&
(![X]:(brave(X)=>(~creative(X)<~>~tall(X))))&
(((~strong(alice)<~>~creative(alice)))<=>((~calm(paul)|~happy(paul))))&
(![X]:((~funny(X)<~>humble(X))=>(~humble(X)|~tall(X))))&
(![X]:((kind(X)|old(X))=>~curious(X)))&
((?[X]:((humble(X)&~brave(X))))<=>(?[X]:((~quiet(X)&curious(X)))))&
((?[X]:((old(X)<~>~funny(X))))=>(?[X]:((patient(X)|~curious(X)))))&
((creative(alice)|rich(alice)))&
(?[X]:(strong(X)))&
(~funny(alice))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:(~humble(X)))&
(~happy(paul))&
((brave(lucy)|~curious(lucy)))&
(?[X]:((quiet(X)&humble(X)))) | ~strong(alice) | [] | null | 0 |
If john is brave then someone is quiet. If alice is not generous then susan is both not tall and not strong and vice versa. If alice is old then john is curious and vice versa. Everyone who is old is not creative and vice versa. Everyone who is tall is both humble and strong. If someone is quiet or generous then someone is either wise or kind and vice versa. Everyone who is not happy is creative. Everyone who is creative or happy is either not creative or happy. Everyone who is not rich or not brave is either tall or not patient. Everyone who is creative or calm is either not rich or old and vice versa. If alice is both not generous and kind then alice is both not brave and humble and vice versa. Everyone who is old is either not creative or rich and vice versa. If susan is brave then susan is either not kind or not strong and vice versa. If someone is either not wise or wise then alice is both not kind and not old and vice versa. If someone is not funny or happy then lucy is kind and vice versa. Everyone who is both generous and not humble is either not curious or patient. Someone is either strong or tall. Fred is both not generous and curious. Paul is not strong. John is both calm and not kind. Alice is either not calm or curious. Susan is either not calm or not wise. | Susan is not old. | entailment | ((brave(john))=>(?[X]:(quiet(X))))&
((~generous(alice))<=>((~tall(susan)&~strong(susan))))&
((old(alice))<=>(curious(john)))&
(![X]:(old(X)<=>~creative(X)))&
(![X]:(tall(X)=>(humble(X)&strong(X))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(~happy(X)=>creative(X)))&
(![X]:((creative(X)|happy(X))=>(~creative(X)<~>happy(X))))&
(![X]:((~rich(X)|~brave(X))=>(tall(X)<~>~patient(X))))&
(![X]:((creative(X)|calm(X))<=>(~rich(X)<~>old(X))))&
(((~generous(alice)&kind(alice)))<=>((~brave(alice)&humble(alice))))&
(![X]:(old(X)<=>(~creative(X)<~>rich(X))))&
((brave(susan))<=>((~kind(susan)<~>~strong(susan))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((~kind(alice)&~old(alice))))&
((?[X]:((~funny(X)|happy(X))))<=>(kind(lucy)))&
(![X]:((generous(X)&~humble(X))=>(~curious(X)<~>patient(X))))&
(?[X]:((strong(X)<~>tall(X))))&
((~generous(fred)&curious(fred)))&
(~strong(paul))&
((calm(john)&~kind(john)))&
((~calm(alice)<~>curious(alice)))&
((~calm(susan)<~>~wise(susan))) | ~old(susan) | [
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4771459031393808951306295
% SZS output start Proof for 4771459031393808951306295
4. ! [X0] : (old(X0) <=> ~creative(X0)) [input p3]
7. ! [X0] : (~happy(X0) => creative(X0)) [input p6]
8. ! [X0] : ((happy(X0) | creative(X0)) => (~creative(X0) <~> happy(X0))) [input p7]
23. old(susan) [input hypothesis]
27. ! [X0] : (creative(X0) | happy(X0)) [ennf transformation 7]
28. ! [X0] : ((~creative(X0) <~> happy(X0)) | (~happy(X0) & ~creative(X0))) [ennf transformation 8]
37. ! [X0] : ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))) [nnf transformation 4]
43. ! [X0] : (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~happy(X0) & ~creative(X0))) [nnf transformation 28]
72. ~creative(X0) | ~old(X0) [cnf transformation 37]
82. creative(X0) | happy(X0) [cnf transformation 27]
86. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 43]
131. old(susan) [cnf transformation 23]
137. ~happy(X0) | creative(X0) [duplicate literal removal 86]
206. creative(X0) [subsumption resolution 137,82]
270. ~old(X0) [resolution 72,206]
272. $false [resolution 270,131]
% SZS output end Proof for 4771459031393808951306295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble or strong then lucy is either rich or creative and vice versa.
If alice is both not brave and not generous then someone is tall or not wise.
Everyone who is not brave is either quiet or not funny.
Everyone who is calm is either not calm or quiet and vice versa.
Everyone who is either not happy or funny is both not wise and old.
If someone is both not strong and brave then someone is both not patient and not brave and vice versa.
Everyone who is not funny or calm is either quiet or not calm and vice versa.
If someone is either kind or patient then paul is generous and vice versa.
Everyone who is funny is rich or happy and vice versa.
Everyone who is brave is either curious or kind.
Everyone who is either strong or not calm is either calm or not patient and vice versa.
If fred is wise or not brave then someone is either generous or not rich and vice versa.
Everyone who is generous or creative is curious or calm and vice versa.
If paul is patient or creative then lucy is both old and curious and vice versa.
Everyone who is either not kind or humble is either not patient or happy.
Everyone who is generous is both strong and not creative and vice versa.
Someone is not strong.
Someone is either generous or not generous.
Someone is either not creative or strong.
Lucy is tall.
Someone is not creative or not tall.
Someone is kind.
John is both wise and creative. | Paul is quiet. | entailment | (((~humble(john)|strong(john)))<=>((rich(lucy)<~>creative(lucy))))&
(((~brave(alice)&~generous(alice)))=>(?[X]:((tall(X)|~wise(X)))))&
(![X]:(~brave(X)=>(quiet(X)<~>~funny(X))))&
(![X]:(calm(X)<=>(~calm(X)<~>quiet(X))))&
(![X]:((~happy(X)<~>funny(X))=>(~wise(X)&old(X))))&
((?[X]:((~strong(X)&brave(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~funny(X)|calm(X))<=>(quiet(X)<~>~calm(X))))&
((?[X]:((kind(X)<~>patient(X))))<=>(generous(paul)))&
(![X]:(funny(X)<=>(rich(X)|happy(X))))&
(![X]:(brave(X)=>(curious(X)<~>kind(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(calm(X)<~>~patient(X))))&
(((wise(fred)|~brave(fred)))<=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:((generous(X)|creative(X))<=>(curious(X)|calm(X))))&
(((patient(paul)|creative(paul)))<=>((old(lucy)&curious(lucy))))&
(![X]:((~kind(X)<~>humble(X))=>(~patient(X)<~>happy(X))))&
(![X]:(generous(X)<=>(strong(X)&~creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
(tall(lucy))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:(kind(X)))&
((wise(john)&creative(john))) | quiet(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8567229931934146291955178
% SZS output start Proof for 8567229931934146291955178
4. ! [X0] : (calm(X0) <=> (~calm(X0) <~> quiet(X0))) [input p3]
24. ~quiet(paul) [input hypothesis]
37. ! [X0] : ((calm(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ~calm(X0))) [nnf transformation 4]
87. quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
89. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 37]
154. ~quiet(paul) [cnf transformation 24]
161. quiet(X0) | ~calm(X0) [duplicate literal removal 87]
162. calm(X0) | quiet(X0) [duplicate literal removal 89]
202. quiet(X0) [subsumption resolution 161,162]
322. $false [subsumption resolution 154,202]
% SZS output end Proof for 8567229931934146291955178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and patient is either not old or not patient.
Everyone who is both not funny and not creative is either funny or strong and vice versa.
Everyone who is either not brave or not tall is both wise and not generous.
Everyone who is both quiet and funny is either not kind or not humble and vice versa.
If someone is not old or happy then fred is both old and not tall and vice versa.
Everyone who is either not brave or creative is not tall and vice versa.
If someone is not rich then someone is not tall and vice versa.
If lucy is either patient or not funny then someone is rich and vice versa.
If someone is either kind or not humble then someone is either generous or funny and vice versa.
Everyone who is kind is either quiet or calm and vice versa.
Everyone who is rich is either not rich or not kind.
Everyone who is kind is either not calm or quiet.
If someone is both old and rich then lucy is both not wise and calm and vice versa.
Everyone who is both not generous and rich is either not brave or funny.
Everyone who is not funny is not calm or patient and vice versa.
If someone is not old or not happy then someone is wise.
Paul is old.
Paul is both not calm and not tall.
Someone is either humble or strong.
Someone is both rich and not funny.
Alice is not funny or happy.
Someone is either not wise or not happy.
Lucy is humble or not strong.
Someone is either wise or curious. | Lucy is strong. | contradiction | (![X]:((~calm(X)&patient(X))=>(~old(X)<~>~patient(X))))&
(![X]:((~funny(X)&~creative(X))<=>(funny(X)<~>strong(X))))&
(![X]:((~brave(X)<~>~tall(X))=>(wise(X)&~generous(X))))&
(![X]:((quiet(X)&funny(X))<=>(~kind(X)<~>~humble(X))))&
((?[X]:((~old(X)|happy(X))))<=>((old(fred)&~tall(fred))))&
(![X]:((~brave(X)<~>creative(X))<=>~tall(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(~tall(X))))&
(((patient(lucy)<~>~funny(lucy)))<=>(?[X]:(rich(X))))&
((?[X]:((kind(X)<~>~humble(X))))<=>(?[X]:((generous(X)<~>funny(X)))))&
(![X]:(kind(X)<=>(quiet(X)<~>calm(X))))&
(![X]:(rich(X)=>(~rich(X)<~>~kind(X))))&
(![X]:(kind(X)=>(~calm(X)<~>quiet(X))))&
((?[X]:((old(X)&rich(X))))<=>((~wise(lucy)&calm(lucy))))&
(![X]:((~generous(X)&rich(X))=>(~brave(X)<~>funny(X))))&
(![X]:(~funny(X)<=>(~calm(X)|patient(X))))&
((?[X]:((~old(X)|~happy(X))))=>(?[X]:(wise(X))))&
(old(paul))&
((~calm(paul)&~tall(paul)))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:((rich(X)&~funny(X))))&
((~funny(alice)|happy(alice)))&
(?[X]:((~wise(X)<~>~happy(X))))&
((humble(lucy)|~strong(lucy)))&
(?[X]:((wise(X)<~>curious(X)))) | strong(lucy) | [
"p3",
"p7",
"p9",
"p11",
"p14",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6173821229706948194905892
% SZS output start Proof for 6173821229706948194905892
4. ! [X0] : ((funny(X0) & quiet(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p3]
8. (patient(lucy) <~> ~funny(lucy)) <=> ? [X0] : rich(X0) [input p7]
10. ! [X0] : (kind(X0) <=> (quiet(X0) <~> calm(X0))) [input p9]
12. ! [X0] : (kind(X0) => (~calm(X0) <~> quiet(X0))) [input p11]
15. ! [X0] : (~funny(X0) <=> (patient(X0) | ~calm(X0))) [input p14]
20. ? [X0] : (~funny(X0) & rich(X0)) [input p19]
23. ~strong(lucy) | humble(lucy) [input p22]
25. strong(lucy) [input hypothesis]
33. ! [X0] : ((~calm(X0) <~> quiet(X0)) | ~kind(X0)) [ennf transformation 12]
41. ! [X0] : (((funny(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 4]
42. ! [X0] : (((funny(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | ~funny(X0) | ~quiet(X0))) [flattening 41]
54. (((funny(lucy) | ~patient(lucy)) & (~funny(lucy) | patient(lucy))) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ((patient(lucy) | funny(lucy)) & (~funny(lucy) | ~patient(lucy)))) [nnf transformation 8]
55. (((funny(lucy) | ~patient(lucy)) & (~funny(lucy) | patient(lucy))) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ((patient(lucy) | funny(lucy)) & (~funny(lucy) | ~patient(lucy)))) [rectify 54]
56. ? [X1] : rich(X1) => rich(sK3) [choice axiom]
57. (((funny(lucy) | ~patient(lucy)) & (~funny(lucy) | patient(lucy))) | ! [X0] : ~rich(X0)) & (rich(sK3) | ((patient(lucy) | funny(lucy)) & (~funny(lucy) | ~patient(lucy)))) [skolemisation 55,56]
63. ! [X0] : ((kind(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~kind(X0))) [nnf transformation 10]
65. ! [X0] : (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ~kind(X0)) [nnf transformation 33]
72. ! [X0] : ((~funny(X0) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | funny(X0))) [nnf transformation 15]
73. ! [X0] : ((~funny(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | funny(X0))) [flattening 72]
80. ? [X0] : (~funny(X0) & rich(X0)) => (~funny(sK9) & rich(sK9)) [choice axiom]
81. ~funny(sK9) & rich(sK9) [skolemisation 20,80]
102. ~humble(X0) | quiet(X0) | kind(X0) [cnf transformation 42]
104. ~humble(X0) | funny(X0) | kind(X0) [cnf transformation 42]
119. ~funny(lucy) | patient(lucy) | ~rich(X0) [cnf transformation 57]
129. ~kind(X0) | quiet(X0) | calm(X0) [cnf transformation 63]
130. ~kind(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 63]
135. quiet(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 65]
136. ~quiet(X0) | calm(X0) | ~kind(X0) [cnf transformation 65]
145. ~funny(X0) | ~patient(X0) [cnf transformation 73]
153. rich(sK9) [cnf transformation 81]
158. ~strong(lucy) | humble(lucy) [cnf transformation 23]
161. strong(lucy) [cnf transformation 25]
211. 11 <=> ! [X0] : ~rich(X0) [avatar definition]
212. ~rich(X0) <- (11) [avatar component clause 211]
214. 12 <=> patient(lucy) [avatar definition]
215. patient(lucy) <- (12) [avatar component clause 214]
218. 13 <=> funny(lucy) [avatar definition]
219. ~funny(lucy) <- (~13) [avatar component clause 218]
220. funny(lucy) <- (13) [avatar component clause 218]
222. 11 | 12 | ~13 [avatar split clause 119,218,214,211]
265. ~kind(X0) | calm(X0) [subsumption resolution 136,129]
266. ~kind(X0) | quiet(X0) [subsumption resolution 135,129]
272. 24 <=> calm(lucy) [avatar definition]
329. 36 <=> humble(lucy) [avatar definition]
331. humble(lucy) <- (36) [avatar component clause 329]
333. 37 <=> strong(lucy) [avatar definition]
336. 36 | ~37 [avatar split clause 158,333,329]
347. 37 [avatar split clause 161,333]
356. $false <- (11) [resolution 212,153]
357. ~11 [avatar contradiction clause 356]
359. ~patient(lucy) <- (13) [resolution 145,220]
360. $false <- (12, 13) [subsumption resolution 359,215]
361. ~12 | ~13 [avatar contradiction clause 360]
394. quiet(lucy) | kind(lucy) <- (36) [resolution 102,331]
396. quiet(lucy) <- (36) [subsumption resolution 394,266]
398. funny(lucy) | kind(lucy) <- (36) [resolution 104,331]
408. kind(lucy) <- (~13, 36) [subsumption resolution 398,219]
418. calm(lucy) <- (~13, 36) [resolution 408,265]
420. ~quiet(lucy) | ~calm(lucy) <- (~13, 36) [resolution 130,408]
421. ~calm(lucy) <- (~13, 36) [subsumption resolution 420,396]
424. ~24 | 13 | ~36 [avatar split clause 421,329,218,272]
425. 24 | 13 | ~36 [avatar split clause 418,329,218,272]
428. $false [avatar sat refutation 222,336,347,357,361,424,425]
% SZS output end Proof for 6173821229706948194905892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either rich or not calm then someone is both quiet and not patient and vice versa. Everyone who is either happy or not strong is both not brave and not happy. If someone is rich then susan is happy and vice versa. If someone is patient or not curious then someone is creative and vice versa. Everyone who is not wise or not humble is not creative or rich. Everyone who is not happy or patient is both not kind and funny. If lucy is either not funny or happy then fred is either not humble or not funny and vice versa. Everyone who is both not generous and not kind is either not generous or generous and vice versa. If paul is both kind and patient then someone is both not calm and happy and vice versa. If fred is not generous then fred is old. Everyone who is both patient and quiet is both not kind and not humble. If someone is either not quiet or rich then someone is not creative or not strong and vice versa. If someone is old or not curious then someone is creative and vice versa. Everyone who is both not rich and strong is both brave and not rich and vice versa. If someone is either rich or generous then someone is not quiet and vice versa. Everyone who is calm is not calm. Susan is rich or wise. Susan is not brave or not kind. Paul is either not creative or brave. Someone is not tall or curious. Someone is happy or curious. Someone is not kind or not quiet. Someone is not calm or patient. | Susan is not kind. | entailment | (((rich(alice)<~>~calm(alice)))<=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((happy(X)<~>~strong(X))=>(~brave(X)&~happy(X))))&
((?[X]:(rich(X)))<=>(happy(susan)))&
((?[X]:((patient(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(![X]:((~wise(X)|~humble(X))=>(~creative(X)|rich(X))))&
(![X]:((~happy(X)|patient(X))=>(~kind(X)&funny(X))))&
(((~funny(lucy)<~>happy(lucy)))<=>((~humble(fred)<~>~funny(fred))))&
(![X]:((~generous(X)&~kind(X))<=>(~generous(X)<~>generous(X))))&
(((kind(paul)&patient(paul)))<=>(?[X]:((~calm(X)&happy(X)))))&
((~generous(fred))=>(old(fred)))&
(![X]:((patient(X)&quiet(X))=>(~kind(X)&~humble(X))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(![X]:((~rich(X)&strong(X))<=>(brave(X)&~rich(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(calm(X)=>~calm(X)))&
((rich(susan)|wise(susan)))&
((~brave(susan)|~kind(susan)))&
((~creative(paul)<~>brave(paul)))&
(?[X]:((~tall(X)|curious(X))))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~kind(X)|~quiet(X))))&
(?[X]:((~calm(X)|patient(X)))) | ~kind(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3870626548826768109310989
% SZS output start Proof for 3870626548826768109310989
8. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (~generous(X0) <~> generous(X0))) [input p7]
24. kind(susan) [input hypothesis]
55. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (kind(X0) | generous(X0)))) [nnf transformation 8]
56. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | kind(X0) | generous(X0))) [flattening 55]
118. ~kind(X0) | generous(X0) | generous(X0) [cnf transformation 56]
119. ~kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 56]
151. kind(susan) [cnf transformation 24]
157. ~kind(X0) | generous(X0) [duplicate literal removal 118]
158. ~kind(X0) | ~generous(X0) [duplicate literal removal 119]
248. ~kind(X0) [subsumption resolution 157,158]
346. $false [subsumption resolution 151,248]
% SZS output end Proof for 3870626548826768109310989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or patient is both not creative and not brave and vice versa.
Everyone who is not old or not kind is either not curious or creative.
If someone is not calm then someone is not happy or not funny and vice versa.
Everyone who is not wise is either wise or not calm and vice versa.
If someone is not calm then someone is quiet.
Everyone who is both not curious and quiet is not quiet and vice versa.
Everyone who is either quiet or tall is both quiet and patient and vice versa.
Everyone who is not rich or old is not curious or not happy and vice versa.
If someone is both tall and not calm then someone is humble or creative.
If someone is not patient then mary is both not funny and not rich.
If someone is both funny and not wise then someone is both strong and not strong.
Everyone who is both not strong and not creative is tall or not kind.
If someone is not funny then someone is not happy.
If paul is not happy then someone is not rich.
Everyone who is strong or not wise is either patient or tall and vice versa.
Everyone who is calm or not patient is calm or strong.
Alice is both tall and not generous.
Someone is either humble or brave.
Paul is not humble.
Someone is either not creative or not tall.
Paul is both quiet and rich.
Someone is not kind.
Someone is either not strong or curious. | Alice is quiet. | entailment | (![X]:((humble(X)|patient(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~old(X)|~kind(X))=>(~curious(X)<~>creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:(~wise(X)<=>(wise(X)<~>~calm(X))))&
((?[X]:(~calm(X)))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&quiet(X))<=>~quiet(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(quiet(X)&patient(X))))&
(![X]:((~rich(X)|old(X))<=>(~curious(X)|~happy(X))))&
((?[X]:((tall(X)&~calm(X))))=>(?[X]:((humble(X)|creative(X)))))&
((?[X]:(~patient(X)))=>((~funny(mary)&~rich(mary))))&
((?[X]:((funny(X)&~wise(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)&~creative(X))=>(tall(X)|~kind(X))))&
((?[X]:(~funny(X)))=>(?[X]:(~happy(X))))&
((~happy(paul))=>(?[X]:(~rich(X))))&
(![X]:((strong(X)|~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((calm(X)|~patient(X))=>(calm(X)|strong(X))))&
((tall(alice)&~generous(alice)))&
(?[X]:((humble(X)<~>brave(X))))&
(~humble(paul))&
(?[X]:((~creative(X)<~>~tall(X))))&
((quiet(paul)&rich(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((~strong(X)<~>curious(X)))) | quiet(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3599618645448771561102598
% SZS output start Proof for 3599618645448771561102598
6. ! [X0] : ((quiet(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p5]
24. ~quiet(alice) [input hypothesis]
54. ! [X0] : (((quiet(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) | curious(X0)))) [nnf transformation 6]
55. ! [X0] : (((quiet(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | ~quiet(X0) | curious(X0))) [flattening 54]
103. quiet(X0) | quiet(X0) [cnf transformation 55]
141. ~quiet(alice) [cnf transformation 24]
145. quiet(X0) [duplicate literal removal 103]
252. $false [subsumption resolution 141,145]
% SZS output end Proof for 3599618645448771561102598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet then someone is either generous or happy and vice versa. Everyone who is not quiet or rich is not creative and vice versa. If john is quiet then paul is either rich or not funny and vice versa. Everyone who is either not happy or not quiet is both creative and not generous. Everyone who is both creative and not curious is both not tall and not old. Everyone who is not generous is both not happy and not funny and vice versa. Everyone who is rich is kind or strong and vice versa. Everyone who is creative or not kind is happy and vice versa. If lucy is tall then susan is both rich and not creative and vice versa. Everyone who is happy or not kind is either not brave or not quiet and vice versa. If someone is not curious or humble then someone is either brave or not humble. If someone is not wise or humble then someone is either brave or kind and vice versa. Everyone who is rich or not funny is both funny and not happy and vice versa. If someone is both kind and not wise then john is either not strong or patient. If someone is creative or curious then fred is creative or happy. Everyone who is both not curious and kind is both not calm and not rich and vice versa. Someone is both tall and not calm. Someone is creative or not rich. Paul is either rich or not generous. Paul is both wise and not old. Paul is kind or patient. Someone is either patient or not wise. | Lucy is generous. | entailment | ((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((~quiet(X)|rich(X))<=>~creative(X)))&
((quiet(john))<=>((rich(paul)<~>~funny(paul))))&
(![X]:((~happy(X)<~>~quiet(X))=>(creative(X)&~generous(X))))&
(![X]:((creative(X)&~curious(X))=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~funny(X))))&
(![X]:(rich(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)|~kind(X))<=>happy(X)))&
((tall(lucy))<=>((rich(susan)&~creative(susan))))&
(![X]:((happy(X)|~kind(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((~curious(X)|humble(X))))=>(?[X]:((brave(X)<~>~humble(X)))))&
((?[X]:((~wise(X)|humble(X))))<=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((rich(X)|~funny(X))<=>(funny(X)&~happy(X))))&
((?[X]:((kind(X)&~wise(X))))=>((~strong(john)<~>patient(john))))&
((?[X]:((creative(X)|curious(X))))=>((creative(fred)|happy(fred))))&
(![X]:((~curious(X)&kind(X))<=>(~calm(X)&~rich(X))))&
(?[X]:((tall(X)&~calm(X))))&
(?[X]:((creative(X)|~rich(X))))&
((rich(paul)<~>~generous(paul)))&
((wise(paul)&~old(paul)))&
((kind(paul)|patient(paul)))&
(?[X]:((patient(X)<~>~wise(X)))) | generous(lucy) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5437842588067937899695334
% SZS output start Proof for 5437842588067937899695334
6. ! [X0] : (~generous(X0) <=> (~funny(X0) & ~happy(X0))) [input p5]
13. ! [X0] : ((~funny(X0) | rich(X0)) <=> (~happy(X0) & funny(X0))) [input p12]
23. ~generous(lucy) [input hypothesis]
45. ! [X0] : ((~generous(X0) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | generous(X0))) [nnf transformation 6]
46. ! [X0] : ((~generous(X0) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | generous(X0))) [flattening 45]
64. ! [X0] : (((~funny(X0) | rich(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (funny(X0) & ~rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((~funny(X0) | rich(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (funny(X0) & ~rich(X0)))) [flattening 64]
96. ~funny(X0) | generous(X0) [cnf transformation 46]
124. funny(X0) | funny(X0) [cnf transformation 65]
145. ~generous(lucy) [cnf transformation 23]
146. funny(X0) [duplicate literal removal 124]
330. generous(X0) [resolution 96,146]
331. $false [resolution 330,145]
% SZS output end Proof for 5437842588067937899695334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both creative and calm is creative. Everyone who is wise is humble and vice versa. If someone is both not strong and old then someone is either not rich or rich. If susan is brave or not patient then someone is either not old or curious. If someone is either not old or not wise then someone is wise. Everyone who is both wise and calm is not kind or happy. Everyone who is both not curious and not wise is both not generous and not strong and vice versa. If mary is not generous then alice is both not strong and funny and vice versa. Everyone who is curious or creative is rich or creative and vice versa. Everyone who is not brave or not generous is not generous or old and vice versa. If paul is either quiet or wise then someone is both not rich and brave and vice versa. If someone is strong or not wise then mary is both patient and not humble. Everyone who is both rich and not quiet is happy and vice versa. Everyone who is both not old and calm is both patient and not strong. If someone is both not tall and kind then lucy is both creative and not tall. If someone is not curious then lucy is both quiet and kind and vice versa. John is not tall. Susan is both not kind and humble. Paul is not funny. Paul is calm or tall. Someone is both funny and not curious. John is not strong or kind. Susan is brave. Someone is either not curious or tall. | Alice is funny. | neutral | (![X]:((creative(X)&calm(X))=>creative(X)))&
(![X]:(wise(X)<=>humble(X)))&
((?[X]:((~strong(X)&old(X))))=>(?[X]:((~rich(X)<~>rich(X)))))&
(((brave(susan)|~patient(susan)))=>(?[X]:((~old(X)<~>curious(X)))))&
((?[X]:((~old(X)<~>~wise(X))))=>(?[X]:(wise(X))))&
(![X]:((wise(X)&calm(X))=>(~kind(X)|happy(X))))&
(![X]:((~curious(X)&~wise(X))<=>(~generous(X)&~strong(X))))&
((~generous(mary))<=>((~strong(alice)&funny(alice))))&
(![X]:((curious(X)|creative(X))<=>(rich(X)|creative(X))))&
(![X]:((~brave(X)|~generous(X))<=>(~generous(X)|old(X))))&
(((quiet(paul)<~>wise(paul)))<=>(?[X]:((~rich(X)&brave(X)))))&
((?[X]:((strong(X)|~wise(X))))=>((patient(mary)&~humble(mary))))&
(![X]:((rich(X)&~quiet(X))<=>happy(X)))&
(![X]:((~old(X)&calm(X))=>(patient(X)&~strong(X))))&
((?[X]:((~tall(X)&kind(X))))=>((creative(lucy)&~tall(lucy))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)&kind(lucy))))&
(~tall(john))&
((~kind(susan)&humble(susan)))&
(~funny(paul))&
((calm(paul)|tall(paul)))&
(?[X]:((funny(X)&~curious(X))))&
((~strong(john)|kind(john)))&
(brave(susan))&
(?[X]:((~curious(X)<~>tall(X)))) | funny(alice) | [] | null | 0 |
If someone is not humble then paul is either funny or creative.
Everyone who is either not wise or not calm is either happy or kind and vice versa.
Everyone who is old or not kind is not strong or not old.
Everyone who is both curious and funny is generous and vice versa.
If mary is curious then fred is both kind and not curious and vice versa.
Everyone who is old or not calm is either not curious or funny.
Everyone who is either strong or not curious is not humble and vice versa.
Everyone who is funny or strong is both creative and not old and vice versa.
Everyone who is both not happy and not generous is both kind and curious.
If someone is both happy and not happy then someone is both not tall and not strong and vice versa.
Everyone who is either not brave or not strong is both tall and calm and vice versa.
Everyone who is either not creative or funny is both not strong and not quiet and vice versa.
If susan is both not rich and curious then susan is either generous or not calm and vice versa.
If susan is generous or not strong then lucy is both not brave and patient.
Everyone who is both not tall and not generous is not generous or humble.
If someone is old then someone is either curious or happy.
Mary is not old.
Someone is both creative and humble.
Someone is both creative and curious.
Someone is patient.
Someone is both not quiet and brave.
Someone is tall.
Fred is quiet or not humble.
Someone is old or patient. | Lucy is not wise. | neutral | ((?[X]:(~humble(X)))=>((funny(paul)<~>creative(paul))))&
(![X]:((~wise(X)<~>~calm(X))<=>(happy(X)<~>kind(X))))&
(![X]:((old(X)|~kind(X))=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&funny(X))<=>generous(X)))&
((curious(mary))<=>((kind(fred)&~curious(fred))))&
(![X]:((old(X)|~calm(X))=>(~curious(X)<~>funny(X))))&
(![X]:((strong(X)<~>~curious(X))<=>~humble(X)))&
(![X]:((funny(X)|strong(X))<=>(creative(X)&~old(X))))&
(![X]:((~happy(X)&~generous(X))=>(kind(X)&curious(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(tall(X)&calm(X))))&
(![X]:((~creative(X)<~>funny(X))<=>(~strong(X)&~quiet(X))))&
(((~rich(susan)&curious(susan)))<=>((generous(susan)<~>~calm(susan))))&
(((generous(susan)|~strong(susan)))=>((~brave(lucy)&patient(lucy))))&
(![X]:((~tall(X)&~generous(X))=>(~generous(X)|humble(X))))&
((?[X]:(old(X)))=>(?[X]:((curious(X)<~>happy(X)))))&
(~old(mary))&
(?[X]:((creative(X)&humble(X))))&
(?[X]:((creative(X)&curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:(tall(X)))&
((quiet(fred)|~humble(fred)))&
(?[X]:((old(X)|patient(X)))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either wise or not humble is kind and vice versa. Everyone who is either not strong or not generous is both humble and kind. Everyone who is patient or rich is not generous. Everyone who is either not calm or funny is tall or not rich. If someone is not happy or not patient then someone is old and vice versa. If john is happy or calm then someone is either not creative or not strong and vice versa. Everyone who is patient is not quiet. If someone is not humble or not curious then alice is both rich and not creative. Everyone who is both not generous and funny is either curious or not brave and vice versa. Everyone who is either generous or quiet is not happy and vice versa. Everyone who is brave 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. Everyone who is quiet is not quiet or not humble and vice versa. Everyone who is brave or patient is not tall and vice versa. If someone is both not old and not strong then susan is tall and vice versa. Alice is creative or quiet. Someone is either not tall or strong. Alice is both not creative and not strong. Susan is either not generous or not curious. | Alice is calm. | entailment | (![X]:((wise(X)<~>~humble(X))<=>kind(X)))&
(![X]:((~strong(X)<~>~generous(X))=>(humble(X)&kind(X))))&
(![X]:((patient(X)|rich(X))=>~generous(X)))&
(![X]:((~calm(X)<~>funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:(old(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))=>((rich(alice)&~creative(alice))))&
(![X]:((~generous(X)&funny(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|patient(X))<=>~tall(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
((creative(alice)|quiet(alice)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~creative(alice)&~strong(alice)))&
((~generous(susan)<~>~curious(susan))) | calm(alice) | [
"p6",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5510450167443740837936682
% SZS output start Proof for 5510450167443740837936682
7. ! [X0] : (patient(X0) => ~quiet(X0)) [input p6]
8. ? [X0] : (~curious(X0) | ~humble(X0)) => (~creative(alice) & rich(alice)) [input p7]
13. (~rich(alice) | patient(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~humble(X0) | ~quiet(X0))) [input p13]
21. ~calm(alice) [input hypothesis]
29. ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 7]
30. (~creative(alice) & rich(alice)) | ! [X0] : (curious(X0) & humble(X0)) [ennf transformation 8]
50. ((~rich(alice) | patient(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [nnf transformation 13]
51. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [flattening 50]
52. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | (rich(alice) & ~patient(alice))) [rectify 51]
53. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK3) | ~curious(sK3)) [choice axiom]
54. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK3) | ~curious(sK3)) | (rich(alice) & ~patient(alice))) [skolemisation 52,53]
55. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 55]
86. ~quiet(X0) | ~patient(X0) [cnf transformation 29]
87. rich(alice) | humble(X0) [cnf transformation 30]
109. ~rich(alice) | patient(alice) | calm(X0) [cnf transformation 54]
110. ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
111. quiet(X0) | quiet(X0) [cnf transformation 56]
126. ~calm(alice) [cnf transformation 21]
127. ~humble(X0) | ~quiet(X0) [duplicate literal removal 110]
128. quiet(X0) [duplicate literal removal 111]
190. 15 <=> ! [X0] : humble(X0) [avatar definition]
191. humble(X0) <- (15) [avatar component clause 190]
194. 16 <=> rich(alice) [avatar definition]
198. 15 | 16 [avatar split clause 87,194,190]
200. 17 <=> ! [X0] : calm(X0) [avatar definition]
201. calm(X0) <- (17) [avatar component clause 200]
203. 18 <=> patient(alice) [avatar definition]
205. patient(alice) <- (18) [avatar component clause 203]
206. 17 | 18 | ~16 [avatar split clause 109,194,203,200]
218. ~humble(X0) [subsumption resolution 127,128]
258. $false <- (15) [subsumption resolution 191,218]
259. ~15 [avatar contradiction clause 258]
260. $false <- (17) [resolution 201,126]
263. ~17 [avatar contradiction clause 260]
268. ~patient(X0) [resolution 86,128]
269. $false <- (18) [resolution 268,205]
270. ~18 [avatar contradiction clause 269]
271. $false [avatar sat refutation 198,206,259,263,270]
% SZS output end Proof for 5510450167443740837936682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then susan is funny or tall and vice versa. Everyone who is strong or not quiet is not quiet. Everyone who is either not old or not quiet is both not rich and wise. Everyone who is strong or not happy is both rich and patient. Everyone who is not kind or not tall is not happy and vice versa. Everyone who is not funny is not old and vice versa. If lucy is both generous and not happy then lucy is rich or patient and vice versa. Everyone who is not strong or not funny is not creative and vice versa. If someone is not curious or calm then mary is patient or not humble. If mary is both not humble and old then lucy is quiet or rich. Everyone who is either quiet or brave is not humble or wise and vice versa. If alice is either generous or rich then john is either tall or rich and vice versa. If someone is strong then someone is not rich. Everyone who is both not old and not tall is happy. If susan is funny or not rich then someone is either quiet or funny. Everyone who is generous or patient is not patient and vice versa. Someone is either not patient or not kind. Mary is either tall or not kind. Someone is either not rich or not kind. Someone is not brave or tall. Someone is not funny or humble. Someone is creative or not old. | Lucy is tall. | entailment | ((?[X]:((curious(X)|~curious(X))))<=>((funny(susan)|tall(susan))))&
(![X]:((strong(X)|~quiet(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~quiet(X))=>(~rich(X)&wise(X))))&
(![X]:((strong(X)|~happy(X))=>(rich(X)&patient(X))))&
(![X]:((~kind(X)|~tall(X))<=>~happy(X)))&
(![X]:(~funny(X)<=>~old(X)))&
(((generous(lucy)&~happy(lucy)))<=>((rich(lucy)|patient(lucy))))&
(![X]:((~strong(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~curious(X)|calm(X))))=>((patient(mary)|~humble(mary))))&
(((~humble(mary)&old(mary)))=>((quiet(lucy)|rich(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(~humble(X)|wise(X))))&
(((generous(alice)<~>rich(alice)))<=>((tall(john)<~>rich(john))))&
((?[X]:(strong(X)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&~tall(X))=>happy(X)))&
(((funny(susan)|~rich(susan)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((generous(X)|patient(X))<=>~patient(X)))&
(?[X]:((~patient(X)<~>~kind(X))))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((creative(X)|~old(X)))) | tall(lucy) | [
"p3",
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 234827385004238773016832
% SZS output start Proof for 234827385004238773016832
4. ! [X0] : ((~happy(X0) | strong(X0)) => (patient(X0) & rich(X0))) [input p3]
5. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> ~happy(X0)) [input p4]
16. ! [X0] : ((patient(X0) | generous(X0)) <=> ~patient(X0)) [input p15]
23. ~tall(lucy) [input hypothesis]
29. ! [X0] : ((patient(X0) & rich(X0)) | (happy(X0) & ~strong(X0))) [ennf transformation 4]
45. ! [X0] : (((~tall(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) & kind(X0)))) [nnf transformation 5]
46. ! [X0] : ((~tall(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (tall(X0) & kind(X0)))) [flattening 45]
59. ! [X0] : (((patient(X0) | generous(X0)) | patient(X0)) & (~patient(X0) | (~patient(X0) & ~generous(X0)))) [nnf transformation 16]
60. ! [X0] : ((patient(X0) | generous(X0) | patient(X0)) & (~patient(X0) | (~patient(X0) & ~generous(X0)))) [flattening 59]
87. patient(X0) | happy(X0) [cnf transformation 29]
89. ~happy(X0) | tall(X0) [cnf transformation 46]
123. ~patient(X0) | ~patient(X0) [cnf transformation 60]
134. ~tall(lucy) [cnf transformation 23]
135. ~patient(X0) [duplicate literal removal 123]
291. happy(X0) [resolution 87,135]
299. tall(X0) [resolution 89,291]
302. $false [resolution 299,134]
% SZS output end Proof for 234827385004238773016832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and calm then someone is creative or funny and vice versa.
Everyone who is not patient is not kind or creative and vice versa.
Everyone who is both patient and happy is not tall or not happy.
If someone is not rich or not curious then someone is creative.
Everyone who is not curious is not brave and vice versa.
If paul is either not creative or strong then paul is either quiet or kind.
Everyone who is either funny or not quiet is both not generous and creative.
If someone is not old or not brave then someone is either funny or humble.
Everyone who is both patient and curious is creative or not funny and vice versa.
Everyone who is not humble or not patient is either creative or happy.
If someone is not happy then mary is not creative and vice versa.
If someone is either calm or tall then someone is not quiet and vice versa.
If alice is both generous and not patient then fred is not funny and vice versa.
If someone is either quiet or kind then paul is not curious and vice versa.
If fred is either patient or not quiet then mary is both not happy and not strong.
Everyone who is not generous is either happy or not humble and vice versa.
Someone is patient or not wise.
Susan is calm or happy.
Someone is calm.
Someone is not wise or quiet.
Lucy is tall.
Fred is not humble or quiet.
Fred is patient or not strong. | Mary is creative. | contradiction | ((?[X]:((wise(X)&calm(X))))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:(~patient(X)<=>(~kind(X)|creative(X))))&
(![X]:((patient(X)&happy(X))=>(~tall(X)|~happy(X))))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:(creative(X))))&
(![X]:(~curious(X)<=>~brave(X)))&
(((~creative(paul)<~>strong(paul)))=>((quiet(paul)<~>kind(paul))))&
(![X]:((funny(X)<~>~quiet(X))=>(~generous(X)&creative(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:((patient(X)&curious(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)|~patient(X))=>(creative(X)<~>happy(X))))&
((?[X]:(~happy(X)))<=>(~creative(mary)))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(~quiet(X))))&
(((generous(alice)&~patient(alice)))<=>(~funny(fred)))&
((?[X]:((quiet(X)<~>kind(X))))<=>(~curious(paul)))&
(((patient(fred)<~>~quiet(fred)))=>((~happy(mary)&~strong(mary))))&
(![X]:(~generous(X)<=>(happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~wise(X))))&
((calm(susan)|happy(susan)))&
(?[X]:(calm(X)))&
(?[X]:((~wise(X)|quiet(X))))&
(tall(lucy))&
((~humble(fred)|quiet(fred)))&
((patient(fred)|~strong(fred))) | creative(mary) | [
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1585809123596098070369337
% SZS output start Proof for 1585809123596098070369337
2. ! [X0] : (~patient(X0) <=> (creative(X0) | ~kind(X0))) [input p1]
9. ! [X0] : ((curious(X0) & patient(X0)) <=> (~funny(X0) | creative(X0))) [input p8]
24. creative(mary) [input hypothesis]
44. ! [X0] : ((~patient(X0) | (~creative(X0) & kind(X0))) & ((creative(X0) | ~kind(X0)) | patient(X0))) [nnf transformation 2]
45. ! [X0] : ((~patient(X0) | (~creative(X0) & kind(X0))) & (creative(X0) | ~kind(X0) | patient(X0))) [flattening 44]
56. ! [X0] : (((curious(X0) & patient(X0)) | (funny(X0) & ~creative(X0))) & ((~funny(X0) | creative(X0)) | (~curious(X0) | ~patient(X0)))) [nnf transformation 9]
57. ! [X0] : (((curious(X0) & patient(X0)) | (funny(X0) & ~creative(X0))) & (~funny(X0) | creative(X0) | ~curious(X0) | ~patient(X0))) [flattening 56]
89. ~patient(X0) | ~creative(X0) [cnf transformation 45]
105. patient(X0) | ~creative(X0) [cnf transformation 57]
141. creative(mary) [cnf transformation 24]
152. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
153. ~creative(X1) <- (3) [avatar component clause 152]
214. ~creative(X0) [subsumption resolution 105,89]
215. 3 [avatar split clause 214,152]
219. 17 <=> creative(mary) [avatar definition]
221. creative(mary) <- (17) [avatar component clause 219]
350. 17 [avatar split clause 141,219]
351. $false <- (3, 17) [resolution 221,153]
352. ~3 | ~17 [avatar contradiction clause 351]
353. $false [avatar sat refutation 215,350,352]
% SZS output end Proof for 1585809123596098070369337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either patient or tall then someone is both brave and rich and vice versa.
If alice is kind or not calm then someone is both funny and not quiet.
If someone is calm then someone is not wise or funny.
Everyone who is either strong or not wise is both tall and kind and vice versa.
Everyone who is both humble and strong is either rich or not funny and vice versa.
If someone is not strong or tall then john is not tall or not rich and vice versa.
If someone is curious or not patient then someone is not curious or calm.
Everyone who is either not tall or old is both tall and humble and vice versa.
Everyone who is funny is rich.
If lucy is either humble or tall then paul is both happy and rich.
If mary is not humble or generous then lucy is not quiet.
Everyone who is kind is both not strong and generous and vice versa.
Everyone who is happy is not curious or not rich.
Everyone who is wise is both not kind and not curious.
Everyone who is either not funny or generous is either wise or rich and vice versa.
Everyone who is patient is both not happy and calm and vice versa.
Susan is both not old and brave.
Someone is generous or not quiet.
Susan is either patient or curious.
Someone is either not rich or not strong.
Alice is both not funny and quiet.
Paul is kind or not calm.
Alice is both not wise and not happy. | Mary is not humble. | neutral | (((patient(lucy)<~>tall(lucy)))<=>(?[X]:((brave(X)&rich(X)))))&
(((kind(alice)|~calm(alice)))=>(?[X]:((funny(X)&~quiet(X)))))&
((?[X]:(calm(X)))=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((strong(X)<~>~wise(X))<=>(tall(X)&kind(X))))&
(![X]:((humble(X)&strong(X))<=>(rich(X)<~>~funny(X))))&
((?[X]:((~strong(X)|tall(X))))<=>((~tall(john)|~rich(john))))&
((?[X]:((curious(X)|~patient(X))))=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~tall(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:(funny(X)=>rich(X)))&
(((humble(lucy)<~>tall(lucy)))=>((happy(paul)&rich(paul))))&
(((~humble(mary)|generous(mary)))=>(~quiet(lucy)))&
(![X]:(kind(X)<=>(~strong(X)&generous(X))))&
(![X]:(happy(X)=>(~curious(X)|~rich(X))))&
(![X]:(wise(X)=>(~kind(X)&~curious(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(wise(X)<~>rich(X))))&
(![X]:(patient(X)<=>(~happy(X)&calm(X))))&
((~old(susan)&brave(susan)))&
(?[X]:((generous(X)|~quiet(X))))&
((patient(susan)<~>curious(susan)))&
(?[X]:((~rich(X)<~>~strong(X))))&
((~funny(alice)&quiet(alice)))&
((kind(paul)|~calm(paul)))&
((~wise(alice)&~happy(alice))) | ~humble(mary) | [] | null | 0 |
Everyone who is either happy or calm is both curious and calm.
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.
If john is not kind then paul is both creative and curious and vice versa.
Everyone who is both strong and rich is not happy and vice versa.
Everyone who is not curious or not creative is either not generous or not rich.
Everyone who is both not calm and happy is either curious or funny.
If someone is not rich then someone is kind or calm and vice versa.
If john is both not funny and not generous then someone is curious.
Everyone who is humble is either not curious or curious and vice versa.
Everyone who is not generous is not happy or not brave and vice versa.
John is not quiet or not funny.
Lucy is calm.
John is both old and tall.
Someone is wise or patient.
Someone is funny.
Someone is creative or not curious.
Someone is not kind.
Someone is either generous or humble. | John is not curious. | neutral | (![X]:((happy(X)<~>calm(X))=>(curious(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)))&
((~kind(john))<=>((creative(paul)&curious(paul))))&
(![X]:((strong(X)&rich(X))<=>~happy(X)))&
(![X]:((~curious(X)|~creative(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)&happy(X))=>(curious(X)<~>funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((kind(X)|calm(X)))))&
(((~funny(john)&~generous(john)))=>(?[X]:(curious(X))))&
(![X]:(humble(X)<=>(~curious(X)<~>curious(X))))&
(![X]:(~generous(X)<=>(~happy(X)|~brave(X))))&
((~quiet(john)|~funny(john)))&
(calm(lucy))&
((old(john)&tall(john)))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)<~>humble(X)))) | ~curious(john) | [] | null | 0 |
Everyone who is not patient is not rich or kind and vice versa.
If someone is not brave then john is not patient and vice versa.
If someone is not kind then susan is both not generous and not kind.
Everyone who is not rich or not kind is both not strong and not curious.
If susan is either kind or quiet then lucy is both kind and curious and vice versa.
If lucy is either patient or not curious then someone is either not tall or humble and vice versa.
If someone is both brave and happy then alice is both not patient and old and vice versa.
If mary is both creative and kind then paul is both not curious and creative.
Everyone who is either not quiet or old is old.
Everyone who is curious is either wise or curious and vice versa.
If susan is either not funny or not calm then someone is both not tall and not wise and vice versa.
If fred is quiet or not patient then paul is either not happy or not kind and vice versa.
If someone is generous or brave then someone is both not quiet and creative.
If lucy is not humble or patient then someone is either patient or not old.
Everyone who is either not patient or not generous is either funny or rich.
Someone is both happy and not quiet.
Someone is both happy and generous.
Someone is either tall or quiet.
Someone is generous or not brave.
Alice is funny.
Susan is rich. | Fred is not funny. | neutral | (![X]:(~patient(X)<=>(~rich(X)|kind(X))))&
((?[X]:(~brave(X)))<=>(~patient(john)))&
((?[X]:(~kind(X)))=>((~generous(susan)&~kind(susan))))&
(![X]:((~rich(X)|~kind(X))=>(~strong(X)&~curious(X))))&
(((kind(susan)<~>quiet(susan)))<=>((kind(lucy)&curious(lucy))))&
(((patient(lucy)<~>~curious(lucy)))<=>(?[X]:((~tall(X)<~>humble(X)))))&
((?[X]:((brave(X)&happy(X))))<=>((~patient(alice)&old(alice))))&
(((creative(mary)&kind(mary)))=>((~curious(paul)&creative(paul))))&
(![X]:((~quiet(X)<~>old(X))=>old(X)))&
(![X]:(curious(X)<=>(wise(X)<~>curious(X))))&
(((~funny(susan)<~>~calm(susan)))<=>(?[X]:((~tall(X)&~wise(X)))))&
(((quiet(fred)|~patient(fred)))<=>((~happy(paul)<~>~kind(paul))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((~quiet(X)&creative(X)))))&
(((~humble(lucy)|patient(lucy)))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((~patient(X)<~>~generous(X))=>(funny(X)<~>rich(X))))&
(?[X]:((happy(X)&~quiet(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:((generous(X)|~brave(X))))&
(funny(alice))&
(rich(susan)) | ~funny(fred) | [] | null | 0 |
Everyone who is either not rich or tall is generous or not calm.
If susan is both kind and curious then someone is either curious or not patient.
Everyone who is both patient and strong is happy or not kind.
Everyone who is both not quiet and rich is both brave and old.
Everyone who is not patient or not creative is both generous and not generous.
Everyone who is either not creative or not generous is not rich and vice versa.
Everyone who is curious or creative is both not curious and wise and vice versa.
If someone is quiet then someone is not patient or wise.
Everyone who is both not strong and strong is tall and vice versa.
If someone is both curious and wise then someone is not wise.
Everyone who is quiet is strong.
Everyone who is humble or not humble is creative.
Everyone who is either not curious or not funny is both not quiet and old.
Everyone who is either tall or creative is both calm and wise.
Everyone who is generous or not quiet is not quiet or kind.
Everyone who is both not old and calm is both not curious and not funny and vice versa.
Paul is both strong and generous.
Someone is kind or not creative.
Fred is humble.
Fred is strong.
Someone is either not strong or humble. | Fred is kind. | neutral | (![X]:((~rich(X)<~>tall(X))=>(generous(X)|~calm(X))))&
(((kind(susan)&curious(susan)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((patient(X)&strong(X))=>(happy(X)|~kind(X))))&
(![X]:((~quiet(X)&rich(X))=>(brave(X)&old(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)&~generous(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((curious(X)|creative(X))<=>(~curious(X)&wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
((strong(paul)&generous(paul)))&
(?[X]:((kind(X)|~creative(X))))&
(humble(fred))&
(strong(fred))&
(?[X]:((~strong(X)<~>humble(X)))) | kind(fred) | [] | null | 0 |
Everyone who is either humble or patient is either not curious or old and vice versa.
Everyone who is either old or not strong is not brave or not quiet and vice versa.
If susan is both not funny and old then someone is not happy and vice versa.
If mary is both wise and happy then alice is calm and vice versa.
If fred is both kind and rich then someone is either not quiet or not wise.
If lucy is either not tall or not calm then someone is not quiet or old and vice versa.
Everyone who is strong is both not strong and brave.
If someone is rich or wise then someone is not quiet or not patient and vice versa.
Everyone who is rich is not quiet or calm.
Everyone who is not quiet is not strong or not happy and vice versa.
Everyone who is both not calm and happy is not happy.
If someone is both not wise and not old then someone is not old.
If someone is strong or not funny then someone is either not brave or not old.
If alice is either not funny or kind then paul is either not curious or not tall.
If susan is not funny or not brave then susan is patient.
Everyone who is not tall is not wise or not brave.
Someone is both not brave and not wise.
Susan is not creative or not generous.
Alice is both not kind and not creative.
Paul is rich.
Someone is not wise or not calm.
Someone is not rich. | Alice is not calm. | contradiction | (![X]:((humble(X)<~>patient(X))<=>(~curious(X)<~>old(X))))&
(![X]:((old(X)<~>~strong(X))<=>(~brave(X)|~quiet(X))))&
(((~funny(susan)&old(susan)))<=>(?[X]:(~happy(X))))&
(((wise(mary)&happy(mary)))<=>(calm(alice)))&
(((kind(fred)&rich(fred)))=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(((~tall(lucy)<~>~calm(lucy)))<=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:(strong(X)=>(~strong(X)&brave(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~quiet(X)|~patient(X)))))&
(![X]:(rich(X)=>(~quiet(X)|calm(X))))&
(![X]:(~quiet(X)<=>(~strong(X)|~happy(X))))&
(![X]:((~calm(X)&happy(X))=>~happy(X)))&
((?[X]:((~wise(X)&~old(X))))=>(?[X]:(~old(X))))&
((?[X]:((strong(X)|~funny(X))))=>(?[X]:((~brave(X)<~>~old(X)))))&
(((~funny(alice)<~>kind(alice)))=>((~curious(paul)<~>~tall(paul))))&
(((~funny(susan)|~brave(susan)))=>(patient(susan)))&
(![X]:(~tall(X)=>(~wise(X)|~brave(X))))&
(?[X]:((~brave(X)&~wise(X))))&
((~creative(susan)|~generous(susan)))&
((~kind(alice)&~creative(alice)))&
(rich(paul))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:(~rich(X))) | ~calm(alice) | [
"p1",
"p2",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 775551967655723125183441
% SZS output start Proof for 775551967655723125183441
2. ! [X0] : ((old(X0) <~> ~strong(X0)) <=> (~quiet(X0) | ~brave(X0))) [input p1]
3. (old(susan) & ~funny(susan)) <=> ? [X0] : ~happy(X0) [input p2]
7. ! [X0] : (strong(X0) => (brave(X0) & ~strong(X0))) [input p6]
10. ! [X0] : (~quiet(X0) <=> (~happy(X0) | ~strong(X0))) [input p9]
11. ! [X0] : ((happy(X0) & ~calm(X0)) => ~happy(X0)) [input p10]
23. ~calm(alice) [input hypothesis]
31. ! [X0] : ((brave(X0) & ~strong(X0)) | ~strong(X0)) [ennf transformation 7]
34. ! [X0] : (~happy(X0) | (~happy(X0) | calm(X0))) [ennf transformation 11]
35. ! [X0] : (~happy(X0) | ~happy(X0) | calm(X0)) [flattening 34]
43. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | (quiet(X0) & brave(X0))) & ((~quiet(X0) | ~brave(X0)) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [nnf transformation 2]
44. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | (quiet(X0) & brave(X0))) & (~quiet(X0) | ~brave(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [flattening 43]
45. ((old(susan) & ~funny(susan)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (~old(susan) | funny(susan))) [nnf transformation 3]
46. ((old(susan) & ~funny(susan)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ~old(susan) | funny(susan)) [flattening 45]
47. ((old(susan) & ~funny(susan)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ~old(susan) | funny(susan)) [rectify 46]
48. ? [X1] : ~happy(X1) => ~happy(sK0) [choice axiom]
49. ((old(susan) & ~funny(susan)) | ! [X0] : happy(X0)) & (~happy(sK0) | ~old(susan) | funny(susan)) [skolemisation 47,48]
64. ! [X0] : ((~quiet(X0) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | quiet(X0))) [nnf transformation 10]
65. ! [X0] : ((~quiet(X0) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | quiet(X0))) [flattening 64]
93. ~old(X0) | strong(X0) | quiet(X0) [cnf transformation 44]
96. old(susan) | happy(X0) [cnf transformation 49]
108. ~strong(X0) | ~strong(X0) [cnf transformation 31]
116. ~quiet(X0) | strong(X0) [cnf transformation 65]
118. ~happy(X0) | ~happy(X0) | calm(X0) [cnf transformation 35]
137. ~calm(alice) [cnf transformation 23]
138. ~happy(X0) | calm(X0) [duplicate literal removal 118]
139. ~strong(X0) [duplicate literal removal 108]
141. 1 <=> ! [X0] : happy(X0) [avatar definition]
142. happy(X0) <- (1) [avatar component clause 141]
144. 2 <=> old(susan) [avatar definition]
146. old(susan) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 96,144,141]
159. 5 <=> calm(alice) [avatar definition]
161. ~calm(alice) <- (~5) [avatar component clause 159]
248. ~quiet(X0) [subsumption resolution 116,139]
310. ~5 [avatar split clause 137,159]
320. strong(susan) | quiet(susan) <- (2) [resolution 93,146]
321. quiet(susan) <- (2) [subsumption resolution 320,139]
322. $false <- (2) [subsumption resolution 321,248]
323. ~2 [avatar contradiction clause 322]
326. calm(X0) <- (1) [resolution 142,138]
329. $false <- (1, ~5) [resolution 326,161]
334. ~1 | 5 [avatar contradiction clause 329]
335. $false [avatar sat refutation 147,310,323,334]
% SZS output end Proof for 775551967655723125183441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not happy then mary is either patient or not humble.
Everyone who is either not creative or not rich is both old and strong.
If someone is both not tall and tall then someone is either not rich or brave and vice versa.
If someone is patient or rich then someone is curious and vice versa.
If susan is either not patient or old then someone is not creative or not curious.
If someone is strong then john is happy or funny.
If lucy is either tall or not old then lucy is either not strong or not old and vice versa.
Everyone who is not wise is either not generous or not quiet and vice versa.
If someone is not calm then someone is not generous and vice versa.
Everyone who is either wise or humble is curious.
If someone is patient or not kind then john is rich or patient and vice versa.
If someone is not curious then someone is old and vice versa.
Everyone who is both not rich and not tall is both not kind and not happy.
If someone is tall or not funny then susan is strong or generous and vice versa.
Everyone who is not old is not tall.
If someone is not strong then paul is not old or humble and vice versa.
Lucy is either wise or not kind.
Mary is both not wise and creative.
Lucy is not brave or not rich.
Someone is rich or not funny.
Someone is either not brave or not wise.
Someone is both not curious and happy.
Someone is either wise or not calm.
Someone is old. | Mary is creative. | entailment | ((~happy(john))=>((patient(mary)<~>~humble(mary))))&
(![X]:((~creative(X)<~>~rich(X))=>(old(X)&strong(X))))&
((?[X]:((~tall(X)&tall(X))))<=>(?[X]:((~rich(X)<~>brave(X)))))&
((?[X]:((patient(X)|rich(X))))<=>(?[X]:(curious(X))))&
(((~patient(susan)<~>old(susan)))=>(?[X]:((~creative(X)|~curious(X)))))&
((?[X]:(strong(X)))=>((happy(john)|funny(john))))&
(((tall(lucy)<~>~old(lucy)))<=>((~strong(lucy)<~>~old(lucy))))&
(![X]:(~wise(X)<=>(~generous(X)<~>~quiet(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~generous(X))))&
(![X]:((wise(X)<~>humble(X))=>curious(X)))&
((?[X]:((patient(X)|~kind(X))))<=>((rich(john)|patient(john))))&
((?[X]:(~curious(X)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~tall(X))=>(~kind(X)&~happy(X))))&
((?[X]:((tall(X)|~funny(X))))<=>((strong(susan)|generous(susan))))&
(![X]:(~old(X)=>~tall(X)))&
((?[X]:(~strong(X)))<=>((~old(paul)|humble(paul))))&
((wise(lucy)<~>~kind(lucy)))&
((~wise(mary)&creative(mary)))&
((~brave(lucy)|~rich(lucy)))&
(?[X]:((rich(X)|~funny(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(?[X]:(old(X))) | creative(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2773805152036259208784464
% SZS output start Proof for 2773805152036259208784464
18. creative(mary) & ~wise(mary) [input p17]
25. ~creative(mary) [input hypothesis]
148. creative(mary) [cnf transformation 18]
158. ~creative(mary) [cnf transformation 25]
404. $false [subsumption resolution 158,148]
% SZS output end Proof for 2773805152036259208784464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is not strong or not humble and vice versa.
If someone is either not brave or strong then someone is both not calm and not old.
Everyone who is either creative or not humble is not tall or kind.
If someone is either quiet or creative then someone is not quiet or happy.
If someone is not funny or curious then someone is not tall and vice versa.
If someone is either creative or calm then someone is humble or not creative.
If someone is not tall or curious then someone is humble or quiet and vice versa.
If someone is both tall and funny then someone is both patient and generous.
If fred is not calm or curious then mary is kind or not creative.
If fred is either happy or tall then someone is creative or not calm and vice versa.
Everyone who is either not curious or humble is humble or not happy and vice versa.
If someone is not generous or humble then someone is either old or patient and vice versa.
If someone is not rich or not brave then someone is happy or not rich.
Everyone who is generous or not brave is not rich.
If someone is either happy or not brave then mary is both not funny and not strong.
Everyone who is not creative is either wise or not brave and vice versa.
Someone is either not creative or kind.
Someone is not old.
Fred is not strong.
Fred is either not humble or creative.
Lucy is both happy and not kind.
Someone is not funny or not brave.
Mary is not patient or not kind.
Someone is either not strong or rich. | Fred is tall. | neutral | (![X]:(patient(X)<=>(~strong(X)|~humble(X))))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((creative(X)<~>~humble(X))=>(~tall(X)|kind(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
((?[X]:((~funny(X)|curious(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((creative(X)<~>calm(X))))=>(?[X]:((humble(X)|~creative(X)))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((humble(X)|quiet(X)))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((patient(X)&generous(X)))))&
(((~calm(fred)|curious(fred)))=>((kind(mary)|~creative(mary))))&
(((happy(fred)<~>tall(fred)))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~curious(X)<~>humble(X))<=>(humble(X)|~happy(X))))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((~rich(X)|~brave(X))))=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((generous(X)|~brave(X))=>~rich(X)))&
((?[X]:((happy(X)<~>~brave(X))))=>((~funny(mary)&~strong(mary))))&
(![X]:(~creative(X)<=>(wise(X)<~>~brave(X))))&
(?[X]:((~creative(X)<~>kind(X))))&
(?[X]:(~old(X)))&
(~strong(fred))&
((~humble(fred)<~>creative(fred)))&
((happy(lucy)&~kind(lucy)))&
(?[X]:((~funny(X)|~brave(X))))&
((~patient(mary)|~kind(mary)))&
(?[X]:((~strong(X)<~>rich(X)))) | tall(fred) | [] | null | 0 |
If alice is both calm and not humble then alice is curious. Everyone who is not quiet is both funny and strong. Everyone who is both strong and creative is either not calm or not humble. If someone is not strong then lucy is not funny or not tall and vice versa. Everyone who is either old or wise is curious or patient. If lucy is both generous and rich then someone is either wise or curious and vice versa. If someone is quiet or old then mary is not kind or not creative and vice versa. If someone is not happy then alice is both generous and quiet and vice versa. Everyone who is not kind or not generous is both not tall and not old and vice versa. If someone is both funny and patient then lucy is not rich and vice versa. Everyone who is creative is quiet or tall and vice versa. Everyone who is wise or humble is not kind or not happy. Everyone who is not happy is generous or patient and vice versa. Everyone who is either not tall or not kind is either tall or not generous. Everyone who is quiet or tall is either not rich or brave. Everyone who is wise is both strong and funny. Someone is both brave and not generous. Someone is patient. Someone is either old or not curious. Someone is both humble and not strong. Someone is not strong. Lucy is not kind or kind. Susan is both not curious and strong. John is both not rich and humble. | Alice is generous. | entailment | (((calm(alice)&~humble(alice)))=>(curious(alice)))&
(![X]:(~quiet(X)=>(funny(X)&strong(X))))&
(![X]:((strong(X)&creative(X))=>(~calm(X)<~>~humble(X))))&
((?[X]:(~strong(X)))<=>((~funny(lucy)|~tall(lucy))))&
(![X]:((old(X)<~>wise(X))=>(curious(X)|patient(X))))&
(((generous(lucy)&rich(lucy)))<=>(?[X]:((wise(X)<~>curious(X)))))&
((?[X]:((quiet(X)|old(X))))<=>((~kind(mary)|~creative(mary))))&
((?[X]:(~happy(X)))<=>((generous(alice)&quiet(alice))))&
(![X]:((~kind(X)|~generous(X))<=>(~tall(X)&~old(X))))&
((?[X]:((funny(X)&patient(X))))<=>(~rich(lucy)))&
(![X]:(creative(X)<=>(quiet(X)|tall(X))))&
(![X]:((wise(X)|humble(X))=>(~kind(X)|~happy(X))))&
(![X]:(~happy(X)<=>(generous(X)|patient(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(tall(X)<~>~generous(X))))&
(![X]:((quiet(X)|tall(X))=>(~rich(X)<~>brave(X))))&
(![X]:(wise(X)=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:(patient(X)))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((humble(X)&~strong(X))))&
(?[X]:(~strong(X)))&
((~kind(lucy)|kind(lucy)))&
((~curious(susan)&strong(susan)))&
((~rich(john)&humble(john))) | generous(alice) | [
"p7",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 40589798602976785155853
% SZS output start Proof for 40589798602976785155853
8. ? [X0] : ~happy(X0) <=> (quiet(alice) & generous(alice)) [input p7]
13. ! [X0] : (~happy(X0) <=> (patient(X0) | generous(X0))) [input p12]
18. ? [X0] : patient(X0) [input p17]
25. ~generous(alice) [input hypothesis]
55. (? [X0] : ~happy(X0) | (~quiet(alice) | ~generous(alice))) & ((quiet(alice) & generous(alice)) | ! [X0] : happy(X0)) [nnf transformation 8]
56. (? [X0] : ~happy(X0) | ~quiet(alice) | ~generous(alice)) & ((quiet(alice) & generous(alice)) | ! [X0] : happy(X0)) [flattening 55]
57. (? [X0] : ~happy(X0) | ~quiet(alice) | ~generous(alice)) & ((quiet(alice) & generous(alice)) | ! [X1] : happy(X1)) [rectify 56]
58. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
59. (~happy(sK3) | ~quiet(alice) | ~generous(alice)) & ((quiet(alice) & generous(alice)) | ! [X1] : happy(X1)) [skolemisation 57,58]
68. ! [X0] : ((~happy(X0) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | happy(X0))) [nnf transformation 13]
69. ! [X0] : ((~happy(X0) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | happy(X0))) [flattening 68]
74. ? [X0] : patient(X0) => patient(sK6) [choice axiom]
75. patient(sK6) [skolemisation 18,74]
103. generous(alice) | happy(X1) [cnf transformation 59]
121. ~happy(X0) | ~patient(X0) [cnf transformation 69]
134. patient(sK6) [cnf transformation 75]
145. ~generous(alice) [cnf transformation 25]
234. 20 <=> generous(alice) [avatar definition]
247. 23 <=> ! [X1] : happy(X1) [avatar definition]
248. happy(X1) <- (23) [avatar component clause 247]
250. 23 | 20 [avatar split clause 103,234,247]
275. ~20 [avatar split clause 145,234]
284. ~patient(X0) <- (23) [resolution 121,248]
285. $false <- (23) [resolution 284,134]
288. ~23 [avatar contradiction clause 285]
289. $false [avatar sat refutation 250,275,288]
% SZS output end Proof for 40589798602976785155853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not rich then someone is kind or wise.
Everyone who is both not rich and not brave is not happy or tall and vice versa.
If mary is both curious and happy then someone is either old or rich and vice versa.
If someone is rich or wise then paul is both not patient and not funny.
If someone is either not humble or not old then alice is happy.
If someone is tall or not creative then fred is not calm.
Everyone who is strong or wise is not patient and vice versa.
Everyone who is either not patient or not funny is quiet and vice versa.
Everyone who is either patient or not brave is either not strong or not creative.
Everyone who is kind is humble.
Everyone who is patient is not brave or kind.
Everyone who is generous or not kind is strong or not old.
Everyone who is strong is either not creative or curious.
If paul is not happy or curious then someone is wise.
Everyone who is both brave and wise is either not quiet or patient.
Everyone who is quiet is either happy or not curious and vice versa.
Someone is both creative and not happy.
Someone is not curious or not patient.
Someone is curious.
Someone is not humble.
Someone is not patient.
Fred is not creative or quiet.
Paul is either not old or not brave.
Lucy is brave or not curious. | Alice is happy. | neutral | ((?[X]:((wise(X)&~rich(X))))=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((~rich(X)&~brave(X))<=>(~happy(X)|tall(X))))&
(((curious(mary)&happy(mary)))<=>(?[X]:((old(X)<~>rich(X)))))&
((?[X]:((rich(X)|wise(X))))=>((~patient(paul)&~funny(paul))))&
((?[X]:((~humble(X)<~>~old(X))))=>(happy(alice)))&
((?[X]:((tall(X)|~creative(X))))=>(~calm(fred)))&
(![X]:((strong(X)|wise(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>quiet(X)))&
(![X]:((patient(X)<~>~brave(X))=>(~strong(X)<~>~creative(X))))&
(![X]:(kind(X)=>humble(X)))&
(![X]:(patient(X)=>(~brave(X)|kind(X))))&
(![X]:((generous(X)|~kind(X))=>(strong(X)|~old(X))))&
(![X]:(strong(X)=>(~creative(X)<~>curious(X))))&
(((~happy(paul)|curious(paul)))=>(?[X]:(wise(X))))&
(![X]:((brave(X)&wise(X))=>(~quiet(X)<~>patient(X))))&
(![X]:(quiet(X)<=>(happy(X)<~>~curious(X))))&
(?[X]:((creative(X)&~happy(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(curious(X)))&
(?[X]:(~humble(X)))&
(?[X]:(~patient(X)))&
((~creative(fred)|quiet(fred)))&
((~old(paul)<~>~brave(paul)))&
((brave(lucy)|~curious(lucy))) | happy(alice) | [] | null | 0 |
Everyone who is not generous is either not creative or not funny and vice versa.
Everyone who is generous or happy is tall and vice versa.
If someone is either not tall or not creative then mary is both rich and not wise.
Everyone who is not humble is either happy or strong and vice versa.
If someone is both creative and not old then someone is either wise or generous and vice versa.
Everyone who is both curious and not curious is both rich and quiet and vice versa.
If mary is humble or happy then alice is not patient or not strong.
If alice is both calm and not kind then mary is not wise or creative and vice versa.
Everyone who is kind or not humble is rich and vice versa.
If paul is either kind or not strong then someone is rich or patient and vice versa.
Everyone who is not strong is not curious and vice versa.
If someone is either not brave or not curious then someone is either tall or happy and vice versa.
If someone is both not happy and brave then someone is rich or happy and vice versa.
Everyone who is either wise or kind is generous and vice versa.
Everyone who is both not old and not funny is not generous or humble and vice versa.
Everyone who is rich is not creative and vice versa.
Paul is generous.
Fred is happy or not funny.
Lucy is either generous or not humble.
Lucy is both not wise and not patient.
John is wise or happy.
Someone is not funny.
Someone is not happy or calm.
Alice is not wise. | Paul is rich. | entailment | (![X]:(~generous(X)<=>(~creative(X)<~>~funny(X))))&
(![X]:((generous(X)|happy(X))<=>tall(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((rich(mary)&~wise(mary))))&
(![X]:(~humble(X)<=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)&quiet(X))))&
(((humble(mary)|happy(mary)))=>((~patient(alice)|~strong(alice))))&
(((calm(alice)&~kind(alice)))<=>((~wise(mary)|creative(mary))))&
(![X]:((kind(X)|~humble(X))<=>rich(X)))&
(((kind(paul)<~>~strong(paul)))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(~strong(X)<=>~curious(X)))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((wise(X)<~>kind(X))<=>generous(X)))&
(![X]:((~old(X)&~funny(X))<=>(~generous(X)|humble(X))))&
(![X]:(rich(X)<=>~creative(X)))&
(generous(paul))&
((happy(fred)|~funny(fred)))&
((generous(lucy)<~>~humble(lucy)))&
((~wise(lucy)&~patient(lucy)))&
((wise(john)|happy(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)|calm(X))))&
(~wise(alice)) | rich(paul) | [
"p0",
"p8",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5924681840032471067770546
% SZS output start Proof for 5924681840032471067770546
1. ! [X0] : (~generous(X0) <=> (~creative(X0) <~> ~funny(X0))) [input p0]
9. ! [X0] : ((~humble(X0) | kind(X0)) <=> rich(X0)) [input p8]
15. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (humble(X0) | ~generous(X0))) [input p14]
16. ! [X0] : (rich(X0) <=> ~creative(X0)) [input p15]
17. generous(paul) [input p16]
25. ~rich(paul) [input hypothesis]
32. ! [X0] : ((~generous(X0) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0)))) & (((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | generous(X0))) [nnf transformation 1]
46. ! [X0] : (((~humble(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [flattening 46]
64. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (funny(X0) | old(X0)))) [nnf transformation 15]
65. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | funny(X0) | old(X0))) [flattening 64]
66. ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))) [nnf transformation 16]
75. ~creative(X0) | ~generous(X0) | funny(X0) [cnf transformation 32]
105. humble(X0) | rich(X0) [cnf transformation 47]
136. ~humble(X0) | ~funny(X0) [cnf transformation 65]
138. rich(X0) | creative(X0) [cnf transformation 66]
139. generous(paul) [cnf transformation 17]
149. ~rich(paul) [cnf transformation 25]
377. creative(paul) [resolution 138,149]
453. ~generous(paul) | funny(paul) [resolution 75,377]
457. funny(paul) [subsumption resolution 453,139]
494. 54 <=> humble(paul) [avatar definition]
495. ~humble(paul) <- (~54) [avatar component clause 494]
496. humble(paul) <- (54) [avatar component clause 494]
515. ~funny(paul) <- (54) [resolution 496,136]
518. $false <- (54) [subsumption resolution 515,457]
519. ~54 [avatar contradiction clause 518]
520. rich(paul) <- (~54) [resolution 495,105]
521. $false <- (~54) [subsumption resolution 520,149]
522. 54 [avatar contradiction clause 521]
523. $false [avatar sat refutation 519,522]
% SZS output end Proof for 5924681840032471067770546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not calm is funny and vice versa. If someone is not calm or kind then someone is old. Everyone who is either calm or not wise is both not calm and kind and vice versa. If someone is generous then alice is both curious and rich and vice versa. If someone is both not brave and kind then someone is not curious or not generous and vice versa. If someone is not kind or strong then someone is both not old and not creative. Everyone who is calm is patient or not happy. Everyone who is patient is not wise or not old and vice versa. Everyone who is either not rich or rich is not patient or strong and vice versa. Everyone who is either creative or curious is humble or not quiet. If someone is either humble or not kind then alice is not wise or wise and vice versa. Everyone who is both funny and rich is either not quiet or not patient and vice versa. Everyone who is tall or not generous is not calm or creative. Everyone who is not strong is not quiet and vice versa. If someone is either generous or not humble then susan is not old and vice versa. Everyone who is either happy or funny is curious or happy and vice versa. Someone is both happy and patient. Someone is either wise or not brave. Someone is both tall and not funny. Susan is not generous or happy. Someone is either not patient or not humble. Someone is both patient and kind. Paul is both old and tall. Someone is both not funny and brave. | Susan is not happy. | neutral | (![X]:((~humble(X)&~calm(X))<=>funny(X)))&
((?[X]:((~calm(X)|kind(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~calm(X)&kind(X))))&
((?[X]:(generous(X)))<=>((curious(alice)&rich(alice))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:((~kind(X)|strong(X))))=>(?[X]:((~old(X)&~creative(X)))))&
(![X]:(calm(X)=>(patient(X)|~happy(X))))&
(![X]:(patient(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~patient(X)|strong(X))))&
(![X]:((creative(X)<~>curious(X))=>(humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((tall(X)&~funny(X))))&
((~generous(susan)|happy(susan)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((patient(X)&kind(X))))&
((old(paul)&tall(paul)))&
(?[X]:((~funny(X)&brave(X)))) | ~happy(susan) | [] | null | 0 |
If susan is happy then someone is not kind or happy.
Everyone who is calm is not kind and vice versa.
If susan is not generous or not curious then mary is both strong and happy and vice versa.
Everyone who is not calm is both not brave and wise and vice versa.
If someone is calm or curious then someone is both not happy and not kind.
If john is strong or not strong then fred is brave.
Everyone who is not curious is not rich or calm and vice versa.
If someone is both happy and not quiet then alice is brave.
If someone is calm then someone is brave.
Everyone who is creative is strong or calm and vice versa.
Everyone who is not strong is both not strong and not old and vice versa.
If someone is not curious then fred is both wise and not strong.
Everyone who is both not tall and not quiet is both not kind and generous.
Everyone who is either not happy or not old is either old or patient and vice versa.
Everyone who is not old or not strong is either humble or patient and vice versa.
Everyone who is either calm or not rich is either not funny or quiet and vice versa.
Paul is tall or quiet.
Someone is not curious.
Fred is either funny or not brave.
John is not humble or brave.
Susan is not creative.
Someone is strong.
Someone is both not curious and not calm. | Mary is strong. | neutral | ((happy(susan))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:(calm(X)<=>~kind(X)))&
(((~generous(susan)|~curious(susan)))<=>((strong(mary)&happy(mary))))&
(![X]:(~calm(X)<=>(~brave(X)&wise(X))))&
((?[X]:((calm(X)|curious(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
(((strong(john)|~strong(john)))=>(brave(fred)))&
(![X]:(~curious(X)<=>(~rich(X)|calm(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(brave(alice)))&
((?[X]:(calm(X)))=>(?[X]:(brave(X))))&
(![X]:(creative(X)<=>(strong(X)|calm(X))))&
(![X]:(~strong(X)<=>(~strong(X)&~old(X))))&
((?[X]:(~curious(X)))=>((wise(fred)&~strong(fred))))&
(![X]:((~tall(X)&~quiet(X))=>(~kind(X)&generous(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(old(X)<~>patient(X))))&
(![X]:((~old(X)|~strong(X))<=>(humble(X)<~>patient(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(~funny(X)<~>quiet(X))))&
((tall(paul)|quiet(paul)))&
(?[X]:(~curious(X)))&
((funny(fred)<~>~brave(fred)))&
((~humble(john)|brave(john)))&
(~creative(susan))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&~calm(X)))) | strong(mary) | [] | null | 0 |
If someone is wise or not old then susan is not calm and vice versa.
If someone is not humble then someone is both not wise and not happy and vice versa.
If someone is tall then someone is not rich or curious and vice versa.
Everyone who is both wise and not brave is both not strong and happy.
Everyone who is either not kind or strong is both rich and old.
If someone is both not rich and not patient then mary is either not kind or not old and vice versa.
Everyone who is humble is both not creative and tall.
If lucy is either not strong or creative then someone is either not old or wise.
If john is both patient and happy then lucy is not tall or not quiet.
Everyone who is patient is both not creative and wise.
If alice is happy then someone is either not patient or brave and vice versa.
Everyone who is rich is quiet or humble and vice versa.
Everyone who is either not kind or not strong is both wise and happy.
Everyone who is either calm or not generous is not generous.
Everyone who is patient is old or not patient and vice versa.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Someone is curious or creative.
Alice is either not calm or not rich.
Someone is rich.
Someone is either not quiet or kind.
Someone is not brave or not wise.
Someone is not creative.
Lucy is old. | Alice is not old. | contradiction | ((?[X]:((wise(X)|~old(X))))<=>(~calm(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)&~happy(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))=>(~strong(X)&happy(X))))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&old(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>((~kind(mary)<~>~old(mary))))&
(![X]:(humble(X)=>(~creative(X)&tall(X))))&
(((~strong(lucy)<~>creative(lucy)))=>(?[X]:((~old(X)<~>wise(X)))))&
(((patient(john)&happy(john)))=>((~tall(lucy)|~quiet(lucy))))&
(![X]:(patient(X)=>(~creative(X)&wise(X))))&
((happy(alice))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:(rich(X)<=>(quiet(X)|humble(X))))&
(![X]:((~kind(X)<~>~strong(X))=>(wise(X)&happy(X))))&
(![X]:((calm(X)<~>~generous(X))=>~generous(X)))&
(![X]:(patient(X)<=>(old(X)|~patient(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(?[X]:((curious(X)|creative(X))))&
((~calm(alice)<~>~rich(alice)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:(~creative(X)))&
(old(lucy)) | ~old(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8961051594279635230749192
% SZS output start Proof for 8961051594279635230749192
15. ! [X0] : (patient(X0) <=> (~patient(X0) | old(X0))) [input p14]
24. ~old(alice) [input hypothesis]
67. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | ~patient(X0))) [nnf transformation 15]
68. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~patient(X0))) [flattening 67]
125. ~patient(X0) | old(X0) | ~patient(X0) [cnf transformation 68]
127. patient(X0) | patient(X0) [cnf transformation 68]
145. ~old(alice) [cnf transformation 24]
150. ~patient(X0) | old(X0) [duplicate literal removal 125]
151. patient(X0) [duplicate literal removal 127]
167. 4 <=> ! [X1] : old(X1) [avatar definition]
168. old(X1) <- (4) [avatar component clause 167]
303. old(X0) [subsumption resolution 150,151]
304. 4 [avatar split clause 303,167]
352. $false <- (4) [resolution 168,145]
353. ~4 [avatar contradiction clause 352]
354. $false [avatar sat refutation 304,353]
% SZS output end Proof for 8961051594279635230749192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not tall or not old then someone is curious or not calm.
Everyone who is not patient or wise is patient or creative and vice versa.
If paul is not old or patient then someone is creative or brave and vice versa.
If alice is not rich or not generous then someone is patient and vice versa.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Susan is brave. | neutral | (((~tall(alice)<~>~old(alice)))=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((~patient(X)|wise(X))<=>(patient(X)|creative(X))))&
(((~old(paul)|patient(paul)))<=>(?[X]:((creative(X)|brave(X)))))&
(((~rich(alice)|~generous(alice)))<=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | brave(susan) | [] | null | 0 |
If someone is either tall or not kind then someone is not tall. Everyone who is not rich or not kind is either wise or not humble. Everyone who is not wise is both humble and strong and vice versa. Everyone who is not humble is not quiet. Everyone who is not humble is wise. If mary is either creative or not rich then paul is wise or not brave. If susan is rich or not creative then mary is either not generous or not strong. If someone is creative or not curious then paul is strong or not humble and vice versa. If fred is both brave and quiet then mary is either not calm or not creative. Everyone who is not wise is either funny or not strong and vice versa. If john is either not patient or not funny then someone is not wise and vice versa. If susan is both not humble and not happy then someone is calm or happy. If mary is not humble or not calm then alice is either not quiet or humble. If someone is either not old or quiet then susan is both strong and patient and vice versa. Everyone who is either creative or calm is both not kind and curious. Everyone who is either not kind or curious is either generous or wise and vice versa. Someone is not funny. Mary is not wise. Paul is not kind or not quiet. Someone is both brave and curious. Someone is not old or brave. Someone is either humble or calm. Someone is both quiet and curious. Susan is not kind or not quiet. | Mary is not funny. | contradiction | ((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|~kind(X))=>(wise(X)<~>~humble(X))))&
(![X]:(~wise(X)<=>(humble(X)&strong(X))))&
(![X]:(~humble(X)=>~quiet(X)))&
(![X]:(~humble(X)=>wise(X)))&
(((creative(mary)<~>~rich(mary)))=>((wise(paul)|~brave(paul))))&
(((rich(susan)|~creative(susan)))=>((~generous(mary)<~>~strong(mary))))&
((?[X]:((creative(X)|~curious(X))))<=>((strong(paul)|~humble(paul))))&
(((brave(fred)&quiet(fred)))=>((~calm(mary)<~>~creative(mary))))&
(![X]:(~wise(X)<=>(funny(X)<~>~strong(X))))&
(((~patient(john)<~>~funny(john)))<=>(?[X]:(~wise(X))))&
(((~humble(susan)&~happy(susan)))=>(?[X]:((calm(X)|happy(X)))))&
(((~humble(mary)|~calm(mary)))=>((~quiet(alice)<~>humble(alice))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((strong(susan)&patient(susan))))&
(![X]:((creative(X)<~>calm(X))=>(~kind(X)&curious(X))))&
(![X]:((~kind(X)<~>curious(X))<=>(generous(X)<~>wise(X))))&
(?[X]:(~funny(X)))&
(~wise(mary))&
((~kind(paul)|~quiet(paul)))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~old(X)|brave(X))))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:((quiet(X)&curious(X))))&
((~kind(susan)|~quiet(susan))) | ~funny(mary) | [
"p2",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2530170129741806610610698
% SZS output start Proof for 2530170129741806610610698
3. ! [X0] : (~wise(X0) <=> (strong(X0) & humble(X0))) [input p2]
10. ! [X0] : (~wise(X0) <=> (funny(X0) <~> ~strong(X0))) [input p9]
18. ~wise(mary) [input p17]
25. ~funny(mary) [input hypothesis]
44. ! [X0] : ((~wise(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | wise(X0))) [nnf transformation 3]
45. ! [X0] : ((~wise(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | wise(X0))) [flattening 44]
54. ! [X0] : ((~wise(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | wise(X0))) [nnf transformation 10]
85. strong(X0) | wise(X0) [cnf transformation 45]
101. ~strong(X0) | funny(X0) | wise(X0) [cnf transformation 54]
104. ~wise(X0) | funny(X0) | strong(X0) [cnf transformation 54]
132. ~wise(mary) [cnf transformation 18]
142. ~funny(mary) [cnf transformation 25]
233. funny(X0) | strong(X0) [subsumption resolution 104,85]
234. funny(X0) | wise(X0) [subsumption resolution 101,233]
344. wise(mary) [resolution 234,142]
346. $false [subsumption resolution 344,132]
% SZS output end Proof for 2530170129741806610610698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not rich is both wise and not humble and vice versa.
Everyone who is both not quiet and not strong is either generous or not curious.
Everyone who is not kind is patient or not wise and vice versa.
Everyone who is not humble is not old.
Everyone who is not happy or calm is both not funny and not curious and vice versa.
Everyone who is calm is not funny and vice versa.
Everyone who is either curious or not funny is both not funny and happy.
If someone is not old then someone is both not humble and rich.
Everyone who is tall is either patient or brave.
If someone is old or not strong then susan is rich or not funny.
Everyone who is tall or not funny is either not happy or not strong and vice versa.
Everyone who is both humble and not curious is either calm or strong and vice versa.
If someone is both kind and not funny then john is not quiet.
Everyone who is either not old or not humble is patient or not quiet.
If someone is both not tall and not happy then someone is both not generous and not funny.
Lucy is both tall and kind.
Someone is both calm and wise.
Susan is either strong or not quiet.
Susan is funny.
Someone is quiet.
Someone is both not rich and not old.
Someone is not funny or not wise.
Lucy is either strong or not patient. | Susan is not curious. | entailment | (![X]:((wise(X)&~rich(X))<=>(wise(X)&~humble(X))))&
(![X]:((~quiet(X)&~strong(X))=>(generous(X)<~>~curious(X))))&
(![X]:(~kind(X)<=>(patient(X)|~wise(X))))&
(![X]:(~humble(X)=>~old(X)))&
(![X]:((~happy(X)|calm(X))<=>(~funny(X)&~curious(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(![X]:((curious(X)<~>~funny(X))=>(~funny(X)&happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(tall(X)=>(patient(X)<~>brave(X))))&
((?[X]:((old(X)|~strong(X))))=>((rich(susan)|~funny(susan))))&
(![X]:((tall(X)|~funny(X))<=>(~happy(X)<~>~strong(X))))&
(![X]:((humble(X)&~curious(X))<=>(calm(X)<~>strong(X))))&
((?[X]:((kind(X)&~funny(X))))=>(~quiet(john)))&
(![X]:((~old(X)<~>~humble(X))=>(patient(X)|~quiet(X))))&
((?[X]:((~tall(X)&~happy(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
((tall(lucy)&kind(lucy)))&
(?[X]:((calm(X)&wise(X))))&
((strong(susan)<~>~quiet(susan)))&
(funny(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((strong(lucy)<~>~patient(lucy))) | ~curious(susan) | [
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 781637662886655017846136
% SZS output start Proof for 781637662886655017846136
7. ! [X0] : ((curious(X0) <~> ~funny(X0)) => (happy(X0) & ~funny(X0))) [input p6]
19. funny(susan) [input p18]
24. curious(susan) [input hypothesis]
30. ! [X0] : ((happy(X0) & ~funny(X0)) | (curious(X0) <=> ~funny(X0))) [ennf transformation 7]
47. ! [X0] : ((happy(X0) & ~funny(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) [nnf transformation 30]
87. ~funny(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 47]
120. funny(susan) [cnf transformation 19]
127. curious(susan) [cnf transformation 24]
128. ~funny(X0) | ~curious(X0) [duplicate literal removal 87]
152. 6 <=> funny(susan) [avatar definition]
153. funny(susan) <- (6) [avatar component clause 152]
183. 6 [avatar split clause 120,152]
210. ~curious(susan) <- (6) [resolution 128,153]
212. $false <- (6) [subsumption resolution 210,127]
213. ~6 [avatar contradiction clause 212]
215. $false [avatar sat refutation 183,213]
% SZS output end Proof for 781637662886655017846136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not rich and not generous.
Everyone who is old is both generous and not creative.
If susan is not rich then mary is either humble or not rich.
If someone is not curious or creative then alice is strong.
Everyone who is calm or humble is both not wise and not happy and vice versa.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
Someone is happy.
Someone is tall or not kind.
Fred is wise.
Someone is not brave.
Someone is either rich or wise.
Someone is not old.
Mary is either not funny or patient.
Alice is either not tall or not patient. | Mary is humble. | contradiction | (![X]:(~quiet(X)=>(~rich(X)&~generous(X))))&
(![X]:(old(X)=>(generous(X)&~creative(X))))&
((~rich(susan))=>((humble(mary)<~>~rich(mary))))&
((?[X]:((~curious(X)|creative(X))))=>(strong(alice)))&
(![X]:((calm(X)|humble(X))<=>(~wise(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
(?[X]:(happy(X)))&
(?[X]:((tall(X)|~kind(X))))&
(wise(fred))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((~funny(mary)<~>patient(mary)))&
((~tall(alice)<~>~patient(alice))) | humble(mary) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6862532295136159097183137
% SZS output start Proof for 6862532295136159097183137
1. ! [X0] : (~quiet(X0) => (~generous(X0) & ~rich(X0))) [input p0]
5. ! [X0] : ((humble(X0) | calm(X0)) <=> (~happy(X0) & ~wise(X0))) [input p4]
7. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p9]
16. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~generous(X0) & ~curious(X0))) [input p15]
23. ~funny(mary) <~> patient(mary) [input p22]
25. humble(mary) [input hypothesis]
27. ! [X0] : ((~generous(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 1]
33. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 10]
39. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 16]
41. ! [X0] : (((humble(X0) | calm(X0)) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 5]
42. ! [X0] : ((humble(X0) | calm(X0) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 41]
45. ! [X0] : (((~creative(X0) | ~funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((~creative(X0) | ~funny(X0) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [flattening 45]
47. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 9]
57. ! [X0] : ((~generous(X0) & ~curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 39]
69. (~patient(mary) | funny(mary)) & (patient(mary) | ~funny(mary)) [nnf transformation 23]
72. ~generous(X0) | quiet(X0) [cnf transformation 27]
82. ~happy(X0) | ~humble(X0) [cnf transformation 42]
87. funny(X0) | curious(X0) [cnf transformation 46]
93. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 47]
97. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 47]
100. ~brave(X0) | happy(X0) [cnf transformation 33]
102. happy(X0) | generous(X0) [cnf transformation 33]
117. ~curious(X0) | brave(X0) | funny(X0) [cnf transformation 57]
128. patient(mary) | ~funny(mary) [cnf transformation 69]
132. humble(mary) [cnf transformation 25]
133. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 93]
135. ~patient(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 97]
142. 2 <=> humble(mary) [avatar definition]
143. humble(mary) <- (2) [avatar component clause 142]
164. ~patient(X0) | ~quiet(X0) [subsumption resolution 133,135]
189. brave(X0) | funny(X0) [subsumption resolution 117,87]
210. 16 <=> funny(mary) [avatar definition]
211. ~funny(mary) <- (~16) [avatar component clause 210]
214. 17 <=> patient(mary) [avatar definition]
215. patient(mary) <- (17) [avatar component clause 214]
218. ~16 | 17 [avatar split clause 128,214,210]
229. 2 [avatar split clause 132,142]
238. ~humble(X0) | generous(X0) [resolution 102,82]
248. funny(X2) | happy(X2) [resolution 189,100]
249. generous(mary) <- (2) [resolution 238,143]
252. quiet(mary) <- (2) [resolution 249,72]
270. ~quiet(mary) <- (17) [resolution 215,164]
276. $false <- (2, 17) [subsumption resolution 252,270]
277. ~2 | ~17 [avatar contradiction clause 276]
301. 23 <=> happy(mary) [avatar definition]
303. happy(mary) <- (23) [avatar component clause 301]
410. happy(mary) <- (~16) [resolution 248,211]
413. 23 | 16 [avatar split clause 410,210,301]
414. ~humble(mary) <- (23) [resolution 303,82]
416. $false <- (2, 23) [subsumption resolution 414,143]
417. ~2 | ~23 [avatar contradiction clause 416]
418. $false [avatar sat refutation 218,229,277,413,417]
% SZS output end Proof for 6862532295136159097183137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and not creative then someone is wise or humble.
Everyone who is not humble or generous is either not quiet or old and vice versa.
Everyone who is generous or creative is either not creative or not old and vice versa.
Everyone who is both curious and not patient is both strong and curious and vice versa.
Everyone who is both generous and not happy is not happy.
Everyone who is either not creative or funny is both not creative and old.
Everyone who is not tall or not strong is not happy or kind.
If john is not calm then someone is not funny and vice versa.
Everyone who is either not wise or not funny is not strong or not calm.
Everyone who is not strong or not generous is brave and vice versa.
If paul is not kind then someone is not calm and vice versa.
Everyone who is either not funny or humble is both quiet and humble.
Everyone who is not old is both old and not rich.
Everyone who is not calm is generous.
Everyone who is not rich or old is not curious and vice versa.
Everyone who is both quiet and generous is patient and vice versa.
John is not humble or not calm.
Someone is both tall and generous.
Alice is creative or not happy.
Lucy is tall or curious.
Someone is patient or not wise.
Someone is either not rich or humble. | Lucy is not strong. | neutral | ((?[X]:((brave(X)&~creative(X))))=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~humble(X)|generous(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((generous(X)|creative(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((curious(X)&~patient(X))<=>(strong(X)&curious(X))))&
(![X]:((generous(X)&~happy(X))=>~happy(X)))&
(![X]:((~creative(X)<~>funny(X))=>(~creative(X)&old(X))))&
(![X]:((~tall(X)|~strong(X))=>(~happy(X)|kind(X))))&
((~calm(john))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>~funny(X))=>(~strong(X)|~calm(X))))&
(![X]:((~strong(X)|~generous(X))<=>brave(X)))&
((~kind(paul))<=>(?[X]:(~calm(X))))&
(![X]:((~funny(X)<~>humble(X))=>(quiet(X)&humble(X))))&
(![X]:(~old(X)=>(old(X)&~rich(X))))&
(![X]:(~calm(X)=>generous(X)))&
(![X]:((~rich(X)|old(X))<=>~curious(X)))&
(![X]:((quiet(X)&generous(X))<=>patient(X)))&
((~humble(john)|~calm(john)))&
(?[X]:((tall(X)&generous(X))))&
((creative(alice)|~happy(alice)))&
((tall(lucy)|curious(lucy)))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((~rich(X)<~>humble(X)))) | ~strong(lucy) | [] | null | 0 |
If susan is either patient or not rich then someone is not tall.
If someone is both not curious and not patient then someone is not creative or old.
Everyone who is both calm and old is either not curious or brave.
Everyone who is both creative and rich is funny or quiet.
If paul is not kind then someone is not quiet or happy.
Everyone who is not kind is either tall or not kind and vice versa.
If someone is either calm or not rich then someone is both not calm and happy and vice versa.
Everyone who is tall or not humble is creative or rich.
If mary is patient then susan is either not tall or happy and vice versa.
Everyone who is both creative and not creative is either old or not curious.
Everyone who is both rich and humble is not funny and vice versa.
If fred is both not patient and not wise then lucy is strong or not patient and vice versa.
Everyone who is either wise or old is wise.
If someone is not quiet or not generous then mary is either not generous or not patient.
Everyone who is either kind or wise is not generous or generous and vice versa.
Everyone who is both rich and not curious is not strong.
Paul is happy.
Fred is not happy or tall.
Mary is wise or not brave.
Mary is curious or not creative.
Susan is both not brave and not curious.
Someone is curious. | Paul is generous. | neutral | (((patient(susan)<~>~rich(susan)))=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)&~patient(X))))=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((calm(X)&old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((creative(X)&rich(X))=>(funny(X)|quiet(X))))&
((~kind(paul))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:(~kind(X)<=>(tall(X)<~>~kind(X))))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:((tall(X)|~humble(X))=>(creative(X)|rich(X))))&
((patient(mary))<=>((~tall(susan)<~>happy(susan))))&
(![X]:((creative(X)&~creative(X))=>(old(X)<~>~curious(X))))&
(![X]:((rich(X)&humble(X))<=>~funny(X)))&
(((~patient(fred)&~wise(fred)))<=>((strong(lucy)|~patient(lucy))))&
(![X]:((wise(X)<~>old(X))=>wise(X)))&
((?[X]:((~quiet(X)|~generous(X))))=>((~generous(mary)<~>~patient(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~generous(X)|generous(X))))&
(![X]:((rich(X)&~curious(X))=>~strong(X)))&
(happy(paul))&
((~happy(fred)|tall(fred)))&
((wise(mary)|~brave(mary)))&
((curious(mary)|~creative(mary)))&
((~brave(susan)&~curious(susan)))&
(?[X]:(curious(X))) | generous(paul) | [] | null | 0 |
If lucy is either rich or strong then someone is either tall or old.
Everyone who is quiet or funny is old or curious.
Everyone who is tall or creative is both not humble and generous.
If someone is either not funny or strong then someone is either quiet or not funny and vice versa.
Everyone who is not kind is not wise or wise and vice versa.
Everyone who is patient or not happy is rich.
If susan is both strong and wise then lucy is both brave and not generous.
If fred is both not curious and happy then someone is not curious.
Everyone who is wise is either tall or not wise.
Everyone who is both not kind and wise is kind or not kind and vice versa.
Everyone who is curious or creative is wise and vice versa.
If susan is not brave or not rich then mary is both happy and not rich and vice versa.
If fred is brave or not humble then paul is not patient.
Everyone who is both not humble and funny is both not brave and not quiet.
If mary is creative then someone is either not calm or funny.
Lucy is quiet.
Someone is either strong or not generous.
Lucy is either not quiet or not creative.
John is not kind.
Someone is both old and rich.
Alice is both not calm and not happy.
Someone is not calm or patient.
Someone is brave or generous. | Fred is wise. | entailment | (((rich(lucy)<~>strong(lucy)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((quiet(X)|funny(X))=>(old(X)|curious(X))))&
(![X]:((tall(X)|creative(X))=>(~humble(X)&generous(X))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:(~kind(X)<=>(~wise(X)|wise(X))))&
(![X]:((patient(X)|~happy(X))=>rich(X)))&
(((strong(susan)&wise(susan)))=>((brave(lucy)&~generous(lucy))))&
(((~curious(fred)&happy(fred)))=>(?[X]:(~curious(X))))&
(![X]:(wise(X)=>(tall(X)<~>~wise(X))))&
(![X]:((~kind(X)&wise(X))<=>(kind(X)|~kind(X))))&
(![X]:((curious(X)|creative(X))<=>wise(X)))&
(((~brave(susan)|~rich(susan)))<=>((happy(mary)&~rich(mary))))&
(((brave(fred)|~humble(fred)))=>(~patient(paul)))&
(![X]:((~humble(X)&funny(X))=>(~brave(X)&~quiet(X))))&
((creative(mary))=>(?[X]:((~calm(X)<~>funny(X)))))&
(quiet(lucy))&
(?[X]:((strong(X)<~>~generous(X))))&
((~quiet(lucy)<~>~creative(lucy)))&
(~kind(john))&
(?[X]:((old(X)&rich(X))))&
((~calm(alice)&~happy(alice)))&
(?[X]:((~calm(X)|patient(X))))&
(?[X]:((brave(X)|generous(X)))) | wise(fred) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8303589042821972794218623
% SZS output start Proof for 8303589042821972794218623
5. ! [X0] : (~kind(X0) <=> (wise(X0) | ~wise(X0))) [input p4]
10. ! [X0] : ((wise(X0) & ~kind(X0)) <=> (~kind(X0) | kind(X0))) [input p9]
24. ~wise(fred) [input hypothesis]
48. ! [X0] : ((~kind(X0) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | kind(X0))) [nnf transformation 5]
49. ! [X0] : ((~kind(X0) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | kind(X0))) [flattening 48]
53. ! [X0] : (((wise(X0) & ~kind(X0)) | (kind(X0) & ~kind(X0))) & ((~kind(X0) | kind(X0)) | (~wise(X0) | kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((wise(X0) & ~kind(X0)) | (kind(X0) & ~kind(X0))) & (~kind(X0) | kind(X0) | ~wise(X0) | kind(X0))) [flattening 53]
91. ~kind(X0) | wise(X0) [cnf transformation 49]
92. ~kind(X0) | ~wise(X0) [cnf transformation 49]
104. wise(X0) | kind(X0) [cnf transformation 54]
131. ~wise(fred) [cnf transformation 24]
191. ~kind(X0) [subsumption resolution 91,92]
223. wise(X0) [subsumption resolution 104,191]
304. $false [subsumption resolution 131,223]
% SZS output end Proof for 8303589042821972794218623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not generous is either not brave or not humble.
Everyone who is not creative or not kind is either not strong or tall and vice versa.
Everyone who is funny or not rich is not wise.
If susan is either not creative or brave then lucy is not tall and vice versa.
If john is not humble or creative then mary is both not kind and not humble.
Everyone who is either strong or not patient is either not kind or not happy and vice versa.
Everyone who is both not patient and tall is either generous or wise.
Everyone who is either not curious or not tall is rich or not kind.
If paul is kind or not creative then john is both not strong and not tall and vice versa.
If lucy is rich or quiet then someone is not old or kind and vice versa.
Everyone who is either rich or not creative is either humble or not wise and vice versa.
If mary is both rich and patient then john is creative or old and vice versa.
Everyone who is not tall or not patient is rich and vice versa.
Everyone who is funny or creative is old or not humble.
If lucy is rich then fred is curious or tall.
If someone is not kind or happy then mary is not rich and vice versa.
Fred is not patient.
Someone is funny or not creative.
Someone is brave or quiet.
Paul is both not patient and not wise.
Someone is not calm.
Susan is tall or old.
Someone is not tall or kind.
Mary is either kind or not funny. | John is not creative. | entailment | (![X]:((~calm(X)&~generous(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~strong(X)<~>tall(X))))&
(![X]:((funny(X)|~rich(X))=>~wise(X)))&
(((~creative(susan)<~>brave(susan)))<=>(~tall(lucy)))&
(((~humble(john)|creative(john)))=>((~kind(mary)&~humble(mary))))&
(![X]:((strong(X)<~>~patient(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((~patient(X)&tall(X))=>(generous(X)<~>wise(X))))&
(![X]:((~curious(X)<~>~tall(X))=>(rich(X)|~kind(X))))&
(((kind(paul)|~creative(paul)))<=>((~strong(john)&~tall(john))))&
(((rich(lucy)|quiet(lucy)))<=>(?[X]:((~old(X)|kind(X)))))&
(![X]:((rich(X)<~>~creative(X))<=>(humble(X)<~>~wise(X))))&
(((rich(mary)&patient(mary)))<=>((creative(john)|old(john))))&
(![X]:((~tall(X)|~patient(X))<=>rich(X)))&
(![X]:((funny(X)|creative(X))=>(old(X)|~humble(X))))&
((rich(lucy))=>((curious(fred)|tall(fred))))&
((?[X]:((~kind(X)|happy(X))))<=>(~rich(mary)))&
(~patient(fred))&
(?[X]:((funny(X)|~creative(X))))&
(?[X]:((brave(X)|quiet(X))))&
((~patient(paul)&~wise(paul)))&
(?[X]:(~calm(X)))&
((tall(susan)|old(susan)))&
(?[X]:((~tall(X)|kind(X))))&
((kind(mary)<~>~funny(mary))) | ~creative(john) | [
"p4",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4860792533847089767417500
% SZS output start Proof for 4860792533847089767417500
5. (creative(john) | ~humble(john)) => (~humble(mary) & ~kind(mary)) [input p4]
12. (patient(mary) & rich(mary)) <=> (old(john) | creative(john)) [input p11]
16. ? [X0] : (happy(X0) | ~kind(X0)) <=> ~rich(mary) [input p15]
25. creative(john) [input hypothesis]
29. (~humble(mary) & ~kind(mary)) | (~creative(john) & humble(john)) [ennf transformation 5]
53. ((patient(mary) & rich(mary)) | (~old(john) & ~creative(john))) & ((old(john) | creative(john)) | (~patient(mary) | ~rich(mary))) [nnf transformation 12]
54. ((patient(mary) & rich(mary)) | (~old(john) & ~creative(john))) & (old(john) | creative(john) | ~patient(mary) | ~rich(mary)) [flattening 53]
57. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~happy(X0) & kind(X0))) [nnf transformation 16]
58. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [rectify 57]
59. ? [X0] : (happy(X0) | ~kind(X0)) => (happy(sK1) | ~kind(sK1)) [choice axiom]
60. ((happy(sK1) | ~kind(sK1)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [skolemisation 58,59]
85. ~kind(mary) | ~creative(john) [cnf transformation 29]
118. rich(mary) | ~creative(john) [cnf transformation 54]
128. ~rich(mary) | kind(X1) [cnf transformation 60]
141. creative(john) [cnf transformation 25]
159. 4 <=> creative(john) [avatar definition]
173. 7 <=> kind(mary) [avatar definition]
175. ~kind(mary) <- (~7) [avatar component clause 173]
176. ~4 | ~7 [avatar split clause 85,173,159]
240. 20 <=> rich(mary) [avatar definition]
244. ~4 | 20 [avatar split clause 118,240,159]
269. 26 <=> ! [X1] : kind(X1) [avatar definition]
270. kind(X1) <- (26) [avatar component clause 269]
271. 26 | ~20 [avatar split clause 128,240,269]
314. 4 [avatar split clause 141,159]
315. $false <- (~7, 26) [subsumption resolution 175,270]
316. 7 | ~26 [avatar contradiction clause 315]
317. $false [avatar sat refutation 176,244,271,314,316]
% SZS output end Proof for 4860792533847089767417500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not funny is either rich or not rich. If someone is both creative and not generous then someone is both humble and kind. Everyone who is patient or rich is not generous. Everyone who is either not calm or funny is tall or not rich. If someone is not happy or not patient then someone is old and vice versa. If john is happy or calm then someone is either not creative or not strong and vice versa. Everyone who is patient is not quiet. If someone is not humble or not curious then alice is both rich and not creative. Everyone who is both not generous and funny is either curious or not brave and vice versa. Everyone who is either generous or quiet is not happy and vice versa. Everyone who is brave 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. Everyone who is quiet is not quiet or not humble and vice versa. Everyone who is brave or patient is not tall and vice versa. If someone is both not old and not strong then susan is tall and vice versa. Alice is creative or quiet. Susan is both not kind and not funny. Alice is both not generous and not kind. Someone is either not tall or strong. Alice is both not creative and not strong. Susan is either not generous or not curious. | Alice is not funny. | entailment | (![X]:((~calm(X)|~funny(X))=>(rich(X)<~>~rich(X))))&
((?[X]:((creative(X)&~generous(X))))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((patient(X)|rich(X))=>~generous(X)))&
(![X]:((~calm(X)<~>funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:(old(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))=>((rich(alice)&~creative(alice))))&
(![X]:((~generous(X)&funny(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|patient(X))<=>~tall(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
((creative(alice)|quiet(alice)))&
((~kind(susan)&~funny(susan)))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~creative(alice)&~strong(alice)))&
((~generous(susan)<~>~curious(susan))) | ~funny(alice) | [
"p3",
"p6",
"p7",
"p8",
"p11",
"p12",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 652665586348350458512903
% SZS output start Proof for 652665586348350458512903
4. ! [X0] : ((~calm(X0) <~> funny(X0)) => (~rich(X0) | tall(X0))) [input p3]
7. ! [X0] : (patient(X0) => ~quiet(X0)) [input p6]
8. ? [X0] : (~curious(X0) | ~humble(X0)) => (~creative(alice) & rich(alice)) [input p7]
9. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((~patient(X0) | quiet(X0)) => curious(X0)) [input p11]
13. (~rich(alice) | patient(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~humble(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((patient(X0) | brave(X0)) <=> ~tall(X0)) [input p14]
19. ~kind(alice) & ~generous(alice) [input p18]
23. funny(alice) [input hypothesis]
29. ! [X0] : ((~rich(X0) | tall(X0)) | (~calm(X0) <=> funny(X0))) [ennf transformation 4]
30. ! [X0] : (~rich(X0) | tall(X0) | (~calm(X0) <=> funny(X0))) [flattening 29]
31. ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 7]
32. (~creative(alice) & rich(alice)) | ! [X0] : (curious(X0) & humble(X0)) [ennf transformation 8]
33. ! [X0] : (curious(X0) | (patient(X0) & ~quiet(X0))) [ennf transformation 12]
38. ! [X0] : (~rich(X0) | tall(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [nnf transformation 30]
49. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~funny(X0) | generous(X0)))) [nnf transformation 9]
50. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~funny(X0) | generous(X0))) [flattening 49]
54. ((~rich(alice) | patient(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [nnf transformation 13]
55. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [flattening 54]
56. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | (rich(alice) & ~patient(alice))) [rectify 55]
57. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK4) | ~curious(sK4)) [choice axiom]
58. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK4) | ~curious(sK4)) | (rich(alice) & ~patient(alice))) [skolemisation 56,57]
59. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 14]
60. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 59]
61. ! [X0] : (((patient(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [nnf transformation 15]
62. ! [X0] : ((patient(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [flattening 61]
80. ~rich(X0) | tall(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 38]
90. ~quiet(X0) | ~patient(X0) [cnf transformation 31]
91. rich(alice) | humble(X0) [cnf transformation 32]
96. ~curious(X0) | brave(X0) | ~funny(X0) | generous(X0) [cnf transformation 50]
109. curious(X0) | patient(X0) [cnf transformation 33]
113. ~rich(alice) | patient(alice) | calm(X0) [cnf transformation 58]
114. ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 60]
115. quiet(X0) | quiet(X0) [cnf transformation 60]
117. ~brave(X0) | ~tall(X0) [cnf transformation 62]
126. ~generous(alice) [cnf transformation 19]
134. funny(alice) [cnf transformation 23]
135. ~humble(X0) | ~quiet(X0) [duplicate literal removal 114]
136. quiet(X0) [duplicate literal removal 115]
211. 18 <=> ! [X0] : humble(X0) [avatar definition]
212. humble(X0) <- (18) [avatar component clause 211]
215. 19 <=> rich(alice) [avatar definition]
217. rich(alice) <- (19) [avatar component clause 215]
219. 18 | 19 [avatar split clause 91,215,211]
221. 20 <=> ! [X0] : calm(X0) [avatar definition]
222. calm(X0) <- (20) [avatar component clause 221]
224. 21 <=> patient(alice) [avatar definition]
226. patient(alice) <- (21) [avatar component clause 224]
227. 20 | 21 | ~19 [avatar split clause 113,215,224,221]
239. ~humble(X0) [subsumption resolution 135,136]
279. $false <- (18) [subsumption resolution 212,239]
280. ~18 [avatar contradiction clause 279]
289. ~patient(X0) [resolution 90,136]
290. $false <- (21) [resolution 289,226]
291. ~21 [avatar contradiction clause 290]
340. tall(alice) | ~calm(alice) | ~funny(alice) <- (19) [resolution 80,217]
341. tall(alice) | ~funny(alice) <- (19, 20) [subsumption resolution 340,222]
342. tall(alice) <- (19, 20) [subsumption resolution 341,134]
351. brave(X0) | ~funny(X0) | generous(X0) | patient(X0) [resolution 96,109]
354. ~funny(X0) | brave(X0) | generous(X0) [subsumption resolution 351,289]
357. brave(alice) | generous(alice) [resolution 354,134]
359. brave(alice) [subsumption resolution 357,126]
377. ~tall(alice) [resolution 359,117]
379. $false <- (19, 20) [subsumption resolution 377,342]
380. ~19 | ~20 [avatar contradiction clause 379]
381. $false [avatar sat refutation 219,227,280,291,380]
% SZS output end Proof for 652665586348350458512903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and quiet is not kind or calm. Everyone who is either not curious or brave is happy or old and vice versa. If someone is not strong or not funny then susan is both wise and happy. Everyone who is strong or humble is generous or calm. If someone is happy or not generous then someone is brave. Everyone who is not curious is funny. If john is not tall then alice is not wise and vice versa. If someone is either not creative or not strong then someone is either not creative or not rich and vice versa. Everyone who is old or wise is both funny and not curious and vice versa. If someone is quiet then someone is strong or not wise. If someone is brave or not kind then john is either not generous or not quiet and vice versa. If someone is generous or old then paul is both not old and not tall and vice versa. Everyone who is both not old and curious is kind. Everyone who is not humble is not funny. If someone is calm then someone is both calm and rich. Everyone who is rich or not creative is either not calm or strong. Someone is either not brave or not wise. John is not kind. Mary is not strong or wise. Mary is both not happy and not generous. Someone is both not rich and not funny. Lucy is funny. Fred is both calm and patient. Someone is both not quiet and not calm. | Fred is calm. | entailment | (![X]:((~old(X)&quiet(X))=>(~kind(X)|calm(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(happy(X)|old(X))))&
((?[X]:((~strong(X)|~funny(X))))=>((wise(susan)&happy(susan))))&
(![X]:((strong(X)|humble(X))=>(generous(X)|calm(X))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:(brave(X))))&
(![X]:(~curious(X)=>funny(X)))&
((~tall(john))<=>(~wise(alice)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((old(X)|wise(X))<=>(funny(X)&~curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((brave(X)|~kind(X))))<=>((~generous(john)<~>~quiet(john))))&
((?[X]:((generous(X)|old(X))))<=>((~old(paul)&~tall(paul))))&
(![X]:((~old(X)&curious(X))=>kind(X)))&
(![X]:(~humble(X)=>~funny(X)))&
((?[X]:(calm(X)))=>(?[X]:((calm(X)&rich(X)))))&
(![X]:((rich(X)|~creative(X))=>(~calm(X)<~>strong(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(~kind(john))&
((~strong(mary)|wise(mary)))&
((~happy(mary)&~generous(mary)))&
(?[X]:((~rich(X)&~funny(X))))&
(funny(lucy))&
((calm(fred)&patient(fred)))&
(?[X]:((~quiet(X)&~calm(X)))) | calm(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5973935729594410985936756
% SZS output start Proof for 5973935729594410985936756
23. patient(fred) & calm(fred) [input p22]
25. ~calm(fred) [input hypothesis]
30. calm(fred) [pure predicate removal 23]
140. calm(fred) [cnf transformation 30]
143. ~calm(fred) [cnf transformation 25]
321. $false [subsumption resolution 143,140]
% SZS output end Proof for 5973935729594410985936756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or generous then someone is not patient and vice versa. Everyone who is either not happy or curious is generous. If alice is not calm then someone is not brave and vice versa. Everyone who is not old or tall is both not patient and curious and vice versa. Everyone who is not happy or calm is either not patient or not wise and vice versa. Everyone who is not rich is happy and vice versa. If someone is both not humble and strong then someone is either funny or calm and vice versa. If someone is not happy or not humble then susan is either rich or patient and vice versa. Everyone who is not calm is either wise or not quiet. If john is not humble then fred is not brave or calm. Everyone who is either not funny or not tall is not funny and vice versa. If someone is both not wise and not brave then mary is either not happy or humble and vice versa. If someone is either kind or not calm then susan is both not wise and not funny and vice versa. Everyone who is either kind or strong is either calm or humble. If mary is not old then someone is generous or not curious and vice versa. Everyone who is either not happy or generous is humble and vice versa. Lucy is not wise or not curious. Susan is old. Paul is not wise. Someone is both rich and not quiet. Someone is not creative. Mary is either not generous or tall. | Susan is kind. | neutral | ((?[X]:((~calm(X)|generous(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~happy(X)<~>curious(X))=>generous(X)))&
((~calm(alice))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|tall(X))<=>(~patient(X)&curious(X))))&
(![X]:((~happy(X)|calm(X))<=>(~patient(X)<~>~wise(X))))&
(![X]:(~rich(X)<=>happy(X)))&
((?[X]:((~humble(X)&strong(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
((?[X]:((~happy(X)|~humble(X))))<=>((rich(susan)<~>patient(susan))))&
(![X]:(~calm(X)=>(wise(X)<~>~quiet(X))))&
((~humble(john))=>((~brave(fred)|calm(fred))))&
(![X]:((~funny(X)<~>~tall(X))<=>~funny(X)))&
((?[X]:((~wise(X)&~brave(X))))<=>((~happy(mary)<~>humble(mary))))&
((?[X]:((kind(X)<~>~calm(X))))<=>((~wise(susan)&~funny(susan))))&
(![X]:((kind(X)<~>strong(X))=>(calm(X)<~>humble(X))))&
((~old(mary))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((~happy(X)<~>generous(X))<=>humble(X)))&
((~wise(lucy)|~curious(lucy)))&
(old(susan))&
(~wise(paul))&
(?[X]:((rich(X)&~quiet(X))))&
(?[X]:(~creative(X)))&
((~generous(mary)<~>tall(mary))) | kind(susan) | [] | null | 0 |
Everyone who is not calm or creative is either not creative or funny and vice versa.
Everyone who is both not creative and not old is both not curious and not generous.
If someone is patient or strong then lucy is kind or quiet and vice versa.
If someone is not happy or not kind then someone is not patient or not generous.
If someone is either rich or not creative then lucy is both not tall and not kind.
Everyone who is not strong is rich.
If mary is not tall then john is not patient or not curious and vice versa.
Everyone who is not creative is both not tall and not generous and vice versa.
If john is either kind or rich then someone is both quiet and not calm and vice versa.
If paul is not happy or brave then someone is both not patient and not old.
Everyone who is either calm or humble is not rich or not brave and vice versa.
If susan is either not happy or funny then someone is not calm or humble and vice versa.
If someone is rich then mary is both not rich and strong and vice versa.
If someone is both tall and not funny then someone is either curious or not old.
Everyone who is both curious and not happy is not humble.
Everyone who is not patient or generous is not wise.
John is both old and generous.
Someone is either not creative or humble.
John is rich.
Someone is both not brave and tall.
Mary is both not generous and not creative.
Someone is funny or not humble.
Someone is either not funny or calm.
Fred is either not brave or tall. | Lucy is not quiet. | contradiction | (![X]:((~calm(X)|creative(X))<=>(~creative(X)<~>funny(X))))&
(![X]:((~creative(X)&~old(X))=>(~curious(X)&~generous(X))))&
((?[X]:((patient(X)|strong(X))))<=>((kind(lucy)|quiet(lucy))))&
((?[X]:((~happy(X)|~kind(X))))=>(?[X]:((~patient(X)|~generous(X)))))&
((?[X]:((rich(X)<~>~creative(X))))=>((~tall(lucy)&~kind(lucy))))&
(![X]:(~strong(X)=>rich(X)))&
((~tall(mary))<=>((~patient(john)|~curious(john))))&
(![X]:(~creative(X)<=>(~tall(X)&~generous(X))))&
(((kind(john)<~>rich(john)))<=>(?[X]:((quiet(X)&~calm(X)))))&
(((~happy(paul)|brave(paul)))=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((calm(X)<~>humble(X))<=>(~rich(X)|~brave(X))))&
(((~happy(susan)<~>funny(susan)))<=>(?[X]:((~calm(X)|humble(X)))))&
((?[X]:(rich(X)))<=>((~rich(mary)&strong(mary))))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((curious(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
((old(john)&generous(john)))&
(?[X]:((~creative(X)<~>humble(X))))&
(rich(john))&
(?[X]:((~brave(X)&tall(X))))&
((~generous(mary)&~creative(mary)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((~brave(fred)<~>tall(fred))) | ~quiet(lucy) | [
"p2",
"p4",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8165923111099356001104315
% SZS output start Proof for 8165923111099356001104315
3. ? [X0] : (strong(X0) | patient(X0)) <=> (quiet(lucy) | kind(lucy)) [input p2]
5. ? [X0] : (rich(X0) <~> ~creative(X0)) => (~kind(lucy) & ~tall(lucy)) [input p4]
13. ? [X0] : rich(X0) <=> (strong(mary) & ~rich(mary)) [input p12]
19. rich(john) [input p18]
21. ~creative(mary) & ~generous(mary) [input p20]
25. ~quiet(lucy) [input hypothesis]
32. (~kind(lucy) & ~tall(lucy)) | ! [X0] : (rich(X0) <=> ~creative(X0)) [ennf transformation 5]
40. (? [X0] : (strong(X0) | patient(X0)) | (~quiet(lucy) & ~kind(lucy))) & ((quiet(lucy) | kind(lucy)) | ! [X0] : (~strong(X0) & ~patient(X0))) [nnf transformation 3]
41. (? [X0] : (strong(X0) | patient(X0)) | (~quiet(lucy) & ~kind(lucy))) & (quiet(lucy) | kind(lucy) | ! [X0] : (~strong(X0) & ~patient(X0))) [flattening 40]
42. (? [X0] : (strong(X0) | patient(X0)) | (~quiet(lucy) & ~kind(lucy))) & (quiet(lucy) | kind(lucy) | ! [X1] : (~strong(X1) & ~patient(X1))) [rectify 41]
43. ? [X0] : (strong(X0) | patient(X0)) => (strong(sK0) | patient(sK0)) [choice axiom]
44. ((strong(sK0) | patient(sK0)) | (~quiet(lucy) & ~kind(lucy))) & (quiet(lucy) | kind(lucy) | ! [X1] : (~strong(X1) & ~patient(X1))) [skolemisation 42,43]
48. (~kind(lucy) & ~tall(lucy)) | ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))) [nnf transformation 32]
65. (? [X0] : rich(X0) | (~strong(mary) | rich(mary))) & ((strong(mary) & ~rich(mary)) | ! [X0] : ~rich(X0)) [nnf transformation 13]
66. (? [X0] : rich(X0) | ~strong(mary) | rich(mary)) & ((strong(mary) & ~rich(mary)) | ! [X0] : ~rich(X0)) [flattening 65]
67. (? [X0] : rich(X0) | ~strong(mary) | rich(mary)) & ((strong(mary) & ~rich(mary)) | ! [X1] : ~rich(X1)) [rectify 66]
68. ? [X0] : rich(X0) => rich(sK5) [choice axiom]
69. (rich(sK5) | ~strong(mary) | rich(mary)) & ((strong(mary) & ~rich(mary)) | ! [X1] : ~rich(X1)) [skolemisation 67,68]
94. quiet(lucy) | kind(lucy) | ~strong(X1) [cnf transformation 44]
102. ~kind(lucy) | rich(X0) | creative(X0) [cnf transformation 48]
132. ~rich(mary) | ~rich(X1) [cnf transformation 69]
133. strong(mary) | ~rich(X1) [cnf transformation 69]
142. rich(john) [cnf transformation 19]
146. ~creative(mary) [cnf transformation 21]
152. ~quiet(lucy) [cnf transformation 25]
156. 1 <=> quiet(lucy) [avatar definition]
169. 4 <=> kind(lucy) [avatar definition]
174. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
175. ~strong(X1) <- (5) [avatar component clause 174]
176. 5 | 4 | 1 [avatar split clause 94,156,169,174]
198. 11 <=> ! [X0] : (rich(X0) | creative(X0)) [avatar definition]
199. rich(X0) | creative(X0) <- (11) [avatar component clause 198]
200. 11 | ~4 [avatar split clause 102,169,198]
234. 19 <=> rich(john) [avatar definition]
235. rich(john) <- (19) [avatar component clause 234]
301. 32 <=> rich(mary) [avatar definition]
302. ~rich(mary) <- (~32) [avatar component clause 301]
310. 34 <=> ! [X1] : ~rich(X1) [avatar definition]
311. ~rich(X1) <- (34) [avatar component clause 310]
313. 35 <=> strong(mary) [avatar definition]
315. strong(mary) <- (35) [avatar component clause 313]
316. 34 | 35 [avatar split clause 133,313,310]
317. 34 | ~32 [avatar split clause 132,301,310]
341. 19 [avatar split clause 142,234]
371. ~1 [avatar split clause 152,156]
374. $false <- (19, 34) [subsumption resolution 235,311]
375. ~19 | ~34 [avatar contradiction clause 374]
376. $false <- (5, 35) [subsumption resolution 315,175]
377. ~5 | ~35 [avatar contradiction clause 376]
385. creative(mary) <- (11, ~32) [resolution 199,302]
386. $false <- (11, ~32) [subsumption resolution 385,146]
387. ~11 | 32 [avatar contradiction clause 386]
388. $false [avatar sat refutation 176,200,316,317,341,371,375,377,387]
% SZS output end Proof for 8165923111099356001104315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or wise then someone is not old or not kind and vice versa. Everyone who is either generous or funny is humble or not curious. Everyone who is not curious or creative is patient or not generous and vice versa. If susan is not tall then paul is both happy and not funny. If someone is generous then alice is creative and vice versa. Everyone who is either not curious or rich is either tall or not calm and vice versa. Everyone who is both not wise and not kind is either wise or not wise. Everyone who is kind is both rich and not strong. If paul is calm or not brave then paul is wise and vice versa. Everyone who is wise is either calm or happy and vice versa. If someone is either old or brave then john is not old or not creative. If someone is kind then paul is not patient or kind and vice versa. Everyone who is funny is creative or not brave and vice versa. If someone is humble then lucy is not old or not quiet and vice versa. Everyone who is both patient and old is either not tall or not strong and vice versa. Everyone who is brave is both not strong and happy. Paul is either humble or not old. John is both not old and not tall. Susan is wise. Lucy is either generous or kind. Someone is both funny and rich. Susan is funny or patient. Fred is calm. Fred is strong or not tall. | Lucy is old. | neutral | ((?[X]:((happy(X)|wise(X))))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((generous(X)<~>funny(X))=>(humble(X)|~curious(X))))&
(![X]:((~curious(X)|creative(X))<=>(patient(X)|~generous(X))))&
((~tall(susan))=>((happy(paul)&~funny(paul))))&
((?[X]:(generous(X)))<=>(creative(alice)))&
(![X]:((~curious(X)<~>rich(X))<=>(tall(X)<~>~calm(X))))&
(![X]:((~wise(X)&~kind(X))=>(wise(X)<~>~wise(X))))&
(![X]:(kind(X)=>(rich(X)&~strong(X))))&
(((calm(paul)|~brave(paul)))<=>(wise(paul)))&
(![X]:(wise(X)<=>(calm(X)<~>happy(X))))&
((?[X]:((old(X)<~>brave(X))))=>((~old(john)|~creative(john))))&
((?[X]:(kind(X)))<=>((~patient(paul)|kind(paul))))&
(![X]:(funny(X)<=>(creative(X)|~brave(X))))&
((?[X]:(humble(X)))<=>((~old(lucy)|~quiet(lucy))))&
(![X]:((patient(X)&old(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:(brave(X)=>(~strong(X)&happy(X))))&
((humble(paul)<~>~old(paul)))&
((~old(john)&~tall(john)))&
(wise(susan))&
((generous(lucy)<~>kind(lucy)))&
(?[X]:((funny(X)&rich(X))))&
((funny(susan)|patient(susan)))&
(calm(fred))&
((strong(fred)|~tall(fred))) | old(lucy) | [] | null | 0 |
If someone is not calm then mary is both kind and not brave.
If someone is either not generous or not brave then paul is old and vice versa.
If someone is curious then someone is both strong and not tall.
Everyone who is both not wise and not calm is creative and vice versa.
Everyone who is creative is either not kind or not rich and vice versa.
If paul is brave or old then mary is either rich or not funny and vice versa.
Everyone who is rich or not rich is either calm or funny.
Everyone who is quiet is tall or quiet.
Everyone who is both not curious and not quiet is not happy.
If someone is wise then fred is not generous and vice versa.
If lucy is not calm then someone is either not creative or not rich.
If someone is both not patient and wise then someone is wise or funny and vice versa.
If lucy is not rich then lucy is both not old and calm.
If someone is not kind then someone is either curious or creative and vice versa.
If fred is strong or not generous then paul is not rich and vice versa.
If susan is both not brave and not quiet then someone is not calm or not humble.
Someone is either happy or wise.
Mary is both not strong and not funny.
Someone is tall or strong.
Paul is both not rich and kind.
Someone is both kind and happy.
Someone is not wise or humble. | Paul is brave. | contradiction | ((?[X]:(~calm(X)))=>((kind(mary)&~brave(mary))))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(old(paul)))&
((?[X]:(curious(X)))=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((~wise(X)&~calm(X))<=>creative(X)))&
(![X]:(creative(X)<=>(~kind(X)<~>~rich(X))))&
(((brave(paul)|old(paul)))<=>((rich(mary)<~>~funny(mary))))&
(![X]:((rich(X)|~rich(X))=>(calm(X)<~>funny(X))))&
(![X]:(quiet(X)=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&~quiet(X))=>~happy(X)))&
((?[X]:(wise(X)))<=>(~generous(fred)))&
((~calm(lucy))=>(?[X]:((~creative(X)<~>~rich(X)))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((wise(X)|funny(X)))))&
((~rich(lucy))=>((~old(lucy)&calm(lucy))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>creative(X)))))&
(((strong(fred)|~generous(fred)))<=>(~rich(paul)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((~calm(X)|~humble(X)))))&
(?[X]:((happy(X)<~>wise(X))))&
((~strong(mary)&~funny(mary)))&
(?[X]:((tall(X)|strong(X))))&
((~rich(paul)&kind(paul)))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:((~wise(X)|humble(X)))) | brave(paul) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8645255035874329721465545
% SZS output start Proof for 8645255035874329721465545
1. ? [X0] : ~calm(X0) => (~brave(mary) & kind(mary)) [input p0]
4. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> creative(X0)) [input p3]
5. ! [X0] : (creative(X0) <=> (~kind(X0) <~> ~rich(X0))) [input p4]
6. (old(paul) | brave(paul)) <=> (rich(mary) <~> ~funny(mary)) [input p5]
7. ! [X0] : ((~rich(X0) | rich(X0)) => (calm(X0) <~> funny(X0))) [input p6]
18. ~funny(mary) & ~strong(mary) [input p17]
20. kind(paul) & ~rich(paul) [input p19]
23. brave(paul) [input hypothesis]
27. (~brave(mary) & kind(mary)) | ! [X0] : calm(X0) [ennf transformation 1]
29. ! [X0] : ((calm(X0) <~> funny(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 7]
45. ! [X0] : (((~calm(X0) & ~wise(X0)) | ~creative(X0)) & (creative(X0) | (calm(X0) | wise(X0)))) [nnf transformation 4]
46. ! [X0] : (((~calm(X0) & ~wise(X0)) | ~creative(X0)) & (creative(X0) | calm(X0) | wise(X0))) [flattening 45]
47. ! [X0] : ((creative(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 5]
48. ((old(paul) | brave(paul)) | ((rich(mary) | funny(mary)) & (~funny(mary) | ~rich(mary)))) & (((funny(mary) | ~rich(mary)) & (~funny(mary) | rich(mary))) | (~old(paul) & ~brave(paul))) [nnf transformation 6]
49. (old(paul) | brave(paul) | ((rich(mary) | funny(mary)) & (~funny(mary) | ~rich(mary)))) & (((funny(mary) | ~rich(mary)) & (~funny(mary) | rich(mary))) | (~old(paul) & ~brave(paul))) [flattening 48]
50. ! [X0] : (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (rich(X0) & ~rich(X0))) [nnf transformation 29]
81. kind(mary) | calm(X0) [cnf transformation 27]
91. ~creative(X0) | ~calm(X0) [cnf transformation 46]
95. ~kind(X0) | creative(X0) | rich(X0) [cnf transformation 47]
98. funny(mary) | ~rich(mary) | ~brave(paul) [cnf transformation 49]
102. funny(X0) | calm(X0) | ~rich(X0) [cnf transformation 50]
103. funny(X0) | calm(X0) | rich(X0) [cnf transformation 50]
130. ~funny(mary) [cnf transformation 18]
132. ~rich(paul) [cnf transformation 20]
133. kind(paul) [cnf transformation 20]
137. brave(paul) [cnf transformation 23]
139. 1 <=> ! [X0] : calm(X0) [avatar definition]
140. calm(X0) <- (1) [avatar component clause 139]
147. 3 <=> kind(mary) [avatar definition]
149. kind(mary) <- (3) [avatar component clause 147]
150. 1 | 3 [avatar split clause 81,147,139]
187. 12 <=> funny(mary) [avatar definition]
188. ~funny(mary) <- (~12) [avatar component clause 187]
191. 13 <=> rich(mary) [avatar definition]
192. ~rich(mary) <- (~13) [avatar component clause 191]
195. 14 <=> brave(paul) [avatar definition]
201. ~14 | ~13 | 12 [avatar split clause 98,187,191,195]
205. funny(X0) | calm(X0) [subsumption resolution 102,103]
296. 35 <=> rich(paul) [avatar definition]
297. ~rich(paul) <- (~35) [avatar component clause 296]
333. ~12 [avatar split clause 130,187]
343. ~35 [avatar split clause 132,296]
353. 14 [avatar split clause 137,195]
362. calm(mary) <- (~12) [resolution 188,205]
373. creative(paul) | rich(paul) [resolution 95,133]
395. creative(paul) <- (~35) [subsumption resolution 373,297]
405. creative(mary) | rich(mary) <- (3) [resolution 149,95]
406. creative(mary) <- (3, ~13) [subsumption resolution 405,192]
450. ~calm(paul) <- (~35) [resolution 395,91]
497. ~calm(mary) <- (3, ~13) [resolution 406,91]
499. $false <- (3, ~12, ~13) [subsumption resolution 497,362]
500. ~3 | 12 | 13 [avatar contradiction clause 499]
510. $false <- (1, ~35) [resolution 450,140]
511. ~1 | 35 [avatar contradiction clause 510]
512. $false [avatar sat refutation 150,201,333,343,353,500,511]
% SZS output end Proof for 8645255035874329721465545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or not kind is wise and vice versa.
Everyone who is not curious is either not curious or wise and vice versa.
If john is brave or not happy then someone is not rich and vice versa.
Everyone who is either happy or wise is both creative and quiet and vice versa.
If someone is both happy and not happy then john is curious or not wise.
Everyone who is both not calm and not quiet is not quiet or not kind.
If someone is either kind or not happy then someone is both not generous and kind.
Everyone who is both calm and tall is both not strong and not kind and vice versa.
If lucy is not rich then paul is not curious and vice versa.
If someone is wise or strong then someone is humble or not funny.
Everyone who is either quiet or generous is either not strong or not rich and vice versa.
Everyone who is funny is not strong and vice versa.
Everyone who is patient or not kind is not strong or not happy and vice versa.
If someone is not humble then someone is not strong.
If someone is either not tall or not humble then someone is not quiet.
Everyone who is quiet is not old or not quiet.
Someone is not rich.
Alice is funny or not old.
Someone is both rich and not patient.
Someone is generous or not strong.
Someone is kind or strong.
Someone is not kind or brave.
John is either rich or not wise. | Paul is not rich. | neutral | (![X]:((~strong(X)<~>~kind(X))<=>wise(X)))&
(![X]:(~curious(X)<=>(~curious(X)<~>wise(X))))&
(((brave(john)|~happy(john)))<=>(?[X]:(~rich(X))))&
(![X]:((happy(X)<~>wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((happy(X)&~happy(X))))=>((curious(john)|~wise(john))))&
(![X]:((~calm(X)&~quiet(X))=>(~quiet(X)|~kind(X))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((calm(X)&tall(X))<=>(~strong(X)&~kind(X))))&
((~rich(lucy))<=>(~curious(paul)))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:(funny(X)<=>~strong(X)))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~old(X)|~quiet(X))))&
(?[X]:(~rich(X)))&
((funny(alice)|~old(alice)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((generous(X)|~strong(X))))&
(?[X]:((kind(X)|strong(X))))&
(?[X]:((~kind(X)|brave(X))))&
((rich(john)<~>~wise(john))) | ~rich(paul) | [] | null | 0 |
If someone is not patient or funny then someone is both humble and curious.
If alice is not tall then someone is not brave or creative.
If susan is not calm then someone is both brave and happy.
If paul is wise then someone is either not kind or not funny and vice versa.
Everyone who is either not calm or funny is not creative or not curious and vice versa.
Everyone who is not curious or patient is either not creative or not funny.
If someone is both generous and funny then lucy is not calm.
If alice is both patient and curious then mary is happy or strong.
Everyone who is rich is either patient or wise and vice versa.
Everyone who is either wise or creative is calm or not old and vice versa.
Everyone who is not tall or not calm is either calm or not kind and vice versa.
If mary is not strong or not patient then alice is both not calm and not happy.
Everyone who is not funny is both creative and tall and vice versa.
If lucy is both patient and not kind then someone is either funny or curious and vice versa.
If someone is not creative then someone is either not patient or not quiet and vice versa.
If alice is tall or kind then paul is tall and vice versa.
Someone is not happy.
Someone is either humble or not funny.
Paul is both not happy and patient.
Someone is not old.
John is both curious and not calm.
Someone is either funny or wise.
Alice is either not humble or not tall. | John is not tall. | entailment | ((?[X]:((~patient(X)|funny(X))))=>(?[X]:((humble(X)&curious(X)))))&
((~tall(alice))=>(?[X]:((~brave(X)|creative(X)))))&
((~calm(susan))=>(?[X]:((brave(X)&happy(X)))))&
((wise(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:((~calm(X)<~>funny(X))<=>(~creative(X)|~curious(X))))&
(![X]:((~curious(X)|patient(X))=>(~creative(X)<~>~funny(X))))&
((?[X]:((generous(X)&funny(X))))=>(~calm(lucy)))&
(((patient(alice)&curious(alice)))=>((happy(mary)|strong(mary))))&
(![X]:(rich(X)<=>(patient(X)<~>wise(X))))&
(![X]:((wise(X)<~>creative(X))<=>(calm(X)|~old(X))))&
(![X]:((~tall(X)|~calm(X))<=>(calm(X)<~>~kind(X))))&
(((~strong(mary)|~patient(mary)))=>((~calm(alice)&~happy(alice))))&
(![X]:(~funny(X)<=>(creative(X)&tall(X))))&
(((patient(lucy)&~kind(lucy)))<=>(?[X]:((funny(X)<~>curious(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((tall(alice)|kind(alice)))<=>(tall(paul)))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~funny(X))))&
((~happy(paul)&patient(paul)))&
(?[X]:(~old(X)))&
((curious(john)&~calm(john)))&
(?[X]:((funny(X)<~>wise(X))))&
((~humble(alice)<~>~tall(alice))) | ~tall(john) | [
"p4",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1759751091791038847994469
% SZS output start Proof for 1759751091791038847994469
5. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~curious(X0) | ~creative(X0))) [input p4]
13. ! [X0] : (~funny(X0) <=> (tall(X0) & creative(X0))) [input p12]
21. ~calm(john) & curious(john) [input p20]
24. tall(john) [input hypothesis]
46. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (curious(X0) & creative(X0))) & ((~curious(X0) | ~creative(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 5]
47. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (curious(X0) & creative(X0))) & (~curious(X0) | ~creative(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [flattening 46]
53. ! [X0] : ((~funny(X0) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | funny(X0))) [nnf transformation 13]
54. ! [X0] : ((~funny(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | funny(X0))) [flattening 53]
89. ~creative(X0) | ~curious(X0) | funny(X0) | calm(X0) [cnf transformation 47]
93. ~funny(X0) | calm(X0) | creative(X0) [cnf transformation 47]
113. creative(X0) | funny(X0) [cnf transformation 54]
115. ~creative(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 54]
135. curious(john) [cnf transformation 21]
136. ~calm(john) [cnf transformation 21]
141. tall(john) [cnf transformation 24]
406. ~curious(X1) | funny(X1) | calm(X1) | funny(X1) [resolution 89,113]
408. ~curious(X1) | funny(X1) | calm(X1) [duplicate literal removal 406]
648. funny(john) | calm(john) [resolution 408,135]
652. funny(john) [subsumption resolution 648,136]
699. calm(john) | creative(john) [resolution 652,93]
700. creative(john) [subsumption resolution 699,136]
712. ~tall(john) | ~funny(john) [resolution 700,115]
715. ~funny(john) [subsumption resolution 712,141]
716. $false [subsumption resolution 715,652]
% SZS output end Proof for 1759751091791038847994469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is funny or patient then someone is not patient and vice versa.
Everyone who is quiet or not brave is both not old and wise.
Everyone who is both strong and not calm is not funny or funny and vice versa.
If someone is either not funny or not creative then fred is not wise or not creative and vice versa.
If john is either funny or humble then susan is not generous or quiet and vice versa.
If alice is tall then someone is not humble and vice versa.
Everyone who is either happy or quiet is not funny and vice versa.
Everyone who is either not humble or not tall is both not funny and not patient and vice versa.
If susan is funny or quiet then someone is either not funny or calm and vice versa.
Everyone who is not creative or not humble is either kind or not wise.
Everyone who is either not old or old is curious or not rich.
Everyone who is either calm or not creative is both quiet and tall and vice versa.
Everyone who is not old or not happy is funny and vice versa.
Everyone who is patient or curious is generous or brave and vice versa.
If someone is not humble then mary is not curious or not strong and vice versa.
Someone is both happy and not funny.
Fred is not curious.
John is either creative or kind.
Someone is not wise or rich.
Someone is both wise and happy.
Someone is not kind or not generous. | John is not strong. | contradiction | ((?[X]:((funny(X)|patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)|~brave(X))=>(~old(X)&wise(X))))&
(![X]:((strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((~wise(fred)|~creative(fred))))&
(((funny(john)<~>humble(john)))<=>((~generous(susan)|quiet(susan))))&
((tall(alice))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>quiet(X))<=>~funny(X)))&
(![X]:((~humble(X)<~>~tall(X))<=>(~funny(X)&~patient(X))))&
(((funny(susan)|quiet(susan)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((~creative(X)|~humble(X))=>(kind(X)<~>~wise(X))))&
(![X]:((~old(X)<~>old(X))=>(curious(X)|~rich(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(quiet(X)&tall(X))))&
(![X]:((~old(X)|~happy(X))<=>funny(X)))&
(![X]:((patient(X)|curious(X))<=>(generous(X)|brave(X))))&
((?[X]:(~humble(X)))<=>((~curious(mary)|~strong(mary))))&
(?[X]:((happy(X)&~funny(X))))&
(~curious(fred))&
((creative(john)<~>kind(john)))&
(?[X]:((~wise(X)|rich(X))))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:((~kind(X)|~generous(X)))) | ~strong(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6960777752398910873432708
% SZS output start Proof for 6960777752398910873432708
3. ! [X0] : ((~calm(X0) & strong(X0)) <=> (funny(X0) | ~funny(X0))) [input p2]
22. ~strong(john) [input hypothesis]
33. ! [X0] : (((~calm(X0) & strong(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~calm(X0) & strong(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | calm(X0) | ~strong(X0))) [flattening 33]
84. strong(X0) | funny(X0) [cnf transformation 34]
85. strong(X0) | ~funny(X0) [cnf transformation 34]
149. ~strong(john) [cnf transformation 22]
177. strong(X0) [subsumption resolution 84,85]
301. $false [subsumption resolution 149,177]
% SZS output end Proof for 6960777752398910873432708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy and curious then someone is either not humble or not quiet and vice versa. If fred is patient or not rich then alice is not wise. If fred is not brave or not old then someone is both kind and not strong. If susan is either kind or funny then susan is not patient. Everyone who is both not curious and not tall is either not kind or not quiet and vice versa. If someone is not humble or calm then someone is quiet or not strong and vice versa. Everyone who is both not curious and not brave is both quiet and not strong. Everyone who is not patient is not strong and vice versa. If someone is creative or not strong then paul is either kind or not strong and vice versa. If alice is either not patient or not creative then fred is either kind or rich. If someone is humble or generous then someone is either not happy or happy. Everyone who is both not tall and not calm is both not humble and not creative and vice versa. If someone is either not wise or not curious then john is either not happy or not quiet and vice versa. Everyone who is either tall or brave is not tall or not old. If mary is both tall and not tall then alice is both not funny and generous. Everyone who is not calm or not patient is both humble and patient. Paul is kind or not quiet. John is not patient or calm. Mary is either strong or calm. Fred is both curious and not humble. Someone is not wise or wise. John is either brave or not old. | Fred is quiet. | neutral | ((?[X]:((~happy(X)&curious(X))))<=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(((patient(fred)|~rich(fred)))=>(~wise(alice)))&
(((~brave(fred)|~old(fred)))=>(?[X]:((kind(X)&~strong(X)))))&
(((kind(susan)<~>funny(susan)))=>(~patient(susan)))&
(![X]:((~curious(X)&~tall(X))<=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~humble(X)|calm(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:((~curious(X)&~brave(X))=>(quiet(X)&~strong(X))))&
(![X]:(~patient(X)<=>~strong(X)))&
((?[X]:((creative(X)|~strong(X))))<=>((kind(paul)<~>~strong(paul))))&
(((~patient(alice)<~>~creative(alice)))=>((kind(fred)<~>rich(fred))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((~happy(john)<~>~quiet(john))))&
(![X]:((tall(X)<~>brave(X))=>(~tall(X)|~old(X))))&
(((tall(mary)&~tall(mary)))=>((~funny(alice)&generous(alice))))&
(![X]:((~calm(X)|~patient(X))=>(humble(X)&patient(X))))&
((kind(paul)|~quiet(paul)))&
((~patient(john)|calm(john)))&
((strong(mary)<~>calm(mary)))&
((curious(fred)&~humble(fred)))&
(?[X]:((~wise(X)|wise(X))))&
((brave(john)<~>~old(john))) | quiet(fred) | [] | null | 0 |
If alice is tall or not generous then fred is either happy or strong and vice versa. Everyone who is either not rich or not happy is both happy and calm and vice versa. Everyone who is both not patient and not creative is both not curious and happy. If susan is both not creative and funny then alice is calm and vice versa. If john is either curious or calm then someone is wise and vice versa. If mary is not brave then someone is both not kind and not old and vice versa. If alice is not patient or creative then lucy is curious. Everyone who is either funny or curious is either rich or not old. Everyone who is not tall is funny and vice versa. Everyone who is not wise or generous is creative. Everyone who is not funny is rich or not curious and vice versa. Everyone who is quiet or strong is either curious or not kind and vice versa. If someone is either not humble or old then someone is either brave or not calm. Everyone who is humble or not happy is not rich and vice versa. If paul is either not kind or quiet then someone is not creative or curious and vice versa. Everyone who is tall or not kind is rich or not patient and vice versa. Mary is both strong and not brave. Someone is not tall or creative. Someone is both wise and funny. Alice is happy. Fred is both not kind and calm. Someone is brave. Someone is both calm and not quiet. Fred is tall or not kind. | Fred is brave. | neutral | (((tall(alice)|~generous(alice)))<=>((happy(fred)<~>strong(fred))))&
(![X]:((~rich(X)<~>~happy(X))<=>(happy(X)&calm(X))))&
(![X]:((~patient(X)&~creative(X))=>(~curious(X)&happy(X))))&
(((~creative(susan)&funny(susan)))<=>(calm(alice)))&
(((curious(john)<~>calm(john)))<=>(?[X]:(wise(X))))&
((~brave(mary))<=>(?[X]:((~kind(X)&~old(X)))))&
(((~patient(alice)|creative(alice)))=>(curious(lucy)))&
(![X]:((funny(X)<~>curious(X))=>(rich(X)<~>~old(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~wise(X)|generous(X))=>creative(X)))&
(![X]:(~funny(X)<=>(rich(X)|~curious(X))))&
(![X]:((quiet(X)|strong(X))<=>(curious(X)<~>~kind(X))))&
((?[X]:((~humble(X)<~>old(X))))=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((humble(X)|~happy(X))<=>~rich(X)))&
(((~kind(paul)<~>quiet(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((tall(X)|~kind(X))<=>(rich(X)|~patient(X))))&
((strong(mary)&~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((wise(X)&funny(X))))&
(happy(alice))&
((~kind(fred)&calm(fred)))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)&~quiet(X))))&
((tall(fred)|~kind(fred))) | brave(fred) | [] | null | 0 |
Everyone who is either curious or not patient is both not humble and funny and vice versa. If alice is funny or not rich then fred is both funny and old and vice versa. Everyone who is both generous and wise is kind and vice versa. If someone is not happy then alice is either creative or old and vice versa. Everyone who is both not brave and not tall is either old or curious and vice versa. If paul is either not tall or not calm then lucy is either not old or not kind and vice versa. Everyone who is either wise or not calm is either creative or strong and vice versa. If someone is tall then someone is either tall or not strong and vice versa. Everyone who is either not kind or not strong is wise and vice versa. Everyone who is old is not happy or curious. Everyone who is rich is either calm or generous. Everyone who is both not rich and not tall is both funny and not old. Everyone who is not tall is quiet or not old. If someone is either not creative or not patient then someone is both not patient and not wise and vice versa. Everyone who is either creative or curious is both rich and tall. Everyone who is both happy and patient is both wise and curious. Someone is either not happy or not quiet. Fred is both old and not kind. Someone is curious or funny. John is not happy. Fred is not wise. Lucy is both creative and not kind. Mary is both not quiet and creative. Lucy is old or happy. | Mary is quiet. | contradiction | (![X]:((curious(X)<~>~patient(X))<=>(~humble(X)&funny(X))))&
(((funny(alice)|~rich(alice)))<=>((funny(fred)&old(fred))))&
(![X]:((generous(X)&wise(X))<=>kind(X)))&
((?[X]:(~happy(X)))<=>((creative(alice)<~>old(alice))))&
(![X]:((~brave(X)&~tall(X))<=>(old(X)<~>curious(X))))&
(((~tall(paul)<~>~calm(paul)))<=>((~old(lucy)<~>~kind(lucy))))&
(![X]:((wise(X)<~>~calm(X))<=>(creative(X)<~>strong(X))))&
((?[X]:(tall(X)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((~kind(X)<~>~strong(X))<=>wise(X)))&
(![X]:(old(X)=>(~happy(X)|curious(X))))&
(![X]:(rich(X)=>(calm(X)<~>generous(X))))&
(![X]:((~rich(X)&~tall(X))=>(funny(X)&~old(X))))&
(![X]:(~tall(X)=>(quiet(X)|~old(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((creative(X)<~>curious(X))=>(rich(X)&tall(X))))&
(![X]:((happy(X)&patient(X))=>(wise(X)&curious(X))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((old(fred)&~kind(fred)))&
(?[X]:((curious(X)|funny(X))))&
(~happy(john))&
(~wise(fred))&
((creative(lucy)&~kind(lucy)))&
((~quiet(mary)&creative(mary)))&
((old(lucy)|happy(lucy))) | quiet(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8183256703014042245223185
% SZS output start Proof for 8183256703014042245223185
23. creative(mary) & ~quiet(mary) [input p22]
25. quiet(mary) [input hypothesis]
145. ~quiet(mary) [cnf transformation 23]
148. quiet(mary) [cnf transformation 25]
297. $false [subsumption resolution 148,145]
% SZS output end Proof for 8183256703014042245223185
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not brave or not strong then someone is funny.
Everyone who is either strong or curious is not strong or brave and vice versa.
Everyone who is creative or kind is not happy.
If someone is both not generous and not curious then lucy is not generous or not wise.
Everyone who is either calm or not brave is not creative or not calm.
If someone is both not brave and quiet then lucy is either not old or not creative and vice versa.
Everyone who is humble is either rich or kind and vice versa.
If someone is not old or strong then someone is not wise or not strong.
If someone is humble then someone is not quiet.
If someone is rich or not funny then susan is not rich or not calm.
Everyone who is both not humble and strong is either kind or strong.
If someone is humble or strong then john is both not wise and rich.
Everyone who is happy or brave is both not rich and happy.
If someone is not quiet or not kind then alice is not humble or quiet.
If someone is either calm or happy then alice is not quiet or not rich and vice versa.
Everyone who is both happy and curious is wise or rich and vice versa.
Someone is either not old or not generous.
John is either brave or not curious.
Someone is not wise or not curious.
Someone is both not creative and not funny.
Someone is either strong or not rich.
Someone is both curious and not rich.
Someone is brave or not kind. | Susan is curious. | entailment | (((~brave(john)|~strong(john)))=>(?[X]:(funny(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~strong(X)|brave(X))))&
(![X]:((creative(X)|kind(X))=>~happy(X)))&
((?[X]:((~generous(X)&~curious(X))))=>((~generous(lucy)|~wise(lucy))))&
(![X]:((calm(X)<~>~brave(X))=>(~creative(X)|~calm(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>((~old(lucy)<~>~creative(lucy))))&
(![X]:(humble(X)<=>(rich(X)<~>kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((~wise(X)|~strong(X)))))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)|~funny(X))))=>((~rich(susan)|~calm(susan))))&
(![X]:((~humble(X)&strong(X))=>(kind(X)<~>strong(X))))&
((?[X]:((humble(X)|strong(X))))=>((~wise(john)&rich(john))))&
(![X]:((happy(X)|brave(X))=>(~rich(X)&happy(X))))&
((?[X]:((~quiet(X)|~kind(X))))=>((~humble(alice)|quiet(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~quiet(alice)|~rich(alice))))&
(![X]:((happy(X)&curious(X))<=>(wise(X)|rich(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
((brave(john)<~>~curious(john)))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((strong(X)<~>~rich(X))))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((brave(X)|~kind(X)))) | curious(susan) | [
"p1",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 330559064360742109805360
% SZS output start Proof for 330559064360742109805360
2. ! [X0] : ((strong(X0) <~> curious(X0)) <=> (brave(X0) | ~strong(X0))) [input p1]
12. ? [X0] : (strong(X0) | humble(X0)) => (rich(john) & ~wise(john)) [input p11]
13. ! [X0] : ((brave(X0) | happy(X0)) => (happy(X0) & ~rich(X0))) [input p12]
16. ! [X0] : ((curious(X0) & happy(X0)) <=> (rich(X0) | wise(X0))) [input p15]
24. ~curious(susan) [input hypothesis]
39. (rich(john) & ~wise(john)) | ! [X0] : (~strong(X0) & ~humble(X0)) [ennf transformation 12]
40. ! [X0] : ((happy(X0) & ~rich(X0)) | (~brave(X0) & ~happy(X0))) [ennf transformation 13]
45. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [nnf transformation 2]
46. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [flattening 45]
65. ! [X0] : (((curious(X0) & happy(X0)) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 16]
66. ! [X0] : (((curious(X0) & happy(X0)) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | ~curious(X0) | ~happy(X0))) [flattening 65]
86. curious(X0) | strong(X0) | strong(X0) [cnf transformation 46]
115. rich(john) | ~strong(X0) [cnf transformation 39]
116. ~rich(X0) | ~happy(X0) [cnf transformation 40]
130. happy(X0) | ~rich(X0) [cnf transformation 66]
145. ~curious(susan) [cnf transformation 24]
149. curious(X0) | strong(X0) [duplicate literal removal 86]
203. 12 <=> ! [X1] : ~strong(X1) [avatar definition]
204. ~strong(X1) <- (12) [avatar component clause 203]
239. 21 <=> ! [X0] : ~rich(X0) [avatar definition]
240. ~rich(X0) <- (21) [avatar component clause 239]
243. 22 <=> rich(john) [avatar definition]
245. rich(john) <- (22) [avatar component clause 243]
246. 12 | 22 [avatar split clause 115,243,203]
294. ~rich(X0) [subsumption resolution 130,116]
295. 21 [avatar split clause 294,239]
333. strong(susan) [resolution 149,145]
334. $false <- (12) [subsumption resolution 333,204]
335. ~12 [avatar contradiction clause 334]
336. $false <- (21, 22) [subsumption resolution 245,240]
337. ~21 | ~22 [avatar contradiction clause 336]
338. $false [avatar sat refutation 246,295,335,337]
% SZS output end Proof for 330559064360742109805360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not strong is both not kind and rich. Everyone who is not funny or funny is not creative and vice versa. Everyone who is both calm and strong is rich and vice versa. If fred is not kind or strong then susan is either not strong or quiet and vice versa. Everyone who is brave is both not generous and creative and vice versa. Everyone who is kind or generous is either not tall or kind. Everyone who is both not tall and wise is both not old and wise and vice versa. If someone is either happy or not calm then paul is both not funny and happy. If john is rich then someone is both funny and not funny and vice versa. Everyone who is both not rich and patient is both old and brave and vice versa. Everyone who is calm or brave is either not old or wise and vice versa. If susan is both old and quiet then john is either creative or not humble. If lucy is either kind or not funny then someone is not calm or funny. Everyone who is either humble or patient is either not creative or generous and vice versa. Everyone who is either brave or rich is rich and vice versa. If fred is old then someone is funny or rich. Someone is kind or curious. Susan is both not curious and calm. Someone is both not quiet and happy. John is not humble or strong. Someone is either not humble or brave. Susan is both kind and not humble. | Paul is tall. | neutral | (![X]:((~kind(X)|~strong(X))=>(~kind(X)&rich(X))))&
(![X]:((~funny(X)|funny(X))<=>~creative(X)))&
(![X]:((calm(X)&strong(X))<=>rich(X)))&
(((~kind(fred)|strong(fred)))<=>((~strong(susan)<~>quiet(susan))))&
(![X]:(brave(X)<=>(~generous(X)&creative(X))))&
(![X]:((kind(X)|generous(X))=>(~tall(X)<~>kind(X))))&
(![X]:((~tall(X)&wise(X))<=>(~old(X)&wise(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>((~funny(paul)&happy(paul))))&
((rich(john))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~rich(X)&patient(X))<=>(old(X)&brave(X))))&
(![X]:((calm(X)|brave(X))<=>(~old(X)<~>wise(X))))&
(((old(susan)&quiet(susan)))=>((creative(john)<~>~humble(john))))&
(((kind(lucy)<~>~funny(lucy)))=>(?[X]:((~calm(X)|funny(X)))))&
(![X]:((humble(X)<~>patient(X))<=>(~creative(X)<~>generous(X))))&
(![X]:((brave(X)<~>rich(X))<=>rich(X)))&
((old(fred))=>(?[X]:((funny(X)|rich(X)))))&
(?[X]:((kind(X)|curious(X))))&
((~curious(susan)&calm(susan)))&
(?[X]:((~quiet(X)&happy(X))))&
((~humble(john)|strong(john)))&
(?[X]:((~humble(X)<~>brave(X))))&
((kind(susan)&~humble(susan))) | tall(paul) | [] | null | 0 |
Everyone who is both curious and kind is either not old or not humble.
If someone is not happy or not funny then paul is happy or tall and vice versa.
If someone is quiet then someone is either quiet or rich and vice versa.
If fred is either not curious or strong then someone is old or not curious.
If someone is curious then mary is both not old and generous and vice versa.
Everyone who is not curious is both not generous and not old and vice versa.
Everyone who is not kind or wise is funny.
Everyone who is either brave or rich is tall.
Everyone who is not old is both not generous and not calm.
If susan is either old or not strong then fred is strong or funny.
If paul is not generous then john is not kind and vice versa.
If someone is either not brave or wise then mary is both not old and generous.
If alice is humble or patient then paul is not generous and vice versa.
If someone is not kind then someone is happy.
If someone is either rich or tall then someone is not quiet or humble.
Everyone who is both generous and happy is either brave or tall and vice versa.
John is both not quiet and humble.
Paul is both not kind and not curious.
Someone is not humble or not curious.
Someone is quiet.
Someone is generous or not happy.
Paul is not curious. | Susan is not generous. | entailment | (![X]:((curious(X)&kind(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((~happy(X)|~funny(X))))<=>((happy(paul)|tall(paul))))&
((?[X]:(quiet(X)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(((~curious(fred)<~>strong(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:(curious(X)))<=>((~old(mary)&generous(mary))))&
(![X]:(~curious(X)<=>(~generous(X)&~old(X))))&
(![X]:((~kind(X)|wise(X))=>funny(X)))&
(![X]:((brave(X)<~>rich(X))=>tall(X)))&
(![X]:(~old(X)=>(~generous(X)&~calm(X))))&
(((old(susan)<~>~strong(susan)))=>((strong(fred)|funny(fred))))&
((~generous(paul))<=>(~kind(john)))&
((?[X]:((~brave(X)<~>wise(X))))=>((~old(mary)&generous(mary))))&
(((humble(alice)|patient(alice)))<=>(~generous(paul)))&
((?[X]:(~kind(X)))=>(?[X]:(happy(X))))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
((~quiet(john)&humble(john)))&
((~kind(paul)&~curious(paul)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
(~curious(paul)) | ~generous(susan) | [
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4564465407778995729772876
% SZS output start Proof for 4564465407778995729772876
5. ? [X0] : curious(X0) <=> (generous(mary) & ~old(mary)) [input p4]
6. ! [X0] : (~curious(X0) <=> (~old(X0) & ~generous(X0))) [input p5]
9. ! [X0] : (~old(X0) => (~calm(X0) & ~generous(X0))) [input p8]
23. generous(susan) [input hypothesis]
27. ! [X0] : (~old(X0) => ~generous(X0)) [pure predicate removal 9]
33. ! [X0] : (~generous(X0) | old(X0)) [ennf transformation 27]
53. (? [X0] : curious(X0) | (~generous(mary) | old(mary))) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [nnf transformation 5]
54. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [flattening 53]
55. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [rectify 54]
56. ? [X0] : curious(X0) => curious(sK4) [choice axiom]
57. (curious(sK4) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [skolemisation 55,56]
58. ! [X0] : ((~curious(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | curious(X0))) [nnf transformation 6]
59. ! [X0] : ((~curious(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | curious(X0))) [flattening 58]
93. ~old(mary) | ~curious(X1) [cnf transformation 57]
94. generous(mary) | ~curious(X1) [cnf transformation 57]
96. ~generous(X0) | curious(X0) [cnf transformation 59]
103. ~generous(X0) | old(X0) [cnf transformation 33]
132. generous(susan) [cnf transformation 23]
203. 17 <=> old(mary) [avatar definition]
204. ~old(mary) <- (~17) [avatar component clause 203]
207. 18 <=> generous(mary) [avatar definition]
208. generous(mary) <- (18) [avatar component clause 207]
216. 20 <=> ! [X1] : ~curious(X1) [avatar definition]
217. ~curious(X1) <- (20) [avatar component clause 216]
218. 20 | 18 [avatar split clause 94,207,216]
219. 20 | ~17 [avatar split clause 93,203,216]
314. curious(susan) [resolution 96,132]
320. old(mary) <- (18) [resolution 103,208]
322. $false <- (~17, 18) [subsumption resolution 320,204]
323. 17 | ~18 [avatar contradiction clause 322]
325. $false <- (20) [resolution 217,314]
326. ~20 [avatar contradiction clause 325]
328. $false [avatar sat refutation 218,219,323,326]
% SZS output end Proof for 4564465407778995729772876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not strong or not brave then someone is either humble or rich. If someone is tall then someone is both calm and creative. If someone is either strong or not curious then fred is old or wise. Everyone who is not old is both not strong and not calm. If someone is not kind or quiet then someone is both not generous and kind. Everyone who is either not happy or curious is old or not quiet and vice versa. Everyone who is either kind or strong is both not humble and not calm and vice versa. If john is happy then alice is strong or generous and vice versa. If john is not patient or not generous then someone is patient. If mary is either not rich or not strong then mary is both not wise and rich. Everyone who is both not wise and old is both creative and old. Everyone who is brave is both not generous and patient. Everyone who is either humble or funny is quiet or kind. Everyone who is both rich and generous is either not generous or generous. Everyone who is not wise or not curious is both not funny and not old. If john is not generous or not tall then mary is happy and vice versa. John is patient. Someone is either not patient or wise. Mary is both quiet and old. Alice is either rich or happy. Someone is not strong or creative. Someone is both not happy and not rich. Someone is either brave or calm. Alice is either quiet or strong. | Alice is strong. | neutral | (((~strong(john)|~brave(john)))=>(?[X]:((humble(X)<~>rich(X)))))&
((?[X]:(tall(X)))=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((strong(X)<~>~curious(X))))=>((old(fred)|wise(fred))))&
(![X]:(~old(X)=>(~strong(X)&~calm(X))))&
((?[X]:((~kind(X)|quiet(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((~happy(X)<~>curious(X))<=>(old(X)|~quiet(X))))&
(![X]:((kind(X)<~>strong(X))<=>(~humble(X)&~calm(X))))&
((happy(john))<=>((strong(alice)|generous(alice))))&
(((~patient(john)|~generous(john)))=>(?[X]:(patient(X))))&
(((~rich(mary)<~>~strong(mary)))=>((~wise(mary)&rich(mary))))&
(![X]:((~wise(X)&old(X))=>(creative(X)&old(X))))&
(![X]:(brave(X)=>(~generous(X)&patient(X))))&
(![X]:((humble(X)<~>funny(X))=>(quiet(X)|kind(X))))&
(![X]:((rich(X)&generous(X))=>(~generous(X)<~>generous(X))))&
(![X]:((~wise(X)|~curious(X))=>(~funny(X)&~old(X))))&
(((~generous(john)|~tall(john)))<=>(happy(mary)))&
(patient(john))&
(?[X]:((~patient(X)<~>wise(X))))&
((quiet(mary)&old(mary)))&
((rich(alice)<~>happy(alice)))&
(?[X]:((~strong(X)|creative(X))))&
(?[X]:((~happy(X)&~rich(X))))&
(?[X]:((brave(X)<~>calm(X))))&
((quiet(alice)<~>strong(alice))) | strong(alice) | [] | null | 0 |
Everyone who is wise or not humble is either old or happy.
If someone is generous or kind then someone is calm and vice versa.
If mary is either brave or calm then fred is not humble or not generous and vice versa.
If someone is either not curious or not quiet then john is not strong or not brave.
Everyone who is either not tall or not wise is calm or strong.
Everyone who is either funny or not brave is both generous and not rich.
If someone is not humble then susan is either not generous or not strong and vice versa.
If paul is either calm or patient then someone is not quiet.
If fred is either not creative or not generous then someone is not generous or quiet and vice versa.
Everyone who is either not rich or wise is either quiet or not curious and vice versa.
Everyone who is both creative and patient is either rich or creative and vice versa.
Everyone who is either funny or not calm is not funny and vice versa.
If susan is not wise or not creative then lucy is either tall or not kind and vice versa.
Everyone who is wise or not wise is both wise and humble and vice versa.
Everyone who is creative is both not happy and not kind.
Everyone who is either not humble or not tall is either kind or not humble.
Fred is not wise or not calm.
Someone is strong or not curious.
Someone is wise.
Someone is not curious.
Paul is humble or not tall.
Someone is funny.
Alice is both creative and brave. | Fred is not old. | contradiction | (![X]:((wise(X)|~humble(X))=>(old(X)<~>happy(X))))&
((?[X]:((generous(X)|kind(X))))<=>(?[X]:(calm(X))))&
(((brave(mary)<~>calm(mary)))<=>((~humble(fred)|~generous(fred))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>((~strong(john)|~brave(john))))&
(![X]:((~tall(X)<~>~wise(X))=>(calm(X)|strong(X))))&
(![X]:((funny(X)<~>~brave(X))=>(generous(X)&~rich(X))))&
((?[X]:(~humble(X)))<=>((~generous(susan)<~>~strong(susan))))&
(((calm(paul)<~>patient(paul)))=>(?[X]:(~quiet(X))))&
(((~creative(fred)<~>~generous(fred)))<=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((~rich(X)<~>wise(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((creative(X)&patient(X))<=>(rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>~calm(X))<=>~funny(X)))&
(((~wise(susan)|~creative(susan)))<=>((tall(lucy)<~>~kind(lucy))))&
(![X]:((wise(X)|~wise(X))<=>(wise(X)&humble(X))))&
(![X]:(creative(X)=>(~happy(X)&~kind(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(kind(X)<~>~humble(X))))&
((~wise(fred)|~calm(fred)))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:(~curious(X)))&
((humble(paul)|~tall(paul)))&
(?[X]:(funny(X)))&
((creative(alice)&brave(alice))) | ~old(fred) | [
"p0",
"p1",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2097311177502942464838258
% SZS output start Proof for 2097311177502942464838258
1. ! [X0] : ((~humble(X0) | wise(X0)) => (old(X0) <~> happy(X0))) [input p0]
2. ? [X0] : (kind(X0) | generous(X0)) <=> ? [X0] : calm(X0) [input p1]
9. (~creative(fred) <~> ~generous(fred)) <=> ? [X0] : (quiet(X0) | ~generous(X0)) [input p8]
12. ! [X0] : ((funny(X0) <~> ~calm(X0)) <=> ~funny(X0)) [input p11]
14. ! [X0] : ((~wise(X0) | wise(X0)) <=> (humble(X0) & wise(X0))) [input p13]
15. ! [X0] : (creative(X0) => (~kind(X0) & ~happy(X0))) [input p14]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (kind(X0) | generous(X0)) <=> ? [X1] : calm(X1) [rectify 2]
26. ! [X0] : ((old(X0) <~> happy(X0)) | (humble(X0) & ~wise(X0))) [ennf transformation 1]
33. ! [X0] : ((~kind(X0) & ~happy(X0)) | ~creative(X0)) [ennf transformation 15]
35. ! [X0] : (((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (humble(X0) & ~wise(X0))) [nnf transformation 26]
36. (? [X0] : (kind(X0) | generous(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~kind(X0) & ~generous(X0))) [nnf transformation 25]
37. (? [X0] : (kind(X0) | generous(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~kind(X3) & ~generous(X3))) [rectify 36]
38. ? [X0] : (kind(X0) | generous(X0)) => (kind(sK0) | generous(sK0)) [choice axiom]
39. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
40. ((kind(sK0) | generous(sK0)) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : (~kind(X3) & ~generous(X3))) [skolemisation 37,39,38]
53. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & (? [X0] : (quiet(X0) | ~generous(X0)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [nnf transformation 9]
54. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & (? [X1] : (quiet(X1) | ~generous(X1)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [rectify 53]
55. ? [X1] : (quiet(X1) | ~generous(X1)) => (quiet(sK4) | ~generous(sK4)) [choice axiom]
56. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & ((quiet(sK4) | ~generous(sK4)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [skolemisation 54,55]
60. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [nnf transformation 12]
63. ! [X0] : (((~wise(X0) | wise(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | wise(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [flattening 63]
74. ~wise(X0) | old(X0) | happy(X0) [cnf transformation 35]
78. calm(sK1) | ~generous(X3) [cnf transformation 40]
105. generous(fred) | creative(fred) | generous(X0) [cnf transformation 56]
121. ~funny(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 60]
123. ~calm(X0) | funny(X0) | funny(X0) [cnf transformation 60]
132. wise(X0) | wise(X0) [cnf transformation 64]
136. ~creative(X0) | ~happy(X0) [cnf transformation 33]
150. ~old(fred) [cnf transformation 24]
153. wise(X0) [duplicate literal removal 132]
155. ~funny(X0) | ~calm(X0) [duplicate literal removal 121]
156. ~calm(X0) | funny(X0) [duplicate literal removal 123]
160. 1 <=> ! [X1] : ~calm(X1) [avatar definition]
161. ~calm(X1) <- (1) [avatar component clause 160]
175. 5 <=> calm(sK1) [avatar definition]
177. calm(sK1) <- (5) [avatar component clause 175]
180. 6 <=> ! [X3] : ~generous(X3) [avatar definition]
181. ~generous(X3) <- (6) [avatar component clause 180]
182. 6 | 5 [avatar split clause 78,175,180]
184. 7 <=> generous(fred) [avatar definition]
186. generous(fred) <- (7) [avatar component clause 184]
258. 23 <=> creative(fred) [avatar definition]
260. creative(fred) <- (23) [avatar component clause 258]
263. 24 <=> ! [X0] : generous(X0) [avatar definition]
264. generous(X0) <- (24) [avatar component clause 263]
265. 24 | 23 | 7 [avatar split clause 105,184,258,263]
279. ~calm(X0) [subsumption resolution 155,156]
280. 1 [avatar split clause 279,160]
328. $false <- (1, 5) [resolution 177,161]
329. ~1 | ~5 [avatar contradiction clause 328]
330. $false <- (6, 7) [resolution 186,181]
331. ~6 | ~7 [avatar contradiction clause 330]
333. ~happy(fred) <- (23) [resolution 136,260]
336. happy(X0) | old(X0) [resolution 74,153]
340. old(fred) <- (23) [resolution 336,333]
341. $false <- (23) [subsumption resolution 340,150]
342. ~23 [avatar contradiction clause 341]
343. $false <- (6, 24) [subsumption resolution 264,181]
344. ~6 | ~24 [avatar contradiction clause 343]
345. $false [avatar sat refutation 182,265,280,329,331,342,344]
% SZS output end Proof for 2097311177502942464838258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If john is both rich and humble then fred is not happy or old.
Everyone who is not funny is either not happy or old.
Everyone who is both brave and kind is either wise or not generous and vice versa.
Everyone who is not wise is kind and vice versa.
Everyone who is either calm or happy is both not creative and not tall.
Everyone who is both not kind and not quiet is calm.
If john is not calm then alice is either not rich or not quiet.
If someone is creative then susan is not patient or not happy.
Everyone who is both patient and kind is wise or strong.
If someone is generous or not brave then fred is tall or rich and vice versa.
If fred is either humble or calm then someone is funny.
Everyone who is either not brave or not creative is not happy or not creative.
If someone is patient then fred is both humble and not kind.
If someone is either not rich or wise then someone is not funny.
If someone is either not brave or rich then mary is both not patient and not kind.
Everyone who is not curious or curious is either not strong or generous and vice versa.
Fred is either quiet or curious.
Someone is both calm and not tall.
Mary is quiet.
Lucy is either creative or curious.
Someone is kind.
Someone is not patient.
Someone is either calm or not creative. | Lucy is creative. | neutral | (((rich(john)&humble(john)))=>((~happy(fred)|old(fred))))&
(![X]:(~funny(X)=>(~happy(X)<~>old(X))))&
(![X]:((brave(X)&kind(X))<=>(wise(X)<~>~generous(X))))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((calm(X)<~>happy(X))=>(~creative(X)&~tall(X))))&
(![X]:((~kind(X)&~quiet(X))=>calm(X)))&
((~calm(john))=>((~rich(alice)<~>~quiet(alice))))&
((?[X]:(creative(X)))=>((~patient(susan)|~happy(susan))))&
(![X]:((patient(X)&kind(X))=>(wise(X)|strong(X))))&
((?[X]:((generous(X)|~brave(X))))<=>((tall(fred)|rich(fred))))&
(((humble(fred)<~>calm(fred)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~happy(X)|~creative(X))))&
((?[X]:(patient(X)))=>((humble(fred)&~kind(fred))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>rich(X))))=>((~patient(mary)&~kind(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~strong(X)<~>generous(X))))&
((quiet(fred)<~>curious(fred)))&
(?[X]:((calm(X)&~tall(X))))&
(quiet(mary))&
((creative(lucy)<~>curious(lucy)))&
(?[X]:(kind(X)))&
(?[X]:(~patient(X)))&
(?[X]:((calm(X)<~>~creative(X)))) | creative(lucy) | [] | null | 0 |
Everyone who is not funny is not wise.
If someone is both tall and not old then someone is either rich or not quiet.
If fred is wise then susan is not tall.
Everyone who is either quiet or happy is not patient.
If someone is not humble then fred is either not creative or wise and vice versa.
Everyone who is either not funny or creative is not brave or old.
If someone is not happy then mary is creative and vice versa.
If someone is humble then lucy is generous and vice versa.
Everyone who is either not old or not funny is either not kind or not funny.
Everyone who is both not funny and not tall is both quiet and not curious.
Everyone who is either not humble or humble is old and vice versa.
Everyone who is not creative or not funny is either not funny or funny.
Everyone who is curious is creative or wise.
If someone is either not brave or not happy then mary is either not calm or not rich.
Everyone who is not patient is either not brave or generous.
Everyone who is kind or funny is wise or not strong and vice versa.
John is not patient.
Someone is kind.
Susan is strong or not calm.
Someone is either not wise or kind.
John is calm.
Paul is humble or not old.
Alice is not generous or not kind.
Fred is funny or rich. | Alice is old. | entailment | (![X]:(~funny(X)=>~wise(X)))&
((?[X]:((tall(X)&~old(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((wise(fred))=>(~tall(susan)))&
(![X]:((quiet(X)<~>happy(X))=>~patient(X)))&
((?[X]:(~humble(X)))<=>((~creative(fred)<~>wise(fred))))&
(![X]:((~funny(X)<~>creative(X))=>(~brave(X)|old(X))))&
((?[X]:(~happy(X)))<=>(creative(mary)))&
((?[X]:(humble(X)))<=>(generous(lucy)))&
(![X]:((~old(X)<~>~funny(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((~funny(X)&~tall(X))=>(quiet(X)&~curious(X))))&
(![X]:((~humble(X)<~>humble(X))<=>old(X)))&
(![X]:((~creative(X)|~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:(curious(X)=>(creative(X)|wise(X))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~calm(mary)<~>~rich(mary))))&
(![X]:(~patient(X)=>(~brave(X)<~>generous(X))))&
(![X]:((kind(X)|funny(X))<=>(wise(X)|~strong(X))))&
(~patient(john))&
(?[X]:(kind(X)))&
((strong(susan)|~calm(susan)))&
(?[X]:((~wise(X)<~>kind(X))))&
(calm(john))&
((humble(paul)|~old(paul)))&
((~generous(alice)|~kind(alice)))&
((funny(fred)|rich(fred))) | old(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5706828424816494927277731
% SZS output start Proof for 5706828424816494927277731
11. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> old(X0)) [input p10]
25. ~old(alice) [input hypothesis]
60. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~old(X0)) & (old(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 11]
92. old(X0) | humble(X0) | humble(X0) [cnf transformation 60]
93. old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 60]
119. ~old(alice) [cnf transformation 25]
122. old(X0) | humble(X0) [duplicate literal removal 92]
123. old(X0) | ~humble(X0) [duplicate literal removal 93]
189. old(X0) [subsumption resolution 122,123]
246. $false [subsumption resolution 119,189]
% SZS output end Proof for 5706828424816494927277731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or quiet is strong. If someone is happy then mary is either patient or generous and vice versa. If someone is both not humble and rich then someone is wise or not generous and vice versa. If someone is either not brave or funny then lucy is either not quiet or not brave. Everyone who is not kind or not quiet is both happy and quiet. Everyone who is not funny or not generous is not kind and vice versa. If john is not rich then someone is not quiet. Everyone who is either generous or wise is both calm and brave. Everyone who is not curious is not calm or not creative. Everyone who is curious is both generous and not rich. If someone is not strong or strong then someone is either wise or patient and vice versa. Everyone who is funny or wise is both not patient and wise. Everyone who is either generous or wise is either not wise or not happy. If someone is either not kind or not happy then someone is both strong and not patient and vice versa. If paul is not rich or curious then someone is kind and vice versa. Everyone who is either not wise or not happy is not funny and vice versa. Mary is kind or not kind. Paul is not brave or happy. Someone is both happy and not kind. Someone is not wise or calm. Paul is kind or not curious. Someone is not brave. Lucy is not curious. Mary is both generous and humble. | John is not curious. | entailment | (![X]:((~strong(X)<~>quiet(X))=>strong(X)))&
((?[X]:(happy(X)))<=>((patient(mary)<~>generous(mary))))&
((?[X]:((~humble(X)&rich(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
((?[X]:((~brave(X)<~>funny(X))))=>((~quiet(lucy)<~>~brave(lucy))))&
(![X]:((~kind(X)|~quiet(X))=>(happy(X)&quiet(X))))&
(![X]:((~funny(X)|~generous(X))<=>~kind(X)))&
((~rich(john))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)<~>wise(X))=>(calm(X)&brave(X))))&
(![X]:(~curious(X)=>(~calm(X)|~creative(X))))&
(![X]:(curious(X)=>(generous(X)&~rich(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((funny(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
(((~rich(paul)|curious(paul)))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)<~>~happy(X))<=>~funny(X)))&
((kind(mary)|~kind(mary)))&
((~brave(paul)|happy(paul)))&
(?[X]:((happy(X)&~kind(X))))&
(?[X]:((~wise(X)|calm(X))))&
((kind(paul)|~curious(paul)))&
(?[X]:(~brave(X)))&
(~curious(lucy))&
((generous(mary)&humble(mary))) | ~curious(john) | [
"p4",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6071780974649144924407034
% SZS output start Proof for 6071780974649144924407034
5. ! [X0] : ((~quiet(X0) | ~kind(X0)) => (quiet(X0) & happy(X0))) [input p4]
7. ~rich(john) => ? [X0] : ~quiet(X0) [input p6]
10. ! [X0] : (curious(X0) => (~rich(X0) & generous(X0))) [input p9]
25. curious(john) [input hypothesis]
34. ! [X0] : ((quiet(X0) & happy(X0)) | (quiet(X0) & kind(X0))) [ennf transformation 5]
35. ? [X0] : ~quiet(X0) | rich(john) [ennf transformation 7]
37. ! [X0] : ((~rich(X0) & generous(X0)) | ~curious(X0)) [ennf transformation 10]
53. ? [X0] : ~quiet(X0) => ~quiet(sK3) [choice axiom]
54. ~quiet(sK3) | rich(john) [skolemisation 35,53]
95. quiet(X0) | quiet(X0) [cnf transformation 34]
99. ~quiet(sK3) | rich(john) [cnf transformation 54]
103. ~curious(X0) | ~rich(X0) [cnf transformation 37]
140. curious(john) [cnf transformation 25]
143. quiet(X0) [duplicate literal removal 95]
212. rich(john) [subsumption resolution 99,143]
308. ~rich(john) [resolution 103,140]
309. $false [subsumption resolution 308,212]
% SZS output end Proof for 6071780974649144924407034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and strong then mary is creative and vice versa.
Everyone who is not funny is not old or not quiet.
If someone is both wise and strong then someone is both not brave and not quiet.
If someone is both not wise and not funny then mary is both tall and not old and vice versa.
Everyone who is tall or not old is both calm and brave.
Everyone who is happy or not kind is not rich and vice versa.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
If someone is brave then paul is not patient and vice versa.
Fred is wise.
Someone is either wise or curious.
Mary is not funny or creative.
Fred is either not patient or not tall.
Susan is either funny or quiet. | Fred is not wise. | contradiction | ((?[X]:((~curious(X)&strong(X))))<=>(creative(mary)))&
(![X]:(~funny(X)=>(~old(X)|~quiet(X))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:((~wise(X)&~funny(X))))<=>((tall(mary)&~old(mary))))&
(![X]:((tall(X)|~old(X))=>(calm(X)&brave(X))))&
(![X]:((happy(X)|~kind(X))<=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
(wise(fred))&
(?[X]:((wise(X)<~>curious(X))))&
((~funny(mary)|creative(mary)))&
((~patient(fred)<~>~tall(fred)))&
((funny(susan)<~>quiet(susan))) | ~wise(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 779253855442776313656707
% SZS output start Proof for 779253855442776313656707
16. wise(fred) [input p15]
21. ~wise(fred) [input hypothesis]
114. wise(fred) [cnf transformation 16]
122. ~wise(fred) [cnf transformation 21]
200. 16 <=> wise(fred) [avatar definition]
240. 16 [avatar split clause 114,200]
271. ~16 [avatar split clause 122,200]
272. $false [avatar sat refutation 240,271]
% SZS output end Proof for 779253855442776313656707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or curious then someone is not quiet or kind. Everyone who is not kind or old is both generous and not generous and vice versa. Everyone who is kind is curious or not tall. If fred is both not happy and funny then alice is either not funny or kind. Everyone who is both generous and not patient is rich or happy and vice versa. If mary is calm or not rich then fred is creative or not patient and vice versa. Everyone who is humble is both rich and old and vice versa. Everyone who is both not curious and not strong is both not calm and patient. If lucy is both not wise and patient then someone is both not brave and funny and vice versa. Everyone who is not humble or happy is either not tall or not humble and vice versa. Everyone who is either not rich or not old is both strong and funny and vice versa. If john is strong or creative then susan is not brave or not old and vice versa. Everyone who is brave or calm is not kind. Everyone who is not old is brave or not brave. If john is not wise or not quiet then susan is both not old and rich and vice versa. Someone is not generous. Lucy is either not kind or happy. Lucy is patient or not old. Someone is tall. Mary is not quiet. Paul is either not old or not patient. Someone is curious or not humble. | Fred is not rich. | entailment | ((?[X]:((humble(X)<~>curious(X))))=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~kind(X)|old(X))<=>(generous(X)&~generous(X))))&
(![X]:(kind(X)=>(curious(X)|~tall(X))))&
(((~happy(fred)&funny(fred)))=>((~funny(alice)<~>kind(alice))))&
(![X]:((generous(X)&~patient(X))<=>(rich(X)|happy(X))))&
(((calm(mary)|~rich(mary)))<=>((creative(fred)|~patient(fred))))&
(![X]:(humble(X)<=>(rich(X)&old(X))))&
(![X]:((~curious(X)&~strong(X))=>(~calm(X)&patient(X))))&
(((~wise(lucy)&patient(lucy)))<=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(strong(X)&funny(X))))&
(((strong(john)|creative(john)))<=>((~brave(susan)|~old(susan))))&
(![X]:((brave(X)|calm(X))=>~kind(X)))&
(![X]:(~old(X)=>(brave(X)|~brave(X))))&
(((~wise(john)|~quiet(john)))<=>((~old(susan)&rich(susan))))&
(?[X]:(~generous(X)))&
((~kind(lucy)<~>happy(lucy)))&
((patient(lucy)|~old(lucy)))&
(?[X]:(tall(X)))&
(~quiet(mary))&
((~old(paul)<~>~patient(paul)))&
(?[X]:((curious(X)|~humble(X)))) | ~rich(fred) | [
"p1",
"p4",
"p8",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4254838258690483168118203
% SZS output start Proof for 4254838258690483168118203
2. ! [X0] : ((old(X0) | ~kind(X0)) <=> (~generous(X0) & generous(X0))) [input p1]
5. ! [X0] : ((~patient(X0) & generous(X0)) <=> (happy(X0) | rich(X0))) [input p4]
9. (patient(lucy) & ~wise(lucy)) <=> ? [X0] : (funny(X0) & ~brave(X0)) [input p8]
11. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (funny(X0) & strong(X0))) [input p10]
13. ! [X0] : ((calm(X0) | brave(X0)) => ~kind(X0)) [input p12]
17. ~kind(lucy) <~> happy(lucy) [input p16]
23. rich(fred) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~calm(X0) & ~brave(X0))) [ennf transformation 13]
39. ! [X0] : (((old(X0) | ~kind(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (~old(X0) & kind(X0)))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | ~kind(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (~old(X0) & kind(X0)))) [flattening 39]
42. ! [X0] : (((~patient(X0) & generous(X0)) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | (patient(X0) | ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((~patient(X0) & generous(X0)) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | patient(X0) | ~generous(X0))) [flattening 42]
48. ((patient(lucy) & ~wise(lucy)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X0] : (funny(X0) & ~brave(X0)) | (~patient(lucy) | wise(lucy))) [nnf transformation 9]
49. ((patient(lucy) & ~wise(lucy)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X0] : (funny(X0) & ~brave(X0)) | ~patient(lucy) | wise(lucy)) [flattening 48]
50. ((patient(lucy) & ~wise(lucy)) | ! [X0] : (~funny(X0) | brave(X0))) & (? [X1] : (funny(X1) & ~brave(X1)) | ~patient(lucy) | wise(lucy)) [rectify 49]
51. ? [X1] : (funny(X1) & ~brave(X1)) => (funny(sK1) & ~brave(sK1)) [choice axiom]
52. ((patient(lucy) & ~wise(lucy)) | ! [X0] : (~funny(X0) | brave(X0))) & ((funny(sK1) & ~brave(sK1)) | ~patient(lucy) | wise(lucy)) [skolemisation 50,51]
55. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 11]
56. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [flattening 55]
63. (~happy(lucy) | kind(lucy)) & (happy(lucy) | ~kind(lucy)) [nnf transformation 17]
71. generous(X0) | kind(X0) [cnf transformation 40]
72. generous(X0) | ~old(X0) [cnf transformation 40]
73. ~generous(X0) | kind(X0) [cnf transformation 40]
74. ~generous(X0) | ~old(X0) [cnf transformation 40]
83. ~patient(X0) | ~happy(X0) [cnf transformation 43]
96. patient(lucy) | ~funny(X0) | brave(X0) [cnf transformation 52]
106. funny(X0) | ~rich(X0) | old(X0) [cnf transformation 56]
113. ~kind(X0) | ~brave(X0) [cnf transformation 32]
122. happy(lucy) | ~kind(lucy) [cnf transformation 63]
130. rich(fred) [cnf transformation 23]
149. ~old(X0) [subsumption resolution 72,74]
150. kind(X0) [subsumption resolution 71,73]
188. 12 <=> ! [X0] : (~funny(X0) | brave(X0)) [avatar definition]
189. ~funny(X0) | brave(X0) <- (12) [avatar component clause 188]
191. 13 <=> patient(lucy) [avatar definition]
193. patient(lucy) <- (13) [avatar component clause 191]
194. 12 | 13 [avatar split clause 96,191,188]
213. ~rich(X0) | funny(X0) [subsumption resolution 106,149]
231. ~brave(X0) [subsumption resolution 113,150]
248. happy(lucy) [subsumption resolution 122,150]
250. ~funny(X0) <- (12) [subsumption resolution 189,231]
265. funny(fred) [resolution 213,130]
267. $false <- (12) [subsumption resolution 265,250]
268. ~12 [avatar contradiction clause 267]
274. ~happy(lucy) <- (13) [resolution 193,83]
275. $false <- (13) [subsumption resolution 274,248]
276. ~13 [avatar contradiction clause 275]
277. $false [avatar sat refutation 194,268,276]
% SZS output end Proof for 4254838258690483168118203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not funny is either not old or old and vice versa. If john is not quiet or not happy then alice is wise. Everyone who is either happy or not kind is not strong or brave. Everyone who is either not happy or not curious is either not quiet or happy and vice versa. Everyone who is both curious and not curious is both not curious and calm. Everyone who is either creative or humble is not wise or quiet and vice versa. Everyone who is both not strong and not kind is quiet or not quiet and vice versa. Everyone who is curious is either funny or not wise and vice versa. Everyone who is either quiet or not rich is either wise or kind and vice versa. If someone is humble then someone is rich or happy. If susan is either tall or not tall then fred is both old and not calm and vice versa. Everyone who is either not rich or not old is either old or not kind and vice versa. Everyone who is either curious or humble is both happy and calm. If lucy is rich then alice is either quiet or creative and vice versa. Everyone who is both rich and not wise is strong and vice versa. Everyone who is not tall is not funny. Alice is either curious or generous. Mary is happy or old. Fred is not strong or humble. Someone is both creative and happy. Mary is not strong or not brave. Someone is not happy or not creative. Alice is both quiet and not funny. | Susan is funny. | contradiction | (![X]:((~calm(X)|~funny(X))<=>(~old(X)<~>old(X))))&
(((~quiet(john)|~happy(john)))=>(wise(alice)))&
(![X]:((happy(X)<~>~kind(X))=>(~strong(X)|brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((curious(X)&~curious(X))=>(~curious(X)&calm(X))))&
(![X]:((creative(X)<~>humble(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~strong(X)&~kind(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(curious(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((rich(X)|happy(X)))))&
(((tall(susan)<~>~tall(susan)))<=>((old(fred)&~calm(fred))))&
(![X]:((~rich(X)<~>~old(X))<=>(old(X)<~>~kind(X))))&
(![X]:((curious(X)<~>humble(X))=>(happy(X)&calm(X))))&
((rich(lucy))<=>((quiet(alice)<~>creative(alice))))&
(![X]:((rich(X)&~wise(X))<=>strong(X)))&
(![X]:(~tall(X)=>~funny(X)))&
((curious(alice)<~>generous(alice)))&
((happy(mary)|old(mary)))&
((~strong(fred)|humble(fred)))&
(?[X]:((creative(X)&happy(X))))&
((~strong(mary)|~brave(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((quiet(alice)&~funny(alice))) | funny(susan) | [
"p3",
"p6",
"p7",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6884551630799906218663569
% SZS output start Proof for 6884551630799906218663569
4. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (~quiet(X0) <~> happy(X0))) [input p3]
7. ! [X0] : ((~kind(X0) & ~strong(X0)) <=> (~quiet(X0) | quiet(X0))) [input p6]
8. ! [X0] : (curious(X0) <=> (funny(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (wise(X0) <~> kind(X0))) [input p8]
12. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (old(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~wise(X0) & rich(X0)) <=> strong(X0)) [input p14]
24. funny(susan) [input hypothesis]
37. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 4]
40. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | (kind(X0) | strong(X0)))) [nnf transformation 7]
41. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | kind(X0) | strong(X0))) [flattening 40]
42. ! [X0] : ((curious(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~curious(X0))) [nnf transformation 8]
43. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 9]
49. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 12]
52. ! [X0] : (((~wise(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | (wise(X0) | ~rich(X0)))) [nnf transformation 15]
53. ! [X0] : (((~wise(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | wise(X0) | ~rich(X0))) [flattening 52]
69. happy(X0) | ~quiet(X0) | ~curious(X0) | happy(X0) [cnf transformation 37]
74. ~curious(X0) | ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 37]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 41]
87. ~strong(X0) | quiet(X0) [cnf transformation 41]
88. ~kind(X0) | ~quiet(X0) [cnf transformation 41]
89. ~kind(X0) | quiet(X0) [cnf transformation 41]
92. ~wise(X0) | curious(X0) | ~funny(X0) [cnf transformation 42]
98. ~rich(X0) | quiet(X0) | kind(X0) | ~wise(X0) [cnf transformation 43]
111. kind(X0) | ~old(X0) | ~old(X0) | rich(X0) [cnf transformation 49]
116. old(X0) | rich(X0) | old(X0) | kind(X0) [cnf transformation 49]
125. strong(X0) | wise(X0) | ~rich(X0) [cnf transformation 53]
139. funny(susan) [cnf transformation 24]
141. kind(X0) | ~old(X0) | rich(X0) [duplicate literal removal 111]
143. old(X0) | rich(X0) | kind(X0) [duplicate literal removal 116]
149. happy(X0) | ~quiet(X0) | ~curious(X0) [duplicate literal removal 69]
151. ~curious(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 74]
171. ~curious(X0) | ~quiet(X0) [subsumption resolution 149,151]
172. ~kind(X0) [subsumption resolution 88,89]
173. ~strong(X0) [subsumption resolution 86,87]
175. ~rich(X0) | quiet(X0) | ~wise(X0) [subsumption resolution 98,172]
206. rich(X0) | old(X0) [subsumption resolution 143,172]
207. ~old(X0) | rich(X0) [subsumption resolution 141,172]
208. rich(X0) [subsumption resolution 207,206]
221. wise(X0) | ~rich(X0) [subsumption resolution 125,173]
222. wise(X0) [subsumption resolution 221,208]
271. ~funny(X0) | curious(X0) [resolution 92,222]
272. curious(susan) [resolution 271,139]
281. ~quiet(susan) [resolution 272,171]
324. quiet(X1) | ~wise(X1) [resolution 175,208]
326. quiet(X1) [subsumption resolution 324,222]
330. $false [resolution 326,281]
% SZS output end Proof for 6884551630799906218663569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not happy is either not happy or curious and vice versa.
If lucy is both not curious and not strong then someone is either not brave or not patient and vice versa.
Everyone who is either not tall or quiet is brave or not calm.
Everyone who is either not kind or not rich is either not quiet or generous.
Everyone who is tall or not funny is not wise or wise and vice versa.
Everyone who is either funny or rich is both not wise and not rich and vice versa.
Everyone who is both not generous and not creative is either humble or not generous.
Everyone who is either creative or calm is strong or not old and vice versa.
If susan is patient or not brave then susan is both not patient and not old and vice versa.
If someone is happy or tall then john is either not calm or tall.
Everyone who is not calm is generous and vice versa.
Everyone who is not tall or not funny is either rich or not calm and vice versa.
Everyone who is either not kind or not wise is brave and vice versa.
If someone is either not brave or not patient then someone is not funny or not curious.
Everyone who is not humble or not calm is not patient or not creative and vice versa.
If someone is generous then alice is either happy or funny and vice versa.
Fred is not calm or funny.
Mary is both not creative and not kind.
Someone is wise or not rich.
Fred is both creative and not generous.
John is creative or not wise.
Alice is both funny and not brave.
John is either tall or not happy. | Fred is calm. | entailment | (![X]:((~humble(X)<~>~happy(X))<=>(~happy(X)<~>curious(X))))&
(((~curious(lucy)&~strong(lucy)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((tall(X)|~funny(X))<=>(~wise(X)|wise(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~generous(X)&~creative(X))=>(humble(X)<~>~generous(X))))&
(![X]:((creative(X)<~>calm(X))<=>(strong(X)|~old(X))))&
(((patient(susan)|~brave(susan)))<=>((~patient(susan)&~old(susan))))&
((?[X]:((happy(X)|tall(X))))=>((~calm(john)<~>tall(john))))&
(![X]:(~calm(X)<=>generous(X)))&
(![X]:((~tall(X)|~funny(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>brave(X)))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(~patient(X)|~creative(X))))&
((?[X]:(generous(X)))<=>((happy(alice)<~>funny(alice))))&
((~calm(fred)|funny(fred)))&
((~creative(mary)&~kind(mary)))&
(?[X]:((wise(X)|~rich(X))))&
((creative(fred)&~generous(fred)))&
((creative(john)|~wise(john)))&
((funny(alice)&~brave(alice)))&
((tall(john)<~>~happy(john))) | calm(fred) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 12336116058334607230239
% SZS output start Proof for 12336116058334607230239
11. ! [X0] : (~calm(X0) <=> generous(X0)) [input p10]
20. ~generous(fred) & creative(fred) [input p19]
24. ~calm(fred) [input hypothesis]
51. ! [X0] : ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))) [nnf transformation 11]
115. generous(X0) | calm(X0) [cnf transformation 51]
142. ~generous(fred) [cnf transformation 20]
148. ~calm(fred) [cnf transformation 24]
284. calm(fred) [resolution 115,142]
285. $false [subsumption resolution 284,148]
% SZS output end Proof for 12336116058334607230239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not wise is both kind and not curious.
If lucy is both not kind and tall then john is strong or not wise and vice versa.
If someone is both not rich and old then someone is both not rich and curious and vice versa.
Everyone who is kind is both not strong and quiet and vice versa.
If fred is rich then john is not curious and vice versa.
Everyone who is either not kind or patient is creative and vice versa.
If someone is both not funny and kind then fred is not wise or funny and vice versa.
Everyone who is either not wise or curious is not wise.
Everyone who is not happy or not humble is quiet.
If someone is both not funny and not curious then someone is both kind and not generous and vice versa.
Everyone who is not rich or not funny is both not happy and not old and vice versa.
If someone is either not brave or not curious then paul is either not creative or tall.
If someone is either not calm or not old then susan is old.
Everyone who is either not happy or rich is both not happy and not humble.
If someone is both not calm and curious then someone is not calm or not quiet.
Everyone who is either wise or not tall is not calm and vice versa.
Someone is either not quiet or strong.
Lucy is creative or quiet.
Lucy is either not happy or strong.
Paul is generous.
Someone is humble or wise.
Someone is old. | Lucy is not kind. | contradiction | (![X]:((rich(X)|~wise(X))=>(kind(X)&~curious(X))))&
(((~kind(lucy)&tall(lucy)))<=>((strong(john)|~wise(john))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:(kind(X)<=>(~strong(X)&quiet(X))))&
((rich(fred))<=>(~curious(john)))&
(![X]:((~kind(X)<~>patient(X))<=>creative(X)))&
((?[X]:((~funny(X)&kind(X))))<=>((~wise(fred)|funny(fred))))&
(![X]:((~wise(X)<~>curious(X))=>~wise(X)))&
(![X]:((~happy(X)|~humble(X))=>quiet(X)))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((~rich(X)|~funny(X))<=>(~happy(X)&~old(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>((~creative(paul)<~>tall(paul))))&
((?[X]:((~calm(X)<~>~old(X))))=>(old(susan)))&
(![X]:((~happy(X)<~>rich(X))=>(~happy(X)&~humble(X))))&
((?[X]:((~calm(X)&curious(X))))=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:((wise(X)<~>~tall(X))<=>~calm(X)))&
(?[X]:((~quiet(X)<~>strong(X))))&
((creative(lucy)|quiet(lucy)))&
((~happy(lucy)<~>strong(lucy)))&
(generous(paul))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:(old(X))) | ~kind(lucy) | [
"p3",
"p8",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7852489008826582995633221
% SZS output start Proof for 7852489008826582995633221
4. ! [X0] : (kind(X0) <=> (quiet(X0) & ~strong(X0))) [input p3]
9. ! [X0] : ((~humble(X0) | ~happy(X0)) => quiet(X0)) [input p8]
11. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (~old(X0) & ~happy(X0))) [input p10]
14. ! [X0] : ((~happy(X0) <~> rich(X0)) => (~humble(X0) & ~happy(X0))) [input p13]
19. ~happy(lucy) <~> strong(lucy) [input p18]
23. ~kind(lucy) [input hypothesis]
29. ! [X0] : (quiet(X0) | (humble(X0) & happy(X0))) [ennf transformation 9]
32. ! [X0] : ((~humble(X0) & ~happy(X0)) | (~happy(X0) <=> rich(X0))) [ennf transformation 14]
41. ! [X0] : ((kind(X0) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ~kind(X0))) [nnf transformation 4]
42. ! [X0] : ((kind(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~kind(X0))) [flattening 41]
56. ! [X0] : (((~funny(X0) | ~rich(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (funny(X0) & rich(X0)))) [nnf transformation 11]
57. ! [X0] : ((~funny(X0) | ~rich(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | (funny(X0) & rich(X0)))) [flattening 56]
60. ! [X0] : ((~humble(X0) & ~happy(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) [nnf transformation 32]
68. (~strong(lucy) | happy(lucy)) & (strong(lucy) | ~happy(lucy)) [nnf transformation 19]
88. ~quiet(X0) | kind(X0) | strong(X0) [cnf transformation 42]
102. happy(X0) | quiet(X0) [cnf transformation 29]
108. ~happy(X0) | rich(X0) [cnf transformation 57]
120. ~happy(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 60]
132. ~strong(lucy) | happy(lucy) [cnf transformation 68]
136. ~kind(lucy) [cnf transformation 23]
137. ~happy(X0) | ~rich(X0) [duplicate literal removal 120]
154. 4 <=> kind(lucy) [avatar definition]
156. ~kind(lucy) <- (~4) [avatar component clause 154]
283. ~happy(X0) [subsumption resolution 137,108]
315. ~strong(lucy) [subsumption resolution 132,283]
325. ~4 [avatar split clause 136,154]
333. quiet(X0) [resolution 102,283]
381. strong(X0) | kind(X0) [resolution 88,333]
442. kind(lucy) [resolution 381,315]
443. $false <- (~4) [subsumption resolution 442,156]
444. 4 [avatar contradiction clause 443]
445. $false [avatar sat refutation 325,444]
% SZS output end Proof for 7852489008826582995633221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not generous or wise then susan is either happy or patient.
If lucy is either patient or creative then mary is both calm and funny.
Everyone who is both not wise and not generous is both funny and not generous and vice versa.
If fred is not patient then lucy is not wise and vice versa.
Everyone who is both happy and funny is either rich or generous and vice versa.
If alice is either not kind or not creative then someone is not brave or wise.
Everyone who is either not creative or calm is either strong or tall and vice versa.
Everyone who is not patient is humble.
Everyone who is not quiet is not rich and vice versa.
Everyone who is wise or patient is humble and vice versa.
Everyone who is not happy is not curious or not calm.
If someone is not humble or patient then susan is both not funny and wise and vice versa.
Everyone who is both not humble and calm is either tall or not humble.
Everyone who is both brave and not wise is both not kind and brave.
If susan is not quiet or rich then mary is either patient or not wise and vice versa.
Alice is either not kind or quiet.
Someone is either not wise or calm.
Mary is both not old and generous.
Someone is either humble or kind.
Lucy is generous or not curious.
Someone is either calm or funny. | Susan is not funny. | entailment | (((~generous(lucy)<~>wise(lucy)))=>((happy(susan)<~>patient(susan))))&
(((patient(lucy)<~>creative(lucy)))=>((calm(mary)&funny(mary))))&
(![X]:((~wise(X)&~generous(X))<=>(funny(X)&~generous(X))))&
((~patient(fred))<=>(~wise(lucy)))&
(![X]:((happy(X)&funny(X))<=>(rich(X)<~>generous(X))))&
(((~kind(alice)<~>~creative(alice)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(strong(X)<~>tall(X))))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:((wise(X)|patient(X))<=>humble(X)))&
(![X]:(~happy(X)=>(~curious(X)|~calm(X))))&
((?[X]:((~humble(X)|patient(X))))<=>((~funny(susan)&wise(susan))))&
(![X]:((~humble(X)&calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((brave(X)&~wise(X))=>(~kind(X)&brave(X))))&
(((~quiet(susan)|rich(susan)))<=>((patient(mary)<~>~wise(mary))))&
((~kind(alice)<~>quiet(alice)))&
(?[X]:((~wise(X)<~>calm(X))))&
((~old(mary)&generous(mary)))&
(?[X]:((humble(X)<~>kind(X))))&
((generous(lucy)|~curious(lucy)))&
(?[X]:((calm(X)<~>funny(X)))) | ~funny(susan) | [
"p7",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3567266105950648560278658
% SZS output start Proof for 3567266105950648560278658
8. ! [X0] : (~patient(X0) => humble(X0)) [input p7]
9. ! [X0] : (~quiet(X0) <=> ~rich(X0)) [input p8]
10. ! [X0] : ((patient(X0) | wise(X0)) <=> humble(X0)) [input p9]
12. ? [X0] : (patient(X0) | ~humble(X0)) <=> (wise(susan) & ~funny(susan)) [input p11]
15. (rich(susan) | ~quiet(susan)) <=> (patient(mary) <~> ~wise(mary)) [input p14]
22. funny(susan) [input hypothesis]
29. ! [X0] : (humble(X0) | patient(X0)) [ennf transformation 8]
45. ! [X0] : ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0))) [nnf transformation 9]
46. ! [X0] : (((patient(X0) | wise(X0)) | ~humble(X0)) & (humble(X0) | (~patient(X0) & ~wise(X0)))) [nnf transformation 10]
47. ! [X0] : ((patient(X0) | wise(X0) | ~humble(X0)) & (humble(X0) | (~patient(X0) & ~wise(X0)))) [flattening 46]
48. (? [X0] : (patient(X0) | ~humble(X0)) | (~wise(susan) | funny(susan))) & ((wise(susan) & ~funny(susan)) | ! [X0] : (~patient(X0) & humble(X0))) [nnf transformation 12]
49. (? [X0] : (patient(X0) | ~humble(X0)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X0] : (~patient(X0) & humble(X0))) [flattening 48]
50. (? [X0] : (patient(X0) | ~humble(X0)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X1] : (~patient(X1) & humble(X1))) [rectify 49]
51. ? [X0] : (patient(X0) | ~humble(X0)) => (patient(sK1) | ~humble(sK1)) [choice axiom]
52. ((patient(sK1) | ~humble(sK1)) | ~wise(susan) | funny(susan)) & ((wise(susan) & ~funny(susan)) | ! [X1] : (~patient(X1) & humble(X1))) [skolemisation 50,51]
54. ((rich(susan) | ~quiet(susan)) | ((patient(mary) | wise(mary)) & (~wise(mary) | ~patient(mary)))) & (((wise(mary) | ~patient(mary)) & (~wise(mary) | patient(mary))) | (~rich(susan) & quiet(susan))) [nnf transformation 15]
55. (rich(susan) | ~quiet(susan) | ((patient(mary) | wise(mary)) & (~wise(mary) | ~patient(mary)))) & (((wise(mary) | ~patient(mary)) & (~wise(mary) | patient(mary))) | (~rich(susan) & quiet(susan))) [flattening 54]
96. humble(X0) | patient(X0) [cnf transformation 29]
98. ~quiet(X0) | rich(X0) [cnf transformation 45]
101. patient(X0) | wise(X0) | ~humble(X0) [cnf transformation 47]
103. ~funny(susan) | ~patient(X1) [cnf transformation 52]
111. ~wise(mary) | patient(mary) | quiet(susan) [cnf transformation 55]
112. ~wise(mary) | patient(mary) | ~rich(susan) [cnf transformation 55]
126. funny(susan) [cnf transformation 22]
192. patient(X0) | wise(X0) [subsumption resolution 101,96]
196. 14 <=> funny(susan) [avatar definition]
209. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
210. ~patient(X1) <- (17) [avatar component clause 209]
212. 17 | ~14 [avatar split clause 103,196,209]
215. 18 <=> rich(susan) [avatar definition]
225. 20 <=> quiet(susan) [avatar definition]
227. quiet(susan) <- (20) [avatar component clause 225]
229. patient(mary) | ~rich(susan) [subsumption resolution 112,192]
231. 21 <=> patient(mary) [avatar definition]
233. patient(mary) <- (21) [avatar component clause 231]
234. ~18 | 21 [avatar split clause 229,231,215]
235. patient(mary) | quiet(susan) [subsumption resolution 111,192]
236. 20 | 21 [avatar split clause 235,231,225]
264. 14 [avatar split clause 126,196]
265. rich(susan) <- (20) [resolution 98,227]
268. 18 | ~20 [avatar split clause 265,225,215]
269. $false <- (17, 21) [subsumption resolution 233,210]
270. ~17 | ~21 [avatar contradiction clause 269]
271. $false [avatar sat refutation 212,234,236,264,268,270]
% SZS output end Proof for 3567266105950648560278658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or funny then alice is not kind or not generous and vice versa.
Everyone who is wise or tall is not happy and vice versa.
Everyone who is not patient is not quiet.
Everyone who is not kind is both generous and wise and vice versa.
If john is both not old and curious then someone is not patient or wise and vice versa.
Everyone who is both calm and not calm is not happy or funny and vice versa.
If someone is either not rich or not humble then someone is both tall and not strong and vice versa.
If someone is both not curious and strong then someone is both generous and not wise.
Everyone who is either not curious or funny is both happy and not rich.
If mary is either not funny or curious then someone is either funny or brave.
If paul is not wise then someone is rich or tall.
Everyone who is both not funny and funny is not creative.
Everyone who is not funny is both patient and rich.
Everyone who is not wise is not generous or not kind and vice versa.
Everyone who is either not quiet or quiet is both not brave and quiet and vice versa.
If paul is both old and not creative then someone is both brave and not generous.
Paul is calm.
Paul is both not generous and quiet.
Susan is generous or not creative.
Someone is patient or not humble.
Someone is both humble and not tall. | Susan is quiet. | entailment | ((?[X]:((~wise(X)<~>funny(X))))<=>((~kind(alice)|~generous(alice))))&
(![X]:((wise(X)|tall(X))<=>~happy(X)))&
(![X]:(~patient(X)=>~quiet(X)))&
(![X]:(~kind(X)<=>(generous(X)&wise(X))))&
(((~old(john)&curious(john)))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~happy(X)|funny(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~curious(X)<~>funny(X))=>(happy(X)&~rich(X))))&
(((~funny(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>brave(X)))))&
((~wise(paul))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~funny(X)&funny(X))=>~creative(X)))&
(![X]:(~funny(X)=>(patient(X)&rich(X))))&
(![X]:(~wise(X)<=>(~generous(X)|~kind(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~brave(X)&quiet(X))))&
(((old(paul)&~creative(paul)))=>(?[X]:((brave(X)&~generous(X)))))&
(calm(paul))&
((~generous(paul)&quiet(paul)))&
((generous(susan)|~creative(susan)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((humble(X)&~tall(X)))) | quiet(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3797725430802951281426787
% SZS output start Proof for 3797725430802951281426787
15. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (quiet(X0) & ~brave(X0))) [input p14]
22. ~quiet(susan) [input hypothesis]
67. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [flattening 67]
123. quiet(X0) | quiet(X0) | quiet(X0) [cnf transformation 68]
136. ~quiet(susan) [cnf transformation 22]
139. quiet(X0) [duplicate literal removal 123]
308. $false [subsumption resolution 136,139]
% SZS output end Proof for 3797725430802951281426787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not funny then someone is not wise and vice versa.
Everyone who is either not wise or happy is funny or old and vice versa.
If mary is creative or not wise then mary is tall or old.
Everyone who is both not strong and rich is both not generous and not old.
Everyone who is both kind and not rich is either not calm or not happy.
Everyone who is not old is either wise or humble and vice versa.
Everyone who is either not tall or not wise is not wise or not creative and vice versa.
If mary is not curious then someone is not patient or tall.
If someone is either not strong or brave then paul is either patient or not funny.
Everyone who is both old and generous is happy or not kind.
Everyone who is either not funny or not generous is both kind and not rich.
If someone is not quiet or not rich then someone is both generous and not generous and vice versa.
If mary is both not humble and humble then susan is funny and vice versa.
If someone is both not strong and wise then someone is not calm and vice versa.
If someone is not rich then alice is old or not wise.
If someone is not brave or generous then someone is either not creative or not tall and vice versa.
Someone is not strong or not funny.
Someone is not humble.
Someone is patient or not curious.
Susan is either creative or not creative.
John is old or not tall.
Susan is either curious or happy.
Susan is wise or rich. | John is quiet. | entailment | ((~funny(john))<=>(?[X]:(~wise(X))))&
(![X]:((~wise(X)<~>happy(X))<=>(funny(X)|old(X))))&
(((creative(mary)|~wise(mary)))=>((tall(mary)|old(mary))))&
(![X]:((~strong(X)&rich(X))=>(~generous(X)&~old(X))))&
(![X]:((kind(X)&~rich(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(wise(X)<~>humble(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~wise(X)|~creative(X))))&
((~curious(mary))=>(?[X]:((~patient(X)|tall(X)))))&
((?[X]:((~strong(X)<~>brave(X))))=>((patient(paul)<~>~funny(paul))))&
(![X]:((old(X)&generous(X))=>(happy(X)|~kind(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(kind(X)&~rich(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((generous(X)&~generous(X)))))&
(((~humble(mary)&humble(mary)))<=>(funny(susan)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~rich(X)))=>((old(alice)|~wise(alice))))&
((?[X]:((~brave(X)|generous(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:((patient(X)|~curious(X))))&
((creative(susan)<~>~creative(susan)))&
((old(john)|~tall(john)))&
((curious(susan)<~>happy(susan)))&
((wise(susan)|rich(susan))) | quiet(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8576167940953997358858487
% SZS output start Proof for 8576167940953997358858487
12. ? [X0] : (~rich(X0) | ~quiet(X0)) <=> ? [X0] : (~generous(X0) & generous(X0)) [input p11]
24. ~quiet(john) [input hypothesis]
25. ? [X0] : (~rich(X0) | ~quiet(X0)) <=> ? [X1] : (~generous(X1) & generous(X1)) [rectify 12]
55. (? [X0] : (~rich(X0) | ~quiet(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X1] : (~generous(X1) & generous(X1)) | ! [X0] : (rich(X0) & quiet(X0))) [nnf transformation 25]
56. (? [X0] : (~rich(X0) | ~quiet(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X2] : (~generous(X2) & generous(X2)) | ! [X3] : (rich(X3) & quiet(X3))) [rectify 55]
57. ? [X0] : (~rich(X0) | ~quiet(X0)) => (~rich(sK2) | ~quiet(sK2)) [choice axiom]
58. ? [X2] : (~generous(X2) & generous(X2)) => (~generous(sK3) & generous(sK3)) [choice axiom]
59. ((~rich(sK2) | ~quiet(sK2)) | ! [X1] : (generous(X1) | ~generous(X1))) & ((~generous(sK3) & generous(sK3)) | ! [X3] : (rich(X3) & quiet(X3))) [skolemisation 56,58,57]
114. generous(sK3) | quiet(X3) [cnf transformation 59]
116. ~generous(sK3) | quiet(X3) [cnf transformation 59]
141. ~quiet(john) [cnf transformation 24]
211. 16 <=> generous(sK3) [avatar definition]
216. 17 <=> ! [X3] : quiet(X3) [avatar definition]
217. quiet(X3) <- (17) [avatar component clause 216]
218. 17 | ~16 [avatar split clause 116,211,216]
220. 17 | 16 [avatar split clause 114,211,216]
341. $false <- (17) [resolution 217,141]
342. ~17 [avatar contradiction clause 341]
343. $false [avatar sat refutation 218,220,342]
% SZS output end Proof for 8576167940953997358858487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or patient then susan is not strong.
Everyone who is calm is not wise and vice versa.
Everyone who is both not old and tall is either not quiet or generous.
Everyone who is not quiet or generous is both creative and not old.
Everyone who is both not curious and not funny is funny and vice versa.
If someone is either creative or old then alice is both not creative and strong.
If mary is both humble and not tall then someone is not patient.
Everyone who is quiet is happy or calm.
If someone is calm or tall then paul is either not brave or not old.
If fred is not happy or patient then someone is both wise and brave.
Everyone who is either not generous or quiet is both not funny and not strong.
If john is both not curious and strong then paul is not humble.
If alice is both calm and not kind then someone is both humble and funny and vice versa.
If someone is both not wise and not tall then fred is either not tall or not patient and vice versa.
If someone is both patient and wise then someone is both not generous and not tall and vice versa.
Someone is not brave.
Alice is not old.
Someone is old or kind.
Susan is not calm or brave.
Someone is both not patient and not funny.
Fred is both not rich and not calm.
Someone is either not strong or patient. | Fred is not wise. | contradiction | (((~brave(lucy)|patient(lucy)))=>(~strong(susan)))&
(![X]:(calm(X)<=>~wise(X)))&
(![X]:((~old(X)&tall(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~quiet(X)|generous(X))=>(creative(X)&~old(X))))&
(![X]:((~curious(X)&~funny(X))<=>funny(X)))&
((?[X]:((creative(X)<~>old(X))))=>((~creative(alice)&strong(alice))))&
(((humble(mary)&~tall(mary)))=>(?[X]:(~patient(X))))&
(![X]:(quiet(X)=>(happy(X)|calm(X))))&
((?[X]:((calm(X)|tall(X))))=>((~brave(paul)<~>~old(paul))))&
(((~happy(fred)|patient(fred)))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:((~generous(X)<~>quiet(X))=>(~funny(X)&~strong(X))))&
(((~curious(john)&strong(john)))=>(~humble(paul)))&
(((calm(alice)&~kind(alice)))<=>(?[X]:((humble(X)&funny(X)))))&
((?[X]:((~wise(X)&~tall(X))))<=>((~tall(fred)<~>~patient(fred))))&
((?[X]:((patient(X)&wise(X))))<=>(?[X]:((~generous(X)&~tall(X)))))&
(?[X]:(~brave(X)))&
(~old(alice))&
(?[X]:((old(X)|kind(X))))&
((~calm(susan)|brave(susan)))&
(?[X]:((~patient(X)&~funny(X))))&
((~rich(fred)&~calm(fred)))&
(?[X]:((~strong(X)<~>patient(X)))) | ~wise(fred) | [
"p1",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2370886220044508665942012
% SZS output start Proof for 2370886220044508665942012
2. ! [X0] : (calm(X0) <=> ~wise(X0)) [input p1]
21. ~calm(fred) & ~rich(fred) [input p20]
23. ~wise(fred) [input hypothesis]
25. ~calm(fred) [pure predicate removal 21]
40. ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))) [nnf transformation 2]
77. wise(X0) | calm(X0) [cnf transformation 40]
123. ~calm(fred) [cnf transformation 25]
126. ~wise(fred) [cnf transformation 23]
298. calm(fred) [resolution 77,126]
301. $false [subsumption resolution 298,123]
% SZS output end Proof for 2370886220044508665942012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or wise then someone is wise or not tall and vice versa. If someone is not quiet or old then someone is calm or creative and vice versa. If mary is not curious then someone is both kind and not tall. If susan is tall then alice is either wise or generous. If fred is curious then alice is not curious and vice versa. Everyone who is either not wise or rich is generous. If someone is not tall then someone is either not generous or not wise. If someone is either not tall or tall then someone is either not strong or not humble and vice versa. Everyone who is either not kind or kind is not kind and vice versa. If lucy is generous then lucy is both not humble and not calm. Everyone who is not calm or curious is quiet or rich and vice versa. Everyone who is not quiet or funny is either curious or kind and vice versa. Everyone who is either not calm or not happy is either brave or calm. If someone is either not strong or happy then lucy is either old or tall. If paul is either not quiet or not humble then someone is both not brave and wise and vice versa. If someone is both calm and not wise then john is either not generous or not creative. Susan is not curious or humble. Mary is both strong and not wise. Lucy is either creative or not calm. Someone is either creative or not calm. Mary is not creative or funny. John is both not strong and not calm. Mary is not rich. | Mary is not funny. | contradiction | (((curious(john)<~>wise(john)))<=>(?[X]:((wise(X)|~tall(X)))))&
((?[X]:((~quiet(X)|old(X))))<=>(?[X]:((calm(X)|creative(X)))))&
((~curious(mary))=>(?[X]:((kind(X)&~tall(X)))))&
((tall(susan))=>((wise(alice)<~>generous(alice))))&
((curious(fred))<=>(~curious(alice)))&
(![X]:((~wise(X)<~>rich(X))=>generous(X)))&
((?[X]:(~tall(X)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((~tall(X)<~>tall(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((~kind(X)<~>kind(X))<=>~kind(X)))&
((generous(lucy))=>((~humble(lucy)&~calm(lucy))))&
(![X]:((~calm(X)|curious(X))<=>(quiet(X)|rich(X))))&
(![X]:((~quiet(X)|funny(X))<=>(curious(X)<~>kind(X))))&
(![X]:((~calm(X)<~>~happy(X))=>(brave(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>happy(X))))=>((old(lucy)<~>tall(lucy))))&
(((~quiet(paul)<~>~humble(paul)))<=>(?[X]:((~brave(X)&wise(X)))))&
((?[X]:((calm(X)&~wise(X))))=>((~generous(john)<~>~creative(john))))&
((~curious(susan)|humble(susan)))&
((strong(mary)&~wise(mary)))&
((creative(lucy)<~>~calm(lucy)))&
(?[X]:((creative(X)<~>~calm(X))))&
((~creative(mary)|funny(mary)))&
((~strong(john)&~calm(john)))&
(~rich(mary)) | ~funny(mary) | [
"p2",
"p8",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3364091710150946248291639
% SZS output start Proof for 3364091710150946248291639
3. ~curious(mary) => ? [X0] : (~tall(X0) & kind(X0)) [input p2]
9. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> ~kind(X0)) [input p8]
11. ! [X0] : ((curious(X0) | ~calm(X0)) <=> (rich(X0) | quiet(X0))) [input p10]
12. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (curious(X0) <~> kind(X0))) [input p11]
23. ~rich(mary) [input p22]
24. ~funny(mary) [input hypothesis]
28. ? [X0] : (~tall(X0) & kind(X0)) | curious(mary) [ennf transformation 3]
45. ? [X0] : (~tall(X0) & kind(X0)) => (~tall(sK3) & kind(sK3)) [choice axiom]
46. (~tall(sK3) & kind(sK3)) | curious(mary) [skolemisation 28,45]
59. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 9]
60. ! [X0] : (((curious(X0) | ~calm(X0)) | (~rich(X0) & ~quiet(X0))) & ((rich(X0) | quiet(X0)) | (~curious(X0) & calm(X0)))) [nnf transformation 11]
61. ! [X0] : ((curious(X0) | ~calm(X0) | (~rich(X0) & ~quiet(X0))) & (rich(X0) | quiet(X0) | (~curious(X0) & calm(X0)))) [flattening 60]
62. ! [X0] : (((funny(X0) | ~quiet(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~funny(X0) & quiet(X0)))) [nnf transformation 12]
63. ! [X0] : ((funny(X0) | ~quiet(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~funny(X0) & quiet(X0)))) [flattening 62]
85. kind(sK3) | curious(mary) [cnf transformation 46]
104. ~kind(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 59]
110. ~curious(X0) | quiet(X0) | rich(X0) [cnf transformation 61]
117. funny(X0) | ~quiet(X0) | kind(X0) | ~curious(X0) [cnf transformation 63]
145. ~rich(mary) [cnf transformation 23]
146. ~funny(mary) [cnf transformation 24]
150. ~kind(X0) [duplicate literal removal 104]
218. 15 <=> curious(mary) [avatar definition]
220. curious(mary) <- (15) [avatar component clause 218]
227. 17 <=> kind(sK3) [avatar definition]
229. kind(sK3) <- (17) [avatar component clause 227]
230. 15 | 17 [avatar split clause 85,227,218]
294. ~quiet(X0) | funny(X0) | ~curious(X0) [subsumption resolution 117,150]
383. 49 <=> funny(mary) [avatar definition]
384. ~funny(mary) <- (~49) [avatar component clause 383]
387. ~49 [avatar split clause 146,383]
403. 51 <=> quiet(mary) [avatar definition]
405. quiet(mary) <- (51) [avatar component clause 403]
411. quiet(mary) | rich(mary) <- (15) [resolution 110,220]
424. quiet(mary) <- (15) [subsumption resolution 411,145]
425. 51 | ~15 [avatar split clause 424,218,403]
437. $false <- (17) [subsumption resolution 229,150]
438. ~17 [avatar contradiction clause 437]
494. funny(mary) | ~curious(mary) <- (51) [resolution 294,405]
495. ~curious(mary) <- (~49, 51) [subsumption resolution 494,384]
496. $false <- (15, ~49, 51) [subsumption resolution 495,220]
497. ~15 | 49 | ~51 [avatar contradiction clause 496]
498. $false [avatar sat refutation 230,387,425,438,497]
% SZS output end Proof for 3364091710150946248291639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not funny or generous then someone is both not strong and brave.
If someone is either not creative or not funny then someone is not creative and vice versa.
If fred is not creative then mary is either curious or not happy and vice versa.
Everyone who is humble is both not generous and kind.
Everyone who is not humble is either generous or tall and vice versa.
Everyone who is either not creative or not old is either not funny or not generous.
If lucy is either not wise or not creative then someone is both curious and not creative and vice versa.
Everyone who is either not funny or generous is both not patient and not creative.
If mary is not happy then someone is both funny and wise and vice versa.
If lucy is either not humble or not brave then lucy is either not quiet or tall and vice versa.
If someone is not patient then someone is humble or not patient.
If someone is not wise then someone is either not generous or old.
Everyone who is calm is quiet.
Everyone who is curious is either not generous or strong.
If someone is both not brave and calm then someone is both not curious and curious.
Everyone who is either not happy or tall is either not funny or generous and vice versa.
Fred is patient or not old.
Someone is either tall or humble.
Someone is both not wise and strong.
Someone is both not tall and brave.
Susan is not brave.
Someone is both humble and not generous.
Alice is both humble and not curious. | Susan is brave. | contradiction | (((~funny(alice)<~>generous(alice)))=>(?[X]:((~strong(X)&brave(X)))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:(~creative(X))))&
((~creative(fred))<=>((curious(mary)<~>~happy(mary))))&
(![X]:(humble(X)=>(~generous(X)&kind(X))))&
(![X]:(~humble(X)<=>(generous(X)<~>tall(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~funny(X)<~>~generous(X))))&
(((~wise(lucy)<~>~creative(lucy)))<=>(?[X]:((curious(X)&~creative(X)))))&
(![X]:((~funny(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
((~happy(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(((~humble(lucy)<~>~brave(lucy)))<=>((~quiet(lucy)<~>tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:(calm(X)=>quiet(X)))&
(![X]:(curious(X)=>(~generous(X)<~>strong(X))))&
((?[X]:((~brave(X)&calm(X))))=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(~funny(X)<~>generous(X))))&
((patient(fred)|~old(fred)))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((~tall(X)&brave(X))))&
(~brave(susan))&
(?[X]:((humble(X)&~generous(X))))&
((humble(alice)&~curious(alice))) | brave(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1933512935865530401596625
% SZS output start Proof for 1933512935865530401596625
21. ~brave(susan) [input p20]
24. brave(susan) [input hypothesis]
140. ~brave(susan) [cnf transformation 21]
145. brave(susan) [cnf transformation 24]
321. $false [subsumption resolution 145,140]
% SZS output end Proof for 1933512935865530401596625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is both not rich and curious.
Everyone who is both not rich and not happy is patient and vice versa.
Everyone who is not brave or not creative is either not calm or not curious.
Everyone who is not generous or not patient is creative.
If alice is wise then mary is not old or kind and vice versa.
If someone is not tall or not strong then susan is not funny.
If susan is either funny or not patient then paul is either calm or not rich and vice versa.
Everyone who is creative or strong is both not tall and wise.
Everyone who is not quiet is both not rich and not strong and vice versa.
Everyone who is both not curious and not kind is not wise and vice versa.
Everyone who is both humble and not funny is both old and not funny and vice versa.
If someone is tall then someone is either quiet or funny and vice versa.
If someone is not old then alice is both tall and not happy and vice versa.
Everyone who is either brave or strong is both patient and not generous and vice versa.
If lucy is either not funny or not calm then someone is both rich and not patient.
Everyone who is not curious is not humble or not calm.
John is both tall and not humble.
Lucy is not kind or kind.
Someone is wise or humble.
John is not creative or not strong.
Someone is not humble.
Alice is both not wise and not brave.
Fred is not calm or creative.
John is either not creative or not kind. | John is happy. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((~rich(X)&~happy(X))<=>patient(X)))&
(![X]:((~brave(X)|~creative(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((~generous(X)|~patient(X))=>creative(X)))&
((wise(alice))<=>((~old(mary)|kind(mary))))&
((?[X]:((~tall(X)|~strong(X))))=>(~funny(susan)))&
(((funny(susan)<~>~patient(susan)))<=>((calm(paul)<~>~rich(paul))))&
(![X]:((creative(X)|strong(X))=>(~tall(X)&wise(X))))&
(![X]:(~quiet(X)<=>(~rich(X)&~strong(X))))&
(![X]:((~curious(X)&~kind(X))<=>~wise(X)))&
(![X]:((humble(X)&~funny(X))<=>(old(X)&~funny(X))))&
((?[X]:(tall(X)))<=>(?[X]:((quiet(X)<~>funny(X)))))&
((?[X]:(~old(X)))<=>((tall(alice)&~happy(alice))))&
(![X]:((brave(X)<~>strong(X))<=>(patient(X)&~generous(X))))&
(((~funny(lucy)<~>~calm(lucy)))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:(~curious(X)=>(~humble(X)|~calm(X))))&
((tall(john)&~humble(john)))&
((~kind(lucy)|kind(lucy)))&
(?[X]:((wise(X)|humble(X))))&
((~creative(john)|~strong(john)))&
(?[X]:(~humble(X)))&
((~wise(alice)&~brave(alice)))&
((~calm(fred)|creative(fred)))&
((~creative(john)<~>~kind(john))) | happy(john) | [
"p1",
"p3",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6168094712856725195414080
% SZS output start Proof for 6168094712856725195414080
2. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> patient(X0)) [input p1]
4. ! [X0] : ((~patient(X0) | ~generous(X0)) => creative(X0)) [input p3]
8. ! [X0] : ((strong(X0) | creative(X0)) => (wise(X0) & ~tall(X0))) [input p7]
17. ~humble(john) & tall(john) [input p16]
25. happy(john) [input hypothesis]
30. ! [X0] : (creative(X0) | (patient(X0) & generous(X0))) [ennf transformation 4]
32. ! [X0] : ((wise(X0) & ~tall(X0)) | (~strong(X0) & ~creative(X0))) [ennf transformation 8]
39. ! [X0] : (((~happy(X0) & ~rich(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) | rich(X0)))) [nnf transformation 2]
40. ! [X0] : (((~happy(X0) & ~rich(X0)) | ~patient(X0)) & (patient(X0) | happy(X0) | rich(X0))) [flattening 39]
75. ~patient(X0) | ~happy(X0) [cnf transformation 40]
81. creative(X0) | patient(X0) [cnf transformation 30]
95. ~tall(X0) | ~creative(X0) [cnf transformation 32]
127. tall(john) [cnf transformation 17]
138. happy(john) [cnf transformation 25]
272. 29 <=> creative(john) [avatar definition]
274. ~creative(john) <- (~29) [avatar component clause 272]
300. ~creative(john) [resolution 95,127]
304. ~29 [avatar split clause 300,272]
305. patient(john) <- (~29) [resolution 274,81]
307. ~happy(john) <- (~29) [resolution 305,75]
309. $false <- (~29) [subsumption resolution 307,138]
310. 29 [avatar contradiction clause 309]
311. $false [avatar sat refutation 304,310]
% SZS output end Proof for 6168094712856725195414080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not curious and not funny and vice versa.
If paul is not humble or calm then someone is either not strong or not wise and vice versa.
If someone is funny or kind then someone is either generous or tall and vice versa.
Everyone who is both not funny and not quiet is either humble or strong and vice versa.
Everyone who is both not kind and brave is both calm and not calm and vice versa.
If someone is both funny and tall then someone is wise or calm.
If paul is not wise or not happy then mary is calm or curious and vice versa.
Everyone who is not brave or strong is old and vice versa.
If someone is creative or not curious then lucy is both not patient and patient.
If mary is both wise and not old then someone is kind or not tall and vice versa.
Everyone who is creative is both strong and not brave.
Everyone who is curious or happy is either not rich or brave.
If someone is both not patient and not humble then john is either not funny or quiet and vice versa.
If someone is either tall or not creative then mary is not creative.
Everyone who is not humble is both not kind and not brave.
If john is either old or tall then someone is not happy.
John is not quiet.
Paul is either curious or not happy.
Fred is humble or not kind.
Someone is either quiet or not curious.
Alice is either not old or not generous.
Someone is either not kind or creative.
Someone is either not humble or old. | Lucy is not brave. | entailment | (![X]:(~old(X)<=>(~curious(X)&~funny(X))))&
(((~humble(paul)|calm(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(humble(X)<~>strong(X))))&
(![X]:((~kind(X)&brave(X))<=>(calm(X)&~calm(X))))&
((?[X]:((funny(X)&tall(X))))=>(?[X]:((wise(X)|calm(X)))))&
(((~wise(paul)|~happy(paul)))<=>((calm(mary)|curious(mary))))&
(![X]:((~brave(X)|strong(X))<=>old(X)))&
((?[X]:((creative(X)|~curious(X))))=>((~patient(lucy)&patient(lucy))))&
(((wise(mary)&~old(mary)))<=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(creative(X)=>(strong(X)&~brave(X))))&
(![X]:((curious(X)|happy(X))=>(~rich(X)<~>brave(X))))&
((?[X]:((~patient(X)&~humble(X))))<=>((~funny(john)<~>quiet(john))))&
((?[X]:((tall(X)<~>~creative(X))))=>(~creative(mary)))&
(![X]:(~humble(X)=>(~kind(X)&~brave(X))))&
(((old(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
(~quiet(john))&
((curious(paul)<~>~happy(paul)))&
((humble(fred)|~kind(fred)))&
(?[X]:((quiet(X)<~>~curious(X))))&
((~old(alice)<~>~generous(alice)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((~humble(X)<~>old(X)))) | ~brave(lucy) | [
"p0",
"p4",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6534312807410509673284895
% SZS output start Proof for 6534312807410509673284895
1. ! [X0] : (~old(X0) <=> (~funny(X0) & ~curious(X0))) [input p0]
5. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (~calm(X0) & calm(X0))) [input p4]
9. ? [X0] : (~curious(X0) | creative(X0)) => (patient(lucy) & ~patient(lucy)) [input p8]
10. (~old(mary) & wise(mary)) <=> ? [X0] : (~tall(X0) | kind(X0)) [input p9]
24. brave(lucy) [input hypothesis]
28. (patient(lucy) & ~patient(lucy)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 9]
34. ! [X0] : ((~old(X0) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | old(X0))) [nnf transformation 1]
35. ! [X0] : ((~old(X0) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | old(X0))) [flattening 34]
48. ! [X0] : (((brave(X0) & ~kind(X0)) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 5]
49. ! [X0] : (((brave(X0) & ~kind(X0)) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | ~brave(X0) | kind(X0))) [flattening 48]
57. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X0] : (~tall(X0) | kind(X0)) | (old(mary) | ~wise(mary))) [nnf transformation 10]
58. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X0] : (~tall(X0) | kind(X0)) | old(mary) | ~wise(mary)) [flattening 57]
59. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X1] : (~tall(X1) | kind(X1)) | old(mary) | ~wise(mary)) [rectify 58]
60. ? [X1] : (~tall(X1) | kind(X1)) => (~tall(sK4) | kind(sK4)) [choice axiom]
61. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & ((~tall(sK4) | kind(sK4)) | old(mary) | ~wise(mary)) [skolemisation 59,60]
82. ~curious(X0) | old(X0) [cnf transformation 35]
103. calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 49]
104. ~calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 49]
116. ~patient(lucy) | curious(X0) [cnf transformation 28]
118. patient(lucy) | curious(X0) [cnf transformation 28]
122. ~old(mary) | ~kind(X0) [cnf transformation 61]
154. brave(lucy) [cnf transformation 24]
200. 11 <=> ! [X3] : ~kind(X3) [avatar definition]
201. ~kind(X3) <- (11) [avatar component clause 200]
217. ~brave(X0) | kind(X0) [subsumption resolution 103,104]
251. 22 <=> ! [X0] : curious(X0) [avatar definition]
252. curious(X0) <- (22) [avatar component clause 251]
254. 23 <=> patient(lucy) [avatar definition]
257. 22 | 23 [avatar split clause 118,254,251]
262. 22 | ~23 [avatar split clause 116,254,251]
268. 26 <=> old(mary) [avatar definition]
270. ~old(mary) <- (~26) [avatar component clause 268]
272. 11 | ~26 [avatar split clause 122,268,200]
403. old(X0) <- (22) [resolution 82,252]
412. kind(lucy) [resolution 217,154]
414. $false <- (11) [subsumption resolution 412,201]
415. ~11 [avatar contradiction clause 414]
416. $false <- (22, ~26) [subsumption resolution 270,403]
417. ~22 | 26 [avatar contradiction clause 416]
418. $false [avatar sat refutation 257,262,272,415,417]
% SZS output end Proof for 6534312807410509673284895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not humble is calm and vice versa.
If someone is curious then alice is curious or not happy and vice versa.
If someone is both strong and old then someone is not patient.
Everyone who is both humble and not funny is either creative or not creative.
Everyone who is either tall or humble is either generous or wise.
Everyone who is either tall or not rich is not kind or wise and vice versa.
If someone is strong or not rich then lucy is either not wise or not patient.
Everyone who is not kind is old and vice versa.
If someone is not rich or funny then someone is both not tall and not humble.
If someone is both not brave and not happy then lucy is either not old or not humble.
Everyone who is either not calm or quiet is both not curious and wise.
If fred is not brave or not funny then fred is not tall.
If someone is either humble or not brave then lucy is both not humble and not kind.
Everyone who is either not old or not curious is humble.
Everyone who is not generous or humble is either not brave or not creative.
Everyone who is patient or brave is kind.
Someone is happy.
Fred is either not tall or not old.
Someone is brave.
Alice is either not brave or not funny.
Someone is kind or not kind.
John is not strong or not creative.
Someone is not calm or calm.
Fred is both creative and not funny. | Fred is creative. | entailment | (![X]:((~happy(X)&~humble(X))<=>calm(X)))&
((?[X]:(curious(X)))<=>((curious(alice)|~happy(alice))))&
((?[X]:((strong(X)&old(X))))=>(?[X]:(~patient(X))))&
(![X]:((humble(X)&~funny(X))=>(creative(X)<~>~creative(X))))&
(![X]:((tall(X)<~>humble(X))=>(generous(X)<~>wise(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(~kind(X)|wise(X))))&
((?[X]:((strong(X)|~rich(X))))=>((~wise(lucy)<~>~patient(lucy))))&
(![X]:(~kind(X)<=>old(X)))&
((?[X]:((~rich(X)|funny(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>((~old(lucy)<~>~humble(lucy))))&
(![X]:((~calm(X)<~>quiet(X))=>(~curious(X)&wise(X))))&
(((~brave(fred)|~funny(fred)))=>(~tall(fred)))&
((?[X]:((humble(X)<~>~brave(X))))=>((~humble(lucy)&~kind(lucy))))&
(![X]:((~old(X)<~>~curious(X))=>humble(X)))&
(![X]:((~generous(X)|humble(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((patient(X)|brave(X))=>kind(X)))&
(?[X]:(happy(X)))&
((~tall(fred)<~>~old(fred)))&
(?[X]:(brave(X)))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((kind(X)|~kind(X))))&
((~strong(john)|~creative(john)))&
(?[X]:((~calm(X)|calm(X))))&
((creative(fred)&~funny(fred))) | creative(fred) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 587042105833488791771949
% SZS output start Proof for 587042105833488791771949
24. ~funny(fred) & creative(fred) [input p23]
25. ~creative(fred) [input hypothesis]
128. creative(fred) [cnf transformation 24]
130. ~creative(fred) [cnf transformation 25]
235. $false [subsumption resolution 130,128]
% SZS output end Proof for 587042105833488791771949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and strong is old and vice versa. Everyone who is both patient and not kind is not kind. Everyone who is either not happy or strong is happy or humble and vice versa. If someone is humble or not wise then someone is rich. Everyone who is not patient is either not quiet or kind and vice versa. If someone is either strong or calm then susan is curious or not generous and vice versa. If someone is quiet then alice is not wise or not strong. Everyone who is both not curious and not brave is either creative or not wise and vice versa. Everyone who is calm is both not wise and happy and vice versa. Everyone who is either not kind or happy is not old. If fred is both not generous and not curious then someone is not curious. If john is not curious or humble then someone is both quiet and not calm. Everyone who is old or humble is both curious and brave. If mary is either quiet or not patient then someone is not rich. Everyone who is not old or not creative is both quiet and not curious and vice versa. If mary is both tall and not happy then someone is tall or not rich and vice versa. John is not tall or not kind. Paul is both kind and not calm. Someone is not humble or not happy. Alice is not strong or not quiet. John is not curious. Susan is either curious or not wise. Fred is both happy and not humble. Mary is not patient. | Alice is not creative. | contradiction | (![X]:((humble(X)&strong(X))<=>old(X)))&
(![X]:((patient(X)&~kind(X))=>~kind(X)))&
(![X]:((~happy(X)<~>strong(X))<=>(happy(X)|humble(X))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>kind(X))))&
((?[X]:((strong(X)<~>calm(X))))<=>((curious(susan)|~generous(susan))))&
((?[X]:(quiet(X)))=>((~wise(alice)|~strong(alice))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:(calm(X)<=>(~wise(X)&happy(X))))&
(![X]:((~kind(X)<~>happy(X))=>~old(X)))&
(((~generous(fred)&~curious(fred)))=>(?[X]:(~curious(X))))&
(((~curious(john)|humble(john)))=>(?[X]:((quiet(X)&~calm(X)))))&
(![X]:((old(X)|humble(X))=>(curious(X)&brave(X))))&
(((quiet(mary)<~>~patient(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)|~creative(X))<=>(quiet(X)&~curious(X))))&
(((tall(mary)&~happy(mary)))<=>(?[X]:((tall(X)|~rich(X)))))&
((~tall(john)|~kind(john)))&
((kind(paul)&~calm(paul)))&
(?[X]:((~humble(X)|~happy(X))))&
((~strong(alice)|~quiet(alice)))&
(~curious(john))&
((curious(susan)<~>~wise(susan)))&
((happy(fred)&~humble(fred)))&
(~patient(mary)) | ~creative(alice) | [
"p2",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6625445821957785039132145
% SZS output start Proof for 6625445821957785039132145
3. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> (humble(X0) | happy(X0))) [input p2]
13. ! [X0] : ((humble(X0) | old(X0)) => (brave(X0) & curious(X0))) [input p12]
15. ! [X0] : ((~creative(X0) | ~old(X0)) <=> (~curious(X0) & quiet(X0))) [input p14]
20. ~quiet(alice) | ~strong(alice) [input p19]
25. ~creative(alice) [input hypothesis]
36. ! [X0] : ((brave(X0) & curious(X0)) | (~humble(X0) & ~old(X0))) [ennf transformation 13]
40. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [flattening 40]
63. ! [X0] : (((~creative(X0) | ~old(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (creative(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((~creative(X0) | ~old(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | (creative(X0) & old(X0)))) [flattening 63]
77. humble(X0) | happy(X0) | strong(X0) | happy(X0) [cnf transformation 41]
79. strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 41]
113. ~humble(X0) | curious(X0) [cnf transformation 36]
119. creative(X0) | quiet(X0) [cnf transformation 64]
121. ~curious(X0) | creative(X0) [cnf transformation 64]
132. ~quiet(alice) | ~strong(alice) [cnf transformation 20]
139. ~creative(alice) [cnf transformation 25]
140. humble(X0) | happy(X0) | strong(X0) [duplicate literal removal 77]
141. ~happy(X0) | strong(X0) [duplicate literal removal 79]
142. strong(X0) | humble(X0) [subsumption resolution 140,141]
191. 12 <=> strong(alice) [avatar definition]
193. ~strong(alice) <- (~12) [avatar component clause 191]
288. 33 <=> quiet(alice) [avatar definition]
291. ~12 | ~33 [avatar split clause 132,288,191]
302. quiet(alice) [resolution 119,139]
303. 33 [avatar split clause 302,288]
305. humble(alice) <- (~12) [resolution 142,193]
307. curious(alice) <- (~12) [resolution 305,113]
324. creative(alice) <- (~12) [resolution 307,121]
326. $false <- (~12) [subsumption resolution 324,139]
327. 12 [avatar contradiction clause 326]
328. $false [avatar sat refutation 291,303,327]
% SZS output end Proof for 6625445821957785039132145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not happy is both not brave and happy.
If someone is either not wise or not strong then someone is both strong and funny.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not humble is either not curious or strong.
If someone is not brave or not kind then mary is not patient or kind and vice versa.
Everyone who is not strong is either not funny or not patient.
If someone is old or wise then someone is strong or not old and vice versa.
If someone is both not brave and not wise then susan is not old or not happy and vice versa.
If alice is both not generous and not rich then someone is either not strong or not funny and vice versa.
If john is both not humble and strong then someone is not old.
Everyone who is either not old or humble is not old or not curious.
Everyone who is either curious or funny is either generous or not tall and vice versa.
Everyone who is both not rich and curious is both not strong and generous and vice versa.
Everyone who is happy is rich.
If someone is not brave then john is either not tall or creative and vice versa.
If someone is both not old and not humble then mary is either not wise or not generous.
Someone is not happy.
Someone is not humble.
Mary is not quiet or curious.
John is not generous.
Someone is not generous.
Susan is tall.
Lucy is either not tall or not curious.
Someone is not happy or not curious. | Susan is not happy. | neutral | (![X]:((old(X)&~happy(X))=>(~brave(X)&happy(X))))&
((?[X]:((~wise(X)<~>~strong(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~humble(X)=>(~curious(X)<~>strong(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>((~patient(mary)|kind(mary))))&
(![X]:(~strong(X)=>(~funny(X)<~>~patient(X))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((strong(X)|~old(X)))))&
((?[X]:((~brave(X)&~wise(X))))<=>((~old(susan)|~happy(susan))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~humble(john)&strong(john)))=>(?[X]:(~old(X))))&
(![X]:((~old(X)<~>humble(X))=>(~old(X)|~curious(X))))&
(![X]:((curious(X)<~>funny(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~rich(X)&curious(X))<=>(~strong(X)&generous(X))))&
(![X]:(happy(X)=>rich(X)))&
((?[X]:(~brave(X)))<=>((~tall(john)<~>creative(john))))&
((?[X]:((~old(X)&~humble(X))))=>((~wise(mary)<~>~generous(mary))))&
(?[X]:(~happy(X)))&
(?[X]:(~humble(X)))&
((~quiet(mary)|curious(mary)))&
(~generous(john))&
(?[X]:(~generous(X)))&
(tall(susan))&
((~tall(lucy)<~>~curious(lucy)))&
(?[X]:((~happy(X)|~curious(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is not curious or not strong is either not patient or patient and vice versa. Everyone who is not patient or not quiet is both humble and not happy and vice versa. If paul is not strong or not brave then someone is not funny. Everyone who is both rich and generous is both not curious and quiet. Everyone who is either not wise or patient is not humble and vice versa. Everyone who is both not tall and not happy is not brave or not wise. If susan is both brave and tall then someone is both wise and strong and vice versa. Everyone who is both funny and not strong is funny. Everyone who is both tall and not curious is brave. If someone is either rich or happy then someone is funny or not tall. If someone is both happy and tall then paul is tall or not rich. Everyone who is both rich and not funny is curious. If john is either funny or strong then lucy is either strong or not patient. If susan is calm or wise then someone is not patient or creative and vice versa. If fred is curious then lucy is not creative. If someone is not calm or calm then lucy is not quiet. Susan is calm or not creative. Paul is either not wise or strong. Someone is happy or not patient. Lucy is curious or not tall. Lucy is rich. Someone is either not funny or not happy. Someone is both not funny and wise. Someone is both not generous and humble. | Susan is not strong. | neutral | (![X]:((~curious(X)|~strong(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(humble(X)&~happy(X))))&
(((~strong(paul)|~brave(paul)))=>(?[X]:(~funny(X))))&
(![X]:((rich(X)&generous(X))=>(~curious(X)&quiet(X))))&
(![X]:((~wise(X)<~>patient(X))<=>~humble(X)))&
(![X]:((~tall(X)&~happy(X))=>(~brave(X)|~wise(X))))&
(((brave(susan)&tall(susan)))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((funny(X)&~strong(X))=>funny(X)))&
(![X]:((tall(X)&~curious(X))=>brave(X)))&
((?[X]:((rich(X)<~>happy(X))))=>(?[X]:((funny(X)|~tall(X)))))&
((?[X]:((happy(X)&tall(X))))=>((tall(paul)|~rich(paul))))&
(![X]:((rich(X)&~funny(X))=>curious(X)))&
(((funny(john)<~>strong(john)))=>((strong(lucy)<~>~patient(lucy))))&
(((calm(susan)|wise(susan)))<=>(?[X]:((~patient(X)|creative(X)))))&
((curious(fred))=>(~creative(lucy)))&
((?[X]:((~calm(X)|calm(X))))=>(~quiet(lucy)))&
((calm(susan)|~creative(susan)))&
((~wise(paul)<~>strong(paul)))&
(?[X]:((happy(X)|~patient(X))))&
((curious(lucy)|~tall(lucy)))&
(rich(lucy))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((~generous(X)&humble(X)))) | ~strong(susan) | [] | null | 0 |
If mary is not humble or funny then john is not quiet and vice versa.
If someone is both not humble and not rich then alice is either not old or not calm.
Everyone who is both not quiet and not kind is not rich or generous.
Everyone who is not tall is both kind and not generous.
If someone is curious or creative then someone is quiet and vice versa.
If john is rich then someone is strong or funny and vice versa.
Everyone who is strong or not creative is not wise and vice versa.
Everyone who is both brave and not brave is calm or wise and vice versa.
Everyone who is both not strong and not quiet is not generous and vice versa.
If fred is not happy then mary is not quiet or not tall.
Everyone who is both not happy and not strong is either not patient or not funny.
Everyone who is both quiet and not generous is both not curious and old and vice versa.
Everyone who is either not kind or not funny is strong.
Everyone who is not quiet or old is both brave and tall and vice versa.
Everyone who is both not curious and not generous is both not quiet and not calm.
Everyone who is both not kind and generous is creative or brave.
John is not kind.
Mary is both kind and not wise.
Fred is both generous and humble.
Fred is either generous or kind.
Fred is both happy and not patient.
Someone is generous or patient.
Someone is not funny. | Mary is happy. | neutral | (((~humble(mary)|funny(mary)))<=>(~quiet(john)))&
((?[X]:((~humble(X)&~rich(X))))=>((~old(alice)<~>~calm(alice))))&
(![X]:((~quiet(X)&~kind(X))=>(~rich(X)|generous(X))))&
(![X]:(~tall(X)=>(kind(X)&~generous(X))))&
((?[X]:((curious(X)|creative(X))))<=>(?[X]:(quiet(X))))&
((rich(john))<=>(?[X]:((strong(X)|funny(X)))))&
(![X]:((strong(X)|~creative(X))<=>~wise(X)))&
(![X]:((brave(X)&~brave(X))<=>(calm(X)|wise(X))))&
(![X]:((~strong(X)&~quiet(X))<=>~generous(X)))&
((~happy(fred))=>((~quiet(mary)|~tall(mary))))&
(![X]:((~happy(X)&~strong(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((quiet(X)&~generous(X))<=>(~curious(X)&old(X))))&
(![X]:((~kind(X)<~>~funny(X))=>strong(X)))&
(![X]:((~quiet(X)|old(X))<=>(brave(X)&tall(X))))&
(![X]:((~curious(X)&~generous(X))=>(~quiet(X)&~calm(X))))&
(![X]:((~kind(X)&generous(X))=>(creative(X)|brave(X))))&
(~kind(john))&
((kind(mary)&~wise(mary)))&
((generous(fred)&humble(fred)))&
((generous(fred)<~>kind(fred)))&
((happy(fred)&~patient(fred)))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:(~funny(X))) | happy(mary) | [] | null | 0 |
If someone is generous or not happy then paul is quiet or not quiet.
If someone is not patient or calm then fred is both not wise and humble.
Everyone who is happy is both not generous and not patient.
If susan is not rich or creative then john is both curious and tall and vice versa.
Everyone who is both not old and not humble is not kind or not funny.
If fred is both not funny and generous then susan is either kind or tall.
Everyone who is not humble is not calm or kind and vice versa.
Everyone who is calm is not old or not tall and vice versa.
If someone is both not calm and not kind then paul is both patient and not kind and vice versa.
Everyone who is not curious or happy is both strong and not humble and vice versa.
If someone is both not calm and strong then someone is either not quiet or strong.
Everyone who is both old and calm is both generous and funny.
If lucy is calm or generous then alice is not creative.
If alice is both not kind and not strong then susan is both curious and old and vice versa.
Everyone who is either not curious or not creative is both not tall and not calm.
If someone is not calm then someone is not patient.
Someone is curious or generous.
Someone is not brave.
Susan is both not creative and quiet.
Someone is tall.
Mary is both not humble and not funny.
Someone is not curious.
Alice is not kind or tall.
Someone is both not rich and patient. | Susan is not humble. | entailment | ((?[X]:((generous(X)|~happy(X))))=>((quiet(paul)|~quiet(paul))))&
((?[X]:((~patient(X)|calm(X))))=>((~wise(fred)&humble(fred))))&
(![X]:(happy(X)=>(~generous(X)&~patient(X))))&
(((~rich(susan)|creative(susan)))<=>((curious(john)&tall(john))))&
(![X]:((~old(X)&~humble(X))=>(~kind(X)|~funny(X))))&
(((~funny(fred)&generous(fred)))=>((kind(susan)<~>tall(susan))))&
(![X]:(~humble(X)<=>(~calm(X)|kind(X))))&
(![X]:(calm(X)<=>(~old(X)|~tall(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>((patient(paul)&~kind(paul))))&
(![X]:((~curious(X)|happy(X))<=>(strong(X)&~humble(X))))&
((?[X]:((~calm(X)&strong(X))))=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:((old(X)&calm(X))=>(generous(X)&funny(X))))&
(((calm(lucy)|generous(lucy)))=>(~creative(alice)))&
(((~kind(alice)&~strong(alice)))<=>((curious(susan)&old(susan))))&
(![X]:((~curious(X)<~>~creative(X))=>(~tall(X)&~calm(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~patient(X))))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:(~brave(X)))&
((~creative(susan)&quiet(susan)))&
(?[X]:(tall(X)))&
((~humble(mary)&~funny(mary)))&
(?[X]:(~curious(X)))&
((~kind(alice)|tall(alice)))&
(?[X]:((~rich(X)&patient(X)))) | ~humble(susan) | [
"p6",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8510005625621570282273438
% SZS output start Proof for 8510005625621570282273438
7. ! [X0] : (~humble(X0) <=> (kind(X0) | ~calm(X0))) [input p6]
10. ! [X0] : ((happy(X0) | ~curious(X0)) <=> (~humble(X0) & strong(X0))) [input p9]
15. ! [X0] : ((~curious(X0) <~> ~creative(X0)) => (~calm(X0) & ~tall(X0))) [input p14]
19. quiet(susan) & ~creative(susan) [input p18]
25. humble(susan) [input hypothesis]
42. ! [X0] : ((~calm(X0) & ~tall(X0)) | (~curious(X0) <=> ~creative(X0))) [ennf transformation 15]
47. ! [X0] : ((~humble(X0) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | humble(X0))) [nnf transformation 7]
48. ! [X0] : ((~humble(X0) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | humble(X0))) [flattening 47]
56. ! [X0] : (((happy(X0) | ~curious(X0)) | (humble(X0) | ~strong(X0))) & ((~humble(X0) & strong(X0)) | (~happy(X0) & curious(X0)))) [nnf transformation 10]
57. ! [X0] : ((happy(X0) | ~curious(X0) | humble(X0) | ~strong(X0)) & ((~humble(X0) & strong(X0)) | (~happy(X0) & curious(X0)))) [flattening 56]
64. ! [X0] : ((~calm(X0) & ~tall(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) [nnf transformation 42]
91. ~humble(X0) | calm(X0) [cnf transformation 48]
102. ~humble(X0) | curious(X0) [cnf transformation 57]
118. ~curious(X0) | ~calm(X0) | creative(X0) [cnf transformation 64]
121. ~creative(susan) [cnf transformation 19]
130. humble(susan) [cnf transformation 25]
156. 7 <=> creative(susan) [avatar definition]
157. ~creative(susan) <- (~7) [avatar component clause 156]
233. 23 <=> curious(susan) [avatar definition]
234. curious(susan) <- (23) [avatar component clause 233]
269. ~7 [avatar split clause 121,156]
277. calm(susan) [resolution 91,130]
281. curious(susan) [resolution 102,130]
320. ~calm(susan) | creative(susan) <- (23) [resolution 118,234]
326. creative(susan) <- (23) [subsumption resolution 320,277]
327. $false <- (~7, 23) [subsumption resolution 326,157]
328. 7 | ~23 [avatar contradiction clause 327]
348. 23 [avatar split clause 281,233]
349. $false [avatar sat refutation 269,328,348]
% SZS output end Proof for 8510005625621570282273438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or patient then john is wise or not quiet and vice versa.
Everyone who is both funny and strong is generous.
If someone is both wise and not creative then someone is either funny or not patient and vice versa.
Everyone who is not creative or funny is creative or tall and vice versa.
Everyone who is either old or calm is both not wise and not calm.
Everyone who is either curious or patient is not strong or quiet and vice versa.
Everyone who is funny or not wise is not creative.
Everyone who is both not calm and tall is either brave or not wise.
Everyone who is not creative is either funny or not creative and vice versa.
Everyone who is both strong and not strong is generous or not curious and vice versa.
Everyone who is both calm and not generous is not funny or creative.
Everyone who is creative or wise is humble or tall and vice versa.
If susan is either rich or patient then someone is funny or not tall and vice versa.
Someone is either calm or not calm.
Fred is both humble and rich.
Someone is either old or not humble.
Lucy is not brave or funny.
Someone is both not calm and not happy. | Lucy is not generous. | entailment | ((?[X]:((generous(X)<~>patient(X))))<=>((wise(john)|~quiet(john))))&
(![X]:((funny(X)&strong(X))=>generous(X)))&
((?[X]:((wise(X)&~creative(X))))<=>(?[X]:((funny(X)<~>~patient(X)))))&
(![X]:((~creative(X)|funny(X))<=>(creative(X)|tall(X))))&
(![X]:((old(X)<~>calm(X))=>(~wise(X)&~calm(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~strong(X)|quiet(X))))&
(![X]:((funny(X)|~wise(X))=>~creative(X)))&
(![X]:((~calm(X)&tall(X))=>(brave(X)<~>~wise(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((calm(X)&~generous(X))=>(~funny(X)|creative(X))))&
(![X]:((creative(X)|wise(X))<=>(humble(X)|tall(X))))&
(((rich(susan)<~>patient(susan)))<=>(?[X]:((funny(X)|~tall(X)))))&
(?[X]:((calm(X)<~>~calm(X))))&
((humble(fred)&rich(fred)))&
(?[X]:((old(X)<~>~humble(X))))&
((~brave(lucy)|funny(lucy)))&
(?[X]:((~calm(X)&~happy(X)))) | ~generous(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 63967795572045177608675
% SZS output start Proof for 63967795572045177608675
10. ! [X0] : ((~strong(X0) & strong(X0)) <=> (~curious(X0) | generous(X0))) [input p9]
19. generous(lucy) [input hypothesis]
47. ! [X0] : (((~strong(X0) & strong(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 10]
48. ! [X0] : (((~strong(X0) & strong(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | strong(X0) | ~strong(X0))) [flattening 47]
99. strong(X0) | ~generous(X0) [cnf transformation 48]
101. ~strong(X0) | ~generous(X0) [cnf transformation 48]
122. generous(lucy) [cnf transformation 19]
190. ~generous(X0) [subsumption resolution 99,101]
225. $false [subsumption resolution 122,190]
% SZS output end Proof for 63967795572045177608675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not old is both patient and funny. If someone is either old or brave then susan is rich and vice versa. If lucy is not generous then susan is old and vice versa. Everyone who is not quiet is both patient and not humble and vice versa. Everyone who is not patient or not quiet is quiet or funny and vice versa. If someone is humble then john is kind. If paul is both calm and not rich then someone is both not brave and funny. If paul is kind or rich then alice is not brave or quiet. Everyone who is patient is happy or humble and vice versa. Everyone who is tall or kind is both old and wise. Everyone who is not curious is both creative and not humble. Everyone who is brave or strong is either not curious or not kind. Everyone who is not quiet is both happy and not funny. If john is either not wise or tall then someone is either quiet or not brave. Everyone who is not patient or not humble is both not wise and not generous. If someone is not wise then someone is either not funny or not quiet and vice versa. Mary is kind or not calm. Someone is creative or not generous. Someone is not humble. Someone is creative or not creative. Lucy is either not generous or creative. Someone is either funny or not generous. Lucy is either not funny or strong. | Paul is not rich. | contradiction | (![X]:((~rich(X)|~old(X))=>(patient(X)&funny(X))))&
((?[X]:((old(X)<~>brave(X))))<=>(rich(susan)))&
((~generous(lucy))<=>(old(susan)))&
(![X]:(~quiet(X)<=>(patient(X)&~humble(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(quiet(X)|funny(X))))&
((?[X]:(humble(X)))=>(kind(john)))&
(((calm(paul)&~rich(paul)))=>(?[X]:((~brave(X)&funny(X)))))&
(((kind(paul)|rich(paul)))=>((~brave(alice)|quiet(alice))))&
(![X]:(patient(X)<=>(happy(X)|humble(X))))&
(![X]:((tall(X)|kind(X))=>(old(X)&wise(X))))&
(![X]:(~curious(X)=>(creative(X)&~humble(X))))&
(![X]:((brave(X)|strong(X))=>(~curious(X)<~>~kind(X))))&
(![X]:(~quiet(X)=>(happy(X)&~funny(X))))&
(((~wise(john)<~>tall(john)))=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~humble(X))=>(~wise(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
((kind(mary)|~calm(mary)))&
(?[X]:((creative(X)|~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((creative(X)|~creative(X))))&
((~generous(lucy)<~>creative(lucy)))&
(?[X]:((funny(X)<~>~generous(X))))&
((~funny(lucy)<~>strong(lucy))) | ~rich(paul) | [
"p0",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1703296947270213504435432
% SZS output start Proof for 1703296947270213504435432
1. ! [X0] : ((~old(X0) | ~rich(X0)) => (funny(X0) & patient(X0))) [input p0]
5. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> (funny(X0) | quiet(X0))) [input p4]
13. ! [X0] : (~quiet(X0) => (~funny(X0) & happy(X0))) [input p12]
24. ~rich(paul) [input hypothesis]
28. ! [X0] : ((funny(X0) & patient(X0)) | (old(X0) & rich(X0))) [ennf transformation 1]
35. ! [X0] : ((~funny(X0) & happy(X0)) | quiet(X0)) [ennf transformation 13]
45. ! [X0] : (((~quiet(X0) | ~patient(X0)) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | (quiet(X0) & patient(X0)))) [nnf transformation 5]
46. ! [X0] : ((~quiet(X0) | ~patient(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | (quiet(X0) & patient(X0)))) [flattening 45]
69. patient(X0) | rich(X0) [cnf transformation 28]
83. funny(X0) | quiet(X0) | quiet(X0) [cnf transformation 46]
84. ~quiet(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 46]
103. ~funny(X0) | quiet(X0) [cnf transformation 35]
125. ~rich(paul) [cnf transformation 24]
126. quiet(X0) | funny(X0) [duplicate literal removal 83]
127. ~quiet(X0) | ~patient(X0) [duplicate literal removal 84]
169. 10 <=> rich(paul) [avatar definition]
171. ~rich(paul) <- (~10) [avatar component clause 169]
186. quiet(X0) [subsumption resolution 103,126]
258. ~10 [avatar split clause 125,169]
268. ~patient(X2) [resolution 127,186]
270. rich(X1) [resolution 268,69]
278. $false <- (~10) [resolution 270,171]
279. 10 [avatar contradiction clause 278]
281. $false [avatar sat refutation 258,279]
% SZS output end Proof for 1703296947270213504435432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or rich is not funny and vice versa. If someone is both wise and not patient then john is creative or not generous. If mary is either brave or not tall then alice is either generous or not humble. Everyone who is either not funny or not rich is either not tall or not happy and vice versa. Everyone who is not curious or not rich is not rich or not calm and vice versa. Everyone who is generous is either not quiet or not happy. If someone is either old or not rich then alice is not wise and vice versa. Everyone who is wise or humble is either not calm or not quiet and vice versa. Everyone who is generous is not kind and vice versa. If someone is not kind or creative then lucy is both happy and rich. Everyone who is not quiet or not patient is either patient or humble. Everyone who is not rich or curious is old or not calm. If mary is creative then someone is kind or curious. If alice is either brave or not quiet then fred is either humble or not curious. Everyone who is rich or not old is tall and vice versa. If someone is quiet or tall then someone is not old or not brave and vice versa. John is either not quiet or patient. Fred is both calm and tall. Fred is curious or not creative. Someone is both not calm and not curious. Someone is not curious or wise. Someone is either calm or not funny. Someone is either happy or not calm. | John is tall. | neutral | (![X]:((~wise(X)|rich(X))<=>~funny(X)))&
((?[X]:((wise(X)&~patient(X))))=>((creative(john)|~generous(john))))&
(((brave(mary)<~>~tall(mary)))=>((generous(alice)<~>~humble(alice))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:(generous(X)=>(~quiet(X)<~>~happy(X))))&
((?[X]:((old(X)<~>~rich(X))))<=>(~wise(alice)))&
(![X]:((wise(X)|humble(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>~kind(X)))&
((?[X]:((~kind(X)|creative(X))))=>((happy(lucy)&rich(lucy))))&
(![X]:((~quiet(X)|~patient(X))=>(patient(X)<~>humble(X))))&
(![X]:((~rich(X)|curious(X))=>(old(X)|~calm(X))))&
((creative(mary))=>(?[X]:((kind(X)|curious(X)))))&
(((brave(alice)<~>~quiet(alice)))=>((humble(fred)<~>~curious(fred))))&
(![X]:((rich(X)|~old(X))<=>tall(X)))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:((~old(X)|~brave(X)))))&
((~quiet(john)<~>patient(john)))&
((calm(fred)&tall(fred)))&
((curious(fred)|~creative(fred)))&
(?[X]:((~calm(X)&~curious(X))))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((calm(X)<~>~funny(X))))&
(?[X]:((happy(X)<~>~calm(X)))) | tall(john) | [] | null | 0 |
If someone is brave then john is both not kind and not patient and vice versa.
Everyone who is not brave is both not tall and not old and vice versa.
Everyone who is not strong or not quiet is not happy.
Everyone who is funny is both not patient and generous and vice versa.
Everyone who is not kind or not strong is either not tall or happy and vice versa.
Everyone who is tall is both not strong and not patient and vice versa.
Everyone who is not rich is either not humble or wise and vice versa.
Everyone who is either not wise or calm is old and vice versa.
Everyone who is either not curious or rich is both brave and not funny.
Everyone who is either happy or not creative is both not brave and tall and vice versa.
Everyone who is not patient or not kind is not curious or not calm.
Everyone who is not calm is brave or generous and vice versa.
If someone is either not humble or old then someone is either happy or curious and vice versa.
If someone is not patient then lucy is not happy.
Everyone who is rich or not calm is either not humble or humble and vice versa.
If paul is either not happy or not tall then someone is either old or not tall and vice versa.
John is strong or not tall.
Someone is both not quiet and not wise.
Someone is either patient or humble.
Someone is either calm or not tall.
Mary is not calm or not strong.
Someone is both not old and funny.
Susan is quiet or not patient.
Someone is not creative or quiet. | Paul is not strong. | contradiction | ((?[X]:(brave(X)))<=>((~kind(john)&~patient(john))))&
(![X]:(~brave(X)<=>(~tall(X)&~old(X))))&
(![X]:((~strong(X)|~quiet(X))=>~happy(X)))&
(![X]:(funny(X)<=>(~patient(X)&generous(X))))&
(![X]:((~kind(X)|~strong(X))<=>(~tall(X)<~>happy(X))))&
(![X]:(tall(X)<=>(~strong(X)&~patient(X))))&
(![X]:(~rich(X)<=>(~humble(X)<~>wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>old(X)))&
(![X]:((~curious(X)<~>rich(X))=>(brave(X)&~funny(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&tall(X))))&
(![X]:((~patient(X)|~kind(X))=>(~curious(X)|~calm(X))))&
(![X]:(~calm(X)<=>(brave(X)|generous(X))))&
((?[X]:((~humble(X)<~>old(X))))<=>(?[X]:((happy(X)<~>curious(X)))))&
((?[X]:(~patient(X)))=>(~happy(lucy)))&
(![X]:((rich(X)|~calm(X))<=>(~humble(X)<~>humble(X))))&
(((~happy(paul)<~>~tall(paul)))<=>(?[X]:((old(X)<~>~tall(X)))))&
((strong(john)|~tall(john)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((calm(X)<~>~tall(X))))&
((~calm(mary)|~strong(mary)))&
(?[X]:((~old(X)&funny(X))))&
((quiet(susan)|~patient(susan)))&
(?[X]:((~creative(X)|quiet(X)))) | ~strong(paul) | [
"p2",
"p4",
"p5",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7273891100756740742723706
% SZS output start Proof for 7273891100756740742723706
3. ! [X0] : ((~quiet(X0) | ~strong(X0)) => ~happy(X0)) [input p2]
5. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (~tall(X0) <~> happy(X0))) [input p4]
6. ! [X0] : (tall(X0) <=> (~patient(X0) & ~strong(X0))) [input p5]
16. (~happy(paul) <~> ~tall(paul)) <=> ? [X0] : (old(X0) <~> ~tall(X0)) [input p15]
22. ? [X0] : (funny(X0) & ~old(X0)) [input p21]
25. ~strong(paul) [input hypothesis]
27. ! [X0] : (~happy(X0) | (quiet(X0) & strong(X0))) [ennf transformation 3]
41. ! [X0] : (((~strong(X0) | ~kind(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (strong(X0) & kind(X0)))) [nnf transformation 5]
42. ! [X0] : ((~strong(X0) | ~kind(X0) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) & (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (strong(X0) & kind(X0)))) [flattening 41]
43. ! [X0] : ((tall(X0) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ~tall(X0))) [nnf transformation 6]
44. ! [X0] : ((tall(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ~tall(X0))) [flattening 43]
59. (((tall(paul) | happy(paul)) & (~tall(paul) | ~happy(paul))) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | ((~happy(paul) | tall(paul)) & (~tall(paul) | happy(paul)))) [nnf transformation 16]
60. (((tall(paul) | happy(paul)) & (~tall(paul) | ~happy(paul))) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) | ((~happy(paul) | tall(paul)) & (~tall(paul) | happy(paul)))) [rectify 59]
61. ? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) => ((tall(sK3) | ~old(sK3)) & (~tall(sK3) | old(sK3))) [choice axiom]
62. (((tall(paul) | happy(paul)) & (~tall(paul) | ~happy(paul))) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(sK3) | ~old(sK3)) & (~tall(sK3) | old(sK3))) | ((~happy(paul) | tall(paul)) & (~tall(paul) | happy(paul)))) [skolemisation 60,61]
71. ? [X0] : (funny(X0) & ~old(X0)) => (funny(sK7) & ~old(sK7)) [choice axiom]
72. funny(sK7) & ~old(sK7) [skolemisation 22,71]
81. ~happy(X0) | strong(X0) [cnf transformation 27]
87. happy(X0) | ~tall(X0) | strong(X0) [cnf transformation 42]
92. ~strong(X0) | ~tall(X0) [cnf transformation 44]
140. tall(paul) | happy(paul) | old(X0) | tall(X0) [cnf transformation 62]
149. ~old(sK7) [cnf transformation 72]
153. ~strong(paul) [cnf transformation 25]
175. ~tall(X0) | strong(X0) [subsumption resolution 87,81]
177. ~tall(X0) [subsumption resolution 92,175]
225. happy(paul) | old(X0) | tall(X0) [subsumption resolution 140,177]
226. happy(paul) | old(X0) [subsumption resolution 225,177]
228. 15 <=> ! [X0] : old(X0) [avatar definition]
229. old(X0) <- (15) [avatar component clause 228]
231. 16 <=> happy(paul) [avatar definition]
233. happy(paul) <- (16) [avatar component clause 231]
234. 15 | 16 [avatar split clause 226,231,228]
282. $false <- (15) [resolution 229,149]
283. ~15 [avatar contradiction clause 282]
286. strong(paul) <- (16) [resolution 81,233]
287. $false <- (16) [subsumption resolution 286,153]
288. ~16 [avatar contradiction clause 287]
289. $false [avatar sat refutation 234,283,288]
% SZS output end Proof for 7273891100756740742723706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or wise is either not wise or not old.
If someone is both patient and not patient then mary is either funny or not calm and vice versa.
Everyone who is either not creative or brave is both not tall and happy.
If someone is either funny or not funny then someone is both not happy and brave and vice versa.
If someone is calm then someone is not brave or wise and vice versa.
If alice is brave then someone is both quiet and not creative.
Everyone who is both not rich and not funny is either not rich or rich and vice versa.
Everyone who is both not rich and not humble is both strong and not kind.
If someone is not kind or happy then someone is happy or wise.
Everyone who is both not kind and happy is not strong and vice versa.
Everyone who is not generous or brave is either happy or old and vice versa.
If someone is old then someone is both not creative and not patient and vice versa.
Everyone who is either rich or brave is either not wise or generous.
If someone is both rich and not kind then someone is kind and vice versa.
Everyone who is either not humble or old is tall or strong.
If someone is both not humble and not funny then susan is either not patient or not rich.
Fred is not old or not humble.
Fred is both not calm and not tall.
John is not calm.
Someone is both not humble and not calm.
Someone is creative or not quiet.
Fred is not creative or strong.
Paul is not quiet.
Someone is curious or not kind. | Fred is not kind. | entailment | (![X]:((funny(X)|wise(X))=>(~wise(X)<~>~old(X))))&
((?[X]:((patient(X)&~patient(X))))<=>((funny(mary)<~>~calm(mary))))&
(![X]:((~creative(X)<~>brave(X))=>(~tall(X)&happy(X))))&
((?[X]:((funny(X)<~>~funny(X))))<=>(?[X]:((~happy(X)&brave(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)|wise(X)))))&
((brave(alice))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~rich(X)&~funny(X))<=>(~rich(X)<~>rich(X))))&
(![X]:((~rich(X)&~humble(X))=>(strong(X)&~kind(X))))&
((?[X]:((~kind(X)|happy(X))))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~kind(X)&happy(X))<=>~strong(X)))&
(![X]:((~generous(X)|brave(X))<=>(happy(X)<~>old(X))))&
((?[X]:(old(X)))<=>(?[X]:((~creative(X)&~patient(X)))))&
(![X]:((rich(X)<~>brave(X))=>(~wise(X)<~>generous(X))))&
((?[X]:((rich(X)&~kind(X))))<=>(?[X]:(kind(X))))&
(![X]:((~humble(X)<~>old(X))=>(tall(X)|strong(X))))&
((?[X]:((~humble(X)&~funny(X))))=>((~patient(susan)<~>~rich(susan))))&
((~old(fred)|~humble(fred)))&
((~calm(fred)&~tall(fred)))&
(~calm(john))&
(?[X]:((~humble(X)&~calm(X))))&
(?[X]:((creative(X)|~quiet(X))))&
((~creative(fred)|strong(fred)))&
(~quiet(paul))&
(?[X]:((curious(X)|~kind(X)))) | ~kind(fred) | [
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8260736100508097613334824
% SZS output start Proof for 8260736100508097613334824
7. ! [X0] : ((~funny(X0) & ~rich(X0)) <=> (~rich(X0) <~> rich(X0))) [input p6]
14. ? [X0] : (~kind(X0) & rich(X0)) <=> ? [X0] : kind(X0) [input p13]
25. kind(fred) [input hypothesis]
30. ? [X0] : (~kind(X0) & rich(X0)) <=> ? [X1] : kind(X1) [rectify 14]
63. ! [X0] : (((~funny(X0) & ~rich(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (funny(X0) | rich(X0)))) [nnf transformation 7]
64. ! [X0] : (((~funny(X0) & ~rich(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | funny(X0) | rich(X0))) [flattening 63]
76. (? [X0] : (~kind(X0) & rich(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (kind(X0) | ~rich(X0))) [nnf transformation 30]
77. (? [X0] : (~kind(X0) & rich(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (kind(X3) | ~rich(X3))) [rectify 76]
78. ? [X0] : (~kind(X0) & rich(X0)) => (~kind(sK9) & rich(sK9)) [choice axiom]
79. ? [X2] : kind(X2) => kind(sK10) [choice axiom]
80. ((~kind(sK9) & rich(sK9)) | ! [X1] : ~kind(X1)) & (kind(sK10) | ! [X3] : (kind(X3) | ~rich(X3))) [skolemisation 77,79,78]
115. ~rich(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 64]
137. rich(sK9) | ~kind(X1) [cnf transformation 80]
152. kind(fred) [cnf transformation 25]
156. ~rich(X0) [duplicate literal removal 115]
280. 26 <=> ! [X1] : ~kind(X1) [avatar definition]
281. ~kind(X1) <- (26) [avatar component clause 280]
287. ~kind(X1) [subsumption resolution 137,156]
288. 26 [avatar split clause 287,280]
330. $false <- (26) [resolution 281,152]
331. ~26 [avatar contradiction clause 330]
332. $false [avatar sat refutation 288,331]
% SZS output end Proof for 8260736100508097613334824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or creative is either happy or funny and vice versa. Everyone who is not curious or not brave is not creative or curious and vice versa. If fred is not tall or funny then someone is strong or humble. Everyone who is not quiet or funny is wise or not generous. If lucy is generous then susan is not curious. If someone is both not kind and curious then someone is kind or humble and vice versa. Everyone who is humble is tall or curious. Everyone who is either not old or not quiet is brave or not curious and vice versa. Everyone who is not kind is either not generous or not brave and vice versa. Everyone who is either funny or curious is not funny and vice versa. Everyone who is curious is not humble and vice versa. If someone is tall or not curious then alice is both quiet and not humble and vice versa. Everyone who is both not calm and happy is either calm or not humble. If someone is both kind and quiet then someone is both funny and tall. Everyone who is either not brave or not quiet is both not wise and not funny and vice versa. If someone is both not kind and kind then someone is either generous or creative. Someone is both not generous and kind. Paul is either tall or creative. Alice is humble or not tall. Someone is creative. John is either not tall or not creative. John is curious or brave. Someone is both not tall and not quiet. | John is old. | neutral | (![X]:((tall(X)|creative(X))<=>(happy(X)<~>funny(X))))&
(![X]:((~curious(X)|~brave(X))<=>(~creative(X)|curious(X))))&
(((~tall(fred)|funny(fred)))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:(humble(X)=>(tall(X)|curious(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(brave(X)|~curious(X))))&
(![X]:(~kind(X)<=>(~generous(X)<~>~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>~funny(X)))&
(![X]:(curious(X)<=>~humble(X)))&
((?[X]:((tall(X)|~curious(X))))<=>((quiet(alice)&~humble(alice))))&
(![X]:((~calm(X)&happy(X))=>(calm(X)<~>~humble(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((funny(X)&tall(X)))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((~kind(X)&kind(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
(?[X]:((~generous(X)&kind(X))))&
((tall(paul)<~>creative(paul)))&
((humble(alice)|~tall(alice)))&
(?[X]:(creative(X)))&
((~tall(john)<~>~creative(john)))&
((curious(john)|brave(john)))&
(?[X]:((~tall(X)&~quiet(X)))) | old(john) | [] | null | 0 |
Everyone who is not funny or creative is not quiet or patient and vice versa. Everyone who is kind or rich is both tall and not calm. Everyone who is wise or curious is quiet or happy. Everyone who is both not wise and creative is both not funny and not creative and vice versa. If susan is brave then lucy is calm or not rich and vice versa. Everyone who is funny is both not curious and curious and vice versa. If someone is not strong then someone is humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. Everyone who is creative is calm or not funny. Everyone who is wise is not strong or not rich and vice versa. If someone is patient or not funny then fred is both not generous and patient. Everyone who is both not patient and not tall is calm and vice versa. If someone is both not patient and rich then someone is not curious. Someone is happy. Someone is either brave or not rich. Someone is not quiet or rich. Someone is both not humble and generous. Someone is not quiet. Someone is patient. Someone is not wise or wise. | Susan is not happy. | contradiction | (![X]:((~funny(X)|creative(X))<=>(~quiet(X)|patient(X))))&
(![X]:((kind(X)|rich(X))=>(tall(X)&~calm(X))))&
(![X]:((wise(X)|curious(X))=>(quiet(X)|happy(X))))&
(![X]:((~wise(X)&creative(X))<=>(~funny(X)&~creative(X))))&
((brave(susan))<=>((calm(lucy)|~rich(lucy))))&
(![X]:(funny(X)<=>(~curious(X)&curious(X))))&
((?[X]:(~strong(X)))=>(?[X]:(humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
(![X]:((~patient(X)&~tall(X))<=>calm(X)))&
((?[X]:((~patient(X)&rich(X))))=>(?[X]:(~curious(X))))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|wise(X)))) | ~happy(susan) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4663935583415515943235474
% SZS output start Proof for 4663935583415515943235474
2. ! [X0] : ((rich(X0) | kind(X0)) => (~calm(X0) & tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | tall(X0)) => (wise(X0) & happy(X0))) [input p10]
24. ~happy(susan) [input hypothesis]
27. ! [X0] : ((~calm(X0) & tall(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 2]
32. ! [X0] : ((wise(X0) & happy(X0)) | (kind(X0) & ~tall(X0))) [ennf transformation 11]
81. ~kind(X0) | tall(X0) [cnf transformation 27]
111. ~tall(X0) | happy(X0) [cnf transformation 32]
112. happy(X0) | kind(X0) [cnf transformation 32]
136. ~happy(susan) [cnf transformation 24]
247. kind(susan) [resolution 112,136]
248. tall(susan) [resolution 247,81]
249. happy(susan) [resolution 248,111]
250. $false [subsumption resolution 249,136]
% SZS output end Proof for 4663935583415515943235474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not patient is both calm and generous and vice versa. Everyone who is both not curious and not brave is both not patient and strong. Everyone who is both not kind and not happy is both not strong and not patient and vice versa. Everyone who is both brave and happy is not creative and vice versa. If john is both not strong and kind then someone is either calm or rich and vice versa. Everyone who is both not happy and creative is both not calm and not generous and vice versa. Everyone who is either kind or not tall is not old or not tall and vice versa. Everyone who is both funny and wise is not calm and vice versa. Everyone who is both funny and not wise is calm or old and vice versa. Everyone who is not patient is not humble and vice versa. Everyone who is happy or generous is not curious or not old and vice versa. Everyone who is not quiet or patient is patient and vice versa. If someone is both not brave and kind then paul is not kind or not quiet and vice versa. Everyone who is kind or not calm is curious or not wise. If alice is not patient or wise then fred is either not happy or not generous and vice versa. Everyone who is either brave or not creative is both not quiet and quiet. Someone is not kind. Mary is creative or calm. Someone is not generous. Paul is either not funny or not rich. Someone is not tall or not funny. Mary is not calm. Susan is not creative. Alice is humble. | Susan is not brave. | contradiction | (![X]:((happy(X)<~>~patient(X))<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&~brave(X))=>(~patient(X)&strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)&wise(X))<=>~calm(X)))&
(![X]:((funny(X)&~wise(X))<=>(calm(X)|old(X))))&
(![X]:(~patient(X)<=>~humble(X)))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)|~old(X))))&
(![X]:((~quiet(X)|patient(X))<=>patient(X)))&
((?[X]:((~brave(X)&kind(X))))<=>((~kind(paul)|~quiet(paul))))&
(![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
(![X]:((brave(X)<~>~creative(X))=>(~quiet(X)&quiet(X))))&
(?[X]:(~kind(X)))&
((creative(mary)|calm(mary)))&
(?[X]:(~generous(X)))&
((~funny(paul)<~>~rich(paul)))&
(?[X]:((~tall(X)|~funny(X))))&
(~calm(mary))&
(~creative(susan))&
(humble(alice)) | ~brave(susan) | [
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5984508194478587259125855
% SZS output start Proof for 5984508194478587259125855
4. ! [X0] : ((happy(X0) & brave(X0)) <=> ~creative(X0)) [input p3]
23. ~creative(susan) [input p22]
25. ~brave(susan) [input hypothesis]
35. ! [X0] : (((happy(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | (~happy(X0) | ~brave(X0)))) [nnf transformation 4]
36. ! [X0] : (((happy(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | ~happy(X0) | ~brave(X0))) [flattening 35]
83. creative(X0) | brave(X0) [cnf transformation 36]
142. ~creative(susan) [cnf transformation 23]
144. ~brave(susan) [cnf transformation 25]
244. brave(susan) [resolution 83,142]
245. $false [subsumption resolution 244,144]
% SZS output end Proof for 5984508194478587259125855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is calm then someone is not old or not brave and vice versa. Everyone who is not calm is either not curious or not humble and vice versa. If mary is not rich then someone is curious or not humble. Everyone who is both not rich and old is both wise and patient. Everyone who is not happy or old is both not calm and curious and vice versa. Everyone who is either humble or not generous is old. If someone is both not calm and not quiet then someone is either not wise or not funny. If someone is old or wise then someone is both not curious and not funny and vice versa. Everyone who is not strong is not kind or old. If alice is tall then john is not funny or curious and vice versa. Everyone who is not brave or patient is either not calm or tall. Everyone who is both not happy and not curious is not kind or not funny and vice versa. If fred is not humble then mary is both kind and not old. Everyone who is funny or not wise is not tall and vice versa. If someone is not humble then someone is not old and vice versa. Everyone who is either not calm or generous is both not patient and not creative. Someone is not rich. Someone is either not quiet or funny. Someone is either not creative or not kind. Alice is both strong and not wise. Someone is old or not tall. Someone is either not creative or creative. | Alice is tall. | contradiction | ((calm(mary))<=>(?[X]:((~old(X)|~brave(X)))))&
(![X]:(~calm(X)<=>(~curious(X)<~>~humble(X))))&
((~rich(mary))=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~rich(X)&old(X))=>(wise(X)&patient(X))))&
(![X]:((~happy(X)|old(X))<=>(~calm(X)&curious(X))))&
(![X]:((humble(X)<~>~generous(X))=>old(X)))&
((?[X]:((~calm(X)&~quiet(X))))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~strong(X)=>(~kind(X)|old(X))))&
((tall(alice))<=>((~funny(john)|curious(john))))&
(![X]:((~brave(X)|patient(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)|~funny(X))))&
((~humble(fred))=>((kind(mary)&~old(mary))))&
(![X]:((funny(X)|~wise(X))<=>~tall(X)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~quiet(X)<~>funny(X))))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(alice)&~wise(alice)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~creative(X)<~>creative(X)))) | tall(alice) | [
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1411143420229265315405803
% SZS output start Proof for 1411143420229265315405803
5. ! [X0] : ((old(X0) | ~happy(X0)) <=> (curious(X0) & ~calm(X0))) [input p4]
12. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (~funny(X0) | ~kind(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | funny(X0)) <=> ~tall(X0)) [input p13]
23. tall(alice) [input hypothesis]
44. ! [X0] : (((old(X0) | ~happy(X0)) | (~curious(X0) | calm(X0))) & ((curious(X0) & ~calm(X0)) | (~old(X0) & happy(X0)))) [nnf transformation 5]
45. ! [X0] : ((old(X0) | ~happy(X0) | ~curious(X0) | calm(X0)) & ((curious(X0) & ~calm(X0)) | (~old(X0) & happy(X0)))) [flattening 44]
59. ! [X0] : (((~curious(X0) & ~happy(X0)) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 12]
60. ! [X0] : (((~curious(X0) & ~happy(X0)) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | curious(X0) | happy(X0))) [flattening 59]
61. ! [X0] : (((~wise(X0) | funny(X0)) | tall(X0)) & (~tall(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 14]
62. ! [X0] : ((~wise(X0) | funny(X0) | tall(X0)) & (~tall(X0) | (wise(X0) & ~funny(X0)))) [flattening 61]
94. happy(X0) | curious(X0) [cnf transformation 45]
115. ~happy(X0) | funny(X0) [cnf transformation 60]
117. ~curious(X0) | funny(X0) [cnf transformation 60]
120. ~tall(X0) | ~funny(X0) [cnf transformation 62]
138. tall(alice) [cnf transformation 23]
221. 20 <=> tall(alice) [avatar definition]
223. tall(alice) <- (20) [avatar component clause 221]
287. 20 [avatar split clause 138,221]
303. funny(X0) | curious(X0) [resolution 115,94]
304. funny(X0) [subsumption resolution 303,117]
317. ~funny(alice) <- (20) [resolution 120,223]
318. $false <- (20) [subsumption resolution 317,304]
319. ~20 [avatar contradiction clause 318]
320. $false [avatar sat refutation 287,319]
% SZS output end Proof for 1411143420229265315405803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and wise is not happy and vice versa.
Everyone who is brave or generous is not wise or kind and vice versa.
Everyone who is patient is not curious or strong.
Everyone who is either not funny or creative is either kind or not kind and vice versa.
If mary is old then someone is both not wise and brave.
Everyone who is both not tall and calm is both generous and not calm.
Everyone who is either happy or kind is strong or kind and vice versa.
If fred is both wise and not tall then someone is either not generous or kind and vice versa.
If alice is either not creative or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Everyone who is either not brave or calm is either rich or not funny.
If paul is both funny and not old then someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise.
Paul is both old and calm.
Someone is rich.
Lucy is both calm and wise.
Paul is both not kind and quiet.
Fred is either quiet or rich. | Paul is happy. | entailment | (![X]:((quiet(X)&wise(X))<=>~happy(X)))&
(![X]:((brave(X)|generous(X))<=>(~wise(X)|kind(X))))&
(![X]:(patient(X)=>(~curious(X)|strong(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(kind(X)<~>~kind(X))))&
((old(mary))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((~tall(X)&calm(X))=>(generous(X)&~calm(X))))&
(![X]:((happy(X)<~>kind(X))<=>(strong(X)|kind(X))))&
(((wise(fred)&~tall(fred)))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(((~creative(alice)<~>brave(alice)))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>calm(X))=>(rich(X)<~>~funny(X))))&
(((funny(paul)&~old(paul)))=>(?[X]:((curious(X)|~calm(X)))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X)))&
((calm(lucy)&wise(lucy)))&
((~kind(paul)&quiet(paul)))&
((quiet(fred)<~>rich(fred))) | happy(paul) | [
"p0",
"p1",
"p5",
"p7",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3022266495384614930433721
% SZS output start Proof for 3022266495384614930433721
1. ! [X0] : ((wise(X0) & quiet(X0)) <=> ~happy(X0)) [input p0]
2. ! [X0] : ((generous(X0) | brave(X0)) <=> (kind(X0) | ~wise(X0))) [input p1]
6. ! [X0] : ((calm(X0) & ~tall(X0)) => (~calm(X0) & generous(X0))) [input p5]
8. (~tall(fred) & wise(fred)) <=> ? [X0] : (~generous(X0) <~> kind(X0)) [input p7]
12. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p11]
23. quiet(paul) & ~kind(paul) [input p22]
25. ~happy(paul) [input hypothesis]
29. ! [X0] : ((~calm(X0) & generous(X0)) | (~calm(X0) | tall(X0))) [ennf transformation 6]
30. ! [X0] : ((~calm(X0) & generous(X0)) | ~calm(X0) | tall(X0)) [flattening 29]
39. ! [X0] : (((wise(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | (~wise(X0) | ~quiet(X0)))) [nnf transformation 1]
40. ! [X0] : (((wise(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | ~wise(X0) | ~quiet(X0))) [flattening 39]
41. ! [X0] : (((generous(X0) | brave(X0)) | (~kind(X0) & wise(X0))) & ((kind(X0) | ~wise(X0)) | (~generous(X0) & ~brave(X0)))) [nnf transformation 2]
42. ! [X0] : ((generous(X0) | brave(X0) | (~kind(X0) & wise(X0))) & (kind(X0) | ~wise(X0) | (~generous(X0) & ~brave(X0)))) [flattening 41]
48. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X0] : ((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (tall(fred) | ~wise(fred))) [nnf transformation 8]
49. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X0] : ((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | tall(fred) | ~wise(fred)) [flattening 48]
50. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X1] : ((~kind(X1) | generous(X1)) & (kind(X1) | ~generous(X1))) | tall(fred) | ~wise(fred)) [rectify 49]
51. ? [X1] : ((~kind(X1) | generous(X1)) & (kind(X1) | ~generous(X1))) => ((~kind(sK1) | generous(sK1)) & (kind(sK1) | ~generous(sK1))) [choice axiom]
52. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(sK1) | generous(sK1)) & (kind(sK1) | ~generous(sK1))) | tall(fred) | ~wise(fred)) [skolemisation 50,51]
57. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 12]
58. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 57]
77. happy(X0) | wise(X0) [cnf transformation 40]
79. ~generous(X0) | ~wise(X0) | kind(X0) [cnf transformation 42]
94. ~calm(X0) | ~calm(X0) | tall(X0) [cnf transformation 30]
103. wise(fred) | kind(X0) | generous(X0) [cnf transformation 52]
105. ~tall(fred) | kind(X0) | generous(X0) [cnf transformation 52]
123. ~wise(X0) | calm(X0) [cnf transformation 58]
147. ~kind(paul) [cnf transformation 23]
151. ~happy(paul) [cnf transformation 25]
154. ~calm(X0) | tall(X0) [duplicate literal removal 94]
180. 5 <=> tall(fred) [avatar definition]
182. ~tall(fred) <- (~5) [avatar component clause 180]
185. 6 <=> ! [X0] : (kind(X0) | generous(X0)) [avatar definition]
186. kind(X0) | generous(X0) <- (6) [avatar component clause 185]
187. 6 | ~5 [avatar split clause 105,180,185]
189. 7 <=> wise(fred) [avatar definition]
191. wise(fred) <- (7) [avatar component clause 189]
193. 6 | 7 [avatar split clause 103,189,185]
309. wise(paul) [resolution 77,151]
322. generous(paul) <- (6) [resolution 186,147]
329. ~wise(paul) | kind(paul) <- (6) [resolution 79,322]
331. kind(paul) <- (6) [subsumption resolution 329,309]
332. $false <- (6) [subsumption resolution 331,147]
333. ~6 [avatar contradiction clause 332]
341. calm(fred) <- (7) [resolution 191,123]
375. tall(fred) <- (7) [resolution 341,154]
376. $false <- (~5, 7) [subsumption resolution 375,182]
377. 5 | ~7 [avatar contradiction clause 376]
378. $false [avatar sat refutation 187,193,333,377]
% SZS output end Proof for 3022266495384614930433721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or generous then mary is brave or not brave and vice versa.
Everyone who is either not brave or not creative is either wise or rich and vice versa.
Everyone who is not wise is happy or not creative and vice versa.
Everyone who is brave is not calm or rich and vice versa.
Everyone who is not creative or not brave is wise or funny and vice versa.
If fred is not quiet then paul is rich and vice versa.
Everyone who is patient or not funny is curious.
Everyone who is both not tall and not creative is both brave and happy.
Everyone who is both humble and kind is not happy and vice versa.
Everyone who is brave is rich or not wise and vice versa.
Everyone who is creative is creative or not quiet.
Everyone who is not brave is both not calm and calm and vice versa.
Everyone who is not old is both brave and not funny and vice versa.
Everyone who is either not patient or kind is both not funny and quiet and vice versa.
Everyone who is either old or not rich is both generous and not kind.
Everyone who is either not funny or kind is both strong and old.
Someone is not calm or not rich.
Someone is calm or not quiet.
Mary is either quiet or not funny. | Paul is creative. | contradiction | ((?[X]:((~generous(X)<~>generous(X))))<=>((brave(mary)|~brave(mary))))&
(![X]:((~brave(X)<~>~creative(X))<=>(wise(X)<~>rich(X))))&
(![X]:(~wise(X)<=>(happy(X)|~creative(X))))&
(![X]:(brave(X)<=>(~calm(X)|rich(X))))&
(![X]:((~creative(X)|~brave(X))<=>(wise(X)|funny(X))))&
((~quiet(fred))<=>(rich(paul)))&
(![X]:((patient(X)|~funny(X))=>curious(X)))&
(![X]:((~tall(X)&~creative(X))=>(brave(X)&happy(X))))&
(![X]:((humble(X)&kind(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(rich(X)|~wise(X))))&
(![X]:(creative(X)=>(creative(X)|~quiet(X))))&
(![X]:(~brave(X)<=>(~calm(X)&calm(X))))&
(![X]:(~old(X)<=>(brave(X)&~funny(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((old(X)<~>~rich(X))=>(generous(X)&~kind(X))))&
(![X]:((~funny(X)<~>kind(X))=>(strong(X)&old(X))))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:((calm(X)|~quiet(X))))&
((quiet(mary)<~>~funny(mary))) | creative(paul) | [
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6814486047276155431721629
% SZS output start Proof for 6814486047276155431721629
2. ! [X0] : ((~brave(X0) <~> ~creative(X0)) <=> (wise(X0) <~> rich(X0))) [input p1]
3. ! [X0] : (~wise(X0) <=> (~creative(X0) | happy(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (rich(X0) | ~calm(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (funny(X0) | wise(X0))) [input p4]
12. ! [X0] : (~brave(X0) <=> (calm(X0) & ~calm(X0))) [input p11]
13. ! [X0] : (~old(X0) <=> (~funny(X0) & brave(X0))) [input p12]
15. ! [X0] : ((old(X0) <~> ~rich(X0)) => (~kind(X0) & generous(X0))) [input p14]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) => (old(X0) & strong(X0))) [input p15]
20. creative(paul) [input hypothesis]
21. ! [X0] : ((~funny(X0) <~> kind(X0)) => old(X0)) [pure predicate removal 16]
26. ! [X0] : ((~kind(X0) & generous(X0)) | (old(X0) <=> ~rich(X0))) [ennf transformation 15]
27. ! [X0] : (old(X0) | (~funny(X0) <=> kind(X0))) [ennf transformation 21]
33. ! [X0] : ((((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0)))) & (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))))) [nnf transformation 2]
34. ! [X0] : ((~wise(X0) | (creative(X0) & ~happy(X0))) & ((~creative(X0) | happy(X0)) | wise(X0))) [nnf transformation 3]
35. ! [X0] : ((~wise(X0) | (creative(X0) & ~happy(X0))) & (~creative(X0) | happy(X0) | wise(X0))) [flattening 34]
36. ! [X0] : ((brave(X0) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 4]
37. ! [X0] : ((brave(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~brave(X0))) [flattening 36]
38. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 5]
39. ! [X0] : ((~brave(X0) | ~creative(X0) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | (brave(X0) & creative(X0)))) [flattening 38]
45. ! [X0] : ((~brave(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | brave(X0))) [nnf transformation 12]
46. ! [X0] : ((~brave(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | brave(X0))) [flattening 45]
47. ! [X0] : ((~old(X0) | (funny(X0) | ~brave(X0))) & ((~funny(X0) & brave(X0)) | old(X0))) [nnf transformation 13]
48. ! [X0] : ((~old(X0) | funny(X0) | ~brave(X0)) & ((~funny(X0) & brave(X0)) | old(X0))) [flattening 47]
51. ! [X0] : ((~kind(X0) & generous(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0)))) [nnf transformation 26]
52. ! [X0] : (old(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 27]
65. ~brave(X0) | wise(X0) | rich(X0) | creative(X0) [cnf transformation 33]
69. ~rich(X0) | ~brave(X0) | wise(X0) | ~creative(X0) [cnf transformation 33]
74. ~wise(X0) | creative(X0) [cnf transformation 35]
76. calm(X0) | brave(X0) [cnf transformation 37]
80. ~brave(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 39]
81. ~funny(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
91. ~calm(X0) | brave(X0) [cnf transformation 46]
95. ~funny(X0) | old(X0) [cnf transformation 48]
96. ~old(X0) | funny(X0) | ~brave(X0) [cnf transformation 48]
106. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 51]
107. old(X0) | kind(X0) | funny(X0) [cnf transformation 52]
113. creative(paul) [cnf transformation 20]
116. ~wise(X0) | ~brave(X0) [subsumption resolution 80,74]
128. brave(X0) [subsumption resolution 91,76]
129. ~old(X0) | funny(X0) [subsumption resolution 96,128]
130. old(X0) | kind(X0) [subsumption resolution 107,95]
163. kind(X0) | funny(X0) [resolution 130,129]
167. 9 <=> wise(paul) [avatar definition]
168. ~wise(paul) <- (~9) [avatar component clause 167]
169. wise(paul) <- (9) [avatar component clause 167]
185. ~brave(paul) <- (9) [resolution 169,116]
187. $false <- (9) [subsumption resolution 185,128]
188. ~9 [avatar contradiction clause 187]
239. old(X0) | rich(X0) | funny(X0) [resolution 106,163]
242. old(X0) | rich(X0) [subsumption resolution 239,95]
247. funny(X2) | rich(X2) [resolution 242,129]
248. wise(X0) | rich(X0) | creative(X0) [resolution 65,128]
249. rich(X0) | creative(X0) [subsumption resolution 248,74]
284. rich(X1) | ~creative(X1) | ~brave(X1) [resolution 247,81]
287. rich(X1) | ~creative(X1) [subsumption resolution 284,128]
288. rich(X1) [subsumption resolution 287,249]
294. ~brave(X1) | wise(X1) | ~creative(X1) [resolution 288,69]
299. ~creative(X1) | wise(X1) [subsumption resolution 294,128]
300. wise(paul) [resolution 299,113]
302. $false <- (~9) [subsumption resolution 300,168]
303. 9 [avatar contradiction clause 302]
306. $false [avatar sat refutation 188,303]
% SZS output end Proof for 6814486047276155431721629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not curious is not quiet and vice versa.
If someone is not calm then someone is either not funny or calm and vice versa.
Everyone who is either quiet or rich is not wise and vice versa.
Everyone who is calm is not humble or not tall and vice versa.
If susan is not rich or not funny then fred is not calm.
Everyone who is brave is kind and vice versa.
If alice is both happy and not quiet then alice is not tall or not brave and vice versa.
Everyone who is not rich is not creative.
Everyone who is not quiet or kind is either not creative or kind and vice versa.
If someone is not funny or not old then susan is either calm or not kind.
Everyone who is either funny or not creative is both not rich and humble.
If someone is rich then someone is not strong and vice versa.
Everyone who is either not humble or creative is either calm or not wise and vice versa.
Everyone who is not creative or strong is not creative and vice versa.
Fred is humble or not humble.
Someone is either not wise or not kind.
Someone is creative.
John is either not old or not happy.
Susan is either curious or not funny. | Fred is not kind. | contradiction | (![X]:((kind(X)&~curious(X))<=>~quiet(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(~humble(X)|~tall(X))))&
(((~rich(susan)|~funny(susan)))=>(~calm(fred)))&
(![X]:(brave(X)<=>kind(X)))&
(((happy(alice)&~quiet(alice)))<=>((~tall(alice)|~brave(alice))))&
(![X]:(~rich(X)=>~creative(X)))&
(![X]:((~quiet(X)|kind(X))<=>(~creative(X)<~>kind(X))))&
((?[X]:((~funny(X)|~old(X))))=>((calm(susan)<~>~kind(susan))))&
(![X]:((funny(X)<~>~creative(X))=>(~rich(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(calm(X)<~>~wise(X))))&
(![X]:((~creative(X)|strong(X))<=>~creative(X)))&
((humble(fred)|~humble(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:(creative(X)))&
((~old(john)<~>~happy(john)))&
((curious(susan)<~>~funny(susan))) | ~kind(fred) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2558801087986546165221015
% SZS output start Proof for 2558801087986546165221015
1. ! [X0] : ((~curious(X0) & kind(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : (calm(X0) <=> (~tall(X0) | ~humble(X0))) [input p3]
5. (~funny(susan) | ~rich(susan)) => ~calm(fred) [input p4]
8. ! [X0] : (~rich(X0) => ~creative(X0)) [input p7]
9. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (~creative(X0) <~> kind(X0))) [input p8]
11. ! [X0] : ((funny(X0) <~> ~creative(X0)) => (humble(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((~humble(X0) <~> creative(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p12]
20. ~kind(fred) [input hypothesis]
23. ~calm(fred) | (funny(susan) & rich(susan)) [ennf transformation 5]
24. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 8]
26. ! [X0] : ((humble(X0) & ~rich(X0)) | (funny(X0) <=> ~creative(X0))) [ennf transformation 11]
27. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | (curious(X0) | ~kind(X0)))) [nnf transformation 1]
28. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | curious(X0) | ~kind(X0))) [flattening 27]
34. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 3]
35. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ~calm(X0))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ~calm(X0))) [flattening 35]
40. ! [X0] : (((kind(X0) | ~quiet(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [nnf transformation 9]
41. ! [X0] : ((kind(X0) | ~quiet(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [flattening 40]
43. ! [X0] : ((humble(X0) & ~rich(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) [nnf transformation 26]
49. ! [X0] : ((((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))))) [nnf transformation 13]
60. quiet(X0) | kind(X0) [cnf transformation 28]
69. ~rich(X0) | ~quiet(X0) | wise(X0) [cnf transformation 34]
71. humble(X0) | calm(X0) [cnf transformation 36]
74. ~calm(fred) | funny(susan) [cnf transformation 23]
82. ~creative(X0) | rich(X0) [cnf transformation 24]
86. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 41]
87. kind(X0) | ~quiet(X0) | kind(X0) | creative(X0) [cnf transformation 41]
93. ~rich(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 43]
100. ~wise(X0) | calm(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 49]
105. ~creative(X0) | humble(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 49]
118. ~kind(fred) [cnf transformation 20]
119. ~kind(X0) | creative(X0) [duplicate literal removal 86]
120. kind(X0) | ~quiet(X0) | creative(X0) [duplicate literal removal 87]
147. 7 <=> funny(susan) [avatar definition]
149. funny(susan) <- (7) [avatar component clause 147]
151. 8 <=> calm(fred) [avatar definition]
153. ~calm(fred) <- (~8) [avatar component clause 151]
154. 7 | ~8 [avatar split clause 74,151,147]
181. creative(X0) | kind(X0) [subsumption resolution 120,60]
182. creative(X0) [subsumption resolution 119,181]
202. ~rich(X0) | ~funny(X0) [subsumption resolution 93,182]
219. humble(X0) | ~wise(X0) | ~calm(X0) [subsumption resolution 105,182]
220. ~wise(X0) | humble(X0) [subsumption resolution 219,71]
222. ~wise(X0) | calm(X0) | ~humble(X0) [subsumption resolution 100,182]
223. ~wise(X0) | calm(X0) [subsumption resolution 222,220]
255. rich(X0) [resolution 82,182]
258. ~funny(X0) [resolution 202,255]
273. ~quiet(X0) | wise(X0) [resolution 69,255]
299. wise(X0) | kind(X0) [resolution 273,60]
303. calm(X2) | kind(X2) [resolution 299,223]
306. kind(fred) <- (~8) [resolution 303,153]
312. $false <- (~8) [subsumption resolution 306,118]
313. 8 [avatar contradiction clause 312]
314. $false <- (7) [subsumption resolution 149,258]
315. ~7 [avatar contradiction clause 314]
316. $false [avatar sat refutation 154,313,315]
% SZS output end Proof for 2558801087986546165221015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and brave is humble and vice versa.
Everyone who is both calm and not tall is both not strong and generous and vice versa.
Everyone who is either not kind or wise is not generous or generous.
If paul is not wise or not rich then someone is not generous or not kind.
Everyone who is both not quiet and kind is either generous or not old and vice versa.
Everyone who is old is both not wise and strong and vice versa.
Everyone who is both humble and strong is not strong or not creative.
If john is calm then susan is either rich or not humble.
Everyone who is both brave and not strong is not rich and vice versa.
Everyone who is either happy or not humble is both not strong and brave.
If mary is not strong or not old then susan is rich or not wise and vice versa.
Everyone who is not old is not wise or rich.
If susan is not creative or patient then someone is not happy.
If someone is generous then someone is strong or not creative and vice versa.
Everyone who is either not tall or not calm is both not humble and humble.
If someone is not calm then someone is not creative and vice versa.
Someone is not kind or kind.
Someone is not quiet or not tall.
Susan is both brave and curious.
Someone is generous.
Alice is not rich.
John is humble or not rich.
Someone is either not humble or strong.
Susan is either not wise or wise. | Paul is wise. | neutral | (![X]:((tall(X)&brave(X))<=>humble(X)))&
(![X]:((calm(X)&~tall(X))<=>(~strong(X)&generous(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~generous(X)|generous(X))))&
(((~wise(paul)|~rich(paul)))=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)<=>(~wise(X)&strong(X))))&
(![X]:((humble(X)&strong(X))=>(~strong(X)|~creative(X))))&
((calm(john))=>((rich(susan)<~>~humble(susan))))&
(![X]:((brave(X)&~strong(X))<=>~rich(X)))&
(![X]:((happy(X)<~>~humble(X))=>(~strong(X)&brave(X))))&
(((~strong(mary)|~old(mary)))<=>((rich(susan)|~wise(susan))))&
(![X]:(~old(X)=>(~wise(X)|rich(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:(~happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((~tall(X)<~>~calm(X))=>(~humble(X)&humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~creative(X))))&
(?[X]:((~kind(X)|kind(X))))&
(?[X]:((~quiet(X)|~tall(X))))&
((brave(susan)&curious(susan)))&
(?[X]:(generous(X)))&
(~rich(alice))&
((humble(john)|~rich(john)))&
(?[X]:((~humble(X)<~>strong(X))))&
((~wise(susan)<~>wise(susan))) | wise(paul) | [] | null | 0 |
If someone is not calm then fred is not curious or strong and vice versa.
If john is both old and rich then someone is both not wise and not kind.
Everyone who is not brave is either not patient or tall and vice versa.
Everyone who is not strong is either rich or not old and vice versa.
If john is both not curious and not humble then someone is not humble and vice versa.
Everyone who is not patient or not creative is either not calm or not happy.
If someone is patient then someone is either not happy or not calm and vice versa.
Everyone who is not calm or kind is either not calm or not wise and vice versa.
Everyone who is both strong and not generous is both rich and generous.
Everyone who is not rich or not generous is both not calm and generous.
Everyone who is not humble is both kind and tall.
If someone is both kind and not old then someone is rich or tall.
Everyone who is not brave or generous is both not wise and not funny and vice versa.
Everyone who is not funny is not strong or not humble and vice versa.
If someone is not quiet then someone is happy.
Someone is humble.
Lucy is not humble.
Someone is either not strong or brave.
Someone is both not wise and humble.
Someone is not creative or strong. | Lucy is not calm. | contradiction | ((?[X]:(~calm(X)))<=>((~curious(fred)|strong(fred))))&
(((old(john)&rich(john)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(~brave(X)<=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~creative(X)|strong(X)))) | ~calm(lucy) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4253462877869147318168189
% SZS output start Proof for 4253462877869147318168189
8. ! [X0] : ((kind(X0) | ~calm(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p7]
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (generous(X0) & ~calm(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (~funny(X0) & ~wise(X0))) [input p12]
21. ~calm(lucy) [input hypothesis]
31. ! [X0] : ((generous(X0) & ~calm(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
54. ! [X0] : (((kind(X0) | ~calm(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | ~calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [flattening 54]
59. ! [X0] : (((generous(X0) | ~brave(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [nnf transformation 13]
60. ! [X0] : ((generous(X0) | ~brave(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [flattening 59]
98. wise(X0) | calm(X0) | calm(X0) [cnf transformation 55]
107. generous(X0) | generous(X0) [cnf transformation 31]
112. ~wise(X0) | ~generous(X0) [cnf transformation 60]
126. ~calm(lucy) [cnf transformation 21]
127. generous(X0) [duplicate literal removal 107]
129. wise(X0) | calm(X0) [duplicate literal removal 98]
146. 4 <=> ! [X1] : calm(X1) [avatar definition]
147. calm(X1) <- (4) [avatar component clause 146]
223. ~wise(X0) [subsumption resolution 112,127]
252. calm(X0) [resolution 129,223]
253. 4 [avatar split clause 252,146]
254. $false <- (4) [resolution 147,126]
258. ~4 [avatar contradiction clause 254]
259. $false [avatar sat refutation 253,258]
% SZS output end Proof for 4253462877869147318168189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or calm then someone is either not brave or not curious.
If someone is not wise then mary is either brave or not wise and vice versa.
Everyone who is both not curious and not humble is calm and vice versa.
Everyone who is brave is not brave.
If someone is happy then someone is not strong or not happy.
Everyone who is not kind is not wise or not calm and vice versa.
Everyone who is either old or tall is both not quiet and not funny.
If susan is both not kind and funny then someone is not humble and vice versa.
If john is either happy or not humble then susan is both curious and not wise.
If susan is both quiet and not old then alice is not kind or wise.
Everyone who is either wise or not tall is kind and vice versa.
Everyone who is both quiet and not generous is both not quiet and humble and vice versa.
Everyone who is both wise and not curious is both brave and patient.
If someone is both not creative and not brave then paul is both not quiet and not old and vice versa.
If alice is happy or tall then someone is not quiet or strong and vice versa.
If lucy is both not strong and not patient then someone is both curious and not brave and vice versa.
Susan is both not funny and humble.
Lucy is old or creative.
John is either not brave or not rich.
Someone is wise or not funny.
Fred is not tall. | Susan is not generous. | contradiction | ((?[X]:((~humble(X)|calm(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:(~wise(X)))<=>((brave(mary)<~>~wise(mary))))&
(![X]:((~curious(X)&~humble(X))<=>calm(X)))&
(![X]:(brave(X)=>~brave(X)))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(~kind(X)<=>(~wise(X)|~calm(X))))&
(![X]:((old(X)<~>tall(X))=>(~quiet(X)&~funny(X))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:(~humble(X))))&
(((happy(john)<~>~humble(john)))=>((curious(susan)&~wise(susan))))&
(((quiet(susan)&~old(susan)))=>((~kind(alice)|wise(alice))))&
(![X]:((wise(X)<~>~tall(X))<=>kind(X)))&
(![X]:((quiet(X)&~generous(X))<=>(~quiet(X)&humble(X))))&
(![X]:((wise(X)&~curious(X))=>(brave(X)&patient(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>((~quiet(paul)&~old(paul))))&
(((happy(alice)|tall(alice)))<=>(?[X]:((~quiet(X)|strong(X)))))&
(((~strong(lucy)&~patient(lucy)))<=>(?[X]:((curious(X)&~brave(X)))))&
((~funny(susan)&humble(susan)))&
((old(lucy)|creative(lucy)))&
((~brave(john)<~>~rich(john)))&
(?[X]:((wise(X)|~funny(X))))&
(~tall(fred)) | ~generous(susan) | [
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6373329595087394890758078
% SZS output start Proof for 6373329595087394890758078
8. (funny(susan) & ~kind(susan)) <=> ? [X0] : ~humble(X0) [input p7]
12. ! [X0] : ((~generous(X0) & quiet(X0)) <=> (humble(X0) & ~quiet(X0))) [input p11]
17. humble(susan) & ~funny(susan) [input p16]
22. ~generous(susan) [input hypothesis]
50. ((funny(susan) & ~kind(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (~funny(susan) | kind(susan))) [nnf transformation 8]
51. ((funny(susan) & ~kind(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ~funny(susan) | kind(susan)) [flattening 50]
52. ((funny(susan) & ~kind(susan)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ~funny(susan) | kind(susan)) [rectify 51]
53. ? [X1] : ~humble(X1) => ~humble(sK3) [choice axiom]
54. ((funny(susan) & ~kind(susan)) | ! [X0] : humble(X0)) & (~humble(sK3) | ~funny(susan) | kind(susan)) [skolemisation 52,53]
57. ! [X0] : (((~generous(X0) & quiet(X0)) | (~humble(X0) | quiet(X0))) & ((humble(X0) & ~quiet(X0)) | (generous(X0) | ~quiet(X0)))) [nnf transformation 12]
58. ! [X0] : (((~generous(X0) & quiet(X0)) | ~humble(X0) | quiet(X0)) & ((humble(X0) & ~quiet(X0)) | generous(X0) | ~quiet(X0))) [flattening 57]
99. funny(susan) | humble(X0) [cnf transformation 54]
109. ~quiet(X0) | generous(X0) | ~quiet(X0) [cnf transformation 58]
111. quiet(X0) | ~humble(X0) | quiet(X0) [cnf transformation 58]
127. ~funny(susan) [cnf transformation 17]
134. ~generous(susan) [cnf transformation 22]
135. ~quiet(X0) | generous(X0) [duplicate literal removal 109]
136. ~humble(X0) | quiet(X0) [duplicate literal removal 111]
151. 4 <=> ! [X1] : humble(X1) [avatar definition]
152. humble(X1) <- (4) [avatar component clause 151]
188. 12 <=> funny(susan) [avatar definition]
191. 4 | 12 [avatar split clause 99,188,151]
258. 26 <=> ! [X0] : quiet(X0) [avatar definition]
259. quiet(X0) <- (26) [avatar component clause 258]
291. ~12 [avatar split clause 127,188]
318. quiet(X0) <- (4) [resolution 136,152]
320. 26 | ~4 [avatar split clause 318,151,258]
323. generous(X0) <- (26) [resolution 259,135]
332. $false <- (26) [resolution 323,134]
333. ~26 [avatar contradiction clause 332]
334. $false [avatar sat refutation 191,291,320,333]
% SZS output end Proof for 6373329595087394890758078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not humble then someone is happy or curious.
Everyone who is not happy is not rich.
If mary is either not kind or not old then alice is not brave and vice versa.
Everyone who is not funny is not old.
Everyone who is both not patient and humble is both not tall and not creative.
If john is both not tall and patient then john is both not creative and quiet and vice versa.
If john is both patient and not wise then alice is both not creative and not rich.
If someone is either not creative or creative then john is either not tall or not curious and vice versa.
Everyone who is not funny is either not quiet or not funny.
If someone is not quiet then someone is either patient or not curious and vice versa.
Everyone who is brave or not old is both happy and not generous.
If someone is both not rich and brave then fred is both not calm and strong.
If mary is not happy or not old then someone is either tall or not generous and vice versa.
Everyone who is both brave and curious is either generous or not calm and vice versa.
Everyone who is curious is wise or not curious.
Everyone who is wise is either not rich or not wise.
Mary is not funny.
Someone is either happy or brave.
Susan is tall.
Paul is brave or generous.
Someone is not rich.
Someone is curious or not kind.
Someone is both old and generous.
Someone is not wise or not strong. | Paul is not creative. | neutral | ((?[X]:((funny(X)&~humble(X))))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
(((~kind(mary)<~>~old(mary)))<=>(~brave(alice)))&
(![X]:(~funny(X)=>~old(X)))&
(![X]:((~patient(X)&humble(X))=>(~tall(X)&~creative(X))))&
(((~tall(john)&patient(john)))<=>((~creative(john)&quiet(john))))&
(((patient(john)&~wise(john)))=>((~creative(alice)&~rich(alice))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((~tall(john)<~>~curious(john))))&
(![X]:(~funny(X)=>(~quiet(X)<~>~funny(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((brave(X)|~old(X))=>(happy(X)&~generous(X))))&
((?[X]:((~rich(X)&brave(X))))=>((~calm(fred)&strong(fred))))&
(((~happy(mary)|~old(mary)))<=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((brave(X)&curious(X))<=>(generous(X)<~>~calm(X))))&
(![X]:(curious(X)=>(wise(X)|~curious(X))))&
(![X]:(wise(X)=>(~rich(X)<~>~wise(X))))&
(~funny(mary))&
(?[X]:((happy(X)<~>brave(X))))&
(tall(susan))&
((brave(paul)|generous(paul)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is both not patient and not quiet is not tall or not rich.
Everyone who is not calm or old is both brave and tall and vice versa.
Everyone who is kind is both not kind and humble.
Everyone who is happy or strong is kind.
Everyone who is happy or funny is both not tall and brave.
Everyone who is old is both not patient and patient and vice versa.
Everyone who is either patient or not funny is patient.
If john is not tall then someone is either not rich or not happy.
If paul is either not kind or not brave then someone is either not brave or funny.
If someone is not quiet then john is either not kind or not quiet and vice versa.
Everyone who is either generous or happy is happy or kind and vice versa.
If someone is humble or not tall then fred is both not kind and not wise and vice versa.
Everyone who is rich is either not generous or curious and vice versa.
Everyone who is humble or not rich is both rich and calm.
If john is either not wise or not tall then someone is both patient and old.
Everyone who is either happy or not humble is not happy or curious and vice versa.
Paul is not humble.
Someone is wise or not wise.
Someone is either old or not humble.
Paul is not humble or not creative.
Someone is either not happy or strong.
Someone is either not brave or patient.
Fred is both tall and not wise. | John is not quiet. | contradiction | (![X]:((~patient(X)&~quiet(X))=>(~tall(X)|~rich(X))))&
(![X]:((~calm(X)|old(X))<=>(brave(X)&tall(X))))&
(![X]:(kind(X)=>(~kind(X)&humble(X))))&
(![X]:((happy(X)|strong(X))=>kind(X)))&
(![X]:((happy(X)|funny(X))=>(~tall(X)&brave(X))))&
(![X]:(old(X)<=>(~patient(X)&patient(X))))&
(![X]:((patient(X)<~>~funny(X))=>patient(X)))&
((~tall(john))=>(?[X]:((~rich(X)<~>~happy(X)))))&
(((~kind(paul)<~>~brave(paul)))=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:(~quiet(X)))<=>((~kind(john)<~>~quiet(john))))&
(![X]:((generous(X)<~>happy(X))<=>(happy(X)|kind(X))))&
((?[X]:((humble(X)|~tall(X))))<=>((~kind(fred)&~wise(fred))))&
(![X]:(rich(X)<=>(~generous(X)<~>curious(X))))&
(![X]:((humble(X)|~rich(X))=>(rich(X)&calm(X))))&
(((~wise(john)<~>~tall(john)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(~happy(X)|curious(X))))&
(~humble(paul))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((old(X)<~>~humble(X))))&
((~humble(paul)|~creative(paul)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
((tall(fred)&~wise(fred))) | ~quiet(john) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7891506262262607865722892
% SZS output start Proof for 7891506262262607865722892
3. ! [X0] : (kind(X0) => (humble(X0) & ~kind(X0))) [input p2]
10. ? [X0] : ~quiet(X0) <=> (~kind(john) <~> ~quiet(john)) [input p9]
24. ~quiet(john) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~kind(X0)) | ~kind(X0)) [ennf transformation 3]
47. (? [X0] : ~quiet(X0) | ((~kind(john) | quiet(john)) & (~quiet(john) | kind(john)))) & (((quiet(john) | kind(john)) & (~quiet(john) | ~kind(john))) | ! [X0] : quiet(X0)) [nnf transformation 10]
48. (? [X0] : ~quiet(X0) | ((~kind(john) | quiet(john)) & (~quiet(john) | kind(john)))) & (((quiet(john) | kind(john)) & (~quiet(john) | ~kind(john))) | ! [X1] : quiet(X1)) [rectify 47]
49. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
50. (~quiet(sK2) | ((~kind(john) | quiet(john)) & (~quiet(john) | kind(john)))) & (((quiet(john) | kind(john)) & (~quiet(john) | ~kind(john))) | ! [X1] : quiet(X1)) [skolemisation 48,49]
81. ~kind(X0) | ~kind(X0) [cnf transformation 28]
101. quiet(john) | kind(john) | quiet(X1) [cnf transformation 50]
143. ~quiet(john) [cnf transformation 24]
150. ~kind(X0) [duplicate literal removal 81]
180. 6 <=> quiet(john) [avatar definition]
182. ~quiet(john) <- (~6) [avatar component clause 180]
188. quiet(john) | quiet(X1) [subsumption resolution 101,150]
190. 8 <=> ! [X1] : quiet(X1) [avatar definition]
191. quiet(X1) <- (8) [avatar component clause 190]
192. 8 | 6 [avatar split clause 188,180,190]
248. ~6 [avatar split clause 143,180]
249. $false <- (~6, 8) [subsumption resolution 182,191]
250. 6 | ~8 [avatar contradiction clause 249]
251. $false [avatar sat refutation 192,248,250]
% SZS output end Proof for 7891506262262607865722892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not old is quiet or not humble.
If fred is either happy or strong then alice is either not rich or not calm.
Everyone who is either quiet or generous is not calm.
If someone is both not rich and not happy then someone is not rich or humble.
Everyone who is both patient and funny is both funny and old and vice versa.
Everyone who is both not wise and curious is not quiet.
Everyone who is tall or not happy is both curious and happy and vice versa.
Everyone who is strong is tall.
If someone is calm then lucy is not patient or not calm.
Everyone who is calm is curious and vice versa.
If alice is not rich then lucy is not generous.
If someone is both not curious and creative then someone is not happy or funny.
Everyone who is not creative is funny or not humble and vice versa.
If someone is happy or brave then someone is both not generous and funny.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
Fred is either wise or happy.
Someone is either calm or not generous.
Paul is either not kind or not creative.
Alice is not brave.
Someone is both patient and not wise.
Someone is tall.
Someone is patient. | Lucy is not happy. | contradiction | (![X]:((~generous(X)|~old(X))=>(quiet(X)|~humble(X))))&
(((happy(fred)<~>strong(fred)))=>((~rich(alice)<~>~calm(alice))))&
(![X]:((quiet(X)<~>generous(X))=>~calm(X)))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((patient(X)&funny(X))<=>(funny(X)&old(X))))&
(![X]:((~wise(X)&curious(X))=>~quiet(X)))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)&happy(X))))&
(![X]:(strong(X)=>tall(X)))&
((?[X]:(calm(X)))=>((~patient(lucy)|~calm(lucy))))&
(![X]:(calm(X)<=>curious(X)))&
((~rich(alice))=>(~generous(lucy)))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((wise(fred)<~>happy(fred)))&
(?[X]:((calm(X)<~>~generous(X))))&
((~kind(paul)<~>~creative(paul)))&
(~brave(alice))&
(?[X]:((patient(X)&~wise(X))))&
(?[X]:(tall(X)))&
(?[X]:(patient(X))) | ~happy(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 660310568335460358538467
% SZS output start Proof for 660310568335460358538467
7. ! [X0] : ((~happy(X0) | tall(X0)) <=> (happy(X0) & curious(X0))) [input p6]
24. ~happy(lucy) [input hypothesis]
51. ! [X0] : (((~happy(X0) | tall(X0)) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | (happy(X0) & ~tall(X0)))) [nnf transformation 7]
52. ! [X0] : ((~happy(X0) | tall(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | (happy(X0) & ~tall(X0)))) [flattening 51]
92. happy(X0) | happy(X0) [cnf transformation 52]
123. ~happy(lucy) [cnf transformation 24]
124. happy(X0) [duplicate literal removal 92]
224. $false [subsumption resolution 123,124]
% SZS output end Proof for 660310568335460358538467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then alice is not calm and vice versa. Everyone who is either not creative or funny is both not brave and tall and vice versa. Everyone who is either kind or not generous is both kind and not curious and vice versa. Everyone who is funny is either not wise or not brave. If someone is either brave or curious then john is not humble. Everyone who is patient or generous is both quiet and curious. If someone is rich or not old then someone is rich or not rich. Everyone who is not curious or creative is either not calm or not humble. If paul is not wise then alice is both not generous and funny. Everyone who is rich is not funny or not patient and vice versa. If someone is not rich or old then john is both humble and rich. Everyone who is not strong is either tall or not patient and vice versa. If someone is either brave or not calm then mary is both old and not curious and vice versa. If someone is not old then lucy is either not kind or quiet and vice versa. If someone is both not tall and not kind then someone is patient. If fred is either funny or not patient then someone is not brave and vice versa. John is old. Someone is not wise or not rich. Alice is not humble. Susan is both rich and not old. John is both not kind and not happy. Someone is both not creative and not humble. Someone is generous. Someone is curious or not generous. | Fred is brave. | entailment | ((?[X]:(generous(X)))<=>(~calm(alice)))&
(![X]:((~creative(X)<~>funny(X))<=>(~brave(X)&tall(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(kind(X)&~curious(X))))&
(![X]:(funny(X)=>(~wise(X)<~>~brave(X))))&
((?[X]:((brave(X)<~>curious(X))))=>(~humble(john)))&
(![X]:((patient(X)|generous(X))=>(quiet(X)&curious(X))))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((~curious(X)|creative(X))=>(~calm(X)<~>~humble(X))))&
((~wise(paul))=>((~generous(alice)&funny(alice))))&
(![X]:(rich(X)<=>(~funny(X)|~patient(X))))&
((?[X]:((~rich(X)|old(X))))=>((humble(john)&rich(john))))&
(![X]:(~strong(X)<=>(tall(X)<~>~patient(X))))&
((?[X]:((brave(X)<~>~calm(X))))<=>((old(mary)&~curious(mary))))&
((?[X]:(~old(X)))<=>((~kind(lucy)<~>quiet(lucy))))&
((?[X]:((~tall(X)&~kind(X))))=>(?[X]:(patient(X))))&
(((funny(fred)<~>~patient(fred)))<=>(?[X]:(~brave(X))))&
(old(john))&
(?[X]:((~wise(X)|~rich(X))))&
(~humble(alice))&
((rich(susan)&~old(susan)))&
((~kind(john)&~happy(john)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((curious(X)|~generous(X)))) | brave(fred) | [
"p2",
"p4",
"p5",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 899094342384133970742036
% SZS output start Proof for 899094342384133970742036
3. ! [X0] : ((kind(X0) <~> ~generous(X0)) <=> (~curious(X0) & kind(X0))) [input p2]
5. ? [X0] : (brave(X0) <~> curious(X0)) => ~humble(john) [input p4]
6. ! [X0] : ((generous(X0) | patient(X0)) => (curious(X0) & quiet(X0))) [input p5]
11. ? [X0] : (old(X0) | ~rich(X0)) => (rich(john) & humble(john)) [input p10]
17. old(john) [input p16]
25. ~brave(fred) [input hypothesis]
30. ~humble(john) | ! [X0] : (brave(X0) <=> curious(X0)) [ennf transformation 5]
31. ! [X0] : ((curious(X0) & quiet(X0)) | (~generous(X0) & ~patient(X0))) [ennf transformation 6]
35. (rich(john) & humble(john)) | ! [X0] : (~old(X0) & rich(X0)) [ennf transformation 11]
43. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [nnf transformation 3]
44. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [flattening 43]
46. ~humble(john) | ! [X0] : ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))) [nnf transformation 30]
86. kind(X0) | kind(X0) | generous(X0) [cnf transformation 44]
90. generous(X0) | ~kind(X0) | curious(X0) | ~kind(X0) [cnf transformation 44]
94. ~humble(john) | brave(X0) | ~curious(X0) [cnf transformation 46]
98. ~generous(X0) | curious(X0) [cnf transformation 31]
111. humble(john) | ~old(X0) [cnf transformation 35]
129. old(john) [cnf transformation 17]
139. ~brave(fred) [cnf transformation 25]
140. kind(X0) | generous(X0) [duplicate literal removal 86]
141. ~kind(X0) | generous(X0) | curious(X0) [duplicate literal removal 90]
156. 4 <=> ! [X0] : (brave(X0) | ~curious(X0)) [avatar definition]
157. ~curious(X0) | brave(X0) <- (4) [avatar component clause 156]
159. 5 <=> humble(john) [avatar definition]
162. 4 | ~5 [avatar split clause 94,159,156]
182. 10 <=> ! [X0] : ~old(X0) [avatar definition]
183. ~old(X0) <- (10) [avatar component clause 182]
193. 10 | 5 [avatar split clause 111,159,182]
251. 25 <=> ! [X0] : brave(X0) [avatar definition]
252. brave(X0) <- (25) [avatar component clause 251]
437. generous(X1) | curious(X1) | generous(X1) [resolution 141,140]
439. generous(X1) | curious(X1) [duplicate literal removal 437]
441. curious(X1) [subsumption resolution 439,98]
448. brave(X2) <- (4) [resolution 441,157]
450. 25 | ~4 [avatar split clause 448,156,251]
457. $false <- (10) [resolution 183,129]
460. ~10 [avatar contradiction clause 457]
469. $false <- (25) [resolution 252,139]
474. ~25 [avatar contradiction clause 469]
475. $false [avatar sat refutation 162,193,450,460,474]
% SZS output end Proof for 899094342384133970742036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not creative or not quiet. If alice is not humble then paul is either rich or strong. If john is old then susan is both kind and humble. Everyone who is both curious and funny is both brave and kind. Everyone who is patient or not wise is not tall or not generous and vice versa. If someone is not happy then someone is kind. Everyone who is curious or rich is both not wise and strong and vice versa. Everyone who is either not brave or not happy is kind or brave. Everyone who is both not patient and not curious is either not rich or not wise. If someone is both funny and not funny then alice is humble or happy and vice versa. Everyone who is not rich is either wise or not happy. Everyone who is not old or calm is not generous. If alice is not kind or old then fred is either not patient or not strong and vice versa. If paul is not rich then lucy is both strong and not tall. If paul is not rich then alice is both calm and not patient. If alice is not humble or creative then john is not humble or old. John is either curious or brave. John is generous or not happy. Paul is not calm. Lucy is not creative or not tall. Fred is tall or not calm. Someone is funny. Lucy is humble or not strong. Someone is either not curious or wise. | Alice is old. | neutral | (![X]:(~creative(X)=>(~creative(X)|~quiet(X))))&
((~humble(alice))=>((rich(paul)<~>strong(paul))))&
((old(john))=>((kind(susan)&humble(susan))))&
(![X]:((curious(X)&funny(X))=>(brave(X)&kind(X))))&
(![X]:((patient(X)|~wise(X))<=>(~tall(X)|~generous(X))))&
((?[X]:(~happy(X)))=>(?[X]:(kind(X))))&
(![X]:((curious(X)|rich(X))<=>(~wise(X)&strong(X))))&
(![X]:((~brave(X)<~>~happy(X))=>(kind(X)|brave(X))))&
(![X]:((~patient(X)&~curious(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:((funny(X)&~funny(X))))<=>((humble(alice)|happy(alice))))&
(![X]:(~rich(X)=>(wise(X)<~>~happy(X))))&
(![X]:((~old(X)|calm(X))=>~generous(X)))&
(((~kind(alice)|old(alice)))<=>((~patient(fred)<~>~strong(fred))))&
((~rich(paul))=>((strong(lucy)&~tall(lucy))))&
((~rich(paul))=>((calm(alice)&~patient(alice))))&
(((~humble(alice)|creative(alice)))=>((~humble(john)|old(john))))&
((curious(john)<~>brave(john)))&
((generous(john)|~happy(john)))&
(~calm(paul))&
((~creative(lucy)|~tall(lucy)))&
((tall(fred)|~calm(fred)))&
(?[X]:(funny(X)))&
((humble(lucy)|~strong(lucy)))&
(?[X]:((~curious(X)<~>wise(X)))) | old(alice) | [] | null | 0 |
If alice is wise or quiet then mary is rich and vice versa.
Everyone who is either curious or not curious is both not old and not brave and vice versa.
Everyone who is both wise and brave is not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Everyone who is both not curious and not kind is calm.
Someone is either calm or not wise.
Someone is either not happy or not old.
Someone is not curious.
Someone is rich.
Someone is not quiet or not generous.
Someone is not curious or funny. | Fred is not wise. | entailment | (((wise(alice)|quiet(alice)))<=>(rich(mary)))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((wise(X)&brave(X))<=>~kind(X)))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~curious(X)&~kind(X))=>calm(X)))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~curious(X)|funny(X)))) | ~wise(fred) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 640412111047902252257000
% SZS output start Proof for 640412111047902252257000
2. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~brave(X0) & ~old(X0))) [input p1]
4. ! [X0] : ((creative(X0) | wise(X0)) <=> (brave(X0) & ~quiet(X0))) [input p3]
22. wise(fred) [input hypothesis]
31. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 2]
32. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 31]
35. ! [X0] : (((creative(X0) | wise(X0)) | (~brave(X0) | quiet(X0))) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 4]
36. ! [X0] : ((creative(X0) | wise(X0) | ~brave(X0) | quiet(X0)) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 35]
90. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 32]
91. ~brave(X0) | curious(X0) | curious(X0) [cnf transformation 32]
99. brave(X0) | ~wise(X0) [cnf transformation 36]
153. wise(fred) [cnf transformation 22]
156. ~brave(X0) | ~curious(X0) [duplicate literal removal 90]
157. ~brave(X0) | curious(X0) [duplicate literal removal 91]
173. ~brave(X0) [subsumption resolution 156,157]
177. ~wise(X0) [subsumption resolution 99,173]
273. $false [subsumption resolution 153,177]
% SZS output end Proof for 640412111047902252257000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both rich and happy then someone is brave.
Everyone who is not calm or generous is not kind or tall.
Everyone who is not funny or not quiet is both not patient and not kind and vice versa.
If someone is calm or humble then someone is wise and vice versa.
Everyone who is not tall or tall is generous.
Everyone who is not creative is either quiet or happy and vice versa.
If lucy is creative or curious then lucy is funny.
Everyone who is not curious or calm is not tall.
Everyone who is happy is not quiet.
If someone is both not happy and not humble then someone is either not patient or not happy and vice versa.
Everyone who is both patient and happy is old and vice versa.
Everyone who is not creative is either kind or not generous.
Everyone who is both not strong and not wise is not happy.
Everyone who is both not tall and happy is either not kind or generous and vice versa.
Everyone who is either tall or strong is calm or kind.
If lucy is funny then john is kind or brave and vice versa.
Someone is not kind.
Someone is not strong.
Fred is both wise and not calm.
Fred is wise or not funny.
Paul is both not brave and not old.
John is kind or brave.
Someone is not brave or wise. | John is not brave. | contradiction | (((rich(susan)&happy(susan)))=>(?[X]:(brave(X))))&
(![X]:((~calm(X)|generous(X))=>(~kind(X)|tall(X))))&
(![X]:((~funny(X)|~quiet(X))<=>(~patient(X)&~kind(X))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)|tall(X))=>generous(X)))&
(![X]:(~creative(X)<=>(quiet(X)<~>happy(X))))&
(((creative(lucy)|curious(lucy)))=>(funny(lucy)))&
(![X]:((~curious(X)|calm(X))=>~tall(X)))&
(![X]:(happy(X)=>~quiet(X)))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((patient(X)&happy(X))<=>old(X)))&
(![X]:(~creative(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~strong(X)&~wise(X))=>~happy(X)))&
(![X]:((~tall(X)&happy(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((tall(X)<~>strong(X))=>(calm(X)|kind(X))))&
((funny(lucy))<=>((kind(john)|brave(john))))&
(?[X]:(~kind(X)))&
(?[X]:(~strong(X)))&
((wise(fred)&~calm(fred)))&
((wise(fred)|~funny(fred)))&
((~brave(paul)&~old(paul)))&
((kind(john)|brave(john)))&
(?[X]:((~brave(X)|wise(X)))) | ~brave(john) | [
"p2",
"p4",
"p8",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 656546044424453502562400
% SZS output start Proof for 656546044424453502562400
3. ! [X0] : ((~quiet(X0) | ~funny(X0)) <=> (~kind(X0) & ~patient(X0))) [input p2]
5. ! [X0] : ((tall(X0) | ~tall(X0)) => generous(X0)) [input p4]
9. ! [X0] : (happy(X0) => ~quiet(X0)) [input p8]
14. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (~kind(X0) <~> generous(X0))) [input p13]
22. brave(john) | kind(john) [input p21]
24. ~brave(john) [input hypothesis]
31. ! [X0] : (generous(X0) | (~tall(X0) & tall(X0))) [ennf transformation 5]
34. ! [X0] : (~quiet(X0) | ~happy(X0)) [ennf transformation 9]
42. ! [X0] : (((~quiet(X0) | ~funny(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (quiet(X0) & funny(X0)))) [nnf transformation 3]
43. ! [X0] : ((~quiet(X0) | ~funny(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (quiet(X0) & funny(X0)))) [flattening 42]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~happy(X0) | tall(X0)))) [nnf transformation 14]
57. ! [X0] : (((happy(X0) & ~tall(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ~happy(X0) | tall(X0))) [flattening 56]
72. ~kind(X0) | quiet(X0) [cnf transformation 43]
77. generous(X0) | tall(X0) [cnf transformation 31]
78. ~tall(X0) | generous(X0) [cnf transformation 31]
87. ~quiet(X0) | ~happy(X0) [cnf transformation 34]
103. happy(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 57]
116. brave(john) | kind(john) [cnf transformation 22]
118. ~brave(john) [cnf transformation 24]
143. generous(X0) [subsumption resolution 77,78]
190. ~kind(X0) | happy(X0) [subsumption resolution 103,143]
197. 17 <=> brave(john) [avatar definition]
202. 18 <=> kind(john) [avatar definition]
203. kind(john) <- (18) [avatar component clause 202]
207. 18 | 17 [avatar split clause 116,197,202]
217. ~17 [avatar split clause 118,197]
219. quiet(john) <- (18) [resolution 72,203]
220. ~happy(john) <- (18) [resolution 87,219]
224. happy(john) <- (18) [resolution 190,203]
225. $false <- (18) [subsumption resolution 224,220]
226. ~18 [avatar contradiction clause 225]
227. $false [avatar sat refutation 207,217,226]
% SZS output end Proof for 656546044424453502562400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either funny or not rich then susan is both calm and brave. If someone is wise then someone is rich or not strong. Everyone who is not strong is both not tall and generous and vice versa. Everyone who is both not funny and rich is not curious or not patient and vice versa. Everyone who is not tall or not humble is both not generous and not rich. If someone is quiet or old then someone is humble. If lucy is both not wise and patient then alice is not generous or kind. Everyone who is generous is both old and rich and vice versa. Everyone who is either not kind or not generous is not creative or strong and vice versa. Everyone who is either quiet or not tall is brave and vice versa. Everyone who is brave or quiet is not quiet or not brave and vice versa. If mary is tall or creative then someone is not strong or not happy. Everyone who is tall or patient is either quiet or rich and vice versa. Everyone who is not strong or not rich is either strong or not funny. If someone is either not patient or not rich then mary is rich or not creative and vice versa. Someone is either rich or kind. Someone is not humble or not happy. Mary is not old or patient. Someone is not curious or kind. Fred is either curious or rich. | Fred is not humble. | neutral | (((funny(lucy)<~>~rich(lucy)))=>((calm(susan)&brave(susan))))&
((?[X]:(wise(X)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&generous(X))))&
(![X]:((~funny(X)&rich(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&~rich(X))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:(humble(X))))&
(((~wise(lucy)&patient(lucy)))=>((~generous(alice)|kind(alice))))&
(![X]:(generous(X)<=>(old(X)&rich(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~creative(X)|strong(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>brave(X)))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|~brave(X))))&
(((tall(mary)|creative(mary)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((tall(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~strong(X)|~rich(X))=>(strong(X)<~>~funny(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>((rich(mary)|~creative(mary))))&
(?[X]:((rich(X)<~>kind(X))))&
(?[X]:((~humble(X)|~happy(X))))&
((~old(mary)|patient(mary)))&
(?[X]:((~curious(X)|kind(X))))&
((curious(fred)<~>rich(fred))) | ~humble(fred) | [] | null | 0 |
Everyone who is both quiet and not happy is not tall.
Everyone who is either not generous or not curious is both humble and not patient.
Everyone who is either not funny or generous is happy.
If someone is patient then someone is tall or not kind.
If someone is not humble then alice is brave and vice versa.
If someone is both not calm and not strong then someone is both tall and not kind.
If someone is either generous or not generous then mary is generous or wise.
Everyone who is both kind and not rich is kind or not wise and vice versa.
Everyone who is quiet is both brave and not funny and vice versa.
If susan is both brave and not generous then fred is either patient or wise.
Everyone who is either not tall or not kind is both not rich and not funny and vice versa.
Everyone who is either strong or not happy is either not creative or not tall and vice versa.
Everyone who is both not old and old is both old and kind and vice versa.
Everyone who is not generous or not patient is funny.
If someone is not funny or not creative then someone is generous or not strong and vice versa.
Everyone who is both kind and not creative is not creative and vice versa.
Fred is creative or old.
Someone is both not creative and not rich.
Someone is wise.
Fred is either not quiet or rich.
Someone is funny or not happy.
Fred is either tall or not strong.
Someone is both humble and wise.
Alice is both curious and patient. | Fred is calm. | neutral | (![X]:((quiet(X)&~happy(X))=>~tall(X)))&
(![X]:((~generous(X)<~>~curious(X))=>(humble(X)&~patient(X))))&
(![X]:((~funny(X)<~>generous(X))=>happy(X)))&
((?[X]:(patient(X)))=>(?[X]:((tall(X)|~kind(X)))))&
((?[X]:(~humble(X)))<=>(brave(alice)))&
((?[X]:((~calm(X)&~strong(X))))=>(?[X]:((tall(X)&~kind(X)))))&
((?[X]:((generous(X)<~>~generous(X))))=>((generous(mary)|wise(mary))))&
(![X]:((kind(X)&~rich(X))<=>(kind(X)|~wise(X))))&
(![X]:(quiet(X)<=>(brave(X)&~funny(X))))&
(((brave(susan)&~generous(susan)))=>((patient(fred)<~>wise(fred))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~rich(X)&~funny(X))))&
(![X]:((strong(X)<~>~happy(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~old(X)&old(X))<=>(old(X)&kind(X))))&
(![X]:((~generous(X)|~patient(X))=>funny(X)))&
((?[X]:((~funny(X)|~creative(X))))<=>(?[X]:((generous(X)|~strong(X)))))&
(![X]:((kind(X)&~creative(X))<=>~creative(X)))&
((creative(fred)|old(fred)))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:(wise(X)))&
((~quiet(fred)<~>rich(fred)))&
(?[X]:((funny(X)|~happy(X))))&
((tall(fred)<~>~strong(fred)))&
(?[X]:((humble(X)&wise(X))))&
((curious(alice)&patient(alice))) | calm(fred) | [] | null | 0 |
Everyone who is creative is either tall or not rich.
Everyone who is humble or not creative is both strong and not old and vice versa.
Everyone who is either old or not old is both curious and not tall.
Everyone who is either not quiet or not generous is either calm or humble and vice versa.
If someone is both not humble and not funny then paul is either kind or curious.
If someone is both happy and brave then john is not funny.
If someone is funny then someone is both not patient and not quiet.
Everyone who is both funny and not old is both rich and not happy and vice versa.
If someone is not rich then john is both humble and not creative.
If someone is either patient or tall then lucy is not rich and vice versa.
Everyone who is not rich or not old is generous and vice versa.
If alice is both curious and not rich then paul is not patient or creative.
Everyone who is both generous and humble is both generous and wise and vice versa.
If mary is either patient or not happy then mary is both happy and creative.
Everyone who is kind or not brave is either not quiet or not curious and vice versa.
Everyone who is both happy and not wise is both not generous and not brave and vice versa.
Mary is not happy.
Someone is both humble and happy.
Lucy is creative.
Paul is both not old and wise.
Mary is not tall.
Paul is not brave or calm.
Paul is not kind or creative.
Susan is not creative. | Lucy is not rich. | entailment | (![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(strong(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(curious(X)&~tall(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(calm(X)<~>humble(X))))&
((?[X]:((~humble(X)&~funny(X))))=>((kind(paul)<~>curious(paul))))&
((?[X]:((happy(X)&brave(X))))=>(~funny(john)))&
((?[X]:(funny(X)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(![X]:((funny(X)&~old(X))<=>(rich(X)&~happy(X))))&
((?[X]:(~rich(X)))=>((humble(john)&~creative(john))))&
((?[X]:((patient(X)<~>tall(X))))<=>(~rich(lucy)))&
(![X]:((~rich(X)|~old(X))<=>generous(X)))&
(((curious(alice)&~rich(alice)))=>((~patient(paul)|creative(paul))))&
(![X]:((generous(X)&humble(X))<=>(generous(X)&wise(X))))&
(((patient(mary)<~>~happy(mary)))=>((happy(mary)&creative(mary))))&
(![X]:((kind(X)|~brave(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((happy(X)&~wise(X))<=>(~generous(X)&~brave(X))))&
(~happy(mary))&
(?[X]:((humble(X)&happy(X))))&
(creative(lucy))&
((~old(paul)&wise(paul)))&
(~tall(mary))&
((~brave(paul)|calm(paul)))&
((~kind(paul)|creative(paul)))&
(~creative(susan)) | ~rich(lucy) | [
"p2",
"p9",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4735744233958414614821571
% SZS output start Proof for 4735744233958414614821571
3. ! [X0] : ((old(X0) <~> ~old(X0)) => (~tall(X0) & curious(X0))) [input p2]
10. ? [X0] : (patient(X0) <~> tall(X0)) <=> ~rich(lucy) [input p9]
14. (patient(mary) <~> ~happy(mary)) => (creative(mary) & happy(mary)) [input p13]
17. ~happy(mary) [input p16]
25. rich(lucy) [input hypothesis]
28. ! [X0] : ((~tall(X0) & curious(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 3]
35. (creative(mary) & happy(mary)) | (patient(mary) <=> ~happy(mary)) [ennf transformation 14]
39. ! [X0] : ((~tall(X0) & curious(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 28]
47. (? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | rich(lucy)) & (~rich(lucy) | ! [X0] : ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) [nnf transformation 10]
48. (? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | rich(lucy)) & (~rich(lucy) | ! [X1] : ((patient(X1) | ~tall(X1)) & (tall(X1) | ~patient(X1)))) [rectify 47]
49. ? [X0] : ((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) => ((~tall(sK1) | ~patient(sK1)) & (tall(sK1) | patient(sK1))) [choice axiom]
50. (((~tall(sK1) | ~patient(sK1)) & (tall(sK1) | patient(sK1))) | rich(lucy)) & (~rich(lucy) | ! [X1] : ((patient(X1) | ~tall(X1)) & (tall(X1) | ~patient(X1)))) [skolemisation 48,49]
55. (creative(mary) & happy(mary)) | ((patient(mary) | happy(mary)) & (~happy(mary) | ~patient(mary))) [nnf transformation 35]
71. ~tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 39]
72. ~tall(X0) | old(X0) | old(X0) [cnf transformation 39]
92. ~rich(lucy) | tall(X1) | ~patient(X1) [cnf transformation 50]
105. happy(mary) | patient(mary) | happy(mary) [cnf transformation 55]
118. ~happy(mary) [cnf transformation 17]
128. rich(lucy) [cnf transformation 25]
129. happy(mary) | patient(mary) [duplicate literal removal 105]
132. ~tall(X0) | ~old(X0) [duplicate literal removal 71]
133. ~tall(X0) | old(X0) [duplicate literal removal 72]
134. ~tall(X0) [subsumption resolution 132,133]
181. 11 <=> rich(lucy) [avatar definition]
189. ~rich(lucy) | ~patient(X1) [subsumption resolution 92,134]
191. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
192. ~patient(X1) <- (13) [avatar component clause 191]
193. 13 | ~11 [avatar split clause 189,181,191]
209. 17 <=> happy(mary) [avatar definition]
213. 18 <=> patient(mary) [avatar definition]
215. patient(mary) <- (18) [avatar component clause 213]
222. 18 | 17 [avatar split clause 129,209,213]
226. ~17 [avatar split clause 118,209]
237. 11 [avatar split clause 128,181]
238. $false <- (13, 18) [resolution 215,192]
239. ~13 | ~18 [avatar contradiction clause 238]
240. $false [avatar sat refutation 193,222,226,237,239]
% SZS output end Proof for 4735744233958414614821571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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