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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If mary is both not kind and quiet then someone is both creative and rich. Everyone who is both not humble and not curious is not rich and vice versa. If someone is both not funny and not rich then someone is either not generous or not old. If someone is not generous or happy then someone is not creative and vice versa. Everyone who is rich is both old and happy. Everyone who is both not kind and kind is either old or tall and vice versa. Everyone who is both not old and not generous is either generous or old. Everyone who is either patient or old is either happy or not curious and vice versa. Everyone who is not kind is both not strong and calm. Everyone who is not old or generous is not wise or not old and vice versa. Everyone who is either not happy or brave is either not calm or rich and vice versa. Everyone who is generous or rich is either old or rich. If someone is either funny or humble then someone is creative. If someone is either not quiet or not kind then someone is either humble or not humble. If someone is not curious or funny then someone is calm. If mary is quiet then lucy is both creative and humble and vice versa. Fred is either brave or quiet. Mary is strong. Lucy is either funny or generous. Someone is tall. Someone is not funny or not kind. Someone is either happy or not curious. Fred is both not brave and quiet. | Fred is not curious. | entailment | (((~kind(mary)&quiet(mary)))=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
((quiet(mary))<=>((creative(lucy)&humble(lucy))))&
((brave(fred)<~>quiet(fred)))&
(strong(mary))&
((funny(lucy)<~>generous(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
((~brave(fred)&quiet(fred))) | ~curious(fred) | [
"p1",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6677608589707044189090
% SZS output start Proof for 6677608589707044189090
2. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> ~rich(X0)) [input p1]
5. ! [X0] : (rich(X0) => (happy(X0) & old(X0))) [input p4]
12. ! [X0] : ((rich(X0) | generous(X0)) => (old(X0) <~> rich(X0))) [input p11]
24. curious(fred) [input hypothesis]
33. ! [X0] : ((happy(X0) & old(X0)) | ~rich(X0)) [ennf transformation 5]
37. ! [X0] : ((old(X0) <~> rich(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 12]
43. ! [X0] : (((~curious(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | (curious(X0) | humble(X0)))) [nnf transformation 2]
44. ! [X0] : (((~curious(X0) & ~humble(X0)) | rich(X0)) & (~rich(X0) | curious(X0) | humble(X0))) [flattening 43]
61. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 37]
88. ~curious(X0) | rich(X0) [cnf transformation 44]
94. old(X0) | ~rich(X0) [cnf transformation 33]
129. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 61]
152. curious(fred) [cnf transformation 24]
153. ~rich(X0) | ~old(X0) [duplicate literal removal 129]
217. ~rich(X0) [subsumption resolution 153,94]
297. rich(fred) [resolution 88,152]
298. $false [subsumption resolution 297,217]
% SZS output end Proof for 6677608589707044189090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or generous then someone is either creative or not patient and vice versa.
Everyone who is either creative or kind is both not generous and tall.
If someone is wise or not funny then someone is either not generous or not creative.
Everyone who is not generous or curious is either patient or funny and vice versa.
Everyone who is not funny is patient or not kind.
If someone is not generous then fred is rich.
If someone is both not patient and tall then mary is both not humble and not generous.
Everyone who is not calm or rich is both funny and not quiet and vice versa.
Everyone who is funny is not quiet and vice versa.
If someone is both strong and quiet then someone is not old and vice versa.
Everyone who is both not creative and creative is tall and vice versa.
If alice is creative or not tall then someone is both old and not humble and vice versa.
Everyone who is not strong is both not tall and not humble and vice versa.
Everyone who is either not quiet or not happy is rich or happy.
Everyone who is not calm or not old is both wise and tall.
If someone is both strong and not patient then john is either not quiet or not creative and vice versa.
Fred is funny.
Susan is both not creative and happy.
Lucy is patient or generous.
Someone is not funny or not generous.
Someone is either strong or not quiet.
Someone is either not generous or humble.
John is either not tall or not brave. | Fred is not brave. | neutral | (((~patient(lucy)|generous(lucy)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((creative(X)<~>kind(X))=>(~generous(X)&tall(X))))&
((?[X]:((wise(X)|~funny(X))))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((~generous(X)|curious(X))<=>(patient(X)<~>funny(X))))&
(![X]:(~funny(X)=>(patient(X)|~kind(X))))&
((?[X]:(~generous(X)))=>(rich(fred)))&
((?[X]:((~patient(X)&tall(X))))=>((~humble(mary)&~generous(mary))))&
(![X]:((~calm(X)|rich(X))<=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&creative(X))<=>tall(X)))&
(((creative(alice)|~tall(alice)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(funny(fred))&
((~creative(susan)&happy(susan)))&
((patient(lucy)|generous(lucy)))&
(?[X]:((~funny(X)|~generous(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~generous(X)<~>humble(X))))&
((~tall(john)<~>~brave(john))) | ~brave(fred) | [] | null | 0 |
Everyone who is not funny is patient or wise and vice versa. Everyone who is old is rich and vice versa. Everyone who is creative is either funny or not funny. If someone is both strong and not old then someone is kind or not funny. Everyone who is brave or not wise is either creative or quiet and vice versa. Everyone who is either not funny or curious is not brave or not generous. Everyone who is both not humble and not strong is both calm and curious and vice versa. Everyone who is not patient is not creative or tall and vice versa. Everyone who is both not generous and not humble is both kind and not strong. If mary is both not funny and not curious then someone is calm or rich and vice versa. If someone is quiet then someone is either kind or generous. If someone is either not happy or not kind then someone is both generous and old. If lucy is both not tall and wise then susan is either not tall or not humble. Everyone who is not patient or not happy is not old. Everyone who is strong is both not generous and creative and vice versa. If someone is either creative or not humble then someone is both not creative and rich. Susan is both brave and not humble. Someone is not rich. Someone is either rich or wise. Someone is either calm or not old. Alice is either not brave or not generous. Someone is not funny or not rich. Paul is curious or not kind. Someone is either not calm or not old. | Susan is not generous. | contradiction | (![X]:(~funny(X)<=>(patient(X)|wise(X))))&
(![X]:(old(X)<=>rich(X)))&
(![X]:(creative(X)=>(funny(X)<~>~funny(X))))&
((?[X]:((strong(X)&~old(X))))=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((brave(X)|~wise(X))<=>(creative(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>curious(X))=>(~brave(X)|~generous(X))))&
(![X]:((~humble(X)&~strong(X))<=>(calm(X)&curious(X))))&
(![X]:(~patient(X)<=>(~creative(X)|tall(X))))&
(![X]:((~generous(X)&~humble(X))=>(kind(X)&~strong(X))))&
(((~funny(mary)&~curious(mary)))<=>(?[X]:((calm(X)|rich(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(?[X]:((generous(X)&old(X)))))&
(((~tall(lucy)&wise(lucy)))=>((~tall(susan)<~>~humble(susan))))&
(![X]:((~patient(X)|~happy(X))=>~old(X)))&
(![X]:(strong(X)<=>(~generous(X)&creative(X))))&
((?[X]:((creative(X)<~>~humble(X))))=>(?[X]:((~creative(X)&rich(X)))))&
((brave(susan)&~humble(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:((calm(X)<~>~old(X))))&
((~brave(alice)<~>~generous(alice)))&
(?[X]:((~funny(X)|~rich(X))))&
((curious(paul)|~kind(paul)))&
(?[X]:((~calm(X)<~>~old(X)))) | ~generous(susan) | [
"p1",
"p7",
"p8",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8528094176531103097895567
% SZS output start Proof for 8528094176531103097895567
2. ! [X0] : (old(X0) <=> rich(X0)) [input p1]
8. ! [X0] : (~patient(X0) <=> (tall(X0) | ~creative(X0))) [input p7]
9. ! [X0] : ((~humble(X0) & ~generous(X0)) => (~strong(X0) & kind(X0))) [input p8]
14. ! [X0] : ((~happy(X0) | ~patient(X0)) => ~old(X0)) [input p13]
15. ! [X0] : (strong(X0) <=> (creative(X0) & ~generous(X0))) [input p14]
16. ? [X0] : (creative(X0) <~> ~humble(X0)) => ? [X0] : (rich(X0) & ~creative(X0)) [input p15]
17. ~humble(susan) & brave(susan) [input p16]
25. ~generous(susan) [input hypothesis]
29. ? [X0] : (creative(X0) <~> ~humble(X0)) => ? [X1] : (rich(X1) & ~creative(X1)) [rectify 16]
34. ! [X0] : ((~strong(X0) & kind(X0)) | (humble(X0) | generous(X0))) [ennf transformation 9]
35. ! [X0] : ((~strong(X0) & kind(X0)) | humble(X0) | generous(X0)) [flattening 34]
40. ! [X0] : (~old(X0) | (happy(X0) & patient(X0))) [ennf transformation 14]
41. ? [X1] : (rich(X1) & ~creative(X1)) | ! [X0] : (creative(X0) <=> ~humble(X0)) [ennf transformation 29]
44. ! [X0] : ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0))) [nnf transformation 2]
54. ! [X0] : ((~patient(X0) | (~tall(X0) & creative(X0))) & ((tall(X0) | ~creative(X0)) | patient(X0))) [nnf transformation 8]
55. ! [X0] : ((~patient(X0) | (~tall(X0) & creative(X0))) & (tall(X0) | ~creative(X0) | patient(X0))) [flattening 54]
70. ! [X0] : ((strong(X0) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | ~strong(X0))) [nnf transformation 15]
71. ! [X0] : ((strong(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | ~strong(X0))) [flattening 70]
72. ? [X1] : (rich(X1) & ~creative(X1)) | ! [X0] : ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))) [nnf transformation 41]
73. ? [X0] : (rich(X0) & ~creative(X0)) | ! [X1] : ((creative(X1) | humble(X1)) & (~humble(X1) | ~creative(X1))) [rectify 72]
74. ? [X0] : (rich(X0) & ~creative(X0)) => (rich(sK4) & ~creative(sK4)) [choice axiom]
75. (rich(sK4) & ~creative(sK4)) | ! [X1] : ((creative(X1) | humble(X1)) & (~humble(X1) | ~creative(X1))) [skolemisation 73,74]
94. ~rich(X0) | old(X0) [cnf transformation 44]
111. ~patient(X0) | creative(X0) [cnf transformation 55]
114. ~strong(X0) | humble(X0) | generous(X0) [cnf transformation 35]
128. ~old(X0) | patient(X0) [cnf transformation 40]
132. ~creative(X0) | strong(X0) | generous(X0) [cnf transformation 71]
134. ~creative(sK4) | creative(X1) | humble(X1) [cnf transformation 75]
136. rich(sK4) | creative(X1) | humble(X1) [cnf transformation 75]
138. ~humble(susan) [cnf transformation 17]
150. ~generous(susan) [cnf transformation 25]
234. 20 <=> humble(susan) [avatar definition]
235. ~humble(susan) <- (~20) [avatar component clause 234]
240. 21 <=> ! [X1] : (creative(X1) | humble(X1)) [avatar definition]
241. humble(X1) | creative(X1) <- (21) [avatar component clause 240]
243. 22 <=> rich(sK4) [avatar definition]
245. rich(sK4) <- (22) [avatar component clause 243]
246. 21 | 22 [avatar split clause 136,243,240]
252. 24 <=> creative(sK4) [avatar definition]
254. ~creative(sK4) <- (~24) [avatar component clause 252]
255. 21 | ~24 [avatar split clause 134,252,240]
257. ~20 [avatar split clause 138,234]
324. old(sK4) <- (22) [resolution 94,245]
331. patient(sK4) <- (22) [resolution 128,324]
342. creative(sK4) <- (22) [resolution 331,111]
344. $false <- (22, ~24) [subsumption resolution 342,254]
345. ~22 | 24 [avatar contradiction clause 344]
349. creative(susan) <- (~20, 21) [resolution 241,235]
386. 40 <=> strong(susan) [avatar definition]
388. strong(susan) <- (40) [avatar component clause 386]
429. strong(susan) | generous(susan) <- (~20, 21) [resolution 132,349]
435. strong(susan) <- (~20, 21) [subsumption resolution 429,150]
436. 40 | 20 | ~21 [avatar split clause 435,240,234,386]
521. humble(susan) | generous(susan) <- (40) [resolution 388,114]
523. generous(susan) <- (~20, 40) [subsumption resolution 521,235]
524. $false <- (~20, 40) [subsumption resolution 523,150]
525. 20 | ~40 [avatar contradiction clause 524]
526. $false [avatar sat refutation 246,255,257,345,436,525]
% SZS output end Proof for 8528094176531103097895567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is either not happy or not humble and vice versa.
Everyone who is both strong and not funny is kind.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Everyone who is old is tall or curious.
If someone is wise then mary is not rich or not humble.
Everyone who is either curious or not generous is humble and vice versa.
Susan is tall.
Someone is either curious or rich.
Someone is not quiet or brave.
John is either not strong or not generous.
Fred is curious or not strong.
Someone is both not creative and not rich. | Fred is not patient. | neutral | (![X]:(tall(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((strong(X)&~funny(X))=>kind(X)))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(![X]:(old(X)=>(tall(X)|curious(X))))&
((?[X]:(wise(X)))=>((~rich(mary)|~humble(mary))))&
(![X]:((curious(X)<~>~generous(X))<=>humble(X)))&
(tall(susan))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~quiet(X)|brave(X))))&
((~strong(john)<~>~generous(john)))&
((curious(fred)|~strong(fred)))&
(?[X]:((~creative(X)&~rich(X)))) | ~patient(fred) | [] | null | 0 |
Everyone who is both not humble and not old is not patient or quiet and vice versa.
If alice is both not strong and not quiet then someone is either not brave or not strong and vice versa.
Everyone who is both happy and kind is both not wise and not old and vice versa.
Everyone who is either kind or not rich is happy.
Everyone who is curious is old or not funny.
Everyone who is either not funny or brave is either not humble or not tall and vice versa.
If fred is quiet or not humble then someone is curious or not generous and vice versa.
Everyone who is both not happy and not brave is both not tall and patient.
Everyone who is not humble is both kind and not happy and vice versa.
Everyone who is tall or not old is both happy and not old.
Everyone who is both not tall and not kind is strong.
Everyone who is both quiet and brave is both old and not creative.
Everyone who is either not humble or funny is either not patient or patient and vice versa.
Everyone who is not creative is both not tall and not brave and vice versa.
If john is not wise then someone is either tall or generous.
Everyone who is both calm and strong is not brave and vice versa.
Someone is not tall.
Lucy is both not old and not brave.
John is both not happy and not curious.
Someone is not quiet.
Susan is either not strong or brave.
Someone is calm. | Alice is not funny. | neutral | (![X]:((~humble(X)&~old(X))<=>(~patient(X)|quiet(X))))&
(((~strong(alice)&~quiet(alice)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((happy(X)&kind(X))<=>(~wise(X)&~old(X))))&
(![X]:((kind(X)<~>~rich(X))=>happy(X)))&
(![X]:(curious(X)=>(old(X)|~funny(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(~humble(X)<~>~tall(X))))&
(((quiet(fred)|~humble(fred)))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((~happy(X)&~brave(X))=>(~tall(X)&patient(X))))&
(![X]:(~humble(X)<=>(kind(X)&~happy(X))))&
(![X]:((tall(X)|~old(X))=>(happy(X)&~old(X))))&
(![X]:((~tall(X)&~kind(X))=>strong(X)))&
(![X]:((quiet(X)&brave(X))=>(old(X)&~creative(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(~patient(X)<~>patient(X))))&
(![X]:(~creative(X)<=>(~tall(X)&~brave(X))))&
((~wise(john))=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((calm(X)&strong(X))<=>~brave(X)))&
(?[X]:(~tall(X)))&
((~old(lucy)&~brave(lucy)))&
((~happy(john)&~curious(john)))&
(?[X]:(~quiet(X)))&
((~strong(susan)<~>brave(susan)))&
(?[X]:(calm(X))) | ~funny(alice) | [] | null | 0 |
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Everyone who is either not tall or not funny is not tall and vice versa.
If someone is kind then someone is quiet.
If susan is either old or not creative then someone is humble or not kind.
Everyone who is both not tall and not quiet is either humble or not happy and vice versa.
Everyone who is both generous and not funny is old and vice versa.
Everyone who is not humble or kind is not patient.
If someone is both not creative and not generous then lucy is not humble.
Everyone who is not calm is both funny and old.
Everyone who is not happy is not kind.
Everyone who is both not wise and not generous is both not curious and creative.
Everyone who is funny or rich is not brave.
If paul is not generous or not curious then someone is not calm.
Everyone who is brave is not wise or not patient and vice versa.
Susan is generous or not calm.
Someone is wise or not humble.
John is not creative.
Someone is happy or not humble.
Alice is happy or not creative. | Paul is generous. | entailment | (((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
(((old(susan)<~>~creative(susan)))=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((generous(X)&~funny(X))<=>old(X)))&
(![X]:((~humble(X)|kind(X))=>~patient(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(~humble(lucy)))&
(![X]:(~calm(X)=>(funny(X)&old(X))))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:((~wise(X)&~generous(X))=>(~curious(X)&creative(X))))&
(![X]:((funny(X)|rich(X))=>~brave(X)))&
(((~generous(paul)|~curious(paul)))=>(?[X]:(~calm(X))))&
(![X]:(brave(X)<=>(~wise(X)|~patient(X))))&
((generous(susan)|~calm(susan)))&
(?[X]:((wise(X)|~humble(X))))&
(~creative(john))&
(?[X]:((happy(X)|~humble(X))))&
((happy(alice)|~creative(alice))) | generous(paul) | [
"p2",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6448395828851566552207349
% SZS output start Proof for 6448395828851566552207349
3. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p2]
7. ! [X0] : ((~funny(X0) & generous(X0)) <=> old(X0)) [input p6]
10. ! [X0] : (~calm(X0) => (old(X0) & funny(X0))) [input p9]
14. (~curious(paul) | ~generous(paul)) => ? [X0] : ~calm(X0) [input p13]
21. ~generous(paul) [input hypothesis]
28. ! [X0] : ((old(X0) & funny(X0)) | calm(X0)) [ennf transformation 10]
33. ? [X0] : ~calm(X0) | (curious(paul) & generous(paul)) [ennf transformation 14]
41. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | tall(X0)) & (~tall(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 3]
50. ! [X0] : (((~funny(X0) & generous(X0)) | ~old(X0)) & (old(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 7]
51. ! [X0] : (((~funny(X0) & generous(X0)) | ~old(X0)) & (old(X0) | funny(X0) | ~generous(X0))) [flattening 50]
52. ? [X0] : ~calm(X0) => ~calm(sK3) [choice axiom]
53. ~calm(sK3) | (curious(paul) & generous(paul)) [skolemisation 33,52]
68. ~tall(X0) | ~tall(X0) | funny(X0) [cnf transformation 41]
70. funny(X0) | tall(X0) | tall(X0) [cnf transformation 41]
82. ~old(X0) | ~funny(X0) [cnf transformation 51]
87. calm(X0) | old(X0) [cnf transformation 28]
92. ~calm(sK3) | generous(paul) [cnf transformation 53]
102. ~generous(paul) [cnf transformation 21]
103. ~tall(X0) | funny(X0) [duplicate literal removal 68]
104. funny(X0) | tall(X0) [duplicate literal removal 70]
106. 1 <=> ! [X0] : funny(X0) [avatar definition]
107. funny(X0) <- (1) [avatar component clause 106]
131. funny(X0) [subsumption resolution 103,104]
132. 1 [avatar split clause 131,106]
172. 16 <=> calm(sK3) [avatar definition]
174. ~calm(sK3) <- (~16) [avatar component clause 172]
177. 17 <=> generous(paul) [avatar definition]
180. 17 | ~16 [avatar split clause 92,172,177]
217. ~17 [avatar split clause 102,177]
225. old(sK3) <- (~16) [resolution 87,174]
234. ~funny(sK3) <- (~16) [resolution 225,82]
236. $false <- (1, ~16) [subsumption resolution 234,107]
237. ~1 | 16 [avatar contradiction clause 236]
238. $false [avatar sat refutation 132,180,217,237]
% SZS output end Proof for 6448395828851566552207349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Susan is either brave or strong.
John is not creative.
Susan is not calm.
Someone is both old and generous.
Someone is not wise or tall.
Someone is either not patient or tall.
Someone is not humble. | Mary is not happy. | contradiction | (![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
((brave(susan)<~>strong(susan)))&
(~creative(john))&
(~calm(susan))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:(~humble(X))) | ~happy(mary) | [
"p0",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 956967966509012913360840
% SZS output start Proof for 956967966509012913360840
1. ! [X0] : (brave(X0) => (strong(X0) | happy(X0))) [input p0]
5. ! [X0] : ((brave(X0) | ~funny(X0)) => (~calm(X0) & brave(X0))) [input p4]
6. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p5]
7. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p6]
9. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p8]
11. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (~rich(X0) | generous(X0))) [input p10]
12. ? [X0] : (curious(X0) & ~creative(X0)) => (creative(mary) | ~strong(mary)) [input p11]
13. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p12]
23. ~happy(mary) [input hypothesis]
26. ! [X0] : ((strong(X0) | happy(X0)) | ~brave(X0)) [ennf transformation 1]
27. ! [X0] : (strong(X0) | happy(X0) | ~brave(X0)) [flattening 26]
32. ! [X0] : ((~calm(X0) & brave(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 5]
35. (creative(mary) | ~strong(mary)) | ! [X0] : (~curious(X0) | creative(X0)) [ennf transformation 12]
36. creative(mary) | ~strong(mary) | ! [X0] : (~curious(X0) | creative(X0)) [flattening 35]
40. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 6]
41. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 40]
42. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 41]
43. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK0) | creative(sK0)) [choice axiom]
44. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK0) | creative(sK0)) | ~tall(fred) | old(fred)) [skolemisation 42,43]
45. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 7]
46. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 9]
47. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 46]
48. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 11]
49. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [flattening 48]
50. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 13]
51. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 50]
63. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 27]
68. funny(X0) | brave(X0) [cnf transformation 32]
70. ~calm(X0) | funny(X0) [cnf transformation 32]
75. tall(fred) | ~creative(X0) [cnf transformation 44]
76. tall(fred) | ~funny(X0) [cnf transformation 44]
78. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 45]
82. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 45]
89. ~tall(X0) | wise(X0) [cnf transformation 47]
94. rich(X0) | calm(X0) | curious(X0) [cnf transformation 49]
97. creative(mary) | ~strong(mary) | ~curious(X0) | creative(X0) [cnf transformation 36]
98. ~rich(fred) | ~wise(fred) [cnf transformation 51]
99. ~rich(fred) | calm(fred) [cnf transformation 51]
119. ~happy(mary) [cnf transformation 23]
120. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 78]
122. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 82]
139. 4 <=> creative(mary) [avatar definition]
140. creative(mary) <- (4) [avatar component clause 139]
144. 5 <=> ! [X0] : ~funny(X0) [avatar definition]
145. ~funny(X0) <- (5) [avatar component clause 144]
147. 6 <=> tall(fred) [avatar definition]
149. tall(fred) <- (6) [avatar component clause 147]
150. 5 | 6 [avatar split clause 76,147,144]
152. 7 <=> ! [X0] : ~creative(X0) [avatar definition]
153. ~creative(X0) <- (7) [avatar component clause 152]
154. 7 | 6 [avatar split clause 75,147,152]
171. ~tall(X0) | rich(X0) [subsumption resolution 120,122]
173. 11 <=> ! [X0] : (~curious(X0) | creative(X0)) [avatar definition]
174. ~curious(X0) | creative(X0) <- (11) [avatar component clause 173]
176. 12 <=> strong(mary) [avatar definition]
178. ~strong(mary) <- (~12) [avatar component clause 176]
179. 11 | ~12 | 4 [avatar split clause 97,139,176,173]
181. 13 <=> calm(fred) [avatar definition]
182. ~calm(fred) <- (~13) [avatar component clause 181]
183. calm(fred) <- (13) [avatar component clause 181]
190. 15 <=> wise(fred) [avatar definition]
192. ~wise(fred) <- (~15) [avatar component clause 190]
195. 16 <=> rich(fred) [avatar definition]
197. ~rich(fred) <- (~16) [avatar component clause 195]
198. 13 | ~16 [avatar split clause 99,195,181]
199. ~15 | ~16 [avatar split clause 98,195,190]
246. funny(fred) <- (13) [resolution 70,183]
247. $false <- (5, 13) [subsumption resolution 246,145]
248. ~5 | ~13 [avatar contradiction clause 247]
256. wise(fred) <- (6) [resolution 89,149]
257. $false <- (6, ~15) [subsumption resolution 256,192]
258. ~6 | 15 [avatar contradiction clause 257]
274. calm(fred) | curious(fred) <- (~16) [resolution 94,197]
285. curious(fred) <- (~13, ~16) [subsumption resolution 274,182]
288. rich(fred) <- (6) [resolution 149,171]
290. $false <- (6, ~16) [subsumption resolution 288,197]
291. ~6 | 16 [avatar contradiction clause 290]
292. brave(X0) <- (5) [resolution 145,68]
299. strong(X0) | happy(X0) <- (5) [resolution 292,63]
300. happy(mary) <- (5, ~12) [resolution 299,178]
302. $false <- (5, ~12) [subsumption resolution 300,119]
303. ~5 | 12 [avatar contradiction clause 302]
304. $false <- (4, 7) [subsumption resolution 140,153]
305. ~4 | ~7 [avatar contradiction clause 304]
306. ~curious(X0) <- (7, 11) [subsumption resolution 174,153]
309. $false <- (7, 11, ~13, ~16) [resolution 306,285]
310. ~7 | ~11 | 13 | 16 [avatar contradiction clause 309]
313. $false [avatar sat refutation 150,154,179,198,199,248,258,291,303,305,310]
% SZS output end Proof for 956967966509012913360840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is 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. | John is not creative. | 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)))) | ~creative(john) | [
"p1",
"p2",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 741139129589794078478755
% SZS output start Proof for 741139129589794078478755
2. ! [X0] : ((strong(X0) <~> curious(X0)) <=> (brave(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((kind(X0) | creative(X0)) => ~happy(X0)) [input p2]
13. ! [X0] : ((brave(X0) | happy(X0)) => (happy(X0) & ~rich(X0))) [input p12]
18. brave(john) <~> ~curious(john) [input p17]
24. creative(john) [input hypothesis]
28. ! [X0] : (~happy(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 3]
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]
70. (curious(john) | ~brave(john)) & (~curious(john) | brave(john)) [nnf transformation 18]
84. brave(X0) | ~strong(X0) | curious(X0) | ~strong(X0) [cnf transformation 46]
86. curious(X0) | strong(X0) | strong(X0) [cnf transformation 46]
90. ~happy(X0) | ~creative(X0) [cnf transformation 28]
119. ~brave(X0) | happy(X0) [cnf transformation 40]
135. ~curious(john) | brave(john) [cnf transformation 70]
136. curious(john) | ~brave(john) [cnf transformation 70]
145. creative(john) [cnf transformation 24]
148. brave(X0) | ~strong(X0) | curious(X0) [duplicate literal removal 84]
149. curious(X0) | strong(X0) [duplicate literal removal 86]
160. 3 <=> brave(john) [avatar definition]
162. brave(john) <- (3) [avatar component clause 160]
164. brave(X0) | curious(X0) [subsumption resolution 148,149]
307. curious(john) [subsumption resolution 136,164]
308. brave(john) [subsumption resolution 135,307]
309. 3 [avatar split clause 308,160]
330. happy(john) <- (3) [resolution 119,162]
332. ~creative(john) <- (3) [resolution 330,90]
333. $false <- (3) [subsumption resolution 332,145]
334. ~3 [avatar contradiction clause 333]
335. $false [avatar sat refutation 309,334]
% SZS output end Proof for 741139129589794078478755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or curious then paul is both not funny and wise.
If mary is not kind or humble then someone is either quiet or not tall.
If someone is both not kind and happy then someone is not creative and vice versa.
Everyone who is both not creative and not old is either quiet or brave.
Everyone who is either not calm or rich is both not happy and kind.
If fred is both not wise and not patient then someone is both not funny and not creative.
If fred is not tall or humble then someone is either not patient or calm and vice versa.
If paul is old then paul is happy.
If someone is not tall then someone is not kind and vice versa.
If susan is both not brave and not patient then someone is either not rich or not patient.
If someone is either patient or not happy then lucy is not quiet and vice versa.
If someone is not quiet or not patient then someone is both strong and not kind.
If someone is happy or not curious then paul is both brave and not curious and vice versa.
Everyone who is both not tall and not quiet is either not generous or not old.
Everyone who is old is not generous or creative.
If fred is either curious or not tall then john is not old or creative and vice versa.
Someone is curious.
Someone is tall.
Someone is both kind and not old.
Alice is both not funny and kind.
Someone is not funny.
Someone is not strong.
John is quiet or not generous.
Mary is either not calm or not generous. | Alice is not kind. | contradiction | ((?[X]:((old(X)|curious(X))))=>((~funny(paul)&wise(paul))))&
(((~kind(mary)|humble(mary)))=>(?[X]:((quiet(X)<~>~tall(X)))))&
((?[X]:((~kind(X)&happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~creative(X)&~old(X))=>(quiet(X)<~>brave(X))))&
(![X]:((~calm(X)<~>rich(X))=>(~happy(X)&kind(X))))&
(((~wise(fred)&~patient(fred)))=>(?[X]:((~funny(X)&~creative(X)))))&
(((~tall(fred)|humble(fred)))<=>(?[X]:((~patient(X)<~>calm(X)))))&
((old(paul))=>(happy(paul)))&
((?[X]:(~tall(X)))<=>(?[X]:(~kind(X))))&
(((~brave(susan)&~patient(susan)))=>(?[X]:((~rich(X)<~>~patient(X)))))&
((?[X]:((patient(X)<~>~happy(X))))<=>(~quiet(lucy)))&
((?[X]:((~quiet(X)|~patient(X))))=>(?[X]:((strong(X)&~kind(X)))))&
((?[X]:((happy(X)|~curious(X))))<=>((brave(paul)&~curious(paul))))&
(![X]:((~tall(X)&~quiet(X))=>(~generous(X)<~>~old(X))))&
(![X]:(old(X)=>(~generous(X)|creative(X))))&
(((curious(fred)<~>~tall(fred)))<=>((~old(john)|creative(john))))&
(?[X]:(curious(X)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)&~old(X))))&
((~funny(alice)&kind(alice)))&
(?[X]:(~funny(X)))&
(?[X]:(~strong(X)))&
((quiet(john)|~generous(john)))&
((~calm(mary)<~>~generous(mary))) | ~kind(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6133487105643876566488694
% SZS output start Proof for 6133487105643876566488694
20. kind(alice) & ~funny(alice) [input p19]
25. ~kind(alice) [input hypothesis]
33. kind(alice) [pure predicate removal 20]
143. kind(alice) [cnf transformation 33]
148. ~kind(alice) [cnf transformation 25]
365. $false [subsumption resolution 148,143]
% SZS output end Proof for 6133487105643876566488694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then john is old or generous.
Everyone who is rich is both not brave and old and vice versa.
Everyone who is both calm and brave is rich or wise and vice versa.
If someone is both humble and not brave then someone is either not strong or happy and vice versa.
If alice is not rich or not wise then susan is both kind and wise and vice versa.
Everyone who is either not humble or strong is either patient or not quiet.
Everyone who is both tall and not happy is patient or happy.
If someone is both not strong and kind then someone is both calm and not old and vice versa.
If someone is humble then someone is not quiet.
Everyone who is either creative or strong is not creative and vice versa.
Everyone who is patient is either old or not quiet and vice versa.
If susan is both rich and not old then alice is calm.
Everyone who is both not calm and not quiet is not quiet or quiet.
If susan is either calm or not brave then lucy is either generous or rich and vice versa.
Everyone who is both not curious and patient is not tall or curious.
John is both brave and not humble.
Someone is both not wise and not happy.
Fred is either not happy or not calm.
Fred is either kind or not creative.
Someone is not curious or not generous.
Someone is wise or generous. | Alice is old. | neutral | ((?[X]:(wise(X)))=>((old(john)|generous(john))))&
(![X]:(rich(X)<=>(~brave(X)&old(X))))&
(![X]:((calm(X)&brave(X))<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)&~brave(X))))<=>(?[X]:((~strong(X)<~>happy(X)))))&
(((~rich(alice)|~wise(alice)))<=>((kind(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>(patient(X)<~>~quiet(X))))&
(![X]:((tall(X)&~happy(X))=>(patient(X)|happy(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:((calm(X)&~old(X)))))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)<~>strong(X))<=>~creative(X)))&
(![X]:(patient(X)<=>(old(X)<~>~quiet(X))))&
(((rich(susan)&~old(susan)))=>(calm(alice)))&
(![X]:((~calm(X)&~quiet(X))=>(~quiet(X)|quiet(X))))&
(((calm(susan)<~>~brave(susan)))<=>((generous(lucy)<~>rich(lucy))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)|curious(X))))&
((brave(john)&~humble(john)))&
(?[X]:((~wise(X)&~happy(X))))&
((~happy(fred)<~>~calm(fred)))&
((kind(fred)<~>~creative(fred)))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:((wise(X)|generous(X)))) | old(alice) | [] | null | 0 |
If someone is calm or not patient then paul is both not curious and funny.
Everyone who is happy is either not brave or tall and vice versa.
If someone is not humble then someone is quiet or wise and vice versa.
If someone is either not kind or not strong then someone is either funny or old and vice versa.
If someone is humble then alice is not generous or not strong and vice versa.
Everyone who is both wise and not strong is not generous or not creative.
If paul is not rich then john is both strong and not humble and vice versa.
Everyone who is tall is strong or curious and vice versa.
Everyone who is kind is either happy or not tall and vice versa.
Everyone who is not happy is generous.
Everyone who is not generous is not old.
Everyone who is not tall is either not rich or creative.
Everyone who is both old and kind is both calm and curious and vice versa.
Everyone who is either not funny or not happy is tall.
If someone is not wise or not curious then someone is brave and vice versa.
If someone is both not humble and old then someone is either not wise or humble and vice versa.
Someone is creative.
Fred is wise.
John is both not patient and not brave.
Paul is old or not kind.
Someone is either not strong or not tall.
John is curious.
Someone is either not strong or old.
Lucy is either not humble or not wise. | John is not kind. | entailment | ((?[X]:((calm(X)|~patient(X))))=>((~curious(paul)&funny(paul))))&
(![X]:(happy(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)|wise(X)))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>(?[X]:((funny(X)<~>old(X)))))&
((?[X]:(humble(X)))<=>((~generous(alice)|~strong(alice))))&
(![X]:((wise(X)&~strong(X))=>(~generous(X)|~creative(X))))&
((~rich(paul))<=>((strong(john)&~humble(john))))&
(![X]:(tall(X)<=>(strong(X)|curious(X))))&
(![X]:(kind(X)<=>(happy(X)<~>~tall(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:(~generous(X)=>~old(X)))&
(![X]:(~tall(X)=>(~rich(X)<~>creative(X))))&
(![X]:((old(X)&kind(X))<=>(calm(X)&curious(X))))&
(![X]:((~funny(X)<~>~happy(X))=>tall(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~humble(X)&old(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(?[X]:(creative(X)))&
(wise(fred))&
((~patient(john)&~brave(john)))&
((old(paul)|~kind(paul)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(curious(john))&
(?[X]:((~strong(X)<~>old(X))))&
((~humble(lucy)<~>~wise(lucy))) | ~kind(john) | [
"p1",
"p7",
"p8",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3323021503412810632293844
% SZS output start Proof for 3323021503412810632293844
2. ! [X0] : (happy(X0) <=> (~brave(X0) <~> tall(X0))) [input p1]
8. ! [X0] : (tall(X0) <=> (curious(X0) | strong(X0))) [input p7]
9. ! [X0] : (kind(X0) <=> (happy(X0) <~> ~tall(X0))) [input p8]
19. ~brave(john) & ~patient(john) [input p18]
22. curious(john) [input p21]
25. kind(john) [input hypothesis]
37. ! [X0] : ((happy(X0) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0)))) & (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | ~happy(X0))) [nnf transformation 2]
55. ! [X0] : ((tall(X0) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | ~tall(X0))) [nnf transformation 8]
56. ! [X0] : ((tall(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ~tall(X0))) [flattening 55]
57. ! [X0] : ((kind(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ~kind(X0))) [nnf transformation 9]
86. ~tall(X0) | brave(X0) | ~happy(X0) [cnf transformation 37]
109. ~curious(X0) | tall(X0) [cnf transformation 56]
110. ~kind(X0) | happy(X0) | ~tall(X0) [cnf transformation 57]
136. ~brave(john) [cnf transformation 19]
140. curious(john) [cnf transformation 22]
145. kind(john) [cnf transformation 25]
350. tall(john) [resolution 109,140]
388. happy(john) | ~tall(john) [resolution 110,145]
403. 51 <=> tall(john) [avatar definition]
404. tall(john) <- (51) [avatar component clause 403]
407. 52 <=> happy(john) [avatar definition]
409. happy(john) <- (52) [avatar component clause 407]
410. ~51 | 52 [avatar split clause 388,407,403]
411. 51 [avatar split clause 350,403]
451. brave(john) | ~happy(john) <- (51) [resolution 404,86]
452. ~happy(john) <- (51) [subsumption resolution 451,136]
453. $false <- (51, 52) [subsumption resolution 452,409]
454. ~51 | ~52 [avatar contradiction clause 453]
455. $false [avatar sat refutation 410,411,454]
% SZS output end Proof for 3323021503412810632293844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or patient is both not strong and kind.
Everyone who is not tall is either funny or not generous and vice versa.
If susan is not calm then someone is either curious or not rich and vice versa.
Everyone who is humble or not happy is either not happy or not generous and vice versa.
If lucy is strong or quiet then someone is creative and vice versa.
Everyone who is curious or not happy is either generous or not generous.
Everyone who is both quiet and not strong is either not calm or funny and vice versa.
Everyone who is either not wise or patient is patient or not creative and vice versa.
Everyone who is curious is brave and vice versa.
Everyone who is either strong or calm is either not funny or quiet and vice versa.
Everyone who is not rich is not old or tall.
Everyone who is either humble or creative is not wise or generous.
If someone is either quiet or creative then paul is both not kind and not humble.
Everyone who is curious or not humble is both not funny and not happy.
If someone is not happy then susan is not rich.
Everyone who is both quiet and strong is creative or not rich.
Mary is creative.
Alice is both calm and old.
Paul is creative or quiet.
Lucy is either funny or not strong.
Someone is both generous and not wise.
Someone is both rich and wise.
John is both humble and brave.
Susan is either curious or kind. | Mary is wise. | entailment | (![X]:((funny(X)<~>patient(X))=>(~strong(X)&kind(X))))&
(![X]:(~tall(X)<=>(funny(X)<~>~generous(X))))&
((~calm(susan))<=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((humble(X)|~happy(X))<=>(~happy(X)<~>~generous(X))))&
(((strong(lucy)|quiet(lucy)))<=>(?[X]:(creative(X))))&
(![X]:((curious(X)|~happy(X))=>(generous(X)<~>~generous(X))))&
(![X]:((quiet(X)&~strong(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(patient(X)|~creative(X))))&
(![X]:(curious(X)<=>brave(X)))&
(![X]:((strong(X)<~>calm(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(~rich(X)=>(~old(X)|tall(X))))&
(![X]:((humble(X)<~>creative(X))=>(~wise(X)|generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~kind(paul)&~humble(paul))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&~happy(X))))&
((?[X]:(~happy(X)))=>(~rich(susan)))&
(![X]:((quiet(X)&strong(X))=>(creative(X)|~rich(X))))&
(creative(mary))&
((calm(alice)&old(alice)))&
((creative(paul)|quiet(paul)))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((generous(X)&~wise(X))))&
(?[X]:((rich(X)&wise(X))))&
((humble(john)&brave(john)))&
((curious(susan)<~>kind(susan))) | wise(mary) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8633834929326038643900493
% SZS output start Proof for 8633834929326038643900493
8. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> (~creative(X0) | patient(X0))) [input p7]
17. creative(mary) [input p16]
25. ~wise(mary) [input hypothesis]
55. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [flattening 55]
96. ~creative(X0) | patient(X0) | patient(X0) | wise(X0) [cnf transformation 56]
100. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 56]
125. creative(mary) [cnf transformation 17]
139. ~wise(mary) [cnf transformation 25]
140. ~creative(X0) | patient(X0) | wise(X0) [duplicate literal removal 96]
141. ~patient(X0) | wise(X0) [duplicate literal removal 100]
184. ~creative(X0) | wise(X0) [subsumption resolution 140,141]
249. wise(mary) [resolution 184,125]
252. $false [subsumption resolution 249,139]
% SZS output end Proof for 8633834929326038643900493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not calm and generous then mary is both tall and not curious.
If someone is funny or not generous then someone is either patient or quiet.
Everyone who is either not strong or not generous is brave or not creative.
If someone is rich then susan is both not patient and strong.
Everyone who is funny or old is both not strong and kind.
Everyone who is either not calm or happy is tall or not quiet and vice versa.
Everyone who is not old or humble is both not tall and generous and vice versa.
If fred is not wise or humble then someone is both not tall and happy.
Everyone who is either rich or not curious is not patient or not wise.
If paul is creative then john is both not funny and not tall and vice versa.
Everyone who is both quiet and not creative is humble or not old.
If paul is not generous or humble then alice is not generous or not happy.
Everyone who is not tall is not curious.
Everyone who is not brave is not patient and vice versa.
If alice is not patient or not rich then someone is not wise and vice versa.
If someone is either not rich or strong then someone is either not kind or not calm and vice versa.
Someone is both not patient and rich.
Someone is not tall or humble.
Lucy is tall or happy.
Paul is both not humble and not old.
Someone is curious or creative.
Fred is not calm or not strong.
Paul is quiet or not curious.
John is not kind. | Paul is creative. | entailment | (((~calm(susan)&generous(susan)))=>((tall(mary)&~curious(mary))))&
((?[X]:((funny(X)|~generous(X))))=>(?[X]:((patient(X)<~>quiet(X)))))&
(![X]:((~strong(X)<~>~generous(X))=>(brave(X)|~creative(X))))&
((?[X]:(rich(X)))=>((~patient(susan)&strong(susan))))&
(![X]:((funny(X)|old(X))=>(~strong(X)&kind(X))))&
(![X]:((~calm(X)<~>happy(X))<=>(tall(X)|~quiet(X))))&
(![X]:((~old(X)|humble(X))<=>(~tall(X)&generous(X))))&
(((~wise(fred)|humble(fred)))=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:((rich(X)<~>~curious(X))=>(~patient(X)|~wise(X))))&
((creative(paul))<=>((~funny(john)&~tall(john))))&
(![X]:((quiet(X)&~creative(X))=>(humble(X)|~old(X))))&
(((~generous(paul)|humble(paul)))=>((~generous(alice)|~happy(alice))))&
(![X]:(~tall(X)=>~curious(X)))&
(![X]:(~brave(X)<=>~patient(X)))&
(((~patient(alice)|~rich(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(?[X]:((~patient(X)&rich(X))))&
(?[X]:((~tall(X)|humble(X))))&
((tall(lucy)|happy(lucy)))&
((~humble(paul)&~old(paul)))&
(?[X]:((curious(X)|creative(X))))&
((~calm(fred)|~strong(fred)))&
((quiet(paul)|~curious(paul)))&
(~kind(john)) | creative(paul) | [
"p4",
"p6",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3450838280190229577295899
% SZS output start Proof for 3450838280190229577295899
5. ! [X0] : ((old(X0) | funny(X0)) => (kind(X0) & ~strong(X0))) [input p4]
7. ! [X0] : ((humble(X0) | ~old(X0)) <=> (generous(X0) & ~tall(X0))) [input p6]
10. creative(paul) <=> (~tall(john) & ~funny(john)) [input p9]
24. ~kind(john) [input p23]
25. ~creative(paul) [input hypothesis]
35. ! [X0] : ((kind(X0) & ~strong(X0)) | (~old(X0) & ~funny(X0))) [ennf transformation 5]
52. ! [X0] : (((humble(X0) | ~old(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 7]
53. ! [X0] : ((humble(X0) | ~old(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | (~humble(X0) & old(X0)))) [flattening 52]
57. (creative(paul) | (tall(john) | funny(john))) & ((~tall(john) & ~funny(john)) | ~creative(paul)) [nnf transformation 10]
58. (creative(paul) | tall(john) | funny(john)) & ((~tall(john) & ~funny(john)) | ~creative(paul)) [flattening 57]
87. ~funny(X0) | kind(X0) [cnf transformation 35]
88. ~old(X0) | kind(X0) [cnf transformation 35]
95. ~tall(X0) | old(X0) [cnf transformation 53]
108. creative(paul) | tall(john) | funny(john) [cnf transformation 58]
134. ~kind(john) [cnf transformation 24]
135. ~creative(paul) [cnf transformation 25]
206. 16 <=> funny(john) [avatar definition]
208. funny(john) <- (16) [avatar component clause 206]
210. 17 <=> tall(john) [avatar definition]
212. tall(john) <- (17) [avatar component clause 210]
214. 18 <=> creative(paul) [avatar definition]
217. 16 | 17 | 18 [avatar split clause 108,214,210,206]
330. ~18 [avatar split clause 135,214]
334. kind(john) <- (16) [resolution 87,208]
335. $false <- (16) [subsumption resolution 334,134]
336. ~16 [avatar contradiction clause 335]
338. old(john) <- (17) [resolution 95,212]
345. kind(john) <- (17) [resolution 338,88]
347. $false <- (17) [subsumption resolution 345,134]
348. ~17 [avatar contradiction clause 347]
349. $false [avatar sat refutation 217,330,336,348]
% SZS output end Proof for 3450838280190229577295899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not rich is either humble or curious and vice versa. Everyone who is both not patient and not old is both humble and quiet. If someone is calm or brave then paul is not quiet or creative and vice versa. If someone is not old or not creative then paul is both not wise and kind and vice versa. If john is kind or not calm then someone is not kind or not humble and vice versa. If paul is tall then fred is either strong or brave and vice versa. Everyone who is either strong or not kind is not brave or generous. Everyone who is either rich or tall is either funny or not happy and vice versa. Everyone who is either not quiet or not generous is either quiet or patient and vice versa. If someone is happy or creative then mary is both patient and not calm. If john is either patient or not calm then someone is either not patient or old and vice versa. Everyone who is either not patient or not happy is quiet. Everyone who is old is not old. Everyone who is both quiet and not happy is brave and vice versa. Everyone who is both not tall and not rich is either wise or not generous. If mary is both generous and not happy then susan is tall or curious. Paul is rich or not curious. Paul is either not funny or strong. Lucy is brave. Lucy is quiet or calm. Susan is both funny and kind. Lucy is either not old or strong. | Mary is strong. | neutral | (![X]:((funny(X)<~>~rich(X))<=>(humble(X)<~>curious(X))))&
(![X]:((~patient(X)&~old(X))=>(humble(X)&quiet(X))))&
((?[X]:((calm(X)|brave(X))))<=>((~quiet(paul)|creative(paul))))&
((?[X]:((~old(X)|~creative(X))))<=>((~wise(paul)&kind(paul))))&
(((kind(john)|~calm(john)))<=>(?[X]:((~kind(X)|~humble(X)))))&
((tall(paul))<=>((strong(fred)<~>brave(fred))))&
(![X]:((strong(X)<~>~kind(X))=>(~brave(X)|generous(X))))&
(![X]:((rich(X)<~>tall(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(quiet(X)<~>patient(X))))&
((?[X]:((happy(X)|creative(X))))=>((patient(mary)&~calm(mary))))&
(((patient(john)<~>~calm(john)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:((~patient(X)<~>~happy(X))=>quiet(X)))&
(![X]:(old(X)=>~old(X)))&
(![X]:((quiet(X)&~happy(X))<=>brave(X)))&
(![X]:((~tall(X)&~rich(X))=>(wise(X)<~>~generous(X))))&
(((generous(mary)&~happy(mary)))=>((tall(susan)|curious(susan))))&
((rich(paul)|~curious(paul)))&
((~funny(paul)<~>strong(paul)))&
(brave(lucy))&
((quiet(lucy)|calm(lucy)))&
((funny(susan)&kind(susan)))&
((~old(lucy)<~>strong(lucy))) | strong(mary) | [] | null | 0 |
If lucy is both creative and tall then alice is both funny and generous.
If fred is rich or not calm then mary is either kind or not kind and vice versa.
Everyone who is either not curious or not rich is either not wise or wise and vice versa.
If paul is either happy or not wise then someone is both happy and rich.
If someone is patient or old then mary is both not quiet and funny and vice versa.
If someone is either wise or not strong then mary is rich or old.
Everyone who is both not calm and quiet is not old or funny and vice versa.
Everyone who is not kind is both not tall and humble and vice versa.
Everyone who is kind is both funny and calm and vice versa.
Everyone who is not creative is both happy and brave and vice versa.
Everyone who is either patient or not generous is not strong and vice versa.
Everyone who is creative or wise is not old and vice versa.
Everyone who is curious or not funny is not creative.
Everyone who is either not creative or calm is kind and vice versa.
If someone is either not rich or not wise then fred is both patient and not tall.
If lucy is both strong and not rich then lucy is either curious or quiet.
Someone is quiet.
Fred is brave or not curious.
Someone is generous or not happy.
Susan is not wise or not happy.
Susan is not patient or not creative. | Paul is funny. | entailment | (((creative(lucy)&tall(lucy)))=>((funny(alice)&generous(alice))))&
(((rich(fred)|~calm(fred)))<=>((kind(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~wise(X)<~>wise(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((patient(X)|old(X))))<=>((~quiet(mary)&funny(mary))))&
((?[X]:((wise(X)<~>~strong(X))))=>((rich(mary)|old(mary))))&
(![X]:((~calm(X)&quiet(X))<=>(~old(X)|funny(X))))&
(![X]:(~kind(X)<=>(~tall(X)&humble(X))))&
(![X]:(kind(X)<=>(funny(X)&calm(X))))&
(![X]:(~creative(X)<=>(happy(X)&brave(X))))&
(![X]:((patient(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((creative(X)|wise(X))<=>~old(X)))&
(![X]:((curious(X)|~funny(X))=>~creative(X)))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
((?[X]:((~rich(X)<~>~wise(X))))=>((patient(fred)&~tall(fred))))&
(((strong(lucy)&~rich(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(?[X]:(quiet(X)))&
((brave(fred)|~curious(fred)))&
(?[X]:((generous(X)|~happy(X))))&
((~wise(susan)|~happy(susan)))&
((~patient(susan)|~creative(susan))) | funny(paul) | [
"p4",
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8374743825423052919597603
% SZS output start Proof for 8374743825423052919597603
5. ? [X0] : (old(X0) | patient(X0)) <=> (funny(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (funny(X0) | ~old(X0))) [input p6]
9. ! [X0] : (kind(X0) <=> (calm(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~funny(X0) | curious(X0)) => ~creative(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> kind(X0)) [input p13]
22. ~funny(paul) [input hypothesis]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~curious(X0))) [ennf transformation 13]
38. (? [X0] : (old(X0) | patient(X0)) | (~funny(mary) | quiet(mary))) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 5]
39. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 38]
40. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 39]
41. ? [X0] : (old(X0) | patient(X0)) => (old(sK1) | patient(sK1)) [choice axiom]
42. ((old(sK1) | patient(sK1)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 40,41]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
48. ! [X0] : ((kind(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~kind(X0))) [flattening 48]
55. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
83. ~quiet(mary) | ~old(X1) [cnf transformation 42]
85. funny(mary) | ~old(X1) [cnf transformation 42]
90. ~calm(X0) | old(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 45]
98. ~kind(X0) | calm(X0) [cnf transformation 49]
111. ~creative(X0) | funny(X0) [cnf transformation 28]
112. kind(X0) | calm(X0) | creative(X0) [cnf transformation 55]
115. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 55]
127. ~funny(paul) [cnf transformation 22]
189. 12 <=> quiet(mary) [avatar definition]
193. 13 <=> funny(mary) [avatar definition]
194. funny(mary) <- (13) [avatar component clause 193]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 13 [avatar split clause 85,193,206]
213. 16 | ~12 [avatar split clause 83,189,206]
231. ~kind(X0) | creative(X0) [subsumption resolution 115,98]
232. calm(X0) | creative(X0) [subsumption resolution 112,231]
305. quiet(mary) <- (13) [resolution 93,194]
322. old(X1) | creative(X1) [resolution 232,90]
332. 12 | ~13 [avatar split clause 305,193,189]
402. creative(X0) <- (16) [resolution 322,207]
406. funny(X1) <- (16) [resolution 402,111]
412. $false <- (16) [resolution 406,127]
417. ~16 [avatar contradiction clause 412]
418. $false [avatar sat refutation 208,213,332,417]
% SZS output end Proof for 8374743825423052919597603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not generous then someone is either tall or creative.
Everyone who is either not brave or rich is not funny.
If someone is not wise or rich then paul is generous.
Everyone who is both generous and creative is both not happy and not rich and vice versa.
If someone is not creative or tall then someone is quiet.
If someone is either quiet or not curious then someone is either rich or not creative.
If john is patient or not quiet then someone is both not creative and creative and vice versa.
If paul is both funny and generous then john is not old or not generous.
Everyone who is not humble is quiet or brave and vice versa.
Everyone who is both curious and quiet is both not old and not tall and vice versa.
If someone is happy or strong then mary is not generous.
Everyone who is not generous is not patient or not humble and vice versa.
Everyone who is both not patient and not happy is old or not rich.
Everyone who is not creative is not old or not brave.
If susan is not creative or curious then paul is both curious and rich and vice versa.
Everyone who is wise is either quiet or old.
Paul is not brave or not curious.
Someone is not calm or not quiet.
Someone is generous or not rich.
Paul is not happy or not strong.
Lucy is both not calm and quiet.
Someone is quiet.
Lucy is not generous or generous. | Paul is not curious. | neutral | ((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~brave(X)<~>rich(X))=>~funny(X)))&
((?[X]:((~wise(X)|rich(X))))=>(generous(paul)))&
(![X]:((generous(X)&creative(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((~creative(X)|tall(X))))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
(((patient(john)|~quiet(john)))<=>(?[X]:((~creative(X)&creative(X)))))&
(((funny(paul)&generous(paul)))=>((~old(john)|~generous(john))))&
(![X]:(~humble(X)<=>(quiet(X)|brave(X))))&
(![X]:((curious(X)&quiet(X))<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)|strong(X))))=>(~generous(mary)))&
(![X]:(~generous(X)<=>(~patient(X)|~humble(X))))&
(![X]:((~patient(X)&~happy(X))=>(old(X)|~rich(X))))&
(![X]:(~creative(X)=>(~old(X)|~brave(X))))&
(((~creative(susan)|curious(susan)))<=>((curious(paul)&rich(paul))))&
(![X]:(wise(X)=>(quiet(X)<~>old(X))))&
((~brave(paul)|~curious(paul)))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:((generous(X)|~rich(X))))&
((~happy(paul)|~strong(paul)))&
((~calm(lucy)&quiet(lucy)))&
(?[X]:(quiet(X)))&
((~generous(lucy)|generous(lucy))) | ~curious(paul) | [] | null | 0 |
If alice is both generous and not curious then lucy is not tall and vice versa.
If lucy is either old or quiet then someone is not funny.
Everyone who is both not rich and not tall is not strong or funny and vice versa.
Everyone who is both humble and not kind is kind and vice versa.
Everyone who is patient is creative or not generous.
Everyone who is brave or old is either not brave or not rich and vice versa.
Everyone who is not kind is both not funny and not old and vice versa.
Everyone who is not quiet is not patient or not kind.
Everyone who is both not calm and not brave is both wise and rich and vice versa.
Everyone who is both wise and happy is not creative.
Everyone who is either strong or not old is either brave or strong.
Everyone who is tall is not creative or wise.
Everyone who is not strong or calm is not strong.
Everyone who is not happy or creative is not curious or wise.
Everyone who is either not creative or calm is either patient or not generous and vice versa.
If fred is not generous or creative then alice is old and vice versa.
Fred is either tall or generous.
John is both quiet and creative.
Someone is either curious or strong.
Susan is patient or not creative.
Fred is either not old or quiet.
Lucy is curious or strong.
Someone is both patient and not rich. | Susan is not strong. | neutral | (((generous(alice)&~curious(alice)))<=>(~tall(lucy)))&
(((old(lucy)<~>quiet(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)&~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~strong(X)|calm(X))=>~strong(X)))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
((tall(fred)<~>generous(fred)))&
((quiet(john)&creative(john)))&
(?[X]:((curious(X)<~>strong(X))))&
((patient(susan)|~creative(susan)))&
((~old(fred)<~>quiet(fred)))&
((curious(lucy)|strong(lucy)))&
(?[X]:((patient(X)&~rich(X)))) | ~strong(susan) | [] | null | 0 |
If john is not kind then someone is wise or funny.
Everyone who is humble or tall is not quiet or curious.
If someone is strong then alice is creative and vice versa.
If alice is tall or not quiet then someone is humble or not quiet and vice versa.
If alice is not calm then someone is either tall or not tall and vice versa.
Everyone who is not patient is either calm or not generous and vice versa.
Everyone who is not generous or not kind is rich or not patient and vice versa.
If someone is both not kind and rich then someone is creative and vice versa.
Everyone who is funny or generous is either rich or quiet.
If susan is funny or not generous then alice is not rich or not patient.
Everyone who is both not calm and not rich is not wise or kind and vice versa.
If someone is funny then susan is not happy and vice versa.
If someone is not strong then someone is not patient or not humble and vice versa.
Everyone who is both not kind and calm is either strong or not humble and vice versa.
Everyone who is old is either wise or not curious.
If alice is not brave then someone is brave and vice versa.
Someone is both not quiet and not kind.
Someone is both not creative and not generous.
Someone is rich.
Someone is kind or tall.
Someone is either not wise or not strong.
Lucy is either not brave or curious.
Someone is not brave.
Someone is not quiet. | Alice is not kind. | neutral | ((~kind(john))=>(?[X]:((wise(X)|funny(X)))))&
(![X]:((humble(X)|tall(X))=>(~quiet(X)|curious(X))))&
((?[X]:(strong(X)))<=>(creative(alice)))&
(((tall(alice)|~quiet(alice)))<=>(?[X]:((humble(X)|~quiet(X)))))&
((~calm(alice))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:(~patient(X)<=>(calm(X)<~>~generous(X))))&
(![X]:((~generous(X)|~kind(X))<=>(rich(X)|~patient(X))))&
((?[X]:((~kind(X)&rich(X))))<=>(?[X]:(creative(X))))&
(![X]:((funny(X)|generous(X))=>(rich(X)<~>quiet(X))))&
(((funny(susan)|~generous(susan)))=>((~rich(alice)|~patient(alice))))&
(![X]:((~calm(X)&~rich(X))<=>(~wise(X)|kind(X))))&
((?[X]:(funny(X)))<=>(~happy(susan)))&
((?[X]:(~strong(X)))<=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((~kind(X)&calm(X))<=>(strong(X)<~>~humble(X))))&
(![X]:(old(X)=>(wise(X)<~>~curious(X))))&
((~brave(alice))<=>(?[X]:(brave(X))))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((~creative(X)&~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((~wise(X)<~>~strong(X))))&
((~brave(lucy)<~>curious(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X))) | ~kind(alice) | [] | null | 0 |
Everyone who is either not curious or curious is not quiet or not creative.
If someone is curious then someone is not quiet and vice versa.
If lucy is both not rich and not funny then someone is not funny or funny.
Everyone who is either not old or not quiet is both patient and happy and vice versa.
If john is brave or not tall then alice is not humble.
If someone is both kind and old then someone is patient and vice versa.
Everyone who is both funny and old is brave or generous and vice versa.
Everyone who is not rich or humble is both not happy and generous and vice versa.
Everyone who is not humble or not patient is not brave and vice versa.
Everyone who is not strong or rich is both quiet and kind and vice versa.
Everyone who is both not humble and not tall is both rich and wise.
Everyone who is not tall or wise is either patient or not curious and vice versa.
If someone is strong then someone is not funny or not calm and vice versa.
If someone is calm or not calm then someone is not tall or curious.
If someone is either not brave or not creative then alice is both not funny and not humble and vice versa.
Everyone who is wise is either not generous or not curious.
Paul is not wise or not curious.
Someone is happy.
Paul is quiet or not calm.
Alice is not creative.
Fred is both not calm and not funny.
Someone is creative or not happy.
Susan is funny. | Fred is not brave. | entailment | (![X]:((~curious(X)<~>curious(X))=>(~quiet(X)|~creative(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~quiet(X))))&
(((~rich(lucy)&~funny(lucy)))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((~old(X)<~>~quiet(X))<=>(patient(X)&happy(X))))&
(((brave(john)|~tall(john)))=>(~humble(alice)))&
((?[X]:((kind(X)&old(X))))<=>(?[X]:(patient(X))))&
(![X]:((funny(X)&old(X))<=>(brave(X)|generous(X))))&
(![X]:((~rich(X)|humble(X))<=>(~happy(X)&generous(X))))&
(![X]:((~humble(X)|~patient(X))<=>~brave(X)))&
(![X]:((~strong(X)|rich(X))<=>(quiet(X)&kind(X))))&
(![X]:((~humble(X)&~tall(X))=>(rich(X)&wise(X))))&
(![X]:((~tall(X)|wise(X))<=>(patient(X)<~>~curious(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~funny(X)|~calm(X)))))&
((?[X]:((calm(X)|~calm(X))))=>(?[X]:((~tall(X)|curious(X)))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>((~funny(alice)&~humble(alice))))&
(![X]:(wise(X)=>(~generous(X)<~>~curious(X))))&
((~wise(paul)|~curious(paul)))&
(?[X]:(happy(X)))&
((quiet(paul)|~calm(paul)))&
(~creative(alice))&
((~calm(fred)&~funny(fred)))&
(?[X]:((creative(X)|~happy(X))))&
(funny(susan)) | ~brave(fred) | [
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2856578070337217223440692
% SZS output start Proof for 2856578070337217223440692
7. ! [X0] : ((old(X0) & funny(X0)) <=> (generous(X0) | brave(X0))) [input p6]
21. ~funny(fred) & ~calm(fred) [input p20]
24. brave(fred) [input hypothesis]
53. ! [X0] : (((old(X0) & funny(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~old(X0) | ~funny(X0)))) [nnf transformation 7]
54. ! [X0] : (((old(X0) & funny(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~old(X0) | ~funny(X0))) [flattening 53]
98. ~brave(X0) | funny(X0) [cnf transformation 54]
141. ~funny(fred) [cnf transformation 21]
144. brave(fred) [cnf transformation 24]
287. funny(fred) [resolution 98,144]
289. $false [subsumption resolution 287,141]
% SZS output end Proof for 2856578070337217223440692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and not strong then someone is rich and vice versa.
Everyone who is either tall or wise is strong or not kind.
If someone is calm or humble then someone is not creative or curious and vice versa.
If paul is both not humble and not patient then someone is either not funny or calm and vice versa.
Everyone who is patient or not strong is not curious or funny.
Everyone who is not creative is both not patient and not strong.
If someone is not old or creative then someone is either funny or patient and vice versa.
Everyone who is wise is not rich or funny and vice versa.
If someone is not rich or curious then paul is not strong or generous and vice versa.
Everyone who is tall or wise is patient and vice versa.
Everyone who is creative or tall is not brave or not calm and vice versa.
Everyone who is not curious or not quiet is not curious or tall and vice versa.
If someone is not rich then lucy is both not quiet and wise.
Everyone who is not tall is quiet or old and vice versa.
If someone is both rich and tall then someone is both not old and rich.
Everyone who is brave or not brave is not calm and vice versa.
John is both quiet and wise.
Someone is either not curious or curious.
Someone is both not generous and not humble.
Someone is both strong and tall.
Fred is not brave or happy.
Someone is not brave or not humble.
Paul is both not quiet and not funny.
Someone is both not quiet and tall. | Paul is old. | entailment | ((?[X]:((~tall(X)&~strong(X))))<=>(?[X]:(rich(X))))&
(![X]:((tall(X)<~>wise(X))=>(strong(X)|~kind(X))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((patient(X)|~strong(X))=>(~curious(X)|funny(X))))&
(![X]:(~creative(X)=>(~patient(X)&~strong(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((funny(X)<~>patient(X)))))&
(![X]:(wise(X)<=>(~rich(X)|funny(X))))&
((?[X]:((~rich(X)|curious(X))))<=>((~strong(paul)|generous(paul))))&
(![X]:((tall(X)|wise(X))<=>patient(X)))&
(![X]:((creative(X)|tall(X))<=>(~brave(X)|~calm(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(~curious(X)|tall(X))))&
((?[X]:(~rich(X)))=>((~quiet(lucy)&wise(lucy))))&
(![X]:(~tall(X)<=>(quiet(X)|old(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((brave(X)|~brave(X))<=>~calm(X)))&
((quiet(john)&wise(john)))&
(?[X]:((~curious(X)<~>curious(X))))&
(?[X]:((~generous(X)&~humble(X))))&
(?[X]:((strong(X)&tall(X))))&
((~brave(fred)|happy(fred)))&
(?[X]:((~brave(X)|~humble(X))))&
((~quiet(paul)&~funny(paul)))&
(?[X]:((~quiet(X)&tall(X)))) | old(paul) | [
"p3",
"p9",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2421503490128155084768084
% SZS output start Proof for 2421503490128155084768084
4. (~patient(paul) & ~humble(paul)) <=> ? [X0] : (~funny(X0) <~> calm(X0)) [input p3]
10. ! [X0] : ((wise(X0) | tall(X0)) <=> patient(X0)) [input p9]
14. ! [X0] : (~tall(X0) <=> (old(X0) | quiet(X0))) [input p13]
16. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~calm(X0)) [input p15]
23. ~funny(paul) & ~quiet(paul) [input p22]
25. ~old(paul) [input hypothesis]
47. ((~patient(paul) & ~humble(paul)) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X0] : ((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (patient(paul) | humble(paul))) [nnf transformation 4]
48. ((~patient(paul) & ~humble(paul)) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X0] : ((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | patient(paul) | humble(paul)) [flattening 47]
49. ((~patient(paul) & ~humble(paul)) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (? [X1] : ((~calm(X1) | funny(X1)) & (calm(X1) | ~funny(X1))) | patient(paul) | humble(paul)) [rectify 48]
50. ? [X1] : ((~calm(X1) | funny(X1)) & (calm(X1) | ~funny(X1))) => ((~calm(sK4) | funny(sK4)) & (calm(sK4) | ~funny(sK4))) [choice axiom]
51. ((~patient(paul) & ~humble(paul)) | ! [X0] : ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(sK4) | funny(sK4)) & (calm(sK4) | ~funny(sK4))) | patient(paul) | humble(paul)) [skolemisation 49,50]
64. ! [X0] : (((wise(X0) | tall(X0)) | ~patient(X0)) & (patient(X0) | (~wise(X0) & ~tall(X0)))) [nnf transformation 10]
65. ! [X0] : ((wise(X0) | tall(X0) | ~patient(X0)) & (patient(X0) | (~wise(X0) & ~tall(X0)))) [flattening 64]
70. ! [X0] : ((~tall(X0) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | tall(X0))) [nnf transformation 14]
71. ! [X0] : ((~tall(X0) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | tall(X0))) [flattening 70]
75. ! [X0] : (((~brave(X0) | brave(X0)) | calm(X0)) & (~calm(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 16]
76. ! [X0] : ((~brave(X0) | brave(X0) | calm(X0)) & (~calm(X0) | (brave(X0) & ~brave(X0)))) [flattening 75]
99. ~patient(paul) | calm(X0) | funny(X0) [cnf transformation 51]
118. ~tall(X0) | patient(X0) [cnf transformation 65]
131. quiet(X0) | old(X0) | tall(X0) [cnf transformation 71]
136. ~calm(X0) | ~brave(X0) [cnf transformation 76]
137. ~calm(X0) | brave(X0) [cnf transformation 76]
148. ~quiet(paul) [cnf transformation 23]
149. ~funny(paul) [cnf transformation 23]
152. ~old(paul) [cnf transformation 25]
203. 13 <=> ! [X3] : ~calm(X3) [avatar definition]
204. ~calm(X3) <- (13) [avatar component clause 203]
210. 15 <=> patient(paul) [avatar definition]
215. 16 <=> ! [X0] : (calm(X0) | funny(X0)) [avatar definition]
216. calm(X0) | funny(X0) <- (16) [avatar component clause 215]
217. 16 | ~15 [avatar split clause 99,210,215]
314. ~calm(X0) [subsumption resolution 136,137]
315. 13 [avatar split clause 314,203]
454. old(paul) | tall(paul) [resolution 131,148]
457. tall(paul) [subsumption resolution 454,152]
467. patient(paul) [resolution 457,118]
470. 15 [avatar split clause 467,210]
471. funny(X0) <- (13, 16) [subsumption resolution 216,204]
476. $false <- (13, 16) [resolution 471,149]
481. ~13 | ~16 [avatar contradiction clause 476]
482. $false [avatar sat refutation 217,315,470,481]
% SZS output end Proof for 2421503490128155084768084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or calm is not quiet or not wise and vice versa. If someone is not old or kind then john is not wise or not creative and vice versa. If someone is not quiet then someone is strong or kind. If fred is not patient then someone is calm. Everyone who is not happy or not patient is not old or not generous. Everyone who is both not funny and not calm is either not creative or not tall and vice versa. If paul is not strong then someone is not happy and vice versa. Everyone who is either not patient or funny is not quiet. Everyone who is not kind or rich is both strong and generous. If someone is not happy then mary is both kind and not kind. If someone is not quiet or funny then paul is both not tall and not wise. Everyone who is not kind is not calm or not kind and vice versa. Everyone who is either humble or wise is not curious or creative. Everyone who is not creative is either not calm or not wise and vice versa. Everyone who is both strong and not funny is rich and vice versa. If fred is tall then someone is brave and vice versa. Someone is patient. Someone is creative or strong. Fred is not brave. Mary is kind or quiet. Someone is either not rich or creative. Someone is both brave and not curious. Paul is wise. Susan is either patient or wise. | Susan is not tall. | entailment | (![X]:((creative(X)<~>calm(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((~old(X)|kind(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)|kind(X)))))&
((~patient(fred))=>(?[X]:(calm(X))))&
(![X]:((~happy(X)|~patient(X))=>(~old(X)|~generous(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~creative(X)<~>~tall(X))))&
((~strong(paul))<=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)<~>funny(X))=>~quiet(X)))&
(![X]:((~kind(X)|rich(X))=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))=>((kind(mary)&~kind(mary))))&
((?[X]:((~quiet(X)|funny(X))))=>((~tall(paul)&~wise(paul))))&
(![X]:(~kind(X)<=>(~calm(X)|~kind(X))))&
(![X]:((humble(X)<~>wise(X))=>(~curious(X)|creative(X))))&
(![X]:(~creative(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~funny(X))<=>rich(X)))&
((tall(fred))<=>(?[X]:(brave(X))))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)|strong(X))))&
(~brave(fred))&
((kind(mary)|quiet(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((brave(X)&~curious(X))))&
(wise(paul))&
((patient(susan)<~>wise(susan))) | ~tall(susan) | [
"p0",
"p5",
"p7",
"p10",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4201566805401388830435796
% SZS output start Proof for 4201566805401388830435796
1. ! [X0] : ((creative(X0) <~> calm(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p0]
6. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p5]
8. ! [X0] : ((~patient(X0) <~> funny(X0)) => ~quiet(X0)) [input p7]
11. ? [X0] : (funny(X0) | ~quiet(X0)) => (~wise(paul) & ~tall(paul)) [input p10]
23. wise(paul) [input p22]
24. patient(susan) <~> wise(susan) [input p23]
25. tall(susan) [input hypothesis]
33. ! [X0] : (~quiet(X0) | (~patient(X0) <=> funny(X0))) [ennf transformation 8]
36. (~wise(paul) & ~tall(paul)) | ! [X0] : (~funny(X0) & quiet(X0)) [ennf transformation 11]
37. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [flattening 37]
49. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (calm(X0) | funny(X0)))) [nnf transformation 6]
50. ! [X0] : (((~calm(X0) & ~funny(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | calm(X0) | funny(X0))) [flattening 49]
55. ! [X0] : (~quiet(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) [nnf transformation 33]
74. (~wise(susan) | ~patient(susan)) & (wise(susan) | patient(susan)) [nnf transformation 24]
78. wise(X0) | creative(X0) | calm(X0) [cnf transformation 38]
80. ~calm(X0) | ~creative(X0) | wise(X0) [cnf transformation 38]
89. ~tall(X0) | ~creative(X0) | calm(X0) | funny(X0) [cnf transformation 50]
93. ~tall(X0) | ~calm(X0) | creative(X0) [cnf transformation 50]
97. ~quiet(X0) | funny(X0) | patient(X0) [cnf transformation 55]
107. ~wise(paul) | quiet(X0) [cnf transformation 36]
108. ~wise(paul) | ~funny(X0) [cnf transformation 36]
128. wise(paul) [cnf transformation 23]
130. ~wise(susan) | ~patient(susan) [cnf transformation 74]
131. tall(susan) [cnf transformation 25]
159. 7 <=> ! [X1] : quiet(X1) [avatar definition]
160. quiet(X1) <- (7) [avatar component clause 159]
199. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
200. ~funny(X0) <- (16) [avatar component clause 199]
202. 17 <=> wise(paul) [avatar definition]
205. 16 | ~17 [avatar split clause 108,202,199]
206. 7 | ~17 [avatar split clause 107,202,159]
250. 17 [avatar split clause 128,202]
252. 27 <=> patient(susan) [avatar definition]
254. ~patient(susan) <- (~27) [avatar component clause 252]
256. 28 <=> wise(susan) [avatar definition]
258. ~wise(susan) <- (~28) [avatar component clause 256]
259. ~27 | ~28 [avatar split clause 130,256,252]
266. creative(susan) | calm(susan) <- (~28) [resolution 78,258]
268. 29 <=> calm(susan) [avatar definition]
270. calm(susan) <- (29) [avatar component clause 268]
272. 30 <=> creative(susan) [avatar definition]
274. creative(susan) <- (30) [avatar component clause 272]
275. 29 | 30 | 28 [avatar split clause 266,256,272,268]
291. ~calm(susan) | creative(susan) [resolution 93,131]
293. 30 | ~29 [avatar split clause 291,268,272]
305. funny(X1) | patient(X1) <- (7) [resolution 97,160]
307. patient(X1) <- (7, 16) [subsumption resolution 305,200]
308. $false <- (7, 16, ~27) [resolution 307,254]
309. ~7 | ~16 | 27 [avatar contradiction clause 308]
347. ~creative(susan) | calm(susan) | funny(susan) [resolution 89,131]
349. calm(susan) | funny(susan) <- (30) [subsumption resolution 347,274]
356. calm(susan) <- (16, 30) [subsumption resolution 349,200]
357. 29 | ~16 | ~30 [avatar split clause 356,272,199,268]
359. ~creative(susan) | wise(susan) <- (29) [resolution 270,80]
361. wise(susan) <- (29, 30) [subsumption resolution 359,274]
362. $false <- (~28, 29, 30) [subsumption resolution 361,258]
363. 28 | ~29 | ~30 [avatar contradiction clause 362]
364. $false [avatar sat refutation 205,206,250,259,275,293,309,357,363]
% SZS output end Proof for 4201566805401388830435796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not tall and old then someone is either patient or happy and vice versa.
If someone is not patient or not strong then someone is not creative.
If someone is not rich or not strong then someone is not tall and vice versa.
Everyone who is either not happy or funny is either wise or rich.
Everyone who is either curious or not tall is creative.
If someone is wise or not tall then fred is either happy or not old.
If john is both patient and quiet then someone is both quiet and not generous and vice versa.
If lucy is either not creative or humble then someone is brave or funny and vice versa.
Everyone who is not wise or quiet is both curious and not humble and vice versa.
If john is both calm and not tall then paul is both calm and happy.
If mary is both not strong and old then fred is both funny and not brave and vice versa.
If someone is patient or not humble then paul is happy or wise.
Everyone who is either humble or funny is not kind or not strong.
If susan is not kind then susan is both generous and not old and vice versa.
Everyone who is funny or tall is patient and vice versa.
Everyone who is either happy or humble is either not brave or not calm.
Someone is not humble or not kind.
Someone is both funny and strong.
Paul is wise.
Someone is not humble.
Someone is humble.
Someone is generous.
Mary is not generous.
Lucy is both creative and not patient. | Lucy is wise. | entailment | (((~tall(fred)&old(fred)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~patient(X)|~strong(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~rich(X)|~strong(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)<~>funny(X))=>(wise(X)<~>rich(X))))&
(![X]:((curious(X)<~>~tall(X))=>creative(X)))&
((?[X]:((wise(X)|~tall(X))))=>((happy(fred)<~>~old(fred))))&
(((patient(john)&quiet(john)))<=>(?[X]:((quiet(X)&~generous(X)))))&
(((~creative(lucy)<~>humble(lucy)))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:((funny(X)&strong(X))))&
(wise(paul))&
(?[X]:(~humble(X)))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(~generous(mary))&
((creative(lucy)&~patient(lucy))) | wise(lucy) | [
"p7",
"p8",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1295904428087722334777702
% SZS output start Proof for 1295904428087722334777702
8. (~creative(lucy) <~> humble(lucy)) <=> ? [X0] : (funny(X0) | brave(X0)) [input p7]
9. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~humble(X0) & curious(X0))) [input p8]
18. ? [X0] : (strong(X0) & funny(X0)) [input p17]
24. ~patient(lucy) & creative(lucy) [input p23]
25. ~wise(lucy) [input hypothesis]
60. (((~humble(lucy) | creative(lucy)) & (humble(lucy) | ~creative(lucy))) | ! [X0] : (~funny(X0) & ~brave(X0))) & (? [X0] : (funny(X0) | brave(X0)) | ((~creative(lucy) | ~humble(lucy)) & (humble(lucy) | creative(lucy)))) [nnf transformation 8]
61. (((~humble(lucy) | creative(lucy)) & (humble(lucy) | ~creative(lucy))) | ! [X0] : (~funny(X0) & ~brave(X0))) & (? [X1] : (funny(X1) | brave(X1)) | ((~creative(lucy) | ~humble(lucy)) & (humble(lucy) | creative(lucy)))) [rectify 60]
62. ? [X1] : (funny(X1) | brave(X1)) => (funny(sK5) | brave(sK5)) [choice axiom]
63. (((~humble(lucy) | creative(lucy)) & (humble(lucy) | ~creative(lucy))) | ! [X0] : (~funny(X0) & ~brave(X0))) & ((funny(sK5) | brave(sK5)) | ((~creative(lucy) | ~humble(lucy)) & (humble(lucy) | creative(lucy)))) [skolemisation 61,62]
64. ! [X0] : (((quiet(X0) | ~wise(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 9]
65. ! [X0] : ((quiet(X0) | ~wise(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [flattening 64]
76. ? [X0] : (strong(X0) & funny(X0)) => (strong(sK7) & funny(sK7)) [choice axiom]
77. strong(sK7) & funny(sK7) [skolemisation 18,76]
112. humble(lucy) | ~creative(lucy) | ~funny(X0) [cnf transformation 63]
117. ~humble(X0) | wise(X0) [cnf transformation 65]
141. funny(sK7) [cnf transformation 77]
148. creative(lucy) [cnf transformation 24]
150. ~wise(lucy) [cnf transformation 25]
247. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
248. ~funny(X0) <- (22) [avatar component clause 247]
250. 23 <=> creative(lucy) [avatar definition]
254. 24 <=> humble(lucy) [avatar definition]
255. humble(lucy) <- (24) [avatar component clause 254]
262. 22 | ~23 | 24 [avatar split clause 112,254,250,247]
349. 23 [avatar split clause 148,250]
350. $false <- (22) [resolution 248,141]
351. ~22 [avatar contradiction clause 350]
355. wise(lucy) <- (24) [resolution 117,255]
356. $false <- (24) [subsumption resolution 355,150]
357. ~24 [avatar contradiction clause 356]
358. $false [avatar sat refutation 262,349,351,357]
% SZS output end Proof for 1295904428087722334777702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not creative and kind then susan is both happy and not tall.
Everyone who is not quiet or old is not patient or calm and vice versa.
If someone is not creative then paul is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
Someone is either not humble or not strong.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is generous.
Someone is either not generous or quiet. | Paul is generous. | contradiction | (((~creative(paul)&kind(paul)))=>((happy(susan)&~tall(susan))))&
(![X]:((~quiet(X)|old(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~creative(X)))<=>(old(paul)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)<~>quiet(X)))) | generous(paul) | [
"p2",
"p5",
"p7",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4857251866860086610613910
% SZS output start Proof for 4857251866860086610613910
3. ? [X0] : ~creative(X0) <=> old(paul) [input p2]
6. ! [X0] : (funny(X0) <=> (generous(X0) & ~creative(X0))) [input p5]
8. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> rich(X0)) [input p7]
9. ? [X0] : (creative(X0) | ~strong(X0)) <=> ~rich(mary) [input p8]
14. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p13]
16. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p15]
24. generous(paul) [input hypothesis]
35. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 14]
39. (? [X0] : ~creative(X0) | ~old(paul)) & (old(paul) | ! [X0] : creative(X0)) [nnf transformation 3]
40. (? [X0] : ~creative(X0) | ~old(paul)) & (old(paul) | ! [X1] : creative(X1)) [rectify 39]
41. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
42. (~creative(sK0) | ~old(paul)) & (old(paul) | ! [X1] : creative(X1)) [skolemisation 40,41]
44. ! [X0] : ((funny(X0) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | ~funny(X0))) [nnf transformation 6]
45. ! [X0] : ((funny(X0) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | ~funny(X0))) [flattening 44]
48. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((~humble(X0) | ~happy(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [flattening 48]
50. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~creative(X0) & strong(X0))) [nnf transformation 9]
51. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [rectify 50]
52. ? [X0] : (creative(X0) | ~strong(X0)) => (creative(sK1) | ~strong(sK1)) [choice axiom]
53. ((creative(sK1) | ~strong(sK1)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [skolemisation 51,52]
59. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 16]
60. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 59]
78. old(paul) | creative(X1) [cnf transformation 42]
85. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 45]
92. rich(X0) | happy(X0) [cnf transformation 49]
93. humble(X0) | rich(X0) [cnf transformation 49]
96. ~rich(mary) | ~creative(X1) [cnf transformation 53]
106. ~humble(X0) | ~old(X0) [cnf transformation 35]
107. ~funny(X0) | ~old(X0) [cnf transformation 35]
110. ~happy(X0) | old(X0) [cnf transformation 60]
122. generous(paul) [cnf transformation 24]
124. 1 <=> creative(paul) [avatar definition]
125. ~creative(paul) <- (~1) [avatar component clause 124]
126. creative(paul) <- (1) [avatar component clause 124]
142. 5 <=> old(paul) [avatar definition]
151. 7 <=> ! [X1] : creative(X1) [avatar definition]
152. creative(X1) <- (7) [avatar component clause 151]
153. 7 | 5 [avatar split clause 78,142,151]
187. 14 <=> rich(mary) [avatar definition]
188. ~rich(mary) <- (~14) [avatar component clause 187]
200. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
201. ~creative(X1) <- (17) [avatar component clause 200]
202. 17 | ~14 [avatar split clause 96,187,200]
278. happy(mary) <- (~14) [resolution 92,188]
281. ~old(X0) | rich(X0) [resolution 106,93]
283. old(mary) <- (~14) [resolution 110,278]
288. rich(mary) <- (~14) [resolution 281,283]
290. $false <- (~14) [subsumption resolution 288,188]
291. 14 [avatar contradiction clause 290]
311. funny(paul) | creative(paul) [resolution 85,122]
314. funny(paul) <- (~1) [subsumption resolution 311,125]
320. ~old(paul) <- (~1) [resolution 314,107]
325. ~5 | 1 [avatar split clause 320,124,142]
326. $false <- (7, 17) [subsumption resolution 152,201]
327. ~7 | ~17 [avatar contradiction clause 326]
331. $false <- (1, 17) [subsumption resolution 126,201]
332. ~1 | ~17 [avatar contradiction clause 331]
333. $false [avatar sat refutation 153,202,291,325,327,332]
% SZS output end Proof for 4857251866860086610613910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not humble is both strong and not curious.
Everyone who is either not rich or not kind is both not patient and calm.
Everyone who is curious or patient is not patient or not tall and vice versa.
If john is either not tall or not old then someone is not tall and vice versa.
Everyone who is either calm or not curious is not quiet.
Everyone who is generous is both not curious and humble.
If someone is not brave then susan is old and vice versa.
Everyone who is not calm is both not tall and not patient and vice versa.
Everyone who is either tall or not quiet is either not tall or rich and vice versa.
Everyone who is either not happy or not calm is not humble or calm.
If lucy is either not quiet or creative then susan is both not happy and quiet.
Everyone who is either not creative or rich is either not funny or not strong.
Everyone who is both not calm and not generous is generous.
If susan is wise or old then lucy is not brave and vice versa.
If john is both generous and not humble then alice is both not creative and not kind.
If paul is not generous or brave then someone is tall or not curious and vice versa.
Lucy is happy.
John is rich.
Someone is both not generous and not old.
Paul is either wise or not curious.
Susan is not tall.
Someone is not curious.
Mary is not curious or not brave.
John is patient or wise. | Paul is not calm. | contradiction | (![X]:((~rich(X)&~humble(X))=>(strong(X)&~curious(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(~patient(X)&calm(X))))&
(![X]:((curious(X)|patient(X))<=>(~patient(X)|~tall(X))))&
(((~tall(john)<~>~old(john)))<=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>~curious(X))=>~quiet(X)))&
(![X]:(generous(X)=>(~curious(X)&humble(X))))&
((?[X]:(~brave(X)))<=>(old(susan)))&
(![X]:(~calm(X)<=>(~tall(X)&~patient(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(~humble(X)|calm(X))))&
(((~quiet(lucy)<~>creative(lucy)))=>((~happy(susan)&quiet(susan))))&
(![X]:((~creative(X)<~>rich(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)&~generous(X))=>generous(X)))&
(((wise(susan)|old(susan)))<=>(~brave(lucy)))&
(((generous(john)&~humble(john)))=>((~creative(alice)&~kind(alice))))&
(((~generous(paul)|brave(paul)))<=>(?[X]:((tall(X)|~curious(X)))))&
(happy(lucy))&
(rich(john))&
(?[X]:((~generous(X)&~old(X))))&
((wise(paul)<~>~curious(paul)))&
(~tall(susan))&
(?[X]:(~curious(X)))&
((~curious(mary)|~brave(mary)))&
((patient(john)|wise(john))) | ~calm(paul) | [
"p2",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 418241650494531101929862
% SZS output start Proof for 418241650494531101929862
3. ! [X0] : ((patient(X0) | curious(X0)) <=> (~tall(X0) | ~patient(X0))) [input p2]
6. ! [X0] : (generous(X0) => (humble(X0) & ~curious(X0))) [input p5]
8. ! [X0] : (~calm(X0) <=> (~patient(X0) & ~tall(X0))) [input p7]
13. ! [X0] : ((~generous(X0) & ~calm(X0)) => generous(X0)) [input p12]
25. ~calm(paul) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~curious(X0)) | ~generous(X0)) [ennf transformation 6]
35. ! [X0] : (generous(X0) | (generous(X0) | calm(X0))) [ennf transformation 13]
36. ! [X0] : (generous(X0) | generous(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (((patient(X0) | curious(X0)) | (tall(X0) & patient(X0))) & ((~tall(X0) | ~patient(X0)) | (~patient(X0) & ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : ((patient(X0) | curious(X0) | (tall(X0) & patient(X0))) & (~tall(X0) | ~patient(X0) | (~patient(X0) & ~curious(X0)))) [flattening 40]
51. ! [X0] : ((~calm(X0) | (patient(X0) | tall(X0))) & ((~patient(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 8]
52. ! [X0] : ((~calm(X0) | patient(X0) | tall(X0)) & ((~patient(X0) & ~tall(X0)) | calm(X0))) [flattening 51]
77. patient(X0) | curious(X0) | patient(X0) [cnf transformation 41]
85. ~generous(X0) | ~curious(X0) [cnf transformation 30]
90. ~patient(X0) | calm(X0) [cnf transformation 52]
110. generous(X0) | generous(X0) | calm(X0) [cnf transformation 36]
130. ~calm(paul) [cnf transformation 25]
131. generous(X0) | calm(X0) [duplicate literal removal 110]
138. patient(X0) | curious(X0) [duplicate literal removal 77]
263. calm(X1) | ~curious(X1) [resolution 131,85]
272. curious(X0) | calm(X0) [resolution 138,90]
274. calm(X0) [subsumption resolution 272,263]
276. $false [resolution 274,130]
% SZS output end Proof for 418241650494531101929862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is strong then someone is tall and vice versa.
If someone is either old or not funny then susan is patient or happy and vice versa.
If alice is not brave then fred is not wise or brave.
If fred is both kind and creative then someone is both humble and not old.
If alice is either not kind or brave then alice is generous or strong.
Everyone who is not humble is not quiet or strong and vice versa.
Everyone who is both strong and calm is both not funny and calm.
Everyone who is either not curious or quiet is happy or rich.
If someone is either calm or strong then lucy is either calm or not strong and vice versa.
If someone is both not patient and not calm then someone is not wise or not old and vice versa.
Everyone who is generous is not kind or not funny and vice versa.
If lucy is not generous or not kind then someone is calm.
Everyone who is either rich or funny is either not calm or funny.
Everyone who is humble or tall is curious or not curious.
Everyone who is either happy or not generous is both calm and not kind and vice versa.
Everyone who is either not curious or not old is not creative and vice versa.
Alice is not generous.
John is both strong and kind.
Alice is creative or not strong.
Alice is old.
Someone is brave.
Mary is wise or not tall.
Someone is either funny or wise.
Mary is either brave or not old. | Lucy is not strong. | neutral | ((strong(lucy))<=>(?[X]:(tall(X))))&
((?[X]:((old(X)<~>~funny(X))))<=>((patient(susan)|happy(susan))))&
((~brave(alice))=>((~wise(fred)|brave(fred))))&
(((kind(fred)&creative(fred)))=>(?[X]:((humble(X)&~old(X)))))&
(((~kind(alice)<~>brave(alice)))=>((generous(alice)|strong(alice))))&
(![X]:(~humble(X)<=>(~quiet(X)|strong(X))))&
(![X]:((strong(X)&calm(X))=>(~funny(X)&calm(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(happy(X)|rich(X))))&
((?[X]:((calm(X)<~>strong(X))))<=>((calm(lucy)<~>~strong(lucy))))&
((?[X]:((~patient(X)&~calm(X))))<=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~funny(X))))&
(((~generous(lucy)|~kind(lucy)))=>(?[X]:(calm(X))))&
(![X]:((rich(X)<~>funny(X))=>(~calm(X)<~>funny(X))))&
(![X]:((humble(X)|tall(X))=>(curious(X)|~curious(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(calm(X)&~kind(X))))&
(![X]:((~curious(X)<~>~old(X))<=>~creative(X)))&
(~generous(alice))&
((strong(john)&kind(john)))&
((creative(alice)|~strong(alice)))&
(old(alice))&
(?[X]:(brave(X)))&
((wise(mary)|~tall(mary)))&
(?[X]:((funny(X)<~>wise(X))))&
((brave(mary)<~>~old(mary))) | ~strong(lucy) | [] | null | 0 |
If someone is humble then paul is both not old and humble and vice versa.
Everyone who is creative is either not humble or not quiet and vice versa.
If someone is either not tall or not strong then susan is not patient or humble and vice versa.
If someone is both not creative and not curious then mary is either not humble or not creative and vice versa.
If someone is both not funny and kind then someone is both not funny and tall and vice versa.
If someone is not wise then someone is either strong or calm.
Everyone who is both quiet and patient is not calm or calm and vice versa.
Everyone who is either brave or curious is either not brave or not old and vice versa.
Everyone who is both not happy and not brave is funny or not calm and vice versa.
If someone is either not tall or not patient then fred is both kind and not patient.
If fred is not generous or not curious then fred is either not humble or humble and vice versa.
Everyone who is not happy or patient is patient or strong.
If lucy is either happy or generous then someone is either not quiet or not curious.
If lucy is either not strong or not patient then fred is both not quiet and kind and vice versa.
If fred is not funny or not calm then mary is either patient or not wise.
Everyone who is not brave or not kind is quiet or not calm and vice versa.
John is happy.
John is rich or not creative.
Lucy is not funny or old.
Susan is either quiet or brave.
Someone is kind or not patient.
Alice is either not patient or not kind.
John is not humble. | Paul is not brave. | neutral | ((?[X]:(humble(X)))<=>((~old(paul)&humble(paul))))&
(![X]:(creative(X)<=>(~humble(X)<~>~quiet(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((~patient(susan)|humble(susan))))&
((?[X]:((~creative(X)&~curious(X))))<=>((~humble(mary)<~>~creative(mary))))&
((?[X]:((~funny(X)&kind(X))))<=>(?[X]:((~funny(X)&tall(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((quiet(X)&patient(X))<=>(~calm(X)|calm(X))))&
(![X]:((brave(X)<~>curious(X))<=>(~brave(X)<~>~old(X))))&
(![X]:((~happy(X)&~brave(X))<=>(funny(X)|~calm(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(fred)&~patient(fred))))&
(((~generous(fred)|~curious(fred)))<=>((~humble(fred)<~>humble(fred))))&
(![X]:((~happy(X)|patient(X))=>(patient(X)|strong(X))))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((~quiet(X)<~>~curious(X)))))&
(((~strong(lucy)<~>~patient(lucy)))<=>((~quiet(fred)&kind(fred))))&
(((~funny(fred)|~calm(fred)))=>((patient(mary)<~>~wise(mary))))&
(![X]:((~brave(X)|~kind(X))<=>(quiet(X)|~calm(X))))&
(happy(john))&
((rich(john)|~creative(john)))&
((~funny(lucy)|old(lucy)))&
((quiet(susan)<~>brave(susan)))&
(?[X]:((kind(X)|~patient(X))))&
((~patient(alice)<~>~kind(alice)))&
(~humble(john)) | ~brave(paul) | [] | null | 0 |
If mary is generous then lucy is not happy or quiet.
Everyone who is creative or patient is either old or generous and vice versa.
Everyone who is either not old or not generous is either not quiet or curious and vice versa.
Everyone who is patient or brave is not happy or not rich.
If alice is not strong or not curious then lucy is patient and vice versa.
If someone is either creative or not wise then someone is kind.
Everyone who is not wise is patient.
If mary is humble then someone is both rich and curious.
If lucy is not tall then alice is curious and vice versa.
Everyone who is happy or brave is either not quiet or not kind.
Everyone who is old is not happy or brave.
Everyone who is happy is either brave or not kind.
Everyone who is generous or kind is both calm and tall.
Everyone who is calm is both patient and tall and vice versa.
Everyone who is not creative or not patient is kind.
Everyone who is quiet or not creative is rich or not strong.
Susan is strong or generous.
Someone is patient or not funny.
Someone is both creative and not strong.
Mary is rich or curious.
John is either humble or tall.
Someone is both not old and not strong.
Someone is not kind.
Fred is either not generous or not wise. | Fred is creative. | neutral | ((generous(mary))=>((~happy(lucy)|quiet(lucy))))&
(![X]:((creative(X)|patient(X))<=>(old(X)<~>generous(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((patient(X)|brave(X))=>(~happy(X)|~rich(X))))&
(((~strong(alice)|~curious(alice)))<=>(patient(lucy)))&
((?[X]:((creative(X)<~>~wise(X))))=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>patient(X)))&
((humble(mary))=>(?[X]:((rich(X)&curious(X)))))&
((~tall(lucy))<=>(curious(alice)))&
(![X]:((happy(X)|brave(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(old(X)=>(~happy(X)|brave(X))))&
(![X]:(happy(X)=>(brave(X)<~>~kind(X))))&
(![X]:((generous(X)|kind(X))=>(calm(X)&tall(X))))&
(![X]:(calm(X)<=>(patient(X)&tall(X))))&
(![X]:((~creative(X)|~patient(X))=>kind(X)))&
(![X]:((quiet(X)|~creative(X))=>(rich(X)|~strong(X))))&
((strong(susan)|generous(susan)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((creative(X)&~strong(X))))&
((rich(mary)|curious(mary)))&
((humble(john)<~>tall(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>~wise(fred))) | creative(fred) | [] | null | 0 |
Everyone who is humble is not old or happy. Everyone who is tall is not strong and vice versa. Everyone who is either brave or not calm is either strong or wise. Everyone who is not humble is brave or not generous. If someone is either quiet or not quiet then someone is not funny or not creative and vice versa. If fred is not brave or not humble then someone is both old and happy. Everyone who is either not patient or kind is not tall or not old and vice versa. If lucy is not brave then someone is either happy or not rich and vice versa. If mary is both generous and old then someone is wise. Everyone who is patient is not calm and vice versa. Everyone who is generous is not quiet or not generous. If someone is either brave or not humble then someone is either curious or funny and vice versa. Everyone who is both humble and kind is both rich and creative. Everyone who is curious is not funny and vice versa. If alice is both not generous and strong then john is both not tall and not quiet. If someone is brave or quiet then alice is either not strong or wise. Susan is not brave. Someone is curious or patient. Mary is old. Someone is generous or not calm. Someone is either rich or humble. Lucy is either tall or not brave. John is both old and not patient. Someone is not creative or generous. | Fred is not humble. | neutral | (![X]:(humble(X)=>(~old(X)|happy(X))))&
(![X]:(tall(X)<=>~strong(X)))&
(![X]:((brave(X)<~>~calm(X))=>(strong(X)<~>wise(X))))&
(![X]:(~humble(X)=>(brave(X)|~generous(X))))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(?[X]:((~funny(X)|~creative(X)))))&
(((~brave(fred)|~humble(fred)))=>(?[X]:((old(X)&happy(X)))))&
(![X]:((~patient(X)<~>kind(X))<=>(~tall(X)|~old(X))))&
((~brave(lucy))<=>(?[X]:((happy(X)<~>~rich(X)))))&
(((generous(mary)&old(mary)))=>(?[X]:(wise(X))))&
(![X]:(patient(X)<=>~calm(X)))&
(![X]:(generous(X)=>(~quiet(X)|~generous(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)&kind(X))=>(rich(X)&creative(X))))&
(![X]:(curious(X)<=>~funny(X)))&
(((~generous(alice)&strong(alice)))=>((~tall(john)&~quiet(john))))&
((?[X]:((brave(X)|quiet(X))))=>((~strong(alice)<~>wise(alice))))&
(~brave(susan))&
(?[X]:((curious(X)|patient(X))))&
(old(mary))&
(?[X]:((generous(X)|~calm(X))))&
(?[X]:((rich(X)<~>humble(X))))&
((tall(lucy)<~>~brave(lucy)))&
((old(john)&~patient(john)))&
(?[X]:((~creative(X)|generous(X)))) | ~humble(fred) | [] | null | 0 |
Everyone who is both strong and not creative is both patient and not quiet and vice versa.
If someone is either not tall or happy then paul is not curious or not wise.
If someone is patient then lucy is either not humble or wise.
Everyone who is both patient and not tall is either patient or not generous and vice versa.
If someone is old then john is curious or calm and vice versa.
Everyone who is curious or not kind is both creative and not quiet and vice versa.
Everyone who is either not rich or not kind is wise.
If someone is wise or not calm then paul is brave.
Everyone who is either quiet or generous is both not tall and not creative and vice versa.
Everyone who is both not funny and not happy is both happy and not curious and vice versa.
Everyone who is either calm or not generous is patient or not strong and vice versa.
If john is both happy and patient then john is either not rich or not calm.
Everyone who is humble is both not strong and not patient and vice versa.
If fred is old then john is old and vice versa.
Everyone who is not strong is both not tall and generous.
If paul is not kind or funny then john is both not old and humble.
Someone is not strong.
Someone is both creative and not rich.
Someone is wise or quiet.
Alice is not patient.
Someone is brave.
Fred is either not generous or not patient.
Paul is strong. | Lucy is not curious. | entailment | (![X]:((strong(X)&~creative(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>happy(X))))=>((~curious(paul)|~wise(paul))))&
((?[X]:(patient(X)))=>((~humble(lucy)<~>wise(lucy))))&
(![X]:((patient(X)&~tall(X))<=>(patient(X)<~>~generous(X))))&
((?[X]:(old(X)))<=>((curious(john)|calm(john))))&
(![X]:((curious(X)|~kind(X))<=>(creative(X)&~quiet(X))))&
(![X]:((~rich(X)<~>~kind(X))=>wise(X)))&
((?[X]:((wise(X)|~calm(X))))=>(brave(paul)))&
(![X]:((quiet(X)<~>generous(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>(happy(X)&~curious(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(patient(X)|~strong(X))))&
(((happy(john)&patient(john)))=>((~rich(john)<~>~calm(john))))&
(![X]:(humble(X)<=>(~strong(X)&~patient(X))))&
((old(fred))<=>(old(john)))&
(![X]:(~strong(X)=>(~tall(X)&generous(X))))&
(((~kind(paul)|funny(paul)))=>((~old(john)&humble(john))))&
(?[X]:(~strong(X)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((wise(X)|quiet(X))))&
(~patient(alice))&
(?[X]:(brave(X)))&
((~generous(fred)<~>~patient(fred)))&
(strong(paul)) | ~curious(lucy) | [
"p0",
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 558157448286395723195129
% SZS output start Proof for 558157448286395723195129
1. ! [X0] : ((~creative(X0) & strong(X0)) <=> (~quiet(X0) & patient(X0))) [input p0]
4. ! [X0] : ((~tall(X0) & patient(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | curious(X0)) <=> (~quiet(X0) & creative(X0))) [input p5]
9. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~creative(X0) & ~tall(X0))) [input p8]
24. curious(lucy) [input hypothesis]
35. ! [X0] : (((~creative(X0) & strong(X0)) | (quiet(X0) | ~patient(X0))) & ((~quiet(X0) & patient(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((~creative(X0) & strong(X0)) | quiet(X0) | ~patient(X0)) & ((~quiet(X0) & patient(X0)) | creative(X0) | ~strong(X0))) [flattening 35]
39. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (tall(X0) | ~patient(X0)))) [nnf transformation 4]
40. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | tall(X0) | ~patient(X0))) [flattening 39]
46. ! [X0] : (((~kind(X0) | curious(X0)) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [nnf transformation 6]
47. ! [X0] : ((~kind(X0) | curious(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [flattening 46]
49. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 49]
69. ~patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 36]
77. patient(X0) | patient(X0) | generous(X0) [cnf transformation 40]
83. ~curious(X0) | creative(X0) [cnf transformation 47]
85. ~curious(X0) | ~quiet(X0) [cnf transformation 47]
93. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 50]
127. curious(lucy) [cnf transformation 24]
131. generous(X0) | patient(X0) [duplicate literal removal 77]
242. creative(lucy) [resolution 83,127]
243. ~quiet(lucy) [resolution 85,127]
298. quiet(X1) | ~creative(X1) | patient(X1) [resolution 93,131]
302. ~creative(X1) | quiet(X1) [subsumption resolution 298,69]
304. quiet(lucy) [resolution 302,242]
305. $false [subsumption resolution 304,243]
% SZS output end Proof for 558157448286395723195129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or not humble then alice is both not humble and funny. If someone is both not curious and rich then fred is both funny and not curious and vice versa. Everyone who is either not strong or rich is humble or not brave. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Everyone who is not old or curious is calm or rich. If someone is not tall or generous then someone is not strong and vice versa. If lucy is wise then fred is humble or not old. If mary is either not kind or wise then someone is not creative or wise and vice versa. Everyone who is both not old and not curious is either not strong or not kind and vice versa. Someone is calm or rich. Someone is not strong or calm. Fred is not generous or not brave. Mary is wise or not wise. Someone is not creative or not generous. | Fred is humble. | entailment | ((?[X]:((happy(X)|~humble(X))))=>((~humble(alice)&funny(alice))))&
((?[X]:((~curious(X)&rich(X))))<=>((funny(fred)&~curious(fred))))&
(![X]:((~strong(X)<~>rich(X))=>(humble(X)|~brave(X))))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~old(X)|curious(X))=>(calm(X)|rich(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:(~strong(X))))&
((wise(lucy))=>((humble(fred)|~old(fred))))&
(((~kind(mary)<~>wise(mary)))<=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~old(X)&~curious(X))<=>(~strong(X)<~>~kind(X))))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((~strong(X)|calm(X))))&
((~generous(fred)|~brave(fred)))&
((wise(mary)|~wise(mary)))&
(?[X]:((~creative(X)|~generous(X)))) | humble(fred) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4523894591339637070243105
% SZS output start Proof for 4523894591339637070243105
1. ? [X0] : (~humble(X0) | happy(X0)) => (funny(alice) & ~humble(alice)) [input p0]
4. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p3]
7. ! [X0] : ((~funny(X0) | ~curious(X0)) <=> (~humble(X0) & ~brave(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (~curious(X0) | ~old(X0))) [input p7]
9. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p8]
22. ~humble(fred) [input hypothesis]
29. (funny(alice) & ~humble(alice)) | ! [X0] : (humble(X0) & ~happy(X0)) [ennf transformation 1]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 4]
46. ! [X0] : (((~funny(X0) | ~curious(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [nnf transformation 7]
47. ! [X0] : ((~funny(X0) | ~curious(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | (funny(X0) & curious(X0)))) [flattening 46]
48. ! [X0] : (((~funny(X0) & ~patient(X0)) | (curious(X0) & old(X0))) & ((~curious(X0) | ~old(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 8]
49. ! [X0] : (((~funny(X0) & ~patient(X0)) | (curious(X0) & old(X0))) & (~curious(X0) | ~old(X0) | funny(X0) | patient(X0))) [flattening 48]
50. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 50]
70. ~humble(alice) | humble(X0) [cnf transformation 29]
72. funny(alice) | humble(X0) [cnf transformation 29]
80. ~quiet(X0) | ~brave(X0) [cnf transformation 32]
82. ~brave(X0) | patient(X0) [cnf transformation 32]
92. ~curious(X0) | ~funny(X0) | humble(X0) | brave(X0) [cnf transformation 47]
97. ~funny(X0) | curious(X0) [cnf transformation 49]
99. ~patient(X0) | quiet(X0) [cnf transformation 51]
122. ~humble(fred) [cnf transformation 22]
124. 1 <=> ! [X0] : humble(X0) [avatar definition]
125. humble(X0) <- (1) [avatar component clause 124]
127. 2 <=> funny(alice) [avatar definition]
129. funny(alice) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 72,127,124]
136. 4 <=> humble(alice) [avatar definition]
138. ~humble(alice) <- (~4) [avatar component clause 136]
139. 1 | ~4 [avatar split clause 70,136,124]
205. 20 <=> humble(fred) [avatar definition]
206. ~humble(fred) <- (~20) [avatar component clause 205]
259. ~20 [avatar split clause 122,205]
264. curious(alice) <- (2) [resolution 97,129]
318. ~funny(alice) | humble(alice) | brave(alice) <- (2) [resolution 92,264]
319. humble(alice) | brave(alice) <- (2) [subsumption resolution 318,129]
320. brave(alice) <- (2, ~4) [subsumption resolution 319,138]
325. patient(alice) <- (2, ~4) [resolution 320,82]
329. quiet(alice) <- (2, ~4) [resolution 325,99]
356. ~brave(alice) <- (2, ~4) [resolution 329,80]
358. $false <- (2, ~4) [subsumption resolution 356,320]
359. ~2 | 4 [avatar contradiction clause 358]
367. $false <- (1, ~20) [resolution 125,206]
370. ~1 | 20 [avatar contradiction clause 367]
371. $false [avatar sat refutation 130,139,259,359,370]
% SZS output end Proof for 4523894591339637070243105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not old is generous or not curious.
Everyone who is both humble and strong is not calm and vice versa.
Everyone who is not rich is either strong or not happy.
If someone is not brave or not strong then john is both rich and not old.
Everyone who is not kind or not strong is humble and vice versa.
If john is not patient then someone is either not creative or curious.
If someone is both not brave and tall then someone is strong and vice versa.
Everyone who is not curious or not quiet is both not curious and creative.
Everyone who is humble or strong is both quiet and calm.
If someone is not old or not kind then mary is either not creative or not tall.
Everyone who is funny is both not rich and not quiet.
If someone is not happy then mary is wise.
Everyone who is both brave and not kind is not curious or generous and vice versa.
If paul is not patient then mary is not strong.
Everyone who is either not creative or calm is not calm or not curious and vice versa.
Everyone who is both happy and kind is not tall.
Lucy is not brave or not curious.
Susan is either not calm or quiet.
Susan is either quiet or creative.
Someone is strong.
Someone is not patient.
Fred is both quiet and creative.
Mary is either not happy or funny. | Paul is not funny. | entailment | (![X]:((patient(X)<~>~old(X))=>(generous(X)|~curious(X))))&
(![X]:((humble(X)&strong(X))<=>~calm(X)))&
(![X]:(~rich(X)=>(strong(X)<~>~happy(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((rich(john)&~old(john))))&
(![X]:((~kind(X)|~strong(X))<=>humble(X)))&
((~patient(john))=>(?[X]:((~creative(X)<~>curious(X)))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:(strong(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~curious(X)&creative(X))))&
(![X]:((humble(X)|strong(X))=>(quiet(X)&calm(X))))&
((?[X]:((~old(X)|~kind(X))))=>((~creative(mary)<~>~tall(mary))))&
(![X]:(funny(X)=>(~rich(X)&~quiet(X))))&
((?[X]:(~happy(X)))=>(wise(mary)))&
(![X]:((brave(X)&~kind(X))<=>(~curious(X)|generous(X))))&
((~patient(paul))=>(~strong(mary)))&
(![X]:((~creative(X)<~>calm(X))<=>(~calm(X)|~curious(X))))&
(![X]:((happy(X)&kind(X))=>~tall(X)))&
((~brave(lucy)|~curious(lucy)))&
((~calm(susan)<~>quiet(susan)))&
((quiet(susan)<~>creative(susan)))&
(?[X]:(strong(X)))&
(?[X]:(~patient(X)))&
((quiet(fred)&creative(fred)))&
((~happy(mary)<~>funny(mary))) | ~funny(paul) | [
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1607224451797146180502777
% SZS output start Proof for 1607224451797146180502777
5. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> humble(X0)) [input p4]
9. ! [X0] : ((strong(X0) | humble(X0)) => (calm(X0) & quiet(X0))) [input p8]
11. ! [X0] : (funny(X0) => (~quiet(X0) & ~rich(X0))) [input p10]
24. funny(paul) [input hypothesis]
33. ! [X0] : ((calm(X0) & quiet(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 9]
35. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ~funny(X0)) [ennf transformation 11]
43. ! [X0] : (((~strong(X0) | ~kind(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) & kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((~strong(X0) | ~kind(X0) | ~humble(X0)) & (humble(X0) | (strong(X0) & kind(X0)))) [flattening 43]
77. strong(X0) | humble(X0) [cnf transformation 44]
88. ~humble(X0) | quiet(X0) [cnf transformation 33]
89. ~strong(X0) | quiet(X0) [cnf transformation 33]
97. ~funny(X0) | ~quiet(X0) [cnf transformation 35]
122. funny(paul) [cnf transformation 24]
238. quiet(X0) | humble(X0) [resolution 89,77]
239. quiet(X0) [subsumption resolution 238,88]
241. ~quiet(paul) [resolution 97,122]
242. $false [subsumption resolution 241,239]
% SZS output end Proof for 1607224451797146180502777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind then lucy is not quiet and vice versa.
Everyone who is either not quiet or not brave is not curious and vice versa.
If someone is not wise or not patient then someone is both not funny and not kind and vice versa.
If someone is either not curious or old then someone is both quiet and not creative.
Everyone who is either not creative or old is not creative and vice versa.
If someone is either humble or old then alice is not tall or not old.
Everyone who is either rich or not wise is funny and vice versa.
If someone is either not happy or not tall then someone is either not old or not generous and vice versa.
If someone is either humble or not quiet then someone is not generous or curious.
Everyone who is either not creative or happy is both happy and tall and vice versa.
Everyone who is both not happy and not creative is not kind or not tall.
If someone is old then susan is funny and vice versa.
If someone is either not rich or tall then paul is not funny or not humble.
Everyone who is generous or not old is creative and vice versa.
Everyone who is rich or tall is not rich.
Everyone who is both not creative and not funny is either not tall or not curious.
Fred is strong or not quiet.
Someone is not creative or not funny.
Mary is not funny.
Mary is either not curious or not calm.
Someone is humble.
Someone is not strong or calm. | Lucy is old. | contradiction | (((generous(john)|~kind(john)))<=>(~quiet(lucy)))&
(![X]:((~quiet(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~wise(X)|~patient(X))))<=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~curious(X)<~>old(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~creative(X)<~>old(X))<=>~creative(X)))&
((?[X]:((humble(X)<~>old(X))))=>((~tall(alice)|~old(alice))))&
(![X]:((rich(X)<~>~wise(X))<=>funny(X)))&
((?[X]:((~happy(X)<~>~tall(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~creative(X)<~>happy(X))<=>(happy(X)&tall(X))))&
(![X]:((~happy(X)&~creative(X))=>(~kind(X)|~tall(X))))&
((?[X]:(old(X)))<=>(funny(susan)))&
((?[X]:((~rich(X)<~>tall(X))))=>((~funny(paul)|~humble(paul))))&
(![X]:((generous(X)|~old(X))<=>creative(X)))&
(![X]:((rich(X)|tall(X))=>~rich(X)))&
(![X]:((~creative(X)&~funny(X))=>(~tall(X)<~>~curious(X))))&
((strong(fred)|~quiet(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(~funny(mary))&
((~curious(mary)<~>~calm(mary)))&
(?[X]:(humble(X)))&
(?[X]:((~strong(X)|calm(X)))) | old(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3984838048607448102777772
% SZS output start Proof for 3984838048607448102777772
5. ! [X0] : ((~creative(X0) <~> old(X0)) <=> ~creative(X0)) [input p4]
23. old(lucy) [input hypothesis]
51. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | creative(X0)) & (~creative(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 5]
97. ~creative(X0) | ~creative(X0) | ~old(X0) [cnf transformation 51]
99. ~old(X0) | creative(X0) | creative(X0) [cnf transformation 51]
141. old(lucy) [cnf transformation 23]
145. ~creative(X0) | ~old(X0) [duplicate literal removal 97]
146. ~old(X0) | creative(X0) [duplicate literal removal 99]
210. ~old(X0) [subsumption resolution 145,146]
304. $false [subsumption resolution 141,210]
% SZS output end Proof for 3984838048607448102777772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then someone is not wise and vice versa.
If fred is not creative then someone is either not generous or not brave and vice versa.
If lucy is both calm and not rich then lucy is not patient or wise and vice versa.
Everyone who is both not funny and not patient is both not creative and quiet and vice versa.
Everyone who is not tall or generous is happy.
If someone is not kind or creative then susan is both not kind and kind and vice versa.
If someone is either not happy or not curious then someone is generous or curious.
If alice is either not kind or not wise then someone is both not old and patient.
Everyone who is not brave or patient is either happy or not quiet.
If susan is both creative and not generous then fred is quiet.
Everyone who is both kind and calm is both not happy and not generous and vice versa.
If alice is either not rich or not patient then paul is both brave and happy and vice versa.
If someone is either tall or not happy then someone is both creative and quiet.
Everyone who is either curious or not tall is either patient or not humble.
Everyone who is either happy or funny is either wise or not rich and vice versa.
Someone is not brave.
Fred is either wise or not patient.
Susan is either creative or not humble.
Paul is not creative or not funny.
John is either not rich or not funny. | Lucy is not calm. | contradiction | ((?[X]:(humble(X)))<=>(?[X]:(~wise(X))))&
((~creative(fred))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(((calm(lucy)&~rich(lucy)))<=>((~patient(lucy)|wise(lucy))))&
(![X]:((~funny(X)&~patient(X))<=>(~creative(X)&quiet(X))))&
(![X]:((~tall(X)|generous(X))=>happy(X)))&
((?[X]:((~kind(X)|creative(X))))<=>((~kind(susan)&kind(susan))))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:((generous(X)|curious(X)))))&
(((~kind(alice)<~>~wise(alice)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((~brave(X)|patient(X))=>(happy(X)<~>~quiet(X))))&
(((creative(susan)&~generous(susan)))=>(quiet(fred)))&
(![X]:((kind(X)&calm(X))<=>(~happy(X)&~generous(X))))&
(((~rich(alice)<~>~patient(alice)))<=>((brave(paul)&happy(paul))))&
((?[X]:((tall(X)<~>~happy(X))))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((curious(X)<~>~tall(X))=>(patient(X)<~>~humble(X))))&
(![X]:((happy(X)<~>funny(X))<=>(wise(X)<~>~rich(X))))&
(?[X]:(~brave(X)))&
((wise(fred)<~>~patient(fred)))&
((creative(susan)<~>~humble(susan)))&
((~creative(paul)|~funny(paul)))&
((~rich(john)<~>~funny(john))) | ~calm(lucy) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4270168825461190958238890
% SZS output start Proof for 4270168825461190958238890
3. (~rich(lucy) & calm(lucy)) <=> (wise(lucy) | ~patient(lucy)) [input p2]
4. ! [X0] : ((~patient(X0) & ~funny(X0)) <=> (quiet(X0) & ~creative(X0))) [input p3]
5. ! [X0] : ((generous(X0) | ~tall(X0)) => happy(X0)) [input p4]
6. ? [X0] : (creative(X0) | ~kind(X0)) <=> (kind(susan) & ~kind(susan)) [input p5]
9. ! [X0] : ((patient(X0) | ~brave(X0)) => (happy(X0) <~> ~quiet(X0))) [input p8]
11. ! [X0] : ((calm(X0) & kind(X0)) <=> (~generous(X0) & ~happy(X0))) [input p10]
21. ~calm(lucy) [input hypothesis]
26. ! [X0] : (happy(X0) | (~generous(X0) & tall(X0))) [ennf transformation 5]
29. ! [X0] : ((happy(X0) <~> ~quiet(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 9]
43. ((~rich(lucy) & calm(lucy)) | (~wise(lucy) & patient(lucy))) & ((wise(lucy) | ~patient(lucy)) | (rich(lucy) | ~calm(lucy))) [nnf transformation 3]
44. ((~rich(lucy) & calm(lucy)) | (~wise(lucy) & patient(lucy))) & (wise(lucy) | ~patient(lucy) | rich(lucy) | ~calm(lucy)) [flattening 43]
45. ! [X0] : (((~patient(X0) & ~funny(X0)) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | (patient(X0) | funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((~patient(X0) & ~funny(X0)) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | patient(X0) | funny(X0))) [flattening 45]
47. (? [X0] : (creative(X0) | ~kind(X0)) | (~kind(susan) | kind(susan))) & ((kind(susan) & ~kind(susan)) | ! [X0] : (~creative(X0) & kind(X0))) [nnf transformation 6]
48. (? [X0] : (creative(X0) | ~kind(X0)) | ~kind(susan) | kind(susan)) & ((kind(susan) & ~kind(susan)) | ! [X0] : (~creative(X0) & kind(X0))) [flattening 47]
49. (? [X0] : (creative(X0) | ~kind(X0)) | ~kind(susan) | kind(susan)) & ((kind(susan) & ~kind(susan)) | ! [X1] : (~creative(X1) & kind(X1))) [rectify 48]
50. ? [X0] : (creative(X0) | ~kind(X0)) => (creative(sK3) | ~kind(sK3)) [choice axiom]
51. ((creative(sK3) | ~kind(sK3)) | ~kind(susan) | kind(susan)) & ((kind(susan) & ~kind(susan)) | ! [X1] : (~creative(X1) & kind(X1))) [skolemisation 49,50]
59. ! [X0] : (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~patient(X0) & brave(X0))) [nnf transformation 29]
60. ! [X0] : (((calm(X0) & kind(X0)) | (generous(X0) | happy(X0))) & ((~generous(X0) & ~happy(X0)) | (~calm(X0) | ~kind(X0)))) [nnf transformation 11]
61. ! [X0] : (((calm(X0) & kind(X0)) | generous(X0) | happy(X0)) & ((~generous(X0) & ~happy(X0)) | ~calm(X0) | ~kind(X0))) [flattening 60]
82. calm(lucy) | patient(lucy) [cnf transformation 44]
89. ~quiet(X0) | ~patient(X0) | creative(X0) [cnf transformation 46]
91. ~generous(X0) | happy(X0) [cnf transformation 26]
93. ~kind(susan) | ~creative(X1) [cnf transformation 51]
95. kind(susan) | ~creative(X1) [cnf transformation 51]
104. ~happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 59]
109. calm(X0) | generous(X0) | happy(X0) [cnf transformation 61]
140. ~calm(lucy) [cnf transformation 21]
189. 12 <=> patient(lucy) [avatar definition]
191. patient(lucy) <- (12) [avatar component clause 189]
194. 13 <=> calm(lucy) [avatar definition]
195. ~calm(lucy) <- (~13) [avatar component clause 194]
198. 12 | 13 [avatar split clause 82,194,189]
201. 14 <=> ! [X1] : ~creative(X1) [avatar definition]
202. ~creative(X1) <- (14) [avatar component clause 201]
204. 15 <=> kind(susan) [avatar definition]
207. 14 | 15 [avatar split clause 95,204,201]
212. 14 | ~15 [avatar split clause 93,204,201]
257. happy(X0) | calm(X0) [subsumption resolution 109,91]
329. ~13 [avatar split clause 140,194]
359. ~patient(X0) | quiet(X0) | calm(X0) [resolution 104,257]
629. 74 <=> quiet(lucy) [avatar definition]
631. quiet(lucy) <- (74) [avatar component clause 629]
638. quiet(lucy) | calm(lucy) <- (12) [resolution 359,191]
639. quiet(lucy) <- (12, ~13) [subsumption resolution 638,195]
640. 74 | ~12 | 13 [avatar split clause 639,194,189,629]
670. ~patient(lucy) | creative(lucy) <- (74) [resolution 631,89]
673. creative(lucy) <- (12, 74) [subsumption resolution 670,191]
674. $false <- (12, 14, 74) [subsumption resolution 673,202]
675. ~12 | ~14 | ~74 [avatar contradiction clause 674]
677. $false [avatar sat refutation 198,207,212,329,640,675]
% SZS output end Proof for 4270168825461190958238890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is happy then someone is not wise and vice versa.
Everyone who is either curious or not happy is not happy or patient and vice versa.
Everyone who is brave or not kind is not kind.
If alice is both wise and funny then someone is not happy.
If paul is either not calm or not brave then john is quiet or not generous and vice versa.
Everyone who is not generous or rich is either not happy or not curious and vice versa.
Everyone who is curious or wise is not happy or not patient.
Everyone who is not brave or not curious is not quiet or calm.
Everyone who is both calm and kind is curious.
If lucy is not funny then someone is both not wise and brave and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If fred is both not tall and not wise then someone is either curious or not tall and vice versa.
Everyone who is not humble or not happy is both not creative and not old and vice versa.
If someone is calm then susan is both creative and not humble.
If someone is not wise or calm then john is both not calm and not funny and vice versa.
Someone is not brave.
Paul is not humble or not curious.
Someone is either not humble or not wise. | Alice is rich. | contradiction | ((happy(fred))<=>(?[X]:(~wise(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~happy(X)|patient(X))))&
(![X]:((brave(X)|~kind(X))=>~kind(X)))&
(((wise(alice)&funny(alice)))=>(?[X]:(~happy(X))))&
(((~calm(paul)<~>~brave(paul)))<=>((quiet(john)|~generous(john))))&
(![X]:((~generous(X)|rich(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((curious(X)|wise(X))=>(~happy(X)|~patient(X))))&
(![X]:((~brave(X)|~curious(X))=>(~quiet(X)|calm(X))))&
(![X]:((calm(X)&kind(X))=>curious(X)))&
((~funny(lucy))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
(((~tall(fred)&~wise(fred)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~creative(X)&~old(X))))&
((?[X]:(calm(X)))=>((creative(susan)&~humble(susan))))&
((?[X]:((~wise(X)|calm(X))))<=>((~calm(john)&~funny(john))))&
(?[X]:(~brave(X)))&
((~humble(paul)|~curious(paul)))&
(?[X]:((~humble(X)<~>~wise(X)))) | rich(alice) | [
"p1",
"p5",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1589844729691632787685312
% SZS output start Proof for 1589844729691632787685312
2. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (patient(X0) | ~happy(X0))) [input p1]
6. ! [X0] : ((rich(X0) | ~generous(X0)) <=> (~happy(X0) <~> ~curious(X0))) [input p5]
7. ! [X0] : ((wise(X0) | curious(X0)) => (~patient(X0) | ~happy(X0))) [input p6]
11. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p10]
13. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~old(X0) & ~creative(X0))) [input p12]
14. ? [X0] : calm(X0) => (~humble(susan) & creative(susan)) [input p13]
19. rich(alice) [input hypothesis]
23. ! [X0] : ((~patient(X0) | ~happy(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 7]
24. ! [X0] : (~patient(X0) | ~happy(X0) | (~wise(X0) & ~curious(X0))) [flattening 23]
29. (~humble(susan) & creative(susan)) | ! [X0] : ~calm(X0) [ennf transformation 14]
34. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 2]
35. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 34]
40. ! [X0] : (((rich(X0) | ~generous(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~rich(X0) & generous(X0)))) [nnf transformation 6]
41. ! [X0] : ((rich(X0) | ~generous(X0) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~rich(X0) & generous(X0)))) [flattening 40]
46. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 11]
47. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 46]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 13]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [flattening 53]
67. patient(X0) | ~happy(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 35]
70. ~patient(X0) | curious(X0) | ~happy(X0) [cnf transformation 35]
71. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 35]
85. curious(X0) | happy(X0) | ~rich(X0) [cnf transformation 41]
88. ~patient(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 24]
97. calm(X0) | patient(X0) [cnf transformation 47]
105. ~creative(X0) | humble(X0) [cnf transformation 54]
110. creative(susan) | ~calm(X0) [cnf transformation 29]
111. ~humble(susan) | ~calm(X0) [cnf transformation 29]
121. rich(alice) [cnf transformation 19]
122. patient(X0) | ~happy(X0) | ~curious(X0) [duplicate literal removal 67]
123. ~curious(X0) | happy(X0) [duplicate literal removal 71]
137. ~curious(X0) | patient(X0) [subsumption resolution 122,123]
173. ~rich(X0) | happy(X0) [subsumption resolution 85,123]
177. ~patient(X0) | ~curious(X0) [subsumption resolution 88,123]
178. ~curious(X0) [subsumption resolution 177,137]
221. 19 <=> ! [X0] : ~calm(X0) [avatar definition]
222. ~calm(X0) <- (19) [avatar component clause 221]
224. 20 <=> humble(susan) [avatar definition]
226. ~humble(susan) <- (~20) [avatar component clause 224]
227. 19 | ~20 [avatar split clause 111,224,221]
229. 21 <=> creative(susan) [avatar definition]
231. creative(susan) <- (21) [avatar component clause 229]
232. 19 | 21 [avatar split clause 110,229,221]
264. patient(X0) <- (19) [resolution 97,222]
266. happy(alice) [resolution 173,121]
269. curious(X0) | ~happy(X0) <- (19) [resolution 70,264]
270. ~happy(X0) <- (19) [subsumption resolution 269,178]
272. $false <- (19) [resolution 270,266]
273. ~19 [avatar contradiction clause 272]
277. humble(susan) <- (21) [resolution 231,105]
278. $false <- (~20, 21) [subsumption resolution 277,226]
279. 20 | ~21 [avatar contradiction clause 278]
280. $false [avatar sat refutation 227,232,273,279]
% SZS output end Proof for 1589844729691632787685312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or curious is either quiet or kind.
If john is both happy and wise then lucy is both tall and funny.
Everyone who is not kind is either not patient or patient.
If mary is not strong or old then someone is rich or happy and vice versa.
Everyone who is not wise is either humble or not wise.
Everyone who is both quiet and not humble is not curious or not funny and vice versa.
Everyone who is not funny is not brave and vice versa.
If paul is not old or old then someone is both not old and quiet and vice versa.
Everyone who is either wise or humble is not kind or not generous.
If someone is either not wise or old then mary is both funny and not old and vice versa.
Everyone who is both not quiet and tall is either patient or tall.
Everyone who is not patient or funny is not patient and vice versa.
If john is tall or brave then john is both not funny and kind.
If someone is happy or tall then fred is both not happy and not curious and vice versa.
Everyone who is both funny and creative is either not brave or not patient.
If someone is both not kind and not calm then mary is both funny and not creative.
Someone is wise or tall.
Susan is rich.
Mary is either not creative or strong.
Someone is not creative.
Someone is not brave or not humble.
Paul is not rich.
Alice is strong or curious. | Lucy is tall. | neutral | (![X]:((funny(X)<~>curious(X))=>(quiet(X)<~>kind(X))))&
(((happy(john)&wise(john)))=>((tall(lucy)&funny(lucy))))&
(![X]:(~kind(X)=>(~patient(X)<~>patient(X))))&
(((~strong(mary)|old(mary)))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:(~wise(X)=>(humble(X)<~>~wise(X))))&
(![X]:((quiet(X)&~humble(X))<=>(~curious(X)|~funny(X))))&
(![X]:(~funny(X)<=>~brave(X)))&
(((~old(paul)|old(paul)))<=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:((wise(X)<~>humble(X))=>(~kind(X)|~generous(X))))&
((?[X]:((~wise(X)<~>old(X))))<=>((funny(mary)&~old(mary))))&
(![X]:((~quiet(X)&tall(X))=>(patient(X)<~>tall(X))))&
(![X]:((~patient(X)|funny(X))<=>~patient(X)))&
(((tall(john)|brave(john)))=>((~funny(john)&kind(john))))&
((?[X]:((happy(X)|tall(X))))<=>((~happy(fred)&~curious(fred))))&
(![X]:((funny(X)&creative(X))=>(~brave(X)<~>~patient(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((funny(mary)&~creative(mary))))&
(?[X]:((wise(X)|tall(X))))&
(rich(susan))&
((~creative(mary)<~>strong(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)|~humble(X))))&
(~rich(paul))&
((strong(alice)|curious(alice))) | tall(lucy) | [] | null | 0 |
If someone is either brave or not generous then someone is not calm or not curious.
If someone is either not rich or humble then john is either patient or brave.
Everyone who is not creative or not old is not happy.
If someone is not brave then someone is not generous or brave and vice versa.
If lucy is brave then someone is not patient and vice versa.
Everyone who is happy or not humble is not patient or not happy.
If alice is both curious and not tall then someone is not quiet or not calm.
Everyone who is both funny and generous is not calm or quiet and vice versa.
Everyone who is rich is either quiet or patient and vice versa.
Everyone who is not rich is either not creative or not old and vice versa.
If fred is not happy then alice is both kind and not patient and vice versa.
Everyone who is calm is both happy and not brave and vice versa.
Everyone who is brave is either wise or strong and vice versa.
If someone is both not patient and not creative then someone is not wise.
If susan is not tall then alice is both strong and not curious.
Everyone who is not quiet or not old is either not old or kind.
Someone is both not brave and patient.
Fred is not kind or not funny.
Someone is not creative.
Someone is either not humble or not old.
John is not calm or kind.
Fred is either not old or brave.
Mary is either tall or not humble. | Fred is not funny. | contradiction | ((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~rich(X)<~>humble(X))))=>((patient(john)<~>brave(john))))&
(![X]:((~creative(X)|~old(X))=>~happy(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~generous(X)|brave(X)))))&
((brave(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((happy(X)|~humble(X))=>(~patient(X)|~happy(X))))&
(((curious(alice)&~tall(alice)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((funny(X)&generous(X))<=>(~calm(X)|quiet(X))))&
(![X]:(rich(X)<=>(quiet(X)<~>patient(X))))&
(![X]:(~rich(X)<=>(~creative(X)<~>~old(X))))&
((~happy(fred))<=>((kind(alice)&~patient(alice))))&
(![X]:(calm(X)<=>(happy(X)&~brave(X))))&
(![X]:(brave(X)<=>(wise(X)<~>strong(X))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:(~wise(X))))&
((~tall(susan))=>((strong(alice)&~curious(alice))))&
(![X]:((~quiet(X)|~old(X))=>(~old(X)<~>kind(X))))&
(?[X]:((~brave(X)&patient(X))))&
((~kind(fred)|~funny(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)<~>~old(X))))&
((~calm(john)|kind(john)))&
((~old(fred)<~>brave(fred)))&
((tall(mary)<~>~humble(mary))) | ~funny(fred) | [
"p2",
"p7",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4105284759803304803251087
% SZS output start Proof for 4105284759803304803251087
3. ! [X0] : ((~old(X0) | ~creative(X0)) => ~happy(X0)) [input p2]
8. ! [X0] : ((generous(X0) & funny(X0)) <=> (quiet(X0) | ~calm(X0))) [input p7]
12. ! [X0] : (calm(X0) <=> (~brave(X0) & happy(X0))) [input p11]
22. ~old(fred) <~> brave(fred) [input p21]
24. ~funny(fred) [input hypothesis]
32. ! [X0] : (~happy(X0) | (old(X0) & creative(X0))) [ennf transformation 3]
48. ! [X0] : (((generous(X0) & funny(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~generous(X0) | ~funny(X0)))) [nnf transformation 8]
49. ! [X0] : (((generous(X0) & funny(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~generous(X0) | ~funny(X0))) [flattening 48]
54. ! [X0] : ((calm(X0) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | ~calm(X0))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | ~calm(X0))) [flattening 54]
68. (~brave(fred) | old(fred)) & (brave(fred) | ~old(fred)) [nnf transformation 22]
75. ~happy(X0) | old(X0) [cnf transformation 32]
84. funny(X0) | calm(X0) [cnf transformation 49]
99. ~calm(X0) | happy(X0) [cnf transformation 55]
100. ~calm(X0) | ~brave(X0) [cnf transformation 55]
119. brave(fred) | ~old(fred) [cnf transformation 68]
123. ~funny(fred) [cnf transformation 24]
190. 16 <=> happy(fred) [avatar definition]
191. happy(fred) <- (16) [avatar component clause 190]
218. 22 <=> funny(fred) [avatar definition]
220. ~funny(fred) <- (~22) [avatar component clause 218]
242. 27 <=> old(fred) [avatar definition]
246. 28 <=> brave(fred) [avatar definition]
247. brave(fred) <- (28) [avatar component clause 246]
250. ~27 | 28 [avatar split clause 119,246,242]
261. ~22 [avatar split clause 123,218]
264. calm(fred) <- (~22) [resolution 84,220]
266. happy(fred) <- (~22) [resolution 99,264]
270. 16 | 22 [avatar split clause 266,218,190]
271. old(fred) <- (16) [resolution 191,75]
275. 27 | ~16 [avatar split clause 271,190,242]
276. ~brave(fred) <- (~22) [resolution 100,264]
278. $false <- (~22, 28) [subsumption resolution 276,247]
279. 22 | ~28 [avatar contradiction clause 278]
280. $false [avatar sat refutation 250,261,270,275,279]
% SZS output end Proof for 4105284759803304803251087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then paul is both not brave and not patient.
If someone is either creative or humble then paul is either not old or not happy.
If lucy is either not happy or not quiet then lucy is not brave or not strong.
Everyone who is happy is quiet.
If susan is either wise or not strong then susan is wise and vice versa.
If someone is funny then mary is both not calm and not curious and vice versa.
If someone is not funny then someone is not creative.
Everyone who is both not tall and not humble is both not strong and creative and vice versa.
Everyone who is both not generous and old is either not generous or not humble and vice versa.
If alice is both not wise and not brave then susan is patient or not patient and vice versa.
Everyone who is kind or not kind is funny.
Everyone who is either not tall or not strong is both not funny and not humble.
Everyone who is both curious and brave is creative and vice versa.
Everyone who is quiet is rich and vice versa.
If john is both not funny and brave then someone is creative and vice versa.
Everyone who is curious is both funny and brave.
Someone is both not happy and calm.
Alice is not curious or brave.
Someone is either not strong or happy.
Susan is not brave.
Mary is not creative.
Someone is happy.
Susan is both generous and not curious. | Mary is kind. | neutral | ((?[X]:(~kind(X)))=>((~brave(paul)&~patient(paul))))&
((?[X]:((creative(X)<~>humble(X))))=>((~old(paul)<~>~happy(paul))))&
(((~happy(lucy)<~>~quiet(lucy)))=>((~brave(lucy)|~strong(lucy))))&
(![X]:(happy(X)=>quiet(X)))&
(((wise(susan)<~>~strong(susan)))<=>(wise(susan)))&
((?[X]:(funny(X)))<=>((~calm(mary)&~curious(mary))))&
((?[X]:(~funny(X)))=>(?[X]:(~creative(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~strong(X)&creative(X))))&
(![X]:((~generous(X)&old(X))<=>(~generous(X)<~>~humble(X))))&
(((~wise(alice)&~brave(alice)))<=>((patient(susan)|~patient(susan))))&
(![X]:((kind(X)|~kind(X))=>funny(X)))&
(![X]:((~tall(X)<~>~strong(X))=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&brave(X))<=>creative(X)))&
(![X]:(quiet(X)<=>rich(X)))&
(((~funny(john)&brave(john)))<=>(?[X]:(creative(X))))&
(![X]:(curious(X)=>(funny(X)&brave(X))))&
(?[X]:((~happy(X)&calm(X))))&
((~curious(alice)|brave(alice)))&
(?[X]:((~strong(X)<~>happy(X))))&
(~brave(susan))&
(~creative(mary))&
(?[X]:(happy(X)))&
((generous(susan)&~curious(susan))) | kind(mary) | [] | null | 0 |
Everyone who is either not tall or strong is both strong and not kind and vice versa.
If mary is creative then mary is both brave and strong.
Everyone who is not old or humble is quiet and vice versa.
Everyone who is funny or tall is both not tall and kind.
If someone is both not rich and not wise then alice is curious or not generous and vice versa.
Everyone who is both creative and patient is both patient and not curious.
Everyone who is both happy and creative is curious and vice versa.
If paul is funny or not brave then someone is both creative and not wise.
Everyone who is not funny is either not creative or humble and vice versa.
If susan is rich or not curious then someone is both not tall and not rich.
If mary is either not brave or humble then alice is old and vice versa.
If alice is either old or creative then someone is not quiet and vice versa.
Everyone who is not funny or patient is not calm and vice versa.
Everyone who is both not old and not creative is not tall and vice versa.
Everyone who is not rich is either old or humble.
Someone is not happy.
Paul is not humble or quiet.
Someone is not patient or quiet.
Alice is curious or not calm.
Someone is happy.
Mary is both brave and not patient.
Someone is patient.
Someone is not patient. | Mary is old. | contradiction | (![X]:((~tall(X)<~>strong(X))<=>(strong(X)&~kind(X))))&
((creative(mary))=>((brave(mary)&strong(mary))))&
(![X]:((~old(X)|humble(X))<=>quiet(X)))&
(![X]:((funny(X)|tall(X))=>(~tall(X)&kind(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>((curious(alice)|~generous(alice))))&
(![X]:((creative(X)&patient(X))=>(patient(X)&~curious(X))))&
(![X]:((happy(X)&creative(X))<=>curious(X)))&
(((funny(paul)|~brave(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:(~funny(X)<=>(~creative(X)<~>humble(X))))&
(((rich(susan)|~curious(susan)))=>(?[X]:((~tall(X)&~rich(X)))))&
(((~brave(mary)<~>humble(mary)))<=>(old(alice)))&
(((old(alice)<~>creative(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((~funny(X)|patient(X))<=>~calm(X)))&
(![X]:((~old(X)&~creative(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(old(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((~humble(paul)|quiet(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
((curious(alice)|~calm(alice)))&
(?[X]:(happy(X)))&
((brave(mary)&~patient(mary)))&
(?[X]:(patient(X)))&
(?[X]:(~patient(X))) | old(mary) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2177968675414658343605098
% SZS output start Proof for 2177968675414658343605098
4. ! [X0] : ((tall(X0) | funny(X0)) => (kind(X0) & ~tall(X0))) [input p3]
14. ! [X0] : ((~creative(X0) & ~old(X0)) <=> ~tall(X0)) [input p13]
24. old(mary) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~tall(X0)) | (~tall(X0) & ~funny(X0))) [ennf transformation 4]
58. ! [X0] : (((~creative(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) | old(X0)))) [nnf transformation 14]
59. ! [X0] : (((~creative(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | creative(X0) | old(X0))) [flattening 58]
83. ~tall(X0) | ~tall(X0) [cnf transformation 28]
116. ~old(X0) | tall(X0) [cnf transformation 59]
129. old(mary) [cnf transformation 24]
130. ~tall(X0) [duplicate literal removal 83]
233. ~old(X0) [subsumption resolution 116,130]
250. $false [subsumption resolution 129,233]
% SZS output end Proof for 2177968675414658343605098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either strong or not rich.
Everyone who is not curious or curious is not brave or not humble and vice versa.
If john is both not old and not kind then someone is old or not tall and vice versa.
Everyone who is either quiet or funny is either not brave or old and vice versa.
Everyone who is not rich is both strong and not creative.
If mary is quiet then fred is happy or not brave and vice versa.
If someone is either tall or strong then john is not tall.
If someone is not quiet or tall then john is not creative or tall and vice versa.
If alice is either not happy or not kind then alice is not creative and vice versa.
If alice is either not generous or not kind then susan is humble or not wise and vice versa.
If susan is either not humble or not creative then mary is not kind or kind and vice versa.
If fred is not funny or curious then someone is either tall or wise and vice versa.
Everyone who is either quiet or wise is not quiet and vice versa.
If fred is both not curious and not calm then someone is either not humble or not tall.
Everyone who is happy is either not generous or not rich.
If lucy is humble then someone is either creative or not generous and vice versa.
Mary is not brave or tall.
Fred is both not tall and not old.
Someone is rich or not happy.
John is either not kind or patient.
John is both not old and not kind.
John is both not tall and creative. | Alice is not tall. | entailment | (![X]:(wise(X)=>(strong(X)<~>~rich(X))))&
(![X]:((~curious(X)|curious(X))<=>(~brave(X)|~humble(X))))&
(((~old(john)&~kind(john)))<=>(?[X]:((old(X)|~tall(X)))))&
(![X]:((quiet(X)<~>funny(X))<=>(~brave(X)<~>old(X))))&
(![X]:(~rich(X)=>(strong(X)&~creative(X))))&
((quiet(mary))<=>((happy(fred)|~brave(fred))))&
((?[X]:((tall(X)<~>strong(X))))=>(~tall(john)))&
((?[X]:((~quiet(X)|tall(X))))<=>((~creative(john)|tall(john))))&
(((~happy(alice)<~>~kind(alice)))<=>(~creative(alice)))&
(((~generous(alice)<~>~kind(alice)))<=>((humble(susan)|~wise(susan))))&
(((~humble(susan)<~>~creative(susan)))<=>((~kind(mary)|kind(mary))))&
(((~funny(fred)|curious(fred)))<=>(?[X]:((tall(X)<~>wise(X)))))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
((humble(lucy))<=>(?[X]:((creative(X)<~>~generous(X)))))&
((~brave(mary)|tall(mary)))&
((~tall(fred)&~old(fred)))&
(?[X]:((rich(X)|~happy(X))))&
((~kind(john)<~>patient(john)))&
((~old(john)&~kind(john)))&
((~tall(john)&creative(john))) | ~tall(alice) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1916729307037210505105441
% SZS output start Proof for 1916729307037210505105441
8. ? [X0] : (tall(X0) | ~quiet(X0)) <=> (tall(john) | ~creative(john)) [input p7]
22. creative(john) & ~tall(john) [input p21]
23. tall(alice) [input hypothesis]
41. (? [X0] : (tall(X0) | ~quiet(X0)) | (~tall(john) & creative(john))) & ((tall(john) | ~creative(john)) | ! [X0] : (~tall(X0) & quiet(X0))) [nnf transformation 8]
42. (? [X0] : (tall(X0) | ~quiet(X0)) | (~tall(john) & creative(john))) & (tall(john) | ~creative(john) | ! [X0] : (~tall(X0) & quiet(X0))) [flattening 41]
43. (? [X0] : (tall(X0) | ~quiet(X0)) | (~tall(john) & creative(john))) & (tall(john) | ~creative(john) | ! [X1] : (~tall(X1) & quiet(X1))) [rectify 42]
44. ? [X0] : (tall(X0) | ~quiet(X0)) => (tall(sK1) | ~quiet(sK1)) [choice axiom]
45. ((tall(sK1) | ~quiet(sK1)) | (~tall(john) & creative(john))) & (tall(john) | ~creative(john) | ! [X1] : (~tall(X1) & quiet(X1))) [skolemisation 43,44]
92. tall(john) | ~creative(john) | ~tall(X1) [cnf transformation 45]
135. ~tall(john) [cnf transformation 22]
136. creative(john) [cnf transformation 22]
137. tall(alice) [cnf transformation 23]
187. 11 <=> tall(john) [avatar definition]
205. 15 <=> creative(john) [avatar definition]
210. 16 <=> ! [X1] : ~tall(X1) [avatar definition]
211. ~tall(X1) <- (16) [avatar component clause 210]
212. 16 | ~15 | 11 [avatar split clause 92,187,205,210]
340. 15 [avatar split clause 136,205]
341. ~11 [avatar split clause 135,187]
350. $false <- (16) [resolution 211,137]
351. ~16 [avatar contradiction clause 350]
352. $false [avatar sat refutation 212,340,341,351]
% SZS output end Proof for 1916729307037210505105441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both not curious and not calm.
If someone is both kind and curious then someone is patient and vice versa.
Everyone who is strong is either generous or not happy and vice versa.
Everyone who is creative is both not curious and not quiet and vice versa.
If paul is both rich and humble then someone is kind or not kind and vice versa.
Everyone who is brave is both brave and calm.
Everyone who is not generous is funny and vice versa.
If someone is both brave and rich then mary is both not strong and not kind.
Everyone who is not generous or quiet is not strong and vice versa.
Everyone who is rich or tall is funny or not rich and vice versa.
If mary is not wise then someone is either not rich or wise.
If someone is not humble then someone is both not tall and not rich and vice versa.
Everyone who is not quiet or generous is brave or humble and vice versa.
Everyone who is funny or generous is either strong or old.
Everyone who is either not humble or funny is kind or curious and vice versa.
Everyone who is either not tall or not humble is brave or creative and vice versa.
Someone is both not funny and tall.
Mary is not quiet or not curious.
Lucy is either curious or not brave.
Someone is not tall or not generous. | Paul is not funny. | contradiction | (![X]:(curious(X)=>(~curious(X)&~calm(X))))&
((?[X]:((kind(X)&curious(X))))<=>(?[X]:(patient(X))))&
(![X]:(strong(X)<=>(generous(X)<~>~happy(X))))&
(![X]:(creative(X)<=>(~curious(X)&~quiet(X))))&
(((rich(paul)&humble(paul)))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:(brave(X)=>(brave(X)&calm(X))))&
(![X]:(~generous(X)<=>funny(X)))&
((?[X]:((brave(X)&rich(X))))=>((~strong(mary)&~kind(mary))))&
(![X]:((~generous(X)|quiet(X))<=>~strong(X)))&
(![X]:((rich(X)|tall(X))<=>(funny(X)|~rich(X))))&
((~wise(mary))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(brave(X)|humble(X))))&
(![X]:((funny(X)|generous(X))=>(strong(X)<~>old(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(kind(X)|curious(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(brave(X)|creative(X))))&
(?[X]:((~funny(X)&tall(X))))&
((~quiet(mary)|~curious(mary)))&
((curious(lucy)<~>~brave(lucy)))&
(?[X]:((~tall(X)|~generous(X)))) | ~funny(paul) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6767527637627614941999237
% SZS output start Proof for 6767527637627614941999237
5. (humble(paul) & rich(paul)) <=> ? [X0] : (~kind(X0) | kind(X0)) [input p4]
10. ! [X0] : ((tall(X0) | rich(X0)) <=> (~rich(X0) | funny(X0))) [input p9]
21. ~funny(paul) [input hypothesis]
37. ((humble(paul) & rich(paul)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X0] : (~kind(X0) | kind(X0)) | (~humble(paul) | ~rich(paul))) [nnf transformation 5]
38. ((humble(paul) & rich(paul)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X0] : (~kind(X0) | kind(X0)) | ~humble(paul) | ~rich(paul)) [flattening 37]
39. ((humble(paul) & rich(paul)) | ! [X0] : (kind(X0) & ~kind(X0))) & (? [X1] : (~kind(X1) | kind(X1)) | ~humble(paul) | ~rich(paul)) [rectify 38]
40. ? [X1] : (~kind(X1) | kind(X1)) => (~kind(sK2) | kind(sK2)) [choice axiom]
41. ((humble(paul) & rich(paul)) | ! [X0] : (kind(X0) & ~kind(X0))) & ((~kind(sK2) | kind(sK2)) | ~humble(paul) | ~rich(paul)) [skolemisation 39,40]
45. ! [X0] : (((tall(X0) | rich(X0)) | (rich(X0) & ~funny(X0))) & ((~rich(X0) | funny(X0)) | (~tall(X0) & ~rich(X0)))) [nnf transformation 10]
46. ! [X0] : ((tall(X0) | rich(X0) | (rich(X0) & ~funny(X0))) & (~rich(X0) | funny(X0) | (~tall(X0) & ~rich(X0)))) [flattening 45]
80. rich(paul) | ~kind(X0) [cnf transformation 41]
81. rich(paul) | kind(X0) [cnf transformation 41]
93. ~rich(X0) | funny(X0) | ~rich(X0) [cnf transformation 46]
128. ~funny(paul) [cnf transformation 21]
129. ~rich(X0) | funny(X0) [duplicate literal removal 93]
135. 1 <=> ! [X0] : kind(X0) [avatar definition]
136. kind(X0) <- (1) [avatar component clause 135]
143. 3 <=> ! [X0] : ~kind(X0) [avatar definition]
144. ~kind(X0) <- (3) [avatar component clause 143]
147. 4 <=> rich(paul) [avatar definition]
149. rich(paul) <- (4) [avatar component clause 147]
150. 1 | 4 [avatar split clause 81,147,135]
151. 3 | 4 [avatar split clause 80,147,143]
208. funny(paul) <- (4) [resolution 129,149]
209. $false <- (4) [subsumption resolution 208,128]
210. ~4 [avatar contradiction clause 209]
211. $false <- (1, 3) [subsumption resolution 136,144]
212. ~1 | ~3 [avatar contradiction clause 211]
213. $false [avatar sat refutation 150,151,210,212]
% SZS output end Proof for 6767527637627614941999237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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.
Everyone who is both not generous and funny is both brave and not old.
Everyone who is not calm is not wise.
Everyone who is not happy or not old is either not generous or not tall.
Paul is tall or curious.
Someone is either rich or strong.
Someone is wise or curious.
Someone is brave or not rich.
Someone is not wise or generous.
Someone is both not funny and old. | Lucy is tall. | entailment | ((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]:((~generous(X)&funny(X))=>(brave(X)&~old(X))))&
(![X]:(~calm(X)=>~wise(X)))&
(![X]:((~happy(X)|~old(X))=>(~generous(X)<~>~tall(X))))&
((tall(paul)|curious(paul)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((~funny(X)&old(X)))) | tall(lucy) | [
"p1",
"p2",
"p6",
"p7",
"p9",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9112001948093925162893689
% SZS output start Proof for 9112001948093925162893689
2. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~curious(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((patient(X0) | ~curious(X0)) => (~creative(X0) <~> ~funny(X0))) [input p2]
7. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (~old(X0) | calm(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | ~tall(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p7]
10. ! [X0] : (~funny(X0) <=> (tall(X0) & creative(X0))) [input p9]
11. (~kind(lucy) & patient(lucy)) <=> ? [X0] : (funny(X0) <~> curious(X0)) [input p10]
15. ! [X0] : (~calm(X0) => ~wise(X0)) [input p14]
22. ? [X0] : (old(X0) & ~funny(X0)) [input p21]
23. ~tall(lucy) [input hypothesis]
27. ! [X0] : ((~creative(X0) <~> ~funny(X0)) | (~patient(X0) & curious(X0))) [ennf transformation 3]
34. ! [X0] : (~wise(X0) | calm(X0)) [ennf transformation 15]
40. ! [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 2]
41. ! [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 40]
42. ! [X0] : (((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | (~patient(X0) & curious(X0))) [nnf transformation 27]
44. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [flattening 44]
46. ! [X0] : (((~calm(X0) | ~tall(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (calm(X0) & tall(X0)))) [nnf transformation 8]
47. ! [X0] : ((~calm(X0) | ~tall(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (calm(X0) & tall(X0)))) [flattening 46]
48. ! [X0] : ((~funny(X0) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | funny(X0))) [nnf transformation 10]
49. ! [X0] : ((~funny(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | funny(X0))) [flattening 48]
50. ((~kind(lucy) & patient(lucy)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (? [X0] : ((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (kind(lucy) | ~patient(lucy))) [nnf transformation 11]
51. ((~kind(lucy) & patient(lucy)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (? [X0] : ((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | kind(lucy) | ~patient(lucy)) [flattening 50]
52. ((~kind(lucy) & patient(lucy)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (? [X1] : ((~curious(X1) | ~funny(X1)) & (curious(X1) | funny(X1))) | kind(lucy) | ~patient(lucy)) [rectify 51]
53. ? [X1] : ((~curious(X1) | ~funny(X1)) & (curious(X1) | funny(X1))) => ((~curious(sK1) | ~funny(sK1)) & (curious(sK1) | funny(sK1))) [choice axiom]
54. ((~kind(lucy) & patient(lucy)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (((~curious(sK1) | ~funny(sK1)) & (curious(sK1) | funny(sK1))) | kind(lucy) | ~patient(lucy)) [skolemisation 52,53]
70. ? [X0] : (old(X0) & ~funny(X0)) => (old(sK7) & ~funny(sK7)) [choice axiom]
71. old(sK7) & ~funny(sK7) [skolemisation 22,70]
79. ~calm(X0) | funny(X0) | curious(X0) [cnf transformation 41]
80. ~funny(X0) | calm(X0) | creative(X0) [cnf transformation 41]
83. ~patient(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 42]
93. ~old(X0) | calm(X0) | wise(X0) | ~creative(X0) [cnf transformation 45]
100. ~calm(X0) | kind(X0) | tall(X0) [cnf transformation 47]
108. creative(X0) | funny(X0) [cnf transformation 49]
109. tall(X0) | funny(X0) [cnf transformation 49]
114. patient(lucy) | funny(X0) | ~curious(X0) [cnf transformation 54]
116. ~kind(lucy) | funny(X0) | ~curious(X0) [cnf transformation 54]
125. ~wise(X0) | calm(X0) [cnf transformation 34]
135. ~funny(sK7) [cnf transformation 71]
136. old(sK7) [cnf transformation 71]
137. ~tall(lucy) [cnf transformation 23]
166. 7 <=> calm(lucy) [avatar definition]
167. calm(lucy) <- (7) [avatar component clause 166]
204. 15 <=> ! [X0] : (funny(X0) | ~curious(X0)) [avatar definition]
205. ~curious(X0) | funny(X0) <- (15) [avatar component clause 204]
207. 16 <=> kind(lucy) [avatar definition]
209. ~kind(lucy) <- (~16) [avatar component clause 207]
210. 15 | ~16 [avatar split clause 116,207,204]
216. 18 <=> patient(lucy) [avatar definition]
218. patient(lucy) <- (18) [avatar component clause 216]
219. 15 | 18 [avatar split clause 114,216,204]
306. funny(lucy) [resolution 109,137]
326. calm(lucy) | creative(lucy) [resolution 80,306]
370. ~creative(lucy) | ~funny(lucy) <- (18) [resolution 83,218]
374. ~creative(lucy) <- (18) [subsumption resolution 370,306]
375. calm(lucy) <- (18) [subsumption resolution 326,374]
376. 7 | ~18 [avatar split clause 375,216,166]
502. kind(lucy) | tall(lucy) <- (7) [resolution 100,167]
507. tall(lucy) <- (7, ~16) [subsumption resolution 502,209]
508. $false <- (7, ~16) [subsumption resolution 507,137]
509. ~7 | 16 [avatar contradiction clause 508]
727. calm(sK7) | wise(sK7) | ~creative(sK7) [resolution 93,136]
730. calm(sK7) | ~creative(sK7) [subsumption resolution 727,125]
732. 74 <=> creative(sK7) [avatar definition]
734. ~creative(sK7) <- (~74) [avatar component clause 732]
736. 75 <=> calm(sK7) [avatar definition]
738. calm(sK7) <- (75) [avatar component clause 736]
739. ~74 | 75 [avatar split clause 730,736,732]
783. funny(sK7) <- (~74) [resolution 734,108]
784. $false <- (~74) [subsumption resolution 783,135]
785. 74 [avatar contradiction clause 784]
792. funny(sK7) | curious(sK7) <- (75) [resolution 738,79]
803. curious(sK7) <- (75) [subsumption resolution 792,135]
950. funny(sK7) <- (15, 75) [resolution 803,205]
951. $false <- (15, 75) [subsumption resolution 950,135]
952. ~15 | ~75 [avatar contradiction clause 951]
953. $false [avatar sat refutation 210,219,376,509,739,785,952]
% SZS output end Proof for 9112001948093925162893689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is either not patient or wise.
Everyone who is not curious is not wise or happy and vice versa.
Everyone who is not wise is not quiet or not happy and vice versa.
Everyone who is patient or not patient is both generous and funny.
Everyone who is both patient and not strong is not creative or not kind and vice versa.
If lucy is both not kind and not generous then someone is not patient or creative and vice versa.
Everyone who is patient is both not curious and not rich and vice versa.
Everyone who is not strong is either brave or not calm.
Everyone who is either not brave or kind is either creative or not patient and vice versa.
Everyone who is either not kind or generous is not quiet or not patient and vice versa.
If paul is funny then fred is either funny or old and vice versa.
If susan is either strong or kind then someone is either not tall or rich.
John is tall or not calm.
Someone is not rich or not wise.
Alice is both not happy and not brave.
John is either patient or not funny.
Paul is tall or not kind. | Alice is quiet. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:(~curious(X)<=>(~wise(X)|happy(X))))&
(![X]:(~wise(X)<=>(~quiet(X)|~happy(X))))&
(![X]:((patient(X)|~patient(X))=>(generous(X)&funny(X))))&
(![X]:((patient(X)&~strong(X))<=>(~creative(X)|~kind(X))))&
(((~kind(lucy)&~generous(lucy)))<=>(?[X]:((~patient(X)|creative(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~rich(X))))&
(![X]:(~strong(X)=>(brave(X)<~>~calm(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(~quiet(X)|~patient(X))))&
((funny(paul))<=>((funny(fred)<~>old(fred))))&
(((strong(susan)<~>kind(susan)))=>(?[X]:((~tall(X)<~>rich(X)))))&
((tall(john)|~calm(john)))&
(?[X]:((~rich(X)|~wise(X))))&
((~happy(alice)&~brave(alice)))&
((patient(john)<~>~funny(john)))&
((tall(paul)|~kind(paul))) | quiet(alice) | [
"p3",
"p5",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4400347155084256725210430
% SZS output start Proof for 4400347155084256725210430
4. ! [X0] : ((~patient(X0) | patient(X0)) => (funny(X0) & generous(X0))) [input p3]
6. (~generous(lucy) & ~kind(lucy)) <=> ? [X0] : (creative(X0) | ~patient(X0)) [input p5]
9. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p8]
10. ! [X0] : ((~kind(X0) <~> generous(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p9]
15. ~brave(alice) & ~happy(alice) [input p14]
18. quiet(alice) [input hypothesis]
21. ! [X0] : ((funny(X0) & generous(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 4]
34. ((~generous(lucy) & ~kind(lucy)) | ! [X0] : (~creative(X0) & patient(X0))) & (? [X0] : (creative(X0) | ~patient(X0)) | (generous(lucy) | kind(lucy))) [nnf transformation 6]
35. ((~generous(lucy) & ~kind(lucy)) | ! [X0] : (~creative(X0) & patient(X0))) & (? [X0] : (creative(X0) | ~patient(X0)) | generous(lucy) | kind(lucy)) [flattening 34]
36. ((~generous(lucy) & ~kind(lucy)) | ! [X0] : (~creative(X0) & patient(X0))) & (? [X1] : (creative(X1) | ~patient(X1)) | generous(lucy) | kind(lucy)) [rectify 35]
37. ? [X1] : (creative(X1) | ~patient(X1)) => (creative(sK1) | ~patient(sK1)) [choice axiom]
38. ((~generous(lucy) & ~kind(lucy)) | ! [X0] : (~creative(X0) & patient(X0))) & ((creative(sK1) | ~patient(sK1)) | generous(lucy) | kind(lucy)) [skolemisation 36,37]
42. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 9]
43. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [nnf transformation 10]
44. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [flattening 43]
60. generous(X0) | ~patient(X0) [cnf transformation 21]
61. generous(X0) | patient(X0) [cnf transformation 21]
72. ~generous(lucy) | patient(X0) [cnf transformation 38]
73. ~generous(lucy) | ~creative(X0) [cnf transformation 38]
79. ~patient(X0) | creative(X0) | kind(X0) | brave(X0) [cnf transformation 42]
88. ~patient(X0) | ~quiet(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 44]
104. ~brave(alice) [cnf transformation 15]
108. quiet(alice) [cnf transformation 18]
123. generous(X0) [subsumption resolution 60,61]
124. ~creative(X0) [subsumption resolution 73,123]
125. patient(X0) [subsumption resolution 72,123]
130. creative(X0) | kind(X0) | brave(X0) [subsumption resolution 79,125]
131. brave(X0) | kind(X0) [subsumption resolution 130,124]
133. ~quiet(X0) | ~kind(X0) | ~generous(X0) [subsumption resolution 88,125]
134. ~kind(X0) | ~quiet(X0) [subsumption resolution 133,123]
176. kind(alice) [resolution 131,104]
181. ~quiet(alice) [resolution 134,176]
182. $false [subsumption resolution 181,108]
% SZS output end Proof for 4400347155084256725210430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or not quiet then someone is either not calm or happy. If someone is both not old and quiet then mary is both not calm and generous. Everyone who is both humble and not brave is either happy or not generous and vice versa. If john is both not generous and generous then fred is both not creative and not tall and vice versa. Everyone who is strong is either not brave or not quiet. If alice is either calm or not kind then someone is kind or not creative. Everyone who is not kind or quiet is patient and vice versa. Everyone who is curious is either not rich or not creative. If someone is not calm or not old then someone is both brave and not brave. Everyone who is creative or not old is both creative and strong. If someone is not wise or not curious then someone is both not creative and happy and vice versa. If john is not funny or rich then someone is either funny or not humble. If someone is either not generous or wise then someone is both kind and calm. Everyone who is both generous and not creative is strong or not funny and vice versa. Everyone who is both not old and not patient is rich. Everyone who is both not strong and calm is not calm and vice versa. Someone is either rich or curious. Someone is not generous or not curious. Paul is both happy and tall. Someone is rich or strong. Someone is not old or strong. Someone is either not funny or not quiet. | Paul is not generous. | contradiction | ((?[X]:((~calm(X)|~quiet(X))))=>(?[X]:((~calm(X)<~>happy(X)))))&
((?[X]:((~old(X)&quiet(X))))=>((~calm(mary)&generous(mary))))&
(![X]:((humble(X)&~brave(X))<=>(happy(X)<~>~generous(X))))&
(((~generous(john)&generous(john)))<=>((~creative(fred)&~tall(fred))))&
(![X]:(strong(X)=>(~brave(X)<~>~quiet(X))))&
(((calm(alice)<~>~kind(alice)))=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((~kind(X)|quiet(X))<=>patient(X)))&
(![X]:(curious(X)=>(~rich(X)<~>~creative(X))))&
((?[X]:((~calm(X)|~old(X))))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((creative(X)|~old(X))=>(creative(X)&strong(X))))&
((?[X]:((~wise(X)|~curious(X))))<=>(?[X]:((~creative(X)&happy(X)))))&
(((~funny(john)|rich(john)))=>(?[X]:((funny(X)<~>~humble(X)))))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((generous(X)&~creative(X))<=>(strong(X)|~funny(X))))&
(![X]:((~old(X)&~patient(X))=>rich(X)))&
(![X]:((~strong(X)&calm(X))<=>~calm(X)))&
(?[X]:((rich(X)<~>curious(X))))&
(?[X]:((~generous(X)|~curious(X))))&
((happy(paul)&tall(paul)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((~funny(X)<~>~quiet(X)))) | ~generous(paul) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3590860349491783509813247
% SZS output start Proof for 3590860349491783509813247
14. ! [X0] : ((~creative(X0) & generous(X0)) <=> (~funny(X0) | strong(X0))) [input p13]
16. ! [X0] : ((calm(X0) & ~strong(X0)) <=> ~calm(X0)) [input p15]
23. ~generous(paul) [input hypothesis]
70. ! [X0] : (((~creative(X0) & generous(X0)) | (funny(X0) & ~strong(X0))) & ((~funny(X0) | strong(X0)) | (creative(X0) | ~generous(X0)))) [nnf transformation 14]
71. ! [X0] : (((~creative(X0) & generous(X0)) | (funny(X0) & ~strong(X0))) & (~funny(X0) | strong(X0) | creative(X0) | ~generous(X0))) [flattening 70]
72. ! [X0] : (((calm(X0) & ~strong(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) | strong(X0)))) [nnf transformation 16]
73. ! [X0] : (((calm(X0) & ~strong(X0)) | calm(X0)) & (~calm(X0) | ~calm(X0) | strong(X0))) [flattening 72]
131. ~strong(X0) | generous(X0) [cnf transformation 71]
136. ~calm(X0) | ~calm(X0) | strong(X0) [cnf transformation 73]
138. calm(X0) | calm(X0) [cnf transformation 73]
148. ~generous(paul) [cnf transformation 23]
149. ~calm(X0) | strong(X0) [duplicate literal removal 136]
150. calm(X0) [duplicate literal removal 138]
164. 4 <=> ! [X1] : calm(X1) [avatar definition]
165. calm(X1) <- (4) [avatar component clause 164]
295. 4 [avatar split clause 150,164]
347. strong(X0) <- (4) [resolution 149,165]
349. generous(X1) <- (4) [resolution 347,131]
350. $false <- (4) [resolution 349,148]
353. ~4 [avatar contradiction clause 350]
354. $false [avatar sat refutation 295,353]
% SZS output end Proof for 3590860349491783509813247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not happy then someone is either rich or not quiet.
If lucy is either strong or not wise then someone is not creative.
Everyone who is both not strong and not happy is either not funny or not creative and vice versa.
Everyone who is either kind or funny is both not kind and kind and vice versa.
If alice is either curious or strong then fred is humble.
Everyone who is either tall or brave is both curious and creative and vice versa.
Everyone who is old or not curious is not quiet or happy and vice versa.
If mary is either not quiet or creative then john is both wise and not wise.
If someone is rich then someone is both happy and patient and vice versa.
If someone is old then john is not humble or patient.
If lucy is not kind then someone is either curious or wise and vice versa.
If paul is happy then alice is both happy and not generous.
Everyone who is both kind and not calm is either curious or funny and vice versa.
Everyone who is tall is either not humble or not kind and vice versa.
If susan is strong or not happy then susan is either not strong or rich and vice versa.
If someone is not quiet or old then someone is quiet or not funny.
Someone is happy.
Susan is either not kind or funny.
Susan is not humble.
Someone is not brave or not strong.
Someone is either not funny or not patient.
Someone is not rich or wise. | Mary is tall. | neutral | ((?[X]:((rich(X)|~happy(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(((strong(lucy)<~>~wise(lucy)))=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&~happy(X))<=>(~funny(X)<~>~creative(X))))&
(![X]:((kind(X)<~>funny(X))<=>(~kind(X)&kind(X))))&
(((curious(alice)<~>strong(alice)))=>(humble(fred)))&
(![X]:((tall(X)<~>brave(X))<=>(curious(X)&creative(X))))&
(![X]:((old(X)|~curious(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(mary)<~>creative(mary)))=>((wise(john)&~wise(john))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&patient(X)))))&
((?[X]:(old(X)))=>((~humble(john)|patient(john))))&
((~kind(lucy))<=>(?[X]:((curious(X)<~>wise(X)))))&
((happy(paul))=>((happy(alice)&~generous(alice))))&
(![X]:((kind(X)&~calm(X))<=>(curious(X)<~>funny(X))))&
(![X]:(tall(X)<=>(~humble(X)<~>~kind(X))))&
(((strong(susan)|~happy(susan)))<=>((~strong(susan)<~>rich(susan))))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:((quiet(X)|~funny(X)))))&
(?[X]:(happy(X)))&
((~kind(susan)<~>funny(susan)))&
(~humble(susan))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((~rich(X)|wise(X)))) | tall(mary) | [] | null | 0 |
Everyone who is creative is both not humble and not kind. If someone is not patient or not rich then lucy is either happy or patient and vice versa. Everyone who is either not kind or not strong is both calm and not calm. Everyone who is not curious is tall. Everyone who is either not kind or not rich is either kind or not old and vice versa. Everyone who is funny is either not rich or not calm and vice versa. Everyone who is not wise or patient is both creative and funny and vice versa. If lucy is both kind and creative then alice is both happy and creative. Everyone who is either not curious or curious is humble. Everyone who is not kind or quiet is not happy. If someone is either quiet or tall then someone is not patient or not kind and vice versa. Everyone who is happy is humble or not curious and vice versa. Everyone who is either not rich or not old is either not creative or not strong. If susan is humble or generous then fred is both not creative and strong. If someone is both not strong and generous then someone is both not humble and humble and vice versa. Everyone who is both generous and not old is happy and vice versa. Lucy is generous. Alice is quiet or wise. Lucy is not curious. Paul is not brave. | Fred is funny. | neutral | (![X]:(creative(X)=>(~humble(X)&~kind(X))))&
((?[X]:((~patient(X)|~rich(X))))<=>((happy(lucy)<~>patient(lucy))))&
(![X]:((~kind(X)<~>~strong(X))=>(calm(X)&~calm(X))))&
(![X]:(~curious(X)=>tall(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(kind(X)<~>~old(X))))&
(![X]:(funny(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((~wise(X)|patient(X))<=>(creative(X)&funny(X))))&
(((kind(lucy)&creative(lucy)))=>((happy(alice)&creative(alice))))&
(![X]:((~curious(X)<~>curious(X))=>humble(X)))&
(![X]:((~kind(X)|quiet(X))=>~happy(X)))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:(happy(X)<=>(humble(X)|~curious(X))))&
(![X]:((~rich(X)<~>~old(X))=>(~creative(X)<~>~strong(X))))&
(((humble(susan)|generous(susan)))=>((~creative(fred)&strong(fred))))&
((?[X]:((~strong(X)&generous(X))))<=>(?[X]:((~humble(X)&humble(X)))))&
(![X]:((generous(X)&~old(X))<=>happy(X)))&
(generous(lucy))&
((quiet(alice)|wise(alice)))&
(~curious(lucy))&
(~brave(paul)) | funny(fred) | [] | null | 0 |
If lucy is rich or not tall then someone is not tall or not humble. Everyone who is either not curious or old is brave or rich and vice versa. If someone is both not humble and quiet then alice is brave or patient. Everyone who is strong or patient is old or not old and vice versa. Everyone who is humble or generous is both not old and generous and vice versa. If someone is kind then alice is either happy or curious. If susan is not curious then fred is old or not wise and vice versa. If someone is not rich or not happy then paul is either happy or not kind and vice versa. If someone is not strong then lucy is both funny and not curious and vice versa. Everyone who is patient or tall is both generous and quiet and vice versa. If someone is either curious or brave then someone is either not quiet or not funny. Everyone who is not humble or brave is humble. If someone is brave then alice is either not quiet or generous and vice versa. Everyone who is curious is not creative or patient and vice versa. If fred is both funny and happy then someone is humble or not wise and vice versa. If mary is both not kind and not tall then mary is either curious or not brave. Someone is both not quiet and kind. Someone is both curious and tall. Mary is patient or happy. Someone is not creative. John is either rich or brave. Someone is both kind and generous. John is not brave. | Susan is not curious. | neutral | (((rich(lucy)|~tall(lucy)))=>(?[X]:((~tall(X)|~humble(X)))))&
(![X]:((~curious(X)<~>old(X))<=>(brave(X)|rich(X))))&
((?[X]:((~humble(X)&quiet(X))))=>((brave(alice)|patient(alice))))&
(![X]:((strong(X)|patient(X))<=>(old(X)|~old(X))))&
(![X]:((humble(X)|generous(X))<=>(~old(X)&generous(X))))&
((?[X]:(kind(X)))=>((happy(alice)<~>curious(alice))))&
((~curious(susan))<=>((old(fred)|~wise(fred))))&
((?[X]:((~rich(X)|~happy(X))))<=>((happy(paul)<~>~kind(paul))))&
((?[X]:(~strong(X)))<=>((funny(lucy)&~curious(lucy))))&
(![X]:((patient(X)|tall(X))<=>(generous(X)&quiet(X))))&
((?[X]:((curious(X)<~>brave(X))))=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(![X]:((~humble(X)|brave(X))=>humble(X)))&
((?[X]:(brave(X)))<=>((~quiet(alice)<~>generous(alice))))&
(![X]:(curious(X)<=>(~creative(X)|patient(X))))&
(((funny(fred)&happy(fred)))<=>(?[X]:((humble(X)|~wise(X)))))&
(((~kind(mary)&~tall(mary)))=>((curious(mary)<~>~brave(mary))))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((curious(X)&tall(X))))&
((patient(mary)|happy(mary)))&
(?[X]:(~creative(X)))&
((rich(john)<~>brave(john)))&
(?[X]:((kind(X)&generous(X))))&
(~brave(john)) | ~curious(susan) | [] | null | 0 |
Everyone who is either humble or brave is both strong and not quiet and vice versa. If paul is not wise then lucy is strong or creative. Everyone who is both not happy and strong is not funny or not curious and vice versa. Everyone who is both not funny and not happy is not strong or not funny and vice versa. Everyone who is quiet or wise is both not curious and not funny. If mary is either rich or not tall then susan is not quiet and vice versa. If someone is either generous or not quiet then susan is either quiet or rich. If someone is curious then someone is either patient or rich. If susan is calm or not curious then someone is either not brave or not strong and vice versa. If someone is not funny then someone is both not strong and quiet. If someone is tall then mary is both not rich and quiet. Everyone who is either not quiet or not strong is not rich and vice versa. Everyone who is not kind is both tall and humble. If someone is rich then someone is tall or funny. Everyone who is happy is humble or wise. If someone is both wise and funny then john is not kind or not humble. Fred is not quiet. John is both not wise and not curious. Someone is either brave or not calm. Someone is either not curious or wise. Fred is not generous or not rich. | Paul is not funny. | contradiction | (![X]:((humble(X)<~>brave(X))<=>(strong(X)&~quiet(X))))&
((~wise(paul))=>((strong(lucy)|creative(lucy))))&
(![X]:((~happy(X)&strong(X))<=>(~funny(X)|~curious(X))))&
(![X]:((~funny(X)&~happy(X))<=>(~strong(X)|~funny(X))))&
(![X]:((quiet(X)|wise(X))=>(~curious(X)&~funny(X))))&
(((rich(mary)<~>~tall(mary)))<=>(~quiet(susan)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((quiet(susan)<~>rich(susan))))&
((?[X]:(curious(X)))=>(?[X]:((patient(X)<~>rich(X)))))&
(((calm(susan)|~curious(susan)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)&quiet(X)))))&
((?[X]:(tall(X)))=>((~rich(mary)&quiet(mary))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~rich(X)))&
(![X]:(~kind(X)=>(tall(X)&humble(X))))&
((?[X]:(rich(X)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:(happy(X)=>(humble(X)|wise(X))))&
((?[X]:((wise(X)&funny(X))))=>((~kind(john)|~humble(john))))&
(~quiet(fred))&
((~wise(john)&~curious(john)))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((~generous(fred)|~rich(fred))) | ~funny(paul) | [
"p2",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8610136604852759331957651
% SZS output start Proof for 8610136604852759331957651
3. ! [X0] : ((strong(X0) & ~happy(X0)) <=> (~curious(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> (~funny(X0) | ~strong(X0))) [input p3]
10. ? [X0] : ~funny(X0) => ? [X0] : (quiet(X0) & ~strong(X0)) [input p9]
22. ~funny(paul) [input hypothesis]
24. ? [X0] : ~funny(X0) => ? [X1] : (quiet(X1) & ~strong(X1)) [rectify 10]
30. ? [X1] : (quiet(X1) & ~strong(X1)) | ! [X0] : funny(X0) [ennf transformation 24]
40. ! [X0] : (((strong(X0) & ~happy(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~strong(X0) | happy(X0)))) [nnf transformation 3]
41. ! [X0] : (((strong(X0) & ~happy(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~strong(X0) | happy(X0))) [flattening 40]
42. ! [X0] : (((~happy(X0) & ~funny(X0)) | (funny(X0) & strong(X0))) & ((~funny(X0) | ~strong(X0)) | (happy(X0) | funny(X0)))) [nnf transformation 4]
43. ! [X0] : (((~happy(X0) & ~funny(X0)) | (funny(X0) & strong(X0))) & (~funny(X0) | ~strong(X0) | happy(X0) | funny(X0))) [flattening 42]
55. ? [X0] : (quiet(X0) & ~strong(X0)) | ! [X1] : funny(X1) [rectify 30]
56. ? [X0] : (quiet(X0) & ~strong(X0)) => (quiet(sK2) & ~strong(sK2)) [choice axiom]
57. (quiet(sK2) & ~strong(sK2)) | ! [X1] : funny(X1) [skolemisation 55,56]
77. strong(X0) | funny(X0) [cnf transformation 41]
80. ~funny(X0) | strong(X0) [cnf transformation 43]
104. ~strong(sK2) | funny(X1) [cnf transformation 57]
125. ~funny(paul) [cnf transformation 22]
126. strong(X0) [subsumption resolution 80,77]
192. 14 <=> ! [X1] : funny(X1) [avatar definition]
193. funny(X1) <- (14) [avatar component clause 192]
199. funny(X1) [subsumption resolution 104,126]
200. 14 [avatar split clause 199,192]
247. $false <- (14) [resolution 193,125]
248. ~14 [avatar contradiction clause 247]
249. $false [avatar sat refutation 200,248]
% SZS output end Proof for 8610136604852759331957651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not rich is either creative or humble and vice versa. If someone is either not quiet or humble then paul is tall or funny. If someone is either quiet or tall then someone is both wise and not kind and vice versa. Everyone who is not generous or not patient is quiet and vice versa. Everyone who is not wise or funny is kind or strong and vice versa. If mary is either quiet or creative then susan is either tall or not humble. If paul is both wise and tall then alice is not strong or not happy and vice versa. If someone is both funny and not brave then someone is either not calm or rich. Everyone who is strong is tall and vice versa. Everyone who is both quiet and not rich is not curious or creative. Everyone who is wise or humble is both not humble and quiet. If someone is both wise and not old then someone is wise or generous. If someone is either tall or not tall then someone is not calm and vice versa. Everyone who is rich is not quiet and vice versa. If john is either generous or calm then someone is not tall or strong. Everyone who is either not quiet or not generous is tall or not creative and vice versa. Someone is either not brave or strong. Someone is patient. Fred is both not strong and happy. Someone is either not humble or not wise. Lucy is both generous and tall. Someone is both not funny and not calm. Mary is not patient. Someone is brave. | Fred is tall. | contradiction | (![X]:((~brave(X)<~>~rich(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~quiet(X)<~>humble(X))))=>((tall(paul)|funny(paul))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~generous(X)|~patient(X))<=>quiet(X)))&
(![X]:((~wise(X)|funny(X))<=>(kind(X)|strong(X))))&
(((quiet(mary)<~>creative(mary)))=>((tall(susan)<~>~humble(susan))))&
(((wise(paul)&tall(paul)))<=>((~strong(alice)|~happy(alice))))&
((?[X]:((funny(X)&~brave(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
(![X]:(strong(X)<=>tall(X)))&
(![X]:((quiet(X)&~rich(X))=>(~curious(X)|creative(X))))&
(![X]:((wise(X)|humble(X))=>(~humble(X)&quiet(X))))&
((?[X]:((wise(X)&~old(X))))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((tall(X)<~>~tall(X))))<=>(?[X]:(~calm(X))))&
(![X]:(rich(X)<=>~quiet(X)))&
(((generous(john)<~>calm(john)))=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(tall(X)|~creative(X))))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:(patient(X)))&
((~strong(fred)&happy(fred)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((generous(lucy)&tall(lucy)))&
(?[X]:((~funny(X)&~calm(X))))&
(~patient(mary))&
(?[X]:(brave(X))) | tall(fred) | [
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3648559656055027696766607
% SZS output start Proof for 3648559656055027696766607
9. ! [X0] : (strong(X0) <=> tall(X0)) [input p8]
19. happy(fred) & ~strong(fred) [input p18]
25. tall(fred) [input hypothesis]
56. ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 9]
115. ~tall(X0) | strong(X0) [cnf transformation 56]
137. ~strong(fred) [cnf transformation 19]
147. tall(fred) [cnf transformation 25]
280. strong(fred) [resolution 115,147]
282. $false [subsumption resolution 280,137]
% SZS output end Proof for 3648559656055027696766607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or humble is not patient or curious and vice versa.
If fred is both not creative and old then someone is both creative and not happy.
Everyone who is both not calm and not quiet is not quiet and vice versa.
If someone is either curious or funny then someone is not creative or rich.
If paul is old then someone is both generous and kind and vice versa.
Everyone who is not calm is patient and vice versa.
If susan is quiet then someone is not old.
If someone is both happy and calm then someone is both not tall and tall and vice versa.
If someone is either kind or not creative then someone is both not kind and funny and vice versa.
Everyone who is both tall and calm is curious or not calm.
Everyone who is not rich is happy.
If someone is not humble or not patient then someone is patient or not brave.
Everyone who is either not patient or not tall is tall or humble.
Everyone who is not happy is both not wise and not calm.
Everyone who is both not funny and not generous is not rich or not kind and vice versa.
If someone is not curious then john is either not happy or calm.
Lucy is calm or not kind.
Someone is kind.
Someone is not brave.
Susan is either not creative or wise.
Fred is kind.
Mary is either not curious or not patient.
Lucy is either humble or generous. | Lucy is not curious. | entailment | (![X]:((patient(X)<~>humble(X))<=>(~patient(X)|curious(X))))&
(((~creative(fred)&old(fred)))=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>~quiet(X)))&
((?[X]:((curious(X)<~>funny(X))))=>(?[X]:((~creative(X)|rich(X)))))&
((old(paul))<=>(?[X]:((generous(X)&kind(X)))))&
(![X]:(~calm(X)<=>patient(X)))&
((quiet(susan))=>(?[X]:(~old(X))))&
((?[X]:((happy(X)&calm(X))))<=>(?[X]:((~tall(X)&tall(X)))))&
((?[X]:((kind(X)<~>~creative(X))))<=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((tall(X)&calm(X))=>(curious(X)|~calm(X))))&
(![X]:(~rich(X)=>happy(X)))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~patient(X)<~>~tall(X))=>(tall(X)|humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~calm(X))))&
(![X]:((~funny(X)&~generous(X))<=>(~rich(X)|~kind(X))))&
((?[X]:(~curious(X)))=>((~happy(john)<~>calm(john))))&
((calm(lucy)|~kind(lucy)))&
(?[X]:(kind(X)))&
(?[X]:(~brave(X)))&
((~creative(susan)<~>wise(susan)))&
(kind(fred))&
((~curious(mary)<~>~patient(mary)))&
((humble(lucy)<~>generous(lucy))) | ~curious(lucy) | [
"p0",
"p5",
"p7",
"p13",
"p14",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4930315757110043752812559
% SZS output start Proof for 4930315757110043752812559
1. ! [X0] : ((patient(X0) <~> humble(X0)) <=> (curious(X0) | ~patient(X0))) [input p0]
6. ! [X0] : (~calm(X0) <=> patient(X0)) [input p5]
8. ? [X0] : (calm(X0) & happy(X0)) <=> ? [X0] : (tall(X0) & ~tall(X0)) [input p7]
14. ! [X0] : (~happy(X0) => (~calm(X0) & ~wise(X0))) [input p13]
15. ! [X0] : ((~generous(X0) & ~funny(X0)) <=> (~kind(X0) | ~rich(X0))) [input p14]
17. ~kind(lucy) | calm(lucy) [input p16]
23. humble(lucy) <~> generous(lucy) [input p22]
24. curious(lucy) [input hypothesis]
26. ? [X0] : (calm(X0) & happy(X0)) <=> ? [X1] : (tall(X1) & ~tall(X1)) [rectify 8]
40. ! [X0] : ((~calm(X0) & ~wise(X0)) | happy(X0)) [ennf transformation 14]
42. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 1]
43. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [flattening 42]
56. ! [X0] : ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))) [nnf transformation 6]
59. (? [X0] : (calm(X0) & happy(X0)) | ! [X1] : (~tall(X1) | tall(X1))) & (? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : (~calm(X0) | ~happy(X0))) [nnf transformation 26]
60. (? [X0] : (calm(X0) & happy(X0)) | ! [X1] : (~tall(X1) | tall(X1))) & (? [X2] : (tall(X2) & ~tall(X2)) | ! [X3] : (~calm(X3) | ~happy(X3))) [rectify 59]
61. ? [X0] : (calm(X0) & happy(X0)) => (calm(sK4) & happy(sK4)) [choice axiom]
62. ? [X2] : (tall(X2) & ~tall(X2)) => (tall(sK5) & ~tall(sK5)) [choice axiom]
63. ((calm(sK4) & happy(sK4)) | ! [X1] : (~tall(X1) | tall(X1))) & ((tall(sK5) & ~tall(sK5)) | ! [X3] : (~calm(X3) | ~happy(X3))) [skolemisation 60,62,61]
70. ! [X0] : (((~generous(X0) & ~funny(X0)) | (kind(X0) & rich(X0))) & ((~kind(X0) | ~rich(X0)) | (generous(X0) | funny(X0)))) [nnf transformation 15]
71. ! [X0] : (((~generous(X0) & ~funny(X0)) | (kind(X0) & rich(X0))) & (~kind(X0) | ~rich(X0) | generous(X0) | funny(X0))) [flattening 70]
77. (~generous(lucy) | ~humble(lucy)) & (generous(lucy) | humble(lucy)) [nnf transformation 23]
83. ~curious(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 43]
94. calm(X0) | patient(X0) [cnf transformation 56]
97. ~tall(sK5) | ~calm(X3) | ~happy(X3) [cnf transformation 63]
98. tall(sK5) | ~calm(X3) | ~happy(X3) [cnf transformation 63]
112. ~calm(X0) | happy(X0) [cnf transformation 40]
117. ~generous(X0) | kind(X0) [cnf transformation 71]
120. ~kind(lucy) | calm(lucy) [cnf transformation 17]
127. generous(lucy) | humble(lucy) [cnf transformation 77]
129. curious(lucy) [cnf transformation 24]
197. 15 <=> ! [X3] : (~calm(X3) | ~happy(X3)) [avatar definition]
198. ~calm(X3) | ~happy(X3) <- (15) [avatar component clause 197]
200. 16 <=> tall(sK5) [avatar definition]
203. 15 | 16 [avatar split clause 98,200,197]
204. 15 | ~16 [avatar split clause 97,200,197]
251. 27 <=> calm(lucy) [avatar definition]
253. calm(lucy) <- (27) [avatar component clause 251]
255. 28 <=> kind(lucy) [avatar definition]
258. 27 | ~28 [avatar split clause 120,255,251]
280. 33 <=> humble(lucy) [avatar definition]
284. 34 <=> generous(lucy) [avatar definition]
285. generous(lucy) <- (34) [avatar component clause 284]
288. 33 | 34 [avatar split clause 127,284,280]
289. ~calm(X3) <- (15) [subsumption resolution 198,112]
292. patient(X1) <- (15) [resolution 94,289]
311. ~patient(lucy) | ~humble(lucy) [resolution 83,129]
313. ~humble(lucy) <- (15) [subsumption resolution 311,292]
316. ~33 | ~15 [avatar split clause 313,197,280]
323. kind(lucy) <- (34) [resolution 285,117]
327. 28 | ~34 [avatar split clause 323,284,255]
328. $false <- (15, 27) [subsumption resolution 253,289]
329. ~15 | ~27 [avatar contradiction clause 328]
330. $false [avatar sat refutation 203,204,258,288,316,327,329]
% SZS output end Proof for 4930315757110043752812559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not humble or not funny then susan is both not generous and not funny and vice versa.
Everyone who is humble is either wise or humble and vice versa.
If someone is wise or not calm then fred is either not tall or not brave.
Everyone who is not curious or funny is not tall or not quiet.
Everyone who is either kind or patient is both not rich and kind and vice versa.
Everyone who is not funny is either strong or not wise and vice versa.
If someone is either curious or not patient then someone is brave and vice versa.
If lucy is old or funny then someone is patient and vice versa.
If alice is not brave then mary is creative.
If someone is funny or strong then someone is not quiet and vice versa.
Everyone who is not patient is not calm or kind and vice versa.
Everyone who is rich or curious is either patient or humble and vice versa.
If someone is not old or not happy then mary is either not rich or not brave.
Everyone who is both humble and not brave is tall and vice versa.
If someone is both not happy and not rich then someone is not curious or not strong.
Everyone who is either not wise or quiet is not tall and vice versa.
Someone is either wise or not generous.
Someone is rich.
Fred is either curious or not wise.
Someone is not strong.
Paul is both old and not quiet.
Someone is generous. | Alice is quiet. | neutral | ((?[X]:((~humble(X)|~funny(X))))<=>((~generous(susan)&~funny(susan))))&
(![X]:(humble(X)<=>(wise(X)<~>humble(X))))&
((?[X]:((wise(X)|~calm(X))))=>((~tall(fred)<~>~brave(fred))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)|~quiet(X))))&
(![X]:((kind(X)<~>patient(X))<=>(~rich(X)&kind(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~wise(X))))&
((?[X]:((curious(X)<~>~patient(X))))<=>(?[X]:(brave(X))))&
(((old(lucy)|funny(lucy)))<=>(?[X]:(patient(X))))&
((~brave(alice))=>(creative(mary)))&
((?[X]:((funny(X)|strong(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(~patient(X)<=>(~calm(X)|kind(X))))&
(![X]:((rich(X)|curious(X))<=>(patient(X)<~>humble(X))))&
((?[X]:((~old(X)|~happy(X))))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((humble(X)&~brave(X))<=>tall(X)))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~tall(X)))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:(rich(X)))&
((curious(fred)<~>~wise(fred)))&
(?[X]:(~strong(X)))&
((old(paul)&~quiet(paul)))&
(?[X]:(generous(X))) | quiet(alice) | [] | null | 0 |
Everyone who is not rich is either not curious or kind and vice versa.
If someone is either not tall or not patient then someone is not kind or humble and vice versa.
If lucy is both not quiet and old then someone is either brave or creative.
Everyone who is patient or not tall is either tall or not creative and vice versa.
If someone is generous or not old then lucy is wise.
If someone is both humble and not calm then someone is funny or not humble.
Everyone who is rich or not creative is both not tall and wise.
Everyone who is not curious or not old is humble or not tall.
If paul is both not old and not strong then someone is kind or calm and vice versa.
Everyone who is both not creative and humble is either rich or curious.
Everyone who is not patient or not curious is both not wise and not strong and vice versa.
Everyone who is either brave or creative is either not funny or tall.
If susan is either not patient or not tall then someone is both not tall and not humble and vice versa.
Everyone who is not wise or tall is both not kind and humble.
If someone is not funny then someone is generous.
If lucy is both rich and not strong then someone is not quiet or not happy and vice versa.
Someone is not happy.
Susan is both not funny and rich.
Someone is tall.
Alice is either rich or old.
Alice is both humble and quiet.
Paul is either creative or curious.
Mary is strong. | Mary is creative. | contradiction | (![X]:(~rich(X)<=>(~curious(X)<~>kind(X))))&
((?[X]:((~tall(X)<~>~patient(X))))<=>(?[X]:((~kind(X)|humble(X)))))&
(((~quiet(lucy)&old(lucy)))=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:((patient(X)|~tall(X))<=>(tall(X)<~>~creative(X))))&
((?[X]:((generous(X)|~old(X))))=>(wise(lucy)))&
((?[X]:((humble(X)&~calm(X))))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:((rich(X)|~creative(X))=>(~tall(X)&wise(X))))&
(![X]:((~curious(X)|~old(X))=>(humble(X)|~tall(X))))&
(((~old(paul)&~strong(paul)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~creative(X)&humble(X))=>(rich(X)<~>curious(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((brave(X)<~>creative(X))=>(~funny(X)<~>tall(X))))&
(((~patient(susan)<~>~tall(susan)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(![X]:((~wise(X)|tall(X))=>(~kind(X)&humble(X))))&
((?[X]:(~funny(X)))=>(?[X]:(generous(X))))&
(((rich(lucy)&~strong(lucy)))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(?[X]:(~happy(X)))&
((~funny(susan)&rich(susan)))&
(?[X]:(tall(X)))&
((rich(alice)<~>old(alice)))&
((humble(alice)&quiet(alice)))&
((creative(paul)<~>curious(paul)))&
(strong(mary)) | creative(mary) | [
"p0",
"p3",
"p6",
"p10",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 839984664100498015542084
% SZS output start Proof for 839984664100498015542084
1. ! [X0] : (~rich(X0) <=> (~curious(X0) <~> kind(X0))) [input p0]
4. ! [X0] : ((~tall(X0) | patient(X0)) <=> (tall(X0) <~> ~creative(X0))) [input p3]
7. ! [X0] : ((~creative(X0) | rich(X0)) => (wise(X0) & ~tall(X0))) [input p6]
11. ! [X0] : ((~curious(X0) | ~patient(X0)) <=> (~strong(X0) & ~wise(X0))) [input p10]
14. ! [X0] : ((tall(X0) | ~wise(X0)) => (humble(X0) & ~kind(X0))) [input p13]
23. strong(mary) [input p22]
24. creative(mary) [input hypothesis]
32. ! [X0] : ((wise(X0) & ~tall(X0)) | (creative(X0) & ~rich(X0))) [ennf transformation 7]
38. ! [X0] : ((humble(X0) & ~kind(X0)) | (~tall(X0) & wise(X0))) [ennf transformation 14]
40. ! [X0] : ((~rich(X0) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0)))) & (((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | rich(X0))) [nnf transformation 1]
49. ! [X0] : (((~tall(X0) | patient(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (tall(X0) & ~patient(X0)))) [nnf transformation 4]
50. ! [X0] : ((~tall(X0) | patient(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (tall(X0) & ~patient(X0)))) [flattening 49]
60. ! [X0] : (((~curious(X0) | ~patient(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (curious(X0) & patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((~curious(X0) | ~patient(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (curious(X0) & patient(X0)))) [flattening 60]
81. ~curious(X0) | kind(X0) | rich(X0) [cnf transformation 40]
94. ~creative(X0) | tall(X0) | tall(X0) [cnf transformation 50]
102. ~tall(X0) | ~rich(X0) [cnf transformation 32]
118. ~strong(X0) | curious(X0) [cnf transformation 61]
131. ~tall(X0) | ~kind(X0) [cnf transformation 38]
150. strong(mary) [cnf transformation 23]
151. creative(mary) [cnf transformation 24]
152. ~creative(X0) | tall(X0) [duplicate literal removal 94]
373. curious(mary) [resolution 118,150]
384. tall(mary) [resolution 152,151]
388. kind(mary) | rich(mary) [resolution 81,373]
396. ~kind(mary) [resolution 384,131]
398. ~rich(mary) [resolution 384,102]
401. rich(mary) [subsumption resolution 388,396]
402. $false [subsumption resolution 401,398]
% SZS output end Proof for 839984664100498015542084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is kind then someone is not tall. If someone is brave then someone is either not kind or not happy and vice versa. If someone is both rich and generous then alice is calm and vice versa. Everyone who is happy or tall is humble and vice versa. Everyone who is not happy or rich is either funny or rich. Everyone who is both patient and old is humble or not humble and vice versa. Everyone who is not quiet or curious is not tall or not patient and vice versa. If john is both brave and funny then mary is either patient or humble and vice versa. If mary is tall then fred is either brave or not strong and vice versa. Everyone who is tall is both humble and not wise. If someone is both not old and happy then john is tall and vice versa. Everyone who is not brave or not rich is either quiet or not generous and vice versa. Everyone who is curious is either not rich or rich. Everyone who is old or rich is tall or not happy. Everyone who is not curious or quiet is both not creative and not old. Everyone who is either kind or not wise is not happy or calm. Alice is generous. Someone is either wise or not brave. Someone is either rich or not patient. Someone is not tall. Someone is either old or brave. Mary is either not strong or not wise. | John is curious. | entailment | ((?[X]:(kind(X)))=>(?[X]:(~tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((rich(X)&generous(X))))<=>(calm(alice)))&
(![X]:((happy(X)|tall(X))<=>humble(X)))&
(![X]:((~happy(X)|rich(X))=>(funny(X)<~>rich(X))))&
(![X]:((patient(X)&old(X))<=>(humble(X)|~humble(X))))&
(![X]:((~quiet(X)|curious(X))<=>(~tall(X)|~patient(X))))&
(((brave(john)&funny(john)))<=>((patient(mary)<~>humble(mary))))&
((tall(mary))<=>((brave(fred)<~>~strong(fred))))&
(![X]:(tall(X)=>(humble(X)&~wise(X))))&
((?[X]:((~old(X)&happy(X))))<=>(tall(john)))&
(![X]:((~brave(X)|~rich(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(curious(X)=>(~rich(X)<~>rich(X))))&
(![X]:((old(X)|rich(X))=>(tall(X)|~happy(X))))&
(![X]:((~curious(X)|quiet(X))=>(~creative(X)&~old(X))))&
(![X]:((kind(X)<~>~wise(X))=>(~happy(X)|calm(X))))&
(generous(alice))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)<~>brave(X))))&
((~strong(mary)<~>~wise(mary))) | curious(john) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 653447449392243068381559
% SZS output start Proof for 653447449392243068381559
6. ! [X0] : ((old(X0) & patient(X0)) <=> (~humble(X0) | humble(X0))) [input p5]
15. ! [X0] : ((quiet(X0) | ~curious(X0)) => (~old(X0) & ~creative(X0))) [input p14]
23. ~curious(john) [input hypothesis]
26. ! [X0] : ((quiet(X0) | ~curious(X0)) => ~old(X0)) [pure predicate removal 15]
33. ! [X0] : (~old(X0) | (~quiet(X0) & curious(X0))) [ennf transformation 26]
51. ! [X0] : (((old(X0) & patient(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (~old(X0) | ~patient(X0)))) [nnf transformation 6]
52. ! [X0] : (((old(X0) & patient(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ~old(X0) | ~patient(X0))) [flattening 51]
96. old(X0) | ~humble(X0) [cnf transformation 52]
97. old(X0) | humble(X0) [cnf transformation 52]
127. ~old(X0) | curious(X0) [cnf transformation 33]
141. ~curious(john) [cnf transformation 23]
194. old(X0) [subsumption resolution 96,97]
245. curious(X0) [subsumption resolution 127,194]
268. $false [subsumption resolution 141,245]
% SZS output end Proof for 653447449392243068381559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not happy is either wise or rich. Everyone who is either not creative or not rich is not humble and vice versa. If someone is not patient then susan is not patient. If fred is both generous and not strong then someone is not rich or not patient. If someone is not old then lucy is not rich and vice versa. Everyone who is not tall is curious or not generous. If someone is either patient or not rich then someone is either brave or creative. Everyone who is not calm is kind. If lucy is both tall and patient then susan is not curious or humble and vice versa. Everyone who is both not kind and strong is both curious and not patient and vice versa. Everyone who is patient or not humble is both not wise and not strong and vice versa. Everyone who is kind is both generous and rich and vice versa. If someone is generous then someone is not rich or not humble and vice versa. If alice is both not generous and not funny then lucy is tall and vice versa. If someone is not quiet or old then someone is old. If susan is either not humble or calm then someone is both not funny and happy and vice versa. Someone is either not generous or happy. Someone is tall or kind. John is both not strong and old. Someone is either not kind or tall. Mary is quiet or calm. Someone is both not curious and creative. John is either kind or not quiet. | Susan is not old. | contradiction | (![X]:((~wise(X)|~happy(X))=>(wise(X)<~>rich(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>~humble(X)))&
((?[X]:(~patient(X)))=>(~patient(susan)))&
(((generous(fred)&~strong(fred)))=>(?[X]:((~rich(X)|~patient(X)))))&
((?[X]:(~old(X)))<=>(~rich(lucy)))&
(![X]:(~tall(X)=>(curious(X)|~generous(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:(~calm(X)=>kind(X)))&
(((tall(lucy)&patient(lucy)))<=>((~curious(susan)|humble(susan))))&
(![X]:((~kind(X)&strong(X))<=>(curious(X)&~patient(X))))&
(![X]:((patient(X)|~humble(X))<=>(~wise(X)&~strong(X))))&
(![X]:(kind(X)<=>(generous(X)&rich(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~generous(alice)&~funny(alice)))<=>(tall(lucy)))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:(old(X))))&
(((~humble(susan)<~>calm(susan)))<=>(?[X]:((~funny(X)&happy(X)))))&
(?[X]:((~generous(X)<~>happy(X))))&
(?[X]:((tall(X)|kind(X))))&
((~strong(john)&old(john)))&
(?[X]:((~kind(X)<~>tall(X))))&
((quiet(mary)|calm(mary)))&
(?[X]:((~curious(X)&creative(X))))&
((kind(john)<~>~quiet(john))) | ~old(susan) | [
"p0",
"p2",
"p4",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 750401124724547430559051
% SZS output start Proof for 750401124724547430559051
1. ! [X0] : ((~happy(X0) | ~wise(X0)) => (wise(X0) <~> rich(X0))) [input p0]
3. ? [X0] : ~patient(X0) => ~patient(susan) [input p2]
5. ? [X0] : ~old(X0) <=> ~rich(lucy) [input p4]
9. (patient(lucy) & tall(lucy)) <=> (humble(susan) | ~curious(susan)) [input p8]
10. ! [X0] : ((strong(X0) & ~kind(X0)) <=> (~patient(X0) & curious(X0))) [input p9]
11. ! [X0] : ((~humble(X0) | patient(X0)) <=> (~strong(X0) & ~wise(X0))) [input p10]
24. ~old(susan) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> rich(X0)) | (happy(X0) & wise(X0))) [ennf transformation 1]
29. ~patient(susan) | ! [X0] : patient(X0) [ennf transformation 3]
37. ! [X0] : (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (happy(X0) & wise(X0))) [nnf transformation 28]
41. (? [X0] : ~old(X0) | rich(lucy)) & (~rich(lucy) | ! [X0] : old(X0)) [nnf transformation 5]
42. (? [X0] : ~old(X0) | rich(lucy)) & (~rich(lucy) | ! [X1] : old(X1)) [rectify 41]
43. ? [X0] : ~old(X0) => ~old(sK1) [choice axiom]
44. (~old(sK1) | rich(lucy)) & (~rich(lucy) | ! [X1] : old(X1)) [skolemisation 42,43]
49. ((patient(lucy) & tall(lucy)) | (~humble(susan) & curious(susan))) & ((humble(susan) | ~curious(susan)) | (~patient(lucy) | ~tall(lucy))) [nnf transformation 9]
50. ((patient(lucy) & tall(lucy)) | (~humble(susan) & curious(susan))) & (humble(susan) | ~curious(susan) | ~patient(lucy) | ~tall(lucy)) [flattening 49]
51. ! [X0] : (((strong(X0) & ~kind(X0)) | (patient(X0) | ~curious(X0))) & ((~patient(X0) & curious(X0)) | (~strong(X0) | kind(X0)))) [nnf transformation 10]
52. ! [X0] : (((strong(X0) & ~kind(X0)) | patient(X0) | ~curious(X0)) & ((~patient(X0) & curious(X0)) | ~strong(X0) | kind(X0))) [flattening 51]
53. ! [X0] : (((~humble(X0) | patient(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (humble(X0) & ~patient(X0)))) [nnf transformation 11]
54. ! [X0] : ((~humble(X0) | patient(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (humble(X0) & ~patient(X0)))) [flattening 53]
82. rich(X0) | wise(X0) | wise(X0) [cnf transformation 37]
90. ~patient(susan) | patient(X0) [cnf transformation 29]
92. ~rich(lucy) | old(X1) [cnf transformation 44]
103. patient(lucy) | curious(susan) [cnf transformation 50]
104. patient(lucy) | ~humble(susan) [cnf transformation 50]
108. ~curious(X0) | patient(X0) | strong(X0) [cnf transformation 52]
109. ~patient(X0) | ~wise(X0) [cnf transformation 54]
112. ~strong(X0) | humble(X0) [cnf transformation 54]
143. ~old(susan) [cnf transformation 24]
144. rich(X0) | wise(X0) [duplicate literal removal 82]
146. 1 <=> ! [X0] : patient(X0) [avatar definition]
147. patient(X0) <- (1) [avatar component clause 146]
149. 2 <=> patient(susan) [avatar definition]
151. ~patient(susan) <- (~2) [avatar component clause 149]
152. 1 | ~2 [avatar split clause 90,149,146]
171. 7 <=> rich(lucy) [avatar definition]
172. ~rich(lucy) <- (~7) [avatar component clause 171]
180. 9 <=> ! [X1] : old(X1) [avatar definition]
181. old(X1) <- (9) [avatar component clause 180]
182. 9 | ~7 [avatar split clause 92,171,180]
202. 14 <=> humble(susan) [avatar definition]
204. ~humble(susan) <- (~14) [avatar component clause 202]
206. 15 <=> patient(lucy) [avatar definition]
207. ~patient(lucy) <- (~15) [avatar component clause 206]
208. patient(lucy) <- (15) [avatar component clause 206]
209. ~14 | 15 [avatar split clause 104,206,202]
211. 16 <=> curious(susan) [avatar definition]
213. curious(susan) <- (16) [avatar component clause 211]
214. 16 | 15 [avatar split clause 103,206,211]
340. ~wise(lucy) <- (15) [resolution 109,208]
343. wise(lucy) <- (~7) [resolution 144,172]
344. $false <- (~7, 15) [subsumption resolution 343,340]
345. 7 | ~15 [avatar contradiction clause 344]
346. $false <- (9) [resolution 181,143]
349. ~9 [avatar contradiction clause 346]
447. patient(susan) | strong(susan) <- (16) [resolution 108,213]
448. strong(susan) <- (~2, 16) [subsumption resolution 447,151]
476. humble(susan) <- (~2, 16) [resolution 448,112]
478. $false <- (~2, ~14, 16) [subsumption resolution 476,204]
479. 2 | 14 | ~16 [avatar contradiction clause 478]
486. $false <- (1, ~15) [resolution 147,207]
489. ~1 | 15 [avatar contradiction clause 486]
490. $false [avatar sat refutation 152,182,209,214,345,349,479,489]
% SZS output end Proof for 750401124724547430559051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not creative then mary is both happy and creative.
If paul is either not tall or not old then someone is quiet or calm and vice versa.
If lucy is happy or tall then john is both not wise and not humble.
Everyone who is not happy or quiet is not patient and vice versa.
Everyone who is both happy and quiet is not humble or not happy and vice versa.
If mary is not kind or patient then john is generous or kind.
Everyone who is not happy is either not curious or not funny.
Everyone who is both tall and not wise is either tall or not brave.
If someone is not wise or brave then paul is not quiet and vice versa.
Everyone who is both happy and generous is old and vice versa.
Everyone who is both not creative and wise is either kind or curious.
If someone is wise or not funny then mary is quiet and vice versa.
Everyone who is both kind and not patient is either old or not wise and vice versa.
Everyone who is both not curious and funny is either generous or not funny and vice versa.
Someone is either kind or not kind.
Mary is either wise or not humble.
Someone is both not quiet and not brave.
Someone is not tall.
Fred is tall.
Someone is either brave or calm. | Fred is not old. | neutral | ((?[X]:((generous(X)&~creative(X))))=>((happy(mary)&creative(mary))))&
(((~tall(paul)<~>~old(paul)))<=>(?[X]:((quiet(X)|calm(X)))))&
(((happy(lucy)|tall(lucy)))=>((~wise(john)&~humble(john))))&
(![X]:((~happy(X)|quiet(X))<=>~patient(X)))&
(![X]:((happy(X)&quiet(X))<=>(~humble(X)|~happy(X))))&
(((~kind(mary)|patient(mary)))=>((generous(john)|kind(john))))&
(![X]:(~happy(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((tall(X)&~wise(X))=>(tall(X)<~>~brave(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~quiet(paul)))&
(![X]:((happy(X)&generous(X))<=>old(X)))&
(![X]:((~creative(X)&wise(X))=>(kind(X)<~>curious(X))))&
((?[X]:((wise(X)|~funny(X))))<=>(quiet(mary)))&
(![X]:((kind(X)&~patient(X))<=>(old(X)<~>~wise(X))))&
(![X]:((~curious(X)&funny(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
((wise(mary)<~>~humble(mary)))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:(~tall(X)))&
(tall(fred))&
(?[X]:((brave(X)<~>calm(X)))) | ~old(fred) | [] | null | 0 |
If fred is both creative and not old then someone is not happy and vice versa. Everyone who is either rich or not calm is both happy and not old. Everyone who is both happy and not generous is either not old or patient. Everyone who is tall or brave is either happy or strong and vice versa. If someone is kind or calm then john is either rich or curious. If someone is tall or kind then alice is not creative. If paul is both not creative and quiet then someone is not humble and vice versa. Everyone who is kind or not creative is not strong. Everyone who is not strong is creative or strong and vice versa. Everyone who is not brave or rich is either curious or not funny. Everyone who is both not brave and strong is both not kind and funny and vice versa. Everyone who is not tall or not generous is generous or not humble and vice versa. Everyone who is either happy or kind is not tall or not strong and vice versa. If fred is either not brave or not kind then paul is both creative and patient and vice versa. Everyone who is either not generous or not humble is either funny or not creative and vice versa. Alice is not kind or happy. Someone is funny or not calm. Someone is either wise or not happy. Susan is both old and not quiet. | Alice is brave. | entailment | (((creative(fred)&~old(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((rich(X)<~>~calm(X))=>(happy(X)&~old(X))))&
(![X]:((happy(X)&~generous(X))=>(~old(X)<~>patient(X))))&
(![X]:((tall(X)|brave(X))<=>(happy(X)<~>strong(X))))&
((?[X]:((kind(X)|calm(X))))=>((rich(john)<~>curious(john))))&
((?[X]:((tall(X)|kind(X))))=>(~creative(alice)))&
(((~creative(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|~creative(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(creative(X)|strong(X))))&
(![X]:((~brave(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~brave(X)&strong(X))<=>(~kind(X)&funny(X))))&
(![X]:((~tall(X)|~generous(X))<=>(generous(X)|~humble(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~tall(X)|~strong(X))))&
(((~brave(fred)<~>~kind(fred)))<=>((creative(paul)&patient(paul))))&
(![X]:((~generous(X)<~>~humble(X))<=>(funny(X)<~>~creative(X))))&
((~kind(alice)|happy(alice)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:((wise(X)<~>~happy(X))))&
((old(susan)&~quiet(susan))) | brave(alice) | [
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 12873348028972344204288
% SZS output start Proof for 12873348028972344204288
4. ! [X0] : ((brave(X0) | tall(X0)) <=> (happy(X0) <~> strong(X0))) [input p3]
6. ? [X0] : (kind(X0) | tall(X0)) => ~creative(alice) [input p5]
9. ! [X0] : (~strong(X0) <=> (strong(X0) | creative(X0))) [input p8]
13. ! [X0] : ((happy(X0) <~> kind(X0)) <=> (~strong(X0) | ~tall(X0))) [input p12]
20. ~brave(alice) [input hypothesis]
25. ~creative(alice) | ! [X0] : (~kind(X0) & ~tall(X0)) [ennf transformation 6]
35. ! [X0] : (((brave(X0) | tall(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 4]
36. ! [X0] : ((brave(X0) | tall(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 35]
43. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | strong(X0))) [nnf transformation 9]
44. ! [X0] : ((~strong(X0) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | strong(X0))) [flattening 43]
50. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [nnf transformation 13]
51. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [flattening 50]
73. ~happy(X0) | tall(X0) | strong(X0) | brave(X0) [cnf transformation 36]
79. ~creative(alice) | ~tall(X0) [cnf transformation 25]
80. ~creative(alice) | ~kind(X0) [cnf transformation 25]
86. strong(X0) | creative(X0) | strong(X0) [cnf transformation 44]
88. ~strong(X0) | ~strong(X0) [cnf transformation 44]
104. kind(X0) | happy(X0) | strong(X0) [cnf transformation 51]
127. ~brave(alice) [cnf transformation 20]
130. strong(X0) | creative(X0) [duplicate literal removal 86]
131. ~strong(X0) [duplicate literal removal 88]
133. 1 <=> ! [X0] : happy(X0) [avatar definition]
134. happy(X0) <- (1) [avatar component clause 133]
163. 8 <=> ! [X0] : ~kind(X0) [avatar definition]
164. ~kind(X0) <- (8) [avatar component clause 163]
169. 9 <=> creative(alice) [avatar definition]
171. ~creative(alice) <- (~9) [avatar component clause 169]
172. 8 | ~9 [avatar split clause 80,169,163]
174. 10 <=> ! [X0] : ~tall(X0) [avatar definition]
175. ~tall(X0) <- (10) [avatar component clause 174]
176. 10 | ~9 [avatar split clause 79,169,174]
195. creative(X0) [subsumption resolution 130,131]
198. kind(X0) | happy(X0) [subsumption resolution 104,131]
242. $false <- (~9) [subsumption resolution 171,195]
243. 9 [avatar contradiction clause 242]
252. happy(X2) <- (8) [resolution 198,164]
255. 1 | ~8 [avatar split clause 252,163,133]
298. tall(X0) | strong(X0) | brave(X0) <- (1) [resolution 73,134]
301. strong(X0) | brave(X0) <- (1, 10) [subsumption resolution 298,175]
302. brave(X0) <- (1, 10) [subsumption resolution 301,131]
303. $false <- (1, 10) [resolution 302,127]
307. ~1 | ~10 [avatar contradiction clause 303]
308. $false [avatar sat refutation 172,176,243,255,307]
% SZS output end Proof for 12873348028972344204288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and wise is quiet or kind.
Everyone who is both not creative and not quiet is not strong or not humble and vice versa.
If paul is both strong and kind then someone is either funny or rich.
If someone is either not brave or not old then someone is both not brave and not generous.
Everyone who is either quiet or tall is either not happy or generous and vice versa.
If someone is generous or not funny then someone is both not tall and not funny.
Everyone who is calm or kind is both not brave and humble.
Everyone who is either curious or humble is either funny or brave.
Everyone who is both tall and creative is both not brave and not kind.
If alice is not creative then someone is old or patient.
If john is both not curious and not humble then someone is either creative or not kind and vice versa.
Everyone who is not patient or quiet is both not patient and creative and vice versa.
If mary is either not quiet or creative then john is not quiet and vice versa.
Everyone who is either not curious or not tall is not curious and vice versa.
Everyone who is not wise or funny is rich or generous.
Someone is both not kind and calm.
Someone is either not curious or not funny.
Someone is not generous or curious.
Someone is happy or strong.
Mary is not generous.
Someone is not wise or not happy.
Someone is not brave or not tall.
Someone is humble or not kind. | John is generous. | contradiction | (![X]:((strong(X)&wise(X))=>(quiet(X)|kind(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|~humble(X))))&
(((strong(paul)&kind(paul)))=>(?[X]:((funny(X)<~>rich(X)))))&
((?[X]:((~brave(X)<~>~old(X))))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((generous(X)|~funny(X))))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((calm(X)|kind(X))=>(~brave(X)&humble(X))))&
(![X]:((curious(X)<~>humble(X))=>(funny(X)<~>brave(X))))&
(![X]:((tall(X)&creative(X))=>(~brave(X)&~kind(X))))&
((~creative(alice))=>(?[X]:((old(X)|patient(X)))))&
(((~curious(john)&~humble(john)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~patient(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(((~quiet(mary)<~>creative(mary)))<=>(~quiet(john)))&
(![X]:((~curious(X)<~>~tall(X))<=>~curious(X)))&
(![X]:((~wise(X)|funny(X))=>(rich(X)|generous(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((happy(X)|strong(X))))&
(~generous(mary))&
(?[X]:((~wise(X)|~happy(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((humble(X)|~kind(X)))) | generous(john) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3375919308265924486989775
% SZS output start Proof for 3375919308265924486989775
6. ? [X0] : (~funny(X0) | generous(X0)) => ? [X0] : (~funny(X0) & ~tall(X0)) [input p5]
14. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> ~curious(X0)) [input p13]
24. generous(john) [input hypothesis]
26. ? [X0] : (~funny(X0) | generous(X0)) => ? [X1] : (~funny(X1) & ~tall(X1)) [rectify 6]
32. ? [X1] : (~funny(X1) & ~tall(X1)) | ! [X0] : (funny(X0) & ~generous(X0)) [ennf transformation 26]
50. ? [X0] : (~funny(X0) & ~tall(X0)) | ! [X1] : (funny(X1) & ~generous(X1)) [rectify 32]
51. ? [X0] : (~funny(X0) & ~tall(X0)) => (~funny(sK2) & ~tall(sK2)) [choice axiom]
52. (~funny(sK2) & ~tall(sK2)) | ! [X1] : (funny(X1) & ~generous(X1)) [skolemisation 50,51]
64. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | curious(X0)) & (~curious(X0) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 14]
100. ~tall(sK2) | ~generous(X1) [cnf transformation 52]
131. ~curious(X0) | ~curious(X0) | tall(X0) [cnf transformation 64]
133. tall(X0) | curious(X0) | curious(X0) [cnf transformation 64]
146. generous(john) [cnf transformation 24]
147. ~curious(X0) | tall(X0) [duplicate literal removal 131]
148. tall(X0) | curious(X0) [duplicate literal removal 133]
194. 11 <=> ! [X1] : ~generous(X1) [avatar definition]
195. ~generous(X1) <- (11) [avatar component clause 194]
198. 12 <=> tall(sK2) [avatar definition]
200. ~tall(sK2) <- (~12) [avatar component clause 198]
202. 11 | ~12 [avatar split clause 100,198,194]
261. tall(X0) [subsumption resolution 147,148]
300. $false <- (~12) [subsumption resolution 200,261]
301. 12 [avatar contradiction clause 300]
304. $false <- (11) [resolution 195,146]
305. ~11 [avatar contradiction clause 304]
306. $false [avatar sat refutation 202,301,305]
% SZS output end Proof for 3375919308265924486989775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or curious is calm or creative.
Everyone who is both not tall and old is either funny or not calm and vice versa.
Everyone who is either not quiet or not calm is patient and vice versa.
Everyone who is both generous and not curious is not curious or patient and vice versa.
Everyone who is not tall or creative is either not funny or kind and vice versa.
If someone is not rich then paul is both creative and quiet and vice versa.
If someone is brave or old then lucy is quiet or not happy and vice versa.
Everyone who is both not humble and humble is wise or not funny.
Everyone who is not wise or happy is both not calm and humble and vice versa.
Everyone who is quiet or creative is generous.
Everyone who is both not happy and quiet is creative and vice versa.
Everyone who is happy is not humble or not funny and vice versa.
Everyone who is not old is either wise or not humble and vice versa.
If someone is curious then mary is not patient.
If lucy is not creative then someone is not brave and vice versa.
If someone is either strong or rich then mary is not tall or not curious.
Paul is not curious or brave.
Mary is not creative or calm.
Mary is not creative or old.
Susan is brave or not kind.
John is not quiet or tall.
Someone is rich.
Someone is either not wise or rich. | Mary is patient. | contradiction | (![X]:((old(X)<~>curious(X))=>(calm(X)|creative(X))))&
(![X]:((~tall(X)&old(X))<=>(funny(X)<~>~calm(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>patient(X)))&
(![X]:((generous(X)&~curious(X))<=>(~curious(X)|patient(X))))&
(![X]:((~tall(X)|creative(X))<=>(~funny(X)<~>kind(X))))&
((?[X]:(~rich(X)))<=>((creative(paul)&quiet(paul))))&
((?[X]:((brave(X)|old(X))))<=>((quiet(lucy)|~happy(lucy))))&
(![X]:((~humble(X)&humble(X))=>(wise(X)|~funny(X))))&
(![X]:((~wise(X)|happy(X))<=>(~calm(X)&humble(X))))&
(![X]:((quiet(X)|creative(X))=>generous(X)))&
(![X]:((~happy(X)&quiet(X))<=>creative(X)))&
(![X]:(happy(X)<=>(~humble(X)|~funny(X))))&
(![X]:(~old(X)<=>(wise(X)<~>~humble(X))))&
((?[X]:(curious(X)))=>(~patient(mary)))&
((~creative(lucy))<=>(?[X]:(~brave(X))))&
((?[X]:((strong(X)<~>rich(X))))=>((~tall(mary)|~curious(mary))))&
((~curious(paul)|brave(paul)))&
((~creative(mary)|calm(mary)))&
((~creative(mary)|old(mary)))&
((brave(susan)|~kind(susan)))&
((~quiet(john)|tall(john)))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>rich(X)))) | patient(mary) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4000180374993527412951024
% SZS output start Proof for 4000180374993527412951024
1. ! [X0] : ((old(X0) <~> curious(X0)) => (creative(X0) | calm(X0))) [input p0]
2. ! [X0] : ((old(X0) & ~tall(X0)) <=> (funny(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> patient(X0)) [input p2]
9. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (humble(X0) & ~calm(X0))) [input p8]
11. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : (happy(X0) <=> (~funny(X0) | ~humble(X0))) [input p11]
13. ! [X0] : (~old(X0) <=> (wise(X0) <~> ~humble(X0))) [input p12]
14. ? [X0] : curious(X0) => ~patient(mary) [input p13]
18. calm(mary) | ~creative(mary) [input p17]
24. patient(mary) [input hypothesis]
25. ! [X0] : ((creative(X0) | calm(X0)) | (old(X0) <=> curious(X0))) [ennf transformation 1]
26. ! [X0] : (creative(X0) | calm(X0) | (old(X0) <=> curious(X0))) [flattening 25]
30. ~patient(mary) | ! [X0] : ~curious(X0) [ennf transformation 14]
33. ! [X0] : (creative(X0) | calm(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) [nnf transformation 26]
34. ! [X0] : (((old(X0) & ~tall(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) & (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | (~old(X0) | tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((old(X0) & ~tall(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) & (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ~old(X0) | tall(X0))) [flattening 34]
36. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~patient(X0)) & (patient(X0) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 3]
51. ! [X0] : (((happy(X0) | ~wise(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~happy(X0) & wise(X0)))) [nnf transformation 9]
52. ! [X0] : ((happy(X0) | ~wise(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~happy(X0) & wise(X0)))) [flattening 51]
53. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~creative(X0)) & (creative(X0) | (~quiet(X0) | happy(X0)))) [nnf transformation 11]
54. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~creative(X0)) & (creative(X0) | ~quiet(X0) | happy(X0))) [flattening 53]
55. ! [X0] : ((happy(X0) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | ~happy(X0))) [nnf transformation 12]
56. ! [X0] : ((happy(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | ~happy(X0))) [flattening 55]
57. ! [X0] : ((~old(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | old(X0))) [nnf transformation 13]
68. ~old(X0) | calm(X0) | curious(X0) | creative(X0) [cnf transformation 33]
74. ~funny(X0) | ~calm(X0) | old(X0) [cnf transformation 35]
75. funny(X0) | old(X0) | calm(X0) [cnf transformation 35]
79. ~patient(X0) | quiet(X0) | calm(X0) [cnf transformation 36]
99. ~calm(X0) | wise(X0) [cnf transformation 52]
100. ~happy(X0) | ~calm(X0) [cnf transformation 52]
102. ~happy(X0) | humble(X0) [cnf transformation 52]
106. ~quiet(X0) | creative(X0) | happy(X0) [cnf transformation 54]
109. ~funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 56]
110. happy(X0) | humble(X0) [cnf transformation 56]
111. happy(X0) | funny(X0) [cnf transformation 56]
114. ~old(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 57]
116. ~patient(mary) | ~curious(X0) [cnf transformation 30]
122. calm(mary) | ~creative(mary) [cnf transformation 18]
129. patient(mary) [cnf transformation 24]
174. humble(X0) [subsumption resolution 110,102]
175. ~happy(X0) | ~funny(X0) [subsumption resolution 109,174]
176. ~wise(X0) | ~old(X0) [subsumption resolution 114,174]
179. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
180. ~curious(X0) <- (11) [avatar component clause 179]
182. 12 <=> patient(mary) [avatar definition]
183. patient(mary) <- (12) [avatar component clause 182]
185. 11 | ~12 [avatar split clause 116,182,179]
225. 22 <=> creative(mary) [avatar definition]
227. ~creative(mary) <- (~22) [avatar component clause 225]
229. 23 <=> calm(mary) [avatar definition]
230. ~calm(mary) <- (~23) [avatar component clause 229]
231. calm(mary) <- (23) [avatar component clause 229]
232. ~22 | 23 [avatar split clause 122,229,225]
234. 24 <=> old(mary) [avatar definition]
235. ~old(mary) <- (~24) [avatar component clause 234]
236. old(mary) <- (24) [avatar component clause 234]
266. 12 [avatar split clause 129,182]
276. ~calm(X2) | funny(X2) [resolution 111,100]
302. 34 <=> quiet(mary) [avatar definition]
303. quiet(mary) <- (34) [avatar component clause 302]
306. quiet(mary) | calm(mary) <- (12) [resolution 79,183]
309. 23 | 34 | ~12 [avatar split clause 306,182,302,229]
311. funny(mary) <- (23) [resolution 231,276]
312. wise(mary) <- (23) [resolution 231,99]
316. ~old(mary) <- (23) [resolution 312,176]
317. ~24 | ~23 [avatar split clause 316,229,234]
319. ~calm(mary) | old(mary) <- (23) [resolution 311,74]
322. old(mary) <- (23) [subsumption resolution 319,231]
323. $false <- (23, ~24) [subsumption resolution 322,235]
324. ~23 | 24 [avatar contradiction clause 323]
331. creative(mary) | happy(mary) <- (34) [resolution 106,303]
332. happy(mary) <- (~22, 34) [subsumption resolution 331,227]
333. ~funny(mary) <- (~22, 34) [resolution 332,175]
337. old(mary) | calm(mary) <- (~22, 34) [resolution 333,75]
341. old(mary) <- (~22, ~23, 34) [subsumption resolution 337,230]
342. 24 | 22 | 23 | ~34 [avatar split clause 341,302,229,225,234]
343. calm(mary) | curious(mary) | creative(mary) <- (24) [resolution 236,68]
344. curious(mary) | creative(mary) <- (~23, 24) [subsumption resolution 343,230]
345. creative(mary) <- (11, ~23, 24) [subsumption resolution 344,180]
346. $false <- (11, ~22, ~23, 24) [subsumption resolution 345,227]
347. ~11 | 22 | 23 | ~24 [avatar contradiction clause 346]
348. $false [avatar sat refutation 185,232,266,309,317,324,342,347]
% SZS output end Proof for 4000180374993527412951024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or brave is either not humble or kind.
Everyone who is either funny or not happy is either not curious or not creative and vice versa.
Everyone who is both not happy and not generous is curious and vice versa.
Everyone who is not quiet or not creative is not tall and vice versa.
If susan is either old or not calm then fred is either not strong or not tall.
If mary is either not happy or not strong then someone is not humble and vice versa.
If someone is funny or not happy then someone is either kind or brave and vice versa.
Everyone who is funny or brave is either not old or not creative and vice versa.
Everyone who is either not brave or strong is quiet and vice versa.
Everyone who is humble is not calm and vice versa.
Everyone who is both brave and not funny is either not quiet or not rich.
If someone is happy then someone is not curious or not happy and vice versa.
Everyone who is old or not brave is either not funny or not kind.
If alice is both not humble and not funny then someone is both not patient and wise.
Everyone who is not humble is either not happy or not humble and vice versa.
If alice is either not funny or patient then mary is not patient.
Alice is both brave and not funny.
Someone is both not creative and not funny.
Susan is either generous or calm.
Someone is either kind or not strong.
Someone is either not patient or generous.
Mary is not humble.
Susan is either patient or quiet.
Paul is wise. | Alice is tall. | contradiction | (![X]:((~humble(X)|brave(X))=>(~humble(X)<~>kind(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~happy(X)&~generous(X))<=>curious(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(((old(susan)<~>~calm(susan)))=>((~strong(fred)<~>~tall(fred))))&
(((~happy(mary)<~>~strong(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((funny(X)|brave(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>strong(X))<=>quiet(X)))&
(![X]:(humble(X)<=>~calm(X)))&
(![X]:((brave(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((old(X)|~brave(X))=>(~funny(X)<~>~kind(X))))&
(((~humble(alice)&~funny(alice)))=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~humble(X))))&
(((~funny(alice)<~>patient(alice)))=>(~patient(mary)))&
((brave(alice)&~funny(alice)))&
(?[X]:((~creative(X)&~funny(X))))&
((generous(susan)<~>calm(susan)))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
(~humble(mary))&
((patient(susan)<~>quiet(susan)))&
(wise(paul)) | tall(alice) | [
"p1",
"p2",
"p3",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6898457909714216345859417
% SZS output start Proof for 6898457909714216345859417
2. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> curious(X0)) [input p2]
4. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> ~tall(X0)) [input p3]
15. ! [X0] : (~humble(X0) <=> (~happy(X0) <~> ~humble(X0))) [input p14]
17. ~funny(alice) & brave(alice) [input p16]
25. tall(alice) [input hypothesis]
39. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 2]
40. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (generous(X0) | happy(X0)))) [nnf transformation 3]
41. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | generous(X0) | happy(X0))) [flattening 40]
42. ! [X0] : (((~creative(X0) | ~quiet(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) & quiet(X0)))) [nnf transformation 4]
43. ! [X0] : ((~creative(X0) | ~quiet(X0) | tall(X0)) & (~tall(X0) | (creative(X0) & quiet(X0)))) [flattening 42]
67. ! [X0] : ((~humble(X0) | ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0)))) & (((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | humble(X0))) [nnf transformation 15]
87. ~creative(X0) | funny(X0) | ~happy(X0) | curious(X0) [cnf transformation 39]
92. ~curious(X0) | ~happy(X0) [cnf transformation 41]
95. ~tall(X0) | creative(X0) [cnf transformation 43]
134. humble(X0) | happy(X0) | humble(X0) [cnf transformation 67]
135. ~humble(X0) | ~humble(X0) | happy(X0) [cnf transformation 67]
140. ~funny(alice) [cnf transformation 17]
152. tall(alice) [cnf transformation 25]
153. humble(X0) | happy(X0) [duplicate literal removal 134]
154. ~humble(X0) | happy(X0) [duplicate literal removal 135]
212. 13 <=> ! [X3] : happy(X3) [avatar definition]
213. happy(X3) <- (13) [avatar component clause 212]
243. 20 <=> funny(alice) [avatar definition]
244. ~funny(alice) <- (~20) [avatar component clause 243]
251. happy(X0) [subsumption resolution 153,154]
252. 13 [avatar split clause 251,212]
263. ~20 [avatar split clause 140,243]
306. creative(alice) [resolution 95,152]
504. funny(alice) | ~happy(alice) | curious(alice) [resolution 87,306]
508. ~happy(alice) | curious(alice) <- (~20) [subsumption resolution 504,244]
509. curious(alice) <- (13, ~20) [subsumption resolution 508,213]
521. ~happy(alice) <- (13, ~20) [resolution 509,92]
522. $false <- (13, ~20) [subsumption resolution 521,213]
523. ~13 | 20 [avatar contradiction clause 522]
524. $false [avatar sat refutation 252,263,523]
% SZS output end Proof for 6898457909714216345859417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and humble is both quiet and not curious and vice versa. If someone is not creative or old then someone is either not patient or wise. Everyone who is both not generous and not old is either quiet or humble. If fred is tall or patient then someone is both not strong and not wise. Everyone who is both patient and not kind is creative. Everyone who is creative or not patient is both not brave and quiet and vice versa. Everyone who is both calm and not creative is both not humble and strong and vice versa. If someone is not funny or calm then fred is both creative and not brave and vice versa. If paul is not generous or brave then someone is not kind or not funny and vice versa. Everyone who is tall is not quiet or not tall. If someone is not curious or wise then someone is curious or not happy and vice versa. If paul is either calm or strong then someone is either happy or brave and vice versa. If paul is not creative then someone is not kind or not calm and vice versa. Everyone who is either strong or kind is funny or not old. If someone is both humble and brave then someone is both brave and strong and vice versa. Everyone who is both brave and humble is rich or not generous. Someone is either not kind or happy. Someone is curious or not patient. Lucy is calm or curious. Someone is kind or not patient. Paul is either tall or calm. Someone is either happy or brave. Lucy is not quiet. Mary is kind or not funny. | Mary is not kind. | contradiction | (![X]:((~creative(X)&humble(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((~creative(X)|old(X))))=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((~generous(X)&~old(X))=>(quiet(X)<~>humble(X))))&
(((tall(fred)|patient(fred)))=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((patient(X)&~kind(X))=>creative(X)))&
(![X]:((creative(X)|~patient(X))<=>(~brave(X)&quiet(X))))&
(![X]:((calm(X)&~creative(X))<=>(~humble(X)&strong(X))))&
((?[X]:((~funny(X)|calm(X))))<=>((creative(fred)&~brave(fred))))&
(((~generous(paul)|brave(paul)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(tall(X)=>(~quiet(X)|~tall(X))))&
((?[X]:((~curious(X)|wise(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(((calm(paul)<~>strong(paul)))<=>(?[X]:((happy(X)<~>brave(X)))))&
((~creative(paul))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((strong(X)<~>kind(X))=>(funny(X)|~old(X))))&
((?[X]:((humble(X)&brave(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((brave(X)&humble(X))=>(rich(X)|~generous(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((curious(X)|~patient(X))))&
((calm(lucy)|curious(lucy)))&
(?[X]:((kind(X)|~patient(X))))&
((tall(paul)<~>calm(paul)))&
(?[X]:((happy(X)<~>brave(X))))&
(~quiet(lucy))&
((kind(mary)|~funny(mary))) | ~kind(mary) | [
"p0",
"p6",
"p9",
"p11",
"p12",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3233523049529655290853690
% SZS output start Proof for 3233523049529655290853690
1. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (~curious(X0) & quiet(X0))) [input p0]
7. ! [X0] : ((~creative(X0) & calm(X0)) <=> (strong(X0) & ~humble(X0))) [input p6]
10. ! [X0] : (tall(X0) => (~tall(X0) | ~quiet(X0))) [input p9]
12. (calm(paul) <~> strong(paul)) <=> ? [X0] : (happy(X0) <~> brave(X0)) [input p11]
13. ~creative(paul) <=> ? [X0] : (~calm(X0) | ~kind(X0)) [input p12]
21. tall(paul) <~> calm(paul) [input p20]
22. ? [X0] : (happy(X0) <~> brave(X0)) [input p21]
25. ~kind(mary) [input hypothesis]
36. ! [X0] : ((~tall(X0) | ~quiet(X0)) | ~tall(X0)) [ennf transformation 10]
37. ! [X0] : (~tall(X0) | ~quiet(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : (((humble(X0) & ~creative(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 1]
41. ! [X0] : (((humble(X0) & ~creative(X0)) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ~humble(X0) | creative(X0))) [flattening 40]
51. ! [X0] : (((~creative(X0) & calm(X0)) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | (creative(X0) | ~calm(X0)))) [nnf transformation 7]
52. ! [X0] : (((~creative(X0) & calm(X0)) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | creative(X0) | ~calm(X0))) [flattening 51]
68. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [nnf transformation 12]
69. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [rectify 68]
70. ? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) => ((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) [choice axiom]
71. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [skolemisation 69,70]
72. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X0] : (~calm(X0) | ~kind(X0)) | creative(paul)) [nnf transformation 13]
73. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X1] : (~calm(X1) | ~kind(X1)) | creative(paul)) [rectify 72]
74. ? [X1] : (~calm(X1) | ~kind(X1)) => (~calm(sK7) | ~kind(sK7)) [choice axiom]
75. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & ((~calm(sK7) | ~kind(sK7)) | creative(paul)) [skolemisation 73,74]
89. (~calm(paul) | ~tall(paul)) & (calm(paul) | tall(paul)) [nnf transformation 21]
90. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) [nnf transformation 22]
91. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13))) [choice axiom]
92. (~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13)) [skolemisation 90,91]
93. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 41]
113. ~calm(X0) | creative(X0) | ~humble(X0) [cnf transformation 52]
114. ~calm(X0) | creative(X0) | strong(X0) [cnf transformation 52]
115. ~strong(X0) | calm(X0) | humble(X0) [cnf transformation 52]
126. ~tall(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 37]
135. strong(paul) | calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
136. strong(paul) | calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
137. ~strong(paul) | ~calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
138. ~strong(paul) | ~calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
140. ~creative(paul) | kind(X0) [cnf transformation 75]
153. calm(paul) | tall(paul) [cnf transformation 89]
155. brave(sK13) | happy(sK13) [cnf transformation 92]
156. ~brave(sK13) | ~happy(sK13) [cnf transformation 92]
159. ~kind(mary) [cnf transformation 25]
160. ~tall(X0) | ~quiet(X0) [duplicate literal removal 126]
237. 17 <=> ! [X0] : kind(X0) [avatar definition]
238. kind(X0) <- (17) [avatar component clause 237]
283. 28 <=> ! [X0] : (happy(X0) | ~brave(X0)) [avatar definition]
284. ~brave(X0) | happy(X0) <- (28) [avatar component clause 283]
286. 29 <=> calm(paul) [avatar definition]
287. calm(paul) <- (29) [avatar component clause 286]
290. 30 <=> strong(paul) [avatar definition]
291. strong(paul) <- (30) [avatar component clause 290]
292. ~strong(paul) <- (~30) [avatar component clause 290]
293. 28 | ~29 | ~30 [avatar split clause 138,290,286,283]
295. 31 <=> ! [X0] : (brave(X0) | ~happy(X0)) [avatar definition]
296. ~happy(X0) | brave(X0) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~30 [avatar split clause 137,290,286,295]
298. 28 | 29 | 30 [avatar split clause 136,290,286,283]
299. 31 | 29 | 30 [avatar split clause 135,290,286,295]
316. 35 <=> creative(paul) [avatar definition]
318. ~creative(paul) <- (~35) [avatar component clause 316]
320. 17 | ~35 [avatar split clause 140,316,237]
394. 52 <=> tall(paul) [avatar definition]
395. tall(paul) <- (52) [avatar component clause 394]
398. 52 | 29 [avatar split clause 153,286,394]
400. 53 <=> happy(sK13) [avatar definition]
401. happy(sK13) <- (53) [avatar component clause 400]
402. ~happy(sK13) <- (~53) [avatar component clause 400]
404. 54 <=> brave(sK13) [avatar definition]
405. brave(sK13) <- (54) [avatar component clause 404]
406. ~brave(sK13) <- (~54) [avatar component clause 404]
407. ~53 | ~54 [avatar split clause 156,404,400]
408. 53 | 54 [avatar split clause 155,404,400]
410. 55 <=> kind(mary) [avatar definition]
411. ~kind(mary) <- (~55) [avatar component clause 410]
418. ~55 [avatar split clause 159,410]
423. brave(sK13) <- (31, 53) [resolution 296,401]
424. $false <- (31, 53, ~54) [subsumption resolution 423,406]
425. ~31 | ~53 | 54 [avatar contradiction clause 424]
481. creative(paul) | ~humble(paul) <- (29) [resolution 113,287]
493. creative(paul) | strong(paul) <- (29) [resolution 114,287]
503. creative(paul) <- (29, ~30) [subsumption resolution 493,292]
504. 35 | ~29 | 30 [avatar split clause 503,290,286,316]
506. 68 <=> humble(paul) [avatar definition]
507. humble(paul) <- (68) [avatar component clause 506]
509. ~68 | 35 | ~29 [avatar split clause 481,286,316,506]
512. $false <- (17, ~55) [resolution 238,411]
513. ~17 | 55 [avatar contradiction clause 512]
519. ~quiet(paul) <- (52) [resolution 395,160]
520. calm(paul) | humble(paul) <- (30) [resolution 115,291]
524. quiet(paul) | creative(paul) <- (68) [resolution 507,93]
525. creative(paul) <- (52, 68) [subsumption resolution 524,519]
526. $false <- (~35, 52, 68) [subsumption resolution 525,318]
527. 35 | ~52 | ~68 [avatar contradiction clause 526]
528. 68 | 29 | ~30 [avatar split clause 520,290,286,506]
533. happy(sK13) <- (28, 54) [resolution 405,284]
536. $false <- (28, ~53, 54) [subsumption resolution 533,402]
537. ~28 | 53 | ~54 [avatar contradiction clause 536]
538. $false [avatar sat refutation 293,297,298,299,320,398,407,408,418,425,504,509,513,527,528,537]
% SZS output end Proof for 3233523049529655290853690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either tall or happy.
Everyone who is both patient and not curious is either old or patient and vice versa.
Everyone who is not funny or funny is not humble.
Everyone who is either not calm or strong is tall or not creative.
If lucy is brave or not quiet then fred is not humble and vice versa.
If lucy is not quiet then someone is not wise or not kind and vice versa.
If someone is either not calm or not happy then someone is kind or rich and vice versa.
Everyone who is both brave and creative is either tall or generous.
If susan is not creative or kind then paul is happy and vice versa.
If someone is both patient and not curious then paul is brave.
If someone is not rich or wise then paul is strong or not tall.
Everyone who is either not brave or not happy is creative or brave and vice versa.
If someone is wise or happy then someone is not tall and vice versa.
If someone is not creative or not strong then paul is either strong or kind and vice versa.
If mary is both not humble and curious then someone is not brave or creative.
If someone is calm then someone is humble.
Mary is either not wise or curious.
Someone is not generous.
Someone is either curious or quiet.
Susan is either brave or strong.
Someone is both tall and wise.
Paul is both not quiet and rich.
Someone is not humble. | Susan is not calm. | entailment | (![X]:(~patient(X)=>(tall(X)<~>happy(X))))&
(![X]:((patient(X)&~curious(X))<=>(old(X)<~>patient(X))))&
(![X]:((~funny(X)|funny(X))=>~humble(X)))&
(![X]:((~calm(X)<~>strong(X))=>(tall(X)|~creative(X))))&
(((brave(lucy)|~quiet(lucy)))<=>(~humble(fred)))&
((~quiet(lucy))<=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&creative(X))=>(tall(X)<~>generous(X))))&
(((~creative(susan)|kind(susan)))<=>(happy(paul)))&
((?[X]:((patient(X)&~curious(X))))=>(brave(paul)))&
((?[X]:((~rich(X)|wise(X))))=>((strong(paul)|~tall(paul))))&
(![X]:((~brave(X)<~>~happy(X))<=>(creative(X)|brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((strong(paul)<~>kind(paul))))&
(((~humble(mary)&curious(mary)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:(calm(X)))=>(?[X]:(humble(X))))&
((~wise(mary)<~>curious(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>quiet(X))))&
((brave(susan)<~>strong(susan)))&
(?[X]:((tall(X)&wise(X))))&
((~quiet(paul)&rich(paul)))&
(?[X]:(~humble(X))) | ~calm(susan) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7541472531662152215595415
% SZS output start Proof for 7541472531662152215595415
3. ! [X0] : ((funny(X0) | ~funny(X0)) => ~humble(X0)) [input p2]
16. ? [X0] : calm(X0) => ? [X0] : humble(X0) [input p15]
24. calm(susan) [input hypothesis]
27. ? [X0] : calm(X0) => ? [X1] : humble(X1) [rectify 16]
29. ! [X0] : (~humble(X0) | (~funny(X0) & funny(X0))) [ennf transformation 3]
39. ? [X1] : humble(X1) | ! [X0] : ~calm(X0) [ennf transformation 27]
71. ? [X0] : humble(X0) | ! [X1] : ~calm(X1) [rectify 39]
72. ? [X0] : humble(X0) => humble(sK7) [choice axiom]
73. humble(sK7) | ! [X1] : ~calm(X1) [skolemisation 71,72]
93. ~humble(X0) | funny(X0) [cnf transformation 29]
94. ~humble(X0) | ~funny(X0) [cnf transformation 29]
133. humble(sK7) | ~calm(X1) [cnf transformation 73]
146. calm(susan) [cnf transformation 24]
152. ~humble(X0) [subsumption resolution 93,94]
313. ~calm(X1) [subsumption resolution 133,152]
340. $false [subsumption resolution 146,313]
% SZS output end Proof for 7541472531662152215595415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not wise is strong.
Everyone who is not generous or not strong is both happy and wise and vice versa.
Everyone who is not happy is either not curious or not old.
Everyone who is both patient and not humble is either curious or not tall and vice versa.
Everyone who is old is both not strong and not rich.
If someone is wise or not humble then someone is either curious or not brave and vice versa.
Everyone who is both not quiet and brave is both humble and not strong.
Everyone who is not funny is both not strong and strong and vice versa.
Everyone who is either rich or not rich is rich or humble.
If someone is not calm or not rich then alice is not quiet or generous and vice versa.
Everyone who is wise is brave or happy and vice versa.
Everyone who is not quiet or not creative is either wise or humble and vice versa.
Everyone who is creative is either not funny or old and vice versa.
Everyone who is not brave is either humble or old and vice versa.
If alice is both old and happy then paul is creative.
If someone is patient then someone is either curious or not happy.
Mary is either tall or not funny.
Someone is curious.
Someone is both curious and not brave.
Someone is either not strong or curious.
Someone is creative or wise.
Someone is either not old or generous.
John is brave. | Mary is not rich. | contradiction | (![X]:((quiet(X)|~wise(X))=>strong(X)))&
(![X]:((~generous(X)|~strong(X))<=>(happy(X)&wise(X))))&
(![X]:(~happy(X)=>(~curious(X)<~>~old(X))))&
(![X]:((patient(X)&~humble(X))<=>(curious(X)<~>~tall(X))))&
(![X]:(old(X)=>(~strong(X)&~rich(X))))&
((?[X]:((wise(X)|~humble(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~quiet(X)&brave(X))=>(humble(X)&~strong(X))))&
(![X]:(~funny(X)<=>(~strong(X)&strong(X))))&
(![X]:((rich(X)<~>~rich(X))=>(rich(X)|humble(X))))&
((?[X]:((~calm(X)|~rich(X))))<=>((~quiet(alice)|generous(alice))))&
(![X]:(wise(X)<=>(brave(X)|happy(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(wise(X)<~>humble(X))))&
(![X]:(creative(X)<=>(~funny(X)<~>old(X))))&
(![X]:(~brave(X)<=>(humble(X)<~>old(X))))&
(((old(alice)&happy(alice)))=>(creative(paul)))&
((?[X]:(patient(X)))=>(?[X]:((curious(X)<~>~happy(X)))))&
((tall(mary)<~>~funny(mary)))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((~old(X)<~>generous(X))))&
(brave(john)) | ~rich(mary) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p7",
"p8",
"p10",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2859748467718433206661302
% SZS output start Proof for 2859748467718433206661302
1. ! [X0] : ((~wise(X0) | quiet(X0)) => strong(X0)) [input p0]
2. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> (wise(X0) & happy(X0))) [input p1]
3. ! [X0] : (~happy(X0) => (~curious(X0) <~> ~old(X0))) [input p2]
4. ! [X0] : ((~humble(X0) & patient(X0)) <=> (curious(X0) <~> ~tall(X0))) [input p3]
5. ! [X0] : (old(X0) => (~rich(X0) & ~strong(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (strong(X0) & ~strong(X0))) [input p7]
9. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (humble(X0) | rich(X0))) [input p8]
11. ! [X0] : (wise(X0) <=> (happy(X0) | brave(X0))) [input p10]
12. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> (wise(X0) <~> humble(X0))) [input p11]
13. ! [X0] : (creative(X0) <=> (~funny(X0) <~> old(X0))) [input p12]
17. tall(mary) <~> ~funny(mary) [input p16]
24. ~rich(mary) [input hypothesis]
27. ! [X0] : (strong(X0) | (wise(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : ((~curious(X0) <~> ~old(X0)) | happy(X0)) [ennf transformation 3]
29. ! [X0] : ((~rich(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 5]
32. ! [X0] : ((humble(X0) | rich(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 9]
33. ! [X0] : (humble(X0) | rich(X0) | (rich(X0) <=> ~rich(X0))) [flattening 32]
37. ! [X0] : (((~strong(X0) | ~generous(X0)) | (~wise(X0) | ~happy(X0))) & ((wise(X0) & happy(X0)) | (strong(X0) & generous(X0)))) [nnf transformation 2]
38. ! [X0] : ((~strong(X0) | ~generous(X0) | ~wise(X0) | ~happy(X0)) & ((wise(X0) & happy(X0)) | (strong(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | happy(X0)) [nnf transformation 28]
40. ! [X0] : (((~humble(X0) & patient(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (humble(X0) | ~patient(X0)))) [nnf transformation 4]
41. ! [X0] : (((~humble(X0) & patient(X0)) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) & (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | humble(X0) | ~patient(X0))) [flattening 40]
47. ! [X0] : ((~funny(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | funny(X0))) [nnf transformation 8]
48. ! [X0] : ((~funny(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | funny(X0))) [flattening 47]
49. ! [X0] : (humble(X0) | rich(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 33]
55. ! [X0] : ((wise(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~wise(X0))) [nnf transformation 11]
56. ! [X0] : ((wise(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~wise(X0))) [flattening 55]
57. ! [X0] : (((~creative(X0) | ~quiet(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (creative(X0) & quiet(X0)))) [nnf transformation 12]
58. ! [X0] : ((~creative(X0) | ~quiet(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (creative(X0) & quiet(X0)))) [flattening 57]
59. ! [X0] : ((creative(X0) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~creative(X0))) [nnf transformation 13]
65. (funny(mary) | ~tall(mary)) & (~funny(mary) | tall(mary)) [nnf transformation 17]
78. ~quiet(X0) | strong(X0) [cnf transformation 27]
81. happy(X0) | strong(X0) [cnf transformation 38]
86. old(X0) | curious(X0) | happy(X0) [cnf transformation 39]
91. ~tall(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 41]
93. ~old(X0) | ~strong(X0) [cnf transformation 29]
103. ~strong(X0) | funny(X0) [cnf transformation 48]
104. funny(X0) | strong(X0) [cnf transformation 48]
107. humble(X0) | rich(X0) | rich(X0) | rich(X0) [cnf transformation 49]
114. ~happy(X0) | wise(X0) [cnf transformation 56]
117. ~humble(X0) | ~wise(X0) | quiet(X0) [cnf transformation 58]
118. ~humble(X0) | ~wise(X0) | creative(X0) [cnf transformation 58]
121. old(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 59]
132. ~funny(mary) | tall(mary) [cnf transformation 65]
143. ~rich(mary) [cnf transformation 24]
145. rich(X0) | humble(X0) [duplicate literal removal 107]
180. funny(X0) [subsumption resolution 103,104]
208. ~creative(X0) | old(X0) [subsumption resolution 121,180]
235. tall(mary) [subsumption resolution 132,180]
275. humble(mary) [resolution 145,143]
293. curious(X2) | happy(X2) | ~strong(X2) [resolution 86,93]
304. curious(X2) | happy(X2) [subsumption resolution 293,81]
313. 31 <=> curious(mary) [avatar definition]
315. ~curious(mary) <- (~31) [avatar component clause 313]
325. ~humble(mary) | ~curious(mary) [resolution 91,235]
397. ~wise(mary) | quiet(mary) [resolution 117,275]
402. 44 <=> quiet(mary) [avatar definition]
404. quiet(mary) <- (44) [avatar component clause 402]
406. 45 <=> wise(mary) [avatar definition]
409. 44 | ~45 [avatar split clause 397,406,402]
416. ~wise(mary) | creative(mary) [resolution 118,275]
457. 50 <=> old(mary) [avatar definition]
458. old(mary) <- (50) [avatar component clause 457]
556. happy(mary) <- (~31) [resolution 304,315]
653. wise(mary) <- (~31) [resolution 556,114]
656. 45 | 31 [avatar split clause 653,313,406]
658. 65 <=> strong(mary) [avatar definition]
659. strong(mary) <- (65) [avatar component clause 658]
660. ~strong(mary) <- (~65) [avatar component clause 658]
667. 67 <=> creative(mary) [avatar definition]
669. creative(mary) <- (67) [avatar component clause 667]
670. 67 | ~45 [avatar split clause 416,406,667]
671. strong(mary) <- (44) [resolution 404,78]
672. $false <- (44, ~65) [subsumption resolution 671,660]
673. ~44 | 65 [avatar contradiction clause 672]
674. ~curious(mary) [subsumption resolution 325,275]
675. ~31 [avatar split clause 674,313]
763. old(mary) <- (67) [resolution 669,208]
766. 50 | ~67 [avatar split clause 763,667,457]
776. ~strong(mary) <- (50) [resolution 458,93]
777. $false <- (50, 65) [subsumption resolution 776,659]
778. ~50 | ~65 [avatar contradiction clause 777]
779. $false [avatar sat refutation 409,656,670,673,675,766,778]
% SZS output end Proof for 2859748467718433206661302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or kind is both not strong and not old and vice versa. If someone is either not generous or not humble then paul is both creative and not generous. Everyone who is both kind and rich is either patient or not humble and vice versa. If someone is not generous then someone is not strong and vice versa. Everyone who is generous is not happy or strong and vice versa. Everyone who is not calm or not tall is not calm or not quiet. Everyone who is both not tall and not old is patient or not happy. Everyone who is not funny is both not wise and not kind and vice versa. Everyone who is not generous or curious is rich or old. Everyone who is both not curious and not brave is not rich or not funny. Everyone who is not generous is either generous or not rich and vice versa. Everyone who is either rich or calm is either strong or not kind. Everyone who is happy is either not calm or not creative. If john is not tall then someone is either not kind or happy. Everyone who is not wise is patient or not patient and vice versa. If alice is either calm or curious then mary is either not curious or not funny. Alice is kind or not old. Someone is quiet or curious. Mary is not brave or not strong. Alice is happy. Someone is not rich or not curious. Mary is both not kind and strong. Someone is both not quiet and old. | John is not tall. | neutral | (![X]:((funny(X)|kind(X))<=>(~strong(X)&~old(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>((creative(paul)&~generous(paul))))&
(![X]:((kind(X)&rich(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(~happy(X)|strong(X))))&
(![X]:((~calm(X)|~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~happy(X))))&
(![X]:(~funny(X)<=>(~wise(X)&~kind(X))))&
(![X]:((~generous(X)|curious(X))=>(rich(X)|old(X))))&
(![X]:((~curious(X)&~brave(X))=>(~rich(X)|~funny(X))))&
(![X]:(~generous(X)<=>(generous(X)<~>~rich(X))))&
(![X]:((rich(X)<~>calm(X))=>(strong(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~calm(X)<~>~creative(X))))&
((~tall(john))=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
(((calm(alice)<~>curious(alice)))=>((~curious(mary)<~>~funny(mary))))&
((kind(alice)|~old(alice)))&
(?[X]:((quiet(X)|curious(X))))&
((~brave(mary)|~strong(mary)))&
(happy(alice))&
(?[X]:((~rich(X)|~curious(X))))&
((~kind(mary)&strong(mary)))&
(?[X]:((~quiet(X)&old(X)))) | ~tall(john) | [] | null | 0 |
Everyone who is both not brave and not quiet is not generous and vice versa.
If fred is either funny or not kind then someone is both wise and not kind and vice versa.
Everyone who is either creative or tall is brave and vice versa.
Everyone who is strong is not humble or old.
Everyone who is either not humble or kind is curious and vice versa.
Everyone who is both not happy and funny is both not brave and not humble and vice versa.
If someone is both not rich and not generous then paul is both calm and brave and vice versa.
Everyone who is both not funny and creative is not generous or tall and vice versa.
If someone is either not quiet or happy then paul is both brave and wise.
If someone is not wise then mary is not curious.
Everyone who is both not rich and not wise is tall and vice versa.
Everyone who is both not calm and old is tall.
Everyone who is not calm is not funny or not wise.
If someone is not creative or happy then someone is not kind or not funny.
If fred is tall then someone is not strong.
Everyone who is either rich or not generous is either brave or quiet and vice versa.
Someone is both not calm and kind.
Someone is either wise or quiet.
Someone is not tall or curious.
Fred is either creative or not generous.
Someone is old.
John is happy.
Lucy is both rich and not quiet. | Fred is not quiet. | entailment | (![X]:((~brave(X)&~quiet(X))<=>~generous(X)))&
(((funny(fred)<~>~kind(fred)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((creative(X)<~>tall(X))<=>brave(X)))&
(![X]:(strong(X)=>(~humble(X)|old(X))))&
(![X]:((~humble(X)<~>kind(X))<=>curious(X)))&
(![X]:((~happy(X)&funny(X))<=>(~brave(X)&~humble(X))))&
((?[X]:((~rich(X)&~generous(X))))<=>((calm(paul)&brave(paul))))&
(![X]:((~funny(X)&creative(X))<=>(~generous(X)|tall(X))))&
((?[X]:((~quiet(X)<~>happy(X))))=>((brave(paul)&wise(paul))))&
((?[X]:(~wise(X)))=>(~curious(mary)))&
(![X]:((~rich(X)&~wise(X))<=>tall(X)))&
(![X]:((~calm(X)&old(X))=>tall(X)))&
(![X]:(~calm(X)=>(~funny(X)|~wise(X))))&
((?[X]:((~creative(X)|happy(X))))=>(?[X]:((~kind(X)|~funny(X)))))&
((tall(fred))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(brave(X)<~>quiet(X))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((wise(X)<~>quiet(X))))&
(?[X]:((~tall(X)|curious(X))))&
((creative(fred)<~>~generous(fred)))&
(?[X]:(old(X)))&
(happy(john))&
((rich(lucy)&~quiet(lucy))) | ~quiet(fred) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5094120932037352691360942
% SZS output start Proof for 5094120932037352691360942
1. ! [X0] : ((~quiet(X0) & ~brave(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((creative(X0) <~> tall(X0)) <=> brave(X0)) [input p2]
6. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~humble(X0) & ~brave(X0))) [input p5]
7. ? [X0] : (~generous(X0) & ~rich(X0)) <=> (brave(paul) & calm(paul)) [input p6]
8. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (tall(X0) | ~generous(X0))) [input p7]
9. ? [X0] : (~quiet(X0) <~> happy(X0)) => (wise(paul) & brave(paul)) [input p8]
11. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> tall(X0)) [input p10]
13. ! [X0] : (~calm(X0) => (~wise(X0) | ~funny(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (brave(X0) <~> quiet(X0))) [input p15]
20. creative(fred) <~> ~generous(fred) [input p19]
24. quiet(fred) [input hypothesis]
28. (wise(paul) & brave(paul)) | ! [X0] : (~quiet(X0) <=> happy(X0)) [ennf transformation 9]
32. ! [X0] : ((~wise(X0) | ~funny(X0)) | calm(X0)) [ennf transformation 13]
33. ! [X0] : (~wise(X0) | ~funny(X0) | calm(X0)) [flattening 32]
35. ! [X0] : (((~quiet(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | (quiet(X0) | brave(X0)))) [nnf transformation 1]
36. ! [X0] : (((~quiet(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | quiet(X0) | brave(X0))) [flattening 35]
41. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~brave(X0)) & (brave(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 3]
43. ! [X0] : (((funny(X0) & ~happy(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (~funny(X0) | happy(X0)))) [nnf transformation 6]
44. ! [X0] : (((funny(X0) & ~happy(X0)) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | ~funny(X0) | happy(X0))) [flattening 43]
45. (? [X0] : (~generous(X0) & ~rich(X0)) | (~brave(paul) | ~calm(paul))) & ((brave(paul) & calm(paul)) | ! [X0] : (generous(X0) | rich(X0))) [nnf transformation 7]
46. (? [X0] : (~generous(X0) & ~rich(X0)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X0] : (generous(X0) | rich(X0))) [flattening 45]
47. (? [X0] : (~generous(X0) & ~rich(X0)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X1] : (generous(X1) | rich(X1))) [rectify 46]
48. ? [X0] : (~generous(X0) & ~rich(X0)) => (~generous(sK1) & ~rich(sK1)) [choice axiom]
49. ((~generous(sK1) & ~rich(sK1)) | ~brave(paul) | ~calm(paul)) & ((brave(paul) & calm(paul)) | ! [X1] : (generous(X1) | rich(X1))) [skolemisation 47,48]
50. ! [X0] : (((creative(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((creative(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | ~creative(X0) | funny(X0))) [flattening 50]
52. (wise(paul) & brave(paul)) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 28]
53. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | (wise(X0) | rich(X0)))) [nnf transformation 11]
54. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | wise(X0) | rich(X0))) [flattening 53]
58. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 16]
66. (generous(fred) | ~creative(fred)) & (~generous(fred) | creative(fred)) [nnf transformation 20]
69. ~generous(X0) | quiet(X0) | brave(X0) [cnf transformation 36]
70. ~brave(X0) | generous(X0) [cnf transformation 36]
71. ~quiet(X0) | generous(X0) [cnf transformation 36]
78. ~creative(X0) | tall(X0) | brave(X0) [cnf transformation 41]
80. ~brave(X0) | creative(X0) | tall(X0) [cnf transformation 41]
81. ~tall(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 41]
86. ~funny(X0) | ~brave(X0) | happy(X0) [cnf transformation 44]
93. ~generous(sK1) | ~brave(paul) | ~calm(paul) [cnf transformation 49]
94. ~creative(X0) | ~generous(X0) | tall(X0) | funny(X0) [cnf transformation 51]
97. creative(X0) | generous(X0) [cnf transformation 51]
98. ~tall(X0) | creative(X0) [cnf transformation 51]
100. brave(paul) | ~quiet(X0) | ~happy(X0) [cnf transformation 52]
102. wise(paul) | ~quiet(X0) | ~happy(X0) [cnf transformation 52]
105. ~rich(X0) | ~tall(X0) [cnf transformation 54]
108. ~wise(X0) | ~funny(X0) | calm(X0) [cnf transformation 33]
112. quiet(X0) | brave(X0) | rich(X0) | generous(X0) [cnf transformation 58]
116. ~generous(X0) | rich(X0) | brave(X0) | ~quiet(X0) [cnf transformation 58]
124. ~generous(fred) | creative(fred) [cnf transformation 66]
125. generous(fred) | ~creative(fred) [cnf transformation 66]
130. quiet(fred) [cnf transformation 24]
135. 2 <=> funny(fred) [avatar definition]
136. funny(fred) <- (2) [avatar component clause 135]
157. 6 <=> calm(paul) [avatar definition]
161. 7 <=> brave(paul) [avatar definition]
162. brave(paul) <- (7) [avatar component clause 161]
165. 8 <=> generous(sK1) [avatar definition]
167. ~generous(sK1) <- (~8) [avatar component clause 165]
168. ~6 | ~7 | ~8 [avatar split clause 93,165,161,157]
175. 10 <=> ! [X1] : (generous(X1) | rich(X1)) [avatar definition]
176. rich(X1) | generous(X1) <- (10) [avatar component clause 175]
180. 11 <=> ! [X0] : (~quiet(X0) | ~happy(X0)) [avatar definition]
181. ~happy(X0) | ~quiet(X0) <- (11) [avatar component clause 180]
183. 12 <=> wise(paul) [avatar definition]
185. wise(paul) <- (12) [avatar component clause 183]
186. 11 | 12 [avatar split clause 102,183,180]
191. 11 | 7 [avatar split clause 100,161,180]
217. ~generous(X0) | rich(X0) | brave(X0) [subsumption resolution 116,69]
220. brave(X0) | rich(X0) | generous(X0) [subsumption resolution 112,71]
221. rich(X0) | generous(X0) [subsumption resolution 220,70]
222. 10 [avatar split clause 221,175]
242. generous(fred) [subsumption resolution 125,97]
243. creative(fred) [subsumption resolution 124,242]
247. ~tall(X0) | generous(X0) <- (10) [resolution 176,105]
250. tall(fred) | brave(fred) [resolution 78,243]
251. tall(X0) | brave(X0) | generous(X0) [resolution 78,97]
253. 24 <=> brave(fred) [avatar definition]
254. ~brave(fred) <- (~24) [avatar component clause 253]
255. brave(fred) <- (24) [avatar component clause 253]
257. 25 <=> tall(fred) [avatar definition]
259. tall(fred) <- (25) [avatar component clause 257]
260. 24 | 25 [avatar split clause 250,257,253]
261. tall(X0) | generous(X0) [subsumption resolution 251,70]
262. generous(X0) <- (10) [subsumption resolution 261,247]
358. ~funny(paul) | calm(paul) <- (12) [resolution 108,185]
381. rich(X0) | brave(X0) <- (10) [resolution 217,262]
398. ~generous(fred) | tall(fred) | funny(fred) [resolution 94,243]
401. tall(fred) | funny(fred) [subsumption resolution 398,242]
408. ~creative(fred) | ~brave(fred) <- (25) [resolution 259,81]
414. ~brave(fred) <- (25) [subsumption resolution 408,243]
417. ~24 | ~25 [avatar split clause 414,257,253]
495. ~tall(X1) | brave(X1) <- (10) [resolution 381,105]
500. 50 <=> funny(paul) [avatar definition]
503. 6 | ~50 | ~12 [avatar split clause 358,183,500,157]
505. $false <- (~8, 10) [subsumption resolution 167,262]
506. 8 | ~10 [avatar contradiction clause 505]
508. 51 <=> tall(paul) [avatar definition]
509. ~tall(paul) <- (~51) [avatar component clause 508]
510. tall(paul) <- (51) [avatar component clause 508]
544. ~creative(paul) | ~brave(paul) <- (51) [resolution 510,81]
548. creative(paul) <- (51) [resolution 510,98]
554. ~brave(paul) <- (51) [subsumption resolution 544,548]
555. ~7 | ~51 [avatar split clause 554,508,161]
564. creative(paul) | tall(paul) <- (7) [resolution 162,80]
566. creative(paul) <- (7, ~51) [subsumption resolution 564,509]
567. ~generous(paul) | tall(paul) | funny(paul) <- (7, ~51) [resolution 566,94]
569. tall(paul) | funny(paul) <- (7, 10, ~51) [subsumption resolution 567,262]
570. funny(paul) <- (7, 10, ~51) [subsumption resolution 569,509]
573. 50 | ~7 | ~10 | 51 [avatar split clause 570,508,175,161,500]
589. brave(fred) <- (10, 25) [resolution 495,259]
592. $false <- (10, ~24, 25) [subsumption resolution 589,254]
593. ~10 | 24 | ~25 [avatar contradiction clause 592]
594. 2 | 25 [avatar split clause 401,257,135]
610. ~brave(fred) | happy(fred) <- (2) [resolution 136,86]
612. happy(fred) <- (2, 24) [subsumption resolution 610,255]
616. ~quiet(fred) <- (2, 11, 24) [resolution 612,181]
618. $false <- (2, 11, 24) [subsumption resolution 616,130]
619. ~2 | ~11 | ~24 [avatar contradiction clause 618]
620. $false [avatar sat refutation 168,186,191,222,260,417,503,506,555,573,593,594,619]
% SZS output end Proof for 5094120932037352691360942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or humble is calm or kind.
If someone is both not creative and not calm then someone is generous.
Everyone who is either not strong or funny is not creative or humble and vice versa.
Everyone who is both not strong and funny is either not strong or not patient.
Everyone who is either not rich or not wise is either calm or not curious and vice versa.
If someone is not calm or not strong then lucy is both calm and not creative and vice versa.
Everyone who is curious or patient is both funny and old.
Everyone who is both not humble and not calm is both not quiet and humble and vice versa.
Everyone who is tall or not humble is not quiet and vice versa.
Everyone who is either kind or quiet is either not rich or strong and vice versa.
Everyone who is humble is both kind and not wise and vice versa.
If someone is either not calm or not creative then john is both creative and not curious and vice versa.
Everyone who is both quiet and curious is not happy or not kind and vice versa.
Everyone who is not rich is either tall or rich.
Everyone who is either not calm or generous is either not humble or happy and vice versa.
Everyone who is both wise and not tall is not strong or not happy and vice versa.
Someone is not happy or not funny.
Someone is happy.
Someone is either generous or creative.
Someone is creative. | John is not funny. | entailment | (![X]:((brave(X)|humble(X))=>(calm(X)|kind(X))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~creative(X)|humble(X))))&
(![X]:((~strong(X)&funny(X))=>(~strong(X)<~>~patient(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(calm(X)<~>~curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>((calm(lucy)&~creative(lucy))))&
(![X]:((curious(X)|patient(X))=>(funny(X)&old(X))))&
(![X]:((~humble(X)&~calm(X))<=>(~quiet(X)&humble(X))))&
(![X]:((tall(X)|~humble(X))<=>~quiet(X)))&
(![X]:((kind(X)<~>quiet(X))<=>(~rich(X)<~>strong(X))))&
(![X]:(humble(X)<=>(kind(X)&~wise(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>((creative(john)&~curious(john))))&
(![X]:((quiet(X)&curious(X))<=>(~happy(X)|~kind(X))))&
(![X]:(~rich(X)=>(tall(X)<~>rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((wise(X)&~tall(X))<=>(~strong(X)|~happy(X))))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:(happy(X)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(creative(X))) | ~funny(john) | [
"p2",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8567849846591594514830409
% SZS output start Proof for 8567849846591594514830409
3. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) | ~creative(X0))) [input p2]
8. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> (humble(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((~humble(X0) | tall(X0)) <=> ~quiet(X0)) [input p8]
10. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> (~rich(X0) <~> strong(X0))) [input p9]
11. ! [X0] : (humble(X0) <=> (~wise(X0) & kind(X0))) [input p10]
12. ? [X0] : (~calm(X0) <~> ~creative(X0)) <=> (~curious(john) & creative(john)) [input p11]
13. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~kind(X0) | ~happy(X0))) [input p12]
14. ! [X0] : (~rich(X0) => (tall(X0) <~> rich(X0))) [input p13]
16. ! [X0] : ((~tall(X0) & wise(X0)) <=> (~happy(X0) | ~strong(X0))) [input p15]
21. funny(john) [input hypothesis]
31. ! [X0] : ((tall(X0) <~> rich(X0)) | rich(X0)) [ennf transformation 14]
35. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) & creative(X0))) & ((humble(X0) | ~creative(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 3]
36. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) & creative(X0))) & (humble(X0) | ~creative(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 35]
44. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~humble(X0) | quiet(X0))) & ((humble(X0) & ~quiet(X0)) | (calm(X0) | humble(X0)))) [nnf transformation 8]
45. ! [X0] : (((~calm(X0) & ~humble(X0)) | ~humble(X0) | quiet(X0)) & ((humble(X0) & ~quiet(X0)) | calm(X0) | humble(X0))) [flattening 44]
46. ! [X0] : (((~humble(X0) | tall(X0)) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~tall(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | tall(X0) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~tall(X0)))) [flattening 46]
48. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 10]
49. ! [X0] : ((humble(X0) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ~humble(X0))) [nnf transformation 11]
50. ! [X0] : ((humble(X0) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~humble(X0))) [flattening 49]
51. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (curious(john) | ~creative(john))) & ((~curious(john) & creative(john)) | ! [X0] : ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) [nnf transformation 12]
52. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | curious(john) | ~creative(john)) & ((~curious(john) & creative(john)) | ! [X0] : ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) [flattening 51]
53. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | curious(john) | ~creative(john)) & ((~curious(john) & creative(john)) | ! [X1] : ((~calm(X1) | creative(X1)) & (~creative(X1) | calm(X1)))) [rectify 52]
54. ? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) => ((creative(sK2) | calm(sK2)) & (~creative(sK2) | ~calm(sK2))) [choice axiom]
55. (((creative(sK2) | calm(sK2)) & (~creative(sK2) | ~calm(sK2))) | curious(john) | ~creative(john)) & ((~curious(john) & creative(john)) | ! [X1] : ((~calm(X1) | creative(X1)) & (~creative(X1) | calm(X1)))) [skolemisation 53,54]
56. ! [X0] : (((curious(X0) & quiet(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 13]
57. ! [X0] : (((curious(X0) & quiet(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~curious(X0) | ~quiet(X0))) [flattening 56]
58. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | rich(X0)) [nnf transformation 31]
60. ! [X0] : (((~tall(X0) & wise(X0)) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 16]
61. ! [X0] : (((~tall(X0) & wise(X0)) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | tall(X0) | ~wise(X0))) [flattening 60]
74. ~funny(X0) | ~creative(X0) | ~strong(X0) | humble(X0) [cnf transformation 36]
97. humble(X0) | calm(X0) | humble(X0) [cnf transformation 45]
98. ~humble(X0) | ~humble(X0) | quiet(X0) [cnf transformation 45]
100. ~tall(X0) | ~quiet(X0) [cnf transformation 47]
101. ~quiet(X0) | humble(X0) [cnf transformation 47]
103. ~rich(X0) | strong(X0) | quiet(X0) | ~kind(X0) [cnf transformation 48]
105. ~strong(X0) | rich(X0) | quiet(X0) | ~kind(X0) [cnf transformation 48]
110. ~quiet(X0) | ~kind(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 48]
111. ~humble(X0) | kind(X0) [cnf transformation 50]
112. ~wise(X0) | ~humble(X0) [cnf transformation 50]
115. creative(john) | ~calm(X1) | creative(X1) [cnf transformation 55]
122. quiet(X0) | kind(X0) [cnf transformation 57]
125. rich(X0) | tall(X0) | rich(X0) [cnf transformation 58]
136. wise(X0) | strong(X0) [cnf transformation 61]
138. ~tall(X0) | strong(X0) [cnf transformation 61]
145. funny(john) [cnf transformation 21]
146. tall(X0) | rich(X0) [duplicate literal removal 125]
147. calm(X0) | humble(X0) [duplicate literal removal 97]
148. ~humble(X0) | quiet(X0) [duplicate literal removal 98]
176. 7 <=> ! [X1] : strong(X1) [avatar definition]
177. strong(X1) <- (7) [avatar component clause 176]
186. 9 <=> creative(john) [avatar definition]
187. creative(john) <- (9) [avatar component clause 186]
204. 13 <=> ! [X1] : (~calm(X1) | creative(X1)) [avatar definition]
205. ~calm(X1) | creative(X1) <- (13) [avatar component clause 204]
211. 13 | 9 [avatar split clause 115,186,204]
237. kind(X0) | humble(X0) [resolution 122,101]
238. kind(X0) [subsumption resolution 237,111]
245. ~humble(X0) | strong(X0) [resolution 136,112]
247. rich(X1) | strong(X1) [resolution 146,138]
248. ~quiet(X2) | rich(X2) [resolution 146,100]
262. 20 <=> strong(john) [avatar definition]
263. ~strong(john) <- (~20) [avatar component clause 262]
327. ~creative(john) | ~strong(john) | humble(john) [resolution 74,145]
330. 28 <=> humble(john) [avatar definition]
332. humble(john) <- (28) [avatar component clause 330]
414. creative(X0) | humble(X0) <- (13) [resolution 205,147]
425. $false <- (7, ~20) [resolution 177,263]
426. ~7 | 20 [avatar contradiction clause 425]
428. ~creative(john) | humble(john) <- (7) [subsumption resolution 327,177]
429. humble(john) <- (7, 13) [subsumption resolution 428,414]
430. 28 | ~7 | ~13 [avatar split clause 429,204,176,330]
441. quiet(john) <- (28) [resolution 332,148]
443. strong(X0) | quiet(X0) | ~kind(X0) | strong(X0) [resolution 103,247]
446. strong(X0) | quiet(X0) | ~kind(X0) [duplicate literal removal 443]
459. rich(X0) | quiet(X0) | ~kind(X0) <- (7) [resolution 105,177]
462. rich(X0) | quiet(X0) <- (7) [subsumption resolution 459,238]
463. rich(X0) <- (7) [subsumption resolution 462,248]
512. ~kind(john) | ~rich(john) | ~strong(john) <- (28) [resolution 110,441]
517. ~rich(john) | ~strong(john) <- (28) [subsumption resolution 512,238]
518. ~strong(john) <- (7, 28) [subsumption resolution 517,463]
519. $false <- (7, 28) [subsumption resolution 518,177]
520. ~7 | ~28 [avatar contradiction clause 519]
524. quiet(X0) | strong(X0) [subsumption resolution 446,238]
528. ~strong(john) | humble(john) <- (9) [subsumption resolution 327,187]
529. 28 | ~20 | ~9 [avatar split clause 528,186,262,330]
761. strong(X0) | humble(X0) [resolution 524,101]
771. strong(X0) [subsumption resolution 761,245]
772. 7 [avatar split clause 771,176]
775. $false [avatar sat refutation 211,426,430,520,529,772]
% SZS output end Proof for 8567849846591594514830409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is either wise or not patient and vice versa.
Everyone who is both curious and happy is both not funny and not quiet and vice versa.
If paul is both not happy and not quiet then john is both not humble and not kind.
Everyone who is not creative or not tall is funny.
Everyone who is not calm is old or happy and vice versa.
If someone is either not curious or not patient then paul is not old.
Everyone who is either curious or not tall is both brave and old and vice versa.
If someone is both happy and quiet then john is either not wise or not happy.
If john is either humble or brave then someone is not funny and vice versa.
Everyone who is both wise and brave is creative or calm and vice versa.
Everyone who is not rich or not patient is not rich or creative and vice versa.
Everyone who is either patient or wise is both not generous and tall.
Everyone who is either generous or calm is either not quiet or strong and vice versa.
Everyone who is calm or not wise is rich or not strong.
Everyone who is both old and not quiet is patient and vice versa.
Everyone who is both curious and rich is both patient and not quiet.
Someone is wise.
Someone is not happy or curious.
Someone is wise or not generous.
Someone is both happy and not strong.
Someone is both not rich and not happy.
Someone is not wise.
Someone is either not strong or quiet. | John is not funny. | neutral | (![X]:((~calm(X)<~>creative(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((curious(X)&happy(X))<=>(~funny(X)&~quiet(X))))&
(((~happy(paul)&~quiet(paul)))=>((~humble(john)&~kind(john))))&
(![X]:((~creative(X)|~tall(X))=>funny(X)))&
(![X]:(~calm(X)<=>(old(X)|happy(X))))&
((?[X]:((~curious(X)<~>~patient(X))))=>(~old(paul)))&
(![X]:((curious(X)<~>~tall(X))<=>(brave(X)&old(X))))&
((?[X]:((happy(X)&quiet(X))))=>((~wise(john)<~>~happy(john))))&
(((humble(john)<~>brave(john)))<=>(?[X]:(~funny(X))))&
(![X]:((wise(X)&brave(X))<=>(creative(X)|calm(X))))&
(![X]:((~rich(X)|~patient(X))<=>(~rich(X)|creative(X))))&
(![X]:((patient(X)<~>wise(X))=>(~generous(X)&tall(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:((calm(X)|~wise(X))=>(rich(X)|~strong(X))))&
(![X]:((old(X)&~quiet(X))<=>patient(X)))&
(![X]:((curious(X)&rich(X))=>(patient(X)&~quiet(X))))&
(?[X]:(wise(X)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~strong(X)<~>quiet(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is both old and not old is both not quiet and rich and vice versa. Everyone who is not humble or not happy is strong or funny. Everyone who is both calm and funny is happy or strong and vice versa. Everyone who is both not tall and not wise is not old or funny and vice versa. If paul is both not kind and not humble then someone is not calm. If someone is not calm then someone is both humble and quiet and vice versa. Everyone who is humble is not quiet. Everyone who is not humble is not brave. If someone is not curious or not calm then someone is not happy and vice versa. If someone is both not funny and curious then susan is strong or not calm and vice versa. If someone is either not funny or not curious then someone is either humble or creative. Everyone who is creative is both not wise and generous and vice versa. Everyone who is calm or not wise is not brave or quiet. If someone is both not funny and creative then fred is patient or not calm and vice versa. Everyone who is humble or not kind is not brave. Mary is not curious. Someone is not creative. Someone is not old or not brave. Someone is either not patient or not wise. Someone is not generous or not kind. | Fred is curious. | neutral | (![X]:((old(X)&~old(X))<=>(~quiet(X)&rich(X))))&
(![X]:((~humble(X)|~happy(X))=>(strong(X)|funny(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)|strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~old(X)|funny(X))))&
(((~kind(paul)&~humble(paul)))=>(?[X]:(~calm(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:(humble(X)=>~quiet(X)))&
(![X]:(~humble(X)=>~brave(X)))&
((?[X]:((~curious(X)|~calm(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((strong(susan)|~calm(susan))))&
((?[X]:((~funny(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:(creative(X)<=>(~wise(X)&generous(X))))&
(![X]:((calm(X)|~wise(X))=>(~brave(X)|quiet(X))))&
((?[X]:((~funny(X)&creative(X))))<=>((patient(fred)|~calm(fred))))&
(![X]:((humble(X)|~kind(X))=>~brave(X)))&
(~curious(mary))&
(?[X]:(~creative(X)))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((~generous(X)|~kind(X)))) | curious(fred) | [] | null | 0 |
Everyone who is both strong and not creative is both patient and not quiet and vice versa.
If someone is either not tall or happy then paul is not curious or not wise.
If someone is patient then lucy is either not humble or wise.
Everyone who is both patient and not tall is either patient or not generous and vice versa.
If someone is old then john is curious or calm and vice versa.
Everyone who is curious or not kind is both creative and not quiet and vice versa.
Everyone who is either not rich or not kind is wise.
If someone is wise or not calm then paul is brave.
Everyone who is either quiet or generous is both not tall and not creative and vice versa.
Everyone who is both not funny and not happy is both happy and not curious and vice versa.
Everyone who is either calm or not generous is patient or not strong and vice versa.
If john is both happy and patient then john is either not rich or not calm.
Everyone who is humble is both not strong and not patient and vice versa.
If fred is old then john is old and vice versa.
Everyone who is not strong is both not tall and generous.
If paul is not kind or funny then john is both not old and humble.
Someone is not strong.
Someone is both creative and not rich.
Someone is wise or quiet.
Alice is not patient.
Someone is brave.
Fred is either not generous or not patient.
Paul is strong. | Lucy is not curious. | entailment | (![X]:((strong(X)&~creative(X))<=>(patient(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>happy(X))))=>((~curious(paul)|~wise(paul))))&
((?[X]:(patient(X)))=>((~humble(lucy)<~>wise(lucy))))&
(![X]:((patient(X)&~tall(X))<=>(patient(X)<~>~generous(X))))&
((?[X]:(old(X)))<=>((curious(john)|calm(john))))&
(![X]:((curious(X)|~kind(X))<=>(creative(X)&~quiet(X))))&
(![X]:((~rich(X)<~>~kind(X))=>wise(X)))&
((?[X]:((wise(X)|~calm(X))))=>(brave(paul)))&
(![X]:((quiet(X)<~>generous(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>(happy(X)&~curious(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(patient(X)|~strong(X))))&
(((happy(john)&patient(john)))=>((~rich(john)<~>~calm(john))))&
(![X]:(humble(X)<=>(~strong(X)&~patient(X))))&
((old(fred))<=>(old(john)))&
(![X]:(~strong(X)=>(~tall(X)&generous(X))))&
(((~kind(paul)|funny(paul)))=>((~old(john)&humble(john))))&
(?[X]:(~strong(X)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((wise(X)|quiet(X))))&
(~patient(alice))&
(?[X]:(brave(X)))&
((~generous(fred)<~>~patient(fred)))&
(strong(paul)) | ~curious(lucy) | [
"p0",
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5581574482863957231290889
% SZS output start Proof for 5581574482863957231290889
1. ! [X0] : ((~creative(X0) & strong(X0)) <=> (~quiet(X0) & patient(X0))) [input p0]
4. ! [X0] : ((~tall(X0) & patient(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | curious(X0)) <=> (~quiet(X0) & creative(X0))) [input p5]
9. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~creative(X0) & ~tall(X0))) [input p8]
24. curious(lucy) [input hypothesis]
35. ! [X0] : (((~creative(X0) & strong(X0)) | (quiet(X0) | ~patient(X0))) & ((~quiet(X0) & patient(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((~creative(X0) & strong(X0)) | quiet(X0) | ~patient(X0)) & ((~quiet(X0) & patient(X0)) | creative(X0) | ~strong(X0))) [flattening 35]
39. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (tall(X0) | ~patient(X0)))) [nnf transformation 4]
40. ! [X0] : (((~tall(X0) & patient(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | tall(X0) | ~patient(X0))) [flattening 39]
46. ! [X0] : (((~kind(X0) | curious(X0)) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [nnf transformation 6]
47. ! [X0] : ((~kind(X0) | curious(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | (kind(X0) & ~curious(X0)))) [flattening 46]
49. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 49]
69. ~patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 36]
77. patient(X0) | patient(X0) | generous(X0) [cnf transformation 40]
83. ~curious(X0) | creative(X0) [cnf transformation 47]
85. ~curious(X0) | ~quiet(X0) [cnf transformation 47]
93. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 50]
127. curious(lucy) [cnf transformation 24]
131. generous(X0) | patient(X0) [duplicate literal removal 77]
242. creative(lucy) [resolution 83,127]
243. ~quiet(lucy) [resolution 85,127]
298. quiet(X1) | ~creative(X1) | patient(X1) [resolution 93,131]
302. ~creative(X1) | quiet(X1) [subsumption resolution 298,69]
304. quiet(lucy) [resolution 302,242]
305. $false [subsumption resolution 304,243]
% SZS output end Proof for 5581574482863957231290889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then alice is both not calm and tall. Everyone who is both not brave and humble is not wise and vice versa. Everyone who is either patient or not funny is either curious or quiet and vice versa. Everyone who is not humble is both happy and not funny and vice versa. Everyone who is both tall and strong is either not tall or not curious. Everyone who is both calm and old is not wise and vice versa. If someone is both strong and not humble then john is either creative or not calm. Everyone who is not funny is either rich or not curious. Everyone who is not rich or curious is not patient or not old and vice versa. Everyone who is either wise or not old is either happy or kind. If alice is humble then alice is either not humble or not old and vice versa. If paul is not old then someone is either calm or not quiet. If someone is tall or not rich then lucy is not strong or not generous. Everyone who is both not rich and wise is not kind and vice versa. Everyone who is both not tall and not wise is either not kind or not humble. Everyone who is both not funny and not calm is calm or brave and vice versa. John is both humble and not curious. Alice is either not humble or tall. Someone is either not kind or tall. Fred is patient or curious. Alice is either not brave or tall. Someone is not patient or old. Someone is curious or not brave. | John is not happy. | entailment | ((~patient(susan))=>((~calm(alice)&tall(alice))))&
(![X]:((~brave(X)&humble(X))<=>~wise(X)))&
(![X]:((patient(X)<~>~funny(X))<=>(curious(X)<~>quiet(X))))&
(![X]:(~humble(X)<=>(happy(X)&~funny(X))))&
(![X]:((tall(X)&strong(X))=>(~tall(X)<~>~curious(X))))&
(![X]:((calm(X)&old(X))<=>~wise(X)))&
((?[X]:((strong(X)&~humble(X))))=>((creative(john)<~>~calm(john))))&
(![X]:(~funny(X)=>(rich(X)<~>~curious(X))))&
(![X]:((~rich(X)|curious(X))<=>(~patient(X)|~old(X))))&
(![X]:((wise(X)<~>~old(X))=>(happy(X)<~>kind(X))))&
((humble(alice))<=>((~humble(alice)<~>~old(alice))))&
((~old(paul))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((tall(X)|~rich(X))))=>((~strong(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&wise(X))<=>~kind(X)))&
(![X]:((~tall(X)&~wise(X))=>(~kind(X)<~>~humble(X))))&
(![X]:((~funny(X)&~calm(X))<=>(calm(X)|brave(X))))&
((humble(john)&~curious(john)))&
((~humble(alice)<~>tall(alice)))&
(?[X]:((~kind(X)<~>tall(X))))&
((patient(fred)|curious(fred)))&
((~brave(alice)<~>tall(alice)))&
(?[X]:((~patient(X)|old(X))))&
(?[X]:((curious(X)|~brave(X)))) | ~happy(john) | [
"p1",
"p3",
"p5",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7354115821816680164421658
% SZS output start Proof for 7354115821816680164421658
2. ! [X0] : ((humble(X0) & ~brave(X0)) <=> ~wise(X0)) [input p1]
4. ! [X0] : (~humble(X0) <=> (~funny(X0) & happy(X0))) [input p3]
6. ! [X0] : ((old(X0) & calm(X0)) <=> ~wise(X0)) [input p5]
16. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (brave(X0) | calm(X0))) [input p15]
17. ~curious(john) & humble(john) [input p16]
24. happy(john) [input hypothesis]
34. ! [X0] : (((humble(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | (~humble(X0) | brave(X0)))) [nnf transformation 2]
35. ! [X0] : (((humble(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | ~humble(X0) | brave(X0))) [flattening 34]
37. ! [X0] : ((~humble(X0) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | humble(X0))) [nnf transformation 4]
38. ! [X0] : ((~humble(X0) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | humble(X0))) [flattening 37]
39. ! [X0] : (((old(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | (~old(X0) | ~calm(X0)))) [nnf transformation 6]
40. ! [X0] : (((old(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | ~old(X0) | ~calm(X0))) [flattening 39]
52. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~brave(X0) & ~calm(X0))) & ((brave(X0) | calm(X0)) | (calm(X0) | funny(X0)))) [nnf transformation 16]
53. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~brave(X0) & ~calm(X0))) & (brave(X0) | calm(X0) | calm(X0) | funny(X0))) [flattening 52]
65. ~wise(X0) | ~humble(X0) | brave(X0) [cnf transformation 35]
77. ~funny(X0) | humble(X0) [cnf transformation 38]
78. ~happy(X0) | funny(X0) | ~humble(X0) [cnf transformation 38]
80. wise(X0) | calm(X0) [cnf transformation 40]
103. brave(X0) | calm(X0) | calm(X0) | funny(X0) [cnf transformation 53]
105. ~funny(X0) | ~brave(X0) [cnf transformation 53]
106. ~calm(X0) | ~calm(X0) [cnf transformation 53]
108. humble(john) [cnf transformation 17]
119. happy(john) [cnf transformation 24]
120. brave(X0) | calm(X0) | funny(X0) [duplicate literal removal 103]
121. ~calm(X0) [duplicate literal removal 106]
164. funny(X0) | brave(X0) [subsumption resolution 120,121]
215. humble(X1) | brave(X1) [resolution 164,77]
217. ~humble(X1) | brave(X1) | calm(X1) [resolution 65,80]
222. ~humble(X1) | brave(X1) [subsumption resolution 217,121]
223. brave(X1) [subsumption resolution 222,215]
229. funny(john) | ~humble(john) [resolution 78,119]
231. funny(john) [subsumption resolution 229,108]
232. ~brave(john) [resolution 231,105]
234. $false [subsumption resolution 232,223]
% SZS output end Proof for 7354115821816680164421658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not calm and calm.
If someone is either not wise or not humble then someone is either not old or strong.
If someone is not tall then mary is not rich and vice versa.
Everyone who is tall is both calm and not brave.
If someone is wise then john is not funny and vice versa.
If someone is not curious or brave then lucy is both not old and curious and vice versa.
Everyone who is either wise or brave is not generous or creative.
Everyone who is both not old and not calm is both not patient and not old.
If someone is either tall or creative then lucy is rich.
If someone is not kind or humble then susan is either kind or not calm.
If susan is calm then someone is both not kind and not tall.
Everyone who is not happy or humble is either not funny or not brave.
If paul is either not tall or rich then someone is not strong or wise.
Everyone who is calm or not humble is quiet or not strong.
If someone is not funny then alice is both rich and creative and vice versa.
Everyone who is either happy or patient is both humble and not curious.
Mary is either wise or not humble.
Lucy is patient or curious.
Someone is both not rich and happy.
Someone is either calm or curious.
Alice is both funny and not quiet.
Someone is not wise.
Someone is either rich or not generous.
Alice is funny. | Mary is not curious. | contradiction | (![X]:(~old(X)=>(~calm(X)&calm(X))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:((~old(X)<~>strong(X)))))&
((?[X]:(~tall(X)))<=>(~rich(mary)))&
(![X]:(tall(X)=>(calm(X)&~brave(X))))&
((?[X]:(wise(X)))<=>(~funny(john)))&
((?[X]:((~curious(X)|brave(X))))<=>((~old(lucy)&curious(lucy))))&
(![X]:((wise(X)<~>brave(X))=>(~generous(X)|creative(X))))&
(![X]:((~old(X)&~calm(X))=>(~patient(X)&~old(X))))&
((?[X]:((tall(X)<~>creative(X))))=>(rich(lucy)))&
((?[X]:((~kind(X)|humble(X))))=>((kind(susan)<~>~calm(susan))))&
((calm(susan))=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:((~happy(X)|humble(X))=>(~funny(X)<~>~brave(X))))&
(((~tall(paul)<~>rich(paul)))=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((calm(X)|~humble(X))=>(quiet(X)|~strong(X))))&
((?[X]:(~funny(X)))<=>((rich(alice)&creative(alice))))&
(![X]:((happy(X)<~>patient(X))=>(humble(X)&~curious(X))))&
((wise(mary)<~>~humble(mary)))&
((patient(lucy)|curious(lucy)))&
(?[X]:((~rich(X)&happy(X))))&
(?[X]:((calm(X)<~>curious(X))))&
((funny(alice)&~quiet(alice)))&
(?[X]:(~wise(X)))&
(?[X]:((rich(X)<~>~generous(X))))&
(funny(alice)) | ~curious(mary) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4798495661613270880159023
% SZS output start Proof for 4798495661613270880159023
1. ! [X0] : (~old(X0) => (calm(X0) & ~calm(X0))) [input p0]
6. ? [X0] : (brave(X0) | ~curious(X0)) <=> (curious(lucy) & ~old(lucy)) [input p5]
25. ~curious(mary) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~calm(X0)) | old(X0)) [ennf transformation 1]
54. (? [X0] : (brave(X0) | ~curious(X0)) | (~curious(lucy) | old(lucy))) & ((curious(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) [nnf transformation 6]
55. (? [X0] : (brave(X0) | ~curious(X0)) | ~curious(lucy) | old(lucy)) & ((curious(lucy) & ~old(lucy)) | ! [X0] : (~brave(X0) & curious(X0))) [flattening 54]
56. (? [X0] : (brave(X0) | ~curious(X0)) | ~curious(lucy) | old(lucy)) & ((curious(lucy) & ~old(lucy)) | ! [X1] : (~brave(X1) & curious(X1))) [rectify 55]
57. ? [X0] : (brave(X0) | ~curious(X0)) => (brave(sK3) | ~curious(sK3)) [choice axiom]
58. ((brave(sK3) | ~curious(sK3)) | ~curious(lucy) | old(lucy)) & ((curious(lucy) & ~old(lucy)) | ! [X1] : (~brave(X1) & curious(X1))) [skolemisation 56,57]
85. ~calm(X0) | old(X0) [cnf transformation 27]
86. calm(X0) | old(X0) [cnf transformation 27]
97. ~old(lucy) | curious(X1) [cnf transformation 58]
142. ~curious(mary) [cnf transformation 25]
143. old(X0) [subsumption resolution 85,86]
193. 12 <=> ! [X1] : curious(X1) [avatar definition]
194. curious(X1) <- (12) [avatar component clause 193]
198. curious(X1) [subsumption resolution 97,143]
199. 12 [avatar split clause 198,193]
311. $false <- (12) [resolution 194,142]
312. ~12 [avatar contradiction clause 311]
313. $false [avatar sat refutation 199,312]
% SZS output end Proof for 4798495661613270880159023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either patient or humble then alice is both kind and not brave.
If someone is not funny or generous then alice is both not old and quiet.
If someone is not humble or not brave then mary is curious or tall.
Everyone who is not wise is not rich and vice versa.
Everyone who is either not creative or brave is quiet and vice versa.
If someone is both not creative and not kind then susan is happy and vice versa.
Everyone who is calm or kind is curious and vice versa.
If someone is rich then john is either rich or funny.
Everyone who is either wise or creative is either not kind or not strong and vice versa.
Everyone who is happy is either patient or not curious.
If john is either tall or not strong then someone is both curious and not kind and vice versa.
Everyone who is either not humble or quiet is not creative or not strong and vice versa.
Everyone who is not wise is not curious.
If someone is happy or patient then someone is either not kind or not humble and vice versa.
If someone is both not happy and not tall then someone is strong or patient.
Someone is brave.
Someone is both happy and not creative.
John is both quiet and old.
Fred is not creative.
Someone is not tall. | Susan is not funny. | neutral | (((patient(paul)<~>humble(paul)))=>((kind(alice)&~brave(alice))))&
((?[X]:((~funny(X)|generous(X))))=>((~old(alice)&quiet(alice))))&
((?[X]:((~humble(X)|~brave(X))))=>((curious(mary)|tall(mary))))&
(![X]:(~wise(X)<=>~rich(X)))&
(![X]:((~creative(X)<~>brave(X))<=>quiet(X)))&
((?[X]:((~creative(X)&~kind(X))))<=>(happy(susan)))&
(![X]:((calm(X)|kind(X))<=>curious(X)))&
((?[X]:(rich(X)))=>((rich(john)<~>funny(john))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~strong(X))))&
(![X]:(happy(X)=>(patient(X)<~>~curious(X))))&
(((tall(john)<~>~strong(john)))<=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~creative(X)|~strong(X))))&
(![X]:(~wise(X)=>~curious(X)))&
((?[X]:((happy(X)|patient(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((strong(X)|patient(X)))))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)&~creative(X))))&
((quiet(john)&old(john)))&
(~creative(fred))&
(?[X]:(~tall(X))) | ~funny(susan) | [] | null | 0 |
If someone is kind then susan is both strong and humble and vice versa.
Everyone who is both not brave and funny is not wise or wise and vice versa.
Everyone who is either rich or not patient is either not brave or not kind and vice versa.
If someone is both kind and funny then mary is both generous and not kind and vice versa.
If fred is both tall and strong then someone is curious or not generous and vice versa.
If someone is not humble or not generous then someone is not wise.
If someone is both not humble and funny then someone is patient and vice versa.
If someone is both tall and not happy then someone is generous or not rich and vice versa.
If someone is not calm or not generous then lucy is both strong and not humble and vice versa.
Everyone who is either funny or old is both rich and funny.
Everyone who is either patient or not generous is both not rich and funny and vice versa.
Everyone who is not happy is either wise or funny.
Everyone who is either not tall or not brave is not strong or old.
If someone is either not happy or not calm then alice is not funny.
Everyone who is either kind or not calm is both happy and tall and vice versa.
Mary is either not rich or rich.
Someone is either humble or not patient.
Fred is either brave or not brave.
Susan is either not calm or not strong. | Susan is calm. | contradiction | ((?[X]:(kind(X)))<=>((strong(susan)&humble(susan))))&
(![X]:((~brave(X)&funny(X))<=>(~wise(X)|wise(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~brave(X)<~>~kind(X))))&
((?[X]:((kind(X)&funny(X))))<=>((generous(mary)&~kind(mary))))&
(((tall(fred)&strong(fred)))<=>(?[X]:((curious(X)|~generous(X)))))&
((?[X]:((~humble(X)|~generous(X))))=>(?[X]:(~wise(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:(patient(X))))&
((?[X]:((tall(X)&~happy(X))))<=>(?[X]:((generous(X)|~rich(X)))))&
((?[X]:((~calm(X)|~generous(X))))<=>((strong(lucy)&~humble(lucy))))&
(![X]:((funny(X)<~>old(X))=>(rich(X)&funny(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~rich(X)&funny(X))))&
(![X]:(~happy(X)=>(wise(X)<~>funny(X))))&
(![X]:((~tall(X)<~>~brave(X))=>(~strong(X)|old(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(~funny(alice)))&
(![X]:((kind(X)<~>~calm(X))<=>(happy(X)&tall(X))))&
((~rich(mary)<~>rich(mary)))&
(?[X]:((humble(X)<~>~patient(X))))&
((brave(fred)<~>~brave(fred)))&
((~calm(susan)<~>~strong(susan))) | calm(susan) | [
"p0",
"p1",
"p2",
"p7",
"p10",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6119598951661201286306031
% SZS output start Proof for 6119598951661201286306031
1. ? [X0] : kind(X0) <=> (humble(susan) & strong(susan)) [input p0]
2. ! [X0] : ((funny(X0) & ~brave(X0)) <=> (wise(X0) | ~wise(X0))) [input p1]
3. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> (~brave(X0) <~> ~kind(X0))) [input p2]
8. ? [X0] : (~happy(X0) & tall(X0)) <=> ? [X0] : (~rich(X0) | generous(X0)) [input p7]
11. ! [X0] : ((patient(X0) <~> ~generous(X0)) <=> (funny(X0) & ~rich(X0))) [input p10]
14. ? [X0] : (~happy(X0) <~> ~calm(X0)) => ~funny(alice) [input p13]
15. ! [X0] : ((kind(X0) <~> ~calm(X0)) <=> (tall(X0) & happy(X0))) [input p14]
19. ~calm(susan) <~> ~strong(susan) [input p18]
20. calm(susan) [input hypothesis]
23. ? [X0] : (~happy(X0) & tall(X0)) <=> ? [X1] : (~rich(X1) | generous(X1)) [rectify 8]
29. ~funny(alice) | ! [X0] : (~happy(X0) <=> ~calm(X0)) [ennf transformation 14]
30. (? [X0] : kind(X0) | (~humble(susan) | ~strong(susan))) & ((humble(susan) & strong(susan)) | ! [X0] : ~kind(X0)) [nnf transformation 1]
31. (? [X0] : kind(X0) | ~humble(susan) | ~strong(susan)) & ((humble(susan) & strong(susan)) | ! [X0] : ~kind(X0)) [flattening 30]
32. (? [X0] : kind(X0) | ~humble(susan) | ~strong(susan)) & ((humble(susan) & strong(susan)) | ! [X1] : ~kind(X1)) [rectify 31]
33. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
34. (kind(sK0) | ~humble(susan) | ~strong(susan)) & ((humble(susan) & strong(susan)) | ! [X1] : ~kind(X1)) [skolemisation 32,33]
35. ! [X0] : (((funny(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (~funny(X0) | brave(X0)))) [nnf transformation 2]
36. ! [X0] : (((funny(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | ~funny(X0) | brave(X0))) [flattening 35]
37. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 3]
56. (? [X0] : (~happy(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~generous(X1))) & (? [X1] : (~rich(X1) | generous(X1)) | ! [X0] : (happy(X0) | ~tall(X0))) [nnf transformation 23]
57. (? [X0] : (~happy(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~generous(X1))) & (? [X2] : (~rich(X2) | generous(X2)) | ! [X3] : (happy(X3) | ~tall(X3))) [rectify 56]
58. ? [X0] : (~happy(X0) & tall(X0)) => (~happy(sK6) & tall(sK6)) [choice axiom]
59. ? [X2] : (~rich(X2) | generous(X2)) => (~rich(sK7) | generous(sK7)) [choice axiom]
60. ((~happy(sK6) & tall(sK6)) | ! [X1] : (rich(X1) & ~generous(X1))) & ((~rich(sK7) | generous(sK7)) | ! [X3] : (happy(X3) | ~tall(X3))) [skolemisation 57,59,58]
67. ! [X0] : ((((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0))))) [nnf transformation 11]
68. ! [X0] : ((((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0))))) [flattening 67]
71. ~funny(alice) | ! [X0] : ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))) [nnf transformation 29]
72. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~tall(X0) | ~happy(X0))) & ((tall(X0) & happy(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [nnf transformation 15]
73. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ~tall(X0) | ~happy(X0)) & ((tall(X0) & happy(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [flattening 72]
79. (strong(susan) | calm(susan)) & (~strong(susan) | ~calm(susan)) [nnf transformation 19]
80. strong(susan) | ~kind(X1) [cnf transformation 34]
84. ~brave(X0) | wise(X0) [cnf transformation 36]
85. ~wise(X0) | ~brave(X0) [cnf transformation 36]
86. funny(X0) | wise(X0) [cnf transformation 36]
87. ~wise(X0) | funny(X0) [cnf transformation 36]
90. kind(X0) | brave(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 37]
113. ~happy(sK6) | ~generous(X1) [cnf transformation 60]
114. ~happy(sK6) | rich(X1) [cnf transformation 60]
125. ~rich(X0) | patient(X0) | generous(X0) [cnf transformation 68]
134. ~funny(alice) | ~calm(X0) | happy(X0) [cnf transformation 71]
135. ~funny(alice) | ~happy(X0) | calm(X0) [cnf transformation 71]
137. happy(X0) | kind(X0) | calm(X0) [cnf transformation 73]
148. ~strong(susan) | ~calm(susan) [cnf transformation 79]
150. calm(susan) [cnf transformation 20]
153. 1 <=> strong(susan) [avatar definition]
166. 4 <=> ! [X1] : ~kind(X1) [avatar definition]
167. ~kind(X1) <- (4) [avatar component clause 166]
169. 4 | 1 [avatar split clause 80,153,166]
170. funny(X0) [subsumption resolution 86,87]
171. ~brave(X0) [subsumption resolution 84,85]
175. ~patient(X0) | kind(X0) | ~rich(X0) [subsumption resolution 90,171]
244. 19 <=> ! [X1] : rich(X1) [avatar definition]
245. rich(X1) <- (19) [avatar component clause 244]
247. 20 <=> happy(sK6) [avatar definition]
249. ~happy(sK6) <- (~20) [avatar component clause 247]
250. 19 | ~20 [avatar split clause 114,247,244]
252. 21 <=> ! [X1] : ~generous(X1) [avatar definition]
253. ~generous(X1) <- (21) [avatar component clause 252]
254. 21 | ~20 [avatar split clause 113,247,252]
302. ~happy(X0) | calm(X0) [subsumption resolution 135,170]
303. ~calm(X0) | happy(X0) [subsumption resolution 134,170]
305. calm(X0) | kind(X0) [subsumption resolution 137,302]
317. 33 <=> calm(susan) [avatar definition]
321. ~33 | ~1 [avatar split clause 148,153,317]
322. 33 [avatar split clause 150,317]
336. kind(X0) | happy(X0) [resolution 305,303]
339. happy(X0) <- (4) [subsumption resolution 336,167]
341. $false <- (4, ~20) [resolution 339,249]
343. ~4 | 20 [avatar contradiction clause 341]
346. patient(X0) | generous(X0) <- (19) [resolution 125,245]
348. patient(X0) <- (19, 21) [subsumption resolution 346,253]
366. kind(X1) | ~rich(X1) <- (19, 21) [resolution 175,348]
371. ~rich(X1) <- (4, 19, 21) [subsumption resolution 366,167]
372. $false <- (4, 19, 21) [subsumption resolution 371,245]
373. ~4 | ~19 | ~21 [avatar contradiction clause 372]
374. $false [avatar sat refutation 169,250,254,321,322,343,373]
% SZS output end Proof for 6119598951661201286306031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not wise and not old then fred is either creative or wise and vice versa. Everyone who is either funny or not quiet is curious. Everyone who is both not strong and strong is both humble and patient. Everyone who is both curious and not happy is not humble. Everyone who is not patient is both humble and not happy and vice versa. If john is either not quiet or not rich then someone is either not tall or not wise and vice versa. Everyone who is brave is wise or happy and vice versa. If someone is not funny then someone is rich. Everyone who is wise or rich is both strong and kind and vice versa. Everyone who is humble or old is not curious. Everyone who is either not rich or calm is rich and vice versa. If someone is wise then lucy is tall. Everyone who is rich is either funny or not calm. If someone is calm then john is not curious. If fred is not creative then mary is both not brave and strong and vice versa. Everyone who is either happy or not brave is either not calm or strong. Someone is both quiet and calm. Mary is not patient or not kind. Someone is both not wise and not creative. John is old or not kind. Someone is quiet or not happy. Alice is not calm or not humble. Susan is either brave or humble. Someone is not quiet. | Fred is strong. | entailment | ((?[X]:((~wise(X)&~old(X))))<=>((creative(fred)<~>wise(fred))))&
(![X]:((funny(X)<~>~quiet(X))=>curious(X)))&
(![X]:((~strong(X)&strong(X))=>(humble(X)&patient(X))))&
(![X]:((curious(X)&~happy(X))=>~humble(X)))&
(![X]:(~patient(X)<=>(humble(X)&~happy(X))))&
(((~quiet(john)<~>~rich(john)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:(brave(X)<=>(wise(X)|happy(X))))&
((?[X]:(~funny(X)))=>(?[X]:(rich(X))))&
(![X]:((wise(X)|rich(X))<=>(strong(X)&kind(X))))&
(![X]:((humble(X)|old(X))=>~curious(X)))&
(![X]:((~rich(X)<~>calm(X))<=>rich(X)))&
((?[X]:(wise(X)))=>(tall(lucy)))&
(![X]:(rich(X)=>(funny(X)<~>~calm(X))))&
((?[X]:(calm(X)))=>(~curious(john)))&
((~creative(fred))<=>((~brave(mary)&strong(mary))))&
(![X]:((happy(X)<~>~brave(X))=>(~calm(X)<~>strong(X))))&
(?[X]:((quiet(X)&calm(X))))&
((~patient(mary)|~kind(mary)))&
(?[X]:((~wise(X)&~creative(X))))&
((old(john)|~kind(john)))&
(?[X]:((quiet(X)|~happy(X))))&
((~calm(alice)|~humble(alice)))&
((brave(susan)<~>humble(susan)))&
(?[X]:(~quiet(X))) | strong(fred) | [
"p6",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4470032210937465589957150
% SZS output start Proof for 4470032210937465589957150
7. ! [X0] : (brave(X0) <=> (happy(X0) | wise(X0))) [input p6]
9. ! [X0] : ((rich(X0) | wise(X0)) <=> (kind(X0) & strong(X0))) [input p8]
11. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> rich(X0)) [input p10]
16. ! [X0] : ((happy(X0) <~> ~brave(X0)) => (~calm(X0) <~> strong(X0))) [input p15]
25. ~strong(fred) [input hypothesis]
37. ! [X0] : ((~calm(X0) <~> strong(X0)) | (happy(X0) <=> ~brave(X0))) [ennf transformation 16]
49. ! [X0] : ((brave(X0) | (~happy(X0) & ~wise(X0))) & ((happy(X0) | wise(X0)) | ~brave(X0))) [nnf transformation 7]
50. ! [X0] : ((brave(X0) | (~happy(X0) & ~wise(X0))) & (happy(X0) | wise(X0) | ~brave(X0))) [flattening 49]
54. ! [X0] : (((rich(X0) | wise(X0)) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | (~rich(X0) & ~wise(X0)))) [nnf transformation 9]
55. ! [X0] : ((rich(X0) | wise(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | (~rich(X0) & ~wise(X0)))) [flattening 54]
56. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ~rich(X0)) & (rich(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 11]
60. ! [X0] : (((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) [nnf transformation 37]
92. ~brave(X0) | wise(X0) | happy(X0) [cnf transformation 50]
94. ~happy(X0) | brave(X0) [cnf transformation 50]
96. ~wise(X0) | strong(X0) [cnf transformation 55]
103. rich(X0) | calm(X0) | rich(X0) [cnf transformation 56]
105. calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 56]
114. strong(X0) | ~calm(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 60]
115. strong(X0) | ~calm(X0) | happy(X0) | brave(X0) [cnf transformation 60]
129. ~strong(fred) [cnf transformation 25]
130. rich(X0) | calm(X0) [duplicate literal removal 103]
131. ~rich(X0) | calm(X0) [duplicate literal removal 105]
195. calm(X0) [subsumption resolution 130,131]
217. strong(X0) | happy(X0) | brave(X0) [subsumption resolution 115,195]
218. brave(X0) | strong(X0) [subsumption resolution 217,94]
219. strong(X0) | ~brave(X0) | ~happy(X0) [subsumption resolution 114,195]
220. ~happy(X0) | strong(X0) [subsumption resolution 219,218]
271. wise(X0) | happy(X0) | strong(X0) [resolution 92,218]
282. happy(X0) | strong(X0) [subsumption resolution 271,96]
283. strong(X0) [subsumption resolution 282,220]
293. $false [resolution 283,129]
% SZS output end Proof for 4470032210937465589957150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and quiet then fred is either generous or not happy.
Everyone who is not tall is both not happy and generous and vice versa.
If someone is happy or brave then someone is both not tall and old.
If john is either not kind or creative then someone is either not old or tall and vice versa.
If mary is not funny then someone is either not brave or not creative and vice versa.
If someone is either not rich or not tall then alice is not old or not wise and vice versa.
Everyone who is not funny or old is creative or not funny and vice versa.
Everyone who is both not humble and not wise is not curious or not brave.
Everyone who is happy or calm is not quiet.
Everyone who is not kind or not quiet is quiet and vice versa.
Everyone who is both not rich and strong is either not calm or not patient and vice versa.
If mary is patient or not old then susan is not curious or rich.
Everyone who is either not calm or quiet is either old or brave.
If mary is both kind and tall then paul is both patient and not happy.
Everyone who is either not patient or rich is not kind or not generous and vice versa.
Everyone who is both funny and not patient is both not brave and old and vice versa.
Mary is not rich.
Someone is both old and not strong.
Someone is not rich.
Paul is not curious or wise.
Someone is tall or happy.
Fred is not curious. | Fred is happy. | contradiction | ((?[X]:((strong(X)&quiet(X))))=>((generous(fred)<~>~happy(fred))))&
(![X]:(~tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
(((~kind(john)<~>creative(john)))<=>(?[X]:((~old(X)<~>tall(X)))))&
((~funny(mary))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~old(alice)|~wise(alice))))&
(![X]:((~funny(X)|old(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)|~brave(X))))&
(![X]:((happy(X)|calm(X))=>~quiet(X)))&
(![X]:((~kind(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(mary)|~old(mary)))=>((~curious(susan)|rich(susan))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)<~>brave(X))))&
(((kind(mary)&tall(mary)))=>((patient(paul)&~happy(paul))))&
(![X]:((~patient(X)<~>rich(X))<=>(~kind(X)|~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~brave(X)&old(X))))&
(~rich(mary))&
(?[X]:((old(X)&~strong(X))))&
(?[X]:(~rich(X)))&
((~curious(paul)|wise(paul)))&
(?[X]:((tall(X)|happy(X))))&
(~curious(fred)) | happy(fred) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 740901317310377753943277
% SZS output start Proof for 740901317310377753943277
9. ! [X0] : ((calm(X0) | happy(X0)) => ~quiet(X0)) [input p8]
10. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> quiet(X0)) [input p9]
23. happy(fred) [input hypothesis]
31. ! [X0] : (~quiet(X0) | (~calm(X0) & ~happy(X0))) [ennf transformation 9]
56. ! [X0] : (((~quiet(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [nnf transformation 10]
57. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [flattening 56]
102. ~happy(X0) | ~quiet(X0) [cnf transformation 31]
105. quiet(X0) | quiet(X0) [cnf transformation 57]
134. happy(fred) [cnf transformation 23]
135. quiet(X0) [duplicate literal removal 105]
145. 3 <=> happy(fred) [avatar definition]
147. happy(fred) <- (3) [avatar component clause 145]
267. 3 [avatar split clause 134,145]
273. ~quiet(fred) <- (3) [resolution 102,147]
274. $false <- (3) [subsumption resolution 273,135]
275. ~3 [avatar contradiction clause 274]
276. $false [avatar sat refutation 267,275]
% SZS output end Proof for 740901317310377753943277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not quiet then someone is both not wise and patient.
Everyone who is kind is not rich or not wise.
If someone is not happy or not quiet then paul is both quiet and rich.
Everyone who is not wise or brave is both not funny and tall.
If someone is both wise and not humble then someone is curious or not calm and vice versa.
If lucy is not kind then john is both not creative and not rich.
If fred is both not tall and not generous then someone is not rich.
If someone is both calm and creative then susan is kind or not patient.
If john is both calm and curious then someone is both not quiet and tall.
Everyone who is humble or not strong is not curious or not happy.
Everyone who is either quiet or not humble is both not patient and brave.
Everyone who is not old is both not tall and not wise.
If someone is not strong then someone is creative.
Everyone who is both old and not curious is both tall and not brave and vice versa.
If john is not patient then someone is quiet and vice versa.
Everyone who is quiet or funny is not strong or generous and vice versa.
Susan is not creative or curious.
Someone is either not kind or not generous.
Someone is either not patient or kind.
Mary is not tall or wise.
Someone is both wise and not calm.
Someone is wise.
Fred is tall or not wise.
Lucy is both happy and not generous. | Lucy is not tall. | contradiction | ((?[X]:((~old(X)<~>~quiet(X))))=>(?[X]:((~wise(X)&patient(X)))))&
(![X]:(kind(X)=>(~rich(X)|~wise(X))))&
((?[X]:((~happy(X)|~quiet(X))))=>((quiet(paul)&rich(paul))))&
(![X]:((~wise(X)|brave(X))=>(~funny(X)&tall(X))))&
((?[X]:((wise(X)&~humble(X))))<=>(?[X]:((curious(X)|~calm(X)))))&
((~kind(lucy))=>((~creative(john)&~rich(john))))&
(((~tall(fred)&~generous(fred)))=>(?[X]:(~rich(X))))&
((?[X]:((calm(X)&creative(X))))=>((kind(susan)|~patient(susan))))&
(((calm(john)&curious(john)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((humble(X)|~strong(X))=>(~curious(X)|~happy(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(~patient(X)&brave(X))))&
(![X]:(~old(X)=>(~tall(X)&~wise(X))))&
((?[X]:(~strong(X)))=>(?[X]:(creative(X))))&
(![X]:((old(X)&~curious(X))<=>(tall(X)&~brave(X))))&
((~patient(john))<=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)|funny(X))<=>(~strong(X)|generous(X))))&
((~creative(susan)|curious(susan)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((~patient(X)<~>kind(X))))&
((~tall(mary)|wise(mary)))&
(?[X]:((wise(X)&~calm(X))))&
(?[X]:(wise(X)))&
((tall(fred)|~wise(fred)))&
((happy(lucy)&~generous(lucy))) | ~tall(lucy) | [
"p3",
"p9",
"p10",
"p11",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2900206660126756783899740
% SZS output start Proof for 2900206660126756783899740
4. ! [X0] : ((brave(X0) | ~wise(X0)) => (tall(X0) & ~funny(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | humble(X0)) => (~happy(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((quiet(X0) <~> ~humble(X0)) => (brave(X0) & ~patient(X0))) [input p10]
12. ! [X0] : (~old(X0) => (~wise(X0) & ~tall(X0))) [input p11]
14. ! [X0] : ((~curious(X0) & old(X0)) <=> (~brave(X0) & tall(X0))) [input p13]
16. ! [X0] : ((funny(X0) | quiet(X0)) <=> (generous(X0) | ~strong(X0))) [input p15]
24. ~generous(lucy) & happy(lucy) [input p23]
25. ~tall(lucy) [input hypothesis]
33. ! [X0] : ((tall(X0) & ~funny(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 4]
41. ! [X0] : ((~happy(X0) | ~curious(X0)) | (strong(X0) & ~humble(X0))) [ennf transformation 10]
42. ! [X0] : (~happy(X0) | ~curious(X0) | (strong(X0) & ~humble(X0))) [flattening 41]
43. ! [X0] : ((brave(X0) & ~patient(X0)) | (quiet(X0) <=> ~humble(X0))) [ennf transformation 11]
44. ! [X0] : ((~wise(X0) & ~tall(X0)) | old(X0)) [ennf transformation 12]
59. ! [X0] : ((brave(X0) & ~patient(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) [nnf transformation 43]
63. ! [X0] : (((~curious(X0) & old(X0)) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | (curious(X0) | ~old(X0)))) [nnf transformation 14]
64. ! [X0] : (((~curious(X0) & old(X0)) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | curious(X0) | ~old(X0))) [flattening 63]
69. ! [X0] : (((funny(X0) | quiet(X0)) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 16]
70. ! [X0] : ((funny(X0) | quiet(X0) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | (~funny(X0) & ~quiet(X0)))) [flattening 69]
92. tall(X0) | wise(X0) [cnf transformation 33]
93. ~brave(X0) | tall(X0) [cnf transformation 33]
105. ~curious(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 42]
106. ~curious(X0) | ~happy(X0) | strong(X0) [cnf transformation 42]
110. humble(X0) | quiet(X0) | brave(X0) [cnf transformation 59]
111. ~tall(X0) | old(X0) [cnf transformation 44]
112. ~wise(X0) | old(X0) [cnf transformation 44]
114. ~old(X0) | curious(X0) | tall(X0) [cnf transformation 64]
120. ~strong(X0) | generous(X0) | ~quiet(X0) [cnf transformation 70]
134. happy(lucy) [cnf transformation 24]
135. ~generous(lucy) [cnf transformation 24]
136. ~tall(lucy) [cnf transformation 25]
321. old(X0) | wise(X0) [resolution 111,92]
322. old(X0) [subsumption resolution 321,112]
344. curious(X0) | tall(X0) [resolution 114,322]
349. ~happy(X0) | tall(X0) | strong(X0) [resolution 344,106]
350. ~humble(X1) | ~happy(X1) | tall(X1) [resolution 344,105]
370. tall(lucy) | strong(lucy) [resolution 349,134]
371. strong(lucy) [subsumption resolution 370,136]
373. generous(lucy) | ~quiet(lucy) [resolution 371,120]
375. ~quiet(lucy) [subsumption resolution 373,135]
421. ~happy(X0) | tall(X0) | quiet(X0) | brave(X0) [resolution 350,110]
423. ~happy(X0) | tall(X0) | quiet(X0) [subsumption resolution 421,93]
433. tall(lucy) | quiet(lucy) [resolution 423,134]
434. quiet(lucy) [subsumption resolution 433,136]
435. $false [subsumption resolution 434,375]
% SZS output end Proof for 2900206660126756783899740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind then susan is either not generous or not strong and vice versa.
Everyone who is either not kind or kind is humble and vice versa.
Everyone who is not rich or humble is not tall or not generous and vice versa.
Everyone who is funny is either not patient or not calm.
Everyone who is either happy or patient is both not calm and not creative.
Everyone who is rich or curious is both not creative and patient.
If susan is either not kind or quiet then paul is both not calm and happy.
If fred is tall or brave then paul is either not curious or not generous.
Everyone who is kind or not generous is rich and vice versa.
Everyone who is rich is both wise and not rich.
If susan is either not creative or humble then someone is not wise or brave.
Everyone who is not patient is funny or not creative.
Everyone who is not funny or not curious is both not strong and not happy and vice versa.
If someone is not curious or humble then someone is generous or not generous.
Everyone who is both not creative and not curious is creative or not rich.
Everyone who is both not funny and not happy is rich.
Someone is generous or curious.
Someone is either creative or not happy.
Alice is both not old and funny.
John is patient.
Mary is either not rich or kind.
Someone is either kind or creative. | Fred is patient. | neutral | ((~kind(alice))<=>((~generous(susan)<~>~strong(susan))))&
(![X]:((~kind(X)<~>kind(X))<=>humble(X)))&
(![X]:((~rich(X)|humble(X))<=>(~tall(X)|~generous(X))))&
(![X]:(funny(X)=>(~patient(X)<~>~calm(X))))&
(![X]:((happy(X)<~>patient(X))=>(~calm(X)&~creative(X))))&
(![X]:((rich(X)|curious(X))=>(~creative(X)&patient(X))))&
(((~kind(susan)<~>quiet(susan)))=>((~calm(paul)&happy(paul))))&
(((tall(fred)|brave(fred)))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((kind(X)|~generous(X))<=>rich(X)))&
(![X]:(rich(X)=>(wise(X)&~rich(X))))&
(((~creative(susan)<~>humble(susan)))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(~patient(X)=>(funny(X)|~creative(X))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((~curious(X)|humble(X))))=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((~creative(X)&~curious(X))=>(creative(X)|~rich(X))))&
(![X]:((~funny(X)&~happy(X))=>rich(X)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((~old(alice)&funny(alice)))&
(patient(john))&
((~rich(mary)<~>kind(mary)))&
(?[X]:((kind(X)<~>creative(X)))) | patient(fred) | [] | null | 0 |
If someone is either funny or not calm then someone is both not rich and not funny. Everyone who is both kind and not patient is curious or not creative. Everyone who is tall is either tall or funny and vice versa. If someone is either not tall or not calm then john is not old or not generous. Everyone who is both creative and not generous is strong or kind. If fred is calm then alice is either not generous or wise. Everyone who is calm is both not old and quiet and vice versa. Everyone who is not kind or not curious is either not creative or not happy. If someone is both tall and not humble then someone is wise and vice versa. Everyone who is both not patient and not quiet is either not funny or not patient. If paul is not creative or generous then mary is both generous and patient. Everyone who is either quiet or patient is both happy and not old. Everyone who is either kind or old is either not old or funny and vice versa. Everyone who is either calm or not patient is not calm. Everyone who is not old is either funny or not wise and vice versa. Everyone who is either not calm or funny is not old and vice versa. Mary is kind. John is generous. Someone is not generous. Someone is either not funny or not curious. | Alice is not happy. | contradiction | ((?[X]:((funny(X)<~>~calm(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((kind(X)&~patient(X))=>(curious(X)|~creative(X))))&
(![X]:(tall(X)<=>(tall(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>~calm(X))))=>((~old(john)|~generous(john))))&
(![X]:((creative(X)&~generous(X))=>(strong(X)|kind(X))))&
((calm(fred))=>((~generous(alice)<~>wise(alice))))&
(![X]:(calm(X)<=>(~old(X)&quiet(X))))&
(![X]:((~kind(X)|~curious(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((tall(X)&~humble(X))))<=>(?[X]:(wise(X))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~patient(X))))&
(((~creative(paul)|generous(paul)))=>((generous(mary)&patient(mary))))&
(![X]:((quiet(X)<~>patient(X))=>(happy(X)&~old(X))))&
(![X]:((kind(X)<~>old(X))<=>(~old(X)<~>funny(X))))&
(![X]:((calm(X)<~>~patient(X))=>~calm(X)))&
(![X]:(~old(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>funny(X))<=>~old(X)))&
(kind(mary))&
(generous(john))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~curious(X)))) | ~happy(alice) | [
"p2",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7210192873072106602202077
% SZS output start Proof for 7210192873072106602202077
3. ! [X0] : (tall(X0) <=> (tall(X0) <~> funny(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> (quiet(X0) & ~old(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~patient(X0)) => (~funny(X0) <~> ~patient(X0))) [input p9]
12. ! [X0] : ((quiet(X0) <~> patient(X0)) => (~old(X0) & happy(X0))) [input p11]
16. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> ~old(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | (quiet(X0) | patient(X0))) [ennf transformation 10]
34. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | quiet(X0) | patient(X0)) [flattening 33]
36. ! [X0] : ((~old(X0) & happy(X0)) | (quiet(X0) <=> patient(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~tall(X0))) [nnf transformation 3]
45. ! [X0] : ((calm(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [flattening 45]
53. ! [X0] : (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | quiet(X0) | patient(X0)) [nnf transformation 34]
54. ! [X0] : ((~old(X0) & happy(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) [nnf transformation 36]
58. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | old(X0)) & (~old(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 16]
68. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 42]
70. tall(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
75. ~old(X0) | ~calm(X0) [cnf transformation 46]
77. ~quiet(X0) | calm(X0) | old(X0) [cnf transformation 46]
86. patient(X0) | funny(X0) | quiet(X0) | patient(X0) [cnf transformation 53]
92. happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 54]
109. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 58]
111. funny(X0) | ~calm(X0) | old(X0) [cnf transformation 58]
118. ~happy(alice) [cnf transformation 21]
124. patient(X0) | funny(X0) | quiet(X0) [duplicate literal removal 86]
125. ~funny(X0) | ~tall(X0) [duplicate literal removal 68]
126. ~funny(X0) | tall(X0) [duplicate literal removal 70]
139. ~funny(X0) [subsumption resolution 125,126]
191. quiet(X0) | patient(X0) [subsumption resolution 124,139]
214. happy(X0) | quiet(X0) [subsumption resolution 92,191]
221. ~calm(X0) | old(X0) [subsumption resolution 111,139]
222. ~calm(X0) [subsumption resolution 221,75]
223. ~old(X0) | calm(X0) [subsumption resolution 109,139]
224. ~old(X0) [subsumption resolution 223,222]
227. quiet(alice) [resolution 214,118]
236. calm(alice) | old(alice) [resolution 77,227]
239. old(alice) [subsumption resolution 236,222]
240. $false [subsumption resolution 239,224]
% SZS output end Proof for 7210192873072106602202077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or generous then someone is not calm or not rich.
If someone is old or strong then lucy is both rich and calm and vice versa.
Everyone who is not tall or rich is either not quiet or not kind and vice versa.
Everyone who is not wise or not quiet is both kind and rich.
If alice is not creative or not generous then someone is not curious or not old.
If someone is not generous then lucy is both creative and patient.
Everyone who is both rich and kind is both strong and not patient and vice versa.
Everyone who is either not kind or not tall is not creative and vice versa.
Everyone who is both creative and not wise is both not tall and rich and vice versa.
Everyone who is both happy and curious is either not brave or calm and vice versa.
If alice is either not calm or wise then susan is happy or patient.
If someone is either not generous or creative then susan is kind or not humble and vice versa.
If someone is not old then someone is creative and vice versa.
If someone is not patient then someone is both not happy and not tall and vice versa.
If someone is not rich or not generous then someone is either humble or not brave.
Everyone who is humble or not humble is kind or old.
Someone is tall or not tall.
Lucy is either rich or humble.
Someone is generous or rich.
Mary is either not humble or strong.
Someone is either generous or not generous.
Someone is both not generous and tall.
Someone is not rich or not generous.
Fred is both patient and curious. | Susan is creative. | entailment | (((patient(mary)<~>generous(mary)))=>(?[X]:((~calm(X)|~rich(X)))))&
((?[X]:((old(X)|strong(X))))<=>((rich(lucy)&calm(lucy))))&
(![X]:((~tall(X)|rich(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(kind(X)&rich(X))))&
(((~creative(alice)|~generous(alice)))=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:(~generous(X)))=>((creative(lucy)&patient(lucy))))&
(![X]:((rich(X)&kind(X))<=>(strong(X)&~patient(X))))&
(![X]:((~kind(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((creative(X)&~wise(X))<=>(~tall(X)&rich(X))))&
(![X]:((happy(X)&curious(X))<=>(~brave(X)<~>calm(X))))&
(((~calm(alice)<~>wise(alice)))=>((happy(susan)|patient(susan))))&
((?[X]:((~generous(X)<~>creative(X))))<=>((kind(susan)|~humble(susan))))&
((?[X]:(~old(X)))<=>(?[X]:(creative(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:((~rich(X)|~generous(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((humble(X)|~humble(X))=>(kind(X)|old(X))))&
(?[X]:((tall(X)|~tall(X))))&
((rich(lucy)<~>humble(lucy)))&
(?[X]:((generous(X)|rich(X))))&
((~humble(mary)<~>strong(mary)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((~rich(X)|~generous(X))))&
((patient(fred)&curious(fred))) | creative(susan) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4416802406632323840350789
% SZS output start Proof for 4416802406632323840350789
2. ? [X0] : (strong(X0) | old(X0)) <=> (calm(lucy) & rich(lucy)) [input p1]
3. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) | ~wise(X0)) => (rich(X0) & kind(X0))) [input p3]
6. ? [X0] : ~generous(X0) => (patient(lucy) & creative(lucy)) [input p5]
7. ! [X0] : ((kind(X0) & rich(X0)) <=> (~patient(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~kind(X0) <~> ~tall(X0)) <=> ~creative(X0)) [input p7]
9. ! [X0] : ((~wise(X0) & creative(X0)) <=> (rich(X0) & ~tall(X0))) [input p8]
16. ! [X0] : ((~humble(X0) | humble(X0)) => (old(X0) | kind(X0))) [input p15]
22. ? [X0] : (tall(X0) & ~generous(X0)) [input p21]
25. ~creative(susan) [input hypothesis]
30. ! [X0] : ((rich(X0) & kind(X0)) | (quiet(X0) & wise(X0))) [ennf transformation 4]
32. (patient(lucy) & creative(lucy)) | ! [X0] : generous(X0) [ennf transformation 6]
36. ! [X0] : ((old(X0) | kind(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 16]
37. ! [X0] : (old(X0) | kind(X0) | (humble(X0) & ~humble(X0))) [flattening 36]
41. (? [X0] : (strong(X0) | old(X0)) | (~calm(lucy) | ~rich(lucy))) & ((calm(lucy) & rich(lucy)) | ! [X0] : (~strong(X0) & ~old(X0))) [nnf transformation 2]
42. (? [X0] : (strong(X0) | old(X0)) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X0] : (~strong(X0) & ~old(X0))) [flattening 41]
43. (? [X0] : (strong(X0) | old(X0)) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X1] : (~strong(X1) & ~old(X1))) [rectify 42]
44. ? [X0] : (strong(X0) | old(X0)) => (strong(sK1) | old(sK1)) [choice axiom]
45. ((strong(sK1) | old(sK1)) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X1] : (~strong(X1) & ~old(X1))) [skolemisation 43,44]
46. ! [X0] : (((rich(X0) | ~tall(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~rich(X0) & tall(X0)))) [nnf transformation 3]
47. ! [X0] : ((rich(X0) | ~tall(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~rich(X0) & tall(X0)))) [flattening 46]
50. ! [X0] : (((kind(X0) & rich(X0)) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | (~kind(X0) | ~rich(X0)))) [nnf transformation 7]
51. ! [X0] : (((kind(X0) & rich(X0)) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ~kind(X0) | ~rich(X0))) [flattening 50]
52. ! [X0] : ((((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | creative(X0)) & (~creative(X0) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0))))) [nnf transformation 8]
53. ! [X0] : (((~wise(X0) & creative(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (wise(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((~wise(X0) & creative(X0)) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | wise(X0) | ~creative(X0))) [flattening 53]
86. ? [X0] : (tall(X0) & ~generous(X0)) => (tall(sK12) & ~generous(sK12)) [choice axiom]
87. tall(sK12) & ~generous(sK12) [skolemisation 22,86]
92. rich(lucy) | ~old(X1) [cnf transformation 45]
93. rich(lucy) | ~strong(X1) [cnf transformation 45]
97. ~kind(X0) | ~quiet(X0) | tall(X0) [cnf transformation 47]
98. ~kind(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 47]
103. wise(X0) | kind(X0) [cnf transformation 30]
104. kind(X0) | quiet(X0) [cnf transformation 30]
106. quiet(X0) | rich(X0) [cnf transformation 30]
109. creative(lucy) | generous(X0) [cnf transformation 32]
110. patient(lucy) | generous(X0) [cnf transformation 32]
111. ~kind(X0) | strong(X0) | ~rich(X0) [cnf transformation 51]
112. ~kind(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 51]
115. ~creative(X0) | ~tall(X0) | kind(X0) [cnf transformation 52]
117. ~kind(X0) | ~tall(X0) | creative(X0) [cnf transformation 52]
122. ~wise(X0) | ~rich(X0) | tall(X0) [cnf transformation 54]
146. old(X0) | kind(X0) | ~humble(X0) [cnf transformation 37]
147. humble(X0) | kind(X0) | old(X0) [cnf transformation 37]
156. ~generous(sK12) [cnf transformation 87]
161. ~creative(susan) [cnf transformation 25]
181. 5 <=> rich(lucy) [avatar definition]
182. rich(lucy) <- (5) [avatar component clause 181]
198. 9 <=> ! [X1] : ~strong(X1) [avatar definition]
199. ~strong(X1) <- (9) [avatar component clause 198]
202. 10 <=> ! [X1] : ~old(X1) [avatar definition]
203. ~old(X1) <- (10) [avatar component clause 202]
205. 9 | 5 [avatar split clause 93,181,198]
206. 10 | 5 [avatar split clause 92,181,202]
226. 15 <=> ! [X0] : generous(X0) [avatar definition]
227. generous(X0) <- (15) [avatar component clause 226]
229. 16 <=> patient(lucy) [avatar definition]
231. patient(lucy) <- (16) [avatar component clause 229]
232. 15 | 16 [avatar split clause 110,229,226]
234. 17 <=> creative(lucy) [avatar definition]
236. creative(lucy) <- (17) [avatar component clause 234]
237. 15 | 17 [avatar split clause 109,234,226]
270. 25 <=> kind(susan) [avatar definition]
271. kind(susan) <- (25) [avatar component clause 270]
272. ~kind(susan) <- (~25) [avatar component clause 270]
336. kind(X0) | old(X0) [subsumption resolution 146,147]
373. $false <- (15) [resolution 227,156]
374. ~15 [avatar contradiction clause 373]
378. old(susan) <- (~25) [resolution 336,272]
390. strong(X2) | ~rich(X2) | quiet(X2) [resolution 111,104]
392. quiet(X2) | strong(X2) [subsumption resolution 390,106]
395. ~patient(X2) | ~rich(X2) | quiet(X2) [resolution 112,104]
397. ~patient(X2) | quiet(X2) [subsumption resolution 395,106]
399. quiet(lucy) <- (16) [resolution 397,231]
400. ~tall(lucy) | kind(lucy) <- (17) [resolution 115,236]
403. 47 <=> kind(lucy) [avatar definition]
405. kind(lucy) <- (47) [avatar component clause 403]
407. 48 <=> tall(lucy) [avatar definition]
410. 47 | ~48 | ~17 [avatar split clause 400,234,407,403]
463. ~rich(X1) | tall(X1) | kind(X1) [resolution 122,103]
572. tall(lucy) | kind(lucy) <- (5) [resolution 463,182]
577. 47 | 48 | ~5 [avatar split clause 572,181,407,403]
588. ~quiet(lucy) | ~rich(lucy) <- (47) [resolution 405,98]
594. ~rich(lucy) <- (16, 47) [subsumption resolution 588,399]
595. $false <- (5, 16, 47) [subsumption resolution 594,182]
596. ~5 | ~16 | ~47 [avatar contradiction clause 595]
605. $false <- (10, ~25) [resolution 203,378]
616. ~10 | 25 [avatar contradiction clause 605]
618. 65 <=> tall(susan) [avatar definition]
631. ~tall(susan) | creative(susan) <- (25) [resolution 271,117]
635. ~quiet(susan) | tall(susan) <- (25) [resolution 271,97]
636. ~tall(susan) <- (25) [subsumption resolution 631,161]
637. ~65 | ~25 [avatar split clause 636,270,618]
646. 68 <=> quiet(susan) [avatar definition]
648. ~quiet(susan) <- (~68) [avatar component clause 646]
650. 65 | ~68 | ~25 [avatar split clause 635,270,646,618]
710. strong(susan) <- (~68) [resolution 648,392]
715. $false <- (9, ~68) [subsumption resolution 710,199]
716. ~9 | 68 [avatar contradiction clause 715]
719. $false [avatar sat refutation 205,206,232,237,374,410,577,596,616,637,650,716]
% SZS output end Proof for 4416802406632323840350789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not quiet.
If someone is either not tall or brave then paul is creative or humble.
If someone is not wise then alice is both not rich and not curious.
Everyone who is creative is both not humble and happy.
Everyone who is either not tall or strong is both happy and humble and vice versa.
Everyone who is not strong is either not patient or not calm.
If alice is old or curious then someone is humble or funny and vice versa.
If someone is not patient or quiet then someone is both calm and not humble and vice versa.
If someone is not generous or patient then susan is not tall and vice versa.
If someone is both tall and kind then someone is either curious or not curious and vice versa.
If someone is both strong and not creative then someone is not happy or not funny.
Everyone who is either not rich or not patient is wise or not strong and vice versa.
Everyone who is both calm and not humble is quiet or not old and vice versa.
Everyone who is both not old and curious is rich.
Everyone who is tall is generous or strong.
Fred is either creative or not humble.
Alice is not creative or humble.
Fred is both not strong and curious.
Someone is both not creative and kind.
Someone is both rich and not happy.
Susan is both not wise and not calm.
Someone is both wise and not kind.
Someone is both creative and quiet. | Alice is not curious. | entailment | (![X]:(~brave(X)=>~quiet(X)))&
((?[X]:((~tall(X)<~>brave(X))))=>((creative(paul)|humble(paul))))&
((?[X]:(~wise(X)))=>((~rich(alice)&~curious(alice))))&
(![X]:(creative(X)=>(~humble(X)&happy(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(happy(X)&humble(X))))&
(![X]:(~strong(X)=>(~patient(X)<~>~calm(X))))&
(((old(alice)|curious(alice)))<=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:((~generous(X)|patient(X))))<=>(~tall(susan)))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)|~strong(X))))&
(![X]:((calm(X)&~humble(X))<=>(quiet(X)|~old(X))))&
(![X]:((~old(X)&curious(X))=>rich(X)))&
(![X]:(tall(X)=>(generous(X)|strong(X))))&
((creative(fred)<~>~humble(fred)))&
((~creative(alice)|humble(alice)))&
((~strong(fred)&curious(fred)))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((rich(X)&~happy(X))))&
((~wise(susan)&~calm(susan)))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((creative(X)&quiet(X)))) | ~curious(alice) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2169399135134787231862633
% SZS output start Proof for 2169399135134787231862633
3. ? [X0] : ~wise(X0) => (~curious(alice) & ~rich(alice)) [input p2]
21. ~calm(susan) & ~wise(susan) [input p20]
24. curious(alice) [input hypothesis]
31. (~curious(alice) & ~rich(alice)) | ! [X0] : wise(X0) [ennf transformation 3]
82. ~curious(alice) | wise(X0) [cnf transformation 31]
134. ~wise(susan) [cnf transformation 21]
140. curious(alice) [cnf transformation 24]
162. 5 <=> ! [X0] : wise(X0) [avatar definition]
163. wise(X0) <- (5) [avatar component clause 162]
165. 6 <=> curious(alice) [avatar definition]
168. 5 | ~6 [avatar split clause 82,165,162]
280. 6 [avatar split clause 140,165]
287. $false <- (5) [resolution 163,134]
288. ~5 [avatar contradiction clause 287]
289. $false [avatar sat refutation 168,280,288]
% SZS output end Proof for 2169399135134787231862633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not kind then mary is both creative and strong.
Everyone who is both wise and not old is both not quiet and wise and vice versa.
Everyone who is both humble and quiet is calm.
If lucy is not quiet or not creative then mary is both not patient and quiet.
Everyone who is not wise is not kind and vice versa.
Everyone who is either tall or not curious is calm or not patient.
If paul is happy then fred is either not creative or generous and vice versa.
Everyone who is both quiet and curious is either rich or not brave and vice versa.
If lucy is not kind or not curious then alice is tall.
Everyone who is both wise and not patient is not funny or strong and vice versa.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
John is quiet.
Fred is happy.
Someone is not curious.
Lucy is not generous or funny.
Someone is not quiet or not old.
Someone is kind or not wise.
Mary is generous or not generous.
Someone is either not brave or curious. | Lucy is patient. | contradiction | ((?[X]:((creative(X)<~>~kind(X))))=>((creative(mary)&strong(mary))))&
(![X]:((wise(X)&~old(X))<=>(~quiet(X)&wise(X))))&
(![X]:((humble(X)&quiet(X))=>calm(X)))&
(((~quiet(lucy)|~creative(lucy)))=>((~patient(mary)&quiet(mary))))&
(![X]:(~wise(X)<=>~kind(X)))&
(![X]:((tall(X)<~>~curious(X))=>(calm(X)|~patient(X))))&
((happy(paul))<=>((~creative(fred)<~>generous(fred))))&
(![X]:((quiet(X)&curious(X))<=>(rich(X)<~>~brave(X))))&
(((~kind(lucy)|~curious(lucy)))=>(tall(alice)))&
(![X]:((wise(X)&~patient(X))<=>(~funny(X)|strong(X))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
(quiet(john))&
(happy(fred))&
(?[X]:(~curious(X)))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:((kind(X)|~wise(X))))&
((generous(mary)|~generous(mary)))&
(?[X]:((~brave(X)<~>curious(X)))) | patient(lucy) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 793221620244709256361515
% SZS output start Proof for 793221620244709256361515
10. ! [X0] : ((~patient(X0) & wise(X0)) <=> (strong(X0) | ~funny(X0))) [input p9]
13. ! [X0] : (patient(X0) <=> strong(X0)) [input p12]
25. patient(lucy) [input hypothesis]
42. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 10]
43. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | patient(X0) | ~wise(X0))) [flattening 42]
47. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 13]
94. ~patient(X0) | ~strong(X0) [cnf transformation 43]
100. strong(X0) | ~patient(X0) [cnf transformation 47]
101. patient(X0) | ~strong(X0) [cnf transformation 47]
119. patient(lucy) [cnf transformation 25]
200. ~strong(X0) [subsumption resolution 101,94]
201. ~patient(X0) [subsumption resolution 100,200]
223. $false [subsumption resolution 119,201]
% SZS output end Proof for 793221620244709256361515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not old is both not calm and not strong.
If someone is both not humble and creative then someone is both not happy and wise and vice versa.
Everyone who is both not strong and humble is both old and not humble and vice versa.
Everyone who is not kind or not creative is not creative or wise.
Everyone who is both not patient and not wise is not creative and vice versa.
Everyone who is both not tall and not happy is strong.
If alice is both not curious and creative then someone is both generous and not funny and vice versa.
Everyone who is not strong or not creative is both funny and not kind.
If susan is not kind or not rich then someone is both old and not old.
Everyone who is either not patient or creative is both not wise and not creative.
If alice is not brave then fred is either not humble or strong and vice versa.
Everyone who is either old or happy is either not calm or calm.
Everyone who is not happy or creative is either calm or not old.
Everyone who is not brave or creative is both old and happy.
If paul is either not calm or not curious then mary is not brave.
If paul is either not happy or not generous then john is calm.
Someone is kind.
Paul is both curious and not quiet.
John is either not calm or not old.
Someone is both tall and not creative.
Someone is not patient.
Alice is both strong and generous. | Mary is kind. | neutral | (![X]:((~creative(X)<~>~old(X))=>(~calm(X)&~strong(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~strong(X)&humble(X))<=>(old(X)&~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~creative(X)|wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>~creative(X)))&
(![X]:((~tall(X)&~happy(X))=>strong(X)))&
(((~curious(alice)&creative(alice)))<=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((~strong(X)|~creative(X))=>(funny(X)&~kind(X))))&
(((~kind(susan)|~rich(susan)))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~wise(X)&~creative(X))))&
((~brave(alice))<=>((~humble(fred)<~>strong(fred))))&
(![X]:((old(X)<~>happy(X))=>(~calm(X)<~>calm(X))))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((~brave(X)|creative(X))=>(old(X)&happy(X))))&
(((~calm(paul)<~>~curious(paul)))=>(~brave(mary)))&
(((~happy(paul)<~>~generous(paul)))=>(calm(john)))&
(?[X]:(kind(X)))&
((curious(paul)&~quiet(paul)))&
((~calm(john)<~>~old(john)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:(~patient(X)))&
((strong(alice)&generous(alice))) | kind(mary) | [] | null | 0 |
If lucy is both strong and not wise then someone is both humble and not quiet and vice versa.
Everyone who is not strong is kind and vice versa.
Everyone who is both not patient and not curious is not creative.
If paul is either funny or brave then lucy is either not humble or not funny and vice versa.
Everyone who is not brave is both not calm and not strong.
Everyone who is not happy or not calm is either not humble or patient and vice versa.
If alice is both not rich and tall then someone is either not tall or not funny.
Everyone who is either not patient or quiet is not calm and vice versa.
Everyone who is generous or not generous is either wise or funny and vice versa.
Everyone who is both not strong and not wise is not kind.
If mary is both patient and not happy then john is both not calm and rich and vice versa.
If mary is either not rich or not humble then fred is both not patient and generous and vice versa.
If mary is either not tall or old then someone is either not brave or not kind and vice versa.
Everyone who is not generous is not patient or kind.
If mary is either creative or not old then someone is either not calm or calm and vice versa.
Everyone who is curious is quiet and vice versa.
Alice is either not old or humble.
Fred is old or tall.
Fred is not calm or not humble.
Someone is not old or strong.
Someone is not brave.
Someone is either not brave or quiet.
Someone is both not kind and not tall.
Mary is both funny and humble. | Lucy is not tall. | neutral | (((strong(lucy)&~wise(lucy)))<=>(?[X]:((humble(X)&~quiet(X)))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~patient(X)&~curious(X))=>~creative(X)))&
(((funny(paul)<~>brave(paul)))<=>((~humble(lucy)<~>~funny(lucy))))&
(![X]:(~brave(X)=>(~calm(X)&~strong(X))))&
(![X]:((~happy(X)|~calm(X))<=>(~humble(X)<~>patient(X))))&
(((~rich(alice)&tall(alice)))=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>~calm(X)))&
(![X]:((generous(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
(![X]:((~strong(X)&~wise(X))=>~kind(X)))&
(((patient(mary)&~happy(mary)))<=>((~calm(john)&rich(john))))&
(((~rich(mary)<~>~humble(mary)))<=>((~patient(fred)&generous(fred))))&
(((~tall(mary)<~>old(mary)))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:(~generous(X)=>(~patient(X)|kind(X))))&
(((creative(mary)<~>~old(mary)))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:(curious(X)<=>quiet(X)))&
((~old(alice)<~>humble(alice)))&
((old(fred)|tall(fred)))&
((~calm(fred)|~humble(fred)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~kind(X)&~tall(X))))&
((funny(mary)&humble(mary))) | ~tall(lucy) | [] | null | 0 |
If someone is generous or not kind then mary is either not curious or not patient and vice versa. Everyone who is either not brave or not patient is both wise and not strong and vice versa. If someone is brave then someone is both wise and not brave and vice versa. Everyone who is not patient is both not old and tall and vice versa. Everyone who is either tall or not funny is not old or not wise and vice versa. If john is both generous and strong then someone is not rich and vice versa. Everyone who is not humble is not calm or not creative. If lucy is tall then someone is not wise or not patient and vice versa. If someone is creative then someone is old or quiet and vice versa. Everyone who is brave is humble or not calm and vice versa. If susan is both not old and tall then john is not wise or generous and vice versa. Everyone who is tall or not patient is both patient and not strong. If someone is both not humble and calm then someone is quiet or rich and vice versa. If someone is not funny then someone is both not generous and strong and vice versa. If someone is curious then someone is either brave or tall. If someone is not rich then susan is either not humble or not happy. Someone is either not kind or not wise. Someone is not kind or brave. Someone is not patient or not creative. Alice is both not quiet and creative. Someone is both wise and brave. Someone is either not curious or not creative. | Mary is not wise. | neutral | ((?[X]:((generous(X)|~kind(X))))<=>((~curious(mary)<~>~patient(mary))))&
(![X]:((~brave(X)<~>~patient(X))<=>(wise(X)&~strong(X))))&
((?[X]:(brave(X)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~patient(X)<=>(~old(X)&tall(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~old(X)|~wise(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~rich(X))))&
(![X]:(~humble(X)=>(~calm(X)|~creative(X))))&
((tall(lucy))<=>(?[X]:((~wise(X)|~patient(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((old(X)|quiet(X)))))&
(![X]:(brave(X)<=>(humble(X)|~calm(X))))&
(((~old(susan)&tall(susan)))<=>((~wise(john)|generous(john))))&
(![X]:((tall(X)|~patient(X))=>(patient(X)&~strong(X))))&
((?[X]:((~humble(X)&calm(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~generous(X)&strong(X)))))&
((?[X]:(curious(X)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:(~rich(X)))=>((~humble(susan)<~>~happy(susan))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((~patient(X)|~creative(X))))&
((~quiet(alice)&creative(alice)))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:((~curious(X)<~>~creative(X)))) | ~wise(mary) | [] | null | 0 |
Everyone who is both tall and not curious is rich and vice versa.
Everyone who is wise or brave is both not generous and funny and vice versa.
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.
If susan is generous then susan is happy and vice versa.
If someone is both kind and not humble then fred is either not funny or creative.
Everyone who is curious or wise is not curious.
Everyone who is both humble and rich is not brave and vice versa.
If mary is not patient or funny then john is either strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
Everyone who is not curious is creative or not patient and vice versa.
Everyone who is old or not quiet is either not creative or not curious and vice versa.
Alice is funny or old.
Lucy is either not curious or brave.
Susan is either funny or not calm.
Fred is not kind.
Paul is tall or brave.
John is creative.
Fred is either creative or tall. | Susan is strong. | neutral | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:((wise(X)|brave(X))<=>(~generous(X)&funny(X))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul)))&
(creative(john))&
((creative(fred)<~>tall(fred))) | strong(susan) | [] | null | 0 |
Everyone who is both funny and not patient is both not calm and curious.
If alice is calm then john is either creative or not funny.
If someone is quiet then paul is tall and vice versa.
If someone is both quiet and brave then someone is both patient and strong.
If someone is kind or not patient then mary is either strong or not humble.
Everyone who is both generous and not tall is both curious and kind and vice versa.
Everyone who is either not happy or happy is both not rich and not wise and vice versa.
If john is either tall or not kind then someone is both not happy and rich and vice versa.
If mary is either generous or creative then lucy is both wise and not funny and vice versa.
If someone is either funny or not tall then susan is not funny and vice versa.
If lucy is both not funny and rich then susan is both not old and happy.
If someone is both kind and patient then someone is both not strong and rich.
Everyone who is old or curious is both quiet and happy and vice versa.
Everyone who is both curious and humble is not old or not tall and vice versa.
Everyone who is either calm or rich is either wise or not quiet.
Lucy is brave or kind.
Someone is both creative and not patient.
Someone is not strong.
Someone is either not humble or brave. | Paul is brave. | neutral | (![X]:((funny(X)&~patient(X))=>(~calm(X)&curious(X))))&
((calm(alice))=>((creative(john)<~>~funny(john))))&
((?[X]:(quiet(X)))<=>(tall(paul)))&
((?[X]:((quiet(X)&brave(X))))=>(?[X]:((patient(X)&strong(X)))))&
((?[X]:((kind(X)|~patient(X))))=>((strong(mary)<~>~humble(mary))))&
(![X]:((generous(X)&~tall(X))<=>(curious(X)&kind(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~rich(X)&~wise(X))))&
(((tall(john)<~>~kind(john)))<=>(?[X]:((~happy(X)&rich(X)))))&
(((generous(mary)<~>creative(mary)))<=>((wise(lucy)&~funny(lucy))))&
((?[X]:((funny(X)<~>~tall(X))))<=>(~funny(susan)))&
(((~funny(lucy)&rich(lucy)))=>((~old(susan)&happy(susan))))&
((?[X]:((kind(X)&patient(X))))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((old(X)|curious(X))<=>(quiet(X)&happy(X))))&
(![X]:((curious(X)&humble(X))<=>(~old(X)|~tall(X))))&
(![X]:((calm(X)<~>rich(X))=>(wise(X)<~>~quiet(X))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((creative(X)&~patient(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~humble(X)<~>brave(X)))) | brave(paul) | [] | null | 0 |
If alice is either not patient or calm then someone is not patient. If fred is rich or not kind then john is not wise or not strong and vice versa. If john is generous or old then someone is not kind or happy and vice versa. Everyone who is both not tall and tall is both patient and calm and vice versa. If alice is both not generous and quiet then someone is quiet or not happy and vice versa. Everyone who is either humble or not happy is either not tall or not happy. If fred is both not funny and not wise then paul is not humble. If john is not quiet or creative then mary is both quiet and not patient and vice versa. Everyone who is not old is both old and not strong and vice versa. If someone is either not rich or wise then susan is curious and vice versa. If someone is generous then paul is both not kind and not happy and vice versa. If fred is patient then paul is calm or generous and vice versa. Everyone who is kind is both not calm and creative and vice versa. Everyone who is either happy or creative is either kind or not brave and vice versa. If someone is both happy and not quiet then someone is both rich and not strong. If someone is not wise then someone is not funny or not curious. Someone is generous. Paul is either humble or not generous. Someone is either not patient or not funny. Someone is humble or not funny. John is not quiet or old. Alice is either not old or not curious. Someone is both not patient and brave. Lucy is either not rich or not kind. | John is not old. | contradiction | (((~patient(alice)<~>calm(alice)))=>(?[X]:(~patient(X))))&
(((rich(fred)|~kind(fred)))<=>((~wise(john)|~strong(john))))&
(((generous(john)|old(john)))<=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~tall(X)&tall(X))<=>(patient(X)&calm(X))))&
(((~generous(alice)&quiet(alice)))<=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((humble(X)<~>~happy(X))=>(~tall(X)<~>~happy(X))))&
(((~funny(fred)&~wise(fred)))=>(~humble(paul)))&
(((~quiet(john)|creative(john)))<=>((quiet(mary)&~patient(mary))))&
(![X]:(~old(X)<=>(old(X)&~strong(X))))&
((?[X]:((~rich(X)<~>wise(X))))<=>(curious(susan)))&
((?[X]:(generous(X)))<=>((~kind(paul)&~happy(paul))))&
((patient(fred))<=>((calm(paul)|generous(paul))))&
(![X]:(kind(X)<=>(~calm(X)&creative(X))))&
(![X]:((happy(X)<~>creative(X))<=>(kind(X)<~>~brave(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((rich(X)&~strong(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)|~curious(X)))))&
(?[X]:(generous(X)))&
((humble(paul)<~>~generous(paul)))&
(?[X]:((~patient(X)<~>~funny(X))))&
(?[X]:((humble(X)|~funny(X))))&
((~quiet(john)|old(john)))&
((~old(alice)<~>~curious(alice)))&
(?[X]:((~patient(X)&brave(X))))&
((~rich(lucy)<~>~kind(lucy))) | ~old(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 391789469490671879335800
% SZS output start Proof for 391789469490671879335800
9. ! [X0] : (~old(X0) <=> (~strong(X0) & old(X0))) [input p8]
25. ~old(john) [input hypothesis]
54. ! [X0] : ((~old(X0) | (strong(X0) | ~old(X0))) & ((~strong(X0) & old(X0)) | old(X0))) [nnf transformation 9]
55. ! [X0] : ((~old(X0) | strong(X0) | ~old(X0)) & ((~strong(X0) & old(X0)) | old(X0))) [flattening 54]
117. old(X0) | old(X0) [cnf transformation 55]
157. ~old(john) [cnf transformation 25]
158. old(X0) [duplicate literal removal 117]
400. $false [subsumption resolution 157,158]
% SZS output end Proof for 391789469490671879335800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then lucy is kind or not patient.
If someone is either wise or tall then someone is not quiet and vice versa.
If someone is both funny and not old then fred is not curious or not funny and vice versa.
If susan is both curious and tall then someone is both patient and not old.
If someone is patient or not humble then john is funny or not calm and vice versa.
Everyone who is either old or tall is not quiet or not wise and vice versa.
Everyone who is not tall is not creative and vice versa.
If someone is either old or humble then fred is not funny and vice versa.
Everyone who is both calm and not quiet is either not generous or not creative and vice versa.
If paul is either calm or rich then someone is either tall or not humble and vice versa.
If john is not tall or calm then paul is both calm and old and vice versa.
If lucy is not tall then someone is brave and vice versa.
Everyone who is both not funny and quiet is not strong.
Everyone who is not creative or not curious is tall.
If john is either curious or not rich then someone is creative and vice versa.
If mary is both not old and strong then fred is quiet or not wise and vice versa.
Mary is either wise or not calm.
Someone is not patient or curious.
Lucy is not curious.
Someone is not brave.
Someone is both not happy and not quiet.
Paul is not calm.
Someone is curious.
Someone is either kind or not humble. | Lucy is not tall. | contradiction | ((?[X]:(funny(X)))=>((kind(lucy)|~patient(lucy))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((funny(X)&~old(X))))<=>((~curious(fred)|~funny(fred))))&
(((curious(susan)&tall(susan)))=>(?[X]:((patient(X)&~old(X)))))&
((?[X]:((patient(X)|~humble(X))))<=>((funny(john)|~calm(john))))&
(![X]:((old(X)<~>tall(X))<=>(~quiet(X)|~wise(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
((?[X]:((old(X)<~>humble(X))))<=>(~funny(fred)))&
(![X]:((calm(X)&~quiet(X))<=>(~generous(X)<~>~creative(X))))&
(((calm(paul)<~>rich(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~tall(john)|calm(john)))<=>((calm(paul)&old(paul))))&
((~tall(lucy))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)&quiet(X))=>~strong(X)))&
(![X]:((~creative(X)|~curious(X))=>tall(X)))&
(((curious(john)<~>~rich(john)))<=>(?[X]:(creative(X))))&
(((~old(mary)&strong(mary)))<=>((quiet(fred)|~wise(fred))))&
((wise(mary)<~>~calm(mary)))&
(?[X]:((~patient(X)|curious(X))))&
(~curious(lucy))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)&~quiet(X))))&
(~calm(paul))&
(?[X]:(curious(X)))&
(?[X]:((kind(X)<~>~humble(X)))) | ~tall(lucy) | [
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 792546317727893201041507
% SZS output start Proof for 792546317727893201041507
7. ! [X0] : (~tall(X0) <=> ~creative(X0)) [input p6]
14. ! [X0] : ((~curious(X0) | ~creative(X0)) => tall(X0)) [input p13]
25. ~tall(lucy) [input hypothesis]
34. ! [X0] : (tall(X0) | (curious(X0) & creative(X0))) [ennf transformation 14]
54. ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 7]
111. ~creative(X0) | tall(X0) [cnf transformation 54]
112. ~tall(X0) | creative(X0) [cnf transformation 54]
139. tall(X0) | creative(X0) [cnf transformation 34]
160. ~tall(lucy) [cnf transformation 25]
331. 38 <=> tall(lucy) [avatar definition]
333. ~tall(lucy) <- (~38) [avatar component clause 331]
340. creative(X0) [subsumption resolution 139,112]
404. ~38 [avatar split clause 160,331]
407. tall(X0) [resolution 111,340]
410. $false <- (~38) [resolution 407,333]
411. 38 [avatar contradiction clause 410]
414. $false [avatar sat refutation 404,411]
% SZS output end Proof for 792546317727893201041507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is patient then someone is either not quiet or not wise.
If mary is not generous then someone is not old or tall and vice versa.
If paul is not wise or not patient then someone is kind or calm.
Everyone who is strong or generous is not tall or not wise and vice versa.
Everyone who is both not creative and not wise is patient and vice versa.
Everyone who is either not creative or generous is both generous and not quiet.
Everyone who is either kind or not wise is patient or tall and vice versa.
Everyone who is not old is either not creative or not strong and vice versa.
If john is not strong or not quiet then paul is both not tall and patient.
Everyone who is both not kind and not curious is either not happy or funny and vice versa.
Everyone who is both not generous and not humble is both generous and not humble and vice versa.
If susan is both not happy and rich then fred is calm or old and vice versa.
If someone is funny then lucy is humble and vice versa.
Everyone who is either not calm or not happy is creative and vice versa.
If mary is both tall and not kind then someone is either not tall or quiet and vice versa.
Everyone who is either not patient or not tall is either not happy or not kind and vice versa.
Someone is not funny.
Someone is not patient.
Someone is not rich.
Susan is not creative or tall.
John is both not tall and quiet.
Lucy is either brave or not strong.
Someone is humble.
Susan is either not tall or not creative. | Susan is not patient. | contradiction | ((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>~wise(X)))))&
((~generous(mary))<=>(?[X]:((~old(X)|tall(X)))))&
(((~wise(paul)|~patient(paul)))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((strong(X)|generous(X))<=>(~tall(X)|~wise(X))))&
(![X]:((~creative(X)&~wise(X))<=>patient(X)))&
(![X]:((~creative(X)<~>generous(X))=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(patient(X)|tall(X))))&
(![X]:(~old(X)<=>(~creative(X)<~>~strong(X))))&
(((~strong(john)|~quiet(john)))=>((~tall(paul)&patient(paul))))&
(![X]:((~kind(X)&~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~generous(X)&~humble(X))<=>(generous(X)&~humble(X))))&
(((~happy(susan)&rich(susan)))<=>((calm(fred)|old(fred))))&
((?[X]:(funny(X)))<=>(humble(lucy)))&
(![X]:((~calm(X)<~>~happy(X))<=>creative(X)))&
(((tall(mary)&~kind(mary)))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~happy(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
(?[X]:(~patient(X)))&
(?[X]:(~rich(X)))&
((~creative(susan)|tall(susan)))&
((~tall(john)&quiet(john)))&
((brave(lucy)<~>~strong(lucy)))&
(?[X]:(humble(X)))&
((~tall(susan)<~>~creative(susan))) | ~patient(susan) | [
"p3",
"p4",
"p5",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6205538359674925967827570
% SZS output start Proof for 6205538359674925967827570
4. ! [X0] : ((generous(X0) | strong(X0)) <=> (~wise(X0) | ~tall(X0))) [input p3]
5. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> patient(X0)) [input p4]
6. ! [X0] : ((~creative(X0) <~> generous(X0)) => (~quiet(X0) & generous(X0))) [input p5]
20. tall(susan) | ~creative(susan) [input p19]
24. ~tall(susan) <~> ~creative(susan) [input p23]
25. ~patient(susan) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & generous(X0)) | (~creative(X0) <=> generous(X0))) [ennf transformation 6]
41. ! [X0] : (((generous(X0) | strong(X0)) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | (~generous(X0) & ~strong(X0)))) [nnf transformation 4]
42. ! [X0] : ((generous(X0) | strong(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | (~generous(X0) & ~strong(X0)))) [flattening 41]
43. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | (wise(X0) | creative(X0)))) [nnf transformation 5]
44. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | wise(X0) | creative(X0))) [flattening 43]
45. ! [X0] : ((~quiet(X0) & generous(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 29]
75. (creative(susan) | tall(susan)) & (~creative(susan) | ~tall(susan)) [nnf transformation 24]
84. ~tall(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 42]
87. creative(X0) | wise(X0) | patient(X0) [cnf transformation 44]
90. generous(X0) | generous(X0) | creative(X0) [cnf transformation 45]
146. tall(susan) | ~creative(susan) [cnf transformation 20]
152. ~creative(susan) | ~tall(susan) [cnf transformation 75]
153. creative(susan) | tall(susan) [cnf transformation 75]
154. ~patient(susan) [cnf transformation 25]
157. creative(X0) | generous(X0) [duplicate literal removal 90]
284. 26 <=> creative(susan) [avatar definition]
286. ~creative(susan) <- (~26) [avatar component clause 284]
288. 27 <=> tall(susan) [avatar definition]
290. tall(susan) <- (27) [avatar component clause 288]
291. ~26 | 27 [avatar split clause 146,288,284]
303. 27 | 26 [avatar split clause 153,284,288]
304. ~27 | ~26 [avatar split clause 152,284,288]
305. generous(susan) <- (~26) [resolution 157,286]
314. ~wise(susan) | ~generous(susan) <- (27) [resolution 84,290]
316. ~wise(susan) <- (~26, 27) [subsumption resolution 314,305]
336. wise(susan) | patient(susan) <- (~26) [resolution 87,286]
338. patient(susan) <- (~26, 27) [subsumption resolution 336,316]
339. $false <- (~26, 27) [subsumption resolution 338,154]
340. 26 | ~27 [avatar contradiction clause 339]
341. $false [avatar sat refutation 291,303,304,340]
% SZS output end Proof for 6205538359674925967827570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not calm is either curious or old and vice versa.
Everyone who is both old and not patient is both happy and patient and vice versa.
Everyone who is either not calm or not strong is either kind or quiet and vice versa.
If lucy is either quiet or not creative then someone is both humble and not generous and vice versa.
Everyone who is both kind and not curious is either not calm or not wise and vice versa.
Everyone who is both old and not creative is both not happy and strong.
Everyone who is either not quiet or old is not happy or not humble and vice versa.
If fred is curious then someone is quiet and vice versa.
If paul is wise or patient then someone is not wise or not creative and vice versa.
Everyone who is both curious and brave is not brave.
Everyone who is not patient is old and vice versa.
Everyone who is not humble or brave is either not creative or not patient.
Everyone who is tall is either patient or wise and vice versa.
If paul is both strong and humble then someone is not strong and vice versa.
If lucy is patient or not generous then someone is either old or not calm and vice versa.
Someone is not humble.
Someone is not funny or not patient.
Someone is either tall or not rich.
Paul is either not calm or not humble.
Someone is old or not tall.
Someone is creative. | Fred is not old. | entailment | (![X]:((strong(X)|~calm(X))<=>(curious(X)<~>old(X))))&
(![X]:((old(X)&~patient(X))<=>(happy(X)&patient(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>quiet(X))))&
(((quiet(lucy)<~>~creative(lucy)))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((old(X)&~creative(X))=>(~happy(X)&strong(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~happy(X)|~humble(X))))&
((curious(fred))<=>(?[X]:(quiet(X))))&
(((wise(paul)|patient(paul)))<=>(?[X]:((~wise(X)|~creative(X)))))&
(![X]:((curious(X)&brave(X))=>~brave(X)))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~humble(X)|brave(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(patient(X)<~>wise(X))))&
(((strong(paul)&humble(paul)))<=>(?[X]:(~strong(X))))&
(((patient(lucy)|~generous(lucy)))<=>(?[X]:((old(X)<~>~calm(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
((~calm(paul)<~>~humble(paul)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:(creative(X))) | ~old(fred) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8073818990242667113135885
% SZS output start Proof for 8073818990242667113135885
2. ! [X0] : ((~patient(X0) & old(X0)) <=> (patient(X0) & happy(X0))) [input p1]
11. ! [X0] : (~patient(X0) <=> old(X0)) [input p10]
22. old(fred) [input hypothesis]
31. ! [X0] : (((~patient(X0) & old(X0)) | (~patient(X0) | ~happy(X0))) & ((patient(X0) & happy(X0)) | (patient(X0) | ~old(X0)))) [nnf transformation 2]
32. ! [X0] : (((~patient(X0) & old(X0)) | ~patient(X0) | ~happy(X0)) & ((patient(X0) & happy(X0)) | patient(X0) | ~old(X0))) [flattening 31]
51. ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))) [nnf transformation 11]
81. patient(X0) | patient(X0) | ~old(X0) [cnf transformation 32]
119. ~patient(X0) | ~old(X0) [cnf transformation 51]
142. old(fred) [cnf transformation 22]
143. patient(X0) | ~old(X0) [duplicate literal removal 81]
209. ~old(X0) [subsumption resolution 119,143]
262. $false [subsumption resolution 142,209]
% SZS output end Proof for 8073818990242667113135885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not strong and quiet then someone is rich or not happy.
If someone is both not brave and not creative then paul is not rich and vice versa.
If susan is not calm then alice is either not wise or calm and vice versa.
If john is either kind or not happy then someone is either happy or not brave and vice versa.
Everyone who is not wise is both not quiet and brave.
Everyone who is not patient or not humble is brave and vice versa.
Everyone who is both kind and not calm is both not tall and happy.
Everyone who is both not curious and calm is both humble and strong.
If paul is not tall or not happy then paul is either strong or not calm and vice versa.
If alice is not curious or not strong then lucy is either not quiet or brave and vice versa.
Everyone who is not old is both generous and tall and vice versa.
Everyone who is not humble is both tall and calm.
Everyone who is either quiet or funny is happy or brave and vice versa.
Everyone who is both not tall and not humble is both not generous and not old and vice versa.
Everyone who is either creative or brave is both generous and not humble and vice versa.
If someone is both not happy and patient then someone is both not funny and quiet.
Alice is either strong or not patient.
Paul is both funny and creative.
Lucy is either not funny or funny.
Paul is not old.
Alice is either not strong or kind.
Someone is wise.
Mary is not patient or old.
Someone is not brave. | Lucy is funny. | neutral | ((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:((~brave(X)&~creative(X))))<=>(~rich(paul)))&
((~calm(susan))<=>((~wise(alice)<~>calm(alice))))&
(((kind(john)<~>~happy(john)))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:(~wise(X)=>(~quiet(X)&brave(X))))&
(![X]:((~patient(X)|~humble(X))<=>brave(X)))&
(![X]:((kind(X)&~calm(X))=>(~tall(X)&happy(X))))&
(![X]:((~curious(X)&calm(X))=>(humble(X)&strong(X))))&
(((~tall(paul)|~happy(paul)))<=>((strong(paul)<~>~calm(paul))))&
(((~curious(alice)|~strong(alice)))<=>((~quiet(lucy)<~>brave(lucy))))&
(![X]:(~old(X)<=>(generous(X)&tall(X))))&
(![X]:(~humble(X)=>(tall(X)&calm(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(happy(X)|brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~generous(X)&~old(X))))&
(![X]:((creative(X)<~>brave(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~happy(X)&patient(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
((strong(alice)<~>~patient(alice)))&
((funny(paul)&creative(paul)))&
((~funny(lucy)<~>funny(lucy)))&
(~old(paul))&
((~strong(alice)<~>kind(alice)))&
(?[X]:(wise(X)))&
((~patient(mary)|old(mary)))&
(?[X]:(~brave(X))) | funny(lucy) | [] | null | 0 |
Everyone who is both strong and quiet is not curious or not creative and vice versa.
If someone is both tall and not kind then alice is strong and vice versa.
If someone is not rich then someone is both not curious and quiet.
Everyone who is not kind is both kind and tall and vice versa.
Everyone who is humble or quiet is either not rich or not strong.
Everyone who is not humble is either curious or quiet.
If fred is not kind then alice is either generous or wise and vice versa.
If someone is both funny and not curious then fred is creative or not curious.
Everyone who is either not old or brave is patient.
Everyone who is funny is both tall and not humble and vice versa.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is both tall and old then fred is not brave or creative.
Everyone who is tall is wise and vice versa.
Everyone who is happy is both humble and wise and vice versa.
Everyone who is either not creative or not quiet is not strong and vice versa.
John is both not calm and not old.
Someone is not kind or strong.
Someone is not old or not quiet.
Susan is both not patient and quiet.
Someone is either not patient or not old.
Someone is either brave or not quiet. | Alice is curious. | entailment | (![X]:((strong(X)&quiet(X))<=>(~curious(X)|~creative(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(strong(alice)))&
((?[X]:(~rich(X)))=>(?[X]:((~curious(X)&quiet(X)))))&
(![X]:(~kind(X)<=>(kind(X)&tall(X))))&
(![X]:((humble(X)|quiet(X))=>(~rich(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(curious(X)<~>quiet(X))))&
((~kind(fred))<=>((generous(alice)<~>wise(alice))))&
((?[X]:((funny(X)&~curious(X))))=>((creative(fred)|~curious(fred))))&
(![X]:((~old(X)<~>brave(X))=>patient(X)))&
(![X]:(funny(X)<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((tall(X)&old(X))))=>((~brave(fred)|creative(fred))))&
(![X]:(tall(X)<=>wise(X)))&
(![X]:(happy(X)<=>(humble(X)&wise(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>~strong(X)))&
((~calm(john)&~old(john)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~old(X)|~quiet(X))))&
((~patient(susan)&quiet(susan)))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((brave(X)<~>~quiet(X)))) | curious(alice) | [
"p0",
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8355870466187936878765718
% SZS output start Proof for 8355870466187936878765718
1. ! [X0] : ((quiet(X0) & strong(X0)) <=> (~creative(X0) | ~curious(X0))) [input p0]
2. ? [X0] : (~kind(X0) & tall(X0)) <=> strong(alice) [input p1]
4. ! [X0] : (~kind(X0) <=> (tall(X0) & kind(X0))) [input p3]
22. ~curious(alice) [input hypothesis]
36. ! [X0] : (((quiet(X0) & strong(X0)) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | (~quiet(X0) | ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : (((quiet(X0) & strong(X0)) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | ~quiet(X0) | ~strong(X0))) [flattening 36]
38. (? [X0] : (~kind(X0) & tall(X0)) | ~strong(alice)) & (strong(alice) | ! [X0] : (kind(X0) | ~tall(X0))) [nnf transformation 2]
39. (? [X0] : (~kind(X0) & tall(X0)) | ~strong(alice)) & (strong(alice) | ! [X1] : (kind(X1) | ~tall(X1))) [rectify 38]
40. ? [X0] : (~kind(X0) & tall(X0)) => (~kind(sK0) & tall(sK0)) [choice axiom]
41. ((~kind(sK0) & tall(sK0)) | ~strong(alice)) & (strong(alice) | ! [X1] : (kind(X1) | ~tall(X1))) [skolemisation 39,40]
45. ! [X0] : ((~kind(X0) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | kind(X0))) [nnf transformation 4]
46. ! [X0] : ((~kind(X0) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | kind(X0))) [flattening 45]
68. curious(X0) | strong(X0) [cnf transformation 37]
74. ~kind(sK0) | ~strong(alice) [cnf transformation 41]
77. kind(X0) | kind(X0) [cnf transformation 46]
118. ~curious(alice) [cnf transformation 22]
119. kind(X0) [duplicate literal removal 77]
122. 1 <=> strong(alice) [avatar definition]
126. 2 <=> kind(sK0) [avatar definition]
128. ~kind(sK0) <- (~2) [avatar component clause 126]
129. ~1 | ~2 [avatar split clause 74,126,122]
218. strong(alice) [resolution 68,118]
222. 1 [avatar split clause 218,122]
223. $false <- (~2) [subsumption resolution 128,119]
224. 2 [avatar contradiction clause 223]
225. $false [avatar sat refutation 129,222,224]
% SZS output end Proof for 8355870466187936878765718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or not happy is not old or calm and vice versa.
Everyone who is humble is both happy and brave and vice versa.
If john is either not wise or not quiet then john is rich and vice versa.
If mary is not patient or not calm then someone is either quiet or humble and vice versa.
Everyone who is funny or tall is not old or funny and vice versa.
If someone is not generous or not rich then someone is either creative or old.
If john is not creative then paul is both not creative and patient and vice versa.
Everyone who is happy is either not creative or not old and vice versa.
Everyone who is not strong or curious is either not curious or not quiet.
If paul is both not kind and kind then someone is both curious and not generous and vice versa.
Everyone who is calm or not happy is both not tall and funny.
Everyone who is not rich or not old is both not brave and not curious.
If someone is either not kind or patient then lucy is not wise or not rich.
If fred is either creative or rich then someone is not rich.
If someone is both not quiet and creative then susan is either humble or not old.
If someone is curious then someone is not brave.
Someone is not rich.
Someone is kind or calm.
John is not strong.
Someone is calm or not strong.
Susan is either not humble or calm.
Someone is both curious and generous.
Susan is funny.
Lucy is not brave or not curious. | Paul is kind. | neutral | (![X]:((~tall(X)<~>~happy(X))<=>(~old(X)|calm(X))))&
(![X]:(humble(X)<=>(happy(X)&brave(X))))&
(((~wise(john)<~>~quiet(john)))<=>(rich(john)))&
(((~patient(mary)|~calm(mary)))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((funny(X)|tall(X))<=>(~old(X)|funny(X))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:((creative(X)<~>old(X)))))&
((~creative(john))<=>((~creative(paul)&patient(paul))))&
(![X]:(happy(X)<=>(~creative(X)<~>~old(X))))&
(![X]:((~strong(X)|curious(X))=>(~curious(X)<~>~quiet(X))))&
(((~kind(paul)&kind(paul)))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((calm(X)|~happy(X))=>(~tall(X)&funny(X))))&
(![X]:((~rich(X)|~old(X))=>(~brave(X)&~curious(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~wise(lucy)|~rich(lucy))))&
(((creative(fred)<~>rich(fred)))=>(?[X]:(~rich(X))))&
((?[X]:((~quiet(X)&creative(X))))=>((humble(susan)<~>~old(susan))))&
((?[X]:(curious(X)))=>(?[X]:(~brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)|calm(X))))&
(~strong(john))&
(?[X]:((calm(X)|~strong(X))))&
((~humble(susan)<~>calm(susan)))&
(?[X]:((curious(X)&generous(X))))&
(funny(susan))&
((~brave(lucy)|~curious(lucy))) | kind(paul) | [] | null | 0 |
Everyone who is not brave is either not generous or strong and vice versa.
If someone is not calm then lucy is both not wise and not creative.
Everyone who is old or not kind is both not curious and not generous.
Everyone who is both kind and tall is either brave or old.
Everyone who is both not creative and not humble is both not strong and not rich and vice versa.
Everyone who is either humble or tall is quiet and vice versa.
If fred is both patient and not curious then lucy is either old or not happy.
Everyone who is both not funny and not tall is creative or not generous.
Everyone who is either not strong or generous is generous or not kind and vice versa.
Everyone who is brave or not brave is not brave and vice versa.
Everyone who is not quiet or not happy is both wise and strong.
Everyone who is not tall or creative is creative or not patient and vice versa.
Everyone who is both not rich and quiet is either not brave or not humble.
Everyone who is not patient is both quiet and not rich.
Everyone who is quiet is both tall and funny.
Everyone who is not patient is funny or generous.
John is both quiet and not generous.
Alice is either not curious or patient.
John is patient.
Lucy is either not rich or wise.
Someone is not funny or wise.
Paul is either not tall or not kind.
Someone is either not tall or humble. | Paul is not calm. | contradiction | (![X]:(~brave(X)<=>(~generous(X)<~>strong(X))))&
((?[X]:(~calm(X)))=>((~wise(lucy)&~creative(lucy))))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&~generous(X))))&
(![X]:((kind(X)&tall(X))=>(brave(X)<~>old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~strong(X)&~rich(X))))&
(![X]:((humble(X)<~>tall(X))<=>quiet(X)))&
(((patient(fred)&~curious(fred)))=>((old(lucy)<~>~happy(lucy))))&
(![X]:((~funny(X)&~tall(X))=>(creative(X)|~generous(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((brave(X)|~brave(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))=>(wise(X)&strong(X))))&
(![X]:((~tall(X)|creative(X))<=>(creative(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:(~patient(X)=>(quiet(X)&~rich(X))))&
(![X]:(quiet(X)=>(tall(X)&funny(X))))&
(![X]:(~patient(X)=>(funny(X)|generous(X))))&
((quiet(john)&~generous(john)))&
((~curious(alice)<~>patient(alice)))&
(patient(john))&
((~rich(lucy)<~>wise(lucy)))&
(?[X]:((~funny(X)|wise(X))))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:((~tall(X)<~>humble(X)))) | ~calm(paul) | [
"p1",
"p5",
"p9",
"p10",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 320587642383864523952730
% SZS output start Proof for 320587642383864523952730
2. ? [X0] : ~calm(X0) => (~creative(lucy) & ~wise(lucy)) [input p1]
6. ! [X0] : ((humble(X0) <~> tall(X0)) <=> quiet(X0)) [input p5]
10. ! [X0] : ((~brave(X0) | brave(X0)) <=> ~brave(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (strong(X0) & wise(X0))) [input p10]
13. ! [X0] : ((quiet(X0) & ~rich(X0)) => (~brave(X0) <~> ~humble(X0))) [input p12]
15. ! [X0] : (quiet(X0) => (funny(X0) & tall(X0))) [input p14]
20. ~rich(lucy) <~> wise(lucy) [input p19]
24. ~calm(paul) [input hypothesis]
25. (~creative(lucy) & ~wise(lucy)) | ! [X0] : calm(X0) [ennf transformation 2]
33. ! [X0] : ((strong(X0) & wise(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 11]
34. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | (~quiet(X0) | rich(X0))) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~humble(X0)) | ~quiet(X0) | rich(X0)) [flattening 34]
37. ! [X0] : ((funny(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 15]
44. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~quiet(X0)) & (quiet(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 6]
48. ! [X0] : (((~brave(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [nnf transformation 10]
49. ! [X0] : ((~brave(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~brave(X0)))) [flattening 48]
52. ! [X0] : (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | ~quiet(X0) | rich(X0)) [nnf transformation 35]
54. (~wise(lucy) | rich(lucy)) & (wise(lucy) | ~rich(lucy)) [nnf transformation 20]
65. ~wise(lucy) | calm(X0) [cnf transformation 25]
80. ~quiet(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 44]
90. ~brave(X0) | ~brave(X0) [cnf transformation 49]
93. quiet(X0) | wise(X0) [cnf transformation 33]
102. humble(X0) | brave(X0) | ~quiet(X0) | rich(X0) [cnf transformation 52]
105. ~quiet(X0) | tall(X0) [cnf transformation 37]
113. wise(lucy) | ~rich(lucy) [cnf transformation 54]
120. ~calm(paul) [cnf transformation 24]
121. ~brave(X0) [duplicate literal removal 90]
126. 1 <=> ! [X0] : calm(X0) [avatar definition]
127. calm(X0) <- (1) [avatar component clause 126]
134. 3 <=> wise(lucy) [avatar definition]
136. ~wise(lucy) <- (~3) [avatar component clause 134]
137. 1 | ~3 [avatar split clause 65,134,126]
158. ~quiet(X0) | humble(X0) | rich(X0) [subsumption resolution 102,121]
170. 10 <=> rich(lucy) [avatar definition]
171. ~rich(lucy) <- (~10) [avatar component clause 170]
174. ~10 | 3 [avatar split clause 113,134,170]
208. tall(X1) | wise(X1) [resolution 105,93]
264. ~humble(X1) | ~tall(X1) | wise(X1) [resolution 80,93]
269. ~humble(X1) | wise(X1) [subsumption resolution 264,208]
319. humble(X1) | rich(X1) | wise(X1) [resolution 158,93]
324. rich(X1) | wise(X1) [subsumption resolution 319,269]
404. $false <- (1) [resolution 127,120]
405. ~1 [avatar contradiction clause 404]
426. wise(lucy) <- (~10) [resolution 324,171]
427. $false <- (~3, ~10) [subsumption resolution 426,136]
428. 3 | 10 [avatar contradiction clause 427]
429. $false [avatar sat refutation 137,174,405,428]
% SZS output end Proof for 320587642383864523952730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or kind is both not strong and not old and vice versa. If someone is either not generous or not humble then paul is both creative and not generous. Everyone who is both kind and rich is either patient or not humble and vice versa. If someone is not generous then someone is not strong and vice versa. Everyone who is generous is not happy or strong and vice versa. Everyone who is not calm or not tall is not calm or not quiet. Everyone who is both not tall and not old is patient or not happy. Everyone who is not funny is both not wise and not kind and vice versa. Everyone who is not generous or curious is rich or old. Everyone who is both not curious and not brave is not rich or not funny. Everyone who is not generous is either generous or not rich and vice versa. Everyone who is either rich or calm is either strong or not kind. Everyone who is happy is either not calm or not creative. If john is not tall then someone is either not kind or happy. Everyone who is not wise is patient or not patient and vice versa. If alice is either calm or curious then mary is either not curious or not funny. Alice is kind or not old. Someone is quiet or curious. Mary is not brave or not strong. Alice is happy. Someone is not rich or not curious. Mary is both not kind and strong. Someone is both not quiet and old. | Alice is not calm. | entailment | (![X]:((funny(X)|kind(X))<=>(~strong(X)&~old(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>((creative(paul)&~generous(paul))))&
(![X]:((kind(X)&rich(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(~happy(X)|strong(X))))&
(![X]:((~calm(X)|~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~happy(X))))&
(![X]:(~funny(X)<=>(~wise(X)&~kind(X))))&
(![X]:((~generous(X)|curious(X))=>(rich(X)|old(X))))&
(![X]:((~curious(X)&~brave(X))=>(~rich(X)|~funny(X))))&
(![X]:(~generous(X)<=>(generous(X)<~>~rich(X))))&
(![X]:((rich(X)<~>calm(X))=>(strong(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~calm(X)<~>~creative(X))))&
((~tall(john))=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
(((calm(alice)<~>curious(alice)))=>((~curious(mary)<~>~funny(mary))))&
((kind(alice)|~old(alice)))&
(?[X]:((quiet(X)|curious(X))))&
((~brave(mary)|~strong(mary)))&
(happy(alice))&
(?[X]:((~rich(X)|~curious(X))))&
((~kind(mary)&strong(mary)))&
(?[X]:((~quiet(X)&old(X)))) | ~calm(alice) | [
"p0",
"p4",
"p8",
"p10",
"p11",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8942467243617772376208713
% SZS output start Proof for 8942467243617772376208713
1. ! [X0] : ((kind(X0) | funny(X0)) <=> (~old(X0) & ~strong(X0))) [input p0]
5. ! [X0] : (generous(X0) <=> (strong(X0) | ~happy(X0))) [input p4]
9. ! [X0] : ((curious(X0) | ~generous(X0)) => (old(X0) | rich(X0))) [input p8]
11. ! [X0] : (~generous(X0) <=> (generous(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : ((rich(X0) <~> calm(X0)) => (strong(X0) <~> ~kind(X0))) [input p11]
17. ~old(alice) | kind(alice) [input p16]
20. happy(alice) [input p19]
24. calm(alice) [input hypothesis]
32. ! [X0] : ((old(X0) | rich(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 9]
33. ! [X0] : (old(X0) | rich(X0) | (~curious(X0) & generous(X0))) [flattening 32]
36. ! [X0] : ((strong(X0) <~> ~kind(X0)) | (rich(X0) <=> calm(X0))) [ennf transformation 12]
39. ! [X0] : (((kind(X0) | funny(X0)) | (old(X0) | strong(X0))) & ((~old(X0) & ~strong(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 1]
40. ! [X0] : ((kind(X0) | funny(X0) | old(X0) | strong(X0)) & ((~old(X0) & ~strong(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 39]
49. ! [X0] : ((generous(X0) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ~generous(X0))) [nnf transformation 5]
50. ! [X0] : ((generous(X0) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ~generous(X0))) [flattening 49]
53. ! [X0] : ((~generous(X0) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | generous(X0))) [nnf transformation 11]
54. ! [X0] : (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) [nnf transformation 36]
66. ~strong(X0) | ~kind(X0) [cnf transformation 40]
68. ~old(X0) | ~kind(X0) [cnf transformation 40]
82. ~happy(X0) | strong(X0) | ~generous(X0) [cnf transformation 50]
89. rich(X0) | old(X0) | generous(X0) [cnf transformation 33]
92. ~rich(X0) | generous(X0) | generous(X0) [cnf transformation 53]
94. ~generous(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 53]
99. kind(X0) | ~strong(X0) | rich(X0) | ~calm(X0) [cnf transformation 54]
109. ~old(alice) | kind(alice) [cnf transformation 17]
112. happy(alice) [cnf transformation 20]
118. calm(alice) [cnf transformation 24]
119. ~rich(X0) | generous(X0) [duplicate literal removal 92]
120. ~rich(X0) | ~generous(X0) [duplicate literal removal 94]
155. ~rich(X0) [subsumption resolution 119,120]
156. kind(X0) | ~strong(X0) | ~calm(X0) [subsumption resolution 99,155]
157. ~calm(X0) | ~strong(X0) [subsumption resolution 156,66]
166. 10 <=> calm(alice) [avatar definition]
168. calm(alice) <- (10) [avatar component clause 166]
181. ~old(alice) [subsumption resolution 109,68]
201. 10 [avatar split clause 118,166]
208. ~strong(alice) <- (10) [resolution 157,168]
216. strong(alice) | ~generous(alice) [resolution 82,112]
218. ~generous(alice) <- (10) [subsumption resolution 216,208]
220. generous(X1) | old(X1) [resolution 89,155]
223. old(alice) <- (10) [resolution 220,218]
224. $false <- (10) [subsumption resolution 223,181]
225. ~10 [avatar contradiction clause 224]
226. $false [avatar sat refutation 201,225]
% SZS output end Proof for 8942467243617772376208713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and not calm then someone is both wise and rich and vice versa.
If someone is not calm then someone is tall and vice versa.
If susan is either not generous or not strong then someone is not brave.
If lucy is not funny then paul is calm.
Everyone who is wise is both not patient and kind and vice versa.
Everyone who is calm is either humble or creative.
Everyone who is both not brave and funny is happy and vice versa.
Everyone who is generous is not generous or not quiet.
If fred is either wise or not happy then someone is either not quiet or not strong and vice versa.
Everyone who is either not humble or patient is calm or tall and vice versa.
Everyone who is creative is not rich and vice versa.
Everyone who is not patient is both not creative and not quiet and vice versa.
Everyone who is not kind or not creative is curious.
Everyone who is either not strong or creative is either quiet or wise.
Everyone who is tall or not tall is not curious and vice versa.
If someone is quiet then someone is either not rich or not calm.
Alice is either not calm or brave.
Someone is both happy and tall.
John is not quiet.
Alice is not curious or not happy.
Someone is either strong or not wise.
Someone is happy or not generous.
Mary is not rich or creative.
Someone is not old. | Paul is not patient. | contradiction | ((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((wise(X)&rich(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(tall(X))))&
(((~generous(susan)<~>~strong(susan)))=>(?[X]:(~brave(X))))&
((~funny(lucy))=>(calm(paul)))&
(![X]:(wise(X)<=>(~patient(X)&kind(X))))&
(![X]:(calm(X)=>(humble(X)<~>creative(X))))&
(![X]:((~brave(X)&funny(X))<=>happy(X)))&
(![X]:(generous(X)=>(~generous(X)|~quiet(X))))&
(((wise(fred)<~>~happy(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:((~humble(X)<~>patient(X))<=>(calm(X)|tall(X))))&
(![X]:(creative(X)<=>~rich(X)))&
(![X]:(~patient(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((~kind(X)|~creative(X))=>curious(X)))&
(![X]:((~strong(X)<~>creative(X))=>(quiet(X)<~>wise(X))))&
(![X]:((tall(X)|~tall(X))<=>~curious(X)))&
((?[X]:(quiet(X)))=>(?[X]:((~rich(X)<~>~calm(X)))))&
((~calm(alice)<~>brave(alice)))&
(?[X]:((happy(X)&tall(X))))&
(~quiet(john))&
((~curious(alice)|~happy(alice)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:((happy(X)|~generous(X))))&
((~rich(mary)|creative(mary)))&
(?[X]:(~old(X))) | ~patient(paul) | [
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 550750690499911818850047
% SZS output start Proof for 550750690499911818850047
12. ! [X0] : (~patient(X0) <=> (~quiet(X0) & ~creative(X0))) [input p11]
13. ! [X0] : ((~creative(X0) | ~kind(X0)) => curious(X0)) [input p12]
15. ! [X0] : ((~tall(X0) | tall(X0)) <=> ~curious(X0)) [input p14]
25. ~patient(paul) [input hypothesis]
35. ! [X0] : (curious(X0) | (creative(X0) & kind(X0))) [ennf transformation 13]
63. ! [X0] : ((~patient(X0) | (quiet(X0) | creative(X0))) & ((~quiet(X0) & ~creative(X0)) | patient(X0))) [nnf transformation 12]
64. ! [X0] : ((~patient(X0) | quiet(X0) | creative(X0)) & ((~quiet(X0) & ~creative(X0)) | patient(X0))) [flattening 63]
66. ! [X0] : (((~tall(X0) | tall(X0)) | curious(X0)) & (~curious(X0) | (tall(X0) & ~tall(X0)))) [nnf transformation 15]
67. ! [X0] : ((~tall(X0) | tall(X0) | curious(X0)) & (~curious(X0) | (tall(X0) & ~tall(X0)))) [flattening 66]
114. ~creative(X0) | patient(X0) [cnf transformation 64]
118. curious(X0) | creative(X0) [cnf transformation 35]
123. ~curious(X0) | ~tall(X0) [cnf transformation 67]
124. ~curious(X0) | tall(X0) [cnf transformation 67]
138. ~patient(paul) [cnf transformation 25]
235. ~curious(X0) [subsumption resolution 123,124]
296. creative(X0) [resolution 118,235]
297. patient(X0) [resolution 296,114]
301. $false [resolution 297,138]
% SZS output end Proof for 550750690499911818850047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not funny and vice versa.
If someone is either not curious or quiet then someone is not strong.
If susan is either not calm or not rich then susan is old or wise and vice versa.
Everyone who is both not happy and not old is kind.
If someone is not kind or not creative then mary is old or not humble and vice versa.
If alice is brave then susan is either happy or not patient.
Everyone who is brave or wise is curious and vice versa.
If lucy is kind or not generous then fred is calm and vice versa.
Everyone who is either quiet or not tall is either tall or kind.
If john is not quiet then someone is either wise or rich and vice versa.
Everyone who is either not wise or brave is not generous.
If someone is kind or not old then someone is either funny or calm and vice versa.
If lucy is either old or not strong then someone is either not old or generous.
If someone is both quiet and not old then mary is curious and vice versa.
If fred is either not creative or old then someone is patient or old and vice versa.
Everyone who is curious or rich is not strong or not curious.
Alice is old.
Paul is funny or generous.
Someone is not generous or old.
Paul is both creative and not brave.
John is both not kind and old.
Fred is quiet or not happy.
Fred is both wise and brave. | Paul is generous. | neutral | (![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:(~strong(X))))&
(((~calm(susan)<~>~rich(susan)))<=>((old(susan)|wise(susan))))&
(![X]:((~happy(X)&~old(X))=>kind(X)))&
((?[X]:((~kind(X)|~creative(X))))<=>((old(mary)|~humble(mary))))&
((brave(alice))=>((happy(susan)<~>~patient(susan))))&
(![X]:((brave(X)|wise(X))<=>curious(X)))&
(((kind(lucy)|~generous(lucy)))<=>(calm(fred)))&
(![X]:((quiet(X)<~>~tall(X))=>(tall(X)<~>kind(X))))&
((~quiet(john))<=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>brave(X))=>~generous(X)))&
((?[X]:((kind(X)|~old(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
(((old(lucy)<~>~strong(lucy)))=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>(curious(mary)))&
(((~creative(fred)<~>old(fred)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((curious(X)|rich(X))=>(~strong(X)|~curious(X))))&
(old(alice))&
((funny(paul)|generous(paul)))&
(?[X]:((~generous(X)|old(X))))&
((creative(paul)&~brave(paul)))&
((~kind(john)&old(john)))&
((quiet(fred)|~happy(fred)))&
((wise(fred)&brave(fred))) | generous(paul) | [] | null | 0 |
If paul is either happy or quiet then paul is either generous or not funny.
Everyone who is both not generous and rich is not humble and vice versa.
If alice is both generous and humble then someone is wise or not humble.
If fred is kind or wise then someone is either patient or not humble.
If john is calm or not strong then alice is both patient and quiet and vice versa.
Everyone who is not creative or not rich is not generous or not brave and vice versa.
Everyone who is either humble or not tall is curious and vice versa.
Everyone who is either funny or not wise is both not old and humble and vice versa.
If fred is creative or not rich then fred is generous and vice versa.
If someone is rich or not brave then paul is not old or wise.
Everyone who is both not curious and rich is either strong or quiet and vice versa.
Everyone who is both brave and not patient is either not rich or funny and vice versa.
If someone is both not wise and not strong then alice is either not patient or kind.
Everyone who is not happy or not generous is generous.
Everyone who is both creative and patient is either curious or tall.
Everyone who is not strong or rich is either not creative or not curious.
Someone is both creative and calm.
Mary is either not quiet or not humble.
Lucy is not happy.
Someone is both quiet and tall.
Fred is not curious.
Susan is both rich and not brave.
Someone is both humble and not calm.
Someone is generous or strong. | Susan is curious. | entailment | (((happy(paul)<~>quiet(paul)))=>((generous(paul)<~>~funny(paul))))&
(![X]:((~generous(X)&rich(X))<=>~humble(X)))&
(((generous(alice)&humble(alice)))=>(?[X]:((wise(X)|~humble(X)))))&
(((kind(fred)|wise(fred)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(((calm(john)|~strong(john)))<=>((patient(alice)&quiet(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(~generous(X)|~brave(X))))&
(![X]:((humble(X)<~>~tall(X))<=>curious(X)))&
(![X]:((funny(X)<~>~wise(X))<=>(~old(X)&humble(X))))&
(((creative(fred)|~rich(fred)))<=>(generous(fred)))&
((?[X]:((rich(X)|~brave(X))))=>((~old(paul)|wise(paul))))&
(![X]:((~curious(X)&rich(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((brave(X)&~patient(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~patient(alice)<~>kind(alice))))&
(![X]:((~happy(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)&patient(X))=>(curious(X)<~>tall(X))))&
(![X]:((~strong(X)|rich(X))=>(~creative(X)<~>~curious(X))))&
(?[X]:((creative(X)&calm(X))))&
((~quiet(mary)<~>~humble(mary)))&
(~happy(lucy))&
(?[X]:((quiet(X)&tall(X))))&
(~curious(fred))&
((rich(susan)&~brave(susan)))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:((generous(X)|strong(X)))) | curious(susan) | [
"p5",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2803074829094113469347713
% SZS output start Proof for 2803074829094113469347713
6. ! [X0] : ((~rich(X0) | ~creative(X0)) <=> (~brave(X0) | ~generous(X0))) [input p5]
16. ! [X0] : ((rich(X0) | ~strong(X0)) => (~creative(X0) <~> ~curious(X0))) [input p15]
22. ~brave(susan) & rich(susan) [input p21]
25. ~curious(susan) [input hypothesis]
36. ! [X0] : ((~creative(X0) <~> ~curious(X0)) | (~rich(X0) & strong(X0))) [ennf transformation 16]
47. ! [X0] : (((~rich(X0) | ~creative(X0)) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | (rich(X0) & creative(X0)))) [nnf transformation 6]
48. ! [X0] : ((~rich(X0) | ~creative(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | (rich(X0) & creative(X0)))) [flattening 47]
60. ! [X0] : (((curious(X0) | creative(X0)) & (~curious(X0) | ~creative(X0))) | (~rich(X0) & strong(X0))) [nnf transformation 36]
90. ~creative(X0) | ~rich(X0) | brave(X0) [cnf transformation 48]
127. ~rich(X0) | creative(X0) | curious(X0) [cnf transformation 60]
136. rich(susan) [cnf transformation 22]
137. ~brave(susan) [cnf transformation 22]
141. ~curious(susan) [cnf transformation 25]
399. 40 <=> creative(susan) [avatar definition]
401. creative(susan) <- (40) [avatar component clause 399]
409. creative(susan) | curious(susan) [resolution 127,136]
428. creative(susan) [subsumption resolution 409,141]
429. 40 [avatar split clause 428,399]
478. ~rich(susan) | brave(susan) <- (40) [resolution 401,90]
480. brave(susan) <- (40) [subsumption resolution 478,136]
481. $false <- (40) [subsumption resolution 480,137]
482. ~40 [avatar contradiction clause 481]
483. $false [avatar sat refutation 429,482]
% SZS output end Proof for 2803074829094113469347713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and tall then john is both curious and not kind and vice versa.
If someone is both not patient and not creative then john is either not kind or not curious.
Everyone who is not calm is not wise or calm and vice versa.
If someone is either happy or old then john is not patient or not curious.
Everyone who is old or happy is either wise or not quiet and vice versa.
Everyone who is both not rich and wise is funny.
Everyone who is either humble or happy is creative or not calm.
If john is both not calm and not old then someone is calm.
Everyone who is both curious and not old is both not tall and not quiet.
Everyone who is not old or not curious is not humble or happy.
If john is brave then someone is either not brave or generous.
Everyone who is not quiet or funny is both not patient and not tall.
If fred is either kind or not kind then paul is not old.
If someone is either old or not creative then someone is generous or not curious.
Everyone who is either not happy or brave is both humble and not patient and vice versa.
Alice is both generous and funny.
Someone is either funny or strong.
Susan is rich.
Alice is not curious or not tall.
Susan is not kind or generous.
Paul is not patient or not calm.
Susan is not calm. | John is not quiet. | entailment | ((?[X]:((patient(X)&tall(X))))<=>((curious(john)&~kind(john))))&
((?[X]:((~patient(X)&~creative(X))))=>((~kind(john)<~>~curious(john))))&
(![X]:(~calm(X)<=>(~wise(X)|calm(X))))&
((?[X]:((happy(X)<~>old(X))))=>((~patient(john)|~curious(john))))&
(![X]:((old(X)|happy(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~rich(X)&wise(X))=>funny(X)))&
(![X]:((humble(X)<~>happy(X))=>(creative(X)|~calm(X))))&
(((~calm(john)&~old(john)))=>(?[X]:(calm(X))))&
(![X]:((curious(X)&~old(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~old(X)|~curious(X))=>(~humble(X)|happy(X))))&
((brave(john))=>(?[X]:((~brave(X)<~>generous(X)))))&
(![X]:((~quiet(X)|funny(X))=>(~patient(X)&~tall(X))))&
(((kind(fred)<~>~kind(fred)))=>(~old(paul)))&
((?[X]:((old(X)<~>~creative(X))))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(humble(X)&~patient(X))))&
((generous(alice)&funny(alice)))&
(?[X]:((funny(X)<~>strong(X))))&
(rich(susan))&
((~curious(alice)|~tall(alice)))&
((~kind(susan)|generous(susan)))&
((~patient(paul)|~calm(paul)))&
(~calm(susan)) | ~quiet(john) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7996654038414748081656523
% SZS output start Proof for 7996654038414748081656523
3. ! [X0] : (~calm(X0) <=> (calm(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((happy(X0) | old(X0)) <=> (wise(X0) <~> ~quiet(X0))) [input p4]
8. (~old(john) & ~calm(john)) => ? [X0] : calm(X0) [input p7]
23. quiet(john) [input hypothesis]
32. ? [X0] : calm(X0) | (old(john) | calm(john)) [ennf transformation 8]
33. ? [X0] : calm(X0) | old(john) | calm(john) [flattening 32]
48. ! [X0] : ((~calm(X0) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | calm(X0))) [nnf transformation 3]
49. ! [X0] : ((~calm(X0) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | calm(X0))) [flattening 48]
51. ! [X0] : (((happy(X0) | old(X0)) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~happy(X0) & ~old(X0)))) [nnf transformation 5]
52. ! [X0] : ((happy(X0) | old(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~happy(X0) & ~old(X0)))) [flattening 51]
54. ? [X0] : calm(X0) => calm(sK1) [choice axiom]
55. calm(sK1) | old(john) | calm(john) [skolemisation 33,54]
75. calm(X0) | ~wise(X0) | calm(X0) [cnf transformation 49]
77. ~calm(X0) | ~calm(X0) [cnf transformation 49]
80. ~quiet(X0) | wise(X0) | ~old(X0) [cnf transformation 52]
88. calm(sK1) | old(john) | calm(john) [cnf transformation 55]
117. quiet(john) [cnf transformation 23]
120. calm(X0) | ~wise(X0) [duplicate literal removal 75]
121. ~calm(X0) [duplicate literal removal 77]
150. ~wise(X0) [subsumption resolution 120,121]
165. ~quiet(X0) | ~old(X0) [subsumption resolution 80,150]
166. old(john) | calm(john) [subsumption resolution 88,121]
167. old(john) [subsumption resolution 166,121]
243. ~old(john) [resolution 165,117]
244. $false [subsumption resolution 243,167]
% SZS output end Proof for 7996654038414748081656523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is happy or not happy then someone is kind and vice versa.
If someone is either rich or wise then alice is strong or not brave and vice versa.
If mary is both wise and brave then someone is both brave and not happy.
If someone is both creative and tall then someone is strong.
Everyone who is both not rich and calm is not creative or generous and vice versa.
If john is either not brave or not funny then someone is either funny or not wise and vice versa.
If lucy is both not strong and humble then someone is either curious or brave.
Everyone who is generous is old and vice versa.
Everyone who is not creative is either not creative or not funny.
Everyone who is not brave is either not brave or not old and vice versa.
Everyone who is both quiet and creative is both humble and kind.
Everyone who is not creative or funny is both calm and not kind.
Everyone who is either not creative or tall is kind and vice versa.
If someone is both not rich and not generous then someone is not strong and vice versa.
Everyone who is funny or not brave is either brave or strong.
Everyone who is either curious or not curious is not funny or not generous.
Someone is kind.
Someone is either brave or not quiet.
Fred is not quiet or kind.
John is either not kind or patient.
John is not rich or tall.
Someone is not happy. | Fred is calm. | entailment | (((happy(alice)|~happy(alice)))<=>(?[X]:(kind(X))))&
((?[X]:((rich(X)<~>wise(X))))<=>((strong(alice)|~brave(alice))))&
(((wise(mary)&brave(mary)))=>(?[X]:((brave(X)&~happy(X)))))&
((?[X]:((creative(X)&tall(X))))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)&calm(X))<=>(~creative(X)|generous(X))))&
(((~brave(john)<~>~funny(john)))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(((~strong(lucy)&humble(lucy)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~creative(X)=>(~creative(X)<~>~funny(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~old(X))))&
(![X]:((quiet(X)&creative(X))=>(humble(X)&kind(X))))&
(![X]:((~creative(X)|funny(X))=>(calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>tall(X))<=>kind(X)))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~funny(X)|~generous(X))))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)<~>~quiet(X))))&
((~quiet(fred)|kind(fred)))&
((~kind(john)<~>patient(john)))&
((~rich(john)|tall(john)))&
(?[X]:(~happy(X))) | calm(fred) | [
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4842299706883349743955248
% SZS output start Proof for 4842299706883349743955248
5. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (generous(X0) | ~creative(X0))) [input p4]
8. ! [X0] : (generous(X0) <=> old(X0)) [input p7]
10. ! [X0] : (~brave(X0) <=> (~brave(X0) <~> ~old(X0))) [input p9]
23. ~calm(fred) [input hypothesis]
53. ! [X0] : (((calm(X0) & ~rich(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 5]
54. ! [X0] : (((calm(X0) & ~rich(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | ~calm(X0) | rich(X0))) [flattening 53]
62. ! [X0] : ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))) [nnf transformation 8]
64. ! [X0] : ((~brave(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | brave(X0))) [nnf transformation 10]
97. ~generous(X0) | calm(X0) [cnf transformation 54]
109. ~old(X0) | generous(X0) [cnf transformation 62]
113. old(X0) | brave(X0) | brave(X0) [cnf transformation 64]
115. ~brave(X0) | ~brave(X0) | old(X0) [cnf transformation 64]
143. ~calm(fred) [cnf transformation 23]
147. old(X0) | brave(X0) [duplicate literal removal 113]
148. ~brave(X0) | old(X0) [duplicate literal removal 115]
262. old(X0) [subsumption resolution 147,148]
327. generous(X0) [resolution 109,262]
330. calm(X1) [resolution 327,97]
335. $false [resolution 330,143]
% SZS output end Proof for 4842299706883349743955248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not happy or calm then someone is either not curious or not brave and vice versa.
If someone is both not brave and old then mary is either not rich or not wise and vice versa.
Everyone who is both not brave and humble is either funny or not tall.
Everyone who is happy is brave or not old and vice versa.
Everyone who is either not patient or not generous is old.
If someone is either not rich or not generous then mary is both not generous and old.
If someone is not curious then alice is both not strong and not curious and vice versa.
Everyone who is wise or not wise is not creative or wise and vice versa.
Everyone who is not brave is both not kind and strong and vice versa.
Everyone who is either humble or rich is both quiet and not quiet and vice versa.
If someone is either wise or humble then susan is creative and vice versa.
If fred is tall then alice is not humble and vice versa.
If john is not strong then someone is either not calm or patient and vice versa.
If someone is both calm and not old then mary is not kind and vice versa.
If susan is both quiet and not happy then mary is either creative or not generous and vice versa.
Everyone who is either not kind or quiet is not generous.
Someone is either not creative or generous.
Fred is not brave.
John is not funny or tall.
John is not strong.
Fred is not funny or not calm.
Paul is either not rich or tall.
Susan is not tall or not curious.
Susan is either humble or funny. | Mary is generous. | neutral | (((~happy(paul)<~>calm(paul)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:((~brave(X)&old(X))))<=>((~rich(mary)<~>~wise(mary))))&
(![X]:((~brave(X)&humble(X))=>(funny(X)<~>~tall(X))))&
(![X]:(happy(X)<=>(brave(X)|~old(X))))&
(![X]:((~patient(X)<~>~generous(X))=>old(X)))&
((?[X]:((~rich(X)<~>~generous(X))))=>((~generous(mary)&old(mary))))&
((?[X]:(~curious(X)))<=>((~strong(alice)&~curious(alice))))&
(![X]:((wise(X)|~wise(X))<=>(~creative(X)|wise(X))))&
(![X]:(~brave(X)<=>(~kind(X)&strong(X))))&
(![X]:((humble(X)<~>rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(creative(susan)))&
((tall(fred))<=>(~humble(alice)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(~kind(mary)))&
(((quiet(susan)&~happy(susan)))<=>((creative(mary)<~>~generous(mary))))&
(![X]:((~kind(X)<~>quiet(X))=>~generous(X)))&
(?[X]:((~creative(X)<~>generous(X))))&
(~brave(fred))&
((~funny(john)|tall(john)))&
(~strong(john))&
((~funny(fred)|~calm(fred)))&
((~rich(paul)<~>tall(paul)))&
((~tall(susan)|~curious(susan)))&
((humble(susan)<~>funny(susan))) | generous(mary) | [] | null | 0 |
If mary is both generous and not brave then someone is either generous or not happy.
Everyone who is not strong is both not happy and curious and vice versa.
If mary is happy then mary is not quiet or not creative.
If someone is not tall then someone is either patient or not generous and vice versa.
Everyone who is both not strong and calm is not wise and vice versa.
Everyone who is either creative or not wise is humble and vice versa.
Everyone who is both not old and funny is either not humble or patient and vice versa.
Everyone who is brave is old.
If someone is either funny or brave then someone is either generous or not calm and vice versa.
If susan is either generous or not quiet then someone is not brave or tall and vice versa.
Everyone who is quiet is either not funny or wise and vice versa.
Everyone who is not calm is not tall and vice versa.
Everyone who is either generous or not rich is both calm and not calm and vice versa.
Everyone who is both rich and not generous is either quiet or not kind and vice versa.
Everyone who is wise is either wise or not funny and vice versa.
If someone is either kind or quiet then paul is generous.
Mary is calm.
Someone is tall or quiet.
Fred is either happy or not kind.
Mary is not rich.
Someone is not calm or not creative.
Someone is either brave or happy.
Paul is either humble or brave. | Paul is rich. | contradiction | (((generous(mary)&~brave(mary)))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(~strong(X)<=>(~happy(X)&curious(X))))&
((happy(mary))=>((~quiet(mary)|~creative(mary))))&
((?[X]:(~tall(X)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
(![X]:((~strong(X)&calm(X))<=>~wise(X)))&
(![X]:((creative(X)<~>~wise(X))<=>humble(X)))&
(![X]:((~old(X)&funny(X))<=>(~humble(X)<~>patient(X))))&
(![X]:(brave(X)=>old(X)))&
((?[X]:((funny(X)<~>brave(X))))<=>(?[X]:((generous(X)<~>~calm(X)))))&
(((generous(susan)<~>~quiet(susan)))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:(quiet(X)<=>(~funny(X)<~>wise(X))))&
(![X]:(~calm(X)<=>~tall(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(calm(X)&~calm(X))))&
(![X]:((rich(X)&~generous(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~funny(X))))&
((?[X]:((kind(X)<~>quiet(X))))=>(generous(paul)))&
(calm(mary))&
(?[X]:((tall(X)|quiet(X))))&
((happy(fred)<~>~kind(fred)))&
(~rich(mary))&
(?[X]:((~calm(X)|~creative(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((humble(paul)<~>brave(paul))) | rich(paul) | [
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2200199543147714444231593
% SZS output start Proof for 2200199543147714444231593
13. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (~calm(X0) & calm(X0))) [input p12]
14. ! [X0] : ((~generous(X0) & rich(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p13]
16. ? [X0] : (kind(X0) <~> quiet(X0)) => generous(paul) [input p15]
20. ~rich(mary) [input p19]
24. rich(paul) [input hypothesis]
32. generous(paul) | ! [X0] : (kind(X0) <=> quiet(X0)) [ennf transformation 16]
59. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 13]
60. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 59]
61. ! [X0] : (((~generous(X0) & rich(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (generous(X0) | ~rich(X0)))) [nnf transformation 14]
62. ! [X0] : (((~generous(X0) & rich(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | generous(X0) | ~rich(X0))) [flattening 61]
64. generous(paul) | ! [X0] : ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))) [nnf transformation 32]
118. calm(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 60]
119. calm(X0) | generous(X0) | rich(X0) [cnf transformation 60]
120. ~rich(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 60]
121. ~calm(X0) | generous(X0) | rich(X0) [cnf transformation 60]
126. ~kind(X0) | rich(X0) | ~quiet(X0) [cnf transformation 62]
129. ~generous(X0) | quiet(X0) | kind(X0) [cnf transformation 62]
134. generous(paul) | quiet(X0) | ~kind(X0) [cnf transformation 64]
135. generous(paul) | kind(X0) | ~quiet(X0) [cnf transformation 64]
140. ~rich(mary) [cnf transformation 20]
146. rich(paul) [cnf transformation 24]
150. 1 <=> generous(mary) [avatar definition]
151. generous(mary) <- (1) [avatar component clause 150]
172. 6 <=> quiet(mary) [avatar definition]
269. rich(X0) | generous(X0) [subsumption resolution 119,121]
270. ~rich(X0) | ~generous(X0) [subsumption resolution 118,120]
275. 28 <=> ! [X0] : (kind(X0) | ~quiet(X0)) [avatar definition]
276. ~quiet(X0) | kind(X0) <- (28) [avatar component clause 275]
278. 29 <=> generous(paul) [avatar definition]
281. 28 | 29 [avatar split clause 135,278,275]
283. 30 <=> ! [X0] : (quiet(X0) | ~kind(X0)) [avatar definition]
284. ~kind(X0) | quiet(X0) <- (30) [avatar component clause 283]
285. 30 | 29 [avatar split clause 134,278,283]
339. generous(mary) [resolution 269,140]
342. 1 [avatar split clause 339,150]
343. ~generous(paul) [resolution 270,146]
347. ~29 [avatar split clause 343,278]
453. quiet(mary) | kind(mary) <- (1) [resolution 129,151]
454. kind(mary) <- (1, 28) [subsumption resolution 453,276]
456. rich(mary) | ~quiet(mary) <- (1, 28) [resolution 454,126]
457. quiet(mary) <- (1, 28, 30) [resolution 454,284]
460. ~quiet(mary) <- (1, 28) [subsumption resolution 456,140]
461. ~6 | ~1 | ~28 [avatar split clause 460,275,150,172]
462. 6 | ~1 | ~28 | ~30 [avatar split clause 457,283,275,150,172]
463. $false [avatar sat refutation 281,285,342,347,461,462]
% SZS output end Proof for 2200199543147714444231593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits