premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not strong or not tall is both not happy and not patient and vice versa.
Everyone who is either not creative or generous is either not funny or not humble and vice versa.
If mary is either not generous or not brave then mary is happy and vice versa.
Everyone who is strong is not calm or not humble.
Everyone who is not creative is either not calm or brave and vice versa.
Everyone who is patient is either kind or generous and vice versa.
If alice is not creative or generous then someone is not happy.
Everyone who is either not brave or not old is either not tall or humble and vice versa.
Everyone who is either not patient or generous is both not humble and patient and vice versa.
Everyone who is both patient and not happy is both not creative and creative.
If susan is not generous then mary is not generous or strong and vice versa.
If someone is both happy and strong then john is strong and vice versa.
If someone is either creative or not strong then mary is both happy and not creative.
If fred is not generous then someone is not curious or old and vice versa.
Everyone who is kind is humble and vice versa.
If someone is both not patient and curious then fred is either not funny or not tall and vice versa.
Someone is both not happy and old.
Alice is either not creative or not curious.
Lucy is both happy and kind.
Someone is not rich or generous.
Someone is both tall and not quiet.
Someone is strong or generous.
Someone is either curious or not tall.
John is either not curious or not kind. | Fred is not calm. | entailment | (![X]:((~strong(X)|~tall(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~funny(X)<~>~humble(X))))&
(((~generous(mary)<~>~brave(mary)))<=>(happy(mary)))&
(![X]:(strong(X)=>(~calm(X)|~humble(X))))&
(![X]:(~creative(X)<=>(~calm(X)<~>brave(X))))&
(![X]:(patient(X)<=>(kind(X)<~>generous(X))))&
(((~creative(alice)|generous(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~humble(X)&patient(X))))&
(![X]:((patient(X)&~happy(X))=>(~creative(X)&creative(X))))&
((~generous(susan))<=>((~generous(mary)|strong(mary))))&
((?[X]:((happy(X)&strong(X))))<=>(strong(john)))&
((?[X]:((creative(X)<~>~strong(X))))=>((happy(mary)&~creative(mary))))&
((~generous(fred))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:(kind(X)<=>humble(X)))&
((?[X]:((~patient(X)&curious(X))))<=>((~funny(fred)<~>~tall(fred))))&
(?[X]:((~happy(X)&old(X))))&
((~creative(alice)<~>~curious(alice)))&
((happy(lucy)&kind(lucy)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:((curious(X)<~>~tall(X))))&
((~curious(john)<~>~kind(john))) | ~calm(fred) | [
"p0",
"p3",
"p8",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3140831758892847128430198
% SZS output start Proof for 3140831758892847128430198
1. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (~patient(X0) & ~happy(X0))) [input p0]
4. ! [X0] : (strong(X0) => (~humble(X0) | ~calm(X0))) [input p3]
9. ! [X0] : ((~patient(X0) <~> generous(X0)) <=> (patient(X0) & ~humble(X0))) [input p8]
14. ~generous(fred) <=> ? [X0] : (old(X0) | ~curious(X0)) [input p13]
17. ? [X0] : (old(X0) & ~happy(X0)) [input p16]
25. calm(fred) [input hypothesis]
28. ! [X0] : ((~humble(X0) | ~calm(X0)) | ~strong(X0)) [ennf transformation 4]
29. ! [X0] : (~humble(X0) | ~calm(X0) | ~strong(X0)) [flattening 28]
34. ! [X0] : (((~tall(X0) | ~strong(X0)) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | (tall(X0) & strong(X0)))) [nnf transformation 1]
35. ! [X0] : ((~tall(X0) | ~strong(X0) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | (tall(X0) & strong(X0)))) [flattening 34]
43. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (~patient(X0) | humble(X0))) & ((patient(X0) & ~humble(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [nnf transformation 9]
44. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ~patient(X0) | humble(X0)) & ((patient(X0) & ~humble(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [flattening 43]
52. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & (? [X0] : (old(X0) | ~curious(X0)) | generous(fred)) [nnf transformation 14]
53. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & (? [X1] : (old(X1) | ~curious(X1)) | generous(fred)) [rectify 52]
54. ? [X1] : (old(X1) | ~curious(X1)) => (old(sK2) | ~curious(sK2)) [choice axiom]
55. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & ((old(sK2) | ~curious(sK2)) | generous(fred)) [skolemisation 53,54]
61. ? [X0] : (old(X0) & ~happy(X0)) => (old(sK4) & ~happy(sK4)) [choice axiom]
62. old(sK4) & ~happy(sK4) [skolemisation 17,61]
74. ~patient(X0) | strong(X0) [cnf transformation 35]
89. ~calm(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 29]
110. patient(X0) | generous(X0) | patient(X0) [cnf transformation 44]
112. generous(X0) | ~patient(X0) | ~patient(X0) | humble(X0) [cnf transformation 44]
128. ~generous(fred) | ~old(X0) [cnf transformation 55]
138. old(sK4) [cnf transformation 62]
149. calm(fred) [cnf transformation 25]
150. generous(X0) | patient(X0) [duplicate literal removal 110]
151. ~patient(X0) | generous(X0) | humble(X0) [duplicate literal removal 112]
228. 16 <=> ! [X0] : ~old(X0) [avatar definition]
229. ~old(X0) <- (16) [avatar component clause 228]
231. 17 <=> generous(fred) [avatar definition]
233. ~generous(fred) <- (~17) [avatar component clause 231]
234. 16 | ~17 [avatar split clause 128,231,228]
318. patient(fred) <- (~17) [resolution 150,233]
333. strong(fred) <- (~17) [resolution 318,74]
336. ~humble(fred) | ~strong(fred) [resolution 89,149]
337. ~humble(fred) <- (~17) [subsumption resolution 336,333]
409. generous(fred) | humble(fred) <- (~17) [resolution 151,318]
414. humble(fred) <- (~17) [subsumption resolution 409,233]
415. $false <- (~17) [subsumption resolution 414,337]
416. 17 [avatar contradiction clause 415]
419. $false <- (16) [resolution 229,138]
420. ~16 [avatar contradiction clause 419]
421. $false [avatar sat refutation 234,416,420]
% SZS output end Proof for 3140831758892847128430198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous is both not tall and not generous and vice versa.
If paul is strong or humble then someone is tall or not generous and vice versa.
Everyone who is either not happy or generous is both strong and old.
Everyone who is both strong and tall is both happy and calm and vice versa.
Everyone who is not kind is either strong or not rich and vice versa.
Everyone who is either rich or strong is both patient and not funny and vice versa.
If alice is generous then someone is either generous or not wise.
If mary is calm or not happy then someone is creative or not generous and vice versa.
If lucy is both quiet and kind then john is not old.
Everyone who is generous or not humble is strong or not humble.
Everyone who is either kind or not kind is both generous and not patient.
If someone is both not funny and not brave then someone is either generous or not kind and vice versa.
Everyone who is not kind or kind is both not funny and rich.
If someone is generous or not rich then someone is not calm or not rich.
Everyone who is both calm and brave is not calm or humble.
Alice is either not strong or not kind.
Someone is not creative or funny.
Fred is either curious or old.
Someone is not wise or not humble.
Someone is calm or not patient.
Lucy is creative or not strong. | Alice is not kind. | entailment | (![X]:(~generous(X)<=>(~tall(X)&~generous(X))))&
(((strong(paul)|humble(paul)))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~happy(X)<~>generous(X))=>(strong(X)&old(X))))&
(![X]:((strong(X)&tall(X))<=>(happy(X)&calm(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(![X]:((kind(X)<~>~kind(X))=>(generous(X)&~patient(X))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~kind(X)|kind(X))=>(~funny(X)&rich(X))))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((calm(X)&brave(X))=>(~calm(X)|humble(X))))&
((~strong(alice)<~>~kind(alice)))&
(?[X]:((~creative(X)|funny(X))))&
((curious(fred)<~>old(fred)))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((calm(X)|~patient(X))))&
((creative(lucy)|~strong(lucy))) | ~kind(alice) | [
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4598110128855360509935635
% SZS output start Proof for 4598110128855360509935635
6. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (~funny(X0) & patient(X0))) [input p5]
11. ! [X0] : ((kind(X0) <~> ~kind(X0)) => (~patient(X0) & generous(X0))) [input p10]
13. ! [X0] : ((kind(X0) | ~kind(X0)) => (rich(X0) & ~funny(X0))) [input p12]
16. ~strong(alice) <~> ~kind(alice) [input p15]
22. kind(alice) [input hypothesis]
30. ! [X0] : ((~patient(X0) & generous(X0)) | (kind(X0) <=> ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((rich(X0) & ~funny(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 13]
46. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [flattening 46]
56. ! [X0] : ((~patient(X0) & generous(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
65. (kind(alice) | strong(alice)) & (~kind(alice) | ~strong(alice)) [nnf transformation 16]
92. ~rich(X0) | strong(X0) | patient(X0) [cnf transformation 47]
108. ~patient(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
109. ~patient(X0) | kind(X0) | kind(X0) [cnf transformation 56]
118. rich(X0) | kind(X0) [cnf transformation 31]
119. ~kind(X0) | rich(X0) [cnf transformation 31]
123. ~kind(alice) | ~strong(alice) [cnf transformation 65]
131. kind(alice) [cnf transformation 22]
135. ~patient(X0) | ~kind(X0) [duplicate literal removal 108]
136. ~patient(X0) | kind(X0) [duplicate literal removal 109]
200. ~patient(X0) [subsumption resolution 135,136]
231. rich(X0) [subsumption resolution 118,119]
243. 23 <=> strong(alice) [avatar definition]
244. ~strong(alice) <- (~23) [avatar component clause 243]
247. 24 <=> kind(alice) [avatar definition]
251. ~23 | ~24 [avatar split clause 123,247,243]
281. 24 [avatar split clause 131,247]
322. strong(X0) | patient(X0) [resolution 92,231]
323. strong(X0) [subsumption resolution 322,200]
328. $false <- (~23) [resolution 323,244]
331. 23 [avatar contradiction clause 328]
333. $false [avatar sat refutation 251,281,331]
% SZS output end Proof for 4598110128855360509935635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa. Everyone who is old is either happy or not creative. Everyone who is both old and wise is both funny and not humble and vice versa. Everyone who is tall or brave is not kind. If someone is either generous or kind then alice is either strong or not strong. Everyone who is calm is funny. Everyone who is funny or not wise is either wise or quiet. Everyone who is either brave or old is humble or not tall and vice versa. Everyone who is either tall or not funny is either brave or not generous. If someone is calm or not quiet then fred is calm. Everyone who is either not wise or not rich is funny. Everyone who is both strong and not generous is not tall. Everyone who is funny or not humble is not calm or generous and vice versa. If someone is generous then john is tall and vice versa. If alice is both not humble and not tall then fred is not rich or not humble. Everyone who is brave or not brave is not funny or not wise. Someone is both not humble and happy. John is creative. Someone is kind. Fred is either not generous or quiet. John is tall or not humble. Fred is both generous and not kind. Someone is not generous or rich. Someone is humble. | Alice is tall. | neutral | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&wise(X))<=>(funny(X)&~humble(X))))&
(![X]:((tall(X)|brave(X))=>~kind(X)))&
((?[X]:((generous(X)<~>kind(X))))=>((strong(alice)<~>~strong(alice))))&
(![X]:(calm(X)=>funny(X)))&
(![X]:((funny(X)|~wise(X))=>(wise(X)<~>quiet(X))))&
(![X]:((brave(X)<~>old(X))<=>(humble(X)|~tall(X))))&
(![X]:((tall(X)<~>~funny(X))=>(brave(X)<~>~generous(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(calm(fred)))&
(![X]:((~wise(X)<~>~rich(X))=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(?[X]:((~humble(X)&happy(X))))&
(creative(john))&
(?[X]:(kind(X)))&
((~generous(fred)<~>quiet(fred)))&
((tall(john)|~humble(john)))&
((generous(fred)&~kind(fred)))&
(?[X]:((~generous(X)|rich(X))))&
(?[X]:(humble(X))) | tall(alice) | [] | null | 0 |
Everyone who is either humble or kind is both not strong and strong and vice versa. Everyone who is not generous or not quiet is either strong or kind and vice versa. Everyone who is not wise or not creative is both not funny and strong and vice versa. If mary is kind or not patient then alice is either tall or curious and vice versa. Everyone who is not creative is both brave and kind and vice versa. Everyone who is not funny or not patient is not rich and vice versa. Everyone who is not patient or not curious is not happy and vice versa. If john is happy or not creative then someone is wise. Everyone who is not tall or rich is not rich and vice versa. Everyone who is either not happy or not old is calm and vice versa. If mary is both brave and old then someone is either not strong or brave and vice versa. Everyone who is funny is not creative or kind and vice versa. If someone is both creative and calm then someone is either quiet or not calm and vice versa. Everyone who is either not humble or not brave is not strong and vice versa. If john is funny or humble then mary is either quiet or old and vice versa. Everyone who is calm or not brave is either not tall or not happy and vice versa. Someone is not wise. Someone is brave. Someone is both not kind and not rich. Someone is creative or not humble. Someone is patient. | John is not happy. | neutral | (![X]:((humble(X)<~>kind(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(strong(X)<~>kind(X))))&
(![X]:((~wise(X)|~creative(X))<=>(~funny(X)&strong(X))))&
(((kind(mary)|~patient(mary)))<=>((tall(alice)<~>curious(alice))))&
(![X]:(~creative(X)<=>(brave(X)&kind(X))))&
(![X]:((~funny(X)|~patient(X))<=>~rich(X)))&
(![X]:((~patient(X)|~curious(X))<=>~happy(X)))&
(((happy(john)|~creative(john)))=>(?[X]:(wise(X))))&
(![X]:((~tall(X)|rich(X))<=>~rich(X)))&
(![X]:((~happy(X)<~>~old(X))<=>calm(X)))&
(((brave(mary)&old(mary)))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(funny(X)<=>(~creative(X)|kind(X))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>~brave(X))<=>~strong(X)))&
(((funny(john)|humble(john)))<=>((quiet(mary)<~>old(mary))))&
(![X]:((calm(X)|~brave(X))<=>(~tall(X)<~>~happy(X))))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:(patient(X))) | ~happy(john) | [] | null | 0 |
Everyone who is curious or calm is both kind and old.
If someone is patient or not tall then john is either not quiet or not wise.
Everyone who is both not creative and patient is either not strong or rich and vice versa.
Everyone who is both not curious and not calm is either creative or not humble and vice versa.
If someone is wise or rich then alice is tall or creative and vice versa.
If alice is not humble or not creative then someone is either quiet or not strong.
Everyone who is happy is not humble or not old and vice versa.
Everyone who is either curious or tall is calm or happy.
If fred is not generous then alice is brave or not humble and vice versa.
Everyone who is not humble is both not creative and not curious.
If someone is both tall and brave then someone is generous or wise.
Everyone who is either not humble or kind is both kind and not humble and vice versa.
If someone is not calm then someone is not brave or kind and vice versa.
Everyone who is rich or wise is either not rich or not tall.
Someone is both funny and not old.
Fred is not kind or not curious.
Someone is either not humble or humble.
Mary is not funny. | Alice is funny. | neutral | (![X]:((curious(X)|calm(X))=>(kind(X)&old(X))))&
((?[X]:((patient(X)|~tall(X))))=>((~quiet(john)<~>~wise(john))))&
(![X]:((~creative(X)&patient(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|rich(X))))<=>((tall(alice)|creative(alice))))&
(((~humble(alice)|~creative(alice)))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(happy(X)<=>(~humble(X)|~old(X))))&
(![X]:((curious(X)<~>tall(X))=>(calm(X)|happy(X))))&
((~generous(fred))<=>((brave(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((rich(X)|wise(X))=>(~rich(X)<~>~tall(X))))&
(?[X]:((funny(X)&~old(X))))&
((~kind(fred)|~curious(fred)))&
(?[X]:((~humble(X)<~>humble(X))))&
(~funny(mary)) | funny(alice) | [] | null | 0 |
If someone is either not strong or wise then fred is curious and vice versa. If paul is not patient then someone is not wise and vice versa. If someone is both not wise and humble then alice is not wise or happy. Everyone who is both calm and not patient is both funny and not wise and vice versa. If someone is either tall or not tall then someone is kind. If someone is not kind or not wise then someone is not creative and vice versa. If someone is both not old and not funny then lucy is calm or not old and vice versa. Everyone who is both not generous and not curious is not old and vice versa. Everyone who is not brave or happy is either strong or happy and vice versa. Everyone who is either not curious or not patient is not happy or not brave and vice versa. If john is not generous or strong then someone is either rich or kind and vice versa. Everyone who is either tall or not calm is not generous or strong. If susan is both quiet and not kind then someone is not patient or tall and vice versa. Everyone who is creative or not wise is not strong and vice versa. Everyone who is not kind or not happy is both not kind and not happy. If someone is both not kind and not quiet then fred is both old and strong and vice versa. John is both brave and not strong. Alice is not strong. Someone is not creative. Alice is not funny or not creative. Mary is either not brave or not happy. John is creative. Alice is either not funny or old. Someone is not brave. | Paul is creative. | neutral | ((?[X]:((~strong(X)<~>wise(X))))<=>(curious(fred)))&
((~patient(paul))<=>(?[X]:(~wise(X))))&
((?[X]:((~wise(X)&humble(X))))=>((~wise(alice)|happy(alice))))&
(![X]:((calm(X)&~patient(X))<=>(funny(X)&~wise(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)|~wise(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((~old(X)&~funny(X))))<=>((calm(lucy)|~old(lucy))))&
(![X]:((~generous(X)&~curious(X))<=>~old(X)))&
(![X]:((~brave(X)|happy(X))<=>(strong(X)<~>happy(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~happy(X)|~brave(X))))&
(((~generous(john)|strong(john)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((tall(X)<~>~calm(X))=>(~generous(X)|strong(X))))&
(((quiet(susan)&~kind(susan)))<=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((creative(X)|~wise(X))<=>~strong(X)))&
(![X]:((~kind(X)|~happy(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>((old(fred)&strong(fred))))&
((brave(john)&~strong(john)))&
(~strong(alice))&
(?[X]:(~creative(X)))&
((~funny(alice)|~creative(alice)))&
((~brave(mary)<~>~happy(mary)))&
(creative(john))&
((~funny(alice)<~>old(alice)))&
(?[X]:(~brave(X))) | creative(paul) | [] | null | 0 |
Everyone who is generous or humble is either kind or wise and vice versa.
If someone is both quiet and tall then susan is either not rich or generous and vice versa.
Everyone who is not brave is old and vice versa.
If mary is both humble and not humble then john is old and vice versa.
Everyone who is not quiet is either not funny or not kind and vice versa.
If someone is both not patient and funny then paul is either not humble or brave and vice versa.
Everyone who is not strong or not patient is either not funny or not strong.
If someone is either not generous or happy then john is both not old and not calm and vice versa.
Everyone who is either calm or not creative is either not patient or not rich and vice versa.
Everyone who is both humble and not funny is tall.
Everyone who is either creative or not strong is either funny or strong and vice versa.
If someone is both not curious and not funny then alice is both not kind and tall.
If lucy is both wise and not kind then paul is not tall and vice versa.
Everyone who is wise or not creative is humble or not calm.
If susan is either not quiet or brave then alice is either not quiet or not kind.
John is not brave or not quiet.
Someone is quiet.
Alice is not calm.
Someone is both humble and quiet.
Paul is either tall or not quiet.
Susan is both not old and patient.
Mary is not rich or calm.
Susan is both curious and not humble. | Susan is brave. | entailment | (![X]:((generous(X)|humble(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((quiet(X)&tall(X))))<=>((~rich(susan)<~>generous(susan))))&
(![X]:(~brave(X)<=>old(X)))&
(((humble(mary)&~humble(mary)))<=>(old(john)))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~patient(X)&funny(X))))<=>((~humble(paul)<~>brave(paul))))&
(![X]:((~strong(X)|~patient(X))=>(~funny(X)<~>~strong(X))))&
((?[X]:((~generous(X)<~>happy(X))))<=>((~old(john)&~calm(john))))&
(![X]:((calm(X)<~>~creative(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))=>tall(X)))&
(![X]:((creative(X)<~>~strong(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~curious(X)&~funny(X))))=>((~kind(alice)&tall(alice))))&
(((wise(lucy)&~kind(lucy)))<=>(~tall(paul)))&
(![X]:((wise(X)|~creative(X))=>(humble(X)|~calm(X))))&
(((~quiet(susan)<~>brave(susan)))=>((~quiet(alice)<~>~kind(alice))))&
((~brave(john)|~quiet(john)))&
(?[X]:(quiet(X)))&
(~calm(alice))&
(?[X]:((humble(X)&quiet(X))))&
((tall(paul)<~>~quiet(paul)))&
((~old(susan)&patient(susan)))&
((~rich(mary)|calm(mary)))&
((curious(susan)&~humble(susan))) | brave(susan) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3304141178552644908889038
% SZS output start Proof for 3304141178552644908889038
3. ! [X0] : (~brave(X0) <=> old(X0)) [input p2]
21. patient(susan) & ~old(susan) [input p20]
24. ~brave(susan) [input hypothesis]
39. ! [X0] : ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0))) [nnf transformation 3]
75. old(X0) | brave(X0) [cnf transformation 39]
133. ~old(susan) [cnf transformation 21]
137. ~brave(susan) [cnf transformation 24]
246. 21 <=> brave(susan) [avatar definition]
248. ~brave(susan) <- (~21) [avatar component clause 246]
289. ~21 [avatar split clause 137,246]
290. brave(susan) [resolution 75,133]
292. $false <- (~21) [subsumption resolution 290,248]
293. 21 [avatar contradiction clause 292]
296. $false [avatar sat refutation 289,293]
% SZS output end Proof for 3304141178552644908889038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and tall is not old or wise and vice versa. If someone is not calm or old then mary is strong or not kind and vice versa. Everyone who is not humble is rich and vice versa. If someone is not creative then someone is happy or calm. Everyone who is both not funny and kind is not wise or not kind and vice versa. If alice is strong then susan is not creative or not curious and vice versa. If lucy is strong or brave then john is either not creative or brave and vice versa. If mary is creative or kind then john is both not patient and wise. If someone is calm or not strong then someone is not curious or not brave and vice versa. If someone is happy or brave then someone is either strong or not creative. Everyone who is both not wise and not generous is both not creative and generous. Everyone who is either not brave or calm is either funny or rich. Everyone who is both not rich and not happy is either curious or not wise and vice versa. If someone is not wise or generous then someone is not humble or not funny. Everyone who is kind or old is not happy or not old. Someone is brave. Someone is both not strong and not curious. Fred is both not brave and curious. Lucy is either not rich or calm. Lucy is both funny and not rich. John is not generous or not funny. Someone is strong or not patient. | Lucy is humble. | entailment | (![X]:((curious(X)&tall(X))<=>(~old(X)|wise(X))))&
((?[X]:((~calm(X)|old(X))))<=>((strong(mary)|~kind(mary))))&
(![X]:(~humble(X)<=>rich(X)))&
((?[X]:(~creative(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~funny(X)&kind(X))<=>(~wise(X)|~kind(X))))&
((strong(alice))<=>((~creative(susan)|~curious(susan))))&
(((strong(lucy)|brave(lucy)))<=>((~creative(john)<~>brave(john))))&
(((creative(mary)|kind(mary)))=>((~patient(john)&wise(john))))&
((?[X]:((calm(X)|~strong(X))))<=>(?[X]:((~curious(X)|~brave(X)))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((~wise(X)&~generous(X))=>(~creative(X)&generous(X))))&
(![X]:((~brave(X)<~>calm(X))=>(funny(X)<~>rich(X))))&
(![X]:((~rich(X)&~happy(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:((~wise(X)|generous(X))))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((kind(X)|old(X))=>(~happy(X)|~old(X))))&
(?[X]:(brave(X)))&
(?[X]:((~strong(X)&~curious(X))))&
((~brave(fred)&curious(fred)))&
((~rich(lucy)<~>calm(lucy)))&
((funny(lucy)&~rich(lucy)))&
((~generous(john)|~funny(john)))&
(?[X]:((strong(X)|~patient(X)))) | humble(lucy) | [
"p2",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6655851730382540276455783
% SZS output start Proof for 6655851730382540276455783
3. ! [X0] : (~humble(X0) <=> rich(X0)) [input p2]
20. ~rich(lucy) & funny(lucy) [input p19]
23. ~humble(lucy) [input hypothesis]
28. ! [X0] : (~humble(X0) => rich(X0)) [unused predicate definition removal 3]
31. ! [X0] : (rich(X0) | humble(X0)) [ennf transformation 28]
86. rich(X0) | humble(X0) [cnf transformation 31]
136. ~rich(lucy) [cnf transformation 20]
138. ~humble(lucy) [cnf transformation 23]
291. 33 <=> rich(lucy) [avatar definition]
292. ~rich(lucy) <- (~33) [avatar component clause 291]
300. ~33 [avatar split clause 136,291]
316. humble(lucy) <- (~33) [resolution 86,292]
317. $false <- (~33) [subsumption resolution 316,138]
318. 33 [avatar contradiction clause 317]
319. $false [avatar sat refutation 300,318]
% SZS output end Proof for 6655851730382540276455783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either curious or happy. Everyone who is not patient is tall or quiet and vice versa. If someone is not brave then someone is not calm or creative. If lucy is humble or strong then someone is both curious and not strong and vice versa. Everyone who is rich or not funny is either funny or strong. If someone is either happy or not patient then someone is brave or creative. If someone is both funny and not rich then lucy is both not patient and wise. If alice is creative or not creative then someone is not tall or tall and vice versa. Everyone who is not kind or creative is either not kind or not tall and vice versa. If lucy is both not humble and not curious then someone is not humble. Everyone who is not funny is either not generous or brave. Everyone who is not funny or not rich is both not wise and not generous. If someone is both humble and calm then someone is both not brave and tall. Everyone who is patient or wise is creative or old and vice versa. If john is both curious and not happy then mary is not brave and vice versa. If alice is not patient then someone is not wise and vice versa. John is not funny. Someone is generous or not rich. Susan is either not creative or not generous. Someone is quiet or not wise. Paul is both not patient and not brave. John is both not wise and tall. Lucy is not rich. Someone is either not funny or not patient. | John is creative. | contradiction | (![X]:(~tall(X)=>(curious(X)<~>happy(X))))&
(![X]:(~patient(X)<=>(tall(X)|quiet(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)|creative(X)))))&
(((humble(lucy)|strong(lucy)))<=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((rich(X)|~funny(X))=>(funny(X)<~>strong(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((brave(X)|creative(X)))))&
((?[X]:((funny(X)&~rich(X))))=>((~patient(lucy)&wise(lucy))))&
(((creative(alice)|~creative(alice)))<=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~kind(X)<~>~tall(X))))&
(((~humble(lucy)&~curious(lucy)))=>(?[X]:(~humble(X))))&
(![X]:(~funny(X)=>(~generous(X)<~>brave(X))))&
(![X]:((~funny(X)|~rich(X))=>(~wise(X)&~generous(X))))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|old(X))))&
(((curious(john)&~happy(john)))<=>(~brave(mary)))&
((~patient(alice))<=>(?[X]:(~wise(X))))&
(~funny(john))&
(?[X]:((generous(X)|~rich(X))))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((quiet(X)|~wise(X))))&
((~patient(paul)&~brave(paul)))&
((~wise(john)&tall(john)))&
(~rich(lucy))&
(?[X]:((~funny(X)<~>~patient(X)))) | creative(john) | [
"p1",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3972906482410530492668
% SZS output start Proof for 3972906482410530492668
2. ! [X0] : (~patient(X0) <=> (quiet(X0) | tall(X0))) [input p1]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> (old(X0) | creative(X0))) [input p13]
22. tall(john) & ~wise(john) [input p21]
25. creative(john) [input hypothesis]
40. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | patient(X0))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | patient(X0))) [flattening 40]
62. ! [X0] : (((wise(X0) | patient(X0)) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((wise(X0) | patient(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | (~wise(X0) & ~patient(X0)))) [flattening 62]
81. ~patient(X0) | ~tall(X0) [cnf transformation 41]
115. ~creative(X0) | patient(X0) | wise(X0) [cnf transformation 63]
129. ~wise(john) [cnf transformation 22]
130. tall(john) [cnf transformation 22]
134. creative(john) [cnf transformation 25]
309. patient(john) | wise(john) [resolution 115,134]
312. patient(john) [subsumption resolution 309,129]
332. ~tall(john) [resolution 312,81]
333. $false [subsumption resolution 332,130]
% SZS output end Proof for 3972906482410530492668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is not wise.
If someone is creative or funny then someone is either not happy or happy.
If john is either old or not wise then lucy is either not generous or happy and vice versa.
If someone is humble or not tall then mary is not rich.
If someone is both not old and creative then someone is funny.
Everyone who is quiet is not brave or generous and vice versa.
Everyone who is both not funny and not kind is either funny or not funny and vice versa.
Everyone who is either wise or old is both kind and funny and vice versa.
If alice is not generous then john is brave or kind.
If alice is creative then someone is not calm or creative and vice versa.
Everyone who is both patient and old is not quiet.
Everyone who is not wise is creative.
If someone is either funny or curious then someone is both not generous and brave and vice versa.
Everyone who is brave is strong.
If susan is both funny and not happy then someone is funny and vice versa.
Mary is happy or tall.
Someone is not brave.
Someone is either not quiet or not strong.
Someone is either not rich or not brave. | Susan is not humble. | neutral | (![X]:((~calm(X)|brave(X))=>~wise(X)))&
((?[X]:((creative(X)|funny(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(((old(john)<~>~wise(john)))<=>((~generous(lucy)<~>happy(lucy))))&
((?[X]:((humble(X)|~tall(X))))=>(~rich(mary)))&
((?[X]:((~old(X)&creative(X))))=>(?[X]:(funny(X))))&
(![X]:(quiet(X)<=>(~brave(X)|generous(X))))&
(![X]:((~funny(X)&~kind(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(kind(X)&funny(X))))&
((~generous(alice))=>((brave(john)|kind(john))))&
((creative(alice))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((patient(X)&old(X))=>~quiet(X)))&
(![X]:(~wise(X)=>creative(X)))&
((?[X]:((funny(X)<~>curious(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:(brave(X)=>strong(X)))&
(((funny(susan)&~happy(susan)))<=>(?[X]:(funny(X))))&
((happy(mary)|tall(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~humble(susan) | [] | null | 0 |
If someone is both humble and patient then someone is both not calm and humble and vice versa.
If someone is not humble then someone is quiet or not kind and vice versa.
Everyone who is calm or not rich is patient or not rich and vice versa.
If someone is either not creative or brave then alice is either not quiet or calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
Everyone who is not rich or kind is not calm.
Someone is either old or not tall.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative.
Someone is both not humble and not wise.
Someone is both rich and quiet.
Lucy is either not humble or humble.
Someone is either creative or not wise. | Mary is tall. | entailment | ((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~calm(X)&humble(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)|~kind(X)))))&
(![X]:((calm(X)|~rich(X))<=>(patient(X)|~rich(X))))&
((?[X]:((~creative(X)<~>brave(X))))<=>((~quiet(alice)<~>calm(alice))))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((rich(X)&quiet(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X)))) | tall(mary) | [
"p2",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4979131025585030144452871
% SZS output start Proof for 4979131025585030144452871
3. ! [X0] : ((~rich(X0) | calm(X0)) <=> (~rich(X0) | patient(X0))) [input p2]
10. (rich(susan) <~> wise(susan)) <=> ? [X0] : (wise(X0) | calm(X0)) [input p9]
12. ! [X0] : ((~rich(X0) | ~tall(X0)) => calm(X0)) [input p11]
13. (~patient(mary) & humble(mary)) <=> ~kind(susan) [input p12]
15. ! [X0] : ((wise(X0) <~> ~calm(X0)) => (wise(X0) | ~tall(X0))) [input p14]
16. ! [X0] : ((kind(X0) | ~rich(X0)) => ~calm(X0)) [input p15]
25. ~tall(mary) [input hypothesis]
29. ! [X0] : (calm(X0) | (rich(X0) & tall(X0))) [ennf transformation 12]
30. ! [X0] : ((wise(X0) | ~tall(X0)) | (wise(X0) <=> ~calm(X0))) [ennf transformation 15]
31. ! [X0] : (wise(X0) | ~tall(X0) | (wise(X0) <=> ~calm(X0))) [flattening 30]
32. ! [X0] : (~calm(X0) | (~kind(X0) & rich(X0))) [ennf transformation 16]
43. ! [X0] : (((~rich(X0) | calm(X0)) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | (rich(X0) & ~calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((~rich(X0) | calm(X0) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | (rich(X0) & ~calm(X0)))) [flattening 43]
63. (((~wise(susan) | ~rich(susan)) & (wise(susan) | rich(susan))) | ! [X0] : (~wise(X0) & ~calm(X0))) & (? [X0] : (wise(X0) | calm(X0)) | ((rich(susan) | ~wise(susan)) & (wise(susan) | ~rich(susan)))) [nnf transformation 10]
64. (((~wise(susan) | ~rich(susan)) & (wise(susan) | rich(susan))) | ! [X0] : (~wise(X0) & ~calm(X0))) & (? [X1] : (wise(X1) | calm(X1)) | ((rich(susan) | ~wise(susan)) & (wise(susan) | ~rich(susan)))) [rectify 63]
65. ? [X1] : (wise(X1) | calm(X1)) => (wise(sK7) | calm(sK7)) [choice axiom]
66. (((~wise(susan) | ~rich(susan)) & (wise(susan) | rich(susan))) | ! [X0] : (~wise(X0) & ~calm(X0))) & ((wise(sK7) | calm(sK7)) | ((rich(susan) | ~wise(susan)) & (wise(susan) | ~rich(susan)))) [skolemisation 64,65]
68. ((~patient(mary) & humble(mary)) | kind(susan)) & (~kind(susan) | (patient(mary) | ~humble(mary))) [nnf transformation 13]
69. ((~patient(mary) & humble(mary)) | kind(susan)) & (~kind(susan) | patient(mary) | ~humble(mary)) [flattening 68]
74. ! [X0] : (wise(X0) | ~tall(X0) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) [nnf transformation 31]
96. ~rich(X0) | patient(X0) | ~calm(X0) [cnf transformation 44]
135. ~wise(susan) | ~rich(susan) | ~wise(X0) [cnf transformation 66]
140. tall(X0) | calm(X0) [cnf transformation 29]
141. rich(X0) | calm(X0) [cnf transformation 29]
144. ~patient(mary) | kind(susan) [cnf transformation 69]
154. wise(X0) | ~tall(X0) | wise(X0) | calm(X0) [cnf transformation 74]
155. ~calm(X0) | rich(X0) [cnf transformation 32]
156. ~kind(X0) | ~calm(X0) [cnf transformation 32]
172. ~tall(mary) [cnf transformation 25]
173. wise(X0) | ~tall(X0) | calm(X0) [duplicate literal removal 154]
305. 29 <=> ! [X0] : ~wise(X0) [avatar definition]
306. ~wise(X0) <- (29) [avatar component clause 305]
308. 30 <=> rich(susan) [avatar definition]
310. ~rich(susan) <- (~30) [avatar component clause 308]
312. 31 <=> wise(susan) [avatar definition]
314. ~wise(susan) <- (~31) [avatar component clause 312]
315. 29 | ~30 | ~31 [avatar split clause 135,312,308,305]
330. 34 <=> kind(susan) [avatar definition]
332. kind(susan) <- (34) [avatar component clause 330]
334. 35 <=> patient(mary) [avatar definition]
336. ~patient(mary) <- (~35) [avatar component clause 334]
337. 34 | ~35 [avatar split clause 144,334,330]
345. 37 <=> tall(mary) [avatar definition]
347. ~tall(mary) <- (~37) [avatar component clause 345]
349. 38 <=> calm(mary) [avatar definition]
350. calm(mary) <- (38) [avatar component clause 349]
376. wise(X0) | calm(X0) [subsumption resolution 173,140]
377. rich(X0) [subsumption resolution 155,141]
400. ~37 [avatar split clause 172,345]
401. $false <- (~30) [subsumption resolution 310,377]
402. 30 [avatar contradiction clause 401]
412. calm(mary) <- (~37) [resolution 140,347]
413. 38 | 37 [avatar split clause 412,345,349]
414. ~calm(susan) <- (34) [resolution 156,332]
424. calm(X0) <- (29) [resolution 376,306]
427. ~calm(X1) | patient(X1) [resolution 96,377]
430. $false <- (29, 34) [resolution 424,414]
431. ~29 | ~34 [avatar contradiction clause 430]
435. calm(susan) <- (~31) [resolution 314,376]
436. ~calm(susan) <- (34) [resolution 332,156]
437. $false <- (~31, 34) [subsumption resolution 436,435]
438. 31 | ~34 [avatar contradiction clause 437]
508. patient(mary) <- (38) [resolution 427,350]
512. $false <- (~35, 38) [subsumption resolution 508,336]
513. 35 | ~38 [avatar contradiction clause 512]
514. $false [avatar sat refutation 315,337,400,402,413,431,438,513]
% SZS output end Proof for 4979131025585030144452871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is both humble and not creative then someone is patient.
Everyone who is not generous or not happy is both not strong and not curious.
Everyone who is not calm or generous is both generous and not kind and vice versa.
If mary is both not quiet and calm then someone is tall or kind and vice versa.
Everyone who is either tall or calm is rich or humble and vice versa.
If someone is both not rich and tall then paul is both not quiet and brave.
If someone is not patient then alice is both generous and rich and vice versa.
Everyone who is both not wise and not happy is both not quiet and humble and vice versa.
If alice is either not funny or rich then someone is generous or tall.
Everyone who is either happy or not kind is either not quiet or curious.
If someone is not wise or creative then fred is either not curious or brave and vice versa.
Everyone who is happy is either rich or brave and vice versa.
If mary is both patient and calm then fred is not kind and vice versa.
Everyone who is not humble or not calm is both creative and calm and vice versa.
Everyone who is both not calm and not curious is funny.
Everyone who is both wise and not calm is either not rich or not happy and vice versa.
Lucy is wise or strong.
Lucy is tall or calm.
Fred is not patient or patient.
Someone is both rich and kind.
Someone is either not strong or not creative.
Paul is not generous or strong.
Someone is curious or not quiet.
Paul is calm. | Fred is tall. | contradiction | (((humble(lucy)&~creative(lucy)))=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|~happy(X))=>(~strong(X)&~curious(X))))&
(![X]:((~calm(X)|generous(X))<=>(generous(X)&~kind(X))))&
(((~quiet(mary)&calm(mary)))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:((tall(X)<~>calm(X))<=>(rich(X)|humble(X))))&
((?[X]:((~rich(X)&tall(X))))=>((~quiet(paul)&brave(paul))))&
((?[X]:(~patient(X)))<=>((generous(alice)&rich(alice))))&
(![X]:((~wise(X)&~happy(X))<=>(~quiet(X)&humble(X))))&
(((~funny(alice)<~>rich(alice)))=>(?[X]:((generous(X)|tall(X)))))&
(![X]:((happy(X)<~>~kind(X))=>(~quiet(X)<~>curious(X))))&
((?[X]:((~wise(X)|creative(X))))<=>((~curious(fred)<~>brave(fred))))&
(![X]:(happy(X)<=>(rich(X)<~>brave(X))))&
(((patient(mary)&calm(mary)))<=>(~kind(fred)))&
(![X]:((~humble(X)|~calm(X))<=>(creative(X)&calm(X))))&
(![X]:((~calm(X)&~curious(X))=>funny(X)))&
(![X]:((wise(X)&~calm(X))<=>(~rich(X)<~>~happy(X))))&
((wise(lucy)|strong(lucy)))&
((tall(lucy)|calm(lucy)))&
((~patient(fred)|patient(fred)))&
(?[X]:((rich(X)&kind(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
((~generous(paul)|strong(paul)))&
(?[X]:((curious(X)|~quiet(X))))&
(calm(paul)) | tall(fred) | [
"p4",
"p5",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6837234038224797483688216
% SZS output start Proof for 6837234038224797483688216
5. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (humble(X0) | rich(X0))) [input p4]
6. ? [X0] : (tall(X0) & ~rich(X0)) => (brave(paul) & ~quiet(paul)) [input p5]
12. ! [X0] : (happy(X0) <=> (rich(X0) <~> brave(X0))) [input p11]
14. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (calm(X0) & creative(X0))) [input p13]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p15]
25. tall(fred) [input hypothesis]
29. (brave(paul) & ~quiet(paul)) | ! [X0] : (~tall(X0) | rich(X0)) [ennf transformation 6]
43. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 43]
60. ! [X0] : ((happy(X0) | ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0)))) & (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | ~happy(X0))) [nnf transformation 12]
63. ! [X0] : (((~calm(X0) | ~humble(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 14]
64. ! [X0] : ((~calm(X0) | ~humble(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (calm(X0) & humble(X0)))) [flattening 63]
65. ! [X0] : (((~calm(X0) & wise(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
66. ! [X0] : (((~calm(X0) & wise(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | calm(X0) | ~wise(X0))) [flattening 65]
93. ~rich(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 44]
96. brave(paul) | ~tall(X0) | rich(X0) [cnf transformation 29]
117. ~brave(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 60]
119. ~brave(X0) | rich(X0) | happy(X0) [cnf transformation 60]
126. calm(X0) | calm(X0) [cnf transformation 64]
133. ~calm(X0) | ~happy(X0) | rich(X0) [cnf transformation 66]
134. ~calm(X0) | ~rich(X0) | happy(X0) [cnf transformation 66]
145. tall(fred) [cnf transformation 25]
146. calm(X0) [duplicate literal removal 126]
189. 10 <=> ! [X0] : (~tall(X0) | rich(X0)) [avatar definition]
190. ~tall(X0) | rich(X0) <- (10) [avatar component clause 189]
192. 11 <=> brave(paul) [avatar definition]
194. brave(paul) <- (11) [avatar component clause 192]
195. 10 | 11 [avatar split clause 96,192,189]
274. ~rich(X0) | happy(X0) [subsumption resolution 134,146]
275. ~happy(X0) | rich(X0) [subsumption resolution 133,146]
326. rich(fred) <- (10) [resolution 190,145]
340. ~tall(fred) | ~calm(fred) <- (10) [resolution 93,326]
344. ~calm(fred) <- (10) [subsumption resolution 340,145]
345. $false <- (10) [subsumption resolution 344,146]
346. ~10 [avatar contradiction clause 345]
403. ~rich(paul) | ~happy(paul) <- (11) [resolution 117,194]
404. ~rich(paul) <- (11) [subsumption resolution 403,274]
409. rich(paul) | happy(paul) <- (11) [resolution 119,194]
410. happy(paul) <- (11) [subsumption resolution 409,404]
413. rich(paul) <- (11) [resolution 410,275]
415. $false <- (11) [subsumption resolution 413,404]
416. ~11 [avatar contradiction clause 415]
417. $false [avatar sat refutation 195,346,416]
% SZS output end Proof for 6837234038224797483688216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and not creative then someone is curious and vice versa.
If fred is both strong and not patient then john is both creative and not curious and vice versa.
Everyone who is kind is either not strong or generous and vice versa.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
If mary is not brave or not quiet then lucy is wise or curious and vice versa.
Everyone who is both not happy and calm is either not brave or calm and vice versa.
Everyone who is both not old and rich is calm and vice versa.
If susan is rich then alice is both funny and quiet.
Everyone who is rich or not happy is not patient and vice versa.
Everyone who is brave or quiet is generous.
Everyone who is not tall is not kind or not humble and vice versa.
Everyone who is wise is not brave or not rich.
Everyone who is either not happy or calm is not curious or not old and vice versa.
If mary is either happy or curious then john is patient.
Everyone who is patient or not curious is not quiet or patient and vice versa.
Someone is calm.
Someone is not rich.
Mary is old.
Someone is quiet or humble.
Paul is not creative.
Paul is happy or creative.
Mary is funny.
Susan is either not calm or strong. | Fred is not happy. | neutral | ((?[X]:((~old(X)&~creative(X))))<=>(?[X]:(curious(X))))&
(((strong(fred)&~patient(fred)))<=>((creative(john)&~curious(john))))&
(![X]:(kind(X)<=>(~strong(X)<~>generous(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
(![X]:((~happy(X)&calm(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((~old(X)&rich(X))<=>calm(X)))&
((rich(susan))=>((funny(alice)&quiet(alice))))&
(![X]:((rich(X)|~happy(X))<=>~patient(X)))&
(![X]:((brave(X)|quiet(X))=>generous(X)))&
(![X]:(~tall(X)<=>(~kind(X)|~humble(X))))&
(![X]:(wise(X)=>(~brave(X)|~rich(X))))&
(![X]:((~happy(X)<~>calm(X))<=>(~curious(X)|~old(X))))&
(((happy(mary)<~>curious(mary)))=>(patient(john)))&
(![X]:((patient(X)|~curious(X))<=>(~quiet(X)|patient(X))))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
(old(mary))&
(?[X]:((quiet(X)|humble(X))))&
(~creative(paul))&
((happy(paul)|creative(paul)))&
(funny(mary))&
((~calm(susan)<~>strong(susan))) | ~happy(fred) | [] | null | 0 |
Everyone who is tall or not brave is not calm and vice versa. If susan is either tall or calm then paul is strong and vice versa. Everyone who is curious or kind is not generous. Everyone who is not humble is both creative and strong. Everyone who is both not generous and not quiet is either not creative or not wise. Everyone who is not brave is both quiet and not rich and vice versa. If john is either kind or happy then alice is not tall or not quiet. If paul is not creative or quiet then alice is both not strong and not calm. If someone is either not humble or not brave then paul is humble. Everyone who is generous is not quiet or not wise. Everyone who is not generous or not humble is not rich or not generous and vice versa. Everyone who is not quiet or rich is not curious or not generous. Everyone who is both kind and not humble is strong. Everyone who is both humble and funny is both not wise and old and vice versa. Everyone who is both not kind and quiet is not old and vice versa. If someone is not calm or not patient then susan is both humble and not patient. Someone is patient. Alice is rich or happy. Susan is not humble. Someone is both not humble and not curious. Someone is both not tall and not quiet. Someone is both not old and not strong. Someone is strong or creative. Someone is either creative or not curious. | Paul is not creative. | contradiction | (![X]:((tall(X)|~brave(X))<=>~calm(X)))&
(((tall(susan)<~>calm(susan)))<=>(strong(paul)))&
(![X]:((curious(X)|kind(X))=>~generous(X)))&
(![X]:(~humble(X)=>(creative(X)&strong(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~creative(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(quiet(X)&~rich(X))))&
(((kind(john)<~>happy(john)))=>((~tall(alice)|~quiet(alice))))&
(((~creative(paul)|quiet(paul)))=>((~strong(alice)&~calm(alice))))&
((?[X]:((~humble(X)<~>~brave(X))))=>(humble(paul)))&
(![X]:(generous(X)=>(~quiet(X)|~wise(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~rich(X)|~generous(X))))&
(![X]:((~quiet(X)|rich(X))=>(~curious(X)|~generous(X))))&
(![X]:((kind(X)&~humble(X))=>strong(X)))&
(![X]:((humble(X)&funny(X))<=>(~wise(X)&old(X))))&
(![X]:((~kind(X)&quiet(X))<=>~old(X)))&
((?[X]:((~calm(X)|~patient(X))))=>((humble(susan)&~patient(susan))))&
(?[X]:(patient(X)))&
((rich(alice)|happy(alice)))&
(~humble(susan))&
(?[X]:((~humble(X)&~curious(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((strong(X)|creative(X))))&
(?[X]:((creative(X)<~>~curious(X)))) | ~creative(paul) | [
"p7",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1736079936373747221719463
% SZS output start Proof for 1736079936373747221719463
8. (quiet(paul) | ~creative(paul)) => (~calm(alice) & ~strong(alice)) [input p7]
16. ? [X0] : (~patient(X0) | ~calm(X0)) => (~patient(susan) & humble(susan)) [input p15]
19. ~humble(susan) [input p18]
25. ~creative(paul) [input hypothesis]
32. (~calm(alice) & ~strong(alice)) | (~quiet(paul) & creative(paul)) [ennf transformation 8]
40. (~patient(susan) & humble(susan)) | ! [X0] : (patient(X0) & calm(X0)) [ennf transformation 16]
88. ~calm(alice) | creative(paul) [cnf transformation 32]
107. humble(susan) | calm(X0) [cnf transformation 40]
113. ~humble(susan) [cnf transformation 19]
123. ~creative(paul) [cnf transformation 25]
164. 9 <=> calm(alice) [avatar definition]
166. ~calm(alice) <- (~9) [avatar component clause 164]
169. 10 <=> creative(paul) [avatar definition]
172. 10 | ~9 [avatar split clause 88,164,169]
200. 17 <=> ! [X0] : calm(X0) [avatar definition]
201. calm(X0) <- (17) [avatar component clause 200]
204. 18 <=> humble(susan) [avatar definition]
208. 17 | 18 [avatar split clause 107,204,200]
218. ~18 [avatar split clause 113,204]
238. ~10 [avatar split clause 123,169]
239. $false <- (~9, 17) [subsumption resolution 166,201]
240. 9 | ~17 [avatar contradiction clause 239]
243. $false [avatar sat refutation 172,208,218,238,240]
% SZS output end Proof for 1736079936373747221719463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or generous is either not wise or funny.
If fred is not humble or happy then john is happy or curious.
Everyone who is kind is not curious and vice versa.
Everyone who is not tall or curious is both not calm and not funny.
If someone is not creative then paul is both not quiet and not strong.
If someone is both tall and rich then john is both creative and not funny and vice versa.
Everyone who is both happy and not curious is both creative and funny.
If paul is calm then someone is either calm or not old and vice versa.
If someone is either not generous or old then someone is either not brave or not rich and vice versa.
If someone is not kind then someone is not happy and vice versa.
If fred is kind or not quiet then john is not strong or not brave.
Everyone who is both generous and calm is quiet.
Everyone who is not creative or happy is both not humble and tall and vice versa.
If paul is both calm and not calm then paul is either not old or rich.
Everyone who is not creative is not humble.
If paul is not quiet or happy then someone is both not kind and not happy and vice versa.
Alice is either kind or patient.
Someone is rich.
Someone is not wise.
Paul is both happy and not humble.
Someone is creative or not kind.
Someone is both funny and strong.
Susan is either brave or happy. | Paul is tall. | entailment | (![X]:((strong(X)<~>generous(X))=>(~wise(X)<~>funny(X))))&
(((~humble(fred)|happy(fred)))=>((happy(john)|curious(john))))&
(![X]:(kind(X)<=>~curious(X)))&
(![X]:((~tall(X)|curious(X))=>(~calm(X)&~funny(X))))&
((?[X]:(~creative(X)))=>((~quiet(paul)&~strong(paul))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(john)&~funny(john))))&
(![X]:((happy(X)&~curious(X))=>(creative(X)&funny(X))))&
((calm(paul))<=>(?[X]:((calm(X)<~>~old(X)))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:(~happy(X))))&
(((kind(fred)|~quiet(fred)))=>((~strong(john)|~brave(john))))&
(![X]:((generous(X)&calm(X))=>quiet(X)))&
(![X]:((~creative(X)|happy(X))<=>(~humble(X)&tall(X))))&
(((calm(paul)&~calm(paul)))=>((~old(paul)<~>rich(paul))))&
(![X]:(~creative(X)=>~humble(X)))&
(((~quiet(paul)|happy(paul)))<=>(?[X]:((~kind(X)&~happy(X)))))&
((kind(alice)<~>patient(alice)))&
(?[X]:(rich(X)))&
(?[X]:(~wise(X)))&
((happy(paul)&~humble(paul)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((funny(X)&strong(X))))&
((brave(susan)<~>happy(susan))) | tall(paul) | [
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6289892152894083137109136
% SZS output start Proof for 6289892152894083137109136
13. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (tall(X0) & ~humble(X0))) [input p12]
20. ~humble(paul) & happy(paul) [input p19]
24. ~tall(paul) [input hypothesis]
62. ! [X0] : (((happy(X0) | ~creative(X0)) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 13]
63. ! [X0] : ((happy(X0) | ~creative(X0) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | (~happy(X0) & creative(X0)))) [flattening 62]
120. ~happy(X0) | tall(X0) [cnf transformation 63]
134. happy(paul) [cnf transformation 20]
141. ~tall(paul) [cnf transformation 24]
292. 35 <=> happy(paul) [avatar definition]
294. happy(paul) <- (35) [avatar component clause 292]
318. 35 [avatar split clause 134,292]
353. tall(paul) <- (35) [resolution 120,294]
354. $false <- (35) [subsumption resolution 353,141]
355. ~35 [avatar contradiction clause 354]
356. $false [avatar sat refutation 318,355]
% SZS output end Proof for 6289892152894083137109136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not patient is both quiet and tall. Everyone who is both rich and tall is humble or not tall. Everyone who is not kind is both curious and brave and vice versa. Everyone who is not quiet is curious and vice versa. If someone is either generous or not patient then someone is not brave and vice versa. If mary is both old and not generous then someone is both happy and old and vice versa. If someone is generous then fred is not kind or not brave. Everyone who is calm or kind is tall or patient. If fred is not wise or generous then someone is not curious. If someone is both not rich and not curious then someone is both not generous and not quiet and vice versa. Everyone who is either not happy or not calm is tall. If someone is either not quiet or not patient then susan is creative and vice versa. If mary is happy then someone is both not rich and happy and vice versa. If john is not curious or kind then john is strong or funny. If someone is not funny then someone is either not brave or calm and vice versa. Everyone who is not humble or wise is both not calm and wise. Someone is both not curious and old. Susan is tall or not happy. Mary is both rich and not happy. John is either quiet or strong. Someone is either kind or funny. Susan is strong or not kind. Lucy is not patient. Someone is either wise or kind. | Lucy is not quiet. | contradiction | (![X]:((curious(X)|~patient(X))=>(quiet(X)&tall(X))))&
(![X]:((rich(X)&tall(X))=>(humble(X)|~tall(X))))&
(![X]:(~kind(X)<=>(curious(X)&brave(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:(~brave(X))))&
(((old(mary)&~generous(mary)))<=>(?[X]:((happy(X)&old(X)))))&
((?[X]:(generous(X)))=>((~kind(fred)|~brave(fred))))&
(![X]:((calm(X)|kind(X))=>(tall(X)|patient(X))))&
(((~wise(fred)|generous(fred)))=>(?[X]:(~curious(X))))&
((?[X]:((~rich(X)&~curious(X))))<=>(?[X]:((~generous(X)&~quiet(X)))))&
(![X]:((~happy(X)<~>~calm(X))=>tall(X)))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(creative(susan)))&
((happy(mary))<=>(?[X]:((~rich(X)&happy(X)))))&
(((~curious(john)|kind(john)))=>((strong(john)|funny(john))))&
((?[X]:(~funny(X)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((~humble(X)|wise(X))=>(~calm(X)&wise(X))))&
(?[X]:((~curious(X)&old(X))))&
((tall(susan)|~happy(susan)))&
((rich(mary)&~happy(mary)))&
((quiet(john)<~>strong(john)))&
(?[X]:((kind(X)<~>funny(X))))&
((strong(susan)|~kind(susan)))&
(~patient(lucy))&
(?[X]:((wise(X)<~>kind(X)))) | ~quiet(lucy) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8616290385145914513410574
% SZS output start Proof for 8616290385145914513410574
1. ! [X0] : ((~patient(X0) | curious(X0)) => (tall(X0) & quiet(X0))) [input p0]
4. ! [X0] : (~quiet(X0) <=> curious(X0)) [input p3]
25. ~quiet(lucy) [input hypothesis]
32. ! [X0] : ((~patient(X0) | curious(X0)) => quiet(X0)) [pure predicate removal 1]
35. ! [X0] : (quiet(X0) | (patient(X0) & ~curious(X0))) [ennf transformation 32]
44. ! [X0] : ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))) [nnf transformation 4]
84. quiet(X0) | ~curious(X0) [cnf transformation 35]
89. curious(X0) | quiet(X0) [cnf transformation 44]
90. ~quiet(X0) | ~curious(X0) [cnf transformation 44]
133. ~quiet(lucy) [cnf transformation 25]
134. ~curious(X0) [subsumption resolution 90,84]
135. quiet(X0) [subsumption resolution 89,134]
296. $false [subsumption resolution 133,135]
% SZS output end Proof for 8616290385145914513410574
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not brave is either not kind or not funny.
Everyone who is not creative is kind and vice versa.
If lucy is either not wise or strong then mary is not rich and vice versa.
If paul is not creative or not brave then someone is not patient.
If someone is either not wise or not rich then someone is both wise and not strong.
If someone is not patient or not curious then someone is funny and vice versa.
Everyone who is either funny or rich is tall or not curious.
If fred is not rich or creative then someone is both tall and not tall and vice versa.
If someone is strong or not patient then susan is brave or wise.
Everyone who is both strong and not quiet is funny.
Everyone who is not creative is both generous and kind and vice versa.
Everyone who is both not happy and kind is brave or not wise and vice versa.
Everyone who is rich or not creative is brave or wise and vice versa.
Everyone who is either quiet or not funny is both not humble and not funny and vice versa.
Everyone who is both not wise and funny is not happy and vice versa.
Everyone who is not wise is both not humble and not curious and vice versa.
Someone is not quiet.
Someone is happy or funny.
Lucy is not patient or not humble.
Paul is either not happy or quiet.
Someone is both curious and not quiet.
Lucy is not creative.
Someone is rich or wise. | Fred is kind. | entailment | (![X]:((patient(X)|~brave(X))=>(~kind(X)<~>~funny(X))))&
(![X]:(~creative(X)<=>kind(X)))&
(((~wise(lucy)<~>strong(lucy)))<=>(~rich(mary)))&
(((~creative(paul)|~brave(paul)))=>(?[X]:(~patient(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((~patient(X)|~curious(X))))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)<~>rich(X))=>(tall(X)|~curious(X))))&
(((~rich(fred)|creative(fred)))<=>(?[X]:((tall(X)&~tall(X)))))&
((?[X]:((strong(X)|~patient(X))))=>((brave(susan)|wise(susan))))&
(![X]:((strong(X)&~quiet(X))=>funny(X)))&
(![X]:(~creative(X)<=>(generous(X)&kind(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~wise(X))))&
(![X]:((rich(X)|~creative(X))<=>(brave(X)|wise(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~humble(X)&~funny(X))))&
(![X]:((~wise(X)&funny(X))<=>~happy(X)))&
(![X]:(~wise(X)<=>(~humble(X)&~curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)|funny(X))))&
((~patient(lucy)|~humble(lucy)))&
((~happy(paul)<~>quiet(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
(~creative(lucy))&
(?[X]:((rich(X)|wise(X)))) | kind(fred) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3795422723673677022369681
% SZS output start Proof for 3795422723673677022369681
2. ! [X0] : (~creative(X0) <=> kind(X0)) [input p1]
8. (creative(fred) | ~rich(fred)) <=> ? [X0] : (~tall(X0) & tall(X0)) [input p7]
24. ~kind(fred) [input hypothesis]
37. ! [X0] : ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))) [nnf transformation 2]
51. ((creative(fred) | ~rich(fred)) | ! [X0] : (tall(X0) | ~tall(X0))) & (? [X0] : (~tall(X0) & tall(X0)) | (~creative(fred) & rich(fred))) [nnf transformation 8]
52. (creative(fred) | ~rich(fred) | ! [X0] : (tall(X0) | ~tall(X0))) & (? [X0] : (~tall(X0) & tall(X0)) | (~creative(fred) & rich(fred))) [flattening 51]
53. (creative(fred) | ~rich(fred) | ! [X0] : (tall(X0) | ~tall(X0))) & (? [X1] : (~tall(X1) & tall(X1)) | (~creative(fred) & rich(fred))) [rectify 52]
54. ? [X1] : (~tall(X1) & tall(X1)) => (~tall(sK4) & tall(sK4)) [choice axiom]
55. (creative(fred) | ~rich(fred) | ! [X0] : (tall(X0) | ~tall(X0))) & ((~tall(sK4) & tall(sK4)) | (~creative(fred) & rich(fred))) [skolemisation 53,54]
81. creative(X0) | kind(X0) [cnf transformation 37]
99. tall(sK4) | ~creative(fred) [cnf transformation 55]
101. ~tall(sK4) | ~creative(fred) [cnf transformation 55]
139. ~kind(fred) [cnf transformation 24]
215. 17 <=> creative(fred) [avatar definition]
217. ~creative(fred) <- (~17) [avatar component clause 215]
219. 18 <=> tall(sK4) [avatar definition]
222. ~17 | ~18 [avatar split clause 101,219,215]
228. ~17 | 18 [avatar split clause 99,219,215]
272. kind(fred) <- (~17) [resolution 81,217]
273. $false <- (~17) [subsumption resolution 272,139]
274. 17 [avatar contradiction clause 273]
275. $false [avatar sat refutation 222,228,274]
% SZS output end Proof for 3795422723673677022369681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not generous is both creative and generous and vice versa.
Everyone who is both not old and rich is generous.
Everyone who is either not strong or not creative is either not funny or not strong.
Everyone who is both not brave and not rich is not brave or not rich.
Everyone who is strong is quiet.
If alice is either rich or happy then alice is creative or calm.
If john is not old or rich then mary is wise or not kind and vice versa.
Everyone who is not rich or tall is not generous and vice versa.
If someone is either not quiet or not tall then someone is either kind or happy and vice versa.
Everyone who is both creative and not patient is both funny and not tall and vice versa.
Everyone who is not tall is not kind.
Everyone who is both not calm and not patient is patient and vice versa.
Everyone who is not tall or not creative is not quiet and vice versa.
If someone is not old or not kind then someone is either not generous or not curious and vice versa.
If someone is either not humble or strong then susan is either not curious or brave.
John is both not tall and not brave.
Someone is rich.
Susan is both calm and old.
Susan is curious or not old.
Someone is either not brave or not creative. | Susan is not funny. | entailment | (![X]:((strong(X)<~>~generous(X))<=>(creative(X)&generous(X))))&
(![X]:((~old(X)&rich(X))=>generous(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~brave(X)&~rich(X))=>(~brave(X)|~rich(X))))&
(![X]:(strong(X)=>quiet(X)))&
(((rich(alice)<~>happy(alice)))=>((creative(alice)|calm(alice))))&
(((~old(john)|rich(john)))<=>((wise(mary)|~kind(mary))))&
(![X]:((~rich(X)|tall(X))<=>~generous(X)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((creative(X)&~patient(X))<=>(funny(X)&~tall(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~calm(X)&~patient(X))<=>patient(X)))&
(![X]:((~tall(X)|~creative(X))<=>~quiet(X)))&
((?[X]:((~old(X)|~kind(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((~humble(X)<~>strong(X))))=>((~curious(susan)<~>brave(susan))))&
((~tall(john)&~brave(john)))&
(?[X]:(rich(X)))&
((calm(susan)&old(susan)))&
((curious(susan)|~old(susan)))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~funny(susan) | [
"p0",
"p2",
"p4",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 267118524218349059354406
% SZS output start Proof for 267118524218349059354406
1. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> (generous(X0) & creative(X0))) [input p0]
3. ! [X0] : ((~strong(X0) <~> ~creative(X0)) => (~funny(X0) <~> ~strong(X0))) [input p2]
5. ! [X0] : (strong(X0) => quiet(X0)) [input p4]
8. ! [X0] : ((tall(X0) | ~rich(X0)) <=> ~generous(X0)) [input p7]
10. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~tall(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> patient(X0)) [input p11]
13. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> ~quiet(X0)) [input p12]
21. funny(susan) [input hypothesis]
26. ! [X0] : ((~funny(X0) <~> ~strong(X0)) | (~strong(X0) <=> ~creative(X0))) [ennf transformation 3]
29. ! [X0] : (quiet(X0) | ~strong(X0)) [ennf transformation 5]
34. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 1]
35. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [flattening 34]
36. ! [X0] : (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) [nnf transformation 26]
40. ! [X0] : (((tall(X0) | ~rich(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) & rich(X0)))) [nnf transformation 8]
41. ! [X0] : ((tall(X0) | ~rich(X0) | generous(X0)) & (~generous(X0) | (~tall(X0) & rich(X0)))) [flattening 40]
47. ! [X0] : (((~patient(X0) & creative(X0)) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 10]
48. ! [X0] : (((~patient(X0) & creative(X0)) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | patient(X0) | ~creative(X0))) [flattening 47]
49. ! [X0] : (((~patient(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((~patient(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | calm(X0))) [flattening 49]
51. ! [X0] : (((~creative(X0) | ~tall(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [nnf transformation 13]
52. ! [X0] : ((~creative(X0) | ~tall(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [flattening 51]
67. generous(X0) | strong(X0) | generous(X0) [cnf transformation 35]
68. ~generous(X0) | strong(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 35]
72. ~strong(X0) | ~funny(X0) | ~strong(X0) | creative(X0) [cnf transformation 36]
76. ~strong(X0) | quiet(X0) [cnf transformation 29]
84. ~tall(X0) | ~generous(X0) [cnf transformation 41]
95. ~tall(X0) | patient(X0) | ~creative(X0) [cnf transformation 48]
96. ~funny(X0) | tall(X0) | creative(X0) [cnf transformation 48]
101. ~patient(X0) | ~patient(X0) [cnf transformation 50]
102. ~quiet(X0) | tall(X0) [cnf transformation 52]
123. funny(susan) [cnf transformation 21]
125. ~patient(X0) [duplicate literal removal 101]
126. ~funny(X0) | ~strong(X0) | creative(X0) [duplicate literal removal 72]
128. generous(X0) | strong(X0) [duplicate literal removal 67]
129. ~creative(X0) | strong(X0) | ~generous(X0) [duplicate literal removal 68]
187. 13 <=> ! [X3] : (~quiet(X3) | tall(X3)) [avatar definition]
188. ~quiet(X3) | tall(X3) <- (13) [avatar component clause 187]
205. 13 [avatar split clause 102,187]
318. tall(susan) | creative(susan) [resolution 96,123]
320. 36 <=> creative(susan) [avatar definition]
322. creative(susan) <- (36) [avatar component clause 320]
324. 37 <=> tall(susan) [avatar definition]
326. tall(susan) <- (37) [avatar component clause 324]
327. 36 | 37 [avatar split clause 318,324,320]
349. ~strong(susan) | creative(susan) [resolution 126,123]
366. strong(susan) | ~generous(susan) <- (36) [resolution 129,322]
367. strong(susan) <- (36) [subsumption resolution 366,128]
371. quiet(susan) <- (36) [resolution 367,76]
373. tall(susan) <- (13, 36) [resolution 371,188]
375. 37 | ~13 | ~36 [avatar split clause 373,320,187,324]
378. patient(susan) | ~creative(susan) <- (37) [resolution 326,95]
379. ~generous(susan) <- (37) [resolution 326,84]
380. ~creative(susan) <- (37) [subsumption resolution 378,125]
383. ~36 | ~37 [avatar split clause 380,324,320]
391. 41 <=> strong(susan) [avatar definition]
393. ~strong(susan) <- (~41) [avatar component clause 391]
394. 36 | ~41 [avatar split clause 349,391,320]
395. strong(susan) <- (37) [resolution 379,128]
396. $false <- (37, ~41) [subsumption resolution 395,393]
397. ~37 | 41 [avatar contradiction clause 396]
398. $false [avatar sat refutation 205,327,375,383,394,397]
% SZS output end Proof for 267118524218349059354406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is quiet.
Everyone who is not kind or wise is strong and vice versa.
Everyone who is curious is both not calm and not humble.
Everyone who is not calm is old.
Everyone who is not strong or curious is happy or patient.
Everyone who is old is strong and vice versa.
Everyone who is either not patient or not wise is both not funny and not strong and vice versa.
If someone is strong then paul is tall or funny.
Everyone who is not curious or not wise is both humble and not wise.
Everyone who is either old or kind is both not tall and not brave and vice versa.
If someone is either not quiet or tall then someone is both not creative and patient and vice versa.
If someone is both not quiet and patient then someone is both not patient and not brave.
Everyone who is not happy is not brave or happy and vice versa.
If someone is both not curious and not calm then susan is wise or rich.
If someone is not humble then someone is either humble or not happy.
Everyone who is both patient and happy is calm or tall.
Mary is either not funny or not quiet.
Alice is not tall.
Susan is both not happy and not funny.
Mary is not strong.
Someone is either quiet or humble.
Someone is either creative or not generous.
Someone is not humble or creative.
Susan is patient. | Mary is not wise. | entailment | (![X]:(~kind(X)=>quiet(X)))&
(![X]:((~kind(X)|wise(X))<=>strong(X)))&
(![X]:(curious(X)=>(~calm(X)&~humble(X))))&
(![X]:(~calm(X)=>old(X)))&
(![X]:((~strong(X)|curious(X))=>(happy(X)|patient(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~patient(X)<~>~wise(X))<=>(~funny(X)&~strong(X))))&
((?[X]:(strong(X)))=>((tall(paul)|funny(paul))))&
(![X]:((~curious(X)|~wise(X))=>(humble(X)&~wise(X))))&
(![X]:((old(X)<~>kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((~creative(X)&patient(X)))))&
((?[X]:((~quiet(X)&patient(X))))=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:(~happy(X)<=>(~brave(X)|happy(X))))&
((?[X]:((~curious(X)&~calm(X))))=>((wise(susan)|rich(susan))))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((patient(X)&happy(X))=>(calm(X)|tall(X))))&
((~funny(mary)<~>~quiet(mary)))&
(~tall(alice))&
((~happy(susan)&~funny(susan)))&
(~strong(mary))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((~humble(X)|creative(X))))&
(patient(susan)) | ~wise(mary) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6580129592188340401637524
% SZS output start Proof for 6580129592188340401637524
2. ! [X0] : ((wise(X0) | ~kind(X0)) <=> strong(X0)) [input p1]
20. ~strong(mary) [input p19]
25. wise(mary) [input hypothesis]
42. ! [X0] : (((wise(X0) | ~kind(X0)) | ~strong(X0)) & (strong(X0) | (~wise(X0) & kind(X0)))) [nnf transformation 2]
43. ! [X0] : ((wise(X0) | ~kind(X0) | ~strong(X0)) & (strong(X0) | (~wise(X0) & kind(X0)))) [flattening 42]
74. ~wise(X0) | strong(X0) [cnf transformation 43]
119. ~strong(mary) [cnf transformation 20]
126. wise(mary) [cnf transformation 25]
239. strong(mary) [resolution 74,126]
240. $false [subsumption resolution 239,119]
% SZS output end Proof for 6580129592188340401637524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not kind is not brave or not funny and vice versa.
Everyone who is both not calm and not happy is not generous or not rich.
Everyone who is either funny or creative is kind or funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
Everyone who is not rich or kind is not calm.
Someone is either old or not tall.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative.
Someone is both not humble and not wise.
Someone is both rich and quiet.
Lucy is either not humble or humble.
Someone is either creative or not wise. | Mary is not calm. | contradiction | (![X]:((humble(X)<~>~kind(X))<=>(~brave(X)|~funny(X))))&
(![X]:((~calm(X)&~happy(X))=>(~generous(X)|~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(kind(X)|funny(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((rich(X)&quiet(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X)))) | ~calm(mary) | [
"p2",
"p7",
"p11",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2490655251141689616998700
% SZS output start Proof for 2490655251141689616998700
3. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (funny(X0) | kind(X0))) [input p2]
8. ! [X0] : ((humble(X0) & ~tall(X0)) <=> strong(X0)) [input p7]
12. ! [X0] : ((~rich(X0) | ~tall(X0)) => calm(X0)) [input p11]
14. ? [X0] : (~funny(X0) <~> strong(X0)) <=> (tall(mary) <~> ~calm(mary)) [input p13]
16. ! [X0] : ((kind(X0) | ~rich(X0)) => ~calm(X0)) [input p15]
20. rich(alice) <~> ~creative(alice) [input p19]
25. ~calm(mary) [input hypothesis]
30. ! [X0] : (calm(X0) | (rich(X0) & tall(X0))) [ennf transformation 12]
33. ! [X0] : (~calm(X0) | (~kind(X0) & rich(X0))) [ennf transformation 16]
36. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 36]
45. ! [X0] : (((humble(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | (~humble(X0) | tall(X0)))) [nnf transformation 8]
46. ! [X0] : (((humble(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | ~humble(X0) | tall(X0))) [flattening 45]
59. (? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X0] : ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0)))) [nnf transformation 14]
60. (? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X1] : ((~funny(X1) | ~strong(X1)) & (strong(X1) | funny(X1)))) [rectify 59]
61. ? [X0] : ((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) => ((~strong(sK3) | funny(sK3)) & (strong(sK3) | ~funny(sK3))) [choice axiom]
62. (((~strong(sK3) | funny(sK3)) & (strong(sK3) | ~funny(sK3))) | ((tall(mary) | calm(mary)) & (~calm(mary) | ~tall(mary)))) & (((calm(mary) | ~tall(mary)) & (~calm(mary) | tall(mary))) | ! [X1] : ((~funny(X1) | ~strong(X1)) & (strong(X1) | funny(X1)))) [skolemisation 60,61]
69. (creative(alice) | ~rich(alice)) & (~creative(alice) | rich(alice)) [nnf transformation 20]
85. funny(X0) | kind(X0) | funny(X0) | ~creative(X0) [cnf transformation 37]
89. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 37]
106. ~strong(X0) | ~tall(X0) [cnf transformation 46]
123. tall(X0) | calm(X0) [cnf transformation 30]
124. rich(X0) | calm(X0) [cnf transformation 30]
130. calm(mary) | ~tall(mary) | strong(X1) | funny(X1) [cnf transformation 62]
138. ~calm(X0) | rich(X0) [cnf transformation 33]
139. ~calm(X0) | ~kind(X0) [cnf transformation 33]
146. creative(alice) | ~rich(alice) [cnf transformation 69]
155. ~calm(mary) [cnf transformation 25]
158. funny(X0) | kind(X0) | ~creative(X0) [duplicate literal removal 85]
159. ~creative(X0) | ~funny(X0) [duplicate literal removal 89]
160. ~creative(X0) | kind(X0) [subsumption resolution 158,159]
258. 21 <=> calm(mary) [avatar definition]
276. calm(mary) | strong(X1) | funny(X1) [subsumption resolution 130,123]
278. 25 <=> ! [X1] : (strong(X1) | funny(X1)) [avatar definition]
279. strong(X1) | funny(X1) <- (25) [avatar component clause 278]
280. 25 | 21 [avatar split clause 276,258,278]
286. rich(X0) [subsumption resolution 138,124]
298. creative(alice) [subsumption resolution 146,286]
309. ~21 [avatar split clause 155,258]
321. ~funny(alice) [resolution 159,298]
322. kind(alice) [resolution 160,298]
325. ~tall(X2) | funny(X2) <- (25) [resolution 279,106]
420. 41 <=> tall(alice) [avatar definition]
421. ~tall(alice) <- (~41) [avatar component clause 420]
422. tall(alice) <- (41) [avatar component clause 420]
566. funny(alice) <- (25, 41) [resolution 422,325]
572. $false <- (25, 41) [subsumption resolution 566,321]
573. ~25 | ~41 [avatar contradiction clause 572]
588. calm(alice) <- (~41) [resolution 421,123]
716. ~kind(alice) <- (~41) [resolution 588,139]
717. $false <- (~41) [subsumption resolution 716,322]
718. 41 [avatar contradiction clause 717]
719. $false [avatar sat refutation 280,309,573,718]
% SZS output end Proof for 2490655251141689616998700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not quiet is both curious and tall.
If someone is generous then fred is either quiet or not old and vice versa.
Everyone who is both funny and tall is old or not rich and vice versa.
If mary is both not happy and patient then someone is generous.
Everyone who is not funny or not tall is both creative and patient and vice versa.
If lucy is curious then someone is calm or generous and vice versa.
Everyone who is not curious or not funny is both not quiet and humble and vice versa.
If someone is wise then someone is not generous and vice versa.
If someone is either not wise or funny then someone is either humble or not curious.
Everyone who is humble is generous or brave and vice versa.
Everyone who is not quiet or rich is not patient or rich.
If susan is both happy and not tall then someone is either not curious or old and vice versa.
If someone is both not happy and wise then susan is either not creative or not old and vice versa.
If fred is both not generous and not rich then someone is either humble or not kind.
Everyone who is both humble and strong is brave or not wise and vice versa.
If someone is not creative then someone is both not curious and not generous and vice versa.
Lucy is not old.
Someone is not curious or not funny.
Someone is patient or humble.
John is kind.
Someone is generous or brave.
Alice is not calm or curious.
Someone is either quiet or not happy. | Susan is not old. | entailment | (![X]:((~happy(X)|~quiet(X))=>(curious(X)&tall(X))))&
((?[X]:(generous(X)))<=>((quiet(fred)<~>~old(fred))))&
(![X]:((funny(X)&tall(X))<=>(old(X)|~rich(X))))&
(((~happy(mary)&patient(mary)))=>(?[X]:(generous(X))))&
(![X]:((~funny(X)|~tall(X))<=>(creative(X)&patient(X))))&
((curious(lucy))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~curious(X)|~funny(X))<=>(~quiet(X)&humble(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~generous(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(humble(X)<=>(generous(X)|brave(X))))&
(![X]:((~quiet(X)|rich(X))=>(~patient(X)|rich(X))))&
(((happy(susan)&~tall(susan)))<=>(?[X]:((~curious(X)<~>old(X)))))&
((?[X]:((~happy(X)&wise(X))))<=>((~creative(susan)<~>~old(susan))))&
(((~generous(fred)&~rich(fred)))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((humble(X)&strong(X))<=>(brave(X)|~wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
(~old(lucy))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((patient(X)|humble(X))))&
(kind(john))&
(?[X]:((generous(X)|brave(X))))&
((~calm(alice)|curious(alice)))&
(?[X]:((quiet(X)<~>~happy(X)))) | ~old(susan) | [
"p0",
"p2",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6031565660008481638143984
% SZS output start Proof for 6031565660008481638143984
1. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (tall(X0) & curious(X0))) [input p0]
3. ! [X0] : ((tall(X0) & funny(X0)) <=> (~rich(X0) | old(X0))) [input p2]
7. ! [X0] : ((~funny(X0) | ~curious(X0)) <=> (humble(X0) & ~quiet(X0))) [input p6]
12. (~tall(susan) & happy(susan)) <=> ? [X0] : (~curious(X0) <~> old(X0)) [input p11]
24. old(susan) [input hypothesis]
28. ! [X0] : ((tall(X0) & curious(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 1]
40. ! [X0] : (((tall(X0) & funny(X0)) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | (~tall(X0) | ~funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((tall(X0) & funny(X0)) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | ~tall(X0) | ~funny(X0))) [flattening 40]
50. ! [X0] : (((~funny(X0) | ~curious(X0)) | (~humble(X0) | quiet(X0))) & ((humble(X0) & ~quiet(X0)) | (funny(X0) & curious(X0)))) [nnf transformation 7]
51. ! [X0] : ((~funny(X0) | ~curious(X0) | ~humble(X0) | quiet(X0)) & ((humble(X0) & ~quiet(X0)) | (funny(X0) & curious(X0)))) [flattening 50]
63. ((~tall(susan) & happy(susan)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (tall(susan) | ~happy(susan))) [nnf transformation 12]
64. ((~tall(susan) & happy(susan)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | tall(susan) | ~happy(susan)) [flattening 63]
65. ((~tall(susan) & happy(susan)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (? [X1] : ((~old(X1) | curious(X1)) & (old(X1) | ~curious(X1))) | tall(susan) | ~happy(susan)) [rectify 64]
66. ? [X1] : ((~old(X1) | curious(X1)) & (old(X1) | ~curious(X1))) => ((~old(sK6) | curious(sK6)) & (old(sK6) | ~curious(sK6))) [choice axiom]
67. ((~tall(susan) & happy(susan)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(sK6) | curious(sK6)) & (old(sK6) | ~curious(sK6))) | tall(susan) | ~happy(susan)) [skolemisation 65,66]
92. curious(X0) | quiet(X0) [cnf transformation 28]
102. ~old(X0) | tall(X0) [cnf transformation 41]
113. ~quiet(X0) | curious(X0) [cnf transformation 51]
134. ~tall(susan) | ~curious(X0) | ~old(X0) [cnf transformation 67]
159. old(susan) [cnf transformation 24]
211. curious(X0) [subsumption resolution 113,92]
242. ~tall(susan) | ~old(X0) [subsumption resolution 134,211]
244. 19 <=> ! [X0] : ~old(X0) [avatar definition]
245. ~old(X0) <- (19) [avatar component clause 244]
247. 20 <=> tall(susan) [avatar definition]
249. ~tall(susan) <- (~20) [avatar component clause 247]
250. 19 | ~20 [avatar split clause 242,247,244]
265. 23 <=> old(susan) [avatar definition]
267. old(susan) <- (23) [avatar component clause 265]
346. 23 [avatar split clause 159,265]
355. $false <- (19, 23) [resolution 267,245]
356. ~19 | ~23 [avatar contradiction clause 355]
363. tall(susan) <- (23) [resolution 102,267]
365. $false <- (~20, 23) [subsumption resolution 363,249]
366. 20 | ~23 [avatar contradiction clause 365]
367. $false [avatar sat refutation 250,346,356,366]
% SZS output end Proof for 6031565660008481638143984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not old then someone is not humble or kind and vice versa.
Everyone who is both humble and calm is not tall or not brave and vice versa.
Everyone who is either kind or not patient is not wise or not strong and vice versa.
Everyone who is not quiet or old is both patient and happy and vice versa.
If someone is not funny or generous then alice is quiet or not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
If lucy is quiet or tall then susan is humble or not patient.
If john is either not calm or not strong then someone is not creative or not humble and vice versa.
If lucy is not curious then fred is both not patient and curious.
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
Someone is either not creative or not calm.
Someone is either quiet or not curious.
Someone is either funny or not old.
Someone is both not wise and strong.
Someone is either patient or not generous.
Someone is rich or not wise. | Susan is not wise. | neutral | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((humble(X)&calm(X))<=>(~tall(X)|~brave(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(~wise(X)|~strong(X))))&
(![X]:((~quiet(X)|old(X))<=>(patient(X)&happy(X))))&
((?[X]:((~funny(X)|generous(X))))<=>((quiet(alice)|~rich(alice))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(((quiet(lucy)|tall(lucy)))=>((humble(susan)|~patient(susan))))&
(((~calm(john)<~>~strong(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
((~curious(lucy))=>((~patient(fred)&curious(fred))))&
(![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(?[X]:((~creative(X)<~>~calm(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((rich(X)|~wise(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is not wise is not old or wise.
Everyone who is both not generous and not creative is both not brave and wise and vice versa.
Everyone who is both not humble and generous is not generous.
Everyone who is either not old or quiet is both old and not strong and vice versa.
Everyone who is creative or not funny is both not humble and not calm.
If susan is not calm or not brave then mary is both not generous and quiet.
Everyone who is either creative or patient is not calm or not old.
Everyone who is not quiet is both rich and not strong and vice versa.
Everyone who is generous is either not old or quiet.
If mary is rich or humble then someone is humble and vice versa.
If someone is either not generous or not kind then someone is funny or tall and vice versa.
Everyone who is either not rich or not brave is both generous and not humble and vice versa.
Everyone who is kind or not creative is both not patient and not rich.
Everyone who is both curious and not tall is quiet and vice versa.
If someone is either not kind or not patient then paul is funny or calm and vice versa.
If paul is not rich or not calm then alice is both not happy and not patient.
Someone is either not curious or old.
Someone is not funny.
Someone is either old or rich.
Someone is either happy or not curious.
Someone is both calm and wise.
Susan is either not kind or not tall. | Paul is quiet. | entailment | (![X]:(~wise(X)=>(~old(X)|wise(X))))&
(![X]:((~generous(X)&~creative(X))<=>(~brave(X)&wise(X))))&
(![X]:((~humble(X)&generous(X))=>~generous(X)))&
(![X]:((~old(X)<~>quiet(X))<=>(old(X)&~strong(X))))&
(![X]:((creative(X)|~funny(X))=>(~humble(X)&~calm(X))))&
(((~calm(susan)|~brave(susan)))=>((~generous(mary)&quiet(mary))))&
(![X]:((creative(X)<~>patient(X))=>(~calm(X)|~old(X))))&
(![X]:(~quiet(X)<=>(rich(X)&~strong(X))))&
(![X]:(generous(X)=>(~old(X)<~>quiet(X))))&
(((rich(mary)|humble(mary)))<=>(?[X]:(humble(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((~rich(X)<~>~brave(X))<=>(generous(X)&~humble(X))))&
(![X]:((kind(X)|~creative(X))=>(~patient(X)&~rich(X))))&
(![X]:((curious(X)&~tall(X))<=>quiet(X)))&
((?[X]:((~kind(X)<~>~patient(X))))<=>((funny(paul)|calm(paul))))&
(((~rich(paul)|~calm(paul)))=>((~happy(alice)&~patient(alice))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((old(X)<~>rich(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((~kind(susan)<~>~tall(susan))) | quiet(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6929983788988318267350774
% SZS output start Proof for 6929983788988318267350774
4. ! [X0] : ((~old(X0) <~> quiet(X0)) <=> (~strong(X0) & old(X0))) [input p3]
8. ! [X0] : (~quiet(X0) <=> (~strong(X0) & rich(X0))) [input p7]
23. ~quiet(paul) [input hypothesis]
38. ! [X0] : ((((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | (strong(X0) | ~old(X0))) & ((~strong(X0) & old(X0)) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | strong(X0) | ~old(X0)) & ((~strong(X0) & old(X0)) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0))))) [flattening 38]
41. ! [X0] : ((~quiet(X0) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | quiet(X0))) [nnf transformation 8]
42. ! [X0] : ((~quiet(X0) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | quiet(X0))) [flattening 41]
83. old(X0) | quiet(X0) | old(X0) [cnf transformation 39]
87. quiet(X0) | ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 39]
100. ~strong(X0) | quiet(X0) [cnf transformation 42]
147. ~quiet(paul) [cnf transformation 23]
148. quiet(X0) | old(X0) [duplicate literal removal 83]
149. ~old(X0) | quiet(X0) | strong(X0) [duplicate literal removal 87]
328. old(paul) [resolution 148,147]
384. quiet(paul) | strong(paul) [resolution 149,328]
388. strong(paul) [subsumption resolution 384,147]
392. quiet(paul) [resolution 388,100]
393. $false [subsumption resolution 392,147]
% SZS output end Proof for 6929983788988318267350774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or brave is not kind.
Everyone who is either happy or tall is both rich and curious.
Everyone who is not calm or not humble is both happy and wise.
Everyone who is either not tall or not happy is both generous and creative and vice versa.
If someone is both quiet and creative then alice is not patient.
Everyone who is rich or not strong is both happy and brave and vice versa.
Everyone who is rich is patient or not brave.
Everyone who is strong is not patient or happy and vice versa.
Everyone who is old or not wise is either generous or funny.
If someone is either brave or not calm then john is not old or not quiet.
If alice is both creative and patient then someone is either not wise or not quiet and vice versa.
Everyone who is not kind or not old is either not kind or generous.
Everyone who is either not rich or not creative is brave.
If someone is not strong then someone is kind or not wise and vice versa.
If lucy is not happy then mary is creative and vice versa.
Everyone who is either not patient or not strong is either strong or rich and vice versa.
Susan is quiet or not calm.
Someone is not curious or strong.
Fred is brave.
Someone is both not tall and brave. | Fred is calm. | neutral | (![X]:((~wise(X)|brave(X))=>~kind(X)))&
(![X]:((happy(X)<~>tall(X))=>(rich(X)&curious(X))))&
(![X]:((~calm(X)|~humble(X))=>(happy(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(generous(X)&creative(X))))&
((?[X]:((quiet(X)&creative(X))))=>(~patient(alice)))&
(![X]:((rich(X)|~strong(X))<=>(happy(X)&brave(X))))&
(![X]:(rich(X)=>(patient(X)|~brave(X))))&
(![X]:(strong(X)<=>(~patient(X)|happy(X))))&
(![X]:((old(X)|~wise(X))=>(generous(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~calm(X))))=>((~old(john)|~quiet(john))))&
(((creative(alice)&patient(alice)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:((~kind(X)|~old(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~rich(X)<~>~creative(X))=>brave(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)|~wise(X)))))&
((~happy(lucy))<=>(creative(mary)))&
(![X]:((~patient(X)<~>~strong(X))<=>(strong(X)<~>rich(X))))&
((quiet(susan)|~calm(susan)))&
(?[X]:((~curious(X)|strong(X))))&
(brave(fred))&
(?[X]:((~tall(X)&brave(X)))) | calm(fred) | [] | null | 0 |
Everyone who is either strong or not kind is not happy or patient. Everyone who is either wise or not tall is both brave and generous. Everyone who is either not humble or generous is both not generous and not brave. Everyone who is not brave is both strong and not wise. Everyone who is both not old and humble is either funny or not rich. Everyone who is not brave is either strong or not kind and vice versa. If fred is either rich or wise then someone is either not curious or not strong and vice versa. If mary is happy then someone is both brave and not rich and vice versa. Everyone who is quiet or not calm is not kind or patient and vice versa. If someone is tall or calm then someone is rich or not generous and vice versa. If paul is wise then someone is funny or wise and vice versa. If someone is both not calm and creative then john is not quiet and vice versa. Everyone who is either generous or not patient is patient and vice versa. If someone is either not quiet or wise then john is either curious or kind and vice versa. If paul is funny or not strong then mary is either rich or funny and vice versa. If someone is both happy and calm then fred is either not old or not curious. Mary is brave. Someone is rich or kind. Susan is not tall or happy. Mary is either brave or quiet. Someone is both kind and curious. Mary is either not creative or calm. Someone is either humble or not rich. Someone is happy. | Mary is happy. | neutral | (![X]:((strong(X)<~>~kind(X))=>(~happy(X)|patient(X))))&
(![X]:((wise(X)<~>~tall(X))=>(brave(X)&generous(X))))&
(![X]:((~humble(X)<~>generous(X))=>(~generous(X)&~brave(X))))&
(![X]:(~brave(X)=>(strong(X)&~wise(X))))&
(![X]:((~old(X)&humble(X))=>(funny(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>(strong(X)<~>~kind(X))))&
(((rich(fred)<~>wise(fred)))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((happy(mary))<=>(?[X]:((brave(X)&~rich(X)))))&
(![X]:((quiet(X)|~calm(X))<=>(~kind(X)|patient(X))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((rich(X)|~generous(X)))))&
((wise(paul))<=>(?[X]:((funny(X)|wise(X)))))&
((?[X]:((~calm(X)&creative(X))))<=>(~quiet(john)))&
(![X]:((generous(X)<~>~patient(X))<=>patient(X)))&
((?[X]:((~quiet(X)<~>wise(X))))<=>((curious(john)<~>kind(john))))&
(((funny(paul)|~strong(paul)))<=>((rich(mary)<~>funny(mary))))&
((?[X]:((happy(X)&calm(X))))=>((~old(fred)<~>~curious(fred))))&
(brave(mary))&
(?[X]:((rich(X)|kind(X))))&
((~tall(susan)|happy(susan)))&
((brave(mary)<~>quiet(mary)))&
(?[X]:((kind(X)&curious(X))))&
((~creative(mary)<~>calm(mary)))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:(happy(X))) | happy(mary) | [] | null | 0 |
Everyone who is both curious and not rich is brave or quiet.
Everyone who is either wise or not old is not funny or not wise and vice versa.
Everyone who is either not rich or generous is both not calm and not generous and vice versa.
Everyone who is not old or not calm is both not rich and curious.
Everyone who is both not old and not curious is both happy and not patient and vice versa.
Everyone who is both not rich and not generous is both not strong and not funny.
Everyone who is quiet or creative is either not wise or rich and vice versa.
If someone is either funny or not kind then someone is rich or funny and vice versa.
If someone is either not patient or not happy then mary is not wise and vice versa.
Everyone who is quiet or brave is not strong and vice versa.
Everyone who is not funny is both not creative and rich and vice versa.
Everyone who is both not calm and tall is either brave or tall.
If fred is not strong or not creative then lucy is not quiet.
If lucy is humble then someone is not happy and vice versa.
If someone is either not quiet or not happy then john is either rich or happy and vice versa.
If someone is kind then someone is not curious or not happy and vice versa.
Someone is strong or rich.
Susan is not humble.
Someone is not humble.
Someone is either not wise or quiet.
Alice is happy or tall.
Paul is brave or not wise.
Mary is not old or creative. | Susan is not strong. | entailment | (![X]:((curious(X)&~rich(X))=>(brave(X)|quiet(X))))&
(![X]:((wise(X)<~>~old(X))<=>(~funny(X)|~wise(X))))&
(![X]:((~rich(X)<~>generous(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~old(X)|~calm(X))=>(~rich(X)&curious(X))))&
(![X]:((~old(X)&~curious(X))<=>(happy(X)&~patient(X))))&
(![X]:((~rich(X)&~generous(X))=>(~strong(X)&~funny(X))))&
(![X]:((quiet(X)|creative(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>(?[X]:((rich(X)|funny(X)))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(~wise(mary)))&
(![X]:((quiet(X)|brave(X))<=>~strong(X)))&
(![X]:(~funny(X)<=>(~creative(X)&rich(X))))&
(![X]:((~calm(X)&tall(X))=>(brave(X)<~>tall(X))))&
(((~strong(fred)|~creative(fred)))=>(~quiet(lucy)))&
((humble(lucy))<=>(?[X]:(~happy(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((rich(john)<~>happy(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(?[X]:((strong(X)|rich(X))))&
(~humble(susan))&
(?[X]:(~humble(X)))&
(?[X]:((~wise(X)<~>quiet(X))))&
((happy(alice)|tall(alice)))&
((brave(paul)|~wise(paul)))&
((~old(mary)|creative(mary))) | ~strong(susan) | [
"p0",
"p1",
"p3",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3101552580954255900282197
% SZS output start Proof for 3101552580954255900282197
1. ! [X0] : ((~rich(X0) & curious(X0)) => (quiet(X0) | brave(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> ~old(X0)) <=> (~wise(X0) | ~funny(X0))) [input p1]
4. ! [X0] : ((~calm(X0) | ~old(X0)) => (curious(X0) & ~rich(X0))) [input p3]
7. ! [X0] : ((creative(X0) | quiet(X0)) <=> (~wise(X0) <~> rich(X0))) [input p6]
10. ! [X0] : ((brave(X0) | quiet(X0)) <=> ~strong(X0)) [input p9]
11. ! [X0] : (~funny(X0) <=> (rich(X0) & ~creative(X0))) [input p10]
24. strong(susan) [input hypothesis]
27. ! [X0] : ((quiet(X0) | brave(X0)) | (rich(X0) | ~curious(X0))) [ennf transformation 1]
28. ! [X0] : (quiet(X0) | brave(X0) | rich(X0) | ~curious(X0)) [flattening 27]
29. ! [X0] : ((curious(X0) & ~rich(X0)) | (calm(X0) & old(X0))) [ennf transformation 4]
35. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [nnf transformation 2]
36. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [flattening 35]
41. ! [X0] : (((creative(X0) | quiet(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | quiet(X0) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (~creative(X0) & ~quiet(X0)))) [flattening 41]
52. ! [X0] : (((brave(X0) | quiet(X0)) | strong(X0)) & (~strong(X0) | (~brave(X0) & ~quiet(X0)))) [nnf transformation 10]
53. ! [X0] : ((brave(X0) | quiet(X0) | strong(X0)) & (~strong(X0) | (~brave(X0) & ~quiet(X0)))) [flattening 52]
54. ! [X0] : ((~funny(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | funny(X0))) [nnf transformation 11]
55. ! [X0] : ((~funny(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | funny(X0))) [flattening 54]
77. ~curious(X0) | brave(X0) | rich(X0) | quiet(X0) [cnf transformation 28]
78. ~wise(X0) | ~funny(X0) | ~old(X0) | ~wise(X0) [cnf transformation 36]
81. ~old(X0) | wise(X0) | wise(X0) [cnf transformation 36]
90. ~rich(X0) | old(X0) [cnf transformation 29]
92. old(X0) | curious(X0) [cnf transformation 29]
105. ~wise(X0) | quiet(X0) | creative(X0) | ~rich(X0) [cnf transformation 42]
116. ~strong(X0) | ~quiet(X0) [cnf transformation 53]
117. ~strong(X0) | ~brave(X0) [cnf transformation 53]
119. ~creative(X0) | funny(X0) [cnf transformation 55]
120. funny(X0) | rich(X0) [cnf transformation 55]
147. strong(susan) [cnf transformation 24]
151. ~wise(X0) | ~funny(X0) | ~old(X0) [duplicate literal removal 78]
152. ~old(X0) | wise(X0) [duplicate literal removal 81]
153. ~funny(X0) | ~old(X0) [subsumption resolution 151,152]
339. ~quiet(susan) [resolution 116,147]
341. ~brave(susan) [resolution 117,147]
348. ~old(X0) | rich(X0) [resolution 153,120]
388. 46 <=> rich(susan) [avatar definition]
389. ~rich(susan) <- (~46) [avatar component clause 388]
390. rich(susan) <- (46) [avatar component clause 388]
410. old(susan) <- (46) [resolution 390,90]
428. wise(susan) <- (46) [resolution 410,152]
520. quiet(susan) | creative(susan) | ~rich(susan) <- (46) [resolution 105,428]
523. creative(susan) | ~rich(susan) <- (46) [subsumption resolution 520,339]
524. creative(susan) <- (46) [subsumption resolution 523,390]
555. rich(X0) | curious(X0) [resolution 348,92]
676. funny(susan) <- (46) [resolution 524,119]
724. ~old(susan) <- (46) [resolution 676,153]
725. $false <- (46) [subsumption resolution 724,410]
726. ~46 [avatar contradiction clause 725]
727. curious(susan) <- (~46) [resolution 389,555]
729. brave(susan) | rich(susan) | quiet(susan) <- (~46) [resolution 727,77]
730. rich(susan) | quiet(susan) <- (~46) [subsumption resolution 729,341]
731. quiet(susan) <- (~46) [subsumption resolution 730,389]
732. $false <- (~46) [subsumption resolution 731,339]
733. 46 [avatar contradiction clause 732]
734. $false [avatar sat refutation 726,733]
% SZS output end Proof for 3101552580954255900282197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or kind is wise or not patient.
If susan is not strong then john is either humble or not patient and vice versa.
Everyone who is both not creative and calm is patient or curious and vice versa.
If alice is rich or not creative then someone is not patient and vice versa.
If someone is not patient or brave then john is both happy and not patient and vice versa.
If someone is both not calm and not creative then someone is both not calm and not generous and vice versa.
If someone is not strong or not kind then someone is both funny and not calm and vice versa.
Everyone who is both patient and not patient is quiet.
Everyone who is both not strong and patient is not curious or creative and vice versa.
Everyone who is strong or not old is curious or not funny.
Everyone who is both tall and quiet is calm or not tall and vice versa.
If lucy is both patient and not wise then mary is either patient or old and vice versa.
Everyone who is both funny and not rich is not old.
If someone is kind or humble then someone is either strong or funny.
If someone is both not curious and strong then someone is both not old and patient.
Susan is patient.
Someone is both old and strong.
Mary is not old.
Someone is either not happy or quiet.
Someone is either not tall or happy.
Susan is either brave or not generous. | Alice is not generous. | neutral | (![X]:((~generous(X)|kind(X))=>(wise(X)|~patient(X))))&
((~strong(susan))<=>((humble(john)<~>~patient(john))))&
(![X]:((~creative(X)&calm(X))<=>(patient(X)|curious(X))))&
(((rich(alice)|~creative(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~patient(X)|brave(X))))<=>((happy(john)&~patient(john))))&
((?[X]:((~calm(X)&~creative(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:((patient(X)&~patient(X))=>quiet(X)))&
(![X]:((~strong(X)&patient(X))<=>(~curious(X)|creative(X))))&
(![X]:((strong(X)|~old(X))=>(curious(X)|~funny(X))))&
(![X]:((tall(X)&quiet(X))<=>(calm(X)|~tall(X))))&
(((patient(lucy)&~wise(lucy)))<=>((patient(mary)<~>old(mary))))&
(![X]:((funny(X)&~rich(X))=>~old(X)))&
((?[X]:((kind(X)|humble(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((~old(X)&patient(X)))))&
(patient(susan))&
(?[X]:((old(X)&strong(X))))&
(~old(mary))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>happy(X))))&
((brave(susan)<~>~generous(susan))) | ~generous(alice) | [] | null | 0 |
If alice is funny or humble then fred is both brave and not wise and vice versa.
Everyone who is both not quiet and rich is not creative.
If someone is either wise or calm then lucy is either not calm or generous.
If someone is old or not patient then someone is not creative.
If someone is not happy or not kind then susan is tall or creative.
Everyone who is both funny and curious is either not rich or not kind.
If someone is funny or curious then someone is either happy or not brave and vice versa.
Everyone who is not happy or quiet is both old and not brave and vice versa.
Everyone who is both curious and not strong is not kind or not happy and vice versa.
Everyone who is patient is not generous and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not quiet or creative is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
If someone is both kind and not rich then someone is not curious.
Everyone who is rich or not tall is either tall or calm.
Fred is both not humble and not rich.
Someone is both humble and not rich.
Paul is kind or funny.
Someone is either not rich or not wise.
Susan is both not kind and not old.
Fred is funny.
Someone is both brave and not rich.
Someone is either not strong or not wise. | Fred is not wise. | entailment | (((funny(alice)|humble(alice)))<=>((brave(fred)&~wise(fred))))&
(![X]:((~quiet(X)&rich(X))=>~creative(X)))&
((?[X]:((wise(X)<~>calm(X))))=>((~calm(lucy)<~>generous(lucy))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((tall(susan)|creative(susan))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((~humble(fred)&~rich(fred)))&
(?[X]:((humble(X)&~rich(X))))&
((kind(paul)|funny(paul)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((~kind(susan)&~old(susan)))&
(funny(fred))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((~strong(X)<~>~wise(X)))) | ~wise(fred) | [
"p5",
"p8",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 693432889902674194825649
% SZS output start Proof for 693432889902674194825649
6. ! [X0] : ((curious(X0) & funny(X0)) => (~rich(X0) <~> ~kind(X0))) [input p5]
9. ! [X0] : ((~strong(X0) & curious(X0)) <=> (~happy(X0) | ~kind(X0))) [input p8]
14. ! [X0] : ((quiet(X0) | wise(X0)) <=> (~kind(X0) <~> ~funny(X0))) [input p13]
17. ~rich(fred) & ~humble(fred) [input p16]
22. funny(fred) [input p21]
25. wise(fred) [input hypothesis]
36. ! [X0] : ((~rich(X0) <~> ~kind(X0)) | (~curious(X0) | ~funny(X0))) [ennf transformation 6]
37. ! [X0] : ((~rich(X0) <~> ~kind(X0)) | ~curious(X0) | ~funny(X0)) [flattening 36]
49. ! [X0] : (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | ~curious(X0) | ~funny(X0)) [nnf transformation 37]
57. ! [X0] : (((~strong(X0) & curious(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (strong(X0) | ~curious(X0)))) [nnf transformation 9]
58. ! [X0] : (((~strong(X0) & curious(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | strong(X0) | ~curious(X0))) [flattening 57]
65. ! [X0] : (((quiet(X0) | wise(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 14]
66. ! [X0] : ((quiet(X0) | wise(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~quiet(X0) & ~wise(X0)))) [flattening 65]
96. ~curious(X0) | rich(X0) | kind(X0) | ~funny(X0) [cnf transformation 49]
109. curious(X0) | kind(X0) [cnf transformation 58]
124. ~kind(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 66]
136. ~rich(fred) [cnf transformation 17]
144. funny(fred) [cnf transformation 22]
149. wise(fred) [cnf transformation 25]
156. 2 <=> wise(fred) [avatar definition]
158. wise(fred) <- (2) [avatar component clause 156]
311. 2 [avatar split clause 149,156]
444. rich(X1) | kind(X1) | ~funny(X1) | kind(X1) [resolution 96,109]
445. ~funny(X1) | kind(X1) | rich(X1) [duplicate literal removal 444]
599. kind(fred) | rich(fred) [resolution 445,144]
602. kind(fred) [subsumption resolution 599,136]
619. ~funny(fred) | ~wise(fred) [resolution 602,124]
638. ~wise(fred) [subsumption resolution 619,144]
639. $false <- (2) [subsumption resolution 638,158]
640. ~2 [avatar contradiction clause 639]
645. $false [avatar sat refutation 311,640]
% SZS output end Proof for 693432889902674194825649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and quiet then paul is either not patient or not brave and vice versa.
Everyone who is not curious or wise is either not creative or not rich and vice versa.
Everyone who is not humble or not happy is both old and not calm.
If alice is either not brave or old then lucy is rich.
Everyone who is generous is both not rich and not happy and vice versa.
Everyone who is brave or not generous is both humble and patient and vice versa.
Everyone who is not generous or kind is not quiet and vice versa.
Everyone who is either tall or curious is either not creative or rich and vice versa.
If lucy is kind or not humble then lucy is either not curious or not happy and vice versa.
Everyone who is curious or brave is both not rich and not kind and vice versa.
Everyone who is both not funny and wise is not happy or not old and vice versa.
If mary is either quiet or not kind then someone is either creative or not quiet.
Everyone who is both tall and rich is curious or not funny and vice versa.
Everyone who is tall or quiet is either not calm or not generous and vice versa.
If paul is not happy or not rich then mary is not quiet or funny.
Someone is tall or strong.
Lucy is wise.
Someone is both wise and not rich.
Someone is not creative.
Someone is either not funny or not tall.
Someone is both not creative and strong.
Someone is either not tall or curious.
Someone is either not tall or not kind. | Alice is funny. | entailment | ((?[X]:((rich(X)&quiet(X))))<=>((~patient(paul)<~>~brave(paul))))&
(![X]:((~curious(X)|wise(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((~humble(X)|~happy(X))=>(old(X)&~calm(X))))&
(((~brave(alice)<~>old(alice)))=>(rich(lucy)))&
(![X]:(generous(X)<=>(~rich(X)&~happy(X))))&
(![X]:((brave(X)|~generous(X))<=>(humble(X)&patient(X))))&
(![X]:((~generous(X)|kind(X))<=>~quiet(X)))&
(![X]:((tall(X)<~>curious(X))<=>(~creative(X)<~>rich(X))))&
(((kind(lucy)|~humble(lucy)))<=>((~curious(lucy)<~>~happy(lucy))))&
(![X]:((curious(X)|brave(X))<=>(~rich(X)&~kind(X))))&
(![X]:((~funny(X)&wise(X))<=>(~happy(X)|~old(X))))&
(((quiet(mary)<~>~kind(mary)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)&rich(X))<=>(curious(X)|~funny(X))))&
(![X]:((tall(X)|quiet(X))<=>(~calm(X)<~>~generous(X))))&
(((~happy(paul)|~rich(paul)))=>((~quiet(mary)|funny(mary))))&
(?[X]:((tall(X)|strong(X))))&
(wise(lucy))&
(?[X]:((wise(X)&~rich(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~tall(X))))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:((~tall(X)<~>~kind(X)))) | funny(alice) | [
"p1",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6634587065286668556857593
% SZS output start Proof for 6634587065286668556857593
2. ! [X0] : ((wise(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p1]
8. ! [X0] : ((tall(X0) <~> curious(X0)) <=> (~creative(X0) <~> rich(X0))) [input p7]
10. ! [X0] : ((brave(X0) | curious(X0)) <=> (~kind(X0) & ~rich(X0))) [input p9]
13. ! [X0] : ((rich(X0) & tall(X0)) <=> (~funny(X0) | curious(X0))) [input p12]
24. ~funny(alice) [input hypothesis]
36. ! [X0] : (((wise(X0) | ~curious(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~wise(X0) & curious(X0)))) [nnf transformation 2]
37. ! [X0] : ((wise(X0) | ~curious(X0) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~wise(X0) & curious(X0)))) [flattening 36]
45. ! [X0] : ((((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))))) [nnf transformation 8]
48. ! [X0] : (((brave(X0) | curious(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 10]
49. ! [X0] : ((brave(X0) | curious(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 48]
55. ! [X0] : (((rich(X0) & tall(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (~rich(X0) | ~tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((rich(X0) & tall(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~rich(X0) | ~tall(X0))) [flattening 55]
80. ~creative(X0) | ~rich(X0) | curious(X0) [cnf transformation 37]
105. ~rich(X0) | creative(X0) | curious(X0) | ~tall(X0) [cnf transformation 45]
110. ~curious(X0) | ~tall(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 45]
117. ~curious(X0) | ~rich(X0) [cnf transformation 49]
133. funny(X0) | tall(X0) [cnf transformation 56]
134. rich(X0) | ~curious(X0) [cnf transformation 56]
135. funny(X0) | rich(X0) [cnf transformation 56]
155. ~funny(alice) [cnf transformation 24]
195. ~tall(X0) | ~creative(X0) | ~rich(X0) [subsumption resolution 110,80]
197. ~tall(X0) | curious(X0) | ~rich(X0) [subsumption resolution 105,195]
239. ~curious(X0) [subsumption resolution 134,117]
285. tall(alice) [resolution 133,155]
292. rich(alice) [resolution 135,155]
368. curious(alice) | ~rich(alice) [resolution 197,285]
369. ~rich(alice) [subsumption resolution 368,239]
370. $false [subsumption resolution 369,292]
% SZS output end Proof for 6634587065286668556857593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or patient is either not brave or not old. Everyone who is both tall and not quiet is not curious or not tall and vice versa. If someone is not happy then someone is calm or not happy. Everyone who is brave is wise and vice versa. If john is both not creative and patient then someone is not rich or generous. If john is either not calm or not rich then someone is not creative. If someone is either not humble or humble then paul is either not humble or strong. If susan is either curious or not strong then mary is calm or not generous. If alice is either not brave or not patient then someone is not brave or old. If lucy is either curious or not calm then susan is either quiet or funny. Everyone who is both humble and rich is rich or happy. Everyone who is not humble or happy is both not rich and humble. Everyone who is either rich or not curious is quiet and vice versa. If someone is either curious or kind then someone is not creative or old and vice versa. If someone is not tall then someone is both not happy and not wise and vice versa. Everyone who is both generous and curious is both not humble and not calm. Mary is either not calm or funny. Someone is strong. Alice is old. Someone is happy or humble. Paul is either brave or not curious. | Paul is not curious. | contradiction | (![X]:((~quiet(X)<~>patient(X))=>(~brave(X)<~>~old(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~curious(X)|~tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:(brave(X)<=>wise(X)))&
(((~creative(john)&patient(john)))=>(?[X]:((~rich(X)|generous(X)))))&
(((~calm(john)<~>~rich(john)))=>(?[X]:(~creative(X))))&
((?[X]:((~humble(X)<~>humble(X))))=>((~humble(paul)<~>strong(paul))))&
(((curious(susan)<~>~strong(susan)))=>((calm(mary)|~generous(mary))))&
(((~brave(alice)<~>~patient(alice)))=>(?[X]:((~brave(X)|old(X)))))&
(((curious(lucy)<~>~calm(lucy)))=>((quiet(susan)<~>funny(susan))))&
(![X]:((humble(X)&rich(X))=>(rich(X)|happy(X))))&
(![X]:((~humble(X)|happy(X))=>(~rich(X)&humble(X))))&
(![X]:((rich(X)<~>~curious(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~creative(X)|old(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:((generous(X)&curious(X))=>(~humble(X)&~calm(X))))&
((~calm(mary)<~>funny(mary)))&
(?[X]:(strong(X)))&
(old(alice))&
(?[X]:((happy(X)|humble(X))))&
((brave(paul)<~>~curious(paul))) | ~curious(paul) | [
"p1",
"p3",
"p11",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8735013456695634927968026
% SZS output start Proof for 8735013456695634927968026
2. ! [X0] : ((~quiet(X0) & tall(X0)) <=> (~tall(X0) | ~curious(X0))) [input p1]
4. ! [X0] : (brave(X0) <=> wise(X0)) [input p3]
12. ! [X0] : ((happy(X0) | ~humble(X0)) => (humble(X0) & ~rich(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> quiet(X0)) [input p12]
15. ? [X0] : ~tall(X0) <=> ? [X0] : (~wise(X0) & ~happy(X0)) [input p14]
21. brave(paul) <~> ~curious(paul) [input p20]
22. ~curious(paul) [input hypothesis]
25. ? [X0] : ~tall(X0) <=> ? [X1] : (~wise(X1) & ~happy(X1)) [rectify 15]
38. ! [X0] : ((humble(X0) & ~rich(X0)) | (~happy(X0) & humble(X0))) [ennf transformation 12]
42. ! [X0] : (((~quiet(X0) & tall(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (quiet(X0) | ~tall(X0)))) [nnf transformation 2]
43. ! [X0] : (((~quiet(X0) & tall(X0)) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | quiet(X0) | ~tall(X0))) [flattening 42]
47. ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0))) [nnf transformation 4]
59. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~quiet(X0)) & (quiet(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 13]
65. (? [X0] : ~tall(X0) | ! [X1] : (wise(X1) | happy(X1))) & (? [X1] : (~wise(X1) & ~happy(X1)) | ! [X0] : tall(X0)) [nnf transformation 25]
66. (? [X0] : ~tall(X0) | ! [X1] : (wise(X1) | happy(X1))) & (? [X2] : (~wise(X2) & ~happy(X2)) | ! [X3] : tall(X3)) [rectify 65]
67. ? [X0] : ~tall(X0) => ~tall(sK6) [choice axiom]
68. ? [X2] : (~wise(X2) & ~happy(X2)) => (~wise(sK7) & ~happy(sK7)) [choice axiom]
69. (~tall(sK6) | ! [X1] : (wise(X1) | happy(X1))) & ((~wise(sK7) & ~happy(sK7)) | ! [X3] : tall(X3)) [skolemisation 66,68,67]
75. (curious(paul) | ~brave(paul)) & (~curious(paul) | brave(paul)) [nnf transformation 21]
80. ~tall(X0) | ~curious(X0) | quiet(X0) | ~tall(X0) [cnf transformation 43]
82. tall(X0) | tall(X0) [cnf transformation 43]
83. ~quiet(X0) | curious(X0) [cnf transformation 43]
87. ~wise(X0) | brave(X0) [cnf transformation 47]
105. ~rich(X0) | ~happy(X0) [cnf transformation 38]
109. quiet(X0) | rich(X0) | curious(X0) [cnf transformation 59]
110. ~curious(X0) | rich(X0) | ~quiet(X0) [cnf transformation 59]
120. ~tall(sK6) | wise(X1) | happy(X1) [cnf transformation 69]
129. curious(paul) | ~brave(paul) [cnf transformation 75]
130. ~curious(paul) [cnf transformation 22]
136. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 80]
137. tall(X0) [duplicate literal removal 82]
138. ~curious(X0) | quiet(X0) [subsumption resolution 136,137]
257. ~curious(X0) | rich(X0) [subsumption resolution 110,138]
258. rich(X0) | curious(X0) [subsumption resolution 109,83]
259. rich(X0) [subsumption resolution 258,257]
294. wise(X1) | happy(X1) [subsumption resolution 120,137]
303. 36 <=> brave(paul) [avatar definition]
305. ~brave(paul) <- (~36) [avatar component clause 303]
307. 37 <=> curious(paul) [avatar definition]
310. ~36 | 37 [avatar split clause 129,307,303]
312. ~37 [avatar split clause 130,307]
318. ~happy(X0) [resolution 105,259]
323. happy(X0) | brave(X0) [resolution 294,87]
324. brave(X0) [subsumption resolution 323,318]
328. $false <- (~36) [resolution 324,305]
330. 36 [avatar contradiction clause 328]
332. $false [avatar sat refutation 310,312,330]
% SZS output end Proof for 8735013456695634927968026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or rich is both generous and old.
Everyone who is both not strong and not happy is funny or generous and vice versa.
If someone is old then someone is both patient and rich and vice versa.
If someone is either not strong or not generous then someone is both not creative and creative.
If someone is not tall then fred is both patient and not quiet and vice versa.
If someone is not wise or not tall then lucy is not curious or old and vice versa.
Everyone who is either not funny or not quiet is both rich and not creative.
Everyone who is both wise and curious is both strong and not kind and vice versa.
Everyone who is either quiet or not kind is kind.
If paul is creative then someone is both calm and creative.
Everyone who is not strong or not tall is quiet or funny and vice versa.
If susan is either not creative or quiet then susan is not tall or old and vice versa.
If someone is creative then paul is both not tall and not kind.
Someone is patient or strong.
Paul is both not rich and funny.
Lucy is either not quiet or not kind.
Paul is strong or not happy.
Someone is both not old and not creative. | Fred is old. | contradiction | (![X]:((~brave(X)|rich(X))=>(generous(X)&old(X))))&
(![X]:((~strong(X)&~happy(X))<=>(funny(X)|generous(X))))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&rich(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:(~tall(X)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~curious(lucy)|old(lucy))))&
(![X]:((~funny(X)<~>~quiet(X))=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&curious(X))<=>(strong(X)&~kind(X))))&
(![X]:((quiet(X)<~>~kind(X))=>kind(X)))&
((creative(paul))=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(quiet(X)|funny(X))))&
(((~creative(susan)<~>quiet(susan)))<=>((~tall(susan)|old(susan))))&
((?[X]:(creative(X)))=>((~tall(paul)&~kind(paul))))&
(?[X]:((patient(X)|strong(X))))&
((~rich(paul)&funny(paul)))&
((~quiet(lucy)<~>~kind(lucy)))&
((strong(paul)|~happy(paul)))&
(?[X]:((~old(X)&~creative(X)))) | old(fred) | [
"p0",
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3521992022770357956519349
% SZS output start Proof for 3521992022770357956519349
1. ! [X0] : ((rich(X0) | ~brave(X0)) => (old(X0) & generous(X0))) [input p0]
2. ! [X0] : ((~happy(X0) & ~strong(X0)) <=> (generous(X0) | funny(X0))) [input p1]
3. ? [X0] : old(X0) <=> ? [X0] : (rich(X0) & patient(X0)) [input p2]
4. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X0] : (creative(X0) & ~creative(X0)) [input p3]
19. old(fred) [input hypothesis]
20. ? [X0] : old(X0) <=> ? [X1] : (rich(X1) & patient(X1)) [rectify 3]
21. ? [X0] : (~strong(X0) <~> ~generous(X0)) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 4]
23. ! [X0] : (rich(X0) => (old(X0) & generous(X0))) [pure predicate removal 1]
24. ! [X0] : ((old(X0) & generous(X0)) | ~rich(X0)) [ennf transformation 23]
25. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : (~strong(X0) <=> ~generous(X0)) [ennf transformation 21]
30. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (happy(X0) | strong(X0)))) [nnf transformation 2]
31. ! [X0] : (((~happy(X0) & ~strong(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | happy(X0) | strong(X0))) [flattening 30]
32. (? [X0] : old(X0) | ! [X1] : (~rich(X1) | ~patient(X1))) & (? [X1] : (rich(X1) & patient(X1)) | ! [X0] : ~old(X0)) [nnf transformation 20]
33. (? [X0] : old(X0) | ! [X1] : (~rich(X1) | ~patient(X1))) & (? [X2] : (rich(X2) & patient(X2)) | ! [X3] : ~old(X3)) [rectify 32]
34. ? [X0] : old(X0) => old(sK0) [choice axiom]
35. ? [X2] : (rich(X2) & patient(X2)) => (rich(sK1) & patient(sK1)) [choice axiom]
36. (old(sK0) | ! [X1] : (~rich(X1) | ~patient(X1))) & ((rich(sK1) & patient(sK1)) | ! [X3] : ~old(X3)) [skolemisation 33,35,34]
37. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 25]
38. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [rectify 37]
39. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK2) & ~creative(sK2)) [choice axiom]
40. (creative(sK2) & ~creative(sK2)) | ! [X1] : ((~strong(X1) | generous(X1)) & (~generous(X1) | strong(X1))) [skolemisation 38,39]
66. ~rich(X0) | generous(X0) [cnf transformation 24]
70. ~strong(X0) | ~generous(X0) [cnf transformation 31]
74. rich(sK1) | ~old(X3) [cnf transformation 36]
76. ~creative(sK2) | ~generous(X1) | strong(X1) [cnf transformation 40]
78. creative(sK2) | ~generous(X1) | strong(X1) [cnf transformation 40]
118. old(fred) [cnf transformation 19]
129. 3 <=> ! [X3] : ~old(X3) [avatar definition]
130. ~old(X3) <- (3) [avatar component clause 129]
132. 4 <=> rich(sK1) [avatar definition]
134. rich(sK1) <- (4) [avatar component clause 132]
135. 3 | 4 [avatar split clause 74,132,129]
146. 7 <=> creative(sK2) [avatar definition]
150. creative(sK2) | ~generous(X1) [subsumption resolution 78,70]
152. 8 <=> ! [X1] : ~generous(X1) [avatar definition]
153. ~generous(X1) <- (8) [avatar component clause 152]
154. 8 | 7 [avatar split clause 150,146,152]
157. ~creative(sK2) | ~generous(X1) [subsumption resolution 76,70]
158. 8 | ~7 [avatar split clause 157,146,152]
271. generous(sK1) <- (4) [resolution 66,134]
272. $false <- (4, 8) [subsumption resolution 271,153]
273. ~4 | ~8 [avatar contradiction clause 272]
274. $false <- (3) [resolution 130,118]
277. ~3 [avatar contradiction clause 274]
278. $false [avatar sat refutation 135,154,158,273,277]
% SZS output end Proof for 3521992022770357956519349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not strong then lucy is both quiet and not wise. Everyone who is either not happy or not humble is both quiet and humble. If someone is both not tall and not brave then someone is not calm or quiet. Everyone who is both tall and curious is not calm or not humble and vice versa. Everyone who is either wise or not quiet is not creative or not brave and vice versa. Everyone who is strong or not humble is humble. Everyone who is calm is curious or not funny and vice versa. Everyone who is rich or funny is both strong and tall. If someone is both not rich and not calm then someone is both quiet and not strong and vice versa. If lucy is generous or not generous then lucy is both not old and humble and vice versa. Everyone who is kind is generous and vice versa. If susan is not quiet or tall then paul is not patient and vice versa. If mary is not quiet then someone is either tall or not funny and vice versa. If someone is not wise or not tall then someone is strong or creative. If someone is not strong then someone is curious or patient. Someone is not kind. Fred is either not generous or generous. Someone is not old or not wise. Alice is not patient or not creative. Lucy is both curious and not quiet. Susan is not tall or curious. | Lucy is not funny. | entailment | ((?[X]:((~quiet(X)&~strong(X))))=>((quiet(lucy)&~wise(lucy))))&
(![X]:((~happy(X)<~>~humble(X))=>(quiet(X)&humble(X))))&
((?[X]:((~tall(X)&~brave(X))))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((tall(X)&curious(X))<=>(~calm(X)|~humble(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~creative(X)|~brave(X))))&
(![X]:((strong(X)|~humble(X))=>humble(X)))&
(![X]:(calm(X)<=>(curious(X)|~funny(X))))&
(![X]:((rich(X)|funny(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(((generous(lucy)|~generous(lucy)))<=>((~old(lucy)&humble(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(((~quiet(susan)|tall(susan)))<=>(~patient(paul)))&
((~quiet(mary))<=>(?[X]:((tall(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((strong(X)|creative(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)|patient(X)))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>generous(fred)))&
(?[X]:((~old(X)|~wise(X))))&
((~patient(alice)|~creative(alice)))&
((curious(lucy)&~quiet(lucy)))&
((~tall(susan)|curious(susan))) | ~funny(lucy) | [
"p3",
"p5",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4731094671051336843564614
% SZS output start Proof for 4731094671051336843564614
4. ! [X0] : ((curious(X0) & tall(X0)) <=> (~humble(X0) | ~calm(X0))) [input p3]
6. ! [X0] : ((~humble(X0) | strong(X0)) => humble(X0)) [input p5]
7. ! [X0] : (calm(X0) <=> (~funny(X0) | curious(X0))) [input p6]
8. ! [X0] : ((funny(X0) | rich(X0)) => (tall(X0) & strong(X0))) [input p7]
20. ~quiet(lucy) & curious(lucy) [input p19]
22. funny(lucy) [input hypothesis]
31. ! [X0] : (humble(X0) | (humble(X0) & ~strong(X0))) [ennf transformation 6]
32. ! [X0] : ((tall(X0) & strong(X0)) | (~funny(X0) & ~rich(X0))) [ennf transformation 8]
40. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & ((~humble(X0) | ~calm(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & (~humble(X0) | ~calm(X0) | ~curious(X0) | ~tall(X0))) [flattening 40]
44. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | ~calm(X0))) [nnf transformation 7]
45. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~calm(X0))) [flattening 44]
77. ~curious(X0) | ~calm(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 41]
80. curious(X0) | calm(X0) [cnf transformation 41]
89. humble(X0) | humble(X0) [cnf transformation 31]
91. calm(X0) | ~curious(X0) [cnf transformation 45]
96. ~funny(X0) | tall(X0) [cnf transformation 32]
122. curious(lucy) [cnf transformation 20]
125. funny(lucy) [cnf transformation 22]
126. humble(X0) [duplicate literal removal 89]
153. calm(X0) [subsumption resolution 91,80]
259. tall(lucy) [resolution 96,125]
276. ~calm(lucy) | ~humble(lucy) | ~tall(lucy) [resolution 77,122]
279. ~humble(lucy) | ~tall(lucy) [subsumption resolution 276,153]
280. ~tall(lucy) [subsumption resolution 279,126]
281. $false [subsumption resolution 280,259]
% SZS output end Proof for 4731094671051336843564614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not generous and vice versa. Everyone who is either not rich or humble is funny or not generous. Everyone who is funny or humble is not curious and vice versa. Everyone who is not humble is either rich or not tall and vice versa. Everyone who is either funny or not humble is either brave or not wise and vice versa. If someone is strong then lucy is either not humble or not quiet. If someone is either not humble or curious then someone is kind or not generous and vice versa. If fred is both not rich and quiet then susan is brave or not old and vice versa. Everyone who is not humble is not calm and vice versa. If someone is brave then someone is not generous or not brave. Everyone who is strong or creative is both not tall and not humble and vice versa. If fred is both humble and not rich then john is not humble and vice versa. Everyone who is not creative is either brave or not generous. Everyone who is either not tall or not generous is both not tall and not quiet. If susan is both not calm and not funny then mary is both funny and old. Everyone who is not wise or not calm is both not brave and kind and vice versa. Someone is not curious or calm. Someone is generous. Mary is humble. Paul is either not rich or not happy. Paul is not old or not kind. Alice is both patient and wise. Mary is old. Paul is both not kind and not strong. | Susan is not kind. | neutral | (![X]:(~patient(X)<=>~generous(X)))&
(![X]:((~rich(X)<~>humble(X))=>(funny(X)|~generous(X))))&
(![X]:((funny(X)|humble(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(rich(X)<~>~tall(X))))&
(![X]:((funny(X)<~>~humble(X))<=>(brave(X)<~>~wise(X))))&
((?[X]:(strong(X)))=>((~humble(lucy)<~>~quiet(lucy))))&
((?[X]:((~humble(X)<~>curious(X))))<=>(?[X]:((kind(X)|~generous(X)))))&
(((~rich(fred)&quiet(fred)))<=>((brave(susan)|~old(susan))))&
(![X]:(~humble(X)<=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:((~generous(X)|~brave(X)))))&
(![X]:((strong(X)|creative(X))<=>(~tall(X)&~humble(X))))&
(((humble(fred)&~rich(fred)))<=>(~humble(john)))&
(![X]:(~creative(X)=>(brave(X)<~>~generous(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~tall(X)&~quiet(X))))&
(((~calm(susan)&~funny(susan)))=>((funny(mary)&old(mary))))&
(![X]:((~wise(X)|~calm(X))<=>(~brave(X)&kind(X))))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:(generous(X)))&
(humble(mary))&
((~rich(paul)<~>~happy(paul)))&
((~old(paul)|~kind(paul)))&
((patient(alice)&wise(alice)))&
(old(mary))&
((~kind(paul)&~strong(paul))) | ~kind(susan) | [] | null | 0 |
If someone is both wise and not patient then lucy is both not rich and quiet. Everyone who is not wise is not wise or rich and vice versa. If someone is either not quiet or not wise then someone is both old and not calm and vice versa. If someone is both wise and kind then mary is tall or rich. If susan is not quiet or not wise then mary is both not wise and not tall. Everyone who is wise or not creative is either creative or not creative. Everyone who is creative is either brave or curious. Everyone who is strong is either not rich or wise. Everyone who is tall or not tall is not quiet and vice versa. If fred is tall or rich then someone is patient or tall and vice versa. If mary is strong then someone is happy and vice versa. If paul is not funny or not old then someone is not calm or not strong and vice versa. Everyone who is creative or not humble is both not happy and not creative and vice versa. If someone is not tall or not quiet then someone is not strong. Everyone who is either funny or not creative is both not quiet and humble and vice versa. Everyone who is humble is both not brave and not old. Someone is kind or wise. Paul is either humble or not wise. Mary is old or creative. Alice is not kind. Someone is brave. John is both not patient and brave. | Alice is curious. | neutral | ((?[X]:((wise(X)&~patient(X))))=>((~rich(lucy)&quiet(lucy))))&
(![X]:(~wise(X)<=>(~wise(X)|rich(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:((old(X)&~calm(X)))))&
((?[X]:((wise(X)&kind(X))))=>((tall(mary)|rich(mary))))&
(((~quiet(susan)|~wise(susan)))=>((~wise(mary)&~tall(mary))))&
(![X]:((wise(X)|~creative(X))=>(creative(X)<~>~creative(X))))&
(![X]:(creative(X)=>(brave(X)<~>curious(X))))&
(![X]:(strong(X)=>(~rich(X)<~>wise(X))))&
(![X]:((tall(X)|~tall(X))<=>~quiet(X)))&
(((tall(fred)|rich(fred)))<=>(?[X]:((patient(X)|tall(X)))))&
((strong(mary))<=>(?[X]:(happy(X))))&
(((~funny(paul)|~old(paul)))<=>(?[X]:((~calm(X)|~strong(X)))))&
(![X]:((creative(X)|~humble(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:(~strong(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(~quiet(X)&humble(X))))&
(![X]:(humble(X)=>(~brave(X)&~old(X))))&
(?[X]:((kind(X)|wise(X))))&
((humble(paul)<~>~wise(paul)))&
((old(mary)|creative(mary)))&
(~kind(alice))&
(?[X]:(brave(X)))&
((~patient(john)&brave(john))) | curious(alice) | [] | null | 0 |
Everyone who is not rich or not strong is wise. If susan is calm or not strong then john is not generous or tall and vice versa. If someone is either brave or not strong then someone is old or not quiet. If mary is not strong then someone is old or not funny and vice versa. Everyone who is both wise and not curious is both brave and generous. Everyone who is not generous or creative is both not tall and humble. Everyone who is not rich is both not tall and not happy. Everyone who is both tall and old is not patient or brave and vice versa. If mary is both not kind and generous then someone is humble and vice versa. If mary is either humble or generous then someone is either tall or not happy and vice versa. Everyone who is not humble is not old or creative. Everyone who is tall is either tall or humble and vice versa. Everyone who is generous or rich is either not funny or not happy. Everyone who is not quiet is both happy and kind. If paul is happy then fred is patient and vice versa. If someone is calm then susan is funny. Someone is both calm and not wise. Someone is either not kind or tall. Someone is strong. Someone is quiet or strong. Susan is either rich or not strong. Someone is not rich. | Mary is not brave. | entailment | (![X]:((~rich(X)|~strong(X))=>wise(X)))&
(((calm(susan)|~strong(susan)))<=>((~generous(john)|tall(john))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((old(X)|~quiet(X)))))&
((~strong(mary))<=>(?[X]:((old(X)|~funny(X)))))&
(![X]:((wise(X)&~curious(X))=>(brave(X)&generous(X))))&
(![X]:((~generous(X)|creative(X))=>(~tall(X)&humble(X))))&
(![X]:(~rich(X)=>(~tall(X)&~happy(X))))&
(![X]:((tall(X)&old(X))<=>(~patient(X)|brave(X))))&
(((~kind(mary)&generous(mary)))<=>(?[X]:(humble(X))))&
(((humble(mary)<~>generous(mary)))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:(~humble(X)=>(~old(X)|creative(X))))&
(![X]:(tall(X)<=>(tall(X)<~>humble(X))))&
(![X]:((generous(X)|rich(X))=>(~funny(X)<~>~happy(X))))&
(![X]:(~quiet(X)=>(happy(X)&kind(X))))&
((happy(paul))<=>(patient(fred)))&
((?[X]:(calm(X)))=>(funny(susan)))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)|strong(X))))&
((rich(susan)<~>~strong(susan)))&
(?[X]:(~rich(X))) | ~brave(mary) | [
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1676455110989096562412656
% SZS output start Proof for 1676455110989096562412656
6. ! [X0] : ((creative(X0) | ~generous(X0)) => (humble(X0) & ~tall(X0))) [input p5]
8. ! [X0] : ((old(X0) & tall(X0)) <=> (brave(X0) | ~patient(X0))) [input p7]
11. ! [X0] : (~humble(X0) => (creative(X0) | ~old(X0))) [input p10]
12. ! [X0] : (tall(X0) <=> (tall(X0) <~> humble(X0))) [input p11]
23. brave(mary) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~tall(X0)) | (~creative(X0) & generous(X0))) [ennf transformation 6]
30. ! [X0] : ((creative(X0) | ~old(X0)) | humble(X0)) [ennf transformation 11]
31. ! [X0] : (creative(X0) | ~old(X0) | humble(X0)) [flattening 30]
45. ! [X0] : (((old(X0) & tall(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (~old(X0) | ~tall(X0)))) [nnf transformation 8]
46. ! [X0] : (((old(X0) & tall(X0)) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | ~old(X0) | ~tall(X0))) [flattening 45]
56. ! [X0] : ((tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~tall(X0))) [nnf transformation 12]
85. ~creative(X0) | humble(X0) [cnf transformation 28]
92. ~brave(X0) | old(X0) [cnf transformation 46]
104. creative(X0) | ~old(X0) | humble(X0) [cnf transformation 31]
106. ~humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 56]
108. tall(X0) | tall(X0) | ~humble(X0) [cnf transformation 56]
127. brave(mary) [cnf transformation 23]
128. ~humble(X0) | ~tall(X0) [duplicate literal removal 106]
129. ~humble(X0) | tall(X0) [duplicate literal removal 108]
188. 14 <=> ! [X0] : ~humble(X0) [avatar definition]
189. ~humble(X0) <- (14) [avatar component clause 188]
233. ~old(X0) | humble(X0) [subsumption resolution 104,85]
234. ~humble(X0) [subsumption resolution 128,129]
235. 14 [avatar split clause 234,188]
296. old(mary) [resolution 92,127]
303. humble(mary) [resolution 233,296]
306. $false <- (14) [subsumption resolution 303,189]
307. ~14 [avatar contradiction clause 306]
308. $false [avatar sat refutation 235,307]
% SZS output end Proof for 1676455110989096562412656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not strong then someone is both not funny and old.
If someone is both not strong and not brave then john is not wise or not kind.
Everyone who is old or rich is either not humble or not patient and vice versa.
Everyone who is not humble is either generous or not kind.
If someone is not creative or humble then fred is not wise and vice versa.
Everyone who is both rich and humble is not old or tall.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Everyone who is either quiet or not creative is either rich or old and vice versa.
If someone is either not quiet or quiet then fred is not tall or tall and vice versa.
If someone is humble or not funny then someone is not patient or quiet.
Everyone who is brave or curious is not brave.
Everyone who is curious or not old is either wise or not curious and vice versa.
Everyone who is wise or not funny is both brave and not curious.
Everyone who is either not strong or funny is either not wise or not funny and vice versa.
Someone is not generous.
Someone is either quiet or kind.
Paul is happy or not curious.
Fred is humble or not calm.
Paul is both funny and not old.
Someone is strong. | John is brave. | contradiction | ((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>((~wise(john)|~kind(john))))&
(![X]:((old(X)|rich(X))<=>(~humble(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~creative(X)|humble(X))))<=>(~wise(fred)))&
(![X]:((rich(X)&humble(X))=>(~old(X)|tall(X))))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~tall(fred)|tall(fred))))&
((?[X]:((humble(X)|~funny(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((brave(X)|curious(X))=>~brave(X)))&
(![X]:((curious(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>kind(X))))&
((happy(paul)|~curious(paul)))&
((humble(fred)|~calm(fred)))&
((funny(paul)&~old(paul)))&
(?[X]:(strong(X))) | brave(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 36316520495742410835563
% SZS output start Proof for 36316520495742410835563
13. ! [X0] : ((curious(X0) | brave(X0)) => ~brave(X0)) [input p12]
23. brave(john) [input hypothesis]
35. ! [X0] : (~brave(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 13]
116. ~brave(X0) | ~brave(X0) [cnf transformation 35]
143. brave(john) [cnf transformation 23]
150. ~brave(X0) [duplicate literal removal 116]
256. $false [subsumption resolution 143,150]
% SZS output end Proof for 36316520495742410835563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not funny and old then someone is both not creative and not patient and vice versa.
Everyone who is not wise or patient is not creative.
If lucy is both not happy and not humble then someone is both not calm and not quiet.
Everyone who is not funny is not strong and vice versa.
Everyone who is generous is both not humble and not creative and vice versa.
Everyone who is creative is not wise and vice versa.
Everyone who is not funny or not wise is both not funny and creative and vice versa.
Everyone who is not humble is both funny and not calm and vice versa.
Everyone who is either calm or not old is both wise and curious and vice versa.
If someone is strong or not curious then alice is happy.
If someone is both not funny and generous then someone is brave.
Everyone who is either not quiet or not brave is not creative and vice versa.
If someone is not rich then someone is not curious or funny.
If susan is either not patient or not rich then someone is both strong and old and vice versa.
Everyone who is either generous or rich is both calm and creative.
Fred is not brave.
Someone is either not generous or not curious.
Paul is not brave.
Lucy is not quiet. | Susan is not patient. | contradiction | ((?[X]:((~funny(X)&old(X))))<=>(?[X]:((~creative(X)&~patient(X)))))&
(![X]:((~wise(X)|patient(X))=>~creative(X)))&
(((~happy(lucy)&~humble(lucy)))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:(~funny(X)<=>~strong(X)))&
(![X]:(generous(X)<=>(~humble(X)&~creative(X))))&
(![X]:(creative(X)<=>~wise(X)))&
(![X]:((~funny(X)|~wise(X))<=>(~funny(X)&creative(X))))&
(![X]:(~humble(X)<=>(funny(X)&~calm(X))))&
(![X]:((calm(X)<~>~old(X))<=>(wise(X)&curious(X))))&
((?[X]:((strong(X)|~curious(X))))=>(happy(alice)))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>~creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((~curious(X)|funny(X)))))&
(((~patient(susan)<~>~rich(susan)))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:((generous(X)<~>rich(X))=>(calm(X)&creative(X))))&
(~brave(fred))&
(?[X]:((~generous(X)<~>~curious(X))))&
(~brave(paul))&
(~quiet(lucy)) | ~patient(susan) | [
"p0",
"p1",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8377829835768608374675954
% SZS output start Proof for 8377829835768608374675954
1. ? [X0] : (old(X0) & ~funny(X0)) <=> ? [X0] : (~patient(X0) & ~creative(X0)) [input p0]
2. ! [X0] : ((patient(X0) | ~wise(X0)) => ~creative(X0)) [input p1]
6. ! [X0] : (creative(X0) <=> ~wise(X0)) [input p5]
7. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (creative(X0) & ~funny(X0))) [input p6]
20. ~patient(susan) [input hypothesis]
21. ? [X0] : (old(X0) & ~funny(X0)) <=> ? [X1] : (~patient(X1) & ~creative(X1)) [rectify 1]
26. ! [X0] : (~creative(X0) | (~patient(X0) & wise(X0))) [ennf transformation 2]
30. (? [X0] : (old(X0) & ~funny(X0)) | ! [X1] : (patient(X1) | creative(X1))) & (? [X1] : (~patient(X1) & ~creative(X1)) | ! [X0] : (~old(X0) | funny(X0))) [nnf transformation 21]
31. (? [X0] : (old(X0) & ~funny(X0)) | ! [X1] : (patient(X1) | creative(X1))) & (? [X2] : (~patient(X2) & ~creative(X2)) | ! [X3] : (~old(X3) | funny(X3))) [rectify 30]
32. ? [X0] : (old(X0) & ~funny(X0)) => (old(sK0) & ~funny(sK0)) [choice axiom]
33. ? [X2] : (~patient(X2) & ~creative(X2)) => (~patient(sK1) & ~creative(sK1)) [choice axiom]
34. ((old(sK0) & ~funny(sK0)) | ! [X1] : (patient(X1) | creative(X1))) & ((~patient(sK1) & ~creative(sK1)) | ! [X3] : (~old(X3) | funny(X3))) [skolemisation 31,33,32]
38. ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))) [nnf transformation 6]
39. ! [X0] : (((~wise(X0) | ~funny(X0)) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | (wise(X0) & funny(X0)))) [nnf transformation 7]
40. ! [X0] : ((~wise(X0) | ~funny(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | (wise(X0) & funny(X0)))) [flattening 39]
62. ~funny(sK0) | patient(X1) | creative(X1) [cnf transformation 34]
64. ~creative(X0) | wise(X0) [cnf transformation 26]
71. ~wise(X0) | ~creative(X0) [cnf transformation 38]
72. creative(X0) | wise(X0) [cnf transformation 38]
75. creative(X0) | funny(X0) [cnf transformation 40]
108. ~patient(susan) [cnf transformation 20]
110. 1 <=> ! [X1] : (patient(X1) | creative(X1)) [avatar definition]
111. patient(X1) | creative(X1) <- (1) [avatar component clause 110]
118. 3 <=> funny(sK0) [avatar definition]
120. ~funny(sK0) <- (~3) [avatar component clause 118]
121. 1 | ~3 [avatar split clause 62,118,110]
135. wise(X0) [subsumption resolution 72,64]
136. ~creative(X0) [subsumption resolution 71,135]
137. funny(X0) [subsumption resolution 75,136]
147. 8 <=> patient(susan) [avatar definition]
148. ~patient(susan) <- (~8) [avatar component clause 147]
180. ~8 [avatar split clause 108,147]
181. $false <- (~3) [subsumption resolution 120,137]
182. 3 [avatar contradiction clause 181]
183. patient(X1) <- (1) [subsumption resolution 111,136]
185. $false <- (1, ~8) [resolution 183,148]
186. ~1 | 8 [avatar contradiction clause 185]
188. $false [avatar sat refutation 121,180,182,186]
% SZS output end Proof for 8377829835768608374675954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not wise then mary is either patient or not strong.
Everyone who is either not happy or not curious is strong or humble.
Everyone who is either happy or not rich is happy or humble.
Everyone who is not tall is tall or not generous.
If john is both wise and rich then someone is either not wise or calm and vice versa.
If someone is both not funny and not happy then paul is not funny.
Everyone who is both not quiet and funny is curious or not quiet.
Everyone who is tall or creative is wise.
Everyone who is both not quiet and quiet is either not curious or not creative and vice versa.
Everyone who is wise is not curious and vice versa.
If alice is either rich or quiet then lucy is both not tall and not calm.
Everyone who is not tall or wise is not creative.
If someone is both not curious and humble then susan is rich or not brave and vice versa.
Everyone who is either not calm or not generous is both creative and not kind.
If someone is both generous and rich then fred is either not strong or not quiet and vice versa.
Someone is both not generous and rich.
Someone is either rich or old.
John is either kind or brave.
Paul is brave.
Someone is either brave or happy.
Paul is either not tall or not patient.
Susan is brave or patient.
Someone is both old and tall. | Alice is wise. | entailment | ((~wise(alice))=>((patient(mary)<~>~strong(mary))))&
(![X]:((~happy(X)<~>~curious(X))=>(strong(X)|humble(X))))&
(![X]:((happy(X)<~>~rich(X))=>(happy(X)|humble(X))))&
(![X]:(~tall(X)=>(tall(X)|~generous(X))))&
(((wise(john)&rich(john)))<=>(?[X]:((~wise(X)<~>calm(X)))))&
((?[X]:((~funny(X)&~happy(X))))=>(~funny(paul)))&
(![X]:((~quiet(X)&funny(X))=>(curious(X)|~quiet(X))))&
(![X]:((tall(X)|creative(X))=>wise(X)))&
(![X]:((~quiet(X)&quiet(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(((rich(alice)<~>quiet(alice)))=>((~tall(lucy)&~calm(lucy))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
((?[X]:((~curious(X)&humble(X))))<=>((rich(susan)|~brave(susan))))&
(![X]:((~calm(X)<~>~generous(X))=>(creative(X)&~kind(X))))&
((?[X]:((generous(X)&rich(X))))<=>((~strong(fred)<~>~quiet(fred))))&
(?[X]:((~generous(X)&rich(X))))&
(?[X]:((rich(X)<~>old(X))))&
((kind(john)<~>brave(john)))&
(brave(paul))&
(?[X]:((brave(X)<~>happy(X))))&
((~tall(paul)<~>~patient(paul)))&
((brave(susan)|patient(susan)))&
(?[X]:((old(X)&tall(X)))) | wise(alice) | [
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2696398291977851428528951
% SZS output start Proof for 2696398291977851428528951
8. ! [X0] : ((creative(X0) | tall(X0)) => wise(X0)) [input p7]
9. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> ~curious(X0)) [input p9]
12. ! [X0] : ((wise(X0) | ~tall(X0)) => ~creative(X0)) [input p11]
24. ~wise(alice) [input hypothesis]
35. ! [X0] : (wise(X0) | (~creative(X0) & ~tall(X0))) [ennf transformation 8]
37. ! [X0] : (~creative(X0) | (~wise(X0) & tall(X0))) [ennf transformation 12]
47. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~quiet(X0) | quiet(X0)))) [nnf transformation 9]
48. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ~quiet(X0) | quiet(X0))) [flattening 47]
49. ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0))) [nnf transformation 10]
89. ~creative(X0) | wise(X0) [cnf transformation 35]
93. ~quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 48]
95. quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 48]
97. curious(X0) | wise(X0) [cnf transformation 49]
103. ~creative(X0) | ~wise(X0) [cnf transformation 37]
133. ~wise(alice) [cnf transformation 24]
137. 1 <=> wise(alice) [avatar definition]
138. ~wise(alice) <- (~1) [avatar component clause 137]
186. ~curious(X0) | creative(X0) [subsumption resolution 93,95]
208. ~creative(X0) [subsumption resolution 103,89]
305. ~1 [avatar split clause 133,137]
313. creative(X0) | wise(X0) [resolution 186,97]
314. wise(X0) [subsumption resolution 313,208]
315. $false <- (~1) [resolution 314,138]
316. 1 [avatar contradiction clause 315]
317. $false [avatar sat refutation 305,316]
% SZS output end Proof for 2696398291977851428528951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or wise is old or curious and vice versa.
If someone is patient or not patient then paul is either humble or not wise.
Everyone who is tall is humble or not happy and vice versa.
Everyone who is humble or strong is quiet.
If someone is either strong or not patient then alice is humble or wise and vice versa.
If john is not brave or not creative then someone is not funny and vice versa.
If susan is not old or brave then someone is either not curious or rich.
Everyone who is not strong or strong is not tall or creative and vice versa.
If john is both wise and kind then someone is both old and creative and vice versa.
Everyone who is either not funny or not generous is not creative or wise.
Everyone who is not happy or strong is either rich or not calm and vice versa.
If susan is calm or curious then someone is either quiet or not old and vice versa.
If lucy is either patient or not strong then fred is not funny and vice versa.
Everyone who is strong is not wise and vice versa.
Everyone who is either generous or not wise is kind.
Paul is not strong.
Alice is humble or kind.
Someone is either not curious or generous.
Lucy is either not generous or funny.
Someone is not rich or not humble.
Mary is not humble or not funny.
Someone is not old. | Susan is not creative. | neutral | (![X]:((~generous(X)<~>wise(X))<=>(old(X)|curious(X))))&
((?[X]:((patient(X)|~patient(X))))=>((humble(paul)<~>~wise(paul))))&
(![X]:(tall(X)<=>(humble(X)|~happy(X))))&
(![X]:((humble(X)|strong(X))=>quiet(X)))&
((?[X]:((strong(X)<~>~patient(X))))<=>((humble(alice)|wise(alice))))&
(((~brave(john)|~creative(john)))<=>(?[X]:(~funny(X))))&
(((~old(susan)|brave(susan)))=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((~strong(X)|strong(X))<=>(~tall(X)|creative(X))))&
(((wise(john)&kind(john)))<=>(?[X]:((old(X)&creative(X)))))&
(![X]:((~funny(X)<~>~generous(X))=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)|strong(X))<=>(rich(X)<~>~calm(X))))&
(((calm(susan)|curious(susan)))<=>(?[X]:((quiet(X)<~>~old(X)))))&
(((patient(lucy)<~>~strong(lucy)))<=>(~funny(fred)))&
(![X]:(strong(X)<=>~wise(X)))&
(![X]:((generous(X)<~>~wise(X))=>kind(X)))&
(~strong(paul))&
((humble(alice)|kind(alice)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~generous(lucy)<~>funny(lucy)))&
(?[X]:((~rich(X)|~humble(X))))&
((~humble(mary)|~funny(mary)))&
(?[X]:(~old(X))) | ~creative(susan) | [] | null | 0 |
Everyone who is funny is not creative or not kind and vice versa.
Everyone who is either strong or not wise is both not patient and old and vice versa.
If mary is both generous and not brave then paul is not calm or not tall and vice versa.
Everyone who is both not funny and creative is either patient or old.
If fred is quiet then john is not happy and vice versa.
Everyone who is either not calm or wise is tall.
Everyone who is either not generous or tall is not kind.
Everyone who is both generous and not quiet is either generous or not funny.
If mary is both quiet and humble then alice is both not humble and happy and vice versa.
Everyone who is either not patient or happy is not creative.
If alice is both not tall and creative then someone is creative or calm.
Everyone who is either wise or creative is quiet or not creative and vice versa.
Everyone who is either wise or curious is either happy or not funny and vice versa.
If someone is not old then paul is both not patient and not wise and vice versa.
If someone is both not happy and humble then someone is not funny and vice versa.
If john is not kind or tall then someone is both not curious and humble.
Susan is either not curious or not strong.
Someone is not calm or old.
Alice is not rich.
Someone is patient or not kind.
Lucy is both not patient and happy.
John is both not funny and wise.
Someone is either brave or not creative.
Mary is both not patient and not old. | Mary is not funny. | contradiction | (![X]:(funny(X)<=>(~creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~wise(X))<=>(~patient(X)&old(X))))&
(((generous(mary)&~brave(mary)))<=>((~calm(paul)|~tall(paul))))&
(![X]:((~funny(X)&creative(X))=>(patient(X)<~>old(X))))&
((quiet(fred))<=>(~happy(john)))&
(![X]:((~calm(X)<~>wise(X))=>tall(X)))&
(![X]:((~generous(X)<~>tall(X))=>~kind(X)))&
(![X]:((generous(X)&~quiet(X))=>(generous(X)<~>~funny(X))))&
(((quiet(mary)&humble(mary)))<=>((~humble(alice)&happy(alice))))&
(![X]:((~patient(X)<~>happy(X))=>~creative(X)))&
(((~tall(alice)&creative(alice)))=>(?[X]:((creative(X)|calm(X)))))&
(![X]:((wise(X)<~>creative(X))<=>(quiet(X)|~creative(X))))&
(![X]:((wise(X)<~>curious(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:(~old(X)))<=>((~patient(paul)&~wise(paul))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:(~funny(X))))&
(((~kind(john)|tall(john)))=>(?[X]:((~curious(X)&humble(X)))))&
((~curious(susan)<~>~strong(susan)))&
(?[X]:((~calm(X)|old(X))))&
(~rich(alice))&
(?[X]:((patient(X)|~kind(X))))&
((~patient(lucy)&happy(lucy)))&
((~funny(john)&wise(john)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(mary)&~old(mary))) | ~funny(mary) | [
"p0",
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8910369777192186683998371
% SZS output start Proof for 8910369777192186683998371
1. ! [X0] : (funny(X0) <=> (~kind(X0) | ~creative(X0))) [input p0]
4. ! [X0] : ((creative(X0) & ~funny(X0)) => (patient(X0) <~> old(X0))) [input p3]
24. ~old(mary) & ~patient(mary) [input p23]
25. ~funny(mary) [input hypothesis]
28. ! [X0] : ((patient(X0) <~> old(X0)) | (~creative(X0) | funny(X0))) [ennf transformation 4]
29. ! [X0] : ((patient(X0) <~> old(X0)) | ~creative(X0) | funny(X0)) [flattening 28]
38. ! [X0] : ((funny(X0) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | ~funny(X0))) [nnf transformation 1]
39. ! [X0] : ((funny(X0) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0))) [flattening 38]
44. ! [X0] : (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~creative(X0) | funny(X0)) [nnf transformation 29]
78. creative(X0) | funny(X0) [cnf transformation 39]
91. old(X0) | patient(X0) | ~creative(X0) | funny(X0) [cnf transformation 44]
142. ~patient(mary) [cnf transformation 24]
143. ~old(mary) [cnf transformation 24]
144. ~funny(mary) [cnf transformation 25]
170. old(X0) | patient(X0) | funny(X0) [subsumption resolution 91,78]
419. patient(mary) | funny(mary) [resolution 170,143]
423. funny(mary) [subsumption resolution 419,142]
424. $false [subsumption resolution 423,144]
% SZS output end Proof for 8910369777192186683998371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and not happy is either not happy or rich and vice versa. Everyone who is not quiet or not brave is calm or not wise. Everyone who is not tall or tall is brave and vice versa. If john is either quiet or not tall then someone is not old or happy and vice versa. If alice is creative then mary is curious and vice versa. Everyone who is quiet or generous is not curious. Everyone who is not kind is both not brave and funny. If someone is either humble or not tall then susan is both brave and patient and vice versa. If someone is wise or rich then someone is either old or not calm and vice versa. Everyone who is rich or funny is not quiet and vice versa. If someone is either not calm or not tall then mary is both not rich and tall and vice versa. If fred is both patient and calm then john is creative. Everyone who is not rich or rich is either patient or quiet. Everyone who is not tall is not quiet or not wise. If someone is both not old and generous then someone is either not generous or not strong. Everyone who is not funny or brave is either not creative or wise and vice versa. Lucy is either rich or not creative. John is not tall or not quiet. Mary is quiet. Lucy is either not old or strong. Mary is both not wise and tall. | Lucy is quiet. | neutral | (![X]:((kind(X)&~happy(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~quiet(X)|~brave(X))=>(calm(X)|~wise(X))))&
(![X]:((~tall(X)|tall(X))<=>brave(X)))&
(((quiet(john)<~>~tall(john)))<=>(?[X]:((~old(X)|happy(X)))))&
((creative(alice))<=>(curious(mary)))&
(![X]:((quiet(X)|generous(X))=>~curious(X)))&
(![X]:(~kind(X)=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((brave(susan)&patient(susan))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((rich(X)|funny(X))<=>~quiet(X)))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((~rich(mary)&tall(mary))))&
(((patient(fred)&calm(fred)))=>(creative(john)))&
(![X]:((~rich(X)|rich(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(~quiet(X)|~wise(X))))&
((?[X]:((~old(X)&generous(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((~funny(X)|brave(X))<=>(~creative(X)<~>wise(X))))&
((rich(lucy)<~>~creative(lucy)))&
((~tall(john)|~quiet(john)))&
(quiet(mary))&
((~old(lucy)<~>strong(lucy)))&
((~wise(mary)&tall(mary))) | quiet(lucy) | [] | null | 0 |
If someone is not calm or not rich then fred is not humble or kind.
If someone is happy then mary is rich and vice versa.
Everyone who is both old and not kind is both not humble and quiet and vice versa.
Everyone who is both not happy and not quiet is both not quiet and not brave.
Everyone who is kind is both not tall and calm and vice versa.
Everyone who is humble is either not calm or old and vice versa.
If someone is not patient then someone is happy.
If john is either not funny or not happy then fred is both not kind and funny and vice versa.
Everyone who is rich is both curious and old and vice versa.
Everyone who is curious or not old is generous or humble and vice versa.
Everyone who is not patient is kind and vice versa.
If someone is not rich then someone is either old or not kind.
If mary is funny then mary is not strong.
Everyone who is funny or quiet is both not brave and not patient and vice versa.
Everyone who is both not rich and happy is either not calm or tall.
If someone is either not rich or not happy then someone is either kind or calm.
Mary is wise or not kind.
Fred is either funny or brave.
Susan is either not strong or not generous.
Someone is creative.
Fred is rich.
Paul is not rich or calm.
Someone is either not brave or calm.
Paul is strong or not strong. | Fred is not humble. | contradiction | ((?[X]:((~calm(X)|~rich(X))))=>((~humble(fred)|kind(fred))))&
((?[X]:(happy(X)))<=>(rich(mary)))&
(![X]:((old(X)&~kind(X))<=>(~humble(X)&quiet(X))))&
(![X]:((~happy(X)&~quiet(X))=>(~quiet(X)&~brave(X))))&
(![X]:(kind(X)<=>(~tall(X)&calm(X))))&
(![X]:(humble(X)<=>(~calm(X)<~>old(X))))&
((?[X]:(~patient(X)))=>(?[X]:(happy(X))))&
(((~funny(john)<~>~happy(john)))<=>((~kind(fred)&funny(fred))))&
(![X]:(rich(X)<=>(curious(X)&old(X))))&
(![X]:((curious(X)|~old(X))<=>(generous(X)|humble(X))))&
(![X]:(~patient(X)<=>kind(X)))&
((?[X]:(~rich(X)))=>(?[X]:((old(X)<~>~kind(X)))))&
((funny(mary))=>(~strong(mary)))&
(![X]:((funny(X)|quiet(X))<=>(~brave(X)&~patient(X))))&
(![X]:((~rich(X)&happy(X))=>(~calm(X)<~>tall(X))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
((wise(mary)|~kind(mary)))&
((funny(fred)<~>brave(fred)))&
((~strong(susan)<~>~generous(susan)))&
(?[X]:(creative(X)))&
(rich(fred))&
((~rich(paul)|calm(paul)))&
(?[X]:((~brave(X)<~>calm(X))))&
((strong(paul)|~strong(paul))) | ~humble(fred) | [
"p2",
"p4",
"p5",
"p8",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7804935457895575666591374
% SZS output start Proof for 7804935457895575666591374
3. ! [X0] : ((~kind(X0) & old(X0)) <=> (quiet(X0) & ~humble(X0))) [input p2]
5. ! [X0] : (kind(X0) <=> (calm(X0) & ~tall(X0))) [input p4]
6. ! [X0] : (humble(X0) <=> (~calm(X0) <~> old(X0))) [input p5]
9. ! [X0] : (rich(X0) <=> (old(X0) & curious(X0))) [input p8]
11. ! [X0] : (~patient(X0) <=> kind(X0)) [input p10]
14. ! [X0] : ((quiet(X0) | funny(X0)) <=> (~patient(X0) & ~brave(X0))) [input p13]
21. rich(fred) [input p20]
25. ~humble(fred) [input hypothesis]
45. ! [X0] : (((~kind(X0) & old(X0)) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | (kind(X0) | ~old(X0)))) [nnf transformation 3]
46. ! [X0] : (((~kind(X0) & old(X0)) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | kind(X0) | ~old(X0))) [flattening 45]
47. ! [X0] : ((kind(X0) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | ~kind(X0))) [nnf transformation 5]
48. ! [X0] : ((kind(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | ~kind(X0))) [flattening 47]
49. ! [X0] : ((humble(X0) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | ~humble(X0))) [nnf transformation 6]
55. ! [X0] : ((rich(X0) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | ~rich(X0))) [nnf transformation 9]
56. ! [X0] : ((rich(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | ~rich(X0))) [flattening 55]
59. ! [X0] : ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))) [nnf transformation 11]
64. ! [X0] : (((quiet(X0) | funny(X0)) | (patient(X0) | brave(X0))) & ((~patient(X0) & ~brave(X0)) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 14]
65. ! [X0] : ((quiet(X0) | funny(X0) | patient(X0) | brave(X0)) & ((~patient(X0) & ~brave(X0)) | (~quiet(X0) & ~funny(X0)))) [flattening 64]
81. ~old(X0) | kind(X0) | quiet(X0) [cnf transformation 46]
87. ~kind(X0) | calm(X0) [cnf transformation 48]
92. ~old(X0) | ~calm(X0) | humble(X0) [cnf transformation 49]
101. ~rich(X0) | old(X0) [cnf transformation 56]
107. patient(X0) | kind(X0) [cnf transformation 59]
115. ~patient(X0) | ~quiet(X0) [cnf transformation 65]
127. rich(fred) [cnf transformation 21]
132. ~humble(fred) [cnf transformation 25]
137. 2 <=> humble(fred) [avatar definition]
139. ~humble(fred) <- (~2) [avatar component clause 137]
141. 3 <=> kind(fred) [avatar definition]
143. kind(fred) <- (3) [avatar component clause 141]
263. ~2 [avatar split clause 132,137]
264. calm(fred) <- (3) [resolution 87,143]
267. old(fred) [resolution 101,127]
276. ~quiet(X0) | kind(X0) [resolution 115,107]
298. kind(fred) | quiet(fred) [resolution 81,267]
377. ~calm(fred) | humble(fred) [resolution 92,267]
382. humble(fred) <- (3) [subsumption resolution 377,264]
383. $false <- (~2, 3) [subsumption resolution 382,139]
384. 2 | ~3 [avatar contradiction clause 383]
393. kind(fred) [subsumption resolution 298,276]
394. 3 [avatar split clause 393,141]
400. $false [avatar sat refutation 263,384,394]
% SZS output end Proof for 7804935457895575666591374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not curious then alice is both creative and not generous.
If susan is either kind or creative then john is tall and vice versa.
Everyone who is not old is not tall.
Everyone who is either not patient or not funny is both not quiet and brave.
Everyone who is either not wise or not brave is tall or not curious.
Everyone who is generous or curious is not quiet.
Everyone who is not old or calm is calm.
Everyone who is not wise is either curious or kind.
If susan is either not old or not curious then susan is both not patient and calm and vice versa.
Everyone who is not patient is either kind or calm and vice versa.
Everyone who is not strong is both calm and not tall and vice versa.
Everyone who is both curious and rich is not rich and vice versa.
If someone is not wise then someone is either humble or not brave and vice versa.
Everyone who is not rich or not old is both not curious and curious and vice versa.
Everyone who is not generous is not curious and vice versa.
Someone is generous or wise.
Someone is either not strong or rich.
Paul is either kind or calm.
Susan is not brave.
Mary is either not kind or not generous.
Someone is either not creative or funny.
Someone is both not quiet and not wise.
Someone is either calm or funny. | Mary is not generous. | entailment | ((?[X]:((generous(X)&~curious(X))))=>((creative(alice)&~generous(alice))))&
(((kind(susan)<~>creative(susan)))<=>(tall(john)))&
(![X]:(~old(X)=>~tall(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(~quiet(X)&brave(X))))&
(![X]:((~wise(X)<~>~brave(X))=>(tall(X)|~curious(X))))&
(![X]:((generous(X)|curious(X))=>~quiet(X)))&
(![X]:((~old(X)|calm(X))=>calm(X)))&
(![X]:(~wise(X)=>(curious(X)<~>kind(X))))&
(((~old(susan)<~>~curious(susan)))<=>((~patient(susan)&calm(susan))))&
(![X]:(~patient(X)<=>(kind(X)<~>calm(X))))&
(![X]:(~strong(X)<=>(calm(X)&~tall(X))))&
(![X]:((curious(X)&rich(X))<=>~rich(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~old(X))<=>(~curious(X)&curious(X))))&
(![X]:(~generous(X)<=>~curious(X)))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((kind(paul)<~>calm(paul)))&
(~brave(susan))&
((~kind(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)<~>funny(X))))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((calm(X)<~>funny(X)))) | ~generous(mary) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 725225157484976507629254
% SZS output start Proof for 725225157484976507629254
12. ! [X0] : ((rich(X0) & curious(X0)) <=> ~rich(X0)) [input p11]
15. ! [X0] : (~generous(X0) <=> ~curious(X0)) [input p14]
24. generous(mary) [input hypothesis]
45. ! [X0] : (((rich(X0) & curious(X0)) | rich(X0)) & (~rich(X0) | (~rich(X0) | ~curious(X0)))) [nnf transformation 12]
46. ! [X0] : (((rich(X0) & curious(X0)) | rich(X0)) & (~rich(X0) | ~rich(X0) | ~curious(X0))) [flattening 45]
54. ! [X0] : ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))) [nnf transformation 15]
98. ~rich(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 46]
100. rich(X0) | rich(X0) [cnf transformation 46]
111. ~generous(X0) | curious(X0) [cnf transformation 54]
125. generous(mary) [cnf transformation 24]
126. ~rich(X0) | ~curious(X0) [duplicate literal removal 98]
127. rich(X0) [duplicate literal removal 100]
180. ~curious(X0) [subsumption resolution 126,127]
207. ~generous(X0) [subsumption resolution 111,180]
241. $false [subsumption resolution 125,207]
% SZS output end Proof for 725225157484976507629254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or brave is either happy or not funny and vice versa. If paul is not calm or strong then paul is generous and vice versa. Everyone who is either not happy or calm is both wise and not rich. If someone is either not strong or not kind then alice is either not wise or happy and vice versa. Everyone who is either curious or not kind is not happy. Everyone who is tall is either generous or not creative. Everyone who is either happy or quiet is either humble or not rich. Everyone who is brave is either quiet or kind. If alice is brave then someone is either curious or not rich. Everyone who is either not quiet or not creative is happy and vice versa. Everyone who is either old or not funny is either humble or not funny and vice versa. Everyone who is either creative or funny is either not generous or not brave and vice versa. Everyone who is not kind is either brave or not old and vice versa. Everyone who is both creative and happy is not kind. If someone is wise or not patient then someone is not calm or not rich. Everyone who is either rich or not strong is brave or curious and vice versa. Fred is kind or not happy. Someone is either not patient or kind. Lucy is creative or humble. Someone is both not tall and kind. John is both tall and kind. John is calm or tall. | Fred is not calm. | neutral | (![X]:((~generous(X)<~>brave(X))<=>(happy(X)<~>~funny(X))))&
(((~calm(paul)|strong(paul)))<=>(generous(paul)))&
(![X]:((~happy(X)<~>calm(X))=>(wise(X)&~rich(X))))&
((?[X]:((~strong(X)<~>~kind(X))))<=>((~wise(alice)<~>happy(alice))))&
(![X]:((curious(X)<~>~kind(X))=>~happy(X)))&
(![X]:(tall(X)=>(generous(X)<~>~creative(X))))&
(![X]:((happy(X)<~>quiet(X))=>(humble(X)<~>~rich(X))))&
(![X]:(brave(X)=>(quiet(X)<~>kind(X))))&
((brave(alice))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>happy(X)))&
(![X]:((old(X)<~>~funny(X))<=>(humble(X)<~>~funny(X))))&
(![X]:((creative(X)<~>funny(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:(~kind(X)<=>(brave(X)<~>~old(X))))&
(![X]:((creative(X)&happy(X))=>~kind(X)))&
((?[X]:((wise(X)|~patient(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((rich(X)<~>~strong(X))<=>(brave(X)|curious(X))))&
((kind(fred)|~happy(fred)))&
(?[X]:((~patient(X)<~>kind(X))))&
((creative(lucy)|humble(lucy)))&
(?[X]:((~tall(X)&kind(X))))&
((tall(john)&kind(john)))&
((calm(john)|tall(john))) | ~calm(fred) | [] | null | 0 |
If lucy is either not kind or generous then someone is not happy or old. If someone is both not humble and funny then paul is either not calm or not wise. Everyone who is brave or rich is not humble and vice versa. If someone is rich or not calm then someone is not patient or not generous. Everyone who is both tall and not rich is not creative or not funny and vice versa. Everyone who is humble or not generous is both rich and not kind and vice versa. If paul is kind or not quiet then paul is quiet and vice versa. If someone is brave or quiet then alice is not kind or curious and vice versa. If someone is either not kind or strong then someone is not kind. If mary is generous then alice is either not brave or tall. If paul is generous or not generous then fred is both not patient and not old. Everyone who is both humble and wise is curious or funny and vice versa. If someone is tall or strong then someone is not creative and vice versa. Everyone who is not strong is either not creative or not curious. Everyone who is both strong and tall is either not rich or not wise. Everyone who is not strong or kind is kind or strong. Someone is not happy. Paul is brave or patient. Someone is either strong or old. Someone is either curious or not old. Someone is either quiet or old. | Paul is calm. | neutral | (((~kind(lucy)<~>generous(lucy)))=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~humble(X)&funny(X))))=>((~calm(paul)<~>~wise(paul))))&
(![X]:((brave(X)|rich(X))<=>~humble(X)))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((tall(X)&~rich(X))<=>(~creative(X)|~funny(X))))&
(![X]:((humble(X)|~generous(X))<=>(rich(X)&~kind(X))))&
(((kind(paul)|~quiet(paul)))<=>(quiet(paul)))&
((?[X]:((brave(X)|quiet(X))))<=>((~kind(alice)|curious(alice))))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
((generous(mary))=>((~brave(alice)<~>tall(alice))))&
(((generous(paul)|~generous(paul)))=>((~patient(fred)&~old(fred))))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|funny(X))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>~curious(X))))&
(![X]:((strong(X)&tall(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((~strong(X)|kind(X))=>(kind(X)|strong(X))))&
(?[X]:(~happy(X)))&
((brave(paul)|patient(paul)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((quiet(X)<~>old(X)))) | calm(paul) | [] | null | 0 |
If someone is not funny then someone is kind and vice versa.
Everyone who is both strong and not humble is either not humble or quiet and vice versa.
Everyone who is both calm and rich is both not quiet and not creative.
If susan is not wise or not creative then someone is both not funny and not brave.
If john is either not strong or not patient then someone is not old.
Everyone who is quiet is either not calm or not creative.
If mary is not happy or brave then someone is not creative.
If lucy is brave or not funny then someone is not funny.
Everyone who is either kind or not funny is both not tall and kind and vice versa.
Everyone who is kind or not generous is both patient and funny.
If fred is both generous and not calm then someone is not generous or quiet and vice versa.
If someone is calm then someone is either not curious or strong and vice versa.
Everyone who is strong or not happy is either not strong or not old.
If lucy is not wise or not patient then someone is not wise or not happy.
Everyone who is both strong and rich is both not happy and strong and vice versa.
Everyone who is not creative or not quiet is quiet or not quiet and vice versa.
Someone is not kind.
Lucy is not kind.
John is creative or not quiet.
Someone is not old or calm.
Someone is not creative or funny.
Mary is both rich and generous.
Fred is strong or not wise.
John is either curious or not generous. | Lucy is not brave. | entailment | ((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((strong(X)&~humble(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:((calm(X)&rich(X))=>(~quiet(X)&~creative(X))))&
(((~wise(susan)|~creative(susan)))=>(?[X]:((~funny(X)&~brave(X)))))&
(((~strong(john)<~>~patient(john)))=>(?[X]:(~old(X))))&
(![X]:(quiet(X)=>(~calm(X)<~>~creative(X))))&
(((~happy(mary)|brave(mary)))=>(?[X]:(~creative(X))))&
(((brave(lucy)|~funny(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~tall(X)&kind(X))))&
(![X]:((kind(X)|~generous(X))=>(patient(X)&funny(X))))&
(((generous(fred)&~calm(fred)))<=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((strong(X)|~happy(X))=>(~strong(X)<~>~old(X))))&
(((~wise(lucy)|~patient(lucy)))=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:((strong(X)&rich(X))<=>(~happy(X)&strong(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(quiet(X)|~quiet(X))))&
(?[X]:(~kind(X)))&
(~kind(lucy))&
((creative(john)|~quiet(john)))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:((~creative(X)|funny(X))))&
((rich(mary)&generous(mary)))&
((strong(fred)|~wise(fred)))&
((curious(john)<~>~generous(john))) | ~brave(lucy) | [
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2443698896035643634726988
% SZS output start Proof for 2443698896035643634726988
8. (~funny(lucy) | brave(lucy)) => ? [X0] : ~funny(X0) [input p7]
9. ! [X0] : ((kind(X0) <~> ~funny(X0)) <=> (kind(X0) & ~tall(X0))) [input p8]
10. ! [X0] : ((~generous(X0) | kind(X0)) => (funny(X0) & patient(X0))) [input p9]
25. brave(lucy) [input hypothesis]
34. ? [X0] : ~funny(X0) | (funny(lucy) & ~brave(lucy)) [ennf transformation 8]
35. ! [X0] : ((funny(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) [ennf transformation 10]
53. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
54. ~funny(sK5) | (funny(lucy) & ~brave(lucy)) [skolemisation 34,53]
55. ! [X0] : ((((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (~kind(X0) | tall(X0))) & ((kind(X0) & ~tall(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))))) [nnf transformation 9]
56. ! [X0] : ((((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | ~kind(X0) | tall(X0)) & ((kind(X0) & ~tall(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))))) [flattening 55]
101. ~funny(sK5) | ~brave(lucy) [cnf transformation 54]
106. kind(X0) | kind(X0) | funny(X0) [cnf transformation 56]
111. funny(X0) | ~kind(X0) [cnf transformation 35]
146. brave(lucy) [cnf transformation 25]
150. kind(X0) | funny(X0) [duplicate literal removal 106]
163. 3 <=> ! [X3] : funny(X3) [avatar definition]
164. funny(X3) <- (3) [avatar component clause 163]
224. 16 <=> funny(sK5) [avatar definition]
226. ~funny(sK5) <- (~16) [avatar component clause 224]
229. 17 <=> brave(lucy) [avatar definition]
232. ~17 | ~16 [avatar split clause 101,224,229]
233. funny(X0) [subsumption resolution 111,150]
234. 3 [avatar split clause 233,163]
343. 17 [avatar split clause 146,229]
348. $false <- (3, ~16) [resolution 226,164]
349. ~3 | 16 [avatar contradiction clause 348]
350. $false [avatar sat refutation 232,234,343,349]
% SZS output end Proof for 2443698896035643634726988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not funny then fred is not patient.
If someone is either not patient or generous then someone is both not strong and not tall and vice versa.
If someone is not old or not funny then alice is either not brave or not strong and vice versa.
If someone is brave then mary is curious or not rich.
Everyone who is old is wise.
Everyone who is either humble or not funny is creative and vice versa.
If someone is both wise and quiet then lucy is both brave and generous.
Everyone who is not brave or not humble is happy.
If someone is curious or funny then someone is not wise and vice versa.
If someone is not brave or not patient then someone is either not tall or humble and vice versa.
If someone is both calm and not creative then someone is quiet or curious.
Everyone who is not calm or not old is rich and vice versa.
If john is either quiet or generous then someone is either not quiet or rich.
Everyone who is both generous and not creative is both curious and happy.
Everyone who is both not calm and not patient is brave and vice versa.
Everyone who is not humble or old is either happy or rich and vice versa.
Someone is either not creative or creative.
Someone is calm.
Someone is not creative or generous.
John is both not curious and not patient.
Someone is either not wise or old.
Paul is not rich or not tall.
Mary is both not tall and creative.
Someone is either strong or not happy. | Mary is curious. | neutral | ((?[X]:((tall(X)<~>~funny(X))))=>(~patient(fred)))&
((?[X]:((~patient(X)<~>generous(X))))<=>(?[X]:((~strong(X)&~tall(X)))))&
((?[X]:((~old(X)|~funny(X))))<=>((~brave(alice)<~>~strong(alice))))&
((?[X]:(brave(X)))=>((curious(mary)|~rich(mary))))&
(![X]:(old(X)=>wise(X)))&
(![X]:((humble(X)<~>~funny(X))<=>creative(X)))&
((?[X]:((wise(X)&quiet(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:((~brave(X)|~humble(X))=>happy(X)))&
((?[X]:((curious(X)|funny(X))))<=>(?[X]:(~wise(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((~tall(X)<~>humble(X)))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~calm(X)|~old(X))<=>rich(X)))&
(((quiet(john)<~>generous(john)))=>(?[X]:((~quiet(X)<~>rich(X)))))&
(![X]:((generous(X)&~creative(X))=>(curious(X)&happy(X))))&
(![X]:((~calm(X)&~patient(X))<=>brave(X)))&
(![X]:((~humble(X)|old(X))<=>(happy(X)<~>rich(X))))&
(?[X]:((~creative(X)<~>creative(X))))&
(?[X]:(calm(X)))&
(?[X]:((~creative(X)|generous(X))))&
((~curious(john)&~patient(john)))&
(?[X]:((~wise(X)<~>old(X))))&
((~rich(paul)|~tall(paul)))&
((~tall(mary)&creative(mary)))&
(?[X]:((strong(X)<~>~happy(X)))) | curious(mary) | [] | null | 0 |
Everyone who is both not wise and not funny is both generous and calm.
Everyone who is not brave or not funny is not brave and vice versa.
If someone is both not patient and quiet then susan is either not old or not happy.
If someone is both not old and happy then someone is humble.
Everyone who is not tall or old is either quiet or kind.
Everyone who is either not happy or tall is both old and creative and vice versa.
If susan is both wise and brave then lucy is old or happy and vice versa.
Everyone who is brave or quiet is not creative and vice versa.
If paul is kind or not wise then fred is brave and vice versa.
If lucy is either kind or strong then someone is not wise or not quiet and vice versa.
Everyone who is not old is strong and vice versa.
Everyone who is calm is creative or not happy and vice versa.
If john is funny or quiet then mary is both kind and not tall and vice versa.
If someone is tall or humble then someone is not funny or not quiet and vice versa.
If someone is funny then someone is either strong or not creative.
Everyone who is both not quiet and not funny is not humble and vice versa.
Mary is both kind and not wise.
Alice is either not tall or patient.
Someone is happy or not rich.
John is both strong and not generous.
Someone is not strong.
John is not generous.
Lucy is both not generous and strong.
Lucy is brave. | Fred is brave. | neutral | (![X]:((~wise(X)&~funny(X))=>(generous(X)&calm(X))))&
(![X]:((~brave(X)|~funny(X))<=>~brave(X)))&
((?[X]:((~patient(X)&quiet(X))))=>((~old(susan)<~>~happy(susan))))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(((kind(paul)|~wise(paul)))<=>(brave(fred)))&
(((kind(lucy)<~>strong(lucy)))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:(~old(X)<=>strong(X)))&
(![X]:(calm(X)<=>(creative(X)|~happy(X))))&
(((funny(john)|quiet(john)))<=>((kind(mary)&~tall(mary))))&
((?[X]:((tall(X)|humble(X))))<=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((~quiet(X)&~funny(X))<=>~humble(X)))&
((kind(mary)&~wise(mary)))&
((~tall(alice)<~>patient(alice)))&
(?[X]:((happy(X)|~rich(X))))&
((strong(john)&~generous(john)))&
(?[X]:(~strong(X)))&
(~generous(john))&
((~generous(lucy)&strong(lucy)))&
(brave(lucy)) | brave(fred) | [] | null | 0 |
If someone is both funny and not quiet then someone is not funny or quiet.
Everyone who is either not humble or not rich is calm and vice versa.
Everyone who is either humble or calm is either strong or rich.
Everyone who is not happy is either not happy or not humble and vice versa.
Everyone who is both not humble and kind is both not humble and quiet and vice versa.
If fred is either humble or curious then someone is both not humble and not calm.
Everyone who is rich or not generous is old or not rich and vice versa.
Everyone who is not wise is curious.
Everyone who is both old and creative is both not rich and not old and vice versa.
If lucy is either not generous or generous then mary is both humble and not patient and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is old is either not tall or strong.
Everyone who is not rich or not old is creative or not old.
If mary is funny or not kind then john is not funny or humble and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is both not quiet and rich is strong and vice versa.
John is both rich and curious.
John is either brave or creative.
Someone is not funny.
Someone is not creative.
Someone is wise.
Paul is happy or not calm.
Paul is generous. | Lucy is not curious. | neutral | ((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~rich(X))<=>calm(X)))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)<~>rich(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((~humble(X)&kind(X))<=>(~humble(X)&quiet(X))))&
(((humble(fred)<~>curious(fred)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((rich(X)|~generous(X))<=>(old(X)|~rich(X))))&
(![X]:(~wise(X)=>curious(X)))&
(![X]:((old(X)&creative(X))<=>(~rich(X)&~old(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>((humble(mary)&~patient(mary))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:(old(X)=>(~tall(X)<~>strong(X))))&
(![X]:((~rich(X)|~old(X))=>(creative(X)|~old(X))))&
(((funny(mary)|~kind(mary)))<=>((~funny(john)|humble(john))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)&rich(X))<=>strong(X)))&
((rich(john)&curious(john)))&
((brave(john)<~>creative(john)))&
(?[X]:(~funny(X)))&
(?[X]:(~creative(X)))&
(?[X]:(wise(X)))&
((happy(paul)|~calm(paul)))&
(generous(paul)) | ~curious(lucy) | [] | null | 0 |
If someone is both creative and not creative then alice is old or not calm.
Everyone who is strong is either generous or not kind.
If someone is not happy or not generous then susan is not patient and vice versa.
If someone is kind or tall then fred is not humble or curious.
Everyone who is both not calm and rich is both patient and funny and vice versa.
If mary is not old then someone is both not tall and curious and vice versa.
Everyone who is both not funny and not old is both brave and patient.
Everyone who is creative is both not rich and not tall and vice versa.
If susan is either wise or not generous then someone is either not brave or rich and vice versa.
If alice is both not calm and not curious then someone is either happy or strong and vice versa.
Everyone who is tall or not tall is both kind and humble.
If someone is generous then john is both brave and curious.
Everyone who is both old and not rich is either humble or not brave.
If someone is not patient then lucy is calm and vice versa.
Everyone who is both humble and not kind is rich or creative and vice versa.
Everyone who is both not brave and not curious is either creative or not happy and vice versa.
Someone is both patient and not old.
Alice is both not creative and curious.
Someone is either not curious or not funny.
John is not happy or not wise.
Lucy is either not wise or quiet. | Mary is not brave. | contradiction | ((?[X]:((creative(X)&~creative(X))))=>((old(alice)|~calm(alice))))&
(![X]:(strong(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>(~patient(susan)))&
((?[X]:((kind(X)|tall(X))))=>((~humble(fred)|curious(fred))))&
(![X]:((~calm(X)&rich(X))<=>(patient(X)&funny(X))))&
((~old(mary))<=>(?[X]:((~tall(X)&curious(X)))))&
(![X]:((~funny(X)&~old(X))=>(brave(X)&patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&~tall(X))))&
(((wise(susan)<~>~generous(susan)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(((~calm(alice)&~curious(alice)))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((tall(X)|~tall(X))=>(kind(X)&humble(X))))&
((?[X]:(generous(X)))=>((brave(john)&curious(john))))&
(![X]:((old(X)&~rich(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(~patient(X)))<=>(calm(lucy)))&
(![X]:((humble(X)&~kind(X))<=>(rich(X)|creative(X))))&
(![X]:((~brave(X)&~curious(X))<=>(creative(X)<~>~happy(X))))&
(?[X]:((patient(X)&~old(X))))&
((~creative(alice)&curious(alice)))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~happy(john)|~wise(john)))&
((~wise(lucy)<~>quiet(lucy))) | ~brave(mary) | [
"p5",
"p7",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4862539760519197606549714
% SZS output start Proof for 4862539760519197606549714
6. ~old(mary) <=> ? [X0] : (curious(X0) & ~tall(X0)) [input p5]
8. ! [X0] : (creative(X0) <=> (~tall(X0) & ~rich(X0))) [input p7]
11. ! [X0] : ((~tall(X0) | tall(X0)) => (humble(X0) & kind(X0))) [input p10]
13. ! [X0] : ((~rich(X0) & old(X0)) => (humble(X0) <~> ~brave(X0))) [input p12]
15. ! [X0] : ((~kind(X0) & humble(X0)) <=> (creative(X0) | rich(X0))) [input p14]
22. ~brave(mary) [input hypothesis]
30. ! [X0] : ((humble(X0) & kind(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 11]
32. ! [X0] : ((humble(X0) <~> ~brave(X0)) | (rich(X0) | ~old(X0))) [ennf transformation 13]
33. ! [X0] : ((humble(X0) <~> ~brave(X0)) | rich(X0) | ~old(X0)) [flattening 32]
41. (~old(mary) | ! [X0] : (~curious(X0) | tall(X0))) & (? [X0] : (curious(X0) & ~tall(X0)) | old(mary)) [nnf transformation 6]
42. (~old(mary) | ! [X0] : (~curious(X0) | tall(X0))) & (? [X1] : (curious(X1) & ~tall(X1)) | old(mary)) [rectify 41]
43. ? [X1] : (curious(X1) & ~tall(X1)) => (curious(sK1) & ~tall(sK1)) [choice axiom]
44. (~old(mary) | ! [X0] : (~curious(X0) | tall(X0))) & ((curious(sK1) & ~tall(sK1)) | old(mary)) [skolemisation 42,43]
45. ! [X0] : ((creative(X0) | (tall(X0) | rich(X0))) & ((~tall(X0) & ~rich(X0)) | ~creative(X0))) [nnf transformation 8]
46. ! [X0] : ((creative(X0) | tall(X0) | rich(X0)) & ((~tall(X0) & ~rich(X0)) | ~creative(X0))) [flattening 45]
56. ! [X0] : (((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | rich(X0) | ~old(X0)) [nnf transformation 33]
61. ! [X0] : (((~kind(X0) & humble(X0)) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | (kind(X0) | ~humble(X0)))) [nnf transformation 15]
62. ! [X0] : (((~kind(X0) & humble(X0)) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | kind(X0) | ~humble(X0))) [flattening 61]
83. ~tall(sK1) | old(mary) [cnf transformation 44]
90. rich(X0) | tall(X0) | creative(X0) [cnf transformation 46]
105. kind(X0) | ~tall(X0) [cnf transformation 30]
106. tall(X0) | kind(X0) [cnf transformation 30]
107. humble(X0) | ~tall(X0) [cnf transformation 30]
108. humble(X0) | tall(X0) [cnf transformation 30]
112. brave(X0) | ~humble(X0) | rich(X0) | ~old(X0) [cnf transformation 56]
118. ~kind(X0) | ~rich(X0) [cnf transformation 62]
119. ~kind(X0) | ~creative(X0) [cnf transformation 62]
135. ~brave(mary) [cnf transformation 22]
177. 11 <=> old(mary) [avatar definition]
178. old(mary) <- (11) [avatar component clause 177]
187. 13 <=> tall(sK1) [avatar definition]
189. ~tall(sK1) <- (~13) [avatar component clause 187]
190. 11 | ~13 [avatar split clause 83,187,177]
249. humble(X0) [subsumption resolution 107,108]
250. kind(X0) [subsumption resolution 105,106]
264. ~old(X0) | rich(X0) | brave(X0) [subsumption resolution 112,249]
278. ~creative(X0) [subsumption resolution 119,250]
279. ~rich(X0) [subsumption resolution 118,250]
381. tall(X3) | creative(X3) [resolution 90,279]
384. tall(X3) [subsumption resolution 381,278]
385. rich(mary) | brave(mary) <- (11) [resolution 264,178]
387. brave(mary) <- (11) [subsumption resolution 385,279]
388. $false <- (11) [subsumption resolution 387,135]
389. ~11 [avatar contradiction clause 388]
396. $false <- (~13) [subsumption resolution 189,384]
397. 13 [avatar contradiction clause 396]
398. $false [avatar sat refutation 190,389,397]
% SZS output end Proof for 4862539760519197606549714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and rich is calm and vice versa.
Everyone who is funny or tall is tall and vice versa.
Everyone who is either not quiet or not strong is funny or not kind.
If someone is both wise and funny then someone is either happy or not generous.
Everyone who is not calm is not kind or old.
Everyone who is either not quiet or not kind is both not funny and kind.
Everyone who is funny or not wise is not tall or humble and vice versa.
Everyone who is both not calm and not tall is both not rich and brave.
If paul is not rich then someone is not creative or calm and vice versa.
Everyone who is either tall or not humble is old.
If someone is either not tall or brave then someone is kind or not funny.
If alice is happy or not kind then lucy is both not happy and strong.
Everyone who is either not creative or kind is either funny or not kind and vice versa.
Everyone who is either patient or not old is either not brave or wise and vice versa.
Everyone who is either old or curious is either generous or patient and vice versa.
Everyone who is generous or quiet is not wise or not humble and vice versa.
Someone is not generous or not strong.
Someone is patient.
Someone is not curious.
Someone is funny or not funny.
Someone is either not funny or rich.
Alice is both not generous and tall.
Susan is either quiet or generous.
Alice is either kind or not curious. | Alice is happy. | neutral | (![X]:((happy(X)&rich(X))<=>calm(X)))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>~strong(X))=>(funny(X)|~kind(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:(~calm(X)=>(~kind(X)|old(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~funny(X)&kind(X))))&
(![X]:((funny(X)|~wise(X))<=>(~tall(X)|humble(X))))&
(![X]:((~calm(X)&~tall(X))=>(~rich(X)&brave(X))))&
((~rich(paul))<=>(?[X]:((~creative(X)|calm(X)))))&
(![X]:((tall(X)<~>~humble(X))=>old(X)))&
((?[X]:((~tall(X)<~>brave(X))))=>(?[X]:((kind(X)|~funny(X)))))&
(((happy(alice)|~kind(alice)))=>((~happy(lucy)&strong(lucy))))&
(![X]:((~creative(X)<~>kind(X))<=>(funny(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~old(X))<=>(~brave(X)<~>wise(X))))&
(![X]:((old(X)<~>curious(X))<=>(generous(X)<~>patient(X))))&
(![X]:((generous(X)|quiet(X))<=>(~wise(X)|~humble(X))))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:(patient(X)))&
(?[X]:(~curious(X)))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((~funny(X)<~>rich(X))))&
((~generous(alice)&tall(alice)))&
((quiet(susan)<~>generous(susan)))&
((kind(alice)<~>~curious(alice))) | happy(alice) | [] | null | 0 |
Everyone who is both funny and not happy is not creative or happy and vice versa.
Everyone who is both brave and kind is not funny or happy and vice versa.
If paul is both not kind and happy then someone is kind or not tall.
If paul is either not old or not humble then someone is not creative and vice versa.
If lucy is not funny or funny then mary is both creative and not rich and vice versa.
Everyone who is either not creative or not quiet is both wise and not happy and vice versa.
If lucy is wise then alice is both not curious and not brave.
If paul is kind or calm then someone is not quiet.
If lucy is either not creative or not tall then lucy is old or not happy.
If lucy is either not old or not calm then someone is happy and vice versa.
Everyone who is both not wise and calm is both happy and humble.
Everyone who is patient is either not wise or not quiet.
If someone is kind or tall then someone is creative or not tall and vice versa.
Everyone who is both not wise and not happy is either not brave or calm and vice versa.
Everyone who is tall or not strong is not patient and vice versa.
If someone is both not wise and not old then fred is either wise or not patient and vice versa.
Someone is not strong.
Fred is happy or not brave.
Mary is tall.
Someone is both curious and generous.
Someone is either not generous or not brave. | Mary is not happy. | entailment | (![X]:((funny(X)&~happy(X))<=>(~creative(X)|happy(X))))&
(![X]:((brave(X)&kind(X))<=>(~funny(X)|happy(X))))&
(((~kind(paul)&happy(paul)))=>(?[X]:((kind(X)|~tall(X)))))&
(((~old(paul)<~>~humble(paul)))<=>(?[X]:(~creative(X))))&
(((~funny(lucy)|funny(lucy)))<=>((creative(mary)&~rich(mary))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(wise(X)&~happy(X))))&
((wise(lucy))=>((~curious(alice)&~brave(alice))))&
(((kind(paul)|calm(paul)))=>(?[X]:(~quiet(X))))&
(((~creative(lucy)<~>~tall(lucy)))=>((old(lucy)|~happy(lucy))))&
(((~old(lucy)<~>~calm(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)&calm(X))=>(happy(X)&humble(X))))&
(![X]:(patient(X)=>(~wise(X)<~>~quiet(X))))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((creative(X)|~tall(X)))))&
(![X]:((~wise(X)&~happy(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((tall(X)|~strong(X))<=>~patient(X)))&
((?[X]:((~wise(X)&~old(X))))<=>((wise(fred)<~>~patient(fred))))&
(?[X]:(~strong(X)))&
((happy(fred)|~brave(fred)))&
(tall(mary))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:((~generous(X)<~>~brave(X)))) | ~happy(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8742015034698606682750073
% SZS output start Proof for 8742015034698606682750073
1. ! [X0] : ((~happy(X0) & funny(X0)) <=> (happy(X0) | ~creative(X0))) [input p0]
22. happy(mary) [input hypothesis]
33. ! [X0] : (((~happy(X0) & funny(X0)) | (~happy(X0) & creative(X0))) & ((happy(X0) | ~creative(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : (((~happy(X0) & funny(X0)) | (~happy(X0) & creative(X0))) & (happy(X0) | ~creative(X0) | happy(X0) | ~funny(X0))) [flattening 33]
79. ~happy(X0) | ~happy(X0) [cnf transformation 34]
141. happy(mary) [cnf transformation 22]
143. ~happy(X0) [duplicate literal removal 79]
295. $false [subsumption resolution 141,143]
% SZS output end Proof for 8742015034698606682750073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not creative is both generous and not wise and vice versa.
If mary is both kind and not patient then paul is either old or not quiet.
If someone is kind or calm then lucy is not old.
If someone is either happy or funny then someone is not strong or not quiet.
If someone is both not calm and rich then someone is not funny or patient.
If someone is not calm then paul is either calm or not wise and vice versa.
If alice is both generous and old then someone is patient or curious.
Everyone who is both happy and not tall is calm.
If paul is calm or not kind then mary is patient.
Everyone who is humble is not kind or not tall and vice versa.
Everyone who is tall is either not humble or not old and vice versa.
If someone is either not old or not calm then someone is generous and vice versa.
Everyone who is both not old and not kind is humble and vice versa.
If someone is both creative and not generous then fred is not tall or humble and vice versa.
Everyone who is either not tall or quiet is both curious and not happy.
If fred is either not humble or not curious then someone is either not patient or not curious.
Someone is either not happy or not funny.
Someone is curious.
Someone is either brave or humble.
Someone is both not funny and calm.
Susan is tall.
Fred is both happy and brave.
John is not tall or not rich. | Lucy is not humble. | contradiction | (![X]:((~brave(X)|~creative(X))<=>(generous(X)&~wise(X))))&
(((kind(mary)&~patient(mary)))=>((old(paul)<~>~quiet(paul))))&
((?[X]:((kind(X)|calm(X))))=>(~old(lucy)))&
((?[X]:((happy(X)<~>funny(X))))=>(?[X]:((~strong(X)|~quiet(X)))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:(~calm(X)))<=>((calm(paul)<~>~wise(paul))))&
(((generous(alice)&old(alice)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((happy(X)&~tall(X))=>calm(X)))&
(((calm(paul)|~kind(paul)))=>(patient(mary)))&
(![X]:(humble(X)<=>(~kind(X)|~tall(X))))&
(![X]:(tall(X)<=>(~humble(X)<~>~old(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(generous(X))))&
(![X]:((~old(X)&~kind(X))<=>humble(X)))&
((?[X]:((creative(X)&~generous(X))))<=>((~tall(fred)|humble(fred))))&
(![X]:((~tall(X)<~>quiet(X))=>(curious(X)&~happy(X))))&
(((~humble(fred)<~>~curious(fred)))=>(?[X]:((~patient(X)<~>~curious(X)))))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((~funny(X)&calm(X))))&
(tall(susan))&
((happy(fred)&brave(fred)))&
((~tall(john)|~rich(john))) | ~humble(lucy) | [
"p2",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5504641517651084643430580
% SZS output start Proof for 5504641517651084643430580
3. ? [X0] : (calm(X0) | kind(X0)) => ~old(lucy) [input p2]
10. ! [X0] : (humble(X0) <=> (~tall(X0) | ~kind(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> (~humble(X0) <~> ~old(X0))) [input p10]
20. ? [X0] : (calm(X0) & ~funny(X0)) [input p19]
24. ~humble(lucy) [input hypothesis]
33. ~old(lucy) | ! [X0] : (~calm(X0) & ~kind(X0)) [ennf transformation 3]
50. ! [X0] : ((humble(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | ~humble(X0))) [nnf transformation 10]
51. ! [X0] : ((humble(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | ~humble(X0))) [flattening 50]
52. ! [X0] : ((tall(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~tall(X0))) [nnf transformation 11]
77. ? [X0] : (calm(X0) & ~funny(X0)) => (calm(sK9) & ~funny(sK9)) [choice axiom]
78. calm(sK9) & ~funny(sK9) [skolemisation 20,77]
87. ~old(lucy) | ~calm(X0) [cnf transformation 33]
98. humble(X0) | tall(X0) [cnf transformation 51]
100. old(X0) | humble(X0) | ~tall(X0) [cnf transformation 52]
129. calm(sK9) [cnf transformation 78]
133. ~humble(lucy) [cnf transformation 24]
153. 5 <=> ! [X0] : ~calm(X0) [avatar definition]
154. ~calm(X0) <- (5) [avatar component clause 153]
156. 6 <=> old(lucy) [avatar definition]
159. 5 | ~6 [avatar split clause 87,156,153]
207. humble(X0) | old(X0) [subsumption resolution 100,98]
310. old(lucy) [resolution 207,133]
315. 6 [avatar split clause 310,156]
316. $false <- (5) [resolution 154,129]
317. ~5 [avatar contradiction clause 316]
318. $false [avatar sat refutation 159,315,317]
% SZS output end Proof for 5504641517651084643430580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is either humble or not calm.
Everyone who is not old is both not kind and not tall and vice versa.
Everyone who is both not happy and not creative is curious or not patient.
Everyone who is not funny is tall or humble.
Everyone who is both wise and not wise is not generous or not humble and vice versa.
Everyone who is brave is not humble or tall.
If paul is either wise or not strong then mary is both not wise and not old and vice versa.
If someone is both not strong and wise then lucy is kind and vice versa.
If john is either kind or calm then someone is brave or funny.
If someone is not humble then someone is not old.
If someone is not brave or happy then someone is not wise and vice versa.
Everyone who is happy or not creative is both creative and funny and vice versa.
If someone is both creative and not tall then someone is patient.
Everyone who is funny is not strong or rich.
If someone is wise or strong then paul is not strong.
Everyone who is either happy or not strong is generous.
Someone is generous or not kind.
Mary is either not wise or not strong.
Someone is curious.
Someone is both creative and not funny.
Susan is not rich.
Fred is both not wise and patient.
Someone is not brave or not tall. | Susan is creative. | entailment | (![X]:(quiet(X)=>(humble(X)<~>~calm(X))))&
(![X]:(~old(X)<=>(~kind(X)&~tall(X))))&
(![X]:((~happy(X)&~creative(X))=>(curious(X)|~patient(X))))&
(![X]:(~funny(X)=>(tall(X)|humble(X))))&
(![X]:((wise(X)&~wise(X))<=>(~generous(X)|~humble(X))))&
(![X]:(brave(X)=>(~humble(X)|tall(X))))&
(((wise(paul)<~>~strong(paul)))<=>((~wise(mary)&~old(mary))))&
((?[X]:((~strong(X)&wise(X))))<=>(kind(lucy)))&
(((kind(john)<~>calm(john)))=>(?[X]:((brave(X)|funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:(~old(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((happy(X)|~creative(X))<=>(creative(X)&funny(X))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:(patient(X))))&
(![X]:(funny(X)=>(~strong(X)|rich(X))))&
((?[X]:((wise(X)|strong(X))))=>(~strong(paul)))&
(![X]:((happy(X)<~>~strong(X))=>generous(X)))&
(?[X]:((generous(X)|~kind(X))))&
((~wise(mary)<~>~strong(mary)))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)&~funny(X))))&
(~rich(susan))&
((~wise(fred)&patient(fred)))&
(?[X]:((~brave(X)|~tall(X)))) | creative(susan) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 316062642475381502437771
% SZS output start Proof for 316062642475381502437771
12. ! [X0] : ((~creative(X0) | happy(X0)) <=> (funny(X0) & creative(X0))) [input p11]
24. ~creative(susan) [input hypothesis]
64. ! [X0] : (((~creative(X0) | happy(X0)) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | (creative(X0) & ~happy(X0)))) [nnf transformation 12]
65. ! [X0] : ((~creative(X0) | happy(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | (creative(X0) & ~happy(X0)))) [flattening 64]
100. creative(X0) | creative(X0) [cnf transformation 65]
117. ~creative(susan) [cnf transformation 24]
118. creative(X0) [duplicate literal removal 100]
220. $false [subsumption resolution 117,118]
% SZS output end Proof for 316062642475381502437771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is not kind and vice versa. If someone is either not generous or not brave then someone is either not generous or strong and vice versa. Everyone who is creative is either patient or wise. If someone is either strong or not calm then lucy is either not old or not quiet. If someone is not curious then alice is strong. Everyone who is not rich or brave is not quiet. Everyone who is both not funny and generous is curious or happy. If someone is happy or not patient then someone is old or not rich and vice versa. Everyone who is not creative is not wise. Everyone who is both brave and creative is not strong. If someone is either not funny or not happy then fred is both wise and not tall. If someone is creative then john is quiet. If someone is generous or not rich then someone is either not generous or wise. Everyone who is both generous and quiet is strong. If someone is either not funny or tall then john is both generous and kind. Paul is both happy and tall. Someone is not creative. Someone is not old. Lucy is not old or curious. Someone is either not creative or not wise. Someone is not funny or not patient. Someone is not patient. | John is not kind. | entailment | (![X]:((~old(X)<~>old(X))<=>~kind(X)))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(creative(X)=>(patient(X)<~>wise(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~old(lucy)<~>~quiet(lucy))))&
((?[X]:(~curious(X)))=>(strong(alice)))&
(![X]:((~rich(X)|brave(X))=>~quiet(X)))&
(![X]:((~funny(X)&generous(X))=>(curious(X)|happy(X))))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:(~creative(X)=>~wise(X)))&
(![X]:((brave(X)&creative(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~happy(X))))=>((wise(fred)&~tall(fred))))&
((?[X]:(creative(X)))=>(quiet(john)))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((generous(X)&quiet(X))=>strong(X)))&
((?[X]:((~funny(X)<~>tall(X))))=>((generous(john)&kind(john))))&
((happy(paul)&tall(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(~old(X)))&
((~old(lucy)|curious(lucy)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | ~kind(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5751338348824959039780724
% SZS output start Proof for 5751338348824959039780724
1. ! [X0] : ((~old(X0) <~> old(X0)) <=> ~kind(X0)) [input p0]
23. kind(john) [input hypothesis]
27. ! [X0] : ((~old(X0) <~> old(X0)) => ~kind(X0)) [unused predicate definition removal 1]
31. ! [X0] : (~kind(X0) | (~old(X0) <=> old(X0))) [ennf transformation 27]
44. ! [X0] : (~kind(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 31]
74. ~kind(X0) | old(X0) | old(X0) [cnf transformation 44]
75. ~kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 44]
120. kind(john) [cnf transformation 23]
121. ~kind(X0) | old(X0) [duplicate literal removal 74]
122. ~kind(X0) | ~old(X0) [duplicate literal removal 75]
123. ~kind(X0) [subsumption resolution 121,122]
264. $false [subsumption resolution 120,123]
% SZS output end Proof for 5751338348824959039780724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not funny is either calm or not patient. Everyone who is not tall is both not quiet and funny and vice versa. If someone is either rich or quiet then mary is not happy or wise and vice versa. Everyone who is not quiet is both quiet and kind and vice versa. If john is not generous or not calm then alice is either not tall or not strong and vice versa. Everyone who is either calm or not old is both generous and funny and vice versa. If alice is either not kind or not generous then paul is not creative. Everyone who is either not old or brave is not funny or wise. If someone is rich then someone is either strong or funny. Everyone who is both not humble and patient is both wise and calm. If paul is both kind and quiet then paul is either strong or creative and vice versa. Everyone who is either not calm or not brave is both not strong and tall. Everyone who is curious or wise is not funny and vice versa. Everyone who is not funny is not rich. If someone is brave then lucy is both not happy and not kind. Everyone who is both calm and not kind is either curious or not happy and vice versa. Susan is calm. Someone is both happy and funny. Paul is quiet or patient. Someone is wise or old. Susan is calm or not quiet. Lucy is generous. Someone is not rich or curious. Someone is not strong. | Susan is not tall. | contradiction | (![X]:((creative(X)|~funny(X))=>(calm(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(~quiet(X)&funny(X))))&
((?[X]:((rich(X)<~>quiet(X))))<=>((~happy(mary)|wise(mary))))&
(![X]:(~quiet(X)<=>(quiet(X)&kind(X))))&
(((~generous(john)|~calm(john)))<=>((~tall(alice)<~>~strong(alice))))&
(![X]:((calm(X)<~>~old(X))<=>(generous(X)&funny(X))))&
(((~kind(alice)<~>~generous(alice)))=>(~creative(paul)))&
(![X]:((~old(X)<~>brave(X))=>(~funny(X)|wise(X))))&
((?[X]:(rich(X)))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~humble(X)&patient(X))=>(wise(X)&calm(X))))&
(((kind(paul)&quiet(paul)))<=>((strong(paul)<~>creative(paul))))&
(![X]:((~calm(X)<~>~brave(X))=>(~strong(X)&tall(X))))&
(![X]:((curious(X)|wise(X))<=>~funny(X)))&
(![X]:(~funny(X)=>~rich(X)))&
((?[X]:(brave(X)))=>((~happy(lucy)&~kind(lucy))))&
(![X]:((calm(X)&~kind(X))<=>(curious(X)<~>~happy(X))))&
(calm(susan))&
(?[X]:((happy(X)&funny(X))))&
((quiet(paul)|patient(paul)))&
(?[X]:((wise(X)|old(X))))&
((calm(susan)|~quiet(susan)))&
(generous(lucy))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:(~strong(X))) | ~tall(susan) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3378682901852956399349681
% SZS output start Proof for 3378682901852956399349681
2. ! [X0] : (~tall(X0) <=> (funny(X0) & ~quiet(X0))) [input p1]
4. ! [X0] : (~quiet(X0) <=> (kind(X0) & quiet(X0))) [input p3]
25. ~tall(susan) [input hypothesis]
37. ! [X0] : ((~tall(X0) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | tall(X0))) [nnf transformation 2]
38. ! [X0] : ((~tall(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | tall(X0))) [flattening 37]
44. ! [X0] : ((~quiet(X0) | (~kind(X0) | ~quiet(X0))) & ((kind(X0) & quiet(X0)) | quiet(X0))) [nnf transformation 4]
45. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & ((kind(X0) & quiet(X0)) | quiet(X0))) [flattening 44]
75. ~quiet(X0) | tall(X0) [cnf transformation 38]
84. quiet(X0) | quiet(X0) [cnf transformation 45]
136. ~tall(susan) [cnf transformation 25]
137. quiet(X0) [duplicate literal removal 84]
264. tall(X0) [resolution 75,137]
265. $false [resolution 264,136]
% SZS output end Proof for 3378682901852956399349681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and rich is not strong. If john is funny or not wise then john is not strong. Everyone who is brave or not kind is both not curious and not creative and vice versa. Everyone who is humble is not creative and vice versa. If lucy is both creative and not happy then someone is patient or kind. Everyone who is both not old and not happy is either tall or happy and vice versa. If someone is generous then mary is kind or not humble and vice versa. If mary is either wise or not curious then john is calm. If paul is either not humble or old then paul is both funny and not curious. Everyone who is either generous or quiet is both not patient and old and vice versa. Everyone who is either old or not strong is not old and vice versa. If alice is either not patient or not kind then susan is either creative or funny. If fred is wise then john is either creative or not kind. Everyone who is both not patient and curious is funny and vice versa. If alice is both quiet and not happy then lucy is strong and vice versa. If paul is not rich then someone is not tall or not happy. Susan is generous. Paul is strong or not patient. Paul is not tall. Paul is not strong or not quiet. Someone is tall or quiet. Someone is not funny. Someone is both not humble and not wise. Someone is either not quiet or brave. | Paul is tall. | contradiction | (![X]:((~brave(X)&rich(X))=>~strong(X)))&
(((funny(john)|~wise(john)))=>(~strong(john)))&
(![X]:((brave(X)|~kind(X))<=>(~curious(X)&~creative(X))))&
(![X]:(humble(X)<=>~creative(X)))&
(((creative(lucy)&~happy(lucy)))=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((~old(X)&~happy(X))<=>(tall(X)<~>happy(X))))&
((?[X]:(generous(X)))<=>((kind(mary)|~humble(mary))))&
(((wise(mary)<~>~curious(mary)))=>(calm(john)))&
(((~humble(paul)<~>old(paul)))=>((funny(paul)&~curious(paul))))&
(![X]:((generous(X)<~>quiet(X))<=>(~patient(X)&old(X))))&
(![X]:((old(X)<~>~strong(X))<=>~old(X)))&
(((~patient(alice)<~>~kind(alice)))=>((creative(susan)<~>funny(susan))))&
((wise(fred))=>((creative(john)<~>~kind(john))))&
(![X]:((~patient(X)&curious(X))<=>funny(X)))&
(((quiet(alice)&~happy(alice)))<=>(strong(lucy)))&
((~rich(paul))=>(?[X]:((~tall(X)|~happy(X)))))&
(generous(susan))&
((strong(paul)|~patient(paul)))&
(~tall(paul))&
((~strong(paul)|~quiet(paul)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((~quiet(X)<~>brave(X)))) | tall(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4979025442191931669132834
% SZS output start Proof for 4979025442191931669132834
19. ~tall(paul) [input p18]
25. tall(paul) [input hypothesis]
118. ~tall(paul) [cnf transformation 19]
126. tall(paul) [cnf transformation 25]
275. $false [subsumption resolution 126,118]
% SZS output end Proof for 4979025442191931669132834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not calm and vice versa.
Everyone who is both happy and creative is not calm or kind.
Everyone who is humble is tall.
If john is not generous then someone is happy and vice versa.
If susan is both not quiet and generous then someone is both not quiet and not humble.
Everyone who is not generous is not creative or wise and vice versa.
If someone is generous or not brave then lucy is not rich.
Everyone who is funny or not old is either curious or not creative.
If mary is either patient or not happy then mary is not rich or tall.
If fred is brave then someone is either kind or not happy and vice versa.
If someone is not curious or not generous then lucy is both not old and funny and vice versa.
Everyone who is humble is both not patient and not humble and vice versa.
If someone is happy or not generous then someone is both kind and old.
If someone is both not funny and not strong then someone is not old or curious and vice versa.
Everyone who is either not calm or not strong is patient or not brave and vice versa.
If someone is funny or not kind then john is either quiet or kind.
Someone is strong or not old.
Susan is not funny or not brave.
Fred is both not quiet and kind.
Lucy is not rich.
Paul is either not brave or not funny.
Someone is either curious or humble.
Someone is both not quiet and kind.
Someone is both tall and generous. | Fred is not strong. | contradiction | (![X]:(~quiet(X)<=>~calm(X)))&
(![X]:((happy(X)&creative(X))=>(~calm(X)|kind(X))))&
(![X]:(humble(X)=>tall(X)))&
((~generous(john))<=>(?[X]:(happy(X))))&
(((~quiet(susan)&generous(susan)))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(~generous(X)<=>(~creative(X)|wise(X))))&
((?[X]:((generous(X)|~brave(X))))=>(~rich(lucy)))&
(![X]:((funny(X)|~old(X))=>(curious(X)<~>~creative(X))))&
(((patient(mary)<~>~happy(mary)))=>((~rich(mary)|tall(mary))))&
((brave(fred))<=>(?[X]:((kind(X)<~>~happy(X)))))&
((?[X]:((~curious(X)|~generous(X))))<=>((~old(lucy)&funny(lucy))))&
(![X]:(humble(X)<=>(~patient(X)&~humble(X))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:((kind(X)&old(X)))))&
((?[X]:((~funny(X)&~strong(X))))<=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((~calm(X)<~>~strong(X))<=>(patient(X)|~brave(X))))&
((?[X]:((funny(X)|~kind(X))))=>((quiet(john)<~>kind(john))))&
(?[X]:((strong(X)|~old(X))))&
((~funny(susan)|~brave(susan)))&
((~quiet(fred)&kind(fred)))&
(~rich(lucy))&
((~brave(paul)<~>~funny(paul)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((tall(X)&generous(X)))) | ~strong(fred) | [
"p0",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8913514304635045347998075
% SZS output start Proof for 8913514304635045347998075
1. ! [X0] : (~quiet(X0) <=> ~calm(X0)) [input p0]
12. ! [X0] : (humble(X0) <=> (~humble(X0) & ~patient(X0))) [input p11]
15. ! [X0] : ((~calm(X0) <~> ~strong(X0)) <=> (~brave(X0) | patient(X0))) [input p14]
19. kind(fred) & ~quiet(fred) [input p18]
25. ~strong(fred) [input hypothesis]
40. ! [X0] : ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))) [nnf transformation 1]
59. ! [X0] : ((humble(X0) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | ~humble(X0))) [nnf transformation 12]
60. ! [X0] : ((humble(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | ~humble(X0))) [flattening 59]
69. ! [X0] : ((((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0))))) [nnf transformation 15]
70. ! [X0] : ((((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0))))) [flattening 69]
82. ~calm(X0) | quiet(X0) [cnf transformation 40]
106. ~humble(X0) | ~humble(X0) [cnf transformation 60]
107. humble(X0) | humble(X0) | patient(X0) [cnf transformation 60]
121. ~patient(X0) | calm(X0) | strong(X0) [cnf transformation 70]
129. ~quiet(fred) [cnf transformation 19]
138. ~strong(fred) [cnf transformation 25]
139. ~humble(X0) [duplicate literal removal 106]
140. patient(X0) | humble(X0) [duplicate literal removal 107]
361. calm(X0) | strong(X0) | humble(X0) [resolution 121,140]
362. strong(X0) | calm(X0) [subsumption resolution 361,139]
407. 52 <=> calm(fred) [avatar definition]
408. calm(fred) <- (52) [avatar component clause 407]
441. calm(fred) [resolution 362,138]
454. 52 [avatar split clause 441,407]
465. quiet(fred) <- (52) [resolution 408,82]
466. $false <- (52) [subsumption resolution 465,129]
467. ~52 [avatar contradiction clause 466]
468. $false [avatar sat refutation 454,467]
% SZS output end Proof for 8913514304635045347998075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or strong is either quiet or rich.
If paul is not kind then alice is both tall and not creative.
Everyone who is either not curious or not rich is either not kind or quiet and vice versa.
If alice is both patient and not kind then fred is both calm and patient and vice versa.
Everyone who is not happy is not creative or generous.
Everyone who is either tall or not generous is not rich and vice versa.
Everyone who is both quiet and not brave is either brave or not old and vice versa.
Everyone who is both brave and not wise is kind or not old and vice versa.
If someone is both not quiet and not creative then john is not tall.
Everyone who is either not funny or not wise is not quiet and vice versa.
If someone is not generous then alice is tall or not creative and vice versa.
Everyone who is both not patient and calm is quiet.
If lucy is either funny or not quiet then fred is quiet and vice versa.
If mary is generous then someone is either not calm or old and vice versa.
Everyone who is not tall is both strong and old.
Everyone who is curious is either not calm or generous and vice versa.
Mary is both brave and quiet.
Someone is wise or strong.
Alice is not brave or curious.
Mary is both curious and not wise.
Someone is tall.
Someone is either kind or quiet. | Mary is not rich. | entailment | (![X]:((creative(X)<~>strong(X))=>(quiet(X)<~>rich(X))))&
((~kind(paul))=>((tall(alice)&~creative(alice))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~kind(X)<~>quiet(X))))&
(((patient(alice)&~kind(alice)))<=>((calm(fred)&patient(fred))))&
(![X]:(~happy(X)=>(~creative(X)|generous(X))))&
(![X]:((tall(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((quiet(X)&~brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:((brave(X)&~wise(X))<=>(kind(X)|~old(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(~tall(john)))&
(![X]:((~funny(X)<~>~wise(X))<=>~quiet(X)))&
((?[X]:(~generous(X)))<=>((tall(alice)|~creative(alice))))&
(![X]:((~patient(X)&calm(X))=>quiet(X)))&
(((funny(lucy)<~>~quiet(lucy)))<=>(quiet(fred)))&
((generous(mary))<=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~tall(X)=>(strong(X)&old(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>generous(X))))&
((brave(mary)&quiet(mary)))&
(?[X]:((wise(X)|strong(X))))&
((~brave(alice)|curious(alice)))&
((curious(mary)&~wise(mary)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)<~>quiet(X)))) | ~rich(mary) | [
"p5",
"p6",
"p13",
"p14",
"p15",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6823751494844206035969717
% SZS output start Proof for 6823751494844206035969717
6. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> ~rich(X0)) [input p5]
7. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (brave(X0) <~> ~old(X0))) [input p6]
14. generous(mary) <=> ? [X0] : (~calm(X0) <~> old(X0)) [input p13]
15. ! [X0] : (~tall(X0) => (old(X0) & strong(X0))) [input p14]
16. ! [X0] : (curious(X0) <=> (~calm(X0) <~> generous(X0))) [input p15]
17. quiet(mary) & brave(mary) [input p16]
20. ~wise(mary) & curious(mary) [input p19]
23. rich(mary) [input hypothesis]
30. ! [X0] : ((old(X0) & strong(X0)) | tall(X0)) [ennf transformation 15]
35. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | rich(X0)) & (~rich(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 6]
36. ! [X0] : (((~brave(X0) & quiet(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((~brave(X0) & quiet(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | brave(X0) | ~quiet(X0))) [flattening 36]
47. (generous(mary) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (? [X0] : ((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | ~generous(mary)) [nnf transformation 14]
48. (generous(mary) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (? [X1] : ((~old(X1) | calm(X1)) & (old(X1) | ~calm(X1))) | ~generous(mary)) [rectify 47]
49. ? [X1] : ((~old(X1) | calm(X1)) & (old(X1) | ~calm(X1))) => ((~old(sK1) | calm(sK1)) & (old(sK1) | ~calm(sK1))) [choice axiom]
50. (generous(mary) | ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(sK1) | calm(sK1)) & (old(sK1) | ~calm(sK1))) | ~generous(mary)) [skolemisation 48,49]
51. ! [X0] : ((curious(X0) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0)))) & (((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | ~curious(X0))) [nnf transformation 16]
77. ~generous(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 35]
81. ~old(X0) | brave(X0) | brave(X0) | ~quiet(X0) [cnf transformation 37]
85. ~brave(X0) | ~old(X0) | ~brave(X0) [cnf transformation 37]
107. generous(mary) | old(X0) | calm(X0) [cnf transformation 50]
110. old(X0) | tall(X0) [cnf transformation 30]
111. ~calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 51]
115. brave(mary) [cnf transformation 17]
116. quiet(mary) [cnf transformation 17]
119. curious(mary) [cnf transformation 20]
124. rich(mary) [cnf transformation 23]
125. ~old(X0) | brave(X0) | ~quiet(X0) [duplicate literal removal 81]
126. ~old(X0) | ~brave(X0) [duplicate literal removal 85]
161. ~old(X0) | ~quiet(X0) [subsumption resolution 125,126]
200. 16 <=> generous(mary) [avatar definition]
201. ~generous(mary) <- (~16) [avatar component clause 200]
202. generous(mary) <- (16) [avatar component clause 200]
205. 17 <=> ! [X0] : (old(X0) | calm(X0)) [avatar definition]
206. old(X0) | calm(X0) <- (17) [avatar component clause 205]
207. 17 | 16 [avatar split clause 107,200,205]
252. ~brave(X0) | tall(X0) [resolution 126,110]
295. 32 <=> tall(mary) [avatar definition]
302. ~rich(mary) | ~tall(mary) <- (16) [resolution 202,77]
303. ~tall(mary) <- (16) [subsumption resolution 302,124]
304. ~32 | ~16 [avatar split clause 303,200,295]
314. ~quiet(X0) | calm(X0) <- (17) [resolution 206,161]
520. tall(mary) [resolution 252,115]
524. 32 [avatar split clause 520,295]
596. calm(mary) <- (17) [resolution 314,116]
691. generous(mary) | ~curious(mary) <- (17) [resolution 596,111]
693. ~curious(mary) <- (~16, 17) [subsumption resolution 691,201]
694. $false <- (~16, 17) [subsumption resolution 693,119]
695. 16 | ~17 [avatar contradiction clause 694]
696. $false [avatar sat refutation 207,304,524,695]
% SZS output end Proof for 6823751494844206035969717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If john is both not wise and not generous then someone is wise or tall.
If someone is either kind or not wise then someone is funny or not strong and vice versa.
Everyone who is both patient and creative is both not kind and funny and vice versa.
Everyone who is rich or tall is either generous or brave.
Everyone who is not creative is not tall and vice versa.
If susan is both not old and not rich then someone is both funny and patient and vice versa.
Everyone who is both not humble and not tall is happy and vice versa.
If someone is both generous and not tall then someone is happy.
If paul is both brave and not funny then someone is both rich and not curious and vice versa.
If mary is both not strong and not generous then someone is both wise and not rich.
If someone is not humble then someone is both generous and not brave and vice versa.
If someone is either humble or not wise then alice is both not tall and not patient.
If someone is both humble and not curious then fred is old and vice versa.
If someone is either not funny or not calm then someone is brave or not quiet and vice versa.
Everyone who is both wise and rich is not wise or not kind and vice versa.
Everyone who is either strong or not patient is quiet.
Someone is either creative or not calm.
Someone is both not humble and not creative.
Someone is humble.
John is brave.
Someone is both funny and brave.
Someone is not rich.
Someone is happy or not happy. | John is creative. | neutral | (((~wise(john)&~generous(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((kind(X)<~>~wise(X))))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((patient(X)&creative(X))<=>(~kind(X)&funny(X))))&
(![X]:((rich(X)|tall(X))=>(generous(X)<~>brave(X))))&
(![X]:(~creative(X)<=>~tall(X)))&
(((~old(susan)&~rich(susan)))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:((~humble(X)&~tall(X))<=>happy(X)))&
((?[X]:((generous(X)&~tall(X))))=>(?[X]:(happy(X))))&
(((brave(paul)&~funny(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
(((~strong(mary)&~generous(mary)))=>(?[X]:((wise(X)&~rich(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((humble(X)<~>~wise(X))))=>((~tall(alice)&~patient(alice))))&
((?[X]:((humble(X)&~curious(X))))<=>(old(fred)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((wise(X)&rich(X))<=>(~wise(X)|~kind(X))))&
(![X]:((strong(X)<~>~patient(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:(humble(X)))&
(brave(john))&
(?[X]:((funny(X)&brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((happy(X)|~happy(X)))) | creative(john) | [] | null | 0 |
Everyone who is both not quiet and creative is both not funny and strong.
Everyone who is either not curious or not creative is either not curious or wise.
Everyone who is not strong is either not tall or not wise and vice versa.
If someone is not wise or not old then paul is quiet or brave.
If someone is old or curious then mary is either not calm or old and vice versa.
If susan is either not kind or calm then someone is tall or brave and vice versa.
If susan is either curious or not patient then mary is both strong and not curious.
Everyone who is both not patient and not strong is either generous or not brave and vice versa.
Everyone who is either not humble or not curious is wise.
Everyone who is old or happy is not old.
Everyone who is not humble is old or not old.
If someone is humble then mary is both rich and kind and vice versa.
If someone is either not happy or not brave then someone is both not quiet and happy and vice versa.
If someone is either kind or tall then alice is not funny.
Everyone who is not strong is generous.
If susan is both not calm and calm then someone is strong and vice versa.
Alice is both calm and not patient.
Someone is patient or tall.
Mary is both funny and not calm.
Someone is not brave.
Someone is creative or generous.
Fred is not brave.
Someone is either not kind or creative. | Mary is not old. | entailment | (![X]:((~quiet(X)&creative(X))=>(~funny(X)&strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(~curious(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~wise(X)|~old(X))))=>((quiet(paul)|brave(paul))))&
((?[X]:((old(X)|curious(X))))<=>((~calm(mary)<~>old(mary))))&
(((~kind(susan)<~>calm(susan)))<=>(?[X]:((tall(X)|brave(X)))))&
(((curious(susan)<~>~patient(susan)))=>((strong(mary)&~curious(mary))))&
(![X]:((~patient(X)&~strong(X))<=>(generous(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
(((~calm(susan)&calm(susan)))<=>(?[X]:(strong(X))))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
((funny(mary)&~calm(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | ~old(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 805460369952446696991943
% SZS output start Proof for 805460369952446696991943
10. ! [X0] : ((happy(X0) | old(X0)) => ~old(X0)) [input p9]
24. old(mary) [input hypothesis]
33. ! [X0] : (~old(X0) | (~happy(X0) & ~old(X0))) [ennf transformation 10]
113. ~old(X0) | ~old(X0) [cnf transformation 33]
141. old(mary) [cnf transformation 24]
142. ~old(X0) [duplicate literal removal 113]
162. 5 <=> old(mary) [avatar definition]
163. old(mary) <- (5) [avatar component clause 162]
184. 10 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (10) [avatar component clause 184]
237. 10 [avatar split clause 142,184]
333. 5 [avatar split clause 141,162]
334. $false <- (5, 10) [subsumption resolution 163,185]
335. ~5 | ~10 [avatar contradiction clause 334]
336. $false [avatar sat refutation 237,333,335]
% SZS output end Proof for 805460369952446696991943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and patient is humble or quiet and vice versa.
Everyone who is not calm or funny is either not wise or not brave.
If lucy is humble then someone is both strong and rich and vice versa.
Everyone who is not funny is not old or not wise.
Everyone who is either not generous or not creative is both creative and generous.
Everyone who is both quiet and not quiet is kind or not humble.
Everyone who is either tall or not old is curious and vice versa.
Everyone who is either patient or not quiet is both not creative and not kind and vice versa.
Everyone who is both not old and strong is not funny or not creative and vice versa.
Everyone who is not strong or creative is either not wise or generous and vice versa.
Everyone who is both not strong and not happy is either happy or not humble and vice versa.
If someone is both old and curious then lucy is both brave and wise and vice versa.
Everyone who is tall is both wise and not rich.
Everyone who is not wise or old is either humble or not generous and vice versa.
Everyone who is both not old and not funny is either calm or creative and vice versa.
If paul is not old then john is either generous or not old.
Someone is not creative.
Someone is both not quiet and not humble.
Alice is brave or humble.
Someone is funny.
Fred is humble or not curious.
Someone is not funny or not patient.
Someone is not creative or creative.
Someone is either not kind or not creative. | Alice is creative. | contradiction | (![X]:((~generous(X)&patient(X))<=>(humble(X)|quiet(X))))&
(![X]:((~calm(X)|funny(X))=>(~wise(X)<~>~brave(X))))&
((humble(lucy))<=>(?[X]:((strong(X)&rich(X)))))&
(![X]:(~funny(X)=>(~old(X)|~wise(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(creative(X)&generous(X))))&
(![X]:((quiet(X)&~quiet(X))=>(kind(X)|~humble(X))))&
(![X]:((tall(X)<~>~old(X))<=>curious(X)))&
(![X]:((patient(X)<~>~quiet(X))<=>(~creative(X)&~kind(X))))&
(![X]:((~old(X)&strong(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~strong(X)|creative(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((~strong(X)&~happy(X))<=>(happy(X)<~>~humble(X))))&
((?[X]:((old(X)&curious(X))))<=>((brave(lucy)&wise(lucy))))&
(![X]:(tall(X)=>(wise(X)&~rich(X))))&
(![X]:((~wise(X)|old(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((~old(X)&~funny(X))<=>(calm(X)<~>creative(X))))&
((~old(paul))=>((generous(john)<~>~old(john))))&
(?[X]:(~creative(X)))&
(?[X]:((~quiet(X)&~humble(X))))&
((brave(alice)|humble(alice)))&
(?[X]:(funny(X)))&
((humble(fred)|~curious(fred)))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((~kind(X)<~>~creative(X)))) | creative(alice) | [
"p0",
"p1",
"p4",
"p8",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3580586092141003405379482
% SZS output start Proof for 3580586092141003405379482
1. ! [X0] : ((patient(X0) & ~generous(X0)) <=> (quiet(X0) | humble(X0))) [input p0]
2. ! [X0] : ((funny(X0) | ~calm(X0)) => (~wise(X0) <~> ~brave(X0))) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (generous(X0) & creative(X0))) [input p4]
9. ! [X0] : ((strong(X0) & ~old(X0)) <=> (~creative(X0) | ~funny(X0))) [input p8]
10. ! [X0] : ((creative(X0) | ~strong(X0)) <=> (~wise(X0) <~> generous(X0))) [input p9]
15. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (calm(X0) <~> creative(X0))) [input p14]
19. humble(alice) | brave(alice) [input p18]
25. creative(alice) [input hypothesis]
26. ! [X0] : ((~wise(X0) <~> ~brave(X0)) | (~funny(X0) & calm(X0))) [ennf transformation 2]
29. ! [X0] : ((generous(X0) & creative(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 5]
34. ! [X0] : (((patient(X0) & ~generous(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~patient(X0) | generous(X0)))) [nnf transformation 1]
35. ! [X0] : (((patient(X0) & ~generous(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ~patient(X0) | generous(X0))) [flattening 34]
36. ! [X0] : (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~funny(X0) & calm(X0))) [nnf transformation 26]
41. ! [X0] : ((generous(X0) & creative(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 29]
45. ! [X0] : (((strong(X0) & ~old(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 9]
46. ! [X0] : (((strong(X0) & ~old(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~strong(X0) | old(X0))) [flattening 45]
47. ! [X0] : (((creative(X0) | ~strong(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & strong(X0)))) [nnf transformation 10]
48. ! [X0] : ((creative(X0) | ~strong(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & strong(X0)))) [flattening 47]
58. ! [X0] : (((~funny(X0) & ~old(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (funny(X0) | old(X0)))) [nnf transformation 15]
59. ! [X0] : (((~funny(X0) & ~old(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | funny(X0) | old(X0))) [flattening 58]
75. ~humble(X0) | ~generous(X0) [cnf transformation 35]
79. ~brave(X0) | ~wise(X0) | calm(X0) [cnf transformation 36]
80. ~brave(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 36]
88. creative(X0) | ~generous(X0) | creative(X0) [cnf transformation 41]
89. generous(X0) | ~creative(X0) | generous(X0) [cnf transformation 41]
103. ~old(X0) | funny(X0) [cnf transformation 46]
106. creative(X0) | strong(X0) [cnf transformation 46]
110. ~generous(X0) | wise(X0) | ~creative(X0) [cnf transformation 48]
111. creative(X0) | ~strong(X0) | generous(X0) | wise(X0) [cnf transformation 48]
132. ~creative(X0) | ~calm(X0) | funny(X0) | old(X0) [cnf transformation 59]
142. humble(alice) | brave(alice) [cnf transformation 19]
149. creative(alice) [cnf transformation 25]
152. ~generous(X0) | creative(X0) [duplicate literal removal 88]
153. ~creative(X0) | generous(X0) [duplicate literal removal 89]
176. creative(X0) | ~strong(X0) | wise(X0) [subsumption resolution 111,152]
177. creative(X0) | wise(X0) [subsumption resolution 176,106]
178. wise(X0) | ~creative(X0) [subsumption resolution 110,153]
179. wise(X0) [subsumption resolution 178,177]
206. ~creative(X0) | ~calm(X0) | funny(X0) [subsumption resolution 132,103]
225. 12 <=> brave(alice) [avatar definition]
227. brave(alice) <- (12) [avatar component clause 225]
229. 13 <=> humble(alice) [avatar definition]
231. humble(alice) <- (13) [avatar component clause 229]
232. 12 | 13 [avatar split clause 142,229,225]
267. generous(alice) [resolution 153,149]
291. ~wise(alice) | calm(alice) <- (12) [resolution 79,227]
292. calm(alice) <- (12) [subsumption resolution 291,179]
293. ~wise(alice) | ~funny(alice) <- (12) [resolution 80,227]
294. ~funny(alice) <- (12) [subsumption resolution 293,179]
416. ~calm(alice) | funny(alice) [resolution 206,149]
420. funny(alice) <- (12) [subsumption resolution 416,292]
421. $false <- (12) [subsumption resolution 420,294]
422. ~12 [avatar contradiction clause 421]
438. ~generous(alice) <- (13) [resolution 231,75]
439. $false <- (13) [subsumption resolution 438,267]
440. ~13 [avatar contradiction clause 439]
441. $false [avatar sat refutation 232,422,440]
% SZS output end Proof for 3580586092141003405379482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 curious. | neutral | (((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))) | curious(paul) | [] | null | 0 |
If mary is either not patient or humble then someone is either not humble or rich and vice versa.
Everyone who is not kind or quiet is either not kind or tall.
Everyone who is not calm is quiet.
Everyone who is kind is not old.
Everyone who is not funny is not rich or not tall.
Everyone who is not rich or not happy is not calm or brave.
Everyone who is creative is funny or kind.
Everyone who is both not funny and tall is quiet or brave and vice versa.
Everyone who is both patient and kind is either not happy or not quiet.
Everyone who is creative or rich is not rich.
Everyone who is generous is both calm and not creative.
If someone is either not funny or not humble then susan is not patient.
Everyone who is either not funny or not old is calm or not kind.
If someone is not creative then john is both strong and not tall and vice versa.
Everyone who is patient or not calm is both not wise and old.
If john is funny or curious then lucy is either generous or tall.
Someone is either humble or curious.
John is calm.
Fred is wise or rich.
Someone is not tall or not quiet.
Susan is both curious and not rich. | John is not humble. | neutral | (((~patient(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|~kind(X))))&
((?[X]:(~creative(X)))<=>((strong(john)&~tall(john))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>curious(X))))&
(calm(john))&
((wise(fred)|rich(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
((curious(susan)&~rich(susan))) | ~humble(john) | [] | null | 0 |
Everyone who is calm or not quiet is kind or not funny and vice versa.
If someone is generous then someone is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Lucy is strong. | neutral | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|~funny(X))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is both not creative and calm is both wise and not calm and vice versa. If mary is both quiet and calm then fred is happy or not rich and vice versa. If john is both strong and humble then someone is calm and vice versa. Everyone who is not kind is not humble or not patient and vice versa. Everyone who is either not strong or not funny is quiet and vice versa. If john is either curious or not patient then someone is patient and vice versa. Everyone who is both not kind and not creative is not patient or humble and vice versa. If someone is both quiet and not patient then someone is not old or not patient. Everyone who is not strong or not old is not strong or brave and vice versa. If someone is not tall then someone is both brave and old and vice versa. If someone is both not curious and strong then someone is both not quiet and not calm. If someone is either patient or not creative then someone is not curious or not tall. Everyone who is not creative or not humble is either not wise or brave and vice versa. Everyone who is either brave or not kind is both not happy and tall and vice versa. Everyone who is both not tall and not creative is either wise or not patient and vice versa. Someone is either not kind or not creative. Paul is not rich. Someone is brave or strong. Someone is both not calm and old. | Fred is brave. | contradiction | (![X]:((~creative(X)&calm(X))<=>(wise(X)&~calm(X))))&
(((quiet(mary)&calm(mary)))<=>((happy(fred)|~rich(fred))))&
(((strong(john)&humble(john)))<=>(?[X]:(calm(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~patient(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>quiet(X)))&
(((curious(john)<~>~patient(john)))<=>(?[X]:(patient(X))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)|humble(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~strong(X)|~old(X))<=>(~strong(X)|brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((~quiet(X)&~calm(X)))))&
((?[X]:((patient(X)<~>~creative(X))))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((~creative(X)|~humble(X))<=>(~wise(X)<~>brave(X))))&
(![X]:((brave(X)<~>~kind(X))<=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~creative(X))<=>(wise(X)<~>~patient(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(~rich(paul))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((~calm(X)&old(X)))) | brave(fred) | [
"p0",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7231257277429461808613310
% SZS output start Proof for 7231257277429461808613310
1. ! [X0] : ((calm(X0) & ~creative(X0)) <=> (~calm(X0) & wise(X0))) [input p0]
7. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (humble(X0) | ~patient(X0))) [input p6]
13. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> (~wise(X0) <~> brave(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & ~tall(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p14]
20. brave(fred) [input hypothesis]
28. ! [X0] : (((calm(X0) & ~creative(X0)) | (calm(X0) | ~wise(X0))) & ((~calm(X0) & wise(X0)) | (~calm(X0) | creative(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & ~creative(X0)) | calm(X0) | ~wise(X0)) & ((~calm(X0) & wise(X0)) | ~calm(X0) | creative(X0))) [flattening 28]
44. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | creative(X0) | kind(X0))) [flattening 44]
63. ! [X0] : (((~humble(X0) | ~creative(X0)) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | (humble(X0) & creative(X0)))) [nnf transformation 13]
64. ! [X0] : ((~humble(X0) | ~creative(X0) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | (humble(X0) & creative(X0)))) [flattening 63]
67. ! [X0] : (((~creative(X0) & ~tall(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (creative(X0) | tall(X0)))) [nnf transformation 15]
68. ! [X0] : (((~creative(X0) & ~tall(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | creative(X0) | tall(X0))) [flattening 67]
77. ~calm(X0) | ~calm(X0) | creative(X0) [cnf transformation 29]
79. calm(X0) | calm(X0) | ~wise(X0) [cnf transformation 29]
102. ~creative(X0) | patient(X0) [cnf transformation 45]
103. ~humble(X0) | ~creative(X0) [cnf transformation 45]
118. ~brave(X0) | wise(X0) | creative(X0) [cnf transformation 64]
119. ~brave(X0) | wise(X0) | humble(X0) [cnf transformation 64]
132. ~creative(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 68]
140. brave(fred) [cnf transformation 20]
141. ~calm(X0) | creative(X0) [duplicate literal removal 77]
142. ~wise(X0) | calm(X0) [duplicate literal removal 79]
270. ~wise(X0) | ~creative(X0) [subsumption resolution 132,102]
356. wise(fred) | creative(fred) [resolution 118,140]
361. 36 <=> creative(fred) [avatar definition]
362. ~creative(fred) <- (~36) [avatar component clause 361]
363. creative(fred) <- (36) [avatar component clause 361]
365. 37 <=> wise(fred) [avatar definition]
367. wise(fred) <- (37) [avatar component clause 365]
368. 36 | 37 [avatar split clause 356,365,361]
390. ~creative(fred) <- (37) [resolution 367,270]
391. calm(fred) <- (37) [resolution 367,142]
392. ~36 | ~37 [avatar split clause 390,365,361]
393. wise(fred) | humble(fred) [resolution 119,140]
501. creative(fred) <- (37) [resolution 391,141]
502. $false <- (~36, 37) [subsumption resolution 501,362]
503. 36 | ~37 [avatar contradiction clause 502]
505. 50 <=> humble(fred) [avatar definition]
507. humble(fred) <- (50) [avatar component clause 505]
508. 50 | 37 [avatar split clause 393,365,505]
510. ~creative(fred) <- (50) [resolution 507,103]
511. $false <- (36, 50) [subsumption resolution 510,363]
512. ~36 | ~50 [avatar contradiction clause 511]
513. $false [avatar sat refutation 368,392,503,508,512]
% SZS output end Proof for 7231257277429461808613310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not patient then someone is both not curious and rich and vice versa. If fred is both rich and not strong then someone is wise. If someone is quiet or not rich then someone is both not kind and generous and vice versa. If lucy is rich then john is both not creative and not funny. If paul is both patient and not brave then someone is not kind and vice versa. Everyone who is both patient and humble is both not generous and happy and vice versa. Everyone who is both patient and rich is strong or not calm. Everyone who is either not funny or brave is either calm or rich and vice versa. If paul is both brave and kind then someone is both not funny and not patient and vice versa. Everyone who is generous or not rich is both calm and brave. Everyone who is both not patient and not old is not old. If mary is both kind and not tall then someone is not quiet or kind and vice versa. Everyone who is both rich and patient is tall or curious. If paul is not funny or creative then someone is not old and vice versa. If someone is either calm or not calm then lucy is not happy or wise. If susan is either not brave or rich then alice is both brave and generous and vice versa. Susan is patient or not old. John is not brave. Someone is not old. Fred is both not rich and not wise. Fred is calm or generous. Mary is not tall or not calm. Lucy is quiet. Someone is quiet or patient. | Lucy is generous. | neutral | ((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((~curious(X)&rich(X)))))&
(((rich(fred)&~strong(fred)))=>(?[X]:(wise(X))))&
((?[X]:((quiet(X)|~rich(X))))<=>(?[X]:((~kind(X)&generous(X)))))&
((rich(lucy))=>((~creative(john)&~funny(john))))&
(((patient(paul)&~brave(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((patient(X)&humble(X))<=>(~generous(X)&happy(X))))&
(![X]:((patient(X)&rich(X))=>(strong(X)|~calm(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(calm(X)<~>rich(X))))&
(((brave(paul)&kind(paul)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((generous(X)|~rich(X))=>(calm(X)&brave(X))))&
(![X]:((~patient(X)&~old(X))=>~old(X)))&
(((kind(mary)&~tall(mary)))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((rich(X)&patient(X))=>(tall(X)|curious(X))))&
(((~funny(paul)|creative(paul)))<=>(?[X]:(~old(X))))&
((?[X]:((calm(X)<~>~calm(X))))=>((~happy(lucy)|wise(lucy))))&
(((~brave(susan)<~>rich(susan)))<=>((brave(alice)&generous(alice))))&
((patient(susan)|~old(susan)))&
(~brave(john))&
(?[X]:(~old(X)))&
((~rich(fred)&~wise(fred)))&
((calm(fred)|generous(fred)))&
((~tall(mary)|~calm(mary)))&
(quiet(lucy))&
(?[X]:((quiet(X)|patient(X)))) | generous(lucy) | [] | null | 0 |
If someone is either funny or not quiet then paul is rich and vice versa. Everyone who is either not calm or not quiet is both not strong and not rich and vice versa. If mary is creative or not strong then susan is both not kind and kind and vice versa. If mary is both not rich and not old then alice is both not tall and tall. Everyone who is both not old and not generous is both old and not creative and vice versa. Everyone who is brave is wise and vice versa. Everyone who is both not calm and not funny is curious or calm. If paul is not happy then susan is either not strong or generous. Everyone who is either not patient or not creative is both not happy and not generous and vice versa. Everyone who is both generous and not strong is both rich and not brave and vice versa. If alice is both not rich and not brave then someone is either not wise or not patient and vice versa. Everyone who is wise or kind is old or kind and vice versa. Everyone who is old or not strong is brave or not humble. Everyone who is either not happy or not wise is not curious and vice versa. If someone is generous then fred is both old and calm and vice versa. Everyone who is not wise is not happy. John is not happy or wise. Someone is either not wise or not rich. Paul is brave. Lucy is not brave. Someone is either wise or curious. Lucy is both tall and humble. Someone is not rich or wise. | Mary is rich. | entailment | ((?[X]:((funny(X)<~>~quiet(X))))<=>(rich(paul)))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~strong(X)&~rich(X))))&
(((creative(mary)|~strong(mary)))<=>((~kind(susan)&kind(susan))))&
(((~rich(mary)&~old(mary)))=>((~tall(alice)&tall(alice))))&
(![X]:((~old(X)&~generous(X))<=>(old(X)&~creative(X))))&
(![X]:(brave(X)<=>wise(X)))&
(![X]:((~calm(X)&~funny(X))=>(curious(X)|calm(X))))&
((~happy(paul))=>((~strong(susan)<~>generous(susan))))&
(![X]:((~patient(X)<~>~creative(X))<=>(~happy(X)&~generous(X))))&
(![X]:((generous(X)&~strong(X))<=>(rich(X)&~brave(X))))&
(((~rich(alice)&~brave(alice)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:((wise(X)|kind(X))<=>(old(X)|kind(X))))&
(![X]:((old(X)|~strong(X))=>(brave(X)|~humble(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>~curious(X)))&
((?[X]:(generous(X)))<=>((old(fred)&calm(fred))))&
(![X]:(~wise(X)=>~happy(X)))&
((~happy(john)|wise(john)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(brave(paul))&
(~brave(lucy))&
(?[X]:((wise(X)<~>curious(X))))&
((tall(lucy)&humble(lucy)))&
(?[X]:((~rich(X)|wise(X)))) | rich(mary) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1240895505685251123437475
% SZS output start Proof for 1240895505685251123437475
3. (~strong(mary) | creative(mary)) <=> (kind(susan) & ~kind(susan)) [input p2]
4. (~old(mary) & ~rich(mary)) => (tall(alice) & ~tall(alice)) [input p3]
5. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (~creative(X0) & old(X0))) [input p4]
24. ~rich(mary) [input hypothesis]
25. (tall(alice) & ~tall(alice)) | (old(mary) | rich(mary)) [ennf transformation 4]
26. (tall(alice) & ~tall(alice)) | old(mary) | rich(mary) [flattening 25]
39. ((~strong(mary) | creative(mary)) | (~kind(susan) | kind(susan))) & ((kind(susan) & ~kind(susan)) | (strong(mary) & ~creative(mary))) [nnf transformation 3]
40. (~strong(mary) | creative(mary) | ~kind(susan) | kind(susan)) & ((kind(susan) & ~kind(susan)) | (strong(mary) & ~creative(mary))) [flattening 39]
41. ! [X0] : (((~generous(X0) & ~old(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (generous(X0) | old(X0)))) [nnf transformation 5]
42. ! [X0] : (((~generous(X0) & ~old(X0)) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | generous(X0) | old(X0))) [flattening 41]
80. ~kind(susan) | ~creative(mary) [cnf transformation 40]
82. kind(susan) | ~creative(mary) [cnf transformation 40]
85. ~tall(alice) | old(mary) | rich(mary) [cnf transformation 26]
86. tall(alice) | old(mary) | rich(mary) [cnf transformation 26]
89. ~old(X0) | creative(X0) | ~old(X0) [cnf transformation 42]
136. ~rich(mary) [cnf transformation 24]
139. ~old(X0) | creative(X0) [duplicate literal removal 89]
167. 7 <=> kind(susan) [avatar definition]
172. 8 <=> creative(mary) [avatar definition]
174. ~creative(mary) <- (~8) [avatar component clause 172]
175. ~8 | 7 [avatar split clause 82,167,172]
177. ~8 | ~7 [avatar split clause 80,167,172]
179. 9 <=> rich(mary) [avatar definition]
183. 10 <=> old(mary) [avatar definition]
185. old(mary) <- (10) [avatar component clause 183]
187. 11 <=> tall(alice) [avatar definition]
190. 9 | 10 | 11 [avatar split clause 86,187,183,179]
191. 9 | 10 | ~11 [avatar split clause 85,187,183,179]
281. ~9 [avatar split clause 136,179]
291. creative(mary) <- (10) [resolution 139,185]
293. $false <- (~8, 10) [subsumption resolution 291,174]
294. 8 | ~10 [avatar contradiction clause 293]
295. $false [avatar sat refutation 175,177,190,191,281,294]
% SZS output end Proof for 1240895505685251123437475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then someone is not creative or wise. Everyone who is not kind is brave. Everyone who is brave is either kind or not curious and vice versa. If paul is not creative then someone is both not patient and calm and vice versa. Everyone who is both quiet and funny is curious or calm and vice versa. Everyone who is not funny or calm is not quiet and vice versa. Everyone who is old is humble. Everyone who is funny is both not happy and tall and vice versa. Everyone who is brave is not funny. If lucy is brave then lucy is tall or patient and vice versa. If mary is not wise then someone is both patient and not kind. Everyone who is either curious or brave is either funny or tall. Everyone who is not tall or not humble is calm or brave. If mary is quiet or not rich then lucy is not rich and vice versa. Everyone who is both not creative and not curious is both kind and not funny. Alice is not generous. Mary is strong. Someone is kind or old. Someone is both not humble and generous. Someone is not patient. | Alice is happy. | entailment | ((curious(mary))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:(~kind(X)=>brave(X)))&
(![X]:(brave(X)<=>(kind(X)<~>~curious(X))))&
((~creative(paul))<=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((quiet(X)&funny(X))<=>(curious(X)|calm(X))))&
(![X]:((~funny(X)|calm(X))<=>~quiet(X)))&
(![X]:(old(X)=>humble(X)))&
(![X]:(funny(X)<=>(~happy(X)&tall(X))))&
(![X]:(brave(X)=>~funny(X)))&
((brave(lucy))<=>((tall(lucy)|patient(lucy))))&
((~wise(mary))=>(?[X]:((patient(X)&~kind(X)))))&
(![X]:((curious(X)<~>brave(X))=>(funny(X)<~>tall(X))))&
(![X]:((~tall(X)|~humble(X))=>(calm(X)|brave(X))))&
(((quiet(mary)|~rich(mary)))<=>(~rich(lucy)))&
(![X]:((~creative(X)&~curious(X))=>(kind(X)&~funny(X))))&
(~generous(alice))&
(strong(mary))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:(~patient(X))) | happy(alice) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7032250630902769568924658
% SZS output start Proof for 7032250630902769568924658
2. ! [X0] : (~kind(X0) => brave(X0)) [input p1]
3. ! [X0] : (brave(X0) <=> (kind(X0) <~> ~curious(X0))) [input p2]
5. ! [X0] : ((funny(X0) & quiet(X0)) <=> (calm(X0) | curious(X0))) [input p4]
6. ! [X0] : ((calm(X0) | ~funny(X0)) <=> ~quiet(X0)) [input p5]
8. ! [X0] : (funny(X0) <=> (tall(X0) & ~happy(X0))) [input p7]
9. ! [X0] : (brave(X0) => ~funny(X0)) [input p8]
12. ! [X0] : ((curious(X0) <~> brave(X0)) => (funny(X0) <~> tall(X0))) [input p11]
13. ! [X0] : ((~humble(X0) | ~tall(X0)) => (brave(X0) | calm(X0))) [input p12]
21. ~happy(alice) [input hypothesis]
25. ! [X0] : (brave(X0) | kind(X0)) [ennf transformation 2]
27. ! [X0] : (~funny(X0) | ~brave(X0)) [ennf transformation 9]
28. ! [X0] : ((funny(X0) <~> tall(X0)) | (curious(X0) <=> brave(X0))) [ennf transformation 12]
29. ! [X0] : ((brave(X0) | calm(X0)) | (humble(X0) & tall(X0))) [ennf transformation 13]
30. ! [X0] : (brave(X0) | calm(X0) | (humble(X0) & tall(X0))) [flattening 29]
33. ! [X0] : ((brave(X0) | ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0)))) & (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ~brave(X0))) [nnf transformation 3]
38. ! [X0] : (((funny(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 5]
39. ! [X0] : (((funny(X0) & quiet(X0)) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | ~funny(X0) | ~quiet(X0))) [flattening 38]
40. ! [X0] : (((calm(X0) | ~funny(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & funny(X0)))) [nnf transformation 6]
41. ! [X0] : ((calm(X0) | ~funny(X0) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & funny(X0)))) [flattening 40]
42. ! [X0] : ((funny(X0) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | ~funny(X0))) [nnf transformation 8]
43. ! [X0] : ((funny(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | ~funny(X0))) [flattening 42]
46. ! [X0] : (((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) [nnf transformation 28]
55. brave(X0) | kind(X0) [cnf transformation 25]
56. ~curious(X0) | kind(X0) | ~brave(X0) [cnf transformation 33]
57. ~brave(X0) | ~kind(X0) | curious(X0) [cnf transformation 33]
58. brave(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 33]
63. ~funny(X0) | curious(X0) | calm(X0) | ~quiet(X0) [cnf transformation 39]
64. ~curious(X0) | quiet(X0) [cnf transformation 39]
65. ~calm(X0) | quiet(X0) [cnf transformation 39]
66. ~curious(X0) | funny(X0) [cnf transformation 39]
69. ~quiet(X0) | ~calm(X0) [cnf transformation 41]
70. calm(X0) | ~funny(X0) | quiet(X0) [cnf transformation 41]
74. ~tall(X0) | funny(X0) | happy(X0) [cnf transformation 43]
75. ~funny(X0) | ~brave(X0) [cnf transformation 27]
80. tall(X0) | funny(X0) | curious(X0) | ~brave(X0) [cnf transformation 46]
83. brave(X0) | calm(X0) | tall(X0) [cnf transformation 30]
95. ~happy(alice) [cnf transformation 21]
96. ~curious(X0) | brave(X0) [subsumption resolution 58,55]
97. ~curious(X0) | kind(X0) [subsumption resolution 56,96]
116. ~funny(X0) | quiet(X0) [subsumption resolution 70,65]
117. ~calm(X0) [subsumption resolution 69,65]
133. ~brave(X0) | curious(X0) | tall(X0) [subsumption resolution 80,75]
135. tall(X0) | brave(X0) [subsumption resolution 83,117]
190. happy(X0) | funny(X0) | brave(X0) [resolution 74,135]
193. curious(X0) | tall(X0) | kind(X0) [resolution 133,55]
196. tall(X0) | kind(X0) [subsumption resolution 193,97]
212. happy(X0) | funny(X0) | kind(X0) [resolution 196,74]
220. funny(alice) | brave(alice) [resolution 190,95]
223. 18 <=> brave(alice) [avatar definition]
224. ~brave(alice) <- (~18) [avatar component clause 223]
225. brave(alice) <- (18) [avatar component clause 223]
227. 19 <=> funny(alice) [avatar definition]
228. ~funny(alice) <- (~19) [avatar component clause 227]
229. funny(alice) <- (19) [avatar component clause 227]
230. 18 | 19 [avatar split clause 220,227,223]
271. 23 <=> curious(alice) [avatar definition]
273. curious(alice) <- (23) [avatar component clause 271]
276. 24 <=> kind(alice) [avatar definition]
282. curious(alice) | calm(alice) | ~quiet(alice) <- (19) [resolution 229,63]
284. quiet(alice) <- (19) [resolution 229,116]
287. curious(alice) | ~quiet(alice) <- (19) [subsumption resolution 282,117]
289. 25 <=> quiet(alice) [avatar definition]
292. ~25 | 23 | ~19 [avatar split clause 287,227,271,289]
298. 25 | ~19 [avatar split clause 284,227,289]
301. ~kind(alice) | curious(alice) <- (18) [resolution 225,57]
323. funny(alice) <- (23) [resolution 273,66]
324. quiet(alice) <- (23) [resolution 273,64]
325. $false <- (~19, 23) [subsumption resolution 323,228]
326. 19 | ~23 [avatar contradiction clause 325]
327. 25 | ~23 [avatar split clause 324,271,289]
328. 23 | ~24 | ~18 [avatar split clause 301,223,276,271]
330. funny(alice) | kind(alice) [resolution 212,95]
335. 24 | 19 [avatar split clause 330,227,276]
339. ~brave(alice) <- (19) [resolution 229,75]
343. ~18 | ~19 [avatar split clause 339,227,223]
347. brave(alice) <- (23) [resolution 273,96]
350. $false <- (~18, 23) [subsumption resolution 347,224]
351. 18 | ~23 [avatar contradiction clause 350]
352. $false [avatar sat refutation 230,292,298,326,327,328,335,343,351]
% SZS output end Proof for 7032250630902769568924658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and not quiet then someone is either tall or creative.
Everyone who is not happy or not creative is rich and vice versa.
Everyone who is not rich is calm or not generous.
If someone is not calm then someone is both not brave and happy.
Everyone who is not humble or not strong is both not kind and patient.
Everyone who is brave or kind is not kind or strong and vice versa.
Everyone who is both generous and not humble is kind.
If someone is curious then mary is not calm and vice versa.
If someone is both happy and curious then someone is curious.
If paul is not patient or not curious then alice is not kind.
If paul is either patient or brave then fred is not kind or funny.
If someone is not calm then someone is not patient.
Everyone who is patient or not happy is either humble or not humble.
If someone is not kind or tall then someone is wise or not funny and vice versa.
Everyone who is strong is not brave and vice versa.
Everyone who is both strong and calm is both not quiet and not patient.
Susan is both not calm and not rich.
Someone is either kind or funny.
Someone is not happy or kind.
Fred is brave or humble.
Mary is not generous.
Someone is humble or not quiet.
Paul is both curious and not creative.
Susan is humble or calm. | Alice is calm. | neutral | ((?[X]:((patient(X)&~quiet(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~happy(X)|~creative(X))<=>rich(X)))&
(![X]:(~rich(X)=>(calm(X)|~generous(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~brave(X)&happy(X)))))&
(![X]:((~humble(X)|~strong(X))=>(~kind(X)&patient(X))))&
(![X]:((brave(X)|kind(X))<=>(~kind(X)|strong(X))))&
(![X]:((generous(X)&~humble(X))=>kind(X)))&
((?[X]:(curious(X)))<=>(~calm(mary)))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:(curious(X))))&
(((~patient(paul)|~curious(paul)))=>(~kind(alice)))&
(((patient(paul)<~>brave(paul)))=>((~kind(fred)|funny(fred))))&
((?[X]:(~calm(X)))=>(?[X]:(~patient(X))))&
(![X]:((patient(X)|~happy(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~kind(X)|tall(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(strong(X)<=>~brave(X)))&
(![X]:((strong(X)&calm(X))=>(~quiet(X)&~patient(X))))&
((~calm(susan)&~rich(susan)))&
(?[X]:((kind(X)<~>funny(X))))&
(?[X]:((~happy(X)|kind(X))))&
((brave(fred)|humble(fred)))&
(~generous(mary))&
(?[X]:((humble(X)|~quiet(X))))&
((curious(paul)&~creative(paul)))&
((humble(susan)|calm(susan))) | calm(alice) | [] | null | 0 |
If someone is humble then fred is humble and vice versa.
Everyone who is both not patient and not humble is both quiet and creative.
If someone is both strong and not wise then someone is either not kind or not curious.
If alice is both tall and brave then someone is both kind and not kind.
If someone is not rich or not funny then someone is both humble and not rich.
If someone is not happy then mary is both creative and tall and vice versa.
Everyone who is either strong or not tall is both humble and brave.
Everyone who is both old and tall is both not humble and funny.
If lucy is kind or not patient then someone is both wise and happy and vice versa.
Everyone who is either not humble or not happy is happy.
Everyone who is either not humble or calm is calm or not funny and vice versa.
Everyone who is rich is patient.
Everyone who is both brave and tall is either quiet or not happy.
Everyone who is rich or not humble is either generous or humble.
If fred is either not curious or happy then someone is either not happy or happy.
Everyone who is either brave or not creative is not humble or happy.
Fred is either not happy or not calm.
Someone is not funny.
Someone is both brave and tall.
Lucy is strong.
Someone is happy.
Someone is curious or not strong. | Fred is calm. | contradiction | ((?[X]:(humble(X)))<=>(humble(fred)))&
(![X]:((~patient(X)&~humble(X))=>(quiet(X)&creative(X))))&
((?[X]:((strong(X)&~wise(X))))=>(?[X]:((~kind(X)<~>~curious(X)))))&
(((tall(alice)&brave(alice)))=>(?[X]:((kind(X)&~kind(X)))))&
((?[X]:((~rich(X)|~funny(X))))=>(?[X]:((humble(X)&~rich(X)))))&
((?[X]:(~happy(X)))<=>((creative(mary)&tall(mary))))&
(![X]:((strong(X)<~>~tall(X))=>(humble(X)&brave(X))))&
(![X]:((old(X)&tall(X))=>(~humble(X)&funny(X))))&
(((kind(lucy)|~patient(lucy)))<=>(?[X]:((wise(X)&happy(X)))))&
(![X]:((~humble(X)<~>~happy(X))=>happy(X)))&
(![X]:((~humble(X)<~>calm(X))<=>(calm(X)|~funny(X))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((brave(X)&tall(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((rich(X)|~humble(X))=>(generous(X)<~>humble(X))))&
(((~curious(fred)<~>happy(fred)))=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((brave(X)<~>~creative(X))=>(~humble(X)|happy(X))))&
((~happy(fred)<~>~calm(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((brave(X)&tall(X))))&
(strong(lucy))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)|~strong(X)))) | calm(fred) | [
"p0",
"p4",
"p9",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7589979146323414393497049
% SZS output start Proof for 7589979146323414393497049
1. ? [X0] : humble(X0) <=> humble(fred) [input p0]
5. ? [X0] : (~funny(X0) | ~rich(X0)) => ? [X0] : (~rich(X0) & humble(X0)) [input p4]
10. ! [X0] : ((~humble(X0) <~> ~happy(X0)) => happy(X0)) [input p9]
17. ~happy(fred) <~> ~calm(fred) [input p16]
18. ? [X0] : ~funny(X0) [input p17]
23. calm(fred) [input hypothesis]
25. ? [X0] : (~funny(X0) | ~rich(X0)) => ? [X1] : (~rich(X1) & humble(X1)) [rectify 5]
32. ? [X1] : (~rich(X1) & humble(X1)) | ! [X0] : (funny(X0) & rich(X0)) [ennf transformation 25]
34. ! [X0] : (happy(X0) | (~humble(X0) <=> ~happy(X0))) [ennf transformation 10]
42. (? [X0] : humble(X0) | ~humble(fred)) & (humble(fred) | ! [X0] : ~humble(X0)) [nnf transformation 1]
43. (? [X0] : humble(X0) | ~humble(fred)) & (humble(fred) | ! [X1] : ~humble(X1)) [rectify 42]
44. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
45. (humble(sK0) | ~humble(fred)) & (humble(fred) | ! [X1] : ~humble(X1)) [skolemisation 43,44]
52. ? [X0] : (~rich(X0) & humble(X0)) | ! [X1] : (funny(X1) & rich(X1)) [rectify 32]
53. ? [X0] : (~rich(X0) & humble(X0)) => (~rich(sK3) & humble(sK3)) [choice axiom]
54. (~rich(sK3) & humble(sK3)) | ! [X1] : (funny(X1) & rich(X1)) [skolemisation 52,53]
66. ! [X0] : (happy(X0) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) [nnf transformation 34]
75. (calm(fred) | happy(fred)) & (~calm(fred) | ~happy(fred)) [nnf transformation 17]
76. ? [X0] : ~funny(X0) => ~funny(sK7) [choice axiom]
77. ~funny(sK7) [skolemisation 18,76]
84. humble(fred) | ~humble(X1) [cnf transformation 45]
93. humble(sK3) | funny(X1) [cnf transformation 54]
109. happy(X0) | ~humble(X0) | happy(X0) [cnf transformation 66]
129. ~calm(fred) | ~happy(fred) [cnf transformation 75]
131. ~funny(sK7) [cnf transformation 77]
137. calm(fred) [cnf transformation 23]
141. ~humble(X0) | happy(X0) [duplicate literal removal 109]
143. 1 <=> humble(fred) [avatar definition]
144. humble(fred) <- (1) [avatar component clause 143]
152. 3 <=> ! [X1] : ~humble(X1) [avatar definition]
153. ~humble(X1) <- (3) [avatar component clause 152]
154. 3 | 1 [avatar split clause 84,143,152]
183. 10 <=> ! [X1] : funny(X1) [avatar definition]
184. funny(X1) <- (10) [avatar component clause 183]
195. 13 <=> humble(sK3) [avatar definition]
197. humble(sK3) <- (13) [avatar component clause 195]
198. 10 | 13 [avatar split clause 93,195,183]
244. 23 <=> happy(fred) [avatar definition]
245. ~happy(fred) <- (~23) [avatar component clause 244]
248. 24 <=> calm(fred) [avatar definition]
252. ~23 | ~24 [avatar split clause 129,248,244]
262. 24 [avatar split clause 137,248]
263. $false <- (10) [resolution 184,131]
264. ~10 [avatar contradiction clause 263]
265. $false <- (3, 13) [subsumption resolution 197,153]
266. ~3 | ~13 [avatar contradiction clause 265]
270. happy(fred) <- (1) [resolution 141,144]
273. $false <- (1, ~23) [subsumption resolution 270,245]
274. ~1 | 23 [avatar contradiction clause 273]
275. $false [avatar sat refutation 154,198,252,262,264,266,274]
% SZS output end Proof for 7589979146323414393497049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is either old or happy.
If susan is not strong or not funny then mary is not quiet or happy.
Everyone who is both tall and not funny is either not happy or not strong.
If mary is both patient and not kind then someone is not happy or not generous and vice versa.
If mary is either calm or not tall then alice is either not curious or not quiet.
If john is either not calm or funny then paul is both not wise and not happy.
Everyone who is both happy and not quiet is not tall or kind.
If someone is either curious or not patient then susan is curious or not brave.
Everyone who is either quiet or not humble is either not wise or funny.
Everyone who is either quiet or not quiet is not wise or wise and vice versa.
If susan is not generous or quiet then paul is funny or not patient and vice versa.
Everyone who is both tall and not old is either not kind or not brave.
If fred is not curious then someone is both not strong and funny and vice versa.
Everyone who is both funny and happy is both humble and generous and vice versa.
Everyone who is both not patient and old is not strong or not generous.
Everyone who is not rich is either quiet or not rich.
Someone is calm or not calm.
Someone is both not curious and not generous.
Someone is not strong or rich.
Someone is both brave and patient.
John is funny or not funny.
Someone is not quiet.
Paul is not funny.
Someone is brave. | John is funny. | neutral | (![X]:((~tall(X)<~>~creative(X))=>(old(X)<~>happy(X))))&
(((~strong(susan)|~funny(susan)))=>((~quiet(mary)|happy(mary))))&
(![X]:((tall(X)&~funny(X))=>(~happy(X)<~>~strong(X))))&
(((patient(mary)&~kind(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(((calm(mary)<~>~tall(mary)))=>((~curious(alice)<~>~quiet(alice))))&
(((~calm(john)<~>funny(john)))=>((~wise(paul)&~happy(paul))))&
(![X]:((happy(X)&~quiet(X))=>(~tall(X)|kind(X))))&
((?[X]:((curious(X)<~>~patient(X))))=>((curious(susan)|~brave(susan))))&
(![X]:((quiet(X)<~>~humble(X))=>(~wise(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~wise(X)|wise(X))))&
(((~generous(susan)|quiet(susan)))<=>((funny(paul)|~patient(paul))))&
(![X]:((tall(X)&~old(X))=>(~kind(X)<~>~brave(X))))&
((~curious(fred))<=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:((funny(X)&happy(X))<=>(humble(X)&generous(X))))&
(![X]:((~patient(X)&old(X))=>(~strong(X)|~generous(X))))&
(![X]:(~rich(X)=>(quiet(X)<~>~rich(X))))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~curious(X)&~generous(X))))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:((brave(X)&patient(X))))&
((funny(john)|~funny(john)))&
(?[X]:(~quiet(X)))&
(~funny(paul))&
(?[X]:(brave(X))) | funny(john) | [] | null | 0 |
If lucy is kind then someone is either not old or old. Everyone who is either funny or not calm is curious or not kind and vice versa. If fred is either not generous or wise then lucy is both brave and not rich and vice versa. Everyone who is either not calm or not old is strong or not wise and vice versa. Everyone who is not generous or not creative is patient or kind and vice versa. If someone is both strong and creative then someone is both curious and patient and vice versa. If someone is either calm or not funny then susan is patient and vice versa. Everyone who is both creative and humble is both old and creative and vice versa. If lucy is both not kind and not generous then someone is either not brave or creative. Everyone who is both not calm and not patient is not brave and vice versa. Everyone who is both humble and not humble is not happy. Everyone who is not brave or brave is both calm and generous and vice versa. Everyone who is both not old and brave is not humble and vice versa. If someone is both not old and generous then someone is not happy and vice versa. If mary is both humble and not happy then mary is funny and vice versa. If someone is not generous or not tall then paul is either not quiet or not brave. Someone is both brave and not rich. Alice is both not tall and brave. Someone is both not tall and not wise. Someone is either quiet or not happy. John is both old and happy. Someone is either not funny or not generous. Someone is rich or not generous. | Lucy is humble. | neutral | ((kind(lucy))=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((funny(X)<~>~calm(X))<=>(curious(X)|~kind(X))))&
(((~generous(fred)<~>wise(fred)))<=>((brave(lucy)&~rich(lucy))))&
(![X]:((~calm(X)<~>~old(X))<=>(strong(X)|~wise(X))))&
(![X]:((~generous(X)|~creative(X))<=>(patient(X)|kind(X))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((calm(X)<~>~funny(X))))<=>(patient(susan)))&
(![X]:((creative(X)&humble(X))<=>(old(X)&creative(X))))&
(((~kind(lucy)&~generous(lucy)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:((~calm(X)&~patient(X))<=>~brave(X)))&
(![X]:((humble(X)&~humble(X))=>~happy(X)))&
(![X]:((~brave(X)|brave(X))<=>(calm(X)&generous(X))))&
(![X]:((~old(X)&brave(X))<=>~humble(X)))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:(~happy(X))))&
(((humble(mary)&~happy(mary)))<=>(funny(mary)))&
((?[X]:((~generous(X)|~tall(X))))=>((~quiet(paul)<~>~brave(paul))))&
(?[X]:((brave(X)&~rich(X))))&
((~tall(alice)&brave(alice)))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
((old(john)&happy(john)))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((rich(X)|~generous(X)))) | humble(lucy) | [] | null | 0 |
Everyone who is not wise or funny is tall. Everyone who is not patient is humble or curious and vice versa. Everyone who is both strong and rich is both not funny and patient. If someone is either kind or brave then someone is not quiet or not kind. Everyone who is happy or kind is both generous and not generous and vice versa. Everyone who is generous or strong is not calm or not humble and vice versa. If john is both not creative and tall then someone is both generous and curious and vice versa. Everyone who is either not rich or not generous is either not wise or rich and vice versa. If someone is either not calm or not wise then lucy is both not kind and not strong and vice versa. Everyone who is both rich and not humble is both tall and rich and vice versa. If john is generous or humble then alice is both not generous and not brave and vice versa. Everyone who is either brave or rich is not generous or quiet. If someone is brave or not calm then someone is not patient or not old and vice versa. Everyone who is humble or not humble is either not happy or not funny and vice versa. Everyone who is not wise is not old or not creative and vice versa. Everyone who is either not strong or wise is either curious or not wise and vice versa. Susan is either not generous or rich. Someone is not humble. Lucy is strong. Mary is calm or not kind. Susan is not patient or not calm. John is either tall or not creative. Lucy is either old or not quiet. | Lucy is humble. | contradiction | (![X]:((~wise(X)|funny(X))=>tall(X)))&
(![X]:(~patient(X)<=>(humble(X)|curious(X))))&
(![X]:((strong(X)&rich(X))=>(~funny(X)&patient(X))))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((happy(X)|kind(X))<=>(generous(X)&~generous(X))))&
(![X]:((generous(X)|strong(X))<=>(~calm(X)|~humble(X))))&
(((~creative(john)&tall(john)))<=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((~kind(lucy)&~strong(lucy))))&
(![X]:((rich(X)&~humble(X))<=>(tall(X)&rich(X))))&
(((generous(john)|humble(john)))<=>((~generous(alice)&~brave(alice))))&
(![X]:((brave(X)<~>rich(X))=>(~generous(X)|quiet(X))))&
((?[X]:((brave(X)|~calm(X))))<=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((humble(X)|~humble(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:(~wise(X)<=>(~old(X)|~creative(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(curious(X)<~>~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:(~humble(X)))&
(strong(lucy))&
((calm(mary)|~kind(mary)))&
((~patient(susan)|~calm(susan)))&
((tall(john)<~>~creative(john)))&
((old(lucy)<~>~quiet(lucy))) | humble(lucy) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p13",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6750976116611948935337981
% SZS output start Proof for 6750976116611948935337981
1. ! [X0] : ((funny(X0) | ~wise(X0)) => tall(X0)) [input p0]
5. ! [X0] : ((kind(X0) | happy(X0)) <=> (~generous(X0) & generous(X0))) [input p4]
6. ! [X0] : ((strong(X0) | generous(X0)) <=> (~humble(X0) | ~calm(X0))) [input p5]
7. (tall(john) & ~creative(john)) <=> ? [X0] : (curious(X0) & generous(X0)) [input p6]
8. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> (~wise(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~calm(X0) <~> ~wise(X0)) <=> (~strong(lucy) & ~kind(lucy)) [input p8]
14. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p15]
19. strong(lucy) [input p18]
22. tall(john) <~> ~creative(john) [input p21]
24. humble(lucy) [input hypothesis]
27. ! [X0] : (tall(X0) | (~funny(X0) & wise(X0))) [ennf transformation 1]
39. ! [X0] : (((kind(X0) | happy(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [nnf transformation 5]
40. ! [X0] : ((kind(X0) | happy(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [flattening 39]
41. ! [X0] : (((strong(X0) | generous(X0)) | (humble(X0) & calm(X0))) & ((~humble(X0) | ~calm(X0)) | (~strong(X0) & ~generous(X0)))) [nnf transformation 6]
42. ! [X0] : ((strong(X0) | generous(X0) | (humble(X0) & calm(X0))) & (~humble(X0) | ~calm(X0) | (~strong(X0) & ~generous(X0)))) [flattening 41]
43. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | (~tall(john) | creative(john))) [nnf transformation 7]
44. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | ~tall(john) | creative(john)) [flattening 43]
45. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X1] : (curious(X1) & generous(X1)) | ~tall(john) | creative(john)) [rectify 44]
46. ? [X1] : (curious(X1) & generous(X1)) => (curious(sK1) & generous(sK1)) [choice axiom]
47. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & ((curious(sK1) & generous(sK1)) | ~tall(john) | creative(john)) [skolemisation 45,46]
48. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 8]
49. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (strong(lucy) | kind(lucy))) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [nnf transformation 9]
50. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [flattening 49]
51. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [rectify 50]
52. ? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) => ((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) [choice axiom]
53. (((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [skolemisation 51,52]
64. ! [X0] : (((~humble(X0) | humble(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [nnf transformation 14]
65. ! [X0] : ((~humble(X0) | humble(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [flattening 64]
68. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 16]
72. (creative(john) | ~tall(john)) & (~creative(john) | tall(john)) [nnf transformation 22]
75. ~funny(X0) | tall(X0) [cnf transformation 27]
83. generous(X0) | ~happy(X0) [cnf transformation 40]
85. ~generous(X0) | ~happy(X0) [cnf transformation 40]
89. ~calm(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 42]
94. ~creative(john) | ~curious(X0) | ~generous(X0) [cnf transformation 47]
99. ~rich(X0) | wise(X0) | ~rich(X0) | generous(X0) [cnf transformation 48]
102. generous(X0) | rich(X0) | rich(X0) | wise(X0) [cnf transformation 48]
106. ~strong(lucy) | ~wise(X1) | calm(X1) [cnf transformation 53]
127. funny(X0) | happy(X0) | ~humble(X0) [cnf transformation 65]
128. funny(X0) | happy(X0) | humble(X0) [cnf transformation 65]
135. ~wise(X0) | curious(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 68]
139. wise(X0) | ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 68]
145. strong(lucy) [cnf transformation 19]
149. creative(john) | ~tall(john) [cnf transformation 72]
152. humble(lucy) [cnf transformation 24]
153. ~wise(X0) | curious(X0) | ~strong(X0) [duplicate literal removal 135]
155. ~strong(X0) | wise(X0) | curious(X0) [duplicate literal removal 139]
158. ~rich(X0) | wise(X0) | generous(X0) [duplicate literal removal 99]
160. generous(X0) | rich(X0) | wise(X0) [duplicate literal removal 102]
178. ~happy(X0) [subsumption resolution 83,85]
180. 5 <=> ! [X0] : (~curious(X0) | ~generous(X0)) [avatar definition]
181. ~generous(X0) | ~curious(X0) <- (5) [avatar component clause 180]
183. 6 <=> tall(john) [avatar definition]
184. ~tall(john) <- (~6) [avatar component clause 183]
188. 7 <=> creative(john) [avatar definition]
191. 5 | ~7 [avatar split clause 94,188,180]
202. generous(X0) | wise(X0) [subsumption resolution 158,160]
206. 10 <=> strong(lucy) [avatar definition]
208. strong(lucy) <- (10) [avatar component clause 206]
225. 14 <=> ! [X1] : (~wise(X1) | calm(X1)) [avatar definition]
226. ~wise(X1) | calm(X1) <- (14) [avatar component clause 225]
227. 14 | ~10 [avatar split clause 106,206,225]
281. humble(X0) | funny(X0) [subsumption resolution 128,178]
282. funny(X0) | ~humble(X0) [subsumption resolution 127,178]
283. funny(X0) [subsumption resolution 282,281]
285. ~strong(X0) | curious(X0) [subsumption resolution 153,155]
296. 10 [avatar split clause 145,206]
306. ~6 | 7 [avatar split clause 149,188,183]
319. tall(X0) [resolution 75,283]
320. $false <- (~6) [resolution 319,184]
321. 6 [avatar contradiction clause 320]
328. ~curious(X0) | wise(X0) <- (5) [resolution 202,181]
348. curious(lucy) <- (10) [resolution 285,208]
497. wise(lucy) <- (5, 10) [resolution 328,348]
521. calm(lucy) <- (5, 10, 14) [resolution 497,226]
547. ~humble(lucy) | ~strong(lucy) <- (5, 10, 14) [resolution 521,89]
550. ~strong(lucy) <- (5, 10, 14) [subsumption resolution 547,152]
551. $false <- (5, 10, 14) [subsumption resolution 550,208]
552. ~5 | ~10 | ~14 [avatar contradiction clause 551]
554. $false [avatar sat refutation 191,227,296,306,321,552]
% SZS output end Proof for 6750976116611948935337981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is either strong or wise and vice versa.
Everyone who is not curious or funny is either not strong or not generous and vice versa.
If someone is not wise or calm then mary is either old or not kind and vice versa.
If alice is not funny or not old then someone is both curious and not patient.
Everyone who is not old or not strong is both not generous and tall and vice versa.
Everyone who is either humble or happy is not quiet.
If alice is not quiet or happy then alice is both not brave and not calm and vice versa.
If someone is brave or not funny then lucy is either funny or calm.
If someone is not funny then someone is kind and vice versa.
Everyone who is not funny or tall is both generous and funny and vice versa.
Everyone who is either not curious or happy is both brave and calm.
If mary is not wise or not patient then alice is quiet or kind and vice versa.
Everyone who is either not creative or old is not happy or generous and vice versa.
Everyone who is happy or not humble is not strong.
Everyone who is both not strong and not generous is tall or not creative.
Everyone who is creative is funny or creative and vice versa.
Mary is humble or not patient.
Lucy is patient.
Someone is both brave and not kind.
Paul is not quiet.
Someone is either not kind or patient.
Someone is curious. | Paul is old. | entailment | (![X]:((~creative(X)&curious(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~curious(X)|funny(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:((~wise(X)|calm(X))))<=>((old(mary)<~>~kind(mary))))&
(((~funny(alice)|~old(alice)))=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~generous(X)&tall(X))))&
(![X]:((humble(X)<~>happy(X))=>~quiet(X)))&
(((~quiet(alice)|happy(alice)))<=>((~brave(alice)&~calm(alice))))&
((?[X]:((brave(X)|~funny(X))))=>((funny(lucy)<~>calm(lucy))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((~funny(X)|tall(X))<=>(generous(X)&funny(X))))&
(![X]:((~curious(X)<~>happy(X))=>(brave(X)&calm(X))))&
(((~wise(mary)|~patient(mary)))<=>((quiet(alice)|kind(alice))))&
(![X]:((~creative(X)<~>old(X))<=>(~happy(X)|generous(X))))&
(![X]:((happy(X)|~humble(X))=>~strong(X)))&
(![X]:((~strong(X)&~generous(X))=>(tall(X)|~creative(X))))&
(![X]:(creative(X)<=>(funny(X)|creative(X))))&
((humble(mary)|~patient(mary)))&
(patient(lucy))&
(?[X]:((brave(X)&~kind(X))))&
(~quiet(paul))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:(curious(X))) | old(paul) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7558522077594830608359513
% SZS output start Proof for 7558522077594830608359513
5. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (funny(X0) & generous(X0))) [input p9]
23. ~old(paul) [input hypothesis]
42. ! [X0] : (((~strong(X0) | ~old(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [nnf transformation 5]
43. ! [X0] : ((~strong(X0) | ~old(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [flattening 42]
53. ! [X0] : (((tall(X0) | ~funny(X0)) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((tall(X0) | ~funny(X0) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [flattening 53]
91. ~generous(X0) | old(X0) [cnf transformation 43]
93. tall(X0) | old(X0) [cnf transformation 43]
110. ~tall(X0) | generous(X0) [cnf transformation 54]
142. ~old(paul) [cnf transformation 23]
284. generous(X1) | old(X1) [resolution 110,93]
286. old(X1) [subsumption resolution 284,91]
289. $false [resolution 286,142]
% SZS output end Proof for 7558522077594830608359513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or tall is either funny or not strong and vice versa. If someone is curious then susan is not strong and vice versa. Everyone who is not tall is not quiet or old. If fred is not kind then fred is either not wise or not rich. Everyone who is not patient is curious and vice versa. If someone is both wise and rich then someone is not rich and vice versa. If mary is not quiet then someone is not calm or not tall. Everyone who is funny or calm is either not humble or not tall and vice versa. Everyone who is humble is curious or not humble and vice versa. If someone is either generous or kind then someone is both not calm and not funny. If mary is happy or quiet then someone is both not brave and not funny and vice versa. Everyone who is not curious or not strong is kind. Everyone who is strong or not old is both not kind and not happy. If mary is not old or rich then someone is both not brave and tall and vice versa. If alice is old then someone is both creative and not patient. If someone is either kind or not brave then someone is either wise or curious and vice versa. Someone is either strong or not tall. Lucy is not humble or not generous. Someone is either funny or generous. Paul is wise or not tall. Susan is either not funny or happy. Someone is creative or not creative. Lucy is not creative. Alice is both calm and not happy. | Mary is not quiet. | neutral | (![X]:((~quiet(X)<~>tall(X))<=>(funny(X)<~>~strong(X))))&
((?[X]:(curious(X)))<=>(~strong(susan)))&
(![X]:(~tall(X)=>(~quiet(X)|old(X))))&
((~kind(fred))=>((~wise(fred)<~>~rich(fred))))&
(![X]:(~patient(X)<=>curious(X)))&
((?[X]:((wise(X)&rich(X))))<=>(?[X]:(~rich(X))))&
((~quiet(mary))=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:((funny(X)|calm(X))<=>(~humble(X)<~>~tall(X))))&
(![X]:(humble(X)<=>(curious(X)|~humble(X))))&
((?[X]:((generous(X)<~>kind(X))))=>(?[X]:((~calm(X)&~funny(X)))))&
(((happy(mary)|quiet(mary)))<=>(?[X]:((~brave(X)&~funny(X)))))&
(![X]:((~curious(X)|~strong(X))=>kind(X)))&
(![X]:((strong(X)|~old(X))=>(~kind(X)&~happy(X))))&
(((~old(mary)|rich(mary)))<=>(?[X]:((~brave(X)&tall(X)))))&
((old(alice))=>(?[X]:((creative(X)&~patient(X)))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((wise(X)<~>curious(X)))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~humble(lucy)|~generous(lucy)))&
(?[X]:((funny(X)<~>generous(X))))&
((wise(paul)|~tall(paul)))&
((~funny(susan)<~>happy(susan)))&
(?[X]:((creative(X)|~creative(X))))&
(~creative(lucy))&
((calm(alice)&~happy(alice))) | ~quiet(mary) | [] | null | 0 |
Everyone who is either rich or brave is either curious or not quiet and vice versa.
Everyone who is either not quiet or not wise is either not happy or happy and vice versa.
If someone is both generous and creative then someone is humble or happy.
If someone is both wise and generous then alice is both not patient and creative and vice versa.
If someone is either happy or not quiet then paul is not quiet or not curious.
Everyone who is quiet is humble or strong.
Everyone who is either not happy or happy is either strong or not tall.
Everyone who is both not curious and tall is either strong or wise and vice versa.
Everyone who is not wise is generous or not brave and vice versa.
If someone is either wise or rich then someone is either patient or rich and vice versa.
If lucy is either not creative or not quiet then someone is happy and vice versa.
If someone is both not happy and wise then someone is both not old and not funny.
Everyone who is either tall or calm is not patient or creative.
Everyone who is not rich is not happy or rich and vice versa.
If someone is brave or not happy then alice is both not tall and not wise and vice versa.
If someone is patient or not calm then someone is both humble and not generous.
Mary is either not generous or patient.
Someone is either generous or old.
Lucy is tall or not tall.
Paul is not kind or happy.
Someone is both humble and not rich.
Someone is either not quiet or not strong.
Someone is old or curious.
John is either not calm or old. | Paul is not rich. | entailment | (![X]:((rich(X)<~>brave(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~happy(X)<~>happy(X))))&
((?[X]:((generous(X)&creative(X))))=>(?[X]:((humble(X)|happy(X)))))&
((?[X]:((wise(X)&generous(X))))<=>((~patient(alice)&creative(alice))))&
((?[X]:((happy(X)<~>~quiet(X))))=>((~quiet(paul)|~curious(paul))))&
(![X]:(quiet(X)=>(humble(X)|strong(X))))&
(![X]:((~happy(X)<~>happy(X))=>(strong(X)<~>~tall(X))))&
(![X]:((~curious(X)&tall(X))<=>(strong(X)<~>wise(X))))&
(![X]:(~wise(X)<=>(generous(X)|~brave(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(((~creative(lucy)<~>~quiet(lucy)))<=>(?[X]:(happy(X))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((tall(X)<~>calm(X))=>(~patient(X)|creative(X))))&
(![X]:(~rich(X)<=>(~happy(X)|rich(X))))&
((?[X]:((brave(X)|~happy(X))))<=>((~tall(alice)&~wise(alice))))&
((?[X]:((patient(X)|~calm(X))))=>(?[X]:((humble(X)&~generous(X)))))&
((~generous(mary)<~>patient(mary)))&
(?[X]:((generous(X)<~>old(X))))&
((tall(lucy)|~tall(lucy)))&
((~kind(paul)|happy(paul)))&
(?[X]:((humble(X)&~rich(X))))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((old(X)|curious(X))))&
((~calm(john)<~>old(john))) | ~rich(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7009337266841693475361047
% SZS output start Proof for 7009337266841693475361047
14. ! [X0] : (~rich(X0) <=> (rich(X0) | ~happy(X0))) [input p13]
25. rich(paul) [input hypothesis]
69. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | rich(X0))) [nnf transformation 14]
70. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | rich(X0))) [flattening 69]
143. ~rich(X0) | ~rich(X0) [cnf transformation 70]
162. rich(paul) [cnf transformation 25]
164. ~rich(X0) [duplicate literal removal 143]
372. $false [subsumption resolution 162,164]
% SZS output end Proof for 7009337266841693475361047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is creative or old then john is old or not kind and vice versa.
Everyone who is quiet or creative is not humble or not strong.
If john is not funny then alice is not tall and vice versa.
Everyone who is not kind is either not curious or not kind and vice versa.
If someone is both wise and not brave then someone is not generous and vice versa.
Everyone who is not creative or not generous is kind and vice versa.
If susan is not tall or not strong then someone is kind and vice versa.
Everyone who is not funny is either tall or not rich.
If paul is both not kind and wise then someone is both not curious and not quiet and vice versa.
If someone is either strong or not old then fred is kind or not generous and vice versa.
If lucy is not curious or strong then alice is both not tall and not rich and vice versa.
If paul is either not creative or not humble then lucy is either strong or creative and vice versa.
If someone is both curious and not funny then susan is humble or not generous and vice versa.
Everyone who is both wise and not old is both not curious and not creative and vice versa.
If mary is either not tall or not funny then mary is either humble or not rich and vice versa.
If paul is both not calm and curious then mary is funny and vice versa.
Fred is either generous or not calm.
Someone is both generous and not rich.
Someone is not kind or not old.
Lucy is not tall or not creative.
Lucy is humble or happy.
Someone is not creative or not brave.
Susan is not humble.
Susan is either creative or rich. | Susan is not humble. | entailment | (((creative(alice)|old(alice)))<=>((old(john)|~kind(john))))&
(![X]:((quiet(X)|creative(X))=>(~humble(X)|~strong(X))))&
((~funny(john))<=>(~tall(alice)))&
(![X]:(~kind(X)<=>(~curious(X)<~>~kind(X))))&
((?[X]:((wise(X)&~brave(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~creative(X)|~generous(X))<=>kind(X)))&
(((~tall(susan)|~strong(susan)))<=>(?[X]:(kind(X))))&
(![X]:(~funny(X)=>(tall(X)<~>~rich(X))))&
(((~kind(paul)&wise(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
((?[X]:((strong(X)<~>~old(X))))<=>((kind(fred)|~generous(fred))))&
(((~curious(lucy)|strong(lucy)))<=>((~tall(alice)&~rich(alice))))&
(((~creative(paul)<~>~humble(paul)))<=>((strong(lucy)<~>creative(lucy))))&
((?[X]:((curious(X)&~funny(X))))<=>((humble(susan)|~generous(susan))))&
(![X]:((wise(X)&~old(X))<=>(~curious(X)&~creative(X))))&
(((~tall(mary)<~>~funny(mary)))<=>((humble(mary)<~>~rich(mary))))&
(((~calm(paul)&curious(paul)))<=>(funny(mary)))&
((generous(fred)<~>~calm(fred)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((~kind(X)|~old(X))))&
((~tall(lucy)|~creative(lucy)))&
((humble(lucy)|happy(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(~humble(susan))&
((creative(susan)<~>rich(susan))) | ~humble(susan) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8718364584616779105359707
% SZS output start Proof for 8718364584616779105359707
23. ~humble(susan) [input p22]
25. humble(susan) [input hypothesis]
152. ~humble(susan) [cnf transformation 23]
155. humble(susan) [cnf transformation 25]
315. 32 <=> humble(susan) [avatar definition]
387. ~32 [avatar split clause 152,315]
398. 32 [avatar split clause 155,315]
399. $false [avatar sat refutation 387,398]
% SZS output end Proof for 8718364584616779105359707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not humble is either patient or quiet. Everyone who is not tall is patient or wise. Everyone who is both not tall and calm is not curious or not generous and vice versa. Everyone who is both strong and not calm is either humble or brave and vice versa. Everyone who is not tall or strong is not curious or not brave and vice versa. If fred is not kind then someone is humble and vice versa. If someone is wise or happy then fred is funny. Everyone who is either not happy or not funny is both not generous and curious. Everyone who is not happy is either not tall or not rich. Everyone who is creative or kind is both not kind and rich and vice versa. If someone is both calm and not strong then alice is both not curious and kind. If someone is not tall then paul is both wise and rich. If someone is either not quiet or old then someone is creative or quiet and vice versa. Everyone who is either not brave or not curious is both curious and creative and vice versa. If someone is both happy and quiet then someone is either quiet or not kind and vice versa. If john is either old or not old then someone is both not creative and calm and vice versa. Someone is both not brave and not old. Someone is not creative or patient. Fred is either generous or curious. Someone is either not old or not patient. Fred is not rich or tall. Mary is not tall. | Alice is old. | neutral | (![X]:((generous(X)<~>~humble(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|wise(X))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)|~generous(X))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~tall(X)|strong(X))<=>(~curious(X)|~brave(X))))&
((~kind(fred))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)|happy(X))))=>(funny(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(((old(john)<~>~old(john)))<=>(?[X]:((~creative(X)&calm(X)))))&
(?[X]:((~brave(X)&~old(X))))&
(?[X]:((~creative(X)|patient(X))))&
((generous(fred)<~>curious(fred)))&
(?[X]:((~old(X)<~>~patient(X))))&
((~rich(fred)|tall(fred)))&
(~tall(mary)) | old(alice) | [] | null | 0 |
If mary is not wise or kind then susan is either not strong or not curious and vice versa. If lucy is strong or not old then someone is both calm and not strong. If paul is either kind or generous then susan is not curious. Everyone who is not humble is not kind. Everyone who is not brave or kind is not happy. If someone is either patient or not kind then someone is either funny or quiet and vice versa. If someone is not old or wise then someone is both rich and calm. If someone is not creative then paul is not rich and vice versa. Everyone who is both not wise and not tall is not patient or patient and vice versa. Everyone who is either not happy or not strong is not calm. If alice is not humble or not strong then fred is strong or not generous. If someone is strong or tall then someone is kind. If susan is both strong and not brave then susan is either creative or funny and vice versa. If someone is tall then someone is not humble and vice versa. Everyone who is calm or not old is both not strong and strong and vice versa. Everyone who is not generous is not tall or quiet and vice versa. Alice is not funny or curious. Paul is patient or not calm. Someone is not rich. Someone is not curious. Paul is brave or not curious. Lucy is tall or happy. | Lucy is quiet. | neutral | (((~wise(mary)|kind(mary)))<=>((~strong(susan)<~>~curious(susan))))&
(((strong(lucy)|~old(lucy)))=>(?[X]:((calm(X)&~strong(X)))))&
(((kind(paul)<~>generous(paul)))=>(~curious(susan)))&
(![X]:(~humble(X)=>~kind(X)))&
(![X]:((~brave(X)|kind(X))=>~happy(X)))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
((?[X]:((~old(X)|wise(X))))=>(?[X]:((rich(X)&calm(X)))))&
((?[X]:(~creative(X)))<=>(~rich(paul)))&
(![X]:((~wise(X)&~tall(X))<=>(~patient(X)|patient(X))))&
(![X]:((~happy(X)<~>~strong(X))=>~calm(X)))&
(((~humble(alice)|~strong(alice)))=>((strong(fred)|~generous(fred))))&
((?[X]:((strong(X)|tall(X))))=>(?[X]:(kind(X))))&
(((strong(susan)&~brave(susan)))<=>((creative(susan)<~>funny(susan))))&
((?[X]:(tall(X)))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~old(X))<=>(~strong(X)&strong(X))))&
(![X]:(~generous(X)<=>(~tall(X)|quiet(X))))&
((~funny(alice)|curious(alice)))&
((patient(paul)|~calm(paul)))&
(?[X]:(~rich(X)))&
(?[X]:(~curious(X)))&
((brave(paul)|~curious(paul)))&
((tall(lucy)|happy(lucy))) | quiet(lucy) | [] | null | 0 |
If someone is not quiet then alice is both not quiet and not happy.
If alice is not curious or tall then someone is not rich.
Everyone who is not brave or not wise is both not generous and patient.
Everyone who is both curious and tall is either tall or rich.
If john is humble then someone is not tall or creative.
Everyone who is kind or tall is not rich.
If someone is either not happy or kind then lucy is both tall and not quiet.
Everyone who is both not old and happy is calm or happy and vice versa.
Everyone who is not patient or not funny is either not rich or not tall.
Everyone who is both not old and not brave is tall or not kind and vice versa.
If fred is either creative or not kind then paul is not old or not patient.
Everyone who is either strong or not old is both not kind and patient and vice versa.
If someone is either not brave or tall then someone is either generous or old and vice versa.
Everyone who is either not patient or not funny is strong.
Everyone who is either rich or not generous is either kind or happy and vice versa.
If john is both patient and brave then someone is either not quiet or not calm and vice versa.
Someone is wise.
Alice is quiet.
John is not happy.
Someone is either not humble or not kind.
Someone is not curious or not funny.
Lucy is both not rich and not funny.
Someone is not tall. | Alice is not rich. | entailment | ((?[X]:(~quiet(X)))=>((~quiet(alice)&~happy(alice))))&
(((~curious(alice)|tall(alice)))=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)|~wise(X))=>(~generous(X)&patient(X))))&
(![X]:((curious(X)&tall(X))=>(tall(X)<~>rich(X))))&
((humble(john))=>(?[X]:((~tall(X)|creative(X)))))&
(![X]:((kind(X)|tall(X))=>~rich(X)))&
((?[X]:((~happy(X)<~>kind(X))))=>((tall(lucy)&~quiet(lucy))))&
(![X]:((~old(X)&happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~patient(X)|~funny(X))=>(~rich(X)<~>~tall(X))))&
(![X]:((~old(X)&~brave(X))<=>(tall(X)|~kind(X))))&
(((creative(fred)<~>~kind(fred)))=>((~old(paul)|~patient(paul))))&
(![X]:((strong(X)<~>~old(X))<=>(~kind(X)&patient(X))))&
((?[X]:((~brave(X)<~>tall(X))))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~patient(X)<~>~funny(X))=>strong(X)))&
(![X]:((rich(X)<~>~generous(X))<=>(kind(X)<~>happy(X))))&
(((patient(john)&brave(john)))<=>(?[X]:((~quiet(X)<~>~calm(X)))))&
(?[X]:(wise(X)))&
(quiet(alice))&
(~happy(john))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((~curious(X)|~funny(X))))&
((~rich(lucy)&~funny(lucy)))&
(?[X]:(~tall(X))) | ~rich(alice) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7697797670255634214972973
% SZS output start Proof for 7697797670255634214972973
1. ? [X0] : ~quiet(X0) => (~happy(alice) & ~quiet(alice)) [input p0]
3. ! [X0] : ((~wise(X0) | ~brave(X0)) => (patient(X0) & ~generous(X0))) [input p2]
6. ! [X0] : ((tall(X0) | kind(X0)) => ~rich(X0)) [input p5]
7. ? [X0] : (~happy(X0) <~> kind(X0)) => (~quiet(lucy) & tall(lucy)) [input p6]
10. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (~kind(X0) | tall(X0))) [input p9]
15. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (kind(X0) <~> happy(X0))) [input p14]
18. quiet(alice) [input p17]
24. rich(alice) [input hypothesis]
26. ! [X0] : (~brave(X0) => (patient(X0) & ~generous(X0))) [pure predicate removal 3]
28. (~happy(alice) & ~quiet(alice)) | ! [X0] : quiet(X0) [ennf transformation 1]
30. ! [X0] : ((patient(X0) & ~generous(X0)) | brave(X0)) [ennf transformation 26]
34. ! [X0] : (~rich(X0) | (~tall(X0) & ~kind(X0))) [ennf transformation 6]
35. (~quiet(lucy) & tall(lucy)) | ! [X0] : (~happy(X0) <=> kind(X0)) [ennf transformation 7]
45. (~quiet(lucy) & tall(lucy)) | ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 35]
49. ! [X0] : (((~brave(X0) & ~old(X0)) | (kind(X0) & ~tall(X0))) & ((~kind(X0) | tall(X0)) | (brave(X0) | old(X0)))) [nnf transformation 10]
50. ! [X0] : (((~brave(X0) & ~old(X0)) | (kind(X0) & ~tall(X0))) & (~kind(X0) | tall(X0) | brave(X0) | old(X0))) [flattening 49]
60. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 15]
73. ~quiet(alice) | quiet(X0) [cnf transformation 28]
77. ~generous(X0) | brave(X0) [cnf transformation 30]
82. ~kind(X0) | ~rich(X0) [cnf transformation 34]
86. ~quiet(lucy) | kind(X0) | happy(X0) [cnf transformation 45]
101. ~brave(X0) | kind(X0) [cnf transformation 50]
127. generous(X0) | ~rich(X0) | kind(X0) | ~happy(X0) [cnf transformation 60]
134. quiet(alice) [cnf transformation 18]
142. rich(alice) [cnf transformation 24]
145. 1 <=> ! [X0] : quiet(X0) [avatar definition]
146. quiet(X0) <- (1) [avatar component clause 145]
148. 2 <=> happy(alice) [avatar definition]
149. happy(alice) <- (2) [avatar component clause 148]
153. 3 <=> quiet(alice) [avatar definition]
156. 1 | ~3 [avatar split clause 73,153,145]
188. 11 <=> quiet(lucy) [avatar definition]
190. ~quiet(lucy) <- (~11) [avatar component clause 188]
193. 12 <=> ! [X0] : (kind(X0) | happy(X0)) [avatar definition]
194. kind(X0) | happy(X0) <- (12) [avatar component clause 193]
195. 12 | ~11 [avatar split clause 86,188,193]
257. ~rich(X0) | generous(X0) | ~happy(X0) [subsumption resolution 127,82]
289. 3 [avatar split clause 134,153]
313. ~rich(X1) | happy(X1) <- (12) [resolution 194,82]
356. happy(alice) <- (12) [resolution 313,142]
357. 2 | ~12 [avatar split clause 356,193,148]
358. $false <- (1, ~11) [subsumption resolution 190,146]
359. ~1 | 11 [avatar contradiction clause 358]
380. generous(alice) | ~happy(alice) [resolution 257,142]
381. generous(alice) <- (2) [subsumption resolution 380,149]
383. brave(alice) <- (2) [resolution 381,77]
399. kind(alice) <- (2) [resolution 383,101]
428. ~rich(alice) <- (2) [resolution 399,82]
440. $false <- (2) [subsumption resolution 428,142]
441. ~2 [avatar contradiction clause 440]
442. $false [avatar sat refutation 156,195,289,357,359,441]
% SZS output end Proof for 7697797670255634214972973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or wise then alice is either not quiet or calm and vice versa.
Everyone who is brave is either patient or funny.
Everyone who is either not wise or not rich is wise.
Everyone who is both not creative and not curious is not tall or not creative and vice versa.
If john is either not creative or not kind then paul is both kind and calm and vice versa.
Everyone who is both not wise and not humble is both not generous and quiet.
Everyone who is old or not kind is not strong.
If someone is both brave and kind then someone is both not funny and not creative.
Everyone who is not funny or calm is tall.
If someone is rich or not patient then lucy is both not humble and humble.
Everyone who is both not generous and tall is both curious and not strong and vice versa.
Everyone who is both patient and kind is not happy or generous and vice versa.
Everyone who is not tall or not patient is both happy and brave.
Everyone who is not happy or not kind is both creative and kind and vice versa.
Everyone who is not generous is not wise or funny and vice versa.
Everyone who is not quiet or humble is both generous and not wise.
John is curious or rich.
Someone is both generous and tall.
Susan is either old or patient.
Mary is both brave and curious.
Paul is calm or not brave.
Someone is not rich or rich.
Fred is calm or not strong.
Mary is curious. | Lucy is brave. | neutral | ((?[X]:((~wise(X)<~>wise(X))))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:(brave(X)=>(patient(X)<~>funny(X))))&
(![X]:((~wise(X)<~>~rich(X))=>wise(X)))&
(![X]:((~creative(X)&~curious(X))<=>(~tall(X)|~creative(X))))&
(((~creative(john)<~>~kind(john)))<=>((kind(paul)&calm(paul))))&
(![X]:((~wise(X)&~humble(X))=>(~generous(X)&quiet(X))))&
(![X]:((old(X)|~kind(X))=>~strong(X)))&
((?[X]:((brave(X)&kind(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((~funny(X)|calm(X))=>tall(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:((~generous(X)&tall(X))<=>(curious(X)&~strong(X))))&
(![X]:((patient(X)&kind(X))<=>(~happy(X)|generous(X))))&
(![X]:((~tall(X)|~patient(X))=>(happy(X)&brave(X))))&
(![X]:((~happy(X)|~kind(X))<=>(creative(X)&kind(X))))&
(![X]:(~generous(X)<=>(~wise(X)|funny(X))))&
(![X]:((~quiet(X)|humble(X))=>(generous(X)&~wise(X))))&
((curious(john)|rich(john)))&
(?[X]:((generous(X)&tall(X))))&
((old(susan)<~>patient(susan)))&
((brave(mary)&curious(mary)))&
((calm(paul)|~brave(paul)))&
(?[X]:((~rich(X)|rich(X))))&
((calm(fred)|~strong(fred)))&
(curious(mary)) | brave(lucy) | [] | null | 0 |
Everyone who is patient or not funny is both generous and not funny and vice versa. Everyone who is either strong or not tall is rich. Everyone who is not creative is not funny or not generous. Everyone who is both not funny and not quiet is not calm and vice versa. If someone is both not wise and rich then someone is either old or not creative. If someone is humble then paul is not kind or humble. Everyone who is either not patient or kind is not tall. If alice is both strong and not quiet then someone is quiet or not wise and vice versa. Everyone who is not rich is calm or funny and vice versa. Everyone who is curious is either not happy or humble. Everyone who is tall or quiet is both not patient and not strong. Everyone who is either not rich or funny is not happy and vice versa. If someone is calm then someone is not creative. Everyone who is patient or rich is old or tall and vice versa. If someone is either not creative or not humble then someone is both not brave and old and vice versa. Everyone who is not rich or generous is both not creative and rich. Alice is both curious and kind. Mary is brave. Someone is not happy or curious. Someone is both not curious and not old. Someone is not funny. Someone is either creative or not patient. | Paul is not creative. | entailment | (![X]:((patient(X)|~funny(X))<=>(generous(X)&~funny(X))))&
(![X]:((strong(X)<~>~tall(X))=>rich(X)))&
(![X]:(~creative(X)=>(~funny(X)|~generous(X))))&
(![X]:((~funny(X)&~quiet(X))<=>~calm(X)))&
((?[X]:((~wise(X)&rich(X))))=>(?[X]:((old(X)<~>~creative(X)))))&
((?[X]:(humble(X)))=>((~kind(paul)|humble(paul))))&
(![X]:((~patient(X)<~>kind(X))=>~tall(X)))&
(((strong(alice)&~quiet(alice)))<=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:(~rich(X)<=>(calm(X)|funny(X))))&
(![X]:(curious(X)=>(~happy(X)<~>humble(X))))&
(![X]:((tall(X)|quiet(X))=>(~patient(X)&~strong(X))))&
(![X]:((~rich(X)<~>funny(X))<=>~happy(X)))&
((?[X]:(calm(X)))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)|rich(X))<=>(old(X)|tall(X))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&rich(X))))&
((curious(alice)&kind(alice)))&
(brave(mary))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>~patient(X)))) | ~creative(paul) | [
"p0",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4353041089220478053323126
% SZS output start Proof for 4353041089220478053323126
1. ! [X0] : ((~funny(X0) | patient(X0)) <=> (~funny(X0) & generous(X0))) [input p0]
9. ! [X0] : (~rich(X0) <=> (funny(X0) | calm(X0))) [input p8]
16. ! [X0] : ((generous(X0) | ~rich(X0)) => (rich(X0) & ~creative(X0))) [input p15]
23. creative(paul) [input hypothesis]
37. ! [X0] : ((rich(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 16]
38. ! [X0] : (((~funny(X0) | patient(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (funny(X0) & ~patient(X0)))) [nnf transformation 1]
39. ! [X0] : ((~funny(X0) | patient(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (funny(X0) & ~patient(X0)))) [flattening 38]
53. ! [X0] : ((~rich(X0) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | rich(X0))) [nnf transformation 9]
54. ! [X0] : ((~rich(X0) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | rich(X0))) [flattening 53]
77. generous(X0) | funny(X0) [cnf transformation 39]
99. ~rich(X0) | ~funny(X0) [cnf transformation 54]
122. ~creative(X0) | ~generous(X0) [cnf transformation 37]
123. rich(X0) | rich(X0) [cnf transformation 37]
134. creative(paul) [cnf transformation 23]
135. rich(X0) [duplicate literal removal 123]
253. ~funny(X0) [resolution 99,135]
254. ~generous(paul) [resolution 122,134]
255. funny(paul) [resolution 254,77]
256. $false [subsumption resolution 255,253]
% SZS output end Proof for 4353041089220478053323126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both not rich and not generous.
Everyone who is old is both generous and not creative.
If fred is not funny then lucy is either old or curious.
Everyone who is not happy is either not humble or not quiet and vice versa.
Everyone who is either not humble or humble is both not wise and not happy and vice versa.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
Someone is tall or not kind.
Someone is not brave.
Someone is either rich or wise.
Someone is not old.
Alice is either not tall or not patient. | Alice is humble. | contradiction | (![X]:(~quiet(X)=>(~rich(X)&~generous(X))))&
(![X]:(old(X)=>(generous(X)&~creative(X))))&
((~funny(fred))=>((old(lucy)<~>curious(lucy))))&
(![X]:(~happy(X)<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(~wise(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((~tall(alice)<~>~patient(alice))) | humble(alice) | [
"p0",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1403233426784160273714902
% SZS output start Proof for 1403233426784160273714902
1. ! [X0] : (~quiet(X0) => (~generous(X0) & ~rich(X0))) [input p0]
4. ! [X0] : (~happy(X0) <=> (~humble(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~happy(X0) & ~wise(X0))) [input p4]
10. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p9]
22. humble(alice) [input hypothesis]
24. ! [X0] : ((~generous(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 1]
29. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 10]
37. ! [X0] : ((~happy(X0) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | happy(X0))) [nnf transformation 4]
38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 38]
66. ~generous(X0) | quiet(X0) [cnf transformation 24]
71. ~humble(X0) | ~quiet(X0) | happy(X0) [cnf transformation 37]
77. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 39]
78. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 39]
99. generous(X0) | happy(X0) [cnf transformation 29]
125. humble(alice) [cnf transformation 22]
132. ~happy(X0) | humble(X0) [duplicate literal removal 77]
133. ~humble(X0) | ~happy(X0) [duplicate literal removal 78]
148. ~happy(X0) [subsumption resolution 132,133]
152. generous(X0) [subsumption resolution 99,148]
196. quiet(X0) [resolution 66,152]
213. ~quiet(alice) | happy(alice) [resolution 71,125]
214. happy(alice) [subsumption resolution 213,196]
215. $false [subsumption resolution 214,148]
% SZS output end Proof for 1403233426784160273714902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and quiet is humble or not humble. Everyone who is funny or not generous is not kind and vice versa. If paul is old or happy then someone is either strong or brave and vice versa. If paul is either old or rich then someone is curious or humble and vice versa. If mary is happy then someone is either tall or not quiet. If paul is happy then someone is both not calm and funny and vice versa. Everyone who is kind is not creative or generous. Everyone who is not patient is wise or quiet and vice versa. Everyone who is not brave is either not quiet or quiet. Everyone who is both not strong and calm is tall and vice versa. If john is either rich or not calm then susan is either not curious or not generous. If paul is either not happy or not calm then someone is not patient or not strong and vice versa. If susan is both calm and wise then lucy is either strong or not calm and vice versa. Everyone who is either not creative or old is either curious or not happy. Everyone who is not brave is either tall or not humble and vice versa. If fred is either generous or funny then alice is patient or brave and vice versa. Someone is tall or not rich. Lucy is happy. Someone is humble. Susan is both tall and not humble. John is either not happy or not strong. Alice is either not quiet or happy. Someone is both strong and not happy. | Susan is creative. | neutral | (![X]:((strong(X)&quiet(X))=>(humble(X)|~humble(X))))&
(![X]:((funny(X)|~generous(X))<=>~kind(X)))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:((~strong(X)&calm(X))<=>tall(X)))&
(((rich(john)<~>~calm(john)))=>((~curious(susan)<~>~generous(susan))))&
(((~happy(paul)<~>~calm(paul)))<=>(?[X]:((~patient(X)|~strong(X)))))&
(((calm(susan)&wise(susan)))<=>((strong(lucy)<~>~calm(lucy))))&
(![X]:((~creative(X)<~>old(X))=>(curious(X)<~>~happy(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~humble(X))))&
(((generous(fred)<~>funny(fred)))<=>((patient(alice)|brave(alice))))&
(?[X]:((tall(X)|~rich(X))))&
(happy(lucy))&
(?[X]:(humble(X)))&
((tall(susan)&~humble(susan)))&
((~happy(john)<~>~strong(john)))&
((~quiet(alice)<~>happy(alice)))&
(?[X]:((strong(X)&~happy(X)))) | creative(susan) | [] | null | 0 |
Everyone who is not brave or not rich is both tall and wise and vice versa.
If someone is either strong or not happy then susan is both patient and not patient and vice versa.
Everyone who is not rich is funny or calm and vice versa.
If lucy is tall or calm then someone is funny and vice versa.
Everyone who is either not curious or curious is not kind and vice versa.
If paul is both curious and patient then mary is not brave and vice versa.
Everyone who is either funny or not kind is curious or rich.
If mary is happy then paul is either humble or not calm and vice versa.
Everyone who is humble is happy or not curious.
Everyone who is not wise is both not humble and calm and vice versa.
Everyone who is creative or not happy is either not old or not curious and vice versa.
Everyone who is humble is either generous or not brave and vice versa.
If someone is not tall then susan is both not kind and calm.
If alice is either not old or not humble then alice is not funny or not wise and vice versa.
If susan is rich then john is not curious.
If alice is either strong or creative then someone is not happy.
Paul is generous.
Someone is brave or not creative.
Someone is old or not curious.
Alice is not quiet.
Susan is both not humble and happy.
Someone is both not old and not calm.
John is kind or not patient.
Someone is not happy or brave. | Alice is tall. | entailment | (![X]:((~brave(X)|~rich(X))<=>(tall(X)&wise(X))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((patient(susan)&~patient(susan))))&
(![X]:(~rich(X)<=>(funny(X)|calm(X))))&
(((tall(lucy)|calm(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~kind(X)))&
(((curious(paul)&patient(paul)))<=>(~brave(mary)))&
(![X]:((funny(X)<~>~kind(X))=>(curious(X)|rich(X))))&
((happy(mary))<=>((humble(paul)<~>~calm(paul))))&
(![X]:(humble(X)=>(happy(X)|~curious(X))))&
(![X]:(~wise(X)<=>(~humble(X)&calm(X))))&
(![X]:((creative(X)|~happy(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(humble(X)<=>(generous(X)<~>~brave(X))))&
((?[X]:(~tall(X)))=>((~kind(susan)&calm(susan))))&
(((~old(alice)<~>~humble(alice)))<=>((~funny(alice)|~wise(alice))))&
((rich(susan))=>(~curious(john)))&
(((strong(alice)<~>creative(alice)))=>(?[X]:(~happy(X))))&
(generous(paul))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:((old(X)|~curious(X))))&
(~quiet(alice))&
((~humble(susan)&happy(susan)))&
(?[X]:((~old(X)&~calm(X))))&
((kind(john)|~patient(john)))&
(?[X]:((~happy(X)|brave(X)))) | tall(alice) | [
"p0",
"p2",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7480157058907530037474246
% SZS output start Proof for 7480157058907530037474246
1. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> (wise(X0) & tall(X0))) [input p0]
3. ! [X0] : (~rich(X0) <=> (calm(X0) | funny(X0))) [input p2]
10. ! [X0] : (~wise(X0) <=> (calm(X0) & ~humble(X0))) [input p9]
13. ? [X0] : ~tall(X0) => (calm(susan) & ~kind(susan)) [input p12]
21. happy(susan) & ~humble(susan) [input p20]
25. ~tall(alice) [input hypothesis]
31. (calm(susan) & ~kind(susan)) | ! [X0] : tall(X0) [ennf transformation 13]
34. ! [X0] : (((~rich(X0) | ~brave(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (rich(X0) & brave(X0)))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | ~brave(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (rich(X0) & brave(X0)))) [flattening 34]
41. ! [X0] : ((~rich(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | rich(X0))) [nnf transformation 3]
42. ! [X0] : ((~rich(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | rich(X0))) [flattening 41]
53. ! [X0] : ((~wise(X0) | (~calm(X0) | humble(X0))) & ((calm(X0) & ~humble(X0)) | wise(X0))) [nnf transformation 10]
54. ! [X0] : ((~wise(X0) | ~calm(X0) | humble(X0)) & ((calm(X0) & ~humble(X0)) | wise(X0))) [flattening 53]
74. wise(X0) | rich(X0) [cnf transformation 35]
84. ~calm(X0) | ~rich(X0) [cnf transformation 42]
103. calm(X0) | wise(X0) [cnf transformation 54]
104. ~calm(X0) | ~wise(X0) | humble(X0) [cnf transformation 54]
116. calm(susan) | tall(X0) [cnf transformation 31]
129. ~humble(susan) [cnf transformation 21]
135. ~tall(alice) [cnf transformation 25]
204. 14 <=> ! [X0] : tall(X0) [avatar definition]
205. tall(X0) <- (14) [avatar component clause 204]
207. 15 <=> calm(susan) [avatar definition]
209. calm(susan) <- (15) [avatar component clause 207]
210. 14 | 15 [avatar split clause 116,207,204]
296. wise(X0) | ~rich(X0) [resolution 103,84]
297. wise(X0) [subsumption resolution 296,74]
310. ~wise(susan) | humble(susan) <- (15) [resolution 104,209]
316. humble(susan) <- (15) [subsumption resolution 310,297]
317. $false <- (15) [subsumption resolution 316,129]
318. ~15 [avatar contradiction clause 317]
326. $false <- (14) [resolution 205,135]
329. ~14 [avatar contradiction clause 326]
330. $false [avatar sat refutation 210,318,329]
% SZS output end Proof for 7480157058907530037474246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both strong and not brave then alice is both patient and not strong.
Everyone who is not creative is both humble and not old.
Everyone who is not kind is both not wise and happy.
Everyone who is both old and not generous is both brave and funny and vice versa.
If someone is either not calm or not humble then someone is both brave and not patient and vice versa.
Everyone who is not old is either not humble or calm and vice versa.
If someone is not strong or not wise then someone is both old and not old and vice versa.
If john is both not humble and tall then john is both not old and rich and vice versa.
Everyone who is either strong or not happy is not patient or generous and vice versa.
If someone is either not happy or calm then someone is either curious or not rich.
If susan is not funny or not wise then john is rich.
Everyone who is either wise or patient is both not kind and tall and vice versa.
Everyone who is patient is not quiet.
Everyone who is not quiet or rich is both not humble and not quiet.
Everyone who is creative or not generous is kind or tall.
If alice is kind or patient then someone is not brave.
Paul is both not curious and strong.
Someone is not tall.
Mary is both not tall and generous.
Lucy is not happy.
John is generous or not kind.
Someone is either patient or happy.
Someone is either not rich or tall. | Paul is not old. | entailment | (((strong(mary)&~brave(mary)))=>((patient(alice)&~strong(alice))))&
(![X]:(~creative(X)=>(humble(X)&~old(X))))&
(![X]:(~kind(X)=>(~wise(X)&happy(X))))&
(![X]:((old(X)&~generous(X))<=>(brave(X)&funny(X))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(?[X]:((brave(X)&~patient(X)))))&
(![X]:(~old(X)<=>(~humble(X)<~>calm(X))))&
((?[X]:((~strong(X)|~wise(X))))<=>(?[X]:((old(X)&~old(X)))))&
(((~humble(john)&tall(john)))<=>((~old(john)&rich(john))))&
(![X]:((strong(X)<~>~happy(X))<=>(~patient(X)|generous(X))))&
((?[X]:((~happy(X)<~>calm(X))))=>(?[X]:((curious(X)<~>~rich(X)))))&
(((~funny(susan)|~wise(susan)))=>(rich(john)))&
(![X]:((wise(X)<~>patient(X))<=>(~kind(X)&tall(X))))&
(![X]:(patient(X)=>~quiet(X)))&
(![X]:((~quiet(X)|rich(X))=>(~humble(X)&~quiet(X))))&
(![X]:((creative(X)|~generous(X))=>(kind(X)|tall(X))))&
(((kind(alice)|patient(alice)))=>(?[X]:(~brave(X))))&
((~curious(paul)&strong(paul)))&
(?[X]:(~tall(X)))&
((~tall(mary)&generous(mary)))&
(~happy(lucy))&
((generous(john)|~kind(john)))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((~rich(X)<~>tall(X)))) | ~old(paul) | [
"p2",
"p4",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7529307559649481977315353
% SZS output start Proof for 7529307559649481977315353
3. ! [X0] : (~kind(X0) => (happy(X0) & ~wise(X0))) [input p2]
5. ? [X0] : (~calm(X0) <~> ~humble(X0)) <=> ? [X0] : (~patient(X0) & brave(X0)) [input p4]
6. ! [X0] : (~old(X0) <=> (~humble(X0) <~> calm(X0))) [input p5]
7. ? [X0] : (~wise(X0) | ~strong(X0)) <=> ? [X0] : (~old(X0) & old(X0)) [input p6]
12. ! [X0] : ((wise(X0) <~> patient(X0)) <=> (tall(X0) & ~kind(X0))) [input p11]
24. old(paul) [input hypothesis]
25. ? [X0] : (~calm(X0) <~> ~humble(X0)) <=> ? [X1] : (~patient(X1) & brave(X1)) [rectify 5]
26. ? [X0] : (~wise(X0) | ~strong(X0)) <=> ? [X1] : (~old(X1) & old(X1)) [rectify 7]
31. ! [X0] : ((happy(X0) & ~wise(X0)) | kind(X0)) [ennf transformation 3]
41. (? [X0] : ((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | ! [X1] : (patient(X1) | ~brave(X1))) & (? [X1] : (~patient(X1) & brave(X1)) | ! [X0] : ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0)))) [nnf transformation 25]
42. (? [X0] : ((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | ! [X1] : (patient(X1) | ~brave(X1))) & (? [X2] : (~patient(X2) & brave(X2)) | ! [X3] : ((~calm(X3) | humble(X3)) & (~humble(X3) | calm(X3)))) [rectify 41]
43. ? [X0] : ((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) => ((humble(sK0) | calm(sK0)) & (~humble(sK0) | ~calm(sK0))) [choice axiom]
44. ? [X2] : (~patient(X2) & brave(X2)) => (~patient(sK1) & brave(sK1)) [choice axiom]
45. (((humble(sK0) | calm(sK0)) & (~humble(sK0) | ~calm(sK0))) | ! [X1] : (patient(X1) | ~brave(X1))) & ((~patient(sK1) & brave(sK1)) | ! [X3] : ((~calm(X3) | humble(X3)) & (~humble(X3) | calm(X3)))) [skolemisation 42,44,43]
46. ! [X0] : ((~old(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | old(X0))) [nnf transformation 6]
47. (? [X0] : (~wise(X0) | ~strong(X0)) | ! [X1] : (old(X1) | ~old(X1))) & (? [X1] : (~old(X1) & old(X1)) | ! [X0] : (wise(X0) & strong(X0))) [nnf transformation 26]
48. (? [X0] : (~wise(X0) | ~strong(X0)) | ! [X1] : (old(X1) | ~old(X1))) & (? [X2] : (~old(X2) & old(X2)) | ! [X3] : (wise(X3) & strong(X3))) [rectify 47]
49. ? [X0] : (~wise(X0) | ~strong(X0)) => (~wise(sK2) | ~strong(sK2)) [choice axiom]
50. ? [X2] : (~old(X2) & old(X2)) => (~old(sK3) & old(sK3)) [choice axiom]
51. ((~wise(sK2) | ~strong(sK2)) | ! [X1] : (old(X1) | ~old(X1))) & ((~old(sK3) & old(sK3)) | ! [X3] : (wise(X3) & strong(X3))) [skolemisation 48,50,49]
60. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 12]
61. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [flattening 60]
76. ~wise(X0) | kind(X0) [cnf transformation 31]
84. ~patient(sK1) | ~humble(X3) | calm(X3) [cnf transformation 45]
85. ~patient(sK1) | ~calm(X3) | humble(X3) [cnf transformation 45]
90. ~old(X0) | calm(X0) | humble(X0) [cnf transformation 46]
91. ~calm(X0) | ~humble(X0) | ~old(X0) [cnf transformation 46]
93. old(sK3) | wise(X3) [cnf transformation 51]
95. ~old(sK3) | wise(X3) [cnf transformation 51]
113. ~kind(X0) | patient(X0) | ~wise(X0) [cnf transformation 61]
139. old(paul) [cnf transformation 24]
172. 8 <=> ! [X3] : (~calm(X3) | humble(X3)) [avatar definition]
173. ~calm(X3) | humble(X3) <- (8) [avatar component clause 172]
175. 9 <=> patient(sK1) [avatar definition]
177. ~patient(sK1) <- (~9) [avatar component clause 175]
178. 8 | ~9 [avatar split clause 85,175,172]
180. 10 <=> ! [X3] : (~humble(X3) | calm(X3)) [avatar definition]
181. ~humble(X3) | calm(X3) <- (10) [avatar component clause 180]
182. 10 | ~9 [avatar split clause 84,175,180]
190. 12 <=> ! [X3] : wise(X3) [avatar definition]
191. wise(X3) <- (12) [avatar component clause 190]
193. 13 <=> old(sK3) [avatar definition]
196. 12 | ~13 [avatar split clause 95,193,190]
201. 12 | 13 [avatar split clause 93,193,190]
252. ~wise(X0) | patient(X0) [subsumption resolution 113,76]
307. patient(X0) <- (12) [resolution 252,191]
308. $false <- (~9, 12) [resolution 307,177]
309. 9 | ~12 [avatar contradiction clause 308]
336. calm(paul) | humble(paul) [resolution 90,139]
338. humble(paul) <- (8) [subsumption resolution 336,173]
341. calm(paul) <- (8, 10) [resolution 338,181]
350. ~humble(paul) | ~old(paul) <- (8, 10) [resolution 341,91]
353. ~old(paul) <- (8, 10) [subsumption resolution 350,338]
354. $false <- (8, 10) [subsumption resolution 353,139]
355. ~8 | ~10 [avatar contradiction clause 354]
356. $false [avatar sat refutation 178,182,196,201,309,355]
% SZS output end Proof for 7529307559649481977315353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not wise or funny.
If someone is not curious or not kind then alice is either not patient or quiet.
Everyone who is either not wise or brave is either not rich or kind and vice versa.
If paul is not brave then susan is either funny or not calm.
Everyone who is not humble or calm is both brave and not kind and vice versa.
If susan is either not curious or happy then someone is not wise or not funny and vice versa.
Everyone who is patient is both not kind and not quiet and vice versa.
Everyone who is either not calm or not creative is either rich or patient.
If someone is both strong and not old then john is both calm and not rich.
Everyone who is creative or not brave is not humble.
If someone is not old or not rich then someone is either not calm or not kind and vice versa.
Everyone who is patient is both curious and not curious and vice versa.
Everyone who is either strong or not old is kind or not wise and vice versa.
Everyone who is either calm or curious is not humble and vice versa.
If john is both wise and not tall then someone is both happy and tall and vice versa.
If alice is both not rich and creative then alice is not old or calm.
Lucy is either not happy or not old.
Someone is either patient or curious.
Someone is not tall.
Someone is either not generous or wise.
Someone is both not tall and brave.
Someone is not generous or not calm.
Someone is not wise or brave. | John is not kind. | neutral | (![X]:(~kind(X)=>(~wise(X)<~>funny(X))))&
((?[X]:((~curious(X)|~kind(X))))=>((~patient(alice)<~>quiet(alice))))&
(![X]:((~wise(X)<~>brave(X))<=>(~rich(X)<~>kind(X))))&
((~brave(paul))=>((funny(susan)<~>~calm(susan))))&
(![X]:((~humble(X)|calm(X))<=>(brave(X)&~kind(X))))&
(((~curious(susan)<~>happy(susan)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(patient(X)<=>(~kind(X)&~quiet(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(rich(X)<~>patient(X))))&
((?[X]:((strong(X)&~old(X))))=>((calm(john)&~rich(john))))&
(![X]:((creative(X)|~brave(X))=>~humble(X)))&
((?[X]:((~old(X)|~rich(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:(patient(X)<=>(curious(X)&~curious(X))))&
(![X]:((strong(X)<~>~old(X))<=>(kind(X)|~wise(X))))&
(![X]:((calm(X)<~>curious(X))<=>~humble(X)))&
(((wise(john)&~tall(john)))<=>(?[X]:((happy(X)&tall(X)))))&
(((~rich(alice)&creative(alice)))=>((~old(alice)|calm(alice))))&
((~happy(lucy)<~>~old(lucy)))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((~tall(X)&brave(X))))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((~wise(X)|brave(X)))) | ~kind(john) | [] | null | 0 |
Everyone who is not brave is both not brave and not creative.
Everyone who is both not tall and not humble is both not curious and not tall and vice versa.
Everyone who is not brave or not generous is both not kind and strong and vice versa.
Everyone who is both not humble and not generous is curious and vice versa.
Everyone who is wise is not strong.
Everyone who is both not calm and rich is not brave or calm.
Everyone who is not patient or rich is either not creative or not quiet and vice versa.
Everyone who is either not funny or not rich is quiet and vice versa.
If someone is not rich then someone is curious and vice versa.
Everyone who is both not funny and calm is funny or not patient.
If someone is not happy or not brave then someone is patient and vice versa.
Everyone who is not generous or kind is both not brave and not creative.
Everyone who is either not old or not creative is not old or not quiet.
Everyone who is not happy or not strong is either wise or not strong.
If john is not happy or not quiet then someone is either not quiet or wise.
Everyone who is both curious and strong is either strong or tall and vice versa.
John is not generous.
Someone is both not wise and not curious.
Someone is either generous or not tall.
Someone is not strong.
Someone is happy.
Paul is both not curious and brave.
Someone is either patient or not humble. | Paul is not tall. | entailment | (![X]:(~brave(X)=>(~brave(X)&~creative(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~curious(X)&~tall(X))))&
(![X]:((~brave(X)|~generous(X))<=>(~kind(X)&strong(X))))&
(![X]:((~humble(X)&~generous(X))<=>curious(X)))&
(![X]:(wise(X)=>~strong(X)))&
(![X]:((~calm(X)&rich(X))=>(~brave(X)|calm(X))))&
(![X]:((~patient(X)|rich(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>quiet(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(curious(X))))&
(![X]:((~funny(X)&calm(X))=>(funny(X)|~patient(X))))&
((?[X]:((~happy(X)|~brave(X))))<=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((~old(X)<~>~creative(X))=>(~old(X)|~quiet(X))))&
(![X]:((~happy(X)|~strong(X))=>(wise(X)<~>~strong(X))))&
(((~happy(john)|~quiet(john)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:((curious(X)&strong(X))<=>(strong(X)<~>tall(X))))&
(~generous(john))&
(?[X]:((~wise(X)&~curious(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:(~strong(X)))&
(?[X]:(happy(X)))&
((~curious(paul)&brave(paul)))&
(?[X]:((patient(X)<~>~humble(X)))) | ~tall(paul) | [
"p2",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5427737686038561618725612
% SZS output start Proof for 5427737686038561618725612
3. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> (strong(X0) & ~kind(X0))) [input p2]
12. ! [X0] : ((kind(X0) | ~generous(X0)) => (~creative(X0) & ~brave(X0))) [input p11]
16. ! [X0] : ((strong(X0) & curious(X0)) <=> (strong(X0) <~> tall(X0))) [input p15]
22. brave(paul) & ~curious(paul) [input p21]
24. tall(paul) [input hypothesis]
33. ! [X0] : ((~creative(X0) & ~brave(X0)) | (~kind(X0) & generous(X0))) [ennf transformation 12]
40. ! [X0] : (((~generous(X0) | ~brave(X0)) | (~strong(X0) | kind(X0))) & ((strong(X0) & ~kind(X0)) | (generous(X0) & brave(X0)))) [nnf transformation 3]
41. ! [X0] : ((~generous(X0) | ~brave(X0) | ~strong(X0) | kind(X0)) & ((strong(X0) & ~kind(X0)) | (generous(X0) & brave(X0)))) [flattening 40]
62. ! [X0] : (((strong(X0) & curious(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | (~strong(X0) | ~curious(X0)))) [nnf transformation 16]
63. ! [X0] : (((strong(X0) & curious(X0)) | ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | ~strong(X0) | ~curious(X0))) [flattening 62]
82. ~kind(X0) | brave(X0) [cnf transformation 41]
86. ~strong(X0) | ~brave(X0) | ~generous(X0) | kind(X0) [cnf transformation 41]
108. ~brave(X0) | generous(X0) [cnf transformation 33]
109. ~brave(X0) | ~kind(X0) [cnf transformation 33]
127. strong(X0) | strong(X0) | ~tall(X0) [cnf transformation 63]
136. brave(paul) [cnf transformation 22]
139. tall(paul) [cnf transformation 24]
141. ~tall(X0) | strong(X0) [duplicate literal removal 127]
186. ~kind(X0) [subsumption resolution 109,82]
231. generous(paul) [resolution 108,136]
234. strong(paul) [resolution 141,139]
315. ~brave(paul) | ~generous(paul) | kind(paul) [resolution 86,234]
317. ~generous(paul) | kind(paul) [subsumption resolution 315,136]
318. kind(paul) [subsumption resolution 317,231]
319. $false [subsumption resolution 318,186]
% SZS output end Proof for 5427737686038561618725612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not humble is either not creative or not humble and vice versa.
Everyone who is happy is either funny or wise and vice versa.
Everyone who is not old is generous.
If paul is both not happy and not calm then someone is both tall and not happy.
Everyone who is old or not funny is either rich or happy and vice versa.
If fred is tall or old then someone is either quiet or not quiet.
Everyone who is either not wise or happy is not brave and vice versa.
If susan is not quiet then someone is either old or strong.
If someone is either tall or generous then alice is both not humble and not tall.
Everyone who is generous or not tall is kind and vice versa.
Everyone who is either not patient or not funny is both not tall and patient and vice versa.
If someone is either rich or patient then someone is either happy or not funny and vice versa.
Everyone who is not creative or old is both wise and funny.
If someone is funny or tall then lucy is both not tall and old.
Everyone who is both not calm and kind is tall.
Everyone who is both rich and not wise is not creative.
Someone is happy or not old.
John is humble.
Fred is generous or not quiet.
Someone is either generous or not kind. | Lucy is not happy. | contradiction | (![X]:((happy(X)&~humble(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(happy(X)<=>(funny(X)<~>wise(X))))&
(![X]:(~old(X)=>generous(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((old(X)|~funny(X))<=>(rich(X)<~>happy(X))))&
(((tall(fred)|old(fred)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~brave(X)))&
((~quiet(susan))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((~humble(alice)&~tall(alice))))&
(![X]:((generous(X)|~tall(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~creative(X)|old(X))=>(wise(X)&funny(X))))&
((?[X]:((funny(X)|tall(X))))=>((~tall(lucy)&old(lucy))))&
(![X]:((~calm(X)&kind(X))=>tall(X)))&
(![X]:((rich(X)&~wise(X))=>~creative(X)))&
(?[X]:((happy(X)|~old(X))))&
(humble(john))&
((generous(fred)|~quiet(fred)))&
(?[X]:((generous(X)<~>~kind(X)))) | ~happy(lucy) | [
"p1",
"p4",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6198819407546655249795063
% SZS output start Proof for 6198819407546655249795063
2. ! [X0] : (happy(X0) <=> (funny(X0) <~> wise(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | old(X0)) <=> (rich(X0) <~> happy(X0))) [input p4]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (patient(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~creative(X0)) => (funny(X0) & wise(X0))) [input p12]
14. ? [X0] : (tall(X0) | funny(X0)) => (old(lucy) & ~tall(lucy)) [input p13]
16. ! [X0] : ((~wise(X0) & rich(X0)) => ~creative(X0)) [input p15]
21. ~happy(lucy) [input hypothesis]
29. ! [X0] : ((funny(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 13]
30. (old(lucy) & ~tall(lucy)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 14]
31. ! [X0] : (~creative(X0) | (wise(X0) | ~rich(X0))) [ennf transformation 16]
32. ! [X0] : (~creative(X0) | wise(X0) | ~rich(X0)) [flattening 31]
35. ! [X0] : ((happy(X0) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) & (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~happy(X0))) [nnf transformation 2]
36. ! [X0] : (((~funny(X0) | old(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [nnf transformation 5]
37. ! [X0] : ((~funny(X0) | old(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [flattening 36]
47. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
48. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 47]
65. ~happy(X0) | funny(X0) | wise(X0) [cnf transformation 35]
68. ~wise(X0) | funny(X0) | happy(X0) [cnf transformation 35]
71. rich(X0) | happy(X0) | funny(X0) [cnf transformation 37]
91. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 48]
93. ~funny(X0) | ~patient(X0) | ~patient(X0) | tall(X0) [cnf transformation 48]
103. wise(X0) | creative(X0) [cnf transformation 29]
106. ~old(X0) | funny(X0) [cnf transformation 29]
107. ~tall(lucy) | ~funny(X0) [cnf transformation 30]
109. old(lucy) | ~funny(X0) [cnf transformation 30]
111. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 32]
117. ~happy(lucy) [cnf transformation 21]
118. ~funny(X0) | patient(X0) [duplicate literal removal 91]
119. ~patient(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 93]
195. 17 <=> old(lucy) [avatar definition]
197. old(lucy) <- (17) [avatar component clause 195]
200. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
201. ~funny(X0) <- (18) [avatar component clause 200]
202. 18 | 17 [avatar split clause 109,195,200]
204. 19 <=> tall(lucy) [avatar definition]
206. ~tall(lucy) <- (~19) [avatar component clause 204]
208. 18 | ~19 [avatar split clause 107,204,200]
209. ~rich(X0) | wise(X0) [subsumption resolution 111,103]
243. funny(lucy) <- (17) [resolution 106,197]
247. patient(lucy) <- (17) [resolution 243,118]
281. happy(X0) | funny(X0) | wise(X0) [resolution 71,209]
283. wise(X0) | funny(X0) [subsumption resolution 281,65]
310. ~funny(lucy) | tall(lucy) <- (17) [resolution 119,247]
313. tall(lucy) <- (17) [subsumption resolution 310,243]
314. $false <- (17, ~19) [subsumption resolution 313,206]
315. ~17 | 19 [avatar contradiction clause 314]
334. funny(X0) | funny(X0) | happy(X0) [resolution 283,68]
336. funny(X0) | happy(X0) [duplicate literal removal 334]
337. happy(X0) <- (18) [subsumption resolution 336,201]
340. $false <- (18) [resolution 337,117]
343. ~18 [avatar contradiction clause 340]
344. $false [avatar sat refutation 202,208,315,343]
% SZS output end Proof for 6198819407546655249795063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not strong is both not wise and not happy.
If someone is either funny or strong then alice is not generous or calm.
If paul is either patient or not brave then someone is not strong.
Everyone who is calm or old is either strong or quiet and vice versa.
Everyone who is creative is both brave and not quiet and vice versa.
Everyone who is not wise is either not creative or not tall and vice versa.
If mary is either patient or not kind then lucy is happy or old and vice versa.
If susan is both not curious and not wise then john is either happy or not funny.
Everyone who is both not creative and curious is either brave or not brave and vice versa.
If fred is not generous then lucy is either tall or not calm.
If someone is not rich or not patient then someone is both funny and not quiet and vice versa.
Everyone who is both not kind and not generous is not wise or not funny.
If someone is not funny or calm then someone is kind or not creative and vice versa.
If someone is both not wise and generous then john is both not curious and strong.
Everyone who is both calm and not kind is both calm and curious.
Everyone who is both not kind and brave is not old or not quiet and vice versa.
Susan is either brave or creative.
Paul is either not quiet or quiet.
Someone is not happy or not calm.
Susan is either creative or not old.
Paul is either not quiet or not strong.
Lucy is both curious and funny.
Someone is either old or not generous. | Susan is quiet. | entailment | (![X]:((~funny(X)|~strong(X))=>(~wise(X)&~happy(X))))&
((?[X]:((funny(X)<~>strong(X))))=>((~generous(alice)|calm(alice))))&
(((patient(paul)<~>~brave(paul)))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|old(X))<=>(strong(X)<~>quiet(X))))&
(![X]:(creative(X)<=>(brave(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(~creative(X)<~>~tall(X))))&
(((patient(mary)<~>~kind(mary)))<=>((happy(lucy)|old(lucy))))&
(((~curious(susan)&~wise(susan)))=>((happy(john)<~>~funny(john))))&
(![X]:((~creative(X)&curious(X))<=>(brave(X)<~>~brave(X))))&
((~generous(fred))=>((tall(lucy)<~>~calm(lucy))))&
((?[X]:((~rich(X)|~patient(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(![X]:((~kind(X)&~generous(X))=>(~wise(X)|~funny(X))))&
((?[X]:((~funny(X)|calm(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((~wise(X)&generous(X))))=>((~curious(john)&strong(john))))&
(![X]:((calm(X)&~kind(X))=>(calm(X)&curious(X))))&
(![X]:((~kind(X)&brave(X))<=>(~old(X)|~quiet(X))))&
((brave(susan)<~>creative(susan)))&
((~quiet(paul)<~>quiet(paul)))&
(?[X]:((~happy(X)|~calm(X))))&
((creative(susan)<~>~old(susan)))&
((~quiet(paul)<~>~strong(paul)))&
((curious(lucy)&funny(lucy)))&
(?[X]:((old(X)<~>~generous(X)))) | quiet(susan) | [
"p4",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6995937902401651025552803
% SZS output start Proof for 6995937902401651025552803
5. ! [X0] : (creative(X0) <=> (~quiet(X0) & brave(X0))) [input p4]
9. ! [X0] : ((curious(X0) & ~creative(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p8]
17. brave(susan) <~> creative(susan) [input p16]
24. ~quiet(susan) [input hypothesis]
45. ! [X0] : ((creative(X0) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | ~creative(X0))) [nnf transformation 5]
46. ! [X0] : ((creative(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~creative(X0))) [flattening 45]
51. ! [X0] : (((curious(X0) & ~creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~curious(X0) | creative(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~curious(X0) | creative(X0))) [flattening 51]
66. (~creative(susan) | ~brave(susan)) & (creative(susan) | brave(susan)) [nnf transformation 17]
89. ~creative(X0) | brave(X0) [cnf transformation 46]
91. ~brave(X0) | quiet(X0) | creative(X0) [cnf transformation 46]
106. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
131. creative(susan) | brave(susan) [cnf transformation 66]
144. ~quiet(susan) [cnf transformation 24]
145. ~creative(X0) | ~brave(X0) [duplicate literal removal 106]
219. ~creative(X0) [subsumption resolution 145,89]
289. brave(susan) [subsumption resolution 131,219]
339. quiet(susan) | creative(susan) [resolution 91,289]
342. creative(susan) [subsumption resolution 339,144]
343. $false [subsumption resolution 342,219]
% SZS output end Proof for 6995937902401651025552803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or curious then someone is kind. If mary is either not patient or not generous then paul is either not patient or brave and vice versa. Everyone who is funny or humble is either not happy or brave and vice versa. Everyone who is both not quiet and patient is patient or not humble and vice versa. If fred is not generous or patient then mary is both not wise and not rich. If fred is rich or not calm then someone is either calm or happy and vice versa. Everyone who is not quiet is both wise and not funny and vice versa. If mary is not brave then mary is humble or not calm and vice versa. If someone is not brave or not humble then lucy is either wise or not quiet and vice versa. If someone is not quiet then alice is calm. Everyone who is both not rich and curious is both not strong and not calm and vice versa. If lucy is either humble or not wise then someone is both not calm and not rich. Everyone who is either tall or happy is tall. If susan is not humble then someone is not calm or not happy. Everyone who is not old is both strong and generous. If someone is funny or patient then someone is both not wise and not curious and vice versa. Fred is not humble. Fred is both happy and creative. Someone is either humble or brave. Someone is not funny or curious. Susan is not humble or creative. Someone is not rich or curious. Someone is both generous and quiet. Someone is strong or funny. | Lucy is humble. | entailment | ((?[X]:((kind(X)|curious(X))))=>(?[X]:(kind(X))))&
(((~patient(mary)<~>~generous(mary)))<=>((~patient(paul)<~>brave(paul))))&
(![X]:((funny(X)|humble(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~quiet(X)&patient(X))<=>(patient(X)|~humble(X))))&
(((~generous(fred)|patient(fred)))=>((~wise(mary)&~rich(mary))))&
(((rich(fred)|~calm(fred)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(~quiet(X)<=>(wise(X)&~funny(X))))&
((~brave(mary))<=>((humble(mary)|~calm(mary))))&
((?[X]:((~brave(X)|~humble(X))))<=>((wise(lucy)<~>~quiet(lucy))))&
((?[X]:(~quiet(X)))=>(calm(alice)))&
(![X]:((~rich(X)&curious(X))<=>(~strong(X)&~calm(X))))&
(((humble(lucy)<~>~wise(lucy)))=>(?[X]:((~calm(X)&~rich(X)))))&
(![X]:((tall(X)<~>happy(X))=>tall(X)))&
((~humble(susan))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~old(X)=>(strong(X)&generous(X))))&
((?[X]:((funny(X)|patient(X))))<=>(?[X]:((~wise(X)&~curious(X)))))&
(~humble(fred))&
((happy(fred)&creative(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((~funny(X)|curious(X))))&
((~humble(susan)|creative(susan)))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:((generous(X)&quiet(X))))&
(?[X]:((strong(X)|funny(X)))) | humble(lucy) | [
"p3",
"p6",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4150218984719201623929409
% SZS output start Proof for 4150218984719201623929409
4. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (~humble(X0) | patient(X0))) [input p3]
7. ! [X0] : (~quiet(X0) <=> (~funny(X0) & wise(X0))) [input p6]
9. ? [X0] : (~humble(X0) | ~brave(X0)) <=> (wise(lucy) <~> ~quiet(lucy)) [input p8]
17. ~humble(fred) [input p16]
25. ~humble(lucy) [input hypothesis]
43. ! [X0] : (((patient(X0) & ~quiet(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (~patient(X0) | quiet(X0)))) [nnf transformation 4]
44. ! [X0] : (((patient(X0) & ~quiet(X0)) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | ~patient(X0) | quiet(X0))) [flattening 43]
50. ! [X0] : ((~quiet(X0) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | quiet(X0))) [nnf transformation 7]
51. ! [X0] : ((~quiet(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | quiet(X0))) [flattening 50]
54. (? [X0] : (~humble(X0) | ~brave(X0)) | ((wise(lucy) | quiet(lucy)) & (~quiet(lucy) | ~wise(lucy)))) & (((quiet(lucy) | ~wise(lucy)) & (~quiet(lucy) | wise(lucy))) | ! [X0] : (humble(X0) & brave(X0))) [nnf transformation 9]
55. (? [X0] : (~humble(X0) | ~brave(X0)) | ((wise(lucy) | quiet(lucy)) & (~quiet(lucy) | ~wise(lucy)))) & (((quiet(lucy) | ~wise(lucy)) & (~quiet(lucy) | wise(lucy))) | ! [X1] : (humble(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (~humble(X0) | ~brave(X0)) => (~humble(sK2) | ~brave(sK2)) [choice axiom]
57. ((~humble(sK2) | ~brave(sK2)) | ((wise(lucy) | quiet(lucy)) & (~quiet(lucy) | ~wise(lucy)))) & (((quiet(lucy) | ~wise(lucy)) & (~quiet(lucy) | wise(lucy))) | ! [X1] : (humble(X1) & brave(X1))) [skolemisation 55,56]
100. ~quiet(X0) | humble(X0) [cnf transformation 44]
113. wise(X0) | quiet(X0) [cnf transformation 51]
122. quiet(lucy) | ~wise(lucy) | humble(X1) [cnf transformation 57]
142. ~humble(fred) [cnf transformation 17]
151. ~humble(lucy) [cnf transformation 25]
257. 22 <=> quiet(lucy) [avatar definition]
258. quiet(lucy) <- (22) [avatar component clause 257]
269. quiet(lucy) | humble(X1) [subsumption resolution 122,113]
271. 25 <=> ! [X1] : humble(X1) [avatar definition]
272. humble(X1) <- (25) [avatar component clause 271]
273. 25 | 22 [avatar split clause 269,257,271]
292. 29 <=> humble(lucy) [avatar definition]
293. ~humble(lucy) <- (~29) [avatar component clause 292]
387. ~29 [avatar split clause 151,292]
393. humble(lucy) <- (22) [resolution 100,258]
394. $false <- (22, ~29) [subsumption resolution 393,293]
395. ~22 | 29 [avatar contradiction clause 394]
396. $false <- (25) [resolution 272,142]
401. ~25 [avatar contradiction clause 396]
402. $false [avatar sat refutation 273,387,395,401]
% SZS output end Proof for 4150218984719201623929409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is both not tall and not curious. Everyone who is either strong or wise is not wise or not kind and vice versa. If someone is calm then susan is both rich and wise. If someone is not calm then john is kind or quiet. Everyone who is either not humble or not strong is both tall and funny and vice versa. If lucy is old or generous then mary is both not humble and strong and vice versa. Everyone who is not calm or tall is not calm or curious and vice versa. Everyone who is both not tall and strong is quiet or strong and vice versa. If alice is tall or not patient then fred is not rich and vice versa. If fred is both wise and not creative then someone is not creative or not strong and vice versa. If someone is either old or not generous then fred is not wise. If someone is rich then paul is humble. If lucy is both not strong and curious then mary is either not strong or not wise. Everyone who is kind is both tall and brave and vice versa. If lucy is wise then someone is quiet. Everyone who is either not quiet or kind is not old. Someone is both creative and not brave. Susan is either generous or tall. Paul is either not kind or not brave. Lucy is either generous or humble. Someone is both not kind and not old. Susan is either patient or rich. | Mary is humble. | entailment | (![X]:((patient(X)|~calm(X))=>(~tall(X)&~curious(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:(calm(X)))=>((rich(susan)&wise(susan))))&
((?[X]:(~calm(X)))=>((kind(john)|quiet(john))))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((~humble(mary)&strong(mary))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|curious(X))))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|strong(X))))&
(((tall(alice)|~patient(alice)))<=>(~rich(fred)))&
(((wise(fred)&~creative(fred)))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)<~>~generous(X))))=>(~wise(fred)))&
((?[X]:(rich(X)))=>(humble(paul)))&
(((~strong(lucy)&curious(lucy)))=>((~strong(mary)<~>~wise(mary))))&
(![X]:(kind(X)<=>(tall(X)&brave(X))))&
((wise(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~old(X)))&
(?[X]:((creative(X)&~brave(X))))&
((generous(susan)<~>tall(susan)))&
((~kind(paul)<~>~brave(paul)))&
((generous(lucy)<~>humble(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
((patient(susan)<~>rich(susan))) | humble(mary) | [
"p4",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6294777985970261934690065
% SZS output start Proof for 6294777985970261934690065
5. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (funny(X0) & tall(X0))) [input p4]
6. (generous(lucy) | old(lucy)) <=> (strong(mary) & ~humble(mary)) [input p5]
8. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (strong(X0) | quiet(X0))) [input p7]
10. (~creative(fred) & wise(fred)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p9]
11. ? [X0] : (old(X0) <~> ~generous(X0)) => ~wise(fred) [input p10]
23. ~humble(mary) [input hypothesis]
28. ~wise(fred) | ! [X0] : (old(X0) <=> ~generous(X0)) [ennf transformation 11]
36. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 5]
37. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 36]
38. ((generous(lucy) | old(lucy)) | (~strong(mary) | humble(mary))) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [nnf transformation 6]
39. (generous(lucy) | old(lucy) | ~strong(mary) | humble(mary)) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [flattening 38]
42. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 8]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | ~strong(X0) | tall(X0))) [flattening 42]
46. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | (creative(fred) | ~wise(fred))) [nnf transformation 10]
47. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | creative(fred) | ~wise(fred)) [flattening 46]
48. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X1] : (~strong(X1) | ~creative(X1)) | creative(fred) | ~wise(fred)) [rectify 47]
49. ? [X1] : (~strong(X1) | ~creative(X1)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
50. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & ((~strong(sK0) | ~creative(sK0)) | creative(fred) | ~wise(fred)) [skolemisation 48,49]
51. ~wise(fred) | ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 28]
79. ~strong(X0) | tall(X0) | humble(X0) [cnf transformation 37]
87. strong(mary) | ~old(lucy) [cnf transformation 39]
88. strong(mary) | ~generous(lucy) [cnf transformation 39]
96. ~strong(X0) | ~tall(X0) [cnf transformation 43]
104. wise(fred) | strong(X0) [cnf transformation 50]
108. ~wise(fred) | old(X0) | generous(X0) [cnf transformation 51]
130. ~humble(mary) [cnf transformation 23]
160. 7 <=> humble(mary) [avatar definition]
161. ~humble(mary) <- (~7) [avatar component clause 160]
164. 8 <=> strong(mary) [avatar definition]
165. strong(mary) <- (8) [avatar component clause 164]
166. ~strong(mary) <- (~8) [avatar component clause 164]
168. 9 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~9) [avatar component clause 168]
172. 10 <=> generous(lucy) [avatar definition]
173. ~generous(lucy) <- (~10) [avatar component clause 172]
176. ~10 | 8 [avatar split clause 88,164,172]
177. ~9 | 8 [avatar split clause 87,164,168]
199. 14 <=> ! [X0] : strong(X0) [avatar definition]
200. strong(X0) <- (14) [avatar component clause 199]
211. 17 <=> wise(fred) [avatar definition]
214. 14 | 17 [avatar split clause 104,211,199]
226. 20 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
227. generous(X0) | old(X0) <- (20) [avatar component clause 226]
228. 20 | ~17 [avatar split clause 108,211,226]
287. ~7 [avatar split clause 130,160]
321. tall(mary) | humble(mary) <- (8) [resolution 165,79]
322. ~tall(mary) <- (8) [resolution 165,96]
323. tall(mary) <- (~7, 8) [subsumption resolution 321,161]
324. $false <- (~7, 8) [subsumption resolution 322,323]
325. 7 | ~8 [avatar contradiction clause 324]
338. old(lucy) <- (~10, 20) [resolution 227,173]
339. $false <- (~9, ~10, 20) [subsumption resolution 338,169]
340. 9 | 10 | ~20 [avatar contradiction clause 339]
344. $false <- (~8, 14) [resolution 200,166]
347. 8 | ~14 [avatar contradiction clause 344]
349. $false [avatar sat refutation 176,177,214,228,287,325,340,347]
% SZS output end Proof for 6294777985970261934690065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not kind or not brave and vice versa.
If paul is either not calm or calm then someone is either strong or not funny.
Everyone who is either old or happy is either humble or not kind and vice versa.
Everyone who is both kind and not patient is not humble and vice versa.
Everyone who is either calm or kind is not humble and vice versa.
Everyone who is both funny and not old is both not kind and rich.
If susan is both old and not happy then mary is both not calm and not humble.
Everyone who is not calm or not old is generous or not rich and vice versa.
Everyone who is not kind or not creative is both kind and not brave and vice versa.
If john is both not happy and not patient then someone is not humble.
If paul is both not funny and creative then mary is both not strong and not funny.
Everyone who is either strong or curious is not strong.
Everyone who is both not kind and strong is either wise or not humble.
If someone is both not kind and funny then someone is both not happy and calm and vice versa.
Everyone who is not rich is funny or quiet.
Everyone who is generous or not kind is both wise and rich and vice versa.
Someone is quiet.
Someone is both wise and not creative.
Someone is not kind or old.
Someone is either not old or quiet.
Someone is old or not happy.
John is both not rich and not funny.
Paul is either not quiet or not wise. | John is kind. | entailment | (![X]:(quiet(X)<=>(~kind(X)|~brave(X))))&
(((~calm(paul)<~>calm(paul)))=>(?[X]:((strong(X)<~>~funny(X)))))&
(![X]:((old(X)<~>happy(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((kind(X)&~patient(X))<=>~humble(X)))&
(![X]:((calm(X)<~>kind(X))<=>~humble(X)))&
(![X]:((funny(X)&~old(X))=>(~kind(X)&rich(X))))&
(((old(susan)&~happy(susan)))=>((~calm(mary)&~humble(mary))))&
(![X]:((~calm(X)|~old(X))<=>(generous(X)|~rich(X))))&
(![X]:((~kind(X)|~creative(X))<=>(kind(X)&~brave(X))))&
(((~happy(john)&~patient(john)))=>(?[X]:(~humble(X))))&
(((~funny(paul)&creative(paul)))=>((~strong(mary)&~funny(mary))))&
(![X]:((strong(X)<~>curious(X))=>~strong(X)))&
(![X]:((~kind(X)&strong(X))=>(wise(X)<~>~humble(X))))&
((?[X]:((~kind(X)&funny(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(~rich(X)=>(funny(X)|quiet(X))))&
(![X]:((generous(X)|~kind(X))<=>(wise(X)&rich(X))))&
(?[X]:(quiet(X)))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
(?[X]:((old(X)|~happy(X))))&
((~rich(john)&~funny(john)))&
((~quiet(paul)<~>~wise(paul))) | kind(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3403678250252227097394215
% SZS output start Proof for 3403678250252227097394215
9. ! [X0] : ((~creative(X0) | ~kind(X0)) <=> (~brave(X0) & kind(X0))) [input p8]
24. ~kind(john) [input hypothesis]
51. ! [X0] : (((~creative(X0) | ~kind(X0)) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | (creative(X0) & kind(X0)))) [nnf transformation 9]
52. ! [X0] : ((~creative(X0) | ~kind(X0) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | (creative(X0) & kind(X0)))) [flattening 51]
106. kind(X0) | kind(X0) [cnf transformation 52]
139. ~kind(john) [cnf transformation 24]
141. kind(X0) [duplicate literal removal 106]
255. $false [subsumption resolution 139,141]
% SZS output end Proof for 3403678250252227097394215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or tall is creative and vice versa.
If lucy is not generous or funny then susan is not wise.
Everyone who is either brave or not quiet is both quiet and curious.
If someone is both creative and not strong then john is either creative or quiet and vice versa.
If someone is not happy or not brave then someone is not old or quiet.
If someone is either not curious or not old then someone is either not patient or tall and vice versa.
Everyone who is not generous or generous is not rich.
Everyone who is rich is both not funny and not quiet and vice versa.
If alice is not patient or not strong then lucy is both funny and not quiet and vice versa.
Everyone who is kind or not wise is funny and vice versa.
Everyone who is both not old and strong is both funny and not generous and vice versa.
If john is both patient and not kind then someone is either not wise or humble and vice versa.
Everyone who is not calm is not brave or not strong.
Everyone who is funny is both wise and not wise.
If someone is not rich then someone is brave.
Everyone who is happy is either not generous or not rich and vice versa.
Paul is not kind or not strong.
Someone is brave.
Someone is either creative or not rich.
Someone is both curious and tall.
John is not brave or not quiet.
Paul is rich or not kind.
Paul is both strong and tall. | Alice is not strong. | contradiction | (![X]:((~old(X)<~>tall(X))<=>creative(X)))&
(((~generous(lucy)|funny(lucy)))=>(~wise(susan)))&
(![X]:((brave(X)<~>~quiet(X))=>(quiet(X)&curious(X))))&
((?[X]:((creative(X)&~strong(X))))<=>((creative(john)<~>quiet(john))))&
((?[X]:((~happy(X)|~brave(X))))=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((~curious(X)<~>~old(X))))<=>(?[X]:((~patient(X)<~>tall(X)))))&
(![X]:((~generous(X)|generous(X))=>~rich(X)))&
(![X]:(rich(X)<=>(~funny(X)&~quiet(X))))&
(((~patient(alice)|~strong(alice)))<=>((funny(lucy)&~quiet(lucy))))&
(![X]:((kind(X)|~wise(X))<=>funny(X)))&
(![X]:((~old(X)&strong(X))<=>(funny(X)&~generous(X))))&
(((patient(john)&~kind(john)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(~calm(X)=>(~brave(X)|~strong(X))))&
(![X]:(funny(X)=>(wise(X)&~wise(X))))&
((?[X]:(~rich(X)))=>(?[X]:(brave(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>~rich(X))))&
((~kind(paul)|~strong(paul)))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)<~>~rich(X))))&
(?[X]:((curious(X)&tall(X))))&
((~brave(john)|~quiet(john)))&
((rich(paul)|~kind(paul)))&
((strong(paul)&tall(paul))) | ~strong(alice) | [
"p1",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1536075413700039654419199
% SZS output start Proof for 1536075413700039654419199
2. (funny(lucy) | ~generous(lucy)) => ~wise(susan) [input p1]
9. (~strong(alice) | ~patient(alice)) <=> (~quiet(lucy) & funny(lucy)) [input p8]
10. ! [X0] : ((~wise(X0) | kind(X0)) <=> funny(X0)) [input p9]
14. ! [X0] : (funny(X0) => (~wise(X0) & wise(X0))) [input p13]
24. ~strong(alice) [input hypothesis]
30. ~wise(susan) | (~funny(lucy) & generous(lucy)) [ennf transformation 2]
34. ! [X0] : ((~wise(X0) & wise(X0)) | ~funny(X0)) [ennf transformation 14]
53. ((~strong(alice) | ~patient(alice)) | (quiet(lucy) | ~funny(lucy))) & ((~quiet(lucy) & funny(lucy)) | (strong(alice) & patient(alice))) [nnf transformation 9]
54. (~strong(alice) | ~patient(alice) | quiet(lucy) | ~funny(lucy)) & ((~quiet(lucy) & funny(lucy)) | (strong(alice) & patient(alice))) [flattening 53]
55. ! [X0] : (((~wise(X0) | kind(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) & ~kind(X0)))) [nnf transformation 10]
56. ! [X0] : ((~wise(X0) | kind(X0) | ~funny(X0)) & (funny(X0) | (wise(X0) & ~kind(X0)))) [flattening 55]
80. ~wise(susan) | ~funny(lucy) [cnf transformation 30]
107. funny(lucy) | strong(alice) [cnf transformation 54]
112. funny(X0) | wise(X0) [cnf transformation 56]
124. wise(X0) | ~funny(X0) [cnf transformation 34]
139. ~strong(alice) [cnf transformation 24]
142. 1 <=> funny(lucy) [avatar definition]
146. 2 <=> wise(susan) [avatar definition]
148. ~wise(susan) <- (~2) [avatar component clause 146]
149. ~1 | ~2 [avatar split clause 80,146,142]
244. 23 <=> strong(alice) [avatar definition]
250. 23 | 1 [avatar split clause 107,142,244]
280. wise(X0) [subsumption resolution 124,112]
301. ~23 [avatar split clause 139,244]
303. $false <- (~2) [subsumption resolution 148,280]
304. 2 [avatar contradiction clause 303]
305. $false [avatar sat refutation 149,250,301,304]
% SZS output end Proof for 1536075413700039654419199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not calm and vice versa. If someone is both tall and patient then john is curious and vice versa. Everyone who is either generous or not humble is either tall or funny. Everyone who is not quiet or humble is both old and not calm and vice versa. If someone is curious then someone is funny and vice versa. Everyone who is not funny or generous is both not old and not generous. If lucy is wise or not patient then someone is patient. Everyone who is both humble and not kind is either not wise or not quiet and vice versa. If alice is both happy and not strong then someone is rich or not brave. Everyone who is quiet is both creative and not creative. Everyone who is humble or wise is rich or not quiet and vice versa. If john is either not funny or not calm then someone is old and vice versa. Everyone who is brave is either humble or rich and vice versa. If someone is not humble then mary is not old or generous. Everyone who is happy or not strong is kind. Everyone who is both not brave and not creative is not creative or wise. Someone is either patient or not creative. Susan is calm or strong. Susan is not old or not tall. Someone is not funny or not brave. Someone is tall or patient. Someone is either not funny or not quiet. | Mary is creative. | neutral | (![X]:(~tall(X)<=>~calm(X)))&
((?[X]:((tall(X)&patient(X))))<=>(curious(john)))&
(![X]:((generous(X)<~>~humble(X))=>(tall(X)<~>funny(X))))&
(![X]:((~quiet(X)|humble(X))<=>(old(X)&~calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)|generous(X))=>(~old(X)&~generous(X))))&
(((wise(lucy)|~patient(lucy)))=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~kind(X))<=>(~wise(X)<~>~quiet(X))))&
(((happy(alice)&~strong(alice)))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:(quiet(X)=>(creative(X)&~creative(X))))&
(![X]:((humble(X)|wise(X))<=>(rich(X)|~quiet(X))))&
(((~funny(john)<~>~calm(john)))<=>(?[X]:(old(X))))&
(![X]:(brave(X)<=>(humble(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>((~old(mary)|generous(mary))))&
(![X]:((happy(X)|~strong(X))=>kind(X)))&
(![X]:((~brave(X)&~creative(X))=>(~creative(X)|wise(X))))&
(?[X]:((patient(X)<~>~creative(X))))&
((calm(susan)|strong(susan)))&
((~old(susan)|~tall(susan)))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~funny(X)<~>~quiet(X)))) | creative(mary) | [] | null | 0 |
If someone is humble or funny then someone is not tall.
Everyone who is both happy and not generous is either not wise or not happy and vice versa.
If susan is not tall or not funny then lucy is either creative or not creative and vice versa.
Everyone who is either old or quiet is not patient or curious and vice versa.
Everyone who is both not quiet and not rich is both patient and not tall.
Everyone who is not wise or calm is both not generous and calm and vice versa.
Everyone who is either quiet or not calm is brave or curious.
Everyone who is both humble and not wise is not calm or patient and vice versa.
If fred is wise or happy then someone is old or brave and vice versa.
If lucy is both quiet and not brave then paul is not tall or curious.
Everyone who is both rich and patient is not calm.
Everyone who is calm is both tall and quiet.
Everyone who is not strong or creative is not humble and vice versa.
Everyone who is strong or generous is either not humble or wise.
Paul is strong or not brave.
Fred is either not funny or not strong.
Someone is either not curious or not humble.
Someone is not creative.
Lucy is either calm or old.
Someone is either old or not happy. | Lucy is creative. | neutral | ((?[X]:((humble(X)|funny(X))))=>(?[X]:(~tall(X))))&
(![X]:((happy(X)&~generous(X))<=>(~wise(X)<~>~happy(X))))&
(((~tall(susan)|~funny(susan)))<=>((creative(lucy)<~>~creative(lucy))))&
(![X]:((old(X)<~>quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~quiet(X)&~rich(X))=>(patient(X)&~tall(X))))&
(![X]:((~wise(X)|calm(X))<=>(~generous(X)&calm(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(brave(X)|curious(X))))&
(![X]:((humble(X)&~wise(X))<=>(~calm(X)|patient(X))))&
(((wise(fred)|happy(fred)))<=>(?[X]:((old(X)|brave(X)))))&
(((quiet(lucy)&~brave(lucy)))=>((~tall(paul)|curious(paul))))&
(![X]:((rich(X)&patient(X))=>~calm(X)))&
(![X]:(calm(X)=>(tall(X)&quiet(X))))&
(![X]:((~strong(X)|creative(X))<=>~humble(X)))&
(![X]:((strong(X)|generous(X))=>(~humble(X)<~>wise(X))))&
((strong(paul)|~brave(paul)))&
((~funny(fred)<~>~strong(fred)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~creative(X)))&
((calm(lucy)<~>old(lucy)))&
(?[X]:((old(X)<~>~happy(X)))) | creative(lucy) | [] | null | 0 |
If someone is either not happy or not quiet then susan is both not old and kind and vice versa.
If lucy is quiet or not tall then someone is not funny.
Everyone who is not calm or not quiet is generous and vice versa.
Everyone who is curious is not curious.
Everyone who is both not kind and generous is strong or calm and vice versa.
Everyone who is not strong is not strong or not brave and vice versa.
If someone is both humble and rich then someone is either brave or curious and vice versa.
Everyone who is generous is either calm or not calm.
If john is not generous then alice is kind or not old and vice versa.
If someone is tall or not funny then someone is either not tall or not brave and vice versa.
If susan is either not patient or curious then someone is either kind or not rich.
If someone is both not kind and not wise then john is both not quiet and not rich.
If someone is not generous or not calm then lucy is not kind.
If someone is either generous or not strong then paul is not kind and vice versa.
Someone is both not humble and creative.
Lucy is funny.
Someone is either not quiet or wise.
John is both calm and funny.
Someone is both humble and quiet.
Mary is both not quiet and not humble.
Alice is both not curious and tall. | Paul is not curious. | entailment | ((?[X]:((~happy(X)<~>~quiet(X))))<=>((~old(susan)&kind(susan))))&
(((quiet(lucy)|~tall(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)|~quiet(X))<=>generous(X)))&
(![X]:(curious(X)=>~curious(X)))&
(![X]:((~kind(X)&generous(X))<=>(strong(X)|calm(X))))&
(![X]:(~strong(X)<=>(~strong(X)|~brave(X))))&
((?[X]:((humble(X)&rich(X))))<=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:(generous(X)=>(calm(X)<~>~calm(X))))&
((~generous(john))<=>((kind(alice)|~old(alice))))&
((?[X]:((tall(X)|~funny(X))))<=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~patient(susan)<~>curious(susan)))=>(?[X]:((kind(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&~wise(X))))=>((~quiet(john)&~rich(john))))&
((?[X]:((~generous(X)|~calm(X))))=>(~kind(lucy)))&
((?[X]:((generous(X)<~>~strong(X))))<=>(~kind(paul)))&
(?[X]:((~humble(X)&creative(X))))&
(funny(lucy))&
(?[X]:((~quiet(X)<~>wise(X))))&
((calm(john)&funny(john)))&
(?[X]:((humble(X)&quiet(X))))&
((~quiet(mary)&~humble(mary)))&
((~curious(alice)&tall(alice))) | ~curious(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3363322358389630905125164
% SZS output start Proof for 3363322358389630905125164
4. ! [X0] : (curious(X0) => ~curious(X0)) [input p3]
22. curious(paul) [input hypothesis]
27. ! [X0] : (~curious(X0) | ~curious(X0)) [ennf transformation 4]
83. ~curious(X0) | ~curious(X0) [cnf transformation 27]
133. curious(paul) [cnf transformation 22]
134. ~curious(X0) [duplicate literal removal 83]
301. $false [subsumption resolution 133,134]
% SZS output end Proof for 3363322358389630905125164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is humble. Everyone who is both happy and calm is both happy and not rich. Everyone who is both brave and not humble is not brave. Everyone who is both not rich and kind is not creative or not happy and vice versa. If someone is either not brave or creative then someone is brave. Everyone who is funny is quiet or not curious and vice versa. Everyone who is funny is not creative and vice versa. If someone is quiet then paul is not curious or kind and vice versa. Everyone who is not kind or not brave is rich. If lucy is tall then someone is creative. Everyone who is either not creative or not old is both funny and creative and vice versa. Everyone who is not creative is kind or not generous and vice versa. If lucy is either old or not rich then paul is either not funny or not humble and vice versa. If mary is either not tall or tall then susan is not quiet and vice versa. If someone is both not patient and creative then someone is either not happy or not curious. Everyone who is calm is either quiet or strong. Fred is either rich or not strong. Someone is not kind or curious. Someone is happy. Someone is either brave or creative. Susan is rich or not funny. Someone is both not curious and not rich. Alice is both wise and not humble. Susan is both happy and rich. | Mary is not quiet. | entailment | ((kind(susan))=>(?[X]:(humble(X))))&
(![X]:((happy(X)&calm(X))=>(happy(X)&~rich(X))))&
(![X]:((brave(X)&~humble(X))=>~brave(X)))&
(![X]:((~rich(X)&kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((?[X]:(quiet(X)))<=>((~curious(paul)|kind(paul))))&
(![X]:((~kind(X)|~brave(X))=>rich(X)))&
((tall(lucy))=>(?[X]:(creative(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(funny(X)&creative(X))))&
(![X]:(~creative(X)<=>(kind(X)|~generous(X))))&
(((old(lucy)<~>~rich(lucy)))<=>((~funny(paul)<~>~humble(paul))))&
(((~tall(mary)<~>tall(mary)))<=>(~quiet(susan)))&
((?[X]:((~patient(X)&creative(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:(calm(X)=>(quiet(X)<~>strong(X))))&
((rich(fred)<~>~strong(fred)))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>creative(X))))&
((rich(susan)|~funny(susan)))&
(?[X]:((~curious(X)&~rich(X))))&
((wise(alice)&~humble(alice)))&
((happy(susan)&rich(susan))) | ~quiet(mary) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2189207420947139061567154
% SZS output start Proof for 2189207420947139061567154
3. ! [X0] : ((~humble(X0) & brave(X0)) => ~brave(X0)) [input p2]
4. ! [X0] : ((kind(X0) & ~rich(X0)) <=> (~happy(X0) | ~creative(X0))) [input p3]
6. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p5]
7. ! [X0] : (funny(X0) <=> ~creative(X0)) [input p6]
8. ? [X0] : quiet(X0) <=> (kind(paul) | ~curious(paul)) [input p7]
9. ! [X0] : ((~brave(X0) | ~kind(X0)) => rich(X0)) [input p8]
11. ! [X0] : ((~creative(X0) <~> ~old(X0)) <=> (creative(X0) & funny(X0))) [input p10]
12. ! [X0] : (~creative(X0) <=> (~generous(X0) | kind(X0))) [input p11]
13. (old(lucy) <~> ~rich(lucy)) <=> (~funny(paul) <~> ~humble(paul)) [input p12]
25. quiet(mary) [input hypothesis]
33. ! [X0] : (~brave(X0) | (humble(X0) | ~brave(X0))) [ennf transformation 3]
34. ! [X0] : (~brave(X0) | humble(X0) | ~brave(X0)) [flattening 33]
36. ! [X0] : (rich(X0) | (brave(X0) & kind(X0))) [ennf transformation 9]
40. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~kind(X0) | rich(X0)))) [nnf transformation 4]
41. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~kind(X0) | rich(X0))) [flattening 40]
46. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 6]
47. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 46]
48. ! [X0] : ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))) [nnf transformation 7]
49. (? [X0] : quiet(X0) | (~kind(paul) & curious(paul))) & ((kind(paul) | ~curious(paul)) | ! [X0] : ~quiet(X0)) [nnf transformation 8]
50. (? [X0] : quiet(X0) | (~kind(paul) & curious(paul))) & (kind(paul) | ~curious(paul) | ! [X0] : ~quiet(X0)) [flattening 49]
51. (? [X0] : quiet(X0) | (~kind(paul) & curious(paul))) & (kind(paul) | ~curious(paul) | ! [X1] : ~quiet(X1)) [rectify 50]
52. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
53. (quiet(sK2) | (~kind(paul) & curious(paul))) & (kind(paul) | ~curious(paul) | ! [X1] : ~quiet(X1)) [skolemisation 51,52]
56. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [nnf transformation 11]
57. ! [X0] : ((((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0))))) [flattening 56]
58. ! [X0] : ((~creative(X0) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | creative(X0))) [nnf transformation 12]
59. ! [X0] : ((~creative(X0) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | creative(X0))) [flattening 58]
60. (((rich(lucy) | ~old(lucy)) & (~rich(lucy) | old(lucy))) | ((~funny(paul) | humble(paul)) & (~humble(paul) | funny(paul)))) & (((humble(paul) | funny(paul)) & (~humble(paul) | ~funny(paul))) | ((old(lucy) | rich(lucy)) & (~rich(lucy) | ~old(lucy)))) [nnf transformation 13]
73. ~brave(X0) | humble(X0) | ~brave(X0) [cnf transformation 34]
75. ~rich(X0) | creative(X0) [cnf transformation 41]
83. curious(X0) | funny(X0) [cnf transformation 47]
84. ~funny(X0) | ~creative(X0) [cnf transformation 48]
85. funny(X0) | creative(X0) [cnf transformation 48]
86. kind(paul) | ~curious(paul) | ~quiet(X1) [cnf transformation 53]
89. rich(X0) | kind(X0) [cnf transformation 36]
90. brave(X0) | rich(X0) [cnf transformation 36]
93. funny(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
94. creative(X0) | ~old(X0) | creative(X0) [cnf transformation 57]
99. ~creative(X0) | ~kind(X0) [cnf transformation 59]
101. ~humble(paul) | ~funny(paul) | ~rich(lucy) | ~old(lucy) [cnf transformation 60]
102. ~humble(paul) | ~funny(paul) | old(lucy) | rich(lucy) [cnf transformation 60]
125. quiet(mary) [cnf transformation 25]
128. ~old(X0) | creative(X0) [duplicate literal removal 94]
130. ~brave(X0) | humble(X0) [duplicate literal removal 73]
153. 6 <=> kind(paul) [avatar definition]
162. 8 <=> curious(paul) [avatar definition]
163. ~curious(paul) <- (~8) [avatar component clause 162]
167. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
168. ~quiet(X1) <- (9) [avatar component clause 167]
169. 9 | ~8 | 6 [avatar split clause 86,153,162,167]
179. old(X0) | funny(X0) [subsumption resolution 93,85]
181. 12 <=> humble(paul) [avatar definition]
185. 13 <=> funny(paul) [avatar definition]
186. funny(paul) <- (13) [avatar component clause 185]
187. ~funny(paul) <- (~13) [avatar component clause 185]
189. 14 <=> old(lucy) [avatar definition]
190. old(lucy) <- (14) [avatar component clause 189]
191. ~old(lucy) <- (~14) [avatar component clause 189]
193. 15 <=> rich(lucy) [avatar definition]
194. ~rich(lucy) <- (~15) [avatar component clause 193]
195. rich(lucy) <- (15) [avatar component clause 193]
202. 15 | 14 | ~13 | ~12 [avatar split clause 102,181,185,189,193]
203. ~14 | ~15 | ~13 | ~12 [avatar split clause 101,181,185,193,189]
259. funny(paul) <- (~8) [resolution 83,163]
260. $false <- (~8, ~13) [subsumption resolution 259,187]
261. 8 | 13 [avatar contradiction clause 260]
264. creative(paul) <- (~13) [resolution 85,187]
269. kind(lucy) <- (~15) [resolution 89,194]
274. ~kind(paul) <- (~13) [resolution 99,264]
277. ~6 | 13 [avatar split clause 274,185,153]
278. $false <- (9) [resolution 168,125]
281. ~9 [avatar contradiction clause 278]
283. ~creative(paul) <- (13) [resolution 186,84]
288. rich(X0) | humble(X0) [resolution 130,90]
302. creative(X1) | humble(X1) [resolution 288,75]
311. humble(paul) <- (13) [resolution 302,283]
319. 12 | ~13 [avatar split clause 311,185,181]
320. creative(lucy) <- (14) [resolution 190,128]
323. ~kind(lucy) <- (14) [resolution 320,99]
326. $false <- (14, ~15) [subsumption resolution 323,269]
327. ~14 | 15 [avatar contradiction clause 326]
328. funny(lucy) <- (~14) [resolution 191,179]
330. creative(lucy) <- (15) [resolution 195,75]
331. ~creative(lucy) <- (~14) [resolution 328,84]
332. $false <- (~14, 15) [subsumption resolution 331,330]
333. 14 | ~15 [avatar contradiction clause 332]
334. $false [avatar sat refutation 169,202,203,261,277,281,319,327,333]
% SZS output end Proof for 2189207420947139061567154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not patient then someone is calm or not funny.
Everyone who is brave is either quiet or not kind.
Everyone who is not humble or rich is either not generous or not creative.
If alice is both not old and not happy then someone is calm and vice versa.
Everyone who is both not brave and creative is both generous and rich.
Everyone who is not patient is not wise and vice versa.
Everyone who is generous or wise is not patient or curious and vice versa.
If someone is either happy or not quiet then paul is either not curious or creative and vice versa.
If susan is both creative and not kind then alice is not kind or tall.
Everyone who is both rich and curious is either not kind or rich and vice versa.
Everyone who is either not curious or happy is both not humble and not creative and vice versa.
Everyone who is both brave and not generous is both funny and kind.
Everyone who is either brave or kind is not kind.
If someone is both funny and not strong then someone is generous and vice versa.
Everyone who is either not wise or happy is generous or old and vice versa.
If someone is either calm or not old then mary is not humble.
Mary is either not humble or curious.
Paul is both curious and not tall.
John is both not happy and brave.
Susan is both not happy and quiet.
Alice is happy.
Someone is either not kind or not creative.
Alice is either not rich or not humble. | Mary is happy. | contradiction | ((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(brave(X)=>(quiet(X)<~>~kind(X))))&
(![X]:((~humble(X)|rich(X))=>(~generous(X)<~>~creative(X))))&
(((~old(alice)&~happy(alice)))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)&creative(X))=>(generous(X)&rich(X))))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((generous(X)|wise(X))<=>(~patient(X)|curious(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((~curious(paul)<~>creative(paul))))&
(((creative(susan)&~kind(susan)))=>((~kind(alice)|tall(alice))))&
(![X]:((rich(X)&curious(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(~humble(X)&~creative(X))))&
(![X]:((brave(X)&~generous(X))=>(funny(X)&kind(X))))&
(![X]:((brave(X)<~>kind(X))=>~kind(X)))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:(generous(X))))&
(![X]:((~wise(X)<~>happy(X))<=>(generous(X)|old(X))))&
((?[X]:((calm(X)<~>~old(X))))=>(~humble(mary)))&
((~humble(mary)<~>curious(mary)))&
((curious(paul)&~tall(paul)))&
((~happy(john)&brave(john)))&
((~happy(susan)&quiet(susan)))&
(happy(alice))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~rich(alice)<~>~humble(alice))) | happy(mary) | [
"p5",
"p6",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7104849122205407181966276
% SZS output start Proof for 7104849122205407181966276
6. ! [X0] : (~patient(X0) <=> ~wise(X0)) [input p5]
7. ! [X0] : ((wise(X0) | generous(X0)) <=> (curious(X0) | ~patient(X0))) [input p6]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (~creative(X0) & ~humble(X0))) [input p10]
15. ! [X0] : ((~wise(X0) <~> happy(X0)) <=> (old(X0) | generous(X0))) [input p14]
17. ~humble(mary) <~> curious(mary) [input p16]
24. happy(mary) [input hypothesis]
48. ! [X0] : ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))) [nnf transformation 6]
49. ! [X0] : (((wise(X0) | generous(X0)) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | (~wise(X0) & ~generous(X0)))) [nnf transformation 7]
50. ! [X0] : ((wise(X0) | generous(X0) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | (~wise(X0) & ~generous(X0)))) [flattening 49]
57. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11]
58. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 57]
65. ! [X0] : ((((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | (~old(X0) & ~generous(X0))) & ((old(X0) | generous(X0)) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))))) [nnf transformation 15]
66. ! [X0] : ((((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | (~old(X0) & ~generous(X0))) & (old(X0) | generous(X0) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))))) [flattening 65]
68. (~curious(mary) | humble(mary)) & (curious(mary) | ~humble(mary)) [nnf transformation 17]
86. ~wise(X0) | patient(X0) [cnf transformation 48]
87. ~patient(X0) | wise(X0) [cnf transformation 48]
89. curious(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 50]
90. wise(X0) | generous(X0) | patient(X0) [cnf transformation 50]
108. ~curious(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 58]
124. ~happy(X0) | wise(X0) | ~generous(X0) [cnf transformation 66]
129. ~curious(mary) | humble(mary) [cnf transformation 68]
141. happy(mary) [cnf transformation 24]
179. wise(X0) | generous(X0) [subsumption resolution 90,87]
180. ~wise(X0) | curious(X0) [subsumption resolution 89,86]
250. ~happy(X0) | wise(X0) [subsumption resolution 124,179]
256. 25 <=> humble(mary) [avatar definition]
257. humble(mary) <- (25) [avatar component clause 256]
265. 27 <=> curious(mary) [avatar definition]
266. curious(mary) <- (27) [avatar component clause 265]
268. 25 | ~27 [avatar split clause 129,265,256]
301. wise(mary) [resolution 250,141]
308. curious(mary) [resolution 301,180]
312. 27 [avatar split clause 308,265]
464. ~humble(mary) | ~happy(mary) <- (27) [resolution 108,266]
471. ~happy(mary) <- (25, 27) [subsumption resolution 464,257]
472. $false <- (25, 27) [subsumption resolution 471,141]
473. ~25 | ~27 [avatar contradiction clause 472]
474. $false [avatar sat refutation 268,312,473]
% SZS output end Proof for 7104849122205407181966276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
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