premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is quiet is strong or humble and vice versa.
Everyone who is both not happy and tall is happy or kind and vice versa.
If someone is not old then paul is either creative or not humble and vice versa.
If someone is either funny or not creative then someone is not generous or kind and vice versa.
Everyone who is either wise or not calm is not patient or kind.
Everyone who is both not funny and not kind is generous or not creative.
If fred is not old or not quiet then someone is kind.
Everyone who is both calm and strong is not curious or not tall.
Everyone who is not humble is not strong or generous.
Everyone who is rich is both quiet and not rich and vice versa.
If lucy is either rich or not creative then someone is generous or calm.
If someone is brave or rich then susan is either curious or not calm.
Everyone who is humble or strong is either curious or not rich.
Fred is both not creative and not happy.
Fred is old or brave.
Alice is either not wise or not generous.
Someone is both not creative and not happy.
Someone is not wise.
Paul is either not old or not kind.
Someone is not strong. | Alice is not strong. | entailment | (![X]:(quiet(X)<=>(strong(X)|humble(X))))&
(![X]:((~happy(X)&tall(X))<=>(happy(X)|kind(X))))&
((?[X]:(~old(X)))<=>((creative(paul)<~>~humble(paul))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((wise(X)<~>~calm(X))=>(~patient(X)|kind(X))))&
(![X]:((~funny(X)&~kind(X))=>(generous(X)|~creative(X))))&
(((~old(fred)|~quiet(fred)))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&strong(X))=>(~curious(X)|~tall(X))))&
(![X]:(~humble(X)=>(~strong(X)|generous(X))))&
(![X]:(rich(X)<=>(quiet(X)&~rich(X))))&
(((rich(lucy)<~>~creative(lucy)))=>(?[X]:((generous(X)|calm(X)))))&
((?[X]:((brave(X)|rich(X))))=>((curious(susan)<~>~calm(susan))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
((~creative(fred)&~happy(fred)))&
((old(fred)|brave(fred)))&
((~wise(alice)<~>~generous(alice)))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:(~wise(X)))&
((~old(paul)<~>~kind(paul)))&
(?[X]:(~strong(X))) | ~strong(alice) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4359293682331901819135469
% SZS output start Proof for 4359293682331901819135469
1. ! [X0] : (quiet(X0) <=> (humble(X0) | strong(X0))) [input p0]
10. ! [X0] : (rich(X0) <=> (~rich(X0) & quiet(X0))) [input p9]
21. strong(alice) [input hypothesis]
34. ! [X0] : ((quiet(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 1]
35. ! [X0] : ((quiet(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ~quiet(X0))) [flattening 34]
49. ! [X0] : ((rich(X0) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | ~rich(X0))) [nnf transformation 10]
50. ! [X0] : ((rich(X0) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | ~rich(X0))) [flattening 49]
65. ~strong(X0) | quiet(X0) [cnf transformation 35]
88. ~rich(X0) | ~rich(X0) [cnf transformation 50]
89. rich(X0) | rich(X0) | ~quiet(X0) [cnf transformation 50]
111. strong(alice) [cnf transformation 21]
112. ~rich(X0) [duplicate literal removal 88]
113. ~quiet(X0) | rich(X0) [duplicate literal removal 89]
238. quiet(alice) [resolution 65,111]
240. rich(alice) [resolution 113,238]
243. $false [subsumption resolution 240,112]
% SZS output end Proof for 4359293682331901819135469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not creative is either generous or not calm. If someone is generous or wise then fred is not calm. If someone is creative then someone is either not patient or creative and vice versa. If someone is both generous and humble then mary is kind and vice versa. Everyone who is both curious and not wise is both old and not curious. Everyone who is not tall is both generous and not generous. Everyone who is not generous or happy is wise or not creative and vice versa. If someone is either curious or generous then someone is either not patient or not generous and vice versa. If someone is either not rich or not tall then susan is either not funny or not rich and vice versa. Everyone who is either generous or tall is both brave and not rich and vice versa. If someone is both not happy and creative then someone is both wise and rich. Everyone who is both not brave and creative is either funny or not calm and vice versa. If someone is not quiet or tall then someone is not old. If lucy is either not creative or not strong then john is either not happy or rich. If someone is both rich and not rich then someone is not curious and vice versa. Everyone who is strong or calm is both not brave and not tall and vice versa. Lucy is either funny or not wise. Someone is generous. Someone is not kind. Someone is both not funny and happy. Alice is either tall or not patient. Mary is humble. Someone is either not brave or humble. | Susan is not funny. | contradiction | (![X]:((rich(X)|~creative(X))=>(generous(X)<~>~calm(X))))&
((?[X]:((generous(X)|wise(X))))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)<~>creative(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(kind(mary)))&
(![X]:((curious(X)&~wise(X))=>(old(X)&~curious(X))))&
(![X]:(~tall(X)=>(generous(X)&~generous(X))))&
(![X]:((~generous(X)|happy(X))<=>(wise(X)|~creative(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~funny(susan)<~>~rich(susan))))&
(![X]:((generous(X)<~>tall(X))<=>(brave(X)&~rich(X))))&
((?[X]:((~happy(X)&creative(X))))=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((~brave(X)&creative(X))<=>(funny(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|tall(X))))=>(?[X]:(~old(X))))&
(((~creative(lucy)<~>~strong(lucy)))=>((~happy(john)<~>rich(john))))&
((?[X]:((rich(X)&~rich(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)|calm(X))<=>(~brave(X)&~tall(X))))&
((funny(lucy)<~>~wise(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)&happy(X))))&
((tall(alice)<~>~patient(alice)))&
(humble(mary))&
(?[X]:((~brave(X)<~>humble(X)))) | ~funny(susan) | [
"p0",
"p5",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 294520199072970134180052
% SZS output start Proof for 294520199072970134180052
1. ! [X0] : ((~creative(X0) | rich(X0)) => (generous(X0) <~> ~calm(X0))) [input p0]
6. ! [X0] : (~tall(X0) => (~generous(X0) & generous(X0))) [input p5]
9. ? [X0] : (~rich(X0) <~> ~tall(X0)) <=> (~funny(susan) <~> ~rich(susan)) [input p8]
10. ! [X0] : ((generous(X0) <~> tall(X0)) <=> (~rich(X0) & brave(X0))) [input p9]
16. ! [X0] : ((calm(X0) | strong(X0)) <=> (~tall(X0) & ~brave(X0))) [input p15]
24. ~funny(susan) [input hypothesis]
31. ! [X0] : ((generous(X0) <~> ~calm(X0)) | (creative(X0) & ~rich(X0))) [ennf transformation 1]
35. ! [X0] : ((~generous(X0) & generous(X0)) | tall(X0)) [ennf transformation 6]
39. ! [X0] : (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (creative(X0) & ~rich(X0))) [nnf transformation 31]
56. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X0] : ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [nnf transformation 9]
57. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [rectify 56]
58. ? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) => ((tall(sK5) | rich(sK5)) & (~tall(sK5) | ~rich(sK5))) [choice axiom]
59. (((tall(sK5) | rich(sK5)) & (~tall(sK5) | ~rich(sK5))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [skolemisation 57,58]
60. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (rich(X0) | ~brave(X0))) & ((~rich(X0) & brave(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 10]
61. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | rich(X0) | ~brave(X0)) & ((~rich(X0) & brave(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [flattening 60]
76. ! [X0] : (((calm(X0) | strong(X0)) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 16]
77. ! [X0] : ((calm(X0) | strong(X0) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 76]
91. ~generous(X0) | calm(X0) | ~rich(X0) [cnf transformation 39]
104. generous(X0) | tall(X0) [cnf transformation 35]
105. ~generous(X0) | tall(X0) [cnf transformation 35]
120. rich(susan) | funny(susan) | ~tall(X1) | rich(X1) [cnf transformation 59]
129. ~rich(X0) | generous(X0) | ~tall(X0) [cnf transformation 61]
151. ~tall(X0) | ~calm(X0) [cnf transformation 77]
164. ~funny(susan) [cnf transformation 24]
221. tall(X0) [subsumption resolution 104,105]
260. 22 <=> rich(susan) [avatar definition]
261. ~rich(susan) <- (~22) [avatar component clause 260]
262. rich(susan) <- (22) [avatar component clause 260]
264. 23 <=> funny(susan) [avatar definition]
274. rich(susan) | funny(susan) | rich(X1) [subsumption resolution 120,221]
276. 25 <=> ! [X1] : rich(X1) [avatar definition]
277. rich(X1) <- (25) [avatar component clause 276]
278. 25 | 23 | 22 [avatar split clause 274,260,264,276]
282. ~rich(X0) | generous(X0) [subsumption resolution 129,221]
327. ~calm(X0) [subsumption resolution 151,221]
350. ~23 [avatar split clause 164,264]
356. generous(susan) <- (22) [resolution 282,262]
361. calm(susan) | ~rich(susan) <- (22) [resolution 91,356]
365. ~rich(susan) <- (22) [subsumption resolution 361,327]
366. $false <- (22) [subsumption resolution 365,262]
367. ~22 [avatar contradiction clause 366]
371. $false <- (~22, 25) [subsumption resolution 261,277]
372. 22 | ~25 [avatar contradiction clause 371]
373. $false [avatar sat refutation 278,350,367,372]
% SZS output end Proof for 294520199072970134180052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both creative and strong then someone is both not wise and calm and vice versa.
Everyone who is both not old and not funny is rich.
Everyone who is wise or not funny is both happy and generous and vice versa.
If someone is either curious or not strong then susan is both not creative and not old and vice versa.
Everyone who is not calm or curious is old.
Everyone who is not humble is both tall and not happy and vice versa.
Everyone who is not patient or wise is either creative or not brave and vice versa.
If someone is not rich then someone is either happy or not strong and vice versa.
Everyone who is not old is either wise or strong.
Everyone who is either creative or funny is not patient or calm.
If someone is either creative or brave then someone is tall and vice versa.
Everyone who is both kind and not happy is patient or not curious.
Everyone who is both calm and not brave is old and vice versa.
If john is tall or kind then someone is not quiet.
If someone is old or kind then mary is not funny or not old and vice versa.
If fred is not humble or not happy then someone is old and vice versa.
Someone is kind or patient.
Someone is not tall or strong.
Paul is either rich or wise.
Alice is both not strong and not old.
Paul is not strong or not patient.
John is both curious and old. | John is not strong. | neutral | ((?[X]:((creative(X)&strong(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((~old(X)&~funny(X))=>rich(X)))&
(![X]:((wise(X)|~funny(X))<=>(happy(X)&generous(X))))&
((?[X]:((curious(X)<~>~strong(X))))<=>((~creative(susan)&~old(susan))))&
(![X]:((~calm(X)|curious(X))=>old(X)))&
(![X]:(~humble(X)<=>(tall(X)&~happy(X))))&
(![X]:((~patient(X)|wise(X))<=>(creative(X)<~>~brave(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(~old(X)=>(wise(X)<~>strong(X))))&
(![X]:((creative(X)<~>funny(X))=>(~patient(X)|calm(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~happy(X))=>(patient(X)|~curious(X))))&
(![X]:((calm(X)&~brave(X))<=>old(X)))&
(((tall(john)|kind(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((old(X)|kind(X))))<=>((~funny(mary)|~old(mary))))&
(((~humble(fred)|~happy(fred)))<=>(?[X]:(old(X))))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:((~tall(X)|strong(X))))&
((rich(paul)<~>wise(paul)))&
((~strong(alice)&~old(alice)))&
((~strong(paul)|~patient(paul)))&
((curious(john)&old(john))) | ~strong(john) | [] | null | 0 |
Everyone who is patient or generous is curious or not old and vice versa. Everyone who is not humble is kind and vice versa. Everyone who is not calm is not humble and vice versa. Everyone who is either calm or not generous is curious or not creative. If paul is not wise or happy then mary is curious and vice versa. If fred is either not wise or not creative then someone is either curious or strong and vice versa. If someone is not humble or curious then john is not funny or not old and vice versa. If someone is either calm or not brave then susan is not kind and vice versa. Everyone who is not patient or rich is tall or not patient. Everyone who is wise or not rich is either curious or generous. If mary is both not curious and not happy then alice is not happy and vice versa. If someone is not quiet then susan is either not wise or creative. If someone is strong or not creative then someone is either not creative or brave. If someone is either brave or rich then susan is not tall and vice versa. If john is humble then mary is either patient or not quiet and vice versa. Everyone who is kind or patient is not kind and vice versa. Someone is both not kind and not tall. Someone is not tall. Alice is quiet or not tall. Someone is either not strong or not curious. Alice is funny. Someone is either wise or not curious. Someone is not generous. | Mary is wise. | neutral | (![X]:((patient(X)|generous(X))<=>(curious(X)|~old(X))))&
(![X]:(~humble(X)<=>kind(X)))&
(![X]:(~calm(X)<=>~humble(X)))&
(![X]:((calm(X)<~>~generous(X))=>(curious(X)|~creative(X))))&
(((~wise(paul)|happy(paul)))<=>(curious(mary)))&
(((~wise(fred)<~>~creative(fred)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((?[X]:((~humble(X)|curious(X))))<=>((~funny(john)|~old(john))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(~kind(susan)))&
(![X]:((~patient(X)|rich(X))=>(tall(X)|~patient(X))))&
(![X]:((wise(X)|~rich(X))=>(curious(X)<~>generous(X))))&
(((~curious(mary)&~happy(mary)))<=>(~happy(alice)))&
((?[X]:(~quiet(X)))=>((~wise(susan)<~>creative(susan))))&
((?[X]:((strong(X)|~creative(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
((?[X]:((brave(X)<~>rich(X))))<=>(~tall(susan)))&
((humble(john))<=>((patient(mary)<~>~quiet(mary))))&
(![X]:((kind(X)|patient(X))<=>~kind(X)))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:(~tall(X)))&
((quiet(alice)|~tall(alice)))&
(?[X]:((~strong(X)<~>~curious(X))))&
(funny(alice))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:(~generous(X))) | wise(mary) | [] | null | 0 |
Everyone who is either not funny or humble is happy.
If someone is tall then fred is either not creative or patient.
If susan is not strong or funny then lucy is not tall.
If someone is not wise then susan is creative.
Everyone who is both not quiet and kind is not patient and vice versa.
If susan is not old then alice is quiet.
If susan is both not quiet and calm then someone is generous or kind.
Everyone who is wise or not humble is both funny and not funny and vice versa.
If someone is not patient or not old then someone is both not curious and not old and vice versa.
Everyone who is both not funny and tall is both strong and not quiet.
If someone is not quiet then mary is not tall and vice versa.
Everyone who is brave or not calm is patient or quiet and vice versa.
If susan is both old and happy then alice is either not old or not strong and vice versa.
Everyone who is strong or curious is both old and not quiet and vice versa.
Everyone who is tall or curious is not funny.
Everyone who is either not wise or tall is not happy or wise and vice versa.
Someone is curious or calm.
Lucy is patient or not quiet.
Mary is either wise or not kind.
Someone is calm.
Someone is old.
Someone is not funny or not calm.
Someone is both not curious and kind.
Someone is not tall or rich. | Fred is funny. | contradiction | (![X]:((~funny(X)<~>humble(X))=>happy(X)))&
((?[X]:(tall(X)))=>((~creative(fred)<~>patient(fred))))&
(((~strong(susan)|funny(susan)))=>(~tall(lucy)))&
((?[X]:(~wise(X)))=>(creative(susan)))&
(![X]:((~quiet(X)&kind(X))<=>~patient(X)))&
((~old(susan))=>(quiet(alice)))&
(((~quiet(susan)&calm(susan)))=>(?[X]:((generous(X)|kind(X)))))&
(![X]:((wise(X)|~humble(X))<=>(funny(X)&~funny(X))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((~funny(X)&tall(X))=>(strong(X)&~quiet(X))))&
((?[X]:(~quiet(X)))<=>(~tall(mary)))&
(![X]:((brave(X)|~calm(X))<=>(patient(X)|quiet(X))))&
(((old(susan)&happy(susan)))<=>((~old(alice)<~>~strong(alice))))&
(![X]:((strong(X)|curious(X))<=>(old(X)&~quiet(X))))&
(![X]:((tall(X)|curious(X))=>~funny(X)))&
(![X]:((~wise(X)<~>tall(X))<=>(~happy(X)|wise(X))))&
(?[X]:((curious(X)|calm(X))))&
((patient(lucy)|~quiet(lucy)))&
((wise(mary)<~>~kind(mary)))&
(?[X]:(calm(X)))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)|~calm(X))))&
(?[X]:((~curious(X)&kind(X))))&
(?[X]:((~tall(X)|rich(X)))) | funny(fred) | [
"p0",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7273041755092382679679223
% SZS output start Proof for 7273041755092382679679223
1. ! [X0] : ((~funny(X0) <~> humble(X0)) => happy(X0)) [input p0]
8. ! [X0] : ((~humble(X0) | wise(X0)) <=> (~funny(X0) & funny(X0))) [input p7]
15. ! [X0] : ((curious(X0) | tall(X0)) => ~funny(X0)) [input p14]
16. ! [X0] : ((~wise(X0) <~> tall(X0)) <=> (wise(X0) | ~happy(X0))) [input p15]
25. funny(fred) [input hypothesis]
29. ! [X0] : (happy(X0) | (~funny(X0) <=> humble(X0))) [ennf transformation 1]
36. ! [X0] : (~funny(X0) | (~curious(X0) & ~tall(X0))) [ennf transformation 15]
37. ! [X0] : (happy(X0) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0)))) [nnf transformation 29]
41. ! [X0] : (((~humble(X0) | wise(X0)) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | (humble(X0) & ~wise(X0)))) [nnf transformation 8]
42. ! [X0] : ((~humble(X0) | wise(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | (humble(X0) & ~wise(X0)))) [flattening 41]
58. ! [X0] : ((((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | (~wise(X0) & happy(X0))) & ((wise(X0) | ~happy(X0)) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))))) [nnf transformation 16]
59. ! [X0] : ((((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | (~wise(X0) & happy(X0))) & (wise(X0) | ~happy(X0) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))))) [flattening 58]
72. ~humble(X0) | ~funny(X0) | happy(X0) [cnf transformation 37]
82. funny(X0) | ~wise(X0) [cnf transformation 42]
83. funny(X0) | humble(X0) [cnf transformation 42]
84. ~wise(X0) | ~funny(X0) [cnf transformation 42]
85. ~funny(X0) | humble(X0) [cnf transformation 42]
111. ~tall(X0) | ~funny(X0) [cnf transformation 36]
113. wise(X0) | ~happy(X0) | tall(X0) | wise(X0) [cnf transformation 59]
128. funny(fred) [cnf transformation 25]
129. wise(X0) | ~happy(X0) | tall(X0) [duplicate literal removal 113]
175. humble(X0) [subsumption resolution 83,85]
176. ~wise(X0) [subsumption resolution 82,84]
241. ~happy(X0) | tall(X0) [subsumption resolution 129,176]
271. ~funny(X0) | happy(X0) [resolution 72,175]
272. happy(fred) [resolution 271,128]
284. tall(fred) [resolution 272,241]
287. ~funny(fred) [resolution 284,111]
288. $false [subsumption resolution 287,128]
% SZS output end Proof for 7273041755092382679679223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is not strong then someone is not calm. Everyone who is not patient is strong or quiet. If someone is either not quiet or not calm then susan is either patient or not old and vice versa. If someone is both brave and not tall then susan is not wise or calm and vice versa. Everyone who is both not old and not curious is strong or curious and vice versa. Everyone who is funny or not strong is quiet or not quiet. Everyone who is patient or quiet is both not creative and not strong and vice versa. Everyone who is both tall and humble is not tall and vice versa. Everyone who is either not calm or old is calm. If someone is either tall or not humble then mary is humble. If someone is both not rich and not kind then someone is not curious or not rich and vice versa. If someone is either not wise or not creative then someone is both happy and not wise and vice versa. If someone is either kind or old then someone is either not patient or kind and vice versa. Everyone who is both not patient and calm is either curious or old. Alice is patient. Someone is not humble or not brave. Someone is not happy or not brave. Fred is either not happy or not kind. Mary is not happy or not curious. Someone is both not brave and not rich. | Susan is not funny. | neutral | ((~strong(john))=>(?[X]:(~calm(X))))&
(![X]:(~patient(X)=>(strong(X)|quiet(X))))&
((?[X]:((~quiet(X)<~>~calm(X))))<=>((patient(susan)<~>~old(susan))))&
((?[X]:((brave(X)&~tall(X))))<=>((~wise(susan)|calm(susan))))&
(![X]:((~old(X)&~curious(X))<=>(strong(X)|curious(X))))&
(![X]:((funny(X)|~strong(X))=>(quiet(X)|~quiet(X))))&
(![X]:((patient(X)|quiet(X))<=>(~creative(X)&~strong(X))))&
(![X]:((tall(X)&humble(X))<=>~tall(X)))&
(![X]:((~calm(X)<~>old(X))=>calm(X)))&
((?[X]:((tall(X)<~>~humble(X))))=>(humble(mary)))&
((?[X]:((~rich(X)&~kind(X))))<=>(?[X]:((~curious(X)|~rich(X)))))&
((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
((?[X]:((kind(X)<~>old(X))))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((~patient(X)&calm(X))=>(curious(X)<~>old(X))))&
(patient(alice))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
((~happy(fred)<~>~kind(fred)))&
((~happy(mary)|~curious(mary)))&
(?[X]:((~brave(X)&~rich(X)))) | ~funny(susan) | [] | null | 0 |
If someone is brave then alice is both not funny and wise and vice versa. If lucy is not curious then someone is both funny and not kind. Everyone who is not kind or calm is old or wise and vice versa. If john is not strong or not rich then alice is either calm or not happy. Everyone who is not humble is both generous and creative. If someone is not quiet or rich then someone is creative. If paul is not old then someone is either not quiet or curious. If someone is either humble or not tall then lucy is either not quiet or not creative. Everyone who is not patient is not quiet. Everyone who is both not kind and wise is calm or generous and vice versa. If someone is generous or creative then someone is both not funny and funny. Everyone who is not calm is not humble and vice versa. If someone is either not strong or generous then someone is old or calm and vice versa. Everyone who is both not generous and not patient is both not strong and strong and vice versa. Everyone who is both not generous and not strong is not kind. Paul is humble or not curious. Fred is both wise and not generous. Someone is brave. Paul is either old or not calm. Someone is not strong or not humble. | Lucy is not rich. | entailment | ((?[X]:(brave(X)))<=>((~funny(alice)&wise(alice))))&
((~curious(lucy))=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((~kind(X)|calm(X))<=>(old(X)|wise(X))))&
(((~strong(john)|~rich(john)))=>((calm(alice)<~>~happy(alice))))&
(![X]:(~humble(X)=>(generous(X)&creative(X))))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:(creative(X))))&
((~old(paul))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((humble(X)<~>~tall(X))))=>((~quiet(lucy)<~>~creative(lucy))))&
(![X]:(~patient(X)=>~quiet(X)))&
(![X]:((~kind(X)&wise(X))<=>(calm(X)|generous(X))))&
((?[X]:((generous(X)|creative(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
((humble(paul)|~curious(paul)))&
((wise(fred)&~generous(fred)))&
(?[X]:(brave(X)))&
((old(paul)<~>~calm(paul)))&
(?[X]:((~strong(X)|~humble(X)))) | ~rich(lucy) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7185924828604399433663324
% SZS output start Proof for 7185924828604399433663324
6. ? [X0] : (rich(X0) | ~quiet(X0)) => ? [X0] : creative(X0) [input p5]
11. ? [X0] : (creative(X0) | generous(X0)) => ? [X0] : (funny(X0) & ~funny(X0)) [input p10]
21. rich(lucy) [input hypothesis]
22. ? [X0] : (rich(X0) | ~quiet(X0)) => ? [X1] : creative(X1) [rectify 6]
23. ? [X0] : (creative(X0) | generous(X0)) => ? [X1] : (funny(X1) & ~funny(X1)) [rectify 11]
28. ? [X1] : creative(X1) | ! [X0] : (~rich(X0) & quiet(X0)) [ennf transformation 22]
32. ? [X1] : (funny(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & ~generous(X0)) [ennf transformation 23]
45. ? [X0] : creative(X0) | ! [X1] : (~rich(X1) & quiet(X1)) [rectify 28]
46. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
47. creative(sK2) | ! [X1] : (~rich(X1) & quiet(X1)) [skolemisation 45,46]
54. ? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & ~generous(X1)) [rectify 32]
55. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK4) & ~funny(sK4)) [choice axiom]
56. (funny(sK4) & ~funny(sK4)) | ! [X1] : (~creative(X1) & ~generous(X1)) [skolemisation 54,55]
86. creative(sK2) | ~rich(X1) [cnf transformation 47]
100. ~funny(sK4) | ~creative(X1) [cnf transformation 56]
102. funny(sK4) | ~creative(X1) [cnf transformation 56]
123. rich(lucy) [cnf transformation 21]
177. 12 <=> ! [X1] : ~rich(X1) [avatar definition]
178. ~rich(X1) <- (12) [avatar component clause 177]
180. 13 <=> creative(sK2) [avatar definition]
182. creative(sK2) <- (13) [avatar component clause 180]
183. 12 | 13 [avatar split clause 86,180,177]
222. 22 <=> ! [X1] : ~creative(X1) [avatar definition]
223. ~creative(X1) <- (22) [avatar component clause 222]
225. 23 <=> funny(sK4) [avatar definition]
228. 22 | 23 [avatar split clause 102,225,222]
233. 22 | ~23 [avatar split clause 100,225,222]
295. $false <- (13, 22) [subsumption resolution 182,223]
296. ~13 | ~22 [avatar contradiction clause 295]
299. $false <- (12) [resolution 178,123]
300. ~12 [avatar contradiction clause 299]
301. $false [avatar sat refutation 183,228,233,296,300]
% SZS output end Proof for 7185924828604399433663324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not happy is old and vice versa. Everyone who is not rich is rich or not wise. Everyone who is both not humble and brave is either not creative or old. If someone is generous or tall then john is either quiet or tall and vice versa. Everyone who is both quiet and not tall is both calm and not patient. Everyone who is kind is both funny and generous and vice versa. Everyone who is both not strong and not tall is not creative. If someone is strong or not quiet then someone is both calm and not funny. If susan is both old and funny then fred is not calm or creative and vice versa. If someone is not wise then john is strong and vice versa. Everyone who is strong or not humble is either patient or not calm. Everyone who is both not generous and calm is not tall or not funny. Everyone who is kind or not creative is creative or not brave and vice versa. If alice is not tall then someone is both quiet and calm and vice versa. Everyone who is either calm or not calm is either kind or not rich. If mary is not creative then someone is both not curious and quiet and vice versa. Fred is either curious or quiet. Susan is both creative and tall. John is both patient and generous. Someone is wise or not wise. Mary is generous. Someone is not funny or strong. Mary is patient or not wise. Someone is both not generous and not wise. | Fred is not calm. | neutral | (![X]:((~quiet(X)&~happy(X))<=>old(X)))&
(![X]:(~rich(X)=>(rich(X)|~wise(X))))&
(![X]:((~humble(X)&brave(X))=>(~creative(X)<~>old(X))))&
((?[X]:((generous(X)|tall(X))))<=>((quiet(john)<~>tall(john))))&
(![X]:((quiet(X)&~tall(X))=>(calm(X)&~patient(X))))&
(![X]:(kind(X)<=>(funny(X)&generous(X))))&
(![X]:((~strong(X)&~tall(X))=>~creative(X)))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((calm(X)&~funny(X)))))&
(((old(susan)&funny(susan)))<=>((~calm(fred)|creative(fred))))&
((?[X]:(~wise(X)))<=>(strong(john)))&
(![X]:((strong(X)|~humble(X))=>(patient(X)<~>~calm(X))))&
(![X]:((~generous(X)&calm(X))=>(~tall(X)|~funny(X))))&
(![X]:((kind(X)|~creative(X))<=>(creative(X)|~brave(X))))&
((~tall(alice))<=>(?[X]:((quiet(X)&calm(X)))))&
(![X]:((calm(X)<~>~calm(X))=>(kind(X)<~>~rich(X))))&
((~creative(mary))<=>(?[X]:((~curious(X)&quiet(X)))))&
((curious(fred)<~>quiet(fred)))&
((creative(susan)&tall(susan)))&
((patient(john)&generous(john)))&
(?[X]:((wise(X)|~wise(X))))&
(generous(mary))&
(?[X]:((~funny(X)|strong(X))))&
((patient(mary)|~wise(mary)))&
(?[X]:((~generous(X)&~wise(X)))) | ~calm(fred) | [] | null | 0 |
If someone is either not funny or generous then john is both not rich and not generous.
If someone is rich then mary is either generous or calm.
Everyone who is both not brave and tall is quiet or not quiet and vice versa.
Everyone who is quiet is not strong and vice versa.
Everyone who is not curious or not brave is both not rich and not curious and vice versa.
Everyone who is both calm and patient is not wise and vice versa.
Everyone who is either not calm or generous is rich.
Everyone who is both calm and old is either not generous or not old.
Everyone who is tall is both quiet and kind and vice versa.
If someone is humble or brave then someone is calm.
Everyone who is not creative is both calm and not strong and vice versa.
Everyone who is both not kind and not brave is humble or curious.
If lucy is not patient then someone is either wise or creative and vice versa.
Everyone who is brave or curious is either not kind or creative and vice versa.
Everyone who is not patient is quiet and vice versa.
If mary is either not patient or not brave then someone is either generous or strong.
John is not patient.
Mary is not creative.
John is not brave or not creative.
Paul is either not funny or quiet.
Someone is either not funny or not rich.
Someone is funny or curious. | Paul is not wise. | contradiction | ((?[X]:((~funny(X)<~>generous(X))))=>((~rich(john)&~generous(john))))&
((?[X]:(rich(X)))=>((generous(mary)<~>calm(mary))))&
(![X]:((~brave(X)&tall(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(quiet(X)<=>~strong(X)))&
(![X]:((~curious(X)|~brave(X))<=>(~rich(X)&~curious(X))))&
(![X]:((calm(X)&patient(X))<=>~wise(X)))&
(![X]:((~calm(X)<~>generous(X))=>rich(X)))&
(![X]:((calm(X)&old(X))=>(~generous(X)<~>~old(X))))&
(![X]:(tall(X)<=>(quiet(X)&kind(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(calm(X))))&
(![X]:(~creative(X)<=>(calm(X)&~strong(X))))&
(![X]:((~kind(X)&~brave(X))=>(humble(X)|curious(X))))&
((~patient(lucy))<=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:((brave(X)|curious(X))<=>(~kind(X)<~>creative(X))))&
(![X]:(~patient(X)<=>quiet(X)))&
(((~patient(mary)<~>~brave(mary)))=>(?[X]:((generous(X)<~>strong(X)))))&
(~patient(john))&
(~creative(mary))&
((~brave(john)|~creative(john)))&
((~funny(paul)<~>quiet(paul)))&
(?[X]:((~funny(X)<~>~rich(X))))&
(?[X]:((funny(X)|curious(X)))) | ~wise(paul) | [
"p2",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 113125164839476148328425
% SZS output start Proof for 113125164839476148328425
3. ! [X0] : ((tall(X0) & ~brave(X0)) <=> (~quiet(X0) | quiet(X0))) [input p2]
6. ! [X0] : ((patient(X0) & calm(X0)) <=> ~wise(X0)) [input p5]
9. ! [X0] : (tall(X0) <=> (kind(X0) & quiet(X0))) [input p8]
15. ! [X0] : (~patient(X0) <=> quiet(X0)) [input p14]
23. ~wise(paul) [input hypothesis]
36. ! [X0] : (((tall(X0) & ~brave(X0)) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | (~tall(X0) | brave(X0)))) [nnf transformation 3]
37. ! [X0] : (((tall(X0) & ~brave(X0)) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | ~tall(X0) | brave(X0))) [flattening 36]
41. ! [X0] : (((patient(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) | ~calm(X0)))) [nnf transformation 6]
42. ! [X0] : (((patient(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | ~patient(X0) | ~calm(X0))) [flattening 41]
45. ! [X0] : ((tall(X0) | (~kind(X0) | ~quiet(X0))) & ((kind(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 9]
46. ! [X0] : ((tall(X0) | ~kind(X0) | ~quiet(X0)) & ((kind(X0) & quiet(X0)) | ~tall(X0))) [flattening 45]
58. ! [X0] : ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))) [nnf transformation 15]
77. tall(X0) | ~quiet(X0) [cnf transformation 37]
78. quiet(X0) | tall(X0) [cnf transformation 37]
88. wise(X0) | patient(X0) [cnf transformation 42]
93. quiet(X0) | ~tall(X0) [cnf transformation 46]
113. ~patient(X0) | ~quiet(X0) [cnf transformation 58]
126. ~wise(paul) [cnf transformation 23]
159. tall(X0) [subsumption resolution 77,78]
167. quiet(X0) [subsumption resolution 93,159]
201. ~patient(X0) [subsumption resolution 113,167]
221. patient(paul) [resolution 88,126]
222. $false [subsumption resolution 221,201]
% SZS output end Proof for 113125164839476148328425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not strong is quiet or creative. Everyone who is strong is humble or not rich and vice versa. If someone is not curious then alice is both not wise and not humble and vice versa. If someone is both generous and calm then someone is not happy and vice versa. If someone is either not curious or not creative then someone is not rich or not humble and vice versa. If someone is wise or not generous then someone is either not wise or brave and vice versa. If someone is old or rich then someone is not curious. Everyone who is both creative and not creative is not kind or curious. Everyone who is creative or funny is either not tall or humble. Everyone who is patient or not humble is wise. Everyone who is happy is either not strong or quiet. Everyone who is both wise and not humble is both not brave and not happy and vice versa. Everyone who is brave or rich is not happy. Everyone who is rich is not happy. Everyone who is both not patient and not kind is either not calm or wise and vice versa. If someone is not wise then mary is either patient or not old and vice versa. Mary is either not creative or not curious. Alice is creative or not generous. Someone is both not old and not generous. Paul is both not tall and quiet. Mary is both tall and not brave. Alice is either patient or not kind. Someone is creative. | Paul is not curious. | contradiction | (![X]:((kind(X)|~strong(X))=>(quiet(X)|creative(X))))&
(![X]:(strong(X)<=>(humble(X)|~rich(X))))&
((?[X]:(~curious(X)))<=>((~wise(alice)&~humble(alice))))&
((?[X]:((generous(X)&calm(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((~rich(X)|~humble(X)))))&
((?[X]:((wise(X)|~generous(X))))<=>(?[X]:((~wise(X)<~>brave(X)))))&
((?[X]:((old(X)|rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((creative(X)&~creative(X))=>(~kind(X)|curious(X))))&
(![X]:((creative(X)|funny(X))=>(~tall(X)<~>humble(X))))&
(![X]:((patient(X)|~humble(X))=>wise(X)))&
(![X]:(happy(X)=>(~strong(X)<~>quiet(X))))&
(![X]:((wise(X)&~humble(X))<=>(~brave(X)&~happy(X))))&
(![X]:((brave(X)|rich(X))=>~happy(X)))&
(![X]:(rich(X)=>~happy(X)))&
(![X]:((~patient(X)&~kind(X))<=>(~calm(X)<~>wise(X))))&
((?[X]:(~wise(X)))<=>((patient(mary)<~>~old(mary))))&
((~creative(mary)<~>~curious(mary)))&
((creative(alice)|~generous(alice)))&
(?[X]:((~old(X)&~generous(X))))&
((~tall(paul)&quiet(paul)))&
((tall(mary)&~brave(mary)))&
((patient(alice)<~>~kind(alice)))&
(?[X]:(creative(X))) | ~curious(paul) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 475242752485891264601733
% SZS output start Proof for 475242752485891264601733
3. ? [X0] : ~curious(X0) <=> (~humble(alice) & ~wise(alice)) [input p2]
10. ! [X0] : ((~humble(X0) | patient(X0)) => wise(X0)) [input p9]
24. ~curious(paul) [input hypothesis]
36. ! [X0] : (wise(X0) | (humble(X0) & ~patient(X0))) [ennf transformation 10]
42. (? [X0] : ~curious(X0) | (humble(alice) | wise(alice))) & ((~humble(alice) & ~wise(alice)) | ! [X0] : curious(X0)) [nnf transformation 3]
43. (? [X0] : ~curious(X0) | humble(alice) | wise(alice)) & ((~humble(alice) & ~wise(alice)) | ! [X0] : curious(X0)) [flattening 42]
44. (? [X0] : ~curious(X0) | humble(alice) | wise(alice)) & ((~humble(alice) & ~wise(alice)) | ! [X1] : curious(X1)) [rectify 43]
45. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
46. (~curious(sK0) | humble(alice) | wise(alice)) & ((~humble(alice) & ~wise(alice)) | ! [X1] : curious(X1)) [skolemisation 44,45]
86. ~wise(alice) | curious(X1) [cnf transformation 46]
87. ~humble(alice) | curious(X1) [cnf transformation 46]
110. wise(X0) | humble(X0) [cnf transformation 36]
142. ~curious(paul) [cnf transformation 24]
144. 1 <=> wise(alice) [avatar definition]
145. ~wise(alice) <- (~1) [avatar component clause 144]
148. 2 <=> humble(alice) [avatar definition]
149. ~humble(alice) <- (~2) [avatar component clause 148]
157. 4 <=> ! [X1] : curious(X1) [avatar definition]
158. curious(X1) <- (4) [avatar component clause 157]
159. 4 | ~2 [avatar split clause 87,148,157]
160. 4 | ~1 [avatar split clause 86,144,157]
317. humble(alice) <- (~1) [resolution 110,145]
320. $false <- (~1, ~2) [subsumption resolution 317,149]
321. 1 | 2 [avatar contradiction clause 320]
323. $false <- (4) [resolution 158,142]
328. ~4 [avatar contradiction clause 323]
330. $false [avatar sat refutation 159,160,321,328]
% SZS output end Proof for 475242752485891264601733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not patient then john is not rich.
Everyone who is both not generous and not wise is either not old or tall.
If paul is either kind or calm then fred is both curious and not brave.
If someone is not funny then fred is not humble or patient and vice versa.
Everyone who is not strong is not rich or not patient and vice versa.
If someone is not generous or humble then someone is not calm or humble.
Everyone who is both humble and not creative is either patient or not old and vice versa.
If someone is both creative and not humble then mary is either not patient or rich and vice versa.
Everyone who is not curious is either curious or kind and vice versa.
Everyone who is both calm and not patient is not funny or brave.
Everyone who is both patient and not strong is tall or funny and vice versa.
Everyone who is both not creative and kind is patient or not curious.
If paul is both quiet and not humble then fred is old.
Everyone who is quiet or curious is both creative and not strong and vice versa.
Everyone who is not creative is brave and vice versa.
If someone is both strong and not rich then susan is both humble and not tall.
Someone is both not generous and creative.
Lucy is not rich or not kind.
Someone is not calm.
Paul is either happy or brave.
Alice is rich.
Someone is happy or strong.
Susan is both wise and not calm.
Someone is not strong. | Alice is old. | neutral | ((?[X]:((wise(X)&~patient(X))))=>(~rich(john)))&
(![X]:((~generous(X)&~wise(X))=>(~old(X)<~>tall(X))))&
(((kind(paul)<~>calm(paul)))=>((curious(fred)&~brave(fred))))&
((?[X]:(~funny(X)))<=>((~humble(fred)|patient(fred))))&
(![X]:(~strong(X)<=>(~rich(X)|~patient(X))))&
((?[X]:((~generous(X)|humble(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((humble(X)&~creative(X))<=>(patient(X)<~>~old(X))))&
((?[X]:((creative(X)&~humble(X))))<=>((~patient(mary)<~>rich(mary))))&
(![X]:(~curious(X)<=>(curious(X)<~>kind(X))))&
(![X]:((calm(X)&~patient(X))=>(~funny(X)|brave(X))))&
(![X]:((patient(X)&~strong(X))<=>(tall(X)|funny(X))))&
(![X]:((~creative(X)&kind(X))=>(patient(X)|~curious(X))))&
(((quiet(paul)&~humble(paul)))=>(old(fred)))&
(![X]:((quiet(X)|curious(X))<=>(creative(X)&~strong(X))))&
(![X]:(~creative(X)<=>brave(X)))&
((?[X]:((strong(X)&~rich(X))))=>((humble(susan)&~tall(susan))))&
(?[X]:((~generous(X)&creative(X))))&
((~rich(lucy)|~kind(lucy)))&
(?[X]:(~calm(X)))&
((happy(paul)<~>brave(paul)))&
(rich(alice))&
(?[X]:((happy(X)|strong(X))))&
((wise(susan)&~calm(susan)))&
(?[X]:(~strong(X))) | old(alice) | [] | null | 0 |
Everyone who is not funny is either not funny or not curious.
If someone is either not kind or not generous then someone is patient or not wise and vice versa.
If someone is either kind or old then alice is not calm or creative and vice versa.
Everyone who is either not creative or not brave is either not kind or not creative.
If susan is not quiet then someone is either strong or not funny.
If alice is creative then someone is both not calm and not kind and vice versa.
Everyone who is not old is either not funny or creative and vice versa.
Everyone who is both not curious and strong is either not funny or quiet and vice versa.
If someone is curious then someone is both not brave and brave and vice versa.
If alice is wise or not rich then susan is brave and vice versa.
Everyone who is both not quiet and curious is both humble and not tall.
Everyone who is not rich or brave is rich and vice versa.
If susan is calm then someone is generous and vice versa.
Everyone who is either not humble or not funny is both not kind and not humble and vice versa.
If lucy is both funny and happy then paul is either not old or tall.
Mary is not kind.
John is either not brave or quiet.
Lucy is not strong or humble.
Someone is quiet or creative.
Someone is wise or not calm.
Susan is humble. | Mary is not brave. | contradiction | (![X]:(~funny(X)=>(~funny(X)<~>~curious(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:((kind(X)<~>old(X))))<=>((~calm(alice)|creative(alice))))&
(![X]:((~creative(X)<~>~brave(X))=>(~kind(X)<~>~creative(X))))&
((~quiet(susan))=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(alice))<=>(?[X]:((~calm(X)&~kind(X)))))&
(![X]:(~old(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((~curious(X)&strong(X))<=>(~funny(X)<~>quiet(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)&brave(X)))))&
(((wise(alice)|~rich(alice)))<=>(brave(susan)))&
(![X]:((~quiet(X)&curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~rich(X)|brave(X))<=>rich(X)))&
((calm(susan))<=>(?[X]:(generous(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~kind(X)&~humble(X))))&
(((funny(lucy)&happy(lucy)))=>((~old(paul)<~>tall(paul))))&
(~kind(mary))&
((~brave(john)<~>quiet(john)))&
((~strong(lucy)|humble(lucy)))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((wise(X)|~calm(X))))&
(humble(susan)) | ~brave(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 963229267548227118788235
% SZS output start Proof for 963229267548227118788235
12. ! [X0] : ((brave(X0) | ~rich(X0)) <=> rich(X0)) [input p11]
22. ~brave(mary) [input hypothesis]
61. ! [X0] : (((brave(X0) | ~rich(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & rich(X0)))) [nnf transformation 12]
62. ! [X0] : ((brave(X0) | ~rich(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & rich(X0)))) [flattening 61]
114. rich(X0) | rich(X0) [cnf transformation 62]
116. brave(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 62]
132. ~brave(mary) [cnf transformation 22]
135. rich(X0) [duplicate literal removal 114]
136. ~rich(X0) | brave(X0) [duplicate literal removal 116]
310. brave(X0) [resolution 136,135]
312. $false [resolution 310,132]
% SZS output end Proof for 963229267548227118788235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If mary is tall or not patient then alice is either not humble or curious.
Everyone who is not calm is either generous or not strong and vice versa.
Everyone who is old or not tall is curious or wise and vice versa.
If susan is not kind or quiet then someone is not patient and vice versa.
Everyone who is not quiet is strong or not tall and vice versa.
If paul is either tall or happy then someone is not generous and vice versa.
Everyone who is either not generous or not strong is not old.
Everyone who is not kind is funny or not rich.
Everyone who is happy or rich is not happy and vice versa.
If fred is humble or funny then someone is rich.
If someone is not creative or funny then someone is wise or not wise and vice versa.
If someone is both not generous and not calm then john is funny.
Everyone who is either creative or humble is either not kind or not brave and vice versa.
Everyone who is both calm and humble is not calm and vice versa.
If alice is both generous and not generous then someone is not patient or generous and vice versa.
If mary is both not strong and not rich then john is either rich or not happy and vice versa.
Susan is either wise or curious.
Someone is either quiet or not happy.
John is patient or calm.
Alice is kind.
Someone is not kind.
Someone is strong.
Someone is not brave. | John is calm. | entailment | (((tall(mary)|~patient(mary)))=>((~humble(alice)<~>curious(alice))))&
(![X]:(~calm(X)<=>(generous(X)<~>~strong(X))))&
(![X]:((old(X)|~tall(X))<=>(curious(X)|wise(X))))&
(((~kind(susan)|quiet(susan)))<=>(?[X]:(~patient(X))))&
(![X]:(~quiet(X)<=>(strong(X)|~tall(X))))&
(((tall(paul)<~>happy(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>~strong(X))=>~old(X)))&
(![X]:(~kind(X)=>(funny(X)|~rich(X))))&
(![X]:((happy(X)|rich(X))<=>~happy(X)))&
(((humble(fred)|funny(fred)))=>(?[X]:(rich(X))))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((wise(X)|~wise(X)))))&
((?[X]:((~generous(X)&~calm(X))))=>(funny(john)))&
(![X]:((creative(X)<~>humble(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((calm(X)&humble(X))<=>~calm(X)))&
(((generous(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|generous(X)))))&
(((~strong(mary)&~rich(mary)))<=>((rich(john)<~>~happy(john))))&
((wise(susan)<~>curious(susan)))&
(?[X]:((quiet(X)<~>~happy(X))))&
((patient(john)|calm(john)))&
(kind(alice))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X))) | calm(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7040984487830898088452531
% SZS output start Proof for 7040984487830898088452531
14. ! [X0] : ((humble(X0) & calm(X0)) <=> ~calm(X0)) [input p13]
24. ~calm(john) [input hypothesis]
58. ! [X0] : (((humble(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
59. ! [X0] : (((humble(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | ~humble(X0) | ~calm(X0))) [flattening 58]
121. calm(X0) | calm(X0) [cnf transformation 59]
143. ~calm(john) [cnf transformation 24]
145. calm(X0) [duplicate literal removal 121]
280. $false [subsumption resolution 143,145]
% SZS output end Proof for 7040984487830898088452531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or happy is tall and vice versa. Everyone who is either not patient or brave is tall or humble. Everyone who is not wise is either quiet or not wise and vice versa. Everyone who is either not wise or not curious is rich. If fred is curious or quiet then susan is not creative or not calm and vice versa. Everyone who is both not humble and not strong is either kind or not old and vice versa. If someone is either brave or happy then john is either not happy or wise. Everyone who is brave or old is not quiet and vice versa. If mary is either funny or tall then someone is not quiet or kind and vice versa. Everyone who is both not happy and not generous is not kind and vice versa. Everyone who is not happy or not tall is not curious or strong. If someone is patient or not old then someone is not kind. If someone is not creative then paul is both tall and not calm. If alice is patient or quiet then fred is both not rich and not generous. If someone is patient then paul is not strong. Someone is either not quiet or not humble. Paul is calm or rich. Mary is both old and not patient. Someone is curious or tall. Someone is either not wise or curious. Someone is not funny or not humble. Someone is brave or funny. | Paul is not quiet. | entailment | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>brave(X))=>(tall(X)|humble(X))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>~curious(X))=>rich(X)))&
(((curious(fred)|quiet(fred)))<=>((~creative(susan)|~calm(susan))))&
(![X]:((~humble(X)&~strong(X))<=>(kind(X)<~>~old(X))))&
((?[X]:((brave(X)<~>happy(X))))=>((~happy(john)<~>wise(john))))&
(![X]:((brave(X)|old(X))<=>~quiet(X)))&
(((funny(mary)<~>tall(mary)))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~happy(X)&~generous(X))<=>~kind(X)))&
(![X]:((~happy(X)|~tall(X))=>(~curious(X)|strong(X))))&
((?[X]:((patient(X)|~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~creative(X)))=>((tall(paul)&~calm(paul))))&
(((patient(alice)|quiet(alice)))=>((~rich(fred)&~generous(fred))))&
((?[X]:(patient(X)))=>(~strong(paul)))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((calm(paul)|rich(paul)))&
((old(mary)&~patient(mary)))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((brave(X)|funny(X)))) | ~quiet(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4498616147072602742243202
% SZS output start Proof for 4498616147072602742243202
3. ! [X0] : (~wise(X0) <=> (quiet(X0) <~> ~wise(X0))) [input p2]
23. quiet(paul) [input hypothesis]
37. ! [X0] : ((~wise(X0) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | wise(X0))) [nnf transformation 3]
74. wise(X0) | ~quiet(X0) | wise(X0) [cnf transformation 37]
75. ~wise(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 37]
126. quiet(paul) [cnf transformation 23]
127. wise(X0) | ~quiet(X0) [duplicate literal removal 74]
128. ~wise(X0) | ~quiet(X0) [duplicate literal removal 75]
132. ~quiet(X0) [subsumption resolution 127,128]
254. $false [subsumption resolution 126,132]
% SZS output end Proof for 4498616147072602742243202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then lucy is humble and vice versa. If someone is not strong then john is both humble and not wise and vice versa. Everyone who is not kind or not curious is both rich and not calm. If mary is both not old and not tall then susan is not calm. Everyone who is either curious or strong is patient and vice versa. If someone is either happy or old then mary is not funny and vice versa. Everyone who is not patient is brave and vice versa. Everyone who is not tall is both not funny and not old and vice versa. If someone is either not humble or strong then someone is not strong and vice versa. If someone is strong then someone is quiet or calm. If lucy is both not creative and curious then someone is either funny or not tall and vice versa. Everyone who is both creative and funny is either creative or not curious and vice versa. Everyone who is either not strong or quiet is wise and vice versa. If susan is calm or not quiet then mary is curious or not quiet and vice versa. Everyone who is not brave or creative is not quiet and vice versa. Everyone who is curious is not creative. Someone is either not strong or not kind. Someone is not funny or not creative. Someone is either not generous or not curious. Paul is not tall. Someone is either not kind or tall. Someone is both not calm and tall. Someone is not happy. | John is calm. | contradiction | ((?[X]:(strong(X)))<=>(humble(lucy)))&
((?[X]:(~strong(X)))<=>((humble(john)&~wise(john))))&
(![X]:((~kind(X)|~curious(X))=>(rich(X)&~calm(X))))&
(((~old(mary)&~tall(mary)))=>(~calm(susan)))&
(![X]:((curious(X)<~>strong(X))<=>patient(X)))&
((?[X]:((happy(X)<~>old(X))))<=>(~funny(mary)))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:(~tall(X)<=>(~funny(X)&~old(X))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:(~strong(X))))&
((?[X]:(strong(X)))=>(?[X]:((quiet(X)|calm(X)))))&
(((~creative(lucy)&curious(lucy)))<=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((creative(X)&funny(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>wise(X)))&
(((calm(susan)|~quiet(susan)))<=>((curious(mary)|~quiet(mary))))&
(![X]:((~brave(X)|creative(X))<=>~quiet(X)))&
(![X]:(curious(X)=>~creative(X)))&
(?[X]:((~strong(X)<~>~kind(X))))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:((~generous(X)<~>~curious(X))))&
(~tall(paul))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:((~calm(X)&tall(X))))&
(?[X]:(~happy(X))) | calm(john) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p8",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5826494988929043830446903
% SZS output start Proof for 5826494988929043830446903
1. ? [X0] : strong(X0) <=> humble(lucy) [input p0]
2. ? [X0] : ~strong(X0) <=> (~wise(john) & humble(john)) [input p1]
3. ! [X0] : ((~curious(X0) | ~kind(X0)) => (~calm(X0) & rich(X0))) [input p2]
5. ! [X0] : ((curious(X0) <~> strong(X0)) <=> patient(X0)) [input p4]
7. ! [X0] : (~patient(X0) <=> brave(X0)) [input p6]
9. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X0] : ~strong(X0) [input p8]
12. ! [X0] : ((funny(X0) & creative(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p11]
13. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> wise(X0)) [input p12]
15. ! [X0] : ((creative(X0) | ~brave(X0)) <=> ~quiet(X0)) [input p14]
16. ! [X0] : (curious(X0) => ~creative(X0)) [input p15]
24. calm(john) [input hypothesis]
25. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X1] : ~strong(X1) [rectify 9]
27. ! [X0] : ((~curious(X0) | ~kind(X0)) => ~calm(X0)) [pure predicate removal 3]
28. ! [X0] : (~calm(X0) | (curious(X0) & kind(X0))) [ennf transformation 27]
32. ! [X0] : (~creative(X0) | ~curious(X0)) [ennf transformation 16]
33. (? [X0] : strong(X0) | ~humble(lucy)) & (humble(lucy) | ! [X0] : ~strong(X0)) [nnf transformation 1]
34. (? [X0] : strong(X0) | ~humble(lucy)) & (humble(lucy) | ! [X1] : ~strong(X1)) [rectify 33]
35. ? [X0] : strong(X0) => strong(sK0) [choice axiom]
36. (strong(sK0) | ~humble(lucy)) & (humble(lucy) | ! [X1] : ~strong(X1)) [skolemisation 34,35]
37. (? [X0] : ~strong(X0) | (wise(john) | ~humble(john))) & ((~wise(john) & humble(john)) | ! [X0] : strong(X0)) [nnf transformation 2]
38. (? [X0] : ~strong(X0) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X0] : strong(X0)) [flattening 37]
39. (? [X0] : ~strong(X0) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X1] : strong(X1)) [rectify 38]
40. ? [X0] : ~strong(X0) => ~strong(sK1) [choice axiom]
41. (~strong(sK1) | wise(john) | ~humble(john)) & ((~wise(john) & humble(john)) | ! [X1] : strong(X1)) [skolemisation 39,40]
42. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | ~patient(X0)) & (patient(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [nnf transformation 5]
47. ! [X0] : ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0))) [nnf transformation 7]
50. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 25]
51. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [rectify 50]
52. ? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) => ((~strong(sK3) | humble(sK3)) & (strong(sK3) | ~humble(sK3))) [choice axiom]
53. ? [X2] : ~strong(X2) => ~strong(sK4) [choice axiom]
54. (((~strong(sK3) | humble(sK3)) & (strong(sK3) | ~humble(sK3))) | ! [X1] : strong(X1)) & (~strong(sK4) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [skolemisation 51,53,52]
63. ! [X0] : (((funny(X0) & creative(X0)) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | (~funny(X0) | ~creative(X0)))) [nnf transformation 12]
64. ! [X0] : (((funny(X0) & creative(X0)) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | ~funny(X0) | ~creative(X0))) [flattening 63]
65. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | ~wise(X0)) & (wise(X0) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 13]
68. ! [X0] : (((creative(X0) | ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & brave(X0)))) [nnf transformation 15]
69. ! [X0] : ((creative(X0) | ~brave(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & brave(X0)))) [flattening 68]
85. humble(lucy) | ~strong(X1) [cnf transformation 36]
88. ~wise(john) | strong(X1) [cnf transformation 41]
91. ~calm(X0) | curious(X0) [cnf transformation 28]
93. ~curious(X0) | strong(X0) | patient(X0) [cnf transformation 42]
96. ~patient(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 42]
101. brave(X0) | patient(X0) [cnf transformation 47]
102. ~brave(X0) | ~patient(X0) [cnf transformation 47]
107. ~strong(sK4) | ~humble(X3) | ~strong(X3) [cnf transformation 54]
120. creative(X0) | creative(X0) | curious(X0) [cnf transformation 64]
123. quiet(X0) | wise(X0) | strong(X0) [cnf transformation 65]
124. ~quiet(X0) | ~strong(X0) | wise(X0) [cnf transformation 65]
131. ~quiet(X0) | brave(X0) [cnf transformation 69]
132. ~creative(X0) | ~quiet(X0) [cnf transformation 69]
133. ~brave(X0) | creative(X0) | quiet(X0) [cnf transformation 69]
134. ~creative(X0) | ~curious(X0) [cnf transformation 32]
146. calm(john) [cnf transformation 24]
148. creative(X0) | curious(X0) [duplicate literal removal 120]
150. 1 <=> humble(lucy) [avatar definition]
151. humble(lucy) <- (1) [avatar component clause 150]
159. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
160. ~strong(X1) <- (3) [avatar component clause 159]
161. 3 | 1 [avatar split clause 85,150,159]
167. 5 <=> wise(john) [avatar definition]
168. ~wise(john) <- (~5) [avatar component clause 167]
176. 7 <=> ! [X1] : strong(X1) [avatar definition]
177. strong(X1) <- (7) [avatar component clause 176]
178. 7 | ~5 [avatar split clause 88,167,176]
226. 18 <=> ! [X3] : (~humble(X3) | ~strong(X3)) [avatar definition]
227. ~humble(X3) | ~strong(X3) <- (18) [avatar component clause 226]
229. 19 <=> strong(sK4) [avatar definition]
231. ~strong(sK4) <- (~19) [avatar component clause 229]
232. 18 | ~19 [avatar split clause 107,229,226]
336. curious(john) [resolution 91,146]
341. ~quiet(X1) | curious(X1) [resolution 148,132]
379. curious(X0) | strong(X0) | wise(X0) [resolution 123,341]
380. brave(X1) | strong(X1) | wise(X1) [resolution 123,131]
397. creative(X1) | quiet(X1) | patient(X1) [resolution 133,101]
402. ~curious(X1) | patient(X1) | quiet(X1) [resolution 397,134]
407. $false <- (3, 7) [subsumption resolution 177,160]
408. ~3 | ~7 [avatar contradiction clause 407]
434. $false <- (7, ~19) [resolution 177,231]
435. ~7 | 19 [avatar contradiction clause 434]
438. ~humble(X3) <- (7, 18) [subsumption resolution 227,177]
450. $false <- (1, 7, 18) [resolution 438,151]
451. ~1 | ~7 | ~18 [avatar contradiction clause 450]
469. 49 <=> patient(john) [avatar definition]
471. patient(john) <- (49) [avatar component clause 469]
473. 50 <=> strong(john) [avatar definition]
475. strong(john) <- (50) [avatar component clause 473]
619. ~patient(X1) | wise(X1) | strong(X1) [resolution 380,102]
637. ~curious(john) | ~strong(john) <- (49) [resolution 471,96]
639. ~strong(john) <- (49) [subsumption resolution 637,336]
640. ~50 | ~49 [avatar split clause 639,469,473]
664. strong(X0) | wise(X0) | strong(X0) | patient(X0) [resolution 379,93]
665. strong(X0) | wise(X0) | patient(X0) [duplicate literal removal 664]
675. wise(X0) | strong(X0) [subsumption resolution 665,619]
679. patient(john) | quiet(john) [resolution 402,336]
764. strong(john) <- (~5) [resolution 675,168]
773. 75 <=> quiet(john) [avatar definition]
775. quiet(john) <- (75) [avatar component clause 773]
777. 75 | 49 [avatar split clause 679,469,773]
778. 50 | 5 [avatar split clause 764,167,473]
781. ~strong(john) | wise(john) <- (75) [resolution 775,124]
784. wise(john) <- (50, 75) [subsumption resolution 781,475]
785. $false <- (~5, 50, 75) [subsumption resolution 784,168]
786. 5 | ~50 | ~75 [avatar contradiction clause 785]
787. $false [avatar sat refutation 161,178,232,408,435,451,640,777,778,786]
% SZS output end Proof for 5826494988929043830446903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not rich is both kind and not quiet. If mary is curious or rich then susan is not wise and vice versa. If someone is not wise or not calm then alice is not wise. Everyone who is either not brave or not funny is creative. Everyone who is both not generous and funny is kind or not rich. Everyone who is not wise or happy is both kind and not creative and vice versa. Everyone who is either not strong or not kind is either not happy or not old and vice versa. Everyone who is both not happy and not strong is either old or creative and vice versa. If someone is not rich then someone is both not creative and not wise and vice versa. Everyone who is both not generous and not wise is wise. If someone is either not tall or strong then john is both not quiet and not happy and vice versa. Everyone who is not generous or not funny is either calm or not kind and vice versa. If someone is not creative or creative then someone is old or not kind and vice versa. Everyone who is either not patient or happy is both not old and not calm. Everyone who is either not rich or not wise is wise or not tall. If someone is calm or kind then someone is rich or calm and vice versa. John is either not generous or calm. John is both humble and not kind. Mary is either not old or creative. Someone is either calm or patient. Someone is either brave or humble. Someone is either quiet or creative. Alice is both not quiet and rich. Someone is not quiet. | Alice is kind. | entailment | (![X]:((calm(X)<~>~rich(X))=>(kind(X)&~quiet(X))))&
(((curious(mary)|rich(mary)))<=>(~wise(susan)))&
((?[X]:((~wise(X)|~calm(X))))=>(~wise(alice)))&
(![X]:((~brave(X)<~>~funny(X))=>creative(X)))&
(![X]:((~generous(X)&funny(X))=>(kind(X)|~rich(X))))&
(![X]:((~wise(X)|happy(X))<=>(kind(X)&~creative(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((~happy(X)&~strong(X))<=>(old(X)<~>creative(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((~generous(X)&~wise(X))=>wise(X)))&
((?[X]:((~tall(X)<~>strong(X))))<=>((~quiet(john)&~happy(john))))&
(![X]:((~generous(X)|~funny(X))<=>(calm(X)<~>~kind(X))))&
((?[X]:((~creative(X)|creative(X))))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((~patient(X)<~>happy(X))=>(~old(X)&~calm(X))))&
(![X]:((~rich(X)<~>~wise(X))=>(wise(X)|~tall(X))))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((rich(X)|calm(X)))))&
((~generous(john)<~>calm(john)))&
((humble(john)&~kind(john)))&
((~old(mary)<~>creative(mary)))&
(?[X]:((calm(X)<~>patient(X))))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((quiet(X)<~>creative(X))))&
((~quiet(alice)&rich(alice)))&
(?[X]:(~quiet(X))) | kind(alice) | [
"p1",
"p2",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5544275980696583766420331
% SZS output start Proof for 5544275980696583766420331
2. (rich(mary) | curious(mary)) <=> ~wise(susan) [input p1]
3. ? [X0] : (~calm(X0) | ~wise(X0)) => ~wise(alice) [input p2]
6. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (~creative(X0) & kind(X0))) [input p5]
9. ? [X0] : ~rich(X0) <=> ? [X0] : (~wise(X0) & ~creative(X0)) [input p8]
25. ~kind(alice) [input hypothesis]
26. ? [X0] : ~rich(X0) <=> ? [X1] : (~wise(X1) & ~creative(X1)) [rectify 9]
30. ~wise(alice) | ! [X0] : (calm(X0) & wise(X0)) [ennf transformation 3]
40. ((rich(mary) | curious(mary)) | wise(susan)) & (~wise(susan) | (~rich(mary) & ~curious(mary))) [nnf transformation 2]
41. (rich(mary) | curious(mary) | wise(susan)) & (~wise(susan) | (~rich(mary) & ~curious(mary))) [flattening 40]
43. ! [X0] : (((happy(X0) | ~wise(X0)) | (creative(X0) | ~kind(X0))) & ((~creative(X0) & kind(X0)) | (~happy(X0) & wise(X0)))) [nnf transformation 6]
44. ! [X0] : ((happy(X0) | ~wise(X0) | creative(X0) | ~kind(X0)) & ((~creative(X0) & kind(X0)) | (~happy(X0) & wise(X0)))) [flattening 43]
48. (? [X0] : ~rich(X0) | ! [X1] : (wise(X1) | creative(X1))) & (? [X1] : (~wise(X1) & ~creative(X1)) | ! [X0] : rich(X0)) [nnf transformation 26]
49. (? [X0] : ~rich(X0) | ! [X1] : (wise(X1) | creative(X1))) & (? [X2] : (~wise(X2) & ~creative(X2)) | ! [X3] : rich(X3)) [rectify 48]
50. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
51. ? [X2] : (~wise(X2) & ~creative(X2)) => (~wise(sK1) & ~creative(sK1)) [choice axiom]
52. (~rich(sK0) | ! [X1] : (wise(X1) | creative(X1))) & ((~wise(sK1) & ~creative(sK1)) | ! [X3] : rich(X3)) [skolemisation 49,51,50]
90. ~wise(susan) | ~rich(mary) [cnf transformation 41]
92. ~wise(alice) | wise(X0) [cnf transformation 30]
97. wise(X0) | kind(X0) [cnf transformation 44]
117. ~wise(sK1) | rich(X3) [cnf transformation 52]
161. ~kind(alice) [cnf transformation 25]
165. 1 <=> wise(susan) [avatar definition]
166. ~wise(susan) <- (~1) [avatar component clause 165]
173. 3 <=> rich(mary) [avatar definition]
174. ~rich(mary) <- (~3) [avatar component clause 173]
177. ~3 | ~1 [avatar split clause 90,165,173]
183. 5 <=> wise(alice) [avatar definition]
185. ~wise(alice) <- (~5) [avatar component clause 183]
188. 6 <=> ! [X0] : wise(X0) [avatar definition]
189. wise(X0) <- (6) [avatar component clause 188]
190. 6 | ~5 [avatar split clause 92,183,188]
204. 8 <=> ! [X3] : rich(X3) [avatar definition]
205. rich(X3) <- (8) [avatar component clause 204]
207. 9 <=> wise(sK1) [avatar definition]
209. ~wise(sK1) <- (~9) [avatar component clause 207]
210. 8 | ~9 [avatar split clause 117,207,204]
349. kind(alice) <- (~5) [resolution 97,185]
351. $false <- (~5) [subsumption resolution 349,161]
352. 5 [avatar contradiction clause 351]
361. $false <- (~1, 6) [resolution 189,166]
362. $false <- (6, ~9) [resolution 189,209]
363. ~6 | 9 [avatar contradiction clause 362]
364. 1 | ~6 [avatar contradiction clause 361]
365. $false <- (~3, 8) [subsumption resolution 174,205]
366. 3 | ~8 [avatar contradiction clause 365]
367. $false [avatar sat refutation 177,190,210,352,363,364,366]
% SZS output end Proof for 5544275980696583766420331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not happy is patient and vice versa.
Everyone who is both brave and not calm is both not old and humble.
If someone is patient or wise then fred is tall or calm.
If someone is not funny or rich then alice is both not funny and tall and vice versa.
Everyone who is not rich is both not calm and not creative.
Everyone who is not old is old or not rich.
Everyone who is either rich or not patient is not old or not quiet and vice versa.
If someone is both not humble and not generous then someone is either brave or not generous and vice versa.
Everyone who is either not curious or not patient is either calm or not creative and vice versa.
If someone is not kind then someone is funny or patient and vice versa.
Everyone who is both wise and quiet is either not quiet or calm and vice versa.
If someone is not old or curious then lucy is either not kind or old and vice versa.
Everyone who is happy is not happy.
Everyone who is not calm or not generous is either calm or not happy and vice versa.
Everyone who is not tall or not rich is not humble or tall and vice versa.
If someone is quiet or kind then fred is calm and vice versa.
Someone is curious.
John is either not creative or not quiet.
Someone is either not tall or not kind.
Someone is both humble and not kind.
Susan is either generous or rich.
Someone is not brave or brave. | Fred is humble. | contradiction | (![X]:((strong(X)|~happy(X))<=>patient(X)))&
(![X]:((brave(X)&~calm(X))=>(~old(X)&humble(X))))&
((?[X]:((patient(X)|wise(X))))=>((tall(fred)|calm(fred))))&
((?[X]:((~funny(X)|rich(X))))<=>((~funny(alice)&tall(alice))))&
(![X]:(~rich(X)=>(~calm(X)&~creative(X))))&
(![X]:(~old(X)=>(old(X)|~rich(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~old(X)|~quiet(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~curious(X)<~>~patient(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~old(X)|curious(X))))<=>((~kind(lucy)<~>old(lucy))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((~calm(X)|~generous(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~humble(X)|tall(X))))&
((?[X]:((quiet(X)|kind(X))))<=>(calm(fred)))&
(?[X]:(curious(X)))&
((~creative(john)<~>~quiet(john)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((humble(X)&~kind(X))))&
((generous(susan)<~>rich(susan)))&
(?[X]:((~brave(X)|brave(X)))) | humble(fred) | [
"p0",
"p4",
"p5",
"p6",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1234266936984642995496310
% SZS output start Proof for 1234266936984642995496310
1. ! [X0] : ((~happy(X0) | strong(X0)) <=> patient(X0)) [input p0]
5. ! [X0] : (~rich(X0) => (~creative(X0) & ~calm(X0))) [input p4]
6. ! [X0] : (~old(X0) => (~rich(X0) | old(X0))) [input p5]
7. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> (~quiet(X0) | ~old(X0))) [input p6]
12. ? [X0] : (curious(X0) | ~old(X0)) <=> (~kind(lucy) <~> old(lucy)) [input p11]
13. ! [X0] : (happy(X0) => ~happy(X0)) [input p12]
15. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> (tall(X0) | ~humble(X0))) [input p14]
16. ? [X0] : (kind(X0) | quiet(X0)) <=> calm(fred) [input p15]
17. ? [X0] : curious(X0) [input p16]
23. humble(fred) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~calm(X0)) | rich(X0)) [ennf transformation 5]
31. ! [X0] : ((~rich(X0) | old(X0)) | old(X0)) [ennf transformation 6]
32. ! [X0] : (~rich(X0) | old(X0) | old(X0)) [flattening 31]
33. ! [X0] : (~happy(X0) | ~happy(X0)) [ennf transformation 13]
34. ! [X0] : (((~happy(X0) | strong(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : ((~happy(X0) | strong(X0) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [flattening 34]
41. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 7]
42. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [flattening 41]
56. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X0] : (~curious(X0) & old(X0))) [nnf transformation 12]
57. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [rectify 56]
58. ? [X0] : (curious(X0) | ~old(X0)) => (curious(sK5) | ~old(sK5)) [choice axiom]
59. ((curious(sK5) | ~old(sK5)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [skolemisation 57,58]
62. ! [X0] : (((~rich(X0) | ~tall(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (rich(X0) & tall(X0)))) [nnf transformation 15]
63. ! [X0] : ((~rich(X0) | ~tall(X0) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | (rich(X0) & tall(X0)))) [flattening 62]
64. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X0] : (~kind(X0) & ~quiet(X0))) [nnf transformation 16]
65. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [rectify 64]
66. ? [X0] : (kind(X0) | quiet(X0)) => (kind(sK6) | quiet(sK6)) [choice axiom]
67. ((kind(sK6) | quiet(sK6)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [skolemisation 65,66]
68. ? [X0] : curious(X0) => curious(sK7) [choice axiom]
69. curious(sK7) [skolemisation 17,68]
80. patient(X0) | happy(X0) [cnf transformation 35]
91. ~calm(X0) | rich(X0) [cnf transformation 30]
93. ~rich(X0) | old(X0) | old(X0) [cnf transformation 32]
96. ~patient(X0) | rich(X0) | old(X0) [cnf transformation 42]
126. ~old(lucy) | kind(lucy) | ~curious(X1) [cnf transformation 59]
129. ~happy(X0) | ~happy(X0) [cnf transformation 33]
136. tall(X0) | ~humble(X0) | tall(X0) [cnf transformation 63]
139. ~rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 63]
141. calm(fred) | ~kind(X1) [cnf transformation 67]
143. curious(sK7) [cnf transformation 69]
153. humble(fred) [cnf transformation 23]
154. ~humble(X0) | tall(X0) [duplicate literal removal 136]
155. ~rich(X0) | ~tall(X0) [duplicate literal removal 139]
158. ~happy(X0) [duplicate literal removal 129]
161. ~rich(X0) | old(X0) [duplicate literal removal 93]
166. 2 <=> tall(fred) [avatar definition]
168. tall(fred) <- (2) [avatar component clause 166]
170. 3 <=> calm(fred) [avatar definition]
172. calm(fred) <- (3) [avatar component clause 170]
205. ~patient(X0) | old(X0) [subsumption resolution 96,161]
261. 23 <=> old(lucy) [avatar definition]
263. ~old(lucy) <- (~23) [avatar component clause 261]
265. 24 <=> kind(lucy) [avatar definition]
266. kind(lucy) <- (24) [avatar component clause 265]
279. 27 <=> ! [X1] : ~curious(X1) [avatar definition]
280. ~curious(X1) <- (27) [avatar component clause 279]
281. 27 | 24 | ~23 [avatar split clause 126,261,265,279]
283. 28 <=> ! [X1] : old(X1) [avatar definition]
284. old(X1) <- (28) [avatar component clause 283]
299. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
300. ~kind(X1) <- (31) [avatar component clause 299]
301. 31 | 3 [avatar split clause 141,170,299]
345. rich(fred) <- (3) [resolution 91,172]
348. tall(fred) [resolution 154,153]
349. 2 [avatar split clause 348,166]
350. ~tall(fred) <- (3) [resolution 155,345]
351. $false <- (2, 3) [subsumption resolution 350,168]
352. ~2 | ~3 [avatar contradiction clause 351]
359. old(X0) | happy(X0) [resolution 205,80]
360. old(X0) [subsumption resolution 359,158]
361. 28 [avatar split clause 360,283]
362. $false <- (~23, 28) [resolution 284,263]
365. 23 | ~28 [avatar contradiction clause 362]
366. $false <- (24, 31) [subsumption resolution 266,300]
367. ~24 | ~31 [avatar contradiction clause 366]
368. $false <- (27) [resolution 280,143]
371. ~27 [avatar contradiction clause 368]
372. $false [avatar sat refutation 281,301,349,352,361,365,367,371]
% SZS output end Proof for 1234266936984642995496310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not patient is happy or not rich and vice versa.
Everyone who is either happy or strong is quiet or kind.
Everyone who is both kind and not happy is both strong and quiet and vice versa.
If mary is not kind then lucy is funny or not curious.
Everyone who is either creative or not brave is both creative and wise and vice versa.
If someone is either creative or kind then paul is both calm and not rich and vice versa.
Everyone who is either not creative or calm is not curious and vice versa.
If someone is happy then john is either not strong or brave and vice versa.
If susan is both tall and not kind then someone is both creative and not calm and vice versa.
If someone is not rich or wise then someone is not wise and vice versa.
Everyone who is old is not humble.
If john is not brave or not wise then someone is kind.
If someone is not generous then lucy is both not funny and generous and vice versa.
If paul is funny or not quiet then someone is either not calm or patient and vice versa.
Paul is both not funny and tall.
Someone is either creative or not calm.
Mary is either happy or funny.
Someone is either not creative or not curious.
Someone is either funny or calm.
Someone is both tall and not curious. | Susan is rich. | entailment | (![X]:((patient(X)&~patient(X))<=>(happy(X)|~rich(X))))&
(![X]:((happy(X)<~>strong(X))=>(quiet(X)|kind(X))))&
(![X]:((kind(X)&~happy(X))<=>(strong(X)&quiet(X))))&
((~kind(mary))=>((funny(lucy)|~curious(lucy))))&
(![X]:((creative(X)<~>~brave(X))<=>(creative(X)&wise(X))))&
((?[X]:((creative(X)<~>kind(X))))<=>((calm(paul)&~rich(paul))))&
(![X]:((~creative(X)<~>calm(X))<=>~curious(X)))&
((?[X]:(happy(X)))<=>((~strong(john)<~>brave(john))))&
(((tall(susan)&~kind(susan)))<=>(?[X]:((creative(X)&~calm(X)))))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:(~wise(X))))&
(![X]:(old(X)=>~humble(X)))&
(((~brave(john)|~wise(john)))=>(?[X]:(kind(X))))&
((?[X]:(~generous(X)))<=>((~funny(lucy)&generous(lucy))))&
(((funny(paul)|~quiet(paul)))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((~funny(paul)&tall(paul)))&
(?[X]:((creative(X)<~>~calm(X))))&
((happy(mary)<~>funny(mary)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((funny(X)<~>calm(X))))&
(?[X]:((tall(X)&~curious(X)))) | rich(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3459649912919576521723734
% SZS output start Proof for 3459649912919576521723734
1. ! [X0] : ((~patient(X0) & patient(X0)) <=> (~rich(X0) | happy(X0))) [input p0]
21. ~rich(susan) [input hypothesis]
29. ! [X0] : (((~patient(X0) & patient(X0)) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | (patient(X0) | ~patient(X0)))) [nnf transformation 1]
30. ! [X0] : (((~patient(X0) & patient(X0)) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | patient(X0) | ~patient(X0))) [flattening 29]
82. patient(X0) | rich(X0) [cnf transformation 30]
84. ~patient(X0) | rich(X0) [cnf transformation 30]
142. ~rich(susan) [cnf transformation 21]
145. rich(X0) [subsumption resolution 82,84]
302. $false [subsumption resolution 142,145]
% SZS output end Proof for 3459649912919576521723734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both not brave and not wise. Everyone who is either not old or quiet is kind and vice versa. Everyone who is both not calm and calm is either not rich or not patient. Everyone who is both not quiet and not rich is both generous and curious. If someone is both kind and not old then someone is tall or creative. Everyone who is either creative or tall is either funny or not happy. If lucy is both not generous and not creative then alice is both not wise and tall and vice versa. If someone is both not old and not funny then someone is not funny and vice versa. Everyone who is both not patient and generous is curious and vice versa. If susan is humble then someone is either not generous or not curious. If someone is brave or funny then someone is both not old and not happy and vice versa. Everyone who is either not creative or rich is both not calm and patient. If someone is either not generous or not curious then someone is not creative and vice versa. Everyone who is both not brave and not kind is strong. If someone is both quiet and happy then lucy is both humble and not quiet. Someone is not rich. Mary is not tall or not happy. Someone is not creative or not old. Fred is either not humble or old. Lucy is both not brave and generous. Lucy is either happy or calm. Fred is not humble or wise. John is quiet. | Fred is not old. | neutral | (![X]:(~curious(X)=>(~brave(X)&~wise(X))))&
(![X]:((~old(X)<~>quiet(X))<=>kind(X)))&
(![X]:((~calm(X)&calm(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~rich(X))=>(generous(X)&curious(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((tall(X)|creative(X)))))&
(![X]:((creative(X)<~>tall(X))=>(funny(X)<~>~happy(X))))&
(((~generous(lucy)&~creative(lucy)))<=>((~wise(alice)&tall(alice))))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&generous(X))<=>curious(X)))&
((humble(susan))=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((brave(X)|funny(X))))<=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~calm(X)&patient(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~brave(X)&~kind(X))=>strong(X)))&
((?[X]:((quiet(X)&happy(X))))=>((humble(lucy)&~quiet(lucy))))&
(?[X]:(~rich(X)))&
((~tall(mary)|~happy(mary)))&
(?[X]:((~creative(X)|~old(X))))&
((~humble(fred)<~>old(fred)))&
((~brave(lucy)&generous(lucy)))&
((happy(lucy)<~>calm(lucy)))&
((~humble(fred)|wise(fred)))&
(quiet(john)) | ~old(fred) | [] | null | 0 |
If someone is patient or not quiet then someone is wise and vice versa. Everyone who is kind or not strong is either generous or not kind. Everyone who is not quiet or not rich is both not happy and not patient. Everyone who is not old or not wise is either rich or not tall and vice versa. If someone is both brave and tall then someone is both not wise and not creative and vice versa. Everyone who is curious is not happy and vice versa. Everyone who is both not generous and quiet is not generous or not kind. Everyone who is either not kind or happy is both not curious and creative. Everyone who is not generous is not kind or not tall and vice versa. Everyone who is both patient and curious is either not calm or happy and vice versa. Everyone who is not happy or curious is either old or not wise and vice versa. If mary is either not strong or humble then someone is not wise or tall. Everyone who is both not creative and not kind is humble or generous and vice versa. If someone is either wise or quiet then someone is tall and vice versa. Everyone who is kind or not creative is both not quiet and generous and vice versa. John is not wise. Paul is either happy or not happy. Someone is generous or happy. Susan is wise or not funny. Someone is both happy and quiet. Someone is not old. Fred is either not strong or not curious. | Susan is calm. | contradiction | ((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~curious(X)&creative(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~tall(X))))&
(![X]:((patient(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~happy(X)|curious(X))<=>(old(X)<~>~wise(X))))&
(((~strong(mary)<~>humble(mary)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(humble(X)|generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)|~creative(X))<=>(~quiet(X)&generous(X))))&
(~wise(john))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((generous(X)|happy(X))))&
((wise(susan)|~funny(susan)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:(~old(X)))&
((~strong(fred)<~>~curious(fred))) | calm(susan) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1667213874482012727652038
% SZS output start Proof for 1667213874482012727652038
2. ! [X0] : ((~strong(X0) | kind(X0)) => (generous(X0) <~> ~kind(X0))) [input p1]
6. ! [X0] : (curious(X0) <=> ~happy(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> happy(X0)) => (creative(X0) & ~curious(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (~tall(X0) | ~kind(X0))) [input p8]
10. ! [X0] : ((curious(X0) & patient(X0)) <=> (~calm(X0) <~> happy(X0))) [input p9]
13. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (generous(X0) | humble(X0))) [input p12]
23. calm(susan) [input hypothesis]
28. ! [X0] : ((generous(X0) <~> ~kind(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 2]
32. ! [X0] : ((creative(X0) & ~curious(X0)) | (~kind(X0) <=> happy(X0))) [ennf transformation 8]
39. ! [X0] : (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (strong(X0) & ~kind(X0))) [nnf transformation 28]
47. ! [X0] : ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))) [nnf transformation 6]
48. ! [X0] : ((creative(X0) & ~curious(X0)) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 32]
49. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 9]
50. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | generous(X0))) [flattening 49]
51. ! [X0] : (((curious(X0) & patient(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~curious(X0) | ~patient(X0)))) [nnf transformation 10]
52. ! [X0] : (((curious(X0) & patient(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~curious(X0) | ~patient(X0))) [flattening 51]
58. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 13]
59. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | kind(X0) | creative(X0))) [flattening 58]
78. ~kind(X0) | generous(X0) | ~kind(X0) [cnf transformation 39]
96. ~curious(X0) | ~happy(X0) [cnf transformation 47]
97. curious(X0) | happy(X0) [cnf transformation 47]
99. ~curious(X0) | happy(X0) | kind(X0) [cnf transformation 48]
104. ~generous(X0) | kind(X0) [cnf transformation 50]
111. curious(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 52]
124. ~kind(X0) | ~generous(X0) [cnf transformation 59]
143. calm(susan) [cnf transformation 23]
144. ~kind(X0) | generous(X0) [duplicate literal removal 78]
195. ~curious(X0) | kind(X0) [subsumption resolution 99,96]
196. ~calm(X0) | curious(X0) [subsumption resolution 111,97]
219. ~generous(X0) [subsumption resolution 124,104]
271. curious(susan) [resolution 196,143]
273. kind(susan) [resolution 271,195]
276. generous(susan) [resolution 273,144]
279. $false [subsumption resolution 276,219]
% SZS output end Proof for 1667213874482012727652038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not curious then paul is either funny or not rich.
If someone is both kind and brave then someone is strong.
Everyone who is both tall and not funny is both not creative and strong and vice versa.
Everyone who is curious or not patient is either not old or tall and vice versa.
If susan is both rich and happy then mary is generous and vice versa.
Everyone who is funny or kind is both not calm and not rich and vice versa.
If someone is either strong or quiet then someone is both not wise and funny and vice versa.
If someone is not strong or strong then paul is both calm and not tall and vice versa.
If someone is both not patient and tall then fred is either calm or not curious and vice versa.
Everyone who is patient is both not calm and generous and vice versa.
Everyone who is calm or strong is humble or brave and vice versa.
Everyone who is either not tall or calm is not generous or not quiet.
Everyone who is not humble is not old.
If lucy is not wise or generous then someone is strong or not wise.
Everyone who is either not brave or humble is not kind or tall and vice versa.
If someone is both calm and not strong then someone is both curious and strong and vice versa.
Someone is either humble or not patient.
Lucy is not kind or not happy.
Fred is kind.
Susan is patient or old.
Mary is wise.
Fred is not wise or not creative.
Someone is not funny.
Someone is not quiet. | Fred is rich. | contradiction | ((~curious(fred))=>((funny(paul)<~>~rich(paul))))&
((?[X]:((kind(X)&brave(X))))=>(?[X]:(strong(X))))&
(![X]:((tall(X)&~funny(X))<=>(~creative(X)&strong(X))))&
(![X]:((curious(X)|~patient(X))<=>(~old(X)<~>tall(X))))&
(((rich(susan)&happy(susan)))<=>(generous(mary)))&
(![X]:((funny(X)|kind(X))<=>(~calm(X)&~rich(X))))&
((?[X]:((strong(X)<~>quiet(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>((calm(paul)&~tall(paul))))&
((?[X]:((~patient(X)&tall(X))))<=>((calm(fred)<~>~curious(fred))))&
(![X]:(patient(X)<=>(~calm(X)&generous(X))))&
(![X]:((calm(X)|strong(X))<=>(humble(X)|brave(X))))&
(![X]:((~tall(X)<~>calm(X))=>(~generous(X)|~quiet(X))))&
(![X]:(~humble(X)=>~old(X)))&
(((~wise(lucy)|generous(lucy)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((~brave(X)<~>humble(X))<=>(~kind(X)|tall(X))))&
((?[X]:((calm(X)&~strong(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~kind(lucy)|~happy(lucy)))&
(kind(fred))&
((patient(susan)|old(susan)))&
(wise(mary))&
((~wise(fred)|~creative(fred)))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X))) | rich(fred) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7189494871401108316997531
% SZS output start Proof for 7189494871401108316997531
6. ! [X0] : ((kind(X0) | funny(X0)) <=> (~rich(X0) & ~calm(X0))) [input p5]
19. kind(fred) [input p18]
25. rich(fred) [input hypothesis]
45. ! [X0] : (((kind(X0) | funny(X0)) | (rich(X0) | calm(X0))) & ((~rich(X0) & ~calm(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 6]
46. ! [X0] : ((kind(X0) | funny(X0) | rich(X0) | calm(X0)) & ((~rich(X0) & ~calm(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 45]
101. ~kind(X0) | ~rich(X0) [cnf transformation 46]
145. kind(fred) [cnf transformation 19]
151. rich(fred) [cnf transformation 25]
345. ~rich(fred) [resolution 101,145]
346. $false [subsumption resolution 345,151]
% SZS output end Proof for 7189494871401108316997531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is funny.
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 brave.
If someone is either calm or not happy then someone is either calm or creative.
If john is not calm then fred is either strong or funny and vice versa.
Everyone who is either not brave or not tall is not brave.
If john is either humble or quiet then susan is rich or not old.
Everyone who is not brave or not humble is tall or happy.
Everyone who is brave is either brave or not rich.
If john is generous then lucy is not quiet.
Everyone who is either quiet or not quiet is both not old and rich and vice versa.
Everyone who is not curious is both not funny and not brave.
Everyone who is not wise is both tall and wise and vice versa.
Everyone who is not wise is either creative or not funny.
Someone is either not creative or strong.
Paul is either not strong or not curious.
Fred is old or creative.
Someone is not quiet.
Mary is either not generous or not happy.
Fred is either not generous or not curious.
Someone is either strong or wise.
Someone is both not old and calm. | John is not happy. | contradiction | ((?[X]:(rich(X)))=>(?[X]:(funny(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)|brave(alice))))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
((~calm(john))<=>((strong(fred)<~>funny(fred))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&wise(X))))&
(![X]:(~wise(X)=>(creative(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
((~strong(paul)<~>~curious(paul)))&
((old(fred)|creative(fred)))&
(?[X]:(~quiet(X)))&
((~generous(mary)<~>~happy(mary)))&
((~generous(fred)<~>~curious(fred)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~old(X)&calm(X)))) | ~happy(john) | [
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5762246621324503761757154
% SZS output start Proof for 5762246621324503761757154
8. ! [X0] : ((~brave(X0) <~> ~tall(X0)) => ~brave(X0)) [input p7]
10. ! [X0] : ((~humble(X0) | ~brave(X0)) => (happy(X0) | tall(X0))) [input p9]
15. ! [X0] : (~wise(X0) <=> (wise(X0) & tall(X0))) [input p14]
25. ~happy(john) [input hypothesis]
36. ! [X0] : (~brave(X0) | (~brave(X0) <=> ~tall(X0))) [ennf transformation 8]
39. ! [X0] : ((happy(X0) | tall(X0)) | (humble(X0) & brave(X0))) [ennf transformation 10]
40. ! [X0] : (happy(X0) | tall(X0) | (humble(X0) & brave(X0))) [flattening 39]
55. ! [X0] : (~brave(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) [nnf transformation 36]
60. ! [X0] : ((~wise(X0) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | wise(X0))) [nnf transformation 15]
61. ! [X0] : ((~wise(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | wise(X0))) [flattening 60]
94. ~brave(X0) | ~brave(X0) | tall(X0) [cnf transformation 55]
97. happy(X0) | tall(X0) | brave(X0) [cnf transformation 40]
111. wise(X0) | wise(X0) [cnf transformation 61]
112. ~wise(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 61]
129. ~happy(john) [cnf transformation 25]
130. wise(X0) [duplicate literal removal 111]
131. ~wise(X0) | ~tall(X0) [duplicate literal removal 112]
137. ~brave(X0) | tall(X0) [duplicate literal removal 94]
218. tall(X0) | happy(X0) [subsumption resolution 97,137]
280. ~tall(X0) [resolution 131,130]
283. happy(X0) [resolution 218,280]
284. $false [resolution 283,129]
% SZS output end Proof for 5762246621324503761757154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is happy or not kind then someone is calm or kind.
Everyone who is not humble or kind is not strong.
Everyone who is not calm or calm is both not tall and humble and vice versa.
Everyone who is old is both not quiet and not strong.
If susan is either humble or rich then someone is both generous and curious and vice versa.
Everyone who is not wise or not calm is either strong or quiet.
Everyone who is either tall or strong is strong or not brave and vice versa.
Everyone who is patient is either not brave or not strong and vice versa.
Everyone who is both not calm and calm is funny and vice versa.
Everyone who is old is both not funny and patient and vice versa.
If fred is both not creative and calm then mary is kind and vice versa.
If someone is not old or not strong then lucy is old.
Everyone who is both not creative and generous is strong.
If susan is not humble then someone is not wise or not humble and vice versa.
If someone is strong or brave then john is strong or not patient and vice versa.
If paul is not strong or not wise then someone is patient.
Someone is either not funny or not curious.
Fred is either not tall or not calm.
Someone is either wise or not kind.
Someone is either quiet or not calm.
Someone is not creative or not humble.
John is creative.
Someone is either not patient or rich. | Susan is not brave. | contradiction | (((happy(alice)|~kind(alice)))=>(?[X]:((calm(X)|kind(X)))))&
(![X]:((~humble(X)|kind(X))=>~strong(X)))&
(![X]:((~calm(X)|calm(X))<=>(~tall(X)&humble(X))))&
(![X]:(old(X)=>(~quiet(X)&~strong(X))))&
(((humble(susan)<~>rich(susan)))<=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~wise(X)|~calm(X))=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)<~>strong(X))<=>(strong(X)|~brave(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&calm(X))<=>funny(X)))&
(![X]:(old(X)<=>(~funny(X)&patient(X))))&
(((~creative(fred)&calm(fred)))<=>(kind(mary)))&
((?[X]:((~old(X)|~strong(X))))=>(old(lucy)))&
(![X]:((~creative(X)&generous(X))=>strong(X)))&
((~humble(susan))<=>(?[X]:((~wise(X)|~humble(X)))))&
((?[X]:((strong(X)|brave(X))))<=>((strong(john)|~patient(john))))&
(((~strong(paul)|~wise(paul)))=>(?[X]:(patient(X))))&
(?[X]:((~funny(X)<~>~curious(X))))&
((~tall(fred)<~>~calm(fred)))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(creative(john))&
(?[X]:((~patient(X)<~>rich(X)))) | ~brave(susan) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4140330679691396070133675
% SZS output start Proof for 4140330679691396070133675
3. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (humble(X0) & ~tall(X0))) [input p2]
4. ! [X0] : (old(X0) => (~strong(X0) & ~quiet(X0))) [input p3]
7. ! [X0] : ((tall(X0) <~> strong(X0)) <=> (~brave(X0) | strong(X0))) [input p6]
8. ! [X0] : (patient(X0) <=> (~brave(X0) <~> ~strong(X0))) [input p7]
9. ! [X0] : ((calm(X0) & ~calm(X0)) <=> funny(X0)) [input p8]
10. ! [X0] : (old(X0) <=> (patient(X0) & ~funny(X0))) [input p9]
24. ~brave(susan) [input hypothesis]
28. ! [X0] : ((~strong(X0) & ~quiet(X0)) | ~old(X0)) [ennf transformation 4]
36. ! [X0] : (((calm(X0) | ~calm(X0)) | (~humble(X0) | tall(X0))) & ((humble(X0) & ~tall(X0)) | (~calm(X0) & calm(X0)))) [nnf transformation 3]
37. ! [X0] : ((calm(X0) | ~calm(X0) | ~humble(X0) | tall(X0)) & ((humble(X0) & ~tall(X0)) | (~calm(X0) & calm(X0)))) [flattening 36]
43. ! [X0] : ((((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))))) [nnf transformation 7]
44. ! [X0] : ((((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))))) [flattening 43]
45. ! [X0] : ((patient(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | ~patient(X0))) [nnf transformation 8]
46. ! [X0] : (((calm(X0) & ~calm(X0)) | ~funny(X0)) & (funny(X0) | (~calm(X0) | calm(X0)))) [nnf transformation 9]
47. ! [X0] : (((calm(X0) & ~calm(X0)) | ~funny(X0)) & (funny(X0) | ~calm(X0) | calm(X0))) [flattening 46]
48. ! [X0] : ((old(X0) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | ~old(X0))) [nnf transformation 10]
49. ! [X0] : ((old(X0) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | ~old(X0))) [flattening 48]
81. ~tall(X0) | calm(X0) [cnf transformation 37]
82. ~tall(X0) | ~calm(X0) [cnf transformation 37]
87. ~old(X0) | ~strong(X0) [cnf transformation 28]
101. strong(X0) | tall(X0) | brave(X0) [cnf transformation 44]
106. patient(X0) | ~strong(X0) | brave(X0) [cnf transformation 45]
109. ~calm(X0) | ~funny(X0) [cnf transformation 47]
110. ~funny(X0) | calm(X0) [cnf transformation 47]
113. old(X0) | ~patient(X0) | funny(X0) [cnf transformation 49]
141. ~brave(susan) [cnf transformation 24]
158. ~tall(X0) [subsumption resolution 81,82]
180. brave(X0) | strong(X0) [subsumption resolution 101,158]
182. patient(X0) | brave(X0) [subsumption resolution 106,180]
183. ~funny(X0) [subsumption resolution 109,110]
184. ~patient(X0) | old(X0) [subsumption resolution 113,183]
270. strong(susan) [resolution 180,141]
278. brave(X0) | old(X0) [resolution 184,182]
289. old(susan) [resolution 278,141]
294. ~strong(susan) [resolution 289,87]
295. $false [subsumption resolution 294,270]
% SZS output end Proof for 4140330679691396070133675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not quiet then lucy is both wise and creative and vice versa.
If susan is either not strong or rich then paul is not funny or rich and vice versa.
Everyone who is humble or strong is rich.
If paul is not curious or brave then susan is not patient.
If someone is either not rich or not generous then someone is both not strong and brave.
Everyone who is old is either not funny or not kind and vice versa.
Everyone who is creative is not happy or not tall and vice versa.
If someone is either not humble or brave then someone is patient or happy and vice versa.
If paul is both not quiet and calm then someone is not humble and vice versa.
If mary is not calm then someone is either kind or not wise.
If susan is not humble then someone is calm and vice versa.
If paul is either not humble or generous then someone is both patient and tall.
If alice is either not happy or strong then lucy is not strong or funny and vice versa.
Everyone who is both not humble and patient is not wise or calm and vice versa.
Everyone who is not wise or quiet is not funny or strong.
Everyone who is both tall and not creative is both funny and quiet.
Lucy is either not generous or creative.
Fred is either not old or humble.
John is not strong.
Lucy is not calm.
Someone is funny or not humble.
Someone is either not humble or patient.
Someone is both humble and kind.
Mary is tall. | John is not creative. | contradiction | ((?[X]:((~patient(X)|~quiet(X))))<=>((wise(lucy)&creative(lucy))))&
(((~strong(susan)<~>rich(susan)))<=>((~funny(paul)|rich(paul))))&
(![X]:((humble(X)|strong(X))=>rich(X)))&
(((~curious(paul)|brave(paul)))=>(~patient(susan)))&
((?[X]:((~rich(X)<~>~generous(X))))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:(old(X)<=>(~funny(X)<~>~kind(X))))&
(![X]:(creative(X)<=>(~happy(X)|~tall(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((patient(X)|happy(X)))))&
(((~quiet(paul)&calm(paul)))<=>(?[X]:(~humble(X))))&
((~calm(mary))=>(?[X]:((kind(X)<~>~wise(X)))))&
((~humble(susan))<=>(?[X]:(calm(X))))&
(((~humble(paul)<~>generous(paul)))=>(?[X]:((patient(X)&tall(X)))))&
(((~happy(alice)<~>strong(alice)))<=>((~strong(lucy)|funny(lucy))))&
(![X]:((~humble(X)&patient(X))<=>(~wise(X)|calm(X))))&
(![X]:((~wise(X)|quiet(X))=>(~funny(X)|strong(X))))&
(![X]:((tall(X)&~creative(X))=>(funny(X)&quiet(X))))&
((~generous(lucy)<~>creative(lucy)))&
((~old(fred)<~>humble(fred)))&
(~strong(john))&
(~calm(lucy))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~humble(X)<~>patient(X))))&
(?[X]:((humble(X)&kind(X))))&
(tall(mary)) | ~creative(john) | [
"p6",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3239583210756647326426036
% SZS output start Proof for 3239583210756647326426036
7. ! [X0] : (creative(X0) <=> (~tall(X0) | ~happy(X0))) [input p6]
15. ! [X0] : ((quiet(X0) | ~wise(X0)) => (strong(X0) | ~funny(X0))) [input p14]
16. ! [X0] : ((~creative(X0) & tall(X0)) => (quiet(X0) & funny(X0))) [input p15]
19. ~strong(john) [input p18]
25. ~creative(john) [input hypothesis]
34. ! [X0] : ((strong(X0) | ~funny(X0)) | (~quiet(X0) & wise(X0))) [ennf transformation 15]
35. ! [X0] : (strong(X0) | ~funny(X0) | (~quiet(X0) & wise(X0))) [flattening 34]
36. ! [X0] : ((quiet(X0) & funny(X0)) | (creative(X0) | ~tall(X0))) [ennf transformation 16]
37. ! [X0] : ((quiet(X0) & funny(X0)) | creative(X0) | ~tall(X0)) [flattening 36]
50. ! [X0] : ((creative(X0) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | ~creative(X0))) [nnf transformation 7]
51. ! [X0] : ((creative(X0) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | ~creative(X0))) [flattening 50]
109. tall(X0) | creative(X0) [cnf transformation 51]
139. ~funny(X0) | strong(X0) | ~quiet(X0) [cnf transformation 35]
140. funny(X0) | creative(X0) | ~tall(X0) [cnf transformation 37]
141. quiet(X0) | creative(X0) | ~tall(X0) [cnf transformation 37]
146. ~strong(john) [cnf transformation 19]
154. ~creative(john) [cnf transformation 25]
352. creative(X0) | quiet(X0) [subsumption resolution 141,109]
353. funny(X0) | creative(X0) [subsumption resolution 140,109]
480. strong(X0) | ~quiet(X0) | creative(X0) [resolution 139,353]
481. strong(X0) | creative(X0) [subsumption resolution 480,352]
504. creative(john) [resolution 481,146]
506. $false [subsumption resolution 504,154]
% SZS output end Proof for 3239583210756647326426036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not rich is not happy. If someone is either not patient or not generous then someone is calm. Everyone who is generous or rich is happy and vice versa. Everyone who is calm or not generous is both not wise and old and vice versa. If john is either curious or not quiet then someone is tall or not happy and vice versa. Everyone who is either tall or not generous is tall or rich and vice versa. Everyone who is curious is both not creative and not funny and vice versa. Everyone who is not brave is both tall and calm and vice versa. Everyone who is both not creative and kind is both not strong and happy and vice versa. Everyone who is both not creative and curious is both not tall and happy. Everyone who is either tall or not generous is both wise and tall. Everyone who is either not happy or not wise is both rich and funny and vice versa. Everyone who is curious or not kind is happy and vice versa. Everyone who is not humble or not brave is not generous and vice versa. If lucy is both not calm and not brave then alice is either calm or humble. If john is both not strong and not calm then mary is not happy or not brave. Mary is either not generous or not kind. Someone is tall. Mary is either happy or not tall. Paul is not happy or generous. Someone is rich or quiet. John is either not old or kind. | Paul is not generous. | contradiction | (![X]:((quiet(X)|~rich(X))=>~happy(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(calm(X))))&
(![X]:((generous(X)|rich(X))<=>happy(X)))&
(![X]:((calm(X)|~generous(X))<=>(~wise(X)&old(X))))&
(((curious(john)<~>~quiet(john)))<=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((tall(X)<~>~generous(X))<=>(tall(X)|rich(X))))&
(![X]:(curious(X)<=>(~creative(X)&~funny(X))))&
(![X]:(~brave(X)<=>(tall(X)&calm(X))))&
(![X]:((~creative(X)&kind(X))<=>(~strong(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))=>(~tall(X)&happy(X))))&
(![X]:((tall(X)<~>~generous(X))=>(wise(X)&tall(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>(rich(X)&funny(X))))&
(![X]:((curious(X)|~kind(X))<=>happy(X)))&
(![X]:((~humble(X)|~brave(X))<=>~generous(X)))&
(((~calm(lucy)&~brave(lucy)))=>((calm(alice)<~>humble(alice))))&
(((~strong(john)&~calm(john)))=>((~happy(mary)|~brave(mary))))&
((~generous(mary)<~>~kind(mary)))&
(?[X]:(tall(X)))&
((happy(mary)<~>~tall(mary)))&
((~happy(paul)|generous(paul)))&
(?[X]:((rich(X)|quiet(X))))&
((~old(john)<~>kind(john))) | ~generous(paul) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 812082683773403261457974
% SZS output start Proof for 812082683773403261457974
6. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (rich(X0) | tall(X0))) [input p5]
11. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (tall(X0) & wise(X0))) [input p10]
23. ~generous(paul) [input hypothesis]
29. ! [X0] : ((tall(X0) & wise(X0)) | (tall(X0) <=> ~generous(X0))) [ennf transformation 11]
46. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 6]
47. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 46]
54. ! [X0] : ((tall(X0) & wise(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 29]
91. generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 47]
108. tall(X0) | tall(X0) | generous(X0) [cnf transformation 54]
133. ~generous(paul) [cnf transformation 23]
134. tall(X0) | generous(X0) [duplicate literal removal 108]
136. generous(X0) | ~tall(X0) [duplicate literal removal 91]
180. generous(X0) [subsumption resolution 134,136]
226. $false [subsumption resolution 133,180]
% SZS output end Proof for 812082683773403261457974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both calm and funny then someone is not wise and vice versa.
Everyone who is either not strong or patient is not creative and vice versa.
Everyone who is not patient or humble is both humble and not wise.
If someone is kind then someone is not wise or not tall.
Everyone who is both happy and not creative is not strong.
Everyone who is not old is either brave or rich and vice versa.
Everyone who is not tall is either not curious or not brave and vice versa.
Everyone who is not generous or not funny is both generous and humble.
Everyone who is tall is not quiet and vice versa.
If john is not patient then susan is not strong.
If fred is quiet then john is either not patient or curious.
If john is creative or calm then someone is not humble.
If someone is both tall and not creative then fred is either calm or not patient.
Everyone who is both wise and kind is either not calm or funny and vice versa.
If someone is either not generous or quiet then alice is not humble or rich and vice versa.
Everyone who is either not quiet or funny is not patient and vice versa.
Lucy is either not generous or generous.
Someone is both not patient and calm.
Someone is not old.
Susan is either kind or curious.
Fred is generous.
Susan is not wise.
Susan is not humble or tall. | Susan is tall. | entailment | (((calm(fred)&funny(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~creative(X)))&
(![X]:((~patient(X)|humble(X))=>(humble(X)&~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)|~tall(X)))))&
(![X]:((happy(X)&~creative(X))=>~strong(X)))&
(![X]:(~old(X)<=>(brave(X)<~>rich(X))))&
(![X]:(~tall(X)<=>(~curious(X)<~>~brave(X))))&
(![X]:((~generous(X)|~funny(X))=>(generous(X)&humble(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
((~patient(john))=>(~strong(susan)))&
((quiet(fred))=>((~patient(john)<~>curious(john))))&
(((creative(john)|calm(john)))=>(?[X]:(~humble(X))))&
((?[X]:((tall(X)&~creative(X))))=>((calm(fred)<~>~patient(fred))))&
(![X]:((wise(X)&kind(X))<=>(~calm(X)<~>funny(X))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((~humble(alice)|rich(alice))))&
(![X]:((~quiet(X)<~>funny(X))<=>~patient(X)))&
((~generous(lucy)<~>generous(lucy)))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:(~old(X)))&
((kind(susan)<~>curious(susan)))&
(generous(fred))&
(~wise(susan))&
((~humble(susan)|tall(susan))) | tall(susan) | [
"p2",
"p7",
"p8",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7183399299281379757437617
% SZS output start Proof for 7183399299281379757437617
3. ! [X0] : ((humble(X0) | ~patient(X0)) => (~wise(X0) & humble(X0))) [input p2]
8. ! [X0] : ((~funny(X0) | ~generous(X0)) => (humble(X0) & generous(X0))) [input p7]
9. ! [X0] : (tall(X0) <=> ~quiet(X0)) [input p8]
16. ! [X0] : ((~quiet(X0) <~> funny(X0)) <=> ~patient(X0)) [input p15]
23. tall(susan) | ~humble(susan) [input p22]
24. ~tall(susan) [input hypothesis]
28. ! [X0] : ((~wise(X0) & humble(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 3]
31. ! [X0] : ((humble(X0) & generous(X0)) | (funny(X0) & generous(X0))) [ennf transformation 8]
47. ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))) [nnf transformation 9]
59. ! [X0] : ((((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | patient(X0)) & (~patient(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0))))) [nnf transformation 16]
73. humble(X0) | patient(X0) [cnf transformation 28]
87. humble(X0) | funny(X0) [cnf transformation 31]
89. quiet(X0) | tall(X0) [cnf transformation 47]
110. ~quiet(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 59]
122. tall(susan) | ~humble(susan) [cnf transformation 23]
123. ~tall(susan) [cnf transformation 24]
229. 23 <=> humble(susan) [avatar definition]
231. ~humble(susan) <- (~23) [avatar component clause 229]
233. 24 <=> tall(susan) [avatar definition]
234. ~tall(susan) <- (~24) [avatar component clause 233]
236. ~23 | 24 [avatar split clause 122,233,229]
237. ~24 [avatar split clause 123,233]
240. patient(susan) <- (~23) [resolution 73,231]
243. funny(susan) <- (~23) [resolution 87,231]
410. ~patient(X0) | ~funny(X0) | tall(X0) [resolution 110,89]
488. ~funny(susan) | tall(susan) <- (~23) [resolution 410,240]
491. tall(susan) <- (~23) [subsumption resolution 488,243]
492. $false <- (~23, ~24) [subsumption resolution 491,234]
493. 23 | 24 [avatar contradiction clause 492]
494. $false [avatar sat refutation 236,237,493]
% SZS output end Proof for 7183399299281379757437617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not rich or calm is both not happy and calm and vice versa.
If someone is not strong or not funny then someone is either not calm or funny and vice versa.
If someone is not curious or kind then john is either not patient or not wise.
If someone is both not happy and wise then someone is either not patient or wise and vice versa.
Everyone who is both rich and not quiet is happy or not brave.
If alice is strong then mary is both not strong and not curious.
Everyone who is either generous or not wise is both humble and not brave and vice versa.
Everyone who is either not patient or generous is both not wise and patient and vice versa.
Everyone who is humble is both not humble and rich and vice versa.
If someone is both creative and brave then fred is either rich or brave.
If john is both quiet and humble then alice is both not old and old and vice versa.
Everyone who is both not happy and old is not patient or not quiet.
If susan is both not happy and calm then someone is either not tall or not quiet and vice versa.
If someone is either rich or not humble then someone is generous and vice versa.
Everyone who is not rich or curious is not curious.
Everyone who is either not funny or not rich is funny and vice versa.
Someone is patient.
Mary is both not rich and patient.
Someone is not rich.
Susan is both creative and patient.
Susan is not kind or not humble.
Susan is either brave or not kind. | John is not generous. | contradiction | (![X]:((~rich(X)<~>calm(X))<=>(~happy(X)&calm(X))))&
((?[X]:((~strong(X)|~funny(X))))<=>(?[X]:((~calm(X)<~>funny(X)))))&
((?[X]:((~curious(X)|kind(X))))=>((~patient(john)<~>~wise(john))))&
((?[X]:((~happy(X)&wise(X))))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((rich(X)&~quiet(X))=>(happy(X)|~brave(X))))&
((strong(alice))=>((~strong(mary)&~curious(mary))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)&~brave(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~wise(X)&patient(X))))&
(![X]:(humble(X)<=>(~humble(X)&rich(X))))&
((?[X]:((creative(X)&brave(X))))=>((rich(fred)<~>brave(fred))))&
(((quiet(john)&humble(john)))<=>((~old(alice)&old(alice))))&
(![X]:((~happy(X)&old(X))=>(~patient(X)|~quiet(X))))&
(((~happy(susan)&calm(susan)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((rich(X)<~>~humble(X))))<=>(?[X]:(generous(X))))&
(![X]:((~rich(X)|curious(X))=>~curious(X)))&
(![X]:((~funny(X)<~>~rich(X))<=>funny(X)))&
(?[X]:(patient(X)))&
((~rich(mary)&patient(mary)))&
(?[X]:(~rich(X)))&
((creative(susan)&patient(susan)))&
((~kind(susan)|~humble(susan)))&
((brave(susan)<~>~kind(susan))) | ~generous(john) | [
"p2",
"p6",
"p7",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7000340541375566404187673
% SZS output start Proof for 7000340541375566404187673
3. ? [X0] : (kind(X0) | ~curious(X0)) => (~patient(john) <~> ~wise(john)) [input p2]
7. ! [X0] : ((generous(X0) <~> ~wise(X0)) <=> (~brave(X0) & humble(X0))) [input p6]
8. ! [X0] : ((~patient(X0) <~> generous(X0)) <=> (patient(X0) & ~wise(X0))) [input p7]
9. ! [X0] : (humble(X0) <=> (rich(X0) & ~humble(X0))) [input p8]
15. ! [X0] : ((curious(X0) | ~rich(X0)) => ~curious(X0)) [input p14]
16. ! [X0] : ((~funny(X0) <~> ~rich(X0)) <=> funny(X0)) [input p15]
23. ~generous(john) [input hypothesis]
27. (~patient(john) <~> ~wise(john)) | ! [X0] : (~kind(X0) & curious(X0)) [ennf transformation 3]
34. ! [X0] : (~curious(X0) | (~curious(X0) & rich(X0))) [ennf transformation 15]
42. ((wise(john) | patient(john)) & (~wise(john) | ~patient(john))) | ! [X0] : (~kind(X0) & curious(X0)) [nnf transformation 27]
48. ! [X0] : ((((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))))) [nnf transformation 7]
49. ! [X0] : ((((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))))) [flattening 48]
50. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [nnf transformation 8]
51. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [flattening 50]
52. ! [X0] : ((humble(X0) | (~rich(X0) | humble(X0))) & ((rich(X0) & ~humble(X0)) | ~humble(X0))) [nnf transformation 9]
53. ! [X0] : ((humble(X0) | ~rich(X0) | humble(X0)) & ((rich(X0) & ~humble(X0)) | ~humble(X0))) [flattening 52]
67. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ~funny(X0)) & (funny(X0) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [nnf transformation 16]
85. ~wise(john) | ~patient(john) | curious(X0) [cnf transformation 42]
99. humble(X0) | generous(X0) | wise(X0) [cnf transformation 49]
106. patient(X0) | generous(X0) | patient(X0) [cnf transformation 51]
111. ~humble(X0) | rich(X0) [cnf transformation 53]
131. ~curious(X0) | ~curious(X0) [cnf transformation 34]
132. funny(X0) | ~rich(X0) | funny(X0) [cnf transformation 67]
134. ~rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 67]
145. ~generous(john) [cnf transformation 23]
146. funny(X0) | ~rich(X0) [duplicate literal removal 132]
147. ~funny(X0) | ~rich(X0) [duplicate literal removal 134]
148. ~curious(X0) [duplicate literal removal 131]
151. generous(X0) | patient(X0) [duplicate literal removal 106]
193. 10 <=> patient(john) [avatar definition]
197. 11 <=> wise(john) [avatar definition]
202. 12 <=> ! [X0] : curious(X0) [avatar definition]
203. curious(X0) <- (12) [avatar component clause 202]
206. 12 | ~10 | ~11 [avatar split clause 85,197,193,202]
302. ~rich(X0) [subsumption resolution 146,147]
315. patient(john) [resolution 151,145]
329. generous(X0) | wise(X0) | rich(X0) [resolution 99,111]
331. generous(X0) | wise(X0) [subsumption resolution 329,302]
335. wise(john) [resolution 331,145]
340. 10 [avatar split clause 315,193]
341. 11 [avatar split clause 335,197]
342. $false <- (12) [subsumption resolution 203,148]
343. ~12 [avatar contradiction clause 342]
344. $false [avatar sat refutation 206,340,341,343]
% SZS output end Proof for 7000340541375566404187673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not tall then someone is not strong and vice versa.
Everyone who is either strong or creative is wise and vice versa.
Everyone who is creative is not quiet or generous and vice versa.
Everyone who is not brave or curious is both not rich and not quiet and vice versa.
Everyone who is not quiet is both not creative and kind and vice versa.
If someone is rich then someone is both brave and tall and vice versa.
Everyone who is calm or wise is not creative.
Everyone who is not patient is both generous and not humble.
Everyone who is rich is either creative or not quiet.
Everyone who is either not patient or not funny is both not curious and funny and vice versa.
Everyone who is not curious or patient is not kind or curious.
If lucy is either quiet or humble then paul is not rich and vice versa.
Everyone who is both brave and not humble is funny and vice versa.
If fred is not brave then susan is creative or not wise.
Everyone who is both rich and not quiet is both not creative and not happy.
Everyone who is both not funny and quiet is rich or not old.
John is either tall or kind.
Lucy is patient or not happy.
Someone is not old or strong.
Someone is creative.
Alice is rich or generous. | John is not funny. | contradiction | ((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(X)<~>creative(X))<=>wise(X)))&
(![X]:(creative(X)<=>(~quiet(X)|generous(X))))&
(![X]:((~brave(X)|curious(X))<=>(~rich(X)&~quiet(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)|wise(X))=>~creative(X)))&
(![X]:(~patient(X)=>(generous(X)&~humble(X))))&
(![X]:(rich(X)=>(creative(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~curious(X)&funny(X))))&
(![X]:((~curious(X)|patient(X))=>(~kind(X)|curious(X))))&
(((quiet(lucy)<~>humble(lucy)))<=>(~rich(paul)))&
(![X]:((brave(X)&~humble(X))<=>funny(X)))&
((~brave(fred))=>((creative(susan)|~wise(susan))))&
(![X]:((rich(X)&~quiet(X))=>(~creative(X)&~happy(X))))&
(![X]:((~funny(X)&quiet(X))=>(rich(X)|~old(X))))&
((tall(john)<~>kind(john)))&
((patient(lucy)|~happy(lucy)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(creative(X)))&
((rich(alice)|generous(alice))) | ~funny(john) | [
"p2",
"p3",
"p4",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4197550081300939013448523
% SZS output start Proof for 4197550081300939013448523
3. ! [X0] : (creative(X0) <=> (generous(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((curious(X0) | ~brave(X0)) <=> (~quiet(X0) & ~rich(X0))) [input p3]
5. ! [X0] : (~quiet(X0) <=> (kind(X0) & ~creative(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (~humble(X0) & generous(X0))) [input p7]
10. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (funny(X0) & ~curious(X0))) [input p9]
13. ! [X0] : ((~humble(X0) & brave(X0)) <=> funny(X0)) [input p12]
22. ~funny(john) [input hypothesis]
33. ! [X0] : ((~humble(X0) & generous(X0)) | patient(X0)) [ennf transformation 8]
47. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 3]
48. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
49. ! [X0] : (((curious(X0) | ~brave(X0)) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [nnf transformation 4]
50. ! [X0] : ((curious(X0) | ~brave(X0) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [flattening 49]
51. ! [X0] : ((~quiet(X0) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [nnf transformation 5]
52. ! [X0] : ((~quiet(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [flattening 51]
59. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 10]
60. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 59]
62. ! [X0] : (((~humble(X0) & brave(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) | ~brave(X0)))) [nnf transformation 13]
63. ! [X0] : (((~humble(X0) & brave(X0)) | ~funny(X0)) & (funny(X0) | humble(X0) | ~brave(X0))) [flattening 62]
73. quiet(X0) | creative(X0) [cnf transformation 48]
77. ~quiet(X0) | brave(X0) [cnf transformation 50]
80. ~creative(X0) | quiet(X0) [cnf transformation 52]
88. ~humble(X0) | patient(X0) [cnf transformation 33]
94. funny(X0) | ~patient(X0) | funny(X0) [cnf transformation 60]
103. ~brave(X0) | humble(X0) | funny(X0) [cnf transformation 63]
112. ~funny(john) [cnf transformation 22]
114. ~patient(X0) | funny(X0) [duplicate literal removal 94]
138. quiet(X0) [subsumption resolution 80,73]
207. brave(X1) [resolution 77,138]
278. funny(X1) | humble(X1) [resolution 103,207]
335. humble(john) [resolution 278,112]
359. patient(john) [resolution 335,88]
367. funny(john) [resolution 359,114]
368. $false [subsumption resolution 367,112]
% SZS output end Proof for 4197550081300939013448523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and creative is not quiet.
Everyone who is generous is not brave or not generous.
If mary is either tall or not quiet then someone is either quiet or wise and vice versa.
Everyone who is not funny is quiet.
Everyone who is both not creative and tall is either rich or humble and vice versa.
If someone is both not kind and not happy then alice is not brave or not rich.
Everyone who is both not old and old is both calm and not generous.
Everyone who is both patient and calm is either not calm or not curious.
If alice is either funny or humble then someone is old or not curious.
If susan is both wise and quiet then mary is quiet or strong and vice versa.
Everyone who is strong or rich is either not wise or not kind and vice versa.
If lucy is either not wise or old then john is both not brave and generous.
Everyone who is not calm or creative is kind and vice versa.
Everyone who is not curious or wise is both not generous and not creative.
If john is not old then john is creative or humble and vice versa.
If someone is creative then someone is either quiet or not happy and vice versa.
Someone is not quiet or not rich.
Lucy is both not old and wise.
Someone is both not patient and not quiet.
Someone is quiet or generous.
Paul is both patient and not quiet.
John is creative or not brave.
Lucy is not humble.
Fred is both quiet and tall. | Lucy is strong. | neutral | (![X]:((old(X)&creative(X))=>~quiet(X)))&
(![X]:(generous(X)=>(~brave(X)|~generous(X))))&
(((tall(mary)<~>~quiet(mary)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:(~funny(X)=>quiet(X)))&
(![X]:((~creative(X)&tall(X))<=>(rich(X)<~>humble(X))))&
((?[X]:((~kind(X)&~happy(X))))=>((~brave(alice)|~rich(alice))))&
(![X]:((~old(X)&old(X))=>(calm(X)&~generous(X))))&
(![X]:((patient(X)&calm(X))=>(~calm(X)<~>~curious(X))))&
(((funny(alice)<~>humble(alice)))=>(?[X]:((old(X)|~curious(X)))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(((~wise(lucy)<~>old(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((~calm(X)|creative(X))<=>kind(X)))&
(![X]:((~curious(X)|wise(X))=>(~generous(X)&~creative(X))))&
((~old(john))<=>((creative(john)|humble(john))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
(?[X]:((~quiet(X)|~rich(X))))&
((~old(lucy)&wise(lucy)))&
(?[X]:((~patient(X)&~quiet(X))))&
(?[X]:((quiet(X)|generous(X))))&
((patient(paul)&~quiet(paul)))&
((creative(john)|~brave(john)))&
(~humble(lucy))&
((quiet(fred)&tall(fred))) | strong(lucy) | [] | null | 0 |
Everyone who is either humble or not curious is either funny or not patient and vice versa.
Everyone who is rich is both curious and not wise.
Everyone who is both old and not brave is both happy and not humble.
Everyone who is both not creative and not generous is either patient or not humble and vice versa.
Everyone who is generous or curious is not curious and vice versa.
If lucy is not curious or old then someone is either not brave or not wise and vice versa.
If someone is kind or creative then someone is either creative or tall and vice versa.
If someone is both not brave and kind then someone is either brave or not rich.
If someone is either not humble or not quiet then fred is both not brave and brave.
Everyone who is tall or not strong is both funny and not patient and vice versa.
Everyone who is both creative and not brave is not strong.
If john is either tall or not quiet then someone is tall.
If someone is not old then paul is not generous or not rich.
Someone is not kind.
Susan is both not curious and old.
Someone is both not curious and not patient.
Fred is not wise.
Paul is kind or not calm. | John is not brave. | neutral | (![X]:((humble(X)<~>~curious(X))<=>(funny(X)<~>~patient(X))))&
(![X]:(rich(X)=>(curious(X)&~wise(X))))&
(![X]:((old(X)&~brave(X))=>(happy(X)&~humble(X))))&
(![X]:((~creative(X)&~generous(X))<=>(patient(X)<~>~humble(X))))&
(![X]:((generous(X)|curious(X))<=>~curious(X)))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((creative(X)<~>tall(X)))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~humble(X)<~>~quiet(X))))=>((~brave(fred)&brave(fred))))&
(![X]:((tall(X)|~strong(X))<=>(funny(X)&~patient(X))))&
(![X]:((creative(X)&~brave(X))=>~strong(X)))&
(((tall(john)<~>~quiet(john)))=>(?[X]:(tall(X))))&
((?[X]:(~old(X)))=>((~generous(paul)|~rich(paul))))&
(?[X]:(~kind(X)))&
((~curious(susan)&old(susan)))&
(?[X]:((~curious(X)&~patient(X))))&
(~wise(fred))&
((kind(paul)|~calm(paul))) | ~brave(john) | [] | null | 0 |
If mary is both curious and not creative then fred is either kind or wise.
Everyone who is patient is humble or not brave.
Everyone who is either not tall or brave is curious.
If alice is not generous or creative then paul is quiet or kind and vice versa.
Everyone who is creative or generous is not curious or not happy.
Everyone who is both not creative and not wise is not curious and vice versa.
If alice is curious or not kind then someone is both strong and not curious.
If susan is both kind and not generous then someone is either not kind or not tall.
Everyone who is either rich or not calm is either brave or not happy.
If someone is either not creative or not curious then someone is both not quiet and not kind.
Everyone who is either wise or calm is either old or not brave and vice versa.
If someone is not humble then someone is both quiet and tall.
Everyone who is quiet is calm or not generous and vice versa.
If paul is not curious or wise then someone is not patient.
If paul is both not old and not generous then susan is patient or not curious.
Everyone who is tall is creative and vice versa.
Mary is not funny or not generous.
Mary is patient.
Lucy is either not creative or tall.
Susan is not calm.
Mary is creative.
Someone is kind or quiet.
Someone is kind or not rich.
Someone is both strong and generous. | Paul is not curious. | neutral | (((curious(mary)&~creative(mary)))=>((kind(fred)<~>wise(fred))))&
(![X]:(patient(X)=>(humble(X)|~brave(X))))&
(![X]:((~tall(X)<~>brave(X))=>curious(X)))&
(((~generous(alice)|creative(alice)))<=>((quiet(paul)|kind(paul))))&
(![X]:((creative(X)|generous(X))=>(~curious(X)|~happy(X))))&
(![X]:((~creative(X)&~wise(X))<=>~curious(X)))&
(((curious(alice)|~kind(alice)))=>(?[X]:((strong(X)&~curious(X)))))&
(((kind(susan)&~generous(susan)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((rich(X)<~>~calm(X))=>(brave(X)<~>~happy(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>(?[X]:((~quiet(X)&~kind(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(old(X)<~>~brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:(quiet(X)<=>(calm(X)|~generous(X))))&
(((~curious(paul)|wise(paul)))=>(?[X]:(~patient(X))))&
(((~old(paul)&~generous(paul)))=>((patient(susan)|~curious(susan))))&
(![X]:(tall(X)<=>creative(X)))&
((~funny(mary)|~generous(mary)))&
(patient(mary))&
((~creative(lucy)<~>tall(lucy)))&
(~calm(susan))&
(creative(mary))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((kind(X)|~rich(X))))&
(?[X]:((strong(X)&generous(X)))) | ~curious(paul) | [] | null | 0 |
If john is either wise or brave then john is not calm.
Everyone who is patient is generous or rich and vice versa.
Everyone who is both not rich and rich is not tall and vice versa.
Everyone who is kind is either humble or not rich and vice versa.
If someone is tall then paul is both not curious and not strong.
Everyone who is brave is either not brave or patient.
Everyone who is both not brave and kind is patient and vice versa.
Everyone who is both funny and humble is both not patient and not humble.
Everyone who is both old and not generous is both not creative and curious.
Everyone who is humble or strong is both not creative and not funny.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is both not old and old is not kind and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
Someone is happy.
Alice is not humble or not creative.
Fred is tall or generous.
Someone is not tall or not happy.
Lucy is either curious or rich.
Someone is either not humble or funny.
Someone is either not rich or curious. | Lucy is curious. | entailment | (((wise(john)<~>brave(john)))=>(~calm(john)))&
(![X]:(patient(X)<=>(generous(X)|rich(X))))&
(![X]:((~rich(X)&rich(X))<=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(![X]:((~brave(X)&kind(X))<=>patient(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)&~humble(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~old(X)&old(X))<=>~kind(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(?[X]:(happy(X)))&
((~humble(alice)|~creative(alice)))&
((tall(fred)|generous(fred)))&
(?[X]:((~tall(X)|~happy(X))))&
((curious(lucy)<~>rich(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((~rich(X)<~>curious(X)))) | curious(lucy) | [
"p3",
"p7",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5007676699417175274178310
% SZS output start Proof for 5007676699417175274178310
4. ! [X0] : (kind(X0) <=> (humble(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((humble(X0) & funny(X0)) => (~humble(X0) & ~patient(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | wise(X0)) => (~patient(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~rich(X0) <~> funny(X0))) [input p12]
14. ! [X0] : ((old(X0) & ~old(X0)) <=> ~kind(X0)) [input p13]
20. curious(lucy) <~> rich(lucy) [input p19]
23. ~curious(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) & ~patient(X0)) | (~humble(X0) | ~funny(X0))) [ennf transformation 8]
33. ! [X0] : ((~humble(X0) & ~patient(X0)) | ~humble(X0) | ~funny(X0)) [flattening 32]
37. ! [X0] : ((~patient(X0) & ~rich(X0)) | (generous(X0) & ~wise(X0))) [ennf transformation 11]
44. ! [X0] : ((kind(X0) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0)))) & (((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | ~kind(X0))) [nnf transformation 4]
53. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 13]
54. ! [X0] : (((old(X0) & ~old(X0)) | kind(X0)) & (~kind(X0) | (~old(X0) | old(X0)))) [nnf transformation 14]
55. ! [X0] : (((old(X0) & ~old(X0)) | kind(X0)) & (~kind(X0) | ~old(X0) | old(X0))) [flattening 54]
61. (~rich(lucy) | ~curious(lucy)) & (rich(lucy) | curious(lucy)) [nnf transformation 20]
76. ~kind(X0) | humble(X0) | ~rich(X0) [cnf transformation 44]
87. ~humble(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 33]
90. ~rich(X0) | ~wise(X0) [cnf transformation 37]
101. funny(X0) | ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 53]
109. ~old(X0) | kind(X0) [cnf transformation 55]
110. old(X0) | kind(X0) [cnf transformation 55]
118. rich(lucy) | curious(lucy) [cnf transformation 61]
124. ~curious(lucy) [cnf transformation 23]
127. funny(X0) | ~rich(X0) | wise(X0) [duplicate literal removal 101]
130. ~funny(X0) | ~humble(X0) [duplicate literal removal 87]
175. ~rich(X0) | funny(X0) [subsumption resolution 127,90]
176. kind(X0) [subsumption resolution 109,110]
179. 9 <=> curious(lucy) [avatar definition]
183. 10 <=> rich(lucy) [avatar definition]
184. rich(lucy) <- (10) [avatar component clause 183]
187. 9 | 10 [avatar split clause 118,183,179]
200. ~9 [avatar split clause 124,179]
213. funny(lucy) <- (10) [resolution 175,184]
215. ~humble(lucy) <- (10) [resolution 213,130]
218. ~rich(X0) | humble(X0) [resolution 76,176]
219. humble(lucy) <- (10) [resolution 218,184]
220. $false <- (10) [subsumption resolution 219,215]
221. ~10 [avatar contradiction clause 220]
222. $false [avatar sat refutation 187,200,221]
% SZS output end Proof for 5007676699417175274178310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not old is both not creative and curious and vice versa.
Everyone who is quiet is either curious or not kind.
If susan is both not creative and not humble then paul is funny or not generous.
Everyone who is calm or happy is either old or creative and vice versa.
Everyone who is either creative or strong is either brave or funny and vice versa.
Everyone who is not old is both patient and quiet and vice versa.
Everyone who is either quiet or curious is both rich and happy and vice versa.
Everyone who is both strong and funny is quiet or not brave.
If paul is not funny or generous then someone is both wise and not happy.
Everyone who is both not rich and strong is either not rich or calm and vice versa.
If someone is not rich then someone is not calm or kind.
Everyone who is either quiet or creative is both not funny and generous and vice versa.
If someone is both not kind and not calm then someone is not rich and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is not rich or not happy then paul is both strong and rich and vice versa.
Everyone who is happy or not creative is both not wise and creative.
Susan is both not tall and not generous.
Someone is not happy.
Lucy is not patient.
Someone is not old or not curious.
Someone is brave or not brave.
Someone is not generous or humble. | Lucy is generous. | neutral | (![X]:((~creative(X)|~old(X))<=>(~creative(X)&curious(X))))&
(![X]:(quiet(X)=>(curious(X)<~>~kind(X))))&
(((~creative(susan)&~humble(susan)))=>((funny(paul)|~generous(paul))))&
(![X]:((calm(X)|happy(X))<=>(old(X)<~>creative(X))))&
(![X]:((creative(X)<~>strong(X))<=>(brave(X)<~>funny(X))))&
(![X]:(~old(X)<=>(patient(X)&quiet(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(rich(X)&happy(X))))&
(![X]:((strong(X)&funny(X))=>(quiet(X)|~brave(X))))&
(((~funny(paul)|generous(paul)))=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)<~>calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((quiet(X)<~>creative(X))<=>(~funny(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~rich(X)|~happy(X))))<=>((strong(paul)&rich(paul))))&
(![X]:((happy(X)|~creative(X))=>(~wise(X)&creative(X))))&
((~tall(susan)&~generous(susan)))&
(?[X]:(~happy(X)))&
(~patient(lucy))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~generous(X)|humble(X)))) | generous(lucy) | [] | null | 0 |
If someone is not quiet or not old then john is kind and vice versa.
If mary is happy then someone is not creative or humble and vice versa.
Everyone who is either not generous or patient is both not wise and not humble and vice versa.
If paul is both generous and not curious then fred is not patient or funny.
Everyone who is either not calm or rich is either funny or humble.
Everyone who is happy is both not humble and not quiet.
Everyone who is brave or calm is not happy or happy.
Everyone who is either wise or curious is not rich.
Everyone who is either curious or humble is either not humble or old.
Everyone who is either not strong or humble is not quiet and vice versa.
Everyone who is either rich or not kind is both generous and funny and vice versa.
Everyone who is quiet is not generous and vice versa.
If someone is kind or tall then someone is either rich or humble and vice versa.
If someone is either strong or rich then someone is both rich and calm and vice versa.
If someone is either not humble or not strong then fred is not humble or rich and vice versa.
Everyone who is not old or old is either tall or happy and vice versa.
Someone is not curious.
Someone is both not funny and wise.
Someone is both rich and not old.
Susan is not wise or curious.
Someone is either not curious or quiet.
Paul is brave or rich.
Mary is both quiet and brave.
Someone is either not curious or not humble. | Susan is not humble. | entailment | ((?[X]:((~quiet(X)|~old(X))))<=>(kind(john)))&
((happy(mary))<=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((~generous(X)<~>patient(X))<=>(~wise(X)&~humble(X))))&
(((generous(paul)&~curious(paul)))=>((~patient(fred)|funny(fred))))&
(![X]:((~calm(X)<~>rich(X))=>(funny(X)<~>humble(X))))&
(![X]:(happy(X)=>(~humble(X)&~quiet(X))))&
(![X]:((brave(X)|calm(X))=>(~happy(X)|happy(X))))&
(![X]:((wise(X)<~>curious(X))=>~rich(X)))&
(![X]:((curious(X)<~>humble(X))=>(~humble(X)<~>old(X))))&
(![X]:((~strong(X)<~>humble(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~kind(X))<=>(generous(X)&funny(X))))&
(![X]:(quiet(X)<=>~generous(X)))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((rich(X)&calm(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>((~humble(fred)|rich(fred))))&
(![X]:((~old(X)|old(X))<=>(tall(X)<~>happy(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((rich(X)&~old(X))))&
((~wise(susan)|curious(susan)))&
(?[X]:((~curious(X)<~>quiet(X))))&
((brave(paul)|rich(paul)))&
((quiet(mary)&brave(mary)))&
(?[X]:((~curious(X)<~>~humble(X)))) | ~humble(susan) | [
"p1",
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8518738971493527027517962
% SZS output start Proof for 8518738971493527027517962
2. happy(mary) <=> ? [X0] : (humble(X0) | ~creative(X0)) [input p1]
6. ! [X0] : (happy(X0) => (~quiet(X0) & ~humble(X0))) [input p5]
23. brave(mary) & quiet(mary) [input p22]
25. humble(susan) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~humble(X0)) | ~happy(X0)) [ennf transformation 6]
40. (happy(mary) | ! [X0] : (~humble(X0) & creative(X0))) & (? [X0] : (humble(X0) | ~creative(X0)) | ~happy(mary)) [nnf transformation 2]
41. (happy(mary) | ! [X0] : (~humble(X0) & creative(X0))) & (? [X1] : (humble(X1) | ~creative(X1)) | ~happy(mary)) [rectify 40]
42. ? [X1] : (humble(X1) | ~creative(X1)) => (humble(sK1) | ~creative(sK1)) [choice axiom]
43. (happy(mary) | ! [X0] : (~humble(X0) & creative(X0))) & ((humble(sK1) | ~creative(sK1)) | ~happy(mary)) [skolemisation 41,42]
87. happy(mary) | ~humble(X0) [cnf transformation 43]
100. ~happy(X0) | ~quiet(X0) [cnf transformation 31]
154. quiet(mary) [cnf transformation 23]
158. humble(susan) [cnf transformation 25]
183. 6 <=> ! [X0] : ~humble(X0) [avatar definition]
184. ~humble(X0) <- (6) [avatar component clause 183]
186. 7 <=> happy(mary) [avatar definition]
188. happy(mary) <- (7) [avatar component clause 186]
189. 6 | 7 [avatar split clause 87,186,183]
359. ~quiet(mary) <- (7) [resolution 100,188]
360. $false <- (7) [subsumption resolution 359,154]
361. ~7 [avatar contradiction clause 360]
362. $false <- (6) [resolution 184,158]
365. ~6 [avatar contradiction clause 362]
366. $false [avatar sat refutation 189,361,365]
% SZS output end Proof for 8518738971493527027517962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or humble then someone is not patient and vice versa. If paul is both not calm and old then someone is both not generous and not kind and vice versa. Everyone who is curious or wise is rich or calm. If someone is not calm or tall then paul is curious and vice versa. Everyone who is rich is either funny or strong. If fred is both wise and humble then alice is either not strong or tall. Everyone who is patient is either not wise or not strong. Everyone who is not calm is both not tall and not quiet and vice versa. If john is either kind or not curious then someone is either not humble or generous. If someone is not happy then someone is happy or patient. If someone is not kind or strong then mary is either humble or not tall. Everyone who is not rich is not old or not calm. Everyone who is wise or not wise is not calm and vice versa. Everyone who is both not quiet and not brave is both funny and creative. Everyone who is tall or calm is not strong or not old and vice versa. Everyone who is either not curious or not brave is generous. Fred is not patient. Alice is both kind and not brave. Someone is either not curious or wise. Lucy is not generous. Alice is not curious or not creative. Mary is either creative or rich. Paul is brave or quiet. | Mary is not tall. | entailment | ((?[X]:((happy(X)<~>humble(X))))<=>(?[X]:(~patient(X))))&
(((~calm(paul)&old(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:((curious(X)|wise(X))=>(rich(X)|calm(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(curious(paul)))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((wise(fred)&humble(fred)))=>((~strong(alice)<~>tall(alice))))&
(![X]:(patient(X)=>(~wise(X)<~>~strong(X))))&
(![X]:(~calm(X)<=>(~tall(X)&~quiet(X))))&
(((kind(john)<~>~curious(john)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((humble(mary)<~>~tall(mary))))&
(![X]:(~rich(X)=>(~old(X)|~calm(X))))&
(![X]:((wise(X)|~wise(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~brave(X))=>(funny(X)&creative(X))))&
(![X]:((tall(X)|calm(X))<=>(~strong(X)|~old(X))))&
(![X]:((~curious(X)<~>~brave(X))=>generous(X)))&
(~patient(fred))&
((kind(alice)&~brave(alice)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~generous(lucy))&
((~curious(alice)|~creative(alice)))&
((creative(mary)<~>rich(mary)))&
((brave(paul)|quiet(paul))) | ~tall(mary) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 872114229275081626046483
% SZS output start Proof for 872114229275081626046483
8. ! [X0] : (~calm(X0) <=> (~quiet(X0) & ~tall(X0))) [input p7]
13. ! [X0] : ((~wise(X0) | wise(X0)) <=> ~calm(X0)) [input p12]
24. tall(mary) [input hypothesis]
58. ! [X0] : ((~calm(X0) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 8]
59. ! [X0] : ((~calm(X0) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [flattening 58]
67. ! [X0] : (((~wise(X0) | wise(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) & ~wise(X0)))) [nnf transformation 13]
68. ! [X0] : ((~wise(X0) | wise(X0) | calm(X0)) & (~calm(X0) | (wise(X0) & ~wise(X0)))) [flattening 67]
95. ~tall(X0) | calm(X0) [cnf transformation 59]
108. ~calm(X0) | ~wise(X0) [cnf transformation 68]
109. ~calm(X0) | wise(X0) [cnf transformation 68]
129. tall(mary) [cnf transformation 24]
257. 30 <=> tall(mary) [avatar definition]
259. tall(mary) <- (30) [avatar component clause 257]
267. ~calm(X0) [subsumption resolution 108,109]
308. 30 [avatar split clause 129,257]
309. calm(mary) <- (30) [resolution 95,259]
310. $false <- (30) [subsumption resolution 309,267]
311. ~30 [avatar contradiction clause 310]
312. $false [avatar sat refutation 308,311]
% SZS output end Proof for 872114229275081626046483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not creative or not rich then alice is either not calm or not kind. If someone is calm or old then alice is either not funny or not curious. Everyone who is not funny is not kind or old. If paul is both not creative and strong then someone is either happy or not kind and vice versa. If someone is both funny and not strong then someone is both humble and not strong. If someone is calm then someone is not calm or not wise and vice versa. If lucy is either generous or strong then someone is quiet or patient and vice versa. If lucy is both not rich and generous then lucy is both not quiet and old and vice versa. If fred is not quiet or not strong then mary is not calm and vice versa. If mary is either not curious or not quiet then someone is both not kind and curious and vice versa. Everyone who is either old or brave is not tall and vice versa. If someone is old then alice is both not happy and brave and vice versa. Everyone who is humble or not generous is either quiet or tall and vice versa. If someone is either not calm or not rich then paul is both not humble and rich. Everyone who is generous or not tall is both not happy and not brave. Everyone who is not quiet or rich is both quiet and not humble and vice versa. Paul is not humble or wise. Someone is both not calm and not creative. Alice is tall or calm. Someone is not strong or curious. Lucy is rich or not strong. Paul is not kind. Someone is not creative. | Paul is not rich. | contradiction | (((~creative(paul)|~rich(paul)))=>((~calm(alice)<~>~kind(alice))))&
((?[X]:((calm(X)|old(X))))=>((~funny(alice)<~>~curious(alice))))&
(![X]:(~funny(X)=>(~kind(X)|old(X))))&
(((~creative(paul)&strong(paul)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((humble(X)&~strong(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((~calm(X)|~wise(X)))))&
(((generous(lucy)<~>strong(lucy)))<=>(?[X]:((quiet(X)|patient(X)))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
((~humble(paul)|wise(paul)))&
(?[X]:((~calm(X)&~creative(X))))&
((tall(alice)|calm(alice)))&
(?[X]:((~strong(X)|curious(X))))&
((rich(lucy)|~strong(lucy)))&
(~kind(paul))&
(?[X]:(~creative(X))) | ~rich(paul) | [
"p10",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7428676975073269140974863
% SZS output start Proof for 7428676975073269140974863
11. ! [X0] : ((old(X0) <~> brave(X0)) <=> ~tall(X0)) [input p10]
12. ? [X0] : old(X0) <=> (brave(alice) & ~happy(alice)) [input p11]
13. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p14]
16. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p15]
24. ~rich(paul) [input hypothesis]
33. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 15]
61. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | tall(X0)) & (~tall(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 11]
62. (? [X0] : old(X0) | (~brave(alice) | happy(alice))) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [nnf transformation 12]
63. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [flattening 62]
64. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [rectify 63]
65. ? [X0] : old(X0) => old(sK6) [choice axiom]
66. (old(sK6) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [skolemisation 64,65]
67. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 13]
68. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 67]
70. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 16]
71. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 70]
118. ~tall(X0) | old(X0) | ~brave(X0) [cnf transformation 61]
119. tall(X0) | old(X0) | brave(X0) [cnf transformation 61]
122. brave(alice) | ~old(X1) [cnf transformation 66]
126. ~tall(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 68]
127. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 68]
136. ~brave(X0) | ~generous(X0) [cnf transformation 33]
137. ~brave(X0) | tall(X0) [cnf transformation 33]
138. quiet(X0) | quiet(X0) [cnf transformation 71]
142. rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0) [cnf transformation 71]
151. ~rich(paul) [cnf transformation 24]
152. quiet(X0) [duplicate literal removal 138]
153. ~quiet(X0) | rich(X0) | humble(X0) [duplicate literal removal 142]
155. 1 <=> rich(paul) [avatar definition]
156. ~rich(paul) <- (~1) [avatar component clause 155]
175. 5 <=> ! [X0] : ~old(X0) [avatar definition]
176. ~old(X0) <- (5) [avatar component clause 175]
339. 40 <=> brave(alice) [avatar definition]
340. brave(alice) <- (40) [avatar component clause 339]
347. 5 | 40 [avatar split clause 122,339,175]
358. 44 <=> humble(paul) [avatar definition]
359. humble(paul) <- (44) [avatar component clause 358]
360. ~humble(paul) <- (~44) [avatar component clause 358]
369. 46 <=> tall(alice) [avatar definition]
371. tall(alice) <- (46) [avatar component clause 369]
383. ~1 [avatar split clause 151,155]
414. ~quiet(X1) | ~humble(X1) | old(X1) | brave(X1) [resolution 126,119]
416. ~humble(X1) | old(X1) | brave(X1) [subsumption resolution 414,152]
417. ~humble(X1) | brave(X1) <- (5) [subsumption resolution 416,176]
425. humble(X0) | rich(X0) [resolution 153,152]
437. rich(paul) <- (~44) [resolution 425,360]
443. $false <- (~1, ~44) [subsumption resolution 437,156]
444. 1 | 44 [avatar contradiction clause 443]
445. brave(paul) <- (5, 44) [resolution 359,417]
457. tall(paul) <- (5, 44) [resolution 445,137]
462. old(paul) | ~brave(paul) <- (5, 44) [resolution 457,118]
470. ~brave(paul) <- (5, 44) [subsumption resolution 462,176]
471. $false <- (5, 44) [subsumption resolution 470,445]
472. ~5 | ~44 [avatar contradiction clause 471]
489. tall(alice) <- (40) [resolution 340,137]
490. ~generous(alice) <- (40) [resolution 340,136]
495. 46 | ~40 [avatar split clause 489,339,369]
498. ~quiet(alice) | generous(alice) <- (46) [resolution 371,127]
502. generous(alice) <- (46) [subsumption resolution 498,152]
503. $false <- (40, 46) [subsumption resolution 502,490]
504. ~40 | ~46 [avatar contradiction clause 503]
506. $false [avatar sat refutation 347,383,444,472,495,504]
% SZS output end Proof for 7428676975073269140974863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or quiet is rich or strong and vice versa.
If fred is brave or generous then susan is either kind or rich.
Everyone who is old or tall is kind and vice versa.
Everyone who is both wise and not humble is kind and vice versa.
If john is funny or not curious then someone is both not calm and not patient.
Everyone who is not quiet or generous is either creative or tall and vice versa.
Everyone who is both kind and not happy is generous or happy and vice versa.
If lucy is either not creative or not happy then someone is quiet and vice versa.
Everyone who is funny is not humble and vice versa.
If someone is either not tall or funny then someone is not brave and vice versa.
Everyone who is either not kind or happy is not brave.
If someone is both curious and not quiet then someone is not strong and vice versa.
Everyone who is not quiet is both not tall and not kind.
Everyone who is tall is not curious or generous and vice versa.
Everyone who is not quiet or not creative is not tall.
If alice is not patient then someone is either kind or not tall.
Paul is not happy.
Susan is not funny or generous.
Someone is humble or not patient.
Someone is either not humble or quiet.
Someone is not tall or brave. | Susan is not humble. | contradiction | (![X]:((~strong(X)|quiet(X))<=>(rich(X)|strong(X))))&
(((brave(fred)|generous(fred)))=>((kind(susan)<~>rich(susan))))&
(![X]:((old(X)|tall(X))<=>kind(X)))&
(![X]:((wise(X)&~humble(X))<=>kind(X)))&
(((funny(john)|~curious(john)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(creative(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)|happy(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(funny(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>~brave(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~kind(X))))&
(![X]:(tall(X)<=>(~curious(X)|generous(X))))&
(![X]:((~quiet(X)|~creative(X))=>~tall(X)))&
((~patient(alice))=>(?[X]:((kind(X)<~>~tall(X)))))&
(~happy(paul))&
((~funny(susan)|generous(susan)))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~tall(X)|brave(X)))) | ~humble(susan) | [
"p5",
"p8",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 67612277499109552745554
% SZS output start Proof for 67612277499109552745554
6. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (creative(X0) <~> tall(X0))) [input p5]
9. ! [X0] : (funny(X0) <=> ~humble(X0)) [input p8]
14. ! [X0] : (tall(X0) <=> (generous(X0) | ~curious(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | ~quiet(X0)) => ~tall(X0)) [input p14]
18. generous(susan) | ~funny(susan) [input p17]
22. ~humble(susan) [input hypothesis]
30. ! [X0] : (~tall(X0) | (creative(X0) & quiet(X0))) [ennf transformation 15]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [nnf transformation 6]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [flattening 41]
49. ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))) [nnf transformation 9]
61. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | ~tall(X0))) [flattening 61]
92. ~creative(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 42]
105. funny(X0) | humble(X0) [cnf transformation 49]
119. ~generous(X0) | tall(X0) [cnf transformation 62]
121. ~tall(X0) | creative(X0) [cnf transformation 30]
125. generous(susan) | ~funny(susan) [cnf transformation 18]
130. ~humble(susan) [cnf transformation 22]
246. 25 <=> funny(susan) [avatar definition]
248. ~funny(susan) <- (~25) [avatar component clause 246]
250. 26 <=> generous(susan) [avatar definition]
252. generous(susan) <- (26) [avatar component clause 250]
253. ~25 | 26 [avatar split clause 125,250,246]
285. humble(susan) <- (~25) [resolution 105,248]
287. $false <- (~25) [subsumption resolution 285,130]
288. 25 [avatar contradiction clause 287]
297. tall(susan) <- (26) [resolution 119,252]
298. creative(susan) <- (26) [resolution 297,121]
312. ~tall(susan) | ~generous(susan) <- (26) [resolution 92,298]
315. ~generous(susan) <- (26) [subsumption resolution 312,297]
316. $false <- (26) [subsumption resolution 315,252]
317. ~26 [avatar contradiction clause 316]
318. $false [avatar sat refutation 253,288,317]
% SZS output end Proof for 67612277499109552745554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not humble then susan is not strong. If lucy is either not tall or not wise then fred is not kind or not old. Everyone who is brave or wise is both humble and not curious and vice versa. Everyone who is curious is both not wise and strong. Everyone who is both not quiet and wise is either old or happy and vice versa. If mary is funny then someone is not patient or not creative and vice versa. If alice is wise or not brave then someone is not humble or happy and vice versa. Everyone who is patient is humble or patient and vice versa. Everyone who is both not brave and not tall is wise. Everyone who is kind is either not funny or creative. Everyone who is both not humble and not creative is either brave or patient. Everyone who is either humble or calm is either humble or not kind. If someone is either tall or not funny then someone is either funny or curious and vice versa. Everyone who is either not curious or not calm is both not rich and not funny. Everyone who is calm or not happy is both not creative and not kind. Everyone who is not creative is curious or not happy and vice versa. Someone is either rich or calm. Susan is either not creative or rich. Paul is not generous. Mary is both funny and curious. Someone is funny or not rich. Someone is not curious or old. Mary is either not funny or strong. Someone is not kind or patient. | Mary is strong. | entailment | ((?[X]:((~old(X)&~humble(X))))=>(~strong(susan)))&
(((~tall(lucy)<~>~wise(lucy)))=>((~kind(fred)|~old(fred))))&
(![X]:((brave(X)|wise(X))<=>(humble(X)&~curious(X))))&
(![X]:(curious(X)=>(~wise(X)&strong(X))))&
(![X]:((~quiet(X)&wise(X))<=>(old(X)<~>happy(X))))&
((funny(mary))<=>(?[X]:((~patient(X)|~creative(X)))))&
(((wise(alice)|~brave(alice)))<=>(?[X]:((~humble(X)|happy(X)))))&
(![X]:(patient(X)<=>(humble(X)|patient(X))))&
(![X]:((~brave(X)&~tall(X))=>wise(X)))&
(![X]:(kind(X)=>(~funny(X)<~>creative(X))))&
(![X]:((~humble(X)&~creative(X))=>(brave(X)<~>patient(X))))&
(![X]:((humble(X)<~>calm(X))=>(humble(X)<~>~kind(X))))&
((?[X]:((tall(X)<~>~funny(X))))<=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>(~rich(X)&~funny(X))))&
(![X]:((calm(X)|~happy(X))=>(~creative(X)&~kind(X))))&
(![X]:(~creative(X)<=>(curious(X)|~happy(X))))&
(?[X]:((rich(X)<~>calm(X))))&
((~creative(susan)<~>rich(susan)))&
(~generous(paul))&
((funny(mary)&curious(mary)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((~curious(X)|old(X))))&
((~funny(mary)<~>strong(mary)))&
(?[X]:((~kind(X)|patient(X)))) | strong(mary) | [
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6753887871876204205238696
% SZS output start Proof for 6753887871876204205238696
20. curious(mary) & funny(mary) [input p19]
23. ~funny(mary) <~> strong(mary) [input p22]
25. ~strong(mary) [input hypothesis]
75. (~strong(mary) | funny(mary)) & (strong(mary) | ~funny(mary)) [nnf transformation 23]
136. funny(mary) [cnf transformation 20]
140. strong(mary) | ~funny(mary) [cnf transformation 75]
143. ~strong(mary) [cnf transformation 25]
176. 8 <=> funny(mary) [avatar definition]
276. 8 [avatar split clause 136,176]
296. 34 <=> strong(mary) [avatar definition]
300. ~8 | 34 [avatar split clause 140,296,176]
310. ~34 [avatar split clause 143,296]
311. $false [avatar sat refutation 276,300,310]
% SZS output end Proof for 6753887871876204205238696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not calm is not rich. Everyone who is either calm or not quiet is not creative or funny and vice versa. If alice is either not quiet or not wise then john is both wise and curious. If someone is not old or not wise then someone is not kind and vice versa. Everyone who is either not humble or wise is not brave and vice versa. Everyone who is both not old and not happy is both not strong and curious and vice versa. Everyone who is not generous is either not curious or humble. Everyone who is happy or calm is both humble and not happy and vice versa. If someone is either quiet or not rich then susan is either wise or brave. If paul is tall then john is both not tall and not rich and vice versa. Everyone who is either not calm or strong is wise. If someone is both tall and not funny then someone is not brave or rich. Everyone who is patient or strong is rich and vice versa. Everyone who is creative or not strong is both not calm and strong and vice versa. If fred is both not rich and not humble then susan is both not funny and quiet and vice versa. Everyone who is strong is tall or not funny. Susan is patient or creative. Alice is both not kind and strong. Someone is both calm and tall. Fred is either not kind or not creative. John is either brave or generous. Alice is curious or tall. Someone is not happy. | Susan is funny. | entailment | (![X]:((~funny(X)&~calm(X))=>~rich(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(~creative(X)|funny(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((patient(susan)|creative(susan)))&
((~kind(alice)&strong(alice)))&
(?[X]:((calm(X)&tall(X))))&
((~kind(fred)<~>~creative(fred)))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X))) | funny(susan) | [
"p0",
"p1",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8986454706427697250511448
% SZS output start Proof for 8986454706427697250511448
1. ! [X0] : ((~calm(X0) & ~funny(X0)) => ~rich(X0)) [input p0]
2. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (funny(X0) | ~creative(X0))) [input p1]
13. ! [X0] : ((strong(X0) | patient(X0)) <=> rich(X0)) [input p12]
14. ! [X0] : ((~strong(X0) | creative(X0)) <=> (strong(X0) & ~calm(X0))) [input p13]
15. (~humble(fred) & ~rich(fred)) <=> (quiet(susan) & ~funny(susan)) [input p14]
17. creative(susan) | patient(susan) [input p16]
24. ~funny(susan) [input hypothesis]
27. ! [X0] : (~rich(X0) | (calm(X0) | funny(X0))) [ennf transformation 1]
28. ! [X0] : (~rich(X0) | calm(X0) | funny(X0)) [flattening 27]
36. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~funny(X0) & creative(X0))) & ((funny(X0) | ~creative(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 2]
37. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~funny(X0) & creative(X0))) & (funny(X0) | ~creative(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 36]
57. ! [X0] : (((strong(X0) | patient(X0)) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((strong(X0) | patient(X0) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [flattening 57]
59. ! [X0] : (((~strong(X0) | creative(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 14]
60. ! [X0] : ((~strong(X0) | creative(X0) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [flattening 59]
61. ((~humble(fred) & ~rich(fred)) | (~quiet(susan) | funny(susan))) & ((quiet(susan) & ~funny(susan)) | (humble(fred) | rich(fred))) [nnf transformation 15]
62. ((~humble(fred) & ~rich(fred)) | ~quiet(susan) | funny(susan)) & ((quiet(susan) & ~funny(susan)) | humble(fred) | rich(fred)) [flattening 61]
69. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 28]
74. ~calm(X0) | quiet(X0) | creative(X0) [cnf transformation 37]
108. ~patient(X0) | rich(X0) [cnf transformation 58]
109. ~strong(X0) | rich(X0) [cnf transformation 58]
111. ~creative(X0) | ~calm(X0) [cnf transformation 60]
114. strong(X0) | strong(X0) [cnf transformation 60]
118. ~rich(fred) | ~quiet(susan) | funny(susan) [cnf transformation 62]
121. creative(susan) | patient(susan) [cnf transformation 17]
132. ~funny(susan) [cnf transformation 24]
133. strong(X0) [duplicate literal removal 114]
227. 21 <=> funny(susan) [avatar definition]
228. ~funny(susan) <- (~21) [avatar component clause 227]
231. 22 <=> quiet(susan) [avatar definition]
233. ~quiet(susan) <- (~22) [avatar component clause 231]
240. 24 <=> rich(fred) [avatar definition]
242. ~rich(fred) <- (~24) [avatar component clause 240]
243. 21 | ~22 | ~24 [avatar split clause 118,240,231,227]
248. 25 <=> patient(susan) [avatar definition]
250. patient(susan) <- (25) [avatar component clause 248]
252. 26 <=> creative(susan) [avatar definition]
254. creative(susan) <- (26) [avatar component clause 252]
255. 25 | 26 [avatar split clause 121,252,248]
285. ~21 [avatar split clause 132,227]
287. rich(susan) <- (25) [resolution 108,250]
288. rich(X0) [resolution 109,133]
289. $false <- (~24) [resolution 288,242]
290. 24 [avatar contradiction clause 289]
291. calm(susan) | funny(susan) <- (25) [resolution 69,287]
292. calm(X0) | funny(X0) [resolution 69,288]
293. calm(susan) <- (~21, 25) [subsumption resolution 291,228]
296. quiet(susan) | creative(susan) <- (~21, 25) [resolution 74,293]
306. creative(susan) <- (~21, ~22, 25) [subsumption resolution 296,233]
307. 26 | 21 | 22 | ~25 [avatar split clause 306,248,231,227,252]
308. ~calm(susan) <- (26) [resolution 254,111]
364. funny(susan) <- (26) [resolution 292,308]
365. $false <- (~21, 26) [subsumption resolution 364,228]
366. 21 | ~26 [avatar contradiction clause 365]
367. $false [avatar sat refutation 243,255,285,290,307,366]
% SZS output end Proof for 8986454706427697250511448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or rich then someone is humble.
Everyone who is old is either not quiet or curious and vice versa.
If someone is generous then someone is not creative and vice versa.
Everyone who is brave or not patient is not tall.
Everyone who is either not patient or not funny is not rich or not patient.
Everyone who is both wise and not patient is not generous or not curious.
If susan is not quiet then mary is brave or old and vice versa.
Everyone who is both not humble and not strong is either curious or not kind.
Everyone who is wise or not tall is tall and vice versa.
If someone is not creative then lucy is both wise and not curious and vice versa.
If lucy is not funny or brave then susan is not wise.
Everyone who is either rich or not brave is creative or not patient and vice versa.
If susan is either curious or kind then someone is tall.
Everyone who is not old is not tall and vice versa.
Everyone who is not happy or not funny is either brave or not curious.
Someone is strong.
John is not happy.
Alice is both not quiet and not creative.
Someone is happy.
Someone is rich.
Someone is either curious or brave.
Susan is strong.
Susan is not quiet or not humble. | Lucy is not funny. | contradiction | ((?[X]:((~generous(X)<~>rich(X))))=>(?[X]:(humble(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>curious(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~creative(X))))&
(![X]:((brave(X)|~patient(X))=>~tall(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(~rich(X)|~patient(X))))&
(![X]:((wise(X)&~patient(X))=>(~generous(X)|~curious(X))))&
((~quiet(susan))<=>((brave(mary)|old(mary))))&
(![X]:((~humble(X)&~strong(X))=>(curious(X)<~>~kind(X))))&
(![X]:((wise(X)|~tall(X))<=>tall(X)))&
((?[X]:(~creative(X)))<=>((wise(lucy)&~curious(lucy))))&
(((~funny(lucy)|brave(lucy)))=>(~wise(susan)))&
(![X]:((rich(X)<~>~brave(X))<=>(creative(X)|~patient(X))))&
(((curious(susan)<~>kind(susan)))=>(?[X]:(tall(X))))&
(![X]:(~old(X)<=>~tall(X)))&
(![X]:((~happy(X)|~funny(X))=>(brave(X)<~>~curious(X))))&
(?[X]:(strong(X)))&
(~happy(john))&
((~quiet(alice)&~creative(alice)))&
(?[X]:(happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((curious(X)<~>brave(X))))&
(strong(susan))&
((~quiet(susan)|~humble(susan))) | ~funny(lucy) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6053474259144016498453219
% SZS output start Proof for 6053474259144016498453219
9. ! [X0] : ((~tall(X0) | wise(X0)) <=> tall(X0)) [input p8]
11. (brave(lucy) | ~funny(lucy)) => ~wise(susan) [input p10]
24. ~funny(lucy) [input hypothesis]
36. ~wise(susan) | (~brave(lucy) & funny(lucy)) [ennf transformation 11]
52. ! [X0] : (((~tall(X0) | wise(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) & ~wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((~tall(X0) | wise(X0) | ~tall(X0)) & (tall(X0) | (tall(X0) & ~wise(X0)))) [flattening 52]
90. tall(X0) | tall(X0) [cnf transformation 53]
91. ~tall(X0) | wise(X0) | ~tall(X0) [cnf transformation 53]
95. ~wise(susan) | funny(lucy) [cnf transformation 36]
119. ~funny(lucy) [cnf transformation 24]
120. tall(X0) [duplicate literal removal 90]
121. ~tall(X0) | wise(X0) [duplicate literal removal 91]
186. 15 <=> wise(susan) [avatar definition]
188. ~wise(susan) <- (~15) [avatar component clause 186]
191. 16 <=> funny(lucy) [avatar definition]
194. 16 | ~15 [avatar split clause 95,186,191]
211. ~16 [avatar split clause 119,191]
216. wise(X0) [resolution 121,120]
217. $false <- (~15) [resolution 216,188]
218. 15 [avatar contradiction clause 217]
219. $false [avatar sat refutation 194,211,218]
% SZS output end Proof for 6053474259144016498453219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or generous then fred is not brave or funny.
If someone is not tall or not generous then mary is both strong and not wise and vice versa.
Everyone who is brave is either quiet or wise and vice versa.
Everyone who is kind is either not calm or curious.
Everyone who is not humble or not quiet is kind and vice versa.
If mary is both wise and happy then alice is generous or not humble and vice versa.
If someone is not patient or not happy then someone is either not kind or humble.
Everyone who is both tall and brave is kind or calm and vice versa.
If susan is both not happy and not funny then someone is both not calm and kind and vice versa.
If fred is both humble and not wise then someone is not funny or patient.
If someone is not creative then mary is either not brave or not tall and vice versa.
Everyone who is either not old or not tall is not wise and vice versa.
Everyone who is not generous is not tall or not brave.
Everyone who is either curious or calm is not patient or calm.
If someone is funny or not quiet then someone is either not funny or curious.
Everyone who is wise or funny is either wise or not kind.
Someone is not quiet or kind.
Susan is not strong.
Alice is not rich.
Someone is not curious.
Fred is either not happy or not wise.
Someone is not tall.
Someone is not wise. | Alice is quiet. | entailment | ((?[X]:((~strong(X)|generous(X))))=>((~brave(fred)|funny(fred))))&
((?[X]:((~tall(X)|~generous(X))))<=>((strong(mary)&~wise(mary))))&
(![X]:(brave(X)<=>(quiet(X)<~>wise(X))))&
(![X]:(kind(X)=>(~calm(X)<~>curious(X))))&
(![X]:((~humble(X)|~quiet(X))<=>kind(X)))&
(((wise(mary)&happy(mary)))<=>((generous(alice)|~humble(alice))))&
((?[X]:((~patient(X)|~happy(X))))=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((tall(X)&brave(X))<=>(kind(X)|calm(X))))&
(((~happy(susan)&~funny(susan)))<=>(?[X]:((~calm(X)&kind(X)))))&
(((humble(fred)&~wise(fred)))=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:(~creative(X)))<=>((~brave(mary)<~>~tall(mary))))&
(![X]:((~old(X)<~>~tall(X))<=>~wise(X)))&
(![X]:(~generous(X)=>(~tall(X)|~brave(X))))&
(![X]:((curious(X)<~>calm(X))=>(~patient(X)|calm(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((wise(X)|funny(X))=>(wise(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|kind(X))))&
(~strong(susan))&
(~rich(alice))&
(?[X]:(~curious(X)))&
((~happy(fred)<~>~wise(fred)))&
(?[X]:(~tall(X)))&
(?[X]:(~wise(X))) | quiet(alice) | [
"p1",
"p4",
"p5",
"p7",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4741811844301333137917528
% SZS output start Proof for 4741811844301333137917528
2. ? [X0] : (~generous(X0) | ~tall(X0)) <=> (~wise(mary) & strong(mary)) [input p1]
5. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> kind(X0)) [input p4]
6. (happy(mary) & wise(mary)) <=> (~humble(alice) | generous(alice)) [input p5]
8. ! [X0] : ((brave(X0) & tall(X0)) <=> (calm(X0) | kind(X0))) [input p7]
13. ! [X0] : (~generous(X0) => (~brave(X0) | ~tall(X0))) [input p12]
22. ? [X0] : ~tall(X0) [input p21]
24. ~quiet(alice) [input hypothesis]
34. ! [X0] : ((~brave(X0) | ~tall(X0)) | generous(X0)) [ennf transformation 13]
35. ! [X0] : (~brave(X0) | ~tall(X0) | generous(X0)) [flattening 34]
40. (? [X0] : (~generous(X0) | ~tall(X0)) | (wise(mary) | ~strong(mary))) & ((~wise(mary) & strong(mary)) | ! [X0] : (generous(X0) & tall(X0))) [nnf transformation 2]
41. (? [X0] : (~generous(X0) | ~tall(X0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X0] : (generous(X0) & tall(X0))) [flattening 40]
42. (? [X0] : (~generous(X0) | ~tall(X0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X1] : (generous(X1) & tall(X1))) [rectify 41]
43. ? [X0] : (~generous(X0) | ~tall(X0)) => (~generous(sK0) | ~tall(sK0)) [choice axiom]
44. ((~generous(sK0) | ~tall(sK0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X1] : (generous(X1) & tall(X1))) [skolemisation 42,43]
47. ! [X0] : (((~quiet(X0) | ~humble(X0)) | ~kind(X0)) & (kind(X0) | (quiet(X0) & humble(X0)))) [nnf transformation 5]
48. ! [X0] : ((~quiet(X0) | ~humble(X0) | ~kind(X0)) & (kind(X0) | (quiet(X0) & humble(X0)))) [flattening 47]
49. ((happy(mary) & wise(mary)) | (humble(alice) & ~generous(alice))) & ((~humble(alice) | generous(alice)) | (~happy(mary) | ~wise(mary))) [nnf transformation 6]
50. ((happy(mary) & wise(mary)) | (humble(alice) & ~generous(alice))) & (~humble(alice) | generous(alice) | ~happy(mary) | ~wise(mary)) [flattening 49]
55. ! [X0] : (((brave(X0) & tall(X0)) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 8]
56. ! [X0] : (((brave(X0) & tall(X0)) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | ~brave(X0) | ~tall(X0))) [flattening 55]
80. ? [X0] : ~tall(X0) => ~tall(sK8) [choice axiom]
81. ~tall(sK8) [skolemisation 22,80]
88. ~wise(mary) | tall(X1) [cnf transformation 44]
98. kind(X0) | quiet(X0) [cnf transformation 48]
101. wise(mary) | ~generous(alice) [cnf transformation 50]
110. ~kind(X0) | tall(X0) [cnf transformation 56]
112. ~kind(X0) | brave(X0) [cnf transformation 56]
127. ~tall(X0) | ~brave(X0) | generous(X0) [cnf transformation 35]
143. ~tall(sK8) [cnf transformation 81]
145. ~quiet(alice) [cnf transformation 24]
169. 6 <=> wise(mary) [avatar definition]
186. 10 <=> ! [X1] : tall(X1) [avatar definition]
187. tall(X1) <- (10) [avatar component clause 186]
188. 10 | ~6 [avatar split clause 88,169,186]
201. 13 <=> generous(alice) [avatar definition]
206. ~13 | 6 [avatar split clause 101,169,201]
318. quiet(X0) | tall(X0) [resolution 110,98]
321. quiet(X0) | brave(X0) [resolution 112,98]
398. tall(alice) [resolution 318,145]
403. ~brave(alice) | generous(alice) [resolution 398,127]
409. brave(alice) [resolution 321,145]
418. generous(alice) [subsumption resolution 403,409]
419. 13 [avatar split clause 418,201]
437. $false <- (10) [resolution 187,143]
440. ~10 [avatar contradiction clause 437]
442. $false [avatar sat refutation 188,206,419,440]
% SZS output end Proof for 4741811844301333137917528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and generous then john is kind or brave.
Everyone who is both not calm and not happy is not brave and vice versa.
Everyone who is not funny is both not funny and calm.
If mary is not brave or not patient then mary is either kind or not creative and vice versa.
Everyone who is either not happy or not strong is either kind or not calm and vice versa.
If john is either not curious or calm then alice is funny and vice versa.
Everyone who is tall or not calm is either not old or not quiet.
Everyone who is happy or not happy is both rich and not creative.
If lucy is not wise or old then someone is both generous and creative.
If someone is either not quiet or not creative then john is kind.
If mary is either not rich or humble then someone is kind and vice versa.
Everyone who is not wise is not humble or strong.
Everyone who is tall or not strong is not kind or not generous.
Everyone who is either kind or not calm is both wise and calm and vice versa.
If susan is rich then someone is both not tall and humble and vice versa.
Everyone who is kind is either not wise or generous.
Someone is both not kind and not old.
Someone is not humble or not old.
Someone is both not strong and curious.
Mary is tall or not calm.
Someone is either not curious or quiet.
Someone is either not tall or not old.
Susan is not funny.
Someone is both not patient and strong. | Alice is not rich. | contradiction | ((?[X]:((funny(X)&generous(X))))=>((kind(john)|brave(john))))&
(![X]:((~calm(X)&~happy(X))<=>~brave(X)))&
(![X]:(~funny(X)=>(~funny(X)&calm(X))))&
(((~brave(mary)|~patient(mary)))<=>((kind(mary)<~>~creative(mary))))&
(![X]:((~happy(X)<~>~strong(X))<=>(kind(X)<~>~calm(X))))&
(((~curious(john)<~>calm(john)))<=>(funny(alice)))&
(![X]:((tall(X)|~calm(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((happy(X)|~happy(X))=>(rich(X)&~creative(X))))&
(((~wise(lucy)|old(lucy)))=>(?[X]:((generous(X)&creative(X)))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>(kind(john)))&
(((~rich(mary)<~>humble(mary)))<=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>(~humble(X)|strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~generous(X))))&
(![X]:((kind(X)<~>~calm(X))<=>(wise(X)&calm(X))))&
((rich(susan))<=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:(kind(X)=>(~wise(X)<~>generous(X))))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~strong(X)&curious(X))))&
((tall(mary)|~calm(mary)))&
(?[X]:((~curious(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>~old(X))))&
(~funny(susan))&
(?[X]:((~patient(X)&strong(X)))) | ~rich(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 279170348462112770981275
% SZS output start Proof for 279170348462112770981275
8. ! [X0] : ((~happy(X0) | happy(X0)) => (~creative(X0) & rich(X0))) [input p7]
25. ~rich(alice) [input hypothesis]
30. ! [X0] : ((~creative(X0) & rich(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 8]
101. rich(X0) | ~happy(X0) [cnf transformation 30]
102. rich(X0) | happy(X0) [cnf transformation 30]
142. ~rich(alice) [cnf transformation 25]
196. rich(X0) [subsumption resolution 101,102]
259. $false [subsumption resolution 142,196]
% SZS output end Proof for 279170348462112770981275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both wise and not happy and vice versa. If paul is either kind or wise then someone is both generous and not humble. Everyone who is both not rich and not quiet is either not brave or creative and vice versa. If someone is quiet then lucy is both happy and not happy and vice versa. Everyone who is not tall or not wise is both funny and old. If fred is not quiet or not kind then paul is either not wise or not curious and vice versa. Everyone who is both generous and wise is not tall or funny and vice versa. Everyone who is either old or creative is either not rich or not wise and vice versa. Everyone who is either happy or not creative is humble or not funny and vice versa. Everyone who is either quiet or generous is either not strong or not rich and vice versa. Everyone who is funny is not strong and vice versa. Everyone who is patient or not kind is not strong or not happy and vice versa. If someone is not humble then someone is not strong. If someone is either not tall or not humble then someone is not quiet. Everyone who is quiet is not old or not quiet. If someone is either not wise or humble then lucy is both not rich and funny. Someone is not funny. Susan is creative or calm. Susan is not kind or not creative. Susan is not calm. Someone is happy. Lucy is either generous or rich. Alice is not tall. John is both calm and not generous. | Susan is humble. | contradiction | (![X]:(~happy(X)<=>(wise(X)&~happy(X))))&
(((kind(paul)<~>wise(paul)))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~rich(X)&~quiet(X))<=>(~brave(X)<~>creative(X))))&
((?[X]:(quiet(X)))<=>((happy(lucy)&~happy(lucy))))&
(![X]:((~tall(X)|~wise(X))=>(funny(X)&old(X))))&
(((~quiet(fred)|~kind(fred)))<=>((~wise(paul)<~>~curious(paul))))&
(![X]:((generous(X)&wise(X))<=>(~tall(X)|funny(X))))&
(![X]:((old(X)<~>creative(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(humble(X)|~funny(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:(funny(X)<=>~strong(X)))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~old(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))=>((~rich(lucy)&funny(lucy))))&
(?[X]:(~funny(X)))&
((creative(susan)|calm(susan)))&
((~kind(susan)|~creative(susan)))&
(~calm(susan))&
(?[X]:(happy(X)))&
((generous(lucy)<~>rich(lucy)))&
(~tall(alice))&
((calm(john)&~generous(john))) | humble(susan) | [
"p3",
"p4",
"p6",
"p9",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6952531102796758696182734
% SZS output start Proof for 6952531102796758696182734
4. ? [X0] : quiet(X0) <=> (~happy(lucy) & happy(lucy)) [input p3]
5. ! [X0] : ((~wise(X0) | ~tall(X0)) => (old(X0) & funny(X0))) [input p4]
7. ! [X0] : ((wise(X0) & generous(X0)) <=> (funny(X0) | ~tall(X0))) [input p6]
10. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~strong(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : (funny(X0) <=> ~strong(X0)) [input p10]
16. ? [X0] : (~wise(X0) <~> humble(X0)) => (funny(lucy) & ~rich(lucy)) [input p15]
22. generous(lucy) <~> rich(lucy) [input p21]
25. humble(susan) [input hypothesis]
29. ! [X0] : ((old(X0) & funny(X0)) | (wise(X0) & tall(X0))) [ennf transformation 5]
34. (funny(lucy) & ~rich(lucy)) | ! [X0] : (~wise(X0) <=> humble(X0)) [ennf transformation 16]
42. (? [X0] : quiet(X0) | (happy(lucy) | ~happy(lucy))) & ((~happy(lucy) & happy(lucy)) | ! [X0] : ~quiet(X0)) [nnf transformation 4]
43. (? [X0] : quiet(X0) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X0] : ~quiet(X0)) [flattening 42]
44. (? [X0] : quiet(X0) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X1] : ~quiet(X1)) [rectify 43]
45. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
46. (quiet(sK1) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X1] : ~quiet(X1)) [skolemisation 44,45]
49. ! [X0] : (((wise(X0) & generous(X0)) | (~funny(X0) & tall(X0))) & ((funny(X0) | ~tall(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 7]
50. ! [X0] : (((wise(X0) & generous(X0)) | (~funny(X0) & tall(X0))) & (funny(X0) | ~tall(X0) | ~wise(X0) | ~generous(X0))) [flattening 49]
54. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0)))) & (((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 10]
55. ! [X0] : ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))) [nnf transformation 11]
65. (funny(lucy) & ~rich(lucy)) | ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 34]
70. (~rich(lucy) | ~generous(lucy)) & (rich(lucy) | generous(lucy)) [nnf transformation 22]
84. happy(lucy) | ~quiet(X1) [cnf transformation 46]
85. ~happy(lucy) | ~quiet(X1) [cnf transformation 46]
88. funny(X0) | wise(X0) [cnf transformation 29]
101. wise(X0) | ~funny(X0) [cnf transformation 50]
119. ~generous(X0) | strong(X0) | quiet(X0) | rich(X0) [cnf transformation 54]
124. ~strong(X0) | ~funny(X0) [cnf transformation 55]
135. ~rich(lucy) | ~wise(X0) | ~humble(X0) [cnf transformation 65]
137. funny(lucy) | ~wise(X0) | ~humble(X0) [cnf transformation 65]
143. rich(lucy) | generous(lucy) [cnf transformation 70]
148. humble(susan) [cnf transformation 25]
171. 5 <=> ! [X1] : ~quiet(X1) [avatar definition]
172. ~quiet(X1) <- (5) [avatar component clause 171]
174. 6 <=> happy(lucy) [avatar definition]
177. 5 | ~6 [avatar split clause 85,174,171]
178. 5 | 6 [avatar split clause 84,174,171]
197. wise(X0) [subsumption resolution 101,88]
224. funny(lucy) | ~humble(X0) [subsumption resolution 137,197]
226. 15 <=> ! [X0] : ~humble(X0) [avatar definition]
227. ~humble(X0) <- (15) [avatar component clause 226]
229. 16 <=> funny(lucy) [avatar definition]
231. funny(lucy) <- (16) [avatar component clause 229]
232. 15 | 16 [avatar split clause 224,229,226]
233. ~rich(lucy) | ~humble(X0) [subsumption resolution 135,197]
235. 17 <=> rich(lucy) [avatar definition]
237. ~rich(lucy) <- (~17) [avatar component clause 235]
238. 15 | ~17 [avatar split clause 233,235,226]
255. 21 <=> generous(lucy) [avatar definition]
256. generous(lucy) <- (21) [avatar component clause 255]
259. 21 | 17 [avatar split clause 143,235,255]
262. $false <- (15) [resolution 227,148]
263. ~15 [avatar contradiction clause 262]
431. strong(lucy) | quiet(lucy) | rich(lucy) <- (21) [resolution 119,256]
435. strong(lucy) | rich(lucy) <- (5, 21) [subsumption resolution 431,172]
436. strong(lucy) <- (5, ~17, 21) [subsumption resolution 435,237]
499. ~funny(lucy) <- (5, ~17, 21) [resolution 436,124]
500. $false <- (5, 16, ~17, 21) [subsumption resolution 499,231]
501. ~5 | ~16 | 17 | ~21 [avatar contradiction clause 500]
502. $false [avatar sat refutation 177,178,232,238,259,263,501]
% SZS output end Proof for 6952531102796758696182734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and tall then john is either funny or generous. If fred is both wise and humble then someone is brave and vice versa. Everyone who is curious or wise is either curious or not strong and vice versa. Everyone who is kind or tall is either quiet or not rich and vice versa. Everyone who is both not funny and quiet is both not strong and tall. Everyone who is either not happy or not patient is calm or generous. Everyone who is not brave is either tall or kind and vice versa. Everyone who is either wise or not wise is either brave or humble and vice versa. If someone is both not funny and not creative then someone is brave or not kind. Everyone who is both strong and not creative is not brave or patient. If paul is not curious then someone is either not calm or not humble and vice versa. Everyone who is not quiet is either not kind or quiet. Everyone who is both not quiet and tall is both patient and not rich. If someone is both not quiet and not patient then someone is either quiet or wise. Everyone who is kind is both brave and not brave and vice versa. If someone is both not generous and not funny then someone is not wise or not tall and vice versa. Susan is both not quiet and happy. Susan is both not creative and not calm. John is either curious or not wise. Susan is either not funny or not wise. Susan is wise or generous. Someone is funny or kind. Mary is not humble or wise. | Susan is quiet. | contradiction | ((?[X]:((humble(X)&tall(X))))=>((funny(john)<~>generous(john))))&
(((wise(fred)&humble(fred)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)|wise(X))<=>(curious(X)<~>~strong(X))))&
(![X]:((kind(X)|tall(X))<=>(quiet(X)<~>~rich(X))))&
(![X]:((~funny(X)&quiet(X))=>(~strong(X)&tall(X))))&
(![X]:((~happy(X)<~>~patient(X))=>(calm(X)|generous(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>kind(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(brave(X)<~>humble(X))))&
((?[X]:((~funny(X)&~creative(X))))=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((strong(X)&~creative(X))=>(~brave(X)|patient(X))))&
((~curious(paul))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(![X]:(~quiet(X)=>(~kind(X)<~>quiet(X))))&
(![X]:((~quiet(X)&tall(X))=>(patient(X)&~rich(X))))&
((?[X]:((~quiet(X)&~patient(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:(kind(X)<=>(brave(X)&~brave(X))))&
((?[X]:((~generous(X)&~funny(X))))<=>(?[X]:((~wise(X)|~tall(X)))))&
((~quiet(susan)&happy(susan)))&
((~creative(susan)&~calm(susan)))&
((curious(john)<~>~wise(john)))&
((~funny(susan)<~>~wise(susan)))&
((wise(susan)|generous(susan)))&
(?[X]:((funny(X)|kind(X))))&
((~humble(mary)|wise(mary))) | quiet(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6321734196182395983383947
% SZS output start Proof for 6321734196182395983383947
17. happy(susan) & ~quiet(susan) [input p16]
24. quiet(susan) [input hypothesis]
129. ~quiet(susan) [cnf transformation 17]
140. quiet(susan) [cnf transformation 24]
294. $false [subsumption resolution 140,129]
% SZS output end Proof for 6321734196182395983383947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is not tall then mary is not creative and vice versa. Everyone who is both not tall and strong is not quiet or not funny and vice versa. If mary is not curious or kind then fred is both creative and funny. Everyone who is generous is either happy or not quiet and vice versa. If paul is happy then john is quiet and vice versa. Everyone who is both not calm and not kind is funny. Everyone who is not strong or not rich is not humble or patient. Everyone who is both not quiet and not old is both not funny and not curious and vice versa. Everyone who is both curious and humble is either not humble or not quiet and vice versa. Everyone who is either tall or not happy is not creative and vice versa. Everyone who is both not strong and not old is not quiet and vice versa. Everyone who is kind or generous is wise. If someone is both happy and not curious then john is either not patient or not tall. Everyone who is either not patient or not wise is quiet or strong. Everyone who is both not wise and not tall is not humble or happy. Mary is not funny or creative. Fred is creative. Someone is either not humble or old. Someone is strong or not creative. Someone is either brave or not funny. Someone is either curious or not calm. | Paul is not funny. | contradiction | ((~tall(lucy))<=>(~creative(mary)))&
(![X]:((~tall(X)&strong(X))<=>(~quiet(X)|~funny(X))))&
(((~curious(mary)|kind(mary)))=>((creative(fred)&funny(fred))))&
(![X]:(generous(X)<=>(happy(X)<~>~quiet(X))))&
((happy(paul))<=>(quiet(john)))&
(![X]:((~calm(X)&~kind(X))=>funny(X)))&
(![X]:((~strong(X)|~rich(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)&~old(X))<=>(~funny(X)&~curious(X))))&
(![X]:((curious(X)&humble(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>~happy(X))<=>~creative(X)))&
(![X]:((~strong(X)&~old(X))<=>~quiet(X)))&
(![X]:((kind(X)|generous(X))=>wise(X)))&
((?[X]:((happy(X)&~curious(X))))=>((~patient(john)<~>~tall(john))))&
(![X]:((~patient(X)<~>~wise(X))=>(quiet(X)|strong(X))))&
(![X]:((~wise(X)&~tall(X))=>(~humble(X)|happy(X))))&
((~funny(mary)|creative(mary)))&
(creative(fred))&
(?[X]:((~humble(X)<~>old(X))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((curious(X)<~>~calm(X)))) | ~funny(paul) | [
"p1",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6494216264439688982203157
% SZS output start Proof for 6494216264439688982203157
2. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p1]
8. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (~curious(X0) & ~funny(X0))) [input p7]
9. ! [X0] : ((humble(X0) & curious(X0)) <=> (~humble(X0) <~> ~quiet(X0))) [input p8]
11. ! [X0] : ((~old(X0) & ~strong(X0)) <=> ~quiet(X0)) [input p10]
22. ~funny(paul) [input hypothesis]
38. ! [X0] : (((strong(X0) & ~tall(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((strong(X0) & ~tall(X0)) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | ~strong(X0) | tall(X0))) [flattening 38]
42. ! [X0] : (((~old(X0) & ~quiet(X0)) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | (old(X0) | quiet(X0)))) [nnf transformation 8]
43. ! [X0] : (((~old(X0) & ~quiet(X0)) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | old(X0) | quiet(X0))) [flattening 42]
44. ! [X0] : (((humble(X0) & curious(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (~humble(X0) | ~curious(X0)))) [nnf transformation 9]
45. ! [X0] : (((humble(X0) & curious(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | ~humble(X0) | ~curious(X0))) [flattening 44]
47. ! [X0] : (((~old(X0) & ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | strong(X0)))) [nnf transformation 11]
48. ! [X0] : (((~old(X0) & ~strong(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | strong(X0))) [flattening 47]
67. quiet(X0) | strong(X0) [cnf transformation 39]
81. ~quiet(X0) | curious(X0) | funny(X0) [cnf transformation 43]
83. ~quiet(X0) | ~humble(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 45]
87. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 45]
94. ~strong(X0) | quiet(X0) [cnf transformation 48]
112. ~funny(paul) [cnf transformation 22]
113. ~quiet(X0) | ~humble(X0) | ~curious(X0) [duplicate literal removal 83]
114. ~quiet(X0) | humble(X0) [duplicate literal removal 87]
155. ~curious(X0) | ~quiet(X0) [subsumption resolution 113,114]
156. quiet(X0) [subsumption resolution 94,67]
257. curious(X1) | funny(X1) [resolution 81,156]
259. funny(X1) | ~quiet(X1) [resolution 257,155]
261. funny(X1) [subsumption resolution 259,156]
266. $false [resolution 261,112]
% SZS output end Proof for 6494216264439688982203157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or creative is both brave and curious. If lucy is funny then someone is either not rich or not kind. Everyone who is either not quiet or quiet is rich and vice versa. Everyone who is creative is tall and vice versa. Everyone who is either not old or brave is both not funny and funny and vice versa. Everyone who is funny or strong is both not happy and not brave. Everyone who is both strong and rich is both strong and brave and vice versa. If susan is either not rich or not brave then someone is both not curious and curious and vice versa. Everyone who is not happy or creative is either not wise or old. Everyone who is kind is both not tall and calm and vice versa. If lucy is creative or not kind then someone is either not funny or not kind and vice versa. Everyone who is either tall or not happy is either not humble or not strong and vice versa. If susan is not brave or quiet then someone is quiet or not creative and vice versa. Everyone who is old or curious is both not patient and patient and vice versa. If someone is not old then someone is not happy or not wise. If john is patient or quiet then someone is both kind and brave and vice versa. Fred is not rich or not curious. Someone is either kind or not patient. Someone is kind or not quiet. Alice is not strong. Someone is strong or happy. Someone is either humble or not brave. | Susan is quiet. | entailment | (![X]:((funny(X)<~>creative(X))=>(brave(X)&curious(X))))&
((funny(lucy))=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>rich(X)))&
(![X]:(creative(X)<=>tall(X)))&
(![X]:((~old(X)<~>brave(X))<=>(~funny(X)&funny(X))))&
(![X]:((funny(X)|strong(X))=>(~happy(X)&~brave(X))))&
(![X]:((strong(X)&rich(X))<=>(strong(X)&brave(X))))&
(((~rich(susan)<~>~brave(susan)))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~happy(X)|creative(X))=>(~wise(X)<~>old(X))))&
(![X]:(kind(X)<=>(~tall(X)&calm(X))))&
(((creative(lucy)|~kind(lucy)))<=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:((tall(X)<~>~happy(X))<=>(~humble(X)<~>~strong(X))))&
(((~brave(susan)|quiet(susan)))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((old(X)|curious(X))<=>(~patient(X)&patient(X))))&
((?[X]:(~old(X)))=>(?[X]:((~happy(X)|~wise(X)))))&
(((patient(john)|quiet(john)))<=>(?[X]:((kind(X)&brave(X)))))&
((~rich(fred)|~curious(fred)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((kind(X)|~quiet(X))))&
(~strong(alice))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((humble(X)<~>~brave(X)))) | quiet(susan) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8488758673274179257129543
% SZS output start Proof for 8488758673274179257129543
3. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> rich(X0)) [input p2]
4. ! [X0] : (creative(X0) <=> tall(X0)) [input p3]
5. ! [X0] : ((~old(X0) <~> brave(X0)) <=> (funny(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((strong(X0) | funny(X0)) => (~brave(X0) & ~happy(X0))) [input p5]
8. (~rich(susan) <~> ~brave(susan)) <=> ? [X0] : (curious(X0) & ~curious(X0)) [input p7]
10. ! [X0] : (kind(X0) <=> (calm(X0) & ~tall(X0))) [input p9]
11. (~kind(lucy) | creative(lucy)) <=> ? [X0] : (~funny(X0) <~> ~kind(X0)) [input p10]
13. (quiet(susan) | ~brave(susan)) <=> ? [X0] : (~creative(X0) | quiet(X0)) [input p12]
14. ! [X0] : ((curious(X0) | old(X0)) <=> (patient(X0) & ~patient(X0))) [input p13]
23. ~quiet(susan) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (~strong(X0) & ~funny(X0))) [ennf transformation 6]
34. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~rich(X0)) & (rich(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 3]
35. ! [X0] : ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))) [nnf transformation 4]
36. ! [X0] : ((((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0))))) [flattening 36]
40. (((brave(susan) | rich(susan)) & (~brave(susan) | ~rich(susan))) | ! [X0] : (~curious(X0) | curious(X0))) & (? [X0] : (curious(X0) & ~curious(X0)) | ((~rich(susan) | brave(susan)) & (~brave(susan) | rich(susan)))) [nnf transformation 8]
41. (((brave(susan) | rich(susan)) & (~brave(susan) | ~rich(susan))) | ! [X0] : (~curious(X0) | curious(X0))) & (? [X1] : (curious(X1) & ~curious(X1)) | ((~rich(susan) | brave(susan)) & (~brave(susan) | rich(susan)))) [rectify 40]
42. ? [X1] : (curious(X1) & ~curious(X1)) => (curious(sK1) & ~curious(sK1)) [choice axiom]
43. (((brave(susan) | rich(susan)) & (~brave(susan) | ~rich(susan))) | ! [X0] : (~curious(X0) | curious(X0))) & ((curious(sK1) & ~curious(sK1)) | ((~rich(susan) | brave(susan)) & (~brave(susan) | rich(susan)))) [skolemisation 41,42]
45. ! [X0] : ((kind(X0) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | ~kind(X0))) [nnf transformation 10]
46. ! [X0] : ((kind(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | ~kind(X0))) [flattening 45]
47. ((~kind(lucy) | creative(lucy)) | ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (? [X0] : ((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (kind(lucy) & ~creative(lucy))) [nnf transformation 11]
48. (~kind(lucy) | creative(lucy) | ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (? [X0] : ((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (kind(lucy) & ~creative(lucy))) [flattening 47]
49. (~kind(lucy) | creative(lucy) | ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (? [X1] : ((kind(X1) | funny(X1)) & (~kind(X1) | ~funny(X1))) | (kind(lucy) & ~creative(lucy))) [rectify 48]
50. ? [X1] : ((kind(X1) | funny(X1)) & (~kind(X1) | ~funny(X1))) => ((kind(sK2) | funny(sK2)) & (~kind(sK2) | ~funny(sK2))) [choice axiom]
51. (~kind(lucy) | creative(lucy) | ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) & (((kind(sK2) | funny(sK2)) & (~kind(sK2) | ~funny(sK2))) | (kind(lucy) & ~creative(lucy))) [skolemisation 49,50]
53. ((quiet(susan) | ~brave(susan)) | ! [X0] : (creative(X0) & ~quiet(X0))) & (? [X0] : (~creative(X0) | quiet(X0)) | (~quiet(susan) & brave(susan))) [nnf transformation 13]
54. (quiet(susan) | ~brave(susan) | ! [X0] : (creative(X0) & ~quiet(X0))) & (? [X0] : (~creative(X0) | quiet(X0)) | (~quiet(susan) & brave(susan))) [flattening 53]
55. (quiet(susan) | ~brave(susan) | ! [X0] : (creative(X0) & ~quiet(X0))) & (? [X1] : (~creative(X1) | quiet(X1)) | (~quiet(susan) & brave(susan))) [rectify 54]
56. ? [X1] : (~creative(X1) | quiet(X1)) => (~creative(sK3) | quiet(sK3)) [choice axiom]
57. (quiet(susan) | ~brave(susan) | ! [X0] : (creative(X0) & ~quiet(X0))) & ((~creative(sK3) | quiet(sK3)) | (~quiet(susan) & brave(susan))) [skolemisation 55,56]
58. ! [X0] : (((curious(X0) | old(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~curious(X0) & ~old(X0)))) [nnf transformation 14]
59. ! [X0] : ((curious(X0) | old(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~curious(X0) & ~old(X0)))) [flattening 58]
84. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 34]
85. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 34]
88. ~creative(X0) | tall(X0) [cnf transformation 35]
90. ~funny(X0) | brave(X0) | old(X0) [cnf transformation 37]
92. funny(X0) | brave(X0) | old(X0) [cnf transformation 37]
98. ~brave(X0) | ~funny(X0) [cnf transformation 27]
105. ~curious(sK1) | ~rich(susan) | brave(susan) [cnf transformation 43]
107. curious(sK1) | ~rich(susan) | brave(susan) [cnf transformation 43]
114. ~tall(X0) | ~kind(X0) [cnf transformation 46]
119. kind(sK2) | funny(sK2) | ~creative(lucy) [cnf transformation 51]
134. quiet(susan) | ~brave(susan) | creative(X0) [cnf transformation 57]
135. ~patient(X0) | ~old(X0) [cnf transformation 59]
137. ~old(X0) | patient(X0) [cnf transformation 59]
154. ~quiet(susan) [cnf transformation 23]
155. rich(X0) | quiet(X0) [duplicate literal removal 84]
156. ~quiet(X0) | rich(X0) [duplicate literal removal 85]
171. rich(X0) [subsumption resolution 155,156]
173. old(X0) | brave(X0) [subsumption resolution 90,92]
176. curious(sK1) | brave(susan) [subsumption resolution 107,171]
178. 4 <=> brave(susan) [avatar definition]
182. 5 <=> curious(sK1) [avatar definition]
185. 4 | 5 [avatar split clause 176,182,178]
186. ~curious(sK1) | brave(susan) [subsumption resolution 105,171]
187. 4 | ~5 [avatar split clause 186,182,178]
192. 7 <=> creative(lucy) [avatar definition]
193. ~creative(lucy) <- (~7) [avatar component clause 192]
205. 10 <=> funny(sK2) [avatar definition]
207. funny(sK2) <- (10) [avatar component clause 205]
209. 11 <=> kind(sK2) [avatar definition]
211. kind(sK2) <- (11) [avatar component clause 209]
213. ~7 | 10 | 11 [avatar split clause 119,209,205,192]
221. 12 <=> ! [X0] : creative(X0) [avatar definition]
222. creative(X0) <- (12) [avatar component clause 221]
224. 13 <=> quiet(susan) [avatar definition]
227. 12 | ~4 | 13 [avatar split clause 134,224,178,221]
243. ~old(X0) [subsumption resolution 135,137]
308. ~13 [avatar split clause 154,224]
309. $false <- (~7, 12) [subsumption resolution 193,222]
310. 7 | ~12 [avatar contradiction clause 309]
311. tall(X0) <- (12) [resolution 88,222]
316. ~kind(X0) <- (12) [resolution 114,311]
321. brave(X2) [resolution 173,243]
326. ~funny(X0) [resolution 321,98]
328. $false <- (10) [resolution 326,207]
329. ~10 [avatar contradiction clause 328]
330. $false <- (11, 12) [subsumption resolution 211,316]
331. ~11 | ~12 [avatar contradiction clause 330]
332. $false [avatar sat refutation 185,187,213,227,308,310,329,331]
% SZS output end Proof for 8488758673274179257129543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not generous or not calm then mary is not brave. If someone is strong then mary is either funny or not tall and vice versa. Everyone who is both calm and tall is not happy and vice versa. Everyone who is kind or humble is both tall and not calm. Everyone who is not old is not patient. If susan is tall then someone is either not humble or not kind and vice versa. If mary is either not tall or not brave then someone is either generous or not patient. Everyone who is either generous or not quiet is either tall or generous. Everyone who is not wise or strong is both not calm and not kind. Everyone who is generous is both not tall and rich. If mary is humble then alice is not wise or not generous and vice versa. If paul is not funny or not kind then someone is both not funny and not happy. Everyone who is either not funny or funny is either not generous or not rich and vice versa. If someone is old then someone is creative. Everyone who is either tall or not funny is not tall. If someone is not funny or brave then someone is creative or not creative and vice versa. Paul is either generous or humble. Someone is rich. Someone is not quiet. Alice is rich. Paul is either not brave or kind. Susan is either not tall or not happy. Someone is either funny or strong. Someone is not generous. | Mary is not happy. | contradiction | (((~generous(lucy)<~>~calm(lucy)))=>(~brave(mary)))&
((?[X]:(strong(X)))<=>((funny(mary)<~>~tall(mary))))&
(![X]:((calm(X)&tall(X))<=>~happy(X)))&
(![X]:((kind(X)|humble(X))=>(tall(X)&~calm(X))))&
(![X]:(~old(X)=>~patient(X)))&
((tall(susan))<=>(?[X]:((~humble(X)<~>~kind(X)))))&
(((~tall(mary)<~>~brave(mary)))=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:((generous(X)<~>~quiet(X))=>(tall(X)<~>generous(X))))&
(![X]:((~wise(X)|strong(X))=>(~calm(X)&~kind(X))))&
(![X]:(generous(X)=>(~tall(X)&rich(X))))&
((humble(mary))<=>((~wise(alice)|~generous(alice))))&
(((~funny(paul)|~kind(paul)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~generous(X)<~>~rich(X))))&
((?[X]:(old(X)))=>(?[X]:(creative(X))))&
(![X]:((tall(X)<~>~funny(X))=>~tall(X)))&
((?[X]:((~funny(X)|brave(X))))<=>(?[X]:((creative(X)|~creative(X)))))&
((generous(paul)<~>humble(paul)))&
(?[X]:(rich(X)))&
(?[X]:(~quiet(X)))&
(rich(alice))&
((~brave(paul)<~>kind(paul)))&
((~tall(susan)<~>~happy(susan)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:(~generous(X))) | ~happy(mary) | [
"p2",
"p3",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4614031989245927461987707
% SZS output start Proof for 4614031989245927461987707
3. ! [X0] : ((tall(X0) & calm(X0)) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((humble(X0) | kind(X0)) => (~calm(X0) & tall(X0))) [input p3]
10. ! [X0] : (generous(X0) => (rich(X0) & ~tall(X0))) [input p9]
11. humble(mary) <=> (~generous(alice) | ~wise(alice)) [input p10]
13. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~generous(X0) <~> ~rich(X0))) [input p12]
25. ~happy(mary) [input hypothesis]
29. ! [X0] : ((~calm(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 4]
34. ! [X0] : ((rich(X0) & ~tall(X0)) | ~generous(X0)) [ennf transformation 10]
43. ! [X0] : (((tall(X0) & calm(X0)) | happy(X0)) & (~happy(X0) | (~tall(X0) | ~calm(X0)))) [nnf transformation 3]
44. ! [X0] : (((tall(X0) & calm(X0)) | happy(X0)) & (~happy(X0) | ~tall(X0) | ~calm(X0))) [flattening 43]
53. (humble(mary) | (generous(alice) & wise(alice))) & ((~generous(alice) | ~wise(alice)) | ~humble(mary)) [nnf transformation 11]
54. (humble(mary) | (generous(alice) & wise(alice))) & (~generous(alice) | ~wise(alice) | ~humble(mary)) [flattening 53]
57. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) & (((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 13]
86. happy(X0) | calm(X0) [cnf transformation 44]
91. ~humble(X0) | ~calm(X0) [cnf transformation 29]
110. rich(X0) | ~generous(X0) [cnf transformation 34]
113. humble(mary) | generous(alice) [cnf transformation 54]
118. ~rich(X0) | ~generous(X0) | funny(X0) | funny(X0) [cnf transformation 57]
119. ~rich(X0) | ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
120. rich(X0) | generous(X0) | funny(X0) | funny(X0) [cnf transformation 57]
121. rich(X0) | generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
145. ~happy(mary) [cnf transformation 25]
147. ~rich(X0) | ~generous(X0) | funny(X0) [duplicate literal removal 118]
148. ~rich(X0) | ~generous(X0) | ~funny(X0) [duplicate literal removal 119]
149. rich(X0) | generous(X0) | funny(X0) [duplicate literal removal 120]
150. rich(X0) | generous(X0) | ~funny(X0) [duplicate literal removal 121]
221. 15 <=> generous(alice) [avatar definition]
223. generous(alice) <- (15) [avatar component clause 221]
225. 16 <=> humble(mary) [avatar definition]
227. humble(mary) <- (16) [avatar component clause 225]
228. 15 | 16 [avatar split clause 113,225,221]
255. rich(X0) | ~funny(X0) [subsumption resolution 150,110]
256. rich(X0) | funny(X0) [subsumption resolution 149,110]
257. rich(X0) [subsumption resolution 256,255]
258. ~generous(X0) | ~funny(X0) [subsumption resolution 148,257]
259. ~generous(X0) | funny(X0) [subsumption resolution 147,257]
260. ~generous(X0) [subsumption resolution 259,258]
307. calm(mary) [resolution 86,145]
318. ~calm(mary) <- (16) [resolution 91,227]
320. $false <- (16) [subsumption resolution 318,307]
321. ~16 [avatar contradiction clause 320]
322. $false <- (15) [subsumption resolution 223,260]
323. ~15 [avatar contradiction clause 322]
324. $false [avatar sat refutation 228,321,323]
% SZS output end Proof for 4614031989245927461987707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is not creative or not brave and vice versa. Everyone who is generous is calm or strong and vice versa. If lucy is not tall then someone is not brave or kind. Everyone who is tall or not brave is not kind or not humble and vice versa. Everyone who is not humble is not quiet or not strong and vice versa. If someone is patient or humble then john is either quiet or patient and vice versa. If alice is old or not brave then lucy is both not quiet and not brave and vice versa. Everyone who is both rich and creative is both not generous and strong and vice versa. Everyone who is creative is both not happy and not creative and vice versa. Everyone who is not brave or not happy is old. Everyone who is either wise or curious is either quiet or not old and vice versa. If alice is both curious and not patient then susan is both not generous and patient. If mary is either not strong or not funny then alice is rich and vice versa. If someone is wise or not calm then someone is both not tall and not funny and vice versa. Everyone who is either not wise or not quiet is calm. Someone is either not quiet or not tall. Mary is both not generous and curious. Fred is not kind. Someone is both generous and wise. John is rich. Someone is quiet or not tall. | Mary is not brave. | contradiction | ((?[X]:(~funny(X)))<=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:(generous(X)<=>(calm(X)|strong(X))))&
((~tall(lucy))=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((tall(X)|~brave(X))<=>(~kind(X)|~humble(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~strong(X))))&
((?[X]:((patient(X)|humble(X))))<=>((quiet(john)<~>patient(john))))&
(((old(alice)|~brave(alice)))<=>((~quiet(lucy)&~brave(lucy))))&
(![X]:((rich(X)&creative(X))<=>(~generous(X)&strong(X))))&
(![X]:(creative(X)<=>(~happy(X)&~creative(X))))&
(![X]:((~brave(X)|~happy(X))=>old(X)))&
(![X]:((wise(X)<~>curious(X))<=>(quiet(X)<~>~old(X))))&
(((curious(alice)&~patient(alice)))=>((~generous(susan)&patient(susan))))&
(((~strong(mary)<~>~funny(mary)))<=>(rich(alice)))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((~wise(X)<~>~quiet(X))=>calm(X)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
((~generous(mary)&curious(mary)))&
(~kind(fred))&
(?[X]:((generous(X)&wise(X))))&
(rich(john))&
(?[X]:((quiet(X)|~tall(X)))) | ~brave(mary) | [
"p1",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7499985468205437154434152
% SZS output start Proof for 7499985468205437154434152
2. ! [X0] : (generous(X0) <=> (strong(X0) | calm(X0))) [input p1]
10. ! [X0] : ((~happy(X0) | ~brave(X0)) => old(X0)) [input p9]
11. ! [X0] : ((wise(X0) <~> curious(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p10]
15. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) => calm(X0)) [input p14]
17. curious(mary) & ~generous(mary) [input p16]
22. ~brave(mary) [input hypothesis]
26. ! [X0] : (old(X0) | (happy(X0) & brave(X0))) [ennf transformation 10]
29. ! [X0] : (calm(X0) | (~wise(X0) <=> ~quiet(X0))) [ennf transformation 15]
35. ! [X0] : ((generous(X0) | (~strong(X0) & ~calm(X0))) & ((strong(X0) | calm(X0)) | ~generous(X0))) [nnf transformation 2]
36. ! [X0] : ((generous(X0) | (~strong(X0) & ~calm(X0))) & (strong(X0) | calm(X0) | ~generous(X0))) [flattening 35]
53. ! [X0] : ((((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0))))) [nnf transformation 11]
60. ! [X0] : (calm(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) [nnf transformation 29]
72. ~calm(X0) | generous(X0) [cnf transformation 36]
100. old(X0) | brave(X0) [cnf transformation 26]
103. ~curious(X0) | quiet(X0) | wise(X0) | ~old(X0) [cnf transformation 53]
108. ~curious(X0) | ~wise(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 53]
121. ~quiet(X0) | calm(X0) | wise(X0) [cnf transformation 60]
122. ~wise(X0) | calm(X0) | quiet(X0) [cnf transformation 60]
125. ~generous(mary) [cnf transformation 17]
126. curious(mary) [cnf transformation 17]
132. ~brave(mary) [cnf transformation 22]
355. quiet(mary) | wise(mary) | ~old(mary) [resolution 103,126]
357. 47 <=> old(mary) [avatar definition]
358. old(mary) <- (47) [avatar component clause 357]
359. ~old(mary) <- (~47) [avatar component clause 357]
361. 48 <=> wise(mary) [avatar definition]
363. wise(mary) <- (48) [avatar component clause 361]
365. 49 <=> quiet(mary) [avatar definition]
366. ~quiet(mary) <- (~49) [avatar component clause 365]
367. quiet(mary) <- (49) [avatar component clause 365]
368. ~47 | 48 | 49 [avatar split clause 355,365,361,357]
376. brave(mary) <- (~47) [resolution 359,100]
377. $false <- (~47) [subsumption resolution 376,132]
378. 47 [avatar contradiction clause 377]
396. calm(mary) | wise(mary) <- (49) [resolution 367,121]
399. 52 <=> calm(mary) [avatar definition]
400. ~calm(mary) <- (~52) [avatar component clause 399]
401. calm(mary) <- (52) [avatar component clause 399]
402. 48 | 52 | ~49 [avatar split clause 396,365,399,361]
403. ~wise(mary) | ~old(mary) | ~quiet(mary) [resolution 108,126]
405. ~wise(mary) | ~quiet(mary) <- (47) [subsumption resolution 403,358]
524. generous(mary) <- (52) [resolution 401,72]
525. $false <- (52) [subsumption resolution 524,125]
526. ~52 [avatar contradiction clause 525]
527. ~49 | ~48 | ~47 [avatar split clause 405,357,361,365]
530. calm(mary) | quiet(mary) <- (48) [resolution 363,122]
531. quiet(mary) <- (48, ~52) [subsumption resolution 530,400]
532. $false <- (48, ~49, ~52) [subsumption resolution 531,366]
533. ~48 | 49 | 52 [avatar contradiction clause 532]
534. $false [avatar sat refutation 368,378,402,526,527,533]
% SZS output end Proof for 7499985468205437154434152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either calm or humble then someone is not funny or brave and vice versa. If susan is both tall and not quiet then someone is not rich or not generous and vice versa. If lucy is both wise and tall then someone is funny or not strong and vice versa. Everyone who is not tall or not humble is both not strong and humble and vice versa. If susan is kind then john is both not brave and not calm. Everyone who is not old is both generous and not happy and vice versa. Everyone who is not happy is either humble or tall and vice versa. Everyone who is not rich is both rich and humble. Everyone who is not old is both creative and not curious. If john is either generous or not happy then someone is either not patient or not generous and vice versa. If someone is kind then john is both not calm and old and vice versa. Everyone who is both calm and not creative is generous or not wise and vice versa. Everyone who is calm or kind is not tall or brave. If alice is curious then someone is both creative and not quiet. Everyone who is not old is either not calm or quiet. Everyone who is generous is both not wise and patient and vice versa. Susan is either strong or not curious. Someone is either creative or not rich. Mary is not patient. Someone is both funny and not patient. Someone is not funny or not strong. Someone is old or patient. Someone is both not creative and not tall. Someone is not creative or not humble. | Lucy is not brave. | neutral | (((calm(fred)<~>humble(fred)))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(susan)&~quiet(susan)))<=>(?[X]:((~rich(X)|~generous(X)))))&
(((wise(lucy)&tall(lucy)))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((~tall(X)|~humble(X))<=>(~strong(X)&humble(X))))&
((kind(susan))=>((~brave(john)&~calm(john))))&
(![X]:(~old(X)<=>(generous(X)&~happy(X))))&
(![X]:(~happy(X)<=>(humble(X)<~>tall(X))))&
(![X]:(~rich(X)=>(rich(X)&humble(X))))&
(![X]:(~old(X)=>(creative(X)&~curious(X))))&
(((generous(john)<~>~happy(john)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:(kind(X)))<=>((~calm(john)&old(john))))&
(![X]:((calm(X)&~creative(X))<=>(generous(X)|~wise(X))))&
(![X]:((calm(X)|kind(X))=>(~tall(X)|brave(X))))&
((curious(alice))=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~old(X)=>(~calm(X)<~>quiet(X))))&
(![X]:(generous(X)<=>(~wise(X)&patient(X))))&
((strong(susan)<~>~curious(susan)))&
(?[X]:((creative(X)<~>~rich(X))))&
(~patient(mary))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:((~funny(X)|~strong(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((~creative(X)&~tall(X))))&
(?[X]:((~creative(X)|~humble(X)))) | ~brave(lucy) | [] | null | 0 |
Everyone who is generous is both curious and not tall.
Everyone who is either not creative or tall is either happy or not wise and vice versa.
Everyone who is curious is not old and vice versa.
Everyone who is both not humble and not funny is either funny or kind and vice versa.
If paul is both brave and not creative then someone is creative or not calm.
Everyone who is both not tall and funny is both not quiet and calm and vice versa.
Everyone who is wise is kind or brave.
Everyone who is generous or not calm is not rich.
If paul is generous then someone is curious.
If someone is brave then someone is either not kind or brave and vice versa.
If fred is not humble or curious then susan is curious or brave.
If fred is generous then someone is both not funny and not brave.
Everyone who is either not tall or not wise is both creative and old.
If someone is both not patient and humble then someone is curious or not patient and vice versa.
If someone is not patient or not kind then mary is not brave and vice versa.
If someone is not patient then someone is both not brave and not old and vice versa.
Paul is both kind and humble.
Lucy is not funny or patient.
Someone is not strong or strong.
Susan is either not calm or creative.
Someone is not quiet or quiet.
Fred is either strong or creative.
Someone is not curious or not tall. | Lucy is not funny. | neutral | (![X]:(generous(X)=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)<~>tall(X))<=>(happy(X)<~>~wise(X))))&
(![X]:(curious(X)<=>~old(X)))&
(![X]:((~humble(X)&~funny(X))<=>(funny(X)<~>kind(X))))&
(((brave(paul)&~creative(paul)))=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~tall(X)&funny(X))<=>(~quiet(X)&calm(X))))&
(![X]:(wise(X)=>(kind(X)|brave(X))))&
(![X]:((generous(X)|~calm(X))=>~rich(X)))&
((generous(paul))=>(?[X]:(curious(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)<~>brave(X)))))&
(((~humble(fred)|curious(fred)))=>((curious(susan)|brave(susan))))&
((generous(fred))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>(creative(X)&old(X))))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((~patient(X)|~kind(X))))<=>(~brave(mary)))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((kind(paul)&humble(paul)))&
((~funny(lucy)|patient(lucy)))&
(?[X]:((~strong(X)|strong(X))))&
((~calm(susan)<~>creative(susan)))&
(?[X]:((~quiet(X)|quiet(X))))&
((strong(fred)<~>creative(fred)))&
(?[X]:((~curious(X)|~tall(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is either creative or strong is happy or not wise.
Everyone who is either not rich or not humble is either rich or wise and vice versa.
Everyone who is humble or not generous is brave and vice versa.
If alice is both funny and not happy then lucy is both not creative and strong.
If fred is both curious and not humble then someone is curious or not happy.
If someone is either not curious or not quiet then someone is either not strong or not happy and vice versa.
Everyone who is kind or not calm is either creative or not tall and vice versa.
Everyone who is either curious or quiet is both not old and not curious and vice versa.
If paul is not patient then someone is both generous and not wise and vice versa.
If susan is both not strong and not brave then susan is both happy and not funny and vice versa.
If john is either not curious or wise then paul is either tall or not brave and vice versa.
Everyone who is patient or not kind is happy.
Everyone who is both not wise and funny is either not humble or not rich.
Everyone who is both not happy and not old is both creative and not curious and vice versa.
Everyone who is not curious or not humble is not humble or not curious and vice versa.
Everyone who is not wise or not humble is both calm and not old.
Someone is both not patient and rich.
John is wise or not humble.
Someone is calm or not strong.
Someone is both quiet and tall.
Alice is not kind or generous.
Someone is both not tall and strong.
Paul is humble.
Someone is either old or not generous. | Paul is brave. | entailment | (![X]:((creative(X)<~>strong(X))=>(happy(X)|~wise(X))))&
(![X]:((~rich(X)<~>~humble(X))<=>(rich(X)<~>wise(X))))&
(![X]:((humble(X)|~generous(X))<=>brave(X)))&
(((funny(alice)&~happy(alice)))=>((~creative(lucy)&strong(lucy))))&
(((curious(fred)&~humble(fred)))=>(?[X]:((curious(X)|~happy(X)))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(![X]:((kind(X)|~calm(X))<=>(creative(X)<~>~tall(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~old(X)&~curious(X))))&
((~patient(paul))<=>(?[X]:((generous(X)&~wise(X)))))&
(((~strong(susan)&~brave(susan)))<=>((happy(susan)&~funny(susan))))&
(((~curious(john)<~>wise(john)))<=>((tall(paul)<~>~brave(paul))))&
(![X]:((patient(X)|~kind(X))=>happy(X)))&
(![X]:((~wise(X)&funny(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((~happy(X)&~old(X))<=>(creative(X)&~curious(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~humble(X)|~curious(X))))&
(![X]:((~wise(X)|~humble(X))=>(calm(X)&~old(X))))&
(?[X]:((~patient(X)&rich(X))))&
((wise(john)|~humble(john)))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((quiet(X)&tall(X))))&
((~kind(alice)|generous(alice)))&
(?[X]:((~tall(X)&strong(X))))&
(humble(paul))&
(?[X]:((old(X)<~>~generous(X)))) | brave(paul) | [
"p2",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2401391046549451986879617
% SZS output start Proof for 2401391046549451986879617
3. ! [X0] : ((~generous(X0) | humble(X0)) <=> brave(X0)) [input p2]
23. humble(paul) [input p22]
25. ~brave(paul) [input hypothesis]
39. ! [X0] : (((~generous(X0) | humble(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) & ~humble(X0)))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | humble(X0) | ~brave(X0)) & (brave(X0) | (generous(X0) & ~humble(X0)))) [flattening 39]
85. ~humble(X0) | brave(X0) [cnf transformation 40]
151. humble(paul) [cnf transformation 23]
154. ~brave(paul) [cnf transformation 25]
274. 25 <=> brave(paul) [avatar definition]
275. ~brave(paul) <- (~25) [avatar component clause 274]
326. ~25 [avatar split clause 154,274]
327. brave(paul) [resolution 85,151]
328. $false <- (~25) [subsumption resolution 327,275]
329. 25 [avatar contradiction clause 328]
330. $false [avatar sat refutation 326,329]
% SZS output end Proof for 2401391046549451986879617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is tall or funny.
Everyone who is not funny is both not kind and humble.
Everyone who is not tall is both happy and not creative and vice versa.
If alice is patient or strong then someone is either kind or not patient and vice versa.
Everyone who is calm or creative is not tall or creative and vice versa.
Everyone who is humble or not tall is both kind and not calm.
If alice is both not calm and calm then susan is both rich and strong and vice versa.
Everyone who is not creative or wise is calm.
Everyone who is both funny and calm is both funny and not curious.
If lucy is creative then someone is either not brave or funny.
Everyone who is both not generous and not old is wise.
If fred is not kind or not rich then someone is creative and vice versa.
If someone is not kind or not funny then someone is either generous or not brave.
If someone is both not kind and tall then someone is not patient.
If someone is both patient and curious then mary is happy or not rich and vice versa.
Everyone who is both tall and not curious is both quiet and not generous.
Fred is quiet.
Fred is both not curious and not calm.
John is happy or not strong.
Susan is either not rich or tall.
Lucy is both not old and not quiet.
Lucy is humble.
Someone is either calm or not brave.
Someone is not patient. | Mary is tall. | entailment | (![X]:(humble(X)=>(tall(X)|funny(X))))&
(![X]:(~funny(X)=>(~kind(X)&humble(X))))&
(![X]:(~tall(X)<=>(happy(X)&~creative(X))))&
(((patient(alice)|strong(alice)))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:((calm(X)|creative(X))<=>(~tall(X)|creative(X))))&
(![X]:((humble(X)|~tall(X))=>(kind(X)&~calm(X))))&
(((~calm(alice)&calm(alice)))<=>((rich(susan)&strong(susan))))&
(![X]:((~creative(X)|wise(X))=>calm(X)))&
(![X]:((funny(X)&calm(X))=>(funny(X)&~curious(X))))&
((creative(lucy))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:((~generous(X)&~old(X))=>wise(X)))&
(((~kind(fred)|~rich(fred)))<=>(?[X]:(creative(X))))&
((?[X]:((~kind(X)|~funny(X))))=>(?[X]:((generous(X)<~>~brave(X)))))&
((?[X]:((~kind(X)&tall(X))))=>(?[X]:(~patient(X))))&
((?[X]:((patient(X)&curious(X))))<=>((happy(mary)|~rich(mary))))&
(![X]:((tall(X)&~curious(X))=>(quiet(X)&~generous(X))))&
(quiet(fred))&
((~curious(fred)&~calm(fred)))&
((happy(john)|~strong(john)))&
((~rich(susan)<~>tall(susan)))&
((~old(lucy)&~quiet(lucy)))&
(humble(lucy))&
(?[X]:((calm(X)<~>~brave(X))))&
(?[X]:(~patient(X))) | tall(mary) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1933433489560245132454706
% SZS output start Proof for 1933433489560245132454706
3. ! [X0] : (~tall(X0) <=> (~creative(X0) & happy(X0))) [input p2]
5. ! [X0] : ((creative(X0) | calm(X0)) <=> (creative(X0) | ~tall(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | humble(X0)) => (~calm(X0) & kind(X0))) [input p5]
25. ~tall(mary) [input hypothesis]
31. ! [X0] : ((~calm(X0) & kind(X0)) | (tall(X0) & ~humble(X0))) [ennf transformation 6]
42. ! [X0] : ((~tall(X0) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | tall(X0))) [nnf transformation 3]
43. ! [X0] : ((~tall(X0) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | tall(X0))) [flattening 42]
49. ! [X0] : (((creative(X0) | calm(X0)) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 5]
50. ! [X0] : ((creative(X0) | calm(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | (~creative(X0) & ~calm(X0)))) [flattening 49]
83. ~creative(X0) | tall(X0) [cnf transformation 43]
93. creative(X0) | calm(X0) | tall(X0) [cnf transformation 50]
98. ~calm(X0) | tall(X0) [cnf transformation 31]
137. ~tall(mary) [cnf transformation 25]
166. calm(X0) | tall(X0) [subsumption resolution 93,83]
167. tall(X0) [subsumption resolution 98,166]
285. $false [subsumption resolution 137,167]
% SZS output end Proof for 1933433489560245132454706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not wise is either quiet or generous.
Everyone who is not generous is not humble or not tall and vice versa.
Everyone who is either creative or not curious is both not brave and not patient and vice versa.
Everyone who is both funny and not calm is not happy or kind and vice versa.
Everyone who is both not brave and rich is not wise and vice versa.
Everyone who is both kind and patient is both strong and not brave and vice versa.
If someone is either not strong or curious then someone is funny and vice versa.
Everyone who is not happy is either tall or not wise.
Everyone who is either humble or not tall is kind and vice versa.
Everyone who is either not calm or humble is either not patient or not quiet.
Everyone who is either tall or funny is both generous and quiet and vice versa.
Everyone who is either not wise or not brave is either brave or not tall and vice versa.
If john is not rich or not creative then someone is both rich and creative.
If john is not wise or happy then john is either not old or happy.
Everyone who is funny or quiet is both rich and old.
If someone is either tall or not strong then someone is either brave or not patient.
Paul is calm or funny.
Someone is either old or not brave.
Paul is not curious.
Someone is strong or old.
Susan is both generous and not quiet.
Alice is either curious or creative.
Someone is either tall or old. | Susan is not happy. | contradiction | (![X]:((old(X)<~>~wise(X))=>(quiet(X)<~>generous(X))))&
(![X]:(~generous(X)<=>(~humble(X)|~tall(X))))&
(![X]:((creative(X)<~>~curious(X))<=>(~brave(X)&~patient(X))))&
(![X]:((funny(X)&~calm(X))<=>(~happy(X)|kind(X))))&
(![X]:((~brave(X)&rich(X))<=>~wise(X)))&
(![X]:((kind(X)&patient(X))<=>(strong(X)&~brave(X))))&
((?[X]:((~strong(X)<~>curious(X))))<=>(?[X]:(funny(X))))&
(![X]:(~happy(X)=>(tall(X)<~>~wise(X))))&
(![X]:((humble(X)<~>~tall(X))<=>kind(X)))&
(![X]:((~calm(X)<~>humble(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>funny(X))<=>(generous(X)&quiet(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)<~>~tall(X))))&
(((~rich(john)|~creative(john)))=>(?[X]:((rich(X)&creative(X)))))&
(((~wise(john)|happy(john)))=>((~old(john)<~>happy(john))))&
(![X]:((funny(X)|quiet(X))=>(rich(X)&old(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>(?[X]:((brave(X)<~>~patient(X)))))&
((calm(paul)|funny(paul)))&
(?[X]:((old(X)<~>~brave(X))))&
(~curious(paul))&
(?[X]:((strong(X)|old(X))))&
((generous(susan)&~quiet(susan)))&
((curious(alice)<~>creative(alice)))&
(?[X]:((tall(X)<~>old(X)))) | ~happy(susan) | [
"p1",
"p4",
"p7",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5652870081944310778375069
% SZS output start Proof for 5652870081944310778375069
2. ! [X0] : (~generous(X0) <=> (~tall(X0) | ~humble(X0))) [input p1]
5. ! [X0] : ((rich(X0) & ~brave(X0)) <=> ~wise(X0)) [input p4]
8. ! [X0] : (~happy(X0) => (tall(X0) <~> ~wise(X0))) [input p7]
12. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (brave(X0) <~> ~tall(X0))) [input p11]
21. ~quiet(susan) & generous(susan) [input p20]
24. ~happy(susan) [input hypothesis]
28. ! [X0] : ((tall(X0) <~> ~wise(X0)) | happy(X0)) [ennf transformation 8]
35. ! [X0] : ((~generous(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | generous(X0))) [nnf transformation 2]
36. ! [X0] : ((~generous(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | generous(X0))) [flattening 35]
41. ! [X0] : (((rich(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | (~rich(X0) | brave(X0)))) [nnf transformation 5]
42. ! [X0] : (((rich(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | ~rich(X0) | brave(X0))) [flattening 41]
50. ! [X0] : (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | happy(X0)) [nnf transformation 28]
55. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 12]
78. ~generous(X0) | tall(X0) [cnf transformation 36]
91. ~brave(X0) | wise(X0) [cnf transformation 42]
102. ~tall(X0) | wise(X0) | happy(X0) [cnf transformation 50]
118. ~tall(X0) | brave(X0) | ~wise(X0) | brave(X0) [cnf transformation 55]
121. ~brave(X0) | ~wise(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 55]
124. brave(X0) | wise(X0) | brave(X0) | tall(X0) [cnf transformation 55]
146. generous(susan) [cnf transformation 21]
152. ~happy(susan) [cnf transformation 24]
154. ~tall(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 118]
156. ~brave(X0) | ~wise(X0) | ~tall(X0) [duplicate literal removal 121]
157. brave(X0) | wise(X0) | tall(X0) [duplicate literal removal 124]
185. tall(X0) | wise(X0) [subsumption resolution 157,91]
186. ~brave(X0) | ~tall(X0) [subsumption resolution 156,91]
187. ~tall(X0) | ~wise(X0) [subsumption resolution 154,186]
290. tall(susan) [resolution 78,146]
305. ~wise(susan) [resolution 187,290]
367. wise(X0) | happy(X0) | wise(X0) [resolution 102,185]
371. happy(X0) | wise(X0) [duplicate literal removal 367]
595. wise(susan) [resolution 371,152]
597. $false [subsumption resolution 595,305]
% SZS output end Proof for 5652870081944310778375069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not funny or not humble and vice versa. Everyone who is both not calm and not patient is both generous and tall. Everyone who is curious is rich. If paul is both kind and not wise then mary is both not strong and generous and vice versa. Everyone who is not happy or brave is either not rich or tall and vice versa. Everyone who is not old or strong is both creative and curious and vice versa. If fred is either quiet or not quiet then someone is kind or not wise and vice versa. Everyone who is generous or tall is brave or calm. If someone is not happy then susan is tall. If fred is rich or brave then susan is either patient or not brave and vice versa. Everyone who is both not creative and not quiet is either generous or not tall. Everyone who is either not rich or not old is either not curious or generous. Everyone who is either not happy or curious is tall or not rich. If susan is generous or not strong then susan is either not creative or curious and vice versa. Everyone who is both not brave and not curious is strong. Everyone who is either not rich or kind is not old or not creative. Someone is kind. Someone is either funny or not curious. John is either tall or not quiet. Someone is not creative or not calm. Someone is either not generous or not kind. Susan is both not rich and not curious. Someone is either happy or not rich. Mary is not calm. | Susan is generous. | contradiction | (![X]:((patient(X)|~kind(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~calm(X)&~patient(X))=>(generous(X)&tall(X))))&
(![X]:(curious(X)=>rich(X)))&
(((kind(paul)&~wise(paul)))<=>((~strong(mary)&generous(mary))))&
(![X]:((~happy(X)|brave(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~old(X)|strong(X))<=>(creative(X)&curious(X))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((generous(X)|tall(X))=>(brave(X)|calm(X))))&
((?[X]:(~happy(X)))=>(tall(susan)))&
(((rich(fred)|brave(fred)))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>~old(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~happy(X)<~>curious(X))=>(tall(X)|~rich(X))))&
(((generous(susan)|~strong(susan)))<=>((~creative(susan)<~>curious(susan))))&
(![X]:((~brave(X)&~curious(X))=>strong(X)))&
(![X]:((~rich(X)<~>kind(X))=>(~old(X)|~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((funny(X)<~>~curious(X))))&
((tall(john)<~>~quiet(john)))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((~generous(X)<~>~kind(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:((happy(X)<~>~rich(X))))&
(~calm(mary)) | generous(susan) | [
"p2",
"p5",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8541935264873672876542618
% SZS output start Proof for 8541935264873672876542618
3. ! [X0] : (curious(X0) => rich(X0)) [input p2]
6. ! [X0] : ((strong(X0) | ~old(X0)) <=> (curious(X0) & creative(X0))) [input p5]
12. ! [X0] : ((~rich(X0) <~> ~old(X0)) => (~curious(X0) <~> generous(X0))) [input p11]
14. (~strong(susan) | generous(susan)) <=> (~creative(susan) <~> curious(susan)) [input p13]
22. ~curious(susan) & ~rich(susan) [input p21]
25. generous(susan) [input hypothesis]
28. ! [X0] : (rich(X0) | ~curious(X0)) [ennf transformation 3]
34. ! [X0] : ((~curious(X0) <~> generous(X0)) | (~rich(X0) <=> ~old(X0))) [ennf transformation 12]
47. ! [X0] : (((strong(X0) | ~old(X0)) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [nnf transformation 6]
48. ! [X0] : ((strong(X0) | ~old(X0) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [flattening 47]
56. ! [X0] : (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) [nnf transformation 34]
58. ((~strong(susan) | generous(susan)) | ((~creative(susan) | ~curious(susan)) & (curious(susan) | creative(susan)))) & (((~curious(susan) | creative(susan)) & (curious(susan) | ~creative(susan))) | (strong(susan) & ~generous(susan))) [nnf transformation 14]
59. (~strong(susan) | generous(susan) | ((~creative(susan) | ~curious(susan)) & (curious(susan) | creative(susan)))) & (((~curious(susan) | creative(susan)) & (curious(susan) | ~creative(susan))) | (strong(susan) & ~generous(susan))) [flattening 58]
81. ~curious(X0) | rich(X0) [cnf transformation 28]
92. creative(X0) | old(X0) [cnf transformation 48]
116. ~generous(X0) | curious(X0) | ~old(X0) | rich(X0) [cnf transformation 56]
120. curious(susan) | ~creative(susan) | ~generous(susan) [cnf transformation 59]
137. ~rich(susan) [cnf transformation 22]
138. ~curious(susan) [cnf transformation 22]
142. generous(susan) [cnf transformation 25]
209. ~old(X0) | ~generous(X0) | rich(X0) [subsumption resolution 116,81]
215. 14 <=> generous(susan) [avatar definition]
217. generous(susan) <- (14) [avatar component clause 215]
225. 16 <=> creative(susan) [avatar definition]
226. ~creative(susan) <- (~16) [avatar component clause 225]
229. 17 <=> curious(susan) [avatar definition]
236. ~14 | ~16 | 17 [avatar split clause 120,229,225,215]
277. ~17 [avatar split clause 138,229]
288. 14 [avatar split clause 142,215]
291. old(susan) <- (~16) [resolution 92,226]
397. ~generous(susan) | rich(susan) <- (~16) [resolution 209,291]
399. rich(susan) <- (14, ~16) [subsumption resolution 397,217]
400. $false <- (14, ~16) [subsumption resolution 399,137]
401. ~14 | 16 [avatar contradiction clause 400]
403. $false [avatar sat refutation 236,277,288,401]
% SZS output end Proof for 8541935264873672876542618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is either curious or not generous and vice versa.
Everyone who is both tall and wise is not happy and vice versa.
Everyone who is brave or generous is not wise or kind and vice versa.
Everyone who is patient is not curious or strong.
Everyone who is either not funny or creative is either kind or not kind and vice versa.
If mary is old then someone is both not wise and brave.
Everyone who is both not tall and calm is both generous and not calm.
Everyone who is either happy or kind is strong or kind and vice versa.
If fred is both wise and not tall then someone is either not generous or kind and vice versa.
If alice is either not creative or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Everyone who is either not brave or calm is either rich or not funny.
Lucy is old.
Paul is either not kind or strong.
Someone is either tall or not patient.
Someone is both not patient and old. | Susan is tall. | entailment | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&wise(X))<=>~happy(X)))&
(![X]:((brave(X)|generous(X))<=>(~wise(X)|kind(X))))&
(![X]:(patient(X)=>(~curious(X)|strong(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(kind(X)<~>~kind(X))))&
((old(mary))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((~tall(X)&calm(X))=>(generous(X)&~calm(X))))&
(![X]:((happy(X)<~>kind(X))<=>(strong(X)|kind(X))))&
(((wise(fred)&~tall(fred)))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(((~creative(alice)<~>brave(alice)))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>calm(X))=>(rich(X)<~>~funny(X))))&
(old(lucy))&
((~kind(paul)<~>strong(paul)))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:((~patient(X)&old(X)))) | tall(susan) | [
"p0",
"p4",
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8530978156685628349631171
% SZS output start Proof for 8530978156685628349631171
1. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p0]
5. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4]
7. ! [X0] : ((calm(X0) & ~tall(X0)) => (~calm(X0) & generous(X0))) [input p6]
9. (~tall(fred) & wise(fred)) <=> ? [X0] : (~generous(X0) <~> kind(X0)) [input p8]
13. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p12]
14. ! [X0] : ((creative(X0) <~> kind(X0)) <=> curious(X0)) [input p13]
21. ~tall(susan) [input hypothesis]
25. ! [X0] : ((~calm(X0) & generous(X0)) | (~calm(X0) | tall(X0))) [ennf transformation 7]
26. ! [X0] : ((~calm(X0) & generous(X0)) | ~calm(X0) | tall(X0)) [flattening 25]
33. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (funny(X0) | ~quiet(X0)))) [nnf transformation 1]
34. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | funny(X0) | ~quiet(X0))) [flattening 33]
39. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 5]
44. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X0] : ((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (tall(fred) | ~wise(fred))) [nnf transformation 9]
45. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X0] : ((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | tall(fred) | ~wise(fred)) [flattening 44]
46. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (? [X1] : ((~kind(X1) | generous(X1)) & (kind(X1) | ~generous(X1))) | tall(fred) | ~wise(fred)) [rectify 45]
47. ? [X1] : ((~kind(X1) | generous(X1)) & (kind(X1) | ~generous(X1))) => ((~kind(sK1) | generous(sK1)) & (kind(sK1) | ~generous(sK1))) [choice axiom]
48. ((~tall(fred) & wise(fred)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(sK1) | generous(sK1)) & (kind(sK1) | ~generous(sK1))) | tall(fred) | ~wise(fred)) [skolemisation 46,47]
53. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 13]
54. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 53]
55. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ~curious(X0)) & (curious(X0) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 14]
68. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 34]
69. ~funny(X0) | curious(X0) | generous(X0) [cnf transformation 34]
82. creative(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39]
83. creative(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 39]
89. ~calm(X0) | ~calm(X0) | tall(X0) [cnf transformation 26]
98. wise(fred) | kind(X0) | generous(X0) [cnf transformation 48]
99. wise(fred) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
100. ~tall(fred) | kind(X0) | generous(X0) [cnf transformation 48]
101. ~tall(fred) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
117. calm(X0) | funny(X0) [cnf transformation 54]
118. ~wise(X0) | calm(X0) [cnf transformation 54]
121. ~creative(X0) | kind(X0) | curious(X0) [cnf transformation 55]
124. ~creative(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 55]
138. ~tall(susan) [cnf transformation 21]
141. ~calm(X0) | tall(X0) [duplicate literal removal 89]
142. creative(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 82]
143. ~funny(X0) | creative(X0) | kind(X0) [duplicate literal removal 83]
147. ~funny(X0) | creative(X0) [subsumption resolution 142,143]
164. 4 <=> ! [X0] : (~generous(X0) | ~kind(X0)) [avatar definition]
165. ~kind(X0) | ~generous(X0) <- (4) [avatar component clause 164]
167. 5 <=> tall(fred) [avatar definition]
169. ~tall(fred) <- (~5) [avatar component clause 167]
170. 4 | ~5 [avatar split clause 101,167,164]
172. 6 <=> ! [X0] : (kind(X0) | generous(X0)) [avatar definition]
173. kind(X0) | generous(X0) <- (6) [avatar component clause 172]
174. 6 | ~5 [avatar split clause 100,167,172]
176. 7 <=> wise(fred) [avatar definition]
178. wise(fred) <- (7) [avatar component clause 176]
179. 4 | 7 [avatar split clause 99,176,164]
180. 6 | 7 [avatar split clause 98,176,172]
216. 14 <=> generous(susan) [avatar definition]
217. generous(susan) <- (14) [avatar component clause 216]
218. ~generous(susan) <- (~14) [avatar component clause 216]
259. tall(X0) | funny(X0) [resolution 141,117]
284. funny(susan) [resolution 259,138]
297. curious(susan) | generous(susan) [resolution 284,69]
298. creative(susan) [resolution 284,147]
300. 26 <=> curious(susan) [avatar definition]
301. ~curious(susan) <- (~26) [avatar component clause 300]
303. 14 | 26 [avatar split clause 297,300,216]
304. ~funny(susan) | ~curious(susan) <- (14) [resolution 217,68]
306. ~curious(susan) <- (14) [subsumption resolution 304,284]
307. ~26 | ~14 [avatar split clause 306,216,300]
389. kind(susan) | curious(susan) [resolution 121,298]
391. kind(susan) <- (~26) [subsumption resolution 389,301]
395. ~kind(susan) | ~curious(susan) [resolution 124,298]
399. ~generous(susan) <- (4, ~26) [resolution 391,165]
401. $false <- (4, 14, ~26) [subsumption resolution 399,217]
402. ~4 | ~14 | 26 [avatar contradiction clause 401]
404. 39 <=> kind(susan) [avatar definition]
406. ~kind(susan) <- (~39) [avatar component clause 404]
407. ~26 | ~39 [avatar split clause 395,404,300]
408. 26 | 39 [avatar split clause 389,404,300]
419. generous(susan) <- (6, ~39) [resolution 406,173]
420. $false <- (6, ~14, ~39) [subsumption resolution 419,218]
421. ~6 | 14 | 39 [avatar contradiction clause 420]
430. calm(fred) <- (7) [resolution 178,118]
466. tall(fred) <- (7) [resolution 430,141]
467. $false <- (~5, 7) [subsumption resolution 466,169]
468. 5 | ~7 [avatar contradiction clause 467]
469. $false [avatar sat refutation 170,174,179,180,303,307,402,407,408,421,468]
% SZS output end Proof for 8530978156685628349631171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is happy is old and vice versa.
Everyone who is not brave is funny and vice versa.
If susan is both humble and patient then someone is not rich.
Everyone who is humble or not creative is both not brave and tall and vice versa.
If someone is tall then mary is either calm or strong.
Everyone who is curious is happy and vice versa.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is kind or old is brave or not quiet and vice versa.
Everyone who is not kind or calm is not brave or not funny.
Everyone who is wise is not humble.
Everyone who is humble or wise is both not generous and not creative.
Everyone who is humble is rich or brave and vice versa.
If someone is brave then lucy is not patient or not generous and vice versa.
If someone is not quiet or calm then someone is not happy and vice versa.
If alice is either wise or not generous then someone is both not brave and old and vice versa.
Someone is either not tall or rich.
Someone is strong or rich.
Someone is not quiet or quiet.
John is either not calm or happy.
Fred is both tall and not patient.
Someone is not humble.
Susan is not rich or creative. | Mary is not quiet. | entailment | (![X]:(happy(X)<=>old(X)))&
(![X]:(~brave(X)<=>funny(X)))&
(((humble(susan)&patient(susan)))=>(?[X]:(~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((~calm(john)<~>happy(john)))&
((tall(fred)&~patient(fred)))&
(?[X]:(~humble(X)))&
((~rich(susan)|creative(susan))) | ~quiet(mary) | [
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2698812808335052193662330
% SZS output start Proof for 2698812808335052193662330
4. ! [X0] : ((~creative(X0) | humble(X0)) <=> (tall(X0) & ~brave(X0))) [input p3]
7. ! [X0] : ((~kind(X0) & brave(X0)) <=> quiet(X0)) [input p6]
12. ! [X0] : (humble(X0) <=> (brave(X0) | rich(X0))) [input p11]
23. quiet(mary) [input hypothesis]
36. ! [X0] : (((~creative(X0) | humble(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : ((~creative(X0) | humble(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [flattening 36]
39. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 7]
40. ! [X0] : (((~kind(X0) & brave(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 12]
44. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0))) [flattening 43]
74. ~humble(X0) | ~brave(X0) [cnf transformation 37]
82. ~quiet(X0) | brave(X0) [cnf transformation 40]
97. humble(X0) | ~brave(X0) [cnf transformation 44]
120. quiet(mary) [cnf transformation 23]
147. ~brave(X0) [subsumption resolution 97,74]
239. brave(mary) [resolution 82,120]
240. $false [subsumption resolution 239,147]
% SZS output end Proof for 2698812808335052193662330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or not rich then susan is wise and vice versa. If someone is wise then mary is not wise and vice versa. If someone is creative then someone is not tall and vice versa. Everyone who is not kind or not funny is brave or not calm and vice versa. Everyone who is both happy and not tall is not old. Everyone who is not generous or not quiet is patient or not humble and vice versa. Everyone who is both not calm and happy is rich. If mary is either not patient or brave then mary is curious or rich. Everyone who is both not quiet and not happy is either not brave or strong and vice versa. Everyone who is both rich and not old is either rich or not happy and vice versa. Everyone who is old or not rich is patient or not funny and vice versa. If john is calm or not calm then mary is curious and vice versa. If someone is both rich and not calm then someone is both not curious and curious and vice versa. Everyone who is generous or calm is not patient or brave and vice versa. Everyone who is not old or strong is both not humble and not generous and vice versa. Someone is either not funny or not wise. Susan is not wise or not patient. Someone is not generous. Susan is both not happy and tall. Alice is humble. Susan is rich or tall. Susan is generous. | Alice is not kind. | neutral | (((~patient(mary)|~rich(mary)))<=>(wise(susan)))&
((?[X]:(wise(X)))<=>(~wise(mary)))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)|~funny(X))<=>(brave(X)|~calm(X))))&
(![X]:((happy(X)&~tall(X))=>~old(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(patient(X)|~humble(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(((~patient(mary)<~>brave(mary)))=>((curious(mary)|rich(mary))))&
(![X]:((~quiet(X)&~happy(X))<=>(~brave(X)<~>strong(X))))&
(![X]:((rich(X)&~old(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((old(X)|~rich(X))<=>(patient(X)|~funny(X))))&
(((calm(john)|~calm(john)))<=>(curious(mary)))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
(?[X]:(~generous(X)))&
((~happy(susan)&tall(susan)))&
(humble(alice))&
((rich(susan)|tall(susan)))&
(generous(susan)) | ~kind(alice) | [] | null | 0 |
If someone is either not calm or not generous then paul is either quiet or not quiet.
If fred is both curious and wise then alice is not generous or not funny and vice versa.
Everyone who is both calm and happy is not patient.
Everyone who is brave is humble and vice versa.
Everyone who is not strong or calm is either brave or generous and vice versa.
If someone is tall then fred is either curious or not old.
Everyone who is both not strong and not wise is not funny and vice versa.
Everyone who is happy is both not quiet and strong.
Everyone who is tall or humble is not creative and vice versa.
Everyone who is not happy is either patient or quiet and vice versa.
Everyone who is both not funny and not curious is both not happy and generous and vice versa.
If someone is not funny then john is kind and vice versa.
If mary is funny or not curious then fred is either not rich or quiet and vice versa.
Everyone who is either not creative or curious is not humble or patient and vice versa.
Everyone who is not curious is either wise or funny and vice versa.
If paul is quiet then someone is either not brave or not generous and vice versa.
Paul is either not funny or rich.
Alice is both humble and not quiet.
Susan is rich or not funny.
Fred is not old or not humble.
Susan is creative or not funny.
Susan is either not tall or kind.
John is generous.
Alice is not tall or strong. | Alice is funny. | entailment | ((?[X]:((~calm(X)<~>~generous(X))))=>((quiet(paul)<~>~quiet(paul))))&
(((curious(fred)&wise(fred)))<=>((~generous(alice)|~funny(alice))))&
(![X]:((calm(X)&happy(X))=>~patient(X)))&
(![X]:(brave(X)<=>humble(X)))&
(![X]:((~strong(X)|calm(X))<=>(brave(X)<~>generous(X))))&
((?[X]:(tall(X)))=>((curious(fred)<~>~old(fred))))&
(![X]:((~strong(X)&~wise(X))<=>~funny(X)))&
(![X]:(happy(X)=>(~quiet(X)&strong(X))))&
(![X]:((tall(X)|humble(X))<=>~creative(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~happy(X)&generous(X))))&
((?[X]:(~funny(X)))<=>(kind(john)))&
(((funny(mary)|~curious(mary)))<=>((~rich(fred)<~>quiet(fred))))&
(![X]:((~creative(X)<~>curious(X))<=>(~humble(X)|patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>funny(X))))&
((quiet(paul))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((~funny(paul)<~>rich(paul)))&
((humble(alice)&~quiet(alice)))&
((rich(susan)|~funny(susan)))&
((~old(fred)|~humble(fred)))&
((creative(susan)|~funny(susan)))&
((~tall(susan)<~>kind(susan)))&
(generous(john))&
((~tall(alice)|strong(alice))) | funny(alice) | [
"p6",
"p7",
"p8",
"p9",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5328211890166586330720625
% SZS output start Proof for 5328211890166586330720625
7. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> ~funny(X0)) [input p6]
8. ! [X0] : (happy(X0) => (strong(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((humble(X0) | tall(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : (~happy(X0) <=> (patient(X0) <~> quiet(X0))) [input p9]
14. ! [X0] : ((~creative(X0) <~> curious(X0)) <=> (patient(X0) | ~humble(X0))) [input p13]
15. ! [X0] : (~curious(X0) <=> (wise(X0) <~> funny(X0))) [input p14]
18. ~quiet(alice) & humble(alice) [input p17]
25. ~funny(alice) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~happy(X0)) [ennf transformation 8]
38. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (wise(X0) | strong(X0)))) [nnf transformation 7]
39. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | wise(X0) | strong(X0))) [flattening 38]
40. ! [X0] : (((humble(X0) | tall(X0)) | creative(X0)) & (~creative(X0) | (~humble(X0) & ~tall(X0)))) [nnf transformation 9]
41. ! [X0] : ((humble(X0) | tall(X0) | creative(X0)) & (~creative(X0) | (~humble(X0) & ~tall(X0)))) [flattening 40]
42. ! [X0] : ((~happy(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | happy(X0))) [nnf transformation 10]
51. ! [X0] : ((((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0))))) [nnf transformation 14]
52. ! [X0] : ((((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0))))) [flattening 51]
53. ! [X0] : ((~curious(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | curious(X0))) [nnf transformation 15]
81. ~strong(X0) | funny(X0) [cnf transformation 39]
82. ~wise(X0) | funny(X0) [cnf transformation 39]
84. ~happy(X0) | strong(X0) [cnf transformation 30]
86. ~creative(X0) | ~humble(X0) [cnf transformation 41]
88. patient(X0) | quiet(X0) | happy(X0) [cnf transformation 42]
109. ~patient(X0) | creative(X0) | ~curious(X0) [cnf transformation 52]
110. funny(X0) | wise(X0) | curious(X0) [cnf transformation 53]
111. ~funny(X0) | ~wise(X0) | curious(X0) [cnf transformation 53]
120. humble(alice) [cnf transformation 18]
121. ~quiet(alice) [cnf transformation 18]
129. ~funny(alice) [cnf transformation 25]
131. 1 <=> funny(alice) [avatar definition]
132. ~funny(alice) <- (~1) [avatar component clause 131]
199. ~wise(X0) | curious(X0) [subsumption resolution 111,82]
200. funny(X0) | curious(X0) [subsumption resolution 110,199]
267. 28 <=> strong(alice) [avatar definition]
269. strong(alice) <- (28) [avatar component clause 267]
271. ~1 [avatar split clause 129,131]
277. curious(alice) <- (~1) [resolution 200,132]
385. ~curious(X0) | creative(X0) | quiet(X0) | happy(X0) [resolution 109,88]
458. creative(alice) | quiet(alice) | happy(alice) <- (~1) [resolution 385,277]
462. creative(alice) | happy(alice) <- (~1) [subsumption resolution 458,121]
464. 46 <=> happy(alice) [avatar definition]
466. happy(alice) <- (46) [avatar component clause 464]
468. 47 <=> creative(alice) [avatar definition]
470. creative(alice) <- (47) [avatar component clause 468]
471. 46 | 47 | 1 [avatar split clause 462,131,468,464]
531. strong(alice) <- (46) [resolution 466,84]
533. 28 | ~46 [avatar split clause 531,464,267]
536. funny(alice) <- (28) [resolution 269,81]
539. $false <- (~1, 28) [subsumption resolution 536,132]
540. 1 | ~28 [avatar contradiction clause 539]
545. ~humble(alice) <- (47) [resolution 470,86]
547. $false <- (47) [subsumption resolution 545,120]
548. ~47 [avatar contradiction clause 547]
549. $false [avatar sat refutation 271,471,533,540,548]
% SZS output end Proof for 5328211890166586330720625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not creative or not old then mary is both creative and not patient and vice versa.
Everyone who is not generous is not quiet and vice versa.
Everyone who is either strong or not old is both not humble and strong.
If someone is not funny or not kind then someone is not creative and vice versa.
Everyone who is not happy or old is either curious or not creative and vice versa.
If someone is not brave then john is both tall and not funny and vice versa.
If john is not calm or strong then paul is both not tall and not humble and vice versa.
If fred is both not quiet and not wise then lucy is either not rich or patient.
If susan is both strong and not curious then paul is not funny or funny.
Everyone who is not curious is rich.
If paul is either not creative or not strong then someone is old or not generous and vice versa.
Everyone who is not generous or creative is either curious or not brave and vice versa.
Everyone who is kind is curious or wise.
If someone is either not creative or not patient then fred is generous or tall and vice versa.
If someone is not quiet or curious then mary is both not curious and generous.
Everyone who is not creative is both old and not patient and vice versa.
Alice is either kind or generous.
Someone is both not creative and not calm.
Susan is not kind.
Someone is not generous or not old.
Alice is not generous or not kind.
Someone is both not strong and not generous.
Mary is not humble or rich.
Alice is both humble and generous. | John is not funny. | entailment | ((?[X]:((~creative(X)<~>~old(X))))<=>((creative(mary)&~patient(mary))))&
(![X]:(~generous(X)<=>~quiet(X)))&
(![X]:((strong(X)<~>~old(X))=>(~humble(X)&strong(X))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)|old(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(~brave(X)))<=>((tall(john)&~funny(john))))&
(((~calm(john)|strong(john)))<=>((~tall(paul)&~humble(paul))))&
(((~quiet(fred)&~wise(fred)))=>((~rich(lucy)<~>patient(lucy))))&
(((strong(susan)&~curious(susan)))=>((~funny(paul)|funny(paul))))&
(![X]:(~curious(X)=>rich(X)))&
(((~creative(paul)<~>~strong(paul)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~generous(X)|creative(X))<=>(curious(X)<~>~brave(X))))&
(![X]:(kind(X)=>(curious(X)|wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(fred)|tall(fred))))&
((?[X]:((~quiet(X)|curious(X))))=>((~curious(mary)&generous(mary))))&
(![X]:(~creative(X)<=>(old(X)&~patient(X))))&
((kind(alice)<~>generous(alice)))&
(?[X]:((~creative(X)&~calm(X))))&
(~kind(susan))&
(?[X]:((~generous(X)|~old(X))))&
((~generous(alice)|~kind(alice)))&
(?[X]:((~strong(X)&~generous(X))))&
((~humble(mary)|rich(mary)))&
((humble(alice)&generous(alice))) | ~funny(john) | [
"p0",
"p5",
"p11",
"p14",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1625760758443184168648310
% SZS output start Proof for 1625760758443184168648310
1. ? [X0] : (~creative(X0) <~> ~old(X0)) <=> (~patient(mary) & creative(mary)) [input p0]
6. ? [X0] : ~brave(X0) <=> (~funny(john) & tall(john)) [input p5]
12. ! [X0] : ((creative(X0) | ~generous(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p11]
15. ? [X0] : (curious(X0) | ~quiet(X0)) => (generous(mary) & ~curious(mary)) [input p14]
16. ! [X0] : (~creative(X0) <=> (~patient(X0) & old(X0))) [input p15]
18. ? [X0] : (~calm(X0) & ~creative(X0)) [input p17]
22. ? [X0] : (~generous(X0) & ~strong(X0)) [input p21]
25. funny(john) [input hypothesis]
34. (generous(mary) & ~curious(mary)) | ! [X0] : (~curious(X0) & quiet(X0)) [ennf transformation 15]
35. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (patient(mary) | ~creative(mary))) & ((~patient(mary) & creative(mary)) | ! [X0] : ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 1]
36. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X0] : ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [flattening 35]
37. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [rectify 36]
38. ? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) => ((old(sK0) | creative(sK0)) & (~old(sK0) | ~creative(sK0))) [choice axiom]
39. (((old(sK0) | creative(sK0)) & (~old(sK0) | ~creative(sK0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [skolemisation 37,38]
49. (? [X0] : ~brave(X0) | (funny(john) | ~tall(john))) & ((~funny(john) & tall(john)) | ! [X0] : brave(X0)) [nnf transformation 6]
50. (? [X0] : ~brave(X0) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X0] : brave(X0)) [flattening 49]
51. (? [X0] : ~brave(X0) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X1] : brave(X1)) [rectify 50]
52. ? [X0] : ~brave(X0) => ~brave(sK3) [choice axiom]
53. (~brave(sK3) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X1] : brave(X1)) [skolemisation 51,52]
60. ! [X0] : (((creative(X0) | ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~creative(X0) & generous(X0)))) [nnf transformation 12]
61. ! [X0] : ((creative(X0) | ~generous(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~creative(X0) & generous(X0)))) [flattening 60]
67. ! [X0] : ((~creative(X0) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | creative(X0))) [nnf transformation 16]
68. ! [X0] : ((~creative(X0) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | creative(X0))) [flattening 67]
70. ? [X0] : (~calm(X0) & ~creative(X0)) => (~calm(sK6) & ~creative(sK6)) [choice axiom]
71. ~calm(sK6) & ~creative(sK6) [skolemisation 18,70]
74. ? [X0] : (~generous(X0) & ~strong(X0)) => (~generous(sK8) & ~strong(sK8)) [choice axiom]
75. ~generous(sK8) & ~strong(sK8) [skolemisation 22,74]
76. creative(mary) | ~old(X1) | creative(X1) [cnf transformation 39]
98. ~funny(john) | brave(X1) [cnf transformation 53]
112. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 61]
113. ~brave(X0) | curious(X0) | ~creative(X0) [cnf transformation 61]
125. ~curious(mary) | ~curious(X0) [cnf transformation 34]
128. old(X0) | creative(X0) [cnf transformation 68]
133. ~creative(sK6) [cnf transformation 71]
139. ~generous(sK8) [cnf transformation 75]
142. funny(john) [cnf transformation 25]
145. 1 <=> creative(mary) [avatar definition]
146. creative(mary) <- (1) [avatar component clause 145]
167. 6 <=> ! [X1] : (~old(X1) | creative(X1)) [avatar definition]
168. ~old(X1) | creative(X1) <- (6) [avatar component clause 167]
171. 6 | 1 [avatar split clause 76,145,167]
173. 7 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (7) [avatar component clause 173]
201. 14 <=> funny(john) [avatar definition]
210. 16 <=> ! [X1] : brave(X1) [avatar definition]
211. brave(X1) <- (16) [avatar component clause 210]
212. 16 | ~14 [avatar split clause 98,201,210]
236. 21 <=> ! [X0] : generous(X0) [avatar definition]
237. generous(X0) <- (21) [avatar component clause 236]
292. 33 <=> ! [X0] : ~curious(X0) [avatar definition]
293. ~curious(X0) <- (33) [avatar component clause 292]
304. 36 <=> curious(mary) [avatar definition]
307. 33 | ~36 [avatar split clause 125,304,292]
331. 14 [avatar split clause 142,201]
332. creative(X1) <- (6) [subsumption resolution 168,128]
333. 7 | ~6 [avatar split clause 332,167,173]
335. $false <- (7) [resolution 174,133]
338. ~7 [avatar contradiction clause 335]
418. curious(X0) | generous(X0) <- (16) [resolution 112,211]
419. ~creative(X0) | curious(X0) <- (16) [resolution 113,211]
446. curious(mary) <- (1, 16) [resolution 419,146]
453. 36 | ~1 | ~16 [avatar split clause 446,210,145,304]
459. generous(X0) <- (16, 33) [resolution 293,418]
460. 21 | ~16 | ~33 [avatar split clause 459,292,210,236]
465. $false <- (21) [resolution 237,139]
466. ~21 [avatar contradiction clause 465]
470. $false [avatar sat refutation 171,212,307,331,333,338,453,460,466]
% SZS output end Proof for 1625760758443184168648310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not old is either brave or not happy and vice versa.
Everyone who is either quiet or tall is not happy or not humble and vice versa.
Everyone who is not generous or not kind is both generous and creative and vice versa.
Everyone who is both old and not strong is both humble and old and vice versa.
Everyone who is not kind is either not rich or humble.
Everyone who is not patient is funny.
Everyone who is funny is either old or not happy and vice versa.
If john is funny then fred is either wise or creative.
Everyone who is either quiet or happy is both not old and not tall and vice versa.
If lucy is either patient or not calm then alice is both wise and not tall and vice versa.
If paul is both not calm and tall then someone is both curious and kind.
If someone is both not curious and kind then susan is both not wise and not curious.
Everyone who is both rich and not calm is either not brave or not rich and vice versa.
Everyone who is both not happy and not rich is both generous and not old.
If someone is not calm then someone is both not wise and not quiet and vice versa.
Everyone who is not happy or not brave is not quiet.
Lucy is either quiet or not generous.
Someone is both curious and not old.
Paul is calm.
Someone is not kind or tall.
Mary is not curious or not old.
Susan is not kind or not old.
Someone is either rich or not brave.
Someone is happy or not creative. | Lucy is not humble. | contradiction | (![X]:((~happy(X)<~>~old(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)|~humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>(generous(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(humble(X)&old(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>humble(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(funny(X)<=>(old(X)<~>~happy(X))))&
((funny(john))=>((wise(fred)<~>creative(fred))))&
(![X]:((quiet(X)<~>happy(X))<=>(~old(X)&~tall(X))))&
(((patient(lucy)<~>~calm(lucy)))<=>((wise(alice)&~tall(alice))))&
(((~calm(paul)&tall(paul)))=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:((~curious(X)&kind(X))))=>((~wise(susan)&~curious(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~happy(X)&~rich(X))=>(generous(X)&~old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((quiet(lucy)<~>~generous(lucy)))&
(?[X]:((curious(X)&~old(X))))&
(calm(paul))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)|~old(mary)))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:((happy(X)|~creative(X)))) | ~humble(lucy) | [
"p0",
"p1",
"p2",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 308387659545868960970593
% SZS output start Proof for 308387659545868960970593
1. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~humble(X0) | ~happy(X0))) [input p1]
3. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (creative(X0) & generous(X0))) [input p2]
9. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> (~tall(X0) & ~old(X0))) [input p8]
16. ! [X0] : ((~brave(X0) | ~happy(X0)) => ~quiet(X0)) [input p15]
17. quiet(lucy) <~> ~generous(lucy) [input p16]
25. ~humble(lucy) [input hypothesis]
35. ! [X0] : (~quiet(X0) | (brave(X0) & happy(X0))) [ennf transformation 16]
36. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (humble(X0) & happy(X0))) & ((~humble(X0) | ~happy(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (humble(X0) & happy(X0))) & (~humble(X0) | ~happy(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [flattening 37]
39. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~creative(X0) | ~generous(X0))) & ((creative(X0) & generous(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 3]
40. ! [X0] : ((~kind(X0) | ~generous(X0) | ~creative(X0) | ~generous(X0)) & ((creative(X0) & generous(X0)) | (kind(X0) & generous(X0)))) [flattening 39]
46. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [flattening 46]
59. (generous(lucy) | ~quiet(lucy)) & (~generous(lucy) | quiet(lucy)) [nnf transformation 17]
71. happy(X0) | ~brave(X0) | ~old(X0) | happy(X0) [cnf transformation 36]
73. ~old(X0) | ~happy(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 36]
82. ~tall(X0) | ~quiet(X0) | humble(X0) [cnf transformation 38]
83. generous(X0) | generous(X0) [cnf transformation 40]
106. ~quiet(X0) | ~happy(X0) | tall(X0) | old(X0) [cnf transformation 47]
128. ~quiet(X0) | happy(X0) [cnf transformation 35]
129. ~quiet(X0) | brave(X0) [cnf transformation 35]
130. ~generous(lucy) | quiet(lucy) [cnf transformation 59]
141. ~humble(lucy) [cnf transformation 25]
144. generous(X0) [duplicate literal removal 83]
147. happy(X0) | ~brave(X0) | ~old(X0) [duplicate literal removal 71]
148. ~brave(X0) | ~happy(X0) | ~old(X0) [duplicate literal removal 73]
150. ~brave(X0) | ~old(X0) [subsumption resolution 147,148]
241. quiet(lucy) [subsumption resolution 130,144]
292. happy(lucy) [resolution 128,241]
293. brave(lucy) [resolution 129,241]
295. ~old(lucy) [resolution 150,293]
482. ~happy(lucy) | tall(lucy) | old(lucy) [resolution 106,241]
483. tall(lucy) | old(lucy) [subsumption resolution 482,292]
484. tall(lucy) [subsumption resolution 483,295]
486. ~quiet(lucy) | humble(lucy) [resolution 484,82]
488. humble(lucy) [subsumption resolution 486,241]
489. $false [subsumption resolution 488,141]
% SZS output end Proof for 308387659545868960970593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not brave or not happy and vice versa.
If fred is both not creative and wise then someone is either not wise or not old.
Everyone who is calm or happy is either patient or not patient.
If someone is both patient and generous then someone is both brave and not generous.
If someone is either not tall or curious then alice is either not curious or old and vice versa.
Everyone who is both not wise and not humble is creative or not kind and vice versa.
Everyone who is curious is not generous or not curious.
Everyone who is not rich or not brave is both funny and not happy.
If someone is both wise and quiet then fred is both not funny and not humble and vice versa.
If alice is tall or not happy then alice is calm or patient.
Everyone who is not happy or not strong is both not wise and tall and vice versa.
Everyone who is either strong or not kind is both curious and not old.
If susan is either quiet or creative then someone is either not old or curious and vice versa.
If paul is not quiet then john is not brave.
If someone is wise or quiet then someone is not generous and vice versa.
Everyone who is not creative is either not wise or not brave and vice versa.
Lucy is brave or rich.
Someone is either old or not quiet.
Paul is not quiet or not funny.
John is old or strong.
Fred is rich.
Susan is not strong or not brave.
Alice is either quiet or generous.
Alice is either not creative or curious. | Alice is curious. | contradiction | (![X]:(~brave(X)<=>(~brave(X)<~>~happy(X))))&
(((~creative(fred)&wise(fred)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((calm(X)|happy(X))=>(patient(X)<~>~patient(X))))&
((?[X]:((patient(X)&generous(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~tall(X)<~>curious(X))))<=>((~curious(alice)<~>old(alice))))&
(![X]:((~wise(X)&~humble(X))<=>(creative(X)|~kind(X))))&
(![X]:(curious(X)=>(~generous(X)|~curious(X))))&
(![X]:((~rich(X)|~brave(X))=>(funny(X)&~happy(X))))&
((?[X]:((wise(X)&quiet(X))))<=>((~funny(fred)&~humble(fred))))&
(((tall(alice)|~happy(alice)))=>((calm(alice)|patient(alice))))&
(![X]:((~happy(X)|~strong(X))<=>(~wise(X)&tall(X))))&
(![X]:((strong(X)<~>~kind(X))=>(curious(X)&~old(X))))&
(((quiet(susan)<~>creative(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
((~quiet(paul))=>(~brave(john)))&
((?[X]:((wise(X)|quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(~wise(X)<~>~brave(X))))&
((brave(lucy)|rich(lucy)))&
(?[X]:((old(X)<~>~quiet(X))))&
((~quiet(paul)|~funny(paul)))&
((old(john)|strong(john)))&
(rich(fred))&
((~strong(susan)|~brave(susan)))&
((quiet(alice)<~>generous(alice)))&
((~creative(alice)<~>curious(alice))) | curious(alice) | [
"p0",
"p5",
"p7",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8418661287689156048221680
% SZS output start Proof for 8418661287689156048221680
1. ! [X0] : (~brave(X0) <=> (~brave(X0) <~> ~happy(X0))) [input p0]
6. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (~kind(X0) | creative(X0))) [input p5]
8. ! [X0] : ((~brave(X0) | ~rich(X0)) => (~happy(X0) & funny(X0))) [input p7]
16. ! [X0] : (~creative(X0) <=> (~wise(X0) <~> ~brave(X0))) [input p15]
24. ~creative(alice) <~> curious(alice) [input p23]
25. curious(alice) [input hypothesis]
29. ! [X0] : (~brave(X0) => (~happy(X0) & funny(X0))) [pure predicate removal 8]
37. ! [X0] : ((~happy(X0) & funny(X0)) | brave(X0)) [ennf transformation 29]
42. ! [X0] : ((~brave(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0)))) & (((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | brave(X0))) [nnf transformation 1]
54. ! [X0] : (((~humble(X0) & ~wise(X0)) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 6]
55. ! [X0] : (((~humble(X0) & ~wise(X0)) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | humble(X0) | wise(X0))) [flattening 54]
73. ! [X0] : ((~creative(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | creative(X0))) [nnf transformation 16]
78. (~curious(alice) | creative(alice)) & (curious(alice) | ~creative(alice)) [nnf transformation 24]
80. happy(X0) | brave(X0) | brave(X0) [cnf transformation 42]
82. ~brave(X0) | ~brave(X0) | happy(X0) [cnf transformation 42]
100. ~wise(X0) | ~creative(X0) [cnf transformation 55]
106. ~happy(X0) | brave(X0) [cnf transformation 37]
136. ~creative(X0) | ~brave(X0) | wise(X0) [cnf transformation 73]
146. ~curious(alice) | creative(alice) [cnf transformation 78]
147. curious(alice) [cnf transformation 25]
149. happy(X0) | brave(X0) [duplicate literal removal 80]
150. ~brave(X0) | happy(X0) [duplicate literal removal 82]
151. happy(X0) [subsumption resolution 149,150]
188. 9 <=> curious(alice) [avatar definition]
213. brave(X0) [subsumption resolution 106,151]
306. ~creative(X0) | wise(X0) [subsumption resolution 136,213]
307. ~creative(X0) [subsumption resolution 306,100]
342. ~curious(alice) [subsumption resolution 146,307]
343. ~9 [avatar split clause 342,188]
344. 9 [avatar split clause 147,188]
345. $false [avatar sat refutation 343,344]
% SZS output end Proof for 8418661287689156048221680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or generous is both brave and generous and vice versa. Everyone who is not rich is both not strong and not humble and vice versa. If fred is both funny and brave then someone is either wise or generous. Everyone who is either not calm or not generous is both calm and not generous and vice versa. Everyone who is funny is both not kind and calm. If fred is not strong or not generous then someone is both tall and not calm. If fred is patient then john is both calm and not old and vice versa. Everyone who is either not funny or not quiet is not strong and vice versa. Everyone who is either kind or old is either quiet or patient and vice versa. Everyone who is both not kind and funny is either calm or not curious. If someone is tall then john is wise and vice versa. If someone is not old or rich then someone is strong. Everyone who is either not wise or quiet is either old or strong. Everyone who is kind or not quiet is not rich. If someone is both kind and not patient then someone is not happy or not patient. Everyone who is creative or not humble is generous or not wise and vice versa. Someone is both not generous and wise. Alice is not rich. Fred is either not wise or not patient. Mary is both calm and not happy. Susan is both old and brave. Someone is patient. Someone is not kind or old. Alice is either not kind or old. | Fred is not curious. | contradiction | (![X]:((tall(X)<~>generous(X))<=>(brave(X)&generous(X))))&
(![X]:(~rich(X)<=>(~strong(X)&~humble(X))))&
(((funny(fred)&brave(fred)))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((~calm(X)<~>~generous(X))<=>(calm(X)&~generous(X))))&
(![X]:(funny(X)=>(~kind(X)&calm(X))))&
(((~strong(fred)|~generous(fred)))=>(?[X]:((tall(X)&~calm(X)))))&
((patient(fred))<=>((calm(john)&~old(john))))&
(![X]:((~funny(X)<~>~quiet(X))<=>~strong(X)))&
(![X]:((kind(X)<~>old(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~kind(X)&funny(X))=>(calm(X)<~>~curious(X))))&
((?[X]:(tall(X)))<=>(wise(john)))&
((?[X]:((~old(X)|rich(X))))=>(?[X]:(strong(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(old(X)<~>strong(X))))&
(![X]:((kind(X)|~quiet(X))=>~rich(X)))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((creative(X)|~humble(X))<=>(generous(X)|~wise(X))))&
(?[X]:((~generous(X)&wise(X))))&
(~rich(alice))&
((~wise(fred)<~>~patient(fred)))&
((calm(mary)&~happy(mary)))&
((old(susan)&brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)|old(X))))&
((~kind(alice)<~>old(alice))) | ~curious(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8319620706796015439792896
% SZS output start Proof for 8319620706796015439792896
1. ! [X0] : ((tall(X0) <~> generous(X0)) <=> (generous(X0) & brave(X0))) [input p0]
2. ! [X0] : (~rich(X0) <=> (~humble(X0) & ~strong(X0))) [input p1]
4. ! [X0] : ((~calm(X0) <~> ~generous(X0)) <=> (~generous(X0) & calm(X0))) [input p3]
5. ! [X0] : (funny(X0) => (calm(X0) & ~kind(X0))) [input p4]
6. (~generous(fred) | ~strong(fred)) => ? [X0] : (~calm(X0) & tall(X0)) [input p5]
8. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) <=> ~strong(X0)) [input p7]
10. ! [X0] : ((funny(X0) & ~kind(X0)) => (calm(X0) <~> ~curious(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) | kind(X0)) => ~rich(X0)) [input p13]
25. ~curious(fred) [input hypothesis]
28. ! [X0] : (~rich(X0) => (~humble(X0) & ~strong(X0))) [unused predicate definition removal 2]
31. ! [X0] : ((~humble(X0) & ~strong(X0)) | rich(X0)) [ennf transformation 28]
34. ! [X0] : ((calm(X0) & ~kind(X0)) | ~funny(X0)) [ennf transformation 5]
35. ? [X0] : (~calm(X0) & tall(X0)) | (generous(fred) & strong(fred)) [ennf transformation 6]
36. ! [X0] : ((calm(X0) <~> ~curious(X0)) | (~funny(X0) | kind(X0))) [ennf transformation 10]
37. ! [X0] : ((calm(X0) <~> ~curious(X0)) | ~funny(X0) | kind(X0)) [flattening 36]
40. ! [X0] : (~rich(X0) | (quiet(X0) & ~kind(X0))) [ennf transformation 14]
41. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 1]
42. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [flattening 41]
46. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (generous(X0) | ~calm(X0))) & ((~generous(X0) & calm(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [nnf transformation 4]
47. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | generous(X0) | ~calm(X0)) & ((~generous(X0) & calm(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [flattening 46]
48. ? [X0] : (~calm(X0) & tall(X0)) => (~calm(sK1) & tall(sK1)) [choice axiom]
49. (~calm(sK1) & tall(sK1)) | (generous(fred) & strong(fred)) [skolemisation 35,48]
52. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | strong(X0)) & (~strong(X0) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [nnf transformation 8]
54. ! [X0] : (((curious(X0) | ~calm(X0)) & (~curious(X0) | calm(X0))) | ~funny(X0) | kind(X0)) [nnf transformation 37]
75. generous(X0) | generous(X0) | ~tall(X0) [cnf transformation 42]
79. ~strong(X0) | rich(X0) [cnf transformation 31]
85. ~generous(X0) | ~generous(X0) | calm(X0) [cnf transformation 47]
89. ~kind(X0) | ~funny(X0) [cnf transformation 34]
90. ~funny(X0) | calm(X0) [cnf transformation 34]
91. tall(sK1) | strong(fred) [cnf transformation 49]
93. ~calm(sK1) | strong(fred) [cnf transformation 49]
98. ~quiet(X0) | ~strong(X0) | funny(X0) [cnf transformation 52]
111. curious(X0) | ~calm(X0) | ~funny(X0) | kind(X0) [cnf transformation 54]
121. ~rich(X0) | quiet(X0) [cnf transformation 40]
138. ~curious(fred) [cnf transformation 25]
140. ~generous(X0) | calm(X0) [duplicate literal removal 85]
143. ~tall(X0) | generous(X0) [duplicate literal removal 75]
146. 1 <=> funny(fred) [avatar definition]
147. funny(fred) <- (1) [avatar component clause 146]
148. ~funny(fred) <- (~1) [avatar component clause 146]
168. 6 <=> calm(sK1) [avatar definition]
170. ~calm(sK1) <- (~6) [avatar component clause 168]
173. 7 <=> strong(fred) [avatar definition]
175. strong(fred) <- (7) [avatar component clause 173]
176. 7 | ~6 [avatar split clause 93,168,173]
178. 8 <=> tall(sK1) [avatar definition]
180. tall(sK1) <- (8) [avatar component clause 178]
182. 7 | 8 [avatar split clause 91,178,173]
198. curious(X0) | ~funny(X0) | kind(X0) [subsumption resolution 111,90]
199. ~funny(X0) | curious(X0) [subsumption resolution 198,89]
250. rich(fred) <- (7) [resolution 79,175]
252. quiet(fred) <- (7) [resolution 121,250]
264. generous(sK1) <- (8) [resolution 180,143]
265. ~strong(fred) | funny(fred) <- (7) [resolution 98,252]
266. funny(fred) <- (7) [subsumption resolution 265,175]
267. $false <- (~1, 7) [subsumption resolution 266,148]
268. 1 | ~7 [avatar contradiction clause 267]
270. calm(sK1) <- (8) [resolution 264,140]
271. $false <- (~6, 8) [subsumption resolution 270,170]
272. 6 | ~8 [avatar contradiction clause 271]
274. curious(fred) <- (1) [resolution 147,199]
277. $false <- (1) [subsumption resolution 274,138]
278. ~1 [avatar contradiction clause 277]
279. $false [avatar sat refutation 176,182,268,272,278]
% SZS output end Proof for 8319620706796015439792896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not generous or tall then susan is both not tall and not patient and vice versa.
If susan is not happy or not curious then someone is kind or not curious.
Everyone who is both not wise and not tall is strong.
Everyone who is either calm or not calm is both not wise and rich.
Everyone who is not wise or curious is happy and vice versa.
Everyone who is not old or not funny is not generous and vice versa.
Everyone who is curious or wise is humble or not funny.
Everyone who is brave or wise is not rich and vice versa.
Everyone who is either not old or not curious is strong or not strong and vice versa.
Everyone who is both funny and humble is creative or funny and vice versa.
Everyone who is strong or not humble is either rich or not strong.
Everyone who is both calm and quiet is not brave and vice versa.
If alice is both happy and strong then fred is both not quiet and quiet.
Everyone who is not kind or not creative is not rich.
Everyone who is both curious and not generous is either strong or not quiet and vice versa.
Paul is curious.
Paul is either rich or not quiet.
Someone is kind.
Alice is either calm or not tall.
Mary is creative.
Someone is not rich or generous. | Fred is not quiet. | contradiction | (((~generous(fred)<~>tall(fred)))<=>((~tall(susan)&~patient(susan))))&
(((~happy(susan)|~curious(susan)))=>(?[X]:((kind(X)|~curious(X)))))&
(![X]:((~wise(X)&~tall(X))=>strong(X)))&
(![X]:((calm(X)<~>~calm(X))=>(~wise(X)&rich(X))))&
(![X]:((~wise(X)|curious(X))<=>happy(X)))&
(![X]:((~old(X)|~funny(X))<=>~generous(X)))&
(![X]:((curious(X)|wise(X))=>(humble(X)|~funny(X))))&
(![X]:((brave(X)|wise(X))<=>~rich(X)))&
(![X]:((~old(X)<~>~curious(X))<=>(strong(X)|~strong(X))))&
(![X]:((funny(X)&humble(X))<=>(creative(X)|funny(X))))&
(![X]:((strong(X)|~humble(X))=>(rich(X)<~>~strong(X))))&
(![X]:((calm(X)&quiet(X))<=>~brave(X)))&
(((happy(alice)&strong(alice)))=>((~quiet(fred)&quiet(fred))))&
(![X]:((~kind(X)|~creative(X))=>~rich(X)))&
(![X]:((curious(X)&~generous(X))<=>(strong(X)<~>~quiet(X))))&
(curious(paul))&
((rich(paul)<~>~quiet(paul)))&
(?[X]:(kind(X)))&
((calm(alice)<~>~tall(alice)))&
(creative(mary))&
(?[X]:((~rich(X)|generous(X)))) | ~quiet(fred) | [
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6294090837991780492286261
% SZS output start Proof for 6294090837991780492286261
4. ! [X0] : ((calm(X0) <~> ~calm(X0)) => (rich(X0) & ~wise(X0))) [input p3]
8. ! [X0] : ((wise(X0) | brave(X0)) <=> ~rich(X0)) [input p7]
12. ! [X0] : ((quiet(X0) & calm(X0)) <=> ~brave(X0)) [input p11]
22. ~quiet(fred) [input hypothesis]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | (calm(X0) <=> ~calm(X0))) [ennf transformation 4]
39. ! [X0] : ((rich(X0) & ~wise(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) [nnf transformation 29]
42. ! [X0] : (((wise(X0) | brave(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~brave(X0)))) [nnf transformation 8]
43. ! [X0] : ((wise(X0) | brave(X0) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~brave(X0)))) [flattening 42]
49. ! [X0] : (((quiet(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | (~quiet(X0) | ~calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((quiet(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | ~quiet(X0) | ~calm(X0))) [flattening 49]
66. rich(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 39]
67. rich(X0) | calm(X0) | calm(X0) [cnf transformation 39]
75. ~rich(X0) | ~brave(X0) [cnf transformation 43]
95. quiet(X0) | brave(X0) [cnf transformation 50]
112. ~quiet(fred) [cnf transformation 22]
116. rich(X0) | ~calm(X0) [duplicate literal removal 66]
117. rich(X0) | calm(X0) [duplicate literal removal 67]
140. rich(X0) [subsumption resolution 116,117]
143. ~brave(X0) [subsumption resolution 75,140]
147. quiet(X0) [subsumption resolution 95,143]
157. $false [subsumption resolution 112,147]
% SZS output end Proof for 6294090837991780492286261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous then someone is not rich and vice versa. If alice is both not rich and not happy then someone is not patient or not curious and vice versa. If mary is both not tall and quiet then someone is not creative or not happy. If mary is both not funny and not generous then someone is funny or patient and vice versa. Everyone who is both generous and old is both not happy and not curious and vice versa. Everyone who is not generous or funny is humble or patient. Everyone who is either humble or brave is both wise and generous. If someone is both not strong and creative then susan is both strong and not creative and vice versa. Everyone who is either not quiet or happy is both old and wise. Everyone who is both not happy and quiet is both brave and rich and vice versa. If alice is both rich and kind then fred is either not wise or quiet and vice versa. If someone is both kind and not kind then john is not calm or patient. Everyone who is brave is either rich or curious. If susan is either wise or not strong then john is either not quiet or kind and vice versa. Everyone who is both not wise and not brave is not humble and vice versa. Everyone who is either not wise or curious is both not strong and strong and vice versa. Someone is kind. Someone is either not generous or not happy. Mary is not patient or not happy. Someone is both happy and not kind. Someone is both strong and not rich. Someone is funny or tall. Alice is either not rich or kind. Someone is both not brave and not wise. | Alice is not happy. | entailment | ((~generous(susan))<=>(?[X]:(~rich(X))))&
(((~rich(alice)&~happy(alice)))<=>(?[X]:((~patient(X)|~curious(X)))))&
(((~tall(mary)&quiet(mary)))=>(?[X]:((~creative(X)|~happy(X)))))&
(((~funny(mary)&~generous(mary)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((generous(X)&old(X))<=>(~happy(X)&~curious(X))))&
(![X]:((~generous(X)|funny(X))=>(humble(X)|patient(X))))&
(![X]:((humble(X)<~>brave(X))=>(wise(X)&generous(X))))&
((?[X]:((~strong(X)&creative(X))))<=>((strong(susan)&~creative(susan))))&
(![X]:((~quiet(X)<~>happy(X))=>(old(X)&wise(X))))&
(![X]:((~happy(X)&quiet(X))<=>(brave(X)&rich(X))))&
(((rich(alice)&kind(alice)))<=>((~wise(fred)<~>quiet(fred))))&
((?[X]:((kind(X)&~kind(X))))=>((~calm(john)|patient(john))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(((wise(susan)<~>~strong(susan)))<=>((~quiet(john)<~>kind(john))))&
(![X]:((~wise(X)&~brave(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>curious(X))<=>(~strong(X)&strong(X))))&
(?[X]:(kind(X)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((~patient(mary)|~happy(mary)))&
(?[X]:((happy(X)&~kind(X))))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:((funny(X)|tall(X))))&
((~rich(alice)<~>kind(alice)))&
(?[X]:((~brave(X)&~wise(X)))) | ~happy(alice) | [
"p1",
"p8",
"p9",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3894067402775415106180036
% SZS output start Proof for 3894067402775415106180036
2. (~happy(alice) & ~rich(alice)) <=> ? [X0] : (~curious(X0) | ~patient(X0)) [input p1]
9. ! [X0] : ((~quiet(X0) <~> happy(X0)) => (wise(X0) & old(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (rich(X0) & brave(X0))) [input p9]
13. ! [X0] : (brave(X0) => (rich(X0) <~> curious(X0))) [input p12]
16. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (strong(X0) & ~strong(X0))) [input p15]
19. ~happy(mary) | ~patient(mary) [input p18]
25. happy(alice) [input hypothesis]
32. ! [X0] : ((wise(X0) & old(X0)) | (~quiet(X0) <=> happy(X0))) [ennf transformation 9]
33. ! [X0] : ((rich(X0) <~> curious(X0)) | ~brave(X0)) [ennf transformation 13]
38. ((~happy(alice) & ~rich(alice)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | (happy(alice) | rich(alice))) [nnf transformation 2]
39. ((~happy(alice) & ~rich(alice)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | happy(alice) | rich(alice)) [flattening 38]
40. ((~happy(alice) & ~rich(alice)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X1] : (~curious(X1) | ~patient(X1)) | happy(alice) | rich(alice)) [rectify 39]
41. ? [X1] : (~curious(X1) | ~patient(X1)) => (~curious(sK1) | ~patient(sK1)) [choice axiom]
42. ((~happy(alice) & ~rich(alice)) | ! [X0] : (curious(X0) & patient(X0))) & ((~curious(sK1) | ~patient(sK1)) | happy(alice) | rich(alice)) [skolemisation 40,41]
56. ! [X0] : ((wise(X0) & old(X0)) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) [nnf transformation 32]
57. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
58. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | ~quiet(X0) | happy(X0))) [flattening 57]
61. ! [X0] : (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ~brave(X0)) [nnf transformation 33]
65. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 16]
66. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 65]
84. ~happy(alice) | patient(X0) [cnf transformation 42]
85. ~happy(alice) | curious(X0) [cnf transformation 42]
107. wise(X0) | happy(X0) | quiet(X0) [cnf transformation 56]
109. ~quiet(X0) | brave(X0) | happy(X0) [cnf transformation 58]
110. ~quiet(X0) | rich(X0) | happy(X0) [cnf transformation 58]
120. ~brave(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 61]
133. ~strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 66]
135. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 66]
141. ~happy(mary) | ~patient(mary) [cnf transformation 19]
150. happy(alice) [cnf transformation 25]
165. 4 <=> ! [X0] : curious(X0) [avatar definition]
166. curious(X0) <- (4) [avatar component clause 165]
168. 5 <=> happy(alice) [avatar definition]
171. 4 | ~5 [avatar split clause 85,168,165]
173. 6 <=> ! [X0] : patient(X0) [avatar definition]
174. patient(X0) <- (6) [avatar component clause 173]
175. 6 | ~5 [avatar split clause 84,168,173]
279. ~wise(X0) | ~curious(X0) [subsumption resolution 133,135]
292. 29 <=> patient(mary) [avatar definition]
294. ~patient(mary) <- (~29) [avatar component clause 292]
296. 30 <=> happy(mary) [avatar definition]
298. ~happy(mary) <- (~30) [avatar component clause 296]
299. ~29 | ~30 [avatar split clause 141,296,292]
302. 5 [avatar split clause 150,168]
307. $false <- (6, ~29) [resolution 294,174]
308. ~6 | 29 [avatar contradiction clause 307]
333. happy(X0) | quiet(X0) | ~curious(X0) [resolution 107,279]
338. quiet(X0) | happy(X0) <- (4) [subsumption resolution 333,166]
344. brave(X0) | happy(X0) | happy(X0) <- (4) [resolution 109,338]
345. brave(X0) | happy(X0) <- (4) [duplicate literal removal 344]
373. rich(X0) | happy(X0) | happy(X0) <- (4) [resolution 110,338]
374. happy(X0) | rich(X0) <- (4) [duplicate literal removal 373]
385. ~rich(X0) | ~curious(X0) | happy(X0) <- (4) [resolution 120,345]
386. ~rich(X0) | happy(X0) <- (4) [subsumption resolution 385,166]
387. happy(X0) <- (4) [subsumption resolution 386,374]
390. $false <- (4, ~30) [resolution 387,298]
391. ~4 | 30 [avatar contradiction clause 390]
393. $false [avatar sat refutation 171,175,299,302,308,391]
% SZS output end Proof for 3894067402775415106180036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or kind is not old or strong. Everyone who is both not humble and not creative is not patient or old. If susan is both not old and not tall then someone is both not happy and old. Everyone who is patient or rich is not patient and vice versa. If mary is not generous or patient then someone is either quiet or funny. Everyone who is not generous or strong is rich or not old. If alice is either not funny or happy then someone is either brave or not wise and vice versa. If someone is not rich then alice is not brave and vice versa. Everyone who is either not creative or quiet is humble or not patient. Everyone who is not old is both not brave and old and vice versa. Everyone who is either patient or tall is both curious and not rich and vice versa. Everyone who is both calm and patient is either not calm or patient. Everyone who is either not happy or kind is calm. Everyone who is wise or generous is not strong or curious and vice versa. Everyone who is either not old or old is not strong. Someone is not funny or strong. Someone is both creative and not calm. John is not tall or brave. Someone is both not creative and not generous. Susan is not happy. Alice is both not creative and kind. | Susan is quiet. | neutral | (![X]:((~tall(X)<~>kind(X))=>(~old(X)|strong(X))))&
(![X]:((~humble(X)&~creative(X))=>(~patient(X)|old(X))))&
(((~old(susan)&~tall(susan)))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((patient(X)|rich(X))<=>~patient(X)))&
(((~generous(mary)|patient(mary)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~generous(X)|strong(X))=>(rich(X)|~old(X))))&
(((~funny(alice)<~>happy(alice)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:(~old(X)<=>(~brave(X)&old(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
(![X]:((~happy(X)<~>kind(X))=>calm(X)))&
(![X]:((wise(X)|generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((~old(X)<~>old(X))=>~strong(X)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~tall(john)|brave(john)))&
(?[X]:((~creative(X)&~generous(X))))&
(~happy(susan))&
((~creative(alice)&kind(alice))) | quiet(susan) | [] | null | 0 |
If alice is either not brave or patient then someone is either kind or not creative and vice versa.
If lucy is humble or not patient then paul is either old or happy.
Everyone who is both quiet and not kind is either not kind or not humble and vice versa.
Everyone who is not tall is strong and vice versa.
Everyone who is old or not kind is brave and vice versa.
Everyone who is both not brave and not calm is curious.
If someone is creative then susan is either patient or calm.
If someone is humble then someone is both not creative and not brave and vice versa.
Everyone who is not funny or not strong is wise or calm.
If someone is not kind or generous then someone is not rich or not calm.
If alice is either not funny or not wise then someone is either not humble or creative.
Everyone who is both kind and happy is patient and vice versa.
Everyone who is both tall and strong is curious or not generous and vice versa.
Everyone who is creative or not happy is both not humble and not happy.
If someone is not wise then susan is both strong and not brave.
If lucy is both old and brave then lucy is both not kind and humble.
Mary is not happy.
Susan is either strong or creative.
Alice is not kind.
Someone is humble.
Lucy is both not rich and not curious.
Paul is either tall or not patient.
Someone is both wise and old. | Susan is patient. | neutral | (((~brave(alice)<~>patient(alice)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
(((humble(lucy)|~patient(lucy)))=>((old(paul)<~>happy(paul))))&
(![X]:((quiet(X)&~kind(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:(~tall(X)<=>strong(X)))&
(![X]:((old(X)|~kind(X))<=>brave(X)))&
(![X]:((~brave(X)&~calm(X))=>curious(X)))&
((?[X]:(creative(X)))=>((patient(susan)<~>calm(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~funny(X)|~strong(X))=>(wise(X)|calm(X))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((~rich(X)|~calm(X)))))&
(((~funny(alice)<~>~wise(alice)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((kind(X)&happy(X))<=>patient(X)))&
(![X]:((tall(X)&strong(X))<=>(curious(X)|~generous(X))))&
(![X]:((creative(X)|~happy(X))=>(~humble(X)&~happy(X))))&
((?[X]:(~wise(X)))=>((strong(susan)&~brave(susan))))&
(((old(lucy)&brave(lucy)))=>((~kind(lucy)&humble(lucy))))&
(~happy(mary))&
((strong(susan)<~>creative(susan)))&
(~kind(alice))&
(?[X]:(humble(X)))&
((~rich(lucy)&~curious(lucy)))&
((tall(paul)<~>~patient(paul)))&
(?[X]:((wise(X)&old(X)))) | patient(susan) | [] | null | 0 |
Everyone who is either calm or quiet is not tall or not brave and vice versa.
Everyone who is calm is not patient and vice versa.
If mary is either not strong or not tall then john is both old and not old.
Everyone who is both not creative and funny is strong or rich.
Everyone who is both wise and strong is not creative and vice versa.
Everyone who is either brave or happy is not rich.
Everyone who is creative or not kind is not strong.
If alice is not curious or quiet then someone is either wise or not brave.
If someone is both not tall and funny then someone is generous or calm and vice versa.
Everyone who is not creative or strong is not kind or not calm and vice versa.
Everyone who is humble is both kind and not tall.
Everyone who is not strong is both quiet and not humble.
If someone is wise or patient then someone is not humble and vice versa.
If paul is creative then john is not old and vice versa.
If paul is tall then paul is both old and patient.
Everyone who is not curious or tall is wise or patient.
Lucy is happy.
Fred is both happy and not tall.
Alice is not kind or happy.
Alice is either wise or not happy.
Lucy is either not old or calm.
John is both curious and not humble.
Someone is either not kind or funny.
Mary is both not curious and generous. | Mary is wise. | entailment | (![X]:((calm(X)<~>quiet(X))<=>(~tall(X)|~brave(X))))&
(![X]:(calm(X)<=>~patient(X)))&
(((~strong(mary)<~>~tall(mary)))=>((old(john)&~old(john))))&
(![X]:((~creative(X)&funny(X))=>(strong(X)|rich(X))))&
(![X]:((wise(X)&strong(X))<=>~creative(X)))&
(![X]:((brave(X)<~>happy(X))=>~rich(X)))&
(![X]:((creative(X)|~kind(X))=>~strong(X)))&
(((~curious(alice)|quiet(alice)))=>(?[X]:((wise(X)<~>~brave(X)))))&
((?[X]:((~tall(X)&funny(X))))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~creative(X)|strong(X))<=>(~kind(X)|~calm(X))))&
(![X]:(humble(X)=>(kind(X)&~tall(X))))&
(![X]:(~strong(X)=>(quiet(X)&~humble(X))))&
((?[X]:((wise(X)|patient(X))))<=>(?[X]:(~humble(X))))&
((creative(paul))<=>(~old(john)))&
((tall(paul))=>((old(paul)&patient(paul))))&
(![X]:((~curious(X)|tall(X))=>(wise(X)|patient(X))))&
(happy(lucy))&
((happy(fred)&~tall(fred)))&
((~kind(alice)|happy(alice)))&
((wise(alice)<~>~happy(alice)))&
((~old(lucy)<~>calm(lucy)))&
((curious(john)&~humble(john)))&
(?[X]:((~kind(X)<~>funny(X))))&
((~curious(mary)&generous(mary))) | wise(mary) | [
"p0",
"p2",
"p4",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8024786551790564643304899
% SZS output start Proof for 8024786551790564643304899
1. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> (~brave(X0) | ~tall(X0))) [input p0]
3. (~strong(mary) <~> ~tall(mary)) => (~old(john) & old(john)) [input p2]
5. ! [X0] : ((strong(X0) & wise(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : ((~kind(X0) | creative(X0)) => ~strong(X0)) [input p6]
10. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~calm(X0) | ~kind(X0))) [input p9]
12. ! [X0] : (~strong(X0) => (~humble(X0) & quiet(X0))) [input p11]
25. ~wise(mary) [input hypothesis]
28. (~old(john) & old(john)) | (~strong(mary) <=> ~tall(mary)) [ennf transformation 3]
32. ! [X0] : (~strong(X0) | (kind(X0) & ~creative(X0))) [ennf transformation 7]
35. ! [X0] : ((~humble(X0) & quiet(X0)) | strong(X0)) [ennf transformation 12]
39. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (brave(X0) & tall(X0))) & ((~brave(X0) | ~tall(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 1]
40. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (brave(X0) & tall(X0))) & (~brave(X0) | ~tall(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [flattening 39]
42. (~old(john) & old(john)) | ((~strong(mary) | tall(mary)) & (~tall(mary) | strong(mary))) [nnf transformation 28]
43. ! [X0] : (((strong(X0) & wise(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & wise(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | ~wise(X0))) [flattening 43]
54. ! [X0] : (((strong(X0) | ~creative(X0)) | (calm(X0) & kind(X0))) & ((~calm(X0) | ~kind(X0)) | (~strong(X0) & creative(X0)))) [nnf transformation 10]
55. ! [X0] : ((strong(X0) | ~creative(X0) | (calm(X0) & kind(X0))) & (~calm(X0) | ~kind(X0) | (~strong(X0) & creative(X0)))) [flattening 54]
71. ~quiet(X0) | ~calm(X0) | tall(X0) [cnf transformation 40]
75. old(john) | ~tall(mary) | strong(mary) [cnf transformation 42]
77. ~old(john) | ~tall(mary) | strong(mary) [cnf transformation 42]
81. wise(X0) | creative(X0) [cnf transformation 44]
82. creative(X0) | strong(X0) [cnf transformation 44]
85. ~creative(X0) | ~strong(X0) [cnf transformation 32]
99. strong(X0) | ~creative(X0) | calm(X0) [cnf transformation 55]
102. strong(X0) | quiet(X0) [cnf transformation 35]
127. ~wise(mary) [cnf transformation 25]
129. 1 <=> tall(mary) [avatar definition]
130. ~tall(mary) <- (~1) [avatar component clause 129]
133. 2 <=> strong(mary) [avatar definition]
135. ~strong(mary) <- (~2) [avatar component clause 133]
137. 3 <=> old(john) [avatar definition]
141. 2 | ~1 | ~3 [avatar split clause 77,137,129,133]
143. 2 | ~1 | 3 [avatar split clause 75,137,129,133]
194. strong(X0) | calm(X0) [subsumption resolution 99,82]
259. creative(mary) [resolution 81,127]
262. ~strong(mary) [resolution 85,259]
266. quiet(mary) <- (~2) [resolution 102,135]
275. calm(mary) <- (~2) [resolution 194,135]
294. ~calm(mary) | tall(mary) <- (~2) [resolution 71,266]
298. tall(mary) <- (~2) [subsumption resolution 294,275]
299. $false <- (~1, ~2) [subsumption resolution 298,130]
300. 1 | 2 [avatar contradiction clause 299]
303. ~2 [avatar split clause 262,133]
305. $false [avatar sat refutation 141,143,300,303]
% SZS output end Proof for 8024786551790564643304899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or quiet is both happy and wise.
If someone is quiet then someone is both not generous and not tall and vice versa.
If someone is both not old and brave then someone is both humble and curious and vice versa.
If someone is both not happy and funny then alice is both wise and brave.
If john is either brave or happy then someone is both not brave and not strong and vice versa.
Everyone who is not quiet or wise is both happy and not wise.
Everyone who is not funny or funny is either calm or not strong.
Everyone who is both not quiet and generous is both happy and not calm and vice versa.
Everyone who is not old or not tall is calm or funny and vice versa.
If someone is either rich or brave then alice is either funny or wise.
Everyone who is not strong is both wise and not kind.
Everyone who is either not quiet or not creative is either quiet or humble and vice versa.
If someone is not wise then someone is either not brave or creative.
Everyone who is rich is either wise or happy and vice versa.
Everyone who is not rich is not old and vice versa.
If someone is not generous then someone is either not generous or not strong and vice versa.
Lucy is either kind or not funny.
Someone is both not happy and quiet.
Someone is not happy.
Susan is not wise.
Lucy is not strong or not creative.
Susan is creative. | Susan is not happy. | neutral | (![X]:((~brave(X)<~>quiet(X))=>(happy(X)&wise(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~generous(X)&~tall(X)))))&
((?[X]:((~old(X)&brave(X))))<=>(?[X]:((humble(X)&curious(X)))))&
((?[X]:((~happy(X)&funny(X))))=>((wise(alice)&brave(alice))))&
(((brave(john)<~>happy(john)))<=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:((~quiet(X)|wise(X))=>(happy(X)&~wise(X))))&
(![X]:((~funny(X)|funny(X))=>(calm(X)<~>~strong(X))))&
(![X]:((~quiet(X)&generous(X))<=>(happy(X)&~calm(X))))&
(![X]:((~old(X)|~tall(X))<=>(calm(X)|funny(X))))&
((?[X]:((rich(X)<~>brave(X))))=>((funny(alice)<~>wise(alice))))&
(![X]:(~strong(X)=>(wise(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:(rich(X)<=>(wise(X)<~>happy(X))))&
(![X]:(~rich(X)<=>~old(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
((kind(lucy)<~>~funny(lucy)))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:(~happy(X)))&
(~wise(susan))&
((~strong(lucy)|~creative(lucy)))&
(creative(susan)) | ~happy(susan) | [] | null | 0 |
If someone is either not kind or not humble then someone is calm or not rich and vice versa.
Everyone who is generous or not happy is both calm and not creative and vice versa.
Everyone who is either quiet or not calm is both funny and creative and vice versa.
If fred is both funny and humble then fred is creative.
Everyone who is old is either not happy or not strong and vice versa.
If someone is either generous or not rich then susan is both not creative and not happy.
If fred is not brave or wise then susan is humble or generous and vice versa.
Everyone who is not quiet or tall is generous and vice versa.
If someone is tall then someone is not funny and vice versa.
If mary is brave then john is not generous and vice versa.
If someone is either not generous or not patient then someone is not old.
Everyone who is quiet or generous is either generous or calm and vice versa.
Everyone who is either not calm or old is both tall and curious.
Everyone who is both curious and rich is generous and vice versa.
Everyone who is both not quiet and not curious is not patient or not quiet.
If paul is both not old and not quiet then someone is calm or not wise.
Paul is either generous or wise.
Someone is not patient or not tall.
Mary is not humble.
Someone is not tall.
Someone is not patient.
Lucy is not curious. | Lucy is not creative. | contradiction | ((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((generous(X)|~happy(X))<=>(calm(X)&~creative(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(funny(X)&creative(X))))&
(((funny(fred)&humble(fred)))=>(creative(fred)))&
(![X]:(old(X)<=>(~happy(X)<~>~strong(X))))&
((?[X]:((generous(X)<~>~rich(X))))=>((~creative(susan)&~happy(susan))))&
(((~brave(fred)|wise(fred)))<=>((humble(susan)|generous(susan))))&
(![X]:((~quiet(X)|tall(X))<=>generous(X)))&
((?[X]:(tall(X)))<=>(?[X]:(~funny(X))))&
((brave(mary))<=>(~generous(john)))&
((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|generous(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~calm(X)<~>old(X))=>(tall(X)&curious(X))))&
(![X]:((curious(X)&rich(X))<=>generous(X)))&
(![X]:((~quiet(X)&~curious(X))=>(~patient(X)|~quiet(X))))&
(((~old(paul)&~quiet(paul)))=>(?[X]:((calm(X)|~wise(X)))))&
((generous(paul)<~>wise(paul)))&
(?[X]:((~patient(X)|~tall(X))))&
(~humble(mary))&
(?[X]:(~tall(X)))&
(?[X]:(~patient(X)))&
(~curious(lucy)) | ~creative(lucy) | [
"p1",
"p2",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1509511978346873273242103
% SZS output start Proof for 1509511978346873273242103
2. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~creative(X0) & calm(X0))) [input p1]
3. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (creative(X0) & funny(X0))) [input p2]
8. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> generous(X0)) [input p7]
12. ! [X0] : ((generous(X0) | quiet(X0)) <=> (generous(X0) <~> calm(X0))) [input p11]
23. ~creative(lucy) [input hypothesis]
41. ! [X0] : (((~happy(X0) | generous(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 2]
42. ! [X0] : ((~happy(X0) | generous(X0) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | (happy(X0) & ~generous(X0)))) [flattening 41]
43. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 3]
44. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 43]
49. ! [X0] : (((tall(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (~tall(X0) & quiet(X0)))) [flattening 49]
61. ! [X0] : (((generous(X0) | quiet(X0)) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 12]
62. ! [X0] : ((generous(X0) | quiet(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~generous(X0) & ~quiet(X0)))) [flattening 61]
81. ~generous(X0) | calm(X0) [cnf transformation 42]
88. ~quiet(X0) | ~calm(X0) | creative(X0) [cnf transformation 44]
105. quiet(X0) | generous(X0) [cnf transformation 50]
114. calm(X0) | generous(X0) | ~quiet(X0) [cnf transformation 62]
117. ~calm(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 62]
136. ~creative(lucy) [cnf transformation 23]
137. ~calm(X0) | ~generous(X0) [duplicate literal removal 117]
262. ~generous(X0) [subsumption resolution 137,81]
263. ~quiet(X0) | calm(X0) [subsumption resolution 114,262]
304. calm(X0) | generous(X0) [resolution 263,105]
305. calm(X0) [subsumption resolution 304,262]
307. ~calm(X0) | creative(X0) | generous(X0) [resolution 88,105]
308. creative(X0) | generous(X0) [subsumption resolution 307,305]
309. creative(X0) [subsumption resolution 308,262]
310. $false [resolution 309,136]
% SZS output end Proof for 1509511978346873273242103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or patient then john is funny. If john is both humble and not brave then john is not brave or not curious and vice versa. If susan is not creative or not tall then mary is either patient or funny. If someone is not brave or tall then someone is either not funny or not tall and vice versa. If fred is either strong or curious then someone is brave. Everyone who is kind is funny and vice versa. Everyone who is not quiet or not humble is both not strong and not tall. Everyone who is creative or wise is curious or not generous. Everyone who is kind is patient. Everyone who is either not brave or humble is not creative and vice versa. Everyone who is not kind is either brave or patient and vice versa. Everyone who is either calm or not quiet is both curious and happy. Everyone who is wise is strong or creative. If paul is both kind and not curious then john is not quiet. Everyone who is both wise and kind is not old. Someone is either wise or not strong. John is not calm. John is quiet. Lucy is both not generous and not old. Someone is both not humble and funny. Alice is not creative. | Lucy is tall. | neutral | ((?[X]:((~curious(X)|patient(X))))=>(funny(john)))&
(((humble(john)&~brave(john)))<=>((~brave(john)|~curious(john))))&
(((~creative(susan)|~tall(susan)))=>((patient(mary)<~>funny(mary))))&
((?[X]:((~brave(X)|tall(X))))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
(((strong(fred)<~>curious(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)<=>funny(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)|wise(X))=>(curious(X)|~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((~brave(X)<~>humble(X))<=>~creative(X)))&
(![X]:(~kind(X)<=>(brave(X)<~>patient(X))))&
(![X]:((calm(X)<~>~quiet(X))=>(curious(X)&happy(X))))&
(![X]:(wise(X)=>(strong(X)|creative(X))))&
(((kind(paul)&~curious(paul)))=>(~quiet(john)))&
(![X]:((wise(X)&kind(X))=>~old(X)))&
(?[X]:((wise(X)<~>~strong(X))))&
(~calm(john))&
(quiet(john))&
((~generous(lucy)&~old(lucy)))&
(?[X]:((~humble(X)&funny(X))))&
(~creative(alice)) | tall(lucy) | [] | null | 0 |
Everyone who is curious is either quiet or not happy and vice versa.
If someone is funny then paul is either not funny or not creative and vice versa.
Everyone who is both not tall and old is creative or not brave and vice versa.
If someone is either brave or not happy then someone is not patient.
If lucy is either not happy or generous then lucy is kind or not happy.
Everyone who is either curious or not patient is either not old or not kind.
Everyone who is humble is both quiet and not humble and vice versa.
Everyone who is both quiet and humble is both calm and not curious.
Everyone who is either not rich or not calm is either not generous or not rich.
Everyone who is generous is either funny or not generous and vice versa.
If someone is not old or patient then john is not humble or not calm and vice versa.
Everyone who is either tall or generous is strong or not generous.
Everyone who is both wise and not tall is either humble or rich.
Everyone who is not rich is either not patient or not funny and vice versa.
If someone is not strong or not curious then john is either brave or not creative and vice versa.
Everyone who is either not kind or strong is not rich or patient and vice versa.
Someone is creative.
Someone is kind or not quiet.
Fred is not kind.
John is rich.
Someone is quiet or not brave. | Fred is not tall. | neutral | (![X]:(curious(X)<=>(quiet(X)<~>~happy(X))))&
((?[X]:(funny(X)))<=>((~funny(paul)<~>~creative(paul))))&
(![X]:((~tall(X)&old(X))<=>(creative(X)|~brave(X))))&
((?[X]:((brave(X)<~>~happy(X))))=>(?[X]:(~patient(X))))&
(((~happy(lucy)<~>generous(lucy)))=>((kind(lucy)|~happy(lucy))))&
(![X]:((curious(X)<~>~patient(X))=>(~old(X)<~>~kind(X))))&
(![X]:(humble(X)<=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)&humble(X))=>(calm(X)&~curious(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~generous(X)<~>~rich(X))))&
(![X]:(generous(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:((~old(X)|patient(X))))<=>((~humble(john)|~calm(john))))&
(![X]:((tall(X)<~>generous(X))=>(strong(X)|~generous(X))))&
(![X]:((wise(X)&~tall(X))=>(humble(X)<~>rich(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~funny(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>((brave(john)<~>~creative(john))))&
(![X]:((~kind(X)<~>strong(X))<=>(~rich(X)|patient(X))))&
(?[X]:(creative(X)))&
(?[X]:((kind(X)|~quiet(X))))&
(~kind(fred))&
(rich(john))&
(?[X]:((quiet(X)|~brave(X)))) | ~tall(fred) | [] | null | 0 |
If fred is either humble or not tall then someone is not kind or not wise.
Everyone who is brave is both rich and not curious and vice versa.
Everyone who is both not calm and not quiet is not brave and vice versa.
Everyone who is funny or creative is happy and vice versa.
If susan is both brave and not wise then someone is not kind and vice versa.
If someone is old then susan is rich or not quiet.
If mary is both tall and not kind then someone is old.
Everyone who is both not wise and not patient is not brave and vice versa.
Everyone who is both creative and funny is either quiet or humble.
Everyone who is quiet or generous is not old or not happy.
If lucy is both kind and not tall then someone is curious.
If someone is rich then someone is either not tall or not wise.
If someone is either not humble or wise then susan is old or kind.
Everyone who is not calm or not curious is brave and vice versa.
If someone is not patient or not tall then someone is not patient and vice versa.
If lucy is both not old and not creative then lucy is happy or patient and vice versa.
Someone is both not tall and not strong.
Paul is not kind or humble.
Someone is happy.
Paul is not patient or brave.
Someone is both not generous and happy.
Mary is generous or not quiet. | Mary is tall. | neutral | (((humble(fred)<~>~tall(fred)))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:(brave(X)<=>(rich(X)&~curious(X))))&
(![X]:((~calm(X)&~quiet(X))<=>~brave(X)))&
(![X]:((funny(X)|creative(X))<=>happy(X)))&
(((brave(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(old(X)))=>((rich(susan)|~quiet(susan))))&
(((tall(mary)&~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~patient(X))<=>~brave(X)))&
(![X]:((creative(X)&funny(X))=>(quiet(X)<~>humble(X))))&
(![X]:((quiet(X)|generous(X))=>(~old(X)|~happy(X))))&
(((kind(lucy)&~tall(lucy)))=>(?[X]:(curious(X))))&
((?[X]:(rich(X)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~humble(X)<~>wise(X))))=>((old(susan)|kind(susan))))&
(![X]:((~calm(X)|~curious(X))<=>brave(X)))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~patient(X))))&
(((~old(lucy)&~creative(lucy)))<=>((happy(lucy)|patient(lucy))))&
(?[X]:((~tall(X)&~strong(X))))&
((~kind(paul)|humble(paul)))&
(?[X]:(happy(X)))&
((~patient(paul)|brave(paul)))&
(?[X]:((~generous(X)&happy(X))))&
((generous(mary)|~quiet(mary))) | tall(mary) | [] | null | 0 |
Everyone who is not old or old is not happy or happy and vice versa.
If someone is both tall and wise then paul is not happy or humble and vice versa.
Everyone who is either not wise or strong is not creative.
Everyone who is not tall is either wise or not humble and vice versa.
If fred is humble or strong then someone is not quiet and vice versa.
Everyone who is not old is happy or not brave and vice versa.
Everyone who is rich is not patient or patient and vice versa.
Everyone who is not patient or patient is not kind.
If paul is either not generous or old then paul is not funny and vice versa.
Everyone who is not humble is funny.
If alice is either not quiet or not strong then lucy is either humble or kind.
Everyone who is not funny is both calm and rich and vice versa.
If susan is both not rich and brave then alice is either not humble or not patient and vice versa.
If alice is humble then susan is either generous or not tall.
Someone is either not generous or not quiet.
Lucy is either happy or not strong.
Someone is either not rich or not tall.
Alice is generous.
Paul is not rich or not curious.
Susan is not quiet or brave.
John is both not happy and calm.
Paul is either strong or curious. | Fred is not kind. | entailment | (![X]:((~old(X)|old(X))<=>(~happy(X)|happy(X))))&
((?[X]:((tall(X)&wise(X))))<=>((~happy(paul)|humble(paul))))&
(![X]:((~wise(X)<~>strong(X))=>~creative(X)))&
(![X]:(~tall(X)<=>(wise(X)<~>~humble(X))))&
(((humble(fred)|strong(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(happy(X)|~brave(X))))&
(![X]:(rich(X)<=>(~patient(X)|patient(X))))&
(![X]:((~patient(X)|patient(X))=>~kind(X)))&
(((~generous(paul)<~>old(paul)))<=>(~funny(paul)))&
(![X]:(~humble(X)=>funny(X)))&
(((~quiet(alice)<~>~strong(alice)))=>((humble(lucy)<~>kind(lucy))))&
(![X]:(~funny(X)<=>(calm(X)&rich(X))))&
(((~rich(susan)&brave(susan)))<=>((~humble(alice)<~>~patient(alice))))&
((humble(alice))=>((generous(susan)<~>~tall(susan))))&
(?[X]:((~generous(X)<~>~quiet(X))))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~rich(X)<~>~tall(X))))&
(generous(alice))&
((~rich(paul)|~curious(paul)))&
((~quiet(susan)|brave(susan)))&
((~happy(john)&calm(john)))&
((strong(paul)<~>curious(paul))) | ~kind(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 45578600634238954577098
% SZS output start Proof for 45578600634238954577098
8. ! [X0] : ((patient(X0) | ~patient(X0)) => ~kind(X0)) [input p7]
23. kind(fred) [input hypothesis]
25. ! [X0] : (~kind(X0) | (~patient(X0) & patient(X0))) [ennf transformation 8]
83. ~kind(X0) | patient(X0) [cnf transformation 25]
84. ~kind(X0) | ~patient(X0) [cnf transformation 25]
118. kind(fred) [cnf transformation 23]
162. ~kind(X0) [subsumption resolution 83,84]
252. $false [subsumption resolution 118,162]
% SZS output end Proof for 45578600634238954577098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not strong is not calm and vice versa.
Everyone who is not brave or generous is strong.
Everyone who is both not brave and generous is either calm or not kind.
If fred is both not happy and generous then fred is humble and vice versa.
Everyone who is both wise and not calm is either not creative or calm.
Everyone who is either not humble or not quiet is not brave or not humble and vice versa.
Everyone who is curious or wise is not brave and vice versa.
If paul is either not rich or generous then fred is both kind and not old and vice versa.
If fred is both not tall and not calm then someone is tall or humble and vice versa.
Everyone who is both not happy and patient is not strong.
Everyone who is both brave and curious is either not patient or creative and vice versa.
If someone is both creative and not creative then someone is not calm.
If someone is both kind and not strong then someone is not happy.
Everyone who is both not rich and not funny is both quiet and funny and vice versa.
Everyone who is not calm or not funny is either patient or creative and vice versa.
Everyone who is happy or not brave is brave.
Someone is rich.
Someone is both patient and kind.
Someone is kind.
Lucy is not humble or not brave.
John is not wise or not quiet.
Someone is either quiet or not happy. | Lucy is generous. | neutral | (![X]:((curious(X)<~>~strong(X))<=>~calm(X)))&
(![X]:((~brave(X)|generous(X))=>strong(X)))&
(![X]:((~brave(X)&generous(X))=>(calm(X)<~>~kind(X))))&
(((~happy(fred)&generous(fred)))<=>(humble(fred)))&
(![X]:((wise(X)&~calm(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)|wise(X))<=>~brave(X)))&
(((~rich(paul)<~>generous(paul)))<=>((kind(fred)&~old(fred))))&
(((~tall(fred)&~calm(fred)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((~happy(X)&patient(X))=>~strong(X)))&
(![X]:((brave(X)&curious(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:(~calm(X))))&
((?[X]:((kind(X)&~strong(X))))=>(?[X]:(~happy(X))))&
(![X]:((~rich(X)&~funny(X))<=>(quiet(X)&funny(X))))&
(![X]:((~calm(X)|~funny(X))<=>(patient(X)<~>creative(X))))&
(![X]:((happy(X)|~brave(X))=>brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:(kind(X)))&
((~humble(lucy)|~brave(lucy)))&
((~wise(john)|~quiet(john)))&
(?[X]:((quiet(X)<~>~happy(X)))) | generous(lucy) | [] | null | 0 |
If someone is quiet then fred is either creative or generous.
Everyone who is not kind or not old is creative and vice versa.
Everyone who is either not funny or not rich is curious and vice versa.
If someone is creative then someone is either not tall or patient and vice versa.
Everyone who is both happy and curious is not happy or curious and vice versa.
Everyone who is not curious is both not generous and not humble.
If someone is either patient or funny then someone is either brave or wise and vice versa.
Everyone who is not creative is not patient.
If someone is not old then someone is both not brave and not tall.
Everyone who is both calm and not old is either brave or not tall.
Everyone who is both not generous and not rich is either not creative or rich and vice versa.
Everyone who is both not quiet and kind is creative or not generous.
If someone is old or not tall then alice is both patient and calm and vice versa.
Everyone who is either tall or calm is not tall or not rich and vice versa.
Everyone who is humble or not funny is either not tall or not kind and vice versa.
If someone is both creative and generous then someone is either calm or rich and vice versa.
Fred is either not wise or wise.
Someone is both curious and rich.
Someone is not funny.
Paul is brave.
Paul is either kind or not funny.
Fred is either happy or creative.
John is either funny or tall.
Alice is funny. | Alice is tall. | contradiction | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~rich(X))<=>curious(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((happy(X)&curious(X))<=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | tall(alice) | [
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 29591308818628936245573
% SZS output start Proof for 29591308818628936245573
8. ! [X0] : (~creative(X0) => ~patient(X0)) [input p7]
9. ? [X0] : ~old(X0) => ? [X0] : (~tall(X0) & ~brave(X0)) [input p8]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) <~> rich(X0))) [input p10]
13. ? [X0] : (~tall(X0) | old(X0)) <=> (calm(alice) & patient(alice)) [input p12]
14. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (~rich(X0) | ~tall(X0))) [input p13]
25. tall(alice) [input hypothesis]
28. ? [X0] : ~old(X0) => ? [X1] : (~tall(X1) & ~brave(X1)) [rectify 9]
32. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 8]
33. ? [X1] : (~tall(X1) & ~brave(X1)) | ! [X0] : old(X0) [ennf transformation 28]
54. ? [X0] : (~tall(X0) & ~brave(X0)) | ! [X1] : old(X1) [rectify 33]
55. ? [X0] : (~tall(X0) & ~brave(X0)) => (~tall(sK4) & ~brave(sK4)) [choice axiom]
56. (~tall(sK4) & ~brave(sK4)) | ! [X1] : old(X1) [skolemisation 54,55]
58. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (rich(X0) | generous(X0)))) [nnf transformation 11]
59. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | rich(X0) | generous(X0))) [flattening 58]
60. (? [X0] : (~tall(X0) | old(X0)) | (~calm(alice) | ~patient(alice))) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [nnf transformation 13]
61. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [flattening 60]
62. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [rectify 61]
63. ? [X0] : (~tall(X0) | old(X0)) => (~tall(sK5) | old(sK5)) [choice axiom]
64. ((~tall(sK5) | old(sK5)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [skolemisation 62,63]
65. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 14]
66. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 65]
110. ~patient(X0) | creative(X0) [cnf transformation 32]
112. ~tall(sK4) | old(X1) [cnf transformation 56]
120. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 59]
122. patient(alice) | ~old(X1) [cnf transformation 64]
123. patient(alice) | tall(X1) [cnf transformation 64]
124. calm(alice) | ~old(X1) [cnf transformation 64]
125. calm(alice) | tall(X1) [cnf transformation 64]
132. ~calm(X0) | ~tall(X0) | rich(X0) [cnf transformation 66]
158. tall(alice) [cnf transformation 25]
162. ~rich(X0) | ~creative(X0) [duplicate literal removal 120]
241. 18 <=> ! [X1] : old(X1) [avatar definition]
242. old(X1) <- (18) [avatar component clause 241]
244. 19 <=> tall(sK4) [avatar definition]
246. ~tall(sK4) <- (~19) [avatar component clause 244]
247. 18 | ~19 [avatar split clause 112,244,241]
256. 21 <=> patient(alice) [avatar definition]
257. patient(alice) <- (21) [avatar component clause 256]
260. 22 <=> calm(alice) [avatar definition]
261. calm(alice) <- (22) [avatar component clause 260]
273. 25 <=> ! [X1] : tall(X1) [avatar definition]
274. tall(X1) <- (25) [avatar component clause 273]
275. 25 | 22 [avatar split clause 125,260,273]
277. 26 <=> ! [X1] : ~old(X1) [avatar definition]
278. ~old(X1) <- (26) [avatar component clause 277]
279. 26 | 22 [avatar split clause 124,260,277]
280. 25 | 21 [avatar split clause 123,256,273]
281. 26 | 21 [avatar split clause 122,256,277]
404. 42 <=> rich(alice) [avatar definition]
406. rich(alice) <- (42) [avatar component clause 404]
423. $false <- (~19, 25) [resolution 274,246]
426. 19 | ~25 [avatar contradiction clause 423]
428. $false <- (18, 26) [subsumption resolution 242,278]
429. ~18 | ~26 [avatar contradiction clause 428]
432. creative(alice) <- (21) [resolution 257,110]
468. ~tall(alice) | rich(alice) <- (22) [resolution 132,261]
472. rich(alice) <- (22) [subsumption resolution 468,158]
476. 42 | ~22 [avatar split clause 472,260,404]
479. ~creative(alice) <- (42) [resolution 406,162]
480. $false <- (21, 42) [subsumption resolution 479,432]
481. ~21 | ~42 [avatar contradiction clause 480]
482. $false [avatar sat refutation 247,275,279,280,281,426,429,476,481]
% SZS output end Proof for 29591308818628936245573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not rich or quiet then john is not tall or not patient.
If john is curious or happy then someone is creative or not curious and vice versa.
If someone is tall or not funny then paul is not wise and vice versa.
Everyone who is not humble is not funny or strong.
If paul is rich or patient then someone is both rich and brave.
Everyone who is curious is both not calm and kind and vice versa.
Everyone who is not curious is rich.
Everyone who is funny or not funny is not rich and vice versa.
If susan is either not rich or tall then someone is not quiet or not generous and vice versa.
If alice is either kind or not calm then someone is not patient.
If someone is wise or not strong then someone is not funny or not curious.
If paul is both generous and creative then someone is both not brave and wise and vice versa.
Everyone who is both funny and brave is wise or rich and vice versa.
If someone is strong or not wise then lucy is happy and vice versa.
If someone is either not wise or not tall then alice is either quiet or old.
If paul is both not rich and not funny then alice is either not calm or not tall.
Paul is not rich or not strong.
Someone is creative or not tall.
Someone is not old.
Susan is generous.
Someone is not humble or not rich.
Someone is happy. | John is calm. | contradiction | ((?[X]:((~rich(X)|quiet(X))))=>((~tall(john)|~patient(john))))&
(((curious(john)|happy(john)))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((tall(X)|~funny(X))))<=>(~wise(paul)))&
(![X]:(~humble(X)=>(~funny(X)|strong(X))))&
(((rich(paul)|patient(paul)))=>(?[X]:((rich(X)&brave(X)))))&
(![X]:(curious(X)<=>(~calm(X)&kind(X))))&
(![X]:(~curious(X)=>rich(X)))&
(![X]:((funny(X)|~funny(X))<=>~rich(X)))&
(((~rich(susan)<~>tall(susan)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((kind(alice)<~>~calm(alice)))=>(?[X]:(~patient(X))))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:((funny(X)&brave(X))<=>(wise(X)|rich(X))))&
((?[X]:((strong(X)|~wise(X))))<=>(happy(lucy)))&
((?[X]:((~wise(X)<~>~tall(X))))=>((quiet(alice)<~>old(alice))))&
(((~rich(paul)&~funny(paul)))=>((~calm(alice)<~>~tall(alice))))&
((~rich(paul)|~strong(paul)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(~old(X)))&
(generous(susan))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:(happy(X))) | calm(john) | [
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7156600235619055673248419
% SZS output start Proof for 7156600235619055673248419
6. ! [X0] : (curious(X0) <=> (kind(X0) & ~calm(X0))) [input p5]
7. ! [X0] : (~curious(X0) => rich(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | funny(X0)) <=> ~rich(X0)) [input p7]
23. calm(john) [input hypothesis]
31. ! [X0] : (rich(X0) | curious(X0)) [ennf transformation 7]
47. ! [X0] : ((curious(X0) | (~kind(X0) | calm(X0))) & ((kind(X0) & ~calm(X0)) | ~curious(X0))) [nnf transformation 6]
48. ! [X0] : ((curious(X0) | ~kind(X0) | calm(X0)) & ((kind(X0) & ~calm(X0)) | ~curious(X0))) [flattening 47]
49. ! [X0] : (((~funny(X0) | funny(X0)) | rich(X0)) & (~rich(X0) | (funny(X0) & ~funny(X0)))) [nnf transformation 8]
50. ! [X0] : ((~funny(X0) | funny(X0) | rich(X0)) & (~rich(X0) | (funny(X0) & ~funny(X0)))) [flattening 49]
89. ~calm(X0) | ~curious(X0) [cnf transformation 48]
92. curious(X0) | rich(X0) [cnf transformation 31]
93. ~rich(X0) | ~funny(X0) [cnf transformation 50]
94. ~rich(X0) | funny(X0) [cnf transformation 50]
128. calm(john) [cnf transformation 23]
133. 2 <=> curious(john) [avatar definition]
134. ~curious(john) <- (~2) [avatar component clause 133]
190. ~rich(X0) [subsumption resolution 93,94]
320. ~curious(john) [resolution 89,128]
323. ~2 [avatar split clause 320,133]
325. rich(john) <- (~2) [resolution 92,134]
329. $false <- (~2) [subsumption resolution 325,190]
330. 2 [avatar contradiction clause 329]
332. $false [avatar sat refutation 323,330]
% SZS output end Proof for 7156600235619055673248419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or old then mary is not humble.
If paul is not kind or curious then susan is not rich or not old.
Everyone who is not kind is either not kind or calm.
Everyone who is patient is either not rich or old and vice versa.
If someone is rich then paul is kind and vice versa.
If someone is calm or old then lucy is wise or quiet and vice versa.
Everyone who is either humble or not strong is both quiet and funny and vice versa.
Everyone who is not calm is both not calm and quiet and vice versa.
Everyone who is either wise or humble is either not quiet or not funny and vice versa.
Everyone who is either brave or not old is both wise and old.
Everyone who is both brave and generous is both quiet and brave and vice versa.
Everyone who is kind or not curious is calm.
If susan is kind then someone is funny or not generous and vice versa.
If lucy is both not generous and humble then someone is both wise and not kind.
If susan is either rich or not old then alice is both not creative and strong and vice versa.
If someone is either wise or humble then mary is either not curious or creative.
Alice is patient or not funny.
Someone is humble or funny.
Someone is kind.
Someone is rich or not calm.
Someone is both humble and wise.
Someone is both not wise and funny. | Lucy is not strong. | neutral | ((?[X]:((wise(X)|old(X))))=>(~humble(mary)))&
(((~kind(paul)|curious(paul)))=>((~rich(susan)|~old(susan))))&
(![X]:(~kind(X)=>(~kind(X)<~>calm(X))))&
(![X]:(patient(X)<=>(~rich(X)<~>old(X))))&
((?[X]:(rich(X)))<=>(kind(paul)))&
((?[X]:((calm(X)|old(X))))<=>((wise(lucy)|quiet(lucy))))&
(![X]:((humble(X)<~>~strong(X))<=>(quiet(X)&funny(X))))&
(![X]:(~calm(X)<=>(~calm(X)&quiet(X))))&
(![X]:((wise(X)<~>humble(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((brave(X)<~>~old(X))=>(wise(X)&old(X))))&
(![X]:((brave(X)&generous(X))<=>(quiet(X)&brave(X))))&
(![X]:((kind(X)|~curious(X))=>calm(X)))&
((kind(susan))<=>(?[X]:((funny(X)|~generous(X)))))&
(((~generous(lucy)&humble(lucy)))=>(?[X]:((wise(X)&~kind(X)))))&
(((rich(susan)<~>~old(susan)))<=>((~creative(alice)&strong(alice))))&
((?[X]:((wise(X)<~>humble(X))))=>((~curious(mary)<~>creative(mary))))&
((patient(alice)|~funny(alice)))&
(?[X]:((humble(X)|funny(X))))&
(?[X]:(kind(X)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((~wise(X)&funny(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either curious or old is both curious and funny. Everyone who is happy or tall is both wise and not strong and vice versa. Everyone who is either curious or not old is not brave or not quiet. If someone is rich or not quiet then john is both kind and happy. If someone is either not patient or wise then someone is either brave or not patient and vice versa. If someone is wise or old then someone is old or curious. Everyone who is strong is both happy and not curious. If someone is either not tall or patient then susan is either not curious or brave. If alice is happy or not patient then mary is happy. Everyone who is both patient and not tall is either tall or not tall. Everyone who is both not kind and not humble is tall and vice versa. If someone is either not curious or not strong then paul is not happy and vice versa. Everyone who is not tall is kind and vice versa. Everyone who is either humble or creative is both strong and not calm. Everyone who is either not quiet or not old is not humble or brave. If paul is both quiet and calm then someone is either not calm or not rich and vice versa. Someone is not kind. Susan is both happy and not curious. Paul is patient or rich. Someone is not wise or not strong. Someone is both not strong and not rich. Alice is kind or humble. Someone is either old or tall. | Paul is happy. | contradiction | (![X]:((curious(X)<~>old(X))=>(curious(X)&funny(X))))&
(![X]:((happy(X)|tall(X))<=>(wise(X)&~strong(X))))&
(![X]:((curious(X)<~>~old(X))=>(~brave(X)|~quiet(X))))&
((?[X]:((rich(X)|~quiet(X))))=>((kind(john)&happy(john))))&
((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(strong(X)=>(happy(X)&~curious(X))))&
((?[X]:((~tall(X)<~>patient(X))))=>((~curious(susan)<~>brave(susan))))&
(((happy(alice)|~patient(alice)))=>(happy(mary)))&
(![X]:((patient(X)&~tall(X))=>(tall(X)<~>~tall(X))))&
(![X]:((~kind(X)&~humble(X))<=>tall(X)))&
((?[X]:((~curious(X)<~>~strong(X))))<=>(~happy(paul)))&
(![X]:(~tall(X)<=>kind(X)))&
(![X]:((humble(X)<~>creative(X))=>(strong(X)&~calm(X))))&
(![X]:((~quiet(X)<~>~old(X))=>(~humble(X)|brave(X))))&
(((quiet(paul)&calm(paul)))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
(?[X]:(~kind(X)))&
((happy(susan)&~curious(susan)))&
((patient(paul)|rich(paul)))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~strong(X)&~rich(X))))&
((kind(alice)|humble(alice)))&
(?[X]:((old(X)<~>tall(X)))) | happy(paul) | [
"p0",
"p1",
"p5",
"p6",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2972394003585580877776547
% SZS output start Proof for 2972394003585580877776547
1. ! [X0] : ((curious(X0) <~> old(X0)) => (funny(X0) & curious(X0))) [input p0]
2. ! [X0] : ((tall(X0) | happy(X0)) <=> (~strong(X0) & wise(X0))) [input p1]
6. ? [X0] : (old(X0) | wise(X0)) => ? [X0] : (curious(X0) | old(X0)) [input p5]
7. ! [X0] : (strong(X0) => (~curious(X0) & happy(X0))) [input p6]
12. ? [X0] : (~curious(X0) <~> ~strong(X0)) <=> ~happy(paul) [input p11]
18. ~curious(susan) & happy(susan) [input p17]
24. happy(paul) [input hypothesis]
26. ? [X0] : (old(X0) | wise(X0)) => ? [X1] : (curious(X1) | old(X1)) [rectify 6]
27. ! [X0] : ((curious(X0) <~> old(X0)) => curious(X0)) [pure predicate removal 1]
28. ! [X0] : (curious(X0) | (curious(X0) <=> old(X0))) [ennf transformation 27]
32. ? [X1] : (curious(X1) | old(X1)) | ! [X0] : (~old(X0) & ~wise(X0)) [ennf transformation 26]
33. ! [X0] : ((~curious(X0) & happy(X0)) | ~strong(X0)) [ennf transformation 7]
41. ! [X0] : (curious(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0)))) [nnf transformation 28]
42. ! [X0] : (((tall(X0) | happy(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 2]
43. ! [X0] : ((tall(X0) | happy(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 42]
50. ? [X0] : (curious(X0) | old(X0)) | ! [X1] : (~old(X1) & ~wise(X1)) [rectify 32]
51. ? [X0] : (curious(X0) | old(X0)) => (curious(sK2) | old(sK2)) [choice axiom]
52. (curious(sK2) | old(sK2)) | ! [X1] : (~old(X1) & ~wise(X1)) [skolemisation 50,51]
57. (? [X0] : ((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | happy(paul)) & (~happy(paul) | ! [X0] : ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) [nnf transformation 12]
58. (? [X0] : ((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | happy(paul)) & (~happy(paul) | ! [X1] : ((~curious(X1) | strong(X1)) & (~strong(X1) | curious(X1)))) [rectify 57]
59. ? [X0] : ((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) => ((strong(sK3) | curious(sK3)) & (~strong(sK3) | ~curious(sK3))) [choice axiom]
60. (((strong(sK3) | curious(sK3)) & (~strong(sK3) | ~curious(sK3))) | happy(paul)) & (~happy(paul) | ! [X1] : ((~curious(X1) | strong(X1)) & (~strong(X1) | curious(X1)))) [skolemisation 58,59]
79. curious(X0) | curious(X0) | ~old(X0) [cnf transformation 41]
80. ~happy(X0) | wise(X0) [cnf transformation 43]
82. ~strong(X0) | ~happy(X0) [cnf transformation 43]
99. curious(sK2) | old(sK2) | ~wise(X1) [cnf transformation 52]
101. happy(X0) | ~strong(X0) [cnf transformation 33]
115. ~happy(paul) | ~curious(X1) | strong(X1) [cnf transformation 60]
133. happy(susan) [cnf transformation 18]
142. happy(paul) [cnf transformation 24]
145. curious(X0) | ~old(X0) [duplicate literal removal 79]
207. 14 <=> curious(sK2) [avatar definition]
209. curious(sK2) <- (14) [avatar component clause 207]
211. curious(sK2) | ~wise(X1) [subsumption resolution 99,145]
213. 15 <=> ! [X1] : ~wise(X1) [avatar definition]
214. ~wise(X1) <- (15) [avatar component clause 213]
215. 15 | 14 [avatar split clause 211,207,213]
216. ~strong(X0) [subsumption resolution 101,82]
251. 23 <=> happy(paul) [avatar definition]
259. ~happy(paul) | ~curious(X1) [subsumption resolution 115,216]
261. 25 <=> ! [X1] : ~curious(X1) [avatar definition]
262. ~curious(X1) <- (25) [avatar component clause 261]
263. 25 | ~23 [avatar split clause 259,251,261]
323. 23 [avatar split clause 142,251]
324. $false <- (14, 25) [subsumption resolution 209,262]
325. ~14 | ~25 [avatar contradiction clause 324]
328. wise(susan) [resolution 80,133]
331. $false <- (15) [subsumption resolution 328,214]
332. ~15 [avatar contradiction clause 331]
337. $false [avatar sat refutation 215,263,323,325,332]
% SZS output end Proof for 2972394003585580877776547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not patient is not creative or not tall.
Everyone who is funny or not strong is both patient and brave.
If mary is not old then someone is kind or quiet and vice versa.
If paul is either creative or not rich then someone is old or not rich and vice versa.
If someone is not old then paul is funny and vice versa.
Everyone who is funny or tall is not funny or not quiet.
If someone is both not creative and not happy then someone is both not quiet and not wise.
Everyone who is both brave and not tall is both not old and creative.
Everyone who is happy or not kind is strong and vice versa.
Everyone who is both not strong and not rich is both quiet and not funny.
If someone is either not humble or not calm then paul is either creative or not rich and vice versa.
Everyone who is either not rich or not calm is both not curious and not happy.
If lucy is not patient or not rich then paul is both not strong and not old.
If someone is both tall and funny then someone is not calm and vice versa.
Everyone who is either not calm or brave is not happy.
Everyone who is strong is both creative and strong.
Lucy is both humble and quiet.
Someone is both funny and old.
Someone is either not old or not patient.
Someone is not rich or not creative.
Someone is both not wise and not calm.
Alice is not curious or patient.
Someone is both not patient and not wise.
Susan is both kind and creative. | Alice is not kind. | neutral | (![X]:((~humble(X)<~>~patient(X))=>(~creative(X)|~tall(X))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(((creative(paul)<~>~rich(paul)))<=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:(~old(X)))<=>(funny(paul)))&
(![X]:((funny(X)|tall(X))=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)&~happy(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(![X]:((brave(X)&~tall(X))=>(~old(X)&creative(X))))&
(![X]:((happy(X)|~kind(X))<=>strong(X)))&
(![X]:((~strong(X)&~rich(X))=>(quiet(X)&~funny(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((creative(paul)<~>~rich(paul))))&
(![X]:((~rich(X)<~>~calm(X))=>(~curious(X)&~happy(X))))&
(((~patient(lucy)|~rich(lucy)))=>((~strong(paul)&~old(paul))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~calm(X)<~>brave(X))=>~happy(X)))&
(![X]:(strong(X)=>(creative(X)&strong(X))))&
((humble(lucy)&quiet(lucy)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~wise(X)&~calm(X))))&
((~curious(alice)|patient(alice)))&
(?[X]:((~patient(X)&~wise(X))))&
((kind(susan)&creative(susan))) | ~kind(alice) | [] | null | 0 |
If mary is either creative or not tall then susan is quiet.
Everyone who is not curious is not rich and vice versa.
If someone is not quiet then susan is both generous and rich and vice versa.
Everyone who is either not kind or curious is either not patient or happy.
If susan is creative then alice is either tall or kind.
Everyone who is both not generous and not happy is generous and vice versa.
If someone is not kind then susan is not rich or not strong and vice versa.
If someone is not humble then lucy is not happy or creative and vice versa.
Everyone who is both not calm and not curious is not patient or curious.
If mary is either creative or kind then fred is both quiet and not happy and vice versa.
Everyone who is both wise and not brave is either kind or not brave and vice versa.
Everyone who is not generous or funny is not rich.
If mary is creative or not generous then john is humble or not calm and vice versa.
If john is both generous and calm then mary is curious and vice versa.
Susan is either brave or happy.
Susan is not tall or not happy.
Someone is either not brave or happy.
Mary is either wise or not humble.
Mary is both happy and quiet. | John is brave. | neutral | (((creative(mary)<~>~tall(mary)))=>(quiet(susan)))&
(![X]:(~curious(X)<=>~rich(X)))&
((?[X]:(~quiet(X)))<=>((generous(susan)&rich(susan))))&
(![X]:((~kind(X)<~>curious(X))=>(~patient(X)<~>happy(X))))&
((creative(susan))=>((tall(alice)<~>kind(alice))))&
(![X]:((~generous(X)&~happy(X))<=>generous(X)))&
((?[X]:(~kind(X)))<=>((~rich(susan)|~strong(susan))))&
((?[X]:(~humble(X)))<=>((~happy(lucy)|creative(lucy))))&
(![X]:((~calm(X)&~curious(X))=>(~patient(X)|curious(X))))&
(((creative(mary)<~>kind(mary)))<=>((quiet(fred)&~happy(fred))))&
(![X]:((wise(X)&~brave(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~generous(X)|funny(X))=>~rich(X)))&
(((creative(mary)|~generous(mary)))<=>((humble(john)|~calm(john))))&
(((generous(john)&calm(john)))<=>(curious(mary)))&
((brave(susan)<~>happy(susan)))&
((~tall(susan)|~happy(susan)))&
(?[X]:((~brave(X)<~>happy(X))))&
((wise(mary)<~>~humble(mary)))&
((happy(mary)&quiet(mary))) | brave(john) | [] | null | 0 |
If someone is patient then john is both rich and not tall and vice versa.
Everyone who is both rich and humble is kind and vice versa.
Everyone who is both not wise and not tall is curious or tall and vice versa.
Everyone who is either not happy or happy is both brave and strong and vice versa.
If susan is generous or wise then susan is both not humble and strong and vice versa.
If someone is both not brave and not curious then someone is either not calm or creative and vice versa.
Everyone who is either not generous or old is old or not brave and vice versa.
If someone is not patient or calm then mary is kind and vice versa.
Everyone who is either creative or strong is wise or not patient.
If mary is not curious or not humble then someone is strong or curious.
If someone is both not calm and not kind then someone is not generous and vice versa.
Everyone who is not creative is happy or creative and vice versa.
Everyone who is humble is not patient and vice versa.
Everyone who is either strong or creative is not tall and vice versa.
If mary is patient then paul is both not happy and not generous and vice versa.
Someone is not funny or rich.
Alice is either not strong or humble.
Someone is not creative or not tall.
Someone is both patient and old.
Fred is rich.
Someone is quiet. | Fred is not kind. | neutral | ((?[X]:(patient(X)))<=>((rich(john)&~tall(john))))&
(![X]:((rich(X)&humble(X))<=>kind(X)))&
(![X]:((~wise(X)&~tall(X))<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(brave(X)&strong(X))))&
(((generous(susan)|wise(susan)))<=>((~humble(susan)&strong(susan))))&
((?[X]:((~brave(X)&~curious(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~generous(X)<~>old(X))<=>(old(X)|~brave(X))))&
((?[X]:((~patient(X)|calm(X))))<=>(kind(mary)))&
(![X]:((creative(X)<~>strong(X))=>(wise(X)|~patient(X))))&
(((~curious(mary)|~humble(mary)))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(happy(X)|creative(X))))&
(![X]:(humble(X)<=>~patient(X)))&
(![X]:((strong(X)<~>creative(X))<=>~tall(X)))&
((patient(mary))<=>((~happy(paul)&~generous(paul))))&
(?[X]:((~funny(X)|rich(X))))&
((~strong(alice)<~>humble(alice)))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((patient(X)&old(X))))&
(rich(fred))&
(?[X]:(quiet(X))) | ~kind(fred) | [] | null | 0 |
Everyone who is both not rich and not quiet is either not brave or creative and vice versa.
If someone is quiet then lucy is both happy and not happy and vice versa.
Everyone who is not tall or not wise is both funny and old.
If fred is not quiet or not kind then paul is either not wise or not curious and vice versa.
Everyone who is both generous and wise is not tall or funny and vice versa.
Everyone who is either old or creative is either not rich or not wise and vice versa.
Everyone who is either happy or not creative is humble or not funny and vice versa.
Everyone who is either quiet or generous is either not strong or not rich and vice versa.
Everyone who is funny is not strong and vice versa.
Everyone who is patient or not kind is not strong or not happy and vice versa.
If someone is not humble then someone is not strong.
If someone is either not tall or not humble then someone is not quiet.
Everyone who is quiet is not old or not quiet.
If someone is either not wise or humble then lucy is both not rich and funny.
Everyone who is not quiet or not old is not strong and vice versa.
Everyone who is not brave or not curious is brave or not humble.
Someone is not strong or not creative.
Mary is either old or quiet.
Susan is both not creative and calm.
Fred is strong or not kind.
Alice is tall.
John is either calm or generous.
Someone is both wise and not old. | Lucy is not humble. | entailment | (![X]:((~rich(X)&~quiet(X))<=>(~brave(X)<~>creative(X))))&
((?[X]:(quiet(X)))<=>((happy(lucy)&~happy(lucy))))&
(![X]:((~tall(X)|~wise(X))=>(funny(X)&old(X))))&
(((~quiet(fred)|~kind(fred)))<=>((~wise(paul)<~>~curious(paul))))&
(![X]:((generous(X)&wise(X))<=>(~tall(X)|funny(X))))&
(![X]:((old(X)<~>creative(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(humble(X)|~funny(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:(funny(X)<=>~strong(X)))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~old(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))=>((~rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>~strong(X)))&
(![X]:((~brave(X)|~curious(X))=>(brave(X)|~humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
((old(mary)<~>quiet(mary)))&
((~creative(susan)&calm(susan)))&
((strong(fred)|~kind(fred)))&
(tall(alice))&
((calm(john)<~>generous(john)))&
(?[X]:((wise(X)&~old(X)))) | ~humble(lucy) | [
"p1",
"p2",
"p4",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5371650689183559170900578
% SZS output start Proof for 5371650689183559170900578
2. ? [X0] : quiet(X0) <=> (~happy(lucy) & happy(lucy)) [input p1]
3. ! [X0] : ((~wise(X0) | ~tall(X0)) => (old(X0) & funny(X0))) [input p2]
5. ! [X0] : ((wise(X0) & generous(X0)) <=> (funny(X0) | ~tall(X0))) [input p4]
8. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~strong(X0) <~> ~rich(X0))) [input p7]
9. ! [X0] : (funny(X0) <=> ~strong(X0)) [input p8]
14. ? [X0] : (~wise(X0) <~> humble(X0)) => (funny(lucy) & ~rich(lucy)) [input p13]
15. ! [X0] : ((~old(X0) | ~quiet(X0)) <=> ~strong(X0)) [input p14]
24. humble(lucy) [input hypothesis]
27. ! [X0] : ((old(X0) & funny(X0)) | (wise(X0) & tall(X0))) [ennf transformation 3]
32. (funny(lucy) & ~rich(lucy)) | ! [X0] : (~wise(X0) <=> humble(X0)) [ennf transformation 14]
37. (? [X0] : quiet(X0) | (happy(lucy) | ~happy(lucy))) & ((~happy(lucy) & happy(lucy)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
38. (? [X0] : quiet(X0) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X0] : ~quiet(X0)) [flattening 37]
39. (? [X0] : quiet(X0) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X1] : ~quiet(X1)) [rectify 38]
40. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
41. (quiet(sK0) | happy(lucy) | ~happy(lucy)) & ((~happy(lucy) & happy(lucy)) | ! [X1] : ~quiet(X1)) [skolemisation 39,40]
44. ! [X0] : (((wise(X0) & generous(X0)) | (~funny(X0) & tall(X0))) & ((funny(X0) | ~tall(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 5]
45. ! [X0] : (((wise(X0) & generous(X0)) | (~funny(X0) & tall(X0))) & (funny(X0) | ~tall(X0) | ~wise(X0) | ~generous(X0))) [flattening 44]
49. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0)))) & (((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 8]
50. ! [X0] : ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))) [nnf transformation 9]
60. (funny(lucy) & ~rich(lucy)) | ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 32]
61. ! [X0] : (((~old(X0) | ~quiet(X0)) | strong(X0)) & (~strong(X0) | (old(X0) & quiet(X0)))) [nnf transformation 15]
62. ! [X0] : ((~old(X0) | ~quiet(X0) | strong(X0)) & (~strong(X0) | (old(X0) & quiet(X0)))) [flattening 61]
75. happy(lucy) | ~quiet(X1) [cnf transformation 41]
76. ~happy(lucy) | ~quiet(X1) [cnf transformation 41]
79. funny(X0) | wise(X0) [cnf transformation 27]
90. ~funny(X0) | generous(X0) [cnf transformation 45]
92. wise(X0) | ~funny(X0) [cnf transformation 45]
110. ~generous(X0) | strong(X0) | quiet(X0) | rich(X0) [cnf transformation 49]
116. strong(X0) | funny(X0) [cnf transformation 50]
126. ~rich(lucy) | ~wise(X0) | ~humble(X0) [cnf transformation 60]
129. ~strong(X0) | quiet(X0) [cnf transformation 62]
145. humble(lucy) [cnf transformation 24]
149. 1 <=> ! [X1] : ~quiet(X1) [avatar definition]
150. ~quiet(X1) <- (1) [avatar component clause 149]
152. 2 <=> happy(lucy) [avatar definition]
155. 1 | ~2 [avatar split clause 76,152,149]
156. 1 | 2 [avatar split clause 75,152,149]
179. wise(X0) [subsumption resolution 92,79]
208. 12 <=> ! [X0] : ~humble(X0) [avatar definition]
209. ~humble(X0) <- (12) [avatar component clause 208]
215. ~rich(lucy) | ~humble(X0) [subsumption resolution 126,179]
217. 14 <=> rich(lucy) [avatar definition]
219. ~rich(lucy) <- (~14) [avatar component clause 217]
220. 12 | ~14 [avatar split clause 215,217,208]
256. $false <- (12) [resolution 209,145]
257. ~12 [avatar contradiction clause 256]
267. quiet(X0) | funny(X0) [resolution 129,116]
268. funny(X0) <- (1) [subsumption resolution 267,150]
271. generous(X0) <- (1) [resolution 268,90]
373. strong(X0) | quiet(X0) | rich(X0) <- (1) [resolution 110,271]
379. strong(X0) | rich(X0) <- (1) [subsumption resolution 373,150]
386. rich(X4) | quiet(X4) <- (1) [resolution 379,129]
388. rich(X4) <- (1) [subsumption resolution 386,150]
429. $false <- (1, ~14) [resolution 388,219]
435. ~1 | 14 [avatar contradiction clause 429]
436. $false [avatar sat refutation 155,156,220,257,435]
% SZS output end Proof for 5371650689183559170900578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not wise is happy and vice versa. Everyone who is either happy or quiet is either not calm or wise. If someone is both not rich and creative then someone is both creative and not brave and vice versa. If someone is not curious then alice is not happy and vice versa. If someone is either not creative or not funny then susan is calm. Everyone who is either rich or generous is not curious or not creative. Everyone who is curious or not kind is either not rich or not calm. If lucy is not kind or funny then someone is either rich or not wise. Everyone who is tall is both humble and not humble and vice versa. Everyone who is either not creative or not quiet is tall and vice versa. If someone is not generous then someone is kind or not old. Everyone who is both not funny and rich is not patient or not brave and vice versa. Everyone who is either brave or tall is not kind or happy. Everyone who is either kind or patient is tall or not quiet and vice versa. Everyone who is both happy and not tall is generous or calm. Everyone who is either not creative or not happy is not wise. Someone is not happy. Someone is both not old and wise. Fred is either creative or not calm. John is both not happy and kind. John is either generous or not generous. Fred is creative. Someone is not kind or not happy. Someone is not strong. | Lucy is tall. | contradiction | (![X]:((tall(X)|~wise(X))<=>happy(X)))&
(![X]:((happy(X)<~>quiet(X))=>(~calm(X)<~>wise(X))))&
((?[X]:((~rich(X)&creative(X))))<=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:(~curious(X)))<=>(~happy(alice)))&
((?[X]:((~creative(X)<~>~funny(X))))=>(calm(susan)))&
(![X]:((rich(X)<~>generous(X))=>(~curious(X)|~creative(X))))&
(![X]:((curious(X)|~kind(X))=>(~rich(X)<~>~calm(X))))&
(((~kind(lucy)|funny(lucy)))=>(?[X]:((rich(X)<~>~wise(X)))))&
(![X]:(tall(X)<=>(humble(X)&~humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>tall(X)))&
((?[X]:(~generous(X)))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((~funny(X)&rich(X))<=>(~patient(X)|~brave(X))))&
(![X]:((brave(X)<~>tall(X))=>(~kind(X)|happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>(tall(X)|~quiet(X))))&
(![X]:((happy(X)&~tall(X))=>(generous(X)|calm(X))))&
(![X]:((~creative(X)<~>~happy(X))=>~wise(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~old(X)&wise(X))))&
((creative(fred)<~>~calm(fred)))&
((~happy(john)&kind(john)))&
((generous(john)<~>~generous(john)))&
(creative(fred))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:(~strong(X))) | tall(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 61571045015888961452381
% SZS output start Proof for 61571045015888961452381
9. ! [X0] : (tall(X0) <=> (~humble(X0) & humble(X0))) [input p8]
25. tall(lucy) [input hypothesis]
60. ! [X0] : ((tall(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 9]
61. ! [X0] : ((tall(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [flattening 60]
102. humble(X0) | ~tall(X0) [cnf transformation 61]
103. ~humble(X0) | ~tall(X0) [cnf transformation 61]
135. tall(lucy) [cnf transformation 25]
209. ~tall(X0) [subsumption resolution 102,103]
237. $false [subsumption resolution 135,209]
% SZS output end Proof for 61571045015888961452381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or funny is both not wise and tall.
If paul is either not strong or not quiet then someone is either not kind or quiet.
If someone is not calm then someone is curious or quiet.
If lucy is both rich and not creative then someone is calm.
Everyone who is kind or not creative is both strong and not funny and vice versa.
If someone is either humble or not rich then someone is both not creative and tall and vice versa.
Everyone who is either not funny or not old is not tall or creative.
Everyone who is both wise and quiet is not happy and vice versa.
Everyone who is tall or not calm is wise.
Everyone who is either not creative or not generous is quiet or curious.
Everyone who is funny or not happy is funny.
Everyone who is not wise is old and vice versa.
Everyone who is both not quiet and not funny is either wise or rich.
If someone is both not quiet and wise then someone is rich.
If someone is happy then mary is either humble or not quiet and vice versa.
Everyone who is either not strong or not happy is both quiet and not old and vice versa.
Someone is both not funny and wise.
Someone is not old.
Someone is not creative or not patient.
Someone is both not generous and not tall.
Paul is not humble.
Someone is rich or strong. | Lucy is rich. | neutral | (![X]:((~kind(X)|funny(X))=>(~wise(X)&tall(X))))&
(((~strong(paul)<~>~quiet(paul)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((curious(X)|quiet(X)))))&
(((rich(lucy)&~creative(lucy)))=>(?[X]:(calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(strong(X)&~funny(X))))&
((?[X]:((humble(X)<~>~rich(X))))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((~funny(X)<~>~old(X))=>(~tall(X)|creative(X))))&
(![X]:((wise(X)&quiet(X))<=>~happy(X)))&
(![X]:((tall(X)|~calm(X))=>wise(X)))&
(![X]:((~creative(X)<~>~generous(X))=>(quiet(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))=>funny(X)))&
(![X]:(~wise(X)<=>old(X)))&
(![X]:((~quiet(X)&~funny(X))=>(wise(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))=>(?[X]:(rich(X))))&
((?[X]:(happy(X)))<=>((humble(mary)<~>~quiet(mary))))&
(![X]:((~strong(X)<~>~happy(X))<=>(quiet(X)&~old(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)|~patient(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(~humble(paul))&
(?[X]:((rich(X)|strong(X)))) | rich(lucy) | [] | null | 0 |
If john is not calm then mary is not kind or happy.
Everyone who is not funny or not wise is both funny and not humble.
If someone is humble or not tall then someone is either not tall or not patient.
Everyone who is both not strong and not tall is either not creative or funny and vice versa.
If fred is both tall and humble then someone is either kind or not strong.
If someone is either funny or curious then mary is either generous or wise.
Everyone who is either not happy or calm is either happy or humble.
Everyone who is either strong or not humble is either happy or tall and vice versa.
Everyone who is both calm and funny is both happy and not curious and vice versa.
Everyone who is not funny is either humble or not wise and vice versa.
If fred is not kind then someone is curious or not patient and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
Everyone who is both not creative and rich is both not creative and not strong.
If lucy is either not humble or generous then someone is either kind or generous and vice versa.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Paul is not quiet or not rich.
Mary is curious or humble.
Someone is either quiet or curious.
Susan is rich or not strong.
Susan is not brave or rich. | Fred is not curious. | neutral | ((~calm(john))=>((~kind(mary)|happy(mary))))&
(![X]:((~funny(X)|~wise(X))=>(funny(X)&~humble(X))))&
((?[X]:((humble(X)|~tall(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(~creative(X)<~>funny(X))))&
(((tall(fred)&humble(fred)))=>(?[X]:((kind(X)<~>~strong(X)))))&
((?[X]:((funny(X)<~>curious(X))))=>((generous(mary)<~>wise(mary))))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)<~>humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)<~>tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
((~kind(fred))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
(![X]:((~creative(X)&rich(X))=>(~creative(X)&~strong(X))))&
(((~humble(lucy)<~>generous(lucy)))<=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
((~quiet(paul)|~rich(paul)))&
((curious(mary)|humble(mary)))&
(?[X]:((quiet(X)<~>curious(X))))&
((rich(susan)|~strong(susan)))&
((~brave(susan)|rich(susan))) | ~curious(fred) | [] | null | 0 |
Everyone who is either quiet or not happy is not patient and vice versa. Everyone who is either not patient or not generous is patient and vice versa. Everyone who is funny or not brave is both not generous and kind. If susan is happy then john is either not quiet or humble. If mary is both not strong and brave then paul is either not calm or not patient. Everyone who is not generous is not quiet and vice versa. Everyone who is kind is quiet or not quiet and vice versa. If mary is not calm or generous then someone is funny or not brave and vice versa. Everyone who is tall is either funny or not calm. Everyone who is both not happy and not generous is either quiet or rich and vice versa. Everyone who is not old or funny is not quiet or not funny and vice versa. If someone is curious then someone is not humble or happy and vice versa. Everyone who is calm or not curious is not calm. If susan is quiet or patient then someone is both not old and humble. Everyone who is both brave and creative is both old and strong. Everyone who is wise or not generous is both rich and not strong and vice versa. John is not wise. Fred is old. Someone is kind or not calm. John is not calm or not patient. Paul is brave. Someone is tall. Fred is either humble or not humble. | Paul is not generous. | entailment | (![X]:((quiet(X)<~>~happy(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>~generous(X))<=>patient(X)))&
(![X]:((funny(X)|~brave(X))=>(~generous(X)&kind(X))))&
((happy(susan))=>((~quiet(john)<~>humble(john))))&
(((~strong(mary)&brave(mary)))=>((~calm(paul)<~>~patient(paul))))&
(![X]:(~generous(X)<=>~quiet(X)))&
(![X]:(kind(X)<=>(quiet(X)|~quiet(X))))&
(((~calm(mary)|generous(mary)))<=>(?[X]:((funny(X)|~brave(X)))))&
(![X]:(tall(X)=>(funny(X)<~>~calm(X))))&
(![X]:((~happy(X)&~generous(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~old(X)|funny(X))<=>(~quiet(X)|~funny(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|happy(X)))))&
(![X]:((calm(X)|~curious(X))=>~calm(X)))&
(((quiet(susan)|patient(susan)))=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((brave(X)&creative(X))=>(old(X)&strong(X))))&
(![X]:((wise(X)|~generous(X))<=>(rich(X)&~strong(X))))&
(~wise(john))&
(old(fred))&
(?[X]:((kind(X)|~calm(X))))&
((~calm(john)|~patient(john)))&
(brave(paul))&
(?[X]:(tall(X)))&
((humble(fred)<~>~humble(fred))) | ~generous(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2846702345695439780991656
% SZS output start Proof for 2846702345695439780991656
2. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> patient(X0)) [input p1]
24. generous(paul) [input hypothesis]
38. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 2]
70. patient(X0) | ~generous(X0) | patient(X0) [cnf transformation 38]
72. ~generous(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 38]
123. generous(paul) [cnf transformation 24]
127. patient(X0) | ~generous(X0) [duplicate literal removal 70]
128. ~generous(X0) | ~patient(X0) [duplicate literal removal 72]
129. ~generous(X0) [subsumption resolution 127,128]
229. $false [subsumption resolution 123,129]
% SZS output end Proof for 2846702345695439780991656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If mary is funny then fred is not humble and vice versa.
Everyone who is both not calm and not strong is not brave or generous and vice versa.
Everyone who is not curious is both brave and not tall and vice versa.
Everyone who is either not calm or not creative is not strong or calm and vice versa.
Everyone who is either not strong or kind is both not tall and not creative and vice versa.
If fred is either not curious or not funny then fred is either not humble or humble.
If someone is not generous or rich then john is creative or not brave.
If paul is both not generous and humble then john is not kind.
Everyone who is both generous and not calm is not kind and vice versa.
Everyone who is quiet is patient or curious.
If someone is either not strong or not creative then someone is either humble or not curious.
Everyone who is not curious is calm or patient and vice versa.
Everyone who is both old and not brave is either creative or not old and vice versa.
Everyone who is both creative and not generous is old and vice versa.
Everyone who is either old or not happy is not creative and vice versa.
John is funny or patient.
Susan is old or happy.
Someone is either not rich or humble.
Someone is not funny. | Fred is generous. | contradiction | ((funny(mary))<=>(~humble(fred)))&
(![X]:((~calm(X)&~strong(X))<=>(~brave(X)|generous(X))))&
(![X]:(~curious(X)<=>(brave(X)&~tall(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~tall(X)&~creative(X))))&
(((~curious(fred)<~>~funny(fred)))=>((~humble(fred)<~>humble(fred))))&
((?[X]:((~generous(X)|rich(X))))=>((creative(john)|~brave(john))))&
(((~generous(paul)&humble(paul)))=>(~kind(john)))&
(![X]:((generous(X)&~calm(X))<=>~kind(X)))&
(![X]:(quiet(X)=>(patient(X)|curious(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>(calm(X)|patient(X))))&
(![X]:((old(X)&~brave(X))<=>(creative(X)<~>~old(X))))&
(![X]:((creative(X)&~generous(X))<=>old(X)))&
(![X]:((old(X)<~>~happy(X))<=>~creative(X)))&
((funny(john)|patient(john)))&
((old(susan)|happy(susan)))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~funny(X))) | generous(fred) | [
"p1",
"p3",
"p4",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7903472386070368641435147
% SZS output start Proof for 7903472386070368641435147
2. ! [X0] : ((~strong(X0) & ~calm(X0)) <=> (generous(X0) | ~brave(X0))) [input p1]
4. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (calm(X0) | ~strong(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~creative(X0) & ~tall(X0))) [input p4]
9. ! [X0] : ((~calm(X0) & generous(X0)) <=> ~kind(X0)) [input p8]
13. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p12]
14. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p13]
20. generous(fred) [input hypothesis]
30. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (strong(X0) | calm(X0)))) [nnf transformation 2]
31. ! [X0] : (((~strong(X0) & ~calm(X0)) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | strong(X0) | calm(X0))) [flattening 30]
34. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 4]
35. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 34]
36. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 36]
39. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 9]
40. ! [X0] : (((~calm(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | calm(X0) | ~generous(X0))) [flattening 39]
47. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (brave(X0) | ~old(X0)))) [nnf transformation 13]
48. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | brave(X0) | ~old(X0))) [flattening 47]
49. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 14]
50. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 49]
61. ~generous(X0) | ~calm(X0) [cnf transformation 31]
67. calm(X0) | ~strong(X0) | ~creative(X0) | calm(X0) [cnf transformation 35]
70. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 35]
75. ~creative(X0) | kind(X0) | strong(X0) [cnf transformation 37]
86. ~kind(X0) | calm(X0) | ~generous(X0) [cnf transformation 40]
99. old(X0) | creative(X0) | old(X0) [cnf transformation 48]
103. creative(X0) | ~old(X0) [cnf transformation 50]
114. generous(fred) [cnf transformation 20]
116. old(X0) | creative(X0) [duplicate literal removal 99]
117. calm(X0) | ~strong(X0) | ~creative(X0) [duplicate literal removal 67]
118. ~creative(X0) | ~calm(X0) [duplicate literal removal 70]
129. ~creative(X0) | ~strong(X0) [subsumption resolution 117,118]
131. ~creative(X0) | kind(X0) [subsumption resolution 75,129]
161. ~kind(X0) | ~generous(X0) [subsumption resolution 86,61]
185. creative(X0) [subsumption resolution 103,116]
219. kind(X0) [resolution 131,185]
222. ~generous(X0) [resolution 219,161]
224. $false [resolution 222,114]
% SZS output end Proof for 7903472386070368641435147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is patient or not generous then susan is either generous or not tall.
If someone is both not quiet and brave then someone is either not generous or brave.
If someone is generous then someone is not brave.
Everyone who is either wise or not creative is not humble or kind and vice versa.
If lucy is either happy or not happy then john is humble or strong and vice versa.
Everyone who is not rich is either not brave or not wise.
Everyone who is either not funny or not generous is not calm or not creative.
If someone is either not creative or not kind then someone is calm.
Everyone who is both not wise and kind is both curious and not curious and vice versa.
Everyone who is strong or not quiet is both not wise and not strong and vice versa.
Everyone who is kind or calm is not happy and vice versa.
If lucy is not kind or not curious then susan is not old or not strong.
If someone is either not wise or not happy then john is either not wise or not patient and vice versa.
If john is either calm or not curious then someone is not humble or brave and vice versa.
If someone is not patient or not happy then someone is either strong or not patient and vice versa.
Someone is not kind or not strong.
Mary is either funny or not rich.
Someone is both not happy and not kind.
John is both not generous and old.
Lucy is both tall and not patient.
Someone is both quiet and not patient.
John is quiet or tall.
Someone is not happy. | Lucy is not strong. | entailment | (((patient(paul)|~generous(paul)))=>((generous(susan)<~>~tall(susan))))&
((?[X]:((~quiet(X)&brave(X))))=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:(generous(X)))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)<~>~creative(X))<=>(~humble(X)|kind(X))))&
(((happy(lucy)<~>~happy(lucy)))<=>((humble(john)|strong(john))))&
(![X]:(~rich(X)=>(~brave(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(~calm(X)|~creative(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:(calm(X))))&
(![X]:((~wise(X)&kind(X))<=>(curious(X)&~curious(X))))&
(![X]:((strong(X)|~quiet(X))<=>(~wise(X)&~strong(X))))&
(![X]:((kind(X)|calm(X))<=>~happy(X)))&
(((~kind(lucy)|~curious(lucy)))=>((~old(susan)|~strong(susan))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~wise(john)<~>~patient(john))))&
(((calm(john)<~>~curious(john)))<=>(?[X]:((~humble(X)|brave(X)))))&
((?[X]:((~patient(X)|~happy(X))))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(?[X]:((~kind(X)|~strong(X))))&
((funny(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)&~kind(X))))&
((~generous(john)&old(john)))&
((tall(lucy)&~patient(lucy)))&
(?[X]:((quiet(X)&~patient(X))))&
((quiet(john)|tall(john)))&
(?[X]:(~happy(X))) | ~strong(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4601602636553560618556611
% SZS output start Proof for 4601602636553560618556611
10. ! [X0] : ((~quiet(X0) | strong(X0)) <=> (~strong(X0) & ~wise(X0))) [input p9]
24. strong(lucy) [input hypothesis]
58. ! [X0] : (((~quiet(X0) | strong(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (quiet(X0) & ~strong(X0)))) [nnf transformation 10]
59. ! [X0] : ((~quiet(X0) | strong(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (quiet(X0) & ~strong(X0)))) [flattening 58]
115. ~strong(X0) | ~strong(X0) [cnf transformation 59]
156. strong(lucy) [cnf transformation 24]
157. ~strong(X0) [duplicate literal removal 115]
330. $false [subsumption resolution 156,157]
% SZS output end Proof for 4601602636553560618556611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not old is patient.
If paul is funny or not old then paul is both curious and quiet.
Everyone who is either humble or patient is not humble or funny and vice versa.
If someone is not generous then someone is not quiet or not kind and vice versa.
If susan is not wise or brave then susan is both tall and not generous.
If someone is strong then someone is tall or not old and vice versa.
If someone is both humble and creative then fred is both tall and quiet.
Everyone who is humble is either calm or curious and vice versa.
Everyone who is not tall is not quiet or not calm and vice versa.
Everyone who is happy is calm and vice versa.
If lucy is funny or calm then fred is not wise or not funny and vice versa.
Everyone who is both happy and humble is not brave.
Everyone who is both not curious and patient is not rich or not old.
Everyone who is both not calm and generous is not humble.
Everyone who is both not curious and humble is funny.
Everyone who is not generous is either funny or not wise.
John is creative.
Someone is either humble or kind.
Susan is not wise.
Someone is not generous.
Lucy is both not patient and not wise.
Someone is not humble.
Alice is curious.
Someone is either creative or wise. | Susan is quiet. | entailment | (![X]:((~happy(X)&~old(X))=>patient(X)))&
(((funny(paul)|~old(paul)))=>((curious(paul)&quiet(paul))))&
(![X]:((humble(X)<~>patient(X))<=>(~humble(X)|funny(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~quiet(X)|~kind(X)))))&
(((~wise(susan)|brave(susan)))=>((tall(susan)&~generous(susan))))&
((?[X]:(strong(X)))<=>(?[X]:((tall(X)|~old(X)))))&
((?[X]:((humble(X)&creative(X))))=>((tall(fred)&quiet(fred))))&
(![X]:(humble(X)<=>(calm(X)<~>curious(X))))&
(![X]:(~tall(X)<=>(~quiet(X)|~calm(X))))&
(![X]:(happy(X)<=>calm(X)))&
(((funny(lucy)|calm(lucy)))<=>((~wise(fred)|~funny(fred))))&
(![X]:((happy(X)&humble(X))=>~brave(X)))&
(![X]:((~curious(X)&patient(X))=>(~rich(X)|~old(X))))&
(![X]:((~calm(X)&generous(X))=>~humble(X)))&
(![X]:((~curious(X)&humble(X))=>funny(X)))&
(![X]:(~generous(X)=>(funny(X)<~>~wise(X))))&
(creative(john))&
(?[X]:((humble(X)<~>kind(X))))&
(~wise(susan))&
(?[X]:(~generous(X)))&
((~patient(lucy)&~wise(lucy)))&
(?[X]:(~humble(X)))&
(curious(alice))&
(?[X]:((creative(X)<~>wise(X)))) | quiet(susan) | [
"p4",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5973537426387048961559796
% SZS output start Proof for 5973537426387048961559796
5. (brave(susan) | ~wise(susan)) => (~generous(susan) & tall(susan)) [input p4]
9. ! [X0] : (~tall(X0) <=> (~calm(X0) | ~quiet(X0))) [input p8]
19. ~wise(susan) [input p18]
25. ~quiet(susan) [input hypothesis]
29. ~wise(susan) => (~generous(susan) & tall(susan)) [pure predicate removal 5]
35. (~generous(susan) & tall(susan)) | wise(susan) [ennf transformation 29]
56. ! [X0] : ((~tall(X0) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | tall(X0))) [nnf transformation 9]
57. ! [X0] : ((~tall(X0) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | tall(X0))) [flattening 56]
85. tall(susan) | wise(susan) [cnf transformation 35]
97. ~tall(X0) | quiet(X0) [cnf transformation 57]
111. ~wise(susan) [cnf transformation 19]
119. ~quiet(susan) [cnf transformation 25]
168. 11 <=> wise(susan) [avatar definition]
177. 13 <=> tall(susan) [avatar definition]
179. tall(susan) <- (13) [avatar component clause 177]
180. 11 | 13 [avatar split clause 85,177,168]
248. ~11 [avatar split clause 111,168]
259. quiet(susan) <- (13) [resolution 97,179]
260. $false <- (13) [subsumption resolution 259,119]
261. ~13 [avatar contradiction clause 260]
262. $false [avatar sat refutation 180,248,261]
% SZS output end Proof for 5973537426387048961559796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is both not tall and humble and vice versa.
Everyone who is both quiet and not brave is either not funny or brave and vice versa.
Everyone who is either funny or rich is happy.
If someone is not funny then someone is either not calm or not patient.
If mary is both happy and funny then someone is both not kind and creative and vice versa.
Everyone who is either calm or old is both not patient and patient and vice versa.
Everyone who is not wise is patient.
If alice is either patient or rich then someone is not curious and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not creative and curious is either not tall or not funny and vice versa.
If someone is rich then someone is both not kind and patient.
Everyone who is not old is both quiet and not wise.
Everyone who is both generous and not quiet is not patient and vice versa.
Everyone who is either tall or not creative is funny or not patient and vice versa.
If someone is either generous or tall then fred is not patient.
If someone is either not patient or curious then someone is both not curious and not calm and vice versa.
Mary is both strong and old.
Lucy is both not quiet and rich.
Susan is either humble or not wise.
Lucy is happy.
Someone is patient or wise.
Someone is creative.
Someone is not kind or strong.
John is brave. | Fred is wise. | neutral | (![X]:((wise(X)|quiet(X))<=>(~tall(X)&humble(X))))&
(![X]:((quiet(X)&~brave(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>happy(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((calm(X)<~>old(X))<=>(~patient(X)&patient(X))))&
(![X]:(~wise(X)=>patient(X)))&
(((patient(alice)<~>rich(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~creative(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:(~old(X)=>(quiet(X)&~wise(X))))&
(![X]:((generous(X)&~quiet(X))<=>~patient(X)))&
(![X]:((tall(X)<~>~creative(X))<=>(funny(X)|~patient(X))))&
((?[X]:((generous(X)<~>tall(X))))=>(~patient(fred)))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((~curious(X)&~calm(X)))))&
((strong(mary)&old(mary)))&
((~quiet(lucy)&rich(lucy)))&
((humble(susan)<~>~wise(susan)))&
(happy(lucy))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|strong(X))))&
(brave(john)) | wise(fred) | [] | null | 0 |
If someone is both not kind and not funny then alice is either not funny or not rich. If fred is curious then someone is creative or not happy and vice versa. If someone is either not patient or curious then someone is not humble. Everyone who is either generous or brave is wise and vice versa. If susan is both not happy and kind then someone is either not calm or wise and vice versa. Everyone who is either happy or not humble is humble or tall and vice versa. Everyone who is kind or calm is both patient and not quiet and vice versa. Everyone who is not rich or happy is not kind. Everyone who is either patient or generous is both kind and happy and vice versa. If john is either not rich or old then paul is either humble or rich and vice versa. If someone is both creative and quiet then someone is rich and vice versa. Everyone who is calm is kind. If someone is either not funny or happy then paul is both rich and not old and vice versa. If someone is both not old and tall then paul is generous and vice versa. If someone is not humble or brave then susan is rich or not curious. Everyone who is happy is calm and vice versa. Someone is either not curious or old. Someone is either generous or wise. Alice is either not kind or not creative. Someone is wise or not patient. Lucy is either curious or rich. | Fred is not tall. | contradiction | ((?[X]:((~kind(X)&~funny(X))))=>((~funny(alice)<~>~rich(alice))))&
((curious(fred))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~patient(X)<~>curious(X))))=>(?[X]:(~humble(X))))&
(![X]:((generous(X)<~>brave(X))<=>wise(X)))&
(((~happy(susan)&kind(susan)))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(humble(X)|tall(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&~quiet(X))))&
(![X]:((~rich(X)|happy(X))=>~kind(X)))&
(![X]:((patient(X)<~>generous(X))<=>(kind(X)&happy(X))))&
(((~rich(john)<~>old(john)))<=>((humble(paul)<~>rich(paul))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:(calm(X)=>kind(X)))&
((?[X]:((~funny(X)<~>happy(X))))<=>((rich(paul)&~old(paul))))&
((?[X]:((~old(X)&tall(X))))<=>(generous(paul)))&
((?[X]:((~humble(X)|brave(X))))=>((rich(susan)|~curious(susan))))&
(![X]:(happy(X)<=>calm(X)))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((generous(X)<~>wise(X))))&
((~kind(alice)<~>~creative(alice)))&
(?[X]:((wise(X)|~patient(X))))&
((curious(lucy)<~>rich(lucy))) | ~tall(fred) | [
"p5",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1351903816690566071128552
% SZS output start Proof for 1351903816690566071128552
6. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> (tall(X0) | humble(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~rich(X0)) => ~kind(X0)) [input p7]
12. ! [X0] : (calm(X0) => kind(X0)) [input p11]
16. ! [X0] : (happy(X0) <=> calm(X0)) [input p15]
22. ~tall(fred) [input hypothesis]
27. ! [X0] : (~kind(X0) | (~happy(X0) & rich(X0))) [ennf transformation 8]
28. ! [X0] : (kind(X0) | ~calm(X0)) [ennf transformation 12]
46. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 6]
47. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [flattening 46]
67. ! [X0] : ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))) [nnf transformation 16]
96. tall(X0) | humble(X0) | happy(X0) | humble(X0) [cnf transformation 47]
97. ~humble(X0) | happy(X0) | ~humble(X0) [cnf transformation 47]
107. ~happy(X0) | ~kind(X0) [cnf transformation 27]
125. ~calm(X0) | kind(X0) [cnf transformation 28]
137. ~happy(X0) | calm(X0) [cnf transformation 67]
148. ~tall(fred) [cnf transformation 22]
149. tall(X0) | humble(X0) | happy(X0) [duplicate literal removal 96]
150. ~humble(X0) | happy(X0) [duplicate literal removal 97]
225. tall(X0) | happy(X0) [subsumption resolution 149,150]
407. happy(fred) [resolution 225,148]
408. calm(fred) [resolution 407,137]
409. ~kind(fred) [resolution 407,107]
463. kind(fred) [resolution 408,125]
465. $false [subsumption resolution 463,409]
% SZS output end Proof for 1351903816690566071128552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not wise and not kind then lucy is not rich or calm and vice versa. If john is both not humble and funny then someone is not curious or generous and vice versa. If alice is rich or humble then paul is either not curious or patient. If someone is not kind or not humble then fred is either kind or not patient and vice versa. If someone is either not quiet or tall then someone is either strong or not rich. Everyone who is both rich and funny is both not funny and not calm. If someone is wise then alice is creative or not kind and vice versa. Everyone who is not quiet is not creative or not old and vice versa. Everyone who is both not happy and not curious is rich and vice versa. If someone is both funny and not happy then mary is both quiet and calm. If someone is either not tall or old then mary is not quiet or patient. If someone is both generous and not calm then lucy is not rich and vice versa. Everyone who is not strong or happy is either calm or not strong. Everyone who is generous is either quiet or not generous and vice versa. Everyone who is both creative and not tall is either not funny or not strong. Lucy is either not patient or tall. John is not wise or not creative. Susan is either patient or calm. Someone is both brave and not kind. Alice is both not strong and generous. Someone is both funny and generous. Alice is quiet or humble. | John is not creative. | contradiction | (((~wise(lucy)&~kind(lucy)))<=>((~rich(lucy)|calm(lucy))))&
(((~humble(john)&funny(john)))<=>(?[X]:((~curious(X)|generous(X)))))&
(((rich(alice)|humble(alice)))=>((~curious(paul)<~>patient(paul))))&
((?[X]:((~kind(X)|~humble(X))))<=>((kind(fred)<~>~patient(fred))))&
((?[X]:((~quiet(X)<~>tall(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((rich(X)&funny(X))=>(~funny(X)&~calm(X))))&
((?[X]:(wise(X)))<=>((creative(alice)|~kind(alice))))&
(![X]:(~quiet(X)<=>(~creative(X)|~old(X))))&
(![X]:((~happy(X)&~curious(X))<=>rich(X)))&
((?[X]:((funny(X)&~happy(X))))=>((quiet(mary)&calm(mary))))&
((?[X]:((~tall(X)<~>old(X))))=>((~quiet(mary)|patient(mary))))&
((?[X]:((generous(X)&~calm(X))))<=>(~rich(lucy)))&
(![X]:((~strong(X)|happy(X))=>(calm(X)<~>~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
((~patient(lucy)<~>tall(lucy)))&
((~wise(john)|~creative(john)))&
((patient(susan)<~>calm(susan)))&
(?[X]:((brave(X)&~kind(X))))&
((~strong(alice)&generous(alice)))&
(?[X]:((funny(X)&generous(X))))&
((quiet(alice)|humble(alice))) | ~creative(john) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7445035563046764821139874
% SZS output start Proof for 7445035563046764821139874
8. ! [X0] : (~quiet(X0) <=> (~old(X0) | ~creative(X0))) [input p7]
14. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p13]
23. ~creative(john) [input hypothesis]
57. ! [X0] : ((~quiet(X0) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | quiet(X0))) [nnf transformation 8]
58. ! [X0] : ((~quiet(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | quiet(X0))) [flattening 57]
67. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 14]
105. ~quiet(X0) | creative(X0) [cnf transformation 58]
121. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 67]
124. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 67]
138. ~creative(john) [cnf transformation 23]
139. ~generous(X0) | quiet(X0) [duplicate literal removal 121]
140. generous(X0) | quiet(X0) [duplicate literal removal 124]
314. quiet(X0) [subsumption resolution 139,140]
330. 41 <=> creative(john) [avatar definition]
332. ~creative(john) <- (~41) [avatar component clause 330]
344. ~41 [avatar split clause 138,330]
347. creative(X0) [resolution 105,314]
348. $false <- (~41) [resolution 347,332]
349. 41 [avatar contradiction clause 348]
350. $false [avatar sat refutation 344,349]
% SZS output end Proof for 7445035563046764821139874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not kind then someone is both wise and rich and vice versa.
If someone is both not generous and rich then someone is not creative and vice versa.
Everyone who is wise is both funny and not kind and vice versa.
Everyone who is not patient or not generous is both not tall and not generous and vice versa.
Everyone who is either not curious or happy is both brave and wise and vice versa.
If someone is not creative then someone is not old or quiet and vice versa.
If someone is either happy or not brave then mary is happy and vice versa.
Everyone who is either kind or not strong is both not rich and happy and vice versa.
If someone is old then john is either patient or not wise.
If alice is happy then someone is humble or calm and vice versa.
If john is both not patient and quiet then someone is brave or rich and vice versa.
Everyone who is both tall and wise is patient or not calm and vice versa.
Everyone who is both tall and not curious is both tall and wise.
Everyone who is both not brave and wise is both strong and wise.
Everyone who is not kind is both not calm and quiet and vice versa.
Everyone who is either funny or not creative is both creative and not kind and vice versa.
Someone is either not old or not brave.
Someone is generous or not patient.
Someone is either not funny or not happy.
Someone is both patient and not calm.
Someone is not strong. | John is wise. | contradiction | (((~happy(fred)|~kind(fred)))<=>(?[X]:((wise(X)&rich(X)))))&
((?[X]:((~generous(X)&rich(X))))<=>(?[X]:(~creative(X))))&
(![X]:(wise(X)<=>(funny(X)&~kind(X))))&
(![X]:((~patient(X)|~generous(X))<=>(~tall(X)&~generous(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(brave(X)&wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(happy(mary)))&
(![X]:((kind(X)<~>~strong(X))<=>(~rich(X)&happy(X))))&
((?[X]:(old(X)))=>((patient(john)<~>~wise(john))))&
((happy(alice))<=>(?[X]:((humble(X)|calm(X)))))&
(((~patient(john)&quiet(john)))<=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((tall(X)&wise(X))<=>(patient(X)|~calm(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)&wise(X))))&
(![X]:((~brave(X)&wise(X))=>(strong(X)&wise(X))))&
(![X]:(~kind(X)<=>(~calm(X)&quiet(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~kind(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
(?[X]:((generous(X)|~patient(X))))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(~strong(X))) | wise(john) | [
"p1",
"p2",
"p3",
"p5",
"p10",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7326003089161832100641498
% SZS output start Proof for 7326003089161832100641498
2. ? [X0] : (rich(X0) & ~generous(X0)) <=> ? [X0] : ~creative(X0) [input p1]
3. ! [X0] : (wise(X0) <=> (~kind(X0) & funny(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~generous(X0) & ~tall(X0))) [input p3]
6. ? [X0] : ~creative(X0) <=> ? [X0] : (quiet(X0) | ~old(X0)) [input p5]
11. (quiet(john) & ~patient(john)) <=> ? [X0] : (rich(X0) | brave(X0)) [input p10]
12. ! [X0] : ((wise(X0) & tall(X0)) <=> (~calm(X0) | patient(X0))) [input p11]
15. ! [X0] : (~kind(X0) <=> (quiet(X0) & ~calm(X0))) [input p14]
20. ? [X0] : (~calm(X0) & patient(X0)) [input p19]
22. wise(john) [input hypothesis]
23. ? [X0] : (rich(X0) & ~generous(X0)) <=> ? [X1] : ~creative(X1) [rectify 2]
24. ? [X0] : ~creative(X0) <=> ? [X1] : (quiet(X1) | ~old(X1)) [rectify 6]
35. (? [X0] : (rich(X0) & ~generous(X0)) | ! [X1] : creative(X1)) & (? [X1] : ~creative(X1) | ! [X0] : (~rich(X0) | generous(X0))) [nnf transformation 23]
36. (? [X0] : (rich(X0) & ~generous(X0)) | ! [X1] : creative(X1)) & (? [X2] : ~creative(X2) | ! [X3] : (~rich(X3) | generous(X3))) [rectify 35]
37. ? [X0] : (rich(X0) & ~generous(X0)) => (rich(sK1) & ~generous(sK1)) [choice axiom]
38. ? [X2] : ~creative(X2) => ~creative(sK2) [choice axiom]
39. ((rich(sK1) & ~generous(sK1)) | ! [X1] : creative(X1)) & (~creative(sK2) | ! [X3] : (~rich(X3) | generous(X3))) [skolemisation 36,38,37]
40. ! [X0] : ((wise(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | ~wise(X0))) [nnf transformation 3]
41. ! [X0] : ((wise(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | ~wise(X0))) [flattening 40]
42. ! [X0] : (((~generous(X0) | ~patient(X0)) | (generous(X0) | tall(X0))) & ((~generous(X0) & ~tall(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 4]
43. ! [X0] : ((~generous(X0) | ~patient(X0) | generous(X0) | tall(X0)) & ((~generous(X0) & ~tall(X0)) | (generous(X0) & patient(X0)))) [flattening 42]
46. (? [X0] : ~creative(X0) | ! [X1] : (~quiet(X1) & old(X1))) & (? [X1] : (quiet(X1) | ~old(X1)) | ! [X0] : creative(X0)) [nnf transformation 24]
47. (? [X0] : ~creative(X0) | ! [X1] : (~quiet(X1) & old(X1))) & (? [X2] : (quiet(X2) | ~old(X2)) | ! [X3] : creative(X3)) [rectify 46]
48. ? [X0] : ~creative(X0) => ~creative(sK3) [choice axiom]
49. ? [X2] : (quiet(X2) | ~old(X2)) => (quiet(sK4) | ~old(sK4)) [choice axiom]
50. (~creative(sK3) | ! [X1] : (~quiet(X1) & old(X1))) & ((quiet(sK4) | ~old(sK4)) | ! [X3] : creative(X3)) [skolemisation 47,49,48]
62. ((quiet(john) & ~patient(john)) | ! [X0] : (~rich(X0) & ~brave(X0))) & (? [X0] : (rich(X0) | brave(X0)) | (~quiet(john) | patient(john))) [nnf transformation 11]
63. ((quiet(john) & ~patient(john)) | ! [X0] : (~rich(X0) & ~brave(X0))) & (? [X0] : (rich(X0) | brave(X0)) | ~quiet(john) | patient(john)) [flattening 62]
64. ((quiet(john) & ~patient(john)) | ! [X0] : (~rich(X0) & ~brave(X0))) & (? [X1] : (rich(X1) | brave(X1)) | ~quiet(john) | patient(john)) [rectify 63]
65. ? [X1] : (rich(X1) | brave(X1)) => (rich(sK7) | brave(sK7)) [choice axiom]
66. ((quiet(john) & ~patient(john)) | ! [X0] : (~rich(X0) & ~brave(X0))) & ((rich(sK7) | brave(sK7)) | ~quiet(john) | patient(john)) [skolemisation 64,65]
67. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~wise(X0) | ~tall(X0)))) [nnf transformation 12]
68. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ~wise(X0) | ~tall(X0))) [flattening 67]
69. ! [X0] : ((~kind(X0) | (~quiet(X0) | calm(X0))) & ((quiet(X0) & ~calm(X0)) | kind(X0))) [nnf transformation 15]
70. ! [X0] : ((~kind(X0) | ~quiet(X0) | calm(X0)) & ((quiet(X0) & ~calm(X0)) | kind(X0))) [flattening 69]
81. ? [X0] : (~calm(X0) & patient(X0)) => (~calm(sK11) & patient(sK11)) [choice axiom]
82. ~calm(sK11) & patient(sK11) [skolemisation 20,81]
92. rich(sK1) | creative(X1) [cnf transformation 39]
94. ~wise(X0) | ~kind(X0) [cnf transformation 41]
96. ~tall(X0) | patient(X0) [cnf transformation 43]
109. ~creative(sK3) | ~quiet(X1) [cnf transformation 50]
127. ~patient(john) | ~rich(X0) [cnf transformation 66]
132. calm(X0) | tall(X0) [cnf transformation 68]
133. ~patient(X0) | wise(X0) [cnf transformation 68]
139. ~calm(X0) | kind(X0) [cnf transformation 70]
140. quiet(X0) | kind(X0) [cnf transformation 70]
153. patient(sK11) [cnf transformation 82]
156. wise(john) [cnf transformation 22]
184. 6 <=> ! [X1] : creative(X1) [avatar definition]
185. creative(X1) <- (6) [avatar component clause 184]
187. 7 <=> rich(sK1) [avatar definition]
189. rich(sK1) <- (7) [avatar component clause 187]
190. 6 | 7 [avatar split clause 92,187,184]
205. 11 <=> ! [X1] : ~quiet(X1) [avatar definition]
206. ~quiet(X1) <- (11) [avatar component clause 205]
208. 12 <=> creative(sK3) [avatar definition]
210. ~creative(sK3) <- (~12) [avatar component clause 208]
211. 11 | ~12 [avatar split clause 109,208,205]
251. 22 <=> patient(john) [avatar definition]
253. ~patient(john) <- (~22) [avatar component clause 251]
255. 23 <=> wise(john) [avatar definition]
257. wise(john) <- (23) [avatar component clause 255]
282. 29 <=> ! [X0] : ~rich(X0) [avatar definition]
283. ~rich(X0) <- (29) [avatar component clause 282]
293. 29 | ~22 [avatar split clause 127,251,282]
333. 23 [avatar split clause 156,255]
347. ~kind(john) <- (23) [resolution 94,257]
355. wise(sK11) [resolution 133,153]
356. ~kind(sK11) [resolution 355,94]
363. tall(X1) | kind(X1) [resolution 139,132]
368. $false <- (6, ~12) [resolution 185,210]
369. ~6 | 12 [avatar contradiction clause 368]
406. patient(X1) | kind(X1) [resolution 363,96]
575. kind(john) <- (~22) [resolution 406,253]
579. $false <- (~22, 23) [subsumption resolution 575,347]
580. 22 | ~23 [avatar contradiction clause 579]
599. $false <- (7, 29) [resolution 283,189]
600. ~7 | ~29 [avatar contradiction clause 599]
608. kind(X0) <- (11) [resolution 206,140]
637. $false <- (11) [resolution 608,356]
638. ~11 [avatar contradiction clause 637]
644. $false [avatar sat refutation 190,211,293,333,369,580,600,638]
% SZS output end Proof for 7326003089161832100641498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not generous then fred is kind or not tall and vice versa.
If alice is both not generous and not patient then someone is either tall or humble.
Everyone who is not patient is not old.
If susan is not humble or not calm then fred is not old or not rich.
If someone is both not kind and kind then someone is either not strong or humble.
If lucy is either not strong or rich then lucy is funny or not patient and vice versa.
If someone is not quiet or not creative then someone is not rich.
Everyone who is both strong and creative is not quiet and vice versa.
If someone is both not strong and funny then paul is either humble or not tall and vice versa.
Everyone who is kind is not funny and vice versa.
Everyone who is old is either calm or strong.
If someone is not wise then someone is humble.
Everyone who is not quiet or not creative is both calm and happy.
Everyone who is rich is either tall or strong and vice versa.
Everyone who is either old or strong is calm or not wise.
Everyone who is both not happy and humble is either strong or curious and vice versa.
Susan is either strong or not quiet.
Someone is either not tall or happy.
Someone is brave or not wise.
Paul is not generous.
Someone is either calm or not funny.
Someone is not generous.
Someone is either not rich or patient.
Someone is tall. | Susan is old. | contradiction | ((?[X]:((quiet(X)|~generous(X))))<=>((kind(fred)|~tall(fred))))&
(((~generous(alice)&~patient(alice)))=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:(~patient(X)=>~old(X)))&
(((~humble(susan)|~calm(susan)))=>((~old(fred)|~rich(fred))))&
((?[X]:((~kind(X)&kind(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(((~strong(lucy)<~>rich(lucy)))<=>((funny(lucy)|~patient(lucy))))&
((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:(~rich(X))))&
(![X]:((strong(X)&creative(X))<=>~quiet(X)))&
((?[X]:((~strong(X)&funny(X))))<=>((humble(paul)<~>~tall(paul))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:(old(X)=>(calm(X)<~>strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|~creative(X))=>(calm(X)&happy(X))))&
(![X]:(rich(X)<=>(tall(X)<~>strong(X))))&
(![X]:((old(X)<~>strong(X))=>(calm(X)|~wise(X))))&
(![X]:((~happy(X)&humble(X))<=>(strong(X)<~>curious(X))))&
((strong(susan)<~>~quiet(susan)))&
(?[X]:((~tall(X)<~>happy(X))))&
(?[X]:((brave(X)|~wise(X))))&
(~generous(paul))&
(?[X]:((calm(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:(tall(X))) | old(susan) | [
"p7",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 443363566890150303628463
% SZS output start Proof for 443363566890150303628463
8. ! [X0] : ((creative(X0) & strong(X0)) <=> ~quiet(X0)) [input p7]
11. ! [X0] : (old(X0) => (calm(X0) <~> strong(X0))) [input p10]
13. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (happy(X0) & calm(X0))) [input p12]
17. strong(susan) <~> ~quiet(susan) [input p16]
25. old(susan) [input hypothesis]
37. ! [X0] : ((calm(X0) <~> strong(X0)) | ~old(X0)) [ennf transformation 11]
39. ! [X0] : ((happy(X0) & calm(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 13]
59. ! [X0] : (((creative(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) | ~strong(X0)))) [nnf transformation 8]
60. ! [X0] : (((creative(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | ~creative(X0) | ~strong(X0))) [flattening 59]
66. ! [X0] : (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | ~old(X0)) [nnf transformation 37]
74. (quiet(susan) | ~strong(susan)) & (~quiet(susan) | strong(susan)) [nnf transformation 17]
107. ~creative(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 60]
108. strong(X0) | quiet(X0) [cnf transformation 60]
119. ~strong(X0) | ~calm(X0) | ~old(X0) [cnf transformation 66]
121. calm(X0) | quiet(X0) [cnf transformation 39]
122. creative(X0) | calm(X0) [cnf transformation 39]
137. ~quiet(susan) | strong(susan) [cnf transformation 74]
138. quiet(susan) | ~strong(susan) [cnf transformation 74]
148. old(susan) [cnf transformation 25]
194. 11 <=> calm(susan) [avatar definition]
195. ~calm(susan) <- (~11) [avatar component clause 194]
278. quiet(susan) [subsumption resolution 138,108]
279. strong(susan) [subsumption resolution 137,278]
319. ~quiet(X0) | ~strong(X0) | calm(X0) [resolution 107,122]
321. ~strong(X0) | calm(X0) [subsumption resolution 319,121]
326. ~calm(susan) | ~old(susan) [resolution 119,279]
328. ~calm(susan) [subsumption resolution 326,148]
329. ~11 [avatar split clause 328,194]
332. calm(susan) [resolution 321,279]
334. $false <- (~11) [subsumption resolution 332,195]
335. 11 [avatar contradiction clause 334]
336. $false [avatar sat refutation 329,335]
% SZS output end Proof for 443363566890150303628463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and kind is either rich or not old and vice versa.
Everyone who is not humble is not rich or not patient and vice versa.
If lucy is either not kind or not happy then someone is wise.
If someone is either rich or funny then paul is not funny.
If someone is either happy or tall then someone is both old and kind and vice versa.
Everyone who is either creative or not wise is either quiet or not kind and vice versa.
If alice is either creative or not brave then alice is either creative or curious and vice versa.
If mary is either not kind or not humble then susan is either not old or not tall.
Everyone who is not strong or strong is creative.
Everyone who is strong or not patient is either not calm or curious and vice versa.
If someone is wise then someone is either not brave or not quiet.
If someone is both kind and not creative then fred is not curious and vice versa.
If someone is not generous or not kind then paul is either not patient or old.
Everyone who is not patient is both humble and wise.
Everyone who is either not humble or humble is both creative and not rich and vice versa.
If lucy is old then lucy is not kind or calm.
Susan is either not strong or not funny.
Mary is either kind or not happy.
Someone is not curious or not funny.
Someone is patient or curious.
Alice is happy.
Someone is both strong and not tall.
Someone is either humble or generous. | Lucy is patient. | entailment | (![X]:((~kind(X)&kind(X))<=>(rich(X)<~>~old(X))))&
(![X]:(~humble(X)<=>(~rich(X)|~patient(X))))&
(((~kind(lucy)<~>~happy(lucy)))=>(?[X]:(wise(X))))&
((?[X]:((rich(X)<~>funny(X))))=>(~funny(paul)))&
((?[X]:((happy(X)<~>tall(X))))<=>(?[X]:((old(X)&kind(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>(quiet(X)<~>~kind(X))))&
(((creative(alice)<~>~brave(alice)))<=>((creative(alice)<~>curious(alice))))&
(((~kind(mary)<~>~humble(mary)))=>((~old(susan)<~>~tall(susan))))&
(![X]:((~strong(X)|strong(X))=>creative(X)))&
(![X]:((strong(X)|~patient(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:(wise(X)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~creative(X))))<=>(~curious(fred)))&
((?[X]:((~generous(X)|~kind(X))))=>((~patient(paul)<~>old(paul))))&
(![X]:(~patient(X)=>(humble(X)&wise(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(creative(X)&~rich(X))))&
((old(lucy))=>((~kind(lucy)|calm(lucy))))&
((~strong(susan)<~>~funny(susan)))&
((kind(mary)<~>~happy(mary)))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((patient(X)|curious(X))))&
(happy(alice))&
(?[X]:((strong(X)&~tall(X))))&
(?[X]:((humble(X)<~>generous(X)))) | patient(lucy) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6281968333189056179914905
% SZS output start Proof for 6281968333189056179914905
2. ! [X0] : (~humble(X0) <=> (~patient(X0) | ~rich(X0))) [input p1]
14. ! [X0] : (~patient(X0) => (wise(X0) & humble(X0))) [input p13]
24. ~patient(lucy) [input hypothesis]
33. ! [X0] : ((wise(X0) & humble(X0)) | patient(X0)) [ennf transformation 14]
38. ! [X0] : ((~humble(X0) | (patient(X0) & rich(X0))) & ((~patient(X0) | ~rich(X0)) | humble(X0))) [nnf transformation 2]
39. ! [X0] : ((~humble(X0) | (patient(X0) & rich(X0))) & (~patient(X0) | ~rich(X0) | humble(X0))) [flattening 38]
84. ~humble(X0) | patient(X0) [cnf transformation 39]
132. humble(X0) | patient(X0) [cnf transformation 33]
152. ~patient(lucy) [cnf transformation 24]
289. patient(X0) [subsumption resolution 132,84]
327. $false [subsumption resolution 152,289]
% SZS output end Proof for 6281968333189056179914905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not strong is both not creative and curious and vice versa. Everyone who is both curious and brave is not creative or not brave. Everyone who is curious or not strong is kind or curious and vice versa. If someone is either rich or quiet then someone is both wise and not curious. If paul is strong or patient then someone is either calm or creative. Everyone who is both curious and brave is either tall or not humble. If someone is both old and strong then lucy is both patient and not generous and vice versa. Everyone who is not tall or not strong is not generous or humble and vice versa. Everyone who is not funny or not generous is both not quiet and wise. If someone is either calm or not curious then someone is not wise or funny and vice versa. Everyone who is not curious or not generous is not creative or not wise and vice versa. If someone is not humble then someone is both not old and strong. Everyone who is not patient is brave or not calm. If someone is tall then lucy is either not brave or not strong. Everyone who is not brave is old or quiet and vice versa. If someone is both not happy and not humble then someone is not old and vice versa. Someone is either generous or not calm. Lucy is both not humble and not kind. Susan is both creative and quiet. Alice is strong. Fred is brave. John is not curious or kind. Someone is not brave or kind. Someone is both curious and not kind. | Lucy is not humble. | entailment | (![X]:((~rich(X)|~strong(X))<=>(~creative(X)&curious(X))))&
(![X]:((curious(X)&brave(X))=>(~creative(X)|~brave(X))))&
(![X]:((curious(X)|~strong(X))<=>(kind(X)|curious(X))))&
((?[X]:((rich(X)<~>quiet(X))))=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(paul)|patient(paul)))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((curious(X)&brave(X))=>(tall(X)<~>~humble(X))))&
((?[X]:((old(X)&strong(X))))<=>((patient(lucy)&~generous(lucy))))&
(![X]:((~tall(X)|~strong(X))<=>(~generous(X)|humble(X))))&
(![X]:((~funny(X)|~generous(X))=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((?[X]:(tall(X)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:(~brave(X)<=>(old(X)|quiet(X))))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:(~old(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
((~humble(lucy)&~kind(lucy)))&
((creative(susan)&quiet(susan)))&
(strong(alice))&
(brave(fred))&
((~curious(john)|kind(john)))&
(?[X]:((~brave(X)|kind(X))))&
(?[X]:((curious(X)&~kind(X)))) | ~humble(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5097269844028008678211574
% SZS output start Proof for 5097269844028008678211574
18. ~kind(lucy) & ~humble(lucy) [input p17]
25. humble(lucy) [input hypothesis]
140. ~humble(lucy) [cnf transformation 18]
150. humble(lucy) [cnf transformation 25]
323. $false [subsumption resolution 150,140]
% SZS output end Proof for 5097269844028008678211574
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then susan is not kind or not wise.
Everyone who is happy or not humble is patient or humble.
Everyone who is not brave or tall is both not patient and not humble and vice versa.
Everyone who is both not old and tall is both not calm and not tall and vice versa.
If john is not kind or not strong then fred is either not kind or wise and vice versa.
Everyone who is either not funny or patient is either not humble or not quiet.
Everyone who is either happy or calm is tall.
If someone is not tall or not brave then susan is either rich or funny and vice versa.
If fred is both not patient and not wise then someone is both not rich and not generous and vice versa.
Everyone who is not happy or generous is kind or generous.
Everyone who is not wise is humble and vice versa.
Everyone who is old is both curious and quiet and vice versa.
If fred is both kind and strong then lucy is calm and vice versa.
Everyone who is patient or generous is curious or kind.
If someone is both not quiet and not rich then someone is not humble or not brave and vice versa.
If mary is patient or funny then someone is both not curious and not happy and vice versa.
Lucy is either not happy or not funny.
Fred is rich or not curious.
Someone is strong or kind.
Someone is either generous or rich.
Lucy is either brave or not strong.
Fred is both humble and rich. | Fred is not rich. | contradiction | ((?[X]:(wise(X)))=>((~kind(susan)|~wise(susan))))&
(![X]:((happy(X)|~humble(X))=>(patient(X)|humble(X))))&
(![X]:((~brave(X)|tall(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)&~tall(X))))&
(((~kind(john)|~strong(john)))<=>((~kind(fred)<~>wise(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((happy(X)<~>calm(X))=>tall(X)))&
((?[X]:((~tall(X)|~brave(X))))<=>((rich(susan)<~>funny(susan))))&
(((~patient(fred)&~wise(fred)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~happy(X)|generous(X))=>(kind(X)|generous(X))))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:(old(X)<=>(curious(X)&quiet(X))))&
(((kind(fred)&strong(fred)))<=>(calm(lucy)))&
(![X]:((patient(X)|generous(X))=>(curious(X)|kind(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~humble(X)|~brave(X)))))&
(((patient(mary)|funny(mary)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((~happy(lucy)<~>~funny(lucy)))&
((rich(fred)|~curious(fred)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((brave(lucy)<~>~strong(lucy)))&
((humble(fred)&rich(fred))) | ~rich(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5863331862621950893319721
% SZS output start Proof for 5863331862621950893319721
22. rich(fred) & humble(fred) [input p21]
23. ~rich(fred) [input hypothesis]
139. rich(fred) [cnf transformation 22]
140. ~rich(fred) [cnf transformation 23]
298. 32 <=> rich(fred) [avatar definition]
335. 32 [avatar split clause 139,298]
336. ~32 [avatar split clause 140,298]
337. $false [avatar sat refutation 335,336]
% SZS output end Proof for 5863331862621950893319721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is patient then someone is not curious or patient and vice versa. If susan is funny then lucy is either calm or kind and vice versa. If someone is wise or tall then someone is not strong. Everyone who is not patient is creative or not creative and vice versa. If lucy is old then fred is not old or creative and vice versa. If someone is funny then someone is kind. If susan is either not wise or not brave then someone is not curious and vice versa. Everyone who is happy or not generous is either not old or not tall and vice versa. Everyone who is either not tall or patient is both strong and not generous. If someone is either happy or not tall then susan is both old and not generous and vice versa. If john is happy then someone is not kind and vice versa. If susan is either not creative or not kind then someone is not old or not curious and vice versa. Everyone who is both creative and patient is both strong and quiet. If someone is both not generous and kind then fred is happy and vice versa. If someone is kind then someone is both brave and not brave. Everyone who is either not curious or not tall is old. Paul is not generous or not tall. Lucy is either creative or not patient. Someone is either brave or not rich. John is either generous or tall. Someone is happy. Someone is either not brave or rich. Paul is not tall. | Susan is not tall. | entailment | ((patient(paul))<=>(?[X]:((~curious(X)|patient(X)))))&
((funny(susan))<=>((calm(lucy)<~>kind(lucy))))&
((?[X]:((wise(X)|tall(X))))=>(?[X]:(~strong(X))))&
(![X]:(~patient(X)<=>(creative(X)|~creative(X))))&
((old(lucy))<=>((~old(fred)|creative(fred))))&
((?[X]:(funny(X)))=>(?[X]:(kind(X))))&
(((~wise(susan)<~>~brave(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)|~generous(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~tall(X)<~>patient(X))=>(strong(X)&~generous(X))))&
((?[X]:((happy(X)<~>~tall(X))))<=>((old(susan)&~generous(susan))))&
((happy(john))<=>(?[X]:(~kind(X))))&
(((~creative(susan)<~>~kind(susan)))<=>(?[X]:((~old(X)|~curious(X)))))&
(![X]:((creative(X)&patient(X))=>(strong(X)&quiet(X))))&
((?[X]:((~generous(X)&kind(X))))<=>(happy(fred)))&
((?[X]:(kind(X)))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((~curious(X)<~>~tall(X))=>old(X)))&
((~generous(paul)|~tall(paul)))&
((creative(lucy)<~>~patient(lucy)))&
(?[X]:((brave(X)<~>~rich(X))))&
((generous(john)<~>tall(john)))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)<~>rich(X))))&
(~tall(paul)) | ~tall(susan) | [
"p3",
"p7",
"p8",
"p9",
"p10",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9109839161348284760930256
% SZS output start Proof for 9109839161348284760930256
4. ! [X0] : (~patient(X0) <=> (~creative(X0) | creative(X0))) [input p3]
8. ! [X0] : ((~generous(X0) | happy(X0)) <=> (~old(X0) <~> ~tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) <~> patient(X0)) => (~generous(X0) & strong(X0))) [input p8]
10. ? [X0] : (happy(X0) <~> ~tall(X0)) <=> (~generous(susan) & old(susan)) [input p9]
11. happy(john) <=> ? [X0] : ~kind(X0) [input p10]
15. ? [X0] : kind(X0) => ? [X0] : (~brave(X0) & brave(X0)) [input p14]
20. generous(john) <~> tall(john) [input p19]
24. tall(susan) [input hypothesis]
27. ? [X0] : kind(X0) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 15]
31. ! [X0] : ((~generous(X0) & strong(X0)) | (~tall(X0) <=> patient(X0))) [ennf transformation 9]
34. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : ~kind(X0) [ennf transformation 27]
44. ! [X0] : ((~patient(X0) | (creative(X0) & ~creative(X0))) & ((~creative(X0) | creative(X0)) | patient(X0))) [nnf transformation 4]
45. ! [X0] : ((~patient(X0) | (creative(X0) & ~creative(X0))) & (~creative(X0) | creative(X0) | patient(X0))) [flattening 44]
55. ! [X0] : (((~generous(X0) | happy(X0)) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | (generous(X0) & ~happy(X0)))) [nnf transformation 8]
56. ! [X0] : ((~generous(X0) | happy(X0) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | (generous(X0) & ~happy(X0)))) [flattening 55]
57. ! [X0] : ((~generous(X0) & strong(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) [nnf transformation 31]
58. (? [X0] : ((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (generous(susan) | ~old(susan))) & ((~generous(susan) & old(susan)) | ! [X0] : ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) [nnf transformation 10]
59. (? [X0] : ((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | generous(susan) | ~old(susan)) & ((~generous(susan) & old(susan)) | ! [X0] : ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) [flattening 58]
60. (? [X0] : ((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | generous(susan) | ~old(susan)) & ((~generous(susan) & old(susan)) | ! [X1] : ((happy(X1) | tall(X1)) & (~tall(X1) | ~happy(X1)))) [rectify 59]
61. ? [X0] : ((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) => ((tall(sK4) | ~happy(sK4)) & (~tall(sK4) | happy(sK4))) [choice axiom]
62. (((tall(sK4) | ~happy(sK4)) & (~tall(sK4) | happy(sK4))) | generous(susan) | ~old(susan)) & ((~generous(susan) & old(susan)) | ! [X1] : ((happy(X1) | tall(X1)) & (~tall(X1) | ~happy(X1)))) [skolemisation 60,61]
63. (happy(john) | ! [X0] : kind(X0)) & (? [X0] : ~kind(X0) | ~happy(john)) [nnf transformation 11]
64. (happy(john) | ! [X0] : kind(X0)) & (? [X1] : ~kind(X1) | ~happy(john)) [rectify 63]
65. ? [X1] : ~kind(X1) => ~kind(sK5) [choice axiom]
66. (happy(john) | ! [X0] : kind(X0)) & (~kind(sK5) | ~happy(john)) [skolemisation 64,65]
75. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ~kind(X1) [rectify 34]
76. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK8) & brave(sK8)) [choice axiom]
77. (~brave(sK8) & brave(sK8)) | ! [X1] : ~kind(X1) [skolemisation 75,76]
83. (~tall(john) | ~generous(john)) & (tall(john) | generous(john)) [nnf transformation 20]
99. ~patient(X0) | ~creative(X0) [cnf transformation 45]
100. ~patient(X0) | creative(X0) [cnf transformation 45]
110. ~old(X0) | ~tall(X0) | generous(X0) [cnf transformation 56]
117. ~generous(X0) | patient(X0) | tall(X0) [cnf transformation 57]
119. old(susan) | ~tall(X1) | ~happy(X1) [cnf transformation 62]
121. ~generous(susan) | ~tall(X1) | ~happy(X1) [cnf transformation 62]
126. happy(john) | kind(X0) [cnf transformation 66]
137. brave(sK8) | ~kind(X1) [cnf transformation 77]
138. ~brave(sK8) | ~kind(X1) [cnf transformation 77]
146. tall(john) | generous(john) [cnf transformation 83]
152. tall(susan) [cnf transformation 24]
154. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
155. ~patient(X0) <- (1) [avatar component clause 154]
202. ~patient(X0) [subsumption resolution 99,100]
203. 1 [avatar split clause 202,154]
244. 20 <=> old(susan) [avatar definition]
245. old(susan) <- (20) [avatar component clause 244]
248. 21 <=> generous(susan) [avatar definition]
266. 25 <=> ! [X1] : (~tall(X1) | ~happy(X1)) [avatar definition]
267. ~happy(X1) | ~tall(X1) <- (25) [avatar component clause 266]
268. 25 | ~21 [avatar split clause 121,248,266]
270. 25 | 20 [avatar split clause 119,244,266]
272. 26 <=> ! [X0] : kind(X0) [avatar definition]
273. kind(X0) <- (26) [avatar component clause 272]
275. 27 <=> happy(john) [avatar definition]
277. happy(john) <- (27) [avatar component clause 275]
278. 26 | 27 [avatar split clause 126,275,272]
329. 38 <=> ! [X1] : ~kind(X1) [avatar definition]
330. ~kind(X1) <- (38) [avatar component clause 329]
332. 39 <=> brave(sK8) [avatar definition]
335. 38 | ~39 [avatar split clause 138,332,329]
336. 38 | 39 [avatar split clause 137,332,329]
366. 46 <=> generous(john) [avatar definition]
367. generous(john) <- (46) [avatar component clause 366]
370. 47 <=> tall(john) [avatar definition]
372. ~tall(john) <- (~47) [avatar component clause 370]
374. 46 | 47 [avatar split clause 146,370,366]
388. $false <- (26, 38) [subsumption resolution 273,330]
389. ~26 | ~38 [avatar contradiction clause 388]
404. ~tall(susan) | generous(susan) <- (20) [resolution 110,245]
414. generous(susan) <- (20) [subsumption resolution 404,152]
417. 21 | ~20 [avatar split clause 414,244,248]
425. ~tall(john) <- (25, 27) [resolution 267,277]
443. patient(john) | tall(john) <- (46) [resolution 117,367]
447. tall(john) <- (1, 46) [subsumption resolution 443,155]
448. $false <- (1, 46, ~47) [subsumption resolution 447,372]
449. ~1 | ~46 | 47 [avatar contradiction clause 448]
450. ~47 | ~25 | ~27 [avatar split clause 425,275,266,370]
456. $false [avatar sat refutation 203,268,270,278,335,336,374,389,417,449,450]
% SZS output end Proof for 9109839161348284760930256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise and curious is wise and vice versa. Everyone who is quiet or not generous is quiet or not funny and vice versa. Everyone who is creative or not humble is both creative and not funny. Everyone who is wise is not patient or not kind and vice versa. Everyone who is wise is both not humble and not happy. Everyone who is either not strong or rich is either not tall or not patient. Everyone who is not old or not quiet is wise or curious. If someone is either tall or not curious then someone is either not happy or humble. Everyone who is humble is not wise and vice versa. If someone is not generous then someone is either not curious or not strong. If mary is both kind and quiet then someone is both humble and happy and vice versa. Everyone who is both brave and not rich is both patient and rich. If someone is either kind or not humble then alice is not calm or old and vice versa. If someone is curious or not quiet then someone is strong or not tall. If someone is both curious and humble then alice is generous or not patient. Everyone who is tall is not rich or not happy and vice versa. Someone is both not wise and generous. Paul is not tall or not kind. John is happy or generous. Susan is both happy and not wise. Fred is either funny or generous. Someone is generous or not patient. Mary is either not calm or old. Alice is not quiet or patient. | Fred is humble. | entailment | (![X]:((~wise(X)&curious(X))<=>wise(X)))&
(![X]:((quiet(X)|~generous(X))<=>(quiet(X)|~funny(X))))&
(![X]:((creative(X)|~humble(X))=>(creative(X)&~funny(X))))&
(![X]:(wise(X)<=>(~patient(X)|~kind(X))))&
(![X]:(wise(X)=>(~humble(X)&~happy(X))))&
(![X]:((~strong(X)<~>rich(X))=>(~tall(X)<~>~patient(X))))&
(![X]:((~old(X)|~quiet(X))=>(wise(X)|curious(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((~happy(X)<~>humble(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)<~>~strong(X)))))&
(((kind(mary)&quiet(mary)))<=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((brave(X)&~rich(X))=>(patient(X)&rich(X))))&
((?[X]:((kind(X)<~>~humble(X))))<=>((~calm(alice)|old(alice))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:((strong(X)|~tall(X)))))&
((?[X]:((curious(X)&humble(X))))=>((generous(alice)|~patient(alice))))&
(![X]:(tall(X)<=>(~rich(X)|~happy(X))))&
(?[X]:((~wise(X)&generous(X))))&
((~tall(paul)|~kind(paul)))&
((happy(john)|generous(john)))&
((happy(susan)&~wise(susan)))&
((funny(fred)<~>generous(fred)))&
(?[X]:((generous(X)|~patient(X))))&
((~calm(mary)<~>old(mary)))&
((~quiet(alice)|patient(alice))) | humble(fred) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5068135627110297747178150
% SZS output start Proof for 5068135627110297747178150
1. ! [X0] : ((curious(X0) & ~wise(X0)) <=> wise(X0)) [input p0]
9. ! [X0] : (humble(X0) <=> ~wise(X0)) [input p8]
25. ~humble(fred) [input hypothesis]
40. ! [X0] : (((curious(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) | wise(X0)))) [nnf transformation 1]
41. ! [X0] : (((curious(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | ~curious(X0) | wise(X0))) [flattening 40]
51. ! [X0] : ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0))) [nnf transformation 9]
78. ~wise(X0) | ~wise(X0) [cnf transformation 41]
104. humble(X0) | wise(X0) [cnf transformation 51]
135. ~humble(fred) [cnf transformation 25]
137. ~wise(X0) [duplicate literal removal 78]
162. humble(X0) [subsumption resolution 104,137]
196. $false [subsumption resolution 135,162]
% SZS output end Proof for 5068135627110297747178150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is not creative.
If someone is both not creative and not old then lucy is not quiet and vice versa.
If mary is strong or funny then someone is both not generous and not rich and vice versa.
Everyone who is both not curious and patient is happy and vice versa.
If paul is not old then someone is both not kind and not curious and vice versa.
Everyone who is either rich or not humble is both kind and humble.
If alice is not happy or not brave then susan is either not quiet or generous.
If mary is not tall then someone is not curious or funny.
If susan is either not quiet or not generous then someone is either not rich or generous and vice versa.
If susan is both not tall and not wise then someone is both humble and not old.
If someone is either funny or tall then someone is calm and vice versa.
Everyone who is either quiet or generous is not rich or curious.
Everyone who is both not calm and wise is both patient and not patient.
If john is both quiet and patient then lucy is either not tall or not patient and vice versa.
Everyone who is kind or quiet is humble and vice versa.
If paul is both not wise and not creative then someone is both not old and happy.
Someone is both curious and not generous.
Fred is tall.
Fred is calm.
Someone is not curious or rich.
Lucy is not patient.
Mary is both not creative and funny.
Someone is both not quiet and not creative. | Alice is not patient. | contradiction | (![X]:(rich(X)=>~creative(X)))&
((?[X]:((~creative(X)&~old(X))))<=>(~quiet(lucy)))&
(((strong(mary)|funny(mary)))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~curious(X)&patient(X))<=>happy(X)))&
((~old(paul))<=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((rich(X)<~>~humble(X))=>(kind(X)&humble(X))))&
(((~happy(alice)|~brave(alice)))=>((~quiet(susan)<~>generous(susan))))&
((~tall(mary))=>(?[X]:((~curious(X)|funny(X)))))&
(((~quiet(susan)<~>~generous(susan)))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(((~tall(susan)&~wise(susan)))=>(?[X]:((humble(X)&~old(X)))))&
((?[X]:((funny(X)<~>tall(X))))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)|curious(X))))&
(![X]:((~calm(X)&wise(X))=>(patient(X)&~patient(X))))&
(((quiet(john)&patient(john)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:((kind(X)|quiet(X))<=>humble(X)))&
(((~wise(paul)&~creative(paul)))=>(?[X]:((~old(X)&happy(X)))))&
(?[X]:((curious(X)&~generous(X))))&
(tall(fred))&
(calm(fred))&
(?[X]:((~curious(X)|rich(X))))&
(~patient(lucy))&
((~creative(mary)&funny(mary)))&
(?[X]:((~quiet(X)&~creative(X)))) | ~patient(alice) | [
"p2",
"p3",
"p6",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2876296779034556422843722
% SZS output start Proof for 2876296779034556422843722
3. (funny(mary) | strong(mary)) <=> ? [X0] : (~rich(X0) & ~generous(X0)) [input p2]
4. ! [X0] : ((patient(X0) & ~curious(X0)) <=> happy(X0)) [input p3]
7. (~brave(alice) | ~happy(alice)) => (~quiet(susan) <~> generous(susan)) [input p6]
9. (~quiet(susan) <~> ~generous(susan)) <=> ? [X0] : (~rich(X0) <~> generous(X0)) [input p8]
22. funny(mary) & ~creative(mary) [input p21]
24. ~patient(alice) [input hypothesis]
26. ! [X0] : (happy(X0) => (patient(X0) & ~curious(X0))) [unused predicate definition removal 4]
27. ~happy(alice) => (~quiet(susan) <~> generous(susan)) [pure predicate removal 7]
29. ! [X0] : ((patient(X0) & ~curious(X0)) | ~happy(X0)) [ennf transformation 26]
31. (~quiet(susan) <~> generous(susan)) | happy(alice) [ennf transformation 27]
45. ((funny(mary) | strong(mary)) | ! [X0] : (rich(X0) | generous(X0))) & (? [X0] : (~rich(X0) & ~generous(X0)) | (~funny(mary) & ~strong(mary))) [nnf transformation 3]
46. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & (? [X0] : (~rich(X0) & ~generous(X0)) | (~funny(mary) & ~strong(mary))) [flattening 45]
47. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & (? [X1] : (~rich(X1) & ~generous(X1)) | (~funny(mary) & ~strong(mary))) [rectify 46]
48. ? [X1] : (~rich(X1) & ~generous(X1)) => (~rich(sK1) & ~generous(sK1)) [choice axiom]
49. (funny(mary) | strong(mary) | ! [X0] : (rich(X0) | generous(X0))) & ((~rich(sK1) & ~generous(sK1)) | (~funny(mary) & ~strong(mary))) [skolemisation 47,48]
55. ((~generous(susan) | quiet(susan)) & (generous(susan) | ~quiet(susan))) | happy(alice) [nnf transformation 31]
58. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X0] : ((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [nnf transformation 9]
59. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [rectify 58]
60. ? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) => ((~generous(sK4) | rich(sK4)) & (generous(sK4) | ~rich(sK4))) [choice axiom]
61. (((generous(susan) | quiet(susan)) & (~generous(susan) | ~quiet(susan))) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(sK4) | rich(sK4)) & (generous(sK4) | ~rich(sK4))) | ((~quiet(susan) | generous(susan)) & (~generous(susan) | quiet(susan)))) [skolemisation 59,60]
87. ~generous(sK1) | ~funny(mary) [cnf transformation 49]
89. ~rich(sK1) | ~funny(mary) [cnf transformation 49]
92. ~happy(X0) | patient(X0) [cnf transformation 29]
100. generous(susan) | ~quiet(susan) | happy(alice) [cnf transformation 55]
101. ~generous(susan) | quiet(susan) | happy(alice) [cnf transformation 55]
107. ~generous(susan) | ~quiet(susan) | generous(X0) | rich(X0) [cnf transformation 61]
109. generous(susan) | quiet(susan) | generous(X0) | rich(X0) [cnf transformation 61]
139. funny(mary) [cnf transformation 22]
142. ~patient(alice) [cnf transformation 24]
163. 5 <=> ! [X0] : (rich(X0) | generous(X0)) [avatar definition]
164. generous(X0) | rich(X0) <- (5) [avatar component clause 163]
170. 7 <=> funny(mary) [avatar definition]
175. 8 <=> rich(sK1) [avatar definition]
177. ~rich(sK1) <- (~8) [avatar component clause 175]
178. ~7 | ~8 [avatar split clause 89,175,170]
181. 9 <=> generous(sK1) [avatar definition]
183. ~generous(sK1) <- (~9) [avatar component clause 181]
184. ~7 | ~9 [avatar split clause 87,181,170]
205. 14 <=> happy(alice) [avatar definition]
207. happy(alice) <- (14) [avatar component clause 205]
209. 15 <=> quiet(susan) [avatar definition]
213. 16 <=> generous(susan) [avatar definition]
216. 14 | 15 | ~16 [avatar split clause 101,213,209,205]
217. 14 | ~15 | 16 [avatar split clause 100,213,209,205]
235. 5 | 15 | 16 [avatar split clause 109,213,209,163]
237. 5 | ~15 | ~16 [avatar split clause 107,213,209,163]
344. 7 [avatar split clause 139,170]
348. patient(alice) <- (14) [resolution 92,207]
349. $false <- (14) [subsumption resolution 348,142]
350. ~14 [avatar contradiction clause 349]
352. rich(sK1) <- (5, ~9) [resolution 164,183]
355. $false <- (5, ~8, ~9) [subsumption resolution 352,177]
356. ~5 | 8 | 9 [avatar contradiction clause 355]
359. $false [avatar sat refutation 178,184,216,217,235,237,344,350,356]
% SZS output end Proof for 2876296779034556422843722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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