premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If alice is wise then someone is kind and vice versa. Everyone who is either not quiet or calm is either not kind or not wise and vice versa. Everyone who is brave or calm is both not strong and rich and vice versa. If susan is tall or not wise then someone is wise or not kind and vice versa. Everyone who is either wise or not humble is either patient or not humble. Everyone who is either humble or curious is either tall or patient and vice versa. Everyone who is either calm or strong is either not old or old. Everyone who is wise or not old is patient or not wise. Everyone who is either happy or not generous is not brave or not curious and vice versa. If someone is either not patient or rich then someone is either not brave or happy. If someone is both curious and happy then someone is patient or tall and vice versa. If fred is funny then fred is kind. Everyone who is not calm is either brave or curious and vice versa. If fred is both rich and not humble then someone is either not patient or curious. Everyone who is happy is generous and vice versa. Everyone who is creative or not patient is either old or brave. Fred is either not strong or humble. Someone is strong or calm. Someone is humble or not quiet. Susan is old or calm. Someone is either not kind or old. Susan is not humble. Fred is not rich or not old. Paul is rich. | Fred is not strong. | neutral | ((wise(alice))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(~kind(X)<~>~wise(X))))&
(![X]:((brave(X)|calm(X))<=>(~strong(X)&rich(X))))&
(((tall(susan)|~wise(susan)))<=>(?[X]:((wise(X)|~kind(X)))))&
(![X]:((wise(X)<~>~humble(X))=>(patient(X)<~>~humble(X))))&
(![X]:((humble(X)<~>curious(X))<=>(tall(X)<~>patient(X))))&
(![X]:((calm(X)<~>strong(X))=>(~old(X)<~>old(X))))&
(![X]:((wise(X)|~old(X))=>(patient(X)|~wise(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~brave(X)|~curious(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:((~brave(X)<~>happy(X)))))&
((?[X]:((curious(X)&happy(X))))<=>(?[X]:((patient(X)|tall(X)))))&
((funny(fred))=>(kind(fred)))&
(![X]:(~calm(X)<=>(brave(X)<~>curious(X))))&
(((rich(fred)&~humble(fred)))=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>(old(X)<~>brave(X))))&
((~strong(fred)<~>humble(fred)))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((old(susan)|calm(susan)))&
(?[X]:((~kind(X)<~>old(X))))&
(~humble(susan))&
((~rich(fred)|~old(fred)))&
(rich(paul)) | ~strong(fred) | [] | null | 0 |
Everyone who is either not generous or old is both funny and not curious and vice versa.
If someone is creative then mary is calm and vice versa.
If someone is funny then john is creative and vice versa.
If someone is not humble or not strong then john is both happy and not old.
If mary is generous then susan is creative and vice versa.
Everyone who is either old or not funny is patient or quiet and vice versa.
If someone is both not generous and not patient then paul is either calm or rich.
If someone is either funny or not patient then mary is both creative and generous.
Everyone who is not calm is both funny and creative.
If someone is either kind or not strong then someone is either not strong or not humble and vice versa.
If fred is either not funny or humble then someone is not quiet or not wise.
If someone is both generous and wise then someone is both quiet and not happy.
Everyone who is either strong or not rich is either not tall or old and vice versa.
Everyone who is creative or not humble is kind or humble and vice versa.
Everyone who is both not creative and brave is humble and vice versa.
If alice is either quiet or humble then someone is either rich or quiet and vice versa.
Paul is either brave or not old.
Someone is not calm or humble.
John is both patient and wise.
John is both patient and happy.
Someone is both not patient and not old.
Fred is not tall.
Fred is either brave or not creative. | Fred is not creative. | neutral | (![X]:((~generous(X)<~>old(X))<=>(funny(X)&~curious(X))))&
((?[X]:(creative(X)))<=>(calm(mary)))&
((?[X]:(funny(X)))<=>(creative(john)))&
((?[X]:((~humble(X)|~strong(X))))=>((happy(john)&~old(john))))&
((generous(mary))<=>(creative(susan)))&
(![X]:((old(X)<~>~funny(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((calm(paul)<~>rich(paul))))&
((?[X]:((funny(X)<~>~patient(X))))=>((creative(mary)&generous(mary))))&
(![X]:(~calm(X)=>(funny(X)&creative(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(((~funny(fred)<~>humble(fred)))=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((generous(X)&wise(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((strong(X)<~>~rich(X))<=>(~tall(X)<~>old(X))))&
(![X]:((creative(X)|~humble(X))<=>(kind(X)|humble(X))))&
(![X]:((~creative(X)&brave(X))<=>humble(X)))&
(((quiet(alice)<~>humble(alice)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
((brave(paul)<~>~old(paul)))&
(?[X]:((~calm(X)|humble(X))))&
((patient(john)&wise(john)))&
((patient(john)&happy(john)))&
(?[X]:((~patient(X)&~old(X))))&
(~tall(fred))&
((brave(fred)<~>~creative(fred))) | ~creative(fred) | [] | null | 0 |
Everyone who is not happy is either not tall or calm and vice versa. Everyone who is rich is not quiet or funny and vice versa. Everyone who is patient is wise or patient and vice versa. If someone is both quiet and not generous then fred is not funny or not quiet. If susan is either generous or not brave then someone is both not creative and happy and vice versa. Everyone who is either old or not quiet is not strong. Everyone who is both not tall and patient is creative or strong and vice versa. If someone is either creative or not happy then someone is either not patient or strong and vice versa. Everyone who is both humble and happy is both curious and creative and vice versa. If someone is not old or tall then fred is both not funny and funny and vice versa. Everyone who is both creative and not old is either not generous or not rich. Everyone who is curious or not patient is both not humble and brave and vice versa. Everyone who is both curious and not rich is old or quiet and vice versa. Everyone who is funny is either not funny or not old. Everyone who is strong is either not creative or humble. If susan is both not quiet and creative then someone is either not brave or not curious. Fred is not humble. Lucy is both not calm and quiet. Someone is either old or rich. Fred is not tall. John is kind. Alice is either not strong or rich. Someone is not creative. Someone is not kind or kind. | Alice is funny. | contradiction | (![X]:(~happy(X)<=>(~tall(X)<~>calm(X))))&
(![X]:(rich(X)<=>(~quiet(X)|funny(X))))&
(![X]:(patient(X)<=>(wise(X)|patient(X))))&
((?[X]:((quiet(X)&~generous(X))))=>((~funny(fred)|~quiet(fred))))&
(((generous(susan)<~>~brave(susan)))<=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((old(X)<~>~quiet(X))=>~strong(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)|strong(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((humble(X)&happy(X))<=>(curious(X)&creative(X))))&
((?[X]:((~old(X)|tall(X))))<=>((~funny(fred)&funny(fred))))&
(![X]:((creative(X)&~old(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((curious(X)|~patient(X))<=>(~humble(X)&brave(X))))&
(![X]:((curious(X)&~rich(X))<=>(old(X)|quiet(X))))&
(![X]:(funny(X)=>(~funny(X)<~>~old(X))))&
(![X]:(strong(X)=>(~creative(X)<~>humble(X))))&
(((~quiet(susan)&creative(susan)))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(~humble(fred))&
((~calm(lucy)&quiet(lucy)))&
(?[X]:((old(X)<~>rich(X))))&
(~tall(fred))&
(kind(john))&
((~strong(alice)<~>rich(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((~kind(X)|kind(X)))) | funny(alice) | [
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7172499747787632261886324
% SZS output start Proof for 7172499747787632261886324
2. ! [X0] : (rich(X0) <=> (funny(X0) | ~quiet(X0))) [input p1]
10. ? [X0] : (tall(X0) | ~old(X0)) <=> (funny(fred) & ~funny(fred)) [input p9]
13. ! [X0] : ((~rich(X0) & curious(X0)) <=> (quiet(X0) | old(X0))) [input p12]
25. funny(alice) [input hypothesis]
37. ! [X0] : ((rich(X0) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | ~rich(X0))) [nnf transformation 2]
38. ! [X0] : ((rich(X0) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | ~rich(X0))) [flattening 37]
55. (? [X0] : (tall(X0) | ~old(X0)) | (~funny(fred) | funny(fred))) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [nnf transformation 10]
56. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [flattening 55]
57. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [rectify 56]
58. ? [X0] : (tall(X0) | ~old(X0)) => (tall(sK3) | ~old(sK3)) [choice axiom]
59. ((tall(sK3) | ~old(sK3)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [skolemisation 57,58]
63. ! [X0] : (((~rich(X0) & curious(X0)) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | (rich(X0) | ~curious(X0)))) [nnf transformation 13]
64. ! [X0] : (((~rich(X0) & curious(X0)) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | rich(X0) | ~curious(X0))) [flattening 63]
84. ~funny(X0) | rich(X0) [cnf transformation 38]
114. ~funny(fred) | old(X1) [cnf transformation 59]
116. funny(fred) | old(X1) [cnf transformation 59]
129. ~old(X0) | ~rich(X0) [cnf transformation 64]
148. funny(alice) [cnf transformation 25]
154. 2 <=> funny(fred) [avatar definition]
230. 18 <=> ! [X1] : old(X1) [avatar definition]
231. old(X1) <- (18) [avatar component clause 230]
232. 18 | 2 [avatar split clause 116,154,230]
234. 18 | ~2 [avatar split clause 114,154,230]
269. 26 <=> rich(alice) [avatar definition]
270. rich(alice) <- (26) [avatar component clause 269]
275. rich(alice) [resolution 84,148]
278. 26 [avatar split clause 275,269]
290. ~rich(X0) <- (18) [resolution 129,231]
293. $false <- (18, 26) [resolution 290,270]
294. ~18 | ~26 [avatar contradiction clause 293]
296. $false [avatar sat refutation 232,234,278,294]
% SZS output end Proof for 7172499747787632261886324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and rich is both old and not creative. If john is both not kind and not patient then john is curious. Everyone who is tall is either curious or not wise and vice versa. Everyone who is either calm or not patient is strong and vice versa. Everyone who is both not generous and tall is both strong and generous. Everyone who is either not generous or not curious is either not rich or generous. Everyone who is happy or patient is not creative or not generous and vice versa. Everyone who is generous or patient is both not calm and not generous. If lucy is not happy or not strong then lucy is not funny or not strong and vice versa. Everyone who is not calm or kind is either not generous or not patient. If someone is creative then susan is both not generous and patient. Everyone who is strong is both not calm and not kind and vice versa. Everyone who is both rich and creative is old and vice versa. Everyone who is not funny is both happy and old. Everyone who is tall or not kind is brave or curious. Everyone who is both humble and not creative is happy. Mary is happy or not strong. Someone is both quiet and not rich. Mary is not tall. Lucy is not rich or not curious. Someone is old. Someone is either tall or old. | John is not curious. | neutral | (![X]:((brave(X)&rich(X))=>(old(X)&~creative(X))))&
(((~kind(john)&~patient(john)))=>(curious(john)))&
(![X]:(tall(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((calm(X)<~>~patient(X))<=>strong(X)))&
(![X]:((~generous(X)&tall(X))=>(strong(X)&generous(X))))&
(![X]:((~generous(X)<~>~curious(X))=>(~rich(X)<~>generous(X))))&
(![X]:((happy(X)|patient(X))<=>(~creative(X)|~generous(X))))&
(![X]:((generous(X)|patient(X))=>(~calm(X)&~generous(X))))&
(((~happy(lucy)|~strong(lucy)))<=>((~funny(lucy)|~strong(lucy))))&
(![X]:((~calm(X)|kind(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:(creative(X)))=>((~generous(susan)&patient(susan))))&
(![X]:(strong(X)<=>(~calm(X)&~kind(X))))&
(![X]:((rich(X)&creative(X))<=>old(X)))&
(![X]:(~funny(X)=>(happy(X)&old(X))))&
(![X]:((tall(X)|~kind(X))=>(brave(X)|curious(X))))&
(![X]:((humble(X)&~creative(X))=>happy(X)))&
((happy(mary)|~strong(mary)))&
(?[X]:((quiet(X)&~rich(X))))&
(~tall(mary))&
((~rich(lucy)|~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:((tall(X)<~>old(X)))) | ~curious(john) | [] | null | 0 |
If someone is both not strong and not old then paul is either not humble or tall and vice versa.
Everyone who is rich is either humble or calm and vice versa.
Everyone who is brave is funny and vice versa.
Everyone who is either not old or kind is both funny and curious.
If alice is humble or not kind then someone is either curious or tall.
Everyone who is not humble or calm is either not strong or quiet.
If someone is not curious or generous then someone is both not brave and not kind.
Everyone who is either not happy or not old is either quiet or generous and vice versa.
Everyone who is not generous is not quiet or creative and vice versa.
Everyone who is not kind or strong is either not brave or not kind and vice versa.
If alice is not quiet then someone is both rich and not generous and vice versa.
Everyone who is either not humble or quiet is quiet or patient and vice versa.
Everyone who is not wise is not generous and vice versa.
If fred is humble then someone is either rich or not humble.
If fred is either not kind or curious then someone is not kind and vice versa.
If lucy is both kind and not quiet then alice is not funny or not kind and vice versa.
Alice is not generous or not rich.
Someone is both old and curious.
Fred is either creative or not happy.
Alice is not rich.
Someone is either humble or old.
Mary is either not humble or calm. | Alice is wise. | contradiction | ((?[X]:((~strong(X)&~old(X))))<=>((~humble(paul)<~>tall(paul))))&
(![X]:(rich(X)<=>(humble(X)<~>calm(X))))&
(![X]:(brave(X)<=>funny(X)))&
(![X]:((~old(X)<~>kind(X))=>(funny(X)&curious(X))))&
(((humble(alice)|~kind(alice)))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~humble(X)|calm(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((~curious(X)|generous(X))))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~happy(X)<~>~old(X))<=>(quiet(X)<~>generous(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|creative(X))))&
(![X]:((~kind(X)|strong(X))<=>(~brave(X)<~>~kind(X))))&
((~quiet(alice))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~humble(X)<~>quiet(X))<=>(quiet(X)|patient(X))))&
(![X]:(~wise(X)<=>~generous(X)))&
((humble(fred))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~kind(fred)<~>curious(fred)))<=>(?[X]:(~kind(X))))&
(((kind(lucy)&~quiet(lucy)))<=>((~funny(alice)|~kind(alice))))&
((~generous(alice)|~rich(alice)))&
(?[X]:((old(X)&curious(X))))&
((creative(fred)<~>~happy(fred)))&
(~rich(alice))&
(?[X]:((humble(X)<~>old(X))))&
((~humble(mary)<~>calm(mary))) | wise(alice) | [
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3681678738455230758468403
% SZS output start Proof for 3681678738455230758468403
7. ? [X0] : (generous(X0) | ~curious(X0)) => ? [X0] : (~kind(X0) & ~brave(X0)) [input p6]
10. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (~brave(X0) <~> ~kind(X0))) [input p9]
13. ! [X0] : (~wise(X0) <=> ~generous(X0)) [input p12]
23. wise(alice) [input hypothesis]
24. ? [X0] : (generous(X0) | ~curious(X0)) => ? [X1] : (~kind(X1) & ~brave(X1)) [rectify 7]
25. ! [X0] : (~generous(X0) => ~wise(X0)) [unused predicate definition removal 13]
29. ? [X1] : (~kind(X1) & ~brave(X1)) | ! [X0] : (~generous(X0) & curious(X0)) [ennf transformation 24]
30. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 25]
43. ? [X0] : (~kind(X0) & ~brave(X0)) | ! [X1] : (~generous(X1) & curious(X1)) [rectify 29]
44. ? [X0] : (~kind(X0) & ~brave(X0)) => (~kind(sK2) & ~brave(sK2)) [choice axiom]
45. (~kind(sK2) & ~brave(sK2)) | ! [X1] : (~generous(X1) & curious(X1)) [skolemisation 43,44]
49. ! [X0] : (((strong(X0) | ~kind(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~strong(X0) & kind(X0)))) [nnf transformation 10]
50. ! [X0] : ((strong(X0) | ~kind(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) & (((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~strong(X0) & kind(X0)))) [flattening 49]
98. ~brave(sK2) | ~generous(X1) [cnf transformation 45]
100. ~kind(sK2) | ~generous(X1) [cnf transformation 45]
114. kind(X0) | brave(X0) | kind(X0) [cnf transformation 50]
127. ~wise(X0) | generous(X0) [cnf transformation 30]
149. wise(alice) [cnf transformation 23]
152. kind(X0) | brave(X0) [duplicate literal removal 114]
200. 10 <=> ! [X1] : ~generous(X1) [avatar definition]
201. ~generous(X1) <- (10) [avatar component clause 200]
203. 11 <=> kind(sK2) [avatar definition]
205. ~kind(sK2) <- (~11) [avatar component clause 203]
206. 10 | ~11 [avatar split clause 100,203,200]
212. 13 <=> brave(sK2) [avatar definition]
214. ~brave(sK2) <- (~13) [avatar component clause 212]
215. 10 | ~13 [avatar split clause 98,212,200]
287. 28 <=> generous(alice) [avatar definition]
288. generous(alice) <- (28) [avatar component clause 287]
328. generous(alice) [resolution 127,149]
329. 28 [avatar split clause 328,287]
337. brave(sK2) <- (~11) [resolution 152,205]
339. $false <- (~11, ~13) [subsumption resolution 337,214]
340. 11 | 13 [avatar contradiction clause 339]
341. $false <- (10, 28) [resolution 201,288]
342. ~10 | ~28 [avatar contradiction clause 341]
343. $false [avatar sat refutation 206,215,329,340,342]
% SZS output end Proof for 3681678738455230758468403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not curious is not rich or creative and vice versa.
Everyone who is funny or not humble is both not funny and not kind and vice versa.
Everyone who is not patient is not generous.
If mary is not old then alice is old and vice versa.
If paul is not wise then someone is both generous and strong and vice versa.
Everyone who is either happy or brave is either generous or calm.
If susan is both not wise and not tall then alice is both not rich and old.
Everyone who is either generous or not brave is not kind and vice versa.
If john is either brave or tall then someone is funny or happy.
If someone is either not funny or patient then fred is not curious and vice versa.
If john is either happy or tall then someone is both not humble and not strong and vice versa.
Everyone who is both not tall and not creative is either rich or strong.
Everyone who is both curious and not old is either not old or strong.
If someone is not humble then someone is not creative.
If someone is either not wise or old then lucy is both not kind and not funny.
Everyone who is either not tall or wise is not generous and vice versa.
Fred is both not patient and not tall.
John is both happy and not quiet.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Mary is either not wise or happy. | John is quiet. | contradiction | (![X]:((~brave(X)|~curious(X))<=>(~rich(X)|creative(X))))&
(![X]:((funny(X)|~humble(X))<=>(~funny(X)&~kind(X))))&
(![X]:(~patient(X)=>~generous(X)))&
((~old(mary))<=>(old(alice)))&
((~wise(paul))<=>(?[X]:((generous(X)&strong(X)))))&
(![X]:((happy(X)<~>brave(X))=>(generous(X)<~>calm(X))))&
(((~wise(susan)&~tall(susan)))=>((~rich(alice)&old(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>~kind(X)))&
(((brave(john)<~>tall(john)))=>(?[X]:((funny(X)|happy(X)))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
(![X]:((~tall(X)<~>wise(X))<=>~generous(X)))&
((~patient(fred)&~tall(fred)))&
((happy(john)&~quiet(john)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((~wise(mary)<~>happy(mary))) | quiet(john) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4851360517870757849229367
% SZS output start Proof for 4851360517870757849229367
18. ~quiet(john) & happy(john) [input p17]
24. quiet(john) [input hypothesis]
127. ~quiet(john) [cnf transformation 18]
135. quiet(john) [cnf transformation 24]
292. $false [subsumption resolution 135,127]
% SZS output end Proof for 4851360517870757849229367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or funny is either funny or strong and vice versa. Everyone who is both not happy and not calm is both brave and happy and vice versa. If someone is funny or not happy then paul is both not humble and not creative. If someone is either curious or wise then someone is not quiet and vice versa. If someone is not wise then someone is not happy or funny and vice versa. If someone is calm or not patient then someone is generous and vice versa. Everyone who is either not funny or tall is either tall or patient and vice versa. Everyone who is humble or brave is not strong or not generous and vice versa. Everyone who is humble is both kind and not humble and vice versa. Everyone who is not tall is either creative or quiet and vice versa. If someone is either tall or not calm then someone is both humble and not calm. Everyone who is either happy or not curious is either not generous or wise and vice versa. Everyone who is not old or generous is either tall or wise and vice versa. Everyone who is not generous or generous is not old and vice versa. Everyone who is either patient or not kind is either quiet or not wise and vice versa. Alice is not tall or humble. Someone is creative or calm. John is not tall. | Alice is calm. | entailment | (![X]:((tall(X)|funny(X))<=>(funny(X)<~>strong(X))))&
(![X]:((~happy(X)&~calm(X))<=>(brave(X)&happy(X))))&
((?[X]:((funny(X)|~happy(X))))=>((~humble(paul)&~creative(paul))))&
((?[X]:((curious(X)<~>wise(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~happy(X)|funny(X)))))&
((?[X]:((calm(X)|~patient(X))))<=>(?[X]:(generous(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(tall(X)<~>patient(X))))&
(![X]:((humble(X)|brave(X))<=>(~strong(X)|~generous(X))))&
(![X]:(humble(X)<=>(kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(creative(X)<~>quiet(X))))&
((?[X]:((tall(X)<~>~calm(X))))=>(?[X]:((humble(X)&~calm(X)))))&
(![X]:((happy(X)<~>~curious(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
((~tall(alice)|humble(alice)))&
(?[X]:((creative(X)|calm(X))))&
(~tall(john)) | calm(alice) | [
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2210663225559173920262568
% SZS output start Proof for 2210663225559173920262568
9. ! [X0] : (humble(X0) <=> (~humble(X0) & kind(X0))) [input p8]
11. ? [X0] : (tall(X0) <~> ~calm(X0)) => ? [X0] : (~calm(X0) & humble(X0)) [input p10]
16. humble(alice) | ~tall(alice) [input p15]
19. ~calm(alice) [input hypothesis]
23. ? [X0] : (tall(X0) <~> ~calm(X0)) => ? [X1] : (~calm(X1) & humble(X1)) [rectify 11]
25. ? [X1] : (~calm(X1) & humble(X1)) | ! [X0] : (tall(X0) <=> ~calm(X0)) [ennf transformation 23]
48. ! [X0] : ((humble(X0) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ~humble(X0))) [nnf transformation 9]
49. ! [X0] : ((humble(X0) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ~humble(X0))) [flattening 48]
51. ? [X1] : (~calm(X1) & humble(X1)) | ! [X0] : ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))) [nnf transformation 25]
52. ? [X0] : (~calm(X0) & humble(X0)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1))) [rectify 51]
53. ? [X0] : (~calm(X0) & humble(X0)) => (~calm(sK6) & humble(sK6)) [choice axiom]
54. (~calm(sK6) & humble(sK6)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1))) [skolemisation 52,53]
100. ~humble(X0) | ~humble(X0) [cnf transformation 49]
107. humble(sK6) | tall(X1) | calm(X1) [cnf transformation 54]
135. humble(alice) | ~tall(alice) [cnf transformation 16]
138. ~calm(alice) [cnf transformation 19]
139. ~humble(X0) [duplicate literal removal 100]
237. 21 <=> ! [X1] : (tall(X1) | calm(X1)) [avatar definition]
238. calm(X1) | tall(X1) <- (21) [avatar component clause 237]
248. tall(X1) | calm(X1) [subsumption resolution 107,139]
249. 21 [avatar split clause 248,237]
253. ~tall(alice) [subsumption resolution 135,139]
268. tall(alice) <- (21) [resolution 238,138]
269. $false <- (21) [subsumption resolution 268,253]
270. ~21 [avatar contradiction clause 269]
271. $false [avatar sat refutation 249,270]
% SZS output end Proof for 2210663225559173920262568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both rich and not generous then mary is either rich or not generous.
If someone is not quiet or kind then someone is not quiet.
Everyone who is either not humble or not tall is happy or kind.
Everyone who is not brave is either calm or not strong and vice versa.
Everyone who is wise is either not generous or brave.
Everyone who is both happy and calm is both not humble and old.
Everyone who is rich is old and vice versa.
If fred is either calm or not kind then someone is both brave and not generous.
If mary is kind or not patient then mary is either not happy or not quiet.
Everyone who is not funny is not strong.
If john is brave or quiet then paul is both not calm and strong and vice versa.
Everyone who is not tall or not quiet is funny or not generous.
Everyone who is both not old and not happy is not old.
If fred is rich or not strong then someone is not creative or not rich and vice versa.
Everyone who is not strong is both calm and kind and vice versa.
Everyone who is patient or brave is either not calm or brave and vice versa.
Alice is either not funny or brave.
Someone is both not brave and not patient.
Fred is both funny and old.
Someone is either not happy or not old.
Lucy is either not rich or not humble.
John is kind or rich.
Someone is both not kind and funny. | Fred is not patient. | neutral | (((rich(susan)&~generous(susan)))=>((rich(mary)<~>~generous(mary))))&
((?[X]:((~quiet(X)|kind(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(happy(X)|kind(X))))&
(![X]:(~brave(X)<=>(calm(X)<~>~strong(X))))&
(![X]:(wise(X)=>(~generous(X)<~>brave(X))))&
(![X]:((happy(X)&calm(X))=>(~humble(X)&old(X))))&
(![X]:(rich(X)<=>old(X)))&
(((calm(fred)<~>~kind(fred)))=>(?[X]:((brave(X)&~generous(X)))))&
(((kind(mary)|~patient(mary)))=>((~happy(mary)<~>~quiet(mary))))&
(![X]:(~funny(X)=>~strong(X)))&
(((brave(john)|quiet(john)))<=>((~calm(paul)&strong(paul))))&
(![X]:((~tall(X)|~quiet(X))=>(funny(X)|~generous(X))))&
(![X]:((~old(X)&~happy(X))=>~old(X)))&
(((rich(fred)|~strong(fred)))<=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:(~strong(X)<=>(calm(X)&kind(X))))&
(![X]:((patient(X)|brave(X))<=>(~calm(X)<~>brave(X))))&
((~funny(alice)<~>brave(alice)))&
(?[X]:((~brave(X)&~patient(X))))&
((funny(fred)&old(fred)))&
(?[X]:((~happy(X)<~>~old(X))))&
((~rich(lucy)<~>~humble(lucy)))&
((kind(john)|rich(john)))&
(?[X]:((~kind(X)&funny(X)))) | ~patient(fred) | [] | null | 0 |
If mary is not calm or happy then alice is not calm and vice versa.
Everyone who is happy is both not curious and not creative and vice versa.
Everyone who is both strong and creative is wise.
Everyone who is rich is not patient.
Everyone who is both not humble and not kind is not happy.
Everyone who is both curious and not wise is not brave and vice versa.
If someone is either not funny or not creative then paul is both not curious and not calm.
Everyone who is not patient or not wise is either not patient or not creative and vice versa.
Everyone who is not strong is rich.
If someone is both wise and happy then mary is both rich and happy and vice versa.
Everyone who is both generous and patient is either curious or creative.
Everyone who is not strong is not calm or strong and vice versa.
Everyone who is both strong and humble is creative.
If susan is wise or not funny then someone is either quiet or not rich and vice versa.
If john is either quiet or not patient then someone is both not quiet and not humble.
If someone is either not strong or patient then someone is either not rich or wise and vice versa.
Mary is kind.
Someone is both generous and kind.
Lucy is either not rich or not wise.
Alice is strong or tall.
Susan is not happy.
Someone is rich.
Susan is not quiet.
Someone is curious or quiet. | Mary is strong. | contradiction | (((~calm(mary)|happy(mary)))<=>(~calm(alice)))&
(![X]:(happy(X)<=>(~curious(X)&~creative(X))))&
(![X]:((strong(X)&creative(X))=>wise(X)))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((~humble(X)&~kind(X))=>~happy(X)))&
(![X]:((curious(X)&~wise(X))<=>~brave(X)))&
((?[X]:((~funny(X)<~>~creative(X))))=>((~curious(paul)&~calm(paul))))&
(![X]:((~patient(X)|~wise(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:(~strong(X)=>rich(X)))&
((?[X]:((wise(X)&happy(X))))<=>((rich(mary)&happy(mary))))&
(![X]:((generous(X)&patient(X))=>(curious(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(~calm(X)|strong(X))))&
(![X]:((strong(X)&humble(X))=>creative(X)))&
(((wise(susan)|~funny(susan)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((quiet(john)<~>~patient(john)))=>(?[X]:((~quiet(X)&~humble(X)))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((~rich(X)<~>wise(X)))))&
(kind(mary))&
(?[X]:((generous(X)&kind(X))))&
((~rich(lucy)<~>~wise(lucy)))&
((strong(alice)|tall(alice)))&
(~happy(susan))&
(?[X]:(rich(X)))&
(~quiet(susan))&
(?[X]:((curious(X)|quiet(X)))) | strong(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7179700325352395069487486
% SZS output start Proof for 7179700325352395069487486
12. ! [X0] : (~strong(X0) <=> (strong(X0) | ~calm(X0))) [input p11]
25. strong(mary) [input hypothesis]
54. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | strong(X0))) [nnf transformation 12]
55. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | strong(X0))) [flattening 54]
103. ~strong(X0) | ~strong(X0) [cnf transformation 55]
127. strong(mary) [cnf transformation 25]
129. ~strong(X0) [duplicate literal removal 103]
276. $false [subsumption resolution 127,129]
% SZS output end Proof for 7179700325352395069487486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or rich is either rich or kind.
If someone is either not calm or curious then susan is happy or not generous.
Everyone who is either wise or not patient is wise or not quiet.
If mary is both not strong and not brave then someone is quiet or not calm.
If someone is either wise or old then john is both tall and not kind and vice versa.
If susan is both old and calm then susan is either not funny or not calm.
Everyone who is tall or not strong is both not happy and strong and vice versa.
If someone is either not funny or not strong then someone is either not curious or not generous and vice versa.
If mary is not happy or patient then paul is not generous.
Everyone who is not humble or not strong is both strong and not wise and vice versa.
Everyone who is both quiet and kind is both tall and not strong.
Everyone who is both not happy and happy is either not old or funny.
If mary is either curious or not kind then someone is quiet or patient.
Everyone who is both curious and kind is both not creative and strong and vice versa.
Everyone who is humble or not patient is either not old or not quiet and vice versa.
Someone is not creative or old.
Someone is both patient and not old.
Someone is either rich or not humble.
John is both not calm and rich.
Someone is not calm.
Mary is kind or not old.
Paul is either patient or not quiet.
Someone is both not funny and not calm. | Susan is not rich. | neutral | (![X]:((~brave(X)|rich(X))=>(rich(X)<~>kind(X))))&
((?[X]:((~calm(X)<~>curious(X))))=>((happy(susan)|~generous(susan))))&
(![X]:((wise(X)<~>~patient(X))=>(wise(X)|~quiet(X))))&
(((~strong(mary)&~brave(mary)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:((wise(X)<~>old(X))))<=>((tall(john)&~kind(john))))&
(((old(susan)&calm(susan)))=>((~funny(susan)<~>~calm(susan))))&
(![X]:((tall(X)|~strong(X))<=>(~happy(X)&strong(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(((~happy(mary)|patient(mary)))=>(~generous(paul)))&
(![X]:((~humble(X)|~strong(X))<=>(strong(X)&~wise(X))))&
(![X]:((quiet(X)&kind(X))=>(tall(X)&~strong(X))))&
(![X]:((~happy(X)&happy(X))=>(~old(X)<~>funny(X))))&
(((curious(mary)<~>~kind(mary)))=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:((curious(X)&kind(X))<=>(~creative(X)&strong(X))))&
(![X]:((humble(X)|~patient(X))<=>(~old(X)<~>~quiet(X))))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((patient(X)&~old(X))))&
(?[X]:((rich(X)<~>~humble(X))))&
((~calm(john)&rich(john)))&
(?[X]:(~calm(X)))&
((kind(mary)|~old(mary)))&
((patient(paul)<~>~quiet(paul)))&
(?[X]:((~funny(X)&~calm(X)))) | ~rich(susan) | [] | null | 0 |
If alice is funny or creative then fred is both calm and not happy and vice versa.
Everyone who is not humble is both not happy and creative and vice versa.
Everyone who is either old or not old is curious.
Everyone who is either wise or creative is funny and vice versa.
Everyone who is patient or not humble is both old and tall.
If someone is either brave or not curious then lucy is not brave.
Everyone who is not happy or creative is both not curious and funny and vice versa.
Everyone who is both not calm and not curious is either not funny or rich and vice versa.
If someone is either happy or not wise then someone is calm or brave.
If someone is not tall then john is either not generous or rich and vice versa.
Everyone who is not rich or curious is calm or not old and vice versa.
If alice is either brave or not humble then someone is either not curious or funny and vice versa.
Everyone who is generous is either happy or not tall and vice versa.
Alice is either patient or wise.
Someone is rich or old.
Someone is tall or wise.
Someone is either not humble or not old.
Lucy is either not quiet or humble.
Someone is either humble or not curious.
Fred is either strong or creative. | Lucy is calm. | neutral | (((funny(alice)|creative(alice)))<=>((calm(fred)&~happy(fred))))&
(![X]:(~humble(X)<=>(~happy(X)&creative(X))))&
(![X]:((old(X)<~>~old(X))=>curious(X)))&
(![X]:((wise(X)<~>creative(X))<=>funny(X)))&
(![X]:((patient(X)|~humble(X))=>(old(X)&tall(X))))&
((?[X]:((brave(X)<~>~curious(X))))=>(~brave(lucy)))&
(![X]:((~happy(X)|creative(X))<=>(~curious(X)&funny(X))))&
(![X]:((~calm(X)&~curious(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((happy(X)<~>~wise(X))))=>(?[X]:((calm(X)|brave(X)))))&
((?[X]:(~tall(X)))<=>((~generous(john)<~>rich(john))))&
(![X]:((~rich(X)|curious(X))<=>(calm(X)|~old(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
((patient(alice)<~>wise(alice)))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((tall(X)|wise(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
((~quiet(lucy)<~>humble(lucy)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(fred)<~>creative(fred))) | calm(lucy) | [] | null | 0 |
Everyone who is both not wise and not old is not calm. If someone is both not happy and not wise then alice is kind or not wise and vice versa. Everyone who is patient is either not tall or not generous. Everyone who is brave is not brave or humble and vice versa. Everyone who is both wise and not quiet is both not wise and strong and vice versa. If someone is either tall or brave then alice is rich. Everyone who is kind or not generous is both old and not generous and vice versa. Everyone who is old or not funny is either old or not quiet and vice versa. Everyone who is either funny or not calm is both kind and patient and vice versa. If mary is both brave and not quiet then mary is either generous or not wise and vice versa. Everyone who is quiet or strong is rich or generous. If someone is either wise or not brave then someone is not generous and vice versa. If john is wise then someone is not generous and vice versa. Everyone who is either not brave or rich is either brave or not creative. Everyone who is not happy is strong. If alice is not quiet or brave then someone is funny and vice versa. Someone is quiet. Fred is rich or not wise. Susan is patient or not generous. Someone is both old and patient. Alice is either not old or quiet. Lucy is both not old and curious. Someone is either old or not quiet. | Lucy is not generous. | contradiction | (![X]:((~wise(X)&~old(X))=>~calm(X)))&
((?[X]:((~happy(X)&~wise(X))))<=>((kind(alice)|~wise(alice))))&
(![X]:(patient(X)=>(~tall(X)<~>~generous(X))))&
(![X]:(brave(X)<=>(~brave(X)|humble(X))))&
(![X]:((wise(X)&~quiet(X))<=>(~wise(X)&strong(X))))&
((?[X]:((tall(X)<~>brave(X))))=>(rich(alice)))&
(![X]:((kind(X)|~generous(X))<=>(old(X)&~generous(X))))&
(![X]:((old(X)|~funny(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((funny(X)<~>~calm(X))<=>(kind(X)&patient(X))))&
(((brave(mary)&~quiet(mary)))<=>((generous(mary)<~>~wise(mary))))&
(![X]:((quiet(X)|strong(X))=>(rich(X)|generous(X))))&
((?[X]:((wise(X)<~>~brave(X))))<=>(?[X]:(~generous(X))))&
((wise(john))<=>(?[X]:(~generous(X))))&
(![X]:((~brave(X)<~>rich(X))=>(brave(X)<~>~creative(X))))&
(![X]:(~happy(X)=>strong(X)))&
(((~quiet(alice)|brave(alice)))<=>(?[X]:(funny(X))))&
(?[X]:(quiet(X)))&
((rich(fred)|~wise(fred)))&
((patient(susan)|~generous(susan)))&
(?[X]:((old(X)&patient(X))))&
((~old(alice)<~>quiet(alice)))&
((~old(lucy)&curious(lucy)))&
(?[X]:((old(X)<~>~quiet(X)))) | ~generous(lucy) | [
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8677321261987104313646852
% SZS output start Proof for 8677321261987104313646852
7. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~generous(X0) & old(X0))) [input p6]
22. curious(lucy) & ~old(lucy) [input p21]
24. ~generous(lucy) [input hypothesis]
26. ~old(lucy) [pure predicate removal 22]
46. ! [X0] : (((~generous(X0) | kind(X0)) | (generous(X0) | ~old(X0))) & ((~generous(X0) & old(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 7]
47. ! [X0] : ((~generous(X0) | kind(X0) | generous(X0) | ~old(X0)) & ((~generous(X0) & old(X0)) | (generous(X0) & ~kind(X0)))) [flattening 46]
95. generous(X0) | old(X0) [cnf transformation 47]
140. ~old(lucy) [cnf transformation 26]
143. ~generous(lucy) [cnf transformation 24]
276. old(lucy) [resolution 95,143]
279. $false [subsumption resolution 276,140]
% SZS output end Proof for 8677321261987104313646852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not happy is humble or calm and vice versa.
If lucy is both not quiet and not brave then someone is either not old or calm and vice versa.
Everyone who is not humble or tall is not rich.
If someone is either not quiet or kind then paul is wise or not quiet and vice versa.
Everyone who is both humble and not wise is kind and vice versa.
Everyone who is calm or tall is both not strong and not tall.
If someone is either funny or not brave then alice is either not old or not rich and vice versa.
Everyone who is both humble and curious is both not happy and not old.
If paul is both not funny and not happy then lucy is either curious or funny and vice versa.
Everyone who is either funny or brave is not brave or curious and vice versa.
If someone is both not wise and humble then someone is not humble and vice versa.
If mary is not creative then someone is not generous and vice versa.
If someone is rich or not humble then lucy is not quiet or not funny and vice versa.
Everyone who is both not patient and not strong is not tall and vice versa.
Everyone who is old is not curious or not funny and vice versa.
Everyone who is brave is either tall or happy.
Susan is both not wise and not creative.
Fred is not rich.
Someone is either not happy or quiet.
Alice is both happy and not curious.
Lucy is either quiet or not quiet.
Someone is wise.
Paul is both creative and curious. | Lucy is not old. | entailment | (![X]:((~rich(X)|~happy(X))<=>(humble(X)|calm(X))))&
(((~quiet(lucy)&~brave(lucy)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~humble(X)|tall(X))=>~rich(X)))&
((?[X]:((~quiet(X)<~>kind(X))))<=>((wise(paul)|~quiet(paul))))&
(![X]:((humble(X)&~wise(X))<=>kind(X)))&
(![X]:((calm(X)|tall(X))=>(~strong(X)&~tall(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>((~old(alice)<~>~rich(alice))))&
(![X]:((humble(X)&curious(X))=>(~happy(X)&~old(X))))&
(((~funny(paul)&~happy(paul)))<=>((curious(lucy)<~>funny(lucy))))&
(![X]:((funny(X)<~>brave(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~wise(X)&humble(X))))<=>(?[X]:(~humble(X))))&
((~creative(mary))<=>(?[X]:(~generous(X))))&
((?[X]:((rich(X)|~humble(X))))<=>((~quiet(lucy)|~funny(lucy))))&
(![X]:((~patient(X)&~strong(X))<=>~tall(X)))&
(![X]:(old(X)<=>(~curious(X)|~funny(X))))&
(![X]:(brave(X)=>(tall(X)<~>happy(X))))&
((~wise(susan)&~creative(susan)))&
(~rich(fred))&
(?[X]:((~happy(X)<~>quiet(X))))&
((happy(alice)&~curious(alice)))&
((quiet(lucy)<~>~quiet(lucy)))&
(?[X]:(wise(X)))&
((creative(paul)&curious(paul))) | ~old(lucy) | [
"p5",
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5790455047218579279198530
% SZS output start Proof for 5790455047218579279198530
6. ! [X0] : ((tall(X0) | calm(X0)) => (~tall(X0) & ~strong(X0))) [input p5]
9. (~happy(paul) & ~funny(paul)) <=> (curious(lucy) <~> funny(lucy)) [input p8]
10. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (curious(X0) | ~brave(X0))) [input p9]
15. ! [X0] : (old(X0) <=> (~funny(X0) | ~curious(X0))) [input p14]
16. ! [X0] : (brave(X0) => (tall(X0) <~> happy(X0))) [input p15]
24. old(lucy) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~strong(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 6]
30. ! [X0] : ((tall(X0) <~> happy(X0)) | ~brave(X0)) [ennf transformation 16]
49. ((~happy(paul) & ~funny(paul)) | ((curious(lucy) | ~funny(lucy)) & (funny(lucy) | ~curious(lucy)))) & (((~funny(lucy) | ~curious(lucy)) & (funny(lucy) | curious(lucy))) | (happy(paul) | funny(paul))) [nnf transformation 9]
50. ((~happy(paul) & ~funny(paul)) | ((curious(lucy) | ~funny(lucy)) & (funny(lucy) | ~curious(lucy)))) & (((~funny(lucy) | ~curious(lucy)) & (funny(lucy) | curious(lucy))) | happy(paul) | funny(paul)) [flattening 49]
51. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 51]
69. ! [X0] : ((old(X0) | (funny(X0) & curious(X0))) & ((~funny(X0) | ~curious(X0)) | ~old(X0))) [nnf transformation 15]
70. ! [X0] : ((old(X0) | (funny(X0) & curious(X0))) & (~funny(X0) | ~curious(X0) | ~old(X0))) [flattening 69]
71. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | ~brave(X0)) [nnf transformation 30]
102. ~tall(X0) | ~tall(X0) [cnf transformation 27]
115. ~funny(paul) | funny(lucy) | ~curious(lucy) [cnf transformation 50]
116. ~funny(paul) | curious(lucy) | ~funny(lucy) [cnf transformation 50]
117. ~happy(paul) | funny(lucy) | ~curious(lucy) [cnf transformation 50]
118. ~happy(paul) | curious(lucy) | ~funny(lucy) [cnf transformation 50]
120. curious(X0) | ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 52]
121. brave(X0) | funny(X0) | brave(X0) [cnf transformation 52]
137. ~curious(X0) | ~funny(X0) | ~old(X0) [cnf transformation 70]
140. happy(X0) | tall(X0) | ~brave(X0) [cnf transformation 71]
154. old(lucy) [cnf transformation 24]
155. ~brave(X0) | curious(X0) | funny(X0) [duplicate literal removal 120]
156. brave(X0) | funny(X0) [duplicate literal removal 121]
157. ~tall(X0) [duplicate literal removal 102]
162. 2 <=> brave(lucy) [avatar definition]
163. brave(lucy) <- (2) [avatar component clause 162]
164. ~brave(lucy) <- (~2) [avatar component clause 162]
235. 17 <=> ! [X1] : (funny(X1) | brave(X1)) [avatar definition]
236. funny(X1) | brave(X1) <- (17) [avatar component clause 235]
245. 19 <=> funny(lucy) [avatar definition]
246. funny(lucy) <- (19) [avatar component clause 245]
247. ~funny(lucy) <- (~19) [avatar component clause 245]
249. 20 <=> curious(lucy) [avatar definition]
250. ~curious(lucy) <- (~20) [avatar component clause 249]
251. curious(lucy) <- (20) [avatar component clause 249]
253. 21 <=> happy(paul) [avatar definition]
256. ~19 | 20 | ~21 [avatar split clause 118,253,249,245]
257. ~20 | 19 | ~21 [avatar split clause 117,253,245,249]
259. 22 <=> funny(paul) [avatar definition]
261. ~funny(paul) <- (~22) [avatar component clause 259]
262. ~19 | 20 | ~22 [avatar split clause 116,259,249,245]
263. ~20 | 19 | ~22 [avatar split clause 115,259,245,249]
266. 17 [avatar split clause 156,235]
318. ~brave(X0) | happy(X0) [subsumption resolution 140,157]
341. brave(paul) <- (17, ~22) [resolution 236,261]
345. happy(paul) <- (17, ~22) [resolution 341,318]
348. 21 | ~17 | 22 [avatar split clause 345,259,235,253]
349. brave(lucy) <- (17, ~19) [resolution 247,236]
351. $false <- (~2, 17, ~19) [subsumption resolution 349,164]
352. 2 | ~17 | 19 [avatar contradiction clause 351]
419. ~funny(lucy) | ~old(lucy) <- (20) [resolution 137,251]
420. ~old(lucy) <- (19, 20) [subsumption resolution 419,246]
421. $false <- (19, 20) [subsumption resolution 420,154]
422. ~19 | ~20 [avatar contradiction clause 421]
440. curious(lucy) | funny(lucy) <- (2) [resolution 155,163]
441. funny(lucy) <- (2, ~20) [subsumption resolution 440,250]
442. $false <- (2, ~19, ~20) [subsumption resolution 441,247]
443. ~2 | 19 | 20 [avatar contradiction clause 442]
444. $false [avatar sat refutation 256,257,262,263,266,348,352,422,443]
% SZS output end Proof for 5790455047218579279198530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or calm is rich or not quiet.
If paul is both happy and calm then mary is not tall or happy and vice versa.
If mary is not funny or old then paul is both not kind and patient.
If john is not calm or not strong then someone is either calm or humble.
If someone is creative or calm then susan is either not happy or not humble and vice versa.
If john is both not wise and happy then someone is patient and vice versa.
Everyone who is both humble and not strong is both happy and kind.
Everyone who is both not happy and not funny is funny and vice versa.
If alice is wise then someone is both quiet and creative.
Everyone who is both calm and generous is not funny or not strong and vice versa.
If someone is kind then someone is either strong or not happy.
If someone is not generous or creative then someone is both creative and not kind.
Everyone who is not strong or brave is rich or tall and vice versa.
If lucy is patient then someone is either not patient or calm.
If paul is both funny and not brave then lucy is not old or creative and vice versa.
Fred is both not funny and not quiet.
Susan is both tall and not brave.
Someone is not patient or quiet.
Susan is either not creative or not patient.
Someone is not tall.
John is not rich or curious.
Someone is creative or not humble. | Fred is generous. | entailment | (![X]:((rich(X)|calm(X))=>(rich(X)|~quiet(X))))&
(((happy(paul)&calm(paul)))<=>((~tall(mary)|happy(mary))))&
(((~funny(mary)|old(mary)))=>((~kind(paul)&patient(paul))))&
(((~calm(john)|~strong(john)))=>(?[X]:((calm(X)<~>humble(X)))))&
((?[X]:((creative(X)|calm(X))))<=>((~happy(susan)<~>~humble(susan))))&
(((~wise(john)&happy(john)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~strong(X))=>(happy(X)&kind(X))))&
(![X]:((~happy(X)&~funny(X))<=>funny(X)))&
((wise(alice))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((calm(X)&generous(X))<=>(~funny(X)|~strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)<~>~happy(X)))))&
((?[X]:((~generous(X)|creative(X))))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>(rich(X)|tall(X))))&
((patient(lucy))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((funny(paul)&~brave(paul)))<=>((~old(lucy)|creative(lucy))))&
((~funny(fred)&~quiet(fred)))&
((tall(susan)&~brave(susan)))&
(?[X]:((~patient(X)|quiet(X))))&
((~creative(susan)<~>~patient(susan)))&
(?[X]:(~tall(X)))&
((~rich(john)|curious(john)))&
(?[X]:((creative(X)|~humble(X)))) | generous(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7862586664245044891422242
% SZS output start Proof for 7862586664245044891422242
8. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> funny(X0)) [input p7]
10. ! [X0] : ((generous(X0) & calm(X0)) <=> (~strong(X0) | ~funny(X0))) [input p9]
23. ~generous(fred) [input hypothesis]
51. ! [X0] : (((~funny(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) | happy(X0)))) [nnf transformation 8]
52. ! [X0] : (((~funny(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | funny(X0) | happy(X0))) [flattening 51]
55. ! [X0] : (((generous(X0) & calm(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (~generous(X0) | ~calm(X0)))) [nnf transformation 10]
56. ! [X0] : (((generous(X0) & calm(X0)) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ~generous(X0) | ~calm(X0))) [flattening 55]
106. ~funny(X0) | ~funny(X0) [cnf transformation 52]
112. generous(X0) | funny(X0) [cnf transformation 56]
140. ~generous(fred) [cnf transformation 23]
142. ~funny(X0) [duplicate literal removal 106]
265. generous(X0) [subsumption resolution 112,142]
342. $false [subsumption resolution 140,265]
% SZS output end Proof for 7862586664245044891422242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not brave then lucy is either calm or quiet and vice versa. Everyone who is both not old and not strong is either not funny or not generous. Everyone who is both not humble and humble is brave and vice versa. Everyone who is both funny and not humble is humble. If someone is either not curious or wise then alice is both not wise and not quiet. Everyone who is both curious and brave is either not generous or not brave and vice versa. If someone is kind then someone is not rich or rich and vice versa. If fred is either funny or generous then paul is creative. Everyone who is funny or not patient is patient and vice versa. If someone is creative then lucy is either rich or patient. Everyone who is both happy and old is both not funny and funny and vice versa. Everyone who is curious is either old or kind and vice versa. Everyone who is tall or creative is not tall and vice versa. Everyone who is both not funny and not generous is either not kind or rich. Everyone who is both old and not kind is not wise and vice versa. Someone is both rich and not kind. Someone is not brave or not tall. Someone is not generous or wise. John is both happy and not generous. Someone is not curious. | Paul is not wise. | neutral | ((?[X]:((kind(X)|~brave(X))))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:((~old(X)&~strong(X))=>(~funny(X)<~>~generous(X))))&
(![X]:((~humble(X)&humble(X))<=>brave(X)))&
(![X]:((funny(X)&~humble(X))=>humble(X)))&
((?[X]:((~curious(X)<~>wise(X))))=>((~wise(alice)&~quiet(alice))))&
(![X]:((curious(X)&brave(X))<=>(~generous(X)<~>~brave(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((funny(fred)<~>generous(fred)))=>(creative(paul)))&
(![X]:((funny(X)|~patient(X))<=>patient(X)))&
((?[X]:(creative(X)))=>((rich(lucy)<~>patient(lucy))))&
(![X]:((happy(X)&old(X))<=>(~funny(X)&funny(X))))&
(![X]:(curious(X)<=>(old(X)<~>kind(X))))&
(![X]:((tall(X)|creative(X))<=>~tall(X)))&
(![X]:((~funny(X)&~generous(X))=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)&~kind(X))<=>~wise(X)))&
(?[X]:((rich(X)&~kind(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~generous(X)|wise(X))))&
((happy(john)&~generous(john)))&
(?[X]:(~curious(X))) | ~wise(paul) | [] | null | 0 |
If lucy is both not patient and not tall then someone is wise and vice versa.
Everyone who is either not calm or not creative is both not strong and not creative.
If someone is both calm and old then alice is either not patient or not creative.
Everyone who is both funny and patient is not strong.
If paul is not strong then someone is both not tall and rich and vice versa.
If john is calm or not patient then fred is both not kind and not rich.
Everyone who is either curious or not calm is both not generous and not brave.
If someone is not brave or brave then lucy is either curious or creative.
If someone is either not patient or creative then someone is both strong and not wise.
If susan is brave or curious then someone is either not brave or not quiet.
Everyone who is either generous or not tall is either not brave or funny.
Everyone who is both funny and strong is both not tall and humble.
Everyone who is both not humble and humble is not happy or generous and vice versa.
Everyone who is both not creative and not wise is both not quiet and not curious.
If john is either not tall or not old then susan is both rich and happy.
Everyone who is either not happy or happy is brave.
Someone is either not wise or happy.
Susan is both not generous and not creative.
Susan is either brave or creative.
Mary is not brave or not curious.
Paul is not curious.
Susan is not generous or not wise.
Someone is not creative or strong.
Someone is humble. | Mary is calm. | entailment | (((~patient(lucy)&~tall(lucy)))<=>(?[X]:(wise(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(~strong(X)&~creative(X))))&
((?[X]:((calm(X)&old(X))))=>((~patient(alice)<~>~creative(alice))))&
(![X]:((funny(X)&patient(X))=>~strong(X)))&
((~strong(paul))<=>(?[X]:((~tall(X)&rich(X)))))&
(((calm(john)|~patient(john)))=>((~kind(fred)&~rich(fred))))&
(![X]:((curious(X)<~>~calm(X))=>(~generous(X)&~brave(X))))&
((?[X]:((~brave(X)|brave(X))))=>((curious(lucy)<~>creative(lucy))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((strong(X)&~wise(X)))))&
(((brave(susan)|curious(susan)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~brave(X)<~>funny(X))))&
(![X]:((funny(X)&strong(X))=>(~tall(X)&humble(X))))&
(![X]:((~humble(X)&humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((~creative(X)&~wise(X))=>(~quiet(X)&~curious(X))))&
(((~tall(john)<~>~old(john)))=>((rich(susan)&happy(susan))))&
(![X]:((~happy(X)<~>happy(X))=>brave(X)))&
(?[X]:((~wise(X)<~>happy(X))))&
((~generous(susan)&~creative(susan)))&
((brave(susan)<~>creative(susan)))&
((~brave(mary)|~curious(mary)))&
(~curious(paul))&
((~generous(susan)|~wise(susan)))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(humble(X))) | calm(mary) | [
"p6",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5702921899494520402753329
% SZS output start Proof for 5702921899494520402753329
7. ! [X0] : ((curious(X0) <~> ~calm(X0)) => (~brave(X0) & ~generous(X0))) [input p6]
13. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (generous(X0) | ~happy(X0))) [input p12]
16. ! [X0] : ((~happy(X0) <~> happy(X0)) => brave(X0)) [input p15]
20. ~curious(mary) | ~brave(mary) [input p19]
25. ~calm(mary) [input hypothesis]
33. ! [X0] : ((~brave(X0) & ~generous(X0)) | (curious(X0) <=> ~calm(X0))) [ennf transformation 7]
43. ! [X0] : (brave(X0) | (~happy(X0) <=> happy(X0))) [ennf transformation 16]
55. ! [X0] : ((~brave(X0) & ~generous(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) [nnf transformation 33]
65. ! [X0] : (((humble(X0) & ~humble(X0)) | (~generous(X0) & happy(X0))) & ((generous(X0) | ~happy(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 13]
66. ! [X0] : (((humble(X0) & ~humble(X0)) | (~generous(X0) & happy(X0))) & (generous(X0) | ~happy(X0) | ~humble(X0) | humble(X0))) [flattening 65]
68. ! [X0] : (brave(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 43]
95. ~brave(X0) | curious(X0) | calm(X0) [cnf transformation 55]
115. ~humble(X0) | happy(X0) [cnf transformation 66]
117. happy(X0) | humble(X0) [cnf transformation 66]
126. brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 68]
133. ~curious(mary) | ~brave(mary) [cnf transformation 20]
138. ~calm(mary) [cnf transformation 25]
140. brave(X0) | ~happy(X0) [duplicate literal removal 126]
218. 18 <=> ! [X0] : brave(X0) [avatar definition]
219. brave(X0) <- (18) [avatar component clause 218]
262. happy(X0) [subsumption resolution 115,117]
277. brave(X0) [subsumption resolution 140,262]
278. 18 [avatar split clause 277,218]
283. 30 <=> brave(mary) [avatar definition]
285. ~brave(mary) <- (~30) [avatar component clause 283]
287. 31 <=> curious(mary) [avatar definition]
289. ~curious(mary) <- (~31) [avatar component clause 287]
290. ~30 | ~31 [avatar split clause 133,287,283]
302. $false <- (18, ~30) [resolution 285,219]
303. ~18 | 30 [avatar contradiction clause 302]
328. curious(X0) | calm(X0) <- (18) [resolution 95,219]
335. calm(mary) <- (18, ~31) [resolution 328,289]
338. $false <- (18, ~31) [subsumption resolution 335,138]
339. ~18 | 31 [avatar contradiction clause 338]
340. $false [avatar sat refutation 278,290,303,339]
% SZS output end Proof for 5702921899494520402753329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or curious then lucy is not quiet or not wise.
If lucy is not rich then fred is old.
If susan is either kind or not strong then someone is creative or strong and vice versa.
Everyone who is wise or not strong is creative or not creative.
If paul is either not strong or not quiet then someone is both creative and calm and vice versa.
If mary is happy or funny then someone is quiet or not calm and vice versa.
Everyone who is either wise or not strong is strong.
Everyone who is not creative or generous is funny and vice versa.
If lucy is not kind or funny then paul is both not old and old.
Everyone who is both not rich and not quiet is both quiet and not quiet.
Everyone who is not creative or not rich is both not brave and not quiet.
If paul is not curious or humble then susan is funny and vice versa.
If someone is not happy or patient then susan is both wise and strong and vice versa.
If fred is either not strong or kind then fred is happy and vice versa.
If john is either funny or brave then someone is kind or creative and vice versa.
Everyone who is not wise is not generous.
Someone is not strong or funny.
Fred is not funny.
Mary is either not calm or calm.
Someone is either old or not rich.
Paul is both not happy and not kind.
Paul is not calm or not patient.
Alice is both generous and not humble.
Alice is rich. | Lucy is not funny. | entailment | ((?[X]:((wise(X)<~>curious(X))))=>((~quiet(lucy)|~wise(lucy))))&
((~rich(lucy))=>(old(fred)))&
(((kind(susan)<~>~strong(susan)))<=>(?[X]:((creative(X)|strong(X)))))&
(![X]:((wise(X)|~strong(X))=>(creative(X)|~creative(X))))&
(((~strong(paul)<~>~quiet(paul)))<=>(?[X]:((creative(X)&calm(X)))))&
(((happy(mary)|funny(mary)))<=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((wise(X)<~>~strong(X))=>strong(X)))&
(![X]:((~creative(X)|generous(X))<=>funny(X)))&
(((~kind(lucy)|funny(lucy)))=>((~old(paul)&old(paul))))&
(![X]:((~rich(X)&~quiet(X))=>(quiet(X)&~quiet(X))))&
(![X]:((~creative(X)|~rich(X))=>(~brave(X)&~quiet(X))))&
(((~curious(paul)|humble(paul)))<=>(funny(susan)))&
((?[X]:((~happy(X)|patient(X))))<=>((wise(susan)&strong(susan))))&
(((~strong(fred)<~>kind(fred)))<=>(happy(fred)))&
(((funny(john)<~>brave(john)))<=>(?[X]:((kind(X)|creative(X)))))&
(![X]:(~wise(X)=>~generous(X)))&
(?[X]:((~strong(X)|funny(X))))&
(~funny(fred))&
((~calm(mary)<~>calm(mary)))&
(?[X]:((old(X)<~>~rich(X))))&
((~happy(paul)&~kind(paul)))&
((~calm(paul)|~patient(paul)))&
((generous(alice)&~humble(alice)))&
(rich(alice)) | ~funny(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 302966766032284121549716
% SZS output start Proof for 302966766032284121549716
9. (funny(lucy) | ~kind(lucy)) => (old(paul) & ~old(paul)) [input p8]
25. funny(lucy) [input hypothesis]
32. (old(paul) & ~old(paul)) | (~funny(lucy) & kind(lucy)) [ennf transformation 9]
99. ~old(paul) | ~funny(lucy) [cnf transformation 32]
101. old(paul) | ~funny(lucy) [cnf transformation 32]
139. funny(lucy) [cnf transformation 25]
247. 24 <=> funny(lucy) [avatar definition]
251. 25 <=> old(paul) [avatar definition]
254. ~24 | 25 [avatar split clause 101,251,247]
260. ~24 | ~25 [avatar split clause 99,251,247]
361. 24 [avatar split clause 139,247]
362. $false [avatar sat refutation 254,260,361]
% SZS output end Proof for 302966766032284121549716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and happy is either tall or happy and vice versa. Everyone who is both kind and not old is calm or not wise and vice versa. If alice is either strong or rich then paul is either not calm or quiet. If someone is either not generous or not patient then someone is not quiet. Everyone who is both not calm and rich is not creative or quiet and vice versa. If someone is not patient then lucy is both curious and funny. If fred is both not quiet and quiet then someone is wise and vice versa. Everyone who is kind is both creative and not strong and vice versa. Everyone who is both calm and humble is not curious or not funny and vice versa. If lucy is creative or patient then alice is funny and vice versa. Everyone who is wise or calm is not generous and vice versa. If mary is patient then john is not rich or patient and vice versa. Everyone who is not brave is not happy or not quiet and vice versa. If someone is brave or tall then someone is either not patient or not happy and vice versa. If fred is brave then alice is not happy or wise and vice versa. Everyone who is either not patient or not strong is either curious or not happy. Mary is rich. Someone is creative. Someone is not generous. Mary is generous or curious. Someone is both not wise and humble. Someone is either humble or not generous. | Alice is happy. | neutral | (![X]:((~humble(X)&happy(X))<=>(tall(X)<~>happy(X))))&
(![X]:((kind(X)&~old(X))<=>(calm(X)|~wise(X))))&
(((strong(alice)<~>rich(alice)))=>((~calm(paul)<~>quiet(paul))))&
((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~calm(X)&rich(X))<=>(~creative(X)|quiet(X))))&
((?[X]:(~patient(X)))=>((curious(lucy)&funny(lucy))))&
(((~quiet(fred)&quiet(fred)))<=>(?[X]:(wise(X))))&
(![X]:(kind(X)<=>(creative(X)&~strong(X))))&
(![X]:((calm(X)&humble(X))<=>(~curious(X)|~funny(X))))&
(((creative(lucy)|patient(lucy)))<=>(funny(alice)))&
(![X]:((wise(X)|calm(X))<=>~generous(X)))&
((patient(mary))<=>((~rich(john)|patient(john))))&
(![X]:(~brave(X)<=>(~happy(X)|~quiet(X))))&
((?[X]:((brave(X)|tall(X))))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
((brave(fred))<=>((~happy(alice)|wise(alice))))&
(![X]:((~patient(X)<~>~strong(X))=>(curious(X)<~>~happy(X))))&
(rich(mary))&
(?[X]:(creative(X)))&
(?[X]:(~generous(X)))&
((generous(mary)|curious(mary)))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((humble(X)<~>~generous(X)))) | happy(alice) | [] | null | 0 |
Everyone who is not creative or not curious is patient and vice versa. If someone is calm or tall then susan is both old and creative and vice versa. Everyone who is not generous is either creative or not rich and vice versa. Everyone who is not generous is not wise. Everyone who is both not curious and not creative is not strong and vice versa. If someone is not tall then mary is not humble or wise. If alice is curious then someone is either not rich or generous and vice versa. Everyone who is not tall is both not quiet and not curious. If someone is either tall or happy then lucy is both humble and brave. Everyone who is not patient or quiet is both not curious and generous and vice versa. Everyone who is either rich or not tall is either generous or not happy and vice versa. If paul is not old then someone is either wise or not generous. If someone is brave then someone is either not calm or not happy. If someone is both not kind and not curious then someone is not brave or not creative and vice versa. Everyone who is quiet or generous is curious or happy and vice versa. If someone is not calm then someone is brave or generous and vice versa. Paul is both quiet and not kind. Someone is both not calm and happy. Susan is humble or calm. Someone is either kind or humble. Lucy is both not wise and not strong. Someone is either not creative or kind. | Alice is strong. | entailment | (![X]:((~creative(X)|~curious(X))<=>patient(X)))&
((?[X]:((calm(X)|tall(X))))<=>((old(susan)&creative(susan))))&
(![X]:(~generous(X)<=>(creative(X)<~>~rich(X))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~curious(X)&~creative(X))<=>~strong(X)))&
((?[X]:(~tall(X)))=>((~humble(mary)|wise(mary))))&
((curious(alice))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(![X]:(~tall(X)=>(~quiet(X)&~curious(X))))&
((?[X]:((tall(X)<~>happy(X))))=>((humble(lucy)&brave(lucy))))&
(![X]:((~patient(X)|quiet(X))<=>(~curious(X)&generous(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~happy(X))))&
((~old(paul))=>(?[X]:((wise(X)<~>~generous(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
((?[X]:((~kind(X)&~curious(X))))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((quiet(X)|generous(X))<=>(curious(X)|happy(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((brave(X)|generous(X)))))&
((quiet(paul)&~kind(paul)))&
(?[X]:((~calm(X)&happy(X))))&
((humble(susan)|calm(susan)))&
(?[X]:((kind(X)<~>humble(X))))&
((~wise(lucy)&~strong(lucy)))&
(?[X]:((~creative(X)<~>kind(X)))) | strong(alice) | [
"p2",
"p4",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8064670595704245740432480
% SZS output start Proof for 8064670595704245740432480
3. ! [X0] : (~generous(X0) <=> (creative(X0) <~> ~rich(X0))) [input p2]
5. ! [X0] : ((~creative(X0) & ~curious(X0)) <=> ~strong(X0)) [input p4]
7. curious(alice) <=> ? [X0] : (~rich(X0) <~> generous(X0)) [input p6]
21. ~strong(lucy) & ~wise(lucy) [input p20]
23. ~strong(alice) [input hypothesis]
27. ! [X0] : (~strong(X0) => (~creative(X0) & ~curious(X0))) [unused predicate definition removal 5]
29. ! [X0] : ((~creative(X0) & ~curious(X0)) | strong(X0)) [ennf transformation 27]
43. ! [X0] : ((~generous(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | generous(X0))) [nnf transformation 3]
44. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X0] : ((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~curious(alice)) [nnf transformation 7]
45. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) | ~curious(alice)) [rectify 44]
46. ? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) => ((~generous(sK1) | rich(sK1)) & (generous(sK1) | ~rich(sK1))) [choice axiom]
47. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(sK1) | rich(sK1)) & (generous(sK1) | ~rich(sK1))) | ~curious(alice)) [skolemisation 45,46]
87. ~rich(X0) | creative(X0) | generous(X0) [cnf transformation 43]
90. ~generous(X0) | creative(X0) | rich(X0) [cnf transformation 43]
92. ~curious(X0) | strong(X0) [cnf transformation 29]
93. ~creative(X0) | strong(X0) [cnf transformation 29]
97. curious(alice) | generous(X0) | rich(X0) [cnf transformation 47]
98. curious(alice) | ~rich(X0) | ~generous(X0) [cnf transformation 47]
142. ~strong(lucy) [cnf transformation 21]
145. ~strong(alice) [cnf transformation 23]
186. 10 <=> ! [X0] : (~rich(X0) | ~generous(X0)) [avatar definition]
187. ~rich(X0) | ~generous(X0) <- (10) [avatar component clause 186]
189. 11 <=> curious(alice) [avatar definition]
191. curious(alice) <- (11) [avatar component clause 189]
192. 10 | 11 [avatar split clause 98,189,186]
194. 12 <=> ! [X0] : (generous(X0) | rich(X0)) [avatar definition]
195. rich(X0) | generous(X0) <- (12) [avatar component clause 194]
196. 12 | 11 [avatar split clause 97,189,194]
254. 25 <=> ! [X1] : creative(X1) [avatar definition]
255. creative(X1) <- (25) [avatar component clause 254]
344. strong(alice) <- (11) [resolution 92,191]
345. $false <- (11) [subsumption resolution 344,145]
346. ~11 [avatar contradiction clause 345]
375. creative(X0) | generous(X0) | generous(X0) <- (12) [resolution 87,195]
377. generous(X0) | creative(X0) <- (12) [duplicate literal removal 375]
387. creative(X0) | rich(X0) | creative(X0) <- (12) [resolution 90,377]
392. rich(X0) | creative(X0) <- (12) [duplicate literal removal 387]
434. creative(X3) | ~generous(X3) <- (10, 12) [resolution 392,187]
436. creative(X3) <- (10, 12) [subsumption resolution 434,377]
437. 25 | ~10 | ~12 [avatar split clause 436,194,186,254]
439. strong(X1) <- (25) [resolution 255,93]
446. $false <- (25) [resolution 439,142]
449. ~25 [avatar contradiction clause 446]
450. $false [avatar sat refutation 192,196,346,437,449]
% SZS output end Proof for 8064670595704245740432480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not strong is both quiet and not strong and vice versa.
Everyone who is strong is either not rich or not happy.
Everyone who is strong or not humble is not patient.
Everyone who is strong is not creative or humble and vice versa.
Everyone who is not strong or happy is both funny and not patient.
If someone is not quiet then mary is curious.
If mary is either not generous or patient then someone is not strong and vice versa.
If someone is not strong then someone is not quiet.
If someone is either not tall or not creative then john is both not curious and not kind.
Everyone who is both strong and not rich is both not generous and funny and vice versa.
If john is not generous then susan is both old and quiet.
If someone is quiet or not quiet then someone is either wise or not wise and vice versa.
Everyone who is either happy or not kind is both not humble and not brave and vice versa.
Everyone who is both not happy and not brave is either happy or not generous and vice versa.
Everyone who is wise or generous is either patient or old.
Everyone who is not wise or curious is both quiet and not brave.
Mary is both rich and quiet.
Someone is happy.
Someone is not creative.
Lucy is not kind or funny.
Someone is both not rich and wise.
Someone is not funny. | John is humble. | neutral | (![X]:((~brave(X)<~>~strong(X))<=>(quiet(X)&~strong(X))))&
(![X]:(strong(X)=>(~rich(X)<~>~happy(X))))&
(![X]:((strong(X)|~humble(X))=>~patient(X)))&
(![X]:(strong(X)<=>(~creative(X)|humble(X))))&
(![X]:((~strong(X)|happy(X))=>(funny(X)&~patient(X))))&
((?[X]:(~quiet(X)))=>(curious(mary)))&
(((~generous(mary)<~>patient(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~curious(john)&~kind(john))))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)&funny(X))))&
((~generous(john))=>((old(susan)&quiet(susan))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>~kind(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((wise(X)|generous(X))=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)|curious(X))=>(quiet(X)&~brave(X))))&
((rich(mary)&quiet(mary)))&
(?[X]:(happy(X)))&
(?[X]:(~creative(X)))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~rich(X)&wise(X))))&
(?[X]:(~funny(X))) | humble(john) | [] | null | 0 |
Everyone who is either humble or tall is both happy and not rich and vice versa.
Everyone who is either calm or creative is not patient or not generous and vice versa.
Everyone who is both happy and patient is both strong and not quiet.
If someone is both not rich and calm then someone is not kind or not humble.
Everyone who is either not funny or not calm is strong or happy.
If someone is tall then susan is not wise and vice versa.
If someone is not strong or rich then alice is either funny or not generous and vice versa.
Everyone who is either not quiet or not funny is not calm.
If someone is either strong or not old then someone is calm or curious.
Everyone who is patient is both rich and brave and vice versa.
Everyone who is both generous and happy is not calm.
If someone is both not old and humble then someone is creative or not happy and vice versa.
If mary is rich then someone is strong or old and vice versa.
Everyone who is not funny is both curious and not brave.
If john is generous then alice is both not old and not patient and vice versa.
Everyone who is not creative or not calm is not rich.
Someone is both not humble and old.
John is both patient and tall.
Someone is both creative and not kind.
Someone is not humble.
John is both not kind and brave.
Mary is kind or not brave.
Someone is either not happy or not old. | Mary is not kind. | contradiction | (![X]:((humble(X)<~>tall(X))<=>(happy(X)&~rich(X))))&
(![X]:((calm(X)<~>creative(X))<=>(~patient(X)|~generous(X))))&
(![X]:((happy(X)&patient(X))=>(strong(X)&~quiet(X))))&
((?[X]:((~rich(X)&calm(X))))=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(strong(X)|happy(X))))&
((?[X]:(tall(X)))<=>(~wise(susan)))&
((?[X]:((~strong(X)|rich(X))))<=>((funny(alice)<~>~generous(alice))))&
(![X]:((~quiet(X)<~>~funny(X))=>~calm(X)))&
((?[X]:((strong(X)<~>~old(X))))=>(?[X]:((calm(X)|curious(X)))))&
(![X]:(patient(X)<=>(rich(X)&brave(X))))&
(![X]:((generous(X)&happy(X))=>~calm(X)))&
((?[X]:((~old(X)&humble(X))))<=>(?[X]:((creative(X)|~happy(X)))))&
((rich(mary))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:(~funny(X)=>(curious(X)&~brave(X))))&
((generous(john))<=>((~old(alice)&~patient(alice))))&
(![X]:((~creative(X)|~calm(X))=>~rich(X)))&
(?[X]:((~humble(X)&old(X))))&
((patient(john)&tall(john)))&
(?[X]:((creative(X)&~kind(X))))&
(?[X]:(~humble(X)))&
((~kind(john)&brave(john)))&
((kind(mary)|~brave(mary)))&
(?[X]:((~happy(X)<~>~old(X)))) | ~kind(mary) | [
"p1",
"p9",
"p12",
"p15",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4645207736991306869204797
% SZS output start Proof for 4645207736991306869204797
2. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (~generous(X0) | ~patient(X0))) [input p1]
10. ! [X0] : (patient(X0) <=> (brave(X0) & rich(X0))) [input p9]
13. rich(mary) <=> ? [X0] : (old(X0) | strong(X0)) [input p12]
16. ! [X0] : ((~calm(X0) | ~creative(X0)) => ~rich(X0)) [input p15]
17. ? [X0] : (old(X0) & ~humble(X0)) [input p16]
22. ~brave(mary) | kind(mary) [input p21]
24. ~kind(mary) [input hypothesis]
39. ! [X0] : (~rich(X0) | (calm(X0) & creative(X0))) [ennf transformation 16]
42. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 2]
43. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 42]
57. ! [X0] : ((patient(X0) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ~patient(X0))) [nnf transformation 10]
58. ! [X0] : ((patient(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~patient(X0))) [flattening 57]
64. (rich(mary) | ! [X0] : (~old(X0) & ~strong(X0))) & (? [X0] : (old(X0) | strong(X0)) | ~rich(mary)) [nnf transformation 13]
65. (rich(mary) | ! [X0] : (~old(X0) & ~strong(X0))) & (? [X1] : (old(X1) | strong(X1)) | ~rich(mary)) [rectify 64]
66. ? [X1] : (old(X1) | strong(X1)) => (old(sK5) | strong(sK5)) [choice axiom]
67. (rich(mary) | ! [X0] : (~old(X0) & ~strong(X0))) & ((old(sK5) | strong(sK5)) | ~rich(mary)) [skolemisation 65,66]
70. ? [X0] : (old(X0) & ~humble(X0)) => (old(sK6) & ~humble(sK6)) [choice axiom]
71. old(sK6) & ~humble(sK6) [skolemisation 17,70]
89. ~creative(X0) | ~calm(X0) | patient(X0) [cnf transformation 43]
107. ~patient(X0) | brave(X0) [cnf transformation 58]
117. rich(mary) | ~old(X0) [cnf transformation 67]
122. ~rich(X0) | creative(X0) [cnf transformation 39]
123. ~rich(X0) | calm(X0) [cnf transformation 39]
125. old(sK6) [cnf transformation 71]
133. ~brave(mary) | kind(mary) [cnf transformation 22]
136. ~kind(mary) [cnf transformation 24]
221. 20 <=> ! [X0] : ~old(X0) [avatar definition]
222. ~old(X0) <- (20) [avatar component clause 221]
224. 21 <=> rich(mary) [avatar definition]
226. rich(mary) <- (21) [avatar component clause 224]
227. 20 | 21 [avatar split clause 117,224,221]
257. 28 <=> kind(mary) [avatar definition]
261. 29 <=> brave(mary) [avatar definition]
263. ~brave(mary) <- (~29) [avatar component clause 261]
264. 28 | ~29 [avatar split clause 133,261,257]
275. ~28 [avatar split clause 136,257]
276. $false <- (20) [resolution 222,125]
277. ~20 [avatar contradiction clause 276]
283. creative(mary) <- (21) [resolution 122,226]
285. calm(mary) <- (21) [resolution 123,226]
331. ~calm(mary) | patient(mary) <- (21) [resolution 89,283]
335. patient(mary) <- (21) [subsumption resolution 331,285]
370. brave(mary) <- (21) [resolution 335,107]
373. $false <- (21, ~29) [subsumption resolution 370,263]
374. ~21 | 29 [avatar contradiction clause 373]
375. $false [avatar sat refutation 227,264,275,277,374]
% SZS output end Proof for 4645207736991306869204797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall or brave then someone is not old and vice versa.
If someone is rich then someone is either kind or rich and vice versa.
Everyone who is funny or not generous is kind and vice versa.
If susan is either patient or not kind then someone is both old and wise and vice versa.
If alice is both humble and not humble then someone is both strong and humble and vice versa.
Everyone who is old or brave is both wise and not curious and vice versa.
If alice is both kind and generous then someone is either generous or not curious and vice versa.
If someone is wise or not creative then fred is either generous or humble and vice versa.
Everyone who is brave is both not happy and not old and vice versa.
Everyone who is not tall or quiet is not quiet or humble.
If someone is not creative then someone is not wise.
Everyone who is not brave is kind or not quiet and vice versa.
Everyone who is not generous or generous is both not strong and creative and vice versa.
If lucy is either not humble or creative then someone is not creative.
If someone is wise then someone is not old or not kind.
Everyone who is not humble or not brave is not happy or brave.
Fred is either not calm or kind.
Alice is wise or rich.
Someone is either not brave or not generous.
Alice is either not humble or brave. | Fred is curious. | contradiction | ((?[X]:((tall(X)|brave(X))))<=>(?[X]:(~old(X))))&
((?[X]:(rich(X)))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((funny(X)|~generous(X))<=>kind(X)))&
(((patient(susan)<~>~kind(susan)))<=>(?[X]:((old(X)&wise(X)))))&
(((humble(alice)&~humble(alice)))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((old(X)|brave(X))<=>(wise(X)&~curious(X))))&
(((kind(alice)&generous(alice)))<=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:((wise(X)|~creative(X))))<=>((generous(fred)<~>humble(fred))))&
(![X]:(brave(X)<=>(~happy(X)&~old(X))))&
(![X]:((~tall(X)|quiet(X))=>(~quiet(X)|humble(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(kind(X)|~quiet(X))))&
(![X]:((~generous(X)|generous(X))<=>(~strong(X)&creative(X))))&
(((~humble(lucy)<~>creative(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((~humble(X)|~brave(X))=>(~happy(X)|brave(X))))&
((~calm(fred)<~>kind(fred)))&
((wise(alice)|rich(alice)))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~humble(alice)<~>brave(alice))) | curious(fred) | [
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5872836420721207409256037
% SZS output start Proof for 5872836420721207409256037
6. ! [X0] : ((brave(X0) | old(X0)) <=> (~curious(X0) & wise(X0))) [input p5]
9. ! [X0] : (brave(X0) <=> (~old(X0) & ~happy(X0))) [input p8]
16. ! [X0] : ((~brave(X0) | ~humble(X0)) => (brave(X0) | ~happy(X0))) [input p15]
21. curious(fred) [input hypothesis]
31. ! [X0] : ((brave(X0) | ~happy(X0)) | (brave(X0) & humble(X0))) [ennf transformation 16]
32. ! [X0] : (brave(X0) | ~happy(X0) | (brave(X0) & humble(X0))) [flattening 31]
54. ! [X0] : (((brave(X0) | old(X0)) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | (~brave(X0) & ~old(X0)))) [nnf transformation 6]
55. ! [X0] : ((brave(X0) | old(X0) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | (~brave(X0) & ~old(X0)))) [flattening 54]
65. ! [X0] : ((brave(X0) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | ~brave(X0))) [nnf transformation 9]
66. ! [X0] : ((brave(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ~brave(X0))) [flattening 65]
107. ~curious(X0) | ~old(X0) [cnf transformation 55]
108. ~curious(X0) | ~brave(X0) [cnf transformation 55]
122. ~happy(X0) | ~brave(X0) [cnf transformation 66]
124. happy(X0) | old(X0) | brave(X0) [cnf transformation 66]
140. brave(X0) | ~happy(X0) | brave(X0) [cnf transformation 32]
148. curious(fred) [cnf transformation 21]
149. brave(X0) | ~happy(X0) [duplicate literal removal 140]
321. ~happy(X0) [subsumption resolution 149,122]
372. ~old(fred) [resolution 107,148]
373. ~brave(fred) [resolution 108,148]
398. old(X1) | brave(X1) [resolution 124,321]
429. brave(fred) [resolution 398,372]
434. $false [subsumption resolution 429,373]
% SZS output end Proof for 5872836420721207409256037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is happy or creative then lucy is not creative or quiet and vice versa.
If susan is curious then someone is not curious and vice versa.
Everyone who is both kind and not rich is either not old or not strong.
Everyone who is funny is not patient or not brave.
If someone is not strong or not generous then alice is either quiet or not brave and vice versa.
Everyone who is not curious or generous is not generous or creative and vice versa.
Everyone who is both strong and not tall is both patient and curious and vice versa.
If someone is not generous or kind then someone is both not funny and not generous and vice versa.
Everyone who is tall or not wise is either brave or humble and vice versa.
If alice is not wise then someone is either strong or not generous and vice versa.
If susan is either brave or wise then someone is not quiet.
Everyone who is creative is either humble or not tall.
Everyone who is either old or not generous is either not happy or not tall.
Everyone who is either not patient or curious is generous or strong and vice versa.
Everyone who is either old or not patient is not brave or not curious and vice versa.
If lucy is not happy then fred is tall or not creative.
Alice is either not patient or quiet.
Paul is both not happy and not patient.
Lucy is kind or rich.
Fred is either quiet or not happy.
Fred is both not brave and kind.
Someone is both brave and calm.
Fred is either funny or not curious. | Alice is quiet. | neutral | (((happy(susan)|creative(susan)))<=>((~creative(lucy)|quiet(lucy))))&
((curious(susan))<=>(?[X]:(~curious(X))))&
(![X]:((kind(X)&~rich(X))=>(~old(X)<~>~strong(X))))&
(![X]:(funny(X)=>(~patient(X)|~brave(X))))&
((?[X]:((~strong(X)|~generous(X))))<=>((quiet(alice)<~>~brave(alice))))&
(![X]:((~curious(X)|generous(X))<=>(~generous(X)|creative(X))))&
(![X]:((strong(X)&~tall(X))<=>(patient(X)&curious(X))))&
((?[X]:((~generous(X)|kind(X))))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:((tall(X)|~wise(X))<=>(brave(X)<~>humble(X))))&
((~wise(alice))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(((brave(susan)<~>wise(susan)))=>(?[X]:(~quiet(X))))&
(![X]:(creative(X)=>(humble(X)<~>~tall(X))))&
(![X]:((old(X)<~>~generous(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>curious(X))<=>(generous(X)|strong(X))))&
(![X]:((old(X)<~>~patient(X))<=>(~brave(X)|~curious(X))))&
((~happy(lucy))=>((tall(fred)|~creative(fred))))&
((~patient(alice)<~>quiet(alice)))&
((~happy(paul)&~patient(paul)))&
((kind(lucy)|rich(lucy)))&
((quiet(fred)<~>~happy(fred)))&
((~brave(fred)&kind(fred)))&
(?[X]:((brave(X)&calm(X))))&
((funny(fred)<~>~curious(fred))) | quiet(alice) | [] | null | 0 |
If mary is either not curious or strong then someone is both calm and not kind and vice versa.
If someone is either tall or strong then someone is humble and vice versa.
Everyone who is not quiet or kind is happy or calm.
Everyone who is both not old and happy is both not curious and not creative and vice versa.
Everyone who is kind or tall is either wise or happy.
Everyone who is not humble or funny is either not strong or not calm.
Everyone who is wise is not humble or kind and vice versa.
If mary is both not humble and patient then alice is generous or not patient and vice versa.
Everyone who is both generous and rich is not generous.
If someone is not generous then someone is either wise or not strong and vice versa.
If fred is either not calm or wise then lucy is not strong.
Everyone who is both old and patient is either not tall or patient and vice versa.
If someone is not calm or not happy then john is both curious and not patient.
Everyone who is both not brave and not old is old.
Everyone who is old or not rich is both not tall and rich.
Everyone who is both not generous and not humble is not tall or tall and vice versa.
Someone is either happy or not happy.
Alice is both patient and not old.
John is either old or not old.
Someone is both not kind and quiet.
Mary is not humble.
Someone is not patient or tall. | Lucy is not curious. | neutral | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(happy(X)|calm(X))))&
(![X]:((~old(X)&happy(X))<=>(~curious(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))=>(wise(X)<~>happy(X))))&
(![X]:((~humble(X)|funny(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~humble(X)|kind(X))))&
(((~humble(mary)&patient(mary)))<=>((generous(alice)|~patient(alice))))&
(![X]:((generous(X)&rich(X))=>~generous(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
((patient(alice)&~old(alice)))&
((old(john)<~>~old(john)))&
(?[X]:((~kind(X)&quiet(X))))&
(~humble(mary))&
(?[X]:((~patient(X)|tall(X)))) | ~curious(lucy) | [] | null | 0 |
Everyone who is both brave and not curious is not humble or not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Everyone who is not wise or not old is not brave and vice versa.
Everyone who is either not kind or wise is not calm or old and vice versa.
Everyone who is both not creative and not curious is not happy or kind and vice versa.
If john is both curious and not funny then alice is wise and vice versa.
If someone is humble then someone is not quiet.
If someone is either not creative or not curious then alice is not quiet or calm.
Everyone who is not creative or generous is creative.
If someone is either not calm or not brave then fred is either not patient or not humble and vice versa.
Everyone who is generous is not funny or generous.
If someone is either quiet or not patient then someone is not happy and vice versa.
Everyone who is wise or not funny is generous or happy.
Someone is patient or kind.
Mary is not strong.
Someone is not strong.
Someone is either funny or not wise.
Someone is either not tall or not creative.
Someone is not curious. | Mary is funny. | entailment | (![X]:((brave(X)&~curious(X))=>(~humble(X)|~creative(X))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(![X]:((~wise(X)|~old(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|old(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~happy(X)|kind(X))))&
(((curious(john)&~funny(john)))<=>(wise(alice)))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>((~quiet(alice)|calm(alice))))&
(![X]:((~creative(X)|generous(X))=>creative(X)))&
((?[X]:((~calm(X)<~>~brave(X))))<=>((~patient(fred)<~>~humble(fred))))&
(![X]:(generous(X)=>(~funny(X)|generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))=>(generous(X)|happy(X))))&
(?[X]:((patient(X)|kind(X))))&
(~strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~curious(X))) | funny(mary) | [
"p2",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7846187681640562870967463
% SZS output start Proof for 7846187681640562870967463
3. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X0] : brave(X0) [input p2]
6. ! [X0] : ((~old(X0) | ~wise(X0)) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (old(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (kind(X0) | ~happy(X0))) [input p7]
12. ! [X0] : ((generous(X0) | ~creative(X0)) => creative(X0)) [input p11]
23. ~funny(mary) [input hypothesis]
24. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X1] : brave(X1) [rectify 3]
29. ? [X1] : brave(X1) | ! [X0] : (~creative(X0) | funny(X0)) [ennf transformation 24]
34. ! [X0] : (creative(X0) | (~generous(X0) & creative(X0))) [ennf transformation 12]
44. ? [X0] : brave(X0) | ! [X1] : (~creative(X1) | funny(X1)) [rectify 29]
45. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
46. brave(sK1) | ! [X1] : (~creative(X1) | funny(X1)) [skolemisation 44,45]
52. ! [X0] : (((~old(X0) | ~wise(X0)) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [nnf transformation 6]
53. ! [X0] : ((~old(X0) | ~wise(X0) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 54]
56. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 8]
57. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | curious(X0) | creative(X0))) [flattening 56]
91. brave(sK1) | ~creative(X1) | funny(X1) [cnf transformation 46]
99. ~brave(X0) | wise(X0) [cnf transformation 53]
100. ~brave(X0) | old(X0) [cnf transformation 53]
107. ~old(X0) | kind(X0) | ~wise(X0) [cnf transformation 55]
110. ~kind(X0) | ~creative(X0) [cnf transformation 57]
119. creative(X0) | creative(X0) [cnf transformation 34]
144. ~funny(mary) [cnf transformation 23]
145. creative(X0) [duplicate literal removal 119]
176. 7 <=> ! [X1] : (~creative(X1) | funny(X1)) [avatar definition]
177. ~creative(X1) | funny(X1) <- (7) [avatar component clause 176]
179. 8 <=> brave(sK1) [avatar definition]
181. brave(sK1) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 91,179,176]
327. funny(X1) <- (7) [subsumption resolution 177,145]
328. $false <- (7) [resolution 327,144]
333. ~7 [avatar contradiction clause 328]
334. wise(sK1) <- (8) [resolution 99,181]
335. old(sK1) <- (8) [resolution 100,181]
365. 43 <=> kind(sK1) [avatar definition]
367. kind(sK1) <- (43) [avatar component clause 365]
369. kind(sK1) | ~wise(sK1) <- (8) [resolution 107,335]
370. kind(sK1) <- (8) [subsumption resolution 369,334]
371. 43 | ~8 [avatar split clause 370,179,365]
376. ~creative(sK1) <- (43) [resolution 367,110]
377. $false <- (43) [subsumption resolution 376,145]
378. ~43 [avatar contradiction clause 377]
379. $false [avatar sat refutation 182,333,371,378]
% SZS output end Proof for 7846187681640562870967463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or wise then lucy is both not strong and patient and vice versa.
Everyone who is not calm or not curious is either tall or not creative and vice versa.
If someone is both not creative and not old then john is not curious.
If paul is both old and humble then fred is either not curious or not tall.
Everyone who is both not kind and wise is either not tall or not humble and vice versa.
Everyone who is either brave or strong is not wise or not old.
If someone is not brave or happy then someone is happy and vice versa.
If alice is both not creative and not happy then someone is not strong or tall and vice versa.
Everyone who is old is both not creative and patient.
Everyone who is either not funny or not tall is both curious and not funny and vice versa.
If john is both not kind and creative then someone is not creative and vice versa.
If someone is both not patient and brave then someone is wise and vice versa.
If someone is patient then john is either quiet or not curious and vice versa.
If fred is not patient then fred is both funny and not strong and vice versa.
Everyone who is calm is either not generous or creative and vice versa.
Everyone who is not curious is both not funny and quiet.
Lucy is both creative and not funny.
Paul is wise or not curious.
Fred is both curious and happy.
Paul is kind.
Someone is both not brave and not humble.
Paul is funny.
Someone is both tall and not rich.
Lucy is both rich and creative. | John is tall. | entailment | (((kind(fred)<~>wise(fred)))<=>((~strong(lucy)&patient(lucy))))&
(![X]:((~calm(X)|~curious(X))<=>(tall(X)<~>~creative(X))))&
((?[X]:((~creative(X)&~old(X))))=>(~curious(john)))&
(((old(paul)&humble(paul)))=>((~curious(fred)<~>~tall(fred))))&
(![X]:((~kind(X)&wise(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((brave(X)<~>strong(X))=>(~wise(X)|~old(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(happy(X))))&
(((~creative(alice)&~happy(alice)))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:(old(X)=>(~creative(X)&patient(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>(curious(X)&~funny(X))))&
(((~kind(john)&creative(john)))<=>(?[X]:(~creative(X))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:(wise(X))))&
((?[X]:(patient(X)))<=>((quiet(john)<~>~curious(john))))&
((~patient(fred))<=>((funny(fred)&~strong(fred))))&
(![X]:(calm(X)<=>(~generous(X)<~>creative(X))))&
(![X]:(~curious(X)=>(~funny(X)&quiet(X))))&
((creative(lucy)&~funny(lucy)))&
((wise(paul)|~curious(paul)))&
((curious(fred)&happy(fred)))&
(kind(paul))&
(?[X]:((~brave(X)&~humble(X))))&
(funny(paul))&
(?[X]:((tall(X)&~rich(X))))&
((rich(lucy)&creative(lucy))) | tall(john) | [
"p1",
"p7",
"p9",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7249440693440265287364787
% SZS output start Proof for 7249440693440265287364787
2. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (tall(X0) <~> ~creative(X0))) [input p1]
8. (~happy(alice) & ~creative(alice)) <=> ? [X0] : (tall(X0) | ~strong(X0)) [input p7]
10. ! [X0] : ((~funny(X0) <~> ~tall(X0)) <=> (~funny(X0) & curious(X0))) [input p9]
11. (creative(john) & ~kind(john)) <=> ? [X0] : ~creative(X0) [input p10]
22. funny(paul) [input p21]
25. ~tall(john) [input hypothesis]
37. ! [X0] : (((~curious(X0) | ~calm(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (curious(X0) & calm(X0)))) [nnf transformation 2]
38. ! [X0] : ((~curious(X0) | ~calm(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (curious(X0) & calm(X0)))) [flattening 37]
48. ((~happy(alice) & ~creative(alice)) | ! [X0] : (~tall(X0) & strong(X0))) & (? [X0] : (tall(X0) | ~strong(X0)) | (happy(alice) | creative(alice))) [nnf transformation 8]
49. ((~happy(alice) & ~creative(alice)) | ! [X0] : (~tall(X0) & strong(X0))) & (? [X0] : (tall(X0) | ~strong(X0)) | happy(alice) | creative(alice)) [flattening 48]
50. ((~happy(alice) & ~creative(alice)) | ! [X0] : (~tall(X0) & strong(X0))) & (? [X1] : (tall(X1) | ~strong(X1)) | happy(alice) | creative(alice)) [rectify 49]
51. ? [X1] : (tall(X1) | ~strong(X1)) => (tall(sK2) | ~strong(sK2)) [choice axiom]
52. ((~happy(alice) & ~creative(alice)) | ! [X0] : (~tall(X0) & strong(X0))) & ((tall(sK2) | ~strong(sK2)) | happy(alice) | creative(alice)) [skolemisation 50,51]
53. ! [X0] : ((((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (funny(X0) | ~curious(X0))) & ((~funny(X0) & curious(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))))) [nnf transformation 10]
54. ! [X0] : ((((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | funny(X0) | ~curious(X0)) & ((~funny(X0) & curious(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))))) [flattening 53]
55. ((creative(john) & ~kind(john)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~creative(john) | kind(john))) [nnf transformation 11]
56. ((creative(john) & ~kind(john)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~creative(john) | kind(john)) [flattening 55]
57. ((creative(john) & ~kind(john)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~creative(john) | kind(john)) [rectify 56]
58. ? [X1] : ~creative(X1) => ~creative(sK3) [choice axiom]
59. ((creative(john) & ~kind(john)) | ! [X0] : creative(X0)) & (~creative(sK3) | ~creative(john) | kind(john)) [skolemisation 57,58]
83. ~creative(X0) | tall(X0) | curious(X0) [cnf transformation 38]
104. ~creative(alice) | ~tall(X0) [cnf transformation 52]
112. ~funny(X0) | ~funny(X0) | tall(X0) [cnf transformation 54]
114. tall(X0) | funny(X0) | funny(X0) | ~curious(X0) [cnf transformation 54]
117. creative(john) | creative(X0) [cnf transformation 59]
142. funny(paul) [cnf transformation 22]
147. ~tall(john) [cnf transformation 25]
148. ~funny(X0) | tall(X0) [duplicate literal removal 112]
149. ~curious(X0) | funny(X0) | tall(X0) [duplicate literal removal 114]
176. 6 <=> curious(john) [avatar definition]
177. curious(john) <- (6) [avatar component clause 176]
220. 16 <=> ! [X0] : ~tall(X0) [avatar definition]
221. ~tall(X0) <- (16) [avatar component clause 220]
232. 19 <=> creative(alice) [avatar definition]
234. ~creative(alice) <- (~19) [avatar component clause 232]
235. 16 | ~19 [avatar split clause 104,232,220]
247. 22 <=> ! [X0] : creative(X0) [avatar definition]
248. creative(X0) <- (22) [avatar component clause 247]
250. 23 <=> creative(john) [avatar definition]
252. creative(john) <- (23) [avatar component clause 250]
253. 22 | 23 [avatar split clause 117,250,247]
325. $false <- (~19, 22) [subsumption resolution 234,248]
326. 19 | ~22 [avatar contradiction clause 325]
345. tall(paul) [resolution 148,142]
367. tall(john) | curious(john) <- (23) [resolution 83,252]
489. funny(john) | tall(john) <- (6) [resolution 149,177]
492. funny(john) <- (6) [subsumption resolution 489,147]
493. tall(john) <- (6) [resolution 492,148]
495. $false <- (6) [subsumption resolution 493,147]
496. ~6 [avatar contradiction clause 495]
497. curious(john) <- (23) [subsumption resolution 367,147]
498. 6 | ~23 [avatar split clause 497,250,176]
501. $false <- (16) [resolution 221,345]
504. ~16 [avatar contradiction clause 501]
507. $false [avatar sat refutation 235,253,326,496,498,504]
% SZS output end Proof for 7249440693440265287364787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not kind is patient or old and vice versa. If someone is both not rich and not kind then susan is both patient and not calm. Everyone who is not happy is either kind or not funny and vice versa. If someone is either not brave or not old then someone is both happy and kind and vice versa. Everyone who is either creative or not humble is patient and vice versa. Everyone who is either not happy or not old is tall and vice versa. Everyone who is either creative or not brave is not curious and vice versa. If lucy is not generous or not happy then john is creative or not brave and vice versa. If someone is either curious or brave then paul is either not rich or humble and vice versa. Everyone who is not old or humble is either not wise or not calm and vice versa. If someone is patient or happy then susan is either quiet or not calm and vice versa. If lucy is not wise or calm then someone is humble. Everyone who is quiet is either not humble or quiet and vice versa. Everyone who is both not wise and not rich is both not tall and curious. Everyone who is calm or not brave is not happy and vice versa. Everyone who is funny or not creative is either not curious or not patient. Alice is quiet or strong. Someone is either patient or not patient. Someone is brave or not generous. John is brave. Paul is not strong or not rich. Someone is either not wise or happy. | John is not patient. | neutral | (![X]:((~quiet(X)<~>~kind(X))<=>(patient(X)|old(X))))&
((?[X]:((~rich(X)&~kind(X))))=>((patient(susan)&~calm(susan))))&
(![X]:(~happy(X)<=>(kind(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>~old(X))))<=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((creative(X)<~>~humble(X))<=>patient(X)))&
(![X]:((~happy(X)<~>~old(X))<=>tall(X)))&
(![X]:((creative(X)<~>~brave(X))<=>~curious(X)))&
(((~generous(lucy)|~happy(lucy)))<=>((creative(john)|~brave(john))))&
((?[X]:((curious(X)<~>brave(X))))<=>((~rich(paul)<~>humble(paul))))&
(![X]:((~old(X)|humble(X))<=>(~wise(X)<~>~calm(X))))&
((?[X]:((patient(X)|happy(X))))<=>((quiet(susan)<~>~calm(susan))))&
(((~wise(lucy)|calm(lucy)))=>(?[X]:(humble(X))))&
(![X]:(quiet(X)<=>(~humble(X)<~>quiet(X))))&
(![X]:((~wise(X)&~rich(X))=>(~tall(X)&curious(X))))&
(![X]:((calm(X)|~brave(X))<=>~happy(X)))&
(![X]:((funny(X)|~creative(X))=>(~curious(X)<~>~patient(X))))&
((quiet(alice)|strong(alice)))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((brave(X)|~generous(X))))&
(brave(john))&
((~strong(paul)|~rich(paul)))&
(?[X]:((~wise(X)<~>happy(X)))) | ~patient(john) | [] | null | 0 |
Everyone who is not happy is patient and vice versa. Everyone who is quiet or patient is both creative and not funny. Everyone who is both calm and not curious is either wise or not kind and vice versa. Everyone who is generous is both quiet and funny. Everyone who is not old or not funny is not creative or happy. Everyone who is both not patient and not wise is both creative and brave and vice versa. If someone is not strong or not old then someone is generous. Everyone who is not patient is both not curious and not wise. If paul is either not rich or not wise then someone is either wise or not brave. Everyone who is not patient or generous is not kind. Everyone who is both not old and humble is both not kind and curious and vice versa. If someone is either not brave or happy then someone is calm or not generous. Everyone who is not patient is humble and vice versa. If someone is both not tall and not wise then fred is both brave and not rich and vice versa. If someone is not creative then someone is both quiet and not creative and vice versa. Everyone who is either not brave or happy is not generous. Alice is kind or tall. Someone is not curious or not generous. Mary is either humble or curious. John is both not kind and creative. Someone is either funny or not creative. | Paul is kind. | contradiction | (![X]:(~happy(X)<=>patient(X)))&
(![X]:((quiet(X)|patient(X))=>(creative(X)&~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>(wise(X)<~>~kind(X))))&
(![X]:(generous(X)=>(quiet(X)&funny(X))))&
(![X]:((~old(X)|~funny(X))=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)&~wise(X))<=>(creative(X)&brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:(generous(X))))&
(![X]:(~patient(X)=>(~curious(X)&~wise(X))))&
(((~rich(paul)<~>~wise(paul)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((~old(X)&humble(X))<=>(~kind(X)&curious(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:(~patient(X)<=>humble(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>((brave(fred)&~rich(fred))))&
((?[X]:(~creative(X)))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~brave(X)<~>happy(X))=>~generous(X)))&
((kind(alice)|tall(alice)))&
(?[X]:((~curious(X)|~generous(X))))&
((humble(mary)<~>curious(mary)))&
((~kind(john)&creative(john)))&
(?[X]:((funny(X)<~>~creative(X)))) | kind(paul) | [
"p0",
"p1",
"p4",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2472764728426769164362912
% SZS output start Proof for 2472764728426769164362912
1. ! [X0] : (~happy(X0) <=> patient(X0)) [input p0]
2. ! [X0] : ((patient(X0) | quiet(X0)) => (~funny(X0) & creative(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | ~old(X0)) => (happy(X0) | ~creative(X0))) [input p4]
10. ! [X0] : ((generous(X0) | ~patient(X0)) => ~kind(X0)) [input p9]
15. ? [X0] : ~creative(X0) <=> ? [X0] : (~creative(X0) & quiet(X0)) [input p14]
22. kind(paul) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : (~creative(X1) & quiet(X1)) [rectify 15]
27. ! [X0] : ((~funny(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) [ennf transformation 2]
29. ! [X0] : ((happy(X0) | ~creative(X0)) | (funny(X0) & old(X0))) [ennf transformation 5]
30. ! [X0] : (happy(X0) | ~creative(X0) | (funny(X0) & old(X0))) [flattening 29]
34. ! [X0] : (~kind(X0) | (~generous(X0) & patient(X0))) [ennf transformation 10]
37. ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))) [nnf transformation 1]
60. (? [X0] : ~creative(X0) | ! [X1] : (creative(X1) | ~quiet(X1))) & (? [X1] : (~creative(X1) & quiet(X1)) | ! [X0] : creative(X0)) [nnf transformation 25]
61. (? [X0] : ~creative(X0) | ! [X1] : (creative(X1) | ~quiet(X1))) & (? [X2] : (~creative(X2) & quiet(X2)) | ! [X3] : creative(X3)) [rectify 60]
62. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
63. ? [X2] : (~creative(X2) & quiet(X2)) => (~creative(sK5) & quiet(sK5)) [choice axiom]
64. (~creative(sK4) | ! [X1] : (creative(X1) | ~quiet(X1))) & ((~creative(sK5) & quiet(sK5)) | ! [X3] : creative(X3)) [skolemisation 61,63,62]
73. ~patient(X0) | ~happy(X0) [cnf transformation 37]
74. ~quiet(X0) | creative(X0) [cnf transformation 27]
77. ~funny(X0) | ~patient(X0) [cnf transformation 27]
87. ~creative(X0) | happy(X0) | funny(X0) [cnf transformation 30]
99. ~kind(X0) | patient(X0) [cnf transformation 34]
113. quiet(sK5) | creative(X3) [cnf transformation 64]
114. ~creative(sK5) | creative(X3) [cnf transformation 64]
126. kind(paul) [cnf transformation 22]
197. 16 <=> ! [X3] : creative(X3) [avatar definition]
198. creative(X3) <- (16) [avatar component clause 197]
200. 17 <=> creative(sK5) [avatar definition]
202. ~creative(sK5) <- (~17) [avatar component clause 200]
203. 16 | ~17 [avatar split clause 114,200,197]
205. 18 <=> quiet(sK5) [avatar definition]
207. quiet(sK5) <- (18) [avatar component clause 205]
208. 16 | 18 [avatar split clause 113,205,197]
250. creative(sK5) <- (18) [resolution 74,207]
251. $false <- (~17, 18) [subsumption resolution 250,202]
252. 17 | ~18 [avatar contradiction clause 251]
266. patient(paul) [resolution 99,126]
313. funny(X0) | happy(X0) <- (16) [resolution 87,198]
338. happy(X0) | ~patient(X0) <- (16) [resolution 313,77]
340. ~patient(X0) <- (16) [subsumption resolution 338,73]
342. $false <- (16) [resolution 340,266]
345. ~16 [avatar contradiction clause 342]
346. $false [avatar sat refutation 203,208,252,345]
% SZS output end Proof for 2472764728426769164362912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and wise is not funny or rich and vice versa.
If someone is either generous or not generous then someone is both not funny and not humble and vice versa.
Everyone who is both not brave and not kind is both not humble and not quiet and vice versa.
Everyone who is curious is either kind or generous.
If fred is tall then someone is rich or not calm.
Everyone who is both not kind and not brave is either not generous or patient.
Everyone who is either not patient or rich is not strong or not wise.
Everyone who is both not tall and not old is not wise and vice versa.
Everyone who is not rich is brave and vice versa.
Everyone who is either funny or not quiet is not funny and vice versa.
If fred is not patient then john is either tall or quiet and vice versa.
Everyone who is both not calm and not curious is either happy or humble and vice versa.
If paul is either not rich or not happy then someone is either kind or not curious and vice versa.
If someone is strong or humble then someone is either not wise or tall and vice versa.
If someone is not patient then someone is curious.
Someone is both not tall and not rich.
Mary is tall or not old.
Someone is generous or strong.
Someone is either wise or rich.
Someone is curious.
John is not calm or not old.
Someone is not patient or not tall.
Fred is both patient and brave. | Fred is not humble. | contradiction | (![X]:((~strong(X)&wise(X))<=>(~funny(X)|rich(X))))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:((~brave(X)&~kind(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(curious(X)=>(kind(X)<~>generous(X))))&
((tall(fred))=>(?[X]:((rich(X)|~calm(X)))))&
(![X]:((~kind(X)&~brave(X))=>(~generous(X)<~>patient(X))))&
(![X]:((~patient(X)<~>rich(X))=>(~strong(X)|~wise(X))))&
(![X]:((~tall(X)&~old(X))<=>~wise(X)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>~funny(X)))&
((~patient(fred))<=>((tall(john)<~>quiet(john))))&
(![X]:((~calm(X)&~curious(X))<=>(happy(X)<~>humble(X))))&
(((~rich(paul)<~>~happy(paul)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~patient(X)))=>(?[X]:(curious(X))))&
(?[X]:((~tall(X)&~rich(X))))&
((tall(mary)|~old(mary)))&
(?[X]:((generous(X)|strong(X))))&
(?[X]:((wise(X)<~>rich(X))))&
(?[X]:(curious(X)))&
((~calm(john)|~old(john)))&
(?[X]:((~patient(X)|~tall(X))))&
((patient(fred)&brave(fred))) | ~humble(fred) | [
"p2",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8314059506775015712816464
% SZS output start Proof for 8314059506775015712816464
3. ! [X0] : ((~kind(X0) & ~brave(X0)) <=> (~quiet(X0) & ~humble(X0))) [input p2]
10. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> ~funny(X0)) [input p9]
23. brave(fred) & patient(fred) [input p22]
24. ~humble(fred) [input hypothesis]
42. ! [X0] : (((~kind(X0) & ~brave(X0)) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | (kind(X0) | brave(X0)))) [nnf transformation 3]
43. ! [X0] : (((~kind(X0) & ~brave(X0)) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | kind(X0) | brave(X0))) [flattening 42]
52. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 10]
92. ~brave(X0) | quiet(X0) | humble(X0) [cnf transformation 43]
106. ~funny(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 52]
108. ~quiet(X0) | funny(X0) | funny(X0) [cnf transformation 52]
145. brave(fred) [cnf transformation 23]
146. ~humble(fred) [cnf transformation 24]
147. ~funny(X0) | ~quiet(X0) [duplicate literal removal 106]
148. ~quiet(X0) | funny(X0) [duplicate literal removal 108]
185. ~quiet(X0) [subsumption resolution 147,148]
315. quiet(fred) | humble(fred) [resolution 92,145]
317. humble(fred) [subsumption resolution 315,185]
318. $false [subsumption resolution 317,146]
% SZS output end Proof for 8314059506775015712816464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or humble is humble or not old.
If susan is rich or not old then alice is either not generous or not brave.
Everyone who is creative is both not humble and not curious and vice versa.
If alice is both generous and wise then someone is strong and vice versa.
Everyone who is both patient and not humble is patient or curious and vice versa.
If lucy is not old or wise then someone is either creative or not curious and vice versa.
If someone is not strong then alice is both not humble and not funny and vice versa.
If someone is wise then someone is either strong or not quiet.
Everyone who is both quiet and not patient is not brave.
Everyone who is either not curious or not strong is either not curious or not tall.
Everyone who is strong is either strong or not old and vice versa.
If mary is funny or humble then someone is quiet or not funny.
If someone is not happy or not tall then paul is wise and vice versa.
Everyone who is not wise is either not brave or quiet and vice versa.
If susan is kind or old then susan is either wise or quiet and vice versa.
John is wise or kind.
Someone is either not old or creative.
John is both patient and not creative.
Someone is both happy and not curious.
Someone is not wise or tall.
Lucy is both kind and not strong.
Fred is either not brave or not kind. | Alice is brave. | entailment | (![X]:((~brave(X)|humble(X))=>(humble(X)|~old(X))))&
(((rich(susan)|~old(susan)))=>((~generous(alice)<~>~brave(alice))))&
(![X]:(creative(X)<=>(~humble(X)&~curious(X))))&
(((generous(alice)&wise(alice)))<=>(?[X]:(strong(X))))&
(![X]:((patient(X)&~humble(X))<=>(patient(X)|curious(X))))&
(((~old(lucy)|wise(lucy)))<=>(?[X]:((creative(X)<~>~curious(X)))))&
((?[X]:(~strong(X)))<=>((~humble(alice)&~funny(alice))))&
((?[X]:(wise(X)))=>(?[X]:((strong(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~patient(X))=>~brave(X)))&
(![X]:((~curious(X)<~>~strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>(strong(X)<~>~old(X))))&
(((funny(mary)|humble(mary)))=>(?[X]:((quiet(X)|~funny(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>(wise(paul)))&
(![X]:(~wise(X)<=>(~brave(X)<~>quiet(X))))&
(((kind(susan)|old(susan)))<=>((wise(susan)<~>quiet(susan))))&
((wise(john)|kind(john)))&
(?[X]:((~old(X)<~>creative(X))))&
((patient(john)&~creative(john)))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:((~wise(X)|tall(X))))&
((kind(lucy)&~strong(lucy)))&
((~brave(fred)<~>~kind(fred))) | brave(alice) | [
"p0",
"p6",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6525801214953528957733627
% SZS output start Proof for 6525801214953528957733627
1. ! [X0] : ((humble(X0) | ~brave(X0)) => (~old(X0) | humble(X0))) [input p0]
7. ? [X0] : ~strong(X0) <=> (~funny(alice) & ~humble(alice)) [input p6]
11. ! [X0] : (strong(X0) <=> (strong(X0) <~> ~old(X0))) [input p10]
21. ~strong(lucy) & kind(lucy) [input p20]
23. ~brave(alice) [input hypothesis]
26. ! [X0] : ((~old(X0) | humble(X0)) | (~humble(X0) & brave(X0))) [ennf transformation 1]
27. ! [X0] : (~old(X0) | humble(X0) | (~humble(X0) & brave(X0))) [flattening 26]
49. (? [X0] : ~strong(X0) | (funny(alice) | humble(alice))) & ((~funny(alice) & ~humble(alice)) | ! [X0] : strong(X0)) [nnf transformation 7]
50. (? [X0] : ~strong(X0) | funny(alice) | humble(alice)) & ((~funny(alice) & ~humble(alice)) | ! [X0] : strong(X0)) [flattening 49]
51. (? [X0] : ~strong(X0) | funny(alice) | humble(alice)) & ((~funny(alice) & ~humble(alice)) | ! [X1] : strong(X1)) [rectify 50]
52. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
53. (~strong(sK2) | funny(alice) | humble(alice)) & ((~funny(alice) & ~humble(alice)) | ! [X1] : strong(X1)) [skolemisation 51,52]
59. ! [X0] : ((strong(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~strong(X0))) [nnf transformation 11]
77. ~old(X0) | humble(X0) | brave(X0) [cnf transformation 27]
98. ~humble(alice) | strong(X1) [cnf transformation 53]
109. old(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 59]
111. strong(X0) | strong(X0) | old(X0) [cnf transformation 59]
136. ~strong(lucy) [cnf transformation 21]
139. ~brave(alice) [cnf transformation 23]
140. old(X0) | ~strong(X0) [duplicate literal removal 109]
141. strong(X0) | old(X0) [duplicate literal removal 111]
153. 3 <=> brave(alice) [avatar definition]
154. ~brave(alice) <- (~3) [avatar component clause 153]
201. 12 <=> humble(alice) [avatar definition]
202. ~humble(alice) <- (~12) [avatar component clause 201]
214. 15 <=> ! [X1] : strong(X1) [avatar definition]
215. strong(X1) <- (15) [avatar component clause 214]
217. 15 | ~12 [avatar split clause 98,201,214]
231. old(X0) [subsumption resolution 140,141]
318. ~3 [avatar split clause 139,153]
335. humble(X0) | brave(X0) [resolution 77,231]
336. brave(alice) <- (~12) [resolution 335,202]
339. $false <- (~3, ~12) [subsumption resolution 336,154]
340. 3 | 12 [avatar contradiction clause 339]
343. $false <- (15) [resolution 215,136]
348. ~15 [avatar contradiction clause 343]
349. $false [avatar sat refutation 217,318,340,348]
% SZS output end Proof for 6525801214953528957733627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and kind is happy and vice versa.
If lucy is strong or happy then susan is not brave.
Everyone who is both not old and wise is rich or not old.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Everyone who is both rich and strong is tall or not tall and vice versa.
Fred is both quiet and funny.
Lucy is both not brave and creative.
Someone is not kind or not tall.
Mary is both not humble and brave.
Someone is not patient.
Lucy is either not humble or funny. | Mary is tall. | contradiction | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((strong(lucy)|happy(lucy)))=>(~brave(susan)))&
(![X]:((~old(X)&wise(X))=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
((quiet(fred)&funny(fred)))&
((~brave(lucy)&creative(lucy)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(mary)&brave(mary)))&
(?[X]:(~patient(X)))&
((~humble(lucy)<~>funny(lucy))) | tall(mary) | [
"p0",
"p5",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6138429369870053897451862
% SZS output start Proof for 6138429369870053897451862
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
6. ! [X0] : ((~tall(X0) | brave(X0)) <=> (~rich(X0) | calm(X0))) [input p5]
12. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p11]
13. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p12]
15. ! [X0] : ((strong(X0) & rich(X0)) <=> (~tall(X0) | tall(X0))) [input p14]
19. brave(mary) & ~humble(mary) [input p18]
22. tall(mary) [input hypothesis]
33. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 33]
40. ! [X0] : (((~tall(X0) | brave(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 6]
41. ! [X0] : ((~tall(X0) | brave(X0) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | (tall(X0) & ~brave(X0)))) [flattening 40]
48. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 12]
49. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 48]
50. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 13]
52. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 15]
53. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ~strong(X0) | ~rich(X0))) [flattening 52]
60. ~happy(X0) | ~curious(X0) [cnf transformation 34]
70. ~rich(X0) | calm(X0) | ~brave(X0) [cnf transformation 41]
87. curious(X0) | curious(X0) [cnf transformation 49]
90. ~calm(X0) | ~tall(X0) | happy(X0) [cnf transformation 50]
103. rich(X0) | ~tall(X0) [cnf transformation 53]
104. tall(X0) | rich(X0) [cnf transformation 53]
113. brave(mary) [cnf transformation 19]
117. tall(mary) [cnf transformation 22]
118. curious(X0) [duplicate literal removal 87]
201. rich(X0) [subsumption resolution 103,104]
222. ~brave(X0) | calm(X0) [resolution 70,201]
224. calm(mary) [resolution 222,113]
232. ~tall(mary) | happy(mary) [resolution 90,224]
234. happy(mary) [subsumption resolution 232,117]
245. ~curious(mary) [resolution 234,60]
246. $false [subsumption resolution 245,118]
% SZS output end Proof for 6138429369870053897451862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not strong is not creative.
Everyone who is not tall is not funny or quiet and vice versa.
If susan is both rich and not old then paul is both not happy and not strong and vice versa.
Everyone who is both kind and not kind is creative and vice versa.
Everyone who is either kind or not creative is creative or not creative and vice versa.
If mary is brave then mary is not calm or curious and vice versa.
Everyone who is not happy is not patient or not creative and vice versa.
Everyone who is not old or funny is either not humble or strong and vice versa.
If someone is not wise then john is either not funny or not wise.
Everyone who is both not funny and funny is not old and vice versa.
Everyone who is either kind or not funny is either not generous or not humble.
If fred is brave then someone is not humble or not patient.
If john is not funny or not calm then someone is happy.
Everyone who is both calm and humble is happy.
If paul is either not quiet or funny then someone is both curious and wise and vice versa.
Paul is both not patient and calm.
Susan is funny.
Fred is not strong.
Mary is either creative or not humble.
Lucy is both not generous and patient. | Mary is creative. | contradiction | (![X]:((~wise(X)|~strong(X))=>~creative(X)))&
(![X]:(~tall(X)<=>(~funny(X)|quiet(X))))&
(((rich(susan)&~old(susan)))<=>((~happy(paul)&~strong(paul))))&
(![X]:((kind(X)&~kind(X))<=>creative(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(creative(X)|~creative(X))))&
((brave(mary))<=>((~calm(mary)|curious(mary))))&
(![X]:(~happy(X)<=>(~patient(X)|~creative(X))))&
(![X]:((~old(X)|funny(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:(~wise(X)))=>((~funny(john)<~>~wise(john))))&
(![X]:((~funny(X)&funny(X))<=>~old(X)))&
(![X]:((kind(X)<~>~funny(X))=>(~generous(X)<~>~humble(X))))&
((brave(fred))=>(?[X]:((~humble(X)|~patient(X)))))&
(((~funny(john)|~calm(john)))=>(?[X]:(happy(X))))&
(![X]:((calm(X)&humble(X))=>happy(X)))&
(((~quiet(paul)<~>funny(paul)))<=>(?[X]:((curious(X)&wise(X)))))&
((~patient(paul)&calm(paul)))&
(funny(susan))&
(~strong(fred))&
((creative(mary)<~>~humble(mary)))&
((~generous(lucy)&patient(lucy))) | creative(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8910266153727837027912136
% SZS output start Proof for 8910266153727837027912136
4. ! [X0] : ((~kind(X0) & kind(X0)) <=> creative(X0)) [input p3]
21. creative(mary) [input hypothesis]
31. ! [X0] : (((~kind(X0) & kind(X0)) | ~creative(X0)) & (creative(X0) | (kind(X0) | ~kind(X0)))) [nnf transformation 4]
32. ! [X0] : (((~kind(X0) & kind(X0)) | ~creative(X0)) & (creative(X0) | kind(X0) | ~kind(X0))) [flattening 31]
61. kind(X0) | ~creative(X0) [cnf transformation 32]
62. ~kind(X0) | ~creative(X0) [cnf transformation 32]
108. creative(mary) [cnf transformation 21]
133. ~creative(X0) [subsumption resolution 61,62]
210. $false [subsumption resolution 108,133]
% SZS output end Proof for 8910266153727837027912136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is not calm or patient and vice versa.
Everyone who is either not calm or not generous is both patient and tall and vice versa.
If someone is calm then someone is both old and happy.
If susan is both rich and generous then someone is both quiet and happy and vice versa.
Everyone who is not quiet or not tall is both kind and not funny.
If someone is curious or tall then someone is both kind and not kind and vice versa.
Everyone who is either rich or not kind is either tall or calm and vice versa.
If someone is strong then someone is either not tall or not brave.
If susan is not humble then john is tall.
Everyone who is not strong is both wise and not humble and vice versa.
If someone is brave then paul is both quiet and rich.
Everyone who is either happy or rich is not calm or not creative and vice versa.
If someone is kind then fred is rich and vice versa.
If someone is creative or brave then someone is both wise and kind and vice versa.
Mary is not humble.
John is either not old or not generous.
Someone is either funny or not calm.
Someone is either not patient or not kind. | John is not wise. | neutral | ((?[X]:(~brave(X)))<=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~calm(X)<~>~generous(X))<=>(patient(X)&tall(X))))&
((?[X]:(calm(X)))=>(?[X]:((old(X)&happy(X)))))&
(((rich(susan)&generous(susan)))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((~quiet(X)|~tall(X))=>(kind(X)&~funny(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((rich(X)<~>~kind(X))<=>(tall(X)<~>calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~tall(X)<~>~brave(X)))))&
((~humble(susan))=>(tall(john)))&
(![X]:(~strong(X)<=>(wise(X)&~humble(X))))&
((?[X]:(brave(X)))=>((quiet(paul)&rich(paul))))&
(![X]:((happy(X)<~>rich(X))<=>(~calm(X)|~creative(X))))&
((?[X]:(kind(X)))<=>(rich(fred)))&
((?[X]:((creative(X)|brave(X))))<=>(?[X]:((wise(X)&kind(X)))))&
(~humble(mary))&
((~old(john)<~>~generous(john)))&
(?[X]:((funny(X)<~>~calm(X))))&
(?[X]:((~patient(X)<~>~kind(X)))) | ~wise(john) | [] | null | 0 |
Everyone who is generous is either not tall or old and vice versa.
Everyone who is wise or creative is both funny and not old and vice versa.
If paul is not humble or not tall then mary is not patient.
If paul is not happy or generous then fred is both not quiet and not strong and vice versa.
Everyone who is either not kind or funny is either calm or funny and vice versa.
Everyone who is kind is happy or not brave.
Everyone who is not curious or humble is both not brave and happy and vice versa.
Everyone who is not wise or not brave is creative and vice versa.
Everyone who is either not patient or not strong is both quiet and happy.
Everyone who is either creative or not happy is not generous and vice versa.
If someone is both not quiet and not happy then john is either creative or quiet and vice versa.
If fred is happy then someone is both not calm and not generous.
Everyone who is patient is both not curious and not strong and vice versa.
If someone is humble then susan is both brave and patient and vice versa.
If susan is not wise then someone is not wise or strong and vice versa.
Everyone who is either not quiet or not kind is strong or curious and vice versa.
Mary is not rich.
Paul is rich.
Someone is not kind or not humble.
Someone is both curious and not rich.
Lucy is happy or not creative.
Lucy is wise.
Paul is either humble or not generous.
Someone is not rich or not quiet. | Paul is tall. | entailment | (![X]:(generous(X)<=>(~tall(X)<~>old(X))))&
(![X]:((wise(X)|creative(X))<=>(funny(X)&~old(X))))&
(((~humble(paul)|~tall(paul)))=>(~patient(mary)))&
(((~happy(paul)|generous(paul)))<=>((~quiet(fred)&~strong(fred))))&
(![X]:((~kind(X)<~>funny(X))<=>(calm(X)<~>funny(X))))&
(![X]:(kind(X)=>(happy(X)|~brave(X))))&
(![X]:((~curious(X)|humble(X))<=>(~brave(X)&happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>creative(X)))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((?[X]:(humble(X)))<=>((brave(susan)&patient(susan))))&
((~wise(susan))<=>(?[X]:((~wise(X)|strong(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(strong(X)|curious(X))))&
(~rich(mary))&
(rich(paul))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((curious(X)&~rich(X))))&
((happy(lucy)|~creative(lucy)))&
(wise(lucy))&
((humble(paul)<~>~generous(paul)))&
(?[X]:((~rich(X)|~quiet(X)))) | tall(paul) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 607633989993371087064469
% SZS output start Proof for 607633989993371087064469
1. ! [X0] : (generous(X0) <=> (~tall(X0) <~> old(X0))) [input p0]
2. ! [X0] : ((creative(X0) | wise(X0)) <=> (~old(X0) & funny(X0))) [input p1]
7. ! [X0] : ((humble(X0) | ~curious(X0)) <=> (happy(X0) & ~brave(X0))) [input p6]
8. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> creative(X0)) [input p7]
13. ! [X0] : (patient(X0) <=> (~strong(X0) & ~curious(X0))) [input p12]
14. ? [X0] : humble(X0) <=> (patient(susan) & brave(susan)) [input p13]
23. humble(paul) <~> ~generous(paul) [input p22]
25. ~tall(paul) [input hypothesis]
31. ! [X0] : ((generous(X0) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) & (((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ~generous(X0))) [nnf transformation 1]
32. ! [X0] : (((creative(X0) | wise(X0)) | (old(X0) | ~funny(X0))) & ((~old(X0) & funny(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 2]
33. ! [X0] : ((creative(X0) | wise(X0) | old(X0) | ~funny(X0)) & ((~old(X0) & funny(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 32]
37. ! [X0] : (((humble(X0) | ~curious(X0)) | (~happy(X0) | brave(X0))) & ((happy(X0) & ~brave(X0)) | (~humble(X0) & curious(X0)))) [nnf transformation 7]
38. ! [X0] : ((humble(X0) | ~curious(X0) | ~happy(X0) | brave(X0)) & ((happy(X0) & ~brave(X0)) | (~humble(X0) & curious(X0)))) [flattening 37]
39. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~creative(X0)) & (creative(X0) | (brave(X0) & wise(X0)))) [nnf transformation 8]
40. ! [X0] : ((~brave(X0) | ~wise(X0) | ~creative(X0)) & (creative(X0) | (brave(X0) & wise(X0)))) [flattening 39]
49. ! [X0] : ((patient(X0) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [nnf transformation 13]
50. ! [X0] : ((patient(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [flattening 49]
51. (? [X0] : humble(X0) | (~patient(susan) | ~brave(susan))) & ((patient(susan) & brave(susan)) | ! [X0] : ~humble(X0)) [nnf transformation 14]
52. (? [X0] : humble(X0) | ~patient(susan) | ~brave(susan)) & ((patient(susan) & brave(susan)) | ! [X0] : ~humble(X0)) [flattening 51]
53. (? [X0] : humble(X0) | ~patient(susan) | ~brave(susan)) & ((patient(susan) & brave(susan)) | ! [X1] : ~humble(X1)) [rectify 52]
54. ? [X0] : humble(X0) => humble(sK2) [choice axiom]
55. (humble(sK2) | ~patient(susan) | ~brave(susan)) & ((patient(susan) & brave(susan)) | ! [X1] : ~humble(X1)) [skolemisation 53,54]
66. (generous(paul) | ~humble(paul)) & (~generous(paul) | humble(paul)) [nnf transformation 23]
71. old(X0) | generous(X0) | tall(X0) [cnf transformation 31]
75. ~wise(X0) | ~old(X0) [cnf transformation 33]
76. ~creative(X0) | ~old(X0) [cnf transformation 33]
94. ~brave(X0) | curious(X0) [cnf transformation 38]
99. creative(X0) | wise(X0) [cnf transformation 40]
118. ~curious(X0) | ~patient(X0) [cnf transformation 50]
121. brave(susan) | ~humble(X1) [cnf transformation 55]
122. patient(susan) | ~humble(X1) [cnf transformation 55]
140. ~generous(paul) | humble(paul) [cnf transformation 66]
143. ~tall(paul) [cnf transformation 25]
149. 1 <=> tall(paul) [avatar definition]
150. ~tall(paul) <- (~1) [avatar component clause 149]
158. 3 <=> humble(paul) [avatar definition]
160. humble(paul) <- (3) [avatar component clause 158]
175. 7 <=> generous(paul) [avatar definition]
225. 16 <=> brave(susan) [avatar definition]
226. brave(susan) <- (16) [avatar component clause 225]
229. 17 <=> patient(susan) [avatar definition]
238. 19 <=> ! [X1] : ~humble(X1) [avatar definition]
239. ~humble(X1) <- (19) [avatar component clause 238]
240. 19 | 17 [avatar split clause 122,229,238]
241. 19 | 16 [avatar split clause 121,225,238]
282. 3 | ~7 [avatar split clause 140,175,158]
292. ~1 [avatar split clause 143,149]
295. curious(susan) <- (16) [resolution 94,226]
300. wise(X0) | ~old(X0) [resolution 99,76]
302. ~old(X0) [subsumption resolution 300,75]
309. ~patient(susan) <- (16) [resolution 118,295]
313. ~17 | ~16 [avatar split clause 309,225,229]
320. tall(X1) | generous(X1) [resolution 71,302]
346. generous(paul) <- (~1) [resolution 320,150]
350. 7 | 1 [avatar split clause 346,149,175]
351. $false <- (3, 19) [subsumption resolution 160,239]
352. ~3 | ~19 [avatar contradiction clause 351]
353. $false [avatar sat refutation 240,241,282,292,313,350,352]
% SZS output end Proof for 607633989993371087064469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not curious is both not patient and humble and vice versa. If susan is old or curious then someone is not rich or not strong. If mary is both old and quiet then someone is funny. If alice is not rich then mary is generous. Everyone who is not tall is not strong or kind. Everyone who is both not humble and creative is both creative and not wise. Everyone who is either not old or curious is both not wise and not tall and vice versa. Everyone who is curious or humble is both not rich and not calm. Everyone who is both humble and not generous is tall. Everyone who is either rich or not kind is not calm or not wise and vice versa. Everyone who is not curious or not funny is generous or not old. If susan is brave then fred is either not brave or happy. If susan is strong then someone is patient. Everyone who is wise or not quiet is either not happy or not calm. Everyone who is either not creative or quiet is either not creative or not tall and vice versa. If alice is either curious or not generous then susan is both humble and not brave. Mary is not quiet. John is not curious or not kind. Someone is wise or funny. Someone is not old. Lucy is both not generous and kind. Someone is old or not patient. | Lucy is not humble. | entailment | (![X]:((~calm(X)<~>~curious(X))<=>(~patient(X)&humble(X))))&
(((old(susan)|curious(susan)))=>(?[X]:((~rich(X)|~strong(X)))))&
(((old(mary)&quiet(mary)))=>(?[X]:(funny(X))))&
((~rich(alice))=>(generous(mary)))&
(![X]:(~tall(X)=>(~strong(X)|kind(X))))&
(![X]:((~humble(X)&creative(X))=>(creative(X)&~wise(X))))&
(![X]:((~old(X)<~>curious(X))<=>(~wise(X)&~tall(X))))&
(![X]:((curious(X)|humble(X))=>(~rich(X)&~calm(X))))&
(![X]:((humble(X)&~generous(X))=>tall(X)))&
(![X]:((rich(X)<~>~kind(X))<=>(~calm(X)|~wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(generous(X)|~old(X))))&
((brave(susan))=>((~brave(fred)<~>happy(fred))))&
((strong(susan))=>(?[X]:(patient(X))))&
(![X]:((wise(X)|~quiet(X))=>(~happy(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>(~creative(X)<~>~tall(X))))&
(((curious(alice)<~>~generous(alice)))=>((humble(susan)&~brave(susan))))&
(~quiet(mary))&
((~curious(john)|~kind(john)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:(~old(X)))&
((~generous(lucy)&kind(lucy)))&
(?[X]:((old(X)|~patient(X)))) | ~humble(lucy) | [
"p7",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2539751679782248992710439
% SZS output start Proof for 2539751679782248992710439
8. ! [X0] : ((humble(X0) | curious(X0)) => (~calm(X0) & ~rich(X0))) [input p7]
10. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> (~wise(X0) | ~calm(X0))) [input p9]
21. kind(lucy) & ~generous(lucy) [input p20]
23. humble(lucy) [input hypothesis]
33. ! [X0] : ((~calm(X0) & ~rich(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 8]
45. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (wise(X0) & calm(X0))) & ((~wise(X0) | ~calm(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 10]
46. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (wise(X0) & calm(X0))) & (~wise(X0) | ~calm(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [flattening 45]
71. ~rich(X0) | ~humble(X0) [cnf transformation 33]
73. ~humble(X0) | ~calm(X0) [cnf transformation 33]
77. ~kind(X0) | rich(X0) | calm(X0) [cnf transformation 46]
104. kind(lucy) [cnf transformation 21]
106. humble(lucy) [cnf transformation 23]
170. ~calm(lucy) [resolution 73,106]
189. rich(lucy) | calm(lucy) [resolution 77,104]
190. rich(lucy) [subsumption resolution 189,170]
191. ~humble(lucy) [resolution 190,71]
193. $false [subsumption resolution 191,106]
% SZS output end Proof for 2539751679782248992710439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or calm is either curious or not generous.
Everyone who is both creative and strong is not kind.
Everyone who is both not wise and not strong is either not wise or patient and vice versa.
Everyone who is not kind or not rich is either quiet or not brave.
Everyone who is curious is generous or not rich.
If mary is either kind or curious then someone is either funny or not funny.
Everyone who is both not wise and old is not kind or not brave and vice versa.
Everyone who is either tall or not quiet is not strong.
If someone is calm then paul is both not rich and generous and vice versa.
If someone is not wise or not strong then john is both patient and tall.
Everyone who is calm or kind is creative or wise and vice versa.
If susan is both not creative and not old then paul is either not strong or wise.
If someone is either strong or not kind then someone is not quiet or not humble.
Everyone who is both old and curious is both not brave and not generous and vice versa.
If lucy is both strong and happy then alice is not tall or quiet and vice versa.
If someone is either not rich or not funny then alice is quiet or humble and vice versa.
Fred is both not old and not curious.
Someone is either not curious or generous.
Alice is either not patient or old.
Paul is old or not tall.
Susan is either old or humble.
Someone is either not funny or rich. | Lucy is not kind. | contradiction | (![X]:((~calm(X)|calm(X))=>(curious(X)<~>~generous(X))))&
(![X]:((creative(X)&strong(X))=>~kind(X)))&
(![X]:((~wise(X)&~strong(X))<=>(~wise(X)<~>patient(X))))&
(![X]:((~kind(X)|~rich(X))=>(quiet(X)<~>~brave(X))))&
(![X]:(curious(X)=>(generous(X)|~rich(X))))&
(((kind(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((~wise(X)&old(X))<=>(~kind(X)|~brave(X))))&
(![X]:((tall(X)<~>~quiet(X))=>~strong(X)))&
((?[X]:(calm(X)))<=>((~rich(paul)&generous(paul))))&
((?[X]:((~wise(X)|~strong(X))))=>((patient(john)&tall(john))))&
(![X]:((calm(X)|kind(X))<=>(creative(X)|wise(X))))&
(((~creative(susan)&~old(susan)))=>((~strong(paul)<~>wise(paul))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)&~generous(X))))&
(((strong(lucy)&happy(lucy)))<=>((~tall(alice)|quiet(alice))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>((quiet(alice)|humble(alice))))&
((~old(fred)&~curious(fred)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~patient(alice)<~>old(alice)))&
((old(paul)|~tall(paul)))&
((old(susan)<~>humble(susan)))&
(?[X]:((~funny(X)<~>rich(X)))) | ~kind(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5344884473379203779462082
% SZS output start Proof for 5344884473379203779462082
1. ! [X0] : ((calm(X0) | ~calm(X0)) => (curious(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : ((strong(X0) & creative(X0)) => ~kind(X0)) [input p1]
3. ! [X0] : ((~strong(X0) & ~wise(X0)) <=> (~wise(X0) <~> patient(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | ~kind(X0)) => (quiet(X0) <~> ~brave(X0))) [input p3]
7. ! [X0] : ((old(X0) & ~wise(X0)) <=> (~brave(X0) | ~kind(X0))) [input p6]
8. ! [X0] : ((tall(X0) <~> ~quiet(X0)) => ~strong(X0)) [input p7]
10. ? [X0] : (~strong(X0) | ~wise(X0)) => (tall(john) & patient(john)) [input p9]
11. ! [X0] : ((kind(X0) | calm(X0)) <=> (wise(X0) | creative(X0))) [input p10]
14. ! [X0] : ((curious(X0) & old(X0)) <=> (~generous(X0) & ~brave(X0))) [input p13]
23. ~kind(lucy) [input hypothesis]
25. ! [X0] : ((curious(X0) <~> ~generous(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 1]
26. ! [X0] : (~kind(X0) | (~strong(X0) | ~creative(X0))) [ennf transformation 2]
27. ! [X0] : (~kind(X0) | ~strong(X0) | ~creative(X0)) [flattening 26]
28. ! [X0] : ((quiet(X0) <~> ~brave(X0)) | (rich(X0) & kind(X0))) [ennf transformation 4]
32. ! [X0] : (~strong(X0) | (tall(X0) <=> ~quiet(X0))) [ennf transformation 8]
33. (tall(john) & patient(john)) | ! [X0] : (strong(X0) & wise(X0)) [ennf transformation 10]
37. ! [X0] : (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~calm(X0) & calm(X0))) [nnf transformation 25]
38. ! [X0] : (((~strong(X0) & ~wise(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (strong(X0) | wise(X0)))) [nnf transformation 3]
39. ! [X0] : (((~strong(X0) & ~wise(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | strong(X0) | wise(X0))) [flattening 38]
40. ! [X0] : (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (rich(X0) & kind(X0))) [nnf transformation 28]
44. ! [X0] : (((old(X0) & ~wise(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 7]
45. ! [X0] : (((old(X0) & ~wise(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~old(X0) | wise(X0))) [flattening 44]
46. ! [X0] : (~strong(X0) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 32]
52. ! [X0] : (((kind(X0) | calm(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~kind(X0) & ~calm(X0)))) [nnf transformation 11]
53. ! [X0] : ((kind(X0) | calm(X0) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | (~kind(X0) & ~calm(X0)))) [flattening 52]
59. ! [X0] : (((curious(X0) & old(X0)) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 14]
60. ! [X0] : (((curious(X0) & old(X0)) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | ~curious(X0) | ~old(X0))) [flattening 59]
76. ~generous(X0) | curious(X0) | calm(X0) [cnf transformation 37]
77. ~generous(X0) | curious(X0) | ~calm(X0) [cnf transformation 37]
78. generous(X0) | ~curious(X0) | calm(X0) [cnf transformation 37]
79. ~curious(X0) | generous(X0) | ~calm(X0) [cnf transformation 37]
80. ~kind(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 27]
82. ~patient(X0) | wise(X0) | strong(X0) | wise(X0) [cnf transformation 39]
84. ~wise(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 39]
87. ~brave(X0) | quiet(X0) | kind(X0) [cnf transformation 40]
97. ~wise(X0) | kind(X0) [cnf transformation 45]
99. old(X0) | kind(X0) [cnf transformation 45]
101. ~tall(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 46]
106. patient(john) | wise(X0) [cnf transformation 33]
108. tall(john) | wise(X0) [cnf transformation 33]
111. ~kind(X0) | creative(X0) | wise(X0) [cnf transformation 53]
119. ~generous(X0) | ~curious(X0) | ~old(X0) [cnf transformation 60]
121. curious(X0) | generous(X0) | brave(X0) [cnf transformation 60]
144. ~kind(lucy) [cnf transformation 23]
145. ~patient(X0) | wise(X0) | strong(X0) [duplicate literal removal 82]
146. ~patient(X0) | ~wise(X0) [duplicate literal removal 84]
147. ~curious(X0) | generous(X0) [subsumption resolution 78,79]
148. ~generous(X0) | curious(X0) [subsumption resolution 76,77]
149. ~patient(X0) | strong(X0) [subsumption resolution 145,146]
172. 6 <=> tall(john) [avatar definition]
174. tall(john) <- (6) [avatar component clause 172]
177. 7 <=> ! [X0] : wise(X0) [avatar definition]
178. wise(X0) <- (7) [avatar component clause 177]
179. 7 | 6 [avatar split clause 108,172,177]
181. 8 <=> patient(john) [avatar definition]
183. patient(john) <- (8) [avatar component clause 181]
185. 7 | 8 [avatar split clause 106,181,177]
220. brave(X0) | generous(X0) [subsumption resolution 121,147]
221. ~old(X0) | ~curious(X0) [subsumption resolution 119,147]
302. kind(X0) <- (7) [resolution 97,178]
303. $false <- (7) [resolution 302,144]
304. ~7 [avatar contradiction clause 303]
309. ~wise(john) <- (8) [resolution 146,183]
311. strong(john) <- (8) [resolution 149,183]
315. ~curious(X1) | kind(X1) [resolution 221,99]
327. quiet(X0) | kind(X0) | generous(X0) [resolution 87,220]
350. ~quiet(john) | ~strong(john) <- (6) [resolution 101,174]
430. 42 <=> generous(john) [avatar definition]
432. generous(john) <- (42) [avatar component clause 430]
434. 43 <=> kind(john) [avatar definition]
436. kind(john) <- (43) [avatar component clause 434]
479. curious(john) <- (42) [resolution 432,148]
485. 49 <=> curious(john) [avatar definition]
487. curious(john) <- (49) [avatar component clause 485]
489. 49 | ~42 [avatar split clause 479,430,485]
560. 63 <=> strong(john) [avatar definition]
561. strong(john) <- (63) [avatar component clause 560]
564. 64 <=> quiet(john) [avatar definition]
566. ~quiet(john) <- (~64) [avatar component clause 564]
567. ~63 | ~64 | ~6 [avatar split clause 350,172,564,560]
592. 63 | ~8 [avatar split clause 311,181,560]
619. kind(john) | generous(john) <- (~64) [resolution 566,327]
642. kind(john) <- (49) [resolution 487,315]
646. 43 | ~49 [avatar split clause 642,485,434]
647. creative(john) | wise(john) <- (43) [resolution 436,111]
648. ~strong(john) | ~creative(john) <- (43) [resolution 436,80]
649. creative(john) <- (8, 43) [subsumption resolution 647,309]
650. ~creative(john) <- (43, 63) [subsumption resolution 648,561]
651. $false <- (8, 43, 63) [subsumption resolution 650,649]
652. ~8 | ~43 | ~63 [avatar contradiction clause 651]
653. 42 | 43 | 64 [avatar split clause 619,564,434,430]
659. $false [avatar sat refutation 179,185,304,489,567,592,646,652,653]
% SZS output end Proof for 5344884473379203779462082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and patient is either kind or not old. Everyone who is both not quiet and not humble is not humble or not curious. If someone is both old and not quiet then paul is both not quiet and not generous. Everyone who is brave is both not old and wise. Everyone who is either happy or quiet is not wise and vice versa. If paul is both calm and not curious then someone is both not kind and not wise and vice versa. Everyone who is funny or not brave is either not brave or kind and vice versa. Everyone who is either not rich or humble is either strong or funny and vice versa. If alice is not wise or creative then alice is either kind or brave and vice versa. If someone is both patient and not calm then paul is creative or not strong. Everyone who is both curious and wise is kind or strong and vice versa. Everyone who is not calm or calm is not quiet and vice versa. If someone is both funny and not kind then someone is either not generous or tall and vice versa. If someone is funny then mary is not old and vice versa. Everyone who is not humble is not funny and vice versa. If someone is either not curious or quiet then someone is not strong. Alice is creative or not tall. Someone is both not curious and not humble. Someone is either not happy or not wise. Someone is either curious or tall. Someone is not old or not humble. Lucy is both wise and not brave. Someone is not strong. | Lucy is not brave. | entailment | (![X]:((~rich(X)&patient(X))=>(kind(X)<~>~old(X))))&
(![X]:((~quiet(X)&~humble(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)&~quiet(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:(brave(X)=>(~old(X)&wise(X))))&
(![X]:((happy(X)<~>quiet(X))<=>~wise(X)))&
(((calm(paul)&~curious(paul)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((funny(X)|~brave(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((~rich(X)<~>humble(X))<=>(strong(X)<~>funny(X))))&
(((~wise(alice)|creative(alice)))<=>((kind(alice)<~>brave(alice))))&
((?[X]:((patient(X)&~calm(X))))=>((creative(paul)|~strong(paul))))&
(![X]:((curious(X)&wise(X))<=>(kind(X)|strong(X))))&
(![X]:((~calm(X)|calm(X))<=>~quiet(X)))&
((?[X]:((funny(X)&~kind(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:(funny(X)))<=>(~old(mary)))&
(![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:(~strong(X))))&
((creative(alice)|~tall(alice)))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~old(X)|~humble(X))))&
((wise(lucy)&~brave(lucy)))&
(?[X]:(~strong(X))) | ~brave(lucy) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2792384536895742581598907
% SZS output start Proof for 2792384536895742581598907
22. ~brave(lucy) & wise(lucy) [input p21]
24. brave(lucy) [input hypothesis]
137. ~brave(lucy) [cnf transformation 22]
139. brave(lucy) [cnf transformation 24]
290. $false [subsumption resolution 139,137]
% SZS output end Proof for 2792384536895742581598907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not humble or not calm then susan is not strong or not calm and vice versa.
If alice is either not tall or wise then paul is not rich.
Everyone who is kind or rich is not happy or not patient and vice versa.
If lucy is not strong or not patient then someone is not curious.
Everyone who is both not strong and not brave is both tall and curious.
Everyone who is curious is either kind or calm.
If someone is either wise or quiet then someone is both humble and old.
Everyone who is both not funny and tall is either not rich or brave and vice versa.
If someone is both not tall and not creative then alice is either not calm or not patient.
If john is either not generous or not wise then lucy is humble or generous and vice versa.
Everyone who is not patient or wise is not funny or kind.
If paul is wise or not generous then alice is patient.
Everyone who is both curious and not strong is not strong or not kind.
If someone is both not rich and funny then someone is either calm or not strong.
Everyone who is happy or not generous is either wise or not curious.
If alice is both not rich and not happy then fred is creative and vice versa.
Fred is both not rich and quiet.
Someone is either not calm or not tall.
Someone is not funny.
John is both generous and funny.
Someone is curious.
John is curious or not patient.
Fred is not quiet or not curious. | Fred is rich. | contradiction | (((~humble(susan)<~>~calm(susan)))<=>((~strong(susan)|~calm(susan))))&
(((~tall(alice)<~>wise(alice)))=>(~rich(paul)))&
(![X]:((kind(X)|rich(X))<=>(~happy(X)|~patient(X))))&
(((~strong(lucy)|~patient(lucy)))=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)&~brave(X))=>(tall(X)&curious(X))))&
(![X]:(curious(X)=>(kind(X)<~>calm(X))))&
((?[X]:((wise(X)<~>quiet(X))))=>(?[X]:((humble(X)&old(X)))))&
(![X]:((~funny(X)&tall(X))<=>(~rich(X)<~>brave(X))))&
((?[X]:((~tall(X)&~creative(X))))=>((~calm(alice)<~>~patient(alice))))&
(((~generous(john)<~>~wise(john)))<=>((humble(lucy)|generous(lucy))))&
(![X]:((~patient(X)|wise(X))=>(~funny(X)|kind(X))))&
(((wise(paul)|~generous(paul)))=>(patient(alice)))&
(![X]:((curious(X)&~strong(X))=>(~strong(X)|~kind(X))))&
((?[X]:((~rich(X)&funny(X))))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((happy(X)|~generous(X))=>(wise(X)<~>~curious(X))))&
(((~rich(alice)&~happy(alice)))<=>(creative(fred)))&
((~rich(fred)&quiet(fred)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(~funny(X)))&
((generous(john)&funny(john)))&
(?[X]:(curious(X)))&
((curious(john)|~patient(john)))&
((~quiet(fred)|~curious(fred))) | rich(fred) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7474143594595127864430810
% SZS output start Proof for 7474143594595127864430810
17. quiet(fred) & ~rich(fred) [input p16]
24. rich(fred) [input hypothesis]
121. ~rich(fred) [cnf transformation 17]
131. rich(fred) [cnf transformation 24]
284. $false [subsumption resolution 131,121]
% SZS output end Proof for 7474143594595127864430810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not humble then someone is not funny and vice versa. Everyone who is both funny and not quiet is funny. If paul is either not creative or not patient then someone is both brave and not wise and vice versa. If someone is either tall or not creative then mary is both not rich and not tall. Everyone who is both not strong and generous is not kind or not curious. Everyone who is either not strong or generous is rich and vice versa. If someone is both kind and not generous then mary is both not creative and funny. If john is happy or not creative then paul is either patient or not tall and vice versa. If someone is both not kind and wise then susan is either creative or not kind. Everyone who is both kind and funny is generous and vice versa. If someone is either not tall or not wise then someone is old and vice versa. Everyone who is either calm or funny is either not old or not strong. If john is both kind and not humble then susan is both not quiet and not calm and vice versa. Everyone who is either curious or patient is either curious or not calm and vice versa. Everyone who is both humble and strong is patient or kind and vice versa. If someone is either not kind or patient then fred is patient. Someone is either wise or not curious. Someone is both brave and not old. Someone is happy or quiet. Someone is both not happy and calm. Someone is either not generous or brave. Mary is not funny. Fred is calm. Someone is both calm and old. | Mary is not strong. | contradiction | (((patient(susan)|~humble(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((funny(X)&~quiet(X))=>funny(X)))&
(((~creative(paul)<~>~patient(paul)))<=>(?[X]:((brave(X)&~wise(X)))))&
((?[X]:((tall(X)<~>~creative(X))))=>((~rich(mary)&~tall(mary))))&
(![X]:((~strong(X)&generous(X))=>(~kind(X)|~curious(X))))&
(![X]:((~strong(X)<~>generous(X))<=>rich(X)))&
((?[X]:((kind(X)&~generous(X))))=>((~creative(mary)&funny(mary))))&
(((happy(john)|~creative(john)))<=>((patient(paul)<~>~tall(paul))))&
((?[X]:((~kind(X)&wise(X))))=>((creative(susan)<~>~kind(susan))))&
(![X]:((kind(X)&funny(X))<=>generous(X)))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>funny(X))=>(~old(X)<~>~strong(X))))&
(((kind(john)&~humble(john)))<=>((~quiet(susan)&~calm(susan))))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)&strong(X))<=>(patient(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(patient(fred)))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:((happy(X)|quiet(X))))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
(~funny(mary))&
(calm(fred))&
(?[X]:((calm(X)&old(X)))) | ~strong(mary) | [
"p13",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7671578708574641934452862
% SZS output start Proof for 7671578708574641934452862
14. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (curious(X0) <~> ~calm(X0))) [input p13]
15. ! [X0] : ((strong(X0) & humble(X0)) <=> (kind(X0) | patient(X0))) [input p14]
16. ? [X0] : (~kind(X0) <~> patient(X0)) => patient(fred) [input p15]
23. calm(fred) [input p22]
25. ~strong(mary) [input hypothesis]
37. patient(fred) | ! [X0] : (~kind(X0) <=> patient(X0)) [ennf transformation 16]
62. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) & (((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 14]
63. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~strong(X0) | ~humble(X0)))) [nnf transformation 15]
64. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~strong(X0) | ~humble(X0))) [flattening 63]
65. patient(fred) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))) [nnf transformation 37]
123. ~calm(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 62]
128. ~patient(X0) | ~curious(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 62]
133. ~patient(X0) | strong(X0) [cnf transformation 64]
134. ~kind(X0) | strong(X0) [cnf transformation 64]
135. patient(fred) | patient(X0) | kind(X0) [cnf transformation 65]
147. calm(fred) [cnf transformation 23]
150. ~strong(mary) [cnf transformation 25]
151. ~calm(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 123]
154. ~patient(X0) | ~curious(X0) | ~calm(X0) [duplicate literal removal 128]
306. ~calm(X0) | ~patient(X0) [subsumption resolution 151,154]
311. 34 <=> patient(fred) [avatar definition]
316. 35 <=> ! [X0] : (patient(X0) | kind(X0)) [avatar definition]
317. kind(X0) | patient(X0) <- (35) [avatar component clause 316]
318. 35 | 34 [avatar split clause 135,311,316]
355. ~patient(fred) [resolution 306,147]
360. ~34 [avatar split clause 355,311]
365. patient(X2) | strong(X2) <- (35) [resolution 317,134]
368. strong(X2) <- (35) [subsumption resolution 365,133]
381. $false <- (35) [resolution 368,150]
382. ~35 [avatar contradiction clause 381]
383. $false [avatar sat refutation 318,360,382]
% SZS output end Proof for 7671578708574641934452862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both curious and patient then someone is either rich or calm and vice versa. Everyone who is both not old and funny is both old and not kind. If someone is not tall then john is either generous or wise and vice versa. Everyone who is both not brave and funny is not patient or funny and vice versa. Everyone who is either kind or not creative is not kind or not wise and vice versa. Everyone who is either not rich or wise is both quiet and strong and vice versa. Everyone who is both wise and patient is either rich or not tall and vice versa. If someone is either happy or not old then someone is not strong. Everyone who is not strong is not tall or rich. Everyone who is either generous or funny is either not creative or not patient. Everyone who is happy is funny and vice versa. If paul is not patient then mary is not creative or not brave and vice versa. Everyone who is calm is both brave and humble and vice versa. If paul is not calm then fred is both generous and creative and vice versa. If mary is either generous or not calm then someone is not curious or brave. If alice is both not tall and wise then john is both not calm and not brave. Someone is funny or wise. Someone is generous. John is not brave. Someone is not kind. Fred is either not generous or not old. Someone is humble or not curious. Someone is both curious and not calm. | Paul is not patient. | contradiction | ((?[X]:((curious(X)&patient(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:((~old(X)&funny(X))=>(old(X)&~kind(X))))&
((?[X]:(~tall(X)))<=>((generous(john)<~>wise(john))))&
(![X]:((~brave(X)&funny(X))<=>(~patient(X)|funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(quiet(X)&strong(X))))&
(![X]:((wise(X)&patient(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((happy(X)<~>~old(X))))=>(?[X]:(~strong(X))))&
(![X]:(~strong(X)=>(~tall(X)|rich(X))))&
(![X]:((generous(X)<~>funny(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(happy(X)<=>funny(X)))&
((~patient(paul))<=>((~creative(mary)|~brave(mary))))&
(![X]:(calm(X)<=>(brave(X)&humble(X))))&
((~calm(paul))<=>((generous(fred)&creative(fred))))&
(((generous(mary)<~>~calm(mary)))=>(?[X]:((~curious(X)|brave(X)))))&
(((~tall(alice)&wise(alice)))=>((~calm(john)&~brave(john))))&
(?[X]:((funny(X)|wise(X))))&
(?[X]:(generous(X)))&
(~brave(john))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>~old(fred)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((curious(X)&~calm(X)))) | ~patient(paul) | [
"p1",
"p3",
"p9",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7978849541432204647991633
% SZS output start Proof for 7978849541432204647991633
2. ! [X0] : ((funny(X0) & ~old(X0)) => (~kind(X0) & old(X0))) [input p1]
4. ! [X0] : ((funny(X0) & ~brave(X0)) <=> (funny(X0) | ~patient(X0))) [input p3]
10. ! [X0] : ((generous(X0) <~> funny(X0)) => (~creative(X0) <~> ~patient(X0))) [input p9]
13. ! [X0] : (calm(X0) <=> (humble(X0) & brave(X0))) [input p12]
14. ~calm(paul) <=> (creative(fred) & generous(fred)) [input p13]
21. ~generous(fred) <~> ~old(fred) [input p20]
24. ~patient(paul) [input hypothesis]
27. ! [X0] : ((~kind(X0) & old(X0)) | (~funny(X0) | old(X0))) [ennf transformation 2]
28. ! [X0] : ((~kind(X0) & old(X0)) | ~funny(X0) | old(X0)) [flattening 27]
32. ! [X0] : ((~creative(X0) <~> ~patient(X0)) | (generous(X0) <=> funny(X0))) [ennf transformation 10]
45. ! [X0] : (((funny(X0) & ~brave(X0)) | (~funny(X0) & patient(X0))) & ((funny(X0) | ~patient(X0)) | (~funny(X0) | brave(X0)))) [nnf transformation 4]
46. ! [X0] : (((funny(X0) & ~brave(X0)) | (~funny(X0) & patient(X0))) & (funny(X0) | ~patient(X0) | ~funny(X0) | brave(X0))) [flattening 45]
57. ! [X0] : (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) [nnf transformation 32]
61. ! [X0] : ((calm(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | ~calm(X0))) [nnf transformation 13]
62. ! [X0] : ((calm(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | ~calm(X0))) [flattening 61]
63. (~calm(paul) | (~creative(fred) | ~generous(fred))) & ((creative(fred) & generous(fred)) | calm(paul)) [nnf transformation 14]
64. (~calm(paul) | ~creative(fred) | ~generous(fred)) & ((creative(fred) & generous(fred)) | calm(paul)) [flattening 63]
74. (old(fred) | generous(fred)) & (~old(fred) | ~generous(fred)) [nnf transformation 21]
85. old(X0) | ~funny(X0) | old(X0) [cnf transformation 28]
92. ~brave(X0) | patient(X0) [cnf transformation 46]
94. funny(X0) | patient(X0) [cnf transformation 46]
117. ~patient(X0) | ~creative(X0) | funny(X0) | ~generous(X0) [cnf transformation 57]
126. ~calm(X0) | brave(X0) [cnf transformation 62]
129. generous(fred) | calm(paul) [cnf transformation 64]
130. creative(fred) | calm(paul) [cnf transformation 64]
140. ~old(fred) | ~generous(fred) [cnf transformation 74]
145. ~patient(paul) [cnf transformation 24]
148. ~funny(X0) | old(X0) [duplicate literal removal 85]
213. ~creative(X0) | funny(X0) | ~generous(X0) [subsumption resolution 117,94]
219. 16 <=> patient(paul) [avatar definition]
221. ~patient(paul) <- (~16) [avatar component clause 219]
230. 18 <=> generous(fred) [avatar definition]
231. generous(fred) <- (18) [avatar component clause 230]
234. 19 <=> creative(fred) [avatar definition]
235. creative(fred) <- (19) [avatar component clause 234]
238. 20 <=> calm(paul) [avatar definition]
239. calm(paul) <- (20) [avatar component clause 238]
242. 20 | 19 [avatar split clause 130,234,238]
243. 20 | 18 [avatar split clause 129,230,238]
291. 31 <=> old(fred) [avatar definition]
292. ~old(fred) <- (~31) [avatar component clause 291]
295. ~18 | ~31 [avatar split clause 140,291,230]
305. ~16 [avatar split clause 145,219]
346. brave(paul) <- (20) [resolution 239,126]
367. patient(paul) <- (20) [resolution 346,92]
382. $false <- (~16, 20) [subsumption resolution 367,221]
383. 16 | ~20 [avatar contradiction clause 382]
425. funny(fred) | ~generous(fred) <- (19) [resolution 213,235]
427. funny(fred) <- (18, 19) [subsumption resolution 425,231]
428. old(fred) <- (18, 19) [resolution 427,148]
430. $false <- (18, 19, ~31) [subsumption resolution 428,292]
431. ~18 | ~19 | 31 [avatar contradiction clause 430]
432. $false [avatar sat refutation 242,243,295,305,383,431]
% SZS output end Proof for 7978849541432204647991633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or quiet is both wise and not brave. Everyone who is not happy or patient is not curious or not generous and vice versa. Everyone who is not patient or curious is not creative and vice versa. Everyone who is patient or not calm is tall. If susan is not kind or not patient then someone is either not quiet or happy and vice versa. If paul is not quiet then someone is not brave or not generous. If someone is either not strong or not rich then someone is either tall or not curious. Everyone who is not happy is either not kind or funny and vice versa. If john is both patient and not quiet then someone is both not brave and quiet and vice versa. If lucy is happy then alice is not calm or rich. Everyone who is not happy or not curious is both tall and brave. If someone is not happy then someone is both not brave and wise and vice versa. Everyone who is not patient is both not strong and creative and vice versa. Everyone who is both quiet and not calm is not happy or happy and vice versa. Everyone who is either curious or strong is not quiet or not brave and vice versa. Someone is wise. Someone is both patient and happy. Someone is both not old and quiet. Fred is not calm or not humble. Paul is both strong and rich. Lucy is either not calm or not rich. | Fred is tall. | entailment | (![X]:((curious(X)<~>quiet(X))=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|patient(X))<=>(~curious(X)|~generous(X))))&
(![X]:((~patient(X)|curious(X))<=>~creative(X)))&
(![X]:((patient(X)|~calm(X))=>tall(X)))&
(((~kind(susan)|~patient(susan)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
((~quiet(paul))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>funny(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~brave(X)&quiet(X)))))&
((happy(lucy))=>((~calm(alice)|rich(alice))))&
(![X]:((~happy(X)|~curious(X))=>(tall(X)&brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~old(X)&quiet(X))))&
((~calm(fred)|~humble(fred)))&
((strong(paul)&rich(paul)))&
((~calm(lucy)<~>~rich(lucy))) | tall(fred) | [
"p2",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6485609304184241572152495
% SZS output start Proof for 6485609304184241572152495
3. ! [X0] : ((curious(X0) | ~patient(X0)) <=> ~creative(X0)) [input p2]
4. ! [X0] : ((~calm(X0) | patient(X0)) => tall(X0)) [input p3]
13. ! [X0] : (~patient(X0) <=> (creative(X0) & ~strong(X0))) [input p12]
22. ~tall(fred) [input hypothesis]
28. ! [X0] : (tall(X0) | (calm(X0) & ~patient(X0))) [ennf transformation 4]
37. ! [X0] : (((curious(X0) | ~patient(X0)) | creative(X0)) & (~creative(X0) | (~curious(X0) & patient(X0)))) [nnf transformation 3]
38. ! [X0] : ((curious(X0) | ~patient(X0) | creative(X0)) & (~creative(X0) | (~curious(X0) & patient(X0)))) [flattening 37]
61. ! [X0] : ((~patient(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | patient(X0))) [nnf transformation 13]
62. ! [X0] : ((~patient(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | patient(X0))) [flattening 61]
82. ~creative(X0) | patient(X0) [cnf transformation 38]
85. ~patient(X0) | tall(X0) [cnf transformation 28]
115. creative(X0) | patient(X0) [cnf transformation 62]
136. ~tall(fred) [cnf transformation 22]
254. patient(X0) [subsumption resolution 115,82]
273. tall(X0) [resolution 85,254]
274. $false [resolution 273,136]
% SZS output end Proof for 6485609304184241572152495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is not happy. If someone is not curious then susan is either not strong or funny. If someone is either calm or curious then someone is either wise or not happy and vice versa. If someone is either happy or not old then lucy is strong. If someone is both curious and patient then someone is either not curious or wise and vice versa. If susan is both happy and not generous then someone is both patient and happy. If john is not wise or happy then someone is curious. Everyone who is either calm or rich is not wise or not brave and vice versa. Everyone who is both tall and curious is humble. Everyone who is either not humble or humble is wise and vice versa. If fred is either not generous or not wise then someone is quiet or not curious and vice versa. If john is not generous then paul is both strong and not humble and vice versa. If fred is not happy or generous then john is either old or not rich. If someone is not happy then susan is both calm and quiet and vice versa. Everyone who is both not humble and kind is quiet. Everyone who is either not generous or not strong is both not happy and not old. Fred is strong or rich. Paul is either not patient or creative. Someone is not funny or not calm. Someone is wise. Susan is tall. Someone is either creative or kind. Alice is not strong or wise. | Paul is wise. | entailment | (![X]:(kind(X)=>~happy(X)))&
((?[X]:(~curious(X)))=>((~strong(susan)<~>funny(susan))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
((?[X]:((happy(X)<~>~old(X))))=>(strong(lucy)))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((happy(susan)&~generous(susan)))=>(?[X]:((patient(X)&happy(X)))))&
(((~wise(john)|happy(john)))=>(?[X]:(curious(X))))&
(![X]:((calm(X)<~>rich(X))<=>(~wise(X)|~brave(X))))&
(![X]:((tall(X)&curious(X))=>humble(X)))&
(![X]:((~humble(X)<~>humble(X))<=>wise(X)))&
(((~generous(fred)<~>~wise(fred)))<=>(?[X]:((quiet(X)|~curious(X)))))&
((~generous(john))<=>((strong(paul)&~humble(paul))))&
(((~happy(fred)|generous(fred)))=>((old(john)<~>~rich(john))))&
((?[X]:(~happy(X)))<=>((calm(susan)&quiet(susan))))&
(![X]:((~humble(X)&kind(X))=>quiet(X)))&
(![X]:((~generous(X)<~>~strong(X))=>(~happy(X)&~old(X))))&
((strong(fred)|rich(fred)))&
((~patient(paul)<~>creative(paul)))&
(?[X]:((~funny(X)|~calm(X))))&
(?[X]:(wise(X)))&
(tall(susan))&
(?[X]:((creative(X)<~>kind(X))))&
((~strong(alice)|wise(alice))) | wise(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 173304292240314591300026
% SZS output start Proof for 173304292240314591300026
10. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> wise(X0)) [input p9]
24. ~wise(paul) [input hypothesis]
57. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~wise(X0)) & (wise(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 10]
109. wise(X0) | humble(X0) | humble(X0) [cnf transformation 57]
110. wise(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 57]
143. ~wise(paul) [cnf transformation 24]
144. wise(X0) | humble(X0) [duplicate literal removal 109]
145. wise(X0) | ~humble(X0) [duplicate literal removal 110]
270. wise(X0) [subsumption resolution 144,145]
379. $false [subsumption resolution 143,270]
% SZS output end Proof for 173304292240314591300026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not rich is calm or creative and vice versa. If alice is not brave then alice is both humble and strong. If susan is both rich and not old then alice is both not old and not calm and vice versa. Everyone who is generous or not creative is creative. Everyone who is happy or strong is either not calm or not tall and vice versa. Everyone who is both curious and strong is both tall and curious. If lucy is not quiet then susan is not generous or not rich and vice versa. If alice is not quiet or generous then mary is wise or kind and vice versa. Everyone who is curious or not calm is both not humble and tall. Everyone who is not funny or not brave is not humble. If someone is not kind or wise then someone is both brave and not tall and vice versa. If paul is both funny and not brave then someone is both not happy and old and vice versa. If fred is either strong or patient then lucy is both not tall and not rich and vice versa. If paul is either rich or not strong then paul is both wise and calm and vice versa. If someone is both rich and quiet then someone is not creative or not old. Everyone who is not quiet is either happy or not quiet. Someone is either not strong or not generous. Paul is generous. Someone is not quiet or not tall. Someone is not old or not curious. Mary is generous or not happy. Someone is not curious. John is either not old or not creative. | Susan is not rich. | neutral | (![X]:((strong(X)|~rich(X))<=>(calm(X)|creative(X))))&
((~brave(alice))=>((humble(alice)&strong(alice))))&
(((rich(susan)&~old(susan)))<=>((~old(alice)&~calm(alice))))&
(![X]:((generous(X)|~creative(X))=>creative(X)))&
(![X]:((happy(X)|strong(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((curious(X)&strong(X))=>(tall(X)&curious(X))))&
((~quiet(lucy))<=>((~generous(susan)|~rich(susan))))&
(((~quiet(alice)|generous(alice)))<=>((wise(mary)|kind(mary))))&
(![X]:((curious(X)|~calm(X))=>(~humble(X)&tall(X))))&
(![X]:((~funny(X)|~brave(X))=>~humble(X)))&
((?[X]:((~kind(X)|wise(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(((funny(paul)&~brave(paul)))<=>(?[X]:((~happy(X)&old(X)))))&
(((strong(fred)<~>patient(fred)))<=>((~tall(lucy)&~rich(lucy))))&
(((rich(paul)<~>~strong(paul)))<=>((wise(paul)&calm(paul))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:(~quiet(X)=>(happy(X)<~>~quiet(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
(generous(paul))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:((~old(X)|~curious(X))))&
((generous(mary)|~happy(mary)))&
(?[X]:(~curious(X)))&
((~old(john)<~>~creative(john))) | ~rich(susan) | [] | null | 0 |
If someone is both not funny and quiet then someone is either not brave or tall.
If someone is not wise or curious then susan is not generous.
If fred is either not kind or not patient then alice is both patient and not creative.
Everyone who is not quiet or not creative is both not curious and not rich.
Everyone who is either not creative or not strong is either creative or not funny.
If john is not old then someone is kind and vice versa.
Everyone who is not wise is either funny or not wise.
If someone is both not kind and quiet then mary is quiet and vice versa.
Everyone who is not brave or funny is not old.
Everyone who is both not calm and rich is either not patient or not humble and vice versa.
Everyone who is not happy or patient is not generous.
If fred is either curious or not generous then someone is both not old and not quiet.
If someone is not curious or rich then someone is either not kind or rich and vice versa.
If john is both curious and not strong then lucy is rich or not tall.
Everyone who is happy or not wise is not curious or not tall.
Everyone who is both not curious and not generous is either strong or not generous and vice versa.
Paul is brave or not old.
Susan is both not humble and calm.
Someone is not humble.
Someone is not wise.
Someone is quiet or rich.
Paul is not old or not funny.
Mary is both not tall and rich.
Someone is not quiet. | Alice is not generous. | neutral | ((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:((~wise(X)|curious(X))))=>(~generous(susan)))&
(((~kind(fred)<~>~patient(fred)))=>((patient(alice)&~creative(alice))))&
(![X]:((~quiet(X)|~creative(X))=>(~curious(X)&~rich(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(creative(X)<~>~funny(X))))&
((~old(john))<=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>(funny(X)<~>~wise(X))))&
((?[X]:((~kind(X)&quiet(X))))<=>(quiet(mary)))&
(![X]:((~brave(X)|funny(X))=>~old(X)))&
(![X]:((~calm(X)&rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~happy(X)|patient(X))=>~generous(X)))&
(((curious(fred)<~>~generous(fred)))=>(?[X]:((~old(X)&~quiet(X)))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((curious(john)&~strong(john)))=>((rich(lucy)|~tall(lucy))))&
(![X]:((happy(X)|~wise(X))=>(~curious(X)|~tall(X))))&
(![X]:((~curious(X)&~generous(X))<=>(strong(X)<~>~generous(X))))&
((brave(paul)|~old(paul)))&
((~humble(susan)&calm(susan)))&
(?[X]:(~humble(X)))&
(?[X]:(~wise(X)))&
(?[X]:((quiet(X)|rich(X))))&
((~old(paul)|~funny(paul)))&
((~tall(mary)&rich(mary)))&
(?[X]:(~quiet(X))) | ~generous(alice) | [] | null | 0 |
Everyone who is both not funny and not rich is either not happy or quiet.
Everyone who is not patient is not wise or calm and vice versa.
If someone is brave then someone is both not brave and not humble.
Everyone who is either not rich or patient is happy.
Everyone who is either kind or not strong is tall and vice versa.
Everyone who is kind or rich is not strong or calm.
If fred is creative then someone is not funny and vice versa.
Everyone who is both not brave and patient is brave and vice versa.
If someone is both patient and brave then fred is not quiet.
Everyone who is funny or not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Someone is generous.
Mary is not kind or curious.
Lucy is either not old or wise.
Mary is either not strong or brave.
Someone is old or not wise.
Someone is not old.
Someone is either not funny or old.
Susan is either not curious or not brave. | Fred is not patient. | entailment | (![X]:((~funny(X)&~rich(X))=>(~happy(X)<~>quiet(X))))&
(![X]:(~patient(X)<=>(~wise(X)|calm(X))))&
((?[X]:(brave(X)))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((~rich(X)<~>patient(X))=>happy(X)))&
(![X]:((kind(X)<~>~strong(X))<=>tall(X)))&
(![X]:((kind(X)|rich(X))=>(~strong(X)|calm(X))))&
((creative(fred))<=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&patient(X))<=>brave(X)))&
((?[X]:((patient(X)&brave(X))))=>(~quiet(fred)))&
(![X]:((funny(X)|~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(?[X]:(generous(X)))&
((~kind(mary)|curious(mary)))&
((~old(lucy)<~>wise(lucy)))&
((~strong(mary)<~>brave(mary)))&
(?[X]:((old(X)|~wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)<~>old(X))))&
((~curious(susan)<~>~brave(susan))) | ~patient(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2117972813780546066415448
% SZS output start Proof for 2117972813780546066415448
8. ! [X0] : ((patient(X0) & ~brave(X0)) <=> brave(X0)) [input p7]
25. patient(fred) [input hypothesis]
50. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~patient(X0) | brave(X0))) [flattening 50]
92. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 51]
93. ~brave(X0) | ~brave(X0) [cnf transformation 51]
134. patient(fred) [cnf transformation 25]
135. ~patient(X0) | brave(X0) [duplicate literal removal 92]
136. ~brave(X0) [duplicate literal removal 93]
138. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
139. ~brave(X1) <- (1) [avatar component clause 138]
163. 1 [avatar split clause 136,138]
288. brave(fred) [resolution 135,134]
289. $false <- (1) [subsumption resolution 288,139]
290. ~1 [avatar contradiction clause 289]
291. $false [avatar sat refutation 163,290]
% SZS output end Proof for 2117972813780546066415448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or generous is both not tall and not happy and vice versa. Everyone who is both not calm and creative is not creative and vice versa. Everyone who is not strong or not creative is both strong and kind and vice versa. If mary is patient or not humble then mary is both not tall and humble. Everyone who is quiet is not rich or not patient. If someone is either not old or tall then alice is both funny and not quiet. Everyone who is both wise and humble is both not strong and not quiet. Everyone who is either rich or old is happy or not tall and vice versa. Everyone who is not funny or patient is either quiet or rich and vice versa. Everyone who is not funny or happy is either not old or not patient. If fred is either not calm or kind then john is either rich or not brave and vice versa. Everyone who is both patient and generous is both not brave and not curious and vice versa. Everyone who is either not brave or not quiet is both not brave and funny and vice versa. If someone is either curious or tall then john is either not wise or generous and vice versa. If john is not kind or creative then someone is both curious and quiet. Someone is either patient or quiet. Someone is brave. Mary is generous or rich. Alice is brave. | Alice is rich. | contradiction | (![X]:((~strong(X)<~>generous(X))<=>(~tall(X)&~happy(X))))&
(![X]:((~calm(X)&creative(X))<=>~creative(X)))&
(![X]:((~strong(X)|~creative(X))<=>(strong(X)&kind(X))))&
(((patient(mary)|~humble(mary)))=>((~tall(mary)&humble(mary))))&
(![X]:(quiet(X)=>(~rich(X)|~patient(X))))&
((?[X]:((~old(X)<~>tall(X))))=>((funny(alice)&~quiet(alice))))&
(![X]:((wise(X)&humble(X))=>(~strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))<=>(happy(X)|~tall(X))))&
(![X]:((~funny(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~funny(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(((~calm(fred)<~>kind(fred)))<=>((rich(john)<~>~brave(john))))&
(![X]:((patient(X)&generous(X))<=>(~brave(X)&~curious(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~brave(X)&funny(X))))&
((?[X]:((curious(X)<~>tall(X))))<=>((~wise(john)<~>generous(john))))&
(((~kind(john)|creative(john)))=>(?[X]:((curious(X)&quiet(X)))))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:(brave(X)))&
((generous(mary)|rich(mary)))&
(brave(alice)) | rich(alice) | [
"p4",
"p5",
"p7",
"p9",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 694784423228471523532
% SZS output start Proof for 694784423228471523532
5. ! [X0] : (quiet(X0) => (~patient(X0) | ~rich(X0))) [input p4]
6. ? [X0] : (~old(X0) <~> tall(X0)) => (~quiet(alice) & funny(alice)) [input p5]
8. ! [X0] : ((rich(X0) <~> old(X0)) <=> (~tall(X0) | happy(X0))) [input p7]
10. ! [X0] : ((happy(X0) | ~funny(X0)) => (~old(X0) <~> ~patient(X0))) [input p9]
13. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) <=> (funny(X0) & ~brave(X0))) [input p12]
19. brave(alice) [input p18]
20. rich(alice) [input hypothesis]
22. ! [X0] : ((~patient(X0) | ~rich(X0)) | ~quiet(X0)) [ennf transformation 5]
23. ! [X0] : (~patient(X0) | ~rich(X0) | ~quiet(X0)) [flattening 22]
24. (~quiet(alice) & funny(alice)) | ! [X0] : (~old(X0) <=> tall(X0)) [ennf transformation 6]
27. ! [X0] : ((~old(X0) <~> ~patient(X0)) | (~happy(X0) & funny(X0))) [ennf transformation 10]
35. (~quiet(alice) & funny(alice)) | ! [X0] : ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))) [nnf transformation 24]
36. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [nnf transformation 8]
37. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [flattening 36]
40. ! [X0] : (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~happy(X0) & funny(X0))) [nnf transformation 27]
44. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~funny(X0) | brave(X0))) & ((funny(X0) & ~brave(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [nnf transformation 13]
45. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~funny(X0) | brave(X0)) & ((funny(X0) & ~brave(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [flattening 44]
75. ~rich(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 23]
78. ~quiet(alice) | tall(X0) | old(X0) [cnf transformation 35]
79. ~quiet(alice) | ~old(X0) | ~tall(X0) [cnf transformation 35]
82. ~rich(X0) | happy(X0) | old(X0) | ~tall(X0) [cnf transformation 37]
87. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 37]
97. ~happy(X0) | old(X0) | patient(X0) [cnf transformation 40]
111. ~brave(X0) | ~brave(X0) | quiet(X0) [cnf transformation 45]
132. brave(alice) [cnf transformation 19]
133. rich(alice) [cnf transformation 20]
134. ~brave(X0) | quiet(X0) [duplicate literal removal 111]
153. 3 <=> ! [X0] : (~old(X0) | ~tall(X0)) [avatar definition]
154. ~old(X0) | ~tall(X0) <- (3) [avatar component clause 153]
156. 4 <=> quiet(alice) [avatar definition]
157. quiet(alice) <- (4) [avatar component clause 156]
159. 3 | ~4 [avatar split clause 79,156,153]
161. 5 <=> ! [X0] : (tall(X0) | old(X0)) [avatar definition]
162. old(X0) | tall(X0) <- (5) [avatar component clause 161]
163. 5 | ~4 [avatar split clause 78,156,161]
244. quiet(alice) [resolution 134,132]
248. 4 [avatar split clause 244,156]
251. ~patient(alice) | ~quiet(alice) [resolution 75,133]
252. ~patient(alice) <- (4) [subsumption resolution 251,157]
257. ~rich(X1) | tall(X1) | tall(X1) <- (5) [resolution 87,162]
258. ~rich(X1) | tall(X1) <- (5) [duplicate literal removal 257]
260. tall(alice) <- (5) [resolution 258,133]
349. happy(alice) | old(alice) | ~tall(alice) [resolution 82,133]
352. happy(alice) | old(alice) <- (5) [subsumption resolution 349,260]
354. 28 <=> old(alice) [avatar definition]
355. ~old(alice) <- (~28) [avatar component clause 354]
356. old(alice) <- (28) [avatar component clause 354]
358. 29 <=> happy(alice) [avatar definition]
360. happy(alice) <- (29) [avatar component clause 358]
361. 28 | 29 | ~5 [avatar split clause 352,161,358,354]
377. ~tall(alice) <- (3, 28) [resolution 356,154]
380. $false <- (3, 5, 28) [subsumption resolution 377,260]
381. ~3 | ~5 | ~28 [avatar contradiction clause 380]
400. old(alice) | patient(alice) <- (29) [resolution 360,97]
404. patient(alice) <- (~28, 29) [subsumption resolution 400,355]
405. $false <- (4, ~28, 29) [subsumption resolution 404,252]
406. ~4 | 28 | ~29 [avatar contradiction clause 405]
407. $false [avatar sat refutation 159,163,248,361,381,406]
% SZS output end Proof for 694784423228471523532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is not curious and vice versa. Everyone who is both not tall and not old is quiet or not brave and vice versa. If paul is either not kind or not generous then john is either creative or brave. Everyone who is both not strong and not happy is both brave and humble. If someone is patient or not wise then fred is kind and vice versa. If someone is tall then someone is either not funny or not happy. Everyone who is either not funny or old is not calm. Everyone who is either not kind or not strong is both kind and curious. Everyone who is both creative and kind is humble and vice versa. If someone is tall then someone is brave or tall and vice versa. If someone is both brave and not kind then someone is not quiet or strong. Everyone who is creative is both not strong and generous. Everyone who is not tall is not happy and vice versa. Everyone who is either patient or curious is both humble and not quiet. Everyone who is both kind and not quiet is not funny. Everyone who is either patient or rich is both not wise and quiet. Someone is not calm. John is both curious and not old. Lucy is not kind or kind. John is quiet. Someone is either not funny or funny. Someone is not calm or tall. John is not old or strong. Susan is brave or not rich. | John is humble. | contradiction | (![X]:(brave(X)<=>~curious(X)))&
(![X]:((~tall(X)&~old(X))<=>(quiet(X)|~brave(X))))&
(((~kind(paul)<~>~generous(paul)))=>((creative(john)<~>brave(john))))&
(![X]:((~strong(X)&~happy(X))=>(brave(X)&humble(X))))&
((?[X]:((patient(X)|~wise(X))))<=>(kind(fred)))&
((?[X]:(tall(X)))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~funny(X)<~>old(X))=>~calm(X)))&
(![X]:((~kind(X)<~>~strong(X))=>(kind(X)&curious(X))))&
(![X]:((creative(X)&kind(X))<=>humble(X)))&
((?[X]:(tall(X)))<=>(?[X]:((brave(X)|tall(X)))))&
((?[X]:((brave(X)&~kind(X))))=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:(creative(X)=>(~strong(X)&generous(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((patient(X)<~>curious(X))=>(humble(X)&~quiet(X))))&
(![X]:((kind(X)&~quiet(X))=>~funny(X)))&
(![X]:((patient(X)<~>rich(X))=>(~wise(X)&quiet(X))))&
(?[X]:(~calm(X)))&
((curious(john)&~old(john)))&
((~kind(lucy)|kind(lucy)))&
(quiet(john))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:((~calm(X)|tall(X))))&
((~old(john)|strong(john)))&
((brave(susan)|~rich(susan))) | humble(john) | [
"p0",
"p1",
"p3",
"p8",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6043228361118455724572562
% SZS output start Proof for 6043228361118455724572562
1. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p0]
2. ! [X0] : ((~old(X0) & ~tall(X0)) <=> (~brave(X0) | quiet(X0))) [input p1]
4. ! [X0] : ((~happy(X0) & ~strong(X0)) => (humble(X0) & brave(X0))) [input p3]
9. ! [X0] : ((kind(X0) & creative(X0)) <=> humble(X0)) [input p8]
12. ! [X0] : (creative(X0) => (generous(X0) & ~strong(X0))) [input p11]
13. ! [X0] : (~tall(X0) <=> ~happy(X0)) [input p12]
18. ~old(john) & curious(john) [input p17]
25. humble(john) [input hypothesis]
29. ! [X0] : (humble(X0) => (kind(X0) & creative(X0))) [unused predicate definition removal 9]
34. ! [X0] : ((humble(X0) & brave(X0)) | (happy(X0) | strong(X0))) [ennf transformation 4]
35. ! [X0] : ((humble(X0) & brave(X0)) | happy(X0) | strong(X0)) [flattening 34]
38. ! [X0] : ((kind(X0) & creative(X0)) | ~humble(X0)) [ennf transformation 29]
40. ! [X0] : ((generous(X0) & ~strong(X0)) | ~creative(X0)) [ennf transformation 12]
45. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 1]
46. ! [X0] : (((~old(X0) & ~tall(X0)) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | (old(X0) | tall(X0)))) [nnf transformation 2]
47. ! [X0] : (((~old(X0) & ~tall(X0)) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | old(X0) | tall(X0))) [flattening 46]
66. ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 13]
72. ~curious(X0) | ~brave(X0) [cnf transformation 45]
76. ~tall(X0) | brave(X0) [cnf transformation 47]
83. happy(X0) | brave(X0) | strong(X0) [cnf transformation 35]
94. ~humble(X0) | creative(X0) [cnf transformation 38]
100. ~strong(X0) | ~creative(X0) [cnf transformation 40]
102. ~happy(X0) | tall(X0) [cnf transformation 66]
113. curious(john) [cnf transformation 18]
121. humble(john) [cnf transformation 25]
132. 3 <=> creative(john) [avatar definition]
133. creative(john) <- (3) [avatar component clause 132]
136. 4 <=> brave(john) [avatar definition]
138. ~brave(john) <- (~4) [avatar component clause 136]
215. ~brave(john) [resolution 72,113]
219. creative(john) [resolution 94,121]
220. 3 [avatar split clause 219,132]
223. brave(X0) | strong(X0) | tall(X0) [resolution 83,102]
233. strong(X0) | brave(X0) [subsumption resolution 223,76]
234. ~4 [avatar split clause 215,136]
298. ~creative(X2) | brave(X2) [resolution 233,100]
316. brave(john) <- (3) [resolution 298,133]
317. $false <- (3, ~4) [subsumption resolution 316,138]
318. ~3 | 4 [avatar contradiction clause 317]
319. $false [avatar sat refutation 220,234,318]
% SZS output end Proof for 6043228361118455724572562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either wise or happy then someone is old or not strong.
If someone is either not old or quiet then mary is both not happy and not rich and vice versa.
If paul is either not curious or not generous then someone is not rich and vice versa.
If someone is patient or not rich then susan is both rich and strong and vice versa.
Everyone who is not calm is funny.
If someone is both quiet and curious then susan is both strong and wise and vice versa.
If fred is either calm or kind then paul is both not tall and patient and vice versa.
If lucy is both happy and not kind then someone is not rich and vice versa.
If susan is not calm then john is both not patient and not strong and vice versa.
If paul is either happy or not strong then fred is not generous and vice versa.
Everyone who is not strong is funny or not funny and vice versa.
Everyone who is old is not generous and vice versa.
If someone is not happy then someone is not wise or curious.
If lucy is either humble or not funny then susan is both happy and curious and vice versa.
If alice is calm then john is either creative or not funny.
If someone is quiet then paul is tall and vice versa.
Mary is either rich or strong.
John is both quiet and not happy.
Someone is either rich or patient.
Someone is kind or curious.
Someone is either tall or not happy.
Someone is wise or humble.
Someone is either not calm or not rich. | Fred is not rich. | contradiction | (((wise(lucy)<~>happy(lucy)))=>(?[X]:((old(X)|~strong(X)))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((~happy(mary)&~rich(mary))))&
(((~curious(paul)<~>~generous(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((patient(X)|~rich(X))))<=>((rich(susan)&strong(susan))))&
(![X]:(~calm(X)=>funny(X)))&
((?[X]:((quiet(X)&curious(X))))<=>((strong(susan)&wise(susan))))&
(((calm(fred)<~>kind(fred)))<=>((~tall(paul)&patient(paul))))&
(((happy(lucy)&~kind(lucy)))<=>(?[X]:(~rich(X))))&
((~calm(susan))<=>((~patient(john)&~strong(john))))&
(((happy(paul)<~>~strong(paul)))<=>(~generous(fred)))&
(![X]:(~strong(X)<=>(funny(X)|~funny(X))))&
(![X]:(old(X)<=>~generous(X)))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|curious(X)))))&
(((humble(lucy)<~>~funny(lucy)))<=>((happy(susan)&curious(susan))))&
((calm(alice))=>((creative(john)<~>~funny(john))))&
((?[X]:(quiet(X)))<=>(tall(paul)))&
((rich(mary)<~>strong(mary)))&
((quiet(john)&~happy(john)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:((kind(X)|curious(X))))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~calm(X)<~>~rich(X)))) | ~rich(fred) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8471833666770954145347803
% SZS output start Proof for 8471833666770954145347803
4. ? [X0] : (~rich(X0) | patient(X0)) <=> (strong(susan) & rich(susan)) [input p3]
11. ! [X0] : (~strong(X0) <=> (~funny(X0) | funny(X0))) [input p10]
24. ~rich(fred) [input hypothesis]
42. (? [X0] : (~rich(X0) | patient(X0)) | (~strong(susan) | ~rich(susan))) & ((strong(susan) & rich(susan)) | ! [X0] : (rich(X0) & ~patient(X0))) [nnf transformation 4]
43. (? [X0] : (~rich(X0) | patient(X0)) | ~strong(susan) | ~rich(susan)) & ((strong(susan) & rich(susan)) | ! [X0] : (rich(X0) & ~patient(X0))) [flattening 42]
44. (? [X0] : (~rich(X0) | patient(X0)) | ~strong(susan) | ~rich(susan)) & ((strong(susan) & rich(susan)) | ! [X1] : (rich(X1) & ~patient(X1))) [rectify 43]
45. ? [X0] : (~rich(X0) | patient(X0)) => (~rich(sK3) | patient(sK3)) [choice axiom]
46. ((~rich(sK3) | patient(sK3)) | ~strong(susan) | ~rich(susan)) & ((strong(susan) & rich(susan)) | ! [X1] : (rich(X1) & ~patient(X1))) [skolemisation 44,45]
62. ! [X0] : ((~strong(X0) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | strong(X0))) [nnf transformation 11]
63. ! [X0] : ((~strong(X0) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | strong(X0))) [flattening 62]
104. strong(susan) | rich(X1) [cnf transformation 46]
128. ~strong(X0) | ~funny(X0) [cnf transformation 63]
129. ~strong(X0) | funny(X0) [cnf transformation 63]
155. ~rich(fred) [cnf transformation 24]
203. 11 <=> ! [X0] : rich(X0) [avatar definition]
204. rich(X0) <- (11) [avatar component clause 203]
226. 16 <=> strong(susan) [avatar definition]
227. strong(susan) <- (16) [avatar component clause 226]
238. 11 | 16 [avatar split clause 104,226,203]
328. ~strong(X0) [subsumption resolution 128,129]
436. $false <- (16) [subsumption resolution 227,328]
437. ~16 [avatar contradiction clause 436]
438. $false <- (11) [resolution 204,155]
439. ~11 [avatar contradiction clause 438]
440. $false [avatar sat refutation 238,437,439]
% SZS output end Proof for 8471833666770954145347803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or not funny is not rich or not funny and vice versa.
Everyone who is old or not quiet is both curious and creative and vice versa.
Everyone who is either wise or quiet is either not creative or not humble.
Everyone who is not tall is not patient or rich.
Everyone who is generous is either not curious or not tall and vice versa.
Everyone who is strong is patient and vice versa.
If mary is both not old and not quiet then someone is wise or not creative.
Everyone who is not old or tall is rich or kind.
Everyone who is not kind is both happy and curious.
If someone is either kind or wise then lucy is either not strong or calm.
Everyone who is not humble or not happy is funny and vice versa.
Everyone who is both calm and funny is not brave or not creative.
Everyone who is either not generous or strong is tall or kind and vice versa.
If alice is funny or calm then alice is not creative and vice versa.
If someone is both quiet and not tall then someone is not generous and vice versa.
Everyone who is not quiet is not old.
Someone is patient.
Someone is old.
Someone is both generous and not patient.
Someone is either quiet or not humble.
Mary is not strong.
John is either old or not tall.
Alice is either creative or kind. | Alice is strong. | neutral | (![X]:((~rich(X)<~>~funny(X))<=>(~rich(X)|~funny(X))))&
(![X]:((old(X)|~quiet(X))<=>(curious(X)&creative(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(~patient(X)|rich(X))))&
(![X]:(generous(X)<=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>patient(X)))&
(((~old(mary)&~quiet(mary)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~old(X)|tall(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)=>(happy(X)&curious(X))))&
((?[X]:((kind(X)<~>wise(X))))=>((~strong(lucy)<~>calm(lucy))))&
(![X]:((~humble(X)|~happy(X))<=>funny(X)))&
(![X]:((calm(X)&funny(X))=>(~brave(X)|~creative(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)|kind(X))))&
(((funny(alice)|calm(alice)))<=>(~creative(alice)))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~quiet(X)=>~old(X)))&
(?[X]:(patient(X)))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(~strong(mary))&
((old(john)<~>~tall(john)))&
((creative(alice)<~>kind(alice))) | strong(alice) | [] | null | 0 |
Everyone who is not old is either happy or not calm and vice versa. If someone is not strong then someone is either curious or patient. If fred is either not old or not brave then someone is either not calm or kind. If someone is not patient then someone is both not wise and kind. Everyone who is tall is funny and vice versa. Everyone who is patient or not rich is not patient or rich. If someone is both wise and not strong then someone is not generous or calm. If someone is funny then john is not brave or patient and vice versa. Everyone who is not strong is both not generous and calm and vice versa. If someone is not brave or strong then susan is not humble or not tall. Everyone who is either happy or not humble is humble. Everyone who is either not old or creative is not quiet. If paul is funny then someone is not patient or not rich and vice versa. If someone is both calm and not creative then someone is rich or not happy and vice versa. If someone is patient or strong then paul is either generous or not rich. If someone is either not patient or not old then someone is both not rich and not funny. Susan is either humble or old. Fred is not kind. Paul is either not humble or not quiet. Someone is kind or not wise. Someone is both funny and patient. Paul is both creative and wise. Someone is not funny or not rich. Susan is either not humble or not calm. | Susan is not humble. | contradiction | (![X]:(~old(X)<=>(happy(X)<~>~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)<~>patient(X)))))&
(((~old(fred)<~>~brave(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:(tall(X)<=>funny(X)))&
(![X]:((patient(X)|~rich(X))=>(~patient(X)|rich(X))))&
((?[X]:((wise(X)&~strong(X))))=>(?[X]:((~generous(X)|calm(X)))))&
((?[X]:(funny(X)))<=>((~brave(john)|patient(john))))&
(![X]:(~strong(X)<=>(~generous(X)&calm(X))))&
((?[X]:((~brave(X)|strong(X))))=>((~humble(susan)|~tall(susan))))&
(![X]:((happy(X)<~>~humble(X))=>humble(X)))&
(![X]:((~old(X)<~>creative(X))=>~quiet(X)))&
((funny(paul))<=>(?[X]:((~patient(X)|~rich(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:((patient(X)|strong(X))))=>((generous(paul)<~>~rich(paul))))&
((?[X]:((~patient(X)<~>~old(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
((humble(susan)<~>old(susan)))&
(~kind(fred))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((funny(X)&patient(X))))&
((creative(paul)&wise(paul)))&
(?[X]:((~funny(X)|~rich(X))))&
((~humble(susan)<~>~calm(susan))) | ~humble(susan) | [
"p0",
"p10",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2631011240431197227630313
% SZS output start Proof for 2631011240431197227630313
1. ! [X0] : (~old(X0) <=> (happy(X0) <~> ~calm(X0))) [input p0]
11. ! [X0] : ((happy(X0) <~> ~humble(X0)) => humble(X0)) [input p10]
17. humble(susan) <~> old(susan) [input p16]
24. ~humble(susan) <~> ~calm(susan) [input p23]
25. ~humble(susan) [input hypothesis]
41. ! [X0] : (humble(X0) | (happy(X0) <=> ~humble(X0))) [ennf transformation 11]
45. ! [X0] : ((~old(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | old(X0))) [nnf transformation 1]
66. ! [X0] : (humble(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 41]
82. (~old(susan) | ~humble(susan)) & (old(susan) | humble(susan)) [nnf transformation 17]
90. (calm(susan) | humble(susan)) & (~calm(susan) | ~humble(susan)) [nnf transformation 24]
93. ~calm(X0) | ~old(X0) | ~happy(X0) [cnf transformation 45]
116. humble(X0) | happy(X0) | humble(X0) [cnf transformation 66]
135. old(susan) | humble(susan) [cnf transformation 82]
147. calm(susan) | humble(susan) [cnf transformation 90]
148. ~humble(susan) [cnf transformation 25]
149. humble(X0) | happy(X0) [duplicate literal removal 116]
232. 19 <=> humble(susan) [avatar definition]
234. ~humble(susan) <- (~19) [avatar component clause 232]
323. 39 <=> old(susan) [avatar definition]
324. old(susan) <- (39) [avatar component clause 323]
327. 19 | 39 [avatar split clause 135,323,232]
357. 46 <=> calm(susan) [avatar definition]
359. calm(susan) <- (46) [avatar component clause 357]
360. 19 | 46 [avatar split clause 147,357,232]
362. ~19 [avatar split clause 148,232]
372. happy(susan) <- (~19) [resolution 149,234]
389. ~old(susan) | ~happy(susan) <- (46) [resolution 93,359]
392. ~happy(susan) <- (39, 46) [subsumption resolution 389,324]
393. $false <- (~19, 39, 46) [subsumption resolution 392,372]
394. 19 | ~39 | ~46 [avatar contradiction clause 393]
395. $false [avatar sat refutation 327,360,362,394]
% SZS output end Proof for 2631011240431197227630313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or calm then susan is not rich or not curious.
Everyone who is creative is either strong or not quiet.
Everyone who is both not wise and patient is both not calm and not old.
Everyone who is both funny and old is funny or wise.
If john is both funny and calm then fred is funny or not rich and vice versa.
Everyone who is kind is wise.
Everyone who is happy is both curious and humble and vice versa.
Everyone who is calm or not kind is either kind or happy and vice versa.
Everyone who is old or tall is both kind and funny and vice versa.
Everyone who is both not patient and funny is both funny and not brave.
If mary is strong then paul is both not calm and not generous.
If someone is either not creative or not quiet then someone is either not brave or brave and vice versa.
Everyone who is not funny is not tall and vice versa.
Everyone who is curious or not calm is both kind and not wise and vice versa.
Everyone who is either not rich or not calm is both not rich and generous and vice versa.
If alice is generous or patient then someone is either humble or generous and vice versa.
Someone is calm.
Someone is either creative or not wise.
Mary is not old or not kind.
Lucy is not curious or creative.
Susan is either tall or rich.
Paul is either not calm or not patient. | Paul is strong. | neutral | (((~happy(lucy)|calm(lucy)))=>((~rich(susan)|~curious(susan))))&
(![X]:(creative(X)=>(strong(X)<~>~quiet(X))))&
(![X]:((~wise(X)&patient(X))=>(~calm(X)&~old(X))))&
(![X]:((funny(X)&old(X))=>(funny(X)|wise(X))))&
(((funny(john)&calm(john)))<=>((funny(fred)|~rich(fred))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:(happy(X)<=>(curious(X)&humble(X))))&
(![X]:((calm(X)|~kind(X))<=>(kind(X)<~>happy(X))))&
(![X]:((old(X)|tall(X))<=>(kind(X)&funny(X))))&
(![X]:((~patient(X)&funny(X))=>(funny(X)&~brave(X))))&
((strong(mary))=>((~calm(paul)&~generous(paul))))&
((?[X]:((~creative(X)<~>~quiet(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((curious(X)|~calm(X))<=>(kind(X)&~wise(X))))&
(![X]:((~rich(X)<~>~calm(X))<=>(~rich(X)&generous(X))))&
(((generous(alice)|patient(alice)))<=>(?[X]:((humble(X)<~>generous(X)))))&
(?[X]:(calm(X)))&
(?[X]:((creative(X)<~>~wise(X))))&
((~old(mary)|~kind(mary)))&
((~curious(lucy)|creative(lucy)))&
((tall(susan)<~>rich(susan)))&
((~calm(paul)<~>~patient(paul))) | strong(paul) | [] | null | 0 |
If someone is either calm or not rich then someone is both not rich and brave.
Everyone who is not generous or brave is either curious or happy.
Everyone who is both patient and not strong is curious.
Everyone who is either generous or humble is either not kind or funny.
Everyone who is either not old or brave is calm or not old and vice versa.
Everyone who is both not calm and not happy is both not curious and not rich and vice versa.
If someone is not generous then lucy is calm.
Everyone who is not strong or not wise is either curious or not curious and vice versa.
Everyone who is not happy is both not calm and not wise.
Everyone who is not funny is not wise or calm and vice versa.
If someone is either generous or patient then someone is both not wise and strong and vice versa.
Everyone who is not quiet is either quiet or creative.
Everyone who is both not funny and patient is both humble and not tall and vice versa.
If alice is generous or not brave then someone is not kind and vice versa.
If fred is both brave and tall then paul is calm and vice versa.
Everyone who is either brave or not calm is generous or not happy and vice versa.
John is wise.
Someone is both old and not wise.
Susan is both curious and strong.
Someone is either not funny or not strong.
Someone is not generous or not patient.
Someone is rich.
Paul is both not old and not funny. | Lucy is not generous. | contradiction | ((?[X]:((calm(X)<~>~rich(X))))=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:((~generous(X)|brave(X))=>(curious(X)<~>happy(X))))&
(![X]:((patient(X)&~strong(X))=>curious(X)))&
(![X]:((generous(X)<~>humble(X))=>(~kind(X)<~>funny(X))))&
(![X]:((~old(X)<~>brave(X))<=>(calm(X)|~old(X))))&
(![X]:((~calm(X)&~happy(X))<=>(~curious(X)&~rich(X))))&
((?[X]:(~generous(X)))=>(calm(lucy)))&
(![X]:((~strong(X)|~wise(X))<=>(curious(X)<~>~curious(X))))&
(![X]:(~happy(X)=>(~calm(X)&~wise(X))))&
(![X]:(~funny(X)<=>(~wise(X)|calm(X))))&
((?[X]:((generous(X)<~>patient(X))))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:(~quiet(X)=>(quiet(X)<~>creative(X))))&
(![X]:((~funny(X)&patient(X))<=>(humble(X)&~tall(X))))&
(((generous(alice)|~brave(alice)))<=>(?[X]:(~kind(X))))&
(((brave(fred)&tall(fred)))<=>(calm(paul)))&
(![X]:((brave(X)<~>~calm(X))<=>(generous(X)|~happy(X))))&
(wise(john))&
(?[X]:((old(X)&~wise(X))))&
((curious(susan)&strong(susan)))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((~generous(X)|~patient(X))))&
(?[X]:(rich(X)))&
((~old(paul)&~funny(paul))) | ~generous(lucy) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8686022991778568342440708
% SZS output start Proof for 8686022991778568342440708
1. ? [X0] : (calm(X0) <~> ~rich(X0)) => ? [X0] : (brave(X0) & ~rich(X0)) [input p0]
2. ! [X0] : ((brave(X0) | ~generous(X0)) => (curious(X0) <~> happy(X0))) [input p1]
5. ! [X0] : ((~old(X0) <~> brave(X0)) <=> (~old(X0) | calm(X0))) [input p4]
6. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~rich(X0) & ~curious(X0))) [input p5]
7. ? [X0] : ~generous(X0) => calm(lucy) [input p6]
9. ! [X0] : (~happy(X0) => (~wise(X0) & ~calm(X0))) [input p8]
24. ~generous(lucy) [input hypothesis]
25. ? [X0] : (calm(X0) <~> ~rich(X0)) => ? [X1] : (brave(X1) & ~rich(X1)) [rectify 1]
27. ? [X1] : (brave(X1) & ~rich(X1)) | ! [X0] : (calm(X0) <=> ~rich(X0)) [ennf transformation 25]
28. ! [X0] : ((curious(X0) <~> happy(X0)) | (~brave(X0) & generous(X0))) [ennf transformation 2]
32. calm(lucy) | ! [X0] : generous(X0) [ennf transformation 7]
33. ! [X0] : ((~wise(X0) & ~calm(X0)) | happy(X0)) [ennf transformation 9]
35. ? [X1] : (brave(X1) & ~rich(X1)) | ! [X0] : ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))) [nnf transformation 27]
36. ? [X0] : (brave(X0) & ~rich(X0)) | ! [X1] : ((calm(X1) | rich(X1)) & (~rich(X1) | ~calm(X1))) [rectify 35]
37. ? [X0] : (brave(X0) & ~rich(X0)) => (brave(sK0) & ~rich(sK0)) [choice axiom]
38. (brave(sK0) & ~rich(sK0)) | ! [X1] : ((calm(X1) | rich(X1)) & (~rich(X1) | ~calm(X1))) [skolemisation 36,37]
39. ! [X0] : (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (~brave(X0) & generous(X0))) [nnf transformation 28]
41. ! [X0] : ((((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0))))) [flattening 41]
43. ! [X0] : (((~happy(X0) & ~calm(X0)) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 6]
44. ! [X0] : (((~happy(X0) & ~calm(X0)) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | happy(X0) | calm(X0))) [flattening 43]
75. ~rich(sK0) | ~rich(X1) | ~calm(X1) [cnf transformation 38]
77. brave(sK0) | ~rich(X1) | ~calm(X1) [cnf transformation 38]
81. ~happy(X0) | ~curious(X0) | generous(X0) [cnf transformation 39]
82. ~happy(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 39]
89. ~old(X0) | calm(X0) | ~old(X0) | ~brave(X0) [cnf transformation 42]
93. ~brave(X0) | old(X0) | old(X0) [cnf transformation 42]
96. ~calm(X0) | rich(X0) | curious(X0) [cnf transformation 44]
98. calm(lucy) | generous(X0) [cnf transformation 32]
105. ~calm(X0) | happy(X0) [cnf transformation 33]
145. ~generous(lucy) [cnf transformation 24]
149. ~old(X0) | calm(X0) | ~brave(X0) [duplicate literal removal 89]
150. ~brave(X0) | old(X0) [duplicate literal removal 93]
155. 2 <=> brave(sK0) [avatar definition]
157. brave(sK0) <- (2) [avatar component clause 155]
160. 3 <=> ! [X1] : (~rich(X1) | ~calm(X1)) [avatar definition]
161. ~rich(X1) | ~calm(X1) <- (3) [avatar component clause 160]
162. 3 | 2 [avatar split clause 77,155,160]
164. 4 <=> rich(sK0) [avatar definition]
168. 3 | ~4 [avatar split clause 75,164,160]
169. ~brave(X0) | calm(X0) [subsumption resolution 149,150]
171. 5 <=> ! [X0] : generous(X0) [avatar definition]
172. generous(X0) <- (5) [avatar component clause 171]
174. 6 <=> calm(lucy) [avatar definition]
176. calm(lucy) <- (6) [avatar component clause 174]
177. 5 | 6 [avatar split clause 98,174,171]
266. $false <- (5) [resolution 172,145]
267. ~5 [avatar contradiction clause 266]
270. happy(lucy) <- (6) [resolution 105,176]
276. calm(sK0) <- (2) [resolution 169,157]
277. happy(sK0) <- (2) [resolution 276,105]
282. ~curious(lucy) | generous(lucy) <- (6) [resolution 81,270]
287. ~curious(lucy) <- (6) [subsumption resolution 282,145]
302. 28 <=> curious(sK0) [avatar definition]
318. ~curious(sK0) | ~brave(sK0) <- (2) [resolution 82,277]
355. rich(lucy) | curious(lucy) <- (6) [resolution 96,176]
356. rich(sK0) | curious(sK0) <- (2) [resolution 96,276]
357. rich(lucy) <- (6) [subsumption resolution 355,287]
362. ~curious(sK0) <- (2) [subsumption resolution 318,157]
363. ~28 | ~2 [avatar split clause 362,155,302]
364. 28 | 4 | ~2 [avatar split clause 356,155,164,302]
371. ~calm(lucy) <- (3, 6) [resolution 161,357]
374. $false <- (3, 6) [subsumption resolution 371,176]
375. ~3 | ~6 [avatar contradiction clause 374]
378. $false [avatar sat refutation 162,168,177,267,363,364,375]
% SZS output end Proof for 8686022991778568342440708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm or curious then someone is strong.
Everyone who is not old or creative is either curious or kind and vice versa.
Everyone who is either quiet or not old is either not curious or kind.
Everyone who is both tall and old is either tall or calm and vice versa.
Everyone who is kind is quiet.
Everyone who is both not kind and not humble is old or curious and vice versa.
Everyone who is either not curious or quiet is happy or rich.
If someone is either calm or strong then lucy is either calm or not strong and vice versa.
If someone is both not patient and not calm then someone is not wise or not old and vice versa.
Everyone who is generous is not kind or not funny and vice versa.
If lucy is not generous or not kind then someone is calm.
Everyone who is either rich or funny is either not calm or funny.
Everyone who is humble or tall is curious or not curious.
Everyone who is either happy or not generous is both calm and not kind and vice versa.
Everyone who is either not curious or not old is not creative and vice versa.
Everyone who is not curious or funny is funny or kind and vice versa.
Alice is not quiet or quiet.
Alice is both not generous and rich.
Someone is happy.
Paul is both not quiet and brave.
Someone is quiet.
Fred is not happy.
Alice is rich. | Alice is not curious. | entailment | (((calm(fred)|curious(fred)))=>(?[X]:(strong(X))))&
(![X]:((~old(X)|creative(X))<=>(curious(X)<~>kind(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~curious(X)<~>kind(X))))&
(![X]:((tall(X)&old(X))<=>(tall(X)<~>calm(X))))&
(![X]:(kind(X)=>quiet(X)))&
(![X]:((~kind(X)&~humble(X))<=>(old(X)|curious(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(happy(X)|rich(X))))&
((?[X]:((calm(X)<~>strong(X))))<=>((calm(lucy)<~>~strong(lucy))))&
((?[X]:((~patient(X)&~calm(X))))<=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~funny(X))))&
(((~generous(lucy)|~kind(lucy)))=>(?[X]:(calm(X))))&
(![X]:((rich(X)<~>funny(X))=>(~calm(X)<~>funny(X))))&
(![X]:((humble(X)|tall(X))=>(curious(X)|~curious(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(calm(X)&~kind(X))))&
(![X]:((~curious(X)<~>~old(X))<=>~creative(X)))&
(![X]:((~curious(X)|funny(X))<=>(funny(X)|kind(X))))&
((~quiet(alice)|quiet(alice)))&
((~generous(alice)&rich(alice)))&
(?[X]:(happy(X)))&
((~quiet(paul)&brave(paul)))&
(?[X]:(quiet(X)))&
(~happy(fred))&
(rich(alice)) | ~curious(alice) | [
"p5",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 292305925128310670245189
% SZS output start Proof for 292305925128310670245189
6. ! [X0] : ((~humble(X0) & ~kind(X0)) <=> (curious(X0) | old(X0))) [input p5]
10. ! [X0] : (generous(X0) <=> (~funny(X0) | ~kind(X0))) [input p9]
18. rich(alice) & ~generous(alice) [input p17]
24. curious(alice) [input hypothesis]
43. ! [X0] : (((~humble(X0) & ~kind(X0)) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | (humble(X0) | kind(X0)))) [nnf transformation 6]
44. ! [X0] : (((~humble(X0) & ~kind(X0)) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | humble(X0) | kind(X0))) [flattening 43]
55. ! [X0] : ((generous(X0) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | ~generous(X0))) [nnf transformation 10]
56. ! [X0] : ((generous(X0) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | ~generous(X0))) [flattening 55]
90. ~kind(X0) | ~curious(X0) [cnf transformation 44]
109. generous(X0) | kind(X0) [cnf transformation 56]
134. ~generous(alice) [cnf transformation 18]
141. curious(alice) [cnf transformation 24]
240. kind(alice) [resolution 109,134]
241. ~curious(alice) [resolution 240,90]
244. $false [subsumption resolution 241,141]
% SZS output end Proof for 292305925128310670245189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or humble is calm.
Everyone who is both old and not creative is quiet and vice versa.
If susan is both not happy and tall then someone is both not old and not funny.
Everyone who is tall or calm is either not patient or not kind.
If paul is brave or quiet then someone is either not humble or not happy.
If john is old or creative then lucy is either strong or not old.
If fred is creative or tall then susan is funny or not brave and vice versa.
Everyone who is both not wise and not calm is not rich or not curious and vice versa.
If mary is both brave and not calm then someone is either not old or not tall and vice versa.
Everyone who is not old or not humble is not generous and vice versa.
If john is both not patient and humble then lucy is both not strong and old.
If john is creative or not wise then someone is either not calm or not rich and vice versa.
If someone is funny then someone is not rich.
Everyone who is either funny or not curious is both not quiet and rich and vice versa.
If fred is not wise then someone is brave or creative.
Everyone who is quiet or not strong is either wise or not quiet and vice versa.
John is both happy and old.
Mary is either humble or tall.
Fred is either not happy or rich.
Paul is not humble.
Alice is patient.
Mary is either not calm or calm.
Someone is tall.
Fred is strong. | Alice is patient. | entailment | (![X]:((quiet(X)<~>humble(X))=>calm(X)))&
(![X]:((old(X)&~creative(X))<=>quiet(X)))&
(((~happy(susan)&tall(susan)))=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((tall(X)|calm(X))=>(~patient(X)<~>~kind(X))))&
(((brave(paul)|quiet(paul)))=>(?[X]:((~humble(X)<~>~happy(X)))))&
(((old(john)|creative(john)))=>((strong(lucy)<~>~old(lucy))))&
(((creative(fred)|tall(fred)))<=>((funny(susan)|~brave(susan))))&
(![X]:((~wise(X)&~calm(X))<=>(~rich(X)|~curious(X))))&
(((brave(mary)&~calm(mary)))<=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((~old(X)|~humble(X))<=>~generous(X)))&
(((~patient(john)&humble(john)))=>((~strong(lucy)&old(lucy))))&
(((creative(john)|~wise(john)))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:(funny(X)))=>(?[X]:(~rich(X))))&
(![X]:((funny(X)<~>~curious(X))<=>(~quiet(X)&rich(X))))&
((~wise(fred))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((quiet(X)|~strong(X))<=>(wise(X)<~>~quiet(X))))&
((happy(john)&old(john)))&
((humble(mary)<~>tall(mary)))&
((~happy(fred)<~>rich(fred)))&
(~humble(paul))&
(patient(alice))&
((~calm(mary)<~>calm(mary)))&
(?[X]:(tall(X)))&
(strong(fred)) | patient(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6985033790164454052138980
% SZS output start Proof for 6985033790164454052138980
21. patient(alice) [input p20]
25. ~patient(alice) [input hypothesis]
138. patient(alice) [cnf transformation 21]
143. ~patient(alice) [cnf transformation 25]
328. $false [subsumption resolution 143,138]
% SZS output end Proof for 6985033790164454052138980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and tall then someone is not funny and vice versa.
If mary is not patient then john is rich and vice versa.
Everyone who is either strong or happy is both patient and generous and vice versa.
Everyone who is both wise and not creative is not curious and vice versa.
Everyone who is both not happy and curious is either not calm or creative.
If someone is either not happy or not curious then paul is not brave and vice versa.
If someone is either patient or strong then alice is both not old and not quiet.
If someone is not patient or generous then someone is rich.
If lucy is curious or creative then someone is not quiet.
Everyone who is kind is not tall or tall and vice versa.
If someone is both not creative and generous then someone is both not funny and quiet.
Everyone who is creative or kind is either quiet or not kind and vice versa.
If mary is both not patient and funny then paul is both not happy and generous.
Everyone who is both quiet and kind is tall.
Everyone who is not calm is both not kind and not wise and vice versa.
Everyone who is patient or quiet is generous.
John is either not calm or calm.
Susan is not curious.
Someone is wise or not kind.
Someone is either humble or not calm.
Paul is funny or not brave. | Susan is not happy. | entailment | ((?[X]:((~curious(X)&tall(X))))<=>(?[X]:(~funny(X))))&
((~patient(mary))<=>(rich(john)))&
(![X]:((strong(X)<~>happy(X))<=>(patient(X)&generous(X))))&
(![X]:((wise(X)&~creative(X))<=>~curious(X)))&
(![X]:((~happy(X)&curious(X))=>(~calm(X)<~>creative(X))))&
((?[X]:((~happy(X)<~>~curious(X))))<=>(~brave(paul)))&
((?[X]:((patient(X)<~>strong(X))))=>((~old(alice)&~quiet(alice))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:(rich(X))))&
(((curious(lucy)|creative(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:(kind(X)<=>(~tall(X)|tall(X))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
(![X]:((creative(X)|kind(X))<=>(quiet(X)<~>~kind(X))))&
(((~patient(mary)&funny(mary)))=>((~happy(paul)&generous(paul))))&
(![X]:((quiet(X)&kind(X))=>tall(X)))&
(![X]:(~calm(X)<=>(~kind(X)&~wise(X))))&
(![X]:((patient(X)|quiet(X))=>generous(X)))&
((~calm(john)<~>calm(john)))&
(~curious(susan))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((funny(paul)|~brave(paul))) | ~happy(susan) | [
"p2",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2839314150920831416548107
% SZS output start Proof for 2839314150920831416548107
3. ! [X0] : ((strong(X0) <~> happy(X0)) <=> (generous(X0) & patient(X0))) [input p2]
7. ? [X0] : (patient(X0) <~> strong(X0)) => (~quiet(alice) & ~old(alice)) [input p6]
10. ! [X0] : (kind(X0) <=> (tall(X0) | ~tall(X0))) [input p9]
12. ! [X0] : ((kind(X0) | creative(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | patient(X0)) => generous(X0)) [input p15]
22. happy(susan) [input hypothesis]
26. ? [X0] : (patient(X0) <~> strong(X0)) => ~quiet(alice) [pure predicate removal 7]
29. ~quiet(alice) | ! [X0] : (patient(X0) <=> strong(X0)) [ennf transformation 26]
37. ! [X0] : (generous(X0) | (~quiet(X0) & ~patient(X0))) [ennf transformation 16]
44. ! [X0] : ((((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0))))) [flattening 44]
53. ~quiet(alice) | ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 29]
59. ! [X0] : ((kind(X0) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | ~kind(X0))) [nnf transformation 10]
60. ! [X0] : ((kind(X0) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | ~kind(X0))) [flattening 59]
64. ! [X0] : (((kind(X0) | creative(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~kind(X0) & ~creative(X0)))) [nnf transformation 12]
65. ! [X0] : ((kind(X0) | creative(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~kind(X0) & ~creative(X0)))) [flattening 64]
80. ~happy(X0) | strong(X0) | patient(X0) [cnf transformation 45]
84. ~generous(X0) | ~strong(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 45]
94. ~quiet(alice) | strong(X0) | ~patient(X0) [cnf transformation 53]
95. ~quiet(alice) | patient(X0) | ~strong(X0) [cnf transformation 53]
101. kind(X0) | tall(X0) [cnf transformation 60]
102. ~tall(X0) | kind(X0) [cnf transformation 60]
106. ~kind(X0) | quiet(X0) | ~kind(X0) [cnf transformation 65]
118. generous(X0) | ~quiet(X0) [cnf transformation 37]
126. happy(susan) [cnf transformation 22]
127. ~kind(X0) | quiet(X0) [duplicate literal removal 106]
184. 13 <=> ! [X0] : (patient(X0) | ~strong(X0)) [avatar definition]
185. ~strong(X0) | patient(X0) <- (13) [avatar component clause 184]
187. 14 <=> quiet(alice) [avatar definition]
189. ~quiet(alice) <- (~14) [avatar component clause 187]
190. 13 | ~14 [avatar split clause 95,187,184]
192. 15 <=> ! [X0] : (strong(X0) | ~patient(X0)) [avatar definition]
193. ~patient(X0) | strong(X0) <- (15) [avatar component clause 192]
194. 15 | ~14 [avatar split clause 94,187,192]
221. kind(X0) [subsumption resolution 101,102]
235. quiet(X0) [subsumption resolution 127,221]
253. generous(X0) [subsumption resolution 118,235]
264. $false <- (~14) [subsumption resolution 189,235]
265. 14 [avatar contradiction clause 264]
271. strong(susan) | patient(susan) [resolution 80,126]
273. patient(susan) <- (13) [subsumption resolution 271,185]
297. ~strong(X0) | ~happy(X0) | ~patient(X0) [resolution 84,253]
298. ~happy(X0) | ~patient(X0) <- (15) [subsumption resolution 297,193]
299. ~patient(susan) <- (15) [resolution 298,126]
301. $false <- (13, 15) [subsumption resolution 299,273]
302. ~13 | ~15 [avatar contradiction clause 301]
305. $false [avatar sat refutation 190,194,265,302]
% SZS output end Proof for 2839314150920831416548107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and humble then susan is both not quiet and brave and vice versa. Everyone who is both humble and patient is calm and vice versa. Everyone who is not strong is either not kind or not calm and vice versa. If fred is not rich or not patient then someone is both not strong and creative and vice versa. If lucy is funny or not creative then paul is either not wise or old and vice versa. Everyone who is either not happy or strong is not patient and vice versa. Everyone who is not patient is either not kind or generous. Everyone who is not funny is both old and calm and vice versa. If paul is both curious and not generous then someone is not kind or not old and vice versa. Everyone who is quiet or patient is not patient or quiet. Everyone who is not happy is not tall or patient and vice versa. Everyone who is not curious is either generous or not patient and vice versa. Everyone who is either funny or kind is not curious or not patient and vice versa. If mary is strong then mary is either creative or not patient and vice versa. Everyone who is both not strong and curious is both not funny and not curious. If someone is not old then someone is humble. Someone is both wise and not funny. Lucy is either tall or generous. Someone is both not curious and not rich. Susan is both not kind and old. Fred is not calm. Someone is both wise and humble. Someone is either patient or rich. | Susan is quiet. | neutral | ((?[X]:((happy(X)&humble(X))))<=>((~quiet(susan)&brave(susan))))&
(![X]:((humble(X)&patient(X))<=>calm(X)))&
(![X]:(~strong(X)<=>(~kind(X)<~>~calm(X))))&
(((~rich(fred)|~patient(fred)))<=>(?[X]:((~strong(X)&creative(X)))))&
(((funny(lucy)|~creative(lucy)))<=>((~wise(paul)<~>old(paul))))&
(![X]:((~happy(X)<~>strong(X))<=>~patient(X)))&
(![X]:(~patient(X)=>(~kind(X)<~>generous(X))))&
(![X]:(~funny(X)<=>(old(X)&calm(X))))&
(((curious(paul)&~generous(paul)))<=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((quiet(X)|patient(X))=>(~patient(X)|quiet(X))))&
(![X]:(~happy(X)<=>(~tall(X)|patient(X))))&
(![X]:(~curious(X)<=>(generous(X)<~>~patient(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~curious(X)|~patient(X))))&
((strong(mary))<=>((creative(mary)<~>~patient(mary))))&
(![X]:((~strong(X)&curious(X))=>(~funny(X)&~curious(X))))&
((?[X]:(~old(X)))=>(?[X]:(humble(X))))&
(?[X]:((wise(X)&~funny(X))))&
((tall(lucy)<~>generous(lucy)))&
(?[X]:((~curious(X)&~rich(X))))&
((~kind(susan)&old(susan)))&
(~calm(fred))&
(?[X]:((wise(X)&humble(X))))&
(?[X]:((patient(X)<~>rich(X)))) | quiet(susan) | [] | null | 0 |
Everyone who is either not funny or not generous is humble or not brave.
If someone is not funny or tall then someone is both curious and creative and vice versa.
If someone is not kind then someone is either curious or humble.
If someone is either generous or brave then paul is not rich or quiet.
If someone is old then susan is not curious.
If someone is both not quiet and generous then someone is tall or wise and vice versa.
Everyone who is either not brave or not wise is strong and vice versa.
Everyone who is either brave or not curious is not humble or not brave.
If someone is rich then lucy is humble.
If someone is both old and not wise then mary is not happy.
If someone is both generous and old then someone is not humble or wise and vice versa.
If someone is either not old or not patient then paul is not brave and vice versa.
Everyone who is both not wise and not calm is either not old or patient.
If someone is calm or not quiet then lucy is both quiet and not old.
Everyone who is not curious is not humble or calm.
Everyone who is wise is either creative or not rich and vice versa.
John is not happy or quiet.
Someone is either not happy or not kind.
Someone is patient.
Someone is either not wise or not patient.
Mary is not humble or wise.
Fred is not tall.
Alice is not rich or strong.
Lucy is either strong or patient. | Susan is curious. | contradiction | (![X]:((~funny(X)<~>~generous(X))=>(humble(X)|~brave(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((curious(X)&creative(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)<~>humble(X)))))&
((?[X]:((generous(X)<~>brave(X))))=>((~rich(paul)|quiet(paul))))&
((?[X]:(old(X)))=>(~curious(susan)))&
((?[X]:((~quiet(X)&generous(X))))<=>(?[X]:((tall(X)|wise(X)))))&
(![X]:((~brave(X)<~>~wise(X))<=>strong(X)))&
(![X]:((brave(X)<~>~curious(X))=>(~humble(X)|~brave(X))))&
((?[X]:(rich(X)))=>(humble(lucy)))&
((?[X]:((old(X)&~wise(X))))=>(~happy(mary)))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:((~humble(X)|wise(X)))))&
((?[X]:((~old(X)<~>~patient(X))))<=>(~brave(paul)))&
(![X]:((~wise(X)&~calm(X))=>(~old(X)<~>patient(X))))&
((?[X]:((calm(X)|~quiet(X))))=>((quiet(lucy)&~old(lucy))))&
(![X]:(~curious(X)=>(~humble(X)|calm(X))))&
(![X]:(wise(X)<=>(creative(X)<~>~rich(X))))&
((~happy(john)|quiet(john)))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)<~>~patient(X))))&
((~humble(mary)|wise(mary)))&
(~tall(fred))&
((~rich(alice)|strong(alice)))&
((strong(lucy)<~>patient(lucy))) | curious(susan) | [
"p4",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5442870499607202775728871
% SZS output start Proof for 5442870499607202775728871
5. ? [X0] : old(X0) => ~curious(susan) [input p4]
11. ? [X0] : (old(X0) & generous(X0)) <=> ? [X0] : (wise(X0) | ~humble(X0)) [input p10]
21. wise(mary) | ~humble(mary) [input p20]
25. curious(susan) [input hypothesis]
29. ? [X0] : (old(X0) & generous(X0)) <=> ? [X1] : (wise(X1) | ~humble(X1)) [rectify 11]
35. ~curious(susan) | ! [X0] : ~old(X0) [ennf transformation 5]
63. (? [X0] : (old(X0) & generous(X0)) | ! [X1] : (~wise(X1) & humble(X1))) & (? [X1] : (wise(X1) | ~humble(X1)) | ! [X0] : (~old(X0) | ~generous(X0))) [nnf transformation 29]
64. (? [X0] : (old(X0) & generous(X0)) | ! [X1] : (~wise(X1) & humble(X1))) & (? [X2] : (wise(X2) | ~humble(X2)) | ! [X3] : (~old(X3) | ~generous(X3))) [rectify 63]
65. ? [X0] : (old(X0) & generous(X0)) => (old(sK5) & generous(sK5)) [choice axiom]
66. ? [X2] : (wise(X2) | ~humble(X2)) => (wise(sK6) | ~humble(sK6)) [choice axiom]
67. ((old(sK5) & generous(sK5)) | ! [X1] : (~wise(X1) & humble(X1))) & ((wise(sK6) | ~humble(sK6)) | ! [X3] : (~old(X3) | ~generous(X3))) [skolemisation 64,66,65]
94. ~curious(susan) | ~old(X0) [cnf transformation 35]
111. old(sK5) | humble(X1) [cnf transformation 67]
112. old(sK5) | ~wise(X1) [cnf transformation 67]
134. wise(mary) | ~humble(mary) [cnf transformation 21]
139. curious(susan) [cnf transformation 25]
201. 15 <=> ! [X0] : ~old(X0) [avatar definition]
202. ~old(X0) <- (15) [avatar component clause 201]
204. 16 <=> curious(susan) [avatar definition]
207. 15 | ~16 [avatar split clause 94,204,201]
209. 17 <=> ! [X1] : ~wise(X1) [avatar definition]
210. ~wise(X1) <- (17) [avatar component clause 209]
252. 27 <=> old(sK5) [avatar definition]
254. old(sK5) <- (27) [avatar component clause 252]
255. 17 | 27 [avatar split clause 112,252,209]
257. 28 <=> ! [X1] : humble(X1) [avatar definition]
258. humble(X1) <- (28) [avatar component clause 257]
259. 28 | 27 [avatar split clause 111,252,257]
348. 48 <=> humble(mary) [avatar definition]
350. ~humble(mary) <- (~48) [avatar component clause 348]
352. 49 <=> wise(mary) [avatar definition]
354. wise(mary) <- (49) [avatar component clause 352]
355. ~48 | 49 [avatar split clause 134,352,348]
375. 16 [avatar split clause 139,204]
380. $false <- (15, 27) [subsumption resolution 254,202]
381. ~15 | ~27 [avatar contradiction clause 380]
390. $false <- (28, ~48) [resolution 350,258]
391. ~28 | 48 [avatar contradiction clause 390]
392. $false <- (17, 49) [subsumption resolution 354,210]
393. ~17 | ~49 [avatar contradiction clause 392]
394. $false [avatar sat refutation 207,255,259,355,375,381,391,393]
% SZS output end Proof for 5442870499607202775728871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or patient is strong or creative and vice versa.
If paul is calm or rich then john is either kind or not patient and vice versa.
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Fred is wise.
Alice is either kind or patient.
Fred is creative or not creative.
Paul is both wise and strong.
Fred is funny or not quiet.
Mary is calm or not calm.
Someone is either brave or funny. | Fred is tall. | contradiction | (![X]:((~creative(X)|patient(X))<=>(strong(X)|creative(X))))&
(((calm(paul)|rich(paul)))<=>((kind(john)<~>~patient(john))))&
(![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(wise(fred))&
((kind(alice)<~>patient(alice)))&
((creative(fred)|~creative(fred)))&
((wise(paul)&strong(paul)))&
((funny(fred)|~quiet(fred)))&
((calm(mary)|~calm(mary)))&
(?[X]:((brave(X)<~>funny(X)))) | tall(fred) | [
"p0",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3003641443589010407620420
% SZS output start Proof for 3003641443589010407620420
1. ! [X0] : ((patient(X0) | ~creative(X0)) <=> (creative(X0) | strong(X0))) [input p0]
10. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (curious(X0) | tall(X0))) [input p9]
14. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p13]
16. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p15]
24. tall(fred) [input hypothesis]
36. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 16]
37. ! [X0] : (((patient(X0) | ~creative(X0)) | (~creative(X0) & ~strong(X0))) & ((creative(X0) | strong(X0)) | (~patient(X0) & creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((patient(X0) | ~creative(X0) | (~creative(X0) & ~strong(X0))) & (creative(X0) | strong(X0) | (~patient(X0) & creative(X0)))) [flattening 37]
52. ! [X0] : (((~strong(X0) | ~old(X0)) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | (strong(X0) & old(X0)))) [nnf transformation 10]
53. ! [X0] : ((~strong(X0) | ~old(X0) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | (strong(X0) & old(X0)))) [flattening 52]
65. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 14]
66. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 65]
73. creative(X0) | strong(X0) | creative(X0) [cnf transformation 38]
76. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 38]
103. ~old(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 53]
115. happy(X0) | curious(X0) [cnf transformation 66]
116. ~curious(X0) | happy(X0) [cnf transformation 66]
126. ~patient(X0) | ~happy(X0) [cnf transformation 36]
128. old(X0) | ~happy(X0) [cnf transformation 36]
140. tall(fred) [cnf transformation 24]
141. strong(X0) | creative(X0) [duplicate literal removal 73]
142. ~creative(X0) | patient(X0) [duplicate literal removal 76]
189. 11 <=> strong(fred) [avatar definition]
190. ~strong(fred) <- (~11) [avatar component clause 189]
229. happy(X0) [subsumption resolution 115,116]
230. old(X0) [subsumption resolution 128,229]
231. ~patient(X0) [subsumption resolution 126,229]
305. ~tall(X1) | ~strong(X1) [resolution 103,230]
310. ~strong(fred) [resolution 305,140]
313. ~11 [avatar split clause 310,189]
314. creative(fred) <- (~11) [resolution 190,141]
315. patient(fred) <- (~11) [resolution 314,142]
316. $false <- (~11) [subsumption resolution 315,231]
317. 11 [avatar contradiction clause 316]
318. $false [avatar sat refutation 313,317]
% SZS output end Proof for 3003641443589010407620420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and funny is strong or not kind. Everyone who is brave is not generous or not brave and vice versa. Everyone who is not rich is not creative and vice versa. If paul is not funny then john is rich. If paul is calm then john is both kind and not funny and vice versa. Everyone who is either strong or not kind is both curious and not calm. Everyone who is both patient and not happy is both not kind and not strong and vice versa. Everyone who is funny or not tall is either generous or tall and vice versa. Everyone who is both old and not tall is either not happy or not curious and vice versa. Everyone who is both not old and not wise is not brave or not tall. Everyone who is not brave or humble is happy or not rich. If paul is both not curious and not tall then john is both not curious and happy. Everyone who is both humble and strong is both kind and curious. Everyone who is both not calm and brave is either curious or not strong. If fred is both creative and not tall then someone is either generous or curious and vice versa. Someone is quiet or not wise. Someone is humble. Paul is humble. Susan is old. Someone is either not tall or wise. Paul is both quiet and not strong. | Paul is not tall. | contradiction | (![X]:((happy(X)&funny(X))=>(strong(X)|~kind(X))))&
(![X]:(brave(X)<=>(~generous(X)|~brave(X))))&
(![X]:(~rich(X)<=>~creative(X)))&
((~funny(paul))=>(rich(john)))&
((calm(paul))<=>((kind(john)&~funny(john))))&
(![X]:((strong(X)<~>~kind(X))=>(curious(X)&~calm(X))))&
(![X]:((patient(X)&~happy(X))<=>(~kind(X)&~strong(X))))&
(![X]:((funny(X)|~tall(X))<=>(generous(X)<~>tall(X))))&
(![X]:((old(X)&~tall(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((~old(X)&~wise(X))=>(~brave(X)|~tall(X))))&
(![X]:((~brave(X)|humble(X))=>(happy(X)|~rich(X))))&
(((~curious(paul)&~tall(paul)))=>((~curious(john)&happy(john))))&
(![X]:((humble(X)&strong(X))=>(kind(X)&curious(X))))&
(![X]:((~calm(X)&brave(X))=>(curious(X)<~>~strong(X))))&
(((creative(fred)&~tall(fred)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:(humble(X)))&
(humble(paul))&
(old(susan))&
(?[X]:((~tall(X)<~>wise(X))))&
((quiet(paul)&~strong(paul))) | ~tall(paul) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 87373686057679911864454
% SZS output start Proof for 87373686057679911864454
2. ! [X0] : (brave(X0) <=> (~brave(X0) | ~generous(X0))) [input p1]
8. ! [X0] : ((~tall(X0) | funny(X0)) <=> (generous(X0) <~> tall(X0))) [input p7]
22. ~tall(paul) [input hypothesis]
39. ! [X0] : ((brave(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | ~brave(X0))) [flattening 39]
47. ! [X0] : (((~tall(X0) | funny(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (tall(X0) & ~funny(X0)))) [nnf transformation 8]
48. ! [X0] : ((~tall(X0) | funny(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (tall(X0) & ~funny(X0)))) [flattening 47]
63. ~brave(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 40]
65. brave(X0) | brave(X0) [cnf transformation 40]
81. tall(X0) | generous(X0) | tall(X0) [cnf transformation 48]
113. ~tall(paul) [cnf transformation 22]
114. tall(X0) | generous(X0) [duplicate literal removal 81]
116. ~brave(X0) | ~generous(X0) [duplicate literal removal 63]
117. brave(X0) [duplicate literal removal 65]
118. ~generous(X0) [subsumption resolution 116,117]
144. tall(X0) [subsumption resolution 114,118]
154. $false [subsumption resolution 113,144]
% SZS output end Proof for 87373686057679911864454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich then lucy is either generous or not strong and vice versa.
Everyone who is not generous is curious.
Everyone who is not humble is strong or not patient and vice versa.
If mary is either not funny or not generous then someone is either generous or not old.
If someone is rich then susan is creative and vice versa.
If someone is either not funny or not patient then alice is both not quiet and not patient.
If lucy is not humble or humble then paul is either not humble or quiet.
Everyone who is curious is both tall and wise.
If fred is either strong or not patient then john is either patient or kind.
If someone is either curious or not brave then mary is strong or not happy.
If fred is not humble or not rich then alice is generous.
Everyone who is wise or not strong is both wise and not creative and vice versa.
If john is either generous or brave then mary is both old and not rich.
Everyone who is both strong and curious is either wise or happy.
If someone is both not curious and not patient then paul is not patient.
Everyone who is not wise is curious or not calm and vice versa.
Someone is both not kind and not curious.
Mary is not patient.
Someone is not funny.
Susan is either not patient or creative.
Lucy is both wise and brave.
Alice is both rich and not curious.
John is not rich. | Lucy is not creative. | entailment | ((rich(john))<=>((generous(lucy)<~>~strong(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:(~humble(X)<=>(strong(X)|~patient(X))))&
(((~funny(mary)<~>~generous(mary)))=>(?[X]:((generous(X)<~>~old(X)))))&
((?[X]:(rich(X)))<=>(creative(susan)))&
((?[X]:((~funny(X)<~>~patient(X))))=>((~quiet(alice)&~patient(alice))))&
(((~humble(lucy)|humble(lucy)))=>((~humble(paul)<~>quiet(paul))))&
(![X]:(curious(X)=>(tall(X)&wise(X))))&
(((strong(fred)<~>~patient(fred)))=>((patient(john)<~>kind(john))))&
((?[X]:((curious(X)<~>~brave(X))))=>((strong(mary)|~happy(mary))))&
(((~humble(fred)|~rich(fred)))=>(generous(alice)))&
(![X]:((wise(X)|~strong(X))<=>(wise(X)&~creative(X))))&
(((generous(john)<~>brave(john)))=>((old(mary)&~rich(mary))))&
(![X]:((strong(X)&curious(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~curious(X)&~patient(X))))=>(~patient(paul)))&
(![X]:(~wise(X)<=>(curious(X)|~calm(X))))&
(?[X]:((~kind(X)&~curious(X))))&
(~patient(mary))&
(?[X]:(~funny(X)))&
((~patient(susan)<~>creative(susan)))&
((wise(lucy)&brave(lucy)))&
((rich(alice)&~curious(alice)))&
(~rich(john)) | ~creative(lucy) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3772933725262975843457326
% SZS output start Proof for 3772933725262975843457326
12. ! [X0] : ((~strong(X0) | wise(X0)) <=> (~creative(X0) & wise(X0))) [input p11]
21. brave(lucy) & wise(lucy) [input p20]
24. creative(lucy) [input hypothesis]
53. ! [X0] : (((~strong(X0) | wise(X0)) | (creative(X0) | ~wise(X0))) & ((~creative(X0) & wise(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 12]
54. ! [X0] : ((~strong(X0) | wise(X0) | creative(X0) | ~wise(X0)) & ((~creative(X0) & wise(X0)) | (strong(X0) & ~wise(X0)))) [flattening 53]
97. ~wise(X0) | ~creative(X0) [cnf transformation 54]
116. wise(lucy) [cnf transformation 21]
121. creative(lucy) [cnf transformation 24]
303. ~creative(lucy) [resolution 97,116]
305. $false [subsumption resolution 303,121]
% SZS output end Proof for 3772933725262975843457326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or kind then someone is both not kind and not creative. If someone is either funny or kind then mary is both generous and funny. Everyone who is either rich or old is not strong and vice versa. Everyone who is strong or not wise is brave or funny. Everyone who is both not kind and patient is either strong or not quiet. If someone is both funny and not old then someone is both not old and humble. If fred is both kind and happy then alice is strong and vice versa. Everyone who is calm is not funny and vice versa. If fred is both wise and not strong then alice is both wise and rich. If someone is calm or kind then mary is both wise and not tall. If paul is humble then someone is either kind or not strong. Everyone who is old is brave. If someone is either rich or not creative then someone is either not kind or not funny. Everyone who is not happy or not old is brave or wise and vice versa. If someone is both kind and happy then someone is old. Everyone who is kind is both not wise and calm. Someone is either calm or not curious. Susan is not brave or tall. Someone is either not curious or kind. Someone is not tall. Someone is not quiet. Mary is both strong and not wise. Someone is both quiet and not strong. | Susan is funny. | entailment | ((?[X]:((~strong(X)|kind(X))))=>(?[X]:((~kind(X)&~creative(X)))))&
((?[X]:((funny(X)<~>kind(X))))=>((generous(mary)&funny(mary))))&
(![X]:((rich(X)<~>old(X))<=>~strong(X)))&
(![X]:((strong(X)|~wise(X))=>(brave(X)|funny(X))))&
(![X]:((~kind(X)&patient(X))=>(strong(X)<~>~quiet(X))))&
((?[X]:((funny(X)&~old(X))))=>(?[X]:((~old(X)&humble(X)))))&
(((kind(fred)&happy(fred)))<=>(strong(alice)))&
(![X]:(calm(X)<=>~funny(X)))&
(((wise(fred)&~strong(fred)))=>((wise(alice)&rich(alice))))&
((?[X]:((calm(X)|kind(X))))=>((wise(mary)&~tall(mary))))&
((humble(paul))=>(?[X]:((kind(X)<~>~strong(X)))))&
(![X]:(old(X)=>brave(X)))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:((~happy(X)|~old(X))<=>(brave(X)|wise(X))))&
((?[X]:((kind(X)&happy(X))))=>(?[X]:(old(X))))&
(![X]:(kind(X)=>(~wise(X)&calm(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
((~brave(susan)|tall(susan)))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:(~quiet(X)))&
((strong(mary)&~wise(mary)))&
(?[X]:((quiet(X)&~strong(X)))) | funny(susan) | [
"p7",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7664159044482597679795676
% SZS output start Proof for 7664159044482597679795676
8. ! [X0] : (calm(X0) <=> ~funny(X0)) [input p7]
10. ? [X0] : (kind(X0) | calm(X0)) => (~tall(mary) & wise(mary)) [input p9]
22. ~wise(mary) & strong(mary) [input p21]
24. ~funny(susan) [input hypothesis]
38. (~tall(mary) & wise(mary)) | ! [X0] : (~kind(X0) & ~calm(X0)) [ennf transformation 10]
54. ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))) [nnf transformation 8]
97. calm(X0) | funny(X0) [cnf transformation 54]
100. wise(mary) | ~calm(X0) [cnf transformation 38]
126. ~wise(mary) [cnf transformation 22]
129. ~funny(susan) [cnf transformation 24]
212. 19 <=> ! [X0] : ~calm(X0) [avatar definition]
213. ~calm(X0) <- (19) [avatar component clause 212]
216. 20 <=> wise(mary) [avatar definition]
220. 19 | 20 [avatar split clause 100,216,212]
292. ~20 [avatar split clause 126,216]
296. funny(X1) <- (19) [resolution 97,213]
298. $false <- (19) [resolution 296,129]
299. ~19 [avatar contradiction clause 298]
300. $false [avatar sat refutation 220,292,299]
% SZS output end Proof for 7664159044482597679795676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or creative then someone is both calm and not rich and vice versa. If paul is rich or happy then lucy is not curious or tall. Everyone who is wise is strong and vice versa. Everyone who is either creative or rich is either not kind or quiet. Everyone who is brave or humble is not generous and vice versa. If susan is either old or funny then someone is kind. If fred is old then someone is either generous or humble and vice versa. If mary is not creative then mary is either calm or brave and vice versa. Everyone who is old is funny and vice versa. If someone is not old then fred is either not humble or not tall and vice versa. Everyone who is either strong or not wise is brave and vice versa. If alice is not wise then someone is curious. Everyone who is quiet or not rich is patient or not generous. Everyone who is either not humble or kind is both kind and curious and vice versa. Everyone who is not strong is strong. If john is not tall then mary is both not curious and not old. Someone is tall. Mary is both patient and not curious. Susan is not rich or tall. John is either curious or not old. Mary is quiet. Lucy is not creative. | Paul is not patient. | neutral | ((?[X]:((~curious(X)|creative(X))))<=>(?[X]:((calm(X)&~rich(X)))))&
(((rich(paul)|happy(paul)))=>((~curious(lucy)|tall(lucy))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((creative(X)<~>rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)|humble(X))<=>~generous(X)))&
(((old(susan)<~>funny(susan)))=>(?[X]:(kind(X))))&
((old(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((~creative(mary))<=>((calm(mary)<~>brave(mary))))&
(![X]:(old(X)<=>funny(X)))&
((?[X]:(~old(X)))<=>((~humble(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>~wise(X))<=>brave(X)))&
((~wise(alice))=>(?[X]:(curious(X))))&
(![X]:((quiet(X)|~rich(X))=>(patient(X)|~generous(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&curious(X))))&
(![X]:(~strong(X)=>strong(X)))&
((~tall(john))=>((~curious(mary)&~old(mary))))&
(?[X]:(tall(X)))&
((patient(mary)&~curious(mary)))&
((~rich(susan)|tall(susan)))&
((curious(john)<~>~old(john)))&
(quiet(mary))&
(~creative(lucy)) | ~patient(paul) | [] | null | 0 |
Everyone who is either not quiet or not generous is both generous and curious.
If someone is tall then someone is both humble and wise and vice versa.
Everyone who is not creative or brave is both not curious and not strong and vice versa.
If lucy is either happy or brave then mary is generous or not rich.
If someone is not humble or not quiet then mary is either not patient or strong.
Everyone who is curious or funny is either not happy or not creative.
Everyone who is either not wise or not quiet is both old and creative.
If mary is curious or not quiet then someone is either not curious or funny and vice versa.
Everyone who is humble is either calm or not humble and vice versa.
Everyone who is not humble or patient is curious.
Everyone who is either humble or happy is both brave and patient and vice versa.
Everyone who is not happy is either not happy or brave and vice versa.
If lucy is both not rich and not patient then fred is both not tall and not old and vice versa.
Everyone who is both creative and not rich is both not happy and rich and vice versa.
Everyone who is not generous is generous.
Fred is not curious or wise.
Someone is both not brave and kind.
Someone is not tall. | Lucy is not quiet. | contradiction | (![X]:((~quiet(X)<~>~generous(X))=>(generous(X)&curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((~creative(X)|brave(X))<=>(~curious(X)&~strong(X))))&
(((happy(lucy)<~>brave(lucy)))=>((generous(mary)|~rich(mary))))&
((?[X]:((~humble(X)|~quiet(X))))=>((~patient(mary)<~>strong(mary))))&
(![X]:((curious(X)|funny(X))=>(~happy(X)<~>~creative(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(old(X)&creative(X))))&
(((curious(mary)|~quiet(mary)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(humble(X)<=>(calm(X)<~>~humble(X))))&
(![X]:((~humble(X)|patient(X))=>curious(X)))&
(![X]:((humble(X)<~>happy(X))<=>(brave(X)&patient(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>brave(X))))&
(((~rich(lucy)&~patient(lucy)))<=>((~tall(fred)&~old(fred))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:(~tall(X))) | ~quiet(lucy) | [
"p0",
"p2",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1358976522270508427884648
% SZS output start Proof for 1358976522270508427884648
1. ! [X0] : ((~quiet(X0) <~> ~generous(X0)) => (curious(X0) & generous(X0))) [input p0]
3. ! [X0] : ((brave(X0) | ~creative(X0)) <=> (~strong(X0) & ~curious(X0))) [input p2]
6. ! [X0] : ((funny(X0) | curious(X0)) => (~happy(X0) <~> ~creative(X0))) [input p5]
8. (~quiet(mary) | curious(mary)) <=> ? [X0] : (~curious(X0) <~> funny(X0)) [input p7]
14. ! [X0] : ((~rich(X0) & creative(X0)) <=> (rich(X0) & ~happy(X0))) [input p13]
15. ! [X0] : (~generous(X0) => generous(X0)) [input p14]
19. ~quiet(lucy) [input hypothesis]
22. ! [X0] : ((curious(X0) & generous(X0)) | (~quiet(X0) <=> ~generous(X0))) [ennf transformation 1]
26. ! [X0] : ((~happy(X0) <~> ~creative(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 6]
29. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 15]
30. ! [X0] : ((curious(X0) & generous(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) [nnf transformation 22]
36. ! [X0] : (((brave(X0) | ~creative(X0)) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | (~brave(X0) & creative(X0)))) [nnf transformation 3]
37. ! [X0] : ((brave(X0) | ~creative(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | (~brave(X0) & creative(X0)))) [flattening 36]
40. ! [X0] : (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 26]
42. ((~quiet(mary) | curious(mary)) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (quiet(mary) & ~curious(mary))) [nnf transformation 8]
43. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (quiet(mary) & ~curious(mary))) [flattening 42]
44. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X1] : ((~funny(X1) | curious(X1)) & (funny(X1) | ~curious(X1))) | (quiet(mary) & ~curious(mary))) [rectify 43]
45. ? [X1] : ((~funny(X1) | curious(X1)) & (funny(X1) | ~curious(X1))) => ((~funny(sK2) | curious(sK2)) & (funny(sK2) | ~curious(sK2))) [choice axiom]
46. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(sK2) | curious(sK2)) & (funny(sK2) | ~curious(sK2))) | (quiet(mary) & ~curious(mary))) [skolemisation 44,45]
53. ! [X0] : (((~rich(X0) & creative(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 14]
54. ! [X0] : (((~rich(X0) & creative(X0)) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | rich(X0) | ~creative(X0))) [flattening 53]
61. ~generous(X0) | curious(X0) | quiet(X0) [cnf transformation 30]
66. ~curious(X0) | creative(X0) [cnf transformation 37]
77. ~creative(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 40]
80. ~funny(X0) | happy(X0) | creative(X0) [cnf transformation 40]
89. ~quiet(mary) | curious(mary) | funny(X0) | curious(X0) [cnf transformation 46]
112. rich(X0) | rich(X0) | ~creative(X0) [cnf transformation 54]
114. ~rich(X0) | ~rich(X0) | happy(X0) [cnf transformation 54]
115. generous(X0) | generous(X0) [cnf transformation 29]
119. ~quiet(lucy) [cnf transformation 19]
120. generous(X0) [duplicate literal removal 115]
121. ~creative(X0) | rich(X0) [duplicate literal removal 112]
122. ~rich(X0) | happy(X0) [duplicate literal removal 114]
154. 7 <=> happy(lucy) [avatar definition]
155. ~happy(lucy) <- (~7) [avatar component clause 154]
156. happy(lucy) <- (7) [avatar component clause 154]
162. 9 <=> rich(mary) [avatar definition]
163. rich(mary) <- (9) [avatar component clause 162]
185. ~happy(X0) | ~curious(X0) [subsumption resolution 77,66]
190. 15 <=> curious(mary) [avatar definition]
191. ~curious(mary) <- (~15) [avatar component clause 190]
192. curious(mary) <- (15) [avatar component clause 190]
194. 16 <=> quiet(mary) [avatar definition]
196. ~quiet(mary) <- (~16) [avatar component clause 194]
199. 17 <=> ! [X0] : (funny(X0) | curious(X0)) [avatar definition]
200. funny(X0) | curious(X0) <- (17) [avatar component clause 199]
201. 17 | 15 | ~16 [avatar split clause 89,194,190,199]
230. 23 <=> rich(lucy) [avatar definition]
231. rich(lucy) <- (23) [avatar component clause 230]
232. ~rich(lucy) <- (~23) [avatar component clause 230]
247. curious(X0) | quiet(X0) [resolution 61,120]
249. quiet(mary) <- (~15) [resolution 247,191]
252. $false <- (~15, ~16) [subsumption resolution 249,196]
253. 15 | 16 [avatar contradiction clause 252]
254. creative(mary) <- (15) [resolution 192,66]
255. rich(mary) <- (15) [resolution 254,121]
258. 9 | ~15 [avatar split clause 255,190,162]
259. happy(mary) <- (9) [resolution 163,122]
260. ~curious(mary) <- (9) [resolution 259,185]
264. ~15 | ~9 [avatar split clause 260,162,190]
279. happy(X0) | creative(X0) | curious(X0) <- (17) [resolution 80,200]
280. happy(X0) | creative(X0) <- (17) [subsumption resolution 279,66]
397. creative(lucy) <- (~7, 17) [resolution 280,155]
406. rich(lucy) <- (~7, 17) [resolution 397,121]
407. $false <- (~7, 17, ~23) [subsumption resolution 406,232]
408. 7 | ~17 | 23 [avatar contradiction clause 407]
412. ~curious(lucy) <- (7) [resolution 156,185]
415. quiet(lucy) <- (7) [resolution 412,247]
416. $false <- (7) [subsumption resolution 415,119]
417. ~7 [avatar contradiction clause 416]
420. happy(lucy) <- (23) [resolution 231,122]
421. $false <- (~7, 23) [subsumption resolution 420,155]
422. 7 | ~23 [avatar contradiction clause 421]
423. $false [avatar sat refutation 201,253,258,264,408,417,422]
% SZS output end Proof for 1358976522270508427884648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not creative is kind.
If someone is either curious or not humble then paul is generous.
Everyone who is kind is both not humble and not creative and vice versa.
Everyone who is happy is humble.
If someone is either patient or kind then paul is not patient.
If someone is either brave or not happy then john is both not calm and not curious and vice versa.
If john is creative or not generous then someone is either kind or creative and vice versa.
Everyone who is patient is creative or not wise.
Everyone who is generous is either not wise or not generous and vice versa.
Everyone who is either not creative or not calm is humble or funny and vice versa.
If someone is not tall then john is not happy.
Everyone who is not happy is not brave.
If someone is either happy or not creative then mary is not patient and vice versa.
If someone is not wise then someone is both kind and not rich and vice versa.
If john is tall then someone is either calm or creative and vice versa.
Everyone who is not humble is generous.
Alice is not calm.
Susan is calm.
Someone is both not brave and happy.
Someone is creative or kind.
Mary is either happy or rich.
John is both not wise and funny.
Someone is either not brave or old.
Susan is either not tall or not generous. | John is kind. | contradiction | (![X]:((rich(X)&~creative(X))=>kind(X)))&
((?[X]:((curious(X)<~>~humble(X))))=>(generous(paul)))&
(![X]:(kind(X)<=>(~humble(X)&~creative(X))))&
(![X]:(happy(X)=>humble(X)))&
((?[X]:((patient(X)<~>kind(X))))=>(~patient(paul)))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~calm(john)&~curious(john))))&
(((creative(john)|~generous(john)))<=>(?[X]:((kind(X)<~>creative(X)))))&
(![X]:(patient(X)=>(creative(X)|~wise(X))))&
(![X]:(generous(X)<=>(~wise(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(humble(X)|funny(X))))&
((?[X]:(~tall(X)))=>(~happy(john)))&
(![X]:(~happy(X)=>~brave(X)))&
((?[X]:((happy(X)<~>~creative(X))))<=>(~patient(mary)))&
((?[X]:(~wise(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
((tall(john))<=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:(~humble(X)=>generous(X)))&
(~calm(alice))&
(calm(susan))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((creative(X)|kind(X))))&
((happy(mary)<~>rich(mary)))&
((~wise(john)&funny(john)))&
(?[X]:((~brave(X)<~>old(X))))&
((~tall(susan)<~>~generous(susan))) | kind(john) | [
"p2",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4526486601619707383475357
% SZS output start Proof for 4526486601619707383475357
3. ! [X0] : (kind(X0) <=> (~creative(X0) & ~humble(X0))) [input p2]
7. (~generous(john) | creative(john)) <=> ? [X0] : (kind(X0) <~> creative(X0)) [input p6]
16. ! [X0] : (~humble(X0) => generous(X0)) [input p15]
25. kind(john) [input hypothesis]
36. ! [X0] : (generous(X0) | humble(X0)) [ennf transformation 16]
38. ! [X0] : ((kind(X0) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | ~kind(X0))) [nnf transformation 3]
39. ! [X0] : ((kind(X0) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | ~kind(X0))) [flattening 38]
46. ((~generous(john) | creative(john)) | ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (? [X0] : ((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (generous(john) & ~creative(john))) [nnf transformation 7]
47. (~generous(john) | creative(john) | ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (? [X0] : ((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (generous(john) & ~creative(john))) [flattening 46]
48. (~generous(john) | creative(john) | ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (? [X1] : ((~creative(X1) | ~kind(X1)) & (creative(X1) | kind(X1))) | (generous(john) & ~creative(john))) [rectify 47]
49. ? [X1] : ((~creative(X1) | ~kind(X1)) & (creative(X1) | kind(X1))) => ((~creative(sK1) | ~kind(sK1)) & (creative(sK1) | kind(sK1))) [choice axiom]
50. (~generous(john) | creative(john) | ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(sK1) | ~kind(sK1)) & (creative(sK1) | kind(sK1))) | (generous(john) & ~creative(john))) [skolemisation 48,49]
79. ~humble(X0) | ~kind(X0) [cnf transformation 39]
80. ~kind(X0) | ~creative(X0) [cnf transformation 39]
95. ~generous(john) | creative(john) | creative(X0) | ~kind(X0) [cnf transformation 50]
121. generous(X0) | humble(X0) [cnf transformation 36]
135. kind(john) [cnf transformation 25]
195. 14 <=> creative(john) [avatar definition]
199. 15 <=> generous(john) [avatar definition]
201. ~generous(john) <- (~15) [avatar component clause 199]
203. ~generous(john) | creative(john) | ~kind(X0) [subsumption resolution 95,80]
205. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
206. ~kind(X0) <- (16) [avatar component clause 205]
207. 16 | 14 | ~15 [avatar split clause 203,199,195,205]
312. $false <- (16) [resolution 206,135]
313. ~16 [avatar contradiction clause 312]
316. ~creative(john) [resolution 80,135]
324. humble(john) <- (~15) [resolution 121,201]
326. ~kind(john) <- (~15) [resolution 324,79]
327. $false <- (~15) [subsumption resolution 326,135]
328. 15 [avatar contradiction clause 327]
329. ~14 [avatar split clause 316,195]
330. $false [avatar sat refutation 207,313,328,329]
% SZS output end Proof for 4526486601619707383475357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not rich and vice versa. Everyone who is both not brave and not strong is not kind and vice versa. Everyone who is both not kind and humble is not wise or not rich. Everyone who is not rich or curious is both not wise and generous. Everyone who is both not rich and not calm is not kind. Everyone who is kind or not rich is either not generous or not curious and vice versa. Everyone who is not wise or not curious is not creative or rich and vice versa. If fred is brave or funny then someone is happy or not generous and vice versa. If someone is not happy then someone is patient. Everyone who is not patient or not wise is not strong or wise and vice versa. Everyone who is either strong or brave is humble. Everyone who is funny is not old. If john is both patient and quiet then someone is both generous and not brave. Everyone who is both generous and calm is brave and vice versa. Everyone who is either humble or not quiet is either not wise or old. If fred is not tall then alice is not wise or not humble and vice versa. Someone is rich. Alice is not wise or not old. Someone is generous or not wise. Someone is either not brave or tall. Susan is either happy or not wise. Someone is not happy. Susan is creative or kind. Lucy is both not calm and happy. | Lucy is not creative. | entailment | (![X]:(happy(X)<=>~rich(X)))&
(![X]:((~brave(X)&~strong(X))<=>~kind(X)))&
(![X]:((~kind(X)&humble(X))=>(~wise(X)|~rich(X))))&
(![X]:((~rich(X)|curious(X))=>(~wise(X)&generous(X))))&
(![X]:((~rich(X)&~calm(X))=>~kind(X)))&
(![X]:((kind(X)|~rich(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:((~wise(X)|~curious(X))<=>(~creative(X)|rich(X))))&
(((brave(fred)|funny(fred)))<=>(?[X]:((happy(X)|~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:(patient(X))))&
(![X]:((~patient(X)|~wise(X))<=>(~strong(X)|wise(X))))&
(![X]:((strong(X)<~>brave(X))=>humble(X)))&
(![X]:(funny(X)=>~old(X)))&
(((patient(john)&quiet(john)))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((generous(X)&calm(X))<=>brave(X)))&
(![X]:((humble(X)<~>~quiet(X))=>(~wise(X)<~>old(X))))&
((~tall(fred))<=>((~wise(alice)|~humble(alice))))&
(?[X]:(rich(X)))&
((~wise(alice)|~old(alice)))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
((happy(susan)<~>~wise(susan)))&
(?[X]:(~happy(X)))&
((creative(susan)|kind(susan)))&
((~calm(lucy)&happy(lucy))) | ~creative(lucy) | [
"p0",
"p3",
"p5",
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3592422898624818339139908
% SZS output start Proof for 3592422898624818339139908
1. ! [X0] : (happy(X0) <=> ~rich(X0)) [input p0]
4. ! [X0] : ((curious(X0) | ~rich(X0)) => (generous(X0) & ~wise(X0))) [input p3]
6. ! [X0] : ((~rich(X0) | kind(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p5]
7. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> (rich(X0) | ~creative(X0))) [input p6]
24. happy(lucy) & ~calm(lucy) [input p23]
25. creative(lucy) [input hypothesis]
29. ! [X0] : ((generous(X0) & ~wise(X0)) | (~curious(X0) & rich(X0))) [ennf transformation 4]
38. ! [X0] : ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))) [nnf transformation 1]
41. ! [X0] : (((~rich(X0) | kind(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (rich(X0) & ~kind(X0)))) [nnf transformation 6]
42. ! [X0] : ((~rich(X0) | kind(X0) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (rich(X0) & ~kind(X0)))) [flattening 41]
43. ! [X0] : (((~curious(X0) | ~wise(X0)) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | (curious(X0) & wise(X0)))) [nnf transformation 7]
44. ! [X0] : ((~curious(X0) | ~wise(X0) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | (curious(X0) & wise(X0)))) [flattening 43]
73. ~rich(X0) | ~happy(X0) [cnf transformation 38]
82. ~curious(X0) | generous(X0) [cnf transformation 29]
85. ~curious(X0) | ~generous(X0) | rich(X0) [cnf transformation 42]
91. rich(X0) | ~creative(X0) | curious(X0) [cnf transformation 44]
128. happy(lucy) [cnf transformation 24]
129. creative(lucy) [cnf transformation 25]
133. ~curious(X0) | rich(X0) [subsumption resolution 85,82]
135. ~creative(X0) | rich(X0) [subsumption resolution 91,133]
258. rich(lucy) [resolution 135,129]
260. ~happy(lucy) [resolution 258,73]
261. $false [subsumption resolution 260,128]
% SZS output end Proof for 3592422898624818339139908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and strong is either old or not funny.
If susan is not kind then someone is both happy and not rich.
Everyone who is either funny or kind is creative or not strong and vice versa.
Everyone who is both tall and not kind is curious.
If john is either not brave or rich then someone is not rich or patient.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
If someone is not tall then fred is not wise or not rich and vice versa.
Everyone who is not strong is patient or happy and vice versa.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Someone is either creative or strong.
Mary is either not patient or not wise.
Someone is not funny or kind. | Mary is curious. | entailment | (![X]:((~generous(X)&strong(X))=>(old(X)<~>~funny(X))))&
((~kind(susan))=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((funny(X)<~>kind(X))<=>(creative(X)|~strong(X))))&
(![X]:((tall(X)&~kind(X))=>curious(X)))&
(((~brave(john)<~>rich(john)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
(![X]:(~strong(X)<=>(patient(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
(?[X]:((creative(X)<~>strong(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | curious(mary) | [
"p5",
"p6",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1298942190548615127656635
% SZS output start Proof for 1298942190548615127656635
6. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
16. ! [X0] : (~strong(X0) <=> (happy(X0) | patient(X0))) [input p15]
25. ~curious(mary) [input hypothesis]
32. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 6]
33. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
57. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
58. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 57]
67. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | strong(X0))) [nnf transformation 16]
68. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | strong(X0))) [flattening 67]
97. patient(X0) | curious(X0) [cnf transformation 32]
100. ~patient(X0) | ~generous(X0) [cnf transformation 33]
126. strong(X0) | generous(X0) [cnf transformation 58]
142. ~patient(X0) | ~strong(X0) [cnf transformation 68]
158. ~curious(mary) [cnf transformation 25]
277. 26 <=> generous(mary) [avatar definition]
303. 31 <=> patient(mary) [avatar definition]
304. ~patient(mary) <- (~31) [avatar component clause 303]
305. patient(mary) <- (31) [avatar component clause 303]
326. ~generous(mary) <- (31) [resolution 100,305]
339. ~strong(mary) <- (31) [resolution 142,305]
341. generous(mary) <- (31) [resolution 339,126]
344. 26 | ~31 [avatar split clause 341,303,277]
345. ~26 | ~31 [avatar split clause 326,303,277]
347. curious(mary) <- (~31) [resolution 304,97]
348. $false <- (~31) [subsumption resolution 347,158]
349. 31 [avatar contradiction clause 348]
350. $false [avatar sat refutation 344,345,349]
% SZS output end Proof for 1298942190548615127656635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not happy is either curious or quiet and vice versa.
Everyone who is patient is not calm.
Everyone who is happy is old or happy and vice versa.
If paul is either not humble or funny then someone is old or not generous and vice versa.
Everyone who is either happy or humble is either creative or old and vice versa.
Everyone who is both humble and curious is not tall and vice versa.
Everyone who is not curious is not quiet and vice versa.
Everyone who is not creative or not quiet is either not strong or not curious and vice versa.
If someone is not creative or not rich then john is kind or quiet and vice versa.
If someone is not quiet then john is both calm and not funny.
If someone is calm or not calm then someone is curious or not tall.
Everyone who is not kind or calm is either not patient or not creative.
If fred is not quiet or generous then someone is old or not curious.
If someone is both strong and not patient then someone is rich or patient and vice versa.
Everyone who is both humble and old is both brave and not generous and vice versa.
If paul is both not generous and brave then someone is tall or happy and vice versa.
Someone is both not quiet and not happy.
Susan is both not rich and quiet.
Someone is either not patient or strong.
Someone is both wise and not curious.
Someone is both brave and not funny.
Susan is generous.
Someone is humble or not humble.
Someone is either not calm or not happy. | Fred is calm. | neutral | (![X]:((brave(X)&~happy(X))<=>(curious(X)<~>quiet(X))))&
(![X]:(patient(X)=>~calm(X)))&
(![X]:(happy(X)<=>(old(X)|happy(X))))&
(((~humble(paul)<~>funny(paul)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((happy(X)<~>humble(X))<=>(creative(X)<~>old(X))))&
(![X]:((humble(X)&curious(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>~quiet(X)))&
(![X]:((~creative(X)|~quiet(X))<=>(~strong(X)<~>~curious(X))))&
((?[X]:((~creative(X)|~rich(X))))<=>((kind(john)|quiet(john))))&
((?[X]:(~quiet(X)))=>((calm(john)&~funny(john))))&
((?[X]:((calm(X)|~calm(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(![X]:((~kind(X)|calm(X))=>(~patient(X)<~>~creative(X))))&
(((~quiet(fred)|generous(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:((humble(X)&old(X))<=>(brave(X)&~generous(X))))&
(((~generous(paul)&brave(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(?[X]:((~quiet(X)&~happy(X))))&
((~rich(susan)&quiet(susan)))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((wise(X)&~curious(X))))&
(?[X]:((brave(X)&~funny(X))))&
(generous(susan))&
(?[X]:((humble(X)|~humble(X))))&
(?[X]:((~calm(X)<~>~happy(X)))) | calm(fred) | [] | null | 0 |
If someone is either not strong or not rich then john is either not generous or rich.
If alice is either not curious or not quiet then alice is humble or creative.
If alice is both not generous and not happy then fred is both not calm and patient.
Everyone who is either not quiet or not creative is not wise and vice versa.
Everyone who is not old is both old and creative and vice versa.
Everyone who is happy or not wise is not wise.
If someone is either not patient or strong then john is both not calm and strong.
Everyone who is either not humble or funny is both not old and curious.
If alice is either strong or quiet then someone is happy or not happy and vice versa.
Everyone who is kind or not kind is both not quiet and patient and vice versa.
Everyone who is strong is not kind.
If john is either brave or not rich then someone is not wise or curious and vice versa.
If alice is either not happy or not funny then paul is both not quiet and happy and vice versa.
Everyone who is either kind or strong is not rich.
Everyone who is not wise or kind is either not tall or not creative and vice versa.
Someone is either not tall or not generous.
Fred is not generous or not wise.
Alice is both not brave and humble.
Someone is funny.
Susan is both humble and curious.
Someone is brave. | John is not tall. | entailment | ((?[X]:((~strong(X)<~>~rich(X))))=>((~generous(john)<~>rich(john))))&
(((~curious(alice)<~>~quiet(alice)))=>((humble(alice)|creative(alice))))&
(((~generous(alice)&~happy(alice)))=>((~calm(fred)&patient(fred))))&
(![X]:((~quiet(X)<~>~creative(X))<=>~wise(X)))&
(![X]:(~old(X)<=>(old(X)&creative(X))))&
(![X]:((happy(X)|~wise(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>strong(X))))=>((~calm(john)&strong(john))))&
(![X]:((~humble(X)<~>funny(X))=>(~old(X)&curious(X))))&
(((strong(alice)<~>quiet(alice)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((kind(X)|~kind(X))<=>(~quiet(X)&patient(X))))&
(![X]:(strong(X)=>~kind(X)))&
(((brave(john)<~>~rich(john)))<=>(?[X]:((~wise(X)|curious(X)))))&
(((~happy(alice)<~>~funny(alice)))<=>((~quiet(paul)&happy(paul))))&
(![X]:((kind(X)<~>strong(X))=>~rich(X)))&
(![X]:((~wise(X)|kind(X))<=>(~tall(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>~generous(X))))&
((~generous(fred)|~wise(fred)))&
((~brave(alice)&humble(alice)))&
(?[X]:(funny(X)))&
((humble(susan)&curious(susan)))&
(?[X]:(brave(X))) | ~tall(john) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7793462230003651511150454
% SZS output start Proof for 7793462230003651511150454
4. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) <=> ~wise(X0)) [input p3]
5. ! [X0] : (~old(X0) <=> (creative(X0) & old(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | happy(X0)) => ~wise(X0)) [input p5]
7. ? [X0] : (~patient(X0) <~> strong(X0)) => (strong(john) & ~calm(john)) [input p6]
9. (strong(alice) <~> quiet(alice)) <=> ? [X0] : (~happy(X0) | happy(X0)) [input p8]
10. ! [X0] : ((~kind(X0) | kind(X0)) <=> (patient(X0) & ~quiet(X0))) [input p9]
11. ! [X0] : (strong(X0) => ~kind(X0)) [input p10]
15. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p14]
22. tall(john) [input hypothesis]
24. ? [X0] : (~patient(X0) <~> strong(X0)) => strong(john) [pure predicate removal 7]
30. ! [X0] : (~wise(X0) | (wise(X0) & ~happy(X0))) [ennf transformation 6]
31. strong(john) | ! [X0] : (~patient(X0) <=> strong(X0)) [ennf transformation 24]
33. ! [X0] : (~kind(X0) | ~strong(X0)) [ennf transformation 11]
37. ! [X0] : ((((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | wise(X0)) & (~wise(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | old(X0))) [nnf transformation 5]
39. ! [X0] : ((~old(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | old(X0))) [flattening 38]
40. strong(john) | ! [X0] : ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))) [nnf transformation 31]
42. (((~quiet(alice) | ~strong(alice)) & (quiet(alice) | strong(alice))) | ! [X0] : (happy(X0) & ~happy(X0))) & (? [X0] : (~happy(X0) | happy(X0)) | ((strong(alice) | ~quiet(alice)) & (quiet(alice) | ~strong(alice)))) [nnf transformation 9]
43. (((~quiet(alice) | ~strong(alice)) & (quiet(alice) | strong(alice))) | ! [X0] : (happy(X0) & ~happy(X0))) & (? [X1] : (~happy(X1) | happy(X1)) | ((strong(alice) | ~quiet(alice)) & (quiet(alice) | ~strong(alice)))) [rectify 42]
44. ? [X1] : (~happy(X1) | happy(X1)) => (~happy(sK0) | happy(sK0)) [choice axiom]
45. (((~quiet(alice) | ~strong(alice)) & (quiet(alice) | strong(alice))) | ! [X0] : (happy(X0) & ~happy(X0))) & ((~happy(sK0) | happy(sK0)) | ((strong(alice) | ~quiet(alice)) & (quiet(alice) | ~strong(alice)))) [skolemisation 43,44]
46. ! [X0] : (((~kind(X0) | kind(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [nnf transformation 10]
47. ! [X0] : ((~kind(X0) | kind(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (kind(X0) & ~kind(X0)))) [flattening 46]
55. ! [X0] : (((kind(X0) | ~wise(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~kind(X0) & wise(X0)))) [nnf transformation 15]
56. ! [X0] : ((kind(X0) | ~wise(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~kind(X0) & wise(X0)))) [flattening 55]
74. wise(X0) | quiet(X0) | creative(X0) [cnf transformation 37]
75. old(X0) | old(X0) [cnf transformation 39]
77. ~old(X0) | ~creative(X0) | ~old(X0) [cnf transformation 39]
78. ~wise(X0) | ~happy(X0) [cnf transformation 30]
81. strong(john) | ~patient(X0) | ~strong(X0) [cnf transformation 40]
89. quiet(alice) | strong(alice) | happy(X0) [cnf transformation 45]
92. ~quiet(X0) | ~kind(X0) [cnf transformation 47]
93. ~quiet(X0) | kind(X0) [cnf transformation 47]
94. patient(X0) | ~kind(X0) [cnf transformation 47]
95. kind(X0) | patient(X0) [cnf transformation 47]
97. ~kind(X0) | ~strong(X0) [cnf transformation 33]
117. ~tall(X0) | ~wise(X0) | kind(X0) | creative(X0) [cnf transformation 56]
127. tall(john) [cnf transformation 22]
128. old(X0) [duplicate literal removal 75]
129. ~old(X0) | ~creative(X0) [duplicate literal removal 77]
149. 5 <=> quiet(alice) [avatar definition]
151. quiet(alice) <- (5) [avatar component clause 149]
180. 12 <=> ! [X0] : (~patient(X0) | ~strong(X0)) [avatar definition]
181. ~patient(X0) | ~strong(X0) <- (12) [avatar component clause 180]
183. 13 <=> strong(john) [avatar definition]
185. strong(john) <- (13) [avatar component clause 183]
186. 12 | 13 [avatar split clause 81,183,180]
194. 15 <=> ! [X0] : happy(X0) [avatar definition]
195. happy(X0) <- (15) [avatar component clause 194]
197. 16 <=> strong(alice) [avatar definition]
198. strong(alice) <- (16) [avatar component clause 197]
202. 17 <=> ! [X0] : ~happy(X0) [avatar definition]
203. ~happy(X0) <- (17) [avatar component clause 202]
205. 15 | 16 | 5 [avatar split clause 89,149,197,194]
207. patient(X0) [subsumption resolution 94,95]
208. ~quiet(X0) [subsumption resolution 92,93]
269. $false <- (5) [subsumption resolution 151,208]
270. ~5 [avatar contradiction clause 269]
273. ~creative(X1) [resolution 129,128]
282. quiet(X2) | creative(X2) | ~happy(X2) [resolution 74,78]
291. creative(X2) | ~happy(X2) [subsumption resolution 282,208]
292. ~happy(X2) [subsumption resolution 291,273]
293. 17 [avatar split clause 292,202]
298. ~strong(X0) <- (12) [subsumption resolution 181,207]
310. $false <- (12, 16) [resolution 298,198]
311. ~12 | ~16 [avatar contradiction clause 310]
330. ~wise(john) | kind(john) | creative(john) [resolution 117,127]
344. $false <- (15, 17) [subsumption resolution 195,203]
345. ~15 | ~17 [avatar contradiction clause 344]
357. ~wise(john) | kind(john) [subsumption resolution 330,273]
359. 31 <=> kind(john) [avatar definition]
361. kind(john) <- (31) [avatar component clause 359]
363. 32 <=> wise(john) [avatar definition]
365. ~wise(john) <- (~32) [avatar component clause 363]
366. 31 | ~32 [avatar split clause 357,363,359]
376. quiet(john) | creative(john) <- (~32) [resolution 365,74]
377. creative(john) <- (~32) [subsumption resolution 376,208]
378. $false <- (~32) [subsumption resolution 377,273]
379. 32 [avatar contradiction clause 378]
382. ~strong(john) <- (31) [resolution 361,97]
383. $false <- (13, 31) [subsumption resolution 382,185]
384. ~13 | ~31 [avatar contradiction clause 383]
385. $false [avatar sat refutation 186,205,270,293,311,345,366,379,384]
% SZS output end Proof for 7793462230003651511150454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not rich and vice versa.
Everyone who is either not happy or wise is either happy or not humble and vice versa.
Everyone who is either happy or humble is brave and vice versa.
Everyone who is not generous is old or not strong and vice versa.
Everyone who is generous or not creative is both funny and not creative and vice versa.
If susan is not funny then john is either not creative or not humble and vice versa.
If lucy is either not old or not patient then alice is not strong or humble.
Everyone who is either not patient or funny is funny and vice versa.
If someone is both kind and old then lucy is both wise and not strong and vice versa.
If john is either not calm or not humble then lucy is not generous or not calm.
If someone is both kind and not kind then paul is either not quiet or happy and vice versa.
Everyone who is either not rich or not happy is not generous.
Everyone who is either strong or calm is strong or not wise and vice versa.
If fred is both not funny and happy then paul is not quiet or kind.
If someone is both rich and not patient then susan is either not generous or not funny.
Everyone who is rich is either not calm or rich and vice versa.
Someone is not brave.
Lucy is curious or not funny.
Lucy is not old or not tall.
Fred is not funny or not happy.
Paul is either calm or strong.
Someone is either not brave or not wise. | Alice is not tall. | neutral | (![X]:(~creative(X)<=>~rich(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((happy(X)<~>humble(X))<=>brave(X)))&
(![X]:(~generous(X)<=>(old(X)|~strong(X))))&
(![X]:((generous(X)|~creative(X))<=>(funny(X)&~creative(X))))&
((~funny(susan))<=>((~creative(john)<~>~humble(john))))&
(((~old(lucy)<~>~patient(lucy)))=>((~strong(alice)|humble(alice))))&
(![X]:((~patient(X)<~>funny(X))<=>funny(X)))&
((?[X]:((kind(X)&old(X))))<=>((wise(lucy)&~strong(lucy))))&
(((~calm(john)<~>~humble(john)))=>((~generous(lucy)|~calm(lucy))))&
((?[X]:((kind(X)&~kind(X))))<=>((~quiet(paul)<~>happy(paul))))&
(![X]:((~rich(X)<~>~happy(X))=>~generous(X)))&
(![X]:((strong(X)<~>calm(X))<=>(strong(X)|~wise(X))))&
(((~funny(fred)&happy(fred)))=>((~quiet(paul)|kind(paul))))&
((?[X]:((rich(X)&~patient(X))))=>((~generous(susan)<~>~funny(susan))))&
(![X]:(rich(X)<=>(~calm(X)<~>rich(X))))&
(?[X]:(~brave(X)))&
((curious(lucy)|~funny(lucy)))&
((~old(lucy)|~tall(lucy)))&
((~funny(fred)|~happy(fred)))&
((calm(paul)<~>strong(paul)))&
(?[X]:((~brave(X)<~>~wise(X)))) | ~tall(alice) | [] | null | 0 |
Everyone who is both happy and not humble is either not creative or not humble and vice versa.
Everyone who is happy is either funny or wise and vice versa.
Everyone who is not old is generous.
If paul is both not happy and not calm then someone is both tall and not happy.
Everyone who is old or not funny is either rich or happy and vice versa.
If fred is tall or old then someone is either quiet or not quiet.
Everyone who is either not wise or happy is not brave and vice versa.
If susan is not quiet then someone is either old or strong.
If someone is either tall or generous then alice is both not humble and not tall.
Everyone who is generous or not tall is kind and vice versa.
Everyone who is either not patient or not funny is both not tall and patient and vice versa.
If someone is either rich or patient then someone is either happy or not funny and vice versa.
Everyone who is not creative or old is both wise and funny.
If someone is funny or tall then lucy is both not tall and old.
Everyone who is both not calm and kind is tall.
Everyone who is both rich and not wise is not creative.
Someone is happy or not old.
John is humble.
Fred is generous or not quiet.
Someone is either generous or not kind. | Susan is brave. | contradiction | (![X]:((happy(X)&~humble(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(happy(X)<=>(funny(X)<~>wise(X))))&
(![X]:(~old(X)=>generous(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((old(X)|~funny(X))<=>(rich(X)<~>happy(X))))&
(((tall(fred)|old(fred)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~brave(X)))&
((~quiet(susan))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((~humble(alice)&~tall(alice))))&
(![X]:((generous(X)|~tall(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~creative(X)|old(X))=>(wise(X)&funny(X))))&
((?[X]:((funny(X)|tall(X))))=>((~tall(lucy)&old(lucy))))&
(![X]:((~calm(X)&kind(X))=>tall(X)))&
(![X]:((rich(X)&~wise(X))=>~creative(X)))&
(?[X]:((happy(X)|~old(X))))&
(humble(john))&
((generous(fred)|~quiet(fred)))&
(?[X]:((generous(X)<~>~kind(X)))) | brave(susan) | [
"p1",
"p4",
"p6",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 25868220202577144654358
% SZS output start Proof for 25868220202577144654358
2. ! [X0] : (happy(X0) <=> (funny(X0) <~> wise(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | old(X0)) <=> (rich(X0) <~> happy(X0))) [input p4]
7. ! [X0] : ((~wise(X0) <~> happy(X0)) <=> ~brave(X0)) [input p6]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (patient(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~creative(X0)) => (funny(X0) & wise(X0))) [input p12]
14. ? [X0] : (tall(X0) | funny(X0)) => (old(lucy) & ~tall(lucy)) [input p13]
16. ! [X0] : ((~wise(X0) & rich(X0)) => ~creative(X0)) [input p15]
21. brave(susan) [input hypothesis]
23. ! [X0] : ((~wise(X0) <~> happy(X0)) => ~brave(X0)) [unused predicate definition removal 7]
28. ! [X0] : (~brave(X0) | (~wise(X0) <=> happy(X0))) [ennf transformation 23]
31. ! [X0] : ((funny(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 13]
32. (old(lucy) & ~tall(lucy)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 14]
33. ! [X0] : (~creative(X0) | (wise(X0) | ~rich(X0))) [ennf transformation 16]
34. ! [X0] : (~creative(X0) | wise(X0) | ~rich(X0)) [flattening 33]
37. ! [X0] : ((happy(X0) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) & (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~happy(X0))) [nnf transformation 2]
38. ! [X0] : (((~funny(X0) | old(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [nnf transformation 5]
39. ! [X0] : ((~funny(X0) | old(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [flattening 38]
43. ! [X0] : (~brave(X0) | ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0)))) [nnf transformation 28]
50. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
51. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 50]
68. ~happy(X0) | funny(X0) | wise(X0) [cnf transformation 37]
71. ~wise(X0) | funny(X0) | happy(X0) [cnf transformation 37]
74. rich(X0) | happy(X0) | funny(X0) [cnf transformation 39]
84. ~brave(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 43]
96. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 51]
98. ~funny(X0) | ~patient(X0) | ~patient(X0) | tall(X0) [cnf transformation 51]
108. wise(X0) | creative(X0) [cnf transformation 31]
111. ~old(X0) | funny(X0) [cnf transformation 31]
112. ~tall(lucy) | ~funny(X0) [cnf transformation 32]
114. old(lucy) | ~funny(X0) [cnf transformation 32]
116. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 34]
122. brave(susan) [cnf transformation 21]
123. ~funny(X0) | patient(X0) [duplicate literal removal 96]
124. ~patient(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 98]
200. 17 <=> old(lucy) [avatar definition]
202. old(lucy) <- (17) [avatar component clause 200]
205. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
206. ~funny(X0) <- (18) [avatar component clause 205]
207. 18 | 17 [avatar split clause 114,200,205]
209. 19 <=> tall(lucy) [avatar definition]
213. 18 | ~19 [avatar split clause 112,209,205]
214. ~rich(X0) | wise(X0) [subsumption resolution 116,108]
248. funny(lucy) <- (17) [resolution 111,202]
252. patient(lucy) <- (17) [resolution 248,123]
287. happy(X0) | funny(X0) | wise(X0) [resolution 74,214]
289. wise(X0) | funny(X0) [subsumption resolution 287,68]
305. 28 <=> wise(susan) [avatar definition]
306. ~wise(susan) <- (~28) [avatar component clause 305]
307. wise(susan) <- (28) [avatar component clause 305]
309. 29 <=> happy(susan) [avatar definition]
311. happy(susan) <- (29) [avatar component clause 309]
313. funny(susan) | happy(susan) <- (28) [resolution 307,71]
316. 30 <=> funny(susan) [avatar definition]
317. ~funny(susan) <- (~30) [avatar component clause 316]
318. funny(susan) <- (30) [avatar component clause 316]
319. 29 | 30 | ~28 [avatar split clause 313,305,316,309]
321. ~wise(susan) | ~happy(susan) [resolution 84,122]
325. ~wise(susan) <- (29) [subsumption resolution 321,311]
326. ~28 | ~29 [avatar split clause 325,309,305]
340. ~funny(lucy) | tall(lucy) <- (17) [resolution 124,252]
343. tall(lucy) <- (17) [subsumption resolution 340,248]
348. 19 | ~17 [avatar split clause 343,200,209]
373. funny(susan) <- (~28) [resolution 289,306]
376. $false <- (~28, ~30) [subsumption resolution 373,317]
377. 28 | 30 [avatar contradiction clause 376]
380. $false <- (18, 30) [subsumption resolution 318,206]
381. ~18 | ~30 [avatar contradiction clause 380]
382. $false [avatar sat refutation 207,213,319,326,348,377,381]
% SZS output end Proof for 25868220202577144654358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then fred is not patient and vice versa.
Everyone who is either not quiet or not patient is either tall or kind.
Everyone who is either not wise or not strong is either not patient or not quiet.
Everyone who is brave or not patient is not humble or not generous and vice versa.
Everyone who is humble is generous or wise and vice versa.
Everyone who is both generous and funny is brave or happy.
Everyone who is either not quiet or wise is curious.
Everyone who is either not creative or not generous is funny and vice versa.
If john is not rich or rich then fred is creative.
Everyone who is not funny or generous is either humble or rich and vice versa.
If someone is both not quiet and not generous then paul is both not funny and not generous and vice versa.
If alice is both funny and not curious then susan is either creative or not quiet.
Everyone who is either not quiet or creative is not rich or quiet and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is either wise or patient is both not funny and wise and vice versa.
If someone is either not quiet or not rich then someone is not quiet or funny and vice versa.
Someone is quiet.
Someone is strong or patient.
Someone is either not tall or not quiet.
Someone is generous or not happy.
Someone is both patient and not generous.
Lucy is not funny or not quiet.
John is either not tall or generous.
Someone is not funny or generous. | Fred is not humble. | entailment | ((?[X]:(creative(X)))<=>(~patient(fred)))&
(![X]:((~quiet(X)<~>~patient(X))=>(tall(X)<~>kind(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((brave(X)|~patient(X))<=>(~humble(X)|~generous(X))))&
(![X]:(humble(X)<=>(generous(X)|wise(X))))&
(![X]:((generous(X)&funny(X))=>(brave(X)|happy(X))))&
(![X]:((~quiet(X)<~>wise(X))=>curious(X)))&
(![X]:((~creative(X)<~>~generous(X))<=>funny(X)))&
(((~rich(john)|rich(john)))=>(creative(fred)))&
(![X]:((~funny(X)|generous(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~funny(paul)&~generous(paul))))&
(((funny(alice)&~curious(alice)))=>((creative(susan)<~>~quiet(susan))))&
(![X]:((~quiet(X)<~>creative(X))<=>(~rich(X)|quiet(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((wise(X)<~>patient(X))<=>(~funny(X)&wise(X))))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>(?[X]:((~quiet(X)|funny(X)))))&
(?[X]:(quiet(X)))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((patient(X)&~generous(X))))&
((~funny(lucy)|~quiet(lucy)))&
((~tall(john)<~>generous(john)))&
(?[X]:((~funny(X)|generous(X)))) | ~humble(fred) | [
"p0",
"p3",
"p4",
"p7",
"p8",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1291720686109624273470247
% SZS output start Proof for 1291720686109624273470247
1. ? [X0] : creative(X0) <=> ~patient(fred) [input p0]
4. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~generous(X0) | ~humble(X0))) [input p3]
5. ! [X0] : (humble(X0) <=> (wise(X0) | generous(X0))) [input p4]
8. ! [X0] : ((~creative(X0) <~> ~generous(X0)) <=> funny(X0)) [input p7]
9. (rich(john) | ~rich(john)) => creative(fred) [input p8]
13. ! [X0] : ((~quiet(X0) <~> creative(X0)) <=> (quiet(X0) | ~rich(X0))) [input p12]
15. ! [X0] : ((wise(X0) <~> patient(X0)) <=> (wise(X0) & ~funny(X0))) [input p14]
17. ? [X0] : quiet(X0) [input p16]
25. humble(fred) [input hypothesis]
33. creative(fred) | (~rich(john) & rich(john)) [ennf transformation 9]
36. (? [X0] : creative(X0) | patient(fred)) & (~patient(fred) | ! [X0] : ~creative(X0)) [nnf transformation 1]
37. (? [X0] : creative(X0) | patient(fred)) & (~patient(fred) | ! [X1] : ~creative(X1)) [rectify 36]
38. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
39. (creative(sK0) | patient(fred)) & (~patient(fred) | ! [X1] : ~creative(X1)) [skolemisation 37,38]
42. ! [X0] : (((~patient(X0) | brave(X0)) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 4]
43. ! [X0] : ((~patient(X0) | brave(X0) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | (patient(X0) & ~brave(X0)))) [flattening 42]
44. ! [X0] : ((humble(X0) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | ~humble(X0))) [nnf transformation 5]
45. ! [X0] : ((humble(X0) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ~humble(X0))) [flattening 44]
46. ! [X0] : ((((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | ~funny(X0)) & (funny(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [flattening 54]
56. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [flattening 56]
63. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
64. quiet(sK4) [skolemisation 17,63]
77. ~patient(fred) | ~creative(X1) [cnf transformation 39]
88. ~generous(X0) | ~humble(X0) | patient(X0) [cnf transformation 43]
91. ~humble(X0) | generous(X0) | wise(X0) [cnf transformation 45]
96. ~creative(X0) | funny(X0) | generous(X0) [cnf transformation 46]
99. creative(fred) | rich(john) [cnf transformation 33]
100. creative(fred) | ~rich(john) [cnf transformation 33]
114. creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 55]
118. ~funny(X0) | patient(X0) | ~wise(X0) [cnf transformation 57]
130. quiet(sK4) [cnf transformation 64]
141. humble(fred) [cnf transformation 25]
145. ~quiet(X0) | creative(X0) [duplicate literal removal 114]
147. 1 <=> patient(fred) [avatar definition]
148. ~patient(fred) <- (~1) [avatar component clause 147]
156. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
157. ~creative(X1) <- (3) [avatar component clause 156]
158. 3 | ~1 [avatar split clause 77,147,156]
160. 4 <=> rich(john) [avatar definition]
164. 5 <=> creative(fred) [avatar definition]
166. creative(fred) <- (5) [avatar component clause 164]
167. ~4 | 5 [avatar split clause 100,164,160]
168. 4 | 5 [avatar split clause 99,164,160]
286. creative(sK4) [resolution 145,130]
292. generous(fred) | wise(fred) [resolution 91,141]
295. 31 <=> wise(fred) [avatar definition]
297. wise(fred) <- (31) [avatar component clause 295]
299. 32 <=> generous(fred) [avatar definition]
301. generous(fred) <- (32) [avatar component clause 299]
302. 31 | 32 [avatar split clause 292,299,295]
304. funny(fred) | generous(fred) <- (5) [resolution 96,166]
309. 33 <=> funny(fred) [avatar definition]
311. funny(fred) <- (33) [avatar component clause 309]
312. 32 | 33 | ~5 [avatar split clause 304,164,309,299]
344. $false <- (3) [resolution 157,286]
345. ~3 [avatar contradiction clause 344]
352. ~humble(fred) | patient(fred) <- (32) [resolution 301,88]
355. patient(fred) <- (32) [subsumption resolution 352,141]
356. $false <- (~1, 32) [subsumption resolution 355,148]
357. 1 | ~32 [avatar contradiction clause 356]
424. patient(fred) | ~wise(fred) <- (33) [resolution 118,311]
426. ~wise(fred) <- (~1, 33) [subsumption resolution 424,148]
427. $false <- (~1, 31, 33) [subsumption resolution 426,297]
428. 1 | ~31 | ~33 [avatar contradiction clause 427]
434. $false [avatar sat refutation 158,167,168,302,312,345,357,428]
% SZS output end Proof for 1291720686109624273470247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and old is either not curious or creative.
Everyone who is both generous and not rich is not generous or humble and vice versa.
Everyone who is both quiet and tall is not patient or funny and vice versa.
Everyone who is not kind is both not generous and not kind.
Everyone who is both strong and brave is not old or not wise and vice versa.
If someone is both not funny and generous then john is brave.
If someone is either humble or brave then someone is patient.
Everyone who is curious is either quiet or brave.
If someone is both not creative and not humble then someone is either creative or funny and vice versa.
If alice is both not generous and kind then lucy is both not humble and generous.
If someone is either kind or not brave then susan is not generous or old and vice versa.
If paul is either not generous or strong then fred is happy or humble and vice versa.
Everyone who is kind is both patient and not calm.
If someone is not generous then john is both tall and creative.
If mary is not happy then susan is not calm or kind and vice versa.
Someone is either humble or not curious.
Someone is patient or calm.
Mary is both curious and not wise.
Lucy is patient or not funny.
John is either not curious or humble.
Alice is either old or not brave. | Paul is not funny. | neutral | (![X]:((~generous(X)&old(X))=>(~curious(X)<~>creative(X))))&
(![X]:((generous(X)&~rich(X))<=>(~generous(X)|humble(X))))&
(![X]:((quiet(X)&tall(X))<=>(~patient(X)|funny(X))))&
(![X]:(~kind(X)=>(~generous(X)&~kind(X))))&
(![X]:((strong(X)&brave(X))<=>(~old(X)|~wise(X))))&
((?[X]:((~funny(X)&generous(X))))=>(brave(john)))&
((?[X]:((humble(X)<~>brave(X))))=>(?[X]:(patient(X))))&
(![X]:(curious(X)=>(quiet(X)<~>brave(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((creative(X)<~>funny(X)))))&
(((~generous(alice)&kind(alice)))=>((~humble(lucy)&generous(lucy))))&
((?[X]:((kind(X)<~>~brave(X))))<=>((~generous(susan)|old(susan))))&
(((~generous(paul)<~>strong(paul)))<=>((happy(fred)|humble(fred))))&
(![X]:(kind(X)=>(patient(X)&~calm(X))))&
((?[X]:(~generous(X)))=>((tall(john)&creative(john))))&
((~happy(mary))<=>((~calm(susan)|kind(susan))))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((patient(X)|calm(X))))&
((curious(mary)&~wise(mary)))&
((patient(lucy)|~funny(lucy)))&
((~curious(john)<~>humble(john)))&
((old(alice)<~>~brave(alice))) | ~funny(paul) | [] | null | 0 |
If someone is both generous and not creative then mary is both happy and creative.
If paul is either not tall or not old then someone is quiet or calm and vice versa.
If lucy is happy or tall then john is both not wise and not humble.
Everyone who is not happy or quiet is not patient and vice versa.
Everyone who is both happy and quiet is not humble or not happy and vice versa.
If mary is not kind or patient then john is generous or kind.
Everyone who is not happy is either not curious or not funny.
Everyone who is both tall and not wise is either tall or not brave.
If someone is not wise or brave then paul is not quiet and vice versa.
Everyone who is both happy and generous is old and vice versa.
Everyone who is both not creative and wise is either kind or curious.
If someone is wise or not funny then mary is quiet and vice versa.
Everyone who is both kind and not patient is either old or not wise and vice versa.
Everyone who is both not curious and funny is either generous or not funny and vice versa.
Someone is either kind or not kind.
Mary is either wise or not humble.
Someone is both not quiet and not brave.
Someone is not tall.
Fred is tall.
Someone is either brave or calm. | Fred is not calm. | neutral | ((?[X]:((generous(X)&~creative(X))))=>((happy(mary)&creative(mary))))&
(((~tall(paul)<~>~old(paul)))<=>(?[X]:((quiet(X)|calm(X)))))&
(((happy(lucy)|tall(lucy)))=>((~wise(john)&~humble(john))))&
(![X]:((~happy(X)|quiet(X))<=>~patient(X)))&
(![X]:((happy(X)&quiet(X))<=>(~humble(X)|~happy(X))))&
(((~kind(mary)|patient(mary)))=>((generous(john)|kind(john))))&
(![X]:(~happy(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((tall(X)&~wise(X))=>(tall(X)<~>~brave(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~quiet(paul)))&
(![X]:((happy(X)&generous(X))<=>old(X)))&
(![X]:((~creative(X)&wise(X))=>(kind(X)<~>curious(X))))&
((?[X]:((wise(X)|~funny(X))))<=>(quiet(mary)))&
(![X]:((kind(X)&~patient(X))<=>(old(X)<~>~wise(X))))&
(![X]:((~curious(X)&funny(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
((wise(mary)<~>~humble(mary)))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:(~tall(X)))&
(tall(fred))&
(?[X]:((brave(X)<~>calm(X)))) | ~calm(fred) | [] | null | 0 |
Everyone who is wise or not tall is curious.
Everyone who is either not creative or humble is happy or not creative and vice versa.
If alice is either generous or not tall then fred is not creative and vice versa.
If paul is creative then john is both not strong and not happy and vice versa.
Everyone who is not kind or creative is not quiet or not happy and vice versa.
Everyone who is not calm is creative or not tall.
Everyone who is funny is not humble or not quiet.
If susan is both not happy and not wise then someone is either humble or wise.
Everyone who is either wise or tall is not curious.
Everyone who is curious is not quiet and vice versa.
If someone is both wise and tall then john is creative or not patient and vice versa.
If someone is funny then fred is not funny.
Everyone who is both not humble and curious is either rich or old and vice versa.
If someone is not tall then paul is not kind or curious.
Everyone who is old or generous is either wise or not quiet and vice versa.
Everyone who is calm or not creative is either calm or not generous and vice versa.
Someone is not curious or not tall.
Mary is calm.
Mary is both not funny and not happy.
Someone is humble.
Alice is both not rich and not strong.
Someone is both calm and kind.
Someone is not old. | Paul is curious. | entailment | (![X]:((wise(X)|~tall(X))=>curious(X)))&
(![X]:((~creative(X)<~>humble(X))<=>(happy(X)|~creative(X))))&
(((generous(alice)<~>~tall(alice)))<=>(~creative(fred)))&
((creative(paul))<=>((~strong(john)&~happy(john))))&
(![X]:((~kind(X)|creative(X))<=>(~quiet(X)|~happy(X))))&
(![X]:(~calm(X)=>(creative(X)|~tall(X))))&
(![X]:(funny(X)=>(~humble(X)|~quiet(X))))&
(((~happy(susan)&~wise(susan)))=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:((wise(X)<~>tall(X))=>~curious(X)))&
(![X]:(curious(X)<=>~quiet(X)))&
((?[X]:((wise(X)&tall(X))))<=>((creative(john)|~patient(john))))&
((?[X]:(funny(X)))=>(~funny(fred)))&
(![X]:((~humble(X)&curious(X))<=>(rich(X)<~>old(X))))&
((?[X]:(~tall(X)))=>((~kind(paul)|curious(paul))))&
(![X]:((old(X)|generous(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((calm(X)|~creative(X))<=>(calm(X)<~>~generous(X))))&
(?[X]:((~curious(X)|~tall(X))))&
(calm(mary))&
((~funny(mary)&~happy(mary)))&
(?[X]:(humble(X)))&
((~rich(alice)&~strong(alice)))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:(~old(X))) | curious(paul) | [
"p0",
"p5",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8149936226825947713662497
% SZS output start Proof for 8149936226825947713662497
1. ! [X0] : ((~tall(X0) | wise(X0)) => curious(X0)) [input p0]
6. ! [X0] : (~calm(X0) => (~tall(X0) | creative(X0))) [input p5]
10. ! [X0] : (curious(X0) <=> ~quiet(X0)) [input p9]
15. ! [X0] : ((generous(X0) | old(X0)) <=> (wise(X0) <~> ~quiet(X0))) [input p14]
16. ! [X0] : ((~creative(X0) | calm(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p15]
24. ~curious(paul) [input hypothesis]
28. ! [X0] : (curious(X0) | (tall(X0) & ~wise(X0))) [ennf transformation 1]
29. ! [X0] : ((~tall(X0) | creative(X0)) | calm(X0)) [ennf transformation 6]
30. ! [X0] : (~tall(X0) | creative(X0) | calm(X0)) [flattening 29]
47. ! [X0] : ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0))) [nnf transformation 10]
55. ! [X0] : (((generous(X0) | old(X0)) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~generous(X0) & ~old(X0)))) [nnf transformation 15]
56. ! [X0] : ((generous(X0) | old(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~generous(X0) & ~old(X0)))) [flattening 55]
57. ! [X0] : (((~creative(X0) | calm(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (creative(X0) & ~calm(X0)))) [nnf transformation 16]
58. ! [X0] : ((~creative(X0) | calm(X0) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (creative(X0) & ~calm(X0)))) [flattening 57]
67. ~wise(X0) | curious(X0) [cnf transformation 28]
68. curious(X0) | tall(X0) [cnf transformation 28]
86. ~tall(X0) | creative(X0) | calm(X0) [cnf transformation 30]
92. quiet(X0) | curious(X0) [cnf transformation 47]
106. ~quiet(X0) | wise(X0) | ~generous(X0) [cnf transformation 56]
113. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 58]
114. ~calm(X0) | generous(X0) | creative(X0) [cnf transformation 58]
116. ~creative(X0) | calm(X0) | calm(X0) | generous(X0) [cnf transformation 58]
126. ~curious(paul) [cnf transformation 24]
127. ~calm(X0) | generous(X0) [duplicate literal removal 113]
128. ~creative(X0) | calm(X0) | generous(X0) [duplicate literal removal 116]
157. 6 <=> creative(paul) [avatar definition]
158. ~creative(paul) <- (~6) [avatar component clause 157]
159. creative(paul) <- (6) [avatar component clause 157]
215. 18 <=> curious(paul) [avatar definition]
216. ~curious(paul) <- (~18) [avatar component clause 215]
228. ~18 [avatar split clause 126,215]
230. tall(paul) <- (~18) [resolution 68,216]
262. creative(paul) | calm(paul) <- (~18) [resolution 86,230]
275. wise(X0) | ~generous(X0) | curious(X0) [resolution 106,92]
276. ~generous(X0) | curious(X0) [subsumption resolution 275,67]
312. calm(paul) | generous(paul) <- (6) [resolution 128,159]
315. generous(paul) <- (6) [subsumption resolution 312,127]
319. curious(paul) <- (6) [resolution 315,276]
329. $false <- (6, ~18) [subsumption resolution 319,216]
330. ~6 | 18 [avatar contradiction clause 329]
332. 33 <=> calm(paul) [avatar definition]
334. calm(paul) <- (33) [avatar component clause 332]
335. 33 | 6 | 18 [avatar split clause 262,215,157,332]
391. generous(paul) | creative(paul) <- (33) [resolution 334,114]
393. generous(paul) <- (~6, 33) [subsumption resolution 391,158]
527. curious(paul) <- (~6, 33) [resolution 393,276]
529. $false <- (~6, ~18, 33) [subsumption resolution 527,216]
530. 6 | 18 | ~33 [avatar contradiction clause 529]
531. $false [avatar sat refutation 228,330,335,530]
% SZS output end Proof for 8149936226825947713662497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is kind or quiet then someone is kind. If mary is not quiet or not kind then someone is tall and vice versa. If mary is patient then someone is tall and vice versa. If someone is both wise and humble then paul is both calm and not curious and vice versa. Everyone who is not brave is both not calm and not tall. Everyone who is either not calm or not wise is wise and vice versa. If lucy is not funny then john is either not wise or not old. If susan is either not humble or happy then john is both not humble and kind and vice versa. If alice is both old and not creative then someone is not happy or generous and vice versa. Everyone who is not rich is both not calm and wise. Everyone who is not curious is not funny or not strong and vice versa. If someone is either not quiet or old then someone is not happy. Everyone who is funny is both not generous and not old and vice versa. Everyone who is both old and creative is either old or not brave and vice versa. If fred is not humble then someone is not curious and vice versa. Everyone who is tall is either happy or not funny. Susan is both curious and not patient. Someone is tall. Someone is either happy or creative. Susan is either not funny or not happy. Paul is funny or curious. Someone is both not wise and not happy. Lucy is rich. Someone is not happy. | Paul is not old. | entailment | (((kind(john)|quiet(john)))=>(?[X]:(kind(X))))&
(((~quiet(mary)|~kind(mary)))<=>(?[X]:(tall(X))))&
((patient(mary))<=>(?[X]:(tall(X))))&
((?[X]:((wise(X)&humble(X))))<=>((calm(paul)&~curious(paul))))&
(![X]:(~brave(X)=>(~calm(X)&~tall(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>wise(X)))&
((~funny(lucy))=>((~wise(john)<~>~old(john))))&
(((~humble(susan)<~>happy(susan)))<=>((~humble(john)&kind(john))))&
(((old(alice)&~creative(alice)))<=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:(~rich(X)=>(~calm(X)&wise(X))))&
(![X]:(~curious(X)<=>(~funny(X)|~strong(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>(?[X]:(~happy(X))))&
(![X]:(funny(X)<=>(~generous(X)&~old(X))))&
(![X]:((old(X)&creative(X))<=>(old(X)<~>~brave(X))))&
((~humble(fred))<=>(?[X]:(~curious(X))))&
(![X]:(tall(X)=>(happy(X)<~>~funny(X))))&
((curious(susan)&~patient(susan)))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)<~>creative(X))))&
((~funny(susan)<~>~happy(susan)))&
((funny(paul)|curious(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(rich(lucy))&
(?[X]:(~happy(X))) | ~old(paul) | [
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2607693714003500204888349
% SZS output start Proof for 2607693714003500204888349
11. ! [X0] : (~curious(X0) <=> (~strong(X0) | ~funny(X0))) [input p10]
13. ! [X0] : (funny(X0) <=> (~old(X0) & ~generous(X0))) [input p12]
21. curious(paul) | funny(paul) [input p20]
25. old(paul) [input hypothesis]
59. ! [X0] : ((~curious(X0) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | curious(X0))) [nnf transformation 11]
60. ! [X0] : ((~curious(X0) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | curious(X0))) [flattening 59]
65. ! [X0] : ((funny(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ~funny(X0))) [nnf transformation 13]
66. ! [X0] : ((funny(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ~funny(X0))) [flattening 65]
115. ~curious(X0) | funny(X0) [cnf transformation 60]
120. ~old(X0) | ~funny(X0) [cnf transformation 66]
139. curious(paul) | funny(paul) [cnf transformation 21]
143. old(paul) [cnf transformation 25]
315. funny(paul) [subsumption resolution 139,115]
332. ~funny(paul) [resolution 120,143]
334. $false [subsumption resolution 332,315]
% SZS output end Proof for 2607693714003500204888349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and not rich then susan is either quiet or strong and vice versa.
If someone is either not brave or humble then susan is both not kind and not old and vice versa.
Everyone who is quiet or not quiet is both generous and old.
If someone is both not generous and not tall then someone is either not happy or not curious.
If fred is both not funny and humble then someone is either not patient or not funny and vice versa.
Everyone who is both wise and funny is both humble and not old.
Everyone who is brave or wise is humble or old and vice versa.
Everyone who is either happy or not humble is funny.
If lucy is not funny or humble then lucy is either not rich or not tall.
If someone is not curious then someone is both not rich and brave and vice versa.
If john is both rich and funny then someone is curious and vice versa.
If someone is rich or not rich then mary is both kind and not humble and vice versa.
If someone is either not brave or not patient then john is not humble or brave.
Everyone who is both not funny and patient is not humble or not generous and vice versa.
If someone is not quiet or not brave then paul is either not old or not rich and vice versa.
If someone is humble or creative then someone is not strong.
Susan is not rich.
Someone is patient or not generous.
Mary is generous.
Mary is both old and strong.
Alice is both creative and kind.
Someone is either not generous or patient.
Someone is not humble. | John is curious. | contradiction | ((?[X]:((~funny(X)&~rich(X))))<=>((quiet(susan)<~>strong(susan))))&
((?[X]:((~brave(X)<~>humble(X))))<=>((~kind(susan)&~old(susan))))&
(![X]:((quiet(X)|~quiet(X))=>(generous(X)&old(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(((~funny(fred)&humble(fred)))<=>(?[X]:((~patient(X)<~>~funny(X)))))&
(![X]:((wise(X)&funny(X))=>(humble(X)&~old(X))))&
(![X]:((brave(X)|wise(X))<=>(humble(X)|old(X))))&
(![X]:((happy(X)<~>~humble(X))=>funny(X)))&
(((~funny(lucy)|humble(lucy)))=>((~rich(lucy)<~>~tall(lucy))))&
((?[X]:(~curious(X)))<=>(?[X]:((~rich(X)&brave(X)))))&
(((rich(john)&funny(john)))<=>(?[X]:(curious(X))))&
((?[X]:((rich(X)|~rich(X))))<=>((kind(mary)&~humble(mary))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~humble(john)|brave(john))))&
(![X]:((~funny(X)&patient(X))<=>(~humble(X)|~generous(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((~old(paul)<~>~rich(paul))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:(~strong(X))))&
(~rich(susan))&
(?[X]:((patient(X)|~generous(X))))&
(generous(mary))&
((old(mary)&strong(mary)))&
((creative(alice)&kind(alice)))&
(?[X]:((~generous(X)<~>patient(X))))&
(?[X]:(~humble(X))) | curious(john) | [
"p1",
"p2",
"p5",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5307473720263317479296579
% SZS output start Proof for 5307473720263317479296579
2. ? [X0] : (~brave(X0) <~> humble(X0)) <=> (~old(susan) & ~kind(susan)) [input p1]
3. ! [X0] : ((~quiet(X0) | quiet(X0)) => (old(X0) & generous(X0))) [input p2]
6. ! [X0] : ((funny(X0) & wise(X0)) => (~old(X0) & humble(X0))) [input p5]
7. ! [X0] : ((wise(X0) | brave(X0)) <=> (old(X0) | humble(X0))) [input p6]
11. (funny(john) & rich(john)) <=> ? [X0] : curious(X0) [input p10]
14. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (~generous(X0) | ~humble(X0))) [input p13]
24. curious(john) [input hypothesis]
28. ! [X0] : ((old(X0) & generous(X0)) | (quiet(X0) & ~quiet(X0))) [ennf transformation 3]
30. ! [X0] : ((~old(X0) & humble(X0)) | (~funny(X0) | ~wise(X0))) [ennf transformation 6]
31. ! [X0] : ((~old(X0) & humble(X0)) | ~funny(X0) | ~wise(X0)) [flattening 30]
41. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | (old(susan) | kind(susan))) & ((~old(susan) & ~kind(susan)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [nnf transformation 2]
42. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [flattening 41]
43. (? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1)))) [rectify 42]
44. ? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) => ((~humble(sK1) | brave(sK1)) & (humble(sK1) | ~brave(sK1))) [choice axiom]
45. (((~humble(sK1) | brave(sK1)) & (humble(sK1) | ~brave(sK1))) | old(susan) | kind(susan)) & ((~old(susan) & ~kind(susan)) | ! [X1] : ((~brave(X1) | ~humble(X1)) & (humble(X1) | brave(X1)))) [skolemisation 43,44]
55. ! [X0] : (((wise(X0) | brave(X0)) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 7]
56. ! [X0] : ((wise(X0) | brave(X0) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | (~wise(X0) & ~brave(X0)))) [flattening 55]
64. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~funny(john) | ~rich(john))) [nnf transformation 11]
65. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~funny(john) | ~rich(john)) [flattening 64]
66. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~funny(john) | ~rich(john)) [rectify 65]
67. ? [X1] : curious(X1) => curious(sK6) [choice axiom]
68. ((funny(john) & rich(john)) | ! [X0] : ~curious(X0)) & (curious(sK6) | ~funny(john) | ~rich(john)) [skolemisation 66,67]
75. ! [X0] : (((patient(X0) & ~funny(X0)) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | (~patient(X0) | funny(X0)))) [nnf transformation 14]
76. ! [X0] : (((patient(X0) & ~funny(X0)) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | ~patient(X0) | funny(X0))) [flattening 75]
100. ~old(susan) | ~brave(X1) | ~humble(X1) [cnf transformation 45]
105. old(X0) | ~quiet(X0) [cnf transformation 28]
106. old(X0) | quiet(X0) [cnf transformation 28]
116. ~old(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 31]
120. wise(X0) | brave(X0) | ~old(X0) [cnf transformation 56]
132. funny(john) | ~curious(X0) [cnf transformation 68]
141. ~funny(X0) | humble(X0) [cnf transformation 76]
163. curious(john) [cnf transformation 24]
194. 7 <=> old(susan) [avatar definition]
195. ~old(susan) <- (~7) [avatar component clause 194]
208. 10 <=> ! [X1] : (~brave(X1) | ~humble(X1)) [avatar definition]
209. ~humble(X1) | ~brave(X1) <- (10) [avatar component clause 208]
210. 10 | ~7 [avatar split clause 100,194,208]
217. old(X0) [subsumption resolution 105,106]
247. ~wise(X0) | ~funny(X0) [subsumption resolution 116,217]
248. wise(X0) | brave(X0) [subsumption resolution 120,217]
291. 27 <=> ! [X0] : ~curious(X0) [avatar definition]
292. ~curious(X0) <- (27) [avatar component clause 291]
294. 28 <=> funny(john) [avatar definition]
296. funny(john) <- (28) [avatar component clause 294]
297. 27 | 28 [avatar split clause 132,294,291]
330. 36 <=> humble(john) [avatar definition]
331. humble(john) <- (36) [avatar component clause 330]
334. 37 <=> brave(john) [avatar definition]
335. ~brave(john) <- (~37) [avatar component clause 334]
387. $false <- (~7) [subsumption resolution 195,217]
388. 7 [avatar contradiction clause 387]
389. $false <- (27) [resolution 292,163]
390. ~27 [avatar contradiction clause 389]
393. humble(john) <- (28) [resolution 141,296]
396. 36 | ~28 [avatar split clause 393,294,330]
397. ~brave(john) <- (10, 36) [resolution 209,331]
400. ~37 | ~10 | ~36 [avatar split clause 397,330,208,334]
414. ~funny(X0) | brave(X0) [resolution 248,247]
485. brave(john) <- (28) [resolution 414,296]
487. $false <- (28, ~37) [subsumption resolution 485,335]
488. ~28 | 37 [avatar contradiction clause 487]
491. $false [avatar sat refutation 210,297,388,390,396,400,488]
% SZS output end Proof for 5307473720263317479296579
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm is not creative or rich and vice versa. If mary is both humble and kind then susan is either calm or not old and vice versa. Everyone who is happy is either not happy or brave. If someone is both brave and happy then alice is either quiet or not old and vice versa. Everyone who is both not curious and creative is not humble. Everyone who is funny or not creative is both not old and kind. Everyone who is both old and happy is kind or old and vice versa. If someone is either funny or not calm then someone is patient and vice versa. If lucy is either strong or not old then someone is not happy. If someone is either not brave or happy then someone is not old and vice versa. Everyone who is either not generous or not quiet is either old or not curious and vice versa. Everyone who is either not calm or not strong is both creative and rich. If lucy is old then alice is not quiet or tall. If mary is not tall then alice is not generous or calm and vice versa. Everyone who is either happy or not brave is brave and vice versa. Paul is either not strong or kind. Someone is curious or not patient. Lucy is both not wise and humble. Someone is either not old or not patient. | Paul is funny. | contradiction | (![X]:(~calm(X)<=>(~creative(X)|rich(X))))&
(((humble(mary)&kind(mary)))<=>((calm(susan)<~>~old(susan))))&
(![X]:(happy(X)=>(~happy(X)<~>brave(X))))&
((?[X]:((brave(X)&happy(X))))<=>((quiet(alice)<~>~old(alice))))&
(![X]:((~curious(X)&creative(X))=>~humble(X)))&
(![X]:((funny(X)|~creative(X))=>(~old(X)&kind(X))))&
(![X]:((old(X)&happy(X))<=>(kind(X)|old(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>(?[X]:(patient(X))))&
(((strong(lucy)<~>~old(lucy)))=>(?[X]:(~happy(X))))&
((?[X]:((~brave(X)<~>happy(X))))<=>(?[X]:(~old(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(old(X)<~>~curious(X))))&
(![X]:((~calm(X)<~>~strong(X))=>(creative(X)&rich(X))))&
((old(lucy))=>((~quiet(alice)|tall(alice))))&
((~tall(mary))<=>((~generous(alice)|calm(alice))))&
(![X]:((happy(X)<~>~brave(X))<=>brave(X)))&
((~strong(paul)<~>kind(paul)))&
(?[X]:((curious(X)|~patient(X))))&
((~wise(lucy)&humble(lucy)))&
(?[X]:((~old(X)<~>~patient(X)))) | funny(paul) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6076402494074152333126541
% SZS output start Proof for 6076402494074152333126541
6. ! [X0] : ((~creative(X0) | funny(X0)) => (kind(X0) & ~old(X0))) [input p5]
7. ! [X0] : ((happy(X0) & old(X0)) <=> (old(X0) | kind(X0))) [input p6]
20. funny(paul) [input hypothesis]
27. ! [X0] : ((kind(X0) & ~old(X0)) | (creative(X0) & ~funny(X0))) [ennf transformation 6]
41. ! [X0] : (((happy(X0) & old(X0)) | (~old(X0) & ~kind(X0))) & ((old(X0) | kind(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 7]
42. ! [X0] : (((happy(X0) & old(X0)) | (~old(X0) & ~kind(X0))) & (old(X0) | kind(X0) | ~happy(X0) | ~old(X0))) [flattening 41]
85. ~funny(X0) | ~old(X0) [cnf transformation 27]
87. ~funny(X0) | kind(X0) [cnf transformation 27]
90. ~kind(X0) | old(X0) [cnf transformation 42]
130. funny(paul) [cnf transformation 20]
274. 29 <=> kind(paul) [avatar definition]
275. kind(paul) <- (29) [avatar component clause 274]
304. ~old(paul) [resolution 85,130]
306. kind(paul) [resolution 87,130]
309. 29 [avatar split clause 306,274]
311. old(paul) <- (29) [resolution 90,275]
313. $false <- (29) [subsumption resolution 311,304]
314. ~29 [avatar contradiction clause 313]
316. $false [avatar sat refutation 309,314]
% SZS output end Proof for 6076402494074152333126541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either funny or quiet and vice versa.
Everyone who is not brave or wise is both not calm and calm.
Everyone who is funny is either quiet or not kind and vice versa.
If someone is both not old and not calm then someone is both not wise and not brave.
If someone is happy then someone is not brave and vice versa.
Everyone who is both not generous and curious is both not tall and patient.
Everyone who is not generous is both brave and not rich and vice versa.
If someone is either not curious or curious then someone is calm.
If someone is not funny or funny then someone is either not rich or strong and vice versa.
Everyone who is both not wise and old is both not tall and happy and vice versa.
If someone is either not old or not wise then mary is rich or not brave.
Everyone who is either tall or not brave is kind or not funny and vice versa.
If fred is either not tall or wise then fred is kind and vice versa.
Everyone who is not calm or not funny is brave.
If lucy is either not funny or old then someone is quiet or generous and vice versa.
If someone is both rich and brave then someone is tall or calm and vice versa.
Someone is patient.
Mary is both not funny and not generous.
John is rich.
Someone is both not strong and not old.
Someone is not humble. | Fred is creative. | contradiction | (![X]:(~creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)|wise(X))=>(~calm(X)&calm(X))))&
(![X]:(funny(X)<=>(quiet(X)<~>~kind(X))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((~wise(X)&~brave(X)))))&
((?[X]:(happy(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)&curious(X))=>(~tall(X)&patient(X))))&
(![X]:(~generous(X)<=>(brave(X)&~rich(X))))&
((?[X]:((~curious(X)<~>curious(X))))=>(?[X]:(calm(X))))&
((?[X]:((~funny(X)|funny(X))))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~wise(X)&old(X))<=>(~tall(X)&happy(X))))&
((?[X]:((~old(X)<~>~wise(X))))=>((rich(mary)|~brave(mary))))&
(![X]:((tall(X)<~>~brave(X))<=>(kind(X)|~funny(X))))&
(((~tall(fred)<~>wise(fred)))<=>(kind(fred)))&
(![X]:((~calm(X)|~funny(X))=>brave(X)))&
(((~funny(lucy)<~>old(lucy)))<=>(?[X]:((quiet(X)|generous(X)))))&
((?[X]:((rich(X)&brave(X))))<=>(?[X]:((tall(X)|calm(X)))))&
(?[X]:(patient(X)))&
((~funny(mary)&~generous(mary)))&
(rich(john))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:(~humble(X))) | creative(fred) | [
"p0",
"p1",
"p2",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4382496955140805858321760
% SZS output start Proof for 4382496955140805858321760
1. ! [X0] : (~creative(X0) <=> (funny(X0) <~> quiet(X0))) [input p0]
2. ! [X0] : ((wise(X0) | ~brave(X0)) => (calm(X0) & ~calm(X0))) [input p1]
3. ! [X0] : (funny(X0) <=> (quiet(X0) <~> ~kind(X0))) [input p2]
12. ! [X0] : ((tall(X0) <~> ~brave(X0)) <=> (~funny(X0) | kind(X0))) [input p11]
13. (~tall(fred) <~> wise(fred)) <=> kind(fred) [input p12]
22. creative(fred) [input hypothesis]
28. ! [X0] : ((funny(X0) <~> quiet(X0)) => ~creative(X0)) [unused predicate definition removal 1]
32. ! [X0] : (~creative(X0) | (funny(X0) <=> quiet(X0))) [ennf transformation 28]
33. ! [X0] : ((calm(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) [ennf transformation 2]
41. ! [X0] : (~creative(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) [nnf transformation 32]
42. ! [X0] : ((funny(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~funny(X0))) [nnf transformation 3]
65. ! [X0] : ((((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | (funny(X0) & ~kind(X0))) & ((~funny(X0) | kind(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))))) [nnf transformation 12]
66. ! [X0] : ((((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | (funny(X0) & ~kind(X0))) & (~funny(X0) | kind(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))))) [flattening 65]
67. (((~wise(fred) | tall(fred)) & (wise(fred) | ~tall(fred))) | ~kind(fred)) & (kind(fred) | ((~tall(fred) | ~wise(fred)) & (wise(fred) | tall(fred)))) [nnf transformation 13]
79. ~funny(X0) | quiet(X0) | ~creative(X0) [cnf transformation 41]
80. ~quiet(X0) | funny(X0) | ~creative(X0) [cnf transformation 41]
81. ~calm(X0) | brave(X0) [cnf transformation 33]
82. ~calm(X0) | ~wise(X0) [cnf transformation 33]
83. calm(X0) | brave(X0) [cnf transformation 33]
84. ~wise(X0) | calm(X0) [cnf transformation 33]
86. ~quiet(X0) | kind(X0) | ~funny(X0) [cnf transformation 42]
88. kind(X0) | quiet(X0) | funny(X0) [cnf transformation 42]
113. ~brave(X0) | tall(X0) | ~kind(X0) [cnf transformation 66]
119. wise(fred) | ~tall(fred) | ~kind(fred) [cnf transformation 67]
139. creative(fred) [cnf transformation 22]
142. ~wise(X0) [subsumption resolution 82,84]
143. brave(X0) [subsumption resolution 81,83]
180. ~kind(X0) | tall(X0) [subsumption resolution 113,143]
182. ~tall(fred) | ~kind(fred) [subsumption resolution 119,142]
183. ~kind(fred) [subsumption resolution 182,180]
268. quiet(fred) | funny(fred) [resolution 88,183]
275. 22 <=> funny(fred) [avatar definition]
277. funny(fred) <- (22) [avatar component clause 275]
279. 23 <=> quiet(fred) [avatar definition]
281. quiet(fred) <- (23) [avatar component clause 279]
282. 22 | 23 [avatar split clause 268,279,275]
283. quiet(fred) | ~creative(fred) <- (22) [resolution 277,79]
284. quiet(fred) <- (22) [subsumption resolution 283,139]
285. 23 | ~22 [avatar split clause 284,275,279]
307. kind(fred) | ~funny(fred) <- (23) [resolution 281,86]
308. funny(fred) | ~creative(fred) <- (23) [resolution 281,80]
309. ~funny(fred) <- (23) [subsumption resolution 307,183]
312. funny(fred) <- (23) [subsumption resolution 308,139]
313. 22 | ~23 [avatar split clause 312,279,275]
314. ~22 | ~23 [avatar split clause 309,279,275]
315. $false [avatar sat refutation 282,285,313,314]
% SZS output end Proof for 4382496955140805858321760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not kind is not calm and vice versa.
Everyone who is both not brave and not quiet is happy or not funny and vice versa.
Everyone who is both strong and not tall is both not rich and calm.
Everyone who is calm or not curious is wise and vice versa.
If someone is not humble or not funny then someone is both not tall and brave.
If paul is either not wise or happy then fred is not funny or not old.
If someone is wise or not kind then someone is not patient or happy and vice versa.
If mary is both not strong and curious then someone is tall.
If lucy is either not wise or old then paul is both calm and quiet.
If someone is both humble and not tall then someone is not creative.
If susan is not funny or not patient then someone is quiet or strong and vice versa.
If paul is not brave or not curious then someone is both generous and not old and vice versa.
Everyone who is either humble or quiet is both patient and not happy.
Everyone who is not generous is not rich and vice versa.
Everyone who is both old and happy is either wise or not creative.
Everyone who is not tall or strong is either tall or wise and vice versa.
Someone is both not wise and not happy.
Someone is not strong or not patient.
Alice is not brave or not quiet.
Fred is both not strong and tall.
Mary is both humble and not tall.
Mary is wise or kind.
Someone is not humble or tall.
John is not wise. | Susan is not generous. | neutral | (![X]:((quiet(X)|~kind(X))<=>~calm(X)))&
(![X]:((~brave(X)&~quiet(X))<=>(happy(X)|~funny(X))))&
(![X]:((strong(X)&~tall(X))=>(~rich(X)&calm(X))))&
(![X]:((calm(X)|~curious(X))<=>wise(X)))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(((~wise(paul)<~>happy(paul)))=>((~funny(fred)|~old(fred))))&
((?[X]:((wise(X)|~kind(X))))<=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(mary)&curious(mary)))=>(?[X]:(tall(X))))&
(((~wise(lucy)<~>old(lucy)))=>((calm(paul)&quiet(paul))))&
((?[X]:((humble(X)&~tall(X))))=>(?[X]:(~creative(X))))&
(((~funny(susan)|~patient(susan)))<=>(?[X]:((quiet(X)|strong(X)))))&
(((~brave(paul)|~curious(paul)))<=>(?[X]:((generous(X)&~old(X)))))&
(![X]:((humble(X)<~>quiet(X))=>(patient(X)&~happy(X))))&
(![X]:(~generous(X)<=>~rich(X)))&
(![X]:((old(X)&happy(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)<~>wise(X))))&
(?[X]:((~wise(X)&~happy(X))))&
(?[X]:((~strong(X)|~patient(X))))&
((~brave(alice)|~quiet(alice)))&
((~strong(fred)&tall(fred)))&
((humble(mary)&~tall(mary)))&
((wise(mary)|kind(mary)))&
(?[X]:((~humble(X)|tall(X))))&
(~wise(john)) | ~generous(susan) | [] | null | 0 |
Everyone who is either rich or tall is either humble or rich.
Everyone who is patient is old or not strong.
Everyone who is both funny and not tall is either not kind or humble.
If susan is either not curious or patient then someone is not funny.
Everyone who is strong or not humble is not old.
If someone is both wise and rich then john is either patient or brave and vice versa.
Everyone who is brave or rich is either not tall or not curious and vice versa.
Everyone who is either humble or not tall is funny and vice versa.
Everyone who is funny or not funny is brave and vice versa.
Everyone who is both creative and not calm is not brave or not strong.
If lucy is both brave and humble then lucy is strong or patient.
Everyone who is brave or not funny is both strong and not funny.
If susan is both not old and curious then someone is kind or not wise and vice versa.
Everyone who is both creative and not generous is happy or not happy and vice versa.
Everyone who is not humble or rich is either wise or not creative.
Alice is not kind or creative.
Someone is not curious or curious.
Someone is not rich or tall.
Someone is either kind or not happy. | John is calm. | entailment | (![X]:((rich(X)<~>tall(X))=>(humble(X)<~>rich(X))))&
(![X]:(patient(X)=>(old(X)|~strong(X))))&
(![X]:((funny(X)&~tall(X))=>(~kind(X)<~>humble(X))))&
(((~curious(susan)<~>patient(susan)))=>(?[X]:(~funny(X))))&
(![X]:((strong(X)|~humble(X))=>~old(X)))&
((?[X]:((wise(X)&rich(X))))<=>((patient(john)<~>brave(john))))&
(![X]:((brave(X)|rich(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)<~>~tall(X))<=>funny(X)))&
(![X]:((funny(X)|~funny(X))<=>brave(X)))&
(![X]:((creative(X)&~calm(X))=>(~brave(X)|~strong(X))))&
(((brave(lucy)&humble(lucy)))=>((strong(lucy)|patient(lucy))))&
(![X]:((brave(X)|~funny(X))=>(strong(X)&~funny(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((creative(X)&~generous(X))<=>(happy(X)|~happy(X))))&
(![X]:((~humble(X)|rich(X))=>(wise(X)<~>~creative(X))))&
((~kind(alice)|creative(alice)))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((~rich(X)|tall(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | calm(john) | [
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 348825828232412104311429
% SZS output start Proof for 348825828232412104311429
9. ! [X0] : ((~funny(X0) | funny(X0)) <=> brave(X0)) [input p8]
10. ! [X0] : ((~calm(X0) & creative(X0)) => (~strong(X0) | ~brave(X0))) [input p9]
12. ! [X0] : ((~funny(X0) | brave(X0)) => (~funny(X0) & strong(X0))) [input p11]
14. ! [X0] : ((~generous(X0) & creative(X0)) <=> (~happy(X0) | happy(X0))) [input p13]
20. ~calm(john) [input hypothesis]
28. ! [X0] : ((~strong(X0) | ~brave(X0)) | (calm(X0) | ~creative(X0))) [ennf transformation 10]
29. ! [X0] : (~strong(X0) | ~brave(X0) | calm(X0) | ~creative(X0)) [flattening 28]
32. ! [X0] : ((~funny(X0) & strong(X0)) | (funny(X0) & ~brave(X0))) [ennf transformation 12]
46. ! [X0] : (((~funny(X0) | funny(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~funny(X0)))) [nnf transformation 9]
47. ! [X0] : ((~funny(X0) | funny(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~funny(X0)))) [flattening 46]
53. ! [X0] : (((~generous(X0) & creative(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (generous(X0) | ~creative(X0)))) [nnf transformation 14]
54. ! [X0] : (((~generous(X0) & creative(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | generous(X0) | ~creative(X0))) [flattening 53]
90. brave(X0) | ~funny(X0) [cnf transformation 47]
91. brave(X0) | funny(X0) [cnf transformation 47]
93. ~strong(X0) | ~brave(X0) | calm(X0) | ~creative(X0) [cnf transformation 29]
96. strong(X0) | funny(X0) [cnf transformation 32]
97. ~funny(X0) | ~brave(X0) [cnf transformation 32]
105. creative(X0) | ~happy(X0) [cnf transformation 54]
106. happy(X0) | creative(X0) [cnf transformation 54]
118. ~calm(john) [cnf transformation 20]
160. brave(X0) [subsumption resolution 90,91]
161. ~creative(X0) | calm(X0) | ~strong(X0) [subsumption resolution 93,160]
176. ~funny(X0) [subsumption resolution 97,160]
177. strong(X0) [subsumption resolution 96,176]
202. creative(X0) [subsumption resolution 105,106]
268. calm(X0) | ~strong(X0) [resolution 161,202]
269. calm(X0) [subsumption resolution 268,177]
270. $false [resolution 269,118]
% SZS output end Proof for 348825828232412104311429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not brave is both not creative and rich.
Everyone who is either humble or old is humble.
Everyone who is tall or not strong is not old or brave and vice versa.
Everyone who is happy or not rich is rich or curious and vice versa.
Everyone who is either not funny or not strong is both kind and not patient and vice versa.
Everyone who is not curious is both not funny and strong and vice versa.
If fred is kind or old then someone is not rich and vice versa.
Everyone who is both wise and rich is both not curious and happy.
Everyone who is both calm and tall is either not kind or not curious.
If fred is both tall and funny then someone is both curious and not kind.
If someone is not humble then paul is not tall and vice versa.
Everyone who is both kind and strong is not humble and vice versa.
Everyone who is wise is both humble and not happy and vice versa.
If alice is both tall and not happy then paul is strong or humble and vice versa.
If someone is funny then john is funny or brave and vice versa.
If someone is either quiet or calm then someone is both not happy and humble.
Lucy is either not kind or not old.
Lucy is both not creative and strong.
Lucy is not strong or not patient.
Lucy is either generous or strong.
Alice is not brave or not kind.
Susan is not quiet or humble.
Paul is either not rich or rich. | Alice is not tall. | contradiction | (![X]:((~wise(X)&~brave(X))=>(~creative(X)&rich(X))))&
(![X]:((humble(X)<~>old(X))=>humble(X)))&
(![X]:((tall(X)|~strong(X))<=>(~old(X)|brave(X))))&
(![X]:((happy(X)|~rich(X))<=>(rich(X)|curious(X))))&
(![X]:((~funny(X)<~>~strong(X))<=>(kind(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~funny(X)&strong(X))))&
(((kind(fred)|old(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&rich(X))=>(~curious(X)&happy(X))))&
(![X]:((calm(X)&tall(X))=>(~kind(X)<~>~curious(X))))&
(((tall(fred)&funny(fred)))=>(?[X]:((curious(X)&~kind(X)))))&
((?[X]:(~humble(X)))<=>(~tall(paul)))&
(![X]:((kind(X)&strong(X))<=>~humble(X)))&
(![X]:(wise(X)<=>(humble(X)&~happy(X))))&
(((tall(alice)&~happy(alice)))<=>((strong(paul)|humble(paul))))&
((?[X]:(funny(X)))<=>((funny(john)|brave(john))))&
((?[X]:((quiet(X)<~>calm(X))))=>(?[X]:((~happy(X)&humble(X)))))&
((~kind(lucy)<~>~old(lucy)))&
((~creative(lucy)&strong(lucy)))&
((~strong(lucy)|~patient(lucy)))&
((generous(lucy)<~>strong(lucy)))&
((~brave(alice)|~kind(alice)))&
((~quiet(susan)|humble(susan)))&
((~rich(paul)<~>rich(paul))) | ~tall(alice) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9058073160517189588282439
% SZS output start Proof for 9058073160517189588282439
12. ! [X0] : ((strong(X0) & kind(X0)) <=> ~humble(X0)) [input p11]
14. (~happy(alice) & tall(alice)) <=> (humble(paul) | strong(paul)) [input p13]
24. ~tall(alice) [input hypothesis]
59. ! [X0] : (((strong(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | (~strong(X0) | ~kind(X0)))) [nnf transformation 12]
60. ! [X0] : (((strong(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | ~strong(X0) | ~kind(X0))) [flattening 59]
63. ((~happy(alice) & tall(alice)) | (~humble(paul) & ~strong(paul))) & ((humble(paul) | strong(paul)) | (happy(alice) | ~tall(alice))) [nnf transformation 14]
64. ((~happy(alice) & tall(alice)) | (~humble(paul) & ~strong(paul))) & (humble(paul) | strong(paul) | happy(alice) | ~tall(alice)) [flattening 63]
110. strong(X0) | humble(X0) [cnf transformation 60]
115. tall(alice) | ~strong(paul) [cnf transformation 64]
116. tall(alice) | ~humble(paul) [cnf transformation 64]
136. ~tall(alice) [cnf transformation 24]
190. 12 <=> humble(paul) [avatar definition]
192. ~humble(paul) <- (~12) [avatar component clause 190]
199. 14 <=> strong(paul) [avatar definition]
201. ~strong(paul) <- (~14) [avatar component clause 199]
204. 15 <=> tall(alice) [avatar definition]
207. ~12 | 15 [avatar split clause 116,204,190]
208. ~14 | 15 [avatar split clause 115,204,199]
275. ~15 [avatar split clause 136,204]
277. humble(paul) <- (~14) [resolution 110,201]
278. $false <- (~12, ~14) [subsumption resolution 277,192]
279. 12 | 14 [avatar contradiction clause 278]
280. $false [avatar sat refutation 207,208,275,279]
% SZS output end Proof for 9058073160517189588282439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either curious or not patient and vice versa.
If someone is not brave then someone is both not creative and not old.
Everyone who is both not patient and not happy is either generous or curious and vice versa.
Everyone who is wise is either brave or not generous.
If mary is both not humble and not happy then lucy is curious and vice versa.
Everyone who is both not wise and not happy is kind and vice versa.
Everyone who is both not patient and curious is not tall and vice versa.
If someone is either tall or calm then john is funny or old.
If alice is both not quiet and happy then someone is both rich and strong and vice versa.
If mary is not funny or not humble then lucy is both not kind and not rich.
Everyone who is not brave is rich.
Everyone who is either not rich or tall is not funny or not happy.
If paul is not patient or funny then john is either not creative or not old and vice versa.
If john is both not humble and not patient then someone is not humble and vice versa.
If susan is not strong then someone is either not brave or not happy.
If someone is patient then someone is not old.
Someone is either patient or old.
Susan is old or not old.
Fred is quiet.
Someone is either not quiet or wise.
Someone is both generous and not humble.
Someone is either old or humble.
Fred is either not rich or not happy.
Someone is not brave. | John is not humble. | entailment | (![X]:(wise(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(generous(X)<~>curious(X))))&
(![X]:(wise(X)=>(brave(X)<~>~generous(X))))&
(((~humble(mary)&~happy(mary)))<=>(curious(lucy)))&
(![X]:((~wise(X)&~happy(X))<=>kind(X)))&
(![X]:((~patient(X)&curious(X))<=>~tall(X)))&
((?[X]:((tall(X)<~>calm(X))))=>((funny(john)|old(john))))&
(((~quiet(alice)&happy(alice)))<=>(?[X]:((rich(X)&strong(X)))))&
(((~funny(mary)|~humble(mary)))=>((~kind(lucy)&~rich(lucy))))&
(![X]:(~brave(X)=>rich(X)))&
(![X]:((~rich(X)<~>tall(X))=>(~funny(X)|~happy(X))))&
(((~patient(paul)|funny(paul)))<=>((~creative(john)<~>~old(john))))&
(((~humble(john)&~patient(john)))<=>(?[X]:(~humble(X))))&
((~strong(susan))=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:(patient(X)))=>(?[X]:(~old(X))))&
(?[X]:((patient(X)<~>old(X))))&
((old(susan)|~old(susan)))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((old(X)<~>humble(X))))&
((~rich(fred)<~>~happy(fred)))&
(?[X]:(~brave(X))) | ~humble(john) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3169413244859689628259118
% SZS output start Proof for 3169413244859689628259118
14. (~patient(john) & ~humble(john)) <=> ? [X0] : ~humble(X0) [input p13]
21. ? [X0] : (~humble(X0) & generous(X0)) [input p20]
25. humble(john) [input hypothesis]
61. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (patient(john) | humble(john))) [nnf transformation 14]
62. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | patient(john) | humble(john)) [flattening 61]
63. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | patient(john) | humble(john)) [rectify 62]
64. ? [X1] : ~humble(X1) => ~humble(sK2) [choice axiom]
65. ((~patient(john) & ~humble(john)) | ! [X0] : humble(X0)) & (~humble(sK2) | patient(john) | humble(john)) [skolemisation 63,64]
78. ? [X0] : (~humble(X0) & generous(X0)) => (~humble(sK7) & generous(sK7)) [choice axiom]
79. ~humble(sK7) & generous(sK7) [skolemisation 21,78]
127. ~humble(john) | humble(X0) [cnf transformation 65]
139. ~humble(sK7) [cnf transformation 79]
145. humble(john) [cnf transformation 25]
248. 22 <=> ! [X0] : humble(X0) [avatar definition]
249. humble(X0) <- (22) [avatar component clause 248]
256. 24 <=> humble(john) [avatar definition]
259. 22 | ~24 [avatar split clause 127,256,248]
327. 24 [avatar split clause 145,256]
330. $false <- (22) [resolution 249,139]
331. ~22 [avatar contradiction clause 330]
332. $false [avatar sat refutation 259,327,331]
% SZS output end Proof for 3169413244859689628259118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not patient is either not generous or creative. Everyone who is not kind or humble is wise and vice versa. If someone is both not rich and funny then someone is not tall or kind. If someone is brave then john is either happy or brave. If someone is both not rich and not patient then someone is either rich or not brave and vice versa. Everyone who is either tall or not generous is either not old or not tall. If someone is patient or not kind then someone is either kind or happy and vice versa. Everyone who is both happy and humble is curious and vice versa. If fred is funny then someone is either not curious or not creative and vice versa. If susan is either not happy or kind then someone is not old or calm. Everyone who is not kind is not old and vice versa. Everyone who is both not generous and not curious is kind or not brave and vice versa. If fred is not calm then someone is calm and vice versa. If someone is both not calm and not rich then lucy is funny or not curious. If someone is both happy and humble then paul is both not wise and not generous and vice versa. Everyone who is both not old and not quiet is tall or kind and vice versa. Someone is not happy. Paul is either not calm or happy. Someone is wise. Someone is either not strong or old. Paul is either not rich or not humble. | Susan is creative. | neutral | (![X]:((rich(X)<~>~patient(X))=>(~generous(X)<~>creative(X))))&
(![X]:((~kind(X)|humble(X))<=>wise(X)))&
((?[X]:((~rich(X)&funny(X))))=>(?[X]:((~tall(X)|kind(X)))))&
((?[X]:(brave(X)))=>((happy(john)<~>brave(john))))&
((?[X]:((~rich(X)&~patient(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((tall(X)<~>~generous(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((happy(X)&humble(X))<=>curious(X)))&
((funny(fred))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
(((~happy(susan)<~>kind(susan)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:(~kind(X)<=>~old(X)))&
(![X]:((~generous(X)&~curious(X))<=>(kind(X)|~brave(X))))&
((~calm(fred))<=>(?[X]:(calm(X))))&
((?[X]:((~calm(X)&~rich(X))))=>((funny(lucy)|~curious(lucy))))&
((?[X]:((happy(X)&humble(X))))<=>((~wise(paul)&~generous(paul))))&
(![X]:((~old(X)&~quiet(X))<=>(tall(X)|kind(X))))&
(?[X]:(~happy(X)))&
((~calm(paul)<~>happy(paul)))&
(?[X]:(wise(X)))&
(?[X]:((~strong(X)<~>old(X))))&
((~rich(paul)<~>~humble(paul))) | creative(susan) | [] | null | 0 |
If john is not strong or not kind then someone is either tall or not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
If someone is not old or happy then lucy is either not creative or not wise and vice versa.
Everyone who is either funny or tall is strong.
Alice is either not curious or brave.
John is either not quiet or not creative.
Alice is either creative or not wise.
Someone is either not calm or not wise.
Someone is both not curious and brave.
Someone is either kind or not kind.
Lucy is brave. | Mary is not funny. | neutral | (((~strong(john)|~kind(john)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
((?[X]:((~old(X)|happy(X))))<=>((~creative(lucy)<~>~wise(lucy))))&
(![X]:((funny(X)<~>tall(X))=>strong(X)))&
((~curious(alice)<~>brave(alice)))&
((~quiet(john)<~>~creative(john)))&
((creative(alice)<~>~wise(alice)))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(brave(lucy)) | ~funny(mary) | [] | null | 0 |
If someone is either not old or not curious then someone is not happy and vice versa. If someone is not rich then alice is kind or not creative and vice versa. If someone is creative then fred is happy. Everyone who is brave or curious is not curious or not wise. Everyone who is either not rich or generous is curious or not happy. If someone is both tall and patient then someone is rich or not happy. If someone is strong or patient then someone is both not calm and wise and vice versa. If paul is not humble or creative then fred is both not calm and not wise and vice versa. Everyone who is funny is both funny and not patient. If john is either not brave or not funny then susan is humble or old. Everyone who is tall or not happy is funny and vice versa. Everyone who is either happy or old is both not old and not humble. Everyone who is not strong is both not creative and happy and vice versa. Everyone who is either happy or not quiet is patient or tall. Everyone who is both wise and not patient is creative and vice versa. Everyone who is both brave and not old is either old or not funny. Someone is not strong or generous. Lucy is both not funny and generous. Alice is quiet or not patient. Alice is not kind or rich. Someone is either not strong or curious. Someone is not rich. Someone is either not happy or not quiet. Mary is either rich or not generous. | Lucy is tall. | contradiction | ((?[X]:((~old(X)<~>~curious(X))))<=>(?[X]:(~happy(X))))&
((?[X]:(~rich(X)))<=>((kind(alice)|~creative(alice))))&
((?[X]:(creative(X)))=>(happy(fred)))&
(![X]:((brave(X)|curious(X))=>(~curious(X)|~wise(X))))&
(![X]:((~rich(X)<~>generous(X))=>(curious(X)|~happy(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:((strong(X)|patient(X))))<=>(?[X]:((~calm(X)&wise(X)))))&
(((~humble(paul)|creative(paul)))<=>((~calm(fred)&~wise(fred))))&
(![X]:(funny(X)=>(funny(X)&~patient(X))))&
(((~brave(john)<~>~funny(john)))=>((humble(susan)|old(susan))))&
(![X]:((tall(X)|~happy(X))<=>funny(X)))&
(![X]:((happy(X)<~>old(X))=>(~old(X)&~humble(X))))&
(![X]:(~strong(X)<=>(~creative(X)&happy(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(patient(X)|tall(X))))&
(![X]:((wise(X)&~patient(X))<=>creative(X)))&
(![X]:((brave(X)&~old(X))=>(old(X)<~>~funny(X))))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(lucy)&generous(lucy)))&
((quiet(alice)|~patient(alice)))&
((~kind(alice)|rich(alice)))&
(?[X]:((~strong(X)<~>curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((rich(mary)<~>~generous(mary))) | tall(lucy) | [
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6461927811573536824579422
% SZS output start Proof for 6461927811573536824579422
11. ! [X0] : ((~happy(X0) | tall(X0)) <=> funny(X0)) [input p10]
18. generous(lucy) & ~funny(lucy) [input p17]
25. tall(lucy) [input hypothesis]
65. ! [X0] : (((~happy(X0) | tall(X0)) | ~funny(X0)) & (funny(X0) | (happy(X0) & ~tall(X0)))) [nnf transformation 11]
66. ! [X0] : ((~happy(X0) | tall(X0) | ~funny(X0)) & (funny(X0) | (happy(X0) & ~tall(X0)))) [flattening 65]
112. ~tall(X0) | funny(X0) [cnf transformation 66]
130. ~funny(lucy) [cnf transformation 18]
141. tall(lucy) [cnf transformation 25]
330. funny(lucy) [resolution 112,141]
331. $false [subsumption resolution 330,130]
% SZS output end Proof for 6461927811573536824579422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either strong or not curious and vice versa.
If alice is quiet then alice is not tall or tall and vice versa.
If someone is either funny or tall then someone is both not wise and not brave.
Everyone who is either not quiet or not calm is both old and not creative and vice versa.
If lucy is both not quiet and not happy then someone is not rich and vice versa.
Everyone who is either brave or not happy is creative.
Everyone who is either not wise or funny is either curious or kind and vice versa.
Everyone who is patient or happy is creative or brave and vice versa.
Everyone who is old or calm is funny or curious.
Everyone who is not brave is either strong or not patient.
If paul is either not quiet or old then lucy is quiet and vice versa.
Everyone who is both not kind and not humble is not kind or generous and vice versa.
If someone is wise or humble then someone is either not calm or not wise and vice versa.
Everyone who is wise or not generous is generous or kind and vice versa.
Everyone who is not patient or not calm is not kind or humble.
If someone is curious or not kind then paul is not calm.
Paul is both not rich and funny.
Someone is either not generous or not happy.
Lucy is not generous or not kind.
Someone is not brave or not generous.
Someone is both old and not generous.
Someone is not quiet or not wise.
Paul is either not curious or not wise.
John is not generous or brave. | John is not funny. | neutral | (![X]:(~happy(X)<=>(strong(X)<~>~curious(X))))&
((quiet(alice))<=>((~tall(alice)|tall(alice))))&
((?[X]:((funny(X)<~>tall(X))))=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(old(X)&~creative(X))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:(~rich(X))))&
(![X]:((brave(X)<~>~happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>funny(X))<=>(curious(X)<~>kind(X))))&
(![X]:((patient(X)|happy(X))<=>(creative(X)|brave(X))))&
(![X]:((old(X)|calm(X))=>(funny(X)|curious(X))))&
(![X]:(~brave(X)=>(strong(X)<~>~patient(X))))&
(((~quiet(paul)<~>old(paul)))<=>(quiet(lucy)))&
(![X]:((~kind(X)&~humble(X))<=>(~kind(X)|generous(X))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(![X]:((wise(X)|~generous(X))<=>(generous(X)|kind(X))))&
(![X]:((~patient(X)|~calm(X))=>(~kind(X)|humble(X))))&
((?[X]:((curious(X)|~kind(X))))=>(~calm(paul)))&
((~rich(paul)&funny(paul)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((~generous(lucy)|~kind(lucy)))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((old(X)&~generous(X))))&
(?[X]:((~quiet(X)|~wise(X))))&
((~curious(paul)<~>~wise(paul)))&
((~generous(john)|brave(john))) | ~funny(john) | [] | null | 0 |
Everyone who is funny is not creative or not kind and vice versa.
Everyone who is either strong or not wise is both not patient and old and vice versa.
If mary is both generous and not brave then paul is not calm or not tall and vice versa.
Everyone who is both not funny and creative is either patient or old.
If fred is quiet then john is not happy and vice versa.
Everyone who is either not calm or wise is tall.
Everyone who is either not generous or tall is not kind.
Everyone who is both generous and not quiet is either generous or not funny.
If mary is both quiet and humble then alice is both not humble and happy and vice versa.
Everyone who is either not patient or happy is not creative.
If alice is both not tall and creative then someone is creative or calm.
Everyone who is either wise or creative is quiet or not creative and vice versa.
Everyone who is either wise or curious is either happy or not funny and vice versa.
If someone is not old then paul is both not patient and not wise and vice versa.
If someone is both not happy and humble then someone is not funny and vice versa.
If john is not kind or tall then someone is both not curious and humble.
Susan is either not curious or not strong.
Someone is not calm or old.
Alice is not rich.
Someone is patient or not kind.
Lucy is both not patient and happy.
John is both not funny and wise.
Someone is either brave or not creative.
Mary is both not patient and not old. | Lucy is not creative. | neutral | (![X]:(funny(X)<=>(~creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~wise(X))<=>(~patient(X)&old(X))))&
(((generous(mary)&~brave(mary)))<=>((~calm(paul)|~tall(paul))))&
(![X]:((~funny(X)&creative(X))=>(patient(X)<~>old(X))))&
((quiet(fred))<=>(~happy(john)))&
(![X]:((~calm(X)<~>wise(X))=>tall(X)))&
(![X]:((~generous(X)<~>tall(X))=>~kind(X)))&
(![X]:((generous(X)&~quiet(X))=>(generous(X)<~>~funny(X))))&
(((quiet(mary)&humble(mary)))<=>((~humble(alice)&happy(alice))))&
(![X]:((~patient(X)<~>happy(X))=>~creative(X)))&
(((~tall(alice)&creative(alice)))=>(?[X]:((creative(X)|calm(X)))))&
(![X]:((wise(X)<~>creative(X))<=>(quiet(X)|~creative(X))))&
(![X]:((wise(X)<~>curious(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:(~old(X)))<=>((~patient(paul)&~wise(paul))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:(~funny(X))))&
(((~kind(john)|tall(john)))=>(?[X]:((~curious(X)&humble(X)))))&
((~curious(susan)<~>~strong(susan)))&
(?[X]:((~calm(X)|old(X))))&
(~rich(alice))&
(?[X]:((patient(X)|~kind(X))))&
((~patient(lucy)&happy(lucy)))&
((~funny(john)&wise(john)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(mary)&~old(mary))) | ~creative(lucy) | [] | null | 0 |
Everyone who is generous is not humble. Everyone who is not kind or not tall is not patient or not calm. If john is both not creative and humble then lucy is curious and vice versa. Everyone who is both wise and old is happy. Everyone who is not creative is either not quiet or not old. Everyone who is both calm and brave is both not strong and funny. If fred is old or wise then someone is both not wise and not patient. If someone is not wise then john is creative and vice versa. Everyone who is both not creative and tall is both wise and not kind. If lucy is wise then someone is not patient or generous. If fred is both funny and not generous then lucy is both strong and not quiet and vice versa. If someone is either happy or not brave then someone is not humble and vice versa. Everyone who is either generous or not happy is either calm or not brave. If paul is both wise and tall then paul is both funny and not kind. Everyone who is quiet or old is not kind. Everyone who is either not generous or funny is either not creative or not kind and vice versa. Someone is either brave or curious. Someone is either curious or tall. Fred is not funny. Alice is not patient. Someone is either not brave or quiet. Alice is not wise or not quiet. Someone is calm. | Alice is not quiet. | neutral | (![X]:(generous(X)=>~humble(X)))&
(![X]:((~kind(X)|~tall(X))=>(~patient(X)|~calm(X))))&
(((~creative(john)&humble(john)))<=>(curious(lucy)))&
(![X]:((wise(X)&old(X))=>happy(X)))&
(![X]:(~creative(X)=>(~quiet(X)<~>~old(X))))&
(![X]:((calm(X)&brave(X))=>(~strong(X)&funny(X))))&
(((old(fred)|wise(fred)))=>(?[X]:((~wise(X)&~patient(X)))))&
((?[X]:(~wise(X)))<=>(creative(john)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&~kind(X))))&
((wise(lucy))=>(?[X]:((~patient(X)|generous(X)))))&
(((funny(fred)&~generous(fred)))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:(~humble(X))))&
(![X]:((generous(X)<~>~happy(X))=>(calm(X)<~>~brave(X))))&
(((wise(paul)&tall(paul)))=>((funny(paul)&~kind(paul))))&
(![X]:((quiet(X)|old(X))=>~kind(X)))&
(![X]:((~generous(X)<~>funny(X))<=>(~creative(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(~funny(fred))&
(~patient(alice))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~wise(alice)|~quiet(alice)))&
(?[X]:(calm(X))) | ~quiet(alice) | [] | null | 0 |
Everyone who is both quiet and not happy is rich or not kind and vice versa. If fred is either not curious or rich then someone is both not old and not funny and vice versa. Everyone who is both happy and not tall is both brave and not wise. Everyone who is not old is creative or not funny and vice versa. If someone is not quiet then john is either not strong or not old. Everyone who is either not quiet or not funny is not strong. Everyone who is funny or strong is patient and vice versa. Everyone who is either not creative or curious is not strong. If someone is both humble and calm then someone is tall or not quiet and vice versa. If susan is either old or not old then someone is quiet or kind and vice versa. Everyone who is not old is happy and vice versa. If susan is both not quiet and not brave then someone is both not calm and not brave and vice versa. If someone is both strong and wise then someone is not curious and vice versa. If someone is either brave or old then mary is rich and vice versa. Everyone who is either not strong or not patient is happy and vice versa. Everyone who is not wise or old is either quiet or funny. Someone is patient or not curious. Lucy is funny. Someone is not happy or not old. Someone is either not strong or not patient. Someone is either generous or creative. | Mary is tall. | entailment | (![X]:((quiet(X)&~happy(X))<=>(rich(X)|~kind(X))))&
(((~curious(fred)<~>rich(fred)))<=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((happy(X)&~tall(X))=>(brave(X)&~wise(X))))&
(![X]:(~old(X)<=>(creative(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>((~strong(john)<~>~old(john))))&
(![X]:((~quiet(X)<~>~funny(X))=>~strong(X)))&
(![X]:((funny(X)|strong(X))<=>patient(X)))&
(![X]:((~creative(X)<~>curious(X))=>~strong(X)))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:((tall(X)|~quiet(X)))))&
(((old(susan)<~>~old(susan)))<=>(?[X]:((quiet(X)|kind(X)))))&
(![X]:(~old(X)<=>happy(X)))&
(((~quiet(susan)&~brave(susan)))<=>(?[X]:((~calm(X)&~brave(X)))))&
((?[X]:((strong(X)&wise(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)<~>old(X))))<=>(rich(mary)))&
(![X]:((~strong(X)<~>~patient(X))<=>happy(X)))&
(![X]:((~wise(X)|old(X))=>(quiet(X)<~>funny(X))))&
(?[X]:((patient(X)|~curious(X))))&
(funny(lucy))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((generous(X)<~>creative(X)))) | tall(mary) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6527826999239613545950491
% SZS output start Proof for 6527826999239613545950491
1. ! [X0] : ((~happy(X0) & quiet(X0)) <=> (~kind(X0) | rich(X0))) [input p0]
2. (~curious(fred) <~> rich(fred)) <=> ? [X0] : (~funny(X0) & ~old(X0)) [input p1]
3. ! [X0] : ((~tall(X0) & happy(X0)) => (~wise(X0) & brave(X0))) [input p2]
4. ! [X0] : (~old(X0) <=> (~funny(X0) | creative(X0))) [input p3]
5. ? [X0] : ~quiet(X0) => (~strong(john) <~> ~old(john)) [input p4]
7. ! [X0] : ((strong(X0) | funny(X0)) <=> patient(X0)) [input p6]
11. ! [X0] : (~old(X0) <=> happy(X0)) [input p10]
13. ? [X0] : (wise(X0) & strong(X0)) <=> ? [X0] : ~curious(X0) [input p12]
15. ! [X0] : ((~strong(X0) <~> ~patient(X0)) <=> happy(X0)) [input p14]
16. ! [X0] : ((old(X0) | ~wise(X0)) => (quiet(X0) <~> funny(X0))) [input p15]
22. ~tall(mary) [input hypothesis]
24. ? [X0] : (wise(X0) & strong(X0)) <=> ? [X1] : ~curious(X1) [rectify 13]
25. ! [X0] : ((~wise(X0) & brave(X0)) | (tall(X0) | ~happy(X0))) [ennf transformation 3]
26. ! [X0] : ((~wise(X0) & brave(X0)) | tall(X0) | ~happy(X0)) [flattening 25]
27. (~strong(john) <~> ~old(john)) | ! [X0] : quiet(X0) [ennf transformation 5]
30. ! [X0] : ((quiet(X0) <~> funny(X0)) | (~old(X0) & wise(X0))) [ennf transformation 16]
31. ! [X0] : (((~happy(X0) & quiet(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (happy(X0) | ~quiet(X0)))) [nnf transformation 1]
32. ! [X0] : (((~happy(X0) & quiet(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | happy(X0) | ~quiet(X0))) [flattening 31]
33. (((~rich(fred) | curious(fred)) & (rich(fred) | ~curious(fred))) | ! [X0] : (funny(X0) | old(X0))) & (? [X0] : (~funny(X0) & ~old(X0)) | ((~curious(fred) | ~rich(fred)) & (rich(fred) | curious(fred)))) [nnf transformation 2]
34. (((~rich(fred) | curious(fred)) & (rich(fred) | ~curious(fred))) | ! [X0] : (funny(X0) | old(X0))) & (? [X1] : (~funny(X1) & ~old(X1)) | ((~curious(fred) | ~rich(fred)) & (rich(fred) | curious(fred)))) [rectify 33]
35. ? [X1] : (~funny(X1) & ~old(X1)) => (~funny(sK0) & ~old(sK0)) [choice axiom]
36. (((~rich(fred) | curious(fred)) & (rich(fred) | ~curious(fred))) | ! [X0] : (funny(X0) | old(X0))) & ((~funny(sK0) & ~old(sK0)) | ((~curious(fred) | ~rich(fred)) & (rich(fred) | curious(fred)))) [skolemisation 34,35]
37. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & ((~funny(X0) | creative(X0)) | old(X0))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & (~funny(X0) | creative(X0) | old(X0))) [flattening 37]
39. ((old(john) | strong(john)) & (~old(john) | ~strong(john))) | ! [X0] : quiet(X0) [nnf transformation 27]
41. ! [X0] : (((strong(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((strong(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [flattening 41]
53. ! [X0] : ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))) [nnf transformation 11]
59. (? [X0] : (wise(X0) & strong(X0)) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : (~wise(X0) | ~strong(X0))) [nnf transformation 24]
60. (? [X0] : (wise(X0) & strong(X0)) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : (~wise(X3) | ~strong(X3))) [rectify 59]
61. ? [X0] : (wise(X0) & strong(X0)) => (wise(sK5) & strong(sK5)) [choice axiom]
62. ? [X2] : ~curious(X2) => ~curious(sK6) [choice axiom]
63. ((wise(sK5) & strong(sK5)) | ! [X1] : curious(X1)) & (~curious(sK6) | ! [X3] : (~wise(X3) | ~strong(X3))) [skolemisation 60,62,61]
68. ! [X0] : ((((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~happy(X0)) & (happy(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))))) [nnf transformation 15]
69. ! [X0] : (((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | (~old(X0) & wise(X0))) [nnf transformation 30]
83. ~rich(X0) | ~happy(X0) [cnf transformation 32]
89. rich(fred) | ~curious(fred) | funny(X0) | old(X0) [cnf transformation 36]
92. ~wise(X0) | tall(X0) | ~happy(X0) [cnf transformation 26]
95. ~old(X0) | funny(X0) [cnf transformation 38]
96. ~old(john) | ~strong(john) | quiet(X0) [cnf transformation 39]
97. old(john) | strong(john) | quiet(X0) [cnf transformation 39]
100. ~funny(X0) | patient(X0) [cnf transformation 42]
101. ~strong(X0) | patient(X0) [cnf transformation 42]
116. old(X0) | happy(X0) [cnf transformation 53]
117. ~old(X0) | ~happy(X0) [cnf transformation 53]
123. strong(sK5) | curious(X1) [cnf transformation 63]
129. ~patient(X0) | happy(X0) | strong(X0) [cnf transformation 68]
131. ~patient(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 68]
132. patient(X0) | strong(X0) | ~happy(X0) [cnf transformation 68]
135. ~funny(X0) | ~quiet(X0) | wise(X0) [cnf transformation 69]
136. ~funny(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 69]
144. ~tall(mary) [cnf transformation 22]
148. 1 <=> ! [X0] : (funny(X0) | old(X0)) [avatar definition]
149. funny(X0) | old(X0) <- (1) [avatar component clause 148]
151. 2 <=> curious(fred) [avatar definition]
152. ~curious(fred) <- (~2) [avatar component clause 151]
155. 3 <=> rich(fred) [avatar definition]
156. rich(fred) <- (3) [avatar component clause 155]
159. 1 | ~2 | 3 [avatar split clause 89,155,151,148]
173. 6 <=> ! [X0] : quiet(X0) [avatar definition]
174. quiet(X0) <- (6) [avatar component clause 173]
176. 7 <=> strong(john) [avatar definition]
177. ~strong(john) <- (~7) [avatar component clause 176]
178. strong(john) <- (7) [avatar component clause 176]
180. 8 <=> old(john) [avatar definition]
181. ~old(john) <- (~8) [avatar component clause 180]
182. old(john) <- (8) [avatar component clause 180]
183. 6 | 7 | 8 [avatar split clause 97,180,176,173]
184. 6 | ~7 | ~8 [avatar split clause 96,180,176,173]
236. 20 <=> ! [X1] : curious(X1) [avatar definition]
237. curious(X1) <- (20) [avatar component clause 236]
244. 22 <=> strong(sK5) [avatar definition]
246. strong(sK5) <- (22) [avatar component clause 244]
247. 20 | 22 [avatar split clause 123,244,236]
278. ~happy(X0) | patient(X0) [subsumption resolution 132,101]
279. ~strong(X0) | ~happy(X0) [subsumption resolution 131,278]
280. ~old(X0) | ~quiet(X0) [subsumption resolution 136,95]
302. $false <- (~2, 20) [subsumption resolution 152,237]
303. 2 | ~20 [avatar contradiction clause 302]
308. funny(john) <- (8) [resolution 95,182]
310. patient(john) <- (8) [resolution 100,308]
316. ~happy(john) <- (8) [resolution 117,182]
323. ~quiet(X0) | happy(X0) [resolution 280,116]
391. ~happy(sK5) <- (22) [resolution 246,279]
397. happy(john) | strong(john) <- (8) [resolution 129,310]
400. strong(john) <- (8) [subsumption resolution 397,316]
401. $false <- (~7, 8) [subsumption resolution 400,177]
402. 7 | ~8 [avatar contradiction clause 401]
409. ~happy(john) <- (7) [resolution 178,279]
431. happy(john) <- (~8) [resolution 181,116]
432. $false <- (7, ~8) [subsumption resolution 431,409]
433. ~7 | 8 [avatar contradiction clause 432]
496. happy(X0) <- (6) [resolution 323,174]
549. $false <- (6, 22) [subsumption resolution 391,496]
550. ~6 | ~22 [avatar contradiction clause 549]
561. funny(X0) <- (1) [subsumption resolution 149,95]
573. ~quiet(X0) | wise(X0) <- (1) [resolution 561,135]
577. wise(X0) <- (1, 6) [subsumption resolution 573,174]
578. tall(X0) | ~happy(X0) <- (1, 6) [resolution 577,92]
579. tall(X0) <- (1, 6) [subsumption resolution 578,496]
627. $false <- (1, 6) [resolution 579,144]
628. ~1 | ~6 [avatar contradiction clause 627]
629. ~happy(fred) <- (3) [resolution 156,83]
631. $false <- (3, 6) [subsumption resolution 629,496]
632. ~3 | ~6 [avatar contradiction clause 631]
633. $false [avatar sat refutation 159,183,184,247,303,402,433,550,628,632]
% SZS output end Proof for 6527826999239613545950491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not calm is not old. Everyone who is both old and rich is both not curious and rich and vice versa. If john is both not patient and strong then someone is not tall. If someone is not quiet then someone is not calm or not old and vice versa. Everyone who is not generous or not calm is either not humble or patient. If mary is happy or not calm then lucy is not kind or not happy. Everyone who is wise or not generous is both generous and not tall and vice versa. Everyone who is not patient is curious. Everyone who is not brave is not curious or not old and vice versa. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. If someone is both brave and creative then someone is both patient and not old and vice versa. Everyone who is both rich and not happy is rich. Everyone who is funny or not generous is kind and vice versa. Someone is humble. Fred is not kind. Someone is generous or curious. Someone is both strong and not creative. Someone is both funny and patient. Someone is quiet. | John is not tall. | neutral | (![X]:((curious(X)&~calm(X))=>~old(X)))&
(![X]:((old(X)&rich(X))<=>(~curious(X)&rich(X))))&
(((~patient(john)&strong(john)))=>(?[X]:(~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|~old(X)))))&
(![X]:((~generous(X)|~calm(X))=>(~humble(X)<~>patient(X))))&
(((happy(mary)|~calm(mary)))=>((~kind(lucy)|~happy(lucy))))&
(![X]:((wise(X)|~generous(X))<=>(generous(X)&~tall(X))))&
(![X]:(~patient(X)=>curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(![X]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~happy(X))=>rich(X)))&
(![X]:((funny(X)|~generous(X))<=>kind(X)))&
(?[X]:(humble(X)))&
(~kind(fred))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:(quiet(X))) | ~tall(john) | [] | null | 0 |
If lucy is both not patient and not tall then someone is wise and vice versa.
Everyone who is either not calm or not creative is both not strong and not creative.
If someone is both calm and old then alice is either not patient or not creative.
Everyone who is both funny and patient is not strong.
If paul is not strong then someone is both not tall and rich and vice versa.
If john is calm or not patient then fred is both not kind and not rich.
Everyone who is either curious or not calm is both not generous and not brave.
If someone is not brave or brave then lucy is either curious or creative.
If someone is either not patient or creative then someone is both strong and not wise.
If susan is brave or curious then someone is either not brave or not quiet.
Everyone who is either generous or not tall is either not brave or funny.
Everyone who is both funny and strong is both not tall and humble.
Everyone who is both not humble and humble is not happy or generous and vice versa.
Everyone who is both not creative and not wise is both not quiet and not curious.
If john is either not tall or not old then susan is both rich and happy.
Everyone who is either not happy or happy is brave.
Someone is either not wise or happy.
Susan is both not generous and not creative.
Susan is either brave or creative.
Mary is not brave or not curious.
Paul is not curious.
Susan is not generous or not wise.
Someone is not creative or strong.
Someone is humble. | Lucy is not tall. | entailment | (((~patient(lucy)&~tall(lucy)))<=>(?[X]:(wise(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(~strong(X)&~creative(X))))&
((?[X]:((calm(X)&old(X))))=>((~patient(alice)<~>~creative(alice))))&
(![X]:((funny(X)&patient(X))=>~strong(X)))&
((~strong(paul))<=>(?[X]:((~tall(X)&rich(X)))))&
(((calm(john)|~patient(john)))=>((~kind(fred)&~rich(fred))))&
(![X]:((curious(X)<~>~calm(X))=>(~generous(X)&~brave(X))))&
((?[X]:((~brave(X)|brave(X))))=>((curious(lucy)<~>creative(lucy))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((strong(X)&~wise(X)))))&
(((brave(susan)|curious(susan)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~brave(X)<~>funny(X))))&
(![X]:((funny(X)&strong(X))=>(~tall(X)&humble(X))))&
(![X]:((~humble(X)&humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((~creative(X)&~wise(X))=>(~quiet(X)&~curious(X))))&
(((~tall(john)<~>~old(john)))=>((rich(susan)&happy(susan))))&
(![X]:((~happy(X)<~>happy(X))=>brave(X)))&
(?[X]:((~wise(X)<~>happy(X))))&
((~generous(susan)&~creative(susan)))&
((brave(susan)<~>creative(susan)))&
((~brave(mary)|~curious(mary)))&
(~curious(paul))&
((~generous(susan)|~wise(susan)))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(humble(X))) | ~tall(lucy) | [
"p0",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6749957597650090928914775
% SZS output start Proof for 6749957597650090928914775
1. (~tall(lucy) & ~patient(lucy)) <=> ? [X0] : wise(X0) [input p0]
13. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (generous(X0) | ~happy(X0))) [input p12]
17. ? [X0] : (~wise(X0) <~> happy(X0)) [input p16]
25. tall(lucy) [input hypothesis]
44. ((~tall(lucy) & ~patient(lucy)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (tall(lucy) | patient(lucy))) [nnf transformation 1]
45. ((~tall(lucy) & ~patient(lucy)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | tall(lucy) | patient(lucy)) [flattening 44]
46. ((~tall(lucy) & ~patient(lucy)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | tall(lucy) | patient(lucy)) [rectify 45]
47. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
48. ((~tall(lucy) & ~patient(lucy)) | ! [X0] : ~wise(X0)) & (wise(sK0) | tall(lucy) | patient(lucy)) [skolemisation 46,47]
65. ! [X0] : (((humble(X0) & ~humble(X0)) | (~generous(X0) & happy(X0))) & ((generous(X0) | ~happy(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 13]
66. ! [X0] : (((humble(X0) & ~humble(X0)) | (~generous(X0) & happy(X0))) & (generous(X0) | ~happy(X0) | ~humble(X0) | humble(X0))) [flattening 65]
69. ? [X0] : ((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) [nnf transformation 17]
70. ? [X0] : ((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) => ((~happy(sK4) | wise(sK4)) & (happy(sK4) | ~wise(sK4))) [choice axiom]
71. (~happy(sK4) | wise(sK4)) & (happy(sK4) | ~wise(sK4)) [skolemisation 69,70]
79. ~tall(lucy) | ~wise(X0) [cnf transformation 48]
115. ~humble(X0) | happy(X0) [cnf transformation 66]
117. humble(X0) | happy(X0) [cnf transformation 66]
128. ~happy(sK4) | wise(sK4) [cnf transformation 71]
138. tall(lucy) [cnf transformation 25]
143. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
144. ~wise(X0) <- (1) [avatar component clause 143]
146. 2 <=> tall(lucy) [avatar definition]
149. 1 | ~2 [avatar split clause 79,146,143]
262. happy(X0) [subsumption resolution 115,117]
279. wise(sK4) [subsumption resolution 128,262]
300. 2 [avatar split clause 138,146]
303. $false <- (1) [resolution 279,144]
304. ~1 [avatar contradiction clause 303]
305. $false [avatar sat refutation 149,300,304]
% SZS output end Proof for 6749957597650090928914775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not tall is brave and vice versa.
Everyone who is both calm and generous is strong or not brave.
If someone is both not funny and not happy then paul is both not patient and not creative and vice versa.
If someone is either brave or not brave then john is both not tall and not old and vice versa.
Everyone who is either not wise or not curious is either creative or not funny.
Everyone who is not curious or not rich is old and vice versa.
Everyone who is either not creative or creative is not curious or humble.
Everyone who is calm is either kind or not quiet and vice versa.
Everyone who is both strong and not happy is either not calm or not brave.
Everyone who is both funny and not rich is either generous or patient and vice versa.
If john is rich then someone is both not curious and not funny.
Everyone who is not quiet is not patient or wise and vice versa.
Everyone who is quiet or not rich is both quiet and not quiet and vice versa.
If someone is not brave then john is both creative and brave.
If paul is both curious and tall then lucy is either curious or calm.
If fred is either not patient or not curious then someone is not old and vice versa.
Susan is tall.
John is rich or quiet.
Susan is both not curious and not quiet.
Someone is either curious or not quiet.
John is either creative or humble.
Someone is not patient or kind.
Someone is either calm or quiet. | John is not happy. | contradiction | (![X]:((~happy(X)<~>~tall(X))<=>brave(X)))&
(![X]:((calm(X)&generous(X))=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~tall(john)&~old(john))))&
(![X]:((~wise(X)<~>~curious(X))=>(creative(X)<~>~funny(X))))&
(![X]:((~curious(X)|~rich(X))<=>old(X)))&
(![X]:((~creative(X)<~>creative(X))=>(~curious(X)|humble(X))))&
(![X]:(calm(X)<=>(kind(X)<~>~quiet(X))))&
(![X]:((strong(X)&~happy(X))=>(~calm(X)<~>~brave(X))))&
(![X]:((funny(X)&~rich(X))<=>(generous(X)<~>patient(X))))&
((rich(john))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~quiet(X)<=>(~patient(X)|wise(X))))&
(![X]:((quiet(X)|~rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:(~brave(X)))=>((creative(john)&brave(john))))&
(((curious(paul)&tall(paul)))=>((curious(lucy)<~>calm(lucy))))&
(((~patient(fred)<~>~curious(fred)))<=>(?[X]:(~old(X))))&
(tall(susan))&
((rich(john)|quiet(john)))&
((~curious(susan)&~quiet(susan)))&
(?[X]:((curious(X)<~>~quiet(X))))&
((creative(john)<~>humble(john)))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:((calm(X)<~>quiet(X)))) | ~happy(john) | [
"p0",
"p3",
"p5",
"p6",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7966272974947577141707543
% SZS output start Proof for 7966272974947577141707543
1. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> brave(X0)) [input p0]
4. ? [X0] : (brave(X0) <~> ~brave(X0)) <=> (~old(john) & ~tall(john)) [input p3]
6. ! [X0] : ((~rich(X0) | ~curious(X0)) <=> old(X0)) [input p5]
7. ! [X0] : ((~creative(X0) <~> creative(X0)) => (humble(X0) | ~curious(X0))) [input p6]
14. ? [X0] : ~brave(X0) => (brave(john) & creative(john)) [input p13]
21. creative(john) <~> humble(john) [input p20]
24. ~happy(john) [input hypothesis]
28. ! [X0] : ((humble(X0) | ~curious(X0)) | (~creative(X0) <=> creative(X0))) [ennf transformation 7]
29. ! [X0] : (humble(X0) | ~curious(X0) | (~creative(X0) <=> creative(X0))) [flattening 28]
33. (brave(john) & creative(john)) | ! [X0] : brave(X0) [ennf transformation 14]
36. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | ~brave(X0)) & (brave(X0) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 1]
42. (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (old(john) | tall(john))) & ((~old(john) & ~tall(john)) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 4]
43. (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | old(john) | tall(john)) & ((~old(john) & ~tall(john)) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [flattening 42]
44. (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | old(john) | tall(john)) & ((~old(john) & ~tall(john)) | ! [X1] : ((brave(X1) | brave(X1)) & (~brave(X1) | ~brave(X1)))) [rectify 43]
45. ? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) => ((brave(sK1) | ~brave(sK1)) & (~brave(sK1) | brave(sK1))) [choice axiom]
46. (((brave(sK1) | ~brave(sK1)) & (~brave(sK1) | brave(sK1))) | old(john) | tall(john)) & ((~old(john) & ~tall(john)) | ! [X1] : ((brave(X1) | brave(X1)) & (~brave(X1) | ~brave(X1)))) [skolemisation 44,45]
48. ! [X0] : (((~rich(X0) | ~curious(X0)) | ~old(X0)) & (old(X0) | (rich(X0) & curious(X0)))) [nnf transformation 6]
49. ! [X0] : ((~rich(X0) | ~curious(X0) | ~old(X0)) & (old(X0) | (rich(X0) & curious(X0)))) [flattening 48]
50. ! [X0] : (humble(X0) | ~curious(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 29]
69. (~humble(john) | ~creative(john)) & (humble(john) | creative(john)) [nnf transformation 21]
78. ~brave(X0) | happy(X0) | tall(X0) [cnf transformation 36]
84. ~tall(john) | ~brave(X1) | ~brave(X1) [cnf transformation 46]
87. ~old(john) | brave(X1) | brave(X1) [cnf transformation 46]
94. curious(X0) | old(X0) [cnf transformation 49]
97. humble(X0) | ~curious(X0) | creative(X0) | creative(X0) [cnf transformation 50]
98. humble(X0) | ~curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 50]
121. creative(john) | brave(X0) [cnf transformation 33]
136. ~humble(john) | ~creative(john) [cnf transformation 69]
140. ~happy(john) [cnf transformation 24]
143. humble(X0) | ~curious(X0) | creative(X0) [duplicate literal removal 97]
144. humble(X0) | ~curious(X0) | ~creative(X0) [duplicate literal removal 98]
145. ~tall(john) | ~brave(X1) [duplicate literal removal 84]
148. ~old(john) | brave(X1) [duplicate literal removal 87]
173. 6 <=> ! [X1] : brave(X1) [avatar definition]
174. brave(X1) <- (6) [avatar component clause 173]
176. 7 <=> old(john) [avatar definition]
178. ~old(john) <- (~7) [avatar component clause 176]
179. 6 | ~7 [avatar split clause 148,176,173]
181. 8 <=> ! [X1] : ~brave(X1) [avatar definition]
182. ~brave(X1) <- (8) [avatar component clause 181]
185. 9 <=> tall(john) [avatar definition]
187. ~tall(john) <- (~9) [avatar component clause 185]
189. 8 | ~9 [avatar split clause 145,185,181]
190. ~curious(X0) | humble(X0) [subsumption resolution 143,144]
212. 14 <=> creative(john) [avatar definition]
215. 6 | 14 [avatar split clause 121,212,173]
255. 23 <=> humble(john) [avatar definition]
257. ~humble(john) <- (~23) [avatar component clause 255]
258. ~14 | ~23 [avatar split clause 136,255,212]
274. $false <- (6, 8) [subsumption resolution 182,174]
275. ~6 | ~8 [avatar contradiction clause 274]
281. humble(X0) | old(X0) [resolution 190,94]
282. old(john) <- (~23) [resolution 281,257]
283. $false <- (~7, ~23) [subsumption resolution 282,178]
284. 7 | 23 [avatar contradiction clause 283]
288. tall(X0) | happy(X0) <- (6) [resolution 78,174]
291. happy(john) <- (6, ~9) [resolution 288,187]
295. $false <- (6, ~9) [subsumption resolution 291,140]
296. ~6 | 9 [avatar contradiction clause 295]
297. $false [avatar sat refutation 179,189,215,258,275,284,296]
% SZS output end Proof for 7966272974947577141707543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not creative or not quiet then mary is creative and vice versa.
Everyone who is both patient and brave is tall or not curious and vice versa.
If lucy is brave or old then someone is either rich or not curious and vice versa.
Everyone who is rich is either generous or quiet and vice versa.
If someone is calm or not wise then someone is tall.
Everyone who is not strong is both strong and not quiet.
If susan is not rich then john is either not tall or calm.
Everyone who is generous is not brave.
Everyone who is not happy is either not patient or brave.
Everyone who is both strong and not kind is not patient and vice versa.
If john is curious then someone is either strong or not generous.
Everyone who is not strong is not tall and vice versa.
Everyone who is both humble and quiet is rich and vice versa.
Everyone who is humble or not rich is not calm and vice versa.
Everyone who is either not funny or not happy is either not quiet or not generous and vice versa.
If someone is happy then fred is both not strong and brave and vice versa.
Alice is curious.
Fred is either not wise or tall.
Fred is not creative.
Someone is either not curious or not strong.
Someone is either funny or strong.
Paul is curious.
Someone is either not happy or not funny. | Mary is not rich. | neutral | (((~creative(alice)|~quiet(alice)))<=>(creative(mary)))&
(![X]:((patient(X)&brave(X))<=>(tall(X)|~curious(X))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(rich(X)<=>(generous(X)<~>quiet(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:(tall(X))))&
(![X]:(~strong(X)=>(strong(X)&~quiet(X))))&
((~rich(susan))=>((~tall(john)<~>calm(john))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:(~happy(X)=>(~patient(X)<~>brave(X))))&
(![X]:((strong(X)&~kind(X))<=>~patient(X)))&
((curious(john))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
(![X]:((humble(X)&quiet(X))<=>rich(X)))&
(![X]:((humble(X)|~rich(X))<=>~calm(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(~quiet(X)<~>~generous(X))))&
((?[X]:(happy(X)))<=>((~strong(fred)&brave(fred))))&
(curious(alice))&
((~wise(fred)<~>tall(fred)))&
(~creative(fred))&
(?[X]:((~curious(X)<~>~strong(X))))&
(?[X]:((funny(X)<~>strong(X))))&
(curious(paul))&
(?[X]:((~happy(X)<~>~funny(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is calm or kind is both quiet and not patient.
If john is not happy then someone is tall or not tall.
Everyone who is not happy is humble or not strong and vice versa.
If susan is either creative or curious then lucy is not calm and vice versa.
If someone is creative then someone is strong or tall and vice versa.
If mary is either not creative or generous then john is both not wise and not generous.
If someone is not wise then alice is both not generous and not tall and vice versa.
If someone is calm then someone is patient or not patient and vice versa.
Everyone who is either humble or patient is not rich or strong.
If someone is either not tall or not rich then someone is humble.
Everyone who is either old or not tall is both not tall and wise and vice versa.
Everyone who is both curious and not calm is either generous or quiet and vice versa.
Everyone who is either humble or not tall is either brave or not brave and vice versa.
If someone is humble then alice is both not wise and not kind.
Everyone who is not funny is not brave and vice versa.
Everyone who is quiet is kind.
Someone is happy or strong.
Paul is either not quiet or patient.
Someone is either not funny or generous.
John is not old.
Someone is either not creative or not calm.
John is patient.
Someone is tall or not funny. | Mary is not old. | neutral | (![X]:((calm(X)|kind(X))=>(quiet(X)&~patient(X))))&
((~happy(john))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
(((creative(susan)<~>curious(susan)))<=>(~calm(lucy)))&
((?[X]:(creative(X)))<=>(?[X]:((strong(X)|tall(X)))))&
(((~creative(mary)<~>generous(mary)))=>((~wise(john)&~generous(john))))&
((?[X]:(~wise(X)))<=>((~generous(alice)&~tall(alice))))&
((?[X]:(calm(X)))<=>(?[X]:((patient(X)|~patient(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~rich(X)|strong(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(humble(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~tall(X)&wise(X))))&
(![X]:((curious(X)&~calm(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~brave(X))))&
((?[X]:(humble(X)))=>((~wise(alice)&~kind(alice))))&
(![X]:(~funny(X)<=>~brave(X)))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((happy(X)|strong(X))))&
((~quiet(paul)<~>patient(paul)))&
(?[X]:((~funny(X)<~>generous(X))))&
(~old(john))&
(?[X]:((~creative(X)<~>~calm(X))))&
(patient(john))&
(?[X]:((tall(X)|~funny(X)))) | ~old(mary) | [] | null | 0 |
Everyone who is both generous and not kind is strong and vice versa. If someone is either calm or happy then someone is both kind and generous. If someone is either not rich or calm then someone is curious or not strong and vice versa. If alice is not wise then someone is both curious and not happy and vice versa. Everyone who is not curious or happy is quiet or not funny and vice versa. If paul is funny then susan is either not humble or funny and vice versa. If someone is rich then someone is not tall and vice versa. Everyone who is tall is both calm and not humble and vice versa. If someone is both not brave and curious then paul is tall. Everyone who is not quiet is both not brave and not humble and vice versa. Everyone who is both generous and rich is both rich and not funny and vice versa. Everyone who is kind or brave is not old or old. If someone is either not old or not quiet then paul is generous and vice versa. If john is not wise or not happy then someone is rich or brave and vice versa. Everyone who is not wise or curious is curious and vice versa. Everyone who is not creative is either strong or rich and vice versa. Someone is either wise or not patient. Someone is either not wise or old. Susan is strong or humble. Someone is both not strong and not generous. Alice is both patient and not wise. Someone is both not creative and not curious. Fred is not kind or not humble. Lucy is not rich or strong. | Paul is not calm. | contradiction | (![X]:((generous(X)&~kind(X))<=>strong(X)))&
((?[X]:((calm(X)<~>happy(X))))=>(?[X]:((kind(X)&generous(X)))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:((curious(X)|~strong(X)))))&
((~wise(alice))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)|~funny(X))))&
((funny(paul))<=>((~humble(susan)<~>funny(susan))))&
((?[X]:(rich(X)))<=>(?[X]:(~tall(X))))&
(![X]:(tall(X)<=>(calm(X)&~humble(X))))&
((?[X]:((~brave(X)&curious(X))))=>(tall(paul)))&
(![X]:(~quiet(X)<=>(~brave(X)&~humble(X))))&
(![X]:((generous(X)&rich(X))<=>(rich(X)&~funny(X))))&
(![X]:((kind(X)|brave(X))=>(~old(X)|old(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(generous(paul)))&
(((~wise(john)|~happy(john)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((~wise(X)|curious(X))<=>curious(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>rich(X))))&
(?[X]:((wise(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>old(X))))&
((strong(susan)|humble(susan)))&
(?[X]:((~strong(X)&~generous(X))))&
((patient(alice)&~wise(alice)))&
(?[X]:((~creative(X)&~curious(X))))&
((~kind(fred)|~humble(fred)))&
((~rich(lucy)|strong(lucy))) | ~calm(paul) | [
"p3",
"p4",
"p7",
"p8",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2970316884872622846237549
% SZS output start Proof for 2970316884872622846237549
4. ~wise(alice) <=> ? [X0] : (~happy(X0) & curious(X0)) [input p3]
5. ! [X0] : ((happy(X0) | ~curious(X0)) <=> (~funny(X0) | quiet(X0))) [input p4]
8. ! [X0] : (tall(X0) <=> (~humble(X0) & calm(X0))) [input p7]
9. ? [X0] : (curious(X0) & ~brave(X0)) => tall(paul) [input p8]
10. ! [X0] : (~quiet(X0) <=> (~humble(X0) & ~brave(X0))) [input p9]
21. ~wise(alice) & patient(alice) [input p20]
25. ~calm(paul) [input hypothesis]
31. tall(paul) | ! [X0] : (~curious(X0) | brave(X0)) [ennf transformation 9]
46. (~wise(alice) | ! [X0] : (happy(X0) | ~curious(X0))) & (? [X0] : (~happy(X0) & curious(X0)) | wise(alice)) [nnf transformation 4]
47. (~wise(alice) | ! [X0] : (happy(X0) | ~curious(X0))) & (? [X1] : (~happy(X1) & curious(X1)) | wise(alice)) [rectify 46]
48. ? [X1] : (~happy(X1) & curious(X1)) => (~happy(sK3) & curious(sK3)) [choice axiom]
49. (~wise(alice) | ! [X0] : (happy(X0) | ~curious(X0))) & ((~happy(sK3) & curious(sK3)) | wise(alice)) [skolemisation 47,48]
50. ! [X0] : (((happy(X0) | ~curious(X0)) | (funny(X0) & ~quiet(X0))) & ((~funny(X0) | quiet(X0)) | (~happy(X0) & curious(X0)))) [nnf transformation 5]
51. ! [X0] : ((happy(X0) | ~curious(X0) | (funny(X0) & ~quiet(X0))) & (~funny(X0) | quiet(X0) | (~happy(X0) & curious(X0)))) [flattening 50]
58. ! [X0] : ((tall(X0) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | ~tall(X0))) [nnf transformation 8]
59. ! [X0] : ((tall(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | ~tall(X0))) [flattening 58]
60. ! [X0] : ((~quiet(X0) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | quiet(X0))) [nnf transformation 10]
61. ! [X0] : ((~quiet(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | quiet(X0))) [flattening 60]
99. curious(sK3) | wise(alice) [cnf transformation 49]
100. ~happy(sK3) | wise(alice) [cnf transformation 49]
104. ~quiet(X0) | ~curious(X0) | happy(X0) [cnf transformation 51]
112. ~tall(X0) | calm(X0) [cnf transformation 59]
115. tall(paul) | ~curious(X0) | brave(X0) [cnf transformation 31]
116. ~brave(X0) | quiet(X0) [cnf transformation 61]
146. ~wise(alice) [cnf transformation 21]
151. ~calm(paul) [cnf transformation 25]
208. 14 <=> wise(alice) [avatar definition]
213. 15 <=> happy(sK3) [avatar definition]
215. ~happy(sK3) <- (~15) [avatar component clause 213]
216. 14 | ~15 [avatar split clause 100,213,208]
218. 16 <=> curious(sK3) [avatar definition]
220. curious(sK3) <- (16) [avatar component clause 218]
221. 14 | 16 [avatar split clause 99,218,208]
255. 24 <=> ! [X0] : (~curious(X0) | brave(X0)) [avatar definition]
256. ~curious(X0) | brave(X0) <- (24) [avatar component clause 255]
258. 25 <=> tall(paul) [avatar definition]
260. tall(paul) <- (25) [avatar component clause 258]
261. 24 | 25 [avatar split clause 115,258,255]
332. ~14 [avatar split clause 146,208]
362. calm(paul) <- (25) [resolution 260,112]
363. $false <- (25) [subsumption resolution 362,151]
364. ~25 [avatar contradiction clause 363]
369. brave(sK3) <- (16, 24) [resolution 256,220]
384. quiet(sK3) <- (16, 24) [resolution 369,116]
531. ~curious(sK3) | happy(sK3) <- (16, 24) [resolution 384,104]
532. happy(sK3) <- (16, 24) [subsumption resolution 531,220]
533. $false <- (~15, 16, 24) [subsumption resolution 532,215]
534. 15 | ~16 | ~24 [avatar contradiction clause 533]
535. $false [avatar sat refutation 216,221,261,332,364,534]
% SZS output end Proof for 2970316884872622846237549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is tall and vice versa. Everyone who is either not creative or strong is both kind and funny. If someone is both humble and not curious then someone is either not humble or rich. Everyone who is either humble or not tall is curious. If someone is not kind or happy then someone is both curious and rich. Everyone who is either rich or quiet is both not brave and not tall. If someone is either not tall or not calm then alice is both calm and patient. Everyone who is either not creative or tall is calm. Everyone who is not kind or not quiet is patient. Everyone who is patient or not humble is not rich and vice versa. Everyone who is generous is either not happy or patient. Everyone who is not curious or not quiet is either not wise or not strong and vice versa. Everyone who is happy is both old and happy. Everyone who is not tall or not strong is not strong or not quiet and vice versa. If someone is both patient and generous then someone is not rich. Someone is kind or tall. Someone is not calm or kind. Fred is either not calm or funny. Someone is not brave or not old. Alice is both not wise and curious. Alice is creative or not funny. | Alice is strong. | neutral | (![X]:(calm(X)<=>tall(X)))&
(![X]:((~creative(X)<~>strong(X))=>(kind(X)&funny(X))))&
((?[X]:((humble(X)&~curious(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((humble(X)<~>~tall(X))=>curious(X)))&
((?[X]:((~kind(X)|happy(X))))=>(?[X]:((curious(X)&rich(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(~brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~calm(X))))=>((calm(alice)&patient(alice))))&
(![X]:((~creative(X)<~>tall(X))=>calm(X)))&
(![X]:((~kind(X)|~quiet(X))=>patient(X)))&
(![X]:((patient(X)|~humble(X))<=>~rich(X)))&
(![X]:(generous(X)=>(~happy(X)<~>patient(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:(happy(X)=>(old(X)&happy(X))))&
(![X]:((~tall(X)|~strong(X))<=>(~strong(X)|~quiet(X))))&
((?[X]:((patient(X)&generous(X))))=>(?[X]:(~rich(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((~calm(X)|kind(X))))&
((~calm(fred)<~>funny(fred)))&
(?[X]:((~brave(X)|~old(X))))&
((~wise(alice)&curious(alice)))&
((creative(alice)|~funny(alice))) | strong(alice) | [] | null | 0 |
If alice is both not brave and not calm then someone is wise or creative.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.
Everyone who is both old and not old is both rich and funny and vice versa.
If someone is either not wise or not funny then mary is both not humble and not happy.
If someone is kind or tall then susan is either not patient or not happy and vice versa.
Everyone who is brave is both kind and not kind and vice versa.
Everyone who is both generous and not creative is quiet or not happy and vice versa.
If susan is not creative then mary is both not strong and patient and vice versa.
If mary is not strong or kind then paul is not tall and vice versa.
Everyone who is either not generous or patient is not brave and vice versa.
Everyone who is both not rich and not patient is either calm or not old and vice versa.
Everyone who is not happy or rich is not patient or rich and vice versa.
Everyone who is happy or not strong is either not curious or not patient.
If someone is both happy and brave then someone is not brave.
Everyone who is wise is not creative and vice versa.
Someone is either creative or brave.
Alice is either not creative or not curious.
John is either not kind or not patient.
Susan is either not brave or not strong.
John is either old or not humble.
Alice is not humble.
Alice is happy or not old.
Fred is patient or not kind. | Mary is kind. | neutral | (((~brave(alice)&~calm(alice)))=>(?[X]:((wise(X)|creative(X)))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~humble(mary)&~happy(mary))))&
((?[X]:((kind(X)|tall(X))))<=>((~patient(susan)<~>~happy(susan))))&
(![X]:(brave(X)<=>(kind(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(quiet(X)|~happy(X))))&
((~creative(susan))<=>((~strong(mary)&patient(mary))))&
(((~strong(mary)|kind(mary)))<=>(~tall(paul)))&
(![X]:((~generous(X)<~>patient(X))<=>~brave(X)))&
(![X]:((~rich(X)&~patient(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((?[X]:((happy(X)&brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(wise(X)<=>~creative(X)))&
(?[X]:((creative(X)<~>brave(X))))&
((~creative(alice)<~>~curious(alice)))&
((~kind(john)<~>~patient(john)))&
((~brave(susan)<~>~strong(susan)))&
((old(john)<~>~humble(john)))&
(~humble(alice))&
((happy(alice)|~old(alice)))&
((patient(fred)|~kind(fred))) | kind(mary) | [] | null | 0 |
Everyone who is either tall or old is both humble and not patient and vice versa.
If someone is not tall then susan is either not rich or not wise and vice versa.
Everyone who is both not happy and kind is strong.
If lucy is both not patient and not creative then someone is either not generous or not tall and vice versa.
If john is not funny or not quiet then someone is both not humble and curious.
If alice is not curious then susan is not funny and vice versa.
If someone is both not quiet and funny then someone is not happy or old.
If susan is both not happy and brave then someone is not tall.
If someone is funny then john is strong or not curious and vice versa.
Everyone who is not quiet is both not brave and not calm.
If mary is not creative or not strong then alice is both not kind and not old and vice versa.
If alice is either not creative or patient then susan is both brave and not kind and vice versa.
Everyone who is both not curious and not creative is both tall and generous.
If mary is either humble or creative then someone is both not quiet and generous and vice versa.
If fred is not calm then someone is funny and vice versa.
Everyone who is not calm is either creative or strong and vice versa.
Mary is either not brave or patient.
Alice is humble.
Mary is creative or not creative.
John is both not old and not wise.
Someone is either patient or curious.
Mary is not quiet.
Alice is either brave or not kind.
Alice is not brave. | Alice is not old. | entailment | (![X]:((tall(X)<~>old(X))<=>(humble(X)&~patient(X))))&
((?[X]:(~tall(X)))<=>((~rich(susan)<~>~wise(susan))))&
(![X]:((~happy(X)&kind(X))=>strong(X)))&
(((~patient(lucy)&~creative(lucy)))<=>(?[X]:((~generous(X)<~>~tall(X)))))&
(((~funny(john)|~quiet(john)))=>(?[X]:((~humble(X)&curious(X)))))&
((~curious(alice))<=>(~funny(susan)))&
((?[X]:((~quiet(X)&funny(X))))=>(?[X]:((~happy(X)|old(X)))))&
(((~happy(susan)&brave(susan)))=>(?[X]:(~tall(X))))&
((?[X]:(funny(X)))<=>((strong(john)|~curious(john))))&
(![X]:(~quiet(X)=>(~brave(X)&~calm(X))))&
(((~creative(mary)|~strong(mary)))<=>((~kind(alice)&~old(alice))))&
(((~creative(alice)<~>patient(alice)))<=>((brave(susan)&~kind(susan))))&
(![X]:((~curious(X)&~creative(X))=>(tall(X)&generous(X))))&
(((humble(mary)<~>creative(mary)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((~calm(fred))<=>(?[X]:(funny(X))))&
(![X]:(~calm(X)<=>(creative(X)<~>strong(X))))&
((~brave(mary)<~>patient(mary)))&
(humble(alice))&
((creative(mary)|~creative(mary)))&
((~old(john)&~wise(john)))&
(?[X]:((patient(X)<~>curious(X))))&
(~quiet(mary))&
((brave(alice)<~>~kind(alice)))&
(~brave(alice)) | ~old(alice) | [
"p9",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8118043234733218624753448
% SZS output start Proof for 8118043234733218624753448
10. ! [X0] : (~quiet(X0) => (~calm(X0) & ~brave(X0))) [input p9]
11. (~strong(mary) | ~creative(mary)) <=> (~old(alice) & ~kind(alice)) [input p10]
16. ! [X0] : (~calm(X0) <=> (creative(X0) <~> strong(X0))) [input p15]
22. ~quiet(mary) [input p21]
25. old(alice) [input hypothesis]
33. ! [X0] : ((~calm(X0) & ~brave(X0)) | quiet(X0)) [ennf transformation 10]
60. ((~strong(mary) | ~creative(mary)) | (old(alice) | kind(alice))) & ((~old(alice) & ~kind(alice)) | (strong(mary) & creative(mary))) [nnf transformation 11]
61. (~strong(mary) | ~creative(mary) | old(alice) | kind(alice)) & ((~old(alice) & ~kind(alice)) | (strong(mary) & creative(mary))) [flattening 60]
72. ! [X0] : ((~calm(X0) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0)))) & (((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | calm(X0))) [nnf transformation 16]
107. ~calm(X0) | quiet(X0) [cnf transformation 33]
110. ~old(alice) | creative(mary) [cnf transformation 61]
111. ~old(alice) | strong(mary) [cnf transformation 61]
130. ~creative(X0) | ~strong(X0) | calm(X0) [cnf transformation 72]
141. ~quiet(mary) [cnf transformation 22]
145. old(alice) [cnf transformation 25]
271. 28 <=> old(alice) [avatar definition]
275. 29 <=> creative(mary) [avatar definition]
276. creative(mary) <- (29) [avatar component clause 275]
279. 30 <=> strong(mary) [avatar definition]
280. strong(mary) <- (30) [avatar component clause 279]
283. 30 | ~28 [avatar split clause 111,271,279]
284. 29 | ~28 [avatar split clause 110,271,275]
363. 28 [avatar split clause 145,271]
392. ~strong(mary) | calm(mary) <- (29) [resolution 130,276]
403. calm(mary) <- (29, 30) [subsumption resolution 392,280]
426. quiet(mary) <- (29, 30) [resolution 403,107]
427. $false <- (29, 30) [subsumption resolution 426,141]
428. ~29 | ~30 [avatar contradiction clause 427]
429. $false [avatar sat refutation 283,284,363,428]
% SZS output end Proof for 8118043234733218624753448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not humble or not quiet is not generous or not tall.
Everyone who is either not calm or not curious is either funny or creative and vice versa.
If lucy is kind or not generous then someone is both wise and not brave and vice versa.
Everyone who is not curious is funny and vice versa.
Everyone who is both generous and kind is both not wise and not old and vice versa.
If mary is either tall or quiet then someone is both not old and not quiet.
Everyone who is either curious or not curious is not old or kind and vice versa.
Everyone who is not brave or curious is not curious and vice versa.
If someone is curious or humble then john is creative.
If someone is either not kind or not happy then alice is both funny and not humble and vice versa.
Everyone who is both generous and not generous is generous.
Everyone who is both brave and not patient is either wise or not quiet.
Everyone who is either tall or patient is both not quiet and not creative.
Everyone who is either not funny or not kind is curious or not patient and vice versa.
If someone is either creative or brave then someone is wise or kind.
Everyone who is both creative and strong is patient or old and vice versa.
Paul is not curious.
Alice is both creative and not happy.
Susan is patient.
Someone is happy or brave.
Someone is both not tall and not quiet.
Lucy is patient.
Someone is both not old and not curious.
John is either curious or old. | Susan is curious. | contradiction | (![X]:((~humble(X)<~>~quiet(X))=>(~generous(X)|~tall(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(funny(X)<~>creative(X))))&
(((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
(~curious(paul))&
((creative(alice)&~happy(alice)))&
(patient(susan))&
(?[X]:((happy(X)|brave(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(patient(lucy))&
(?[X]:((~old(X)&~curious(X))))&
((curious(john)<~>old(john))) | curious(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 66105422070104599526153
% SZS output start Proof for 66105422070104599526153
8. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p7]
25. curious(susan) [input hypothesis]
52. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 8]
53. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 52]
108. ~curious(X0) | ~curious(X0) [cnf transformation 53]
150. curious(susan) [cnf transformation 25]
152. ~curious(X0) [duplicate literal removal 108]
264. $false [subsumption resolution 150,152]
% SZS output end Proof for 66105422070104599526153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not kind is not humble and vice versa. If someone is not curious then someone is either funny or not generous. Everyone who is both not kind and not curious is not patient. Everyone who is both not humble and not creative is either not curious or not patient. Everyone who is old or rich is not rich or strong and vice versa. If alice is both old and not generous then someone is both old and not creative. Everyone who is not quiet or patient is not patient. Everyone who is funny is wise. If someone is either not patient or wise then someone is both not quiet and not old. If mary is both not curious and tall then someone is old or wise and vice versa. Everyone who is not curious is funny and vice versa. If someone is both not tall and wise then lucy is either patient or not curious and vice versa. If someone is both wise and not curious then someone is both not humble and patient. If someone is generous or wise then someone is either not quiet or wise and vice versa. If someone is either not creative or patient then mary is both strong and not strong and vice versa. Someone is calm. Someone is creative or curious. Alice is not funny. Susan is either brave or tall. | Lucy is wise. | contradiction | (![X]:((~rich(X)&~kind(X))<=>~humble(X)))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)<~>~generous(X)))))&
(![X]:((~kind(X)&~curious(X))=>~patient(X)))&
(![X]:((~humble(X)&~creative(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((old(X)|rich(X))<=>(~rich(X)|strong(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~creative(X)<~>patient(X))))<=>((strong(mary)&~strong(mary))))&
(?[X]:(calm(X)))&
(?[X]:((creative(X)|curious(X))))&
(~funny(alice))&
((brave(susan)<~>tall(susan))) | wise(lucy) | [
"p6",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3425742625688767063624677
% SZS output start Proof for 3425742625688767063624677
7. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : (funny(X0) => wise(X0)) [input p7]
10. (tall(mary) & ~curious(mary)) <=> ? [X0] : (wise(X0) | old(X0)) [input p9]
11. ! [X0] : (~curious(X0) <=> funny(X0)) [input p10]
13. ? [X0] : (~curious(X0) & wise(X0)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p12]
20. wise(lucy) [input hypothesis]
23. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : (patient(X1) & ~humble(X1)) [rectify 13]
33. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 7]
34. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 8]
36. ? [X1] : (patient(X1) & ~humble(X1)) | ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 23]
52. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | (~tall(mary) | curious(mary))) [nnf transformation 10]
53. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | ~tall(mary) | curious(mary)) [flattening 52]
54. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X1] : (wise(X1) | old(X1)) | ~tall(mary) | curious(mary)) [rectify 53]
55. ? [X1] : (wise(X1) | old(X1)) => (wise(sK3) | old(sK3)) [choice axiom]
56. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & ((wise(sK3) | old(sK3)) | ~tall(mary) | curious(mary)) [skolemisation 54,55]
57. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 11]
62. ? [X0] : (patient(X0) & ~humble(X0)) | ! [X1] : (curious(X1) | ~wise(X1)) [rectify 36]
63. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK5) & ~humble(sK5)) [choice axiom]
64. (patient(sK5) & ~humble(sK5)) | ! [X1] : (curious(X1) | ~wise(X1)) [skolemisation 62,63]
93. ~patient(X0) | ~patient(X0) [cnf transformation 33]
94. ~funny(X0) | wise(X0) [cnf transformation 34]
101. ~curious(mary) | ~wise(X0) [cnf transformation 56]
104. funny(X0) | curious(X0) [cnf transformation 57]
113. patient(sK5) | curious(X1) | ~wise(X1) [cnf transformation 64]
130. wise(lucy) [cnf transformation 20]
131. ~patient(X0) [duplicate literal removal 93]
135. 1 <=> ! [X1] : curious(X1) [avatar definition]
136. curious(X1) <- (1) [avatar component clause 135]
181. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
182. ~wise(X0) <- (11) [avatar component clause 181]
193. 14 <=> curious(mary) [avatar definition]
195. ~curious(mary) <- (~14) [avatar component clause 193]
196. 11 | ~14 [avatar split clause 101,193,181]
228. curious(X1) | ~wise(X1) [subsumption resolution 113,131]
290. $false <- (11) [resolution 182,130]
291. ~11 [avatar contradiction clause 290]
296. curious(X0) | wise(X0) [resolution 104,94]
297. curious(X0) [subsumption resolution 296,228]
298. 1 [avatar split clause 297,135]
299. $false <- (1, ~14) [resolution 136,195]
302. ~1 | 14 [avatar contradiction clause 299]
303. $false [avatar sat refutation 196,291,298,302]
% SZS output end Proof for 3425742625688767063624677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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