premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is creative or not strong is both funny and generous. Everyone who is not curious is not old and vice versa. If john is not old then fred is either not humble or not happy. If lucy is either generous or not funny then someone is quiet. If lucy is rich then someone is both wise and not brave. Everyone who is happy or not strong is either quiet or curious and vice versa. If someone is creative then john is strong or generous and vice versa. If fred is both curious and generous then someone is not quiet and vice versa. Everyone who is both not wise and happy is either not kind or tall. Everyone who is not wise or not happy is not curious or not rich and vice versa. Everyone who is quiet or brave is either curious or kind. Everyone who is not happy is not curious or not funny. If fred is either not generous or humble then susan is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Fred is calm. Alice is not old. Paul is not curious. Mary is not creative. Lucy is rich or not brave. Fred is not curious. Someone is either not wise or quiet. Someone is not humble. | Lucy is not happy. | entailment | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
(![X]:((quiet(X)|brave(X))=>(curious(X)<~>kind(X))))&
(![X]:(~happy(X)=>(~curious(X)|~funny(X))))&
(((~generous(fred)<~>humble(fred)))<=>((patient(susan)|~old(susan))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(calm(fred))&
(~old(alice))&
(~curious(paul))&
(~creative(mary))&
((rich(lucy)|~brave(lucy)))&
(~curious(fred))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | ~happy(lucy) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3545876538847440947818948
% SZS output start Proof for 3545876538847440947818948
2. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p1]
6. ! [X0] : ((~strong(X0) | happy(X0)) <=> (quiet(X0) <~> curious(X0))) [input p5]
8. (generous(fred) & curious(fred)) <=> ? [X0] : ~quiet(X0) [input p7]
9. ! [X0] : ((happy(X0) & ~wise(X0)) => (~kind(X0) <~> tall(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~rich(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((brave(X0) | quiet(X0)) => (curious(X0) <~> kind(X0))) [input p10]
15. ! [X0] : (tall(X0) <=> (rich(X0) <~> ~old(X0))) [input p14]
16. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p15]
22. ~curious(fred) [input p21]
25. happy(lucy) [input hypothesis]
31. ! [X0] : ((~kind(X0) <~> tall(X0)) | (~happy(X0) | wise(X0))) [ennf transformation 9]
32. ! [X0] : ((~kind(X0) <~> tall(X0)) | ~happy(X0) | wise(X0)) [flattening 31]
33. ! [X0] : ((curious(X0) <~> kind(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 11]
36. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 16]
37. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 2]
44. ! [X0] : (((~strong(X0) | happy(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~strong(X0) | happy(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [flattening 44]
51. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~generous(fred) | ~curious(fred))) [nnf transformation 8]
52. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~generous(fred) | ~curious(fred)) [flattening 51]
53. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~generous(fred) | ~curious(fred)) [rectify 52]
54. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
55. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~generous(fred) | ~curious(fred)) [skolemisation 53,54]
56. ! [X0] : (((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ~happy(X0) | wise(X0)) [nnf transformation 32]
57. ! [X0] : (((~happy(X0) | ~wise(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 10]
58. ! [X0] : ((~happy(X0) | ~wise(X0) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | (happy(X0) & wise(X0)))) [flattening 57]
59. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33]
64. ! [X0] : ((tall(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0))) [nnf transformation 15]
65. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 36]
75. ~old(X0) | curious(X0) [cnf transformation 37]
76. ~curious(X0) | old(X0) [cnf transformation 37]
85. ~quiet(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 45]
93. curious(fred) | quiet(X0) [cnf transformation 55]
95. ~kind(X0) | tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 56]
99. ~wise(X0) | ~happy(X0) | curious(X0) [cnf transformation 58]
101. ~quiet(X0) | curious(X0) | kind(X0) [cnf transformation 59]
119. ~tall(X0) | ~rich(X0) | old(X0) [cnf transformation 64]
123. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 65]
128. ~curious(fred) [cnf transformation 22]
132. happy(lucy) [cnf transformation 25]
162. 7 <=> rich(lucy) [avatar definition]
163. rich(lucy) <- (7) [avatar component clause 162]
164. ~rich(lucy) <- (~7) [avatar component clause 162]
190. 13 <=> ! [X0] : quiet(X0) [avatar definition]
191. quiet(X0) <- (13) [avatar component clause 190]
198. 15 <=> curious(fred) [avatar definition]
201. 13 | 15 [avatar split clause 93,198,190]
226. ~15 [avatar split clause 128,198]
249. ~happy(X1) | ~curious(X1) <- (13) [resolution 85,191]
253. ~curious(lucy) <- (13) [resolution 249,132]
259. kind(X1) | curious(X1) <- (13) [resolution 101,191]
283. old(X1) | rich(X1) | curious(X1) <- (13) [resolution 123,259]
284. rich(X1) | old(X1) <- (13) [subsumption resolution 283,76]
288. old(lucy) <- (~7, 13) [resolution 284,164]
292. curious(lucy) <- (~7, 13) [resolution 288,75]
293. $false <- (~7, 13) [subsumption resolution 292,253]
294. 7 | ~13 [avatar contradiction clause 293]
299. 22 <=> tall(lucy) [avatar definition]
301. tall(lucy) <- (22) [avatar component clause 299]
303. 23 <=> old(lucy) [avatar definition]
304. old(lucy) <- (23) [avatar component clause 303]
322. tall(X1) | ~happy(X1) | wise(X1) | curious(X1) <- (13) [resolution 95,259]
323. tall(X1) | ~happy(X1) | curious(X1) <- (13) [subsumption resolution 322,99]
324. ~happy(X1) | tall(X1) <- (13) [subsumption resolution 323,249]
328. tall(lucy) <- (13) [resolution 324,132]
330. 22 | ~13 [avatar split clause 328,190,299]
334. ~rich(lucy) | old(lucy) <- (22) [resolution 301,119]
346. old(lucy) <- (7, 22) [subsumption resolution 334,163]
349. 23 | ~7 | ~22 [avatar split clause 346,299,162,303]
350. curious(lucy) <- (23) [resolution 304,75]
351. $false <- (13, 23) [subsumption resolution 350,253]
352. ~13 | ~23 [avatar contradiction clause 351]
353. $false [avatar sat refutation 201,226,294,330,349,352]
% SZS output end Proof for 3545876538847440947818948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then john is not brave or creative. Everyone who is curious or not old is either not creative or not wise. Everyone who is both not strong and wise is not curious or creative. Everyone who is old or not brave is both not curious and tall. Everyone who is not happy or not strong is generous. Everyone who is humble is kind or not funny. If mary is patient or not wise then someone is kind or calm. Everyone who is rich or tall is strong or humble. Everyone who is rich or not humble is either creative or old. If someone is not old then someone is both not curious and kind and vice versa. Everyone who is both patient and funny is either patient or not humble. Everyone who is both not rich and wise is either not wise or generous. If someone is happy then mary is humble and vice versa. Everyone who is both rich and old is either not humble or humble and vice versa. Everyone who is both not calm and patient is both not rich and strong and vice versa. If someone is either strong or not quiet then paul is not patient and vice versa. Someone is calm or not calm. Mary is funny or humble. Fred is either kind or not funny. Someone is both happy and tall. Someone is not calm. Someone is rich or generous. | Paul is calm. | neutral | ((?[X]:(old(X)))=>((~brave(john)|creative(john))))&
(![X]:((curious(X)|~old(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((~strong(X)&wise(X))=>(~curious(X)|creative(X))))&
(![X]:((old(X)|~brave(X))=>(~curious(X)&tall(X))))&
(![X]:((~happy(X)|~strong(X))=>generous(X)))&
(![X]:(humble(X)=>(kind(X)|~funny(X))))&
(((patient(mary)|~wise(mary)))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((rich(X)|tall(X))=>(strong(X)|humble(X))))&
(![X]:((rich(X)|~humble(X))=>(creative(X)<~>old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((patient(X)&funny(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(happy(X)))<=>(humble(mary)))&
(![X]:((rich(X)&old(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~rich(X)&strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(~patient(paul)))&
(?[X]:((calm(X)|~calm(X))))&
((funny(mary)|humble(mary)))&
((kind(fred)<~>~funny(fred)))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|generous(X)))) | calm(paul) | [] | null | 0 |
Everyone who is kind is both curious and generous.
If someone is not humble then someone is both not generous and not patient.
If lucy is generous or not tall then someone is not brave or old.
If lucy is either calm or strong then someone is not wise and vice versa.
If someone is kind or humble then lucy is both brave and not happy and vice versa.
Everyone who is either rich or patient is both tall and not funny and vice versa.
If lucy is both brave and not curious then john is either funny or creative and vice versa.
If john is funny then someone is both not brave and not patient.
Everyone who is happy is either not funny or humble.
Everyone who is both not wise and funny is either not tall or not strong and vice versa.
If someone is both funny and not old then someone is quiet.
Everyone who is not curious or not humble is old.
Everyone who is both tall and rich is either kind or creative and vice versa.
Everyone who is either happy or not calm is old and vice versa.
Everyone who is quiet is not old or not strong and vice versa.
Everyone who is both not quiet and humble is not funny or not strong and vice versa.
Someone is funny or not funny.
Someone is quiet or not wise.
Someone is calm or rich.
Someone is either not kind or not old.
Lucy is not brave or patient.
Lucy is both patient and strong.
Someone is not generous.
Alice is kind or not old. | Lucy is not creative. | neutral | (![X]:(kind(X)=>(curious(X)&generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~generous(X)&~patient(X)))))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~brave(X)|old(X)))))&
(((calm(lucy)<~>strong(lucy)))<=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|humble(X))))<=>((brave(lucy)&~happy(lucy))))&
(![X]:((rich(X)<~>patient(X))<=>(tall(X)&~funny(X))))&
(((brave(lucy)&~curious(lucy)))<=>((funny(john)<~>creative(john))))&
((funny(john))=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:(happy(X)=>(~funny(X)<~>humble(X))))&
(![X]:((~wise(X)&funny(X))<=>(~tall(X)<~>~strong(X))))&
((?[X]:((funny(X)&~old(X))))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)|~humble(X))=>old(X)))&
(![X]:((tall(X)&rich(X))<=>(kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>~calm(X))<=>old(X)))&
(![X]:(quiet(X)<=>(~old(X)|~strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~funny(X)|~strong(X))))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
((~brave(lucy)|patient(lucy)))&
((patient(lucy)&strong(lucy)))&
(?[X]:(~generous(X)))&
((kind(alice)|~old(alice))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both not old and not rich is both rich and not tall and vice versa.
Everyone who is not old or not humble is both kind and creative.
If mary is either not happy or curious then mary is brave and vice versa.
If mary is both happy and not tall then someone is not funny.
If lucy is creative or humble then alice is not calm or not creative and vice versa.
Everyone who is not creative or funny is not rich or not generous and vice versa.
Everyone who is both not curious and not funny is both curious and kind and vice versa.
Everyone who is both wise and not funny is curious or happy and vice versa.
Everyone who is either kind or not generous is patient or not generous.
Everyone who is not curious or kind is not creative and vice versa.
Everyone who is not funny is either strong or not old.
If fred is either not creative or tall then alice is both funny and happy and vice versa.
If fred is either not patient or curious then paul is either quiet or happy and vice versa.
Everyone who is both not quiet and rich is either not kind or brave.
If paul is both tall and not creative then lucy is not wise and vice versa.
Everyone who is both not tall and not creative is not brave.
Paul is either not funny or patient.
Someone is either not wise or not old.
Someone is calm or not strong.
Lucy is both not patient and not tall. | Alice is not humble. | contradiction | (![X]:((~old(X)&~rich(X))<=>(rich(X)&~tall(X))))&
(![X]:((~old(X)|~humble(X))=>(kind(X)&creative(X))))&
(((~happy(mary)<~>curious(mary)))<=>(brave(mary)))&
(((happy(mary)&~tall(mary)))=>(?[X]:(~funny(X))))&
(((creative(lucy)|humble(lucy)))<=>((~calm(alice)|~creative(alice))))&
(![X]:((~creative(X)|funny(X))<=>(~rich(X)|~generous(X))))&
(![X]:((~curious(X)&~funny(X))<=>(curious(X)&kind(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)|happy(X))))&
(![X]:((kind(X)<~>~generous(X))=>(patient(X)|~generous(X))))&
(![X]:((~curious(X)|kind(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(strong(X)<~>~old(X))))&
(((~creative(fred)<~>tall(fred)))<=>((funny(alice)&happy(alice))))&
(((~patient(fred)<~>curious(fred)))<=>((quiet(paul)<~>happy(paul))))&
(![X]:((~quiet(X)&rich(X))=>(~kind(X)<~>brave(X))))&
(((tall(paul)&~creative(paul)))<=>(~wise(lucy)))&
(![X]:((~tall(X)&~creative(X))=>~brave(X)))&
((~funny(paul)<~>patient(paul)))&
(?[X]:((~wise(X)<~>~old(X))))&
(?[X]:((calm(X)|~strong(X))))&
((~patient(lucy)&~tall(lucy))) | ~humble(alice) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 145517672147236931117748
% SZS output start Proof for 145517672147236931117748
2. ! [X0] : ((~humble(X0) | ~old(X0)) => (creative(X0) & kind(X0))) [input p1]
10. ! [X0] : ((kind(X0) | ~curious(X0)) <=> ~creative(X0)) [input p9]
21. ~humble(alice) [input hypothesis]
22. ! [X0] : ((creative(X0) & kind(X0)) | (humble(X0) & old(X0))) [ennf transformation 2]
46. ! [X0] : (((kind(X0) | ~curious(X0)) | creative(X0)) & (~creative(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 10]
47. ! [X0] : ((kind(X0) | ~curious(X0) | creative(X0)) & (~creative(X0) | (~kind(X0) & curious(X0)))) [flattening 46]
66. kind(X0) | humble(X0) [cnf transformation 22]
68. creative(X0) | humble(X0) [cnf transformation 22]
94. ~creative(X0) | ~kind(X0) [cnf transformation 47]
125. ~humble(alice) [cnf transformation 21]
269. ~kind(X0) | humble(X0) [resolution 94,68]
271. humble(X0) [subsumption resolution 269,66]
277. $false [resolution 271,125]
% SZS output end Proof for 145517672147236931117748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not old then someone is either not wise or humble and vice versa.
Everyone who is strong is generous or not brave.
Everyone who is funny or brave is not strong.
Everyone who is not wise is not strong or happy.
If someone is either not kind or brave then someone is not strong or not old and vice versa.
Everyone who is both rich and tall is old or strong.
Everyone who is rich or happy is both quiet and not strong.
Everyone who is not quiet is both not tall and not strong and vice versa.
Everyone who is not creative or not quiet is either old or not rich and vice versa.
Everyone who is either humble or not tall is both wise and not patient and vice versa.
If mary is quiet then lucy is not old or not quiet and vice versa.
If john is either tall or rich then someone is strong.
If someone is rich then lucy is both not quiet and not humble and vice versa.
Everyone who is wise is not wise or not patient and vice versa.
Everyone who is not creative is patient or wise and vice versa.
Everyone who is both calm and funny is not curious and vice versa.
Someone is not kind.
Fred is rich or not brave.
Alice is either rich or curious.
Lucy is both wise and not brave.
Susan is either not patient or not brave.
John is not curious or calm.
Someone is not generous. | Susan is not wise. | contradiction | (((quiet(susan)|~old(susan)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(strong(X)=>(generous(X)|~brave(X))))&
(![X]:((funny(X)|brave(X))=>~strong(X)))&
(![X]:(~wise(X)=>(~strong(X)|happy(X))))&
((?[X]:((~kind(X)<~>brave(X))))<=>(?[X]:((~strong(X)|~old(X)))))&
(![X]:((rich(X)&tall(X))=>(old(X)|strong(X))))&
(![X]:((rich(X)|happy(X))=>(quiet(X)&~strong(X))))&
(![X]:(~quiet(X)<=>(~tall(X)&~strong(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(old(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(wise(X)&~patient(X))))&
((quiet(mary))<=>((~old(lucy)|~quiet(lucy))))&
(((tall(john)<~>rich(john)))=>(?[X]:(strong(X))))&
((?[X]:(rich(X)))<=>((~quiet(lucy)&~humble(lucy))))&
(![X]:(wise(X)<=>(~wise(X)|~patient(X))))&
(![X]:(~creative(X)<=>(patient(X)|wise(X))))&
(![X]:((calm(X)&funny(X))<=>~curious(X)))&
(?[X]:(~kind(X)))&
((rich(fred)|~brave(fred)))&
((rich(alice)<~>curious(alice)))&
((wise(lucy)&~brave(lucy)))&
((~patient(susan)<~>~brave(susan)))&
((~curious(john)|calm(john)))&
(?[X]:(~generous(X))) | ~wise(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 718872209690923454241299
% SZS output start Proof for 718872209690923454241299
14. ! [X0] : (wise(X0) <=> (~patient(X0) | ~wise(X0))) [input p13]
24. ~wise(susan) [input hypothesis]
61. ! [X0] : ((wise(X0) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | ~wise(X0))) [flattening 61]
118. wise(X0) | wise(X0) [cnf transformation 62]
136. ~wise(susan) [cnf transformation 24]
138. wise(X0) [duplicate literal removal 118]
270. $false [subsumption resolution 136,138]
% SZS output end Proof for 718872209690923454241299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong then lucy is rich. Everyone who is not patient or not creative is generous. Everyone who is humble or not happy is both humble and not humble and vice versa. Everyone who is both happy and generous is both not wise and old. If someone is not wise then lucy is both not brave and curious. Everyone who is not old or old is either rich or curious and vice versa. If john is both not generous and not curious then someone is old. If someone is creative or not creative then mary is either not creative or not old and vice versa. Everyone who is both creative and not kind is both tall and not patient. If paul is both kind and quiet then someone is not humble and vice versa. If someone is not patient then someone is both not tall and not patient and vice versa. If john is happy or not calm then paul is wise. Everyone who is either not happy or calm is either happy or humble. Everyone who is either strong or not humble is either happy or tall and vice versa. Everyone who is both calm and funny is both happy and not curious and vice versa. Everyone who is not funny is either humble or not wise and vice versa. Someone is both happy and not strong. Someone is not creative. Someone is both rich and patient. Lucy is either not quiet or humble. Someone is not humble. Someone is either kind or generous. | Alice is not kind. | contradiction | (((~rich(alice)|~strong(alice)))=>(rich(lucy)))&
(![X]:((~patient(X)|~creative(X))=>generous(X)))&
(![X]:((humble(X)|~happy(X))<=>(humble(X)&~humble(X))))&
(![X]:((happy(X)&generous(X))=>(~wise(X)&old(X))))&
((?[X]:(~wise(X)))=>((~brave(lucy)&curious(lucy))))&
(![X]:((~old(X)|old(X))<=>(rich(X)<~>curious(X))))&
(((~generous(john)&~curious(john)))=>(?[X]:(old(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(mary)<~>~old(mary))))&
(![X]:((creative(X)&~kind(X))=>(tall(X)&~patient(X))))&
(((kind(paul)&quiet(paul)))<=>(?[X]:(~humble(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(((happy(john)|~calm(john)))=>(wise(paul)))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)<~>humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)<~>tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)&patient(X))))&
((~quiet(lucy)<~>humble(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)<~>generous(X)))) | ~kind(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p8",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3537872797227168015131861
% SZS output start Proof for 3537872797227168015131861
1. (~strong(alice) | ~rich(alice)) => rich(lucy) [input p0]
2. ! [X0] : ((~creative(X0) | ~patient(X0)) => generous(X0)) [input p1]
3. ! [X0] : ((~happy(X0) | humble(X0)) <=> (~humble(X0) & humble(X0))) [input p2]
4. ! [X0] : ((generous(X0) & happy(X0)) => (old(X0) & ~wise(X0))) [input p3]
5. ? [X0] : ~wise(X0) => (curious(lucy) & ~brave(lucy)) [input p4]
6. ! [X0] : ((old(X0) | ~old(X0)) <=> (rich(X0) <~> curious(X0))) [input p5]
9. ! [X0] : ((~kind(X0) & creative(X0)) => (~patient(X0) & tall(X0))) [input p8]
15. ! [X0] : ((funny(X0) & calm(X0)) <=> (~curious(X0) & happy(X0))) [input p14]
16. ! [X0] : (~funny(X0) <=> (humble(X0) <~> ~wise(X0))) [input p15]
18. ? [X0] : ~creative(X0) [input p17]
23. ~kind(alice) [input hypothesis]
25. ? [X0] : ~wise(X0) => curious(lucy) [pure predicate removal 5]
26. rich(lucy) | (strong(alice) & rich(alice)) [ennf transformation 1]
27. ! [X0] : (generous(X0) | (creative(X0) & patient(X0))) [ennf transformation 2]
28. ! [X0] : ((old(X0) & ~wise(X0)) | (~generous(X0) | ~happy(X0))) [ennf transformation 4]
29. ! [X0] : ((old(X0) & ~wise(X0)) | ~generous(X0) | ~happy(X0)) [flattening 28]
30. curious(lucy) | ! [X0] : wise(X0) [ennf transformation 25]
33. ! [X0] : ((~patient(X0) & tall(X0)) | (kind(X0) | ~creative(X0))) [ennf transformation 9]
34. ! [X0] : ((~patient(X0) & tall(X0)) | kind(X0) | ~creative(X0)) [flattening 33]
37. ! [X0] : (((~happy(X0) | humble(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 3]
38. ! [X0] : ((~happy(X0) | humble(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (happy(X0) & ~humble(X0)))) [flattening 37]
39. ! [X0] : (((old(X0) | ~old(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) & (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (~old(X0) & old(X0)))) [nnf transformation 6]
40. ! [X0] : ((old(X0) | ~old(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) & (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (~old(X0) & old(X0)))) [flattening 39]
59. ! [X0] : (((funny(X0) & calm(X0)) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 15]
60. ! [X0] : (((funny(X0) & calm(X0)) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | ~funny(X0) | ~calm(X0))) [flattening 59]
61. ! [X0] : ((~funny(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | funny(X0))) [nnf transformation 16]
64. ? [X0] : ~creative(X0) => ~creative(sK6) [choice axiom]
65. ~creative(sK6) [skolemisation 18,64]
74. rich(lucy) | rich(alice) [cnf transformation 26]
76. generous(X0) | patient(X0) [cnf transformation 27]
77. generous(X0) | creative(X0) [cnf transformation 27]
79. humble(X0) | happy(X0) [cnf transformation 38]
80. ~humble(X0) | ~humble(X0) [cnf transformation 38]
83. ~wise(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 29]
85. curious(lucy) | wise(X0) [cnf transformation 30]
88. ~curious(X0) | ~rich(X0) | old(X0) [cnf transformation 40]
89. ~curious(X0) | ~rich(X0) | ~old(X0) [cnf transformation 40]
100. ~creative(X0) | kind(X0) | ~patient(X0) [cnf transformation 34]
124. funny(X0) | curious(X0) | ~happy(X0) [cnf transformation 60]
128. ~funny(X0) | humble(X0) | wise(X0) [cnf transformation 61]
131. ~creative(sK6) [cnf transformation 65]
139. ~kind(alice) [cnf transformation 23]
142. ~humble(X0) [duplicate literal removal 80]
149. 2 <=> rich(lucy) [avatar definition]
154. 3 <=> rich(alice) [avatar definition]
156. rich(alice) <- (3) [avatar component clause 154]
157. 3 | 2 [avatar split clause 74,149,154]
158. happy(X0) [subsumption resolution 79,142]
160. ~wise(X0) | ~generous(X0) [subsumption resolution 83,158]
162. 4 <=> ! [X0] : wise(X0) [avatar definition]
163. wise(X0) <- (4) [avatar component clause 162]
165. 5 <=> curious(lucy) [avatar definition]
167. curious(lucy) <- (5) [avatar component clause 165]
168. 4 | 5 [avatar split clause 85,165,162]
169. ~curious(X0) | ~rich(X0) [subsumption resolution 88,89]
185. 9 <=> ! [X1] : creative(X1) [avatar definition]
186. creative(X1) <- (9) [avatar component clause 185]
240. funny(X0) | curious(X0) [subsumption resolution 124,158]
242. ~funny(X0) | wise(X0) [subsumption resolution 128,142]
260. ~generous(X0) <- (4) [resolution 160,163]
263. creative(X0) <- (4) [resolution 260,77]
266. 9 | ~4 [avatar split clause 263,162,185]
268. ~rich(lucy) <- (5) [resolution 167,169]
271. ~2 | ~5 [avatar split clause 268,165,149]
277. curious(X0) | wise(X0) [resolution 242,240]
301. ~rich(X1) | wise(X1) [resolution 277,169]
305. wise(alice) <- (3) [resolution 301,156]
328. ~generous(alice) <- (3) [resolution 305,160]
354. creative(alice) <- (3) [resolution 328,77]
355. patient(alice) <- (3) [resolution 328,76]
367. kind(alice) | ~patient(alice) <- (3) [resolution 354,100]
369. ~patient(alice) <- (3) [subsumption resolution 367,139]
370. $false <- (3) [subsumption resolution 369,355]
371. ~3 [avatar contradiction clause 370]
392. $false <- (9) [resolution 186,131]
397. ~9 [avatar contradiction clause 392]
399. $false [avatar sat refutation 157,168,266,271,371,397]
% SZS output end Proof for 3537872797227168015131861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either quiet or not funny and vice versa.
If susan is both not happy and not humble then susan is either not quiet or not old.
Everyone who is both not happy and not rich is strong or not creative.
If lucy is not patient then lucy is patient.
Everyone who is not creative is both not creative and not brave.
If fred is both rich and not creative then lucy is not quiet and vice versa.
Everyone who is generous is either happy or humble and vice versa.
Everyone who is not tall is both happy and not quiet and vice versa.
Everyone who is either generous or not rich is not strong and vice versa.
If lucy is humble then someone is both not patient and strong and vice versa.
If someone is either not patient or not generous then susan is humble and vice versa.
Everyone who is both generous and kind is humble and vice versa.
If someone is either not strong or not wise then alice is not tall or rich.
If alice is both tall and not old then someone is both humble and not creative and vice versa.
Everyone who is rich is both not happy and not creative.
Everyone who is both not generous and rich is both strong and not funny.
Paul is either wise or not brave.
Someone is either happy or not brave.
Someone is both curious and not creative.
Someone is funny or not old.
Someone is creative or not funny.
Someone is wise or not generous.
John is either not patient or humble.
Someone is not generous. | Lucy is patient. | entailment | (![X]:(~curious(X)<=>(quiet(X)<~>~funny(X))))&
(((~happy(susan)&~humble(susan)))=>((~quiet(susan)<~>~old(susan))))&
(![X]:((~happy(X)&~rich(X))=>(strong(X)|~creative(X))))&
((~patient(lucy))=>(patient(lucy)))&
(![X]:(~creative(X)=>(~creative(X)&~brave(X))))&
(((rich(fred)&~creative(fred)))<=>(~quiet(lucy)))&
(![X]:(generous(X)<=>(happy(X)<~>humble(X))))&
(![X]:(~tall(X)<=>(happy(X)&~quiet(X))))&
(![X]:((generous(X)<~>~rich(X))<=>~strong(X)))&
((humble(lucy))<=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(humble(susan)))&
(![X]:((generous(X)&kind(X))<=>humble(X)))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~tall(alice)|rich(alice))))&
(((tall(alice)&~old(alice)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:(rich(X)=>(~happy(X)&~creative(X))))&
(![X]:((~generous(X)&rich(X))=>(strong(X)&~funny(X))))&
((wise(paul)<~>~brave(paul)))&
(?[X]:((happy(X)<~>~brave(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:((funny(X)|~old(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~patient(john)<~>humble(john)))&
(?[X]:(~generous(X))) | patient(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9195998067260573985507689
% SZS output start Proof for 9195998067260573985507689
4. ~patient(lucy) => patient(lucy) [input p3]
25. ~patient(lucy) [input hypothesis]
32. patient(lucy) | patient(lucy) [ennf transformation 4]
83. patient(lucy) | patient(lucy) [cnf transformation 32]
132. ~patient(lucy) [cnf transformation 25]
133. patient(lucy) [duplicate literal removal 83]
295. $false [subsumption resolution 132,133]
% SZS output end Proof for 9195998067260573985507689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is either funny or not wise and vice versa. Everyone who is either kind or not curious is rich or not creative. If lucy is either old or not strong then someone is tall or not happy and vice versa. Everyone who is not calm or not tall is not quiet and vice versa. If john is both not wise and quiet then paul is both happy and curious and vice versa. If someone is either not humble or calm then paul is wise. If someone is not kind then alice is both tall and not old and vice versa. Everyone who is either not rich or brave is not brave. If fred is happy then alice is quiet and vice versa. If someone is not calm or brave then someone is both not kind and not wise. If someone is old then someone is not patient and vice versa. If someone is both not old and not creative then someone is not funny. Everyone who is either not tall or tall is both not happy and kind. If lucy is calm then paul is both not happy and not creative. If fred is both brave and patient then someone is generous. Everyone who is both kind and patient is humble or not kind and vice versa. Someone is creative or not brave. Fred is both patient and not tall. Someone is both humble and quiet. Paul is curious. Someone is generous or tall. | Fred is not curious. | neutral | (![X]:((brave(X)&~wise(X))<=>(funny(X)<~>~wise(X))))&
(![X]:((kind(X)<~>~curious(X))=>(rich(X)|~creative(X))))&
(((old(lucy)<~>~strong(lucy)))<=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((~calm(X)|~tall(X))<=>~quiet(X)))&
(((~wise(john)&quiet(john)))<=>((happy(paul)&curious(paul))))&
((?[X]:((~humble(X)<~>calm(X))))=>(wise(paul)))&
((?[X]:(~kind(X)))<=>((tall(alice)&~old(alice))))&
(![X]:((~rich(X)<~>brave(X))=>~brave(X)))&
((happy(fred))<=>(quiet(alice)))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:((~kind(X)&~wise(X)))))&
((?[X]:(old(X)))<=>(?[X]:(~patient(X))))&
((?[X]:((~old(X)&~creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)<~>tall(X))=>(~happy(X)&kind(X))))&
((calm(lucy))=>((~happy(paul)&~creative(paul))))&
(((brave(fred)&patient(fred)))=>(?[X]:(generous(X))))&
(![X]:((kind(X)&patient(X))<=>(humble(X)|~kind(X))))&
(?[X]:((creative(X)|~brave(X))))&
((patient(fred)&~tall(fred)))&
(?[X]:((humble(X)&quiet(X))))&
(curious(paul))&
(?[X]:((generous(X)|tall(X)))) | ~curious(fred) | [] | null | 0 |
Everyone who is either patient or curious is strong or not quiet.
Everyone who is either brave or not rich is both quiet and not old.
If john is either not old or not wise then alice is either not happy or not quiet and vice versa.
Everyone who is both generous and humble is both happy and old and vice versa.
If someone is not kind or not curious then lucy is generous or not patient and vice versa.
If someone is either not kind or not quiet then someone is both calm and not patient and vice versa.
Everyone who is patient is either calm or not creative.
If susan is both not calm and not strong then someone is not humble and vice versa.
If john is both not happy and not brave then john is both calm and not kind and vice versa.
Everyone who is both quiet and funny is not calm and vice versa.
If paul is both not quiet and creative then paul is both creative and not curious.
Everyone who is strong is both not kind and happy and vice versa.
Everyone who is not curious or tall is both brave and not strong.
Everyone who is happy is both curious and not strong.
Everyone who is both kind and curious is not wise.
If someone is not strong or not funny then lucy is not brave and vice versa.
Lucy is strong or not humble.
Fred is either not kind or strong.
Fred is both generous and not tall.
Alice is either kind or not funny.
Paul is not brave or strong.
John is tall or not kind.
Alice is humble. | Lucy is funny. | neutral | (![X]:((patient(X)<~>curious(X))=>(strong(X)|~quiet(X))))&
(![X]:((brave(X)<~>~rich(X))=>(quiet(X)&~old(X))))&
(((~old(john)<~>~wise(john)))<=>((~happy(alice)<~>~quiet(alice))))&
(![X]:((generous(X)&humble(X))<=>(happy(X)&old(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(patient(X)=>(calm(X)<~>~creative(X))))&
(((~calm(susan)&~strong(susan)))<=>(?[X]:(~humble(X))))&
(((~happy(john)&~brave(john)))<=>((calm(john)&~kind(john))))&
(![X]:((quiet(X)&funny(X))<=>~calm(X)))&
(((~quiet(paul)&creative(paul)))=>((creative(paul)&~curious(paul))))&
(![X]:(strong(X)<=>(~kind(X)&happy(X))))&
(![X]:((~curious(X)|tall(X))=>(brave(X)&~strong(X))))&
(![X]:(happy(X)=>(curious(X)&~strong(X))))&
(![X]:((kind(X)&curious(X))=>~wise(X)))&
((?[X]:((~strong(X)|~funny(X))))<=>(~brave(lucy)))&
((strong(lucy)|~humble(lucy)))&
((~kind(fred)<~>strong(fred)))&
((generous(fred)&~tall(fred)))&
((kind(alice)<~>~funny(alice)))&
((~brave(paul)|strong(paul)))&
((tall(john)|~kind(john)))&
(humble(alice)) | funny(lucy) | [] | null | 0 |
Everyone who is either not brave or funny is rich. Everyone who is both rich and generous is not old. If paul is not quiet then someone is both not rich and rich. Everyone who is both creative and generous is either not curious or not calm. If someone is either not kind or strong then mary is tall or humble and vice versa. If someone is both not creative and humble then mary is creative. Everyone who is both not generous and generous is not happy or not patient and vice versa. If paul is either happy or tall then someone is both not happy and curious. Everyone who is both not brave and creative is rich. Everyone who is both curious and not rich is humble or funny. Everyone who is strong or not creative is humble. Everyone who is not creative or generous is calm and vice versa. Everyone who is calm or creative is quiet and vice versa. Everyone who is either humble or happy is strong. Everyone who is quiet is both rich and not calm and vice versa. If mary is either kind or not quiet then fred is strong and vice versa. Paul is not generous or not calm. Someone is not humble or humble. Someone is both kind and not tall. Lucy is not curious or not brave. | Lucy is not funny. | neutral | (![X]:((~brave(X)<~>funny(X))=>rich(X)))&
(![X]:((rich(X)&generous(X))=>~old(X)))&
((~quiet(paul))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((creative(X)&generous(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>strong(X))))<=>((tall(mary)|humble(mary))))&
((?[X]:((~creative(X)&humble(X))))=>(creative(mary)))&
(![X]:((~generous(X)&generous(X))<=>(~happy(X)|~patient(X))))&
(((happy(paul)<~>tall(paul)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~brave(X)&creative(X))=>rich(X)))&
(![X]:((curious(X)&~rich(X))=>(humble(X)|funny(X))))&
(![X]:((strong(X)|~creative(X))=>humble(X)))&
(![X]:((~creative(X)|generous(X))<=>calm(X)))&
(![X]:((calm(X)|creative(X))<=>quiet(X)))&
(![X]:((humble(X)<~>happy(X))=>strong(X)))&
(![X]:(quiet(X)<=>(rich(X)&~calm(X))))&
(((kind(mary)<~>~quiet(mary)))<=>(strong(fred)))&
((~generous(paul)|~calm(paul)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((kind(X)&~tall(X))))&
((~curious(lucy)|~brave(lucy))) | ~funny(lucy) | [] | null | 0 |
Everyone who is both not creative and not generous is rich or not kind and vice versa.
If alice is both not creative and calm then paul is either strong or not curious and vice versa.
If someone is wise then john is funny and vice versa.
Everyone who is not patient or old is generous or not quiet.
If someone is either not rich or humble then someone is both not calm and not funny and vice versa.
Everyone who is not curious or funny is old.
Everyone who is strong is either curious or not wise.
Everyone who is not brave is either tall or not funny and vice versa.
If fred is both not humble and not happy then someone is not creative or humble and vice versa.
If someone is strong then someone is both brave and creative.
Everyone who is generous or not quiet is either curious or not curious.
If someone is old or wise then fred is either not wise or not creative and vice versa.
If susan is happy or not wise then someone is both generous and curious and vice versa.
If mary is either old or not brave then someone is either humble or not curious and vice versa.
Everyone who is kind or not wise is generous and vice versa.
If someone is not calm or wise then mary is wise and vice versa.
Mary is either not old or funny.
Someone is both quiet and not humble.
Someone is either kind or old.
Alice is either not brave or generous.
Paul is either old or not kind.
Susan is both curious and creative.
Alice is either rich or not rich.
Someone is both old and strong. | Susan is not kind. | contradiction | (![X]:((~creative(X)&~generous(X))<=>(rich(X)|~kind(X))))&
(((~creative(alice)&calm(alice)))<=>((strong(paul)<~>~curious(paul))))&
((?[X]:(wise(X)))<=>(funny(john)))&
(![X]:((~patient(X)|old(X))=>(generous(X)|~quiet(X))))&
((?[X]:((~rich(X)<~>humble(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~curious(X)|funny(X))=>old(X)))&
(![X]:(strong(X)=>(curious(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~funny(X))))&
(((~humble(fred)&~happy(fred)))<=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:(strong(X)))=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((generous(X)|~quiet(X))=>(curious(X)<~>~curious(X))))&
((?[X]:((old(X)|wise(X))))<=>((~wise(fred)<~>~creative(fred))))&
(((happy(susan)|~wise(susan)))<=>(?[X]:((generous(X)&curious(X)))))&
(((old(mary)<~>~brave(mary)))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((kind(X)|~wise(X))<=>generous(X)))&
((?[X]:((~calm(X)|wise(X))))<=>(wise(mary)))&
((~old(mary)<~>funny(mary)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((kind(X)<~>old(X))))&
((~brave(alice)<~>generous(alice)))&
((old(paul)<~>~kind(paul)))&
((curious(susan)&creative(susan)))&
((rich(alice)<~>~rich(alice)))&
(?[X]:((old(X)&strong(X)))) | ~kind(susan) | [
"p0",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8215876324705218430185747
% SZS output start Proof for 8215876324705218430185747
1. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (~kind(X0) | rich(X0))) [input p0]
22. creative(susan) & curious(susan) [input p21]
25. ~kind(susan) [input hypothesis]
35. ! [X0] : (((~generous(X0) & ~creative(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 1]
36. ! [X0] : (((~generous(X0) & ~creative(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | generous(X0) | creative(X0))) [flattening 35]
91. ~creative(X0) | kind(X0) [cnf transformation 36]
164. creative(susan) [cnf transformation 22]
169. ~kind(susan) [cnf transformation 25]
412. kind(susan) [resolution 91,164]
415. $false [subsumption resolution 412,169]
% SZS output end Proof for 8215876324705218430185747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is creative or not tall and vice versa.
Everyone who is both happy and not patient is either not strong or generous and vice versa.
Everyone who is generous is not tall and vice versa.
If susan is not humble then someone is humble or funny.
Everyone who is either not calm or patient is not old and vice versa.
Everyone who is tall is not strong or not generous.
Everyone who is either humble or not quiet is both not rich and not generous.
If fred is calm then lucy is either rich or not strong.
If mary is strong then alice is curious or not brave and vice versa.
Everyone who is either not wise or not calm is either funny or not curious.
Everyone who is both not tall and not wise is not old or quiet and vice versa.
Everyone who is either generous or old is either humble or quiet and vice versa.
Everyone who is not tall is patient.
Everyone who is either not generous or not calm is both not creative and humble and vice versa.
Everyone who is not happy is both not old and not funny.
Fred is not brave.
John is kind or rich.
John is generous or wise.
Susan is funny or patient.
Someone is not old or not rich. | Alice is not wise. | entailment | (![X]:(~creative(X)<=>(creative(X)|~tall(X))))&
(![X]:((happy(X)&~patient(X))<=>(~strong(X)<~>generous(X))))&
(![X]:(generous(X)<=>~tall(X)))&
((~humble(susan))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((~calm(X)<~>patient(X))<=>~old(X)))&
(![X]:(tall(X)=>(~strong(X)|~generous(X))))&
(![X]:((humble(X)<~>~quiet(X))=>(~rich(X)&~generous(X))))&
((calm(fred))=>((rich(lucy)<~>~strong(lucy))))&
((strong(mary))<=>((curious(alice)|~brave(alice))))&
(![X]:((~wise(X)<~>~calm(X))=>(funny(X)<~>~curious(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~old(X)|quiet(X))))&
(![X]:((generous(X)<~>old(X))<=>(humble(X)<~>quiet(X))))&
(![X]:(~tall(X)=>patient(X)))&
(![X]:((~generous(X)<~>~calm(X))<=>(~creative(X)&humble(X))))&
(![X]:(~happy(X)=>(~old(X)&~funny(X))))&
(~brave(fred))&
((kind(john)|rich(john)))&
((generous(john)|wise(john)))&
((funny(susan)|patient(susan)))&
(?[X]:((~old(X)|~rich(X)))) | ~wise(alice) | [
"p0",
"p2",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9203849101250017531307079
% SZS output start Proof for 9203849101250017531307079
1. ! [X0] : (~creative(X0) <=> (~tall(X0) | creative(X0))) [input p0]
3. ! [X0] : (generous(X0) <=> ~tall(X0)) [input p2]
7. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => (~generous(X0) & ~rich(X0))) [input p6]
11. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (quiet(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((generous(X0) <~> old(X0)) <=> (humble(X0) <~> quiet(X0))) [input p11]
21. wise(alice) [input hypothesis]
26. ! [X0] : ((~generous(X0) & ~rich(X0)) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 7]
31. ! [X0] : ((~creative(X0) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | creative(X0))) [nnf transformation 1]
32. ! [X0] : ((~creative(X0) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | creative(X0))) [flattening 31]
35. ! [X0] : ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0))) [nnf transformation 3]
39. ! [X0] : ((~generous(X0) & ~rich(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 26]
44. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 11]
45. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | wise(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 12]
51. ~tall(X0) | creative(X0) | creative(X0) [cnf transformation 32]
52. ~creative(X0) | ~creative(X0) [cnf transformation 32]
61. generous(X0) | tall(X0) [cnf transformation 35]
70. ~generous(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 39]
71. ~generous(X0) | humble(X0) | quiet(X0) [cnf transformation 39]
84. ~wise(X0) | old(X0) [cnf transformation 45]
92. ~old(X0) | ~generous(X0) | quiet(X0) | ~humble(X0) [cnf transformation 46]
93. ~old(X0) | ~generous(X0) | humble(X0) | ~quiet(X0) [cnf transformation 46]
107. wise(alice) [cnf transformation 21]
108. ~tall(X0) | creative(X0) [duplicate literal removal 51]
109. ~creative(X0) [duplicate literal removal 52]
110. ~tall(X0) [subsumption resolution 108,109]
111. generous(X0) [subsumption resolution 61,110]
125. quiet(X0) | humble(X0) [subsumption resolution 71,111]
126. ~quiet(X0) | ~humble(X0) [subsumption resolution 70,111]
157. ~old(X0) | humble(X0) | ~quiet(X0) [subsumption resolution 93,111]
158. ~quiet(X0) | ~old(X0) [subsumption resolution 157,126]
159. ~old(X0) | quiet(X0) | ~humble(X0) [subsumption resolution 92,111]
160. ~old(X0) | ~humble(X0) [subsumption resolution 159,126]
174. old(alice) [resolution 84,107]
179. ~old(X0) | humble(X0) [resolution 158,125]
180. ~old(X0) [subsumption resolution 179,160]
181. $false [resolution 180,174]
% SZS output end Proof for 9203849101250017531307079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is both rich and not old and vice versa. Everyone who is both calm and old is either not strong or old. If paul is both not happy and strong then fred is both generous and not calm and vice versa. If paul is either not funny or wise then alice is either not tall or creative. Everyone who is both generous and brave is not calm. If someone is both curious and not old then lucy is both patient and not patient and vice versa. If someone is not strong then someone is both humble and creative and vice versa. If lucy is both kind and creative then someone is either not kind or kind and vice versa. Everyone who is not creative or old is rich or not curious and vice versa. Everyone who is happy or old is both not strong and not patient. Everyone who is both not calm and generous is either not curious or funny and vice versa. Everyone who is brave is either quiet or not quiet. Everyone who is not brave or patient is calm or old and vice versa. Everyone who is not creative is strong and vice versa. Everyone who is not old is not kind. If someone is either not wise or not curious then someone is not strong and vice versa. Someone is either not quiet or not brave. Susan is not rich. Susan is both strong and not funny. Someone is not kind or not tall. Someone is both wise and generous. Someone is not calm. Someone is not curious. Someone is both patient and quiet. | Susan is curious. | contradiction | (![X]:(funny(X)<=>(rich(X)&~old(X))))&
(![X]:((calm(X)&old(X))=>(~strong(X)<~>old(X))))&
(((~happy(paul)&strong(paul)))<=>((generous(fred)&~calm(fred))))&
(((~funny(paul)<~>wise(paul)))=>((~tall(alice)<~>creative(alice))))&
(![X]:((generous(X)&brave(X))=>~calm(X)))&
((?[X]:((curious(X)&~old(X))))<=>((patient(lucy)&~patient(lucy))))&
((?[X]:(~strong(X)))<=>(?[X]:((humble(X)&creative(X)))))&
(((kind(lucy)&creative(lucy)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:((~creative(X)|old(X))<=>(rich(X)|~curious(X))))&
(![X]:((happy(X)|old(X))=>(~strong(X)&~patient(X))))&
(![X]:((~calm(X)&generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:(brave(X)=>(quiet(X)<~>~quiet(X))))&
(![X]:((~brave(X)|patient(X))<=>(calm(X)|old(X))))&
(![X]:(~creative(X)<=>strong(X)))&
(![X]:(~old(X)=>~kind(X)))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(~strong(X))))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(~rich(susan))&
((strong(susan)&~funny(susan)))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((wise(X)&generous(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)&quiet(X)))) | curious(susan) | [
"p5",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3452768681070437205690974
% SZS output start Proof for 3452768681070437205690974
6. ? [X0] : (~old(X0) & curious(X0)) <=> (~patient(lucy) & patient(lucy)) [input p5]
10. ! [X0] : ((old(X0) | happy(X0)) => (~patient(X0) & ~strong(X0))) [input p9]
19. ~funny(susan) & strong(susan) [input p18]
25. curious(susan) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~strong(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 10]
42. (? [X0] : (~old(X0) & curious(X0)) | (patient(lucy) | ~patient(lucy))) & ((~patient(lucy) & patient(lucy)) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 6]
43. (? [X0] : (~old(X0) & curious(X0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X0] : (old(X0) | ~curious(X0))) [flattening 42]
44. (? [X0] : (~old(X0) & curious(X0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : (old(X1) | ~curious(X1))) [rectify 43]
45. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK0) & curious(sK0)) [choice axiom]
46. ((~old(sK0) & curious(sK0)) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : (old(X1) | ~curious(X1))) [skolemisation 44,45]
97. patient(lucy) | old(X1) | ~curious(X1) [cnf transformation 46]
98. ~patient(lucy) | old(X1) | ~curious(X1) [cnf transformation 46]
115. ~strong(X0) | ~old(X0) [cnf transformation 33]
140. strong(susan) [cnf transformation 19]
149. curious(susan) [cnf transformation 25]
196. 9 <=> ! [X1] : (old(X1) | ~curious(X1)) [avatar definition]
197. ~curious(X1) | old(X1) <- (9) [avatar component clause 196]
199. 10 <=> patient(lucy) [avatar definition]
202. 9 | ~10 [avatar split clause 98,199,196]
203. 9 | 10 [avatar split clause 97,199,196]
300. ~old(susan) [resolution 115,140]
313. old(susan) <- (9) [resolution 197,149]
322. $false <- (9) [subsumption resolution 313,300]
323. ~9 [avatar contradiction clause 322]
324. $false [avatar sat refutation 202,203,323]
% SZS output end Proof for 3452768681070437205690974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not curious then fred is both tall and happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not happy or not calm is either not tall or not brave.
If susan is both not humble and generous then someone is both rich and not humble.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
Everyone who is not old is happy or kind.
Fred is either wise or not curious.
Mary is both old and not humble.
Someone is either not quiet or not brave.
Susan is not generous.
Someone is both strong and not patient.
Alice is either not kind or not happy. | Alice is not calm. | entailment | ((~curious(fred))=>((tall(fred)&happy(fred))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((~happy(X)|~calm(X))=>(~tall(X)<~>~brave(X))))&
(((~humble(susan)&generous(susan)))=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
(![X]:(~old(X)=>(happy(X)|kind(X))))&
((wise(fred)<~>~curious(fred)))&
((old(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(~generous(susan))&
(?[X]:((strong(X)&~patient(X))))&
((~kind(alice)<~>~happy(alice))) | ~calm(alice) | [
"p2",
"p3",
"p4",
"p5",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7489511533910283121181382
% SZS output start Proof for 7489511533910283121181382
3. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p2]
4. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p3]
5. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p4]
6. ! [X0] : (~old(X0) <=> wise(X0)) [input p5]
11. ! [X0] : (~rich(X0) <=> humble(X0)) [input p10]
18. ~humble(mary) & old(mary) [input p17]
23. calm(alice) [input hypothesis]
36. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 36]
38. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 4]
39. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 38]
40. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK0) | ~rich(sK0)) & (happy(sK0) | rich(sK0))) [choice axiom]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK0) | ~rich(sK0)) & (happy(sK0) | rich(sK0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 39,40]
42. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 5]
43. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 42]
44. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK1) | calm(sK1)) [choice axiom]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK1) | calm(sK1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 43,44]
46. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 6]
59. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 11]
74. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 37]
75. ~humble(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 37]
76. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 37]
77. ~quiet(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 37]
84. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 41]
90. strong(paul) | ~quiet(paul) | ~calm(X0) [cnf transformation 45]
92. ~strong(paul) | quiet(paul) | ~calm(X0) [cnf transformation 45]
95. ~old(X0) | ~wise(X0) [cnf transformation 46]
110. rich(X0) | humble(X0) [cnf transformation 59]
121. old(mary) [cnf transformation 18]
122. ~humble(mary) [cnf transformation 18]
130. calm(alice) [cnf transformation 23]
162. 8 <=> humble(mary) [avatar definition]
166. 9 <=> wise(mary) [avatar definition]
171. 10 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
172. ~rich(X0) | happy(X0) <- (10) [avatar component clause 171]
175. 10 | 8 | 9 [avatar split clause 84,166,162,171]
192. 14 <=> quiet(paul) [avatar definition]
193. ~quiet(paul) <- (~14) [avatar component clause 192]
194. quiet(paul) <- (14) [avatar component clause 192]
196. 15 <=> strong(paul) [avatar definition]
197. strong(paul) <- (15) [avatar component clause 196]
198. ~strong(paul) <- (~15) [avatar component clause 196]
201. 16 <=> ! [X0] : ~calm(X0) [avatar definition]
202. ~calm(X0) <- (16) [avatar component clause 201]
203. 16 | 14 | ~15 [avatar split clause 92,196,192,201]
205. 16 | ~14 | 15 [avatar split clause 90,196,192,201]
281. ~8 [avatar split clause 122,162]
303. ~wise(mary) [resolution 95,121]
316. humble(X0) | happy(X0) <- (10) [resolution 172,110]
350. $false <- (16) [resolution 202,130]
351. ~16 [avatar contradiction clause 350]
412. happy(X1) | quiet(X1) | strong(X1) <- (10) [resolution 316,74]
417. quiet(X1) | strong(X1) <- (10) [subsumption resolution 412,76]
437. strong(paul) <- (10, ~14) [resolution 417,193]
443. $false <- (10, ~14, ~15) [subsumption resolution 437,198]
444. ~10 | 14 | 15 [avatar contradiction clause 443]
445. ~9 [avatar split clause 303,166]
467. humble(X0) | happy(X0) <- (10) [resolution 172,110]
501. happy(X0) | ~strong(X0) | ~quiet(X0) <- (10) [resolution 467,75]
506. ~quiet(X0) | ~strong(X0) <- (10) [subsumption resolution 501,77]
530. ~strong(paul) <- (10, 14) [resolution 506,194]
531. $false <- (10, 14, 15) [subsumption resolution 530,197]
532. ~10 | ~14 | ~15 [avatar contradiction clause 531]
533. $false [avatar sat refutation 175,203,205,281,351,444,445,532]
% SZS output end Proof for 7489511533910283121181382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or old is both not rich and old. If susan is kind or tall then mary is both not calm and happy and vice versa. Everyone who is either generous or not tall is humble or strong. If someone is humble or creative then someone is patient. Everyone who is not calm or strong is tall. Everyone who is both curious and not generous is rich and vice versa. If someone is both wise and not tall 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. Everyone who is patient is curious or brave. Everyone who is both not brave and brave is either not tall or generous. Lucy is not calm. Someone is not patient. Someone is both curious and not kind. Alice is calm. Someone is not calm. Alice is not creative or not strong. | John is not generous. | entailment | (![X]:((wise(X)<~>old(X))=>(~rich(X)&old(X))))&
(((kind(susan)|tall(susan)))<=>((~calm(mary)&happy(mary))))&
(![X]:((generous(X)<~>~tall(X))=>(humble(X)|strong(X))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~calm(X)|strong(X))=>tall(X)))&
(![X]:((curious(X)&~generous(X))<=>rich(X)))&
((?[X]:((wise(X)&~tall(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]:(patient(X)=>(curious(X)|brave(X))))&
(![X]:((~brave(X)&brave(X))=>(~tall(X)<~>generous(X))))&
(~calm(lucy))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&~kind(X))))&
(calm(alice))&
(?[X]:(~calm(X)))&
((~creative(alice)|~strong(alice))) | ~generous(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4504786835400346023533006
% SZS output start Proof for 4504786835400346023533006
13. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (tall(X0) | ~tall(X0))) [input p12]
22. generous(john) [input hypothesis]
58. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 13]
59. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | humble(X0) | generous(X0))) [flattening 58]
108. ~generous(X0) | tall(X0) [cnf transformation 59]
109. ~generous(X0) | ~tall(X0) [cnf transformation 59]
121. generous(john) [cnf transformation 22]
223. ~generous(X0) [subsumption resolution 108,109]
224. $false [subsumption resolution 121,223]
% SZS output end Proof for 4504786835400346023533006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then someone is tall or curious. If someone is not quiet or not brave then someone is happy and vice versa. Everyone who is either not wise or not creative is curious or not humble and vice versa. If someone is either generous or not happy then someone is kind. Everyone who is either curious or patient is curious and vice versa. Everyone who is curious is not happy. Everyone who is either rich or not old is kind or not curious. Everyone who is not creative or kind is kind and vice versa. Everyone who is either kind or happy is both happy and not patient and vice versa. If fred is old or not funny then lucy is either not curious or not quiet and vice versa. If someone is not wise then lucy is not curious or calm and vice versa. Everyone who is both not calm and patient is both not happy and curious. If lucy is both not generous and calm then someone is both wise and generous. If someone is either not generous or funny then someone is funny and vice versa. Everyone who is curious is either not humble or not rich. Everyone who is not creative is wise or tall and vice versa. Susan is not wise or not calm. Someone is creative or not curious. Lucy is either not wise or tall. Susan is both not patient and not generous. Fred is both not brave and strong. Someone is either not funny or not strong. | Lucy is tall. | contradiction | ((?[X]:(wise(X)))=>(?[X]:((tall(X)|curious(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(curious(X)|~humble(X))))&
((?[X]:((generous(X)<~>~happy(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>patient(X))<=>curious(X)))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((rich(X)<~>~old(X))=>(kind(X)|~curious(X))))&
(![X]:((~creative(X)|kind(X))<=>kind(X)))&
(![X]:((kind(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(((old(fred)|~funny(fred)))<=>((~curious(lucy)<~>~quiet(lucy))))&
((?[X]:(~wise(X)))<=>((~curious(lucy)|calm(lucy))))&
(![X]:((~calm(X)&patient(X))=>(~happy(X)&curious(X))))&
(((~generous(lucy)&calm(lucy)))=>(?[X]:((wise(X)&generous(X)))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:(funny(X))))&
(![X]:(curious(X)=>(~humble(X)<~>~rich(X))))&
(![X]:(~creative(X)<=>(wise(X)|tall(X))))&
((~wise(susan)|~calm(susan)))&
(?[X]:((creative(X)|~curious(X))))&
((~wise(lucy)<~>tall(lucy)))&
((~patient(susan)&~generous(susan)))&
((~brave(fred)&strong(fred)))&
(?[X]:((~funny(X)<~>~strong(X)))) | tall(lucy) | [
"p4",
"p7",
"p8",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8060429751529794372512676
% SZS output start Proof for 8060429751529794372512676
5. ! [X0] : ((curious(X0) <~> patient(X0)) <=> curious(X0)) [input p4]
8. ! [X0] : ((kind(X0) | ~creative(X0)) <=> kind(X0)) [input p7]
9. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (~patient(X0) & happy(X0))) [input p8]
16. ! [X0] : (~creative(X0) <=> (tall(X0) | wise(X0))) [input p15]
19. ~wise(lucy) <~> tall(lucy) [input p18]
23. tall(lucy) [input hypothesis]
52. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 5]
54. ! [X0] : (((kind(X0) | ~creative(X0)) | ~kind(X0)) & (kind(X0) | (~kind(X0) & creative(X0)))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | ~creative(X0) | ~kind(X0)) & (kind(X0) | (~kind(X0) & creative(X0)))) [flattening 54]
56. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 9]
57. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 56]
73. ! [X0] : ((~creative(X0) | (~tall(X0) & ~wise(X0))) & ((tall(X0) | wise(X0)) | creative(X0))) [nnf transformation 16]
74. ! [X0] : ((~creative(X0) | (~tall(X0) & ~wise(X0))) & (tall(X0) | wise(X0) | creative(X0))) [flattening 73]
77. (~tall(lucy) | wise(lucy)) & (tall(lucy) | ~wise(lucy)) [nnf transformation 19]
94. curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 52]
96. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
100. kind(X0) | creative(X0) [cnf transformation 55]
103. happy(X0) | happy(X0) | ~kind(X0) [cnf transformation 57]
108. ~happy(X0) | ~kind(X0) | patient(X0) | ~happy(X0) [cnf transformation 57]
129. ~creative(X0) | ~wise(X0) [cnf transformation 74]
134. ~tall(lucy) | wise(lucy) [cnf transformation 77]
141. tall(lucy) [cnf transformation 23]
142. happy(X0) | ~kind(X0) [duplicate literal removal 103]
143. ~happy(X0) | ~kind(X0) | patient(X0) [duplicate literal removal 108]
144. curious(X0) | ~patient(X0) [duplicate literal removal 94]
145. ~patient(X0) | ~curious(X0) [duplicate literal removal 96]
147. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
148. ~wise(X1) <- (1) [avatar component clause 147]
194. ~patient(X0) [subsumption resolution 144,145]
195. ~happy(X0) | ~kind(X0) [subsumption resolution 143,194]
196. ~kind(X0) [subsumption resolution 142,195]
291. 33 <=> wise(lucy) [avatar definition]
293. wise(lucy) <- (33) [avatar component clause 291]
295. 34 <=> tall(lucy) [avatar definition]
298. 33 | ~34 [avatar split clause 134,295,291]
310. 34 [avatar split clause 141,295]
314. creative(X0) [resolution 100,196]
315. ~wise(X0) [resolution 314,129]
316. 1 [avatar split clause 315,147]
317. $false <- (1, 33) [resolution 148,293]
318. ~1 | ~33 [avatar contradiction clause 317]
319. $false [avatar sat refutation 298,310,316,318]
% SZS output end Proof for 8060429751529794372512676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not kind and not happy then someone is both strong and curious and vice versa.
If john is both old and not generous then someone is either tall or kind.
Everyone who is patient is either calm or curious and vice versa.
If someone is not strong then someone is either quiet or humble.
If someone is not calm then john is not patient and vice versa.
If susan is either wise or not wise then alice is both kind and not humble.
Everyone who is not humble or creative is generous or not generous and vice versa.
Everyone who is not funny or calm is funny or not humble and vice versa.
Everyone who is either not creative or humble is not calm.
Everyone who is either funny or strong is either brave or creative and vice versa.
Everyone who is either not strong or tall is either not wise or creative and vice versa.
Everyone who is strong is creative or not curious and vice versa.
If someone is brave then paul is not patient and vice versa.
If lucy is both not brave and not generous then alice is not patient.
If someone is not kind then alice is either kind or not curious and vice versa.
If lucy is wise then someone is both calm and patient and vice versa.
Fred is either strong or tall.
Susan is both not creative and curious.
Lucy is rich.
Paul is creative.
Lucy is not rich or patient.
Someone is both rich and wise.
Paul is either strong or calm. | Paul is calm. | contradiction | (((~kind(susan)&~happy(susan)))<=>(?[X]:((strong(X)&curious(X)))))&
(((old(john)&~generous(john)))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(patient(X)<=>(calm(X)<~>curious(X))))&
((?[X]:(~strong(X)))=>(?[X]:((quiet(X)<~>humble(X)))))&
((?[X]:(~calm(X)))<=>(~patient(john)))&
(((wise(susan)<~>~wise(susan)))=>((kind(alice)&~humble(alice))))&
(![X]:((~humble(X)|creative(X))<=>(generous(X)|~generous(X))))&
(![X]:((~funny(X)|calm(X))<=>(funny(X)|~humble(X))))&
(![X]:((~creative(X)<~>humble(X))=>~calm(X)))&
(![X]:((funny(X)<~>strong(X))<=>(brave(X)<~>creative(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~wise(X)<~>creative(X))))&
(![X]:(strong(X)<=>(creative(X)|~curious(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
(((~brave(lucy)&~generous(lucy)))=>(~patient(alice)))&
((?[X]:(~kind(X)))<=>((kind(alice)<~>~curious(alice))))&
((wise(lucy))<=>(?[X]:((calm(X)&patient(X)))))&
((strong(fred)<~>tall(fred)))&
((~creative(susan)&curious(susan)))&
(rich(lucy))&
(creative(paul))&
((~rich(lucy)|patient(lucy)))&
(?[X]:((rich(X)&wise(X))))&
((strong(paul)<~>calm(paul))) | calm(paul) | [
"p11",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4938260270602794064491187
% SZS output start Proof for 4938260270602794064491187
12. ! [X0] : (strong(X0) <=> (~curious(X0) | creative(X0))) [input p11]
20. creative(paul) [input p19]
23. strong(paul) <~> calm(paul) [input p22]
24. calm(paul) [input hypothesis]
54. ! [X0] : ((strong(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~strong(X0))) [nnf transformation 12]
55. ! [X0] : ((strong(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~strong(X0))) [flattening 54]
71. (~calm(paul) | ~strong(paul)) & (calm(paul) | strong(paul)) [nnf transformation 23]
115. ~creative(X0) | strong(X0) [cnf transformation 55]
132. creative(paul) [cnf transformation 20]
137. ~calm(paul) | ~strong(paul) [cnf transformation 71]
138. calm(paul) [cnf transformation 24]
284. 30 <=> strong(paul) [avatar definition]
286. ~strong(paul) <- (~30) [avatar component clause 284]
288. 31 <=> calm(paul) [avatar definition]
291. ~30 | ~31 [avatar split clause 137,288,284]
293. 31 [avatar split clause 138,288]
294. strong(paul) [resolution 115,132]
295. $false <- (~30) [subsumption resolution 294,286]
296. 30 [avatar contradiction clause 295]
297. $false [avatar sat refutation 291,293,296]
% SZS output end Proof for 4938260270602794064491187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not patient is brave.
If fred is both not old and not happy then someone is funny or brave and vice versa.
If someone is either tall or creative then fred is both not quiet and not calm.
If someone is creative then alice is calm or wise and vice versa.
If someone is either wise or generous then someone is both not creative and not old and vice versa.
If someone is either not humble or patient then lucy is not tall and vice versa.
Everyone who is not generous is either kind or creative.
If fred is either kind or not tall then someone is both old and not funny and vice versa.
Everyone who is both old and patient is both not old and not humble and vice versa.
If someone is both happy and calm then someone is both brave and old.
If someone is not creative or not kind then alice is patient and vice versa.
If someone is humble or strong then someone is both funny and not strong and vice versa.
If alice is not brave then someone is both wise and tall.
Everyone who is not old is either not funny or not quiet and vice versa.
Everyone who is either curious or not creative is not rich and vice versa.
If someone is both curious and old then someone is both not tall and not quiet.
Someone is not tall or not wise.
Someone is not patient.
Someone is both not strong and tall.
Someone is either calm or curious.
Fred is not brave or not quiet.
Someone is either calm or not curious.
Someone is curious.
Someone is both not brave and creative. | Fred is kind. | neutral | (![X]:((~wise(X)&~patient(X))=>brave(X)))&
(((~old(fred)&~happy(fred)))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:((tall(X)<~>creative(X))))=>((~quiet(fred)&~calm(fred))))&
((?[X]:(creative(X)))<=>((calm(alice)|wise(alice))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(~tall(lucy)))&
(![X]:(~generous(X)=>(kind(X)<~>creative(X))))&
(((kind(fred)<~>~tall(fred)))<=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((old(X)&patient(X))<=>(~old(X)&~humble(X))))&
((?[X]:((happy(X)&calm(X))))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~creative(X)|~kind(X))))<=>(patient(alice)))&
((?[X]:((humble(X)|strong(X))))<=>(?[X]:((funny(X)&~strong(X)))))&
((~brave(alice))=>(?[X]:((wise(X)&tall(X)))))&
(![X]:(~old(X)<=>(~funny(X)<~>~quiet(X))))&
(![X]:((curious(X)<~>~creative(X))<=>~rich(X)))&
((?[X]:((curious(X)&old(X))))=>(?[X]:((~tall(X)&~quiet(X)))))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~strong(X)&tall(X))))&
(?[X]:((calm(X)<~>curious(X))))&
((~brave(fred)|~quiet(fred)))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)&creative(X)))) | kind(fred) | [] | null | 0 |
Everyone who is not curious or not brave is patient and vice versa.
If someone is both not humble and patient then lucy is patient or happy.
Everyone who is curious or rich is not happy or curious.
If someone is both not generous and strong then alice is both not old and humble.
Everyone who is both wise and not calm is not curious and vice versa.
Everyone who is not humble or tall is either not generous or not creative.
Everyone who is patient is both humble and curious.
Everyone who is both curious and not old is either rich or strong and vice versa.
If someone is either calm or not curious then fred is not calm.
Everyone who is rich is not happy and vice versa.
If lucy is either not funny or not wise then john is both not tall and tall.
If someone is either patient or happy then someone is either happy or wise.
If someone is not brave then fred is funny.
Everyone who is not wise is both not generous and brave and vice versa.
If someone is both not kind and not generous then someone is either not wise or generous and vice versa.
Everyone who is both not old and not strong is not patient or not tall.
Someone is either rich or not generous.
Lucy is not curious or old.
Someone is not old.
Paul is not funny or not strong.
Alice is both not creative and not calm.
Someone is both happy and not funny.
Mary is either wise or not funny.
Someone is both not strong and not old. | Alice is not humble. | contradiction | (![X]:((~curious(X)|~brave(X))<=>patient(X)))&
((?[X]:((~humble(X)&patient(X))))=>((patient(lucy)|happy(lucy))))&
(![X]:((curious(X)|rich(X))=>(~happy(X)|curious(X))))&
((?[X]:((~generous(X)&strong(X))))=>((~old(alice)&humble(alice))))&
(![X]:((wise(X)&~calm(X))<=>~curious(X)))&
(![X]:((~humble(X)|tall(X))=>(~generous(X)<~>~creative(X))))&
(![X]:(patient(X)=>(humble(X)&curious(X))))&
(![X]:((curious(X)&~old(X))<=>(rich(X)<~>strong(X))))&
((?[X]:((calm(X)<~>~curious(X))))=>(~calm(fred)))&
(![X]:(rich(X)<=>~happy(X)))&
(((~funny(lucy)<~>~wise(lucy)))=>((~tall(john)&tall(john))))&
((?[X]:((patient(X)<~>happy(X))))=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:(~brave(X)))=>(funny(fred)))&
(![X]:(~wise(X)<=>(~generous(X)&brave(X))))&
((?[X]:((~kind(X)&~generous(X))))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((~old(X)&~strong(X))=>(~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
((~curious(lucy)|old(lucy)))&
(?[X]:(~old(X)))&
((~funny(paul)|~strong(paul)))&
((~creative(alice)&~calm(alice)))&
(?[X]:((happy(X)&~funny(X))))&
((wise(mary)<~>~funny(mary)))&
(?[X]:((~strong(X)&~old(X)))) | ~humble(alice) | [
"p0",
"p4",
"p5",
"p6",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1714277265792038687185153
% SZS output start Proof for 1714277265792038687185153
1. ! [X0] : ((~brave(X0) | ~curious(X0)) <=> patient(X0)) [input p0]
5. ! [X0] : ((~calm(X0) & wise(X0)) <=> ~curious(X0)) [input p4]
6. ! [X0] : ((tall(X0) | ~humble(X0)) => (~generous(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : (patient(X0) => (curious(X0) & humble(X0))) [input p6]
14. ! [X0] : (~wise(X0) <=> (brave(X0) & ~generous(X0))) [input p13]
21. ~calm(alice) & ~creative(alice) [input p20]
25. ~humble(alice) [input hypothesis]
33. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | (~tall(X0) & humble(X0))) [ennf transformation 6]
34. ! [X0] : ((curious(X0) & humble(X0)) | ~patient(X0)) [ennf transformation 7]
41. ! [X0] : (((~brave(X0) | ~curious(X0)) | ~patient(X0)) & (patient(X0) | (brave(X0) & curious(X0)))) [nnf transformation 1]
42. ! [X0] : ((~brave(X0) | ~curious(X0) | ~patient(X0)) & (patient(X0) | (brave(X0) & curious(X0)))) [flattening 41]
43. ! [X0] : (((~calm(X0) & wise(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~wise(X0)))) [nnf transformation 5]
44. ! [X0] : (((~calm(X0) & wise(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~wise(X0))) [flattening 43]
45. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~tall(X0) & humble(X0))) [nnf transformation 33]
55. ! [X0] : ((~wise(X0) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | wise(X0))) [nnf transformation 14]
56. ! [X0] : ((~wise(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | wise(X0))) [flattening 55]
72. patient(X0) | curious(X0) [cnf transformation 42]
80. ~wise(X0) | calm(X0) | ~curious(X0) [cnf transformation 44]
85. creative(X0) | generous(X0) | humble(X0) [cnf transformation 45]
88. curious(X0) | ~patient(X0) [cnf transformation 34]
108. ~generous(X0) | wise(X0) [cnf transformation 56]
123. ~creative(alice) [cnf transformation 21]
124. ~calm(alice) [cnf transformation 21]
131. ~humble(alice) [cnf transformation 25]
148. 5 <=> humble(alice) [avatar definition]
149. ~humble(alice) <- (~5) [avatar component clause 148]
157. curious(X0) [subsumption resolution 88,72]
276. ~5 [avatar split clause 131,148]
294. generous(alice) | humble(alice) [resolution 85,123]
298. generous(alice) <- (~5) [subsumption resolution 294,149]
299. wise(alice) <- (~5) [resolution 298,108]
320. calm(alice) | ~curious(alice) <- (~5) [resolution 299,80]
321. ~curious(alice) <- (~5) [subsumption resolution 320,124]
322. $false <- (~5) [subsumption resolution 321,157]
323. 5 [avatar contradiction clause 322]
324. $false [avatar sat refutation 276,323]
% SZS output end Proof for 1714277265792038687185153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or not strong then john is not humble and vice versa.
Everyone who is both not funny and not tall is not strong or not calm.
If fred is either generous or funny then someone is funny or not tall and vice versa.
If someone is not tall then someone is both calm and quiet and vice versa.
If someone is either patient or not generous then someone is both funny and not brave.
Everyone who is either not creative or not patient is not patient and vice versa.
Everyone who is strong or not patient is either not generous or not humble and vice versa.
Everyone who is not calm or kind is both not patient and not tall.
Everyone who is not tall is both brave and happy.
Everyone who is curious is both not rich and curious and vice versa.
Everyone who is both calm and creative is both curious and tall.
If someone is both not quiet and wise then john is not wise or creative.
If someone is both tall and not curious then someone is not calm or curious.
Everyone who is not tall is not calm and vice versa.
Everyone who is either not generous or not happy is old or humble and vice versa.
If lucy is not patient then someone is both not curious and not strong and vice versa.
Alice is not calm.
Susan is kind.
Someone is both calm and not happy.
John is both not curious and happy.
Fred is either not tall or strong.
Someone is not kind or not wise. | Susan is not happy. | contradiction | ((?[X]:((funny(X)|~strong(X))))<=>(~humble(john)))&
(![X]:((~funny(X)&~tall(X))=>(~strong(X)|~calm(X))))&
(((generous(fred)<~>funny(fred)))<=>(?[X]:((funny(X)|~tall(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)&quiet(X)))))&
((?[X]:((patient(X)<~>~generous(X))))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~creative(X)<~>~patient(X))<=>~patient(X)))&
(![X]:((strong(X)|~patient(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((~calm(X)|kind(X))=>(~patient(X)&~tall(X))))&
(![X]:(~tall(X)=>(brave(X)&happy(X))))&
(![X]:(curious(X)<=>(~rich(X)&curious(X))))&
(![X]:((calm(X)&creative(X))=>(curious(X)&tall(X))))&
((?[X]:((~quiet(X)&wise(X))))=>((~wise(john)|creative(john))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:(~tall(X)<=>~calm(X)))&
(![X]:((~generous(X)<~>~happy(X))<=>(old(X)|humble(X))))&
((~patient(lucy))<=>(?[X]:((~curious(X)&~strong(X)))))&
(~calm(alice))&
(kind(susan))&
(?[X]:((calm(X)&~happy(X))))&
((~curious(john)&happy(john)))&
((~tall(fred)<~>strong(fred)))&
(?[X]:((~kind(X)|~wise(X)))) | ~happy(susan) | [
"p7",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2384154383071196610260987
% SZS output start Proof for 2384154383071196610260987
8. ! [X0] : ((kind(X0) | ~calm(X0)) => (~tall(X0) & ~patient(X0))) [input p7]
9. ! [X0] : (~tall(X0) => (happy(X0) & brave(X0))) [input p8]
18. kind(susan) [input p17]
23. ~happy(susan) [input hypothesis]
32. ! [X0] : ((~tall(X0) & ~patient(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 8]
33. ! [X0] : ((happy(X0) & brave(X0)) | tall(X0)) [ennf transformation 9]
102. ~kind(X0) | ~tall(X0) [cnf transformation 32]
104. happy(X0) | tall(X0) [cnf transformation 33]
123. kind(susan) [cnf transformation 18]
130. ~happy(susan) [cnf transformation 23]
257. ~tall(susan) [resolution 102,123]
259. tall(susan) [resolution 104,130]
260. $false [subsumption resolution 259,257]
% SZS output end Proof for 2384154383071196610260987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not creative is not kind.
Everyone who is either not quiet or not curious is both not funny and humble.
If someone is wise or not generous then lucy is both not curious and humble.
Everyone who is not tall is not generous or not calm.
Everyone who is both kind and not strong is not strong and vice versa.
Everyone who is both not calm and wise is not happy and vice versa.
Everyone who is either not happy or patient is both creative and not quiet.
Everyone who is creative or not happy is not creative and vice versa.
If fred is both not rich and rich then someone is either curious or brave and vice versa.
If someone is brave then someone is not calm.
Everyone who is both not curious and not funny is not rich and vice versa.
Everyone who is either calm or humble is either not quiet or not brave.
Everyone who is old or rich is not generous or not curious and vice versa.
Someone is happy or funny.
Someone is humble.
Someone is both not funny and not creative.
Mary is kind or not old.
Alice is wise or not calm.
Mary is both wise and not humble. | Fred is not wise. | contradiction | (![X]:((~kind(X)<~>~creative(X))=>~kind(X)))&
(![X]:((~quiet(X)<~>~curious(X))=>(~funny(X)&humble(X))))&
((?[X]:((wise(X)|~generous(X))))=>((~curious(lucy)&humble(lucy))))&
(![X]:(~tall(X)=>(~generous(X)|~calm(X))))&
(![X]:((kind(X)&~strong(X))<=>~strong(X)))&
(![X]:((~calm(X)&wise(X))<=>~happy(X)))&
(![X]:((~happy(X)<~>patient(X))=>(creative(X)&~quiet(X))))&
(![X]:((creative(X)|~happy(X))<=>~creative(X)))&
(((~rich(fred)&rich(fred)))<=>(?[X]:((curious(X)<~>brave(X)))))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>~rich(X)))&
(![X]:((calm(X)<~>humble(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((old(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:(humble(X)))&
(?[X]:((~funny(X)&~creative(X))))&
((kind(mary)|~old(mary)))&
((wise(alice)|~calm(alice)))&
((wise(mary)&~humble(mary))) | ~wise(fred) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7230766523766265821355959
% SZS output start Proof for 7230766523766265821355959
6. ! [X0] : ((wise(X0) & ~calm(X0)) <=> ~happy(X0)) [input p5]
8. ! [X0] : ((~happy(X0) | creative(X0)) <=> ~creative(X0)) [input p7]
20. ~wise(fred) [input hypothesis]
33. ! [X0] : (((wise(X0) & ~calm(X0)) | happy(X0)) & (~happy(X0) | (~wise(X0) | calm(X0)))) [nnf transformation 6]
34. ! [X0] : (((wise(X0) & ~calm(X0)) | happy(X0)) & (~happy(X0) | ~wise(X0) | calm(X0))) [flattening 33]
36. ! [X0] : (((~happy(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (happy(X0) & ~creative(X0)))) [nnf transformation 8]
37. ! [X0] : ((~happy(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (happy(X0) & ~creative(X0)))) [flattening 36]
72. happy(X0) | wise(X0) [cnf transformation 34]
77. ~creative(X0) | ~creative(X0) [cnf transformation 37]
79. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 37]
106. ~wise(fred) [cnf transformation 20]
107. ~creative(X0) [duplicate literal removal 77]
108. ~happy(X0) | creative(X0) [duplicate literal removal 79]
180. creative(X0) | wise(X0) [resolution 108,72]
183. wise(X0) [subsumption resolution 180,107]
186. $false [resolution 183,106]
% SZS output end Proof for 7230766523766265821355959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or creative is either humble or not wise.
If paul is not rich then alice is generous or not wise.
If someone is either not calm or strong then susan is wise and vice versa.
Everyone who is not tall is either generous or creative.
Everyone who is not curious or not generous is both not kind and wise and vice versa.
If lucy is happy then someone is either wise or not strong.
Everyone who is creative is both not tall and humble and vice versa.
If paul is not calm or not humble then someone is not curious.
Everyone who is both patient and old is both not quiet and not rich.
Everyone who is not creative or not humble is both not tall and not old and vice versa.
Everyone who is either strong or generous is not wise or not generous.
If someone is not happy then lucy is either not rich or not calm and vice versa.
Everyone who is happy is either not humble or not creative and vice versa.
Everyone who is not funny is not humble or not curious.
If john is happy then someone is not funny or not strong.
Everyone who is both generous and tall is patient and vice versa.
Someone is quiet or old.
Mary is strong or not wise.
Mary is either not happy or creative.
Someone is generous or not old.
Mary is both not tall and not quiet.
Someone is either calm or quiet.
Someone is either rich or brave.
Paul is either not happy or not curious. | Mary is not old. | entailment | (![X]:((~quiet(X)<~>creative(X))=>(humble(X)<~>~wise(X))))&
((~rich(paul))=>((generous(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>strong(X))))<=>(wise(susan)))&
(![X]:(~tall(X)=>(generous(X)<~>creative(X))))&
(![X]:((~curious(X)|~generous(X))<=>(~kind(X)&wise(X))))&
((happy(lucy))=>(?[X]:((wise(X)<~>~strong(X)))))&
(![X]:(creative(X)<=>(~tall(X)&humble(X))))&
(((~calm(paul)|~humble(paul)))=>(?[X]:(~curious(X))))&
(![X]:((patient(X)&old(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>(~tall(X)&~old(X))))&
(![X]:((strong(X)<~>generous(X))=>(~wise(X)|~generous(X))))&
((?[X]:(~happy(X)))<=>((~rich(lucy)<~>~calm(lucy))))&
(![X]:(happy(X)<=>(~humble(X)<~>~creative(X))))&
(![X]:(~funny(X)=>(~humble(X)|~curious(X))))&
((happy(john))=>(?[X]:((~funny(X)|~strong(X)))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
(?[X]:((quiet(X)|old(X))))&
((strong(mary)|~wise(mary)))&
((~happy(mary)<~>creative(mary)))&
(?[X]:((generous(X)|~old(X))))&
((~tall(mary)&~quiet(mary)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((~happy(paul)<~>~curious(paul))) | ~old(mary) | [
"p6",
"p9",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1321506331859220454535539
% SZS output start Proof for 1321506331859220454535539
7. ! [X0] : (creative(X0) <=> (humble(X0) & ~tall(X0))) [input p6]
10. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> (~old(X0) & ~tall(X0))) [input p9]
13. ! [X0] : (happy(X0) <=> (~humble(X0) <~> ~creative(X0))) [input p12]
19. ~happy(mary) <~> creative(mary) [input p18]
25. old(mary) [input hypothesis]
53. ! [X0] : ((creative(X0) | (~humble(X0) | tall(X0))) & ((humble(X0) & ~tall(X0)) | ~creative(X0))) [nnf transformation 7]
54. ! [X0] : ((creative(X0) | ~humble(X0) | tall(X0)) & ((humble(X0) & ~tall(X0)) | ~creative(X0))) [flattening 53]
57. ! [X0] : (((~humble(X0) | ~creative(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (humble(X0) & creative(X0)))) [nnf transformation 10]
58. ! [X0] : ((~humble(X0) | ~creative(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (humble(X0) & creative(X0)))) [flattening 57]
64. ! [X0] : ((happy(X0) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~happy(X0))) [nnf transformation 13]
69. (~creative(mary) | happy(mary)) & (creative(mary) | ~happy(mary)) [nnf transformation 19]
98. ~creative(X0) | humble(X0) [cnf transformation 54]
106. ~old(X0) | creative(X0) [cnf transformation 58]
115. ~creative(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 64]
116. creative(X0) | humble(X0) | ~happy(X0) [cnf transformation 64]
125. ~creative(mary) | happy(mary) [cnf transformation 69]
135. old(mary) [cnf transformation 25]
222. humble(X0) | ~happy(X0) [subsumption resolution 116,98]
223. ~creative(X0) | ~happy(X0) [subsumption resolution 115,222]
255. ~creative(mary) [subsumption resolution 125,223]
298. creative(mary) [resolution 106,135]
299. $false [subsumption resolution 298,255]
% SZS output end Proof for 1321506331859220454535539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not strong is either not old or calm. Everyone who is either quiet or curious is either wise or old. Everyone who is either curious or not patient is not curious and vice versa. Everyone who is not quiet is both quiet and calm and vice versa. If someone is both curious and not strong then lucy is old or curious and vice versa. Everyone who is either brave or creative is not quiet or quiet and vice versa. Everyone who is not wise is both old and not tall. Everyone who is not kind is either not patient or not strong. If mary is not kind or not tall then john is not quiet or not calm. Everyone who is both not quiet and humble is humble or not happy and vice versa. Everyone who is both not quiet and quiet is calm or not rich and vice versa. If someone is either wise or generous then someone is either not strong or old and vice versa. If lucy is calm then someone is both not funny and curious and vice versa. If john is either brave or funny then lucy is not generous or not quiet and vice versa. Everyone who is creative or not generous is both funny and creative. Someone is either not humble or not old. Someone is not strong. Someone is not tall or not creative. Paul is rich. Someone is kind. Fred is not kind or not funny. Lucy is tall. | Fred is not funny. | neutral | (![X]:((~curious(X)<~>~strong(X))=>(~old(X)<~>calm(X))))&
(![X]:((quiet(X)<~>curious(X))=>(wise(X)<~>old(X))))&
(![X]:((curious(X)<~>~patient(X))<=>~curious(X)))&
(![X]:(~quiet(X)<=>(quiet(X)&calm(X))))&
((?[X]:((curious(X)&~strong(X))))<=>((old(lucy)|curious(lucy))))&
(![X]:((brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~wise(X)=>(old(X)&~tall(X))))&
(![X]:(~kind(X)=>(~patient(X)<~>~strong(X))))&
(((~kind(mary)|~tall(mary)))=>((~quiet(john)|~calm(john))))&
(![X]:((~quiet(X)&humble(X))<=>(humble(X)|~happy(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(calm(X)|~rich(X))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~strong(X)<~>old(X)))))&
((calm(lucy))<=>(?[X]:((~funny(X)&curious(X)))))&
(((brave(john)<~>funny(john)))<=>((~generous(lucy)|~quiet(lucy))))&
(![X]:((creative(X)|~generous(X))=>(funny(X)&creative(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|~creative(X))))&
(rich(paul))&
(?[X]:(kind(X)))&
((~kind(fred)|~funny(fred)))&
(tall(lucy)) | ~funny(fred) | [] | null | 0 |
Everyone who is either tall or humble is both not rich and not kind.
Everyone who is either quiet or wise is both not brave and not tall and vice versa.
If someone is either tall or not tall then fred is both not old and not brave.
If mary is both not creative and tall then someone is not strong.
Everyone who is both kind and not calm is not brave or patient and vice versa.
Everyone who is either not rich or not tall is strong or generous and vice versa.
Everyone who is either not tall or wise is both not quiet and not strong and vice versa.
If someone is not humble then susan is not rich.
Everyone who is either not wise or not curious is both rich and funny.
If someone is both not funny and not tall then john is creative and vice versa.
If john is either not rich or funny then someone is both wise and not rich.
Everyone who is not happy or old is creative.
If someone is not humble or brave then someone is quiet and vice versa.
If someone is both generous and not funny then paul is both not wise and brave.
Everyone who is either old or not calm is either not generous or generous and vice versa.
If someone is both creative and happy then fred is not wise.
Mary is both tall and calm.
Paul is curious or not quiet.
Lucy is either calm or wise.
Susan is calm.
Someone is old.
Someone is funny.
Someone is generous.
Susan is generous. | Fred is not strong. | contradiction | (![X]:((tall(X)<~>humble(X))=>(~rich(X)&~kind(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>((~old(fred)&~brave(fred))))&
(((~creative(mary)&tall(mary)))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)&~calm(X))<=>(~brave(X)|patient(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>(strong(X)|generous(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(~quiet(X)&~strong(X))))&
((?[X]:(~humble(X)))=>(~rich(susan)))&
(![X]:((~wise(X)<~>~curious(X))=>(rich(X)&funny(X))))&
((?[X]:((~funny(X)&~tall(X))))<=>(creative(john)))&
(((~rich(john)<~>funny(john)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~happy(X)|old(X))=>creative(X)))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((generous(X)&~funny(X))))=>((~wise(paul)&brave(paul))))&
(![X]:((old(X)<~>~calm(X))<=>(~generous(X)<~>generous(X))))&
((?[X]:((creative(X)&happy(X))))=>(~wise(fred)))&
((tall(mary)&calm(mary)))&
((curious(paul)|~quiet(paul)))&
((calm(lucy)<~>wise(lucy)))&
(calm(susan))&
(?[X]:(old(X)))&
(?[X]:(funny(X)))&
(?[X]:(generous(X)))&
(generous(susan)) | ~strong(fred) | [
"p1",
"p2",
"p4",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6945053584391304794780382
% SZS output start Proof for 6945053584391304794780382
2. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~tall(X0) & ~brave(X0))) [input p1]
3. ? [X0] : (tall(X0) <~> ~tall(X0)) => (~brave(fred) & ~old(fred)) [input p2]
5. ! [X0] : ((~calm(X0) & kind(X0)) <=> (patient(X0) | ~brave(X0))) [input p4]
7. ! [X0] : ((~tall(X0) <~> wise(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p6]
13. ? [X0] : (brave(X0) | ~humble(X0)) <=> ? [X0] : quiet(X0) [input p12]
20. calm(susan) [input p19]
25. ~strong(fred) [input hypothesis]
26. ? [X0] : (brave(X0) | ~humble(X0)) <=> ? [X1] : quiet(X1) [rectify 13]
28. (~brave(fred) & ~old(fred)) | ! [X0] : (tall(X0) <=> ~tall(X0)) [ennf transformation 3]
38. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 38]
40. (~brave(fred) & ~old(fred)) | ! [X0] : ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))) [nnf transformation 28]
43. ! [X0] : (((~calm(X0) & kind(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (calm(X0) | ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((~calm(X0) & kind(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | calm(X0) | ~kind(X0))) [flattening 43]
47. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [flattening 47]
57. (? [X0] : (brave(X0) | ~humble(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~brave(X0) & humble(X0))) [nnf transformation 26]
58. (? [X0] : (brave(X0) | ~humble(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~brave(X3) & humble(X3))) [rectify 57]
59. ? [X0] : (brave(X0) | ~humble(X0)) => (brave(sK3) | ~humble(sK3)) [choice axiom]
60. ? [X2] : quiet(X2) => quiet(sK4) [choice axiom]
61. ((brave(sK3) | ~humble(sK3)) | ! [X1] : ~quiet(X1)) & (quiet(sK4) | ! [X3] : (~brave(X3) & humble(X3))) [skolemisation 58,60,59]
76. ~quiet(X0) | wise(X0) | ~tall(X0) [cnf transformation 39]
77. ~wise(X0) | quiet(X0) | ~tall(X0) [cnf transformation 39]
78. brave(X0) | quiet(X0) | tall(X0) | wise(X0) [cnf transformation 39]
79. ~wise(X0) | ~quiet(X0) | tall(X0) | brave(X0) [cnf transformation 39]
83. ~brave(fred) | tall(X0) | tall(X0) [cnf transformation 40]
88. ~calm(X0) | brave(X0) [cnf transformation 44]
96. ~quiet(X0) | wise(X0) | tall(X0) [cnf transformation 48]
97. ~quiet(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 48]
100. wise(X0) | ~tall(X0) | strong(X0) | quiet(X0) [cnf transformation 48]
101. ~wise(X0) | tall(X0) | strong(X0) | quiet(X0) [cnf transformation 48]
117. quiet(sK4) | ~brave(X3) [cnf transformation 61]
135. calm(susan) [cnf transformation 20]
140. ~strong(fred) [cnf transformation 25]
148. ~brave(fred) | tall(X0) [duplicate literal removal 83]
150. 1 <=> ! [X0] : tall(X0) [avatar definition]
151. tall(X0) <- (1) [avatar component clause 150]
153. 2 <=> brave(fred) [avatar definition]
155. ~brave(fred) <- (~2) [avatar component clause 153]
156. 1 | ~2 [avatar split clause 148,153,150]
180. ~wise(X0) | strong(X0) | quiet(X0) [subsumption resolution 101,77]
181. ~tall(X0) | strong(X0) | quiet(X0) [subsumption resolution 100,180]
182. ~wise(X0) | ~tall(X0) [subsumption resolution 97,77]
183. ~quiet(X0) | wise(X0) [subsumption resolution 96,76]
243. 21 <=> ! [X3] : ~brave(X3) [avatar definition]
244. ~brave(X3) <- (21) [avatar component clause 243]
246. 22 <=> quiet(sK4) [avatar definition]
248. quiet(sK4) <- (22) [avatar component clause 246]
249. 21 | 22 [avatar split clause 117,246,243]
270. 27 <=> wise(fred) [avatar definition]
271. wise(fred) <- (27) [avatar component clause 270]
272. ~wise(fred) <- (~27) [avatar component clause 270]
298. brave(susan) [resolution 88,135]
302. $false <- (21) [subsumption resolution 298,244]
303. ~21 [avatar contradiction clause 302]
310. wise(sK4) <- (22) [resolution 183,248]
313. ~tall(sK4) <- (22) [resolution 310,182]
327. 32 <=> tall(fred) [avatar definition]
328. tall(fred) <- (32) [avatar component clause 327]
329. ~tall(fred) <- (~32) [avatar component clause 327]
514. strong(fred) | quiet(fred) <- (32) [resolution 328,181]
525. quiet(fred) <- (32) [subsumption resolution 514,140]
617. wise(fred) <- (32) [resolution 525,183]
621. $false <- (~27, 32) [subsumption resolution 617,272]
622. 27 | ~32 [avatar contradiction clause 621]
630. $false <- (1, 22) [resolution 151,313]
631. ~1 | ~22 [avatar contradiction clause 630]
633. quiet(fred) | tall(fred) | wise(fred) <- (~2) [resolution 155,78]
636. ~quiet(fred) | tall(fred) | brave(fred) <- (27) [resolution 271,79]
639. strong(fred) | quiet(fred) <- (27) [resolution 271,180]
640. ~tall(fred) <- (27) [resolution 271,182]
646. ~32 | ~27 [avatar split clause 640,270,327]
647. quiet(fred) <- (27) [subsumption resolution 639,140]
648. tall(fred) | brave(fred) <- (27) [subsumption resolution 636,647]
649. tall(fred) <- (~2, 27) [subsumption resolution 648,155]
650. 32 | 2 | ~27 [avatar split clause 649,270,153,327]
658. quiet(fred) | wise(fred) <- (~2, ~32) [subsumption resolution 633,329]
659. wise(fred) <- (~2, ~32) [subsumption resolution 658,183]
660. 27 | 2 | 32 [avatar split clause 659,327,153,270]
661. $false [avatar sat refutation 156,249,303,622,631,646,650,660]
% SZS output end Proof for 6945053584391304794780382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is both curious and not funny.
If john is both creative and tall then lucy is not rich or rich and vice versa.
Everyone who is both strong and patient is either quiet or not quiet and vice versa.
If someone is either not rich or old then someone is both curious and not patient.
If mary is calm then someone is either quiet or wise and vice versa.
If lucy is either humble or not happy then john is not kind or not humble.
Everyone who is either not generous or not tall is both not happy and funny and vice versa.
If someone is not quiet then someone is tall or not strong and vice versa.
Everyone who is not curious or rich is not brave.
If someone is either not humble or not brave then someone is kind or not strong.
Everyone who is both not strong and not calm is either not old or quiet.
Everyone who is both creative and not happy is both not humble and funny and vice versa.
Everyone who is either funny or not quiet is curious or not calm and vice versa.
Everyone who is calm or not humble is not kind and vice versa.
Everyone who is not calm is quiet or not quiet and vice versa.
If lucy is not strong or not curious then fred is both not generous and patient and vice versa.
Alice is either strong or not quiet.
Someone is both not curious and not creative.
Someone is strong.
Someone is either quiet or not rich.
Lucy is both funny and not old.
Someone is not kind.
John is both not rich and humble. | John is wise. | contradiction | (![X]:((~tall(X)|happy(X))=>(curious(X)&~funny(X))))&
(((creative(john)&tall(john)))<=>((~rich(lucy)|rich(lucy))))&
(![X]:((strong(X)&patient(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~rich(X)<~>old(X))))=>(?[X]:((curious(X)&~patient(X)))))&
((calm(mary))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(((humble(lucy)<~>~happy(lucy)))=>((~kind(john)|~humble(john))))&
(![X]:((~generous(X)<~>~tall(X))<=>(~happy(X)&funny(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:((~curious(X)|rich(X))=>~brave(X)))&
((?[X]:((~humble(X)<~>~brave(X))))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~strong(X)&~calm(X))=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)&~happy(X))<=>(~humble(X)&funny(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(curious(X)|~calm(X))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(((~strong(lucy)|~curious(lucy)))<=>((~generous(fred)&patient(fred))))&
((strong(alice)<~>~quiet(alice)))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((funny(lucy)&~old(lucy)))&
(?[X]:(~kind(X)))&
((~rich(john)&humble(john))) | wise(john) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"p14",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 494501674757542172026579
% SZS output start Proof for 494501674757542172026579
1. ! [X0] : ((happy(X0) | ~tall(X0)) => (~funny(X0) & curious(X0))) [input p0]
2. (tall(john) & creative(john)) <=> (rich(lucy) | ~rich(lucy)) [input p1]
3. ! [X0] : ((patient(X0) & strong(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p2]
4. ? [X0] : (~rich(X0) <~> old(X0)) => ? [X0] : (~patient(X0) & curious(X0)) [input p3]
5. calm(mary) <=> ? [X0] : (quiet(X0) <~> wise(X0)) [input p4]
12. ! [X0] : ((~happy(X0) & creative(X0)) <=> (funny(X0) & ~humble(X0))) [input p11]
13. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> (~calm(X0) | curious(X0))) [input p12]
15. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p14]
21. ~old(lucy) & funny(lucy) [input p20]
23. humble(john) & ~rich(john) [input p22]
24. wise(john) [input hypothesis]
25. ? [X0] : (~rich(X0) <~> old(X0)) => ? [X1] : (~patient(X1) & curious(X1)) [rectify 4]
28. ! [X0] : ((~funny(X0) & curious(X0)) | (~happy(X0) & tall(X0))) [ennf transformation 1]
29. ? [X1] : (~patient(X1) & curious(X1)) | ! [X0] : (~rich(X0) <=> old(X0)) [ennf transformation 25]
36. ((tall(john) & creative(john)) | (~rich(lucy) & rich(lucy))) & ((rich(lucy) | ~rich(lucy)) | (~tall(john) | ~creative(john))) [nnf transformation 2]
37. ((tall(john) & creative(john)) | (~rich(lucy) & rich(lucy))) & (rich(lucy) | ~rich(lucy) | ~tall(john) | ~creative(john)) [flattening 36]
38. ! [X0] : (((patient(X0) & strong(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (~patient(X0) | ~strong(X0)))) [nnf transformation 3]
39. ! [X0] : (((patient(X0) & strong(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | ~patient(X0) | ~strong(X0))) [flattening 38]
40. ? [X1] : (~patient(X1) & curious(X1)) | ! [X0] : ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))) [nnf transformation 29]
41. ? [X0] : (~patient(X0) & curious(X0)) | ! [X1] : ((~rich(X1) | ~old(X1)) & (old(X1) | rich(X1))) [rectify 40]
42. ? [X0] : (~patient(X0) & curious(X0)) => (~patient(sK0) & curious(sK0)) [choice axiom]
43. (~patient(sK0) & curious(sK0)) | ! [X1] : ((~rich(X1) | ~old(X1)) & (old(X1) | rich(X1))) [skolemisation 41,42]
44. (calm(mary) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~calm(mary)) [nnf transformation 5]
45. (calm(mary) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (? [X1] : ((~wise(X1) | ~quiet(X1)) & (wise(X1) | quiet(X1))) | ~calm(mary)) [rectify 44]
46. ? [X1] : ((~wise(X1) | ~quiet(X1)) & (wise(X1) | quiet(X1))) => ((~wise(sK1) | ~quiet(sK1)) & (wise(sK1) | quiet(sK1))) [choice axiom]
47. (calm(mary) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(sK1) | ~quiet(sK1)) & (wise(sK1) | quiet(sK1))) | ~calm(mary)) [skolemisation 45,46]
61. ! [X0] : (((~happy(X0) & creative(X0)) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | (happy(X0) | ~creative(X0)))) [nnf transformation 12]
62. ! [X0] : (((~happy(X0) & creative(X0)) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | happy(X0) | ~creative(X0))) [flattening 61]
63. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 13]
64. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [flattening 63]
67. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 15]
68. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 67]
84. ~funny(X0) | ~happy(X0) [cnf transformation 28]
87. creative(john) | ~rich(lucy) [cnf transformation 37]
94. patient(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 39]
95. patient(X0) | quiet(X0) | quiet(X0) [cnf transformation 39]
98. ~patient(sK0) | old(X1) | rich(X1) [cnf transformation 43]
103. calm(mary) | quiet(X0) | ~wise(X0) [cnf transformation 47]
121. ~humble(X0) | happy(X0) | ~creative(X0) [cnf transformation 62]
128. ~quiet(X0) | funny(X0) | calm(X0) [cnf transformation 64]
135. ~calm(X0) | ~quiet(X0) [cnf transformation 68]
136. ~calm(X0) | quiet(X0) [cnf transformation 68]
150. ~old(lucy) [cnf transformation 21]
153. humble(john) [cnf transformation 23]
154. wise(john) [cnf transformation 24]
157. patient(X0) | ~quiet(X0) [duplicate literal removal 94]
158. quiet(X0) | patient(X0) [duplicate literal removal 95]
160. 1 <=> rich(lucy) [avatar definition]
170. 3 <=> creative(john) [avatar definition]
172. creative(john) <- (3) [avatar component clause 170]
173. ~1 | 3 [avatar split clause 87,170,160]
175. patient(X0) [subsumption resolution 157,158]
178. old(X1) | rich(X1) [subsumption resolution 98,175]
180. 4 <=> ! [X0] : (quiet(X0) | ~wise(X0)) [avatar definition]
181. ~wise(X0) | quiet(X0) <- (4) [avatar component clause 180]
183. 5 <=> calm(mary) [avatar definition]
185. calm(mary) <- (5) [avatar component clause 183]
186. 4 | 5 [avatar split clause 103,183,180]
214. 12 <=> humble(john) [avatar definition]
215. humble(john) <- (12) [avatar component clause 214]
253. ~calm(X0) [subsumption resolution 135,136]
277. 12 [avatar split clause 153,214]
294. rich(lucy) [resolution 178,150]
298. 1 [avatar split clause 294,160]
299. quiet(john) <- (4) [resolution 181,154]
314. 25 <=> funny(john) [avatar definition]
316. funny(john) <- (25) [avatar component clause 314]
339. happy(john) | ~creative(john) <- (12) [resolution 121,215]
341. happy(john) <- (3, 12) [subsumption resolution 339,172]
381. funny(john) | calm(john) <- (4) [resolution 128,299]
387. funny(john) <- (4) [subsumption resolution 381,253]
388. 25 | ~4 [avatar split clause 387,180,314]
397. ~happy(john) <- (25) [resolution 316,84]
399. $false <- (3, 12, 25) [subsumption resolution 397,341]
400. ~3 | ~12 | ~25 [avatar contradiction clause 399]
401. $false <- (5) [subsumption resolution 185,253]
402. ~5 [avatar contradiction clause 401]
403. $false [avatar sat refutation 173,186,277,298,388,400,402]
% SZS output end Proof for 494501674757542172026579
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is humble or not strong and vice versa.
If someone is either kind or not curious then paul is both not wise and funny and vice versa.
If someone is not rich or not brave then someone is both not generous and calm.
If someone is not quiet then mary is kind or not kind.
Everyone who is both curious and happy is either wise or not patient and vice versa.
Everyone who is either wise or not happy is not strong or tall.
Everyone who is both brave and not patient is either creative or not kind.
If someone is not brave or not strong then john is not quiet or not curious and vice versa.
If mary is either not strong or not brave then someone is not humble and vice versa.
If someone is calm then mary is generous or wise and vice versa.
If john is either tall or creative then john is either not humble or not tall and vice versa.
If someone is both funny and not wise then paul is not funny or calm.
If someone is humble then someone is not calm and vice versa.
Everyone who is both creative and not strong is both not strong and old.
Everyone who is either not curious or brave is quiet and vice versa.
If lucy is not happy or wise then someone is old.
Someone is either happy or funny.
Someone is quiet or not rich.
Alice is not generous.
John is not rich or not tall.
Susan is strong.
Someone is happy.
Someone is either curious or not funny.
Someone is calm. | John is strong. | entailment | (![X]:(strong(X)<=>(humble(X)|~strong(X))))&
((?[X]:((kind(X)<~>~curious(X))))<=>((~wise(paul)&funny(paul))))&
((?[X]:((~rich(X)|~brave(X))))=>(?[X]:((~generous(X)&calm(X)))))&
((?[X]:(~quiet(X)))=>((kind(mary)|~kind(mary))))&
(![X]:((curious(X)&happy(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((wise(X)<~>~happy(X))=>(~strong(X)|tall(X))))&
(![X]:((brave(X)&~patient(X))=>(creative(X)<~>~kind(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>((~quiet(john)|~curious(john))))&
(((~strong(mary)<~>~brave(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:(calm(X)))<=>((generous(mary)|wise(mary))))&
(((tall(john)<~>creative(john)))<=>((~humble(john)<~>~tall(john))))&
((?[X]:((funny(X)&~wise(X))))=>((~funny(paul)|calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&~strong(X))=>(~strong(X)&old(X))))&
(![X]:((~curious(X)<~>brave(X))<=>quiet(X)))&
(((~happy(lucy)|wise(lucy)))=>(?[X]:(old(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((quiet(X)|~rich(X))))&
(~generous(alice))&
((~rich(john)|~tall(john)))&
(strong(susan))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:(calm(X))) | strong(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8125671041570592871304804
% SZS output start Proof for 8125671041570592871304804
1. ! [X0] : (strong(X0) <=> (~strong(X0) | humble(X0))) [input p0]
25. ~strong(john) [input hypothesis]
41. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 1]
42. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~strong(X0))) [flattening 41]
90. strong(X0) | strong(X0) [cnf transformation 42]
149. ~strong(john) [cnf transformation 25]
155. strong(X0) [duplicate literal removal 90]
297. $false [subsumption resolution 149,155]
% SZS output end Proof for 8125671041570592871304804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or old then someone is either humble or curious and vice versa.
Everyone who is both calm and not happy is calm and vice versa.
Everyone who is calm or generous is both brave and not tall and vice versa.
If someone is either not tall or not strong then someone is both happy and not quiet and vice versa.
Everyone who is not strong or old is both creative and patient.
If mary is either quiet or patient then fred is either not patient or not calm.
If john is both not quiet and not patient then fred is both patient and not strong and vice versa.
Everyone who is rich or patient is either not kind or not happy and vice versa.
If alice is both curious and not kind then alice is not humble or tall and vice versa.
If someone is both not calm and not happy then john is either not old or strong.
If mary is either not funny or not creative then mary is not humble and vice versa.
Everyone who is not old is both not humble and funny and vice versa.
If susan is either not creative or not humble then paul is curious and vice versa.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
Someone is either not kind or not happy.
Lucy is not kind or funny.
Someone is not patient or quiet.
John is both quiet and kind.
Someone is not calm.
Someone is both generous and rich.
Someone is both brave and curious. | Fred is generous. | contradiction | ((?[X]:((~strong(X)<~>old(X))))<=>(?[X]:((humble(X)<~>curious(X)))))&
(![X]:((calm(X)&~happy(X))<=>calm(X)))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|quiet(X))))&
((quiet(john)&kind(john)))&
(?[X]:(~calm(X)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((brave(X)&curious(X)))) | generous(fred) | [
"p2",
"p3",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8460171999914658958806807
% SZS output start Proof for 8460171999914658958806807
3. ! [X0] : ((generous(X0) | calm(X0)) <=> (~tall(X0) & brave(X0))) [input p2]
4. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X0] : (~quiet(X0) & happy(X0)) [input p3]
5. ! [X0] : ((old(X0) | ~strong(X0)) => (patient(X0) & creative(X0))) [input p4]
7. (~patient(john) & ~quiet(john)) <=> (~strong(fred) & patient(fred)) [input p6]
14. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p13]
24. generous(fred) [input hypothesis]
26. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X1] : (~quiet(X1) & happy(X1)) [rectify 4]
27. ! [X0] : ((patient(X0) & creative(X0)) | (~old(X0) & strong(X0))) [ennf transformation 5]
37. ! [X0] : (((generous(X0) | calm(X0)) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 3]
38. ! [X0] : ((generous(X0) | calm(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 37]
39. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X1] : (~quiet(X1) & happy(X1)) | ! [X0] : ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 26]
40. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X2] : (~quiet(X2) & happy(X2)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [rectify 39]
41. ? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) => ((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) [choice axiom]
42. ? [X2] : (~quiet(X2) & happy(X2)) => (~quiet(sK3) & happy(sK3)) [choice axiom]
43. (((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) | ! [X1] : (quiet(X1) | ~happy(X1))) & ((~quiet(sK3) & happy(sK3)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [skolemisation 40,42,41]
45. ((~patient(john) & ~quiet(john)) | (strong(fred) | ~patient(fred))) & ((~strong(fred) & patient(fred)) | (patient(john) | quiet(john))) [nnf transformation 7]
46. ((~patient(john) & ~quiet(john)) | strong(fred) | ~patient(fred)) & ((~strong(fred) & patient(fred)) | patient(john) | quiet(john)) [flattening 45]
56. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 14]
86. ~tall(X0) | ~generous(X0) [cnf transformation 38]
90. ~quiet(sK3) | ~strong(X3) | tall(X3) [cnf transformation 43]
96. patient(X0) | strong(X0) [cnf transformation 27]
104. ~quiet(john) | strong(fred) | ~patient(fred) [cnf transformation 46]
130. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 56]
133. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 56]
154. generous(fred) [cnf transformation 24]
157. wise(X0) | quiet(X0) [duplicate literal removal 130]
158. ~wise(X0) | quiet(X0) [duplicate literal removal 133]
212. 13 <=> quiet(sK3) [avatar definition]
214. ~quiet(sK3) <- (~13) [avatar component clause 212]
217. 14 <=> ! [X3] : (~strong(X3) | tall(X3)) [avatar definition]
218. ~strong(X3) | tall(X3) <- (14) [avatar component clause 217]
219. 14 | ~13 [avatar split clause 90,212,217]
248. 20 <=> strong(fred) [avatar definition]
250. strong(fred) <- (20) [avatar component clause 248]
256. ~quiet(john) | strong(fred) [subsumption resolution 104,96]
258. 22 <=> quiet(john) [avatar definition]
260. ~quiet(john) <- (~22) [avatar component clause 258]
261. 20 | ~22 [avatar split clause 256,258,248]
330. quiet(X0) [subsumption resolution 157,158]
350. $false <- (~22) [subsumption resolution 260,330]
351. 22 [avatar contradiction clause 350]
373. tall(fred) <- (14, 20) [resolution 218,250]
377. ~generous(fred) <- (14, 20) [resolution 373,86]
379. $false <- (14, 20) [subsumption resolution 377,154]
380. ~14 | ~20 [avatar contradiction clause 379]
381. $false <- (~13) [subsumption resolution 214,330]
382. 13 [avatar contradiction clause 381]
383. $false [avatar sat refutation 219,261,351,380,382]
% SZS output end Proof for 8460171999914658958806807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either humble or not tall then someone is not kind or not wise. Everyone who is either tall or quiet is strong and vice versa. Everyone who is brave is both rich and not curious. Everyone who is both not calm and not quiet is not brave and vice versa. Everyone who is funny or creative is happy and vice versa. If susan is both brave and not wise then someone is not kind and vice versa. If someone is old then susan is rich or not quiet. If mary is both tall and not kind then someone is old. Everyone who is both not wise and not patient is not brave and vice versa. Everyone who is both creative and funny is either quiet or humble. Everyone who is quiet or generous is not old or not happy. If lucy is both kind and not tall then someone is curious. If someone is rich then someone is either not tall or not wise. If someone is either not humble or wise then susan is old or kind. Everyone who is not calm or not curious is brave and vice versa. If someone is not patient or not tall then someone is not patient and vice versa. John is not old. Someone is both wise and not kind. Someone is both not patient and brave. Susan is not curious. Someone is both not tall and not strong. Paul is not kind or humble. Someone is happy. | Lucy is not rich. | contradiction | (((humble(fred)<~>~tall(fred)))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((tall(X)<~>quiet(X))<=>strong(X)))&
(![X]:(brave(X)=>(rich(X)&~curious(X))))&
(![X]:((~calm(X)&~quiet(X))<=>~brave(X)))&
(![X]:((funny(X)|creative(X))<=>happy(X)))&
(((brave(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(old(X)))=>((rich(susan)|~quiet(susan))))&
(((tall(mary)&~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~patient(X))<=>~brave(X)))&
(![X]:((creative(X)&funny(X))=>(quiet(X)<~>humble(X))))&
(![X]:((quiet(X)|generous(X))=>(~old(X)|~happy(X))))&
(((kind(lucy)&~tall(lucy)))=>(?[X]:(curious(X))))&
((?[X]:(rich(X)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~humble(X)<~>wise(X))))=>((old(susan)|kind(susan))))&
(![X]:((~calm(X)|~curious(X))<=>brave(X)))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~patient(X))))&
(~old(john))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((~patient(X)&brave(X))))&
(~curious(susan))&
(?[X]:((~tall(X)&~strong(X))))&
((~kind(paul)|humble(paul)))&
(?[X]:(happy(X))) | ~rich(lucy) | [
"p2",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8575486179054052525432671
% SZS output start Proof for 8575486179054052525432671
3. ! [X0] : (brave(X0) => (~curious(X0) & rich(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> ~brave(X0)) [input p3]
15. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> brave(X0)) [input p14]
24. ~rich(lucy) [input hypothesis]
31. ! [X0] : ((~curious(X0) & rich(X0)) | ~brave(X0)) [ennf transformation 3]
49. ! [X0] : (((~quiet(X0) & ~calm(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) | calm(X0)))) [nnf transformation 4]
50. ! [X0] : (((~quiet(X0) & ~calm(X0)) | brave(X0)) & (~brave(X0) | quiet(X0) | calm(X0))) [flattening 49]
70. ! [X0] : (((~curious(X0) | ~calm(X0)) | ~brave(X0)) & (brave(X0) | (curious(X0) & calm(X0)))) [nnf transformation 15]
71. ! [X0] : ((~curious(X0) | ~calm(X0) | ~brave(X0)) & (brave(X0) | (curious(X0) & calm(X0)))) [flattening 70]
89. ~brave(X0) | rich(X0) [cnf transformation 31]
92. ~calm(X0) | brave(X0) [cnf transformation 50]
113. brave(X0) | calm(X0) [cnf transformation 71]
129. ~rich(lucy) [cnf transformation 24]
233. brave(X0) [subsumption resolution 113,92]
266. rich(X0) [resolution 89,233]
269. $false [resolution 266,129]
% SZS output end Proof for 8575486179054052525432671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Fred is curious. | contradiction | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | curious(fred) | [
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4025878976706923752332047
% SZS output start Proof for 4025878976706923752332047
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p13]
22. curious(fred) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 9]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
49. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | brave(X0)) & (~brave(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 8]
56. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 14]
57. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 56]
99. ~rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 48]
105. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 49]
108. ~quiet(X0) | ~brave(X0) [cnf transformation 32]
110. ~brave(X0) | patient(X0) [cnf transformation 32]
127. ~patient(X0) | quiet(X0) [cnf transformation 57]
139. curious(fred) [cnf transformation 22]
140. ~rich(X0) | ~creative(X0) [duplicate literal removal 99]
141. ~rich(X0) | creative(X0) [duplicate literal removal 100]
243. ~rich(X0) [subsumption resolution 140,141]
244. ~curious(X0) | brave(X0) [subsumption resolution 105,243]
272. brave(fred) [resolution 244,139]
274. patient(fred) [resolution 272,110]
278. quiet(fred) [resolution 274,127]
286. ~brave(fred) [resolution 278,108]
288. $false [subsumption resolution 286,272]
% SZS output end Proof for 4025878976706923752332047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or humble is both quiet and humble and vice versa.
If lucy is both kind and not calm then paul is not generous.
Everyone who is curious is either not strong or not rich.
If someone is calm or not humble then someone is either rich or not creative.
Everyone who is not kind is kind or humble.
If someone is both kind and not quiet then john is not tall or not funny and vice versa.
Everyone who is happy or creative is brave or happy and vice versa.
Everyone who is not patient or not calm is both brave and kind.
Everyone who is not kind or not generous is both not old and not tall.
Everyone who is either creative or not happy is both tall and creative.
Everyone who is not brave or not tall is curious and vice versa.
If someone is creative then susan is both generous and not wise.
If someone is not brave or curious then lucy is not strong and vice versa.
Everyone who is both not happy and not generous is not patient and vice versa.
If alice is not patient or happy then john is brave or not wise and vice versa.
If alice is both not humble and not strong then someone is either not humble or not rich and vice versa.
Someone is creative.
Someone is generous or not calm.
Fred is either patient or creative.
Susan is not calm or not brave.
John is either not patient or curious.
Lucy is rich or not strong.
John is not quiet or happy.
Susan is not creative or humble. | Lucy is not strong. | entailment | (![X]:((~wise(X)|humble(X))<=>(quiet(X)&humble(X))))&
(((kind(lucy)&~calm(lucy)))=>(~generous(paul)))&
(![X]:(curious(X)=>(~strong(X)<~>~rich(X))))&
((?[X]:((calm(X)|~humble(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:(~kind(X)=>(kind(X)|humble(X))))&
((?[X]:((kind(X)&~quiet(X))))<=>((~tall(john)|~funny(john))))&
(![X]:((happy(X)|creative(X))<=>(brave(X)|happy(X))))&
(![X]:((~patient(X)|~calm(X))=>(brave(X)&kind(X))))&
(![X]:((~kind(X)|~generous(X))=>(~old(X)&~tall(X))))&
(![X]:((creative(X)<~>~happy(X))=>(tall(X)&creative(X))))&
(![X]:((~brave(X)|~tall(X))<=>curious(X)))&
((?[X]:(creative(X)))=>((generous(susan)&~wise(susan))))&
((?[X]:((~brave(X)|curious(X))))<=>(~strong(lucy)))&
(![X]:((~happy(X)&~generous(X))<=>~patient(X)))&
(((~patient(alice)|happy(alice)))<=>((brave(john)|~wise(john))))&
(((~humble(alice)&~strong(alice)))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(?[X]:(creative(X)))&
(?[X]:((generous(X)|~calm(X))))&
((patient(fred)<~>creative(fred)))&
((~calm(susan)|~brave(susan)))&
((~patient(john)<~>curious(john)))&
((rich(lucy)|~strong(lucy)))&
((~quiet(john)|happy(john)))&
((~creative(susan)|humble(susan))) | ~strong(lucy) | [
"p8",
"p10",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8403422101579781143978375
% SZS output start Proof for 8403422101579781143978375
9. ! [X0] : ((~generous(X0) | ~kind(X0)) => (~tall(X0) & ~old(X0))) [input p8]
11. ! [X0] : ((~tall(X0) | ~brave(X0)) <=> curious(X0)) [input p10]
13. ? [X0] : (curious(X0) | ~brave(X0)) <=> ~strong(lucy) [input p12]
14. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> ~patient(X0)) [input p13]
21. ~patient(john) <~> curious(john) [input p20]
25. strong(lucy) [input hypothesis]
27. ! [X0] : ((~generous(X0) | ~kind(X0)) => ~tall(X0)) [pure predicate removal 9]
35. ! [X0] : (~tall(X0) | (generous(X0) & kind(X0))) [ennf transformation 27]
53. ! [X0] : (((~tall(X0) | ~brave(X0)) | ~curious(X0)) & (curious(X0) | (tall(X0) & brave(X0)))) [nnf transformation 11]
54. ! [X0] : ((~tall(X0) | ~brave(X0) | ~curious(X0)) & (curious(X0) | (tall(X0) & brave(X0)))) [flattening 53]
55. (? [X0] : (curious(X0) | ~brave(X0)) | strong(lucy)) & (~strong(lucy) | ! [X0] : (~curious(X0) & brave(X0))) [nnf transformation 13]
56. (? [X0] : (curious(X0) | ~brave(X0)) | strong(lucy)) & (~strong(lucy) | ! [X1] : (~curious(X1) & brave(X1))) [rectify 55]
57. ? [X0] : (curious(X0) | ~brave(X0)) => (curious(sK2) | ~brave(sK2)) [choice axiom]
58. ((curious(sK2) | ~brave(sK2)) | strong(lucy)) & (~strong(lucy) | ! [X1] : (~curious(X1) & brave(X1))) [skolemisation 56,57]
59. ! [X0] : (((~generous(X0) & ~happy(X0)) | patient(X0)) & (~patient(X0) | (generous(X0) | happy(X0)))) [nnf transformation 14]
60. ! [X0] : (((~generous(X0) & ~happy(X0)) | patient(X0)) & (~patient(X0) | generous(X0) | happy(X0))) [flattening 59]
73. (~curious(john) | patient(john)) & (curious(john) | ~patient(john)) [nnf transformation 21]
101. ~tall(X0) | generous(X0) [cnf transformation 35]
107. tall(X0) | curious(X0) [cnf transformation 54]
112. ~strong(lucy) | ~curious(X1) [cnf transformation 58]
116. ~generous(X0) | patient(X0) [cnf transformation 60]
132. curious(john) | ~patient(john) [cnf transformation 73]
137. strong(lucy) [cnf transformation 25]
210. 16 <=> strong(lucy) [avatar definition]
219. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
220. ~curious(X1) <- (18) [avatar component clause 219]
221. 18 | ~16 [avatar split clause 112,210,219]
303. 36 <=> patient(john) [avatar definition]
304. ~patient(john) <- (~36) [avatar component clause 303]
307. 37 <=> curious(john) [avatar definition]
308. curious(john) <- (37) [avatar component clause 307]
311. ~36 | 37 [avatar split clause 132,307,303]
335. 16 [avatar split clause 137,210]
354. curious(X0) | generous(X0) [resolution 107,101]
356. generous(X0) <- (18) [subsumption resolution 354,220]
363. patient(X0) <- (18) [resolution 116,356]
366. $false <- (18, ~36) [resolution 363,304]
369. ~18 | 36 [avatar contradiction clause 366]
370. $false <- (18, 37) [subsumption resolution 308,220]
371. ~18 | ~37 [avatar contradiction clause 370]
372. $false [avatar sat refutation 221,311,335,369,371]
% SZS output end Proof for 8403422101579781143978375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or old is not tall and vice versa.
If someone is curious then someone is either quiet or funny and vice versa.
Everyone who is not patient is both not brave and creative and vice versa.
If john is brave then paul is either humble or creative.
Everyone who is not creative or not rich is both not rich and not calm.
Everyone who is not creative is both tall and not rich.
Everyone who is not calm or not tall is tall or happy.
If someone is both humble and not brave then mary is either brave or curious and vice versa.
If someone is humble or brave then paul is not generous or not patient.
Everyone who is either not generous or patient is both wise and not strong and vice versa.
If someone is wise or not calm then someone is brave and vice versa.
Everyone who is brave or patient is happy or creative.
If someone is calm then someone is either quiet or rich.
Everyone who is either not curious or wise is both rich and quiet and vice versa.
If someone is both not generous and not calm then someone is both tall and not happy.
Everyone who is either patient or not curious is funny.
Someone is not curious.
Paul is both funny and not strong.
Mary is both rich and strong.
Paul is wise.
Someone is tall.
Someone is both not rich and not wise.
Someone is calm. | Paul is not brave. | entailment | (![X]:((humble(X)<~>old(X))<=>~tall(X)))&
((?[X]:(curious(X)))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:(~patient(X)<=>(~brave(X)&creative(X))))&
((brave(john))=>((humble(paul)<~>creative(paul))))&
(![X]:((~creative(X)|~rich(X))=>(~rich(X)&~calm(X))))&
(![X]:(~creative(X)=>(tall(X)&~rich(X))))&
(![X]:((~calm(X)|~tall(X))=>(tall(X)|happy(X))))&
((?[X]:((humble(X)&~brave(X))))<=>((brave(mary)<~>curious(mary))))&
((?[X]:((humble(X)|brave(X))))=>((~generous(paul)|~patient(paul))))&
(![X]:((~generous(X)<~>patient(X))<=>(wise(X)&~strong(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:(brave(X))))&
(![X]:((brave(X)|patient(X))=>(happy(X)|creative(X))))&
((?[X]:(calm(X)))=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((~curious(X)<~>wise(X))<=>(rich(X)&quiet(X))))&
((?[X]:((~generous(X)&~calm(X))))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((patient(X)<~>~curious(X))=>funny(X)))&
(?[X]:(~curious(X)))&
((funny(paul)&~strong(paul)))&
((rich(mary)&strong(mary)))&
(wise(paul))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:(calm(X))) | ~brave(paul) | [
"p2",
"p8",
"p9",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1555296654253367147732334
% SZS output start Proof for 1555296654253367147732334
3. ! [X0] : (~patient(X0) <=> (creative(X0) & ~brave(X0))) [input p2]
9. ? [X0] : (brave(X0) | humble(X0)) => (~patient(paul) | ~generous(paul)) [input p8]
10. ! [X0] : ((~generous(X0) <~> patient(X0)) <=> (~strong(X0) & wise(X0))) [input p9]
18. ~strong(paul) & funny(paul) [input p17]
20. wise(paul) [input p19]
24. brave(paul) [input hypothesis]
36. (~patient(paul) | ~generous(paul)) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 9]
37. ~patient(paul) | ~generous(paul) | ! [X0] : (~brave(X0) & ~humble(X0)) [flattening 36]
49. ! [X0] : ((~patient(X0) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 3]
50. ! [X0] : ((~patient(X0) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | patient(X0))) [flattening 49]
56. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [nnf transformation 10]
57. ! [X0] : ((((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))))) [flattening 56]
87. ~brave(X0) | patient(X0) [cnf transformation 50]
107. ~patient(paul) | ~generous(paul) | ~brave(X0) [cnf transformation 37]
113. ~wise(X0) | generous(X0) | strong(X0) | ~patient(X0) [cnf transformation 57]
133. ~strong(paul) [cnf transformation 18]
136. wise(paul) [cnf transformation 20]
141. brave(paul) [cnf transformation 24]
208. 15 <=> ! [X0] : ~brave(X0) [avatar definition]
209. ~brave(X0) <- (15) [avatar component clause 208]
211. 16 <=> generous(paul) [avatar definition]
215. 17 <=> patient(paul) [avatar definition]
216. patient(paul) <- (17) [avatar component clause 215]
218. 15 | ~16 | ~17 [avatar split clause 107,215,211,208]
273. patient(paul) [resolution 87,141]
275. 17 [avatar split clause 273,215]
383. generous(paul) | strong(paul) | ~patient(paul) [resolution 113,136]
392. generous(paul) | ~patient(paul) [subsumption resolution 383,133]
393. generous(paul) <- (17) [subsumption resolution 392,216]
394. 16 | ~17 [avatar split clause 393,215,211]
395. $false <- (15) [resolution 209,141]
398. ~15 [avatar contradiction clause 395]
399. $false [avatar sat refutation 218,275,394,398]
% SZS output end Proof for 1555296654253367147732334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is both not curious and not kind and vice versa.
If someone is both not strong and not creative then someone is not strong or rich.
If paul is either not tall or rich then someone is either not curious or kind and vice versa.
Everyone who is not patient is funny or creative and vice versa.
Everyone who is happy or not curious is not strong and vice versa.
If someone is not strong or funny then john is both not strong and not calm.
If someone is kind then someone is not humble or humble and vice versa.
If john is either not curious or calm then alice is either not rich or not strong and vice versa.
If someone is humble then someone is not rich or not brave and vice versa.
If someone is both quiet and old then john is not quiet or not humble.
If someone is not quiet then lucy is creative.
Everyone who is not happy is calm or not strong and vice versa.
Everyone who is not calm or happy is not funny or rich and vice versa.
Everyone who is old or creative is either not kind or calm and vice versa.
Everyone who is not calm is both wise and not strong.
If paul is either tall or old then mary is not quiet or not rich and vice versa.
Susan is not kind or wise.
Someone is both creative and not tall.
Susan is either not happy or not tall.
Paul is funny or calm.
Paul is either creative or calm.
Paul is old or humble.
Someone is both not wise and not patient. | Alice is not happy. | entailment | (![X]:(old(X)<=>(~curious(X)&~kind(X))))&
((?[X]:((~strong(X)&~creative(X))))=>(?[X]:((~strong(X)|rich(X)))))&
(((~tall(paul)<~>rich(paul)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(~patient(X)<=>(funny(X)|creative(X))))&
(![X]:((happy(X)|~curious(X))<=>~strong(X)))&
((?[X]:((~strong(X)|funny(X))))=>((~strong(john)&~calm(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)|humble(X)))))&
(((~curious(john)<~>calm(john)))<=>((~rich(alice)<~>~strong(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)|~brave(X)))))&
((?[X]:((quiet(X)&old(X))))=>((~quiet(john)|~humble(john))))&
((?[X]:(~quiet(X)))=>(creative(lucy)))&
(![X]:(~happy(X)<=>(calm(X)|~strong(X))))&
(![X]:((~calm(X)|happy(X))<=>(~funny(X)|rich(X))))&
(![X]:((old(X)|creative(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(~calm(X)=>(wise(X)&~strong(X))))&
(((tall(paul)<~>old(paul)))<=>((~quiet(mary)|~rich(mary))))&
((~kind(susan)|wise(susan)))&
(?[X]:((creative(X)&~tall(X))))&
((~happy(susan)<~>~tall(susan)))&
((funny(paul)|calm(paul)))&
((creative(paul)<~>calm(paul)))&
((old(paul)|humble(paul)))&
(?[X]:((~wise(X)&~patient(X)))) | ~happy(alice) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3188883235882571743138190
% SZS output start Proof for 3188883235882571743138190
5. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~strong(X0)) [input p4]
12. ! [X0] : (~happy(X0) <=> (~strong(X0) | calm(X0))) [input p11]
24. happy(alice) [input hypothesis]
46. ! [X0] : (((~curious(X0) | happy(X0)) | strong(X0)) & (~strong(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 5]
47. ! [X0] : ((~curious(X0) | happy(X0) | strong(X0)) & (~strong(X0) | (curious(X0) & ~happy(X0)))) [flattening 46]
59. ! [X0] : ((~happy(X0) | (strong(X0) & ~calm(X0))) & ((~strong(X0) | calm(X0)) | happy(X0))) [nnf transformation 12]
60. ! [X0] : ((~happy(X0) | (strong(X0) & ~calm(X0))) & (~strong(X0) | calm(X0) | happy(X0))) [flattening 59]
86. ~strong(X0) | ~happy(X0) [cnf transformation 47]
111. ~happy(X0) | strong(X0) [cnf transformation 60]
141. happy(alice) [cnf transformation 24]
275. ~happy(X0) [subsumption resolution 111,86]
325. $false [subsumption resolution 141,275]
% SZS output end Proof for 3188883235882571743138190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not funny and kind then alice is both funny and not funny and vice versa.
Everyone who is either patient or not wise is both humble and patient.
Everyone who is either wise or not funny is curious and vice versa.
If someone is both not curious and not old then mary is either funny or not strong and vice versa.
If mary is not funny or strong then someone is either not happy or creative and vice versa.
If john is not wise or old then fred is both brave and old and vice versa.
If someone is tall or not creative then susan is not rich and vice versa.
Everyone who is both not strong and calm is either not old or wise.
Everyone who is not strong or funny is generous and vice versa.
If fred is either creative or calm then someone is not quiet.
Everyone who is both tall and not old is not calm and vice versa.
Everyone who is both not calm and strong is not creative.
If alice is both kind and not rich then lucy is old or funny.
Everyone who is happy is both not generous and not old.
Everyone who is not patient or not curious is both quiet and not brave.
Everyone who is creative or not humble is either tall or generous and vice versa.
John is both not kind and patient.
Someone is either not kind or kind.
Someone is not tall.
Someone is creative.
Someone is either not patient or not quiet.
John is both not tall and not kind.
Lucy is happy. | Lucy is not creative. | entailment | (((~funny(mary)&kind(mary)))<=>((funny(alice)&~funny(alice))))&
(![X]:((patient(X)<~>~wise(X))=>(humble(X)&patient(X))))&
(![X]:((wise(X)<~>~funny(X))<=>curious(X)))&
((?[X]:((~curious(X)&~old(X))))<=>((funny(mary)<~>~strong(mary))))&
(((~funny(mary)|strong(mary)))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~wise(john)|old(john)))<=>((brave(fred)&old(fred))))&
((?[X]:((tall(X)|~creative(X))))<=>(~rich(susan)))&
(![X]:((~strong(X)&calm(X))=>(~old(X)<~>wise(X))))&
(![X]:((~strong(X)|funny(X))<=>generous(X)))&
(((creative(fred)<~>calm(fred)))=>(?[X]:(~quiet(X))))&
(![X]:((tall(X)&~old(X))<=>~calm(X)))&
(![X]:((~calm(X)&strong(X))=>~creative(X)))&
(((kind(alice)&~rich(alice)))=>((old(lucy)|funny(lucy))))&
(![X]:(happy(X)=>(~generous(X)&~old(X))))&
(![X]:((~patient(X)|~curious(X))=>(quiet(X)&~brave(X))))&
(![X]:((creative(X)|~humble(X))<=>(tall(X)<~>generous(X))))&
((~kind(john)&patient(john)))&
(?[X]:((~kind(X)<~>kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
((~tall(john)&~kind(john)))&
(happy(lucy)) | ~creative(lucy) | [
"p8",
"p10",
"p11",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 853650356291015592369993
% SZS output start Proof for 853650356291015592369993
9. ! [X0] : ((funny(X0) | ~strong(X0)) <=> generous(X0)) [input p8]
11. ! [X0] : ((~old(X0) & tall(X0)) <=> ~calm(X0)) [input p10]
12. ! [X0] : ((strong(X0) & ~calm(X0)) => ~creative(X0)) [input p11]
14. ! [X0] : (happy(X0) => (~old(X0) & ~generous(X0))) [input p13]
16. ! [X0] : ((~humble(X0) | creative(X0)) <=> (tall(X0) <~> generous(X0))) [input p15]
23. happy(lucy) [input p22]
24. creative(lucy) [input hypothesis]
29. ! [X0] : (~creative(X0) | (~strong(X0) | calm(X0))) [ennf transformation 12]
30. ! [X0] : (~creative(X0) | ~strong(X0) | calm(X0)) [flattening 29]
33. ! [X0] : ((~old(X0) & ~generous(X0)) | ~happy(X0)) [ennf transformation 14]
55. ! [X0] : (((funny(X0) | ~strong(X0)) | ~generous(X0)) & (generous(X0) | (~funny(X0) & strong(X0)))) [nnf transformation 9]
56. ! [X0] : ((funny(X0) | ~strong(X0) | ~generous(X0)) & (generous(X0) | (~funny(X0) & strong(X0)))) [flattening 55]
60. ! [X0] : (((~old(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~tall(X0)))) [nnf transformation 11]
61. ! [X0] : (((~old(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~tall(X0))) [flattening 60]
62. ! [X0] : (((~humble(X0) | creative(X0)) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | (humble(X0) & ~creative(X0)))) [nnf transformation 16]
63. ! [X0] : ((~humble(X0) | creative(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0)))) & (((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | (humble(X0) & ~creative(X0)))) [flattening 62]
108. generous(X0) | strong(X0) [cnf transformation 56]
113. ~calm(X0) | old(X0) | ~tall(X0) [cnf transformation 61]
116. ~creative(X0) | ~strong(X0) | calm(X0) [cnf transformation 30]
118. ~generous(X0) | ~happy(X0) [cnf transformation 33]
119. ~happy(X0) | ~old(X0) [cnf transformation 33]
124. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 63]
140. happy(lucy) [cnf transformation 23]
141. creative(lucy) [cnf transformation 24]
263. 26 <=> old(lucy) [avatar definition]
264. ~old(lucy) <- (~26) [avatar component clause 263]
283. ~old(lucy) [resolution 119,140]
284. ~26 [avatar split clause 283,263]
371. ~strong(lucy) | calm(lucy) [resolution 116,141]
382. 41 <=> calm(lucy) [avatar definition]
384. calm(lucy) <- (41) [avatar component clause 382]
386. 42 <=> strong(lucy) [avatar definition]
389. 41 | ~42 [avatar split clause 371,386,382]
391. tall(lucy) | generous(lucy) [resolution 124,141]
402. 45 <=> generous(lucy) [avatar definition]
403. ~generous(lucy) <- (~45) [avatar component clause 402]
404. generous(lucy) <- (45) [avatar component clause 402]
406. 46 <=> tall(lucy) [avatar definition]
408. tall(lucy) <- (46) [avatar component clause 406]
409. 45 | 46 [avatar split clause 391,406,402]
426. ~happy(lucy) <- (45) [resolution 404,118]
434. $false <- (45) [subsumption resolution 426,140]
435. ~45 [avatar contradiction clause 434]
442. strong(lucy) <- (~45) [resolution 403,108]
445. 42 | 45 [avatar split clause 442,402,386]
451. old(lucy) | ~tall(lucy) <- (41) [resolution 384,113]
452. ~tall(lucy) <- (~26, 41) [subsumption resolution 451,264]
453. $false <- (~26, 41, 46) [subsumption resolution 452,408]
454. 26 | ~41 | ~46 [avatar contradiction clause 453]
455. $false [avatar sat refutation 284,389,409,435,445,454]
% SZS output end Proof for 853650356291015592369993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not brave is not happy.
If someone is either not kind or wise then alice is not happy or tall.
Everyone who is not calm is both happy and creative and vice versa.
Everyone who is either not wise or not funny is funny or brave and vice versa.
Everyone who is both happy and not wise is not kind.
Everyone who is either not creative or not patient is both generous and not quiet and vice versa.
If fred is not patient then alice is either brave or rich.
If john is both not creative and curious then susan is both kind and not generous.
If someone is either not happy or quiet then fred is quiet or happy.
Everyone who is either not tall or not old is not funny and vice versa.
Everyone who is both patient and calm is brave.
Everyone who is humble or creative is not wise and vice versa.
If someone is curious or not calm then john is both not happy and patient and vice versa.
If mary is not patient or patient then susan is quiet.
If fred is both old and not wise then someone is either funny or not generous.
Everyone who is strong or rich is not generous and vice versa.
Someone is happy.
Paul is calm or not curious.
Someone is both happy and kind.
Lucy is either not strong or tall.
Someone is not tall.
Lucy is both humble and funny.
Someone is not strong.
Paul is either not old or not rich. | Susan is not quiet. | contradiction | (![X]:((kind(X)&~brave(X))=>~happy(X)))&
((?[X]:((~kind(X)<~>wise(X))))=>((~happy(alice)|tall(alice))))&
(![X]:(~calm(X)<=>(happy(X)&creative(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>(funny(X)|brave(X))))&
(![X]:((happy(X)&~wise(X))=>~kind(X)))&
(![X]:((~creative(X)<~>~patient(X))<=>(generous(X)&~quiet(X))))&
((~patient(fred))=>((brave(alice)<~>rich(alice))))&
(((~creative(john)&curious(john)))=>((kind(susan)&~generous(susan))))&
((?[X]:((~happy(X)<~>quiet(X))))=>((quiet(fred)|happy(fred))))&
(![X]:((~tall(X)<~>~old(X))<=>~funny(X)))&
(![X]:((patient(X)&calm(X))=>brave(X)))&
(![X]:((humble(X)|creative(X))<=>~wise(X)))&
((?[X]:((curious(X)|~calm(X))))<=>((~happy(john)&patient(john))))&
(((~patient(mary)|patient(mary)))=>(quiet(susan)))&
(((old(fred)&~wise(fred)))=>(?[X]:((funny(X)<~>~generous(X)))))&
(![X]:((strong(X)|rich(X))<=>~generous(X)))&
(?[X]:(happy(X)))&
((calm(paul)|~curious(paul)))&
(?[X]:((happy(X)&kind(X))))&
((~strong(lucy)<~>tall(lucy)))&
(?[X]:(~tall(X)))&
((humble(lucy)&funny(lucy)))&
(?[X]:(~strong(X)))&
((~old(paul)<~>~rich(paul))) | ~quiet(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4739512488142816585562904
% SZS output start Proof for 4739512488142816585562904
14. (patient(mary) | ~patient(mary)) => quiet(susan) [input p13]
25. ~quiet(susan) [input hypothesis]
39. quiet(susan) | (~patient(mary) & patient(mary)) [ennf transformation 14]
112. quiet(susan) | patient(mary) [cnf transformation 39]
113. quiet(susan) | ~patient(mary) [cnf transformation 39]
131. ~quiet(susan) [cnf transformation 25]
227. 22 <=> patient(mary) [avatar definition]
231. 23 <=> quiet(susan) [avatar definition]
234. ~22 | 23 [avatar split clause 113,231,227]
235. 22 | 23 [avatar split clause 112,231,227]
283. ~23 [avatar split clause 131,231]
284. $false [avatar sat refutation 234,235,283]
% SZS output end Proof for 4739512488142816585562904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or not quiet then someone is wise and vice versa. Everyone who is kind or not strong is either generous or not kind. Everyone who is not quiet or not rich is both not happy and not patient. Everyone who is not old or not wise is either rich or not tall and vice versa. If someone is both brave and tall then someone is both not wise and not creative and vice versa. Everyone who is curious is not happy and vice versa. Everyone who is both not generous and quiet is not generous or not kind. Everyone who is either not kind or happy is both not curious and creative. Everyone who is not generous is not kind or not tall and vice versa. Everyone who is both patient and curious is either not calm or happy and vice versa. Everyone who is not happy or curious is either old or not wise and vice versa. If mary is either not strong or humble then someone is not wise or tall. Everyone who is both not creative and not kind is humble or generous and vice versa. If someone is either wise or quiet then someone is tall and vice versa. Everyone who is kind or not creative is both not quiet and generous and vice versa. John is not wise. Paul is either happy or not happy. Someone is generous or happy. Susan is wise or not funny. Someone is both happy and quiet. Someone is not old. Fred is either not strong or not curious. | Mary is not curious. | entailment | ((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~happy(X)&~patient(X))))&
(![X]:((~old(X)|~wise(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:(curious(X)<=>~happy(X)))&
(![X]:((~generous(X)&quiet(X))=>(~generous(X)|~kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~curious(X)&creative(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~tall(X))))&
(![X]:((patient(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~happy(X)|curious(X))<=>(old(X)<~>~wise(X))))&
(((~strong(mary)<~>humble(mary)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(humble(X)|generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)|~creative(X))<=>(~quiet(X)&generous(X))))&
(~wise(john))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((generous(X)|happy(X))))&
((wise(susan)|~funny(susan)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:(~old(X)))&
((~strong(fred)<~>~curious(fred))) | ~curious(mary) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 154044908091063823602861
% SZS output start Proof for 154044908091063823602861
2. ! [X0] : ((~strong(X0) | kind(X0)) => (generous(X0) <~> ~kind(X0))) [input p1]
6. ! [X0] : (curious(X0) <=> ~happy(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> happy(X0)) => (creative(X0) & ~curious(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (~tall(X0) | ~kind(X0))) [input p8]
13. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (generous(X0) | humble(X0))) [input p12]
23. curious(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) <~> ~kind(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 2]
32. ! [X0] : ((creative(X0) & ~curious(X0)) | (~kind(X0) <=> happy(X0))) [ennf transformation 8]
39. ! [X0] : (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (strong(X0) & ~kind(X0))) [nnf transformation 28]
47. ! [X0] : ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))) [nnf transformation 6]
48. ! [X0] : ((creative(X0) & ~curious(X0)) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) [nnf transformation 32]
49. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 9]
50. ! [X0] : ((~generous(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | generous(X0))) [flattening 49]
58. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 13]
59. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | kind(X0) | creative(X0))) [flattening 58]
78. ~kind(X0) | generous(X0) | ~kind(X0) [cnf transformation 39]
96. ~curious(X0) | ~happy(X0) [cnf transformation 47]
99. ~curious(X0) | happy(X0) | kind(X0) [cnf transformation 48]
104. ~generous(X0) | kind(X0) [cnf transformation 50]
124. ~kind(X0) | ~generous(X0) [cnf transformation 59]
143. curious(mary) [cnf transformation 23]
144. ~kind(X0) | generous(X0) [duplicate literal removal 78]
195. ~curious(X0) | kind(X0) [subsumption resolution 99,96]
219. ~generous(X0) [subsumption resolution 124,104]
271. kind(mary) [resolution 195,143]
273. generous(mary) [resolution 271,144]
275. $false [subsumption resolution 273,219]
% SZS output end Proof for 154044908091063823602861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not funny. Everyone who is either calm or creative is strong. Everyone who is either not rich or not strong is happy. If someone is both tall and not creative then someone is kind and vice versa. Everyone who is either funny or rich is either not curious or creative and vice versa. Everyone who is both not brave and not kind is either not patient or kind. Everyone who is either not happy or rich is humble or rich and vice versa. Everyone who is either kind or not old is both rich and patient and vice versa. Everyone who is brave or tall is either rich or not strong and vice versa. Everyone who is either brave or not rich is not brave. If lucy is not old or creative then someone is both tall and not rich and vice versa. Everyone who is patient or not kind is both not kind and kind and vice versa. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. John is quiet or curious. Lucy is either humble or creative. Someone is either not curious or quiet. Fred is funny or not funny. Fred is either not kind or humble. Someone is not creative. | Fred is not quiet. | neutral | (![X]:(curious(X)=>~funny(X)))&
(![X]:((calm(X)<~>creative(X))=>strong(X)))&
(![X]:((~rich(X)<~>~strong(X))=>happy(X)))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:(kind(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~brave(X)&~kind(X))=>(~patient(X)<~>kind(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(humble(X)|rich(X))))&
(![X]:((kind(X)<~>~old(X))<=>(rich(X)&patient(X))))&
(![X]:((brave(X)|tall(X))<=>(rich(X)<~>~strong(X))))&
(![X]:((brave(X)<~>~rich(X))=>~brave(X)))&
(((~old(lucy)|creative(lucy)))<=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
((quiet(john)|curious(john)))&
((humble(lucy)<~>creative(lucy)))&
(?[X]:((~curious(X)<~>quiet(X))))&
((funny(fred)|~funny(fred)))&
((~kind(fred)<~>humble(fred)))&
(?[X]:(~creative(X))) | ~quiet(fred) | [] | null | 0 |
Everyone who is generous is both not calm and wise.
If someone is either funny or quiet then mary is not kind or not creative and vice versa.
Everyone who is humble is kind or brave and vice versa.
Everyone who is either not generous or not calm is not brave or not funny and vice versa.
Everyone who is happy or not curious is not happy and vice versa.
If paul is not tall then john is tall and vice versa.
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Everyone who is either not tall or not funny is not tall and vice versa.
If someone is kind then someone is quiet.
If susan is either old or not creative then someone is humble or not kind.
Everyone who is both not tall and not quiet is either humble or not happy and vice versa.
Everyone who is not humble or kind is not patient.
If someone is both not creative and not generous then lucy is not humble.
Everyone who is not calm is both funny and old.
Someone is both not strong and not curious.
Lucy is either patient or creative.
Paul is not generous or strong.
Someone is both old and strong.
Someone is either not humble or patient.
Susan is wise or happy. | John is funny. | entailment | (![X]:(generous(X)=>(~calm(X)&wise(X))))&
((?[X]:((funny(X)<~>quiet(X))))<=>((~kind(mary)|~creative(mary))))&
(![X]:(humble(X)<=>(kind(X)|brave(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~brave(X)|~funny(X))))&
(![X]:((happy(X)|~curious(X))<=>~happy(X)))&
((~tall(paul))<=>(tall(john)))&
(((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
(((old(susan)<~>~creative(susan)))=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((~humble(X)|kind(X))=>~patient(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(~humble(lucy)))&
(![X]:(~calm(X)=>(funny(X)&old(X))))&
(?[X]:((~strong(X)&~curious(X))))&
((patient(lucy)<~>creative(lucy)))&
((~generous(paul)|strong(paul)))&
(?[X]:((old(X)&strong(X))))&
(?[X]:((~humble(X)<~>patient(X))))&
((wise(susan)|happy(susan))) | funny(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3214074678829728382952475
% SZS output start Proof for 3214074678829728382952475
9. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p8]
22. ~funny(john) [input hypothesis]
49. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | tall(X0)) & (~tall(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 9]
96. ~tall(X0) | ~tall(X0) | funny(X0) [cnf transformation 49]
98. funny(X0) | tall(X0) | tall(X0) [cnf transformation 49]
123. ~funny(john) [cnf transformation 22]
124. ~tall(X0) | funny(X0) [duplicate literal removal 96]
125. funny(X0) | tall(X0) [duplicate literal removal 98]
169. 9 <=> ! [X0] : funny(X0) [avatar definition]
170. funny(X0) <- (9) [avatar component clause 169]
196. funny(X0) [subsumption resolution 124,125]
197. 9 [avatar split clause 196,169]
246. $false <- (9) [resolution 170,123]
247. ~9 [avatar contradiction clause 246]
248. $false [avatar sat refutation 197,247]
% SZS output end Proof for 3214074678829728382952475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is wise then john is not wise or not tall. Everyone who is either not curious or patient is old or not kind. Everyone who is not happy is both not strong and not patient. Everyone who is both brave and happy is not creative and vice versa. If john is both not strong and kind then someone is either calm or rich and vice versa. Everyone who is both not happy and creative is both not calm and not generous and vice versa. Everyone who is either kind or not tall is not old or not tall and vice versa. Everyone who is both funny and wise is not calm and vice versa. Everyone who is both funny and not wise is calm or old and vice versa. Everyone who is not patient is not humble and vice versa. Everyone who is happy or generous is not curious or not old and vice versa. Everyone who is not quiet or patient is patient and vice versa. If someone is both not brave and kind then paul is not kind or not quiet and vice versa. Everyone who is kind or not calm is curious or not wise. If alice is not patient or wise then fred is either not happy or not generous and vice versa. Everyone who is either brave or not creative is both not quiet and quiet. Someone is not kind. Mary is creative or calm. Someone is not generous. Paul is either not funny or not rich. Someone is not tall or not funny. Mary is not calm. Susan is not creative. Alice is humble. | John is not wise. | neutral | ((wise(mary))=>((~wise(john)|~tall(john))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~kind(X))))&
(![X]:(~happy(X)=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)&wise(X))<=>~calm(X)))&
(![X]:((funny(X)&~wise(X))<=>(calm(X)|old(X))))&
(![X]:(~patient(X)<=>~humble(X)))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)|~old(X))))&
(![X]:((~quiet(X)|patient(X))<=>patient(X)))&
((?[X]:((~brave(X)&kind(X))))<=>((~kind(paul)|~quiet(paul))))&
(![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
(![X]:((brave(X)<~>~creative(X))=>(~quiet(X)&quiet(X))))&
(?[X]:(~kind(X)))&
((creative(mary)|calm(mary)))&
(?[X]:(~generous(X)))&
((~funny(paul)<~>~rich(paul)))&
(?[X]:((~tall(X)|~funny(X))))&
(~calm(mary))&
(~creative(susan))&
(humble(alice)) | ~wise(john) | [] | null | 0 |
Everyone who is wise is not rich.
If someone is funny then john is creative or strong.
Everyone who is both calm and not humble is patient.
If someone is happy or wise then john is either not happy or not quiet and vice versa.
Everyone who is rich is either patient or not old and vice versa.
If alice is not generous then fred is both not curious and not quiet.
Everyone who is not creative or calm is either not patient or humble.
Everyone who is not rich is not generous or happy.
If someone is both not brave and curious then someone is both not brave and funny and vice versa.
Everyone who is either not tall or strong is not rich or not patient.
Everyone who is brave is both not patient and not calm and vice versa.
If someone is not curious or not happy then someone is both humble and not curious and vice versa.
Everyone who is both not humble and funny is old or kind.
If someone is not brave or generous then mary is both tall and generous and vice versa.
If alice is both not humble and funny then susan is both rich and old.
If paul is both not quiet and not generous then susan is quiet or rich and vice versa.
Someone is both generous and old.
Susan is not generous.
Alice is generous.
Fred is both not old and not tall.
Someone is not generous or strong.
Someone is curious.
Someone is both tall and quiet.
Someone is generous. | Fred is not quiet. | neutral | (![X]:(wise(X)=>~rich(X)))&
((?[X]:(funny(X)))=>((creative(john)|strong(john))))&
(![X]:((calm(X)&~humble(X))=>patient(X)))&
((?[X]:((happy(X)|wise(X))))<=>((~happy(john)<~>~quiet(john))))&
(![X]:(rich(X)<=>(patient(X)<~>~old(X))))&
((~generous(alice))=>((~curious(fred)&~quiet(fred))))&
(![X]:((~creative(X)|calm(X))=>(~patient(X)<~>humble(X))))&
(![X]:(~rich(X)=>(~generous(X)|happy(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~tall(X)<~>strong(X))=>(~rich(X)|~patient(X))))&
(![X]:(brave(X)<=>(~patient(X)&~calm(X))))&
((?[X]:((~curious(X)|~happy(X))))<=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~humble(X)&funny(X))=>(old(X)|kind(X))))&
((?[X]:((~brave(X)|generous(X))))<=>((tall(mary)&generous(mary))))&
(((~humble(alice)&funny(alice)))=>((rich(susan)&old(susan))))&
(((~quiet(paul)&~generous(paul)))<=>((quiet(susan)|rich(susan))))&
(?[X]:((generous(X)&old(X))))&
(~generous(susan))&
(generous(alice))&
((~old(fred)&~tall(fred)))&
(?[X]:((~generous(X)|strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:(generous(X))) | ~quiet(fred) | [] | null | 0 |
If john is not old or brave then susan is both not calm and humble.
Everyone who is old or calm is not wise and vice versa.
Everyone who is not patient is either creative or not calm.
If lucy is not happy then alice is not creative or not generous.
Everyone who is not curious is both not rich and funny and vice versa.
If mary is not happy then someone is not wise or not rich.
If someone is not happy then someone is brave or not quiet.
Everyone who is brave or strong is either not creative or not humble.
Everyone who is strong or not wise is both patient and not brave and vice versa.
If john is both not quiet and humble then mary is either funny or not calm and vice versa.
If someone is both generous and funny then lucy is patient.
Everyone who is not rich or not old is not funny.
Everyone who is either not kind or not generous is not old or not strong and vice versa.
Everyone who is both curious and not calm is rich or curious and vice versa.
Everyone who is brave or rich is both not quiet and quiet.
Fred is both old and not tall.
Susan is happy.
Someone is both wise and tall.
Paul is not generous.
Mary is not old.
Someone is either funny or humble. | Alice is strong. | neutral | (((~old(john)|brave(john)))=>((~calm(susan)&humble(susan))))&
(![X]:((old(X)|calm(X))<=>~wise(X)))&
(![X]:(~patient(X)=>(creative(X)<~>~calm(X))))&
((~happy(lucy))=>((~creative(alice)|~generous(alice))))&
(![X]:(~curious(X)<=>(~rich(X)&funny(X))))&
((~happy(mary))=>(?[X]:((~wise(X)|~rich(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((brave(X)|strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((strong(X)|~wise(X))<=>(patient(X)&~brave(X))))&
(((~quiet(john)&humble(john)))<=>((funny(mary)<~>~calm(mary))))&
((?[X]:((generous(X)&funny(X))))=>(patient(lucy)))&
(![X]:((~rich(X)|~old(X))=>~funny(X)))&
(![X]:((~kind(X)<~>~generous(X))<=>(~old(X)|~strong(X))))&
(![X]:((curious(X)&~calm(X))<=>(rich(X)|curious(X))))&
(![X]:((brave(X)|rich(X))=>(~quiet(X)&quiet(X))))&
((old(fred)&~tall(fred)))&
(happy(susan))&
(?[X]:((wise(X)&tall(X))))&
(~generous(paul))&
(~old(mary))&
(?[X]:((funny(X)<~>humble(X)))) | strong(alice) | [] | null | 0 |
Everyone who is not happy or strong is either happy or not quiet.
If susan is either curious or not old then lucy is either not funny or humble and vice versa.
If someone is patient then mary is not quiet or kind.
Everyone who is not brave or not funny is calm or creative.
If someone is both not strong and not rich then john is both not happy and rich.
If mary is both strong and curious then mary is either not rich or not old and vice versa.
Everyone who is either creative or rich is old.
If fred is both funny and not calm then someone is kind or not quiet and vice versa.
Everyone who is not quiet or happy is both patient and generous and vice versa.
If someone is happy then mary is either kind or not patient and vice versa.
If someone is not humble or not patient then someone is not kind or happy.
Everyone who is both not brave and humble is not happy or old and vice versa.
Everyone who is either not calm or kind is both not wise and not funny.
If someone is both kind and creative then someone is either not wise or old and vice versa.
If mary is rich then someone is not humble or not strong.
Everyone who is either creative or not generous is either brave or not rich and vice versa.
Someone is tall or not humble.
Susan is old or kind.
Someone is either calm or not strong.
Someone is not generous or not curious.
Mary is either not old or tall.
Someone is both kind and wise.
Alice is either curious or not kind.
Someone is generous or not patient. | Fred is not calm. | entailment | (![X]:((~happy(X)|strong(X))=>(happy(X)<~>~quiet(X))))&
(((curious(susan)<~>~old(susan)))<=>((~funny(lucy)<~>humble(lucy))))&
((?[X]:(patient(X)))=>((~quiet(mary)|kind(mary))))&
(![X]:((~brave(X)|~funny(X))=>(calm(X)|creative(X))))&
((?[X]:((~strong(X)&~rich(X))))=>((~happy(john)&rich(john))))&
(((strong(mary)&curious(mary)))<=>((~rich(mary)<~>~old(mary))))&
(![X]:((creative(X)<~>rich(X))=>old(X)))&
(((funny(fred)&~calm(fred)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~quiet(X)|happy(X))<=>(patient(X)&generous(X))))&
((?[X]:(happy(X)))<=>((kind(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((~brave(X)&humble(X))<=>(~happy(X)|old(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~wise(X)&~funny(X))))&
((?[X]:((kind(X)&creative(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
((rich(mary))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((creative(X)<~>~generous(X))<=>(brave(X)<~>~rich(X))))&
(?[X]:((tall(X)|~humble(X))))&
((old(susan)|kind(susan)))&
(?[X]:((calm(X)<~>~strong(X))))&
(?[X]:((~generous(X)|~curious(X))))&
((~old(mary)<~>tall(mary)))&
(?[X]:((kind(X)&wise(X))))&
((curious(alice)<~>~kind(alice)))&
(?[X]:((generous(X)|~patient(X)))) | ~calm(fred) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3813446556927394630672749
% SZS output start Proof for 3813446556927394630672749
8. (~calm(fred) & funny(fred)) <=> ? [X0] : (~quiet(X0) | kind(X0)) [input p7]
22. ? [X0] : (wise(X0) & kind(X0)) [input p21]
25. calm(fred) [input hypothesis]
43. ((~calm(fred) & funny(fred)) | ! [X0] : (quiet(X0) & ~kind(X0))) & (? [X0] : (~quiet(X0) | kind(X0)) | (calm(fred) | ~funny(fred))) [nnf transformation 8]
44. ((~calm(fred) & funny(fred)) | ! [X0] : (quiet(X0) & ~kind(X0))) & (? [X0] : (~quiet(X0) | kind(X0)) | calm(fred) | ~funny(fred)) [flattening 43]
45. ((~calm(fred) & funny(fred)) | ! [X0] : (quiet(X0) & ~kind(X0))) & (? [X1] : (~quiet(X1) | kind(X1)) | calm(fred) | ~funny(fred)) [rectify 44]
46. ? [X1] : (~quiet(X1) | kind(X1)) => (~quiet(sK0) | kind(sK0)) [choice axiom]
47. ((~calm(fred) & funny(fred)) | ! [X0] : (quiet(X0) & ~kind(X0))) & ((~quiet(sK0) | kind(sK0)) | calm(fred) | ~funny(fred)) [skolemisation 45,46]
76. ? [X0] : (wise(X0) & kind(X0)) => (wise(sK9) & kind(sK9)) [choice axiom]
77. wise(sK9) & kind(sK9) [skolemisation 22,76]
109. ~calm(fred) | ~kind(X0) [cnf transformation 47]
153. kind(sK9) [cnf transformation 77]
158. calm(fred) [cnf transformation 25]
235. 16 <=> calm(fred) [avatar definition]
240. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
241. ~kind(X0) <- (17) [avatar component clause 240]
242. 17 | ~16 [avatar split clause 109,235,240]
387. 16 [avatar split clause 158,235]
390. $false <- (17) [resolution 241,153]
391. ~17 [avatar contradiction clause 390]
392. $false [avatar sat refutation 242,387,391]
% SZS output end Proof for 3813446556927394630672749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is funny or not funny then john is brave and vice versa. Everyone who is both quiet and generous is both not brave and not humble. Everyone who is funny is tall and vice versa. Everyone who is both curious and not humble is happy or not tall and vice versa. Everyone who is tall or kind is old. If lucy is not brave then john is old or strong. Everyone who is not old or not strong is both funny and kind and vice versa. Everyone who is either not curious or happy is not calm. Everyone who is not generous is brave or kind and vice versa. Everyone who is strong or calm is quiet and vice versa. Everyone who is not generous is humble. Everyone who is both not rich and generous is not kind and vice versa. Everyone who is not calm is not rich and vice versa. Everyone who is either patient or not quiet is not curious or wise and vice versa. If mary is both not funny and not calm then someone is not happy or happy and vice versa. If paul is not quiet then someone is funny or not creative and vice versa. Lucy is not tall. Someone is either quiet or wise. Alice is either not strong or not rich. Paul is both not creative and curious. Alice is either funny or not patient. | Paul is generous. | contradiction | (((funny(john)|~funny(john)))<=>(brave(john)))&
(![X]:((quiet(X)&generous(X))=>(~brave(X)&~humble(X))))&
(![X]:(funny(X)<=>tall(X)))&
(![X]:((curious(X)&~humble(X))<=>(happy(X)|~tall(X))))&
(![X]:((tall(X)|kind(X))=>old(X)))&
((~brave(lucy))=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(![X]:((patient(X)<~>~quiet(X))<=>(~curious(X)|wise(X))))&
(((~funny(mary)&~calm(mary)))<=>(?[X]:((~happy(X)|happy(X)))))&
((~quiet(paul))<=>(?[X]:((funny(X)|~creative(X)))))&
(~tall(lucy))&
(?[X]:((quiet(X)<~>wise(X))))&
((~strong(alice)<~>~rich(alice)))&
((~creative(paul)&curious(paul)))&
((funny(alice)<~>~patient(alice))) | generous(paul) | [
"p6",
"p8",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6819146444393640534934027
% SZS output start Proof for 6819146444393640534934027
7. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (kind(X0) & funny(X0))) [input p6]
9. ! [X0] : (~generous(X0) <=> (kind(X0) | brave(X0))) [input p8]
10. ! [X0] : ((calm(X0) | strong(X0)) <=> quiet(X0)) [input p9]
16. ~quiet(paul) <=> ? [X0] : (~creative(X0) | funny(X0)) [input p15]
20. curious(paul) & ~creative(paul) [input p19]
22. generous(paul) [input hypothesis]
35. ! [X0] : (((~strong(X0) | ~old(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (strong(X0) & old(X0)))) [nnf transformation 7]
36. ! [X0] : ((~strong(X0) | ~old(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (strong(X0) & old(X0)))) [flattening 35]
38. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | generous(X0))) [nnf transformation 9]
39. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | generous(X0))) [flattening 38]
40. ! [X0] : (((calm(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 10]
41. ! [X0] : ((calm(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [flattening 40]
52. (~quiet(paul) | ! [X0] : (creative(X0) & ~funny(X0))) & (? [X0] : (~creative(X0) | funny(X0)) | quiet(paul)) [nnf transformation 16]
53. (~quiet(paul) | ! [X0] : (creative(X0) & ~funny(X0))) & (? [X1] : (~creative(X1) | funny(X1)) | quiet(paul)) [rectify 52]
54. ? [X1] : (~creative(X1) | funny(X1)) => (~creative(sK1) | funny(sK1)) [choice axiom]
55. (~quiet(paul) | ! [X0] : (creative(X0) & ~funny(X0))) & ((~creative(sK1) | funny(sK1)) | quiet(paul)) [skolemisation 53,54]
79. strong(X0) | kind(X0) [cnf transformation 36]
85. ~kind(X0) | ~generous(X0) [cnf transformation 39]
86. ~strong(X0) | quiet(X0) [cnf transformation 41]
108. ~quiet(paul) | creative(X0) [cnf transformation 55]
114. ~creative(paul) [cnf transformation 20]
118. generous(paul) [cnf transformation 22]
165. 10 <=> ! [X0] : creative(X0) [avatar definition]
166. creative(X0) <- (10) [avatar component clause 165]
168. 11 <=> quiet(paul) [avatar definition]
171. 10 | ~11 [avatar split clause 108,168,165]
217. kind(X0) | quiet(X0) [resolution 86,79]
222. ~generous(X0) | quiet(X0) [resolution 217,85]
271. quiet(paul) [resolution 222,118]
276. 11 [avatar split clause 271,168]
277. $false <- (10) [resolution 166,114]
280. ~10 [avatar contradiction clause 277]
281. $false [avatar sat refutation 171,276,280]
% SZS output end Proof for 6819146444393640534934027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or not brave then someone is not strong or humble.
Everyone who is either calm or not happy is not creative or patient and vice versa.
If someone is not kind or kind then someone is either humble or not happy and vice versa.
Everyone who is generous or not wise is wise and vice versa.
If someone is both not happy and not tall then john is either quiet or calm.
Everyone who is both creative and not happy is either tall or humble and vice versa.
If someone is both old and not brave then someone is tall or not creative.
Everyone who is not humble is both not rich and tall.
If alice is not quiet or not humble then someone is calm and vice versa.
Everyone who is quiet or curious is either not kind or not calm and vice versa.
If fred is either quiet or rich then mary is not quiet or creative and vice versa.
Everyone who is either patient or old is both not calm and not strong and vice versa.
If someone is strong then someone is both not rich and not wise and vice versa.
If someone is either not rich or not quiet then someone is not kind or not tall.
If someone is not rich or calm then alice is not old or wise.
Everyone who is not brave or not kind is curious and vice versa.
Fred is not humble.
John is both brave and not tall.
Paul is not wise or not patient.
Someone is not kind.
Someone is both not kind and quiet.
John is not brave or not strong.
Alice is both happy and funny. | Fred is not strong. | entailment | ((?[X]:((~generous(X)|~brave(X))))=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:((calm(X)<~>~happy(X))<=>(~creative(X)|patient(X))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((generous(X)|~wise(X))<=>wise(X)))&
((?[X]:((~happy(X)&~tall(X))))=>((quiet(john)<~>calm(john))))&
(![X]:((creative(X)&~happy(X))<=>(tall(X)<~>humble(X))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:(~humble(X)=>(~rich(X)&tall(X))))&
(((~quiet(alice)|~humble(alice)))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)|curious(X))<=>(~kind(X)<~>~calm(X))))&
(((quiet(fred)<~>rich(fred)))<=>((~quiet(mary)|creative(mary))))&
(![X]:((patient(X)<~>old(X))<=>(~calm(X)&~strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~rich(X)&~wise(X)))))&
((?[X]:((~rich(X)<~>~quiet(X))))=>(?[X]:((~kind(X)|~tall(X)))))&
((?[X]:((~rich(X)|calm(X))))=>((~old(alice)|wise(alice))))&
(![X]:((~brave(X)|~kind(X))<=>curious(X)))&
(~humble(fred))&
((brave(john)&~tall(john)))&
((~wise(paul)|~patient(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)&quiet(X))))&
((~brave(john)|~strong(john)))&
((happy(alice)&funny(alice))) | ~strong(fred) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2807063240069883091448723
% SZS output start Proof for 2807063240069883091448723
4. ! [X0] : ((~wise(X0) | generous(X0)) <=> wise(X0)) [input p3]
13. ? [X0] : strong(X0) <=> ? [X0] : (~wise(X0) & ~rich(X0)) [input p12]
24. strong(fred) [input hypothesis]
28. ? [X0] : strong(X0) <=> ? [X1] : (~wise(X1) & ~rich(X1)) [rectify 13]
48. ! [X0] : (((~wise(X0) | generous(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~generous(X0)))) [nnf transformation 4]
49. ! [X0] : ((~wise(X0) | generous(X0) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~generous(X0)))) [flattening 48]
67. (? [X0] : strong(X0) | ! [X1] : (wise(X1) | rich(X1))) & (? [X1] : (~wise(X1) & ~rich(X1)) | ! [X0] : ~strong(X0)) [nnf transformation 28]
68. (? [X0] : strong(X0) | ! [X1] : (wise(X1) | rich(X1))) & (? [X2] : (~wise(X2) & ~rich(X2)) | ! [X3] : ~strong(X3)) [rectify 67]
69. ? [X0] : strong(X0) => strong(sK5) [choice axiom]
70. ? [X2] : (~wise(X2) & ~rich(X2)) => (~wise(sK6) & ~rich(sK6)) [choice axiom]
71. (strong(sK5) | ! [X1] : (wise(X1) | rich(X1))) & ((~wise(sK6) & ~rich(sK6)) | ! [X3] : ~strong(X3)) [skolemisation 68,70,69]
97. wise(X0) | wise(X0) [cnf transformation 49]
132. ~wise(sK6) | ~strong(X3) [cnf transformation 71]
150. strong(fred) [cnf transformation 24]
151. wise(X0) [duplicate literal removal 97]
252. ~strong(X3) [subsumption resolution 132,151]
270. $false [subsumption resolution 150,252]
% SZS output end Proof for 2807063240069883091448723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not rich and not strong.
Everyone who is either not calm or not curious is both funny and not old and vice versa.
Everyone who is both not humble and not strong is either not rich or not strong and vice versa.
If someone is both happy and not curious then alice is both generous and not old and vice versa.
Everyone who is not wise is either not happy or wise.
Everyone who is not rich or not humble is both not kind and rich.
Everyone who is happy or not brave is either quiet or old and vice versa.
Everyone who is wise or not curious is not strong and vice versa.
Everyone who is not patient is patient.
If susan is brave then someone is tall.
Everyone who is not old or happy is both old and not wise and vice versa.
If someone is either funny or kind then someone is strong.
Everyone who is both not strong and not wise is either not generous or old.
If someone is not brave then john is not calm or funny.
If someone is either not kind or generous then lucy is both not brave and not creative.
Lucy is not humble.
Someone is either not rich or quiet.
Someone is both not creative and not calm. | Alice is kind. | contradiction | ((?[X]:(~brave(X)))=>((~rich(paul)&~strong(paul))))&
(![X]:((~calm(X)<~>~curious(X))<=>(funny(X)&~old(X))))&
(![X]:((~humble(X)&~strong(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((happy(X)&~curious(X))))<=>((generous(alice)&~old(alice))))&
(![X]:(~wise(X)=>(~happy(X)<~>wise(X))))&
(![X]:((~rich(X)|~humble(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)|~brave(X))<=>(quiet(X)<~>old(X))))&
(![X]:((wise(X)|~curious(X))<=>~strong(X)))&
(![X]:(~patient(X)=>patient(X)))&
((brave(susan))=>(?[X]:(tall(X))))&
(![X]:((~old(X)|happy(X))<=>(old(X)&~wise(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~wise(X))=>(~generous(X)<~>old(X))))&
((?[X]:(~brave(X)))=>((~calm(john)|funny(john))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~brave(lucy)&~creative(lucy))))&
(~humble(lucy))&
(?[X]:((~rich(X)<~>quiet(X))))&
(?[X]:((~creative(X)&~calm(X)))) | kind(alice) | [
"p2",
"p4",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 130717915421536288212021
% SZS output start Proof for 130717915421536288212021
3. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p2]
5. ! [X0] : (~wise(X0) => (~happy(X0) <~> wise(X0))) [input p4]
6. ! [X0] : ((~humble(X0) | ~rich(X0)) => (rich(X0) & ~kind(X0))) [input p5]
8. ! [X0] : ((~curious(X0) | wise(X0)) <=> ~strong(X0)) [input p7]
11. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~wise(X0) & old(X0))) [input p10]
19. kind(alice) [input hypothesis]
26. ! [X0] : ((~happy(X0) <~> wise(X0)) | wise(X0)) [ennf transformation 5]
27. ! [X0] : ((rich(X0) & ~kind(X0)) | (humble(X0) & rich(X0))) [ennf transformation 6]
36. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (strong(X0) | humble(X0)))) [nnf transformation 3]
37. ! [X0] : (((~strong(X0) & ~humble(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | strong(X0) | humble(X0))) [flattening 36]
43. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | wise(X0)) [nnf transformation 26]
46. ! [X0] : (((~curious(X0) | wise(X0)) | strong(X0)) & (~strong(X0) | (curious(X0) & ~wise(X0)))) [nnf transformation 8]
47. ! [X0] : ((~curious(X0) | wise(X0) | strong(X0)) & (~strong(X0) | (curious(X0) & ~wise(X0)))) [flattening 46]
48. ! [X0] : (((happy(X0) | ~old(X0)) | (wise(X0) | ~old(X0))) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 11]
49. ! [X0] : ((happy(X0) | ~old(X0) | wise(X0) | ~old(X0)) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [flattening 48]
72. ~humble(X0) | ~rich(X0) | strong(X0) [cnf transformation 37]
79. wise(X0) | ~happy(X0) | wise(X0) [cnf transformation 43]
82. ~kind(X0) | humble(X0) [cnf transformation 27]
83. rich(X0) | rich(X0) [cnf transformation 27]
91. ~wise(X0) | ~strong(X0) [cnf transformation 47]
94. old(X0) | old(X0) [cnf transformation 49]
98. happy(X0) | ~old(X0) | wise(X0) | ~old(X0) [cnf transformation 49]
110. kind(alice) [cnf transformation 19]
111. old(X0) [duplicate literal removal 94]
112. happy(X0) | ~old(X0) | wise(X0) [duplicate literal removal 98]
113. rich(X0) [duplicate literal removal 83]
114. ~happy(X0) | wise(X0) [duplicate literal removal 79]
154. ~old(X0) | wise(X0) [subsumption resolution 112,114]
198. humble(alice) [resolution 82,110]
202. wise(X0) [resolution 154,111]
204. ~strong(X1) [resolution 202,91]
220. ~rich(alice) | strong(alice) [resolution 72,198]
222. strong(alice) [subsumption resolution 220,113]
223. $false [subsumption resolution 222,204]
% SZS output end Proof for 130717915421536288212021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not brave and not strong and vice versa. If alice is both not brave and patient then susan is not patient. Everyone who is rich or old is not patient and vice versa. If someone is either not happy or happy then paul is both not quiet and not tall and vice versa. If fred is either calm or not curious then someone is both generous and not quiet. If someone is quiet then mary is not humble or not generous. If mary is either tall or not old then someone is both humble and quiet. Everyone who is either not funny or not rich is both curious and not kind and vice versa. If someone is either old or not patient then lucy is quiet and vice versa. If someone is either not strong or not wise then susan is either curious or funny and vice versa. Everyone who is not funny is either rich or not strong and vice versa. Everyone who is either kind or generous is either old or brave and vice versa. Everyone who is both humble and quiet is brave or funny and vice versa. Everyone who is kind or happy is creative or old and vice versa. If fred is not old then fred is both wise and kind. Everyone who is not calm or not quiet is rich or not tall. Alice is not old. Someone is both not happy and not curious. Mary is not humble. John is not old. Paul is not curious. John is both not rich and not generous. John is both not kind and not calm. Someone is not wise. | John is not patient. | contradiction | (![X]:(old(X)<=>(~brave(X)&~strong(X))))&
(((~brave(alice)&patient(alice)))=>(~patient(susan)))&
(![X]:((rich(X)|old(X))<=>~patient(X)))&
((?[X]:((~happy(X)<~>happy(X))))<=>((~quiet(paul)&~tall(paul))))&
(((calm(fred)<~>~curious(fred)))=>(?[X]:((generous(X)&~quiet(X)))))&
((?[X]:(quiet(X)))=>((~humble(mary)|~generous(mary))))&
(((tall(mary)<~>~old(mary)))=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((~funny(X)<~>~rich(X))<=>(curious(X)&~kind(X))))&
((?[X]:((old(X)<~>~patient(X))))<=>(quiet(lucy)))&
((?[X]:((~strong(X)<~>~wise(X))))<=>((curious(susan)<~>funny(susan))))&
(![X]:(~funny(X)<=>(rich(X)<~>~strong(X))))&
(![X]:((kind(X)<~>generous(X))<=>(old(X)<~>brave(X))))&
(![X]:((humble(X)&quiet(X))<=>(brave(X)|funny(X))))&
(![X]:((kind(X)|happy(X))<=>(creative(X)|old(X))))&
((~old(fred))=>((wise(fred)&kind(fred))))&
(![X]:((~calm(X)|~quiet(X))=>(rich(X)|~tall(X))))&
(~old(alice))&
(?[X]:((~happy(X)&~curious(X))))&
(~humble(mary))&
(~old(john))&
(~curious(paul))&
((~rich(john)&~generous(john)))&
((~kind(john)&~calm(john)))&
(?[X]:(~wise(X))) | ~patient(john) | [
"p2",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4746516203851612875383309
% SZS output start Proof for 4746516203851612875383309
3. ! [X0] : ((old(X0) | rich(X0)) <=> ~patient(X0)) [input p2]
20. ~old(john) [input p19]
22. ~generous(john) & ~rich(john) [input p21]
25. ~patient(john) [input hypothesis]
37. ! [X0] : (((old(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : ((old(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~rich(X0)))) [flattening 37]
76. rich(X0) | old(X0) | patient(X0) [cnf transformation 38]
139. ~old(john) [cnf transformation 20]
141. ~rich(john) [cnf transformation 22]
146. ~patient(john) [cnf transformation 25]
307. old(john) | patient(john) [resolution 76,141]
309. patient(john) [subsumption resolution 307,139]
310. $false [subsumption resolution 309,146]
% SZS output end Proof for 4746516203851612875383309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or rich is both not wise and not calm.
If susan is either rich or not curious then paul is both rich and kind and vice versa.
If someone is either creative or calm then john is both patient and not funny and vice versa.
Everyone who is not calm or not humble is not happy or generous and vice versa.
Everyone who is both generous and not brave is not patient or not quiet and vice versa.
Everyone who is not quiet is not curious or patient and vice versa.
Everyone who is both not generous and brave is either not funny or not calm.
If john is either not calm or strong then john is tall and vice versa.
Everyone who is both wise and not rich is either not creative or rich.
Everyone who is not wise is funny and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Fred is generous. | entailment | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
(((rich(susan)<~>~curious(susan)))<=>((rich(paul)&kind(paul))))&
((?[X]:((creative(X)<~>calm(X))))<=>((patient(john)&~funny(john))))&
(![X]:((~calm(X)|~humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((generous(X)&~brave(X))<=>(~patient(X)|~quiet(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|patient(X))))&
(![X]:((~generous(X)&brave(X))=>(~funny(X)<~>~calm(X))))&
(((~calm(john)<~>strong(john)))<=>(tall(john)))&
(![X]:((wise(X)&~rich(X))=>(~creative(X)<~>rich(X))))&
(![X]:(~wise(X)<=>funny(X)))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | generous(fred) | [
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4404028840039661325423886
% SZS output start Proof for 4404028840039661325423886
5. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p4]
6. ! [X0] : (~quiet(X0) <=> (patient(X0) | ~curious(X0))) [input p5]
25. ~generous(fred) [input hypothesis]
43. ! [X0] : (((~brave(X0) & generous(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~brave(X0) & generous(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | brave(X0) | ~generous(X0))) [flattening 43]
45. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | quiet(X0))) [nnf transformation 6]
46. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | quiet(X0))) [flattening 45]
97. patient(X0) | generous(X0) [cnf transformation 44]
98. quiet(X0) | generous(X0) [cnf transformation 44]
103. ~quiet(X0) | ~patient(X0) [cnf transformation 46]
151. ~generous(fred) [cnf transformation 25]
320. ~patient(X0) | generous(X0) [resolution 103,98]
328. generous(X0) [subsumption resolution 320,97]
332. $false [resolution 328,151]
% SZS output end Proof for 4404028840039661325423886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is funny.
Everyone who is either not strong or not creative is either not funny or not strong.
Everyone who is both not brave and not rich is not brave or not rich.
Everyone who is strong is quiet.
If alice is either rich or happy then alice is creative or brave.
If someone is either calm or not happy then someone is either calm or creative.
If john is not calm then fred is either strong or funny and vice versa.
Everyone who is either not brave or not tall is not brave.
If john is either humble or quiet then susan is rich or not old.
Everyone who is not brave or not humble is tall or happy.
Everyone who is brave is either brave or not rich.
If john is generous then lucy is not quiet.
Everyone who is either quiet or not quiet is both not old and rich and vice versa.
Everyone who is not curious is both not funny and not brave.
Everyone who is not wise is both tall and wise and vice versa.
Everyone who is not wise is either creative or not funny.
Someone is either not creative or strong.
Paul is either not strong or not curious.
Fred is old or creative.
Someone is not quiet.
Mary is either not generous or not happy.
Fred is either not generous or not curious.
Someone is either strong or wise.
Someone is both not old and calm. | Lucy is tall. | contradiction | ((?[X]:(rich(X)))=>(?[X]:(funny(X))))&
(![X]:((~strong(X)<~>~creative(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~brave(X)&~rich(X))=>(~brave(X)|~rich(X))))&
(![X]:(strong(X)=>quiet(X)))&
(((rich(alice)<~>happy(alice)))=>((creative(alice)|brave(alice))))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
((~calm(john))<=>((strong(fred)<~>funny(fred))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&wise(X))))&
(![X]:(~wise(X)=>(creative(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
((~strong(paul)<~>~curious(paul)))&
((old(fred)|creative(fred)))&
(?[X]:(~quiet(X)))&
((~generous(mary)<~>~happy(mary)))&
((~generous(fred)<~>~curious(fred)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~old(X)&calm(X)))) | tall(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7623190258815525467794941
% SZS output start Proof for 7623190258815525467794941
15. ! [X0] : (~wise(X0) <=> (wise(X0) & tall(X0))) [input p14]
25. tall(lucy) [input hypothesis]
60. ! [X0] : ((~wise(X0) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | wise(X0))) [nnf transformation 15]
61. ! [X0] : ((~wise(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | wise(X0))) [flattening 60]
111. wise(X0) | wise(X0) [cnf transformation 61]
112. ~wise(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 61]
129. tall(lucy) [cnf transformation 25]
130. wise(X0) [duplicate literal removal 111]
131. ~wise(X0) | ~tall(X0) [duplicate literal removal 112]
280. ~tall(X0) [resolution 131,130]
281. $false [resolution 280,129]
% SZS output end Proof for 7623190258815525467794941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or kind then someone is either not wise or humble and vice versa.
Everyone who is happy is not old and vice versa.
Everyone who is not happy is both generous and calm.
Everyone who is old or rich is kind.
Everyone who is funny is not creative or not kind.
Everyone who is not humble or old is rich or not curious.
If lucy is curious then fred is either strong or creative.
Everyone who is both humble and generous is both kind and happy.
Everyone who is either not generous or not curious is either not brave or not tall and vice versa.
Everyone who is not creative is tall or not old and vice versa.
Everyone who is humble or generous is humble.
Everyone who is both happy and not rich is funny.
Everyone who is not wise is quiet or not kind and vice versa.
If lucy is either patient or not funny then someone is both not patient and not tall and vice versa.
If susan is both quiet and not creative then lucy is both curious and not calm.
If someone is not generous then john is either not tall or not patient and vice versa.
Someone is not happy or not quiet.
John is both not brave and not humble.
John is either tall or not generous.
Someone is not wise.
Lucy is both patient and not funny.
Susan is either not happy or not humble.
Someone is not calm.
Mary is not wise. | Susan is humble. | contradiction | ((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(tall(X)|~old(X))))&
(![X]:((humble(X)|generous(X))=>humble(X)))&
(![X]:((happy(X)&~rich(X))=>funny(X)))&
(![X]:(~wise(X)<=>(quiet(X)|~kind(X))))&
(((patient(lucy)<~>~funny(lucy)))<=>(?[X]:((~patient(X)&~tall(X)))))&
(((quiet(susan)&~creative(susan)))=>((curious(lucy)&~calm(lucy))))&
((?[X]:(~generous(X)))<=>((~tall(john)<~>~patient(john))))&
(?[X]:((~happy(X)|~quiet(X))))&
((~brave(john)&~humble(john)))&
((tall(john)<~>~generous(john)))&
(?[X]:(~wise(X)))&
((patient(lucy)&~funny(lucy)))&
((~happy(susan)<~>~humble(susan)))&
(?[X]:(~calm(X)))&
(~wise(mary)) | humble(susan) | [
"p2",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7619997996235127745421528
% SZS output start Proof for 7619997996235127745421528
3. ! [X0] : (~happy(X0) => (calm(X0) & generous(X0))) [input p2]
8. ! [X0] : ((generous(X0) & humble(X0)) => (happy(X0) & kind(X0))) [input p7]
22. ~happy(susan) <~> ~humble(susan) [input p21]
25. humble(susan) [input hypothesis]
27. ! [X0] : ((calm(X0) & generous(X0)) | happy(X0)) [ennf transformation 3]
34. ! [X0] : ((happy(X0) & kind(X0)) | (~generous(X0) | ~humble(X0))) [ennf transformation 8]
35. ! [X0] : ((happy(X0) & kind(X0)) | ~generous(X0) | ~humble(X0)) [flattening 34]
66. (humble(susan) | happy(susan)) & (~humble(susan) | ~happy(susan)) [nnf transformation 22]
77. generous(X0) | happy(X0) [cnf transformation 27]
87. happy(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 35]
125. ~humble(susan) | ~happy(susan) [cnf transformation 66]
126. humble(susan) | happy(susan) [cnf transformation 66]
129. humble(susan) [cnf transformation 25]
178. happy(X0) | ~humble(X0) [subsumption resolution 87,77]
254. happy(susan) [subsumption resolution 126,178]
255. ~humble(susan) [subsumption resolution 125,254]
256. $false [subsumption resolution 129,255]
% SZS output end Proof for 7619997996235127745421528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or not rich then susan is not patient and vice versa.
If someone is not quiet or generous then alice is not happy or wise.
Everyone who is humble is calm.
Everyone who is patient is both strong and old.
If someone is both quiet and not quiet then someone is both wise and not curious and vice versa.
If susan is either strong or patient then john is calm.
If someone is both tall and not happy then alice is either not brave or not curious.
If someone is strong then someone is not funny.
Everyone who is not happy is both not creative and patient and vice versa.
Everyone who is both creative and not funny is both patient and not calm and vice versa.
Everyone who is either curious or not creative is kind and vice versa.
If alice is generous or funny then someone is either happy or strong.
Everyone who is both creative and not quiet is either calm or not tall.
Everyone who is both quiet and not creative is both generous and not rich and vice versa.
If someone is both brave and calm then paul is patient and vice versa.
If someone is either creative or calm then fred is both creative and strong and vice versa.
Paul is strong.
Someone is either not patient or creative.
John is either not patient or not humble.
Lucy is tall.
Lucy is either rich or curious.
Susan is both happy and not rich.
Lucy is creative.
Someone is not tall or curious. | Alice is not generous. | neutral | ((?[X]:((humble(X)<~>~rich(X))))<=>(~patient(susan)))&
((?[X]:((~quiet(X)|generous(X))))=>((~happy(alice)|wise(alice))))&
(![X]:(humble(X)=>calm(X)))&
(![X]:(patient(X)=>(strong(X)&old(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(susan)<~>patient(susan)))=>(calm(john)))&
((?[X]:((tall(X)&~happy(X))))=>((~brave(alice)<~>~curious(alice))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(![X]:(~happy(X)<=>(~creative(X)&patient(X))))&
(![X]:((creative(X)&~funny(X))<=>(patient(X)&~calm(X))))&
(![X]:((curious(X)<~>~creative(X))<=>kind(X)))&
(((generous(alice)|funny(alice)))=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((creative(X)&~quiet(X))=>(calm(X)<~>~tall(X))))&
(![X]:((quiet(X)&~creative(X))<=>(generous(X)&~rich(X))))&
((?[X]:((brave(X)&calm(X))))<=>(patient(paul)))&
((?[X]:((creative(X)<~>calm(X))))<=>((creative(fred)&strong(fred))))&
(strong(paul))&
(?[X]:((~patient(X)<~>creative(X))))&
((~patient(john)<~>~humble(john)))&
(tall(lucy))&
((rich(lucy)<~>curious(lucy)))&
((happy(susan)&~rich(susan)))&
(creative(lucy))&
(?[X]:((~tall(X)|curious(X)))) | ~generous(alice) | [] | null | 0 |
Everyone who is not wise is both not wise and not humble and vice versa.
Everyone who is either not rich or not quiet is either wise or brave.
Everyone who is either not calm or not strong is curious or old and vice versa.
Everyone who is humble is either funny or humble and vice versa.
If alice is either brave or not generous then someone is not wise.
Everyone who is not funny or not wise is either patient or not old and vice versa.
Everyone who is either not rich or not wise is either not generous or curious and vice versa.
If lucy is strong or curious then someone is not strong and vice versa.
Everyone who is either rich or not kind is either old or not brave and vice versa.
If someone is brave or calm then mary is not brave.
If someone is either rich or brave then someone is not calm.
Everyone who is both funny and kind is not creative or strong and vice versa.
If john is either not curious or not creative then someone is both not creative and curious.
If fred is not happy then someone is not quiet or calm.
If alice is both quiet and not strong then paul is calm or not patient and vice versa.
Someone is wise.
Mary is not humble or rich.
Alice is humble.
Lucy is either quiet or not curious.
Someone is old.
Someone is humble or not generous. | John is not generous. | neutral | (![X]:(~wise(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(curious(X)|old(X))))&
(![X]:(humble(X)<=>(funny(X)<~>humble(X))))&
(((brave(alice)<~>~generous(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~generous(X)<~>curious(X))))&
(((strong(lucy)|curious(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(old(X)<~>~brave(X))))&
((?[X]:((brave(X)|calm(X))))=>(~brave(mary)))&
((?[X]:((rich(X)<~>brave(X))))=>(?[X]:(~calm(X))))&
(![X]:((funny(X)&kind(X))<=>(~creative(X)|strong(X))))&
(((~curious(john)<~>~creative(john)))=>(?[X]:((~creative(X)&curious(X)))))&
((~happy(fred))=>(?[X]:((~quiet(X)|calm(X)))))&
(((quiet(alice)&~strong(alice)))<=>((calm(paul)|~patient(paul))))&
(?[X]:(wise(X)))&
((~humble(mary)|rich(mary)))&
(humble(alice))&
((quiet(lucy)<~>~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:((humble(X)|~generous(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both calm and rich is not strong or humble. If lucy is quiet or not patient then someone is funny. Everyone who is either not patient or not brave is either not humble or not happy and vice versa. Everyone who is brave is both brave and not strong. If someone is both tall and rich then someone is both tall and not generous and vice versa. If someone is both curious and patient then mary is creative and vice versa. Everyone who is either rich or not rich is not wise and vice versa. Everyone who is calm or not wise is either wise or not curious and vice versa. If someone is generous or patient then mary is not curious or not wise and vice versa. If someone is generous then john is both curious and not kind. Everyone who is both not patient and not tall is either not patient or creative. If alice is either calm or kind then someone is either not funny or happy. Everyone who is either not old or not wise is not creative. If someone is both not kind and not quiet then someone is happy and vice versa. If mary is both calm and not kind then someone is not curious and vice versa. Mary is both patient and happy. Someone is either old or funny. Fred is not old. Alice is not quiet. John is not old or wise. Susan is either not wise or tall. Susan is not kind. Someone is both not brave and kind. | Mary is not wise. | entailment | (![X]:((calm(X)&rich(X))=>(~strong(X)|humble(X))))&
(((quiet(lucy)|~patient(lucy)))=>(?[X]:(funny(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(brave(X)=>(brave(X)&~strong(X))))&
((?[X]:((tall(X)&rich(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
((?[X]:((curious(X)&patient(X))))<=>(creative(mary)))&
(![X]:((rich(X)<~>~rich(X))<=>~wise(X)))&
(![X]:((calm(X)|~wise(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~curious(mary)|~wise(mary))))&
((?[X]:(generous(X)))=>((curious(john)&~kind(john))))&
(![X]:((~patient(X)&~tall(X))=>(~patient(X)<~>creative(X))))&
(((calm(alice)<~>kind(alice)))=>(?[X]:((~funny(X)<~>happy(X)))))&
(![X]:((~old(X)<~>~wise(X))=>~creative(X)))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:(happy(X))))&
(((calm(mary)&~kind(mary)))<=>(?[X]:(~curious(X))))&
((patient(mary)&happy(mary)))&
(?[X]:((old(X)<~>funny(X))))&
(~old(fred))&
(~quiet(alice))&
((~old(john)|wise(john)))&
((~wise(susan)<~>tall(susan)))&
(~kind(susan))&
(?[X]:((~brave(X)&kind(X)))) | ~wise(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6272304544453052151112154
% SZS output start Proof for 6272304544453052151112154
7. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> ~wise(X0)) [input p6]
24. wise(mary) [input hypothesis]
48. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | wise(X0)) & (~wise(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 7]
95. ~wise(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
96. ~wise(X0) | rich(X0) | rich(X0) [cnf transformation 48]
137. wise(mary) [cnf transformation 24]
141. ~wise(X0) | ~rich(X0) [duplicate literal removal 95]
142. ~wise(X0) | rich(X0) [duplicate literal removal 96]
201. ~wise(X0) [subsumption resolution 141,142]
281. $false [subsumption resolution 137,201]
% SZS output end Proof for 6272304544453052151112154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then alice is either quiet or patient and vice versa.
If lucy is both creative and not creative then someone is not quiet and vice versa.
If someone is either not generous or patient then someone is either not brave or calm.
Everyone who is both not kind and curious is either wise or not happy and vice versa.
If someone is either not generous or kind then mary is both not happy and not curious.
Everyone who is both not calm and patient is either curious or not creative.
If lucy is either not brave or not humble then someone is both not patient and funny and vice versa.
If susan is kind or not tall then paul is both not creative and brave and vice versa.
If someone is either curious or rich then someone is either generous or not rich.
Everyone who is both generous and not wise is either wise or happy and vice versa.
If alice is either quiet or not strong then john is not creative and vice versa.
If someone is either funny or not generous then someone is not tall or creative and vice versa.
If mary is not wise or humble then someone is either humble or not wise and vice versa.
If john is not strong then someone is not curious.
If someone is not creative then susan is both happy and patient and vice versa.
If paul is either happy or not humble then fred is calm or strong and vice versa.
Fred is quiet.
Someone is not funny.
Susan is not creative.
Fred is calm or not funny.
Mary is not patient.
John is not quiet or not patient. | Mary is not rich. | neutral | ((brave(fred))<=>((quiet(alice)<~>patient(alice))))&
(((creative(lucy)&~creative(lucy)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((~kind(X)&curious(X))<=>(wise(X)<~>~happy(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>((~happy(mary)&~curious(mary))))&
(![X]:((~calm(X)&patient(X))=>(curious(X)<~>~creative(X))))&
(((~brave(lucy)<~>~humble(lucy)))<=>(?[X]:((~patient(X)&funny(X)))))&
(((kind(susan)|~tall(susan)))<=>((~creative(paul)&brave(paul))))&
((?[X]:((curious(X)<~>rich(X))))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:((generous(X)&~wise(X))<=>(wise(X)<~>happy(X))))&
(((quiet(alice)<~>~strong(alice)))<=>(~creative(john)))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|creative(X)))))&
(((~wise(mary)|humble(mary)))<=>(?[X]:((humble(X)<~>~wise(X)))))&
((~strong(john))=>(?[X]:(~curious(X))))&
((?[X]:(~creative(X)))<=>((happy(susan)&patient(susan))))&
(((happy(paul)<~>~humble(paul)))<=>((calm(fred)|strong(fred))))&
(quiet(fred))&
(?[X]:(~funny(X)))&
(~creative(susan))&
((calm(fred)|~funny(fred)))&
(~patient(mary))&
((~quiet(john)|~patient(john))) | ~rich(mary) | [] | null | 0 |
Everyone who is not old or not tall is funny or happy and vice versa.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Everyone who is rich is either not brave or wise.
Paul is not rich or not patient.
Susan is either brave or not quiet.
Alice is not humble.
Someone is either not old or old.
Fred is old or not patient.
Paul is wise.
Someone is either not quiet or not strong. | Alice is not patient. | entailment | (![X]:((~old(X)|~tall(X))<=>(funny(X)|happy(X))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((~rich(paul)|~patient(paul)))&
((brave(susan)<~>~quiet(susan)))&
(~humble(alice))&
(?[X]:((~old(X)<~>old(X))))&
((old(fred)|~patient(fred)))&
(wise(paul))&
(?[X]:((~quiet(X)<~>~strong(X)))) | ~patient(alice) | [
"p3",
"p4",
"p7",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6747996989703059661127886
% SZS output start Proof for 6747996989703059661127886
4. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p4]
8. (happy(alice) <~> calm(alice)) => (quiet(susan) & ~quiet(susan)) [input p7]
10. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p10]
13. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~generous(X0))) [input p12]
15. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p14]
24. patient(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 5]
32. (quiet(susan) & ~quiet(susan)) | (happy(alice) <=> calm(alice)) [ennf transformation 8]
33. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 10]
40. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 40]
45. (quiet(susan) & ~quiet(susan)) | ((happy(alice) | ~calm(alice)) & (calm(alice) | ~happy(alice))) [nnf transformation 32]
50. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 50]
57. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ~quiet(X0))) [nnf transformation 13]
58. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ~quiet(X0))) [flattening 57]
63. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 15]
81. quiet(X0) | ~generous(X0) | quiet(X0) [cnf transformation 41]
84. ~kind(X0) | ~happy(X0) [cnf transformation 30]
94. ~quiet(susan) | happy(alice) | ~calm(alice) [cnf transformation 45]
102. ~patient(X0) | old(X0) [cnf transformation 33]
105. kind(X0) | kind(X0) [cnf transformation 51]
115. quiet(X0) | generous(X0) [cnf transformation 58]
121. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 63]
128. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 63]
141. patient(alice) [cnf transformation 24]
142. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 121]
145. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 128]
146. kind(X0) [duplicate literal removal 105]
151. ~generous(X0) | quiet(X0) [duplicate literal removal 81]
186. 8 <=> calm(alice) [avatar definition]
190. 9 <=> happy(alice) [avatar definition]
192. happy(alice) <- (9) [avatar component clause 190]
194. 10 <=> quiet(susan) [avatar definition]
195. ~quiet(susan) <- (~10) [avatar component clause 194]
199. ~8 | 9 | ~10 [avatar split clause 94,194,190,186]
239. quiet(X0) [subsumption resolution 115,151]
261. ~old(X0) | calm(X0) [subsumption resolution 142,145]
273. $false <- (~10) [subsumption resolution 195,239]
274. 10 [avatar contradiction clause 273]
277. ~happy(X0) [resolution 84,146]
281. old(alice) [resolution 102,141]
288. calm(alice) [resolution 261,281]
291. 8 [avatar split clause 288,186]
292. $false <- (9) [subsumption resolution 192,277]
293. ~9 [avatar contradiction clause 292]
294. $false [avatar sat refutation 199,274,291,293]
% SZS output end Proof for 6747996989703059661127886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is not humble. If lucy is both not brave and curious then fred is patient and vice versa. Everyone who is either rich or brave is both kind and happy. Everyone who is not rich or rich is both not calm and not strong and vice versa. Everyone who is not funny or not strong is not quiet and vice versa. Everyone who is both not humble and kind is either rich or not generous and vice versa. If fred is either not humble or patient then alice is either not brave or not wise and vice versa. If paul is not brave or curious then someone is not strong. Everyone who is rich is not wise and vice versa. If john is not strong then susan is not rich or generous and vice versa. Everyone who is both strong and quiet is either curious or rich. Everyone who is either wise or quiet is wise. Everyone who is either quiet or not tall is not calm or not quiet. Everyone who is not old or happy is strong or not curious and vice versa. Everyone who is both not wise and generous is creative. Someone is both happy and not tall. Someone is not wise or patient. Someone is patient. Someone is both not rich and happy. Someone is either not kind or patient. | John is not wise. | neutral | (![X]:((old(X)|happy(X))=>~humble(X)))&
(((~brave(lucy)&curious(lucy)))<=>(patient(fred)))&
(![X]:((rich(X)<~>brave(X))=>(kind(X)&happy(X))))&
(![X]:((~rich(X)|rich(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~funny(X)|~strong(X))<=>~quiet(X)))&
(![X]:((~humble(X)&kind(X))<=>(rich(X)<~>~generous(X))))&
(((~humble(fred)<~>patient(fred)))<=>((~brave(alice)<~>~wise(alice))))&
(((~brave(paul)|curious(paul)))=>(?[X]:(~strong(X))))&
(![X]:(rich(X)<=>~wise(X)))&
((~strong(john))<=>((~rich(susan)|generous(susan))))&
(![X]:((strong(X)&quiet(X))=>(curious(X)<~>rich(X))))&
(![X]:((wise(X)<~>quiet(X))=>wise(X)))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~old(X)|happy(X))<=>(strong(X)|~curious(X))))&
(![X]:((~wise(X)&generous(X))=>creative(X)))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)&happy(X))))&
(?[X]:((~kind(X)<~>patient(X)))) | ~wise(john) | [] | null | 0 |
Everyone who is either patient or kind is either not calm or brave. If mary is either strong or kind then paul is kind or strong and vice versa. If john is not quiet or not generous then someone is both funny and not curious and vice versa. If someone is generous or not humble then someone is creative or not funny. If someone is either not rich or not tall then mary is not strong or brave and vice versa. If fred is both not kind and not rich then someone is either curious or patient and vice versa. If alice is strong or not quiet then paul is not wise or curious and vice versa. Everyone who is either not kind or not curious is both not wise and generous and vice versa. If someone is either not old or brave then someone is either wise or not generous and vice versa. Everyone who is not old or wise is wise and vice versa. If fred is either not calm or not wise then alice is not humble and vice versa. Everyone who is wise or not wise is strong. Everyone who is either funny or not curious is both not quiet and not calm and vice versa. If someone is creative then mary is both not happy and not funny and vice versa. If susan is both not rich and not patient then someone is either not funny or not strong. Everyone who is not kind is either not patient or brave. Fred is both not curious and happy. Lucy is both quiet and not happy. Someone is both not calm and kind. Someone is kind or old. Someone is not old. Fred is either not happy or generous. Paul is either not quiet or not wise. | Susan is humble. | neutral | (![X]:((patient(X)<~>kind(X))=>(~calm(X)<~>brave(X))))&
(((strong(mary)<~>kind(mary)))<=>((kind(paul)|strong(paul))))&
(((~quiet(john)|~generous(john)))<=>(?[X]:((funny(X)&~curious(X)))))&
((?[X]:((generous(X)|~humble(X))))=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~strong(mary)|brave(mary))))&
(((~kind(fred)&~rich(fred)))<=>(?[X]:((curious(X)<~>patient(X)))))&
(((strong(alice)|~quiet(alice)))<=>((~wise(paul)|curious(paul))))&
(![X]:((~kind(X)<~>~curious(X))<=>(~wise(X)&generous(X))))&
((?[X]:((~old(X)<~>brave(X))))<=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((~old(X)|wise(X))<=>wise(X)))&
(((~calm(fred)<~>~wise(fred)))<=>(~humble(alice)))&
(![X]:((wise(X)|~wise(X))=>strong(X)))&
(![X]:((funny(X)<~>~curious(X))<=>(~quiet(X)&~calm(X))))&
((?[X]:(creative(X)))<=>((~happy(mary)&~funny(mary))))&
(((~rich(susan)&~patient(susan)))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>brave(X))))&
((~curious(fred)&happy(fred)))&
((quiet(lucy)&~happy(lucy)))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:(~old(X)))&
((~happy(fred)<~>generous(fred)))&
((~quiet(paul)<~>~wise(paul))) | humble(susan) | [] | null | 0 |
If susan is both wise and not kind then someone is both funny and not wise and vice versa.
Everyone who is both not funny and calm is brave and vice versa.
If someone is not generous or strong then someone is not happy and vice versa.
Everyone who is not patient or generous is wise or quiet.
Everyone who is not old or not happy is either patient or calm.
Everyone who is tall is not kind or tall.
If alice is quiet then john is strong or not kind and vice versa.
If lucy is happy then someone is old and vice versa.
If alice is humble or funny then someone is both calm and wise.
Everyone who is not humble or generous is both not generous and tall and vice versa.
If someone is either not generous or not humble then paul is both not old and generous and vice versa.
If someone is brave then fred is patient and vice versa.
Everyone who is both calm and curious is either old or not curious.
Everyone who is not funny or brave is not rich.
Everyone who is not wise or not calm is generous.
If mary is either wise or quiet then someone is either not rich or not quiet and vice versa.
Someone is both curious and not patient.
Someone is curious or generous.
Someone is humble or not funny.
Someone is not kind or not brave.
Paul is either funny or not rich.
Susan is not humble or not brave.
Alice is either wise or rich.
Someone is both quiet and not happy. | John is tall. | entailment | (((wise(susan)&~kind(susan)))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((~funny(X)&calm(X))<=>brave(X)))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)|generous(X))=>(wise(X)|quiet(X))))&
(![X]:((~old(X)|~happy(X))=>(patient(X)<~>calm(X))))&
(![X]:(tall(X)=>(~kind(X)|tall(X))))&
((quiet(alice))<=>((strong(john)|~kind(john))))&
((happy(lucy))<=>(?[X]:(old(X))))&
(((humble(alice)|funny(alice)))=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~humble(X)|generous(X))<=>(~generous(X)&tall(X))))&
((?[X]:((~generous(X)<~>~humble(X))))<=>((~old(paul)&generous(paul))))&
((?[X]:(brave(X)))<=>(patient(fred)))&
(![X]:((calm(X)&curious(X))=>(old(X)<~>~curious(X))))&
(![X]:((~funny(X)|brave(X))=>~rich(X)))&
(![X]:((~wise(X)|~calm(X))=>generous(X)))&
(((wise(mary)<~>quiet(mary)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(?[X]:((curious(X)&~patient(X))))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((~kind(X)|~brave(X))))&
((funny(paul)<~>~rich(paul)))&
((~humble(susan)|~brave(susan)))&
((wise(alice)<~>rich(alice)))&
(?[X]:((quiet(X)&~happy(X)))) | tall(john) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7153400703065502208198047
% SZS output start Proof for 7153400703065502208198047
10. ! [X0] : ((generous(X0) | ~humble(X0)) <=> (tall(X0) & ~generous(X0))) [input p9]
11. ? [X0] : (~generous(X0) <~> ~humble(X0)) <=> (generous(paul) & ~old(paul)) [input p10]
25. ~tall(john) [input hypothesis]
58. ! [X0] : (((generous(X0) | ~humble(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (~generous(X0) & humble(X0)))) [nnf transformation 10]
59. ! [X0] : ((generous(X0) | ~humble(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (~generous(X0) & humble(X0)))) [flattening 58]
60. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (~generous(paul) | old(paul))) & ((generous(paul) & ~old(paul)) | ! [X0] : ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) [nnf transformation 11]
61. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X0] : ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) [flattening 60]
62. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X1] : ((~generous(X1) | humble(X1)) & (~humble(X1) | generous(X1)))) [rectify 61]
63. ? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) => ((humble(sK5) | generous(sK5)) & (~humble(sK5) | ~generous(sK5))) [choice axiom]
64. (((humble(sK5) | generous(sK5)) & (~humble(sK5) | ~generous(sK5))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X1] : ((~generous(X1) | humble(X1)) & (~humble(X1) | generous(X1)))) [skolemisation 62,63]
113. ~generous(X0) | ~generous(X0) [cnf transformation 59]
114. humble(X0) | tall(X0) [cnf transformation 59]
119. generous(paul) | ~humble(X1) | generous(X1) [cnf transformation 64]
151. ~tall(john) [cnf transformation 25]
153. ~generous(X0) [duplicate literal removal 113]
250. ~humble(X1) | generous(X1) [subsumption resolution 119,153]
251. ~humble(X1) [subsumption resolution 250,153]
318. tall(X0) [resolution 114,251]
319. $false [resolution 318,151]
% SZS output end Proof for 7153400703065502208198047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not humble then paul is either tall or not old and vice versa. Everyone who is funny is either creative or not creative and vice versa. If susan is tall then john is wise or strong and vice versa. Everyone who is not humble is either not wise or wise and vice versa. Everyone who is either not wise or not quiet is happy or tall and vice versa. If someone is generous then someone is both wise and generous. Everyone who is patient or creative is not quiet and vice versa. If mary is not strong then someone is patient or old and vice versa. Everyone who is both not creative and happy is not creative and vice versa. Everyone who is not rich or strong is patient. Everyone who is not wise is not rich and vice versa. If mary is both not curious and not tall then lucy is not tall or rich and vice versa. Everyone who is generous or rich is both generous and not creative. If fred is both not quiet and old then someone is not brave or happy and vice versa. If mary is brave then paul is not kind. Someone is both curious and not quiet. Mary is either humble or not humble. Alice is not calm or not quiet. Someone is either not brave or brave. Susan is either not old or not tall. Someone is generous. | John is not patient. | contradiction | ((?[X]:((tall(X)<~>~humble(X))))<=>((tall(paul)<~>~old(paul))))&
(![X]:(funny(X)<=>(creative(X)<~>~creative(X))))&
((tall(susan))<=>((wise(john)|strong(john))))&
(![X]:(~humble(X)<=>(~wise(X)<~>wise(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(happy(X)|tall(X))))&
((?[X]:(generous(X)))=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((patient(X)|creative(X))<=>~quiet(X)))&
((~strong(mary))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((~creative(X)&happy(X))<=>~creative(X)))&
(![X]:((~rich(X)|strong(X))=>patient(X)))&
(![X]:(~wise(X)<=>~rich(X)))&
(((~curious(mary)&~tall(mary)))<=>((~tall(lucy)|rich(lucy))))&
(![X]:((generous(X)|rich(X))=>(generous(X)&~creative(X))))&
(((~quiet(fred)&old(fred)))<=>(?[X]:((~brave(X)|happy(X)))))&
((brave(mary))=>(~kind(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
((humble(mary)<~>~humble(mary)))&
((~calm(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>brave(X))))&
((~old(susan)<~>~tall(susan)))&
(?[X]:(generous(X))) | ~patient(john) | [
"p4",
"p6",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2200310381425265975243517
% SZS output start Proof for 2200310381425265975243517
5. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> (tall(X0) | happy(X0))) [input p4]
7. ! [X0] : ((creative(X0) | patient(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((happy(X0) & ~creative(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((strong(X0) | ~rich(X0)) => patient(X0)) [input p9]
11. ! [X0] : (~wise(X0) <=> ~rich(X0)) [input p10]
13. ! [X0] : ((rich(X0) | generous(X0)) => (~creative(X0) & generous(X0))) [input p12]
22. ~patient(john) [input hypothesis]
27. ! [X0] : (patient(X0) | (~strong(X0) & rich(X0))) [ennf transformation 10]
28. ! [X0] : ((~creative(X0) & generous(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 13]
36. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (~tall(X0) & ~happy(X0))) & ((tall(X0) | happy(X0)) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 5]
37. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (~tall(X0) & ~happy(X0))) & (tall(X0) | happy(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [flattening 36]
41. ! [X0] : (((creative(X0) | patient(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & ~patient(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | patient(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & ~patient(X0)))) [flattening 41]
47. ! [X0] : (((happy(X0) & ~creative(X0)) | creative(X0)) & (~creative(X0) | (~happy(X0) | creative(X0)))) [nnf transformation 9]
48. ! [X0] : (((happy(X0) & ~creative(X0)) | creative(X0)) & (~creative(X0) | ~happy(X0) | creative(X0))) [flattening 47]
49. ! [X0] : ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))) [nnf transformation 11]
83. ~happy(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 37]
89. ~patient(X0) | ~quiet(X0) [cnf transformation 42]
90. ~quiet(X0) | ~creative(X0) [cnf transformation 42]
91. patient(X0) | creative(X0) | quiet(X0) [cnf transformation 42]
97. happy(X0) | creative(X0) [cnf transformation 48]
98. rich(X0) | patient(X0) [cnf transformation 27]
100. ~rich(X0) | wise(X0) [cnf transformation 49]
101. ~wise(X0) | rich(X0) [cnf transformation 49]
110. ~rich(X0) | ~creative(X0) [cnf transformation 28]
125. ~patient(john) [cnf transformation 22]
168. 9 <=> wise(john) [avatar definition]
169. wise(john) <- (9) [avatar component clause 168]
274. patient(X0) | wise(X0) [resolution 100,98]
276. rich(john) <- (9) [resolution 101,169]
286. ~creative(john) <- (9) [resolution 110,276]
290. ~wise(X0) | ~quiet(X0) | creative(X0) [resolution 83,97]
291. ~wise(X0) | ~quiet(X0) [subsumption resolution 290,90]
292. wise(john) [resolution 274,125]
293. wise(X0) | ~quiet(X0) [resolution 274,89]
294. ~quiet(X0) [subsumption resolution 293,291]
301. creative(john) | quiet(john) [resolution 91,125]
303. quiet(john) <- (9) [subsumption resolution 301,286]
304. $false <- (9) [subsumption resolution 303,294]
305. ~9 [avatar contradiction clause 304]
307. 9 [avatar split clause 292,168]
308. $false [avatar sat refutation 305,307]
% SZS output end Proof for 2200310381425265975243517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and generous is either tall or not curious and vice versa.
If someone is not humble or not generous then alice is either quiet or not brave and vice versa.
If fred is either not strong or creative then alice is either brave or curious.
If someone is strong then someone is rich or not humble.
If someone is not quiet or not creative then someone is rich or not happy and vice versa.
Everyone who is both brave and not strong is either not tall or not creative and vice versa.
If someone is both kind and brave then someone is not curious or not humble and vice versa.
If fred is both not patient and generous then someone is curious.
If someone is both not generous and not creative then someone is not patient or humble.
If mary is patient or not wise then john is not happy.
Everyone who is either not calm or wise is not brave and vice versa.
If someone is either not humble or not funny then mary is both not creative and tall and vice versa.
If john is either not patient or rich then someone is either not kind or not brave.
Everyone who is not brave or rich is not rich and vice versa.
Everyone who is either not humble or brave is either not patient or happy.
If fred is old or not curious then someone is either quiet or not brave.
Lucy is funny or happy.
Susan is not generous.
Someone is either not creative or calm.
Someone is not brave or wise.
John is not creative or funny.
Paul is not tall or not old. | Fred is not calm. | neutral | (![X]:((~quiet(X)&generous(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>((quiet(alice)<~>~brave(alice))))&
(((~strong(fred)<~>creative(fred)))=>((brave(alice)<~>curious(alice))))&
((?[X]:(strong(X)))=>(?[X]:((rich(X)|~humble(X)))))&
((?[X]:((~quiet(X)|~creative(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:((brave(X)&~strong(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~patient(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~patient(X)|humble(X)))))&
(((patient(mary)|~wise(mary)))=>(~happy(john)))&
(![X]:((~calm(X)<~>wise(X))<=>~brave(X)))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~creative(mary)&tall(mary))))&
(((~patient(john)<~>rich(john)))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((~brave(X)|rich(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>brave(X))=>(~patient(X)<~>happy(X))))&
(((old(fred)|~curious(fred)))=>(?[X]:((quiet(X)<~>~brave(X)))))&
((funny(lucy)|happy(lucy)))&
(~generous(susan))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((~brave(X)|wise(X))))&
((~creative(john)|funny(john)))&
((~tall(paul)|~old(paul))) | ~calm(fred) | [] | null | 0 |
Everyone who is both not funny and funny is both not patient and patient and vice versa.
Everyone who is either quiet or not old is either not tall or rich.
Everyone who is not quiet or generous is kind or not old and vice versa.
Everyone who is both generous and not creative is rich or not funny and vice versa.
If mary is both creative and not patient then someone is either not generous or patient and vice versa.
Everyone who is both rich and not humble is not rich or not funny.
Everyone who is wise is not strong and vice versa.
If lucy is funny then fred is kind and vice versa.
Everyone who is brave or happy is either happy or not humble and vice versa.
If alice is not funny or humble then someone is either calm or not old.
Everyone who is not old or not patient is both rich and creative and vice versa.
Everyone who is both old and rich is brave and vice versa.
Everyone who is both not funny and generous is not old.
Everyone who is not kind or tall is either happy or tall and vice versa.
If someone is not kind then someone is both brave and strong and vice versa.
Everyone who is tall or rich is either humble or not funny.
Someone is patient or not tall.
Someone is either generous or funny.
John is either funny or not strong.
Lucy is either humble or generous. | Lucy is creative. | neutral | (![X]:((~funny(X)&funny(X))<=>(~patient(X)&patient(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~tall(X)<~>rich(X))))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)|~old(X))))&
(![X]:((generous(X)&~creative(X))<=>(rich(X)|~funny(X))))&
(((creative(mary)&~patient(mary)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(![X]:((rich(X)&~humble(X))=>(~rich(X)|~funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
((funny(lucy))<=>(kind(fred)))&
(![X]:((brave(X)|happy(X))<=>(happy(X)<~>~humble(X))))&
(((~funny(alice)|humble(alice)))=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:((~old(X)|~patient(X))<=>(rich(X)&creative(X))))&
(![X]:((old(X)&rich(X))<=>brave(X)))&
(![X]:((~funny(X)&generous(X))=>~old(X)))&
(![X]:((~kind(X)|tall(X))<=>(happy(X)<~>tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((tall(X)|rich(X))=>(humble(X)<~>~funny(X))))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((generous(X)<~>funny(X))))&
((funny(john)<~>~strong(john)))&
((humble(lucy)<~>generous(lucy))) | creative(lucy) | [] | null | 0 |
If someone is old or not happy then lucy is both not curious and strong.
Everyone who is either creative or not brave is either not creative or curious.
Everyone who is both old and not brave is not humble.
Everyone who is either not wise or not brave is either not tall or strong.
Everyone who is both not happy and not calm is patient or not kind and vice versa.
Everyone who is either not humble or calm is happy and vice versa.
If mary is both quiet and not tall then alice is either not wise or creative.
Everyone who is either strong or kind is either generous or not patient and vice versa.
If someone is generous or not humble then mary is both kind and not happy and vice versa.
If susan is either not tall or creative then someone is either not old or humble.
Everyone who is not generous or happy is not brave and vice versa.
If john is both generous and happy then someone is either quiet or not calm and vice versa.
Everyone who is either not generous or not funny is funny and vice versa.
Everyone who is curious or not old is rich and vice versa.
Everyone who is both not tall and not quiet is not humble and vice versa.
Everyone who is not tall or brave is either wise or not brave and vice versa.
Someone is not wise.
Alice is both funny and strong.
Someone is not old or generous.
Someone is either curious or not generous.
Someone is rich.
Someone is either tall or humble. | Mary is not happy. | entailment | ((?[X]:((old(X)|~happy(X))))=>((~curious(lucy)&strong(lucy))))&
(![X]:((creative(X)<~>~brave(X))=>(~creative(X)<~>curious(X))))&
(![X]:((old(X)&~brave(X))=>~humble(X)))&
(![X]:((~wise(X)<~>~brave(X))=>(~tall(X)<~>strong(X))))&
(![X]:((~happy(X)&~calm(X))<=>(patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>calm(X))<=>happy(X)))&
(((quiet(mary)&~tall(mary)))=>((~wise(alice)<~>creative(alice))))&
(![X]:((strong(X)<~>kind(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:((generous(X)|~humble(X))))<=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(?[X]:(~wise(X)))&
((funny(alice)&strong(alice)))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((curious(X)<~>~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((tall(X)<~>humble(X)))) | ~happy(mary) | [
"p3",
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3597848631046825171178744
% SZS output start Proof for 3597848631046825171178744
4. ! [X0] : ((~wise(X0) <~> ~brave(X0)) => (~tall(X0) <~> strong(X0))) [input p3]
5. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> (~kind(X0) | patient(X0))) [input p4]
6. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> happy(X0)) [input p5]
8. ! [X0] : ((strong(X0) <~> kind(X0)) <=> (generous(X0) <~> ~patient(X0))) [input p7]
9. ? [X0] : (~humble(X0) | generous(X0)) <=> (~happy(mary) & kind(mary)) [input p8]
11. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~brave(X0)) [input p10]
12. (happy(john) & generous(john)) <=> ? [X0] : (quiet(X0) <~> ~calm(X0)) [input p11]
13. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> funny(X0)) [input p12]
15. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> ~humble(X0)) [input p14]
16. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p15]
23. happy(mary) [input hypothesis]
29. ! [X0] : ((~tall(X0) <~> strong(X0)) | (~wise(X0) <=> ~brave(X0))) [ennf transformation 4]
36. ! [X0] : (((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) [nnf transformation 29]
37. ! [X0] : (((~calm(X0) & ~happy(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (calm(X0) | happy(X0)))) [nnf transformation 5]
38. ! [X0] : (((~calm(X0) & ~happy(X0)) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | calm(X0) | happy(X0))) [flattening 37]
39. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ~happy(X0)) & (happy(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 6]
41. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0)))) & (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [nnf transformation 8]
42. (? [X0] : (~humble(X0) | generous(X0)) | (happy(mary) | ~kind(mary))) & ((~happy(mary) & kind(mary)) | ! [X0] : (humble(X0) & ~generous(X0))) [nnf transformation 9]
43. (? [X0] : (~humble(X0) | generous(X0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X0] : (humble(X0) & ~generous(X0))) [flattening 42]
44. (? [X0] : (~humble(X0) | generous(X0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X1] : (humble(X1) & ~generous(X1))) [rectify 43]
45. ? [X0] : (~humble(X0) | generous(X0)) => (~humble(sK0) | generous(sK0)) [choice axiom]
46. ((~humble(sK0) | generous(sK0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X1] : (humble(X1) & ~generous(X1))) [skolemisation 44,45]
50. ! [X0] : (((happy(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 11]
51. ! [X0] : ((happy(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [flattening 50]
52. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~happy(john) | ~generous(john))) [nnf transformation 12]
53. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~happy(john) | ~generous(john)) [flattening 52]
54. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X1] : ((calm(X1) | ~quiet(X1)) & (~calm(X1) | quiet(X1))) | ~happy(john) | ~generous(john)) [rectify 53]
55. ? [X1] : ((calm(X1) | ~quiet(X1)) & (~calm(X1) | quiet(X1))) => ((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) [choice axiom]
56. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) | ~happy(john) | ~generous(john)) [skolemisation 54,55]
57. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 13]
58. ! [X0] : (((~quiet(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) | tall(X0)))) [nnf transformation 15]
59. ! [X0] : (((~quiet(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | quiet(X0) | tall(X0))) [flattening 58]
60. ! [X0] : (((brave(X0) | ~tall(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~brave(X0) & tall(X0)))) [nnf transformation 16]
61. ! [X0] : ((brave(X0) | ~tall(X0) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~brave(X0) & tall(X0)))) [flattening 60]
84. ~tall(X0) | strong(X0) | ~wise(X0) | brave(X0) [cnf transformation 36]
88. ~patient(X0) | ~happy(X0) [cnf transformation 38]
89. ~happy(X0) | kind(X0) [cnf transformation 38]
94. ~humble(X0) | calm(X0) | ~happy(X0) [cnf transformation 39]
105. ~kind(X0) | ~strong(X0) | generous(X0) | patient(X0) [cnf transformation 41]
109. ~happy(mary) | humble(X1) [cnf transformation 46]
116. ~brave(X0) | ~happy(X0) [cnf transformation 51]
120. generous(john) | ~calm(X0) | ~quiet(X0) [cnf transformation 56]
125. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 57]
126. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 57]
129. ~humble(X0) | quiet(X0) | tall(X0) [cnf transformation 59]
133. ~brave(X0) | wise(X0) | ~brave(X0) [cnf transformation 61]
137. brave(X0) | ~tall(X0) | wise(X0) | brave(X0) [cnf transformation 61]
147. happy(mary) [cnf transformation 23]
148. ~brave(X0) | wise(X0) [duplicate literal removal 133]
149. ~tall(X0) | brave(X0) | wise(X0) [duplicate literal removal 137]
150. funny(X0) | ~generous(X0) [duplicate literal removal 125]
151. ~funny(X0) | ~generous(X0) [duplicate literal removal 126]
173. 5 <=> quiet(mary) [avatar definition]
174. quiet(mary) <- (5) [avatar component clause 173]
175. ~quiet(mary) <- (~5) [avatar component clause 173]
177. 6 <=> tall(mary) [avatar definition]
179. tall(mary) <- (6) [avatar component clause 177]
191. 9 <=> kind(mary) [avatar definition]
192. kind(mary) <- (9) [avatar component clause 191]
195. 10 <=> happy(mary) [avatar definition]
197. happy(mary) <- (10) [avatar component clause 195]
208. 13 <=> ! [X1] : humble(X1) [avatar definition]
209. humble(X1) <- (13) [avatar component clause 208]
210. 13 | ~10 [avatar split clause 109,195,208]
212. 14 <=> ! [X1] : ~generous(X1) [avatar definition]
213. ~generous(X1) <- (14) [avatar component clause 212]
246. 21 <=> ! [X0] : (~calm(X0) | ~quiet(X0)) [avatar definition]
247. ~quiet(X0) | ~calm(X0) <- (21) [avatar component clause 246]
250. 22 <=> generous(john) [avatar definition]
252. generous(john) <- (22) [avatar component clause 250]
254. 21 | 22 [avatar split clause 120,250,246]
265. ~generous(X0) [subsumption resolution 150,151]
266. 14 [avatar split clause 265,212]
288. 10 [avatar split clause 147,195]
291. kind(mary) <- (10) [resolution 89,197]
292. 9 | ~10 [avatar split clause 291,195,191]
304. ~happy(X0) | calm(X0) <- (13) [resolution 94,209]
309. calm(mary) <- (10, 13) [resolution 304,197]
320. quiet(X0) | tall(X0) <- (13) [resolution 129,209]
322. tall(mary) <- (~5, 13) [resolution 320,175]
325. 6 | 5 | ~13 [avatar split clause 322,208,173,177]
326. ~calm(mary) <- (5, 21) [resolution 174,247]
328. $false <- (5, 10, 13, 21) [subsumption resolution 326,309]
329. ~5 | ~10 | ~13 | ~21 [avatar contradiction clause 328]
330. $false <- (14, 22) [subsumption resolution 252,213]
331. ~14 | ~22 [avatar contradiction clause 330]
349. brave(mary) | wise(mary) <- (6) [resolution 149,179]
350. wise(mary) <- (6) [subsumption resolution 349,148]
363. strong(mary) | ~wise(mary) | brave(mary) <- (6) [resolution 84,179]
365. strong(mary) | brave(mary) <- (6) [subsumption resolution 363,350]
367. 31 <=> brave(mary) [avatar definition]
369. brave(mary) <- (31) [avatar component clause 367]
371. 32 <=> strong(mary) [avatar definition]
373. strong(mary) <- (32) [avatar component clause 371]
374. 31 | 32 | ~6 [avatar split clause 365,177,371,367]
388. ~happy(mary) <- (31) [resolution 369,116]
399. $false <- (10, 31) [subsumption resolution 388,197]
400. ~10 | ~31 [avatar contradiction clause 399]
422. ~strong(mary) | generous(mary) | patient(mary) <- (9) [resolution 105,192]
425. generous(mary) | patient(mary) <- (9, 32) [subsumption resolution 422,373]
426. patient(mary) <- (9, 14, 32) [subsumption resolution 425,213]
429. ~happy(mary) <- (9, 14, 32) [resolution 426,88]
432. $false <- (9, 10, 14, 32) [subsumption resolution 429,197]
433. ~9 | ~10 | ~14 | ~32 [avatar contradiction clause 432]
434. $false [avatar sat refutation 210,254,266,288,292,325,329,331,374,400,433]
% SZS output end Proof for 3597848631046825171178744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not wise is both not rich and generous and vice versa.
Everyone who is both happy and brave is quiet and vice versa.
If mary is either happy or calm then paul is rich and vice versa.
Everyone who is both old and strong is not kind or tall.
If john is calm or strong then someone is not happy and vice versa.
If someone is not old then someone is either not funny or not brave.
Everyone who is either not funny or not creative is both kind and funny.
Everyone who is humble is both not strong and tall and vice versa.
Everyone who is not wise or not humble is generous.
Everyone who is not creative or strong is happy.
Everyone who is not kind or not tall is either not happy or not strong.
Everyone who is quiet is wise.
Everyone who is both not rich and calm is both not old and rich and vice versa.
Everyone who is quiet or not strong is calm and vice versa.
If susan is either patient or happy then john is either not creative or rich and vice versa.
Everyone who is not creative or not tall is either not quiet or creative and vice versa.
Paul is either not generous or humble.
John is not rich or not funny.
Fred is both not brave and rich.
Susan is not humble or not curious.
Someone is both not brave and patient.
Someone is old or not curious. | Fred is not curious. | neutral | (![X]:((happy(X)|~wise(X))<=>(~rich(X)&generous(X))))&
(![X]:((happy(X)&brave(X))<=>quiet(X)))&
(((happy(mary)<~>calm(mary)))<=>(rich(paul)))&
(![X]:((old(X)&strong(X))=>(~kind(X)|tall(X))))&
(((calm(john)|strong(john)))<=>(?[X]:(~happy(X))))&
((?[X]:(~old(X)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(kind(X)&funny(X))))&
(![X]:(humble(X)<=>(~strong(X)&tall(X))))&
(![X]:((~wise(X)|~humble(X))=>generous(X)))&
(![X]:((~creative(X)|strong(X))=>happy(X)))&
(![X]:((~kind(X)|~tall(X))=>(~happy(X)<~>~strong(X))))&
(![X]:(quiet(X)=>wise(X)))&
(![X]:((~rich(X)&calm(X))<=>(~old(X)&rich(X))))&
(![X]:((quiet(X)|~strong(X))<=>calm(X)))&
(((patient(susan)<~>happy(susan)))<=>((~creative(john)<~>rich(john))))&
(![X]:((~creative(X)|~tall(X))<=>(~quiet(X)<~>creative(X))))&
((~generous(paul)<~>humble(paul)))&
((~rich(john)|~funny(john)))&
((~brave(fred)&rich(fred)))&
((~humble(susan)|~curious(susan)))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:((old(X)|~curious(X)))) | ~curious(fred) | [] | null | 0 |
If paul is not rich then john is both kind and calm.
Everyone who is patient or kind is not creative and vice versa.
Everyone who is not generous is either humble or wise and vice versa.
If someone is not curious then john is both not kind and kind.
Everyone who is either not quiet or not calm is not strong or not calm and vice versa.
Everyone who is creative is not quiet or kind and vice versa.
If someone is kind then someone is tall.
If alice is either not creative or patient then someone is either creative or not happy.
If john is both quiet and not tall then someone is both not strong and not tall.
If alice is both not calm and calm then someone is either tall or happy.
Everyone who is both not funny and not calm is either happy or not funny and vice versa.
Everyone who is either not creative or happy is not happy or old and vice versa.
Everyone who is both wise and humble is not old and vice versa.
Everyone who is either wise or not quiet is not quiet.
Everyone who is either humble or not quiet is strong or not patient and vice versa.
If someone is not creative then someone is both funny and not kind and vice versa.
John is happy or kind.
Lucy is both creative and rich.
Mary is patient.
Mary is calm or happy.
Alice is calm or happy. | John is strong. | contradiction | ((~rich(paul))=>((kind(john)&calm(john))))&
(![X]:((patient(X)|kind(X))<=>~creative(X)))&
(![X]:(~generous(X)<=>(humble(X)<~>wise(X))))&
((?[X]:(~curious(X)))=>((~kind(john)&kind(john))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)|~calm(X))))&
(![X]:(creative(X)<=>(~quiet(X)|kind(X))))&
((?[X]:(kind(X)))=>(?[X]:(tall(X))))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((creative(X)<~>~happy(X)))))&
(((quiet(john)&~tall(john)))=>(?[X]:((~strong(X)&~tall(X)))))&
(((~calm(alice)&calm(alice)))=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(~happy(X)|old(X))))&
(![X]:((wise(X)&humble(X))<=>~old(X)))&
(![X]:((wise(X)<~>~quiet(X))=>~quiet(X)))&
(![X]:((humble(X)<~>~quiet(X))<=>(strong(X)|~patient(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)&~kind(X)))))&
((happy(john)|kind(john)))&
((creative(lucy)&rich(lucy)))&
(patient(mary))&
((calm(mary)|happy(mary)))&
((calm(alice)|happy(alice))) | strong(john) | [
"p1",
"p4",
"p5",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 749686250312485818604500
% SZS output start Proof for 749686250312485818604500
2. ! [X0] : ((kind(X0) | patient(X0)) <=> ~creative(X0)) [input p1]
5. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~calm(X0) | ~strong(X0))) [input p4]
6. ! [X0] : (creative(X0) <=> (kind(X0) | ~quiet(X0))) [input p5]
12. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (old(X0) | ~happy(X0))) [input p11]
13. ! [X0] : ((humble(X0) & wise(X0)) <=> ~old(X0)) [input p12]
14. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => ~quiet(X0)) [input p13]
17. kind(john) | happy(john) [input p16]
22. strong(john) [input hypothesis]
34. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 14]
35. ! [X0] : (((kind(X0) | patient(X0)) | creative(X0)) & (~creative(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 2]
36. ! [X0] : ((kind(X0) | patient(X0) | creative(X0)) & (~creative(X0) | (~kind(X0) & ~patient(X0)))) [flattening 35]
37. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 5]
38. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 37]
39. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 6]
40. ! [X0] : ((creative(X0) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0))) [flattening 39]
54. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 12]
55. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 54]
56. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 13]
57. ! [X0] : (((humble(X0) & wise(X0)) | old(X0)) & (~old(X0) | ~humble(X0) | ~wise(X0))) [flattening 56]
58. ! [X0] : (~quiet(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 34]
67. ~creative(X0) | ~kind(X0) [cnf transformation 36]
69. ~calm(X0) | ~strong(X0) | ~calm(X0) | quiet(X0) [cnf transformation 38]
74. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 38]
75. kind(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 40]
76. quiet(X0) | creative(X0) [cnf transformation 40]
77. creative(X0) | ~kind(X0) [cnf transformation 40]
98. ~old(X0) | creative(X0) | ~happy(X0) [cnf transformation 55]
100. old(X0) | wise(X0) [cnf transformation 57]
102. ~quiet(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 58]
113. kind(john) | happy(john) [cnf transformation 17]
118. strong(john) [cnf transformation 22]
119. ~quiet(X0) | ~wise(X0) [duplicate literal removal 102]
124. ~calm(X0) | ~strong(X0) | quiet(X0) [duplicate literal removal 69]
125. quiet(X0) | calm(X0) [duplicate literal removal 74]
126. ~strong(X0) | quiet(X0) [subsumption resolution 124,125]
127. ~kind(X0) [subsumption resolution 77,67]
128. ~quiet(X0) | ~creative(X0) [subsumption resolution 75,127]
148. 5 <=> quiet(john) [avatar definition]
149. quiet(john) <- (5) [avatar component clause 148]
186. happy(john) [subsumption resolution 113,127]
206. ~wise(X0) | creative(X0) [resolution 119,76]
213. quiet(john) [resolution 126,118]
216. 5 [avatar split clause 213,148]
220. ~creative(john) <- (5) [resolution 128,149]
273. creative(X1) | ~happy(X1) | wise(X1) [resolution 98,100]
276. ~happy(X1) | creative(X1) [subsumption resolution 273,206]
379. creative(john) [resolution 276,186]
383. $false <- (5) [subsumption resolution 379,220]
384. ~5 [avatar contradiction clause 383]
386. $false [avatar sat refutation 216,384]
% SZS output end Proof for 749686250312485818604500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then fred is tall.
Everyone who is both not kind and not creative is not kind or not quiet.
Everyone who is wise is either patient or funny and vice versa.
If someone is either humble or creative then someone is not calm or not old.
If mary is not brave or not happy then paul is creative or brave and vice versa.
Everyone who is both tall and kind is both not curious and not old.
Everyone who is not tall or funny is both not kind and tall and vice versa.
Everyone who is both not old and happy is either not kind or not curious and vice versa.
If someone is not wise or not happy then someone is not old or happy and vice versa.
If someone is either not humble or not old then fred is not humble.
If someone is wise then paul is both calm and not generous and vice versa.
Everyone who is not funny or old is not rich or not creative and vice versa.
Everyone who is funny or rich is either generous or not tall and vice versa.
Everyone who is either quiet or not kind is either calm or rich and vice versa.
If mary is old or patient then someone is either not funny or happy and vice versa.
If lucy is either not rich or not old then fred is either tall or not wise.
Someone is not strong or funny.
Someone is happy.
Paul is both patient and rich.
John is either old or humble.
Someone is either funny or happy.
Someone is happy or not quiet.
Someone is either happy or not humble.
John is not patient. | Paul is not kind. | entailment | ((?[X]:(creative(X)))=>(tall(fred)))&
(![X]:((~kind(X)&~creative(X))=>(~kind(X)|~quiet(X))))&
(![X]:(wise(X)<=>(patient(X)<~>funny(X))))&
((?[X]:((humble(X)<~>creative(X))))=>(?[X]:((~calm(X)|~old(X)))))&
(((~brave(mary)|~happy(mary)))<=>((creative(paul)|brave(paul))))&
(![X]:((tall(X)&kind(X))=>(~curious(X)&~old(X))))&
(![X]:((~tall(X)|funny(X))<=>(~kind(X)&tall(X))))&
(![X]:((~old(X)&happy(X))<=>(~kind(X)<~>~curious(X))))&
((?[X]:((~wise(X)|~happy(X))))<=>(?[X]:((~old(X)|happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(~humble(fred)))&
((?[X]:(wise(X)))<=>((calm(paul)&~generous(paul))))&
(![X]:((~funny(X)|old(X))<=>(~rich(X)|~creative(X))))&
(![X]:((funny(X)|rich(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((quiet(X)<~>~kind(X))<=>(calm(X)<~>rich(X))))&
(((old(mary)|patient(mary)))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(((~rich(lucy)<~>~old(lucy)))=>((tall(fred)<~>~wise(fred))))&
(?[X]:((~strong(X)|funny(X))))&
(?[X]:(happy(X)))&
((patient(paul)&rich(paul)))&
((old(john)<~>humble(john)))&
(?[X]:((funny(X)<~>happy(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(~patient(john)) | ~kind(paul) | [
"p2",
"p6",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7393823369697514067386939
% SZS output start Proof for 7393823369697514067386939
3. ! [X0] : (wise(X0) <=> (patient(X0) <~> funny(X0))) [input p2]
7. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (tall(X0) & ~kind(X0))) [input p6]
11. ? [X0] : wise(X0) <=> (~generous(paul) & calm(paul)) [input p10]
13. ! [X0] : ((rich(X0) | funny(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p12]
19. rich(paul) & patient(paul) [input p18]
25. kind(paul) [input hypothesis]
37. ! [X0] : ((wise(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ~wise(X0))) [nnf transformation 3]
44. ! [X0] : (((funny(X0) | ~tall(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 7]
45. ! [X0] : ((funny(X0) | ~tall(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (~funny(X0) & tall(X0)))) [flattening 44]
54. (? [X0] : wise(X0) | (generous(paul) | ~calm(paul))) & ((~generous(paul) & calm(paul)) | ! [X0] : ~wise(X0)) [nnf transformation 11]
55. (? [X0] : wise(X0) | generous(paul) | ~calm(paul)) & ((~generous(paul) & calm(paul)) | ! [X0] : ~wise(X0)) [flattening 54]
56. (? [X0] : wise(X0) | generous(paul) | ~calm(paul)) & ((~generous(paul) & calm(paul)) | ! [X1] : ~wise(X1)) [rectify 55]
57. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
58. (wise(sK3) | generous(paul) | ~calm(paul)) & ((~generous(paul) & calm(paul)) | ! [X1] : ~wise(X1)) [skolemisation 56,57]
61. ! [X0] : (((rich(X0) | funny(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (~rich(X0) & ~funny(X0)))) [nnf transformation 13]
62. ! [X0] : ((rich(X0) | funny(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (~rich(X0) & ~funny(X0)))) [flattening 61]
85. ~patient(X0) | funny(X0) | wise(X0) [cnf transformation 37]
96. ~funny(X0) | ~kind(X0) [cnf transformation 45]
97. tall(X0) | tall(X0) [cnf transformation 45]
113. ~generous(paul) | ~wise(X1) [cnf transformation 58]
120. ~tall(X0) | generous(X0) | ~rich(X0) [cnf transformation 62]
144. patient(paul) [cnf transformation 19]
145. rich(paul) [cnf transformation 19]
154. kind(paul) [cnf transformation 25]
155. tall(X0) [duplicate literal removal 97]
250. 23 <=> generous(paul) [avatar definition]
259. 25 <=> ! [X1] : ~wise(X1) [avatar definition]
260. ~wise(X1) <- (25) [avatar component clause 259]
261. 25 | ~23 [avatar split clause 113,250,259]
264. ~rich(X0) | generous(X0) [subsumption resolution 120,155]
351. generous(paul) [resolution 264,145]
354. 23 [avatar split clause 351,250]
359. funny(paul) | wise(paul) [resolution 85,144]
360. funny(paul) <- (25) [subsumption resolution 359,260]
367. ~kind(paul) <- (25) [resolution 360,96]
368. $false <- (25) [subsumption resolution 367,154]
369. ~25 [avatar contradiction clause 368]
370. $false [avatar sat refutation 261,354,369]
% SZS output end Proof for 7393823369697514067386939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is strong or quiet. Everyone who is tall is both not curious and old. If someone is both not tall and generous then someone is both not humble and happy. If fred is either not strong or rich then someone is either curious or tall. Everyone who is both humble and not old is both not generous and curious and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not generous and not brave is both patient and not old and vice versa. Everyone who is either old or not creative is either tall or not wise. Everyone who is either quiet or not calm is wise or not strong. If mary is either not wise or not tall then someone is creative. Everyone who is both not tall and tall is old and vice versa. Everyone who is both not generous and creative is not quiet and vice versa. Everyone who is not happy or not strong is both not tall and not generous. Everyone who is either not happy or not funny is curious. If john is either not funny or not strong then fred is not rich or wise and vice versa. If someone is either not tall or brave then john is both not kind and old and vice versa. Alice is not kind or generous. Someone is either strong or calm. Someone is brave. John is kind. Someone is either old or not strong. Mary is funny or curious. Someone is quiet. Alice is generous. | Alice is humble. | contradiction | (![X]:(humble(X)=>(strong(X)|quiet(X))))&
(![X]:(tall(X)=>(~curious(X)&old(X))))&
((?[X]:((~tall(X)&generous(X))))=>(?[X]:((~humble(X)&happy(X)))))&
(((~strong(fred)<~>rich(fred)))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((humble(X)&~old(X))<=>(~generous(X)&curious(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~generous(X)&~brave(X))<=>(patient(X)&~old(X))))&
(![X]:((old(X)<~>~creative(X))=>(tall(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(wise(X)|~strong(X))))&
(((~wise(mary)<~>~tall(mary)))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)&tall(X))<=>old(X)))&
(![X]:((~generous(X)&creative(X))<=>~quiet(X)))&
(![X]:((~happy(X)|~strong(X))=>(~tall(X)&~generous(X))))&
(![X]:((~happy(X)<~>~funny(X))=>curious(X)))&
(((~funny(john)<~>~strong(john)))<=>((~rich(fred)|wise(fred))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((~kind(john)&old(john))))&
((~kind(alice)|generous(alice)))&
(?[X]:((strong(X)<~>calm(X))))&
(?[X]:(brave(X)))&
(kind(john))&
(?[X]:((old(X)<~>~strong(X))))&
((funny(mary)|curious(mary)))&
(?[X]:(quiet(X)))&
(generous(alice)) | humble(alice) | [
"p4",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 747217004555772986729257
% SZS output start Proof for 747217004555772986729257
5. ! [X0] : ((~old(X0) & humble(X0)) <=> (curious(X0) & ~generous(X0))) [input p4]
11. ! [X0] : ((tall(X0) & ~tall(X0)) <=> old(X0)) [input p10]
24. generous(alice) [input p23]
25. humble(alice) [input hypothesis]
44. ! [X0] : (((~old(X0) & humble(X0)) | (~curious(X0) | generous(X0))) & ((curious(X0) & ~generous(X0)) | (old(X0) | ~humble(X0)))) [nnf transformation 5]
45. ! [X0] : (((~old(X0) & humble(X0)) | ~curious(X0) | generous(X0)) & ((curious(X0) & ~generous(X0)) | old(X0) | ~humble(X0))) [flattening 44]
54. ! [X0] : (((tall(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & ~tall(X0)) | ~old(X0)) & (old(X0) | ~tall(X0) | tall(X0))) [flattening 54]
85. ~generous(X0) | old(X0) | ~humble(X0) [cnf transformation 45]
104. ~tall(X0) | ~old(X0) [cnf transformation 55]
105. ~old(X0) | tall(X0) [cnf transformation 55]
136. generous(alice) [cnf transformation 24]
137. humble(alice) [cnf transformation 25]
185. ~old(X0) [subsumption resolution 104,105]
211. 15 <=> generous(alice) [avatar definition]
213. generous(alice) <- (15) [avatar component clause 211]
235. 15 [avatar split clause 136,211]
251. old(alice) | ~humble(alice) <- (15) [resolution 85,213]
252. ~humble(alice) <- (15) [subsumption resolution 251,185]
253. $false <- (15) [subsumption resolution 252,137]
254. ~15 [avatar contradiction clause 253]
255. $false [avatar sat refutation 235,254]
% SZS output end Proof for 747217004555772986729257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not strong is both not patient and old and vice versa.
Everyone who is happy is both brave and kind and vice versa.
If fred is not old then someone is both happy and creative.
Everyone who is either creative or kind is both not tall and curious and vice versa.
If someone is generous or brave then someone is curious.
Everyone who is tall or not old is both not brave and not curious and vice versa.
Everyone who is not creative or curious is not happy and vice versa.
Everyone who is patient is not curious or not brave.
Everyone who is not tall or rich is creative and vice versa.
If someone is both creative and curious then alice is either not brave or not old and vice versa.
If someone is either calm or not curious then someone is either quiet or not generous and vice versa.
If fred is both generous and strong then mary is both not wise and patient.
If someone is not funny then paul is both kind and strong and vice versa.
If someone is creative or not rich then fred is not calm and vice versa.
If someone is both not brave and calm then john is either rich or generous.
If someone is not generous or brave then someone is both curious and not patient and vice versa.
Someone is not generous.
Alice is both not rich and not generous.
Someone is not old.
Someone is either quiet or not curious.
Someone is both patient and not tall.
John is not quiet or not happy.
Paul is either brave or old.
John is generous. | Alice is kind. | contradiction | (![X]:((generous(X)|~strong(X))<=>(~patient(X)&old(X))))&
(![X]:(happy(X)<=>(brave(X)&kind(X))))&
((~old(fred))=>(?[X]:((happy(X)&creative(X)))))&
(![X]:((creative(X)<~>kind(X))<=>(~tall(X)&curious(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~old(X))<=>(~brave(X)&~curious(X))))&
(![X]:((~creative(X)|curious(X))<=>~happy(X)))&
(![X]:(patient(X)=>(~curious(X)|~brave(X))))&
(![X]:((~tall(X)|rich(X))<=>creative(X)))&
((?[X]:((creative(X)&curious(X))))<=>((~brave(alice)<~>~old(alice))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(((generous(fred)&strong(fred)))=>((~wise(mary)&patient(mary))))&
((?[X]:(~funny(X)))<=>((kind(paul)&strong(paul))))&
((?[X]:((creative(X)|~rich(X))))<=>(~calm(fred)))&
((?[X]:((~brave(X)&calm(X))))=>((rich(john)<~>generous(john))))&
((?[X]:((~generous(X)|brave(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
(?[X]:(~generous(X)))&
((~rich(alice)&~generous(alice)))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((patient(X)&~tall(X))))&
((~quiet(john)|~happy(john)))&
((brave(paul)<~>old(paul)))&
(generous(john)) | kind(alice) | [
"p3",
"p5",
"p8",
"p9",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4260819096092087283815938
% SZS output start Proof for 4260819096092087283815938
4. ! [X0] : ((creative(X0) <~> kind(X0)) <=> (curious(X0) & ~tall(X0))) [input p3]
6. ! [X0] : ((~old(X0) | tall(X0)) <=> (~curious(X0) & ~brave(X0))) [input p5]
9. ! [X0] : ((rich(X0) | ~tall(X0)) <=> creative(X0)) [input p8]
10. ? [X0] : (curious(X0) & creative(X0)) <=> (~brave(alice) <~> ~old(alice)) [input p9]
16. ? [X0] : (brave(X0) | ~generous(X0)) <=> ? [X0] : (~patient(X0) & curious(X0)) [input p15]
17. ? [X0] : ~generous(X0) [input p16]
18. ~generous(alice) & ~rich(alice) [input p17]
25. kind(alice) [input hypothesis]
28. ? [X0] : (brave(X0) | ~generous(X0)) <=> ? [X1] : (~patient(X1) & curious(X1)) [rectify 16]
43. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [flattening 43]
48. ! [X0] : (((~old(X0) | tall(X0)) | (curious(X0) | brave(X0))) & ((~curious(X0) & ~brave(X0)) | (old(X0) & ~tall(X0)))) [nnf transformation 6]
49. ! [X0] : ((~old(X0) | tall(X0) | curious(X0) | brave(X0)) & ((~curious(X0) & ~brave(X0)) | (old(X0) & ~tall(X0)))) [flattening 48]
52. ! [X0] : (((rich(X0) | ~tall(X0)) | ~creative(X0)) & (creative(X0) | (~rich(X0) & tall(X0)))) [nnf transformation 9]
53. ! [X0] : ((rich(X0) | ~tall(X0) | ~creative(X0)) & (creative(X0) | (~rich(X0) & tall(X0)))) [flattening 52]
54. (? [X0] : (curious(X0) & creative(X0)) | ((~brave(alice) | old(alice)) & (~old(alice) | brave(alice)))) & (((old(alice) | brave(alice)) & (~old(alice) | ~brave(alice))) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 10]
55. (? [X0] : (curious(X0) & creative(X0)) | ((~brave(alice) | old(alice)) & (~old(alice) | brave(alice)))) & (((old(alice) | brave(alice)) & (~old(alice) | ~brave(alice))) | ! [X1] : (~curious(X1) | ~creative(X1))) [rectify 54]
56. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK2) & creative(sK2)) [choice axiom]
57. ((curious(sK2) & creative(sK2)) | ((~brave(alice) | old(alice)) & (~old(alice) | brave(alice)))) & (((old(alice) | brave(alice)) & (~old(alice) | ~brave(alice))) | ! [X1] : (~curious(X1) | ~creative(X1))) [skolemisation 55,56]
73. (? [X0] : (brave(X0) | ~generous(X0)) | ! [X1] : (patient(X1) | ~curious(X1))) & (? [X1] : (~patient(X1) & curious(X1)) | ! [X0] : (~brave(X0) & generous(X0))) [nnf transformation 28]
74. (? [X0] : (brave(X0) | ~generous(X0)) | ! [X1] : (patient(X1) | ~curious(X1))) & (? [X2] : (~patient(X2) & curious(X2)) | ! [X3] : (~brave(X3) & generous(X3))) [rectify 73]
75. ? [X0] : (brave(X0) | ~generous(X0)) => (brave(sK7) | ~generous(sK7)) [choice axiom]
76. ? [X2] : (~patient(X2) & curious(X2)) => (~patient(sK8) & curious(sK8)) [choice axiom]
77. ((brave(sK7) | ~generous(sK7)) | ! [X1] : (patient(X1) | ~curious(X1))) & ((~patient(sK8) & curious(sK8)) | ! [X3] : (~brave(X3) & generous(X3))) [skolemisation 74,76,75]
78. ? [X0] : ~generous(X0) => ~generous(sK9) [choice axiom]
79. ~generous(sK9) [skolemisation 17,78]
99. ~tall(X0) | creative(X0) | ~kind(X0) [cnf transformation 44]
103. ~curious(X0) | ~creative(X0) | ~kind(X0) | tall(X0) [cnf transformation 44]
107. ~brave(X0) | old(X0) [cnf transformation 49]
108. ~curious(X0) | ~tall(X0) [cnf transformation 49]
110. ~old(X0) | tall(X0) | curious(X0) | brave(X0) [cnf transformation 49]
115. tall(X0) | creative(X0) [cnf transformation 53]
117. ~tall(X0) | rich(X0) | ~creative(X0) [cnf transformation 53]
118. ~old(alice) | ~brave(alice) | ~curious(X1) | ~creative(X1) [cnf transformation 57]
119. old(alice) | brave(alice) | ~curious(X1) | ~creative(X1) [cnf transformation 57]
141. curious(sK8) | generous(X3) [cnf transformation 77]
146. ~generous(sK9) [cnf transformation 79]
147. ~rich(alice) [cnf transformation 18]
158. kind(alice) [cnf transformation 25]
186. 7 <=> brave(alice) [avatar definition]
187. ~brave(alice) <- (~7) [avatar component clause 186]
190. 8 <=> old(alice) [avatar definition]
191. old(alice) <- (8) [avatar component clause 190]
203. old(alice) | ~curious(X1) | ~creative(X1) [subsumption resolution 119,107]
205. 11 <=> ! [X1] : (~curious(X1) | ~creative(X1)) [avatar definition]
206. ~curious(X1) | ~creative(X1) <- (11) [avatar component clause 205]
207. 11 | 8 [avatar split clause 203,190,205]
208. ~brave(alice) | ~curious(X1) | ~creative(X1) [subsumption resolution 118,107]
209. 11 | ~7 [avatar split clause 208,186,205]
320. 37 <=> ! [X3] : generous(X3) [avatar definition]
321. generous(X3) <- (37) [avatar component clause 320]
324. 38 <=> curious(sK8) [avatar definition]
326. curious(sK8) <- (38) [avatar component clause 324]
328. 37 | 38 [avatar split clause 141,324,320]
355. $false <- (37) [resolution 321,146]
358. ~37 [avatar contradiction clause 355]
370. ~tall(sK8) <- (38) [resolution 108,326]
380. creative(sK8) <- (38) [resolution 115,370]
390. creative(X0) | ~kind(X0) | creative(X0) [resolution 99,115]
391. ~kind(X0) | creative(X0) [duplicate literal removal 390]
416. 47 <=> curious(alice) [avatar definition]
418. curious(alice) <- (47) [avatar component clause 416]
420. 48 <=> creative(alice) [avatar definition]
422. creative(alice) <- (48) [avatar component clause 420]
443. ~tall(alice) <- (47) [resolution 418,108]
525. ~creative(alice) | ~kind(alice) | tall(alice) <- (47) [resolution 103,418]
530. ~creative(alice) | tall(alice) <- (47) [subsumption resolution 525,158]
531. ~creative(alice) <- (47) [subsumption resolution 530,443]
532. ~48 | ~47 [avatar split clause 531,416,420]
544. tall(alice) | curious(alice) | brave(alice) <- (8) [resolution 110,191]
684. creative(alice) [resolution 391,158]
687. tall(alice) | curious(alice) <- (~7, 8) [subsumption resolution 544,187]
689. 78 <=> tall(alice) [avatar definition]
691. tall(alice) <- (78) [avatar component clause 689]
692. 47 | 78 | 7 | ~8 [avatar split clause 687,190,186,689,416]
693. 48 [avatar split clause 684,420]
703. ~creative(sK8) <- (11, 38) [resolution 206,326]
715. $false <- (11, 38) [subsumption resolution 703,380]
716. ~11 | ~38 [avatar contradiction clause 715]
726. rich(alice) | ~creative(alice) <- (78) [resolution 691,117]
730. ~creative(alice) <- (78) [subsumption resolution 726,147]
731. $false <- (48, 78) [subsumption resolution 730,422]
732. ~48 | ~78 [avatar contradiction clause 731]
733. $false [avatar sat refutation 207,209,328,358,532,692,693,716,732]
% SZS output end Proof for 4260819096092087283815938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and not brave.
If someone is humble then lucy is creative or tall and vice versa.
If someone is either humble or not funny then someone is rich or not brave.
Everyone who is both not old and generous is both not generous and wise.
Everyone who is both not calm and humble is either not happy or not funny.
Everyone who is not curious is not humble.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
If someone is both funny and creative then someone is not humble.
Everyone who is both kind and brave is not calm and vice versa.
Someone is not funny or not patient.
Paul is both not tall and happy.
Alice is either not wise or curious.
Lucy is both creative and not strong.
Someone is kind.
John is not humble.
Someone is not rich.
John is either wise or not kind. | Paul is wise. | contradiction | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:(humble(X)))<=>((creative(lucy)|tall(lucy))))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~old(X)&generous(X))=>(~generous(X)&wise(X))))&
(![X]:((~calm(X)&humble(X))=>(~happy(X)<~>~funny(X))))&
(![X]:(~curious(X)=>~humble(X)))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(~humble(X))))&
(![X]:((kind(X)&brave(X))<=>~calm(X)))&
(?[X]:((~funny(X)|~patient(X))))&
((~tall(paul)&happy(paul)))&
((~wise(alice)<~>curious(alice)))&
((creative(lucy)&~strong(lucy)))&
(?[X]:(kind(X)))&
(~humble(john))&
(?[X]:(~rich(X)))&
((wise(john)<~>~kind(john))) | wise(paul) | [
"p0",
"p8",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2988943678408343719282650
% SZS output start Proof for 2988943678408343719282650
1. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (~brave(X0) & old(X0))) [input p0]
9. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (humble(X0) & quiet(X0))) [input p8]
10. ? [X0] : (wise(X0) <~> ~quiet(X0)) <=> (humble(alice) & creative(alice)) [input p9]
13. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (calm(X0) | ~generous(X0))) [input p12]
16. ! [X0] : ((brave(X0) & kind(X0)) <=> ~calm(X0)) [input p15]
25. wise(paul) [input hypothesis]
28. ! [X0] : ((~calm(X0) <~> quiet(X0)) => ~brave(X0)) [pure predicate removal 1]
30. ! [X0] : (~brave(X0) | (~calm(X0) <=> quiet(X0))) [ennf transformation 28]
40. ! [X0] : (~brave(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 30]
53. ! [X0] : (((humble(X0) & ~creative(X0)) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((humble(X0) & ~creative(X0)) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ~humble(X0) | creative(X0))) [flattening 53]
55. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~humble(alice) | ~creative(alice))) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 10]
56. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [flattening 55]
57. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [rectify 56]
58. ? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) => ((quiet(sK2) | ~wise(sK2)) & (~quiet(sK2) | wise(sK2))) [choice axiom]
59. (((quiet(sK2) | ~wise(sK2)) & (~quiet(sK2) | wise(sK2))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [skolemisation 57,58]
63. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 13]
64. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | ~quiet(X0) | strong(X0))) [flattening 63]
73. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~kind(X0)))) [nnf transformation 16]
74. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~kind(X0))) [flattening 73]
83. ~brave(X0) | quiet(X0) | calm(X0) [cnf transformation 40]
103. ~creative(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 54]
105. creative(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 59]
107. humble(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 59]
123. ~calm(X0) | quiet(X0) [cnf transformation 64]
131. brave(X0) | calm(X0) [cnf transformation 74]
144. wise(paul) [cnf transformation 25]
187. 9 <=> creative(alice) [avatar definition]
188. creative(alice) <- (9) [avatar component clause 187]
191. 10 <=> humble(alice) [avatar definition]
192. humble(alice) <- (10) [avatar component clause 191]
209. 14 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
210. ~wise(X1) | ~quiet(X1) <- (14) [avatar component clause 209]
211. 14 | 10 [avatar split clause 107,191,209]
213. 14 | 9 [avatar split clause 105,187,209]
316. ~quiet(paul) <- (14) [resolution 210,144]
318. quiet(X0) | calm(X0) | calm(X0) [resolution 83,131]
319. quiet(X0) | calm(X0) [duplicate literal removal 318]
320. quiet(X0) [subsumption resolution 319,123]
321. $false <- (14) [resolution 320,316]
322. ~14 [avatar contradiction clause 321]
354. ~humble(alice) | ~quiet(alice) <- (9) [resolution 103,188]
357. ~quiet(alice) <- (9, 10) [subsumption resolution 354,192]
358. $false <- (9, 10) [subsumption resolution 357,320]
359. ~9 | ~10 [avatar contradiction clause 358]
360. $false [avatar sat refutation 211,213,322,359]
% SZS output end Proof for 2988943678408343719282650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not humble is either rich or tall.
If john is quiet or not funny then john is not humble.
If someone is both old and not quiet then paul is either creative or humble.
If mary is both curious and kind then someone is brave.
If someone is not funny then alice is either curious or not wise and vice versa.
If someone is both not brave and not happy then someone is funny and vice versa.
If someone is not wise or not humble then paul is not strong or not happy and vice versa.
Everyone who is not brave is kind and vice versa.
Everyone who is rich or not calm is both not strong and humble.
Everyone who is either calm or generous is not calm and vice versa.
Everyone who is either kind or not happy is both tall and curious and vice versa.
If someone is both not patient and not strong then someone is both calm and rich and vice versa.
Everyone who is not humble is not old or rich and vice versa.
If someone is either old or generous then lucy is both humble and kind and vice versa.
Everyone who is both not happy and creative is brave and vice versa.
If mary is both not rich and not funny then someone is both rich and patient and vice versa.
Someone is either calm or kind.
Someone is kind or not strong.
Susan is happy.
Someone is either not kind or wise.
Lucy is either kind or tall.
John is either not kind or not old.
Lucy is either curious or not quiet. | Paul is humble. | entailment | (![X]:((humble(X)|~humble(X))=>(rich(X)<~>tall(X))))&
(((quiet(john)|~funny(john)))=>(~humble(john)))&
((?[X]:((old(X)&~quiet(X))))=>((creative(paul)<~>humble(paul))))&
(((curious(mary)&kind(mary)))=>(?[X]:(brave(X))))&
((?[X]:(~funny(X)))<=>((curious(alice)<~>~wise(alice))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>((~strong(paul)|~happy(paul))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((rich(X)|~calm(X))=>(~strong(X)&humble(X))))&
(![X]:((calm(X)<~>generous(X))<=>~calm(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)&curious(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:(~humble(X)<=>(~old(X)|rich(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((humble(lucy)&kind(lucy))))&
(![X]:((~happy(X)&creative(X))<=>brave(X)))&
(((~rich(mary)&~funny(mary)))<=>(?[X]:((rich(X)&patient(X)))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((kind(X)|~strong(X))))&
(happy(susan))&
(?[X]:((~kind(X)<~>wise(X))))&
((kind(lucy)<~>tall(lucy)))&
((~kind(john)<~>~old(john)))&
((curious(lucy)<~>~quiet(lucy))) | humble(paul) | [
"p0",
"p8",
"p9",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8555790512759162780121257
% SZS output start Proof for 8555790512759162780121257
1. ! [X0] : ((~humble(X0) | humble(X0)) => (rich(X0) <~> tall(X0))) [input p0]
9. ! [X0] : ((~calm(X0) | rich(X0)) => (humble(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((calm(X0) <~> generous(X0)) <=> ~calm(X0)) [input p9]
13. ! [X0] : (~humble(X0) <=> (rich(X0) | ~old(X0))) [input p12]
14. ? [X0] : (old(X0) <~> generous(X0)) <=> (kind(lucy) & humble(lucy)) [input p13]
21. kind(lucy) <~> tall(lucy) [input p20]
24. ~humble(paul) [input hypothesis]
27. ! [X0] : ((rich(X0) <~> tall(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 1]
32. ! [X0] : ((humble(X0) & ~strong(X0)) | (calm(X0) & ~rich(X0))) [ennf transformation 9]
33. ! [X0] : (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (humble(X0) & ~humble(X0))) [nnf transformation 27]
52. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | calm(X0)) & (~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 10]
60. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | humble(X0))) [nnf transformation 13]
61. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | humble(X0))) [flattening 60]
62. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~kind(lucy) | ~humble(lucy))) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 14]
63. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [flattening 62]
64. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [rectify 63]
65. ? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) => ((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) [choice axiom]
66. (((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [skolemisation 64,65]
82. (~tall(lucy) | ~kind(lucy)) & (tall(lucy) | kind(lucy)) [nnf transformation 21]
85. tall(X0) | rich(X0) | ~humble(X0) [cnf transformation 33]
86. tall(X0) | rich(X0) | humble(X0) [cnf transformation 33]
109. ~rich(X0) | humble(X0) [cnf transformation 32]
111. ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 52]
113. generous(X0) | calm(X0) | calm(X0) [cnf transformation 52]
125. rich(X0) | ~old(X0) | humble(X0) [cnf transformation 61]
127. ~humble(X0) | ~rich(X0) [cnf transformation 61]
131. kind(lucy) | old(X1) | ~generous(X1) [cnf transformation 66]
148. ~tall(lucy) | ~kind(lucy) [cnf transformation 82]
153. ~humble(paul) [cnf transformation 24]
154. ~calm(X0) | generous(X0) [duplicate literal removal 111]
155. generous(X0) | calm(X0) [duplicate literal removal 113]
157. tall(X0) | rich(X0) [subsumption resolution 85,86]
180. 6 <=> humble(paul) [avatar definition]
182. ~humble(paul) <- (~6) [avatar component clause 180]
257. 23 <=> ! [X1] : humble(X1) [avatar definition]
258. humble(X1) <- (23) [avatar component clause 257]
264. generous(X0) [subsumption resolution 154,155]
291. ~rich(X0) [subsumption resolution 127,109]
292. ~old(X0) | humble(X0) [subsumption resolution 125,291]
299. 32 <=> kind(lucy) [avatar definition]
307. kind(lucy) | old(X1) [subsumption resolution 131,264]
309. 34 <=> ! [X1] : old(X1) [avatar definition]
310. old(X1) <- (34) [avatar component clause 309]
311. 34 | 32 [avatar split clause 307,299,309]
357. 43 <=> tall(lucy) [avatar definition]
359. ~tall(lucy) <- (~43) [avatar component clause 357]
360. ~32 | ~43 [avatar split clause 148,357,299]
382. ~6 [avatar split clause 153,180]
389. rich(lucy) <- (~43) [resolution 157,359]
391. $false <- (~43) [subsumption resolution 389,291]
392. 43 [avatar contradiction clause 391]
416. humble(X0) <- (34) [resolution 292,310]
417. 23 | ~34 [avatar split clause 416,309,257]
419. $false <- (~6, 23) [resolution 258,182]
421. 6 | ~23 [avatar contradiction clause 419]
423. $false [avatar sat refutation 311,360,382,392,417,421]
% SZS output end Proof for 8555790512759162780121257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not generous is either not happy or happy and vice versa.
Everyone who is both generous and creative is either humble or not generous and vice versa.
Everyone who is patient is either not creative or kind.
If someone is not quiet then paul is both quiet and not old.
If someone is not old then someone is tall or happy.
Everyone who is both rich and not curious is either not kind or not rich and vice versa.
Everyone who is both not quiet and wise is not calm or creative.
Everyone who is not curious or funny is not calm or calm.
If someone is patient or happy then someone is both strong and creative.
If someone is either not strong or generous then someone is old or calm and vice versa.
Everyone who is both not generous and not patient is both not strong and strong and vice versa.
Everyone who is both not generous and not strong is not kind.
Everyone who is either tall or quiet is both patient and brave.
If someone is wise then john is not kind or calm.
Everyone who is humble or not creative is both calm and not funny and vice versa.
Everyone who is curious is not brave or old and vice versa.
Mary is wise or not strong.
Someone is either creative or not creative.
Paul is wise.
Someone is both curious and not wise.
Someone is either not curious or not quiet.
Paul is not rich or tall.
Someone is either not generous or creative.
Susan is creative. | Susan is not humble. | contradiction | (![X]:((~calm(X)|~generous(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((generous(X)&creative(X))<=>(humble(X)<~>~generous(X))))&
(![X]:(patient(X)=>(~creative(X)<~>kind(X))))&
((?[X]:(~quiet(X)))=>((quiet(paul)&~old(paul))))&
((?[X]:(~old(X)))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((rich(X)&~curious(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((~quiet(X)&wise(X))=>(~calm(X)|creative(X))))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)|calm(X))))&
((?[X]:((patient(X)|happy(X))))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
(![X]:((tall(X)<~>quiet(X))=>(patient(X)&brave(X))))&
((?[X]:(wise(X)))=>((~kind(john)|calm(john))))&
(![X]:((humble(X)|~creative(X))<=>(calm(X)&~funny(X))))&
(![X]:(curious(X)<=>(~brave(X)|old(X))))&
((wise(mary)|~strong(mary)))&
(?[X]:((creative(X)<~>~creative(X))))&
(wise(paul))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((~rich(paul)|tall(paul)))&
(?[X]:((~generous(X)<~>creative(X))))&
(creative(susan)) | ~humble(susan) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6937541480862238876283890
% SZS output start Proof for 6937541480862238876283890
2. ! [X0] : ((creative(X0) & generous(X0)) <=> (humble(X0) <~> ~generous(X0))) [input p1]
24. creative(susan) [input p23]
25. ~humble(susan) [input hypothesis]
44. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (~creative(X0) | ~generous(X0)))) [nnf transformation 2]
45. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ~creative(X0) | ~generous(X0))) [flattening 44]
84. ~generous(X0) | humble(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 45]
87. generous(X0) | humble(X0) | generous(X0) [cnf transformation 45]
143. creative(susan) [cnf transformation 24]
144. ~humble(susan) [cnf transformation 25]
147. ~generous(X0) | humble(X0) | ~creative(X0) [duplicate literal removal 84]
148. humble(X0) | generous(X0) [duplicate literal removal 87]
152. ~creative(X0) | humble(X0) [subsumption resolution 147,148]
295. humble(susan) [resolution 152,143]
297. $false [subsumption resolution 295,144]
% SZS output end Proof for 6937541480862238876283890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not patient is either not humble or not creative and vice versa.
If someone is rich then john is not wise.
If someone is not creative then mary is quiet and vice versa.
Everyone who is both not wise and not calm is not old or patient and vice versa.
Everyone who is both rich and not brave is patient and vice versa.
If someone is not old then paul is not kind and vice versa.
Everyone who is humble or not generous is either not kind or not funny.
Everyone who is quiet is happy or not wise and vice versa.
Everyone who is patient or not kind is wise or not quiet.
If john is either kind or curious then someone is not happy or happy and vice versa.
Everyone who is calm or not rich is both not strong and humble.
Everyone who is both funny and rich is not wise or not happy and vice versa.
If someone is both not rich and tall then someone is both tall and quiet and vice versa.
Everyone who is both not strong and not wise is both strong and old and vice versa.
Everyone who is not patient or not calm is not rich and vice versa.
If someone is either generous or not brave then someone is rich.
Someone is either not funny or not wise.
Someone is either brave or not kind.
Paul is both not generous and humble.
Lucy is calm or not curious.
Paul is either not curious or not brave.
Lucy is either not tall or not creative. | Mary is not strong. | entailment | (![X]:((calm(X)&~patient(X))<=>(~humble(X)<~>~creative(X))))&
((?[X]:(rich(X)))=>(~wise(john)))&
((?[X]:(~creative(X)))<=>(quiet(mary)))&
(![X]:((~wise(X)&~calm(X))<=>(~old(X)|patient(X))))&
(![X]:((rich(X)&~brave(X))<=>patient(X)))&
((?[X]:(~old(X)))<=>(~kind(paul)))&
(![X]:((humble(X)|~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:(quiet(X)<=>(happy(X)|~wise(X))))&
(![X]:((patient(X)|~kind(X))=>(wise(X)|~quiet(X))))&
(((kind(john)<~>curious(john)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((calm(X)|~rich(X))=>(~strong(X)&humble(X))))&
(![X]:((funny(X)&rich(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~strong(X)&~wise(X))<=>(strong(X)&old(X))))&
(![X]:((~patient(X)|~calm(X))<=>~rich(X)))&
((?[X]:((generous(X)<~>~brave(X))))=>(?[X]:(rich(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((~generous(paul)&humble(paul)))&
((calm(lucy)|~curious(lucy)))&
((~curious(paul)<~>~brave(paul)))&
((~tall(lucy)<~>~creative(lucy))) | ~strong(mary) | [
"p3",
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1920649596760390903660518
% SZS output start Proof for 1920649596760390903660518
4. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> (patient(X0) | ~old(X0))) [input p3]
8. ! [X0] : (quiet(X0) <=> (~wise(X0) | happy(X0))) [input p7]
9. ! [X0] : ((~kind(X0) | patient(X0)) => (~quiet(X0) | wise(X0))) [input p8]
11. ! [X0] : ((~rich(X0) | calm(X0)) => (humble(X0) & ~strong(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> ~rich(X0)) [input p14]
23. strong(mary) [input hypothesis]
28. ! [X0] : ((~quiet(X0) | wise(X0)) | (kind(X0) & ~patient(X0))) [ennf transformation 9]
29. ! [X0] : (~quiet(X0) | wise(X0) | (kind(X0) & ~patient(X0))) [flattening 28]
30. ! [X0] : ((humble(X0) & ~strong(X0)) | (rich(X0) & ~calm(X0))) [ennf transformation 11]
38. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~patient(X0) & old(X0))) & ((patient(X0) | ~old(X0)) | (calm(X0) | wise(X0)))) [nnf transformation 4]
39. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~patient(X0) & old(X0))) & (patient(X0) | ~old(X0) | calm(X0) | wise(X0))) [flattening 38]
47. ! [X0] : ((quiet(X0) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | ~quiet(X0))) [nnf transformation 8]
48. ! [X0] : ((quiet(X0) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ~quiet(X0))) [flattening 47]
62. ! [X0] : (((~calm(X0) | ~patient(X0)) | rich(X0)) & (~rich(X0) | (calm(X0) & patient(X0)))) [nnf transformation 15]
63. ! [X0] : ((~calm(X0) | ~patient(X0) | rich(X0)) & (~rich(X0) | (calm(X0) & patient(X0)))) [flattening 62]
87. ~wise(X0) | ~patient(X0) [cnf transformation 39]
101. quiet(X0) | wise(X0) [cnf transformation 48]
102. ~quiet(X0) | wise(X0) | ~patient(X0) [cnf transformation 29]
111. ~strong(X0) | rich(X0) [cnf transformation 30]
127. ~rich(X0) | patient(X0) [cnf transformation 63]
143. strong(mary) [cnf transformation 23]
147. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
148. ~rich(X0) <- (1) [avatar component clause 147]
181. wise(X0) | ~patient(X0) [subsumption resolution 102,101]
182. ~patient(X0) [subsumption resolution 181,87]
229. ~rich(X0) [subsumption resolution 127,182]
230. 1 [avatar split clause 229,147]
294. rich(mary) [resolution 111,143]
295. $false <- (1) [subsumption resolution 294,148]
296. ~1 [avatar contradiction clause 295]
297. $false [avatar sat refutation 230,296]
% SZS output end Proof for 1920649596760390903660518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then lucy is old or not humble and vice versa.
If john is either quiet or curious then mary is both not funny and generous.
Everyone who is either not tall or old is happy.
If someone is either brave or curious then paul is either curious or generous and vice versa.
If someone is both creative and old then lucy is not kind.
Everyone who is not curious is both not funny and quiet.
Everyone who is quiet or tall is both brave and creative.
If someone is either happy or not calm then someone is brave or not creative.
If someone is not happy or not calm then someone is both brave and strong and vice versa.
If mary is not wise or not calm then someone is either not wise or old.
Everyone who is either generous or strong is both not patient and not quiet.
If someone is either funny or quiet then someone is both tall and not creative and vice versa.
Everyone who is both kind and curious is both not curious and not creative.
If someone is either curious or old then someone is either old or humble.
Everyone who is happy is either not curious or not kind.
If susan is either not curious or creative then mary is not creative.
Paul is not happy or not generous.
Mary is both strong and funny.
Someone is both not old and strong.
Someone is old or not quiet.
Lucy is tall.
Susan is not curious or not quiet.
Someone is not humble or quiet.
Someone is wise or patient. | Lucy is curious. | entailment | ((?[X]:(~calm(X)))<=>((old(lucy)|~humble(lucy))))&
(((quiet(john)<~>curious(john)))=>((~funny(mary)&generous(mary))))&
(![X]:((~tall(X)<~>old(X))=>happy(X)))&
((?[X]:((brave(X)<~>curious(X))))<=>((curious(paul)<~>generous(paul))))&
((?[X]:((creative(X)&old(X))))=>(~kind(lucy)))&
(![X]:(~curious(X)=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(brave(X)&creative(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((brave(X)|~creative(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(((~wise(mary)|~calm(mary)))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((generous(X)<~>strong(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((funny(X)<~>quiet(X))))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((kind(X)&curious(X))=>(~curious(X)&~creative(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:(happy(X)=>(~curious(X)<~>~kind(X))))&
(((~curious(susan)<~>creative(susan)))=>(~creative(mary)))&
((~happy(paul)|~generous(paul)))&
((strong(mary)&funny(mary)))&
(?[X]:((~old(X)&strong(X))))&
(?[X]:((old(X)|~quiet(X))))&
(tall(lucy))&
((~curious(susan)|~quiet(susan)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((wise(X)|patient(X)))) | curious(lucy) | [
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2469696646934460175984031
% SZS output start Proof for 2469696646934460175984031
6. ! [X0] : (~curious(X0) => (quiet(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((tall(X0) | quiet(X0)) => (creative(X0) & brave(X0))) [input p6]
12. ? [X0] : (funny(X0) <~> quiet(X0)) <=> ? [X0] : (~creative(X0) & tall(X0)) [input p11]
25. ~curious(lucy) [input hypothesis]
28. ? [X0] : (funny(X0) <~> quiet(X0)) <=> ? [X1] : (~creative(X1) & tall(X1)) [rectify 12]
33. ! [X0] : ((quiet(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 6]
34. ! [X0] : ((creative(X0) & brave(X0)) | (~tall(X0) & ~quiet(X0))) [ennf transformation 7]
67. (? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X1] : (~creative(X1) & tall(X1)) | ! [X0] : ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) [nnf transformation 28]
68. (? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X2] : (~creative(X2) & tall(X2)) | ! [X3] : ((funny(X3) | ~quiet(X3)) & (quiet(X3) | ~funny(X3)))) [rectify 67]
69. ? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) => ((~quiet(sK6) | ~funny(sK6)) & (quiet(sK6) | funny(sK6))) [choice axiom]
70. ? [X2] : (~creative(X2) & tall(X2)) => (~creative(sK7) & tall(sK7)) [choice axiom]
71. (((~quiet(sK6) | ~funny(sK6)) & (quiet(sK6) | funny(sK6))) | ! [X1] : (creative(X1) | ~tall(X1))) & ((~creative(sK7) & tall(sK7)) | ! [X3] : ((funny(X3) | ~quiet(X3)) & (quiet(X3) | ~funny(X3)))) [skolemisation 68,70,69]
104. ~funny(X0) | curious(X0) [cnf transformation 33]
105. curious(X0) | quiet(X0) [cnf transformation 33]
109. ~tall(X0) | creative(X0) [cnf transformation 34]
126. tall(sK7) | funny(X3) | ~quiet(X3) [cnf transformation 71]
128. ~creative(sK7) | funny(X3) | ~quiet(X3) [cnf transformation 71]
151. ~curious(lucy) [cnf transformation 25]
293. 31 <=> ! [X3] : (funny(X3) | ~quiet(X3)) [avatar definition]
294. ~quiet(X3) | funny(X3) <- (31) [avatar component clause 293]
296. 32 <=> creative(sK7) [avatar definition]
298. ~creative(sK7) <- (~32) [avatar component clause 296]
299. 31 | ~32 [avatar split clause 128,296,293]
305. 34 <=> tall(sK7) [avatar definition]
307. tall(sK7) <- (34) [avatar component clause 305]
308. 31 | 34 [avatar split clause 126,305,293]
389. quiet(lucy) [resolution 105,151]
410. funny(lucy) <- (31) [resolution 294,389]
422. creative(sK7) <- (34) [resolution 307,109]
424. $false <- (~32, 34) [subsumption resolution 422,298]
425. 32 | ~34 [avatar contradiction clause 424]
499. curious(lucy) <- (31) [resolution 410,104]
500. $false <- (31) [subsumption resolution 499,151]
501. ~31 [avatar contradiction clause 500]
502. $false [avatar sat refutation 299,308,425,501]
% SZS output end Proof for 2469696646934460175984031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and rich then susan is not tall or not patient and vice versa. If someone is both not wise and humble then someone is not happy or strong and vice versa. Everyone who is not generous or not calm is either generous or not quiet and vice versa. If susan is quiet then someone is either not calm or not funny and vice versa. If susan is patient then susan is kind or not curious and vice versa. Everyone who is humble is not wise or not patient. If lucy is funny or happy then mary is happy or not curious. If someone is either brave or funny then someone is both patient and not generous. If someone is humble or brave then john is both kind and patient and vice versa. If someone is both not curious and curious then someone is not brave and vice versa. If mary is both not humble and not old then someone is either tall or not rich. If someone is both tall and brave then susan is both wise and not rich. Everyone who is happy is humble. Everyone who is both humble and quiet is not brave. Everyone who is both not wise and kind is either not generous or not strong and vice versa. Everyone who is happy is patient or not rich. Someone is funny. Susan is not old or not calm. Someone is both not old and not funny. Someone is not curious. Paul is both quiet and tall. John is not humble or creative. Someone is not quiet or funny. John is not rich. | Paul is happy. | contradiction | ((?[X]:((~tall(X)&rich(X))))<=>((~tall(susan)|~patient(susan))))&
((?[X]:((~wise(X)&humble(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(generous(X)<~>~quiet(X))))&
((quiet(susan))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
((patient(susan))<=>((kind(susan)|~curious(susan))))&
(![X]:(humble(X)=>(~wise(X)|~patient(X))))&
(((funny(lucy)|happy(lucy)))=>((happy(mary)|~curious(mary))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((patient(X)&~generous(X)))))&
((?[X]:((humble(X)|brave(X))))<=>((kind(john)&patient(john))))&
((?[X]:((~curious(X)&curious(X))))<=>(?[X]:(~brave(X))))&
(((~humble(mary)&~old(mary)))=>(?[X]:((tall(X)<~>~rich(X)))))&
((?[X]:((tall(X)&brave(X))))=>((wise(susan)&~rich(susan))))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((humble(X)&quiet(X))=>~brave(X)))&
(![X]:((~wise(X)&kind(X))<=>(~generous(X)<~>~strong(X))))&
(![X]:(happy(X)=>(patient(X)|~rich(X))))&
(?[X]:(funny(X)))&
((~old(susan)|~calm(susan)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:(~curious(X)))&
((quiet(paul)&tall(paul)))&
((~humble(john)|creative(john)))&
(?[X]:((~quiet(X)|funny(X))))&
(~rich(john)) | happy(paul) | [
"p9",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3879625137244060429449062
% SZS output start Proof for 3879625137244060429449062
10. ? [X0] : (curious(X0) & ~curious(X0)) <=> ? [X0] : ~brave(X0) [input p9]
13. ! [X0] : (happy(X0) => humble(X0)) [input p12]
14. ! [X0] : ((quiet(X0) & humble(X0)) => ~brave(X0)) [input p13]
21. tall(paul) & quiet(paul) [input p20]
25. happy(paul) [input hypothesis]
28. ? [X0] : (curious(X0) & ~curious(X0)) <=> ? [X1] : ~brave(X1) [rectify 10]
38. ! [X0] : (humble(X0) | ~happy(X0)) [ennf transformation 13]
39. ! [X0] : (~brave(X0) | (~quiet(X0) | ~humble(X0))) [ennf transformation 14]
40. ! [X0] : (~brave(X0) | ~quiet(X0) | ~humble(X0)) [flattening 39]
70. (? [X0] : (curious(X0) & ~curious(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (~curious(X0) | curious(X0))) [nnf transformation 28]
71. (? [X0] : (curious(X0) & ~curious(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (~curious(X3) | curious(X3))) [rectify 70]
72. ? [X0] : (curious(X0) & ~curious(X0)) => (curious(sK6) & ~curious(sK6)) [choice axiom]
73. ? [X2] : ~brave(X2) => ~brave(sK7) [choice axiom]
74. ((curious(sK6) & ~curious(sK6)) | ! [X1] : brave(X1)) & (~brave(sK7) | ! [X3] : (~curious(X3) | curious(X3))) [skolemisation 71,73,72]
124. ~curious(sK6) | brave(X1) [cnf transformation 74]
125. curious(sK6) | brave(X1) [cnf transformation 74]
130. ~happy(X0) | humble(X0) [cnf transformation 38]
131. ~brave(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 40]
144. quiet(paul) [cnf transformation 21]
148. happy(paul) [cnf transformation 25]
302. 34 <=> ! [X1] : brave(X1) [avatar definition]
303. brave(X1) <- (34) [avatar component clause 302]
305. 35 <=> curious(sK6) [avatar definition]
308. 34 | 35 [avatar split clause 125,305,302]
309. 34 | ~35 [avatar split clause 124,305,302]
363. humble(paul) [resolution 130,148]
393. ~quiet(X0) | ~humble(X0) <- (34) [resolution 131,303]
395. ~humble(paul) <- (34) [resolution 393,144]
396. $false <- (34) [subsumption resolution 395,363]
397. ~34 [avatar contradiction clause 396]
398. $false [avatar sat refutation 308,309,397]
% SZS output end Proof for 3879625137244060429449062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not humble.
Everyone who is either not strong or not curious is not patient and vice versa.
If someone is either wise or not strong then someone is calm.
Everyone who is both kind and not wise is either not kind or not calm and vice versa.
Everyone who is either old or not tall is funny or brave and vice versa.
Everyone who is both not funny and not curious is strong.
Everyone who is both patient and not curious is not curious or not strong and vice versa.
Everyone who is not strong or brave is strong and vice versa.
If someone is either not patient or not generous then someone is not patient.
Everyone who is not quiet or strong is both not humble and not creative and vice versa.
Everyone who is both kind and wise is either not creative or not patient.
Everyone who is not quiet is calm or funny and vice versa.
Everyone who is not old is both not creative and not calm and vice versa.
Everyone who is either not tall or not generous is not generous and vice versa.
If someone is calm then mary is rich or not funny and vice versa.
Someone is brave or not patient.
Susan is both rich and not quiet.
Lucy is either not rich or tall.
Someone is strong. | Susan is not generous. | contradiction | (![X]:(~kind(X)=>~humble(X)))&
(![X]:((~strong(X)<~>~curious(X))<=>~patient(X)))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:(calm(X))))&
(![X]:((kind(X)&~wise(X))<=>(~kind(X)<~>~calm(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|brave(X))))&
(![X]:((~funny(X)&~curious(X))=>strong(X)))&
(![X]:((patient(X)&~curious(X))<=>(~curious(X)|~strong(X))))&
(![X]:((~strong(X)|brave(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:((kind(X)&wise(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~quiet(X)<=>(calm(X)|funny(X))))&
(![X]:(~old(X)<=>(~creative(X)&~calm(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>~generous(X)))&
((?[X]:(calm(X)))<=>((rich(mary)|~funny(mary))))&
(?[X]:((brave(X)|~patient(X))))&
((rich(susan)&~quiet(susan)))&
((~rich(lucy)<~>tall(lucy)))&
(?[X]:(strong(X))) | ~generous(susan) | [
"p1",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6495170754985507138794996
% SZS output start Proof for 6495170754985507138794996
2. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> ~patient(X0)) [input p1]
7. ! [X0] : ((~curious(X0) & patient(X0)) <=> (~strong(X0) | ~curious(X0))) [input p6]
8. ! [X0] : ((brave(X0) | ~strong(X0)) <=> strong(X0)) [input p7]
9. ? [X0] : (~patient(X0) <~> ~generous(X0)) => ? [X0] : ~patient(X0) [input p8]
20. ~generous(susan) [input hypothesis]
22. ? [X0] : (~patient(X0) <~> ~generous(X0)) => ? [X1] : ~patient(X1) [rectify 9]
27. ? [X1] : ~patient(X1) | ! [X0] : (~patient(X0) <=> ~generous(X0)) [ennf transformation 22]
30. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | patient(X0)) & (~patient(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 2]
39. ! [X0] : (((~curious(X0) & patient(X0)) | (strong(X0) & curious(X0))) & ((~strong(X0) | ~curious(X0)) | (curious(X0) | ~patient(X0)))) [nnf transformation 7]
40. ! [X0] : (((~curious(X0) & patient(X0)) | (strong(X0) & curious(X0))) & (~strong(X0) | ~curious(X0) | curious(X0) | ~patient(X0))) [flattening 39]
41. ! [X0] : (((brave(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 8]
42. ! [X0] : ((brave(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [flattening 41]
43. ? [X1] : ~patient(X1) | ! [X0] : ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))) [nnf transformation 27]
44. ? [X0] : ~patient(X0) | ! [X1] : ((~patient(X1) | generous(X1)) & (~generous(X1) | patient(X1))) [rectify 43]
45. ? [X0] : ~patient(X0) => ~patient(sK1) [choice axiom]
46. ~patient(sK1) | ! [X1] : ((~patient(X1) | generous(X1)) & (~generous(X1) | patient(X1))) [skolemisation 44,45]
67. ~patient(X0) | ~strong(X0) | curious(X0) [cnf transformation 30]
68. ~curious(X0) | ~strong(X0) | patient(X0) [cnf transformation 30]
86. patient(X0) | curious(X0) [cnf transformation 40]
90. strong(X0) | strong(X0) [cnf transformation 42]
94. ~patient(sK1) | ~patient(X1) | generous(X1) [cnf transformation 46]
121. ~generous(susan) [cnf transformation 20]
124. strong(X0) [duplicate literal removal 90]
142. 4 <=> ! [X1] : (~patient(X1) | generous(X1)) [avatar definition]
143. ~patient(X1) | generous(X1) <- (4) [avatar component clause 142]
145. 5 <=> patient(sK1) [avatar definition]
147. ~patient(sK1) <- (~5) [avatar component clause 145]
148. 4 | ~5 [avatar split clause 94,145,142]
186. curious(sK1) <- (~5) [resolution 86,147]
207. ~strong(X1) | curious(X1) | curious(X1) [resolution 67,86]
208. ~strong(X1) | curious(X1) [duplicate literal removal 207]
209. curious(X1) [subsumption resolution 208,124]
210. ~strong(sK1) | patient(sK1) <- (~5) [resolution 68,186]
212. patient(sK1) <- (~5) [subsumption resolution 210,124]
213. $false <- (~5) [subsumption resolution 212,147]
214. 5 [avatar contradiction clause 213]
222. ~strong(X0) | patient(X0) [resolution 209,68]
224. patient(X0) [subsumption resolution 222,124]
237. generous(X0) <- (4) [resolution 224,143]
242. $false <- (4) [resolution 237,121]
244. ~4 [avatar contradiction clause 242]
245. $false [avatar sat refutation 148,214,244]
% SZS output end Proof for 6495170754985507138794996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not funny is calm or not brave.
Everyone who is either not old or kind is curious or quiet and vice versa.
Everyone who is patient is both patient and old and vice versa.
Everyone who is both brave and old is both not calm and tall.
If someone is generous then someone is both not old and funny.
If mary is both not curious and not old then fred is old and vice versa.
If alice is funny or not generous then someone is kind or funny.
If fred is creative then someone is either old or not generous.
Everyone who is both not humble and strong is either tall or kind.
If someone is rich or not brave then someone is patient or humble and vice versa.
If someone is not generous then someone is both old and curious.
Everyone who is both brave and funny is both not old and tall.
If fred is brave then paul is both not funny and not creative and vice versa.
Everyone who is not happy is not tall or funny.
If someone is not kind then someone is not funny or calm.
Everyone who is not generous or not kind is kind or tall and vice versa.
Someone is not funny or not curious.
Paul is kind or brave.
Someone is both kind and not calm.
Someone is not kind.
Someone is brave or tall.
Someone is not wise or not funny.
Fred is not funny or not wise.
Someone is both happy and generous. | Paul is not happy. | neutral | (![X]:((calm(X)&~funny(X))=>(calm(X)|~brave(X))))&
(![X]:((~old(X)<~>kind(X))<=>(curious(X)|quiet(X))))&
(![X]:(patient(X)<=>(patient(X)&old(X))))&
(![X]:((brave(X)&old(X))=>(~calm(X)&tall(X))))&
((?[X]:(generous(X)))=>(?[X]:((~old(X)&funny(X)))))&
(((~curious(mary)&~old(mary)))<=>(old(fred)))&
(((funny(alice)|~generous(alice)))=>(?[X]:((kind(X)|funny(X)))))&
((creative(fred))=>(?[X]:((old(X)<~>~generous(X)))))&
(![X]:((~humble(X)&strong(X))=>(tall(X)<~>kind(X))))&
((?[X]:((rich(X)|~brave(X))))<=>(?[X]:((patient(X)|humble(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((brave(X)&funny(X))=>(~old(X)&tall(X))))&
((brave(fred))<=>((~funny(paul)&~creative(paul))))&
(![X]:(~happy(X)=>(~tall(X)|funny(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~funny(X)|calm(X)))))&
(![X]:((~generous(X)|~kind(X))<=>(kind(X)|tall(X))))&
(?[X]:((~funny(X)|~curious(X))))&
((kind(paul)|brave(paul)))&
(?[X]:((kind(X)&~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:((~wise(X)|~funny(X))))&
((~funny(fred)|~wise(fred)))&
(?[X]:((happy(X)&generous(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is both not strong and not rich is tall and vice versa.
Everyone who is both kind and not patient is either not funny or quiet and vice versa.
Everyone who is quiet is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Everyone who is both old and not calm is not rich or not funny and vice versa.
Everyone who is both rich and not wise is both curious and quiet.
If john is both curious and old then susan is rich and vice versa.
Everyone who is either patient or happy is funny or not curious and vice versa.
If someone is rich or calm then alice is rich or not old and vice versa.
Everyone who is either tall or not funny is both strong and funny and vice versa.
Someone is both brave and not strong.
Lucy is either generous or not brave.
Someone is not strong or not quiet.
Someone is rich.
Someone is either quiet or not curious.
Someone is either humble or not wise. | Alice is not brave. | neutral | (![X]:((~strong(X)&~rich(X))<=>tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(quiet(X)<=>(happy(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(![X]:((tall(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~strong(X))))&
((generous(lucy)<~>~brave(lucy)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~wise(X)))) | ~brave(alice) | [] | null | 0 |
If fred is both not funny and not curious then someone is not strong.
If someone is either not calm or kind then someone is happy or creative and vice versa.
If alice is not brave then someone is creative.
Everyone who is funny is both calm and old and vice versa.
If someone is not wise then someone is not rich and vice versa.
Everyone who is generous or tall is either not funny or brave.
If someone is wise or old then someone is both not strong and not humble.
If susan is both curious and wise then someone is either not patient or not wise.
If susan is both not brave and not tall then someone is both funny and not strong.
If someone is either humble or not patient then someone is both not rich and quiet and vice versa.
Everyone who is not curious or not strong is both patient and quiet.
Everyone who is either calm or not tall is curious or humble.
If mary is not quiet then someone is both not old and not funny and vice versa.
Everyone who is not strong is happy and vice versa.
If someone is patient then mary is both not patient and not humble.
Everyone who is not humble is not curious.
John is either curious or not humble.
Fred is both curious and not happy.
Paul is either not calm or strong.
Mary is not old.
Mary is both not brave and not creative.
Someone is both not generous and not tall.
Paul is not funny or not humble. | Mary is strong. | entailment | (((~funny(fred)&~curious(fred)))=>(?[X]:(~strong(X))))&
((?[X]:((~calm(X)<~>kind(X))))<=>(?[X]:((happy(X)|creative(X)))))&
((~brave(alice))=>(?[X]:(creative(X))))&
(![X]:(funny(X)<=>(calm(X)&old(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)|tall(X))=>(~funny(X)<~>brave(X))))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((~strong(X)&~humble(X)))))&
(((curious(susan)&wise(susan)))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(((~brave(susan)&~tall(susan)))=>(?[X]:((funny(X)&~strong(X)))))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((~rich(X)&quiet(X)))))&
(![X]:((~curious(X)|~strong(X))=>(patient(X)&quiet(X))))&
(![X]:((calm(X)<~>~tall(X))=>(curious(X)|humble(X))))&
((~quiet(mary))<=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
((?[X]:(patient(X)))=>((~patient(mary)&~humble(mary))))&
(![X]:(~humble(X)=>~curious(X)))&
((curious(john)<~>~humble(john)))&
((curious(fred)&~happy(fred)))&
((~calm(paul)<~>strong(paul)))&
(~old(mary))&
((~brave(mary)&~creative(mary)))&
(?[X]:((~generous(X)&~tall(X))))&
((~funny(paul)|~humble(paul))) | strong(mary) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7800096045047289323464816
% SZS output start Proof for 7800096045047289323464816
11. ! [X0] : ((~strong(X0) | ~curious(X0)) => (quiet(X0) & patient(X0))) [input p10]
15. ? [X0] : patient(X0) => (~humble(mary) & ~patient(mary)) [input p14]
24. ~strong(mary) [input hypothesis]
40. ! [X0] : ((quiet(X0) & patient(X0)) | (strong(X0) & curious(X0))) [ennf transformation 11]
43. (~humble(mary) & ~patient(mary)) | ! [X0] : ~patient(X0) [ennf transformation 15]
115. patient(X0) | strong(X0) [cnf transformation 40]
125. ~patient(mary) | ~patient(X0) [cnf transformation 43]
139. ~strong(mary) [cnf transformation 24]
317. 41 <=> ! [X0] : ~patient(X0) [avatar definition]
318. ~patient(X0) <- (41) [avatar component clause 317]
325. 43 <=> patient(mary) [avatar definition]
326. patient(mary) <- (43) [avatar component clause 325]
327. ~patient(mary) <- (~43) [avatar component clause 325]
328. 41 | ~43 [avatar split clause 125,325,317]
361. strong(mary) <- (~43) [resolution 115,327]
362. $false <- (~43) [subsumption resolution 361,139]
363. 43 [avatar contradiction clause 362]
366. $false <- (41, 43) [resolution 326,318]
367. ~41 | ~43 [avatar contradiction clause 366]
368. $false [avatar sat refutation 328,363,367]
% SZS output end Proof for 7800096045047289323464816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or funny then alice is either funny or not wise and vice versa.
Everyone who is either not happy or tall is not wise or wise and vice versa.
If lucy is either not brave or rich then john is both not tall and not strong and vice versa.
Everyone who is not generous is both not quiet and not strong and vice versa.
Everyone who is rich is both not tall and brave and vice versa.
Everyone who is both quiet and not humble is both not old and not patient.
Everyone who is calm or not strong is happy or not funny and vice versa.
Everyone who is brave or humble is both generous and not humble and vice versa.
Everyone who is both not curious and curious is either creative or not quiet.
Everyone who is both not brave and strong is strong or curious and vice versa.
Everyone who is both not rich and not tall is either not patient or calm.
If someone is not wise or not brave then someone is not old or strong and vice versa.
Everyone who is not happy is tall or not brave and vice versa.
If someone is old then alice is either calm or tall.
Everyone who is either wise or rich is both not old and creative and vice versa.
If susan is both not old and funny then mary is not generous.
Someone is both old and not happy.
Someone is not funny.
Someone is either brave or not brave.
Lucy is kind.
Someone is either funny or not tall.
Someone is not old or not brave.
Paul is either not strong or brave.
John is funny or wise. | John is curious. | contradiction | ((?[X]:((~calm(X)<~>funny(X))))<=>((funny(alice)<~>~wise(alice))))&
(![X]:((~happy(X)<~>tall(X))<=>(~wise(X)|wise(X))))&
(((~brave(lucy)<~>rich(lucy)))<=>((~tall(john)&~strong(john))))&
(![X]:(~generous(X)<=>(~quiet(X)&~strong(X))))&
(![X]:(rich(X)<=>(~tall(X)&brave(X))))&
(![X]:((quiet(X)&~humble(X))=>(~old(X)&~patient(X))))&
(![X]:((calm(X)|~strong(X))<=>(happy(X)|~funny(X))))&
(![X]:((brave(X)|humble(X))<=>(generous(X)&~humble(X))))&
(![X]:((~curious(X)&curious(X))=>(creative(X)<~>~quiet(X))))&
(![X]:((~brave(X)&strong(X))<=>(strong(X)|curious(X))))&
(![X]:((~rich(X)&~tall(X))=>(~patient(X)<~>calm(X))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(![X]:(~happy(X)<=>(tall(X)|~brave(X))))&
((?[X]:(old(X)))=>((calm(alice)<~>tall(alice))))&
(![X]:((wise(X)<~>rich(X))<=>(~old(X)&creative(X))))&
(((~old(susan)&funny(susan)))=>(~generous(mary)))&
(?[X]:((old(X)&~happy(X))))&
(?[X]:(~funny(X)))&
(?[X]:((brave(X)<~>~brave(X))))&
(kind(lucy))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:((~old(X)|~brave(X))))&
((~strong(paul)<~>brave(paul)))&
((funny(john)|wise(john))) | curious(john) | [
"p1",
"p2",
"p4",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3571968515780308299440846
% SZS output start Proof for 3571968515780308299440846
2. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (wise(X0) | ~wise(X0))) [input p1]
3. (~brave(lucy) <~> rich(lucy)) <=> (~strong(john) & ~tall(john)) [input p2]
5. ! [X0] : (rich(X0) <=> (brave(X0) & ~tall(X0))) [input p4]
10. ! [X0] : ((strong(X0) & ~brave(X0)) <=> (curious(X0) | strong(X0))) [input p9]
13. ! [X0] : (~happy(X0) <=> (~brave(X0) | tall(X0))) [input p12]
25. curious(john) [input hypothesis]
41. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 41]
43. (((~rich(lucy) | brave(lucy)) & (rich(lucy) | ~brave(lucy))) | (strong(john) | tall(john))) & ((~strong(john) & ~tall(john)) | ((~brave(lucy) | ~rich(lucy)) & (rich(lucy) | brave(lucy)))) [nnf transformation 3]
44. (((~rich(lucy) | brave(lucy)) & (rich(lucy) | ~brave(lucy))) | strong(john) | tall(john)) & ((~strong(john) & ~tall(john)) | ((~brave(lucy) | ~rich(lucy)) & (rich(lucy) | brave(lucy)))) [flattening 43]
47. ! [X0] : ((rich(X0) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | ~rich(X0))) [nnf transformation 5]
48. ! [X0] : ((rich(X0) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | ~rich(X0))) [flattening 47]
54. ! [X0] : (((strong(X0) & ~brave(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (~strong(X0) | brave(X0)))) [nnf transformation 10]
55. ! [X0] : (((strong(X0) & ~brave(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ~strong(X0) | brave(X0))) [flattening 54]
62. ! [X0] : ((~happy(X0) | (brave(X0) & ~tall(X0))) & ((~brave(X0) | tall(X0)) | happy(X0))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | (brave(X0) & ~tall(X0))) & (~brave(X0) | tall(X0) | happy(X0))) [flattening 62]
90. tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 42]
91. tall(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 42]
92. ~tall(X0) | happy(X0) | wise(X0) [cnf transformation 42]
93. ~tall(X0) | happy(X0) | ~wise(X0) [cnf transformation 42]
96. ~strong(john) | rich(lucy) | brave(lucy) [cnf transformation 44]
104. ~rich(X0) | brave(X0) [cnf transformation 48]
123. ~curious(X0) | strong(X0) [cnf transformation 55]
130. ~brave(X0) | tall(X0) | happy(X0) [cnf transformation 63]
131. ~happy(X0) | ~tall(X0) [cnf transformation 63]
153. curious(john) [cnf transformation 25]
186. ~tall(X0) | happy(X0) [subsumption resolution 92,93]
187. ~happy(X0) | tall(X0) [subsumption resolution 90,91]
193. 8 <=> strong(john) [avatar definition]
197. 9 <=> brave(lucy) [avatar definition]
198. ~brave(lucy) <- (~9) [avatar component clause 197]
199. brave(lucy) <- (9) [avatar component clause 197]
201. 10 <=> rich(lucy) [avatar definition]
202. rich(lucy) <- (10) [avatar component clause 201]
207. 9 | 10 | ~8 [avatar split clause 96,193,201,197]
242. ~tall(X0) [subsumption resolution 131,186]
243. ~brave(X0) | happy(X0) [subsumption resolution 130,242]
290. strong(john) [resolution 123,153]
293. 8 [avatar split clause 290,193]
297. happy(lucy) <- (9) [resolution 243,199]
298. tall(lucy) <- (9) [resolution 297,187]
300. $false <- (9) [subsumption resolution 298,242]
301. ~9 [avatar contradiction clause 300]
302. brave(lucy) <- (10) [resolution 202,104]
304. $false <- (~9, 10) [subsumption resolution 302,198]
305. 9 | ~10 [avatar contradiction clause 304]
306. $false [avatar sat refutation 207,293,301,305]
% SZS output end Proof for 3571968515780308299440846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not humble is either not curious or not brave. If someone is not wise then susan is curious. If someone is both not strong and not kind then someone is not humble or funny. Everyone who is either happy or not calm is either not generous or not old. If alice is humble or old then someone is both not happy and brave and vice versa. If john is either not quiet or not generous then john is both not wise and not generous. Everyone who is both not generous and wise is both brave and not patient. If lucy is not humble then mary is either not rich or generous. Everyone who is both old and rich is humble or brave and vice versa. Everyone who is creative is not calm and vice versa. Everyone who is curious is creative. Everyone who is not tall is calm or brave. If john is not rich or not kind then alice is both not quiet and quiet. Everyone who is funny is not generous or rich and vice versa. If susan is both not curious and strong then someone is both strong and humble and vice versa. Everyone who is strong or not happy is not rich and vice versa. Someone is not quiet. Mary is not generous or not happy. Someone is not generous. Lucy is both not kind and not quiet. Someone is not kind or curious. | Mary is not funny. | neutral | (![X]:((~creative(X)&~humble(X))=>(~curious(X)<~>~brave(X))))&
((?[X]:(~wise(X)))=>(curious(susan)))&
((?[X]:((~strong(X)&~kind(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(~generous(X)<~>~old(X))))&
(((humble(alice)|old(alice)))<=>(?[X]:((~happy(X)&brave(X)))))&
(((~quiet(john)<~>~generous(john)))=>((~wise(john)&~generous(john))))&
(![X]:((~generous(X)&wise(X))=>(brave(X)&~patient(X))))&
((~humble(lucy))=>((~rich(mary)<~>generous(mary))))&
(![X]:((old(X)&rich(X))<=>(humble(X)|brave(X))))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:(curious(X)=>creative(X)))&
(![X]:(~tall(X)=>(calm(X)|brave(X))))&
(((~rich(john)|~kind(john)))=>((~quiet(alice)&quiet(alice))))&
(![X]:(funny(X)<=>(~generous(X)|rich(X))))&
(((~curious(susan)&strong(susan)))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((strong(X)|~happy(X))<=>~rich(X)))&
(?[X]:(~quiet(X)))&
((~generous(mary)|~happy(mary)))&
(?[X]:(~generous(X)))&
((~kind(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)|curious(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is both not funny and calm is both humble and not humble and vice versa. Everyone who is either not brave or kind is both not wise and not strong and vice versa. If john is not wise or not quiet then someone is wise and vice versa. If someone is both not wise and generous then lucy is old. If john is either not old or strong then lucy is both wise and calm. If someone is not tall or tall then someone is happy or humble and vice versa. Everyone who is both not wise and creative is either curious or rich and vice versa. Everyone who is either not tall or quiet is either not tall or not wise and vice versa. Everyone who is both funny and not rich is either not funny or rich and vice versa. Everyone who is creative or funny is not quiet or not happy. Everyone who is tall is both not strong and quiet and vice versa. If susan is quiet then someone is calm and vice versa. If someone is both not kind and curious then someone is either generous or not curious. If someone is not rich then paul is either creative or not patient. Everyone who is either not happy or generous is curious or strong. Everyone who is both not patient and generous is not creative. John is funny or strong. Lucy is either old or funny. Someone is either not brave or not funny. Someone is both not patient and happy. Someone is brave or not strong. Fred is wise. Alice is not kind or wise. | Alice is not creative. | neutral | (![X]:((~funny(X)&calm(X))<=>(humble(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~wise(X)&~strong(X))))&
(((~wise(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
((?[X]:((~wise(X)&generous(X))))=>(old(lucy)))&
(((~old(john)<~>strong(john)))=>((wise(lucy)&calm(lucy))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~wise(X)&creative(X))<=>(curious(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>~wise(X))))&
(![X]:((funny(X)&~rich(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((creative(X)|funny(X))=>(~quiet(X)|~happy(X))))&
(![X]:(tall(X)<=>(~strong(X)&quiet(X))))&
((quiet(susan))<=>(?[X]:(calm(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:(~rich(X)))=>((creative(paul)<~>~patient(paul))))&
(![X]:((~happy(X)<~>generous(X))=>(curious(X)|strong(X))))&
(![X]:((~patient(X)&generous(X))=>~creative(X)))&
((funny(john)|strong(john)))&
((old(lucy)<~>funny(lucy)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((brave(X)|~strong(X))))&
(wise(fred))&
((~kind(alice)|wise(alice))) | ~creative(alice) | [] | null | 0 |
If john is both patient and rich then john is quiet or not happy and vice versa.
If someone is both not generous and patient then someone is not patient or not generous and vice versa.
Everyone who is both not patient and rich is both generous and happy.
Everyone who is both not tall and tall is either not humble or not generous and vice versa.
If fred is not tall then susan is both not old and not curious.
Everyone who is funny is not kind or curious.
If lucy is kind or not happy then someone is curious and vice versa.
If alice is both quiet and not generous then someone is not patient or patient and vice versa.
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Someone is not humble.
Someone is not happy or humble.
Paul is either kind or not old.
Someone is not quiet.
Someone is both not brave and not calm.
Someone is both not rich and not happy.
Someone is either kind or happy. | Paul is humble. | neutral | (((patient(john)&rich(john)))<=>((quiet(john)|~happy(john))))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~patient(X)&rich(X))=>(generous(X)&happy(X))))&
(![X]:((~tall(X)&tall(X))<=>(~humble(X)<~>~generous(X))))&
((~tall(fred))=>((~old(susan)&~curious(susan))))&
(![X]:(funny(X)=>(~kind(X)|curious(X))))&
(((kind(lucy)|~happy(lucy)))<=>(?[X]:(curious(X))))&
(((quiet(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|patient(X)))))&
((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|humble(X))))&
((kind(paul)<~>~old(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)&~calm(X))))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((kind(X)<~>happy(X)))) | humble(paul) | [] | null | 0 |
If someone is both generous and funny then someone is quiet or not tall and vice versa. Everyone who is not strong or not calm is not happy and vice versa. Everyone who is both strong and not kind is both not quiet and strong and vice versa. Everyone who is either patient or not creative is both not curious and not generous and vice versa. If fred is funny or not humble then john is either not generous or not calm and vice versa. Everyone who is both strong and curious is either not kind or not rich. Everyone who is both not calm and not patient is both not calm and tall. Everyone who is both not calm and wise is not old. Everyone who is not strong is either old or not curious and vice versa. Everyone who is both not brave and not kind is kind and vice versa. If someone is both old and not curious then someone is kind or not creative and vice versa. If someone is generous or wise then alice is not tall or wise and vice versa. If someone is either not humble or not brave then someone is strong or funny and vice versa. Everyone who is either quiet or not rich is not quiet or not humble. Everyone who is both not calm and old is either not rich or funny. Everyone who is both not tall and patient is quiet or funny and vice versa. Mary is not funny or brave. Paul is either quiet or curious. Someone is funny. Someone is not generous or not calm. Alice is both not patient and rich. Someone is both not funny and not strong. Someone is not funny. | Paul is not calm. | neutral | ((?[X]:((generous(X)&funny(X))))<=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~strong(X)|~calm(X))<=>~happy(X)))&
(![X]:((strong(X)&~kind(X))<=>(~quiet(X)&strong(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~curious(X)&~generous(X))))&
(((funny(fred)|~humble(fred)))<=>((~generous(john)<~>~calm(john))))&
(![X]:((strong(X)&curious(X))=>(~kind(X)<~>~rich(X))))&
(![X]:((~calm(X)&~patient(X))=>(~calm(X)&tall(X))))&
(![X]:((~calm(X)&wise(X))=>~old(X)))&
(![X]:(~strong(X)<=>(old(X)<~>~curious(X))))&
(![X]:((~brave(X)&~kind(X))<=>kind(X)))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((generous(X)|wise(X))))<=>((~tall(alice)|wise(alice))))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(?[X]:((strong(X)|funny(X)))))&
(![X]:((quiet(X)<~>~rich(X))=>(~quiet(X)|~humble(X))))&
(![X]:((~calm(X)&old(X))=>(~rich(X)<~>funny(X))))&
(![X]:((~tall(X)&patient(X))<=>(quiet(X)|funny(X))))&
((~funny(mary)|brave(mary)))&
((quiet(paul)<~>curious(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|~calm(X))))&
((~patient(alice)&rich(alice)))&
(?[X]:((~funny(X)&~strong(X))))&
(?[X]:(~funny(X))) | ~calm(paul) | [] | null | 0 |
If someone is either brave or not curious then someone is strong or curious.
If someone is either generous or calm then fred is both not kind and rich and vice versa.
Everyone who is either wise or not strong is either calm or not calm.
If lucy is humble or not wise then susan is not funny or strong.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
If someone is either quiet or not tall then someone is both not creative and not curious and vice versa.
If someone is either wise or not old then someone is either not tall or not happy and vice versa.
Everyone who is not brave or not old is both kind and not generous.
Everyone who is brave or happy is both humble and strong and vice versa.
Everyone who is both not generous and tall is both not patient and brave.
If someone is either quiet or not tall then fred is not old and vice versa.
Someone is kind or brave.
Someone is not happy or not brave.
Someone is funny.
Someone is either not brave or kind.
Paul is either not curious or tall. | Paul is patient. | entailment | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((generous(X)<~>calm(X))))<=>((~kind(fred)&rich(fred))))&
(![X]:((wise(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(((humble(lucy)|~wise(lucy)))=>((~funny(susan)|strong(susan))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((brave(X)|happy(X))<=>(humble(X)&strong(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~curious(paul)<~>tall(paul))) | patient(paul) | [
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 473525871914149539846317
% SZS output start Proof for 473525871914149539846317
7. ! [X0] : (patient(X0) <=> strong(X0)) [input p6]
9. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~brave(X0)) [input p8]
14. ! [X0] : ((happy(X0) | brave(X0)) <=> (strong(X0) & humble(X0))) [input p13]
22. ~patient(paul) [input hypothesis]
48. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~patient(X0) | creative(X0))) [flattening 50]
64. ! [X0] : (((happy(X0) | brave(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 14]
65. ! [X0] : ((happy(X0) | brave(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 64]
99. ~patient(X0) | strong(X0) [cnf transformation 48]
100. ~strong(X0) | patient(X0) [cnf transformation 48]
105. patient(X0) | brave(X0) [cnf transformation 51]
129. ~brave(X0) | strong(X0) [cnf transformation 65]
145. ~patient(paul) [cnf transformation 22]
324. brave(X0) | strong(X0) [resolution 105,99]
325. strong(X0) [subsumption resolution 324,129]
327. patient(X0) [resolution 325,100]
347. $false [resolution 327,145]
% SZS output end Proof for 473525871914149539846317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is calm or not tall and vice versa.
Everyone who is either kind or creative is kind or not quiet and vice versa.
If john is not strong or tall then someone is either not creative or quiet and vice versa.
Everyone who is patient or not tall is wise.
Everyone who is creative or not generous is either not happy or not rich and vice versa.
Everyone who is either old or quiet is funny and vice versa.
Everyone who is either not humble or not tall is brave or not happy.
Everyone who is rich or not brave is quiet or brave and vice versa.
Everyone who is either wise or tall is either curious or not generous and vice versa.
If someone is not calm or not creative then someone is not kind or calm.
Everyone who is not old is both calm and not quiet.
Everyone who is both not creative and not old is both creative and strong.
If someone is not rich or generous then someone is both brave and not happy and vice versa.
Everyone who is either not curious or not calm is both not funny and funny.
If someone is not wise or not creative then mary is either not creative or kind.
If someone is either not humble or humble then someone is rich or creative and vice versa.
Someone is either not funny or rich.
Paul is either not wise or generous.
Alice is either curious or patient.
Lucy is not humble or happy.
Someone is either not humble or quiet.
Someone is either not creative or not calm. | Mary is curious. | neutral | (![X]:(~tall(X)<=>(calm(X)|~tall(X))))&
(![X]:((kind(X)<~>creative(X))<=>(kind(X)|~quiet(X))))&
(((~strong(john)|tall(john)))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:((patient(X)|~tall(X))=>wise(X)))&
(![X]:((creative(X)|~generous(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((old(X)<~>quiet(X))<=>funny(X)))&
(![X]:((~humble(X)<~>~tall(X))=>(brave(X)|~happy(X))))&
(![X]:((rich(X)|~brave(X))<=>(quiet(X)|brave(X))))&
(![X]:((wise(X)<~>tall(X))<=>(curious(X)<~>~generous(X))))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:(~old(X)=>(calm(X)&~quiet(X))))&
(![X]:((~creative(X)&~old(X))=>(creative(X)&strong(X))))&
((?[X]:((~rich(X)|generous(X))))<=>(?[X]:((brave(X)&~happy(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>(~funny(X)&funny(X))))&
((?[X]:((~wise(X)|~creative(X))))=>((~creative(mary)<~>kind(mary))))&
((?[X]:((~humble(X)<~>humble(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(?[X]:((~funny(X)<~>rich(X))))&
((~wise(paul)<~>generous(paul)))&
((curious(alice)<~>patient(alice)))&
((~humble(lucy)|happy(lucy)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~creative(X)<~>~calm(X)))) | curious(mary) | [] | null | 0 |
Everyone who is either tall or not old is humble or not old.
Everyone who is calm or generous is both not tall and not patient.
Everyone who is both not funny and funny is strong or tall.
If someone is not curious or curious then someone is either rich or brave.
If someone is either not quiet or not strong then mary is not old or quiet and vice versa.
Everyone who is either not patient or strong is both not tall and not creative and vice versa.
Everyone who is both not rich and not wise is quiet or not kind and vice versa.
Everyone who is both funny and not creative is either not calm or kind and vice versa.
If fred is both not funny and not creative then someone is both not old and humble and vice versa.
Everyone who is happy or not kind is both not tall and not quiet.
Everyone who is either not old or curious is either wise or not quiet and vice versa.
Everyone who is both not funny and old is both patient and funny.
Everyone who is both brave and funny is both not humble and curious.
If someone is not calm or not generous then mary is not rich or not creative and vice versa.
Everyone who is both rich and not calm is either generous or happy.
Everyone who is both not patient and funny is either rich or kind and vice versa.
Someone is both not funny and not curious.
Someone is either old or not calm.
Paul is wise or creative.
Fred is not funny or calm.
Fred is both not humble and not quiet.
Someone is not old.
Lucy is quiet.
Someone is not rich or not strong. | Lucy is not tall. | neutral | (![X]:((tall(X)<~>~old(X))=>(humble(X)|~old(X))))&
(![X]:((calm(X)|generous(X))=>(~tall(X)&~patient(X))))&
(![X]:((~funny(X)&funny(X))=>(strong(X)|tall(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((rich(X)<~>brave(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>((~old(mary)|quiet(mary))))&
(![X]:((~patient(X)<~>strong(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~rich(X)&~wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:((funny(X)&~creative(X))<=>(~calm(X)<~>kind(X))))&
(((~funny(fred)&~creative(fred)))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((happy(X)|~kind(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~old(X)<~>curious(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~funny(X)&old(X))=>(patient(X)&funny(X))))&
(![X]:((brave(X)&funny(X))=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~rich(mary)|~creative(mary))))&
(![X]:((rich(X)&~calm(X))=>(generous(X)<~>happy(X))))&
(![X]:((~patient(X)&funny(X))<=>(rich(X)<~>kind(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((old(X)<~>~calm(X))))&
((wise(paul)|creative(paul)))&
((~funny(fred)|calm(fred)))&
((~humble(fred)&~quiet(fred)))&
(?[X]:(~old(X)))&
(quiet(lucy))&
(?[X]:((~rich(X)|~strong(X)))) | ~tall(lucy) | [] | null | 0 |
If someone is not old or not calm then mary is both not curious and quiet.
Everyone who is not generous or creative is either not kind or humble.
If paul is calm then someone is either strong or funny.
Everyone who is not calm or rich is either wise or patient.
Everyone who is either funny or not humble is both curious and happy.
Everyone who is not calm is both not generous and rich.
If alice is both not old and calm then someone is not strong and vice versa.
If someone is either generous or not patient then mary is brave or not funny.
Everyone who is either not patient or wise is curious.
If someone is tall then paul is not curious or not kind and vice versa.
If fred is old then john is not brave.
If someone is not humble then someone is not old and vice versa.
If someone is not funny or rich then lucy is both not brave and not calm and vice versa.
Everyone who is either happy or not curious is tall.
Everyone who is both brave and not brave is not generous and vice versa.
Everyone who is both not calm and not curious is both rich and quiet.
Paul is curious.
Someone is not patient or strong.
Someone is either not funny or calm.
Someone is not old or not happy. | Paul is not quiet. | neutral | ((?[X]:((~old(X)|~calm(X))))=>((~curious(mary)&quiet(mary))))&
(![X]:((~generous(X)|creative(X))=>(~kind(X)<~>humble(X))))&
((calm(paul))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~calm(X)|rich(X))=>(wise(X)<~>patient(X))))&
(![X]:((funny(X)<~>~humble(X))=>(curious(X)&happy(X))))&
(![X]:(~calm(X)=>(~generous(X)&rich(X))))&
(((~old(alice)&calm(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)<~>~patient(X))))=>((brave(mary)|~funny(mary))))&
(![X]:((~patient(X)<~>wise(X))=>curious(X)))&
((?[X]:(tall(X)))<=>((~curious(paul)|~kind(paul))))&
((old(fred))=>(~brave(john)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((~funny(X)|rich(X))))<=>((~brave(lucy)&~calm(lucy))))&
(![X]:((happy(X)<~>~curious(X))=>tall(X)))&
(![X]:((brave(X)&~brave(X))<=>~generous(X)))&
(![X]:((~calm(X)&~curious(X))=>(rich(X)&quiet(X))))&
(curious(paul))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~old(X)|~happy(X)))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not strong or funny is both not tall and creative and vice versa.
Everyone who is both brave and not kind is not generous and vice versa.
If alice is both wise and not happy then alice is quiet or kind.
If fred is curious then someone is both not happy and not brave.
Everyone who is not tall is happy.
Everyone who is either happy or not funny is either rich or not kind and vice versa.
Everyone who is funny is quiet or not curious and vice versa.
Everyone who is not rich is either not happy or rich.
Everyone who is not strong is not strong or generous and vice versa.
If someone is either quiet or not funny then paul is both brave and not humble.
If john is kind or not calm then susan is either happy or not old.
Everyone who is not funny is quiet.
Everyone who is both not rich and humble is both not strong and humble and vice versa.
If paul is both not happy and not generous then fred is both not patient and not happy.
Everyone who is either kind or creative is both brave and not strong.
If john is both creative and happy then alice is old.
Someone is either not tall or not curious.
Someone is not old.
Someone is not kind or not strong.
Someone is old.
Paul is curious.
Alice is not brave or calm. | Fred is not creative. | contradiction | (![X]:((~strong(X)|funny(X))<=>(~tall(X)&creative(X))))&
(![X]:((brave(X)&~kind(X))<=>~generous(X)))&
(((wise(alice)&~happy(alice)))=>((quiet(alice)|kind(alice))))&
((curious(fred))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(~tall(X)=>happy(X)))&
(![X]:((happy(X)<~>~funny(X))<=>(rich(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(~rich(X)=>(~happy(X)<~>rich(X))))&
(![X]:(~strong(X)<=>(~strong(X)|generous(X))))&
((?[X]:((quiet(X)<~>~funny(X))))=>((brave(paul)&~humble(paul))))&
(((kind(john)|~calm(john)))=>((happy(susan)<~>~old(susan))))&
(![X]:(~funny(X)=>quiet(X)))&
(![X]:((~rich(X)&humble(X))<=>(~strong(X)&humble(X))))&
(((~happy(paul)&~generous(paul)))=>((~patient(fred)&~happy(fred))))&
(![X]:((kind(X)<~>creative(X))=>(brave(X)&~strong(X))))&
(((creative(john)&happy(john)))=>(old(alice)))&
(?[X]:((~tall(X)<~>~curious(X))))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:(old(X)))&
(curious(paul))&
((~brave(alice)|calm(alice))) | ~creative(fred) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7777160693637065611376219
% SZS output start Proof for 7777160693637065611376219
1. ! [X0] : ((funny(X0) | ~strong(X0)) <=> (creative(X0) & ~tall(X0))) [input p0]
7. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p6]
12. ! [X0] : (~funny(X0) => quiet(X0)) [input p11]
23. ~creative(fred) [input hypothesis]
33. ! [X0] : (quiet(X0) | funny(X0)) [ennf transformation 12]
39. ! [X0] : (((funny(X0) | ~strong(X0)) | (~creative(X0) | tall(X0))) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & strong(X0)))) [nnf transformation 1]
40. ! [X0] : ((funny(X0) | ~strong(X0) | ~creative(X0) | tall(X0)) & ((creative(X0) & ~tall(X0)) | (~funny(X0) & strong(X0)))) [flattening 39]
46. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 7]
47. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 46]
68. ~funny(X0) | creative(X0) [cnf transformation 40]
85. funny(X0) | ~quiet(X0) [cnf transformation 47]
98. quiet(X0) | funny(X0) [cnf transformation 33]
115. ~creative(fred) [cnf transformation 23]
133. 4 <=> ! [X0] : funny(X0) [avatar definition]
134. funny(X0) <- (4) [avatar component clause 133]
167. funny(X0) [subsumption resolution 98,85]
168. 4 [avatar split clause 167,133]
220. creative(X0) <- (4) [resolution 68,134]
221. $false <- (4) [resolution 220,115]
222. ~4 [avatar contradiction clause 221]
223. $false [avatar sat refutation 168,222]
% SZS output end Proof for 7777160693637065611376219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not patient then alice is both strong and not creative. If someone is not rich or rich then paul is either not kind or not calm. Everyone who is curious or tall is both brave and generous and vice versa. If lucy is both not quiet and not rich then someone is calm. Everyone who is either not patient or not kind is not creative or not patient. If mary is not old then someone is generous. Everyone who is either creative or generous is either not kind or strong and vice versa. Everyone who is either not calm or not old is not curious. Everyone who is either tall or not calm is both not old and not humble. If someone is generous or patient then lucy is either not patient or funny and vice versa. Everyone who is kind or patient is both not kind and creative and vice versa. Everyone who is humble is either not kind or patient. Everyone who is not quiet or not generous is creative and vice versa. If someone is either rich or not calm then someone is both brave and patient and vice versa. If lucy is either creative or not generous then susan is both not brave and creative and vice versa. Everyone who is not strong is either not curious or not brave and vice versa. Someone is not strong. Susan is rich or creative. Someone is both not happy and not humble. Someone is both generous and not funny. Someone is not funny. | Alice is quiet. | entailment | ((?[X]:((~happy(X)<~>~patient(X))))=>((strong(alice)&~creative(alice))))&
((?[X]:((~rich(X)|rich(X))))=>((~kind(paul)<~>~calm(paul))))&
(![X]:((curious(X)|tall(X))<=>(brave(X)&generous(X))))&
(((~quiet(lucy)&~rich(lucy)))=>(?[X]:(calm(X))))&
(![X]:((~patient(X)<~>~kind(X))=>(~creative(X)|~patient(X))))&
((~old(mary))=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>generous(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~calm(X)<~>~old(X))=>~curious(X)))&
(![X]:((tall(X)<~>~calm(X))=>(~old(X)&~humble(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~patient(lucy)<~>funny(lucy))))&
(![X]:((kind(X)|patient(X))<=>(~kind(X)&creative(X))))&
(![X]:(humble(X)=>(~kind(X)<~>patient(X))))&
(![X]:((~quiet(X)|~generous(X))<=>creative(X)))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((brave(X)&patient(X)))))&
(((creative(lucy)<~>~generous(lucy)))<=>((~brave(susan)&creative(susan))))&
(![X]:(~strong(X)<=>(~curious(X)<~>~brave(X))))&
(?[X]:(~strong(X)))&
((rich(susan)|creative(susan)))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:((generous(X)&~funny(X))))&
(?[X]:(~funny(X))) | quiet(alice) | [
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2819835093171218016112978
% SZS output start Proof for 2819835093171218016112978
5. ! [X0] : ((~patient(X0) <~> ~kind(X0)) => (~patient(X0) | ~creative(X0))) [input p4]
11. ! [X0] : ((patient(X0) | kind(X0)) <=> (creative(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> creative(X0)) [input p12]
22. ~quiet(alice) [input hypothesis]
31. ! [X0] : ((~patient(X0) | ~creative(X0)) | (~patient(X0) <=> ~kind(X0))) [ennf transformation 5]
32. ! [X0] : (~patient(X0) | ~creative(X0) | (~patient(X0) <=> ~kind(X0))) [flattening 31]
42. ! [X0] : (~patient(X0) | ~creative(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) [nnf transformation 32]
52. ! [X0] : (((patient(X0) | kind(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (~patient(X0) & ~kind(X0)))) [nnf transformation 11]
53. ! [X0] : ((patient(X0) | kind(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | (~patient(X0) & ~kind(X0)))) [flattening 52]
54. ! [X0] : (((~generous(X0) | ~quiet(X0)) | ~creative(X0)) & (creative(X0) | (generous(X0) & quiet(X0)))) [nnf transformation 13]
55. ! [X0] : ((~generous(X0) | ~quiet(X0) | ~creative(X0)) & (creative(X0) | (generous(X0) & quiet(X0)))) [flattening 54]
87. ~patient(X0) | ~creative(X0) | ~patient(X0) | kind(X0) [cnf transformation 42]
107. ~kind(X0) | ~kind(X0) [cnf transformation 53]
111. patient(X0) | kind(X0) | ~creative(X0) | kind(X0) [cnf transformation 53]
112. quiet(X0) | creative(X0) [cnf transformation 55]
137. ~quiet(alice) [cnf transformation 22]
138. ~kind(X0) [duplicate literal removal 107]
139. patient(X0) | kind(X0) | ~creative(X0) [duplicate literal removal 111]
140. ~patient(X0) | ~creative(X0) | kind(X0) [duplicate literal removal 87]
145. 2 <=> creative(alice) [avatar definition]
146. creative(alice) <- (2) [avatar component clause 145]
227. ~creative(X0) | kind(X0) [subsumption resolution 139,140]
288. creative(alice) [resolution 112,137]
291. 2 [avatar split clause 288,145]
295. kind(alice) <- (2) [resolution 227,146]
298. $false <- (2) [subsumption resolution 295,138]
299. ~2 [avatar contradiction clause 298]
300. $false [avatar sat refutation 291,299]
% SZS output end Proof for 2819835093171218016112978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not brave is both calm and not quiet and vice versa.
Everyone who is either tall or not humble is both not wise and not old and vice versa.
Everyone who is not generous is not creative.
If someone is not brave then someone is both not creative and not curious and vice versa.
If susan is funny or not patient then mary is both not happy and not generous and vice versa.
Everyone who is happy or patient is calm and vice versa.
Everyone who is not rich or brave is old.
Everyone who is quiet or not tall is either humble or not rich and vice versa.
Everyone who is either quiet or tall is both not kind and strong and vice versa.
Everyone who is either kind or old is either tall or not creative and vice versa.
Everyone who is both not humble and wise is both not curious and not old and vice versa.
If fred is kind then someone is either not strong or funny.
If someone is not curious then someone is either rich or not tall and vice versa.
If someone is both not quiet and creative then susan is both not curious and strong.
If paul is not curious then someone is not calm and vice versa.
If susan is not quiet or not kind then lucy is both funny and rich.
Fred is both not quiet and old.
Susan is not kind or happy.
Alice is either not strong or tall.
Lucy is either not rich or humble.
Someone is both not old and tall.
Someone is patient. | Lucy is creative. | neutral | (![X]:((~creative(X)|~brave(X))<=>(calm(X)&~quiet(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(~wise(X)&~old(X))))&
(![X]:(~generous(X)=>~creative(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~creative(X)&~curious(X)))))&
(((funny(susan)|~patient(susan)))<=>((~happy(mary)&~generous(mary))))&
(![X]:((happy(X)|patient(X))<=>calm(X)))&
(![X]:((~rich(X)|brave(X))=>old(X)))&
(![X]:((quiet(X)|~tall(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~kind(X)&strong(X))))&
(![X]:((kind(X)<~>old(X))<=>(tall(X)<~>~creative(X))))&
(![X]:((~humble(X)&wise(X))<=>(~curious(X)&~old(X))))&
((kind(fred))=>(?[X]:((~strong(X)<~>funny(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&creative(X))))=>((~curious(susan)&strong(susan))))&
((~curious(paul))<=>(?[X]:(~calm(X))))&
(((~quiet(susan)|~kind(susan)))=>((funny(lucy)&rich(lucy))))&
((~quiet(fred)&old(fred)))&
((~kind(susan)|happy(susan)))&
((~strong(alice)<~>tall(alice)))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:(patient(X))) | creative(lucy) | [] | null | 0 |
If john is not rich or not tall then someone is either not humble or not funny and vice versa. If someone is not calm or curious then paul is either not rich or generous. Everyone who is both not generous and not rich is both not patient and not strong. If alice is calm or not old then someone is either generous or brave and vice versa. Everyone who is funny is either tall or happy. If someone is either not strong or not patient then mary is not strong or not happy and vice versa. Everyone who is not happy or not old is not funny or not generous. Everyone who is not happy is tall. If john is not generous or not tall then mary is both humble and tall and vice versa. Everyone who is either not brave or humble is strong or not calm. If someone is calm then someone is either tall or not patient. Everyone who is kind is either not happy or strong and vice versa. If fred is not old or not rich then susan is both not curious and wise and vice versa. If someone is old then fred is both not wise and curious and vice versa. Everyone who is both not curious and brave is either rich or strong and vice versa. If john is either not generous or not old then someone is either wise or happy and vice versa. Someone is either not brave or not humble. Someone is either rich or not creative. Someone is both not generous and kind. Alice is not funny or not old. Someone is both not calm and not humble. Someone is kind. Alice is not calm. | Fred is not rich. | neutral | (((~rich(john)|~tall(john)))<=>(?[X]:((~humble(X)<~>~funny(X)))))&
((?[X]:((~calm(X)|curious(X))))=>((~rich(paul)<~>generous(paul))))&
(![X]:((~generous(X)&~rich(X))=>(~patient(X)&~strong(X))))&
(((calm(alice)|~old(alice)))<=>(?[X]:((generous(X)<~>brave(X)))))&
(![X]:(funny(X)=>(tall(X)<~>happy(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((~strong(mary)|~happy(mary))))&
(![X]:((~happy(X)|~old(X))=>(~funny(X)|~generous(X))))&
(![X]:(~happy(X)=>tall(X)))&
(((~generous(john)|~tall(john)))<=>((humble(mary)&tall(mary))))&
(![X]:((~brave(X)<~>humble(X))=>(strong(X)|~calm(X))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
((?[X]:(old(X)))<=>((~wise(fred)&curious(fred))))&
(![X]:((~curious(X)&brave(X))<=>(rich(X)<~>strong(X))))&
(((~generous(john)<~>~old(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~generous(X)&kind(X))))&
((~funny(alice)|~old(alice)))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:(kind(X)))&
(~calm(alice)) | ~rich(fred) | [] | null | 0 |
If someone is not creative or funny then mary is not happy and vice versa. If someone is either not generous or not old then someone is brave or not brave. If someone is not patient or quiet then mary is brave and vice versa. Everyone who is not funny or tall is both not brave and strong and vice versa. If fred is either not calm or not humble then john is not wise and vice versa. If lucy is old then someone is both calm and not wise. If fred is either calm or funny then someone is either not humble or not quiet. Everyone who is calm or not generous is either quiet or wise. Everyone who is not calm or funny is not tall. If someone is patient or not funny then fred is kind and vice versa. If lucy is both rich and curious then someone is either wise or not brave. Everyone who is either rich or happy is both not calm and funny. Everyone who is calm or not patient is not brave and vice versa. Everyone who is patient or humble is either not generous or not quiet and vice versa. Everyone who is either kind or funny is not strong. Everyone who is either not tall or quiet is both not patient and wise. Someone is either not generous or quiet. Alice is both quiet and not generous. Someone is not old or not funny. Someone is both not kind and funny. Someone is both calm and generous. Alice is curious. Someone is not curious or not calm. | Alice is quiet. | entailment | ((?[X]:((~creative(X)|funny(X))))<=>(~happy(mary)))&
((?[X]:((~generous(X)<~>~old(X))))=>(?[X]:((brave(X)|~brave(X)))))&
((?[X]:((~patient(X)|quiet(X))))<=>(brave(mary)))&
(![X]:((~funny(X)|tall(X))<=>(~brave(X)&strong(X))))&
(((~calm(fred)<~>~humble(fred)))<=>(~wise(john)))&
((old(lucy))=>(?[X]:((calm(X)&~wise(X)))))&
(((calm(fred)<~>funny(fred)))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((calm(X)|~generous(X))=>(quiet(X)<~>wise(X))))&
(![X]:((~calm(X)|funny(X))=>~tall(X)))&
((?[X]:((patient(X)|~funny(X))))<=>(kind(fred)))&
(((rich(lucy)&curious(lucy)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((rich(X)<~>happy(X))=>(~calm(X)&funny(X))))&
(![X]:((calm(X)|~patient(X))<=>~brave(X)))&
(![X]:((patient(X)|humble(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>funny(X))=>~strong(X)))&
(![X]:((~tall(X)<~>quiet(X))=>(~patient(X)&wise(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((quiet(alice)&~generous(alice)))&
(?[X]:((~old(X)|~funny(X))))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:((calm(X)&generous(X))))&
(curious(alice))&
(?[X]:((~curious(X)|~calm(X)))) | quiet(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 754644446632723642850894
% SZS output start Proof for 754644446632723642850894
18. ~generous(alice) & quiet(alice) [input p17]
24. ~quiet(alice) [input hypothesis]
137. quiet(alice) [cnf transformation 18]
146. ~quiet(alice) [cnf transformation 24]
303. $false [subsumption resolution 146,137]
% SZS output end Proof for 754644446632723642850894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not humble is not rich or not calm and vice versa. Everyone who is curious or patient is either not funny or not happy. Everyone who is either rich or not strong is either not curious or tall. Everyone who is either not rich or strong is either not funny or not rich and vice versa. If lucy is strong or not brave then susan is either not strong or not happy. If paul is both not kind and not calm then someone is creative and vice versa. Everyone who is wise or generous is rich or creative and vice versa. Everyone who is either not creative or not strong is either calm or not calm. Everyone who is strong or tall is curious or not curious. Everyone who is either not creative or not funny is not happy or generous and vice versa. Everyone who is not tall is either not rich or calm. Everyone who is either wise or not curious is not quiet and vice versa. Everyone who is creative is happy. If alice is humble or curious then someone is funny or not happy. Everyone who is patient or kind is both brave and not old. Everyone who is either not kind or curious is humble or patient. Lucy is either not humble or not tall. Mary is generous. Someone is not strong or not creative. Fred is either not quiet or rich. Someone is wise. Susan is either not generous or calm. | Paul is patient. | neutral | (![X]:((~quiet(X)&~humble(X))<=>(~rich(X)|~calm(X))))&
(![X]:((curious(X)|patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~strong(X))=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~funny(X)<~>~rich(X))))&
(((strong(lucy)|~brave(lucy)))=>((~strong(susan)<~>~happy(susan))))&
(((~kind(paul)&~calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)|generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(![X]:((strong(X)|tall(X))=>(curious(X)|~curious(X))))&
(![X]:((~creative(X)<~>~funny(X))<=>(~happy(X)|generous(X))))&
(![X]:(~tall(X)=>(~rich(X)<~>calm(X))))&
(![X]:((wise(X)<~>~curious(X))<=>~quiet(X)))&
(![X]:(creative(X)=>happy(X)))&
(((humble(alice)|curious(alice)))=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:((patient(X)|kind(X))=>(brave(X)&~old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(humble(X)|patient(X))))&
((~humble(lucy)<~>~tall(lucy)))&
(generous(mary))&
(?[X]:((~strong(X)|~creative(X))))&
((~quiet(fred)<~>rich(fred)))&
(?[X]:(wise(X)))&
((~generous(susan)<~>calm(susan))) | patient(paul) | [] | null | 0 |
If john is not quiet then someone is brave or not curious.
Everyone who is either creative or not old is either not calm or not old and vice versa.
If someone is calm then someone is either not brave or not generous and vice versa.
If alice is old then someone is either not calm or not happy and vice versa.
Everyone who is either tall or old is not tall or kind and vice versa.
If someone is either humble or not kind then someone is not patient or not tall and vice versa.
Everyone who is not calm or not curious is both patient and wise.
If susan is either not strong or not happy then someone is either not wise or not old.
Everyone who is both not generous and creative is either not patient or humble and vice versa.
Everyone who is wise or tall is both patient and not kind and vice versa.
Everyone who is not creative or not kind is not funny or not patient.
If paul is generous then someone is both not happy and not funny and vice versa.
Everyone who is not kind is either creative or wise and vice versa.
If paul is either not funny or not wise then fred is not generous or humble and vice versa.
Everyone who is both not humble and not wise is both not humble and kind and vice versa.
Everyone who is either not strong or funny is not kind.
John is curious or not calm.
Someone is both not kind and patient.
Someone is not patient or not wise.
Fred is brave or not kind.
Someone is either quiet or happy.
Fred is not brave. | Susan is strong. | neutral | ((~quiet(john))=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((creative(X)<~>~old(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((old(alice))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((tall(X)<~>old(X))<=>(~tall(X)|kind(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~calm(X)|~curious(X))=>(patient(X)&wise(X))))&
(((~strong(susan)<~>~happy(susan)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((wise(X)|tall(X))<=>(patient(X)&~kind(X))))&
(![X]:((~creative(X)|~kind(X))=>(~funny(X)|~patient(X))))&
((generous(paul))<=>(?[X]:((~happy(X)&~funny(X)))))&
(![X]:(~kind(X)<=>(creative(X)<~>wise(X))))&
(((~funny(paul)<~>~wise(paul)))<=>((~generous(fred)|humble(fred))))&
(![X]:((~humble(X)&~wise(X))<=>(~humble(X)&kind(X))))&
(![X]:((~strong(X)<~>funny(X))=>~kind(X)))&
((curious(john)|~calm(john)))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((~patient(X)|~wise(X))))&
((brave(fred)|~kind(fred)))&
(?[X]:((quiet(X)<~>happy(X))))&
(~brave(fred)) | strong(susan) | [] | null | 0 |
Everyone who is either humble or calm is not brave and vice versa. If someone is not tall then mary is either calm or not rich and vice versa. Everyone who is generous or not kind is happy or not tall. Everyone who is funny or not generous is both not happy and patient. Everyone who is either kind or not funny is either not calm or strong and vice versa. If someone is both creative and kind then someone is either not wise or not creative. Everyone who is not rich or not old is both old and quiet and vice versa. Everyone who is both not rich and not generous is both not tall and curious and vice versa. If john is either not strong or not generous then someone is rich or happy. Everyone who is both patient and not curious is not strong and vice versa. Everyone who is kind or not curious is calm or funny and vice versa. Everyone who is humble is both not brave and old. If someone is both not tall and not rich then someone is both not wise and not old. If susan is either not happy or kind then susan is generous and vice versa. Everyone who is both wise and humble is either generous or brave and vice versa. Everyone who is either not generous or brave is old. Someone is either not humble or not strong. Fred is both not curious and funny. John is old. Someone is not strong or not curious. Someone is either generous or wise. Lucy is both not happy and not tall. | Fred is not humble. | neutral | (![X]:((humble(X)<~>calm(X))<=>~brave(X)))&
((?[X]:(~tall(X)))<=>((calm(mary)<~>~rich(mary))))&
(![X]:((generous(X)|~kind(X))=>(happy(X)|~tall(X))))&
(![X]:((funny(X)|~generous(X))=>(~happy(X)&patient(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~calm(X)<~>strong(X))))&
((?[X]:((creative(X)&kind(X))))=>(?[X]:((~wise(X)<~>~creative(X)))))&
(![X]:((~rich(X)|~old(X))<=>(old(X)&quiet(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~tall(X)&curious(X))))&
(((~strong(john)<~>~generous(john)))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((patient(X)&~curious(X))<=>~strong(X)))&
(![X]:((kind(X)|~curious(X))<=>(calm(X)|funny(X))))&
(![X]:(humble(X)=>(~brave(X)&old(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((~wise(X)&~old(X)))))&
(((~happy(susan)<~>kind(susan)))<=>(generous(susan)))&
(![X]:((wise(X)&humble(X))<=>(generous(X)<~>brave(X))))&
(![X]:((~generous(X)<~>brave(X))=>old(X)))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~curious(fred)&funny(fred)))&
(old(john))&
(?[X]:((~strong(X)|~curious(X))))&
(?[X]:((generous(X)<~>wise(X))))&
((~happy(lucy)&~tall(lucy))) | ~humble(fred) | [] | null | 0 |
Everyone who is both not brave and old is either not quiet or not creative and vice versa.
Everyone who is creative or not generous is both not curious and not creative and vice versa.
If lucy is either not rich or curious then john is funny.
Everyone who is not tall is both strong and not old and vice versa.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Fred is not generous or not quiet.
Someone is both patient and not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous. | Mary is calm. | neutral | (![X]:((~brave(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((creative(X)|~generous(X))<=>(~curious(X)&~creative(X))))&
(((~rich(lucy)<~>curious(lucy)))=>(funny(john)))&
(![X]:(~tall(X)<=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
((~generous(fred)|~quiet(fred)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X)))) | calm(mary) | [] | null | 0 |
If lucy is both humble and funny then someone is both not creative and not kind.
If john is quiet then paul is creative and vice versa.
If paul is old or rich then someone is not brave or happy.
Everyone who is rich or not curious is both kind and calm and vice versa.
Everyone who is not funny or curious is strong and vice versa.
If alice is either generous or not happy then lucy is rich.
If someone is not rich or not funny then john is both happy and not kind and vice versa.
Everyone who is both not tall and kind is either calm or creative.
If john is both funny and generous then someone is both kind and tall.
Everyone who is curious or not brave is not calm or creative.
Everyone who is not wise is both brave and curious and vice versa.
If someone is not strong or not humble then someone is both quiet and generous and vice versa.
If alice is not quiet or not wise then alice is not calm or generous.
If lucy is not rich then mary is brave or creative and vice versa.
If someone is both not humble and tall then someone is not creative and vice versa.
If lucy is happy then paul is both happy and not rich and vice versa.
Someone is rich.
Alice is not creative.
Someone is not old.
John is either wise or strong.
Someone is calm or tall.
Mary is both wise and calm.
Someone is not strong or brave.
Mary is not tall. | Alice is not generous. | neutral | (((humble(lucy)&funny(lucy)))=>(?[X]:((~creative(X)&~kind(X)))))&
((quiet(john))<=>(creative(paul)))&
(((old(paul)|rich(paul)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((rich(X)|~curious(X))<=>(kind(X)&calm(X))))&
(![X]:((~funny(X)|curious(X))<=>strong(X)))&
(((generous(alice)<~>~happy(alice)))=>(rich(lucy)))&
((?[X]:((~rich(X)|~funny(X))))<=>((happy(john)&~kind(john))))&
(![X]:((~tall(X)&kind(X))=>(calm(X)<~>creative(X))))&
(((funny(john)&generous(john)))=>(?[X]:((kind(X)&tall(X)))))&
(![X]:((curious(X)|~brave(X))=>(~calm(X)|creative(X))))&
(![X]:(~wise(X)<=>(brave(X)&curious(X))))&
((?[X]:((~strong(X)|~humble(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
(((~quiet(alice)|~wise(alice)))=>((~calm(alice)|generous(alice))))&
((~rich(lucy))<=>((brave(mary)|creative(mary))))&
((?[X]:((~humble(X)&tall(X))))<=>(?[X]:(~creative(X))))&
((happy(lucy))<=>((happy(paul)&~rich(paul))))&
(?[X]:(rich(X)))&
(~creative(alice))&
(?[X]:(~old(X)))&
((wise(john)<~>strong(john)))&
(?[X]:((calm(X)|tall(X))))&
((wise(mary)&calm(mary)))&
(?[X]:((~strong(X)|brave(X))))&
(~tall(mary)) | ~generous(alice) | [] | null | 0 |
Everyone who is kind is happy or not tall. If john is both not quiet and humble then susan is funny. Everyone who is both kind and brave is both wise and funny. Everyone who is not happy or patient is patient and vice versa. Everyone who is both not humble and old is not kind. Everyone who is not humble is not creative. If someone is not funny then someone is both not humble and patient. Everyone who is old is either wise or calm and vice versa. Everyone who is not funny is both brave and creative and vice versa. If lucy is both strong and not strong then someone is either not happy or not humble. If someone is kind then susan is tall and vice versa. Everyone who is not tall is either not curious or not funny and vice versa. If lucy is either not old or strong then someone is either not patient or tall and vice versa. Everyone who is either not curious or creative is both not happy and patient and vice versa. Everyone who is both happy and not rich is both kind and happy. If susan is both rich and curious then mary is curious or not brave. Someone is both not funny and not rich. Someone is either not quiet or not old. Someone is not calm. Someone is wise. Alice is either tall or not creative. Paul is both kind and not calm. Someone is generous. Someone is not kind or not brave. | John is not curious. | neutral | (![X]:(kind(X)=>(happy(X)|~tall(X))))&
(((~quiet(john)&humble(john)))=>(funny(susan)))&
(![X]:((kind(X)&brave(X))=>(wise(X)&funny(X))))&
(![X]:((~happy(X)|patient(X))<=>patient(X)))&
(![X]:((~humble(X)&old(X))=>~kind(X)))&
(![X]:(~humble(X)=>~creative(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(old(X)<=>(wise(X)<~>calm(X))))&
(![X]:(~funny(X)<=>(brave(X)&creative(X))))&
(((strong(lucy)&~strong(lucy)))=>(?[X]:((~happy(X)<~>~humble(X)))))&
((?[X]:(kind(X)))<=>(tall(susan)))&
(![X]:(~tall(X)<=>(~curious(X)<~>~funny(X))))&
(((~old(lucy)<~>strong(lucy)))<=>(?[X]:((~patient(X)<~>tall(X)))))&
(![X]:((~curious(X)<~>creative(X))<=>(~happy(X)&patient(X))))&
(![X]:((happy(X)&~rich(X))=>(kind(X)&happy(X))))&
(((rich(susan)&curious(susan)))=>((curious(mary)|~brave(mary))))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((~quiet(X)<~>~old(X))))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
((tall(alice)<~>~creative(alice)))&
((kind(paul)&~calm(paul)))&
(?[X]:(generous(X)))&
(?[X]:((~kind(X)|~brave(X)))) | ~curious(john) | [] | null | 0 |
Everyone who is not rich is both calm and tall.
Everyone who is both old and humble is not funny and vice versa.
Everyone who is either humble or not quiet is both brave and humble and vice versa.
Everyone who is not humble is humble.
Everyone who is curious is both wise and rich.
Everyone who is not rich or not curious is either not calm or not happy.
If fred is either not funny or not curious then mary is rich or not quiet and vice versa.
Everyone who is not humble is not generous or brave.
Everyone who is both rich and not old is either rich or not happy and vice versa.
Everyone who is old or not rich is patient or not funny and vice versa.
If john is calm or not calm then mary is curious and vice versa.
If someone is both rich and not calm then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
Everyone who is not brave or happy is both not generous and not funny and vice versa.
Someone is either brave or rich.
Alice is both not funny and brave.
Mary is not funny.
Lucy is not quiet.
Someone is either wise or not patient.
Susan is not creative or not strong. | Lucy is rich. | entailment | (![X]:(~rich(X)=>(calm(X)&tall(X))))&
(![X]:((old(X)&humble(X))<=>~funny(X)))&
(![X]:((humble(X)<~>~quiet(X))<=>(brave(X)&humble(X))))&
(![X]:(~humble(X)=>humble(X)))&
(![X]:(curious(X)=>(wise(X)&rich(X))))&
(![X]:((~rich(X)|~curious(X))=>(~calm(X)<~>~happy(X))))&
(((~funny(fred)<~>~curious(fred)))<=>((rich(mary)|~quiet(mary))))&
(![X]:(~humble(X)=>(~generous(X)|brave(X))))&
(![X]:((rich(X)&~old(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((old(X)|~rich(X))<=>(patient(X)|~funny(X))))&
(((calm(john)|~calm(john)))<=>(curious(mary)))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(![X]:((~brave(X)|happy(X))<=>(~generous(X)&~funny(X))))&
(?[X]:((brave(X)<~>rich(X))))&
((~funny(alice)&brave(alice)))&
(~funny(mary))&
(~quiet(lucy))&
(?[X]:((wise(X)<~>~patient(X))))&
((~creative(susan)|~strong(susan))) | rich(lucy) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3358794876395192136372497
% SZS output start Proof for 3358794876395192136372497
1. ! [X0] : (~rich(X0) => (tall(X0) & calm(X0))) [input p0]
6. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~calm(X0) <~> ~happy(X0))) [input p5]
9. ! [X0] : ((~old(X0) & rich(X0)) <=> (rich(X0) <~> ~happy(X0))) [input p8]
23. ~rich(lucy) [input hypothesis]
26. ! [X0] : (~rich(X0) => calm(X0)) [pure predicate removal 1]
27. ! [X0] : (calm(X0) | rich(X0)) [ennf transformation 26]
30. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (curious(X0) & rich(X0))) [ennf transformation 6]
37. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | (curious(X0) & rich(X0))) [nnf transformation 30]
40. ! [X0] : (((~old(X0) & rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 9]
41. ! [X0] : (((~old(X0) & rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | old(X0) | ~rich(X0))) [flattening 40]
64. calm(X0) | rich(X0) [cnf transformation 27]
77. ~happy(X0) | ~calm(X0) | rich(X0) [cnf transformation 37]
91. rich(X0) | rich(X0) | happy(X0) [cnf transformation 41]
131. ~rich(lucy) [cnf transformation 23]
133. rich(X0) | happy(X0) [duplicate literal removal 91]
137. ~happy(X0) | rich(X0) [subsumption resolution 77,64]
162. rich(X0) [subsumption resolution 133,137]
201. $false [subsumption resolution 131,162]
% SZS output end Proof for 3358794876395192136372497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or not calm then alice is not rich or strong and vice versa. Everyone who is both not creative and not funny is either wise or funny and vice versa. If paul is not old or brave then someone is not calm and vice versa. If lucy is brave or not rich then mary is either not quiet or generous and vice versa. Everyone who is not wise or not funny is either generous or rich. Everyone who is either not curious or patient is not quiet or tall and vice versa. Everyone who is both not rich and generous is either calm or not happy and vice versa. If someone is not calm then john is quiet and vice versa. Everyone who is not kind or not funny is either not funny or quiet. Everyone who is both not funny and not strong is tall. Everyone who is humble is both not wise and not patient and vice versa. Everyone who is quiet or creative is both not strong and humble and vice versa. Everyone who is either not kind or humble is either generous or strong. Everyone who is either old or not tall is old. Paul is either not tall or calm. Someone is either happy or not humble. Mary is not generous or not funny. Someone is strong. Someone is both not old and not quiet. | Alice is not calm. | contradiction | ((?[X]:((funny(X)|~calm(X))))<=>((~rich(alice)|strong(alice))))&
(![X]:((~creative(X)&~funny(X))<=>(wise(X)<~>funny(X))))&
(((~old(paul)|brave(paul)))<=>(?[X]:(~calm(X))))&
(((brave(lucy)|~rich(lucy)))<=>((~quiet(mary)<~>generous(mary))))&
(![X]:((~wise(X)|~funny(X))=>(generous(X)<~>rich(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~quiet(X)|tall(X))))&
(![X]:((~rich(X)&generous(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:(~calm(X)))<=>(quiet(john)))&
(![X]:((~kind(X)|~funny(X))=>(~funny(X)<~>quiet(X))))&
(![X]:((~funny(X)&~strong(X))=>tall(X)))&
(![X]:(humble(X)<=>(~wise(X)&~patient(X))))&
(![X]:((quiet(X)|creative(X))<=>(~strong(X)&humble(X))))&
(![X]:((~kind(X)<~>humble(X))=>(generous(X)<~>strong(X))))&
(![X]:((old(X)<~>~tall(X))=>old(X)))&
((~tall(paul)<~>calm(paul)))&
(?[X]:((happy(X)<~>~humble(X))))&
((~generous(mary)|~funny(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&~quiet(X)))) | ~calm(alice) | [
"p1",
"p7",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2326344145977149103402193
% SZS output start Proof for 2326344145977149103402193
2. ! [X0] : ((~funny(X0) & ~creative(X0)) <=> (wise(X0) <~> funny(X0))) [input p1]
8. ? [X0] : ~calm(X0) <=> quiet(john) [input p7]
9. ! [X0] : ((~funny(X0) | ~kind(X0)) => (~funny(X0) <~> quiet(X0))) [input p8]
11. ! [X0] : (humble(X0) <=> (~patient(X0) & ~wise(X0))) [input p10]
12. ! [X0] : ((creative(X0) | quiet(X0)) <=> (humble(X0) & ~strong(X0))) [input p11]
20. ~calm(alice) [input hypothesis]
22. ! [X0] : ((~funny(X0) <~> quiet(X0)) | (funny(X0) & kind(X0))) [ennf transformation 9]
32. ! [X0] : (((~funny(X0) & ~creative(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (funny(X0) | creative(X0)))) [nnf transformation 2]
33. ! [X0] : (((~funny(X0) & ~creative(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | funny(X0) | creative(X0))) [flattening 32]
46. (? [X0] : ~calm(X0) | ~quiet(john)) & (quiet(john) | ! [X0] : calm(X0)) [nnf transformation 8]
47. (? [X0] : ~calm(X0) | ~quiet(john)) & (quiet(john) | ! [X1] : calm(X1)) [rectify 46]
48. ? [X0] : ~calm(X0) => ~calm(sK2) [choice axiom]
49. (~calm(sK2) | ~quiet(john)) & (quiet(john) | ! [X1] : calm(X1)) [skolemisation 47,48]
50. ! [X0] : (((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | (funny(X0) & kind(X0))) [nnf transformation 22]
51. ! [X0] : ((humble(X0) | (patient(X0) | wise(X0))) & ((~patient(X0) & ~wise(X0)) | ~humble(X0))) [nnf transformation 11]
52. ! [X0] : ((humble(X0) | patient(X0) | wise(X0)) & ((~patient(X0) & ~wise(X0)) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((creative(X0) | quiet(X0)) | (~humble(X0) | strong(X0))) & ((humble(X0) & ~strong(X0)) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 12]
54. ! [X0] : ((creative(X0) | quiet(X0) | ~humble(X0) | strong(X0)) & ((humble(X0) & ~strong(X0)) | (~creative(X0) & ~quiet(X0)))) [flattening 53]
74. ~funny(X0) | wise(X0) | ~funny(X0) [cnf transformation 33]
100. quiet(john) | calm(X1) [cnf transformation 49]
105. ~quiet(X0) | funny(X0) | funny(X0) [cnf transformation 50]
107. ~humble(X0) | ~wise(X0) [cnf transformation 52]
112. ~quiet(X0) | humble(X0) [cnf transformation 54]
129. ~calm(alice) [cnf transformation 20]
131. ~quiet(X0) | funny(X0) [duplicate literal removal 105]
133. ~funny(X0) | wise(X0) [duplicate literal removal 74]
153. 5 <=> ! [X1] : calm(X1) [avatar definition]
154. calm(X1) <- (5) [avatar component clause 153]
199. 14 <=> quiet(john) [avatar definition]
200. quiet(john) <- (14) [avatar component clause 199]
207. 5 | 14 [avatar split clause 100,199,153]
235. $false <- (5) [resolution 154,129]
236. ~5 [avatar contradiction clause 235]
238. humble(john) <- (14) [resolution 112,200]
240. ~wise(john) <- (14) [resolution 238,107]
245. funny(john) <- (14) [resolution 131,200]
248. wise(john) <- (14) [resolution 133,245]
249. $false <- (14) [subsumption resolution 248,240]
250. ~14 [avatar contradiction clause 249]
251. $false [avatar sat refutation 207,236,250]
% SZS output end Proof for 2326344145977149103402193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not happy or not strong then fred is either not funny or tall and vice versa.
Everyone who is tall or not quiet is both not calm and not funny and vice versa.
If john is curious or not wise then mary is either calm or happy.
Everyone who is either curious or creative is not funny or curious and vice versa.
If alice is not creative or not humble then someone is both happy and not old and vice versa.
If someone is either generous or not generous then someone is either calm or rich and vice versa.
Everyone who is both not creative and not wise is either curious or not tall.
Everyone who is both not curious and not generous is calm and vice versa.
Everyone who is curious or rich is either kind or brave.
Everyone who is both not kind and not generous is creative or rich and vice versa.
If someone is generous or not old then someone is not old and vice versa.
If john is not creative then lucy is either not generous or calm.
If mary is not strong or not wise then someone is either not creative or happy.
Everyone who is creative or old is either not creative or not calm.
If someone is either not creative or tall then paul is both creative and old.
Someone is not curious or quiet.
Someone is not kind.
Susan is either not generous or not wise.
Someone is funny or wise.
Susan is patient. | Susan is not calm. | entailment | (((~happy(lucy)<~>~strong(lucy)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((tall(X)|~quiet(X))<=>(~calm(X)&~funny(X))))&
(((curious(john)|~wise(john)))=>((calm(mary)<~>happy(mary))))&
(![X]:((curious(X)<~>creative(X))<=>(~funny(X)|curious(X))))&
(((~creative(alice)|~humble(alice)))<=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~creative(X)&~wise(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~curious(X)&~generous(X))<=>calm(X)))&
(![X]:((curious(X)|rich(X))=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&~generous(X))<=>(creative(X)|rich(X))))&
((?[X]:((generous(X)|~old(X))))<=>(?[X]:(~old(X))))&
((~creative(john))=>((~generous(lucy)<~>calm(lucy))))&
(((~strong(mary)|~wise(mary)))=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((creative(X)|old(X))=>(~creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>((creative(paul)&old(paul))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:(~kind(X)))&
((~generous(susan)<~>~wise(susan)))&
(?[X]:((funny(X)|wise(X))))&
(patient(susan)) | ~calm(susan) | [
"p1",
"p3",
"p7",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1816360636119735441463656
% SZS output start Proof for 1816360636119735441463656
2. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~funny(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((curious(X0) <~> creative(X0)) <=> (curious(X0) | ~funny(X0))) [input p3]
8. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> calm(X0)) [input p7]
10. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (rich(X0) | creative(X0))) [input p9]
14. ! [X0] : ((old(X0) | creative(X0)) => (~creative(X0) <~> ~calm(X0))) [input p13]
15. ? [X0] : (~creative(X0) <~> tall(X0)) => (old(paul) & creative(paul)) [input p14]
21. calm(susan) [input hypothesis]
31. ! [X0] : ((~creative(X0) <~> ~calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 14]
32. (old(paul) & creative(paul)) | ! [X0] : (~creative(X0) <=> tall(X0)) [ennf transformation 15]
34. ! [X0] : (((~quiet(X0) | tall(X0)) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : ((~quiet(X0) | tall(X0) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 34]
37. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))))) [flattening 37]
50. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) | curious(X0)))) [nnf transformation 8]
51. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | generous(X0) | curious(X0))) [flattening 50]
53. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 10]
54. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | generous(X0) | kind(X0))) [flattening 53]
64. ! [X0] : (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 31]
65. (old(paul) & creative(paul)) | ! [X0] : ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))) [nnf transformation 32]
81. ~calm(X0) | ~tall(X0) [cnf transformation 35]
95. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 38]
111. generous(X0) | calm(X0) | curious(X0) [cnf transformation 51]
121. ~generous(X0) | ~creative(X0) [cnf transformation 54]
132. ~calm(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 64]
136. creative(paul) | tall(X0) | creative(X0) [cnf transformation 65]
145. calm(susan) [cnf transformation 21]
146. ~creative(X0) | ~calm(X0) [duplicate literal removal 132]
152. ~creative(X0) | ~curious(X0) [duplicate literal removal 95]
304. 31 <=> ! [X0] : (tall(X0) | creative(X0)) [avatar definition]
305. creative(X0) | tall(X0) <- (31) [avatar component clause 304]
308. 32 <=> creative(paul) [avatar definition]
310. creative(paul) <- (32) [avatar component clause 308]
312. 31 | 32 [avatar split clause 136,308,304]
341. ~tall(susan) [resolution 81,145]
396. calm(X0) | curious(X0) | ~creative(X0) [resolution 111,121]
400. curious(X0) | ~creative(X0) [subsumption resolution 396,146]
401. ~creative(X0) [subsumption resolution 400,152]
440. $false <- (32) [resolution 401,310]
443. ~32 [avatar contradiction clause 440]
446. tall(X0) <- (31) [subsumption resolution 305,401]
454. $false <- (31) [resolution 446,341]
457. ~31 [avatar contradiction clause 454]
460. $false [avatar sat refutation 312,443,457]
% SZS output end Proof for 1816360636119735441463656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not strong or generous then someone is either not funny or not strong. If paul is not humble or creative then someone is either tall or brave and vice versa. If someone is both not brave and not tall then someone is either not curious or funny. Everyone who is quiet or brave is both not wise and humble and vice versa. Everyone who is generous is either brave or not curious and vice versa. Everyone who is both not rich and not wise is not happy or not calm and vice versa. Everyone who is either not happy or humble is calm or not quiet and vice versa. If susan is both brave and not strong then mary is not quiet or not patient and vice versa. If lucy is not kind or calm then someone is either not old or not kind and vice versa. If lucy is either kind or old then lucy is both not quiet and not calm. If fred is strong or not wise then john is brave and vice versa. If alice is generous then someone is both calm and strong. Everyone who is either not happy or not strong is curious or not curious and vice versa. If fred is not funny or wise then susan is generous or calm and vice versa. If lucy is not funny then lucy is either not patient or funny. Everyone who is not quiet or funny is funny or not calm. Fred is either funny or not calm. Fred is both generous and not tall. Lucy is happy or not humble. Paul is both humble and not curious. Susan is funny. Mary is either curious or happy. Lucy is both not tall and strong. John is both not happy and not patient. | John is patient. | contradiction | (((~strong(paul)|generous(paul)))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(((~humble(paul)|creative(paul)))<=>(?[X]:((tall(X)<~>brave(X)))))&
((?[X]:((~brave(X)&~tall(X))))=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:((quiet(X)|brave(X))<=>(~wise(X)&humble(X))))&
(![X]:(generous(X)<=>(brave(X)<~>~curious(X))))&
(![X]:((~rich(X)&~wise(X))<=>(~happy(X)|~calm(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(calm(X)|~quiet(X))))&
(((brave(susan)&~strong(susan)))<=>((~quiet(mary)|~patient(mary))))&
(((~kind(lucy)|calm(lucy)))<=>(?[X]:((~old(X)<~>~kind(X)))))&
(((kind(lucy)<~>old(lucy)))=>((~quiet(lucy)&~calm(lucy))))&
(((strong(fred)|~wise(fred)))<=>(brave(john)))&
((generous(alice))=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)|~curious(X))))&
(((~funny(fred)|wise(fred)))<=>((generous(susan)|calm(susan))))&
((~funny(lucy))=>((~patient(lucy)<~>funny(lucy))))&
(![X]:((~quiet(X)|funny(X))=>(funny(X)|~calm(X))))&
((funny(fred)<~>~calm(fred)))&
((generous(fred)&~tall(fred)))&
((happy(lucy)|~humble(lucy)))&
((humble(paul)&~curious(paul)))&
(funny(susan))&
((curious(mary)<~>happy(mary)))&
((~tall(lucy)&strong(lucy)))&
((~happy(john)&~patient(john))) | patient(john) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6213618975403847456678914
% SZS output start Proof for 6213618975403847456678914
24. ~patient(john) & ~happy(john) [input p23]
25. patient(john) [input hypothesis]
151. ~patient(john) [cnf transformation 24]
152. patient(john) [cnf transformation 25]
360. $false [subsumption resolution 152,151]
% SZS output end Proof for 6213618975403847456678914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is either calm or generous then someone is both quiet and not wise.
If someone is both not patient and not wise then paul is quiet or wise and vice versa.
If alice is both not curious and old then susan is generous and vice versa.
If someone is either not strong or not creative then someone is both brave and generous and vice versa.
Everyone who is both brave and not curious is happy or not wise and vice versa.
If someone is either curious or happy then someone is both humble and not calm.
If someone is not rich then someone is either not strong or rich and vice versa.
If john is either not funny or happy then someone is rich or not tall.
Everyone who is not rich is curious and vice versa.
Everyone who is both strong and not creative is both not tall and not strong and vice versa.
If mary is tall then someone is both not generous and happy and vice versa.
Everyone who is either calm or not strong is both not wise and not rich and vice versa.
Everyone who is both not quiet and not calm is calm and vice versa.
If someone is both tall and not quiet then someone is both wise and not creative.
If someone is both not generous and not strong then someone is both not tall and not wise.
Everyone who is either quiet or funny is not strong.
Someone is happy or not rich.
Alice is either not funny or happy.
Someone is either not old or patient.
Susan is either curious or not happy.
Someone is not rich or rich.
Paul is kind or tall.
Mary is either generous or happy.
Someone is not brave or tall. | John is not funny. | contradiction | (((calm(paul)<~>generous(paul)))=>(?[X]:((quiet(X)&~wise(X)))))&
((?[X]:((~patient(X)&~wise(X))))<=>((quiet(paul)|wise(paul))))&
(((~curious(alice)&old(alice)))<=>(generous(susan)))&
((?[X]:((~strong(X)<~>~creative(X))))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((brave(X)&~curious(X))<=>(happy(X)|~wise(X))))&
((?[X]:((curious(X)<~>happy(X))))=>(?[X]:((humble(X)&~calm(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(((~funny(john)<~>happy(john)))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(~rich(X)<=>curious(X)))&
(![X]:((strong(X)&~creative(X))<=>(~tall(X)&~strong(X))))&
((tall(mary))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((calm(X)<~>~strong(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~quiet(X)&~calm(X))<=>calm(X)))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((wise(X)&~creative(X)))))&
((?[X]:((~generous(X)&~strong(X))))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((quiet(X)<~>funny(X))=>~strong(X)))&
(?[X]:((happy(X)|~rich(X))))&
((~funny(alice)<~>happy(alice)))&
(?[X]:((~old(X)<~>patient(X))))&
((curious(susan)<~>~happy(susan)))&
(?[X]:((~rich(X)|rich(X))))&
((kind(paul)|tall(paul)))&
((generous(mary)<~>happy(mary)))&
(?[X]:((~brave(X)|tall(X)))) | ~funny(john) | [
"p4",
"p8",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2890416062354800530787078
% SZS output start Proof for 2890416062354800530787078
5. ! [X0] : ((~curious(X0) & brave(X0)) <=> (~wise(X0) | happy(X0))) [input p4]
9. ! [X0] : (~rich(X0) <=> curious(X0)) [input p8]
12. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (~rich(X0) & ~wise(X0))) [input p11]
13. ! [X0] : ((~calm(X0) & ~quiet(X0)) <=> calm(X0)) [input p12]
16. ! [X0] : ((quiet(X0) <~> funny(X0)) => ~strong(X0)) [input p15]
25. ~funny(john) [input hypothesis]
38. ! [X0] : (~strong(X0) | (quiet(X0) <=> funny(X0))) [ennf transformation 16]
54. ! [X0] : (((~curious(X0) & brave(X0)) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | (curious(X0) | ~brave(X0)))) [nnf transformation 5]
55. ! [X0] : (((~curious(X0) & brave(X0)) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | curious(X0) | ~brave(X0))) [flattening 54]
68. ! [X0] : ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))) [nnf transformation 9]
75. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (rich(X0) | wise(X0))) & ((~rich(X0) & ~wise(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 12]
76. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | rich(X0) | wise(X0)) & ((~rich(X0) & ~wise(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [flattening 75]
77. ! [X0] : (((~calm(X0) & ~quiet(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | quiet(X0)))) [nnf transformation 13]
78. ! [X0] : (((~calm(X0) & ~quiet(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | quiet(X0))) [flattening 77]
85. ! [X0] : (~strong(X0) | ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) [nnf transformation 38]
120. ~curious(X0) | wise(X0) [cnf transformation 55]
129. rich(X0) | curious(X0) [cnf transformation 68]
139. ~wise(X0) | calm(X0) | strong(X0) [cnf transformation 76]
141. ~rich(X0) | calm(X0) | strong(X0) [cnf transformation 76]
144. calm(X0) | calm(X0) | quiet(X0) [cnf transformation 78]
146. ~calm(X0) | ~calm(X0) [cnf transformation 78]
151. ~strong(X0) | funny(X0) | ~quiet(X0) [cnf transformation 85]
164. ~funny(john) [cnf transformation 25]
165. calm(X0) | quiet(X0) [duplicate literal removal 144]
166. ~calm(X0) [duplicate literal removal 146]
303. 30 <=> funny(john) [avatar definition]
305. ~funny(john) <- (~30) [avatar component clause 303]
335. quiet(X0) [subsumption resolution 165,166]
349. ~strong(X0) | funny(X0) [subsumption resolution 151,335]
400. ~30 [avatar split clause 164,303]
457. calm(X0) | strong(X0) | curious(X0) [resolution 141,129]
459. strong(X0) | curious(X0) [subsumption resolution 457,166]
526. funny(X2) | curious(X2) [resolution 459,349]
579. curious(john) <- (~30) [resolution 526,305]
599. wise(john) <- (~30) [resolution 579,120]
606. calm(john) | strong(john) <- (~30) [resolution 599,139]
607. strong(john) <- (~30) [subsumption resolution 606,166]
610. funny(john) <- (~30) [resolution 607,349]
612. $false <- (~30) [subsumption resolution 610,305]
613. 30 [avatar contradiction clause 612]
614. $false [avatar sat refutation 400,613]
% SZS output end Proof for 2890416062354800530787078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
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