premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not tall or not calm is rich.
Everyone who is calm is brave and vice versa.
If someone is both not rich and not brave then john is not calm or quiet.
If paul is not generous then paul is not calm and vice versa.
If john is curious then someone is rich.
If someone is strong or brave then mary is either not strong or not curious and vice versa.
If paul is quiet then someone is either not strong or not rich.
If someone is either curious or not old then paul is either brave or generous and vice versa.
If fred is not old or happy then mary is curious or strong and vice versa.
If someone is rich then john is both not funny and not curious.
Everyone who is either not curious or happy is brave or old and vice versa.
If fred is creative or strong then john is either not patient or brave.
Everyone who is kind or not humble is both quiet and not brave and vice versa.
If someone is either strong or not curious then someone is either not tall or not humble and vice versa.
Everyone who is generous is either old or not happy and vice versa.
Paul is humble.
Mary is brave or wise.
John is humble or happy.
Someone is not happy.
Someone is either not generous or not happy.
Mary is both strong and not tall. | Paul is not happy. | entailment | (![X]:((~tall(X)|~calm(X))=>rich(X)))&
(![X]:(calm(X)<=>brave(X)))&
((?[X]:((~rich(X)&~brave(X))))=>((~calm(john)|quiet(john))))&
((~generous(paul))<=>(~calm(paul)))&
((curious(john))=>(?[X]:(rich(X))))&
((?[X]:((strong(X)|brave(X))))<=>((~strong(mary)<~>~curious(mary))))&
((quiet(paul))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((curious(X)<~>~old(X))))<=>((brave(paul)<~>generous(paul))))&
(((~old(fred)|happy(fred)))<=>((curious(mary)|strong(mary))))&
((?[X]:(rich(X)))=>((~funny(john)&~curious(john))))&
(![X]:((~curious(X)<~>happy(X))<=>(brave(X)|old(X))))&
(((creative(fred)|strong(fred)))=>((~patient(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~happy(X))))&
(humble(paul))&
((brave(mary)|wise(mary)))&
((humble(john)|happy(john)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((strong(mary)&~tall(mary))) | ~happy(paul) | [
"p1",
"p3",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8456531112978016355467328
% SZS output start Proof for 8456531112978016355467328
2. ! [X0] : (calm(X0) <=> brave(X0)) [input p1]
4. ~generous(paul) <=> ~calm(paul) [input p3]
8. ? [X0] : (curious(X0) <~> ~old(X0)) <=> (brave(paul) <~> generous(paul)) [input p7]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (old(X0) | brave(X0))) [input p10]
15. ! [X0] : (generous(X0) <=> (old(X0) <~> ~happy(X0))) [input p14]
22. happy(paul) [input hypothesis]
34. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 2]
35. (~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul)) [nnf transformation 4]
45. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 8]
46. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [rectify 45]
47. ? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) => ((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) [choice axiom]
48. (((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [skolemisation 46,47]
51. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 51]
61. ! [X0] : ((generous(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~generous(X0))) [nnf transformation 15]
69. ~calm(X0) | brave(X0) [cnf transformation 34]
70. ~brave(X0) | calm(X0) [cnf transformation 34]
72. ~calm(paul) | generous(paul) [cnf transformation 35]
73. ~generous(paul) | calm(paul) [cnf transformation 35]
83. generous(paul) | brave(paul) | ~old(X1) | ~curious(X1) [cnf transformation 48]
84. generous(paul) | brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
85. ~generous(paul) | ~brave(paul) | ~old(X1) | ~curious(X1) [cnf transformation 48]
97. ~happy(X0) | brave(X0) | ~curious(X0) | old(X0) [cnf transformation 52]
101. ~happy(X0) | curious(X0) | ~old(X0) [cnf transformation 52]
117. ~happy(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
128. happy(paul) [cnf transformation 22]
142. 4 <=> calm(paul) [avatar definition]
143. ~calm(paul) <- (~4) [avatar component clause 142]
144. calm(paul) <- (4) [avatar component clause 142]
146. 5 <=> generous(paul) [avatar definition]
149. 4 | ~5 [avatar split clause 73,146,142]
150. 5 | ~4 [avatar split clause 72,142,146]
203. 17 <=> brave(paul) [avatar definition]
204. ~brave(paul) <- (~17) [avatar component clause 203]
205. brave(paul) <- (17) [avatar component clause 203]
219. 20 <=> ! [X1] : (curious(X1) | old(X1)) [avatar definition]
220. old(X1) | curious(X1) <- (20) [avatar component clause 219]
223. 21 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
224. ~old(X1) | ~curious(X1) <- (21) [avatar component clause 223]
225. 21 | ~17 | ~5 [avatar split clause 85,146,203,223]
226. 20 | 17 | 5 [avatar split clause 84,146,203,219]
227. 21 | 17 | 5 [avatar split clause 83,146,203,223]
314. brave(paul) <- (4) [resolution 69,144]
315. $false <- (4, ~17) [subsumption resolution 314,204]
316. ~4 | 17 [avatar contradiction clause 315]
317. calm(paul) <- (17) [resolution 70,205]
318. $false <- (~4, 17) [subsumption resolution 317,143]
319. 4 | ~17 [avatar contradiction clause 318]
345. curious(paul) | ~old(paul) [resolution 101,128]
346. ~old(paul) <- (21) [subsumption resolution 345,224]
347. old(paul) | ~generous(paul) [resolution 117,128]
348. curious(paul) <- (20, 21) [resolution 346,220]
378. brave(paul) | ~curious(paul) | old(paul) [resolution 97,128]
388. ~generous(paul) <- (21) [subsumption resolution 347,346]
389. ~5 | ~21 [avatar split clause 388,223,146]
390. brave(paul) | old(paul) <- (20, 21) [subsumption resolution 378,348]
391. brave(paul) <- (20, 21) [subsumption resolution 390,346]
392. 17 | ~20 | ~21 [avatar split clause 391,223,219,203]
393. $false [avatar sat refutation 149,150,225,226,227,316,319,389,392]
% SZS output end Proof for 8456531112978016355467328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either strong or curious then alice is patient or not curious.
Everyone who is either strong or creative is not calm or not brave and vice versa.
Everyone who is generous or not brave is rich or not brave and vice versa.
If someone is not calm or generous then someone is not wise or wise and vice versa.
Everyone who is both brave and not strong is either not happy or not humble.
Everyone who is creative is not rich or not generous and vice versa.
If alice is either not patient or tall then someone is either not tall or brave.
If alice is not strong then someone is both not creative and strong and vice versa.
Everyone who is both humble and curious is old or not kind.
Everyone who is either funny or not generous is generous.
Everyone who is happy or creative is not rich or rich.
Everyone who is not funny or not kind is not kind or kind and vice versa.
If someone is either not tall or not brave then someone is not wise or creative.
Everyone who is both not kind and not wise is not strong.
Everyone who is rich or brave is calm.
If susan is not rich then someone is either brave or not tall and vice versa.
Paul is both not creative and quiet.
Someone is either not brave or not strong.
Someone is both not old and not tall.
Someone is humble.
Mary is wise.
Someone is not tall or old.
Fred is wise. | Paul is not creative. | entailment | ((?[X]:((strong(X)<~>curious(X))))=>((patient(alice)|~curious(alice))))&
(![X]:((strong(X)<~>creative(X))<=>(~calm(X)|~brave(X))))&
(![X]:((generous(X)|~brave(X))<=>(rich(X)|~brave(X))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:((~wise(X)|wise(X)))))&
(![X]:((brave(X)&~strong(X))=>(~happy(X)<~>~humble(X))))&
(![X]:(creative(X)<=>(~rich(X)|~generous(X))))&
(((~patient(alice)<~>tall(alice)))=>(?[X]:((~tall(X)<~>brave(X)))))&
((~strong(alice))<=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((humble(X)&curious(X))=>(old(X)|~kind(X))))&
(![X]:((funny(X)<~>~generous(X))=>generous(X)))&
(![X]:((happy(X)|creative(X))=>(~rich(X)|rich(X))))&
(![X]:((~funny(X)|~kind(X))<=>(~kind(X)|kind(X))))&
((?[X]:((~tall(X)<~>~brave(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((~kind(X)&~wise(X))=>~strong(X)))&
(![X]:((rich(X)|brave(X))=>calm(X)))&
((~rich(susan))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((~creative(paul)&quiet(paul)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:(humble(X)))&
(wise(mary))&
(?[X]:((~tall(X)|old(X))))&
(wise(fred)) | ~creative(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1908015571353838797130288
% SZS output start Proof for 1908015571353838797130288
17. quiet(paul) & ~creative(paul) [input p16]
24. creative(paul) [input hypothesis]
27. ~creative(paul) [pure predicate removal 17]
128. ~creative(paul) [cnf transformation 27]
137. creative(paul) [cnf transformation 24]
264. $false [subsumption resolution 137,128]
% SZS output end Proof for 1908015571353838797130288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both happy and curious then paul is not humble and vice versa.
If someone is both not patient and not humble then someone is not funny and vice versa.
If someone is both kind and humble then fred is not strong and vice versa.
Everyone who is both not strong and not wise is both not patient and not happy.
If susan is either happy or generous then someone is both not rich and generous.
If someone is either not wise or not happy then someone is both funny and not calm and vice versa.
Everyone who is both quiet and rich is happy.
Everyone who is both not brave and quiet is not tall or humble and vice versa.
Everyone who is not rich is both old and not happy and vice versa.
If alice is either tall or funny then john is either tall or patient.
If paul is either not funny or tall then someone is both funny and not patient and vice versa.
If fred is not curious or not rich then paul is both brave and rich and vice versa.
If someone is both not humble and not wise then someone is tall and vice versa.
Everyone who is both creative and not rich is either not happy or rich and vice versa.
If paul is curious or strong then lucy is either not rich or quiet and vice versa.
Everyone who is both humble and funny is both not patient and not calm and vice versa.
Susan is not funny.
Lucy is curious.
Someone is both not creative and not funny.
Someone is either tall or not humble.
Paul is both not strong and not kind.
Someone is both funny and not happy.
Lucy is strong or humble.
Paul is either strong or curious. | Alice is not curious. | neutral | (((happy(paul)&curious(paul)))<=>(~humble(paul)))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((kind(X)&humble(X))))<=>(~strong(fred)))&
(![X]:((~strong(X)&~wise(X))=>(~patient(X)&~happy(X))))&
(((happy(susan)<~>generous(susan)))=>(?[X]:((~rich(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:((quiet(X)&rich(X))=>happy(X)))&
(![X]:((~brave(X)&quiet(X))<=>(~tall(X)|humble(X))))&
(![X]:(~rich(X)<=>(old(X)&~happy(X))))&
(((tall(alice)<~>funny(alice)))=>((tall(john)<~>patient(john))))&
(((~funny(paul)<~>tall(paul)))<=>(?[X]:((funny(X)&~patient(X)))))&
(((~curious(fred)|~rich(fred)))<=>((brave(paul)&rich(paul))))&
((?[X]:((~humble(X)&~wise(X))))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)<~>rich(X))))&
(((curious(paul)|strong(paul)))<=>((~rich(lucy)<~>quiet(lucy))))&
(![X]:((humble(X)&funny(X))<=>(~patient(X)&~calm(X))))&
(~funny(susan))&
(curious(lucy))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((tall(X)<~>~humble(X))))&
((~strong(paul)&~kind(paul)))&
(?[X]:((funny(X)&~happy(X))))&
((strong(lucy)|humble(lucy)))&
((strong(paul)<~>curious(paul))) | ~curious(alice) | [] | null | 0 |
If fred is either not kind or rich then fred is both not curious and not generous and vice versa.
If someone is either not strong or not old then someone is both not generous and not rich.
Everyone who is not quiet or not brave is tall and vice versa.
Everyone who is both not tall and curious is either not patient or happy and vice versa.
Everyone who is both not rich and not old is old and vice versa.
Everyone who is not patient or not calm is either not happy or not quiet and vice versa.
If someone is both not brave and wise then john is either curious or tall.
If fred is either old or happy then lucy is either curious or not quiet and vice versa.
Everyone who is either rich or happy is humble or quiet and vice versa.
Everyone who is not funny is either kind or not happy.
Everyone who is not curious is curious or not strong and vice versa.
If someone is creative or calm then someone is both wise and not calm and vice versa.
Everyone who is kind or not humble is either not old or not curious and vice versa.
If paul is not old then lucy is either creative or not rich.
Everyone who is humble or not generous is either happy or creative and vice versa.
Someone is wise or quiet.
Paul is humble.
Someone is not funny or funny.
Someone is either not tall or not patient.
Paul is either not rich or rich.
Alice is kind or not strong.
Susan is patient. | John is patient. | entailment | (((~kind(fred)<~>rich(fred)))<=>((~curious(fred)&~generous(fred))))&
((?[X]:((~strong(X)<~>~old(X))))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>tall(X)))&
(![X]:((~tall(X)&curious(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~rich(X)&~old(X))<=>old(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~happy(X)<~>~quiet(X))))&
((?[X]:((~brave(X)&wise(X))))=>((curious(john)<~>tall(john))))&
(((old(fred)<~>happy(fred)))<=>((curious(lucy)<~>~quiet(lucy))))&
(![X]:((rich(X)<~>happy(X))<=>(humble(X)|quiet(X))))&
(![X]:(~funny(X)=>(kind(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(curious(X)|~strong(X))))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((kind(X)|~humble(X))<=>(~old(X)<~>~curious(X))))&
((~old(paul))=>((creative(lucy)<~>~rich(lucy))))&
(![X]:((humble(X)|~generous(X))<=>(happy(X)<~>creative(X))))&
(?[X]:((wise(X)|quiet(X))))&
(humble(paul))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~rich(paul)<~>rich(paul)))&
((kind(alice)|~strong(alice)))&
(patient(susan)) | patient(john) | [
"p3",
"p4",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3947943789952860732131642
% SZS output start Proof for 3947943789952860732131642
4. ! [X0] : ((curious(X0) & ~tall(X0)) <=> (~patient(X0) <~> happy(X0))) [input p3]
5. ! [X0] : ((~old(X0) & ~rich(X0)) <=> old(X0)) [input p4]
9. ! [X0] : ((rich(X0) <~> happy(X0)) <=> (quiet(X0) | humble(X0))) [input p8]
11. ! [X0] : (~curious(X0) <=> (~strong(X0) | curious(X0))) [input p10]
13. ! [X0] : ((~humble(X0) | kind(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p12]
23. ~patient(john) [input hypothesis]
38. ! [X0] : (((curious(X0) & ~tall(X0)) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0)))) & (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | (~curious(X0) | tall(X0)))) [nnf transformation 4]
39. ! [X0] : (((curious(X0) & ~tall(X0)) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0)))) & (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ~curious(X0) | tall(X0))) [flattening 38]
40. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (old(X0) | rich(X0)))) [nnf transformation 5]
41. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | old(X0) | rich(X0))) [flattening 40]
46. ! [X0] : ((((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))))) [flattening 46]
49. ! [X0] : ((~curious(X0) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | curious(X0))) [nnf transformation 11]
50. ! [X0] : ((~curious(X0) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | curious(X0))) [flattening 49]
56. ! [X0] : (((~humble(X0) | kind(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [nnf transformation 13]
57. ! [X0] : ((~humble(X0) | kind(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [flattening 56]
86. happy(X0) | curious(X0) | patient(X0) [cnf transformation 39]
88. old(X0) | old(X0) | rich(X0) [cnf transformation 41]
90. ~old(X0) | ~old(X0) [cnf transformation 41]
111. ~happy(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 47]
116. ~curious(X0) | ~curious(X0) [cnf transformation 50]
126. curious(X0) | old(X0) | humble(X0) [cnf transformation 57]
146. ~patient(john) [cnf transformation 23]
148. ~curious(X0) [duplicate literal removal 116]
149. old(X0) | rich(X0) [duplicate literal removal 88]
150. ~old(X0) [duplicate literal removal 90]
191. rich(X0) [subsumption resolution 149,150]
226. ~humble(X0) | ~happy(X0) [subsumption resolution 111,191]
259. old(X0) | humble(X0) [subsumption resolution 126,148]
260. humble(X0) [subsumption resolution 259,150]
300. ~happy(X0) [resolution 226,260]
328. curious(X1) | patient(X1) [resolution 86,300]
331. patient(X1) [subsumption resolution 328,148]
334. $false [resolution 331,146]
% SZS output end Proof for 3947943789952860732131642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or brave and vice versa. Everyone who is not patient is not strong or not wise and vice versa. If paul is either not quiet or not strong then someone is both not kind and happy. Everyone who is not funny or old is either happy or not happy. If someone is not creative or not humble then john is either not funny or rich. If fred is not funny then susan is not humble or not wise and vice versa. Everyone who is creative or not rich is both not kind and not humble. If john is either wise or not tall then someone is either kind or not creative. If paul is not curious then someone is either not calm or wise. If someone is not quiet or not patient then someone is both wise and not happy and vice versa. Everyone who is both not calm and not patient is either not happy or not generous and vice versa. Everyone who is funny or not rich is not old or strong and vice versa. Everyone who is either not old or strong is strong. Everyone who is strong or happy is kind. Everyone who is either rich or not calm is either not rich or old and vice versa. Everyone who is either not strong or generous is humble and vice versa. Lucy is not kind. Someone is either generous or tall. Someone is both rich and curious. Someone is wise or not old. Mary is calm or not tall. Someone is calm or creative. Paul is not quiet or not strong. | Fred is not tall. | neutral | (![X]:(~kind(X)<=>(~calm(X)<~>brave(X))))&
(![X]:(~patient(X)<=>(~strong(X)|~wise(X))))&
(((~quiet(paul)<~>~strong(paul)))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((~funny(X)|old(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((~funny(john)<~>rich(john))))&
((~funny(fred))<=>((~humble(susan)|~wise(susan))))&
(![X]:((creative(X)|~rich(X))=>(~kind(X)&~humble(X))))&
(((wise(john)<~>~tall(john)))=>(?[X]:((kind(X)<~>~creative(X)))))&
((~curious(paul))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:((~quiet(X)|~patient(X))))<=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~calm(X)&~patient(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((funny(X)|~rich(X))<=>(~old(X)|strong(X))))&
(![X]:((~old(X)<~>strong(X))=>strong(X)))&
(![X]:((strong(X)|happy(X))=>kind(X)))&
(![X]:((rich(X)<~>~calm(X))<=>(~rich(X)<~>old(X))))&
(![X]:((~strong(X)<~>generous(X))<=>humble(X)))&
(~kind(lucy))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((calm(mary)|~tall(mary)))&
(?[X]:((calm(X)|creative(X))))&
((~quiet(paul)|~strong(paul))) | ~tall(fred) | [] | null | 0 |
If someone is either happy or not brave then susan is either not generous or generous.
Everyone who is both not wise and tall is either kind or old and vice versa.
If someone is kind then someone is not rich or strong.
If someone is rich or not patient then lucy is brave and vice versa.
Everyone who is both not brave and not calm is both humble and not funny and vice versa.
Everyone who is not creative is both not happy and quiet and vice versa.
Everyone who is either not quiet or not calm is both not funny and not generous and vice versa.
If susan is not calm or strong then someone is calm.
If someone is both generous and not generous then fred is not strong.
If mary is old or calm then mary is both not creative and patient and vice versa.
Everyone who is both not creative and quiet is happy and vice versa.
Everyone who is brave is either humble or wise and vice versa.
If susan is either not strong or rich then someone is either not humble or creative.
Everyone who is not patient or rich is patient and vice versa.
Everyone who is both not funny and not humble is either creative or not kind and vice versa.
Paul is funny.
Lucy is both not happy and generous.
Alice is not brave or not curious.
Someone is quiet or brave.
Someone is either quiet or curious.
Someone is not old. | Alice is strong. | neutral | ((?[X]:((happy(X)<~>~brave(X))))=>((~generous(susan)<~>generous(susan))))&
(![X]:((~wise(X)&tall(X))<=>(kind(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~rich(X)|strong(X)))))&
((?[X]:((rich(X)|~patient(X))))<=>(brave(lucy)))&
(![X]:((~brave(X)&~calm(X))<=>(humble(X)&~funny(X))))&
(![X]:(~creative(X)<=>(~happy(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~funny(X)&~generous(X))))&
(((~calm(susan)|strong(susan)))=>(?[X]:(calm(X))))&
((?[X]:((generous(X)&~generous(X))))=>(~strong(fred)))&
(((old(mary)|calm(mary)))<=>((~creative(mary)&patient(mary))))&
(![X]:((~creative(X)&quiet(X))<=>happy(X)))&
(![X]:(brave(X)<=>(humble(X)<~>wise(X))))&
(((~strong(susan)<~>rich(susan)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((~patient(X)|rich(X))<=>patient(X)))&
(![X]:((~funny(X)&~humble(X))<=>(creative(X)<~>~kind(X))))&
(funny(paul))&
((~happy(lucy)&generous(lucy)))&
((~brave(alice)|~curious(alice)))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:(~old(X))) | strong(alice) | [] | null | 0 |
Everyone who is either not strong or old is both patient and generous and vice versa.
Everyone who is either strong or not rich is generous or brave.
Everyone who is patient is either not strong or quiet and vice versa.
If john is strong or wise then someone is old or not patient and vice versa.
If mary is not wise then mary is not humble and vice versa.
Everyone who is not wise is either not tall or not humble.
Everyone who is both not old and not brave is creative or not tall and vice versa.
Everyone who is strong or creative is both not quiet and funny.
Everyone who is both not patient and not creative is not wise.
If someone is humble or not generous then susan is wise or not calm.
Everyone who is creative is both generous and not patient.
Everyone who is either funny or curious is not creative or not kind and vice versa.
If someone is rich or not strong then john is both strong and not funny and vice versa.
If lucy is old or rich then fred is both tall and brave and vice versa.
If lucy is calm or tall then someone is both strong and brave and vice versa.
Everyone who is not kind or not curious is both kind and not happy and vice versa.
Lucy is not old.
Someone is either happy or not funny.
Someone is either quiet or not old.
Someone is not strong or not tall.
Someone is not quiet or not kind. | John is not wise. | neutral | (![X]:((~strong(X)<~>old(X))<=>(patient(X)&generous(X))))&
(![X]:((strong(X)<~>~rich(X))=>(generous(X)|brave(X))))&
(![X]:(patient(X)<=>(~strong(X)<~>quiet(X))))&
(((strong(john)|wise(john)))<=>(?[X]:((old(X)|~patient(X)))))&
((~wise(mary))<=>(~humble(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~humble(X))))&
(![X]:((~old(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(![X]:((strong(X)|creative(X))=>(~quiet(X)&funny(X))))&
(![X]:((~patient(X)&~creative(X))=>~wise(X)))&
((?[X]:((humble(X)|~generous(X))))=>((wise(susan)|~calm(susan))))&
(![X]:(creative(X)=>(generous(X)&~patient(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((rich(X)|~strong(X))))<=>((strong(john)&~funny(john))))&
(((old(lucy)|rich(lucy)))<=>((tall(fred)&brave(fred))))&
(((calm(lucy)|tall(lucy)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(kind(X)&~happy(X))))&
(~old(lucy))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((~quiet(X)|~kind(X)))) | ~wise(john) | [] | null | 0 |
If someone is quiet or old then mary is not rich or not humble. Everyone who is both not kind and funny is strong or happy and vice versa. If someone is both not tall and not patient then someone is not strong and vice versa. Everyone who is either kind or not brave is not old and vice versa. Everyone who is generous or not generous is not rich. If susan is both patient and happy then susan is not rich and vice versa. Everyone who is both not generous and rich is either not calm or rich. Everyone who is not quiet or not humble is strong. Everyone who is not funny or not rich is both not old and happy and vice versa. Everyone who is either strong or not tall is both strong and not curious. Everyone who is either not generous or old is not patient. If susan is either not curious or not kind then fred is strong and vice versa. Everyone who is either not brave or creative is both generous and not curious. If lucy is not patient then lucy is both strong and not patient and vice versa. Everyone who is either quiet or not curious is funny and vice versa. Lucy is not generous. John is either not humble or kind. Someone is both wise and calm. Someone is not quiet or strong. Someone is not humble or curious. Someone is either quiet or wise. | Susan is not funny. | contradiction | ((?[X]:((quiet(X)|old(X))))=>((~rich(mary)|~humble(mary))))&
(![X]:((~kind(X)&funny(X))<=>(strong(X)|happy(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~strong(X))))&
(![X]:((kind(X)<~>~brave(X))<=>~old(X)))&
(![X]:((generous(X)|~generous(X))=>~rich(X)))&
(((patient(susan)&happy(susan)))<=>(~rich(susan)))&
(![X]:((~generous(X)&rich(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>strong(X)))&
(![X]:((~funny(X)|~rich(X))<=>(~old(X)&happy(X))))&
(![X]:((strong(X)<~>~tall(X))=>(strong(X)&~curious(X))))&
(![X]:((~generous(X)<~>old(X))=>~patient(X)))&
(((~curious(susan)<~>~kind(susan)))<=>(strong(fred)))&
(![X]:((~brave(X)<~>creative(X))=>(generous(X)&~curious(X))))&
((~patient(lucy))<=>((strong(lucy)&~patient(lucy))))&
(![X]:((quiet(X)<~>~curious(X))<=>funny(X)))&
(~generous(lucy))&
((~humble(john)<~>kind(john)))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:((quiet(X)<~>wise(X)))) | ~funny(susan) | [
"p1",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5740051530623145715634413
% SZS output start Proof for 5740051530623145715634413
2. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (happy(X0) | strong(X0))) [input p1]
5. ! [X0] : ((~generous(X0) | generous(X0)) => ~rich(X0)) [input p4]
6. (happy(susan) & patient(susan)) <=> ~rich(susan) [input p5]
22. ~funny(susan) [input hypothesis]
26. ! [X0] : (~rich(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 5]
33. ! [X0] : (((funny(X0) & ~kind(X0)) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | (~funny(X0) | kind(X0)))) [nnf transformation 2]
34. ! [X0] : (((funny(X0) & ~kind(X0)) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | ~funny(X0) | kind(X0))) [flattening 33]
41. ((happy(susan) & patient(susan)) | rich(susan)) & (~rich(susan) | (~happy(susan) | ~patient(susan))) [nnf transformation 6]
42. ((happy(susan) & patient(susan)) | rich(susan)) & (~rich(susan) | ~happy(susan) | ~patient(susan)) [flattening 41]
69. ~happy(X0) | funny(X0) [cnf transformation 34]
77. ~rich(X0) | ~generous(X0) [cnf transformation 26]
78. ~rich(X0) | generous(X0) [cnf transformation 26]
81. happy(susan) | rich(susan) [cnf transformation 42]
121. ~funny(susan) [cnf transformation 22]
161. ~rich(X0) [subsumption resolution 77,78]
162. happy(susan) [subsumption resolution 81,161]
226. funny(susan) [resolution 69,162]
228. $false [subsumption resolution 226,121]
% SZS output end Proof for 5740051530623145715634413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not creative is not rich and vice versa.
If lucy is either happy or generous then someone is patient or not curious.
Everyone who is strong or tall is old.
If lucy is either not funny or kind then fred is calm and vice versa.
Everyone who is both calm and happy is either not old or not quiet.
Everyone who is not patient or tall is either not old or not rich and vice versa.
Everyone who is not old is strong and vice versa.
If mary is either not happy or not wise then someone is not tall and vice versa.
Everyone who is either not creative or old is generous or brave.
Everyone who is funny or not creative is both generous and quiet.
If susan is both brave and generous then fred is not curious or tall and vice versa.
If john is not patient or creative then mary is both strong and curious and vice versa.
If mary is both not patient and rich then susan is either not kind or not tall.
Everyone who is either not brave or not curious is humble.
If paul is humble or not happy then alice is rich or not kind.
Everyone who is not tall is either not happy or not patient and vice versa.
Alice is funny.
Paul is both not kind and not brave.
Someone is wise or happy.
Someone is either old or not happy.
Alice is either generous or rich. | John is patient. | entailment | (![X]:((~patient(X)&~creative(X))<=>~rich(X)))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:((strong(X)|tall(X))=>old(X)))&
(((~funny(lucy)<~>kind(lucy)))<=>(calm(fred)))&
(![X]:((calm(X)&happy(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(~old(X)<=>strong(X)))&
(((~happy(mary)<~>~wise(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)<~>old(X))=>(generous(X)|brave(X))))&
(![X]:((funny(X)|~creative(X))=>(generous(X)&quiet(X))))&
(((brave(susan)&generous(susan)))<=>((~curious(fred)|tall(fred))))&
(((~patient(john)|creative(john)))<=>((strong(mary)&curious(mary))))&
(((~patient(mary)&rich(mary)))=>((~kind(susan)<~>~tall(susan))))&
(![X]:((~brave(X)<~>~curious(X))=>humble(X)))&
(((humble(paul)|~happy(paul)))=>((rich(alice)|~kind(alice))))&
(![X]:(~tall(X)<=>(~happy(X)<~>~patient(X))))&
(funny(alice))&
((~kind(paul)&~brave(paul)))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:((old(X)<~>~happy(X))))&
((generous(alice)<~>rich(alice))) | patient(john) | [
"p2",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2619383201762522962291871
% SZS output start Proof for 2619383201762522962291871
3. ! [X0] : ((tall(X0) | strong(X0)) => old(X0)) [input p2]
7. ! [X0] : (~old(X0) <=> strong(X0)) [input p6]
12. (creative(john) | ~patient(john)) <=> (curious(mary) & strong(mary)) [input p11]
22. ~patient(john) [input hypothesis]
24. ! [X0] : (old(X0) | (~tall(X0) & ~strong(X0))) [ennf transformation 3]
44. ! [X0] : ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))) [nnf transformation 7]
52. ((creative(john) | ~patient(john)) | (~curious(mary) | ~strong(mary))) & ((curious(mary) & strong(mary)) | (~creative(john) & patient(john))) [nnf transformation 12]
53. (creative(john) | ~patient(john) | ~curious(mary) | ~strong(mary)) & ((curious(mary) & strong(mary)) | (~creative(john) & patient(john))) [flattening 52]
68. old(X0) | ~strong(X0) [cnf transformation 24]
83. ~old(X0) | ~strong(X0) [cnf transformation 44]
99. strong(mary) | patient(john) [cnf transformation 53]
122. ~patient(john) [cnf transformation 22]
161. ~strong(X0) [subsumption resolution 83,68]
214. 18 <=> patient(john) [avatar definition]
220. patient(john) [subsumption resolution 99,161]
221. 18 [avatar split clause 220,214]
274. ~18 [avatar split clause 122,214]
275. $false [avatar sat refutation 221,274]
% SZS output end Proof for 2619383201762522962291871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both creative and not generous then lucy is either happy or not generous and vice versa.
If someone is both rich and not generous then someone is not strong.
Everyone who is not wise or rich is either not old or not brave and vice versa.
If someone is both not brave and tall then lucy is rich or not strong.
Everyone who is not curious is not brave or not kind.
Everyone who is calm or tall is either funny or not humble and vice versa.
If someone is either not happy or not generous then fred is creative and vice versa.
Everyone who is not humble or not happy is either kind or not old.
If someone is rich or not strong then someone is not funny and vice versa.
Everyone who is quiet or not creative is either not calm or humble and vice versa.
If john is happy or kind then someone is either happy or not strong.
Everyone who is either kind or not happy is both generous and wise and vice versa.
Everyone who is both not quiet and not old is both strong and not curious and vice versa.
If fred is humble or tall then someone is both happy and not generous.
Everyone who is either not strong or not tall is happy or curious.
Everyone who is funny or not happy is funny or creative and vice versa.
Lucy is either not funny or wise.
Paul is either not creative or patient.
Someone is both not kind and old.
Someone is old.
Alice is both not creative and old.
Someone is happy or not patient.
Someone is both brave and not wise.
Someone is both happy and calm. | Alice is not old. | contradiction | (((creative(john)&~generous(john)))<=>((happy(lucy)<~>~generous(lucy))))&
((?[X]:((rich(X)&~generous(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)|rich(X))<=>(~old(X)<~>~brave(X))))&
((?[X]:((~brave(X)&tall(X))))=>((rich(lucy)|~strong(lucy))))&
(![X]:(~curious(X)=>(~brave(X)|~kind(X))))&
(![X]:((calm(X)|tall(X))<=>(funny(X)<~>~humble(X))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>(creative(fred)))&
(![X]:((~humble(X)|~happy(X))=>(kind(X)<~>~old(X))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)<~>humble(X))))&
(((happy(john)|kind(john)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(strong(X)&~curious(X))))&
(((humble(fred)|tall(fred)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))<=>(funny(X)|creative(X))))&
((~funny(lucy)<~>wise(lucy)))&
((~creative(paul)<~>patient(paul)))&
(?[X]:((~kind(X)&old(X))))&
(?[X]:(old(X)))&
((~creative(alice)&old(alice)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((happy(X)&calm(X)))) | ~old(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4526052553232261225909949
% SZS output start Proof for 4526052553232261225909949
21. old(alice) & ~creative(alice) [input p20]
25. ~old(alice) [input hypothesis]
153. old(alice) [cnf transformation 21]
159. ~old(alice) [cnf transformation 25]
317. $false [subsumption resolution 159,153]
% SZS output end Proof for 4526052553232261225909949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or patient then someone is creative and vice versa. If someone is both strong and not strong then someone is not humble or rich and vice versa. Everyone who is old is humble. If someone is not quiet or not humble then someone is not wise. Everyone who is happy or not quiet is both calm and not rich and vice versa. Everyone who is either wise or not humble is generous. Everyone who is either generous or not tall is both not calm and not funny and vice versa. Everyone who is both calm and funny is funny. If someone is both not curious and not tall then someone is both creative and brave and vice versa. If susan is either creative or not patient then john is not funny or not generous. If someone is both happy and not patient then john is either not happy or not creative and vice versa. If someone is both not patient and not tall then alice is either quiet or not rich and vice versa. Everyone who is either not tall or not funny is creative or not curious and vice versa. Everyone who is either not calm or curious is both not creative and not generous. Everyone who is kind is tall. If alice is both not generous and strong then john is both creative and not strong. Mary is calm. Paul is not generous or not tall. Mary is old or not wise. Someone is not funny or wise. Mary is either not patient or generous. Someone is both not wise and not generous. Susan is not rich. | Paul is not humble. | contradiction | ((?[X]:((kind(X)<~>patient(X))))<=>(?[X]:(creative(X))))&
((?[X]:((strong(X)&~strong(X))))<=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(old(X)=>humble(X)))&
((?[X]:((~quiet(X)|~humble(X))))=>(?[X]:(~wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>(calm(X)&~rich(X))))&
(![X]:((wise(X)<~>~humble(X))=>generous(X)))&
(![X]:((generous(X)<~>~tall(X))<=>(~calm(X)&~funny(X))))&
(![X]:((calm(X)&funny(X))=>funny(X)))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(((creative(susan)<~>~patient(susan)))=>((~funny(john)|~generous(john))))&
((?[X]:((happy(X)&~patient(X))))<=>((~happy(john)<~>~creative(john))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)<~>~rich(alice))))&
(![X]:((~tall(X)<~>~funny(X))<=>(creative(X)|~curious(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~creative(X)&~generous(X))))&
(![X]:(kind(X)=>tall(X)))&
(((~generous(alice)&strong(alice)))=>((creative(john)&~strong(john))))&
(calm(mary))&
((~generous(paul)|~tall(paul)))&
((old(mary)|~wise(mary)))&
(?[X]:((~funny(X)|wise(X))))&
((~patient(mary)<~>generous(mary)))&
(?[X]:((~wise(X)&~generous(X))))&
(~rich(susan)) | ~humble(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4746370401912249609118292
% SZS output start Proof for 4746370401912249609118292
2. ? [X0] : (~strong(X0) & strong(X0)) <=> ? [X0] : (rich(X0) | ~humble(X0)) [input p1]
24. ~humble(paul) [input hypothesis]
26. ? [X0] : (~strong(X0) & strong(X0)) <=> ? [X1] : (rich(X1) | ~humble(X1)) [rectify 2]
45. (? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~rich(X1) & humble(X1))) & (? [X1] : (rich(X1) | ~humble(X1)) | ! [X0] : (strong(X0) | ~strong(X0))) [nnf transformation 26]
46. (? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~rich(X1) & humble(X1))) & (? [X2] : (rich(X2) | ~humble(X2)) | ! [X3] : (strong(X3) | ~strong(X3))) [rectify 45]
47. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK2) & strong(sK2)) [choice axiom]
48. ? [X2] : (rich(X2) | ~humble(X2)) => (rich(sK3) | ~humble(sK3)) [choice axiom]
49. ((~strong(sK2) & strong(sK2)) | ! [X1] : (~rich(X1) & humble(X1))) & ((rich(sK3) | ~humble(sK3)) | ! [X3] : (strong(X3) | ~strong(X3))) [skolemisation 46,48,47]
85. strong(sK2) | humble(X1) [cnf transformation 49]
87. ~strong(sK2) | humble(X1) [cnf transformation 49]
146. ~humble(paul) [cnf transformation 24]
176. 8 <=> strong(sK2) [avatar definition]
181. 9 <=> ! [X1] : humble(X1) [avatar definition]
182. humble(X1) <- (9) [avatar component clause 181]
183. 9 | ~8 [avatar split clause 87,176,181]
185. 9 | 8 [avatar split clause 85,176,181]
345. $false <- (9) [resolution 182,146]
346. ~9 [avatar contradiction clause 345]
347. $false [avatar sat refutation 183,185,346]
% SZS output end Proof for 4746370401912249609118292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or wise is not creative.
Everyone who is humble is generous or kind and vice versa.
Everyone who is both patient and not old is both not rich and funny and vice versa.
Everyone who is not patient is both quiet and calm.
Everyone who is either old or not old is happy or curious and vice versa.
Everyone who is strong is either patient or not generous and vice versa.
Everyone who is either kind or patient is not generous or not kind.
Everyone who is not humble is either strong or not calm and vice versa.
Everyone who is either patient or not quiet is not calm and vice versa.
Everyone who is not humble is either humble or not strong and vice versa.
Everyone who is strong is both humble and curious and vice versa.
If someone is not patient then someone is not generous or not humble and vice versa.
If someone is both quiet and not funny then lucy is not happy or rich and vice versa.
If someone is both not creative and not quiet then john is rich or happy and vice versa.
Everyone who is both kind and funny is both not creative and tall and vice versa.
If someone is either not generous or generous then fred is both not generous and funny and vice versa.
Someone is both not kind and funny.
Someone is not rich or calm.
Someone is humble.
Someone is either not curious or not brave.
John is both curious and rich.
Someone is not wise.
Someone is both funny and rich.
Someone is not tall or generous. | John is tall. | contradiction | (![X]:((tall(X)|wise(X))=>~creative(X)))&
(![X]:(humble(X)<=>(generous(X)|kind(X))))&
(![X]:((patient(X)&~old(X))<=>(~rich(X)&funny(X))))&
(![X]:(~patient(X)=>(quiet(X)&calm(X))))&
(![X]:((old(X)<~>~old(X))<=>(happy(X)|curious(X))))&
(![X]:(strong(X)<=>(patient(X)<~>~generous(X))))&
(![X]:((kind(X)<~>patient(X))=>(~generous(X)|~kind(X))))&
(![X]:(~humble(X)<=>(strong(X)<~>~calm(X))))&
(![X]:((patient(X)<~>~quiet(X))<=>~calm(X)))&
(![X]:(~humble(X)<=>(humble(X)<~>~strong(X))))&
(![X]:(strong(X)<=>(humble(X)&curious(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~generous(X)|~humble(X)))))&
((?[X]:((quiet(X)&~funny(X))))<=>((~happy(lucy)|rich(lucy))))&
((?[X]:((~creative(X)&~quiet(X))))<=>((rich(john)|happy(john))))&
(![X]:((kind(X)&funny(X))<=>(~creative(X)&tall(X))))&
((?[X]:((~generous(X)<~>generous(X))))<=>((~generous(fred)&funny(fred))))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:((~rich(X)|calm(X))))&
(?[X]:(humble(X)))&
(?[X]:((~curious(X)<~>~brave(X))))&
((curious(john)&rich(john)))&
(?[X]:(~wise(X)))&
(?[X]:((funny(X)&rich(X))))&
(?[X]:((~tall(X)|generous(X)))) | tall(john) | [
"p0",
"p1",
"p9",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8088461791697833137784078
% SZS output start Proof for 8088461791697833137784078
1. ! [X0] : ((wise(X0) | tall(X0)) => ~creative(X0)) [input p0]
2. ! [X0] : (humble(X0) <=> (kind(X0) | generous(X0))) [input p1]
10. ! [X0] : (~humble(X0) <=> (humble(X0) <~> ~strong(X0))) [input p9]
11. ! [X0] : (strong(X0) <=> (curious(X0) & humble(X0))) [input p10]
15. ! [X0] : ((funny(X0) & kind(X0)) <=> (tall(X0) & ~creative(X0))) [input p14]
21. rich(john) & curious(john) [input p20]
25. tall(john) [input hypothesis]
27. ! [X0] : (tall(X0) => ~creative(X0)) [pure predicate removal 1]
29. ! [X0] : (~creative(X0) | ~tall(X0)) [ennf transformation 27]
33. ! [X0] : ((humble(X0) | (~kind(X0) & ~generous(X0))) & ((kind(X0) | generous(X0)) | ~humble(X0))) [nnf transformation 2]
34. ! [X0] : ((humble(X0) | (~kind(X0) & ~generous(X0))) & (kind(X0) | generous(X0) | ~humble(X0))) [flattening 33]
43. ! [X0] : ((~humble(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0)))) & (((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | humble(X0))) [nnf transformation 10]
44. ! [X0] : ((strong(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 11]
45. ! [X0] : ((strong(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | ~strong(X0))) [flattening 44]
61. ! [X0] : (((funny(X0) & kind(X0)) | (~tall(X0) | creative(X0))) & ((tall(X0) & ~creative(X0)) | (~funny(X0) | ~kind(X0)))) [nnf transformation 15]
62. ! [X0] : (((funny(X0) & kind(X0)) | ~tall(X0) | creative(X0)) & ((tall(X0) & ~creative(X0)) | ~funny(X0) | ~kind(X0))) [flattening 61]
81. ~creative(X0) | ~tall(X0) [cnf transformation 29]
84. ~kind(X0) | humble(X0) [cnf transformation 34]
111. ~strong(X0) | humble(X0) | humble(X0) [cnf transformation 43]
113. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 43]
117. strong(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 45]
133. kind(X0) | ~tall(X0) | creative(X0) [cnf transformation 62]
147. curious(john) [cnf transformation 21]
152. tall(john) [cnf transformation 25]
157. ~strong(X0) | humble(X0) [duplicate literal removal 111]
158. ~strong(X0) | ~humble(X0) [duplicate literal removal 113]
164. ~strong(X0) [subsumption resolution 157,158]
165. ~curious(X0) | ~humble(X0) [subsumption resolution 117,164]
236. ~tall(X0) | kind(X0) [subsumption resolution 133,81]
288. ~humble(john) [resolution 165,147]
292. kind(john) [resolution 236,152]
303. humble(john) [resolution 292,84]
304. $false [subsumption resolution 303,288]
% SZS output end Proof for 8088461791697833137784078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not brave and quiet then someone is tall and vice versa.
Everyone who is both kind and not quiet is old.
Everyone who is both not patient and wise is either not rich or wise and vice versa.
If someone is not brave or not kind then susan is not calm and vice versa.
Everyone who is not funny or funny is either not calm or not tall and vice versa.
If someone is not kind then someone is not strong and vice versa.
Everyone who is either wise or not wise is not tall.
If someone is not quiet or happy then someone is not tall or not kind.
If susan is either not old or not creative then someone is either curious or funny.
If lucy is wise then mary is either not patient or happy and vice versa.
Everyone who is either not curious or quiet is either old or calm and vice versa.
If john is both strong and patient then someone is calm and vice versa.
If someone is calm or curious then fred is either not humble or not calm and vice versa.
If someone is both tall and not strong then someone is both calm and rich.
Someone is either strong or old.
Someone is both not generous and strong.
Someone is either kind or not funny.
Paul is either not creative or curious.
Someone is quiet or not funny.
Someone is either creative or not curious.
Someone is either not curious or brave. | John is strong. | entailment | (((~brave(mary)&quiet(mary)))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~quiet(X))=>old(X)))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~calm(susan)))&
(![X]:((~funny(X)|funny(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)<~>~wise(X))=>~tall(X)))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(((~old(susan)<~>~creative(susan)))=>(?[X]:((curious(X)<~>funny(X)))))&
((wise(lucy))<=>((~patient(mary)<~>happy(mary))))&
(![X]:((~curious(X)<~>quiet(X))<=>(old(X)<~>calm(X))))&
(((strong(john)&patient(john)))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|curious(X))))<=>((~humble(fred)<~>~calm(fred))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)&rich(X)))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:((kind(X)<~>~funny(X))))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((~curious(X)<~>brave(X)))) | strong(john) | [
"p4",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5932546254400247465576699
% SZS output start Proof for 5932546254400247465576699
5. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p4]
7. ! [X0] : ((wise(X0) <~> ~wise(X0)) => ~tall(X0)) [input p6]
12. (patient(john) & strong(john)) <=> ? [X0] : calm(X0) [input p11]
22. ~strong(john) [input hypothesis]
29. ! [X0] : (~tall(X0) | (wise(X0) <=> ~wise(X0))) [ennf transformation 7]
44. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 5]
45. ! [X0] : ((funny(X0) | ~funny(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [flattening 44]
51. ! [X0] : (~tall(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 29]
60. ((patient(john) & strong(john)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~patient(john) | ~strong(john))) [nnf transformation 12]
61. ((patient(john) & strong(john)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~patient(john) | ~strong(john)) [flattening 60]
62. ((patient(john) & strong(john)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~patient(john) | ~strong(john)) [rectify 61]
63. ? [X1] : calm(X1) => calm(sK6) [choice axiom]
64. ((patient(john) & strong(john)) | ! [X0] : ~calm(X0)) & (calm(sK6) | ~patient(john) | ~strong(john)) [skolemisation 62,63]
104. tall(X0) | calm(X0) | funny(X0) [cnf transformation 45]
105. tall(X0) | calm(X0) | ~funny(X0) [cnf transformation 45]
110. ~tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 51]
111. ~tall(X0) | wise(X0) | wise(X0) [cnf transformation 51]
131. strong(john) | ~calm(X0) [cnf transformation 64]
153. ~strong(john) [cnf transformation 22]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 110]
155. ~tall(X0) | wise(X0) [duplicate literal removal 111]
159. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
160. ~tall(X0) <- (1) [avatar component clause 159]
198. calm(X0) | tall(X0) [subsumption resolution 104,105]
213. ~tall(X0) [subsumption resolution 154,155]
214. 1 [avatar split clause 213,159]
268. 24 <=> ! [X0] : ~calm(X0) [avatar definition]
269. ~calm(X0) <- (24) [avatar component clause 268]
276. 26 <=> strong(john) [avatar definition]
279. 24 | 26 [avatar split clause 131,276,268]
382. ~26 [avatar split clause 153,276]
387. tall(X0) <- (24) [resolution 198,269]
388. $false <- (1, 24) [subsumption resolution 387,160]
389. ~1 | ~24 [avatar contradiction clause 388]
390. $false [avatar sat refutation 214,279,382,389]
% SZS output end Proof for 5932546254400247465576699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not patient is brave or not funny. Everyone who is both not old and not creative is calm or tall and vice versa. If someone is either wise or happy then susan is not creative or not patient and vice versa. If someone is either not calm or quiet then someone is either not curious or brave and vice versa. Everyone who is not patient or not quiet is both humble and not patient. If john is brave or not curious then someone is patient or strong and vice versa. Everyone who is happy or not strong is calm and vice versa. Everyone who is not rich is either not quiet or not wise and vice versa. If mary is both not strong and not humble then susan is both kind and funny. Everyone who is either not strong or not humble is both brave and not curious and vice versa. Everyone who is patient is either calm or patient. If john is not strong or not calm then someone is creative and vice versa. Everyone who is either not happy or not creative is either not rich or creative. If fred is both happy and quiet then someone is not happy or not tall and vice versa. If susan is not humble then fred is not rich or curious. Everyone who is not wise is not kind and vice versa. Mary is not happy or not calm. Someone is both not patient and funny. Someone is both not old and not quiet. Someone is humble. Mary is not strong or creative. Susan is humble or generous. Someone is brave. John is humble or not old. | Fred is wise. | contradiction | (![X]:((strong(X)&~patient(X))=>(brave(X)|~funny(X))))&
(![X]:((~old(X)&~creative(X))<=>(calm(X)|tall(X))))&
((?[X]:((wise(X)<~>happy(X))))<=>((~creative(susan)|~patient(susan))))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:((~curious(X)<~>brave(X)))))&
(![X]:((~patient(X)|~quiet(X))=>(humble(X)&~patient(X))))&
(((brave(john)|~curious(john)))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((happy(X)|~strong(X))<=>calm(X)))&
(![X]:(~rich(X)<=>(~quiet(X)<~>~wise(X))))&
(((~strong(mary)&~humble(mary)))=>((kind(susan)&funny(susan))))&
(![X]:((~strong(X)<~>~humble(X))<=>(brave(X)&~curious(X))))&
(![X]:(patient(X)=>(calm(X)<~>patient(X))))&
(((~strong(john)|~calm(john)))<=>(?[X]:(creative(X))))&
(![X]:((~happy(X)<~>~creative(X))=>(~rich(X)<~>creative(X))))&
(((happy(fred)&quiet(fred)))<=>(?[X]:((~happy(X)|~tall(X)))))&
((~humble(susan))=>((~rich(fred)|curious(fred))))&
(![X]:(~wise(X)<=>~kind(X)))&
((~happy(mary)|~calm(mary)))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((~old(X)&~quiet(X))))&
(?[X]:(humble(X)))&
((~strong(mary)|creative(mary)))&
((humble(susan)|generous(susan)))&
(?[X]:(brave(X)))&
((humble(john)|~old(john))) | wise(fred) | [
"p1",
"p6",
"p7",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4365995980015186641951585
% SZS output start Proof for 4365995980015186641951585
2. ! [X0] : ((~creative(X0) & ~old(X0)) <=> (tall(X0) | calm(X0))) [input p1]
7. ! [X0] : ((~strong(X0) | happy(X0)) <=> calm(X0)) [input p6]
8. ! [X0] : (~rich(X0) <=> (~quiet(X0) <~> ~wise(X0))) [input p7]
13. ! [X0] : ((~happy(X0) <~> ~creative(X0)) => (~rich(X0) <~> creative(X0))) [input p12]
14. (quiet(fred) & happy(fred)) <=> ? [X0] : (~tall(X0) | ~happy(X0)) [input p13]
17. ~calm(mary) | ~happy(mary) [input p16]
25. wise(fred) [input hypothesis]
34. ! [X0] : ((~rich(X0) <~> creative(X0)) | (~happy(X0) <=> ~creative(X0))) [ennf transformation 13]
37. ! [X0] : (((~creative(X0) & ~old(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (creative(X0) | old(X0)))) [nnf transformation 2]
38. ! [X0] : (((~creative(X0) & ~old(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | creative(X0) | old(X0))) [flattening 37]
54. ! [X0] : (((~strong(X0) | happy(X0)) | ~calm(X0)) & (calm(X0) | (strong(X0) & ~happy(X0)))) [nnf transformation 7]
55. ! [X0] : ((~strong(X0) | happy(X0) | ~calm(X0)) & (calm(X0) | (strong(X0) & ~happy(X0)))) [flattening 54]
56. ! [X0] : ((~rich(X0) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0)))) & (((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | rich(X0))) [nnf transformation 8]
65. ! [X0] : (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) [nnf transformation 34]
66. ((quiet(fred) & happy(fred)) | ! [X0] : (tall(X0) & happy(X0))) & (? [X0] : (~tall(X0) | ~happy(X0)) | (~quiet(fred) | ~happy(fred))) [nnf transformation 14]
67. ((quiet(fred) & happy(fred)) | ! [X0] : (tall(X0) & happy(X0))) & (? [X0] : (~tall(X0) | ~happy(X0)) | ~quiet(fred) | ~happy(fred)) [flattening 66]
68. ((quiet(fred) & happy(fred)) | ! [X0] : (tall(X0) & happy(X0))) & (? [X1] : (~tall(X1) | ~happy(X1)) | ~quiet(fred) | ~happy(fred)) [rectify 67]
69. ? [X1] : (~tall(X1) | ~happy(X1)) => (~tall(sK5) | ~happy(sK5)) [choice axiom]
70. ((quiet(fred) & happy(fred)) | ! [X0] : (tall(X0) & happy(X0))) & ((~tall(sK5) | ~happy(sK5)) | ~quiet(fred) | ~happy(fred)) [skolemisation 68,69]
84. ~calm(X0) | ~creative(X0) [cnf transformation 38]
108. ~happy(X0) | calm(X0) [cnf transformation 55]
111. ~quiet(X0) | ~wise(X0) | rich(X0) [cnf transformation 56]
129. creative(X0) | ~rich(X0) | ~happy(X0) | creative(X0) [cnf transformation 65]
133. happy(fred) | happy(X0) [cnf transformation 70]
135. quiet(fred) | happy(X0) [cnf transformation 70]
140. ~calm(mary) | ~happy(mary) [cnf transformation 17]
149. wise(fred) [cnf transformation 25]
150. ~rich(X0) | creative(X0) | ~happy(X0) [duplicate literal removal 129]
283. 30 <=> quiet(fred) [avatar definition]
285. quiet(fred) <- (30) [avatar component clause 283]
288. 31 <=> ! [X0] : happy(X0) [avatar definition]
289. happy(X0) <- (31) [avatar component clause 288]
290. 31 | 30 [avatar split clause 135,283,288]
292. 32 <=> happy(fred) [avatar definition]
294. happy(fred) <- (32) [avatar component clause 292]
296. 31 | 32 [avatar split clause 133,292,288]
311. 36 <=> rich(fred) [avatar definition]
312. rich(fred) <- (36) [avatar component clause 311]
319. ~happy(mary) [subsumption resolution 140,108]
345. calm(fred) <- (32) [resolution 108,294]
346. ~creative(fred) <- (32) [resolution 345,84]
362. ~wise(fred) | rich(fred) <- (30) [resolution 111,285]
364. rich(fred) <- (30) [subsumption resolution 362,149]
376. 36 | ~30 [avatar split clause 364,283,311]
434. creative(fred) | ~happy(fred) <- (36) [resolution 150,312]
436. ~happy(fred) <- (32, 36) [subsumption resolution 434,346]
437. $false <- (32, 36) [subsumption resolution 436,294]
438. ~32 | ~36 [avatar contradiction clause 437]
445. $false <- (31) [resolution 289,319]
446. ~31 [avatar contradiction clause 445]
447. $false [avatar sat refutation 290,296,376,438,446]
% SZS output end Proof for 4365995980015186641951585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not generous is both quiet and not happy and vice versa.
Everyone who is both not patient and not kind is not strong and vice versa.
Everyone who is patient or rich is curious.
If paul is either kind or not tall then someone is both humble and not curious.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Everyone who is not rich or wise is not generous and vice versa.
If someone is quiet or not generous then alice is old and vice versa.
Everyone who is both funny and not kind is both not happy and old.
Everyone who is not creative is not brave and vice versa.
Someone is both not calm and not patient.
Susan is not humble.
Someone is both funny and humble.
Someone is both not wise and not curious.
Susan is tall or not curious.
Someone is both not patient and quiet.
Someone is either wise or patient.
Fred is both wise and quiet. | Fred is humble. | contradiction | (![X]:((patient(X)&~generous(X))<=>(quiet(X)&~happy(X))))&
(![X]:((~patient(X)&~kind(X))<=>~strong(X)))&
(![X]:((patient(X)|rich(X))=>curious(X)))&
(((kind(paul)<~>~tall(paul)))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(![X]:((~rich(X)|wise(X))<=>~generous(X)))&
((?[X]:((quiet(X)|~generous(X))))<=>(old(alice)))&
(![X]:((funny(X)&~kind(X))=>(~happy(X)&old(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(~humble(susan))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((tall(susan)|~curious(susan)))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((wise(X)<~>patient(X))))&
((wise(fred)&quiet(fred))) | humble(fred) | [
"p0",
"p4",
"p5",
"p7",
"p9",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5349490401955124590334048
% SZS output start Proof for 5349490401955124590334048
1. ! [X0] : ((~generous(X0) & patient(X0)) <=> (~happy(X0) & quiet(X0))) [input p0]
5. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (humble(X0) | wise(X0))) [input p4]
6. ! [X0] : (~strong(X0) => ~old(X0)) [input p5]
8. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> (~humble(X0) & curious(X0))) [input p7]
10. (old(fred) & ~creative(fred)) <=> (quiet(fred) | strong(fred)) [input p9]
13. ! [X0] : ((wise(X0) | ~rich(X0)) <=> ~generous(X0)) [input p12]
24. quiet(fred) & wise(fred) [input p23]
25. humble(fred) [input hypothesis]
29. ! [X0] : (~old(X0) | strong(X0)) [ennf transformation 6]
37. ! [X0] : (((~generous(X0) & patient(X0)) | (happy(X0) | ~quiet(X0))) & ((~happy(X0) & quiet(X0)) | (generous(X0) | ~patient(X0)))) [nnf transformation 1]
38. ! [X0] : (((~generous(X0) & patient(X0)) | happy(X0) | ~quiet(X0)) & ((~happy(X0) & quiet(X0)) | generous(X0) | ~patient(X0))) [flattening 37]
44. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~humble(X0) & ~wise(X0))) & ((humble(X0) | wise(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 5]
45. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~humble(X0) & ~wise(X0))) & (humble(X0) | wise(X0) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 44]
47. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 8]
48. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [flattening 47]
51. ((old(fred) & ~creative(fred)) | (~quiet(fred) & ~strong(fred))) & ((quiet(fred) | strong(fred)) | (~old(fred) | creative(fred))) [nnf transformation 10]
52. ((old(fred) & ~creative(fred)) | (~quiet(fred) & ~strong(fred))) & (quiet(fred) | strong(fred) | ~old(fred) | creative(fred)) [flattening 51]
54. ! [X0] : (((wise(X0) | ~rich(X0)) | generous(X0)) & (~generous(X0) | (~wise(X0) & rich(X0)))) [nnf transformation 13]
55. ! [X0] : ((wise(X0) | ~rich(X0) | generous(X0)) & (~generous(X0) | (~wise(X0) & rich(X0)))) [flattening 54]
73. ~happy(X0) | generous(X0) | ~patient(X0) [cnf transformation 38]
89. ~wise(X0) | patient(X0) | ~quiet(X0) [cnf transformation 45]
91. ~old(X0) | strong(X0) [cnf transformation 29]
96. ~humble(X0) | ~strong(X0) | happy(X0) [cnf transformation 48]
110. old(fred) | ~quiet(fred) [cnf transformation 52]
115. ~wise(X0) | ~generous(X0) [cnf transformation 55]
135. wise(fred) [cnf transformation 24]
136. quiet(fred) [cnf transformation 24]
137. humble(fred) [cnf transformation 25]
159. 5 <=> quiet(fred) [avatar definition]
160. quiet(fred) <- (5) [avatar component clause 159]
163. 6 <=> old(fred) [avatar definition]
165. old(fred) <- (6) [avatar component clause 163]
166. ~5 | 6 [avatar split clause 110,163,159]
168. 7 <=> strong(fred) [avatar definition]
169. strong(fred) <- (7) [avatar component clause 168]
218. 5 [avatar split clause 136,159]
220. strong(fred) <- (6) [resolution 91,165]
222. 7 | ~6 [avatar split clause 220,163,168]
223. ~generous(fred) [resolution 115,135]
229. 18 <=> patient(fred) [avatar definition]
233. 19 <=> happy(fred) [avatar definition]
235. happy(fred) <- (19) [avatar component clause 233]
281. patient(fred) | ~quiet(fred) [resolution 89,135]
334. ~strong(fred) | happy(fred) [resolution 96,137]
344. happy(fred) <- (7) [subsumption resolution 334,169]
345. 19 | ~7 [avatar split clause 344,168,233]
347. generous(fred) | ~patient(fred) <- (19) [resolution 235,73]
348. ~patient(fred) <- (19) [subsumption resolution 347,223]
351. ~18 | ~19 [avatar split clause 348,233,229]
354. patient(fred) <- (5) [subsumption resolution 281,160]
355. 18 | ~5 [avatar split clause 354,159,229]
361. $false [avatar sat refutation 166,218,222,345,351,355]
% SZS output end Proof for 5349490401955124590334048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not strong then someone is curious or happy.
If fred is either not curious or tall then someone is both funny and not humble and vice versa.
Everyone who is humble is generous.
Everyone who is either quiet or not patient is calm or not creative and vice versa.
If paul is not happy then fred is either kind or not creative and vice versa.
Everyone who is funny or not wise is not curious or tall.
If someone is either patient or kind then someone is funny.
Everyone who is creative or not old is patient or kind and vice versa.
Everyone who is either kind or humble is funny or not kind.
Everyone who is both strong and brave is wise.
Everyone who is both not rich and not generous is humble and vice versa.
If someone is wise then someone is both wise and calm.
If mary is not quiet or wise then paul is not strong and vice versa.
Everyone who is curious or not humble is not quiet or humble.
If paul is not rich then paul is both not strong and brave and vice versa.
Everyone who is brave is not rich and vice versa.
Someone is calm or not creative.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich.
Mary is not happy. | Mary is not kind. | neutral | ((?[X]:((~kind(X)<~>~strong(X))))=>(?[X]:((curious(X)|happy(X)))))&
(((~curious(fred)<~>tall(fred)))<=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:(humble(X)=>generous(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>(calm(X)|~creative(X))))&
((~happy(paul))<=>((kind(fred)<~>~creative(fred))))&
(![X]:((funny(X)|~wise(X))=>(~curious(X)|tall(X))))&
((?[X]:((patient(X)<~>kind(X))))=>(?[X]:(funny(X))))&
(![X]:((creative(X)|~old(X))<=>(patient(X)|kind(X))))&
(![X]:((kind(X)<~>humble(X))=>(funny(X)|~kind(X))))&
(![X]:((strong(X)&brave(X))=>wise(X)))&
(![X]:((~rich(X)&~generous(X))<=>humble(X)))&
((?[X]:(wise(X)))=>(?[X]:((wise(X)&calm(X)))))&
(((~quiet(mary)|wise(mary)))<=>(~strong(paul)))&
(![X]:((curious(X)|~humble(X))=>(~quiet(X)|humble(X))))&
((~rich(paul))<=>((~strong(paul)&brave(paul))))&
(![X]:(brave(X)<=>~rich(X)))&
(?[X]:((calm(X)|~creative(X))))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X))))&
(~happy(mary)) | ~kind(mary) | [] | null | 0 |
Everyone who is either generous or not humble is either patient or quiet. Everyone who is not tall is patient or wise. Everyone who is both not tall and calm is not curious or not generous and vice versa. Everyone who is both strong and not calm is either humble or brave and vice versa. Everyone who is not tall or strong is not curious or not brave and vice versa. If fred is not kind then someone is humble and vice versa. If someone is wise or happy then fred is funny. Everyone who is either not happy or not funny is both not generous and curious. Everyone who is not happy is either not tall or not rich. Everyone who is creative or kind is both not kind and rich and vice versa. If someone is both calm and not strong then alice is both not curious and kind. If someone is not tall then paul is both wise and rich. If someone is either not quiet or old then someone is creative or quiet and vice versa. Everyone who is either not brave or not curious is both curious and creative and vice versa. If someone is both happy and quiet then someone is either quiet or not kind and vice versa. If john is either old or not old then someone is both not creative and calm and vice versa. Someone is both not brave and not old. Someone is not creative or patient. Fred is either generous or curious. Someone is either not old or not patient. Fred is not rich or tall. Mary is not tall. | Fred is not happy. | contradiction | (![X]:((generous(X)<~>~humble(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|wise(X))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)|~generous(X))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~tall(X)|strong(X))<=>(~curious(X)|~brave(X))))&
((~kind(fred))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)|happy(X))))=>(funny(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(((old(john)<~>~old(john)))<=>(?[X]:((~creative(X)&calm(X)))))&
(?[X]:((~brave(X)&~old(X))))&
(?[X]:((~creative(X)|patient(X))))&
((generous(fred)<~>curious(fred)))&
(?[X]:((~old(X)<~>~patient(X))))&
((~rich(fred)|tall(fred)))&
(~tall(mary)) | ~happy(fred) | [
"p2",
"p6",
"p7",
"p8",
"p11",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8332306048763098878881248
% SZS output start Proof for 8332306048763098878881248
3. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~generous(X0) | ~curious(X0))) [input p2]
7. ? [X0] : (happy(X0) | wise(X0)) => funny(fred) [input p6]
8. ! [X0] : ((~happy(X0) <~> ~funny(X0)) => (curious(X0) & ~generous(X0))) [input p7]
9. ! [X0] : (~happy(X0) => (~tall(X0) <~> ~rich(X0))) [input p8]
12. ? [X0] : ~tall(X0) => (rich(paul) & wise(paul)) [input p11]
21. tall(fred) | ~rich(fred) [input p20]
22. ~tall(mary) [input p21]
23. ~happy(fred) [input hypothesis]
29. funny(fred) | ! [X0] : (~happy(X0) & ~wise(X0)) [ennf transformation 7]
30. ! [X0] : ((curious(X0) & ~generous(X0)) | (~happy(X0) <=> ~funny(X0))) [ennf transformation 8]
31. ! [X0] : ((~tall(X0) <~> ~rich(X0)) | happy(X0)) [ennf transformation 9]
33. (rich(paul) & wise(paul)) | ! [X0] : tall(X0) [ennf transformation 12]
35. ! [X0] : (((calm(X0) & ~tall(X0)) | (generous(X0) & curious(X0))) & ((~generous(X0) | ~curious(X0)) | (~calm(X0) | tall(X0)))) [nnf transformation 3]
36. ! [X0] : (((calm(X0) & ~tall(X0)) | (generous(X0) & curious(X0))) & (~generous(X0) | ~curious(X0) | ~calm(X0) | tall(X0))) [flattening 35]
45. ! [X0] : ((curious(X0) & ~generous(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) [nnf transformation 30]
46. ! [X0] : (((rich(X0) | tall(X0)) & (~rich(X0) | ~tall(X0))) | happy(X0)) [nnf transformation 31]
80. ~tall(X0) | generous(X0) [cnf transformation 36]
95. funny(fred) | ~wise(X0) [cnf transformation 29]
97. ~funny(X0) | ~generous(X0) | happy(X0) [cnf transformation 45]
102. rich(X0) | tall(X0) | happy(X0) [cnf transformation 46]
110. wise(paul) | tall(X0) [cnf transformation 33]
143. tall(fred) | ~rich(fred) [cnf transformation 21]
144. ~tall(mary) [cnf transformation 22]
145. ~happy(fred) [cnf transformation 23]
171. 5 <=> funny(fred) [avatar definition]
173. funny(fred) <- (5) [avatar component clause 171]
176. 6 <=> ! [X0] : ~wise(X0) [avatar definition]
177. ~wise(X0) <- (6) [avatar component clause 176]
178. 6 | 5 [avatar split clause 95,171,176]
181. 7 <=> ! [X0] : tall(X0) [avatar definition]
182. tall(X0) <- (7) [avatar component clause 181]
189. 9 <=> wise(paul) [avatar definition]
191. wise(paul) <- (9) [avatar component clause 189]
192. 7 | 9 [avatar split clause 110,189,181]
277. 28 <=> generous(fred) [avatar definition]
279. ~generous(fred) <- (~28) [avatar component clause 277]
297. 32 <=> rich(fred) [avatar definition]
299. ~rich(fred) <- (~32) [avatar component clause 297]
301. 33 <=> tall(fred) [avatar definition]
303. tall(fred) <- (33) [avatar component clause 301]
304. ~32 | 33 [avatar split clause 143,301,297]
309. $false <- (7) [resolution 182,144]
310. ~7 [avatar contradiction clause 309]
311. $false <- (6, 9) [subsumption resolution 191,177]
312. ~6 | ~9 [avatar contradiction clause 311]
354. ~generous(fred) | happy(fred) <- (5) [resolution 97,173]
358. ~generous(fred) <- (5) [subsumption resolution 354,145]
359. ~28 | ~5 [avatar split clause 358,171,277]
389. tall(fred) | happy(fred) <- (~32) [resolution 102,299]
392. tall(fred) <- (~32) [subsumption resolution 389,145]
393. 33 | 32 [avatar split clause 392,297,301]
395. generous(fred) <- (33) [resolution 303,80]
402. $false <- (~28, 33) [subsumption resolution 395,279]
403. 28 | ~33 [avatar contradiction clause 402]
404. $false [avatar sat refutation 178,192,304,310,312,359,393,403]
% SZS output end Proof for 8332306048763098878881248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Mary is rich. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | rich(mary) | [
"p0",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3137900199583298396610372
% SZS output start Proof for 3137900199583298396610372
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
21. rich(mary) [input hypothesis]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
83. ~old(X0) | ~rich(X0) | brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
101. ~funny(X0) | old(X0) [cnf transformation 51]
132. rich(mary) [cnf transformation 21]
151. 5 <=> generous(mary) [avatar definition]
265. ~generous(mary) [resolution 87,132]
267. funny(mary) [resolution 88,132]
272. old(mary) [resolution 101,267]
328. ~rich(mary) | brave(mary) [resolution 83,272]
334. brave(mary) [subsumption resolution 328,132]
346. ~rich(mary) | generous(mary) [resolution 334,67]
349. generous(mary) [subsumption resolution 346,132]
352. 5 [avatar split clause 349,151]
353. ~5 [avatar split clause 265,151]
354. $false [avatar sat refutation 352,353]
% SZS output end Proof for 3137900199583298396610372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or tall then fred is curious or not curious and vice versa.
If lucy is both wise and curious then paul is either funny or tall and vice versa.
If paul is not tall or not kind then mary is tall.
Everyone who is either not calm or not old is both not humble and humble and vice versa.
Everyone who is funny is both humble and patient and vice versa.
If alice is not quiet or not happy then alice is either not funny or curious and vice versa.
Everyone who is not old is old.
Everyone who is tall or not happy is either not humble or not happy.
If someone is either curious or quiet then someone is not funny.
Everyone who is either not kind or not patient is both happy and not happy.
Everyone who is both creative and not brave is not brave or not wise.
Everyone who is either curious or generous is not wise or kind and vice versa.
If mary is both not funny and wise then fred is both not wise and not old and vice versa.
If someone is curious then susan is not strong and vice versa.
If someone is both kind and not strong then someone is both not humble and not funny and vice versa.
Everyone who is funny is not curious or not strong.
Mary is generous or not curious.
Paul is both old and generous.
Fred is curious.
Alice is strong.
Someone is patient.
Someone is brave or patient.
Someone is funny or not kind. | Paul is tall. | neutral | ((?[X]:((~patient(X)|tall(X))))<=>((curious(fred)|~curious(fred))))&
(((wise(lucy)&curious(lucy)))<=>((funny(paul)<~>tall(paul))))&
(((~tall(paul)|~kind(paul)))=>(tall(mary)))&
(![X]:((~calm(X)<~>~old(X))<=>(~humble(X)&humble(X))))&
(![X]:(funny(X)<=>(humble(X)&patient(X))))&
(((~quiet(alice)|~happy(alice)))<=>((~funny(alice)<~>curious(alice))))&
(![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)|~happy(X))=>(~humble(X)<~>~happy(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>~patient(X))=>(happy(X)&~happy(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)|~wise(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~wise(X)|kind(X))))&
(((~funny(mary)&wise(mary)))<=>((~wise(fred)&~old(fred))))&
((?[X]:(curious(X)))<=>(~strong(susan)))&
((?[X]:((kind(X)&~strong(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:(funny(X)=>(~curious(X)|~strong(X))))&
((generous(mary)|~curious(mary)))&
((old(paul)&generous(paul)))&
(curious(fred))&
(strong(alice))&
(?[X]:(patient(X)))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:((funny(X)|~kind(X)))) | tall(paul) | [] | null | 0 |
Everyone who is both not patient and strong is both not kind and kind.
If alice is kind then john is both not generous and kind.
If paul is happy or not strong then someone is not generous.
Everyone who is both not kind and patient is not rich and vice versa.
Everyone who is not quiet or not patient is both quiet and humble and vice versa.
If lucy is generous then mary is patient or wise and vice versa.
If paul is patient or brave then alice is quiet or calm.
Everyone who is not generous is both rich and not patient.
Everyone who is not creative is both old and not generous.
Everyone who is creative or not kind is creative.
If john is either rich or old then paul is both wise and not brave and vice versa.
If paul is not quiet then susan is both not creative and brave.
Everyone who is funny or old is either creative or funny and vice versa.
If fred is generous or humble then someone is either quiet or not generous and vice versa.
Everyone who is both not quiet and not curious is both not happy and old and vice versa.
Everyone who is either quiet or not calm is not generous or curious.
Someone is both kind and not strong.
Susan is tall or not creative.
Lucy is either not brave or old.
Someone is kind or tall.
Someone is both rich and not curious.
Alice is patient.
Someone is funny. | Paul is wise. | neutral | (![X]:((~patient(X)&strong(X))=>(~kind(X)&kind(X))))&
((kind(alice))=>((~generous(john)&kind(john))))&
(((happy(paul)|~strong(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~kind(X)&patient(X))<=>~rich(X)))&
(![X]:((~quiet(X)|~patient(X))<=>(quiet(X)&humble(X))))&
((generous(lucy))<=>((patient(mary)|wise(mary))))&
(((patient(paul)|brave(paul)))=>((quiet(alice)|calm(alice))))&
(![X]:(~generous(X)=>(rich(X)&~patient(X))))&
(![X]:(~creative(X)=>(old(X)&~generous(X))))&
(![X]:((creative(X)|~kind(X))=>creative(X)))&
(((rich(john)<~>old(john)))<=>((wise(paul)&~brave(paul))))&
((~quiet(paul))=>((~creative(susan)&brave(susan))))&
(![X]:((funny(X)|old(X))<=>(creative(X)<~>funny(X))))&
(((generous(fred)|humble(fred)))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(![X]:((~quiet(X)&~curious(X))<=>(~happy(X)&old(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(~generous(X)|curious(X))))&
(?[X]:((kind(X)&~strong(X))))&
((tall(susan)|~creative(susan)))&
((~brave(lucy)<~>old(lucy)))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((rich(X)&~curious(X))))&
(patient(alice))&
(?[X]:(funny(X))) | wise(paul) | [] | null | 0 |
If john is not curious then someone is not curious or calm and vice versa. Everyone who is both not wise and tall is humble or not humble and vice versa. If lucy is both quiet and not quiet then fred is not humble. Everyone who is either not funny or curious is either not funny or creative and vice versa. Everyone who is both wise and not brave is old or not rich and vice versa. If mary is generous or strong then alice is both calm and kind and vice versa. If paul is generous then someone is both not funny and quiet and vice versa. If someone is not wise or not old then susan is generous and vice versa. If mary is rich then someone is humble and vice versa. If someone is not calm then paul is curious. If someone is brave then mary is either calm or happy. Everyone who is both not curious and old is funny. If mary is either strong or quiet then someone is kind or old and vice versa. If susan is either quiet or not kind then someone is both not wise and not patient. Alice is both not generous and brave. Someone is either not rich or not creative. John is either not patient or strong. John is not brave or not generous. Paul is rich or funny. | Lucy is old. | contradiction | ((~curious(john))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~wise(X)&tall(X))<=>(humble(X)|~humble(X))))&
(((quiet(lucy)&~quiet(lucy)))=>(~humble(fred)))&
(![X]:((~funny(X)<~>curious(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((wise(X)&~brave(X))<=>(old(X)|~rich(X))))&
(((generous(mary)|strong(mary)))<=>((calm(alice)&kind(alice))))&
((generous(paul))<=>(?[X]:((~funny(X)&quiet(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>(generous(susan)))&
((rich(mary))<=>(?[X]:(humble(X))))&
((?[X]:(~calm(X)))=>(curious(paul)))&
((?[X]:(brave(X)))=>((calm(mary)<~>happy(mary))))&
(![X]:((~curious(X)&old(X))=>funny(X)))&
(((strong(mary)<~>quiet(mary)))<=>(?[X]:((kind(X)|old(X)))))&
(((quiet(susan)<~>~kind(susan)))=>(?[X]:((~wise(X)&~patient(X)))))&
((~generous(alice)&brave(alice)))&
(?[X]:((~rich(X)<~>~creative(X))))&
((~patient(john)<~>strong(john)))&
((~brave(john)|~generous(john)))&
((rich(paul)|funny(paul))) | old(lucy) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4203977153167411180693130
% SZS output start Proof for 4203977153167411180693130
2. ! [X0] : ((tall(X0) & ~wise(X0)) <=> (~humble(X0) | humble(X0))) [input p1]
5. ! [X0] : ((~brave(X0) & wise(X0)) <=> (~rich(X0) | old(X0))) [input p4]
20. old(lucy) [input hypothesis]
32. ! [X0] : (((tall(X0) & ~wise(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (~tall(X0) | wise(X0)))) [nnf transformation 2]
33. ! [X0] : (((tall(X0) & ~wise(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ~tall(X0) | wise(X0))) [flattening 32]
35. ! [X0] : (((~brave(X0) & wise(X0)) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | (brave(X0) | ~wise(X0)))) [nnf transformation 5]
36. ! [X0] : (((~brave(X0) & wise(X0)) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | brave(X0) | ~wise(X0))) [flattening 35]
67. ~wise(X0) | ~humble(X0) [cnf transformation 33]
68. ~wise(X0) | humble(X0) [cnf transformation 33]
81. wise(X0) | ~old(X0) [cnf transformation 36]
120. old(lucy) [cnf transformation 20]
147. ~wise(X0) [subsumption resolution 67,68]
151. ~old(X0) [subsumption resolution 81,147]
265. $false [subsumption resolution 120,151]
% SZS output end Proof for 4203977153167411180693130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or creative is either not kind or not strong.
Everyone who is not kind is not funny or not humble and vice versa.
If someone is either not rich or not wise then lucy is not wise and vice versa.
Everyone who is not tall or happy is not old or not humble and vice versa.
Everyone who is both not curious and happy is not rich or not funny and vice versa.
Everyone who is both not wise and not curious is quiet.
Everyone who is not calm or wise is not patient or not creative.
Everyone who is tall or not rich is kind.
Everyone who is happy or not wise is both not rich and funny.
Everyone who is either not humble or tall is not strong.
If susan is both not strong and not old then someone is generous.
Everyone who is brave or funny is either not old or funny.
Everyone who is not generous or not tall is kind.
Everyone who is either not creative or old is either old or not kind and vice versa.
If someone is patient or not curious then someone is not creative.
Everyone who is both not strong and not creative is both not brave and not strong and vice versa.
Someone is funny.
Lucy is either not wise or calm.
Paul is quiet.
Someone is either not funny or tall.
Someone is both funny and tall. | Paul is not patient. | entailment | (![X]:((~humble(X)<~>creative(X))=>(~kind(X)<~>~strong(X))))&
(![X]:(~kind(X)<=>(~funny(X)|~humble(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~wise(lucy)))&
(![X]:((~tall(X)|happy(X))<=>(~old(X)|~humble(X))))&
(![X]:((~curious(X)&happy(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~wise(X)&~curious(X))=>quiet(X)))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|~creative(X))))&
(![X]:((tall(X)|~rich(X))=>kind(X)))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&funny(X))))&
(![X]:((~humble(X)<~>tall(X))=>~strong(X)))&
(((~strong(susan)&~old(susan)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|funny(X))=>(~old(X)<~>funny(X))))&
(![X]:((~generous(X)|~tall(X))=>kind(X)))&
(![X]:((~creative(X)<~>old(X))<=>(old(X)<~>~kind(X))))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&~creative(X))<=>(~brave(X)&~strong(X))))&
(?[X]:(funny(X)))&
((~wise(lucy)<~>calm(lucy)))&
(quiet(paul))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((funny(X)&tall(X)))) | ~patient(paul) | [
"p4",
"p7",
"p8",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6170770866836498446737551
% SZS output start Proof for 6170770866836498446737551
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> (~funny(X0) | ~rich(X0))) [input p4]
8. ! [X0] : ((~rich(X0) | tall(X0)) => kind(X0)) [input p7]
9. ! [X0] : ((~wise(X0) | happy(X0)) => (funny(X0) & ~rich(X0))) [input p8]
12. ! [X0] : ((funny(X0) | brave(X0)) => (~old(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((~tall(X0) | ~generous(X0)) => kind(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> old(X0)) <=> (old(X0) <~> ~kind(X0))) [input p13]
15. ? [X0] : (~curious(X0) | patient(X0)) => ? [X0] : ~creative(X0) [input p14]
22. patient(paul) [input hypothesis]
23. ? [X0] : (~curious(X0) | patient(X0)) => ? [X1] : ~creative(X1) [rectify 15]
25. ! [X0] : (~tall(X0) => kind(X0)) [pure predicate removal 13]
31. ! [X0] : (kind(X0) | (rich(X0) & ~tall(X0))) [ennf transformation 8]
32. ! [X0] : ((funny(X0) & ~rich(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 9]
34. ! [X0] : ((~old(X0) <~> funny(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 12]
35. ! [X0] : (kind(X0) | tall(X0)) [ennf transformation 25]
36. ? [X1] : ~creative(X1) | ! [X0] : (curious(X0) & ~patient(X0)) [ennf transformation 23]
46. ! [X0] : (((happy(X0) & ~curious(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
47. ! [X0] : (((happy(X0) & ~curious(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~happy(X0) | curious(X0))) [flattening 46]
49. ! [X0] : (((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | (~funny(X0) & ~brave(X0))) [nnf transformation 34]
50. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 14]
51. ? [X0] : ~creative(X0) | ! [X1] : (curious(X1) & ~patient(X1)) [rectify 36]
52. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
53. ~creative(sK1) | ! [X1] : (curious(X1) & ~patient(X1)) [skolemisation 51,52]
83. happy(X0) | funny(X0) [cnf transformation 47]
86. kind(X0) | ~tall(X0) [cnf transformation 31]
90. funny(X0) | ~happy(X0) [cnf transformation 32]
97. ~funny(X0) | old(X0) | ~funny(X0) [cnf transformation 49]
98. kind(X0) | tall(X0) [cnf transformation 35]
105. ~old(X0) | creative(X0) | ~kind(X0) | ~old(X0) [cnf transformation 50]
107. ~creative(sK1) | ~patient(X1) [cnf transformation 53]
120. patient(paul) [cnf transformation 22]
124. ~old(X0) | creative(X0) | ~kind(X0) [duplicate literal removal 105]
125. ~funny(X0) | old(X0) [duplicate literal removal 97]
148. funny(X0) [subsumption resolution 90,83]
150. old(X0) [subsumption resolution 125,148]
151. kind(X0) [subsumption resolution 98,86]
152. creative(X0) | ~kind(X0) [subsumption resolution 124,150]
153. creative(X0) [subsumption resolution 152,151]
155. ~patient(X1) [subsumption resolution 107,153]
164. $false [subsumption resolution 120,155]
% SZS output end Proof for 6170770866836498446737551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not rich or not curious then alice is not strong or not humble and vice versa. If someone is either not old or brave then someone is not quiet or rich. If someone is creative or kind then someone is both not rich and not creative. If fred is either humble or funny then paul is brave or funny. Everyone who is either not funny or not generous is both not humble and strong and vice versa. If someone is not old or not creative then someone is both not generous and not tall. Everyone who is not curious or not rich is rich and vice versa. Everyone who is either not patient or funny is both not calm and creative and vice versa. Everyone who is either old or rich is not brave. If someone is either not old or not brave then john is both generous and not strong. If alice is either strong or not kind then mary is either calm or not kind and vice versa. If susan is not strong then someone is either funny or not wise and vice versa. Everyone who is either not curious or not happy is both curious and creative and vice versa. Everyone who is not wise or happy is either kind or humble and vice versa. Everyone who is both not happy and not wise is not strong or not old. Lucy is either not humble or patient. John is tall. Someone is calm. Someone is either not brave or not old. Alice is either not old or strong. Susan is funny or not funny. John is either patient or humble. | Fred is curious. | contradiction | (((~rich(john)<~>~curious(john)))<=>((~strong(alice)|~humble(alice))))&
((?[X]:((~old(X)<~>brave(X))))=>(?[X]:((~quiet(X)|rich(X)))))&
((?[X]:((creative(X)|kind(X))))=>(?[X]:((~rich(X)&~creative(X)))))&
(((humble(fred)<~>funny(fred)))=>((brave(paul)|funny(paul))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~humble(X)&strong(X))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((~curious(X)|~rich(X))<=>rich(X)))&
(![X]:((~patient(X)<~>funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((old(X)<~>rich(X))=>~brave(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>((generous(john)&~strong(john))))&
(((strong(alice)<~>~kind(alice)))<=>((calm(mary)<~>~kind(mary))))&
((~strong(susan))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(![X]:((~curious(X)<~>~happy(X))<=>(curious(X)&creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~happy(X)&~wise(X))=>(~strong(X)|~old(X))))&
((~humble(lucy)<~>patient(lucy)))&
(tall(john))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)<~>~old(X))))&
((~old(alice)<~>strong(alice)))&
((funny(susan)|~funny(susan)))&
((patient(john)<~>humble(john))) | curious(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 897354897083316952621935
% SZS output start Proof for 897354897083316952621935
7. ! [X0] : ((~rich(X0) | ~curious(X0)) <=> rich(X0)) [input p6]
23. curious(fred) [input hypothesis]
47. ! [X0] : (((~rich(X0) | ~curious(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) & curious(X0)))) [nnf transformation 7]
48. ! [X0] : ((~rich(X0) | ~curious(X0) | ~rich(X0)) & (rich(X0) | (rich(X0) & curious(X0)))) [flattening 47]
93. rich(X0) | rich(X0) [cnf transformation 48]
94. ~rich(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 48]
143. curious(fred) [cnf transformation 23]
146. rich(X0) [duplicate literal removal 93]
147. ~curious(X0) | ~rich(X0) [duplicate literal removal 94]
310. ~rich(fred) [resolution 147,143]
311. $false [subsumption resolution 310,146]
% SZS output end Proof for 897354897083316952621935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is tall or patient.
If someone is kind then lucy is strong or not tall.
Everyone who is either strong or tall is both wise and not rich.
If someone is not kind or strong then alice is either not strong or strong and vice versa.
Everyone who is not funny or not calm is both creative and calm and vice versa.
Everyone who is either not strong or strong is either not generous or funny.
If alice is not old or generous then someone is either not wise or wise and vice versa.
If fred is both not calm and old then john is either generous or not rich and vice versa.
Everyone who is not old is not quiet and vice versa.
If someone is old then someone is not strong or happy and vice versa.
If paul is strong then susan is not curious or quiet and vice versa.
If someone is quiet then mary is not calm and vice versa.
Everyone who is rich is strong and vice versa.
If someone is both rich and tall then someone is either strong or funny and vice versa.
If someone is not calm or kind then someone is not patient and vice versa.
Everyone who is either not brave or not rich is both calm and not strong.
Lucy is generous or not creative.
Someone is either rich or patient.
Someone is not creative.
Lucy is both calm and humble. | John is patient. | neutral | (![X]:(quiet(X)=>(tall(X)|patient(X))))&
((?[X]:(kind(X)))=>((strong(lucy)|~tall(lucy))))&
(![X]:((strong(X)<~>tall(X))=>(wise(X)&~rich(X))))&
((?[X]:((~kind(X)|strong(X))))<=>((~strong(alice)<~>strong(alice))))&
(![X]:((~funny(X)|~calm(X))<=>(creative(X)&calm(X))))&
(![X]:((~strong(X)<~>strong(X))=>(~generous(X)<~>funny(X))))&
(((~old(alice)|generous(alice)))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(((~calm(fred)&old(fred)))<=>((generous(john)<~>~rich(john))))&
(![X]:(~old(X)<=>~quiet(X)))&
((?[X]:(old(X)))<=>(?[X]:((~strong(X)|happy(X)))))&
((strong(paul))<=>((~curious(susan)|quiet(susan))))&
((?[X]:(quiet(X)))<=>(~calm(mary)))&
(![X]:(rich(X)<=>strong(X)))&
((?[X]:((rich(X)&tall(X))))<=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~calm(X)|kind(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(calm(X)&~strong(X))))&
((generous(lucy)|~creative(lucy)))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
((calm(lucy)&humble(lucy))) | patient(john) | [] | null | 0 |
If fred is either curious or not old then paul is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
If fred is either patient or old then paul is not funny and vice versa.
If someone is both not quiet and not humble then john is both not generous and not funny.
Everyone who is not patient is both patient and not patient and vice versa.
Everyone who is not strong or not curious is both humble and not humble and vice versa.
Everyone who is not funny is either happy or curious and vice versa.
Everyone who is both funny and calm is not calm.
If someone is not curious or not patient then john is either not brave or creative.
If someone is both happy and not old then someone is not curious or creative and vice versa.
Everyone who is not quiet or not patient is both brave and not generous and vice versa.
Everyone who is old is either old or not happy and vice versa.
If someone is not humble or old then mary is both curious and brave and vice versa.
If susan is either not rich or not wise then someone is not rich and vice versa.
Someone is both tall and funny.
Someone is not quiet.
Someone is not brave or not kind.
Fred is happy or not funny.
Lucy is either kind or generous. | Mary is creative. | neutral | (((curious(fred)<~>~old(fred)))<=>((quiet(paul)<~>rich(paul))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(((patient(fred)<~>old(fred)))<=>(~funny(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~generous(john)&~funny(john))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(![X]:((~strong(X)|~curious(X))<=>(humble(X)&~humble(X))))&
(![X]:(~funny(X)<=>(happy(X)<~>curious(X))))&
(![X]:((funny(X)&calm(X))=>~calm(X)))&
((?[X]:((~curious(X)|~patient(X))))=>((~brave(john)<~>creative(john))))&
((?[X]:((happy(X)&~old(X))))<=>(?[X]:((~curious(X)|creative(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(brave(X)&~generous(X))))&
(![X]:(old(X)<=>(old(X)<~>~happy(X))))&
((?[X]:((~humble(X)|old(X))))<=>((curious(mary)&brave(mary))))&
(((~rich(susan)<~>~wise(susan)))<=>(?[X]:(~rich(X))))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)|~kind(X))))&
((happy(fred)|~funny(fred)))&
((kind(lucy)<~>generous(lucy))) | creative(mary) | [] | null | 0 |
If alice is both rich and curious then someone is not rich or not strong. Everyone who is either not creative or humble is quiet or not brave. If someone is either funny or tall then susan is both old and wise and vice versa. If alice is not old then john is humble or not brave. Everyone who is either not tall or generous is happy. If alice is either not old or tall then alice is either not creative or not calm. Everyone who is wise or strong is not quiet or quiet. If someone is wise or brave then alice is either not curious or funny. Everyone who is both not brave and not curious is either not curious or strong and vice versa. If mary is either curious or happy then alice is curious or not happy. Everyone who is either not humble or generous is not humble or creative. Everyone who is both not tall and not strong is not happy or calm and vice versa. If someone is either funny or not strong then someone is curious or not patient. If someone is both not humble and curious then someone is both happy and not curious. Everyone who is either creative or generous is either not creative or not happy and vice versa. If someone is generous or curious then someone is either calm or generous. Mary is not curious or not strong. Someone is not wise. Someone is quiet. Alice is either not creative or not generous. Someone is old. Someone is quiet or not kind. Someone is both not rich and not brave. Alice is curious. | Alice is not creative. | entailment | (((rich(alice)&curious(alice)))=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((~creative(X)<~>humble(X))=>(quiet(X)|~brave(X))))&
((?[X]:((funny(X)<~>tall(X))))<=>((old(susan)&wise(susan))))&
((~old(alice))=>((humble(john)|~brave(john))))&
(![X]:((~tall(X)<~>generous(X))=>happy(X)))&
(((~old(alice)<~>tall(alice)))=>((~creative(alice)<~>~calm(alice))))&
(![X]:((wise(X)|strong(X))=>(~quiet(X)|quiet(X))))&
((?[X]:((wise(X)|brave(X))))=>((~curious(alice)<~>funny(alice))))&
(![X]:((~brave(X)&~curious(X))<=>(~curious(X)<~>strong(X))))&
(((curious(mary)<~>happy(mary)))=>((curious(alice)|~happy(alice))))&
(![X]:((~humble(X)<~>generous(X))=>(~humble(X)|creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~happy(X)|calm(X))))&
((?[X]:((funny(X)<~>~strong(X))))=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((~humble(X)&curious(X))))=>(?[X]:((happy(X)&~curious(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((generous(X)|curious(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
((~curious(mary)|~strong(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(quiet(X)))&
((~creative(alice)<~>~generous(alice)))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)|~kind(X))))&
(?[X]:((~rich(X)&~brave(X))))&
(curious(alice)) | ~creative(alice) | [
"p4",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1631456382351613888150851
% SZS output start Proof for 1631456382351613888150851
5. ! [X0] : ((~tall(X0) <~> generous(X0)) => happy(X0)) [input p4]
12. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (calm(X0) | ~happy(X0))) [input p11]
15. ! [X0] : ((creative(X0) <~> generous(X0)) <=> (~creative(X0) <~> ~happy(X0))) [input p14]
20. ~creative(alice) <~> ~generous(alice) [input p19]
25. creative(alice) [input hypothesis]
37. ! [X0] : (happy(X0) | (~tall(X0) <=> generous(X0))) [ennf transformation 5]
54. ! [X0] : (happy(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) [nnf transformation 37]
61. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (strong(X0) | tall(X0)))) [nnf transformation 12]
62. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | strong(X0) | tall(X0))) [flattening 61]
66. ! [X0] : ((((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0)))) & (((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0))))) [nnf transformation 15]
75. (generous(alice) | creative(alice)) & (~generous(alice) | ~creative(alice)) [nnf transformation 20]
89. happy(X0) | generous(X0) | tall(X0) [cnf transformation 54]
112. ~tall(X0) | happy(X0) [cnf transformation 62]
118. ~happy(X0) | ~creative(X0) | generous(X0) | ~creative(X0) [cnf transformation 66]
121. happy(X0) | creative(X0) | creative(X0) | ~generous(X0) [cnf transformation 66]
122. generous(X0) | creative(X0) | ~happy(X0) | creative(X0) [cnf transformation 66]
125. ~generous(X0) | ~creative(X0) | ~creative(X0) | happy(X0) [cnf transformation 66]
133. ~generous(alice) | ~creative(alice) [cnf transformation 75]
138. creative(alice) [cnf transformation 25]
139. ~happy(X0) | ~creative(X0) | generous(X0) [duplicate literal removal 118]
140. happy(X0) | creative(X0) | ~generous(X0) [duplicate literal removal 121]
141. generous(X0) | creative(X0) | ~happy(X0) [duplicate literal removal 122]
142. ~generous(X0) | ~creative(X0) | happy(X0) [duplicate literal removal 125]
192. 11 <=> creative(alice) [avatar definition]
249. ~generous(X0) | happy(X0) [subsumption resolution 140,142]
250. ~happy(X0) | generous(X0) [subsumption resolution 139,141]
270. 27 <=> generous(alice) [avatar definition]
271. ~generous(alice) <- (~27) [avatar component clause 270]
274. ~11 | ~27 [avatar split clause 133,270,192]
276. 11 [avatar split clause 138,192]
285. generous(X0) | tall(X0) | generous(X0) [resolution 89,250]
286. generous(X0) | tall(X0) [duplicate literal removal 285]
290. tall(X1) | happy(X1) [resolution 286,249]
295. happy(X1) [subsumption resolution 290,112]
307. generous(X0) [resolution 295,250]
316. $false <- (~27) [resolution 307,271]
317. 27 [avatar contradiction clause 316]
318. $false [avatar sat refutation 274,276,317]
% SZS output end Proof for 1631456382351613888150851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or strong is not generous or generous. If someone is either wise or not humble then fred is either not rich or not strong and vice versa. Everyone who is both humble and tall is either humble or not brave. Everyone who is generous is either not creative or not patient and vice versa. If john is not tall or not generous then someone is creative. If someone is both not old and rich then alice is not old or humble and vice versa. Everyone who is both brave and not creative is not brave or not rich and vice versa. If someone is both kind and happy then john is both curious and generous and vice versa. Everyone who is not calm or curious is not humble or not curious. If someone is either old or brave then someone is not rich or wise and vice versa. If someone is both old and not calm then someone is funny or kind and vice versa. Everyone who is both not patient and not brave is not humble or not rich and vice versa. If mary is funny then someone is both not curious and not creative. If fred is not calm then susan is quiet or curious and vice versa. Everyone who is either quiet or creative is both generous and not funny and vice versa. If someone is both not rich and not strong then someone is either not calm or tall and vice versa. Someone is either not patient or not humble. Susan is calm or brave. Someone is not old. Someone is wise. Alice is kind. | Fred is not strong. | entailment | (![X]:((~rich(X)|strong(X))=>(~generous(X)|generous(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>((~rich(fred)<~>~strong(fred))))&
(![X]:((humble(X)&tall(X))=>(humble(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~creative(X)<~>~patient(X))))&
(((~tall(john)|~generous(john)))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)&rich(X))))<=>((~old(alice)|humble(alice))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((kind(X)&happy(X))))<=>((curious(john)&generous(john))))&
(![X]:((~calm(X)|curious(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)<~>brave(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~patient(X)&~brave(X))<=>(~humble(X)|~rich(X))))&
((funny(mary))=>(?[X]:((~curious(X)&~creative(X)))))&
((~calm(fred))<=>((quiet(susan)|curious(susan))))&
(![X]:((quiet(X)<~>creative(X))<=>(generous(X)&~funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((~calm(X)<~>tall(X)))))&
(?[X]:((~patient(X)<~>~humble(X))))&
((calm(susan)|brave(susan)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X)))&
(kind(alice)) | ~strong(fred) | [
"p1",
"p6",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1617155759077506597466589
% SZS output start Proof for 1617155759077506597466589
2. ? [X0] : (wise(X0) <~> ~humble(X0)) <=> (~rich(fred) <~> ~strong(fred)) [input p1]
7. ! [X0] : ((~creative(X0) & brave(X0)) <=> (~rich(X0) | ~brave(X0))) [input p6]
12. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~rich(X0) | ~humble(X0))) [input p11]
20. ? [X0] : wise(X0) [input p19]
22. strong(fred) [input hypothesis]
34. (? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X0] : ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) [nnf transformation 2]
35. (? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X1] : ((wise(X1) | humble(X1)) & (~humble(X1) | ~wise(X1)))) [rectify 34]
36. ? [X0] : ((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) => ((humble(sK0) | ~wise(sK0)) & (~humble(sK0) | wise(sK0))) [choice axiom]
37. (((humble(sK0) | ~wise(sK0)) & (~humble(sK0) | wise(sK0))) | ((~rich(fred) | strong(fred)) & (~strong(fred) | rich(fred)))) & (((strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred))) | ! [X1] : ((wise(X1) | humble(X1)) & (~humble(X1) | ~wise(X1)))) [skolemisation 35,36]
47. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | (creative(X0) | ~brave(X0)))) [nnf transformation 7]
48. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | creative(X0) | ~brave(X0))) [flattening 47]
64. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 12]
65. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | brave(X0) | patient(X0))) [flattening 64]
82. ? [X0] : wise(X0) => wise(sK13) [choice axiom]
83. wise(sK13) [skolemisation 20,82]
86. ~strong(fred) | ~rich(fred) | ~humble(X1) | ~wise(X1) [cnf transformation 37]
108. brave(X0) | brave(X0) [cnf transformation 48]
132. ~brave(X0) | humble(X0) [cnf transformation 65]
133. ~brave(X0) | rich(X0) [cnf transformation 65]
155. wise(sK13) [cnf transformation 83]
157. strong(fred) [cnf transformation 22]
160. brave(X0) [duplicate literal removal 108]
163. 1 <=> strong(fred) [avatar definition]
167. 2 <=> rich(fred) [avatar definition]
169. ~rich(fred) <- (~2) [avatar component clause 167]
187. 6 <=> ! [X1] : (~humble(X1) | ~wise(X1)) [avatar definition]
188. ~humble(X1) | ~wise(X1) <- (6) [avatar component clause 187]
191. 6 | ~2 | ~1 [avatar split clause 86,163,167,187]
252. 19 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (19) [avatar component clause 252]
261. 21 <=> ! [X1] : rich(X1) [avatar definition]
262. rich(X1) <- (21) [avatar component clause 261]
307. rich(X0) [subsumption resolution 133,160]
308. 21 [avatar split clause 307,261]
309. humble(X0) [subsumption resolution 132,160]
371. 1 [avatar split clause 157,163]
376. $false <- (~2, 21) [subsumption resolution 169,262]
377. 2 | ~21 [avatar contradiction clause 376]
378. ~wise(X1) <- (6) [subsumption resolution 188,309]
379. 19 | ~6 [avatar split clause 378,187,252]
380. $false <- (19) [resolution 253,155]
381. ~19 [avatar contradiction clause 380]
382. $false [avatar sat refutation 191,308,371,377,379,381]
% SZS output end Proof for 1617155759077506597466589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either patient or not happy then susan is either not funny or not creative.
Everyone who is strong is both old and not strong and vice versa.
Everyone who is either patient or tall is not quiet or humble and vice versa.
Everyone who is not tall or old is not generous or not funny and vice versa.
Everyone who is creative or not rich is creative and vice versa.
If someone is not rich then someone is both creative and not rich and vice versa.
Everyone who is both not curious and generous is either old or not strong.
If paul is not curious then someone is not patient or strong.
If someone is either not quiet or curious then mary is both rich and brave and vice versa.
Everyone who is either old or not old is tall and vice versa.
Everyone who is either not patient or not happy is not brave and vice versa.
If fred is both not calm and not old then mary is both not quiet and strong and vice versa.
If someone is not happy or not generous then someone is both brave and not strong.
If lucy is quiet or not curious then fred is both brave and not patient.
If someone is tall then lucy is not patient or not tall and vice versa.
Someone is either brave or old.
John is creative or kind.
John is either curious or not calm.
Paul is not funny or generous.
Someone is both not calm and not patient.
Susan is either strong or not calm.
Paul is humble or brave. | Lucy is not generous. | contradiction | (((patient(fred)<~>~happy(fred)))=>((~funny(susan)<~>~creative(susan))))&
(![X]:(strong(X)<=>(old(X)&~strong(X))))&
(![X]:((patient(X)<~>tall(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~tall(X)|old(X))<=>(~generous(X)|~funny(X))))&
(![X]:((creative(X)|~rich(X))<=>creative(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~curious(X)&generous(X))=>(old(X)<~>~strong(X))))&
((~curious(paul))=>(?[X]:((~patient(X)|strong(X)))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>((rich(mary)&brave(mary))))&
(![X]:((old(X)<~>~old(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~happy(X))<=>~brave(X)))&
(((~calm(fred)&~old(fred)))<=>((~quiet(mary)&strong(mary))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((brave(X)&~strong(X)))))&
(((quiet(lucy)|~curious(lucy)))=>((brave(fred)&~patient(fred))))&
((?[X]:(tall(X)))<=>((~patient(lucy)|~tall(lucy))))&
(?[X]:((brave(X)<~>old(X))))&
((creative(john)|kind(john)))&
((curious(john)<~>~calm(john)))&
((~funny(paul)|generous(paul)))&
(?[X]:((~calm(X)&~patient(X))))&
((strong(susan)<~>~calm(susan)))&
((humble(paul)|brave(paul))) | ~generous(lucy) | [
"p1",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4939555114921086006730720
% SZS output start Proof for 4939555114921086006730720
2. ! [X0] : (strong(X0) <=> (~strong(X0) & old(X0))) [input p1]
4. ! [X0] : ((old(X0) | ~tall(X0)) <=> (~funny(X0) | ~generous(X0))) [input p3]
10. ! [X0] : ((old(X0) <~> ~old(X0)) <=> tall(X0)) [input p9]
23. ~generous(lucy) [input hypothesis]
34. ! [X0] : ((strong(X0) | (strong(X0) | ~old(X0))) & ((~strong(X0) & old(X0)) | ~strong(X0))) [nnf transformation 2]
35. ! [X0] : ((strong(X0) | strong(X0) | ~old(X0)) & ((~strong(X0) & old(X0)) | ~strong(X0))) [flattening 34]
38. ! [X0] : (((old(X0) | ~tall(X0)) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | (~old(X0) & tall(X0)))) [nnf transformation 4]
39. ! [X0] : ((old(X0) | ~tall(X0) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | (~old(X0) & tall(X0)))) [flattening 38]
55. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~tall(X0)) & (tall(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 10]
79. ~strong(X0) | ~strong(X0) [cnf transformation 35]
80. strong(X0) | strong(X0) | ~old(X0) [cnf transformation 35]
89. ~tall(X0) | old(X0) | generous(X0) [cnf transformation 39]
107. tall(X0) | old(X0) | old(X0) [cnf transformation 55]
139. ~generous(lucy) [cnf transformation 23]
141. tall(X0) | old(X0) [duplicate literal removal 107]
142. ~strong(X0) [duplicate literal removal 79]
143. ~old(X0) | strong(X0) [duplicate literal removal 80]
314. old(X0) | generous(X0) | old(X0) [resolution 89,141]
316. generous(X0) | old(X0) [duplicate literal removal 314]
317. old(lucy) [resolution 316,139]
323. strong(lucy) [resolution 317,143]
324. $false [subsumption resolution 323,142]
% SZS output end Proof for 4939555114921086006730720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or creative then john is either tall or calm. Everyone who is either happy or strong is not calm. Everyone who is quiet is either not tall or not happy and vice versa. Everyone who is either tall or kind is tall and vice versa. If someone is either not strong or not curious then john is creative or wise. Everyone who is both generous and not humble is rich and vice versa. If someone is not funny or not brave then someone is old and vice versa. If john is not old or not kind then alice is not patient or not humble and vice versa. Everyone who is either not wise or patient is both curious and not creative and vice versa. If someone is not curious or kind then susan is not generous or not strong and vice versa. If john is not kind then someone is both brave and patient and vice versa. If someone is both happy and not calm then paul is either strong or curious. Everyone who is not creative or creative is not wise or kind. If someone is not patient or old then someone is not generous and vice versa. Everyone who is not old or creative is not old and vice versa. Everyone who is both not rich and not wise is both wise and old and vice versa. Lucy is not strong or generous. Fred is both rich and not tall. Someone is both curious and tall. Lucy is happy or not humble. Someone is creative. Someone is both not calm and not curious. | Alice is not patient. | contradiction | ((?[X]:((~quiet(X)<~>creative(X))))=>((tall(john)<~>calm(john))))&
(![X]:((happy(X)<~>strong(X))=>~calm(X)))&
(![X]:(quiet(X)<=>(~tall(X)<~>~happy(X))))&
(![X]:((tall(X)<~>kind(X))<=>tall(X)))&
((?[X]:((~strong(X)<~>~curious(X))))=>((creative(john)|wise(john))))&
(![X]:((generous(X)&~humble(X))<=>rich(X)))&
((?[X]:((~funny(X)|~brave(X))))<=>(?[X]:(old(X))))&
(((~old(john)|~kind(john)))<=>((~patient(alice)|~humble(alice))))&
(![X]:((~wise(X)<~>patient(X))<=>(curious(X)&~creative(X))))&
((?[X]:((~curious(X)|kind(X))))<=>((~generous(susan)|~strong(susan))))&
((~kind(john))<=>(?[X]:((brave(X)&patient(X)))))&
((?[X]:((happy(X)&~calm(X))))=>((strong(paul)<~>curious(paul))))&
(![X]:((~creative(X)|creative(X))=>(~wise(X)|kind(X))))&
((?[X]:((~patient(X)|old(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~old(X)|creative(X))<=>~old(X)))&
(![X]:((~rich(X)&~wise(X))<=>(wise(X)&old(X))))&
((~strong(lucy)|generous(lucy)))&
((rich(fred)&~tall(fred)))&
(?[X]:((curious(X)&tall(X))))&
((happy(lucy)|~humble(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)&~curious(X)))) | ~patient(alice) | [
"p3",
"p5",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3634643089489520217348187
% SZS output start Proof for 3634643089489520217348187
4. ! [X0] : ((tall(X0) <~> kind(X0)) <=> tall(X0)) [input p3]
6. ! [X0] : ((~humble(X0) & generous(X0)) <=> rich(X0)) [input p5]
13. ! [X0] : ((creative(X0) | ~creative(X0)) => (kind(X0) | ~wise(X0))) [input p12]
14. ? [X0] : (old(X0) | ~patient(X0)) <=> ? [X0] : ~generous(X0) [input p13]
16. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (old(X0) & wise(X0))) [input p15]
23. ~patient(alice) [input hypothesis]
25. ? [X0] : (old(X0) | ~patient(X0)) <=> ? [X1] : ~generous(X1) [rectify 14]
31. ! [X0] : ((kind(X0) | ~wise(X0)) | (~creative(X0) & creative(X0))) [ennf transformation 13]
32. ! [X0] : (kind(X0) | ~wise(X0) | (~creative(X0) & creative(X0))) [flattening 31]
36. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ~tall(X0)) & (tall(X0) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 4]
38. ! [X0] : (((~humble(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 6]
39. ! [X0] : (((~humble(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | humble(X0) | ~generous(X0))) [flattening 38]
59. (? [X0] : (old(X0) | ~patient(X0)) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : (~old(X0) & patient(X0))) [nnf transformation 25]
60. (? [X0] : (old(X0) | ~patient(X0)) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : (~old(X3) & patient(X3))) [rectify 59]
61. ? [X0] : (old(X0) | ~patient(X0)) => (old(sK4) | ~patient(sK4)) [choice axiom]
62. ? [X2] : ~generous(X2) => ~generous(sK5) [choice axiom]
63. ((old(sK4) | ~patient(sK4)) | ! [X1] : generous(X1)) & (~generous(sK5) | ! [X3] : (~old(X3) & patient(X3))) [skolemisation 60,62,61]
66. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (wise(X0) | rich(X0)))) [nnf transformation 16]
67. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | wise(X0) | rich(X0))) [flattening 66]
85. tall(X0) | tall(X0) | ~kind(X0) [cnf transformation 36]
87. ~kind(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 36]
91. ~rich(X0) | generous(X0) [cnf transformation 39]
115. kind(X0) | ~wise(X0) | creative(X0) [cnf transformation 32]
116. kind(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 32]
117. ~generous(sK5) | patient(X3) [cnf transformation 63]
123. wise(X0) | wise(X0) | rich(X0) [cnf transformation 67]
136. ~patient(alice) [cnf transformation 23]
137. wise(X0) | rich(X0) [duplicate literal removal 123]
139. tall(X0) | ~kind(X0) [duplicate literal removal 85]
140. ~kind(X0) | ~tall(X0) [duplicate literal removal 87]
159. ~kind(X0) [subsumption resolution 139,140]
202. 15 <=> patient(alice) [avatar definition]
204. ~patient(alice) <- (~15) [avatar component clause 202]
250. ~wise(X0) | ~creative(X0) [subsumption resolution 116,159]
251. ~wise(X0) | creative(X0) [subsumption resolution 115,159]
252. ~wise(X0) [subsumption resolution 251,250]
254. 25 <=> ! [X1] : generous(X1) [avatar definition]
255. generous(X1) <- (25) [avatar component clause 254]
266. 28 <=> generous(sK5) [avatar definition]
268. ~generous(sK5) <- (~28) [avatar component clause 266]
271. 29 <=> ! [X3] : patient(X3) [avatar definition]
272. patient(X3) <- (29) [avatar component clause 271]
273. 29 | ~28 [avatar split clause 117,266,271]
275. rich(X0) [subsumption resolution 137,252]
294. ~15 [avatar split clause 136,202]
295. generous(X0) [resolution 91,275]
296. 25 [avatar split clause 295,254]
298. $false <- (25, ~28) [resolution 255,268]
299. ~25 | 28 [avatar contradiction clause 298]
305. $false <- (~15, 29) [resolution 272,204]
308. 15 | ~29 [avatar contradiction clause 305]
309. $false [avatar sat refutation 273,294,296,299,308]
% SZS output end Proof for 3634643089489520217348187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or wise then lucy is either calm or quiet and vice versa.
Everyone who is not strong or happy is either not kind or kind and vice versa.
Everyone who is either not brave or not tall is patient and vice versa.
Everyone who is not rich is quiet and vice versa.
Everyone who is strong or old is not happy.
Everyone who is not quiet or wise is generous or brave and vice versa.
If fred is old then someone is either not patient or not strong and vice versa.
If someone is not curious then someone is not happy and vice versa.
If someone is either not humble or not curious then someone is humble or not humble and vice versa.
If someone is creative then fred is calm or not calm and vice versa.
Everyone who is either happy or calm is both kind and not patient.
If paul is creative then someone is either not calm or not generous and vice versa.
Everyone who is either not old or not quiet is not curious or not quiet and vice versa.
Everyone who is both funny and not old is either creative or humble.
If someone is not generous or curious then fred is either happy or not funny.
Everyone who is curious is strong or quiet and vice versa.
Someone is humble.
Mary is both calm and not curious.
Someone is either not wise or not humble.
Alice is tall or not strong.
Someone is either not wise or not generous. | Paul is brave. | neutral | ((?[X]:((brave(X)|wise(X))))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>patient(X)))&
(![X]:(~rich(X)<=>quiet(X)))&
(![X]:((strong(X)|old(X))=>~happy(X)))&
(![X]:((~quiet(X)|wise(X))<=>(generous(X)|brave(X))))&
((old(fred))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:(~happy(X))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:(creative(X)))<=>((calm(fred)|~calm(fred))))&
(![X]:((happy(X)<~>calm(X))=>(kind(X)&~patient(X))))&
((creative(paul))<=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((funny(X)&~old(X))=>(creative(X)<~>humble(X))))&
((?[X]:((~generous(X)|curious(X))))=>((happy(fred)<~>~funny(fred))))&
(![X]:(curious(X)<=>(strong(X)|quiet(X))))&
(?[X]:(humble(X)))&
((calm(mary)&~curious(mary)))&
(?[X]:((~wise(X)<~>~humble(X))))&
((tall(alice)|~strong(alice)))&
(?[X]:((~wise(X)<~>~generous(X)))) | brave(paul) | [] | null | 0 |
If someone is both not creative and tall then someone is not old or brave and vice versa. Everyone who is brave is both creative and not happy. Everyone who is happy is both happy and not creative and vice versa. If susan is either generous or strong then susan is either not curious or not funny. If paul is either not tall or not kind then someone is quiet or not rich and vice versa. Everyone who is not rich is patient or quiet. If mary is quiet then alice is quiet and vice versa. If john is both funny and generous then susan is either not humble or not strong and vice versa. If lucy is not tall then fred is not patient or not kind and vice versa. If someone is rich then someone is either not brave or not happy and vice versa. Everyone who is either curious or not tall is either not calm or rich and vice versa. Everyone who is both brave and calm is not patient. If someone is both not patient and not funny then paul is creative. If alice is both generous and not funny then someone is not happy and vice versa. If someone is both not calm and not curious then someone is tall and vice versa. Everyone who is both not strong and not patient is not humble. Susan is not calm or rich. Mary is either not patient or not generous. Alice is kind. Someone is either not creative or not funny. Someone is both not old and not funny. Fred is both not old and creative. Fred is either kind or old. Someone is funny. | Susan is not humble. | neutral | ((?[X]:((~creative(X)&tall(X))))<=>(?[X]:((~old(X)|brave(X)))))&
(![X]:(brave(X)=>(creative(X)&~happy(X))))&
(![X]:(happy(X)<=>(happy(X)&~creative(X))))&
(((generous(susan)<~>strong(susan)))=>((~curious(susan)<~>~funny(susan))))&
(((~tall(paul)<~>~kind(paul)))<=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:(~rich(X)=>(patient(X)|quiet(X))))&
((quiet(mary))<=>(quiet(alice)))&
(((funny(john)&generous(john)))<=>((~humble(susan)<~>~strong(susan))))&
((~tall(lucy))<=>((~patient(fred)|~kind(fred))))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((brave(X)&calm(X))=>~patient(X)))&
((?[X]:((~patient(X)&~funny(X))))=>(creative(paul)))&
(((generous(alice)&~funny(alice)))<=>(?[X]:(~happy(X))))&
((?[X]:((~calm(X)&~curious(X))))<=>(?[X]:(tall(X))))&
(![X]:((~strong(X)&~patient(X))=>~humble(X)))&
((~calm(susan)|rich(susan)))&
((~patient(mary)<~>~generous(mary)))&
(kind(alice))&
(?[X]:((~creative(X)<~>~funny(X))))&
(?[X]:((~old(X)&~funny(X))))&
((~old(fred)&creative(fred)))&
((kind(fred)<~>old(fred)))&
(?[X]:(funny(X))) | ~humble(susan) | [] | null | 0 |
If paul is not funny then susan is either patient or not patient.
Everyone who is strong is not curious or not wise and vice versa.
Everyone who is funny or old is either not quiet or rich and vice versa.
Everyone who is either rich or funny is either not tall or not quiet and vice versa.
Everyone who is kind is funny or wise.
Everyone who is humble or not calm is both not quiet and strong.
If someone is patient then paul is either not brave or patient and vice versa.
Everyone who is both generous and brave is either tall or humble and vice versa.
Everyone who is both not creative and not patient is both not strong and not wise.
Everyone who is funny is either tall or not strong.
Everyone who is calm is both not old and not tall and vice versa.
If someone is both happy and not patient then lucy is both quiet and creative.
If someone is not strong then paul is not generous and vice versa.
Everyone who is either not quiet or not old is not creative and vice versa.
If someone is either not rich or creative then someone is not generous.
Everyone who is either funny or not wise is both not tall and not kind.
Paul is not rich.
Someone is not patient.
Mary is both strong and rich.
Someone is both brave and not calm.
Someone is both kind and patient.
Fred is either old or curious.
Paul is either generous or not generous. | Susan is strong. | entailment | ((~funny(paul))=>((patient(susan)<~>~patient(susan))))&
(![X]:(strong(X)<=>(~curious(X)|~wise(X))))&
(![X]:((funny(X)|old(X))<=>(~quiet(X)<~>rich(X))))&
(![X]:((rich(X)<~>funny(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:(kind(X)=>(funny(X)|wise(X))))&
(![X]:((humble(X)|~calm(X))=>(~quiet(X)&strong(X))))&
((?[X]:(patient(X)))<=>((~brave(paul)<~>patient(paul))))&
(![X]:((generous(X)&brave(X))<=>(tall(X)<~>humble(X))))&
(![X]:((~creative(X)&~patient(X))=>(~strong(X)&~wise(X))))&
(![X]:(funny(X)=>(tall(X)<~>~strong(X))))&
(![X]:(calm(X)<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)&~patient(X))))=>((quiet(lucy)&creative(lucy))))&
((?[X]:(~strong(X)))<=>(~generous(paul)))&
(![X]:((~quiet(X)<~>~old(X))<=>~creative(X)))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:(~generous(X))))&
(![X]:((funny(X)<~>~wise(X))=>(~tall(X)&~kind(X))))&
(~rich(paul))&
(?[X]:(~patient(X)))&
((strong(mary)&rich(mary)))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((kind(X)&patient(X))))&
((old(fred)<~>curious(fred)))&
((generous(paul)<~>~generous(paul))) | strong(susan) | [
"p2",
"p3",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4962149738056725053194534
% SZS output start Proof for 4962149738056725053194534
3. ! [X0] : ((old(X0) | funny(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> funny(X0)) <=> (~tall(X0) <~> ~quiet(X0))) [input p3]
6. ! [X0] : ((~calm(X0) | humble(X0)) => (strong(X0) & ~quiet(X0))) [input p5]
10. ! [X0] : (funny(X0) => (tall(X0) <~> ~strong(X0))) [input p9]
11. ! [X0] : (calm(X0) <=> (~tall(X0) & ~old(X0))) [input p10]
24. ~strong(susan) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~quiet(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 6]
33. ! [X0] : ((tall(X0) <~> ~strong(X0)) | ~funny(X0)) [ennf transformation 10]
39. ! [X0] : (((old(X0) | funny(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (~old(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((old(X0) | funny(X0) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (~old(X0) & ~funny(X0)))) [flattening 39]
41. ! [X0] : ((((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0))))) [nnf transformation 4]
48. ! [X0] : (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | ~funny(X0)) [nnf transformation 33]
49. ! [X0] : ((calm(X0) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 11]
50. ! [X0] : ((calm(X0) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ~calm(X0))) [flattening 49]
74. ~quiet(X0) | rich(X0) | ~funny(X0) [cnf transformation 40]
76. ~rich(X0) | quiet(X0) | ~funny(X0) [cnf transformation 40]
78. rich(X0) | funny(X0) | old(X0) | quiet(X0) [cnf transformation 40]
79. ~rich(X0) | funny(X0) | ~quiet(X0) | old(X0) [cnf transformation 40]
82. quiet(X0) | tall(X0) | funny(X0) | ~rich(X0) [cnf transformation 41]
83. quiet(X0) | tall(X0) | rich(X0) | ~funny(X0) [cnf transformation 41]
84. funny(X0) | rich(X0) | ~quiet(X0) | tall(X0) [cnf transformation 41]
86. ~funny(X0) | ~rich(X0) | ~quiet(X0) | tall(X0) [cnf transformation 41]
92. calm(X0) | strong(X0) [cnf transformation 30]
106. ~tall(X0) | strong(X0) | ~funny(X0) [cnf transformation 48]
107. ~calm(X0) | ~old(X0) [cnf transformation 50]
108. ~calm(X0) | ~tall(X0) [cnf transformation 50]
134. ~strong(susan) [cnf transformation 24]
135. ~rich(X0) | ~funny(X0) | tall(X0) [subsumption resolution 86,76]
136. ~quiet(X0) | rich(X0) | tall(X0) [subsumption resolution 84,74]
137. ~funny(X0) | tall(X0) | quiet(X0) [subsumption resolution 83,76]
138. ~rich(X0) | tall(X0) | quiet(X0) [subsumption resolution 82,137]
168. 7 <=> ! [X1] : strong(X1) [avatar definition]
169. strong(X1) <- (7) [avatar component clause 168]
195. ~old(X0) | strong(X0) [resolution 107,92]
196. ~tall(X0) | strong(X0) [resolution 108,92]
330. funny(X0) | old(X0) | quiet(X0) | tall(X0) | quiet(X0) [resolution 78,138]
336. funny(X0) | old(X0) | quiet(X0) | tall(X0) [duplicate literal removal 330]
350. tall(X0) | quiet(X0) | old(X0) [subsumption resolution 336,137]
419. quiet(X7) | old(X7) | strong(X7) [resolution 350,196]
423. quiet(X7) | strong(X7) [subsumption resolution 419,195]
467. strong(X0) | rich(X0) | tall(X0) [resolution 423,136]
474. rich(X0) | strong(X0) [subsumption resolution 467,196]
643. strong(X0) | funny(X0) | ~quiet(X0) | old(X0) [resolution 474,79]
645. strong(X2) | ~funny(X2) | tall(X2) [resolution 474,135]
648. strong(X0) | funny(X0) | old(X0) [subsumption resolution 643,423]
649. strong(X0) | funny(X0) [subsumption resolution 648,195]
650. strong(X2) | ~funny(X2) [subsumption resolution 645,106]
651. strong(X2) [subsumption resolution 650,649]
652. 7 [avatar split clause 651,168]
655. $false <- (7) [resolution 169,134]
660. ~7 [avatar contradiction clause 655]
661. $false [avatar sat refutation 652,660]
% SZS output end Proof for 4962149738056725053194534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not humble is both generous and not humble and vice versa.
If alice is not funny or strong then someone is both not calm and not rich.
If someone is both calm and not creative then someone is old or not humble and vice versa.
Everyone who is either not patient or not creative is both not calm and not rich and vice versa.
Everyone who is either not kind or not humble is either not old or not tall.
Everyone who is either calm or funny is either not quiet or not strong.
If fred is both not strong and funny then someone is either not kind or kind and vice versa.
Everyone who is either not brave or not generous is both happy and patient and vice versa.
Everyone who is either not wise or curious is calm.
Everyone who is wise is either not wise or not calm and vice versa.
If mary is either not brave or not rich then someone is either humble or patient and vice versa.
Everyone who is both generous and tall is patient or calm and vice versa.
If mary is humble then alice is not tall or not kind and vice versa.
If lucy is either not calm or creative then susan is strong or not kind and vice versa.
Everyone who is either patient or not strong is both strong and generous and vice versa.
If someone is not old or not humble then someone is both quiet and wise.
Mary is not creative or generous.
Someone is both not calm and humble.
Alice is not rich or not brave.
Someone is both not happy and not old.
Someone is either wise or kind. | Lucy is tall. | entailment | (![X]:((~brave(X)|~humble(X))<=>(generous(X)&~humble(X))))&
(((~funny(alice)|strong(alice)))=>(?[X]:((~calm(X)&~rich(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:((old(X)|~humble(X)))))&
(![X]:((~patient(X)<~>~creative(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(~old(X)<~>~tall(X))))&
(![X]:((calm(X)<~>funny(X))=>(~quiet(X)<~>~strong(X))))&
(((~strong(fred)&funny(fred)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:((~brave(X)<~>~generous(X))<=>(happy(X)&patient(X))))&
(![X]:((~wise(X)<~>curious(X))=>calm(X)))&
(![X]:(wise(X)<=>(~wise(X)<~>~calm(X))))&
(((~brave(mary)<~>~rich(mary)))<=>(?[X]:((humble(X)<~>patient(X)))))&
(![X]:((generous(X)&tall(X))<=>(patient(X)|calm(X))))&
((humble(mary))<=>((~tall(alice)|~kind(alice))))&
(((~calm(lucy)<~>creative(lucy)))<=>((strong(susan)|~kind(susan))))&
(![X]:((patient(X)<~>~strong(X))<=>(strong(X)&generous(X))))&
((?[X]:((~old(X)|~humble(X))))=>(?[X]:((quiet(X)&wise(X)))))&
((~creative(mary)|generous(mary)))&
(?[X]:((~calm(X)&humble(X))))&
((~rich(alice)|~brave(alice)))&
(?[X]:((~happy(X)&~old(X))))&
(?[X]:((wise(X)<~>kind(X)))) | tall(lucy) | [
"p0",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6759702023572549921592415
% SZS output start Proof for 6759702023572549921592415
1. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (~humble(X0) & generous(X0))) [input p0]
8. ! [X0] : ((~brave(X0) <~> ~generous(X0)) <=> (patient(X0) & happy(X0))) [input p7]
12. ! [X0] : ((tall(X0) & generous(X0)) <=> (calm(X0) | patient(X0))) [input p11]
15. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (generous(X0) & strong(X0))) [input p14]
22. ~tall(lucy) [input hypothesis]
30. ! [X0] : (((~humble(X0) | ~brave(X0)) | (humble(X0) | ~generous(X0))) & ((~humble(X0) & generous(X0)) | (humble(X0) & brave(X0)))) [nnf transformation 1]
31. ! [X0] : ((~humble(X0) | ~brave(X0) | humble(X0) | ~generous(X0)) & ((~humble(X0) & generous(X0)) | (humble(X0) & brave(X0)))) [flattening 30]
48. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (~patient(X0) | ~happy(X0))) & ((patient(X0) & happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [nnf transformation 8]
49. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~patient(X0) | ~happy(X0)) & ((patient(X0) & happy(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [flattening 48]
56. ! [X0] : (((tall(X0) & generous(X0)) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | (~tall(X0) | ~generous(X0)))) [nnf transformation 12]
57. ! [X0] : (((tall(X0) & generous(X0)) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | ~tall(X0) | ~generous(X0))) [flattening 56]
62. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 15]
63. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 62]
74. generous(X0) | brave(X0) [cnf transformation 31]
111. patient(X0) | ~brave(X0) | generous(X0) [cnf transformation 49]
129. generous(X0) | ~patient(X0) [cnf transformation 57]
131. ~patient(X0) | tall(X0) [cnf transformation 57]
143. strong(X0) | patient(X0) | strong(X0) [cnf transformation 63]
146. ~strong(X0) | patient(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 63]
160. ~tall(lucy) [cnf transformation 22]
161. strong(X0) | patient(X0) [duplicate literal removal 143]
162. ~strong(X0) | patient(X0) | ~generous(X0) [duplicate literal removal 146]
237. patient(X0) | generous(X0) [subsumption resolution 111,74]
272. generous(X0) [subsumption resolution 129,237]
308. ~strong(X0) | patient(X0) [subsumption resolution 162,272]
309. patient(X0) [subsumption resolution 161,308]
355. tall(X0) [resolution 131,309]
362. $false [resolution 355,160]
% SZS output end Proof for 6759702023572549921592415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either funny or strong.
Everyone who is not quiet is both patient and not brave and vice versa.
Everyone who is not tall is not calm.
Everyone who is not humble is curious and vice versa.
If john is not strong then someone is either calm or not humble and vice versa.
Everyone who is both patient and not tall is both not funny and strong.
Everyone who is both not patient and happy is funny and vice versa.
If someone is not strong or tall then paul is not humble or not happy.
If someone is either wise or creative then someone is both happy and wise and vice versa.
Everyone who is both tall and not funny is both wise and not strong.
Everyone who is both not curious and not tall is not patient or not creative.
Everyone who is not tall is kind or tall and vice versa.
Everyone who is both quiet and happy is both quiet and not humble.
Everyone who is either funny or not kind is either humble or not humble.
If someone is both creative and quiet then someone is calm and vice versa.
Someone is both brave and kind.
Fred is either strong or tall.
Someone is either not rich or not happy.
Someone is either not kind or not brave.
John is either brave or not brave.
Someone is wise or not brave. | Fred is kind. | entailment | (![X]:(brave(X)=>(funny(X)<~>strong(X))))&
(![X]:(~quiet(X)<=>(patient(X)&~brave(X))))&
(![X]:(~tall(X)=>~calm(X)))&
(![X]:(~humble(X)<=>curious(X)))&
((~strong(john))<=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:((patient(X)&~tall(X))=>(~funny(X)&strong(X))))&
(![X]:((~patient(X)&happy(X))<=>funny(X)))&
((?[X]:((~strong(X)|tall(X))))=>((~humble(paul)|~happy(paul))))&
((?[X]:((wise(X)<~>creative(X))))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:((tall(X)&~funny(X))=>(wise(X)&~strong(X))))&
(![X]:((~curious(X)&~tall(X))=>(~patient(X)|~creative(X))))&
(![X]:(~tall(X)<=>(kind(X)|tall(X))))&
(![X]:((quiet(X)&happy(X))=>(quiet(X)&~humble(X))))&
(![X]:((funny(X)<~>~kind(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(calm(X))))&
(?[X]:((brave(X)&kind(X))))&
((strong(fred)<~>tall(fred)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((brave(john)<~>~brave(john)))&
(?[X]:((wise(X)|~brave(X)))) | kind(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2492880537946770549718898
% SZS output start Proof for 2492880537946770549718898
12. ! [X0] : (~tall(X0) <=> (tall(X0) | kind(X0))) [input p11]
22. ~kind(fred) [input hypothesis]
53. ! [X0] : ((~tall(X0) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | tall(X0))) [nnf transformation 12]
54. ! [X0] : ((~tall(X0) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | tall(X0))) [flattening 53]
101. tall(X0) | kind(X0) | tall(X0) [cnf transformation 54]
103. ~tall(X0) | ~tall(X0) [cnf transformation 54]
124. ~kind(fred) [cnf transformation 22]
125. kind(X0) | tall(X0) [duplicate literal removal 101]
126. ~tall(X0) [duplicate literal removal 103]
150. 6 <=> ! [X0] : ~tall(X0) [avatar definition]
151. ~tall(X0) <- (6) [avatar component clause 150]
196. 6 [avatar split clause 126,150]
262. tall(fred) [resolution 125,124]
266. $false <- (6) [subsumption resolution 262,151]
267. ~6 [avatar contradiction clause 266]
270. $false [avatar sat refutation 196,267]
% SZS output end Proof for 2492880537946770549718898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or patient then someone is not quiet and vice versa.
Everyone who is both not old and tall is not generous or calm and vice versa.
If paul is not quiet then someone is brave or tall.
If someone is quiet or humble then someone is not wise or kind.
If someone is not old or kind then john is both not patient and happy.
Everyone who is rich is not tall or tall.
If someone is not rich then someone is either brave or calm.
Everyone who is both old and not calm is rich or not humble.
Everyone who is both not happy and patient is either creative or not rich.
If someone is both humble and not creative then someone is not happy or old.
Everyone who is both generous and not curious is both not old and wise and vice versa.
Everyone who is both not brave and tall is kind.
If paul is not quiet then alice is both generous and not wise and vice versa.
Everyone who is either not brave or not happy is either curious or brave and vice versa.
Everyone who is either brave or not kind is not patient or creative.
Everyone who is both creative and not strong is either wise or rich.
Fred is either not kind or happy.
Someone is quiet.
Alice is either not calm or old.
Someone is either happy or old.
Paul is not rich or not wise.
Someone is either kind or rich.
Someone is both not strong and creative.
Fred is both patient and brave. | Alice is curious. | neutral | ((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~old(X)&tall(X))<=>(~generous(X)|calm(X))))&
((~quiet(paul))=>(?[X]:((brave(X)|tall(X)))))&
((?[X]:((quiet(X)|humble(X))))=>(?[X]:((~wise(X)|kind(X)))))&
((?[X]:((~old(X)|kind(X))))=>((~patient(john)&happy(john))))&
(![X]:(rich(X)=>(~tall(X)|tall(X))))&
((?[X]:(~rich(X)))=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:((old(X)&~calm(X))=>(rich(X)|~humble(X))))&
(![X]:((~happy(X)&patient(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((generous(X)&~curious(X))<=>(~old(X)&wise(X))))&
(![X]:((~brave(X)&tall(X))=>kind(X)))&
((~quiet(paul))<=>((generous(alice)&~wise(alice))))&
(![X]:((~brave(X)<~>~happy(X))<=>(curious(X)<~>brave(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~patient(X)|creative(X))))&
(![X]:((creative(X)&~strong(X))=>(wise(X)<~>rich(X))))&
((~kind(fred)<~>happy(fred)))&
(?[X]:(quiet(X)))&
((~calm(alice)<~>old(alice)))&
(?[X]:((happy(X)<~>old(X))))&
((~rich(paul)|~wise(paul)))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:((~strong(X)&creative(X))))&
((patient(fred)&brave(fred))) | curious(alice) | [] | null | 0 |
Everyone who is strong is not humble or funny.
Everyone who is both creative and strong is curious and vice versa.
Everyone who is either wise or not old is generous or not patient and vice versa.
If alice is not quiet then paul is either not rich or happy and vice versa.
Everyone who is not humble is either not generous or not patient and vice versa.
If someone is either not strong or tall then someone is not generous and vice versa.
Everyone who is not tall or not strong is both rich and not strong and vice versa.
Everyone who is brave or generous is either tall or not old and vice versa.
Everyone who is either brave or curious is both kind and not happy.
If someone is both curious and brave then someone is both tall and not generous and vice versa.
If paul is funny or kind then someone is not kind or not curious.
Everyone who is humble is not rich and vice versa.
Everyone who is not rich is either not wise or happy.
If lucy is not quiet then fred is either not generous or tall.
If someone is not patient then someone is not wise.
Everyone who is not quiet is generous and vice versa.
Someone is not strong.
Someone is not happy or not kind.
John is funny or not brave.
Someone is not old.
Fred is not calm.
Someone is funny.
Mary is patient or not tall.
Susan is both kind and not creative. | Fred is not curious. | neutral | (![X]:(strong(X)=>(~humble(X)|funny(X))))&
(![X]:((creative(X)&strong(X))<=>curious(X)))&
(![X]:((wise(X)<~>~old(X))<=>(generous(X)|~patient(X))))&
((~quiet(alice))<=>((~rich(paul)<~>happy(paul))))&
(![X]:(~humble(X)<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)|~strong(X))<=>(rich(X)&~strong(X))))&
(![X]:((brave(X)|generous(X))<=>(tall(X)<~>~old(X))))&
(![X]:((brave(X)<~>curious(X))=>(kind(X)&~happy(X))))&
((?[X]:((curious(X)&brave(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(((funny(paul)|kind(paul)))=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:(humble(X)<=>~rich(X)))&
(![X]:(~rich(X)=>(~wise(X)<~>happy(X))))&
((~quiet(lucy))=>((~generous(fred)<~>tall(fred))))&
((?[X]:(~patient(X)))=>(?[X]:(~wise(X))))&
(![X]:(~quiet(X)<=>generous(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)|~kind(X))))&
((funny(john)|~brave(john)))&
(?[X]:(~old(X)))&
(~calm(fred))&
(?[X]:(funny(X)))&
((patient(mary)|~tall(mary)))&
((kind(susan)&~creative(susan))) | ~curious(fred) | [] | null | 0 |
Everyone who is not funny or old is creative or not funny and vice versa.
Everyone who is both not humble and not wise is not curious or not brave.
Everyone who is happy or calm is not quiet.
Everyone who is not kind or not quiet is quiet and vice versa.
Everyone who is both not rich and strong is either not calm or not patient and vice versa.
If mary is patient or not old then susan is not curious or rich.
Everyone who is either not calm or quiet is either old or brave.
If mary is both kind and tall then paul is both patient and not happy.
Everyone who is either not patient or rich is not kind or not generous and vice versa.
Everyone who is both funny and not patient is both not brave and old and vice versa.
If john is either not generous or not wise then lucy is humble or not wise and vice versa.
If someone is kind then susan is either rich or not generous and vice versa.
Everyone who is not brave is either not strong or not rich and vice versa.
Everyone who is either kind or not curious is both not curious and brave and vice versa.
If someone is both not kind and not creative then someone is not kind and vice versa.
Someone is not curious or not strong.
Lucy is old.
John is both quiet and old.
Susan is both wise and curious. | Paul is creative. | neutral | (![X]:((~funny(X)|old(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)|~brave(X))))&
(![X]:((happy(X)|calm(X))=>~quiet(X)))&
(![X]:((~kind(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(mary)|~old(mary)))=>((~curious(susan)|rich(susan))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)<~>brave(X))))&
(((kind(mary)&tall(mary)))=>((patient(paul)&~happy(paul))))&
(![X]:((~patient(X)<~>rich(X))<=>(~kind(X)|~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~brave(X)&old(X))))&
(((~generous(john)<~>~wise(john)))<=>((humble(lucy)|~wise(lucy))))&
((?[X]:(kind(X)))<=>((rich(susan)<~>~generous(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~rich(X))))&
(![X]:((kind(X)<~>~curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:(~kind(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(old(lucy))&
((quiet(john)&old(john)))&
((wise(susan)&curious(susan))) | creative(paul) | [] | null | 0 |
If lucy is not tall or strong then someone is not old or curious.
Everyone who is both not generous and not tall is both not quiet and wise and vice versa.
Everyone who is not creative or not funny is creative or not quiet.
Everyone who is calm is both old and creative and vice versa.
Everyone who is either calm or patient is curious and vice versa.
Everyone who is creative is either tall or not rich.
Everyone who is either not humble or not happy is both generous and calm.
Everyone who is either not wise or patient is either not curious or rich.
Everyone who is funny is brave and vice versa.
Everyone who is not creative or not funny is not tall or wise and vice versa.
Everyone who is not happy is both old and tall and vice versa.
Everyone who is either not kind or not old is not quiet.
Everyone who is both not rich and not humble is either not curious or wise.
Everyone who is curious is not patient.
Everyone who is either quiet or old is not happy and vice versa.
Everyone who is both not generous and kind is not strong.
Susan is humble or not old.
Lucy is not calm or quiet.
Lucy is either kind or not brave.
Someone is both happy and strong.
Lucy is both not old and not tall.
Someone is not tall or happy.
John is not calm or not creative.
Someone is not happy. | Lucy is not kind. | neutral | (((~tall(lucy)|strong(lucy)))=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((~generous(X)&~tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~creative(X)|~funny(X))=>(creative(X)|~quiet(X))))&
(![X]:(calm(X)<=>(old(X)&creative(X))))&
(![X]:((calm(X)<~>patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(generous(X)&calm(X))))&
(![X]:((~wise(X)<~>patient(X))=>(~curious(X)<~>rich(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~creative(X)|~funny(X))<=>(~tall(X)|wise(X))))&
(![X]:(~happy(X)<=>(old(X)&tall(X))))&
(![X]:((~kind(X)<~>~old(X))=>~quiet(X)))&
(![X]:((~rich(X)&~humble(X))=>(~curious(X)<~>wise(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((quiet(X)<~>old(X))<=>~happy(X)))&
(![X]:((~generous(X)&kind(X))=>~strong(X)))&
((humble(susan)|~old(susan)))&
((~calm(lucy)|quiet(lucy)))&
((kind(lucy)<~>~brave(lucy)))&
(?[X]:((happy(X)&strong(X))))&
((~old(lucy)&~tall(lucy)))&
(?[X]:((~tall(X)|happy(X))))&
((~calm(john)|~creative(john)))&
(?[X]:(~happy(X))) | ~kind(lucy) | [] | null | 0 |
Everyone who is not generous or not funny is either not calm or rich and vice versa.
If mary is either patient or quiet then someone is both not generous and tall and vice versa.
Everyone who is not curious or not funny is either not old or not quiet.
If someone is either calm or not brave then someone is both not calm and not brave and vice versa.
Everyone who is both quiet and not kind is both not creative and kind.
If someone is not tall then someone is both not strong and kind.
If lucy is calm or not quiet then alice is both calm and curious and vice versa.
Everyone who is not kind or strong is either not humble or patient and vice versa.
If someone is not rich then alice is calm.
Everyone who is either quiet or not calm is not humble or wise.
If someone is either not curious or not tall then someone is quiet or creative.
Everyone who is either not humble or not wise is either not patient or rich and vice versa.
If someone is kind then someone is strong.
Everyone who is either old or not curious is not kind or old.
Everyone who is old is either kind or funny.
If lucy is strong then susan is not funny or not rich and vice versa.
Susan is either generous or not kind.
Someone is not wise or not rich.
Someone is both rich and kind.
Alice is not kind or calm.
Lucy is both not wise and funny.
Someone is either strong or not calm.
Someone is not happy.
Mary is either not tall or generous. | Susan is not happy. | neutral | (![X]:((~generous(X)|~funny(X))<=>(~calm(X)<~>rich(X))))&
(((patient(mary)<~>quiet(mary)))<=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)|~funny(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((quiet(X)&~kind(X))=>(~creative(X)&kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((calm(lucy)|~quiet(lucy)))<=>((calm(alice)&curious(alice))))&
(![X]:((~kind(X)|strong(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:(~rich(X)))=>(calm(alice)))&
(![X]:((quiet(X)<~>~calm(X))=>(~humble(X)|wise(X))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((~humble(X)<~>~wise(X))<=>(~patient(X)<~>rich(X))))&
((?[X]:(kind(X)))=>(?[X]:(strong(X))))&
(![X]:((old(X)<~>~curious(X))=>(~kind(X)|old(X))))&
(![X]:(old(X)=>(kind(X)<~>funny(X))))&
((strong(lucy))<=>((~funny(susan)|~rich(susan))))&
((generous(susan)<~>~kind(susan)))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((rich(X)&kind(X))))&
((~kind(alice)|calm(alice)))&
((~wise(lucy)&funny(lucy)))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:(~happy(X)))&
((~tall(mary)<~>generous(mary))) | ~happy(susan) | [] | null | 0 |
Everyone who is either not kind or not humble is both not patient and funny.
Everyone who is either not generous or funny is either not brave or not quiet.
Everyone who is not quiet is not brave or not rich and vice versa.
If someone is not quiet then paul is brave and vice versa.
Everyone who is humble or not brave is not funny or not happy.
If someone is either not humble or not kind then alice is both humble and not quiet and vice versa.
Everyone who is not happy is either not humble or not calm.
Everyone who is both patient and not kind is not wise or not calm and vice versa.
Everyone who is both not generous and creative is both old and not patient.
If someone is either happy or creative then someone is either not calm or funny and vice versa.
Everyone who is both brave and tall is not generous or funny.
Everyone who is not patient or generous is either not calm or not old and vice versa.
Everyone who is not strong or humble is not funny or not tall and vice versa.
Everyone who is not kind is old or quiet.
If mary is either not calm or humble then someone is not rich or not humble and vice versa.
If john is happy or humble then alice is quiet or not funny.
Someone is kind or generous.
Someone is not old or not happy.
Someone is either not creative or not quiet.
John is both not wise and not calm.
Someone is happy.
Alice is both tall and not creative.
Someone is both not creative and curious.
John is both not calm and not brave. | Paul is not old. | neutral | (![X]:((~kind(X)<~>~humble(X))=>(~patient(X)&funny(X))))&
(![X]:((~generous(X)<~>funny(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
((?[X]:(~quiet(X)))<=>(brave(paul)))&
(![X]:((humble(X)|~brave(X))=>(~funny(X)|~happy(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((humble(alice)&~quiet(alice))))&
(![X]:(~happy(X)=>(~humble(X)<~>~calm(X))))&
(![X]:((patient(X)&~kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~generous(X)&creative(X))=>(old(X)&~patient(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:((~calm(X)<~>funny(X)))))&
(![X]:((brave(X)&tall(X))=>(~generous(X)|funny(X))))&
(![X]:((~patient(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((~strong(X)|humble(X))<=>(~funny(X)|~tall(X))))&
(![X]:(~kind(X)=>(old(X)|quiet(X))))&
(((~calm(mary)<~>humble(mary)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((happy(john)|humble(john)))=>((quiet(alice)|~funny(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((~old(X)|~happy(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
((~wise(john)&~calm(john)))&
(?[X]:(happy(X)))&
((tall(alice)&~creative(alice)))&
(?[X]:((~creative(X)&curious(X))))&
((~calm(john)&~brave(john))) | ~old(paul) | [] | null | 0 |
Everyone who is either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
If someone is both not curious and old then mary is tall.
Everyone who is not happy is not patient and vice versa.
Everyone who is calm or curious is both calm and kind.
Everyone who is both not creative and not humble is old or tall.
Everyone who is both not kind and brave is creative or tall.
Alice is either funny or not humble.
Someone is not curious or strong.
Mary is not humble or kind.
Someone is generous.
Someone is both not wise and not generous.
John is old or quiet. | Mary is not quiet. | entailment | (![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
((?[X]:((~curious(X)&old(X))))=>(tall(mary)))&
(![X]:(~happy(X)<=>~patient(X)))&
(![X]:((calm(X)|curious(X))=>(calm(X)&kind(X))))&
(![X]:((~creative(X)&~humble(X))=>(old(X)|tall(X))))&
(![X]:((~kind(X)&brave(X))=>(creative(X)|tall(X))))&
((funny(alice)<~>~humble(alice)))&
(?[X]:((~curious(X)|strong(X))))&
((~humble(mary)|kind(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&~generous(X))))&
((old(john)|quiet(john))) | ~quiet(mary) | [
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2091925500130895474180660
% SZS output start Proof for 2091925500130895474180660
6. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p5]
7. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p6]
8. ! [X0] : ((calm(X0) & happy(X0)) => (strong(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p8]
10. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X0] : (patient(X0) & ~kind(X0)) [input p9]
13. ! [X0] : (~happy(X0) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((curious(X0) | calm(X0)) => (kind(X0) & calm(X0))) [input p13]
23. quiet(mary) [input hypothesis]
24. ? [X0] : (funny(X0) <~> creative(X0)) <=> ? [X1] : (patient(X1) & ~kind(X1)) [rectify 10]
26. ! [X0] : ((calm(X0) & happy(X0)) => ~quiet(X0)) [pure predicate removal 8]
29. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 7]
30. ! [X0] : (~quiet(X0) | (~calm(X0) | ~happy(X0))) [ennf transformation 26]
31. ! [X0] : (~quiet(X0) | ~calm(X0) | ~happy(X0)) [flattening 30]
35. ! [X0] : ((kind(X0) & calm(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 14]
51. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 6]
52. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 9]
53. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 52]
54. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X1] : (patient(X1) & ~kind(X1)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) [nnf transformation 24]
55. (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ! [X1] : (~patient(X1) | kind(X1))) & (? [X2] : (patient(X2) & ~kind(X2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [rectify 54]
56. ? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) => ((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) [choice axiom]
57. ? [X2] : (patient(X2) & ~kind(X2)) => (patient(sK2) & ~kind(sK2)) [choice axiom]
58. (((~creative(sK1) | ~funny(sK1)) & (creative(sK1) | funny(sK1))) | ! [X1] : (~patient(X1) | kind(X1))) & ((patient(sK2) & ~kind(sK2)) | ! [X3] : ((funny(X3) | ~creative(X3)) & (creative(X3) | ~funny(X3)))) [skolemisation 55,57,56]
59. ! [X0] : ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0))) [nnf transformation 13]
90. ~calm(X0) | patient(X0) | funny(X0) [cnf transformation 51]
93. creative(X0) | calm(X0) [cnf transformation 29]
94. ~happy(X0) | calm(X0) [cnf transformation 29]
95. ~quiet(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 31]
99. ~creative(X0) | kind(X0) [cnf transformation 53]
100. ~creative(X0) | ~funny(X0) [cnf transformation 53]
101. ~kind(sK2) | creative(X3) | ~funny(X3) [cnf transformation 58]
102. ~kind(sK2) | funny(X3) | ~creative(X3) [cnf transformation 58]
109. ~patient(X0) | happy(X0) [cnf transformation 59]
113. ~calm(X0) | kind(X0) [cnf transformation 35]
124. quiet(mary) [cnf transformation 23]
152. 6 <=> ! [X1] : kind(X1) [avatar definition]
153. kind(X1) <- (6) [avatar component clause 152]
156. ~quiet(X0) | ~happy(X0) [subsumption resolution 95,94]
171. 10 <=> ! [X3] : ~creative(X3) [avatar definition]
172. ~creative(X3) <- (10) [avatar component clause 171]
180. 12 <=> ! [X3] : ~funny(X3) [avatar definition]
181. ~funny(X3) <- (12) [avatar component clause 180]
183. ~kind(sK2) | ~creative(X3) [subsumption resolution 102,100]
185. 13 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~13) [avatar component clause 185]
188. 10 | ~13 [avatar split clause 183,185,171]
189. ~kind(sK2) | ~funny(X3) [subsumption resolution 101,100]
190. 12 | ~13 [avatar split clause 189,185,180]
228. kind(X0) | calm(X0) [resolution 99,93]
229. kind(X0) [subsumption resolution 228,113]
230. 6 [avatar split clause 229,152]
232. $false <- (6, ~13) [resolution 153,187]
233. ~6 | 13 [avatar contradiction clause 232]
235. calm(X0) <- (10) [resolution 172,93]
243. ~happy(mary) [resolution 156,124]
264. patient(X0) | funny(X0) <- (10) [resolution 90,235]
266. patient(X0) <- (10, 12) [subsumption resolution 264,181]
276. happy(X3) <- (10, 12) [resolution 266,109]
292. $false <- (10, 12) [resolution 276,243]
293. ~10 | ~12 [avatar contradiction clause 292]
294. $false [avatar sat refutation 188,190,230,233,293]
% SZS output end Proof for 2091925500130895474180660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or brave is either not brave or not quiet and vice versa. Everyone who is both not quiet and not funny is both generous and tall. If susan is either rich or quiet then someone is either generous or creative and vice versa. Everyone who is humble is quiet or not rich. If alice is kind then alice is tall. If paul is both not strong and not happy then alice is either patient or not old and vice versa. Everyone who is both strong and humble is both creative and not old. If john is either funny or curious then john is either old or not patient and vice versa. Everyone who is strong or rich is either humble or not rich. Everyone who is kind or not tall is either not rich or brave. Everyone who is both not tall and generous is both not brave and patient and vice versa. If lucy is either not calm or not tall then someone is funny or curious and vice versa. Everyone who is not tall is either curious or tall and vice versa. Everyone who is both happy and not tall is both funny and not curious. Everyone who is both not kind and not humble is both not tall and not rich and vice versa. Everyone who is both happy and not calm is not curious and vice versa. Lucy is either quiet or curious. Someone is either tall or not kind. Someone is both quiet and patient. Paul is either happy or strong. Mary is funny or creative. John is either not brave or not rich. Mary is not humble. | Susan is not tall. | neutral | (![X]:((patient(X)<~>brave(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~funny(X))=>(generous(X)&tall(X))))&
(((rich(susan)<~>quiet(susan)))<=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(humble(X)=>(quiet(X)|~rich(X))))&
((kind(alice))=>(tall(alice)))&
(((~strong(paul)&~happy(paul)))<=>((patient(alice)<~>~old(alice))))&
(![X]:((strong(X)&humble(X))=>(creative(X)&~old(X))))&
(((funny(john)<~>curious(john)))<=>((old(john)<~>~patient(john))))&
(![X]:((strong(X)|rich(X))=>(humble(X)<~>~rich(X))))&
(![X]:((kind(X)|~tall(X))=>(~rich(X)<~>brave(X))))&
(![X]:((~tall(X)&generous(X))<=>(~brave(X)&patient(X))))&
(((~calm(lucy)<~>~tall(lucy)))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(~tall(X)<=>(curious(X)<~>tall(X))))&
(![X]:((happy(X)&~tall(X))=>(funny(X)&~curious(X))))&
(![X]:((~kind(X)&~humble(X))<=>(~tall(X)&~rich(X))))&
(![X]:((happy(X)&~calm(X))<=>~curious(X)))&
((quiet(lucy)<~>curious(lucy)))&
(?[X]:((tall(X)<~>~kind(X))))&
(?[X]:((quiet(X)&patient(X))))&
((happy(paul)<~>strong(paul)))&
((funny(mary)|creative(mary)))&
((~brave(john)<~>~rich(john)))&
(~humble(mary)) | ~tall(susan) | [] | null | 0 |
If alice is wise or not patient then john is either not brave or not tall.
Everyone who is funny is not curious or strong and vice versa.
Everyone who is either not humble or not calm is curious.
If alice is not funny then someone is both curious and strong and vice versa.
Everyone who is not tall or calm is either not tall or not humble.
If paul is either kind or not old then fred is either not wise or old and vice versa.
Everyone who is either patient or not old is both humble and old and vice versa.
If john is old then someone is both not curious and curious.
If someone is kind then someone is either not tall or rich and vice versa.
If someone is not rich or creative then someone is not wise or rich.
If someone is both not strong and humble then someone is either not rich or happy and vice versa.
Everyone who is not curious or not creative is curious or strong and vice versa.
Everyone who is kind or not happy is either not patient or creative.
If someone is creative or old then someone is creative or not generous and vice versa.
If john is both not calm and not patient then someone is tall or wise and vice versa.
Lucy is both not tall and not rich.
Mary is quiet.
Mary is both not calm and old.
John is either happy or generous. | Fred is not wise. | entailment | (((wise(alice)|~patient(alice)))=>((~brave(john)<~>~tall(john))))&
(![X]:(funny(X)<=>(~curious(X)|strong(X))))&
(![X]:((~humble(X)<~>~calm(X))=>curious(X)))&
((~funny(alice))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((~tall(X)|calm(X))=>(~tall(X)<~>~humble(X))))&
(((kind(paul)<~>~old(paul)))<=>((~wise(fred)<~>old(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(humble(X)&old(X))))&
((old(john))=>(?[X]:((~curious(X)&curious(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((~tall(X)<~>rich(X)))))&
((?[X]:((~rich(X)|creative(X))))=>(?[X]:((~wise(X)|rich(X)))))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~rich(X)<~>happy(X)))))&
(![X]:((~curious(X)|~creative(X))<=>(curious(X)|strong(X))))&
(![X]:((kind(X)|~happy(X))=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)|old(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(((~calm(john)&~patient(john)))<=>(?[X]:((tall(X)|wise(X)))))&
((~tall(lucy)&~rich(lucy)))&
(quiet(mary))&
((~calm(mary)&old(mary)))&
((happy(john)<~>generous(john))) | ~wise(fred) | [
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5321778941229477376806012
% SZS output start Proof for 5321778941229477376806012
7. ! [X0] : ((patient(X0) <~> ~old(X0)) <=> (old(X0) & humble(X0))) [input p6]
8. old(john) => ? [X0] : (curious(X0) & ~curious(X0)) [input p7]
15. (~patient(john) & ~calm(john)) <=> ? [X0] : (wise(X0) | tall(X0)) [input p14]
20. wise(fred) [input hypothesis]
29. ? [X0] : (curious(X0) & ~curious(X0)) | ~old(john) [ennf transformation 8]
42. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [nnf transformation 7]
43. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [flattening 42]
44. ? [X0] : (curious(X0) & ~curious(X0)) => (curious(sK1) & ~curious(sK1)) [choice axiom]
45. (curious(sK1) & ~curious(sK1)) | ~old(john) [skolemisation 29,44]
67. ((~patient(john) & ~calm(john)) | ! [X0] : (~wise(X0) & ~tall(X0))) & (? [X0] : (wise(X0) | tall(X0)) | (patient(john) | calm(john))) [nnf transformation 15]
68. ((~patient(john) & ~calm(john)) | ! [X0] : (~wise(X0) & ~tall(X0))) & (? [X0] : (wise(X0) | tall(X0)) | patient(john) | calm(john)) [flattening 67]
69. ((~patient(john) & ~calm(john)) | ! [X0] : (~wise(X0) & ~tall(X0))) & (? [X1] : (wise(X1) | tall(X1)) | patient(john) | calm(john)) [rectify 68]
70. ? [X1] : (wise(X1) | tall(X1)) => (wise(sK9) | tall(sK9)) [choice axiom]
71. ((~patient(john) & ~calm(john)) | ! [X0] : (~wise(X0) & ~tall(X0))) & ((wise(sK9) | tall(sK9)) | patient(john) | calm(john)) [skolemisation 69,70]
100. old(X0) | patient(X0) | old(X0) [cnf transformation 43]
103. ~curious(sK1) | ~old(john) [cnf transformation 45]
104. curious(sK1) | ~old(john) [cnf transformation 45]
133. ~patient(john) | ~wise(X0) [cnf transformation 71]
140. wise(fred) [cnf transformation 20]
143. old(X0) | patient(X0) [duplicate literal removal 100]
189. 10 <=> wise(fred) [avatar definition]
190. wise(fred) <- (10) [avatar component clause 189]
209. 13 <=> old(john) [avatar definition]
211. ~old(john) <- (~13) [avatar component clause 209]
213. 14 <=> curious(sK1) [avatar definition]
216. ~13 | 14 [avatar split clause 104,213,209]
217. ~13 | ~14 [avatar split clause 103,213,209]
317. 38 <=> ! [X0] : ~wise(X0) [avatar definition]
318. ~wise(X0) <- (38) [avatar component clause 317]
320. 39 <=> patient(john) [avatar definition]
322. ~patient(john) <- (~39) [avatar component clause 320]
323. 38 | ~39 [avatar split clause 133,320,317]
353. 10 [avatar split clause 140,189]
354. $false <- (10, 38) [subsumption resolution 190,318]
355. ~10 | ~38 [avatar contradiction clause 354]
367. patient(john) <- (~13) [resolution 143,211]
368. $false <- (~13, ~39) [subsumption resolution 367,322]
369. 13 | 39 [avatar contradiction clause 368]
370. $false [avatar sat refutation 216,217,323,353,355,369]
% SZS output end Proof for 5321778941229477376806012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is calm then lucy is either not patient or humble and vice versa.
Everyone who is not humble or not rich is both creative and kind and vice versa.
If someone is not creative then fred is either not tall or not brave.
If someone is either brave or creative then someone is not quiet or not brave.
If someone is not humble then someone is either not wise or generous and vice versa.
Everyone who is not funny or not generous is not brave.
If john is both not happy and not generous then john is either brave or not quiet.
Everyone who is either tall or not rich is either quiet or not brave and vice versa.
Everyone who is not curious or curious is either not generous or rich and vice versa.
Everyone who is either not tall or not quiet is both quiet and not quiet.
Everyone who is either not calm or not old is not happy and vice versa.
Everyone who is both not kind and not funny is strong or generous and vice versa.
If someone is not strong or not old then someone is both not brave and not humble.
If someone is either not wise or tall then someone is generous or not tall and vice versa.
If mary is both funny and curious then someone is quiet.
If someone is brave or not calm then paul is both brave and creative.
Susan is either not generous or not kind.
John is kind.
John is tall.
Someone is either not creative or not rich.
Someone is funny or not quiet.
Mary is not tall. | Lucy is not strong. | entailment | ((calm(fred))<=>((~patient(lucy)<~>humble(lucy))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)&kind(X))))&
((?[X]:(~creative(X)))=>((~tall(fred)<~>~brave(fred))))&
((?[X]:((brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)|~brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((~funny(X)|~generous(X))=>~brave(X)))&
(((~happy(john)&~generous(john)))=>((brave(john)<~>~quiet(john))))&
(![X]:((tall(X)<~>~rich(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~curious(X)|curious(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(quiet(X)&~quiet(X))))&
(![X]:((~calm(X)<~>~old(X))<=>~happy(X)))&
(![X]:((~kind(X)&~funny(X))<=>(strong(X)|generous(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((generous(X)|~tall(X)))))&
(((funny(mary)&curious(mary)))=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~calm(X))))=>((brave(paul)&creative(paul))))&
((~generous(susan)<~>~kind(susan)))&
(kind(john))&
(tall(john))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((funny(X)|~quiet(X))))&
(~tall(mary)) | ~strong(lucy) | [
"p1",
"p5",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4500040602956014882280059
% SZS output start Proof for 4500040602956014882280059
2. ! [X0] : ((~rich(X0) | ~humble(X0)) <=> (kind(X0) & creative(X0))) [input p1]
6. ! [X0] : ((~generous(X0) | ~funny(X0)) => ~brave(X0)) [input p5]
8. ! [X0] : ((tall(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p7]
10. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) => (~quiet(X0) & quiet(X0))) [input p9]
12. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (generous(X0) | strong(X0))) [input p11]
16. ? [X0] : (~calm(X0) | brave(X0)) => (creative(paul) & brave(paul)) [input p15]
23. strong(lucy) [input hypothesis]
31. ! [X0] : (~brave(X0) | (generous(X0) & funny(X0))) [ennf transformation 6]
34. ! [X0] : ((~quiet(X0) & quiet(X0)) | (~tall(X0) <=> ~quiet(X0))) [ennf transformation 10]
39. (creative(paul) & brave(paul)) | ! [X0] : (calm(X0) & ~brave(X0)) [ennf transformation 16]
41. ! [X0] : (((~rich(X0) | ~humble(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [nnf transformation 2]
42. ! [X0] : ((~rich(X0) | ~humble(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (rich(X0) & humble(X0)))) [flattening 41]
54. ! [X0] : ((((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))))) [nnf transformation 8]
57. ! [X0] : ((~quiet(X0) & quiet(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) [nnf transformation 34]
59. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & ((generous(X0) | strong(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 12]
60. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & (generous(X0) | strong(X0) | funny(X0) | kind(X0))) [flattening 59]
84. kind(X0) | rich(X0) [cnf transformation 42]
94. ~brave(X0) | funny(X0) [cnf transformation 31]
95. ~brave(X0) | generous(X0) [cnf transformation 31]
100. ~quiet(X0) | brave(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 54]
103. ~rich(X0) | tall(X0) | quiet(X0) | brave(X0) [cnf transformation 54]
113. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 57]
114. ~quiet(X0) | ~quiet(X0) | tall(X0) [cnf transformation 57]
119. ~strong(X0) | ~kind(X0) [cnf transformation 60]
122. ~funny(X0) | ~generous(X0) [cnf transformation 60]
134. brave(paul) | ~brave(X0) [cnf transformation 39]
146. strong(lucy) [cnf transformation 23]
147. ~tall(X0) | quiet(X0) [duplicate literal removal 113]
148. ~quiet(X0) | tall(X0) [duplicate literal removal 114]
309. 37 <=> ! [X0] : ~brave(X0) [avatar definition]
310. ~brave(X0) <- (37) [avatar component clause 309]
313. 38 <=> brave(paul) [avatar definition]
315. brave(paul) <- (38) [avatar component clause 313]
317. 37 | 38 [avatar split clause 134,313,309]
349. funny(paul) <- (38) [resolution 94,315]
350. generous(paul) <- (38) [resolution 95,315]
351. ~kind(lucy) [resolution 119,146]
352. rich(lucy) [resolution 351,84]
363. ~generous(paul) <- (38) [resolution 122,349]
364. $false <- (38) [subsumption resolution 363,350]
365. ~38 [avatar contradiction clause 364]
396. tall(lucy) | quiet(lucy) | brave(lucy) [resolution 103,352]
399. tall(lucy) | quiet(lucy) <- (37) [subsumption resolution 396,310]
400. tall(lucy) <- (37) [subsumption resolution 399,148]
403. quiet(lucy) <- (37) [resolution 400,147]
432. brave(lucy) | ~rich(lucy) | ~tall(lucy) <- (37) [resolution 403,100]
434. ~rich(lucy) | ~tall(lucy) <- (37) [subsumption resolution 432,310]
435. ~tall(lucy) <- (37) [subsumption resolution 434,352]
436. $false <- (37) [subsumption resolution 435,400]
437. ~37 [avatar contradiction clause 436]
438. $false [avatar sat refutation 317,365,437]
% SZS output end Proof for 4500040602956014882280059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or happy is generous or happy and vice versa.
If someone is strong then someone is both tall and old.
If someone is either not strong or not rich then paul is quiet.
Everyone who is generous is not rich.
If fred is not tall then john is either funny or old.
Everyone who is not creative or strong is not happy.
If someone is either not generous or rich then someone is either wise or not funny and vice versa.
Everyone who is not calm is not quiet or happy and vice versa.
If someone is both not kind and strong then someone is both not creative and not wise and vice versa.
Everyone who is wise or not rich is not patient and vice versa.
If paul is generous then mary is funny or generous.
If john is rich then someone is curious or funny.
Everyone who is not wise is not generous or funny.
If john is either rich or quiet then someone is both not old and not rich.
If someone is both creative and not rich then someone is both curious and rich and vice versa.
Everyone who is not strong or tall is either rich or generous and vice versa.
Mary is either tall or happy.
Mary is not creative.
Lucy is not calm.
Someone is either not creative or tall.
Paul is both happy and not old.
Someone is both not old and not brave.
Someone is both curious and not old.
John is rich. | John is not generous. | entailment | (![X]:((~patient(X)|happy(X))<=>(generous(X)|happy(X))))&
((?[X]:(strong(X)))=>(?[X]:((tall(X)&old(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(quiet(paul)))&
(![X]:(generous(X)=>~rich(X)))&
((~tall(fred))=>((funny(john)<~>old(john))))&
(![X]:((~creative(X)|strong(X))=>~happy(X)))&
((?[X]:((~generous(X)<~>rich(X))))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(![X]:(~calm(X)<=>(~quiet(X)|happy(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((wise(X)|~rich(X))<=>~patient(X)))&
((generous(paul))=>((funny(mary)|generous(mary))))&
((rich(john))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:(~wise(X)=>(~generous(X)|funny(X))))&
(((rich(john)<~>quiet(john)))=>(?[X]:((~old(X)&~rich(X)))))&
((?[X]:((creative(X)&~rich(X))))<=>(?[X]:((curious(X)&rich(X)))))&
(![X]:((~strong(X)|tall(X))<=>(rich(X)<~>generous(X))))&
((tall(mary)<~>happy(mary)))&
(~creative(mary))&
(~calm(lucy))&
(?[X]:((~creative(X)<~>tall(X))))&
((happy(paul)&~old(paul)))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((curious(X)&~old(X))))&
(rich(john)) | ~generous(john) | [
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7348571434189777864583942
% SZS output start Proof for 7348571434189777864583942
4. ! [X0] : (generous(X0) => ~rich(X0)) [input p3]
24. rich(john) [input p23]
25. generous(john) [input hypothesis]
34. ! [X0] : (~rich(X0) | ~generous(X0)) [ennf transformation 4]
92. ~rich(X0) | ~generous(X0) [cnf transformation 34]
141. rich(john) [cnf transformation 24]
142. generous(john) [cnf transformation 25]
257. 26 <=> rich(john) [avatar definition]
258. rich(john) <- (26) [avatar component clause 257]
333. 26 [avatar split clause 141,257]
334. ~generous(john) <- (26) [resolution 92,258]
335. $false <- (26) [subsumption resolution 334,142]
336. ~26 [avatar contradiction clause 335]
337. $false [avatar sat refutation 333,336]
% SZS output end Proof for 7348571434189777864583942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or tall then john is rich or not curious.
Everyone who is brave or curious is not kind and vice versa.
Everyone who is both happy and brave is either brave or not strong and vice versa.
Everyone who is kind is both old and not old.
If fred is not generous then someone is both generous and not kind.
Everyone who is quiet is not creative and vice versa.
Everyone who is patient is either not kind or curious and vice versa.
If someone is wise or curious then someone is tall or not strong and vice versa.
If john is not old or rich then fred is both humble and generous and vice versa.
If someone is curious then lucy is either not kind or rich.
If someone is either not strong or patient then someone is kind or strong and vice versa.
Everyone who is old or not old is humble or not tall.
Everyone who is not wise or not strong is not humble and vice versa.
Everyone who is not patient or brave is both not calm and not creative and vice versa.
If susan is not happy then someone is either not happy or tall and vice versa.
Everyone who is either happy or quiet is not patient and vice versa.
Someone is both not creative and strong.
Paul is both not creative and not kind.
Fred is funny or not calm.
Someone is either humble or not kind.
Someone is curious or not wise.
Mary is not rich or not kind.
Paul is wise. | Mary is not creative. | entailment | ((?[X]:((humble(X)|tall(X))))=>((rich(john)|~curious(john))))&
(![X]:((brave(X)|curious(X))<=>~kind(X)))&
(![X]:((happy(X)&brave(X))<=>(brave(X)<~>~strong(X))))&
(![X]:(kind(X)=>(old(X)&~old(X))))&
((~generous(fred))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(![X]:(patient(X)<=>(~kind(X)<~>curious(X))))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:((tall(X)|~strong(X)))))&
(((~old(john)|rich(john)))<=>((humble(fred)&generous(fred))))&
((?[X]:(curious(X)))=>((~kind(lucy)<~>rich(lucy))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:((old(X)|~old(X))=>(humble(X)|~tall(X))))&
(![X]:((~wise(X)|~strong(X))<=>~humble(X)))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)&~creative(X))))&
((~happy(susan))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((happy(X)<~>quiet(X))<=>~patient(X)))&
(?[X]:((~creative(X)&strong(X))))&
((~creative(paul)&~kind(paul)))&
((funny(fred)|~calm(fred)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:((curious(X)|~wise(X))))&
((~rich(mary)|~kind(mary)))&
(wise(paul)) | ~creative(mary) | [
"p1",
"p3",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7750743064071315178637470
% SZS output start Proof for 7750743064071315178637470
2. ! [X0] : ((curious(X0) | brave(X0)) <=> ~kind(X0)) [input p1]
4. ! [X0] : (kind(X0) => (~old(X0) & old(X0))) [input p3]
7. ! [X0] : (patient(X0) <=> (~kind(X0) <~> curious(X0))) [input p6]
14. ! [X0] : ((brave(X0) | ~patient(X0)) <=> (~creative(X0) & ~calm(X0))) [input p13]
24. creative(mary) [input hypothesis]
30. ! [X0] : ((~old(X0) & old(X0)) | ~kind(X0)) [ennf transformation 4]
35. ! [X0] : (((curious(X0) | brave(X0)) | kind(X0)) & (~kind(X0) | (~curious(X0) & ~brave(X0)))) [nnf transformation 2]
36. ! [X0] : ((curious(X0) | brave(X0) | kind(X0)) & (~kind(X0) | (~curious(X0) & ~brave(X0)))) [flattening 35]
42. ! [X0] : ((patient(X0) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | ~patient(X0))) [nnf transformation 7]
58. ! [X0] : (((brave(X0) | ~patient(X0)) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | (~brave(X0) & patient(X0)))) [nnf transformation 14]
59. ! [X0] : ((brave(X0) | ~patient(X0) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | (~brave(X0) & patient(X0)))) [flattening 58]
76. kind(X0) | brave(X0) | curious(X0) [cnf transformation 36]
83. old(X0) | ~kind(X0) [cnf transformation 30]
84. ~old(X0) | ~kind(X0) [cnf transformation 30]
90. ~curious(X0) | kind(X0) | ~patient(X0) [cnf transformation 42]
117. ~creative(X0) | patient(X0) [cnf transformation 59]
118. ~creative(X0) | ~brave(X0) [cnf transformation 59]
137. creative(mary) [cnf transformation 24]
157. ~kind(X0) [subsumption resolution 83,84]
168. ~patient(X0) | ~curious(X0) [subsumption resolution 90,157]
283. patient(mary) [resolution 117,137]
285. ~brave(mary) [resolution 118,137]
290. ~curious(mary) [resolution 168,283]
296. brave(X2) | curious(X2) [resolution 76,157]
393. curious(mary) [resolution 296,285]
397. $false [subsumption resolution 393,290]
% SZS output end Proof for 7750743064071315178637470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or wise is either not wise or tall and vice versa.
If fred is both calm and not humble then someone is rich and vice versa.
Everyone who is strong is wise or not patient and vice versa.
Everyone who is calm or rich is both quiet and happy.
Everyone who is happy is not tall or kind and vice versa.
Everyone who is not calm or not patient is quiet.
Everyone who is not curious is quiet.
If fred is both not wise and not tall then paul is not old or curious and vice versa.
Everyone who is both curious and funny is not calm or not generous and vice versa.
Everyone who is both not old and not strong is either not happy or not old and vice versa.
If someone is both not quiet and not wise then someone is both rich and not curious and vice versa.
If someone is humble or curious then fred is either curious or not curious and vice versa.
Everyone who is old is both rich and not humble and vice versa.
Everyone who is wise or creative is both not quiet and not patient.
If someone is both happy and not happy then someone is either not tall or strong and vice versa.
Alice is either not patient or brave.
Someone is brave.
John is either funny or not patient.
Alice is tall or funny.
Someone is not generous or creative.
Someone is both calm and brave. | John is strong. | contradiction | (![X]:((~generous(X)<~>wise(X))<=>(~wise(X)<~>tall(X))))&
(((calm(fred)&~humble(fred)))<=>(?[X]:(rich(X))))&
(![X]:(strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((calm(X)|rich(X))=>(quiet(X)&happy(X))))&
(![X]:(happy(X)<=>(~tall(X)|kind(X))))&
(![X]:((~calm(X)|~patient(X))=>quiet(X)))&
(![X]:(~curious(X)=>quiet(X)))&
(((~wise(fred)&~tall(fred)))<=>((~old(paul)|curious(paul))))&
(![X]:((curious(X)&funny(X))<=>(~calm(X)|~generous(X))))&
(![X]:((~old(X)&~strong(X))<=>(~happy(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((rich(X)&~curious(X)))))&
((?[X]:((humble(X)|curious(X))))<=>((curious(fred)<~>~curious(fred))))&
(![X]:(old(X)<=>(rich(X)&~humble(X))))&
(![X]:((wise(X)|creative(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
((~patient(alice)<~>brave(alice)))&
(?[X]:(brave(X)))&
((funny(john)<~>~patient(john)))&
((tall(alice)|funny(alice)))&
(?[X]:((~generous(X)|creative(X))))&
(?[X]:((calm(X)&brave(X)))) | strong(john) | [
"p0",
"p2",
"p3",
"p5",
"p8",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4909987775052372564315255
% SZS output start Proof for 4909987775052372564315255
1. ! [X0] : ((~generous(X0) <~> wise(X0)) <=> (~wise(X0) <~> tall(X0))) [input p0]
3. ! [X0] : (strong(X0) <=> (~patient(X0) | wise(X0))) [input p2]
4. ! [X0] : ((rich(X0) | calm(X0)) => (happy(X0) & quiet(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | ~calm(X0)) => quiet(X0)) [input p5]
9. ! [X0] : ((funny(X0) & curious(X0)) <=> (~generous(X0) | ~calm(X0))) [input p8]
14. ! [X0] : ((creative(X0) | wise(X0)) => (~patient(X0) & ~quiet(X0))) [input p13]
15. ? [X0] : (~happy(X0) & happy(X0)) <=> ? [X0] : (~tall(X0) <~> strong(X0)) [input p14]
18. funny(john) <~> ~patient(john) [input p17]
22. strong(john) [input hypothesis]
24. ? [X0] : (~happy(X0) & happy(X0)) <=> ? [X1] : (~tall(X1) <~> strong(X1)) [rectify 15]
25. ! [X0] : ((happy(X0) & quiet(X0)) | (~rich(X0) & ~calm(X0))) [ennf transformation 4]
26. ! [X0] : (quiet(X0) | (patient(X0) & calm(X0))) [ennf transformation 6]
28. ! [X0] : ((~patient(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0))) [ennf transformation 14]
29. ! [X0] : ((((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))))) [nnf transformation 1]
35. ! [X0] : ((strong(X0) | (patient(X0) & ~wise(X0))) & ((~patient(X0) | wise(X0)) | ~strong(X0))) [nnf transformation 3]
36. ! [X0] : ((strong(X0) | (patient(X0) & ~wise(X0))) & (~patient(X0) | wise(X0) | ~strong(X0))) [flattening 35]
41. ! [X0] : (((funny(X0) & curious(X0)) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | (~funny(X0) | ~curious(X0)))) [nnf transformation 9]
42. ! [X0] : (((funny(X0) & curious(X0)) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ~funny(X0) | ~curious(X0))) [flattening 41]
56. (? [X0] : (~happy(X0) & happy(X0)) | ! [X1] : ((~tall(X1) | ~strong(X1)) & (strong(X1) | tall(X1)))) & (? [X1] : ((~strong(X1) | tall(X1)) & (strong(X1) | ~tall(X1))) | ! [X0] : (happy(X0) | ~happy(X0))) [nnf transformation 24]
57. (? [X0] : (~happy(X0) & happy(X0)) | ! [X1] : ((~tall(X1) | ~strong(X1)) & (strong(X1) | tall(X1)))) & (? [X2] : ((~strong(X2) | tall(X2)) & (strong(X2) | ~tall(X2))) | ! [X3] : (happy(X3) | ~happy(X3))) [rectify 56]
58. ? [X0] : (~happy(X0) & happy(X0)) => (~happy(sK4) & happy(sK4)) [choice axiom]
59. ? [X2] : ((~strong(X2) | tall(X2)) & (strong(X2) | ~tall(X2))) => ((~strong(sK5) | tall(sK5)) & (strong(sK5) | ~tall(sK5))) [choice axiom]
60. ((~happy(sK4) & happy(sK4)) | ! [X1] : ((~tall(X1) | ~strong(X1)) & (strong(X1) | tall(X1)))) & (((~strong(sK5) | tall(sK5)) & (strong(sK5) | ~tall(sK5))) | ! [X3] : (happy(X3) | ~happy(X3))) [skolemisation 57,59,58]
64. (patient(john) | ~funny(john)) & (~patient(john) | funny(john)) [nnf transformation 18]
70. tall(X0) | ~wise(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 29]
73. wise(X0) | ~generous(X0) | tall(X0) | wise(X0) [cnf transformation 29]
80. ~patient(X0) | wise(X0) | ~strong(X0) [cnf transformation 36]
83. ~calm(X0) | quiet(X0) [cnf transformation 25]
90. quiet(X0) | calm(X0) [cnf transformation 26]
102. funny(X0) | generous(X0) [cnf transformation 42]
122. ~quiet(X0) | ~wise(X0) [cnf transformation 28]
129. happy(sK4) | ~tall(X1) | ~strong(X1) [cnf transformation 60]
131. ~happy(sK4) | ~tall(X1) | ~strong(X1) [cnf transformation 60]
136. patient(john) | ~funny(john) [cnf transformation 64]
141. strong(john) [cnf transformation 22]
146. tall(X0) | ~wise(X0) | ~generous(X0) [duplicate literal removal 70]
148. wise(X0) | ~generous(X0) | tall(X0) [duplicate literal removal 73]
151. ~generous(X0) | tall(X0) [subsumption resolution 146,148]
170. quiet(X0) [subsumption resolution 90,83]
218. ~wise(X0) [subsumption resolution 122,170]
220. 14 <=> ! [X1] : (~tall(X1) | ~strong(X1)) [avatar definition]
221. ~strong(X1) | ~tall(X1) <- (14) [avatar component clause 220]
223. 15 <=> happy(sK4) [avatar definition]
226. 14 | ~15 [avatar split clause 131,223,220]
231. 14 | 15 [avatar split clause 129,223,220]
244. 19 <=> funny(john) [avatar definition]
246. ~funny(john) <- (~19) [avatar component clause 244]
248. 20 <=> patient(john) [avatar definition]
250. patient(john) <- (20) [avatar component clause 248]
251. ~19 | 20 [avatar split clause 136,248,244]
278. generous(john) <- (~19) [resolution 102,246]
282. tall(john) <- (~19) [resolution 151,278]
286. ~tall(john) <- (14) [resolution 221,141]
288. $false <- (14, ~19) [subsumption resolution 286,282]
289. ~14 | 19 [avatar contradiction clause 288]
297. wise(john) | ~strong(john) <- (20) [resolution 80,250]
299. ~strong(john) <- (20) [subsumption resolution 297,218]
300. $false <- (20) [subsumption resolution 299,141]
301. ~20 [avatar contradiction clause 300]
302. $false [avatar sat refutation 226,231,251,289,301]
% SZS output end Proof for 4909987775052372564315255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and generous is not calm. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. If someone is either calm or curious then someone is both curious and not creative and vice versa. If someone is quiet or old then fred is not funny or not creative and vice versa. If someone is either curious or funny then someone is calm and vice versa. Fred is patient or brave. Someone is strong or not funny. Fred is both generous and funny. Alice is not funny or creative. Someone is either humble or not wise. Someone is not curious or not funny. Someone is generous. | Fred is not funny. | contradiction | (![X]:((~quiet(X)&generous(X))=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((quiet(X)|old(X))))<=>((~funny(fred)|~creative(fred))))&
((?[X]:((curious(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
((patient(fred)|brave(fred)))&
(?[X]:((strong(X)|~funny(X))))&
((generous(fred)&funny(fred)))&
((~funny(alice)|creative(alice)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:(generous(X))) | ~funny(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3543943549242537554255907
% SZS output start Proof for 3543943549242537554255907
19. funny(fred) & generous(fred) [input p18]
24. ~funny(fred) [input hypothesis]
132. funny(fred) [cnf transformation 19]
138. ~funny(fred) [cnf transformation 24]
236. 22 <=> funny(fred) [avatar definition]
282. 22 [avatar split clause 132,236]
311. ~22 [avatar split clause 138,236]
312. $false [avatar sat refutation 282,311]
% SZS output end Proof for 3543943549242537554255907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and rich is creative or strong and vice versa.
If someone is either rich or happy then someone is both not funny and not curious and vice versa.
If someone is either not humble or not generous then someone is either brave or strong.
Everyone who is not rich or brave is both not tall and strong.
If mary is both brave and not creative then someone is funny or not quiet and vice versa.
Everyone who is either creative or old is both not patient and not kind and vice versa.
Everyone who is either not curious or generous is not rich or humble.
Everyone who is either not strong or not patient is humble.
Everyone who is not brave is not rich.
If mary is both not wise and curious then someone is either calm or not tall and vice versa.
If someone is not old or not quiet then lucy is both not rich and creative and vice versa.
Everyone who is both not humble and wise is not generous.
Everyone who is both not funny and not kind is curious or patient and vice versa.
Everyone who is either not wise or calm is not curious or not brave.
Everyone who is either not old or not quiet is both humble and strong and vice versa.
Paul is both not funny and not kind.
Someone is either kind or not wise.
Someone is not calm. | Lucy is not happy. | contradiction | (![X]:((creative(X)&rich(X))<=>(creative(X)|strong(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((~funny(X)&~curious(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:((~rich(X)|brave(X))=>(~tall(X)&strong(X))))&
(((brave(mary)&~creative(mary)))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~patient(X)&~kind(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~rich(X)|humble(X))))&
(![X]:((~strong(X)<~>~patient(X))=>humble(X)))&
(![X]:(~brave(X)=>~rich(X)))&
(((~wise(mary)&curious(mary)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~rich(lucy)&creative(lucy))))&
(![X]:((~humble(X)&wise(X))=>~generous(X)))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)|patient(X))))&
(![X]:((~wise(X)<~>calm(X))=>(~curious(X)|~brave(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(humble(X)&strong(X))))&
((~funny(paul)&~kind(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(~calm(X))) | ~happy(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5266570437324052901851233
% SZS output start Proof for 5266570437324052901851233
1. ! [X0] : ((rich(X0) & creative(X0)) <=> (strong(X0) | creative(X0))) [input p0]
2. ? [X0] : (rich(X0) <~> happy(X0)) <=> ? [X0] : (~curious(X0) & ~funny(X0)) [input p1]
3. ? [X0] : (~humble(X0) <~> ~generous(X0)) => ? [X0] : (brave(X0) <~> strong(X0)) [input p2]
4. ! [X0] : ((brave(X0) | ~rich(X0)) => (strong(X0) & ~tall(X0))) [input p3]
7. ! [X0] : ((~curious(X0) <~> generous(X0)) => (humble(X0) | ~rich(X0))) [input p6]
9. ! [X0] : (~brave(X0) => ~rich(X0)) [input p8]
11. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (creative(lucy) & ~rich(lucy)) [input p10]
15. ! [X0] : ((~old(X0) <~> ~quiet(X0)) <=> (strong(X0) & humble(X0))) [input p14]
19. ~happy(lucy) [input hypothesis]
20. ? [X0] : (rich(X0) <~> happy(X0)) <=> ? [X1] : (~curious(X1) & ~funny(X1)) [rectify 2]
21. ? [X0] : (~humble(X0) <~> ~generous(X0)) => ? [X1] : (brave(X1) <~> strong(X1)) [rectify 3]
22. ? [X1] : (brave(X1) <~> strong(X1)) | ! [X0] : (~humble(X0) <=> ~generous(X0)) [ennf transformation 21]
23. ! [X0] : ((strong(X0) & ~tall(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 4]
24. ! [X0] : ((humble(X0) | ~rich(X0)) | (~curious(X0) <=> generous(X0))) [ennf transformation 7]
25. ! [X0] : (humble(X0) | ~rich(X0) | (~curious(X0) <=> generous(X0))) [flattening 24]
27. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 9]
32. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | ~rich(X0) | ~creative(X0))) [flattening 32]
34. (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ! [X1] : (curious(X1) | funny(X1))) & (? [X1] : (~curious(X1) & ~funny(X1)) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) [nnf transformation 20]
35. (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ! [X1] : (curious(X1) | funny(X1))) & (? [X2] : (~curious(X2) & ~funny(X2)) | ! [X3] : ((rich(X3) | ~happy(X3)) & (happy(X3) | ~rich(X3)))) [rectify 34]
36. ? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) => ((~happy(sK0) | ~rich(sK0)) & (happy(sK0) | rich(sK0))) [choice axiom]
37. ? [X2] : (~curious(X2) & ~funny(X2)) => (~curious(sK1) & ~funny(sK1)) [choice axiom]
38. (((~happy(sK0) | ~rich(sK0)) & (happy(sK0) | rich(sK0))) | ! [X1] : (curious(X1) | funny(X1))) & ((~curious(sK1) & ~funny(sK1)) | ! [X3] : ((rich(X3) | ~happy(X3)) & (happy(X3) | ~rich(X3)))) [skolemisation 35,37,36]
39. ? [X1] : ((~strong(X1) | ~brave(X1)) & (strong(X1) | brave(X1))) | ! [X0] : ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))) [nnf transformation 22]
40. ? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | ! [X1] : ((~humble(X1) | generous(X1)) & (~generous(X1) | humble(X1))) [rectify 39]
41. ? [X0] : ((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) => ((~strong(sK2) | ~brave(sK2)) & (strong(sK2) | brave(sK2))) [choice axiom]
42. ((~strong(sK2) | ~brave(sK2)) & (strong(sK2) | brave(sK2))) | ! [X1] : ((~humble(X1) | generous(X1)) & (~generous(X1) | humble(X1))) [skolemisation 40,41]
50. ! [X0] : (humble(X0) | ~rich(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 25]
57. (? [X0] : (~quiet(X0) | ~old(X0)) | (~creative(lucy) | rich(lucy))) & ((creative(lucy) & ~rich(lucy)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 11]
58. (? [X0] : (~quiet(X0) | ~old(X0)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 57]
59. (? [X0] : (~quiet(X0) | ~old(X0)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 58]
60. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK5) | ~old(sK5)) [choice axiom]
61. ((~quiet(sK5) | ~old(sK5)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 59,60]
65. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [nnf transformation 15]
66. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [flattening 65]
76. ~strong(X0) | rich(X0) [cnf transformation 33]
79. ~curious(sK1) | happy(X3) | ~rich(X3) [cnf transformation 38]
85. ~strong(sK2) | ~brave(sK2) | ~generous(X1) | humble(X1) [cnf transformation 42]
89. strong(X0) | rich(X0) [cnf transformation 23]
90. ~brave(X0) | strong(X0) [cnf transformation 23]
102. humble(X0) | ~rich(X0) | generous(X0) | curious(X0) [cnf transformation 50]
106. ~rich(X0) | brave(X0) [cnf transformation 27]
113. ~rich(lucy) | old(X1) [cnf transformation 61]
114. ~rich(lucy) | quiet(X1) [cnf transformation 61]
130. ~old(X0) | ~quiet(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 66]
137. ~happy(lucy) [cnf transformation 19]
155. 5 <=> curious(sK1) [avatar definition]
157. ~curious(sK1) <- (~5) [avatar component clause 155]
160. 6 <=> ! [X3] : (happy(X3) | ~rich(X3)) [avatar definition]
161. happy(X3) | ~rich(X3) <- (6) [avatar component clause 160]
162. 6 | ~5 [avatar split clause 79,155,160]
173. 9 <=> brave(sK2) [avatar definition]
175. ~brave(sK2) <- (~9) [avatar component clause 173]
177. 10 <=> strong(sK2) [avatar definition]
179. ~strong(sK2) <- (~10) [avatar component clause 177]
182. 11 <=> ! [X1] : (~generous(X1) | humble(X1)) [avatar definition]
183. ~generous(X1) | humble(X1) <- (11) [avatar component clause 182]
184. 11 | ~9 | ~10 [avatar split clause 85,177,173,182]
187. rich(X0) [subsumption resolution 89,76]
189. 12 <=> ! [X0] : quiet(X0) [avatar definition]
190. quiet(X0) <- (12) [avatar component clause 189]
216. generous(X0) | humble(X0) | curious(X0) [subsumption resolution 102,187]
217. brave(X0) [subsumption resolution 106,187]
252. 25 <=> ! [X1] : old(X1) [avatar definition]
253. old(X1) <- (25) [avatar component clause 252]
255. quiet(X1) [subsumption resolution 114,187]
256. 12 [avatar split clause 255,189]
257. old(X1) [subsumption resolution 113,187]
258. 25 [avatar split clause 257,252]
276. strong(X0) [resolution 90,217]
278. $false <- (~10) [resolution 276,179]
281. 10 [avatar contradiction clause 278]
282. $false <- (~9) [subsumption resolution 175,217]
283. 9 [avatar contradiction clause 282]
296. humble(X1) | curious(X1) | humble(X1) <- (11) [resolution 216,183]
297. humble(X1) | curious(X1) <- (11) [duplicate literal removal 296]
331. ~quiet(X0) | ~strong(X0) | ~humble(X0) <- (25) [resolution 130,253]
332. ~strong(X0) | ~humble(X0) <- (12, 25) [subsumption resolution 331,190]
333. ~humble(X0) <- (12, 25) [subsumption resolution 332,276]
334. curious(X0) <- (11, 12, 25) [resolution 333,297]
340. $false <- (~5, 11, 12, 25) [resolution 334,157]
343. 5 | ~11 | ~12 | ~25 [avatar contradiction clause 340]
344. happy(X3) <- (6) [subsumption resolution 161,187]
345. $false <- (6) [resolution 344,137]
348. ~6 [avatar contradiction clause 345]
349. $false [avatar sat refutation 162,184,256,258,281,283,343,348]
% SZS output end Proof for 5266570437324052901851233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not rich is both not brave and humble and vice versa.
Everyone who is tall or not curious is old.
If paul is not curious then someone is not strong.
Everyone who is generous is either quiet or not wise and vice versa.
Everyone who is either brave or quiet is either quiet or not calm.
Everyone who is not creative or old is both generous and creative.
If someone is both curious and rich then susan is not curious or not humble.
Everyone who is both not rich and patient is not calm or not curious.
Everyone who is funny is both not generous and not quiet and vice versa.
Everyone who is tall is curious or happy and vice versa.
Everyone who is kind or not creative is either happy or curious.
Everyone who is brave or funny is either creative or humble.
Everyone who is either generous or not tall is both not creative and not happy and vice versa.
If someone is either not rich or not kind then someone is both not happy and not old.
Paul is not quiet.
John is not quiet or not rich.
Paul is old or not humble.
Alice is both not curious and strong. | John is not brave. | entailment | (![X]:((brave(X)|~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((tall(X)|~curious(X))=>old(X)))&
((~curious(paul))=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~wise(X))))&
(![X]:((brave(X)<~>quiet(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((~creative(X)|old(X))=>(generous(X)&creative(X))))&
((?[X]:((curious(X)&rich(X))))=>((~curious(susan)|~humble(susan))))&
(![X]:((~rich(X)&patient(X))=>(~calm(X)|~curious(X))))&
(![X]:(funny(X)<=>(~generous(X)&~quiet(X))))&
(![X]:(tall(X)<=>(curious(X)|happy(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)<~>curious(X))))&
(![X]:((brave(X)|funny(X))=>(creative(X)<~>humble(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((~rich(X)<~>~kind(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(~quiet(paul))&
((~quiet(john)|~rich(john)))&
((old(paul)|~humble(paul)))&
((~curious(alice)&strong(alice))) | ~brave(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1613925930798426657306592
% SZS output start Proof for 1613925930798426657306592
1. ! [X0] : ((~rich(X0) | brave(X0)) <=> (humble(X0) & ~brave(X0))) [input p0]
19. brave(john) [input hypothesis]
34. ! [X0] : (((~rich(X0) | brave(X0)) | (~humble(X0) | brave(X0))) & ((humble(X0) & ~brave(X0)) | (rich(X0) & ~brave(X0)))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | brave(X0) | ~humble(X0) | brave(X0)) & ((humble(X0) & ~brave(X0)) | (rich(X0) & ~brave(X0)))) [flattening 34]
50. ~brave(X0) | ~brave(X0) [cnf transformation 35]
98. brave(john) [cnf transformation 19]
102. ~brave(X0) [duplicate literal removal 50]
166. $false [subsumption resolution 98,102]
% SZS output end Proof for 1613925930798426657306592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not quiet and not humble then someone is both rich and happy and vice versa. Everyone who is happy or not patient is patient or not patient. Everyone who is curious or not funny is both creative and not funny and vice versa. Everyone who is tall is not generous. Everyone who is either creative or not kind is not old and vice versa. Everyone who is quiet or not strong is happy or kind. Everyone who is either wise or tall is either not creative or not strong. If susan is both not generous and not patient then paul is both not kind and not patient. Everyone who is not generous or generous is either not tall or humble and vice versa. Everyone who is humble or generous is happy or wise. If fred is either calm or creative then fred is either strong or creative and vice versa. Everyone who is either not calm or not happy is either funny or wise and vice versa. If someone is both kind and brave then someone is creative and vice versa. If alice is both generous and brave then someone is not rich. Everyone who is either quiet or strong is not quiet and vice versa. Everyone who is both rich and calm is happy or creative and vice versa. Fred is not rich or not patient. Mary is brave or not wise. Susan is both generous and rich. Alice is both not funny and humble. Someone is not calm or funny. Mary is funny. Paul is not old. | Fred is tall. | neutral | (((~quiet(alice)&~humble(alice)))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((happy(X)|~patient(X))=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|~funny(X))<=>(creative(X)&~funny(X))))&
(![X]:(tall(X)=>~generous(X)))&
(![X]:((creative(X)<~>~kind(X))<=>~old(X)))&
(![X]:((quiet(X)|~strong(X))=>(happy(X)|kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(~creative(X)<~>~strong(X))))&
(((~generous(susan)&~patient(susan)))=>((~kind(paul)&~patient(paul))))&
(![X]:((~generous(X)|generous(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)|generous(X))=>(happy(X)|wise(X))))&
(((calm(fred)<~>creative(fred)))<=>((strong(fred)<~>creative(fred))))&
(![X]:((~calm(X)<~>~happy(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(creative(X))))&
(((generous(alice)&brave(alice)))=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)<~>strong(X))<=>~quiet(X)))&
(![X]:((rich(X)&calm(X))<=>(happy(X)|creative(X))))&
((~rich(fred)|~patient(fred)))&
((brave(mary)|~wise(mary)))&
((generous(susan)&rich(susan)))&
((~funny(alice)&humble(alice)))&
(?[X]:((~calm(X)|funny(X))))&
(funny(mary))&
(~old(paul)) | tall(fred) | [] | null | 0 |
Everyone who is both not calm and not humble is creative and vice versa.
Everyone who is not curious is brave or curious.
Everyone who is both kind and calm is both funny and not generous.
Everyone who is not calm is either humble or not creative and vice versa.
Everyone who is both not curious and not kind is both patient and not strong.
If john is old or curious then someone is wise or happy.
If lucy is funny or generous then someone is both curious and not rich.
If john is either not quiet or rich then someone is not curious or not wise and vice versa.
If fred is not old then someone is rich or not old and vice versa.
If john is both not calm and not tall then mary is patient or wise and vice versa.
If someone is not tall or brave then mary is either not funny or not rich.
Everyone who is either not strong or not funny is not curious and vice versa.
If someone is either generous or brave then someone is either not curious or creative and vice versa.
Everyone who is humble is either curious or kind and vice versa.
If john is both old and not curious then fred is either not brave or patient and vice versa.
Everyone who is patient or not brave is not generous or not funny.
Alice is both not tall and funny.
Mary is not rich or kind.
Someone is not brave or funny.
Paul is not strong or old.
Mary is both not wise and not kind.
Fred is not happy.
Mary is either happy or not patient.
Someone is wise or not old. | Fred is happy. | contradiction | (![X]:((~calm(X)&~humble(X))<=>creative(X)))&
(![X]:(~curious(X)=>(brave(X)|curious(X))))&
(![X]:((kind(X)&calm(X))=>(funny(X)&~generous(X))))&
(![X]:(~calm(X)<=>(humble(X)<~>~creative(X))))&
(![X]:((~curious(X)&~kind(X))=>(patient(X)&~strong(X))))&
(((old(john)|curious(john)))=>(?[X]:((wise(X)|happy(X)))))&
(((funny(lucy)|generous(lucy)))=>(?[X]:((curious(X)&~rich(X)))))&
(((~quiet(john)<~>rich(john)))<=>(?[X]:((~curious(X)|~wise(X)))))&
((~old(fred))<=>(?[X]:((rich(X)|~old(X)))))&
(((~calm(john)&~tall(john)))<=>((patient(mary)|wise(mary))))&
((?[X]:((~tall(X)|brave(X))))=>((~funny(mary)<~>~rich(mary))))&
(![X]:((~strong(X)<~>~funny(X))<=>~curious(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((~curious(X)<~>creative(X)))))&
(![X]:(humble(X)<=>(curious(X)<~>kind(X))))&
(((old(john)&~curious(john)))<=>((~brave(fred)<~>patient(fred))))&
(![X]:((patient(X)|~brave(X))=>(~generous(X)|~funny(X))))&
((~tall(alice)&funny(alice)))&
((~rich(mary)|kind(mary)))&
(?[X]:((~brave(X)|funny(X))))&
((~strong(paul)|old(paul)))&
((~wise(mary)&~kind(mary)))&
(~happy(fred))&
((happy(mary)<~>~patient(mary)))&
(?[X]:((wise(X)|~old(X)))) | happy(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3374922502813382098809510
% SZS output start Proof for 3374922502813382098809510
22. ~happy(fred) [input p21]
25. happy(fred) [input hypothesis]
137. ~happy(fred) [cnf transformation 22]
141. happy(fred) [cnf transformation 25]
353. $false [subsumption resolution 141,137]
% SZS output end Proof for 3374922502813382098809510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or happy is either not old or not funny and vice versa.
Everyone who is happy or kind is either calm or brave and vice versa.
Everyone who is either quiet or not kind is either wise or not humble and vice versa.
If fred is both quiet and not creative then someone is calm.
Everyone who is both not quiet and curious is both not happy and funny and vice versa.
Everyone who is either curious or not generous is both happy and strong and vice versa.
If someone is both humble and not curious then mary is either not humble or not calm and vice versa.
Everyone who is either creative or kind is both quiet and calm and vice versa.
Everyone who is old is both old and not tall and vice versa.
If someone is happy then someone is not generous or not kind and vice versa.
If someone is either not curious or not generous then mary is humble or not rich.
If someone is both rich and not tall then someone is both not creative and not patient and vice versa.
Everyone who is either not rich or happy is either tall or not rich.
Everyone who is either old or not calm is not kind and vice versa.
If someone is not creative or not humble then someone is wise or tall.
If someone is kind or not strong then someone is either funny or calm and vice versa.
Paul is both tall and strong.
Paul is strong or not calm.
John is both not curious and not calm.
Susan is both old and not brave.
Someone is funny.
John is both creative and humble.
Someone is both not wise and kind.
Paul is both not kind and happy. | Susan is not rich. | entailment | (![X]:((curious(X)<~>happy(X))<=>(~old(X)<~>~funny(X))))&
(![X]:((happy(X)|kind(X))<=>(calm(X)<~>brave(X))))&
(![X]:((quiet(X)<~>~kind(X))<=>(wise(X)<~>~humble(X))))&
(((quiet(fred)&~creative(fred)))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)&curious(X))<=>(~happy(X)&funny(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(happy(X)&strong(X))))&
((?[X]:((humble(X)&~curious(X))))<=>((~humble(mary)<~>~calm(mary))))&
(![X]:((creative(X)<~>kind(X))<=>(quiet(X)&calm(X))))&
(![X]:(old(X)<=>(old(X)&~tall(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~generous(X)|~kind(X)))))&
((?[X]:((~curious(X)<~>~generous(X))))=>((humble(mary)|~rich(mary))))&
((?[X]:((rich(X)&~tall(X))))<=>(?[X]:((~creative(X)&~patient(X)))))&
(![X]:((~rich(X)<~>happy(X))=>(tall(X)<~>~rich(X))))&
(![X]:((old(X)<~>~calm(X))<=>~kind(X)))&
((?[X]:((~creative(X)|~humble(X))))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((kind(X)|~strong(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
((tall(paul)&strong(paul)))&
((strong(paul)|~calm(paul)))&
((~curious(john)&~calm(john)))&
((old(susan)&~brave(susan)))&
(?[X]:(funny(X)))&
((creative(john)&humble(john)))&
(?[X]:((~wise(X)&kind(X))))&
((~kind(paul)&happy(paul))) | ~rich(susan) | [
"p1",
"p8",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4238134936385995979760259
% SZS output start Proof for 4238134936385995979760259
2. ! [X0] : ((kind(X0) | happy(X0)) <=> (calm(X0) <~> brave(X0))) [input p1]
9. ! [X0] : (old(X0) <=> (~tall(X0) & old(X0))) [input p8]
13. ! [X0] : ((~rich(X0) <~> happy(X0)) => (tall(X0) <~> ~rich(X0))) [input p12]
14. ! [X0] : ((old(X0) <~> ~calm(X0)) <=> ~kind(X0)) [input p13]
20. ~brave(susan) & old(susan) [input p19]
25. rich(susan) [input hypothesis]
34. ! [X0] : ((tall(X0) <~> ~rich(X0)) | (~rich(X0) <=> happy(X0))) [ennf transformation 13]
37. ! [X0] : (((kind(X0) | happy(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~kind(X0) & ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : ((kind(X0) | happy(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~kind(X0) & ~happy(X0)))) [flattening 37]
52. ! [X0] : ((old(X0) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | ~old(X0))) [nnf transformation 9]
53. ! [X0] : ((old(X0) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | ~old(X0))) [flattening 52]
65. ! [X0] : (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) [nnf transformation 34]
66. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | kind(X0)) & (~kind(X0) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [nnf transformation 14]
88. ~kind(X0) | calm(X0) | brave(X0) [cnf transformation 38]
91. ~calm(X0) | happy(X0) | brave(X0) | kind(X0) [cnf transformation 38]
125. ~tall(X0) | ~old(X0) [cnf transformation 53]
137. ~rich(X0) | tall(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 65]
140. ~calm(X0) | ~kind(X0) | ~old(X0) [cnf transformation 66]
143. ~old(X0) | calm(X0) | kind(X0) [cnf transformation 66]
157. old(susan) [cnf transformation 20]
158. ~brave(susan) [cnf transformation 20]
166. rich(susan) [cnf transformation 25]
167. ~rich(X0) | tall(X0) | ~happy(X0) [duplicate literal removal 137]
537. calm(susan) | kind(susan) [resolution 143,157]
539. 70 <=> kind(susan) [avatar definition]
540. ~kind(susan) <- (~70) [avatar component clause 539]
541. kind(susan) <- (70) [avatar component clause 539]
543. 71 <=> calm(susan) [avatar definition]
545. calm(susan) <- (71) [avatar component clause 543]
546. 70 | 71 [avatar split clause 537,543,539]
547. tall(susan) | ~happy(susan) [resolution 167,166]
550. 72 <=> happy(susan) [avatar definition]
552. ~happy(susan) <- (~72) [avatar component clause 550]
554. 73 <=> tall(susan) [avatar definition]
556. tall(susan) <- (73) [avatar component clause 554]
557. ~72 | 73 [avatar split clause 547,554,550]
577. calm(susan) | brave(susan) <- (70) [resolution 541,88]
588. calm(susan) <- (70) [subsumption resolution 577,158]
589. 71 | ~70 [avatar split clause 588,539,543]
602. ~kind(susan) | ~old(susan) <- (71) [resolution 545,140]
606. ~kind(susan) <- (71) [subsumption resolution 602,157]
607. ~70 | ~71 [avatar split clause 606,543,539]
689. ~old(susan) <- (73) [resolution 556,125]
690. $false <- (73) [subsumption resolution 689,157]
691. ~73 [avatar contradiction clause 690]
694. happy(susan) | brave(susan) | kind(susan) <- (71) [resolution 91,545]
695. brave(susan) | kind(susan) <- (71, ~72) [subsumption resolution 694,552]
696. kind(susan) <- (71, ~72) [subsumption resolution 695,158]
697. $false <- (~70, 71, ~72) [subsumption resolution 696,540]
698. 70 | ~71 | 72 [avatar contradiction clause 697]
699. $false [avatar sat refutation 546,557,589,607,691,698]
% SZS output end Proof for 4238134936385995979760259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is happy and vice versa.
If john is not strong or patient then susan is strong and vice versa.
Everyone who is not strong is tall and vice versa.
If someone is not old then john is not humble.
If someone is not old then alice is not curious.
Everyone who is either not curious or not humble is both creative and not calm.
If someone is not wise or calm then someone is both not wise and not quiet and vice versa.
If paul is creative or curious then someone is both not wise and not generous.
Everyone who is either wise or old is both strong and not curious.
Everyone who is either not strong or kind is both not generous and kind.
Everyone who is strong or not generous is either not brave or not wise and vice versa.
If lucy is not old then susan is either wise or not happy and vice versa.
Everyone who is both generous and not curious is not happy.
If someone is either not humble or not generous then fred is either tall or calm and vice versa.
Everyone who is not calm or not rich is tall or humble and vice versa.
Everyone who is both not curious and tall is not kind.
Lucy is rich or not quiet.
John is both not quiet and not humble.
Someone is either not curious or funny.
Someone is either curious or not patient.
Someone is funny or curious.
John is strong or not creative.
Paul is either not humble or not wise.
John is wise. | John is not brave. | entailment | (![X]:(~humble(X)<=>happy(X)))&
(((~strong(john)|patient(john)))<=>(strong(susan)))&
(![X]:(~strong(X)<=>tall(X)))&
((?[X]:(~old(X)))=>(~humble(john)))&
((?[X]:(~old(X)))=>(~curious(alice)))&
(![X]:((~curious(X)<~>~humble(X))=>(creative(X)&~calm(X))))&
((?[X]:((~wise(X)|calm(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(((creative(paul)|curious(paul)))=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((wise(X)<~>old(X))=>(strong(X)&~curious(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~generous(X)&kind(X))))&
(![X]:((strong(X)|~generous(X))<=>(~brave(X)<~>~wise(X))))&
((~old(lucy))<=>((wise(susan)<~>~happy(susan))))&
(![X]:((generous(X)&~curious(X))=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&tall(X))=>~kind(X)))&
((rich(lucy)|~quiet(lucy)))&
((~quiet(john)&~humble(john)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john)))&
((~humble(paul)<~>~wise(paul)))&
(wise(john)) | ~brave(john) | [
"p0",
"p5",
"p10",
"p12",
"p17",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6782393385522288965707190
% SZS output start Proof for 6782393385522288965707190
1. ! [X0] : (~humble(X0) <=> happy(X0)) [input p0]
6. ! [X0] : ((~curious(X0) <~> ~humble(X0)) => (~calm(X0) & creative(X0))) [input p5]
11. ! [X0] : ((~generous(X0) | strong(X0)) <=> (~brave(X0) <~> ~wise(X0))) [input p10]
13. ! [X0] : ((~curious(X0) & generous(X0)) => ~happy(X0)) [input p12]
18. ~humble(john) & ~quiet(john) [input p17]
22. ~creative(john) | strong(john) [input p21]
24. wise(john) [input p23]
25. brave(john) [input hypothesis]
29. ! [X0] : ((~calm(X0) & creative(X0)) | (~curious(X0) <=> ~humble(X0))) [ennf transformation 6]
33. ! [X0] : (~happy(X0) | (curious(X0) | ~generous(X0))) [ennf transformation 13]
34. ! [X0] : (~happy(X0) | curious(X0) | ~generous(X0)) [flattening 33]
37. ! [X0] : ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) & creative(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) [nnf transformation 29]
51. ! [X0] : (((~generous(X0) | strong(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 11]
52. ! [X0] : ((~generous(X0) | strong(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (generous(X0) & ~strong(X0)))) [flattening 51]
69. happy(X0) | humble(X0) [cnf transformation 37]
79. ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 41]
99. ~brave(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 52]
100. ~brave(X0) | ~wise(X0) | generous(X0) [cnf transformation 52]
109. ~generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 34]
125. ~humble(john) [cnf transformation 18]
131. ~creative(john) | strong(john) [cnf transformation 22]
134. wise(john) [cnf transformation 24]
135. brave(john) [cnf transformation 25]
142. 2 <=> strong(john) [avatar definition]
156. 5 <=> humble(john) [avatar definition]
158. ~humble(john) <- (~5) [avatar component clause 156]
270. ~5 [avatar split clause 125,156]
301. 35 <=> creative(john) [avatar definition]
303. ~creative(john) <- (~35) [avatar component clause 301]
304. 2 | ~35 [avatar split clause 131,301,142]
362. 44 <=> curious(john) [avatar definition]
363. curious(john) <- (44) [avatar component clause 362]
364. ~curious(john) <- (~44) [avatar component clause 362]
381. ~wise(john) | ~strong(john) [resolution 99,135]
382. ~strong(john) [subsumption resolution 381,134]
385. ~2 [avatar split clause 382,142]
387. ~wise(john) | generous(john) [resolution 100,135]
388. generous(john) [subsumption resolution 387,134]
407. curious(john) | ~happy(john) [resolution 109,388]
408. ~happy(john) <- (~44) [subsumption resolution 407,364]
414. humble(john) <- (~44) [resolution 408,69]
415. $false <- (~5, ~44) [subsumption resolution 414,158]
416. 5 | 44 [avatar contradiction clause 415]
423. creative(john) | humble(john) <- (44) [resolution 363,79]
424. humble(john) <- (~35, 44) [subsumption resolution 423,303]
425. $false <- (~5, ~35, 44) [subsumption resolution 424,158]
426. 5 | 35 | ~44 [avatar contradiction clause 425]
427. $false [avatar sat refutation 270,304,385,416,426]
% SZS output end Proof for 6782393385522288965707190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and patient is both quiet and not curious and vice versa.
If someone is not tall or brave then someone is either not calm or not generous.
Everyone who is wise or not generous is both not kind and generous and vice versa.
If fred is both not curious and not patient then john is generous or not happy and vice versa.
Everyone who is not quiet or old is either not strong or generous and vice versa.
If alice is strong or creative then someone is not quiet or rich and vice versa.
If fred is not tall then someone is not quiet or wise.
Everyone who is not happy is not kind or not funny.
Everyone who is strong is not old or not tall.
If paul is humble then someone is not creative and vice versa.
If susan is not wise or tall then paul is generous and vice versa.
If fred is happy then alice is not kind or generous and vice versa.
If fred is either not wise or not patient then someone is both humble and not funny.
If someone is both not old and wise then lucy is both happy and creative and vice versa.
If alice is either rich or not rich then paul is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
Someone is either not patient or strong.
Mary is either tall or not calm.
John is both not old and not tall.
Someone is not creative.
Someone is either not calm or not rich.
Someone is not creative or humble.
Someone is either old or not tall. | Fred is not curious. | entailment | (![X]:((happy(X)&patient(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((wise(X)|~generous(X))<=>(~kind(X)&generous(X))))&
(((~curious(fred)&~patient(fred)))<=>((generous(john)|~happy(john))))&
(![X]:((~quiet(X)|old(X))<=>(~strong(X)<~>generous(X))))&
(((strong(alice)|creative(alice)))<=>(?[X]:((~quiet(X)|rich(X)))))&
((~tall(fred))=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:(~happy(X)=>(~kind(X)|~funny(X))))&
(![X]:(strong(X)=>(~old(X)|~tall(X))))&
((humble(paul))<=>(?[X]:(~creative(X))))&
(((~wise(susan)|tall(susan)))<=>(generous(paul)))&
((happy(fred))<=>((~kind(alice)|generous(alice))))&
(((~wise(fred)<~>~patient(fred)))=>(?[X]:((humble(X)&~funny(X)))))&
((?[X]:((~old(X)&wise(X))))<=>((happy(lucy)&creative(lucy))))&
(((rich(alice)<~>~rich(alice)))=>(calm(paul)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
(?[X]:((~patient(X)<~>strong(X))))&
((tall(mary)<~>~calm(mary)))&
((~old(john)&~tall(john)))&
(?[X]:(~creative(X)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((old(X)<~>~tall(X)))) | ~curious(fred) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1567478987608776394863909
% SZS output start Proof for 1567478987608776394863909
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (generous(X0) & ~kind(X0))) [input p2]
4. (~patient(fred) & ~curious(fred)) <=> (~happy(john) | generous(john)) [input p3]
24. curious(fred) [input hypothesis]
41. ! [X0] : (((~generous(X0) | wise(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
42. ! [X0] : ((~generous(X0) | wise(X0) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | (generous(X0) & ~wise(X0)))) [flattening 41]
43. ((~patient(fred) & ~curious(fred)) | (happy(john) & ~generous(john))) & ((~happy(john) | generous(john)) | (patient(fred) | curious(fred))) [nnf transformation 4]
44. ((~patient(fred) & ~curious(fred)) | (happy(john) & ~generous(john))) & (~happy(john) | generous(john) | patient(fred) | curious(fred)) [flattening 43]
96. generous(X0) | generous(X0) [cnf transformation 42]
99. ~curious(fred) | ~generous(john) [cnf transformation 44]
146. curious(fred) [cnf transformation 24]
149. generous(X0) [duplicate literal removal 96]
176. 6 <=> curious(fred) [avatar definition]
180. ~curious(fred) [subsumption resolution 99,149]
181. ~6 [avatar split clause 180,176]
348. 6 [avatar split clause 146,176]
349. $false [avatar sat refutation 181,348]
% SZS output end Proof for 1567478987608776394863909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or wise is either not humble or humble and vice versa.
If someone is not brave then mary is either creative or strong and vice versa.
Everyone who is both strong and calm is not happy and vice versa.
Everyone who is calm is either not wise or not humble.
Everyone who is either curious or brave is both not kind and rich and vice versa.
Everyone who is kind or not funny is both not strong and happy.
Everyone who is not curious is either not generous or not patient.
Everyone who is either not funny or quiet is humble or not creative and vice versa.
Everyone who is not funny or not calm is both kind and not strong.
Everyone who is either not brave or happy is either not brave or curious.
If someone is both rich and not humble then mary is both wise and not funny and vice versa.
Everyone who is creative or funny is both happy and not humble and vice versa.
If someone is not tall then john is not funny and vice versa.
Someone is happy or rich.
Someone is generous.
Susan is kind or not kind.
Someone is not quiet or not patient.
Someone is rich or calm.
Alice is both quiet and not creative. | Mary is not creative. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(~humble(X)<~>humble(X))))&
((?[X]:(~brave(X)))<=>((creative(mary)<~>strong(mary))))&
(![X]:((strong(X)&calm(X))<=>~happy(X)))&
(![X]:(calm(X)=>(~wise(X)<~>~humble(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~kind(X)&rich(X))))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~patient(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(humble(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((wise(mary)&~funny(mary))))&
(![X]:((creative(X)|funny(X))<=>(happy(X)&~humble(X))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X))))&
((quiet(alice)&~creative(alice))) | ~creative(mary) | [] | null | 0 |
Everyone who is not happy or not curious is either calm or wise.
If someone is either creative or not brave then someone is calm or not generous.
Everyone who is either creative or kind is not old.
Everyone who is generous is either not calm or wise and vice versa.
Everyone who is wise or not humble is not brave or funny and vice versa.
Everyone who is not quiet or wise is both calm and not curious and vice versa.
Everyone who is not funny or generous is either wise or not funny.
Everyone who is both wise and not curious is not tall or calm and vice versa.
If mary is either not kind or not generous then fred is either creative or not brave and vice versa.
If john is calm or old then alice is brave or tall.
If susan is generous then paul is old or not quiet.
If john is both not brave and humble then fred is both patient and not wise.
If paul is both quiet and happy then lucy is patient or not quiet.
Everyone who is humble is both happy and not patient.
Someone is patient.
Someone is either not brave or not creative.
Someone is either kind or patient.
Paul is not old or not rich.
Someone is either curious or funny. | Alice is happy. | entailment | (![X]:((~happy(X)|~curious(X))=>(calm(X)<~>wise(X))))&
((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((creative(X)<~>kind(X))=>~old(X)))&
(![X]:(generous(X)<=>(~calm(X)<~>wise(X))))&
(![X]:((wise(X)|~humble(X))<=>(~brave(X)|funny(X))))&
(![X]:((~quiet(X)|wise(X))<=>(calm(X)&~curious(X))))&
(![X]:((~funny(X)|generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((wise(X)&~curious(X))<=>(~tall(X)|calm(X))))&
(((~kind(mary)<~>~generous(mary)))<=>((creative(fred)<~>~brave(fred))))&
(((calm(john)|old(john)))=>((brave(alice)|tall(alice))))&
((generous(susan))=>((old(paul)|~quiet(paul))))&
(((~brave(john)&humble(john)))=>((patient(fred)&~wise(fred))))&
(((quiet(paul)&happy(paul)))=>((patient(lucy)|~quiet(lucy))))&
(![X]:(humble(X)=>(happy(X)&~patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~old(paul)|~rich(paul)))&
(?[X]:((curious(X)<~>funny(X)))) | happy(alice) | [
"p0",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 164199262716824717362673
% SZS output start Proof for 164199262716824717362673
1. ! [X0] : ((~curious(X0) | ~happy(X0)) => (calm(X0) <~> wise(X0))) [input p0]
6. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (~curious(X0) & calm(X0))) [input p5]
8. ! [X0] : ((~curious(X0) & wise(X0)) <=> (calm(X0) | ~tall(X0))) [input p7]
20. ~happy(alice) [input hypothesis]
23. ! [X0] : ((calm(X0) <~> wise(X0)) | (curious(X0) & happy(X0))) [ennf transformation 1]
36. ! [X0] : (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | (curious(X0) & happy(X0))) [nnf transformation 23]
45. ! [X0] : (((wise(X0) | ~quiet(X0)) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 6]
46. ! [X0] : ((wise(X0) | ~quiet(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | (~wise(X0) & quiet(X0)))) [flattening 45]
48. ! [X0] : (((~curious(X0) & wise(X0)) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | (curious(X0) | ~wise(X0)))) [nnf transformation 8]
49. ! [X0] : (((~curious(X0) & wise(X0)) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | curious(X0) | ~wise(X0))) [flattening 48]
62. wise(X0) | calm(X0) | happy(X0) [cnf transformation 36]
63. wise(X0) | calm(X0) | curious(X0) [cnf transformation 36]
65. ~wise(X0) | ~calm(X0) | curious(X0) [cnf transformation 36]
79. ~wise(X0) | calm(X0) [cnf transformation 46]
81. ~wise(X0) | ~curious(X0) [cnf transformation 46]
89. ~calm(X0) | wise(X0) [cnf transformation 49]
91. ~calm(X0) | ~curious(X0) [cnf transformation 49]
115. ~happy(alice) [cnf transformation 20]
260. calm(X1) | happy(X1) | ~curious(X1) [resolution 62,81]
261. calm(X2) | happy(X2) | calm(X2) [resolution 62,79]
262. calm(X2) | happy(X2) [duplicate literal removal 261]
263. ~curious(X1) | happy(X1) [subsumption resolution 260,91]
266. wise(X1) | happy(X1) [resolution 262,89]
269. calm(X2) | curious(X2) | calm(X2) [resolution 63,79]
270. calm(X2) | curious(X2) [duplicate literal removal 269]
506. happy(X1) | ~calm(X1) | curious(X1) [resolution 266,65]
513. happy(X1) | curious(X1) [subsumption resolution 506,270]
514. happy(X1) [subsumption resolution 513,263]
533. $false [resolution 514,115]
% SZS output end Proof for 164199262716824717362673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or creative is either happy or generous. Everyone who is not tall is not kind or rich. If mary is tall or not calm then someone is not calm or not happy and vice versa. Everyone who is not old is generous. Everyone who is rich or not patient is not tall and vice versa. If someone is both not rich and kind then fred is either rich or not generous and vice versa. Everyone who is patient or not curious is either not tall or kind. If someone is not old then john is either quiet or strong and vice versa. If someone is not humble or wise then someone is both kind and humble and vice versa. If paul is humble then susan is quiet. If someone is not calm or calm then john is old. If fred is not brave then someone is happy and vice versa. Everyone who is both kind and not creative is creative or calm. If lucy is kind then alice is both not happy and not quiet. Everyone who is not calm is not humble. Everyone who is calm is not curious or not calm and vice versa. Alice is not patient. Someone is either not creative or curious. Lucy is not tall. Paul is funny or wise. John is not wise. Susan is calm. | John is not funny. | neutral | (![X]:((~rich(X)<~>creative(X))=>(happy(X)<~>generous(X))))&
(![X]:(~tall(X)=>(~kind(X)|rich(X))))&
(((tall(mary)|~calm(mary)))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~old(X)=>generous(X)))&
(![X]:((rich(X)|~patient(X))<=>~tall(X)))&
((?[X]:((~rich(X)&kind(X))))<=>((rich(fred)<~>~generous(fred))))&
(![X]:((patient(X)|~curious(X))=>(~tall(X)<~>kind(X))))&
((?[X]:(~old(X)))<=>((quiet(john)<~>strong(john))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((kind(X)&humble(X)))))&
((humble(paul))=>(quiet(susan)))&
((?[X]:((~calm(X)|calm(X))))=>(old(john)))&
((~brave(fred))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)&~creative(X))=>(creative(X)|calm(X))))&
((kind(lucy))=>((~happy(alice)&~quiet(alice))))&
(![X]:(~calm(X)=>~humble(X)))&
(![X]:(calm(X)<=>(~curious(X)|~calm(X))))&
(~patient(alice))&
(?[X]:((~creative(X)<~>curious(X))))&
(~tall(lucy))&
((funny(paul)|wise(paul)))&
(~wise(john))&
(calm(susan)) | ~funny(john) | [] | null | 0 |
If someone is both brave and generous then someone is either rich or not quiet and vice versa.
If mary is either not curious or wise then paul is not brave.
Everyone who is wise is both not tall and funny.
Everyone who is happy is either not patient or not quiet and vice versa.
Everyone who is both not old and not generous is both not calm and not curious.
Everyone who is funny or not generous is not brave and vice versa.
Everyone who is both creative and brave is curious and vice versa.
If fred is both not strong and not old then susan is not calm or not old and vice versa.
If alice is both not creative and not generous then someone is either not kind or calm and vice versa.
Everyone who is both calm and not creative is both tall and not old and vice versa.
If someone is both old and not humble then someone is not kind or wise and vice versa.
If someone is either quiet or wise then someone is not strong and vice versa.
If lucy is either not rich or strong then someone is not curious or happy.
Everyone who is either quiet or not funny is not wise or not patient and vice versa.
Everyone who is not kind is not funny or not patient and vice versa.
If mary is both rich and not funny then alice is not creative and vice versa.
Lucy is both generous and not rich.
Lucy is curious.
Someone is either not curious or not creative.
Someone is not rich.
Fred is either tall or humble.
Someone is either kind or not creative.
Someone is either generous or humble. | Lucy is humble. | neutral | ((?[X]:((brave(X)&generous(X))))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(((~curious(mary)<~>wise(mary)))=>(~brave(paul)))&
(![X]:(wise(X)=>(~tall(X)&funny(X))))&
(![X]:(happy(X)<=>(~patient(X)<~>~quiet(X))))&
(![X]:((~old(X)&~generous(X))=>(~calm(X)&~curious(X))))&
(![X]:((funny(X)|~generous(X))<=>~brave(X)))&
(![X]:((creative(X)&brave(X))<=>curious(X)))&
(((~strong(fred)&~old(fred)))<=>((~calm(susan)|~old(susan))))&
(((~creative(alice)&~generous(alice)))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((calm(X)&~creative(X))<=>(tall(X)&~old(X))))&
((?[X]:((old(X)&~humble(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
((?[X]:((quiet(X)<~>wise(X))))<=>(?[X]:(~strong(X))))&
(((~rich(lucy)<~>strong(lucy)))=>(?[X]:((~curious(X)|happy(X)))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~wise(X)|~patient(X))))&
(![X]:(~kind(X)<=>(~funny(X)|~patient(X))))&
(((rich(mary)&~funny(mary)))<=>(~creative(alice)))&
((generous(lucy)&~rich(lucy)))&
(curious(lucy))&
(?[X]:((~curious(X)<~>~creative(X))))&
(?[X]:(~rich(X)))&
((tall(fred)<~>humble(fred)))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>humble(X)))) | humble(lucy) | [] | null | 0 |
Everyone who is either not patient or kind is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Everyone who is curious is not curious or not happy and vice versa.
Everyone who is both not generous and calm is both strong and not happy and vice versa.
Everyone who is either not kind or generous is either happy or not funny and vice versa.
Everyone who is tall or not old is not funny or not creative and vice versa.
If fred is not patient or quiet then someone is not brave.
Everyone who is either tall or not happy is quiet or not humble and vice versa.
If susan is either funny or not wise then someone is either not funny or not calm.
Everyone who is not happy is humble and vice versa.
Fred is not old or happy.
Susan is not kind.
Alice is patient or old.
Someone is not brave.
Someone is not calm.
Someone is either not creative or not kind.
Fred is either strong or old.
Someone is brave or not wise. | Susan is not generous. | entailment | (![X]:((~patient(X)<~>kind(X))=>(~generous(X)<~>quiet(X))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~curious(X)|~happy(X))))&
(![X]:((~generous(X)&calm(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~funny(X)|~creative(X))))&
(((~patient(fred)|quiet(fred)))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(quiet(X)|~humble(X))))&
(((funny(susan)<~>~wise(susan)))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~happy(X)<=>humble(X)))&
((~old(fred)|happy(fred)))&
(~kind(susan))&
((patient(alice)|old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(fred)<~>old(fred)))&
(?[X]:((brave(X)|~wise(X)))) | ~generous(susan) | [
"p4",
"p7",
"p8",
"p10",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7215549965713249030566654
% SZS output start Proof for 7215549965713249030566654
5. ! [X0] : (~wise(X0) <=> (~creative(X0) | quiet(X0))) [input p4]
8. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : (curious(X0) <=> (~happy(X0) | ~curious(X0))) [input p8]
11. ! [X0] : ((~kind(X0) <~> generous(X0)) <=> (happy(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : ((~old(X0) | tall(X0)) <=> (~creative(X0) | ~funny(X0))) [input p11]
14. ! [X0] : ((tall(X0) <~> ~happy(X0)) <=> (~humble(X0) | quiet(X0))) [input p13]
16. ! [X0] : (~happy(X0) <=> humble(X0)) [input p15]
18. ~kind(susan) [input p17]
25. generous(susan) [input hypothesis]
47. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | wise(X0))) [nnf transformation 5]
48. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | wise(X0))) [flattening 47]
52. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 8]
53. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~curious(X0))) [flattening 53]
57. ! [X0] : ((((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))))) [nnf transformation 11]
58. ! [X0] : (((~old(X0) | tall(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (old(X0) & ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : ((~old(X0) | tall(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | (old(X0) & ~tall(X0)))) [flattening 58]
62. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [nnf transformation 14]
63. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [flattening 62]
67. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 16]
96. ~wise(X0) | ~quiet(X0) [cnf transformation 48]
97. ~wise(X0) | creative(X0) [cnf transformation 48]
109. wise(X0) | wise(X0) | wise(X0) [cnf transformation 52]
110. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 54]
111. curious(X0) | curious(X0) [cnf transformation 54]
124. ~generous(X0) | kind(X0) | happy(X0) | funny(X0) [cnf transformation 57]
125. ~tall(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 59]
132. ~humble(X0) | quiet(X0) | tall(X0) | happy(X0) [cnf transformation 63]
141. humble(X0) | happy(X0) [cnf transformation 67]
144. ~kind(susan) [cnf transformation 18]
153. generous(susan) [cnf transformation 25]
154. ~curious(X0) | ~happy(X0) [duplicate literal removal 110]
155. curious(X0) [duplicate literal removal 111]
159. wise(X0) [duplicate literal removal 109]
193. 8 <=> ! [X1] : curious(X1) [avatar definition]
194. curious(X1) <- (8) [avatar component clause 193]
239. 8 [avatar split clause 155,193]
256. 22 <=> funny(susan) [avatar definition]
257. funny(susan) <- (22) [avatar component clause 256]
314. ~quiet(X0) [resolution 96,159]
315. creative(X0) [resolution 97,159]
318. ~happy(X1) <- (8) [resolution 154,194]
395. kind(susan) | happy(susan) | funny(susan) [resolution 124,153]
398. happy(susan) | funny(susan) [subsumption resolution 395,144]
399. funny(susan) <- (8) [subsumption resolution 398,318]
404. 22 | ~8 [avatar split clause 399,193,256]
455. quiet(X0) | tall(X0) | happy(X0) | happy(X0) [resolution 132,141]
456. quiet(X0) | tall(X0) | happy(X0) [duplicate literal removal 455]
457. tall(X0) | happy(X0) [subsumption resolution 456,314]
458. tall(X0) <- (8) [subsumption resolution 457,318]
466. ~funny(X2) | ~creative(X2) <- (8) [resolution 458,125]
467. ~funny(X2) <- (8) [subsumption resolution 466,315]
470. $false <- (8, 22) [resolution 467,257]
477. ~8 | ~22 [avatar contradiction clause 470]
478. $false [avatar sat refutation 239,404,477]
% SZS output end Proof for 7215549965713249030566654
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not kind or old.
Everyone who is wise or not humble is rich or not strong.
Everyone who is curious is not happy or funny and vice versa.
Everyone who is both not tall and quiet is either wise or not calm and vice versa.
If alice is either old or patient then someone is not tall or humble and vice versa.
If someone is old or curious then susan is strong and vice versa.
If someone is not wise or quiet then paul is either not wise or not calm and vice versa.
Everyone who is wise is either not brave or brave.
Everyone who is old is not generous and vice versa.
If someone is either calm or happy then john is either curious or not patient.
If fred is either funny or old then susan is funny and vice versa.
If fred is either not funny or not curious then someone is both not calm and wise.
If lucy is both not brave and creative then someone is not funny and vice versa.
Everyone who is both tall and not quiet is not creative and vice versa.
If someone is curious or not happy then mary is happy and vice versa.
Everyone who is either not quiet or generous is not rich or not patient.
Lucy is generous.
Someone is quiet.
Someone is both generous and rich.
Someone is not quiet or not rich.
Susan is not happy or not patient.
Alice is humble or quiet.
Someone is both humble and kind.
Lucy is either patient or not old. | Paul is calm. | neutral | (![X]:(wise(X)=>(~kind(X)<~>old(X))))&
(![X]:((wise(X)|~humble(X))=>(rich(X)|~strong(X))))&
(![X]:(curious(X)<=>(~happy(X)|funny(X))))&
(![X]:((~tall(X)&quiet(X))<=>(wise(X)<~>~calm(X))))&
(((old(alice)<~>patient(alice)))<=>(?[X]:((~tall(X)|humble(X)))))&
((?[X]:((old(X)|curious(X))))<=>(strong(susan)))&
((?[X]:((~wise(X)|quiet(X))))<=>((~wise(paul)<~>~calm(paul))))&
(![X]:(wise(X)=>(~brave(X)<~>brave(X))))&
(![X]:(old(X)<=>~generous(X)))&
((?[X]:((calm(X)<~>happy(X))))=>((curious(john)<~>~patient(john))))&
(((funny(fred)<~>old(fred)))<=>(funny(susan)))&
(((~funny(fred)<~>~curious(fred)))=>(?[X]:((~calm(X)&wise(X)))))&
(((~brave(lucy)&creative(lucy)))<=>(?[X]:(~funny(X))))&
(![X]:((tall(X)&~quiet(X))<=>~creative(X)))&
((?[X]:((curious(X)|~happy(X))))<=>(happy(mary)))&
(![X]:((~quiet(X)<~>generous(X))=>(~rich(X)|~patient(X))))&
(generous(lucy))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((~quiet(X)|~rich(X))))&
((~happy(susan)|~patient(susan)))&
((humble(alice)|quiet(alice)))&
(?[X]:((humble(X)&kind(X))))&
((patient(lucy)<~>~old(lucy))) | calm(paul) | [] | null | 0 |
Everyone who is either not generous or not patient is both not old and rich.
If someone is both rich and strong then alice is happy and vice versa.
Everyone who is creative or generous is old or not wise.
If someone is either not kind or strong then someone is both generous and tall and vice versa.
Everyone who is funny or not funny is not tall.
Everyone who is curious or patient is either not patient or strong and vice versa.
If someone is kind or quiet then fred is creative or not tall and vice versa.
Everyone who is either calm or tall is creative and vice versa.
Everyone who is patient is patient or not happy.
Everyone who is either calm or not funny is either brave or happy.
If someone is either old or kind then someone is kind or not wise.
If someone is both not patient and not brave then lucy is not tall or happy and vice versa.
Everyone who is not tall is humble and vice versa.
Everyone who is happy or humble is not rich and vice versa.
Everyone who is both strong and humble is old or wise.
Someone is either tall or not creative.
Fred is either not generous or patient.
Alice is either not curious or quiet.
Someone is generous or not rich.
Someone is not brave or not happy.
Susan is generous.
Someone is both not tall and not rich.
John is both not creative and wise. | Susan is kind. | contradiction | (![X]:((~generous(X)<~>~patient(X))=>(~old(X)&rich(X))))&
((?[X]:((rich(X)&strong(X))))<=>(happy(alice)))&
(![X]:((creative(X)|generous(X))=>(old(X)|~wise(X))))&
((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((funny(X)|~funny(X))=>~tall(X)))&
(![X]:((curious(X)|patient(X))<=>(~patient(X)<~>strong(X))))&
((?[X]:((kind(X)|quiet(X))))<=>((creative(fred)|~tall(fred))))&
(![X]:((calm(X)<~>tall(X))<=>creative(X)))&
(![X]:(patient(X)=>(patient(X)|~happy(X))))&
(![X]:((calm(X)<~>~funny(X))=>(brave(X)<~>happy(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:((~patient(X)&~brave(X))))<=>((~tall(lucy)|happy(lucy))))&
(![X]:(~tall(X)<=>humble(X)))&
(![X]:((happy(X)|humble(X))<=>~rich(X)))&
(![X]:((strong(X)&humble(X))=>(old(X)|wise(X))))&
(?[X]:((tall(X)<~>~creative(X))))&
((~generous(fred)<~>patient(fred)))&
((~curious(alice)<~>quiet(alice)))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((~brave(X)|~happy(X))))&
(generous(susan))&
(?[X]:((~tall(X)&~rich(X))))&
((~creative(john)&wise(john))) | kind(susan) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5447081404485810094583271
% SZS output start Proof for 5447081404485810094583271
1. ! [X0] : ((~generous(X0) <~> ~patient(X0)) => (rich(X0) & ~old(X0))) [input p0]
4. ? [X0] : (~kind(X0) <~> strong(X0)) <=> ? [X0] : (tall(X0) & generous(X0)) [input p3]
5. ! [X0] : ((~funny(X0) | funny(X0)) => ~tall(X0)) [input p4]
6. ! [X0] : ((patient(X0) | curious(X0)) <=> (~patient(X0) <~> strong(X0))) [input p5]
13. ! [X0] : (~tall(X0) <=> humble(X0)) [input p12]
14. ! [X0] : ((humble(X0) | happy(X0)) <=> ~rich(X0)) [input p13]
21. generous(susan) [input p20]
24. kind(susan) [input hypothesis]
25. ? [X0] : (~kind(X0) <~> strong(X0)) <=> ? [X1] : (tall(X1) & generous(X1)) [rectify 4]
27. ! [X0] : ((rich(X0) & ~old(X0)) | (~generous(X0) <=> ~patient(X0))) [ennf transformation 1]
30. ! [X0] : (~tall(X0) | (funny(X0) & ~funny(X0))) [ennf transformation 5]
37. ! [X0] : ((rich(X0) & ~old(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) [nnf transformation 27]
42. (? [X0] : ((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ! [X1] : (~tall(X1) | ~generous(X1))) & (? [X1] : (tall(X1) & generous(X1)) | ! [X0] : ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) [nnf transformation 25]
43. (? [X0] : ((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ! [X1] : (~tall(X1) | ~generous(X1))) & (? [X2] : (tall(X2) & generous(X2)) | ! [X3] : ((~kind(X3) | ~strong(X3)) & (strong(X3) | kind(X3)))) [rectify 42]
44. ? [X0] : ((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) => ((~strong(sK1) | kind(sK1)) & (strong(sK1) | ~kind(sK1))) [choice axiom]
45. ? [X2] : (tall(X2) & generous(X2)) => (tall(sK2) & generous(sK2)) [choice axiom]
46. (((~strong(sK1) | kind(sK1)) & (strong(sK1) | ~kind(sK1))) | ! [X1] : (~tall(X1) | ~generous(X1))) & ((tall(sK2) & generous(sK2)) | ! [X3] : ((~kind(X3) | ~strong(X3)) & (strong(X3) | kind(X3)))) [skolemisation 43,45,44]
47. ! [X0] : (((patient(X0) | curious(X0)) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | (~patient(X0) & ~curious(X0)))) [nnf transformation 6]
48. ! [X0] : ((patient(X0) | curious(X0) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | (~patient(X0) & ~curious(X0)))) [flattening 47]
65. ! [X0] : ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0))) [nnf transformation 13]
66. ! [X0] : (((humble(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (~humble(X0) & ~happy(X0)))) [nnf transformation 14]
67. ! [X0] : ((humble(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (~humble(X0) & ~happy(X0)))) [flattening 66]
82. ~generous(X0) | rich(X0) | patient(X0) [cnf transformation 37]
91. tall(sK2) | ~kind(X3) | ~strong(X3) [cnf transformation 46]
94. ~tall(X0) | ~funny(X0) [cnf transformation 30]
95. ~tall(X0) | funny(X0) [cnf transformation 30]
97. strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 48]
122. humble(X0) | tall(X0) [cnf transformation 65]
125. ~rich(X0) | ~humble(X0) [cnf transformation 67]
136. generous(susan) [cnf transformation 21]
141. kind(susan) [cnf transformation 24]
142. ~patient(X0) | strong(X0) [duplicate literal removal 97]
176. 8 <=> ! [X3] : (~kind(X3) | ~strong(X3)) [avatar definition]
177. ~kind(X3) | ~strong(X3) <- (8) [avatar component clause 176]
179. 9 <=> tall(sK2) [avatar definition]
181. tall(sK2) <- (9) [avatar component clause 179]
182. 8 | 9 [avatar split clause 91,179,176]
193. ~tall(X0) [subsumption resolution 94,95]
245. humble(X0) [subsumption resolution 122,193]
246. ~rich(X0) [subsumption resolution 125,245]
278. ~strong(susan) <- (8) [resolution 177,141]
285. rich(susan) | patient(susan) [resolution 82,136]
286. patient(susan) [subsumption resolution 285,246]
289. strong(susan) [resolution 286,142]
290. $false <- (8) [subsumption resolution 289,278]
291. ~8 [avatar contradiction clause 290]
292. $false <- (9) [subsumption resolution 181,193]
293. ~9 [avatar contradiction clause 292]
294. $false [avatar sat refutation 182,291,293]
% SZS output end Proof for 5447081404485810094583271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is brave.
Everyone who is either kind or not quiet is not funny.
If someone is funny then someone is either not generous or not rich.
Everyone who is kind is rich.
Everyone who is old is either not quiet or curious and vice versa.
If someone is both old and patient then fred is either not tall or tall and vice versa.
If someone is either generous or not funny then fred is calm and vice versa.
Everyone who is either funny or not rich is brave or not brave and vice versa.
If mary is not generous or not rich then mary is not patient and vice versa.
Everyone who is not strong or creative is quiet or tall.
Everyone who is both patient and not rich is either not humble or not curious and vice versa.
Everyone who is not quiet or not humble is either happy or not creative.
Everyone who is strong or not wise is either quiet or not old.
Everyone who is not kind is generous.
If someone is either funny or not patient then someone is humble or not curious.
Everyone who is both tall and kind is patient.
Alice is not strong.
Paul is curious.
Lucy is either quiet or not old.
Mary is either kind or not tall.
Someone is either funny or not old.
Someone is strong or humble.
Someone is either generous or tall.
John is either rich or not generous. | John is rich. | entailment | ((?[X]:(~creative(X)))=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>~quiet(X))=>~funny(X)))&
((?[X]:(funny(X)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
(![X]:(kind(X)=>rich(X)))&
(![X]:(old(X)<=>(~quiet(X)<~>curious(X))))&
((?[X]:((old(X)&patient(X))))<=>((~tall(fred)<~>tall(fred))))&
((?[X]:((generous(X)<~>~funny(X))))<=>(calm(fred)))&
(![X]:((funny(X)<~>~rich(X))<=>(brave(X)|~brave(X))))&
(((~generous(mary)|~rich(mary)))<=>(~patient(mary)))&
(![X]:((~strong(X)|creative(X))=>(quiet(X)|tall(X))))&
(![X]:((patient(X)&~rich(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~quiet(X)|~humble(X))=>(happy(X)<~>~creative(X))))&
(![X]:((strong(X)|~wise(X))=>(quiet(X)<~>~old(X))))&
(![X]:(~kind(X)=>generous(X)))&
((?[X]:((funny(X)<~>~patient(X))))=>(?[X]:((humble(X)|~curious(X)))))&
(![X]:((tall(X)&kind(X))=>patient(X)))&
(~strong(alice))&
(curious(paul))&
((quiet(lucy)<~>~old(lucy)))&
((kind(mary)<~>~tall(mary)))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((generous(X)<~>tall(X))))&
((rich(john)<~>~generous(john))) | rich(john) | [
"p3",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2890791714708559977751142
% SZS output start Proof for 2890791714708559977751142
4. ! [X0] : (kind(X0) => rich(X0)) [input p3]
14. ! [X0] : (~kind(X0) => generous(X0)) [input p13]
24. rich(john) <~> ~generous(john) [input p23]
25. ~rich(john) [input hypothesis]
33. ! [X0] : (rich(X0) | ~kind(X0)) [ennf transformation 4]
38. ! [X0] : (generous(X0) | kind(X0)) [ennf transformation 14]
81. (generous(john) | ~rich(john)) & (~generous(john) | rich(john)) [nnf transformation 24]
87. ~kind(X0) | rich(X0) [cnf transformation 33]
125. generous(X0) | kind(X0) [cnf transformation 38]
140. ~generous(john) | rich(john) [cnf transformation 81]
142. ~rich(john) [cnf transformation 25]
289. 31 <=> rich(john) [avatar definition]
291. ~rich(john) <- (~31) [avatar component clause 289]
293. 32 <=> generous(john) [avatar definition]
294. ~generous(john) <- (~32) [avatar component clause 293]
297. 31 | ~32 [avatar split clause 140,293,289]
298. ~31 [avatar split clause 142,289]
300. kind(john) <- (~32) [resolution 125,294]
302. rich(john) <- (~32) [resolution 300,87]
303. $false <- (~31, ~32) [subsumption resolution 302,291]
304. 31 | 32 [avatar contradiction clause 303]
305. $false [avatar sat refutation 297,298,304]
% SZS output end Proof for 2890791714708559977751142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not strong then susan is both generous and patient.
If someone is either tall or strong then mary is funny.
If someone is not calm or tall then someone is funny or curious.
Everyone who is strong is both not funny and not tall and vice versa.
Everyone who is not happy or not kind is both rich and brave and vice versa.
If someone is quiet or humble then mary is both not old and not funny and vice versa.
Everyone who is old or not rich is not strong or not creative.
If mary is both patient and quiet then susan is either curious or funny.
If paul is either old or not happy then someone is both not creative and calm and vice versa.
If john is both generous and not generous then someone is not humble or calm.
If someone is humble or not creative then john is both wise and not rich.
Everyone who is not tall or not quiet is either not kind or not wise and vice versa.
Everyone who is rich is both happy and creative and vice versa.
If alice is not kind then someone is strong or not strong.
If someone is both creative and calm then someone is not generous or not strong and vice versa.
If fred is both not calm and not old then someone is not rich.
Someone is either creative or not brave.
Susan is either wise or calm.
Someone is old or wise.
Alice is not curious or funny.
Someone is both brave and creative.
Fred is either strong or brave. | Alice is creative. | entailment | ((?[X]:((calm(X)|~strong(X))))=>((generous(susan)&patient(susan))))&
((?[X]:((tall(X)<~>strong(X))))=>(funny(mary)))&
((?[X]:((~calm(X)|tall(X))))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(strong(X)<=>(~funny(X)&~tall(X))))&
(![X]:((~happy(X)|~kind(X))<=>(rich(X)&brave(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((~old(mary)&~funny(mary))))&
(![X]:((old(X)|~rich(X))=>(~strong(X)|~creative(X))))&
(((patient(mary)&quiet(mary)))=>((curious(susan)<~>funny(susan))))&
(((old(paul)<~>~happy(paul)))<=>(?[X]:((~creative(X)&calm(X)))))&
(((generous(john)&~generous(john)))=>(?[X]:((~humble(X)|calm(X)))))&
((?[X]:((humble(X)|~creative(X))))=>((wise(john)&~rich(john))))&
(![X]:((~tall(X)|~quiet(X))<=>(~kind(X)<~>~wise(X))))&
(![X]:(rich(X)<=>(happy(X)&creative(X))))&
((~kind(alice))=>(?[X]:((strong(X)|~strong(X)))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((~generous(X)|~strong(X)))))&
(((~calm(fred)&~old(fred)))=>(?[X]:(~rich(X))))&
(?[X]:((creative(X)<~>~brave(X))))&
((wise(susan)<~>calm(susan)))&
(?[X]:((old(X)|wise(X))))&
((~curious(alice)|funny(alice)))&
(?[X]:((brave(X)&creative(X))))&
((strong(fred)<~>brave(fred))) | creative(alice) | [
"p1",
"p3",
"p4",
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1010905415776707211686867
% SZS output start Proof for 1010905415776707211686867
2. ? [X0] : (tall(X0) <~> strong(X0)) => funny(mary) [input p1]
4. ! [X0] : (strong(X0) <=> (~tall(X0) & ~funny(X0))) [input p3]
5. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (brave(X0) & rich(X0))) [input p4]
6. ? [X0] : (humble(X0) | quiet(X0)) <=> (~funny(mary) & ~old(mary)) [input p5]
11. ? [X0] : (~creative(X0) | humble(X0)) => (~rich(john) & wise(john)) [input p10]
12. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (~kind(X0) <~> ~wise(X0))) [input p11]
23. ~creative(alice) [input hypothesis]
27. funny(mary) | ! [X0] : (tall(X0) <=> strong(X0)) [ennf transformation 2]
35. (~rich(john) & wise(john)) | ! [X0] : (creative(X0) & ~humble(X0)) [ennf transformation 11]
39. funny(mary) | ! [X0] : ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))) [nnf transformation 27]
43. ! [X0] : ((strong(X0) | (tall(X0) | funny(X0))) & ((~tall(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 4]
44. ! [X0] : ((strong(X0) | tall(X0) | funny(X0)) & ((~tall(X0) & ~funny(X0)) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) | ~happy(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (kind(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((~kind(X0) | ~happy(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | (kind(X0) & happy(X0)))) [flattening 45]
47. (? [X0] : (humble(X0) | quiet(X0)) | (funny(mary) | old(mary))) & ((~funny(mary) & ~old(mary)) | ! [X0] : (~humble(X0) & ~quiet(X0))) [nnf transformation 6]
48. (? [X0] : (humble(X0) | quiet(X0)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X0] : (~humble(X0) & ~quiet(X0))) [flattening 47]
49. (? [X0] : (humble(X0) | quiet(X0)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X1] : (~humble(X1) & ~quiet(X1))) [rectify 48]
50. ? [X0] : (humble(X0) | quiet(X0)) => (humble(sK1) | quiet(sK1)) [choice axiom]
51. ((humble(sK1) | quiet(sK1)) | funny(mary) | old(mary)) & ((~funny(mary) & ~old(mary)) | ! [X1] : (~humble(X1) & ~quiet(X1))) [skolemisation 49,50]
59. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (quiet(X0) & tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~quiet(X0) | ~tall(X0) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (quiet(X0) & tall(X0)))) [flattening 59]
85. funny(mary) | strong(X0) | ~tall(X0) [cnf transformation 39]
90. ~tall(X0) | ~strong(X0) [cnf transformation 44]
93. rich(X0) | kind(X0) [cnf transformation 46]
99. ~funny(mary) | ~quiet(X1) [cnf transformation 51]
114. wise(john) | creative(X0) [cnf transformation 35]
116. ~rich(john) | creative(X0) [cnf transformation 35]
117. ~wise(X0) | ~kind(X0) | tall(X0) [cnf transformation 60]
118. ~wise(X0) | ~kind(X0) | quiet(X0) [cnf transformation 60]
143. ~creative(alice) [cnf transformation 23]
166. 6 <=> funny(mary) [avatar definition]
171. 7 <=> ! [X0] : (strong(X0) | ~tall(X0)) [avatar definition]
172. strong(X0) | ~tall(X0) <- (7) [avatar component clause 171]
173. 7 | 6 [avatar split clause 85,166,171]
175. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
176. ~tall(X1) <- (8) [avatar component clause 175]
208. 16 <=> ! [X1] : ~quiet(X1) [avatar definition]
209. ~quiet(X1) <- (16) [avatar component clause 208]
210. 16 | ~6 [avatar split clause 99,166,208]
257. 26 <=> ! [X0] : creative(X0) [avatar definition]
258. creative(X0) <- (26) [avatar component clause 257]
260. 27 <=> rich(john) [avatar definition]
262. ~rich(john) <- (~27) [avatar component clause 260]
263. 26 | ~27 [avatar split clause 116,260,257]
266. 28 <=> wise(john) [avatar definition]
268. wise(john) <- (28) [avatar component clause 266]
269. 26 | 28 [avatar split clause 114,266,257]
363. ~tall(X0) <- (7) [subsumption resolution 172,90]
364. 8 | ~7 [avatar split clause 363,171,175]
366. $false <- (26) [resolution 258,143]
367. ~26 [avatar contradiction clause 366]
376. kind(john) <- (~27) [resolution 93,262]
412. ~kind(john) | tall(john) <- (28) [resolution 117,268]
414. tall(john) <- (~27, 28) [subsumption resolution 412,376]
415. $false <- (8, ~27, 28) [subsumption resolution 414,176]
416. ~8 | 27 | ~28 [avatar contradiction clause 415]
427. ~kind(john) | quiet(john) <- (28) [resolution 118,268]
429. quiet(john) <- (~27, 28) [subsumption resolution 427,376]
430. $false <- (16, ~27, 28) [subsumption resolution 429,209]
431. ~16 | 27 | ~28 [avatar contradiction clause 430]
432. $false [avatar sat refutation 173,210,263,269,364,367,416,431]
% SZS output end Proof for 1010905415776707211686867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not wise is either not curious or strong and vice versa.
If someone is quiet then lucy is both not wise and not creative and vice versa.
Everyone who is both not happy and happy is not old or quiet.
Everyone who is not patient is not curious and vice versa.
Everyone who is funny or curious is not humble and vice versa.
Everyone who is either not wise or kind is wise or rich and vice versa.
Everyone who is not strong or not quiet is not strong and vice versa.
Everyone who is either not quiet or not funny is brave.
Everyone who is either wise or not tall is not kind or not creative.
If lucy is wise then someone is funny and vice versa.
If someone is curious or not old then someone is not tall and vice versa.
Everyone who is either not calm or strong is quiet and vice versa.
If paul is either not generous or not calm then someone is either not quiet or not humble.
Everyone who is creative is either curious or not rich.
If lucy is both not calm and not old then fred is either wise or not calm.
If alice is both brave and not old then john is not creative or happy.
Mary is not quiet or old.
Alice is happy or not funny.
Someone is rich or calm.
Susan is not wise or not curious.
Lucy is both wise and not funny.
Paul is kind or not old.
Someone is either not tall or generous.
Paul is not humble or patient. | Fred is patient. | entailment | (![X]:((strong(X)&~wise(X))<=>(~curious(X)<~>strong(X))))&
((?[X]:(quiet(X)))<=>((~wise(lucy)&~creative(lucy))))&
(![X]:((~happy(X)&happy(X))=>(~old(X)|quiet(X))))&
(![X]:(~patient(X)<=>~curious(X)))&
(![X]:((funny(X)|curious(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>kind(X))<=>(wise(X)|rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~strong(X)))&
(![X]:((~quiet(X)<~>~funny(X))=>brave(X)))&
(![X]:((wise(X)<~>~tall(X))=>(~kind(X)|~creative(X))))&
((wise(lucy))<=>(?[X]:(funny(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>quiet(X)))&
(((~generous(paul)<~>~calm(paul)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:(creative(X)=>(curious(X)<~>~rich(X))))&
(((~calm(lucy)&~old(lucy)))=>((wise(fred)<~>~calm(fred))))&
(((brave(alice)&~old(alice)))=>((~creative(john)|happy(john))))&
((~quiet(mary)|old(mary)))&
((happy(alice)|~funny(alice)))&
(?[X]:((rich(X)|calm(X))))&
((~wise(susan)|~curious(susan)))&
((wise(lucy)&~funny(lucy)))&
((kind(paul)|~old(paul)))&
(?[X]:((~tall(X)<~>generous(X))))&
((~humble(paul)|patient(paul))) | patient(fred) | [
"p0",
"p1",
"p3",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4763153062395748227108931
% SZS output start Proof for 4763153062395748227108931
1. ! [X0] : ((~wise(X0) & strong(X0)) <=> (~curious(X0) <~> strong(X0))) [input p0]
2. ? [X0] : quiet(X0) <=> (~creative(lucy) & ~wise(lucy)) [input p1]
4. ! [X0] : (~patient(X0) <=> ~curious(X0)) [input p3]
7. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> ~strong(X0)) [input p6]
21. ~funny(lucy) & wise(lucy) [input p20]
25. ~patient(fred) [input hypothesis]
38. ! [X0] : (((~wise(X0) & strong(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (wise(X0) | ~strong(X0)))) [nnf transformation 1]
39. ! [X0] : (((~wise(X0) & strong(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0)))) & (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | wise(X0) | ~strong(X0))) [flattening 38]
40. (? [X0] : quiet(X0) | (creative(lucy) | wise(lucy))) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
41. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [flattening 40]
42. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [rectify 41]
43. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
44. (quiet(sK0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [skolemisation 42,43]
45. ! [X0] : ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))) [nnf transformation 4]
50. ! [X0] : (((~quiet(X0) | ~strong(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 7]
51. ! [X0] : ((~quiet(X0) | ~strong(X0) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [flattening 50]
76. strong(X0) | strong(X0) | curious(X0) [cnf transformation 39]
80. ~wise(lucy) | ~quiet(X1) [cnf transformation 44]
84. ~curious(X0) | patient(X0) [cnf transformation 45]
96. ~strong(X0) | quiet(X0) [cnf transformation 51]
124. wise(lucy) [cnf transformation 21]
130. ~patient(fred) [cnf transformation 25]
134. curious(X0) | strong(X0) [duplicate literal removal 76]
137. 1 <=> wise(lucy) [avatar definition]
150. 4 <=> ! [X1] : ~quiet(X1) [avatar definition]
151. ~quiet(X1) <- (4) [avatar component clause 150]
153. 4 | ~1 [avatar split clause 80,137,150]
282. 1 [avatar split clause 124,137]
313. patient(X0) | strong(X0) [resolution 134,84]
326. strong(fred) [resolution 313,130]
330. quiet(fred) [resolution 326,96]
331. $false <- (4) [subsumption resolution 330,151]
332. ~4 [avatar contradiction clause 331]
333. $false [avatar sat refutation 153,282,332]
% SZS output end Proof for 4763153062395748227108931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or quiet then someone is either not tall or wise.
Everyone who is both rich and humble is either funny or brave.
Everyone who is not curious or tall is not calm or quiet.
If mary is patient or rich then paul is not strong or rich and vice versa.
Everyone who is both not patient and curious is happy or not creative.
If someone is not calm then someone is tall and vice versa.
Everyone who is not humble or not tall is both humble and not happy and vice versa.
If someone is funny then lucy is both tall and not calm.
If susan is both not quiet and creative then someone is happy or not quiet and vice versa.
If someone is not calm then john is both creative and brave.
Everyone who is quiet or not happy is not humble or not curious.
Everyone who is creative or not old is both not humble and wise.
Everyone who is both not funny and brave is patient or not kind and vice versa.
Mary is either not calm or rich.
Someone is funny or not strong.
Someone is not rich or quiet.
Alice is either brave or not creative.
Someone is either happy or calm. | Susan is not wise. | neutral | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((rich(X)&humble(X))=>(funny(X)<~>brave(X))))&
(![X]:((~curious(X)|tall(X))=>(~calm(X)|quiet(X))))&
(((patient(mary)|rich(mary)))<=>((~strong(paul)|rich(paul))))&
(![X]:((~patient(X)&curious(X))=>(happy(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(tall(X))))&
(![X]:((~humble(X)|~tall(X))<=>(humble(X)&~happy(X))))&
((?[X]:(funny(X)))=>((tall(lucy)&~calm(lucy))))&
(((~quiet(susan)&creative(susan)))<=>(?[X]:((happy(X)|~quiet(X)))))&
((?[X]:(~calm(X)))=>((creative(john)&brave(john))))&
(![X]:((quiet(X)|~happy(X))=>(~humble(X)|~curious(X))))&
(![X]:((creative(X)|~old(X))=>(~humble(X)&wise(X))))&
(![X]:((~funny(X)&brave(X))<=>(patient(X)|~kind(X))))&
((~calm(mary)<~>rich(mary)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((~rich(X)|quiet(X))))&
((brave(alice)<~>~creative(alice)))&
(?[X]:((happy(X)<~>calm(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is not calm is either generous or humble. If someone is both funny and generous then someone is funny. Everyone who is not rich or brave is either not calm or not curious. Everyone who is either happy or not brave is funny or not wise. If someone is strong then susan is not patient or happy. Everyone who is either not patient or not happy is both not wise and not funny. If john is either patient or not quiet then someone is either not funny or not patient. Everyone who is humble is not wise and vice versa. If someone is humble or not quiet then someone is not happy. Everyone who is not old is both happy and not happy. Everyone who is not happy is happy or brave and vice versa. Everyone who is both not strong and funny is not patient and vice versa. If susan is either wise or curious then someone is not rich. Everyone who is generous is either not wise or not old. Everyone who is either funny or not patient is either not quiet or curious and vice versa. If alice is not tall or generous then someone is both not patient and not brave. Someone is kind. Someone is both generous and not patient. Alice is happy or curious. Someone is not patient. Someone is patient. Someone is old or kind. Mary is either not quiet or old. | Alice is humble. | entailment | (![X]:(~calm(X)=>(generous(X)<~>humble(X))))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:(funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>~brave(X))=>(funny(X)|~wise(X))))&
((?[X]:(strong(X)))=>((~patient(susan)|happy(susan))))&
(![X]:((~patient(X)<~>~happy(X))=>(~wise(X)&~funny(X))))&
(((patient(john)<~>~quiet(john)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
((?[X]:((humble(X)|~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:(~old(X)=>(happy(X)&~happy(X))))&
(![X]:(~happy(X)<=>(happy(X)|brave(X))))&
(![X]:((~strong(X)&funny(X))<=>~patient(X)))&
(((wise(susan)<~>curious(susan)))=>(?[X]:(~rich(X))))&
(![X]:(generous(X)=>(~wise(X)<~>~old(X))))&
(![X]:((funny(X)<~>~patient(X))<=>(~quiet(X)<~>curious(X))))&
(((~tall(alice)|generous(alice)))=>(?[X]:((~patient(X)&~brave(X)))))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)&~patient(X))))&
((happy(alice)|curious(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((old(X)|kind(X))))&
((~quiet(mary)<~>old(mary))) | humble(alice) | [
"p0",
"p2",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9059362280541625555246862
% SZS output start Proof for 9059362280541625555246862
1. ! [X0] : (~calm(X0) => (generous(X0) <~> humble(X0))) [input p0]
3. ! [X0] : ((brave(X0) | ~rich(X0)) => (~calm(X0) <~> ~curious(X0))) [input p2]
11. ! [X0] : (~happy(X0) <=> (brave(X0) | happy(X0))) [input p10]
16. (generous(alice) | ~tall(alice)) => ? [X0] : (~brave(X0) & ~patient(X0)) [input p15]
19. curious(alice) | happy(alice) [input p18]
24. ~humble(alice) [input hypothesis]
29. generous(alice) => ? [X0] : (~brave(X0) & ~patient(X0)) [pure predicate removal 16]
30. ! [X0] : ((generous(X0) <~> humble(X0)) | calm(X0)) [ennf transformation 1]
32. ! [X0] : ((~calm(X0) <~> ~curious(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 3]
43. ? [X0] : (~brave(X0) & ~patient(X0)) | ~generous(alice) [ennf transformation 29]
44. ! [X0] : (((~humble(X0) | ~generous(X0)) & (humble(X0) | generous(X0))) | calm(X0)) [nnf transformation 30]
48. ! [X0] : (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (~brave(X0) & rich(X0))) [nnf transformation 32]
58. ! [X0] : ((~happy(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | happy(X0))) [nnf transformation 11]
59. ! [X0] : ((~happy(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | happy(X0))) [flattening 58]
67. ? [X0] : (~brave(X0) & ~patient(X0)) => (~brave(sK4) & ~patient(sK4)) [choice axiom]
68. (~brave(sK4) & ~patient(sK4)) | ~generous(alice) [skolemisation 43,67]
76. humble(X0) | generous(X0) | calm(X0) [cnf transformation 44]
80. ~curious(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 48]
100. brave(X0) | happy(X0) | happy(X0) [cnf transformation 59]
101. ~happy(X0) | ~happy(X0) [cnf transformation 59]
119. ~brave(sK4) | ~generous(alice) [cnf transformation 68]
122. curious(alice) | happy(alice) [cnf transformation 19]
127. ~humble(alice) [cnf transformation 24]
128. brave(X0) | happy(X0) [duplicate literal removal 100]
129. ~happy(X0) [duplicate literal removal 101]
183. brave(X0) [subsumption resolution 128,129]
203. ~generous(alice) [subsumption resolution 119,183]
204. curious(alice) [subsumption resolution 122,129]
212. generous(alice) | calm(alice) [resolution 76,127]
213. calm(alice) [subsumption resolution 212,203]
218. ~calm(alice) | ~brave(alice) [resolution 80,204]
219. ~brave(alice) [subsumption resolution 218,213]
220. $false [subsumption resolution 219,183]
% SZS output end Proof for 9059362280541625555246862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not patient. Everyone who is brave is both tall and not funny and vice versa. If someone is not strong or not generous then someone is either not funny or not old and vice versa. Everyone who is not wise or happy is not rich and vice versa. Everyone who is both humble and brave is not tall. Everyone who is not curious is both generous and not kind and vice versa. Everyone who is not brave is both quiet and humble. Everyone who is both not quiet and quiet is not humble or kind and vice versa. If someone is not quiet or funny then someone is not creative or old and vice versa. If susan is both humble and calm then someone is not curious or not strong. Everyone who is either creative or quiet is both not patient and not generous. Everyone who is either rich or not humble is old and vice versa. Everyone who is either not happy or patient is both funny and not creative and vice versa. Everyone who is either old or creative is either not calm or not tall. Everyone who is rich is tall or old and vice versa. If someone is tall or not rich then someone is either quiet or creative and vice versa. Someone is not tall or not generous. Someone is either strong or not quiet. Lucy is not patient. John is not generous or generous. Mary is tall or not strong. Lucy is not calm or not humble. Someone is generous or patient. Alice is both generous and not rich. | Alice is creative. | entailment | (![X]:(tall(X)=>~patient(X)))&
(![X]:(brave(X)<=>(tall(X)&~funny(X))))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~wise(X)|happy(X))<=>~rich(X)))&
(![X]:((humble(X)&brave(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(?[X]:((~tall(X)|~generous(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
(~patient(lucy))&
((~generous(john)|generous(john)))&
((tall(mary)|~strong(mary)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice))) | creative(alice) | [
"p1",
"p4",
"p6",
"p7",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6328176020705448417696541
% SZS output start Proof for 6328176020705448417696541
2. ! [X0] : (brave(X0) <=> (~funny(X0) & tall(X0))) [input p1]
5. ! [X0] : ((brave(X0) & humble(X0)) => ~tall(X0)) [input p4]
7. ! [X0] : (~brave(X0) => (humble(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (kind(X0) | ~humble(X0))) [input p7]
11. ! [X0] : ((creative(X0) <~> quiet(X0)) => (~generous(X0) & ~patient(X0))) [input p10]
24. ~rich(alice) & generous(alice) [input p23]
25. ~creative(alice) [input hypothesis]
31. ! [X0] : (~tall(X0) | (~brave(X0) | ~humble(X0))) [ennf transformation 5]
32. ! [X0] : (~tall(X0) | ~brave(X0) | ~humble(X0)) [flattening 31]
34. ! [X0] : ((humble(X0) & quiet(X0)) | brave(X0)) [ennf transformation 7]
37. ! [X0] : ((~generous(X0) & ~patient(X0)) | (creative(X0) <=> quiet(X0))) [ennf transformation 11]
39. ! [X0] : ((brave(X0) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [flattening 39]
48. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 8]
49. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~quiet(X0) | quiet(X0))) [flattening 48]
57. ! [X0] : ((~generous(X0) & ~patient(X0)) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 37]
77. ~brave(X0) | tall(X0) [cnf transformation 40]
89. ~tall(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 32]
92. quiet(X0) | brave(X0) [cnf transformation 34]
95. ~quiet(X0) | humble(X0) [cnf transformation 49]
97. quiet(X0) | humble(X0) [cnf transformation 49]
107. ~quiet(X0) | creative(X0) | ~generous(X0) [cnf transformation 57]
139. generous(alice) [cnf transformation 24]
141. ~creative(alice) [cnf transformation 25]
176. ~humble(X0) | ~brave(X0) [subsumption resolution 89,77]
178. humble(X0) [subsumption resolution 95,97]
311. ~brave(X1) [resolution 176,178]
324. creative(X1) | ~generous(X1) | brave(X1) [resolution 107,92]
328. ~generous(X1) | creative(X1) [subsumption resolution 324,311]
329. creative(alice) [resolution 328,139]
331. $false [subsumption resolution 329,141]
% SZS output end Proof for 6328176020705448417696541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is kind or rich and vice versa.
Everyone who is generous or not funny is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Paul is not generous. | contradiction | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:((generous(X)|~funny(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~generous(paul) | [
"p1",
"p4",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2540041629126743298399981
% SZS output start Proof for 2540041629126743298399981
2. ! [X0] : ((~funny(X0) | generous(X0)) => (creative(X0) <~> ~rich(X0))) [input p1]
5. ! [X0] : ((kind(X0) | ~rich(X0)) => strong(X0)) [input p4]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p10]
12. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p11]
13. ! [X0] : (creative(X0) <=> (patient(X0) | kind(X0))) [input p12]
15. ? [X0] : rich(X0) => kind(paul) [input p14]
16. ! [X0] : (~happy(X0) <=> rich(X0)) [input p15]
22. ~creative(fred) | ~strong(fred) [input p21]
24. ~generous(paul) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~rich(X0)) | (funny(X0) & ~generous(X0))) [ennf transformation 2]
30. ! [X0] : (strong(X0) | (~kind(X0) & rich(X0))) [ennf transformation 5]
33. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
34. kind(paul) | ! [X0] : ~rich(X0) [ennf transformation 15]
37. ! [X0] : (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (funny(X0) & ~generous(X0))) [nnf transformation 27]
51. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 51]
53. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 11]
54. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 53]
55. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 12]
56. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ~creative(X0))) [nnf transformation 13]
57. ! [X0] : ((creative(X0) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ~creative(X0))) [flattening 56]
58. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 16]
76. ~rich(X0) | creative(X0) | funny(X0) [cnf transformation 37]
78. ~creative(X0) | rich(X0) | funny(X0) [cnf transformation 37]
87. strong(X0) | rich(X0) [cnf transformation 30]
100. ~rich(X0) | quiet(X0) [cnf transformation 33]
102. ~funny(X0) | ~rich(X0) [cnf transformation 52]
103. ~funny(X0) | rich(X0) [cnf transformation 52]
106. ~quiet(X0) | generous(X0) [cnf transformation 54]
110. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 55]
111. ~happy(lucy) | ~creative(fred) | ~rich(fred) [cnf transformation 55]
113. ~kind(X0) | creative(X0) [cnf transformation 57]
115. kind(paul) | ~rich(X0) [cnf transformation 34]
116. happy(X0) | rich(X0) [cnf transformation 58]
125. ~creative(fred) | ~strong(fred) [cnf transformation 22]
127. ~generous(paul) [cnf transformation 24]
167. 9 <=> creative(paul) [avatar definition]
168. creative(paul) <- (9) [avatar component clause 167]
179. 12 <=> happy(lucy) [avatar definition]
181. ~happy(lucy) <- (~12) [avatar component clause 179]
195. ~funny(X0) [subsumption resolution 102,103]
197. 15 <=> rich(fred) [avatar definition]
198. rich(fred) <- (15) [avatar component clause 197]
201. 16 <=> creative(fred) [avatar definition]
203. ~creative(fred) <- (~16) [avatar component clause 201]
204. ~15 | ~16 | ~12 [avatar split clause 111,179,201,197]
205. 16 | 15 | ~12 [avatar split clause 110,179,197,201]
209. 17 <=> ! [X0] : ~rich(X0) [avatar definition]
210. ~rich(X0) <- (17) [avatar component clause 209]
212. 18 <=> kind(paul) [avatar definition]
214. kind(paul) <- (18) [avatar component clause 212]
215. 17 | 18 [avatar split clause 115,212,209]
227. 21 <=> strong(fred) [avatar definition]
229. ~strong(fred) <- (~21) [avatar component clause 227]
230. ~21 | ~16 [avatar split clause 125,201,227]
244. rich(lucy) <- (~12) [resolution 116,181]
247. $false <- (~12, 17) [subsumption resolution 244,210]
248. 12 | ~17 [avatar contradiction clause 247]
251. creative(paul) <- (18) [resolution 214,113]
253. 9 | ~18 [avatar split clause 251,212,167]
269. 24 <=> quiet(paul) [avatar definition]
270. quiet(paul) <- (24) [avatar component clause 269]
282. creative(fred) | funny(fred) <- (15) [resolution 76,198]
284. funny(fred) <- (15, ~16) [subsumption resolution 282,203]
285. $false <- (15, ~16) [subsumption resolution 284,195]
286. ~15 | 16 [avatar contradiction clause 285]
288. rich(fred) <- (~21) [resolution 229,87]
291. 15 | 21 [avatar split clause 288,227,197]
328. rich(paul) | funny(paul) <- (9) [resolution 78,168]
331. rich(paul) <- (9) [subsumption resolution 328,195]
369. quiet(paul) <- (9) [resolution 331,100]
372. 24 | ~9 [avatar split clause 369,167,269]
374. generous(paul) <- (24) [resolution 270,106]
376. $false <- (24) [subsumption resolution 374,127]
377. ~24 [avatar contradiction clause 376]
378. $false [avatar sat refutation 204,205,215,230,248,253,286,291,372,377]
% SZS output end Proof for 2540041629126743298399981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not creative is wise or not patient. Everyone who is both generous and not wise is either not creative or patient and vice versa. Everyone who is both not creative and creative is kind. If lucy is both rich and not generous then john is both not creative and funny and vice versa. If john is not quiet or generous then paul is happy or not happy and vice versa. If lucy is not wise then someone is creative or not generous. If someone is tall or creative then fred is not funny and vice versa. Everyone who is not curious or tall is both curious and funny and vice versa. If someone is not calm or not curious then someone is either not old or tall. Everyone who is not strong or not patient is strong or not strong and vice versa. Everyone who is kind or not creative is both patient and not curious and vice versa. If someone is both funny and patient then mary is either happy or not generous. If someone is both not humble and kind then someone is strong. Everyone who is either not happy or humble is both strong and not wise and vice versa. Everyone who is not calm or not brave is both strong and curious and vice versa. If someone is either not wise or funny then paul is both calm and not humble. Lucy is rich. Alice is quiet or not funny. Lucy is both tall and brave. John is generous. Alice is curious. Fred is either not brave or curious. Paul is either not kind or wise. | Lucy is not wise. | contradiction | (![X]:((~wise(X)<~>~creative(X))=>(wise(X)|~patient(X))))&
(![X]:((generous(X)&~wise(X))<=>(~creative(X)<~>patient(X))))&
(![X]:((~creative(X)&creative(X))=>kind(X)))&
(((rich(lucy)&~generous(lucy)))<=>((~creative(john)&funny(john))))&
(((~quiet(john)|generous(john)))<=>((happy(paul)|~happy(paul))))&
((~wise(lucy))=>(?[X]:((creative(X)|~generous(X)))))&
((?[X]:((tall(X)|creative(X))))<=>(~funny(fred)))&
(![X]:((~curious(X)|tall(X))<=>(curious(X)&funny(X))))&
((?[X]:((~calm(X)|~curious(X))))=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:((~strong(X)|~patient(X))<=>(strong(X)|~strong(X))))&
(![X]:((kind(X)|~creative(X))<=>(patient(X)&~curious(X))))&
((?[X]:((funny(X)&patient(X))))=>((happy(mary)<~>~generous(mary))))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(strong(X)&~wise(X))))&
(![X]:((~calm(X)|~brave(X))<=>(strong(X)&curious(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>((calm(paul)&~humble(paul))))&
(rich(lucy))&
((quiet(alice)|~funny(alice)))&
((tall(lucy)&brave(lucy)))&
(generous(john))&
(curious(alice))&
((~brave(fred)<~>curious(fred)))&
((~kind(paul)<~>wise(paul))) | ~wise(lucy) | [
"p0",
"p1",
"p3",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7974063401542377195374096
% SZS output start Proof for 7974063401542377195374096
1. ! [X0] : ((~wise(X0) <~> ~creative(X0)) => (~patient(X0) | wise(X0))) [input p0]
2. ! [X0] : ((~wise(X0) & generous(X0)) <=> (~creative(X0) <~> patient(X0))) [input p1]
4. (~generous(lucy) & rich(lucy)) <=> (funny(john) & ~creative(john)) [input p3]
8. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (funny(X0) & curious(X0))) [input p7]
11. ! [X0] : ((~creative(X0) | kind(X0)) <=> (~curious(X0) & patient(X0))) [input p10]
17. rich(lucy) [input p16]
24. ~wise(lucy) [input hypothesis]
27. ! [X0] : ((~patient(X0) | wise(X0)) | (~wise(X0) <=> ~creative(X0))) [ennf transformation 1]
28. ! [X0] : (~patient(X0) | wise(X0) | (~wise(X0) <=> ~creative(X0))) [flattening 27]
36. ! [X0] : (~patient(X0) | wise(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) [nnf transformation 28]
37. ! [X0] : (((~wise(X0) & generous(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (wise(X0) | ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : (((~wise(X0) & generous(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | wise(X0) | ~generous(X0))) [flattening 37]
39. ((~generous(lucy) & rich(lucy)) | (~funny(john) | creative(john))) & ((funny(john) & ~creative(john)) | (generous(lucy) | ~rich(lucy))) [nnf transformation 4]
40. ((~generous(lucy) & rich(lucy)) | ~funny(john) | creative(john)) & ((funny(john) & ~creative(john)) | generous(lucy) | ~rich(lucy)) [flattening 39]
49. ! [X0] : (((tall(X0) | ~curious(X0)) | (~funny(X0) | ~curious(X0))) & ((funny(X0) & curious(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~curious(X0) | ~funny(X0) | ~curious(X0)) & ((funny(X0) & curious(X0)) | (~tall(X0) & curious(X0)))) [flattening 49]
57. ! [X0] : (((~creative(X0) | kind(X0)) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | (creative(X0) & ~kind(X0)))) [nnf transformation 11]
58. ! [X0] : ((~creative(X0) | kind(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | (creative(X0) & ~kind(X0)))) [flattening 57]
70. ~patient(X0) | wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 36]
72. patient(X0) | ~creative(X0) | wise(X0) | ~generous(X0) [cnf transformation 38]
73. ~patient(X0) | creative(X0) | wise(X0) | ~generous(X0) [cnf transformation 38]
79. ~creative(john) | generous(lucy) | ~rich(lucy) [cnf transformation 40]
91. curious(X0) | curious(X0) [cnf transformation 50]
107. ~curious(X0) | creative(X0) [cnf transformation 58]
127. rich(lucy) [cnf transformation 17]
137. ~wise(lucy) [cnf transformation 24]
140. curious(X0) [duplicate literal removal 91]
142. ~patient(X0) | wise(X0) | ~creative(X0) [duplicate literal removal 70]
144. ~generous(X0) | wise(X0) | ~patient(X0) [subsumption resolution 73,142]
145. ~generous(X0) | wise(X0) | ~creative(X0) [subsumption resolution 72,144]
147. 1 <=> creative(john) [avatar definition]
148. ~creative(john) <- (~1) [avatar component clause 147]
155. 3 <=> generous(lucy) [avatar definition]
156. generous(lucy) <- (3) [avatar component clause 155]
160. 4 <=> rich(lucy) [avatar definition]
165. ~4 | 3 | ~1 [avatar split clause 79,147,155,160]
181. 8 <=> wise(lucy) [avatar definition]
182. ~wise(lucy) <- (~8) [avatar component clause 181]
227. creative(X0) [subsumption resolution 107,140]
261. 4 [avatar split clause 127,160]
274. ~8 [avatar split clause 137,181]
275. $false <- (~1) [subsumption resolution 148,227]
276. 1 [avatar contradiction clause 275]
342. wise(lucy) | ~creative(lucy) <- (3) [resolution 145,156]
345. ~creative(lucy) <- (3, ~8) [subsumption resolution 342,182]
346. $false <- (3, ~8) [subsumption resolution 345,227]
347. ~3 | 8 [avatar contradiction clause 346]
351. $false [avatar sat refutation 165,261,274,276,347]
% SZS output end Proof for 7974063401542377195374096
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient then paul is old or brave.
Everyone who is creative is both funny and not brave.
If mary is either not wise or kind then someone is both kind and wise and vice versa.
If alice is either not funny or tall then alice is not strong or not creative and vice versa.
Everyone who is not quiet or not strong is either not tall or generous.
If alice is both old and curious then someone is not happy and vice versa.
Everyone who is patient or calm is not happy.
Everyone who is not strong or not calm is either tall or kind and vice versa.
Everyone who is wise is both not wise and not calm.
Everyone who is funny is quiet or not tall and vice versa.
If fred is not brave then mary is not brave and vice versa.
Everyone who is both not generous and not brave is both not kind and funny and vice versa.
If fred is creative then john is both tall and rich.
Everyone who is rich or not creative is humble or creative and vice versa.
Everyone who is not quiet or not kind is either humble or not wise.
Everyone who is not calm is both calm and not rich and vice versa.
Paul is patient or wise.
Mary is not curious or calm.
Susan is either strong or rich.
Someone is either not rich or quiet.
John is either not rich or brave.
Someone is strong or creative.
Someone is brave or not calm. | Alice is not curious. | contradiction | ((patient(john))=>((old(paul)|brave(paul))))&
(![X]:(creative(X)=>(funny(X)&~brave(X))))&
(((~wise(mary)<~>kind(mary)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~funny(alice)<~>tall(alice)))<=>((~strong(alice)|~creative(alice))))&
(![X]:((~quiet(X)|~strong(X))=>(~tall(X)<~>generous(X))))&
(((old(alice)&curious(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((patient(X)|calm(X))=>~happy(X)))&
(![X]:((~strong(X)|~calm(X))<=>(tall(X)<~>kind(X))))&
(![X]:(wise(X)=>(~wise(X)&~calm(X))))&
(![X]:(funny(X)<=>(quiet(X)|~tall(X))))&
((~brave(fred))<=>(~brave(mary)))&
(![X]:((~generous(X)&~brave(X))<=>(~kind(X)&funny(X))))&
((creative(fred))=>((tall(john)&rich(john))))&
(![X]:((rich(X)|~creative(X))<=>(humble(X)|creative(X))))&
(![X]:((~quiet(X)|~kind(X))=>(humble(X)<~>~wise(X))))&
(![X]:(~calm(X)<=>(calm(X)&~rich(X))))&
((patient(paul)|wise(paul)))&
((~curious(mary)|calm(mary)))&
((strong(susan)<~>rich(susan)))&
(?[X]:((~rich(X)<~>quiet(X))))&
((~rich(john)<~>brave(john)))&
(?[X]:((strong(X)|creative(X))))&
(?[X]:((brave(X)|~calm(X)))) | ~curious(alice) | [
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3734535027478790675235247
% SZS output start Proof for 3734535027478790675235247
6. (curious(alice) & old(alice)) <=> ? [X0] : ~happy(X0) [input p5]
7. ! [X0] : ((calm(X0) | patient(X0)) => ~happy(X0)) [input p6]
16. ! [X0] : (~calm(X0) <=> (~rich(X0) & calm(X0))) [input p15]
24. ~curious(alice) [input hypothesis]
29. ! [X0] : (~happy(X0) | (~calm(X0) & ~patient(X0))) [ennf transformation 7]
40. ((curious(alice) & old(alice)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (~curious(alice) | ~old(alice))) [nnf transformation 6]
41. ((curious(alice) & old(alice)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ~curious(alice) | ~old(alice)) [flattening 40]
42. ((curious(alice) & old(alice)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ~curious(alice) | ~old(alice)) [rectify 41]
43. ? [X1] : ~happy(X1) => ~happy(sK1) [choice axiom]
44. ((curious(alice) & old(alice)) | ! [X0] : happy(X0)) & (~happy(sK1) | ~curious(alice) | ~old(alice)) [skolemisation 42,43]
55. ! [X0] : ((~calm(X0) | (rich(X0) | ~calm(X0))) & ((~rich(X0) & calm(X0)) | calm(X0))) [nnf transformation 16]
56. ! [X0] : ((~calm(X0) | rich(X0) | ~calm(X0)) & ((~rich(X0) & calm(X0)) | calm(X0))) [flattening 55]
87. curious(alice) | happy(X0) [cnf transformation 44]
89. ~calm(X0) | ~happy(X0) [cnf transformation 29]
117. calm(X0) | calm(X0) [cnf transformation 56]
130. ~curious(alice) [cnf transformation 24]
131. calm(X0) [duplicate literal removal 117]
198. 13 <=> ! [X0] : happy(X0) [avatar definition]
199. happy(X0) <- (13) [avatar component clause 198]
201. 14 <=> curious(alice) [avatar definition]
204. 13 | 14 [avatar split clause 87,201,198]
278. ~14 [avatar split clause 130,201]
282. ~happy(X0) [resolution 89,131]
283. $false <- (13) [subsumption resolution 282,199]
284. ~13 [avatar contradiction clause 283]
285. $false [avatar sat refutation 204,278,284]
% SZS output end Proof for 3734535027478790675235247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not tall is not strong and vice versa. If someone is not humble then mary is not kind and vice versa. Everyone who is funny is not funny or wise and vice versa. Everyone who is not strong or patient is not funny or brave and vice versa. If paul is not happy then someone is either not tall or not old and vice versa. Everyone who is both not quiet and not kind is tall and vice versa. Everyone who is either not curious or not tall is both not quiet and curious and vice versa. If someone is either happy or not calm then someone is both not brave and tall and vice versa. If alice is both not wise and brave then someone is not kind. If paul is either not calm or not rich then someone is not rich or not old. If mary is either not quiet or not strong then susan is both not happy and funny. If paul is both not wise and not curious then someone is curious. Everyone who is both kind and not kind is either not funny or brave. Everyone who is either happy or not quiet is either wise or happy and vice versa. If susan is both not humble and not rich then fred is not brave and vice versa. If mary is not rich or not wise then someone is brave or happy. Someone is curious or not generous. Alice is happy. John is not humble or not happy. Lucy is not calm. Someone is either not brave or humble. | Susan is not quiet. | entailment | (![X]:((quiet(X)<~>~tall(X))<=>~strong(X)))&
((?[X]:(~humble(X)))<=>(~kind(mary)))&
(![X]:(funny(X)<=>(~funny(X)|wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~funny(X)|brave(X))))&
((~happy(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(?[X]:((curious(X)|~generous(X))))&
(happy(alice))&
((~humble(john)|~happy(john)))&
(~calm(lucy))&
(?[X]:((~brave(X)<~>humble(X)))) | ~quiet(susan) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 911177454159139855407054
% SZS output start Proof for 911177454159139855407054
3. ! [X0] : (funny(X0) <=> (wise(X0) | ~funny(X0))) [input p2]
14. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (wise(X0) <~> happy(X0))) [input p13]
22. quiet(susan) [input hypothesis]
39. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 3]
40. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~funny(X0))) [flattening 39]
65. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 14]
79. wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 40]
80. funny(X0) | funny(X0) [cnf transformation 40]
117. ~happy(X0) | ~wise(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 65]
119. ~quiet(X0) | happy(X0) | happy(X0) | ~wise(X0) [cnf transformation 65]
133. quiet(susan) [cnf transformation 22]
135. ~happy(X0) | ~wise(X0) | ~quiet(X0) [duplicate literal removal 117]
136. ~quiet(X0) | happy(X0) | ~wise(X0) [duplicate literal removal 119]
140. wise(X0) | ~funny(X0) [duplicate literal removal 79]
141. funny(X0) [duplicate literal removal 80]
155. wise(X0) [subsumption resolution 140,141]
217. ~quiet(X0) | happy(X0) [subsumption resolution 136,155]
218. ~happy(X0) | ~quiet(X0) [subsumption resolution 135,155]
219. ~quiet(X0) [subsumption resolution 218,217]
267. $false [subsumption resolution 133,219]
% SZS output end Proof for 911177454159139855407054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong then someone is not humble or calm. Everyone who is both curious and funny is either not quiet or patient. Everyone who is tall or not humble is either rich or funny. If someone is curious then susan is both kind and humble and vice versa. If mary is not strong then paul is either not happy or wise and vice versa. If someone is humble or not generous then someone is wise or not funny. Everyone who is not quiet is both creative and strong and vice versa. Everyone who is not rich or not brave is either not quiet or brave. Everyone who is both not humble and creative is both funny and strong and vice versa. Everyone who is either old or humble is either not kind or not creative and vice versa. Everyone who is either not tall or funny is either quiet or happy. Everyone who is either not old or not generous is kind or not generous. Everyone who is either old or humble is either quiet or not quiet and vice versa. If someone is either not curious or not old then lucy is both not old and not humble and vice versa. Everyone who is either not quiet or not strong is brave. If fred is both not quiet and strong then someone is both tall and not funny and vice versa. Someone is wise. Lucy is not strong. Someone is not old. Alice is rich or not brave. Alice is not humble. Someone is either strong or not old. Fred is not tall. | Susan is curious. | contradiction | ((?[X]:((tall(X)|~strong(X))))=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((curious(X)&funny(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((tall(X)|~humble(X))=>(rich(X)<~>funny(X))))&
((?[X]:(curious(X)))<=>((kind(susan)&humble(susan))))&
((~strong(mary))<=>((~happy(paul)<~>wise(paul))))&
((?[X]:((humble(X)|~generous(X))))=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&strong(X))))&
(![X]:((~rich(X)|~brave(X))=>(~quiet(X)<~>brave(X))))&
(![X]:((~humble(X)&creative(X))<=>(funny(X)&strong(X))))&
(![X]:((old(X)<~>humble(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>funny(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)<~>~generous(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)<~>humble(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~curious(X)<~>~old(X))))<=>((~old(lucy)&~humble(lucy))))&
(![X]:((~quiet(X)<~>~strong(X))=>brave(X)))&
(((~quiet(fred)&strong(fred)))<=>(?[X]:((tall(X)&~funny(X)))))&
(?[X]:(wise(X)))&
(~strong(lucy))&
(?[X]:(~old(X)))&
((rich(alice)|~brave(alice)))&
(~humble(alice))&
(?[X]:((strong(X)<~>~old(X))))&
(~tall(fred)) | curious(susan) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5520865977249113262877487
% SZS output start Proof for 5520865977249113262877487
4. ? [X0] : curious(X0) <=> (humble(susan) & kind(susan)) [input p3]
13. ! [X0] : ((old(X0) <~> humble(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p12]
14. ? [X0] : (~curious(X0) <~> ~old(X0)) <=> (~humble(lucy) & ~old(lucy)) [input p13]
24. curious(susan) [input hypothesis]
39. (? [X0] : curious(X0) | (~humble(susan) | ~kind(susan))) & ((humble(susan) & kind(susan)) | ! [X0] : ~curious(X0)) [nnf transformation 4]
40. (? [X0] : curious(X0) | ~humble(susan) | ~kind(susan)) & ((humble(susan) & kind(susan)) | ! [X0] : ~curious(X0)) [flattening 39]
41. (? [X0] : curious(X0) | ~humble(susan) | ~kind(susan)) & ((humble(susan) & kind(susan)) | ! [X1] : ~curious(X1)) [rectify 40]
42. ? [X0] : curious(X0) => curious(sK0) [choice axiom]
43. (curious(sK0) | ~humble(susan) | ~kind(susan)) & ((humble(susan) & kind(susan)) | ! [X1] : ~curious(X1)) [skolemisation 41,42]
56. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 13]
57. (? [X0] : ((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (humble(lucy) | old(lucy))) & ((~humble(lucy) & ~old(lucy)) | ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) [nnf transformation 14]
58. (? [X0] : ((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | humble(lucy) | old(lucy)) & ((~humble(lucy) & ~old(lucy)) | ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) [flattening 57]
59. (? [X0] : ((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | humble(lucy) | old(lucy)) & ((~humble(lucy) & ~old(lucy)) | ! [X1] : ((~curious(X1) | old(X1)) & (~old(X1) | curious(X1)))) [rectify 58]
60. ? [X0] : ((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) => ((old(sK2) | curious(sK2)) & (~old(sK2) | ~curious(sK2))) [choice axiom]
61. (((old(sK2) | curious(sK2)) & (~old(sK2) | ~curious(sK2))) | humble(lucy) | old(lucy)) & ((~humble(lucy) & ~old(lucy)) | ! [X1] : ((~curious(X1) | old(X1)) & (~old(X1) | curious(X1)))) [skolemisation 59,60]
82. humble(susan) | ~curious(X1) [cnf transformation 43]
119. humble(X0) | old(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
120. humble(X0) | old(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
121. ~humble(X0) | ~old(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
122. ~humble(X0) | ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
124. ~old(lucy) | ~curious(X1) | old(X1) [cnf transformation 61]
126. ~humble(lucy) | ~curious(X1) | old(X1) [cnf transformation 61]
143. curious(susan) [cnf transformation 24]
144. humble(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 119]
145. humble(X0) | old(X0) | quiet(X0) [duplicate literal removal 120]
146. ~humble(X0) | ~old(X0) | ~quiet(X0) [duplicate literal removal 121]
147. ~humble(X0) | ~old(X0) | quiet(X0) [duplicate literal removal 122]
155. 2 <=> humble(susan) [avatar definition]
156. humble(susan) <- (2) [avatar component clause 155]
164. 4 <=> ! [X1] : ~curious(X1) [avatar definition]
165. ~curious(X1) <- (4) [avatar component clause 164]
166. 4 | 2 [avatar split clause 82,155,164]
200. ~old(X0) | ~humble(X0) [subsumption resolution 146,147]
201. old(X0) | humble(X0) [subsumption resolution 144,145]
203. 12 <=> ! [X1] : (~curious(X1) | old(X1)) [avatar definition]
204. ~curious(X1) | old(X1) <- (12) [avatar component clause 203]
206. 13 <=> humble(lucy) [avatar definition]
209. 12 | ~13 [avatar split clause 126,206,203]
215. 15 <=> old(lucy) [avatar definition]
217. ~old(lucy) <- (~15) [avatar component clause 215]
218. 12 | ~15 [avatar split clause 124,215,203]
258. $false <- (4) [resolution 165,143]
259. ~4 [avatar contradiction clause 258]
263. humble(lucy) <- (~15) [resolution 201,217]
268. 13 | 15 [avatar split clause 263,215,206]
269. old(susan) <- (12) [resolution 204,143]
273. ~humble(susan) <- (12) [resolution 269,200]
274. $false <- (2, 12) [subsumption resolution 273,156]
275. ~2 | ~12 [avatar contradiction clause 274]
276. $false [avatar sat refutation 166,209,218,259,268,275]
% SZS output end Proof for 5520865977249113262877487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both old and not happy.
Everyone who is both old and not strong is kind or not tall and vice versa.
Everyone who is kind is either not generous or calm.
Everyone who is not tall is either curious or not creative and vice versa.
Everyone who is either humble or tall is both creative and not rich and vice versa.
Everyone who is either not brave or not strong is not brave and vice versa.
If someone is both old and not generous then lucy is wise or not quiet and vice versa.
If john is either humble or generous then someone is both not happy and patient and vice versa.
Everyone who is either not wise or quiet is not creative and vice versa.
Everyone who is either not happy or generous is both patient and kind and vice versa.
If susan is calm then mary is both not curious and tall and vice versa.
Everyone who is either patient or not tall is both curious and funny and vice versa.
If susan is either not patient or not tall then someone is either creative or quiet.
Everyone who is wise is both creative and generous and vice versa.
Everyone who is strong or not humble is strong or not calm.
If someone is both wise and not kind then someone is not curious.
Someone is either strong or not tall.
Mary is not funny.
Someone is both not quiet and not happy.
Someone is curious.
Mary is tall or not quiet.
John is wise. | Lucy is not calm. | neutral | (![X]:(~curious(X)=>(old(X)&~happy(X))))&
(![X]:((old(X)&~strong(X))<=>(kind(X)|~tall(X))))&
(![X]:(kind(X)=>(~generous(X)<~>calm(X))))&
(![X]:(~tall(X)<=>(curious(X)<~>~creative(X))))&
(![X]:((humble(X)<~>tall(X))<=>(creative(X)&~rich(X))))&
(![X]:((~brave(X)<~>~strong(X))<=>~brave(X)))&
((?[X]:((old(X)&~generous(X))))<=>((wise(lucy)|~quiet(lucy))))&
(((humble(john)<~>generous(john)))<=>(?[X]:((~happy(X)&patient(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~creative(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(patient(X)&kind(X))))&
((calm(susan))<=>((~curious(mary)&tall(mary))))&
(![X]:((patient(X)<~>~tall(X))<=>(curious(X)&funny(X))))&
(((~patient(susan)<~>~tall(susan)))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:(wise(X)<=>(creative(X)&generous(X))))&
(![X]:((strong(X)|~humble(X))=>(strong(X)|~calm(X))))&
((?[X]:((wise(X)&~kind(X))))=>(?[X]:(~curious(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
(~funny(mary))&
(?[X]:((~quiet(X)&~happy(X))))&
(?[X]:(curious(X)))&
((tall(mary)|~quiet(mary)))&
(wise(john)) | ~calm(lucy) | [] | null | 0 |
Everyone who is happy or not generous is old and vice versa. If someone is both wise and not calm then susan is calm and vice versa. Everyone who is both not generous and humble is either not calm or not rich. If john is both funny and not calm then lucy is not strong. If someone is both brave and not patient then someone is both tall and not patient. Everyone who is both not creative and quiet is either not tall or not happy. If someone is creative or not patient then someone is either brave or not old. If someone is curious or not generous then alice is strong. If someone is both not quiet and not rich then someone is both not creative and not quiet. If john is calm or creative then someone is both old and not humble and vice versa. Everyone who is not old or old is both not generous and not funny. Everyone who is both wise and not happy is not happy and vice versa. Everyone who is brave or not curious is not brave or not curious and vice versa. Everyone who is generous or not generous is either old or not old. Everyone who is both not brave and not tall is not humble or old and vice versa. If someone is tall then someone is strong or old. Alice is either not happy or not funny. John is calm. Someone is tall or quiet. Someone is either not quiet or not calm. | Alice is creative. | contradiction | (![X]:((happy(X)|~generous(X))<=>old(X)))&
((?[X]:((wise(X)&~calm(X))))<=>(calm(susan)))&
(![X]:((~generous(X)&humble(X))=>(~calm(X)<~>~rich(X))))&
(((funny(john)&~calm(john)))=>(~strong(lucy)))&
((?[X]:((brave(X)&~patient(X))))=>(?[X]:((tall(X)&~patient(X)))))&
(![X]:((~creative(X)&quiet(X))=>(~tall(X)<~>~happy(X))))&
((?[X]:((creative(X)|~patient(X))))=>(?[X]:((brave(X)<~>~old(X)))))&
((?[X]:((curious(X)|~generous(X))))=>(strong(alice)))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
(((calm(john)|creative(john)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((~old(X)|old(X))=>(~generous(X)&~funny(X))))&
(![X]:((wise(X)&~happy(X))<=>~happy(X)))&
(![X]:((brave(X)|~curious(X))<=>(~brave(X)|~curious(X))))&
(![X]:((generous(X)|~generous(X))=>(old(X)<~>~old(X))))&
(![X]:((~brave(X)&~tall(X))<=>(~humble(X)|old(X))))&
((?[X]:(tall(X)))=>(?[X]:((strong(X)|old(X)))))&
((~happy(alice)<~>~funny(alice)))&
(calm(john))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>~calm(X)))) | creative(alice) | [
"p0",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5802972162947724026574758
% SZS output start Proof for 5802972162947724026574758
1. ! [X0] : ((~generous(X0) | happy(X0)) <=> old(X0)) [input p0]
7. ? [X0] : (~patient(X0) | creative(X0)) => ? [X0] : (brave(X0) <~> ~old(X0)) [input p6]
11. ! [X0] : ((old(X0) | ~old(X0)) => (~funny(X0) & ~generous(X0))) [input p10]
15. ! [X0] : ((~tall(X0) & ~brave(X0)) <=> (old(X0) | ~humble(X0))) [input p14]
21. creative(alice) [input hypothesis]
23. ? [X0] : (~patient(X0) | creative(X0)) => ? [X1] : (brave(X1) <~> ~old(X1)) [rectify 7]
33. ? [X1] : (brave(X1) <~> ~old(X1)) | ! [X0] : (patient(X0) & ~creative(X0)) [ennf transformation 23]
36. ! [X0] : ((~funny(X0) & ~generous(X0)) | (~old(X0) & old(X0))) [ennf transformation 11]
39. ! [X0] : (((~generous(X0) | happy(X0)) | ~old(X0)) & (old(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 1]
40. ! [X0] : ((~generous(X0) | happy(X0) | ~old(X0)) & (old(X0) | (generous(X0) & ~happy(X0)))) [flattening 39]
50. ? [X1] : ((old(X1) | ~brave(X1)) & (~old(X1) | brave(X1))) | ! [X0] : (patient(X0) & ~creative(X0)) [nnf transformation 33]
51. ? [X0] : ((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ! [X1] : (patient(X1) & ~creative(X1)) [rectify 50]
52. ? [X0] : ((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) => ((old(sK2) | ~brave(sK2)) & (~old(sK2) | brave(sK2))) [choice axiom]
53. ((old(sK2) | ~brave(sK2)) & (~old(sK2) | brave(sK2))) | ! [X1] : (patient(X1) & ~creative(X1)) [skolemisation 51,52]
67. ! [X0] : (((~tall(X0) & ~brave(X0)) | (~old(X0) & humble(X0))) & ((old(X0) | ~humble(X0)) | (tall(X0) | brave(X0)))) [nnf transformation 15]
68. ! [X0] : (((~tall(X0) & ~brave(X0)) | (~old(X0) & humble(X0))) & (old(X0) | ~humble(X0) | tall(X0) | brave(X0))) [flattening 67]
79. old(X0) | generous(X0) [cnf transformation 40]
91. ~old(sK2) | brave(sK2) | ~creative(X1) [cnf transformation 53]
104. ~generous(X0) | old(X0) [cnf transformation 36]
121. ~brave(X0) | ~old(X0) [cnf transformation 68]
131. creative(alice) [cnf transformation 21]
182. 12 <=> brave(sK2) [avatar definition]
183. brave(sK2) <- (12) [avatar component clause 182]
186. 13 <=> old(sK2) [avatar definition]
187. ~old(sK2) <- (~13) [avatar component clause 186]
191. 14 <=> ! [X1] : ~creative(X1) [avatar definition]
192. ~creative(X1) <- (14) [avatar component clause 191]
195. 14 | 12 | ~13 [avatar split clause 91,186,182,191]
242. old(X0) [subsumption resolution 104,79]
246. ~brave(X0) [subsumption resolution 121,242]
260. $false <- (~13) [subsumption resolution 187,242]
261. 13 [avatar contradiction clause 260]
262. $false <- (12) [subsumption resolution 183,246]
263. ~12 [avatar contradiction clause 262]
264. $false <- (14) [resolution 192,131]
265. ~14 [avatar contradiction clause 264]
266. $false [avatar sat refutation 195,261,263,265]
% SZS output end Proof for 5802972162947724026574758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or wise is both not patient and generous and vice versa.
Everyone who is either not curious or old is either rich or not kind and vice versa.
If paul is not strong then someone is either creative or not creative and vice versa.
Everyone who is kind or curious is both tall and creative and vice versa.
Everyone who is happy or not quiet is brave.
Everyone who is creative is not rich or not quiet and vice versa.
If lucy is not calm then someone is either not wise or wise.
If lucy is both not happy and not humble then lucy is not quiet and vice versa.
If someone is not generous or not strong then fred is both kind and old and vice versa.
If someone is patient or not creative then someone is either humble or not patient and vice versa.
If someone is not old then alice is both not humble and humble and vice versa.
If someone is brave or quiet then someone is not curious and vice versa.
If someone is not humble then someone is either old or funny.
Everyone who is both not tall and happy is both funny and not tall and vice versa.
If someone is either wise or not curious then someone is both not calm and curious and vice versa.
If john is both quiet and not calm then alice is both not quiet and rich.
Someone is not tall.
Susan is not rich or not brave.
Susan is either curious or not rich.
Someone is either not funny or curious.
Mary is both not quiet and calm.
Someone is either not rich or not happy.
Someone is either humble or not quiet. | Fred is kind. | entailment | (![X]:((rich(X)|wise(X))<=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)<~>old(X))<=>(rich(X)<~>~kind(X))))&
((~strong(paul))<=>(?[X]:((creative(X)<~>~creative(X)))))&
(![X]:((kind(X)|curious(X))<=>(tall(X)&creative(X))))&
(![X]:((happy(X)|~quiet(X))=>brave(X)))&
(![X]:(creative(X)<=>(~rich(X)|~quiet(X))))&
((~calm(lucy))=>(?[X]:((~wise(X)<~>wise(X)))))&
(((~happy(lucy)&~humble(lucy)))<=>(~quiet(lucy)))&
((?[X]:((~generous(X)|~strong(X))))<=>((kind(fred)&old(fred))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((humble(X)<~>~patient(X)))))&
((?[X]:(~old(X)))<=>((~humble(alice)&humble(alice))))&
((?[X]:((brave(X)|quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:(~humble(X)))=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~tall(X)&happy(X))<=>(funny(X)&~tall(X))))&
((?[X]:((wise(X)<~>~curious(X))))<=>(?[X]:((~calm(X)&curious(X)))))&
(((quiet(john)&~calm(john)))=>((~quiet(alice)&rich(alice))))&
(?[X]:(~tall(X)))&
((~rich(susan)|~brave(susan)))&
((curious(susan)<~>~rich(susan)))&
(?[X]:((~funny(X)<~>curious(X))))&
((~quiet(mary)&calm(mary)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((humble(X)<~>~quiet(X)))) | kind(fred) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 9019353278567757233819868
% SZS output start Proof for 9019353278567757233819868
3. ~strong(paul) <=> ? [X0] : (creative(X0) <~> ~creative(X0)) [input p2]
9. ? [X0] : (~strong(X0) | ~generous(X0)) <=> (old(fred) & kind(fred)) [input p8]
24. ~kind(fred) [input hypothesis]
37. (~strong(paul) | ! [X0] : ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (? [X0] : ((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | strong(paul)) [nnf transformation 3]
38. (~strong(paul) | ! [X0] : ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (? [X1] : ((creative(X1) | ~creative(X1)) & (~creative(X1) | creative(X1))) | strong(paul)) [rectify 37]
39. ? [X1] : ((creative(X1) | ~creative(X1)) & (~creative(X1) | creative(X1))) => ((creative(sK0) | ~creative(sK0)) & (~creative(sK0) | creative(sK0))) [choice axiom]
40. (~strong(paul) | ! [X0] : ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(sK0) | ~creative(sK0)) & (~creative(sK0) | creative(sK0))) | strong(paul)) [skolemisation 38,39]
50. (? [X0] : (~strong(X0) | ~generous(X0)) | (~old(fred) | ~kind(fred))) & ((old(fred) & kind(fred)) | ! [X0] : (strong(X0) & generous(X0))) [nnf transformation 9]
51. (? [X0] : (~strong(X0) | ~generous(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X0] : (strong(X0) & generous(X0))) [flattening 50]
52. (? [X0] : (~strong(X0) | ~generous(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (strong(X1) & generous(X1))) [rectify 51]
53. ? [X0] : (~strong(X0) | ~generous(X0)) => (~strong(sK2) | ~generous(sK2)) [choice axiom]
54. ((~strong(sK2) | ~generous(sK2)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (strong(X1) & generous(X1))) [skolemisation 52,53]
108. ~strong(paul) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
109. ~strong(paul) | creative(X0) | creative(X0) [cnf transformation 40]
126. kind(fred) | strong(X1) [cnf transformation 54]
168. ~kind(fred) [cnf transformation 24]
169. ~strong(paul) | ~creative(X0) [duplicate literal removal 108]
170. ~strong(paul) | creative(X0) [duplicate literal removal 109]
172. 1 <=> ! [X0] : creative(X0) [avatar definition]
173. creative(X0) <- (1) [avatar component clause 172]
175. 2 <=> strong(paul) [avatar definition]
177. ~strong(paul) <- (~2) [avatar component clause 175]
178. 1 | ~2 [avatar split clause 170,175,172]
180. 3 <=> ! [X0] : ~creative(X0) [avatar definition]
181. ~creative(X0) <- (3) [avatar component clause 180]
182. 3 | ~2 [avatar split clause 169,175,180]
199. 7 <=> kind(fred) [avatar definition]
216. 11 <=> ! [X1] : strong(X1) [avatar definition]
217. strong(X1) <- (11) [avatar component clause 216]
223. 11 | 7 [avatar split clause 126,199,216]
384. ~7 [avatar split clause 168,199]
389. $false <- (~2, 11) [subsumption resolution 177,217]
390. 2 | ~11 [avatar contradiction clause 389]
391. $false <- (1, 3) [subsumption resolution 173,181]
392. ~1 | ~3 [avatar contradiction clause 391]
393. $false [avatar sat refutation 178,182,223,384,390,392]
% SZS output end Proof for 9019353278567757233819868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or happy is not curious and vice versa. Everyone who is not wise or not happy is either not funny or strong and vice versa. Everyone who is not old is both not kind and strong. If someone is happy then lucy is either kind or not creative and vice versa. Everyone who is either not brave or not happy is strong or calm and vice versa. If alice is both strong and not creative then mary is both creative and humble and vice versa. Everyone who is both old and not brave is generous or rich and vice versa. Everyone who is both not happy and not old is calm. If someone is either generous or brave then paul is either not creative or not funny and vice versa. Everyone who is either happy or not kind is either quiet or tall. If someone is not generous then someone is happy. Everyone who is not strong or calm is both wise and kind. If paul is either not creative or not happy then paul is either not quiet or not curious. Everyone who is not brave is patient or wise and vice versa. Everyone who is either not calm or not wise is not brave and vice versa. If someone is either not creative or not strong then fred is calm and vice versa. Someone is either not funny or not happy. Someone is not creative. Alice is not old or funny. Mary is either patient or quiet. Someone is not brave or not funny. Susan is either not rich or rich. Someone is both happy and tall. | Paul is not humble. | neutral | (![X]:((~rich(X)<~>happy(X))<=>~curious(X)))&
(![X]:((~wise(X)|~happy(X))<=>(~funny(X)<~>strong(X))))&
(![X]:(~old(X)=>(~kind(X)&strong(X))))&
((?[X]:(happy(X)))<=>((kind(lucy)<~>~creative(lucy))))&
(![X]:((~brave(X)<~>~happy(X))<=>(strong(X)|calm(X))))&
(((strong(alice)&~creative(alice)))<=>((creative(mary)&humble(mary))))&
(![X]:((old(X)&~brave(X))<=>(generous(X)|rich(X))))&
(![X]:((~happy(X)&~old(X))=>calm(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>((~creative(paul)<~>~funny(paul))))&
(![X]:((happy(X)<~>~kind(X))=>(quiet(X)<~>tall(X))))&
((?[X]:(~generous(X)))=>(?[X]:(happy(X))))&
(![X]:((~strong(X)|calm(X))=>(wise(X)&kind(X))))&
(((~creative(paul)<~>~happy(paul)))=>((~quiet(paul)<~>~curious(paul))))&
(![X]:(~brave(X)<=>(patient(X)|wise(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>~brave(X)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>(calm(fred)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:(~creative(X)))&
((~old(alice)|funny(alice)))&
((patient(mary)<~>quiet(mary)))&
(?[X]:((~brave(X)|~funny(X))))&
((~rich(susan)<~>rich(susan)))&
(?[X]:((happy(X)&tall(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is funny or not rich is both not generous and not brave.
If someone is calm or not happy then susan is not generous or not happy.
Everyone who is both tall and humble is either not quiet or not humble.
Everyone who is both wise and happy is brave and vice versa.
If someone is both kind and not creative then lucy is both happy and not humble and vice versa.
Everyone who is either tall or not quiet is happy or old and vice versa.
Everyone who is funny or not rich is old or humble and vice versa.
Everyone who is either not kind or patient is both not calm and rich.
If someone is both wise and not wise then john is either quiet or strong.
If mary is either rich or strong then alice is strong or humble and vice versa.
If someone is either not brave or calm then alice is creative and vice versa.
If someone is humble then alice is either strong or humble.
If someone is either old or not strong then alice is either not old or creative and vice versa.
Everyone who is not generous or not funny is both not calm and not curious.
Everyone who is both not creative and not funny is creative or not quiet.
If someone is not patient or not quiet then someone is both brave and not happy and vice versa.
Someone is strong or not rich.
John is not creative.
Paul is not happy or not humble.
Alice is either not wise or not quiet.
Someone is either creative or not tall.
John is not patient or not old. | John is tall. | contradiction | (![X]:((funny(X)|~rich(X))=>(~generous(X)&~brave(X))))&
((?[X]:((calm(X)|~happy(X))))=>((~generous(susan)|~happy(susan))))&
(![X]:((tall(X)&humble(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((wise(X)&happy(X))<=>brave(X)))&
((?[X]:((kind(X)&~creative(X))))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((tall(X)<~>~quiet(X))<=>(happy(X)|old(X))))&
(![X]:((funny(X)|~rich(X))<=>(old(X)|humble(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)&~wise(X))))=>((quiet(john)<~>strong(john))))&
(((rich(mary)<~>strong(mary)))<=>((strong(alice)|humble(alice))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(creative(alice)))&
((?[X]:(humble(X)))=>((strong(alice)<~>humble(alice))))&
((?[X]:((old(X)<~>~strong(X))))<=>((~old(alice)<~>creative(alice))))&
(![X]:((~generous(X)|~funny(X))=>(~calm(X)&~curious(X))))&
(![X]:((~creative(X)&~funny(X))=>(creative(X)|~quiet(X))))&
((?[X]:((~patient(X)|~quiet(X))))<=>(?[X]:((brave(X)&~happy(X)))))&
(?[X]:((strong(X)|~rich(X))))&
(~creative(john))&
((~happy(paul)|~humble(paul)))&
((~wise(alice)<~>~quiet(alice)))&
(?[X]:((creative(X)<~>~tall(X))))&
((~patient(john)|~old(john))) | tall(john) | [
"p2",
"p3",
"p6",
"p14",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6218637198378313829734342
% SZS output start Proof for 6218637198378313829734342
3. ! [X0] : ((humble(X0) & tall(X0)) => (~quiet(X0) <~> ~humble(X0))) [input p2]
4. ! [X0] : ((happy(X0) & wise(X0)) <=> brave(X0)) [input p3]
7. ! [X0] : ((~rich(X0) | funny(X0)) <=> (humble(X0) | old(X0))) [input p6]
15. ! [X0] : ((~funny(X0) & ~creative(X0)) => (~quiet(X0) | creative(X0))) [input p14]
16. ? [X0] : (~quiet(X0) | ~patient(X0)) <=> ? [X0] : (~happy(X0) & brave(X0)) [input p15]
18. ~creative(john) [input p17]
22. ~old(john) | ~patient(john) [input p21]
23. tall(john) [input hypothesis]
24. ? [X0] : (~quiet(X0) | ~patient(X0)) <=> ? [X1] : (~happy(X1) & brave(X1)) [rectify 16]
29. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) | (~humble(X0) | ~tall(X0))) [ennf transformation 3]
30. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) | ~humble(X0) | ~tall(X0)) [flattening 29]
35. ! [X0] : ((~quiet(X0) | creative(X0)) | (funny(X0) | creative(X0))) [ennf transformation 15]
36. ! [X0] : (~quiet(X0) | creative(X0) | funny(X0) | creative(X0)) [flattening 35]
37. ! [X0] : (((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | ~humble(X0) | ~tall(X0)) [nnf transformation 30]
38. ! [X0] : (((happy(X0) & wise(X0)) | ~brave(X0)) & (brave(X0) | (~happy(X0) | ~wise(X0)))) [nnf transformation 4]
39. ! [X0] : (((happy(X0) & wise(X0)) | ~brave(X0)) & (brave(X0) | ~happy(X0) | ~wise(X0))) [flattening 38]
47. ! [X0] : (((~rich(X0) | funny(X0)) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | (rich(X0) & ~funny(X0)))) [nnf transformation 7]
48. ! [X0] : ((~rich(X0) | funny(X0) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | (rich(X0) & ~funny(X0)))) [flattening 47]
62. (? [X0] : (~quiet(X0) | ~patient(X0)) | ! [X1] : (happy(X1) | ~brave(X1))) & (? [X1] : (~happy(X1) & brave(X1)) | ! [X0] : (quiet(X0) & patient(X0))) [nnf transformation 24]
63. (? [X0] : (~quiet(X0) | ~patient(X0)) | ! [X1] : (happy(X1) | ~brave(X1))) & (? [X2] : (~happy(X2) & brave(X2)) | ! [X3] : (quiet(X3) & patient(X3))) [rectify 62]
64. ? [X0] : (~quiet(X0) | ~patient(X0)) => (~quiet(sK3) | ~patient(sK3)) [choice axiom]
65. ? [X2] : (~happy(X2) & brave(X2)) => (~happy(sK4) & brave(sK4)) [choice axiom]
66. ((~quiet(sK3) | ~patient(sK3)) | ! [X1] : (happy(X1) | ~brave(X1))) & ((~happy(sK4) & brave(sK4)) | ! [X3] : (quiet(X3) & patient(X3))) [skolemisation 63,65,64]
79. ~humble(X0) | ~quiet(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 37]
83. ~brave(X0) | happy(X0) [cnf transformation 39]
94. ~funny(X0) | old(X0) | humble(X0) [cnf transformation 48]
126. ~quiet(X0) | creative(X0) | funny(X0) | creative(X0) [cnf transformation 36]
127. brave(sK4) | patient(X3) [cnf transformation 66]
128. brave(sK4) | quiet(X3) [cnf transformation 66]
129. ~happy(sK4) | patient(X3) [cnf transformation 66]
130. ~happy(sK4) | quiet(X3) [cnf transformation 66]
133. ~creative(john) [cnf transformation 18]
139. ~old(john) | ~patient(john) [cnf transformation 22]
140. tall(john) [cnf transformation 23]
141. ~quiet(X0) | creative(X0) | funny(X0) [duplicate literal removal 126]
142. ~quiet(X0) | ~humble(X0) | ~tall(X0) [duplicate literal removal 79]
258. 25 <=> ! [X3] : quiet(X3) [avatar definition]
259. quiet(X3) <- (25) [avatar component clause 258]
261. 26 <=> happy(sK4) [avatar definition]
264. 25 | ~26 [avatar split clause 130,261,258]
266. 27 <=> ! [X3] : patient(X3) [avatar definition]
267. patient(X3) <- (27) [avatar component clause 266]
268. 27 | ~26 [avatar split clause 129,261,266]
270. 28 <=> brave(sK4) [avatar definition]
272. brave(sK4) <- (28) [avatar component clause 270]
273. 25 | 28 [avatar split clause 128,270,258]
274. 27 | 28 [avatar split clause 127,270,266]
314. 37 <=> patient(john) [avatar definition]
316. ~patient(john) <- (~37) [avatar component clause 314]
318. 38 <=> old(john) [avatar definition]
321. ~37 | ~38 [avatar split clause 139,318,314]
327. happy(sK4) <- (28) [resolution 83,272]
330. 26 | ~28 [avatar split clause 327,270,261]
387. 42 <=> humble(john) [avatar definition]
389. humble(john) <- (42) [avatar component clause 387]
418. 46 <=> funny(john) [avatar definition]
420. funny(john) <- (46) [avatar component clause 418]
428. creative(X0) | funny(X0) <- (25) [resolution 141,259]
431. ~humble(X0) | ~tall(X0) <- (25) [resolution 142,259]
444. funny(john) <- (25) [resolution 428,133]
446. 46 | ~25 [avatar split clause 444,258,418]
447. old(john) | humble(john) <- (46) [resolution 420,94]
449. ~tall(john) <- (25, 42) [resolution 431,389]
452. $false <- (25, 42) [subsumption resolution 449,140]
453. ~25 | ~42 [avatar contradiction clause 452]
454. 42 | 38 | ~46 [avatar split clause 447,418,318,387]
455. $false <- (27, ~37) [subsumption resolution 316,267]
456. ~27 | 37 [avatar contradiction clause 455]
457. $false [avatar sat refutation 264,268,273,274,321,330,446,453,454,456]
% SZS output end Proof for 6218637198378313829734342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and not patient is happy. Everyone who is either kind or quiet is not tall. Everyone who is not old or wise is not quiet or not curious and vice versa. Everyone who is both not happy and not old is either kind or rich and vice versa. If john is both not rich and funny then someone is either not wise or not quiet and vice versa. Everyone who is curious is either not humble or not tall. Everyone who is quiet or not funny is both not strong and curious and vice versa. Everyone who is rich or not patient is either not wise or not kind. Everyone who is either wise or not funny is not happy or not quiet. If someone is wise or not humble then john is either wise or quiet and vice versa. Everyone who is both not happy and patient is curious and vice versa. Everyone who is calm or rich is both not funny and patient and vice versa. If someone is both patient and humble then alice is both strong and patient. Everyone who is both tall and creative is either not creative or not curious. Everyone who is not patient or kind is creative or patient and vice versa. If someone is funny then lucy is not calm or generous and vice versa. Paul is brave or tall. Fred is not quiet or not wise. Susan is rich or not strong. Paul is not rich or strong. Alice is not quiet or wise. Susan is either not quiet or funny. Someone is calm. Someone is tall or curious. | John is not rich. | entailment | (![X]:((~old(X)&~patient(X))=>happy(X)))&
(![X]:((kind(X)<~>quiet(X))=>~tall(X)))&
(![X]:((~old(X)|wise(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~happy(X)&~old(X))<=>(kind(X)<~>rich(X))))&
(((~rich(john)&funny(john)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:((quiet(X)|~funny(X))<=>(~strong(X)&curious(X))))&
(![X]:((rich(X)|~patient(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~funny(X))=>(~happy(X)|~quiet(X))))&
((?[X]:((wise(X)|~humble(X))))<=>((wise(john)<~>quiet(john))))&
(![X]:((~happy(X)&patient(X))<=>curious(X)))&
(![X]:((calm(X)|rich(X))<=>(~funny(X)&patient(X))))&
((?[X]:((patient(X)&humble(X))))=>((strong(alice)&patient(alice))))&
(![X]:((tall(X)&creative(X))=>(~creative(X)<~>~curious(X))))&
(![X]:((~patient(X)|kind(X))<=>(creative(X)|patient(X))))&
((?[X]:(funny(X)))<=>((~calm(lucy)|generous(lucy))))&
((brave(paul)|tall(paul)))&
((~quiet(fred)|~wise(fred)))&
((rich(susan)|~strong(susan)))&
((~rich(paul)|strong(paul)))&
((~quiet(alice)|wise(alice)))&
((~quiet(susan)<~>funny(susan)))&
(?[X]:(calm(X)))&
(?[X]:((tall(X)|curious(X)))) | ~rich(john) | [
"p2",
"p3",
"p4",
"p6",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 912781248217800837428405
% SZS output start Proof for 912781248217800837428405
3. ! [X0] : ((wise(X0) | ~old(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((~old(X0) & ~happy(X0)) <=> (kind(X0) <~> rich(X0))) [input p3]
5. (funny(john) & ~rich(john)) <=> ? [X0] : (~wise(X0) <~> ~quiet(X0)) [input p4]
7. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (curious(X0) & ~strong(X0))) [input p6]
10. ? [X0] : (~humble(X0) | wise(X0)) <=> (wise(john) <~> quiet(john)) [input p9]
11. ! [X0] : ((patient(X0) & ~happy(X0)) <=> curious(X0)) [input p10]
12. ! [X0] : ((rich(X0) | calm(X0)) <=> (patient(X0) & ~funny(X0))) [input p11]
15. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (patient(X0) | creative(X0))) [input p14]
25. rich(john) [input hypothesis]
38. ! [X0] : (((wise(X0) | ~old(X0)) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 3]
39. ! [X0] : ((wise(X0) | ~old(X0) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | (~wise(X0) & old(X0)))) [flattening 38]
40. ! [X0] : (((~old(X0) & ~happy(X0)) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (old(X0) | happy(X0)))) [nnf transformation 4]
41. ! [X0] : (((~old(X0) & ~happy(X0)) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | old(X0) | happy(X0))) [flattening 40]
42. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (~funny(john) | rich(john))) [nnf transformation 5]
43. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~funny(john) | rich(john)) [flattening 42]
44. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) | ~funny(john) | rich(john)) [rectify 43]
45. ? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) => ((quiet(sK0) | wise(sK0)) & (~quiet(sK0) | ~wise(sK0))) [choice axiom]
46. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(sK0) | wise(sK0)) & (~quiet(sK0) | ~wise(sK0))) | ~funny(john) | rich(john)) [skolemisation 44,45]
48. ! [X0] : (((~funny(X0) | quiet(X0)) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 7]
49. ! [X0] : ((~funny(X0) | quiet(X0) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | (funny(X0) & ~quiet(X0)))) [flattening 48]
52. (? [X0] : (~humble(X0) | wise(X0)) | ((wise(john) | ~quiet(john)) & (quiet(john) | ~wise(john)))) & (((~quiet(john) | ~wise(john)) & (quiet(john) | wise(john))) | ! [X0] : (humble(X0) & ~wise(X0))) [nnf transformation 10]
53. (? [X0] : (~humble(X0) | wise(X0)) | ((wise(john) | ~quiet(john)) & (quiet(john) | ~wise(john)))) & (((~quiet(john) | ~wise(john)) & (quiet(john) | wise(john))) | ! [X1] : (humble(X1) & ~wise(X1))) [rectify 52]
54. ? [X0] : (~humble(X0) | wise(X0)) => (~humble(sK1) | wise(sK1)) [choice axiom]
55. ((~humble(sK1) | wise(sK1)) | ((wise(john) | ~quiet(john)) & (quiet(john) | ~wise(john)))) & (((~quiet(john) | ~wise(john)) & (quiet(john) | wise(john))) | ! [X1] : (humble(X1) & ~wise(X1))) [skolemisation 53,54]
56. ! [X0] : (((patient(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (~patient(X0) | happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((patient(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | ~patient(X0) | happy(X0))) [flattening 56]
58. ! [X0] : (((rich(X0) | calm(X0)) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | calm(X0) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 58]
61. ! [X0] : (((kind(X0) | ~patient(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (~kind(X0) & patient(X0)))) [nnf transformation 15]
62. ! [X0] : ((kind(X0) | ~patient(X0) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | (~kind(X0) & patient(X0)))) [flattening 61]
78. ~old(X0) | wise(X0) | quiet(X0) [cnf transformation 39]
81. ~rich(X0) | ~kind(X0) | old(X0) | happy(X0) [cnf transformation 41]
88. ~rich(john) | ~quiet(X0) | wise(X0) [cnf transformation 46]
89. ~rich(john) | ~wise(X0) | quiet(X0) [cnf transformation 46]
97. funny(X0) | curious(X0) [cnf transformation 49]
105. quiet(john) | wise(john) | ~wise(X1) [cnf transformation 55]
107. ~quiet(john) | ~wise(john) | ~wise(X1) [cnf transformation 55]
112. ~curious(X0) | ~happy(X0) [cnf transformation 57]
115. ~funny(X0) | ~rich(X0) [cnf transformation 59]
117. ~rich(X0) | patient(X0) [cnf transformation 59]
126. kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
138. rich(john) [cnf transformation 25]
140. ~patient(X0) | kind(X0) [duplicate literal removal 126]
143. 1 <=> ! [X0] : (~wise(X0) | quiet(X0)) [avatar definition]
144. ~wise(X0) | quiet(X0) <- (1) [avatar component clause 143]
151. 3 <=> ! [X0] : (~quiet(X0) | wise(X0)) [avatar definition]
152. ~quiet(X0) | wise(X0) <- (3) [avatar component clause 151]
155. 4 <=> rich(john) [avatar definition]
156. rich(john) <- (4) [avatar component clause 155]
158. 1 | ~4 [avatar split clause 89,155,143]
159. 3 | ~4 [avatar split clause 88,155,151]
171. 7 <=> quiet(john) [avatar definition]
172. quiet(john) <- (7) [avatar component clause 171]
173. ~quiet(john) <- (~7) [avatar component clause 171]
175. 8 <=> wise(john) [avatar definition]
176. ~wise(john) <- (~8) [avatar component clause 175]
177. wise(john) <- (8) [avatar component clause 175]
193. 12 <=> ! [X1] : ~wise(X1) [avatar definition]
194. ~wise(X1) <- (12) [avatar component clause 193]
195. 12 | ~8 | ~7 [avatar split clause 107,171,175,193]
197. 12 | 8 | 7 [avatar split clause 105,171,175,193]
284. 4 [avatar split clause 138,155]
294. ~rich(X0) | curious(X0) [resolution 115,97]
296. patient(john) <- (4) [resolution 117,156]
302. wise(john) <- (3, 7) [resolution 152,172]
303. $false <- (3, 7, ~8) [subsumption resolution 302,176]
304. ~3 | ~7 | 8 [avatar contradiction clause 303]
305. quiet(john) <- (1, 8) [resolution 177,144]
306. $false <- (1, ~7, 8) [subsumption resolution 305,173]
307. ~1 | 7 | ~8 [avatar contradiction clause 306]
310. kind(john) <- (4) [resolution 296,140]
377. curious(john) <- (4) [resolution 294,156]
383. ~happy(john) <- (4) [resolution 377,112]
434. ~kind(john) | old(john) | happy(john) <- (4) [resolution 81,156]
437. old(john) | happy(john) <- (4) [subsumption resolution 434,310]
438. old(john) <- (4) [subsumption resolution 437,383]
457. wise(john) | quiet(john) <- (4) [resolution 438,78]
458. quiet(john) <- (4, 12) [subsumption resolution 457,194]
461. 7 | ~4 | ~12 [avatar split clause 458,193,155,171]
462. $false <- (8, 12) [subsumption resolution 177,194]
463. ~8 | ~12 [avatar contradiction clause 462]
464. $false [avatar sat refutation 158,159,195,197,284,304,307,461,463]
% SZS output end Proof for 912781248217800837428405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either old or rich and vice versa.
If someone is both not generous and kind then paul is quiet.
Everyone who is both not creative and funny is both brave and not calm and vice versa.
If mary is both strong and humble then someone is not strong or not tall.
Everyone who is not curious is either not kind or not strong.
If someone is wise then someone is brave and vice versa.
If john is not generous or calm then someone is not quiet or not tall.
Everyone who is either not kind or not calm is either quiet or not curious.
Everyone who is both not curious and curious is not rich or generous and vice versa.
Everyone who is not funny is rich or quiet.
Everyone who is both not happy and not wise is both humble and not funny and vice versa.
Everyone who is both not old and patient is curious or not wise.
Everyone who is both creative and not kind is not happy.
Everyone who is either not wise or brave is brave and vice versa.
If fred is either not old or not brave then someone is curious and vice versa.
If mary is either creative or wise then paul is kind and vice versa.
Someone is either not wise or kind.
Lucy is both quiet and not calm.
Someone is both not quiet and not brave.
Someone is either not creative or humble.
Fred is not brave.
Alice is rich or not strong. | Paul is not happy. | neutral | (![X]:(~kind(X)<=>(old(X)<~>rich(X))))&
((?[X]:((~generous(X)&kind(X))))=>(quiet(paul)))&
(![X]:((~creative(X)&funny(X))<=>(brave(X)&~calm(X))))&
(((strong(mary)&humble(mary)))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:(~curious(X)=>(~kind(X)<~>~strong(X))))&
((?[X]:(wise(X)))<=>(?[X]:(brave(X))))&
(((~generous(john)|calm(john)))=>(?[X]:((~quiet(X)|~tall(X)))))&
(![X]:((~kind(X)<~>~calm(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((~curious(X)&curious(X))<=>(~rich(X)|generous(X))))&
(![X]:(~funny(X)=>(rich(X)|quiet(X))))&
(![X]:((~happy(X)&~wise(X))<=>(humble(X)&~funny(X))))&
(![X]:((~old(X)&patient(X))=>(curious(X)|~wise(X))))&
(![X]:((creative(X)&~kind(X))=>~happy(X)))&
(![X]:((~wise(X)<~>brave(X))<=>brave(X)))&
(((~old(fred)<~>~brave(fred)))<=>(?[X]:(curious(X))))&
(((creative(mary)<~>wise(mary)))<=>(kind(paul)))&
(?[X]:((~wise(X)<~>kind(X))))&
((quiet(lucy)&~calm(lucy)))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
(~brave(fred))&
((rich(alice)|~strong(alice))) | ~happy(paul) | [] | null | 0 |
Everyone who is either not calm or not quiet is both not happy and funny and vice versa. If someone is tall then fred is brave or curious and vice versa. Everyone who is both not tall and not humble is kind. Everyone who is either old or not creative is rich and vice versa. If someone is either curious or tall then someone is both not tall and not strong and vice versa. If john is not kind or not creative then mary is not rich and vice versa. Everyone who is either quiet or not old is both old and not creative and vice versa. Everyone who is both not rich and generous is both brave and patient and vice versa. If someone is quiet or rich then someone is calm. Everyone who is not humble is either not calm or happy and vice versa. If john is both strong and brave then paul is both not humble and not strong and vice versa. If someone is either calm or not wise then alice is not curious or funny. Everyone who is not kind is wise or generous and vice versa. If fred is either not curious or not rich then someone is generous or not wise. Everyone who is either calm or quiet is both not funny and happy and vice versa. Everyone who is either not humble or humble is not humble. Someone is not strong or happy. Someone is either not old or brave. Susan is not tall. Someone is not kind. Someone is either tall or old. Susan is both not humble and not wise. Paul is either curious or not wise. | Alice is not curious. | neutral | (![X]:((~calm(X)<~>~quiet(X))<=>(~happy(X)&funny(X))))&
((?[X]:(tall(X)))<=>((brave(fred)|curious(fred))))&
(![X]:((~tall(X)&~humble(X))=>kind(X)))&
(![X]:((old(X)<~>~creative(X))<=>rich(X)))&
((?[X]:((curious(X)<~>tall(X))))<=>(?[X]:((~tall(X)&~strong(X)))))&
(((~kind(john)|~creative(john)))<=>(~rich(mary)))&
(![X]:((quiet(X)<~>~old(X))<=>(old(X)&~creative(X))))&
(![X]:((~rich(X)&generous(X))<=>(brave(X)&patient(X))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(((strong(john)&brave(john)))<=>((~humble(paul)&~strong(paul))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~curious(alice)|funny(alice))))&
(![X]:(~kind(X)<=>(wise(X)|generous(X))))&
(((~curious(fred)<~>~rich(fred)))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~funny(X)&happy(X))))&
(![X]:((~humble(X)<~>humble(X))=>~humble(X)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(~tall(susan))&
(?[X]:(~kind(X)))&
(?[X]:((tall(X)<~>old(X))))&
((~humble(susan)&~wise(susan)))&
((curious(paul)<~>~wise(paul))) | ~curious(alice) | [] | null | 0 |
If john is not generous or quiet then susan is either not kind or not quiet.
If alice is happy then alice is both calm and not quiet and vice versa.
Everyone who is both not brave and creative is wise and vice versa.
Everyone who is either not old or generous is both not patient and not creative and vice versa.
If someone is both not tall and not calm then someone is either not funny or funny and vice versa.
Everyone who is not curious or tall is both strong and not calm and vice versa.
If fred is creative then someone is not kind or quiet and vice versa.
If someone is both wise and not wise then someone is patient or not humble.
If someone is not funny then john is both not old and not humble and vice versa.
Everyone who is not calm or calm is strong.
Everyone who is both not rich and not humble is brave or humble.
If mary is both not tall and not brave then lucy is rich or quiet.
If alice is either not humble or not happy then alice is not old or generous and vice versa.
If paul is either patient or kind then alice is either not calm or not happy.
Mary is both not kind and not quiet.
Someone is curious or creative.
Someone is old or not generous.
Lucy is tall or not brave.
Someone is not quiet.
Someone is not wise. | John is not brave. | neutral | (((~generous(john)|quiet(john)))=>((~kind(susan)<~>~quiet(susan))))&
((happy(alice))<=>((calm(alice)&~quiet(alice))))&
(![X]:((~brave(X)&creative(X))<=>wise(X)))&
(![X]:((~old(X)<~>generous(X))<=>(~patient(X)&~creative(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>funny(X)))))&
(![X]:((~curious(X)|tall(X))<=>(strong(X)&~calm(X))))&
((creative(fred))<=>(?[X]:((~kind(X)|quiet(X)))))&
((?[X]:((wise(X)&~wise(X))))=>(?[X]:((patient(X)|~humble(X)))))&
((?[X]:(~funny(X)))<=>((~old(john)&~humble(john))))&
(![X]:((~calm(X)|calm(X))=>strong(X)))&
(![X]:((~rich(X)&~humble(X))=>(brave(X)|humble(X))))&
(((~tall(mary)&~brave(mary)))=>((rich(lucy)|quiet(lucy))))&
(((~humble(alice)<~>~happy(alice)))<=>((~old(alice)|generous(alice))))&
(((patient(paul)<~>kind(paul)))=>((~calm(alice)<~>~happy(alice))))&
((~kind(mary)&~quiet(mary)))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((old(X)|~generous(X))))&
((tall(lucy)|~brave(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:(~wise(X))) | ~brave(john) | [] | null | 0 |
If fred is not tall then someone is patient or creative.
Everyone who is either not calm or rich is not rich or wise and vice versa.
If someone is both wise and not creative then someone is either creative or humble.
Everyone who is curious is strong and vice versa.
If someone is both not funny and curious then paul is curious or strong and vice versa.
If someone is both old and not funny then lucy is either rich or funny.
If someone is both happy and not humble then someone is not funny and vice versa.
Everyone who is either not happy or funny is both not generous and patient.
If someone is both funny and not old then alice is both happy and not old.
If fred is both brave and not rich then someone is either strong or not quiet.
Everyone who is either not patient or kind is curious.
Everyone who is both not happy and not humble is not quiet.
Everyone who is not wise is either not calm or not wise.
Everyone who is not rich or brave is happy or calm and vice versa.
If someone is funny or not tall then someone is not happy.
Everyone who is tall or strong is either funny or not old.
Fred is not generous or calm.
Paul is quiet.
Someone is either creative or rich.
Mary is not tall.
Someone is not generous or not wise.
Alice is creative.
Susan is both generous and humble.
Someone is either not quiet or tall. | Paul is not wise. | contradiction | ((~tall(fred))=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((~calm(X)<~>rich(X))<=>(~rich(X)|wise(X))))&
((?[X]:((wise(X)&~creative(X))))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:(curious(X)<=>strong(X)))&
((?[X]:((~funny(X)&curious(X))))<=>((curious(paul)|strong(paul))))&
((?[X]:((old(X)&~funny(X))))=>((rich(lucy)<~>funny(lucy))))&
((?[X]:((happy(X)&~humble(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)<~>funny(X))=>(~generous(X)&patient(X))))&
((?[X]:((funny(X)&~old(X))))=>((happy(alice)&~old(alice))))&
(((brave(fred)&~rich(fred)))=>(?[X]:((strong(X)<~>~quiet(X)))))&
(![X]:((~patient(X)<~>kind(X))=>curious(X)))&
(![X]:((~happy(X)&~humble(X))=>~quiet(X)))&
(![X]:(~wise(X)=>(~calm(X)<~>~wise(X))))&
(![X]:((~rich(X)|brave(X))<=>(happy(X)|calm(X))))&
((?[X]:((funny(X)|~tall(X))))=>(?[X]:(~happy(X))))&
(![X]:((tall(X)|strong(X))=>(funny(X)<~>~old(X))))&
((~generous(fred)|calm(fred)))&
(quiet(paul))&
(?[X]:((creative(X)<~>rich(X))))&
(~tall(mary))&
(?[X]:((~generous(X)|~wise(X))))&
(creative(alice))&
((generous(susan)&humble(susan)))&
(?[X]:((~quiet(X)<~>tall(X)))) | ~wise(paul) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6907885160828755873205453
% SZS output start Proof for 6907885160828755873205453
2. ! [X0] : ((~calm(X0) <~> rich(X0)) <=> (wise(X0) | ~rich(X0))) [input p1]
13. ! [X0] : (~wise(X0) => (~calm(X0) <~> ~wise(X0))) [input p12]
25. ~wise(paul) [input hypothesis]
39. ! [X0] : ((~calm(X0) <~> ~wise(X0)) | wise(X0)) [ennf transformation 13]
44. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [nnf transformation 2]
45. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [flattening 44]
67. ! [X0] : (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | wise(X0)) [nnf transformation 39]
84. wise(X0) | ~rich(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 45]
85. rich(X0) | ~calm(X0) | rich(X0) [cnf transformation 45]
115. wise(X0) | calm(X0) | wise(X0) [cnf transformation 67]
137. ~wise(paul) [cnf transformation 25]
138. wise(X0) | calm(X0) [duplicate literal removal 115]
139. wise(X0) | ~rich(X0) | ~calm(X0) [duplicate literal removal 84]
140. rich(X0) | ~calm(X0) [duplicate literal removal 85]
154. wise(X0) | ~calm(X0) [subsumption resolution 139,140]
258. wise(X0) [subsumption resolution 138,154]
303. $false [subsumption resolution 137,258]
% SZS output end Proof for 6907885160828755873205453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and creative then someone is old or kind and vice versa.
If someone is either not patient or strong then someone is not humble.
Everyone who is not funny or happy is either not kind or strong.
Everyone who is both happy and tall is either not kind or old and vice versa.
Everyone who is not brave is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is not happy. | entailment | ((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((old(X)|kind(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)|happy(X))=>(~kind(X)<~>strong(X))))&
(![X]:((happy(X)&tall(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>~calm(X)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | ~happy(paul) | [
"p0",
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8549099060369399437503879
% SZS output start Proof for 8549099060369399437503879
1. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (kind(X0) | old(X0)) [input p0]
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
15. ? [X0] : creative(X0) <=> (rich(paul) & brave(paul)) [input p14]
20. ? [X0] : old(X0) [input p19]
24. happy(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (kind(X1) | old(X1)) [rectify 1]
40. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X1] : (kind(X1) | old(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X2] : (kind(X2) | old(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 40]
42. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
43. ? [X2] : (kind(X2) | old(X2)) => (kind(sK1) | old(sK1)) [choice axiom]
44. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~kind(X1) & ~old(X1))) & ((kind(sK1) | old(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 41,43,42]
54. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
55. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 54]
67. (? [X0] : creative(X0) | (~rich(paul) | ~brave(paul))) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [nnf transformation 15]
68. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [flattening 67]
69. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [rectify 68]
70. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
71. (creative(sK6) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [skolemisation 69,70]
78. ? [X0] : old(X0) => old(sK10) [choice axiom]
79. old(sK10) [skolemisation 20,78]
88. creative(sK0) | ~old(X1) [cnf transformation 44]
111. ~brave(X0) | ~happy(X0) [cnf transformation 55]
129. brave(paul) | ~creative(X1) [cnf transformation 71]
137. old(sK10) [cnf transformation 79]
142. happy(paul) [cnf transformation 24]
147. 2 <=> creative(sK0) [avatar definition]
149. creative(sK0) <- (2) [avatar component clause 147]
152. 3 <=> ! [X1] : ~old(X1) [avatar definition]
153. ~old(X1) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 88,147,152]
286. 33 <=> brave(paul) [avatar definition]
287. brave(paul) <- (33) [avatar component clause 286]
299. 36 <=> ! [X1] : ~creative(X1) [avatar definition]
300. ~creative(X1) <- (36) [avatar component clause 299]
302. 36 | 33 [avatar split clause 129,286,299]
369. ~happy(paul) <- (33) [resolution 111,287]
370. $false <- (33) [subsumption resolution 369,142]
371. ~33 [avatar contradiction clause 370]
373. $false <- (2, 36) [resolution 300,149]
378. ~2 | ~36 [avatar contradiction clause 373]
379. $false <- (3) [resolution 153,137]
382. ~3 [avatar contradiction clause 379]
383. $false [avatar sat refutation 154,302,371,378,382]
% SZS output end Proof for 8549099060369399437503879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either curious or happy then someone is not old or not funny and vice versa. Everyone who is not tall is wise and vice versa. Everyone who is either not creative or creative is patient. Everyone who is curious is not old and vice versa. Everyone who is both not quiet and wise is strong or wise and vice versa. If someone is not strong or rich then fred is both not creative and funny and vice versa. If alice is not creative or not curious then lucy is funny. If someone is curious then alice is funny or creative. If paul is not brave then paul is either old or kind. Everyone who is generous is not calm and vice versa. Everyone who is either not creative or brave is either not kind or quiet. Everyone who is either not funny or not generous is both not humble and not creative and vice versa. If someone is either not rich or not funny then someone is either not generous or tall and vice versa. Everyone who is both not tall and calm is creative. Everyone who is happy or kind is not rich or not happy. If someone is both not rich and not tall then fred is generous and vice versa. Susan is not generous. Someone is either not kind or funny. Someone is not brave. Lucy is not creative or funny. Paul is kind. Fred is tall or not humble. Someone is not old. Mary is not calm or not generous. | Lucy is not old. | neutral | (((curious(lucy)<~>happy(lucy)))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:(~tall(X)<=>wise(X)))&
(![X]:((~creative(X)<~>creative(X))=>patient(X)))&
(![X]:(curious(X)<=>~old(X)))&
(![X]:((~quiet(X)&wise(X))<=>(strong(X)|wise(X))))&
((?[X]:((~strong(X)|rich(X))))<=>((~creative(fred)&funny(fred))))&
(((~creative(alice)|~curious(alice)))=>(funny(lucy)))&
((?[X]:(curious(X)))=>((funny(alice)|creative(alice))))&
((~brave(paul))=>((old(paul)<~>kind(paul))))&
(![X]:(generous(X)<=>~calm(X)))&
(![X]:((~creative(X)<~>brave(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
(![X]:((~tall(X)&calm(X))=>creative(X)))&
(![X]:((happy(X)|kind(X))=>(~rich(X)|~happy(X))))&
((?[X]:((~rich(X)&~tall(X))))<=>(generous(fred)))&
(~generous(susan))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:(~brave(X)))&
((~creative(lucy)|funny(lucy)))&
(kind(paul))&
((tall(fred)|~humble(fred)))&
(?[X]:(~old(X)))&
((~calm(mary)|~generous(mary))) | ~old(lucy) | [] | null | 0 |
If fred is either not humble or tall then someone is patient and vice versa.
If someone is curious or not old then susan is both tall and not rich and vice versa.
If mary is not patient or not rich then paul is not creative.
If fred is tall then someone is kind or not tall.
Everyone who is both creative and not calm is tall or not kind.
If someone is not quiet or not old then fred is both not patient and not happy and vice versa.
If susan is either wise or not patient then paul is either not curious or not tall.
If someone is curious then someone is not humble and vice versa.
If alice is not quiet then alice is not old or rich and vice versa.
Everyone who is rich is not creative or not tall and vice versa.
Everyone who is both not creative and not tall is rich and vice versa.
If someone is either funny or not humble then susan is creative or not wise.
Everyone who is both brave and creative is either brave or tall and vice versa.
If fred is kind then someone is either calm or not humble.
If lucy is both not humble and old then someone is both rich and not creative.
If someone is both funny and wise then susan is not quiet or generous and vice versa.
Susan is either not funny or brave.
Someone is either not wise or tall.
John is either calm or not old.
Someone is not tall.
Fred is either not wise or not happy.
Someone is either humble or not rich. | Fred is wise. | entailment | (((~humble(fred)<~>tall(fred)))<=>(?[X]:(patient(X))))&
((?[X]:((curious(X)|~old(X))))<=>((tall(susan)&~rich(susan))))&
(((~patient(mary)|~rich(mary)))=>(~creative(paul)))&
((tall(fred))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:((creative(X)&~calm(X))=>(tall(X)|~kind(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>((~patient(fred)&~happy(fred))))&
(((wise(susan)<~>~patient(susan)))=>((~curious(paul)<~>~tall(paul))))&
((?[X]:(curious(X)))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>((~old(alice)|rich(alice))))&
(![X]:(rich(X)<=>(~creative(X)|~tall(X))))&
(![X]:((~creative(X)&~tall(X))<=>rich(X)))&
((?[X]:((funny(X)<~>~humble(X))))=>((creative(susan)|~wise(susan))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>tall(X))))&
((kind(fred))=>(?[X]:((calm(X)<~>~humble(X)))))&
(((~humble(lucy)&old(lucy)))=>(?[X]:((rich(X)&~creative(X)))))&
((?[X]:((funny(X)&wise(X))))<=>((~quiet(susan)|generous(susan))))&
((~funny(susan)<~>brave(susan)))&
(?[X]:((~wise(X)<~>tall(X))))&
((calm(john)<~>~old(john)))&
(?[X]:(~tall(X)))&
((~wise(fred)<~>~happy(fred)))&
(?[X]:((humble(X)<~>~rich(X)))) | wise(fred) | [
"p5",
"p8",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5997310579648641035313332
% SZS output start Proof for 5997310579648641035313332
6. ? [X0] : (~old(X0) | ~quiet(X0)) <=> (~happy(fred) & ~patient(fred)) [input p5]
9. ~quiet(alice) <=> (rich(alice) | ~old(alice)) [input p8]
10. ! [X0] : (rich(X0) <=> (~tall(X0) | ~creative(X0))) [input p9]
13. ! [X0] : ((creative(X0) & brave(X0)) <=> (brave(X0) <~> tall(X0))) [input p12]
21. ~wise(fred) <~> ~happy(fred) [input p20]
23. ~wise(fred) [input hypothesis]
46. (? [X0] : (~old(X0) | ~quiet(X0)) | (happy(fred) | patient(fred))) & ((~happy(fred) & ~patient(fred)) | ! [X0] : (old(X0) & quiet(X0))) [nnf transformation 6]
47. (? [X0] : (~old(X0) | ~quiet(X0)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X0] : (old(X0) & quiet(X0))) [flattening 46]
48. (? [X0] : (~old(X0) | ~quiet(X0)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X1] : (old(X1) & quiet(X1))) [rectify 47]
49. ? [X0] : (~old(X0) | ~quiet(X0)) => (~old(sK3) | ~quiet(sK3)) [choice axiom]
50. ((~old(sK3) | ~quiet(sK3)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X1] : (old(X1) & quiet(X1))) [skolemisation 48,49]
57. (~quiet(alice) | (~rich(alice) & old(alice))) & ((rich(alice) | ~old(alice)) | quiet(alice)) [nnf transformation 9]
58. (~quiet(alice) | (~rich(alice) & old(alice))) & (rich(alice) | ~old(alice) | quiet(alice)) [flattening 57]
59. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~rich(X0))) [nnf transformation 10]
60. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~rich(X0))) [flattening 59]
64. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~creative(X0) | ~brave(X0)))) [nnf transformation 13]
65. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | ~creative(X0) | ~brave(X0))) [flattening 64]
83. (happy(fred) | wise(fred)) & (~happy(fred) | ~wise(fred)) [nnf transformation 21]
102. ~happy(fred) | quiet(X1) [cnf transformation 50]
113. ~quiet(alice) | ~rich(alice) [cnf transformation 58]
115. creative(X0) | rich(X0) [cnf transformation 60]
116. rich(X0) | tall(X0) [cnf transformation 60]
123. ~tall(X0) | ~brave(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 65]
125. brave(X0) | brave(X0) | ~tall(X0) [cnf transformation 65]
145. happy(fred) | wise(fred) [cnf transformation 83]
148. ~wise(fred) [cnf transformation 23]
149. ~tall(X0) | ~brave(X0) | ~creative(X0) [duplicate literal removal 123]
150. ~tall(X0) | brave(X0) [duplicate literal removal 125]
225. 17 <=> happy(fred) [avatar definition]
239. 20 <=> ! [X1] : quiet(X1) [avatar definition]
240. quiet(X1) <- (20) [avatar component clause 239]
241. 20 | ~17 [avatar split clause 102,225,239]
278. 28 <=> rich(alice) [avatar definition]
280. ~rich(alice) <- (~28) [avatar component clause 278]
282. 29 <=> quiet(alice) [avatar definition]
284. ~quiet(alice) <- (~29) [avatar component clause 282]
285. ~28 | ~29 [avatar split clause 113,282,278]
304. ~creative(X0) | ~tall(X0) [subsumption resolution 149,150]
392. 52 <=> wise(fred) [avatar definition]
395. 52 | 17 [avatar split clause 145,225,392]
407. ~52 [avatar split clause 148,392]
412. $false <- (20, ~29) [resolution 284,240]
413. ~20 | 29 [avatar contradiction clause 412]
441. ~tall(X0) | rich(X0) [resolution 304,115]
442. rich(X0) [subsumption resolution 441,116]
446. $false <- (~28) [resolution 442,280]
449. 28 [avatar contradiction clause 446]
451. $false [avatar sat refutation 241,285,395,407,413,449]
% SZS output end Proof for 5997310579648641035313332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not patient then lucy is either not strong or not creative.
If susan is both not tall and not rich then someone is both curious and generous.
Everyone who is not funny is strong or not wise and vice versa.
Everyone who is old is both patient and not curious and vice versa.
If someone is happy or wise then someone is either calm or not strong.
Everyone who is either calm or tall is either strong or patient.
Everyone who is either not generous or quiet is tall or not old and vice versa.
Everyone who is strong is either not wise or curious.
Everyone who is funny or not generous is quiet or not curious.
If fred is both curious and creative then someone is not tall.
If someone is either curious or humble then susan is both creative and not funny.
Everyone who is not generous or happy is both not brave and curious and vice versa.
If someone is either tall or quiet then someone is both wise and not brave.
If someone is either not brave or rich then paul is kind or not curious and vice versa.
Everyone who is strong or quiet is not quiet.
Everyone who is not happy or brave is either not curious or not rich.
Someone is brave or not brave.
Someone is either not humble or strong.
Alice is wise.
Someone is patient. | Susan is not wise. | neutral | (((tall(fred)<~>~patient(fred)))=>((~strong(lucy)<~>~creative(lucy))))&
(((~tall(susan)&~rich(susan)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:(~funny(X)<=>(strong(X)|~wise(X))))&
(![X]:(old(X)<=>(patient(X)&~curious(X))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((calm(X)<~>tall(X))=>(strong(X)<~>patient(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(tall(X)|~old(X))))&
(![X]:(strong(X)=>(~wise(X)<~>curious(X))))&
(![X]:((funny(X)|~generous(X))=>(quiet(X)|~curious(X))))&
(((curious(fred)&creative(fred)))=>(?[X]:(~tall(X))))&
((?[X]:((curious(X)<~>humble(X))))=>((creative(susan)&~funny(susan))))&
(![X]:((~generous(X)|happy(X))<=>(~brave(X)&curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((~brave(X)<~>rich(X))))<=>((kind(paul)|~curious(paul))))&
(![X]:((strong(X)|quiet(X))=>~quiet(X)))&
(![X]:((~happy(X)|brave(X))=>(~curious(X)<~>~rich(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~humble(X)<~>strong(X))))&
(wise(alice))&
(?[X]:(patient(X))) | ~wise(susan) | [] | null | 0 |
Everyone who is both not old and generous is both generous and happy and vice versa. Everyone who is not old or not patient is wise. If someone is both brave and wise then someone is both not calm and not brave and vice versa. If lucy is both humble and quiet then someone is both kind and calm and vice versa. Everyone who is not funny or not generous is both humble and not calm and vice versa. Everyone who is tall or not humble is not patient. Everyone who is creative is funny and vice versa. Everyone who is strong or calm is either not quiet or not calm. If paul is either generous or creative then someone is generous or funny. Everyone who is not strong or rich is both humble and rich. Everyone who is quiet or happy is creative or not calm. If someone is either rich or not creative then lucy is either not happy or old and vice versa. Everyone who is either not patient or not old is both not generous and not happy. Everyone who is not curious is funny or not curious. If fred is either funny or curious then mary is both curious and not creative and vice versa. Everyone who is kind or humble is both not generous and not tall and vice versa. Someone is both not quiet and not old. Someone is not rich. Someone is both not tall and not funny. Fred is either patient or not happy. Paul is either not tall or old. John is not brave. Fred is either not brave or tall. Paul is calm. | John is not humble. | neutral | (![X]:((~old(X)&generous(X))<=>(generous(X)&happy(X))))&
(![X]:((~old(X)|~patient(X))=>wise(X)))&
((?[X]:((brave(X)&wise(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(((humble(lucy)&quiet(lucy)))<=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((~funny(X)|~generous(X))<=>(humble(X)&~calm(X))))&
(![X]:((tall(X)|~humble(X))=>~patient(X)))&
(![X]:(creative(X)<=>funny(X)))&
(![X]:((strong(X)|calm(X))=>(~quiet(X)<~>~calm(X))))&
(((generous(paul)<~>creative(paul)))=>(?[X]:((generous(X)|funny(X)))))&
(![X]:((~strong(X)|rich(X))=>(humble(X)&rich(X))))&
(![X]:((quiet(X)|happy(X))=>(creative(X)|~calm(X))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~happy(lucy)<~>old(lucy))))&
(![X]:((~patient(X)<~>~old(X))=>(~generous(X)&~happy(X))))&
(![X]:(~curious(X)=>(funny(X)|~curious(X))))&
(((funny(fred)<~>curious(fred)))<=>((curious(mary)&~creative(mary))))&
(![X]:((kind(X)|humble(X))<=>(~generous(X)&~tall(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((patient(fred)<~>~happy(fred)))&
((~tall(paul)<~>old(paul)))&
(~brave(john))&
((~brave(fred)<~>tall(fred)))&
(calm(paul)) | ~humble(john) | [] | null | 0 |
Everyone who is either not brave or not happy is not funny.
Everyone who is not quiet or not wise is creative.
If lucy is not generous or tall then paul is humble or not humble and vice versa.
Everyone who is either not brave or not tall is not brave or not tall.
Everyone who is either not kind or calm is both curious and not humble and vice versa.
If someone is both not humble and not tall then someone is both not brave and not creative and vice versa.
If someone is both tall and patient then alice is humble.
If fred is not happy or not kind then someone is either not rich or funny and vice versa.
Everyone who is either kind or funny is not wise and vice versa.
Everyone who is both not old and quiet is both not quiet and patient and vice versa.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
Paul is both quiet and old.
John is not rich or not creative.
Paul is either not brave or happy.
Paul is quiet.
Susan is either happy or not generous.
Someone is both tall and kind. | Fred is not generous. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((~quiet(X)|~wise(X))=>creative(X)))&
(((~generous(lucy)|tall(lucy)))<=>((humble(paul)|~humble(paul))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(curious(X)&~humble(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:((tall(X)&patient(X))))=>(humble(alice)))&
(((~happy(fred)|~kind(fred)))<=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((kind(X)<~>funny(X))<=>~wise(X)))&
(![X]:((~old(X)&quiet(X))<=>(~quiet(X)&patient(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((quiet(paul)&old(paul)))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
(quiet(paul))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is either not rich or brave is not kind or humble.
If lucy is both not patient and curious then paul is quiet or brave.
Everyone who is either not old or not calm is humble.
Everyone who is humble or not humble is not old and vice versa.
Everyone who is creative is both old and not calm.
If someone is kind or wise then someone is either strong or not generous and vice versa.
If paul is not wise or not rich then alice is both not rich and not patient and vice versa.
If alice is either wise or not wise then someone is brave and vice versa.
Everyone who is funny is both strong and not old and vice versa.
If someone is either not old or not strong then paul is creative and vice versa.
If someone is either not quiet or not happy then someone is not rich or not old.
If fred is either calm or quiet then someone is not patient or humble.
Everyone who is humble is patient and vice versa.
Everyone who is old or happy is either not wise or tall and vice versa.
Everyone who is both not happy and not rich is not brave or creative and vice versa.
If someone is both rich and not humble then susan is either calm or patient.
Alice is both not brave and generous.
John is happy or not funny.
Someone is either not happy or not strong.
Someone is happy or wise.
Someone is both not curious and not old.
Alice is patient or not strong.
Someone is not generous or old.
Mary is either tall or kind. | Alice is not strong. | entailment | (![X]:((~rich(X)<~>brave(X))=>(~kind(X)|humble(X))))&
(((~patient(lucy)&curious(lucy)))=>((quiet(paul)|brave(paul))))&
(![X]:((~old(X)<~>~calm(X))=>humble(X)))&
(![X]:((humble(X)|~humble(X))<=>~old(X)))&
(![X]:(creative(X)=>(old(X)&~calm(X))))&
((?[X]:((kind(X)|wise(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(((~wise(paul)|~rich(paul)))<=>((~rich(alice)&~patient(alice))))&
(((wise(alice)<~>~wise(alice)))<=>(?[X]:(brave(X))))&
(![X]:(funny(X)<=>(strong(X)&~old(X))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(creative(paul)))&
((?[X]:((~quiet(X)<~>~happy(X))))=>(?[X]:((~rich(X)|~old(X)))))&
(((calm(fred)<~>quiet(fred)))=>(?[X]:((~patient(X)|humble(X)))))&
(![X]:(humble(X)<=>patient(X)))&
(![X]:((old(X)|happy(X))<=>(~wise(X)<~>tall(X))))&
(![X]:((~happy(X)&~rich(X))<=>(~brave(X)|creative(X))))&
((?[X]:((rich(X)&~humble(X))))=>((calm(susan)<~>patient(susan))))&
((~brave(alice)&generous(alice)))&
((happy(john)|~funny(john)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~curious(X)&~old(X))))&
((patient(alice)|~strong(alice)))&
(?[X]:((~generous(X)|old(X))))&
((tall(mary)<~>kind(mary))) | ~strong(alice) | [
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3830264424937493219757935
% SZS output start Proof for 3830264424937493219757935
4. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~old(X0)) [input p3]
5. ! [X0] : (creative(X0) => (~calm(X0) & old(X0))) [input p4]
10. ? [X0] : (~old(X0) <~> ~strong(X0)) <=> creative(paul) [input p9]
25. strong(alice) [input hypothesis]
34. ! [X0] : ((~calm(X0) & old(X0)) | ~creative(X0)) [ennf transformation 5]
42. ! [X0] : (((~humble(X0) | humble(X0)) | old(X0)) & (~old(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 4]
43. ! [X0] : ((~humble(X0) | humble(X0) | old(X0)) & (~old(X0) | (humble(X0) & ~humble(X0)))) [flattening 42]
55. (? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | ~creative(paul)) & (creative(paul) | ! [X0] : ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0)))) [nnf transformation 10]
56. (? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | ~creative(paul)) & (creative(paul) | ! [X1] : ((~old(X1) | strong(X1)) & (~strong(X1) | old(X1)))) [rectify 55]
57. ? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) => ((strong(sK3) | old(sK3)) & (~strong(sK3) | ~old(sK3))) [choice axiom]
58. (((strong(sK3) | old(sK3)) & (~strong(sK3) | ~old(sK3))) | ~creative(paul)) & (creative(paul) | ! [X1] : ((~old(X1) | strong(X1)) & (~strong(X1) | old(X1)))) [skolemisation 56,57]
86. ~old(X0) | ~humble(X0) [cnf transformation 43]
87. ~old(X0) | humble(X0) [cnf transformation 43]
89. old(X0) | ~creative(X0) [cnf transformation 34]
107. creative(paul) | ~strong(X1) | old(X1) [cnf transformation 58]
141. strong(alice) [cnf transformation 25]
144. ~old(X0) [subsumption resolution 86,87]
145. ~creative(X0) [subsumption resolution 89,144]
212. ~strong(X1) | old(X1) [subsumption resolution 107,145]
213. ~strong(X1) [subsumption resolution 212,144]
278. $false [subsumption resolution 141,213]
% SZS output end Proof for 3830264424937493219757935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not old is either strong or patient.
Everyone who is either quiet or not tall is not creative and vice versa.
Everyone who is both not rich and rich is not generous or not curious.
If someone is both not funny and not quiet then someone is both not humble and not patient.
Everyone who is both not quiet and not funny is both not generous and not curious.
Everyone who is both not brave and tall is either generous or funny and vice versa.
Everyone who is both not rich and tall is either quiet or not old and vice versa.
Everyone who is not curious or not kind is not creative or not kind.
If alice is both kind and not calm then someone is kind or not generous and vice versa.
Everyone who is both not tall and not wise is calm or not happy and vice versa.
Everyone who is patient or not funny is not generous or not rich.
Everyone who is brave or funny is both not happy and not tall.
If lucy is either not generous or old then mary is not curious and vice versa.
If someone is both happy and not humble then fred is not tall or generous.
Everyone who is kind or humble is both tall and generous.
Everyone who is either funny or kind is not rich or not quiet and vice versa.
Someone is both not happy and not patient.
Paul is both happy and generous.
Someone is creative or not kind.
Someone is not old or patient.
Someone is creative or not patient.
Mary is either creative or brave.
Someone is tall or not generous. | Alice is not kind. | contradiction | (![X]:((~tall(X)&~old(X))=>(strong(X)<~>patient(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((~rich(X)&rich(X))=>(~generous(X)|~curious(X))))&
((?[X]:((~funny(X)&~quiet(X))))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((~quiet(X)&~funny(X))=>(~generous(X)&~curious(X))))&
(![X]:((~brave(X)&tall(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~rich(X)&tall(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~creative(X)|~kind(X))))&
(((kind(alice)&~calm(alice)))<=>(?[X]:((kind(X)|~generous(X)))))&
(![X]:((~tall(X)&~wise(X))<=>(calm(X)|~happy(X))))&
(![X]:((patient(X)|~funny(X))=>(~generous(X)|~rich(X))))&
(![X]:((brave(X)|funny(X))=>(~happy(X)&~tall(X))))&
(((~generous(lucy)<~>old(lucy)))<=>(~curious(mary)))&
((?[X]:((happy(X)&~humble(X))))=>((~tall(fred)|generous(fred))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&generous(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~rich(X)|~quiet(X))))&
(?[X]:((~happy(X)&~patient(X))))&
((happy(paul)&generous(paul)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((creative(X)|~patient(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((tall(X)|~generous(X)))) | ~kind(alice) | [
"p8",
"p10",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7688132108629413826425551
% SZS output start Proof for 7688132108629413826425551
9. (~calm(alice) & kind(alice)) <=> ? [X0] : (~generous(X0) | kind(X0)) [input p8]
11. ! [X0] : ((~funny(X0) | patient(X0)) => (~rich(X0) | ~generous(X0))) [input p10]
12. ! [X0] : ((funny(X0) | brave(X0)) => (~tall(X0) & ~happy(X0))) [input p11]
16. ! [X0] : ((funny(X0) <~> kind(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p15]
18. generous(paul) & happy(paul) [input p17]
24. ~kind(alice) [input hypothesis]
35. ! [X0] : ((~rich(X0) | ~generous(X0)) | (funny(X0) & ~patient(X0))) [ennf transformation 11]
36. ! [X0] : (~rich(X0) | ~generous(X0) | (funny(X0) & ~patient(X0))) [flattening 35]
37. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 12]
50. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | (calm(alice) | ~kind(alice))) [nnf transformation 9]
51. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | calm(alice) | ~kind(alice)) [flattening 50]
52. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X1] : (~generous(X1) | kind(X1)) | calm(alice) | ~kind(alice)) [rectify 51]
53. ? [X1] : (~generous(X1) | kind(X1)) => (~generous(sK1) | kind(sK1)) [choice axiom]
54. ((~calm(alice) & kind(alice)) | ! [X0] : (generous(X0) & ~kind(X0))) & ((~generous(sK1) | kind(sK1)) | calm(alice) | ~kind(alice)) [skolemisation 52,53]
58. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [nnf transformation 16]
59. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [flattening 58]
97. kind(alice) | ~kind(X0) [cnf transformation 54]
98. kind(alice) | generous(X0) [cnf transformation 54]
107. ~generous(X0) | ~rich(X0) | funny(X0) [cnf transformation 36]
109. ~happy(X0) | ~funny(X0) [cnf transformation 37]
123. kind(X0) | funny(X0) | rich(X0) [cnf transformation 59]
129. happy(paul) [cnf transformation 18]
137. ~kind(alice) [cnf transformation 24]
152. 4 <=> ! [X0] : generous(X0) [avatar definition]
153. generous(X0) <- (4) [avatar component clause 152]
160. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
161. ~kind(X0) <- (6) [avatar component clause 160]
164. 7 <=> kind(alice) [avatar definition]
167. 4 | 7 [avatar split clause 98,164,152]
168. 6 | 7 [avatar split clause 97,164,160]
252. ~7 [avatar split clause 137,164]
260. ~funny(paul) [resolution 109,129]
357. ~rich(X0) | funny(X0) <- (4) [resolution 107,153]
363. funny(X3) | rich(X3) <- (6) [resolution 123,161]
367. funny(X3) <- (4, 6) [subsumption resolution 363,357]
374. $false <- (4, 6) [resolution 367,260]
379. ~4 | ~6 [avatar contradiction clause 374]
380. $false [avatar sat refutation 167,168,252,379]
% SZS output end Proof for 7688132108629413826425551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not funny then paul is not quiet or not generous and vice versa. Everyone who is quiet is calm or not kind and vice versa. If someone is both kind and not curious then john is wise and vice versa. Everyone who is calm is tall or not brave. If fred is both tall and not happy then john is creative and vice versa. If john is humble then alice is both not funny and not wise and vice versa. Everyone who is tall or brave is both not quiet and not kind. If susan is generous or not wise then someone is both not wise and happy and vice versa. If someone is both strong and generous then paul is not happy. Everyone who is either not wise or not generous is not funny or quiet. Everyone who is not wise is not rich or not tall. If mary is both not old and not humble then lucy is curious. Everyone who is either not old or wise is not strong or humble and vice versa. Everyone who is not patient is both strong and not curious. If someone is not creative then lucy is both strong and not rich and vice versa. Everyone who is either strong or not creative is calm. Someone is either quiet or funny. Mary is either not funny or strong. Someone is wise. Someone is generous or not funny. Mary is not quiet. Alice is either wise or not calm. Mary is not happy. | Fred is kind. | neutral | ((?[X]:((~happy(X)<~>~funny(X))))<=>((~quiet(paul)|~generous(paul))))&
(![X]:(quiet(X)<=>(calm(X)|~kind(X))))&
((?[X]:((kind(X)&~curious(X))))<=>(wise(john)))&
(![X]:(calm(X)=>(tall(X)|~brave(X))))&
(((tall(fred)&~happy(fred)))<=>(creative(john)))&
((humble(john))<=>((~funny(alice)&~wise(alice))))&
(![X]:((tall(X)|brave(X))=>(~quiet(X)&~kind(X))))&
(((generous(susan)|~wise(susan)))<=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((strong(X)&generous(X))))=>(~happy(paul)))&
(![X]:((~wise(X)<~>~generous(X))=>(~funny(X)|quiet(X))))&
(![X]:(~wise(X)=>(~rich(X)|~tall(X))))&
(((~old(mary)&~humble(mary)))=>(curious(lucy)))&
(![X]:((~old(X)<~>wise(X))<=>(~strong(X)|humble(X))))&
(![X]:(~patient(X)=>(strong(X)&~curious(X))))&
((?[X]:(~creative(X)))<=>((strong(lucy)&~rich(lucy))))&
(![X]:((strong(X)<~>~creative(X))=>calm(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~funny(mary)<~>strong(mary)))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)|~funny(X))))&
(~quiet(mary))&
((wise(alice)<~>~calm(alice)))&
(~happy(mary)) | kind(fred) | [] | null | 0 |
Everyone who is both not kind and curious is either old or not happy and vice versa.
If fred is strong or not curious then john is funny and vice versa.
Everyone who is funny is either not funny or funny and vice versa.
If susan is wise then someone is not rich or creative and vice versa.
Everyone who is curious or calm is both wise and old and vice versa.
Everyone who is either not old or old is either strong or generous and vice versa.
If mary is either not curious or brave then paul is not old.
If someone is both old and funny then alice is both strong and not curious.
If lucy is both not calm and not patient then someone is both creative and not old and vice versa.
Everyone who is kind or tall is both not tall and old and vice versa.
Everyone who is quiet is both calm and not funny.
If john is either calm or not happy then someone is both humble and creative.
Everyone who is not happy is either not old or funny and vice versa.
Everyone who is curious is either tall or happy.
Everyone who is calm is either not kind or creative and vice versa.
Mary is either kind or not calm.
Mary is either kind or brave.
Someone is either creative or brave.
Someone is kind or not rich.
Mary is either not brave or not humble.
Someone is not calm.
Paul is calm.
Someone is not happy or wise. | Lucy is calm. | contradiction | (![X]:((~kind(X)&curious(X))<=>(old(X)<~>~happy(X))))&
(((strong(fred)|~curious(fred)))<=>(funny(john)))&
(![X]:(funny(X)<=>(~funny(X)<~>funny(X))))&
((wise(susan))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:((curious(X)|calm(X))<=>(wise(X)&old(X))))&
(![X]:((~old(X)<~>old(X))<=>(strong(X)<~>generous(X))))&
(((~curious(mary)<~>brave(mary)))=>(~old(paul)))&
((?[X]:((old(X)&funny(X))))=>((strong(alice)&~curious(alice))))&
(((~calm(lucy)&~patient(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((kind(X)|tall(X))<=>(~tall(X)&old(X))))&
(![X]:(quiet(X)=>(calm(X)&~funny(X))))&
(((calm(john)<~>~happy(john)))=>(?[X]:((humble(X)&creative(X)))))&
(![X]:(~happy(X)<=>(~old(X)<~>funny(X))))&
(![X]:(curious(X)=>(tall(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~kind(X)<~>creative(X))))&
((kind(mary)<~>~calm(mary)))&
((kind(mary)<~>brave(mary)))&
(?[X]:((creative(X)<~>brave(X))))&
(?[X]:((kind(X)|~rich(X))))&
((~brave(mary)<~>~humble(mary)))&
(?[X]:(~calm(X)))&
(calm(paul))&
(?[X]:((~happy(X)|wise(X)))) | calm(lucy) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1519485826673331458876469
% SZS output start Proof for 1519485826673331458876469
3. ! [X0] : (funny(X0) <=> (~funny(X0) <~> funny(X0))) [input p2]
5. ! [X0] : ((calm(X0) | curious(X0)) <=> (old(X0) & wise(X0))) [input p4]
7. (~curious(mary) <~> brave(mary)) => ~old(paul) [input p6]
9. (~patient(lucy) & ~calm(lucy)) <=> ? [X0] : (~old(X0) & creative(X0)) [input p8]
10. ! [X0] : ((tall(X0) | kind(X0)) <=> (old(X0) & ~tall(X0))) [input p9]
13. ! [X0] : (~happy(X0) <=> (~old(X0) <~> funny(X0))) [input p12]
14. ! [X0] : (curious(X0) => (tall(X0) <~> happy(X0))) [input p13]
15. ! [X0] : (calm(X0) <=> (~kind(X0) <~> creative(X0))) [input p14]
17. kind(mary) <~> brave(mary) [input p16]
22. calm(paul) [input p21]
24. calm(lucy) [input hypothesis]
26. ~old(paul) | (~curious(mary) <=> brave(mary)) [ennf transformation 7]
29. ! [X0] : ((tall(X0) <~> happy(X0)) | ~curious(X0)) [ennf transformation 14]
34. ! [X0] : ((funny(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~funny(X0))) [nnf transformation 3]
39. ! [X0] : (((calm(X0) | curious(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 5]
40. ! [X0] : ((calm(X0) | curious(X0) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | (~calm(X0) & ~curious(X0)))) [flattening 39]
42. ~old(paul) | ((~curious(mary) | ~brave(mary)) & (brave(mary) | curious(mary))) [nnf transformation 26]
43. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X0] : (~old(X0) & creative(X0)) | (patient(lucy) | calm(lucy))) [nnf transformation 9]
44. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X0] : (~old(X0) & creative(X0)) | patient(lucy) | calm(lucy)) [flattening 43]
45. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X1] : (~old(X1) & creative(X1)) | patient(lucy) | calm(lucy)) [rectify 44]
46. ? [X1] : (~old(X1) & creative(X1)) => (~old(sK1) & creative(sK1)) [choice axiom]
47. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & ((~old(sK1) & creative(sK1)) | patient(lucy) | calm(lucy)) [skolemisation 45,46]
48. ! [X0] : (((tall(X0) | kind(X0)) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | kind(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [flattening 48]
53. ! [X0] : ((~happy(X0) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0)))) & (((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | happy(X0))) [nnf transformation 13]
54. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | ~curious(X0)) [nnf transformation 29]
55. ! [X0] : ((calm(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~calm(X0))) [nnf transformation 15]
57. (~brave(mary) | ~kind(mary)) & (brave(mary) | kind(mary)) [nnf transformation 17]
79. funny(X0) | funny(X0) | funny(X0) [cnf transformation 34]
87. ~calm(X0) | old(X0) [cnf transformation 40]
97. ~old(paul) | brave(mary) | curious(mary) [cnf transformation 42]
103. ~calm(lucy) | old(X0) | ~creative(X0) [cnf transformation 47]
106. ~tall(X0) | ~tall(X0) [cnf transformation 49]
107. ~kind(X0) | old(X0) [cnf transformation 49]
109. tall(X0) | kind(X0) | ~old(X0) | tall(X0) [cnf transformation 49]
117. ~happy(X0) | ~old(X0) | ~funny(X0) [cnf transformation 53]
118. happy(X0) | tall(X0) | ~curious(X0) [cnf transformation 54]
122. calm(X0) | creative(X0) | kind(X0) [cnf transformation 55]
127. ~brave(mary) | ~kind(mary) [cnf transformation 57]
134. calm(paul) [cnf transformation 22]
136. calm(lucy) [cnf transformation 24]
137. ~tall(X0) [duplicate literal removal 106]
138. ~old(X0) | kind(X0) | tall(X0) [duplicate literal removal 109]
145. funny(X0) [duplicate literal removal 79]
186. 9 <=> brave(mary) [avatar definition]
190. 10 <=> curious(mary) [avatar definition]
191. curious(mary) <- (10) [avatar component clause 190]
194. 11 <=> old(paul) [avatar definition]
198. 10 | 9 | ~11 [avatar split clause 97,194,186,190]
215. 15 <=> ! [X0] : (old(X0) | ~creative(X0)) [avatar definition]
216. ~creative(X0) | old(X0) <- (15) [avatar component clause 215]
223. 17 <=> calm(lucy) [avatar definition]
226. 15 | ~17 [avatar split clause 103,223,215]
257. ~happy(X0) | ~old(X0) [subsumption resolution 117,145]
259. ~curious(X0) | happy(X0) [subsumption resolution 118,137]
261. 24 <=> kind(mary) [avatar definition]
263. ~kind(mary) <- (~24) [avatar component clause 261]
270. ~24 | ~9 [avatar split clause 127,186,261]
306. 17 [avatar split clause 136,223]
315. old(paul) [resolution 87,134]
321. 11 [avatar split clause 315,194]
364. creative(X2) | kind(X2) | old(X2) [resolution 122,87]
371. creative(X2) | old(X2) [subsumption resolution 364,107]
372. old(X2) <- (15) [subsumption resolution 371,216]
451. kind(X2) | tall(X2) <- (15) [resolution 372,138]
452. kind(X2) <- (15) [subsumption resolution 451,137]
485. $false <- (15, ~24) [resolution 452,263]
488. ~15 | 24 [avatar contradiction clause 485]
490. happy(mary) <- (10) [resolution 191,259]
517. ~old(mary) <- (10) [resolution 490,257]
521. $false <- (10, 15) [subsumption resolution 517,372]
522. ~10 | ~15 [avatar contradiction clause 521]
523. $false [avatar sat refutation 198,226,270,306,321,488,522]
% SZS output end Proof for 1519485826673331458876469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not tall is either not curious or curious and vice versa.
Everyone who is rich or patient is both not curious and calm.
Everyone who is not patient or calm is both not creative and not calm and vice versa.
If mary is either not quiet or kind then paul is either humble or quiet and vice versa.
If mary is kind then alice is tall and vice versa.
If someone is both quiet and not strong then susan is curious.
Everyone who is not calm is rich or not quiet.
If someone is either not funny or not generous then mary is either not curious or not humble.
Everyone who is not kind is both creative and funny.
Everyone who is rich or not happy is wise and vice versa.
Everyone who is tall or not creative is either funny or rich.
Everyone who is both tall and not calm is kind and vice versa.
Everyone who is not funny or curious is both funny and happy and vice versa.
If someone is either old or quiet then someone is both not happy and not humble and vice versa.
Mary is not generous.
John is not wise or curious.
Someone is either quiet or strong.
Someone is generous or happy.
Paul is either not brave or funny. | Mary is tall. | entailment | (![X]:((strong(X)|~tall(X))<=>(~curious(X)<~>curious(X))))&
(![X]:((rich(X)|patient(X))=>(~curious(X)&calm(X))))&
(![X]:((~patient(X)|calm(X))<=>(~creative(X)&~calm(X))))&
(((~quiet(mary)<~>kind(mary)))<=>((humble(paul)<~>quiet(paul))))&
((kind(mary))<=>(tall(alice)))&
((?[X]:((quiet(X)&~strong(X))))=>(curious(susan)))&
(![X]:(~calm(X)=>(rich(X)|~quiet(X))))&
((?[X]:((~funny(X)<~>~generous(X))))=>((~curious(mary)<~>~humble(mary))))&
(![X]:(~kind(X)=>(creative(X)&funny(X))))&
(![X]:((rich(X)|~happy(X))<=>wise(X)))&
(![X]:((tall(X)|~creative(X))=>(funny(X)<~>rich(X))))&
(![X]:((tall(X)&~calm(X))<=>kind(X)))&
(![X]:((~funny(X)|curious(X))<=>(funny(X)&happy(X))))&
((?[X]:((old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)&~humble(X)))))&
(~generous(mary))&
((~wise(john)|curious(john)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((generous(X)|happy(X))))&
((~brave(paul)<~>funny(paul))) | tall(mary) | [
"p1",
"p2",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5822239866913714939185225
% SZS output start Proof for 5822239866913714939185225
2. ! [X0] : ((patient(X0) | rich(X0)) => (calm(X0) & ~curious(X0))) [input p1]
3. ! [X0] : ((calm(X0) | ~patient(X0)) <=> (~calm(X0) & ~creative(X0))) [input p2]
9. ! [X0] : (~kind(X0) => (funny(X0) & creative(X0))) [input p8]
12. ! [X0] : ((~calm(X0) & tall(X0)) <=> kind(X0)) [input p11]
20. ~tall(mary) [input hypothesis]
23. ! [X0] : ((calm(X0) & ~curious(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 2]
28. ! [X0] : ((funny(X0) & creative(X0)) | kind(X0)) [ennf transformation 9]
33. ! [X0] : (((calm(X0) | ~patient(X0)) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | (~calm(X0) & patient(X0)))) [nnf transformation 3]
34. ! [X0] : ((calm(X0) | ~patient(X0) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | (~calm(X0) & patient(X0)))) [flattening 33]
39. ! [X0] : (((~calm(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) | ~tall(X0)))) [nnf transformation 12]
40. ! [X0] : (((~calm(X0) & tall(X0)) | ~kind(X0)) & (kind(X0) | calm(X0) | ~tall(X0))) [flattening 39]
63. ~patient(X0) | calm(X0) [cnf transformation 23]
64. ~creative(X0) | patient(X0) [cnf transformation 34]
67. ~calm(X0) | ~calm(X0) [cnf transformation 34]
85. kind(X0) | creative(X0) [cnf transformation 28]
94. ~kind(X0) | tall(X0) [cnf transformation 40]
114. ~tall(mary) [cnf transformation 20]
117. ~calm(X0) [duplicate literal removal 67]
135. 4 <=> kind(mary) [avatar definition]
136. kind(mary) <- (4) [avatar component clause 135]
137. ~kind(mary) <- (~4) [avatar component clause 135]
240. creative(mary) <- (~4) [resolution 85,137]
241. patient(mary) <- (~4) [resolution 240,64]
242. calm(mary) <- (~4) [resolution 241,63]
244. $false <- (~4) [subsumption resolution 242,117]
245. 4 [avatar contradiction clause 244]
250. tall(mary) <- (4) [resolution 94,136]
251. $false <- (4) [subsumption resolution 250,114]
252. ~4 [avatar contradiction clause 251]
253. $false [avatar sat refutation 245,252]
% SZS output end Proof for 5822239866913714939185225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and calm is not wise or not happy and vice versa.
Everyone who is both not funny and calm is not quiet or not tall.
If someone is funny then alice is not humble or generous.
If paul is both brave and calm then paul is not kind.
If someone is kind or not funny then someone is rich.
Everyone who is both funny and calm is strong or patient.
Everyone who is rich or not old is kind and vice versa.
If alice is not brave or not happy then paul is not quiet and vice versa.
If someone is either not funny or not curious then alice is either not old or not calm and vice versa.
Everyone who is not generous or not creative is not quiet and vice versa.
If someone is both not creative and not curious then someone is funny.
If someone is tall then alice is both humble and not rich and vice versa.
Everyone who is not strong or not funny is either not patient or humble.
Everyone who is not old or calm is not calm.
Everyone who is both not generous and kind is either not strong or tall and vice versa.
If someone is not quiet then john is tall.
Mary is humble.
Someone is kind.
Mary is either not patient or not wise.
Susan is not tall or not funny.
Fred is curious.
Someone is either brave or generous.
Someone is both not rich and strong.
Someone is both not calm and not old. | John is happy. | entailment | (![X]:((humble(X)&calm(X))<=>(~wise(X)|~happy(X))))&
(![X]:((~funny(X)&calm(X))=>(~quiet(X)|~tall(X))))&
((?[X]:(funny(X)))=>((~humble(alice)|generous(alice))))&
(((brave(paul)&calm(paul)))=>(~kind(paul)))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(rich(X))))&
(![X]:((funny(X)&calm(X))=>(strong(X)|patient(X))))&
(![X]:((rich(X)|~old(X))<=>kind(X)))&
(((~brave(alice)|~happy(alice)))<=>(~quiet(paul)))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~old(alice)<~>~calm(alice))))&
(![X]:((~generous(X)|~creative(X))<=>~quiet(X)))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:(funny(X))))&
((?[X]:(tall(X)))<=>((humble(alice)&~rich(alice))))&
(![X]:((~strong(X)|~funny(X))=>(~patient(X)<~>humble(X))))&
(![X]:((~old(X)|calm(X))=>~calm(X)))&
(![X]:((~generous(X)&kind(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:(~quiet(X)))=>(tall(john)))&
(humble(mary))&
(?[X]:(kind(X)))&
((~patient(mary)<~>~wise(mary)))&
((~tall(susan)|~funny(susan)))&
(curious(fred))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((~calm(X)&~old(X)))) | happy(john) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1200874194043014586981712
% SZS output start Proof for 1200874194043014586981712
1. ! [X0] : ((calm(X0) & humble(X0)) <=> (~happy(X0) | ~wise(X0))) [input p0]
14. ! [X0] : ((calm(X0) | ~old(X0)) => ~calm(X0)) [input p13]
25. ~happy(john) [input hypothesis]
39. ! [X0] : (~calm(X0) | (~calm(X0) & old(X0))) [ennf transformation 14]
41. ! [X0] : (((calm(X0) & humble(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~calm(X0) | ~humble(X0)))) [nnf transformation 1]
42. ! [X0] : (((calm(X0) & humble(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~calm(X0) | ~humble(X0))) [flattening 41]
81. happy(X0) | calm(X0) [cnf transformation 42]
114. ~calm(X0) | ~calm(X0) [cnf transformation 39]
134. ~happy(john) [cnf transformation 25]
135. ~calm(X0) [duplicate literal removal 114]
286. calm(john) [resolution 81,134]
287. $false [subsumption resolution 286,135]
% SZS output end Proof for 1200874194043014586981712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or strong then john is curious or not humble and vice versa.
Everyone who is not funny is both not creative and not tall and vice versa.
Everyone who is not tall or old is both creative and old and vice versa.
If lucy is either curious or not tall then someone is either not wise or not kind and vice versa.
Everyone who is not creative is curious or not humble and vice versa.
Everyone who is kind or curious is not kind.
If paul is both not rich and not quiet then someone is either brave or creative and vice versa.
If lucy is both calm and not tall then someone is both wise and not curious and vice versa.
Everyone who is either brave or wise is either not calm or tall.
Everyone who is both not patient and not wise is funny or old and vice versa.
If mary is either not happy or funny then someone is both not creative and not happy and vice versa.
Everyone who is creative is old.
If lucy is not rich or strong then lucy is either not brave or brave and vice versa.
Everyone who is both funny and not quiet is not rich.
If mary is both not tall and quiet then someone is calm or creative and vice versa.
Lucy is not funny or calm.
Someone is strong or not generous.
Someone is not curious or wise. | John is not brave. | neutral | ((?[X]:((~generous(X)|strong(X))))<=>((curious(john)|~humble(john))))&
(![X]:(~funny(X)<=>(~creative(X)&~tall(X))))&
(![X]:((~tall(X)|old(X))<=>(creative(X)&old(X))))&
(((curious(lucy)<~>~tall(lucy)))<=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:(~creative(X)<=>(curious(X)|~humble(X))))&
(![X]:((kind(X)|curious(X))=>~kind(X)))&
(((~rich(paul)&~quiet(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(((calm(lucy)&~tall(lucy)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((brave(X)<~>wise(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&~wise(X))<=>(funny(X)|old(X))))&
(((~happy(mary)<~>funny(mary)))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:(creative(X)=>old(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~brave(lucy)<~>brave(lucy))))&
(![X]:((funny(X)&~quiet(X))=>~rich(X)))&
(((~tall(mary)&quiet(mary)))<=>(?[X]:((calm(X)|creative(X)))))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((strong(X)|~generous(X))))&
(?[X]:((~curious(X)|wise(X)))) | ~brave(john) | [] | null | 0 |
Everyone who is either old or curious is old or rich and vice versa.
Everyone who is not creative or not curious is either not tall or tall.
If someone is patient then mary is happy or rich.
If someone is not wise then fred is both funny and not tall and vice versa.
If someone is not patient then susan is quiet or not funny and vice versa.
Everyone who is curious is not tall or not happy and vice versa.
If mary is both not quiet and strong then someone is not quiet.
Everyone who is either not quiet or tall is both old and funny and vice versa.
If someone is either rich or not old then mary is either not humble or not happy.
If someone is not quiet then paul is brave and vice versa.
Everyone who is either not patient or humble is either not kind or not tall.
If alice is both not kind and not patient then someone is not quiet.
Everyone who is not rich or not curious is either not curious or tall and vice versa.
Everyone who is either not old or quiet is both not rich and not generous and vice versa.
Everyone who is either not rich or not brave is humble.
Everyone who is old is happy.
Someone is kind or old.
Someone is generous or not rich.
Paul is not kind or kind.
Someone is not tall or not creative.
Paul is happy or rich. | Paul is not quiet. | contradiction | (![X]:((old(X)<~>curious(X))<=>(old(X)|rich(X))))&
(![X]:((~creative(X)|~curious(X))=>(~tall(X)<~>tall(X))))&
((?[X]:(patient(X)))=>((happy(mary)|rich(mary))))&
((?[X]:(~wise(X)))<=>((funny(fred)&~tall(fred))))&
((?[X]:(~patient(X)))<=>((quiet(susan)|~funny(susan))))&
(![X]:(curious(X)<=>(~tall(X)|~happy(X))))&
(((~quiet(mary)&strong(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(old(X)&funny(X))))&
((?[X]:((rich(X)<~>~old(X))))=>((~humble(mary)<~>~happy(mary))))&
((?[X]:(~quiet(X)))<=>(brave(paul)))&
(![X]:((~patient(X)<~>humble(X))=>(~kind(X)<~>~tall(X))))&
(((~kind(alice)&~patient(alice)))=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)|~curious(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(~rich(X)&~generous(X))))&
(![X]:((~rich(X)<~>~brave(X))=>humble(X)))&
(![X]:(old(X)=>happy(X)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((generous(X)|~rich(X))))&
((~kind(paul)|kind(paul)))&
(?[X]:((~tall(X)|~creative(X))))&
((happy(paul)|rich(paul))) | ~quiet(paul) | [
"p0",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8439968213552662207635979
% SZS output start Proof for 8439968213552662207635979
1. ! [X0] : ((old(X0) <~> curious(X0)) <=> (rich(X0) | old(X0))) [input p0]
6. ! [X0] : (curious(X0) <=> (~happy(X0) | ~tall(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) <~> tall(X0)) <=> (funny(X0) & old(X0))) [input p7]
13. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> (~curious(X0) <~> tall(X0))) [input p12]
22. ~quiet(paul) [input hypothesis]
33. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 1]
34. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [flattening 33]
46. ! [X0] : ((curious(X0) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ~curious(X0))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ~curious(X0))) [flattening 46]
48. ! [X0] : ((((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | (~funny(X0) | ~old(X0))) & ((funny(X0) & old(X0)) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0))))) [nnf transformation 8]
49. ! [X0] : ((((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ~funny(X0) | ~old(X0)) & ((funny(X0) & old(X0)) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0))))) [flattening 48]
58. ! [X0] : (((~curious(X0) | ~rich(X0)) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | (curious(X0) & rich(X0)))) [nnf transformation 13]
59. ! [X0] : ((~curious(X0) | ~rich(X0) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | (curious(X0) & rich(X0)))) [flattening 58]
70. rich(X0) | old(X0) | old(X0) | ~curious(X0) [cnf transformation 34]
73. ~curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 34]
87. tall(X0) | curious(X0) [cnf transformation 47]
89. quiet(X0) | tall(X0) | old(X0) [cnf transformation 49]
109. ~tall(X0) | curious(X0) | curious(X0) [cnf transformation 59]
111. ~curious(X0) | ~rich(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 59]
126. ~quiet(paul) [cnf transformation 22]
127. ~tall(X0) | curious(X0) [duplicate literal removal 109]
128. ~curious(X0) | ~rich(X0) | ~tall(X0) [duplicate literal removal 111]
129. rich(X0) | old(X0) | ~curious(X0) [duplicate literal removal 70]
130. ~curious(X0) | ~old(X0) [duplicate literal removal 73]
131. ~curious(X0) | rich(X0) [subsumption resolution 129,130]
220. ~tall(X0) | ~curious(X0) [subsumption resolution 128,131]
221. ~tall(X0) [subsumption resolution 127,220]
249. curious(X0) [resolution 87,221]
250. ~old(X0) [resolution 130,249]
260. tall(paul) | old(paul) [resolution 89,126]
263. old(paul) [subsumption resolution 260,221]
264. $false [subsumption resolution 263,250]
% SZS output end Proof for 8439968213552662207635979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not brave or generous.
If someone is not old then john is calm or strong.
Everyone who is not strong or curious is not generous or not kind and vice versa.
Everyone who is strong is calm.
Everyone who is either funny or generous is both not rich and not generous and vice versa.
If susan is both generous and happy then someone is either not old or patient and vice versa.
Everyone who is not calm or humble is either brave or creative.
Everyone who is both not old and not curious is either not patient or old.
Everyone who is calm is not rich.
If lucy is funny then john is either not curious or brave.
Everyone who is not rich or not humble is wise or not curious and vice versa.
Everyone who is either not generous or brave is strong and vice versa.
If someone is not calm or humble then someone is both strong and old.
If someone is wise then susan is curious and vice versa.
If someone is either tall or old then lucy is either not old or not rich and vice versa.
Everyone who is happy is both curious and creative and vice versa.
Alice is not funny.
Someone is generous or quiet.
Lucy is old.
Susan is not kind or tall.
Someone is either not tall or curious.
Paul is quiet or wise.
Susan is either not humble or rich.
Lucy is not happy. | Alice is not curious. | contradiction | (![X]:((humble(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:(~old(X)))=>((calm(john)|strong(john))))&
(![X]:((~strong(X)|curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:(strong(X)=>calm(X)))&
(![X]:((funny(X)<~>generous(X))<=>(~rich(X)&~generous(X))))&
(((generous(susan)&happy(susan)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~calm(X)|humble(X))=>(brave(X)<~>creative(X))))&
(![X]:((~old(X)&~curious(X))=>(~patient(X)<~>old(X))))&
(![X]:(calm(X)=>~rich(X)))&
((funny(lucy))=>((~curious(john)<~>brave(john))))&
(![X]:((~rich(X)|~humble(X))<=>(wise(X)|~curious(X))))&
(![X]:((~generous(X)<~>brave(X))<=>strong(X)))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((strong(X)&old(X)))))&
((?[X]:(wise(X)))<=>(curious(susan)))&
((?[X]:((tall(X)<~>old(X))))<=>((~old(lucy)<~>~rich(lucy))))&
(![X]:(happy(X)<=>(curious(X)&creative(X))))&
(~funny(alice))&
(?[X]:((generous(X)|quiet(X))))&
(old(lucy))&
((~kind(susan)|tall(susan)))&
(?[X]:((~tall(X)<~>curious(X))))&
((quiet(paul)|wise(paul)))&
((~humble(susan)<~>rich(susan)))&
(~happy(lucy)) | ~curious(alice) | [
"p0",
"p2",
"p4",
"p6",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 83969511219757246773643
% SZS output start Proof for 83969511219757246773643
1. ! [X0] : ((humble(X0) <~> ~creative(X0)) => (generous(X0) | ~brave(X0))) [input p0]
3. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~kind(X0) | ~generous(X0))) [input p2]
5. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (~generous(X0) & ~rich(X0))) [input p4]
7. ! [X0] : ((humble(X0) | ~calm(X0)) => (brave(X0) <~> creative(X0))) [input p6]
9. ! [X0] : (calm(X0) => ~rich(X0)) [input p8]
11. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~curious(X0) | wise(X0))) [input p10]
12. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> strong(X0)) [input p11]
17. ~funny(alice) [input p16]
25. ~curious(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) | ~brave(X0)) | (humble(X0) <=> ~creative(X0))) [ennf transformation 1]
30. ! [X0] : (generous(X0) | ~brave(X0) | (humble(X0) <=> ~creative(X0))) [flattening 29]
34. ! [X0] : ((brave(X0) <~> creative(X0)) | (~humble(X0) & calm(X0))) [ennf transformation 7]
37. ! [X0] : (~rich(X0) | ~calm(X0)) [ennf transformation 9]
40. ! [X0] : (generous(X0) | ~brave(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) [nnf transformation 30]
41. ! [X0] : (((curious(X0) | ~strong(X0)) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((curious(X0) | ~strong(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | (~curious(X0) & strong(X0)))) [flattening 41]
43. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (generous(X0) | rich(X0))) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | generous(X0) | rich(X0)) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 43]
50. ! [X0] : (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | (~humble(X0) & calm(X0))) [nnf transformation 34]
53. ! [X0] : (((~humble(X0) | ~rich(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 11]
54. ! [X0] : ((~humble(X0) | ~rich(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (humble(X0) & rich(X0)))) [flattening 53]
55. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ~strong(X0)) & (strong(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 12]
74. ~brave(X0) | generous(X0) | humble(X0) | creative(X0) [cnf transformation 40]
78. ~strong(X0) | curious(X0) | generous(X0) [cnf transformation 42]
84. ~generous(X0) | funny(X0) | ~generous(X0) [cnf transformation 44]
85. generous(X0) | funny(X0) | generous(X0) | rich(X0) [cnf transformation 44]
95. ~brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 50]
99. ~rich(X0) | ~calm(X0) [cnf transformation 37]
105. ~rich(X0) | ~humble(X0) | curious(X0) [cnf transformation 54]
106. strong(X0) | brave(X0) | generous(X0) [cnf transformation 55]
127. ~funny(alice) [cnf transformation 17]
135. ~curious(alice) [cnf transformation 25]
137. ~generous(X0) | funny(X0) [duplicate literal removal 84]
138. rich(X0) | funny(X0) | generous(X0) [duplicate literal removal 85]
291. brave(X1) | generous(X1) | curious(X1) | generous(X1) [resolution 106,78]
293. curious(X1) | generous(X1) | brave(X1) [duplicate literal removal 291]
314. funny(X0) | generous(X0) | ~humble(X0) | curious(X0) [resolution 138,105]
316. funny(X2) | generous(X2) | ~calm(X2) [resolution 138,99]
339. ~calm(X2) | funny(X2) [subsumption resolution 316,137]
388. generous(alice) | brave(alice) [resolution 293,135]
394. 39 <=> brave(alice) [avatar definition]
396. brave(alice) <- (39) [avatar component clause 394]
398. 40 <=> generous(alice) [avatar definition]
400. generous(alice) <- (40) [avatar component clause 398]
401. 39 | 40 [avatar split clause 388,398,394]
430. generous(alice) | humble(alice) | creative(alice) <- (39) [resolution 396,74]
433. ~creative(alice) | calm(alice) <- (39) [resolution 396,95]
436. 45 <=> creative(alice) [avatar definition]
441. 46 <=> calm(alice) [avatar definition]
443. calm(alice) <- (46) [avatar component clause 441]
444. 46 | ~45 | ~39 [avatar split clause 433,394,436,441]
446. 47 <=> humble(alice) [avatar definition]
447. humble(alice) <- (47) [avatar component clause 446]
451. 45 | 47 | 40 | ~39 [avatar split clause 430,394,398,446,436]
475. ~humble(X0) | funny(X0) | curious(X0) [subsumption resolution 314,137]
490. funny(alice) <- (40) [resolution 400,137]
492. $false <- (40) [subsumption resolution 490,127]
493. ~40 [avatar contradiction clause 492]
504. funny(alice) | curious(alice) <- (47) [resolution 447,475]
506. curious(alice) <- (47) [subsumption resolution 504,127]
507. $false <- (47) [subsumption resolution 506,135]
508. ~47 [avatar contradiction clause 507]
512. funny(alice) <- (46) [resolution 443,339]
513. $false <- (46) [subsumption resolution 512,127]
514. ~46 [avatar contradiction clause 513]
515. $false [avatar sat refutation 401,444,451,493,508,514]
% SZS output end Proof for 83969511219757246773643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not rich is happy or not patient.
If someone is curious or wise then paul is both not funny and brave.
Everyone who is both not humble and not wise is old or happy and vice versa.
Everyone who is patient is patient or not creative.
If fred is either not humble or old then someone is wise or creative and vice versa.
If someone is either generous or kind then someone is either strong or not kind and vice versa.
If alice is either not funny or not wise then susan is not creative.
If alice is not humble or humble then someone is both funny and kind and vice versa.
If someone is either not humble or not happy then lucy is wise.
If someone is strong or not tall then someone is strong and vice versa.
If susan is quiet or not humble then alice is both kind and not creative and vice versa.
If someone is strong or not patient then alice is rich and vice versa.
If paul is both funny and humble then someone is either not rich or creative and vice versa.
If lucy is either funny or not kind then someone is not humble.
If paul is curious then someone is either not old or not quiet and vice versa.
Everyone who is either not generous or old is curious and vice versa.
Someone is either not brave or strong.
Someone is both not patient and not calm.
John is wise.
Someone is not calm.
Lucy is curious or brave.
Someone is both brave and patient.
Susan is both tall and curious.
Someone is either curious or tall. | Paul is not brave. | contradiction | (![X]:((~old(X)|~rich(X))=>(happy(X)|~patient(X))))&
((?[X]:((curious(X)|wise(X))))=>((~funny(paul)&brave(paul))))&
(![X]:((~humble(X)&~wise(X))<=>(old(X)|happy(X))))&
(![X]:(patient(X)=>(patient(X)|~creative(X))))&
(((~humble(fred)<~>old(fred)))<=>(?[X]:((wise(X)|creative(X)))))&
((?[X]:((generous(X)<~>kind(X))))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(((~funny(alice)<~>~wise(alice)))=>(~creative(susan)))&
(((~humble(alice)|humble(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
((?[X]:((~humble(X)<~>~happy(X))))=>(wise(lucy)))&
((?[X]:((strong(X)|~tall(X))))<=>(?[X]:(strong(X))))&
(((quiet(susan)|~humble(susan)))<=>((kind(alice)&~creative(alice))))&
((?[X]:((strong(X)|~patient(X))))<=>(rich(alice)))&
(((funny(paul)&humble(paul)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(((funny(lucy)<~>~kind(lucy)))=>(?[X]:(~humble(X))))&
((curious(paul))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((~generous(X)<~>old(X))<=>curious(X)))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:((~patient(X)&~calm(X))))&
(wise(john))&
(?[X]:(~calm(X)))&
((curious(lucy)|brave(lucy)))&
(?[X]:((brave(X)&patient(X))))&
((tall(susan)&curious(susan)))&
(?[X]:((curious(X)<~>tall(X)))) | ~brave(paul) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1220760932886314746198470
% SZS output start Proof for 1220760932886314746198470
2. ? [X0] : (wise(X0) | curious(X0)) => (brave(paul) & ~funny(paul)) [input p1]
19. wise(john) [input p18]
25. ~brave(paul) [input hypothesis]
32. (brave(paul) & ~funny(paul)) | ! [X0] : (~wise(X0) & ~curious(X0)) [ennf transformation 2]
95. brave(paul) | ~wise(X0) [cnf transformation 32]
155. wise(john) [cnf transformation 19]
163. ~brave(paul) [cnf transformation 25]
165. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
166. ~wise(X0) <- (1) [avatar component clause 165]
168. 2 <=> brave(paul) [avatar definition]
171. 1 | 2 [avatar split clause 95,168,165]
439. ~2 [avatar split clause 163,168]
440. $false <- (1) [resolution 166,155]
441. ~1 [avatar contradiction clause 440]
442. $false [avatar sat refutation 171,439,441]
% SZS output end Proof for 1220760932886314746198470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is both not wise and not old and vice versa. If someone is happy then someone is both happy and tall. Everyone who is both rich and not strong is either humble or curious and vice versa. Everyone who is curious is tall. Everyone who is either strong or not curious is calm or not kind and vice versa. Everyone who is either not generous or not curious is not tall or patient and vice versa. If someone is kind then mary is not old and vice versa. Everyone who is either humble or happy is not calm. If john is both not brave and funny then someone is both not tall and not brave and vice versa. Everyone who is either not creative or not humble is both not creative and happy. Everyone who is not generous or old is funny. Everyone who is both not old and not strong is tall or generous. Everyone who is both rich and not calm is calm or generous and vice versa. Everyone who is not generous is not strong and vice versa. Everyone who is not rich or not humble is both generous and strong. Everyone who is both strong and not curious is both happy and not happy and vice versa. Lucy is either happy or not curious. Someone is humble or rich. Someone is old. Alice is not wise. Someone is either wise or strong. Susan is both not quiet and wise. Mary is tall or not old. | John is strong. | entailment | ((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&~old(X)))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((rich(X)&~strong(X))<=>(humble(X)<~>curious(X))))&
(![X]:(curious(X)=>tall(X)))&
(![X]:((strong(X)<~>~curious(X))<=>(calm(X)|~kind(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~tall(X)|patient(X))))&
((?[X]:(kind(X)))<=>(~old(mary)))&
(![X]:((humble(X)<~>happy(X))=>~calm(X)))&
(((~brave(john)&funny(john)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)<~>~humble(X))=>(~creative(X)&happy(X))))&
(![X]:((~generous(X)|old(X))=>funny(X)))&
(![X]:((~old(X)&~strong(X))=>(tall(X)|generous(X))))&
(![X]:((rich(X)&~calm(X))<=>(calm(X)|generous(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:((~rich(X)|~humble(X))=>(generous(X)&strong(X))))&
(![X]:((strong(X)&~curious(X))<=>(happy(X)&~happy(X))))&
((happy(lucy)<~>~curious(lucy)))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:(old(X)))&
(~wise(alice))&
(?[X]:((wise(X)<~>strong(X))))&
((~quiet(susan)&wise(susan)))&
((tall(mary)|~old(mary))) | strong(john) | [
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3593135367479711816973542
% SZS output start Proof for 3593135367479711816973542
13. ! [X0] : ((~calm(X0) & rich(X0)) <=> (generous(X0) | calm(X0))) [input p12]
14. ! [X0] : (~generous(X0) <=> ~strong(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | ~rich(X0)) => (strong(X0) & generous(X0))) [input p14]
24. ~strong(john) [input hypothesis]
35. ! [X0] : ((strong(X0) & generous(X0)) | (humble(X0) & rich(X0))) [ennf transformation 15]
61. ! [X0] : (((~calm(X0) & rich(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 13]
62. ! [X0] : (((~calm(X0) & rich(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | calm(X0) | ~rich(X0))) [flattening 61]
63. ! [X0] : ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))) [nnf transformation 14]
113. generous(X0) | calm(X0) | calm(X0) | ~rich(X0) [cnf transformation 62]
115. ~generous(X0) | rich(X0) [cnf transformation 62]
116. ~calm(X0) | ~calm(X0) [cnf transformation 62]
119. ~generous(X0) | strong(X0) [cnf transformation 63]
120. generous(X0) | rich(X0) [cnf transformation 35]
137. ~strong(john) [cnf transformation 24]
138. generous(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 113]
139. ~calm(X0) [duplicate literal removal 116]
213. ~rich(X0) | generous(X0) [subsumption resolution 138,139]
214. rich(X0) [subsumption resolution 120,115]
260. generous(X0) [resolution 213,214]
262. strong(X0) [resolution 260,119]
266. $false [resolution 262,137]
% SZS output end Proof for 3593135367479711816973542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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