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
|
|---|---|---|---|---|---|---|---|
If fred is either not old or patient then someone is either not curious or tall and vice versa.
Everyone who is not generous or not funny is not quiet and vice versa.
Everyone who is creative is either not creative or patient and vice versa.
If john is not patient or patient then someone is both old and not rich and vice versa.
If mary is calm or kind then lucy is not generous or funny and vice versa.
Everyone who is rich or not funny is creative and vice versa.
Everyone who is quiet is wise or not rich and vice versa.
If someone is curious or not patient then someone is not curious or calm.
Everyone who is either not tall or old is both tall and humble and vice versa.
If lucy is either humble or tall then paul is both happy and rich.
If mary is not humble or generous then lucy is not quiet.
Everyone who is kind is both not strong and generous and vice versa.
Everyone who is happy is not curious or not rich.
Everyone who is wise is both not kind and not curious.
Everyone who is either not funny or generous is either wise or rich and vice versa.
Someone is not quiet or kind.
Fred is either quiet or not old.
Paul is brave.
Alice is both not funny and not brave.
Someone is either not humble or calm.
Someone is quiet or not funny.
Alice is calm. | Lucy is not generous. | neutral | (((~old(fred)<~>patient(fred)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((~generous(X)|~funny(X))<=>~quiet(X)))&
(![X]:(creative(X)<=>(~creative(X)<~>patient(X))))&
(((~patient(john)|patient(john)))<=>(?[X]:((old(X)&~rich(X)))))&
(((calm(mary)|kind(mary)))<=>((~generous(lucy)|funny(lucy))))&
(![X]:((rich(X)|~funny(X))<=>creative(X)))&
(![X]:(quiet(X)<=>(wise(X)|~rich(X))))&
((?[X]:((curious(X)|~patient(X))))=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~tall(X)<~>old(X))<=>(tall(X)&humble(X))))&
(((humble(lucy)<~>tall(lucy)))=>((happy(paul)&rich(paul))))&
(((~humble(mary)|generous(mary)))=>(~quiet(lucy)))&
(![X]:(kind(X)<=>(~strong(X)&generous(X))))&
(![X]:(happy(X)=>(~curious(X)|~rich(X))))&
(![X]:(wise(X)=>(~kind(X)&~curious(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(wise(X)<~>rich(X))))&
(?[X]:((~quiet(X)|kind(X))))&
((quiet(fred)<~>~old(fred)))&
(brave(paul))&
((~funny(alice)&~brave(alice)))&
(?[X]:((~humble(X)<~>calm(X))))&
(?[X]:((quiet(X)|~funny(X))))&
(calm(alice)) | ~generous(lucy) | [] | null | 0 |
If someone is strong or not curious then fred is both quiet and old and vice versa. Everyone who is not generous or calm is either happy or brave and vice versa. Everyone who is both funny and not funny is kind and vice versa. Everyone who is not calm or calm is either kind or not calm and vice versa. If susan is both not quiet and curious then someone is either strong or tall and vice versa. If susan is not quiet then someone is both not strong and brave. If someone is humble then someone is both not patient and generous and vice versa. If susan is either happy or not old then someone is either not rich or not quiet. If fred is not old or kind then lucy is both old and curious. If someone is not patient or not wise then fred is both not funny and not quiet. Everyone who is generous is not happy. If someone is both not strong and calm then someone is either not brave or generous and vice versa. If someone is either not funny or not rich then fred is not rich. If someone is not quiet then fred is happy or kind. Mary is not happy or curious. Someone is generous or not funny. Someone is generous or not quiet. Someone is either brave or not humble. Lucy is either not kind or not rich. Someone is not quiet or not brave. | Fred is wise. | entailment | ((?[X]:((strong(X)|~curious(X))))<=>((quiet(fred)&old(fred))))&
(![X]:((~generous(X)|calm(X))<=>(happy(X)<~>brave(X))))&
(![X]:((funny(X)&~funny(X))<=>kind(X)))&
(![X]:((~calm(X)|calm(X))<=>(kind(X)<~>~calm(X))))&
(((~quiet(susan)&curious(susan)))<=>(?[X]:((strong(X)<~>tall(X)))))&
((~quiet(susan))=>(?[X]:((~strong(X)&brave(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~patient(X)&generous(X)))))&
(((happy(susan)<~>~old(susan)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(((~old(fred)|kind(fred)))=>((old(lucy)&curious(lucy))))&
((?[X]:((~patient(X)|~wise(X))))=>((~funny(fred)&~quiet(fred))))&
(![X]:(generous(X)=>~happy(X)))&
((?[X]:((~strong(X)&calm(X))))<=>(?[X]:((~brave(X)<~>generous(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(~rich(fred)))&
((?[X]:(~quiet(X)))=>((happy(fred)|kind(fred))))&
((~happy(mary)|curious(mary)))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((generous(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:((~quiet(X)|~brave(X)))) | wise(fred) | [
"p1",
"p2",
"p3",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 39871852233504954079154
% SZS output start Proof for 39871852233504954079154
2. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (happy(X0) <~> brave(X0))) [input p1]
3. ! [X0] : ((~funny(X0) & funny(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p3]
10. ? [X0] : (~wise(X0) | ~patient(X0)) => (~quiet(fred) & ~funny(fred)) [input p9]
11. ! [X0] : (generous(X0) => ~happy(X0)) [input p10]
12. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X0] : (~brave(X0) <~> generous(X0)) [input p11]
14. ? [X0] : ~quiet(X0) => (kind(fred) | happy(fred)) [input p13]
21. ~wise(fred) [input hypothesis]
23. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X1] : (~brave(X1) <~> generous(X1)) [rectify 12]
27. (~quiet(fred) & ~funny(fred)) | ! [X0] : (wise(X0) & patient(X0)) [ennf transformation 10]
28. ! [X0] : (~happy(X0) | ~generous(X0)) [ennf transformation 11]
30. (kind(fred) | happy(fred)) | ! [X0] : quiet(X0) [ennf transformation 14]
31. kind(fred) | happy(fred) | ! [X0] : quiet(X0) [flattening 30]
37. ! [X0] : (((calm(X0) | ~generous(X0)) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 2]
38. ! [X0] : ((calm(X0) | ~generous(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | ~funny(X0))) [flattening 39]
41. ! [X0] : (((calm(X0) | ~calm(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [nnf transformation 4]
42. ! [X0] : ((calm(X0) | ~calm(X0) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [flattening 41]
58. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X1] : ((~generous(X1) | brave(X1)) & (generous(X1) | ~brave(X1))) | ! [X0] : (~calm(X0) | strong(X0))) [nnf transformation 23]
59. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) | ! [X3] : (~calm(X3) | strong(X3))) [rectify 58]
60. ? [X0] : (calm(X0) & ~strong(X0)) => (calm(sK6) & ~strong(sK6)) [choice axiom]
61. ? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) => ((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) [choice axiom]
62. ((calm(sK6) & ~strong(sK6)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) | ! [X3] : (~calm(X3) | strong(X3))) [skolemisation 59,61,60]
81. ~brave(X0) | ~happy(X0) | generous(X0) [cnf transformation 38]
86. funny(X0) | ~kind(X0) [cnf transformation 40]
87. ~kind(X0) | ~funny(X0) [cnf transformation 40]
89. ~calm(X0) | kind(X0) | ~calm(X0) [cnf transformation 42]
116. ~quiet(fred) | wise(X0) [cnf transformation 27]
117. ~happy(X0) | ~generous(X0) [cnf transformation 28]
122. calm(sK6) | generous(X1) | brave(X1) [cnf transformation 62]
126. kind(fred) | happy(fred) | quiet(X0) [cnf transformation 31]
135. ~wise(fred) [cnf transformation 21]
136. ~calm(X0) | kind(X0) [duplicate literal removal 89]
141. 1 <=> quiet(fred) [avatar definition]
143. ~quiet(fred) <- (~1) [avatar component clause 141]
167. ~kind(X0) [subsumption resolution 86,87]
168. ~calm(X0) [subsumption resolution 136,167]
259. 26 <=> ! [X0] : wise(X0) [avatar definition]
260. wise(X0) <- (26) [avatar component clause 259]
261. 26 | ~1 [avatar split clause 116,141,259]
273. brave(X1) | generous(X1) [subsumption resolution 122,168]
286. happy(fred) | quiet(X0) [subsumption resolution 126,167]
288. 32 <=> ! [X0] : quiet(X0) [avatar definition]
289. quiet(X0) <- (32) [avatar component clause 288]
291. 33 <=> happy(fred) [avatar definition]
293. happy(fred) <- (33) [avatar component clause 291]
294. 32 | 33 [avatar split clause 286,291,288]
342. $false <- (~1, 32) [subsumption resolution 143,289]
343. 1 | ~32 [avatar contradiction clause 342]
354. ~happy(X1) | generous(X1) | generous(X1) [resolution 81,273]
355. ~happy(X1) | generous(X1) [duplicate literal removal 354]
357. ~happy(X1) [subsumption resolution 355,117]
358. $false <- (33) [resolution 357,293]
359. ~33 [avatar contradiction clause 358]
362. $false <- (26) [resolution 260,135]
363. ~26 [avatar contradiction clause 362]
364. $false [avatar sat refutation 261,294,343,359,363]
% SZS output end Proof for 39871852233504954079154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not rich is not old.
If someone is both brave and humble then susan is tall or not creative and vice versa.
Everyone who is either generous or old is either happy or wise and vice versa.
Everyone who is strong or not curious is either calm or curious and vice versa.
If someone is strong or rich then john is either not wise or not funny and vice versa.
Everyone who is not happy or not brave is either not humble or funny and vice versa.
Everyone who is both curious and quiet is either wise or creative and vice versa.
Everyone who is both not tall and generous is creative or strong.
If john is not curious or not calm then alice is strong or curious and vice versa.
Everyone who is curious or kind is both funny and curious and vice versa.
If susan is either not wise or not creative then alice is both curious and kind.
Everyone who is either brave or funny is both happy and generous and vice versa.
Everyone who is not creative is brave or rich and vice versa.
If someone is either not funny or not happy then mary is not funny or creative and vice versa.
If someone is calm or patient then someone is not calm or old.
Everyone who is either old or happy is both not curious and not strong.
Paul is both quiet and calm.
Susan is tall or not curious.
Someone is either wise or quiet.
Someone is generous.
Mary is not happy.
Susan is either patient or generous.
Someone is strong or not calm.
Someone is either strong or not quiet. | Mary is not kind. | entailment | (![X]:((~humble(X)&~rich(X))=>~old(X)))&
((?[X]:((brave(X)&humble(X))))<=>((tall(susan)|~creative(susan))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)<~>wise(X))))&
(![X]:((strong(X)|~curious(X))<=>(calm(X)<~>curious(X))))&
((?[X]:((strong(X)|rich(X))))<=>((~wise(john)<~>~funny(john))))&
(![X]:((~happy(X)|~brave(X))<=>(~humble(X)<~>funny(X))))&
(![X]:((curious(X)&quiet(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~tall(X)&generous(X))=>(creative(X)|strong(X))))&
(((~curious(john)|~calm(john)))<=>((strong(alice)|curious(alice))))&
(![X]:((curious(X)|kind(X))<=>(funny(X)&curious(X))))&
(((~wise(susan)<~>~creative(susan)))=>((curious(alice)&kind(alice))))&
(![X]:((brave(X)<~>funny(X))<=>(happy(X)&generous(X))))&
(![X]:(~creative(X)<=>(brave(X)|rich(X))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((~funny(mary)|creative(mary))))&
((?[X]:((calm(X)|patient(X))))=>(?[X]:((~calm(X)|old(X)))))&
(![X]:((old(X)<~>happy(X))=>(~curious(X)&~strong(X))))&
((quiet(paul)&calm(paul)))&
((tall(susan)|~curious(susan)))&
(?[X]:((wise(X)<~>quiet(X))))&
(?[X]:(generous(X)))&
(~happy(mary))&
((patient(susan)<~>generous(susan)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((strong(X)<~>~quiet(X)))) | ~kind(mary) | [
"p9",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3079648755470328340343688
% SZS output start Proof for 3079648755470328340343688
10. ! [X0] : ((kind(X0) | curious(X0)) <=> (curious(X0) & funny(X0))) [input p9]
12. ! [X0] : ((brave(X0) <~> funny(X0)) <=> (generous(X0) & happy(X0))) [input p11]
13. ! [X0] : (~creative(X0) <=> (rich(X0) | brave(X0))) [input p12]
14. ? [X0] : (~funny(X0) <~> ~happy(X0)) <=> (creative(mary) | ~funny(mary)) [input p13]
21. ~happy(mary) [input p20]
25. kind(mary) [input hypothesis]
52. ! [X0] : (((kind(X0) | curious(X0)) | (~curious(X0) | ~funny(X0))) & ((curious(X0) & funny(X0)) | (~kind(X0) & ~curious(X0)))) [nnf transformation 10]
53. ! [X0] : ((kind(X0) | curious(X0) | ~curious(X0) | ~funny(X0)) & ((curious(X0) & funny(X0)) | (~kind(X0) & ~curious(X0)))) [flattening 52]
55. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [nnf transformation 12]
56. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [flattening 55]
57. ! [X0] : ((~creative(X0) | (~rich(X0) & ~brave(X0))) & ((rich(X0) | brave(X0)) | creative(X0))) [nnf transformation 13]
58. ! [X0] : ((~creative(X0) | (~rich(X0) & ~brave(X0))) & (rich(X0) | brave(X0) | creative(X0))) [flattening 57]
59. (? [X0] : ((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~creative(mary) & funny(mary))) & ((creative(mary) | ~funny(mary)) | ! [X0] : ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) [nnf transformation 14]
60. (? [X0] : ((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~creative(mary) & funny(mary))) & (creative(mary) | ~funny(mary) | ! [X0] : ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) [flattening 59]
61. (? [X0] : ((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~creative(mary) & funny(mary))) & (creative(mary) | ~funny(mary) | ! [X1] : ((~funny(X1) | happy(X1)) & (~happy(X1) | funny(X1)))) [rectify 60]
62. ? [X0] : ((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) => ((happy(sK2) | funny(sK2)) & (~happy(sK2) | ~funny(sK2))) [choice axiom]
63. (((happy(sK2) | funny(sK2)) & (~happy(sK2) | ~funny(sK2))) | (~creative(mary) & funny(mary))) & (creative(mary) | ~funny(mary) | ! [X1] : ((~funny(X1) | happy(X1)) & (~happy(X1) | funny(X1)))) [skolemisation 61,62]
123. ~kind(X0) | funny(X0) [cnf transformation 53]
132. ~funny(X0) | brave(X0) | happy(X0) [cnf transformation 56]
138. ~creative(X0) | ~brave(X0) [cnf transformation 58]
141. creative(mary) | ~funny(mary) | ~funny(X1) | happy(X1) [cnf transformation 63]
158. ~happy(mary) [cnf transformation 21]
164. kind(mary) [cnf transformation 25]
252. 18 <=> creative(mary) [avatar definition]
253. creative(mary) <- (18) [avatar component clause 252]
265. 21 <=> funny(mary) [avatar definition]
267. funny(mary) <- (21) [avatar component clause 265]
272. 22 <=> ! [X1] : (~funny(X1) | happy(X1)) [avatar definition]
273. ~funny(X1) | happy(X1) <- (22) [avatar component clause 272]
274. 22 | ~21 | 18 [avatar split clause 141,252,265,272]
340. funny(mary) [resolution 123,164]
343. 21 [avatar split clause 340,265]
345. ~brave(mary) <- (18) [resolution 138,253]
456. brave(mary) | happy(mary) <- (21) [resolution 132,267]
459. happy(mary) <- (18, 21) [subsumption resolution 456,345]
460. $false <- (18, 21) [subsumption resolution 459,158]
461. ~18 | ~21 [avatar contradiction clause 460]
466. happy(mary) <- (21, 22) [resolution 273,267]
469. $false <- (21, 22) [subsumption resolution 466,158]
470. ~21 | ~22 [avatar contradiction clause 469]
473. $false [avatar sat refutation 274,343,461,470]
% SZS output end Proof for 3079648755470328340343688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or tall is not creative and vice versa.
If someone is either not funny or not happy then alice is either not happy or kind.
Everyone who is calm is wise.
If paul is either generous or not calm then someone is kind or generous and vice versa.
If alice is not calm or calm then someone is not calm.
Everyone who is both creative and happy is both wise and not happy.
Everyone who is either wise or creative is either calm or not brave and vice versa.
Everyone who is wise is creative and vice versa.
If susan is both not kind and not quiet then someone is either calm or patient and vice versa.
Everyone who is not wise or not happy is not curious or kind and vice versa.
Everyone who is not strong or happy is not brave or not humble and vice versa.
If someone is not old then someone is quiet.
Everyone who is either not happy or not strong is both kind and rich and vice versa.
Everyone who is either creative or curious is both calm and not wise and vice versa.
If someone is calm then someone is not tall or brave and vice versa.
If lucy is quiet or brave then someone is not brave or brave.
Susan is generous or funny.
Someone is quiet or calm.
John is happy or old.
Someone is either not wise or not patient.
Fred is calm or old.
Someone is either not patient or kind.
Someone is not kind or kind.
Paul is not kind. | Paul is calm. | contradiction | (![X]:((~calm(X)|tall(X))<=>~creative(X)))&
((?[X]:((~funny(X)<~>~happy(X))))=>((~happy(alice)<~>kind(alice))))&
(![X]:(calm(X)=>wise(X)))&
(((generous(paul)<~>~calm(paul)))<=>(?[X]:((kind(X)|generous(X)))))&
(((~calm(alice)|calm(alice)))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&happy(X))=>(wise(X)&~happy(X))))&
(![X]:((wise(X)<~>creative(X))<=>(calm(X)<~>~brave(X))))&
(![X]:(wise(X)<=>creative(X)))&
(((~kind(susan)&~quiet(susan)))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|kind(X))))&
(![X]:((~strong(X)|happy(X))<=>(~brave(X)|~humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(quiet(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(kind(X)&rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>(calm(X)&~wise(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)|brave(X)))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:((~brave(X)|brave(X)))))&
((generous(susan)|funny(susan)))&
(?[X]:((quiet(X)|calm(X))))&
((happy(john)|old(john)))&
(?[X]:((~wise(X)<~>~patient(X))))&
((calm(fred)|old(fred)))&
(?[X]:((~patient(X)<~>kind(X))))&
(?[X]:((~kind(X)|kind(X))))&
(~kind(paul)) | calm(paul) | [
"p2",
"p5",
"p7",
"p9",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 680730407376701506310065
% SZS output start Proof for 680730407376701506310065
3. ! [X0] : (calm(X0) => wise(X0)) [input p2]
6. ! [X0] : ((happy(X0) & creative(X0)) => (~happy(X0) & wise(X0))) [input p5]
8. ! [X0] : (wise(X0) <=> creative(X0)) [input p7]
10. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (kind(X0) | ~curious(X0))) [input p9]
14. ! [X0] : ((creative(X0) <~> curious(X0)) <=> (~wise(X0) & calm(X0))) [input p13]
24. ~kind(paul) [input p23]
25. calm(paul) [input hypothesis]
32. ! [X0] : (wise(X0) | ~calm(X0)) [ennf transformation 3]
34. ! [X0] : ((~happy(X0) & wise(X0)) | (~happy(X0) | ~creative(X0))) [ennf transformation 6]
35. ! [X0] : ((~happy(X0) & wise(X0)) | ~happy(X0) | ~creative(X0)) [flattening 34]
47. ! [X0] : ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))) [nnf transformation 8]
53. ! [X0] : (((~happy(X0) | ~wise(X0)) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 10]
54. ! [X0] : ((~happy(X0) | ~wise(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | (happy(X0) & wise(X0)))) [flattening 53]
59. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [flattening 59]
85. ~calm(X0) | wise(X0) [cnf transformation 32]
95. ~happy(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 35]
104. ~wise(X0) | creative(X0) [cnf transformation 47]
113. ~curious(X0) | kind(X0) | happy(X0) [cnf transformation 54]
128. ~wise(X0) | curious(X0) | ~creative(X0) [cnf transformation 60]
144. ~kind(paul) [cnf transformation 24]
145. calm(paul) [cnf transformation 25]
146. ~happy(X0) | ~creative(X0) [duplicate literal removal 95]
173. 7 <=> calm(paul) [avatar definition]
175. calm(paul) <- (7) [avatar component clause 173]
235. ~wise(X0) | curious(X0) [subsumption resolution 128,104]
299. 7 [avatar split clause 145,173]
304. wise(paul) <- (7) [resolution 85,175]
307. creative(paul) <- (7) [resolution 104,304]
322. curious(paul) <- (7) [resolution 235,304]
351. kind(paul) | happy(paul) <- (7) [resolution 113,322]
361. happy(paul) <- (7) [subsumption resolution 351,144]
380. ~creative(paul) <- (7) [resolution 361,146]
381. $false <- (7) [subsumption resolution 380,307]
382. ~7 [avatar contradiction clause 381]
383. $false [avatar sat refutation 299,382]
% SZS output end Proof for 680730407376701506310065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is wise. Everyone who is either not calm or not curious is both not old and not happy. Everyone who is quiet is both brave and not quiet. If susan is not humble or not strong then susan is brave or not curious and vice versa. If someone is not wise then someone is both brave and quiet and vice versa. Everyone who is both not calm and quiet is not tall or rich and vice versa. If someone is both old and patient then someone is old or not humble and vice versa. If susan is not wise then someone is both kind and not generous and vice versa. If john is either calm or not funny then mary is kind and vice versa. Everyone who is kind is both not generous and not creative. Everyone who is not old or not patient is both not wise and kind. Everyone who is not rich is not curious. Everyone who is old is tall and vice versa. Everyone who is curious or not quiet is not curious and vice versa. Everyone who is both not strong and happy is not curious. Everyone who is either not calm or not old is tall or not funny. Someone is either patient or not happy. Mary is not generous or not patient. Someone is old. Susan is not kind or tall. Mary is either not generous or not humble. | Susan is curious. | contradiction | (![X]:(happy(X)=>wise(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(~old(X)&~happy(X))))&
(![X]:(quiet(X)=>(brave(X)&~quiet(X))))&
(((~humble(susan)|~strong(susan)))<=>((brave(susan)|~curious(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:((~calm(X)&quiet(X))<=>(~tall(X)|rich(X))))&
((?[X]:((old(X)&patient(X))))<=>(?[X]:((old(X)|~humble(X)))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(![X]:(kind(X)=>(~generous(X)&~creative(X))))&
(![X]:((~old(X)|~patient(X))=>(~wise(X)&kind(X))))&
(![X]:(~rich(X)=>~curious(X)))&
(![X]:(old(X)<=>tall(X)))&
(![X]:((curious(X)|~quiet(X))<=>~curious(X)))&
(![X]:((~strong(X)&happy(X))=>~curious(X)))&
(![X]:((~calm(X)<~>~old(X))=>(tall(X)|~funny(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
((~generous(mary)|~patient(mary)))&
(?[X]:(old(X)))&
((~kind(susan)|tall(susan)))&
((~generous(mary)<~>~humble(mary))) | curious(susan) | [
"p2",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4792060307700443769936339
% SZS output start Proof for 4792060307700443769936339
3. ! [X0] : (quiet(X0) => (~quiet(X0) & brave(X0))) [input p2]
6. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (rich(X0) | ~tall(X0))) [input p5]
12. ! [X0] : (~rich(X0) => ~curious(X0)) [input p11]
22. curious(susan) [input hypothesis]
28. ! [X0] : ((~quiet(X0) & brave(X0)) | ~quiet(X0)) [ennf transformation 3]
31. ! [X0] : (~curious(X0) | rich(X0)) [ennf transformation 12]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
72. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
84. quiet(X0) | ~rich(X0) [cnf transformation 45]
102. ~curious(X0) | rich(X0) [cnf transformation 31]
118. curious(susan) [cnf transformation 22]
121. ~quiet(X0) [duplicate literal removal 72]
143. ~rich(X0) [subsumption resolution 84,121]
195. ~curious(X0) [subsumption resolution 102,143]
199. $false [subsumption resolution 118,195]
% SZS output end Proof for 4792060307700443769936339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not patient is both funny and wise and vice versa. Everyone who is not brave or happy is either not brave or funny. Everyone who is not curious is humble or creative and vice versa. Everyone who is either creative or kind is either patient or not brave and vice versa. Everyone who is either not tall or not old is not brave or not calm and vice versa. Everyone who is calm is generous. If someone is not creative then someone is both not kind and rich and vice versa. If mary is patient or kind then someone is both not wise and not tall and vice versa. Everyone who is humble is not rich or old. If john is not rich then someone is either not old or patient and vice versa. If mary is not rich or curious then alice is either not patient or not funny. Everyone who is either funny or strong is not patient or curious and vice versa. If fred is tall or not creative then mary is patient or strong. Everyone who is both not generous and tall is either quiet or calm and vice versa. Everyone who is either not funny or tall is both funny and kind. If someone is wise or not happy then alice is both not quiet and not wise. Someone is kind or generous. Someone is both happy and generous. Someone is not curious. Someone is either not happy or not rich. Someone is either not generous or not old. John is not calm. Someone is not calm or calm. Someone is creative. | Mary is generous. | neutral | (![X]:((~quiet(X)|~patient(X))<=>(funny(X)&wise(X))))&
(![X]:((~brave(X)|happy(X))=>(~brave(X)<~>funny(X))))&
(![X]:(~curious(X)<=>(humble(X)|creative(X))))&
(![X]:((creative(X)<~>kind(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~old(X))<=>(~brave(X)|~calm(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~kind(X)&rich(X)))))&
(((patient(mary)|kind(mary)))<=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~calm(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(creative(X))) | generous(mary) | [] | null | 0 |
Everyone who is both happy and brave is both strong and not creative and vice versa.
If someone is both rich and brave then alice is both tall and not calm and vice versa.
Everyone who is both kind and wise is quiet.
Everyone who is both not generous and not wise is not curious and vice versa.
If fred is either not brave or not curious then someone is both not old and not generous and vice versa.
If john is either not generous or generous then someone is wise or quiet.
Everyone who is tall is happy and vice versa.
Everyone who is either kind or not generous is both tall and funny.
Everyone who is quiet or not funny is not calm and vice versa.
If someone is either strong or creative then susan is quiet or not curious.
Everyone who is either brave or wise is either not rich or not quiet and vice versa.
If alice is not humble then susan is both not creative and wise.
If someone is calm then someone is either not generous or humble and vice versa.
If someone is both creative and not kind then someone is not brave or calm and vice versa.
If mary is creative or not brave then paul is both not happy and rich.
If someone is both happy and not brave then someone is both happy and not kind.
Susan is not curious or not calm.
Mary is both rich and not strong.
Fred is both rich and not quiet.
Fred is both not wise and calm.
Someone is both not rich and not curious.
Susan is both calm and happy.
Someone is creative.
Susan is both funny and not patient. | Alice is not calm. | entailment | (![X]:((happy(X)&brave(X))<=>(strong(X)&~creative(X))))&
((?[X]:((rich(X)&brave(X))))<=>((tall(alice)&~calm(alice))))&
(![X]:((kind(X)&wise(X))=>quiet(X)))&
(![X]:((~generous(X)&~wise(X))<=>~curious(X)))&
(((~brave(fred)<~>~curious(fred)))<=>(?[X]:((~old(X)&~generous(X)))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:(tall(X)<=>happy(X)))&
(![X]:((kind(X)<~>~generous(X))=>(tall(X)&funny(X))))&
(![X]:((quiet(X)|~funny(X))<=>~calm(X)))&
((?[X]:((strong(X)<~>creative(X))))=>((quiet(susan)|~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~rich(X)<~>~quiet(X))))&
((~humble(alice))=>((~creative(susan)&wise(susan))))&
((?[X]:(calm(X)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
((?[X]:((creative(X)&~kind(X))))<=>(?[X]:((~brave(X)|calm(X)))))&
(((creative(mary)|~brave(mary)))=>((~happy(paul)&rich(paul))))&
((?[X]:((happy(X)&~brave(X))))=>(?[X]:((happy(X)&~kind(X)))))&
((~curious(susan)|~calm(susan)))&
((rich(mary)&~strong(mary)))&
((rich(fred)&~quiet(fred)))&
((~wise(fred)&calm(fred)))&
(?[X]:((~rich(X)&~curious(X))))&
((calm(susan)&happy(susan)))&
(?[X]:(creative(X)))&
((funny(susan)&~patient(susan))) | ~calm(alice) | [
"p1",
"p10",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4890739306793611952350903
% SZS output start Proof for 4890739306793611952350903
2. ? [X0] : (brave(X0) & rich(X0)) <=> (~calm(alice) & tall(alice)) [input p1]
11. ! [X0] : ((brave(X0) <~> wise(X0)) <=> (~rich(X0) <~> ~quiet(X0))) [input p10]
19. ~quiet(fred) & rich(fred) [input p18]
20. calm(fred) & ~wise(fred) [input p19]
25. calm(alice) [input hypothesis]
41. (? [X0] : (brave(X0) & rich(X0)) | (calm(alice) | ~tall(alice))) & ((~calm(alice) & tall(alice)) | ! [X0] : (~brave(X0) | ~rich(X0))) [nnf transformation 2]
42. (? [X0] : (brave(X0) & rich(X0)) | calm(alice) | ~tall(alice)) & ((~calm(alice) & tall(alice)) | ! [X0] : (~brave(X0) | ~rich(X0))) [flattening 41]
43. (? [X0] : (brave(X0) & rich(X0)) | calm(alice) | ~tall(alice)) & ((~calm(alice) & tall(alice)) | ! [X1] : (~brave(X1) | ~rich(X1))) [rectify 42]
44. ? [X0] : (brave(X0) & rich(X0)) => (brave(sK0) & rich(sK0)) [choice axiom]
45. ((brave(sK0) & rich(sK0)) | calm(alice) | ~tall(alice)) & ((~calm(alice) & tall(alice)) | ! [X1] : (~brave(X1) | ~rich(X1))) [skolemisation 43,44]
60. ! [X0] : ((((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0)))) & (((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0))))) [nnf transformation 11]
83. ~calm(alice) | ~brave(X1) | ~rich(X1) [cnf transformation 45]
114. ~rich(X0) | brave(X0) | wise(X0) | quiet(X0) [cnf transformation 60]
137. rich(fred) [cnf transformation 19]
138. ~quiet(fred) [cnf transformation 19]
139. ~wise(fred) [cnf transformation 20]
147. calm(alice) [cnf transformation 25]
155. 2 <=> calm(alice) [avatar definition]
169. 5 <=> ! [X1] : (~brave(X1) | ~rich(X1)) [avatar definition]
170. ~rich(X1) | ~brave(X1) <- (5) [avatar component clause 169]
171. 5 | ~2 [avatar split clause 83,155,169]
177. 7 <=> brave(fred) [avatar definition]
178. ~brave(fred) <- (~7) [avatar component clause 177]
333. 2 [avatar split clause 147,155]
351. ~brave(fred) <- (5) [resolution 170,137]
356. ~7 | ~5 [avatar split clause 351,169,177]
468. brave(fred) | wise(fred) | quiet(fred) [resolution 114,137]
480. wise(fred) | quiet(fred) <- (~7) [subsumption resolution 468,178]
481. quiet(fred) <- (~7) [subsumption resolution 480,139]
482. $false <- (~7) [subsumption resolution 481,138]
483. 7 [avatar contradiction clause 482]
494. $false [avatar sat refutation 171,333,356,483]
% SZS output end Proof for 4890739306793611952350903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave is both not kind and funny.
If someone is not creative then someone is not rich and vice versa.
Everyone who is not quiet is not tall and vice versa.
If someone is both not quiet and not rich then fred is both humble and not patient and vice versa.
Everyone who is not generous or strong is brave.
Everyone who is either old or kind is old.
Everyone who is not wise or not generous is happy.
If susan is either funny or happy then susan is not quiet and vice versa.
Everyone who is either curious or not tall is both humble and not kind and vice versa.
Everyone who is either humble or old is not quiet and vice versa.
Everyone who is either not old or tall is not tall and vice versa.
Everyone who is both happy and not happy is patient or happy and vice versa.
If susan is not happy then fred is curious or calm.
Everyone who is not quiet is both curious and not brave and vice versa.
If alice is either old or not creative then someone is either strong or not curious.
Everyone who is either wise or creative is both creative and not quiet.
John is not creative or not brave.
Someone is not strong.
Someone is rich.
Someone is either not kind or humble.
Someone is calm or not creative.
Fred is either not strong or calm.
Alice is both quiet and not happy. | Fred is quiet. | entailment | (![X]:(~brave(X)=>(~kind(X)&funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~rich(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&~rich(X))))<=>((humble(fred)&~patient(fred))))&
(![X]:((~generous(X)|strong(X))=>brave(X)))&
(![X]:((old(X)<~>kind(X))=>old(X)))&
(![X]:((~wise(X)|~generous(X))=>happy(X)))&
(((funny(susan)<~>happy(susan)))<=>(~quiet(susan)))&
(![X]:((curious(X)<~>~tall(X))<=>(humble(X)&~kind(X))))&
(![X]:((humble(X)<~>old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>tall(X))<=>~tall(X)))&
(![X]:((happy(X)&~happy(X))<=>(patient(X)|happy(X))))&
((~happy(susan))=>((curious(fred)|calm(fred))))&
(![X]:(~quiet(X)<=>(curious(X)&~brave(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(![X]:((wise(X)<~>creative(X))=>(creative(X)&~quiet(X))))&
((~creative(john)|~brave(john)))&
(?[X]:(~strong(X)))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((calm(X)|~creative(X))))&
((~strong(fred)<~>calm(fred)))&
((quiet(alice)&~happy(alice))) | quiet(fred) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5946089556216387189290344
% SZS output start Proof for 5946089556216387189290344
2. ? [X0] : ~creative(X0) <=> ? [X0] : ~rich(X0) [input p1]
4. ? [X0] : (~rich(X0) & ~quiet(X0)) <=> (~patient(fred) & humble(fred)) [input p3]
7. ! [X0] : ((~generous(X0) | ~wise(X0)) => happy(X0)) [input p6]
10. ! [X0] : ((humble(X0) <~> old(X0)) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((~old(X0) <~> tall(X0)) <=> ~tall(X0)) [input p10]
12. ! [X0] : ((~happy(X0) & happy(X0)) <=> (happy(X0) | patient(X0))) [input p11]
16. ! [X0] : ((wise(X0) <~> creative(X0)) => (~quiet(X0) & creative(X0))) [input p15]
24. ~quiet(fred) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : ~rich(X1) [rectify 2]
26. ! [X0] : (~wise(X0) => happy(X0)) [pure predicate removal 7]
31. ! [X0] : (happy(X0) | wise(X0)) [ennf transformation 26]
35. ! [X0] : ((~quiet(X0) & creative(X0)) | (wise(X0) <=> creative(X0))) [ennf transformation 16]
36. (? [X0] : ~creative(X0) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : creative(X0)) [nnf transformation 25]
37. (? [X0] : ~creative(X0) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : creative(X3)) [rectify 36]
38. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
39. ? [X2] : ~rich(X2) => ~rich(sK1) [choice axiom]
40. (~creative(sK0) | ! [X1] : rich(X1)) & (~rich(sK1) | ! [X3] : creative(X3)) [skolemisation 37,39,38]
42. (? [X0] : (~rich(X0) & ~quiet(X0)) | (patient(fred) | ~humble(fred))) & ((~patient(fred) & humble(fred)) | ! [X0] : (rich(X0) | quiet(X0))) [nnf transformation 4]
43. (? [X0] : (~rich(X0) & ~quiet(X0)) | patient(fred) | ~humble(fred)) & ((~patient(fred) & humble(fred)) | ! [X0] : (rich(X0) | quiet(X0))) [flattening 42]
44. (? [X0] : (~rich(X0) & ~quiet(X0)) | patient(fred) | ~humble(fred)) & ((~patient(fred) & humble(fred)) | ! [X1] : (rich(X1) | quiet(X1))) [rectify 43]
45. ? [X0] : (~rich(X0) & ~quiet(X0)) => (~rich(sK2) & ~quiet(sK2)) [choice axiom]
46. ((~rich(sK2) & ~quiet(sK2)) | patient(fred) | ~humble(fred)) & ((~patient(fred) & humble(fred)) | ! [X1] : (rich(X1) | quiet(X1))) [skolemisation 44,45]
51. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | quiet(X0)) & (~quiet(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | tall(X0)) & (~tall(X0) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 11]
53. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 12]
54. ! [X0] : (((~happy(X0) & happy(X0)) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | happy(X0) | ~happy(X0))) [flattening 53]
60. ! [X0] : ((~quiet(X0) & creative(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) [nnf transformation 35]
74. ~creative(sK0) | rich(X1) [cnf transformation 40]
80. ~rich(sK2) | patient(fred) | ~humble(fred) [cnf transformation 46]
84. happy(X0) | wise(X0) [cnf transformation 31]
97. old(X0) | humble(X0) | quiet(X0) [cnf transformation 51]
100. ~tall(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
101. tall(X0) | ~old(X0) | tall(X0) [cnf transformation 52]
104. happy(X0) | ~patient(X0) [cnf transformation 54]
107. ~happy(X0) | ~happy(X0) [cnf transformation 54]
116. creative(X0) | creative(X0) | ~wise(X0) [cnf transformation 60]
130. ~quiet(fred) [cnf transformation 24]
131. ~wise(X0) | creative(X0) [duplicate literal removal 116]
133. ~happy(X0) [duplicate literal removal 107]
134. ~tall(X0) | ~old(X0) [duplicate literal removal 100]
135. ~old(X0) | tall(X0) [duplicate literal removal 101]
138. 1 <=> ! [X1] : rich(X1) [avatar definition]
139. rich(X1) <- (1) [avatar component clause 138]
141. 2 <=> creative(sK0) [avatar definition]
143. ~creative(sK0) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 74,141,138]
146. 3 <=> ! [X3] : creative(X3) [avatar definition]
147. creative(X3) <- (3) [avatar component clause 146]
154. 5 <=> humble(fred) [avatar definition]
156. ~humble(fred) <- (~5) [avatar component clause 154]
158. 6 <=> patient(fred) [avatar definition]
160. patient(fred) <- (6) [avatar component clause 158]
162. 7 <=> rich(sK2) [avatar definition]
164. ~rich(sK2) <- (~7) [avatar component clause 162]
165. ~5 | 6 | ~7 [avatar split clause 80,162,158,154]
192. ~old(X0) [subsumption resolution 134,135]
193. ~patient(X0) [subsumption resolution 104,133]
259. wise(X0) [resolution 84,133]
264. creative(X0) [resolution 131,259]
265. 3 [avatar split clause 264,146]
266. $false <- (~2, 3) [resolution 147,143]
269. 2 | ~3 [avatar contradiction clause 266]
271. $false <- (1, ~7) [resolution 139,164]
272. ~1 | 7 [avatar contradiction clause 271]
274. $false <- (6) [subsumption resolution 160,193]
275. ~6 [avatar contradiction clause 274]
287. humble(X2) | quiet(X2) [resolution 97,192]
291. quiet(fred) <- (~5) [resolution 287,156]
293. $false <- (~5) [subsumption resolution 291,130]
294. 5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 144,165,265,269,272,275,294]
% SZS output end Proof for 5946089556216387189290344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and funny is either not creative or not generous.
If someone is both quiet and funny then someone is not strong.
If alice is both not calm and not curious then john is creative.
If someone is generous then someone is both old and not curious and vice versa.
Everyone who is tall or not generous is both strong and not happy.
If someone is patient then someone is not brave or patient and vice versa.
If someone is creative or not kind then someone is not patient.
Everyone who is not calm is brave.
If john is both quiet and strong then someone is both quiet and not tall and vice versa.
Everyone who is both not rich and not kind is curious.
Everyone who is not curious is rich or not curious.
Everyone who is not kind or not wise is both not quiet and tall.
If someone is brave then someone is both humble and old and vice versa.
Everyone who is both not humble and not tall is either not humble or kind and vice versa.
Everyone who is not funny is not quiet or not rich.
If alice is both not rich and quiet then alice is patient or curious.
Fred is wise or not brave.
Paul is either wise or not patient.
Someone is strong or tall.
Someone is both old and patient.
Alice is both not funny and not calm.
John is either not wise or patient.
Lucy is both not rich and not humble.
Alice is brave. | Fred is not humble. | neutral | (![X]:((patient(X)&funny(X))=>(~creative(X)<~>~generous(X))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~strong(X))))&
(((~calm(alice)&~curious(alice)))=>(creative(john)))&
((?[X]:(generous(X)))<=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)|~generous(X))=>(strong(X)&~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:(~patient(X))))&
(![X]:(~calm(X)=>brave(X)))&
(((quiet(john)&strong(john)))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~rich(X)&~kind(X))=>curious(X)))&
(![X]:(~curious(X)=>(rich(X)|~curious(X))))&
(![X]:((~kind(X)|~wise(X))=>(~quiet(X)&tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((humble(X)&old(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(~humble(X)<~>kind(X))))&
(![X]:(~funny(X)=>(~quiet(X)|~rich(X))))&
(((~rich(alice)&quiet(alice)))=>((patient(alice)|curious(alice))))&
((wise(fred)|~brave(fred)))&
((wise(paul)<~>~patient(paul)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((old(X)&patient(X))))&
((~funny(alice)&~calm(alice)))&
((~wise(john)<~>patient(john)))&
((~rich(lucy)&~humble(lucy)))&
(brave(alice)) | ~humble(fred) | [] | null | 0 |
If fred is both kind and quiet then someone is either not brave or wise.
If alice is not funny or tall then paul is not patient or kind.
Everyone who is either not rich or rich is both rich and funny and vice versa.
Everyone who is not tall or not patient is either old or not brave and vice versa.
If john is wise or quiet then someone is tall and vice versa.
If mary is funny then someone is not brave or not kind and vice versa.
Everyone who is curious is not brave.
Everyone who is both not wise and not funny is funny or not brave.
If susan is not happy then someone is either kind or not generous.
If mary is creative or patient then mary is not brave and vice versa.
Everyone who is either not happy or not strong is not happy or quiet and vice versa.
If someone is humble then someone is either funny or not wise and vice versa.
If lucy is kind or rich then mary is curious and vice versa.
Everyone who is tall or brave is either wise or not quiet and vice versa.
If mary is both not calm and humble then alice is either creative or tall.
Everyone who is both kind and not tall is not funny.
Lucy is either not creative or not rich.
Paul is either strong or happy.
Someone is either curious or not quiet.
Someone is not curious or creative.
Someone is not generous or strong.
John is both not strong and kind. | John is not generous. | neutral | (((kind(fred)&quiet(fred)))=>(?[X]:((~brave(X)<~>wise(X)))))&
(((~funny(alice)|tall(alice)))=>((~patient(paul)|kind(paul))))&
(![X]:((~rich(X)<~>rich(X))<=>(rich(X)&funny(X))))&
(![X]:((~tall(X)|~patient(X))<=>(old(X)<~>~brave(X))))&
(((wise(john)|quiet(john)))<=>(?[X]:(tall(X))))&
((funny(mary))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(curious(X)=>~brave(X)))&
(![X]:((~wise(X)&~funny(X))=>(funny(X)|~brave(X))))&
((~happy(susan))=>(?[X]:((kind(X)<~>~generous(X)))))&
(((creative(mary)|patient(mary)))<=>(~brave(mary)))&
(![X]:((~happy(X)<~>~strong(X))<=>(~happy(X)|quiet(X))))&
((?[X]:(humble(X)))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(((kind(lucy)|rich(lucy)))<=>(curious(mary)))&
(![X]:((tall(X)|brave(X))<=>(wise(X)<~>~quiet(X))))&
(((~calm(mary)&humble(mary)))=>((creative(alice)<~>tall(alice))))&
(![X]:((kind(X)&~tall(X))=>~funny(X)))&
((~creative(lucy)<~>~rich(lucy)))&
((strong(paul)<~>happy(paul)))&
(?[X]:((curious(X)<~>~quiet(X))))&
(?[X]:((~curious(X)|creative(X))))&
(?[X]:((~generous(X)|strong(X))))&
((~strong(john)&kind(john))) | ~generous(john) | [] | null | 0 |
If susan is not curious then someone is not generous and vice versa.
Everyone who is both creative and not patient is either not curious or not quiet and vice versa.
If someone is brave then someone is both not funny and not brave.
Everyone who is not tall or not strong is strong or not old.
Everyone who is calm or generous is both not patient and not brave and vice versa.
Everyone who is not old or humble is either not generous or funny.
If someone is either not old or quiet then someone is not old or not kind and vice versa.
If someone is either humble or rich then alice is either not rich or not generous and vice versa.
If paul is strong or not brave then someone is either creative or calm and vice versa.
If john is both tall and not humble then someone is either not brave or not humble and vice versa.
Everyone who is both creative and humble is not funny or humble.
Everyone who is not calm is brave or calm.
Everyone who is both not brave and happy is not patient or not generous.
If someone is curious or not generous then someone is not tall or creative.
Everyone who is not strong is both not brave and brave and vice versa.
If someone is either tall or not quiet then someone is both brave and not quiet.
John is strong or not brave.
Someone is either patient or not old.
Alice is wise.
Mary is quiet or not creative.
Someone is happy or not rich.
Alice is calm or wise.
Someone is brave or curious.
Paul is either not funny or not strong. | John is not strong. | contradiction | ((~curious(susan))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)&~patient(X))<=>(~curious(X)<~>~quiet(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~tall(X)|~strong(X))=>(strong(X)|~old(X))))&
(![X]:((calm(X)|generous(X))<=>(~patient(X)&~brave(X))))&
(![X]:((~old(X)|humble(X))=>(~generous(X)<~>funny(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~old(X)|~kind(X)))))&
((?[X]:((humble(X)<~>rich(X))))<=>((~rich(alice)<~>~generous(alice))))&
(((strong(paul)|~brave(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
(((tall(john)&~humble(john)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((creative(X)&humble(X))=>(~funny(X)|humble(X))))&
(![X]:(~calm(X)=>(brave(X)|calm(X))))&
(![X]:((~brave(X)&happy(X))=>(~patient(X)|~generous(X))))&
((?[X]:((curious(X)|~generous(X))))=>(?[X]:((~tall(X)|creative(X)))))&
(![X]:(~strong(X)<=>(~brave(X)&brave(X))))&
((?[X]:((tall(X)<~>~quiet(X))))=>(?[X]:((brave(X)&~quiet(X)))))&
((strong(john)|~brave(john)))&
(?[X]:((patient(X)<~>~old(X))))&
(wise(alice))&
((quiet(mary)|~creative(mary)))&
(?[X]:((happy(X)|~rich(X))))&
((calm(alice)|wise(alice)))&
(?[X]:((brave(X)|curious(X))))&
((~funny(paul)<~>~strong(paul))) | ~strong(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 494650008057827947157412
% SZS output start Proof for 494650008057827947157412
15. ! [X0] : (~strong(X0) <=> (brave(X0) & ~brave(X0))) [input p14]
25. ~strong(john) [input hypothesis]
78. ! [X0] : ((~strong(X0) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | strong(X0))) [nnf transformation 15]
79. ! [X0] : ((~strong(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | strong(X0))) [flattening 78]
144. ~brave(X0) | strong(X0) [cnf transformation 79]
145. brave(X0) | strong(X0) [cnf transformation 79]
159. ~strong(john) [cnf transformation 25]
321. strong(X0) [subsumption resolution 144,145]
378. $false [subsumption resolution 159,321]
% SZS output end Proof for 494650008057827947157412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind or not rich is either kind or not humble.
If john is both not happy and strong then someone is happy or kind.
Everyone who is not brave is tall or not funny and vice versa.
Everyone who is generous is not kind or quiet and vice versa.
Everyone who is both not generous and creative is both patient and tall.
If someone is curious then fred is funny and vice versa.
Everyone who is not rich is both not humble and not curious and vice versa.
Everyone who is brave or generous is either strong or quiet and vice versa.
Everyone who is both tall and quiet is both not happy and rich.
Everyone who is both patient and not calm is happy or not happy and vice versa.
Everyone who is both rich and not strong is not wise.
Everyone who is not calm or patient is not happy or kind.
If paul is both not wise and not patient then someone is quiet.
Everyone who is both not wise and not curious is either creative or not happy.
Everyone who is not rich or patient is not wise and vice versa.
Everyone who is not curious or brave is kind.
Paul is either not calm or not tall.
Someone is not strong.
Someone is both old and not creative.
Susan is not funny or not brave.
Someone is both strong and kind.
Lucy is curious.
Someone is strong.
John is not strong or not happy. | Lucy is patient. | entailment | (![X]:((~kind(X)|~rich(X))=>(kind(X)<~>~humble(X))))&
(((~happy(john)&strong(john)))=>(?[X]:((happy(X)|kind(X)))))&
(![X]:(~brave(X)<=>(tall(X)|~funny(X))))&
(![X]:(generous(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~generous(X)&creative(X))=>(patient(X)&tall(X))))&
((?[X]:(curious(X)))<=>(funny(fred)))&
(![X]:(~rich(X)<=>(~humble(X)&~curious(X))))&
(![X]:((brave(X)|generous(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)&quiet(X))=>(~happy(X)&rich(X))))&
(![X]:((patient(X)&~calm(X))<=>(happy(X)|~happy(X))))&
(![X]:((rich(X)&~strong(X))=>~wise(X)))&
(![X]:((~calm(X)|patient(X))=>(~happy(X)|kind(X))))&
(((~wise(paul)&~patient(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~wise(X)&~curious(X))=>(creative(X)<~>~happy(X))))&
(![X]:((~rich(X)|patient(X))<=>~wise(X)))&
(![X]:((~curious(X)|brave(X))=>kind(X)))&
((~calm(paul)<~>~tall(paul)))&
(?[X]:(~strong(X)))&
(?[X]:((old(X)&~creative(X))))&
((~funny(susan)|~brave(susan)))&
(?[X]:((strong(X)&kind(X))))&
(curious(lucy))&
(?[X]:(strong(X)))&
((~strong(john)|~happy(john))) | patient(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9167392119111311678681986
% SZS output start Proof for 9167392119111311678681986
10. ! [X0] : ((~calm(X0) & patient(X0)) <=> (~happy(X0) | happy(X0))) [input p9]
25. ~patient(lucy) [input hypothesis]
58. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 10]
59. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | calm(X0) | ~patient(X0))) [flattening 58]
101. patient(X0) | ~happy(X0) [cnf transformation 59]
102. patient(X0) | happy(X0) [cnf transformation 59]
126. ~patient(lucy) [cnf transformation 25]
161. patient(X0) [subsumption resolution 101,102]
167. $false [subsumption resolution 126,161]
% SZS output end Proof for 9167392119111311678681986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and creative then alice is either not calm or funny.
Everyone who is both old and funny is not wise and vice versa.
Everyone who is either tall or brave is either humble or curious and vice versa.
Everyone who is not old is both not funny and not kind and vice versa.
Everyone who is not patient or old is both calm and not old and vice versa.
Everyone who is not brave or not humble is both not happy and not patient.
If alice is tall or quiet then someone is not humble and vice versa.
Everyone who is calm is both patient and not generous.
If someone is both patient and not strong then john is quiet or patient.
If paul is patient or not brave then susan is either not patient or not old.
If lucy is both curious and not happy then someone is not humble and vice versa.
Everyone who is both not generous and not tall is either creative or not rich.
If someone is strong then someone is both not patient and not quiet.
Everyone who is not brave is both creative and funny.
If susan is either funny or old then someone is both not kind and kind and vice versa.
Someone is tall.
Fred is brave.
Someone is either quiet or calm.
Paul is either not calm or funny.
Someone is not calm. | Susan is not happy. | neutral | ((?[X]:((~creative(X)&creative(X))))=>((~calm(alice)<~>funny(alice))))&
(![X]:((old(X)&funny(X))<=>~wise(X)))&
(![X]:((tall(X)<~>brave(X))<=>(humble(X)<~>curious(X))))&
(![X]:(~old(X)<=>(~funny(X)&~kind(X))))&
(![X]:((~patient(X)|old(X))<=>(calm(X)&~old(X))))&
(![X]:((~brave(X)|~humble(X))=>(~happy(X)&~patient(X))))&
(((tall(alice)|quiet(alice)))<=>(?[X]:(~humble(X))))&
(![X]:(calm(X)=>(patient(X)&~generous(X))))&
((?[X]:((patient(X)&~strong(X))))=>((quiet(john)|patient(john))))&
(((patient(paul)|~brave(paul)))=>((~patient(susan)<~>~old(susan))))&
(((curious(lucy)&~happy(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)&~tall(X))=>(creative(X)<~>~rich(X))))&
((?[X]:(strong(X)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(![X]:(~brave(X)=>(creative(X)&funny(X))))&
(((funny(susan)<~>old(susan)))<=>(?[X]:((~kind(X)&kind(X)))))&
(?[X]:(tall(X)))&
(brave(fred))&
(?[X]:((quiet(X)<~>calm(X))))&
((~calm(paul)<~>funny(paul)))&
(?[X]:(~calm(X))) | ~happy(susan) | [] | null | 0 |
If someone is both generous and kind then someone is both kind and not quiet. If someone is both not strong and curious then paul is wise and vice versa. Everyone who is not tall or not calm is generous or not curious and vice versa. Everyone who is either not curious or generous is either not happy or not funny. If lucy is rich then alice is funny. Everyone who is generous is not strong or rich and vice versa. If someone is not rich or not funny then mary is kind. Everyone who is quiet or not generous is not creative or happy and vice versa. Everyone who is not generous or not brave is happy and vice versa. If fred is both tall and not happy then mary is either not tall or not patient. If someone is not patient or not happy then mary is both not happy and not funny. Everyone who is either quiet or not tall is either not calm or funny. If fred is not rich then someone is funny. Everyone who is both quiet and wise is not brave. Everyone who is either not creative or kind is either rich or tall. Everyone who is humble or not quiet is not kind. Someone is either strong or not wise. Someone is not tall. Paul is curious. Fred is both not wise and patient. Susan is happy or calm. Someone is either generous or humble. Someone is either not calm or not strong. | Lucy is rich. | neutral | ((?[X]:((generous(X)&kind(X))))=>(?[X]:((kind(X)&~quiet(X)))))&
((?[X]:((~strong(X)&curious(X))))<=>(wise(paul)))&
(![X]:((~tall(X)|~calm(X))<=>(generous(X)|~curious(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~happy(X)<~>~funny(X))))&
((rich(lucy))=>(funny(alice)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~rich(X)|~funny(X))))=>(kind(mary)))&
(![X]:((quiet(X)|~generous(X))<=>(~creative(X)|happy(X))))&
(![X]:((~generous(X)|~brave(X))<=>happy(X)))&
(((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:(~tall(X)))&
(curious(paul))&
((~wise(fred)&patient(fred)))&
((happy(susan)|calm(susan)))&
(?[X]:((generous(X)<~>humble(X))))&
(?[X]:((~calm(X)<~>~strong(X)))) | rich(lucy) | [] | null | 0 |
Everyone who is either tall or rich is both patient and not rich and vice versa.
Everyone who is humble or not rich is not kind and vice versa.
If john is wise or not humble then lucy is either not brave or calm.
If someone is not patient then susan is funny and vice versa.
Everyone who is brave or humble is both humble and not humble and vice versa.
Everyone who is either not strong or not quiet is not calm.
Everyone who is generous is both humble and generous and vice versa.
Everyone who is either rich or not strong is either not quiet or not tall and vice versa.
Everyone who is either funny or happy is both wise and quiet.
If someone is generous or rich then someone is not curious or not humble.
Everyone who is brave is either not generous or tall.
If someone is not curious or wise then someone is either not old or happy.
Everyone who is not generous or not happy is not calm and vice versa.
Everyone who is either wise or not calm is not humble or not curious.
Everyone who is not calm is either not brave or creative.
If fred is either patient or quiet then paul is quiet or brave.
Susan is either not curious or not creative.
Someone is either tall or patient.
Someone is either not quiet or not humble.
Someone is brave or funny.
Lucy is either not happy or not strong. | John is happy. | neutral | (![X]:((tall(X)<~>rich(X))<=>(patient(X)&~rich(X))))&
(![X]:((humble(X)|~rich(X))<=>~kind(X)))&
(((wise(john)|~humble(john)))=>((~brave(lucy)<~>calm(lucy))))&
((?[X]:(~patient(X)))<=>(funny(susan)))&
(![X]:((brave(X)|humble(X))<=>(humble(X)&~humble(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>~calm(X)))&
(![X]:(generous(X)<=>(humble(X)&generous(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)<~>happy(X))=>(wise(X)&quiet(X))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:(brave(X)=>(~generous(X)<~>tall(X))))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~generous(X)|~happy(X))<=>~calm(X)))&
(![X]:((wise(X)<~>~calm(X))=>(~humble(X)|~curious(X))))&
(![X]:(~calm(X)=>(~brave(X)<~>creative(X))))&
(((patient(fred)<~>quiet(fred)))=>((quiet(paul)|brave(paul))))&
((~curious(susan)<~>~creative(susan)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((brave(X)|funny(X))))&
((~happy(lucy)<~>~strong(lucy))) | happy(john) | [] | null | 0 |
Everyone who is either wise or not creative is not old.
Everyone who is both not wise and wise is happy or rich.
If paul is both not rich and not quiet then someone is either not brave or not quiet.
Everyone who is happy is either not funny or not humble.
Everyone who is generous is old or not wise.
If lucy is old then someone is not happy and vice versa.
Everyone who is happy or not strong is either tall or calm and vice versa.
Everyone who is not old or not strong is not humble or funny.
If someone is not tall then someone is not patient.
Everyone who is not brave is creative or strong.
If susan is quiet or not humble then someone is not wise or patient and vice versa.
If someone is either not tall or not wise then someone is not brave and vice versa.
If someone is tall then mary is both strong and not humble and vice versa.
Everyone who is happy or not brave is both funny and rich.
Everyone who is not funny is not humble or generous and vice versa.
Everyone who is both kind and brave is both not patient and quiet.
Someone is brave or wise.
Lucy is both wise and brave.
Lucy is either rich or not creative.
Fred is not brave.
Someone is both quiet and not strong.
Someone is both not strong and creative.
Susan is either funny or not rich. | Mary is not happy. | entailment | (![X]:((wise(X)<~>~creative(X))=>~old(X)))&
(![X]:((~wise(X)&wise(X))=>(happy(X)|rich(X))))&
(((~rich(paul)&~quiet(paul)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:(happy(X)=>(~funny(X)<~>~humble(X))))&
(![X]:(generous(X)=>(old(X)|~wise(X))))&
((old(lucy))<=>(?[X]:(~happy(X))))&
(![X]:((happy(X)|~strong(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~old(X)|~strong(X))=>(~humble(X)|funny(X))))&
((?[X]:(~tall(X)))=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)=>(creative(X)|strong(X))))&
(((quiet(susan)|~humble(susan)))<=>(?[X]:((~wise(X)|patient(X)))))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~humble(mary))))&
(![X]:((happy(X)|~brave(X))=>(funny(X)&rich(X))))&
(![X]:(~funny(X)<=>(~humble(X)|generous(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&quiet(X))))&
(?[X]:((brave(X)|wise(X))))&
((wise(lucy)&brave(lucy)))&
((rich(lucy)<~>~creative(lucy)))&
(~brave(fred))&
(?[X]:((quiet(X)&~strong(X))))&
(?[X]:((~strong(X)&creative(X))))&
((funny(susan)<~>~rich(susan))) | ~happy(mary) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2049350072700299717759365
% SZS output start Proof for 2049350072700299717759365
4. ! [X0] : (happy(X0) => (~funny(X0) <~> ~humble(X0))) [input p3]
14. ! [X0] : ((~brave(X0) | happy(X0)) => (rich(X0) & funny(X0))) [input p13]
15. ! [X0] : (~funny(X0) <=> (generous(X0) | ~humble(X0))) [input p14]
24. happy(mary) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~humble(X0)) | ~happy(X0)) [ennf transformation 4]
41. ! [X0] : ((rich(X0) & funny(X0)) | (brave(X0) & ~happy(X0))) [ennf transformation 14]
46. ! [X0] : (((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | ~happy(X0)) [nnf transformation 33]
71. ! [X0] : ((~funny(X0) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | funny(X0))) [nnf transformation 15]
72. ! [X0] : ((~funny(X0) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | funny(X0))) [flattening 71]
86. ~humble(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 46]
112. ~happy(X0) | funny(X0) [cnf transformation 41]
117. ~funny(X0) | humble(X0) [cnf transformation 72]
131. happy(mary) [cnf transformation 24]
227. 23 <=> humble(mary) [avatar definition]
229. humble(mary) <- (23) [avatar component clause 227]
271. funny(mary) [resolution 112,131]
281. humble(mary) [resolution 117,271]
284. 23 [avatar split clause 281,227]
291. ~funny(mary) | ~happy(mary) <- (23) [resolution 86,229]
292. ~happy(mary) <- (23) [subsumption resolution 291,271]
293. $false <- (23) [subsumption resolution 292,131]
294. ~23 [avatar contradiction clause 293]
295. $false [avatar sat refutation 284,294]
% SZS output end Proof for 2049350072700299717759365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or curious then someone is either not funny or rich.
If someone is funny or not patient then john is not calm or old.
If someone is tall then paul is not happy.
If mary is either old or kind then someone is quiet or not calm and vice versa.
Everyone who is wise or not tall is not strong and vice versa.
Everyone who is both kind and generous is both not calm and not tall and vice versa.
Everyone who is quiet or wise is either not humble or rich and vice versa.
If susan is not generous or not wise then someone is not kind or creative and vice versa.
Everyone who is not tall or strong is both tall and humble and vice versa.
Everyone who is both creative and not tall is not wise or funny and vice versa.
If fred is either not generous or wise then someone is both not wise and not curious and vice versa.
Everyone who is brave or humble is either not quiet or humble and vice versa.
If someone is either not humble or rich then john is wise.
If someone is both rich and not tall then alice is not quiet.
If fred is creative or funny then fred is not old or not tall.
Everyone who is brave or quiet is either not tall or not kind.
Susan is either not curious or not kind.
Mary is not kind or generous.
Lucy is either not happy or not patient.
John is wise or not kind.
John is either not tall or not kind. | John is not wise. | contradiction | ((?[X]:((~brave(X)|curious(X))))=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((funny(X)|~patient(X))))=>((~calm(john)|old(john))))&
((?[X]:(tall(X)))=>(~happy(paul)))&
(((old(mary)<~>kind(mary)))<=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((wise(X)|~tall(X))<=>~strong(X)))&
(![X]:((kind(X)&generous(X))<=>(~calm(X)&~tall(X))))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)&humble(X))))&
(![X]:((creative(X)&~tall(X))<=>(~wise(X)|funny(X))))&
(((~generous(fred)<~>wise(fred)))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|humble(X))<=>(~quiet(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(wise(john)))&
((?[X]:((rich(X)&~tall(X))))=>(~quiet(alice)))&
(((creative(fred)|funny(fred)))=>((~old(fred)|~tall(fred))))&
(![X]:((brave(X)|quiet(X))=>(~tall(X)<~>~kind(X))))&
((~curious(susan)<~>~kind(susan)))&
((~kind(mary)|generous(mary)))&
((~happy(lucy)<~>~patient(lucy)))&
((wise(john)|~kind(john)))&
((~tall(john)<~>~kind(john))) | ~wise(john) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4426089404858932745168832
% SZS output start Proof for 4426089404858932745168832
9. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (humble(X0) & tall(X0))) [input p8]
10. ! [X0] : ((~tall(X0) & creative(X0)) <=> (funny(X0) | ~wise(X0))) [input p9]
22. ~wise(john) [input hypothesis]
52. ! [X0] : (((strong(X0) | ~tall(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 9]
53. ! [X0] : ((strong(X0) | ~tall(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [flattening 52]
54. ! [X0] : (((~tall(X0) & creative(X0)) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | (tall(X0) | ~creative(X0)))) [nnf transformation 10]
55. ! [X0] : (((~tall(X0) & creative(X0)) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | tall(X0) | ~creative(X0))) [flattening 54]
97. tall(X0) | tall(X0) [cnf transformation 53]
105. ~tall(X0) | wise(X0) [cnf transformation 55]
136. ~wise(john) [cnf transformation 22]
139. tall(X0) [duplicate literal removal 97]
239. wise(X0) [subsumption resolution 105,139]
297. $false [subsumption resolution 136,239]
% SZS output end Proof for 4426089404858932745168832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or humble is both not calm and creative. Everyone who is not rich or kind is wise and vice versa. If someone is humble or not creative then fred is not wise and vice versa. If paul is either creative or not humble then someone is not tall and vice versa. If someone is either not curious or kind then susan is quiet or not quiet. Everyone who is funny or generous is kind. If someone is generous then susan is both not generous and rich. Everyone who is not brave or not curious is humble or quiet and vice versa. If fred is both wise and curious then someone is both wise and not generous and vice versa. Everyone who is not humble is patient or tall and vice versa. If mary is happy then john is curious. If john is both not humble and rich then john is calm or creative and vice versa. If someone is creative or not generous then susan is creative or patient and vice versa. If someone is both generous and not funny then paul is wise. Everyone who is both not humble and curious is quiet and vice versa. Everyone who is not quiet or wise is either not kind or not happy and vice versa. Paul is tall or quiet. Someone is both not tall and not strong. Mary is not patient or strong. Someone is either not kind or tall. Someone is both not kind and not calm. Someone is not patient or not strong. John is not rich. Someone is not creative or wise. | Paul is not brave. | entailment | (![X]:((~tall(X)<~>humble(X))=>(~calm(X)&creative(X))))&
(![X]:((~rich(X)|kind(X))<=>wise(X)))&
((?[X]:((humble(X)|~creative(X))))<=>(~wise(fred)))&
(((creative(paul)<~>~humble(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>((quiet(susan)|~quiet(susan))))&
(![X]:((funny(X)|generous(X))=>kind(X)))&
((?[X]:(generous(X)))=>((~generous(susan)&rich(susan))))&
(![X]:((~brave(X)|~curious(X))<=>(humble(X)|quiet(X))))&
(((wise(fred)&curious(fred)))<=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~humble(X)<=>(patient(X)|tall(X))))&
((happy(mary))=>(curious(john)))&
(((~humble(john)&rich(john)))<=>((calm(john)|creative(john))))&
((?[X]:((creative(X)|~generous(X))))<=>((creative(susan)|patient(susan))))&
((?[X]:((generous(X)&~funny(X))))=>(wise(paul)))&
(![X]:((~humble(X)&curious(X))<=>quiet(X)))&
(![X]:((~quiet(X)|wise(X))<=>(~kind(X)<~>~happy(X))))&
((tall(paul)|quiet(paul)))&
(?[X]:((~tall(X)&~strong(X))))&
((~patient(mary)|strong(mary)))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~patient(X)|~strong(X))))&
(~rich(john))&
(?[X]:((~creative(X)|wise(X)))) | ~brave(paul) | [
"p7",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8058159405448070903414672
% SZS output start Proof for 8058159405448070903414672
8. ! [X0] : ((~curious(X0) | ~brave(X0)) <=> (quiet(X0) | humble(X0))) [input p7]
10. ! [X0] : (~humble(X0) <=> (tall(X0) | patient(X0))) [input p9]
15. ! [X0] : ((curious(X0) & ~humble(X0)) <=> quiet(X0)) [input p14]
17. quiet(paul) | tall(paul) [input p16]
25. brave(paul) [input hypothesis]
45. ! [X0] : (((~curious(X0) | ~brave(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (curious(X0) & brave(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | ~brave(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (curious(X0) & brave(X0)))) [flattening 45]
52. ! [X0] : ((~humble(X0) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | humble(X0))) [nnf transformation 10]
53. ! [X0] : ((~humble(X0) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | humble(X0))) [flattening 52]
61. ! [X0] : (((curious(X0) & ~humble(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | humble(X0)))) [nnf transformation 15]
62. ! [X0] : (((curious(X0) & ~humble(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | humble(X0))) [flattening 61]
97. quiet(X0) | humble(X0) | curious(X0) [cnf transformation 46]
99. ~brave(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 46]
106. ~humble(X0) | ~tall(X0) [cnf transformation 53]
118. quiet(X0) | ~curious(X0) | humble(X0) [cnf transformation 62]
120. ~quiet(X0) | curious(X0) [cnf transformation 62]
127. quiet(paul) | tall(paul) [cnf transformation 17]
138. brave(paul) [cnf transformation 25]
168. 8 <=> humble(paul) [avatar definition]
170. humble(paul) <- (8) [avatar component clause 168]
275. quiet(X0) | humble(X0) [subsumption resolution 118,97]
279. 31 <=> tall(paul) [avatar definition]
281. tall(paul) <- (31) [avatar component clause 279]
283. 32 <=> quiet(paul) [avatar definition]
284. ~quiet(paul) <- (~32) [avatar component clause 283]
286. 31 | 32 [avatar split clause 127,283,279]
380. ~curious(paul) | ~quiet(paul) [resolution 99,138]
382. ~quiet(paul) [subsumption resolution 380,120]
383. ~32 [avatar split clause 382,283]
385. humble(paul) <- (~32) [resolution 284,275]
388. 8 | 32 [avatar split clause 385,283,168]
405. ~tall(paul) <- (8) [resolution 170,106]
406. $false <- (8, 31) [subsumption resolution 405,281]
407. ~8 | ~31 [avatar contradiction clause 406]
408. $false [avatar sat refutation 286,383,388,407]
% SZS output end Proof for 8058159405448070903414672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and not wise is patient. Everyone who is tall or not tall is both quiet and not wise and vice versa. Everyone who is either not kind or not curious is old. If someone is not old or not brave then alice is either creative or tall. Everyone who is not old is not brave or kind and vice versa. If susan is either creative or not happy then someone is both happy and generous. Everyone who is not old is both humble and not happy. If someone is quiet then mary is either brave or not tall. If mary is humble then someone is not rich or wise. Everyone who is not rich or not creative is calm or wise and vice versa. Everyone who is either not rich or not strong is both not funny and creative. Everyone who is not calm is both not calm and humble and vice versa. If someone is not old then someone is brave. Everyone who is both not patient and humble is not happy or tall and vice versa. Everyone who is either calm or creative is either strong or tall. John is rich or humble. Fred is not tall or not creative. John is not quiet or not funny. Susan is both not old and not tall. Someone is either generous or not humble. Lucy is either rich or funny. Someone is not generous or brave. | John is not quiet. | contradiction | (![X]:((~humble(X)&~wise(X))=>patient(X)))&
(![X]:((tall(X)|~tall(X))<=>(quiet(X)&~wise(X))))&
(![X]:((~kind(X)<~>~curious(X))=>old(X)))&
((?[X]:((~old(X)|~brave(X))))=>((creative(alice)<~>tall(alice))))&
(![X]:(~old(X)<=>(~brave(X)|kind(X))))&
(((creative(susan)<~>~happy(susan)))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:(~old(X)=>(humble(X)&~happy(X))))&
((?[X]:(quiet(X)))=>((brave(mary)<~>~tall(mary))))&
((humble(mary))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(calm(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~funny(X)&creative(X))))&
(![X]:(~calm(X)<=>(~calm(X)&humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(brave(X))))&
(![X]:((~patient(X)&humble(X))<=>(~happy(X)|tall(X))))&
(![X]:((calm(X)<~>creative(X))=>(strong(X)<~>tall(X))))&
((rich(john)|humble(john)))&
((~tall(fred)|~creative(fred)))&
((~quiet(john)|~funny(john)))&
((~old(susan)&~tall(susan)))&
(?[X]:((generous(X)<~>~humble(X))))&
((rich(lucy)<~>funny(lucy)))&
(?[X]:((~generous(X)|brave(X)))) | ~quiet(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2895994264711666316296211
% SZS output start Proof for 2895994264711666316296211
2. ! [X0] : ((~tall(X0) | tall(X0)) <=> (~wise(X0) & quiet(X0))) [input p1]
23. ~quiet(john) [input hypothesis]
36. ! [X0] : (((~tall(X0) | tall(X0)) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | (tall(X0) & ~tall(X0)))) [nnf transformation 2]
37. ! [X0] : ((~tall(X0) | tall(X0) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | (tall(X0) & ~tall(X0)))) [flattening 36]
66. quiet(X0) | ~tall(X0) [cnf transformation 37]
67. quiet(X0) | tall(X0) [cnf transformation 37]
120. ~quiet(john) [cnf transformation 23]
122. quiet(X0) [subsumption resolution 66,67]
242. $false [subsumption resolution 120,122]
% SZS output end Proof for 2895994264711666316296211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and quiet is either funny or not tall and vice versa.
If someone is either not wise or not generous then someone is not generous.
If paul is not creative or not kind then alice is either not happy or not kind.
Everyone who is not humble or rich is either humble or not quiet and vice versa.
Everyone who is either patient or not happy is calm or not old.
Everyone who is both rich and not brave is not quiet or calm.
Everyone who is rich or not patient is both calm and kind.
Everyone who is both rich and not humble is either not wise or not curious.
Everyone who is funny is not patient or wise and vice versa.
If john is patient or not funny then fred is not quiet and vice versa.
Everyone who is not strong is not creative.
If john is calm then someone is generous.
If someone is either not funny or not patient then someone is both not generous and not patient.
Everyone who is either not funny or curious is patient or not curious and vice versa.
If someone is brave or not brave then susan is curious and vice versa.
If someone is both funny and strong then someone is not rich or strong.
Paul is creative.
Someone is either wise or happy.
Paul is both old and tall.
Susan is both old and not strong.
Alice is not wise or generous.
Fred is both old and kind.
Someone is not old. | Paul is kind. | entailment | (![X]:((funny(X)&quiet(X))<=>(funny(X)<~>~tall(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:(~generous(X))))&
(((~creative(paul)|~kind(paul)))=>((~happy(alice)<~>~kind(alice))))&
(![X]:((~humble(X)|rich(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((patient(X)<~>~happy(X))=>(calm(X)|~old(X))))&
(![X]:((rich(X)&~brave(X))=>(~quiet(X)|calm(X))))&
(![X]:((rich(X)|~patient(X))=>(calm(X)&kind(X))))&
(![X]:((rich(X)&~humble(X))=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)<=>(~patient(X)|wise(X))))&
(((patient(john)|~funny(john)))<=>(~quiet(fred)))&
(![X]:(~strong(X)=>~creative(X)))&
((calm(john))=>(?[X]:(generous(X))))&
((?[X]:((~funny(X)<~>~patient(X))))=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~funny(X)<~>curious(X))<=>(patient(X)|~curious(X))))&
((?[X]:((brave(X)|~brave(X))))<=>(curious(susan)))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(creative(paul))&
(?[X]:((wise(X)<~>happy(X))))&
((old(paul)&tall(paul)))&
((old(susan)&~strong(susan)))&
((~wise(alice)|generous(alice)))&
((old(fred)&kind(fred)))&
(?[X]:(~old(X))) | kind(paul) | [
"p0",
"p3",
"p6",
"p8",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5574159482287786955875513
% SZS output start Proof for 5574159482287786955875513
1. ! [X0] : ((quiet(X0) & funny(X0)) <=> (funny(X0) <~> ~tall(X0))) [input p0]
4. ! [X0] : ((rich(X0) | ~humble(X0)) <=> (humble(X0) <~> ~quiet(X0))) [input p3]
7. ! [X0] : ((~patient(X0) | rich(X0)) => (kind(X0) & calm(X0))) [input p6]
9. ! [X0] : (funny(X0) <=> (wise(X0) | ~patient(X0))) [input p8]
13. ? [X0] : (~funny(X0) <~> ~patient(X0)) => ? [X0] : (~patient(X0) & ~generous(X0)) [input p12]
14. ! [X0] : ((~funny(X0) <~> curious(X0)) <=> (~curious(X0) | patient(X0))) [input p13]
19. tall(paul) & old(paul) [input p18]
24. ~kind(paul) [input hypothesis]
26. ? [X0] : (~funny(X0) <~> ~patient(X0)) => ? [X1] : (~patient(X1) & ~generous(X1)) [rectify 13]
34. ! [X0] : ((kind(X0) & calm(X0)) | (patient(X0) & ~rich(X0))) [ennf transformation 7]
39. ? [X1] : (~patient(X1) & ~generous(X1)) | ! [X0] : (~funny(X0) <=> ~patient(X0)) [ennf transformation 26]
41. ! [X0] : (((quiet(X0) & funny(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) & (((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | (~quiet(X0) | ~funny(X0)))) [nnf transformation 1]
42. ! [X0] : (((quiet(X0) & funny(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) & (((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | ~quiet(X0) | ~funny(X0))) [flattening 41]
48. ! [X0] : (((rich(X0) | ~humble(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) & (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (~rich(X0) & humble(X0)))) [nnf transformation 4]
49. ! [X0] : ((rich(X0) | ~humble(X0) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) & (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (~rich(X0) & humble(X0)))) [flattening 48]
52. ! [X0] : ((funny(X0) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | ~funny(X0))) [nnf transformation 9]
53. ! [X0] : ((funny(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | ~funny(X0))) [flattening 52]
58. ? [X1] : (~patient(X1) & ~generous(X1)) | ! [X0] : ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0))) [nnf transformation 39]
59. ? [X0] : (~patient(X0) & ~generous(X0)) | ! [X1] : ((~funny(X1) | patient(X1)) & (~patient(X1) | funny(X1))) [rectify 58]
60. ? [X0] : (~patient(X0) & ~generous(X0)) => (~patient(sK2) & ~generous(sK2)) [choice axiom]
61. (~patient(sK2) & ~generous(sK2)) | ! [X1] : ((~funny(X1) | patient(X1)) & (~patient(X1) | funny(X1))) [skolemisation 59,60]
62. ! [X0] : ((((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0))))) [nnf transformation 14]
63. ! [X0] : ((((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0))))) [flattening 62]
80. ~tall(X0) | quiet(X0) | ~funny(X0) [cnf transformation 42]
88. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 49]
92. rich(X0) | ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 49]
99. ~rich(X0) | kind(X0) [cnf transformation 34]
104. patient(X0) | funny(X0) [cnf transformation 53]
113. ~patient(sK2) | ~patient(X1) | funny(X1) [cnf transformation 61]
116. ~curious(X0) | patient(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 63]
118. curious(X0) | ~funny(X0) | curious(X0) [cnf transformation 63]
129. tall(paul) [cnf transformation 19]
136. ~kind(paul) [cnf transformation 24]
137. ~curious(X0) | patient(X0) | ~funny(X0) [duplicate literal removal 116]
138. ~funny(X0) | curious(X0) [duplicate literal removal 118]
139. ~quiet(X0) | humble(X0) [duplicate literal removal 88]
140. ~humble(X0) | rich(X0) | ~quiet(X0) [duplicate literal removal 92]
157. 4 <=> kind(paul) [avatar definition]
158. ~kind(paul) <- (~4) [avatar component clause 157]
203. 13 <=> ! [X1] : patient(X1) [avatar definition]
204. patient(X1) <- (13) [avatar component clause 203]
206. 14 <=> patient(sK2) [avatar definition]
208. ~patient(sK2) <- (~14) [avatar component clause 206]
210. ~patient(sK2) | funny(X1) [subsumption resolution 113,104]
212. 15 <=> ! [X1] : funny(X1) [avatar definition]
213. funny(X1) <- (15) [avatar component clause 212]
214. 15 | ~14 [avatar split clause 210,206,212]
224. patient(X0) | ~funny(X0) [subsumption resolution 137,138]
225. patient(X0) [subsumption resolution 224,104]
226. 13 [avatar split clause 225,203]
271. ~4 [avatar split clause 136,157]
272. $false <- (13, ~14) [resolution 208,204]
273. ~13 | 14 [avatar contradiction clause 272]
280. quiet(paul) | ~funny(paul) [resolution 80,129]
282. quiet(paul) <- (15) [subsumption resolution 280,213]
284. humble(paul) <- (15) [resolution 282,139]
297. rich(paul) | ~quiet(paul) <- (15) [resolution 140,284]
298. rich(paul) <- (15) [subsumption resolution 297,282]
301. kind(paul) <- (15) [resolution 298,99]
303. $false <- (~4, 15) [subsumption resolution 301,158]
304. 4 | ~15 [avatar contradiction clause 303]
305. $false [avatar sat refutation 214,226,271,273,304]
% SZS output end Proof for 5574159482287786955875513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not curious or not creative then someone is either not brave or not strong. If susan is both humble and not humble then fred is both calm and old and vice versa. Everyone who is not old is both strong and brave. If mary is not brave then someone is either humble or not creative. Everyone who is either not brave or creative is either brave or not kind and vice versa. Everyone who is either not old or calm is either not brave or brave and vice versa. If someone is not calm or generous then someone is kind and vice versa. If someone is not curious or curious then fred is curious or not wise and vice versa. Everyone who is creative or patient is kind or not quiet and vice versa. Everyone who is happy or not brave is both funny and calm. If john is not patient or creative then fred is either strong or rich and vice versa. Everyone who is either not old or not generous is both not calm and calm. Everyone who is both not happy and not creative is both not wise and not calm. Everyone who is not creative or tall is either patient or brave and vice versa. Mary is both happy and funny. Someone is tall or not old. Someone is happy or not creative. Fred is both patient and creative. Someone is both wise and patient. Lucy is both not funny and not creative. | Mary is not generous. | contradiction | (((~curious(alice)|~creative(alice)))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(((humble(susan)&~humble(susan)))<=>((calm(fred)&old(fred))))&
(![X]:(~old(X)=>(strong(X)&brave(X))))&
((~brave(mary))=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>creative(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((~old(X)<~>calm(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~curious(X)|curious(X))))<=>((curious(fred)|~wise(fred))))&
(![X]:((creative(X)|patient(X))<=>(kind(X)|~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>(funny(X)&calm(X))))&
(((~patient(john)|creative(john)))<=>((strong(fred)<~>rich(fred))))&
(![X]:((~old(X)<~>~generous(X))=>(~calm(X)&calm(X))))&
(![X]:((~happy(X)&~creative(X))=>(~wise(X)&~calm(X))))&
(![X]:((~creative(X)|tall(X))<=>(patient(X)<~>brave(X))))&
((happy(mary)&funny(mary)))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((happy(X)|~creative(X))))&
((patient(fred)&creative(fred)))&
(?[X]:((wise(X)&patient(X))))&
((~funny(lucy)&~creative(lucy))) | ~generous(mary) | [
"p2",
"p5",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8396779965946293414827923
% SZS output start Proof for 8396779965946293414827923
3. ! [X0] : (~old(X0) => (brave(X0) & strong(X0))) [input p2]
6. ! [X0] : ((~old(X0) <~> calm(X0)) <=> (~brave(X0) <~> brave(X0))) [input p5]
10. ! [X0] : ((~brave(X0) | happy(X0)) => (calm(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~old(X0) <~> ~generous(X0)) => (calm(X0) & ~calm(X0))) [input p11]
15. funny(mary) & happy(mary) [input p14]
21. ~generous(mary) [input hypothesis]
24. ! [X0] : ((brave(X0) & strong(X0)) | old(X0)) [ennf transformation 3]
26. ! [X0] : ((calm(X0) & funny(X0)) | (brave(X0) & ~happy(X0))) [ennf transformation 10]
27. ! [X0] : ((calm(X0) & ~calm(X0)) | (~old(X0) <=> ~generous(X0))) [ennf transformation 12]
39. ! [X0] : ((((~calm(X0) | old(X0)) & (calm(X0) | ~old(X0))) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0))))) [nnf transformation 6]
54. ! [X0] : ((calm(X0) & ~calm(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0)))) [nnf transformation 27]
72. old(X0) | brave(X0) [cnf transformation 24]
90. ~calm(X0) | old(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 39]
104. ~happy(X0) | calm(X0) [cnf transformation 26]
113. ~calm(X0) | ~old(X0) | generous(X0) [cnf transformation 54]
124. happy(mary) [cnf transformation 15]
134. ~generous(mary) [cnf transformation 21]
138. ~calm(X0) | old(X0) | ~brave(X0) [duplicate literal removal 90]
193. ~calm(X0) | old(X0) [subsumption resolution 138,72]
258. ~calm(X0) | generous(X0) [subsumption resolution 113,193]
284. calm(mary) [resolution 104,124]
300. generous(mary) [resolution 258,284]
302. $false [subsumption resolution 300,134]
% SZS output end Proof for 8396779965946293414827923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not calm is either not kind or not curious and vice versa.
Everyone who is either not wise or wise is both not calm and not funny.
If fred is both happy and not brave then someone is brave or not patient and vice versa.
Everyone who is strong is both not creative and funny.
Everyone who is both not funny and not creative is both happy and not happy.
Everyone who is either not kind or funny is either not strong or strong.
If john is not quiet then mary is both happy and not generous.
Everyone who is both not kind and rich is not happy.
Everyone who is not generous is either not strong or patient.
If alice is both rich and not curious then john is tall or not happy.
Everyone who is curious is wise or not creative.
If susan is funny then someone is not creative or not tall and vice versa.
Everyone who is both not old and not rich is both not wise and funny and vice versa.
If john is brave or humble then someone is not happy or not calm.
Everyone who is not tall or strong is both patient and not funny and vice versa.
If john is not patient then lucy is either patient or tall and vice versa.
Someone is creative.
Alice is curious or not funny.
Someone is either curious or creative.
Susan is not generous.
Someone is not wise or generous.
Someone is generous.
Someone is not strong or not humble. | Lucy is patient. | contradiction | (![X]:((~brave(X)|~calm(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((~wise(X)<~>wise(X))=>(~calm(X)&~funny(X))))&
(((happy(fred)&~brave(fred)))<=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:(strong(X)=>(~creative(X)&funny(X))))&
(![X]:((~funny(X)&~creative(X))=>(happy(X)&~happy(X))))&
(![X]:((~kind(X)<~>funny(X))=>(~strong(X)<~>strong(X))))&
((~quiet(john))=>((happy(mary)&~generous(mary))))&
(![X]:((~kind(X)&rich(X))=>~happy(X)))&
(![X]:(~generous(X)=>(~strong(X)<~>patient(X))))&
(((rich(alice)&~curious(alice)))=>((tall(john)|~happy(john))))&
(![X]:(curious(X)=>(wise(X)|~creative(X))))&
((funny(susan))<=>(?[X]:((~creative(X)|~tall(X)))))&
(![X]:((~old(X)&~rich(X))<=>(~wise(X)&funny(X))))&
(((brave(john)|humble(john)))=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~tall(X)|strong(X))<=>(patient(X)&~funny(X))))&
((~patient(john))<=>((patient(lucy)<~>tall(lucy))))&
(?[X]:(creative(X)))&
((curious(alice)|~funny(alice)))&
(?[X]:((curious(X)<~>creative(X))))&
(~generous(susan))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:(generous(X)))&
(?[X]:((~strong(X)|~humble(X)))) | patient(lucy) | [
"p1",
"p3",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 658766294358821032723067
% SZS output start Proof for 658766294358821032723067
2. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~funny(X0) & ~calm(X0))) [input p1]
4. ! [X0] : (strong(X0) => (funny(X0) & ~creative(X0))) [input p3]
12. funny(susan) <=> ? [X0] : (~tall(X0) | ~creative(X0)) [input p11]
15. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (~funny(X0) & patient(X0))) [input p14]
24. patient(lucy) [input hypothesis]
28. ! [X0] : ((~funny(X0) & ~calm(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 2]
29. ! [X0] : ((funny(X0) & ~creative(X0)) | ~strong(X0)) [ennf transformation 4]
43. ! [X0] : ((~funny(X0) & ~calm(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 28]
51. (funny(susan) | ! [X0] : (tall(X0) & creative(X0))) & (? [X0] : (~tall(X0) | ~creative(X0)) | ~funny(susan)) [nnf transformation 12]
52. (funny(susan) | ! [X0] : (tall(X0) & creative(X0))) & (? [X1] : (~tall(X1) | ~creative(X1)) | ~funny(susan)) [rectify 51]
53. ? [X1] : (~tall(X1) | ~creative(X1)) => (~tall(sK1) | ~creative(sK1)) [choice axiom]
54. (funny(susan) | ! [X0] : (tall(X0) & creative(X0))) & ((~tall(sK1) | ~creative(sK1)) | ~funny(susan)) [skolemisation 52,53]
59. ! [X0] : (((strong(X0) | ~tall(X0)) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 15]
60. ! [X0] : ((strong(X0) | ~tall(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | (~strong(X0) & tall(X0)))) [flattening 59]
79. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 43]
80. ~funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
87. funny(X0) | ~strong(X0) [cnf transformation 29]
101. funny(susan) | tall(X0) [cnf transformation 54]
111. strong(X0) | ~tall(X0) | funny(X0) | ~patient(X0) [cnf transformation 60]
123. patient(lucy) [cnf transformation 24]
126. ~funny(X0) | wise(X0) [duplicate literal removal 79]
127. ~funny(X0) | ~wise(X0) [duplicate literal removal 80]
128. ~funny(X0) [subsumption resolution 126,127]
157. ~strong(X0) [subsumption resolution 87,128]
180. tall(X0) [subsumption resolution 101,128]
182. ~tall(X0) | funny(X0) | ~patient(X0) [subsumption resolution 111,157]
183. funny(X0) | ~patient(X0) [subsumption resolution 182,180]
184. ~patient(X0) [subsumption resolution 183,128]
195. $false [subsumption resolution 123,184]
% SZS output end Proof for 658766294358821032723067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or generous is curious or old and vice versa. If susan is both not brave and not kind then fred is calm or humble and vice versa. Everyone who is patient or kind is not kind or creative and vice versa. Everyone who is both rich and not rich is humble and vice versa. If someone is both not wise and kind then alice is wise or strong and vice versa. If someone is both humble and generous then paul is funny and vice versa. If susan is not generous or not quiet then fred is either not tall or strong. Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. If someone is curious or old then lucy is both not old and rich and vice versa. Everyone who is not rich or not brave is funny and vice versa. Alice is both not brave and not strong. Alice is not happy. Mary is either not funny or not tall. Someone is both not curious and not happy. Someone is brave. Someone is both generous and funny. Someone is either wise or not kind. | Alice is not rich. | contradiction | (![X]:((~kind(X)<~>generous(X))<=>(curious(X)|old(X))))&
(((~brave(susan)&~kind(susan)))<=>((calm(fred)|humble(fred))))&
(![X]:((patient(X)|kind(X))<=>(~kind(X)|creative(X))))&
(![X]:((rich(X)&~rich(X))<=>humble(X)))&
((?[X]:((~wise(X)&kind(X))))<=>((wise(alice)|strong(alice))))&
((?[X]:((humble(X)&generous(X))))<=>(funny(paul)))&
(((~generous(susan)|~quiet(susan)))=>((~tall(fred)<~>strong(fred))))&
(![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((~brave(alice)&~strong(alice)))&
(~happy(alice))&
((~funny(mary)<~>~tall(mary)))&
(?[X]:((~curious(X)&~happy(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((wise(X)<~>~kind(X)))) | ~rich(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2681199455533518780108731
% SZS output start Proof for 2681199455533518780108731
8. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p7]
24. ~rich(alice) [input hypothesis]
49. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 8]
50. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 49]
119. rich(X0) | ~strong(X0) [cnf transformation 50]
120. rich(X0) | strong(X0) [cnf transformation 50]
163. ~rich(alice) [cnf transformation 24]
243. rich(X0) [subsumption resolution 119,120]
352. $false [subsumption resolution 163,243]
% SZS output end Proof for 2681199455533518780108731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or funny is not happy or not generous and vice versa.
If someone is generous or not strong then someone is either not brave or kind.
Everyone who is not curious is old or wise and vice versa.
If someone is happy or creative then someone is humble.
Everyone who is not rich is both happy and not curious.
If someone is both not patient and not kind then someone is both not curious and tall.
Everyone who is old is not tall or not wise.
If fred is not brave or rich then someone is both not kind and tall.
If someone is either brave or not wise then someone is old or wise and vice versa.
Everyone who is wise or happy is both not happy and not strong and vice versa.
Everyone who is both calm and funny is not kind or not generous.
If paul is either not rich or not strong then someone is either not calm or creative and vice versa.
If someone is creative or not wise then someone is not calm or humble.
Everyone who is both not funny and strong is not kind or not creative.
If someone is wise or generous then someone is quiet or strong.
If someone is both not funny and not old then paul is both not strong and happy.
Someone is strong or tall.
Someone is humble.
Someone is not funny.
Someone is old.
Someone is not old.
Lucy is calm.
Someone is funny or wise. | Lucy is rich. | entailment | (![X]:((strong(X)|funny(X))<=>(~happy(X)|~generous(X))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:(~curious(X)<=>(old(X)|wise(X))))&
((?[X]:((happy(X)|creative(X))))=>(?[X]:(humble(X))))&
(![X]:(~rich(X)=>(happy(X)&~curious(X))))&
((?[X]:((~patient(X)&~kind(X))))=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:(old(X)=>(~tall(X)|~wise(X))))&
(((~brave(fred)|rich(fred)))=>(?[X]:((~kind(X)&tall(X)))))&
((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:((wise(X)|happy(X))<=>(~happy(X)&~strong(X))))&
(![X]:((calm(X)&funny(X))=>(~kind(X)|~generous(X))))&
(((~rich(paul)<~>~strong(paul)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((creative(X)|~wise(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~funny(X)&strong(X))=>(~kind(X)|~creative(X))))&
((?[X]:((wise(X)|generous(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((~funny(X)&~old(X))))=>((~strong(paul)&happy(paul))))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:(humble(X)))&
(?[X]:(~funny(X)))&
(?[X]:(old(X)))&
(?[X]:(~old(X)))&
(calm(lucy))&
(?[X]:((funny(X)|wise(X)))) | rich(lucy) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8723844477932837335857297
% SZS output start Proof for 8723844477932837335857297
5. ! [X0] : (~rich(X0) => (~curious(X0) & happy(X0))) [input p4]
10. ! [X0] : ((happy(X0) | wise(X0)) <=> (~strong(X0) & ~happy(X0))) [input p9]
24. ~rich(lucy) [input hypothesis]
40. ! [X0] : ((~curious(X0) & happy(X0)) | rich(X0)) [ennf transformation 5]
62. ! [X0] : (((happy(X0) | wise(X0)) | (strong(X0) | happy(X0))) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [nnf transformation 10]
63. ! [X0] : ((happy(X0) | wise(X0) | strong(X0) | happy(X0)) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [flattening 62]
87. rich(X0) | happy(X0) [cnf transformation 40]
101. ~happy(X0) | ~happy(X0) [cnf transformation 63]
123. ~rich(lucy) [cnf transformation 24]
124. ~happy(X0) [duplicate literal removal 101]
247. happy(lucy) [resolution 87,123]
248. $false [subsumption resolution 247,124]
% SZS output end Proof for 8723844477932837335857297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or strong is either funny or not generous.
If susan is both not funny and not patient then someone is both not funny and not strong and vice versa.
If lucy is either funny or happy then someone is rich and vice versa.
Everyone who is both rich and funny is humble or not quiet.
If alice is tall or humble then alice is not calm or patient and vice versa.
Everyone who is either generous or not calm is both curious and not calm.
If someone is strong then someone is both humble and not rich.
If paul is happy then someone is either strong or tall and vice versa.
Everyone who is either not humble or not old is either rich or strong and vice versa.
Everyone who is either funny or not tall is creative or not quiet and vice versa.
Everyone who is not calm or not generous is both not patient and quiet.
If someone is both happy and strong then someone is both not patient and quiet and vice versa.
Everyone who is both brave and not rich is both not tall and wise.
Everyone who is not curious is both not quiet and tall and vice versa.
If someone is either not humble or not happy then mary is not rich and vice versa.
Paul is both not rich and kind.
Mary is old.
Fred is not funny or curious.
Someone is brave or humble.
John is not quiet or quiet.
Lucy is wise or old. | Fred is not humble. | neutral | (![X]:((~quiet(X)|strong(X))=>(funny(X)<~>~generous(X))))&
(((~funny(susan)&~patient(susan)))<=>(?[X]:((~funny(X)&~strong(X)))))&
(((funny(lucy)<~>happy(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((rich(X)&funny(X))=>(humble(X)|~quiet(X))))&
(((tall(alice)|humble(alice)))<=>((~calm(alice)|patient(alice))))&
(![X]:((generous(X)<~>~calm(X))=>(curious(X)&~calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((humble(X)&~rich(X)))))&
((happy(paul))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:((~humble(X)<~>~old(X))<=>(rich(X)<~>strong(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~calm(X)|~generous(X))=>(~patient(X)&quiet(X))))&
((?[X]:((happy(X)&strong(X))))<=>(?[X]:((~patient(X)&quiet(X)))))&
(![X]:((brave(X)&~rich(X))=>(~tall(X)&wise(X))))&
(![X]:(~curious(X)<=>(~quiet(X)&tall(X))))&
((?[X]:((~humble(X)<~>~happy(X))))<=>(~rich(mary)))&
((~rich(paul)&kind(paul)))&
(old(mary))&
((~funny(fred)|curious(fred)))&
(?[X]:((brave(X)|humble(X))))&
((~quiet(john)|quiet(john)))&
((wise(lucy)|old(lucy))) | ~humble(fred) | [] | null | 0 |
Everyone who is not old is both not funny and quiet.
Everyone who is both not generous and not creative is not kind or not rich.
Everyone who is both kind and not old is either not generous or quiet.
If fred is funny then mary is both tall and funny and vice versa.
Everyone who is creative or not wise is not tall or calm.
Everyone who is either curious or happy is calm.
If someone is quiet then someone is not humble or curious and vice versa.
Everyone who is rich is either humble or generous.
If someone is curious or happy then someone is both not strong and strong and vice versa.
Everyone who is both not patient and patient is not old and vice versa.
Everyone who is not humble is either not kind or strong and vice versa.
If mary is both generous and not humble then someone is not curious or patient and vice versa.
Everyone who is either humble or not generous is not kind and vice versa.
Everyone who is either not old or strong is either rich or not generous and vice versa.
Everyone who is not rich or brave is both not wise and humble and vice versa.
Everyone who is both not wise and humble is both not tall and generous.
Someone is either not creative or not humble.
Someone is kind or quiet.
Someone is both generous and rich.
Paul is quiet.
Someone is patient.
Someone is either not creative or curious. | Mary is strong. | entailment | (![X]:(~old(X)=>(~funny(X)&quiet(X))))&
(![X]:((~generous(X)&~creative(X))=>(~kind(X)|~rich(X))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>quiet(X))))&
((funny(fred))<=>((tall(mary)&funny(mary))))&
(![X]:((creative(X)|~wise(X))=>(~tall(X)|calm(X))))&
(![X]:((curious(X)<~>happy(X))=>calm(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:(rich(X)=>(humble(X)<~>generous(X))))&
((?[X]:((curious(X)|happy(X))))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((~patient(X)&patient(X))<=>~old(X)))&
(![X]:(~humble(X)<=>(~kind(X)<~>strong(X))))&
(((generous(mary)&~humble(mary)))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((humble(X)<~>~generous(X))<=>~kind(X)))&
(![X]:((~old(X)<~>strong(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((~rich(X)|brave(X))<=>(~wise(X)&humble(X))))&
(![X]:((~wise(X)&humble(X))=>(~tall(X)&generous(X))))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((generous(X)&rich(X))))&
(quiet(paul))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)<~>curious(X)))) | strong(mary) | [
"p10",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1326002955700787269631107
% SZS output start Proof for 1326002955700787269631107
11. ! [X0] : (~humble(X0) <=> (~kind(X0) <~> strong(X0))) [input p10]
12. (~humble(mary) & generous(mary)) <=> ? [X0] : (patient(X0) | ~curious(X0)) [input p11]
13. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> ~kind(X0)) [input p12]
21. ? [X0] : patient(X0) [input p20]
23. ~strong(mary) [input hypothesis]
52. ! [X0] : ((~humble(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | humble(X0))) [nnf transformation 11]
53. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X0] : (patient(X0) | ~curious(X0)) | (humble(mary) | ~generous(mary))) [nnf transformation 12]
54. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X0] : (patient(X0) | ~curious(X0)) | humble(mary) | ~generous(mary)) [flattening 53]
55. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X1] : (patient(X1) | ~curious(X1)) | humble(mary) | ~generous(mary)) [rectify 54]
56. ? [X1] : (patient(X1) | ~curious(X1)) => (patient(sK4) | ~curious(sK4)) [choice axiom]
57. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & ((patient(sK4) | ~curious(sK4)) | humble(mary) | ~generous(mary)) [skolemisation 55,56]
58. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | kind(X0)) & (~kind(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 13]
69. ? [X0] : patient(X0) => patient(sK8) [choice axiom]
70. patient(sK8) [skolemisation 21,69]
95. ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 52]
101. generous(mary) | ~patient(X0) [cnf transformation 57]
103. ~humble(mary) | ~patient(X0) [cnf transformation 57]
106. ~generous(X0) | humble(X0) | kind(X0) [cnf transformation 58]
129. patient(sK8) [cnf transformation 70]
132. ~strong(mary) [cnf transformation 23]
186. 12 <=> ! [X0] : ~patient(X0) [avatar definition]
187. ~patient(X0) <- (12) [avatar component clause 186]
189. 13 <=> humble(mary) [avatar definition]
191. ~humble(mary) <- (~13) [avatar component clause 189]
192. 12 | ~13 [avatar split clause 103,189,186]
198. 15 <=> generous(mary) [avatar definition]
200. generous(mary) <- (15) [avatar component clause 198]
201. 12 | 15 [avatar split clause 101,198,186]
247. $false <- (12) [resolution 187,129]
248. ~12 [avatar contradiction clause 247]
271. humble(mary) | kind(mary) <- (15) [resolution 106,200]
275. kind(mary) <- (~13, 15) [subsumption resolution 271,191]
288. strong(mary) | humble(mary) <- (~13, 15) [resolution 275,95]
289. humble(mary) <- (~13, 15) [subsumption resolution 288,132]
290. $false <- (~13, 15) [subsumption resolution 289,191]
291. 13 | ~15 [avatar contradiction clause 290]
292. $false [avatar sat refutation 192,201,248,291]
% SZS output end Proof for 1326002955700787269631107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not calm is old or not patient. If someone is strong then someone is both not old and not wise. Everyone who is not happy or not generous is not funny and vice versa. Everyone who is either rich or not quiet is happy or patient and vice versa. Everyone who is both not patient and quiet is not creative or not strong and vice versa. Everyone who is either not generous or not funny is both generous and not brave. Everyone who is either not old or patient is both not funny and happy and vice versa. If someone is either wise or quiet then someone is either wise or not rich and vice versa. If someone is either not generous or not tall then john is creative. If alice is not funny or humble then someone is not tall and vice versa. Everyone who is happy or not creative is quiet or old. If mary is both not calm and kind then someone is both not curious and wise and vice versa. Everyone who is both funny and curious is brave and vice versa. Everyone who is not quiet or not creative is tall or brave. Everyone who is happy or not patient is not funny and vice versa. Everyone who is not wise is rich and vice versa. Mary is not humble or not calm. Lucy is brave or not happy. Fred is both calm and creative. Lucy is wise. Someone is humble or not generous. Lucy is not humble or calm. Alice is either not strong or generous. Someone is not old or wise. | Alice is not generous. | entailment | (![X]:((humble(X)&~calm(X))=>(old(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~happy(X)|~generous(X))<=>~funny(X)))&
(![X]:((rich(X)<~>~quiet(X))<=>(happy(X)|patient(X))))&
(![X]:((~patient(X)&quiet(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(generous(X)&~brave(X))))&
(![X]:((~old(X)<~>patient(X))<=>(~funny(X)&happy(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:((~generous(X)<~>~tall(X))))=>(creative(john)))&
(((~funny(alice)|humble(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((happy(X)|~creative(X))=>(quiet(X)|old(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:((funny(X)&curious(X))<=>brave(X)))&
(![X]:((~quiet(X)|~creative(X))=>(tall(X)|brave(X))))&
(![X]:((happy(X)|~patient(X))<=>~funny(X)))&
(![X]:(~wise(X)<=>rich(X)))&
((~humble(mary)|~calm(mary)))&
((brave(lucy)|~happy(lucy)))&
((calm(fred)&creative(fred)))&
(wise(lucy))&
(?[X]:((humble(X)|~generous(X))))&
((~humble(lucy)|calm(lucy)))&
((~strong(alice)<~>generous(alice)))&
(?[X]:((~old(X)|wise(X)))) | ~generous(alice) | [
"p1",
"p3",
"p6",
"p7",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2572305495433569285942250
% SZS output start Proof for 2572305495433569285942250
2. ? [X0] : strong(X0) => ? [X0] : (~wise(X0) & ~old(X0)) [input p1]
4. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (patient(X0) | happy(X0))) [input p3]
7. ! [X0] : ((~old(X0) <~> patient(X0)) <=> (happy(X0) & ~funny(X0))) [input p6]
8. ? [X0] : (wise(X0) <~> quiet(X0)) <=> ? [X0] : (wise(X0) <~> ~rich(X0)) [input p7]
16. ! [X0] : (~wise(X0) <=> rich(X0)) [input p15]
23. ~strong(alice) <~> generous(alice) [input p22]
25. generous(alice) [input hypothesis]
26. ? [X0] : strong(X0) => ? [X1] : (~wise(X1) & ~old(X1)) [rectify 2]
27. ? [X0] : (wise(X0) <~> quiet(X0)) <=> ? [X1] : (wise(X1) <~> ~rich(X1)) [rectify 8]
30. ? [X1] : (~wise(X1) & ~old(X1)) | ! [X0] : ~strong(X0) [ennf transformation 26]
37. ? [X0] : (~wise(X0) & ~old(X0)) | ! [X1] : ~strong(X1) [rectify 30]
38. ? [X0] : (~wise(X0) & ~old(X0)) => (~wise(sK0) & ~old(sK0)) [choice axiom]
39. (~wise(sK0) & ~old(sK0)) | ! [X1] : ~strong(X1) [skolemisation 37,38]
42. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~patient(X0) & ~happy(X0))) & ((patient(X0) | happy(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 4]
43. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~patient(X0) & ~happy(X0))) & (patient(X0) | happy(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 42]
47. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [flattening 47]
49. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (? [X1] : ((rich(X1) | ~wise(X1)) & (~rich(X1) | wise(X1))) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [nnf transformation 27]
50. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (? [X2] : ((rich(X2) | ~wise(X2)) & (~rich(X2) | wise(X2))) | ! [X3] : ((wise(X3) | ~quiet(X3)) & (quiet(X3) | ~wise(X3)))) [rectify 49]
51. ? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) => ((~quiet(sK1) | ~wise(sK1)) & (quiet(sK1) | wise(sK1))) [choice axiom]
52. ? [X2] : ((rich(X2) | ~wise(X2)) & (~rich(X2) | wise(X2))) => ((rich(sK2) | ~wise(sK2)) & (~rich(sK2) | wise(sK2))) [choice axiom]
53. (((~quiet(sK1) | ~wise(sK1)) & (quiet(sK1) | wise(sK1))) | ! [X1] : ((wise(X1) | rich(X1)) & (~rich(X1) | ~wise(X1)))) & (((rich(sK2) | ~wise(sK2)) & (~rich(sK2) | wise(sK2))) | ! [X3] : ((wise(X3) | ~quiet(X3)) & (quiet(X3) | ~wise(X3)))) [skolemisation 50,52,51]
69. ! [X0] : ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))) [nnf transformation 16]
72. (~generous(alice) | strong(alice)) & (generous(alice) | ~strong(alice)) [nnf transformation 23]
76. ~old(sK0) | ~strong(X1) [cnf transformation 39]
77. ~wise(sK0) | ~strong(X1) [cnf transformation 39]
85. ~rich(X0) | quiet(X0) | ~happy(X0) [cnf transformation 43]
86. ~rich(X0) | quiet(X0) | ~patient(X0) [cnf transformation 43]
98. happy(X0) | patient(X0) | old(X0) [cnf transformation 48]
103. ~rich(sK2) | wise(sK2) | wise(X3) | ~quiet(X3) [cnf transformation 53]
105. rich(sK2) | ~wise(sK2) | wise(X3) | ~quiet(X3) [cnf transformation 53]
129. rich(X0) | wise(X0) [cnf transformation 69]
130. ~wise(X0) | ~rich(X0) [cnf transformation 69]
139. ~generous(alice) | strong(alice) [cnf transformation 72]
141. generous(alice) [cnf transformation 25]
144. 1 <=> ! [X1] : ~strong(X1) [avatar definition]
145. ~strong(X1) <- (1) [avatar component clause 144]
147. 2 <=> wise(sK0) [avatar definition]
149. ~wise(sK0) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 77,147,144]
152. 3 <=> old(sK0) [avatar definition]
154. ~old(sK0) <- (~3) [avatar component clause 152]
155. 1 | ~3 [avatar split clause 76,152,144]
157. 4 <=> ! [X1] : (wise(X1) | rich(X1)) [avatar definition]
158. rich(X1) | wise(X1) <- (4) [avatar component clause 157]
169. 7 <=> ! [X1] : (~rich(X1) | ~wise(X1)) [avatar definition]
170. ~rich(X1) | ~wise(X1) <- (7) [avatar component clause 169]
175. 8 <=> ! [X3] : (wise(X3) | ~quiet(X3)) [avatar definition]
176. ~quiet(X3) | wise(X3) <- (8) [avatar component clause 175]
178. 9 <=> wise(sK2) [avatar definition]
179. wise(sK2) <- (9) [avatar component clause 178]
180. ~wise(sK2) <- (~9) [avatar component clause 178]
182. 10 <=> rich(sK2) [avatar definition]
183. ~rich(sK2) <- (~10) [avatar component clause 182]
184. rich(sK2) <- (10) [avatar component clause 182]
185. 8 | ~9 | 10 [avatar split clause 105,182,178,175]
190. 8 | 9 | ~10 [avatar split clause 103,182,178,175]
247. 7 [avatar split clause 130,169]
248. 4 [avatar split clause 129,157]
282. 31 <=> strong(alice) [avatar definition]
284. strong(alice) <- (31) [avatar component clause 282]
286. 32 <=> generous(alice) [avatar definition]
289. 31 | ~32 [avatar split clause 139,286,282]
300. 32 [avatar split clause 141,286]
301. wise(sK2) <- (4, ~10) [resolution 158,183]
302. $false <- (4, ~9, ~10) [subsumption resolution 301,180]
303. ~4 | 9 | 10 [avatar contradiction clause 302]
305. ~wise(sK2) <- (7, 10) [resolution 170,184]
306. $false <- (7, 9, 10) [subsumption resolution 305,179]
307. ~7 | ~9 | ~10 [avatar contradiction clause 306]
335. quiet(X0) | ~happy(X0) | wise(X0) <- (4) [resolution 85,158]
336. ~happy(X0) | wise(X0) <- (4, 8) [subsumption resolution 335,176]
337. quiet(X0) | ~patient(X0) | wise(X0) <- (4) [resolution 86,158]
338. ~patient(X0) | wise(X0) <- (4, 8) [subsumption resolution 337,176]
342. patient(X0) | old(X0) | wise(X0) <- (4, 8) [resolution 98,336]
346. wise(X0) | old(X0) <- (4, 8) [subsumption resolution 342,338]
501. old(sK0) <- (~2, 4, 8) [resolution 346,149]
504. $false <- (~2, ~3, 4, 8) [subsumption resolution 501,154]
505. 2 | 3 | ~4 | ~8 [avatar contradiction clause 504]
506. $false <- (1, 31) [resolution 145,284]
507. ~1 | ~31 [avatar contradiction clause 506]
508. $false [avatar sat refutation 150,155,185,190,247,248,289,300,303,307,505,507]
% SZS output end Proof for 2572305495433569285942250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or funny is strong and vice versa. If paul is either not old or brave then fred is either creative or happy. Everyone who is wise is not curious or quiet and vice versa. If paul is happy then someone is not humble. Everyone who is either happy or not rich is creative or not tall. If alice is happy then mary is not wise. Everyone who is rich or kind is either generous or not funny. If someone is both creative and not calm then alice is either strong or quiet. Everyone who is not calm is both old and not generous and vice versa. If someone is old or not happy then lucy is not kind and vice versa. Everyone who is not old is quiet or funny and vice versa. If lucy is either not curious or not old then someone is not wise or strong. If alice is old then someone is strong. Everyone who is not strong or not patient is creative or not quiet and vice versa. Everyone who is not humble or old is both tall and patient. Everyone who is both not generous and not patient is not patient or wise and vice versa. Someone is not funny. Someone is not funny or curious. Someone is either calm or happy. Someone is strong or not brave. Paul is not tall or rich. Lucy is not happy. Lucy is not brave. | Mary is not brave. | neutral | (![X]:((patient(X)<~>funny(X))<=>strong(X)))&
(((~old(paul)<~>brave(paul)))=>((creative(fred)<~>happy(fred))))&
(![X]:(wise(X)<=>(~curious(X)|quiet(X))))&
((happy(paul))=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>~rich(X))=>(creative(X)|~tall(X))))&
((happy(alice))=>(~wise(mary)))&
(![X]:((rich(X)|kind(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>((strong(alice)<~>quiet(alice))))&
(![X]:(~calm(X)<=>(old(X)&~generous(X))))&
((?[X]:((old(X)|~happy(X))))<=>(~kind(lucy)))&
(![X]:(~old(X)<=>(quiet(X)|funny(X))))&
(((~curious(lucy)<~>~old(lucy)))=>(?[X]:((~wise(X)|strong(X)))))&
((old(alice))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~patient(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~humble(X)|old(X))=>(tall(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((strong(X)|~brave(X))))&
((~tall(paul)|rich(paul)))&
(~happy(lucy))&
(~brave(lucy)) | ~brave(mary) | [] | null | 0 |
Everyone who is not old or not patient is both not old and not brave and vice versa. If someone is strong or not generous then fred is both not kind and calm and vice versa. Everyone who is brave or not happy is both kind and not calm. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. If someone is not funny then lucy is brave. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Susan is either not wise or rich. Someone is not tall. | John is not wise. | contradiction | (![X]:((~old(X)|~patient(X))<=>(~old(X)&~brave(X))))&
((?[X]:((strong(X)|~generous(X))))<=>((~kind(fred)&calm(fred))))&
(![X]:((brave(X)|~happy(X))=>(kind(X)&~calm(X))))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~tall(X))) | ~wise(john) | [
"p1",
"p4",
"p6",
"p7",
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5098546574123742992977144
% SZS output start Proof for 5098546574123742992977144
2. ? [X0] : (~generous(X0) | strong(X0)) <=> (calm(fred) & ~kind(fred)) [input p1]
5. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (calm(X0) & ~calm(X0))) [input p6]
8. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~rich(X0) [input p7]
9. ? [X0] : ~funny(X0) => brave(lucy) [input p8]
12. ? [X0] : (humble(X0) | ~creative(X0)) <=> (~strong(john) & quiet(john)) [input p11]
15. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (funny(X0) & ~wise(X0))) [input p14]
16. ? [X0] : (curious(X0) & humble(X0)) <=> ? [X0] : (humble(X0) <~> ~creative(X0)) [input p15]
22. ~wise(john) [input hypothesis]
23. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~rich(X1) [rectify 8]
24. ? [X0] : (curious(X0) & humble(X0)) <=> ? [X1] : (humble(X1) <~> ~creative(X1)) [rectify 16]
30. ? [X1] : ~rich(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 23]
31. brave(lucy) | ! [X0] : funny(X0) [ennf transformation 9]
38. (? [X0] : (~generous(X0) | strong(X0)) | (~calm(fred) | kind(fred))) & ((calm(fred) & ~kind(fred)) | ! [X0] : (generous(X0) & ~strong(X0))) [nnf transformation 2]
39. (? [X0] : (~generous(X0) | strong(X0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X0] : (generous(X0) & ~strong(X0))) [flattening 38]
40. (? [X0] : (~generous(X0) | strong(X0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X1] : (generous(X1) & ~strong(X1))) [rectify 39]
41. ? [X0] : (~generous(X0) | strong(X0)) => (~generous(sK0) | strong(sK0)) [choice axiom]
42. ((~generous(sK0) | strong(sK0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X1] : (generous(X1) & ~strong(X1))) [skolemisation 40,41]
43. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((~rich(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | rich(X0))) [nnf transformation 7]
46. ! [X0] : ((~rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | rich(X0))) [flattening 45]
47. ? [X0] : ~rich(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 30]
48. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
49. ~rich(sK1) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 47,48]
51. (? [X0] : (humble(X0) | ~creative(X0)) | (strong(john) | ~quiet(john))) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [nnf transformation 12]
52. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [flattening 51]
53. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (humble(X0) | ~creative(X0)) => (humble(sK2) | ~creative(sK2)) [choice axiom]
55. ((humble(sK2) | ~creative(sK2)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [skolemisation 53,54]
61. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 61]
63. (? [X0] : (curious(X0) & humble(X0)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (? [X1] : ((creative(X1) | ~humble(X1)) & (~creative(X1) | humble(X1))) | ! [X0] : (~curious(X0) | ~humble(X0))) [nnf transformation 24]
64. (? [X0] : (curious(X0) & humble(X0)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (? [X2] : ((creative(X2) | ~humble(X2)) & (~creative(X2) | humble(X2))) | ! [X3] : (~curious(X3) | ~humble(X3))) [rectify 63]
65. ? [X0] : (curious(X0) & humble(X0)) => (curious(sK4) & humble(sK4)) [choice axiom]
66. ? [X2] : ((creative(X2) | ~humble(X2)) & (~creative(X2) | humble(X2))) => ((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) [choice axiom]
67. ((curious(sK4) & humble(sK4)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) | ! [X3] : (~curious(X3) | ~humble(X3))) [skolemisation 64,66,65]
80. calm(fred) | ~strong(X1) [cnf transformation 42]
88. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 43]
90. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
95. calm(X0) | rich(X0) [cnf transformation 46]
97. ~rich(sK1) | ~humble(X1) [cnf transformation 49]
98. ~rich(sK1) | ~brave(X1) [cnf transformation 49]
99. brave(lucy) | funny(X0) [cnf transformation 31]
109. humble(sK2) | ~creative(sK2) | strong(john) | ~quiet(john) [cnf transformation 55]
121. calm(X0) | quiet(X0) | ~funny(X0) | wise(X0) [cnf transformation 62]
126. humble(sK4) | humble(X1) | creative(X1) [cnf transformation 67]
138. ~wise(john) [cnf transformation 22]
139. curious(X0) | ~calm(X0) [duplicate literal removal 88]
140. ~curious(X0) | ~calm(X0) [duplicate literal removal 90]
146. 2 <=> calm(fred) [avatar definition]
147. calm(fred) <- (2) [avatar component clause 146]
163. 6 <=> ! [X1] : ~strong(X1) [avatar definition]
164. ~strong(X1) <- (6) [avatar component clause 163]
165. 6 | 2 [avatar split clause 80,146,163]
168. ~calm(X0) [subsumption resolution 139,140]
169. rich(X0) [subsumption resolution 95,168]
170. ~brave(X1) [subsumption resolution 98,169]
171. ~humble(X1) [subsumption resolution 97,169]
172. funny(X0) [subsumption resolution 99,170]
175. ~creative(sK2) | strong(john) | ~quiet(john) [subsumption resolution 109,171]
177. 7 <=> quiet(john) [avatar definition]
179. ~quiet(john) <- (~7) [avatar component clause 177]
181. 8 <=> strong(john) [avatar definition]
183. strong(john) <- (8) [avatar component clause 181]
185. 9 <=> creative(sK2) [avatar definition]
187. ~creative(sK2) <- (~9) [avatar component clause 185]
188. ~7 | 8 | ~9 [avatar split clause 175,185,181,177]
190. 10 <=> ! [X1] : creative(X1) [avatar definition]
191. creative(X1) <- (10) [avatar component clause 190]
231. quiet(X0) | ~funny(X0) | wise(X0) [subsumption resolution 121,168]
232. quiet(X0) | wise(X0) [subsumption resolution 231,172]
240. humble(X1) | creative(X1) [subsumption resolution 126,171]
241. creative(X1) [subsumption resolution 240,171]
242. 10 [avatar split clause 241,190]
255. $false <- (2) [subsumption resolution 147,168]
256. ~2 [avatar contradiction clause 255]
265. wise(john) <- (~7) [resolution 232,179]
266. $false <- (~7) [subsumption resolution 265,138]
267. 7 [avatar contradiction clause 266]
268. $false <- (~9, 10) [subsumption resolution 187,191]
269. 9 | ~10 [avatar contradiction clause 268]
270. $false <- (6, 8) [subsumption resolution 183,164]
271. ~6 | ~8 [avatar contradiction clause 270]
272. $false [avatar sat refutation 165,188,242,256,267,269,271]
% SZS output end Proof for 5098546574123742992977144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or wise is both not old and not wise.
Everyone who is not happy or not humble is quiet.
If someone is both not funny and not curious then someone is both kind and not generous and vice versa.
Everyone who is not rich or not funny is both not happy and not old and vice versa.
If someone is either not brave or not curious then paul is either not creative or tall.
If someone is either not calm or not old then susan is old.
Everyone who is either not happy or rich is both not happy and not humble.
If someone is both not calm and curious then someone is not calm or not quiet.
Everyone who is either wise or not tall is not calm and vice versa.
If alice is generous then someone is both not rich and creative and vice versa.
Everyone who is patient or wise is both not tall and not creative and vice versa.
Everyone who is either humble or quiet is calm or not strong.
If fred is not brave then someone is either calm or rich.
If someone is both rich and not curious then john is either not humble or not old and vice versa.
If john is funny or not humble then someone is both not old and strong.
Everyone who is wise is not strong and vice versa.
Someone is either creative or not strong.
Someone is both generous and not tall.
Someone is not funny or creative.
John is funny or quiet.
Someone is not generous.
Someone is either calm or humble. | Paul is quiet. | entailment | (![X]:((~old(X)|wise(X))=>(~old(X)&~wise(X))))&
(![X]:((~happy(X)|~humble(X))=>quiet(X)))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((~rich(X)|~funny(X))<=>(~happy(X)&~old(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>((~creative(paul)<~>tall(paul))))&
((?[X]:((~calm(X)<~>~old(X))))=>(old(susan)))&
(![X]:((~happy(X)<~>rich(X))=>(~happy(X)&~humble(X))))&
((?[X]:((~calm(X)&curious(X))))=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:((wise(X)<~>~tall(X))<=>~calm(X)))&
((generous(alice))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((patient(X)|wise(X))<=>(~tall(X)&~creative(X))))&
(![X]:((humble(X)<~>quiet(X))=>(calm(X)|~strong(X))))&
((~brave(fred))=>(?[X]:((calm(X)<~>rich(X)))))&
((?[X]:((rich(X)&~curious(X))))<=>((~humble(john)<~>~old(john))))&
(((funny(john)|~humble(john)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(wise(X)<=>~strong(X)))&
(?[X]:((creative(X)<~>~strong(X))))&
(?[X]:((generous(X)&~tall(X))))&
(?[X]:((~funny(X)|creative(X))))&
((funny(john)|quiet(john)))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)<~>humble(X)))) | quiet(paul) | [
"p1",
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6827045214386024635220769
% SZS output start Proof for 6827045214386024635220769
2. ! [X0] : ((~humble(X0) | ~happy(X0)) => quiet(X0)) [input p1]
4. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (~old(X0) & ~happy(X0))) [input p3]
7. ! [X0] : ((~happy(X0) <~> rich(X0)) => (~humble(X0) & ~happy(X0))) [input p6]
23. ~quiet(paul) [input hypothesis]
27. ! [X0] : (quiet(X0) | (humble(X0) & happy(X0))) [ennf transformation 2]
30. ! [X0] : ((~humble(X0) & ~happy(X0)) | (~happy(X0) <=> rich(X0))) [ennf transformation 7]
41. ! [X0] : (((~funny(X0) | ~rich(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (funny(X0) & rich(X0)))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | ~rich(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | (funny(X0) & rich(X0)))) [flattening 41]
45. ! [X0] : ((~humble(X0) & ~happy(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) [nnf transformation 30]
83. quiet(X0) | happy(X0) [cnf transformation 27]
89. ~happy(X0) | rich(X0) [cnf transformation 42]
101. ~happy(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 45]
142. ~quiet(paul) [cnf transformation 23]
143. ~happy(X0) | ~rich(X0) [duplicate literal removal 101]
203. ~happy(X0) [subsumption resolution 143,89]
320. happy(paul) [resolution 83,142]
321. $false [subsumption resolution 320,203]
% SZS output end Proof for 6827045214386024635220769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not happy is not humble or tall and vice versa.
If alice is strong then alice is humble and vice versa.
Everyone who is both wise and creative is patient and vice versa.
If someone is kind or not tall then fred is both not patient and quiet.
Everyone who is both creative and strong is either not calm or not strong and vice versa.
If susan is either brave or calm then someone is not humble.
Everyone who is not tall or strong is both quiet and not strong and vice versa.
If john is both not rich and not quiet then alice is calm.
If someone is both curious and patient then alice is either not humble or old and vice versa.
If someone is either not happy or not funny then someone is brave or not quiet.
If someone is both not generous and not happy then mary is both not old and not happy and vice versa.
Everyone who is both funny and not brave is funny and vice versa.
If john is not curious or quiet then someone is not tall or brave.
Everyone who is both curious and not kind is either curious or not humble.
If someone is both not creative and happy then fred is either generous or not curious and vice versa.
Someone is either not brave or not strong.
Alice is either not humble or not quiet.
Someone is either not rich or not patient.
Susan is either tall or not brave.
John is not wise. | Mary is not curious. | neutral | (![X]:((~old(X)&~happy(X))<=>(~humble(X)|tall(X))))&
((strong(alice))<=>(humble(alice)))&
(![X]:((wise(X)&creative(X))<=>patient(X)))&
((?[X]:((kind(X)|~tall(X))))=>((~patient(fred)&quiet(fred))))&
(![X]:((creative(X)&strong(X))<=>(~calm(X)<~>~strong(X))))&
(((brave(susan)<~>calm(susan)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)|strong(X))<=>(quiet(X)&~strong(X))))&
(((~rich(john)&~quiet(john)))=>(calm(alice)))&
((?[X]:((curious(X)&patient(X))))<=>((~humble(alice)<~>old(alice))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((brave(X)|~quiet(X)))))&
((?[X]:((~generous(X)&~happy(X))))<=>((~old(mary)&~happy(mary))))&
(![X]:((funny(X)&~brave(X))<=>funny(X)))&
(((~curious(john)|quiet(john)))=>(?[X]:((~tall(X)|brave(X)))))&
(![X]:((curious(X)&~kind(X))=>(curious(X)<~>~humble(X))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(?[X]:((~brave(X)<~>~strong(X))))&
((~humble(alice)<~>~quiet(alice)))&
(?[X]:((~rich(X)<~>~patient(X))))&
((tall(susan)<~>~brave(susan)))&
(~wise(john)) | ~curious(mary) | [] | null | 0 |
Everyone who is either wise or not kind is not brave and vice versa. Everyone who is either not funny or not calm is both generous and not kind and vice versa. If someone is not patient then someone is both not quiet and calm and vice versa. If someone is either not happy or not old then paul is both kind and not curious and vice versa. If someone is either calm or not brave then someone is either kind or not calm and vice versa. If someone is kind then lucy is not rich or not brave. If susan is both creative and not kind then someone is funny or not old and vice versa. Everyone who is either not quiet or not rich is either not funny or brave and vice versa. Everyone who is kind or happy is wise and vice versa. Everyone who is either wise or not kind is not generous and vice versa. Everyone who is both not funny and funny is not rich and vice versa. If someone is either funny or not calm then mary is either not patient or not rich and vice versa. Everyone who is patient or kind is wise or not curious and vice versa. Everyone who is quiet or not creative is not humble. Everyone who is brave is both not humble and curious and vice versa. Everyone who is both not strong and creative is either old or quiet and vice versa. Someone is both generous and brave. Someone is calm. Alice is either brave or not wise. Paul is happy. Someone is not funny. | Lucy is curious. | entailment | (![X]:((wise(X)<~>~kind(X))<=>~brave(X)))&
(![X]:((~funny(X)<~>~calm(X))<=>(generous(X)&~kind(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((~happy(X)<~>~old(X))))<=>((kind(paul)&~curious(paul))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((kind(X)<~>~calm(X)))))&
((?[X]:(kind(X)))=>((~rich(lucy)|~brave(lucy))))&
(((creative(susan)&~kind(susan)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((~quiet(X)<~>~rich(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((kind(X)|happy(X))<=>wise(X)))&
(![X]:((wise(X)<~>~kind(X))<=>~generous(X)))&
(![X]:((~funny(X)&funny(X))<=>~rich(X)))&
((?[X]:((funny(X)<~>~calm(X))))<=>((~patient(mary)<~>~rich(mary))))&
(![X]:((patient(X)|kind(X))<=>(wise(X)|~curious(X))))&
(![X]:((quiet(X)|~creative(X))=>~humble(X)))&
(![X]:(brave(X)<=>(~humble(X)&curious(X))))&
(![X]:((~strong(X)&creative(X))<=>(old(X)<~>quiet(X))))&
(?[X]:((generous(X)&brave(X))))&
(?[X]:(calm(X)))&
((brave(alice)<~>~wise(alice)))&
(happy(paul))&
(?[X]:(~funny(X))) | curious(lucy) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6393949093341611483685689
% SZS output start Proof for 6393949093341611483685689
1. ! [X0] : ((wise(X0) <~> ~kind(X0)) <=> ~brave(X0)) [input p0]
2. ! [X0] : ((~funny(X0) <~> ~calm(X0)) <=> (~kind(X0) & generous(X0))) [input p1]
3. ? [X0] : ~patient(X0) <=> ? [X0] : (calm(X0) & ~quiet(X0)) [input p2]
8. ! [X0] : ((~quiet(X0) <~> ~rich(X0)) <=> (~funny(X0) <~> brave(X0))) [input p7]
9. ! [X0] : ((happy(X0) | kind(X0)) <=> wise(X0)) [input p8]
10. ! [X0] : ((wise(X0) <~> ~kind(X0)) <=> ~generous(X0)) [input p9]
11. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~rich(X0)) [input p10]
12. ? [X0] : (funny(X0) <~> ~calm(X0)) <=> (~patient(mary) <~> ~rich(mary)) [input p11]
15. ! [X0] : (brave(X0) <=> (curious(X0) & ~humble(X0))) [input p14]
22. ~curious(lucy) [input hypothesis]
23. ? [X0] : ~patient(X0) <=> ? [X1] : (calm(X1) & ~quiet(X1)) [rectify 3]
28. ! [X0] : ((((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | brave(X0)) & (~brave(X0) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0))))) [nnf transformation 1]
29. ! [X0] : ((((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))))) [nnf transformation 2]
30. ! [X0] : ((((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))))) [flattening 29]
31. (? [X0] : ~patient(X0) | ! [X1] : (~calm(X1) | quiet(X1))) & (? [X1] : (calm(X1) & ~quiet(X1)) | ! [X0] : patient(X0)) [nnf transformation 23]
32. (? [X0] : ~patient(X0) | ! [X1] : (~calm(X1) | quiet(X1))) & (? [X2] : (calm(X2) & ~quiet(X2)) | ! [X3] : patient(X3)) [rectify 31]
33. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
34. ? [X2] : (calm(X2) & ~quiet(X2)) => (calm(sK1) & ~quiet(sK1)) [choice axiom]
35. (~patient(sK0) | ! [X1] : (~calm(X1) | quiet(X1))) & ((calm(sK1) & ~quiet(sK1)) | ! [X3] : patient(X3)) [skolemisation 32,34,33]
51. ! [X0] : ((((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0))))) [nnf transformation 8]
52. ! [X0] : (((happy(X0) | kind(X0)) | ~wise(X0)) & (wise(X0) | (~happy(X0) & ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : ((happy(X0) | kind(X0) | ~wise(X0)) & (wise(X0) | (~happy(X0) & ~kind(X0)))) [flattening 52]
54. ! [X0] : ((((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | generous(X0)) & (~generous(X0) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0))))) [nnf transformation 10]
55. ! [X0] : (((funny(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 11]
56. ! [X0] : (((funny(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | ~funny(X0) | funny(X0))) [flattening 55]
57. (? [X0] : ((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ((~patient(mary) | rich(mary)) & (~rich(mary) | patient(mary)))) & (((rich(mary) | patient(mary)) & (~rich(mary) | ~patient(mary))) | ! [X0] : ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) [nnf transformation 12]
58. (? [X0] : ((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ((~patient(mary) | rich(mary)) & (~rich(mary) | patient(mary)))) & (((rich(mary) | patient(mary)) & (~rich(mary) | ~patient(mary))) | ! [X1] : ((funny(X1) | calm(X1)) & (~calm(X1) | ~funny(X1)))) [rectify 57]
59. ? [X0] : ((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) => ((calm(sK6) | ~funny(sK6)) & (~calm(sK6) | funny(sK6))) [choice axiom]
60. (((calm(sK6) | ~funny(sK6)) & (~calm(sK6) | funny(sK6))) | ((~patient(mary) | rich(mary)) & (~rich(mary) | patient(mary)))) & (((rich(mary) | patient(mary)) & (~rich(mary) | ~patient(mary))) | ! [X1] : ((funny(X1) | calm(X1)) & (~calm(X1) | ~funny(X1)))) [skolemisation 58,59]
63. ! [X0] : ((brave(X0) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | ~brave(X0))) [nnf transformation 15]
64. ! [X0] : ((brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | ~brave(X0))) [flattening 63]
74. ~brave(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 28]
75. ~brave(X0) | wise(X0) | kind(X0) [cnf transformation 28]
77. ~wise(X0) | kind(X0) | brave(X0) [cnf transformation 28]
78. ~calm(X0) | generous(X0) | funny(X0) [cnf transformation 30]
79. ~funny(X0) | generous(X0) | calm(X0) [cnf transformation 30]
80. ~calm(X0) | ~kind(X0) | funny(X0) [cnf transformation 30]
81. ~funny(X0) | ~kind(X0) | calm(X0) [cnf transformation 30]
82. ~generous(X0) | ~funny(X0) | kind(X0) | ~calm(X0) [cnf transformation 30]
84. ~quiet(sK1) | patient(X3) [cnf transformation 35]
85. calm(sK1) | patient(X3) [cnf transformation 35]
107. ~rich(X0) | ~funny(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
109. ~rich(X0) | funny(X0) | ~brave(X0) | quiet(X0) [cnf transformation 51]
115. ~kind(X0) | wise(X0) [cnf transformation 53]
119. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 54]
121. ~wise(X0) | kind(X0) | generous(X0) [cnf transformation 54]
123. ~funny(X0) | rich(X0) [cnf transformation 56]
124. rich(X0) | funny(X0) [cnf transformation 56]
125. ~rich(mary) | ~patient(mary) | ~calm(X1) | ~funny(X1) [cnf transformation 60]
126. ~rich(mary) | ~patient(mary) | funny(X1) | calm(X1) [cnf transformation 60]
140. ~brave(X0) | curious(X0) [cnf transformation 64]
155. ~curious(lucy) [cnf transformation 22]
165. 3 <=> ! [X3] : patient(X3) [avatar definition]
166. patient(X3) <- (3) [avatar component clause 165]
168. 4 <=> calm(sK1) [avatar definition]
170. calm(sK1) <- (4) [avatar component clause 168]
171. 3 | 4 [avatar split clause 85,168,165]
173. 5 <=> quiet(sK1) [avatar definition]
175. ~quiet(sK1) <- (~5) [avatar component clause 173]
176. 3 | ~5 [avatar split clause 84,173,165]
249. 22 <=> brave(lucy) [avatar definition]
250. brave(lucy) <- (22) [avatar component clause 249]
251. ~brave(lucy) <- (~22) [avatar component clause 249]
280. ~generous(X0) | wise(X0) [subsumption resolution 119,115]
282. rich(X0) [subsumption resolution 123,124]
285. 29 <=> patient(mary) [avatar definition]
286. ~patient(mary) <- (~29) [avatar component clause 285]
299. ~patient(mary) | funny(X1) | calm(X1) [subsumption resolution 126,282]
301. 32 <=> ! [X1] : (funny(X1) | calm(X1)) [avatar definition]
302. calm(X1) | funny(X1) <- (32) [avatar component clause 301]
303. 32 | ~29 [avatar split clause 299,285,301]
304. ~patient(mary) | ~calm(X1) | ~funny(X1) [subsumption resolution 125,282]
306. 33 <=> ! [X1] : (~calm(X1) | ~funny(X1)) [avatar definition]
307. ~calm(X1) | ~funny(X1) <- (33) [avatar component clause 306]
308. 33 | ~29 [avatar split clause 304,285,306]
325. $false <- (3, ~29) [resolution 286,166]
326. ~3 | 29 [avatar contradiction clause 325]
414. 36 <=> kind(lucy) [avatar definition]
415. ~kind(lucy) <- (~36) [avatar component clause 414]
416. kind(lucy) <- (36) [avatar component clause 414]
424. ~kind(sK1) | funny(sK1) <- (4) [resolution 170,80]
425. generous(sK1) | funny(sK1) <- (4) [resolution 170,78]
429. 38 <=> funny(sK1) [avatar definition]
430. ~funny(sK1) <- (~38) [avatar component clause 429]
431. funny(sK1) <- (38) [avatar component clause 429]
433. 39 <=> kind(sK1) [avatar definition]
435. ~kind(sK1) <- (~39) [avatar component clause 433]
436. 38 | ~39 | ~4 [avatar split clause 424,168,433,429]
438. 40 <=> generous(sK1) [avatar definition]
440. generous(sK1) <- (40) [avatar component clause 438]
441. 38 | 40 | ~4 [avatar split clause 425,168,438,429]
474. funny(X0) | ~kind(X0) | funny(X0) <- (32) [resolution 302,80]
475. funny(X1) | generous(X1) | funny(X1) <- (32) [resolution 302,78]
480. generous(X1) | funny(X1) <- (32) [duplicate literal removal 475]
481. ~kind(X0) | funny(X0) <- (32) [duplicate literal removal 474]
525. ~funny(X1) | brave(X1) | quiet(X1) [resolution 107,282]
534. funny(X0) | ~brave(X0) | quiet(X0) | funny(X0) [resolution 109,124]
536. ~brave(X0) | funny(X0) | quiet(X0) [duplicate literal removal 534]
585. funny(X3) | wise(X3) <- (32) [resolution 480,280]
592. funny(lucy) <- (32, 36) [resolution 481,416]
593. brave(sK1) | quiet(sK1) <- (38) [resolution 525,431]
596. brave(sK1) <- (~5, 38) [subsumption resolution 593,175]
666. ~kind(lucy) | calm(lucy) <- (32, 36) [resolution 592,81]
669. calm(lucy) <- (32, 36) [subsumption resolution 666,416]
674. wise(sK1) | kind(sK1) <- (~5, 38) [resolution 596,75]
675. ~kind(sK1) | ~wise(sK1) <- (~5, 38) [resolution 596,74]
677. wise(sK1) <- (~5, 38) [subsumption resolution 674,115]
678. ~kind(sK1) <- (~5, 38) [subsumption resolution 675,677]
679. ~39 | 5 | ~38 [avatar split clause 678,429,173,433]
752. wise(X3) | generous(X3) | calm(X3) <- (32) [resolution 585,79]
757. calm(X3) | wise(X3) <- (32) [subsumption resolution 752,280]
852. kind(sK1) | generous(sK1) <- (~5, 38) [resolution 677,121]
856. generous(sK1) <- (~5, 38, ~39) [subsumption resolution 852,435]
857. 40 | 5 | ~38 | 39 [avatar split clause 856,433,429,173,438]
860. ~funny(sK1) | kind(sK1) | ~calm(sK1) <- (40) [resolution 440,82]
862. wise(sK1) <- (40) [resolution 440,280]
909. ~funny(lucy) <- (32, 33, 36) [resolution 307,669]
916. $false <- (32, 33, 36) [subsumption resolution 909,592]
917. ~32 | ~33 | ~36 [avatar contradiction clause 916]
1284. wise(X0) | ~funny(X0) <- (32, 33) [resolution 757,307]
1290. wise(X0) <- (32, 33) [subsumption resolution 1284,585]
1383. brave(X3) | kind(X3) <- (32, 33) [resolution 1290,77]
1440. kind(lucy) <- (~22, 32, 33) [resolution 1383,251]
1442. $false <- (~22, 32, 33, ~36) [subsumption resolution 1440,415]
1443. 22 | ~32 | ~33 | 36 [avatar contradiction clause 1442]
1454. curious(lucy) <- (22) [resolution 250,140]
1455. $false <- (22) [subsumption resolution 1454,155]
1456. ~22 [avatar contradiction clause 1455]
1501. 99 <=> wise(sK1) [avatar definition]
1503. wise(sK1) <- (99) [avatar component clause 1501]
1505. 100 <=> brave(sK1) [avatar definition]
1507. brave(sK1) <- (100) [avatar component clause 1505]
1509. 99 | ~40 [avatar split clause 862,438,1501]
1510. ~funny(sK1) | ~calm(sK1) <- (~39, 40) [subsumption resolution 860,435]
1511. ~4 | ~38 | 39 | ~40 [avatar split clause 1510,438,433,429,168]
1633. kind(sK1) | brave(sK1) <- (99) [resolution 1503,77]
1636. brave(sK1) <- (~39, 99) [subsumption resolution 1633,435]
1637. 100 | 39 | ~99 [avatar split clause 1636,1501,433,1505]
1638. funny(sK1) | quiet(sK1) <- (100) [resolution 1507,536]
1642. quiet(sK1) <- (~38, 100) [subsumption resolution 1638,430]
1643. $false <- (~5, ~38, 100) [subsumption resolution 1642,175]
1644. 5 | 38 | ~100 [avatar contradiction clause 1643]
1645. $false [avatar sat refutation 171,176,303,308,326,436,441,679,857,917,1443,1456,1509,1511,1637,1644]
% SZS output end Proof for 6393949093341611483685689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5756
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not generous is either not humble or quiet and vice versa. Everyone who is wise or not kind is wise. If susan is both not calm and not humble then someone is not quiet or wise and vice versa. If someone is both not curious and quiet then susan is strong. If paul is old or patient then someone is not funny or brave and vice versa. Everyone who is both not happy and patient is not rich or rich and vice versa. Everyone who is both not happy and not brave is either not kind or patient. Everyone who is patient is both not funny and not kind. Everyone who is creative is either brave or not creative. If fred is either not wise or not strong then someone is either not curious or kind and vice versa. If someone is kind then someone is old or creative and vice versa. If someone is quiet then john is either kind or not brave. Everyone who is both brave and wise is not humble or not quiet. Someone is not tall or not brave. Fred is curious or not old. Someone is either not creative or not tall. Lucy is either not creative or not tall. Fred is both not strong and not happy. | Paul is kind. | contradiction | (![X]:((~creative(X)&~generous(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:((wise(X)|~kind(X))=>wise(X)))&
(((~calm(susan)&~humble(susan)))<=>(?[X]:((~quiet(X)|wise(X)))))&
((?[X]:((~curious(X)&quiet(X))))=>(strong(susan)))&
(((old(paul)|patient(paul)))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~happy(X)&patient(X))<=>(~rich(X)|rich(X))))&
(![X]:((~happy(X)&~brave(X))=>(~kind(X)<~>patient(X))))&
(![X]:(patient(X)=>(~funny(X)&~kind(X))))&
(![X]:(creative(X)=>(brave(X)<~>~creative(X))))&
(((~wise(fred)<~>~strong(fred)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((old(X)|creative(X)))))&
((?[X]:(quiet(X)))=>((kind(john)<~>~brave(john))))&
(![X]:((brave(X)&wise(X))=>(~humble(X)|~quiet(X))))&
(?[X]:((~tall(X)|~brave(X))))&
((curious(fred)|~old(fred)))&
(?[X]:((~creative(X)<~>~tall(X))))&
((~creative(lucy)<~>~tall(lucy)))&
((~strong(fred)&~happy(fred))) | kind(paul) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1406104697730832273926983
% SZS output start Proof for 1406104697730832273926983
6. ! [X0] : ((patient(X0) & ~happy(X0)) <=> (rich(X0) | ~rich(X0))) [input p5]
8. ! [X0] : (patient(X0) => (~kind(X0) & ~funny(X0))) [input p7]
19. kind(paul) [input hypothesis]
25. ! [X0] : ((~kind(X0) & ~funny(X0)) | ~patient(X0)) [ennf transformation 8]
42. ! [X0] : (((patient(X0) & ~happy(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (~patient(X0) | happy(X0)))) [nnf transformation 6]
43. ! [X0] : (((patient(X0) & ~happy(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | ~patient(X0) | happy(X0))) [flattening 42]
83. patient(X0) | rich(X0) [cnf transformation 43]
84. patient(X0) | ~rich(X0) [cnf transformation 43]
88. ~kind(X0) | ~patient(X0) [cnf transformation 25]
113. kind(paul) [cnf transformation 19]
176. patient(X0) [subsumption resolution 83,84]
180. ~kind(X0) [subsumption resolution 88,176]
228. $false [subsumption resolution 113,180]
% SZS output end Proof for 1406104697730832273926983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not strong and not rich then susan is funny or not patient and vice versa.
Everyone who is humble or happy is funny or happy.
Everyone who is either quiet or calm is tall or not quiet and vice versa.
If alice is either not quiet or curious then someone is either not wise or funny and vice versa.
If fred is tall then fred is both brave and strong.
Everyone who is wise or not tall is kind and vice versa.
Everyone who is rich is either strong or old and vice versa.
Everyone who is kind or generous is both humble and wise.
Everyone who is either not funny or not brave is either not old or not rich and vice versa.
Everyone who is humble is both not kind and creative and vice versa.
Everyone who is either not happy or rich is either not generous or quiet and vice versa.
Everyone who is not patient or humble is both not kind and brave and vice versa.
If alice is kind or humble then someone is both not humble and brave.
Everyone who is both strong and calm is either not curious or rich and vice versa.
Everyone who is both strong and brave is brave and vice versa.
If someone is either not wise or strong then someone is not calm and vice versa.
Someone is both strong and curious.
Paul is calm or kind.
Mary is not curious or old.
John is patient or quiet.
Someone is tall or not calm.
Someone is not generous or not funny.
Someone is both old and not kind.
John is both not patient and quiet. | Susan is kind. | contradiction | (((~strong(john)&~rich(john)))<=>((funny(susan)|~patient(susan))))&
(![X]:((humble(X)|happy(X))=>(funny(X)|happy(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(tall(X)|~quiet(X))))&
(((~quiet(alice)<~>curious(alice)))<=>(?[X]:((~wise(X)<~>funny(X)))))&
((tall(fred))=>((brave(fred)&strong(fred))))&
(![X]:((wise(X)|~tall(X))<=>kind(X)))&
(![X]:(rich(X)<=>(strong(X)<~>old(X))))&
(![X]:((kind(X)|generous(X))=>(humble(X)&wise(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(~kind(X)&creative(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|humble(X))<=>(~kind(X)&brave(X))))&
(((kind(alice)|humble(alice)))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((strong(X)&calm(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
(?[X]:((strong(X)&curious(X))))&
((calm(paul)|kind(paul)))&
((~curious(mary)|old(mary)))&
((patient(john)|quiet(john)))&
(?[X]:((tall(X)|~calm(X))))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((old(X)&~kind(X))))&
((~patient(john)&quiet(john))) | kind(susan) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2977820791954163749724809
% SZS output start Proof for 2977820791954163749724809
8. ! [X0] : ((generous(X0) | kind(X0)) => (wise(X0) & humble(X0))) [input p7]
10. ! [X0] : (humble(X0) <=> (creative(X0) & ~kind(X0))) [input p9]
25. kind(susan) [input hypothesis]
30. ! [X0] : ((wise(X0) & humble(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 8]
44. ! [X0] : ((humble(X0) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | ~humble(X0))) [nnf transformation 10]
45. ! [X0] : ((humble(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | ~humble(X0))) [flattening 44]
98. humble(X0) | ~kind(X0) [cnf transformation 30]
110. ~kind(X0) | ~humble(X0) [cnf transformation 45]
154. kind(susan) [cnf transformation 25]
224. ~kind(X0) [subsumption resolution 110,98]
296. $false [subsumption resolution 154,224]
% SZS output end Proof for 2977820791954163749724809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or curious then susan is both strong and not strong and vice versa.
Everyone who is not generous is not wise.
Everyone who is both not rich and tall is not generous.
Everyone who is either not funny or rich is patient.
Everyone who is both kind and not generous is either not calm or rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is creative is either rich or not quiet and vice versa.
If someone is kind or not happy then someone is both not generous and not humble and vice versa.
Everyone who is either generous or strong is both not wise and not brave and vice versa.
Everyone who is both curious and not wise is not generous and vice versa.
Everyone who is both generous and not brave is both not wise and not humble and vice versa.
Everyone who is patient or curious is either kind or not kind and vice versa.
Everyone who is calm is not happy and vice versa.
Someone is either calm or happy.
Someone is tall or kind.
Alice is brave.
Someone is either not creative or not wise.
Someone is patient or not humble.
Alice is calm or not old. | Alice is patient. | contradiction | ((?[X]:((strong(X)<~>curious(X))))<=>((strong(susan)&~strong(susan))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(![X]:((generous(X)&~brave(X))<=>(~wise(X)&~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(kind(X)<~>~kind(X))))&
(![X]:(calm(X)<=>~happy(X)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((tall(X)|kind(X))))&
(brave(alice))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((patient(X)|~humble(X))))&
((calm(alice)|~old(alice))) | patient(alice) | [
"p0",
"p5",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1345397497284959218877538
% SZS output start Proof for 1345397497284959218877538
1. ? [X0] : (strong(X0) <~> curious(X0)) <=> (~strong(susan) & strong(susan)) [input p0]
6. ! [X0] : (~generous(X0) <=> patient(X0)) [input p5]
9. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p8]
10. ! [X0] : ((~wise(X0) & curious(X0)) <=> ~generous(X0)) [input p9]
16. brave(alice) [input p15]
20. patient(alice) [input hypothesis]
27. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (strong(susan) | ~strong(susan))) & ((~strong(susan) & strong(susan)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) [nnf transformation 1]
28. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) [flattening 27]
29. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X1] : ((strong(X1) | ~curious(X1)) & (curious(X1) | ~strong(X1)))) [rectify 28]
30. ? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) => ((~curious(sK0) | ~strong(sK0)) & (curious(sK0) | strong(sK0))) [choice axiom]
31. (((~curious(sK0) | ~strong(sK0)) & (curious(sK0) | strong(sK0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X1] : ((strong(X1) | ~curious(X1)) & (curious(X1) | ~strong(X1)))) [skolemisation 29,30]
35. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 6]
42. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 9]
43. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 42]
44. ! [X0] : (((~wise(X0) & curious(X0)) | generous(X0)) & (~generous(X0) | (wise(X0) | ~curious(X0)))) [nnf transformation 10]
45. ! [X0] : (((~wise(X0) & curious(X0)) | generous(X0)) & (~generous(X0) | wise(X0) | ~curious(X0))) [flattening 44]
62. strong(susan) | strong(X1) | ~curious(X1) [cnf transformation 31]
64. ~strong(susan) | strong(X1) | ~curious(X1) [cnf transformation 31]
78. ~patient(X0) | ~generous(X0) [cnf transformation 35]
91. ~brave(X0) | generous(X0) | ~strong(X0) [cnf transformation 43]
95. generous(X0) | curious(X0) [cnf transformation 45]
112. brave(alice) [cnf transformation 16]
116. patient(alice) [cnf transformation 20]
120. 1 <=> ! [X1] : (strong(X1) | ~curious(X1)) [avatar definition]
121. ~curious(X1) | strong(X1) <- (1) [avatar component clause 120]
123. 2 <=> strong(susan) [avatar definition]
126. 1 | ~2 [avatar split clause 64,123,120]
131. 1 | 2 [avatar split clause 62,123,120]
197. ~generous(alice) [resolution 78,116]
200. curious(alice) [resolution 197,95]
203. strong(alice) <- (1) [resolution 121,200]
245. generous(alice) | ~strong(alice) [resolution 91,112]
246. ~strong(alice) [subsumption resolution 245,197]
247. $false <- (1) [subsumption resolution 246,203]
248. ~1 [avatar contradiction clause 247]
249. $false [avatar sat refutation 126,131,248]
% SZS output end Proof for 1345397497284959218877538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is calm or kind then paul is creative and vice versa.
If someone is both old and not happy then john is not rich or not patient.
Everyone who is creative is curious and vice versa.
If someone is generous or not patient then paul is either not curious or not creative.
Everyone who is brave or not patient is not brave or brave.
Everyone who is both brave and humble is not calm and vice versa.
If someone is not humble or humble then mary is either not rich or not happy.
Everyone who is both not patient and funny is both calm and not kind and vice versa.
If alice is both not kind and not wise then mary is either not quiet or humble and vice versa.
Everyone who is not humble is not generous.
If paul is strong or curious then someone is not kind.
If john is both generous and not generous then someone is tall or not funny.
If someone is not quiet then fred is funny and vice versa.
If someone is not tall then someone is not curious.
Everyone who is not quiet is either wise or brave and vice versa.
Everyone who is both not kind and funny is happy or not curious and vice versa.
Someone is not curious or not happy.
Someone is either funny or not curious.
Paul is both not creative and not tall.
Someone is humble.
Mary is wise or tall.
Alice is both not happy and old.
John is not old or not curious. | Paul is brave. | entailment | (((calm(paul)|kind(paul)))<=>(creative(paul)))&
((?[X]:((old(X)&~happy(X))))=>((~rich(john)|~patient(john))))&
(![X]:(creative(X)<=>curious(X)))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(((strong(paul)|curious(paul)))=>(?[X]:(~kind(X))))&
(((generous(john)&~generous(john)))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(~quiet(X)))<=>(funny(fred)))&
((?[X]:(~tall(X)))=>(?[X]:(~curious(X))))&
(![X]:(~quiet(X)<=>(wise(X)<~>brave(X))))&
(![X]:((~kind(X)&funny(X))<=>(happy(X)|~curious(X))))&
(?[X]:((~curious(X)|~happy(X))))&
(?[X]:((funny(X)<~>~curious(X))))&
((~creative(paul)&~tall(paul)))&
(?[X]:(humble(X)))&
((wise(mary)|tall(mary)))&
((~happy(alice)&old(alice)))&
((~old(john)|~curious(john))) | brave(paul) | [
"p0",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1665915785207068765572103
% SZS output start Proof for 1665915785207068765572103
1. (kind(paul) | calm(paul)) <=> creative(paul) [input p0]
6. ! [X0] : ((humble(X0) & brave(X0)) <=> ~calm(X0)) [input p5]
19. ~tall(paul) & ~creative(paul) [input p18]
24. ~brave(paul) [input hypothesis]
38. ((kind(paul) | calm(paul)) | ~creative(paul)) & (creative(paul) | (~kind(paul) & ~calm(paul))) [nnf transformation 1]
39. (kind(paul) | calm(paul) | ~creative(paul)) & (creative(paul) | (~kind(paul) & ~calm(paul))) [flattening 38]
42. ! [X0] : (((humble(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | (~humble(X0) | ~brave(X0)))) [nnf transformation 6]
43. ! [X0] : (((humble(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | ~humble(X0) | ~brave(X0))) [flattening 42]
70. creative(paul) | ~calm(paul) [cnf transformation 39]
83. brave(X0) | calm(X0) [cnf transformation 43]
117. ~creative(paul) [cnf transformation 19]
124. ~brave(paul) [cnf transformation 24]
127. 1 <=> creative(paul) [avatar definition]
131. 2 <=> calm(paul) [avatar definition]
132. ~calm(paul) <- (~2) [avatar component clause 131]
140. ~2 | 1 [avatar split clause 70,127,131]
248. ~1 [avatar split clause 117,127]
269. calm(paul) [resolution 83,124]
270. $false <- (~2) [subsumption resolution 269,132]
271. 2 [avatar contradiction clause 270]
272. $false [avatar sat refutation 140,248,271]
% SZS output end Proof for 1665915785207068765572103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or tall is both not strong and wise.
Everyone who is kind or strong is either not tall or not quiet.
Everyone who is rich or not patient is either not generous or quiet and vice versa.
Everyone who is either tall or not creative is strong or patient and vice versa.
Everyone who is either not wise or not funny is kind and vice versa.
If someone is either happy or wise then someone is both wise and not rich and vice versa.
Everyone who is either not funny or old is both old and patient and vice versa.
If susan is rich or not patient then alice is both not calm and curious.
Everyone who is not funny or not patient is both creative and patient and vice versa.
Everyone who is both not rich and kind is humble.
Everyone who is not kind or not wise is not rich or not tall.
If paul is patient or funny then someone is rich and vice versa.
Everyone who is either not brave or brave is kind or not old and vice versa.
Everyone who is not calm is both not brave and not rich.
If alice is both not patient and quiet then someone is either generous or calm and vice versa.
Alice is not humble or patient.
Fred is both funny and wise.
Someone is either not humble or not strong.
Someone is either not quiet or not happy.
John is either not wise or not strong.
Fred is either quiet or not humble.
Someone is not kind. | Susan is tall. | contradiction | (![X]:((quiet(X)<~>tall(X))=>(~strong(X)&wise(X))))&
(![X]:((kind(X)|strong(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((rich(X)|~patient(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(strong(X)|patient(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~funny(X)<~>old(X))<=>(old(X)&patient(X))))&
(((rich(susan)|~patient(susan)))=>((~calm(alice)&curious(alice))))&
(![X]:((~funny(X)|~patient(X))<=>(creative(X)&patient(X))))&
(![X]:((~rich(X)&kind(X))=>humble(X)))&
(![X]:((~kind(X)|~wise(X))=>(~rich(X)|~tall(X))))&
(((patient(paul)|funny(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(kind(X)|~old(X))))&
(![X]:(~calm(X)=>(~brave(X)&~rich(X))))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~humble(alice)|patient(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:((~humble(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~wise(john)<~>~strong(john)))&
((quiet(fred)<~>~humble(fred)))&
(?[X]:(~kind(X))) | tall(susan) | [
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3572297966089574369260420
% SZS output start Proof for 3572297966089574369260420
4. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (patient(X0) | strong(X0))) [input p3]
7. ! [X0] : ((~funny(X0) <~> old(X0)) <=> (patient(X0) & old(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (patient(X0) & creative(X0))) [input p8]
23. tall(susan) [input hypothesis]
38. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 4]
39. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [flattening 38]
46. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [flattening 46]
48. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~patient(X0) | ~creative(X0))) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0)) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [flattening 48]
91. ~patient(X0) | ~tall(X0) | creative(X0) [cnf transformation 39]
102. old(X0) | old(X0) | funny(X0) [cnf transformation 47]
107. ~old(X0) | funny(X0) | ~patient(X0) | ~old(X0) [cnf transformation 47]
113. patient(X0) | patient(X0) [cnf transformation 49]
114. ~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 49]
147. tall(susan) [cnf transformation 23]
150. patient(X0) [duplicate literal removal 113]
151. ~funny(X0) | ~patient(X0) | ~creative(X0) [duplicate literal removal 114]
152. old(X0) | funny(X0) [duplicate literal removal 102]
153. ~old(X0) | funny(X0) | ~patient(X0) [duplicate literal removal 107]
318. ~tall(X0) | creative(X0) [resolution 91,150]
319. creative(susan) [resolution 318,147]
377. funny(X1) | ~patient(X1) | funny(X1) [resolution 153,152]
378. funny(X1) | ~patient(X1) [duplicate literal removal 377]
380. funny(X1) [subsumption resolution 378,150]
381. ~patient(X0) | ~creative(X0) [resolution 380,151]
384. ~creative(X0) [subsumption resolution 381,150]
389. $false [resolution 384,319]
% SZS output end Proof for 3572297966089574369260420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not tall or not kind then someone is either happy or creative.
Everyone who is tall or rich is either tall or curious and vice versa.
If someone is not kind or rich then mary is calm or wise.
Everyone who is old or wise is strong.
If mary is not happy or not quiet then alice is either curious or funny and vice versa.
Everyone who is both not quiet and old is either not patient or not creative.
Everyone who is either not quiet or old is both funny and kind.
Everyone who is old or brave is quiet and vice versa.
Everyone who is both rich and brave is not calm and vice versa.
Everyone who is not brave or patient is both not creative and not funny.
If someone is not quiet or not curious then lucy is both curious and not rich.
If someone is humble then fred is either not creative or not happy.
If someone is not quiet then someone is either old or not generous.
If fred is not funny then someone is either old or creative and vice versa.
If someone is not old or happy then someone is either not tall or not generous.
Someone is not generous.
John is either not patient or calm.
Someone is either not tall or not happy.
John is not wise or tall.
Lucy is not funny. | Alice is calm. | contradiction | (((~tall(lucy)|~kind(lucy)))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:((tall(X)|rich(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~kind(X)|rich(X))))=>((calm(mary)|wise(mary))))&
(![X]:((old(X)|wise(X))=>strong(X)))&
(((~happy(mary)|~quiet(mary)))<=>((curious(alice)<~>funny(alice))))&
(![X]:((~quiet(X)&old(X))=>(~patient(X)<~>~creative(X))))&
(![X]:((~quiet(X)<~>old(X))=>(funny(X)&kind(X))))&
(![X]:((old(X)|brave(X))<=>quiet(X)))&
(![X]:((rich(X)&brave(X))<=>~calm(X)))&
(![X]:((~brave(X)|patient(X))=>(~creative(X)&~funny(X))))&
((?[X]:((~quiet(X)|~curious(X))))=>((curious(lucy)&~rich(lucy))))&
((?[X]:(humble(X)))=>((~creative(fred)<~>~happy(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~generous(X)))))&
((~funny(fred))<=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:((~old(X)|happy(X))))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(?[X]:(~generous(X)))&
((~patient(john)<~>calm(john)))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~wise(john)|tall(john)))&
(~funny(lucy)) | calm(alice) | [
"p1",
"p6",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5156959464930849352929341
% SZS output start Proof for 5156959464930849352929341
2. ! [X0] : ((rich(X0) | tall(X0)) <=> (tall(X0) <~> curious(X0))) [input p1]
7. ! [X0] : ((~quiet(X0) <~> old(X0)) => (kind(X0) & funny(X0))) [input p6]
8. ! [X0] : ((brave(X0) | old(X0)) <=> quiet(X0)) [input p7]
9. ! [X0] : ((brave(X0) & rich(X0)) <=> ~calm(X0)) [input p8]
10. ! [X0] : ((patient(X0) | ~brave(X0)) => (~funny(X0) & ~creative(X0))) [input p9]
11. ? [X0] : (~curious(X0) | ~quiet(X0)) => (~rich(lucy) & curious(lucy)) [input p10]
21. calm(alice) [input hypothesis]
28. ! [X0] : ((~quiet(X0) <~> old(X0)) => funny(X0)) [pure predicate removal 7]
34. ! [X0] : (funny(X0) | (~quiet(X0) <=> old(X0))) [ennf transformation 28]
35. ! [X0] : ((~funny(X0) & ~creative(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 10]
36. (~rich(lucy) & curious(lucy)) | ! [X0] : (curious(X0) & quiet(X0)) [ennf transformation 11]
42. ! [X0] : (((rich(X0) | tall(X0)) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0)))) & (((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | (~rich(X0) & ~tall(X0)))) [nnf transformation 2]
43. ! [X0] : ((rich(X0) | tall(X0) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0)))) & (((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | (~rich(X0) & ~tall(X0)))) [flattening 42]
47. ! [X0] : (funny(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) [nnf transformation 34]
48. ! [X0] : (((brave(X0) | old(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & ~old(X0)))) [nnf transformation 8]
49. ! [X0] : ((brave(X0) | old(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & ~old(X0)))) [flattening 48]
50. ! [X0] : (((brave(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~rich(X0)))) [nnf transformation 9]
51. ! [X0] : (((brave(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~rich(X0))) [flattening 50]
74. ~curious(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
77. rich(X0) | tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 43]
88. ~quiet(X0) | funny(X0) | ~old(X0) [cnf transformation 47]
91. ~quiet(X0) | old(X0) | brave(X0) [cnf transformation 49]
92. ~brave(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 51]
97. ~funny(X0) | brave(X0) [cnf transformation 35]
100. curious(lucy) | curious(X0) [cnf transformation 36]
101. ~rich(lucy) | quiet(X0) [cnf transformation 36]
102. ~rich(lucy) | curious(X0) [cnf transformation 36]
120. calm(alice) [cnf transformation 21]
121. ~curious(X0) | ~tall(X0) [duplicate literal removal 74]
122. ~curious(X0) | tall(X0) | rich(X0) [duplicate literal removal 77]
124. 1 <=> tall(lucy) [avatar definition]
125. ~tall(lucy) <- (~1) [avatar component clause 124]
150. 7 <=> funny(alice) [avatar definition]
151. funny(alice) <- (7) [avatar component clause 150]
152. ~funny(alice) <- (~7) [avatar component clause 150]
172. 11 <=> ! [X0] : curious(X0) [avatar definition]
173. curious(X0) <- (11) [avatar component clause 172]
175. 12 <=> rich(lucy) [avatar definition]
178. 11 | ~12 [avatar split clause 102,175,172]
180. 13 <=> ! [X0] : quiet(X0) [avatar definition]
181. quiet(X0) <- (13) [avatar component clause 180]
182. 13 | ~12 [avatar split clause 101,175,180]
184. 14 <=> curious(lucy) [avatar definition]
185. ~curious(lucy) <- (~14) [avatar component clause 184]
186. curious(lucy) <- (14) [avatar component clause 184]
187. 11 | 14 [avatar split clause 100,184,172]
286. ~tall(lucy) <- (14) [resolution 186,121]
287. ~1 | ~14 [avatar split clause 286,184,124]
294. ~old(X0) | funny(X0) <- (13) [resolution 88,181]
295. brave(X0) | old(X0) <- (13) [resolution 91,181]
298. ~calm(X0) | old(X0) | ~rich(X0) <- (13) [resolution 295,92]
301. tall(lucy) | rich(lucy) <- (14) [resolution 122,186]
305. rich(lucy) <- (~1, 14) [subsumption resolution 301,125]
308. 12 | 1 | ~14 [avatar split clause 305,184,124,175]
318. brave(alice) <- (7) [resolution 151,97]
319. rich(X0) | tall(X0) <- (11) [resolution 173,122]
321. ~tall(X2) <- (11) [resolution 173,121]
322. $false <- (11, ~14) [resolution 185,173]
323. ~11 | 14 [avatar contradiction clause 322]
326. ~calm(alice) | ~rich(alice) <- (7) [resolution 318,92]
328. ~rich(alice) <- (7) [subsumption resolution 326,120]
339. tall(alice) <- (7, 11) [resolution 328,319]
340. $false <- (7, 11) [subsumption resolution 339,321]
341. ~7 | ~11 [avatar contradiction clause 340]
345. old(alice) | ~rich(alice) <- (13) [resolution 298,120]
357. 36 <=> rich(alice) [avatar definition]
359. ~rich(alice) <- (~36) [avatar component clause 357]
361. 37 <=> old(alice) [avatar definition]
363. old(alice) <- (37) [avatar component clause 361]
364. ~36 | 37 | ~13 [avatar split clause 345,180,361,357]
383. tall(alice) <- (11, ~36) [resolution 359,319]
384. $false <- (11, ~36) [subsumption resolution 383,321]
385. ~11 | 36 [avatar contradiction clause 384]
389. funny(alice) <- (13, 37) [resolution 363,294]
392. $false <- (~7, 13, 37) [subsumption resolution 389,152]
393. 7 | ~13 | ~37 [avatar contradiction clause 392]
394. $false [avatar sat refutation 178,182,187,287,308,323,341,364,385,393]
% SZS output end Proof for 5156959464930849352929341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not wise is not tall or not strong and vice versa. If fred is not wise or not humble then someone is either brave or not happy and vice versa. If paul is not wise or tall then fred is not strong. Everyone who is rich or not strong is not brave or not kind and vice versa. Everyone who is not kind or patient is both not brave and not tall. Everyone who is creative is rich and vice versa. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Everyone who is either not old or not funny is both kind and not strong and vice versa. Everyone who is quiet is generous and vice versa. Someone is brave. Someone is not old. Someone is either not tall or kind. Mary is both not curious and not creative. Someone is either kind or not funny. Someone is wise. | Susan is creative. | neutral | (![X]:((~patient(X)&~wise(X))<=>(~tall(X)|~strong(X))))&
(((~wise(fred)|~humble(fred)))<=>(?[X]:((brave(X)<~>~happy(X)))))&
(((~wise(paul)|tall(paul)))=>(~strong(fred)))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(?[X]:(brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:(wise(X))) | creative(susan) | [] | null | 0 |
Everyone who is both kind and creative is either not curious or kind and vice versa. Everyone who is not brave is kind and vice versa. If someone is both not old and curious then someone is both calm and kind. If fred is both not old and not humble then someone is both wise and not calm. If fred is both not happy and not curious then someone is not brave or not tall and vice versa. Everyone who is not quiet or not wise is funny. If alice is quiet or not humble then someone is happy and vice versa. Everyone who is not calm or strong is both not creative and not happy and vice versa. If someone is humble or not calm then someone is both generous and not humble. Everyone who is either not strong or not curious is tall and vice versa. If someone is not calm or old then john is both brave and not wise and vice versa. Everyone who is not funny or brave is not creative. If john is both not generous and not rich then lucy is rich. If someone is both not calm and old then someone is both not patient and not curious and vice versa. If paul is either not kind or wise then john is both not kind and funny. Everyone who is tall is not strong and vice versa. Someone is either not brave or not wise. Fred is not curious or quiet. Someone is not generous or not curious. Someone is not calm or not kind. Susan is either not brave or curious. Mary is not brave or not creative. | Mary is kind. | contradiction | (![X]:((kind(X)&creative(X))<=>(~curious(X)<~>kind(X))))&
(![X]:(~brave(X)<=>kind(X)))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((calm(X)&kind(X)))))&
(((~old(fred)&~humble(fred)))=>(?[X]:((wise(X)&~calm(X)))))&
(((~happy(fred)&~curious(fred)))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~quiet(X)|~wise(X))=>funny(X)))&
(((quiet(alice)|~humble(alice)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|strong(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((~calm(X)|old(X))))<=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|brave(X))=>~creative(X)))&
(((~generous(john)&~rich(john)))=>(rich(lucy)))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((~kind(paul)<~>wise(paul)))=>((~kind(john)&funny(john))))&
(![X]:(tall(X)<=>~strong(X)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((~curious(fred)|quiet(fred)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((~calm(X)|~kind(X))))&
((~brave(susan)<~>curious(susan)))&
((~brave(mary)|~creative(mary))) | kind(mary) | [
"p1",
"p4",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4405728812442216542191530
% SZS output start Proof for 4405728812442216542191530
2. ! [X0] : (~brave(X0) <=> kind(X0)) [input p1]
5. (~curious(fred) & ~happy(fred)) <=> ? [X0] : (~tall(X0) | ~brave(X0)) [input p4]
10. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> tall(X0)) [input p9]
16. ! [X0] : (tall(X0) <=> ~strong(X0)) [input p15]
23. kind(mary) [input hypothesis]
39. ! [X0] : ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))) [nnf transformation 2]
45. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | (curious(fred) | happy(fred))) [nnf transformation 5]
46. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | curious(fred) | happy(fred)) [flattening 45]
47. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X1] : (~tall(X1) | ~brave(X1)) | curious(fred) | happy(fred)) [rectify 46]
48. ? [X1] : (~tall(X1) | ~brave(X1)) => (~tall(sK2) | ~brave(sK2)) [choice axiom]
49. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & ((~tall(sK2) | ~brave(sK2)) | curious(fred) | happy(fred)) [skolemisation 47,48]
60. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | ~tall(X0)) & (tall(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 10]
72. ! [X0] : ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0))) [nnf transformation 16]
88. ~brave(X0) | ~kind(X0) [cnf transformation 39]
96. ~curious(fred) | brave(X0) [cnf transformation 49]
111. ~strong(X0) | tall(X0) | curious(X0) [cnf transformation 60]
113. ~tall(X0) | strong(X0) | curious(X0) [cnf transformation 60]
126. ~strong(X0) | ~tall(X0) [cnf transformation 72]
127. strong(X0) | tall(X0) [cnf transformation 72]
136. kind(mary) [cnf transformation 23]
175. 9 <=> curious(fred) [avatar definition]
177. ~curious(fred) <- (~9) [avatar component clause 175]
180. 10 <=> ! [X0] : brave(X0) [avatar definition]
181. brave(X0) <- (10) [avatar component clause 180]
182. 10 | ~9 [avatar split clause 96,175,180]
373. tall(X0) | curious(X0) | tall(X0) [resolution 111,127]
374. tall(X0) | curious(X0) [duplicate literal removal 373]
378. strong(X0) | curious(X0) | curious(X0) [resolution 113,374]
379. strong(X0) | curious(X0) [duplicate literal removal 378]
417. curious(X2) | ~tall(X2) [resolution 379,126]
421. curious(X2) [subsumption resolution 417,374]
425. $false <- (~9) [resolution 421,177]
430. 9 [avatar contradiction clause 425]
437. ~kind(X1) <- (10) [resolution 181,88]
451. $false <- (10) [resolution 437,136]
454. ~10 [avatar contradiction clause 451]
455. $false [avatar sat refutation 182,430,454]
% SZS output end Proof for 4405728812442216542191530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is tall.
If someone is both not curious and curious then someone is not curious.
If alice is wise then alice is creative and vice versa.
Everyone who is creative is either funny or not patient.
Everyone who is both not generous and not happy is strong or tall and vice versa.
If someone is not tall or not calm then lucy is either kind or curious.
If someone is either not quiet or not wise then fred is old or calm.
Everyone who is curious is either brave or not rich and vice versa.
Everyone who is quiet is not kind and vice versa.
Everyone who is either not rich or generous is wise or quiet and vice versa.
Everyone who is both not brave and strong is either not curious or not quiet.
Everyone who is both kind and not patient is brave or happy and vice versa.
If alice is not strong or patient then someone is either not quiet or not patient and vice versa.
If fred is not strong or kind then paul is either old or not patient.
Everyone who is not quiet is not tall or old.
Everyone who is both wise and tall is both quiet and generous and vice versa.
Someone is both not patient and not humble.
Alice is either not strong or happy.
Someone is either not calm or calm.
Susan is both not humble and not funny.
Fred is not curious or curious.
Someone is both old and brave.
Lucy is both strong and not creative.
Mary is both creative and not calm. | Susan is humble. | contradiction | ((?[X]:(~happy(X)))=>(tall(fred)))&
((?[X]:((~curious(X)&curious(X))))=>(?[X]:(~curious(X))))&
((wise(alice))<=>(creative(alice)))&
(![X]:(creative(X)=>(funny(X)<~>~patient(X))))&
(![X]:((~generous(X)&~happy(X))<=>(strong(X)|tall(X))))&
((?[X]:((~tall(X)|~calm(X))))=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~quiet(X)<~>~wise(X))))=>((old(fred)|calm(fred))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(![X]:((wise(X)&tall(X))<=>(quiet(X)&generous(X))))&
(?[X]:((~patient(X)&~humble(X))))&
((~strong(alice)<~>happy(alice)))&
(?[X]:((~calm(X)<~>calm(X))))&
((~humble(susan)&~funny(susan)))&
((~curious(fred)|curious(fred)))&
(?[X]:((old(X)&brave(X))))&
((strong(lucy)&~creative(lucy)))&
((creative(mary)&~calm(mary))) | humble(susan) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1281512188689804087929694
% SZS output start Proof for 1281512188689804087929694
20. ~funny(susan) & ~humble(susan) [input p19]
25. humble(susan) [input hypothesis]
127. ~humble(susan) [cnf transformation 20]
136. humble(susan) [cnf transformation 25]
242. $false [subsumption resolution 136,127]
% SZS output end Proof for 1281512188689804087929694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not rich is not generous and vice versa.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is either generous or not rich is both old and kind and vice versa.
Everyone who is generous or kind is strong and vice versa.
Everyone who is not patient or humble is funny and vice versa.
If someone is both creative and old then someone is both old and creative.
Everyone who is generous or happy is either not tall or rich and vice versa.
Everyone who is either not generous or happy is creative.
Everyone who is either not wise or quiet is not rich or creative.
Everyone who is both not patient and creative is wise and vice versa.
Everyone who is either happy or not old is creative and vice versa.
Everyone who is both rich and not kind is wise or quiet and vice versa.
Everyone who is not curious or strong is either humble or kind.
If someone is patient or brave then susan is not old and vice versa.
If someone is either not happy or not humble then fred is both old and creative and vice versa.
Susan is quiet or not humble.
John is either wise or not rich.
Someone is either brave or tall.
Lucy is either wise or not quiet.
Someone is either not patient or not funny. | John is calm. | contradiction | (![X]:((strong(X)|~rich(X))<=>~generous(X)))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(old(X)&kind(X))))&
(![X]:((generous(X)|kind(X))<=>strong(X)))&
(![X]:((~patient(X)|humble(X))<=>funny(X)))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((generous(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~generous(X)<~>happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)|creative(X))))&
(![X]:((~patient(X)&creative(X))<=>wise(X)))&
(![X]:((happy(X)<~>~old(X))<=>creative(X)))&
(![X]:((rich(X)&~kind(X))<=>(wise(X)|quiet(X))))&
(![X]:((~curious(X)|strong(X))=>(humble(X)<~>kind(X))))&
((?[X]:((patient(X)|brave(X))))<=>(~old(susan)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((old(fred)&creative(fred))))&
((quiet(susan)|~humble(susan)))&
((wise(john)<~>~rich(john)))&
(?[X]:((brave(X)<~>tall(X))))&
((wise(lucy)<~>~quiet(lucy)))&
(?[X]:((~patient(X)<~>~funny(X)))) | calm(john) | [
"p0",
"p1",
"p2",
"p3",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1058198845930215122581999
% SZS output start Proof for 1058198845930215122581999
1. ! [X0] : ((~rich(X0) | strong(X0)) <=> ~generous(X0)) [input p0]
2. ! [X0] : (calm(X0) <=> (~strong(X0) <~> humble(X0))) [input p1]
3. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (kind(X0) & old(X0))) [input p2]
4. ! [X0] : ((kind(X0) | generous(X0)) <=> strong(X0)) [input p3]
12. ! [X0] : ((~kind(X0) & rich(X0)) <=> (quiet(X0) | wise(X0))) [input p11]
13. ! [X0] : ((strong(X0) | ~curious(X0)) => (humble(X0) <~> kind(X0))) [input p12]
17. wise(john) <~> ~rich(john) [input p16]
21. calm(john) [input hypothesis]
23. ! [X0] : (calm(X0) => (~strong(X0) <~> humble(X0))) [unused predicate definition removal 2]
24. ! [X0] : (strong(X0) => (humble(X0) <~> kind(X0))) [pure predicate removal 13]
25. ! [X0] : ((~strong(X0) <~> humble(X0)) | ~calm(X0)) [ennf transformation 23]
30. ! [X0] : ((humble(X0) <~> kind(X0)) | ~strong(X0)) [ennf transformation 24]
31. ! [X0] : (((~rich(X0) | strong(X0)) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [nnf transformation 1]
32. ! [X0] : ((~rich(X0) | strong(X0) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [flattening 31]
33. ! [X0] : (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~calm(X0)) [nnf transformation 25]
34. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 3]
35. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 34]
36. ! [X0] : (((kind(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 4]
37. ! [X0] : ((kind(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [flattening 36]
50. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 12]
51. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | kind(X0) | ~rich(X0))) [flattening 50]
52. ! [X0] : (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~strong(X0)) [nnf transformation 30]
62. (rich(john) | ~wise(john)) & (~rich(john) | wise(john)) [nnf transformation 17]
70. ~generous(X0) | ~strong(X0) [cnf transformation 32]
71. ~generous(X0) | rich(X0) [cnf transformation 32]
72. ~rich(X0) | strong(X0) | generous(X0) [cnf transformation 32]
73. ~calm(X0) | ~strong(X0) | humble(X0) [cnf transformation 33]
78. kind(X0) | generous(X0) | rich(X0) [cnf transformation 35]
81. strong(X0) | ~generous(X0) [cnf transformation 37]
82. ~kind(X0) | strong(X0) [cnf transformation 37]
83. kind(X0) | generous(X0) | ~strong(X0) [cnf transformation 37]
109. ~wise(X0) | ~kind(X0) [cnf transformation 51]
112. ~kind(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 52]
123. ~rich(john) | wise(john) [cnf transformation 62]
131. calm(john) [cnf transformation 21]
132. kind(X0) | rich(X0) [subsumption resolution 78,71]
136. ~strong(X0) | kind(X0) [subsumption resolution 83,70]
137. ~generous(X0) [subsumption resolution 81,70]
157. ~kind(X0) | ~humble(X0) [subsumption resolution 112,82]
219. 17 <=> wise(john) [avatar definition]
221. wise(john) <- (17) [avatar component clause 219]
223. 18 <=> rich(john) [avatar definition]
225. ~rich(john) <- (~18) [avatar component clause 223]
226. 17 | ~18 [avatar split clause 123,223,219]
256. rich(X0) | strong(X0) [resolution 132,82]
264. ~humble(X0) | rich(X0) [resolution 157,132]
267. strong(X0) | generous(X0) | strong(X0) [resolution 72,256]
268. strong(X0) | generous(X0) [duplicate literal removal 267]
270. strong(X0) [subsumption resolution 268,137]
272. ~strong(john) | humble(john) [resolution 73,131]
278. kind(X0) [resolution 270,136]
348. humble(john) [subsumption resolution 272,270]
349. ~kind(john) <- (17) [resolution 221,109]
353. $false <- (17) [subsumption resolution 349,278]
354. ~17 [avatar contradiction clause 353]
496. rich(john) [resolution 264,348]
549. $false <- (~18) [subsumption resolution 496,225]
550. 18 [avatar contradiction clause 549]
554. $false [avatar sat refutation 226,354,550]
% SZS output end Proof for 1058198845930215122581999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then paul is quiet or not brave.
Everyone who is both not humble and curious is both humble and not calm.
Everyone who is not wise is either not happy or patient.
If someone is generous then susan is both not calm and old.
Everyone who is either old or strong is generous and vice versa.
Everyone who is either not wise or not quiet is kind or wise.
Everyone who is humble is not tall and vice versa.
Everyone who is both not brave and humble is brave and vice versa.
Everyone who is patient is creative.
Everyone who is wise is humble or tall and vice versa.
If someone is not wise then someone is old and vice versa.
If someone is not curious then someone is either tall or not calm.
If someone is not creative or not happy then someone is either not rich or creative.
If mary is either not kind or happy then someone is funny and vice versa.
Everyone who is both not strong and not rich is not quiet and vice versa.
Everyone who is either rich or not humble is both not brave and wise and vice versa.
Paul is patient or old.
John is either not rich or old.
Someone is either not wise or not kind.
Someone is kind or patient.
Someone is funny.
Someone is both not strong and creative. | John is rich. | contradiction | ((?[X]:(~calm(X)))=>((quiet(paul)|~brave(paul))))&
(![X]:((~humble(X)&curious(X))=>(humble(X)&~calm(X))))&
(![X]:(~wise(X)=>(~happy(X)<~>patient(X))))&
((?[X]:(generous(X)))=>((~calm(susan)&old(susan))))&
(![X]:((old(X)<~>strong(X))<=>generous(X)))&
(![X]:((~wise(X)<~>~quiet(X))=>(kind(X)|wise(X))))&
(![X]:(humble(X)<=>~tall(X)))&
(![X]:((~brave(X)&humble(X))<=>brave(X)))&
(![X]:(patient(X)=>creative(X)))&
(![X]:(wise(X)<=>(humble(X)|tall(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(old(X))))&
((?[X]:(~curious(X)))=>(?[X]:((tall(X)<~>~calm(X)))))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:((~rich(X)<~>creative(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(?[X]:(funny(X))))&
(![X]:((~strong(X)&~rich(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~humble(X))<=>(~brave(X)&wise(X))))&
((patient(paul)|old(paul)))&
((~rich(john)<~>old(john)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~strong(X)&creative(X)))) | rich(john) | [
"p6",
"p7",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 550747929662106219157157
% SZS output start Proof for 550747929662106219157157
7. ! [X0] : (humble(X0) <=> ~tall(X0)) [input p6]
8. ! [X0] : ((humble(X0) & ~brave(X0)) <=> brave(X0)) [input p7]
10. ! [X0] : (wise(X0) <=> (tall(X0) | humble(X0))) [input p9]
11. ? [X0] : ~wise(X0) <=> ? [X0] : old(X0) [input p10]
18. ~rich(john) <~> old(john) [input p17]
23. rich(john) [input hypothesis]
24. ? [X0] : ~wise(X0) <=> ? [X1] : old(X1) [rectify 11]
43. ! [X0] : ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0))) [nnf transformation 7]
44. ! [X0] : (((humble(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~humble(X0) | brave(X0)))) [nnf transformation 8]
45. ! [X0] : (((humble(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~humble(X0) | brave(X0))) [flattening 44]
46. ! [X0] : ((wise(X0) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | ~wise(X0))) [nnf transformation 10]
47. ! [X0] : ((wise(X0) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ~wise(X0))) [flattening 46]
48. (? [X0] : ~wise(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : wise(X0)) [nnf transformation 24]
49. (? [X0] : ~wise(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : wise(X3)) [rectify 48]
50. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
51. ? [X2] : old(X2) => old(sK1) [choice axiom]
52. (~wise(sK0) | ! [X1] : ~old(X1)) & (old(sK1) | ! [X3] : wise(X3)) [skolemisation 49,51,50]
69. (~old(john) | rich(john)) & (old(john) | ~rich(john)) [nnf transformation 18]
91. tall(X0) | humble(X0) [cnf transformation 43]
92. brave(X0) | ~humble(X0) | brave(X0) [cnf transformation 45]
93. ~brave(X0) | ~brave(X0) [cnf transformation 45]
98. ~tall(X0) | wise(X0) [cnf transformation 47]
100. ~wise(sK0) | ~old(X1) [cnf transformation 52]
121. old(john) | ~rich(john) [cnf transformation 69]
129. rich(john) [cnf transformation 23]
130. brave(X0) | ~humble(X0) [duplicate literal removal 92]
131. ~brave(X0) [duplicate literal removal 93]
159. ~humble(X0) [subsumption resolution 130,131]
161. 7 <=> ! [X1] : ~old(X1) [avatar definition]
162. ~old(X1) <- (7) [avatar component clause 161]
164. 8 <=> wise(sK0) [avatar definition]
166. ~wise(sK0) <- (~8) [avatar component clause 164]
167. 7 | ~8 [avatar split clause 100,164,161]
169. 9 <=> ! [X3] : wise(X3) [avatar definition]
170. wise(X3) <- (9) [avatar component clause 169]
239. 24 <=> rich(john) [avatar definition]
243. 25 <=> old(john) [avatar definition]
244. old(john) <- (25) [avatar component clause 243]
247. ~24 | 25 [avatar split clause 121,243,239]
267. 24 [avatar split clause 129,239]
268. $false <- (~8, 9) [subsumption resolution 166,170]
269. 8 | ~9 [avatar contradiction clause 268]
272. $false <- (7, 25) [resolution 244,162]
273. ~7 | ~25 [avatar contradiction clause 272]
280. wise(X0) | humble(X0) [resolution 98,91]
282. wise(X0) [subsumption resolution 280,159]
283. 9 [avatar split clause 282,169]
284. $false [avatar sat refutation 167,247,267,269,273,283]
% SZS output end Proof for 550747929662106219157157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not patient and not calm then susan is either not tall or not curious and vice versa. Everyone who is not old or wise is quiet or not calm and vice versa. Everyone who is both not tall and quiet is both not funny and not rich and vice versa. Everyone who is not rich is rich. Everyone who is not calm or happy is both humble and not rich and vice versa. If someone is not brave or not rich then someone is not strong or not old and vice versa. Everyone who is both funny and not quiet is both quiet and happy and vice versa. If someone is not patient or not tall then someone is either not rich or brave and vice versa. Everyone who is either brave or not generous is not calm or generous. Everyone who is both not humble and rich is both wise and strong and vice versa. If someone is brave then someone is old and vice versa. Everyone who is not patient or creative is both not funny and quiet. Everyone who is happy is either rich or wise. If someone is both funny and not curious then someone is not quiet or not brave and vice versa. If someone is not curious or not old then alice is not patient and vice versa. Everyone who is both not wise and not funny is both not rich and kind. Alice is either calm or not curious. Someone is not generous or not curious. Someone is either rich or not kind. Susan is not happy or not tall. Someone is either not creative or funny. | Mary is old. | neutral | (((~patient(mary)&~calm(mary)))<=>((~tall(susan)<~>~curious(susan))))&
(![X]:((~old(X)|wise(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~tall(X)&quiet(X))<=>(~funny(X)&~rich(X))))&
(![X]:(~rich(X)=>rich(X)))&
(![X]:((~calm(X)|happy(X))<=>(humble(X)&~rich(X))))&
((?[X]:((~brave(X)|~rich(X))))<=>(?[X]:((~strong(X)|~old(X)))))&
(![X]:((funny(X)&~quiet(X))<=>(quiet(X)&happy(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((brave(X)<~>~generous(X))=>(~calm(X)|generous(X))))&
(![X]:((~humble(X)&rich(X))<=>(wise(X)&strong(X))))&
((?[X]:(brave(X)))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)|creative(X))=>(~funny(X)&quiet(X))))&
(![X]:(happy(X)=>(rich(X)<~>wise(X))))&
((?[X]:((funny(X)&~curious(X))))<=>(?[X]:((~quiet(X)|~brave(X)))))&
((?[X]:((~curious(X)|~old(X))))<=>(~patient(alice)))&
(![X]:((~wise(X)&~funny(X))=>(~rich(X)&kind(X))))&
((calm(alice)<~>~curious(alice)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
((~happy(susan)|~tall(susan)))&
(?[X]:((~creative(X)<~>funny(X)))) | old(mary) | [] | null | 0 |
If someone is kind then someone is either wise or patient and vice versa. Everyone who is not creative is brave or not calm and vice versa. Everyone who is not generous or not creative is old or not humble. If someone is either not funny or creative then someone is not humble and vice versa. Everyone who is either kind or curious is both not creative and not kind. Everyone who is both not calm and not generous is both rich and not strong. Everyone who is not calm or not funny is both kind and rich and vice versa. Everyone who is not happy is not wise. If mary is both not tall and kind then lucy is tall. Everyone who is both not kind and old is generous and vice versa. Everyone who is both patient and not funny is old. If susan is not humble then someone is not tall or not kind. If someone is either humble or brave then someone is both not old and humble and vice versa. Everyone who is both funny and kind is not strong or not patient and vice versa. If paul is either not kind or not tall then someone is humble or not kind and vice versa. Everyone who is curious is either not old or not kind and vice versa. Someone is not quiet or funny. Someone is both quiet and funny. Someone is not creative. John is curious or not wise. Someone is not humble or old. Fred is either not curious or creative. Someone is old. Paul is not humble. | John is funny. | entailment | ((?[X]:(kind(X)))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(~creative(X)<=>(brave(X)|~calm(X))))&
(![X]:((~generous(X)|~creative(X))=>(old(X)|~humble(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)<~>curious(X))=>(~creative(X)&~kind(X))))&
(![X]:((~calm(X)&~generous(X))=>(rich(X)&~strong(X))))&
(![X]:((~calm(X)|~funny(X))<=>(kind(X)&rich(X))))&
(![X]:(~happy(X)=>~wise(X)))&
(((~tall(mary)&kind(mary)))=>(tall(lucy)))&
(![X]:((~kind(X)&old(X))<=>generous(X)))&
(![X]:((patient(X)&~funny(X))=>old(X)))&
((~humble(susan))=>(?[X]:((~tall(X)|~kind(X)))))&
((?[X]:((humble(X)<~>brave(X))))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((funny(X)&kind(X))<=>(~strong(X)|~patient(X))))&
(((~kind(paul)<~>~tall(paul)))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:(curious(X)<=>(~old(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(~creative(X)))&
((curious(john)|~wise(john)))&
(?[X]:((~humble(X)|old(X))))&
((~curious(fred)<~>creative(fred)))&
(?[X]:(old(X)))&
(~humble(paul)) | funny(john) | [
"p4",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1591643204850053256885875
% SZS output start Proof for 1591643204850053256885875
5. ! [X0] : ((kind(X0) <~> curious(X0)) => (~kind(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (rich(X0) & kind(X0))) [input p6]
11. ! [X0] : ((~funny(X0) & patient(X0)) => old(X0)) [input p10]
14. ! [X0] : ((kind(X0) & funny(X0)) <=> (~patient(X0) | ~strong(X0))) [input p13]
16. ! [X0] : (curious(X0) <=> (~old(X0) <~> ~kind(X0))) [input p15]
25. ~funny(john) [input hypothesis]
33. ! [X0] : ((~kind(X0) & ~creative(X0)) | (kind(X0) <=> curious(X0))) [ennf transformation 5]
39. ! [X0] : (old(X0) | (funny(X0) | ~patient(X0))) [ennf transformation 11]
40. ! [X0] : (old(X0) | funny(X0) | ~patient(X0)) [flattening 39]
54. ! [X0] : ((~kind(X0) & ~creative(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) [nnf transformation 33]
55. ! [X0] : (((~funny(X0) | ~calm(X0)) | (~rich(X0) | ~kind(X0))) & ((rich(X0) & kind(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 7]
56. ! [X0] : ((~funny(X0) | ~calm(X0) | ~rich(X0) | ~kind(X0)) & ((rich(X0) & kind(X0)) | (funny(X0) & calm(X0)))) [flattening 55]
64. ! [X0] : (((kind(X0) & funny(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (~kind(X0) | ~funny(X0)))) [nnf transformation 14]
65. ! [X0] : (((kind(X0) & funny(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | ~kind(X0) | ~funny(X0))) [flattening 64]
70. ! [X0] : ((curious(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ~curious(X0))) [nnf transformation 16]
97. ~kind(X0) | curious(X0) | ~kind(X0) [cnf transformation 54]
102. funny(X0) | kind(X0) [cnf transformation 56]
109. ~patient(X0) | funny(X0) | old(X0) [cnf transformation 40]
119. funny(X0) | patient(X0) [cnf transformation 65]
128. ~kind(X0) | ~old(X0) | ~curious(X0) [cnf transformation 70]
131. curious(X0) | ~old(X0) | kind(X0) [cnf transformation 70]
142. ~funny(john) [cnf transformation 25]
143. ~kind(X0) | curious(X0) [duplicate literal removal 97]
279. ~old(X0) | curious(X0) [subsumption resolution 131,143]
280. ~old(X0) | ~kind(X0) [subsumption resolution 128,279]
320. kind(john) [resolution 102,142]
322. patient(john) [resolution 119,142]
367. funny(john) | old(john) [resolution 109,322]
370. old(john) [subsumption resolution 367,142]
379. ~kind(john) [resolution 370,280]
381. $false [subsumption resolution 379,320]
% SZS output end Proof for 1591643204850053256885875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not patient then someone is both not kind and not humble.
If alice is quiet or wise then alice is either not patient or not funny.
Everyone who is not brave is either not brave or generous and vice versa.
Everyone who is both rich and not kind is either creative or patient and vice versa.
Everyone who is not rich is not old or funny and vice versa.
If paul is not funny then someone is strong and vice versa.
If someone is not wise then someone is both not curious and rich and vice versa.
Everyone who is not strong or brave is not brave.
If alice is not patient then someone is both not kind and not wise and vice versa.
Everyone who is both not generous and creative is wise and vice versa.
Everyone who is not tall is not brave.
Everyone who is both not happy and not generous is either kind or generous.
Everyone who is both not generous and not humble is brave and vice versa.
If someone is both not strong and tall then fred is not quiet or not generous.
Everyone who is not wise is not strong.
Everyone who is both not wise and strong is both brave and curious and vice versa.
Someone is not humble or not old.
Someone is not rich or humble.
Alice is not brave or not curious.
Mary is not patient.
Someone is both not generous and calm.
Mary is old or generous.
Lucy is either rich or curious.
Someone is happy. | Fred is not humble. | contradiction | ((?[X]:((~curious(X)<~>~patient(X))))=>(?[X]:((~kind(X)&~humble(X)))))&
(((quiet(alice)|wise(alice)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:(~brave(X)<=>(~brave(X)<~>generous(X))))&
(![X]:((rich(X)&~kind(X))<=>(creative(X)<~>patient(X))))&
(![X]:(~rich(X)<=>(~old(X)|funny(X))))&
((~funny(paul))<=>(?[X]:(strong(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~strong(X)|brave(X))=>~brave(X)))&
((~patient(alice))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((~generous(X)&creative(X))<=>wise(X)))&
(![X]:(~tall(X)=>~brave(X)))&
(![X]:((~happy(X)&~generous(X))=>(kind(X)<~>generous(X))))&
(![X]:((~generous(X)&~humble(X))<=>brave(X)))&
((?[X]:((~strong(X)&tall(X))))=>((~quiet(fred)|~generous(fred))))&
(![X]:(~wise(X)=>~strong(X)))&
(![X]:((~wise(X)&strong(X))<=>(brave(X)&curious(X))))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~rich(X)|humble(X))))&
((~brave(alice)|~curious(alice)))&
(~patient(mary))&
(?[X]:((~generous(X)&calm(X))))&
((old(mary)|generous(mary)))&
((rich(lucy)<~>curious(lucy)))&
(?[X]:(happy(X))) | ~humble(fred) | [
"p2",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2774797707909210555424583
% SZS output start Proof for 2774797707909210555424583
3. ! [X0] : (~brave(X0) <=> (~brave(X0) <~> generous(X0))) [input p2]
8. ! [X0] : ((brave(X0) | ~strong(X0)) => ~brave(X0)) [input p7]
13. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> brave(X0)) [input p12]
25. ~humble(fred) [input hypothesis]
36. ! [X0] : (~brave(X0) | (~brave(X0) & strong(X0))) [ennf transformation 8]
43. ! [X0] : ((~brave(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) & (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | brave(X0))) [nnf transformation 3]
63. ! [X0] : (((~humble(X0) & ~generous(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) | generous(X0)))) [nnf transformation 13]
64. ! [X0] : (((~humble(X0) & ~generous(X0)) | ~brave(X0)) & (brave(X0) | humble(X0) | generous(X0))) [flattening 63]
81. ~generous(X0) | brave(X0) | brave(X0) [cnf transformation 43]
83. ~brave(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 43]
99. ~brave(X0) | ~brave(X0) [cnf transformation 36]
106. brave(X0) | humble(X0) | generous(X0) [cnf transformation 64]
122. ~humble(fred) [cnf transformation 25]
123. ~brave(X0) [duplicate literal removal 99]
124. ~generous(X0) | brave(X0) [duplicate literal removal 81]
125. ~brave(X0) | ~generous(X0) [duplicate literal removal 83]
158. ~generous(X0) [subsumption resolution 124,125]
208. humble(X0) | generous(X0) [subsumption resolution 106,123]
209. humble(X0) [subsumption resolution 208,158]
222. $false [subsumption resolution 122,209]
% SZS output end Proof for 2774797707909210555424583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not curious then someone is tall or humble.
If someone is not creative then paul is happy or not brave.
Everyone who is not wise is both funny and not generous and vice versa.
If mary is both humble and creative then someone is not rich and vice versa.
Everyone who is brave is both not funny and curious.
Everyone who is creative or funny is brave or not tall and vice versa.
If paul is not funny or funny then alice is not humble or not creative.
If someone is not happy or calm then mary is both calm and old and vice versa.
If someone is wise or not wise then someone is either wise or humble.
Everyone who is either patient or not curious is not happy and vice versa.
If alice is either funny or not wise then paul is brave or not humble.
If someone is kind or creative then someone is either rich or curious.
If someone is either not generous or patient then lucy is old or wise.
If mary is both rich and not kind then john is both not old and not calm.
If someone is both quiet and not curious then someone is wise or patient.
Everyone who is both not old and not tall is not kind.
Alice is either curious or not humble.
John is strong.
John is creative.
Lucy is either brave or not generous.
John is both not calm and not wise.
Someone is not quiet or kind.
Mary is not generous or creative.
Someone is both rich and wise. | John is tall. | contradiction | ((?[X]:((~generous(X)&~curious(X))))=>(?[X]:((tall(X)|humble(X)))))&
((?[X]:(~creative(X)))=>((happy(paul)|~brave(paul))))&
(![X]:(~wise(X)<=>(funny(X)&~generous(X))))&
(((humble(mary)&creative(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(brave(X)=>(~funny(X)&curious(X))))&
(![X]:((creative(X)|funny(X))<=>(brave(X)|~tall(X))))&
(((~funny(paul)|funny(paul)))=>((~humble(alice)|~creative(alice))))&
((?[X]:((~happy(X)|calm(X))))<=>((calm(mary)&old(mary))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((wise(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~curious(X))<=>~happy(X)))&
(((funny(alice)<~>~wise(alice)))=>((brave(paul)|~humble(paul))))&
((?[X]:((kind(X)|creative(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
((?[X]:((~generous(X)<~>patient(X))))=>((old(lucy)|wise(lucy))))&
(((rich(mary)&~kind(mary)))=>((~old(john)&~calm(john))))&
((?[X]:((quiet(X)&~curious(X))))=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~old(X)&~tall(X))=>~kind(X)))&
((curious(alice)<~>~humble(alice)))&
(strong(john))&
(creative(john))&
((brave(lucy)<~>~generous(lucy)))&
((~calm(john)&~wise(john)))&
(?[X]:((~quiet(X)|kind(X))))&
((~generous(mary)|creative(mary)))&
(?[X]:((rich(X)&wise(X)))) | tall(john) | [
"p2",
"p4",
"p5",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6650954998108987666785389
% SZS output start Proof for 6650954998108987666785389
3. ! [X0] : (~wise(X0) <=> (~generous(X0) & funny(X0))) [input p2]
5. ! [X0] : (brave(X0) => (curious(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((funny(X0) | creative(X0)) <=> (~tall(X0) | brave(X0))) [input p5]
19. creative(john) [input p18]
21. ~wise(john) & ~calm(john) [input p20]
25. tall(john) [input hypothesis]
36. ! [X0] : ((curious(X0) & ~funny(X0)) | ~brave(X0)) [ennf transformation 5]
52. ! [X0] : ((~wise(X0) | (generous(X0) | ~funny(X0))) & ((~generous(X0) & funny(X0)) | wise(X0))) [nnf transformation 3]
53. ! [X0] : ((~wise(X0) | generous(X0) | ~funny(X0)) & ((~generous(X0) & funny(X0)) | wise(X0))) [flattening 52]
59. ! [X0] : (((funny(X0) | creative(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 6]
60. ! [X0] : ((funny(X0) | creative(X0) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | (~funny(X0) & ~creative(X0)))) [flattening 59]
83. funny(X0) | wise(X0) [cnf transformation 53]
89. ~funny(X0) | ~brave(X0) [cnf transformation 36]
91. ~creative(X0) | brave(X0) | ~tall(X0) [cnf transformation 60]
123. creative(john) [cnf transformation 19]
127. ~wise(john) [cnf transformation 21]
131. tall(john) [cnf transformation 25]
322. ~brave(X0) | wise(X0) [resolution 89,83]
325. brave(john) | ~tall(john) [resolution 91,123]
326. brave(john) [subsumption resolution 325,131]
327. wise(john) [resolution 326,322]
330. $false [subsumption resolution 327,127]
% SZS output end Proof for 6650954998108987666785389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or happy is tall and vice versa.
Everyone who is either not patient or not tall is brave or not happy.
Everyone who is both funny and not wise is either quiet or not wise.
Everyone who is either not wise or not curious is rich.
If fred is curious or quiet then susan is not creative or not calm and vice versa.
If susan is quiet then someone is both not quiet and tall and vice versa.
Everyone who is both not humble and not strong is either kind or not old and vice versa.
If someone is either brave or happy then john is either not happy or wise.
Everyone who is brave or old is not quiet and vice versa.
If mary is either funny or tall then someone is not quiet or kind and vice versa.
Everyone who is both not happy and not generous is not kind and vice versa.
Everyone who is not happy or not tall is not curious or strong.
If someone is patient or not old then someone is not kind.
If someone is not creative then paul is both tall and not calm.
If alice is patient or quiet then fred is both not rich and not generous.
If someone is patient then paul is not strong.
Someone is either not quiet or not humble.
Paul is calm or rich.
Mary is both old and not patient.
Someone is curious or tall.
Someone is either not wise or curious.
Someone is not funny or not humble.
Someone is brave or funny. | Paul is not calm. | neutral | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(brave(X)|~happy(X))))&
(![X]:((funny(X)&~wise(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>~curious(X))=>rich(X)))&
(((curious(fred)|quiet(fred)))<=>((~creative(susan)|~calm(susan))))&
((quiet(susan))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~humble(X)&~strong(X))<=>(kind(X)<~>~old(X))))&
((?[X]:((brave(X)<~>happy(X))))=>((~happy(john)<~>wise(john))))&
(![X]:((brave(X)|old(X))<=>~quiet(X)))&
(((funny(mary)<~>tall(mary)))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~happy(X)&~generous(X))<=>~kind(X)))&
(![X]:((~happy(X)|~tall(X))=>(~curious(X)|strong(X))))&
((?[X]:((patient(X)|~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~creative(X)))=>((tall(paul)&~calm(paul))))&
(((patient(alice)|quiet(alice)))=>((~rich(fred)&~generous(fred))))&
((?[X]:(patient(X)))=>(~strong(paul)))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((calm(paul)|rich(paul)))&
((old(mary)&~patient(mary)))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((brave(X)|funny(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is not strong or not humble is both not happy and not rich. Everyone who is either not old or happy is not tall. Everyone who is not brave or not happy is old or not tall and vice versa. Everyone who is kind or generous is either creative or not strong and vice versa. Everyone who is both humble and not generous is both not patient and not humble. Everyone who is patient or not quiet is not patient and vice versa. Everyone who is either not brave or quiet is both generous and not curious. Everyone who is both not curious and old is not wise or not brave and vice versa. If mary is either not happy or curious then john is rich or not brave. Everyone who is old is both strong and not humble. Everyone who is not happy or not creative is funny or calm and vice versa. Everyone who is both not quiet and creative is both creative and quiet and vice versa. If someone is either not funny or not rich then mary is both generous and quiet and vice versa. If someone is both not funny and not brave then someone is either brave or not kind and vice versa. Everyone who is not quiet is curious or rich and vice versa. Everyone who is quiet is generous and vice versa. John is either not tall or not creative. Lucy is brave or not generous. Susan is not rich. Someone is not old or not creative. | Mary is quiet. | contradiction | (![X]:((~strong(X)|~humble(X))=>(~happy(X)&~rich(X))))&
(![X]:((~old(X)<~>happy(X))=>~tall(X)))&
(![X]:((~brave(X)|~happy(X))<=>(old(X)|~tall(X))))&
(![X]:((kind(X)|generous(X))<=>(creative(X)<~>~strong(X))))&
(![X]:((humble(X)&~generous(X))=>(~patient(X)&~humble(X))))&
(![X]:((patient(X)|~quiet(X))<=>~patient(X)))&
(![X]:((~brave(X)<~>quiet(X))=>(generous(X)&~curious(X))))&
(![X]:((~curious(X)&old(X))<=>(~wise(X)|~brave(X))))&
(((~happy(mary)<~>curious(mary)))=>((rich(john)|~brave(john))))&
(![X]:(old(X)=>(strong(X)&~humble(X))))&
(![X]:((~happy(X)|~creative(X))<=>(funny(X)|calm(X))))&
(![X]:((~quiet(X)&creative(X))<=>(creative(X)&quiet(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>((generous(mary)&quiet(mary))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:(~quiet(X)<=>(curious(X)|rich(X))))&
(![X]:(quiet(X)<=>generous(X)))&
((~tall(john)<~>~creative(john)))&
((brave(lucy)|~generous(lucy)))&
(~rich(susan))&
(?[X]:((~old(X)|~creative(X)))) | quiet(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4514933573437294402645351
% SZS output start Proof for 4514933573437294402645351
6. ! [X0] : ((~quiet(X0) | patient(X0)) <=> ~patient(X0)) [input p5]
21. quiet(mary) [input hypothesis]
36. ! [X0] : (((~quiet(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 6]
37. ! [X0] : ((~quiet(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [flattening 36]
80. ~patient(X0) | ~patient(X0) [cnf transformation 37]
82. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 37]
126. quiet(mary) [cnf transformation 21]
129. ~patient(X0) [duplicate literal removal 80]
130. ~quiet(X0) | patient(X0) [duplicate literal removal 82]
156. 6 <=> quiet(mary) [avatar definition]
157. quiet(mary) <- (6) [avatar component clause 156]
220. 6 [avatar split clause 126,156]
234. patient(mary) <- (6) [resolution 130,157]
235. $false <- (6) [subsumption resolution 234,129]
236. ~6 [avatar contradiction clause 235]
237. $false [avatar sat refutation 220,236]
% SZS output end Proof for 4514933573437294402645351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or humble then someone is either generous or brave and vice versa.
Everyone who is not kind is not strong or not generous.
If someone is happy or curious then mary is not old or not curious.
Everyone who is not wise or generous is quiet or not kind.
If someone is kind or humble then someone is both humble and patient.
Everyone who is funny or patient is curious or happy.
Everyone who is both not curious and not rich is both curious and not kind and vice versa.
If paul is not strong or brave then someone is not creative or wise.
Everyone who is quiet is both not brave and not tall.
Everyone who is not tall or not creative is not generous or calm and vice versa.
If alice is happy then paul is curious and vice versa.
If someone is kind then mary is either tall or not patient.
Everyone who is either rich or curious is not curious.
Everyone who is rich is either not happy or curious.
If john is both creative and not creative then someone is either strong or rich.
If paul is both strong and funny then susan is not calm or calm.
Susan is both not humble and not brave.
Lucy is not humble or not funny.
Paul is either calm or not patient.
Someone is both generous and humble.
Susan is either not brave or not generous.
Lucy is either not wise or not generous.
Lucy is curious. | Paul is patient. | neutral | ((?[X]:((old(X)|humble(X))))<=>(?[X]:((generous(X)<~>brave(X)))))&
(![X]:(~kind(X)=>(~strong(X)|~generous(X))))&
((?[X]:((happy(X)|curious(X))))=>((~old(mary)|~curious(mary))))&
(![X]:((~wise(X)|generous(X))=>(quiet(X)|~kind(X))))&
((?[X]:((kind(X)|humble(X))))=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((funny(X)|patient(X))=>(curious(X)|happy(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)&~kind(X))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:(quiet(X)=>(~brave(X)&~tall(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~generous(X)|calm(X))))&
((happy(alice))<=>(curious(paul)))&
((?[X]:(kind(X)))=>((tall(mary)<~>~patient(mary))))&
(![X]:((rich(X)<~>curious(X))=>~curious(X)))&
(![X]:(rich(X)=>(~happy(X)<~>curious(X))))&
(((creative(john)&~creative(john)))=>(?[X]:((strong(X)<~>rich(X)))))&
(((strong(paul)&funny(paul)))=>((~calm(susan)|calm(susan))))&
((~humble(susan)&~brave(susan)))&
((~humble(lucy)|~funny(lucy)))&
((calm(paul)<~>~patient(paul)))&
(?[X]:((generous(X)&humble(X))))&
((~brave(susan)<~>~generous(susan)))&
((~wise(lucy)<~>~generous(lucy)))&
(curious(lucy)) | patient(paul) | [] | null | 0 |
Everyone who is either not old or kind is rich or funny. Everyone who is either not calm or strong is strong and vice versa. Everyone who is either not creative or not wise is either not rich or humble and vice versa. Everyone who is both not old and strong is not patient. Everyone who is both not strong and tall is not creative. Everyone who is both not creative and patient is wise. Everyone who is either old or not wise is both not old and not brave. Everyone who is both not kind and old is either strong or not curious and vice versa. Everyone who is both tall and strong is not quiet or not old and vice versa. If alice is rich then paul is happy and vice versa. Everyone who is happy or wise is not creative and vice versa. If someone is either not tall or not brave then someone is creative or patient and vice versa. If mary is calm or not tall then someone is either tall or not quiet. Everyone who is either not brave or not patient is both not calm and not tall. Everyone who is funny or happy is both wise and not tall and vice versa. If mary is either rich or brave then someone is both not creative and not patient and vice versa. Someone is not patient or not curious. Alice is both not creative and not patient. Someone is either generous or tall. Fred is brave. Someone is not kind or not creative. Lucy is either kind or not quiet. | Paul is wise. | neutral | (![X]:((~old(X)<~>kind(X))=>(rich(X)|funny(X))))&
(![X]:((~calm(X)<~>strong(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((~old(X)&strong(X))=>~patient(X)))&
(![X]:((~strong(X)&tall(X))=>~creative(X)))&
(![X]:((~creative(X)&patient(X))=>wise(X)))&
(![X]:((old(X)<~>~wise(X))=>(~old(X)&~brave(X))))&
(![X]:((~kind(X)&old(X))<=>(strong(X)<~>~curious(X))))&
(![X]:((tall(X)&strong(X))<=>(~quiet(X)|~old(X))))&
((rich(alice))<=>(happy(paul)))&
(![X]:((happy(X)|wise(X))<=>~creative(X)))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(?[X]:((creative(X)|patient(X)))))&
(((calm(mary)|~tall(mary)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>(~calm(X)&~tall(X))))&
(![X]:((funny(X)|happy(X))<=>(wise(X)&~tall(X))))&
(((rich(mary)<~>brave(mary)))<=>(?[X]:((~creative(X)&~patient(X)))))&
(?[X]:((~patient(X)|~curious(X))))&
((~creative(alice)&~patient(alice)))&
(?[X]:((generous(X)<~>tall(X))))&
(brave(fred))&
(?[X]:((~kind(X)|~creative(X))))&
((kind(lucy)<~>~quiet(lucy))) | wise(paul) | [] | null | 0 |
If john is not humble or curious then someone is humble or not patient. If someone is not patient then someone is happy. If someone is not happy then mary is wise and vice versa. Everyone who is both creative and brave is either patient or not quiet and vice versa. Everyone who is either not kind or tall is both not rich and not brave. Everyone who is not calm or generous is quiet or humble. If someone is both generous and not tall then someone is not rich or not curious and vice versa. If someone is both not funny and not quiet then paul is tall or rich and vice versa. Everyone who is not strong or not calm is patient. Everyone who is generous or humble is both calm and not rich and vice versa. Everyone who is either not strong or generous is either generous or brave and vice versa. Everyone who is not old is not tall. Everyone who is both strong and tall is either curious or not creative and vice versa. If someone is quiet then someone is both not strong and curious and vice versa. If lucy is wise or not generous then john is both creative and patient and vice versa. Everyone who is creative or tall is either humble or not strong and vice versa. John is not curious. Someone is either funny or tall. Someone is either not strong or happy. Susan is not curious or patient. Susan is either not patient or not funny. Fred is either not strong or not kind. Susan is not patient. Fred is curious or humble. | Susan is not funny. | contradiction | (((~humble(john)|curious(john)))=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(~patient(X)))=>(?[X]:(happy(X))))&
((?[X]:(~happy(X)))<=>(wise(mary)))&
(![X]:((creative(X)&brave(X))<=>(patient(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>tall(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)|generous(X))=>(quiet(X)|humble(X))))&
((?[X]:((generous(X)&~tall(X))))<=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~funny(X)&~quiet(X))))<=>((tall(paul)|rich(paul))))&
(![X]:((~strong(X)|~calm(X))=>patient(X)))&
(![X]:((generous(X)|humble(X))<=>(calm(X)&~rich(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(generous(X)<~>brave(X))))&
(![X]:(~old(X)=>~tall(X)))&
(![X]:((strong(X)&tall(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~strong(X)&curious(X)))))&
(((wise(lucy)|~generous(lucy)))<=>((creative(john)&patient(john))))&
(![X]:((creative(X)|tall(X))<=>(humble(X)<~>~strong(X))))&
(~curious(john))&
(?[X]:((funny(X)<~>tall(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
((~curious(susan)|patient(susan)))&
((~patient(susan)<~>~funny(susan)))&
((~strong(fred)<~>~kind(fred)))&
(~patient(susan))&
((curious(fred)|humble(fred))) | ~funny(susan) | [
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7985944975575991654126758
% SZS output start Proof for 7985944975575991654126758
21. ~patient(susan) <~> ~funny(susan) [input p20]
23. ~patient(susan) [input p22]
25. ~funny(susan) [input hypothesis]
78. (funny(susan) | patient(susan)) & (~funny(susan) | ~patient(susan)) [nnf transformation 21]
149. funny(susan) | patient(susan) [cnf transformation 78]
152. ~patient(susan) [cnf transformation 23]
154. ~funny(susan) [cnf transformation 25]
322. 36 <=> patient(susan) [avatar definition]
327. 37 <=> funny(susan) [avatar definition]
330. 36 | 37 [avatar split clause 149,327,322]
342. ~36 [avatar split clause 152,322]
352. ~37 [avatar split clause 154,327]
353. $false [avatar sat refutation 330,342,352]
% SZS output end Proof for 7985944975575991654126758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not funny or wise then paul is either not old or not wise and vice versa.
If fred is not kind or patient then someone is either patient or brave and vice versa.
Everyone who is either calm or old is not tall or not old.
Everyone who is not humble or not generous is not calm and vice versa.
Everyone who is both not humble and kind is either calm or happy.
If someone is both not quiet and creative then alice is both quiet and not happy.
If someone is curious then susan is strong and vice versa.
Everyone who is not humble or funny is either funny or rich and vice versa.
If paul is either not funny or generous then someone is not calm or not generous and vice versa.
Everyone who is either curious or not happy is not old.
If someone is not curious or quiet then someone is either not old or brave and vice versa.
Everyone who is rich or quiet is brave or rich.
Everyone who is not old is either humble or not calm and vice versa.
Everyone who is not humble or not kind is both generous and not calm and vice versa.
If susan is either kind or patient then someone is not quiet or brave and vice versa.
If someone is not generous or tall then someone is either curious or generous.
Someone is not quiet.
Mary is kind.
Fred is not rich.
Susan is not generous.
Lucy is not rich or rich.
Paul is both kind and not calm.
Someone is either kind or quiet.
Alice is both kind and wise. | Susan is calm. | contradiction | (((~funny(paul)<~>wise(paul)))<=>((~old(paul)<~>~wise(paul))))&
(((~kind(fred)|patient(fred)))<=>(?[X]:((patient(X)<~>brave(X)))))&
(![X]:((calm(X)<~>old(X))=>(~tall(X)|~old(X))))&
(![X]:((~humble(X)|~generous(X))<=>~calm(X)))&
(![X]:((~humble(X)&kind(X))=>(calm(X)<~>happy(X))))&
((?[X]:((~quiet(X)&creative(X))))=>((quiet(alice)&~happy(alice))))&
((?[X]:(curious(X)))<=>(strong(susan)))&
(![X]:((~humble(X)|funny(X))<=>(funny(X)<~>rich(X))))&
(((~funny(paul)<~>generous(paul)))<=>(?[X]:((~calm(X)|~generous(X)))))&
(![X]:((curious(X)<~>~happy(X))=>~old(X)))&
((?[X]:((~curious(X)|quiet(X))))<=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((rich(X)|quiet(X))=>(brave(X)|rich(X))))&
(![X]:(~old(X)<=>(humble(X)<~>~calm(X))))&
(![X]:((~humble(X)|~kind(X))<=>(generous(X)&~calm(X))))&
(((kind(susan)<~>patient(susan)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((?[X]:((~generous(X)|tall(X))))=>(?[X]:((curious(X)<~>generous(X)))))&
(?[X]:(~quiet(X)))&
(kind(mary))&
(~rich(fred))&
(~generous(susan))&
((~rich(lucy)|rich(lucy)))&
((kind(paul)&~calm(paul)))&
(?[X]:((kind(X)<~>quiet(X))))&
((kind(alice)&wise(alice))) | calm(susan) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1801993274410873369934673
% SZS output start Proof for 1801993274410873369934673
4. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> ~calm(X0)) [input p3]
20. ~generous(susan) [input p19]
25. calm(susan) [input hypothesis]
43. ! [X0] : (((~generous(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) & humble(X0)))) [nnf transformation 4]
44. ! [X0] : ((~generous(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (generous(X0) & humble(X0)))) [flattening 43]
93. ~calm(X0) | generous(X0) [cnf transformation 44]
141. ~generous(susan) [cnf transformation 20]
149. calm(susan) [cnf transformation 25]
323. generous(susan) [resolution 93,149]
324. $false [subsumption resolution 323,141]
% SZS output end Proof for 1801993274410873369934673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not wise is humble or not brave and vice versa.
Everyone who is either not brave or happy is not patient and vice versa.
If susan is either not patient or old then someone is not generous and vice versa.
Everyone who is not curious is curious or creative.
If someone is not brave then john is either generous or calm.
Everyone who is both creative and not patient is kind.
If someone is either not kind or not old then someone is not funny.
Everyone who is both not funny and not tall is either not happy or not patient and vice versa.
Everyone who is both creative and kind is patient.
If mary is either not creative or wise then someone is not tall or wise and vice versa.
Everyone who is either quiet or not curious is not kind.
If john is not happy then someone is both humble and not wise.
Everyone who is not old is either happy or not happy.
Everyone who is not quiet is either not happy or tall and vice versa.
Everyone who is both not tall and not patient is humble or curious and vice versa.
Everyone who is both not generous and not humble is not wise or not funny and vice versa.
Lucy is both not humble and wise.
Lucy is rich or funny.
Someone is either brave or not old.
Fred is both not old and not strong.
Someone is curious or calm.
Paul is both brave and not rich.
Alice is either not generous or brave.
Someone is wise or generous. | Mary is not tall. | entailment | (![X]:((old(X)&~wise(X))<=>(humble(X)|~brave(X))))&
(![X]:((~brave(X)<~>happy(X))<=>~patient(X)))&
(((~patient(susan)<~>old(susan)))<=>(?[X]:(~generous(X))))&
(![X]:(~curious(X)=>(curious(X)|creative(X))))&
((?[X]:(~brave(X)))=>((generous(john)<~>calm(john))))&
(![X]:((creative(X)&~patient(X))=>kind(X)))&
((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:(~funny(X))))&
(![X]:((~funny(X)&~tall(X))<=>(~happy(X)<~>~patient(X))))&
(![X]:((creative(X)&kind(X))=>patient(X)))&
(((~creative(mary)<~>wise(mary)))<=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((quiet(X)<~>~curious(X))=>~kind(X)))&
((~happy(john))=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:(~old(X)=>(happy(X)<~>~happy(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>tall(X))))&
(![X]:((~tall(X)&~patient(X))<=>(humble(X)|curious(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~wise(X)|~funny(X))))&
((~humble(lucy)&wise(lucy)))&
((rich(lucy)|funny(lucy)))&
(?[X]:((brave(X)<~>~old(X))))&
((~old(fred)&~strong(fred)))&
(?[X]:((curious(X)|calm(X))))&
((brave(paul)&~rich(paul)))&
((~generous(alice)<~>brave(alice)))&
(?[X]:((wise(X)|generous(X)))) | ~tall(mary) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6102522386346232650703795
% SZS output start Proof for 6102522386346232650703795
1. ! [X0] : ((~wise(X0) & old(X0)) <=> (~brave(X0) | humble(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> happy(X0)) <=> ~patient(X0)) [input p1]
4. ! [X0] : (~curious(X0) => (creative(X0) | curious(X0))) [input p3]
6. ! [X0] : ((~patient(X0) & creative(X0)) => kind(X0)) [input p5]
8. ! [X0] : ((~tall(X0) & ~funny(X0)) <=> (~happy(X0) <~> ~patient(X0))) [input p7]
9. ! [X0] : ((kind(X0) & creative(X0)) => patient(X0)) [input p8]
10. (~creative(mary) <~> wise(mary)) <=> ? [X0] : (wise(X0) | ~tall(X0)) [input p9]
15. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (curious(X0) | humble(X0))) [input p14]
17. wise(lucy) & ~humble(lucy) [input p16]
25. tall(mary) [input hypothesis]
28. ! [X0] : ((creative(X0) | curious(X0)) | curious(X0)) [ennf transformation 4]
29. ! [X0] : (creative(X0) | curious(X0) | curious(X0)) [flattening 28]
31. ! [X0] : (kind(X0) | (patient(X0) | ~creative(X0))) [ennf transformation 6]
32. ! [X0] : (kind(X0) | patient(X0) | ~creative(X0)) [flattening 31]
34. ! [X0] : (patient(X0) | (~kind(X0) | ~creative(X0))) [ennf transformation 9]
35. ! [X0] : (patient(X0) | ~kind(X0) | ~creative(X0)) [flattening 34]
39. ! [X0] : (((~wise(X0) & old(X0)) | (brave(X0) & ~humble(X0))) & ((~brave(X0) | humble(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 1]
40. ! [X0] : (((~wise(X0) & old(X0)) | (brave(X0) & ~humble(X0))) & (~brave(X0) | humble(X0) | wise(X0) | ~old(X0))) [flattening 39]
41. ! [X0] : ((((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | patient(X0)) & (~patient(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0))))) [nnf transformation 2]
51. ! [X0] : (((~tall(X0) & ~funny(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | (tall(X0) | funny(X0)))) [nnf transformation 8]
52. ! [X0] : (((~tall(X0) & ~funny(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | tall(X0) | funny(X0))) [flattening 51]
53. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X0] : (wise(X0) | ~tall(X0)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [nnf transformation 10]
54. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & (? [X1] : (wise(X1) | ~tall(X1)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [rectify 53]
55. ? [X1] : (wise(X1) | ~tall(X1)) => (wise(sK2) | ~tall(sK2)) [choice axiom]
56. (((~wise(mary) | creative(mary)) & (wise(mary) | ~creative(mary))) | ! [X0] : (~wise(X0) & tall(X0))) & ((wise(sK2) | ~tall(sK2)) | ((~creative(mary) | ~wise(mary)) & (wise(mary) | creative(mary)))) [skolemisation 54,55]
62. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | patient(X0) | tall(X0))) [flattening 62]
78. ~wise(X0) | brave(X0) [cnf transformation 40]
80. ~patient(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 41]
87. creative(X0) | curious(X0) | curious(X0) [cnf transformation 29]
90. ~creative(X0) | patient(X0) | kind(X0) [cnf transformation 32]
97. ~tall(X0) | ~patient(X0) | happy(X0) [cnf transformation 52]
99. patient(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 35]
103. wise(mary) | ~creative(mary) | ~wise(X0) [cnf transformation 56]
118. ~tall(X0) | ~curious(X0) [cnf transformation 63]
127. wise(lucy) [cnf transformation 17]
138. tall(mary) [cnf transformation 25]
139. creative(X0) | curious(X0) [duplicate literal removal 87]
184. ~creative(X0) | patient(X0) [subsumption resolution 99,90]
186. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
187. ~wise(X0) <- (11) [avatar component clause 186]
189. 12 <=> creative(mary) [avatar definition]
190. ~creative(mary) <- (~12) [avatar component clause 189]
191. creative(mary) <- (12) [avatar component clause 189]
193. 13 <=> wise(mary) [avatar definition]
194. wise(mary) <- (13) [avatar component clause 193]
201. 11 | ~12 | 13 [avatar split clause 103,193,189,186]
266. ~curious(mary) [resolution 118,138]
271. curious(mary) <- (~12) [resolution 139,190]
272. $false <- (~12) [subsumption resolution 271,266]
273. 12 [avatar contradiction clause 272]
274. brave(mary) <- (13) [resolution 194,78]
276. patient(mary) <- (12) [resolution 184,191]
281. ~brave(mary) | ~happy(mary) <- (12) [resolution 80,276]
282. ~happy(mary) <- (12, 13) [subsumption resolution 281,274]
347. ~patient(mary) | happy(mary) [resolution 97,138]
348. happy(mary) <- (12) [subsumption resolution 347,276]
349. $false <- (12, 13) [subsumption resolution 348,282]
350. ~12 | ~13 [avatar contradiction clause 349]
353. $false <- (11) [resolution 187,127]
356. ~11 [avatar contradiction clause 353]
358. $false [avatar sat refutation 201,273,350,356]
% SZS output end Proof for 6102522386346232650703795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both humble and not tall is either not tall or not curious.
If mary is either not old or happy then paul is both happy and creative.
Everyone who is both not creative and not kind is not old and vice versa.
If paul is either not calm or not tall then someone is either not strong or not brave and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either not generous or not humble is either not old or quiet and vice versa.
Everyone who is creative or happy is not humble and vice versa.
Everyone who is either not kind or curious is either creative or humble.
If someone is generous or brave then mary is not curious and vice versa.
Everyone who is brave is either humble or not rich and vice versa.
If someone is both not rich and not humble then someone is generous and vice versa.
If someone is both not wise and not creative then someone is either brave or creative.
If alice is either brave or not generous then someone is brave and vice versa.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
Susan is not kind or humble.
Mary is both not creative and not brave.
Someone is happy or not calm.
Someone is either happy or strong.
Alice is either not curious or not kind. | Paul is quiet. | entailment | (![X]:((humble(X)&~tall(X))=>(~tall(X)<~>~curious(X))))&
(((~old(mary)<~>happy(mary)))=>((happy(paul)&creative(paul))))&
(![X]:((~creative(X)&~kind(X))<=>~old(X)))&
(((~calm(paul)<~>~tall(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)|happy(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>(~curious(mary)))&
(![X]:(brave(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(((brave(alice)<~>~generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~kind(susan)|humble(susan)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)<~>strong(X))))&
((~curious(alice)<~>~kind(alice))) | quiet(paul) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1033692721894000960463127
% SZS output start Proof for 1033692721894000960463127
2. (~old(mary) <~> happy(mary)) => (creative(paul) & happy(paul)) [input p1]
3. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~old(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : ((happy(X0) | creative(X0)) <=> ~humble(X0)) [input p6]
14. ! [X0] : ((old(X0) <~> humble(X0)) => generous(X0)) [input p13]
22. ~quiet(paul) [input hypothesis]
28. (creative(paul) & happy(paul)) | (~old(mary) <=> happy(mary)) [ennf transformation 2]
31. ! [X0] : (generous(X0) | (old(X0) <=> humble(X0))) [ennf transformation 14]
34. (creative(paul) & happy(paul)) | ((~old(mary) | ~happy(mary)) & (happy(mary) | old(mary))) [nnf transformation 28]
35. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | (kind(X0) | creative(X0)))) [nnf transformation 3]
36. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | kind(X0) | creative(X0))) [flattening 35]
41. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 5]
42. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 6]
43. ! [X0] : (((happy(X0) | creative(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [nnf transformation 7]
44. ! [X0] : ((happy(X0) | creative(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [flattening 43]
64. ! [X0] : (generous(X0) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) [nnf transformation 31]
76. creative(paul) | happy(mary) | old(mary) [cnf transformation 34]
77. creative(paul) | ~old(mary) | ~happy(mary) [cnf transformation 34]
79. ~creative(X0) | old(X0) [cnf transformation 36]
89. ~happy(X0) | old(X0) [cnf transformation 41]
90. ~old(X0) | happy(X0) [cnf transformation 41]
92. ~generous(X0) | ~old(X0) | quiet(X0) | humble(X0) [cnf transformation 42]
99. ~creative(X0) | ~humble(X0) [cnf transformation 44]
122. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 64]
136. ~quiet(paul) [cnf transformation 22]
139. 1 <=> happy(mary) [avatar definition]
140. happy(mary) <- (1) [avatar component clause 139]
141. ~happy(mary) <- (~1) [avatar component clause 139]
143. 2 <=> old(mary) [avatar definition]
144. old(mary) <- (2) [avatar component clause 143]
145. ~old(mary) <- (~2) [avatar component clause 143]
147. 3 <=> creative(paul) [avatar definition]
149. creative(paul) <- (3) [avatar component clause 147]
150. ~1 | ~2 | 3 [avatar split clause 77,147,143,139]
151. 2 | 1 | 3 [avatar split clause 76,147,139,143]
300. happy(mary) <- (2) [resolution 90,144]
302. $false <- (~1, 2) [subsumption resolution 300,141]
303. 1 | ~2 [avatar contradiction clause 302]
304. old(mary) <- (1) [resolution 140,89]
305. $false <- (1, ~2) [subsumption resolution 304,145]
306. ~1 | 2 [avatar contradiction clause 305]
307. old(paul) <- (3) [resolution 149,79]
309. ~humble(paul) <- (3) [resolution 99,149]
394. humble(paul) | generous(paul) <- (3) [resolution 122,307]
398. generous(paul) <- (3) [subsumption resolution 394,309]
504. ~old(paul) | quiet(paul) | humble(paul) <- (3) [resolution 398,92]
505. quiet(paul) | humble(paul) <- (3) [subsumption resolution 504,307]
506. humble(paul) <- (3) [subsumption resolution 505,136]
507. $false <- (3) [subsumption resolution 506,309]
508. ~3 [avatar contradiction clause 507]
509. $false [avatar sat refutation 150,151,303,306,508]
% SZS output end Proof for 1033692721894000960463127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not rich then paul is not wise and vice versa. If paul is not funny then someone is not rich. Everyone who is not curious is both funny and not funny and vice versa. Everyone who is both not tall and not old is both not creative and patient. Everyone who is not calm is old. Everyone who is happy or not quiet is either happy or not quiet. Everyone who is tall is either rich or curious and vice versa. Everyone who is happy or not quiet is not calm or not generous and vice versa. If mary is both not strong and kind then someone is not quiet and vice versa. Everyone who is either funny or not wise is both wise and not old. Everyone who is both not brave and calm is quiet. If mary is not generous or funny then lucy is calm. If lucy is either old or quiet then alice is either not strong or not wise. Everyone who is either generous or not happy is both not strong and happy and vice versa. If mary is not creative then someone is either not old or not tall. If someone is either not rich or not funny then someone is not kind or generous. Alice is either not brave or tall. Mary is both not quiet and kind. Someone is calm. Someone is generous or not creative. Someone is curious. Someone is not wise. Someone is both not tall and strong. Someone is funny or not tall. | Mary is generous. | entailment | ((~rich(lucy))<=>(~wise(paul)))&
((~funny(paul))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(funny(X)&~funny(X))))&
(![X]:((~tall(X)&~old(X))=>(~creative(X)&patient(X))))&
(![X]:(~calm(X)=>old(X)))&
(![X]:((happy(X)|~quiet(X))=>(happy(X)<~>~quiet(X))))&
(![X]:(tall(X)<=>(rich(X)<~>curious(X))))&
(![X]:((happy(X)|~quiet(X))<=>(~calm(X)|~generous(X))))&
(((~strong(mary)&kind(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)<~>~wise(X))=>(wise(X)&~old(X))))&
(![X]:((~brave(X)&calm(X))=>quiet(X)))&
(((~generous(mary)|funny(mary)))=>(calm(lucy)))&
(((old(lucy)<~>quiet(lucy)))=>((~strong(alice)<~>~wise(alice))))&
(![X]:((generous(X)<~>~happy(X))<=>(~strong(X)&happy(X))))&
((~creative(mary))=>(?[X]:((~old(X)<~>~tall(X)))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:((~kind(X)|generous(X)))))&
((~brave(alice)<~>tall(alice)))&
((~quiet(mary)&kind(mary)))&
(?[X]:(calm(X)))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:(curious(X)))&
(?[X]:(~wise(X)))&
(?[X]:((~tall(X)&strong(X))))&
(?[X]:((funny(X)|~tall(X)))) | generous(mary) | [
"p5",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3144425984370545220165043
% SZS output start Proof for 3144425984370545220165043
6. ! [X0] : ((~quiet(X0) | happy(X0)) => (happy(X0) <~> ~quiet(X0))) [input p5]
14. ! [X0] : ((generous(X0) <~> ~happy(X0)) <=> (happy(X0) & ~strong(X0))) [input p13]
18. kind(mary) & ~quiet(mary) [input p17]
25. ~generous(mary) [input hypothesis]
32. ! [X0] : ((happy(X0) <~> ~quiet(X0)) | (quiet(X0) & ~happy(X0))) [ennf transformation 6]
45. ! [X0] : (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~happy(X0))) [nnf transformation 32]
56. ! [X0] : ((((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))))) [nnf transformation 14]
57. ! [X0] : ((((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))))) [flattening 56]
89. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 45]
115. happy(X0) | generous(X0) | happy(X0) [cnf transformation 57]
124. ~quiet(mary) [cnf transformation 18]
133. ~generous(mary) [cnf transformation 25]
134. generous(X0) | happy(X0) [duplicate literal removal 115]
138. ~happy(X0) | quiet(X0) [duplicate literal removal 89]
189. 11 <=> generous(mary) [avatar definition]
190. ~generous(mary) <- (~11) [avatar component clause 189]
272. ~11 [avatar split clause 133,189]
273. happy(mary) <- (~11) [resolution 134,190]
275. quiet(mary) <- (~11) [resolution 138,273]
276. $false <- (~11) [subsumption resolution 275,124]
277. 11 [avatar contradiction clause 276]
278. $false [avatar sat refutation 272,277]
% SZS output end Proof for 3144425984370545220165043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not funny then someone is either calm or not generous and vice versa.
If fred is both creative and humble then fred is either not humble or curious and vice versa.
Everyone who is either not creative or funny is both generous and wise and vice versa.
Everyone who is either generous or not tall is not brave.
Everyone who is either brave or not humble is either not old or kind and vice versa.
Everyone who is curious is both quiet and generous and vice versa.
If paul is both not generous and not creative then someone is both strong and brave.
Everyone who is both creative and kind is generous.
Everyone who is not creative or wise is either not calm or rich and vice versa.
Everyone who is not curious or tall is both not happy and old and vice versa.
If mary is both calm and not tall then someone is not tall.
Everyone who is either generous or not old is either kind or not curious.
Everyone who is not tall or not humble is both patient and strong.
If fred is either tall or patient then someone is not happy.
Everyone who is both calm and not kind is not patient or not tall and vice versa.
Everyone who is happy or not funny is not kind or not generous.
Someone is creative or not kind.
Alice is both tall and not kind.
Susan is not strong.
Someone is not humble.
Fred is not funny.
Susan is not humble or not calm.
Mary is kind.
Someone is strong. | Alice is curious. | contradiction | ((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(((creative(fred)&humble(fred)))<=>((~humble(fred)<~>curious(fred))))&
(![X]:((~creative(X)<~>funny(X))<=>(generous(X)&wise(X))))&
(![X]:((generous(X)<~>~tall(X))=>~brave(X)))&
(![X]:((brave(X)<~>~humble(X))<=>(~old(X)<~>kind(X))))&
(![X]:(curious(X)<=>(quiet(X)&generous(X))))&
(((~generous(paul)&~creative(paul)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((creative(X)&kind(X))=>generous(X)))&
(![X]:((~creative(X)|wise(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~curious(X)|tall(X))<=>(~happy(X)&old(X))))&
(((calm(mary)&~tall(mary)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~old(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~tall(X)|~humble(X))=>(patient(X)&strong(X))))&
(((tall(fred)<~>patient(fred)))=>(?[X]:(~happy(X))))&
(![X]:((calm(X)&~kind(X))<=>(~patient(X)|~tall(X))))&
(![X]:((happy(X)|~funny(X))=>(~kind(X)|~generous(X))))&
(?[X]:((creative(X)|~kind(X))))&
((tall(alice)&~kind(alice)))&
(~strong(susan))&
(?[X]:(~humble(X)))&
(~funny(fred))&
((~humble(susan)|~calm(susan)))&
(kind(mary))&
(?[X]:(strong(X))) | curious(alice) | [
"p5",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 51698765030536672481566
% SZS output start Proof for 51698765030536672481566
6. ! [X0] : (curious(X0) <=> (generous(X0) & quiet(X0))) [input p5]
10. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (old(X0) & ~happy(X0))) [input p9]
12. ! [X0] : ((generous(X0) <~> ~old(X0)) => (kind(X0) <~> ~curious(X0))) [input p11]
18. ~kind(alice) & tall(alice) [input p17]
25. curious(alice) [input hypothesis]
34. ! [X0] : ((kind(X0) <~> ~curious(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 12]
50. ! [X0] : ((curious(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ~curious(X0))) [nnf transformation 6]
51. ! [X0] : ((curious(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ~curious(X0))) [flattening 50]
56. ! [X0] : (((tall(X0) | ~curious(X0)) | (~old(X0) | happy(X0))) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 10]
57. ! [X0] : ((tall(X0) | ~curious(X0) | ~old(X0) | happy(X0)) & ((old(X0) & ~happy(X0)) | (~tall(X0) & curious(X0)))) [flattening 56]
60. ! [X0] : (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 34]
101. ~curious(X0) | generous(X0) [cnf transformation 51]
115. ~tall(X0) | old(X0) [cnf transformation 57]
118. ~curious(X0) | kind(X0) | ~old(X0) | ~generous(X0) [cnf transformation 60]
136. tall(alice) [cnf transformation 18]
137. ~kind(alice) [cnf transformation 18]
144. curious(alice) [cnf transformation 25]
226. ~old(X0) | kind(X0) | ~curious(X0) [subsumption resolution 118,101]
265. old(alice) [resolution 115,136]
312. kind(alice) | ~curious(alice) [resolution 226,265]
316. ~curious(alice) [subsumption resolution 312,137]
317. $false [subsumption resolution 316,144]
% SZS output end Proof for 51698765030536672481566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not generous is not generous or brave.
Everyone who is both creative and calm is not strong or curious and vice versa.
Everyone who is patient is not brave or not calm.
Everyone who is not strong is not creative and vice versa.
If someone is not rich or not curious then john is patient and vice versa.
If someone is either not curious or strong then someone is not tall or not old.
If someone is quiet or not old then mary is not creative.
If someone is not humble then susan is either old or humble and vice versa.
Everyone who is not quiet is not old or creative.
Everyone who is either humble or not wise is not creative or not brave.
If someone is either calm or tall then mary is strong or happy.
Everyone who is either not humble or wise is either quiet or not old.
Everyone who is not old or not tall is not strong or brave.
Everyone who is strong or not generous is both not kind and wise.
Everyone who is rich or quiet is both old and not generous and vice versa.
Someone is both not kind and tall.
Someone is not funny.
Someone is either patient or happy.
Alice is either not quiet or not generous.
John is not humble or not curious. | John is humble. | contradiction | (![X]:((~calm(X)|~generous(X))=>(~generous(X)|brave(X))))&
(![X]:((creative(X)&calm(X))<=>(~strong(X)|curious(X))))&
(![X]:(patient(X)=>(~brave(X)|~calm(X))))&
(![X]:(~strong(X)<=>~creative(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(patient(john)))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((~tall(X)|~old(X)))))&
((?[X]:((quiet(X)|~old(X))))=>(~creative(mary)))&
((?[X]:(~humble(X)))<=>((old(susan)<~>humble(susan))))&
(![X]:(~quiet(X)=>(~old(X)|creative(X))))&
(![X]:((humble(X)<~>~wise(X))=>(~creative(X)|~brave(X))))&
((?[X]:((calm(X)<~>tall(X))))=>((strong(mary)|happy(mary))))&
(![X]:((~humble(X)<~>wise(X))=>(quiet(X)<~>~old(X))))&
(![X]:((~old(X)|~tall(X))=>(~strong(X)|brave(X))))&
(![X]:((strong(X)|~generous(X))=>(~kind(X)&wise(X))))&
(![X]:((rich(X)|quiet(X))<=>(old(X)&~generous(X))))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)<~>happy(X))))&
((~quiet(alice)<~>~generous(alice)))&
((~humble(john)|~curious(john))) | humble(john) | [
"p1",
"p3",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1860557938397902978633202
% SZS output start Proof for 1860557938397902978633202
2. ! [X0] : ((calm(X0) & creative(X0)) <=> (curious(X0) | ~strong(X0))) [input p1]
4. ! [X0] : (~strong(X0) <=> ~creative(X0)) [input p3]
7. ? [X0] : (~old(X0) | quiet(X0)) => ~creative(mary) [input p6]
12. ! [X0] : ((~humble(X0) <~> wise(X0)) => (quiet(X0) <~> ~old(X0))) [input p11]
14. ! [X0] : ((~generous(X0) | strong(X0)) => (wise(X0) & ~kind(X0))) [input p13]
21. humble(john) [input hypothesis]
25. ! [X0] : ((~generous(X0) | strong(X0)) => wise(X0)) [pure predicate removal 14]
31. ~creative(mary) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 7]
38. ! [X0] : ((quiet(X0) <~> ~old(X0)) | (~humble(X0) <=> wise(X0))) [ennf transformation 12]
41. ! [X0] : (wise(X0) | (generous(X0) & ~strong(X0))) [ennf transformation 25]
42. ! [X0] : (((calm(X0) & creative(X0)) | (~curious(X0) & strong(X0))) & ((curious(X0) | ~strong(X0)) | (~calm(X0) | ~creative(X0)))) [nnf transformation 2]
43. ! [X0] : (((calm(X0) & creative(X0)) | (~curious(X0) & strong(X0))) & (curious(X0) | ~strong(X0) | ~calm(X0) | ~creative(X0))) [flattening 42]
44. ! [X0] : ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))) [nnf transformation 4]
59. ! [X0] : (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) [nnf transformation 38]
71. strong(X0) | creative(X0) [cnf transformation 43]
76. ~creative(X0) | strong(X0) [cnf transformation 44]
77. ~strong(X0) | creative(X0) [cnf transformation 44]
83. ~creative(mary) | ~quiet(X0) [cnf transformation 31]
84. ~creative(mary) | old(X0) [cnf transformation 31]
95. ~old(X0) | quiet(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 59]
100. wise(X0) | ~strong(X0) [cnf transformation 41]
113. humble(john) [cnf transformation 21]
114. creative(X0) [subsumption resolution 77,71]
115. strong(X0) [subsumption resolution 76,114]
150. old(X0) [subsumption resolution 84,114]
151. ~quiet(X0) [subsumption resolution 83,114]
169. quiet(X0) | ~humble(X0) | ~wise(X0) [subsumption resolution 95,150]
170. ~wise(X0) | ~humble(X0) [subsumption resolution 169,151]
174. wise(X0) [subsumption resolution 100,115]
189. 14 <=> humble(john) [avatar definition]
190. humble(john) <- (14) [avatar component clause 189]
197. 14 [avatar split clause 113,189]
205. ~humble(X1) [resolution 170,174]
206. $false <- (14) [resolution 205,190]
207. ~14 [avatar contradiction clause 206]
208. $false [avatar sat refutation 197,207]
% SZS output end Proof for 1860557938397902978633202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or not kind then susan is either not brave or brave and vice versa. If someone is either not old or not humble then someone is either patient or strong and vice versa. If someone is either kind or generous then john is both happy and brave and vice versa. If someone is either not creative or not happy then fred is not tall or not strong. Everyone who is either not curious or patient is not patient and vice versa. Everyone who is both curious and not quiet is either not kind or not brave and vice versa. If someone is creative or curious then john is not quiet or generous. If someone is patient or not strong then someone is both not happy and kind and vice versa. Everyone who is both calm and strong is either not wise or old. If someone is tall or not humble then someone is either creative or generous. Everyone who is not tall or not rich is both old and not curious. If john is either not funny or creative then paul is humble or curious and vice versa. Everyone who is wise is old or strong. Everyone who is not funny or brave is curious and vice versa. Everyone who is humble is both not curious and not kind and vice versa. Everyone who is either not tall or old is both not creative and patient. Someone is either generous or not curious. Someone is either not tall or happy. Fred is not quiet or not tall. Someone is not quiet or strong. Paul is both old and not creative. | Fred is not wise. | neutral | (((~rich(paul)<~>~kind(paul)))<=>((~brave(susan)<~>brave(susan))))&
((?[X]:((~old(X)<~>~humble(X))))<=>(?[X]:((patient(X)<~>strong(X)))))&
((?[X]:((kind(X)<~>generous(X))))<=>((happy(john)&brave(john))))&
((?[X]:((~creative(X)<~>~happy(X))))=>((~tall(fred)|~strong(fred))))&
(![X]:((~curious(X)<~>patient(X))<=>~patient(X)))&
(![X]:((curious(X)&~quiet(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:((creative(X)|curious(X))))=>((~quiet(john)|generous(john))))&
((?[X]:((patient(X)|~strong(X))))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:((~tall(X)<~>happy(X))))&
((~quiet(fred)|~tall(fred)))&
(?[X]:((~quiet(X)|strong(X))))&
((old(paul)&~creative(paul))) | ~wise(fred) | [] | null | 0 |
If alice is both not kind and generous then someone is not calm. Everyone who is both not generous and rich is wise or not kind. If mary is either not patient or funny then susan is not quiet and vice versa. If alice is both old and not strong then someone is patient or not patient and vice versa. If someone is not curious then someone is curious or creative. Everyone who is funny is quiet and vice versa. Everyone who is both not tall and not wise is both brave and not funny and vice versa. Everyone who is both quiet and generous is happy. Everyone who is either not old or not curious is either not tall or not calm and vice versa. Everyone who is either kind or calm is either quiet or not creative. Everyone who is both creative and tall is not curious or curious and vice versa. If john is either kind or not creative then someone is both kind and not strong and vice versa. If someone is funny or not happy then someone is both quiet and not quiet and vice versa. Everyone who is either not wise or not calm is humble and vice versa. If someone is not humble or not tall then susan is not rich. Everyone who is not old or wise is both happy and not rich. Someone is not patient or kind. Someone is not generous. Susan is either old or not patient. Someone is wise or rich. Someone is not humble. Lucy is not old or quiet. Paul is not curious. Someone is brave or not brave. | Lucy is brave. | contradiction | (((~kind(alice)&generous(alice)))=>(?[X]:(~calm(X))))&
(![X]:((~generous(X)&rich(X))=>(wise(X)|~kind(X))))&
(((~patient(mary)<~>funny(mary)))<=>(~quiet(susan)))&
(((old(alice)&~strong(alice)))<=>(?[X]:((patient(X)|~patient(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((curious(X)|creative(X)))))&
(![X]:(funny(X)<=>quiet(X)))&
(![X]:((~tall(X)&~wise(X))<=>(brave(X)&~funny(X))))&
(![X]:((quiet(X)&generous(X))=>happy(X)))&
(![X]:((~old(X)<~>~curious(X))<=>(~tall(X)<~>~calm(X))))&
(![X]:((kind(X)<~>calm(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((creative(X)&tall(X))<=>(~curious(X)|curious(X))))&
(((kind(john)<~>~creative(john)))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>humble(X)))&
((?[X]:((~humble(X)|~tall(X))))=>(~rich(susan)))&
(![X]:((~old(X)|wise(X))=>(happy(X)&~rich(X))))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:(~generous(X)))&
((old(susan)<~>~patient(susan)))&
(?[X]:((wise(X)|rich(X))))&
(?[X]:(~humble(X)))&
((~old(lucy)|quiet(lucy)))&
(~curious(paul))&
(?[X]:((brave(X)|~brave(X)))) | brave(lucy) | [
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7963128164698247614232124
% SZS output start Proof for 7963128164698247614232124
7. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (~funny(X0) & brave(X0))) [input p6]
11. ! [X0] : ((tall(X0) & creative(X0)) <=> (curious(X0) | ~curious(X0))) [input p10]
13. ? [X0] : (~happy(X0) | funny(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p12]
25. brave(lucy) [input hypothesis]
27. ? [X0] : (~happy(X0) | funny(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 13]
50. ! [X0] : (((~wise(X0) & ~tall(X0)) | (funny(X0) | ~brave(X0))) & ((~funny(X0) & brave(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 7]
51. ! [X0] : (((~wise(X0) & ~tall(X0)) | funny(X0) | ~brave(X0)) & ((~funny(X0) & brave(X0)) | wise(X0) | tall(X0))) [flattening 50]
54. ! [X0] : (((tall(X0) & creative(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & creative(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | ~tall(X0) | ~creative(X0))) [flattening 54]
60. (? [X0] : (~happy(X0) | funny(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : (happy(X0) & ~funny(X0))) [nnf transformation 27]
61. (? [X0] : (~happy(X0) | funny(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : (happy(X3) & ~funny(X3))) [rectify 60]
62. ? [X0] : (~happy(X0) | funny(X0)) => (~happy(sK4) | funny(sK4)) [choice axiom]
63. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK5) & quiet(sK5)) [choice axiom]
64. ((~happy(sK4) | funny(sK4)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK5) & quiet(sK5)) | ! [X3] : (happy(X3) & ~funny(X3))) [skolemisation 61,63,62]
93. ~brave(X0) | funny(X0) | ~tall(X0) [cnf transformation 51]
111. tall(X0) | curious(X0) [cnf transformation 55]
112. ~curious(X0) | tall(X0) [cnf transformation 55]
119. quiet(sK5) | ~funny(X3) [cnf transformation 64]
121. ~quiet(sK5) | ~funny(X3) [cnf transformation 64]
143. brave(lucy) [cnf transformation 25]
203. tall(X0) [subsumption resolution 111,112]
230. 19 <=> quiet(sK5) [avatar definition]
235. 20 <=> ! [X3] : ~funny(X3) [avatar definition]
236. ~funny(X3) <- (20) [avatar component clause 235]
237. 20 | ~19 [avatar split clause 121,230,235]
239. 20 | 19 [avatar split clause 119,230,235]
292. funny(lucy) | ~tall(lucy) [resolution 93,143]
294. ~tall(lucy) <- (20) [subsumption resolution 292,236]
295. $false <- (20) [subsumption resolution 294,203]
296. ~20 [avatar contradiction clause 295]
297. $false [avatar sat refutation 237,239,296]
% SZS output end Proof for 7963128164698247614232124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either tall or generous then someone is not strong and vice versa.
Everyone who is either tall or wise is humble.
If someone is both not curious and not old then mary is rich or not old and vice versa.
Everyone who is both quiet and curious is either generous or not old.
Everyone who is either quiet or not curious is creative and vice versa.
If susan is not humble then fred is either patient or tall and vice versa.
Everyone who is both not tall and old is either not calm or not creative and vice versa.
Everyone who is both not humble and not tall is curious or not rich and vice versa.
If alice is both not wise and quiet then susan is both wise and not calm.
If someone is both not calm and not generous then someone is not wise or generous.
If someone is both old and not quiet then fred is not rich or not creative.
Everyone who is either not calm or generous is both quiet and old.
Everyone who is strong is happy.
If paul is patient then john is kind and vice versa.
Everyone who is either not humble or rich is not old or not humble and vice versa.
If someone is either kind or not kind then alice is curious or not happy and vice versa.
John is either not brave or not creative.
Paul is either not kind or curious.
Someone is not generous or curious.
Someone is generous.
Someone is both not wise and old.
Someone is either old or not calm.
Someone is both not generous and funny. | Alice is wise. | neutral | (((tall(john)<~>generous(john)))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>wise(X))=>humble(X)))&
((?[X]:((~curious(X)&~old(X))))<=>((rich(mary)|~old(mary))))&
(![X]:((quiet(X)&curious(X))=>(generous(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>creative(X)))&
((~humble(susan))<=>((patient(fred)<~>tall(fred))))&
(![X]:((~tall(X)&old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~humble(X)&~tall(X))<=>(curious(X)|~rich(X))))&
(((~wise(alice)&quiet(alice)))=>((wise(susan)&~calm(susan))))&
((?[X]:((~calm(X)&~generous(X))))=>(?[X]:((~wise(X)|generous(X)))))&
((?[X]:((old(X)&~quiet(X))))=>((~rich(fred)|~creative(fred))))&
(![X]:((~calm(X)<~>generous(X))=>(quiet(X)&old(X))))&
(![X]:(strong(X)=>happy(X)))&
((patient(paul))<=>(kind(john)))&
(![X]:((~humble(X)<~>rich(X))<=>(~old(X)|~humble(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((curious(alice)|~happy(alice))))&
((~brave(john)<~>~creative(john)))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&old(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~generous(X)&funny(X)))) | wise(alice) | [] | null | 0 |
Everyone who is not old is old or creative and vice versa.
If someone is not wise then mary is not brave.
Everyone who is either not funny or not curious is kind or brave and vice versa.
If john is not rich or not calm then someone is either not happy or not tall and vice versa.
If fred is both tall and happy then someone is not happy or strong.
Everyone who is both not curious and kind is not funny or not creative and vice versa.
If alice is both patient and brave then mary is curious.
If someone is not humble or funny then lucy is either happy or curious and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Everyone who is wise or not kind is both humble and calm and vice versa.
Everyone who is both not humble and not brave is either not tall or not wise.
If someone is calm then mary is both happy and strong and vice versa.
Everyone who is both not patient and not quiet is either rich or curious and vice versa.
Someone is not old.
Mary is both not rich and tall.
Susan is not wise or not curious.
Mary is either old or not old. | Alice is not wise. | contradiction | (![X]:(~old(X)<=>(old(X)|creative(X))))&
((?[X]:(~wise(X)))=>(~brave(mary)))&
(![X]:((~funny(X)<~>~curious(X))<=>(kind(X)|brave(X))))&
(((~rich(john)|~calm(john)))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(((tall(fred)&happy(fred)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~curious(X)&kind(X))<=>(~funny(X)|~creative(X))))&
(((patient(alice)&brave(alice)))=>(curious(mary)))&
((?[X]:((~humble(X)|funny(X))))<=>((happy(lucy)<~>curious(lucy))))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(![X]:((wise(X)|~kind(X))<=>(humble(X)&calm(X))))&
(![X]:((~humble(X)&~brave(X))=>(~tall(X)<~>~wise(X))))&
((?[X]:(calm(X)))<=>((happy(mary)&strong(mary))))&
(![X]:((~patient(X)&~quiet(X))<=>(rich(X)<~>curious(X))))&
(?[X]:(~old(X)))&
((~rich(mary)&tall(mary)))&
((~wise(susan)|~curious(susan)))&
((old(mary)<~>~old(mary))) | ~wise(alice) | [
"p0",
"p1",
"p2",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4173904843411893523663366
% SZS output start Proof for 4173904843411893523663366
1. ! [X0] : (~old(X0) <=> (creative(X0) | old(X0))) [input p0]
2. ? [X0] : ~wise(X0) => ~brave(mary) [input p1]
3. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (brave(X0) | kind(X0))) [input p2]
6. ! [X0] : ((kind(X0) & ~curious(X0)) <=> (~creative(X0) | ~funny(X0))) [input p5]
9. ! [X0] : (~brave(X0) <=> ~humble(X0)) [input p8]
13. ! [X0] : ((~kind(X0) | wise(X0)) <=> (calm(X0) & humble(X0))) [input p12]
21. ~wise(alice) [input hypothesis]
22. ~brave(mary) | ! [X0] : wise(X0) [ennf transformation 2]
31. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & ((creative(X0) | old(X0)) | old(X0))) [nnf transformation 1]
32. ! [X0] : ((~old(X0) | (~creative(X0) & ~old(X0))) & (creative(X0) | old(X0) | old(X0))) [flattening 31]
33. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 3]
34. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [flattening 33]
42. ! [X0] : (((kind(X0) & ~curious(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~kind(X0) | curious(X0)))) [nnf transformation 6]
43. ! [X0] : (((kind(X0) & ~curious(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~kind(X0) | curious(X0))) [flattening 42]
48. ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 9]
53. ! [X0] : (((~kind(X0) | wise(X0)) | (~calm(X0) | ~humble(X0))) & ((calm(X0) & humble(X0)) | (kind(X0) & ~wise(X0)))) [nnf transformation 13]
54. ! [X0] : ((~kind(X0) | wise(X0) | ~calm(X0) | ~humble(X0)) & ((calm(X0) & humble(X0)) | (kind(X0) & ~wise(X0)))) [flattening 53]
66. creative(X0) | old(X0) | old(X0) [cnf transformation 32]
67. ~old(X0) | ~old(X0) [cnf transformation 32]
69. ~brave(mary) | wise(X0) [cnf transformation 22]
72. ~kind(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 34]
74. ~kind(X0) | funny(X0) | curious(X0) [cnf transformation 34]
83. ~creative(X0) | ~funny(X0) | ~kind(X0) | curious(X0) [cnf transformation 43]
84. ~curious(X0) | funny(X0) [cnf transformation 43]
86. kind(X0) | funny(X0) [cnf transformation 43]
95. ~humble(X0) | brave(X0) [cnf transformation 48]
114. humble(X0) | kind(X0) [cnf transformation 54]
135. ~wise(alice) [cnf transformation 21]
138. creative(X0) | old(X0) [duplicate literal removal 66]
139. ~old(X0) [duplicate literal removal 67]
140. creative(X0) [subsumption resolution 138,139]
142. 1 <=> ! [X0] : wise(X0) [avatar definition]
143. wise(X0) <- (1) [avatar component clause 142]
145. 2 <=> brave(mary) [avatar definition]
147. ~brave(mary) <- (~2) [avatar component clause 145]
148. 1 | ~2 [avatar split clause 69,145,142]
194. ~funny(X0) | ~kind(X0) | curious(X0) [subsumption resolution 83,140]
195. ~kind(X0) | curious(X0) [subsumption resolution 194,74]
263. 26 <=> wise(alice) [avatar definition]
264. ~wise(alice) <- (~26) [avatar component clause 263]
311. ~26 [avatar split clause 135,263]
316. kind(X0) | brave(X0) [resolution 114,95]
319. curious(X0) | funny(X0) [resolution 195,86]
322. funny(X0) [subsumption resolution 319,84]
352. brave(X1) | ~funny(X1) | ~curious(X1) [resolution 316,72]
353. brave(X2) | curious(X2) [resolution 316,195]
354. brave(X1) | ~curious(X1) [subsumption resolution 352,322]
355. brave(X2) [subsumption resolution 353,354]
356. $false <- (~2) [resolution 355,147]
361. 2 [avatar contradiction clause 356]
363. $false <- (1, ~26) [resolution 143,264]
368. ~1 | 26 [avatar contradiction clause 363]
369. $false [avatar sat refutation 148,311,361,368]
% SZS output end Proof for 4173904843411893523663366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both brave and not calm and vice versa.
Everyone who is either not funny or not humble is both humble and not patient.
If fred is either not old or old then susan is either quiet or calm.
Everyone who is tall is funny.
If john is not kind then john is either tall or not quiet and vice versa.
Everyone who is patient or not quiet is not tall or funny.
If someone is not strong then someone is not humble or patient.
Everyone who is funny or not kind is not humble and vice versa.
If mary is creative or not quiet then someone is either not old or not rich.
Everyone who is both rich and not old is not calm or strong.
If someone is quiet or not funny then fred is quiet or calm and vice versa.
Everyone who is both happy and not strong is either old or not quiet and vice versa.
Everyone who is curious is either curious or patient and vice versa.
If someone is brave or not creative then fred is old.
If someone is both not rich and not kind then someone is old.
Everyone who is strong or not generous is either not brave or not generous and vice versa.
Someone is either not humble or quiet.
Paul is not happy.
Paul is both not rich and not curious.
Someone is either patient or curious.
Someone is brave.
Fred is not humble or not happy.
Someone is creative or quiet.
Someone is kind or not patient. | Mary is not humble. | neutral | (![X]:(brave(X)<=>(brave(X)&~calm(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(humble(X)&~patient(X))))&
(((~old(fred)<~>old(fred)))=>((quiet(susan)<~>calm(susan))))&
(![X]:(tall(X)=>funny(X)))&
((~kind(john))<=>((tall(john)<~>~quiet(john))))&
(![X]:((patient(X)|~quiet(X))=>(~tall(X)|funny(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((funny(X)|~kind(X))<=>~humble(X)))&
(((creative(mary)|~quiet(mary)))=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((rich(X)&~old(X))=>(~calm(X)|strong(X))))&
((?[X]:((quiet(X)|~funny(X))))<=>((quiet(fred)|calm(fred))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)<~>~quiet(X))))&
(![X]:(curious(X)<=>(curious(X)<~>patient(X))))&
((?[X]:((brave(X)|~creative(X))))=>(old(fred)))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(old(X))))&
(![X]:((strong(X)|~generous(X))<=>(~brave(X)<~>~generous(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(~happy(paul))&
((~rich(paul)&~curious(paul)))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:(brave(X)))&
((~humble(fred)|~happy(fred)))&
(?[X]:((creative(X)|quiet(X))))&
(?[X]:((kind(X)|~patient(X)))) | ~humble(mary) | [] | null | 0 |
Everyone who is both funny and creative is either not wise or not rich and vice versa.
Everyone who is not curious or generous is patient or not wise.
If john is not generous then someone is not wise or not curious and vice versa.
Everyone who is generous is calm or not generous.
Everyone who is both creative and calm is both not patient and strong.
If someone is both brave and creative then mary is either patient or rich and vice versa.
If someone is either not brave or not strong then susan is creative.
If mary is not tall then john is either happy or not happy.
If someone is both not curious and not generous then someone is both not creative and not wise.
If someone is both strong and old then someone is not patient and vice versa.
Everyone who is either curious or quiet is not creative or not old and vice versa.
If someone is either not humble or not happy then john is both old and rich and vice versa.
Everyone who is happy or brave is both quiet and not strong and vice versa.
Everyone who is either not humble or not tall is kind and vice versa.
Everyone who is not strong or not humble is brave.
If someone is curious then someone is not kind or funny and vice versa.
Mary is both calm and not old.
Lucy is not tall or not patient.
Susan is either generous or curious.
Mary is funny.
Someone is either not strong or not brave.
Someone is patient.
Paul is humble.
Someone is either funny or not patient. | Susan is curious. | neutral | (![X]:((funny(X)&creative(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~curious(X)|generous(X))=>(patient(X)|~wise(X))))&
((~generous(john))<=>(?[X]:((~wise(X)|~curious(X)))))&
(![X]:(generous(X)=>(calm(X)|~generous(X))))&
(![X]:((creative(X)&calm(X))=>(~patient(X)&strong(X))))&
((?[X]:((brave(X)&creative(X))))<=>((patient(mary)<~>rich(mary))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(creative(susan)))&
((~tall(mary))=>((happy(john)<~>~happy(john))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~creative(X)&~wise(X)))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:(~patient(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~creative(X)|~old(X))))&
((?[X]:((~humble(X)<~>~happy(X))))<=>((old(john)&rich(john))))&
(![X]:((happy(X)|brave(X))<=>(quiet(X)&~strong(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>kind(X)))&
(![X]:((~strong(X)|~humble(X))=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~kind(X)|funny(X)))))&
((calm(mary)&~old(mary)))&
((~tall(lucy)|~patient(lucy)))&
((generous(susan)<~>curious(susan)))&
(funny(mary))&
(?[X]:((~strong(X)<~>~brave(X))))&
(?[X]:(patient(X)))&
(humble(paul))&
(?[X]:((funny(X)<~>~patient(X)))) | curious(susan) | [] | null | 0 |
If fred is either not strong or brave then someone is either not calm or not funny.
Everyone who is either strong or not tall is both strong and not kind and vice versa.
Everyone who is both not creative and not generous is calm and vice versa.
Everyone who is either not funny or not strong is either tall or not wise and vice versa.
Everyone who is not humble or not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
If paul is not happy or brave then alice is either creative or brave.
If paul is strong or not strong then john is old and vice versa.
Alice is strong or wise.
Someone is wise.
Someone is either creative or not humble.
Someone is either happy or not creative.
Someone is quiet or not patient.
Fred is not patient or rich. | Paul is not kind. | neutral | (((~strong(fred)<~>brave(fred)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((strong(X)<~>~tall(X))<=>(strong(X)&~kind(X))))&
(![X]:((~creative(X)&~generous(X))<=>calm(X)))&
(![X]:((~funny(X)<~>~strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
(((~happy(paul)|brave(paul)))=>((creative(alice)<~>brave(alice))))&
(((strong(paul)|~strong(paul)))<=>(old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((quiet(X)|~patient(X))))&
((~patient(fred)|rich(fred))) | ~kind(paul) | [] | null | 0 |
If someone is brave or not rich then fred is either not funny or not old. Everyone who is either not rich or wise is either not strong or wise and vice versa. If paul is either not happy or not tall then susan is not happy or not strong and vice versa. Everyone who is both wise and not creative is creative or generous and vice versa. If susan is either quiet or not strong then alice is not kind or not brave. Everyone who is either not quiet or not creative is both generous and not tall and vice versa. Everyone who is rich is both curious and not curious and vice versa. Everyone who is calm or patient is generous or wise. Everyone who is tall or creative is both generous and rich and vice versa. If paul is humble then someone is generous or brave. Everyone who is both not tall and happy is curious and vice versa. Everyone who is calm is not funny. If someone is either strong or curious then lucy is generous and vice versa. If fred is either strong or curious then someone is not generous or patient. If alice is either happy or curious then alice is either calm or not rich. Someone is either rich or not funny. John is generous. John is not curious. Someone is both brave and humble. Someone is both patient and not tall. Susan is not calm or not generous. Someone is not patient or not happy. | Lucy is not rich. | entailment | ((?[X]:((brave(X)|~rich(X))))=>((~funny(fred)<~>~old(fred))))&
(![X]:((~rich(X)<~>wise(X))<=>(~strong(X)<~>wise(X))))&
(((~happy(paul)<~>~tall(paul)))<=>((~happy(susan)|~strong(susan))))&
(![X]:((wise(X)&~creative(X))<=>(creative(X)|generous(X))))&
(((quiet(susan)<~>~strong(susan)))=>((~kind(alice)|~brave(alice))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(generous(X)&~tall(X))))&
(![X]:(rich(X)<=>(curious(X)&~curious(X))))&
(![X]:((calm(X)|patient(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)|creative(X))<=>(generous(X)&rich(X))))&
((humble(paul))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~tall(X)&happy(X))<=>curious(X)))&
(![X]:(calm(X)=>~funny(X)))&
((?[X]:((strong(X)<~>curious(X))))<=>(generous(lucy)))&
(((strong(fred)<~>curious(fred)))=>(?[X]:((~generous(X)|patient(X)))))&
(((happy(alice)<~>curious(alice)))=>((calm(alice)<~>~rich(alice))))&
(?[X]:((rich(X)<~>~funny(X))))&
(generous(john))&
(~curious(john))&
(?[X]:((brave(X)&humble(X))))&
(?[X]:((patient(X)&~tall(X))))&
((~calm(susan)|~generous(susan)))&
(?[X]:((~patient(X)|~happy(X)))) | ~rich(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 15961285515745047477153
% SZS output start Proof for 15961285515745047477153
7. ! [X0] : (rich(X0) <=> (~curious(X0) & curious(X0))) [input p6]
23. rich(lucy) [input hypothesis]
40. ! [X0] : ((rich(X0) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | ~rich(X0))) [nnf transformation 7]
41. ! [X0] : ((rich(X0) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | ~rich(X0))) [flattening 40]
94. curious(X0) | ~rich(X0) [cnf transformation 41]
95. ~curious(X0) | ~rich(X0) [cnf transformation 41]
129. rich(lucy) [cnf transformation 23]
182. ~rich(X0) [subsumption resolution 94,95]
251. $false [subsumption resolution 129,182]
% SZS output end Proof for 15961285515745047477153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is old or not quiet then susan is patient or kind and vice versa.
Everyone who is not humble is both not creative and not old and vice versa.
Everyone who is both quiet and happy is both not creative and old.
Everyone who is both not old and brave is both calm and not wise and vice versa.
Everyone who is humble or not rich is either not tall or calm and vice versa.
Everyone who is not kind is either strong or not happy.
If someone is tall or not funny then lucy is not humble and vice versa.
Everyone who is happy is both not patient and not brave and vice versa.
Everyone who is generous is not curious and vice versa.
If fred is patient then someone is either not old or not strong and vice versa.
If lucy is not funny or calm then susan is kind or not happy.
If someone is brave or quiet then someone is both patient and kind and vice versa.
If fred is funny then someone is not strong.
Everyone who is either not old or kind is both not patient and old.
If someone is creative or not wise then paul is both calm and not creative and vice versa.
If susan is humble or generous then mary is both not rich and not humble and vice versa.
Susan is both happy and not generous.
Mary is both old and generous.
Someone is not brave.
Someone is humble or not tall.
Someone is both not creative and not kind.
Someone is calm or happy.
Lucy is tall. | Susan is creative. | contradiction | (((old(mary)|~quiet(mary)))<=>((patient(susan)|kind(susan))))&
(![X]:(~humble(X)<=>(~creative(X)&~old(X))))&
(![X]:((quiet(X)&happy(X))=>(~creative(X)&old(X))))&
(![X]:((~old(X)&brave(X))<=>(calm(X)&~wise(X))))&
(![X]:((humble(X)|~rich(X))<=>(~tall(X)<~>calm(X))))&
(![X]:(~kind(X)=>(strong(X)<~>~happy(X))))&
((?[X]:((tall(X)|~funny(X))))<=>(~humble(lucy)))&
(![X]:(happy(X)<=>(~patient(X)&~brave(X))))&
(![X]:(generous(X)<=>~curious(X)))&
((patient(fred))<=>(?[X]:((~old(X)<~>~strong(X)))))&
(((~funny(lucy)|calm(lucy)))=>((kind(susan)|~happy(susan))))&
((?[X]:((brave(X)|quiet(X))))<=>(?[X]:((patient(X)&kind(X)))))&
((funny(fred))=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>kind(X))=>(~patient(X)&old(X))))&
((?[X]:((creative(X)|~wise(X))))<=>((calm(paul)&~creative(paul))))&
(((humble(susan)|generous(susan)))<=>((~rich(mary)&~humble(mary))))&
((happy(susan)&~generous(susan)))&
((old(mary)&generous(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((calm(X)|happy(X))))&
(tall(lucy)) | creative(susan) | [
"p1",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 359728466312848939656840
% SZS output start Proof for 359728466312848939656840
2. ! [X0] : (~humble(X0) <=> (~old(X0) & ~creative(X0))) [input p1]
16. (generous(susan) | humble(susan)) <=> (~humble(mary) & ~rich(mary)) [input p15]
18. generous(mary) & old(mary) [input p17]
24. creative(susan) [input hypothesis]
35. ! [X0] : ((~humble(X0) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | humble(X0))) [nnf transformation 2]
36. ! [X0] : ((~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | humble(X0))) [flattening 35]
66. ((generous(susan) | humble(susan)) | (humble(mary) | rich(mary))) & ((~humble(mary) & ~rich(mary)) | (~generous(susan) & ~humble(susan))) [nnf transformation 16]
67. (generous(susan) | humble(susan) | humble(mary) | rich(mary)) & ((~humble(mary) & ~rich(mary)) | (~generous(susan) & ~humble(susan))) [flattening 66]
80. ~creative(X0) | humble(X0) [cnf transformation 36]
81. ~old(X0) | humble(X0) [cnf transformation 36]
128. ~humble(mary) | ~humble(susan) [cnf transformation 67]
133. old(mary) [cnf transformation 18]
141. creative(susan) [cnf transformation 24]
148. 2 <=> old(mary) [avatar definition]
150. old(mary) <- (2) [avatar component clause 148]
291. 34 <=> humble(mary) [avatar definition]
292. ~humble(mary) <- (~34) [avatar component clause 291]
295. 35 <=> humble(susan) [avatar definition]
304. ~35 | ~34 [avatar split clause 128,291,295]
309. 2 [avatar split clause 133,148]
328. humble(susan) [resolution 80,141]
331. 35 [avatar split clause 328,295]
332. humble(mary) <- (2) [resolution 81,150]
333. $false <- (2, ~34) [subsumption resolution 332,292]
334. ~2 | 34 [avatar contradiction clause 333]
335. $false [avatar sat refutation 304,309,331,334]
% SZS output end Proof for 359728466312848939656840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not generous is both rich and not funny and vice versa. Everyone who is curious or not wise is creative or tall. Everyone who is both not kind and not calm is both strong and not quiet. Everyone who is rich is not patient or happy and vice versa. If someone is both curious and not old then alice is calm or not brave and vice versa. Everyone who is brave is either not brave or not generous and vice versa. If someone is both not strong and patient then someone is calm or not rich and vice versa. Everyone who is rich is either funny or not curious and vice versa. If alice is both kind and generous then someone is either not quiet or strong and vice versa. If someone is rich then paul is both humble and not happy. If someone is kind then fred is either not funny or rich and vice versa. If someone is not kind or wise then someone is not curious. Everyone who is both old and not kind is rich. Everyone who is either generous or not patient is both patient and tall and vice versa. Everyone who is both patient and not happy is not rich or not creative and vice versa. Alice is old. Someone is both not wise and brave. Someone is either rich or tall. Someone is not curious or not happy. John is both not creative and not generous. Someone is humble. Alice is both not rich and not generous. Someone is either humble or quiet. | Paul is not humble. | contradiction | (![X]:((~quiet(X)&~generous(X))<=>(rich(X)&~funny(X))))&
(![X]:((curious(X)|~wise(X))=>(creative(X)|tall(X))))&
(![X]:((~kind(X)&~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:(rich(X)<=>(~patient(X)|happy(X))))&
((?[X]:((curious(X)&~old(X))))<=>((calm(alice)|~brave(alice))))&
(![X]:(brave(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:((~strong(X)&patient(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(rich(X)<=>(funny(X)<~>~curious(X))))&
(((kind(alice)&generous(alice)))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:(rich(X)))=>((humble(paul)&~happy(paul))))&
((?[X]:(kind(X)))<=>((~funny(fred)<~>rich(fred))))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:(~curious(X))))&
(![X]:((old(X)&~kind(X))=>rich(X)))&
(![X]:((generous(X)<~>~patient(X))<=>(patient(X)&tall(X))))&
(![X]:((patient(X)&~happy(X))<=>(~rich(X)|~creative(X))))&
(old(alice))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~creative(john)&~generous(john)))&
(?[X]:(humble(X)))&
((~rich(alice)&~generous(alice)))&
(?[X]:((humble(X)<~>quiet(X)))) | ~humble(paul) | [
"p3",
"p5",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 69942233911388013420047
% SZS output start Proof for 69942233911388013420047
4. ! [X0] : (rich(X0) <=> (happy(X0) | ~patient(X0))) [input p3]
6. ! [X0] : (brave(X0) <=> (~brave(X0) <~> ~generous(X0))) [input p5]
10. ? [X0] : rich(X0) => (~happy(paul) & humble(paul)) [input p9]
14. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> (tall(X0) & patient(X0))) [input p13]
18. ? [X0] : (rich(X0) <~> tall(X0)) [input p17]
24. ~humble(paul) [input hypothesis]
31. (~happy(paul) & humble(paul)) | ! [X0] : ~rich(X0) [ennf transformation 10]
37. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 4]
38. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~rich(X0))) [flattening 37]
44. ! [X0] : ((brave(X0) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~brave(X0))) [nnf transformation 6]
63. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 14]
64. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [flattening 63]
69. ? [X0] : ((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) [nnf transformation 18]
70. ? [X0] : ((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) => ((~tall(sK7) | ~rich(sK7)) & (tall(sK7) | rich(sK7))) [choice axiom]
71. (~tall(sK7) | ~rich(sK7)) & (tall(sK7) | rich(sK7)) [skolemisation 69,70]
88. patient(X0) | rich(X0) [cnf transformation 38]
95. ~generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
97. brave(X0) | ~generous(X0) | brave(X0) [cnf transformation 44]
114. humble(paul) | ~rich(X0) [cnf transformation 31]
127. ~patient(X0) | generous(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 64]
137. tall(sK7) | rich(sK7) [cnf transformation 71]
147. ~humble(paul) [cnf transformation 24]
149. ~patient(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 127]
150. ~generous(X0) | ~brave(X0) [duplicate literal removal 95]
151. ~generous(X0) | brave(X0) [duplicate literal removal 97]
176. ~generous(X0) [subsumption resolution 150,151]
210. 13 <=> ! [X0] : ~rich(X0) [avatar definition]
211. ~rich(X0) <- (13) [avatar component clause 210]
218. 15 <=> humble(paul) [avatar definition]
221. 13 | 15 [avatar split clause 114,218,210]
253. ~patient(X0) | ~tall(X0) [subsumption resolution 149,176]
257. 23 <=> rich(sK7) [avatar definition]
258. rich(sK7) <- (23) [avatar component clause 257]
261. 24 <=> tall(sK7) [avatar definition]
262. tall(sK7) <- (24) [avatar component clause 261]
265. 23 | 24 [avatar split clause 137,261,257]
285. ~15 [avatar split clause 147,218]
286. $false <- (13, 23) [resolution 258,211]
287. ~13 | ~23 [avatar contradiction clause 286]
290. ~tall(X0) | rich(X0) [resolution 253,88]
292. ~tall(X0) <- (13) [subsumption resolution 290,211]
294. $false <- (13, 24) [resolution 292,262]
295. ~13 | ~24 [avatar contradiction clause 294]
296. $false [avatar sat refutation 221,265,285,287,295]
% SZS output end Proof for 69942233911388013420047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not strong and wise and vice versa.
If someone is humble then susan is both not wise and curious.
If susan is either not humble or tall then someone is either not strong or kind.
Everyone who is kind or not tall is either not funny or not brave.
Everyone who is both not calm and not old is rich or creative and vice versa.
Everyone who is both brave and humble is either not generous or not patient.
Everyone who is wise or not wise is either kind or brave.
If someone is generous then someone is either not happy or calm.
If susan is patient or tall then lucy is either generous or old and vice versa.
Everyone who is both calm and curious is not calm and vice versa.
If someone is both old and not rich then alice is either not rich or brave.
If john is either strong or not curious then someone is tall.
Everyone who is both not kind and not creative is wise or kind and vice versa.
Everyone who is either not wise or not quiet is not curious.
If someone is not strong then someone is not kind or curious and vice versa.
Everyone who is both not quiet and funny is both strong and not generous and vice versa.
Alice is rich or brave.
Someone is not happy or kind.
Someone is both funny and quiet.
Someone is both quiet and funny.
Fred is either not patient or happy.
Susan is both wise and quiet.
Susan is funny or rich. | Fred is creative. | contradiction | (![X]:(wise(X)<=>(~strong(X)&wise(X))))&
((?[X]:(humble(X)))=>((~wise(susan)&curious(susan))))&
(((~humble(susan)<~>tall(susan)))=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:((kind(X)|~tall(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((~calm(X)&~old(X))<=>(rich(X)|creative(X))))&
(![X]:((brave(X)&humble(X))=>(~generous(X)<~>~patient(X))))&
(![X]:((wise(X)|~wise(X))=>(kind(X)<~>brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((~happy(X)<~>calm(X)))))&
(((patient(susan)|tall(susan)))<=>((generous(lucy)<~>old(lucy))))&
(![X]:((calm(X)&curious(X))<=>~calm(X)))&
((?[X]:((old(X)&~rich(X))))=>((~rich(alice)<~>brave(alice))))&
(((strong(john)<~>~curious(john)))=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~creative(X))<=>(wise(X)|kind(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(strong(X)&~generous(X))))&
((rich(alice)|brave(alice)))&
(?[X]:((~happy(X)|kind(X))))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:((quiet(X)&funny(X))))&
((~patient(fred)<~>happy(fred)))&
((wise(susan)&quiet(susan)))&
((funny(susan)|rich(susan))) | creative(fred) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8635543561045952832554709
% SZS output start Proof for 8635543561045952832554709
5. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (creative(X0) | rich(X0))) [input p4]
10. ! [X0] : ((curious(X0) & calm(X0)) <=> ~calm(X0)) [input p9]
24. creative(fred) [input hypothesis]
43. ! [X0] : (((~old(X0) & ~calm(X0)) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | (old(X0) | calm(X0)))) [nnf transformation 5]
44. ! [X0] : (((~old(X0) & ~calm(X0)) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | old(X0) | calm(X0))) [flattening 43]
53. ! [X0] : (((curious(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | (~curious(X0) | ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : (((curious(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | ~curious(X0) | ~calm(X0))) [flattening 53]
91. ~creative(X0) | ~calm(X0) [cnf transformation 44]
109. calm(X0) | calm(X0) [cnf transformation 54]
140. creative(fred) [cnf transformation 24]
144. calm(X0) [duplicate literal removal 109]
267. ~calm(fred) [resolution 91,140]
268. $false [subsumption resolution 267,144]
% SZS output end Proof for 8635543561045952832554709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not curious. Everyone who is both patient and strong is not humble or patient. If alice is both not tall and not wise then john is either not brave or not patient and vice versa. If susan is not funny then someone is either not calm or brave. If lucy is both creative and not humble then fred is not humble and vice versa. Everyone who is either not brave or not calm is not strong. If lucy is either strong or not kind then fred is both funny and old and vice versa. If someone is both not creative and not old then paul is kind. If someone is both quiet and not wise then someone is not humble or not rich and vice versa. If someone is either not strong or not quiet then paul is either curious or brave and vice versa. Everyone who is both not curious and curious is not calm or old. Everyone who is both wise and calm is patient and vice versa. If someone is both not brave and not kind then alice is funny or brave and vice versa. Everyone who is not creative is not happy and vice versa. Everyone who is not funny or calm is curious and vice versa. Everyone who is either not happy or not kind is not old. Someone is not curious. Someone is both not creative and rich. Someone is not funny. Someone is not patient or brave. John is both tall and wise. Fred is not kind or brave. Fred is either kind or not old. Fred is both not calm and tall. | Alice is funny. | neutral | (![X]:(~generous(X)=>~curious(X)))&
(![X]:((patient(X)&strong(X))=>(~humble(X)|patient(X))))&
(((~tall(alice)&~wise(alice)))<=>((~brave(john)<~>~patient(john))))&
((~funny(susan))=>(?[X]:((~calm(X)<~>brave(X)))))&
(((creative(lucy)&~humble(lucy)))<=>(~humble(fred)))&
(![X]:((~brave(X)<~>~calm(X))=>~strong(X)))&
(((strong(lucy)<~>~kind(lucy)))<=>((funny(fred)&old(fred))))&
((?[X]:((~creative(X)&~old(X))))=>(kind(paul)))&
((?[X]:((quiet(X)&~wise(X))))<=>(?[X]:((~humble(X)|~rich(X)))))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>((curious(paul)<~>brave(paul))))&
(![X]:((~curious(X)&curious(X))=>(~calm(X)|old(X))))&
(![X]:((wise(X)&calm(X))<=>patient(X)))&
((?[X]:((~brave(X)&~kind(X))))<=>((funny(alice)|brave(alice))))&
(![X]:(~creative(X)<=>~happy(X)))&
(![X]:((~funny(X)|calm(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~kind(X))=>~old(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~patient(X)|brave(X))))&
((tall(john)&wise(john)))&
((~kind(fred)|brave(fred)))&
((kind(fred)<~>~old(fred)))&
((~calm(fred)&tall(fred))) | funny(alice) | [] | null | 0 |
Everyone who is both not patient and quiet is not happy.
Everyone who is old or kind is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is either not generous or quiet.
Lucy is not funny or strong.
John is not kind or not funny. | Alice is not rich. | contradiction | (![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~funny(lucy)|strong(lucy)))&
((~kind(john)|~funny(john))) | ~rich(alice) | [
"p1",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2684352160878884997197189
% SZS output start Proof for 2684352160878884997197189
2. ! [X0] : ((kind(X0) | old(X0)) <=> old(X0)) [input p1]
7. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> rich(X0)) [input p6]
13. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p12]
15. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p14]
24. ~rich(alice) [input hypothesis]
36. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 13]
37. ! [X0] : (((kind(X0) | old(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 2]
38. ! [X0] : ((kind(X0) | old(X0) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [flattening 37]
44. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [nnf transformation 7]
45. ! [X0] : ((~humble(X0) | ~happy(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [flattening 44]
55. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 15]
56. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 55]
69. ~kind(X0) | old(X0) [cnf transformation 38]
84. humble(X0) | rich(X0) [cnf transformation 45]
97. ~humble(X0) | ~old(X0) [cnf transformation 36]
101. old(X0) | kind(X0) [cnf transformation 56]
117. ~rich(alice) [cnf transformation 24]
206. old(X0) [subsumption resolution 101,69]
282. ~old(X0) | rich(X0) [resolution 97,84]
285. rich(X0) [subsumption resolution 282,206]
288. $false [resolution 285,117]
% SZS output end Proof for 2684352160878884997197189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old then someone is not generous and vice versa.
If john is not funny or not brave then john is humble or creative.
If john is not calm then someone is either patient or not rich.
If mary is not humble or happy then alice is both tall and not brave.
If susan is either not rich or brave then someone is not humble or not wise and vice versa.
Everyone who is rich is not strong or not brave and vice versa.
Everyone who is not generous or not tall is not creative or calm.
Everyone who is funny or not quiet is both rich and not happy and vice versa.
Everyone who is either humble or quiet is wise and vice versa.
If alice is both not old and not calm then susan is both not happy and not old.
Everyone who is not rich or not kind is either old or happy and vice versa.
Everyone who is calm is not patient or not rich and vice versa.
If someone is both funny and happy then someone is either not strong or not quiet and vice versa.
If someone is either brave or not happy then someone is kind.
If someone is both not wise and not strong then someone is not tall or patient.
If fred is not old or calm then paul is both strong and not humble.
Someone is both not strong and brave.
Fred is patient.
Someone is either not calm or tall.
Fred is either not kind or humble.
Mary is both old and not generous.
Lucy is funny or brave.
Mary is not brave or not old.
John is tall. | Susan is not strong. | entailment | ((?[X]:((~happy(X)|old(X))))<=>(?[X]:(~generous(X))))&
(((~funny(john)|~brave(john)))=>((humble(john)|creative(john))))&
((~calm(john))=>(?[X]:((patient(X)<~>~rich(X)))))&
(((~humble(mary)|happy(mary)))=>((tall(alice)&~brave(alice))))&
(((~rich(susan)<~>brave(susan)))<=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:(rich(X)<=>(~strong(X)|~brave(X))))&
(![X]:((~generous(X)|~tall(X))=>(~creative(X)|calm(X))))&
(![X]:((funny(X)|~quiet(X))<=>(rich(X)&~happy(X))))&
(![X]:((humble(X)<~>quiet(X))<=>wise(X)))&
(((~old(alice)&~calm(alice)))=>((~happy(susan)&~old(susan))))&
(![X]:((~rich(X)|~kind(X))<=>(old(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~patient(X)|~rich(X))))&
((?[X]:((funny(X)&happy(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((?[X]:((brave(X)<~>~happy(X))))=>(?[X]:(kind(X))))&
((?[X]:((~wise(X)&~strong(X))))=>(?[X]:((~tall(X)|patient(X)))))&
(((~old(fred)|calm(fred)))=>((strong(paul)&~humble(paul))))&
(?[X]:((~strong(X)&brave(X))))&
(patient(fred))&
(?[X]:((~calm(X)<~>tall(X))))&
((~kind(fred)<~>humble(fred)))&
((old(mary)&~generous(mary)))&
((funny(lucy)|brave(lucy)))&
((~brave(mary)|~old(mary)))&
(tall(john)) | ~strong(susan) | [
"p4",
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4827114494417518994739834
% SZS output start Proof for 4827114494417518994739834
5. (~rich(susan) <~> brave(susan)) <=> ? [X0] : (~wise(X0) | ~humble(X0)) [input p4]
6. ! [X0] : (rich(X0) <=> (~brave(X0) | ~strong(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (~happy(X0) & rich(X0))) [input p7]
9. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> wise(X0)) [input p8]
13. ? [X0] : (happy(X0) & funny(X0)) <=> ? [X0] : (~strong(X0) <~> ~quiet(X0)) [input p12]
25. strong(susan) [input hypothesis]
27. ? [X0] : (happy(X0) & funny(X0)) <=> ? [X1] : (~strong(X1) <~> ~quiet(X1)) [rectify 13]
49. (((~brave(susan) | rich(susan)) & (brave(susan) | ~rich(susan))) | ! [X0] : (wise(X0) & humble(X0))) & (? [X0] : (~wise(X0) | ~humble(X0)) | ((~rich(susan) | ~brave(susan)) & (brave(susan) | rich(susan)))) [nnf transformation 5]
50. (((~brave(susan) | rich(susan)) & (brave(susan) | ~rich(susan))) | ! [X0] : (wise(X0) & humble(X0))) & (? [X1] : (~wise(X1) | ~humble(X1)) | ((~rich(susan) | ~brave(susan)) & (brave(susan) | rich(susan)))) [rectify 49]
51. ? [X1] : (~wise(X1) | ~humble(X1)) => (~wise(sK3) | ~humble(sK3)) [choice axiom]
52. (((~brave(susan) | rich(susan)) & (brave(susan) | ~rich(susan))) | ! [X0] : (wise(X0) & humble(X0))) & ((~wise(sK3) | ~humble(sK3)) | ((~rich(susan) | ~brave(susan)) & (brave(susan) | rich(susan)))) [skolemisation 50,51]
53. ! [X0] : ((rich(X0) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | ~rich(X0))) [nnf transformation 6]
54. ! [X0] : ((rich(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | ~rich(X0))) [flattening 53]
55. ! [X0] : (((~quiet(X0) | funny(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (quiet(X0) & ~funny(X0)))) [nnf transformation 8]
56. ! [X0] : ((~quiet(X0) | funny(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | (quiet(X0) & ~funny(X0)))) [flattening 55]
57. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ~wise(X0)) & (wise(X0) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 9]
62. (? [X0] : (happy(X0) & funny(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X1] : ((quiet(X1) | strong(X1)) & (~quiet(X1) | ~strong(X1))) | ! [X0] : (~happy(X0) | ~funny(X0))) [nnf transformation 27]
63. (? [X0] : (happy(X0) & funny(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) | ! [X3] : (~happy(X3) | ~funny(X3))) [rectify 62]
64. ? [X0] : (happy(X0) & funny(X0)) => (happy(sK4) & funny(sK4)) [choice axiom]
65. ? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) => ((quiet(sK5) | strong(sK5)) & (~quiet(sK5) | ~strong(sK5))) [choice axiom]
66. ((happy(sK4) & funny(sK4)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (((quiet(sK5) | strong(sK5)) & (~quiet(sK5) | ~strong(sK5))) | ! [X3] : (~happy(X3) | ~funny(X3))) [skolemisation 63,65,64]
93. brave(susan) | ~rich(susan) | humble(X0) [cnf transformation 52]
94. brave(susan) | ~rich(susan) | wise(X0) [cnf transformation 52]
95. ~brave(susan) | rich(susan) | humble(X0) [cnf transformation 52]
96. ~brave(susan) | rich(susan) | wise(X0) [cnf transformation 52]
97. ~strong(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 54]
99. rich(X0) | brave(X0) [cnf transformation 54]
104. ~funny(X0) | ~happy(X0) [cnf transformation 56]
110. ~quiet(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 57]
125. funny(sK4) | ~strong(X1) | quiet(X1) [cnf transformation 66]
127. happy(sK4) | ~strong(X1) | quiet(X1) [cnf transformation 66]
147. strong(susan) [cnf transformation 25]
225. 18 <=> ! [X0] : wise(X0) [avatar definition]
226. wise(X0) <- (18) [avatar component clause 225]
228. 19 <=> rich(susan) [avatar definition]
229. ~rich(susan) <- (~19) [avatar component clause 228]
230. rich(susan) <- (19) [avatar component clause 228]
232. 20 <=> brave(susan) [avatar definition]
234. ~brave(susan) <- (~20) [avatar component clause 232]
235. 18 | 19 | ~20 [avatar split clause 96,232,228,225]
237. 21 <=> ! [X0] : humble(X0) [avatar definition]
238. humble(X0) <- (21) [avatar component clause 237]
239. 21 | 19 | ~20 [avatar split clause 95,232,228,237]
240. 18 | ~19 | 20 [avatar split clause 94,232,228,225]
241. 21 | ~19 | 20 [avatar split clause 93,232,228,237]
271. 28 <=> ! [X1] : (~strong(X1) | quiet(X1)) [avatar definition]
272. ~strong(X1) | quiet(X1) <- (28) [avatar component clause 271]
274. 29 <=> happy(sK4) [avatar definition]
276. happy(sK4) <- (29) [avatar component clause 274]
277. 28 | 29 [avatar split clause 127,274,271]
283. 31 <=> funny(sK4) [avatar definition]
285. funny(sK4) <- (31) [avatar component clause 283]
286. 28 | 31 [avatar split clause 125,283,271]
364. brave(susan) <- (~19) [resolution 99,229]
365. $false <- (~19, ~20) [subsumption resolution 364,234]
366. 19 | 20 [avatar contradiction clause 365]
371. quiet(susan) <- (28) [resolution 272,147]
375. ~brave(susan) | ~rich(susan) [resolution 97,147]
380. ~brave(susan) <- (19) [subsumption resolution 375,230]
381. ~20 | ~19 [avatar split clause 380,228,232]
393. ~humble(susan) | ~wise(susan) <- (28) [resolution 110,371]
396. ~wise(susan) <- (21, 28) [subsumption resolution 393,238]
397. $false <- (18, 21, 28) [subsumption resolution 396,226]
398. ~18 | ~21 | ~28 [avatar contradiction clause 397]
400. ~happy(sK4) <- (31) [resolution 285,104]
402. $false <- (29, 31) [subsumption resolution 400,276]
403. ~29 | ~31 [avatar contradiction clause 402]
404. $false [avatar sat refutation 235,239,240,241,277,286,366,381,398,403]
% SZS output end Proof for 4827114494417518994739834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either quiet or not creative.
Everyone who is brave is either not curious or creative and vice versa.
Everyone who is not patient is rich or not creative and vice versa.
If fred is either quiet or not brave then someone is either not strong or not brave.
Everyone who is quiet or old is either curious or not old.
Everyone who is both not funny and humble is not brave or not happy.
Everyone who is strong or patient is generous.
Everyone who is not strong is both not humble and not generous.
If someone is either generous or tall then mary is either not generous or patient.
Everyone who is both creative and calm is not generous or happy and vice versa.
If someone is patient then lucy is tall.
If john is either not funny or not curious then someone is brave or patient.
Everyone who is either tall or not brave is curious or not happy and vice versa.
If mary is not wise or not humble then someone is both strong and brave and vice versa.
If someone is not kind then fred is both rich and not funny.
Everyone who is rich or not old is both patient and not creative.
Alice is both generous and not wise.
Someone is either calm or strong.
Someone is either not generous or happy.
Susan is generous.
Alice is both generous and funny.
Alice is not tall. | Fred is old. | entailment | (![X]:(~wise(X)=>(quiet(X)<~>~creative(X))))&
(![X]:(brave(X)<=>(~curious(X)<~>creative(X))))&
(![X]:(~patient(X)<=>(rich(X)|~creative(X))))&
(((quiet(fred)<~>~brave(fred)))=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:((quiet(X)|old(X))=>(curious(X)<~>~old(X))))&
(![X]:((~funny(X)&humble(X))=>(~brave(X)|~happy(X))))&
(![X]:((strong(X)|patient(X))=>generous(X)))&
(![X]:(~strong(X)=>(~humble(X)&~generous(X))))&
((?[X]:((generous(X)<~>tall(X))))=>((~generous(mary)<~>patient(mary))))&
(![X]:((creative(X)&calm(X))<=>(~generous(X)|happy(X))))&
((?[X]:(patient(X)))=>(tall(lucy)))&
(((~funny(john)<~>~curious(john)))=>(?[X]:((brave(X)|patient(X)))))&
(![X]:((tall(X)<~>~brave(X))<=>(curious(X)|~happy(X))))&
(((~wise(mary)|~humble(mary)))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:(~kind(X)))=>((rich(fred)&~funny(fred))))&
(![X]:((rich(X)|~old(X))=>(patient(X)&~creative(X))))&
((generous(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
(generous(susan))&
((generous(alice)&funny(alice)))&
(~tall(alice)) | old(fred) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2137749777504753922165200
% SZS output start Proof for 2137749777504753922165200
3. ! [X0] : (~patient(X0) <=> (~creative(X0) | rich(X0))) [input p2]
16. ! [X0] : ((~old(X0) | rich(X0)) => (~creative(X0) & patient(X0))) [input p15]
23. ~old(fred) [input hypothesis]
35. ! [X0] : ((~creative(X0) & patient(X0)) | (old(X0) & ~rich(X0))) [ennf transformation 16]
38. ! [X0] : ((~patient(X0) | (creative(X0) & ~rich(X0))) & ((~creative(X0) | rich(X0)) | patient(X0))) [nnf transformation 3]
39. ! [X0] : ((~patient(X0) | (creative(X0) & ~rich(X0))) & (~creative(X0) | rich(X0) | patient(X0))) [flattening 38]
71. ~patient(X0) | creative(X0) [cnf transformation 39]
109. old(X0) | patient(X0) [cnf transformation 35]
111. ~creative(X0) | old(X0) [cnf transformation 35]
122. ~old(fred) [cnf transformation 23]
245. patient(fred) [resolution 109,122]
249. creative(fred) [resolution 245,71]
253. old(fred) [resolution 249,111]
254. $false [subsumption resolution 253,122]
% SZS output end Proof for 2137749777504753922165200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both patient and quiet then someone is both calm and tall.
Everyone who is curious or not strong is generous and vice versa.
Everyone who is both rich and not rich is creative or not curious and vice versa.
If lucy is both not old and strong then john is either rich or not curious.
If alice is either not funny or not strong then someone is either calm or old and vice versa.
If alice is not wise or not calm then paul is either not creative or wise.
If john is both rich and creative then paul is old or strong and vice versa.
If someone is not patient then susan is calm and vice versa.
Everyone who is not curious or tall is tall or calm and vice versa.
Everyone who is both not humble and patient is both calm and patient.
If someone is not kind then someone is both not creative and not brave.
Everyone who is both rich and not happy is not funny.
If someone is either tall or not tall then susan is either patient or not old.
If someone is either old or not strong then fred is both brave and rich.
Someone is not tall or rich.
Paul is not humble or kind.
Someone is both not calm and not tall.
Someone is either wise or not brave.
Someone is both not wise and not happy.
Susan is both not quiet and not wise. | Fred is not brave. | contradiction | (((patient(susan)&quiet(susan)))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:((curious(X)|~strong(X))<=>generous(X)))&
(![X]:((rich(X)&~rich(X))<=>(creative(X)|~curious(X))))&
(((~old(lucy)&strong(lucy)))=>((rich(john)<~>~curious(john))))&
(((~funny(alice)<~>~strong(alice)))<=>(?[X]:((calm(X)<~>old(X)))))&
(((~wise(alice)|~calm(alice)))=>((~creative(paul)<~>wise(paul))))&
(((rich(john)&creative(john)))<=>((old(paul)|strong(paul))))&
((?[X]:(~patient(X)))<=>(calm(susan)))&
(![X]:((~curious(X)|tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&patient(X))=>(calm(X)&patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((rich(X)&~happy(X))=>~funny(X)))&
((?[X]:((tall(X)<~>~tall(X))))=>((patient(susan)<~>~old(susan))))&
((?[X]:((old(X)<~>~strong(X))))=>((brave(fred)&rich(fred))))&
(?[X]:((~tall(X)|rich(X))))&
((~humble(paul)|kind(paul)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~quiet(susan)&~wise(susan))) | ~brave(fred) | [
"p2",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4258626034276159413789880
% SZS output start Proof for 4258626034276159413789880
3. ! [X0] : ((~rich(X0) & rich(X0)) <=> (~curious(X0) | creative(X0))) [input p2]
7. (creative(john) & rich(john)) <=> (strong(paul) | old(paul)) [input p6]
14. ? [X0] : (old(X0) <~> ~strong(X0)) => (rich(fred) & brave(fred)) [input p13]
21. ~brave(fred) [input hypothesis]
34. (rich(fred) & brave(fred)) | ! [X0] : (old(X0) <=> ~strong(X0)) [ennf transformation 14]
35. ! [X0] : (((~rich(X0) & rich(X0)) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 3]
36. ! [X0] : (((~rich(X0) & rich(X0)) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | rich(X0) | ~rich(X0))) [flattening 35]
43. ((creative(john) & rich(john)) | (~strong(paul) & ~old(paul))) & ((strong(paul) | old(paul)) | (~creative(john) | ~rich(john))) [nnf transformation 7]
44. ((creative(john) & rich(john)) | (~strong(paul) & ~old(paul))) & (strong(paul) | old(paul) | ~creative(john) | ~rich(john)) [flattening 43]
52. (rich(fred) & brave(fred)) | ! [X0] : ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))) [nnf transformation 34]
63. rich(X0) | ~creative(X0) [cnf transformation 36]
65. ~creative(X0) | ~rich(X0) [cnf transformation 36]
84. creative(john) | ~old(paul) [cnf transformation 44]
85. creative(john) | ~strong(paul) [cnf transformation 44]
98. brave(fred) | old(X0) | strong(X0) [cnf transformation 52]
109. ~brave(fred) [cnf transformation 21]
115. ~creative(X0) [subsumption resolution 63,65]
176. ~strong(paul) [subsumption resolution 85,115]
177. ~old(paul) [subsumption resolution 84,115]
211. 20 <=> ! [X0] : (old(X0) | strong(X0)) [avatar definition]
212. old(X0) | strong(X0) <- (20) [avatar component clause 211]
223. 23 <=> brave(fred) [avatar definition]
226. 20 | 23 [avatar split clause 98,223,211]
247. ~23 [avatar split clause 109,223]
258. strong(paul) <- (20) [resolution 212,177]
260. $false <- (20) [subsumption resolution 258,176]
261. ~20 [avatar contradiction clause 260]
262. $false [avatar sat refutation 226,247,261]
% SZS output end Proof for 4258626034276159413789880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or kind then someone is both brave and not creative and vice versa.
Everyone who is both not old and not happy is both not humble and not tall.
If someone is not curious then someone is generous or rich and vice versa.
If someone is humble or generous then someone is either tall or funny and vice versa.
Everyone who is both funny and kind is both tall and not patient and vice versa.
If someone is not curious or not funny then mary is not creative and vice versa.
Everyone who is not generous is generous.
Everyone who is either curious or brave is both tall and generous and vice versa.
Everyone who is both brave and strong is not calm.
Everyone who is both not curious and old is both not generous and generous.
Everyone who is both not tall and not wise is calm or not calm and vice versa.
If alice is funny then someone is not kind and vice versa.
Everyone who is not kind is both old and not calm and vice versa.
Everyone who is not strong is either not funny or happy.
Everyone who is both creative and happy is both kind and brave and vice versa.
If someone is either not quiet or old then someone is both not old and curious.
Mary is not quiet.
Someone is both not calm and not brave.
Mary is not humble or creative.
Someone is either not generous or patient.
Fred is not calm or generous.
Someone is strong.
Alice is not rich or funny.
Someone is either strong or not tall. | Alice is not strong. | neutral | ((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((~old(X)&~happy(X))=>(~humble(X)&~tall(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((generous(X)|rich(X)))))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:((funny(X)&kind(X))<=>(tall(X)&~patient(X))))&
((?[X]:((~curious(X)|~funny(X))))<=>(~creative(mary)))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:((curious(X)<~>brave(X))<=>(tall(X)&generous(X))))&
(![X]:((brave(X)&strong(X))=>~calm(X)))&
(![X]:((~curious(X)&old(X))=>(~generous(X)&generous(X))))&
(![X]:((~tall(X)&~wise(X))<=>(calm(X)|~calm(X))))&
((funny(alice))<=>(?[X]:(~kind(X))))&
(![X]:(~kind(X)<=>(old(X)&~calm(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>happy(X))))&
(![X]:((creative(X)&happy(X))<=>(kind(X)&brave(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>(?[X]:((~old(X)&curious(X)))))&
(~quiet(mary))&
(?[X]:((~calm(X)&~brave(X))))&
((~humble(mary)|creative(mary)))&
(?[X]:((~generous(X)<~>patient(X))))&
((~calm(fred)|generous(fred)))&
(?[X]:(strong(X)))&
((~rich(alice)|funny(alice)))&
(?[X]:((strong(X)<~>~tall(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is not old or generous is patient.
If someone is not patient then fred is both not old and not tall and vice versa.
Everyone who is either old or generous is both creative and brave.
Everyone who is both quiet and curious is not patient or not brave.
Everyone who is not quiet or not creative is either curious or not rich.
If susan is both not humble and not old then mary is not happy and vice versa.
Everyone who is both not funny and not old is humble and vice versa.
If mary is either not strong or happy then someone is both not quiet and not humble and vice versa.
Everyone who is both happy and not patient is not generous or not patient and vice versa.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is both curious and patient is not happy or funny and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
If mary is both not curious and creative then lucy is either not generous or not kind.
If someone is not funny or not creative then someone is either tall or old.
Someone is not generous or not calm.
Paul is old or funny.
Someone is either wise or not strong.
Fred is both happy and kind.
Someone is not brave or wise.
Fred is either not wise or curious. | Lucy is quiet. | entailment | (![X]:((~old(X)|generous(X))=>patient(X)))&
((?[X]:(~patient(X)))<=>((~old(fred)&~tall(fred))))&
(![X]:((old(X)<~>generous(X))=>(creative(X)&brave(X))))&
(![X]:((quiet(X)&curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(curious(X)<~>~rich(X))))&
(((~humble(susan)&~old(susan)))<=>(~happy(mary)))&
(![X]:((~funny(X)&~old(X))<=>humble(X)))&
(((~strong(mary)<~>happy(mary)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((curious(X)&patient(X))<=>(~happy(X)|funny(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~curious(mary)&creative(mary)))=>((~generous(lucy)<~>~kind(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(?[X]:((~generous(X)|~calm(X))))&
((old(paul)|funny(paul)))&
(?[X]:((wise(X)<~>~strong(X))))&
((happy(fred)&kind(fred)))&
(?[X]:((~brave(X)|wise(X))))&
((~wise(fred)<~>curious(fred))) | quiet(lucy) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4713944394137224075413300
% SZS output start Proof for 4713944394137224075413300
1. ! [X0] : ((generous(X0) | ~old(X0)) => patient(X0)) [input p0]
2. ? [X0] : ~patient(X0) <=> (~tall(fred) & ~old(fred)) [input p1]
3. ! [X0] : ((old(X0) <~> generous(X0)) => (brave(X0) & creative(X0))) [input p2]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> humble(X0)) [input p6]
8. (~strong(mary) <~> happy(mary)) <=> ? [X0] : (~humble(X0) & ~quiet(X0)) [input p7]
9. ! [X0] : ((~patient(X0) & happy(X0)) <=> (~patient(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (strong(X0) | ~happy(X0))) [input p9]
13. ! [X0] : ((~generous(X0) | happy(X0)) <=> ~creative(X0)) [input p12]
23. ~quiet(lucy) [input hypothesis]
26. ! [X0] : (patient(X0) | (~generous(X0) & old(X0))) [ennf transformation 1]
27. ! [X0] : ((brave(X0) & creative(X0)) | (old(X0) <=> generous(X0))) [ennf transformation 3]
34. (? [X0] : ~patient(X0) | (tall(fred) | old(fred))) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [nnf transformation 2]
35. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [rectify 35]
37. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
38. (~patient(sK0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [skolemisation 36,37]
39. ! [X0] : ((brave(X0) & creative(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 27]
43. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | (old(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | old(X0) | funny(X0))) [flattening 43]
45. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & (? [X0] : (~humble(X0) & ~quiet(X0)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [nnf transformation 8]
46. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & (? [X1] : (~humble(X1) & ~quiet(X1)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [rectify 45]
47. ? [X1] : (~humble(X1) & ~quiet(X1)) => (~humble(sK1) & ~quiet(sK1)) [choice axiom]
48. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & ((~humble(sK1) & ~quiet(sK1)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [skolemisation 46,47]
49. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & ((~patient(X0) | ~generous(X0)) | (patient(X0) | ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & (~patient(X0) | ~generous(X0) | patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 10]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | patient(X0) | creative(X0))) [flattening 51]
56. ! [X0] : (((~generous(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : ((~generous(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [flattening 56]
73. patient(X0) | old(X0) [cnf transformation 26]
74. ~generous(X0) | patient(X0) [cnf transformation 26]
75. ~old(fred) | patient(X1) [cnf transformation 38]
76. ~tall(fred) | patient(X1) [cnf transformation 38]
77. ~patient(sK0) | tall(fred) | old(fred) [cnf transformation 38]
78. ~old(X0) | generous(X0) | creative(X0) [cnf transformation 39]
79. ~generous(X0) | old(X0) | creative(X0) [cnf transformation 39]
92. ~humble(X0) | ~old(X0) [cnf transformation 44]
98. ~happy(mary) | strong(mary) | humble(X0) | quiet(X0) [cnf transformation 48]
101. happy(X0) | patient(X0) [cnf transformation 50]
102. ~patient(X0) | generous(X0) [cnf transformation 50]
107. ~patient(X0) | happy(X0) [cnf transformation 52]
108. ~strong(X0) | ~patient(X0) [cnf transformation 52]
122. ~creative(X0) | ~happy(X0) [cnf transformation 57]
143. ~quiet(lucy) [cnf transformation 23]
145. 1 <=> old(fred) [avatar definition]
149. 2 <=> tall(fred) [avatar definition]
153. 3 <=> patient(sK0) [avatar definition]
155. ~patient(sK0) <- (~3) [avatar component clause 153]
156. 1 | 2 | ~3 [avatar split clause 77,153,149,145]
158. 4 <=> ! [X1] : patient(X1) [avatar definition]
159. patient(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 [avatar split clause 76,149,158]
161. 4 | ~1 [avatar split clause 75,145,158]
163. 5 <=> happy(mary) [avatar definition]
164. ~happy(mary) <- (~5) [avatar component clause 163]
178. 8 <=> ! [X0] : (humble(X0) | quiet(X0)) [avatar definition]
179. humble(X0) | quiet(X0) <- (8) [avatar component clause 178]
181. 9 <=> strong(mary) [avatar definition]
183. strong(mary) <- (9) [avatar component clause 181]
184. 8 | 9 | ~5 [avatar split clause 98,163,181,178]
198. happy(X0) [subsumption resolution 107,101]
205. ~creative(X0) [subsumption resolution 122,198]
263. $false <- (~5) [subsumption resolution 164,198]
264. 5 [avatar contradiction clause 263]
265. old(sK0) <- (~3) [resolution 73,155]
280. generous(sK0) | creative(sK0) <- (~3) [resolution 78,265]
282. generous(sK0) <- (~3) [subsumption resolution 280,205]
303. ~old(X1) | quiet(X1) <- (8) [resolution 179,92]
307. patient(sK0) <- (~3) [resolution 282,74]
308. $false <- (~3) [subsumption resolution 307,155]
309. 3 [avatar contradiction clause 308]
310. generous(X0) <- (4) [resolution 159,102]
312. old(X1) | creative(X1) <- (4) [resolution 310,79]
314. old(X1) <- (4) [subsumption resolution 312,205]
397. quiet(X0) <- (4, 8) [resolution 303,314]
423. $false <- (4, 8) [resolution 397,143]
424. ~4 | ~8 [avatar contradiction clause 423]
448. ~patient(mary) <- (9) [resolution 183,108]
450. $false <- (4, 9) [subsumption resolution 448,159]
451. ~4 | ~9 [avatar contradiction clause 450]
452. $false [avatar sat refutation 156,160,161,184,264,309,424,451]
% SZS output end Proof for 4713944394137224075413300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not creative and not humble.
Everyone who is kind or generous is patient or creative.
Everyone who is both happy and not strong is not brave and vice versa.
Everyone who is not tall or quiet is either not calm or humble and vice versa.
If someone is both old and quiet then someone is either not curious or happy and vice versa.
Everyone who is both rich and wise is funny or kind.
Everyone who is funny or creative is rich.
If someone is either not tall or not strong then john is either patient or not funny and vice versa.
If someone is kind then lucy is funny.
If susan is not curious then mary is both creative and strong and vice versa.
Everyone who is not patient or not curious is not brave.
Everyone who is patient or not strong is either quiet or kind and vice versa.
If lucy is curious then someone is not happy and vice versa.
If someone is not rich or not strong then someone is not funny.
If lucy is strong then someone is either rich or not humble and vice versa.
If someone is not rich or not generous then someone is not patient or not quiet and vice versa.
Someone is either not generous or not patient.
Someone is not wise.
Someone is not calm.
Paul is not calm or generous.
Susan is both happy and humble.
Paul is both strong and tall.
Mary is not creative or not funny. | Lucy is creative. | contradiction | (![X]:(creative(X)=>(~creative(X)&~humble(X))))&
(![X]:((kind(X)|generous(X))=>(patient(X)|creative(X))))&
(![X]:((happy(X)&~strong(X))<=>~brave(X)))&
(![X]:((~tall(X)|quiet(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((old(X)&quiet(X))))<=>(?[X]:((~curious(X)<~>happy(X)))))&
(![X]:((rich(X)&wise(X))=>(funny(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>rich(X)))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((patient(john)<~>~funny(john))))&
((?[X]:(kind(X)))=>(funny(lucy)))&
((~curious(susan))<=>((creative(mary)&strong(mary))))&
(![X]:((~patient(X)|~curious(X))=>~brave(X)))&
(![X]:((patient(X)|~strong(X))<=>(quiet(X)<~>kind(X))))&
((curious(lucy))<=>(?[X]:(~happy(X))))&
((?[X]:((~rich(X)|~strong(X))))=>(?[X]:(~funny(X))))&
((strong(lucy))<=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:((~rich(X)|~generous(X))))<=>(?[X]:((~patient(X)|~quiet(X)))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~calm(X)))&
((~calm(paul)|generous(paul)))&
((happy(susan)&humble(susan)))&
((strong(paul)&tall(paul)))&
((~creative(mary)|~funny(mary))) | creative(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 274894494641579183967230
% SZS output start Proof for 274894494641579183967230
1. ! [X0] : (creative(X0) => (~humble(X0) & ~creative(X0))) [input p0]
24. creative(lucy) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~creative(X0)) | ~creative(X0)) [ennf transformation 1]
75. ~creative(X0) | ~creative(X0) [cnf transformation 31]
136. creative(lucy) [cnf transformation 24]
137. ~creative(X0) [duplicate literal removal 75]
309. $false [subsumption resolution 136,137]
% SZS output end Proof for 274894494641579183967230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not happy is not tall or not funny. If someone is either old or patient then someone is both quiet and wise. If someone is not funny or old then someone is wise or generous and vice versa. If fred is not funny then paul is either calm or not patient and vice versa. Everyone who is either not humble or not quiet is patient or wise and vice versa. If someone is both not patient and not funny then mary is funny and vice versa. If someone is not old then john is not tall or tall and vice versa. If someone is either tall or not creative then mary is either kind or not calm. Everyone who is happy or not kind is both not wise and funny. Everyone who is humble is creative or calm and vice versa. Everyone who is not tall or not brave is both calm and not curious. Everyone who is kind is both humble and not generous. Everyone who is either not tall or old is not happy and vice versa. If someone is strong then someone is both tall and not happy. If fred is either patient or funny then someone is both not humble and not patient. Everyone who is not happy or quiet is kind and vice versa. Someone is kind or creative. Someone is rich or patient. Someone is not creative or brave. Alice is both not creative and quiet. Someone is not brave. Someone is happy or kind. Paul is not patient or kind. Someone is both not quiet and wise. | John is humble. | entailment | (![X]:((~kind(X)<~>~happy(X))=>(~tall(X)|~funny(X))))&
((?[X]:((old(X)<~>patient(X))))=>(?[X]:((quiet(X)&wise(X)))))&
((?[X]:((~funny(X)|old(X))))<=>(?[X]:((wise(X)|generous(X)))))&
((~funny(fred))<=>((calm(paul)<~>~patient(paul))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(patient(X)|wise(X))))&
((?[X]:((~patient(X)&~funny(X))))<=>(funny(mary)))&
((?[X]:(~old(X)))<=>((~tall(john)|tall(john))))&
((?[X]:((tall(X)<~>~creative(X))))=>((kind(mary)<~>~calm(mary))))&
(![X]:((happy(X)|~kind(X))=>(~wise(X)&funny(X))))&
(![X]:(humble(X)<=>(creative(X)|calm(X))))&
(![X]:((~tall(X)|~brave(X))=>(calm(X)&~curious(X))))&
(![X]:(kind(X)=>(humble(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))<=>~happy(X)))&
((?[X]:(strong(X)))=>(?[X]:((tall(X)&~happy(X)))))&
(((patient(fred)<~>funny(fred)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((~happy(X)|quiet(X))<=>kind(X)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((~creative(X)|brave(X))))&
((~creative(alice)&quiet(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((happy(X)|kind(X))))&
((~patient(paul)|kind(paul)))&
(?[X]:((~quiet(X)&wise(X)))) | humble(john) | [
"p0",
"p8",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9060007231050924248691415
% SZS output start Proof for 9060007231050924248691415
1. ! [X0] : ((~kind(X0) <~> ~happy(X0)) => (~funny(X0) | ~tall(X0))) [input p0]
9. ! [X0] : ((~kind(X0) | happy(X0)) => (funny(X0) & ~wise(X0))) [input p8]
10. ! [X0] : (humble(X0) <=> (calm(X0) | creative(X0))) [input p9]
11. ! [X0] : ((~brave(X0) | ~tall(X0)) => (~curious(X0) & calm(X0))) [input p10]
12. ! [X0] : (kind(X0) => (~generous(X0) & humble(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | ~happy(X0)) <=> kind(X0)) [input p15]
25. ~humble(john) [input hypothesis]
31. ! [X0] : ((~brave(X0) | ~tall(X0)) => calm(X0)) [pure predicate removal 11]
32. ! [X0] : ((~funny(X0) | ~tall(X0)) | (~kind(X0) <=> ~happy(X0))) [ennf transformation 1]
33. ! [X0] : (~funny(X0) | ~tall(X0) | (~kind(X0) <=> ~happy(X0))) [flattening 32]
36. ! [X0] : ((funny(X0) & ~wise(X0)) | (kind(X0) & ~happy(X0))) [ennf transformation 9]
37. ! [X0] : (calm(X0) | (brave(X0) & tall(X0))) [ennf transformation 31]
38. ! [X0] : ((~generous(X0) & humble(X0)) | ~kind(X0)) [ennf transformation 12]
40. ! [X0] : (~funny(X0) | ~tall(X0) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) [nnf transformation 33]
63. ! [X0] : ((humble(X0) | (~calm(X0) & ~creative(X0))) & ((calm(X0) | creative(X0)) | ~humble(X0))) [nnf transformation 10]
64. ! [X0] : ((humble(X0) | (~calm(X0) & ~creative(X0))) & (calm(X0) | creative(X0) | ~humble(X0))) [flattening 63]
69. ! [X0] : (((quiet(X0) | ~happy(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) & happy(X0)))) [nnf transformation 16]
70. ! [X0] : ((quiet(X0) | ~happy(X0) | ~kind(X0)) & (kind(X0) | (~quiet(X0) & happy(X0)))) [flattening 69]
81. ~funny(X0) | ~tall(X0) | ~happy(X0) | kind(X0) [cnf transformation 40]
114. funny(X0) | kind(X0) [cnf transformation 36]
117. ~calm(X0) | humble(X0) [cnf transformation 64]
118. calm(X0) | tall(X0) [cnf transformation 37]
120. ~kind(X0) | humble(X0) [cnf transformation 38]
130. happy(X0) | kind(X0) [cnf transformation 70]
142. ~humble(john) [cnf transformation 25]
228. 20 <=> tall(john) [avatar definition]
229. tall(john) <- (20) [avatar component clause 228]
305. humble(X0) | tall(X0) [resolution 118,117]
492. ~tall(X0) | ~happy(X0) | kind(X0) | kind(X0) [resolution 81,114]
496. ~tall(X0) | ~happy(X0) | kind(X0) [duplicate literal removal 492]
497. ~tall(X0) | kind(X0) [subsumption resolution 496,130]
547. tall(john) [resolution 305,142]
553. 20 [avatar split clause 547,228]
568. 63 <=> kind(john) [avatar definition]
569. kind(john) <- (63) [avatar component clause 568]
584. kind(john) <- (20) [resolution 497,229]
595. 63 | ~20 [avatar split clause 584,228,568]
758. humble(john) <- (63) [resolution 569,120]
759. $false <- (63) [subsumption resolution 758,142]
760. ~63 [avatar contradiction clause 759]
761. $false [avatar sat refutation 553,595,760]
% SZS output end Proof for 9060007231050924248691415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is both curious and not tall.
Everyone who is either not tall or creative is quiet or not happy and vice versa.
If paul is either calm or wise then someone is either not wise or not generous.
If someone is either brave or tall then someone is not curious.
Everyone who is generous is both tall and not rich.
If someone is not kind or generous then someone is quiet.
Everyone who is tall is not brave.
Everyone who is tall is not rich.
Everyone who is both not old and strong is either not old or curious and vice versa.
Everyone who is not calm or old is not patient or not curious and vice versa.
Everyone who is not strong is both not happy and not brave and vice versa.
Everyone who is both not curious and not old is either calm or brave.
Everyone who is not creative is kind or curious.
If lucy is both quiet and curious then alice is rich or patient.
If lucy is patient then lucy is tall or calm and vice versa.
Everyone who is both rich and not old is not tall.
Lucy is both not wise and quiet.
Someone is calm.
Paul is not kind or funny.
Someone is not brave or humble.
Alice is both not brave and not happy.
Paul is not humble.
Someone is both tall and quiet.
Lucy is both humble and not curious. | Alice is rich. | neutral | ((?[X]:(~brave(X)))=>(?[X]:((curious(X)&~tall(X)))))&
(![X]:((~tall(X)<~>creative(X))<=>(quiet(X)|~happy(X))))&
(((calm(paul)<~>wise(paul)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
((?[X]:((brave(X)<~>tall(X))))=>(?[X]:(~curious(X))))&
(![X]:(generous(X)=>(tall(X)&~rich(X))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:(quiet(X))))&
(![X]:(tall(X)=>~brave(X)))&
(![X]:(tall(X)=>~rich(X)))&
(![X]:((~old(X)&strong(X))<=>(~old(X)<~>curious(X))))&
(![X]:((~calm(X)|old(X))<=>(~patient(X)|~curious(X))))&
(![X]:(~strong(X)<=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)&~old(X))=>(calm(X)<~>brave(X))))&
(![X]:(~creative(X)=>(kind(X)|curious(X))))&
(((quiet(lucy)&curious(lucy)))=>((rich(alice)|patient(alice))))&
((patient(lucy))<=>((tall(lucy)|calm(lucy))))&
(![X]:((rich(X)&~old(X))=>~tall(X)))&
((~wise(lucy)&quiet(lucy)))&
(?[X]:(calm(X)))&
((~kind(paul)|funny(paul)))&
(?[X]:((~brave(X)|humble(X))))&
((~brave(alice)&~happy(alice)))&
(~humble(paul))&
(?[X]:((tall(X)&quiet(X))))&
((humble(lucy)&~curious(lucy))) | rich(alice) | [] | null | 0 |
Everyone who is not old is both kind and curious and vice versa. If someone is quiet then mary is not tall and vice versa. Everyone who is both not brave and not rich is not kind or not happy and vice versa. Everyone who is not rich is both quiet and brave and vice versa. If lucy is both calm and not tall then fred is calm or not curious. If john is quiet then john is not creative or not patient and vice versa. If alice is old then lucy is both wise and kind and vice versa. Everyone who is either happy or humble is either not strong or not kind and vice versa. Everyone who is generous is either patient or not happy. If alice is patient then fred is either not strong or wise and vice versa. Everyone who is either not brave or not patient is funny. If mary is calm or not calm then susan is either rich or not happy. Everyone who is not funny or creative is happy. If john is curious or humble then someone is not patient or patient. If paul is old or not humble then susan is curious. Everyone who is quiet is brave. Paul is both calm and not wise. John is not funny or not calm. John is both not patient and not old. Someone is wise or humble. Someone is either not tall or brave. Someone is not funny or not generous. Paul is kind. | John is creative. | neutral | (![X]:(~old(X)<=>(kind(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(~tall(mary)))&
(![X]:((~brave(X)&~rich(X))<=>(~kind(X)|~happy(X))))&
(![X]:(~rich(X)<=>(quiet(X)&brave(X))))&
(((calm(lucy)&~tall(lucy)))=>((calm(fred)|~curious(fred))))&
((quiet(john))<=>((~creative(john)|~patient(john))))&
((old(alice))<=>((wise(lucy)&kind(lucy))))&
(![X]:((happy(X)<~>humble(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(generous(X)=>(patient(X)<~>~happy(X))))&
((patient(alice))<=>((~strong(fred)<~>wise(fred))))&
(![X]:((~brave(X)<~>~patient(X))=>funny(X)))&
(((calm(mary)|~calm(mary)))=>((rich(susan)<~>~happy(susan))))&
(![X]:((~funny(X)|creative(X))=>happy(X)))&
(((curious(john)|humble(john)))=>(?[X]:((~patient(X)|patient(X)))))&
(((old(paul)|~humble(paul)))=>(curious(susan)))&
(![X]:(quiet(X)=>brave(X)))&
((calm(paul)&~wise(paul)))&
((~funny(john)|~calm(john)))&
((~patient(john)&~old(john)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~tall(X)<~>brave(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(kind(paul)) | creative(john) | [] | null | 0 |
If lucy is not creative or not humble then john is not curious and vice versa. If paul is quiet then someone is both kind and not strong. If john is both not old and not patient then lucy is either rich or not wise. If someone is not funny or not creative then someone is both not kind and not rich. Everyone who is both tall and happy is patient and vice versa. Everyone who is either humble or tall is not old or not happy and vice versa. If someone is either generous or old then susan is both not patient and brave and vice versa. If lucy is not patient or patient then someone is either tall or not wise and vice versa. If john is either not rich or rich then someone is tall or not patient and vice versa. Everyone who is either not patient or not tall is not kind and vice versa. Everyone who is rich is both not patient and not kind and vice versa. If someone is rich or not patient then someone is either not wise or not rich and vice versa. If someone is either happy or not patient then paul is not rich and vice versa. Everyone who is not kind is either not old or tall and vice versa. Everyone who is either wise or creative is not funny. Paul is both wise and not quiet. Lucy is curious or funny. Someone is both quiet and funny. Someone is not calm or calm. | Lucy is not happy. | neutral | (((~creative(lucy)|~humble(lucy)))<=>(~curious(john)))&
((quiet(paul))=>(?[X]:((kind(X)&~strong(X)))))&
(((~old(john)&~patient(john)))=>((rich(lucy)<~>~wise(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((tall(X)&happy(X))<=>patient(X)))&
(![X]:((humble(X)<~>tall(X))<=>(~old(X)|~happy(X))))&
((?[X]:((generous(X)<~>old(X))))<=>((~patient(susan)&brave(susan))))&
(((~patient(lucy)|patient(lucy)))<=>(?[X]:((tall(X)<~>~wise(X)))))&
(((~rich(john)<~>rich(john)))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>~kind(X)))&
(![X]:(rich(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~rich(paul)))&
(![X]:(~kind(X)<=>(~old(X)<~>tall(X))))&
(![X]:((wise(X)<~>creative(X))=>~funny(X)))&
((wise(paul)&~quiet(paul)))&
((curious(lucy)|funny(lucy)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((~calm(X)|calm(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is not strong or not brave is either tall or not quiet.
Everyone who is not wise or not funny is generous or not quiet and vice versa.
Everyone who is generous is not wise.
Everyone who is either funny or not tall is kind or curious.
Everyone who is funny or strong is brave.
Everyone who is not patient is calm or not calm.
Everyone who is not strong or not tall is rich or creative and vice versa.
Everyone who is not kind is both wise and generous and vice versa.
If mary is not kind or calm then someone is either not humble or tall.
Everyone who is either old or generous is either not calm or not creative and vice versa.
Everyone who is not patient or patient is both tall and not humble and vice versa.
Everyone who is not tall or kind is not happy and vice versa.
Everyone who is not curious or happy is both strong and not tall.
If someone is brave then someone is both humble and not old.
Everyone who is not rich is not calm.
Everyone who is both not wise and not quiet is either not brave or not kind.
Susan is not brave.
Susan is either not generous or quiet.
John is calm or not wise.
Lucy is not quiet or kind.
Someone is calm.
Someone is both not old and not happy. | Lucy is generous. | entailment | (![X]:((~strong(X)|~brave(X))=>(tall(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)|~quiet(X))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:((funny(X)<~>~tall(X))=>(kind(X)|curious(X))))&
(![X]:((funny(X)|strong(X))=>brave(X)))&
(![X]:(~patient(X)=>(calm(X)|~calm(X))))&
(![X]:((~strong(X)|~tall(X))<=>(rich(X)|creative(X))))&
(![X]:(~kind(X)<=>(wise(X)&generous(X))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((old(X)<~>generous(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))<=>(tall(X)&~humble(X))))&
(![X]:((~tall(X)|kind(X))<=>~happy(X)))&
(![X]:((~curious(X)|happy(X))=>(strong(X)&~tall(X))))&
((?[X]:(brave(X)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(~rich(X)=>~calm(X)))&
(![X]:((~wise(X)&~quiet(X))=>(~brave(X)<~>~kind(X))))&
(~brave(susan))&
((~generous(susan)<~>quiet(susan)))&
((calm(john)|~wise(john)))&
((~quiet(lucy)|kind(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~happy(X)))) | generous(lucy) | [
"p0",
"p1",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5439958387149197008990527
% SZS output start Proof for 5439958387149197008990527
1. ! [X0] : ((~brave(X0) | ~strong(X0)) => (tall(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> (~quiet(X0) | generous(X0))) [input p1]
5. ! [X0] : ((strong(X0) | funny(X0)) => brave(X0)) [input p4]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~humble(X0) & tall(X0))) [input p10]
14. ? [X0] : brave(X0) => ? [X0] : (~old(X0) & humble(X0)) [input p13]
23. ~generous(lucy) [input hypothesis]
24. ? [X0] : brave(X0) => ? [X1] : (~old(X1) & humble(X1)) [rectify 14]
28. ! [X0] : ((tall(X0) <~> ~quiet(X0)) | (brave(X0) & strong(X0))) [ennf transformation 1]
30. ! [X0] : (brave(X0) | (~strong(X0) & ~funny(X0))) [ennf transformation 5]
37. ? [X1] : (~old(X1) & humble(X1)) | ! [X0] : ~brave(X0) [ennf transformation 24]
41. ! [X0] : (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (brave(X0) & strong(X0))) [nnf transformation 28]
42. ! [X0] : (((~funny(X0) | ~wise(X0)) | (quiet(X0) & ~generous(X0))) & ((~quiet(X0) | generous(X0)) | (funny(X0) & wise(X0)))) [nnf transformation 2]
43. ! [X0] : ((~funny(X0) | ~wise(X0) | (quiet(X0) & ~generous(X0))) & (~quiet(X0) | generous(X0) | (funny(X0) & wise(X0)))) [flattening 42]
52. ! [X0] : (((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0))) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
53. ! [X0] : ((patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0)) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [flattening 52]
54. ? [X0] : (~old(X0) & humble(X0)) | ! [X1] : ~brave(X1) [rectify 37]
55. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK1) & humble(sK1)) [choice axiom]
56. (~old(sK1) & humble(sK1)) | ! [X1] : ~brave(X1) [skolemisation 54,55]
66. ~tall(X0) | quiet(X0) | brave(X0) [cnf transformation 41]
68. ~quiet(X0) | generous(X0) | funny(X0) [cnf transformation 43]
72. ~funny(X0) | brave(X0) [cnf transformation 30]
94. tall(X0) | patient(X0) [cnf transformation 53]
95. ~patient(X0) | tall(X0) [cnf transformation 53]
96. ~humble(X0) | patient(X0) [cnf transformation 53]
97. ~humble(X0) | ~patient(X0) [cnf transformation 53]
102. humble(sK1) | ~brave(X1) [cnf transformation 56]
115. ~generous(lucy) [cnf transformation 23]
136. ~humble(X0) [subsumption resolution 96,97]
137. tall(X0) [subsumption resolution 94,95]
141. 5 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (5) [avatar component clause 141]
148. ~brave(X1) [subsumption resolution 102,136]
149. 5 [avatar split clause 148,141]
189. quiet(X0) | brave(X0) [resolution 66,137]
190. quiet(X0) <- (5) [subsumption resolution 189,142]
202. generous(X0) | funny(X0) <- (5) [resolution 68,190]
206. funny(lucy) <- (5) [resolution 202,115]
210. brave(lucy) <- (5) [resolution 206,72]
211. $false <- (5) [subsumption resolution 210,142]
212. ~5 [avatar contradiction clause 211]
213. $false [avatar sat refutation 149,212]
% SZS output end Proof for 5439958387149197008990527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not strong is calm or quiet.
Everyone who is both not tall and not calm is funny or not happy.
If someone is both patient and not wise then someone is both not generous and tall.
Everyone who is both not curious and old is either not kind or strong.
Everyone who is either not curious or calm is not old or not strong and vice versa.
If someone is humble then alice is not happy and vice versa.
If mary is either not humble or not brave then someone is old.
Everyone who is either calm or generous is creative or strong and vice versa.
Everyone who is not humble is quiet or not wise and vice versa.
Everyone who is both not patient and happy is either old or curious.
If someone is calm or not rich then someone is either not wise or not rich and vice versa.
If someone is not happy then someone is both not rich and not generous and vice versa.
Everyone who is strong or not strong is not happy and vice versa.
Everyone who is both brave and not old is both curious and old and vice versa.
Everyone who is either funny or not happy is generous or wise and vice versa.
If someone is not wise or not funny then fred is either not creative or patient.
Someone is humble.
Fred is kind or not curious.
Someone is either quiet or calm.
Fred is either not strong or not humble.
Lucy is either calm or happy.
Someone is not wise or patient.
Lucy is either quiet or calm.
Someone is either not humble or not generous. | Alice is happy. | contradiction | (![X]:((~creative(X)&~strong(X))=>(calm(X)|quiet(X))))&
(![X]:((~tall(X)&~calm(X))=>(funny(X)|~happy(X))))&
((?[X]:((patient(X)&~wise(X))))=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)&old(X))=>(~kind(X)<~>strong(X))))&
(![X]:((~curious(X)<~>calm(X))<=>(~old(X)|~strong(X))))&
((?[X]:(humble(X)))<=>(~happy(alice)))&
(((~humble(mary)<~>~brave(mary)))=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>generous(X))<=>(creative(X)|strong(X))))&
(![X]:(~humble(X)<=>(quiet(X)|~wise(X))))&
(![X]:((~patient(X)&happy(X))=>(old(X)<~>curious(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((strong(X)|~strong(X))<=>~happy(X)))&
(![X]:((brave(X)&~old(X))<=>(curious(X)&old(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(generous(X)|wise(X))))&
((?[X]:((~wise(X)|~funny(X))))=>((~creative(fred)<~>patient(fred))))&
(?[X]:(humble(X)))&
((kind(fred)|~curious(fred)))&
(?[X]:((quiet(X)<~>calm(X))))&
((~strong(fred)<~>~humble(fred)))&
((calm(lucy)<~>happy(lucy)))&
(?[X]:((~wise(X)|patient(X))))&
((quiet(lucy)<~>calm(lucy)))&
(?[X]:((~humble(X)<~>~generous(X)))) | happy(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3333754637498234281775790
% SZS output start Proof for 3333754637498234281775790
13. ! [X0] : ((~strong(X0) | strong(X0)) <=> ~happy(X0)) [input p12]
25. happy(alice) [input hypothesis]
68. ! [X0] : (((~strong(X0) | strong(X0)) | happy(X0)) & (~happy(X0) | (strong(X0) & ~strong(X0)))) [nnf transformation 13]
69. ! [X0] : ((~strong(X0) | strong(X0) | happy(X0)) & (~happy(X0) | (strong(X0) & ~strong(X0)))) [flattening 68]
122. ~happy(X0) | ~strong(X0) [cnf transformation 69]
123. ~happy(X0) | strong(X0) [cnf transformation 69]
152. happy(alice) [cnf transformation 25]
245. ~happy(X0) [subsumption resolution 122,123]
317. $false [subsumption resolution 152,245]
% SZS output end Proof for 3333754637498234281775790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and not humble is strong or brave and vice versa.
Everyone who is either tall or kind is generous and vice versa.
If john is kind then lucy is not old and vice versa.
If mary is both not curious and not patient then susan is not calm.
If someone is either generous or calm then someone is either not old or not wise.
If someone is both patient and not tall then someone is not humble and vice versa.
Everyone who is both curious and quiet is not kind.
If someone is not tall then susan is curious.
Everyone who is not kind is both rich and strong.
Everyone who is both not calm and calm is humble or creative and vice versa.
Everyone who is both not funny and not patient is not kind or not patient.
If lucy is both not happy and not patient then someone is quiet or not old and vice versa.
Everyone who is both not old and brave is not funny or happy and vice versa.
If lucy is both creative and not curious then someone is either not funny or humble.
Everyone who is not patient or funny is not funny.
Fred is both not humble and not tall.
Lucy is not patient or not creative.
Someone is not wise.
Susan is either patient or old.
Someone is calm.
Susan is both not kind and brave. | Mary is happy. | neutral | (![X]:((quiet(X)&~humble(X))<=>(strong(X)|brave(X))))&
(![X]:((tall(X)<~>kind(X))<=>generous(X)))&
((kind(john))<=>(~old(lucy)))&
(((~curious(mary)&~patient(mary)))=>(~calm(susan)))&
((?[X]:((generous(X)<~>calm(X))))=>(?[X]:((~old(X)<~>~wise(X)))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~humble(X))))&
(![X]:((curious(X)&quiet(X))=>~kind(X)))&
((?[X]:(~tall(X)))=>(curious(susan)))&
(![X]:(~kind(X)=>(rich(X)&strong(X))))&
(![X]:((~calm(X)&calm(X))<=>(humble(X)|creative(X))))&
(![X]:((~funny(X)&~patient(X))=>(~kind(X)|~patient(X))))&
(((~happy(lucy)&~patient(lucy)))<=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((~old(X)&brave(X))<=>(~funny(X)|happy(X))))&
(((creative(lucy)&~curious(lucy)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:((~patient(X)|funny(X))=>~funny(X)))&
((~humble(fred)&~tall(fred)))&
((~patient(lucy)|~creative(lucy)))&
(?[X]:(~wise(X)))&
((patient(susan)<~>old(susan)))&
(?[X]:(calm(X)))&
((~kind(susan)&brave(susan))) | happy(mary) | [] | null | 0 |
Everyone who is not quiet is both not patient and not curious. Everyone who is either humble or generous is not funny and vice versa. Everyone who is not patient is both kind and rich and vice versa. Everyone who is either old or not happy is generous. If someone is both not quiet and not old then fred is wise or not patient and vice versa. Everyone who is both not old and not curious is not humble and vice versa. If someone is either wise or not rich then susan is happy or calm and vice versa. Everyone who is strong is rich and vice versa. Everyone who is both humble and not calm is not curious and vice versa. Everyone who is both tall and old is humble. Everyone who is not kind is either strong or not rich and vice versa. Everyone who is either rich or strong is both patient and not funny and vice versa. If alice is generous then someone is either generous or not wise. If mary is calm or not happy then someone is creative or not generous and vice versa. If lucy is both quiet and kind then john is not old. Everyone who is generous or not humble is strong or not humble. Paul is not calm. Someone is not wise or curious. Someone is not humble or not brave. Someone is creative or not quiet. Susan is either not quiet or not kind. Lucy is not tall. | Paul is not humble. | contradiction | (![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((humble(X)<~>generous(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(kind(X)&rich(X))))&
(![X]:((old(X)<~>~happy(X))=>generous(X)))&
((?[X]:((~quiet(X)&~old(X))))<=>((wise(fred)|~patient(fred))))&
(![X]:((~old(X)&~curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~rich(X))))<=>((happy(susan)|calm(susan))))&
(![X]:(strong(X)<=>rich(X)))&
(![X]:((humble(X)&~calm(X))<=>~curious(X)))&
(![X]:((tall(X)&old(X))=>humble(X)))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(~calm(paul))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((creative(X)|~quiet(X))))&
((~quiet(susan)<~>~kind(susan)))&
(~tall(lucy)) | ~humble(paul) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3271683189871589767491699
% SZS output start Proof for 3271683189871589767491699
6. ! [X0] : ((~curious(X0) & ~old(X0)) <=> ~humble(X0)) [input p5]
9. ! [X0] : ((~calm(X0) & humble(X0)) <=> ~curious(X0)) [input p8]
23. ~humble(paul) [input hypothesis]
43. ! [X0] : (((~curious(X0) & ~old(X0)) | humble(X0)) & (~humble(X0) | (curious(X0) | old(X0)))) [nnf transformation 6]
44. ! [X0] : (((~curious(X0) & ~old(X0)) | humble(X0)) & (~humble(X0) | curious(X0) | old(X0))) [flattening 43]
51. ! [X0] : (((~calm(X0) & humble(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~humble(X0)))) [nnf transformation 9]
52. ! [X0] : (((~calm(X0) & humble(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~humble(X0))) [flattening 51]
87. ~curious(X0) | humble(X0) [cnf transformation 44]
97. humble(X0) | curious(X0) [cnf transformation 52]
123. ~humble(paul) [cnf transformation 23]
176. humble(X0) [subsumption resolution 97,87]
244. $false [subsumption resolution 123,176]
% SZS output end Proof for 3271683189871589767491699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or generous is both not wise and wise and vice versa.
If fred is either not wise or generous then alice is either not quiet or calm and vice versa.
Everyone who is either not kind or calm is both calm and happy and vice versa.
Everyone who is either not kind or patient is both not happy and generous.
If someone is not old then lucy is not generous or kind and vice versa.
Everyone who is either tall or old is either not generous or old.
Everyone who is both not calm and not strong is not generous or strong.
Everyone who is both generous and happy is both not strong and curious.
Everyone who is funny or wise is both strong and not calm and vice versa.
If someone is either strong or rich then someone is either not calm or creative and vice versa.
Everyone who is both not funny and humble is funny or rich and vice versa.
Everyone who is not curious or not tall is funny or not quiet and vice versa.
Everyone who is wise is both not old and not kind and vice versa.
If someone is either not humble or not wise then alice is not rich.
If someone is rich or not old then someone is both not happy and not tall.
Everyone who is either kind or brave is both old and not calm and vice versa.
Someone is both brave and calm.
Someone is not kind or not brave.
Alice is not happy or creative.
Someone is tall.
Someone is both old and not curious.
Alice is both not calm and brave.
Someone is either not happy or not tall. | Alice is rich. | contradiction | (![X]:((wise(X)<~>generous(X))<=>(~wise(X)&wise(X))))&
(((~wise(fred)<~>generous(fred)))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:((~kind(X)<~>calm(X))<=>(calm(X)&happy(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~happy(X)&generous(X))))&
((?[X]:(~old(X)))<=>((~generous(lucy)|kind(lucy))))&
(![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(~rich(alice)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
(![X]:((kind(X)<~>brave(X))<=>(old(X)&~calm(X))))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~kind(X)|~brave(X))))&
((~happy(alice)|creative(alice)))&
(?[X]:(tall(X)))&
(?[X]:((old(X)&~curious(X))))&
((~calm(alice)&brave(alice)))&
(?[X]:((~happy(X)<~>~tall(X)))) | rich(alice) | [
"p2",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5926379912042018237923718
% SZS output start Proof for 5926379912042018237923718
3. ! [X0] : ((~kind(X0) <~> calm(X0)) <=> (happy(X0) & calm(X0))) [input p2]
9. ! [X0] : ((wise(X0) | funny(X0)) <=> (~calm(X0) & strong(X0))) [input p8]
11. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (rich(X0) | funny(X0))) [input p10]
13. ! [X0] : (wise(X0) <=> (~kind(X0) & ~old(X0))) [input p12]
14. ? [X0] : (~humble(X0) <~> ~wise(X0)) => ~rich(alice) [input p13]
24. rich(alice) [input hypothesis]
33. ~rich(alice) | ! [X0] : (~humble(X0) <=> ~wise(X0)) [ennf transformation 14]
38. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [flattening 38]
47. ! [X0] : (((wise(X0) | funny(X0)) | (calm(X0) | ~strong(X0))) & ((~calm(X0) & strong(X0)) | (~wise(X0) & ~funny(X0)))) [nnf transformation 9]
48. ! [X0] : ((wise(X0) | funny(X0) | calm(X0) | ~strong(X0)) & ((~calm(X0) & strong(X0)) | (~wise(X0) & ~funny(X0)))) [flattening 47]
54. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 11]
55. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~humble(X0) | funny(X0))) [flattening 54]
58. ! [X0] : ((wise(X0) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ~wise(X0))) [nnf transformation 13]
59. ! [X0] : ((wise(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~wise(X0))) [flattening 58]
60. ~rich(alice) | ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 33]
91. calm(X0) | calm(X0) | kind(X0) [cnf transformation 39]
114. ~calm(X0) | ~wise(X0) [cnf transformation 48]
128. ~rich(X0) | humble(X0) [cnf transformation 55]
134. ~kind(X0) | ~wise(X0) [cnf transformation 59]
137. ~rich(alice) | ~humble(X0) | wise(X0) [cnf transformation 60]
159. rich(alice) [cnf transformation 24]
165. kind(X0) | calm(X0) [duplicate literal removal 91]
253. 17 <=> ! [X0] : (~humble(X0) | wise(X0)) [avatar definition]
254. ~humble(X0) | wise(X0) <- (17) [avatar component clause 253]
256. 18 <=> rich(alice) [avatar definition]
257. rich(alice) <- (18) [avatar component clause 256]
259. 17 | ~18 [avatar split clause 137,256,253]
302. 18 [avatar split clause 159,256]
305. humble(alice) <- (18) [resolution 128,257]
307. calm(X0) | ~wise(X0) [resolution 165,134]
308. ~wise(X0) [subsumption resolution 307,114]
310. wise(alice) <- (17, 18) [resolution 254,305]
311. $false <- (17, 18) [subsumption resolution 310,308]
312. ~17 | ~18 [avatar contradiction clause 311]
313. $false [avatar sat refutation 259,302,312]
% SZS output end Proof for 5926379912042018237923718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or generous then alice is curious.
Everyone who is either not kind or humble is both not quiet and quiet and vice versa.
Everyone who is not calm is kind or happy.
If lucy is not old then someone is either kind or happy and vice versa.
Everyone who is not creative is not quiet or strong.
Everyone who is quiet is either not funny or not old.
If mary is not curious then someone is not strong and vice versa.
Everyone who is both not calm and not funny is funny or rich.
Everyone who is strong or not brave is both not brave and not curious.
Everyone who is wise or rich is both not wise and kind and vice versa.
If paul is both not wise and calm then someone is both quiet and not old and vice versa.
If susan is both creative and quiet then alice is either not quiet or wise and vice versa.
Everyone who is both not patient and not creative is not creative or brave and vice versa.
If fred is not creative then mary is either curious or not happy and vice versa.
Everyone who is humble is both not generous and kind.
Everyone who is not humble is either generous or tall and vice versa.
Paul is not tall.
Fred is curious or strong.
Fred is both not calm and quiet.
Someone is both not humble and funny.
Fred is patient or not strong.
Alice is both creative and not quiet. | Alice is not tall. | neutral | (((old(john)<~>generous(john)))=>(curious(alice)))&
(![X]:((~kind(X)<~>humble(X))<=>(~quiet(X)&quiet(X))))&
(![X]:(~calm(X)=>(kind(X)|happy(X))))&
((~old(lucy))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:(~creative(X)=>(~quiet(X)|strong(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~old(X))))&
((~curious(mary))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&~funny(X))=>(funny(X)|rich(X))))&
(![X]:((strong(X)|~brave(X))=>(~brave(X)&~curious(X))))&
(![X]:((wise(X)|rich(X))<=>(~wise(X)&kind(X))))&
(((~wise(paul)&calm(paul)))<=>(?[X]:((quiet(X)&~old(X)))))&
(((creative(susan)&quiet(susan)))<=>((~quiet(alice)<~>wise(alice))))&
(![X]:((~patient(X)&~creative(X))<=>(~creative(X)|brave(X))))&
((~creative(fred))<=>((curious(mary)<~>~happy(mary))))&
(![X]:(humble(X)=>(~generous(X)&kind(X))))&
(![X]:(~humble(X)<=>(generous(X)<~>tall(X))))&
(~tall(paul))&
((curious(fred)|strong(fred)))&
((~calm(fred)&quiet(fred)))&
(?[X]:((~humble(X)&funny(X))))&
((patient(fred)|~strong(fred)))&
((creative(alice)&~quiet(alice))) | ~tall(alice) | [] | null | 0 |
Everyone who is brave is either not wise or not kind and vice versa. Everyone who is either not wise or not curious is either not brave or funny and vice versa. If susan is either not generous or strong then someone is either patient or not funny and vice versa. If someone is not curious or brave then john is either not happy or not generous. If john is not old or generous then paul is patient or old. Everyone who is generous is both strong and not patient. Everyone who is quiet or kind is happy or funny and vice versa. Everyone who is both generous and wise is not humble and vice versa. If someone is both not tall and not old then someone is brave or not generous and vice versa. If susan is kind then someone is both funny and patient and vice versa. Everyone who is not quiet is both creative and funny and vice versa. Everyone who is not kind or not humble is not generous or not curious. If john is not curious then someone is wise or not rich. If someone is kind then someone is both curious and not kind. Everyone who is kind or quiet is both strong and patient and vice versa. Everyone who is both kind and calm is quiet. Someone is either creative or not curious. Paul is both creative and wise. Someone is rich. | Susan is generous. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~brave(X)<~>funny(X))))&
(((~generous(susan)<~>strong(susan)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((~curious(X)|brave(X))))=>((~happy(john)<~>~generous(john))))&
(((~old(john)|generous(john)))=>((patient(paul)|old(paul))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~curious(X))))&
((creative(paul)&wise(paul)))&
(?[X]:(rich(X))) | generous(susan) | [
"p2",
"p5",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8302592813681074267373847
% SZS output start Proof for 8302592813681074267373847
3. (~generous(susan) <~> strong(susan)) <=> ? [X0] : (patient(X0) <~> ~funny(X0)) [input p2]
6. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p5]
10. kind(susan) <=> ? [X0] : (patient(X0) & funny(X0)) [input p9]
11. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p14]
20. generous(susan) [input hypothesis]
28. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 6]
37. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [nnf transformation 3]
38. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [rectify 37]
39. ? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) => ((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) [choice axiom]
40. (((~strong(susan) | generous(susan)) & (strong(susan) | ~generous(susan))) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) | ((~generous(susan) | ~strong(susan)) & (strong(susan) | generous(susan)))) [skolemisation 38,39]
49. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X0] : (patient(X0) & funny(X0)) | ~kind(susan)) [nnf transformation 10]
50. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & (? [X1] : (patient(X1) & funny(X1)) | ~kind(susan)) [rectify 49]
51. ? [X1] : (patient(X1) & funny(X1)) => (patient(sK3) & funny(sK3)) [choice axiom]
52. (kind(susan) | ! [X0] : (~patient(X0) | ~funny(X0))) & ((patient(sK3) & funny(sK3)) | ~kind(susan)) [skolemisation 50,51]
53. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 11]
54. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 53]
60. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 15]
61. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 60]
80. ~funny(sK0) | patient(sK0) | ~generous(susan) | ~strong(susan) [cnf transformation 40]
82. funny(sK0) | ~patient(sK0) | ~generous(susan) | ~strong(susan) [cnf transformation 40]
93. ~generous(X0) | strong(X0) [cnf transformation 28]
94. ~patient(X0) | ~generous(X0) [cnf transformation 28]
107. kind(susan) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
109. quiet(X0) | funny(X0) [cnf transformation 54]
118. ~kind(X0) | patient(X0) [cnf transformation 61]
119. ~quiet(X0) | patient(X0) [cnf transformation 61]
126. generous(susan) [cnf transformation 20]
128. 1 <=> ! [X0] : (patient(X0) | funny(X0)) [avatar definition]
129. patient(X0) | funny(X0) <- (1) [avatar component clause 128]
131. 2 <=> generous(susan) [avatar definition]
133. generous(susan) <- (2) [avatar component clause 131]
135. 3 <=> strong(susan) [avatar definition]
140. 4 <=> ! [X0] : (~funny(X0) | ~patient(X0)) [avatar definition]
141. ~patient(X0) | ~funny(X0) <- (4) [avatar component clause 140]
146. 5 <=> patient(sK0) [avatar definition]
147. patient(sK0) <- (5) [avatar component clause 146]
148. ~patient(sK0) <- (~5) [avatar component clause 146]
150. 6 <=> funny(sK0) [avatar definition]
152. funny(sK0) <- (6) [avatar component clause 150]
153. ~3 | ~2 | ~5 | 6 [avatar split clause 82,150,146,131,135]
155. ~3 | ~2 | 5 | ~6 [avatar split clause 80,150,146,131,135]
217. 20 <=> kind(susan) [avatar definition]
219. kind(susan) <- (20) [avatar component clause 217]
220. 4 | 20 [avatar split clause 107,217,140]
267. 2 [avatar split clause 126,131]
268. strong(susan) <- (2) [resolution 93,133]
273. patient(X0) | funny(X0) [resolution 119,109]
275. 1 [avatar split clause 273,128]
277. funny(sK0) <- (1, ~5) [resolution 129,148]
281. 3 | ~2 [avatar split clause 268,131,135]
282. 6 | ~1 | 5 [avatar split clause 277,146,128,150]
286. ~funny(sK0) <- (4, 5) [resolution 141,147]
288. $false <- (4, 5, 6) [subsumption resolution 286,152]
289. ~4 | ~5 | ~6 [avatar contradiction clause 288]
292. patient(susan) <- (20) [resolution 219,118]
305. ~generous(susan) <- (20) [resolution 292,94]
306. $false <- (2, 20) [subsumption resolution 305,133]
307. ~2 | ~20 [avatar contradiction clause 306]
308. $false [avatar sat refutation 153,155,220,267,275,281,282,289,307]
% SZS output end Proof for 8302592813681074267373847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then lucy is humble and vice versa. Everyone who is not humble or creative is creative or wise and vice versa. Everyone who is either old or strong is both not quiet and not curious and vice versa. If alice is creative or tall then fred is both not creative and happy and vice versa. If mary is either creative or old then someone is patient. Everyone who is not patient or not funny is generous or humble. Everyone who is not curious is either kind or curious and vice versa. Everyone who is both humble and not brave is both not humble and funny. If lucy is not tall or not rich then mary is both creative and not creative. Everyone who is old or not curious is tall and vice versa. Everyone who is either rich or generous is rich and vice versa. If fred is kind then someone is either not funny or tall. Everyone who is both happy and not creative is both old and not humble and vice versa. Everyone who is both not happy and strong is not happy and vice versa. Everyone who is either tall or not generous is curious or not kind. If someone is both quiet and not calm then someone is quiet or happy and vice versa. Someone is either strong or not funny. Mary is both not generous and strong. Paul is not quiet. Someone is not patient or tall. Alice is either not patient or not strong. Susan is both not creative and happy. | Fred is not strong. | neutral | ((?[X]:(~generous(X)))<=>(humble(lucy)))&
(![X]:((~humble(X)|creative(X))<=>(creative(X)|wise(X))))&
(![X]:((old(X)<~>strong(X))<=>(~quiet(X)&~curious(X))))&
(((creative(alice)|tall(alice)))<=>((~creative(fred)&happy(fred))))&
(((creative(mary)<~>old(mary)))=>(?[X]:(patient(X))))&
(![X]:((~patient(X)|~funny(X))=>(generous(X)|humble(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>curious(X))))&
(![X]:((humble(X)&~brave(X))=>(~humble(X)&funny(X))))&
(((~tall(lucy)|~rich(lucy)))=>((creative(mary)&~creative(mary))))&
(![X]:((old(X)|~curious(X))<=>tall(X)))&
(![X]:((rich(X)<~>generous(X))<=>rich(X)))&
((kind(fred))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((happy(X)&~creative(X))<=>(old(X)&~humble(X))))&
(![X]:((~happy(X)&strong(X))<=>~happy(X)))&
(![X]:((tall(X)<~>~generous(X))=>(curious(X)|~kind(X))))&
((?[X]:((quiet(X)&~calm(X))))<=>(?[X]:((quiet(X)|happy(X)))))&
(?[X]:((strong(X)<~>~funny(X))))&
((~generous(mary)&strong(mary)))&
(~quiet(paul))&
(?[X]:((~patient(X)|tall(X))))&
((~patient(alice)<~>~strong(alice)))&
((~creative(susan)&happy(susan))) | ~strong(fred) | [] | null | 0 |
If paul is both quiet and not curious then fred is patient or not curious.
Everyone who is brave or not rich is both kind and happy and vice versa.
Everyone who is either calm or rich is both brave and not patient.
If someone is old then lucy is not patient or not tall.
Everyone who is not brave or not tall is either old or not calm and vice versa.
If someone is calm or not calm then john is not tall or creative.
Everyone who is either creative or funny is not old and vice versa.
Everyone who is not generous or humble is both not curious and old and vice versa.
Everyone who is either happy or calm is not humble and vice versa.
Everyone who is not rich or not patient is either not creative or not funny.
Everyone who is happy or generous is either not wise or not patient.
Everyone who is brave is either not old or happy and vice versa.
If john is either not happy or not tall then susan is both not brave and strong and vice versa.
Everyone who is tall is quiet or not patient and vice versa.
Everyone who is both not rich and quiet is both not quiet and not happy.
Everyone who is both happy and not humble is humble or not tall.
Alice is not calm.
Lucy is either old or strong.
Someone is either brave or patient.
Paul is either calm or kind.
Lucy is both not creative and not generous.
Fred is happy.
Someone is either not patient or not funny.
Someone is both not kind and rich. | Alice is patient. | entailment | (((quiet(paul)&~curious(paul)))=>((patient(fred)|~curious(fred))))&
(![X]:((brave(X)|~rich(X))<=>(kind(X)&happy(X))))&
(![X]:((calm(X)<~>rich(X))=>(brave(X)&~patient(X))))&
((?[X]:(old(X)))=>((~patient(lucy)|~tall(lucy))))&
(![X]:((~brave(X)|~tall(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((calm(X)|~calm(X))))=>((~tall(john)|creative(john))))&
(![X]:((creative(X)<~>funny(X))<=>~old(X)))&
(![X]:((~generous(X)|humble(X))<=>(~curious(X)&old(X))))&
(![X]:((happy(X)<~>calm(X))<=>~humble(X)))&
(![X]:((~rich(X)|~patient(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((happy(X)|generous(X))=>(~wise(X)<~>~patient(X))))&
(![X]:(brave(X)<=>(~old(X)<~>happy(X))))&
(((~happy(john)<~>~tall(john)))<=>((~brave(susan)&strong(susan))))&
(![X]:(tall(X)<=>(quiet(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~quiet(X)&~happy(X))))&
(![X]:((happy(X)&~humble(X))=>(humble(X)|~tall(X))))&
(~calm(alice))&
((old(lucy)<~>strong(lucy)))&
(?[X]:((brave(X)<~>patient(X))))&
((calm(paul)<~>kind(paul)))&
((~creative(lucy)&~generous(lucy)))&
(happy(fred))&
(?[X]:((~patient(X)<~>~funny(X))))&
(?[X]:((~kind(X)&rich(X)))) | patient(alice) | [
"p1",
"p4",
"p8",
"p11",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9069928972017198759957735
% SZS output start Proof for 9069928972017198759957735
2. ! [X0] : ((~rich(X0) | brave(X0)) <=> (happy(X0) & kind(X0))) [input p1]
5. ! [X0] : ((~tall(X0) | ~brave(X0)) <=> (old(X0) <~> ~calm(X0))) [input p4]
9. ! [X0] : ((happy(X0) <~> calm(X0)) <=> ~humble(X0)) [input p8]
12. ! [X0] : (brave(X0) <=> (~old(X0) <~> happy(X0))) [input p11]
14. ! [X0] : (tall(X0) <=> (~patient(X0) | quiet(X0))) [input p13]
16. ! [X0] : ((~humble(X0) & happy(X0)) => (~tall(X0) | humble(X0))) [input p15]
17. ~calm(alice) [input p16]
25. ~patient(alice) [input hypothesis]
37. ! [X0] : ((~tall(X0) | humble(X0)) | (humble(X0) | ~happy(X0))) [ennf transformation 16]
38. ! [X0] : (~tall(X0) | humble(X0) | humble(X0) | ~happy(X0)) [flattening 37]
39. ! [X0] : (((~rich(X0) | brave(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (rich(X0) & ~brave(X0)))) [nnf transformation 2]
40. ! [X0] : ((~rich(X0) | brave(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (rich(X0) & ~brave(X0)))) [flattening 39]
42. ! [X0] : (((~tall(X0) | ~brave(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (tall(X0) & brave(X0)))) [nnf transformation 5]
43. ! [X0] : ((~tall(X0) | ~brave(X0) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (tall(X0) & brave(X0)))) [flattening 42]
47. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | humble(X0)) & (~humble(X0) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 9]
50. ! [X0] : ((brave(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~brave(X0))) [nnf transformation 12]
53. ! [X0] : ((tall(X0) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | ~tall(X0))) [nnf transformation 14]
54. ! [X0] : ((tall(X0) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ~tall(X0))) [flattening 53]
68. ~brave(X0) | happy(X0) [cnf transformation 40]
78. ~old(X0) | calm(X0) | brave(X0) [cnf transformation 43]
93. ~humble(X0) | calm(X0) | ~happy(X0) [cnf transformation 47]
107. brave(X0) | happy(X0) | old(X0) [cnf transformation 50]
117. tall(X0) | patient(X0) [cnf transformation 54]
120. ~tall(X0) | humble(X0) | humble(X0) | ~happy(X0) [cnf transformation 38]
121. ~calm(alice) [cnf transformation 17]
135. ~patient(alice) [cnf transformation 25]
136. ~tall(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 120]
183. old(X0) | happy(X0) [subsumption resolution 107,68]
292. calm(X0) | brave(X0) | happy(X0) [resolution 78,183]
296. calm(X0) | happy(X0) [subsumption resolution 292,68]
397. happy(alice) [resolution 296,121]
465. ~happy(X0) | humble(X0) | patient(X0) [resolution 136,117]
613. humble(alice) | patient(alice) [resolution 465,397]
615. humble(alice) [subsumption resolution 613,135]
647. calm(alice) | ~happy(alice) [resolution 615,93]
650. ~happy(alice) [subsumption resolution 647,121]
651. $false [subsumption resolution 650,397]
% SZS output end Proof for 9069928972017198759957735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either happy or creative then someone is strong and vice versa.
If mary is not humble or happy then someone is not curious and vice versa.
If someone is either not kind or creative then john is either brave or wise.
If someone is either calm or not strong then mary is quiet.
Everyone who is both not wise and not calm is not old or patient and vice versa.
Everyone who is both rich and not brave is patient and vice versa.
If someone is not old then paul is not kind and vice versa.
Everyone who is humble or not generous is either not kind or not funny.
Everyone who is quiet is happy or not wise and vice versa.
Everyone who is patient or not kind is wise or not quiet.
If john is either kind or curious then someone is not happy or happy and vice versa.
Everyone who is calm or not rich is both not strong and humble.
Everyone who is both funny and rich is not wise or not happy and vice versa.
If someone is both not rich and tall then someone is both tall and quiet and vice versa.
Everyone who is both not strong and not wise is both strong and old and vice versa.
Everyone who is not patient or not calm is not rich and vice versa.
Mary is either wise or not brave.
Fred is both not kind and not creative.
Someone is not curious or calm.
Someone is either calm or not curious.
Paul is either not curious or not brave. | Paul is curious. | neutral | (((happy(alice)<~>creative(alice)))<=>(?[X]:(strong(X))))&
(((~humble(mary)|happy(mary)))<=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)<~>creative(X))))=>((brave(john)<~>wise(john))))&
((?[X]:((calm(X)<~>~strong(X))))=>(quiet(mary)))&
(![X]:((~wise(X)&~calm(X))<=>(~old(X)|patient(X))))&
(![X]:((rich(X)&~brave(X))<=>patient(X)))&
((?[X]:(~old(X)))<=>(~kind(paul)))&
(![X]:((humble(X)|~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:(quiet(X)<=>(happy(X)|~wise(X))))&
(![X]:((patient(X)|~kind(X))=>(wise(X)|~quiet(X))))&
(((kind(john)<~>curious(john)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((calm(X)|~rich(X))=>(~strong(X)&humble(X))))&
(![X]:((funny(X)&rich(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~strong(X)&~wise(X))<=>(strong(X)&old(X))))&
(![X]:((~patient(X)|~calm(X))<=>~rich(X)))&
((wise(mary)<~>~brave(mary)))&
((~kind(fred)&~creative(fred)))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
((~curious(paul)<~>~brave(paul))) | curious(paul) | [] | null | 0 |
Everyone who is either not strong or brave is brave and vice versa.
If susan is either wise or humble then mary is both strong and brave.
Everyone who is humble is either tall or brave.
Everyone who is not quiet or creative is quiet or not quiet and vice versa.
Everyone who is both creative and patient is both not brave and rich and vice versa.
Everyone who is both wise and not brave is both not brave and calm.
If someone is brave then alice is either not curious or tall and vice versa.
If susan is either strong or not rich then someone is not old or funny.
Everyone who is either not brave or not funny is either kind or not calm.
Everyone who is not tall or kind is either not generous or brave.
Everyone who is not wise or brave is not funny and vice versa.
Everyone who is not tall is either kind or not quiet.
Everyone who is not tall or old is funny.
If someone is both rich and not humble then alice is either curious or not quiet and vice versa.
Everyone who is generous or not patient is not creative.
Everyone who is both not creative and not brave is brave and vice versa.
Lucy is not generous or creative.
Lucy is both kind and curious.
Mary is both old and strong.
Someone is either quiet or not strong.
Fred is both quiet and not old.
Someone is either happy or not brave. | Alice is not calm. | neutral | (![X]:((~strong(X)<~>brave(X))<=>brave(X)))&
(((wise(susan)<~>humble(susan)))=>((strong(mary)&brave(mary))))&
(![X]:(humble(X)=>(tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|creative(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((creative(X)&patient(X))<=>(~brave(X)&rich(X))))&
(![X]:((wise(X)&~brave(X))=>(~brave(X)&calm(X))))&
((?[X]:(brave(X)))<=>((~curious(alice)<~>tall(alice))))&
(((strong(susan)<~>~rich(susan)))=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((~brave(X)<~>~funny(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~tall(X)|kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~wise(X)|brave(X))<=>~funny(X)))&
(![X]:(~tall(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((~tall(X)|old(X))=>funny(X)))&
((?[X]:((rich(X)&~humble(X))))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((generous(X)|~patient(X))=>~creative(X)))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
((~generous(lucy)|creative(lucy)))&
((kind(lucy)&curious(lucy)))&
((old(mary)&strong(mary)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((quiet(fred)&~old(fred)))&
(?[X]:((happy(X)<~>~brave(X)))) | ~calm(alice) | [] | null | 0 |
If someone is not patient or creative then someone is humble.
If alice is either creative or not creative then someone is both not strong and quiet.
Everyone who is both not funny and not calm is calm and vice versa.
If someone is both rich and not happy then susan is happy or not humble and vice versa.
If john is tall or strong then mary is either generous or not tall.
If someone is not old or calm then someone is not humble or kind.
Everyone who is either not happy or humble is not humble or not patient and vice versa.
If someone is not wise or not humble then someone is not curious and vice versa.
Everyone who is happy is strong or rich.
If someone is both not wise and strong then john is calm or strong.
If someone is both not happy and not humble then someone is either strong or calm and vice versa.
If mary is either not brave or creative then paul is both not rich and old and vice versa.
Everyone who is not old or not calm is creative and vice versa.
Everyone who is humble or rich is not wise or not patient and vice versa.
If someone is either curious or creative then someone is generous and vice versa.
If paul is either rich or not strong then alice is not calm.
Alice is both tall and not patient.
Alice is funny or strong.
Someone is not quiet.
Someone is not happy.
Someone is either not happy or not old.
Lucy is either calm or not tall.
Alice is happy or not quiet. | Susan is creative. | entailment | ((?[X]:((~patient(X)|creative(X))))=>(?[X]:(humble(X))))&
(((creative(alice)<~>~creative(alice)))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((~funny(X)&~calm(X))<=>calm(X)))&
((?[X]:((rich(X)&~happy(X))))<=>((happy(susan)|~humble(susan))))&
(((tall(john)|strong(john)))=>((generous(mary)<~>~tall(mary))))&
((?[X]:((~old(X)|calm(X))))=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((~happy(X)<~>humble(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>(?[X]:(~curious(X))))&
(![X]:(happy(X)=>(strong(X)|rich(X))))&
((?[X]:((~wise(X)&strong(X))))=>((calm(john)|strong(john))))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:((strong(X)<~>calm(X)))))&
(((~brave(mary)<~>creative(mary)))<=>((~rich(paul)&old(paul))))&
(![X]:((~old(X)|~calm(X))<=>creative(X)))&
(![X]:((humble(X)|rich(X))<=>(~wise(X)|~patient(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>(?[X]:(generous(X))))&
(((rich(paul)<~>~strong(paul)))=>(~calm(alice)))&
((tall(alice)&~patient(alice)))&
((funny(alice)|strong(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~old(X))))&
((calm(lucy)<~>~tall(lucy)))&
((happy(alice)|~quiet(alice))) | creative(susan) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6913803163097191144145361
% SZS output start Proof for 6913803163097191144145361
3. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> calm(X0)) [input p2]
13. ! [X0] : ((~calm(X0) | ~old(X0)) <=> creative(X0)) [input p12]
24. ~creative(susan) [input hypothesis]
45. ! [X0] : (((~calm(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) | funny(X0)))) [nnf transformation 3]
46. ! [X0] : (((~calm(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | calm(X0) | funny(X0))) [flattening 45]
67. ! [X0] : (((~calm(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (calm(X0) & old(X0)))) [nnf transformation 13]
68. ! [X0] : ((~calm(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (calm(X0) & old(X0)))) [flattening 67]
93. ~calm(X0) | ~calm(X0) [cnf transformation 46]
127. creative(X0) | calm(X0) [cnf transformation 68]
149. ~creative(susan) [cnf transformation 24]
153. ~calm(X0) [duplicate literal removal 93]
305. creative(X0) [subsumption resolution 127,153]
341. $false [subsumption resolution 149,305]
% SZS output end Proof for 6913803163097191144145361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is humble or creative then mary is either kind or generous and vice versa. Everyone who is not wise is brave and vice versa. Everyone who is generous is both not old and wise. Everyone who is not tall or rich is either not happy or not generous. If paul is not curious then someone is either not humble or creative and vice versa. If alice is not curious or not happy then someone is strong or not strong and vice versa. If mary is patient or not creative then paul is both patient and not patient and vice versa. If alice is patient then someone is not wise or not old. Everyone who is not happy or not kind is not happy. Everyone who is both not humble and not old is not generous and vice versa. If paul is not creative or humble then someone is both not humble and not strong. Everyone who is not rich or curious is both not strong and not patient. Everyone who is both not patient and not generous is curious or not humble and vice versa. Everyone who is both funny and not old is not tall. If alice is both not tall and funny then someone is not funny and vice versa. Everyone who is either funny or calm is either not rich or happy and vice versa. Lucy is not wise. Susan is either calm or creative. Mary is brave or not patient. Susan is not funny. Susan is both not calm and generous. Someone is either old or tall. Fred is not rich. Someone is both kind and not tall. | Alice is tall. | contradiction | (((humble(alice)|creative(alice)))<=>((kind(mary)<~>generous(mary))))&
(![X]:(~wise(X)<=>brave(X)))&
(![X]:(generous(X)=>(~old(X)&wise(X))))&
(![X]:((~tall(X)|rich(X))=>(~happy(X)<~>~generous(X))))&
((~curious(paul))<=>(?[X]:((~humble(X)<~>creative(X)))))&
(((~curious(alice)|~happy(alice)))<=>(?[X]:((strong(X)|~strong(X)))))&
(((patient(mary)|~creative(mary)))<=>((patient(paul)&~patient(paul))))&
((patient(alice))=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:((~happy(X)|~kind(X))=>~happy(X)))&
(![X]:((~humble(X)&~old(X))<=>~generous(X)))&
(((~creative(paul)|humble(paul)))=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~rich(X)|curious(X))=>(~strong(X)&~patient(X))))&
(![X]:((~patient(X)&~generous(X))<=>(curious(X)|~humble(X))))&
(![X]:((funny(X)&~old(X))=>~tall(X)))&
(((~tall(alice)&funny(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((funny(X)<~>calm(X))<=>(~rich(X)<~>happy(X))))&
(~wise(lucy))&
((calm(susan)<~>creative(susan)))&
((brave(mary)|~patient(mary)))&
(~funny(susan))&
((~calm(susan)&generous(susan)))&
(?[X]:((old(X)<~>tall(X))))&
(~rich(fred))&
(?[X]:((kind(X)&~tall(X)))) | tall(alice) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4827554703170052628575372
% SZS output start Proof for 4827554703170052628575372
15. (funny(alice) & ~tall(alice)) <=> ? [X0] : ~funny(X0) [input p14]
20. ~funny(susan) [input p19]
25. tall(alice) [input hypothesis]
57. ((funny(alice) & ~tall(alice)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | (~funny(alice) | tall(alice))) [nnf transformation 15]
58. ((funny(alice) & ~tall(alice)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | ~funny(alice) | tall(alice)) [flattening 57]
59. ((funny(alice) & ~tall(alice)) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | ~funny(alice) | tall(alice)) [rectify 58]
60. ? [X1] : ~funny(X1) => ~funny(sK4) [choice axiom]
61. ((funny(alice) & ~tall(alice)) | ! [X0] : funny(X0)) & (~funny(sK4) | ~funny(alice) | tall(alice)) [skolemisation 59,60]
117. ~tall(alice) | funny(X0) [cnf transformation 61]
131. ~funny(susan) [cnf transformation 20]
139. tall(alice) [cnf transformation 25]
253. 24 <=> ! [X0] : funny(X0) [avatar definition]
254. funny(X0) <- (24) [avatar component clause 253]
261. 26 <=> tall(alice) [avatar definition]
264. 24 | ~26 [avatar split clause 117,261,253]
288. 26 [avatar split clause 139,261]
289. $false <- (24) [resolution 254,131]
290. ~24 [avatar contradiction clause 289]
291. $false [avatar sat refutation 264,288,290]
% SZS output end Proof for 4827554703170052628575372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not creative is not brave and vice versa.
Everyone who is not humble is both old and not patient.
If someone is both not generous and quiet then john is both not brave and not patient.
Everyone who is not rich is either not curious or wise.
If someone is either calm or rich then susan is both not calm and happy and vice versa.
If fred is both not patient and rich then someone is either humble or quiet.
If john is not funny or not tall then john is either rich or not rich and vice versa.
Everyone who is old is both patient and generous and vice versa.
Everyone who is both not kind and not humble is either tall or kind and vice versa.
If someone is humble then lucy is not patient or old and vice versa.
Everyone who is generous or kind is not happy or creative.
If paul is not happy or not funny then someone is either not curious or generous.
If someone is brave or wise then fred is calm or wise.
Everyone who is not funny or not strong is not funny or tall.
If someone is either wise or not brave then susan is either generous or patient.
Everyone who is not old or not curious is humble and vice versa.
Someone is either not wise or not calm.
Someone is humble.
Mary is both not creative and calm.
Someone is calm.
John is old or not curious.
Mary is either not tall or not funny.
Someone is not funny or not happy. | John is not curious. | entailment | (![X]:((happy(X)<~>~creative(X))<=>~brave(X)))&
(![X]:(~humble(X)=>(old(X)&~patient(X))))&
((?[X]:((~generous(X)&quiet(X))))=>((~brave(john)&~patient(john))))&
(![X]:(~rich(X)=>(~curious(X)<~>wise(X))))&
((?[X]:((calm(X)<~>rich(X))))<=>((~calm(susan)&happy(susan))))&
(((~patient(fred)&rich(fred)))=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~funny(john)|~tall(john)))<=>((rich(john)<~>~rich(john))))&
(![X]:(old(X)<=>(patient(X)&generous(X))))&
(![X]:((~kind(X)&~humble(X))<=>(tall(X)<~>kind(X))))&
((?[X]:(humble(X)))<=>((~patient(lucy)|old(lucy))))&
(![X]:((generous(X)|kind(X))=>(~happy(X)|creative(X))))&
(((~happy(paul)|~funny(paul)))=>(?[X]:((~curious(X)<~>generous(X)))))&
((?[X]:((brave(X)|wise(X))))=>((calm(fred)|wise(fred))))&
(![X]:((~funny(X)|~strong(X))=>(~funny(X)|tall(X))))&
((?[X]:((wise(X)<~>~brave(X))))=>((generous(susan)<~>patient(susan))))&
(![X]:((~old(X)|~curious(X))<=>humble(X)))&
(?[X]:((~wise(X)<~>~calm(X))))&
(?[X]:(humble(X)))&
((~creative(mary)&calm(mary)))&
(?[X]:(calm(X)))&
((old(john)|~curious(john)))&
((~tall(mary)<~>~funny(mary)))&
(?[X]:((~funny(X)|~happy(X)))) | ~curious(john) | [
"p1",
"p7",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 83343018922641092379872
% SZS output start Proof for 83343018922641092379872
2. ! [X0] : (~humble(X0) => (~patient(X0) & old(X0))) [input p1]
8. ! [X0] : (old(X0) <=> (generous(X0) & patient(X0))) [input p7]
16. ! [X0] : ((~curious(X0) | ~old(X0)) <=> humble(X0)) [input p15]
21. ~curious(john) | old(john) [input p20]
24. curious(john) [input hypothesis]
26. ! [X0] : ((~patient(X0) & old(X0)) | humble(X0)) [ennf transformation 2]
51. ! [X0] : ((old(X0) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | ~old(X0))) [nnf transformation 8]
52. ! [X0] : ((old(X0) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | ~old(X0))) [flattening 51]
64. ! [X0] : (((~curious(X0) | ~old(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & old(X0)))) [nnf transformation 16]
65. ! [X0] : ((~curious(X0) | ~old(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & old(X0)))) [flattening 64]
80. old(X0) | humble(X0) [cnf transformation 26]
81. ~patient(X0) | humble(X0) [cnf transformation 26]
100. ~old(X0) | patient(X0) [cnf transformation 52]
127. ~curious(X0) | ~old(X0) | ~humble(X0) [cnf transformation 65]
134. ~curious(john) | old(john) [cnf transformation 21]
138. curious(john) [cnf transformation 24]
300. 35 <=> old(john) [avatar definition]
302. old(john) <- (35) [avatar component clause 300]
304. 36 <=> curious(john) [avatar definition]
305. curious(john) <- (36) [avatar component clause 304]
307. 35 | ~36 [avatar split clause 134,304,300]
327. 36 [avatar split clause 138,304]
329. patient(X0) | humble(X0) [resolution 100,80]
332. humble(X0) [subsumption resolution 329,81]
408. ~old(john) | ~humble(john) <- (36) [resolution 127,305]
410. ~humble(john) <- (35, 36) [subsumption resolution 408,302]
411. $false <- (35, 36) [subsumption resolution 410,332]
412. ~35 | ~36 [avatar contradiction clause 411]
413. $false [avatar sat refutation 307,327,412]
% SZS output end Proof for 83343018922641092379872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Lucy is not quiet. | 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)))) | ~quiet(lucy) | [
"p1",
"p4",
"p8",
"p9",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 722769284860952525791090
% SZS output start Proof for 722769284860952525791090
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]
12. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p11]
16. ! [X0] : (~happy(X0) <=> rich(X0)) [input p15]
22. ~creative(fred) | ~strong(fred) [input p21]
24. ~quiet(lucy) [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]
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]
55. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 12]
58. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 16]
76. ~rich(X0) | creative(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]
110. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 55]
111. ~happy(lucy) | ~creative(fred) | ~rich(fred) [cnf transformation 55]
116. happy(X0) | rich(X0) [cnf transformation 58]
125. ~creative(fred) | ~strong(fred) [cnf transformation 22]
127. ~quiet(lucy) [cnf transformation 24]
179. 12 <=> happy(lucy) [avatar definition]
181. ~happy(lucy) <- (~12) [avatar component clause 179]
183. 13 <=> rich(lucy) [avatar definition]
184. rich(lucy) <- (13) [avatar component clause 183]
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]
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]
249. 13 | 12 [avatar split clause 244,179,183]
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]
295. quiet(lucy) <- (13) [resolution 184,100]
297. $false <- (13) [subsumption resolution 295,127]
298. ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 204,205,230,249,286,291,298]
% SZS output end Proof for 722769284860952525791090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then someone is funny and vice versa.
Everyone who is not calm or humble is both creative and old.
If alice is either not kind or funny then john is either funny or old and vice versa.
Everyone who is kind or not quiet is not rich or not kind and vice versa.
Everyone who is either generous or not humble is either kind or quiet.
If someone is both not humble and not calm then someone is either not strong or curious and vice versa.
If someone is kind then someone is both rich and tall and vice versa.
If john is either not humble or not curious then someone is either old or quiet and vice versa.
Everyone who is not generous is creative or not tall.
Everyone who is either strong or tall is wise and vice versa.
If someone is both not quiet and not curious then john is either funny or quiet and vice versa.
If someone is either not creative or quiet then fred is both not patient and not curious and vice versa.
If someone is either not patient or not calm then someone is either not generous or wise and vice versa.
Everyone who is both not old and old is quiet and vice versa.
If someone is both kind and not wise then lucy is generous or calm and vice versa.
Everyone who is not creative is both not creative and not brave and vice versa.
Someone is both not rich and tall.
Someone is both not generous and not wise.
Susan is either strong or not creative.
Someone is either quiet or kind.
Alice is not tall or not generous.
Someone is either not old or not quiet.
Lucy is not wise or strong. | John is not quiet. | entailment | ((?[X]:((brave(X)|curious(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|humble(X))=>(creative(X)&old(X))))&
(((~kind(alice)<~>funny(alice)))<=>((funny(john)<~>old(john))))&
(![X]:((kind(X)|~quiet(X))<=>(~rich(X)|~kind(X))))&
(![X]:((generous(X)<~>~humble(X))=>(kind(X)<~>quiet(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(?[X]:((~strong(X)<~>curious(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)&tall(X)))))&
(((~humble(john)<~>~curious(john)))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:(~generous(X)=>(creative(X)|~tall(X))))&
(![X]:((strong(X)<~>tall(X))<=>wise(X)))&
((?[X]:((~quiet(X)&~curious(X))))<=>((funny(john)<~>quiet(john))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((~patient(fred)&~curious(fred))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((~old(X)&old(X))<=>quiet(X)))&
((?[X]:((kind(X)&~wise(X))))<=>((generous(lucy)|calm(lucy))))&
(![X]:(~creative(X)<=>(~creative(X)&~brave(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((~generous(X)&~wise(X))))&
((strong(susan)<~>~creative(susan)))&
(?[X]:((quiet(X)<~>kind(X))))&
((~tall(alice)|~generous(alice)))&
(?[X]:((~old(X)<~>~quiet(X))))&
((~wise(lucy)|strong(lucy))) | ~quiet(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2033654566557427803511687
% SZS output start Proof for 2033654566557427803511687
14. ! [X0] : ((old(X0) & ~old(X0)) <=> quiet(X0)) [input p13]
24. quiet(john) [input hypothesis]
71. ! [X0] : (((old(X0) & ~old(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) | old(X0)))) [nnf transformation 14]
72. ! [X0] : (((old(X0) & ~old(X0)) | ~quiet(X0)) & (quiet(X0) | ~old(X0) | old(X0))) [flattening 71]
157. ~old(X0) | ~quiet(X0) [cnf transformation 72]
158. old(X0) | ~quiet(X0) [cnf transformation 72]
179. quiet(john) [cnf transformation 24]
287. 23 <=> ! [X0] : (old(X0) | ~quiet(X0)) [avatar definition]
288. old(X0) | ~quiet(X0) <- (23) [avatar component clause 287]
317. 29 <=> quiet(john) [avatar definition]
318. quiet(john) <- (29) [avatar component clause 317]
401. 23 [avatar split clause 158,287]
465. 29 [avatar split clause 179,317]
476. ~quiet(X0) <- (23) [subsumption resolution 288,157]
479. $false <- (23, 29) [resolution 476,318]
482. ~23 | ~29 [avatar contradiction clause 479]
483. $false [avatar sat refutation 401,465,482]
% SZS output end Proof for 2033654566557427803511687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either rich or not curious then fred is not curious or not creative.
Everyone who is not tall or brave is not quiet and vice versa.
If someone is old or quiet then fred is rich or curious and vice versa.
Everyone who is curious is either rich or humble and vice versa.
Everyone who is both brave and tall is not tall or not curious.
Everyone who is humble is either old or not patient and vice versa.
Everyone who is not wise or not funny is either not humble or not brave and vice versa.
Everyone who is both rich and not funny is either patient or funny and vice versa.
If john is either not humble or not generous then alice is tall.
If paul is both not generous and not funny then john is either creative or not brave.
Everyone who is not funny is either patient or not calm and vice versa.
Everyone who is either not wise or curious is either rich or not generous and vice versa.
Everyone who is either curious or not humble is not rich.
If someone is either funny or not curious then someone is both funny and not quiet and vice versa.
Everyone who is both not humble and not kind is kind.
Everyone who is both not creative and not tall is curious.
Paul is old or quiet.
Alice is either not tall or generous.
Someone is either not rich or not calm.
Someone is either not creative or happy.
Susan is happy.
Someone is not kind or not happy.
Someone is not calm. | Fred is not wise. | neutral | (((rich(paul)<~>~curious(paul)))=>((~curious(fred)|~creative(fred))))&
(![X]:((~tall(X)|brave(X))<=>~quiet(X)))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:((rich(X)&~funny(X))<=>(patient(X)<~>funny(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(![X]:(~funny(X)<=>(patient(X)<~>~calm(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((curious(X)<~>~humble(X))=>~rich(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(![X]:((~humble(X)&~kind(X))=>kind(X)))&
(![X]:((~creative(X)&~tall(X))=>curious(X)))&
((old(paul)|quiet(paul)))&
((~tall(alice)<~>generous(alice)))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~creative(X)<~>happy(X))))&
(happy(susan))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:(~calm(X))) | ~wise(fred) | [] | null | 0 |
If susan is funny or not tall then someone is not humble or quiet. Everyone who is not kind is patient. If lucy is not patient then someone is either not curious or tall. If alice is humble or old then someone is patient and vice versa. Everyone who is not humble is not quiet. Everyone who is both tall and kind is not calm or not rich. Everyone who is either wise or not tall is not old and vice versa. Everyone who is tall or strong is not calm and vice versa. If someone is either not humble or funny then someone is patient or humble. Everyone who is either not strong or generous is both tall and quiet. If fred is not generous then someone is both not funny and humble and vice versa. Everyone who is both calm and happy is not happy and vice versa. Everyone who is not old is both not calm and strong. Everyone who is either not brave or patient is either tall or not creative and vice versa. If someone is either not wise or quiet then mary is humble. Everyone who is quiet or not kind is either not calm or quiet. Someone is funny or not strong. Someone is either generous or wise. Paul is quiet or happy. Someone is either strong or old. Someone is not tall. | Alice is not creative. | neutral | (((funny(susan)|~tall(susan)))=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:(~kind(X)=>patient(X)))&
((~patient(lucy))=>(?[X]:((~curious(X)<~>tall(X)))))&
(((humble(alice)|old(alice)))<=>(?[X]:(patient(X))))&
(![X]:(~humble(X)=>~quiet(X)))&
(![X]:((tall(X)&kind(X))=>(~calm(X)|~rich(X))))&
(![X]:((wise(X)<~>~tall(X))<=>~old(X)))&
(![X]:((tall(X)|strong(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>funny(X))))=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~strong(X)<~>generous(X))=>(tall(X)&quiet(X))))&
((~generous(fred))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((calm(X)&happy(X))<=>~happy(X)))&
(![X]:(~old(X)=>(~calm(X)&strong(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(tall(X)<~>~creative(X))))&
((?[X]:((~wise(X)<~>quiet(X))))=>(humble(mary)))&
(![X]:((quiet(X)|~kind(X))=>(~calm(X)<~>quiet(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((generous(X)<~>wise(X))))&
((quiet(paul)|happy(paul)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:(~tall(X))) | ~creative(alice) | [] | null | 0 |
If paul is both humble and rich then someone is both creative and patient and vice versa. If mary is either not brave or not quiet then fred is not brave. Everyone who is both not happy and brave is rich or old and vice versa. Everyone who is not calm is not quiet or kind and vice versa. If someone is not generous or not old then john is either tall or not patient. Everyone who is either humble or patient is either not funny or kind. Everyone who is creative is either not quiet or not old and vice versa. Everyone who is tall or not funny is not funny or not creative and vice versa. Everyone who is both not calm and not rich is happy or not kind and vice versa. If someone is both not generous and not tall then someone is both funny and curious and vice versa. If someone is not patient or not brave then lucy is either not kind or calm. If mary is not quiet then fred is not wise and vice versa. Everyone who is not creative is generous or not calm and vice versa. If alice is both generous and not patient then someone is rich or not tall and vice versa. Everyone who is not funny is either happy or humble. Everyone who is not creative or tall is either calm or brave and vice versa. Someone is not patient or quiet. Fred is not rich. Someone is not tall. Lucy is wise. John is either not tall or patient. Someone is not brave or not kind. Someone is either wise or not curious. | John is not patient. | neutral | (((humble(paul)&rich(paul)))<=>(?[X]:((creative(X)&patient(X)))))&
(((~brave(mary)<~>~quiet(mary)))=>(~brave(fred)))&
(![X]:((~happy(X)&brave(X))<=>(rich(X)|old(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|kind(X))))&
((?[X]:((~generous(X)|~old(X))))=>((tall(john)<~>~patient(john))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>kind(X))))&
(![X]:(creative(X)<=>(~quiet(X)<~>~old(X))))&
(![X]:((tall(X)|~funny(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~calm(X)&~rich(X))<=>(happy(X)|~kind(X))))&
((?[X]:((~generous(X)&~tall(X))))<=>(?[X]:((funny(X)&curious(X)))))&
((?[X]:((~patient(X)|~brave(X))))=>((~kind(lucy)<~>calm(lucy))))&
((~quiet(mary))<=>(~wise(fred)))&
(![X]:(~creative(X)<=>(generous(X)|~calm(X))))&
(((generous(alice)&~patient(alice)))<=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(~funny(X)=>(happy(X)<~>humble(X))))&
(![X]:((~creative(X)|tall(X))<=>(calm(X)<~>brave(X))))&
(?[X]:((~patient(X)|quiet(X))))&
(~rich(fred))&
(?[X]:(~tall(X)))&
(wise(lucy))&
((~tall(john)<~>patient(john)))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((wise(X)<~>~curious(X)))) | ~patient(john) | [] | null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.