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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not rich is not funny or not curious. If alice is quiet or generous then someone is not generous or not rich and vice versa. Everyone who is both not brave and curious is kind and vice versa. Everyone who is both not curious and patient is either funny or rich. Everyone who is both happy and not patient is either happy or kind. Everyone who is not patient or not humble is patient and vice versa. Everyone who is wise or not strong is not patient and vice versa. Everyone who is happy or not wise is tall and vice versa. Everyone who is either not brave or not creative is both rich and not calm and vice versa. Everyone who is both quiet and rich is not calm or kind. If someone is either not kind or not rich then someone is either not brave or humble and vice versa. Everyone who is both not curious and strong is old or generous. Everyone who is rich or wise is either not humble or not funny. Everyone who is tall or not tall is either not creative or not patient and vice versa. If fred is happy or not curious then alice is either kind or not old. If susan is both curious and not funny then fred is both generous and wise and vice versa. Fred is both patient and calm. Fred is curious or humble. Fred is not old or not tall. Fred is both not old and funny. Someone is curious or not calm. Alice is not wise. Alice is either patient or not curious. | Fred is not wise. | entailment | (![X]:(~rich(X)=>(~funny(X)|~curious(X))))&
(((quiet(alice)|generous(alice)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~brave(X)&curious(X))<=>kind(X)))&
(![X]:((~curious(X)&patient(X))=>(funny(X)<~>rich(X))))&
(![X]:((happy(X)&~patient(X))=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)|~humble(X))<=>patient(X)))&
(![X]:((wise(X)|~strong(X))<=>~patient(X)))&
(![X]:((happy(X)|~wise(X))<=>tall(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~calm(X))))&
(![X]:((quiet(X)&rich(X))=>(~calm(X)|kind(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:((~curious(X)&strong(X))=>(old(X)|generous(X))))&
(![X]:((rich(X)|wise(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((tall(X)|~tall(X))<=>(~creative(X)<~>~patient(X))))&
(((happy(fred)|~curious(fred)))=>((kind(alice)<~>~old(alice))))&
(((curious(susan)&~funny(susan)))<=>((generous(fred)&wise(fred))))&
((patient(fred)&calm(fred)))&
((curious(fred)|humble(fred)))&
((~old(fred)|~tall(fred)))&
((~old(fred)&funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice))) | ~wise(fred) | [
"p5",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 7859554326325422735884476
% SZS output start Proof for 7859554326325422735884476
6. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((~strong(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
24. wise(fred) [input hypothesis]
47. ! [X0] : (((~humble(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [flattening 47]
49. ! [X0] : (((~strong(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [nnf transformation 7]
50. ! [X0] : ((~strong(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [flattening 49]
81. patient(X0) | patient(X0) [cnf transformation 48]
84. ~patient(X0) | ~wise(X0) [cnf transformation 50]
134. wise(fred) [cnf transformation 24]
135. patient(X0) [duplicate literal removal 81]
165. ~wise(X0) [subsumption resolution 84,135]
257. $false [subsumption resolution 134,165]
% SZS output end Proof for 7859554326325422735884476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not curious or not tall.
If susan is not funny or wise then fred is kind or not patient and vice versa.
If fred is either not patient or creative then john is brave and vice versa.
If someone is either not wise or calm then lucy is either not creative or not funny and vice versa.
If lucy is either not old or not humble then lucy is not strong or not curious.
Everyone who is not calm or not rich is patient or humble and vice versa.
If someone is either not brave or not generous then someone is both generous and not patient.
If lucy is both not old and curious then someone is both not kind and tall.
If alice is either rich or not calm then john is not kind and vice versa.
If someone is both happy and not kind then lucy is both not rich and happy and vice versa.
Everyone who is not patient is both curious and patient.
If susan is both not tall and tall then mary is not kind.
If john is patient then someone is both humble and rich.
If fred is brave or creative then susan is not curious.
If someone is both tall and calm then susan is not tall or not patient and vice versa.
Someone is either not curious or generous.
Lucy is either old or not curious.
Susan is not old.
Someone is both old and not happy.
Someone is both not old and humble.
Someone is both not kind and not strong.
Susan is strong or not brave. | Mary is not tall. | neutral | (![X]:(rich(X)=>(~curious(X)<~>~tall(X))))&
(((~funny(susan)|wise(susan)))<=>((kind(fred)|~patient(fred))))&
(((~patient(fred)<~>creative(fred)))<=>(brave(john)))&
((?[X]:((~wise(X)<~>calm(X))))<=>((~creative(lucy)<~>~funny(lucy))))&
(((~old(lucy)<~>~humble(lucy)))=>((~strong(lucy)|~curious(lucy))))&
(![X]:((~calm(X)|~rich(X))<=>(patient(X)|humble(X))))&
((?[X]:((~brave(X)<~>~generous(X))))=>(?[X]:((generous(X)&~patient(X)))))&
(((~old(lucy)&curious(lucy)))=>(?[X]:((~kind(X)&tall(X)))))&
(((rich(alice)<~>~calm(alice)))<=>(~kind(john)))&
((?[X]:((happy(X)&~kind(X))))<=>((~rich(lucy)&happy(lucy))))&
(![X]:(~patient(X)=>(curious(X)&patient(X))))&
(((~tall(susan)&tall(susan)))=>(~kind(mary)))&
((patient(john))=>(?[X]:((humble(X)&rich(X)))))&
(((brave(fred)|creative(fred)))=>(~curious(susan)))&
((?[X]:((tall(X)&calm(X))))<=>((~tall(susan)|~patient(susan))))&
(?[X]:((~curious(X)<~>generous(X))))&
((old(lucy)<~>~curious(lucy)))&
(~old(susan))&
(?[X]:((old(X)&~happy(X))))&
(?[X]:((~old(X)&humble(X))))&
(?[X]:((~kind(X)&~strong(X))))&
((strong(susan)|~brave(susan))) | ~tall(mary) | []
| null | 0 |
Everyone who is funny is either kind or patient. If susan is either not generous or not humble then someone is not quiet or rich and vice versa. Everyone who is both funny and generous is not creative and vice versa. Everyone who is patient is both kind and generous. Everyone who is not rich is both not calm and not funny. If someone is not calm or not creative then someone is funny or not creative. Everyone who is either not creative or wise is either old or brave and vice versa. Everyone who is not tall is quiet or not calm. Everyone who is not creative is happy and vice versa. If paul is either not strong or not happy then lucy is both creative and kind. Everyone who is not generous or tall is not old and vice versa. If someone is either not generous or not calm then john is not patient or not old. Everyone who is not humble is creative and vice versa. Everyone who is rich or quiet is both wise and not patient and vice versa. Everyone who is either rich or calm is creative and vice versa. Everyone who is both calm and curious is not wise or not curious. Someone is either not funny or not tall. Someone is rich. Paul is either kind or calm. Someone is either not calm or calm. Someone is either not curious or not brave. Paul is not calm. | John is not wise. | contradiction | (![X]:(funny(X)=>(kind(X)<~>patient(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((funny(X)&generous(X))<=>~creative(X)))&
(![X]:(patient(X)=>(kind(X)&generous(X))))&
(![X]:(~rich(X)=>(~calm(X)&~funny(X))))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>(old(X)<~>brave(X))))&
(![X]:(~tall(X)=>(quiet(X)|~calm(X))))&
(![X]:(~creative(X)<=>happy(X)))&
(((~strong(paul)<~>~happy(paul)))=>((creative(lucy)&kind(lucy))))&
(![X]:((~generous(X)|tall(X))<=>~old(X)))&
((?[X]:((~generous(X)<~>~calm(X))))=>((~patient(john)|~old(john))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:((rich(X)|quiet(X))<=>(wise(X)&~patient(X))))&
(![X]:((rich(X)<~>calm(X))<=>creative(X)))&
(![X]:((calm(X)&curious(X))=>(~wise(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~tall(X))))&
(?[X]:(rich(X)))&
((kind(paul)<~>calm(paul)))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(~calm(paul)) | ~wise(john) | [
"p2",
"p4",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 496912088076921471114971
% SZS output start Proof for 496912088076921471114971
3. ! [X0] : ((generous(X0) & funny(X0)) <=> ~creative(X0)) [input p2]
5. ! [X0] : (~rich(X0) => (~funny(X0) & ~calm(X0))) [input p4]
14. ! [X0] : ((quiet(X0) | rich(X0)) <=> (~patient(X0) & wise(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> calm(X0)) <=> creative(X0)) [input p14]
23. ~wise(john) [input hypothesis]
27. ! [X0] : ((~funny(X0) & ~calm(X0)) | rich(X0)) [ennf transformation 5]
41. ! [X0] : (((generous(X0) & funny(X0)) | creative(X0)) & (~creative(X0) | (~generous(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((generous(X0) & funny(X0)) | creative(X0)) & (~creative(X0) | ~generous(X0) | ~funny(X0))) [flattening 41]
53. ! [X0] : (((quiet(X0) | rich(X0)) | (patient(X0) | ~wise(X0))) & ((~patient(X0) & wise(X0)) | (~quiet(X0) & ~rich(X0)))) [nnf transformation 14]
54. ! [X0] : ((quiet(X0) | rich(X0) | patient(X0) | ~wise(X0)) & ((~patient(X0) & wise(X0)) | (~quiet(X0) & ~rich(X0)))) [flattening 53]
55. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | ~creative(X0)) & (creative(X0) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [nnf transformation 15]
77. creative(X0) | funny(X0) [cnf transformation 42]
81. ~calm(X0) | rich(X0) [cnf transformation 27]
82. ~funny(X0) | rich(X0) [cnf transformation 27]
107. ~rich(X0) | wise(X0) [cnf transformation 54]
114. calm(X0) | rich(X0) | ~creative(X0) [cnf transformation 55]
115. ~calm(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 55]
127. ~wise(john) [cnf transformation 23]
207. ~calm(X0) | ~creative(X0) [subsumption resolution 115,81]
208. ~creative(X0) | rich(X0) [subsumption resolution 114,207]
256. rich(X2) | funny(X2) [resolution 208,77]
258. rich(X2) [subsumption resolution 256,82]
260. wise(X1) [resolution 258,107]
288. $false [resolution 260,127]
% SZS output end Proof for 496912088076921471114971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both curious and not old then alice is old and vice versa. Everyone who is not calm is old or not creative and vice versa. Everyone who is either creative or not tall is either funny or not rich. If someone is generous or not curious then someone is happy or not creative. Everyone who is humble is not strong and vice versa. Everyone who is either not kind or rich is strong or tall and vice versa. Everyone who is either not wise or not creative is either curious or not humble. Everyone who is either not funny or not tall is either not calm or not quiet. If someone is not old then someone is not curious. If someone is both happy and strong then fred is not tall or not kind. Everyone who is either not creative or happy is both creative and not quiet and vice versa. Everyone who is not brave is creative or not rich and vice versa. If someone is not funny then fred is not creative and vice versa. Everyone who is patient is not creative or patient and vice versa. Everyone who is both patient and creative is either quiet or not humble. If susan is either quiet or strong then fred is not quiet and vice versa. Fred is not strong or not curious. Fred is not patient. Someone is both not old and patient. Someone is calm. John is either strong or not kind. Mary is funny or not quiet. Mary is either not patient or rich. Lucy is either not patient or not wise. | John is not funny. | contradiction | (((curious(lucy)&~old(lucy)))<=>(old(alice)))&
(![X]:(~calm(X)<=>(old(X)|~creative(X))))&
(![X]:((creative(X)<~>~tall(X))=>(funny(X)<~>~rich(X))))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:(humble(X)<=>~strong(X)))&
(![X]:((~kind(X)<~>rich(X))<=>(strong(X)|tall(X))))&
(![X]:((~wise(X)<~>~creative(X))=>(curious(X)<~>~humble(X))))&
(![X]:((~funny(X)<~>~tall(X))=>(~calm(X)<~>~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(~curious(X))))&
((?[X]:((happy(X)&strong(X))))=>((~tall(fred)|~kind(fred))))&
(![X]:((~creative(X)<~>happy(X))<=>(creative(X)&~quiet(X))))&
(![X]:(~brave(X)<=>(creative(X)|~rich(X))))&
((?[X]:(~funny(X)))<=>(~creative(fred)))&
(![X]:(patient(X)<=>(~creative(X)|patient(X))))&
(![X]:((patient(X)&creative(X))=>(quiet(X)<~>~humble(X))))&
(((quiet(susan)<~>strong(susan)))<=>(~quiet(fred)))&
((~strong(fred)|~curious(fred)))&
(~patient(fred))&
(?[X]:((~old(X)&patient(X))))&
(?[X]:(calm(X)))&
((strong(john)<~>~kind(john)))&
((funny(mary)|~quiet(mary)))&
((~patient(mary)<~>rich(mary)))&
((~patient(lucy)<~>~wise(lucy))) | ~funny(john) | [
"p12",
"p13",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 8352129283363567980454470
% SZS output start Proof for 8352129283363567980454470
13. ? [X0] : ~funny(X0) <=> ~creative(fred) [input p12]
14. ! [X0] : (patient(X0) <=> (patient(X0) | ~creative(X0))) [input p13]
18. ~patient(fred) [input p17]
25. ~funny(john) [input hypothesis]
56. (? [X0] : ~funny(X0) | creative(fred)) & (~creative(fred) | ! [X0] : funny(X0)) [nnf transformation 13]
57. (? [X0] : ~funny(X0) | creative(fred)) & (~creative(fred) | ! [X1] : funny(X1)) [rectify 56]
58. ? [X0] : ~funny(X0) => ~funny(sK2) [choice axiom]
59. (~funny(sK2) | creative(fred)) & (~creative(fred) | ! [X1] : funny(X1)) [skolemisation 57,58]
60. ! [X0] : ((patient(X0) | (~patient(X0) & creative(X0))) & ((patient(X0) | ~creative(X0)) | ~patient(X0))) [nnf transformation 14]
61. ! [X0] : ((patient(X0) | (~patient(X0) & creative(X0))) & (patient(X0) | ~creative(X0) | ~patient(X0))) [flattening 60]
106. ~creative(fred) | funny(X1) [cnf transformation 59]
109. patient(X0) | creative(X0) [cnf transformation 61]
118. ~patient(fred) [cnf transformation 18]
129. ~funny(john) [cnf transformation 25]
180. 12 <=> creative(fred) [avatar definition]
189. 14 <=> ! [X1] : funny(X1) [avatar definition]
190. funny(X1) <- (14) [avatar component clause 189]
191. 14 | ~12 [avatar split clause 106,180,189]
261. creative(fred) [resolution 109,118]
265. 12 [avatar split clause 261,180]
266. $false <- (14) [resolution 190,129]
269. ~14 [avatar contradiction clause 266]
270. $false [avatar sat refutation 191,265,269]
% SZS output end Proof for 8352129283363567980454470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not happy is both not generous and humble and vice versa.
If someone is not creative then mary is either old or tall.
Everyone who is both curious and not creative is either not brave or not quiet.
Everyone who is either not old or not kind is both not rich and brave and vice versa.
If someone is either not creative or quiet then someone is not generous and vice versa.
Everyone who is either not quiet or kind is either not strong or brave.
If someone is old then paul is both funny and rich.
If paul is not brave then someone is not happy or old and vice versa.
If someone is not tall or creative then paul is both not brave and strong and vice versa.
Everyone who is patient or calm is kind or brave and vice versa.
Everyone who is not curious or not tall is both generous and not strong.
If someone is both not calm and humble then someone is not happy and vice versa.
Everyone who is kind or not brave is not tall.
Everyone who is both creative and patient is either old or not old.
If someone is both not wise and not humble then someone is both strong and not generous.
If mary is not patient or old then someone is brave and vice versa.
Susan is not curious or quiet.
Mary is not rich or wise.
Someone is generous.
Mary is either creative or not patient. | Mary is not curious. | contradiction | (![X]:((calm(X)<~>~happy(X))<=>(~generous(X)&humble(X))))&
((?[X]:(~creative(X)))=>((old(mary)<~>tall(mary))))&
(![X]:((curious(X)&~creative(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(~strong(X)<~>brave(X))))&
((?[X]:(old(X)))=>((funny(paul)&rich(paul))))&
((~brave(paul))<=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~tall(X)|creative(X))))<=>((~brave(paul)&strong(paul))))&
(![X]:((patient(X)|calm(X))<=>(kind(X)|brave(X))))&
(![X]:((~curious(X)|~tall(X))=>(generous(X)&~strong(X))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)|~brave(X))=>~tall(X)))&
(![X]:((creative(X)&patient(X))=>(old(X)<~>~old(X))))&
((?[X]:((~wise(X)&~humble(X))))=>(?[X]:((strong(X)&~generous(X)))))&
(((~patient(mary)|old(mary)))<=>(?[X]:(brave(X))))&
((~curious(susan)|quiet(susan)))&
((~rich(mary)|wise(mary)))&
(?[X]:(generous(X)))&
((creative(mary)<~>~patient(mary))) | ~curious(mary) | [
"p0",
"p7",
"p8",
"p9",
"p10",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8043165078639729803874372
% SZS output start Proof for 8043165078639729803874372
1. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (humble(X0) & ~generous(X0))) [input p0]
8. ~brave(paul) <=> ? [X0] : (old(X0) | ~happy(X0)) [input p7]
9. ? [X0] : (creative(X0) | ~tall(X0)) <=> (strong(paul) & ~brave(paul)) [input p8]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (brave(X0) | kind(X0))) [input p9]
11. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~strong(X0) & generous(X0))) [input p10]
13. ! [X0] : ((~brave(X0) | kind(X0)) => ~tall(X0)) [input p12]
20. creative(mary) <~> ~patient(mary) [input p19]
21. ~curious(mary) [input hypothesis]
33. ! [X0] : ((~strong(X0) & generous(X0)) | (tall(X0) & curious(X0))) [ennf transformation 11]
34. ! [X0] : (~tall(X0) | (brave(X0) & ~kind(X0))) [ennf transformation 13]
37. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 1]
38. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [flattening 37]
49. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X0] : (old(X0) | ~happy(X0)) | brave(paul)) [nnf transformation 8]
50. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X1] : (old(X1) | ~happy(X1)) | brave(paul)) [rectify 49]
51. ? [X1] : (old(X1) | ~happy(X1)) => (old(sK2) | ~happy(sK2)) [choice axiom]
52. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & ((old(sK2) | ~happy(sK2)) | brave(paul)) [skolemisation 50,51]
53. (? [X0] : (creative(X0) | ~tall(X0)) | (~strong(paul) | brave(paul))) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [nnf transformation 9]
54. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [flattening 53]
55. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [rectify 54]
56. ? [X0] : (creative(X0) | ~tall(X0)) => (creative(sK3) | ~tall(sK3)) [choice axiom]
57. ((creative(sK3) | ~tall(sK3)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [skolemisation 55,56]
58. ! [X0] : (((calm(X0) | patient(X0)) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
59. ! [X0] : ((calm(X0) | patient(X0) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | (~calm(X0) & ~patient(X0)))) [flattening 58]
73. (patient(mary) | ~creative(mary)) & (~patient(mary) | creative(mary)) [nnf transformation 20]
74. ~generous(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 38]
100. ~brave(paul) | happy(X0) [cnf transformation 52]
102. ~brave(paul) | tall(X1) [cnf transformation 57]
103. ~brave(paul) | ~creative(X1) [cnf transformation 57]
104. strong(paul) | tall(X1) [cnf transformation 57]
110. ~brave(X0) | patient(X0) | calm(X0) [cnf transformation 59]
111. curious(X0) | generous(X0) [cnf transformation 33]
114. ~strong(X0) | tall(X0) [cnf transformation 33]
119. ~tall(X0) | brave(X0) [cnf transformation 34]
127. ~patient(mary) | creative(mary) [cnf transformation 73]
129. ~curious(mary) [cnf transformation 21]
177. 12 <=> brave(paul) [avatar definition]
179. ~brave(paul) <- (~12) [avatar component clause 177]
182. 13 <=> ! [X0] : happy(X0) [avatar definition]
183. happy(X0) <- (13) [avatar component clause 182]
184. 13 | ~12 [avatar split clause 100,177,182]
195. 16 <=> strong(paul) [avatar definition]
196. strong(paul) <- (16) [avatar component clause 195]
208. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
209. ~creative(X1) <- (19) [avatar component clause 208]
212. 20 <=> ! [X1] : tall(X1) [avatar definition]
213. tall(X1) <- (20) [avatar component clause 212]
214. 20 | 16 [avatar split clause 104,195,212]
215. 19 | ~12 [avatar split clause 103,177,208]
216. 20 | ~12 [avatar split clause 102,177,212]
239. 26 <=> patient(mary) [avatar definition]
241. ~patient(mary) <- (~26) [avatar component clause 239]
259. 30 <=> creative(mary) [avatar definition]
260. creative(mary) <- (30) [avatar component clause 259]
263. 30 | ~26 [avatar split clause 127,239,259]
270. generous(mary) [resolution 111,129]
275. tall(paul) <- (16) [resolution 114,196]
277. brave(paul) <- (16) [resolution 275,119]
278. $false <- (~12, 16) [subsumption resolution 277,179]
279. 12 | ~16 [avatar contradiction clause 278]
282. brave(X0) <- (20) [resolution 213,119]
287. ~happy(mary) | ~calm(mary) [resolution 74,270]
291. 31 <=> calm(mary) [avatar definition]
295. 32 <=> happy(mary) [avatar definition]
297. ~happy(mary) <- (~32) [avatar component clause 295]
298. ~31 | ~32 [avatar split clause 287,295,291]
317. $false <- (~12, 20) [resolution 282,179]
318. 12 | ~20 [avatar contradiction clause 317]
351. patient(X1) | calm(X1) <- (20) [resolution 110,282]
361. $false <- (19, 30) [subsumption resolution 260,209]
362. ~19 | ~30 [avatar contradiction clause 361]
377. calm(mary) <- (20, ~26) [resolution 351,241]
380. 31 | ~20 | 26 [avatar split clause 377,239,212,291]
381. $false <- (13, ~32) [subsumption resolution 297,183]
382. ~13 | 32 [avatar contradiction clause 381]
383. $false [avatar sat refutation 184,214,215,216,263,279,298,318,362,380,382]
% SZS output end Proof for 8043165078639729803874372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong is patient and vice versa.
If someone is both funny and not strong then someone is not happy or old and vice versa.
If mary is quiet then someone is either strong or not strong and vice versa.
Everyone who is curious or not tall is humble or funny.
If someone is calm or rich then someone is both wise and not old.
If someone is either calm or generous then someone is both wise and creative.
Everyone who is either not strong or not funny is not tall and vice versa.
If someone is funny then fred is humble or curious and vice versa.
Everyone who is either not creative or not curious is quiet or patient and vice versa.
Everyone who is humble is not humble.
Everyone who is both calm and creative is both not creative and strong.
Everyone who is not quiet is quiet or brave.
If someone is not old or not wise then alice is quiet.
If alice is either happy or creative then alice is kind or old and vice versa.
If someone is both happy and not funny then someone is not strong or quiet.
If mary is either calm or curious then someone is either not curious or not brave.
Someone is not kind or creative.
Mary is either curious or creative.
Alice is either calm or generous.
Fred is either strong or not curious.
Someone is not happy or strong.
John is not calm.
Someone is happy or patient.
Someone is not generous. | John is old. | neutral | (![X]:((rich(X)|~strong(X))<=>patient(X)))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((~happy(X)|old(X)))))&
((quiet(mary))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((curious(X)|~tall(X))=>(humble(X)|funny(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:((wise(X)&creative(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(funny(X)))<=>((humble(fred)|curious(fred))))&
(![X]:((~creative(X)<~>~curious(X))<=>(quiet(X)|patient(X))))&
(![X]:(humble(X)=>~humble(X)))&
(![X]:((calm(X)&creative(X))=>(~creative(X)&strong(X))))&
(![X]:(~quiet(X)=>(quiet(X)|brave(X))))&
((?[X]:((~old(X)|~wise(X))))=>(quiet(alice)))&
(((happy(alice)<~>creative(alice)))<=>((kind(alice)|old(alice))))&
((?[X]:((happy(X)&~funny(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(?[X]:((~kind(X)|creative(X))))&
((curious(mary)<~>creative(mary)))&
((calm(alice)<~>generous(alice)))&
((strong(fred)<~>~curious(fred)))&
(?[X]:((~happy(X)|strong(X))))&
(~calm(john))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:(~generous(X))) | old(john) | []
| null | 0 |
Everyone who is both tall and not generous is either not happy or kind and vice versa.
Everyone who is both not tall and not brave is creative or tall and vice versa.
Everyone who is not calm or strong is strong or not generous and vice versa.
Everyone who is either wise or not curious is patient and vice versa.
If someone is not tall then someone is either not humble or humble and vice versa.
If someone is both wise and not curious then someone is either not old or not calm and vice versa.
If lucy is not curious or kind then paul is not kind and vice versa.
If lucy is creative then someone is either patient or not tall.
If someone is both not patient and not humble then alice is both funny and not generous and vice versa.
If susan is not funny then someone is not rich or not humble and vice versa.
If lucy is both not funny and brave then someone is either brave or not kind.
If fred is funny or rich then alice is both not kind and not generous.
If alice is not curious then susan is not funny or generous and vice versa.
Everyone who is both brave and not humble is creative or rich and vice versa.
Everyone who is either not creative or not strong is either not brave or not wise and vice versa.
Everyone who is either happy or not happy is generous.
Someone is creative or not kind.
Someone is humble or rich.
Susan is either not kind or generous.
Paul is both patient and brave.
Lucy is not strong.
Alice is both not happy and not creative.
Mary is both not patient and not rich. | Susan is tall. | contradiction | (![X]:((tall(X)&~generous(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~brave(X))<=>(creative(X)|tall(X))))&
(![X]:((~calm(X)|strong(X))<=>(strong(X)|~generous(X))))&
(![X]:((wise(X)<~>~curious(X))<=>patient(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((~humble(X)<~>humble(X)))))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(((~curious(lucy)|kind(lucy)))<=>(~kind(paul)))&
((creative(lucy))=>(?[X]:((patient(X)<~>~tall(X)))))&
((?[X]:((~patient(X)&~humble(X))))<=>((funny(alice)&~generous(alice))))&
((~funny(susan))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~funny(lucy)&brave(lucy)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(((funny(fred)|rich(fred)))=>((~kind(alice)&~generous(alice))))&
((~curious(alice))<=>((~funny(susan)|generous(susan))))&
(![X]:((brave(X)&~humble(X))<=>(creative(X)|rich(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(~brave(X)<~>~wise(X))))&
(![X]:((happy(X)<~>~happy(X))=>generous(X)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((humble(X)|rich(X))))&
((~kind(susan)<~>generous(susan)))&
((patient(paul)&brave(paul)))&
(~strong(lucy))&
((~happy(alice)&~creative(alice)))&
((~patient(mary)&~rich(mary))) | tall(susan) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 5549641344504274631100352
% SZS output start Proof for 5549641344504274631100352
2. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (tall(X0) | creative(X0))) [input p1]
24. tall(susan) [input hypothesis]
34. ! [X0] : (((~brave(X0) & ~tall(X0)) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((~brave(X0) & ~tall(X0)) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | brave(X0) | tall(X0))) [flattening 34]
85. ~tall(X0) | ~tall(X0) [cnf transformation 35]
153. tall(susan) [cnf transformation 24]
159. ~tall(X0) [duplicate literal removal 85]
322. $false [subsumption resolution 153,159]
% SZS output end Proof for 5549641344504274631100352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not kind or happy then someone is either wise or generous and vice versa.
If someone is either not kind or not creative then someone is both not kind and not funny.
Everyone who is either not humble or not wise is old or kind.
If someone is not humble then someone is both not calm and happy.
If someone is not humble then someone is either not patient or kind and vice versa.
If lucy is strong or not patient then susan is not rich and vice versa.
If mary is both brave and not calm then someone is both rich and not rich.
Everyone who is not creative or strong is both not generous and rich.
Everyone who is not rich is old or not creative.
If someone is both not happy and wise then someone is not happy.
Everyone who is not tall or not rich is not curious or not strong and vice versa.
If susan is curious or not wise then fred is not old or not wise and vice versa.
Everyone who is not quiet is generous and vice versa.
If someone is not calm or not humble then fred is either not old or wise.
Everyone who is either not creative or calm is either tall or not patient.
Mary is calm or not generous.
Lucy is generous or funny.
Paul is kind or old.
Mary is both not kind and not creative.
Someone is wise or not brave.
Someone is both calm and not creative.
Someone is not generous.
Alice is not funny or quiet. | Mary is not generous. | entailment | (((~kind(lucy)<~>happy(lucy)))<=>(?[X]:((wise(X)<~>generous(X)))))&
((?[X]:((~kind(X)<~>~creative(X))))=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((~humble(X)<~>~wise(X))=>(old(X)|kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~calm(X)&happy(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(((strong(lucy)|~patient(lucy)))<=>(~rich(susan)))&
(((brave(mary)&~calm(mary)))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((~creative(X)|strong(X))=>(~generous(X)&rich(X))))&
(![X]:(~rich(X)=>(old(X)|~creative(X))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~curious(X)|~strong(X))))&
(((curious(susan)|~wise(susan)))<=>((~old(fred)|~wise(fred))))&
(![X]:(~quiet(X)<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))=>((~old(fred)<~>wise(fred))))&
(![X]:((~creative(X)<~>calm(X))=>(tall(X)<~>~patient(X))))&
((calm(mary)|~generous(mary)))&
((generous(lucy)|funny(lucy)))&
((kind(paul)|old(paul)))&
((~kind(mary)&~creative(mary)))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:(~generous(X)))&
((~funny(alice)|quiet(alice))) | ~generous(mary) | [
"p7",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 2550017063441971333380442
% SZS output start Proof for 2550017063441971333380442
8. ! [X0] : ((strong(X0) | ~creative(X0)) => (rich(X0) & ~generous(X0))) [input p7]
19. ~creative(mary) & ~kind(mary) [input p18]
24. generous(mary) [input hypothesis]
36. ! [X0] : ((rich(X0) & ~generous(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 8]
98. ~generous(X0) | creative(X0) [cnf transformation 36]
125. ~creative(mary) [cnf transformation 19]
130. generous(mary) [cnf transformation 24]
270. 30 <=> generous(mary) [avatar definition]
271. generous(mary) <- (30) [avatar component clause 270]
301. 30 [avatar split clause 130,270]
304. creative(mary) <- (30) [resolution 98,271]
306. $false <- (30) [subsumption resolution 304,125]
307. ~30 [avatar contradiction clause 306]
308. $false [avatar sat refutation 301,307]
% SZS output end Proof for 2550017063441971333380442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is creative and vice versa. If someone is curious then someone is both not kind and strong and vice versa. If someone is calm then john is not rich. Everyone who is either not patient or not curious is not brave and vice versa. If susan is not kind then mary is either not creative or humble. If mary is both wise and old then lucy is not humble. Everyone who is either creative or strong is strong and vice versa. Everyone who is either old or not funny is both not calm and funny. Everyone who is not creative is not calm. If someone is both not wise and not funny then someone is both not generous and brave and vice versa. If someone is either not patient or patient then alice is kind and vice versa. If someone is both not patient and not humble then someone is both rich and not creative. Everyone who is brave or not funny is either calm or not brave. If lucy is both not happy and old then someone is rich. Everyone who is rich or not calm is humble. Everyone who is not humble or not patient is humble or not wise and vice versa. Fred is both not quiet and not patient. Someone is humble or creative. Mary is patient or not tall. Someone is old. Someone is either quiet or creative. Someone is not strong or not kind. | Mary is not curious. | contradiction | (![X]:((~happy(X)<~>kind(X))<=>creative(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:(calm(X)))=>(~rich(john)))&
(![X]:((~patient(X)<~>~curious(X))<=>~brave(X)))&
((~kind(susan))=>((~creative(mary)<~>humble(mary))))&
(((wise(mary)&old(mary)))=>(~humble(lucy)))&
(![X]:((creative(X)<~>strong(X))<=>strong(X)))&
(![X]:((old(X)<~>~funny(X))=>(~calm(X)&funny(X))))&
(![X]:(~creative(X)=>~calm(X)))&
((?[X]:((~wise(X)&~funny(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
((?[X]:((~patient(X)<~>patient(X))))<=>(kind(alice)))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((brave(X)|~funny(X))=>(calm(X)<~>~brave(X))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:((~humble(X)|~patient(X))<=>(humble(X)|~wise(X))))&
((~quiet(fred)&~patient(fred)))&
(?[X]:((humble(X)|creative(X))))&
((patient(mary)|~tall(mary)))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:((~strong(X)|~kind(X)))) | ~curious(mary) | [
"p3",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4213087966945661166804225
% SZS output start Proof for 4213087966945661166804225
4. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p3]
7. ! [X0] : ((creative(X0) <~> strong(X0)) <=> strong(X0)) [input p6]
9. ! [X0] : (~creative(X0) => ~calm(X0)) [input p8]
13. ! [X0] : ((~funny(X0) | brave(X0)) => (calm(X0) <~> ~brave(X0))) [input p12]
15. ! [X0] : ((~calm(X0) | rich(X0)) => humble(X0)) [input p14]
16. ! [X0] : ((~patient(X0) | ~humble(X0)) <=> (~wise(X0) | humble(X0))) [input p15]
23. ~curious(mary) [input hypothesis]
33. ! [X0] : (~calm(X0) | creative(X0)) [ennf transformation 9]
35. ! [X0] : ((calm(X0) <~> ~brave(X0)) | (funny(X0) & ~brave(X0))) [ennf transformation 13]
38. ! [X0] : (humble(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 15]
45. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | brave(X0)) & (~brave(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ~strong(X0)) & (strong(X0) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 7]
61. ! [X0] : (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (funny(X0) & ~brave(X0))) [nnf transformation 35]
64. ! [X0] : (((~patient(X0) | ~humble(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (patient(X0) & humble(X0)))) [nnf transformation 16]
65. ! [X0] : ((~patient(X0) | ~humble(X0) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | (patient(X0) & humble(X0)))) [flattening 64]
86. brave(X0) | patient(X0) | curious(X0) [cnf transformation 45]
90. strong(X0) | strong(X0) | ~creative(X0) [cnf transformation 47]
93. ~strong(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 47]
98. ~calm(X0) | creative(X0) [cnf transformation 33]
109. ~brave(X0) | calm(X0) | ~brave(X0) [cnf transformation 61]
115. humble(X0) | calm(X0) [cnf transformation 38]
118. ~patient(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 65]
127. ~curious(mary) [cnf transformation 23]
129. ~humble(X0) | ~patient(X0) [duplicate literal removal 118]
130. ~brave(X0) | calm(X0) [duplicate literal removal 109]
134. strong(X0) | ~creative(X0) [duplicate literal removal 90]
135. ~strong(X0) | ~creative(X0) [duplicate literal removal 93]
158. 6 <=> ! [X0] : ~calm(X0) [avatar definition]
159. ~calm(X0) <- (6) [avatar component clause 158]
192. ~creative(X0) [subsumption resolution 134,135]
193. ~calm(X0) [subsumption resolution 98,192]
194. 6 [avatar split clause 193,158]
222. 20 <=> ! [X1] : ~patient(X1) [avatar definition]
223. ~patient(X1) <- (20) [avatar component clause 222]
273. ~patient(X0) | calm(X0) [resolution 129,115]
277. ~patient(X0) <- (6) [subsumption resolution 273,159]
278. 20 | ~6 [avatar split clause 277,158,222]
298. patient(X3) | curious(X3) | calm(X3) [resolution 86,130]
303. curious(X3) | calm(X3) <- (20) [subsumption resolution 298,223]
307. curious(X3) <- (6, 20) [subsumption resolution 303,159]
318. $false <- (6, 20) [resolution 307,127]
319. ~6 | ~20 [avatar contradiction clause 318]
320. $false [avatar sat refutation 194,278,319]
% SZS output end Proof for 4213087966945661166804225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not humble is not strong or not brave.
If someone is both brave and not brave then someone is either not wise or old and vice versa.
Everyone who is wise is both calm and brave and vice versa.
Everyone who is funny or brave is not happy and vice versa.
Everyone who is either not curious or not creative is either not calm or old.
Everyone who is either not creative or not generous is calm or not kind.
Everyone who is curious or not happy is wise and vice versa.
Everyone who is not wise is not generous or calm and vice versa.
Everyone who is brave is generous or wise.
Everyone who is not creative or not patient is either not old or not humble.
Everyone who is either generous or creative is not happy or funny and vice versa.
If susan is either not funny or strong then someone is either funny or not generous.
If someone is both curious and not happy then lucy is either not creative or kind and vice versa.
If someone is curious then someone is either not calm or kind and vice versa.
Everyone who is not creative is both not wise and not quiet and vice versa.
If someone is not quiet then susan is not humble and vice versa.
Someone is either old or not calm.
Alice is either not patient or not brave.
Mary is not wise.
Someone is happy.
Fred is not brave. | Fred is not curious. | entailment | (![X]:((funny(X)&~humble(X))=>(~strong(X)|~brave(X))))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(wise(X)<=>(calm(X)&brave(X))))&
(![X]:((funny(X)|brave(X))<=>~happy(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~calm(X)<~>old(X))))&
(![X]:((~creative(X)<~>~generous(X))=>(calm(X)|~kind(X))))&
(![X]:((curious(X)|~happy(X))<=>wise(X)))&
(![X]:(~wise(X)<=>(~generous(X)|calm(X))))&
(![X]:(brave(X)=>(generous(X)|wise(X))))&
(![X]:((~creative(X)|~patient(X))=>(~old(X)<~>~humble(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~happy(X)|funny(X))))&
(((~funny(susan)<~>strong(susan)))=>(?[X]:((funny(X)<~>~generous(X)))))&
((?[X]:((curious(X)&~happy(X))))<=>((~creative(lucy)<~>kind(lucy))))&
((?[X]:(curious(X)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:(~creative(X)<=>(~wise(X)&~quiet(X))))&
((?[X]:(~quiet(X)))<=>(~humble(susan)))&
(?[X]:((old(X)<~>~calm(X))))&
((~patient(alice)<~>~brave(alice)))&
(~wise(mary))&
(?[X]:(happy(X)))&
(~brave(fred)) | ~curious(fred) | [
"p2",
"p6",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 3256529531648268158916303
% SZS output start Proof for 3256529531648268158916303
3. ! [X0] : (wise(X0) <=> (brave(X0) & calm(X0))) [input p2]
7. ! [X0] : ((~happy(X0) | curious(X0)) <=> wise(X0)) [input p6]
8. ! [X0] : (~wise(X0) <=> (calm(X0) | ~generous(X0))) [input p7]
22. curious(fred) [input hypothesis]
39. ! [X0] : ((wise(X0) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ~wise(X0))) [nnf transformation 3]
40. ! [X0] : ((wise(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ~wise(X0))) [flattening 39]
45. ! [X0] : (((~happy(X0) | curious(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & ~curious(X0)))) [nnf transformation 7]
46. ! [X0] : ((~happy(X0) | curious(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & ~curious(X0)))) [flattening 45]
47. ! [X0] : ((~wise(X0) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | wise(X0))) [nnf transformation 8]
48. ! [X0] : ((~wise(X0) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | wise(X0))) [flattening 47]
83. ~wise(X0) | calm(X0) [cnf transformation 40]
95. ~curious(X0) | wise(X0) [cnf transformation 46]
100. ~wise(X0) | ~calm(X0) [cnf transformation 48]
138. curious(fred) [cnf transformation 22]
153. ~wise(X0) [subsumption resolution 100,83]
267. wise(fred) [resolution 95,138]
269. $false [subsumption resolution 267,153]
% SZS output end Proof for 3256529531648268158916303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is either calm or brave.
Everyone who is strong is quiet or funny and vice versa.
Everyone who is not rich is either calm or not strong.
Everyone who is both humble and calm is either not wise or quiet and vice versa.
Everyone who is wise is strong or creative and vice versa.
Everyone who is not generous or kind is happy.
Everyone who is creative or not strong is both happy and not quiet.
If john is both not generous and not creative then someone is either not brave or humble and vice versa.
If someone is both not strong and not wise then alice is not funny or not happy.
If someone is wise then fred is either not rich or humble.
Everyone who is not curious is either rich or patient.
If someone is not funny then john is both curious and kind.
If susan is both old and humble then fred is either patient or happy.
Everyone who is both rich and not old is either wise or calm and vice versa.
Everyone who is humble is not happy and vice versa.
If someone is funny then someone is not kind or not old.
Lucy is either not calm or patient.
Lucy is both not patient and not creative.
Someone is generous or creative.
Someone is creative or tall.
Alice is not creative.
Someone is calm.
Someone is either not wise or creative. | Lucy is quiet. | contradiction | (((~curious(alice)|~brave(alice)))=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:(strong(X)<=>(quiet(X)|funny(X))))&
(![X]:(~rich(X)=>(calm(X)<~>~strong(X))))&
(![X]:((humble(X)&calm(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:(wise(X)<=>(strong(X)|creative(X))))&
(![X]:((~generous(X)|kind(X))=>happy(X)))&
(![X]:((creative(X)|~strong(X))=>(happy(X)&~quiet(X))))&
(((~generous(john)&~creative(john)))<=>(?[X]:((~brave(X)<~>humble(X)))))&
((?[X]:((~strong(X)&~wise(X))))=>((~funny(alice)|~happy(alice))))&
((?[X]:(wise(X)))=>((~rich(fred)<~>humble(fred))))&
(![X]:(~curious(X)=>(rich(X)<~>patient(X))))&
((?[X]:(~funny(X)))=>((curious(john)&kind(john))))&
(((old(susan)&humble(susan)))=>((patient(fred)<~>happy(fred))))&
(![X]:((rich(X)&~old(X))<=>(wise(X)<~>calm(X))))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:(funny(X)))=>(?[X]:((~kind(X)|~old(X)))))&
((~calm(lucy)<~>patient(lucy)))&
((~patient(lucy)&~creative(lucy)))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:((creative(X)|tall(X))))&
(~creative(alice))&
(?[X]:(calm(X)))&
(?[X]:((~wise(X)<~>creative(X)))) | quiet(lucy) | [
"p1",
"p3",
"p4",
"p16",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 3113436005201169203645298
% SZS output start Proof for 3113436005201169203645298
2. ! [X0] : (strong(X0) <=> (funny(X0) | quiet(X0))) [input p1]
4. ! [X0] : ((calm(X0) & humble(X0)) <=> (~wise(X0) <~> quiet(X0))) [input p3]
5. ! [X0] : (wise(X0) <=> (creative(X0) | strong(X0))) [input p4]
17. ~calm(lucy) <~> patient(lucy) [input p16]
18. ~creative(lucy) & ~patient(lucy) [input p17]
24. quiet(lucy) [input hypothesis]
44. ! [X0] : ((strong(X0) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | ~strong(X0))) [nnf transformation 2]
45. ! [X0] : ((strong(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | ~strong(X0))) [flattening 44]
47. ! [X0] : (((calm(X0) & humble(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | (~calm(X0) | ~humble(X0)))) [nnf transformation 4]
48. ! [X0] : (((calm(X0) & humble(X0)) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) & (((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | ~calm(X0) | ~humble(X0))) [flattening 47]
49. ! [X0] : ((wise(X0) | (~creative(X0) & ~strong(X0))) & ((creative(X0) | strong(X0)) | ~wise(X0))) [nnf transformation 5]
50. ! [X0] : ((wise(X0) | (~creative(X0) & ~strong(X0))) & (creative(X0) | strong(X0) | ~wise(X0))) [flattening 49]
64. (~patient(lucy) | calm(lucy)) & (patient(lucy) | ~calm(lucy)) [nnf transformation 17]
75. ~quiet(X0) | strong(X0) [cnf transformation 45]
84. ~wise(X0) | calm(X0) | ~quiet(X0) [cnf transformation 48]
86. ~strong(X0) | wise(X0) [cnf transformation 50]
115. patient(lucy) | ~calm(lucy) [cnf transformation 64]
117. ~patient(lucy) [cnf transformation 18]
124. quiet(lucy) [cnf transformation 24]
232. 25 <=> calm(lucy) [avatar definition]
233. ~calm(lucy) <- (~25) [avatar component clause 232]
236. 26 <=> patient(lucy) [avatar definition]
240. ~25 | 26 [avatar split clause 115,236,232]
241. ~26 [avatar split clause 117,236]
260. strong(lucy) [resolution 75,124]
262. wise(lucy) [resolution 86,260]
339. calm(lucy) | ~quiet(lucy) [resolution 84,262]
344. ~quiet(lucy) <- (~25) [subsumption resolution 339,233]
345. $false <- (~25) [subsumption resolution 344,124]
346. 25 [avatar contradiction clause 345]
347. $false [avatar sat refutation 240,241,346]
% SZS output end Proof for 3113436005201169203645298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or funny is not wise and vice versa.
If alice is either calm or quiet then alice is not brave or patient and vice versa.
If someone is not humble then someone is generous.
If alice is not creative or not quiet then mary is creative and vice versa.
Everyone who is both patient and brave is tall or not curious and vice versa.
If lucy is brave or old then someone is either rich or not curious and vice versa.
Everyone who is rich is either generous or quiet and vice versa.
If someone is calm or not wise then someone is tall.
Everyone who is not strong is both strong and not quiet.
If susan is not rich then john is either not tall or calm.
Everyone who is generous is not brave.
Everyone who is not happy is either not patient or brave.
Everyone who is both strong and not kind is not patient and vice versa.
If john is curious then someone is either strong or not generous.
Everyone who is not strong is not tall and vice versa.
Everyone who is both humble and quiet is rich and vice versa.
Paul is calm or humble.
Someone is not happy.
Lucy is not tall or not curious.
Susan is not wise or not calm.
Someone is not old.
Fred is either not wise or tall. | Mary is humble. | entailment | (![X]:((~brave(X)|funny(X))<=>~wise(X)))&
(((calm(alice)<~>quiet(alice)))<=>((~brave(alice)|patient(alice))))&
((?[X]:(~humble(X)))=>(?[X]:(generous(X))))&
(((~creative(alice)|~quiet(alice)))<=>(creative(mary)))&
(![X]:((patient(X)&brave(X))<=>(tall(X)|~curious(X))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(rich(X)<=>(generous(X)<~>quiet(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:(tall(X))))&
(![X]:(~strong(X)=>(strong(X)&~quiet(X))))&
((~rich(susan))=>((~tall(john)<~>calm(john))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:(~happy(X)=>(~patient(X)<~>brave(X))))&
(![X]:((strong(X)&~kind(X))<=>~patient(X)))&
((curious(john))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
(![X]:((humble(X)&quiet(X))<=>rich(X)))&
((calm(paul)|humble(paul)))&
(?[X]:(~happy(X)))&
((~tall(lucy)|~curious(lucy)))&
((~wise(susan)|~calm(susan)))&
(?[X]:(~old(X)))&
((~wise(fred)<~>tall(fred))) | humble(mary) | [
"p2",
"p4",
"p8",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2452525992215888568108934
% SZS output start Proof for 2452525992215888568108934
3. ? [X0] : ~humble(X0) => ? [X0] : generous(X0) [input p2]
5. ! [X0] : ((brave(X0) & patient(X0)) <=> (~curious(X0) | tall(X0))) [input p4]
9. ! [X0] : (~strong(X0) => (~quiet(X0) & strong(X0))) [input p8]
11. ! [X0] : (generous(X0) => ~brave(X0)) [input p10]
15. ! [X0] : (~strong(X0) <=> ~tall(X0)) [input p14]
23. ~humble(mary) [input hypothesis]
24. ? [X0] : ~humble(X0) => ? [X1] : generous(X1) [rectify 3]
26. ? [X1] : generous(X1) | ! [X0] : humble(X0) [ennf transformation 24]
28. ! [X0] : ((~quiet(X0) & strong(X0)) | strong(X0)) [ennf transformation 9]
30. ! [X0] : (~brave(X0) | ~generous(X0)) [ennf transformation 11]
37. ? [X0] : generous(X0) | ! [X1] : humble(X1) [rectify 26]
38. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
39. generous(sK0) | ! [X1] : humble(X1) [skolemisation 37,38]
42. ! [X0] : (((brave(X0) & patient(X0)) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | (~brave(X0) | ~patient(X0)))) [nnf transformation 5]
43. ! [X0] : (((brave(X0) & patient(X0)) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | ~brave(X0) | ~patient(X0))) [flattening 42]
60. ! [X0] : ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))) [nnf transformation 15]
77. generous(sK0) | humble(X1) [cnf transformation 39]
84. ~tall(X0) | brave(X0) [cnf transformation 43]
98. strong(X0) | strong(X0) [cnf transformation 28]
102. ~generous(X0) | ~brave(X0) [cnf transformation 30]
111. ~strong(X0) | tall(X0) [cnf transformation 60]
122. ~humble(mary) [cnf transformation 23]
123. strong(X0) [duplicate literal removal 98]
147. 5 <=> ! [X1] : humble(X1) [avatar definition]
148. humble(X1) <- (5) [avatar component clause 147]
150. 6 <=> generous(sK0) [avatar definition]
152. generous(sK0) <- (6) [avatar component clause 150]
153. 5 | 6 [avatar split clause 77,150,147]
230. tall(X0) [subsumption resolution 111,123]
253. $false <- (5) [resolution 148,122]
254. ~5 [avatar contradiction clause 253]
261. brave(X0) [resolution 84,230]
270. ~brave(sK0) <- (6) [resolution 102,152]
271. $false <- (6) [subsumption resolution 270,261]
272. ~6 [avatar contradiction clause 271]
273. $false [avatar sat refutation 153,254,272]
% SZS output end Proof for 2452525992215888568108934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and not tall then someone is both old and rich and vice versa.
Everyone who is both not humble and not patient is both strong and kind.
If paul is both not patient and not humble then fred is both not happy and not wise.
Everyone who is either tall or wise is both not tall and calm.
If paul is both funny and not kind then alice is not old and vice versa.
Everyone who is calm or not tall is not wise or not patient.
If lucy is curious or not calm then someone is both not patient and not funny and vice versa.
Everyone who is not kind is not funny or humble.
If fred is either not brave or not kind then someone is both not tall and kind and vice versa.
If mary is not tall then paul is not strong and vice versa.
Everyone who is both not rich and not generous is either not kind or patient and vice versa.
Everyone who is both calm and humble is not humble or not wise and vice versa.
Everyone who is wise or not kind is not strong.
Everyone who is tall is strong or old and vice versa.
If fred is either creative or not patient then someone is strong or creative and vice versa.
Someone is either not strong or not quiet.
Susan is either not strong or curious.
Mary is humble or old.
Someone is either not tall or not rich.
John is old.
Someone is humble or not happy.
Mary is brave.
Paul is rich or not funny. | Susan is not kind. | neutral | (((quiet(paul)&~tall(paul)))<=>(?[X]:((old(X)&rich(X)))))&
(![X]:((~humble(X)&~patient(X))=>(strong(X)&kind(X))))&
(((~patient(paul)&~humble(paul)))=>((~happy(fred)&~wise(fred))))&
(![X]:((tall(X)<~>wise(X))=>(~tall(X)&calm(X))))&
(((funny(paul)&~kind(paul)))<=>(~old(alice)))&
(![X]:((calm(X)|~tall(X))=>(~wise(X)|~patient(X))))&
(((curious(lucy)|~calm(lucy)))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:(~kind(X)=>(~funny(X)|humble(X))))&
(((~brave(fred)<~>~kind(fred)))<=>(?[X]:((~tall(X)&kind(X)))))&
((~tall(mary))<=>(~strong(paul)))&
(![X]:((~rich(X)&~generous(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((calm(X)&humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:((wise(X)|~kind(X))=>~strong(X)))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(((creative(fred)<~>~patient(fred)))<=>(?[X]:((strong(X)|creative(X)))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~strong(susan)<~>curious(susan)))&
((humble(mary)|old(mary)))&
(?[X]:((~tall(X)<~>~rich(X))))&
(old(john))&
(?[X]:((humble(X)|~happy(X))))&
(brave(mary))&
((rich(paul)|~funny(paul))) | ~kind(susan) | []
| null | 0 |
Everyone who is both humble and not humble is not creative or strong and vice versa. If mary is happy or calm then someone is tall. If john is not curious then someone is both not curious and not rich. If susan is not tall or humble then mary is strong or not humble. If fred is old then fred is either not quiet or not calm and vice versa. Everyone who is quiet is both wise and tall and vice versa. If someone is both not happy and not wise then someone is generous and vice versa. If mary is either not brave or not patient then susan is not brave and vice versa. Everyone who is either not brave or quiet is wise or not quiet and vice versa. If someone is both not old and not curious then alice is both calm and not generous and vice versa. If paul is either not wise or not patient then susan is both old and not tall and vice versa. Everyone who is not calm is not brave and vice versa. If someone is not happy then fred is brave or not generous and vice versa. Everyone who is both old and creative is both generous and brave and vice versa. Everyone who is generous is not quiet or not generous. If someone is either brave or not humble then someone is either curious or funny and vice versa. Mary is both not old and not generous. Susan is rich. Someone is creative. Someone is either happy or not calm. John is either calm or strong. Susan is either not creative or creative. | John is humble. | neutral | (![X]:((humble(X)&~humble(X))<=>(~creative(X)|strong(X))))&
(((happy(mary)|calm(mary)))=>(?[X]:(tall(X))))&
((~curious(john))=>(?[X]:((~curious(X)&~rich(X)))))&
(((~tall(susan)|humble(susan)))=>((strong(mary)|~humble(mary))))&
((old(fred))<=>((~quiet(fred)<~>~calm(fred))))&
(![X]:(quiet(X)<=>(wise(X)&tall(X))))&
((?[X]:((~happy(X)&~wise(X))))<=>(?[X]:(generous(X))))&
(((~brave(mary)<~>~patient(mary)))<=>(~brave(susan)))&
(![X]:((~brave(X)<~>quiet(X))<=>(wise(X)|~quiet(X))))&
((?[X]:((~old(X)&~curious(X))))<=>((calm(alice)&~generous(alice))))&
(((~wise(paul)<~>~patient(paul)))<=>((old(susan)&~tall(susan))))&
(![X]:(~calm(X)<=>~brave(X)))&
((?[X]:(~happy(X)))<=>((brave(fred)|~generous(fred))))&
(![X]:((old(X)&creative(X))<=>(generous(X)&brave(X))))&
(![X]:(generous(X)=>(~quiet(X)|~generous(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
((~old(mary)&~generous(mary)))&
(rich(susan))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)<~>~calm(X))))&
((calm(john)<~>strong(john)))&
((~creative(susan)<~>creative(susan))) | humble(john) | []
| null | 0 |
Everyone who is not funny or not brave is not quiet or humble.
Everyone who is curious is either tall or not generous.
If john is both not wise and wise then someone is either happy or not humble.
Everyone who is not patient is either not kind or not creative and vice versa.
If someone is both not wise and not rich then john is not tall.
Everyone who is either not strong or not quiet is both generous and not curious and vice versa.
Everyone who is both curious and not humble is either generous or patient and vice versa.
Everyone who is not happy or not rich is not calm or funny.
If someone is either not old or rich then someone is not kind or not curious and vice versa.
Everyone who is either not generous or not kind is both not humble and quiet.
Everyone who is humble or strong is either not wise or not kind and vice versa.
If alice is curious then someone is not old or generous and vice versa.
If alice is not tall then fred is not humble or curious and vice versa.
Everyone who is either not calm or curious is either quiet or curious.
Everyone who is not kind is wise and vice versa.
If susan is old then someone is patient or not happy.
John is either not rich or not quiet.
Alice is creative or not old.
Someone is both humble and wise.
Fred is either not calm or strong.
Someone is not calm or rich.
Someone is either not wise or not creative.
Someone is not curious or creative. | John is not patient. | neutral | (![X]:((~funny(X)|~brave(X))=>(~quiet(X)|humble(X))))&
(![X]:(curious(X)=>(tall(X)<~>~generous(X))))&
(((~wise(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~patient(X)<=>(~kind(X)<~>~creative(X))))&
((?[X]:((~wise(X)&~rich(X))))=>(~tall(john)))&
(![X]:((~strong(X)<~>~quiet(X))<=>(generous(X)&~curious(X))))&
(![X]:((curious(X)&~humble(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~happy(X)|~rich(X))=>(~calm(X)|funny(X))))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:((~generous(X)<~>~kind(X))=>(~humble(X)&quiet(X))))&
(![X]:((humble(X)|strong(X))<=>(~wise(X)<~>~kind(X))))&
((curious(alice))<=>(?[X]:((~old(X)|generous(X)))))&
((~tall(alice))<=>((~humble(fred)|curious(fred))))&
(![X]:((~calm(X)<~>curious(X))=>(quiet(X)<~>curious(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((old(susan))=>(?[X]:((patient(X)|~happy(X)))))&
((~rich(john)<~>~quiet(john)))&
((creative(alice)|~old(alice)))&
(?[X]:((humble(X)&wise(X))))&
((~calm(fred)<~>strong(fred)))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((~curious(X)|creative(X)))) | ~patient(john) | []
| null | 0 |
Everyone who is both kind and quiet is quiet and vice versa. If someone is not generous then someone is rich or not calm and vice versa. If someone is not kind then lucy is not happy or not creative. Everyone who is not curious is not tall or strong. If someone is either not creative or not funny then someone is either not old or not quiet and vice versa. Everyone who is both not calm and wise is not old. If fred is both not happy and generous then someone is brave or not quiet. Everyone who is both not strong and funny is humble or not happy. If someone is both rich and not calm then someone is either not tall or not patient. If someone is humble or not calm then someone is not patient or old. Everyone who is brave is happy or calm. If someone is either not patient or not humble then susan is not funny. Everyone who is creative is not patient and vice versa. Everyone who is patient or not rich is either patient or not creative and vice versa. If paul is happy then someone is both old and not patient. If someone is both not funny and brave then susan is both not wise and quiet and vice versa. Someone is not kind. Lucy is creative. Someone is both generous and calm. Fred is both generous and strong. Susan is either not brave or not quiet. Someone is quiet or kind. Paul is both wise and calm. Mary is not kind. | Mary is not quiet. | entailment | (![X]:((kind(X)&quiet(X))<=>quiet(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((rich(X)|~calm(X)))))&
((?[X]:(~kind(X)))=>((~happy(lucy)|~creative(lucy))))&
(![X]:(~curious(X)=>(~tall(X)|strong(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((~calm(X)&wise(X))=>~old(X)))&
(((~happy(fred)&generous(fred)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((~strong(X)&funny(X))=>(humble(X)|~happy(X))))&
((?[X]:((rich(X)&~calm(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((~patient(X)|old(X)))))&
(![X]:(brave(X)=>(happy(X)|calm(X))))&
((?[X]:((~patient(X)<~>~humble(X))))=>(~funny(susan)))&
(![X]:(creative(X)<=>~patient(X)))&
(![X]:((patient(X)|~rich(X))<=>(patient(X)<~>~creative(X))))&
((happy(paul))=>(?[X]:((old(X)&~patient(X)))))&
((?[X]:((~funny(X)&brave(X))))<=>((~wise(susan)&quiet(susan))))&
(?[X]:(~kind(X)))&
(creative(lucy))&
(?[X]:((generous(X)&calm(X))))&
((generous(fred)&strong(fred)))&
((~brave(susan)<~>~quiet(susan)))&
(?[X]:((quiet(X)|kind(X))))&
((wise(paul)&calm(paul)))&
(~kind(mary)) | ~quiet(mary) | [
"p0",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 3929984554438144545189171
% SZS output start Proof for 3929984554438144545189171
1. ! [X0] : ((quiet(X0) & kind(X0)) <=> quiet(X0)) [input p0]
24. ~kind(mary) [input p23]
25. quiet(mary) [input hypothesis]
45. ! [X0] : (((quiet(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 1]
46. ! [X0] : (((quiet(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | ~quiet(X0) | ~kind(X0))) [flattening 45]
85. ~quiet(X0) | kind(X0) [cnf transformation 46]
132. ~kind(mary) [cnf transformation 24]
133. quiet(mary) [cnf transformation 25]
307. kind(mary) [resolution 85,133]
309. $false [subsumption resolution 307,132]
% SZS output end Proof for 3929984554438144545189171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is both not patient and not humble. Everyone who is both kind and humble is humble and vice versa. If john is both not quiet and not creative then someone is not happy or not patient and vice versa. If someone is both not rich and not creative then someone is rich. If alice is either kind or funny then someone is not strong or not humble and vice versa. Everyone who is both not strong and not curious is both old and creative and vice versa. Everyone who is either not tall or not generous is both not wise and not calm. If someone is both patient and old then someone is both generous and not strong and vice versa. If someone is both wise and quiet then fred is rich or old and vice versa. Everyone who is either not tall or creative is not kind or not strong and vice versa. If paul is not brave or not quiet then susan is funny and vice versa. If mary is not tall or generous then someone is either calm or strong and vice versa. Everyone who is either wise or tall is both brave and kind. If someone is both not funny and rich then fred is not kind and vice versa. Everyone who is either not old or quiet is not curious or not kind and vice versa. Everyone who is curious is both not brave and old and vice versa. Alice is either not patient or funny. Lucy is patient or not strong. Lucy is kind. Someone is wise. Someone is not patient or not quiet. Someone is either not curious or wise. Fred is both happy and curious. | Susan is creative. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
(![X]:((kind(X)&humble(X))<=>humble(X)))&
(((~quiet(john)&~creative(john)))<=>(?[X]:((~happy(X)|~patient(X)))))&
((?[X]:((~rich(X)&~creative(X))))=>(?[X]:(rich(X))))&
(((kind(alice)<~>funny(alice)))<=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(old(X)&creative(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~wise(X)&~calm(X))))&
((?[X]:((patient(X)&old(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((wise(X)&quiet(X))))<=>((rich(fred)|old(fred))))&
(![X]:((~tall(X)<~>creative(X))<=>(~kind(X)|~strong(X))))&
(((~brave(paul)|~quiet(paul)))<=>(funny(susan)))&
(((~tall(mary)|generous(mary)))<=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((wise(X)<~>tall(X))=>(brave(X)&kind(X))))&
((?[X]:((~funny(X)&rich(X))))<=>(~kind(fred)))&
(![X]:((~old(X)<~>quiet(X))<=>(~curious(X)|~kind(X))))&
(![X]:(curious(X)<=>(~brave(X)&old(X))))&
((~patient(alice)<~>funny(alice)))&
((patient(lucy)|~strong(lucy)))&
(kind(lucy))&
(?[X]:(wise(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((happy(fred)&curious(fred))) | creative(susan) | []
| null | 0 |
If someone is both not quiet and not patient then paul is rich and vice versa. Everyone who is either wise or not strong is not rich or calm. Everyone who is humble is both happy and brave. Everyone who is not calm is not quiet or not funny. If someone is either quiet or generous then alice is not brave or not rich. If john is not humble then mary is either not humble or humble. If someone is both rich and quiet then someone is either wise or not happy and vice versa. Everyone who is not creative or not patient is both humble and not brave and vice versa. If mary is not kind then mary is either not wise or not generous and vice versa. Everyone who is either not creative or strong is either not creative or not brave and vice versa. Everyone who is not happy is both curious and tall. Everyone who is not rich is old or kind and vice versa. If someone is not old or humble then mary is either brave or not brave and vice versa. Everyone who is calm or not brave is both not calm and rich. Everyone who is rich is either generous or not rich. Everyone who is rich is either creative or generous. Someone is either patient or not kind. Fred is either not kind or kind. Someone is either generous or quiet. Someone is either not strong or happy. Lucy is wise. Someone is not strong or tall. | Alice is not humble. | neutral | ((?[X]:((~quiet(X)&~patient(X))))<=>(rich(paul)))&
(![X]:((wise(X)<~>~strong(X))=>(~rich(X)|calm(X))))&
(![X]:(humble(X)=>(happy(X)&brave(X))))&
(![X]:(~calm(X)=>(~quiet(X)|~funny(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>((~brave(alice)|~rich(alice))))&
((~humble(john))=>((~humble(mary)<~>humble(mary))))&
((?[X]:((rich(X)&quiet(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(humble(X)&~brave(X))))&
((~kind(mary))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>strong(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~happy(X)=>(curious(X)&tall(X))))&
(![X]:(~rich(X)<=>(old(X)|kind(X))))&
((?[X]:((~old(X)|humble(X))))<=>((brave(mary)<~>~brave(mary))))&
(![X]:((calm(X)|~brave(X))=>(~calm(X)&rich(X))))&
(![X]:(rich(X)=>(generous(X)<~>~rich(X))))&
(![X]:(rich(X)=>(creative(X)<~>generous(X))))&
(?[X]:((patient(X)<~>~kind(X))))&
((~kind(fred)<~>kind(fred)))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(wise(lucy))&
(?[X]:((~strong(X)|tall(X)))) | ~humble(alice) | []
| null | 0 |
Everyone who is not patient is happy or kind and vice versa.
If someone is not tall or not old then someone is quiet or calm.
If lucy is happy or tall then john is both not wise and not humble.
Everyone who is not happy or quiet is not patient and vice versa.
Everyone who is both happy and quiet is not humble or not happy and vice versa.
If mary is not kind or patient then john is generous or kind.
Everyone who is not happy is either not curious or not funny.
Everyone who is both tall and not wise is either tall or not brave.
Everyone who is both happy and generous is old and vice versa.
Everyone who is both not creative and wise is either kind or curious.
If someone is wise or not funny then mary is quiet and vice versa.
Everyone who is both kind and not patient is either old or not wise and vice versa.
Everyone who is both not curious and funny is either generous or not funny and vice versa.
Someone is either kind or not kind.
Fred is both not humble and not creative.
Someone is not tall.
Fred is tall.
Someone is either brave or calm. | Mary is not brave. | neutral | (![X]:(~patient(X)<=>(happy(X)|kind(X))))&
((?[X]:((~tall(X)|~old(X))))=>(?[X]:((quiet(X)|calm(X)))))&
(((happy(lucy)|tall(lucy)))=>((~wise(john)&~humble(john))))&
(![X]:((~happy(X)|quiet(X))<=>~patient(X)))&
(![X]:((happy(X)&quiet(X))<=>(~humble(X)|~happy(X))))&
(((~kind(mary)|patient(mary)))=>((generous(john)|kind(john))))&
(![X]:(~happy(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((tall(X)&~wise(X))=>(tall(X)<~>~brave(X))))&
(![X]:((happy(X)&generous(X))<=>old(X)))&
(![X]:((~creative(X)&wise(X))=>(kind(X)<~>curious(X))))&
((?[X]:((wise(X)|~funny(X))))<=>(quiet(mary)))&
(![X]:((kind(X)&~patient(X))<=>(old(X)<~>~wise(X))))&
(![X]:((~curious(X)&funny(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
((~humble(fred)&~creative(fred)))&
(?[X]:(~tall(X)))&
(tall(fred))&
(?[X]:((brave(X)<~>calm(X)))) | ~brave(mary) | []
| null | 0 |
Everyone who is not generous or not happy is not tall or kind.
Everyone who is either kind or not quiet is not brave or happy.
Everyone who is either not curious or happy is either humble or not happy.
If someone is tall or curious then alice is either not quiet or calm.
Everyone who is both patient and not happy is either kind or humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
If someone is either funny or not tall then paul is strong.
If someone is old then alice is either not funny or wise and vice versa.
Everyone who is both not curious and not brave is calm or not quiet.
If someone is calm then susan is happy or tall and vice versa.
Everyone who is curious is both not strong and tall.
Everyone who is rich is both wise and strong and vice versa.
Everyone who is creative is both not wise and strong and vice versa.
If someone is wise or quiet then fred is not humble or not generous and vice versa.
Someone is not generous.
Someone is not old.
Someone is either generous or tall.
Fred is not brave.
John is patient.
Susan is either not funny or not generous. | Alice is quiet. | entailment | (![X]:((~generous(X)|~happy(X))=>(~tall(X)|kind(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(![X]:(creative(X)<=>(~wise(X)&strong(X))))&
((?[X]:((wise(X)|quiet(X))))<=>((~humble(fred)|~generous(fred))))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X))))&
(~brave(fred))&
(patient(john))&
((~funny(susan)<~>~generous(susan))) | quiet(alice) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p12",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 1650730122802529419334339
% SZS output start Proof for 1650730122802529419334339
1. ! [X0] : ((~happy(X0) | ~generous(X0)) => (kind(X0) | ~tall(X0))) [input p0]
3. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p2]
4. ? [X0] : (curious(X0) | tall(X0)) => (~quiet(alice) <~> calm(alice)) [input p3]
5. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p4]
7. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p6]
8. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p7]
13. ! [X0] : (curious(X0) => (tall(X0) & ~strong(X0))) [input p12]
19. ? [X0] : (generous(X0) <~> tall(X0)) [input p18]
23. ~quiet(alice) [input hypothesis]
24. ! [X0] : ((kind(X0) | ~tall(X0)) | (happy(X0) & generous(X0))) [ennf transformation 1]
25. ! [X0] : (kind(X0) | ~tall(X0) | (happy(X0) & generous(X0))) [flattening 24]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 3]
29. (~quiet(alice) <~> calm(alice)) | ! [X0] : (~curious(X0) & ~tall(X0)) [ennf transformation 4]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 8]
34. ! [X0] : ((tall(X0) & ~strong(X0)) | ~curious(X0)) [ennf transformation 13]
36. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
37. ((~calm(alice) | quiet(alice)) & (calm(alice) | ~quiet(alice))) | ! [X0] : (~curious(X0) & ~tall(X0)) [nnf transformation 29]
38. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 5]
39. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 38]
42. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 7]
43. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 42]
63. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) [nnf transformation 19]
64. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) => ((~tall(sK5) | ~generous(sK5)) & (tall(sK5) | generous(sK5))) [choice axiom]
65. (~tall(sK5) | ~generous(sK5)) & (tall(sK5) | generous(sK5)) [skolemisation 63,64]
68. ~tall(X0) | kind(X0) | happy(X0) [cnf transformation 25]
73. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 36]
77. ~calm(alice) | quiet(alice) | ~tall(X0) [cnf transformation 37]
84. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 39]
91. ~kind(X0) | ~generous(X0) [cnf transformation 43]
93. humble(paul) | calm(X0) [cnf transformation 30]
94. humble(paul) | kind(X0) [cnf transformation 30]
95. generous(paul) | calm(X0) [cnf transformation 30]
96. generous(paul) | kind(X0) [cnf transformation 30]
108. ~curious(X0) | tall(X0) [cnf transformation 34]
115. tall(sK5) | generous(sK5) [cnf transformation 65]
121. ~quiet(alice) [cnf transformation 23]
123. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 73]
128. 2 <=> quiet(alice) [avatar definition]
132. 3 <=> calm(alice) [avatar definition]
134. ~calm(alice) <- (~3) [avatar component clause 132]
137. 4 <=> ! [X0] : ~tall(X0) [avatar definition]
138. ~tall(X0) <- (4) [avatar component clause 137]
139. 4 | 2 | ~3 [avatar split clause 77,132,128,137]
143. 5 <=> ! [X0] : kind(X0) [avatar definition]
144. kind(X0) <- (5) [avatar component clause 143]
146. 6 <=> generous(paul) [avatar definition]
148. generous(paul) <- (6) [avatar component clause 146]
149. 5 | 6 [avatar split clause 96,146,143]
151. 7 <=> ! [X0] : calm(X0) [avatar definition]
152. calm(X0) <- (7) [avatar component clause 151]
153. 7 | 6 [avatar split clause 95,146,151]
155. 8 <=> humble(paul) [avatar definition]
157. humble(paul) <- (8) [avatar component clause 155]
158. 5 | 8 [avatar split clause 94,155,143]
159. 7 | 8 [avatar split clause 93,155,151]
236. 26 <=> generous(sK5) [avatar definition]
237. generous(sK5) <- (26) [avatar component clause 236]
240. 27 <=> tall(sK5) [avatar definition]
241. tall(sK5) <- (27) [avatar component clause 240]
244. 26 | 27 [avatar split clause 115,240,236]
255. ~2 [avatar split clause 121,128]
256. $false <- (~3, 7) [subsumption resolution 134,152]
257. 3 | ~7 [avatar contradiction clause 256]
264. ~generous(X0) <- (5) [resolution 91,144]
267. $false <- (5, 26) [resolution 264,237]
268. ~5 | ~26 [avatar contradiction clause 267]
327. 34 <=> kind(paul) [avatar definition]
329. kind(paul) <- (34) [avatar component clause 327]
333. kind(paul) | ~happy(paul) <- (8) [resolution 84,157]
335. 35 <=> happy(paul) [avatar definition]
337. ~happy(paul) <- (~35) [avatar component clause 335]
338. ~35 | 34 | ~8 [avatar split clause 333,155,327,335]
341. happy(paul) | curious(paul) <- (8) [resolution 123,157]
342. curious(paul) <- (8, ~35) [subsumption resolution 341,337]
346. tall(paul) <- (8, ~35) [resolution 342,108]
347. kind(paul) | happy(paul) <- (8, ~35) [resolution 346,68]
349. kind(paul) <- (8, ~35) [subsumption resolution 347,337]
350. 34 | ~8 | 35 [avatar split clause 349,335,155,327]
355. ~generous(paul) <- (34) [resolution 329,91]
357. $false <- (6, 34) [subsumption resolution 355,148]
358. ~6 | ~34 [avatar contradiction clause 357]
373. $false <- (4, 27) [resolution 241,138]
376. ~4 | ~27 [avatar contradiction clause 373]
377. $false [avatar sat refutation 139,149,153,158,159,244,255,257,268,338,350,358,376]
% SZS output end Proof for 1650730122802529419334339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not quiet is either not creative or not brave and vice versa.
Everyone who is not tall or calm is calm or not rich and vice versa.
Everyone who is either curious or generous is both quiet and not rich.
Everyone who is either not quiet or not old is either not rich or wise and vice versa.
If lucy is either generous or quiet then lucy is not old.
Everyone who is both not tall and not rich is quiet.
If someone is either patient or humble then paul is funny or generous and vice versa.
Everyone who is not tall is both not kind and not curious and vice versa.
If someone is both wise and not calm then lucy is both not funny and not happy and vice versa.
If someone is either not wise or not generous then someone is either not rich or quiet and vice versa.
Everyone who is old or not kind is both not strong and curious and vice versa.
If someone is old or funny then mary is both not creative and creative and vice versa.
Everyone who is either brave or not wise is either not happy or kind and vice versa.
If john is either not happy or kind then mary is either strong or not patient.
If mary is either not humble or not quiet then susan is either creative or not generous and vice versa.
If someone is not calm or not generous then fred is both not creative and quiet and vice versa.
John is both generous and not kind.
Fred is calm.
Fred is not old or not curious.
Mary is wise.
Mary is not funny or tall.
Paul is either not calm or quiet.
Fred is not humble or humble.
John is both not kind and not patient. | John is tall. | entailment | (![X]:((~strong(X)|~quiet(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:((~tall(X)|calm(X))<=>(calm(X)|~rich(X))))&
(![X]:((curious(X)<~>generous(X))=>(quiet(X)&~rich(X))))&
(![X]:((~quiet(X)<~>~old(X))<=>(~rich(X)<~>wise(X))))&
(((generous(lucy)<~>quiet(lucy)))=>(~old(lucy)))&
(![X]:((~tall(X)&~rich(X))=>quiet(X)))&
((?[X]:((patient(X)<~>humble(X))))<=>((funny(paul)|generous(paul))))&
(![X]:(~tall(X)<=>(~kind(X)&~curious(X))))&
((?[X]:((wise(X)&~calm(X))))<=>((~funny(lucy)&~happy(lucy))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:((old(X)|~kind(X))<=>(~strong(X)&curious(X))))&
((?[X]:((old(X)|funny(X))))<=>((~creative(mary)&creative(mary))))&
(![X]:((brave(X)<~>~wise(X))<=>(~happy(X)<~>kind(X))))&
(((~happy(john)<~>kind(john)))=>((strong(mary)<~>~patient(mary))))&
(((~humble(mary)<~>~quiet(mary)))<=>((creative(susan)<~>~generous(susan))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~creative(fred)&quiet(fred))))&
((generous(john)&~kind(john)))&
(calm(fred))&
((~old(fred)|~curious(fred)))&
(wise(mary))&
((~funny(mary)|tall(mary)))&
((~calm(paul)<~>quiet(paul)))&
((~humble(fred)|humble(fred)))&
((~kind(john)&~patient(john))) | tall(john) | [
"p7",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 444265466987832280668834
% SZS output start Proof for 444265466987832280668834
8. ! [X0] : (~tall(X0) <=> (~curious(X0) & ~kind(X0))) [input p7]
11. ! [X0] : ((~kind(X0) | old(X0)) <=> (curious(X0) & ~strong(X0))) [input p10]
25. ~tall(john) [input hypothesis]
44. ! [X0] : ((~tall(X0) | (curious(X0) | kind(X0))) & ((~curious(X0) & ~kind(X0)) | tall(X0))) [nnf transformation 8]
45. ! [X0] : ((~tall(X0) | curious(X0) | kind(X0)) & ((~curious(X0) & ~kind(X0)) | tall(X0))) [flattening 44]
56. ! [X0] : (((~kind(X0) | old(X0)) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 11]
57. ! [X0] : ((~kind(X0) | old(X0) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | (kind(X0) & ~old(X0)))) [flattening 56]
103. ~kind(X0) | tall(X0) [cnf transformation 45]
104. ~curious(X0) | tall(X0) [cnf transformation 45]
121. kind(X0) | curious(X0) [cnf transformation 57]
164. ~tall(john) [cnf transformation 25]
374. curious(X0) | tall(X0) [resolution 121,103]
375. tall(X0) [subsumption resolution 374,104]
377. $false [resolution 375,164]
% SZS output end Proof for 444265466987832280668834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and patient is old or calm and vice versa. If someone is generous then lucy is either happy or tall and vice versa. Everyone who is either old or not happy is both quiet and not old. Everyone who is either old or not old is both funny and not happy. Everyone who is either curious or old is brave and vice versa. Everyone who is either not quiet or not humble is not rich. If john is both not quiet and brave then someone is either not wise or quiet and vice versa. If someone is both not wise and not strong then fred is both not old and not kind. Everyone who is quiet is both not curious and not patient. Everyone who is kind is wise. Everyone who is quiet or old is either strong or not quiet and vice versa. Everyone who is not curious is not happy. Everyone who is not rich is both tall and generous. If john is both not happy and not rich then susan is either not quiet or wise. Someone is not curious or not rich. Someone is either brave or not wise. Lucy is either not kind or creative. Someone is not humble or rich. Someone is both creative and tall. John is not tall. | Susan is quiet. | entailment | (![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:((quiet(X)|old(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(((~happy(john)&~rich(john)))=>((~quiet(susan)<~>wise(susan))))&
(?[X]:((~curious(X)|~rich(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
((~kind(lucy)<~>creative(lucy)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:((creative(X)&tall(X))))&
(~tall(john)) | quiet(susan) | [
"p0",
"p2",
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 1190972438370716440287978
% SZS output start Proof for 1190972438370716440287978
1. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p0]
3. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p2]
4. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p3]
21. ~quiet(susan) [input hypothesis]
22. ! [X0] : ((old(X0) <~> ~old(X0)) => ~happy(X0)) [pure predicate removal 4]
23. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 3]
24. ! [X0] : (~happy(X0) | (old(X0) <=> ~old(X0))) [ennf transformation 22]
33. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 1]
34. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 33]
39. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 23]
40. ! [X0] : (~happy(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 24]
62. ~patient(X0) | ~old(X0) [cnf transformation 34]
64. ~old(X0) | patient(X0) [cnf transformation 34]
71. quiet(X0) | old(X0) | happy(X0) [cnf transformation 39]
75. ~happy(X0) | old(X0) | old(X0) [cnf transformation 40]
113. ~quiet(susan) [cnf transformation 21]
117. ~happy(X0) | old(X0) [duplicate literal removal 75]
120. ~old(X0) [subsumption resolution 62,64]
140. quiet(X0) | happy(X0) [subsumption resolution 71,120]
141. ~happy(X0) [subsumption resolution 117,120]
188. 14 <=> quiet(susan) [avatar definition]
189. ~quiet(susan) <- (~14) [avatar component clause 188]
236. ~14 [avatar split clause 113,188]
245. happy(susan) <- (~14) [resolution 140,189]
250. $false <- (~14) [subsumption resolution 245,141]
251. 14 [avatar contradiction clause 250]
254. $false [avatar sat refutation 236,251]
% SZS output end Proof for 1190972438370716440287978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or old is not kind. If fred is both not old and wise then someone is not quiet and vice versa. Everyone who is patient or not quiet is both not generous and not rich and vice versa. Everyone who is not strong is both not happy and happy and vice versa. Everyone who is tall or wise is not quiet or quiet. Everyone who is not strong or rich is both happy and funny and vice versa. Everyone who is patient is rich or not kind and vice versa. If lucy is either strong or not wise then someone is not old or rich and vice versa. If someone is both patient and not kind then fred is wise or not funny and vice versa. Everyone who is both not brave and not kind is not wise and vice versa. Everyone who is either generous or quiet is old or not strong and vice versa. If alice is either patient or not old then john is either not patient or happy and vice versa. If someone is either creative or not patient then john is not old or not tall. Everyone who is not brave or funny is not tall and vice versa. Everyone who is both curious and not funny is not funny or rich and vice versa. Everyone who is either tall or happy is not strong and vice versa. Lucy is not creative. Susan is not tall or not calm. Someone is not quiet or not calm. Someone is either not calm or happy. Someone is strong or patient. Paul is either funny or not creative. Someone is not old or not creative. | Susan is not calm. | neutral | (![X]:((curious(X)<~>old(X))=>~kind(X)))&
(((~old(fred)&wise(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((patient(X)|~quiet(X))<=>(~generous(X)&~rich(X))))&
(![X]:(~strong(X)<=>(~happy(X)&happy(X))))&
(![X]:((tall(X)|wise(X))=>(~quiet(X)|quiet(X))))&
(![X]:((~strong(X)|rich(X))<=>(happy(X)&funny(X))))&
(![X]:(patient(X)<=>(rich(X)|~kind(X))))&
(((strong(lucy)<~>~wise(lucy)))<=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((patient(X)&~kind(X))))<=>((wise(fred)|~funny(fred))))&
(![X]:((~brave(X)&~kind(X))<=>~wise(X)))&
(![X]:((generous(X)<~>quiet(X))<=>(old(X)|~strong(X))))&
(((patient(alice)<~>~old(alice)))<=>((~patient(john)<~>happy(john))))&
((?[X]:((creative(X)<~>~patient(X))))=>((~old(john)|~tall(john))))&
(![X]:((~brave(X)|funny(X))<=>~tall(X)))&
(![X]:((curious(X)&~funny(X))<=>(~funny(X)|rich(X))))&
(![X]:((tall(X)<~>happy(X))<=>~strong(X)))&
(~creative(lucy))&
((~tall(susan)|~calm(susan)))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:((strong(X)|patient(X))))&
((funny(paul)<~>~creative(paul)))&
(?[X]:((~old(X)|~creative(X)))) | ~calm(susan) | []
| null | 0 |
Everyone who is not brave or not creative is both generous and not wise and vice versa. If mary is both calm and not funny then someone is not tall. If paul is not rich then someone is not old or funny. If mary is rich then someone is not wise. If someone is not calm or curious then someone is tall. If lucy is both kind and not patient then paul is either old or not quiet and vice versa. If someone is kind or calm then lucy is not old. If someone is either happy or funny then someone is not strong or not quiet. If someone is both not calm and rich then someone is not funny or patient. If someone is not calm then paul is either calm or not wise and vice versa. If alice is both generous and old then someone is patient or curious. Everyone who is both happy and not tall is calm. If paul is calm or not kind then mary is patient. Everyone who is humble is not kind or not tall and vice versa. Everyone who is tall is either not humble or not old and vice versa. If someone is either not old or not calm then someone is generous and vice versa. Lucy is not wise. Mary is either not wise or happy. Someone is patient or not strong. Paul is both creative and not old. Someone is both old and kind. Paul is not rich or kind. Someone is both not quiet and not rich. Someone is not humble. | Lucy is kind. | contradiction | (![X]:((~brave(X)|~creative(X))<=>(generous(X)&~wise(X))))&
(((calm(mary)&~funny(mary)))=>(?[X]:(~tall(X))))&
((~rich(paul))=>(?[X]:((~old(X)|funny(X)))))&
((rich(mary))=>(?[X]:(~wise(X))))&
((?[X]:((~calm(X)|curious(X))))=>(?[X]:(tall(X))))&
(((kind(lucy)&~patient(lucy)))<=>((old(paul)<~>~quiet(paul))))&
((?[X]:((kind(X)|calm(X))))=>(~old(lucy)))&
((?[X]:((happy(X)<~>funny(X))))=>(?[X]:((~strong(X)|~quiet(X)))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:(~calm(X)))<=>((calm(paul)<~>~wise(paul))))&
(((generous(alice)&old(alice)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((happy(X)&~tall(X))=>calm(X)))&
(((calm(paul)|~kind(paul)))=>(patient(mary)))&
(![X]:(humble(X)<=>(~kind(X)|~tall(X))))&
(![X]:(tall(X)<=>(~humble(X)<~>~old(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(generous(X))))&
(~wise(lucy))&
((~wise(mary)<~>happy(mary)))&
(?[X]:((patient(X)|~strong(X))))&
((creative(paul)&~old(paul)))&
(?[X]:((old(X)&kind(X))))&
((~rich(paul)|kind(paul)))&
(?[X]:((~quiet(X)&~rich(X))))&
(?[X]:(~humble(X))) | kind(lucy) | [
"p6",
"p13",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1921537229336553857698594
% SZS output start Proof for 1921537229336553857698594
7. ? [X0] : (calm(X0) | kind(X0)) => ~old(lucy) [input p6]
14. ! [X0] : (humble(X0) <=> (~tall(X0) | ~kind(X0))) [input p13]
15. ! [X0] : (tall(X0) <=> (~humble(X0) <~> ~old(X0))) [input p14]
21. ? [X0] : (kind(X0) & old(X0)) [input p20]
25. kind(lucy) [input hypothesis]
37. ~old(lucy) | ! [X0] : (~calm(X0) & ~kind(X0)) [ennf transformation 7]
66. ! [X0] : ((humble(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | ~humble(X0))) [nnf transformation 14]
67. ! [X0] : ((humble(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | ~humble(X0))) [flattening 66]
68. ! [X0] : ((tall(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~tall(X0))) [nnf transformation 15]
75. ? [X0] : (kind(X0) & old(X0)) => (kind(sK9) & old(sK9)) [choice axiom]
76. kind(sK9) & old(sK9) [skolemisation 21,75]
97. ~old(lucy) | ~kind(X0) [cnf transformation 37]
108. ~humble(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 67]
110. humble(X0) | tall(X0) [cnf transformation 67]
112. old(X0) | humble(X0) | ~tall(X0) [cnf transformation 68]
114. tall(X0) | ~humble(X0) | old(X0) [cnf transformation 68]
125. kind(sK9) [cnf transformation 76]
130. kind(lucy) [cnf transformation 25]
193. 15 <=> kind(lucy) [avatar definition]
195. kind(lucy) <- (15) [avatar component clause 193]
204. 17 <=> old(lucy) [avatar definition]
209. 18 <=> ! [X0] : ~kind(X0) [avatar definition]
210. ~kind(X0) <- (18) [avatar component clause 209]
211. 18 | ~17 [avatar split clause 97,204,209]
267. old(X0) | tall(X0) [subsumption resolution 114,110]
268. humble(X0) | old(X0) [subsumption resolution 112,110]
306. 15 [avatar split clause 130,193]
317. ~kind(X0) | ~tall(X0) | old(X0) [resolution 108,268]
320. ~kind(X0) | old(X0) [subsumption resolution 317,267]
341. old(lucy) <- (15) [resolution 320,195]
348. 17 | ~15 [avatar split clause 341,193,204]
350. $false <- (18) [resolution 210,125]
353. ~18 [avatar contradiction clause 350]
355. $false [avatar sat refutation 211,306,348,353]
% SZS output end Proof for 1921537229336553857698594
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not kind or funny then mary is either patient or not old. Everyone who is not kind or creative is either wise or not strong and vice versa. Everyone who is both happy and tall is both not patient and brave and vice versa. If susan is happy or generous then paul is both brave and not wise. Everyone who is brave or kind is tall or not tall. Everyone who is both tall and not tall is generous or curious and vice versa. If lucy is patient or not strong then someone is wise. If someone is not tall then paul is either not calm or curious and vice versa. If someone is both kind and not quiet then someone is both not tall and not rich and vice versa. If someone is either funny or creative then someone is both patient and not quiet and vice versa. If someone is both not old and not wise then someone is either not rich or not calm and vice versa. If paul is either funny or curious then someone is not curious and vice versa. Everyone who is either generous or funny is not brave or curious. If susan is both not patient and not brave then john is either happy or not patient. If someone is either calm or not patient then paul is not happy or not curious and vice versa. If mary is both brave and not quiet then john is either wise or not kind and vice versa. Someone is not old. Paul is both tall and not quiet. Someone is brave. Lucy is not curious. Someone is not tall. Someone is not wise. Fred is both funny and calm. Lucy is not creative. | Paul is brave. | contradiction | (((~kind(susan)|funny(susan)))=>((patient(mary)<~>~old(mary))))&
(![X]:((~kind(X)|creative(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((happy(X)&tall(X))<=>(~patient(X)&brave(X))))&
(((happy(susan)|generous(susan)))=>((brave(paul)&~wise(paul))))&
(![X]:((brave(X)|kind(X))=>(tall(X)|~tall(X))))&
(![X]:((tall(X)&~tall(X))<=>(generous(X)|curious(X))))&
(((patient(lucy)|~strong(lucy)))=>(?[X]:(wise(X))))&
((?[X]:(~tall(X)))<=>((~calm(paul)<~>curious(paul))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((~tall(X)&~rich(X)))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((patient(X)&~quiet(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:((~rich(X)<~>~calm(X)))))&
(((funny(paul)<~>curious(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>funny(X))=>(~brave(X)|curious(X))))&
(((~patient(susan)&~brave(susan)))=>((happy(john)<~>~patient(john))))&
((?[X]:((calm(X)<~>~patient(X))))<=>((~happy(paul)|~curious(paul))))&
(((brave(mary)&~quiet(mary)))<=>((wise(john)<~>~kind(john))))&
(?[X]:(~old(X)))&
((tall(paul)&~quiet(paul)))&
(?[X]:(brave(X)))&
(~curious(lucy))&
(?[X]:(~tall(X)))&
(?[X]:(~wise(X)))&
((funny(fred)&calm(fred)))&
(~creative(lucy)) | brave(paul) | [
"p5",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 9159028050708211600274515
% SZS output start Proof for 9159028050708211600274515
6. ! [X0] : ((~tall(X0) & tall(X0)) <=> (curious(X0) | generous(X0))) [input p5]
12. (funny(paul) <~> curious(paul)) <=> ? [X0] : ~curious(X0) [input p11]
13. ! [X0] : ((generous(X0) <~> funny(X0)) => (curious(X0) | ~brave(X0))) [input p12]
25. brave(paul) [input hypothesis]
34. ! [X0] : ((curious(X0) | ~brave(X0)) | (generous(X0) <=> funny(X0))) [ennf transformation 13]
35. ! [X0] : (curious(X0) | ~brave(X0) | (generous(X0) <=> funny(X0))) [flattening 34]
43. ! [X0] : (((~tall(X0) & tall(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 6]
44. ! [X0] : (((~tall(X0) & tall(X0)) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | tall(X0) | ~tall(X0))) [flattening 43]
66. (((~curious(paul) | ~funny(paul)) & (curious(paul) | funny(paul))) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ((funny(paul) | ~curious(paul)) & (curious(paul) | ~funny(paul)))) [nnf transformation 12]
67. (((~curious(paul) | ~funny(paul)) & (curious(paul) | funny(paul))) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ((funny(paul) | ~curious(paul)) & (curious(paul) | ~funny(paul)))) [rectify 66]
68. ? [X1] : ~curious(X1) => ~curious(sK8) [choice axiom]
69. (((~curious(paul) | ~funny(paul)) & (curious(paul) | funny(paul))) | ! [X0] : curious(X0)) & (~curious(sK8) | ((funny(paul) | ~curious(paul)) & (curious(paul) | ~funny(paul)))) [skolemisation 67,68]
70. ! [X0] : (curious(X0) | ~brave(X0) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) [nnf transformation 35]
108. tall(X0) | ~generous(X0) [cnf transformation 44]
109. tall(X0) | ~curious(X0) [cnf transformation 44]
110. ~generous(X0) | ~tall(X0) [cnf transformation 44]
111. ~curious(X0) | ~tall(X0) [cnf transformation 44]
136. curious(paul) | funny(paul) | curious(X0) [cnf transformation 69]
139. curious(X0) | ~brave(X0) | generous(X0) | ~funny(X0) [cnf transformation 70]
164. brave(paul) [cnf transformation 25]
200. 8 <=> brave(paul) [avatar definition]
202. brave(paul) <- (8) [avatar component clause 200]
205. ~curious(X0) [subsumption resolution 109,111]
206. ~generous(X0) [subsumption resolution 108,110]
324. funny(paul) | curious(X0) [subsumption resolution 136,205]
325. funny(paul) [subsumption resolution 324,205]
326. ~brave(X0) | generous(X0) | ~funny(X0) [subsumption resolution 139,205]
327. ~brave(X0) | ~funny(X0) [subsumption resolution 326,206]
386. 8 [avatar split clause 164,200]
402. ~funny(paul) <- (8) [resolution 327,202]
403. $false <- (8) [subsumption resolution 402,325]
404. ~8 [avatar contradiction clause 403]
405. $false [avatar sat refutation 386,404]
% SZS output end Proof for 9159028050708211600274515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not happy is happy.
Everyone who is creative is both strong and not tall.
Everyone who is both not tall and not patient is both kind and strong and vice versa.
If someone is either not strong or not quiet then someone is not calm.
Everyone who is quiet is not wise.
Everyone who is rich or not happy is either not quiet or not creative.
Everyone who is either kind or humble is either tall or not kind and vice versa.
Everyone who is patient is both not curious and happy and vice versa.
Everyone who is not old is kind and vice versa.
If someone is not rich then someone is either tall or not creative.
Everyone who is either calm or not happy is either old or not calm.
Everyone who is either rich or old is either not calm or old.
If lucy is both not curious and not tall then someone is both funny and old and vice versa.
If someone is not quiet then john is both humble and not creative.
If someone is both not humble and patient then someone is not happy and vice versa.
Everyone who is not happy is not rich and vice versa.
Susan is either rich or patient.
John is either not patient or not wise.
John is either curious or not funny.
Someone is not kind.
Lucy is generous.
Someone is either quiet or tall.
Someone is either generous or not curious. | John is not patient. | contradiction | (![X]:((~brave(X)|~happy(X))=>happy(X)))&
(![X]:(creative(X)=>(strong(X)&~tall(X))))&
(![X]:((~tall(X)&~patient(X))<=>(kind(X)&strong(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))=>(?[X]:(~calm(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((kind(X)<~>humble(X))<=>(tall(X)<~>~kind(X))))&
(![X]:(patient(X)<=>(~curious(X)&happy(X))))&
(![X]:(~old(X)<=>kind(X)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~creative(X)))))&
(![X]:((calm(X)<~>~happy(X))=>(old(X)<~>~calm(X))))&
(![X]:((rich(X)<~>old(X))=>(~calm(X)<~>old(X))))&
(((~curious(lucy)&~tall(lucy)))<=>(?[X]:((funny(X)&old(X)))))&
((?[X]:(~quiet(X)))=>((humble(john)&~creative(john))))&
((?[X]:((~humble(X)&patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:(~happy(X)<=>~rich(X)))&
((rich(susan)<~>patient(susan)))&
((~patient(john)<~>~wise(john)))&
((curious(john)<~>~funny(john)))&
(?[X]:(~kind(X)))&
(generous(lucy))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((generous(X)<~>~curious(X)))) | ~patient(john) | [
"p0",
"p4",
"p5",
"p13",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 918440014650143637615709
% SZS output start Proof for 918440014650143637615709
1. ! [X0] : ((~happy(X0) | ~brave(X0)) => happy(X0)) [input p0]
5. ! [X0] : (quiet(X0) => ~wise(X0)) [input p4]
6. ! [X0] : ((~happy(X0) | rich(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p5]
14. ? [X0] : ~quiet(X0) => (~creative(john) & humble(john)) [input p13]
16. ! [X0] : (~happy(X0) <=> ~rich(X0)) [input p15]
18. ~patient(john) <~> ~wise(john) [input p17]
24. ~patient(john) [input hypothesis]
28. ! [X0] : (~happy(X0) => happy(X0)) [pure predicate removal 1]
29. ! [X0] : (happy(X0) | happy(X0)) [ennf transformation 28]
32. ! [X0] : (~wise(X0) | ~quiet(X0)) [ennf transformation 5]
33. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 6]
37. (~creative(john) & humble(john)) | ! [X0] : quiet(X0) [ennf transformation 14]
44. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (happy(X0) & ~rich(X0))) [nnf transformation 33]
65. ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))) [nnf transformation 16]
67. (wise(john) | patient(john)) & (~wise(john) | ~patient(john)) [nnf transformation 18]
77. happy(X0) | happy(X0) [cnf transformation 29]
86. ~wise(X0) | ~quiet(X0) [cnf transformation 32]
89. ~rich(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
119. ~creative(john) | quiet(X0) [cnf transformation 37]
124. ~happy(X0) | rich(X0) [cnf transformation 65]
128. wise(john) | patient(john) [cnf transformation 67]
137. ~patient(john) [cnf transformation 24]
146. happy(X0) [duplicate literal removal 77]
164. 4 <=> ! [X1] : rich(X1) [avatar definition]
165. rich(X1) <- (4) [avatar component clause 164]
202. 12 <=> ! [X0] : quiet(X0) [avatar definition]
203. quiet(X0) <- (12) [avatar component clause 202]
205. 13 <=> creative(john) [avatar definition]
207. ~creative(john) <- (~13) [avatar component clause 205]
208. 12 | ~13 [avatar split clause 119,205,202]
215. rich(X0) [subsumption resolution 124,146]
216. 4 [avatar split clause 215,164]
228. 17 <=> patient(john) [avatar definition]
232. 18 <=> wise(john) [avatar definition]
234. wise(john) <- (18) [avatar component clause 232]
235. 17 | 18 [avatar split clause 128,232,228]
267. ~17 [avatar split clause 137,228]
269. ~quiet(john) <- (18) [resolution 86,234]
270. $false <- (12, 18) [subsumption resolution 269,203]
271. ~12 | ~18 [avatar contradiction clause 270]
318. quiet(X0) | creative(X0) <- (4) [resolution 89,165]
326. creative(john) <- (4, 18) [resolution 318,269]
328. $false <- (4, ~13, 18) [subsumption resolution 326,207]
329. ~4 | 13 | ~18 [avatar contradiction clause 328]
330. $false [avatar sat refutation 208,216,235,267,271,329]
% SZS output end Proof for 918440014650143637615709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise then someone is either not rich or not old. If someone is not rich or funny then mary is not brave or old. If someone is either not quiet or not old then someone is not kind. If someone is not creative then paul is either calm or not funny. Everyone who is not generous or rich is both happy and generous and vice versa. If mary is either brave or calm then someone is not quiet or patient and vice versa. Everyone who is curious is either not brave or generous. Everyone who is both not old and not creative is not patient or not humble. Everyone who is both not strong and rich is both tall and not rich. If john is not quiet then someone is both not quiet and not curious. If someone is either not rich or not generous then mary is either not patient or patient and vice versa. If someone is not curious then someone is both not strong and not generous. Everyone who is not curious or not humble is not kind and vice versa. Everyone who is both not curious and generous is either not humble or not kind and vice versa. Everyone who is either not calm or curious is funny. Everyone who is not brave is both not funny and not curious and vice versa. Paul is kind or generous. Someone is generous or not calm. Mary is patient. Someone is either tall or calm. John is either funny or quiet. Lucy is not strong. Alice is not kind. Someone is strong. | John is calm. | contradiction | ((?[X]:((~creative(X)|~wise(X))))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((~rich(X)|funny(X))))=>((~brave(mary)|old(mary))))&
((?[X]:((~quiet(X)<~>~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~creative(X)))=>((calm(paul)<~>~funny(paul))))&
(![X]:((~generous(X)|rich(X))<=>(happy(X)&generous(X))))&
(((brave(mary)<~>calm(mary)))<=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:(curious(X)=>(~brave(X)<~>generous(X))))&
(![X]:((~old(X)&~creative(X))=>(~patient(X)|~humble(X))))&
(![X]:((~strong(X)&rich(X))=>(tall(X)&~rich(X))))&
((~quiet(john))=>(?[X]:((~quiet(X)&~curious(X)))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>((~patient(mary)<~>patient(mary))))&
((?[X]:(~curious(X)))=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~curious(X)|~humble(X))<=>~kind(X)))&
(![X]:((~curious(X)&generous(X))<=>(~humble(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>curious(X))=>funny(X)))&
(![X]:(~brave(X)<=>(~funny(X)&~curious(X))))&
((kind(paul)|generous(paul)))&
(?[X]:((generous(X)|~calm(X))))&
(patient(mary))&
(?[X]:((tall(X)<~>calm(X))))&
((funny(john)<~>quiet(john)))&
(~strong(lucy))&
(~kind(alice))&
(?[X]:(strong(X))) | calm(john) | [
"p4",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 360548905071880754341553
% SZS output start Proof for 360548905071880754341553
5. ! [X0] : ((rich(X0) | ~generous(X0)) <=> (generous(X0) & happy(X0))) [input p4]
10. ~quiet(john) => ? [X0] : (~curious(X0) & ~quiet(X0)) [input p9]
12. ? [X0] : ~curious(X0) => ? [X0] : (~generous(X0) & ~strong(X0)) [input p11]
15. ! [X0] : ((~calm(X0) <~> curious(X0)) => funny(X0)) [input p14]
21. funny(john) <~> quiet(john) [input p20]
25. calm(john) [input hypothesis]
28. ? [X0] : ~curious(X0) => ? [X1] : (~generous(X1) & ~strong(X1)) [rectify 12]
39. ? [X0] : (~curious(X0) & ~quiet(X0)) | quiet(john) [ennf transformation 10]
40. ? [X1] : (~generous(X1) & ~strong(X1)) | ! [X0] : curious(X0) [ennf transformation 28]
41. ! [X0] : (funny(X0) | (~calm(X0) <=> curious(X0))) [ennf transformation 15]
46. ! [X0] : (((rich(X0) | ~generous(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~rich(X0) & generous(X0)))) [nnf transformation 5]
47. ! [X0] : ((rich(X0) | ~generous(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (~rich(X0) & generous(X0)))) [flattening 46]
53. ? [X0] : (~curious(X0) & ~quiet(X0)) => (~curious(sK2) & ~quiet(sK2)) [choice axiom]
54. (~curious(sK2) & ~quiet(sK2)) | quiet(john) [skolemisation 39,53]
59. ? [X0] : (~generous(X0) & ~strong(X0)) | ! [X1] : curious(X1) [rectify 40]
60. ? [X0] : (~generous(X0) & ~strong(X0)) => (~generous(sK4) & ~strong(sK4)) [choice axiom]
61. (~generous(sK4) & ~strong(sK4)) | ! [X1] : curious(X1) [skolemisation 59,60]
66. ! [X0] : (funny(X0) | ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0)))) [nnf transformation 41]
74. (~quiet(john) | ~funny(john)) & (quiet(john) | funny(john)) [nnf transformation 21]
83. generous(X0) | generous(X0) [cnf transformation 47]
97. ~curious(sK2) | quiet(john) [cnf transformation 54]
107. ~generous(sK4) | curious(X1) [cnf transformation 61]
118. funny(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 66]
128. ~quiet(john) | ~funny(john) [cnf transformation 74]
132. calm(john) [cnf transformation 25]
138. generous(X0) [duplicate literal removal 83]
194. 13 <=> quiet(john) [avatar definition]
198. 14 <=> curious(sK2) [avatar definition]
200. ~curious(sK2) <- (~14) [avatar component clause 198]
201. 13 | ~14 [avatar split clause 97,198,194]
219. curious(X1) [subsumption resolution 107,138]
221. ~calm(X0) | funny(X0) [subsumption resolution 118,219]
234. 20 <=> funny(john) [avatar definition]
237. ~20 | ~13 [avatar split clause 128,194,234]
240. funny(john) [resolution 221,132]
243. 20 [avatar split clause 240,234]
244. $false <- (~14) [subsumption resolution 200,219]
245. 14 [avatar contradiction clause 244]
246. $false [avatar sat refutation 201,237,243,245]
% SZS output end Proof for 360548905071880754341553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and humble then john is both not tall and funny. If someone is both curious and strong then fred is both not creative and funny. Everyone who is not patient or strong is both not curious and not humble and vice versa. Everyone who is old is not happy. Everyone who is not wise is either not brave or not happy and vice versa. If john is not creative then someone is either not brave or not creative and vice versa. Everyone who is either strong or not calm is either curious or not brave and vice versa. Everyone who is both not kind and not patient is both not tall and not humble and vice versa. Everyone who is either not humble or patient is both calm and creative. Everyone who is either curious or brave is either old or not wise and vice versa. If someone is not happy or not patient then someone is either not calm or not kind and vice versa. Everyone who is not strong is both happy and brave. Everyone who is not humble is curious. Everyone who is both tall and not funny is not strong and vice versa. If someone is kind or funny then someone is both generous and not quiet and vice versa. If someone is funny or not calm then someone is either not creative or not kind. Someone is either kind or not creative. Someone is either humble or brave. | Fred is not humble. | entailment | ((?[X]:((~tall(X)&humble(X))))=>((~tall(john)&funny(john))))&
((?[X]:((curious(X)&strong(X))))=>((~creative(fred)&funny(fred))))&
(![X]:((~patient(X)|strong(X))<=>(~curious(X)&~humble(X))))&
(![X]:(old(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(~brave(X)<~>~happy(X))))&
((~creative(john))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>~calm(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((~kind(X)&~patient(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~humble(X)<~>patient(X))=>(calm(X)&creative(X))))&
(![X]:((curious(X)<~>brave(X))<=>(old(X)<~>~wise(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:(~strong(X)=>(happy(X)&brave(X))))&
(![X]:(~humble(X)=>curious(X)))&
(![X]:((tall(X)&~funny(X))<=>~strong(X)))&
((?[X]:((kind(X)|funny(X))))<=>(?[X]:((generous(X)&~quiet(X)))))&
((?[X]:((funny(X)|~calm(X))))=>(?[X]:((~creative(X)<~>~kind(X)))))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:((humble(X)<~>brave(X)))) | ~humble(fred) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3106644072074603950183507
% SZS output start Proof for 3106644072074603950183507
3. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~humble(X0) & ~curious(X0))) [input p2]
4. ! [X0] : (old(X0) => ~happy(X0)) [input p3]
5. ! [X0] : (~wise(X0) <=> (~brave(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p6]
8. ! [X0] : ((~patient(X0) & ~kind(X0)) <=> (~humble(X0) & ~tall(X0))) [input p7]
9. ! [X0] : ((~humble(X0) <~> patient(X0)) => (creative(X0) & calm(X0))) [input p8]
10. ! [X0] : ((curious(X0) <~> brave(X0)) <=> (old(X0) <~> ~wise(X0))) [input p9]
11. ? [X0] : (~patient(X0) | ~happy(X0)) <=> ? [X0] : (~calm(X0) <~> ~kind(X0)) [input p10]
12. ! [X0] : (~strong(X0) => (brave(X0) & happy(X0))) [input p11]
13. ! [X0] : (~humble(X0) => curious(X0)) [input p12]
14. ! [X0] : ((~funny(X0) & tall(X0)) <=> ~strong(X0)) [input p13]
15. ? [X0] : (funny(X0) | kind(X0)) <=> ? [X0] : (~quiet(X0) & generous(X0)) [input p14]
19. humble(fred) [input hypothesis]
20. ? [X0] : (~patient(X0) | ~happy(X0)) <=> ? [X1] : (~calm(X1) <~> ~kind(X1)) [rectify 11]
21. ? [X0] : (funny(X0) | kind(X0)) <=> ? [X1] : (~quiet(X1) & generous(X1)) [rectify 15]
25. ! [X0] : (~happy(X0) | ~old(X0)) [ennf transformation 4]
26. ! [X0] : ((creative(X0) & calm(X0)) | (~humble(X0) <=> patient(X0))) [ennf transformation 9]
27. ! [X0] : ((brave(X0) & happy(X0)) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (curious(X0) | humble(X0)) [ennf transformation 13]
30. ! [X0] : (((strong(X0) | ~patient(X0)) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 3]
31. ! [X0] : ((strong(X0) | ~patient(X0) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & patient(X0)))) [flattening 30]
32. ! [X0] : ((~wise(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0)))) & (((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | wise(X0))) [nnf transformation 5]
37. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 7]
38. ! [X0] : (((~patient(X0) & ~kind(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (patient(X0) | kind(X0)))) [nnf transformation 8]
39. ! [X0] : (((~patient(X0) & ~kind(X0)) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | patient(X0) | kind(X0))) [flattening 38]
40. ! [X0] : ((creative(X0) & calm(X0)) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 26]
41. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 10]
42. (? [X0] : (~patient(X0) | ~happy(X0)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (? [X1] : ((kind(X1) | calm(X1)) & (~kind(X1) | ~calm(X1))) | ! [X0] : (patient(X0) & happy(X0))) [nnf transformation 20]
43. (? [X0] : (~patient(X0) | ~happy(X0)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (? [X2] : ((kind(X2) | calm(X2)) & (~kind(X2) | ~calm(X2))) | ! [X3] : (patient(X3) & happy(X3))) [rectify 42]
44. ? [X0] : (~patient(X0) | ~happy(X0)) => (~patient(sK1) | ~happy(sK1)) [choice axiom]
45. ? [X2] : ((kind(X2) | calm(X2)) & (~kind(X2) | ~calm(X2))) => ((kind(sK2) | calm(sK2)) & (~kind(sK2) | ~calm(sK2))) [choice axiom]
46. ((~patient(sK1) | ~happy(sK1)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (((kind(sK2) | calm(sK2)) & (~kind(sK2) | ~calm(sK2))) | ! [X3] : (patient(X3) & happy(X3))) [skolemisation 43,45,44]
47. ! [X0] : (((~funny(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | (funny(X0) | ~tall(X0)))) [nnf transformation 14]
48. ! [X0] : (((~funny(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | funny(X0) | ~tall(X0))) [flattening 47]
49. (? [X0] : (funny(X0) | kind(X0)) | ! [X1] : (quiet(X1) | ~generous(X1))) & (? [X1] : (~quiet(X1) & generous(X1)) | ! [X0] : (~funny(X0) & ~kind(X0))) [nnf transformation 21]
50. (? [X0] : (funny(X0) | kind(X0)) | ! [X1] : (quiet(X1) | ~generous(X1))) & (? [X2] : (~quiet(X2) & generous(X2)) | ! [X3] : (~funny(X3) & ~kind(X3))) [rectify 49]
51. ? [X0] : (funny(X0) | kind(X0)) => (funny(sK3) | kind(sK3)) [choice axiom]
52. ? [X2] : (~quiet(X2) & generous(X2)) => (~quiet(sK4) & generous(sK4)) [choice axiom]
53. ((funny(sK3) | kind(sK3)) | ! [X1] : (quiet(X1) | ~generous(X1))) & ((~quiet(sK4) & generous(sK4)) | ! [X3] : (~funny(X3) & ~kind(X3))) [skolemisation 50,52,51]
68. ~curious(X0) | patient(X0) [cnf transformation 31]
69. ~curious(X0) | ~strong(X0) [cnf transformation 31]
70. ~humble(X0) | patient(X0) [cnf transformation 31]
71. ~strong(X0) | ~humble(X0) [cnf transformation 31]
73. ~happy(X0) | ~old(X0) [cnf transformation 25]
74. ~brave(X0) | ~happy(X0) | wise(X0) [cnf transformation 32]
86. ~calm(X0) | strong(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 37]
93. ~patient(X0) | humble(X0) | tall(X0) [cnf transformation 39]
95. calm(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 40]
99. ~brave(X0) | old(X0) | curious(X0) | ~wise(X0) [cnf transformation 41]
106. ~kind(sK2) | ~calm(sK2) | happy(X3) [cnf transformation 46]
108. kind(sK2) | calm(sK2) | happy(X3) [cnf transformation 46]
110. ~patient(sK1) | ~happy(sK1) | ~kind(X1) | calm(X1) [cnf transformation 46]
111. ~patient(sK1) | ~happy(sK1) | ~calm(X1) | kind(X1) [cnf transformation 46]
112. happy(X0) | strong(X0) [cnf transformation 27]
113. brave(X0) | strong(X0) [cnf transformation 27]
114. curious(X0) | humble(X0) [cnf transformation 28]
115. ~strong(X0) | funny(X0) | ~tall(X0) [cnf transformation 48]
116. strong(X0) | tall(X0) [cnf transformation 48]
117. ~funny(X0) | strong(X0) [cnf transformation 48]
118. generous(sK4) | ~kind(X3) [cnf transformation 53]
120. ~quiet(sK4) | ~kind(X3) [cnf transformation 53]
122. funny(sK3) | kind(sK3) | quiet(X1) | ~generous(X1) [cnf transformation 53]
131. humble(fred) [cnf transformation 19]
133. 1 <=> ! [X0] : (~humble(X0) | tall(X0)) [avatar definition]
134. ~humble(X0) | tall(X0) <- (1) [avatar component clause 133]
146. 4 <=> ! [X0] : (~strong(X0) | ~curious(X0)) [avatar definition]
147. ~strong(X0) | ~curious(X0) <- (4) [avatar component clause 146]
158. 4 [avatar split clause 69,146]
183. ~humble(X0) | calm(X0) [subsumption resolution 95,70]
186. 12 <=> ! [X1] : (~calm(X1) | kind(X1)) [avatar definition]
187. ~calm(X1) | kind(X1) <- (12) [avatar component clause 186]
189. 13 <=> happy(sK1) [avatar definition]
191. ~happy(sK1) <- (~13) [avatar component clause 189]
193. 14 <=> patient(sK1) [avatar definition]
195. ~patient(sK1) <- (~14) [avatar component clause 193]
196. 12 | ~13 | ~14 [avatar split clause 111,193,189,186]
198. 15 <=> ! [X1] : (~kind(X1) | calm(X1)) [avatar definition]
199. ~kind(X1) | calm(X1) <- (15) [avatar component clause 198]
200. 15 | ~13 | ~14 [avatar split clause 110,193,189,198]
202. 16 <=> ! [X3] : patient(X3) [avatar definition]
203. patient(X3) <- (16) [avatar component clause 202]
205. 17 <=> calm(sK2) [avatar definition]
206. ~calm(sK2) <- (~17) [avatar component clause 205]
207. calm(sK2) <- (17) [avatar component clause 205]
209. 18 <=> kind(sK2) [avatar definition]
210. ~kind(sK2) <- (~18) [avatar component clause 209]
211. kind(sK2) <- (18) [avatar component clause 209]
214. 19 <=> ! [X3] : happy(X3) [avatar definition]
215. happy(X3) <- (19) [avatar component clause 214]
216. 19 | 17 | 18 [avatar split clause 108,209,205,214]
218. 19 | ~17 | ~18 [avatar split clause 106,209,205,214]
220. 20 <=> ! [X1] : (quiet(X1) | ~generous(X1)) [avatar definition]
221. ~generous(X1) | quiet(X1) <- (20) [avatar component clause 220]
223. 21 <=> kind(sK3) [avatar definition]
225. kind(sK3) <- (21) [avatar component clause 223]
227. 22 <=> funny(sK3) [avatar definition]
228. ~funny(sK3) <- (~22) [avatar component clause 227]
229. funny(sK3) <- (22) [avatar component clause 227]
230. 20 | 21 | 22 [avatar split clause 122,227,223,220]
235. 24 <=> quiet(sK4) [avatar definition]
237. ~quiet(sK4) <- (~24) [avatar component clause 235]
240. 25 <=> ! [X3] : ~kind(X3) [avatar definition]
241. ~kind(X3) <- (25) [avatar component clause 240]
242. 25 | ~24 [avatar split clause 120,235,240]
244. 26 <=> generous(sK4) [avatar definition]
246. generous(sK4) <- (26) [avatar component clause 244]
248. 25 | 26 [avatar split clause 118,244,240]
288. strong(sK1) <- (~13) [resolution 112,191]
291. ~humble(sK1) <- (~13) [resolution 288,71]
292. humble(X0) | patient(X0) [resolution 114,68]
293. patient(X0) [subsumption resolution 292,70]
294. 16 [avatar split clause 293,202]
295. tall(X0) | ~humble(X0) [resolution 116,71]
296. 1 [avatar split clause 295,133]
303. ~curious(sK1) <- (4, ~13) [resolution 147,288]
316. calm(fred) [resolution 183,131]
318. quiet(sK4) <- (20, 26) [resolution 221,246]
319. $false <- (20, ~24, 26) [subsumption resolution 318,237]
320. ~20 | 24 | ~26 [avatar contradiction clause 319]
323. strong(sK3) <- (22) [resolution 229,117]
366. ~curious(sK3) <- (4, 22) [resolution 323,147]
367. ~humble(sK3) <- (22) [resolution 323,71]
372. humble(sK1) <- (4, ~13) [resolution 303,114]
373. $false <- (4, ~13) [subsumption resolution 372,291]
374. ~4 | 13 [avatar contradiction clause 373]
375. $false <- (~14, 16) [subsumption resolution 195,203]
376. 14 | ~16 [avatar contradiction clause 375]
388. kind(sK2) <- (12, 17) [resolution 187,207]
389. kind(fred) <- (12) [resolution 187,316]
390. $false <- (12, 17, ~18) [subsumption resolution 388,210]
391. ~12 | ~17 | 18 [avatar contradiction clause 390]
393. calm(sK2) <- (15, 18) [resolution 199,211]
394. $false <- (15, ~17, 18) [subsumption resolution 393,206]
395. ~15 | 17 | ~18 [avatar contradiction clause 394]
397. ~old(X0) <- (19) [resolution 215,73]
426. humble(X1) | tall(X1) <- (16) [resolution 93,203]
428. tall(X1) <- (1, 16) [subsumption resolution 426,134]
453. humble(sK3) <- (4, 22) [resolution 366,114]
454. $false <- (4, 22) [subsumption resolution 453,367]
455. ~4 | ~22 [avatar contradiction clause 454]
457. calm(sK3) <- (15, 21) [resolution 225,199]
465. 42 <=> strong(sK3) [avatar definition]
466. strong(sK3) <- (42) [avatar component clause 465]
467. ~strong(sK3) <- (~42) [avatar component clause 465]
469. 43 <=> brave(sK3) [avatar definition]
470. brave(sK3) <- (43) [avatar component clause 469]
471. ~brave(sK3) <- (~43) [avatar component clause 469]
478. strong(sK3) | ~brave(sK3) | ~curious(sK3) <- (15, 21) [resolution 86,457]
481. ~brave(sK3) | ~curious(sK3) <- (15, 21, ~42) [subsumption resolution 478,467]
483. 44 <=> curious(sK3) [avatar definition]
486. ~44 | ~43 | ~15 | ~21 | 42 [avatar split clause 481,465,223,198,469,483]
499. strong(sK3) <- (~43) [resolution 471,113]
502. 42 | 43 [avatar split clause 499,469,465]
505. funny(sK3) | ~tall(sK3) <- (42) [resolution 466,115]
508. ~tall(sK3) <- (~22, 42) [subsumption resolution 505,228]
509. $false <- (1, 16, ~22, 42) [subsumption resolution 508,428]
510. ~1 | ~16 | 22 | ~42 [avatar contradiction clause 509]
577. old(sK3) | curious(sK3) | ~wise(sK3) <- (43) [resolution 470,99]
581. ~happy(sK3) | wise(sK3) <- (43) [resolution 470,74]
582. curious(sK3) | ~wise(sK3) <- (19, 43) [subsumption resolution 577,397]
584. wise(sK3) <- (19, 43) [subsumption resolution 581,215]
587. curious(sK3) <- (19, 43) [subsumption resolution 582,584]
588. 44 | ~19 | ~43 [avatar split clause 587,469,214,483]
589. $false <- (12, 25) [resolution 241,389]
590. ~12 | ~25 [avatar contradiction clause 589]
591. $false [avatar sat refutation 158,196,200,216,218,230,242,248,294,296,320,374,376,391,395,455,486,502,510,588,590]
% SZS output end Proof for 3106644072074603950183507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is rich or not curious and vice versa. If alice is either kind or not brave then someone is not calm. If someone is both not humble and kind then someone is both not happy and wise and vice versa. If lucy is either strong or brave then someone is funny and vice versa. If someone is both calm and not patient then mary is either not strong or strong. Everyone who is either rich or brave is both not curious and kind. If paul is not patient then someone is old or humble. If alice is either not calm or not brave then fred is either happy or not brave. Everyone who is either not creative or patient is not creative. If fred is not wise or curious then someone is both not wise and not humble. Everyone who is both kind and wise is either not patient or humble and vice versa. Everyone who is brave is not creative or rich. Everyone who is both rich and not brave is brave. If fred is either humble or not funny then someone is not wise and vice versa. Everyone who is tall or brave is either patient or happy and vice versa. If someone is generous or not wise then someone is either quiet or not strong and vice versa. Lucy is both happy and tall. Someone is not old or not rich. Someone is humble or quiet. Someone is not generous. Someone is both not humble and not tall. Someone is both not happy and wise. Lucy is both kind and tall. Someone is both not wise and quiet. | Mary is strong. | neutral | ((?[X]:(~generous(X)))<=>(?[X]:((rich(X)|~curious(X)))))&
(((kind(alice)<~>~brave(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((~humble(X)&kind(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(((strong(lucy)<~>brave(lucy)))<=>(?[X]:(funny(X))))&
((?[X]:((calm(X)&~patient(X))))=>((~strong(mary)<~>strong(mary))))&
(![X]:((rich(X)<~>brave(X))=>(~curious(X)&kind(X))))&
((~patient(paul))=>(?[X]:((old(X)|humble(X)))))&
(((~calm(alice)<~>~brave(alice)))=>((happy(fred)<~>~brave(fred))))&
(![X]:((~creative(X)<~>patient(X))=>~creative(X)))&
(((~wise(fred)|curious(fred)))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((kind(X)&wise(X))<=>(~patient(X)<~>humble(X))))&
(![X]:(brave(X)=>(~creative(X)|rich(X))))&
(![X]:((rich(X)&~brave(X))=>brave(X)))&
(((humble(fred)<~>~funny(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((tall(X)|brave(X))<=>(patient(X)<~>happy(X))))&
((?[X]:((generous(X)|~wise(X))))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
((happy(lucy)&tall(lucy)))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~humble(X)&~tall(X))))&
(?[X]:((~happy(X)&wise(X))))&
((kind(lucy)&tall(lucy)))&
(?[X]:((~wise(X)&quiet(X)))) | strong(mary) | []
| null | 0 |
Everyone who is both not brave and humble is either kind or not rich. Everyone who is quiet is either not generous or not funny and vice versa. If alice is not generous or not funny then lucy is both not humble and patient. If someone is patient or calm then mary is not strong or tall. Everyone who is both curious and not generous is both not creative and kind. Everyone who is either not humble or quiet is not humble or not brave and vice versa. If fred is both not funny and not generous then lucy is rich and vice versa. If someone is not curious then someone is both not strong and kind and vice versa. Everyone who is not old or not generous is not wise and vice versa. Everyone who is both not tall and curious is not old or not quiet. If john is both not strong and curious then fred is not generous. If paul is either humble or kind then someone is both happy and old. Everyone who is tall or not wise is creative or tall. If mary is not quiet or not calm then alice is either not quiet or patient. If someone is not humble then someone is not humble or not calm. Everyone who is not old is either humble or calm and vice versa. John is either not quiet or not wise. Someone is not kind. Someone is both curious and not quiet. Lucy is funny. Someone is funny. Paul is either calm or kind. Mary is either old or kind. Someone is funny or brave. | Lucy is patient. | neutral | (![X]:((~brave(X)&humble(X))=>(kind(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>(~generous(X)<~>~funny(X))))&
(((~generous(alice)|~funny(alice)))=>((~humble(lucy)&patient(lucy))))&
((?[X]:((patient(X)|calm(X))))=>((~strong(mary)|tall(mary))))&
(![X]:((curious(X)&~generous(X))=>(~creative(X)&kind(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~humble(X)|~brave(X))))&
(((~funny(fred)&~generous(fred)))<=>(rich(lucy)))&
((?[X]:(~curious(X)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~old(X)|~generous(X))<=>~wise(X)))&
(![X]:((~tall(X)&curious(X))=>(~old(X)|~quiet(X))))&
(((~strong(john)&curious(john)))=>(~generous(fred)))&
(((humble(paul)<~>kind(paul)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((tall(X)|~wise(X))=>(creative(X)|tall(X))))&
(((~quiet(mary)|~calm(mary)))=>((~quiet(alice)<~>patient(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:(~old(X)<=>(humble(X)<~>calm(X))))&
((~quiet(john)<~>~wise(john)))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)&~quiet(X))))&
(funny(lucy))&
(?[X]:(funny(X)))&
((calm(paul)<~>kind(paul)))&
((old(mary)<~>kind(mary)))&
(?[X]:((funny(X)|brave(X)))) | patient(lucy) | []
| null | 0 |
Everyone who is not humble or strong is old and vice versa.
Everyone who is calm or rich is quiet or happy and vice versa.
Everyone who is either patient or not humble is either patient or not tall.
Everyone who is funny is both not funny and wise.
Everyone who is quiet or old is not patient.
Everyone who is both not curious and creative is happy or not wise and vice versa.
Everyone who is both not quiet and not old is not generous or happy.
Everyone who is not calm is both brave and calm.
Everyone who is both happy and kind is both old and not brave and vice versa.
Everyone who is not generous or tall is not old.
Everyone who is either not old or wise is not kind.
Everyone who is generous or curious is quiet.
Everyone who is humble or brave is either not generous or humble and vice versa.
Everyone who is both not strong and creative is either not patient or not old and vice versa.
If mary is both funny and not wise then someone is both rich and not funny and vice versa.
Everyone who is both not humble and not generous is either generous or happy and vice versa.
John is not brave.
Someone is not humble.
John is calm or not tall. | Mary is not brave. | entailment | (![X]:((~humble(X)|strong(X))<=>old(X)))&
(![X]:((calm(X)|rich(X))<=>(quiet(X)|happy(X))))&
(![X]:((patient(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
(![X]:(funny(X)=>(~funny(X)&wise(X))))&
(![X]:((quiet(X)|old(X))=>~patient(X)))&
(![X]:((~curious(X)&creative(X))<=>(happy(X)|~wise(X))))&
(![X]:((~quiet(X)&~old(X))=>(~generous(X)|happy(X))))&
(![X]:(~calm(X)=>(brave(X)&calm(X))))&
(![X]:((happy(X)&kind(X))<=>(old(X)&~brave(X))))&
(![X]:((~generous(X)|tall(X))=>~old(X)))&
(![X]:((~old(X)<~>wise(X))=>~kind(X)))&
(![X]:((generous(X)|curious(X))=>quiet(X)))&
(![X]:((humble(X)|brave(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((~strong(X)&creative(X))<=>(~patient(X)<~>~old(X))))&
(((funny(mary)&~wise(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((~humble(X)&~generous(X))<=>(generous(X)<~>happy(X))))&
(~brave(john))&
(?[X]:(~humble(X)))&
((calm(john)|~tall(john))) | ~brave(mary) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8165549683410191431137442
% SZS output start Proof for 8165549683410191431137442
1. ! [X0] : ((strong(X0) | ~humble(X0)) <=> old(X0)) [input p0]
5. ! [X0] : ((old(X0) | quiet(X0)) => ~patient(X0)) [input p4]
6. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (~wise(X0) | happy(X0))) [input p5]
10. ! [X0] : ((tall(X0) | ~generous(X0)) => ~old(X0)) [input p9]
12. ! [X0] : ((curious(X0) | generous(X0)) => quiet(X0)) [input p11]
13. ! [X0] : ((brave(X0) | humble(X0)) <=> (~generous(X0) <~> humble(X0))) [input p12]
14. ! [X0] : ((creative(X0) & ~strong(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (generous(X0) <~> happy(X0))) [input p15]
20. brave(mary) [input hypothesis]
23. ! [X0] : (~patient(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 5]
27. ! [X0] : (~old(X0) | (~tall(X0) & generous(X0))) [ennf transformation 10]
29. ! [X0] : (quiet(X0) | (~curious(X0) & ~generous(X0))) [ennf transformation 12]
30. ! [X0] : (((strong(X0) | ~humble(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [nnf transformation 1]
31. ! [X0] : ((strong(X0) | ~humble(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [flattening 30]
35. ! [X0] : (((creative(X0) & ~curious(X0)) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | (~creative(X0) | curious(X0)))) [nnf transformation 6]
36. ! [X0] : (((creative(X0) & ~curious(X0)) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ~creative(X0) | curious(X0))) [flattening 35]
40. ! [X0] : (((brave(X0) | humble(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [nnf transformation 13]
41. ! [X0] : ((brave(X0) | humble(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [flattening 40]
42. ! [X0] : (((creative(X0) & ~strong(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~creative(X0) | strong(X0)))) [nnf transformation 14]
43. ! [X0] : (((creative(X0) & ~strong(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~creative(X0) | strong(X0))) [flattening 42]
49. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 16]
50. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | generous(X0) | humble(X0))) [flattening 49]
53. old(X0) | humble(X0) [cnf transformation 31]
54. ~strong(X0) | old(X0) [cnf transformation 31]
55. ~old(X0) | ~humble(X0) | strong(X0) [cnf transformation 31]
66. ~patient(X0) | ~quiet(X0) [cnf transformation 23]
67. ~patient(X0) | ~old(X0) [cnf transformation 23]
71. ~happy(X0) | creative(X0) [cnf transformation 36]
80. ~old(X0) | generous(X0) [cnf transformation 27]
84. ~generous(X0) | quiet(X0) [cnf transformation 29]
87. ~brave(X0) | ~generous(X0) | humble(X0) [cnf transformation 41]
88. ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 41]
93. old(X0) | patient(X0) | ~creative(X0) | strong(X0) [cnf transformation 43]
94. ~strong(X0) | ~old(X0) | patient(X0) [cnf transformation 43]
102. happy(X0) | generous(X0) | generous(X0) | humble(X0) [cnf transformation 50]
106. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 50]
111. brave(mary) [cnf transformation 20]
112. happy(X0) | generous(X0) | humble(X0) [duplicate literal removal 102]
113. ~generous(X0) | happy(X0) [duplicate literal removal 106]
114. ~humble(X0) | generous(X0) [duplicate literal removal 88]
122. ~strong(X0) | ~old(X0) [subsumption resolution 94,67]
123. ~strong(X0) [subsumption resolution 122,54]
124. ~creative(X0) | patient(X0) | old(X0) [subsumption resolution 93,123]
137. happy(X0) | generous(X0) [subsumption resolution 112,114]
138. happy(X0) [subsumption resolution 137,113]
139. creative(X0) [resolution 71,138]
140. generous(X0) | humble(X0) [resolution 80,53]
141. generous(X0) [subsumption resolution 140,114]
142. quiet(X0) [resolution 84,141]
151. ~generous(mary) | humble(mary) [resolution 87,111]
152. humble(mary) [subsumption resolution 151,141]
161. patient(X1) | old(X1) [resolution 124,139]
165. old(X3) | ~quiet(X3) [resolution 161,66]
167. old(X3) [subsumption resolution 165,142]
172. ~humble(X2) | strong(X2) [resolution 167,55]
175. ~humble(X2) [subsumption resolution 172,123]
177. $false [resolution 175,152]
% SZS output end Proof for 8165549683410191431137442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and generous then someone is not wise or not funny.
Everyone who is both not funny and not rich is either not curious or curious and vice versa.
Everyone who is not brave or not strong is both wise and strong and vice versa.
If someone is either curious or not tall then someone is not happy and vice versa.
Everyone who is both old and not rich is either funny or calm and vice versa.
If susan is either strong or generous then someone is not curious and vice versa.
Everyone who is either patient or creative is either not rich or not quiet and vice versa.
If someone is both creative and wise then someone is either strong or brave.
If paul is calm then susan is not curious or funny.
If someone is either not strong or not happy then someone is both not wise and patient and vice versa.
If susan is both tall and happy then someone is both creative and not tall and vice versa.
Everyone who is curious is not calm or not humble.
If someone is not funny or happy then susan is both not funny and kind and vice versa.
Everyone who is either not brave or brave is patient and vice versa.
Everyone who is funny or quiet is either not rich or not kind.
If someone is both happy and patient then paul is either curious or not kind and vice versa.
Someone is both wise and not humble.
Susan is either humble or strong.
Alice is quiet or not humble.
Someone is both happy and not quiet.
Lucy is either humble or not curious.
Fred is both not funny and strong.
John is not humble or creative. | Alice is strong. | entailment | ((?[X]:((happy(X)&generous(X))))=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:((~funny(X)&~rich(X))<=>(~curious(X)<~>curious(X))))&
(![X]:((~brave(X)|~strong(X))<=>(wise(X)&strong(X))))&
((?[X]:((curious(X)<~>~tall(X))))<=>(?[X]:(~happy(X))))&
(![X]:((old(X)&~rich(X))<=>(funny(X)<~>calm(X))))&
(((strong(susan)<~>generous(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((patient(X)<~>creative(X))<=>(~rich(X)<~>~quiet(X))))&
((?[X]:((creative(X)&wise(X))))=>(?[X]:((strong(X)<~>brave(X)))))&
((calm(paul))=>((~curious(susan)|funny(susan))))&
((?[X]:((~strong(X)<~>~happy(X))))<=>(?[X]:((~wise(X)&patient(X)))))&
(((tall(susan)&happy(susan)))<=>(?[X]:((creative(X)&~tall(X)))))&
(![X]:(curious(X)=>(~calm(X)|~humble(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~funny(susan)&kind(susan))))&
(![X]:((~brave(X)<~>brave(X))<=>patient(X)))&
(![X]:((funny(X)|quiet(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((happy(X)&patient(X))))<=>((curious(paul)<~>~kind(paul))))&
(?[X]:((wise(X)&~humble(X))))&
((humble(susan)<~>strong(susan)))&
((quiet(alice)|~humble(alice)))&
(?[X]:((happy(X)&~quiet(X))))&
((humble(lucy)<~>~curious(lucy)))&
((~funny(fred)&strong(fred)))&
((~humble(john)|creative(john))) | strong(alice) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 1026863526368711726937953
% SZS output start Proof for 1026863526368711726937953
3. ! [X0] : ((~strong(X0) | ~brave(X0)) <=> (strong(X0) & wise(X0))) [input p2]
24. ~strong(alice) [input hypothesis]
41. ! [X0] : (((~strong(X0) | ~brave(X0)) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | (strong(X0) & brave(X0)))) [nnf transformation 3]
42. ! [X0] : ((~strong(X0) | ~brave(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | (strong(X0) & brave(X0)))) [flattening 41]
96. strong(X0) | strong(X0) [cnf transformation 42]
165. ~strong(alice) [cnf transformation 24]
168. strong(X0) [duplicate literal removal 96]
357. $false [subsumption resolution 165,168]
% SZS output end Proof for 1026863526368711726937953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and kind then someone is either not brave or kind. If someone is not funny then fred is both generous and funny. Everyone who is creative or not calm is not kind or not curious and vice versa. 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 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. | Alice is not creative. | entailment | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
((?[X]:(~funny(X)))=>((generous(fred)&funny(fred))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![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]:(~old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:(wise(X))) | ~creative(alice) | [
"p2",
"p5",
"p6",
"p9",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 356701977859932140708411
% SZS output start Proof for 356701977859932140708411
3. ! [X0] : ((~calm(X0) | creative(X0)) <=> (~curious(X0) | ~kind(X0))) [input p2]
6. ! [X0] : (creative(X0) <=> rich(X0)) [input p5]
7. rich(alice) <=> (~happy(mary) & patient(mary)) [input p6]
10. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (funny(X0) <~> patient(X0))) [input p9]
14. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p13]
19. ~creative(mary) & ~curious(mary) [input p18]
22. creative(alice) [input hypothesis]
37. ! [X0] : (((~calm(X0) | creative(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 3]
38. ! [X0] : ((~calm(X0) | creative(X0) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | (calm(X0) & ~creative(X0)))) [flattening 37]
41. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 6]
42. (rich(alice) | (happy(mary) | ~patient(mary))) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [nnf transformation 7]
43. (rich(alice) | happy(mary) | ~patient(mary)) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [flattening 42]
46. ! [X0] : (((~calm(X0) | ~generous(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [nnf transformation 10]
47. ! [X0] : ((~calm(X0) | ~generous(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [flattening 46]
51. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 14]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 51]
73. ~calm(X0) | creative(X0) | curious(X0) [cnf transformation 38]
82. ~creative(X0) | rich(X0) [cnf transformation 41]
84. patient(mary) | ~rich(alice) [cnf transformation 43]
85. ~happy(mary) | ~rich(alice) [cnf transformation 43]
93. ~patient(X0) | ~funny(X0) | calm(X0) [cnf transformation 47]
104. ~patient(X0) | happy(X0) | funny(X0) | curious(X0) [cnf transformation 52]
120. ~curious(mary) [cnf transformation 19]
121. ~creative(mary) [cnf transformation 19]
125. creative(alice) [cnf transformation 22]
155. 7 <=> patient(mary) [avatar definition]
156. patient(mary) <- (7) [avatar component clause 155]
159. 8 <=> happy(mary) [avatar definition]
160. ~happy(mary) <- (~8) [avatar component clause 159]
163. 9 <=> rich(alice) [avatar definition]
167. ~9 | ~8 [avatar split clause 85,159,163]
168. ~9 | 7 [avatar split clause 84,155,163]
205. rich(alice) [resolution 82,125]
208. 9 [avatar split clause 205,163]
224. 18 <=> funny(mary) [avatar definition]
225. ~funny(mary) <- (~18) [avatar component clause 224]
237. ~funny(mary) | calm(mary) <- (7) [resolution 93,156]
243. 19 <=> calm(mary) [avatar definition]
245. calm(mary) <- (19) [avatar component clause 243]
246. 19 | ~18 | ~7 [avatar split clause 237,155,224,243]
276. creative(mary) | curious(mary) <- (19) [resolution 245,73]
278. curious(mary) <- (19) [subsumption resolution 276,121]
279. $false <- (19) [subsumption resolution 278,120]
280. ~19 [avatar contradiction clause 279]
322. happy(mary) | funny(mary) | curious(mary) <- (7) [resolution 104,156]
326. funny(mary) | curious(mary) <- (7, ~8) [subsumption resolution 322,160]
327. curious(mary) <- (7, ~8, ~18) [subsumption resolution 326,225]
328. $false <- (7, ~8, ~18) [subsumption resolution 327,120]
329. ~7 | 8 | 18 [avatar contradiction clause 328]
330. $false [avatar sat refutation 167,168,208,246,280,329]
% SZS output end Proof for 356701977859932140708411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or happy is not humble.
Everyone who is not calm or not quiet is old or brave and vice versa.
Everyone who is not generous or not tall is not creative.
Everyone who is both creative and not happy is not generous or curious and vice versa.
Everyone who is brave or not generous is not tall or generous and vice versa.
Everyone who is either curious or not curious is both generous and not wise.
Everyone who is not quiet is both not kind and not humble and vice versa.
Everyone who is humble or wise is either tall or not funny and vice versa.
If someone is both not funny and not rich then someone is not brave.
Everyone who is both curious and not generous is quiet and vice versa.
Everyone who is curious or not kind is both brave and not tall.
Everyone who is not humble is either not funny or brave and vice versa.
Everyone who is either not rich or not humble is not calm.
Everyone who is both generous and curious is curious and vice versa.
If someone is funny or not wise then mary is either strong or rich.
If john is not funny then lucy is brave.
Alice is either tall or happy.
Someone is not wise.
John is old.
Paul is generous. | John is not curious. | entailment | (![X]:((~brave(X)|happy(X))=>~humble(X)))&
(![X]:((~calm(X)|~quiet(X))<=>(old(X)|brave(X))))&
(![X]:((~generous(X)|~tall(X))=>~creative(X)))&
(![X]:((creative(X)&~happy(X))<=>(~generous(X)|curious(X))))&
(![X]:((brave(X)|~generous(X))<=>(~tall(X)|generous(X))))&
(![X]:((curious(X)<~>~curious(X))=>(generous(X)&~wise(X))))&
(![X]:(~quiet(X)<=>(~kind(X)&~humble(X))))&
(![X]:((humble(X)|wise(X))<=>(tall(X)<~>~funny(X))))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:(~brave(X))))&
(![X]:((curious(X)&~generous(X))<=>quiet(X)))&
(![X]:((curious(X)|~kind(X))=>(brave(X)&~tall(X))))&
(![X]:(~humble(X)<=>(~funny(X)<~>brave(X))))&
(![X]:((~rich(X)<~>~humble(X))=>~calm(X)))&
(![X]:((generous(X)&curious(X))<=>curious(X)))&
((?[X]:((funny(X)|~wise(X))))=>((strong(mary)<~>rich(mary))))&
((~funny(john))=>(brave(lucy)))&
((tall(alice)<~>happy(alice)))&
(?[X]:(~wise(X)))&
(old(john))&
(generous(paul)) | ~curious(john) | [
"p2",
"p3",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 4512095991532963201878662
% SZS output start Proof for 4512095991532963201878662
3. ! [X0] : ((~tall(X0) | ~generous(X0)) => ~creative(X0)) [input p2]
4. ! [X0] : ((~happy(X0) & creative(X0)) <=> (curious(X0) | ~generous(X0))) [input p3]
11. ! [X0] : ((~kind(X0) | curious(X0)) => (~tall(X0) & brave(X0))) [input p10]
21. curious(john) [input hypothesis]
24. ! [X0] : (~creative(X0) | (tall(X0) & generous(X0))) [ennf transformation 3]
27. ! [X0] : ((~tall(X0) & brave(X0)) | (kind(X0) & ~curious(X0))) [ennf transformation 11]
33. ! [X0] : (((~happy(X0) & creative(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (happy(X0) | ~creative(X0)))) [nnf transformation 4]
34. ! [X0] : (((~happy(X0) & creative(X0)) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | happy(X0) | ~creative(X0))) [flattening 33]
62. ~creative(X0) | tall(X0) [cnf transformation 24]
65. ~curious(X0) | creative(X0) [cnf transformation 34]
91. ~curious(X0) | ~tall(X0) [cnf transformation 27]
112. curious(john) [cnf transformation 21]
156. creative(john) [resolution 65,112]
157. tall(john) [resolution 156,62]
160. ~tall(john) [resolution 91,112]
161. $false [subsumption resolution 160,157]
% SZS output end Proof for 4512095991532963201878662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is not brave or strong.
If someone is not brave then lucy is either not kind or not strong.
Everyone who is not humble is both not curious and not old.
If someone is both tall and not brave then someone is both wise and rich and vice versa.
Everyone who is not quiet or not wise is both curious and not old.
If mary is not generous or not strong then someone is both not old and not funny and vice versa.
If alice is both wise and humble then alice is not strong and vice versa.
Everyone who is humble is either not tall or humble.
Everyone who is not old is tall.
Everyone who is not kind or happy is both creative and not kind.
If someone is either tall or humble then someone is either patient or not wise.
If someone is patient or brave then someone is either not wise or not curious and vice versa.
Everyone who is not curious is not rich.
Everyone who is both rich and not funny is not rich or humble and vice versa.
Everyone who is not curious is either humble or not rich.
Someone is patient or old.
Someone is not strong.
Mary is either not calm or strong.
Someone is wise or not generous.
John is creative.
Someone is either rich or funny.
Someone is happy or creative. | John is not quiet. | neutral | (![X]:(~rich(X)=>(~brave(X)|strong(X))))&
((?[X]:(~brave(X)))=>((~kind(lucy)<~>~strong(lucy))))&
(![X]:(~humble(X)=>(~curious(X)&~old(X))))&
((?[X]:((tall(X)&~brave(X))))<=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((~quiet(X)|~wise(X))=>(curious(X)&~old(X))))&
(((~generous(mary)|~strong(mary)))<=>(?[X]:((~old(X)&~funny(X)))))&
(((wise(alice)&humble(alice)))<=>(~strong(alice)))&
(![X]:(humble(X)=>(~tall(X)<~>humble(X))))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((~kind(X)|happy(X))=>(creative(X)&~kind(X))))&
((?[X]:((tall(X)<~>humble(X))))=>(?[X]:((patient(X)<~>~wise(X)))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:(~curious(X)=>~rich(X)))&
(![X]:((rich(X)&~funny(X))<=>(~rich(X)|humble(X))))&
(![X]:(~curious(X)=>(humble(X)<~>~rich(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(~strong(X)))&
((~calm(mary)<~>strong(mary)))&
(?[X]:((wise(X)|~generous(X))))&
(creative(john))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((happy(X)|creative(X)))) | ~quiet(john) | []
| null | 0 |
If alice is old then lucy is kind and vice versa. If someone is not calm or not happy then someone is either strong or not old and vice versa. If someone is not brave then someone is humble and vice versa. If someone is either wise or not strong then someone is calm or rich. Everyone who is not rich is not rich or happy and vice versa. Everyone who is not generous is either curious or not curious and vice versa. Everyone who is either rich or not calm is not old or happy and vice versa. Everyone who is humble or not happy is not humble. If alice is not curious then someone is both creative and not old. Everyone who is not happy or not tall is not wise or wise and vice versa. Everyone who is either not funny or patient is either not calm or not rich. If susan is either not happy or not brave then fred is either humble or not tall and vice versa. Everyone who is either not rich or tall is both not brave and generous. If someone is both not creative and rich then someone is both happy and rich. Everyone who is strong or kind is not curious. Someone is not strong. Susan is both kind and creative. Mary is not funny or not creative. Paul is not calm. Someone is both not generous and tall. Someone is either generous or not humble. Fred is tall or brave. | Paul is not happy. | entailment | ((old(alice))<=>(kind(lucy)))&
((?[X]:((~calm(X)|~happy(X))))<=>(?[X]:((strong(X)<~>~old(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((strong(X)|kind(X))=>~curious(X)))&
(?[X]:(~strong(X)))&
((kind(susan)&creative(susan)))&
((~funny(mary)|~creative(mary)))&
(~calm(paul))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
((tall(fred)|brave(fred))) | ~happy(paul) | [
"p4",
"p5",
"p9",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3261065195879030434323864
% SZS output start Proof for 3261065195879030434323864
5. ! [X0] : (~rich(X0) <=> (happy(X0) | ~rich(X0))) [input p4]
6. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~curious(X0))) [input p5]
10. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (wise(X0) | ~wise(X0))) [input p9]
13. ! [X0] : ((~rich(X0) <~> tall(X0)) => (generous(X0) & ~brave(X0))) [input p12]
23. happy(paul) [input hypothesis]
32. ! [X0] : ((generous(X0) & ~brave(X0)) | (~rich(X0) <=> tall(X0))) [ennf transformation 13]
50. ! [X0] : ((~rich(X0) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | rich(X0))) [nnf transformation 5]
51. ! [X0] : ((~rich(X0) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | rich(X0))) [flattening 50]
52. ! [X0] : ((~generous(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0))) [nnf transformation 6]
57. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 10]
58. ! [X0] : ((~tall(X0) | ~happy(X0) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | (tall(X0) & happy(X0)))) [flattening 57]
61. ! [X0] : ((generous(X0) & ~brave(X0)) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) [nnf transformation 32]
86. ~rich(X0) | ~happy(X0) [cnf transformation 51]
89. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
90. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 52]
103. ~tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 58]
104. ~tall(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 58]
119. generous(X0) | tall(X0) | rich(X0) [cnf transformation 61]
135. happy(paul) [cnf transformation 23]
137. ~generous(X0) | ~curious(X0) [duplicate literal removal 89]
138. ~generous(X0) | curious(X0) [duplicate literal removal 90]
215. ~generous(X0) [subsumption resolution 137,138]
233. ~tall(X0) | ~happy(X0) [subsumption resolution 103,104]
259. tall(X0) | rich(X0) [subsumption resolution 119,215]
303. rich(X1) | ~happy(X1) [resolution 259,233]
304. ~happy(X1) [subsumption resolution 303,86]
317. $false [resolution 304,135]
% SZS output end Proof for 3261065195879030434323864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not old is both not calm and not strong.
If someone is both not humble and creative then someone is both not happy and wise and vice versa.
Everyone who is both not strong and humble is both old and not humble and vice versa.
Everyone who is not kind or not creative is not creative or wise.
Everyone who is both not patient and not wise is not creative and vice versa.
Everyone who is both not tall and not happy is strong.
If alice is both not curious and creative then someone is both generous and not funny and vice versa.
Everyone who is not strong or not creative is both funny and not kind.
If susan is not kind or not rich then someone is both old and not old.
Everyone who is either not patient or creative is both not wise and not creative.
If alice is not brave then fred is either not humble or strong and vice versa.
Everyone who is either old or happy is either not calm or calm.
Everyone who is not happy or creative is either calm or not old.
Everyone who is not brave or creative is both old and happy.
If paul is either not calm or not curious then mary is not brave.
If paul is either not happy or not generous then john is calm.
Someone is kind.
Paul is both curious and not quiet.
John is either not calm or not old.
Someone is both tall and not creative.
Someone is not patient.
Alice is both strong and generous. | Susan is humble. | entailment | (![X]:((~creative(X)<~>~old(X))=>(~calm(X)&~strong(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~strong(X)&humble(X))<=>(old(X)&~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~creative(X)|wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>~creative(X)))&
(![X]:((~tall(X)&~happy(X))=>strong(X)))&
(((~curious(alice)&creative(alice)))<=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((~strong(X)|~creative(X))=>(funny(X)&~kind(X))))&
(((~kind(susan)|~rich(susan)))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~wise(X)&~creative(X))))&
((~brave(alice))<=>((~humble(fred)<~>strong(fred))))&
(![X]:((old(X)<~>happy(X))=>(~calm(X)<~>calm(X))))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((~brave(X)|creative(X))=>(old(X)&happy(X))))&
(((~calm(paul)<~>~curious(paul)))=>(~brave(mary)))&
(((~happy(paul)<~>~generous(paul)))=>(calm(john)))&
(?[X]:(kind(X)))&
((curious(paul)&~quiet(paul)))&
((~calm(john)<~>~old(john)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:(~patient(X)))&
((strong(alice)&generous(alice))) | humble(susan) | [
"p1",
"p2",
"p7",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 3435882857338819748139714
% SZS output start Proof for 3435882857338819748139714
2. ? [X0] : (creative(X0) & ~humble(X0)) <=> ? [X0] : (wise(X0) & ~happy(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~strong(X0)) <=> (~humble(X0) & old(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~strong(X0)) => (~kind(X0) & funny(X0))) [input p7]
9. (~rich(susan) | ~kind(susan)) => ? [X0] : (~old(X0) & old(X0)) [input p8]
14. ! [X0] : ((creative(X0) | ~brave(X0)) => (happy(X0) & old(X0))) [input p13]
23. ~humble(susan) [input hypothesis]
24. ? [X0] : (creative(X0) & ~humble(X0)) <=> ? [X1] : (wise(X1) & ~happy(X1)) [rectify 2]
26. ~kind(susan) => ? [X0] : (~old(X0) & old(X0)) [pure predicate removal 9]
32. ! [X0] : ((~kind(X0) & funny(X0)) | (creative(X0) & strong(X0))) [ennf transformation 8]
33. ? [X0] : (~old(X0) & old(X0)) | kind(susan) [ennf transformation 26]
37. ! [X0] : ((happy(X0) & old(X0)) | (~creative(X0) & brave(X0))) [ennf transformation 14]
41. (? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : (~wise(X1) | happy(X1))) & (? [X1] : (wise(X1) & ~happy(X1)) | ! [X0] : (~creative(X0) | humble(X0))) [nnf transformation 24]
42. (? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : (~wise(X1) | happy(X1))) & (? [X2] : (wise(X2) & ~happy(X2)) | ! [X3] : (~creative(X3) | humble(X3))) [rectify 41]
43. ? [X0] : (creative(X0) & ~humble(X0)) => (creative(sK0) & ~humble(sK0)) [choice axiom]
44. ? [X2] : (wise(X2) & ~happy(X2)) => (wise(sK1) & ~happy(sK1)) [choice axiom]
45. ((creative(sK0) & ~humble(sK0)) | ! [X1] : (~wise(X1) | happy(X1))) & ((wise(sK1) & ~happy(sK1)) | ! [X3] : (~creative(X3) | humble(X3))) [skolemisation 42,44,43]
46. ! [X0] : (((humble(X0) & ~strong(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (~humble(X0) | strong(X0)))) [nnf transformation 3]
47. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | ~humble(X0) | strong(X0))) [flattening 46]
55. ? [X0] : (~old(X0) & old(X0)) => (~old(sK3) & old(sK3)) [choice axiom]
56. (~old(sK3) & old(sK3)) | kind(susan) [skolemisation 33,55]
74. ~happy(sK1) | ~creative(X3) | humble(X3) [cnf transformation 45]
75. wise(sK1) | ~creative(X3) | humble(X3) [cnf transformation 45]
76. ~humble(sK0) | ~wise(X1) | happy(X1) [cnf transformation 45]
77. creative(sK0) | ~wise(X1) | happy(X1) [cnf transformation 45]
81. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 47]
94. ~kind(X0) | creative(X0) [cnf transformation 32]
95. old(sK3) | kind(susan) [cnf transformation 56]
96. ~old(sK3) | kind(susan) [cnf transformation 56]
114. ~creative(X0) | old(X0) [cnf transformation 37]
129. ~humble(susan) [cnf transformation 23]
132. ~old(X0) | humble(X0) [duplicate literal removal 81]
134. 1 <=> ! [X1] : (~wise(X1) | happy(X1)) [avatar definition]
135. ~wise(X1) | happy(X1) <- (1) [avatar component clause 134]
137. 2 <=> creative(sK0) [avatar definition]
139. creative(sK0) <- (2) [avatar component clause 137]
140. 1 | 2 [avatar split clause 77,137,134]
142. 3 <=> humble(sK0) [avatar definition]
144. ~humble(sK0) <- (~3) [avatar component clause 142]
145. 1 | ~3 [avatar split clause 76,142,134]
147. 4 <=> ! [X3] : (~creative(X3) | humble(X3)) [avatar definition]
148. ~creative(X3) | humble(X3) <- (4) [avatar component clause 147]
150. 5 <=> wise(sK1) [avatar definition]
152. wise(sK1) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 75,150,147]
155. 6 <=> happy(sK1) [avatar definition]
157. ~happy(sK1) <- (~6) [avatar component clause 155]
158. 4 | ~6 [avatar split clause 74,155,147]
183. 12 <=> kind(susan) [avatar definition]
185. kind(susan) <- (12) [avatar component clause 183]
187. 13 <=> old(sK3) [avatar definition]
190. 12 | ~13 [avatar split clause 96,187,183]
191. 12 | 13 [avatar split clause 95,187,183]
248. creative(susan) <- (12) [resolution 94,185]
251. old(sK0) <- (2) [resolution 114,139]
261. humble(sK0) <- (2) [resolution 251,132]
262. $false <- (2, ~3) [subsumption resolution 261,144]
263. ~2 | 3 [avatar contradiction clause 262]
264. humble(susan) <- (4, 12) [resolution 148,248]
266. $false <- (4, 12) [subsumption resolution 264,129]
267. ~4 | ~12 [avatar contradiction clause 266]
268. happy(sK1) <- (1, 5) [resolution 152,135]
270. $false <- (1, 5, ~6) [subsumption resolution 268,157]
271. ~1 | ~5 | 6 [avatar contradiction clause 270]
272. $false [avatar sat refutation 140,145,153,158,190,191,263,267,271]
% SZS output end Proof for 3435882857338819748139714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is old then someone is generous or tall. Everyone who is patient or not quiet is both wise and kind. Everyone who is creative or patient is both not generous and generous. If someone is either creative or quiet then susan is both not happy and curious and vice versa. Everyone who is both generous and not calm is not happy and vice versa. If someone is both not curious and strong then john is either not quiet or rich and vice versa. Everyone who is both curious and not creative is either curious or not calm. Everyone who is either not patient or not rich is both not calm and not curious and vice versa. Everyone who is both not tall and not calm is wise and vice versa. If someone is not kind or not creative then someone is both old and not creative. Everyone who is happy is not happy or old. If someone is both calm and not rich then someone is happy. If lucy is not funny then mary is both kind and not kind. If lucy is either not happy or not generous then susan is not curious. Everyone who is old or brave is not quiet. Someone is not old. Someone is either not rich or not funny. Mary is both generous and not funny. Mary is not quiet or curious. Mary is either tall or brave. | Susan is generous. | neutral | ((old(alice))=>(?[X]:((generous(X)|tall(X)))))&
(![X]:((patient(X)|~quiet(X))=>(wise(X)&kind(X))))&
(![X]:((creative(X)|patient(X))=>(~generous(X)&generous(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>((~happy(susan)&curious(susan))))&
(![X]:((generous(X)&~calm(X))<=>~happy(X)))&
((?[X]:((~curious(X)&strong(X))))<=>((~quiet(john)<~>rich(john))))&
(![X]:((curious(X)&~creative(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~calm(X)&~curious(X))))&
(![X]:((~tall(X)&~calm(X))<=>wise(X)))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:(happy(X)=>(~happy(X)|old(X))))&
((?[X]:((calm(X)&~rich(X))))=>(?[X]:(happy(X))))&
((~funny(lucy))=>((kind(mary)&~kind(mary))))&
(((~happy(lucy)<~>~generous(lucy)))=>(~curious(susan)))&
(![X]:((old(X)|brave(X))=>~quiet(X)))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((generous(mary)&~funny(mary)))&
((~quiet(mary)|curious(mary)))&
((tall(mary)<~>brave(mary))) | generous(susan) | []
| 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 both kind and strong and vice versa.
If someone is not brave or funny then someone is not brave.
If mary is not strong or strong then john is calm or generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and 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.
Alice is either not curious or not wise.
Paul is not creative.
Someone is not tall.
Fred is not kind.
Paul is both not generous and not creative.
Alice is not creative.
Someone is not calm. | Alice is humble. | entailment | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(kind(X)&strong(X))))&
((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![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))))&
((~curious(alice)<~>~wise(alice)))&
(~creative(paul))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~generous(paul)&~creative(paul)))&
(~creative(alice))&
(?[X]:(~calm(X))) | humble(alice) | [
"p6",
"p8",
"p11",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 6777073599557467074429468
% SZS output start Proof for 6777073599557467074429468
7. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p6]
9. ! [X0] : ((wise(X0) & generous(X0)) <=> ~humble(X0)) [input p8]
12. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p15]
22. ~creative(alice) [input p21]
24. ~humble(alice) [input hypothesis]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 7]
50. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | ~wise(X0) | ~generous(X0))) [flattening 50]
61. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 12]
62. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 61]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
94. ~patient(X0) | ~generous(X0) [cnf transformation 34]
100. humble(X0) | generous(X0) [cnf transformation 51]
110. creative(X0) | quiet(X0) [cnf transformation 62]
121. ~quiet(X0) | patient(X0) [cnf transformation 69]
130. ~creative(alice) [cnf transformation 22]
132. ~humble(alice) [cnf transformation 24]
258. generous(alice) [resolution 100,132]
265. quiet(alice) [resolution 110,130]
271. patient(alice) [resolution 121,265]
275. ~generous(alice) [resolution 271,94]
276. $false [subsumption resolution 275,258]
% SZS output end Proof for 6777073599557467074429468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is creative or not strong then someone is both not happy and funny and vice versa.
If mary is strong then lucy is generous or calm.
Everyone who is both not old and not calm is tall.
Everyone who is both not humble and not generous is not kind and vice versa.
Everyone who is both not creative and kind is both creative and not patient and vice versa.
If someone is kind or quiet then someone is not kind or not brave.
Everyone who is curious is both happy and not strong.
Everyone who is creative is not curious.
Everyone who is both generous and strong is both old and funny.
Everyone who is either quiet or rich is generous.
If someone is not curious or brave then mary is either curious or humble.
If john is not happy then fred is kind and vice versa.
Everyone who is either not creative or creative is happy and vice versa.
Everyone who is both not humble and not brave is either not creative or wise and vice versa.
Everyone who is both not strong and calm is old and vice versa.
If someone is not curious or rich then lucy is either not tall or not old.
Someone is either calm or creative.
John is not calm or not brave.
Alice is either funny or not kind.
Alice is not humble.
Paul is generous or funny.
Alice is either quiet or not curious.
Someone is both kind and not brave. | Fred is funny. | neutral | (((creative(paul)|~strong(paul)))<=>(?[X]:((~happy(X)&funny(X)))))&
((strong(mary))=>((generous(lucy)|calm(lucy))))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
(![X]:((~humble(X)&~generous(X))<=>~kind(X)))&
(![X]:((~creative(X)&kind(X))<=>(creative(X)&~patient(X))))&
((?[X]:((kind(X)|quiet(X))))=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:(curious(X)=>(happy(X)&~strong(X))))&
(![X]:(creative(X)=>~curious(X)))&
(![X]:((generous(X)&strong(X))=>(old(X)&funny(X))))&
(![X]:((quiet(X)<~>rich(X))=>generous(X)))&
((?[X]:((~curious(X)|brave(X))))=>((curious(mary)<~>humble(mary))))&
((~happy(john))<=>(kind(fred)))&
(![X]:((~creative(X)<~>creative(X))<=>happy(X)))&
(![X]:((~humble(X)&~brave(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~strong(X)&calm(X))<=>old(X)))&
((?[X]:((~curious(X)|rich(X))))=>((~tall(lucy)<~>~old(lucy))))&
(?[X]:((calm(X)<~>creative(X))))&
((~calm(john)|~brave(john)))&
((funny(alice)<~>~kind(alice)))&
(~humble(alice))&
((generous(paul)|funny(paul)))&
((quiet(alice)<~>~curious(alice)))&
(?[X]:((kind(X)&~brave(X)))) | funny(fred) | []
| null | 0 |
If someone is either not old or not patient then lucy is creative or not happy. Everyone who is both funny and curious is rich or brave and vice versa. If paul is either tall or curious then alice is both not old and generous and vice versa. Everyone who is not brave or not tall is humble and vice versa. Everyone who is not curious is calm and vice versa. Everyone who is either wise or not generous is not generous. If someone is not funny then someone is either not strong or not generous. Everyone who is rich or not curious is either not humble or strong and vice versa. Everyone who is not quiet is not curious or not calm and vice versa. Everyone who is not generous or brave is both happy and kind and vice versa. Everyone who is either wise or curious is not happy and vice versa. If mary is both not wise and not creative then john is both funny and humble and vice versa. If fred is not old then susan is not humble. If someone is brave then someone is either generous or curious. If mary is not humble or not old then someone is both happy and not quiet and vice versa. If alice is rich or not quiet then someone is generous and vice versa. Someone is either wise or not old. Susan is patient. Mary is wise or not quiet. Alice is both funny and kind. Paul is happy or not funny. Someone is either quiet or not rich. Someone is both not wise and tall. Someone is either brave or not humble. | Alice is creative. | neutral | ((?[X]:((~old(X)<~>~patient(X))))=>((creative(lucy)|~happy(lucy))))&
(![X]:((funny(X)&curious(X))<=>(rich(X)|brave(X))))&
(((tall(paul)<~>curious(paul)))<=>((~old(alice)&generous(alice))))&
(![X]:((~brave(X)|~tall(X))<=>humble(X)))&
(![X]:(~curious(X)<=>calm(X)))&
(![X]:((wise(X)<~>~generous(X))=>~generous(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~humble(X)<~>strong(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|~calm(X))))&
(![X]:((~generous(X)|brave(X))<=>(happy(X)&kind(X))))&
(![X]:((wise(X)<~>curious(X))<=>~happy(X)))&
(((~wise(mary)&~creative(mary)))<=>((funny(john)&humble(john))))&
((~old(fred))=>(~humble(susan)))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)<~>curious(X)))))&
(((~humble(mary)|~old(mary)))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((rich(alice)|~quiet(alice)))<=>(?[X]:(generous(X))))&
(?[X]:((wise(X)<~>~old(X))))&
(patient(susan))&
((wise(mary)|~quiet(mary)))&
((funny(alice)&kind(alice)))&
((happy(paul)|~funny(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((brave(X)<~>~humble(X)))) | creative(alice) | []
| null | 0 |
If someone is creative or calm then fred is not strong.
If someone is both not humble and not happy then someone is funny or rich and vice versa.
Everyone who is both not wise and not tall is patient and vice versa.
If someone is both quiet and tall then fred is both calm and rich and vice versa.
Everyone who is humble or happy is both not patient and strong.
Everyone who is either rich or not old is not patient or not generous.
If mary is either brave or not generous then john is both not old and happy.
If someone is not creative or calm then john is both not patient and rich and vice versa.
Everyone who is both not happy and not calm is both happy and rich.
Everyone who is both not happy and rich is either not strong or not brave.
Everyone who is both not old and creative is kind.
Everyone who is either not calm or calm is kind or humble and vice versa.
If someone is both not tall and not calm then fred is happy or not quiet.
Everyone who is not old is not patient or creative.
If someone is both tall and funny then fred is both not calm and not generous.
Everyone who is calm or not generous is either not rich or not wise.
Paul is either not funny or brave.
Paul is quiet.
Someone is happy or brave.
Lucy is not old.
John is not funny.
Paul is kind or not funny.
Someone is not tall.
Fred is not quiet or strong. | John is not kind. | neutral | ((?[X]:((creative(X)|calm(X))))=>(~strong(fred)))&
((?[X]:((~humble(X)&~happy(X))))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~wise(X)&~tall(X))<=>patient(X)))&
((?[X]:((quiet(X)&tall(X))))<=>((calm(fred)&rich(fred))))&
(![X]:((humble(X)|happy(X))=>(~patient(X)&strong(X))))&
(![X]:((rich(X)<~>~old(X))=>(~patient(X)|~generous(X))))&
(((brave(mary)<~>~generous(mary)))=>((~old(john)&happy(john))))&
((?[X]:((~creative(X)|calm(X))))<=>((~patient(john)&rich(john))))&
(![X]:((~happy(X)&~calm(X))=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&rich(X))=>(~strong(X)<~>~brave(X))))&
(![X]:((~old(X)&creative(X))=>kind(X)))&
(![X]:((~calm(X)<~>calm(X))<=>(kind(X)|humble(X))))&
((?[X]:((~tall(X)&~calm(X))))=>((happy(fred)|~quiet(fred))))&
(![X]:(~old(X)=>(~patient(X)|creative(X))))&
((?[X]:((tall(X)&funny(X))))=>((~calm(fred)&~generous(fred))))&
(![X]:((calm(X)|~generous(X))=>(~rich(X)<~>~wise(X))))&
((~funny(paul)<~>brave(paul)))&
(quiet(paul))&
(?[X]:((happy(X)|brave(X))))&
(~old(lucy))&
(~funny(john))&
((kind(paul)|~funny(paul)))&
(?[X]:(~tall(X)))&
((~quiet(fred)|strong(fred))) | ~kind(john) | []
| null | 0 |
Everyone who is not funny or curious is strong or humble.
Everyone who is both not kind and not wise is calm or not tall.
If fred is both creative and quiet then someone is quiet.
Everyone who is not creative is both not funny and funny.
If john is either not old or not generous then john is either rich or not happy and vice versa.
Everyone who is either curious or not old is either happy or not strong and vice versa.
If someone is not old then someone is not tall and vice versa.
Everyone who is both not rich and quiet is both strong and generous and vice versa.
Everyone who is not patient or not rich is not tall or patient.
If someone is not tall then someone is not generous and vice versa.
Everyone who is not quiet or kind is not old and vice versa.
If john is both kind and brave then someone is funny.
If someone is tall then someone is both rich and quiet.
Everyone who is strong or curious is not strong and vice versa.
Everyone who is not rich is either not curious or humble.
Everyone who is both not tall and not calm is either funny or creative.
Someone is both not calm and not rich.
Someone is patient or not tall.
Fred is either calm or not curious.
Lucy is both wise and not happy.
Lucy is both funny and tall.
Someone is not brave or not rich.
Someone is not happy.
Alice is both not tall and not calm. | Fred is not calm. | contradiction | (![X]:((~funny(X)|curious(X))=>(strong(X)|humble(X))))&
(![X]:((~kind(X)&~wise(X))=>(calm(X)|~tall(X))))&
(((creative(fred)&quiet(fred)))=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)=>(~funny(X)&funny(X))))&
(((~old(john)<~>~generous(john)))<=>((rich(john)<~>~happy(john))))&
(![X]:((curious(X)<~>~old(X))<=>(happy(X)<~>~strong(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)&quiet(X))<=>(strong(X)&generous(X))))&
(![X]:((~patient(X)|~rich(X))=>(~tall(X)|patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|kind(X))<=>~old(X)))&
(((kind(john)&brave(john)))=>(?[X]:(funny(X))))&
((?[X]:(tall(X)))=>(?[X]:((rich(X)&quiet(X)))))&
(![X]:((strong(X)|curious(X))<=>~strong(X)))&
(![X]:(~rich(X)=>(~curious(X)<~>humble(X))))&
(![X]:((~tall(X)&~calm(X))=>(funny(X)<~>creative(X))))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((patient(X)|~tall(X))))&
((calm(fred)<~>~curious(fred)))&
((wise(lucy)&~happy(lucy)))&
((funny(lucy)&tall(lucy)))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:(~happy(X)))&
((~tall(alice)&~calm(alice))) | ~calm(fred) | [
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7684593742294714904448600
% SZS output start Proof for 7684593742294714904448600
14. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p13]
19. calm(fred) <~> ~curious(fred) [input p18]
25. ~calm(fred) [input hypothesis]
65. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [nnf transformation 14]
66. ! [X0] : ((curious(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [flattening 65]
71. (curious(fred) | ~calm(fred)) & (~curious(fred) | calm(fred)) [nnf transformation 19]
108. ~strong(X0) | ~strong(X0) [cnf transformation 66]
110. curious(X0) | strong(X0) | strong(X0) [cnf transformation 66]
117. ~curious(fred) | calm(fred) [cnf transformation 71]
125. ~calm(fred) [cnf transformation 25]
126. ~strong(X0) [duplicate literal removal 108]
127. strong(X0) | curious(X0) [duplicate literal removal 110]
210. 18 <=> calm(fred) [avatar definition]
214. 19 <=> curious(fred) [avatar definition]
215. ~curious(fred) <- (~19) [avatar component clause 214]
218. 18 | ~19 [avatar split clause 117,214,210]
219. ~18 [avatar split clause 125,210]
225. curious(X1) [resolution 127,126]
226. $false <- (~19) [resolution 225,215]
227. 19 [avatar contradiction clause 226]
228. $false [avatar sat refutation 218,219,227]
% SZS output end Proof for 7684593742294714904448600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong and brave is either not strong or old and vice versa. If mary is creative then fred is generous and vice versa. If someone is not calm then susan is either patient or rich and vice versa. Everyone who is brave is rich or not funny and vice versa. Everyone who is either old or strong is brave and vice versa. Everyone who is either wise or creative is either strong or quiet. If mary is both quiet and strong then someone is both not happy and strong. Everyone who is either not rich or funny is not rich. If someone is calm then someone is not strong. If susan is both curious and old then someone is curious or not happy. If alice is not humble or kind then someone is either creative or old and vice versa. Everyone who is not happy or not tall is old or not wise and vice versa. Everyone who is patient is not rich or not humble. Everyone who is strong or not old is either humble or funny. Everyone who is not happy is both quiet and not generous. If someone is both funny and wise then john is both not funny and not rich and vice versa. Someone is not quiet or not generous. Someone is either curious or generous. Someone is either not kind or wise. Someone is both not quiet and not funny. Mary is either not curious or rich. Someone is quiet or not kind. | Fred is not rich. | neutral | (![X]:((~strong(X)&brave(X))<=>(~strong(X)<~>old(X))))&
((creative(mary))<=>(generous(fred)))&
((?[X]:(~calm(X)))<=>((patient(susan)<~>rich(susan))))&
(![X]:(brave(X)<=>(rich(X)|~funny(X))))&
(![X]:((old(X)<~>strong(X))<=>brave(X)))&
(![X]:((wise(X)<~>creative(X))=>(strong(X)<~>quiet(X))))&
(((quiet(mary)&strong(mary)))=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:((~rich(X)<~>funny(X))=>~rich(X)))&
((?[X]:(calm(X)))=>(?[X]:(~strong(X))))&
(((curious(susan)&old(susan)))=>(?[X]:((curious(X)|~happy(X)))))&
(((~humble(alice)|kind(alice)))<=>(?[X]:((creative(X)<~>old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(old(X)|~wise(X))))&
(![X]:(patient(X)=>(~rich(X)|~humble(X))))&
(![X]:((strong(X)|~old(X))=>(humble(X)<~>funny(X))))&
(![X]:(~happy(X)=>(quiet(X)&~generous(X))))&
((?[X]:((funny(X)&wise(X))))<=>((~funny(john)&~rich(john))))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((curious(X)<~>generous(X))))&
(?[X]:((~kind(X)<~>wise(X))))&
(?[X]:((~quiet(X)&~funny(X))))&
((~curious(mary)<~>rich(mary)))&
(?[X]:((quiet(X)|~kind(X)))) | ~rich(fred) | []
| null | 0 |
If susan is both humble and generous then john is either calm or not creative and vice versa.
Everyone who is kind is not curious and vice versa.
If fred is either humble or old then someone is either generous or wise.
If mary is not rich then alice is both strong and not generous and vice versa.
Everyone who is tall or not rich is both tall and not rich and vice versa.
Everyone who is not brave is strong or not creative and vice versa.
Everyone who is not tall or not happy is either calm or happy.
Everyone who is both brave and happy is not creative or generous.
Everyone who is both not humble and curious is either not rich or rich and vice versa.
If someone is not creative then fred is quiet.
If lucy is both wise and calm then fred is both not old and curious and vice versa.
If someone is either not humble or humble then john is patient or generous and vice versa.
Everyone who is both not funny and curious is either not generous or not quiet.
If alice is either generous or not happy then paul is either funny or not brave.
If someone is brave then susan is either calm or not old.
If someone is both kind and not strong then paul is either not quiet or rich.
Someone is both not kind and not tall.
Someone is old.
Susan is both happy and not tall.
Someone is not humble or brave.
Someone is either not funny or not happy.
Fred is both strong and rich.
Paul is kind or happy. | Mary is not curious. | contradiction | (((humble(susan)&generous(susan)))<=>((calm(john)<~>~creative(john))))&
(![X]:(kind(X)<=>~curious(X)))&
(((humble(fred)<~>old(fred)))=>(?[X]:((generous(X)<~>wise(X)))))&
((~rich(mary))<=>((strong(alice)&~generous(alice))))&
(![X]:((tall(X)|~rich(X))<=>(tall(X)&~rich(X))))&
(![X]:(~brave(X)<=>(strong(X)|~creative(X))))&
(![X]:((~tall(X)|~happy(X))=>(calm(X)<~>happy(X))))&
(![X]:((brave(X)&happy(X))=>(~creative(X)|generous(X))))&
(![X]:((~humble(X)&curious(X))<=>(~rich(X)<~>rich(X))))&
((?[X]:(~creative(X)))=>(quiet(fred)))&
(((wise(lucy)&calm(lucy)))<=>((~old(fred)&curious(fred))))&
((?[X]:((~humble(X)<~>humble(X))))<=>((patient(john)|generous(john))))&
(![X]:((~funny(X)&curious(X))=>(~generous(X)<~>~quiet(X))))&
(((generous(alice)<~>~happy(alice)))=>((funny(paul)<~>~brave(paul))))&
((?[X]:(brave(X)))=>((calm(susan)<~>~old(susan))))&
((?[X]:((kind(X)&~strong(X))))=>((~quiet(paul)<~>rich(paul))))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:(old(X)))&
((happy(susan)&~tall(susan)))&
(?[X]:((~humble(X)|brave(X))))&
(?[X]:((~funny(X)<~>~happy(X))))&
((strong(fred)&rich(fred)))&
((kind(paul)|happy(paul))) | ~curious(mary) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 209654852678850743810998
% SZS output start Proof for 209654852678850743810998
9. ! [X0] : ((curious(X0) & ~humble(X0)) <=> (~rich(X0) <~> rich(X0))) [input p8]
24. ~curious(mary) [input hypothesis]
48. ! [X0] : (((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (~curious(X0) | humble(X0)))) [nnf transformation 9]
49. ! [X0] : (((curious(X0) & ~humble(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~curious(X0) | humble(X0))) [flattening 48]
102. curious(X0) | rich(X0) | rich(X0) [cnf transformation 49]
103. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 49]
136. ~curious(mary) [cnf transformation 24]
141. curious(X0) | rich(X0) [duplicate literal removal 102]
142. curious(X0) | ~rich(X0) [duplicate literal removal 103]
202. curious(X0) [subsumption resolution 141,142]
298. $false [subsumption resolution 136,202]
% SZS output end Proof for 209654852678850743810998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or calm is either not tall or not quiet.
Everyone who is funny or not patient is curious or not generous.
Everyone who is tall is funny and vice versa.
Everyone who is either not tall or funny is humble.
If someone is either strong or not calm then john is either not brave or not old and vice versa.
If paul is tall then someone is either not brave or curious and vice versa.
If someone is tall or calm then someone is both happy and not wise.
If someone is either not patient or not curious then someone is either not calm or creative and vice versa.
Everyone who is not strong or not curious is brave.
If someone is both not happy and curious then paul is either strong or wise and vice versa.
Everyone who is not patient is both wise and not old.
Everyone who is either humble or not generous is both not patient and not happy and vice versa.
If alice is both not creative and not old then someone is either quiet or not tall and vice versa.
Everyone who is either not wise or not generous is not wise or creative and vice versa.
If someone is wise then lucy is not calm and vice versa.
Everyone who is generous or not rich is not tall or generous.
Fred is not strong or not humble.
Someone is both not old and wise.
Someone is either not generous or happy.
John is both not brave and strong.
Paul is not generous or creative. | John is not wise. | contradiction | (![X]:((wise(X)<~>calm(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((funny(X)|~patient(X))=>(curious(X)|~generous(X))))&
(![X]:(tall(X)<=>funny(X)))&
(![X]:((~tall(X)<~>funny(X))=>humble(X)))&
((?[X]:((strong(X)<~>~calm(X))))<=>((~brave(john)<~>~old(john))))&
((tall(paul))<=>(?[X]:((~brave(X)<~>curious(X)))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:((happy(X)&~wise(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~strong(X)|~curious(X))=>brave(X)))&
((?[X]:((~happy(X)&curious(X))))<=>((strong(paul)<~>wise(paul))))&
(![X]:(~patient(X)=>(wise(X)&~old(X))))&
(![X]:((humble(X)<~>~generous(X))<=>(~patient(X)&~happy(X))))&
(((~creative(alice)&~old(alice)))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~wise(X)|creative(X))))&
((?[X]:(wise(X)))<=>(~calm(lucy)))&
(![X]:((generous(X)|~rich(X))=>(~tall(X)|generous(X))))&
((~strong(fred)|~humble(fred)))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
((~brave(john)&strong(john)))&
((~generous(paul)|creative(paul))) | ~wise(john) | [
"p2",
"p3",
"p10",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 6222009367217507852505810
% SZS output start Proof for 6222009367217507852505810
3. ! [X0] : (tall(X0) <=> funny(X0)) [input p2]
4. ! [X0] : ((~tall(X0) <~> funny(X0)) => humble(X0)) [input p3]
11. ! [X0] : (~patient(X0) => (~old(X0) & wise(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> (~happy(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (creative(X0) | ~wise(X0))) [input p13]
22. ~wise(john) [input hypothesis]
29. ! [X0] : (humble(X0) | (~tall(X0) <=> funny(X0))) [ennf transformation 4]
32. ! [X0] : ((~old(X0) & wise(X0)) | patient(X0)) [ennf transformation 11]
36. ! [X0] : ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))) [nnf transformation 3]
37. ! [X0] : (humble(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) [nnf transformation 29]
58. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 12]
59. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [flattening 58]
65. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (~creative(X0) & wise(X0))) & ((creative(X0) | ~wise(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 14]
66. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (~creative(X0) & wise(X0))) & (creative(X0) | ~wise(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [flattening 65]
82. ~tall(X0) | funny(X0) [cnf transformation 36]
83. ~funny(X0) | tall(X0) [cnf transformation 36]
84. humble(X0) | funny(X0) | tall(X0) [cnf transformation 37]
85. humble(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 37]
118. patient(X0) | wise(X0) [cnf transformation 32]
120. ~patient(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 59]
136. generous(X0) | wise(X0) | wise(X0) [cnf transformation 66]
149. ~wise(john) [cnf transformation 22]
151. generous(X0) | wise(X0) [duplicate literal removal 136]
152. ~funny(X0) | humble(X0) [subsumption resolution 85,83]
153. humble(X0) | funny(X0) [subsumption resolution 84,82]
154. humble(X0) [subsumption resolution 153,152]
289. ~generous(X0) | ~patient(X0) [subsumption resolution 120,154]
352. ~patient(X0) | wise(X0) [resolution 289,151]
353. wise(X0) [subsumption resolution 352,118]
357. $false [resolution 353,149]
% SZS output end Proof for 6222009367217507852505810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not patient is not strong or humble and vice versa. Everyone who is both not old and funny is not strong or wise and vice versa. If paul is brave or not humble then someone is either not funny or strong and vice versa. If mary is old or not creative then alice is either not kind or quiet. If someone is creative then mary is not generous and vice versa. Everyone who is calm or wise is both not creative and not curious. If someone is either curious or kind then someone is either calm or not tall and vice versa. Everyone who is not strong is either not tall or not kind and vice versa. Everyone who is creative or old is either not strong or not patient and vice versa. Everyone who is both not creative and tall is not calm. Everyone who is old is both not curious and quiet. If susan is brave then someone is both not happy and wise. If someone is either happy or old then paul is either not old or humble and vice versa. If mary is both generous and not creative then alice is either old or not creative and vice versa. Everyone who is old is not funny and vice versa. If john is either happy or not strong then someone is both kind and not rich and vice versa. Someone is creative. Someone is not brave or tall. Susan is not strong or patient. Mary is either kind or not wise. Someone is quiet. Someone is either not quiet or tall. Susan is either not happy or kind. | Alice is not tall. | contradiction | (![X]:((wise(X)|~patient(X))<=>(~strong(X)|humble(X))))&
(![X]:((~old(X)&funny(X))<=>(~strong(X)|wise(X))))&
(((brave(paul)|~humble(paul)))<=>(?[X]:((~funny(X)<~>strong(X)))))&
(((old(mary)|~creative(mary)))=>((~kind(alice)<~>quiet(alice))))&
((?[X]:(creative(X)))<=>(~generous(mary)))&
(![X]:((calm(X)|wise(X))=>(~creative(X)&~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:(~strong(X)<=>(~tall(X)<~>~kind(X))))&
(![X]:((creative(X)|old(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:((~creative(X)&tall(X))=>~calm(X)))&
(![X]:(old(X)=>(~curious(X)&quiet(X))))&
((brave(susan))=>(?[X]:((~happy(X)&wise(X)))))&
((?[X]:((happy(X)<~>old(X))))<=>((~old(paul)<~>humble(paul))))&
(((generous(mary)&~creative(mary)))<=>((old(alice)<~>~creative(alice))))&
(![X]:(old(X)<=>~funny(X)))&
(((happy(john)<~>~strong(john)))<=>(?[X]:((kind(X)&~rich(X)))))&
(?[X]:(creative(X)))&
(?[X]:((~brave(X)|tall(X))))&
((~strong(susan)|patient(susan)))&
((kind(mary)<~>~wise(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((~happy(susan)<~>kind(susan))) | ~tall(alice) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p7",
"p8",
"p10",
"p13",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8594693293037586085456243
% SZS output start Proof for 8594693293037586085456243
1. ! [X0] : ((~patient(X0) | wise(X0)) <=> (humble(X0) | ~strong(X0))) [input p0]
2. ! [X0] : ((funny(X0) & ~old(X0)) <=> (wise(X0) | ~strong(X0))) [input p1]
4. (~creative(mary) | old(mary)) => (~kind(alice) <~> quiet(alice)) [input p3]
5. ? [X0] : creative(X0) <=> ~generous(mary) [input p4]
6. ! [X0] : ((wise(X0) | calm(X0)) => (~curious(X0) & ~creative(X0))) [input p5]
8. ! [X0] : (~strong(X0) <=> (~tall(X0) <~> ~kind(X0))) [input p7]
9. ! [X0] : ((old(X0) | creative(X0)) <=> (~strong(X0) <~> ~patient(X0))) [input p8]
11. ! [X0] : (old(X0) => (quiet(X0) & ~curious(X0))) [input p10]
14. (~creative(mary) & generous(mary)) <=> (old(alice) <~> ~creative(alice)) [input p13]
15. ! [X0] : (old(X0) <=> ~funny(X0)) [input p14]
17. ? [X0] : creative(X0) [input p16]
24. ~tall(alice) [input hypothesis]
26. (~kind(alice) <~> quiet(alice)) | (creative(mary) & ~old(mary)) [ennf transformation 4]
27. ! [X0] : ((~curious(X0) & ~creative(X0)) | (~wise(X0) & ~calm(X0))) [ennf transformation 6]
30. ! [X0] : ((quiet(X0) & ~curious(X0)) | ~old(X0)) [ennf transformation 11]
32. ! [X0] : (((~patient(X0) | wise(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (patient(X0) & ~wise(X0)))) [nnf transformation 1]
33. ! [X0] : ((~patient(X0) | wise(X0) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | (patient(X0) & ~wise(X0)))) [flattening 32]
34. ! [X0] : (((funny(X0) & ~old(X0)) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | (~funny(X0) | old(X0)))) [nnf transformation 2]
35. ! [X0] : (((funny(X0) & ~old(X0)) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | ~funny(X0) | old(X0))) [flattening 34]
41. ((~quiet(alice) | kind(alice)) & (quiet(alice) | ~kind(alice))) | (creative(mary) & ~old(mary)) [nnf transformation 26]
42. (? [X0] : creative(X0) | generous(mary)) & (~generous(mary) | ! [X0] : ~creative(X0)) [nnf transformation 5]
43. (? [X0] : creative(X0) | generous(mary)) & (~generous(mary) | ! [X1] : ~creative(X1)) [rectify 42]
44. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
45. (creative(sK1) | generous(mary)) & (~generous(mary) | ! [X1] : ~creative(X1)) [skolemisation 43,44]
51. ! [X0] : ((~strong(X0) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0)))) & (((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | strong(X0))) [nnf transformation 8]
52. ! [X0] : (((old(X0) | creative(X0)) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) & (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~old(X0) & ~creative(X0)))) [nnf transformation 9]
53. ! [X0] : ((old(X0) | creative(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) & (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~old(X0) & ~creative(X0)))) [flattening 52]
60. ((~creative(mary) & generous(mary)) | ((old(alice) | creative(alice)) & (~creative(alice) | ~old(alice)))) & (((creative(alice) | ~old(alice)) & (~creative(alice) | old(alice))) | (creative(mary) | ~generous(mary))) [nnf transformation 14]
61. ((~creative(mary) & generous(mary)) | ((old(alice) | creative(alice)) & (~creative(alice) | ~old(alice)))) & (((creative(alice) | ~old(alice)) & (~creative(alice) | old(alice))) | creative(mary) | ~generous(mary)) [flattening 60]
62. ! [X0] : ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))) [nnf transformation 15]
67. ? [X0] : creative(X0) => creative(sK7) [choice axiom]
68. creative(sK7) [skolemisation 17,67]
80. ~patient(X0) | wise(X0) | strong(X0) [cnf transformation 33]
82. ~funny(X0) | ~strong(X0) | wise(X0) | old(X0) [cnf transformation 35]
83. ~old(X0) | strong(X0) [cnf transformation 35]
95. ~quiet(alice) | kind(alice) | ~old(mary) [cnf transformation 41]
96. ~quiet(alice) | kind(alice) | creative(mary) [cnf transformation 41]
97. ~generous(mary) | ~creative(X1) [cnf transformation 45]
100. ~creative(X0) | ~wise(X0) [cnf transformation 27]
112. tall(X0) | kind(X0) | strong(X0) [cnf transformation 51]
113. ~kind(X0) | ~strong(X0) | tall(X0) [cnf transformation 51]
117. ~creative(X0) | strong(X0) | patient(X0) [cnf transformation 53]
123. ~old(X0) | quiet(X0) [cnf transformation 30]
137. generous(mary) | old(alice) | creative(alice) [cnf transformation 61]
141. funny(X0) | old(X0) [cnf transformation 62]
148. creative(sK7) [cnf transformation 68]
158. ~tall(alice) [cnf transformation 24]
188. 6 <=> creative(mary) [avatar definition]
190. creative(mary) <- (6) [avatar component clause 188]
192. 7 <=> kind(alice) [avatar definition]
193. ~kind(alice) <- (~7) [avatar component clause 192]
194. kind(alice) <- (7) [avatar component clause 192]
196. 8 <=> quiet(alice) [avatar definition]
198. ~quiet(alice) <- (~8) [avatar component clause 196]
199. 6 | 7 | ~8 [avatar split clause 96,196,192,188]
201. 9 <=> old(mary) [avatar definition]
204. ~9 | 7 | ~8 [avatar split clause 95,196,192,201]
208. 10 <=> generous(mary) [avatar definition]
217. 12 <=> ! [X1] : ~creative(X1) [avatar definition]
218. ~creative(X1) <- (12) [avatar component clause 217]
219. 12 | ~10 [avatar split clause 97,208,217]
301. 29 <=> creative(alice) [avatar definition]
303. creative(alice) <- (29) [avatar component clause 301]
305. 30 <=> old(alice) [avatar definition]
306. ~old(alice) <- (~30) [avatar component clause 305]
307. old(alice) <- (30) [avatar component clause 305]
310. 29 | 30 | 10 [avatar split clause 137,208,305,301]
362. 41 <=> wise(mary) [avatar definition]
363. ~wise(mary) <- (~41) [avatar component clause 362]
387. $false <- (12) [resolution 218,148]
388. ~12 [avatar contradiction clause 387]
424. kind(alice) | strong(alice) [resolution 112,158]
428. strong(alice) <- (~7) [subsumption resolution 424,193]
450. 53 <=> patient(alice) [avatar definition]
451. ~patient(alice) <- (~53) [avatar component clause 450]
452. patient(alice) <- (53) [avatar component clause 450]
501. 62 <=> wise(alice) [avatar definition]
503. ~wise(alice) <- (~62) [avatar component clause 501]
506. quiet(alice) <- (30) [resolution 307,123]
511. $false <- (~8, 30) [subsumption resolution 506,198]
512. 8 | ~30 [avatar contradiction clause 511]
514. ~wise(alice) <- (29) [resolution 303,100]
521. strong(alice) | patient(alice) <- (29) [resolution 117,303]
528. ~strong(X0) | wise(X0) | old(X0) | old(X0) [resolution 82,141]
530. ~strong(X0) | wise(X0) | old(X0) [duplicate literal removal 528]
570. wise(alice) | old(alice) <- (~7) [resolution 530,428]
575. old(alice) <- (~7, ~62) [subsumption resolution 570,503]
576. $false <- (~7, ~30, ~62) [subsumption resolution 575,306]
577. 7 | 30 | 62 [avatar contradiction clause 576]
581. strong(alice) <- (29, ~53) [subsumption resolution 521,451]
582. ~strong(alice) | tall(alice) <- (7) [resolution 194,113]
584. tall(alice) <- (7, 29, ~53) [subsumption resolution 582,581]
585. $false <- (7, 29, ~53) [subsumption resolution 584,158]
586. ~7 | ~29 | 53 [avatar contradiction clause 585]
587. ~62 | ~29 [avatar split clause 514,301,501]
589. 64 <=> strong(alice) [avatar definition]
590. ~strong(alice) <- (~64) [avatar component clause 589]
592. 64 | 7 [avatar split clause 424,192,589]
593. ~strong(alice) | tall(alice) <- (7) [resolution 194,113]
595. ~strong(alice) <- (7) [subsumption resolution 593,158]
596. ~64 | ~7 [avatar split clause 595,192,589]
600. strong(alice) <- (30) [resolution 307,83]
604. 64 | ~30 [avatar split clause 600,305,589]
605. strong(mary) | patient(mary) <- (6) [resolution 190,117]
607. ~wise(mary) <- (6) [resolution 190,100]
609. 65 <=> patient(mary) [avatar definition]
611. patient(mary) <- (65) [avatar component clause 609]
613. 66 <=> strong(mary) [avatar definition]
614. ~strong(mary) <- (~66) [avatar component clause 613]
615. strong(mary) <- (66) [avatar component clause 613]
616. 65 | 66 | ~6 [avatar split clause 605,188,613,609]
623. wise(mary) | strong(mary) <- (65) [resolution 611,80]
627. wise(mary) <- (65, ~66) [subsumption resolution 623,614]
628. 41 | ~65 | 66 [avatar split clause 627,613,609,362]
629. ~41 | ~6 [avatar split clause 607,188,362]
630. wise(mary) | old(mary) <- (66) [resolution 615,530]
634. old(mary) <- (~41, 66) [subsumption resolution 630,363]
638. 9 | 41 | ~66 [avatar split clause 634,613,362,201]
651. wise(alice) | strong(alice) <- (53) [resolution 452,80]
652. strong(alice) <- (53, ~62) [subsumption resolution 651,503]
653. $false <- (53, ~62, ~64) [subsumption resolution 652,590]
654. ~53 | 62 | 64 [avatar contradiction clause 653]
655. $false [avatar sat refutation 199,204,219,310,388,512,577,586,587,592,596,604,616,628,629,638,654]
% SZS output end Proof for 8594693293037586085456243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not calm is not curious or not creative.
Everyone who is calm or kind is either not funny or not curious.
Everyone who is wise or not curious is both not funny and strong.
Everyone who is humble is not strong.
If john is not brave or rich then someone is both not patient and not tall.
If someone is not kind then someone is not kind or not curious.
If someone is not strong then alice is both not creative and not calm.
If alice is either not brave or quiet then someone is either not generous or not patient.
Everyone who is not kind or calm is not kind or kind.
Everyone who is both kind and not old is either not quiet or curious.
Everyone who is both curious and not happy is strong and vice versa.
If someone is both not generous and patient then someone is either funny or generous and vice versa.
Everyone who is both generous and not rich is not happy or not brave and vice versa.
If mary is both humble and not strong then paul is either not generous or rich and vice versa.
Everyone who is patient or curious is either calm or not funny.
If someone is rich or curious then alice is both old and not rich.
Lucy is not humble.
Mary is not generous or not wise.
Someone is tall or old.
Someone is not strong or not happy.
Someone is not strong or not funny.
Someone is not humble or not kind.
Lucy is either not creative or not humble.
John is not tall or not rich. | Alice is not calm. | entailment | (![X]:((~curious(X)&~calm(X))=>(~curious(X)|~creative(X))))&
(![X]:((calm(X)|kind(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((wise(X)|~curious(X))=>(~funny(X)&strong(X))))&
(![X]:(humble(X)=>~strong(X)))&
(((~brave(john)|rich(john)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~kind(X)|~curious(X)))))&
((?[X]:(~strong(X)))=>((~creative(alice)&~calm(alice))))&
(((~brave(alice)<~>quiet(alice)))=>(?[X]:((~generous(X)<~>~patient(X)))))&
(![X]:((~kind(X)|calm(X))=>(~kind(X)|kind(X))))&
(![X]:((kind(X)&~old(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((curious(X)&~happy(X))<=>strong(X)))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~happy(X)|~brave(X))))&
(((humble(mary)&~strong(mary)))<=>((~generous(paul)<~>rich(paul))))&
(![X]:((patient(X)|curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((rich(X)|curious(X))))=>((old(alice)&~rich(alice))))&
(~humble(lucy))&
((~generous(mary)|~wise(mary)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((~strong(X)|~happy(X))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((~humble(X)|~kind(X))))&
((~creative(lucy)<~>~humble(lucy)))&
((~tall(john)|~rich(john))) | ~calm(alice) | [
"p6",
"p10",
"p11",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 4192754514880382045504391
% SZS output start Proof for 4192754514880382045504391
7. ? [X0] : ~strong(X0) => (~calm(alice) & ~creative(alice)) [input p6]
11. ! [X0] : ((~happy(X0) & curious(X0)) <=> strong(X0)) [input p10]
12. ? [X0] : (patient(X0) & ~generous(X0)) <=> ? [X0] : (funny(X0) <~> generous(X0)) [input p11]
13. ! [X0] : ((~rich(X0) & generous(X0)) <=> (~brave(X0) | ~happy(X0))) [input p12]
21. ? [X0] : (~funny(X0) | ~strong(X0)) [input p20]
25. calm(alice) [input hypothesis]
27. ? [X0] : (patient(X0) & ~generous(X0)) <=> ? [X1] : (funny(X1) <~> generous(X1)) [rectify 12]
42. (~calm(alice) & ~creative(alice)) | ! [X0] : strong(X0) [ennf transformation 7]
57. ! [X0] : (((~happy(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | (happy(X0) | ~curious(X0)))) [nnf transformation 11]
58. ! [X0] : (((~happy(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | happy(X0) | ~curious(X0))) [flattening 57]
59. (? [X0] : (patient(X0) & ~generous(X0)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (? [X1] : ((~generous(X1) | ~funny(X1)) & (generous(X1) | funny(X1))) | ! [X0] : (~patient(X0) | generous(X0))) [nnf transformation 27]
60. (? [X0] : (patient(X0) & ~generous(X0)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (? [X2] : ((~generous(X2) | ~funny(X2)) & (generous(X2) | funny(X2))) | ! [X3] : (~patient(X3) | generous(X3))) [rectify 59]
61. ? [X0] : (patient(X0) & ~generous(X0)) => (patient(sK3) & ~generous(sK3)) [choice axiom]
62. ? [X2] : ((~generous(X2) | ~funny(X2)) & (generous(X2) | funny(X2))) => ((~generous(sK4) | ~funny(sK4)) & (generous(sK4) | funny(sK4))) [choice axiom]
63. ((patient(sK3) & ~generous(sK3)) | ! [X1] : ((funny(X1) | ~generous(X1)) & (generous(X1) | ~funny(X1)))) & (((~generous(sK4) | ~funny(sK4)) & (generous(sK4) | funny(sK4))) | ! [X3] : (~patient(X3) | generous(X3))) [skolemisation 60,62,61]
64. ! [X0] : (((~rich(X0) & generous(X0)) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | (rich(X0) | ~generous(X0)))) [nnf transformation 13]
65. ! [X0] : (((~rich(X0) & generous(X0)) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | rich(X0) | ~generous(X0))) [flattening 64]
71. ? [X0] : (~funny(X0) | ~strong(X0)) => (~funny(sK6) | ~strong(sK6)) [choice axiom]
72. ~funny(sK6) | ~strong(sK6) [skolemisation 21,71]
88. ~calm(alice) | strong(X0) [cnf transformation 42]
97. ~happy(X0) | ~strong(X0) [cnf transformation 58]
101. ~generous(sK3) | funny(X1) | ~generous(X1) [cnf transformation 63]
105. happy(X0) | generous(X0) [cnf transformation 65]
123. ~funny(sK6) | ~strong(sK6) [cnf transformation 72]
127. calm(alice) [cnf transformation 25]
156. 7 <=> ! [X0] : strong(X0) [avatar definition]
157. strong(X0) <- (7) [avatar component clause 156]
159. 8 <=> calm(alice) [avatar definition]
162. 7 | ~8 [avatar split clause 88,159,156]
191. 14 <=> ! [X1] : (funny(X1) | ~generous(X1)) [avatar definition]
192. funny(X1) | ~generous(X1) <- (14) [avatar component clause 191]
203. 17 <=> generous(sK3) [avatar definition]
205. ~generous(sK3) <- (~17) [avatar component clause 203]
206. 14 | ~17 [avatar split clause 101,203,191]
249. 25 <=> strong(sK6) [avatar definition]
251. ~strong(sK6) <- (~25) [avatar component clause 249]
253. 26 <=> funny(sK6) [avatar definition]
255. ~funny(sK6) <- (~26) [avatar component clause 253]
256. ~25 | ~26 [avatar split clause 123,253,249]
267. 8 [avatar split clause 127,159]
270. generous(X0) | ~strong(X0) [resolution 105,97]
271. generous(X0) <- (7) [subsumption resolution 270,157]
274. $false <- (7, ~17) [resolution 271,205]
277. ~7 | 17 [avatar contradiction clause 274]
278. funny(X1) <- (7, 14) [subsumption resolution 192,271]
279. $false <- (7, 14, ~26) [resolution 278,255]
281. ~7 | ~14 | 26 [avatar contradiction clause 279]
282. $false <- (7, ~25) [subsumption resolution 251,157]
283. ~7 | 25 [avatar contradiction clause 282]
284. $false [avatar sat refutation 162,206,256,267,277,281,283]
% SZS output end Proof for 4192754514880382045504391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not patient is not calm or not brave and vice versa.
If john is not rich then someone is both rich and curious and vice versa.
If someone is patient then someone is either humble or not funny.
If susan is not old or calm then susan is old.
Everyone who is not old or generous is not brave and vice versa.
Everyone who is rich or not strong is curious or not tall and vice versa.
If lucy is both happy and quiet then mary is either not brave or not old and vice versa.
If mary is both curious and not funny then mary is brave or not funny and vice versa.
Everyone who is either not brave or not wise is either kind or not calm and vice versa.
If someone is either not creative or not generous then someone is old.
Everyone who is both brave and not calm is not kind or not wise and vice versa.
Everyone who is either brave or not happy is not tall or generous.
Everyone who is either not old or tall is both not generous and patient and vice versa.
Everyone who is both kind and brave is not patient.
If paul is strong then alice is quiet or not wise.
Everyone who is either funny or brave is either patient or happy and vice versa.
Someone is both tall and not creative.
John is funny or not creative.
Alice is not wise or patient.
John is both calm and not tall.
Someone is not wise.
Alice is not curious or wise. | John is not old. | contradiction | (![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((~rich(john))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(((~old(susan)|calm(susan)))=>(old(susan)))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(((curious(mary)&~funny(mary)))<=>((brave(mary)|~funny(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((brave(X)&~calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((kind(X)&brave(X))=>~patient(X)))&
((strong(paul))=>((quiet(alice)|~wise(alice))))&
(![X]:((funny(X)<~>brave(X))<=>(patient(X)<~>happy(X))))&
(?[X]:((tall(X)&~creative(X))))&
((funny(john)|~creative(john)))&
((~wise(alice)|patient(alice)))&
((calm(john)&~tall(john)))&
(?[X]:(~wise(X)))&
((~curious(alice)|wise(alice))) | ~old(john) | [
"p0",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7100381251551822908465475
% SZS output start Proof for 7100381251551822908465475
1. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~brave(X0) | ~calm(X0))) [input p0]
11. ! [X0] : ((~calm(X0) & brave(X0)) <=> (~wise(X0) | ~kind(X0))) [input p10]
13. ! [X0] : ((~old(X0) <~> tall(X0)) <=> (patient(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((brave(X0) & kind(X0)) => ~patient(X0)) [input p13]
20. ~tall(john) & calm(john) [input p19]
23. ~old(john) [input hypothesis]
31. ! [X0] : (~patient(X0) | (~brave(X0) | ~kind(X0))) [ennf transformation 14]
32. ! [X0] : (~patient(X0) | ~brave(X0) | ~kind(X0)) [flattening 31]
35. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 1]
36. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | patient(X0) | ~funny(X0))) [flattening 35]
58. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0))) [flattening 58]
61. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | (~patient(X0) | generous(X0))) & ((patient(X0) & ~generous(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 13]
62. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | ~patient(X0) | generous(X0)) & ((patient(X0) & ~generous(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [flattening 61]
72. ~patient(X0) | brave(X0) [cnf transformation 36]
111. ~calm(X0) | kind(X0) [cnf transformation 59]
117. tall(X0) | patient(X0) | old(X0) [cnf transformation 62]
121. ~patient(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 32]
135. calm(john) [cnf transformation 20]
136. ~tall(john) [cnf transformation 20]
139. ~old(john) [cnf transformation 23]
229. ~kind(X0) | ~patient(X0) [subsumption resolution 121,72]
272. kind(john) [resolution 111,135]
278. ~patient(john) [resolution 229,272]
334. patient(john) | old(john) [resolution 117,136]
338. old(john) [subsumption resolution 334,278]
339. $false [subsumption resolution 338,139]
% SZS output end Proof for 7100381251551822908465475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is old. If someone is humble then lucy is not quiet or not old and vice versa. If someone is not tall then lucy is both wise and not tall. If lucy is either not old or not strong then paul is not happy. If susan is wise then someone is happy or wise. Everyone who is both not old and old is kind or wise and vice versa. Everyone who is either not curious or strong is either patient or not generous and vice versa. Everyone who is either calm or generous is not calm or kind and vice versa. If someone is happy or not tall then someone is wise or not generous. Everyone who is not tall or not strong is not rich or not calm and vice versa. Everyone who is either not quiet or not tall is either funny or not brave. If lucy is patient or rich then paul is not patient. If someone is not patient or patient then john is both not funny and not wise. Everyone who is either not generous or not funny is not rich and vice versa. If someone is strong then someone is both not tall and happy and vice versa. Fred is calm or not generous. Someone is funny. Alice is humble or quiet. Someone is either funny or not quiet. Someone is either brave or funny. John is curious. Someone is either quiet or creative. | Lucy is happy. | contradiction | (![X]:(kind(X)=>old(X)))&
((?[X]:(humble(X)))<=>((~quiet(lucy)|~old(lucy))))&
((?[X]:(~tall(X)))=>((wise(lucy)&~tall(lucy))))&
(((~old(lucy)<~>~strong(lucy)))=>(~happy(paul)))&
((wise(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~old(X)&old(X))<=>(kind(X)|wise(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)|kind(X))))&
((?[X]:((happy(X)|~tall(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(funny(X)<~>~brave(X))))&
(((patient(lucy)|rich(lucy)))=>(~patient(paul)))&
((?[X]:((~patient(X)|patient(X))))=>((~funny(john)&~wise(john))))&
(![X]:((~generous(X)<~>~funny(X))<=>~rich(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
((calm(fred)|~generous(fred)))&
(?[X]:(funny(X)))&
((humble(alice)|quiet(alice)))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(curious(john))&
(?[X]:((quiet(X)<~>creative(X)))) | happy(lucy) | [
"p0",
"p5",
"p7",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 5954556739938672849904499
% SZS output start Proof for 5954556739938672849904499
1. ! [X0] : (kind(X0) => old(X0)) [input p0]
6. ! [X0] : ((old(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p5]
8. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (kind(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~tall(X0) | happy(X0)) => ? [X0] : (~generous(X0) | wise(X0)) [input p8]
23. happy(lucy) [input hypothesis]
24. ? [X0] : (~tall(X0) | happy(X0)) => ? [X1] : (~generous(X1) | wise(X1)) [rectify 9]
26. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 1]
30. ? [X1] : (~generous(X1) | wise(X1)) | ! [X0] : (tall(X0) & ~happy(X0)) [ennf transformation 24]
42. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | old(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | old(X0))) [flattening 42]
45. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [flattening 45]
47. ? [X0] : (~generous(X0) | wise(X0)) | ! [X1] : (tall(X1) & ~happy(X1)) [rectify 30]
48. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK2) | wise(sK2)) [choice axiom]
49. (~generous(sK2) | wise(sK2)) | ! [X1] : (tall(X1) & ~happy(X1)) [skolemisation 47,48]
70. old(X0) | ~kind(X0) [cnf transformation 26]
80. ~old(X0) | ~kind(X0) [cnf transformation 43]
81. ~old(X0) | ~wise(X0) [cnf transformation 43]
83. old(X0) | ~wise(X0) [cnf transformation 43]
92. kind(X0) | ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 46]
94. generous(X0) | calm(X0) | calm(X0) [cnf transformation 46]
98. ~generous(sK2) | wise(sK2) | ~happy(X1) [cnf transformation 49]
131. happy(lucy) [cnf transformation 23]
132. kind(X0) | ~calm(X0) | generous(X0) [duplicate literal removal 92]
133. generous(X0) | calm(X0) [duplicate literal removal 94]
188. ~wise(X0) [subsumption resolution 81,83]
189. ~kind(X0) [subsumption resolution 80,70]
190. ~calm(X0) | generous(X0) [subsumption resolution 132,189]
191. generous(X0) [subsumption resolution 190,133]
195. wise(sK2) | ~happy(X1) [subsumption resolution 98,191]
196. ~happy(X1) [subsumption resolution 195,188]
266. $false [subsumption resolution 131,196]
% SZS output end Proof for 5954556739938672849904499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not funny is not calm.
If fred is not creative or old then someone is both not brave and humble and vice versa.
If mary is calm or generous then someone is not brave and vice versa.
Everyone who is both quiet and old is quiet.
Everyone who is both humble and curious is both not strong and not tall and vice versa.
Everyone who is either curious or funny is not tall and vice versa.
Everyone who is tall or curious is either creative or not happy and vice versa.
If someone is both not quiet and curious then fred is either not brave or not humble and vice versa.
If someone is both not old and creative then someone is both brave and not calm and vice versa.
If someone is not funny or calm then john is both quiet and not rich and vice versa.
Everyone who is either generous or not generous is not strong or curious.
If fred is either not kind or happy then someone is rich.
If mary is either rich or tall then someone is not generous or quiet.
If someone is both not funny and not calm then susan is both creative and not happy and vice versa.
If someone is either generous or not wise then someone is creative or not generous.
Everyone who is either happy or patient is not tall or quiet and vice versa.
Mary is not patient.
Lucy is both kind and not funny.
Someone is not kind.
Someone is either not strong or not wise.
Someone is both creative and not wise.
Someone is both strong and wise. | John is not tall. | neutral | (![X]:((~rich(X)<~>~funny(X))=>~calm(X)))&
(((~creative(fred)|old(fred)))<=>(?[X]:((~brave(X)&humble(X)))))&
(((calm(mary)|generous(mary)))<=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)&old(X))=>quiet(X)))&
(![X]:((humble(X)&curious(X))<=>(~strong(X)&~tall(X))))&
(![X]:((curious(X)<~>funny(X))<=>~tall(X)))&
(![X]:((tall(X)|curious(X))<=>(creative(X)<~>~happy(X))))&
((?[X]:((~quiet(X)&curious(X))))<=>((~brave(fred)<~>~humble(fred))))&
((?[X]:((~old(X)&creative(X))))<=>(?[X]:((brave(X)&~calm(X)))))&
((?[X]:((~funny(X)|calm(X))))<=>((quiet(john)&~rich(john))))&
(![X]:((generous(X)<~>~generous(X))=>(~strong(X)|curious(X))))&
(((~kind(fred)<~>happy(fred)))=>(?[X]:(rich(X))))&
(((rich(mary)<~>tall(mary)))=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:((~funny(X)&~calm(X))))<=>((creative(susan)&~happy(susan))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((happy(X)<~>patient(X))<=>(~tall(X)|quiet(X))))&
(~patient(mary))&
((kind(lucy)&~funny(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((strong(X)&wise(X)))) | ~tall(john) | []
| null | 0 |
If lucy is brave then someone is curious.
Everyone who is both curious and not calm is curious or not funny and vice versa.
If alice is rich or not rich then mary is old or not happy.
Everyone who is not quiet or old is either curious or not generous and vice versa.
If mary is generous then alice is not happy or funny.
Everyone who is either not generous or patient is not generous or tall.
If fred is patient or rich then lucy is either not kind or quiet.
If susan is either humble or not funny then mary is funny and vice versa.
If someone is not happy or funny then someone is not calm and vice versa.
Everyone who is either not humble or not curious is both tall and not old.
If someone is old then fred is kind.
Everyone who is wise or calm is both patient and not kind.
If someone is either happy or brave then lucy is funny.
If mary is both not rich and not kind then someone is rich or curious.
If fred is either kind or not rich then someone is both not rich and wise and vice versa.
Everyone who is either patient or curious is not patient or quiet and vice versa.
Alice is rich.
Someone is not calm.
Someone is not humble or not funny.
Fred is humble.
Someone is not happy.
Alice is curious.
Someone is both not wise and not tall.
Someone is funny. | Alice is not calm. | entailment | ((brave(lucy))=>(?[X]:(curious(X))))&
(![X]:((curious(X)&~calm(X))<=>(curious(X)|~funny(X))))&
(((rich(alice)|~rich(alice)))=>((old(mary)|~happy(mary))))&
(![X]:((~quiet(X)|old(X))<=>(curious(X)<~>~generous(X))))&
((generous(mary))=>((~happy(alice)|funny(alice))))&
(![X]:((~generous(X)<~>patient(X))=>(~generous(X)|tall(X))))&
(((patient(fred)|rich(fred)))=>((~kind(lucy)<~>quiet(lucy))))&
(((humble(susan)<~>~funny(susan)))<=>(funny(mary)))&
((?[X]:((~happy(X)|funny(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~humble(X)<~>~curious(X))=>(tall(X)&~old(X))))&
((?[X]:(old(X)))=>(kind(fred)))&
(![X]:((wise(X)|calm(X))=>(patient(X)&~kind(X))))&
((?[X]:((happy(X)<~>brave(X))))=>(funny(lucy)))&
(((~rich(mary)&~kind(mary)))=>(?[X]:((rich(X)|curious(X)))))&
(((kind(fred)<~>~rich(fred)))<=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((patient(X)<~>curious(X))<=>(~patient(X)|quiet(X))))&
(rich(alice))&
(?[X]:(~calm(X)))&
(?[X]:((~humble(X)|~funny(X))))&
(humble(fred))&
(?[X]:(~happy(X)))&
(curious(alice))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:(funny(X))) | ~calm(alice) | [
"p1",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 1604892859971222250502534
% SZS output start Proof for 1604892859971222250502534
2. ! [X0] : ((~calm(X0) & curious(X0)) <=> (~funny(X0) | curious(X0))) [input p1]
22. curious(alice) [input p21]
25. calm(alice) [input hypothesis]
43. ! [X0] : (((~calm(X0) & curious(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (calm(X0) | ~curious(X0)))) [nnf transformation 2]
44. ! [X0] : (((~calm(X0) & curious(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | calm(X0) | ~curious(X0))) [flattening 43]
79. ~calm(X0) | ~curious(X0) [cnf transformation 44]
132. curious(alice) [cnf transformation 22]
136. calm(alice) [cnf transformation 25]
303. ~curious(alice) [resolution 79,136]
304. $false [subsumption resolution 303,132]
% SZS output end Proof for 1604892859971222250502534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If fred is wise or curious then someone is not wise or calm and vice versa.
Everyone who is not strong or brave is either not generous or not old and vice versa.
If lucy is either quiet or not curious then someone is not brave and vice versa.
If alice is calm then someone is patient or old and vice versa.
If someone is both generous and old then someone is not rich or not happy and vice versa.
Everyone who is strong or not rich is either generous or creative.
Everyone who is patient or kind is not generous or not brave and vice versa.
Everyone who is curious is both creative and funny and vice versa.
Everyone who is either not funny or not wise is not curious and vice versa.
Everyone who is both quiet and not curious is either not humble or not curious and vice versa.
Everyone who is funny is not patient.
Everyone who is either not wise or tall is quiet or not happy.
If someone is not wise or not brave then someone is both kind and creative.
Everyone who is patient is creative or not wise.
Everyone who is either not creative or not calm is humble or funny and vice versa.
Someone is either wise or funny.
Paul is old or not funny.
Alice is not happy or old.
Susan is either not brave or creative.
Fred is not generous.
Someone is either wise or calm.
Someone is both not generous and happy. | Susan is curious. | neutral | (((wise(fred)|curious(fred)))<=>(?[X]:((~wise(X)|calm(X)))))&
(![X]:((~strong(X)|brave(X))<=>(~generous(X)<~>~old(X))))&
(((quiet(lucy)<~>~curious(lucy)))<=>(?[X]:(~brave(X))))&
((calm(alice))<=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((strong(X)|~rich(X))=>(generous(X)<~>creative(X))))&
(![X]:((patient(X)|kind(X))<=>(~generous(X)|~brave(X))))&
(![X]:(curious(X)<=>(creative(X)&funny(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>~curious(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(funny(X)=>~patient(X)))&
(![X]:((~wise(X)<~>tall(X))=>(quiet(X)|~happy(X))))&
((?[X]:((~wise(X)|~brave(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(patient(X)=>(creative(X)|~wise(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(humble(X)|funny(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((old(paul)|~funny(paul)))&
((~happy(alice)|old(alice)))&
((~brave(susan)<~>creative(susan)))&
(~generous(fred))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:((~generous(X)&happy(X)))) | curious(susan) | []
| null | 0 |
Everyone who is either strong or not happy is either patient or not brave. If alice is both humble and not brave then susan is either not wise or curious. If someone is either not patient or curious then alice is kind and vice versa. If someone is funny or not wise then susan is either creative or brave. If lucy is not calm or not creative then lucy is either brave or wise. Everyone who is both not strong and not old is either not calm or not creative and vice versa. Everyone who is either not brave or patient is both not happy and old and vice versa. If someone is creative or not rich then someone is tall or brave. If susan is not rich or not happy then someone is tall and vice versa. Everyone who is calm is not generous and vice versa. Everyone who is not brave is strong and vice versa. If someone is generous then someone is kind or not funny. If someone is not humble then someone is old and vice versa. Everyone who is either humble or rich is not quiet. Everyone who is calm is both humble and not quiet and vice versa. If someone is not old or not curious then someone is both generous and not patient. Alice is both not creative and not humble. Mary is patient. Paul is creative. Someone is patient. Paul is both not funny and not tall. Someone is both curious and not quiet. Fred is old. Someone is either not strong or not calm. | Alice is generous. | entailment | (![X]:((strong(X)<~>~happy(X))=>(patient(X)<~>~brave(X))))&
(((humble(alice)&~brave(alice)))=>((~wise(susan)<~>curious(susan))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(kind(alice)))&
((?[X]:((funny(X)|~wise(X))))=>((creative(susan)<~>brave(susan))))&
(((~calm(lucy)|~creative(lucy)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:((~strong(X)&~old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(~happy(X)&old(X))))&
((?[X]:((creative(X)|~rich(X))))=>(?[X]:((tall(X)|brave(X)))))&
(((~rich(susan)|~happy(susan)))<=>(?[X]:(tall(X))))&
(![X]:(calm(X)<=>~generous(X)))&
(![X]:(~brave(X)<=>strong(X)))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)<~>rich(X))=>~quiet(X)))&
(![X]:(calm(X)<=>(humble(X)&~quiet(X))))&
((?[X]:((~old(X)|~curious(X))))=>(?[X]:((generous(X)&~patient(X)))))&
((~creative(alice)&~humble(alice)))&
(patient(mary))&
(creative(paul))&
(?[X]:(patient(X)))&
((~funny(paul)&~tall(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
(old(fred))&
(?[X]:((~strong(X)<~>~calm(X)))) | generous(alice) | [
"p9",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 3002013347097874957657532
% SZS output start Proof for 3002013347097874957657532
10. ! [X0] : (calm(X0) <=> ~generous(X0)) [input p9]
15. ! [X0] : (calm(X0) <=> (~quiet(X0) & humble(X0))) [input p14]
17. ~humble(alice) & ~creative(alice) [input p16]
25. ~generous(alice) [input hypothesis]
61. ! [X0] : ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))) [nnf transformation 10]
69. ! [X0] : ((calm(X0) | (quiet(X0) | ~humble(X0))) & ((~quiet(X0) & humble(X0)) | ~calm(X0))) [nnf transformation 15]
70. ! [X0] : ((calm(X0) | quiet(X0) | ~humble(X0)) & ((~quiet(X0) & humble(X0)) | ~calm(X0))) [flattening 69]
115. generous(X0) | calm(X0) [cnf transformation 61]
122. ~calm(X0) | humble(X0) [cnf transformation 70]
130. ~humble(alice) [cnf transformation 17]
140. ~generous(alice) [cnf transformation 25]
142. 1 <=> humble(alice) [avatar definition]
144. ~humble(alice) <- (~1) [avatar component clause 142]
282. ~1 [avatar split clause 130,142]
303. calm(alice) [resolution 115,140]
309. humble(alice) [resolution 122,303]
310. $false <- (~1) [subsumption resolution 309,144]
311. 1 [avatar contradiction clause 310]
312. $false [avatar sat refutation 282,311]
% SZS output end Proof for 3002013347097874957657532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and kind is either not rich or patient.
Everyone who is brave or not happy is tall or generous and vice versa.
Everyone who is not tall or humble is either wise or curious.
If john is rich then lucy is not generous.
Everyone who is not generous or kind is either not humble or creative and vice versa.
If paul is either not tall or creative then someone is either generous or not brave and vice versa.
Everyone who is either old or generous is either not generous or not patient.
Everyone who is 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.
Fred is quiet or not quiet.
Someone is not old or strong.
Someone is both not old and not brave.
Someone is generous or not wise.
Someone is either not rich or strong.
John is not creative or old.
Alice is strong or wise.
Someone is wise. | Lucy is happy. | entailment | (![X]:((~strong(X)&kind(X))=>(~rich(X)<~>patient(X))))&
(![X]:((brave(X)|~happy(X))<=>(tall(X)|generous(X))))&
(![X]:((~tall(X)|humble(X))=>(wise(X)<~>curious(X))))&
((rich(john))=>(~generous(lucy)))&
(![X]:((~generous(X)|kind(X))<=>(~humble(X)<~>creative(X))))&
(((~tall(paul)<~>creative(paul)))<=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((old(X)<~>generous(X))=>(~generous(X)<~>~patient(X))))&
(![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)))&
((quiet(fred)|~quiet(fred)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
((~creative(john)|old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X))) | happy(lucy) | [
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 215137582123693442792075
% SZS output start Proof for 215137582123693442792075
13. ! [X0] : ((calm(X0) | patient(X0)) <=> (~tall(X0) & creative(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> happy(X0)) [input p14]
25. ~happy(lucy) [input hypothesis]
59. ! [X0] : (((calm(X0) | patient(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 13]
60. ! [X0] : ((calm(X0) | patient(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [flattening 59]
61. ! [X0] : (((~tall(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & calm(X0)))) [nnf transformation 15]
62. ! [X0] : ((~tall(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & calm(X0)))) [flattening 61]
122. ~calm(X0) | ~tall(X0) [cnf transformation 60]
125. calm(X0) | happy(X0) [cnf transformation 62]
126. happy(X0) | tall(X0) [cnf transformation 62]
139. ~happy(lucy) [cnf transformation 25]
252. happy(X0) | ~tall(X0) [resolution 125,122]
254. happy(X0) [subsumption resolution 252,126]
255. $false [resolution 254,139]
% SZS output end Proof for 215137582123693442792075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and strong is either not curious or wise.
Everyone who is either not humble or not wise is either curious or not happy and vice versa.
Everyone who is either not strong or not tall is either calm or rich and vice versa.
If someone is both funny and strong then someone is not tall and vice versa.
If alice is not generous or not rich then someone is strong.
Everyone who is both not curious and not old is either creative or not creative and vice versa.
Everyone who is either strong or not patient is either calm or not rich.
Everyone who is either old or not quiet is not kind or quiet.
Everyone who is humble or not strong is either not humble or humble and vice versa.
Everyone who is wise is creative or tall and vice versa.
Everyone who is both old and not wise is both not creative and funny.
If someone is both kind and rich then someone is both not quiet and not generous and vice versa.
Everyone who is both happy and not brave is not curious.
Everyone who is both wise and not humble is old and vice versa.
If someone is both not creative and brave then alice is both not old and not strong and vice versa.
If lucy is either strong or not funny then fred is kind or patient and vice versa.
John is both tall and not calm.
Someone is both happy and not quiet.
Someone is happy.
Someone is both wise and kind.
Paul is happy or not generous.
Someone is tall.
Someone is both not rich and kind.
Fred is not old or not calm. | John is not patient. | contradiction | (![X]:((tall(X)&strong(X))=>(~curious(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(curious(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(calm(X)<~>rich(X))))&
((?[X]:((funny(X)&strong(X))))<=>(?[X]:(~tall(X))))&
(((~generous(alice)|~rich(alice)))=>(?[X]:(strong(X))))&
(![X]:((~curious(X)&~old(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((strong(X)<~>~patient(X))=>(calm(X)<~>~rich(X))))&
(![X]:((old(X)<~>~quiet(X))=>(~kind(X)|quiet(X))))&
(![X]:((humble(X)|~strong(X))<=>(~humble(X)<~>humble(X))))&
(![X]:(wise(X)<=>(creative(X)|tall(X))))&
(![X]:((old(X)&~wise(X))=>(~creative(X)&funny(X))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:((happy(X)&~brave(X))=>~curious(X)))&
(![X]:((wise(X)&~humble(X))<=>old(X)))&
((?[X]:((~creative(X)&brave(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
((tall(john)&~calm(john)))&
(?[X]:((happy(X)&~quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)&kind(X))))&
((happy(paul)|~generous(paul)))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)&kind(X))))&
((~old(fred)|~calm(fred))) | ~patient(john) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2876916325611783001132560
% SZS output start Proof for 2876916325611783001132560
1. ! [X0] : ((strong(X0) & tall(X0)) => (~curious(X0) <~> wise(X0))) [input p0]
3. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (calm(X0) <~> rich(X0))) [input p2]
6. ! [X0] : ((~old(X0) & ~curious(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p5]
7. ! [X0] : ((strong(X0) <~> ~patient(X0)) => (calm(X0) <~> ~rich(X0))) [input p6]
10. ! [X0] : (wise(X0) <=> (tall(X0) | creative(X0))) [input p9]
17. ~calm(john) & tall(john) [input p16]
25. ~patient(john) [input hypothesis]
28. ! [X0] : ((~curious(X0) <~> wise(X0)) | (~strong(X0) | ~tall(X0))) [ennf transformation 1]
29. ! [X0] : ((~curious(X0) <~> wise(X0)) | ~strong(X0) | ~tall(X0)) [flattening 28]
31. ! [X0] : ((calm(X0) <~> ~rich(X0)) | (strong(X0) <=> ~patient(X0))) [ennf transformation 7]
38. ! [X0] : (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ~strong(X0) | ~tall(X0)) [nnf transformation 29]
40. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 3]
48. ! [X0] : (((~old(X0) & ~curious(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (old(X0) | curious(X0)))) [nnf transformation 6]
49. ! [X0] : (((~old(X0) & ~curious(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | old(X0) | curious(X0))) [flattening 48]
50. ! [X0] : (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) [nnf transformation 31]
54. ! [X0] : ((wise(X0) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | ~wise(X0))) [nnf transformation 10]
55. ! [X0] : ((wise(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | ~wise(X0))) [flattening 54]
81. ~wise(X0) | curious(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 38]
90. ~tall(X0) | calm(X0) | rich(X0) | strong(X0) [cnf transformation 40]
105. ~curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 49]
106. ~curious(X0) | creative(X0) | creative(X0) [cnf transformation 49]
110. ~rich(X0) | calm(X0) | strong(X0) | patient(X0) [cnf transformation 50]
123. ~tall(X0) | wise(X0) [cnf transformation 55]
144. tall(john) [cnf transformation 17]
145. ~calm(john) [cnf transformation 17]
156. ~patient(john) [cnf transformation 25]
162. ~curious(X0) | ~creative(X0) [duplicate literal removal 105]
163. ~curious(X0) | creative(X0) [duplicate literal removal 106]
202. ~curious(X0) [subsumption resolution 162,163]
282. wise(john) [resolution 123,144]
310. curious(john) | ~strong(john) | ~tall(john) [resolution 81,282]
314. ~strong(john) | ~tall(john) [subsumption resolution 310,202]
315. ~strong(john) [subsumption resolution 314,144]
392. calm(john) | rich(john) | strong(john) [resolution 90,144]
395. rich(john) | strong(john) [subsumption resolution 392,145]
396. rich(john) [subsumption resolution 395,315]
504. calm(john) | strong(john) | patient(john) [resolution 110,396]
509. strong(john) | patient(john) [subsumption resolution 504,145]
510. patient(john) [subsumption resolution 509,315]
511. $false [subsumption resolution 510,156]
% SZS output end Proof for 2876916325611783001132560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy is either calm or not creative and vice versa.
If someone is not creative then susan is patient and vice versa.
Everyone who is both generous and tall is not quiet and vice versa.
If alice is humble then lucy is both strong and creative.
If lucy is not old or not happy then john is brave.
Everyone who is either kind or not creative is old or humble and vice versa.
If someone is both not kind and not tall then someone is either not strong or happy.
Everyone who is both rich and humble is not quiet.
Everyone who is both generous and humble is not quiet.
Everyone who is both funny and curious is not brave or calm and vice versa.
Everyone who is both kind and rich is either quiet or not quiet and vice versa.
Everyone who is either generous or not happy is either happy or not rich and vice versa.
Everyone who is not strong is not tall and vice versa.
If someone is patient or not funny then fred is both not tall and calm.
If someone is not quiet or creative then someone is either kind or not old and vice versa.
Everyone who is creative is tall or humble.
Someone is not creative or not strong.
Lucy is either not calm or not brave.
Alice is happy.
Alice is patient.
John is both humble and kind.
Someone is not curious or not quiet.
Someone is not wise. | John is not tall. | contradiction | (![X]:(~happy(X)<=>(calm(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(patient(susan)))&
(![X]:((generous(X)&tall(X))<=>~quiet(X)))&
((humble(alice))=>((strong(lucy)&creative(lucy))))&
(((~old(lucy)|~happy(lucy)))=>(brave(john)))&
(![X]:((kind(X)<~>~creative(X))<=>(old(X)|humble(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((rich(X)&humble(X))=>~quiet(X)))&
(![X]:((generous(X)&humble(X))=>~quiet(X)))&
(![X]:((funny(X)&curious(X))<=>(~brave(X)|calm(X))))&
(![X]:((kind(X)&rich(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:((generous(X)<~>~happy(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~strong(X)<=>~tall(X)))&
((?[X]:((patient(X)|~funny(X))))=>((~tall(fred)&calm(fred))))&
((?[X]:((~quiet(X)|creative(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:(creative(X)=>(tall(X)|humble(X))))&
(?[X]:((~creative(X)|~strong(X))))&
((~calm(lucy)<~>~brave(lucy)))&
(happy(alice))&
(patient(alice))&
((humble(john)&kind(john)))&
(?[X]:((~curious(X)|~quiet(X))))&
(?[X]:(~wise(X))) | ~tall(john) | [
"p2",
"p8",
"p10",
"p11",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 5365004308384269472147658
% SZS output start Proof for 5365004308384269472147658
3. ! [X0] : ((tall(X0) & generous(X0)) <=> ~quiet(X0)) [input p2]
9. ! [X0] : ((humble(X0) & generous(X0)) => ~quiet(X0)) [input p8]
11. ! [X0] : ((rich(X0) & kind(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p10]
12. ! [X0] : ((generous(X0) <~> ~happy(X0)) <=> (happy(X0) <~> ~rich(X0))) [input p11]
21. kind(john) & humble(john) [input p20]
24. ~tall(john) [input hypothesis]
33. ! [X0] : (~quiet(X0) | (~humble(X0) | ~generous(X0))) [ennf transformation 9]
34. ! [X0] : (~quiet(X0) | ~humble(X0) | ~generous(X0)) [flattening 33]
43. ! [X0] : (((tall(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | (~tall(X0) | ~generous(X0)))) [nnf transformation 3]
44. ! [X0] : (((tall(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | ~tall(X0) | ~generous(X0))) [flattening 43]
53. ! [X0] : (((rich(X0) & kind(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (~rich(X0) | ~kind(X0)))) [nnf transformation 11]
54. ! [X0] : (((rich(X0) & kind(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | ~rich(X0) | ~kind(X0))) [flattening 53]
55. ! [X0] : ((((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))))) [nnf transformation 12]
75. quiet(X0) | tall(X0) [cnf transformation 44]
89. ~humble(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 34]
99. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
100. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 54]
102. ~rich(X0) | happy(X0) | generous(X0) | happy(X0) [cnf transformation 55]
105. ~happy(X0) | generous(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 55]
127. humble(john) [cnf transformation 21]
130. ~tall(john) [cnf transformation 24]
131. ~rich(X0) | happy(X0) | generous(X0) [duplicate literal removal 102]
133. ~happy(X0) | generous(X0) | ~rich(X0) [duplicate literal removal 105]
137. rich(X0) | ~quiet(X0) [duplicate literal removal 99]
138. rich(X0) | quiet(X0) [duplicate literal removal 100]
193. rich(X0) [subsumption resolution 137,138]
195. ~happy(X0) | generous(X0) [subsumption resolution 133,193]
196. happy(X0) | generous(X0) [subsumption resolution 131,193]
197. generous(X0) [subsumption resolution 196,195]
353. ~quiet(john) | ~generous(john) [resolution 89,127]
357. ~quiet(john) [subsumption resolution 353,197]
366. tall(john) [resolution 357,75]
368. $false [subsumption resolution 366,130]
% SZS output end Proof for 5365004308384269472147658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both humble and not calm. Everyone who is not happy is creative or not wise and vice versa. If someone is not brave then lucy is not kind. Everyone who is either wise or curious is both not wise and not patient. If mary is either kind or not old then someone is calm or strong and vice versa. Everyone who is either brave or rich is both not old and funny. If lucy is both not generous and not old then someone is not tall. If paul is not creative then someone is tall or not funny and vice versa. Everyone who is humble or calm is either rich or happy and vice versa. If mary is wise or not quiet then lucy is both not quiet and rich and vice versa. Everyone who is humble or not kind is not rich. Everyone who is not humble is either quiet or not kind and vice versa. Everyone who is both not humble and not brave is not old and vice versa. If john is both calm and kind then someone is old and vice versa. Everyone who is both humble and patient is both not generous and quiet and vice versa. If someone is not brave then someone is both brave and not wise. Someone is both rich and not humble. Lucy is either not creative or not funny. Lucy is strong. Someone is not curious or patient. Lucy is brave. Someone is not curious or tall. | Mary is old. | entailment | (![X]:(~strong(X)=>(humble(X)&~calm(X))))&
(![X]:(~happy(X)<=>(creative(X)|~wise(X))))&
((?[X]:(~brave(X)))=>(~kind(lucy)))&
(![X]:((wise(X)<~>curious(X))=>(~wise(X)&~patient(X))))&
(((kind(mary)<~>~old(mary)))<=>(?[X]:((calm(X)|strong(X)))))&
(![X]:((brave(X)<~>rich(X))=>(~old(X)&funny(X))))&
(((~generous(lucy)&~old(lucy)))=>(?[X]:(~tall(X))))&
((~creative(paul))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((humble(X)|calm(X))<=>(rich(X)<~>happy(X))))&
(((wise(mary)|~quiet(mary)))<=>((~quiet(lucy)&rich(lucy))))&
(![X]:((humble(X)|~kind(X))=>~rich(X)))&
(![X]:(~humble(X)<=>(quiet(X)<~>~kind(X))))&
(![X]:((~humble(X)&~brave(X))<=>~old(X)))&
(((calm(john)&kind(john)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)&patient(X))<=>(~generous(X)&quiet(X))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)&~wise(X)))))&
(?[X]:((rich(X)&~humble(X))))&
((~creative(lucy)<~>~funny(lucy)))&
(strong(lucy))&
(?[X]:((~curious(X)|patient(X))))&
(brave(lucy))&
(?[X]:((~curious(X)|tall(X)))) | old(mary) | [
"p2",
"p5",
"p10",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1563552644773010495791575
% SZS output start Proof for 1563552644773010495791575
3. ? [X0] : ~brave(X0) => ~kind(lucy) [input p2]
6. ! [X0] : ((brave(X0) <~> rich(X0)) => (funny(X0) & ~old(X0))) [input p5]
11. ! [X0] : ((~kind(X0) | humble(X0)) => ~rich(X0)) [input p10]
13. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> ~old(X0)) [input p12]
21. brave(lucy) [input p20]
23. ~old(mary) [input hypothesis]
26. ~kind(lucy) | ! [X0] : brave(X0) [ennf transformation 3]
28. ! [X0] : ((funny(X0) & ~old(X0)) | (brave(X0) <=> rich(X0))) [ennf transformation 6]
31. ! [X0] : (~rich(X0) | (kind(X0) & ~humble(X0))) [ennf transformation 11]
40. ! [X0] : ((funny(X0) & ~old(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) [nnf transformation 28]
52. ! [X0] : (((~brave(X0) & ~humble(X0)) | old(X0)) & (~old(X0) | (brave(X0) | humble(X0)))) [nnf transformation 13]
53. ! [X0] : (((~brave(X0) & ~humble(X0)) | old(X0)) & (~old(X0) | brave(X0) | humble(X0))) [flattening 52]
76. ~kind(lucy) | brave(X0) [cnf transformation 26]
87. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 40]
107. ~rich(X0) | kind(X0) [cnf transformation 31]
114. ~brave(X0) | old(X0) [cnf transformation 53]
130. brave(lucy) [cnf transformation 21]
132. ~old(mary) [cnf transformation 23]
135. 1 <=> ! [X0] : brave(X0) [avatar definition]
136. brave(X0) <- (1) [avatar component clause 135]
138. 2 <=> kind(lucy) [avatar definition]
140. ~kind(lucy) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 76,138,135]
150. 5 <=> old(mary) [avatar definition]
151. ~old(mary) <- (~5) [avatar component clause 150]
173. 9 <=> old(lucy) [avatar definition]
175. old(lucy) <- (9) [avatar component clause 173]
207. 17 <=> rich(lucy) [avatar definition]
208. rich(lucy) <- (17) [avatar component clause 207]
279. ~5 [avatar split clause 132,150]
288. kind(lucy) <- (17) [resolution 107,208]
289. $false <- (~2, 17) [subsumption resolution 288,140]
290. 2 | ~17 [avatar contradiction clause 289]
293. old(lucy) [resolution 114,130]
299. 9 [avatar split clause 293,173]
305. rich(lucy) | ~brave(lucy) <- (9) [resolution 87,175]
321. rich(lucy) <- (9) [subsumption resolution 305,130]
322. 17 | ~9 [avatar split clause 321,173,207]
323. old(X0) <- (1) [resolution 136,114]
336. $false <- (1, ~5) [resolution 323,151]
338. ~1 | 5 [avatar contradiction clause 336]
340. $false [avatar sat refutation 141,279,290,299,322,338]
% SZS output end Proof for 1563552644773010495791575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not wise is either generous or not creative. Everyone who is either not brave or not generous is both rich and strong. If lucy is curious or wise then someone is not kind or generous and vice versa. If someone is generous or rich then mary is both wise and creative and vice versa. Everyone who is either not creative or not strong is both strong and not brave and vice versa. Everyone who is curious is creative and vice versa. If someone is not funny or not curious then someone is not strong or not brave and vice versa. If alice is both not humble and quiet then susan is either wise or happy and vice versa. Everyone who is either brave or not tall is both calm and rich. If mary is both not rich and rich then susan is both wise and funny and vice versa. Everyone who is both generous and not strong is humble. If alice is both not patient and wise then john is either not rich or humble and vice versa. Everyone who is either wise or funny is not calm and vice versa. If someone is not calm or not wise then someone is both funny and rich. If someone is not old then alice is old or happy and vice versa. Everyone who is creative or not kind is not kind or brave and vice versa. Someone is not tall or funny. John is both not tall and patient. Someone is both not kind and humble. John is either not strong or kind. Someone is both not generous and kind. Someone is patient or not curious. Someone is wise. | Mary is not wise. | contradiction | (![X]:((generous(X)&~wise(X))=>(generous(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(rich(X)&strong(X))))&
(((curious(lucy)|wise(lucy)))<=>(?[X]:((~kind(X)|generous(X)))))&
((?[X]:((generous(X)|rich(X))))<=>((wise(mary)&creative(mary))))&
(![X]:((~creative(X)<~>~strong(X))<=>(strong(X)&~brave(X))))&
(![X]:(curious(X)<=>creative(X)))&
((?[X]:((~funny(X)|~curious(X))))<=>(?[X]:((~strong(X)|~brave(X)))))&
(((~humble(alice)&quiet(alice)))<=>((wise(susan)<~>happy(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(calm(X)&rich(X))))&
(((~rich(mary)&rich(mary)))<=>((wise(susan)&funny(susan))))&
(![X]:((generous(X)&~strong(X))=>humble(X)))&
(((~patient(alice)&wise(alice)))<=>((~rich(john)<~>humble(john))))&
(![X]:((wise(X)<~>funny(X))<=>~calm(X)))&
((?[X]:((~calm(X)|~wise(X))))=>(?[X]:((funny(X)&rich(X)))))&
((?[X]:(~old(X)))<=>((old(alice)|happy(alice))))&
(![X]:((creative(X)|~kind(X))<=>(~kind(X)|brave(X))))&
(?[X]:((~tall(X)|funny(X))))&
((~tall(john)&patient(john)))&
(?[X]:((~kind(X)&humble(X))))&
((~strong(john)<~>kind(john)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:(wise(X))) | ~wise(mary) | [
"p3",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 6618062561658452616635598
% SZS output start Proof for 6618062561658452616635598
4. ? [X0] : (rich(X0) | generous(X0)) <=> (creative(mary) & wise(mary)) [input p3]
14. ? [X0] : (~wise(X0) | ~calm(X0)) => ? [X0] : (rich(X0) & funny(X0)) [input p13]
24. ~wise(mary) [input hypothesis]
26. ? [X0] : (~wise(X0) | ~calm(X0)) => ? [X1] : (rich(X1) & funny(X1)) [rectify 14]
35. ? [X1] : (rich(X1) & funny(X1)) | ! [X0] : (wise(X0) & calm(X0)) [ennf transformation 26]
43. (? [X0] : (rich(X0) | generous(X0)) | (~creative(mary) | ~wise(mary))) & ((creative(mary) & wise(mary)) | ! [X0] : (~rich(X0) & ~generous(X0))) [nnf transformation 4]
44. (? [X0] : (rich(X0) | generous(X0)) | ~creative(mary) | ~wise(mary)) & ((creative(mary) & wise(mary)) | ! [X0] : (~rich(X0) & ~generous(X0))) [flattening 43]
45. (? [X0] : (rich(X0) | generous(X0)) | ~creative(mary) | ~wise(mary)) & ((creative(mary) & wise(mary)) | ! [X1] : (~rich(X1) & ~generous(X1))) [rectify 44]
46. ? [X0] : (rich(X0) | generous(X0)) => (rich(sK1) | generous(sK1)) [choice axiom]
47. ((rich(sK1) | generous(sK1)) | ~creative(mary) | ~wise(mary)) & ((creative(mary) & wise(mary)) | ! [X1] : (~rich(X1) & ~generous(X1))) [skolemisation 45,46]
64. ? [X0] : (rich(X0) & funny(X0)) | ! [X1] : (wise(X1) & calm(X1)) [rectify 35]
65. ? [X0] : (rich(X0) & funny(X0)) => (rich(sK4) & funny(sK4)) [choice axiom]
66. (rich(sK4) & funny(sK4)) | ! [X1] : (wise(X1) & calm(X1)) [skolemisation 64,65]
96. wise(mary) | ~rich(X1) [cnf transformation 47]
138. rich(sK4) | wise(X1) [cnf transformation 66]
157. ~wise(mary) [cnf transformation 24]
188. 7 <=> wise(mary) [avatar definition]
190. ~wise(mary) <- (~7) [avatar component clause 188]
205. 11 <=> ! [X1] : ~rich(X1) [avatar definition]
206. ~rich(X1) <- (11) [avatar component clause 205]
209. 11 | 7 [avatar split clause 96,188,205]
298. 30 <=> ! [X1] : wise(X1) [avatar definition]
299. wise(X1) <- (30) [avatar component clause 298]
301. 31 <=> rich(sK4) [avatar definition]
303. rich(sK4) <- (31) [avatar component clause 301]
304. 30 | 31 [avatar split clause 138,301,298]
361. ~7 [avatar split clause 157,188]
366. $false <- (~7, 30) [subsumption resolution 190,299]
367. 7 | ~30 [avatar contradiction clause 366]
368. $false <- (11, 31) [subsumption resolution 303,206]
369. ~11 | ~31 [avatar contradiction clause 368]
370. $false [avatar sat refutation 209,304,361,367,369]
% SZS output end Proof for 6618062561658452616635598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is wise or not humble then lucy is not generous or not creative and vice versa. If someone is both humble and wise then someone is not rich. If alice is calm then someone is not happy. Everyone who is either not calm or strong is creative. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. Lucy is not kind. Susan is both generous and not old. Someone is humble or tall. Susan is both wise and humble. Mary is both old and not tall. Someone is not calm. Someone is both not rich and funny. Someone is both not quiet and funny. | Fred is funny. | neutral | (((wise(mary)|~humble(mary)))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:((humble(X)&wise(X))))=>(?[X]:(~rich(X))))&
((calm(alice))=>(?[X]:(~happy(X))))&
(![X]:((~calm(X)<~>strong(X))=>creative(X)))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
(~kind(lucy))&
((generous(susan)&~old(susan)))&
(?[X]:((humble(X)|tall(X))))&
((wise(susan)&humble(susan)))&
((old(mary)&~tall(mary)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((~quiet(X)&funny(X)))) | funny(fred) | []
| null | 0 |
If mary is either not curious or old then someone is both not kind and not funny and vice versa.
If fred is either not humble or humble then someone is either not rich or not tall and vice versa.
If someone is both patient and not tall then mary is generous.
Everyone who is not curious or creative is not curious and vice versa.
If someone is either curious or not funny then paul is curious or not wise.
If someone is either not wise or not humble then someone is both not quiet and not old and vice versa.
Everyone who is not creative or not brave is either old or not humble.
If susan is rich or not quiet then susan is either not creative or not kind and vice versa.
Everyone who is not calm is rich or generous.
Everyone who is both not calm and humble is both generous and not old.
Everyone who is either quiet or happy is creative.
If someone is generous or creative then someone is not calm and vice versa.
If fred is both not strong and not rich then mary is not quiet.
If mary is both not patient and old then someone is not curious or curious and vice versa.
Everyone who is either not kind or not funny is both not humble and not patient and vice versa.
Everyone who is not funny or kind is either patient or not tall.
Paul is patient.
Someone is tall or not old.
Someone is not wise or brave.
Someone is tall.
Paul is both not calm and rich.
Someone is curious or old.
Someone is not funny.
Fred is not tall. | Susan is tall. | neutral | (((~curious(mary)<~>old(mary)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(((~humble(fred)<~>humble(fred)))<=>(?[X]:((~rich(X)<~>~tall(X)))))&
((?[X]:((patient(X)&~tall(X))))=>(generous(mary)))&
(![X]:((~curious(X)|creative(X))<=>~curious(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>((curious(paul)|~wise(paul))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:((~creative(X)|~brave(X))=>(old(X)<~>~humble(X))))&
(((rich(susan)|~quiet(susan)))<=>((~creative(susan)<~>~kind(susan))))&
(![X]:(~calm(X)=>(rich(X)|generous(X))))&
(![X]:((~calm(X)&humble(X))=>(generous(X)&~old(X))))&
(![X]:((quiet(X)<~>happy(X))=>creative(X)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:(~calm(X))))&
(((~strong(fred)&~rich(fred)))=>(~quiet(mary)))&
(((~patient(mary)&old(mary)))<=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~funny(X)|kind(X))=>(patient(X)<~>~tall(X))))&
(patient(paul))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:(tall(X)))&
((~calm(paul)&rich(paul)))&
(?[X]:((curious(X)|old(X))))&
(?[X]:(~funny(X)))&
(~tall(fred)) | tall(susan) | []
| null | 0 |
Everyone who is either not calm or quiet is both not happy and calm.
Everyone who is both patient and old is both curious and calm.
Everyone who is not brave or quiet is not strong and vice versa.
If fred is either not quiet or not kind then susan is either kind or not humble and vice versa.
If john is not happy then someone is both not happy and rich.
Everyone who is both not tall and quiet is both rich and not curious.
If paul is either not wise or not kind then someone is both wise and not kind and vice versa.
If someone is creative or not funny then someone is both not patient and strong and vice versa.
If susan is both not tall and not calm then someone is calm and vice versa.
Everyone who is not humble or patient is funny.
Everyone who is not rich or not quiet is not happy or not funny.
Everyone who is both strong and not tall is either kind or generous.
Everyone who is rich is not old or not quiet and vice versa.
Everyone who is either patient or happy is either brave or generous and vice versa.
Everyone who is tall is not rich or not kind.
Everyone who is not old is not curious.
Paul is either kind or happy.
Susan is not rich.
Susan is patient or not strong.
Someone is generous.
Someone is kind or quiet.
Susan is not creative or not funny.
John is not tall.
Alice is tall. | John is not curious. | entailment | (![X]:((~calm(X)<~>quiet(X))=>(~happy(X)&calm(X))))&
(![X]:((patient(X)&old(X))=>(curious(X)&calm(X))))&
(![X]:((~brave(X)|quiet(X))<=>~strong(X)))&
(((~quiet(fred)<~>~kind(fred)))<=>((kind(susan)<~>~humble(susan))))&
((~happy(john))=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:((~tall(X)&quiet(X))=>(rich(X)&~curious(X))))&
(((~wise(paul)<~>~kind(paul)))<=>(?[X]:((wise(X)&~kind(X)))))&
((?[X]:((creative(X)|~funny(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
(((~tall(susan)&~calm(susan)))<=>(?[X]:(calm(X))))&
(![X]:((~humble(X)|patient(X))=>funny(X)))&
(![X]:((~rich(X)|~quiet(X))=>(~happy(X)|~funny(X))))&
(![X]:((strong(X)&~tall(X))=>(kind(X)<~>generous(X))))&
(![X]:(rich(X)<=>(~old(X)|~quiet(X))))&
(![X]:((patient(X)<~>happy(X))<=>(brave(X)<~>generous(X))))&
(![X]:(tall(X)=>(~rich(X)|~kind(X))))&
(![X]:(~old(X)=>~curious(X)))&
((kind(paul)<~>happy(paul)))&
(~rich(susan))&
((patient(susan)|~strong(susan)))&
(?[X]:(generous(X)))&
(?[X]:((kind(X)|quiet(X))))&
((~creative(susan)|~funny(susan)))&
(~tall(john))&
(tall(alice)) | ~curious(john) | [
"p0",
"p5",
"p8",
"p12",
"p17",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 3585115745536416769935374
% SZS output start Proof for 3585115745536416769935374
1. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (calm(X0) & ~happy(X0))) [input p0]
6. ! [X0] : ((quiet(X0) & ~tall(X0)) => (~curious(X0) & rich(X0))) [input p5]
9. (~calm(susan) & ~tall(susan)) <=> ? [X0] : calm(X0) [input p8]
13. ! [X0] : (rich(X0) <=> (~quiet(X0) | ~old(X0))) [input p12]
18. ~rich(susan) [input p17]
23. ~tall(john) [input p22]
25. curious(john) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~happy(X0)) | (~calm(X0) <=> quiet(X0))) [ennf transformation 1]
31. ! [X0] : ((~curious(X0) & rich(X0)) | (~quiet(X0) | tall(X0))) [ennf transformation 6]
32. ! [X0] : ((~curious(X0) & rich(X0)) | ~quiet(X0) | tall(X0)) [flattening 31]
41. ! [X0] : ((calm(X0) & ~happy(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 27]
56. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (calm(susan) | tall(susan))) [nnf transformation 9]
57. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | calm(susan) | tall(susan)) [flattening 56]
58. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | calm(susan) | tall(susan)) [rectify 57]
59. ? [X1] : calm(X1) => calm(sK4) [choice axiom]
60. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (calm(sK4) | calm(susan) | tall(susan)) [skolemisation 58,59]
62. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 13]
63. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ~rich(X0))) [flattening 62]
72. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 41]
89. ~quiet(X0) | rich(X0) | tall(X0) [cnf transformation 32]
90. ~curious(X0) | ~quiet(X0) | tall(X0) [cnf transformation 32]
103. ~tall(susan) | ~calm(X0) [cnf transformation 60]
113. rich(X0) | quiet(X0) [cnf transformation 63]
126. ~rich(susan) [cnf transformation 18]
131. ~tall(john) [cnf transformation 23]
133. curious(john) [cnf transformation 25]
134. quiet(X0) | calm(X0) [duplicate literal removal 72]
229. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
230. ~calm(X0) <- (20) [avatar component clause 229]
237. 22 <=> tall(susan) [avatar definition]
240. 20 | ~22 [avatar split clause 103,237,229]
285. quiet(susan) [resolution 113,126]
307. rich(susan) | tall(susan) [resolution 89,285]
312. ~quiet(john) | tall(john) [resolution 90,133]
313. ~quiet(john) [subsumption resolution 312,131]
314. calm(john) [resolution 313,134]
315. $false <- (20) [subsumption resolution 314,230]
316. ~20 [avatar contradiction clause 315]
326. tall(susan) [subsumption resolution 307,126]
327. 22 [avatar split clause 326,237]
328. $false [avatar sat refutation 240,316,327]
% SZS output end Proof for 3585115745536416769935374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not happy is either not rich or not tall and vice versa.
Everyone who is humble or not creative is not brave or not wise.
Everyone who is not kind is not old.
If john is both not generous and brave then paul is both not brave and not funny and vice versa.
If someone is either wise or kind then someone is either rich or strong.
If alice is both not wise and not brave then someone is tall or not humble.
Everyone who is both not kind and not rich is not old or not creative and vice versa.
Everyone who is old is strong or not calm.
If someone is both not tall and not strong then someone is funny.
Everyone who is not quiet is not funny and vice versa.
Everyone who is generous is either not brave or not old.
If someone is both not rich and humble then someone is either quiet or not calm and vice versa.
Everyone who is not humble or not generous is either not calm or not tall.
If alice is not creative then fred is either not generous or not tall and vice versa.
If fred is happy then someone is either not happy or not rich.
If someone is brave or funny then someone is either not calm or not funny.
Someone is patient or not kind.
Alice is either not quiet or strong.
Paul is both not patient and calm.
Someone is either kind or brave.
Someone is both old and calm.
Susan is not kind or calm.
Someone is either funny or curious.
Susan is both not kind and not happy. | Susan is rich. | contradiction | (![X]:((brave(X)|~happy(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((humble(X)|~creative(X))=>(~brave(X)|~wise(X))))&
(![X]:(~kind(X)=>~old(X)))&
(((~generous(john)&brave(john)))<=>((~brave(paul)&~funny(paul))))&
((?[X]:((wise(X)<~>kind(X))))=>(?[X]:((rich(X)<~>strong(X)))))&
(((~wise(alice)&~brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~old(X)|~creative(X))))&
(![X]:(old(X)=>(strong(X)|~calm(X))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:(funny(X))))&
(![X]:(~quiet(X)<=>~funny(X)))&
(![X]:(generous(X)=>(~brave(X)<~>~old(X))))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~generous(X))=>(~calm(X)<~>~tall(X))))&
((~creative(alice))<=>((~generous(fred)<~>~tall(fred))))&
((happy(fred))=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((brave(X)|funny(X))))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(?[X]:((patient(X)|~kind(X))))&
((~quiet(alice)<~>strong(alice)))&
((~patient(paul)&calm(paul)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:((old(X)&calm(X))))&
((~kind(susan)|calm(susan)))&
(?[X]:((funny(X)<~>curious(X))))&
((~kind(susan)&~happy(susan))) | rich(susan) | [
"p2",
"p6",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 8258837468839004379504877
% SZS output start Proof for 8258837468839004379504877
3. ! [X0] : (~kind(X0) => ~old(X0)) [input p2]
7. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (~creative(X0) | ~old(X0))) [input p6]
24. ~happy(susan) & ~kind(susan) [input p23]
25. rich(susan) [input hypothesis]
32. ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 3]
53. ! [X0] : (((~rich(X0) & ~kind(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 7]
54. ! [X0] : (((~rich(X0) & ~kind(X0)) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | rich(X0) | kind(X0))) [flattening 53]
93. ~old(X0) | kind(X0) [cnf transformation 32]
106. ~rich(X0) | old(X0) [cnf transformation 54]
146. ~kind(susan) [cnf transformation 24]
148. rich(susan) [cnf transformation 25]
321. 38 <=> kind(susan) [avatar definition]
323. ~kind(susan) <- (~38) [avatar component clause 321]
339. ~38 [avatar split clause 146,321]
346. old(susan) [resolution 106,148]
348. kind(susan) [resolution 346,93]
349. $false <- (~38) [subsumption resolution 348,323]
350. 38 [avatar contradiction clause 349]
351. $false [avatar sat refutation 339,350]
% SZS output end Proof for 8258837468839004379504877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and not quiet then someone is both not creative and not old.
If someone is brave or old then lucy is wise and vice versa.
If paul is not rich then someone is both not strong and not happy.
Everyone who is not rich is kind and vice versa.
Everyone who is either not strong or not generous is either not funny or not patient and vice versa.
Everyone who is not tall is funny or not tall and vice versa.
If someone is kind or not rich then fred is not funny or brave.
If alice is curious or not tall then mary is not old and vice versa.
If someone is not old or generous then someone is either not rich or strong.
If alice is not funny then someone is quiet or not funny.
If fred is not strong or not brave then mary is either funny or quiet.
Everyone who is not rich or not creative is creative or strong and vice versa.
Everyone who is both not generous and curious is both not funny and strong and vice versa.
Everyone who is either humble or not humble is either funny or not happy and vice versa.
Everyone who is brave or not curious is rich.
Everyone who is wise is generous or not wise and vice versa.
Someone is not creative.
Alice is either not quiet or patient.
Alice is strong or not patient.
Mary is not tall.
Alice is either creative or not strong.
Mary is either creative or not calm.
Paul is patient. | Alice is quiet. | entailment | ((?[X]:((~brave(X)&~quiet(X))))=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((brave(X)|old(X))))<=>(wise(lucy)))&
((~rich(paul))=>(?[X]:((~strong(X)&~happy(X)))))&
(![X]:(~rich(X)<=>kind(X)))&
(![X]:((~strong(X)<~>~generous(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|~tall(X))))&
((?[X]:((kind(X)|~rich(X))))=>((~funny(fred)|brave(fred))))&
(((curious(alice)|~tall(alice)))<=>(~old(mary)))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
((~funny(alice))=>(?[X]:((quiet(X)|~funny(X)))))&
(((~strong(fred)|~brave(fred)))=>((funny(mary)<~>quiet(mary))))&
(![X]:((~rich(X)|~creative(X))<=>(creative(X)|strong(X))))&
(![X]:((~generous(X)&curious(X))<=>(~funny(X)&strong(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((brave(X)|~curious(X))=>rich(X)))&
(![X]:(wise(X)<=>(generous(X)|~wise(X))))&
(?[X]:(~creative(X)))&
((~quiet(alice)<~>patient(alice)))&
((strong(alice)|~patient(alice)))&
(~tall(mary))&
((creative(alice)<~>~strong(alice)))&
((creative(mary)<~>~calm(mary)))&
(patient(paul)) | quiet(alice) | [
"p4",
"p11",
"p12",
"p15",
"p17",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 5320780463062108214178381
% SZS output start Proof for 5320780463062108214178381
5. ! [X0] : ((~strong(X0) <~> ~generous(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p4]
12. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (strong(X0) | creative(X0))) [input p11]
13. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (strong(X0) & ~funny(X0))) [input p12]
16. ! [X0] : (wise(X0) <=> (~wise(X0) | generous(X0))) [input p15]
18. ~quiet(alice) <~> patient(alice) [input p17]
21. creative(alice) <~> ~strong(alice) [input p20]
24. ~quiet(alice) [input hypothesis]
45. ! [X0] : ((((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))))) [nnf transformation 5]
57. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 12]
58. ! [X0] : ((~creative(X0) | ~rich(X0) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | (creative(X0) & rich(X0)))) [flattening 57]
59. ! [X0] : (((curious(X0) & ~generous(X0)) | (~strong(X0) | funny(X0))) & ((strong(X0) & ~funny(X0)) | (~curious(X0) | generous(X0)))) [nnf transformation 13]
60. ! [X0] : (((curious(X0) & ~generous(X0)) | ~strong(X0) | funny(X0)) & ((strong(X0) & ~funny(X0)) | ~curious(X0) | generous(X0))) [flattening 59]
62. ! [X0] : ((wise(X0) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | ~wise(X0))) [nnf transformation 16]
63. ! [X0] : ((wise(X0) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | ~wise(X0))) [flattening 62]
66. (~patient(alice) | quiet(alice)) & (patient(alice) | ~quiet(alice)) [nnf transformation 18]
67. (strong(alice) | ~creative(alice)) & (~strong(alice) | creative(alice)) [nnf transformation 21]
83. ~funny(X0) | ~strong(X0) | ~generous(X0) | patient(X0) [cnf transformation 45]
104. strong(X0) | creative(X0) | creative(X0) [cnf transformation 58]
109. ~generous(X0) | ~strong(X0) | funny(X0) [cnf transformation 60]
121. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 63]
123. wise(X0) | wise(X0) [cnf transformation 63]
126. ~patient(alice) | quiet(alice) [cnf transformation 66]
130. strong(alice) | ~creative(alice) [cnf transformation 67]
134. ~quiet(alice) [cnf transformation 24]
135. ~wise(X0) | generous(X0) [duplicate literal removal 121]
136. wise(X0) [duplicate literal removal 123]
141. strong(X0) | creative(X0) [duplicate literal removal 104]
241. 23 <=> funny(alice) [avatar definition]
243. funny(alice) <- (23) [avatar component clause 241]
271. generous(X0) [subsumption resolution 135,136]
273. 29 <=> quiet(alice) [avatar definition]
277. 30 <=> patient(alice) [avatar definition]
279. ~patient(alice) <- (~30) [avatar component clause 277]
280. 29 | ~30 [avatar split clause 126,277,273]
283. 31 <=> strong(alice) [avatar definition]
285. strong(alice) <- (31) [avatar component clause 283]
287. strong(alice) [subsumption resolution 130,141]
288. 31 [avatar split clause 287,283]
300. ~29 [avatar split clause 134,273]
312. ~strong(X0) | funny(X0) [resolution 109,271]
313. funny(alice) <- (31) [resolution 312,285]
315. 23 | ~31 [avatar split clause 313,283,241]
355. ~strong(alice) | ~generous(alice) | patient(alice) <- (23) [resolution 83,243]
367. ~generous(alice) | patient(alice) <- (23, 31) [subsumption resolution 355,285]
368. patient(alice) <- (23, 31) [subsumption resolution 367,271]
369. $false <- (23, ~30, 31) [subsumption resolution 368,279]
370. ~23 | 30 | ~31 [avatar contradiction clause 369]
373. $false [avatar sat refutation 280,288,300,315,370]
% SZS output end Proof for 5320780463062108214178381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not calm and curious then someone is not brave or not creative and vice versa.
Everyone who is either curious or brave is quiet and vice versa.
If someone is quiet then john is not brave and vice versa.
If alice is either patient or strong then mary is both not creative and not tall.
Everyone who is not strong is both tall and not creative.
If someone is kind then someone is not patient.
If someone is generous or not patient then someone is not creative or not funny.
Everyone who is happy or not strong is either not tall or calm.
Everyone who is not generous is both not kind and creative and vice versa.
Everyone who is tall is both not old and funny.
Everyone who is quiet is both tall and calm.
Everyone who is both generous and not happy is funny or not tall.
If someone is either curious or generous then susan is either patient or not brave and vice versa.
Everyone who is either brave or not tall is either strong or not curious and vice versa.
If lucy is not patient then lucy is brave or patient.
John is either funny or not brave.
Someone is either old or curious.
Someone is not humble.
Someone is not old.
Mary is kind or quiet.
Mary is strong.
Alice is happy. | John is not tall. | contradiction | (((~calm(susan)&curious(susan)))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((curious(X)<~>brave(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(((patient(alice)<~>strong(alice)))=>((~creative(mary)&~tall(mary))))&
(![X]:(~strong(X)=>(tall(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:(~patient(X))))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((happy(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:(~generous(X)<=>(~kind(X)&creative(X))))&
(![X]:(tall(X)=>(~old(X)&funny(X))))&
(![X]:(quiet(X)=>(tall(X)&calm(X))))&
(![X]:((generous(X)&~happy(X))=>(funny(X)|~tall(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((brave(X)<~>~tall(X))<=>(strong(X)<~>~curious(X))))&
((~patient(lucy))=>((brave(lucy)|patient(lucy))))&
((funny(john)<~>~brave(john)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
((kind(mary)|quiet(mary)))&
(strong(mary))&
(happy(alice)) | ~tall(john) | [
"p1",
"p2",
"p4",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8862563169033478874803702
% SZS output start Proof for 8862563169033478874803702
2. ! [X0] : ((curious(X0) <~> brave(X0)) <=> quiet(X0)) [input p1]
3. ? [X0] : quiet(X0) <=> ~brave(john) [input p2]
5. ! [X0] : (~strong(X0) => (~creative(X0) & tall(X0))) [input p4]
11. ! [X0] : (quiet(X0) => (calm(X0) & tall(X0))) [input p10]
14. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p13]
23. ~tall(john) [input hypothesis]
28. ! [X0] : ((~creative(X0) & tall(X0)) | strong(X0)) [ennf transformation 5]
33. ! [X0] : ((calm(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 11]
43. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ~quiet(X0)) & (quiet(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 2]
44. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X0] : ~quiet(X0)) [nnf transformation 3]
45. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
47. (quiet(sK1) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
62. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 14]
74. ~curious(X0) | brave(X0) | quiet(X0) [cnf transformation 43]
75. ~brave(X0) | curious(X0) | quiet(X0) [cnf transformation 43]
78. ~brave(john) | ~quiet(X1) [cnf transformation 47]
84. tall(X0) | strong(X0) [cnf transformation 28]
98. ~quiet(X0) | tall(X0) [cnf transformation 33]
112. curious(X0) | ~strong(X0) | brave(X0) | tall(X0) [cnf transformation 62]
115. tall(X0) | ~brave(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 62]
126. ~tall(john) [cnf transformation 23]
156. 7 <=> brave(john) [avatar definition]
157. ~brave(john) <- (~7) [avatar component clause 156]
158. brave(john) <- (7) [avatar component clause 156]
165. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
166. ~quiet(X1) <- (9) [avatar component clause 165]
167. 9 | ~7 [avatar split clause 78,156,165]
243. ~brave(X0) | tall(X0) | ~curious(X0) [subsumption resolution 115,84]
245. tall(X0) | brave(X0) | curious(X0) [subsumption resolution 112,84]
394. brave(john) | curious(john) [resolution 245,126]
397. curious(john) <- (~7) [subsumption resolution 394,157]
420. brave(john) | quiet(john) <- (~7) [resolution 397,74]
421. quiet(john) <- (~7) [subsumption resolution 420,157]
492. tall(john) <- (~7) [resolution 421,98]
493. $false <- (~7) [subsumption resolution 492,126]
494. 7 [avatar contradiction clause 493]
496. 51 <=> curious(john) [avatar definition]
501. tall(john) | ~curious(john) <- (7) [resolution 158,243]
502. curious(john) | quiet(john) <- (7) [resolution 158,75]
503. ~curious(john) <- (7) [subsumption resolution 501,126]
504. ~51 | ~7 [avatar split clause 503,156,496]
505. curious(john) <- (7, 9) [subsumption resolution 502,166]
506. 51 | ~7 | ~9 [avatar split clause 505,165,156,496]
507. $false [avatar sat refutation 167,494,504,506]
% SZS output end Proof for 8862563169033478874803702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both generous and patient then alice is quiet or not calm and vice versa.
Everyone who is both not kind and brave is either humble or quiet and vice versa.
If someone is strong then lucy is both old and calm.
Everyone who is funny is both brave and tall and vice versa.
Everyone who is not patient is both old and funny.
If fred is not happy or wise then someone is both patient and not creative.
If someone is either kind or tall then mary is not happy or humble and vice versa.
Everyone who is either old or not patient is not patient.
If someone is happy or not kind then fred is not brave or not quiet and vice versa.
Everyone who is not curious is both wise and not calm.
Everyone who is both tall and funny is not strong and vice versa.
Everyone who is either brave or not quiet is not old.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is not old or creative is strong and vice versa.
If fred is quiet then paul is either not happy or humble.
Everyone who is rich or calm is both brave and old and vice versa.
Susan is not rich or not kind.
Someone is either not creative or funny.
Someone is happy or funny.
Paul is both patient and not happy.
Someone is either not kind or not generous.
Someone is either old or calm. | Susan is not old. | neutral | (((generous(mary)&patient(mary)))<=>((quiet(alice)|~calm(alice))))&
(![X]:((~kind(X)&brave(X))<=>(humble(X)<~>quiet(X))))&
((?[X]:(strong(X)))=>((old(lucy)&calm(lucy))))&
(![X]:(funny(X)<=>(brave(X)&tall(X))))&
(![X]:(~patient(X)=>(old(X)&funny(X))))&
(((~happy(fred)|wise(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
((?[X]:((kind(X)<~>tall(X))))<=>((~happy(mary)|humble(mary))))&
(![X]:((old(X)<~>~patient(X))=>~patient(X)))&
((?[X]:((happy(X)|~kind(X))))<=>((~brave(fred)|~quiet(fred))))&
(![X]:(~curious(X)=>(wise(X)&~calm(X))))&
(![X]:((tall(X)&funny(X))<=>~strong(X)))&
(![X]:((brave(X)<~>~quiet(X))=>~old(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((~old(X)|creative(X))<=>strong(X)))&
((quiet(fred))=>((~happy(paul)<~>humble(paul))))&
(![X]:((rich(X)|calm(X))<=>(brave(X)&old(X))))&
((~rich(susan)|~kind(susan)))&
(?[X]:((~creative(X)<~>funny(X))))&
(?[X]:((happy(X)|funny(X))))&
((patient(paul)&~happy(paul)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((old(X)<~>calm(X)))) | ~old(susan) | []
| null | 0 |
Everyone who is creative is old or humble.
Everyone who is both not rich and not strong is either humble or not quiet and vice versa.
Everyone who is both not quiet and not patient is generous and vice versa.
If someone is not generous then lucy is both not brave and funny and vice versa.
If fred is either humble or not happy then someone is not old and vice versa.
If susan is calm then someone is either not wise or not rich and vice versa.
Everyone who is both strong and patient is not brave and vice versa.
If mary is creative then someone is happy or generous.
Everyone who is old is either not calm or happy.
Everyone who is both tall and not generous is either wise or old.
Everyone who is tall is either not patient or not generous and vice versa.
Everyone who is both not wise and not brave is both not strong and rich.
Everyone who is both not creative and generous is either old or not generous.
Everyone who is kind or not calm is humble or quiet and vice versa.
If john is strong or not humble then someone is either not humble or not quiet.
If someone is either patient or humble then lucy is not tall or not creative and vice versa.
Someone is both calm and not funny.
Susan is humble.
Someone is not wise.
Someone is not brave.
Lucy is not kind or not calm.
Someone is either not kind or rich.
Someone is either not generous or not tall.
Someone is either not humble or humble. | Fred is not happy. | neutral | (![X]:(creative(X)=>(old(X)|humble(X))))&
(![X]:((~rich(X)&~strong(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~patient(X))<=>generous(X)))&
((?[X]:(~generous(X)))<=>((~brave(lucy)&funny(lucy))))&
(((humble(fred)<~>~happy(fred)))<=>(?[X]:(~old(X))))&
((calm(susan))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:((strong(X)&patient(X))<=>~brave(X)))&
((creative(mary))=>(?[X]:((happy(X)|generous(X)))))&
(![X]:(old(X)=>(~calm(X)<~>happy(X))))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>old(X))))&
(![X]:(tall(X)<=>(~patient(X)<~>~generous(X))))&
(![X]:((~wise(X)&~brave(X))=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)&generous(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)|~calm(X))<=>(humble(X)|quiet(X))))&
(((strong(john)|~humble(john)))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
((?[X]:((patient(X)<~>humble(X))))<=>((~tall(lucy)|~creative(lucy))))&
(?[X]:((calm(X)&~funny(X))))&
(humble(susan))&
(?[X]:(~wise(X)))&
(?[X]:(~brave(X)))&
((~kind(lucy)|~calm(lucy)))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((~humble(X)<~>humble(X)))) | ~happy(fred) | []
| null | 0 |
Everyone who is both not creative and wise is either not patient or not calm and vice versa. If someone is not old then fred is rich or strong. Everyone who is old or curious is both creative and quiet. If someone is either strong or happy then susan is patient or not wise and vice versa. Everyone who is not old is tall and vice versa. Everyone who is not quiet or quiet is quiet or not quiet. If susan is rich then lucy is either not kind or not funny and vice versa. Everyone who is wise or quiet is either not funny or not quiet and vice versa. Everyone who is both not generous and not strong is tall. Everyone who is both brave and creative is both rich and not happy. If someone is both tall and not happy then someone is not humble or not wise. Everyone who is not humble or not brave is not old or rich and vice versa. Everyone who is not rich is not humble and vice versa. Everyone who is patient is both not old and creative. If someone is creative or patient then susan is not patient or generous. Everyone who is calm is wise and vice versa. Someone is both not generous and not funny. John is generous or tall. Fred is either funny or old. John is rich or brave. Someone is both not humble and happy. Someone is not humble. Someone is both brave and kind. Someone is happy or funny. | Fred is happy. | neutral | (![X]:((~creative(X)&wise(X))<=>(~patient(X)<~>~calm(X))))&
((?[X]:(~old(X)))=>((rich(fred)|strong(fred))))&
(![X]:((old(X)|curious(X))=>(creative(X)&quiet(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>((patient(susan)|~wise(susan))))&
(![X]:(~old(X)<=>tall(X)))&
(![X]:((~quiet(X)|quiet(X))=>(quiet(X)|~quiet(X))))&
((rich(susan))<=>((~kind(lucy)<~>~funny(lucy))))&
(![X]:((wise(X)|quiet(X))<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)&creative(X))=>(rich(X)&~happy(X))))&
((?[X]:((tall(X)&~happy(X))))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:(patient(X)=>(~old(X)&creative(X))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(?[X]:((~generous(X)&~funny(X))))&
((generous(john)|tall(john)))&
((funny(fred)<~>old(fred)))&
((rich(john)|brave(john)))&
(?[X]:((~humble(X)&happy(X))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((happy(X)|funny(X)))) | happy(fred) | []
| null | 0 |
Everyone who is both not wise and rich is either brave or creative.
If someone is not rich then someone is both creative and quiet and vice versa.
If alice is both not tall and not creative then lucy is not funny and vice versa.
Everyone who is either old or funny is either not old or not tall and vice versa.
If susan is both wise and not tall then someone is strong and vice versa.
Everyone who is either strong or calm is either calm or old and vice versa.
If someone is either not funny or not patient then lucy is both not rich and rich and vice versa.
Everyone who is both not patient and quiet is not kind and vice versa.
If someone is strong or kind then paul is not brave or humble.
If someone is both not rich and patient then fred is not curious.
Everyone who is not old or not brave is not brave or not happy and vice versa.
If someone is kind or creative then paul is not creative or funny and vice versa.
Everyone who is not tall is funny.
If mary is either not happy or not rich then mary is not kind or humble.
If paul is both creative and not kind then someone is both not tall and not old.
Everyone who is both happy and not wise is either not generous or quiet and vice versa.
Someone is both not generous and curious.
Susan is either not brave or old.
Fred is happy or creative.
Alice is not wise or not brave.
Fred is either not old or not wise.
Someone is either happy or calm.
Fred is either not tall or curious.
Paul is old or not old. | Fred is wise. | entailment | (![X]:((~wise(X)&rich(X))=>(brave(X)<~>creative(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((creative(X)&quiet(X)))))&
(((~tall(alice)&~creative(alice)))<=>(~funny(lucy)))&
(![X]:((old(X)<~>funny(X))<=>(~old(X)<~>~tall(X))))&
(((wise(susan)&~tall(susan)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)<~>calm(X))<=>(calm(X)<~>old(X))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>((~rich(lucy)&rich(lucy))))&
(![X]:((~patient(X)&quiet(X))<=>~kind(X)))&
((?[X]:((strong(X)|kind(X))))=>((~brave(paul)|humble(paul))))&
((?[X]:((~rich(X)&patient(X))))=>(~curious(fred)))&
(![X]:((~old(X)|~brave(X))<=>(~brave(X)|~happy(X))))&
((?[X]:((kind(X)|creative(X))))<=>((~creative(paul)|funny(paul))))&
(![X]:(~tall(X)=>funny(X)))&
(((~happy(mary)<~>~rich(mary)))=>((~kind(mary)|humble(mary))))&
(((creative(paul)&~kind(paul)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((happy(X)&~wise(X))<=>(~generous(X)<~>quiet(X))))&
(?[X]:((~generous(X)&curious(X))))&
((~brave(susan)<~>old(susan)))&
((happy(fred)|creative(fred)))&
((~wise(alice)|~brave(alice)))&
((~old(fred)<~>~wise(fred)))&
(?[X]:((happy(X)<~>calm(X))))&
((~tall(fred)<~>curious(fred)))&
((old(paul)|~old(paul))) | wise(fred) | [
"p3",
"p4",
"p5",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 4705787009610359842175431
% SZS output start Proof for 4705787009610359842175431
4. ! [X0] : ((old(X0) <~> funny(X0)) <=> (~old(X0) <~> ~tall(X0))) [input p3]
5. (~tall(susan) & wise(susan)) <=> ? [X0] : strong(X0) [input p4]
6. ! [X0] : ((strong(X0) <~> calm(X0)) <=> (calm(X0) <~> old(X0))) [input p5]
13. ! [X0] : (~tall(X0) => funny(X0)) [input p12]
21. ~old(fred) <~> ~wise(fred) [input p20]
25. ~wise(fred) [input hypothesis]
32. ! [X0] : (funny(X0) | tall(X0)) [ennf transformation 13]
43. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 4]
44. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (tall(susan) | ~wise(susan))) [nnf transformation 5]
45. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | tall(susan) | ~wise(susan)) [flattening 44]
46. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | tall(susan) | ~wise(susan)) [rectify 45]
47. ? [X1] : strong(X1) => strong(sK2) [choice axiom]
48. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (strong(sK2) | tall(susan) | ~wise(susan)) [skolemisation 46,47]
49. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0)))) & (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [nnf transformation 6]
71. (wise(fred) | old(fred)) & (~wise(fred) | ~old(fred)) [nnf transformation 21]
87. tall(X0) | old(X0) | old(X0) | ~funny(X0) [cnf transformation 43]
91. ~funny(X0) | ~old(X0) | ~old(X0) | tall(X0) [cnf transformation 43]
94. ~tall(susan) | ~strong(X0) [cnf transformation 48]
98. ~old(X0) | ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 49]
100. calm(X0) | strong(X0) | calm(X0) | ~old(X0) [cnf transformation 49]
121. funny(X0) | tall(X0) [cnf transformation 32]
137. wise(fred) | old(fred) [cnf transformation 71]
143. ~wise(fred) [cnf transformation 25]
145. ~old(X0) | ~calm(X0) | strong(X0) [duplicate literal removal 98]
146. calm(X0) | strong(X0) | ~old(X0) [duplicate literal removal 100]
149. tall(X0) | old(X0) | ~funny(X0) [duplicate literal removal 87]
151. ~funny(X0) | ~old(X0) | tall(X0) [duplicate literal removal 91]
188. ~funny(X0) | tall(X0) [subsumption resolution 149,151]
191. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
192. ~strong(X0) <- (9) [avatar component clause 191]
194. 10 <=> tall(susan) [avatar definition]
196. ~tall(susan) <- (~10) [avatar component clause 194]
197. 9 | ~10 [avatar split clause 94,194,191]
208. ~old(X0) | strong(X0) [subsumption resolution 145,146]
258. tall(X0) [subsumption resolution 121,188]
299. 32 <=> old(fred) [avatar definition]
301. old(fred) <- (32) [avatar component clause 299]
303. 33 <=> wise(fred) [avatar definition]
306. 32 | 33 [avatar split clause 137,303,299]
320. ~33 [avatar split clause 143,303]
325. strong(fred) <- (32) [resolution 208,301]
326. $false <- (9, 32) [subsumption resolution 325,192]
327. ~9 | ~32 [avatar contradiction clause 326]
328. $false <- (~10) [subsumption resolution 196,258]
329. 10 [avatar contradiction clause 328]
330. $false [avatar sat refutation 197,306,320,327,329]
% SZS output end Proof for 4705787009610359842175431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not generous then someone is rich.
Everyone who is not kind or not patient is not kind.
If someone is not rich then someone is either generous or not kind and vice versa.
Everyone who is not rich or rich is either not creative or not kind and vice versa.
Everyone who is both not patient and not curious is not curious and vice versa.
Everyone who is either not rich or not tall is both old and not happy and vice versa.
Everyone who is either kind or happy is creative or not patient.
If susan is not happy then fred is not wise and vice versa.
If mary is not curious or quiet then someone is not tall or generous.
If someone is not quiet or humble then susan is calm.
If alice is brave then paul is either not brave or not happy.
If paul is either rich or not wise then someone is either humble or not strong.
Everyone who is curious is brave and vice versa.
If lucy is either happy or not patient then john is patient.
If someone is not generous or patient then alice is not generous and vice versa.
If someone is not kind then john is either humble or generous.
Lucy is happy or not creative.
Lucy is not curious.
Someone is quiet.
Someone is both not wise and brave.
Susan is both not quiet and old. | John is not kind. | neutral | ((?[X]:((~humble(X)&~generous(X))))=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~patient(X))=>~kind(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~rich(X)|rich(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:((~patient(X)&~curious(X))<=>~curious(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(old(X)&~happy(X))))&
(![X]:((kind(X)<~>happy(X))=>(creative(X)|~patient(X))))&
((~happy(susan))<=>(~wise(fred)))&
(((~curious(mary)|quiet(mary)))=>(?[X]:((~tall(X)|generous(X)))))&
((?[X]:((~quiet(X)|humble(X))))=>(calm(susan)))&
((brave(alice))=>((~brave(paul)<~>~happy(paul))))&
(((rich(paul)<~>~wise(paul)))=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:(curious(X)<=>brave(X)))&
(((happy(lucy)<~>~patient(lucy)))=>(patient(john)))&
((?[X]:((~generous(X)|patient(X))))<=>(~generous(alice)))&
((?[X]:(~kind(X)))=>((humble(john)<~>generous(john))))&
((happy(lucy)|~creative(lucy)))&
(~curious(lucy))&
(?[X]:(quiet(X)))&
(?[X]:((~wise(X)&brave(X))))&
((~quiet(susan)&old(susan))) | ~kind(john) | []
| null | 0 |
Everyone who is patient is both tall and not calm.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
If someone is funny or not quiet then someone is wise or not happy.
Everyone who is both not tall and not strong is both happy and not funny.
Everyone who is not creative is either quiet or not humble and vice versa.
If someone is not patient or kind then someone is either calm or curious.
Paul is quiet or not old.
John is tall or strong.
Someone is either not creative or calm.
Someone is both not wise and not generous.
John is both brave and not wise. | John is happy. | contradiction | (![X]:(patient(X)=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((~tall(X)&~strong(X))=>(happy(X)&~funny(X))))&
(![X]:(~creative(X)<=>(quiet(X)<~>~humble(X))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
((quiet(paul)|~old(paul)))&
((tall(john)|strong(john)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((brave(john)&~wise(john))) | happy(john) | [
"p0",
"p3",
"p6",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 6091117338784783212385050
% SZS output start Proof for 6091117338784783212385050
1. ! [X0] : (patient(X0) => (~calm(X0) & tall(X0))) [input p0]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => (calm(X0) & ~rich(X0))) [input p3]
7. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p6]
9. ! [X0] : ((calm(X0) | strong(X0)) <=> (~patient(X0) <~> wise(X0))) [input p8]
10. ? [X0] : wise(X0) <=> ? [X0] : (quiet(X0) & happy(X0)) [input p9]
11. ! [X0] : (~creative(X0) <=> (humble(X0) & brave(X0))) [input p10]
15. ! [X0] : (~creative(X0) <=> (quiet(X0) <~> ~humble(X0))) [input p14]
22. happy(john) [input hypothesis]
23. ? [X0] : wise(X0) <=> ? [X1] : (quiet(X1) & happy(X1)) [rectify 10]
27. ! [X0] : ((~calm(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 1]
29. ! [X0] : ((calm(X0) & ~rich(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
48. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 7]
51. ! [X0] : (((calm(X0) | strong(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~calm(X0) & ~strong(X0)))) [nnf transformation 9]
52. ! [X0] : ((calm(X0) | strong(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~calm(X0) & ~strong(X0)))) [flattening 51]
53. (? [X0] : wise(X0) | ! [X1] : (~quiet(X1) | ~happy(X1))) & (? [X1] : (quiet(X1) & happy(X1)) | ! [X0] : ~wise(X0)) [nnf transformation 23]
54. (? [X0] : wise(X0) | ! [X1] : (~quiet(X1) | ~happy(X1))) & (? [X2] : (quiet(X2) & happy(X2)) | ! [X3] : ~wise(X3)) [rectify 53]
55. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
56. ? [X2] : (quiet(X2) & happy(X2)) => (quiet(sK4) & happy(sK4)) [choice axiom]
57. (wise(sK3) | ! [X1] : (~quiet(X1) | ~happy(X1))) & ((quiet(sK4) & happy(sK4)) | ! [X3] : ~wise(X3)) [skolemisation 54,56,55]
58. ! [X0] : ((~creative(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | creative(X0))) [nnf transformation 11]
59. ! [X0] : ((~creative(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | creative(X0))) [flattening 58]
64. ! [X0] : ((~creative(X0) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) & (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | creative(X0))) [nnf transformation 15]
75. ~calm(X0) | ~patient(X0) [cnf transformation 27]
87. ~quiet(X0) | calm(X0) [cnf transformation 29]
96. ~creative(X0) | brave(X0) [cnf transformation 48]
97. ~brave(X0) | creative(X0) [cnf transformation 48]
104. ~wise(X0) | patient(X0) | ~calm(X0) [cnf transformation 52]
109. wise(sK3) | ~quiet(X1) | ~happy(X1) [cnf transformation 57]
110. brave(X0) | creative(X0) [cnf transformation 59]
112. ~creative(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 59]
124. ~creative(X0) | quiet(X0) | humble(X0) [cnf transformation 64]
135. happy(john) [cnf transformation 22]
233. ~wise(X0) | ~calm(X0) [subsumption resolution 104,75]
235. 21 <=> ! [X1] : (~quiet(X1) | ~happy(X1)) [avatar definition]
236. ~happy(X1) | ~quiet(X1) <- (21) [avatar component clause 235]
238. 22 <=> wise(sK3) [avatar definition]
240. wise(sK3) <- (22) [avatar component clause 238]
241. 21 | 22 [avatar split clause 109,238,235]
255. ~creative(X0) | ~humble(X0) [subsumption resolution 112,96]
256. creative(X0) [subsumption resolution 110,97]
275. quiet(X0) | humble(X0) [subsumption resolution 124,256]
324. ~quiet(john) <- (21) [resolution 236,135]
326. ~humble(X1) [resolution 255,256]
327. humble(X0) | calm(X0) [resolution 275,87]
328. humble(john) <- (21) [resolution 275,324]
329. calm(X0) [subsumption resolution 327,326]
330. $false <- (21) [subsumption resolution 328,326]
331. ~21 [avatar contradiction clause 330]
334. ~calm(sK3) <- (22) [resolution 240,233]
335. $false <- (22) [subsumption resolution 334,329]
336. ~22 [avatar contradiction clause 335]
337. $false [avatar sat refutation 241,331,336]
% SZS output end Proof for 6091117338784783212385050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not strong or not wise.
Everyone who is not tall or not old is kind and vice versa.
If someone is happy then alice is both not tall and not calm.
Everyone who is happy is both not generous and not patient.
Everyone who is not kind or not strong is either calm or rich.
Everyone who is not happy or not tall is both rich and creative and vice versa.
Everyone who is either tall or generous is both rich and not humble.
If mary is not patient or happy then someone is wise.
If someone is either not patient or tall then someone is both generous and patient and vice versa.
Everyone who is not funny or not rich is either quiet or old and vice versa.
Everyone who is not wise or wise is both kind and not tall.
Everyone who is both calm and generous is curious or old and vice versa.
If someone is either not curious or not humble then fred is not creative or not humble.
Everyone who is not quiet is tall and vice versa.
If fred is not funny then someone is quiet or calm.
Everyone who is either not humble or rich is not calm and vice versa.
Someone is both not patient and creative.
Alice is not funny or not quiet.
Susan is creative.
Someone is not strong.
Someone is old or not quiet. | Fred is curious. | neutral | (![X]:(happy(X)=>(~strong(X)|~wise(X))))&
(![X]:((~tall(X)|~old(X))<=>kind(X)))&
((?[X]:(happy(X)))=>((~tall(alice)&~calm(alice))))&
(![X]:(happy(X)=>(~generous(X)&~patient(X))))&
(![X]:((~kind(X)|~strong(X))=>(calm(X)<~>rich(X))))&
(![X]:((~happy(X)|~tall(X))<=>(rich(X)&creative(X))))&
(![X]:((tall(X)<~>generous(X))=>(rich(X)&~humble(X))))&
(((~patient(mary)|happy(mary)))=>(?[X]:(wise(X))))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
(![X]:((~funny(X)|~rich(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~wise(X)|wise(X))=>(kind(X)&~tall(X))))&
(![X]:((calm(X)&generous(X))<=>(curious(X)|old(X))))&
((?[X]:((~curious(X)<~>~humble(X))))=>((~creative(fred)|~humble(fred))))&
(![X]:(~quiet(X)<=>tall(X)))&
((~funny(fred))=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>~calm(X)))&
(?[X]:((~patient(X)&creative(X))))&
((~funny(alice)|~quiet(alice)))&
(creative(susan))&
(?[X]:(~strong(X)))&
(?[X]:((old(X)|~quiet(X)))) | curious(fred) | []
| null | 0 |
Everyone who is not curious is both wise and not generous and vice versa.
If someone is not kind or not strong then paul is not creative.
Everyone who is not creative or not old is both not humble and not creative and vice versa.
If someone is patient or kind then lucy is both curious and not quiet and vice versa.
If fred is either funny or calm then lucy is either not rich or curious and vice versa.
If someone is both not happy and creative then mary is not funny or not creative and vice versa.
Everyone who is not strong or not curious is either curious or humble.
If someone is both not generous and happy then someone is patient.
If someone is either not calm or generous then someone is both not humble and patient and vice versa.
If susan is both not kind and not tall then paul is rich and vice versa.
Everyone who is quiet is both not generous and tall.
If someone is either not old or happy then someone is calm or patient and vice versa.
If someone is either not old or wise then lucy is creative and vice versa.
Everyone who is either not curious or humble is both generous and kind.
If someone is both quiet and not humble then someone is either calm or not brave and vice versa.
Everyone who is creative or not quiet is both not patient and not tall and vice versa.
Susan is rich or not funny.
Fred is either old or rich.
Someone is both brave and not funny.
Someone is funny.
Fred is old.
Paul is creative.
Susan is both old and not patient.
Someone is wise. | Lucy is not patient. | entailment | (![X]:(~curious(X)<=>(wise(X)&~generous(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(~creative(paul)))&
(![X]:((~creative(X)|~old(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((patient(X)|kind(X))))<=>((curious(lucy)&~quiet(lucy))))&
(((funny(fred)<~>calm(fred)))<=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((~happy(X)&creative(X))))<=>((~funny(mary)|~creative(mary))))&
(![X]:((~strong(X)|~curious(X))=>(curious(X)<~>humble(X))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:(patient(X))))&
((?[X]:((~calm(X)<~>generous(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~kind(susan)&~tall(susan)))<=>(rich(paul)))&
(![X]:(quiet(X)=>(~generous(X)&tall(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(generous(X)&kind(X))))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~patient(X)&~tall(X))))&
((rich(susan)|~funny(susan)))&
((old(fred)<~>rich(fred)))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:(funny(X)))&
(old(fred))&
(creative(paul))&
((old(susan)&~patient(susan)))&
(?[X]:(wise(X))) | ~patient(lucy) | [
"p1",
"p3",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 9011891923755170339109396
% SZS output start Proof for 9011891923755170339109396
2. ? [X0] : (~strong(X0) | ~kind(X0)) => ~creative(paul) [input p1]
4. ? [X0] : (kind(X0) | patient(X0)) <=> (~quiet(lucy) & curious(lucy)) [input p3]
16. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (~tall(X0) & ~patient(X0))) [input p15]
22. creative(paul) [input p21]
25. patient(lucy) [input hypothesis]
30. ? [X0] : ~kind(X0) => ~creative(paul) [pure predicate removal 2]
32. ~creative(paul) | ! [X0] : kind(X0) [ennf transformation 30]
41. (? [X0] : (kind(X0) | patient(X0)) | (quiet(lucy) | ~curious(lucy))) & ((~quiet(lucy) & curious(lucy)) | ! [X0] : (~kind(X0) & ~patient(X0))) [nnf transformation 4]
42. (? [X0] : (kind(X0) | patient(X0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X0] : (~kind(X0) & ~patient(X0))) [flattening 41]
43. (? [X0] : (kind(X0) | patient(X0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X1] : (~kind(X1) & ~patient(X1))) [rectify 42]
44. ? [X0] : (kind(X0) | patient(X0)) => (kind(sK0) | patient(sK0)) [choice axiom]
45. ((kind(sK0) | patient(sK0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X1] : (~kind(X1) & ~patient(X1))) [skolemisation 43,44]
78. ! [X0] : (((~quiet(X0) | creative(X0)) | (tall(X0) | patient(X0))) & ((~tall(X0) & ~patient(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 16]
79. ! [X0] : ((~quiet(X0) | creative(X0) | tall(X0) | patient(X0)) & ((~tall(X0) & ~patient(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 78]
90. ~creative(paul) | kind(X0) [cnf transformation 32]
99. ~quiet(lucy) | ~kind(X1) [cnf transformation 45]
149. ~patient(X0) | quiet(X0) [cnf transformation 79]
160. creative(paul) [cnf transformation 22]
164. patient(lucy) [cnf transformation 25]
167. 1 <=> ! [X0] : kind(X0) [avatar definition]
168. kind(X0) <- (1) [avatar component clause 167]
170. 2 <=> creative(paul) [avatar definition]
173. 1 | ~2 [avatar split clause 90,170,167]
179. 4 <=> quiet(lucy) [avatar definition]
180. ~quiet(lucy) <- (~4) [avatar component clause 179]
192. 7 <=> ! [X1] : ~kind(X1) [avatar definition]
193. ~kind(X1) <- (7) [avatar component clause 192]
194. 7 | ~4 [avatar split clause 99,179,192]
403. 2 [avatar split clause 160,170]
404. $false <- (1, 7) [subsumption resolution 168,193]
405. ~1 | ~7 [avatar contradiction clause 404]
420. quiet(lucy) [resolution 149,164]
423. $false <- (~4) [subsumption resolution 420,180]
424. 4 [avatar contradiction clause 423]
425. $false [avatar sat refutation 173,194,403,405,424]
% SZS output end Proof for 9011891923755170339109396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both rich and kind then someone is not brave. If john is either not strong or not creative then paul is both humble and not humble. Everyone who is either not funny or rich is both not creative and not wise and vice versa. If someone is not creative or not humble then someone is either not humble or not curious and vice versa. If paul is not creative then fred is generous or not kind. Everyone who is not generous or strong is patient and vice versa. If lucy is not curious then someone is both happy and calm. Everyone who is both calm and not happy is either not wise or tall. Everyone who is old or not tall is not funny and vice versa. Everyone who is not patient is tall or brave and vice versa. If someone is both strong and not old then john is both creative and funny. If someone is not old then fred is either quiet or not rich. Everyone who is both generous and not tall is both not rich and humble. If lucy is either tall or brave then john is either not wise or funny. If someone is both generous and not old then someone is wise. Everyone who is not humble or wise is either not wise or tall. Someone is either not patient or calm. Paul is not tall. Fred is kind or not patient. John is both not wise and calm. Lucy is both funny and not strong. Paul is either humble or not curious. Someone is creative or not generous. Someone is both brave and not funny. | John is not wise. | entailment | (((rich(john)&kind(john)))=>(?[X]:(~brave(X))))&
(((~strong(john)<~>~creative(john)))=>((humble(paul)&~humble(paul))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
((~creative(paul))=>((generous(fred)|~kind(fred))))&
(![X]:((~generous(X)|strong(X))<=>patient(X)))&
((~curious(lucy))=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((calm(X)&~happy(X))=>(~wise(X)<~>tall(X))))&
(![X]:((old(X)|~tall(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(tall(X)|brave(X))))&
((?[X]:((strong(X)&~old(X))))=>((creative(john)&funny(john))))&
((?[X]:(~old(X)))=>((quiet(fred)<~>~rich(fred))))&
(![X]:((generous(X)&~tall(X))=>(~rich(X)&humble(X))))&
(((tall(lucy)<~>brave(lucy)))=>((~wise(john)<~>funny(john))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:(wise(X))))&
(![X]:((~humble(X)|wise(X))=>(~wise(X)<~>tall(X))))&
(?[X]:((~patient(X)<~>calm(X))))&
(~tall(paul))&
((kind(fred)|~patient(fred)))&
((~wise(john)&calm(john)))&
((funny(lucy)&~strong(lucy)))&
((humble(paul)<~>~curious(paul)))&
(?[X]:((creative(X)|~generous(X))))&
(?[X]:((brave(X)&~funny(X)))) | ~wise(john) | [
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 667237702935323290731611
% SZS output start Proof for 667237702935323290731611
20. calm(john) & ~wise(john) [input p19]
25. wise(john) [input hypothesis]
122. ~wise(john) [cnf transformation 20]
131. wise(john) [cnf transformation 25]
249. 27 <=> wise(john) [avatar definition]
279. ~27 [avatar split clause 122,249]
295. 27 [avatar split clause 131,249]
296. $false [avatar sat refutation 279,295]
% SZS output end Proof for 667237702935323290731611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then alice is not funny or creative.
Everyone who is either generous or creative is either humble or old and vice versa.
Everyone who is either not generous or not old is not humble.
If lucy is not generous then paul is either not funny or not rich and vice versa.
Everyone who is both not old and not curious is not rich or generous and vice versa.
Everyone who is both not old and not curious is not kind or not quiet.
If fred is not brave or humble then alice is not wise or humble.
Everyone who is not rich or not quiet is not patient.
Everyone who is tall or quiet is curious and vice versa.
Everyone who is either not strong or not calm is not happy and vice versa.
Everyone who is not happy or calm is not calm or curious.
Everyone who is not funny or patient is both brave and creative.
Everyone who is both not tall and wise is kind or not creative and vice versa.
If john is both not old and not strong then paul is happy.
Everyone who is not happy or not kind is either happy or not brave and vice versa.
Everyone who is not humble is not kind and vice versa.
Susan is both humble and not old.
Someone is rich or calm.
Fred is not rich or tall.
John is not patient.
Someone is either not wise or old.
Someone is not patient.
Someone is quiet or not patient.
Someone is funny or wise. | Susan is funny. | entailment | ((?[X]:(~generous(X)))=>((~funny(alice)|creative(alice))))&
(![X]:((generous(X)<~>creative(X))<=>(humble(X)<~>old(X))))&
(![X]:((~generous(X)<~>~old(X))=>~humble(X)))&
((~generous(lucy))<=>((~funny(paul)<~>~rich(paul))))&
(![X]:((~old(X)&~curious(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~curious(X))=>(~kind(X)|~quiet(X))))&
(((~brave(fred)|humble(fred)))=>((~wise(alice)|humble(alice))))&
(![X]:((~rich(X)|~quiet(X))=>~patient(X)))&
(![X]:((tall(X)|quiet(X))<=>curious(X)))&
(![X]:((~strong(X)<~>~calm(X))<=>~happy(X)))&
(![X]:((~happy(X)|calm(X))=>(~calm(X)|curious(X))))&
(![X]:((~funny(X)|patient(X))=>(brave(X)&creative(X))))&
(![X]:((~tall(X)&wise(X))<=>(kind(X)|~creative(X))))&
(((~old(john)&~strong(john)))=>(happy(paul)))&
(![X]:((~happy(X)|~kind(X))<=>(happy(X)<~>~brave(X))))&
(![X]:(~humble(X)<=>~kind(X)))&
((humble(susan)&~old(susan)))&
(?[X]:((rich(X)|calm(X))))&
((~rich(fred)|tall(fred)))&
(~patient(john))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((funny(X)|wise(X)))) | funny(susan) | [
"p11",
"p14",
"p15",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2002081703227668313847444
% SZS output start Proof for 2002081703227668313847444
12. ! [X0] : ((patient(X0) | ~funny(X0)) => (creative(X0) & brave(X0))) [input p11]
15. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (happy(X0) <~> ~brave(X0))) [input p14]
16. ! [X0] : (~humble(X0) <=> ~kind(X0)) [input p15]
17. ~old(susan) & humble(susan) [input p16]
25. ~funny(susan) [input hypothesis]
28. ! [X0] : (~funny(X0) => (creative(X0) & brave(X0))) [pure predicate removal 12]
40. ! [X0] : ((creative(X0) & brave(X0)) | funny(X0)) [ennf transformation 28]
53. ! [X0] : (((~kind(X0) | ~happy(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [nnf transformation 15]
54. ! [X0] : ((~kind(X0) | ~happy(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) & (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (kind(X0) & happy(X0)))) [flattening 53]
55. ! [X0] : ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))) [nnf transformation 16]
95. brave(X0) | funny(X0) [cnf transformation 40]
103. ~brave(X0) | happy(X0) | happy(X0) [cnf transformation 54]
107. ~kind(X0) | ~happy(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 54]
110. ~humble(X0) | kind(X0) [cnf transformation 55]
111. humble(susan) [cnf transformation 17]
118. ~funny(susan) [cnf transformation 25]
119. ~brave(X0) | happy(X0) [duplicate literal removal 103]
120. ~happy(X0) | ~kind(X0) | ~brave(X0) [duplicate literal removal 107]
223. kind(susan) [resolution 110,111]
226. happy(X0) | funny(X0) [resolution 119,95]
241. ~kind(X1) | ~brave(X1) | funny(X1) [resolution 120,226]
242. ~kind(X1) | funny(X1) [subsumption resolution 241,95]
243. funny(susan) [resolution 242,223]
244. $false [subsumption resolution 243,118]
% SZS output end Proof for 2002081703227668313847444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not curious or not creative then someone is not curious. If john is not happy then someone is both generous and not creative and vice versa. Everyone who is not patient is either humble or happy. Everyone who is quiet is not old or not kind. If someone is both not patient and strong then paul is quiet or funny and vice versa. Everyone who is either not tall or funny is not funny or not tall and vice versa. Everyone who is either old or not wise is either kind or not tall and vice versa. Everyone who is both not happy and old is both not brave and not wise. Everyone who is not brave is either humble or funny. Everyone who is either not wise or patient is both old and patient. Everyone who is both wise and not kind is brave or not funny and vice versa. If alice is either generous or strong then lucy is either not brave or not happy and vice versa. Everyone who is not calm is either not curious or not generous. Everyone who is either not patient or not tall is old and vice versa. Everyone who is either patient or not tall is humble or not humble. Everyone who is generous or strong is either not happy or not creative and vice versa. Susan is not wise or not tall. Someone is either happy or not patient. Alice is either not happy or calm. Someone is not calm. Someone is not calm or brave. Someone is strong or not humble. John is both strong and not creative. | Susan is not generous. | entailment | (((~curious(lucy)|~creative(lucy)))=>(?[X]:(~curious(X))))&
((~happy(john))<=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:(~patient(X)=>(humble(X)<~>happy(X))))&
(![X]:(quiet(X)=>(~old(X)|~kind(X))))&
((?[X]:((~patient(X)&strong(X))))<=>((quiet(paul)|funny(paul))))&
(![X]:((~tall(X)<~>funny(X))<=>(~funny(X)|~tall(X))))&
(![X]:((old(X)<~>~wise(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((~happy(X)&old(X))=>(~brave(X)&~wise(X))))&
(![X]:(~brave(X)=>(humble(X)<~>funny(X))))&
(![X]:((~wise(X)<~>patient(X))=>(old(X)&patient(X))))&
(![X]:((wise(X)&~kind(X))<=>(brave(X)|~funny(X))))&
(((generous(alice)<~>strong(alice)))<=>((~brave(lucy)<~>~happy(lucy))))&
(![X]:(~calm(X)=>(~curious(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>old(X)))&
(![X]:((patient(X)<~>~tall(X))=>(humble(X)|~humble(X))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)<~>~creative(X))))&
((~wise(susan)|~tall(susan)))&
(?[X]:((happy(X)<~>~patient(X))))&
((~happy(alice)<~>calm(alice)))&
(?[X]:(~calm(X)))&
(?[X]:((~calm(X)|brave(X))))&
(?[X]:((strong(X)|~humble(X))))&
((strong(john)&~creative(john))) | ~generous(susan) | [
"p1",
"p5",
"p6",
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7088728866450233235947246
% SZS output start Proof for 7088728866450233235947246
2. ~happy(john) <=> ? [X0] : (~creative(X0) & generous(X0)) [input p1]
6. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> (~tall(X0) | ~funny(X0))) [input p5]
7. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (kind(X0) <~> ~tall(X0))) [input p6]
8. ! [X0] : ((old(X0) & ~happy(X0)) => (~wise(X0) & ~brave(X0))) [input p7]
10. ! [X0] : ((~wise(X0) <~> patient(X0)) => (patient(X0) & old(X0))) [input p9]
11. ! [X0] : ((~kind(X0) & wise(X0)) <=> (~funny(X0) | brave(X0))) [input p10]
14. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> old(X0)) [input p13]
16. ! [X0] : ((strong(X0) | generous(X0)) <=> (~happy(X0) <~> ~creative(X0))) [input p15]
24. generous(susan) [input hypothesis]
29. ! [X0] : ((~wise(X0) & ~brave(X0)) | (~old(X0) | happy(X0))) [ennf transformation 8]
30. ! [X0] : ((~wise(X0) & ~brave(X0)) | ~old(X0) | happy(X0)) [flattening 29]
32. ! [X0] : ((patient(X0) & old(X0)) | (~wise(X0) <=> patient(X0))) [ennf transformation 10]
38. (~happy(john) | ! [X0] : (creative(X0) | ~generous(X0))) & (? [X0] : (~creative(X0) & generous(X0)) | happy(john)) [nnf transformation 2]
39. (~happy(john) | ! [X0] : (creative(X0) | ~generous(X0))) & (? [X1] : (~creative(X1) & generous(X1)) | happy(john)) [rectify 38]
40. ? [X1] : (~creative(X1) & generous(X1)) => (~creative(sK1) & generous(sK1)) [choice axiom]
41. (~happy(john) | ! [X0] : (creative(X0) | ~generous(X0))) & ((~creative(sK1) & generous(sK1)) | happy(john)) [skolemisation 39,40]
48. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [flattening 48]
50. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) & (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 7]
52. ! [X0] : ((patient(X0) & old(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) [nnf transformation 32]
53. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & ((~funny(X0) | brave(X0)) | (kind(X0) | ~wise(X0)))) [nnf transformation 11]
54. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & (~funny(X0) | brave(X0) | kind(X0) | ~wise(X0))) [flattening 53]
57. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~old(X0)) & (old(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 14]
59. ! [X0] : (((strong(X0) | generous(X0)) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | (~strong(X0) & ~generous(X0)))) [nnf transformation 16]
60. ! [X0] : ((strong(X0) | generous(X0) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | (~strong(X0) & ~generous(X0)))) [flattening 59]
75. ~happy(john) | creative(X0) | ~generous(X0) [cnf transformation 41]
85. ~tall(X0) | ~funny(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 49]
89. ~funny(X0) | tall(X0) | tall(X0) [cnf transformation 49]
95. ~wise(X0) | old(X0) | kind(X0) | tall(X0) [cnf transformation 50]
99. ~wise(X0) | ~old(X0) | happy(X0) [cnf transformation 30]
103. ~wise(X0) | old(X0) | ~patient(X0) [cnf transformation 52]
104. patient(X0) | patient(X0) | wise(X0) [cnf transformation 52]
108. wise(X0) | funny(X0) [cnf transformation 54]
110. ~kind(X0) | funny(X0) [cnf transformation 54]
121. ~tall(X0) | old(X0) | patient(X0) [cnf transformation 57]
124. ~old(X0) | patient(X0) | tall(X0) [cnf transformation 57]
127. ~generous(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 60]
143. generous(susan) [cnf transformation 24]
144. wise(X0) | patient(X0) [duplicate literal removal 104]
145. ~tall(X0) | ~funny(X0) [duplicate literal removal 85]
147. ~funny(X0) | tall(X0) [duplicate literal removal 89]
163. 4 <=> ! [X0] : (creative(X0) | ~generous(X0)) [avatar definition]
164. ~generous(X0) | creative(X0) <- (4) [avatar component clause 163]
166. 5 <=> happy(john) [avatar definition]
168. ~happy(john) <- (~5) [avatar component clause 166]
169. 4 | ~5 [avatar split clause 75,166,163]
204. ~funny(X0) [subsumption resolution 145,147]
206. ~kind(X0) [subsumption resolution 110,204]
207. wise(X0) [subsumption resolution 108,204]
273. creative(susan) <- (4) [resolution 164,143]
292. ~old(X1) | happy(X1) [resolution 99,207]
294. ~patient(X1) | old(X1) [resolution 103,207]
332. ~happy(susan) | ~creative(susan) [resolution 127,143]
334. ~happy(susan) <- (4) [subsumption resolution 332,273]
402. old(X0) | kind(X0) | tall(X0) | patient(X0) [resolution 95,144]
404. old(X0) | tall(X0) | patient(X0) [subsumption resolution 402,206]
405. tall(X0) | patient(X0) [subsumption resolution 404,124]
420. patient(X4) | old(X4) | patient(X4) [resolution 405,121]
422. patient(X4) | old(X4) [duplicate literal removal 420]
423. old(X4) [subsumption resolution 422,294]
440. happy(X3) [resolution 423,292]
453. $false <- (4) [resolution 440,334]
458. ~4 [avatar contradiction clause 453]
464. $false <- (~5) [subsumption resolution 168,440]
465. 5 [avatar contradiction clause 464]
466. $false [avatar sat refutation 169,458,465]
% SZS output end Proof for 7088728866450233235947246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or old then someone is not rich and vice versa. Everyone who is both not creative and not strong is both kind and creative. Everyone who is happy is not brave. If someone is either strong or rich then someone is both not strong and not curious and vice versa. Everyone who is quiet is curious and vice versa. If alice is both old and not old then mary is either not brave or kind and vice versa. Everyone who is both not brave and calm is wise or not wise. If fred is quiet or tall then alice is both happy and humble and vice versa. Everyone who is both wise and curious is either not tall or not creative and vice versa. Everyone who is happy or not patient is both not quiet and wise. If fred is humble then susan is not tall or not calm and vice versa. Everyone who is not tall is both generous and not wise and vice versa. Everyone who is not curious is not funny or not brave. If susan is both brave and not quiet then fred is wise and vice versa. If someone is creative then susan is both happy and generous. If fred is both funny and not tall then someone is either not generous or tall and vice versa. Mary is either rich or strong. Mary is not kind or patient. Someone is both not wise and not kind. Mary is either not funny or tall. Fred is either not creative or not brave. Someone is not calm or not patient. | Fred is brave. | entailment | ((?[X]:((~funny(X)|old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~creative(X)&~strong(X))=>(kind(X)&creative(X))))&
(![X]:(happy(X)=>~brave(X)))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:(quiet(X)<=>curious(X)))&
(((old(alice)&~old(alice)))<=>((~brave(mary)<~>kind(mary))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)|~wise(X))))&
(((quiet(fred)|tall(fred)))<=>((happy(alice)&humble(alice))))&
(![X]:((wise(X)&curious(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((happy(X)|~patient(X))=>(~quiet(X)&wise(X))))&
((humble(fred))<=>((~tall(susan)|~calm(susan))))&
(![X]:(~tall(X)<=>(generous(X)&~wise(X))))&
(![X]:(~curious(X)=>(~funny(X)|~brave(X))))&
(((brave(susan)&~quiet(susan)))<=>(wise(fred)))&
((?[X]:(creative(X)))=>((happy(susan)&generous(susan))))&
(((funny(fred)&~tall(fred)))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((rich(mary)<~>strong(mary)))&
((~kind(mary)|patient(mary)))&
(?[X]:((~wise(X)&~kind(X))))&
((~funny(mary)<~>tall(mary)))&
((~creative(fred)<~>~brave(fred)))&
(?[X]:((~calm(X)|~patient(X)))) | brave(fred) | [
"p8",
"p9",
"p11",
"p14",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 8212811077267243758849097
% SZS output start Proof for 8212811077267243758849097
9. ! [X0] : ((curious(X0) & wise(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p8]
10. ! [X0] : ((~patient(X0) | happy(X0)) => (wise(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : (~tall(X0) <=> (~wise(X0) & generous(X0))) [input p11]
15. ? [X0] : creative(X0) => (generous(susan) & happy(susan)) [input p14]
16. (~tall(fred) & funny(fred)) <=> ? [X0] : (~generous(X0) <~> tall(X0)) [input p15]
21. ~creative(fred) <~> ~brave(fred) [input p20]
23. ~brave(fred) [input hypothesis]
31. ! [X0] : ((wise(X0) & ~quiet(X0)) | (patient(X0) & ~happy(X0))) [ennf transformation 10]
34. (generous(susan) & happy(susan)) | ! [X0] : ~creative(X0) [ennf transformation 15]
50. ! [X0] : (((curious(X0) & wise(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~curious(X0) | ~wise(X0)))) [nnf transformation 9]
51. ! [X0] : (((curious(X0) & wise(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ~curious(X0) | ~wise(X0))) [flattening 50]
54. ! [X0] : ((~tall(X0) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | tall(X0))) [nnf transformation 12]
55. ! [X0] : ((~tall(X0) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | tall(X0))) [flattening 54]
58. ((~tall(fred) & funny(fred)) | ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (? [X0] : ((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (tall(fred) | ~funny(fred))) [nnf transformation 16]
59. ((~tall(fred) & funny(fred)) | ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (? [X0] : ((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | tall(fred) | ~funny(fred)) [flattening 58]
60. ((~tall(fred) & funny(fred)) | ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (? [X1] : ((~tall(X1) | generous(X1)) & (tall(X1) | ~generous(X1))) | tall(fred) | ~funny(fred)) [rectify 59]
61. ? [X1] : ((~tall(X1) | generous(X1)) & (tall(X1) | ~generous(X1))) => ((~tall(sK4) | generous(sK4)) & (tall(sK4) | ~generous(sK4))) [choice axiom]
62. ((~tall(fred) & funny(fred)) | ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(sK4) | generous(sK4)) & (tall(sK4) | ~generous(sK4))) | tall(fred) | ~funny(fred)) [skolemisation 60,61]
67. (brave(fred) | creative(fred)) & (~brave(fred) | ~creative(fred)) [nnf transformation 21]
98. ~creative(X0) | wise(X0) | tall(X0) [cnf transformation 51]
104. ~happy(X0) | wise(X0) [cnf transformation 31]
110. ~wise(X0) | tall(X0) [cnf transformation 55]
116. happy(susan) | ~creative(X0) [cnf transformation 34]
117. generous(susan) | ~creative(X0) [cnf transformation 34]
123. ~tall(fred) | ~generous(X0) | ~tall(X0) [cnf transformation 62]
132. brave(fred) | creative(fred) [cnf transformation 67]
134. ~brave(fred) [cnf transformation 23]
220. 20 <=> tall(fred) [avatar definition]
221. ~tall(fred) <- (~20) [avatar component clause 220]
238. 23 <=> tall(susan) [avatar definition]
240. tall(susan) <- (23) [avatar component clause 238]
244. 24 <=> wise(fred) [avatar definition]
245. wise(fred) <- (24) [avatar component clause 244]
259. 27 <=> ! [X0] : ~creative(X0) [avatar definition]
260. ~creative(X0) <- (27) [avatar component clause 259]
262. 28 <=> generous(susan) [avatar definition]
264. generous(susan) <- (28) [avatar component clause 262]
265. 27 | 28 [avatar split clause 117,262,259]
267. 29 <=> happy(susan) [avatar definition]
269. happy(susan) <- (29) [avatar component clause 267]
270. 27 | 29 [avatar split clause 116,267,259]
272. 30 <=> ! [X0] : (~generous(X0) | ~tall(X0)) [avatar definition]
273. ~generous(X0) | ~tall(X0) <- (30) [avatar component clause 272]
274. 30 | ~20 [avatar split clause 123,220,272]
318. 39 <=> creative(fred) [avatar definition]
320. creative(fred) <- (39) [avatar component clause 318]
322. 40 <=> brave(fred) [avatar definition]
325. 39 | 40 [avatar split clause 132,322,318]
336. ~40 [avatar split clause 134,322]
337. $false <- (27, 39) [resolution 320,260]
338. ~27 | ~39 [avatar contradiction clause 337]
340. wise(susan) <- (29) [resolution 104,269]
341. tall(susan) <- (29) [resolution 110,340]
344. 23 | ~29 [avatar split clause 341,267,238]
351. ~tall(susan) <- (28, 30) [resolution 273,264]
353. $false <- (23, 28, 30) [subsumption resolution 351,240]
354. ~23 | ~28 | ~30 [avatar contradiction clause 353]
355. wise(fred) | tall(fred) <- (39) [resolution 98,320]
363. wise(fred) <- (~20, 39) [subsumption resolution 355,221]
364. 24 | 20 | ~39 [avatar split clause 363,318,220,244]
365. tall(fred) <- (24) [resolution 245,110]
366. $false <- (~20, 24) [subsumption resolution 365,221]
367. 20 | ~24 [avatar contradiction clause 366]
368. $false [avatar sat refutation 265,270,274,325,336,338,344,354,364,367]
% SZS output end Proof for 8212811077267243758849097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both curious and tall and vice versa.
If someone is both not generous and not patient then fred is either not tall or wise.
If paul is both wise and not patient then someone is either not tall or wise.
Everyone who is both strong and not creative is either not creative or kind.
Everyone who is not kind or not rich is both not creative and patient and vice versa.
Everyone who is either creative or old is not quiet or not old.
If mary is either not quiet or old then mary is both rich and not calm and vice versa.
If mary is old then susan is creative.
If paul is both patient and quiet then someone is curious or strong.
If fred is creative then someone is happy and vice versa.
Everyone who is quiet is either not wise or not strong and vice versa.
If mary is not funny or calm then someone is both quiet and not quiet.
Everyone who is both not creative and happy is not patient.
Everyone who is both curious and not old is both happy and not wise and vice versa.
Everyone who is both patient and calm is either strong or kind and vice versa.
If mary is both quiet and funny then someone is both tall and generous and vice versa.
Lucy is either happy or not calm.
Someone is both not patient and not humble.
Someone is patient.
Someone is generous or not brave.
Paul is both calm and kind.
Someone is curious.
Someone is not calm or not brave.
Lucy is both happy and not quiet. | Susan is not rich. | contradiction | (![X]:(~calm(X)<=>(curious(X)&tall(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((~tall(fred)<~>wise(fred))))&
(((wise(paul)&~patient(paul)))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((strong(X)&~creative(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~kind(X)|~rich(X))<=>(~creative(X)&patient(X))))&
(![X]:((creative(X)<~>old(X))=>(~quiet(X)|~old(X))))&
(((~quiet(mary)<~>old(mary)))<=>((rich(mary)&~calm(mary))))&
((old(mary))=>(creative(susan)))&
(((patient(paul)&quiet(paul)))=>(?[X]:((curious(X)|strong(X)))))&
((creative(fred))<=>(?[X]:(happy(X))))&
(![X]:(quiet(X)<=>(~wise(X)<~>~strong(X))))&
(((~funny(mary)|calm(mary)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((~creative(X)&happy(X))=>~patient(X)))&
(![X]:((curious(X)&~old(X))<=>(happy(X)&~wise(X))))&
(![X]:((patient(X)&calm(X))<=>(strong(X)<~>kind(X))))&
(((quiet(mary)&funny(mary)))<=>(?[X]:((tall(X)&generous(X)))))&
((happy(lucy)<~>~calm(lucy)))&
(?[X]:((~patient(X)&~humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((generous(X)|~brave(X))))&
((calm(paul)&kind(paul)))&
(?[X]:(curious(X)))&
(?[X]:((~calm(X)|~brave(X))))&
((happy(lucy)&~quiet(lucy))) | ~rich(susan) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7847867240185525506820375
% SZS output start Proof for 7847867240185525506820375
1. ! [X0] : (~calm(X0) <=> (tall(X0) & curious(X0))) [input p0]
4. ! [X0] : ((~creative(X0) & strong(X0)) => (~creative(X0) <~> kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> (patient(X0) & ~creative(X0))) [input p4]
7. (~quiet(mary) <~> old(mary)) <=> (~calm(mary) & rich(mary)) [input p6]
8. old(mary) => creative(susan) [input p7]
11. ! [X0] : (quiet(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p10]
12. (calm(mary) | ~funny(mary)) => ? [X0] : (~quiet(X0) & quiet(X0)) [input p11]
13. ! [X0] : ((happy(X0) & ~creative(X0)) => ~patient(X0)) [input p12]
14. ! [X0] : ((~old(X0) & curious(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
15. ! [X0] : ((calm(X0) & patient(X0)) <=> (strong(X0) <~> kind(X0))) [input p14]
25. ~rich(susan) [input hypothesis]
32. ! [X0] : ((~creative(X0) <~> kind(X0)) | (creative(X0) | ~strong(X0))) [ennf transformation 4]
33. ! [X0] : ((~creative(X0) <~> kind(X0)) | creative(X0) | ~strong(X0)) [flattening 32]
36. creative(susan) | ~old(mary) [ennf transformation 8]
39. ? [X0] : (~quiet(X0) & quiet(X0)) | (~calm(mary) & funny(mary)) [ennf transformation 12]
40. ! [X0] : (~patient(X0) | (~happy(X0) | creative(X0))) [ennf transformation 13]
41. ! [X0] : (~patient(X0) | ~happy(X0) | creative(X0)) [flattening 40]
42. ! [X0] : ((~calm(X0) | (~tall(X0) | ~curious(X0))) & ((tall(X0) & curious(X0)) | calm(X0))) [nnf transformation 1]
43. ! [X0] : ((~calm(X0) | ~tall(X0) | ~curious(X0)) & ((tall(X0) & curious(X0)) | calm(X0))) [flattening 42]
48. ! [X0] : (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | creative(X0) | ~strong(X0)) [nnf transformation 33]
49. ! [X0] : (((~rich(X0) | ~kind(X0)) | (~patient(X0) | creative(X0))) & ((patient(X0) & ~creative(X0)) | (rich(X0) & kind(X0)))) [nnf transformation 5]
50. ! [X0] : ((~rich(X0) | ~kind(X0) | ~patient(X0) | creative(X0)) & ((patient(X0) & ~creative(X0)) | (rich(X0) & kind(X0)))) [flattening 49]
52. (((~old(mary) | quiet(mary)) & (old(mary) | ~quiet(mary))) | (calm(mary) | ~rich(mary))) & ((~calm(mary) & rich(mary)) | ((~quiet(mary) | ~old(mary)) & (old(mary) | quiet(mary)))) [nnf transformation 7]
53. (((~old(mary) | quiet(mary)) & (old(mary) | ~quiet(mary))) | calm(mary) | ~rich(mary)) & ((~calm(mary) & rich(mary)) | ((~quiet(mary) | ~old(mary)) & (old(mary) | quiet(mary)))) [flattening 52]
60. ! [X0] : ((quiet(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~quiet(X0))) [nnf transformation 11]
61. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK3) & quiet(sK3)) [choice axiom]
62. (~quiet(sK3) & quiet(sK3)) | (~calm(mary) & funny(mary)) [skolemisation 39,61]
63. ! [X0] : (((~old(X0) & curious(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (old(X0) | ~curious(X0)))) [nnf transformation 14]
64. ! [X0] : (((~old(X0) & curious(X0)) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | old(X0) | ~curious(X0))) [flattening 63]
65. ! [X0] : (((calm(X0) & patient(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (~calm(X0) | ~patient(X0)))) [nnf transformation 15]
66. ! [X0] : (((calm(X0) & patient(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | ~calm(X0) | ~patient(X0))) [flattening 65]
79. curious(X0) | calm(X0) [cnf transformation 43]
87. ~kind(X0) | creative(X0) | creative(X0) | ~strong(X0) [cnf transformation 48]
88. ~creative(X0) | kind(X0) [cnf transformation 50]
89. ~creative(X0) | rich(X0) [cnf transformation 50]
90. kind(X0) | patient(X0) [cnf transformation 50]
99. old(mary) | ~quiet(mary) | calm(mary) | ~rich(mary) [cnf transformation 53]
101. creative(susan) | ~old(mary) [cnf transformation 36]
107. ~strong(X0) | quiet(X0) | wise(X0) [cnf transformation 60]
110. quiet(sK3) | ~calm(mary) [cnf transformation 62]
112. ~quiet(sK3) | ~calm(mary) [cnf transformation 62]
113. ~happy(X0) | ~patient(X0) | creative(X0) [cnf transformation 41]
114. ~curious(X0) | old(X0) | happy(X0) [cnf transformation 64]
115. ~wise(X0) | old(X0) | ~curious(X0) [cnf transformation 64]
121. patient(X0) | strong(X0) | ~kind(X0) [cnf transformation 66]
122. ~strong(X0) | kind(X0) | calm(X0) [cnf transformation 66]
123. ~kind(X0) | strong(X0) | calm(X0) [cnf transformation 66]
137. ~rich(susan) [cnf transformation 25]
139. ~kind(X0) | creative(X0) | ~strong(X0) [duplicate literal removal 87]
172. 8 <=> rich(mary) [avatar definition]
174. ~rich(mary) <- (~8) [avatar component clause 172]
176. 9 <=> calm(mary) [avatar definition]
177. ~calm(mary) <- (~9) [avatar component clause 176]
180. 10 <=> quiet(mary) [avatar definition]
181. ~quiet(mary) <- (~10) [avatar component clause 180]
184. 11 <=> old(mary) [avatar definition]
186. ~old(mary) <- (~11) [avatar component clause 184]
188. ~8 | 9 | ~10 | 11 [avatar split clause 99,184,180,176,172]
194. 12 <=> creative(susan) [avatar definition]
196. creative(susan) <- (12) [avatar component clause 194]
197. ~11 | 12 [avatar split clause 101,194,184]
225. 19 <=> quiet(sK3) [avatar definition]
228. ~9 | ~19 [avatar split clause 112,225,176]
234. ~9 | 19 [avatar split clause 110,225,176]
236. strong(X0) | patient(X0) [subsumption resolution 121,90]
284. 28 <=> strong(mary) [avatar definition]
285. strong(mary) <- (28) [avatar component clause 284]
286. ~strong(mary) <- (~28) [avatar component clause 284]
288. 29 <=> wise(mary) [avatar definition]
289. wise(mary) <- (29) [avatar component clause 288]
290. ~wise(mary) <- (~29) [avatar component clause 288]
321. happy(X0) | old(X0) | calm(X0) [resolution 114,79]
331. old(mary) | ~curious(mary) <- (29) [resolution 115,289]
332. ~curious(mary) <- (~11, 29) [subsumption resolution 331,186]
394. creative(X0) | ~strong(X0) | patient(X0) [resolution 139,90]
404. creative(X0) | patient(X0) [subsumption resolution 394,236]
432. calm(mary) <- (~11, 29) [resolution 332,79]
433. $false <- (~9, ~11, 29) [subsumption resolution 432,177]
434. 9 | 11 | ~29 [avatar contradiction clause 433]
449. kind(mary) | calm(mary) <- (28) [resolution 285,122]
451. kind(mary) <- (~9, 28) [subsumption resolution 449,177]
474. old(X2) | calm(X2) | ~patient(X2) | creative(X2) [resolution 321,113]
475. old(X2) | calm(X2) | creative(X2) [subsumption resolution 474,404]
478. creative(mary) | ~strong(mary) <- (~9, 28) [resolution 451,139]
480. creative(mary) <- (~9, 28) [subsumption resolution 478,285]
507. rich(mary) <- (~9, 28) [resolution 480,89]
509. $false <- (~8, ~9, 28) [subsumption resolution 507,174]
510. 8 | 9 | ~28 [avatar contradiction clause 509]
512. 56 <=> creative(mary) [avatar definition]
514. creative(mary) <- (56) [avatar component clause 512]
517. rich(susan) <- (12) [resolution 196,89]
519. $false <- (12) [subsumption resolution 517,137]
520. ~12 [avatar contradiction clause 519]
523. calm(mary) | creative(mary) <- (~11) [resolution 186,475]
532. kind(mary) <- (56) [resolution 514,88]
535. strong(mary) | calm(mary) <- (56) [resolution 532,123]
536. calm(mary) <- (~28, 56) [subsumption resolution 535,286]
537. $false <- (~9, ~28, 56) [subsumption resolution 536,177]
538. 9 | 28 | ~56 [avatar contradiction clause 537]
539. creative(mary) <- (~9, ~11) [subsumption resolution 523,177]
540. 56 | 9 | 11 [avatar split clause 539,184,176,512]
548. quiet(mary) | wise(mary) <- (28) [resolution 285,107]
551. wise(mary) <- (~10, 28) [subsumption resolution 548,181]
552. $false <- (~10, 28, ~29) [subsumption resolution 551,290]
553. 10 | ~28 | 29 [avatar contradiction clause 552]
554. $false [avatar sat refutation 188,197,228,234,434,510,520,538,540,553]
% SZS output end Proof for 7847867240185525506820375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or tall is not wise.
If paul is either not tall or happy then someone is not strong or not calm and vice versa.
Everyone who is either kind or not old is either curious or tall.
Everyone who is either rich or curious is not kind or not patient and vice versa.
Everyone who is not kind or not brave is not kind or funny and vice versa.
If alice is generous then someone is tall.
If susan is either not quiet or not brave then susan is both not kind and calm and vice versa.
Everyone who is kind is both patient and not rich.
If alice is calm then someone is brave or not old.
Everyone who is both humble and funny is either rich or old and vice versa.
Everyone who is either not strong or not curious is funny.
Everyone who is either wise or strong is both not patient and not calm.
Everyone who is not strong is not tall.
Everyone who is strong is either kind or not tall.
If susan is both not creative and not tall then someone is either not wise or tall and vice versa.
If someone is both patient and not generous then mary is not generous or calm and vice versa.
Someone is either not curious or not generous.
Paul is rich.
Paul is patient or quiet.
Someone is both not quiet and funny.
Alice is quiet.
Someone is both kind and calm. | Susan is not wise. | entailment | (![X]:((~kind(X)<~>tall(X))=>~wise(X)))&
(((~tall(paul)<~>happy(paul)))<=>(?[X]:((~strong(X)|~calm(X)))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>tall(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~kind(X)|funny(X))))&
((generous(alice))=>(?[X]:(tall(X))))&
(((~quiet(susan)<~>~brave(susan)))<=>((~kind(susan)&calm(susan))))&
(![X]:(kind(X)=>(patient(X)&~rich(X))))&
((calm(alice))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((humble(X)&funny(X))<=>(rich(X)<~>old(X))))&
(![X]:((~strong(X)<~>~curious(X))=>funny(X)))&
(![X]:((wise(X)<~>strong(X))=>(~patient(X)&~calm(X))))&
(![X]:(~strong(X)=>~tall(X)))&
(![X]:(strong(X)=>(kind(X)<~>~tall(X))))&
(((~creative(susan)&~tall(susan)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:((patient(X)&~generous(X))))<=>((~generous(mary)|calm(mary))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(rich(paul))&
((patient(paul)|quiet(paul)))&
(?[X]:((~quiet(X)&funny(X))))&
(quiet(alice))&
(?[X]:((kind(X)&calm(X)))) | ~wise(susan) | [
"p0",
"p7",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7954030717561882648279354
% SZS output start Proof for 7954030717561882648279354
1. ! [X0] : ((~kind(X0) <~> tall(X0)) => ~wise(X0)) [input p0]
8. ! [X0] : (kind(X0) => (~rich(X0) & patient(X0))) [input p7]
12. ! [X0] : ((wise(X0) <~> strong(X0)) => (~calm(X0) & ~patient(X0))) [input p11]
13. ! [X0] : (~strong(X0) => ~tall(X0)) [input p12]
14. ! [X0] : (strong(X0) => (kind(X0) <~> ~tall(X0))) [input p13]
15. (~tall(susan) & ~creative(susan)) <=> ? [X0] : (~wise(X0) <~> tall(X0)) [input p14]
23. wise(susan) [input hypothesis]
24. ! [X0] : (~wise(X0) | (~kind(X0) <=> tall(X0))) [ennf transformation 1]
27. ! [X0] : ((~rich(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 8]
30. ! [X0] : ((~calm(X0) & ~patient(X0)) | (wise(X0) <=> strong(X0))) [ennf transformation 12]
31. ! [X0] : (~tall(X0) | strong(X0)) [ennf transformation 13]
32. ! [X0] : ((kind(X0) <~> ~tall(X0)) | ~strong(X0)) [ennf transformation 14]
33. ! [X0] : (~wise(X0) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0)))) [nnf transformation 24]
52. ! [X0] : ((~calm(X0) & ~patient(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) [nnf transformation 30]
53. ! [X0] : (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ~strong(X0)) [nnf transformation 32]
54. ((~tall(susan) & ~creative(susan)) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (? [X0] : ((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | (tall(susan) | creative(susan))) [nnf transformation 15]
55. ((~tall(susan) & ~creative(susan)) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (? [X0] : ((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | tall(susan) | creative(susan)) [flattening 54]
56. ((~tall(susan) & ~creative(susan)) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (? [X1] : ((~tall(X1) | wise(X1)) & (tall(X1) | ~wise(X1))) | tall(susan) | creative(susan)) [rectify 55]
57. ? [X1] : ((~tall(X1) | wise(X1)) & (tall(X1) | ~wise(X1))) => ((~tall(sK3) | wise(sK3)) & (tall(sK3) | ~wise(sK3))) [choice axiom]
58. ((~tall(susan) & ~creative(susan)) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (((~tall(sK3) | wise(sK3)) & (tall(sK3) | ~wise(sK3))) | tall(susan) | creative(susan)) [skolemisation 56,57]
71. ~wise(X0) | tall(X0) | kind(X0) [cnf transformation 33]
100. ~kind(X0) | patient(X0) [cnf transformation 27]
111. ~patient(X0) | strong(X0) | ~wise(X0) [cnf transformation 52]
115. ~tall(X0) | strong(X0) [cnf transformation 31]
116. ~tall(X0) | kind(X0) | ~strong(X0) [cnf transformation 53]
117. ~strong(X0) | ~kind(X0) | tall(X0) [cnf transformation 53]
123. ~tall(susan) | ~wise(X0) | ~tall(X0) [cnf transformation 58]
138. wise(susan) [cnf transformation 23]
177. 9 <=> kind(susan) [avatar definition]
179. kind(susan) <- (9) [avatar component clause 177]
211. ~tall(X0) | kind(X0) [subsumption resolution 116,115]
213. 16 <=> ! [X0] : (~wise(X0) | ~tall(X0)) [avatar definition]
214. ~wise(X0) | ~tall(X0) <- (16) [avatar component clause 213]
216. 17 <=> tall(susan) [avatar definition]
218. ~tall(susan) <- (~17) [avatar component clause 216]
219. 16 | ~17 [avatar split clause 123,216,213]
285. tall(susan) | kind(susan) [resolution 71,138]
288. kind(susan) [subsumption resolution 285,211]
289. 9 [avatar split clause 288,177]
290. patient(susan) <- (9) [resolution 179,100]
293. ~tall(susan) <- (16) [resolution 214,138]
296. ~17 | ~16 [avatar split clause 293,213,216]
363. strong(susan) | ~wise(susan) <- (9) [resolution 111,290]
375. strong(susan) <- (9) [subsumption resolution 363,138]
434. ~kind(susan) | tall(susan) <- (9) [resolution 375,117]
436. tall(susan) <- (9) [subsumption resolution 434,179]
437. $false <- (9, ~17) [subsumption resolution 436,218]
438. ~9 | 17 [avatar contradiction clause 437]
439. $false [avatar sat refutation 219,289,296,438]
% SZS output end Proof for 7954030717561882648279354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or not calm then someone is both not rich and not funny. Everyone who is both kind and not patient is curious or not creative. Everyone who is tall is either tall or funny and vice versa. If someone is either not tall or not calm then john is not old or not generous. Everyone who is both creative and not generous is strong or kind. If fred is calm then alice is either not generous or wise. Everyone who is calm is both not old and quiet and vice versa. Everyone who is not kind or not curious is either not creative or not happy. If someone is both tall and not humble then someone is wise and vice versa. Everyone who is both not patient and not quiet is either not funny or not patient. If paul is not creative or generous then mary is both generous and patient. Everyone who is either quiet or patient is both happy and not old. Everyone who is either kind or old is either not old or funny and vice versa. Everyone who is either calm or not patient is not calm. Everyone who is not old is either funny or not wise and vice versa. Everyone who is either not calm or funny is not old and vice versa. Mary is kind. John is generous. Someone is not generous. Someone is either not funny or not curious. | Paul is happy. | entailment | ((?[X]:((funny(X)<~>~calm(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((kind(X)&~patient(X))=>(curious(X)|~creative(X))))&
(![X]:(tall(X)<=>(tall(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>~calm(X))))=>((~old(john)|~generous(john))))&
(![X]:((creative(X)&~generous(X))=>(strong(X)|kind(X))))&
((calm(fred))=>((~generous(alice)<~>wise(alice))))&
(![X]:(calm(X)<=>(~old(X)&quiet(X))))&
(![X]:((~kind(X)|~curious(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((tall(X)&~humble(X))))<=>(?[X]:(wise(X))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~patient(X))))&
(((~creative(paul)|generous(paul)))=>((generous(mary)&patient(mary))))&
(![X]:((quiet(X)<~>patient(X))=>(happy(X)&~old(X))))&
(![X]:((kind(X)<~>old(X))<=>(~old(X)<~>funny(X))))&
(![X]:((calm(X)<~>~patient(X))=>~calm(X)))&
(![X]:(~old(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>funny(X))<=>~old(X)))&
(kind(mary))&
(generous(john))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~curious(X)))) | happy(paul) | [
"p2",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4986033579068620591923225
% SZS output start Proof for 4986033579068620591923225
3. ! [X0] : (tall(X0) <=> (tall(X0) <~> funny(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> (quiet(X0) & ~old(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~patient(X0)) => (~funny(X0) <~> ~patient(X0))) [input p9]
12. ! [X0] : ((quiet(X0) <~> patient(X0)) => (~old(X0) & happy(X0))) [input p11]
16. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> ~old(X0)) [input p15]
21. ~happy(paul) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | (quiet(X0) | patient(X0))) [ennf transformation 10]
34. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | quiet(X0) | patient(X0)) [flattening 33]
36. ! [X0] : ((~old(X0) & happy(X0)) | (quiet(X0) <=> patient(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~tall(X0))) [nnf transformation 3]
45. ! [X0] : ((calm(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [flattening 45]
53. ! [X0] : (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | quiet(X0) | patient(X0)) [nnf transformation 34]
54. ! [X0] : ((~old(X0) & happy(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) [nnf transformation 36]
58. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | old(X0)) & (~old(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 16]
68. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 42]
70. tall(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
75. ~old(X0) | ~calm(X0) [cnf transformation 46]
77. ~quiet(X0) | calm(X0) | old(X0) [cnf transformation 46]
86. patient(X0) | funny(X0) | quiet(X0) | patient(X0) [cnf transformation 53]
92. happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 54]
109. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 58]
111. funny(X0) | ~calm(X0) | old(X0) [cnf transformation 58]
118. ~happy(paul) [cnf transformation 21]
124. patient(X0) | funny(X0) | quiet(X0) [duplicate literal removal 86]
125. ~funny(X0) | ~tall(X0) [duplicate literal removal 68]
126. ~funny(X0) | tall(X0) [duplicate literal removal 70]
139. ~funny(X0) [subsumption resolution 125,126]
191. quiet(X0) | patient(X0) [subsumption resolution 124,139]
214. happy(X0) | quiet(X0) [subsumption resolution 92,191]
221. ~calm(X0) | old(X0) [subsumption resolution 111,139]
222. ~calm(X0) [subsumption resolution 221,75]
223. ~old(X0) | calm(X0) [subsumption resolution 109,139]
224. ~old(X0) [subsumption resolution 223,222]
227. quiet(paul) [resolution 214,118]
236. calm(paul) | old(paul) [resolution 77,227]
239. old(paul) [subsumption resolution 236,222]
240. $false [subsumption resolution 239,224]
% SZS output end Proof for 4986033579068620591923225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not tall or strong then someone is not old or curious.
Everyone who is both not generous and not tall is both not quiet and wise and vice versa.
Everyone who is not creative or not funny is creative or not quiet.
Everyone who is calm is both old and creative and vice versa.
Everyone who is either calm or patient is curious and vice versa.
Everyone who is creative is either tall or not rich.
Everyone who is either not humble or not happy is both generous and calm.
Everyone who is either not wise or patient is either not curious or rich.
Everyone who is funny is brave and vice versa.
Everyone who is not creative or not funny is not tall or wise and vice versa.
Everyone who is not happy is both old and tall and vice versa.
Everyone who is either not kind or not old is not quiet.
Everyone who is both not rich and not humble is either not curious or wise.
Everyone who is curious is not patient.
Everyone who is either quiet or old is not happy and vice versa.
Everyone who is both not generous and kind is not strong.
Susan is humble or not old.
Lucy is not calm or quiet.
Lucy is either kind or not brave.
Someone is both happy and strong.
Lucy is both not old and not tall.
Someone is not tall or happy.
John is not calm or not creative.
Someone is not happy. | Susan is not happy. | neutral | (((~tall(lucy)|strong(lucy)))=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((~generous(X)&~tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~creative(X)|~funny(X))=>(creative(X)|~quiet(X))))&
(![X]:(calm(X)<=>(old(X)&creative(X))))&
(![X]:((calm(X)<~>patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(tall(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(generous(X)&calm(X))))&
(![X]:((~wise(X)<~>patient(X))=>(~curious(X)<~>rich(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~creative(X)|~funny(X))<=>(~tall(X)|wise(X))))&
(![X]:(~happy(X)<=>(old(X)&tall(X))))&
(![X]:((~kind(X)<~>~old(X))=>~quiet(X)))&
(![X]:((~rich(X)&~humble(X))=>(~curious(X)<~>wise(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((quiet(X)<~>old(X))<=>~happy(X)))&
(![X]:((~generous(X)&kind(X))=>~strong(X)))&
((humble(susan)|~old(susan)))&
((~calm(lucy)|quiet(lucy)))&
((kind(lucy)<~>~brave(lucy)))&
(?[X]:((happy(X)&strong(X))))&
((~old(lucy)&~tall(lucy)))&
(?[X]:((~tall(X)|happy(X))))&
((~calm(john)|~creative(john)))&
(?[X]:(~happy(X))) | ~happy(susan) | []
| null | 0 |
Everyone who is not old or creative is both tall and kind.
If someone is wise then fred is old.
Everyone who is both not humble and not brave is wise or brave and vice versa.
Everyone who is both not curious and not old is both strong and not rich.
If mary is not kind then someone is not kind and vice versa.
If someone is strong then someone is either not creative or old and vice versa.
Everyone who is old or not funny is strong.
If fred is either not generous or not rich then someone is either not wise or quiet.
If alice is either not patient or calm then paul is both generous and not creative and vice versa.
If fred is not strong then someone is calm or not funny and vice versa.
If fred is both calm and rich then paul is either not rich or old and vice versa.
Everyone who is either not calm or old is both not wise and kind.
If someone is kind or not brave then someone is not strong or not happy and vice versa.
If someone is both not patient and not rich then someone is funny or rich and vice versa.
If fred is not curious then someone is not humble and vice versa.
Mary is not strong.
Mary is not patient or not rich.
Someone is either not wise or not old.
Alice is not calm.
Someone is old or strong.
Mary is not humble or tall. | Mary is not quiet. | neutral | (![X]:((~old(X)|creative(X))=>(tall(X)&kind(X))))&
((?[X]:(wise(X)))=>(old(fred)))&
(![X]:((~humble(X)&~brave(X))<=>(wise(X)|brave(X))))&
(![X]:((~curious(X)&~old(X))=>(strong(X)&~rich(X))))&
((~kind(mary))<=>(?[X]:(~kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((old(X)|~funny(X))=>strong(X)))&
(((~generous(fred)<~>~rich(fred)))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(((~patient(alice)<~>calm(alice)))<=>((generous(paul)&~creative(paul))))&
((~strong(fred))<=>(?[X]:((calm(X)|~funny(X)))))&
(((calm(fred)&rich(fred)))<=>((~rich(paul)<~>old(paul))))&
(![X]:((~calm(X)<~>old(X))=>(~wise(X)&kind(X))))&
((?[X]:((kind(X)|~brave(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
((?[X]:((~patient(X)&~rich(X))))<=>(?[X]:((funny(X)|rich(X)))))&
((~curious(fred))<=>(?[X]:(~humble(X))))&
(~strong(mary))&
((~patient(mary)|~rich(mary)))&
(?[X]:((~wise(X)<~>~old(X))))&
(~calm(alice))&
(?[X]:((old(X)|strong(X))))&
((~humble(mary)|tall(mary))) | ~quiet(mary) | []
| null | 0 |
Everyone who is rich is both curious and kind.
If john is either not curious or curious then mary is not creative and vice versa.
If someone is not funny then someone is both not wise and not kind and vice versa.
Everyone who is both strong and not kind is not generous or not quiet and vice versa.
If someone is not old then fred is strong and vice versa.
If susan is not funny or not strong then alice is either not brave or not kind and vice versa.
If john is tall or brave then paul is either not strong or happy.
If someone is tall or not rich then someone is not tall or patient.
Everyone who is both wise and quiet is not quiet or not calm and vice versa.
Everyone who is not kind is brave.
Everyone who is both not strong and not humble is both not strong and not old and vice versa.
Everyone who is not humble or not curious is not humble or not patient.
If someone is both not strong and strong then mary is kind and vice versa.
If john is not rich then someone is both not brave and not curious.
If someone is old then mary is both old and creative and vice versa.
Everyone who is brave is creative or not humble.
Paul is both not kind and not rich.
John is both not rich and brave.
Someone is strong.
Someone is not strong.
Someone is not patient.
Lucy is not brave or not happy. | Fred is not strong. | contradiction | (![X]:(rich(X)=>(curious(X)&kind(X))))&
(((~curious(john)<~>curious(john)))<=>(~creative(mary)))&
((?[X]:(~funny(X)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((strong(X)&~kind(X))<=>(~generous(X)|~quiet(X))))&
((?[X]:(~old(X)))<=>(strong(fred)))&
(((~funny(susan)|~strong(susan)))<=>((~brave(alice)<~>~kind(alice))))&
(((tall(john)|brave(john)))=>((~strong(paul)<~>happy(paul))))&
((?[X]:((tall(X)|~rich(X))))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~quiet(X)|~calm(X))))&
(![X]:(~kind(X)=>brave(X)))&
(![X]:((~strong(X)&~humble(X))<=>(~strong(X)&~old(X))))&
(![X]:((~humble(X)|~curious(X))=>(~humble(X)|~patient(X))))&
((?[X]:((~strong(X)&strong(X))))<=>(kind(mary)))&
((~rich(john))=>(?[X]:((~brave(X)&~curious(X)))))&
((?[X]:(old(X)))<=>((old(mary)&creative(mary))))&
(![X]:(brave(X)=>(creative(X)|~humble(X))))&
((~kind(paul)&~rich(paul)))&
((~rich(john)&brave(john)))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
((~brave(lucy)|~happy(lucy))) | ~strong(fred) | [
"p1",
"p4",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 808575768434217047218441
% SZS output start Proof for 808575768434217047218441
2. (~curious(john) <~> curious(john)) <=> ~creative(mary) [input p1]
5. ? [X0] : ~old(X0) <=> strong(fred) [input p4]
15. ? [X0] : old(X0) <=> (creative(mary) & old(mary)) [input p14]
23. ~strong(fred) [input hypothesis]
36. (((~curious(john) | curious(john)) & (curious(john) | ~curious(john))) | creative(mary)) & (~creative(mary) | ((~curious(john) | ~curious(john)) & (curious(john) | curious(john)))) [nnf transformation 2]
44. (? [X0] : ~old(X0) | ~strong(fred)) & (strong(fred) | ! [X0] : old(X0)) [nnf transformation 5]
45. (? [X0] : ~old(X0) | ~strong(fred)) & (strong(fred) | ! [X1] : old(X1)) [rectify 44]
46. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
47. (~old(sK2) | ~strong(fred)) & (strong(fred) | ! [X1] : old(X1)) [skolemisation 45,46]
61. (? [X0] : old(X0) | (~creative(mary) | ~old(mary))) & ((creative(mary) & old(mary)) | ! [X0] : ~old(X0)) [nnf transformation 15]
62. (? [X0] : old(X0) | ~creative(mary) | ~old(mary)) & ((creative(mary) & old(mary)) | ! [X0] : ~old(X0)) [flattening 61]
63. (? [X0] : old(X0) | ~creative(mary) | ~old(mary)) & ((creative(mary) & old(mary)) | ! [X1] : ~old(X1)) [rectify 62]
64. ? [X0] : old(X0) => old(sK5) [choice axiom]
65. (old(sK5) | ~creative(mary) | ~old(mary)) & ((creative(mary) & old(mary)) | ! [X1] : ~old(X1)) [skolemisation 63,64]
72. ~creative(mary) | curious(john) | curious(john) [cnf transformation 36]
73. ~creative(mary) | ~curious(john) | ~curious(john) [cnf transformation 36]
84. strong(fred) | old(X1) [cnf transformation 47]
110. creative(mary) | ~old(X1) [cnf transformation 65]
120. ~strong(fred) [cnf transformation 23]
123. ~creative(mary) | curious(john) [duplicate literal removal 72]
124. ~creative(mary) | ~curious(john) [duplicate literal removal 73]
126. 1 <=> curious(john) [avatar definition]
130. 2 <=> creative(mary) [avatar definition]
133. ~1 | ~2 [avatar split clause 124,130,126]
134. 1 | ~2 [avatar split clause 123,130,126]
157. 8 <=> strong(fred) [avatar definition]
166. 10 <=> ! [X1] : old(X1) [avatar definition]
167. old(X1) <- (10) [avatar component clause 166]
168. 10 | 8 [avatar split clause 84,157,166]
240. 25 <=> ! [X1] : ~old(X1) [avatar definition]
241. ~old(X1) <- (25) [avatar component clause 240]
242. 25 | 2 [avatar split clause 110,130,240]
255. ~8 [avatar split clause 120,157]
256. $false <- (10, 25) [subsumption resolution 167,241]
257. ~10 | ~25 [avatar contradiction clause 256]
258. $false [avatar sat refutation 133,134,168,242,255,257]
% SZS output end Proof for 808575768434217047218441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or rich is both not creative and not wise.
Everyone who is either not kind or not brave is kind.
Everyone who is either not curious or not humble is either patient or not happy and vice versa.
Everyone who is not quiet is either kind or tall and vice versa.
Everyone who is not strong or not generous is not kind or not strong and vice versa.
If someone is both not happy and not quiet then fred is wise or not patient and vice versa.
If someone is either not tall or rich then someone is both funny and not wise and vice versa.
If someone is not old then alice is both kind and not tall.
Everyone who is either not brave or curious is both not patient and not wise and vice versa.
Everyone who is rich or quiet is both not quiet and not brave.
Everyone who is calm or brave is both not wise and brave and vice versa.
Everyone who is generous is both not rich and old and vice versa.
If someone is either funny or not creative then someone is not curious and vice versa.
If someone is both not generous and not tall then someone is not humble or not calm.
Everyone who is curious or generous is either not happy or calm and vice versa.
If someone is both tall and not wise then fred is both not wise and brave and vice versa.
Someone is either not generous or not happy.
Someone is strong.
Mary is old or kind.
Someone is kind or not humble.
Paul is not generous.
Someone is not brave.
Fred is not brave.
Mary is patient or funny. | Alice is kind. | neutral | (![X]:((~strong(X)<~>rich(X))=>(~creative(X)&~wise(X))))&
(![X]:((~kind(X)<~>~brave(X))=>kind(X)))&
(![X]:((~curious(X)<~>~humble(X))<=>(patient(X)<~>~happy(X))))&
(![X]:(~quiet(X)<=>(kind(X)<~>tall(X))))&
(![X]:((~strong(X)|~generous(X))<=>(~kind(X)|~strong(X))))&
((?[X]:((~happy(X)&~quiet(X))))<=>((wise(fred)|~patient(fred))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
((?[X]:(~old(X)))=>((kind(alice)&~tall(alice))))&
(![X]:((~brave(X)<~>curious(X))<=>(~patient(X)&~wise(X))))&
(![X]:((rich(X)|quiet(X))=>(~quiet(X)&~brave(X))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
(![X]:(generous(X)<=>(~rich(X)&old(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:(strong(X)))&
((old(mary)|kind(mary)))&
(?[X]:((kind(X)|~humble(X))))&
(~generous(paul))&
(?[X]:(~brave(X)))&
(~brave(fred))&
((patient(mary)|funny(mary))) | kind(alice) | []
| null | 0 |
If susan is funny or generous then someone is strong or not quiet and vice versa.
If someone is either not funny or not old then someone is funny or not generous and vice versa.
Everyone who is either calm or quiet is either not generous or happy and vice versa.
If someone is wise then someone is not tall or creative and vice versa.
Everyone who is not creative or not generous is not strong or kind and vice versa.
Everyone who is not brave or not strong is both brave and generous and vice versa.
Everyone who is either brave or not calm is both not funny and kind and vice versa.
If john is either rich or curious then someone is not humble and vice versa.
If someone is funny then susan is old or not humble and vice versa.
If lucy is either not quiet or happy then paul is not creative.
If alice is either humble or not quiet then someone is both kind and not creative and vice versa.
If john is both tall and not happy then someone is both happy and creative.
If someone is both funny and not tall then someone is not brave.
Everyone who is either strong or not brave is either generous or not rich and vice versa.
If fred is either funny or not rich then someone is curious or not kind and vice versa.
Everyone who is both brave and not old is both rich and not funny.
Someone is brave.
Someone is both brave and not happy.
Someone is not calm.
Paul is not happy.
Someone is either not humble or kind.
Fred is both not creative and patient. | Lucy is not tall. | neutral | (((funny(susan)|generous(susan)))<=>(?[X]:((strong(X)|~quiet(X)))))&
((?[X]:((~funny(X)<~>~old(X))))<=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~tall(X)|creative(X)))))&
(![X]:((~creative(X)|~generous(X))<=>(~strong(X)|kind(X))))&
(![X]:((~brave(X)|~strong(X))<=>(brave(X)&generous(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~funny(X)&kind(X))))&
(((rich(john)<~>curious(john)))<=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))<=>((old(susan)|~humble(susan))))&
(((~quiet(lucy)<~>happy(lucy)))=>(~creative(paul)))&
(((humble(alice)<~>~quiet(alice)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((tall(john)&~happy(john)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(generous(X)<~>~rich(X))))&
(((funny(fred)<~>~rich(fred)))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((brave(X)&~old(X))=>(rich(X)&~funny(X))))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~happy(X))))&
(?[X]:(~calm(X)))&
(~happy(paul))&
(?[X]:((~humble(X)<~>kind(X))))&
((~creative(fred)&patient(fred))) | ~tall(lucy) | []
| null | 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is either not tall or not wise is either patient or tall and vice versa.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Fred is both not tall and not humble.
Someone is wise.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm. | Fred is not old. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X))) | ~old(fred) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 5890740966137453040993519
% SZS output start Proof for 5890740966137453040993519
1. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> humble(X0)) [input p0]
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) <~> tall(X0))) [input p2]
4. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p3]
5. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (brave(X0) | happy(X0))) [input p6]
16. ~humble(fred) & ~tall(fred) [input p15]
20. ~generous(fred) & ~rich(fred) [input p19]
22. old(fred) [input hypothesis]
24. ! [X0] : ((~curious(X0) <~> generous(X0)) => humble(X0)) [unused predicate definition removal 1]
25. ! [X0] : (humble(X0) | (~curious(X0) <=> generous(X0))) [ennf transformation 24]
26. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
27. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 4]
35. ! [X0] : (humble(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 25]
36. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 26]
37. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 5]
40. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 7]
41. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~wise(X0))) [flattening 40]
73. humble(X0) | generous(X0) | curious(X0) [cnf transformation 35]
75. ~creative(X0) | happy(X0) | ~old(X0) [cnf transformation 36]
76. ~happy(X0) | creative(X0) | ~old(X0) [cnf transformation 36]
77. tall(X0) | patient(X0) | ~wise(X0) | tall(X0) [cnf transformation 37]
82. ~wise(X0) | ~tall(X0) | patient(X0) | ~tall(X0) [cnf transformation 37]
86. ~curious(X0) | happy(X0) [cnf transformation 27]
88. ~patient(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 38]
94. ~happy(X0) | wise(X0) [cnf transformation 41]
127. ~humble(fred) [cnf transformation 16]
132. ~generous(fred) [cnf transformation 20]
134. old(fred) [cnf transformation 22]
137. tall(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 77]
139. ~wise(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 82]
142. ~wise(X0) | patient(X0) [subsumption resolution 137,139]
144. 1 <=> creative(fred) [avatar definition]
145. creative(fred) <- (1) [avatar component clause 144]
162. 5 <=> patient(fred) [avatar definition]
163. ~patient(fred) <- (~5) [avatar component clause 162]
164. patient(fred) <- (5) [avatar component clause 162]
282. generous(fred) | curious(fred) [resolution 73,127]
283. curious(fred) [subsumption resolution 282,132]
286. happy(fred) | ~old(fred) <- (1) [resolution 75,145]
288. happy(fred) <- (1) [subsumption resolution 286,134]
298. happy(fred) [resolution 283,86]
330. wise(fred) <- (1) [resolution 288,94]
446. patient(fred) <- (1) [resolution 330,142]
449. $false <- (1, ~5) [subsumption resolution 446,163]
450. ~1 | 5 [avatar contradiction clause 449]
472. creative(fred) | ~old(fred) [resolution 298,76]
478. creative(fred) [subsumption resolution 472,134]
479. 1 [avatar split clause 478,144]
575. ~happy(fred) | ~creative(fred) <- (5) [resolution 164,88]
578. ~creative(fred) <- (5) [subsumption resolution 575,298]
579. $false <- (1, 5) [subsumption resolution 578,145]
580. ~1 | ~5 [avatar contradiction clause 579]
581. $false [avatar sat refutation 450,479,580]
% SZS output end Proof for 5890740966137453040993519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not generous is tall or generous.
If john is funny then someone is not tall or not strong.
If someone is not creative then fred is not curious and vice versa.
If fred is both not funny and not tall then paul is both not kind and kind and vice versa.
Everyone who is not humble or not patient is humble or rich.
Everyone who is both patient and not quiet is not creative or curious.
Everyone who is both generous and strong is both not humble and not strong.
If someone is funny then someone is both not old and not curious.
Everyone who is either not humble or humble is not happy and vice versa.
If john is either not tall or generous then someone is strong and vice versa.
If paul is both happy and brave then alice is either patient or happy and vice versa.
Everyone who is both not funny and generous is happy.
Everyone who is either not humble or not old is happy or not humble and vice versa.
Everyone who is not brave is either not strong or curious and vice versa.
Everyone who is not quiet or wise is not old.
If fred is not calm then mary is happy and vice versa.
Mary is not curious or not quiet.
Someone is rich.
Someone is either not creative or not generous.
John is not wise or not happy.
Someone is both not curious and humble.
Someone is either not rich or not calm.
Someone is both not funny and brave. | Mary is brave. | contradiction | (![X]:((~humble(X)|~generous(X))=>(tall(X)|generous(X))))&
((funny(john))=>(?[X]:((~tall(X)|~strong(X)))))&
((?[X]:(~creative(X)))<=>(~curious(fred)))&
(((~funny(fred)&~tall(fred)))<=>((~kind(paul)&kind(paul))))&
(![X]:((~humble(X)|~patient(X))=>(humble(X)|rich(X))))&
(![X]:((patient(X)&~quiet(X))=>(~creative(X)|curious(X))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((~humble(X)<~>humble(X))<=>~happy(X)))&
(((~tall(john)<~>generous(john)))<=>(?[X]:(strong(X))))&
(((happy(paul)&brave(paul)))<=>((patient(alice)<~>happy(alice))))&
(![X]:((~funny(X)&generous(X))=>happy(X)))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~humble(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~quiet(X)|wise(X))=>~old(X)))&
((~calm(fred))<=>(happy(mary)))&
((~curious(mary)|~quiet(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)<~>~generous(X))))&
((~wise(john)|~happy(john)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~funny(X)&brave(X)))) | brave(mary) | [
"p0",
"p7",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6649154934509635144414463
% SZS output start Proof for 6649154934509635144414463
1. ! [X0] : ((~generous(X0) | ~humble(X0)) => (generous(X0) | tall(X0))) [input p0]
8. ? [X0] : funny(X0) => ? [X0] : (~curious(X0) & ~old(X0)) [input p7]
9. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~happy(X0)) [input p8]
10. (~tall(john) <~> generous(john)) <=> ? [X0] : strong(X0) [input p9]
12. ! [X0] : ((generous(X0) & ~funny(X0)) => happy(X0)) [input p11]
13. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (~humble(X0) | happy(X0))) [input p12]
14. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> curious(X0))) [input p13]
15. ! [X0] : ((wise(X0) | ~quiet(X0)) => ~old(X0)) [input p14]
17. ~quiet(mary) | ~curious(mary) [input p16]
24. brave(mary) [input hypothesis]
25. ? [X0] : funny(X0) => ? [X1] : (~curious(X1) & ~old(X1)) [rectify 8]
26. ! [X0] : (~quiet(X0) => ~old(X0)) [pure predicate removal 15]
28. ! [X0] : ((generous(X0) | tall(X0)) | (generous(X0) & humble(X0))) [ennf transformation 1]
29. ! [X0] : (generous(X0) | tall(X0) | (generous(X0) & humble(X0))) [flattening 28]
37. ? [X1] : (~curious(X1) & ~old(X1)) | ! [X0] : ~funny(X0) [ennf transformation 25]
38. ! [X0] : (happy(X0) | (~generous(X0) | funny(X0))) [ennf transformation 12]
39. ! [X0] : (happy(X0) | ~generous(X0) | funny(X0)) [flattening 38]
40. ! [X0] : (~old(X0) | quiet(X0)) [ennf transformation 26]
49. ? [X0] : (~curious(X0) & ~old(X0)) | ! [X1] : ~funny(X1) [rectify 37]
50. ? [X0] : (~curious(X0) & ~old(X0)) => (~curious(sK2) & ~old(sK2)) [choice axiom]
51. (~curious(sK2) & ~old(sK2)) | ! [X1] : ~funny(X1) [skolemisation 49,50]
52. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0)) & (~happy(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 9]
53. (((~generous(john) | tall(john)) & (generous(john) | ~tall(john))) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ((~tall(john) | ~generous(john)) & (generous(john) | tall(john)))) [nnf transformation 10]
54. (((~generous(john) | tall(john)) & (generous(john) | ~tall(john))) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ((~tall(john) | ~generous(john)) & (generous(john) | tall(john)))) [rectify 53]
55. ? [X1] : strong(X1) => strong(sK3) [choice axiom]
56. (((~generous(john) | tall(john)) & (generous(john) | ~tall(john))) | ! [X0] : ~strong(X0)) & (strong(sK3) | ((~tall(john) | ~generous(john)) & (generous(john) | tall(john)))) [skolemisation 54,55]
59. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & ((~humble(X0) | happy(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 13]
60. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (humble(X0) & ~happy(X0))) & (~humble(X0) | happy(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 59]
61. ! [X0] : ((~brave(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 14]
76. generous(X0) | tall(X0) | generous(X0) [cnf transformation 29]
89. ~old(sK2) | ~funny(X1) [cnf transformation 51]
91. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 52]
92. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
97. generous(john) | ~tall(john) | ~strong(X0) [cnf transformation 56]
105. happy(X0) | ~generous(X0) | funny(X0) [cnf transformation 39]
107. ~humble(X0) | happy(X0) | ~humble(X0) | old(X0) [cnf transformation 60]
111. old(X0) | humble(X0) | humble(X0) [cnf transformation 60]
114. ~brave(X0) | curious(X0) | strong(X0) [cnf transformation 61]
116. ~old(X0) | quiet(X0) [cnf transformation 40]
119. ~quiet(mary) | ~curious(mary) [cnf transformation 17]
129. brave(mary) [cnf transformation 24]
130. ~humble(X0) | happy(X0) | old(X0) [duplicate literal removal 107]
131. old(X0) | humble(X0) [duplicate literal removal 111]
132. ~happy(X0) | humble(X0) [duplicate literal removal 91]
133. ~happy(X0) | ~humble(X0) [duplicate literal removal 92]
136. tall(X0) | generous(X0) [duplicate literal removal 76]
178. 10 <=> ! [X1] : ~funny(X1) [avatar definition]
179. ~funny(X1) <- (10) [avatar component clause 178]
186. 12 <=> old(sK2) [avatar definition]
188. ~old(sK2) <- (~12) [avatar component clause 186]
189. 10 | ~12 [avatar split clause 89,186,178]
190. ~happy(X0) [subsumption resolution 132,133]
193. 13 <=> ! [X0] : ~strong(X0) [avatar definition]
194. ~strong(X0) <- (13) [avatar component clause 193]
200. generous(john) | ~strong(X0) [subsumption resolution 97,136]
202. 15 <=> generous(john) [avatar definition]
204. generous(john) <- (15) [avatar component clause 202]
205. 13 | 15 [avatar split clause 200,202,193]
224. ~generous(X0) | funny(X0) [subsumption resolution 105,190]
225. ~humble(X0) | old(X0) [subsumption resolution 130,190]
226. old(X0) [subsumption resolution 225,131]
227. quiet(X0) [subsumption resolution 116,226]
229. ~curious(mary) [subsumption resolution 119,227]
250. $false <- (~12) [subsumption resolution 188,226]
251. 12 [avatar contradiction clause 250]
257. curious(mary) | strong(mary) [resolution 114,129]
259. strong(mary) [subsumption resolution 257,229]
260. $false <- (13) [subsumption resolution 259,194]
261. ~13 [avatar contradiction clause 260]
271. funny(john) <- (15) [resolution 204,224]
274. $false <- (10, 15) [subsumption resolution 271,179]
275. ~10 | ~15 [avatar contradiction clause 274]
278. $false [avatar sat refutation 189,205,251,261,275]
% SZS output end Proof for 6649154934509635144414463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old is not wise or funny.
Everyone who is either strong or calm is not brave and vice versa.
Everyone who is both happy and not wise is both not old and not strong.
Everyone who is wise is both curious and not wise.
Everyone who is generous or happy is either creative or funny.
Everyone who is happy or not calm is wise or creative.
Everyone who is not patient is either not curious or old.
If someone is not strong or tall then someone is brave or not patient.
If mary is both funny and not creative then someone is not quiet.
If someone is either not curious or brave then alice is both not patient and generous and vice versa.
If someone is happy then lucy is not rich.
Everyone who is both not strong and curious is both old and curious.
If someone is either wise or creative then alice is funny or not wise and vice versa.
If someone is both funny and not wise then paul is not funny or calm.
If someone is humble then someone is not calm and vice versa.
Everyone who is both creative and not strong is both not strong and old.
Someone is old or generous.
Someone is both not rich and not quiet.
Someone is not generous.
Lucy is both not happy and not funny.
Someone is funny or quiet.
Lucy is either not quiet or humble.
John is not rich or not tall.
Susan is strong. | Paul is not wise. | entailment | (![X]:((funny(X)&~old(X))=>(~wise(X)|funny(X))))&
(![X]:((strong(X)<~>calm(X))<=>~brave(X)))&
(![X]:((happy(X)&~wise(X))=>(~old(X)&~strong(X))))&
(![X]:(wise(X)=>(curious(X)&~wise(X))))&
(![X]:((generous(X)|happy(X))=>(creative(X)<~>funny(X))))&
(![X]:((happy(X)|~calm(X))=>(wise(X)|creative(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>old(X))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(((funny(mary)&~creative(mary)))=>(?[X]:(~quiet(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>((~patient(alice)&generous(alice))))&
((?[X]:(happy(X)))=>(~rich(lucy)))&
(![X]:((~strong(X)&curious(X))=>(old(X)&curious(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>((funny(alice)|~wise(alice))))&
((?[X]:((funny(X)&~wise(X))))=>((~funny(paul)|calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&~strong(X))=>(~strong(X)&old(X))))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((~rich(X)&~quiet(X))))&
(?[X]:(~generous(X)))&
((~happy(lucy)&~funny(lucy)))&
(?[X]:((funny(X)|quiet(X))))&
((~quiet(lucy)<~>humble(lucy)))&
((~rich(john)|~tall(john)))&
(strong(susan)) | ~wise(paul) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 231087312155202741197134
% SZS output start Proof for 231087312155202741197134
4. ! [X0] : (wise(X0) => (~wise(X0) & curious(X0))) [input p3]
25. wise(paul) [input hypothesis]
38. ! [X0] : ((~wise(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 4]
90. ~wise(X0) | ~wise(X0) [cnf transformation 38]
125. wise(paul) [cnf transformation 25]
126. ~wise(X0) [duplicate literal removal 90]
240. $false [subsumption resolution 125,126]
% SZS output end Proof for 231087312155202741197134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and humble is not creative or happy and vice versa. Everyone who is either not generous or not old is not kind or not generous and vice versa. Everyone who is humble is either kind or funny and vice versa. Everyone who is either rich or generous is not brave. If someone is either not curious or kind then john is not old and vice versa. Everyone who is calm is rich and vice versa. Everyone who is calm is either strong or not tall and vice versa. Everyone who is old is generous and vice versa. If someone is old then someone is calm or not happy. Everyone who is both kind and not humble is rich. Everyone who is happy or not rich is calm. Everyone who is not rich or funny is wise or happy. Everyone who is either not quiet or old is either not old or patient. Everyone who is kind or happy is patient or creative and vice versa. If someone is funny or not calm then fred is not rich or not calm. If lucy is happy then susan is old and vice versa. John is rich or not calm. John is both not quiet and generous. Paul is both humble and rich. Someone is not calm or old. Susan is generous or not funny. Lucy is not calm or quiet. Fred is not curious. | Lucy is not curious. | entailment | (![X]:((~wise(X)&humble(X))<=>(~creative(X)|happy(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~kind(X)|~generous(X))))&
(![X]:(humble(X)<=>(kind(X)<~>funny(X))))&
(![X]:((rich(X)<~>generous(X))=>~brave(X)))&
((?[X]:((~curious(X)<~>kind(X))))<=>(~old(john)))&
(![X]:(calm(X)<=>rich(X)))&
(![X]:(calm(X)<=>(strong(X)<~>~tall(X))))&
(![X]:(old(X)<=>generous(X)))&
((?[X]:(old(X)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((kind(X)&~humble(X))=>rich(X)))&
(![X]:((happy(X)|~rich(X))=>calm(X)))&
(![X]:((~rich(X)|funny(X))=>(wise(X)|happy(X))))&
(![X]:((~quiet(X)<~>old(X))=>(~old(X)<~>patient(X))))&
(![X]:((kind(X)|happy(X))<=>(patient(X)|creative(X))))&
((?[X]:((funny(X)|~calm(X))))=>((~rich(fred)|~calm(fred))))&
((happy(lucy))<=>(old(susan)))&
((rich(john)|~calm(john)))&
((~quiet(john)&generous(john)))&
((humble(paul)&rich(paul)))&
(?[X]:((~calm(X)|old(X))))&
((generous(susan)|~funny(susan)))&
((~calm(lucy)|quiet(lucy)))&
(~curious(fred)) | ~curious(lucy) | [
"p1",
"p4",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 1371713772357583723348355
% SZS output start Proof for 1371713772357583723348355
2. ! [X0] : ((~generous(X0) <~> ~old(X0)) <=> (~generous(X0) | ~kind(X0))) [input p1]
5. ? [X0] : (~curious(X0) <~> kind(X0)) <=> ~old(john) [input p4]
8. ! [X0] : (old(X0) <=> generous(X0)) [input p7]
24. curious(lucy) [input hypothesis]
38. ! [X0] : ((((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0))))) [nnf transformation 2]
39. ! [X0] : ((((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0))))) [flattening 38]
41. (? [X0] : ((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | old(john)) & (~old(john) | ! [X0] : ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0)))) [nnf transformation 5]
42. (? [X0] : ((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | old(john)) & (~old(john) | ! [X1] : ((~curious(X1) | ~kind(X1)) & (kind(X1) | curious(X1)))) [rectify 41]
43. ? [X0] : ((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) => ((~kind(sK0) | curious(sK0)) & (kind(sK0) | ~curious(sK0))) [choice axiom]
44. (((~kind(sK0) | curious(sK0)) & (kind(sK0) | ~curious(sK0))) | old(john)) & (~old(john) | ! [X1] : ((~curious(X1) | ~kind(X1)) & (kind(X1) | curious(X1)))) [skolemisation 42,43]
47. ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))) [nnf transformation 8]
64. ~old(X0) | ~generous(X0) | kind(X0) [cnf transformation 39]
67. old(X0) | generous(X0) | generous(X0) [cnf transformation 39]
73. ~old(john) | ~curious(X1) | ~kind(X1) [cnf transformation 44]
82. generous(X0) | ~old(X0) [cnf transformation 47]
83. old(X0) | ~generous(X0) [cnf transformation 47]
111. curious(lucy) [cnf transformation 24]
115. old(X0) | generous(X0) [duplicate literal removal 67]
118. 1 <=> old(john) [avatar definition]
119. ~old(john) <- (~1) [avatar component clause 118]
132. 4 <=> ! [X1] : (~curious(X1) | ~kind(X1)) [avatar definition]
133. ~curious(X1) | ~kind(X1) <- (4) [avatar component clause 132]
134. 4 | ~1 [avatar split clause 73,118,132]
139. old(X0) [subsumption resolution 83,115]
140. generous(X0) [subsumption resolution 82,139]
177. $false <- (~1) [subsumption resolution 119,139]
178. 1 [avatar contradiction clause 177]
189. ~kind(lucy) <- (4) [resolution 133,111]
199. ~generous(X1) | kind(X1) [resolution 64,139]
200. kind(X1) [subsumption resolution 199,140]
205. $false <- (4) [resolution 200,189]
206. ~4 [avatar contradiction clause 205]
208. $false [avatar sat refutation 134,178,206]
% SZS output end Proof for 1371713772357583723348355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or kind then susan is not calm and vice versa.
If john is creative then paul is both brave and curious and vice versa.
If someone is either creative or humble then lucy is either creative or calm and vice versa.
If susan is kind then someone is not rich or not funny and vice versa.
If alice is wise or humble then someone is both not tall and not calm.
If mary is funny then john is either quiet or creative and vice versa.
If mary is not tall then mary is both calm and funny.
Everyone who is tall or kind is tall.
Everyone who is either quiet or not strong is not humble.
Everyone who is not quiet or calm is either not brave or brave and vice versa.
Everyone who is both not brave and brave is not tall or curious and vice versa.
If someone is both not patient and not generous then lucy is both not rich and funny.
If paul is kind or not generous then alice is either not humble or wise.
Everyone who is both not wise and strong is generous or not happy.
If someone is both funny and not strong then john is either patient or not happy and vice versa.
Everyone who is funny is not curious or not funny.
Fred is both rich and not generous.
Alice is both not strong and not patient.
Someone is not quiet.
Susan is not rich or not strong.
Someone is not tall or not happy.
Someone is happy.
Mary is not generous. | Paul is not curious. | entailment | ((?[X]:((strong(X)<~>kind(X))))<=>(~calm(susan)))&
((creative(john))<=>((brave(paul)&curious(paul))))&
((?[X]:((creative(X)<~>humble(X))))<=>((creative(lucy)<~>calm(lucy))))&
((kind(susan))<=>(?[X]:((~rich(X)|~funny(X)))))&
(((wise(alice)|humble(alice)))=>(?[X]:((~tall(X)&~calm(X)))))&
((funny(mary))<=>((quiet(john)<~>creative(john))))&
((~tall(mary))=>((calm(mary)&funny(mary))))&
(![X]:((tall(X)|kind(X))=>tall(X)))&
(![X]:((quiet(X)<~>~strong(X))=>~humble(X)))&
(![X]:((~quiet(X)|calm(X))<=>(~brave(X)<~>brave(X))))&
(![X]:((~brave(X)&brave(X))<=>(~tall(X)|curious(X))))&
((?[X]:((~patient(X)&~generous(X))))=>((~rich(lucy)&funny(lucy))))&
(((kind(paul)|~generous(paul)))=>((~humble(alice)<~>wise(alice))))&
(![X]:((~wise(X)&strong(X))=>(generous(X)|~happy(X))))&
((?[X]:((funny(X)&~strong(X))))<=>((patient(john)<~>~happy(john))))&
(![X]:(funny(X)=>(~curious(X)|~funny(X))))&
((rich(fred)&~generous(fred)))&
((~strong(alice)&~patient(alice)))&
(?[X]:(~quiet(X)))&
((~rich(susan)|~strong(susan)))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:(happy(X)))&
(~generous(mary)) | ~curious(paul) | [
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 9042454727778437297676940
% SZS output start Proof for 9042454727778437297676940
11. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (curious(X0) | ~tall(X0))) [input p10]
24. curious(paul) [input hypothesis]
55. ! [X0] : (((brave(X0) & ~brave(X0)) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((brave(X0) & ~brave(X0)) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | ~brave(X0) | brave(X0))) [flattening 55]
108. ~brave(X0) | ~curious(X0) [cnf transformation 56]
110. brave(X0) | ~curious(X0) [cnf transformation 56]
134. curious(paul) [cnf transformation 24]
269. ~curious(X0) [subsumption resolution 108,110]
331. $false [subsumption resolution 134,269]
% SZS output end Proof for 9042454727778437297676940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not wise is either not quiet or humble. If john is not creative then someone is either not brave or not humble and vice versa. Everyone who is both wise and patient is either quiet or curious and vice versa. If mary is both not patient and quiet then someone is rich and vice versa. If lucy is old then someone is not rich or not happy. Everyone who is not tall or curious is both not kind and not brave. If alice is either not old or calm then someone is kind. If john is not humble or not tall then someone is not wise and vice versa. Everyone who is either not quiet or quiet is either kind or not old and vice versa. If someone is both not funny and happy then paul is both not brave and creative and vice versa. Everyone who is calm or old is not quiet or generous and vice versa. Everyone who is strong or not strong is either happy or curious and vice versa. If john is wise or not tall then alice is rich. Everyone who is not creative or wise is both not funny and humble and vice versa. Everyone who is either brave or happy is not kind or not calm. Everyone who is kind or calm is tall. Someone is either happy or generous. Fred is not quiet or not creative. Susan is both not generous and not happy. Someone is not funny or calm. Paul is not funny. Lucy is not patient or not wise. John is not strong or funny. Someone is not curious. | Alice is not generous. | neutral | (![X]:((~happy(X)&~wise(X))=>(~quiet(X)<~>humble(X))))&
((~creative(john))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)<~>curious(X))))&
(((~patient(mary)&quiet(mary)))<=>(?[X]:(rich(X))))&
((old(lucy))=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((~tall(X)|curious(X))=>(~kind(X)&~brave(X))))&
(((~old(alice)<~>calm(alice)))=>(?[X]:(kind(X))))&
(((~humble(john)|~tall(john)))<=>(?[X]:(~wise(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(kind(X)<~>~old(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~brave(paul)&creative(paul))))&
(![X]:((calm(X)|old(X))<=>(~quiet(X)|generous(X))))&
(![X]:((strong(X)|~strong(X))<=>(happy(X)<~>curious(X))))&
(((wise(john)|~tall(john)))=>(rich(alice)))&
(![X]:((~creative(X)|wise(X))<=>(~funny(X)&humble(X))))&
(![X]:((brave(X)<~>happy(X))=>(~kind(X)|~calm(X))))&
(![X]:((kind(X)|calm(X))=>tall(X)))&
(?[X]:((happy(X)<~>generous(X))))&
((~quiet(fred)|~creative(fred)))&
((~generous(susan)&~happy(susan)))&
(?[X]:((~funny(X)|calm(X))))&
(~funny(paul))&
((~patient(lucy)|~wise(lucy)))&
((~strong(john)|funny(john)))&
(?[X]:(~curious(X))) | ~generous(alice) | []
| null | 0 |
If someone is both wise and curious then someone is generous or calm.
If alice is both old and not brave then someone is either old or not quiet.
Everyone who is both not rich and generous is not patient and vice versa.
Everyone who is brave is both not funny and creative and vice versa.
Everyone who is not tall or humble is not curious.
If fred is either rich or not happy then someone is either not kind or quiet.
Everyone who is not old is quiet and vice versa.
If someone is either not quiet or not rich then someone is rich or not quiet and vice versa.
If mary is either patient or not kind then someone is not calm or not kind and vice versa.
If john is not curious or not calm then fred is not creative or strong.
Everyone who is kind or wise is not calm and vice versa.
Everyone who is not wise is wise or not old and vice versa.
Everyone who is either not curious or not rich is patient.
If lucy is humble then lucy is both patient and not strong.
If alice is both strong and not humble then someone is not strong or brave and vice versa.
Everyone who is both not brave and brave is not brave or not tall and vice versa.
Someone is both not happy and generous.
Someone is either not curious or calm.
Someone is wise or calm.
Someone is either not curious or not calm.
Someone is not strong.
Someone is tall.
Fred is either rich or not old.
Paul is creative or not humble. | Fred is not tall. | contradiction | ((?[X]:((wise(X)&curious(X))))=>(?[X]:((generous(X)|calm(X)))))&
(((old(alice)&~brave(alice)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&generous(X))<=>~patient(X)))&
(![X]:(brave(X)<=>(~funny(X)&creative(X))))&
(![X]:((~tall(X)|humble(X))=>~curious(X)))&
(((rich(fred)<~>~happy(fred)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:(~old(X)<=>quiet(X)))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(((patient(mary)<~>~kind(mary)))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((~curious(john)|~calm(john)))=>((~creative(fred)|strong(fred))))&
(![X]:((kind(X)|wise(X))<=>~calm(X)))&
(![X]:(~wise(X)<=>(wise(X)|~old(X))))&
(![X]:((~curious(X)<~>~rich(X))=>patient(X)))&
((humble(lucy))=>((patient(lucy)&~strong(lucy))))&
(((strong(alice)&~humble(alice)))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:((~brave(X)&brave(X))<=>(~brave(X)|~tall(X))))&
(?[X]:((~happy(X)&generous(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:(~strong(X)))&
(?[X]:(tall(X)))&
((rich(fred)<~>~old(fred)))&
((creative(paul)|~humble(paul))) | ~tall(fred) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6240888408842556187862233
% SZS output start Proof for 6240888408842556187862233
16. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (~tall(X0) | ~brave(X0))) [input p15]
25. ~tall(fred) [input hypothesis]
70. ! [X0] : (((brave(X0) & ~brave(X0)) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 16]
71. ! [X0] : (((brave(X0) & ~brave(X0)) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | ~brave(X0) | brave(X0))) [flattening 70]
135. ~brave(X0) | tall(X0) [cnf transformation 71]
136. brave(X0) | brave(X0) [cnf transformation 71]
150. ~tall(fred) [cnf transformation 25]
152. brave(X0) [duplicate literal removal 136]
328. tall(X0) [subsumption resolution 135,152]
361. $false [subsumption resolution 150,328]
% SZS output end Proof for 6240888408842556187862233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either brave or funny then someone is funny and vice versa.
If someone is quiet or not happy then someone is curious and vice versa.
Everyone who is both quiet and not old is either humble or not quiet and vice versa.
If someone is both rich and not curious then paul is both not wise and quiet.
Everyone who is both not old and not rich is happy or not curious and vice versa.
Everyone who is brave or calm is both not old and humble.
Everyone who is either creative or strong is not happy or not brave.
Everyone who is not humble or quiet is not tall.
Everyone who is not old or not creative is not strong and vice versa.
If mary is either not creative or strong then mary is either patient or wise and vice versa.
If mary is both not happy and rich then fred is generous and vice versa.
Everyone who is both not tall and funny is not quiet.
Everyone who is either not funny or not patient is either not happy or creative and vice versa.
Everyone who is both humble and strong is not happy.
Everyone who is both not funny and not generous is not calm or not happy and vice versa.
If alice is rich then lucy is both curious and not kind and vice versa.
Paul is both not rich and brave.
Paul is either not humble or not quiet.
Someone is either not wise or tall.
Fred is both old and not generous.
Susan is not calm or not brave.
Someone is both patient and not funny. | Lucy is funny. | neutral | (((brave(mary)<~>funny(mary)))<=>(?[X]:(funny(X))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&~old(X))<=>(humble(X)<~>~quiet(X))))&
((?[X]:((rich(X)&~curious(X))))=>((~wise(paul)&quiet(paul))))&
(![X]:((~old(X)&~rich(X))<=>(happy(X)|~curious(X))))&
(![X]:((brave(X)|calm(X))=>(~old(X)&humble(X))))&
(![X]:((creative(X)<~>strong(X))=>(~happy(X)|~brave(X))))&
(![X]:((~humble(X)|quiet(X))=>~tall(X)))&
(![X]:((~old(X)|~creative(X))<=>~strong(X)))&
(((~creative(mary)<~>strong(mary)))<=>((patient(mary)<~>wise(mary))))&
(((~happy(mary)&rich(mary)))<=>(generous(fred)))&
(![X]:((~tall(X)&funny(X))=>~quiet(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((humble(X)&strong(X))=>~happy(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~calm(X)|~happy(X))))&
((rich(alice))<=>((curious(lucy)&~kind(lucy))))&
((~rich(paul)&brave(paul)))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((~wise(X)<~>tall(X))))&
((old(fred)&~generous(fred)))&
((~calm(susan)|~brave(susan)))&
(?[X]:((patient(X)&~funny(X)))) | funny(lucy) | []
| null | 0 |
Everyone who is either kind or calm is tall.
If paul is not curious or kind then paul is kind.
Everyone who is both rich and not brave is not humble.
Everyone who is either not patient or not humble is funny and vice versa.
If paul is not wise or not happy then someone is not brave or wise.
If someone is brave or not kind then someone is both funny and happy.
If someone is both creative and not rich then someone is either not strong or old and vice versa.
If paul is generous or rich then mary is either not old or happy.
If susan is funny then paul is either kind or humble.
If alice is either creative or not curious then paul is rich.
Everyone who is not generous or curious is either not generous or kind.
If someone is either humble or not old then susan is not calm and vice versa.
If mary is not kind or not rich then paul is not patient or creative.
If fred is both not tall and not wise then someone is either curious or not tall and vice versa.
Everyone who is not humble or not happy is both not creative and not old and vice versa.
If someone is calm then susan is both creative and not humble.
Paul is not strong.
Someone is tall.
John is both not calm and not funny.
Someone is kind.
Someone is quiet or not calm.
John is both not wise and not brave.
Paul is not humble or not curious.
Someone is both happy and not tall. | John is funny. | contradiction | (![X]:((kind(X)<~>calm(X))=>tall(X)))&
(((~curious(paul)|kind(paul)))=>(kind(paul)))&
(![X]:((rich(X)&~brave(X))=>~humble(X)))&
(![X]:((~patient(X)<~>~humble(X))<=>funny(X)))&
(((~wise(paul)|~happy(paul)))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((brave(X)|~kind(X))))=>(?[X]:((funny(X)&happy(X)))))&
((?[X]:((creative(X)&~rich(X))))<=>(?[X]:((~strong(X)<~>old(X)))))&
(((generous(paul)|rich(paul)))=>((~old(mary)<~>happy(mary))))&
((funny(susan))=>((kind(paul)<~>humble(paul))))&
(((creative(alice)<~>~curious(alice)))=>(rich(paul)))&
(![X]:((~generous(X)|curious(X))=>(~generous(X)<~>kind(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>(~calm(susan)))&
(((~kind(mary)|~rich(mary)))=>((~patient(paul)|creative(paul))))&
(((~tall(fred)&~wise(fred)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~creative(X)&~old(X))))&
((?[X]:(calm(X)))=>((creative(susan)&~humble(susan))))&
(~strong(paul))&
(?[X]:(tall(X)))&
((~calm(john)&~funny(john)))&
(?[X]:(kind(X)))&
(?[X]:((quiet(X)|~calm(X))))&
((~wise(john)&~brave(john)))&
((~humble(paul)|~curious(paul)))&
(?[X]:((happy(X)&~tall(X)))) | funny(john) | [
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7845136301585985838369723
% SZS output start Proof for 7845136301585985838369723
19. ~funny(john) & ~calm(john) [input p18]
25. funny(john) [input hypothesis]
130. ~funny(john) [cnf transformation 19]
137. funny(john) [cnf transformation 25]
337. $false [subsumption resolution 137,130]
% SZS output end Proof for 7845136301585985838369723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or strong then susan is either not tall or quiet and vice versa.
If someone is not humble then fred is not tall.
If fred is both not patient and tall then someone is not old or kind.
Everyone who is not calm or curious is not happy.
Everyone who is not funny or not humble is humble and vice versa.
If someone is not kind then someone is both brave and not creative.
If someone is both not creative and creative then john is either not generous or not patient.
If someone is both not quiet and creative then someone is either not brave or not tall and vice versa.
Everyone who is either calm or generous is not brave or not happy and vice versa.
Everyone who is not old is kind or not creative and vice versa.
Everyone who is tall is both not calm and not old and vice versa.
Everyone who is not brave is not rich.
If someone is not old or not brave then someone is either quiet or not tall.
Everyone who is either old or not generous is tall and vice versa.
If someone is not quiet then john is both not patient and kind and vice versa.
Everyone who is either not rich or not funny is creative and vice versa.
Someone is either not brave or calm.
Mary is either not quiet or not wise.
Lucy is either not humble or calm.
Someone is quiet.
Fred is not patient or generous.
Lucy is both kind and brave.
Paul is kind or quiet. | John is generous. | entailment | ((?[X]:((~calm(X)|strong(X))))<=>((~tall(susan)<~>quiet(susan))))&
((?[X]:(~humble(X)))=>(~tall(fred)))&
(((~patient(fred)&tall(fred)))=>(?[X]:((~old(X)|kind(X)))))&
(![X]:((~calm(X)|curious(X))=>~happy(X)))&
(![X]:((~funny(X)|~humble(X))<=>humble(X)))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)&~creative(X)))))&
((?[X]:((~creative(X)&creative(X))))=>((~generous(john)<~>~patient(john))))&
((?[X]:((~quiet(X)&creative(X))))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(![X]:((calm(X)<~>generous(X))<=>(~brave(X)|~happy(X))))&
(![X]:(~old(X)<=>(kind(X)|~creative(X))))&
(![X]:(tall(X)<=>(~calm(X)&~old(X))))&
(![X]:(~brave(X)=>~rich(X)))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((old(X)<~>~generous(X))<=>tall(X)))&
((?[X]:(~quiet(X)))<=>((~patient(john)&kind(john))))&
(![X]:((~rich(X)<~>~funny(X))<=>creative(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((~quiet(mary)<~>~wise(mary)))&
((~humble(lucy)<~>calm(lucy)))&
(?[X]:(quiet(X)))&
((~patient(fred)|generous(fred)))&
((kind(lucy)&brave(lucy)))&
((kind(paul)|quiet(paul))) | generous(john) | [
"p3",
"p4",
"p7",
"p8",
"p9",
"p10",
"p13",
"p14",
"p18",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 7472146689048888443384847
% SZS output start Proof for 7472146689048888443384847
4. ! [X0] : ((curious(X0) | ~calm(X0)) => ~happy(X0)) [input p3]
5. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> humble(X0)) [input p4]
8. ? [X0] : (creative(X0) & ~quiet(X0)) <=> ? [X0] : (~brave(X0) <~> ~tall(X0)) [input p7]
9. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (~happy(X0) | ~brave(X0))) [input p8]
10. ! [X0] : (~old(X0) <=> (~creative(X0) | kind(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> (~old(X0) & ~calm(X0))) [input p10]
14. ! [X0] : ((old(X0) <~> ~generous(X0)) <=> tall(X0)) [input p13]
15. ? [X0] : ~quiet(X0) <=> (kind(john) & ~patient(john)) [input p14]
19. ~humble(lucy) <~> calm(lucy) [input p18]
22. brave(lucy) & kind(lucy) [input p21]
24. ~generous(john) [input hypothesis]
26. ? [X0] : (creative(X0) & ~quiet(X0)) <=> ? [X1] : (~brave(X1) <~> ~tall(X1)) [rectify 8]
28. ! [X0] : (~calm(X0) => ~happy(X0)) [pure predicate removal 4]
32. ! [X0] : (~happy(X0) | calm(X0)) [ennf transformation 28]
43. ! [X0] : (((~humble(X0) | ~funny(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) & funny(X0)))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | ~funny(X0) | ~humble(X0)) & (humble(X0) | (humble(X0) & funny(X0)))) [flattening 43]
49. (? [X0] : (creative(X0) & ~quiet(X0)) | ! [X1] : ((~brave(X1) | tall(X1)) & (~tall(X1) | brave(X1)))) & (? [X1] : ((tall(X1) | brave(X1)) & (~tall(X1) | ~brave(X1))) | ! [X0] : (~creative(X0) | quiet(X0))) [nnf transformation 26]
50. (? [X0] : (creative(X0) & ~quiet(X0)) | ! [X1] : ((~brave(X1) | tall(X1)) & (~tall(X1) | brave(X1)))) & (? [X2] : ((tall(X2) | brave(X2)) & (~tall(X2) | ~brave(X2))) | ! [X3] : (~creative(X3) | quiet(X3))) [rectify 49]
51. ? [X0] : (creative(X0) & ~quiet(X0)) => (creative(sK3) & ~quiet(sK3)) [choice axiom]
52. ? [X2] : ((tall(X2) | brave(X2)) & (~tall(X2) | ~brave(X2))) => ((tall(sK4) | brave(sK4)) & (~tall(sK4) | ~brave(sK4))) [choice axiom]
53. ((creative(sK3) & ~quiet(sK3)) | ! [X1] : ((~brave(X1) | tall(X1)) & (~tall(X1) | brave(X1)))) & (((tall(sK4) | brave(sK4)) & (~tall(sK4) | ~brave(sK4))) | ! [X3] : (~creative(X3) | quiet(X3))) [skolemisation 50,52,51]
54. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [flattening 54]
56. ! [X0] : ((~old(X0) | (creative(X0) & ~kind(X0))) & ((~creative(X0) | kind(X0)) | old(X0))) [nnf transformation 10]
57. ! [X0] : ((~old(X0) | (creative(X0) & ~kind(X0))) & (~creative(X0) | kind(X0) | old(X0))) [flattening 56]
58. ! [X0] : ((tall(X0) | (old(X0) | calm(X0))) & ((~old(X0) & ~calm(X0)) | ~tall(X0))) [nnf transformation 11]
59. ! [X0] : ((tall(X0) | old(X0) | calm(X0)) & ((~old(X0) & ~calm(X0)) | ~tall(X0))) [flattening 58]
64. ! [X0] : ((((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | ~tall(X0)) & (tall(X0) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))))) [nnf transformation 14]
65. (? [X0] : ~quiet(X0) | (~kind(john) | patient(john))) & ((kind(john) & ~patient(john)) | ! [X0] : quiet(X0)) [nnf transformation 15]
66. (? [X0] : ~quiet(X0) | ~kind(john) | patient(john)) & ((kind(john) & ~patient(john)) | ! [X0] : quiet(X0)) [flattening 65]
67. (? [X0] : ~quiet(X0) | ~kind(john) | patient(john)) & ((kind(john) & ~patient(john)) | ! [X1] : quiet(X1)) [rectify 66]
68. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
69. (~quiet(sK6) | ~kind(john) | patient(john)) & ((kind(john) & ~patient(john)) | ! [X1] : quiet(X1)) [skolemisation 67,68]
75. (~calm(lucy) | humble(lucy)) & (calm(lucy) | ~humble(lucy)) [nnf transformation 19]
86. ~happy(X0) | calm(X0) [cnf transformation 32]
88. humble(X0) | humble(X0) [cnf transformation 44]
97. ~quiet(sK3) | ~brave(X1) | tall(X1) [cnf transformation 53]
103. generous(X0) | calm(X0) | happy(X0) [cnf transformation 55]
107. ~kind(X0) | ~old(X0) [cnf transformation 57]
109. ~tall(X0) | ~calm(X0) [cnf transformation 59]
110. ~old(X0) | ~tall(X0) [cnf transformation 59]
118. generous(X0) | old(X0) | tall(X0) [cnf transformation 64]
119. ~generous(X0) | old(X0) | ~tall(X0) [cnf transformation 64]
122. kind(john) | quiet(X1) [cnf transformation 69]
132. calm(lucy) | ~humble(lucy) [cnf transformation 75]
137. brave(lucy) [cnf transformation 22]
139. ~generous(john) [cnf transformation 24]
140. humble(X0) [duplicate literal removal 88]
171. 7 <=> ! [X0] : humble(X0) [avatar definition]
172. humble(X0) <- (7) [avatar component clause 171]
191. 7 [avatar split clause 140,171]
206. 15 <=> ! [X1] : (~brave(X1) | tall(X1)) [avatar definition]
207. ~brave(X1) | tall(X1) <- (15) [avatar component clause 206]
218. 18 <=> quiet(sK3) [avatar definition]
220. ~quiet(sK3) <- (~18) [avatar component clause 218]
221. 15 | ~18 [avatar split clause 97,218,206]
236. generous(X0) | calm(X0) [subsumption resolution 103,86]
256. ~generous(X0) | ~tall(X0) [subsumption resolution 119,110]
263. 27 <=> kind(john) [avatar definition]
264. kind(john) <- (27) [avatar component clause 263]
272. 29 <=> ! [X1] : quiet(X1) [avatar definition]
273. quiet(X1) <- (29) [avatar component clause 272]
274. 29 | 27 [avatar split clause 122,263,272]
297. 34 <=> humble(lucy) [avatar definition]
298. ~humble(lucy) <- (~34) [avatar component clause 297]
301. 35 <=> calm(lucy) [avatar definition]
302. calm(lucy) <- (35) [avatar component clause 301]
305. ~34 | 35 [avatar split clause 132,301,297]
320. $false <- (7, ~34) [resolution 298,172]
321. ~7 | 34 [avatar contradiction clause 320]
323. ~old(john) <- (27) [resolution 107,264]
330. tall(lucy) <- (15) [resolution 207,137]
332. ~calm(lucy) <- (15) [resolution 330,109]
333. $false <- (15, 35) [subsumption resolution 332,302]
334. ~15 | ~35 [avatar contradiction clause 333]
336. ~tall(X0) | calm(X0) [resolution 256,236]
337. ~tall(X0) [subsumption resolution 336,109]
362. old(john) | tall(john) [resolution 118,139]
367. tall(john) <- (27) [subsumption resolution 362,323]
368. $false <- (27) [subsumption resolution 367,337]
369. ~27 [avatar contradiction clause 368]
374. $false <- (~18, 29) [resolution 273,220]
379. 18 | ~29 [avatar contradiction clause 374]
381. $false [avatar sat refutation 191,221,274,305,321,334,369,379]
% SZS output end Proof for 7472146689048888443384847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not curious is not humble or kind and vice versa.
If paul is patient then fred is creative or not wise and vice versa.
Everyone who is not old is rich and vice versa.
If someone is old then someone is both funny and creative and vice versa.
Everyone who is either wise or not humble is curious.
If mary is funny or generous then someone is brave or not kind.
Everyone who is humble or curious is not calm or not strong and vice versa.
Everyone who is either quiet or generous is rich.
If someone is kind then someone is either quiet or not strong and vice versa.
Everyone who is not kind is either humble or not curious.
If mary is not quiet or brave then someone is curious or not calm and vice versa.
Everyone who is not creative is not old.
Everyone who is either tall or not generous is both not generous and not quiet and vice versa.
If someone is not brave or brave then someone is not rich.
Everyone who is both old and not creative is both funny and patient and vice versa.
Everyone who is both creative and old is both not kind and wise.
Fred is both patient and not humble.
Mary is either quiet or not humble.
Mary is either not old or kind.
Paul is both not curious and not rich.
Paul is generous.
Lucy is both not curious and creative.
Someone is either not patient or brave.
Susan is both humble and not tall. | Mary is not rich. | contradiction | (![X]:((patient(X)&~curious(X))<=>(~humble(X)|kind(X))))&
((patient(paul))<=>((creative(fred)|~wise(fred))))&
(![X]:(~old(X)<=>rich(X)))&
((?[X]:(old(X)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((wise(X)<~>~humble(X))=>curious(X)))&
(((funny(mary)|generous(mary)))=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)|~strong(X))))&
(![X]:((quiet(X)<~>generous(X))=>rich(X)))&
((?[X]:(kind(X)))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(humble(X)<~>~curious(X))))&
(((~quiet(mary)|brave(mary)))<=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:(~creative(X)=>~old(X)))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)&~creative(X))<=>(funny(X)&patient(X))))&
(![X]:((creative(X)&old(X))=>(~kind(X)&wise(X))))&
((patient(fred)&~humble(fred)))&
((quiet(mary)<~>~humble(mary)))&
((~old(mary)<~>kind(mary)))&
((~curious(paul)&~rich(paul)))&
(generous(paul))&
((~curious(lucy)&creative(lucy)))&
(?[X]:((~patient(X)<~>brave(X))))&
((humble(susan)&~tall(susan))) | ~rich(mary) | [
"p2",
"p11",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 827908155813868979384360
% SZS output start Proof for 827908155813868979384360
3. ! [X0] : (~old(X0) <=> rich(X0)) [input p2]
12. ! [X0] : (~creative(X0) => ~old(X0)) [input p11]
16. ! [X0] : ((old(X0) & creative(X0)) => (wise(X0) & ~kind(X0))) [input p15]
19. ~old(mary) <~> kind(mary) [input p18]
25. ~rich(mary) [input hypothesis]
33. ! [X0] : (~old(X0) | creative(X0)) [ennf transformation 12]
35. ! [X0] : ((wise(X0) & ~kind(X0)) | (~old(X0) | ~creative(X0))) [ennf transformation 16]
36. ! [X0] : ((wise(X0) & ~kind(X0)) | ~old(X0) | ~creative(X0)) [flattening 35]
41. ! [X0] : ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))) [nnf transformation 3]
72. (~kind(mary) | old(mary)) & (kind(mary) | ~old(mary)) [nnf transformation 19]
84. rich(X0) | old(X0) [cnf transformation 41]
109. ~old(X0) | creative(X0) [cnf transformation 33]
122. ~kind(X0) | ~old(X0) | ~creative(X0) [cnf transformation 36]
128. kind(mary) | ~old(mary) [cnf transformation 72]
129. ~kind(mary) | old(mary) [cnf transformation 72]
139. ~rich(mary) [cnf transformation 25]
263. ~kind(X0) | ~old(X0) [subsumption resolution 122,109]
270. ~kind(mary) [subsumption resolution 129,263]
271. ~old(mary) [subsumption resolution 128,270]
287. old(mary) [resolution 84,139]
291. $false [subsumption resolution 287,271]
% SZS output end Proof for 827908155813868979384360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not creative then someone is both humble and strong. If someone is not wise or not funny then someone is either happy or creative. If someone is both tall and creative then someone is not happy and vice versa. Everyone who is tall or not rich is not patient or quiet and vice versa. Everyone who is not happy or not kind is kind and vice versa. If susan is not brave or funny then someone is either not rich or not quiet. If someone is either not patient or not wise then someone is either patient or not curious and vice versa. Everyone who is either not patient or not humble is both not rich and not brave and vice versa. Everyone who is tall is both not old and not strong. Everyone who is not curious is either curious or rich and vice versa. Everyone who is not generous or wise is both not creative and curious. If paul is either not funny or quiet then fred is either not funny or quiet and vice versa. Everyone who is both tall and humble is both wise and strong. If lucy is either not patient or not happy then someone is not calm or old. Everyone who is brave or strong is generous or strong. If someone is either curious or quiet then someone is both not creative and rich. Paul is either strong or not humble. Someone is both curious and not brave. Paul is calm. Someone is generous. Someone is either humble or brave. Someone is funny or curious. | Paul is quiet. | neutral | ((?[X]:((strong(X)&~creative(X))))=>(?[X]:((humble(X)&strong(X)))))&
((?[X]:((~wise(X)|~funny(X))))=>(?[X]:((happy(X)<~>creative(X)))))&
((?[X]:((tall(X)&creative(X))))<=>(?[X]:(~happy(X))))&
(![X]:((tall(X)|~rich(X))<=>(~patient(X)|quiet(X))))&
(![X]:((~happy(X)|~kind(X))<=>kind(X)))&
(((~brave(susan)|funny(susan)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((~patient(X)<~>~humble(X))<=>(~rich(X)&~brave(X))))&
(![X]:(tall(X)=>(~old(X)&~strong(X))))&
(![X]:(~curious(X)<=>(curious(X)<~>rich(X))))&
(![X]:((~generous(X)|wise(X))=>(~creative(X)&curious(X))))&
(((~funny(paul)<~>quiet(paul)))<=>((~funny(fred)<~>quiet(fred))))&
(![X]:((tall(X)&humble(X))=>(wise(X)&strong(X))))&
(((~patient(lucy)<~>~happy(lucy)))=>(?[X]:((~calm(X)|old(X)))))&
(![X]:((brave(X)|strong(X))=>(generous(X)|strong(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((~creative(X)&rich(X)))))&
((strong(paul)<~>~humble(paul)))&
(?[X]:((curious(X)&~brave(X))))&
(calm(paul))&
(?[X]:(generous(X)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((funny(X)|curious(X)))) | quiet(paul) | []
| null | 0 |
Everyone who is either not strong or old is creative or not happy.
Everyone who is both not calm and not quiet is not quiet and vice versa.
If someone is either curious or funny then someone is not creative or rich.
If paul is old then someone is both generous and kind and vice versa.
Everyone who is not calm is patient and vice versa.
If susan is quiet then someone is not old.
If someone is both happy and calm then someone is both not tall and tall and vice versa.
If someone is either kind or not creative then someone is both not kind and funny and vice versa.
Everyone who is both tall and calm is curious or not calm.
Everyone who is not rich is happy.
If someone is not humble or not patient then someone is patient or not brave.
Everyone who is either not patient or not tall is tall or humble.
Everyone who is not happy is both not wise and not calm.
Everyone who is both not funny and not generous is not rich or not kind and vice versa.
If someone is not curious then john is either not happy or calm.
If lucy is humble then fred is either kind or not humble.
Someone is both curious and humble.
Someone is not brave.
Susan is either not creative or wise.
Fred is kind.
Mary is either not curious or not patient.
Lucy is either humble or generous.
Someone is both tall and not funny.
Susan is not curious or not tall. | Fred is not calm. | entailment | (![X]:((~strong(X)<~>old(X))=>(creative(X)|~happy(X))))&
(![X]:((~calm(X)&~quiet(X))<=>~quiet(X)))&
((?[X]:((curious(X)<~>funny(X))))=>(?[X]:((~creative(X)|rich(X)))))&
((old(paul))<=>(?[X]:((generous(X)&kind(X)))))&
(![X]:(~calm(X)<=>patient(X)))&
((quiet(susan))=>(?[X]:(~old(X))))&
((?[X]:((happy(X)&calm(X))))<=>(?[X]:((~tall(X)&tall(X)))))&
((?[X]:((kind(X)<~>~creative(X))))<=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((tall(X)&calm(X))=>(curious(X)|~calm(X))))&
(![X]:(~rich(X)=>happy(X)))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~patient(X)<~>~tall(X))=>(tall(X)|humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~calm(X))))&
(![X]:((~funny(X)&~generous(X))<=>(~rich(X)|~kind(X))))&
((?[X]:(~curious(X)))=>((~happy(john)<~>calm(john))))&
((humble(lucy))=>((kind(fred)<~>~humble(fred))))&
(?[X]:((curious(X)&humble(X))))&
(?[X]:(~brave(X)))&
((~creative(susan)<~>wise(susan)))&
(kind(fred))&
((~curious(mary)<~>~patient(mary)))&
((humble(lucy)<~>generous(lucy)))&
(?[X]:((tall(X)&~funny(X))))&
((~curious(susan)|~tall(susan))) | ~calm(fred) | [
"p6",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 963492587867729174282942
% SZS output start Proof for 963492587867729174282942
7. ? [X0] : (calm(X0) & happy(X0)) <=> ? [X0] : (tall(X0) & ~tall(X0)) [input p6]
13. ! [X0] : (~happy(X0) => (~calm(X0) & ~wise(X0))) [input p12]
25. calm(fred) [input hypothesis]
27. ? [X0] : (calm(X0) & happy(X0)) <=> ? [X1] : (tall(X1) & ~tall(X1)) [rectify 7]
41. ! [X0] : ((~calm(X0) & ~wise(X0)) | happy(X0)) [ennf transformation 13]
58. (? [X0] : (calm(X0) & happy(X0)) | ! [X1] : (~tall(X1) | tall(X1))) & (? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : (~calm(X0) | ~happy(X0))) [nnf transformation 27]
59. (? [X0] : (calm(X0) & happy(X0)) | ! [X1] : (~tall(X1) | tall(X1))) & (? [X2] : (tall(X2) & ~tall(X2)) | ! [X3] : (~calm(X3) | ~happy(X3))) [rectify 58]
60. ? [X0] : (calm(X0) & happy(X0)) => (calm(sK3) & happy(sK3)) [choice axiom]
61. ? [X2] : (tall(X2) & ~tall(X2)) => (tall(sK4) & ~tall(sK4)) [choice axiom]
62. ((calm(sK3) & happy(sK3)) | ! [X1] : (~tall(X1) | tall(X1))) & ((tall(sK4) & ~tall(sK4)) | ! [X3] : (~calm(X3) | ~happy(X3))) [skolemisation 59,61,60]
93. ~tall(sK4) | ~calm(X3) | ~happy(X3) [cnf transformation 62]
94. tall(sK4) | ~calm(X3) | ~happy(X3) [cnf transformation 62]
108. ~calm(X0) | happy(X0) [cnf transformation 41]
130. calm(fred) [cnf transformation 25]
177. 11 <=> ! [X3] : (~calm(X3) | ~happy(X3)) [avatar definition]
178. ~calm(X3) | ~happy(X3) <- (11) [avatar component clause 177]
180. 12 <=> tall(sK4) [avatar definition]
183. 11 | 12 [avatar split clause 94,180,177]
184. 11 | ~12 [avatar split clause 93,180,177]
279. ~calm(X3) <- (11) [subsumption resolution 178,108]
281. $false <- (11) [resolution 279,130]
282. ~11 [avatar contradiction clause 281]
283. $false [avatar sat refutation 183,184,282]
% SZS output end Proof for 963492587867729174282942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both generous and not curious and vice versa. If susan is either humble or not curious then lucy is not rich or old and vice versa. If someone is not brave or not humble then someone is not creative or rich and vice versa. Everyone who is either not patient or humble is either old or curious and vice versa. If john is both not brave and not funny then alice is either funny or patient and vice versa. If someone is calm or wise then someone is not strong or calm. Everyone who is both not happy and creative is wise or brave and vice versa. Everyone who is either brave or not patient is either brave or wise. Everyone who is happy or not wise is both brave and not brave and vice versa. Everyone who is either funny or not kind is kind and vice versa. Everyone who is not generous or quiet is both strong and not tall. Everyone who is not rich or not tall is quiet or patient and vice versa. If john is not generous then paul is both quiet and old and vice versa. If someone is both funny and not humble then alice is both not quiet and tall and vice versa. Mary is either not wise or brave. Someone is either calm or happy. John is not happy. Paul is either not quiet or old. John is not calm or quiet. Someone is not curious or generous. Someone is either brave or strong. | John is not happy. | entailment | (![X]:(rich(X)<=>(generous(X)&~curious(X))))&
(((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))&
((~wise(mary)<~>brave(mary)))&
(?[X]:((calm(X)<~>happy(X))))&
(~happy(john))&
((~quiet(paul)<~>old(paul)))&
((~calm(john)|quiet(john)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((brave(X)<~>strong(X)))) | ~happy(john) | [
"p6",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 1675873563439989659687724
% SZS output start Proof for 1675873563439989659687724
7. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (brave(X0) | wise(X0))) [input p6]
9. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p8]
22. happy(john) [input hypothesis]
43. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~creative(X0) | happy(X0))) [flattening 43]
46. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 9]
47. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 46]
99. ~happy(X0) | ~brave(X0) [cnf transformation 44]
106. brave(X0) | ~happy(X0) [cnf transformation 47]
141. happy(john) [cnf transformation 22]
239. ~happy(X0) [subsumption resolution 106,99]
306. $false [subsumption resolution 141,239]
% SZS output end Proof for 1675873563439989659687724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not calm or not kind then someone is not quiet. Everyone who is either not humble or calm is calm. If mary is both not strong and not generous then someone is either tall or not funny. Everyone who is either wise or patient is either brave or not old. Everyone who is both not happy and brave is both not funny and patient. If someone is patient then someone is tall or humble and vice versa. If alice is both rich and strong then someone is either patient or not funny and vice versa. Everyone who is either not wise or not creative is patient. Everyone who is both not happy and quiet is both funny and not old. Everyone who is wise is not curious or not rich. Everyone who is both not creative and not strong is both quiet and not quiet. If alice is both old and quiet then someone is either wise or humble and vice versa. Everyone who is either not strong or creative is both not funny and patient and vice versa. Everyone who is either not funny or patient is kind. If paul is either not curious or not creative then john is not curious or strong. Everyone who is either patient or not kind is both strong and wise and vice versa. Susan is not wise. Susan is not strong or not quiet. Lucy is humble or brave. Someone is either rich or not happy. Someone is either rich or not patient. Someone is tall or funny. Paul is not patient or brave. Someone is either kind or not quiet. | Susan is not strong. | contradiction | (((~calm(lucy)<~>~kind(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:((~humble(X)<~>calm(X))=>calm(X)))&
(((~strong(mary)&~generous(mary)))=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((wise(X)<~>patient(X))=>(brave(X)<~>~old(X))))&
(![X]:((~happy(X)&brave(X))=>(~funny(X)&patient(X))))&
((?[X]:(patient(X)))<=>(?[X]:((tall(X)|humble(X)))))&
(((rich(alice)&strong(alice)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
(![X]:((~wise(X)<~>~creative(X))=>patient(X)))&
(![X]:((~happy(X)&quiet(X))=>(funny(X)&~old(X))))&
(![X]:(wise(X)=>(~curious(X)|~rich(X))))&
(![X]:((~creative(X)&~strong(X))=>(quiet(X)&~quiet(X))))&
(((old(alice)&quiet(alice)))<=>(?[X]:((wise(X)<~>humble(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>(~funny(X)&patient(X))))&
(![X]:((~funny(X)<~>patient(X))=>kind(X)))&
(((~curious(paul)<~>~creative(paul)))=>((~curious(john)|strong(john))))&
(![X]:((patient(X)<~>~kind(X))<=>(strong(X)&wise(X))))&
(~wise(susan))&
((~strong(susan)|~quiet(susan)))&
((humble(lucy)|brave(lucy)))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:((tall(X)|funny(X))))&
((~patient(paul)|brave(paul)))&
(?[X]:((kind(X)<~>~quiet(X)))) | ~strong(susan) | [
"p7",
"p10",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6127664194013924125866828
% SZS output start Proof for 6127664194013924125866828
8. ! [X0] : ((~wise(X0) <~> ~creative(X0)) => patient(X0)) [input p7]
11. ! [X0] : ((~strong(X0) & ~creative(X0)) => (~quiet(X0) & quiet(X0))) [input p10]
13. ! [X0] : ((~strong(X0) <~> creative(X0)) <=> (patient(X0) & ~funny(X0))) [input p12]
14. ! [X0] : ((~funny(X0) <~> patient(X0)) => kind(X0)) [input p13]
16. ! [X0] : ((patient(X0) <~> ~kind(X0)) <=> (wise(X0) & strong(X0))) [input p15]
17. ~wise(susan) [input p16]
25. ~strong(susan) [input hypothesis]
33. ! [X0] : (patient(X0) | (~wise(X0) <=> ~creative(X0))) [ennf transformation 8]
38. ! [X0] : ((~quiet(X0) & quiet(X0)) | (strong(X0) | creative(X0))) [ennf transformation 11]
39. ! [X0] : ((~quiet(X0) & quiet(X0)) | strong(X0) | creative(X0)) [flattening 38]
40. ! [X0] : (kind(X0) | (~funny(X0) <=> patient(X0))) [ennf transformation 14]
58. ! [X0] : (patient(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) [nnf transformation 33]
64. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [nnf transformation 13]
65. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [flattening 64]
66. ! [X0] : (kind(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) [nnf transformation 40]
68. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~wise(X0) | ~strong(X0))) & ((wise(X0) & strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [nnf transformation 16]
69. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~wise(X0) | ~strong(X0)) & ((wise(X0) & strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [flattening 68]
100. ~creative(X0) | patient(X0) | wise(X0) [cnf transformation 58]
105. quiet(X0) | strong(X0) | creative(X0) [cnf transformation 39]
106. ~quiet(X0) | strong(X0) | creative(X0) [cnf transformation 39]
118. ~creative(X0) | strong(X0) | ~patient(X0) | funny(X0) [cnf transformation 65]
120. ~patient(X0) | ~funny(X0) | kind(X0) [cnf transformation 66]
124. patient(X0) | strong(X0) | kind(X0) [cnf transformation 69]
125. ~patient(X0) | ~kind(X0) | wise(X0) [cnf transformation 69]
129. ~wise(susan) [cnf transformation 17]
140. ~strong(susan) [cnf transformation 25]
208. creative(X0) | strong(X0) [subsumption resolution 105,106]
237. ~patient(X0) | strong(X0) | funny(X0) [subsumption resolution 118,208]
258. 26 <=> strong(susan) [avatar definition]
260. ~strong(susan) <- (~26) [avatar component clause 258]
323. ~26 [avatar split clause 140,258]
343. patient(X0) | wise(X0) | strong(X0) [resolution 100,208]
413. strong(X1) | kind(X1) | ~funny(X1) | kind(X1) [resolution 124,120]
416. strong(X1) | kind(X1) | ~funny(X1) [duplicate literal removal 413]
506. strong(X1) | funny(X1) | strong(X1) | kind(X1) [resolution 237,124]
514. funny(X1) | strong(X1) | kind(X1) [duplicate literal removal 506]
686. wise(X2) | strong(X2) | ~kind(X2) | wise(X2) [resolution 343,125]
695. ~kind(X2) | strong(X2) | wise(X2) [duplicate literal removal 686]
750. strong(X1) | kind(X1) [subsumption resolution 416,514]
765. kind(susan) <- (~26) [resolution 750,260]
807. strong(susan) | wise(susan) <- (~26) [resolution 695,765]
809. wise(susan) <- (~26) [subsumption resolution 807,260]
810. $false <- (~26) [subsumption resolution 809,129]
811. 26 [avatar contradiction clause 810]
812. $false [avatar sat refutation 323,811]
% SZS output end Proof for 6127664194013924125866828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
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