premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either generous or not rich is patient. If someone is either strong or brave then fred is not funny. Everyone who is creative or not wise is curious. Everyone who is not creative or not happy is both curious and wise. Everyone who is rich or not creative is both not kind and not curious and vice versa. If someone is not kind then paul is calm and vice versa. Everyone who is either not humble or quiet is not brave and vice versa. If susan is either not old or not funny then someone is either not wise or not quiet. If susan is not generous then someone is either not curious or not tall. If susan is not creative then someone is both not brave and strong and vice versa. If someone is either old or not tall then susan is either calm or not patient. Everyone who is both old and strong is not strong. Everyone who is either patient or kind is not brave or not wise and vice versa. If john is strong or not tall then someone is rich. Everyone who is happy is either not strong or not happy and vice versa. Alice is quiet or not humble. Someone is curious or rich. Mary is not calm. Lucy is not generous. John is both not humble and kind. Paul is calm or kind. John is either tall or not funny. Mary is either kind or not tall. | Lucy is patient. | entailment | (![X]:((generous(X)<~>~rich(X))=>patient(X)))&
((?[X]:((strong(X)<~>brave(X))))=>(~funny(fred)))&
(![X]:((creative(X)|~wise(X))=>curious(X)))&
(![X]:((~creative(X)|~happy(X))=>(curious(X)&wise(X))))&
(![X]:((rich(X)|~creative(X))<=>(~kind(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(calm(paul)))&
(![X]:((~humble(X)<~>quiet(X))<=>~brave(X)))&
(((~old(susan)<~>~funny(susan)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
((~generous(susan))=>(?[X]:((~curious(X)<~>~tall(X)))))&
((~creative(susan))<=>(?[X]:((~brave(X)&strong(X)))))&
((?[X]:((old(X)<~>~tall(X))))=>((calm(susan)<~>~patient(susan))))&
(![X]:((old(X)&strong(X))=>~strong(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~brave(X)|~wise(X))))&
(((strong(john)|~tall(john)))=>(?[X]:(rich(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~happy(X))))&
((quiet(alice)|~humble(alice)))&
(?[X]:((curious(X)|rich(X))))&
(~calm(mary))&
(~generous(lucy))&
((~humble(john)&kind(john)))&
((calm(paul)|kind(paul)))&
((tall(john)<~>~funny(john)))&
((kind(mary)<~>~tall(mary))) | patient(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7651076436320575957743959
% SZS output start Proof for 7651076436320575957743959
1. ! [X0] : ((generous(X0) <~> ~rich(X0)) => patient(X0)) [input p0]
3. ! [X0] : ((~wise(X0) | creative(X0)) => curious(X0)) [input p2]
4. ! [X0] : ((~happy(X0) | ~creative(X0)) => (wise(X0) & curious(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | rich(X0)) <=> (~curious(X0) & ~kind(X0))) [input p4]
19. ~generous(lucy) [input p18]
24. ~patient(lucy) [input hypothesis]
25. ! [X0] : (patient(X0) | (generous(X0) <=> ~rich(X0))) [ennf transformation 1]
27. ! [X0] : (curious(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 3]
28. ! [X0] : ((wise(X0) & curious(X0)) | (happy(X0) & creative(X0))) [ennf transformation 4]
35. ! [X0] : (patient(X0) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) [nnf transformation 25]
37. ! [X0] : (((~creative(X0) | rich(X0)) | (curious(X0) | kind(X0))) & ((~curious(X0) & ~kind(X0)) | (creative(X0) & ~rich(X0)))) [nnf transformation 5]
38. ! [X0] : ((~creative(X0) | rich(X0) | curious(X0) | kind(X0)) & ((~curious(X0) & ~kind(X0)) | (creative(X0) & ~rich(X0)))) [flattening 37]
65. patient(X0) | generous(X0) | rich(X0) [cnf transformation 35]
68. ~creative(X0) | curious(X0) [cnf transformation 27]
70. curious(X0) | creative(X0) [cnf transformation 28]
76. ~curious(X0) | ~rich(X0) [cnf transformation 38]
114. ~generous(lucy) [cnf transformation 19]
122. ~patient(lucy) [cnf transformation 24]
138. curious(X0) [subsumption resolution 70,68]
140. ~rich(X0) [subsumption resolution 76,138]
233. generous(lucy) | rich(lucy) [resolution 65,122]
235. rich(lucy) [subsumption resolution 233,114]
236. $false [subsumption resolution 235,140]
% SZS output end Proof for 7651076436320575957743959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not generous then susan is either humble or not generous.
Everyone who is not strong or rich is funny or not calm and vice versa.
Everyone who is either generous or not funny is not funny and vice versa.
Everyone who is not strong or old is not calm or tall.
Everyone who is both not wise and creative is either calm or not strong.
Everyone who is both not tall and not brave is both generous and not tall.
Everyone who is both not quiet and not brave is humble and vice versa.
Everyone who is both curious and not kind is not patient and vice versa.
If fred is either creative or not calm then alice is quiet and vice versa.
Everyone who is either not humble or not rich is not tall or creative.
Everyone who is curious or creative is both funny and not wise and vice versa.
If paul is both rich and curious then someone is not tall and vice versa.
Everyone who is patient is not curious or happy and vice versa.
If someone is both not funny and wise then someone is not patient.
Everyone who is not kind is old or kind and vice versa.
Mary is both not curious and tall.
Someone is creative or wise.
Fred is not wise.
Fred is kind or not happy.
Someone is not patient. | Susan is not old. | contradiction | ((?[X]:((~humble(X)|~generous(X))))=>((humble(susan)<~>~generous(susan))))&
(![X]:((~strong(X)|rich(X))<=>(funny(X)|~calm(X))))&
(![X]:((generous(X)<~>~funny(X))<=>~funny(X)))&
(![X]:((~strong(X)|old(X))=>(~calm(X)|tall(X))))&
(![X]:((~wise(X)&creative(X))=>(calm(X)<~>~strong(X))))&
(![X]:((~tall(X)&~brave(X))=>(generous(X)&~tall(X))))&
(![X]:((~quiet(X)&~brave(X))<=>humble(X)))&
(![X]:((curious(X)&~kind(X))<=>~patient(X)))&
(((creative(fred)<~>~calm(fred)))<=>(quiet(alice)))&
(![X]:((~humble(X)<~>~rich(X))=>(~tall(X)|creative(X))))&
(![X]:((curious(X)|creative(X))<=>(funny(X)&~wise(X))))&
(((rich(paul)&curious(paul)))<=>(?[X]:(~tall(X))))&
(![X]:(patient(X)<=>(~curious(X)|happy(X))))&
((?[X]:((~funny(X)&wise(X))))=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)<=>(old(X)|kind(X))))&
((~curious(mary)&tall(mary)))&
(?[X]:((creative(X)|wise(X))))&
(~wise(fred))&
((kind(fred)|~happy(fred)))&
(?[X]:(~patient(X))) | ~old(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4946391112643125829947222
% SZS output start Proof for 4946391112643125829947222
15. ! [X0] : (~kind(X0) <=> (kind(X0) | old(X0))) [input p14]
21. ~old(susan) [input hypothesis]
56. ! [X0] : ((~kind(X0) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | kind(X0))) [nnf transformation 15]
57. ! [X0] : ((~kind(X0) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | kind(X0))) [flattening 56]
104. kind(X0) | old(X0) | kind(X0) [cnf transformation 57]
106. ~kind(X0) | ~kind(X0) [cnf transformation 57]
113. ~old(susan) [cnf transformation 21]
114. kind(X0) | old(X0) [duplicate literal removal 104]
115. ~kind(X0) [duplicate literal removal 106]
180. old(X0) [subsumption resolution 114,115]
191. $false [subsumption resolution 113,180]
% SZS output end Proof for 4946391112643125829947222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either funny or happy then mary is funny and vice versa. Everyone who is both not rich and strong is both brave and kind and vice versa. If lucy is patient then fred is not creative or not quiet and vice versa. Everyone who is either not calm or creative is both not brave and strong and vice versa. Everyone who is both not patient and not humble is either not brave or not wise and vice versa. If john is both brave and humble then susan is not rich or rich. Everyone who is not old or not brave is either not happy or rich. If lucy is not wise or not strong then someone is not wise. Everyone who is either not humble or wise is not rich. If someone is both patient and happy then someone is old or not calm and vice versa. If susan is not patient then someone is either strong or humble and vice versa. Everyone who is either not kind or not funny is funny and vice versa. Everyone who is not quiet or not brave is both not wise and creative. Everyone who is not quiet is not generous or not brave and vice versa. Everyone who is both strong and humble is not strong or humble and vice versa. If someone is funny then alice is either strong or creative and vice versa. Someone is both creative and quiet. John is either not kind or creative. Mary is not curious. Someone is generous. Someone is either strong or old. Someone is both not quiet and patient. Someone is either not old or rich. Paul is tall or not generous. | John is not wise. | contradiction | (((funny(susan)<~>happy(susan)))<=>(funny(mary)))&
(![X]:((~rich(X)&strong(X))<=>(brave(X)&kind(X))))&
((patient(lucy))<=>((~creative(fred)|~quiet(fred))))&
(![X]:((~calm(X)<~>creative(X))<=>(~brave(X)&strong(X))))&
(![X]:((~patient(X)&~humble(X))<=>(~brave(X)<~>~wise(X))))&
(((brave(john)&humble(john)))=>((~rich(susan)|rich(susan))))&
(![X]:((~old(X)|~brave(X))=>(~happy(X)<~>rich(X))))&
(((~wise(lucy)|~strong(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~humble(X)<~>wise(X))=>~rich(X)))&
((?[X]:((patient(X)&happy(X))))<=>(?[X]:((old(X)|~calm(X)))))&
((~patient(susan))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(?[X]:((creative(X)&quiet(X))))&
((~kind(john)<~>creative(john)))&
(~curious(mary))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~quiet(X)&patient(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((tall(paul)|~generous(paul))) | ~wise(john) | [
"p1",
"p4",
"p8",
"p11",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4462836952695316474623196
% SZS output start Proof for 4462836952695316474623196
2. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (kind(X0) & brave(X0))) [input p1]
5. ! [X0] : ((~humble(X0) & ~patient(X0)) <=> (~brave(X0) <~> ~wise(X0))) [input p4]
9. ! [X0] : ((~humble(X0) <~> wise(X0)) => ~rich(X0)) [input p8]
12. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p11]
13. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p12]
15. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p14]
18. ~kind(john) <~> creative(john) [input p17]
25. ~wise(john) [input hypothesis]
33. ! [X0] : (~rich(X0) | (~humble(X0) <=> wise(X0))) [ennf transformation 9]
34. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 13]
36. ! [X0] : (((strong(X0) & ~rich(X0)) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 2]
37. ! [X0] : (((strong(X0) & ~rich(X0)) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | ~strong(X0) | rich(X0))) [flattening 36]
42. ! [X0] : (((~humble(X0) & ~patient(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (humble(X0) | patient(X0)))) [nnf transformation 5]
43. ! [X0] : (((~humble(X0) & ~patient(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | humble(X0) | patient(X0))) [flattening 42]
47. ! [X0] : (~rich(X0) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) [nnf transformation 33]
57. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 12]
60. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 15]
61. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 60]
68. (~creative(john) | kind(john)) & (creative(john) | ~kind(john)) [nnf transformation 18]
84. ~strong(X0) | kind(X0) | rich(X0) [cnf transformation 37]
101. ~humble(X0) | ~brave(X0) | wise(X0) [cnf transformation 43]
109. ~rich(X0) | wise(X0) | humble(X0) [cnf transformation 47]
121. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 57]
122. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 57]
127. creative(X0) | brave(X0) [cnf transformation 34]
133. strong(X0) | ~humble(X0) [cnf transformation 61]
134. humble(X0) | strong(X0) [cnf transformation 61]
143. ~creative(john) | kind(john) [cnf transformation 68]
151. ~wise(john) [cnf transformation 25]
154. funny(X0) | ~kind(X0) [duplicate literal removal 121]
155. ~kind(X0) | ~funny(X0) [duplicate literal removal 122]
253. ~kind(X0) [subsumption resolution 154,155]
254. strong(X0) [subsumption resolution 133,134]
270. ~creative(john) [subsumption resolution 143,253]
289. brave(john) [resolution 127,270]
295. kind(X0) | rich(X0) [resolution 84,254]
296. rich(X0) [subsumption resolution 295,253]
369. wise(X0) | humble(X0) [resolution 109,296]
481. humble(john) [resolution 369,151]
501. ~brave(john) | wise(john) [resolution 481,101]
502. wise(john) [subsumption resolution 501,289]
503. $false [subsumption resolution 502,151]
% SZS output end Proof for 4462836952695316474623196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not generous then john is either quiet or old.
If someone is either brave or tall then paul is either not rich or not patient and vice versa.
If someone is funny then someone is either not happy or rich and vice versa.
Everyone who is not kind is creative or not patient and vice versa.
Everyone who is both brave and curious is both not quiet and generous and vice versa.
If paul is both happy and funny then mary is not funny and vice versa.
Everyone who is either not old or generous is both calm and generous and vice versa.
Everyone who is either not patient or funny is not humble.
If paul is both curious and not kind then someone is not brave.
If someone is not patient then someone is both not brave and not old and vice versa.
If someone is both funny and not brave then paul is both kind and humble.
Everyone who is not strong is either creative or not strong and vice versa.
Everyone who is both strong and old is tall.
Everyone who is strong or not kind is either not funny or not tall and vice versa.
Everyone who is both not strong and tall is happy or kind and vice versa.
Everyone who is not quiet is not tall or generous and vice versa.
Susan is both happy and not strong.
Someone is either not quiet or tall.
Someone is not rich.
Susan is old.
Paul is not old.
Alice is both old and curious.
Paul is curious or not generous. | Mary is not humble. | entailment | ((?[X]:((generous(X)|~generous(X))))=>((quiet(john)<~>old(john))))&
((?[X]:((brave(X)<~>tall(X))))<=>((~rich(paul)<~>~patient(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(creative(X)|~patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~quiet(X)&generous(X))))&
(((happy(paul)&funny(paul)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>generous(X))<=>(calm(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>~humble(X)))&
(((curious(paul)&~kind(paul)))=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((?[X]:((funny(X)&~brave(X))))=>((kind(paul)&humble(paul))))&
(![X]:(~strong(X)<=>(creative(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))=>tall(X)))&
(![X]:((strong(X)|~kind(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~strong(X)&tall(X))<=>(happy(X)|kind(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|generous(X))))&
((happy(susan)&~strong(susan)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~rich(X)))&
(old(susan))&
(~old(paul))&
((old(alice)&curious(alice)))&
((curious(paul)|~generous(paul))) | ~humble(mary) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 891767506861462309337345
% SZS output start Proof for 891767506861462309337345
4. ! [X0] : (~kind(X0) <=> (~patient(X0) | creative(X0))) [input p3]
5. ! [X0] : ((curious(X0) & brave(X0)) <=> (generous(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~old(X0) <~> generous(X0)) <=> (generous(X0) & calm(X0))) [input p6]
8. ! [X0] : ((~patient(X0) <~> funny(X0)) => ~humble(X0)) [input p7]
10. ? [X0] : ~patient(X0) <=> ? [X0] : (~old(X0) & ~brave(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (creative(X0) <~> ~strong(X0))) [input p11]
14. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p13]
15. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (kind(X0) | happy(X0))) [input p14]
16. ! [X0] : (~quiet(X0) <=> (generous(X0) | ~tall(X0))) [input p15]
24. humble(mary) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : (~old(X1) & ~brave(X1)) [rectify 10]
28. ! [X0] : (~humble(X0) | (~patient(X0) <=> funny(X0))) [ennf transformation 8]
44. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | kind(X0))) [nnf transformation 4]
45. ! [X0] : ((~kind(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | kind(X0))) [flattening 44]
46. ! [X0] : (((curious(X0) & brave(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((curious(X0) & brave(X0)) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [flattening 50]
52. ! [X0] : (~humble(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) [nnf transformation 28]
55. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X1] : (~old(X1) & ~brave(X1)) | ! [X0] : patient(X0)) [nnf transformation 26]
56. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X2] : (~old(X2) & ~brave(X2)) | ! [X3] : patient(X3)) [rectify 55]
57. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
58. ? [X2] : (~old(X2) & ~brave(X2)) => (~old(sK5) & ~brave(sK5)) [choice axiom]
59. (~patient(sK4) | ! [X1] : (old(X1) | brave(X1))) & ((~old(sK5) & ~brave(sK5)) | ! [X3] : patient(X3)) [skolemisation 56,58,57]
60. ! [X0] : ((~strong(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | strong(X0))) [nnf transformation 12]
61. ! [X0] : (((~kind(X0) | strong(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : ((~kind(X0) | strong(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (kind(X0) & ~strong(X0)))) [flattening 61]
63. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & ((kind(X0) | happy(X0)) | (~tall(X0) | strong(X0)))) [nnf transformation 15]
64. ! [X0] : (((tall(X0) & ~strong(X0)) | (~kind(X0) & ~happy(X0))) & (kind(X0) | happy(X0) | ~tall(X0) | strong(X0))) [flattening 63]
65. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | quiet(X0))) [flattening 65]
88. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 45]
93. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
100. generous(X0) | generous(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 52]
107. ~brave(sK5) | patient(X3) [cnf transformation 59]
108. ~old(sK5) | patient(X3) [cnf transformation 59]
113. strong(X0) | ~creative(X0) | strong(X0) [cnf transformation 60]
114. ~strong(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 60]
120. kind(X0) | funny(X0) | tall(X0) [cnf transformation 62]
121. ~kind(X0) | strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 62]
125. ~strong(X0) | ~kind(X0) [cnf transformation 64]
127. ~kind(X0) | tall(X0) [cnf transformation 64]
130. ~quiet(X0) | ~generous(X0) [cnf transformation 66]
141. humble(mary) [cnf transformation 24]
142. strong(X0) | ~creative(X0) [duplicate literal removal 113]
143. ~strong(X0) | ~creative(X0) [duplicate literal removal 114]
144. old(X0) | generous(X0) [duplicate literal removal 100]
220. 17 <=> funny(mary) [avatar definition]
221. ~funny(mary) <- (~17) [avatar component clause 220]
256. 25 <=> ! [X3] : patient(X3) [avatar definition]
257. patient(X3) <- (25) [avatar component clause 256]
259. 26 <=> old(sK5) [avatar definition]
261. ~old(sK5) <- (~26) [avatar component clause 259]
262. 25 | ~26 [avatar split clause 108,259,256]
264. 27 <=> brave(sK5) [avatar definition]
266. ~brave(sK5) <- (~27) [avatar component clause 264]
267. 25 | ~27 [avatar split clause 107,264,256]
277. ~creative(X0) [subsumption resolution 142,143]
294. generous(sK5) <- (~26) [resolution 144,261]
328. brave(sK5) | quiet(sK5) <- (~26) [resolution 93,294]
331. quiet(sK5) <- (~26, ~27) [subsumption resolution 328,266]
371. ~patient(mary) | ~funny(mary) [resolution 105,141]
393. funny(X0) | tall(X0) | tall(X0) [resolution 120,127]
395. funny(X0) | tall(X0) [duplicate literal removal 393]
423. ~generous(sK5) <- (~26, ~27) [resolution 331,130]
425. $false <- (~26, ~27) [subsumption resolution 423,294]
426. 26 | 27 [avatar contradiction clause 425]
428. creative(X0) | kind(X0) <- (25) [resolution 257,88]
432. kind(X0) <- (25) [subsumption resolution 428,277]
433. ~funny(mary) <- (25) [subsumption resolution 371,257]
434. ~17 | ~25 [avatar split clause 433,256,220]
450. strong(X1) | ~tall(X1) | funny(X1) <- (25) [resolution 432,121]
454. strong(X1) | funny(X1) <- (25) [subsumption resolution 450,395]
524. funny(X4) | ~kind(X4) <- (25) [resolution 454,125]
528. funny(X4) <- (25) [subsumption resolution 524,432]
533. $false <- (~17, 25) [resolution 528,221]
534. 17 | ~25 [avatar contradiction clause 533]
535. $false [avatar sat refutation 262,267,426,434,534]
% SZS output end Proof for 891767506861462309337345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not kind is not old and vice versa.
If someone is either not tall or not brave then lucy is kind.
If fred is either strong or tall then someone is not calm and vice versa.
Everyone who is either not brave or not wise is not strong or not curious and vice versa.
If someone is both funny and not creative then someone is both not creative and not kind and vice versa.
Everyone who is both not patient and not quiet is old or not kind and vice versa.
If paul is tall or not brave then someone is both strong and not curious and vice versa.
Everyone who is not patient is not patient or old.
If susan is either not generous or not quiet then someone is either generous or not strong.
Everyone who is wise or not old is not strong or calm and vice versa.
Everyone who is either not wise or not quiet is not calm and vice versa.
If someone is either not calm or not curious then someone is either not tall or old.
If fred is both brave and not curious then someone is either generous or not kind and vice versa.
Everyone who is both not kind and happy is not generous and vice versa.
Everyone who is either kind or curious is not brave and vice versa.
Someone is either happy or not kind.
Mary is both curious and humble.
Someone is either rich or strong.
Someone is both humble and not brave.
John is brave or humble.
Someone is both funny and curious.
Lucy is either humble or curious.
Someone is calm or kind. | Mary is kind. | contradiction | (![X]:((~curious(X)|~kind(X))<=>~old(X)))&
((?[X]:((~tall(X)<~>~brave(X))))=>(kind(lucy)))&
(((strong(fred)<~>tall(fred)))<=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~strong(X)|~curious(X))))&
((?[X]:((funny(X)&~creative(X))))<=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:((~patient(X)&~quiet(X))<=>(old(X)|~kind(X))))&
(((tall(paul)|~brave(paul)))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~patient(X)=>(~patient(X)|old(X))))&
(((~generous(susan)<~>~quiet(susan)))=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((wise(X)|~old(X))<=>(~strong(X)|calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>~calm(X)))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~tall(X)<~>old(X)))))&
(((brave(fred)&~curious(fred)))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~kind(X)&happy(X))<=>~generous(X)))&
(![X]:((kind(X)<~>curious(X))<=>~brave(X)))&
(?[X]:((happy(X)<~>~kind(X))))&
((curious(mary)&humble(mary)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((humble(X)&~brave(X))))&
((brave(john)|humble(john)))&
(?[X]:((funny(X)&curious(X))))&
((humble(lucy)<~>curious(lucy)))&
(?[X]:((calm(X)|kind(X)))) | kind(mary) | [
"p0",
"p3",
"p5",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7807008077644993483164772
% SZS output start Proof for 7807008077644993483164772
1. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> ~old(X0)) [input p0]
4. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~curious(X0) | ~strong(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~kind(X0) | old(X0))) [input p5]
10. ! [X0] : ((~old(X0) | wise(X0)) <=> (calm(X0) | ~strong(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> ~calm(X0)) [input p10]
15. ! [X0] : ((kind(X0) <~> curious(X0)) <=> ~brave(X0)) [input p14]
17. humble(mary) & curious(mary) [input p16]
24. kind(mary) [input hypothesis]
32. ! [X0] : (((~kind(X0) | ~curious(X0)) | old(X0)) & (~old(X0) | (kind(X0) & curious(X0)))) [nnf transformation 1]
33. ! [X0] : ((~kind(X0) | ~curious(X0) | old(X0)) & (~old(X0) | (kind(X0) & curious(X0)))) [flattening 32]
39. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 4]
40. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 39]
46. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | quiet(X0) | patient(X0))) [flattening 46]
56. ! [X0] : (((~old(X0) | wise(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (old(X0) & ~wise(X0)))) [nnf transformation 10]
57. ! [X0] : ((~old(X0) | wise(X0) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | (old(X0) & ~wise(X0)))) [flattening 56]
58. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 11]
70. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | brave(X0)) & (~brave(X0) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 15]
86. ~kind(X0) | ~curious(X0) | old(X0) [cnf transformation 33]
95. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 40]
106. ~quiet(X0) | ~old(X0) [cnf transformation 47]
118. ~wise(X0) | ~strong(X0) | calm(X0) [cnf transformation 57]
121. ~calm(X0) | wise(X0) | ~old(X0) [cnf transformation 57]
123. ~wise(X0) | ~calm(X0) | quiet(X0) [cnf transformation 58]
125. quiet(X0) | wise(X0) | calm(X0) [cnf transformation 58]
142. ~kind(X0) | ~curious(X0) | brave(X0) [cnf transformation 70]
145. curious(mary) [cnf transformation 17]
157. kind(mary) [cnf transformation 24]
371. ~curious(mary) | old(mary) [resolution 86,157]
373. old(mary) [subsumption resolution 371,145]
386. 43 <=> strong(mary) [avatar definition]
390. 44 <=> wise(mary) [avatar definition]
392. wise(mary) <- (44) [avatar component clause 390]
414. wise(X3) | calm(X3) | ~old(X3) [resolution 125,106]
417. ~old(X3) | wise(X3) [subsumption resolution 414,121]
418. wise(mary) [resolution 417,373]
419. 44 [avatar split clause 418,390]
421. ~calm(mary) | quiet(mary) <- (44) [resolution 392,123]
422. ~strong(mary) | calm(mary) <- (44) [resolution 392,118]
424. ~brave(mary) | strong(mary) <- (44) [resolution 392,95]
426. 47 <=> quiet(mary) [avatar definition]
428. quiet(mary) <- (47) [avatar component clause 426]
430. 48 <=> calm(mary) [avatar definition]
433. 47 | ~48 | ~44 [avatar split clause 421,390,430,426]
437. 49 <=> brave(mary) [avatar definition]
440. 43 | ~49 | ~44 [avatar split clause 424,390,437,386]
441. 48 | ~43 | ~44 [avatar split clause 422,390,386,430]
485. ~curious(mary) | brave(mary) [resolution 142,157]
487. brave(mary) [subsumption resolution 485,145]
490. 49 [avatar split clause 487,437]
663. ~old(mary) <- (47) [resolution 428,106]
664. $false <- (47) [subsumption resolution 663,373]
665. ~47 [avatar contradiction clause 664]
666. $false [avatar sat refutation 419,433,440,441,490,665]
% SZS output end Proof for 7807008077644993483164772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not funny is not wise or creative.
Everyone who is not brave or not funny is not curious or not patient.
Everyone who is not brave or kind is not brave or brave and vice versa.
Everyone who is funny or not kind is either not strong or curious.
If someone is not rich then lucy is quiet and vice versa.
Everyone who is not happy is both strong and tall.
If mary is both not happy and not kind then fred is both not brave and calm.
Everyone who is both not curious and not tall is tall and vice versa.
Everyone who is not strong is happy.
Everyone who is both not kind and not happy is both not tall and not old and vice versa.
If someone is not kind then lucy is both old and not rich and vice versa.
If someone is not wise or rich then fred is not humble and vice versa.
If someone is either not brave or not funny then fred is both happy and not humble and vice versa.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is both old and not happy is brave.
Everyone who is wise is either not quiet or not brave and vice versa.
Someone is either not brave or not strong.
Someone is happy.
Lucy is not strong or funny.
Someone is generous.
Someone is strong.
Alice is both not quiet and humble. | Mary is not tall. | entailment | (![X]:((~old(X)|~funny(X))=>(~wise(X)|creative(X))))&
(![X]:((~brave(X)|~funny(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)|kind(X))<=>(~brave(X)|brave(X))))&
(![X]:((funny(X)|~kind(X))=>(~strong(X)<~>curious(X))))&
((?[X]:(~rich(X)))<=>(quiet(lucy)))&
(![X]:(~happy(X)=>(strong(X)&tall(X))))&
(((~happy(mary)&~kind(mary)))=>((~brave(fred)&calm(fred))))&
(![X]:((~curious(X)&~tall(X))<=>tall(X)))&
(![X]:(~strong(X)=>happy(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)&~old(X))))&
((?[X]:(~kind(X)))<=>((old(lucy)&~rich(lucy))))&
((?[X]:((~wise(X)|rich(X))))<=>(~humble(fred)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((old(X)&~happy(X))=>brave(X)))&
(![X]:(wise(X)<=>(~quiet(X)<~>~brave(X))))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(happy(X)))&
((~strong(lucy)|funny(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(strong(X)))&
((~quiet(alice)&humble(alice))) | ~tall(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4846933037158227499183876
% SZS output start Proof for 4846933037158227499183876
8. ! [X0] : ((~tall(X0) & ~curious(X0)) <=> tall(X0)) [input p7]
23. tall(mary) [input hypothesis]
42. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) | curious(X0)))) [nnf transformation 8]
43. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | tall(X0) | curious(X0))) [flattening 42]
85. ~tall(X0) | ~tall(X0) [cnf transformation 43]
118. tall(mary) [cnf transformation 23]
122. ~tall(X0) [duplicate literal removal 85]
237. $false [subsumption resolution 118,122]
% SZS output end Proof for 4846933037158227499183876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not generous is not tall and vice versa. If someone is either strong or not calm then mary is not humble and vice versa. Everyone who is curious is calm or tall. If someone is either not quiet or not humble then mary is not creative. If lucy is either not patient or not happy then alice is both not tall and wise and vice versa. Everyone who is not patient or strong is either not old or wise and vice versa. Everyone who is brave is either creative or quiet. If john is either quiet or not strong then someone is both happy and curious. If someone is not strong or calm then someone is not patient or not brave. Everyone who is not funny or not brave is not tall and vice versa. Everyone who is either creative or not brave is wise or not happy and vice versa. If someone is old or not humble then lucy is both not generous and not happy. Everyone who is tall is both humble and tall and vice versa. Everyone who is not creative is both old and funny. If someone is calm or not tall then susan is both not patient and generous. If mary is not wise then lucy is not quiet or humble. Someone is either calm or not kind. Someone is either generous or not tall. John is patient. Mary is either not brave or not calm. Alice is both old and funny. Someone is not humble. Someone is not old. Someone is not creative. | Mary is old. | entailment | (![X]:((curious(X)&~generous(X))<=>~tall(X)))&
((?[X]:((strong(X)<~>~calm(X))))<=>(~humble(mary)))&
(![X]:(curious(X)=>(calm(X)|tall(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(~creative(mary)))&
(((~patient(lucy)<~>~happy(lucy)))<=>((~tall(alice)&wise(alice))))&
(![X]:((~patient(X)|strong(X))<=>(~old(X)<~>wise(X))))&
(![X]:(brave(X)=>(creative(X)<~>quiet(X))))&
(((quiet(john)<~>~strong(john)))=>(?[X]:((happy(X)&curious(X)))))&
((?[X]:((~strong(X)|calm(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((~funny(X)|~brave(X))<=>~tall(X)))&
(![X]:((creative(X)<~>~brave(X))<=>(wise(X)|~happy(X))))&
((?[X]:((old(X)|~humble(X))))=>((~generous(lucy)&~happy(lucy))))&
(![X]:(tall(X)<=>(humble(X)&tall(X))))&
(![X]:(~creative(X)=>(old(X)&funny(X))))&
((?[X]:((calm(X)|~tall(X))))=>((~patient(susan)&generous(susan))))&
((~wise(mary))=>((~quiet(lucy)|humble(lucy))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(patient(john))&
((~brave(mary)<~>~calm(mary)))&
((old(alice)&funny(alice)))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
(?[X]:(~creative(X))) | old(mary) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 691236884103102486421312
% SZS output start Proof for 691236884103102486421312
1. ! [X0] : ((~generous(X0) & curious(X0)) <=> ~tall(X0)) [input p0]
2. ? [X0] : (strong(X0) <~> ~calm(X0)) <=> ~humble(mary) [input p1]
3. ! [X0] : (curious(X0) => (tall(X0) | calm(X0))) [input p2]
4. ? [X0] : (~quiet(X0) <~> ~humble(X0)) => ~creative(mary) [input p3]
6. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~old(X0) <~> wise(X0))) [input p5]
7. ! [X0] : (brave(X0) => (creative(X0) <~> quiet(X0))) [input p6]
10. ! [X0] : ((~brave(X0) | ~funny(X0)) <=> ~tall(X0)) [input p9]
11. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (~happy(X0) | wise(X0))) [input p10]
13. ! [X0] : (tall(X0) <=> (tall(X0) & humble(X0))) [input p12]
14. ! [X0] : (~creative(X0) => (funny(X0) & old(X0))) [input p13]
15. ? [X0] : (~tall(X0) | calm(X0)) => (generous(susan) & ~patient(susan)) [input p14]
25. ~old(mary) [input hypothesis]
27. ! [X0] : ((tall(X0) | calm(X0)) | ~curious(X0)) [ennf transformation 3]
28. ! [X0] : (tall(X0) | calm(X0) | ~curious(X0)) [flattening 27]
29. ~creative(mary) | ! [X0] : (~quiet(X0) <=> ~humble(X0)) [ennf transformation 4]
30. ! [X0] : ((creative(X0) <~> quiet(X0)) | ~brave(X0)) [ennf transformation 7]
34. ! [X0] : ((funny(X0) & old(X0)) | creative(X0)) [ennf transformation 14]
35. (generous(susan) & ~patient(susan)) | ! [X0] : (tall(X0) & ~calm(X0)) [ennf transformation 15]
38. ! [X0] : (((~generous(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | (generous(X0) | ~curious(X0)))) [nnf transformation 1]
39. ! [X0] : (((~generous(X0) & curious(X0)) | tall(X0)) & (~tall(X0) | generous(X0) | ~curious(X0))) [flattening 38]
40. (? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | humble(mary)) & (~humble(mary) | ! [X0] : ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) [nnf transformation 2]
41. (? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | humble(mary)) & (~humble(mary) | ! [X1] : ((strong(X1) | calm(X1)) & (~calm(X1) | ~strong(X1)))) [rectify 40]
42. ? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) => ((calm(sK0) | ~strong(sK0)) & (~calm(sK0) | strong(sK0))) [choice axiom]
43. (((calm(sK0) | ~strong(sK0)) & (~calm(sK0) | strong(sK0))) | humble(mary)) & (~humble(mary) | ! [X1] : ((strong(X1) | calm(X1)) & (~calm(X1) | ~strong(X1)))) [skolemisation 41,42]
44. ~creative(mary) | ! [X0] : ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))) [nnf transformation 29]
47. ! [X0] : (((strong(X0) | ~patient(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) & (((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~strong(X0) & patient(X0)))) [nnf transformation 6]
48. ! [X0] : ((strong(X0) | ~patient(X0) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) & (((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~strong(X0) & patient(X0)))) [flattening 47]
49. ! [X0] : (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~brave(X0)) [nnf transformation 30]
56. ! [X0] : (((~brave(X0) | ~funny(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) & funny(X0)))) [nnf transformation 10]
57. ! [X0] : ((~brave(X0) | ~funny(X0) | tall(X0)) & (~tall(X0) | (brave(X0) & funny(X0)))) [flattening 56]
58. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (happy(X0) & ~wise(X0))) & ((~happy(X0) | wise(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 11]
59. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (happy(X0) & ~wise(X0))) & (~happy(X0) | wise(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [flattening 58]
60. ! [X0] : ((tall(X0) | (~tall(X0) | ~humble(X0))) & ((tall(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 13]
61. ! [X0] : ((tall(X0) | ~tall(X0) | ~humble(X0)) & ((tall(X0) & humble(X0)) | ~tall(X0))) [flattening 60]
76. tall(X0) | curious(X0) [cnf transformation 39]
77. ~generous(X0) | tall(X0) [cnf transformation 39]
79. ~humble(mary) | strong(X1) | calm(X1) [cnf transformation 43]
82. tall(X0) | calm(X0) | ~curious(X0) [cnf transformation 28]
83. ~creative(mary) | ~humble(X0) | quiet(X0) [cnf transformation 44]
91. ~old(X0) | wise(X0) | patient(X0) [cnf transformation 48]
92. ~old(X0) | wise(X0) | ~strong(X0) [cnf transformation 48]
98. ~brave(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 49]
106. ~tall(X0) | brave(X0) [cnf transformation 57]
110. ~brave(X0) | creative(X0) | ~wise(X0) [cnf transformation 59]
118. ~tall(X0) | humble(X0) [cnf transformation 61]
121. old(X0) | creative(X0) [cnf transformation 34]
123. ~patient(susan) | ~calm(X0) [cnf transformation 35]
125. generous(susan) | ~calm(X0) [cnf transformation 35]
140. ~old(mary) [cnf transformation 25]
142. 1 <=> humble(mary) [avatar definition]
143. ~humble(mary) <- (~1) [avatar component clause 142]
156. 4 <=> ! [X1] : (strong(X1) | calm(X1)) [avatar definition]
157. calm(X1) | strong(X1) <- (4) [avatar component clause 156]
158. 4 | ~1 [avatar split clause 79,142,156]
163. calm(X0) | tall(X0) [subsumption resolution 82,76]
168. 7 <=> creative(mary) [avatar definition]
173. 8 <=> ! [X0] : (~humble(X0) | quiet(X0)) [avatar definition]
174. ~humble(X0) | quiet(X0) <- (8) [avatar component clause 173]
175. 8 | ~7 [avatar split clause 83,168,173]
219. 17 <=> ! [X1] : ~calm(X1) [avatar definition]
220. ~calm(X1) <- (17) [avatar component clause 219]
252. 25 <=> generous(susan) [avatar definition]
254. generous(susan) <- (25) [avatar component clause 252]
256. 17 | 25 [avatar split clause 125,252,219]
258. 26 <=> patient(susan) [avatar definition]
260. ~patient(susan) <- (~26) [avatar component clause 258]
262. 17 | ~26 [avatar split clause 123,258,219]
277. 30 <=> calm(sK3) [avatar definition]
278. calm(sK3) <- (30) [avatar component clause 277]
279. ~calm(sK3) <- (~30) [avatar component clause 277]
300. 35 <=> calm(mary) [avatar definition]
301. ~calm(mary) <- (~35) [avatar component clause 300]
302. calm(mary) <- (35) [avatar component clause 300]
308. tall(susan) <- (25) [resolution 77,254]
312. brave(susan) <- (25) [resolution 106,308]
314. humble(susan) <- (25) [resolution 118,308]
316. creative(mary) [resolution 121,140]
319. 7 [avatar split clause 316,168]
321. tall(sK3) <- (~30) [resolution 163,279]
322. tall(mary) <- (~35) [resolution 163,301]
325. humble(sK3) <- (~30) [resolution 321,118]
326. brave(sK3) <- (~30) [resolution 321,106]
328. quiet(susan) <- (8, 25) [resolution 174,314]
329. humble(mary) <- (~35) [resolution 322,118]
332. $false <- (~1, ~35) [subsumption resolution 329,143]
333. 1 | 35 [avatar contradiction clause 332]
360. wise(X0) | patient(X0) | creative(X0) [resolution 91,121]
363. ~strong(X0) | wise(X0) | creative(X0) [resolution 92,121]
365. quiet(sK3) <- (8, ~30) [resolution 325,174]
368. ~creative(susan) | ~quiet(susan) <- (25) [resolution 98,312]
369. ~creative(sK3) | ~quiet(sK3) <- (~30) [resolution 98,326]
370. ~creative(susan) <- (8, 25) [subsumption resolution 368,328]
371. ~creative(sK3) <- (8, ~30) [subsumption resolution 369,365]
381. creative(susan) | ~wise(susan) <- (25) [resolution 110,312]
382. creative(sK3) | ~wise(sK3) <- (~30) [resolution 110,326]
383. ~wise(susan) <- (8, 25) [subsumption resolution 381,370]
384. ~wise(sK3) <- (8, ~30) [subsumption resolution 382,371]
469. strong(sK3) <- (4, ~30) [resolution 157,279]
470. wise(sK3) | creative(sK3) <- (4, ~30) [resolution 469,363]
471. creative(sK3) <- (4, 8, ~30) [subsumption resolution 470,384]
472. $false <- (4, 8, ~30) [subsumption resolution 471,371]
473. ~4 | ~8 | 30 [avatar contradiction clause 472]
571. patient(susan) | creative(susan) <- (8, 25) [resolution 383,360]
572. creative(susan) <- (8, 25, ~26) [subsumption resolution 571,260]
573. $false <- (8, 25, ~26) [subsumption resolution 572,370]
574. ~8 | ~25 | 26 [avatar contradiction clause 573]
577. $false <- (17, 35) [resolution 220,302]
579. $false <- (17, 30) [resolution 220,278]
580. ~17 | ~30 [avatar contradiction clause 579]
582. ~17 | ~35 [avatar contradiction clause 577]
584. $false [avatar sat refutation 158,175,256,262,319,333,473,574,580,582]
% SZS output end Proof for 691236884103102486421312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or kind is both not tall and not brave and vice versa.
If someone is either patient or happy then lucy is not happy and vice versa.
Everyone who is patient is either creative or funny.
Everyone who is either calm or not calm is either wise or not brave and vice versa.
If someone is both happy and patient then paul is old.
If susan is tall then john is wise or not rich and vice versa.
If alice is happy or strong then someone is not old or patient.
If lucy is brave or not generous then someone is wise or creative and vice versa.
Everyone who is either happy or creative is generous or tall and vice versa.
If alice is either not tall or not strong then someone is either kind or not generous and vice versa.
Everyone who is quiet or calm is either happy or not calm and vice versa.
Everyone who is both not strong and funny is both rich and not quiet.
Everyone who is both not happy and brave is either funny or not wise and vice versa.
If someone is both not strong and kind then mary is not strong and vice versa.
If lucy is not rich then someone is not humble and vice versa.
Everyone who is kind or strong is both strong and not brave and vice versa.
Someone is strong.
Fred is either kind or funny.
Someone is not kind.
Someone is both not tall and not funny.
Paul is either not generous or not funny.
Someone is both tall and not funny.
Someone is not tall. | John is not happy. | neutral | (![X]:((curious(X)<~>kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(~happy(lucy)))&
(![X]:(patient(X)=>(creative(X)<~>funny(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(wise(X)<~>~brave(X))))&
((?[X]:((happy(X)&patient(X))))=>(old(paul)))&
((tall(susan))<=>((wise(john)|~rich(john))))&
(((happy(alice)|strong(alice)))=>(?[X]:((~old(X)|patient(X)))))&
(((brave(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((happy(X)<~>creative(X))<=>(generous(X)|tall(X))))&
(((~tall(alice)<~>~strong(alice)))<=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((quiet(X)|calm(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~strong(X)&funny(X))=>(rich(X)&~quiet(X))))&
(![X]:((~happy(X)&brave(X))<=>(funny(X)<~>~wise(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(~strong(mary)))&
((~rich(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|strong(X))<=>(strong(X)&~brave(X))))&
(?[X]:(strong(X)))&
((kind(fred)<~>funny(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((~generous(paul)<~>~funny(paul)))&
(?[X]:((tall(X)&~funny(X))))&
(?[X]:(~tall(X))) | ~happy(john) | [] | null | 0 |
If someone is either not rich or happy then someone is not humble or not patient and vice versa. Everyone who is both curious and happy is funny or tall and vice versa. If someone is quiet or not kind then paul is both strong and wise and vice versa. If someone is not happy or rich then lucy is wise or kind. If alice is not kind or quiet then someone is kind or curious. Everyone who is tall is not generous and vice versa. If paul is creative then someone is either not brave or funny and vice versa. If someone is curious or not quiet then paul is either not creative or funny. If someone is both not curious and quiet then someone is old. Everyone who is tall or not old is not humble or not quiet. Everyone who is either not kind or not strong is both quiet and not calm and vice versa. If someone is both calm and not funny then john is patient and vice versa. Everyone who is not strong or not happy is not generous and vice versa. Everyone who is either not tall or tall is quiet or not tall and vice versa. Everyone who is both not generous and not wise is either tall or brave. Everyone who is both quiet and generous is not funny or not strong and vice versa. Susan is either not old or not brave. Someone is either not patient or rich. Lucy is not rich or kind. Paul is either humble or not happy. Alice is both not brave and patient. Paul is either old or generous. Alice is patient or not calm. Someone is calm. | Lucy is wise. | neutral | ((?[X]:((~rich(X)<~>happy(X))))<=>(?[X]:((~humble(X)|~patient(X)))))&
(![X]:((curious(X)&happy(X))<=>(funny(X)|tall(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((strong(paul)&wise(paul))))&
((?[X]:((~happy(X)|rich(X))))=>((wise(lucy)|kind(lucy))))&
(((~kind(alice)|quiet(alice)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(tall(X)<=>~generous(X)))&
((creative(paul))<=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:((curious(X)|~quiet(X))))=>((~creative(paul)<~>funny(paul))))&
((?[X]:((~curious(X)&quiet(X))))=>(?[X]:(old(X))))&
(![X]:((tall(X)|~old(X))=>(~humble(X)|~quiet(X))))&
(![X]:((~kind(X)<~>~strong(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((calm(X)&~funny(X))))<=>(patient(john)))&
(![X]:((~strong(X)|~happy(X))<=>~generous(X)))&
(![X]:((~tall(X)<~>tall(X))<=>(quiet(X)|~tall(X))))&
(![X]:((~generous(X)&~wise(X))=>(tall(X)<~>brave(X))))&
(![X]:((quiet(X)&generous(X))<=>(~funny(X)|~strong(X))))&
((~old(susan)<~>~brave(susan)))&
(?[X]:((~patient(X)<~>rich(X))))&
((~rich(lucy)|kind(lucy)))&
((humble(paul)<~>~happy(paul)))&
((~brave(alice)&patient(alice)))&
((old(paul)<~>generous(paul)))&
((patient(alice)|~calm(alice)))&
(?[X]:(calm(X))) | wise(lucy) | [] | null | 0 |
If someone is either old or wise then lucy is old.
If fred is both not creative and not happy then susan is either not patient or curious and vice versa.
Everyone who is both not quiet and curious is either wise or kind and vice versa.
If someone is calm then alice is both creative and tall and vice versa.
Everyone who is both not patient and funny is either brave or funny.
Everyone who is either tall or not generous is not calm or not happy.
Everyone who is either not humble or strong is rich.
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Someone is humble or not happy.
John is either not humble or humble.
Paul is both not calm and not creative.
Mary is not calm or not funny. | Alice is patient. | entailment | ((?[X]:((old(X)<~>wise(X))))=>(old(lucy)))&
(((~creative(fred)&~happy(fred)))<=>((~patient(susan)<~>curious(susan))))&
(![X]:((~quiet(X)&curious(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(?[X]:((humble(X)|~happy(X))))&
((~humble(john)<~>humble(john)))&
((~calm(paul)&~creative(paul)))&
((~calm(mary)|~funny(mary))) | patient(alice) | [
"p7",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5511454041503015093341251
% SZS output start Proof for 5511454041503015093341251
8. ! [X0] : ((~patient(X0) | quiet(X0)) => creative(X0)) [input p7]
12. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p11]
13. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p13]
15. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p14]
21. ~patient(alice) [input hypothesis]
22. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 15]
29. ! [X0] : (creative(X0) | (patient(X0) & ~quiet(X0))) [ennf transformation 8]
31. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 12]
54. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 54]
56. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 14]
57. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 56]
58. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 22]
59. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 58]
60. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK3) | quiet(sK3)) [choice axiom]
61. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK4) & ~old(sK4)) [choice axiom]
62. ((~wise(sK3) | quiet(sK3)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK4) & ~old(sK4)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 59,61,60]
91. patient(X0) | creative(X0) [cnf transformation 29]
101. rich(X0) | creative(X0) [cnf transformation 31]
105. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 55]
106. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 55]
113. ~creative(X0) | quiet(X0) [cnf transformation 57]
115. ~old(sK4) | ~quiet(X3) [cnf transformation 62]
117. ~rich(sK4) | ~quiet(X3) [cnf transformation 62]
128. ~patient(alice) [cnf transformation 21]
129. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 105]
130. ~happy(X0) | old(X0) [duplicate literal removal 106]
167. 8 <=> creative(alice) [avatar definition]
168. creative(alice) <- (8) [avatar component clause 167]
220. 20 <=> patient(alice) [avatar definition]
222. ~patient(alice) <- (~20) [avatar component clause 220]
227. ~quiet(X0) | old(X0) [subsumption resolution 129,130]
244. 25 <=> rich(sK4) [avatar definition]
246. ~rich(sK4) <- (~25) [avatar component clause 244]
249. 26 <=> ! [X3] : ~quiet(X3) [avatar definition]
250. ~quiet(X3) <- (26) [avatar component clause 249]
251. 26 | ~25 [avatar split clause 117,244,249]
253. 27 <=> old(sK4) [avatar definition]
255. ~old(sK4) <- (~27) [avatar component clause 253]
257. 26 | ~27 [avatar split clause 115,253,249]
276. ~20 [avatar split clause 128,220]
282. creative(alice) <- (~20) [resolution 91,222]
283. creative(sK4) <- (~25) [resolution 101,246]
288. quiet(alice) <- (8) [resolution 113,168]
289. quiet(sK4) <- (~25) [resolution 113,283]
305. old(sK4) <- (~25) [resolution 289,227]
307. $false <- (~25, ~27) [subsumption resolution 305,255]
308. 25 | 27 [avatar contradiction clause 307]
314. $false <- (8, 26) [resolution 250,288]
315. ~8 | ~26 [avatar contradiction clause 314]
318. 8 | 20 [avatar split clause 282,220,167]
319. $false [avatar sat refutation 251,257,276,308,315,318]
% SZS output end Proof for 5511454041503015093341251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or not happy then paul is either not humble or kind and vice versa. If someone is both humble and old then fred is not rich or not creative. If someone is not creative then someone is either strong or not kind. If paul is quiet or not humble then fred is not happy and vice versa. If susan is rich or not brave then mary is rich. Everyone who is creative is either not brave or not curious and vice versa. Everyone who is not old or not happy is not calm or curious and vice versa. If someone is brave or not calm then mary is either not calm or not old. If someone is humble or brave then susan is old. If mary is old then john is not strong or not tall and vice versa. If someone is calm then someone is not rich or not curious and vice versa. Everyone who is creative is either not quiet or not brave and vice versa. Everyone who is not strong is both funny and patient and vice versa. If someone is not strong or strong then lucy is creative and vice versa. Everyone who is creative or curious is creative. Everyone who is strong is humble or not funny. Susan is either not wise or not strong. Alice is not rich. Alice is humble or curious. Someone is either not quiet or creative. Susan is either calm or not creative. Susan is not generous or not happy. Someone is both patient and not brave. Someone is funny. | Mary is strong. | neutral | (((tall(alice)<~>~happy(alice)))<=>((~humble(paul)<~>kind(paul))))&
((?[X]:((humble(X)&old(X))))=>((~rich(fred)|~creative(fred))))&
((?[X]:(~creative(X)))=>(?[X]:((strong(X)<~>~kind(X)))))&
(((quiet(paul)|~humble(paul)))<=>(~happy(fred)))&
(((rich(susan)|~brave(susan)))=>(rich(mary)))&
(![X]:(creative(X)<=>(~brave(X)<~>~curious(X))))&
(![X]:((~old(X)|~happy(X))<=>(~calm(X)|curious(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~calm(mary)<~>~old(mary))))&
((?[X]:((humble(X)|brave(X))))=>(old(susan)))&
((old(mary))<=>((~strong(john)|~tall(john))))&
((?[X]:(calm(X)))<=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:(creative(X)<=>(~quiet(X)<~>~brave(X))))&
(![X]:(~strong(X)<=>(funny(X)&patient(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(creative(lucy)))&
(![X]:((creative(X)|curious(X))=>creative(X)))&
(![X]:(strong(X)=>(humble(X)|~funny(X))))&
((~wise(susan)<~>~strong(susan)))&
(~rich(alice))&
((humble(alice)|curious(alice)))&
(?[X]:((~quiet(X)<~>creative(X))))&
((calm(susan)<~>~creative(susan)))&
((~generous(susan)|~happy(susan)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:(funny(X))) | strong(mary) | [] | null | 0 |
If susan is either not curious or funny then someone is either not rich or old. Everyone who is either kind or quiet is not rich or tall. Everyone who is not quiet is not kind. If john is quiet then someone is both funny and wise and vice versa. If alice is curious or not happy then someone is either calm or strong. Everyone who is quiet or not strong is either not rich or not calm. Everyone who is not creative is brave or funny. If susan is not old then john is either not rich or patient. Everyone who is both not patient and kind is not wise and vice versa. Everyone who is not funny is curious. If paul is curious then lucy is not tall. Everyone who is both not tall and funny is wise and vice versa. Everyone who is both not tall and happy is either not quiet or humble. Everyone who is not patient or strong is patient and vice versa. Everyone who is humble is not quiet and vice versa. Everyone who is not rich or brave is either not quiet or calm and vice versa. Someone is either not funny or generous. Someone is either not quiet or wise. Paul is old. Susan is creative or kind. Someone is humble or not tall. Susan is happy or curious. Someone is both brave and humble. | Alice is not creative. | neutral | (((~curious(susan)<~>funny(susan)))=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((kind(X)<~>quiet(X))=>(~rich(X)|tall(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
((quiet(john))<=>(?[X]:((funny(X)&wise(X)))))&
(((curious(alice)|~happy(alice)))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)<~>~calm(X))))&
(![X]:(~creative(X)=>(brave(X)|funny(X))))&
((~old(susan))=>((~rich(john)<~>patient(john))))&
(![X]:((~patient(X)&kind(X))<=>~wise(X)))&
(![X]:(~funny(X)=>curious(X)))&
((curious(paul))=>(~tall(lucy)))&
(![X]:((~tall(X)&funny(X))<=>wise(X)))&
(![X]:((~tall(X)&happy(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~patient(X)|strong(X))<=>patient(X)))&
(![X]:(humble(X)<=>~quiet(X)))&
(![X]:((~rich(X)|brave(X))<=>(~quiet(X)<~>calm(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(old(paul))&
((creative(susan)|kind(susan)))&
(?[X]:((humble(X)|~tall(X))))&
((happy(susan)|curious(susan)))&
(?[X]:((brave(X)&humble(X)))) | ~creative(alice) | [] | null | 0 |
If mary is patient or calm then mary is both generous and kind.
If someone is not curious or tall then fred is both not happy and not generous and vice versa.
Everyone who is both not patient and not happy is kind or patient and vice versa.
If someone is not quiet or not kind then fred is either not rich or funny and vice versa.
If lucy is either not kind or not funny then someone is not wise or funny.
Everyone who is not creative or not quiet is happy or kind and vice versa.
Everyone who is both curious and brave is both rich and humble.
If someone is either patient or tall then someone is both not kind and not calm and vice versa.
Everyone who is not rich or not funny is not funny or not tall.
Everyone who is wise or not kind is both not quiet and humble.
If mary is both not strong and kind then john is either funny or tall.
Everyone who is not happy is wise and vice versa.
If susan is not tall or not quiet then mary is funny or not funny.
If paul is either rich or not brave then john is happy or strong and vice versa.
If someone is either not generous or generous then mary is curious.
Everyone who is not patient or strong is creative or not tall.
Alice is both tall and not happy.
Someone is not happy.
Mary is either happy or calm.
Lucy is not happy.
Susan is humble.
Mary is not kind or rich. | Lucy is humble. | entailment | (((patient(mary)|calm(mary)))=>((generous(mary)&kind(mary))))&
((?[X]:((~curious(X)|tall(X))))<=>((~happy(fred)&~generous(fred))))&
(![X]:((~patient(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~quiet(X)|~kind(X))))<=>((~rich(fred)<~>funny(fred))))&
(((~kind(lucy)<~>~funny(lucy)))=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~creative(X)|~quiet(X))<=>(happy(X)|kind(X))))&
(![X]:((curious(X)&brave(X))=>(rich(X)&humble(X))))&
((?[X]:((patient(X)<~>tall(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(![X]:((~rich(X)|~funny(X))=>(~funny(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~quiet(X)&humble(X))))&
(((~strong(mary)&kind(mary)))=>((funny(john)<~>tall(john))))&
(![X]:(~happy(X)<=>wise(X)))&
(((~tall(susan)|~quiet(susan)))=>((funny(mary)|~funny(mary))))&
(((rich(paul)<~>~brave(paul)))<=>((happy(john)|strong(john))))&
((?[X]:((~generous(X)<~>generous(X))))=>(curious(mary)))&
(![X]:((~patient(X)|strong(X))=>(creative(X)|~tall(X))))&
((tall(alice)&~happy(alice)))&
(?[X]:(~happy(X)))&
((happy(mary)<~>calm(mary)))&
(~happy(lucy))&
(humble(susan))&
((~kind(mary)|rich(mary))) | humble(lucy) | [
"p9",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7866081726089785132895593
% SZS output start Proof for 7866081726089785132895593
10. ! [X0] : ((~kind(X0) | wise(X0)) => (humble(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : (~happy(X0) <=> wise(X0)) [input p11]
20. ~happy(lucy) [input p19]
23. ~humble(lucy) [input hypothesis]
31. ! [X0] : ((humble(X0) & ~quiet(X0)) | (kind(X0) & ~wise(X0))) [ennf transformation 10]
61. ! [X0] : ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))) [nnf transformation 12]
106. ~wise(X0) | humble(X0) [cnf transformation 31]
110. wise(X0) | happy(X0) [cnf transformation 61]
129. ~happy(lucy) [cnf transformation 20]
132. ~humble(lucy) [cnf transformation 23]
317. humble(X0) | happy(X0) [resolution 110,106]
344. happy(lucy) [resolution 317,132]
345. $false [subsumption resolution 344,129]
% SZS output end Proof for 7866081726089785132895593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both wise and quiet.
Everyone who is not strong or not quiet is not quiet.
Everyone who is both brave and not patient is either tall or not happy and vice versa.
Everyone who is both not tall and not rich is brave or not brave and vice versa.
Everyone who is either not kind or quiet is not calm.
If john is both quiet and old then someone is either not happy or patient and vice versa.
Everyone who is either not wise or old is both kind and happy.
If lucy is not funny or not rich then someone is not generous and vice versa.
Everyone who is patient or not rich is either tall or calm.
Everyone who is not funny or kind is both not old and creative and vice versa.
If paul is patient or creative then alice is not quiet.
If susan is either creative or not creative then someone is either not brave or not humble and vice versa.
If alice is either strong or calm then someone is not quiet.
If someone is both not funny and not rich then alice is strong and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
Everyone who is not humble is strong or generous.
Someone is either not humble or creative.
Paul is either patient or quiet.
Someone is either not strong or not brave.
Someone is humble or not generous.
Someone is either not strong or quiet.
Alice is not curious or kind.
Paul is not generous. | Paul is not happy. | contradiction | (![X]:(~wise(X)=>(wise(X)&quiet(X))))&
(![X]:((~strong(X)|~quiet(X))=>~quiet(X)))&
(![X]:((brave(X)&~patient(X))<=>(tall(X)<~>~happy(X))))&
(![X]:((~tall(X)&~rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~kind(X)<~>quiet(X))=>~calm(X)))&
(((quiet(john)&old(john)))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>old(X))=>(kind(X)&happy(X))))&
(((~funny(lucy)|~rich(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:((patient(X)|~rich(X))=>(tall(X)<~>calm(X))))&
(![X]:((~funny(X)|kind(X))<=>(~old(X)&creative(X))))&
(((patient(paul)|creative(paul)))=>(~quiet(alice)))&
(((creative(susan)<~>~creative(susan)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((strong(alice)<~>calm(alice)))=>(?[X]:(~quiet(X))))&
((?[X]:((~funny(X)&~rich(X))))<=>(strong(alice)))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(![X]:(~humble(X)=>(strong(X)|generous(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
((patient(paul)<~>quiet(paul)))&
(?[X]:((~strong(X)<~>~brave(X))))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~curious(alice)|kind(alice)))&
(~generous(paul)) | ~happy(paul) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 914721121114879527950832
% SZS output start Proof for 914721121114879527950832
1. ! [X0] : (~wise(X0) => (quiet(X0) & wise(X0))) [input p0]
3. ! [X0] : ((~patient(X0) & brave(X0)) <=> (tall(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (~brave(X0) | brave(X0))) [input p3]
6. (old(john) & quiet(john)) <=> ? [X0] : (~happy(X0) <~> patient(X0)) [input p5]
7. ! [X0] : ((~wise(X0) <~> old(X0)) => (happy(X0) & kind(X0))) [input p6]
10. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (creative(X0) & ~old(X0))) [input p9]
24. ~happy(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) & wise(X0)) | wise(X0)) [ennf transformation 1]
29. ! [X0] : ((happy(X0) & kind(X0)) | (~wise(X0) <=> old(X0))) [ennf transformation 7]
35. ! [X0] : (((~patient(X0) & brave(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (patient(X0) | ~brave(X0)))) [nnf transformation 3]
36. ! [X0] : (((~patient(X0) & brave(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | patient(X0) | ~brave(X0))) [flattening 35]
37. ! [X0] : (((~rich(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (rich(X0) | tall(X0)))) [nnf transformation 4]
38. ! [X0] : (((~rich(X0) & ~tall(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | rich(X0) | tall(X0))) [flattening 37]
40. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (~old(john) | ~quiet(john))) [nnf transformation 6]
41. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~old(john) | ~quiet(john)) [flattening 40]
42. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (? [X1] : ((~patient(X1) | happy(X1)) & (patient(X1) | ~happy(X1))) | ~old(john) | ~quiet(john)) [rectify 41]
43. ? [X1] : ((~patient(X1) | happy(X1)) & (patient(X1) | ~happy(X1))) => ((~patient(sK0) | happy(sK0)) & (patient(sK0) | ~happy(sK0))) [choice axiom]
44. ((old(john) & quiet(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (((~patient(sK0) | happy(sK0)) & (patient(sK0) | ~happy(sK0))) | ~old(john) | ~quiet(john)) [skolemisation 42,43]
45. ! [X0] : ((happy(X0) & kind(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) [nnf transformation 29]
52. ! [X0] : (((kind(X0) | ~funny(X0)) | (~creative(X0) | old(X0))) & ((creative(X0) & ~old(X0)) | (~kind(X0) & funny(X0)))) [nnf transformation 10]
53. ! [X0] : ((kind(X0) | ~funny(X0) | ~creative(X0) | old(X0)) & ((creative(X0) & ~old(X0)) | (~kind(X0) & funny(X0)))) [flattening 52]
78. wise(X0) | wise(X0) [cnf transformation 26]
87. ~patient(X0) | tall(X0) | happy(X0) [cnf transformation 36]
89. ~tall(X0) | ~brave(X0) [cnf transformation 38]
90. ~tall(X0) | brave(X0) [cnf transformation 38]
99. old(john) | patient(X0) | happy(X0) [cnf transformation 44]
102. kind(X0) | ~wise(X0) | ~old(X0) [cnf transformation 45]
113. ~old(X0) | ~kind(X0) [cnf transformation 53]
147. ~happy(paul) [cnf transformation 24]
152. wise(X0) [duplicate literal removal 78]
154. ~tall(X0) [subsumption resolution 89,90]
159. 2 <=> old(john) [avatar definition]
161. old(john) <- (2) [avatar component clause 159]
164. 3 <=> ! [X0] : (patient(X0) | happy(X0)) [avatar definition]
165. happy(X0) | patient(X0) <- (3) [avatar component clause 164]
166. 3 | 2 [avatar split clause 99,159,164]
184. ~old(X0) | kind(X0) [subsumption resolution 102,152]
189. ~old(X0) [subsumption resolution 113,184]
200. 9 <=> patient(paul) [avatar definition]
201. patient(paul) <- (9) [avatar component clause 200]
286. $false <- (2) [subsumption resolution 161,189]
287. ~2 [avatar contradiction clause 286]
293. patient(paul) <- (3) [resolution 165,147]
310. tall(paul) | happy(paul) <- (9) [resolution 87,201]
312. happy(paul) <- (9) [subsumption resolution 310,154]
313. $false <- (9) [subsumption resolution 312,147]
314. ~9 [avatar contradiction clause 313]
319. 9 | ~3 [avatar split clause 293,164,200]
320. $false [avatar sat refutation 166,287,314,319]
% SZS output end Proof for 914721121114879527950832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and generous is either wise or not funny. Everyone who is funny or quiet is not creative. If susan is not old then someone is brave or not brave and vice versa. If someone is patient or not old then lucy is not generous and vice versa. If someone is either wise or humble then mary is both not generous and not old and vice versa. Everyone who is both not generous and generous is both patient and not calm and vice versa. Everyone who is creative is old. If paul is curious then someone is generous. Everyone who is not old is curious or not kind and vice versa. If someone is curious or not generous then someone is both humble and rich and vice versa. If someone is both not tall and tall then someone is strong or funny. If someone is either wise or not quiet then susan is not old or not creative and vice versa. Everyone who is both not happy and not curious is both funny and not calm and vice versa. If someone is not funny then paul is not tall or not curious and vice versa. If someone is funny then paul is not kind or curious and vice versa. Everyone who is brave or not kind is either not wise or not quiet and vice versa. Paul is both curious and not calm. Lucy is either tall or not kind. Someone is both not rich and not kind. Susan is humble. Someone is both not rich and tall. Someone is either kind or not happy. Susan is both not generous and quiet. Someone is not funny. | Susan is kind. | neutral | (![X]:((~happy(X)&generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((funny(X)|quiet(X))=>~creative(X)))&
((~old(susan))<=>(?[X]:((brave(X)|~brave(X)))))&
((?[X]:((patient(X)|~old(X))))<=>(~generous(lucy)))&
((?[X]:((wise(X)<~>humble(X))))<=>((~generous(mary)&~old(mary))))&
(![X]:((~generous(X)&generous(X))<=>(patient(X)&~calm(X))))&
(![X]:(creative(X)=>old(X)))&
((curious(paul))=>(?[X]:(generous(X))))&
(![X]:(~old(X)<=>(curious(X)|~kind(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((strong(X)|funny(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~old(susan)|~creative(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((?[X]:(~funny(X)))<=>((~tall(paul)|~curious(paul))))&
((?[X]:(funny(X)))<=>((~kind(paul)|curious(paul))))&
(![X]:((brave(X)|~kind(X))<=>(~wise(X)<~>~quiet(X))))&
((curious(paul)&~calm(paul)))&
((tall(lucy)<~>~kind(lucy)))&
(?[X]:((~rich(X)&~kind(X))))&
(humble(susan))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((kind(X)<~>~happy(X))))&
((~generous(susan)&quiet(susan)))&
(?[X]:(~funny(X))) | kind(susan) | [] | null | 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. | Mary is generous. | 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)))) | generous(mary) | [] | null | 0 |
If mary is both not brave and kind then susan is rich or quiet.
Everyone who is either rich or not funny is either rich or creative.
Everyone who is strong is either not patient or calm and vice versa.
Everyone who is both kind and generous is both generous and not curious.
Everyone who is both quiet and funny is both not creative and not quiet.
Everyone who is either not curious or rich is curious and vice versa.
Everyone who is calm is both not strong and not curious and vice versa.
If lucy is brave then john is both not strong and not curious and vice versa.
Everyone who is creative or not tall is either not curious or not funny and vice versa.
Everyone who is both curious and not rich is wise.
If fred is old then someone is both strong and not humble and vice versa.
Everyone who is not generous is wise or humble and vice versa.
If someone is both calm and humble then someone is both not old and not brave.
If someone is old or quiet then someone is not rich.
Everyone who is both wise and not rich is both not brave and humble and vice versa.
Everyone who is both calm and not brave is either not patient or not strong and vice versa.
Lucy is both happy and not tall.
Someone is not curious.
Someone is either not brave or calm.
John is either wise or brave.
Someone is generous or not patient.
John is tall or patient.
Someone is not funny. | Mary is wise. | neutral | (((~brave(mary)&kind(mary)))=>((rich(susan)|quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(rich(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)&~curious(X))))&
(![X]:((quiet(X)&funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)<~>rich(X))<=>curious(X)))&
(![X]:(calm(X)<=>(~strong(X)&~curious(X))))&
((brave(lucy))<=>((~strong(john)&~curious(john))))&
(![X]:((creative(X)|~tall(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((curious(X)&~rich(X))=>wise(X)))&
((old(fred))<=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:(~generous(X)<=>(wise(X)|humble(X))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((calm(X)&~brave(X))<=>(~patient(X)<~>~strong(X))))&
((happy(lucy)&~tall(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((wise(john)<~>brave(john)))&
(?[X]:((generous(X)|~patient(X))))&
((tall(john)|patient(john)))&
(?[X]:(~funny(X))) | wise(mary) | [] | null | 0 |
Everyone who is humble is both wise and not quiet and vice versa. Everyone who is both not patient and funny is not tall and vice versa. Everyone who is both not strong and not tall is not curious. If john is either humble or rich then john is either rich or not tall. If someone is not brave then paul is not wise and vice versa. If paul is quiet then someone is patient. If alice is not generous then paul is generous or not happy and vice versa. Everyone who is both quiet and not rich is both not kind and not tall and vice versa. If someone is either not curious or curious then mary is funny or brave and vice versa. If someone is curious or not rich then fred is not quiet or not strong. Everyone who is either funny or curious is either curious or not rich and vice versa. Everyone who is not curious or not strong is not brave or not strong and vice versa. Everyone who is creative or calm is both not kind and not quiet and vice versa. If john is funny or not creative then john is both happy and curious and vice versa. If someone is either strong or tall then alice is both not quiet and not old. If lucy is not creative or rich then john is not tall or not kind and vice versa. Someone is generous. Lucy is old. Mary is both patient and not wise. Paul is curious. Alice is either not rich or not creative. Someone is strong. Someone is not brave. Someone is not quiet. | Alice is not old. | neutral | (![X]:(humble(X)<=>(wise(X)&~quiet(X))))&
(![X]:((~patient(X)&funny(X))<=>~tall(X)))&
(![X]:((~strong(X)&~tall(X))=>~curious(X)))&
(((humble(john)<~>rich(john)))=>((rich(john)<~>~tall(john))))&
((?[X]:(~brave(X)))<=>(~wise(paul)))&
((quiet(paul))=>(?[X]:(patient(X))))&
((~generous(alice))<=>((generous(paul)|~happy(paul))))&
(![X]:((quiet(X)&~rich(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((~curious(X)<~>curious(X))))<=>((funny(mary)|brave(mary))))&
((?[X]:((curious(X)|~rich(X))))=>((~quiet(fred)|~strong(fred))))&
(![X]:((funny(X)<~>curious(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~curious(X)|~strong(X))<=>(~brave(X)|~strong(X))))&
(![X]:((creative(X)|calm(X))<=>(~kind(X)&~quiet(X))))&
(((funny(john)|~creative(john)))<=>((happy(john)&curious(john))))&
((?[X]:((strong(X)<~>tall(X))))=>((~quiet(alice)&~old(alice))))&
(((~creative(lucy)|rich(lucy)))<=>((~tall(john)|~kind(john))))&
(?[X]:(generous(X)))&
(old(lucy))&
((patient(mary)&~wise(mary)))&
(curious(paul))&
((~rich(alice)<~>~creative(alice)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X))) | ~old(alice) | [] | null | 0 |
Everyone who is both generous and not curious is not patient or quiet and vice versa. If fred is quiet then someone is either not patient or generous and vice versa. Everyone who is not calm or calm is curious or not generous. Everyone who is both kind and not rich is both rich and calm. Everyone who is either tall or not funny is brave or quiet and vice versa. Everyone who is both not old and not curious is both wise and patient and vice versa. If someone is either funny or not kind then mary is happy or not old and vice versa. If someone is tall then mary is not funny and vice versa. Everyone who is both generous and brave is either happy or not old and vice versa. If someone is patient or kind then alice is not creative. If someone is either not funny or not happy then alice is brave. Everyone who is both not patient and curious is curious or quiet. If susan is either funny or tall then alice is both patient and not rich and vice versa. Everyone who is not humble is not humble or not tall. If lucy is either funny or not kind then someone is humble or not tall and vice versa. Everyone who is either not happy or not generous is both patient and strong and vice versa. Someone is strong. Alice is tall. Someone is rich. Someone is not kind or patient. Someone is not funny or brave. Someone is not calm. Someone is either not wise or quiet. | Fred is not kind. | neutral | (![X]:((generous(X)&~curious(X))<=>(~patient(X)|quiet(X))))&
((quiet(fred))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:((~calm(X)|calm(X))=>(curious(X)|~generous(X))))&
(![X]:((kind(X)&~rich(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)|quiet(X))))&
(![X]:((~old(X)&~curious(X))<=>(wise(X)&patient(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((happy(mary)|~old(mary))))&
((?[X]:(tall(X)))<=>(~funny(mary)))&
(![X]:((generous(X)&brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((patient(X)|kind(X))))=>(~creative(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(brave(alice)))&
(![X]:((~patient(X)&curious(X))=>(curious(X)|quiet(X))))&
(((funny(susan)<~>tall(susan)))<=>((patient(alice)&~rich(alice))))&
(![X]:(~humble(X)=>(~humble(X)|~tall(X))))&
(((funny(lucy)<~>~kind(lucy)))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)&strong(X))))&
(?[X]:(strong(X)))&
(tall(alice))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~wise(X)<~>quiet(X)))) | ~kind(fred) | [] | null | 0 |
Everyone who is either not calm or humble is brave and vice versa. If someone is either calm or kind then someone is not calm and vice versa. Everyone who is both creative and humble is either wise or not creative. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. Everyone who is both not wise and not rich is not kind or not creative and vice versa. If john is not strong then someone is either quiet or humble and vice versa. Everyone who is old or quiet is not wise. Everyone who is both kind and not curious is either not rich or not curious. If someone is quiet or not creative then someone is not calm. If john is both not brave and not creative then someone is not patient or old and vice versa. Fred is both not strong and not funny. Someone is patient or quiet. Susan is either tall or quiet. Mary is strong. Someone is not rich or not calm. Someone is both not rich and curious. Someone is both funny and wise. Someone is not quiet or not kind. | Susan is tall. | entailment | (![X]:((~calm(X)<~>humble(X))<=>brave(X)))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&humble(X))=>(wise(X)<~>~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
(![X]:((~wise(X)&~rich(X))<=>(~kind(X)|~creative(X))))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((old(X)|quiet(X))=>~wise(X)))&
(![X]:((kind(X)&~curious(X))=>(~rich(X)<~>~curious(X))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:(~calm(X))))&
(((~brave(john)&~creative(john)))<=>(?[X]:((~patient(X)|old(X)))))&
((~strong(fred)&~funny(fred)))&
(?[X]:((patient(X)|quiet(X))))&
((tall(susan)<~>quiet(susan)))&
(strong(mary))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((~rich(X)&curious(X))))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((~quiet(X)|~kind(X)))) | tall(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3208228302691304975778975
% SZS output start Proof for 3208228302691304975778975
1. ! [X0] : ((~calm(X0) <~> humble(X0)) <=> brave(X0)) [input p0]
3. ! [X0] : ((humble(X0) & creative(X0)) => (wise(X0) <~> ~creative(X0))) [input p2]
4. ! [X0] : ((brave(X0) & happy(X0)) <=> (quiet(X0) | ~tall(X0))) [input p3]
5. ! [X0] : (brave(X0) => (humble(X0) | calm(X0))) [input p4]
7. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> rich(X0)) [input p6]
11. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (~creative(X0) | ~kind(X0))) [input p10]
13. ! [X0] : ((quiet(X0) | old(X0)) => ~wise(X0)) [input p12]
19. tall(susan) <~> quiet(susan) [input p18]
25. ~tall(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> ~creative(X0)) | (~humble(X0) | ~creative(X0))) [ennf transformation 3]
30. ! [X0] : ((wise(X0) <~> ~creative(X0)) | ~humble(X0) | ~creative(X0)) [flattening 29]
31. ! [X0] : ((humble(X0) | calm(X0)) | ~brave(X0)) [ennf transformation 5]
32. ! [X0] : (humble(X0) | calm(X0) | ~brave(X0)) [flattening 31]
37. ! [X0] : (~wise(X0) | (~quiet(X0) & ~old(X0))) [ennf transformation 13]
41. ! [X0] : ((((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))))) [nnf transformation 1]
47. ! [X0] : (((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | ~humble(X0) | ~creative(X0)) [nnf transformation 30]
48. ! [X0] : (((brave(X0) & happy(X0)) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | (~brave(X0) | ~happy(X0)))) [nnf transformation 4]
49. ! [X0] : (((brave(X0) & happy(X0)) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ~brave(X0) | ~happy(X0))) [flattening 48]
51. ! [X0] : (((~tall(X0) | ~calm(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) & calm(X0)))) [nnf transformation 7]
52. ! [X0] : ((~tall(X0) | ~calm(X0) | ~rich(X0)) & (rich(X0) | (tall(X0) & calm(X0)))) [flattening 51]
62. ! [X0] : (((~rich(X0) & ~wise(X0)) | (creative(X0) & kind(X0))) & ((~creative(X0) | ~kind(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 11]
63. ! [X0] : (((~rich(X0) & ~wise(X0)) | (creative(X0) & kind(X0))) & (~creative(X0) | ~kind(X0) | rich(X0) | wise(X0))) [flattening 62]
79. (~quiet(susan) | ~tall(susan)) & (quiet(susan) | tall(susan)) [nnf transformation 19]
90. ~brave(X0) | ~calm(X0) | humble(X0) [cnf transformation 41]
91. ~brave(X0) | calm(X0) | ~humble(X0) [cnf transformation 41]
96. ~creative(X0) | wise(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 47]
101. tall(X0) | brave(X0) [cnf transformation 49]
103. humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 32]
107. rich(X0) | tall(X0) [cnf transformation 52]
122. ~rich(X0) | creative(X0) [cnf transformation 63]
128. ~quiet(X0) | ~wise(X0) [cnf transformation 37]
141. quiet(susan) | tall(susan) [cnf transformation 79]
150. ~tall(susan) [cnf transformation 25]
152. ~creative(X0) | wise(X0) | ~humble(X0) [duplicate literal removal 96]
178. ~brave(X0) | calm(X0) [subsumption resolution 103,91]
305. 36 <=> tall(susan) [avatar definition]
307. ~tall(susan) <- (~36) [avatar component clause 305]
309. 37 <=> quiet(susan) [avatar definition]
310. quiet(susan) <- (37) [avatar component clause 309]
313. 36 | 37 [avatar split clause 141,309,305]
332. ~36 [avatar split clause 150,305]
336. brave(susan) <- (~36) [resolution 101,307]
355. tall(X0) | creative(X0) [resolution 122,107]
357. ~wise(susan) <- (37) [resolution 128,310]
360. calm(susan) <- (~36) [resolution 178,336]
373. ~calm(susan) | humble(susan) <- (~36) [resolution 90,336]
416. humble(susan) <- (~36) [subsumption resolution 373,360]
488. creative(susan) <- (~36) [resolution 355,307]
506. wise(susan) | ~humble(susan) <- (~36) [resolution 488,152]
507. ~humble(susan) <- (~36, 37) [subsumption resolution 506,357]
508. $false <- (~36, 37) [subsumption resolution 507,416]
509. 36 | ~37 [avatar contradiction clause 508]
510. $false [avatar sat refutation 313,332,509]
% SZS output end Proof for 3208228302691304975778975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not happy is not strong or quiet. Everyone who is either generous or old is funny or old. Everyone who is either old or brave is either not calm or not creative and vice versa. Everyone who is not humble is not calm and vice versa. If someone is either calm or not old then someone is creative and vice versa. If susan is either generous or happy then someone is wise. Everyone who is calm is either not old or not brave and vice versa. If john is both not brave and not funny then paul is not generous or not old and vice versa. Everyone who is not generous or not rich is not brave or not quiet and vice versa. If susan is wise then someone is not funny or quiet. If lucy is both not generous and calm then alice is not rich or tall and vice versa. If someone is both not calm and happy then john is either not funny or patient. Everyone who is both wise and rich is happy or strong. Everyone who is either not funny or strong is not quiet. Everyone who is either creative or not strong is either patient or not humble and vice versa. Someone is not calm. Lucy is strong or patient. Alice is both curious and not old. Lucy is strong or calm. Someone is either quiet or humble. Someone is either generous or quiet. Mary is strong. Lucy is either not curious or rich. | Susan is not curious. | neutral | (![X]:((curious(X)|~happy(X))=>(~strong(X)|quiet(X))))&
(![X]:((generous(X)<~>old(X))=>(funny(X)|old(X))))&
(![X]:((old(X)<~>brave(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:(~humble(X)<=>~calm(X)))&
((?[X]:((calm(X)<~>~old(X))))<=>(?[X]:(creative(X))))&
(((generous(susan)<~>happy(susan)))=>(?[X]:(wise(X))))&
(![X]:(calm(X)<=>(~old(X)<~>~brave(X))))&
(((~brave(john)&~funny(john)))<=>((~generous(paul)|~old(paul))))&
(![X]:((~generous(X)|~rich(X))<=>(~brave(X)|~quiet(X))))&
((wise(susan))=>(?[X]:((~funny(X)|quiet(X)))))&
(((~generous(lucy)&calm(lucy)))<=>((~rich(alice)|tall(alice))))&
((?[X]:((~calm(X)&happy(X))))=>((~funny(john)<~>patient(john))))&
(![X]:((wise(X)&rich(X))=>(happy(X)|strong(X))))&
(![X]:((~funny(X)<~>strong(X))=>~quiet(X)))&
(![X]:((creative(X)<~>~strong(X))<=>(patient(X)<~>~humble(X))))&
(?[X]:(~calm(X)))&
((strong(lucy)|patient(lucy)))&
((curious(alice)&~old(alice)))&
((strong(lucy)|calm(lucy)))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:((generous(X)<~>quiet(X))))&
(strong(mary))&
((~curious(lucy)<~>rich(lucy))) | ~curious(susan) | [] | null | 0 |
Everyone who is not old is either old or not kind and vice versa.
Everyone who is both happy and not generous is either generous or not happy and vice versa.
If someone is either not funny or not creative then lucy is either curious or kind and vice versa.
If someone is both creative and calm then susan is either quiet or not wise.
Everyone who is old is either not quiet or kind.
If alice is either not curious or not brave then someone is either not humble or wise and vice versa.
Everyone who is either funny or not rich is not creative or brave and vice versa.
If someone is not funny then susan is both quiet and old and vice versa.
Everyone who is not patient or not happy is both patient and quiet.
Everyone who is either humble or not calm is not happy or curious and vice versa.
Everyone who is both generous and not calm is happy.
Everyone who is not old is not tall or tall.
If alice is not brave then someone is both old and not rich and vice versa.
If someone is not kind or not creative then someone is quiet or calm and vice versa.
If someone is both not funny and not humble then john is either not tall or tall.
If someone is either not tall or not strong then someone is kind or strong.
Susan is not wise or not humble.
Alice is tall.
Alice is not wise or not calm.
Someone is humble or not funny.
Someone is either generous or happy.
Someone is either funny or kind. | Susan is creative. | contradiction | (![X]:(~old(X)<=>(old(X)<~>~kind(X))))&
(![X]:((happy(X)&~generous(X))<=>(generous(X)<~>~happy(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((curious(lucy)<~>kind(lucy))))&
((?[X]:((creative(X)&calm(X))))=>((quiet(susan)<~>~wise(susan))))&
(![X]:(old(X)=>(~quiet(X)<~>kind(X))))&
(((~curious(alice)<~>~brave(alice)))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~rich(X))<=>(~creative(X)|brave(X))))&
((?[X]:(~funny(X)))<=>((quiet(susan)&old(susan))))&
(![X]:((~patient(X)|~happy(X))=>(patient(X)&quiet(X))))&
(![X]:((humble(X)<~>~calm(X))<=>(~happy(X)|curious(X))))&
(![X]:((generous(X)&~calm(X))=>happy(X)))&
(![X]:(~old(X)=>(~tall(X)|tall(X))))&
((~brave(alice))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
((?[X]:((~funny(X)&~humble(X))))=>((~tall(john)<~>tall(john))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((kind(X)|strong(X)))))&
((~wise(susan)|~humble(susan)))&
(tall(alice))&
((~wise(alice)|~calm(alice)))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((generous(X)<~>happy(X))))&
(?[X]:((funny(X)<~>kind(X)))) | creative(susan) | [
"p1",
"p3",
"p8",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7922062382634760846541816
% SZS output start Proof for 7922062382634760846541816
2. ! [X0] : ((~generous(X0) & happy(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p1]
4. ? [X0] : (calm(X0) & creative(X0)) => (quiet(susan) <~> ~wise(susan)) [input p3]
9. ! [X0] : ((~happy(X0) | ~patient(X0)) => (quiet(X0) & patient(X0))) [input p8]
10. ! [X0] : ((humble(X0) <~> ~calm(X0)) <=> (curious(X0) | ~happy(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & generous(X0)) => happy(X0)) [input p10]
17. ~humble(susan) | ~wise(susan) [input p16]
23. creative(susan) [input hypothesis]
26. ! [X0] : (~happy(X0) => quiet(X0)) [pure predicate removal 9]
27. (quiet(susan) <~> ~wise(susan)) | ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 4]
29. ! [X0] : (quiet(X0) | happy(X0)) [ennf transformation 26]
30. ! [X0] : (happy(X0) | (calm(X0) | ~generous(X0))) [ennf transformation 11]
31. ! [X0] : (happy(X0) | calm(X0) | ~generous(X0)) [flattening 30]
37. ! [X0] : (((~generous(X0) & happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (generous(X0) | ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((~generous(X0) & happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | generous(X0) | ~happy(X0))) [flattening 37]
43. ((wise(susan) | ~quiet(susan)) & (~wise(susan) | quiet(susan))) | ! [X0] : (~calm(X0) | ~creative(X0)) [nnf transformation 27]
56. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [nnf transformation 10]
57. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [flattening 56]
84. ~happy(X0) | generous(X0) | generous(X0) | ~happy(X0) [cnf transformation 38]
87. happy(X0) | generous(X0) | happy(X0) [cnf transformation 38]
88. ~generous(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 38]
99. wise(susan) | ~quiet(susan) | ~calm(X0) | ~creative(X0) [cnf transformation 43]
119. quiet(X0) | happy(X0) [cnf transformation 29]
122. ~calm(X0) | humble(X0) | happy(X0) [cnf transformation 57]
126. happy(X0) | calm(X0) | ~generous(X0) [cnf transformation 31]
139. ~humble(susan) | ~wise(susan) [cnf transformation 17]
147. creative(susan) [cnf transformation 23]
148. ~happy(X0) | generous(X0) [duplicate literal removal 84]
149. generous(X0) | happy(X0) [duplicate literal removal 87]
150. ~generous(X0) | ~happy(X0) [duplicate literal removal 88]
154. generous(X0) [subsumption resolution 148,149]
182. 6 <=> ! [X0] : (~calm(X0) | ~creative(X0)) [avatar definition]
183. ~calm(X0) | ~creative(X0) <- (6) [avatar component clause 182]
185. 7 <=> quiet(susan) [avatar definition]
187. ~quiet(susan) <- (~7) [avatar component clause 185]
189. 8 <=> wise(susan) [avatar definition]
192. 6 | ~7 | 8 [avatar split clause 99,189,185,182]
234. calm(X0) | happy(X0) [subsumption resolution 126,154]
278. 26 <=> humble(susan) [avatar definition]
280. ~humble(susan) <- (~26) [avatar component clause 278]
281. ~8 | ~26 [avatar split clause 139,278,189]
304. ~happy(X1) [resolution 150,154]
317. happy(X0) | ~creative(X0) <- (6) [resolution 234,183]
318. ~creative(X0) <- (6) [subsumption resolution 317,304]
319. $false <- (6) [resolution 318,147]
320. ~6 [avatar contradiction clause 319]
339. humble(X0) | happy(X0) | happy(X0) [resolution 122,234]
340. humble(X0) | happy(X0) [duplicate literal removal 339]
341. humble(X0) [subsumption resolution 340,304]
343. $false <- (~26) [resolution 341,280]
344. 26 [avatar contradiction clause 343]
346. happy(susan) <- (~7) [resolution 187,119]
347. $false <- (~7) [subsumption resolution 346,304]
348. 7 [avatar contradiction clause 347]
349. $false [avatar sat refutation 192,281,320,344,348]
% SZS output end Proof for 7922062382634760846541816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not funny then susan is both not generous and not funny and vice versa.
Everyone who is humble is either wise or humble and vice versa.
If someone is wise or not calm then fred is either not tall or not brave.
Everyone who is not curious or funny is not tall or not quiet.
Everyone who is either kind or patient is both not rich and kind and vice versa.
Everyone who is not funny is either strong or not wise and vice versa.
If someone is either curious or not patient then someone is brave and vice versa.
If lucy is old or funny then someone is patient and vice versa.
If alice is not brave then mary is creative.
If someone is funny or strong then someone is not quiet and vice versa.
Everyone who is not patient is not calm or kind and vice versa.
Everyone who is rich or curious is either patient or humble and vice versa.
If someone is not old or not happy then mary is either not rich or not brave.
Everyone who is both humble and not brave is tall and vice versa.
If someone is both not happy and not rich then someone is not curious or not strong.
Everyone who is either not wise or quiet is not tall and vice versa.
Someone is either wise or not generous.
Someone is rich.
Fred is either curious or not wise.
Someone is not strong.
Paul is both old and not quiet.
Someone is generous. | Fred is funny. | neutral | ((?[X]:((~humble(X)|~funny(X))))<=>((~generous(susan)&~funny(susan))))&
(![X]:(humble(X)<=>(wise(X)<~>humble(X))))&
((?[X]:((wise(X)|~calm(X))))=>((~tall(fred)<~>~brave(fred))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)|~quiet(X))))&
(![X]:((kind(X)<~>patient(X))<=>(~rich(X)&kind(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~wise(X))))&
((?[X]:((curious(X)<~>~patient(X))))<=>(?[X]:(brave(X))))&
(((old(lucy)|funny(lucy)))<=>(?[X]:(patient(X))))&
((~brave(alice))=>(creative(mary)))&
((?[X]:((funny(X)|strong(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(~patient(X)<=>(~calm(X)|kind(X))))&
(![X]:((rich(X)|curious(X))<=>(patient(X)<~>humble(X))))&
((?[X]:((~old(X)|~happy(X))))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((humble(X)&~brave(X))<=>tall(X)))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~tall(X)))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:(rich(X)))&
((curious(fred)<~>~wise(fred)))&
(?[X]:(~strong(X)))&
((old(paul)&~quiet(paul)))&
(?[X]:(generous(X))) | funny(fred) | [] | null | 0 |
Everyone who is not kind is either wise or not wise and vice versa.
If alice is both not humble and not happy then someone is funny and vice versa.
If john is kind then fred is both happy and not quiet and vice versa.
Everyone who is either quiet or tall is either not patient or not kind and vice versa.
If someone is either tall or quiet then someone is kind or generous and vice versa.
If paul is not brave then fred is either not creative or not generous.
If alice is both calm and not tall then someone is either not humble or old.
If someone is either brave or old then mary is not rich and vice versa.
Everyone who is happy is both not patient and happy.
If alice is both strong and generous then john is both not old and not wise.
Everyone who is kind or tall is strong or quiet and vice versa.
Everyone who is either strong or not quiet is patient.
Everyone who is either not calm or tall is either generous or brave and vice versa.
If mary is both patient and not rich then susan is either brave or not rich and vice versa.
Everyone who is either not funny or humble is creative and vice versa.
Everyone who is both funny and tall is humble or not brave and vice versa.
Paul is either curious or wise.
Someone is both generous and creative.
Fred is creative.
Someone is either quiet or old.
Mary is not funny or not strong.
Mary is either creative or old.
Someone is both wise and not kind.
Someone is not curious or not rich. | Fred is not creative. | contradiction | (![X]:(~kind(X)<=>(wise(X)<~>~wise(X))))&
(((~humble(alice)&~happy(alice)))<=>(?[X]:(funny(X))))&
((kind(john))<=>((happy(fred)&~quiet(fred))))&
(![X]:((quiet(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>(?[X]:((kind(X)|generous(X)))))&
((~brave(paul))=>((~creative(fred)<~>~generous(fred))))&
(((calm(alice)&~tall(alice)))=>(?[X]:((~humble(X)<~>old(X)))))&
((?[X]:((brave(X)<~>old(X))))<=>(~rich(mary)))&
(![X]:(happy(X)=>(~patient(X)&happy(X))))&
(((strong(alice)&generous(alice)))=>((~old(john)&~wise(john))))&
(![X]:((kind(X)|tall(X))<=>(strong(X)|quiet(X))))&
(![X]:((strong(X)<~>~quiet(X))=>patient(X)))&
(![X]:((~calm(X)<~>tall(X))<=>(generous(X)<~>brave(X))))&
(((patient(mary)&~rich(mary)))<=>((brave(susan)<~>~rich(susan))))&
(![X]:((~funny(X)<~>humble(X))<=>creative(X)))&
(![X]:((funny(X)&tall(X))<=>(humble(X)|~brave(X))))&
((curious(paul)<~>wise(paul)))&
(?[X]:((generous(X)&creative(X))))&
(creative(fred))&
(?[X]:((quiet(X)<~>old(X))))&
((~funny(mary)|~strong(mary)))&
((creative(mary)<~>old(mary)))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((~curious(X)|~rich(X)))) | ~creative(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 254327310353898436349642
% SZS output start Proof for 254327310353898436349642
19. creative(fred) [input p18]
25. ~creative(fred) [input hypothesis]
145. creative(fred) [cnf transformation 19]
154. ~creative(fred) [cnf transformation 25]
222. 14 <=> creative(fred) [avatar definition]
320. 14 [avatar split clause 145,222]
359. ~14 [avatar split clause 154,222]
360. $false [avatar sat refutation 320,359]
% SZS output end Proof for 254327310353898436349642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble is not wise or old and vice versa.
If someone is either rich or not patient then someone is rich or not creative and vice versa.
Everyone who is either not brave or calm is both not strong and not quiet and vice versa.
Everyone who is wise is generous or not brave and vice versa.
Everyone who is not happy is both brave and not funny.
Everyone who is kind is not humble.
Everyone who is not strong is tall and vice versa.
Everyone who is brave is either brave or not generous.
Everyone who is both not kind and not tall is tall or not old.
If paul is rich or happy then someone is not old and vice versa.
If alice is kind or creative then someone is either not funny or generous.
Everyone who is rich is kind.
Everyone who is not creative or generous is quiet and vice versa.
Everyone who is quiet is both wise and patient.
If lucy is both patient and old then someone is both not creative and brave.
If someone is either tall or not generous then someone is either tall or not rich and vice versa.
Fred is both tall and not generous.
Mary is not funny or brave.
Paul is brave.
Paul is both curious and rich.
Lucy is curious or calm.
John is either not brave or not happy.
Someone is both not strong and not happy. | Paul is not old. | contradiction | (![X]:(~humble(X)<=>(~wise(X)|old(X))))&
((?[X]:((rich(X)<~>~patient(X))))<=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:(wise(X)<=>(generous(X)|~brave(X))))&
(![X]:(~happy(X)=>(brave(X)&~funny(X))))&
(![X]:(kind(X)=>~humble(X)))&
(![X]:(~strong(X)<=>tall(X)))&
(![X]:(brave(X)=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)&~tall(X))=>(tall(X)|~old(X))))&
(((rich(paul)|happy(paul)))<=>(?[X]:(~old(X))))&
(((kind(alice)|creative(alice)))=>(?[X]:((~funny(X)<~>generous(X)))))&
(![X]:(rich(X)=>kind(X)))&
(![X]:((~creative(X)|generous(X))<=>quiet(X)))&
(![X]:(quiet(X)=>(wise(X)&patient(X))))&
(((patient(lucy)&old(lucy)))=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((tall(X)<~>~rich(X)))))&
((tall(fred)&~generous(fred)))&
((~funny(mary)|brave(mary)))&
(brave(paul))&
((curious(paul)&rich(paul)))&
((curious(lucy)|calm(lucy)))&
((~brave(john)<~>~happy(john)))&
(?[X]:((~strong(X)&~happy(X)))) | ~old(paul) | [
"p0",
"p3",
"p5",
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7837600935314206956664356
% SZS output start Proof for 7837600935314206956664356
1. ! [X0] : (~humble(X0) <=> (old(X0) | ~wise(X0))) [input p0]
4. ! [X0] : (wise(X0) <=> (~brave(X0) | generous(X0))) [input p3]
6. ! [X0] : (kind(X0) => ~humble(X0)) [input p5]
8. ! [X0] : (brave(X0) => (brave(X0) <~> ~generous(X0))) [input p7]
12. ! [X0] : (rich(X0) => kind(X0)) [input p11]
20. rich(paul) & curious(paul) [input p19]
24. ~old(paul) [input hypothesis]
27. ! [X0] : (~humble(X0) => (old(X0) | ~wise(X0))) [unused predicate definition removal 1]
29. rich(paul) [pure predicate removal 20]
30. ! [X0] : ((old(X0) | ~wise(X0)) | humble(X0)) [ennf transformation 27]
31. ! [X0] : (old(X0) | ~wise(X0) | humble(X0)) [flattening 30]
33. ! [X0] : (~humble(X0) | ~kind(X0)) [ennf transformation 6]
34. ! [X0] : ((brave(X0) <~> ~generous(X0)) | ~brave(X0)) [ennf transformation 8]
38. ! [X0] : (kind(X0) | ~rich(X0)) [ennf transformation 12]
49. ! [X0] : ((wise(X0) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | ~wise(X0))) [nnf transformation 4]
50. ! [X0] : ((wise(X0) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~wise(X0))) [flattening 49]
52. ! [X0] : (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | ~brave(X0)) [nnf transformation 34]
73. ~wise(X0) | old(X0) | humble(X0) [cnf transformation 31]
87. ~generous(X0) | wise(X0) [cnf transformation 50]
88. brave(X0) | wise(X0) [cnf transformation 50]
91. ~kind(X0) | ~humble(X0) [cnf transformation 33]
95. generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
104. ~rich(X0) | kind(X0) [cnf transformation 38]
124. rich(paul) [cnf transformation 29]
129. ~old(paul) [cnf transformation 24]
131. ~brave(X0) | generous(X0) [duplicate literal removal 95]
170. 10 <=> rich(paul) [avatar definition]
172. rich(paul) <- (10) [avatar component clause 170]
267. 10 [avatar split clause 124,170]
284. kind(paul) <- (10) [resolution 104,172]
285. ~humble(paul) <- (10) [resolution 284,91]
288. generous(X0) | wise(X0) [resolution 131,88]
292. wise(X0) [subsumption resolution 288,87]
322. old(X0) | humble(X0) [resolution 292,73]
444. humble(paul) [resolution 322,129]
447. $false <- (10) [subsumption resolution 444,285]
448. ~10 [avatar contradiction clause 447]
449. $false [avatar sat refutation 267,448]
% SZS output end Proof for 7837600935314206956664356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both funny and not quiet then someone is old or brave. If alice is not generous or humble then fred is not creative. Everyone who is old is generous or not calm and vice versa. Everyone who is not old or not humble is wise or not brave. Everyone who is not quiet is both funny and not quiet. Everyone who is both not strong and not quiet is not brave or not quiet and vice versa. Everyone who is curious or tall is curious. Everyone who is generous is either not strong or humble. If someone is humble then someone is either not strong or rich and vice versa. Everyone who is both tall and kind is not tall or patient. Everyone who is not quiet or not kind is both not brave and kind and vice versa. If someone is either not curious or happy then paul is happy or not strong and vice versa. Everyone who is both rich and old is not humble and vice versa. Everyone who is not humble or not happy is either kind or calm. If someone is either funny or happy then someone is not brave or not happy. Everyone who is not funny or generous is both rich and humble and vice versa. Someone is quiet or rich. Lucy is either not strong or not rich. Paul is happy or not funny. Lucy is both patient and not tall. Someone is either not rich or humble. Someone is creative. Mary is either not rich or wise. | Susan is not generous. | entailment | (((funny(susan)&~quiet(susan)))=>(?[X]:((old(X)|brave(X)))))&
(((~generous(alice)|humble(alice)))=>(~creative(fred)))&
(![X]:(old(X)<=>(generous(X)|~calm(X))))&
(![X]:((~old(X)|~humble(X))=>(wise(X)|~brave(X))))&
(![X]:(~quiet(X)=>(funny(X)&~quiet(X))))&
(![X]:((~strong(X)&~quiet(X))<=>(~brave(X)|~quiet(X))))&
(![X]:((curious(X)|tall(X))=>curious(X)))&
(![X]:(generous(X)=>(~strong(X)<~>humble(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((tall(X)&kind(X))=>(~tall(X)|patient(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(~brave(X)&kind(X))))&
((?[X]:((~curious(X)<~>happy(X))))<=>((happy(paul)|~strong(paul))))&
(![X]:((rich(X)&old(X))<=>~humble(X)))&
(![X]:((~humble(X)|~happy(X))=>(kind(X)<~>calm(X))))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~funny(X)|generous(X))<=>(rich(X)&humble(X))))&
(?[X]:((quiet(X)|rich(X))))&
((~strong(lucy)<~>~rich(lucy)))&
((happy(paul)|~funny(paul)))&
((patient(lucy)&~tall(lucy)))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(creative(X)))&
((~rich(mary)<~>wise(mary))) | ~generous(susan) | [
"p2",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8109033251854608320476752
% SZS output start Proof for 8109033251854608320476752
3. ! [X0] : (old(X0) <=> (~calm(X0) | generous(X0))) [input p2]
13. ! [X0] : ((old(X0) & rich(X0)) <=> ~humble(X0)) [input p12]
16. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (humble(X0) & rich(X0))) [input p15]
24. generous(susan) [input hypothesis]
43. ! [X0] : ((old(X0) | (calm(X0) & ~generous(X0))) & ((~calm(X0) | generous(X0)) | ~old(X0))) [nnf transformation 3]
44. ! [X0] : ((old(X0) | (calm(X0) & ~generous(X0))) & (~calm(X0) | generous(X0) | ~old(X0))) [flattening 43]
60. ! [X0] : (((old(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | (~old(X0) | ~rich(X0)))) [nnf transformation 13]
61. ! [X0] : (((old(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | ~old(X0) | ~rich(X0))) [flattening 60]
67. ! [X0] : (((generous(X0) | ~funny(X0)) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | (~generous(X0) & funny(X0)))) [nnf transformation 16]
68. ! [X0] : ((generous(X0) | ~funny(X0) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | (~generous(X0) & funny(X0)))) [flattening 67]
82. ~generous(X0) | old(X0) [cnf transformation 44]
111. ~rich(X0) | ~old(X0) | ~humble(X0) [cnf transformation 61]
121. ~generous(X0) | rich(X0) [cnf transformation 68]
123. ~generous(X0) | humble(X0) [cnf transformation 68]
134. generous(susan) [cnf transformation 24]
275. old(susan) [resolution 82,134]
289. rich(susan) [resolution 121,134]
290. humble(susan) [resolution 123,134]
358. ~old(susan) | ~humble(susan) [resolution 111,289]
363. ~humble(susan) [subsumption resolution 358,275]
364. $false [subsumption resolution 363,290]
% SZS output end Proof for 8109033251854608320476752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not tall then someone is either tall or brave.
If mary is not tall or humble then alice is not wise or not kind.
If someone is calm then lucy is not kind or not generous and vice versa.
If someone is both not tall and curious then fred is old or humble.
If someone is both tall and not humble then fred is not generous.
If paul is wise or generous then paul is both not old and not funny and vice versa.
Everyone who is either generous or wise is funny or not generous and vice versa.
Everyone who is not strong is either not old or not calm and vice versa.
Everyone who is either not patient or patient is generous.
Everyone who is not calm or not happy is creative or humble.
Everyone who is happy is either calm or not patient and vice versa.
Everyone who is either not generous or not old is funny or quiet.
If someone is not happy then mary is not quiet or not old and vice versa.
Everyone who is not curious is both not tall and not patient and vice versa.
Everyone who is both not happy and funny is not curious.
Everyone who is either not brave or not kind is either wise or funny.
Someone is not happy.
Someone is not funny or not generous.
John is old.
Someone is both not patient and not tall.
Alice is either patient or not humble. | Lucy is humble. | neutral | ((?[X]:((quiet(X)|~tall(X))))=>(?[X]:((tall(X)<~>brave(X)))))&
(((~tall(mary)|humble(mary)))=>((~wise(alice)|~kind(alice))))&
((?[X]:(calm(X)))<=>((~kind(lucy)|~generous(lucy))))&
((?[X]:((~tall(X)&curious(X))))=>((old(fred)|humble(fred))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(![X]:((generous(X)<~>wise(X))<=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>patient(X))=>generous(X)))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|humble(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((~generous(X)<~>~old(X))=>(funny(X)|quiet(X))))&
((?[X]:(~happy(X)))<=>((~quiet(mary)|~old(mary))))&
(![X]:(~curious(X)<=>(~tall(X)&~patient(X))))&
(![X]:((~happy(X)&funny(X))=>~curious(X)))&
(![X]:((~brave(X)<~>~kind(X))=>(wise(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)|~generous(X))))&
(old(john))&
(?[X]:((~patient(X)&~tall(X))))&
((patient(alice)<~>~humble(alice))) | humble(lucy) | [] | null | 0 |
Everyone who is both patient and not funny is not rich or rich and vice versa.
Everyone who is not creative or not quiet is either not calm or funny and vice versa.
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
Mary is generous.
Someone is kind or strong.
Lucy is not tall or not rich.
Mary is tall.
Fred is generous.
Alice is calm or strong. | Paul is kind. | contradiction | (![X]:((patient(X)&~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(~calm(X)<~>funny(X))))&
(![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
(generous(mary))&
(?[X]:((kind(X)|strong(X))))&
((~tall(lucy)|~rich(lucy)))&
(tall(mary))&
(generous(fred))&
((calm(alice)|strong(alice))) | kind(paul) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5463904374634304073960725
% SZS output start Proof for 5463904374634304073960725
1. ! [X0] : ((~funny(X0) & patient(X0)) <=> (rich(X0) | ~rich(X0))) [input p0]
4. ! [X0] : ((curious(X0) | ~curious(X0)) <=> generous(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p6]
9. ! [X0] : ((~old(X0) | happy(X0)) <=> (~kind(X0) | funny(X0))) [input p8]
21. kind(paul) [input hypothesis]
24. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 6]
29. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 1]
30. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | funny(X0) | ~patient(X0))) [flattening 29]
33. ! [X0] : (((curious(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 4]
34. ! [X0] : ((curious(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [flattening 33]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 7]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | funny(X0) | patient(X0))) [flattening 36]
42. ! [X0] : (((~old(X0) | happy(X0)) | (kind(X0) & ~funny(X0))) & ((~kind(X0) | funny(X0)) | (old(X0) & ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : ((~old(X0) | happy(X0) | (kind(X0) & ~funny(X0))) & (~kind(X0) | funny(X0) | (old(X0) & ~happy(X0)))) [flattening 42]
59. patient(X0) | rich(X0) [cnf transformation 30]
60. ~rich(X0) | patient(X0) [cnf transformation 30]
61. ~funny(X0) | rich(X0) [cnf transformation 30]
62. ~rich(X0) | ~funny(X0) [cnf transformation 30]
71. generous(X0) | curious(X0) [cnf transformation 34]
72. ~curious(X0) | generous(X0) [cnf transformation 34]
78. ~curious(X0) | happy(X0) [cnf transformation 24]
82. ~patient(X0) | ~generous(X0) | curious(X0) [cnf transformation 37]
88. ~kind(X0) | funny(X0) | ~happy(X0) [cnf transformation 43]
113. kind(paul) [cnf transformation 21]
114. ~funny(X0) [subsumption resolution 61,62]
115. patient(X0) [subsumption resolution 59,60]
119. generous(X0) [subsumption resolution 71,72]
120. ~generous(X0) | curious(X0) [subsumption resolution 82,115]
121. curious(X0) [subsumption resolution 120,119]
145. ~happy(X0) | ~kind(X0) [subsumption resolution 88,114]
196. happy(X0) [resolution 78,121]
203. ~kind(X0) [resolution 145,196]
206. $false [resolution 203,113]
% SZS output end Proof for 5463904374634304073960725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or not humble then someone is old or not tall and vice versa. If mary is both humble and not strong then fred is both brave and not generous and vice versa. Everyone who is not calm is happy or creative and vice versa. Everyone who is either quiet or creative is either humble or not strong. Everyone who is both not kind and not patient is calm and vice versa. If someone is either funny or not curious then someone is both not tall and not strong and vice versa. Everyone who is not brave or not humble is not generous or old and vice versa. If john is not rich then paul is not brave or not patient. Everyone who is not calm is both not old and not rich and vice versa. If susan is both wise and calm then someone is patient and vice versa. If someone is not strong or funny then fred is either not rich or old and vice versa. If susan is either not strong or not quiet then someone is funny or not curious and vice versa. If mary is both not quiet and quiet then someone is humble or wise. Everyone who is happy or not patient is not rich and vice versa. Everyone who is both not tall and tall is either tall or funny. Everyone who is both not happy and not old is either brave or old. Someone is either not kind or not old. Someone is not humble. Fred is either quiet or wise. John is old or not old. Lucy is either not patient or happy. Someone is creative. | Susan is rich. | contradiction | (((~rich(lucy)<~>~humble(lucy)))<=>(?[X]:((old(X)|~tall(X)))))&
(((humble(mary)&~strong(mary)))<=>((brave(fred)&~generous(fred))))&
(![X]:(~calm(X)<=>(happy(X)|creative(X))))&
(![X]:((quiet(X)<~>creative(X))=>(humble(X)<~>~strong(X))))&
(![X]:((~kind(X)&~patient(X))<=>calm(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(~generous(X)|old(X))))&
((~rich(john))=>((~brave(paul)|~patient(paul))))&
(![X]:(~calm(X)<=>(~old(X)&~rich(X))))&
(((wise(susan)&calm(susan)))<=>(?[X]:(patient(X))))&
((?[X]:((~strong(X)|funny(X))))<=>((~rich(fred)<~>old(fred))))&
(((~strong(susan)<~>~quiet(susan)))<=>(?[X]:((funny(X)|~curious(X)))))&
(((~quiet(mary)&quiet(mary)))=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((happy(X)|~patient(X))<=>~rich(X)))&
(![X]:((~tall(X)&tall(X))=>(tall(X)<~>funny(X))))&
(![X]:((~happy(X)&~old(X))=>(brave(X)<~>old(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:(~humble(X)))&
((quiet(fred)<~>wise(fred)))&
((old(john)|~old(john)))&
((~patient(lucy)<~>happy(lucy)))&
(?[X]:(creative(X))) | rich(susan) | [
"p4",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8889116426247220561966614
% SZS output start Proof for 8889116426247220561966614
5. ! [X0] : ((~patient(X0) & ~kind(X0)) <=> calm(X0)) [input p4]
9. ! [X0] : (~calm(X0) <=> (~rich(X0) & ~old(X0))) [input p8]
14. ! [X0] : ((~patient(X0) | happy(X0)) <=> ~rich(X0)) [input p13]
23. rich(susan) [input hypothesis]
43. ! [X0] : (((~patient(X0) & ~kind(X0)) | ~calm(X0)) & (calm(X0) | (patient(X0) | kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((~patient(X0) & ~kind(X0)) | ~calm(X0)) & (calm(X0) | patient(X0) | kind(X0))) [flattening 43]
52. ! [X0] : ((~calm(X0) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | calm(X0))) [nnf transformation 9]
53. ! [X0] : ((~calm(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | calm(X0))) [flattening 52]
69. ! [X0] : (((~patient(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (patient(X0) & ~happy(X0)))) [nnf transformation 14]
70. ! [X0] : ((~patient(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (patient(X0) & ~happy(X0)))) [flattening 69]
101. ~patient(X0) | ~calm(X0) [cnf transformation 44]
114. ~rich(X0) | calm(X0) [cnf transformation 53]
133. ~rich(X0) | patient(X0) [cnf transformation 70]
148. rich(susan) [cnf transformation 23]
248. 22 <=> calm(susan) [avatar definition]
250. calm(susan) <- (22) [avatar component clause 248]
351. calm(susan) [resolution 114,148]
353. 22 [avatar split clause 351,248]
354. patient(susan) [resolution 133,148]
374. ~calm(susan) [resolution 354,101]
375. $false <- (22) [subsumption resolution 374,250]
376. ~22 [avatar contradiction clause 375]
377. $false [avatar sat refutation 353,376]
% SZS output end Proof for 8889116426247220561966614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If paul is calm or not strong then alice is wise.
If someone is curious or old then paul is rich or not wise and vice versa.
If fred is not happy then lucy is not tall or not creative.
Everyone who is both not creative and kind is either not quiet or wise and vice versa.
If someone is both not curious and tall then someone is tall and vice versa.
Everyone who is not quiet is both not old and not curious.
If paul is quiet then someone is not funny or wise.
Everyone who is not old is not kind.
If paul is either calm or not rich then john is not humble or kind.
If lucy is not funny then someone is rich.
Everyone who is rich or not tall is both tall and old.
Everyone who is both happy and humble is not generous.
Everyone who is both generous and not creative is not old or not humble.
Everyone who is either generous or not generous is either not curious or funny and vice versa.
Everyone who is both not strong and humble is not humble and vice versa.
If someone is either tall or funny then someone is both kind and strong.
Susan is not happy.
Someone is not kind or wise.
Fred is not calm or curious.
Someone is not calm or not brave.
Alice is not wise or humble.
John is not calm or generous.
Susan is kind or not funny.
Fred is either not curious or not kind. | Fred is humble. | entailment | (((calm(paul)|~strong(paul)))=>(wise(alice)))&
((?[X]:((curious(X)|old(X))))<=>((rich(paul)|~wise(paul))))&
((~happy(fred))=>((~tall(lucy)|~creative(lucy))))&
(![X]:((~creative(X)&kind(X))<=>(~quiet(X)<~>wise(X))))&
((?[X]:((~curious(X)&tall(X))))<=>(?[X]:(tall(X))))&
(![X]:(~quiet(X)=>(~old(X)&~curious(X))))&
((quiet(paul))=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~old(X)=>~kind(X)))&
(((calm(paul)<~>~rich(paul)))=>((~humble(john)|kind(john))))&
((~funny(lucy))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>~generous(X)))&
(![X]:((generous(X)&~creative(X))=>(~old(X)|~humble(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~strong(X)&humble(X))<=>~humble(X)))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:((kind(X)&strong(X)))))&
(~happy(susan))&
(?[X]:((~kind(X)|wise(X))))&
((~calm(fred)|curious(fred)))&
(?[X]:((~calm(X)|~brave(X))))&
((~wise(alice)|humble(alice)))&
((~calm(john)|generous(john)))&
((kind(susan)|~funny(susan)))&
((~curious(fred)<~>~kind(fred))) | humble(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2995407066753604585847290
% SZS output start Proof for 2995407066753604585847290
15. ! [X0] : ((humble(X0) & ~strong(X0)) <=> ~humble(X0)) [input p14]
25. ~humble(fred) [input hypothesis]
62. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | (~humble(X0) | strong(X0)))) [nnf transformation 15]
63. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | ~humble(X0) | strong(X0))) [flattening 62]
110. humble(X0) | humble(X0) [cnf transformation 63]
123. ~humble(fred) [cnf transformation 25]
125. humble(X0) [duplicate literal removal 110]
291. $false [subsumption resolution 123,125]
% SZS output end Proof for 2995407066753604585847290
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not brave is strong and vice versa.
Everyone who is strong or not old is either wise or curious.
Everyone who is not tall or kind is old or not generous and vice versa.
If fred is both humble and not happy then lucy is not wise.
If someone is patient then alice is wise or not brave.
If someone is either tall or not brave then someone is both not quiet and not generous and vice versa.
If someone is creative or not strong then someone is rich.
If someone is not wise or quiet then someone is not brave or old and vice versa.
If someone is funny or tall then paul is not wise.
If someone is both kind and happy then mary is generous.
If someone is quiet then someone is not strong or not kind.
Everyone who is kind is both not brave and not curious and vice versa.
Everyone who is generous is calm or funny.
Everyone who is calm is not humble and vice versa.
If fred is both not old and creative then john is both humble and tall and vice versa.
If someone is not old or not curious then susan is both strong and not creative and vice versa.
John is either kind or rich.
Lucy is both happy and quiet.
Someone is both patient and calm.
Someone is both creative and happy.
Someone is creative or kind.
Susan is not wise.
Susan is both patient and creative. | Fred is quiet. | neutral | (![X]:((~kind(X)|~brave(X))<=>strong(X)))&
(![X]:((strong(X)|~old(X))=>(wise(X)<~>curious(X))))&
(![X]:((~tall(X)|kind(X))<=>(old(X)|~generous(X))))&
(((humble(fred)&~happy(fred)))=>(~wise(lucy)))&
((?[X]:(patient(X)))=>((wise(alice)|~brave(alice))))&
((?[X]:((tall(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((?[X]:((creative(X)|~strong(X))))=>(?[X]:(rich(X))))&
((?[X]:((~wise(X)|quiet(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:((funny(X)|tall(X))))=>(~wise(paul)))&
((?[X]:((kind(X)&happy(X))))=>(generous(mary)))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:(kind(X)<=>(~brave(X)&~curious(X))))&
(![X]:(generous(X)=>(calm(X)|funny(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(((~old(fred)&creative(fred)))<=>((humble(john)&tall(john))))&
((?[X]:((~old(X)|~curious(X))))<=>((strong(susan)&~creative(susan))))&
((kind(john)<~>rich(john)))&
((happy(lucy)&quiet(lucy)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((creative(X)|kind(X))))&
(~wise(susan))&
((patient(susan)&creative(susan))) | quiet(fred) | [] | null | 0 |
If someone is both happy and kind then someone is both quiet and strong and vice versa.
If someone is rich then someone is both quiet and not quiet.
Everyone who is either generous or not funny is either old or brave and vice versa.
Everyone who is not generous or quiet is not humble and vice versa.
Everyone who is rich is either not generous or not humble.
Everyone who is not calm or not strong is either not generous or not brave and vice versa.
Everyone who is both not generous and wise is both not creative and tall.
If fred is not strong or not calm then paul is either not quiet or tall.
If someone is generous or not tall then john is tall or not curious.
If lucy is both generous and not generous then someone is either not calm or funny and vice versa.
Everyone who is tall or not brave is either humble or rich and vice versa.
If someone is either not patient or not strong then mary is not rich or funny.
If paul is either not humble or not brave then paul is not happy and vice versa.
Everyone who is either patient or not brave is not calm or not quiet and vice versa.
If paul is either not humble or not quiet then paul is funny or happy.
Everyone who is calm is either not quiet or not creative and vice versa.
Someone is calm or not calm.
Paul is not creative.
Fred is either rich or not calm.
Someone is either not humble or kind.
Someone is not quiet.
Paul is both not curious and patient.
Someone is brave or old. | Mary is not rich. | entailment | ((?[X]:((happy(X)&kind(X))))<=>(?[X]:((quiet(X)&strong(X)))))&
((?[X]:(rich(X)))=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)<~>brave(X))))&
(![X]:((~generous(X)|quiet(X))<=>~humble(X)))&
(![X]:(rich(X)=>(~generous(X)<~>~humble(X))))&
(![X]:((~calm(X)|~strong(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:((~generous(X)&wise(X))=>(~creative(X)&tall(X))))&
(((~strong(fred)|~calm(fred)))=>((~quiet(paul)<~>tall(paul))))&
((?[X]:((generous(X)|~tall(X))))=>((tall(john)|~curious(john))))&
(((generous(lucy)&~generous(lucy)))<=>(?[X]:((~calm(X)<~>funny(X)))))&
(![X]:((tall(X)|~brave(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>((~rich(mary)|funny(mary))))&
(((~humble(paul)<~>~brave(paul)))<=>(~happy(paul)))&
(![X]:((patient(X)<~>~brave(X))<=>(~calm(X)|~quiet(X))))&
(((~humble(paul)<~>~quiet(paul)))=>((funny(paul)|happy(paul))))&
(![X]:(calm(X)<=>(~quiet(X)<~>~creative(X))))&
(?[X]:((calm(X)|~calm(X))))&
(~creative(paul))&
((rich(fred)<~>~calm(fred)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(~quiet(X)))&
((~curious(paul)&patient(paul)))&
(?[X]:((brave(X)|old(X)))) | ~rich(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4650473076572900395778637
% SZS output start Proof for 4650473076572900395778637
2. ? [X0] : rich(X0) => ? [X0] : (~quiet(X0) & quiet(X0)) [input p1]
24. rich(mary) [input hypothesis]
26. ? [X0] : rich(X0) => ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 2]
30. ? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : ~rich(X0) [ennf transformation 26]
42. ? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : ~rich(X1) [rectify 30]
43. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK2) & quiet(sK2)) [choice axiom]
44. (~quiet(sK2) & quiet(sK2)) | ! [X1] : ~rich(X1) [skolemisation 42,43]
79. quiet(sK2) | ~rich(X1) [cnf transformation 44]
80. ~quiet(sK2) | ~rich(X1) [cnf transformation 44]
143. rich(mary) [cnf transformation 24]
171. 7 <=> ! [X1] : ~rich(X1) [avatar definition]
172. ~rich(X1) <- (7) [avatar component clause 171]
174. 8 <=> quiet(sK2) [avatar definition]
177. 7 | ~8 [avatar split clause 80,174,171]
178. 7 | 8 [avatar split clause 79,174,171]
221. 17 <=> rich(mary) [avatar definition]
222. rich(mary) <- (17) [avatar component clause 221]
282. 17 [avatar split clause 143,221]
283. $false <- (7, 17) [resolution 222,172]
284. ~7 | ~17 [avatar contradiction clause 283]
285. $false [avatar sat refutation 177,178,282,284]
% SZS output end Proof for 4650473076572900395778637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not tall or not brave.
Everyone who is both happy and calm is rich and vice versa.
Everyone who is both not rich and old is patient.
If someone is either not tall or not kind then mary is both rich and creative and vice versa.
If alice is either not old or not curious then someone is both not tall and not strong and vice versa.
Everyone who is both strong and not humble is both not patient and strong and vice versa.
Everyone who is either not tall or not quiet is both tall and not wise.
If john is not kind then mary is both calm and wise.
Everyone who is not quiet is not quiet or not brave.
Everyone who is either not calm or not wise is curious or not humble.
If someone is both quiet and not curious then john is both not patient and funny.
If paul is either not happy or creative then alice is both funny and not patient and vice versa.
Everyone who is both strong and curious is both not funny and not quiet and vice versa.
If fred is creative or not strong then susan is not rich.
If john is not kind then someone is rich or not wise and vice versa.
If someone is not creative then fred is either humble or funny.
Susan is old.
Someone is tall.
Alice is either not generous or not creative.
Someone is either old or not old.
Someone is both patient and humble.
Someone is either curious or not brave.
Alice is either patient or wise.
Someone is not generous or patient. | Alice is not generous. | neutral | (![X]:(~rich(X)=>(~tall(X)<~>~brave(X))))&
(![X]:((happy(X)&calm(X))<=>rich(X)))&
(![X]:((~rich(X)&old(X))=>patient(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>((rich(mary)&creative(mary))))&
(((~old(alice)<~>~curious(alice)))<=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((strong(X)&~humble(X))<=>(~patient(X)&strong(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(tall(X)&~wise(X))))&
((~kind(john))=>((calm(mary)&wise(mary))))&
(![X]:(~quiet(X)=>(~quiet(X)|~brave(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(curious(X)|~humble(X))))&
((?[X]:((quiet(X)&~curious(X))))=>((~patient(john)&funny(john))))&
(((~happy(paul)<~>creative(paul)))<=>((funny(alice)&~patient(alice))))&
(![X]:((strong(X)&curious(X))<=>(~funny(X)&~quiet(X))))&
(((creative(fred)|~strong(fred)))=>(~rich(susan)))&
((~kind(john))<=>(?[X]:((rich(X)|~wise(X)))))&
((?[X]:(~creative(X)))=>((humble(fred)<~>funny(fred))))&
(old(susan))&
(?[X]:(tall(X)))&
((~generous(alice)<~>~creative(alice)))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:((curious(X)<~>~brave(X))))&
((patient(alice)<~>wise(alice)))&
(?[X]:((~generous(X)|patient(X)))) | ~generous(alice) | [] | null | 0 |
If someone is either happy or not patient then fred is humble and vice versa.
If someone is brave then someone is either not strong or not humble and vice versa.
If someone is either happy or not creative then fred is both generous and funny.
Everyone who is either calm or not calm is both quiet and generous.
Everyone who is humble is funny.
Everyone who is both rich and not curious is both funny and not patient.
Everyone who is both not patient and not calm is either tall or not patient.
If someone is humble or not old then mary is patient or not creative and vice versa.
Everyone who is not wise is either quiet or generous.
If fred is generous then mary is not curious and vice versa.
Everyone who is calm or patient is not generous.
If someone is both patient and kind then someone is both tall and not creative.
Everyone who is not generous or not curious is both not patient and rich.
Everyone who is either not strong or wise is both not brave and not old and vice versa.
Everyone who is both happy and brave is not kind and vice versa.
Someone is not quiet or not strong.
Someone is either patient or old.
Fred is either kind or not humble.
Someone is strong.
Mary is either quiet or humble.
Someone is both not humble and not rich. | Mary is funny. | entailment | ((?[X]:((happy(X)<~>~patient(X))))<=>(humble(fred)))&
((?[X]:(brave(X)))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
((?[X]:((happy(X)<~>~creative(X))))=>((generous(fred)&funny(fred))))&
(![X]:((calm(X)<~>~calm(X))=>(quiet(X)&generous(X))))&
(![X]:(humble(X)=>funny(X)))&
(![X]:((rich(X)&~curious(X))=>(funny(X)&~patient(X))))&
(![X]:((~patient(X)&~calm(X))=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|~old(X))))<=>((patient(mary)|~creative(mary))))&
(![X]:(~wise(X)=>(quiet(X)<~>generous(X))))&
((generous(fred))<=>(~curious(mary)))&
(![X]:((calm(X)|patient(X))=>~generous(X)))&
((?[X]:((patient(X)&kind(X))))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~generous(X)|~curious(X))=>(~patient(X)&rich(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(~brave(X)&~old(X))))&
(![X]:((happy(X)&brave(X))<=>~kind(X)))&
(?[X]:((~quiet(X)|~strong(X))))&
(?[X]:((patient(X)<~>old(X))))&
((kind(fred)<~>~humble(fred)))&
(?[X]:(strong(X)))&
((quiet(mary)<~>humble(mary)))&
(?[X]:((~humble(X)&~rich(X)))) | funny(mary) | [
"p3",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2076433255497518609969335
% SZS output start Proof for 2076433255497518609969335
4. ! [X0] : ((calm(X0) <~> ~calm(X0)) => (generous(X0) & quiet(X0))) [input p3]
6. ! [X0] : ((~curious(X0) & rich(X0)) => (~patient(X0) & funny(X0))) [input p5]
10. generous(fred) <=> ~curious(mary) [input p9]
13. ! [X0] : ((~curious(X0) | ~generous(X0)) => (rich(X0) & ~patient(X0))) [input p12]
22. ~funny(mary) [input hypothesis]
26. ! [X0] : ((generous(X0) & quiet(X0)) | (calm(X0) <=> ~calm(X0))) [ennf transformation 4]
28. ! [X0] : ((~patient(X0) & funny(X0)) | (curious(X0) | ~rich(X0))) [ennf transformation 6]
29. ! [X0] : ((~patient(X0) & funny(X0)) | curious(X0) | ~rich(X0)) [flattening 28]
35. ! [X0] : ((rich(X0) & ~patient(X0)) | (curious(X0) & generous(X0))) [ennf transformation 13]
46. ! [X0] : ((generous(X0) & quiet(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) [nnf transformation 26]
54. (generous(fred) | curious(mary)) & (~curious(mary) | ~generous(fred)) [nnf transformation 10]
87. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
88. generous(X0) | calm(X0) | calm(X0) [cnf transformation 46]
90. ~rich(X0) | curious(X0) | funny(X0) [cnf transformation 29]
100. ~curious(mary) | ~generous(fred) [cnf transformation 54]
109. curious(X0) | rich(X0) [cnf transformation 35]
129. ~funny(mary) [cnf transformation 22]
133. generous(X0) | ~calm(X0) [duplicate literal removal 87]
134. calm(X0) | generous(X0) [duplicate literal removal 88]
200. generous(X0) [subsumption resolution 133,134]
230. ~curious(mary) [subsumption resolution 100,200]
248. rich(mary) [resolution 109,230]
263. curious(mary) | funny(mary) [resolution 90,248]
264. funny(mary) [subsumption resolution 263,230]
265. $false [subsumption resolution 264,129]
% SZS output end Proof for 2076433255497518609969335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either old or not kind then someone is both not brave and not strong and vice versa.
Everyone who is kind or not kind is not curious or not humble.
If mary is either quiet or wise then someone is both not brave and tall and vice versa.
Everyone who is either quiet or tall is either old or not humble.
Everyone who is both not strong and kind is both funny and not curious and vice versa.
Everyone who is both patient and not funny is tall and vice versa.
If someone is creative then someone is either patient or calm.
If someone is both not funny and not curious then susan is happy.
If fred is not patient or quiet then john is not calm and vice versa.
Everyone who is either not old or generous is either not creative or not brave and vice versa.
Everyone who is not humble or wise is either humble or not strong.
If susan is both not humble and not old then someone is either curious or not quiet and vice versa.
Everyone who is not curious is strong or not creative and vice versa.
If someone is either creative or not funny then mary is not humble and vice versa.
Everyone who is both curious and not creative is not strong or not patient and vice versa.
If someone is not wise then someone is both creative and not calm.
Alice is strong or not wise.
Someone is both not funny and calm.
Fred is not patient or not old.
Lucy is either brave or patient.
Alice is not brave or not humble.
Susan is either not wise or curious.
Someone is not kind or brave. | John is calm. | contradiction | (((old(paul)<~>~kind(paul)))<=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:((kind(X)|~kind(X))=>(~curious(X)|~humble(X))))&
(((quiet(mary)<~>wise(mary)))<=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((quiet(X)<~>tall(X))=>(old(X)<~>~humble(X))))&
(![X]:((~strong(X)&kind(X))<=>(funny(X)&~curious(X))))&
(![X]:((patient(X)&~funny(X))<=>tall(X)))&
((?[X]:(creative(X)))=>(?[X]:((patient(X)<~>calm(X)))))&
((?[X]:((~funny(X)&~curious(X))))=>(happy(susan)))&
(((~patient(fred)|quiet(fred)))<=>(~calm(john)))&
(![X]:((~old(X)<~>generous(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:((~humble(X)|wise(X))=>(humble(X)<~>~strong(X))))&
(((~humble(susan)&~old(susan)))<=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:(~curious(X)<=>(strong(X)|~creative(X))))&
((?[X]:((creative(X)<~>~funny(X))))<=>(~humble(mary)))&
(![X]:((curious(X)&~creative(X))<=>(~strong(X)|~patient(X))))&
((?[X]:(~wise(X)))=>(?[X]:((creative(X)&~calm(X)))))&
((strong(alice)|~wise(alice)))&
(?[X]:((~funny(X)&calm(X))))&
((~patient(fred)|~old(fred)))&
((brave(lucy)<~>patient(lucy)))&
((~brave(alice)|~humble(alice)))&
((~wise(susan)<~>curious(susan)))&
(?[X]:((~kind(X)|brave(X)))) | calm(john) | [
"p1",
"p8",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 713796507221891249167521
% SZS output start Proof for 713796507221891249167521
2. ! [X0] : ((~kind(X0) | kind(X0)) => (~humble(X0) | ~curious(X0))) [input p1]
9. (quiet(fred) | ~patient(fred)) <=> ~calm(john) [input p8]
11. ! [X0] : ((wise(X0) | ~humble(X0)) => (humble(X0) <~> ~strong(X0))) [input p10]
12. (~old(susan) & ~humble(susan)) <=> ? [X0] : (curious(X0) <~> ~quiet(X0)) [input p11]
13. ! [X0] : (~curious(X0) <=> (~creative(X0) | strong(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & curious(X0)) <=> (~patient(X0) | ~strong(X0))) [input p14]
24. calm(john) [input hypothesis]
28. ! [X0] : ((~humble(X0) | ~curious(X0)) | (kind(X0) & ~kind(X0))) [ennf transformation 2]
29. ! [X0] : (~humble(X0) | ~curious(X0) | (kind(X0) & ~kind(X0))) [flattening 28]
32. ! [X0] : ((humble(X0) <~> ~strong(X0)) | (~wise(X0) & humble(X0))) [ennf transformation 11]
51. ((quiet(fred) | ~patient(fred)) | calm(john)) & (~calm(john) | (~quiet(fred) & patient(fred))) [nnf transformation 9]
52. (quiet(fred) | ~patient(fred) | calm(john)) & (~calm(john) | (~quiet(fred) & patient(fred))) [flattening 51]
54. ! [X0] : (((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (~wise(X0) & humble(X0))) [nnf transformation 32]
55. ((~old(susan) & ~humble(susan)) | ! [X0] : ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (? [X0] : ((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (old(susan) | humble(susan))) [nnf transformation 12]
56. ((~old(susan) & ~humble(susan)) | ! [X0] : ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (? [X0] : ((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | old(susan) | humble(susan)) [flattening 55]
57. ((~old(susan) & ~humble(susan)) | ! [X0] : ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (? [X1] : ((quiet(X1) | ~curious(X1)) & (~quiet(X1) | curious(X1))) | old(susan) | humble(susan)) [rectify 56]
58. ? [X1] : ((quiet(X1) | ~curious(X1)) & (~quiet(X1) | curious(X1))) => ((quiet(sK3) | ~curious(sK3)) & (~quiet(sK3) | curious(sK3))) [choice axiom]
59. ((~old(susan) & ~humble(susan)) | ! [X0] : ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(sK3) | ~curious(sK3)) & (~quiet(sK3) | curious(sK3))) | old(susan) | humble(susan)) [skolemisation 57,58]
60. ! [X0] : ((~curious(X0) | (creative(X0) & ~strong(X0))) & ((~creative(X0) | strong(X0)) | curious(X0))) [nnf transformation 13]
61. ! [X0] : ((~curious(X0) | (creative(X0) & ~strong(X0))) & (~creative(X0) | strong(X0) | curious(X0))) [flattening 60]
66. ! [X0] : (((~creative(X0) & curious(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (creative(X0) | ~curious(X0)))) [nnf transformation 15]
67. ! [X0] : (((~creative(X0) & curious(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | creative(X0) | ~curious(X0))) [flattening 66]
83. ~humble(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 29]
84. ~humble(X0) | ~curious(X0) | kind(X0) [cnf transformation 29]
105. ~calm(john) | ~quiet(fred) [cnf transformation 52]
115. ~strong(X0) | humble(X0) | humble(X0) [cnf transformation 54]
122. ~humble(susan) | curious(X0) | quiet(X0) [cnf transformation 59]
127. ~curious(X0) | creative(X0) [cnf transformation 61]
133. curious(X0) | strong(X0) [cnf transformation 67]
135. ~creative(X0) | strong(X0) [cnf transformation 67]
149. calm(john) [cnf transformation 24]
150. ~strong(X0) | humble(X0) [duplicate literal removal 115]
176. ~humble(X0) | ~curious(X0) [subsumption resolution 83,84]
216. 14 <=> calm(john) [avatar definition]
224. 16 <=> quiet(fred) [avatar definition]
225. ~quiet(fred) <- (~16) [avatar component clause 224]
228. ~16 | ~14 [avatar split clause 105,216,224]
231. 17 <=> ! [X0] : (curious(X0) | quiet(X0)) [avatar definition]
232. quiet(X0) | curious(X0) <- (17) [avatar component clause 231]
243. 20 <=> humble(susan) [avatar definition]
245. ~humble(susan) <- (~20) [avatar component clause 243]
246. 17 | ~20 [avatar split clause 122,243,231]
345. 14 [avatar split clause 149,216]
354. strong(X0) | creative(X0) [resolution 133,127]
356. strong(X0) [subsumption resolution 354,135]
368. humble(X0) [resolution 150,356]
373. ~curious(X0) [resolution 368,176]
375. curious(fred) <- (~16, 17) [resolution 232,225]
377. $false <- (~16, 17) [subsumption resolution 375,373]
378. 16 | ~17 [avatar contradiction clause 377]
383. $false <- (~20) [subsumption resolution 245,368]
384. 20 [avatar contradiction clause 383]
385. $false [avatar sat refutation 228,246,345,378,384]
% SZS output end Proof for 713796507221891249167521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Everyone who is not old or calm is not humble or not wise. If someone is both creative and not quiet then someone is either creative or wise and vice versa. Everyone who is either not calm or not curious is both not funny and calm. If someone is not funny then someone is kind and vice versa. Everyone who is wise or not creative is not strong and vice versa. Everyone who is calm or not funny is either calm or not strong and vice versa. If someone is either tall or not curious then alice is not old and vice versa. Everyone who is both tall and rich is either not creative or not rich and vice versa. Everyone who is calm is tall. Alice is either not strong or not tall. Alice is calm or not brave. John is either not brave or not creative. Someone is not strong. Someone is not patient. Alice is generous. | John is not strong. | entailment | ((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
(![X]:((~old(X)|calm(X))=>(~humble(X)|~wise(X))))&
((?[X]:((creative(X)&~quiet(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~calm(X)<~>~curious(X))=>(~funny(X)&calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((wise(X)|~creative(X))<=>~strong(X)))&
(![X]:((calm(X)|~funny(X))<=>(calm(X)<~>~strong(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(~old(alice)))&
(![X]:((tall(X)&rich(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:(calm(X)=>tall(X)))&
((~strong(alice)<~>~tall(alice)))&
((calm(alice)|~brave(alice)))&
((~brave(john)<~>~creative(john)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
(generous(alice)) | ~strong(john) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8368478849812837891488481
% SZS output start Proof for 8368478849812837891488481
5. ! [X0] : ((rich(X0) | calm(X0)) <=> (~rich(X0) | ~creative(X0))) [input p4]
11. ! [X0] : ((~creative(X0) | wise(X0)) <=> ~strong(X0)) [input p10]
14. ! [X0] : ((rich(X0) & tall(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p13]
22. strong(john) [input hypothesis]
46. ! [X0] : (((rich(X0) | calm(X0)) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((rich(X0) | calm(X0) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | (~rich(X0) & ~calm(X0)))) [flattening 46]
59. ! [X0] : (((~creative(X0) | wise(X0)) | strong(X0)) & (~strong(X0) | (creative(X0) & ~wise(X0)))) [nnf transformation 11]
60. ! [X0] : ((~creative(X0) | wise(X0) | strong(X0)) & (~strong(X0) | (creative(X0) & ~wise(X0)))) [flattening 59]
67. ! [X0] : (((rich(X0) & tall(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~rich(X0) | ~tall(X0)))) [nnf transformation 14]
68. ! [X0] : (((rich(X0) & tall(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~rich(X0) | ~tall(X0))) [flattening 67]
89. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 47]
106. ~strong(X0) | creative(X0) [cnf transformation 60]
123. rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 68]
131. strong(john) [cnf transformation 22]
133. rich(X0) | ~creative(X0) [duplicate literal removal 123]
138. ~rich(X0) | ~creative(X0) [duplicate literal removal 89]
258. ~creative(X0) [subsumption resolution 133,138]
286. creative(john) [resolution 106,131]
288. $false [subsumption resolution 286,258]
% SZS output end Proof for 8368478849812837891488481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not strong is not patient or not humble and vice versa.
Everyone who is patient is both not patient and kind.
Everyone who is funny is both strong and quiet.
Everyone who is not funny or not rich is both patient and not generous and vice versa.
Everyone who is calm or not curious is both not curious and not brave.
If mary is either generous or not kind then someone is both old and brave and vice versa.
If someone is not generous or kind then susan is not creative.
If lucy is calm then someone is tall and vice versa.
Everyone who is either not strong or happy is not rich or wise and vice versa.
If someone is quiet or kind then mary is not old or happy.
If mary is both kind and not curious then mary is rich or kind and vice versa.
If someone is not rich then john is either not kind or brave and vice versa.
If someone is both not creative and wise then someone is funny or old.
Everyone who is either not patient or not quiet is not old.
Everyone who is either not wise or not tall is not funny and vice versa.
Fred is either rich or curious.
Lucy is calm or not humble.
Someone is either curious or not funny.
Lucy is not happy or not quiet.
Susan is both funny and not tall. | Susan is happy. | contradiction | (![X]:((~happy(X)|~strong(X))<=>(~patient(X)|~humble(X))))&
(![X]:(patient(X)=>(~patient(X)&kind(X))))&
(![X]:(funny(X)=>(strong(X)&quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(patient(X)&~generous(X))))&
(![X]:((calm(X)|~curious(X))=>(~curious(X)&~brave(X))))&
(((generous(mary)<~>~kind(mary)))<=>(?[X]:((old(X)&brave(X)))))&
((?[X]:((~generous(X)|kind(X))))=>(~creative(susan)))&
((calm(lucy))<=>(?[X]:(tall(X))))&
(![X]:((~strong(X)<~>happy(X))<=>(~rich(X)|wise(X))))&
((?[X]:((quiet(X)|kind(X))))=>((~old(mary)|happy(mary))))&
(((kind(mary)&~curious(mary)))<=>((rich(mary)|kind(mary))))&
((?[X]:(~rich(X)))<=>((~kind(john)<~>brave(john))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((funny(X)|old(X)))))&
(![X]:((~patient(X)<~>~quiet(X))=>~old(X)))&
(![X]:((~wise(X)<~>~tall(X))<=>~funny(X)))&
((rich(fred)<~>curious(fred)))&
((calm(lucy)|~humble(lucy)))&
(?[X]:((curious(X)<~>~funny(X))))&
((~happy(lucy)|~quiet(lucy)))&
((funny(susan)&~tall(susan))) | happy(susan) | [
"p0",
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3198261075057142940793759
% SZS output start Proof for 3198261075057142940793759
1. ! [X0] : ((~strong(X0) | ~happy(X0)) <=> (~humble(X0) | ~patient(X0))) [input p0]
2. ! [X0] : (patient(X0) => (kind(X0) & ~patient(X0))) [input p1]
3. ! [X0] : (funny(X0) => (quiet(X0) & strong(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~generous(X0) & patient(X0))) [input p3]
21. happy(susan) [input hypothesis]
23. ! [X0] : ((kind(X0) & ~patient(X0)) | ~patient(X0)) [ennf transformation 2]
24. ! [X0] : ((quiet(X0) & strong(X0)) | ~funny(X0)) [ennf transformation 3]
31. ! [X0] : (((~strong(X0) | ~happy(X0)) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | (strong(X0) & happy(X0)))) [nnf transformation 1]
32. ! [X0] : ((~strong(X0) | ~happy(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | (strong(X0) & happy(X0)))) [flattening 31]
33. ! [X0] : (((~rich(X0) | ~funny(X0)) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 4]
34. ! [X0] : ((~rich(X0) | ~funny(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | (rich(X0) & funny(X0)))) [flattening 33]
62. ~strong(X0) | ~happy(X0) | patient(X0) [cnf transformation 32]
64. ~patient(X0) | ~patient(X0) [cnf transformation 23]
66. ~funny(X0) | strong(X0) [cnf transformation 24]
68. patient(X0) | funny(X0) [cnf transformation 34]
119. happy(susan) [cnf transformation 21]
120. ~patient(X0) [duplicate literal removal 64]
122. funny(X0) [subsumption resolution 68,120]
228. strong(X0) [resolution 66,122]
242. ~happy(X0) | patient(X0) [resolution 62,228]
243. ~happy(X0) [subsumption resolution 242,120]
244. $false [resolution 243,119]
% SZS output end Proof for 3198261075057142940793759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or curious then paul is either not curious or not generous.
Everyone who is not rich or not quiet is either not brave or not funny.
Everyone who is both not kind and not generous is both generous and curious and vice versa.
Everyone who is not curious is not old or not patient.
If someone is calm or not kind then mary is either not humble or wise.
If mary is patient or not happy then fred is not happy and vice versa.
If someone is not brave or not humble then alice is not funny and vice versa.
If susan is brave then alice is not kind or strong.
Everyone who is humble is either not generous or kind and vice versa.
If someone is both old and not creative then someone is not rich or funny.
Everyone who is not curious or strong is not kind.
Everyone who is both wise and not happy is both not funny and not tall and vice versa.
Everyone who is kind or strong is either quiet or not patient and vice versa.
Everyone who is both brave and funny is creative.
If fred is both wise and not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Someone is either not strong or not funny.
Lucy is humble or rich.
Someone is tall.
Mary is patient or tall.
Mary is quiet.
Alice is kind.
Paul is patient or curious.
Lucy is both not strong and not curious. | Paul is not patient. | contradiction | ((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((~rich(X)|~quiet(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)&~generous(X))<=>(generous(X)&curious(X))))&
(![X]:(~curious(X)=>(~old(X)|~patient(X))))&
((?[X]:((calm(X)|~kind(X))))=>((~humble(mary)<~>wise(mary))))&
(((patient(mary)|~happy(mary)))<=>(~happy(fred)))&
((?[X]:((~brave(X)|~humble(X))))<=>(~funny(alice)))&
((brave(susan))=>((~kind(alice)|strong(alice))))&
(![X]:(humble(X)<=>(~generous(X)<~>kind(X))))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~curious(X)|strong(X))=>~kind(X)))&
(![X]:((wise(X)&~happy(X))<=>(~funny(X)&~tall(X))))&
(![X]:((kind(X)|strong(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)&funny(X))=>creative(X)))&
(((wise(fred)&~old(fred)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(?[X]:((~strong(X)<~>~funny(X))))&
((humble(lucy)|rich(lucy)))&
(?[X]:(tall(X)))&
((patient(mary)|tall(mary)))&
(quiet(mary))&
(kind(alice))&
((patient(paul)|curious(paul)))&
((~strong(lucy)&~curious(lucy))) | ~patient(paul) | [
"p0",
"p2",
"p8",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8634243718176757634448354
% SZS output start Proof for 8634243718176757634448354
1. ? [X0] : (curious(X0) | brave(X0)) => (~curious(paul) <~> ~generous(paul)) [input p0]
3. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (curious(X0) & generous(X0))) [input p2]
9. ! [X0] : (humble(X0) <=> (~generous(X0) <~> kind(X0))) [input p8]
13. ! [X0] : ((strong(X0) | kind(X0)) <=> (quiet(X0) <~> ~patient(X0))) [input p12]
16. ! [X0] : (~humble(X0) <=> quiet(X0)) [input p15]
23. curious(paul) | patient(paul) [input p22]
25. ~patient(paul) [input hypothesis]
32. (~curious(paul) <~> ~generous(paul)) | ! [X0] : (~curious(X0) & ~brave(X0)) [ennf transformation 1]
40. ((generous(paul) | curious(paul)) & (~generous(paul) | ~curious(paul))) | ! [X0] : (~curious(X0) & ~brave(X0)) [nnf transformation 32]
42. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 3]
43. ! [X0] : (((~generous(X0) & ~kind(X0)) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | generous(X0) | kind(X0))) [flattening 42]
51. ! [X0] : ((humble(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | ~humble(X0))) [nnf transformation 9]
54. ! [X0] : (((strong(X0) | kind(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [nnf transformation 13]
55. ! [X0] : ((strong(X0) | kind(X0) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [flattening 54]
58. ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))) [nnf transformation 16]
65. ~generous(paul) | ~curious(paul) | ~curious(X0) [cnf transformation 40]
70. generous(X0) | generous(X0) | kind(X0) [cnf transformation 43]
85. ~kind(X0) | generous(X0) | ~humble(X0) [cnf transformation 51]
96. ~kind(X0) | ~quiet(X0) | patient(X0) [cnf transformation 55]
105. humble(X0) | quiet(X0) [cnf transformation 58]
113. curious(paul) | patient(paul) [cnf transformation 23]
116. ~patient(paul) [cnf transformation 25]
117. kind(X0) | generous(X0) [duplicate literal removal 70]
120. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
121. ~curious(X0) <- (1) [avatar component clause 120]
123. 2 <=> curious(paul) [avatar definition]
125. curious(paul) <- (2) [avatar component clause 123]
127. 3 <=> generous(paul) [avatar definition]
135. 1 | ~2 | ~3 [avatar split clause 65,127,123,120]
199. ~humble(X0) | generous(X0) [subsumption resolution 85,117]
235. 25 <=> patient(paul) [avatar definition]
236. ~patient(paul) <- (~25) [avatar component clause 235]
238. 25 | 2 [avatar split clause 113,123,235]
239. ~25 [avatar split clause 116,235]
248. quiet(X0) | generous(X0) [resolution 199,105]
378. ~quiet(X1) | patient(X1) | generous(X1) [resolution 96,117]
380. patient(X1) | generous(X1) [subsumption resolution 378,248]
417. generous(paul) <- (~25) [resolution 380,236]
424. 3 | 25 [avatar split clause 417,235,127]
425. $false <- (1, 2) [resolution 121,125]
428. ~1 | ~2 [avatar contradiction clause 425]
429. $false [avatar sat refutation 135,238,239,424,428]
% SZS output end Proof for 8634243718176757634448354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both not humble and not kind and vice versa.
Everyone who is either not happy or not tall is patient and vice versa.
Everyone who is not quiet or not happy is either not humble or happy.
Everyone who is not patient is both kind and not calm.
Everyone who is not generous or not wise is either not wise or not old and vice versa.
If someone is either rich or not quiet then someone is either not patient or brave and vice versa.
Everyone who is either rich or not wise is either funny or patient and vice versa.
If someone is not calm or not quiet then fred is both not humble and not rich.
Everyone who is either old or generous is both tall and rich.
Everyone who is both humble and not tall is not tall or generous and vice versa.
If someone is either not quiet or not humble then susan is not calm.
Everyone who is brave or curious is not happy.
Everyone who is either strong or old is both rich and wise and vice versa.
If someone is not brave then fred is funny or not wise.
If paul is either quiet or wise then alice is either calm or not funny and vice versa.
Everyone who is calm or not rich is brave or strong.
Paul is both curious and not old.
Someone is not old or not curious.
Someone is either strong or calm.
Paul is not happy.
Paul is either generous or funny.
Someone is both not old and kind.
Paul is not quiet. | Alice is tall. | entailment | (![X]:(~curious(X)<=>(~humble(X)&~kind(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>patient(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~humble(X)<~>happy(X))))&
(![X]:(~patient(X)=>(kind(X)&~calm(X))))&
(![X]:((~generous(X)|~wise(X))<=>(~wise(X)<~>~old(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(funny(X)<~>patient(X))))&
((?[X]:((~calm(X)|~quiet(X))))=>((~humble(fred)&~rich(fred))))&
(![X]:((old(X)<~>generous(X))=>(tall(X)&rich(X))))&
(![X]:((humble(X)&~tall(X))<=>(~tall(X)|generous(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(~calm(susan)))&
(![X]:((brave(X)|curious(X))=>~happy(X)))&
(![X]:((strong(X)<~>old(X))<=>(rich(X)&wise(X))))&
((?[X]:(~brave(X)))=>((funny(fred)|~wise(fred))))&
(((quiet(paul)<~>wise(paul)))<=>((calm(alice)<~>~funny(alice))))&
(![X]:((calm(X)|~rich(X))=>(brave(X)|strong(X))))&
((curious(paul)&~old(paul)))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((strong(X)<~>calm(X))))&
(~happy(paul))&
((generous(paul)<~>funny(paul)))&
(?[X]:((~old(X)&kind(X))))&
(~quiet(paul)) | tall(alice) | [
"p0",
"p2",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8036696487667892205502152
% SZS output start Proof for 8036696487667892205502152
1. ! [X0] : (~curious(X0) <=> (~kind(X0) & ~humble(X0))) [input p0]
3. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~humble(X0) <~> happy(X0))) [input p2]
10. ! [X0] : ((~tall(X0) & humble(X0)) <=> (generous(X0) | ~tall(X0))) [input p9]
12. ! [X0] : ((curious(X0) | brave(X0)) => ~happy(X0)) [input p11]
24. ~tall(alice) [input hypothesis]
26. ! [X0] : ((~humble(X0) <~> happy(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 3]
31. ! [X0] : (~happy(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 12]
36. ! [X0] : ((~curious(X0) | (kind(X0) | humble(X0))) & ((~kind(X0) & ~humble(X0)) | curious(X0))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | kind(X0) | humble(X0)) & ((~kind(X0) & ~humble(X0)) | curious(X0))) [flattening 36]
39. ! [X0] : (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | (happy(X0) & quiet(X0))) [nnf transformation 26]
49. ! [X0] : (((~tall(X0) & humble(X0)) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | (tall(X0) | ~humble(X0)))) [nnf transformation 10]
50. ! [X0] : (((~tall(X0) & humble(X0)) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | tall(X0) | ~humble(X0))) [flattening 49]
63. ~humble(X0) | curious(X0) [cnf transformation 37]
71. happy(X0) | ~humble(X0) | happy(X0) [cnf transformation 39]
107. tall(X0) | humble(X0) [cnf transformation 50]
114. ~happy(X0) | ~curious(X0) [cnf transformation 31]
143. ~tall(alice) [cnf transformation 24]
146. ~humble(X0) | happy(X0) [duplicate literal removal 71]
284. humble(alice) [resolution 107,143]
285. curious(alice) [resolution 284,63]
296. happy(alice) [resolution 146,284]
300. ~curious(alice) [resolution 296,114]
301. $false [subsumption resolution 300,285]
% SZS output end Proof for 8036696487667892205502152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or kind is both not tall and not brave and vice versa.
If someone is either patient or happy then lucy is not happy and vice versa.
Everyone who is patient is either creative or funny.
Everyone who is either calm or not calm is either wise or not brave and vice versa.
If someone is both happy and patient then paul is old.
If susan is tall then john is wise or not rich and vice versa.
If alice is happy or strong then someone is not old or patient.
If lucy is brave or not generous then someone is wise or creative and vice versa.
Everyone who is either happy or creative is generous or tall and vice versa.
If alice is either not tall or not strong then someone is either kind or not generous and vice versa.
Everyone who is quiet or calm is either happy or not calm and vice versa.
Everyone who is both not strong and funny is both rich and not quiet.
Everyone who is both not happy and brave is either funny or not wise and vice versa.
If someone is both not strong and kind then mary is not strong and vice versa.
If lucy is not rich then someone is not humble and vice versa.
Everyone who is kind or strong is both strong and not brave and vice versa.
Someone is strong.
Fred is either kind or funny.
Someone is not kind.
Someone is both not tall and not funny.
Paul is either not generous or not funny.
Someone is both tall and not funny.
Someone is not tall. | Lucy is strong. | entailment | (![X]:((curious(X)<~>kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(~happy(lucy)))&
(![X]:(patient(X)=>(creative(X)<~>funny(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(wise(X)<~>~brave(X))))&
((?[X]:((happy(X)&patient(X))))=>(old(paul)))&
((tall(susan))<=>((wise(john)|~rich(john))))&
(((happy(alice)|strong(alice)))=>(?[X]:((~old(X)|patient(X)))))&
(((brave(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((happy(X)<~>creative(X))<=>(generous(X)|tall(X))))&
(((~tall(alice)<~>~strong(alice)))<=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((quiet(X)|calm(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~strong(X)&funny(X))=>(rich(X)&~quiet(X))))&
(![X]:((~happy(X)&brave(X))<=>(funny(X)<~>~wise(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(~strong(mary)))&
((~rich(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|strong(X))<=>(strong(X)&~brave(X))))&
(?[X]:(strong(X)))&
((kind(fred)<~>funny(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((~generous(paul)<~>~funny(paul)))&
(?[X]:((tall(X)&~funny(X))))&
(?[X]:(~tall(X))) | strong(lucy) | [
"p1",
"p2",
"p3",
"p8",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 474361144024213456723744
% SZS output start Proof for 474361144024213456723744
2. ? [X0] : (patient(X0) <~> happy(X0)) <=> ~happy(lucy) [input p1]
3. ! [X0] : (patient(X0) => (creative(X0) <~> funny(X0))) [input p2]
4. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p3]
9. ! [X0] : ((happy(X0) <~> creative(X0)) <=> (tall(X0) | generous(X0))) [input p8]
11. ! [X0] : ((calm(X0) | quiet(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p10]
12. ! [X0] : ((funny(X0) & ~strong(X0)) => (~quiet(X0) & rich(X0))) [input p11]
13. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (funny(X0) <~> ~wise(X0))) [input p12]
22. ? [X0] : (~funny(X0) & tall(X0)) [input p21]
24. ~strong(lucy) [input hypothesis]
25. ! [X0] : ((creative(X0) <~> funny(X0)) | ~patient(X0)) [ennf transformation 3]
28. ! [X0] : ((~quiet(X0) & rich(X0)) | (~funny(X0) | strong(X0))) [ennf transformation 12]
29. ! [X0] : ((~quiet(X0) & rich(X0)) | ~funny(X0) | strong(X0)) [flattening 28]
32. (? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | happy(lucy)) & (~happy(lucy) | ! [X0] : ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) [nnf transformation 2]
33. (? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | happy(lucy)) & (~happy(lucy) | ! [X1] : ((patient(X1) | ~happy(X1)) & (happy(X1) | ~patient(X1)))) [rectify 32]
34. ? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) => ((~happy(sK0) | ~patient(sK0)) & (happy(sK0) | patient(sK0))) [choice axiom]
35. (((~happy(sK0) | ~patient(sK0)) & (happy(sK0) | patient(sK0))) | happy(lucy)) & (~happy(lucy) | ! [X1] : ((patient(X1) | ~happy(X1)) & (happy(X1) | ~patient(X1)))) [skolemisation 33,34]
36. ! [X0] : (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~patient(X0)) [nnf transformation 25]
37. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0))))) [flattening 47]
53. ! [X0] : (((calm(X0) | quiet(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (~calm(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((calm(X0) | quiet(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (~calm(X0) & ~quiet(X0)))) [flattening 53]
55. ! [X0] : (((brave(X0) & ~happy(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 13]
56. ! [X0] : (((brave(X0) & ~happy(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~brave(X0) | happy(X0))) [flattening 55]
75. ? [X0] : (~funny(X0) & tall(X0)) => (~funny(sK9) & tall(sK9)) [choice axiom]
76. ~funny(sK9) & tall(sK9) [skolemisation 22,75]
86. ~happy(lucy) | patient(X1) | ~happy(X1) [cnf transformation 35]
89. ~patient(X0) | creative(X0) | funny(X0) [cnf transformation 36]
91. ~brave(X0) | wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
92. ~brave(X0) | wise(X0) | calm(X0) | calm(X0) [cnf transformation 37]
93. brave(X0) | ~wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
94. brave(X0) | ~wise(X0) | calm(X0) | calm(X0) [cnf transformation 37]
114. ~creative(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 48]
124. ~calm(X0) | happy(X0) | ~calm(X0) [cnf transformation 54]
128. calm(X0) | quiet(X0) | happy(X0) | calm(X0) [cnf transformation 54]
130. ~quiet(X0) | ~funny(X0) | strong(X0) [cnf transformation 29]
131. ~wise(X0) | funny(X0) | ~brave(X0) | happy(X0) [cnf transformation 56]
136. brave(X0) | funny(X0) | wise(X0) [cnf transformation 56]
155. tall(sK9) [cnf transformation 76]
156. ~funny(sK9) [cnf transformation 76]
158. ~strong(lucy) [cnf transformation 24]
159. ~calm(X0) | happy(X0) [duplicate literal removal 124]
160. quiet(X0) | calm(X0) | happy(X0) [duplicate literal removal 128]
161. ~brave(X0) | wise(X0) | ~calm(X0) [duplicate literal removal 91]
162. ~brave(X0) | wise(X0) | calm(X0) [duplicate literal removal 92]
163. brave(X0) | ~wise(X0) | ~calm(X0) [duplicate literal removal 93]
164. ~wise(X0) | brave(X0) | calm(X0) [duplicate literal removal 94]
166. 1 <=> happy(lucy) [avatar definition]
180. 4 <=> ! [X1] : (patient(X1) | ~happy(X1)) [avatar definition]
181. ~happy(X1) | patient(X1) <- (4) [avatar component clause 180]
182. 4 | ~1 [avatar split clause 86,166,180]
187. ~wise(X0) | brave(X0) [subsumption resolution 163,164]
188. ~brave(X0) | wise(X0) [subsumption resolution 161,162]
282. wise(X0) | funny(X0) [subsumption resolution 136,188]
283. ~wise(X0) | funny(X0) | happy(X0) [subsumption resolution 131,187]
284. funny(X0) | happy(X0) [subsumption resolution 283,282]
345. happy(sK9) [resolution 284,156]
423. calm(X0) | happy(X0) | ~funny(X0) | strong(X0) [resolution 160,130]
426. happy(X0) | ~funny(X0) | strong(X0) [subsumption resolution 423,159]
427. strong(X0) | happy(X0) [subsumption resolution 426,284]
629. happy(lucy) [resolution 427,158]
635. 1 [avatar split clause 629,166]
660. patient(sK9) <- (4) [resolution 181,345]
872. creative(sK9) | funny(sK9) <- (4) [resolution 660,89]
873. creative(sK9) <- (4) [subsumption resolution 872,156]
956. ~happy(sK9) | ~tall(sK9) <- (4) [resolution 873,114]
957. ~tall(sK9) <- (4) [subsumption resolution 956,345]
958. $false <- (4) [subsumption resolution 957,155]
959. ~4 [avatar contradiction clause 958]
960. $false [avatar sat refutation 182,635,959]
% SZS output end Proof for 474361144024213456723744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either funny or not generous.
If someone is either calm or strong then mary is not kind or wise and vice versa.
If paul is wise then paul is either not creative or brave.
Everyone who is either not old or kind is not generous and vice versa.
If alice is rich then someone is old.
If someone is kind or not patient then mary is not happy or not curious and vice versa.
If someone is calm or not curious then mary is either happy or not tall and vice versa.
Everyone who is both not creative and brave is either strong or not patient.
Everyone who is strong or creative is both not generous and not wise and vice versa.
Everyone who is humble or not wise is happy or not creative and vice versa.
Everyone who is not generous or old is wise or not old and vice versa.
If someone is not strong or not brave then paul is either quiet or not generous and vice versa.
Everyone who is calm is quiet or calm and vice versa.
If susan is brave then someone is either not patient or rich.
Everyone who is patient or generous is either quiet or not kind and vice versa.
Everyone who is curious or brave is old or patient.
Susan is wise or not kind.
Someone is patient or wise.
Someone is creative or not strong.
Alice is either not curious or brave.
Alice is not curious or humble.
Someone is either quiet or rich.
Someone is both not patient and curious. | Paul is not rich. | neutral | (![X]:(old(X)=>(funny(X)<~>~generous(X))))&
((?[X]:((calm(X)<~>strong(X))))<=>((~kind(mary)|wise(mary))))&
((wise(paul))=>((~creative(paul)<~>brave(paul))))&
(![X]:((~old(X)<~>kind(X))<=>~generous(X)))&
((rich(alice))=>(?[X]:(old(X))))&
((?[X]:((kind(X)|~patient(X))))<=>((~happy(mary)|~curious(mary))))&
((?[X]:((calm(X)|~curious(X))))<=>((happy(mary)<~>~tall(mary))))&
(![X]:((~creative(X)&brave(X))=>(strong(X)<~>~patient(X))))&
(![X]:((strong(X)|creative(X))<=>(~generous(X)&~wise(X))))&
(![X]:((humble(X)|~wise(X))<=>(happy(X)|~creative(X))))&
(![X]:((~generous(X)|old(X))<=>(wise(X)|~old(X))))&
((?[X]:((~strong(X)|~brave(X))))<=>((quiet(paul)<~>~generous(paul))))&
(![X]:(calm(X)<=>(quiet(X)|calm(X))))&
((brave(susan))=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:((patient(X)|generous(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:((curious(X)|brave(X))=>(old(X)|patient(X))))&
((wise(susan)|~kind(susan)))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:((creative(X)|~strong(X))))&
((~curious(alice)<~>brave(alice)))&
((~curious(alice)|humble(alice)))&
(?[X]:((quiet(X)<~>rich(X))))&
(?[X]:((~patient(X)&curious(X)))) | ~rich(paul) | [] | null | 0 |
If someone is both quiet and not tall then someone is either tall or funny. Everyone who is old or humble is generous. Everyone who is either strong or kind is not patient and vice versa. If john is either funny or wise then mary is either not tall or not happy and vice versa. Everyone who is both not funny and tall is not tall and vice versa. If someone is not kind then someone is both not strong and curious. Everyone who is both not humble and curious is not curious or brave and vice versa. Everyone who is both not tall and creative is both happy and not strong. Everyone who is rich or not wise is not curious and vice versa. If susan is both creative and wise then mary is either not curious or happy and vice versa. If someone is both humble and not funny then someone is either not brave or quiet. If fred is either happy or not generous then someone is both quiet and not wise. If susan is funny or generous then paul is not happy or not wise. If someone is both patient and not wise then john is either not patient or not brave and vice versa. Everyone who is either rich or quiet is either strong or old and vice versa. Someone is not brave or curious. Mary is not generous. Someone is creative or not kind. Fred is quiet or not calm. Fred is either creative or calm. Someone is both not quiet and not patient. Mary is funny. | Fred is tall. | entailment | ((?[X]:((quiet(X)&~tall(X))))=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:((old(X)|humble(X))=>generous(X)))&
(![X]:((strong(X)<~>kind(X))<=>~patient(X)))&
(((funny(john)<~>wise(john)))<=>((~tall(mary)<~>~happy(mary))))&
(![X]:((~funny(X)&tall(X))<=>~tall(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:((~humble(X)&curious(X))<=>(~curious(X)|brave(X))))&
(![X]:((~tall(X)&creative(X))=>(happy(X)&~strong(X))))&
(![X]:((rich(X)|~wise(X))<=>~curious(X)))&
(((creative(susan)&wise(susan)))<=>((~curious(mary)<~>happy(mary))))&
((?[X]:((humble(X)&~funny(X))))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((happy(fred)<~>~generous(fred)))=>(?[X]:((quiet(X)&~wise(X)))))&
(((funny(susan)|generous(susan)))=>((~happy(paul)|~wise(paul))))&
((?[X]:((patient(X)&~wise(X))))<=>((~patient(john)<~>~brave(john))))&
(![X]:((rich(X)<~>quiet(X))<=>(strong(X)<~>old(X))))&
(?[X]:((~brave(X)|curious(X))))&
(~generous(mary))&
(?[X]:((creative(X)|~kind(X))))&
((quiet(fred)|~calm(fred)))&
((creative(fred)<~>calm(fred)))&
(?[X]:((~quiet(X)&~patient(X))))&
(funny(mary)) | tall(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7007675339423440220444851
% SZS output start Proof for 7007675339423440220444851
5. ! [X0] : ((tall(X0) & ~funny(X0)) <=> ~tall(X0)) [input p4]
23. ~tall(fred) [input hypothesis]
42. ! [X0] : (((tall(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~tall(X0) | funny(X0)))) [nnf transformation 5]
43. ! [X0] : (((tall(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~tall(X0) | funny(X0))) [flattening 42]
90. tall(X0) | tall(X0) [cnf transformation 43]
140. ~tall(fred) [cnf transformation 23]
144. tall(X0) [duplicate literal removal 90]
285. $false [subsumption resolution 140,144]
% SZS output end Proof for 7007675339423440220444851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not patient is not old and vice versa.
If someone is humble then someone is both humble and not humble.
Everyone who is either patient or not old is either not rich or not kind and vice versa.
Everyone who is both patient and not strong is old and vice versa.
Everyone who is old or not tall is either not calm or quiet and vice versa.
Everyone who is rich is tall or curious and vice versa.
If fred is either not wise or not strong then someone is either not funny or strong.
If someone is happy then susan is not quiet and vice versa.
Everyone who is funny or humble is either not calm or not rich and vice versa.
If john is rich then someone is both not rich and not strong.
If someone is not rich or not patient then someone is both not kind and not old.
Everyone who is quiet or not happy is either strong or quiet and vice versa.
If john is happy or creative then someone is quiet and vice versa.
Everyone who is both not quiet and patient is either brave or not humble.
If someone is kind then someone is not happy.
John is both not happy and old.
Mary is either funny or not old.
John is either not kind or not generous.
John is not humble or not patient.
Fred is both wise and not happy.
Alice is both not wise and curious. | Alice is not humble. | entailment | (![X]:((brave(X)<~>~patient(X))<=>~old(X)))&
((?[X]:(humble(X)))=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((patient(X)<~>~old(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:((patient(X)&~strong(X))<=>old(X)))&
(![X]:((old(X)|~tall(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|curious(X))))&
(((~wise(fred)<~>~strong(fred)))=>(?[X]:((~funny(X)<~>strong(X)))))&
((?[X]:(happy(X)))<=>(~quiet(susan)))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)<~>~rich(X))))&
((rich(john))=>(?[X]:((~rich(X)&~strong(X)))))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)<~>quiet(X))))&
(((happy(john)|creative(john)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&patient(X))=>(brave(X)<~>~humble(X))))&
((?[X]:(kind(X)))=>(?[X]:(~happy(X))))&
((~happy(john)&old(john)))&
((funny(mary)<~>~old(mary)))&
((~kind(john)<~>~generous(john)))&
((~humble(john)|~patient(john)))&
((wise(fred)&~happy(fred)))&
((~wise(alice)&curious(alice))) | ~humble(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 9078332254002253034908936
% SZS output start Proof for 9078332254002253034908936
2. ? [X0] : humble(X0) => ? [X0] : (~humble(X0) & humble(X0)) [input p1]
22. humble(alice) [input hypothesis]
23. ? [X0] : humble(X0) => ? [X1] : (~humble(X1) & humble(X1)) [rectify 2]
26. ? [X1] : (~humble(X1) & humble(X1)) | ! [X0] : ~humble(X0) [ennf transformation 23]
34. ? [X0] : (~humble(X0) & humble(X0)) | ! [X1] : ~humble(X1) [rectify 26]
35. ? [X0] : (~humble(X0) & humble(X0)) => (~humble(sK0) & humble(sK0)) [choice axiom]
36. (~humble(sK0) & humble(sK0)) | ! [X1] : ~humble(X1) [skolemisation 34,35]
75. humble(sK0) | ~humble(X1) [cnf transformation 36]
76. ~humble(sK0) | ~humble(X1) [cnf transformation 36]
138. humble(alice) [cnf transformation 22]
142. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
143. ~humble(X1) <- (1) [avatar component clause 142]
145. 2 <=> humble(sK0) [avatar definition]
148. 1 | ~2 [avatar split clause 76,145,142]
149. 1 | 2 [avatar split clause 75,145,142]
272. $false <- (1) [resolution 143,138]
273. ~1 [avatar contradiction clause 272]
274. $false [avatar sat refutation 148,149,273]
% SZS output end Proof for 9078332254002253034908936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both curious and rich then john is not happy or not humble and vice versa. Everyone who is both not funny and not brave is creative or not tall and vice versa. If fred is both not happy and not tall then someone is either kind or happy and vice versa. If john is both tall and rich then someone is both not humble and funny and vice versa. Everyone who is both not calm and old is either happy or calm and vice versa. If someone is not humble or tall then someone is both strong and not patient and vice versa. If someone is both not strong and brave then someone is either not quiet or not old. If susan is both not generous and not patient then john is both quiet and curious. If someone is both happy and funny then someone is calm. If fred is both creative and curious then lucy is not strong or not funny and vice versa. If someone is both happy and not old then mary is not kind or brave and vice versa. Everyone who is brave is both not quiet and not old and vice versa. Everyone who is funny or curious is brave or not creative and vice versa. Everyone who is both curious and creative is not rich and vice versa. Everyone who is both kind and not curious is old or happy. Everyone who is either old or not strong is both funny and happy and vice versa. Someone is not patient. Someone is either not happy or quiet. Someone is either quiet or humble. Mary is either not curious or kind. John is rich or not brave. Lucy is either old or creative. Someone is either patient or wise. Someone is either generous or not calm. | Lucy is funny. | entailment | (((curious(paul)&rich(paul)))<=>((~happy(john)|~humble(john))))&
(![X]:((~funny(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(((~happy(fred)&~tall(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((tall(john)&rich(john)))<=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((~calm(X)&old(X))<=>(happy(X)<~>calm(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((~generous(susan)&~patient(susan)))=>((quiet(john)&curious(john))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(calm(X))))&
(((creative(fred)&curious(fred)))<=>((~strong(lucy)|~funny(lucy))))&
((?[X]:((happy(X)&~old(X))))<=>((~kind(mary)|brave(mary))))&
(![X]:(brave(X)<=>(~quiet(X)&~old(X))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~creative(X))))&
(![X]:((curious(X)&creative(X))<=>~rich(X)))&
(![X]:((kind(X)&~curious(X))=>(old(X)|happy(X))))&
(![X]:((old(X)<~>~strong(X))<=>(funny(X)&happy(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
((~curious(mary)<~>kind(mary)))&
((rich(john)|~brave(john)))&
((old(lucy)<~>creative(lucy)))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((generous(X)<~>~calm(X)))) | funny(lucy) | [
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1166743293722567653232351
% SZS output start Proof for 1166743293722567653232351
2. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (~tall(X0) | creative(X0))) [input p1]
10. (curious(fred) & creative(fred)) <=> (~funny(lucy) | ~strong(lucy)) [input p9]
13. ! [X0] : ((curious(X0) | funny(X0)) <=> (~creative(X0) | brave(X0))) [input p12]
25. ~funny(lucy) [input hypothesis]
37. ! [X0] : (((~brave(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 2]
38. ! [X0] : (((~brave(X0) & ~funny(X0)) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | brave(X0) | funny(X0))) [flattening 37]
63. ((curious(fred) & creative(fred)) | (funny(lucy) & strong(lucy))) & ((~funny(lucy) | ~strong(lucy)) | (~curious(fred) | ~creative(fred))) [nnf transformation 10]
64. ((curious(fred) & creative(fred)) | (funny(lucy) & strong(lucy))) & (~funny(lucy) | ~strong(lucy) | ~curious(fred) | ~creative(fred)) [flattening 63]
72. ! [X0] : (((curious(X0) | funny(X0)) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 13]
73. ! [X0] : ((curious(X0) | funny(X0) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | (~curious(X0) & ~funny(X0)))) [flattening 72]
102. ~creative(X0) | ~brave(X0) [cnf transformation 38]
132. creative(fred) | funny(lucy) [cnf transformation 64]
134. curious(fred) | funny(lucy) [cnf transformation 64]
144. ~creative(X0) | brave(X0) | ~curious(X0) [cnf transformation 73]
171. ~funny(lucy) [cnf transformation 25]
317. 32 <=> funny(lucy) [avatar definition]
321. 33 <=> curious(fred) [avatar definition]
323. curious(fred) <- (33) [avatar component clause 321]
324. 32 | 33 [avatar split clause 134,321,317]
331. 35 <=> creative(fred) [avatar definition]
333. creative(fred) <- (35) [avatar component clause 331]
334. 32 | 35 [avatar split clause 132,331,317]
361. ~creative(X0) | ~curious(X0) [subsumption resolution 144,102]
426. ~32 [avatar split clause 171,317]
449. ~curious(fred) <- (35) [resolution 361,333]
451. $false <- (33, 35) [subsumption resolution 449,323]
452. ~33 | ~35 [avatar contradiction clause 451]
454. $false [avatar sat refutation 324,334,426,452]
% SZS output end Proof for 1166743293722567653232351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or happy is curious or not creative.
Everyone who is both calm and not funny is either old or quiet.
If susan is either not rich or not patient then someone is both not rich and not tall.
Everyone who is not wise is both not calm and brave and vice versa.
Everyone who is either not quiet or patient is happy and vice versa.
If john is not happy then lucy is either creative or humble.
If someone is not quiet or not curious then lucy is curious or rich and vice versa.
Everyone who is patient or funny is either not calm or generous and vice versa.
Everyone who is either wise or patient is either not tall or not brave and vice versa.
If lucy is not wise or not happy then someone is not happy or happy.
Everyone who is both not calm and not quiet is either strong or wise and vice versa.
Everyone who is both not curious and not brave is both not funny and happy and vice versa.
If alice is generous or not brave then someone is funny or not old and vice versa.
Everyone who is curious or not funny is calm and vice versa.
Everyone who is funny is both happy and not tall and vice versa.
Lucy is patient or not calm.
Fred is funny or calm.
Lucy is not old or calm.
Someone is either not brave or not quiet.
John is both patient and not brave.
Someone is either not quiet or old.
Paul is not humble.
John is not tall. | Lucy is strong. | neutral | (![X]:((~humble(X)<~>happy(X))=>(curious(X)|~creative(X))))&
(![X]:((calm(X)&~funny(X))=>(old(X)<~>quiet(X))))&
(((~rich(susan)<~>~patient(susan)))=>(?[X]:((~rich(X)&~tall(X)))))&
(![X]:(~wise(X)<=>(~calm(X)&brave(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>happy(X)))&
((~happy(john))=>((creative(lucy)<~>humble(lucy))))&
((?[X]:((~quiet(X)|~curious(X))))<=>((curious(lucy)|rich(lucy))))&
(![X]:((patient(X)|funny(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((wise(X)<~>patient(X))<=>(~tall(X)<~>~brave(X))))&
(((~wise(lucy)|~happy(lucy)))=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~curious(X)&~brave(X))<=>(~funny(X)&happy(X))))&
(((generous(alice)|~brave(alice)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((curious(X)|~funny(X))<=>calm(X)))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
((patient(lucy)|~calm(lucy)))&
((funny(fred)|calm(fred)))&
((~old(lucy)|calm(lucy)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((patient(john)&~brave(john)))&
(?[X]:((~quiet(X)<~>old(X))))&
(~humble(paul))&
(~tall(john)) | strong(lucy) | [] | null | 0 |
Everyone who is patient or wise is humble or not tall. Everyone who is happy or not patient is not happy or not tall and vice versa. Everyone who is 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. Everyone who is tall or not funny is either funny or tall. If lucy is both curious and strong then someone is either patient or not tall and vice versa. Everyone who is both quiet and not creative is both not curious and not calm. Fred is either kind or not creative. Someone is rich or not wise. Someone is either not old or not kind. Paul is quiet. Mary is both curious and not old. Someone is both tall and quiet. Someone is either not creative or humble. | Paul is humble. | neutral | (![X]:((patient(X)|wise(X))=>(humble(X)|~tall(X))))&
(![X]:((happy(X)|~patient(X))<=>(~happy(X)|~tall(X))))&
(![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]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(((curious(lucy)&strong(lucy)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((quiet(X)&~creative(X))=>(~curious(X)&~calm(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(quiet(paul))&
((curious(mary)&~old(mary)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~creative(X)<~>humble(X)))) | humble(paul) | [] | null | 0 |
If someone is funny then someone is happy. Everyone who is both not happy and tall is either tall or not kind and vice versa. Everyone who is rich or creative is not wise or old. If someone is both curious and not generous then someone is both not kind and not curious and vice versa. If mary is both generous and curious then someone is both funny and patient. Everyone who is either quiet or not kind is calm or generous. Everyone who is both humble and patient is not brave or not humble and vice versa. If mary is both creative and humble then someone is tall and vice versa. Everyone who is both generous and not quiet is curious or creative. Everyone who is strong is both generous and not quiet and vice versa. If someone is quiet then mary is not humble or not generous. If mary is either tall or not old then someone is both humble and quiet. Everyone who is either not funny or not rich is both curious and not kind and vice versa. If someone is either old or not patient then lucy is quiet and vice versa. If someone is either not strong or not wise then susan is either curious or funny and vice versa. Everyone who is not funny is either rich or not strong and vice versa. Someone is kind or generous. Someone is both old and brave. Someone is rich. Someone is both not tall and generous. Someone is not tall or not funny. Susan is tall. John is either not happy or not patient. Someone is both curious and not calm. | Mary is not patient. | neutral | ((?[X]:(funny(X)))=>(?[X]:(happy(X))))&
(![X]:((~happy(X)&tall(X))<=>(tall(X)<~>~kind(X))))&
(![X]:((rich(X)|creative(X))=>(~wise(X)|old(X))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:((~kind(X)&~curious(X)))))&
(((generous(mary)&curious(mary)))=>(?[X]:((funny(X)&patient(X)))))&
(![X]:((quiet(X)<~>~kind(X))=>(calm(X)|generous(X))))&
(![X]:((humble(X)&patient(X))<=>(~brave(X)|~humble(X))))&
(((creative(mary)&humble(mary)))<=>(?[X]:(tall(X))))&
(![X]:((generous(X)&~quiet(X))=>(curious(X)|creative(X))))&
(![X]:(strong(X)<=>(generous(X)&~quiet(X))))&
((?[X]:(quiet(X)))=>((~humble(mary)|~generous(mary))))&
(((tall(mary)<~>~old(mary)))=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((~funny(X)<~>~rich(X))<=>(curious(X)&~kind(X))))&
((?[X]:((old(X)<~>~patient(X))))<=>(quiet(lucy)))&
((?[X]:((~strong(X)<~>~wise(X))))<=>((curious(susan)<~>funny(susan))))&
(![X]:(~funny(X)<=>(rich(X)<~>~strong(X))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((old(X)&brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((~tall(X)&generous(X))))&
(?[X]:((~tall(X)|~funny(X))))&
(tall(susan))&
((~happy(john)<~>~patient(john)))&
(?[X]:((curious(X)&~calm(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is either humble or not calm is not happy. Everyone who is happy is humble and vice versa. Everyone who is either not curious or not funny is strong and vice versa. Everyone who is either not kind or not rich is either not happy or brave and vice versa. Everyone who is both not calm and not humble is not rich or wise and vice versa. If alice is not calm then someone is not strong or not brave and vice versa. Everyone who is happy is not curious or not happy and vice versa. If lucy is not tall then mary is not kind or not funny and vice versa. Everyone who is either creative or not old is kind and vice versa. If someone is either generous or not calm then paul is either tall or not kind and vice versa. Everyone who is either not happy or not strong is both not creative and strong. If mary is not kind then fred is not old and vice versa. If fred is both not happy and quiet then lucy is either not strong or not quiet. Everyone who is humble is both funny and rich and vice versa. If paul is wise then mary is either tall or quiet. If someone is wise then someone is not happy. Someone is funny or not tall. Susan is both not generous and not kind. Someone is quiet. Someone is quiet or rich. Lucy is brave or wise. Someone is either strong or not rich. | Paul is funny. | entailment | (![X]:((humble(X)<~>~calm(X))=>~happy(X)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~curious(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~calm(X)&~humble(X))<=>(~rich(X)|wise(X))))&
((~calm(alice))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(happy(X)<=>(~curious(X)|~happy(X))))&
((~tall(lucy))<=>((~kind(mary)|~funny(mary))))&
(![X]:((creative(X)<~>~old(X))<=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((tall(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~strong(X))=>(~creative(X)&strong(X))))&
((~kind(mary))<=>(~old(fred)))&
(((~happy(fred)&quiet(fred)))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:(humble(X)<=>(funny(X)&rich(X))))&
((wise(paul))=>((tall(mary)<~>quiet(mary))))&
((?[X]:(wise(X)))=>(?[X]:(~happy(X))))&
(?[X]:((funny(X)|~tall(X))))&
((~generous(susan)&~kind(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)|rich(X))))&
((brave(lucy)|wise(lucy)))&
(?[X]:((strong(X)<~>~rich(X)))) | funny(paul) | [
"p1",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 590982854058639568129538
% SZS output start Proof for 590982854058639568129538
2. ! [X0] : (happy(X0) <=> humble(X0)) [input p1]
7. ! [X0] : (happy(X0) <=> (~happy(X0) | ~curious(X0))) [input p6]
14. ! [X0] : (humble(X0) <=> (rich(X0) & funny(X0))) [input p13]
23. ~funny(paul) [input hypothesis]
32. ! [X0] : ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))) [nnf transformation 2]
41. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~happy(X0))) [nnf transformation 7]
42. ! [X0] : ((happy(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~happy(X0))) [flattening 41]
53. ! [X0] : ((humble(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ~humble(X0))) [nnf transformation 14]
54. ! [X0] : ((humble(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ~humble(X0))) [flattening 53]
70. ~happy(X0) | humble(X0) [cnf transformation 32]
94. happy(X0) | happy(X0) [cnf transformation 42]
118. ~humble(X0) | funny(X0) [cnf transformation 54]
132. ~funny(paul) [cnf transformation 23]
135. happy(X0) [duplicate literal removal 94]
260. humble(X0) [resolution 70,135]
263. funny(X0) [resolution 118,260]
264. $false [resolution 263,132]
% SZS output end Proof for 590982854058639568129538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not funny is either rich or not rich. If someone is both creative and not generous then someone is both humble and kind. Everyone who is patient or rich is not generous. Everyone who is either not calm or funny is tall or not rich. If someone is not happy or not patient then someone is old and vice versa. If john is happy or calm then someone is either not creative or not strong and vice versa. Everyone who is patient is not quiet. If someone is not humble or not curious then alice is both rich and not creative. Everyone who is both not generous and funny is either curious or not brave and vice versa. Everyone who is either generous or quiet is not happy and vice versa. Everyone who is brave is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. Everyone who is quiet is not quiet or not humble and vice versa. Everyone who is brave or patient is not tall and vice versa. If someone is both not old and not strong then susan is tall and vice versa. Alice is creative or quiet. Susan is both not kind and not funny. Alice is both not generous and not kind. Someone is either not tall or strong. Alice is both not creative and not strong. Susan is either not generous or not curious. | Susan is creative. | contradiction | (![X]:((~calm(X)|~funny(X))=>(rich(X)<~>~rich(X))))&
((?[X]:((creative(X)&~generous(X))))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((patient(X)|rich(X))=>~generous(X)))&
(![X]:((~calm(X)<~>funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:(old(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))=>((rich(alice)&~creative(alice))))&
(![X]:((~generous(X)&funny(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|patient(X))<=>~tall(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
((creative(alice)|quiet(alice)))&
((~kind(susan)&~funny(susan)))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~creative(alice)&~strong(alice)))&
((~generous(susan)<~>~curious(susan))) | creative(susan) | [
"p1",
"p6",
"p7",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6156747225258222978460874
% SZS output start Proof for 6156747225258222978460874
2. ? [X0] : (~generous(X0) & creative(X0)) => ? [X0] : (kind(X0) & humble(X0)) [input p1]
7. ! [X0] : (patient(X0) => ~quiet(X0)) [input p6]
8. ? [X0] : (~curious(X0) | ~humble(X0)) => (~creative(alice) & rich(alice)) [input p7]
13. (~rich(alice) | patient(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~humble(X0) | ~quiet(X0))) [input p13]
22. ~generous(susan) <~> ~curious(susan) [input p21]
23. creative(susan) [input hypothesis]
24. ? [X0] : (~generous(X0) & creative(X0)) => ? [X1] : (kind(X1) & humble(X1)) [rectify 2]
27. ? [X1] : (kind(X1) & humble(X1)) | ! [X0] : (generous(X0) | ~creative(X0)) [ennf transformation 24]
31. ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 7]
32. (~creative(alice) & rich(alice)) | ! [X0] : (curious(X0) & humble(X0)) [ennf transformation 8]
35. ? [X0] : (kind(X0) & humble(X0)) | ! [X1] : (generous(X1) | ~creative(X1)) [rectify 27]
36. ? [X0] : (kind(X0) & humble(X0)) => (kind(sK0) & humble(sK0)) [choice axiom]
37. (kind(sK0) & humble(sK0)) | ! [X1] : (generous(X1) | ~creative(X1)) [skolemisation 35,36]
54. ((~rich(alice) | patient(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [nnf transformation 13]
55. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [flattening 54]
56. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | (rich(alice) & ~patient(alice))) [rectify 55]
57. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK4) | ~curious(sK4)) [choice axiom]
58. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK4) | ~curious(sK4)) | (rich(alice) & ~patient(alice))) [skolemisation 56,57]
59. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 14]
60. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 59]
70. (curious(susan) | generous(susan)) & (~curious(susan) | ~generous(susan)) [nnf transformation 22]
75. humble(sK0) | generous(X1) | ~creative(X1) [cnf transformation 37]
90. ~quiet(X0) | ~patient(X0) [cnf transformation 31]
91. rich(alice) | humble(X0) [cnf transformation 32]
112. ~rich(alice) | patient(alice) | curious(X0) [cnf transformation 58]
114. ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 60]
115. quiet(X0) | quiet(X0) [cnf transformation 60]
132. ~curious(susan) | ~generous(susan) [cnf transformation 70]
134. creative(susan) [cnf transformation 23]
135. ~humble(X0) | ~quiet(X0) [duplicate literal removal 114]
136. quiet(X0) [duplicate literal removal 115]
138. 1 <=> ! [X1] : (generous(X1) | ~creative(X1)) [avatar definition]
139. ~creative(X1) | generous(X1) <- (1) [avatar component clause 138]
146. 3 <=> humble(sK0) [avatar definition]
148. humble(sK0) <- (3) [avatar component clause 146]
149. 1 | 3 [avatar split clause 75,146,138]
203. 16 <=> ! [X0] : curious(X0) [avatar definition]
204. curious(X0) <- (16) [avatar component clause 203]
211. 18 <=> ! [X0] : humble(X0) [avatar definition]
212. humble(X0) <- (18) [avatar component clause 211]
215. 19 <=> rich(alice) [avatar definition]
219. 18 | 19 [avatar split clause 91,215,211]
224. 21 <=> patient(alice) [avatar definition]
226. patient(alice) <- (21) [avatar component clause 224]
228. 16 | 21 | ~19 [avatar split clause 112,215,224,203]
239. ~humble(X0) [subsumption resolution 135,136]
270. 30 <=> generous(susan) [avatar definition]
271. ~generous(susan) <- (~30) [avatar component clause 270]
274. 31 <=> curious(susan) [avatar definition]
275. ~curious(susan) <- (~31) [avatar component clause 274]
278. ~30 | ~31 [avatar split clause 132,274,270]
279. $false <- (18) [subsumption resolution 212,239]
280. ~18 [avatar contradiction clause 279]
281. $false <- (3) [subsumption resolution 148,239]
282. ~3 [avatar contradiction clause 281]
289. ~patient(X0) [resolution 90,136]
290. $false <- (21) [resolution 289,226]
291. ~21 [avatar contradiction clause 290]
292. $false <- (16, ~31) [resolution 204,275]
293. ~16 | 31 [avatar contradiction clause 292]
299. generous(susan) <- (1) [resolution 139,134]
301. $false <- (1, ~30) [subsumption resolution 299,271]
302. ~1 | 30 [avatar contradiction clause 301]
303. $false [avatar sat refutation 149,219,228,278,280,282,291,293,302]
% SZS output end Proof for 6156747225258222978460874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and wise then susan is rich.
If someone is not wise or not old then mary is not strong and vice versa.
If mary is not calm then someone is both strong and not wise and vice versa.
Everyone who is rich is not tall and vice versa.
If susan is not tall then fred is both not generous and not creative and vice versa.
Everyone who is either rich or strong is not wise or not humble and vice versa.
Everyone who is not funny is both not happy and not creative and vice versa.
Everyone who is not patient or not humble is either strong or not tall and vice versa.
Everyone who is strong is either not generous or funny.
If alice is either not curious or not calm then john is not humble or not generous.
If someone is either not creative or not tall then someone is both rich and old.
Everyone who is both not old and not curious is not old and vice versa.
If someone is wise or not generous then someone is either not humble or not brave.
Everyone who is both not old and not calm is either not rich or quiet and vice versa.
If someone is old or creative then paul is not wise.
If someone is both not creative and not rich then someone is both brave and not curious.
Lucy is either rich or not patient.
Susan is not tall.
Someone is both brave and strong.
Susan is not happy.
Someone is either creative or not kind.
Someone is either tall or not happy.
Someone is patient or funny.
Alice is either not patient or patient. | Alice is not creative. | neutral | ((?[X]:((~rich(X)&wise(X))))=>(rich(susan)))&
((?[X]:((~wise(X)|~old(X))))<=>(~strong(mary)))&
((~calm(mary))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(rich(X)<=>~tall(X)))&
((~tall(susan))<=>((~generous(fred)&~creative(fred))))&
(![X]:((rich(X)<~>strong(X))<=>(~wise(X)|~humble(X))))&
(![X]:(~funny(X)<=>(~happy(X)&~creative(X))))&
(![X]:((~patient(X)|~humble(X))<=>(strong(X)<~>~tall(X))))&
(![X]:(strong(X)=>(~generous(X)<~>funny(X))))&
(((~curious(alice)<~>~calm(alice)))=>((~humble(john)|~generous(john))))&
((?[X]:((~creative(X)<~>~tall(X))))=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~old(X)&~curious(X))<=>~old(X)))&
((?[X]:((wise(X)|~generous(X))))=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((~old(X)&~calm(X))<=>(~rich(X)<~>quiet(X))))&
((?[X]:((old(X)|creative(X))))=>(~wise(paul)))&
((?[X]:((~creative(X)&~rich(X))))=>(?[X]:((brave(X)&~curious(X)))))&
((rich(lucy)<~>~patient(lucy)))&
(~tall(susan))&
(?[X]:((brave(X)&strong(X))))&
(~happy(susan))&
(?[X]:((creative(X)<~>~kind(X))))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((patient(X)|funny(X))))&
((~patient(alice)<~>patient(alice))) | ~creative(alice) | [] | null | 0 |
Everyone who is either curious or not patient is either not wise or patient and vice versa. Everyone who is not happy is not funny or not creative and vice versa. If lucy is not creative or not humble then someone is both rich and old and vice versa. If susan is both not rich and rich then someone is either kind or brave and vice versa. Everyone who is both not creative and calm is wise or not rich. If susan is both strong and not creative then mary is both strong and tall. Everyone who is both strong and creative is either brave or old and vice versa. Everyone who is both not generous and not strong is both old and happy. Everyone who is quiet is both not curious and not old and vice versa. If someone is brave then someone is not humble or not brave and vice versa. If someone is not happy or not calm then paul is either rich or tall and vice versa. Everyone who is kind is both calm and happy and vice versa. If someone is not creative then john is either tall or curious. If someone is kind then someone is either generous or not wise and vice versa. Everyone who is humble is both rich and not humble. If fred is both rich and not wise then alice is not happy and vice versa. Someone is brave. Someone is calm or not curious. Alice is both not old and patient. Someone is creative. Someone is creative or not generous. John is either rich or not brave. Fred is both quiet and generous. Someone is not kind. | Fred is wise. | contradiction | (![X]:((curious(X)<~>~patient(X))<=>(~wise(X)<~>patient(X))))&
(![X]:(~happy(X)<=>(~funny(X)|~creative(X))))&
(((~creative(lucy)|~humble(lucy)))<=>(?[X]:((rich(X)&old(X)))))&
(((~rich(susan)&rich(susan)))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((~creative(X)&calm(X))=>(wise(X)|~rich(X))))&
(((strong(susan)&~creative(susan)))=>((strong(mary)&tall(mary))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)<~>old(X))))&
(![X]:((~generous(X)&~strong(X))=>(old(X)&happy(X))))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
(![X]:(kind(X)<=>(calm(X)&happy(X))))&
((?[X]:(~creative(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:(humble(X)=>(rich(X)&~humble(X))))&
(((rich(fred)&~wise(fred)))<=>(~happy(alice)))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~old(alice)&patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)|~generous(X))))&
((rich(john)<~>~brave(john)))&
((quiet(fred)&generous(fred)))&
(?[X]:(~kind(X))) | wise(fred) | [
"p0",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5709716629107811737580393
% SZS output start Proof for 5709716629107811737580393
1. ! [X0] : ((curious(X0) <~> ~patient(X0)) <=> (~wise(X0) <~> patient(X0))) [input p0]
9. ! [X0] : (quiet(X0) <=> (~old(X0) & ~curious(X0))) [input p8]
23. generous(fred) & quiet(fred) [input p22]
25. wise(fred) [input hypothesis]
28. ! [X0] : (quiet(X0) => (~old(X0) & ~curious(X0))) [unused predicate definition removal 9]
35. ! [X0] : ((~old(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 28]
38. ! [X0] : ((((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))))) [nnf transformation 1]
84. patient(X0) | ~wise(X0) | curious(X0) | patient(X0) [cnf transformation 38]
88. ~patient(X0) | curious(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 38]
116. ~quiet(X0) | ~curious(X0) [cnf transformation 35]
149. quiet(fred) [cnf transformation 23]
152. wise(fred) [cnf transformation 25]
154. patient(X0) | ~wise(X0) | curious(X0) [duplicate literal removal 84]
156. ~patient(X0) | curious(X0) | ~wise(X0) [duplicate literal removal 88]
159. ~wise(X0) | curious(X0) [subsumption resolution 154,156]
311. 35 <=> wise(fred) [avatar definition]
312. wise(fred) <- (35) [avatar component clause 311]
349. 35 [avatar split clause 152,311]
354. ~curious(fred) [resolution 116,149]
360. curious(fred) <- (35) [resolution 159,312]
361. $false <- (35) [subsumption resolution 360,354]
362. ~35 [avatar contradiction clause 361]
363. $false [avatar sat refutation 349,362]
% SZS output end Proof for 5709716629107811737580393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not happy is both tall and not brave and vice versa. If someone is both not wise and not brave then fred is not generous. Everyone who is either not strong or not old is both not creative and wise. If someone is kind then someone is not calm or not brave and vice versa. If paul is either creative or not creative then john is not quiet and vice versa. Everyone who is not patient is both not humble and not old. If mary is either not creative or not strong then lucy is not strong. If paul is calm or not kind then lucy is both brave and tall and vice versa. If someone is either not funny or humble then someone is not old. Everyone who is happy or not quiet is both funny and wise and vice versa. If susan is brave or not happy then alice is creative. Everyone who is funny or rich is both not old and strong and vice versa. Everyone who is rich is not strong and vice versa. Everyone who is tall is both not creative and calm and vice versa. If fred is both not rich and curious then paul is either funny or not patient. If john is both not calm and not generous then paul is either not calm or not strong. Someone is both brave and not rich. Someone is not creative or wise. Susan is kind or quiet. Someone is either not strong or brave. Paul is either strong or not happy. Susan is either funny or not curious. Fred is either generous or kind. Someone is both not patient and not tall. | John is not wise. | contradiction | (![X]:((~wise(X)&~happy(X))<=>(tall(X)&~brave(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(~generous(fred)))&
(![X]:((~strong(X)<~>~old(X))=>(~creative(X)&wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~calm(X)|~brave(X)))))&
(((creative(paul)<~>~creative(paul)))<=>(~quiet(john)))&
(![X]:(~patient(X)=>(~humble(X)&~old(X))))&
(((~creative(mary)<~>~strong(mary)))=>(~strong(lucy)))&
(((calm(paul)|~kind(paul)))<=>((brave(lucy)&tall(lucy))))&
((?[X]:((~funny(X)<~>humble(X))))=>(?[X]:(~old(X))))&
(![X]:((happy(X)|~quiet(X))<=>(funny(X)&wise(X))))&
(((brave(susan)|~happy(susan)))=>(creative(alice)))&
(![X]:((funny(X)|rich(X))<=>(~old(X)&strong(X))))&
(![X]:(rich(X)<=>~strong(X)))&
(![X]:(tall(X)<=>(~creative(X)&calm(X))))&
(((~rich(fred)&curious(fred)))=>((funny(paul)<~>~patient(paul))))&
(((~calm(john)&~generous(john)))=>((~calm(paul)<~>~strong(paul))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((~creative(X)|wise(X))))&
((kind(susan)|quiet(susan)))&
(?[X]:((~strong(X)<~>brave(X))))&
((strong(paul)<~>~happy(paul)))&
((funny(susan)<~>~curious(susan)))&
((generous(fred)<~>kind(fred)))&
(?[X]:((~patient(X)&~tall(X)))) | ~wise(john) | [
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 981773417748256982994042
% SZS output start Proof for 981773417748256982994042
5. (creative(paul) <~> ~creative(paul)) <=> ~quiet(john) [input p4]
10. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (wise(X0) & funny(X0))) [input p9]
25. ~wise(john) [input hypothesis]
46. (((creative(paul) | ~creative(paul)) & (~creative(paul) | creative(paul))) | quiet(john)) & (~quiet(john) | ((creative(paul) | creative(paul)) & (~creative(paul) | ~creative(paul)))) [nnf transformation 5]
54. ! [X0] : (((~quiet(X0) | happy(X0)) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | (quiet(X0) & ~happy(X0)))) [nnf transformation 10]
55. ! [X0] : ((~quiet(X0) | happy(X0) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | (quiet(X0) & ~happy(X0)))) [flattening 54]
87. ~quiet(john) | ~creative(paul) | ~creative(paul) [cnf transformation 46]
88. ~quiet(john) | creative(paul) | creative(paul) [cnf transformation 46]
105. quiet(X0) | wise(X0) [cnf transformation 55]
137. ~wise(john) [cnf transformation 25]
138. ~quiet(john) | ~creative(paul) [duplicate literal removal 87]
139. ~quiet(john) | creative(paul) [duplicate literal removal 88]
173. 9 <=> creative(paul) [avatar definition]
177. 10 <=> quiet(john) [avatar definition]
179. ~quiet(john) <- (~10) [avatar component clause 177]
180. 9 | ~10 [avatar split clause 139,177,173]
181. ~9 | ~10 [avatar split clause 138,177,173]
319. wise(john) <- (~10) [resolution 105,179]
320. $false <- (~10) [subsumption resolution 319,137]
321. 10 [avatar contradiction clause 320]
322. $false [avatar sat refutation 180,181,321]
% SZS output end Proof for 981773417748256982994042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both tall and not kind then susan is creative and vice versa.
Everyone who is happy is not quiet.
Everyone who is both patient and kind is not patient or patient.
Everyone who is both not tall and not humble is not wise and vice versa.
Everyone who is not happy or not patient is both not happy and generous.
If mary is patient then someone is both creative and not kind and vice versa.
Everyone who is not patient is wise and vice versa.
Everyone who is not strong or not generous is not strong or not brave and vice versa.
If someone is generous then someone is not funny or generous and vice versa.
Everyone who is not wise or calm is brave and vice versa.
If mary is either not patient or not brave then someone is happy or rich and vice versa.
Everyone who is tall is generous or brave.
If someone is both kind and rich then someone is either generous or not happy and vice versa.
If someone is both creative and patient then someone is funny and vice versa.
Everyone who is not curious is not strong.
If susan is not calm or patient then someone is not happy and vice versa.
Someone is either not old or not curious.
Someone is either wise or strong.
Someone is both not happy and not calm.
Susan is both brave and not strong.
John is either quiet or generous.
John is either not brave or wise.
Susan is not wise.
John is not funny or humble. | Susan is not humble. | entailment | (((tall(fred)&~kind(fred)))<=>(creative(susan)))&
(![X]:(happy(X)=>~quiet(X)))&
(![X]:((patient(X)&kind(X))=>(~patient(X)|patient(X))))&
(![X]:((~tall(X)&~humble(X))<=>~wise(X)))&
(![X]:((~happy(X)|~patient(X))=>(~happy(X)&generous(X))))&
((patient(mary))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:(~patient(X)<=>wise(X)))&
(![X]:((~strong(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~wise(X)|calm(X))<=>brave(X)))&
(((~patient(mary)<~>~brave(mary)))<=>(?[X]:((happy(X)|rich(X)))))&
(![X]:(tall(X)=>(generous(X)|brave(X))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((generous(X)<~>~happy(X)))))&
((?[X]:((creative(X)&patient(X))))<=>(?[X]:(funny(X))))&
(![X]:(~curious(X)=>~strong(X)))&
(((~calm(susan)|patient(susan)))<=>(?[X]:(~happy(X))))&
(?[X]:((~old(X)<~>~curious(X))))&
(?[X]:((wise(X)<~>strong(X))))&
(?[X]:((~happy(X)&~calm(X))))&
((brave(susan)&~strong(susan)))&
((quiet(john)<~>generous(john)))&
((~brave(john)<~>wise(john)))&
(~wise(susan))&
((~funny(john)|humble(john))) | ~humble(susan) | [
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 183517190096758282915842
% SZS output start Proof for 183517190096758282915842
4. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> ~wise(X0)) [input p3]
23. ~wise(susan) [input p22]
25. humble(susan) [input hypothesis]
38. ! [X0] : (((~humble(X0) & ~tall(X0)) | wise(X0)) & (~wise(X0) | (humble(X0) | tall(X0)))) [nnf transformation 4]
39. ! [X0] : (((~humble(X0) & ~tall(X0)) | wise(X0)) & (~wise(X0) | humble(X0) | tall(X0))) [flattening 38]
90. ~humble(X0) | wise(X0) [cnf transformation 39]
142. ~wise(susan) [cnf transformation 23]
144. humble(susan) [cnf transformation 25]
333. wise(susan) [resolution 90,144]
334. $false [subsumption resolution 333,142]
% SZS output end Proof for 183517190096758282915842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not wise is not calm.
If lucy is both calm and not rich then someone is not creative.
If fred is wise or not funny then someone is either not happy or curious and vice versa.
Everyone who is either not rich or rich is generous or wise.
If john is not humble then someone is happy.
Everyone who is either humble or not creative is both rich and not patient and vice versa.
If paul is quiet then someone is old.
Everyone who is both generous and not rich is tall or not strong.
If someone is not quiet then someone is not creative or happy.
If someone is either not happy or curious then paul is not tall and vice versa.
If someone is either not quiet or not generous then someone is both quiet and not old and vice versa.
Everyone who is either not tall or not quiet is tall and vice versa.
Everyone who is patient or tall is not happy and vice versa.
Mary is either tall or funny.
Fred is either not funny or calm.
Alice is either not quiet or not calm.
Someone is not kind or not generous.
Mary is not rich or curious. | John is not quiet. | entailment | (![X]:((wise(X)&~wise(X))=>~calm(X)))&
(((calm(lucy)&~rich(lucy)))=>(?[X]:(~creative(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((~rich(X)<~>rich(X))=>(generous(X)|wise(X))))&
((~humble(john))=>(?[X]:(happy(X))))&
(![X]:((humble(X)<~>~creative(X))<=>(rich(X)&~patient(X))))&
((quiet(paul))=>(?[X]:(old(X))))&
(![X]:((generous(X)&~rich(X))=>(tall(X)|~strong(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)|happy(X)))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(~tall(paul)))&
((?[X]:((~quiet(X)<~>~generous(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>tall(X)))&
(![X]:((patient(X)|tall(X))<=>~happy(X)))&
((tall(mary)<~>funny(mary)))&
((~funny(fred)<~>calm(fred)))&
((~quiet(alice)<~>~calm(alice)))&
(?[X]:((~kind(X)|~generous(X))))&
((~rich(mary)|curious(mary))) | ~quiet(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 887300901458616579453386
% SZS output start Proof for 887300901458616579453386
12. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> tall(X0)) [input p11]
19. quiet(john) [input hypothesis]
59. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 12]
94. tall(X0) | ~quiet(X0) | tall(X0) [cnf transformation 59]
96. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 59]
108. quiet(john) [cnf transformation 19]
109. tall(X0) | ~quiet(X0) [duplicate literal removal 94]
110. ~quiet(X0) | ~tall(X0) [duplicate literal removal 96]
232. ~quiet(X0) [subsumption resolution 109,110]
259. $false [subsumption resolution 108,232]
% SZS output end Proof for 887300901458616579453386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not kind is either not kind or old and vice versa.
If alice is both old and not kind then john is strong or brave.
Everyone who is both brave and curious is either patient or generous and vice versa.
If susan is generous then lucy is not kind or wise and vice versa.
If lucy is either quiet or rich then someone is brave or not humble.
Everyone who is kind or rich is either patient or brave and vice versa.
If fred is not brave then alice is both strong and tall.
Everyone who is either not curious or not funny is both patient and not wise and vice versa.
Everyone who is not creative or creative is both not happy and calm and vice versa.
Everyone who is not brave or strong is strong.
If lucy is not wise then fred is both creative and not patient.
Everyone who is both not quiet and not calm is both wise and creative.
Everyone who is both curious and not patient is happy or quiet.
If fred is both calm and not calm then someone is not rich and vice versa.
If someone is both not humble and creative then someone is either old or kind and vice versa.
If alice is either not rich or not quiet then paul is either calm or humble.
Someone is either strong or generous.
Paul is both not wise and brave.
Mary is not funny or not humble.
Someone is brave or not generous.
Susan is both not tall and quiet.
Paul is both humble and funny.
Someone is patient. | Paul is not patient. | entailment | (![X]:((creative(X)&~kind(X))<=>(~kind(X)<~>old(X))))&
(((old(alice)&~kind(alice)))=>((strong(john)|brave(john))))&
(![X]:((brave(X)&curious(X))<=>(patient(X)<~>generous(X))))&
((generous(susan))<=>((~kind(lucy)|wise(lucy))))&
(((quiet(lucy)<~>rich(lucy)))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((kind(X)|rich(X))<=>(patient(X)<~>brave(X))))&
((~brave(fred))=>((strong(alice)&tall(alice))))&
(![X]:((~curious(X)<~>~funny(X))<=>(patient(X)&~wise(X))))&
(![X]:((~creative(X)|creative(X))<=>(~happy(X)&calm(X))))&
(![X]:((~brave(X)|strong(X))=>strong(X)))&
((~wise(lucy))=>((creative(fred)&~patient(fred))))&
(![X]:((~quiet(X)&~calm(X))=>(wise(X)&creative(X))))&
(![X]:((curious(X)&~patient(X))=>(happy(X)|quiet(X))))&
(((calm(fred)&~calm(fred)))<=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((old(X)<~>kind(X)))))&
(((~rich(alice)<~>~quiet(alice)))=>((calm(paul)<~>humble(paul))))&
(?[X]:((strong(X)<~>generous(X))))&
((~wise(paul)&brave(paul)))&
((~funny(mary)|~humble(mary)))&
(?[X]:((brave(X)|~generous(X))))&
((~tall(susan)&quiet(susan)))&
((humble(paul)&funny(paul)))&
(?[X]:(patient(X))) | ~patient(paul) | [
"p5",
"p8",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7538179105134035712957821
% SZS output start Proof for 7538179105134035712957821
6. ! [X0] : ((rich(X0) | kind(X0)) <=> (patient(X0) <~> brave(X0))) [input p5]
9. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (calm(X0) & ~happy(X0))) [input p8]
14. (~calm(fred) & calm(fred)) <=> ? [X0] : ~rich(X0) [input p13]
18. brave(paul) & ~wise(paul) [input p17]
24. patient(paul) [input hypothesis]
46. ! [X0] : (((rich(X0) | kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~rich(X0) & ~kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((rich(X0) | kind(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~rich(X0) & ~kind(X0)))) [flattening 46]
50. ! [X0] : (((creative(X0) | ~creative(X0)) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 9]
51. ! [X0] : ((creative(X0) | ~creative(X0) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | (~creative(X0) & creative(X0)))) [flattening 50]
52. ((~calm(fred) & calm(fred)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (calm(fred) | ~calm(fred))) [nnf transformation 14]
53. ((~calm(fred) & calm(fred)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | calm(fred) | ~calm(fred)) [flattening 52]
54. ((~calm(fred) & calm(fred)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | calm(fred) | ~calm(fred)) [rectify 53]
55. ? [X1] : ~rich(X1) => ~rich(sK1) [choice axiom]
56. ((~calm(fred) & calm(fred)) | ! [X0] : rich(X0)) & (~rich(sK1) | calm(fred) | ~calm(fred)) [skolemisation 54,55]
91. ~rich(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 47]
104. calm(X0) | creative(X0) [cnf transformation 51]
105. ~creative(X0) | calm(X0) [cnf transformation 51]
116. ~calm(fred) | rich(X0) [cnf transformation 56]
130. brave(paul) [cnf transformation 18]
138. patient(paul) [cnf transformation 24]
203. calm(X0) [subsumption resolution 104,105]
216. rich(X0) [subsumption resolution 116,203]
357. ~patient(X0) | ~brave(X0) [resolution 91,216]
377. ~brave(paul) [resolution 357,138]
381. $false [subsumption resolution 377,130]
% SZS output end Proof for 7538179105134035712957821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is strong or curious then john is not curious or not quiet and vice versa.
Everyone who is either calm or not calm is humble and vice versa.
If mary is not creative then susan is not wise.
If john is calm then paul is curious or not quiet.
If lucy is not quiet then someone is both generous and not tall.
Everyone who is old or not wise is either not funny or not curious.
Everyone who is not humble is not rich or generous and vice versa.
If paul is either calm or not happy then john is curious or not brave and vice versa.
Everyone who is funny is both not creative and not curious.
If mary is both not kind and humble then someone is generous and vice versa.
Everyone who is both rich and creative is both not rich and patient.
Everyone who is old or not rich is either rich or not wise.
Everyone who is both not brave and not curious is not happy and vice versa.
Everyone who is both not rich and not wise is not quiet.
Everyone who is either wise or funny is either not humble or humble.
Someone is not kind.
Mary is either generous or not patient.
Fred is curious or not kind.
Someone is not calm or not generous.
John is not curious or not funny.
Mary is rich or creative. | Fred is tall. | neutral | (((strong(paul)|curious(paul)))<=>((~curious(john)|~quiet(john))))&
(![X]:((calm(X)<~>~calm(X))<=>humble(X)))&
((~creative(mary))=>(~wise(susan)))&
((calm(john))=>((curious(paul)|~quiet(paul))))&
((~quiet(lucy))=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~rich(X)|generous(X))))&
(((calm(paul)<~>~happy(paul)))<=>((curious(john)|~brave(john))))&
(![X]:(funny(X)=>(~creative(X)&~curious(X))))&
(((~kind(mary)&humble(mary)))<=>(?[X]:(generous(X))))&
(![X]:((rich(X)&creative(X))=>(~rich(X)&patient(X))))&
(![X]:((old(X)|~rich(X))=>(rich(X)<~>~wise(X))))&
(![X]:((~brave(X)&~curious(X))<=>~happy(X)))&
(![X]:((~rich(X)&~wise(X))=>~quiet(X)))&
(![X]:((wise(X)<~>funny(X))=>(~humble(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
((generous(mary)<~>~patient(mary)))&
((curious(fred)|~kind(fred)))&
(?[X]:((~calm(X)|~generous(X))))&
((~curious(john)|~funny(john)))&
((rich(mary)|creative(mary))) | tall(fred) | [] | null | 0 |
If someone is either patient or not rich then someone is tall and vice versa. Everyone who is humble is generous. Everyone who is both wise and not humble is either patient or not tall and vice versa. If alice is both happy and not brave then someone is both patient and not kind and vice versa. If alice is both old and humble then someone is not curious or patient and vice versa. If someone is both not quiet and not happy then someone is happy or funny and vice versa. If susan is not funny or not rich then susan is either not humble or not old and vice versa. Everyone who is not generous or old is not brave. Everyone who is not creative or not brave is not rich. If someone is old or not rich then someone is not creative or not quiet. Everyone who is both not generous and rich is both creative and funny and vice versa. Everyone who is both happy and creative is kind or not generous. Everyone who is either brave or not old is funny. If john is both quiet and brave then paul is calm or kind and vice versa. If someone is both not brave and strong then mary is creative. Everyone who is calm or patient is either not kind or not patient. John is brave or creative. Someone is strong. Someone is either not funny or not humble. Mary is both quiet and not tall. Someone is curious. Someone is both strong and tall. Someone is not curious. Someone is either not calm or old. | Susan is rich. | neutral | ((?[X]:((patient(X)<~>~rich(X))))<=>(?[X]:(tall(X))))&
(![X]:(humble(X)=>generous(X)))&
(![X]:((wise(X)&~humble(X))<=>(patient(X)<~>~tall(X))))&
(((happy(alice)&~brave(alice)))<=>(?[X]:((patient(X)&~kind(X)))))&
(((old(alice)&humble(alice)))<=>(?[X]:((~curious(X)|patient(X)))))&
((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:((happy(X)|funny(X)))))&
(((~funny(susan)|~rich(susan)))<=>((~humble(susan)<~>~old(susan))))&
(![X]:((~generous(X)|old(X))=>~brave(X)))&
(![X]:((~creative(X)|~brave(X))=>~rich(X)))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((~generous(X)&rich(X))<=>(creative(X)&funny(X))))&
(![X]:((happy(X)&creative(X))=>(kind(X)|~generous(X))))&
(![X]:((brave(X)<~>~old(X))=>funny(X)))&
(((quiet(john)&brave(john)))<=>((calm(paul)|kind(paul))))&
((?[X]:((~brave(X)&strong(X))))=>(creative(mary)))&
(![X]:((calm(X)|patient(X))=>(~kind(X)<~>~patient(X))))&
((brave(john)|creative(john)))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)<~>~humble(X))))&
((quiet(mary)&~tall(mary)))&
(?[X]:(curious(X)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~calm(X)<~>old(X)))) | rich(susan) | [] | null | 0 |
If someone is not strong or not creative then john is both not tall and curious and vice versa. Everyone who is not quiet or patient is old. If someone is either not creative or not generous then someone is not funny and vice versa. Everyone who is not old or not humble is not tall or happy and vice versa. Everyone who is both curious and quiet is not brave. Everyone who is not old is both not tall and not happy. If someone is brave or not creative then susan is both brave and not kind and vice versa. Everyone who is not calm or not humble is not tall and vice versa. Everyone who is not funny or kind is either not patient or humble and vice versa. If someone is either not patient or not creative then someone is humble and vice versa. Everyone who is either not curious or curious is rich and vice versa. Everyone who is either happy or not creative is both not brave and funny and vice versa. If alice is not wise or calm then john is both not kind and old. Everyone who is not patient is both not creative and not old. Everyone who is both brave and not humble is not tall. Everyone who is happy or curious is either not calm or old. John is either not happy or not calm. Alice is not tall. Mary is either tall or generous. Someone is either not rich or creative. Someone is either tall or funny. Someone is both not strong and not patient. Mary is both brave and not calm. Someone is either not generous or humble. | John is not old. | contradiction | ((?[X]:((~strong(X)|~creative(X))))<=>((~tall(john)&curious(john))))&
(![X]:((~quiet(X)|patient(X))=>old(X)))&
((?[X]:((~creative(X)<~>~generous(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
((~happy(john)<~>~calm(john)))&
(~tall(alice))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X)))) | ~old(john) | [
"p0",
"p5",
"p15",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8318178525959259774263977
% SZS output start Proof for 8318178525959259774263977
1. ? [X0] : (~creative(X0) | ~strong(X0)) <=> (curious(john) & ~tall(john)) [input p0]
6. ! [X0] : (~old(X0) => (~happy(X0) & ~tall(X0))) [input p5]
16. ! [X0] : ((curious(X0) | happy(X0)) => (~calm(X0) <~> old(X0))) [input p15]
17. ~happy(john) <~> ~calm(john) [input p16]
22. ? [X0] : (~patient(X0) & ~strong(X0)) [input p21]
25. ~old(john) [input hypothesis]
32. ! [X0] : ((~happy(X0) & ~tall(X0)) | old(X0)) [ennf transformation 6]
37. ! [X0] : ((~calm(X0) <~> old(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 16]
38. (? [X0] : (~creative(X0) | ~strong(X0)) | (~curious(john) | tall(john))) & ((curious(john) & ~tall(john)) | ! [X0] : (creative(X0) & strong(X0))) [nnf transformation 1]
39. (? [X0] : (~creative(X0) | ~strong(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X0] : (creative(X0) & strong(X0))) [flattening 38]
40. (? [X0] : (~creative(X0) | ~strong(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (creative(X1) & strong(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~strong(X0)) => (~creative(sK0) | ~strong(sK0)) [choice axiom]
42. ((~creative(sK0) | ~strong(sK0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (creative(X1) & strong(X1))) [skolemisation 40,41]
67. ! [X0] : (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (~curious(X0) & ~happy(X0))) [nnf transformation 37]
68. (calm(john) | happy(john)) & (~calm(john) | ~happy(john)) [nnf transformation 17]
76. ? [X0] : (~patient(X0) & ~strong(X0)) => (~patient(sK8) & ~strong(sK8)) [choice axiom]
77. ~patient(sK8) & ~strong(sK8) [skolemisation 22,76]
83. curious(john) | strong(X1) [cnf transformation 42]
98. ~happy(X0) | old(X0) [cnf transformation 32]
133. ~calm(X0) | old(X0) | ~curious(X0) [cnf transformation 67]
134. ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 67]
137. calm(john) | happy(john) [cnf transformation 68]
145. ~strong(sK8) [cnf transformation 77]
151. ~old(john) [cnf transformation 25]
159. 2 <=> curious(john) [avatar definition]
176. 6 <=> ! [X1] : strong(X1) [avatar definition]
177. strong(X1) <- (6) [avatar component clause 176]
178. 6 | 2 [avatar split clause 83,159,176]
261. 25 <=> old(john) [avatar definition]
262. ~old(john) <- (~25) [avatar component clause 261]
271. ~happy(X0) | calm(X0) [subsumption resolution 134,98]
272. calm(john) [subsumption resolution 137,271]
305. ~25 [avatar split clause 151,261]
411. old(john) | ~curious(john) [resolution 133,272]
412. ~curious(john) <- (~25) [subsumption resolution 411,262]
415. ~2 | 25 [avatar split clause 412,261,159]
423. $false <- (6) [resolution 177,145]
424. ~6 [avatar contradiction clause 423]
425. $false [avatar sat refutation 178,305,415,424]
% SZS output end Proof for 8318178525959259774263977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not patient and creative then susan is funny.
Everyone who is rich or happy is either brave or not happy and vice versa.
Everyone who is both not humble and quiet is either patient or old and vice versa.
If paul is humble or not patient then someone is old or quiet.
Everyone who is both not kind and funny is quiet.
If alice is either not calm or generous then susan is both not strong and kind.
Everyone who is not tall or calm is either not wise or not funny and vice versa.
Everyone who is either brave or creative is both happy and old.
If susan is either tall or not happy then someone is both generous and not creative.
Everyone who is either not creative or not rich is not funny or creative and vice versa.
Everyone who is brave is both not creative and not generous.
If someone is either not creative or not old then mary is not happy and vice versa.
If paul is either not tall or happy then someone is both brave and tall.
If alice is old or not kind then alice is either tall or wise.
If paul is both brave and funny then susan is not old or not creative and vice versa.
Everyone who is tall is either quiet or rich and vice versa.
Fred is quiet.
Fred is not funny or not humble.
Someone is both generous and not strong.
Someone is humble.
Someone is not wise or tall.
Fred is rich or old.
Lucy is either not old or not rich.
Someone is patient or old. | Paul is funny. | entailment | (((~patient(paul)&creative(paul)))=>(funny(susan)))&
(![X]:((rich(X)|happy(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~humble(X)&quiet(X))<=>(patient(X)<~>old(X))))&
(((humble(paul)|~patient(paul)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~kind(X)&funny(X))=>quiet(X)))&
(((~calm(alice)<~>generous(alice)))=>((~strong(susan)&kind(susan))))&
(![X]:((~tall(X)|calm(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:((brave(X)<~>creative(X))=>(happy(X)&old(X))))&
(((tall(susan)<~>~happy(susan)))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~funny(X)|creative(X))))&
(![X]:(brave(X)=>(~creative(X)&~generous(X))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(~happy(mary)))&
(((~tall(paul)<~>happy(paul)))=>(?[X]:((brave(X)&tall(X)))))&
(((old(alice)|~kind(alice)))=>((tall(alice)<~>wise(alice))))&
(((brave(paul)&funny(paul)))<=>((~old(susan)|~creative(susan))))&
(![X]:(tall(X)<=>(quiet(X)<~>rich(X))))&
(quiet(fred))&
((~funny(fred)|~humble(fred)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((~wise(X)|tall(X))))&
((rich(fred)|old(fred)))&
((~old(lucy)<~>~rich(lucy)))&
(?[X]:((patient(X)|old(X)))) | funny(paul) | [
"p1",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 634730219945456891607864
% SZS output start Proof for 634730219945456891607864
2. ! [X0] : ((happy(X0) | rich(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p1]
8. ! [X0] : ((brave(X0) <~> creative(X0)) => (old(X0) & happy(X0))) [input p7]
11. ! [X0] : (brave(X0) => (~generous(X0) & ~creative(X0))) [input p10]
15. (funny(paul) & brave(paul)) <=> (~creative(susan) | ~old(susan)) [input p14]
25. ~funny(paul) [input hypothesis]
34. ! [X0] : ((old(X0) & happy(X0)) | (brave(X0) <=> creative(X0))) [ennf transformation 8]
36. ! [X0] : ((~generous(X0) & ~creative(X0)) | ~brave(X0)) [ennf transformation 11]
39. ! [X0] : (((happy(X0) | rich(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~happy(X0) & ~rich(X0)))) [nnf transformation 2]
40. ! [X0] : ((happy(X0) | rich(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~happy(X0) & ~rich(X0)))) [flattening 39]
47. ! [X0] : ((old(X0) & happy(X0)) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0)))) [nnf transformation 34]
61. ((funny(paul) & brave(paul)) | (creative(susan) & old(susan))) & ((~creative(susan) | ~old(susan)) | (~funny(paul) | ~brave(paul))) [nnf transformation 15]
62. ((funny(paul) & brave(paul)) | (creative(susan) & old(susan))) & (~creative(susan) | ~old(susan) | ~funny(paul) | ~brave(paul)) [flattening 61]
75. ~happy(X0) | brave(X0) | ~happy(X0) [cnf transformation 40]
95. happy(X0) | brave(X0) | ~creative(X0) [cnf transformation 47]
108. ~creative(X0) | ~brave(X0) [cnf transformation 36]
124. funny(paul) | creative(susan) [cnf transformation 62]
138. ~funny(paul) [cnf transformation 25]
141. ~happy(X0) | brave(X0) [duplicate literal removal 75]
170. brave(X0) | ~creative(X0) [subsumption resolution 95,141]
192. ~creative(X0) [subsumption resolution 108,170]
242. funny(paul) [subsumption resolution 124,192]
290. $false [subsumption resolution 138,242]
% SZS output end Proof for 634730219945456891607864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not old then someone is rich or generous.
Everyone who is not kind is either not brave or rich.
Everyone who is curious or quiet is either calm or creative.
If someone is kind then someone is rich or creative and vice versa.
If john is both not happy and not rich then lucy is generous or tall and vice versa.
If fred is not creative or creative then john is not patient or not happy and vice versa.
Everyone who is not brave or not creative is either not tall or happy.
Everyone who is both not brave and not kind is either strong or quiet and vice versa.
If someone is both not calm and curious then susan is quiet or not old.
Everyone who is either old or kind is strong or not tall and vice versa.
If someone is both not happy and not calm then someone is either not patient or brave and vice versa.
If john is strong then lucy is either not quiet or not calm and vice versa.
If someone is creative then john is calm or not brave.
Everyone who is not tall is not rich and vice versa.
Everyone who is quiet is not rich or not kind.
Everyone who is both kind and creative is both not humble and brave and vice versa.
Someone is both creative and not quiet.
Someone is either not strong or not generous.
Lucy is not creative or rich.
Someone is not funny.
Someone is both strong and not creative.
Someone is brave or creative.
Someone is brave.
Fred is either wise or not quiet. | John is tall. | neutral | ((?[X]:((strong(X)|~old(X))))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(~kind(X)=>(~brave(X)<~>rich(X))))&
(![X]:((curious(X)|quiet(X))=>(calm(X)<~>creative(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|creative(X)))))&
(((~happy(john)&~rich(john)))<=>((generous(lucy)|tall(lucy))))&
(((~creative(fred)|creative(fred)))<=>((~patient(john)|~happy(john))))&
(![X]:((~brave(X)|~creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~brave(X)&~kind(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:((~calm(X)&curious(X))))=>((quiet(susan)|~old(susan))))&
(![X]:((old(X)<~>kind(X))<=>(strong(X)|~tall(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
((strong(john))<=>((~quiet(lucy)<~>~calm(lucy))))&
((?[X]:(creative(X)))=>((calm(john)|~brave(john))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:(quiet(X)=>(~rich(X)|~kind(X))))&
(![X]:((kind(X)&creative(X))<=>(~humble(X)&brave(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~creative(lucy)|rich(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:(brave(X)))&
((wise(fred)<~>~quiet(fred))) | tall(john) | [] | null | 0 |
Everyone who is not happy or not patient is kind and vice versa. If lucy is not kind then someone is either not creative or not curious. If susan is not kind then mary is both not funny and not quiet and vice versa. Everyone who is both humble and not creative is either generous or not generous and vice versa. Everyone who is not quiet or calm is either wise or quiet. Everyone who is either happy or creative is not brave or not wise. If alice is either old or not old then someone is both not patient and generous and vice versa. Everyone who is both quiet and not quiet is either not kind or patient. If someone is either humble or not rich then paul is both old and not generous and vice versa. Everyone who is either not old or not humble is not calm or not humble. If mary is wise or not kind then john is quiet or patient and vice versa. If someone is not old or kind then susan is funny or not happy. Everyone who is either not tall or brave is rich. If mary is either not old or creative then someone is either strong or not kind. Everyone who is both not rich and rich is either not rich or generous and vice versa. Someone is both not happy and tall. Lucy is either not patient or not humble. Someone is either calm or curious. Lucy is either creative or humble. Susan is either not quiet or not calm. Someone is not tall or not humble. | John is creative. | contradiction | (![X]:((~happy(X)|~patient(X))<=>kind(X)))&
((~kind(lucy))=>(?[X]:((~creative(X)<~>~curious(X)))))&
((~kind(susan))<=>((~funny(mary)&~quiet(mary))))&
(![X]:((humble(X)&~creative(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~quiet(X)|calm(X))=>(wise(X)<~>quiet(X))))&
(![X]:((happy(X)<~>creative(X))=>(~brave(X)|~wise(X))))&
(((old(alice)<~>~old(alice)))<=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:((quiet(X)&~quiet(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~rich(X))))<=>((old(paul)&~generous(paul))))&
(![X]:((~old(X)<~>~humble(X))=>(~calm(X)|~humble(X))))&
(((wise(mary)|~kind(mary)))<=>((quiet(john)|patient(john))))&
((?[X]:((~old(X)|kind(X))))=>((funny(susan)|~happy(susan))))&
(![X]:((~tall(X)<~>brave(X))=>rich(X)))&
(((~old(mary)<~>creative(mary)))=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((~rich(X)&rich(X))<=>(~rich(X)<~>generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~patient(lucy)<~>~humble(lucy)))&
(?[X]:((calm(X)<~>curious(X))))&
((creative(lucy)<~>humble(lucy)))&
((~quiet(susan)<~>~calm(susan)))&
(?[X]:((~tall(X)|~humble(X)))) | creative(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3945858957102282886718488
% SZS output start Proof for 3945858957102282886718488
4. ! [X0] : ((~creative(X0) & humble(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p3]
22. creative(john) [input hypothesis]
42. ! [X0] : (((~creative(X0) & humble(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (creative(X0) | ~humble(X0)))) [nnf transformation 4]
43. ! [X0] : (((~creative(X0) & humble(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | creative(X0) | ~humble(X0))) [flattening 42]
87. ~creative(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 43]
88. ~creative(X0) | generous(X0) | generous(X0) [cnf transformation 43]
140. creative(john) [cnf transformation 22]
153. ~creative(X0) | ~generous(X0) [duplicate literal removal 87]
154. ~creative(X0) | generous(X0) [duplicate literal removal 88]
184. ~creative(X0) [subsumption resolution 153,154]
299. $false [subsumption resolution 140,184]
% SZS output end Proof for 3945858957102282886718488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not funny or not curious.
Everyone who is both tall and curious is not humble.
If someone is either curious or old then someone is both not humble and not happy.
Everyone who is curious or not kind is not wise or not tall.
Everyone who is both not patient and rich is both quiet and not generous.
Everyone who is funny or calm is not brave and vice versa.
Everyone who is not generous is kind or not kind and vice versa.
If alice is either not funny or not strong then someone is not strong or not curious.
Everyone who is either creative or not curious is strong and vice versa.
If john is both humble and rich then someone is both calm and brave.
If fred is funny or not creative then someone is kind or not wise and vice versa.
If someone is quiet then paul is not creative or not wise.
If someone is not brave or not funny then fred is both brave and not creative and vice versa.
If someone is quiet then someone is creative and vice versa.
Everyone who is both creative and not rich is both not happy and not wise and vice versa.
Lucy is either not happy or not strong.
Mary is humble.
Paul is strong or curious.
Someone is tall.
Susan is either not curious or funny. | Mary is not old. | neutral | (![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((tall(X)&curious(X))=>~humble(X)))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((curious(X)|~kind(X))=>(~wise(X)|~tall(X))))&
(![X]:((~patient(X)&rich(X))=>(quiet(X)&~generous(X))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
(![X]:(~generous(X)<=>(kind(X)|~kind(X))))&
(((~funny(alice)<~>~strong(alice)))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((creative(X)<~>~curious(X))<=>strong(X)))&
(((humble(john)&rich(john)))=>(?[X]:((calm(X)&brave(X)))))&
(((funny(fred)|~creative(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:(quiet(X)))=>((~creative(paul)|~wise(paul))))&
((?[X]:((~brave(X)|~funny(X))))<=>((brave(fred)&~creative(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:(creative(X))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&~wise(X))))&
((~happy(lucy)<~>~strong(lucy)))&
(humble(mary))&
((strong(paul)|curious(paul)))&
(?[X]:(tall(X)))&
((~curious(susan)<~>funny(susan))) | ~old(mary) | [] | null | 0 |
Everyone who is rich or not wise is not calm.
If someone is either not brave or not happy then paul is not funny or not wise and vice versa.
Everyone who is either not happy or not creative is not creative and vice versa.
Everyone who is not old is creative.
If someone is both kind and not kind then lucy is both not creative and quiet.
Everyone who is not brave is either old or quiet.
If lucy is humble or not funny then john is both not curious and quiet.
If fred is old then john is funny or happy.
Everyone who is not old is funny or not curious and vice versa.
If mary is not old or not kind then someone is patient or not rich and vice versa.
Everyone who is both quiet and not old is either not wise or strong and vice versa.
If fred is happy then someone is not kind or rich.
Everyone who is both happy and not strong is both not creative and not wise and vice versa.
If alice is not old or tall then someone is not brave or not quiet.
Everyone who is kind or not humble is brave or not curious and vice versa.
Everyone who is not funny is tall or rich and vice versa.
Someone is not curious or funny.
Someone is creative or not happy.
John is generous.
Alice is both brave and not generous.
Someone is not calm or strong.
Someone is either not generous or curious.
Susan is not patient or not wise.
Alice is both brave and not old. | Fred is strong. | entailment | (![X]:((rich(X)|~wise(X))=>~calm(X)))&
((?[X]:((~brave(X)<~>~happy(X))))<=>((~funny(paul)|~wise(paul))))&
(![X]:((~happy(X)<~>~creative(X))<=>~creative(X)))&
(![X]:(~old(X)=>creative(X)))&
((?[X]:((kind(X)&~kind(X))))=>((~creative(lucy)&quiet(lucy))))&
(![X]:(~brave(X)=>(old(X)<~>quiet(X))))&
(((humble(lucy)|~funny(lucy)))=>((~curious(john)&quiet(john))))&
((old(fred))=>((funny(john)|happy(john))))&
(![X]:(~old(X)<=>(funny(X)|~curious(X))))&
(((~old(mary)|~kind(mary)))<=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((quiet(X)&~old(X))<=>(~wise(X)<~>strong(X))))&
((happy(fred))=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:((happy(X)&~strong(X))<=>(~creative(X)&~wise(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|~curious(X))))&
(![X]:(~funny(X)<=>(tall(X)|rich(X))))&
(?[X]:((~curious(X)|funny(X))))&
(?[X]:((creative(X)|~happy(X))))&
(generous(john))&
((brave(alice)&~generous(alice)))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~generous(X)<~>curious(X))))&
((~patient(susan)|~wise(susan)))&
((brave(alice)&~old(alice))) | strong(fred) | [
"p2",
"p3",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 929700920803196238451263
% SZS output start Proof for 929700920803196238451263
3. ! [X0] : ((~happy(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p2]
4. ! [X0] : (~old(X0) => creative(X0)) [input p3]
11. ! [X0] : ((~old(X0) & quiet(X0)) <=> (~wise(X0) <~> strong(X0))) [input p10]
13. ! [X0] : ((~strong(X0) & happy(X0)) <=> (~wise(X0) & ~creative(X0))) [input p12]
25. ~strong(fred) [input hypothesis]
28. ! [X0] : (creative(X0) | old(X0)) [ennf transformation 4]
41. ! [X0] : ((((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0))))) [nnf transformation 3]
50. ! [X0] : (((~old(X0) & quiet(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | (old(X0) | ~quiet(X0)))) [nnf transformation 11]
51. ! [X0] : (((~old(X0) & quiet(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) & (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | old(X0) | ~quiet(X0))) [flattening 50]
54. ! [X0] : (((~strong(X0) & happy(X0)) | (wise(X0) | creative(X0))) & ((~wise(X0) & ~creative(X0)) | (strong(X0) | ~happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((~strong(X0) & happy(X0)) | wise(X0) | creative(X0)) & ((~wise(X0) & ~creative(X0)) | strong(X0) | ~happy(X0))) [flattening 54]
75. ~creative(X0) | ~creative(X0) | happy(X0) [cnf transformation 41]
78. creative(X0) | happy(X0) | creative(X0) [cnf transformation 41]
79. old(X0) | creative(X0) [cnf transformation 28]
100. ~old(X0) | strong(X0) | wise(X0) [cnf transformation 51]
103. ~creative(X0) | strong(X0) | ~happy(X0) [cnf transformation 55]
104. ~wise(X0) | strong(X0) | ~happy(X0) [cnf transformation 55]
126. ~strong(fred) [cnf transformation 25]
127. ~creative(X0) | happy(X0) [duplicate literal removal 75]
128. creative(X0) | happy(X0) [duplicate literal removal 78]
157. happy(X0) [subsumption resolution 127,128]
214. ~wise(X0) | strong(X0) [subsumption resolution 104,157]
215. ~creative(X0) | strong(X0) [subsumption resolution 103,157]
328. strong(X0) | wise(X0) | creative(X0) [resolution 100,79]
329. strong(X0) | creative(X0) [subsumption resolution 328,214]
330. strong(X0) [subsumption resolution 329,215]
347. $false [resolution 330,126]
% SZS output end Proof for 929700920803196238451263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or tall is both tall and not creative.
Everyone who is either humble or not old is not strong.
If mary is brave then someone is not quiet.
If mary is both not rich and creative then someone is both brave and not creative and vice versa.
If john is both not funny and patient then someone is both not funny and not rich and vice versa.
If paul is rich then someone is not strong and vice versa.
Everyone who is both not tall and wise is tall.
Everyone who is either rich or calm is both strong and not creative and vice versa.
Everyone who is not brave or kind is quiet or not calm.
If someone is rich then paul is both not creative and not tall and vice versa.
If john is kind or not kind then paul is not strong.
Everyone who is strong or humble is not calm and vice versa.
If john is brave or wise then someone is not generous.
If paul is both not calm and not curious then fred is both quiet and not funny and vice versa.
Everyone who is not happy or not funny is either quiet or not curious.
If someone is either not wise or brave then mary is both not kind and not tall.
Someone is both strong and humble.
Paul is not creative or strong.
Paul is not creative or not wise.
Someone is either calm or tall.
Someone is strong or not calm.
Paul is not curious.
Someone is both brave and not curious.
Mary is either not old or not creative. | Paul is not rich. | contradiction | (![X]:((~kind(X)|tall(X))=>(tall(X)&~creative(X))))&
(![X]:((humble(X)<~>~old(X))=>~strong(X)))&
((brave(mary))=>(?[X]:(~quiet(X))))&
(((~rich(mary)&creative(mary)))<=>(?[X]:((brave(X)&~creative(X)))))&
(((~funny(john)&patient(john)))<=>(?[X]:((~funny(X)&~rich(X)))))&
((rich(paul))<=>(?[X]:(~strong(X))))&
(![X]:((~tall(X)&wise(X))=>tall(X)))&
(![X]:((rich(X)<~>calm(X))<=>(strong(X)&~creative(X))))&
(![X]:((~brave(X)|kind(X))=>(quiet(X)|~calm(X))))&
((?[X]:(rich(X)))<=>((~creative(paul)&~tall(paul))))&
(((kind(john)|~kind(john)))=>(~strong(paul)))&
(![X]:((strong(X)|humble(X))<=>~calm(X)))&
(((brave(john)|wise(john)))=>(?[X]:(~generous(X))))&
(((~calm(paul)&~curious(paul)))<=>((quiet(fred)&~funny(fred))))&
(![X]:((~happy(X)|~funny(X))=>(quiet(X)<~>~curious(X))))&
((?[X]:((~wise(X)<~>brave(X))))=>((~kind(mary)&~tall(mary))))&
(?[X]:((strong(X)&humble(X))))&
((~creative(paul)|strong(paul)))&
((~creative(paul)|~wise(paul)))&
(?[X]:((calm(X)<~>tall(X))))&
(?[X]:((strong(X)|~calm(X))))&
(~curious(paul))&
(?[X]:((brave(X)&~curious(X))))&
((~old(mary)<~>~creative(mary))) | ~rich(paul) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4502322123721949963632580
% SZS output start Proof for 4502322123721949963632580
6. rich(paul) <=> ? [X0] : ~strong(X0) [input p5]
11. (~kind(john) | kind(john)) => ~strong(paul) [input p10]
25. ~rich(paul) [input hypothesis]
35. ~strong(paul) | (kind(john) & ~kind(john)) [ennf transformation 11]
51. (rich(paul) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~rich(paul)) [nnf transformation 6]
52. (rich(paul) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~rich(paul)) [rectify 51]
53. ? [X1] : ~strong(X1) => ~strong(sK3) [choice axiom]
54. (rich(paul) | ! [X0] : strong(X0)) & (~strong(sK3) | ~rich(paul)) [skolemisation 52,53]
94. rich(paul) | strong(X0) [cnf transformation 54]
107. ~strong(paul) | ~kind(john) [cnf transformation 35]
108. ~strong(paul) | kind(john) [cnf transformation 35]
134. ~rich(paul) [cnf transformation 25]
192. 13 <=> ! [X0] : strong(X0) [avatar definition]
193. strong(X0) <- (13) [avatar component clause 192]
195. 14 <=> rich(paul) [avatar definition]
198. 13 | 14 [avatar split clause 94,195,192]
223. 20 <=> kind(john) [avatar definition]
227. 21 <=> strong(paul) [avatar definition]
229. ~strong(paul) <- (~21) [avatar component clause 227]
230. 20 | ~21 [avatar split clause 108,227,223]
231. ~20 | ~21 [avatar split clause 107,227,223]
294. ~14 [avatar split clause 134,195]
295. $false <- (13, ~21) [resolution 229,193]
296. ~13 | 21 [avatar contradiction clause 295]
297. $false [avatar sat refutation 198,230,231,294,296]
% SZS output end Proof for 4502322123721949963632580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not strong is kind or not patient and vice versa.
Everyone who is quiet or patient is both curious and generous and vice versa.
Everyone who is not curious or not happy is happy.
Everyone who is both not funny and not humble is both humble and strong.
If john is both kind and brave then someone is brave or not quiet and vice versa.
Everyone who is both not wise and old is both calm and rich.
Everyone who is either not rich or not brave is both happy and not strong.
Everyone who is both strong and kind is old and vice versa.
Everyone who is generous or not funny is both creative and not kind and vice versa.
Everyone who is both not generous and not kind is not kind or not old.
Everyone who is humble or tall is patient and vice versa.
If john is calm then mary is not creative and vice versa.
Everyone who is not funny or wise is both rich and not kind and vice versa.
If lucy is not creative or patient then someone is both funny and quiet and vice versa.
If someone is creative then fred is both wise and humble.
If mary is patient then john is both old and calm and vice versa.
Someone is brave.
Alice is either humble or patient.
Someone is both generous and rich.
Someone is not old.
Someone is either humble or patient.
Someone is not brave.
Someone is quiet or not old.
Paul is strong or curious. | Alice is not kind. | entailment | (![X]:((patient(X)<~>~strong(X))<=>(kind(X)|~patient(X))))&
(![X]:((quiet(X)|patient(X))<=>(curious(X)&generous(X))))&
(![X]:((~curious(X)|~happy(X))=>happy(X)))&
(![X]:((~funny(X)&~humble(X))=>(humble(X)&strong(X))))&
(((kind(john)&brave(john)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((~wise(X)&old(X))=>(calm(X)&rich(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(happy(X)&~strong(X))))&
(![X]:((strong(X)&kind(X))<=>old(X)))&
(![X]:((generous(X)|~funny(X))<=>(creative(X)&~kind(X))))&
(![X]:((~generous(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:((humble(X)|tall(X))<=>patient(X)))&
((calm(john))<=>(~creative(mary)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)&~kind(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)&quiet(X)))))&
((?[X]:(creative(X)))=>((wise(fred)&humble(fred))))&
((patient(mary))<=>((old(john)&calm(john))))&
(?[X]:(brave(X)))&
((humble(alice)<~>patient(alice)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:(~old(X)))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((quiet(X)|~old(X))))&
((strong(paul)|curious(paul))) | ~kind(alice) | [
"p1",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1303078572713204003756344
% SZS output start Proof for 1303078572713204003756344
2. ! [X0] : ((patient(X0) | quiet(X0)) <=> (generous(X0) & curious(X0))) [input p1]
9. ! [X0] : ((~funny(X0) | generous(X0)) <=> (~kind(X0) & creative(X0))) [input p8]
11. ! [X0] : ((tall(X0) | humble(X0)) <=> patient(X0)) [input p10]
18. humble(alice) <~> patient(alice) [input p17]
25. kind(alice) [input hypothesis]
38. ! [X0] : (((patient(X0) | quiet(X0)) | (~generous(X0) | ~curious(X0))) & ((generous(X0) & curious(X0)) | (~patient(X0) & ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : ((patient(X0) | quiet(X0) | ~generous(X0) | ~curious(X0)) & ((generous(X0) & curious(X0)) | (~patient(X0) & ~quiet(X0)))) [flattening 38]
48. ! [X0] : (((~funny(X0) | generous(X0)) | (kind(X0) | ~creative(X0))) & ((~kind(X0) & creative(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((~funny(X0) | generous(X0) | kind(X0) | ~creative(X0)) & ((~kind(X0) & creative(X0)) | (funny(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((tall(X0) | humble(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~humble(X0)))) [nnf transformation 11]
51. ! [X0] : ((tall(X0) | humble(X0) | ~patient(X0)) & (patient(X0) | (~tall(X0) & ~humble(X0)))) [flattening 50]
64. (~patient(alice) | ~humble(alice)) & (patient(alice) | humble(alice)) [nnf transformation 18]
85. ~patient(X0) | generous(X0) [cnf transformation 39]
103. ~generous(X0) | ~kind(X0) [cnf transformation 49]
107. patient(X0) | ~humble(X0) [cnf transformation 51]
128. patient(alice) | humble(alice) [cnf transformation 64]
129. ~patient(alice) | ~humble(alice) [cnf transformation 64]
138. kind(alice) [cnf transformation 25]
229. ~humble(alice) [subsumption resolution 129,107]
230. patient(alice) [subsumption resolution 128,229]
259. generous(alice) [resolution 85,230]
273. ~kind(alice) [resolution 103,259]
277. $false [subsumption resolution 273,138]
% SZS output end Proof for 1303078572713204003756344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and quiet is either generous or not kind and vice versa.
If someone is not wise or not curious then lucy is not kind.
Everyone who is both wise and not curious is either not patient or humble.
Everyone who is calm is not calm or not strong.
Everyone who is both not curious and funny is either funny or not tall and vice versa.
Everyone who is either creative or calm is not kind or not wise and vice versa.
Everyone who is not patient is both not generous and brave.
Everyone who is either funny or not generous is either humble or not humble and vice versa.
If someone is humble or calm then someone is either generous or not humble and vice versa.
If someone is brave then paul is not calm.
If someone is either quiet or old then someone is either not old or not wise and vice versa.
Everyone who is both curious and not strong is creative or not quiet.
If mary is both not funny and not curious then mary is patient.
Everyone who is generous or not brave is tall and vice versa.
If mary is either patient or rich then someone is humble or curious.
Susan is rich.
Someone is both quiet and brave.
Someone is not generous or generous.
Someone is not generous.
Someone is both wise and not generous.
Someone is either calm or not tall.
Alice is either not patient or old.
Susan is both generous and humble. | Lucy is not patient. | contradiction | (![X]:((~creative(X)&quiet(X))<=>(generous(X)<~>~kind(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(~kind(lucy)))&
(![X]:((wise(X)&~curious(X))=>(~patient(X)<~>humble(X))))&
(![X]:(calm(X)=>(~calm(X)|~strong(X))))&
(![X]:((~curious(X)&funny(X))<=>(funny(X)<~>~tall(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:(~patient(X)=>(~generous(X)&brave(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(humble(X)<~>~humble(X))))&
((?[X]:((humble(X)|calm(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
((?[X]:(brave(X)))=>(~calm(paul)))&
((?[X]:((quiet(X)<~>old(X))))<=>(?[X]:((~old(X)<~>~wise(X)))))&
(![X]:((curious(X)&~strong(X))=>(creative(X)|~quiet(X))))&
(((~funny(mary)&~curious(mary)))=>(patient(mary)))&
(![X]:((generous(X)|~brave(X))<=>tall(X)))&
(((patient(mary)<~>rich(mary)))=>(?[X]:((humble(X)|curious(X)))))&
(rich(susan))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:((calm(X)<~>~tall(X))))&
((~patient(alice)<~>old(alice)))&
((generous(susan)&humble(susan))) | ~patient(lucy) | [
"p4",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2530431905782974268807589
% SZS output start Proof for 2530431905782974268807589
5. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (funny(X0) <~> ~tall(X0))) [input p4]
7. ! [X0] : (~patient(X0) => (brave(X0) & ~generous(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (humble(X0) <~> ~humble(X0))) [input p7]
14. ! [X0] : ((~brave(X0) | generous(X0)) <=> tall(X0)) [input p13]
24. ~patient(lucy) [input hypothesis]
32. ! [X0] : ((brave(X0) & ~generous(X0)) | patient(X0)) [ennf transformation 7]
42. ! [X0] : (((funny(X0) & ~curious(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) & (((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | (~funny(X0) | curious(X0)))) [nnf transformation 5]
43. ! [X0] : (((funny(X0) & ~curious(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) & (((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | ~funny(X0) | curious(X0))) [flattening 42]
46. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 8]
57. ! [X0] : (((~brave(X0) | generous(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~generous(X0)))) [nnf transformation 14]
58. ! [X0] : ((~brave(X0) | generous(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~generous(X0)))) [flattening 57]
90. funny(X0) | funny(X0) | tall(X0) [cnf transformation 43]
97. ~generous(X0) | patient(X0) [cnf transformation 32]
98. brave(X0) | patient(X0) [cnf transformation 32]
105. generous(X0) | ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 46]
106. generous(X0) | ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 46]
126. ~brave(X0) | generous(X0) | ~tall(X0) [cnf transformation 58]
142. ~patient(lucy) [cnf transformation 24]
145. generous(X0) | ~funny(X0) | ~humble(X0) [duplicate literal removal 105]
146. ~funny(X0) | generous(X0) | humble(X0) [duplicate literal removal 106]
148. tall(X0) | funny(X0) [duplicate literal removal 90]
163. ~funny(X0) | generous(X0) [subsumption resolution 145,146]
389. generous(X1) | ~tall(X1) | patient(X1) [resolution 126,98]
399. ~tall(X1) | patient(X1) [subsumption resolution 389,97]
521. funny(X1) | patient(X1) [resolution 399,148]
542. patient(X1) | generous(X1) [resolution 521,163]
546. patient(X1) [subsumption resolution 542,97]
573. $false [resolution 546,142]
% SZS output end Proof for 2530431905782974268807589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny or not generous then someone is either not happy or not quiet.
Everyone who is either not generous or not humble is either not quiet or creative.
Everyone who is not calm or not old is both not calm and calm and vice versa.
Everyone who is both old and kind is not generous and vice versa.
If john is both strong and not happy then someone is both not calm and not wise.
Everyone who is curious or happy is both not quiet and not calm and vice versa.
Everyone who is either old or generous is either not brave or rich.
If lucy is not patient then someone is creative and vice versa.
If john is either not patient or not kind then someone is both not brave and not happy.
Everyone who is both not rich and old is both not brave and generous and vice versa.
Everyone who is both not creative and not funny is both not strong and patient.
Everyone who is not quiet is either not happy or funny and vice versa.
If someone is either not generous or calm then paul is both not patient and patient and vice versa.
Everyone who is both not calm and happy is both not quiet and patient and vice versa.
Everyone who is both not curious and old is either rich or generous and vice versa.
If someone is not creative then someone is not strong and vice versa.
Alice is old.
Someone is funny or not patient.
John is either not humble or not brave.
Lucy is either calm or wise.
Someone is either calm or not patient. | Lucy is not happy. | entailment | (((funny(alice)|~generous(alice)))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(~quiet(X)<~>creative(X))))&
(![X]:((~calm(X)|~old(X))<=>(~calm(X)&calm(X))))&
(![X]:((old(X)&kind(X))<=>~generous(X)))&
(((strong(john)&~happy(john)))=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:((curious(X)|happy(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((old(X)<~>generous(X))=>(~brave(X)<~>rich(X))))&
((~patient(lucy))<=>(?[X]:(creative(X))))&
(((~patient(john)<~>~kind(john)))=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((~rich(X)&old(X))<=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~funny(X))=>(~strong(X)&patient(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>funny(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((~patient(paul)&patient(paul))))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)&patient(X))))&
(![X]:((~curious(X)&old(X))<=>(rich(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~strong(X))))&
(old(alice))&
(?[X]:((funny(X)|~patient(X))))&
((~humble(john)<~>~brave(john)))&
((calm(lucy)<~>wise(lucy)))&
(?[X]:((calm(X)<~>~patient(X)))) | ~happy(lucy) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4743145180224746476437969
% SZS output start Proof for 4743145180224746476437969
3. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (calm(X0) & ~calm(X0))) [input p2]
6. ! [X0] : ((happy(X0) | curious(X0)) <=> (~calm(X0) & ~quiet(X0))) [input p5]
22. happy(lucy) [input hypothesis]
36. ! [X0] : (((~old(X0) | ~calm(X0)) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | (old(X0) & calm(X0)))) [nnf transformation 3]
37. ! [X0] : ((~old(X0) | ~calm(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | (old(X0) & calm(X0)))) [flattening 36]
42. ! [X0] : (((happy(X0) | curious(X0)) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | (~happy(X0) & ~curious(X0)))) [nnf transformation 6]
43. ! [X0] : ((happy(X0) | curious(X0) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | (~happy(X0) & ~curious(X0)))) [flattening 42]
86. calm(X0) | calm(X0) [cnf transformation 37]
97. ~calm(X0) | ~happy(X0) [cnf transformation 43]
145. happy(lucy) [cnf transformation 22]
146. calm(X0) [duplicate literal removal 86]
185. ~happy(X0) [subsumption resolution 97,146]
272. $false [subsumption resolution 145,185]
% SZS output end Proof for 4743145180224746476437969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or strong is either kind or wise. Everyone who is either wise or funny is either not old or old. Everyone who is tall is creative. If someone is both old and not happy then john is not rich or not patient. Everyone who is creative is curious and vice versa. If someone is generous or not patient then paul is either not curious or not creative. Everyone who is brave or not patient is not brave or brave. Everyone who is both brave and humble is not calm and vice versa. If someone is not humble or humble then mary is either not rich or not happy. Everyone who is both not patient and funny is both calm and not kind and vice versa. If alice is both not kind and not wise then mary is either not quiet or humble and vice versa. Everyone who is not humble is not generous. If paul is strong or curious then someone is not kind. If john is both generous and not generous then someone is tall or not funny. If someone is not quiet then fred is funny and vice versa. If someone is not tall then someone is not curious. Someone is not quiet. Fred is both not humble and happy. Paul is rich. Someone is creative. Someone is not rich or not generous. Someone is not quiet or strong. | Paul is not rich. | contradiction | (![X]:((~creative(X)|strong(X))=>(kind(X)<~>wise(X))))&
(![X]:((wise(X)<~>funny(X))=>(~old(X)<~>old(X))))&
(![X]:(tall(X)=>creative(X)))&
((?[X]:((old(X)&~happy(X))))=>((~rich(john)|~patient(john))))&
(![X]:(creative(X)<=>curious(X)))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(((strong(paul)|curious(paul)))=>(?[X]:(~kind(X))))&
(((generous(john)&~generous(john)))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(~quiet(X)))<=>(funny(fred)))&
((?[X]:(~tall(X)))=>(?[X]:(~curious(X))))&
(?[X]:(~quiet(X)))&
((~humble(fred)&happy(fred)))&
(rich(paul))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)|strong(X)))) | ~rich(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7922490926524429736403987
% SZS output start Proof for 7922490926524429736403987
19. rich(paul) [input p18]
23. ~rich(paul) [input hypothesis]
114. rich(paul) [cnf transformation 19]
118. ~rich(paul) [cnf transformation 23]
239. $false [subsumption resolution 118,114]
% SZS output end Proof for 7922490926524429736403987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or funny is either not happy or generous and vice versa. If susan is both creative and kind then someone is generous. If fred is not rich or quiet then someone is either not tall or generous. Everyone who is not brave is either not quiet or old and vice versa. If someone is not patient or funny then mary is both not humble and not funny and vice versa. Everyone who is not tall is either humble or not tall. If someone is both humble and not kind then someone is either calm or strong. If lucy is brave or not old then someone is both wise and not wise and vice versa. Everyone who is not kind is happy or funny. Everyone who is both funny and old is both not curious and not calm and vice versa. If someone is rich or funny then john is creative or not calm. Everyone who is humble is both not funny and not old. Everyone who is not old is not happy and vice versa. Everyone who is quiet is both not humble and wise and vice versa. Everyone who is either not kind or tall is not wise and vice versa. Someone is both not happy and not patient. Fred is either wise or happy. John is not humble or not brave. Paul is wise or funny. Someone is happy or old. Paul is either not humble or curious. Someone is old or quiet. | John is not creative. | neutral | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((creative(susan)&kind(susan)))=>(?[X]:(generous(X))))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:((~patient(X)|funny(X))))<=>((~humble(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(((brave(lucy)|~old(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(?[X]:((~happy(X)&~patient(X))))&
((wise(fred)<~>happy(fred)))&
((~humble(john)|~brave(john)))&
((wise(paul)|funny(paul)))&
(?[X]:((happy(X)|old(X))))&
((~humble(paul)<~>curious(paul)))&
(?[X]:((old(X)|quiet(X)))) | ~creative(john) | [] | null | 0 |
If someone is either creative or strong then fred is calm or not funny.
Everyone who is either not curious or not kind is not wise.
If fred is either brave or not tall then john is either curious or not tall and vice versa.
Everyone who is not kind or not old is both not wise and not generous.
Everyone who is either calm or not kind is not tall or not kind and vice versa.
Everyone who is both not generous and not quiet is either not patient or calm.
Everyone who is both not curious and funny is not curious or not humble.
Everyone who is not funny is both brave and not calm.
Everyone who is both not old and creative is not generous or not rich.
Everyone who is not tall is creative or not funny.
Everyone who is both funny and patient is either tall or not tall and vice versa.
If someone is either not old or not strong then john is brave.
Everyone who is not calm is not rich or calm.
Everyone who is both not calm and calm is kind or not humble.
If mary is either not rich or strong then alice is patient or strong and vice versa.
Everyone who is brave is both funny and not happy and vice versa.
Someone is happy.
Someone is both patient and strong.
John is not calm or not happy.
Someone is either curious or brave.
John is not brave.
Someone is either old or not old.
Someone is not humble.
Alice is both brave and strong. | Fred is creative. | neutral | ((?[X]:((creative(X)<~>strong(X))))=>((calm(fred)|~funny(fred))))&
(![X]:((~curious(X)<~>~kind(X))=>~wise(X)))&
(((brave(fred)<~>~tall(fred)))<=>((curious(john)<~>~tall(john))))&
(![X]:((~kind(X)|~old(X))=>(~wise(X)&~generous(X))))&
(![X]:((calm(X)<~>~kind(X))<=>(~tall(X)|~kind(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~patient(X)<~>calm(X))))&
(![X]:((~curious(X)&funny(X))=>(~curious(X)|~humble(X))))&
(![X]:(~funny(X)=>(brave(X)&~calm(X))))&
(![X]:((~old(X)&creative(X))=>(~generous(X)|~rich(X))))&
(![X]:(~tall(X)=>(creative(X)|~funny(X))))&
(![X]:((funny(X)&patient(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>(brave(john)))&
(![X]:(~calm(X)=>(~rich(X)|calm(X))))&
(![X]:((~calm(X)&calm(X))=>(kind(X)|~humble(X))))&
(((~rich(mary)<~>strong(mary)))<=>((patient(alice)|strong(alice))))&
(![X]:(brave(X)<=>(funny(X)&~happy(X))))&
(?[X]:(happy(X)))&
(?[X]:((patient(X)&strong(X))))&
((~calm(john)|~happy(john)))&
(?[X]:((curious(X)<~>brave(X))))&
(~brave(john))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:(~humble(X)))&
((brave(alice)&strong(alice))) | creative(fred) | [] | null | 0 |
If someone is both not patient and not rich then someone is tall and vice versa.
Everyone who is wise or happy is not strong or strong.
If someone is both calm and curious then someone is wise and vice versa.
If mary is either brave or creative then susan is both not wise and not funny and vice versa.
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is both patient and not tall is rich or not patient and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
If someone is not wise then paul is both brave and creative and vice versa.
Everyone who is either not old or funny is either not quiet or creative and vice versa.
If john is both patient and tall then someone is brave and vice versa.
If someone is both strong and curious then someone is both curious and not patient and vice versa.
Fred is wise or not creative.
Someone is both not happy and quiet.
Mary is both funny and not kind.
Alice is both generous and rich.
Fred is not old or not wise.
Alice is not humble. | Alice is not patient. | contradiction | ((?[X]:((~patient(X)&~rich(X))))<=>(?[X]:(tall(X))))&
(![X]:((wise(X)|happy(X))=>(~strong(X)|strong(X))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:(wise(X))))&
(((brave(mary)<~>creative(mary)))<=>((~wise(susan)&~funny(susan))))&
(((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((patient(X)&~tall(X))<=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
((?[X]:(~wise(X)))<=>((brave(paul)&creative(paul))))&
(![X]:((~old(X)<~>funny(X))<=>(~quiet(X)<~>creative(X))))&
(((patient(john)&tall(john)))<=>(?[X]:(brave(X))))&
((?[X]:((strong(X)&curious(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
((wise(fred)|~creative(fred)))&
(?[X]:((~happy(X)&quiet(X))))&
((funny(mary)&~kind(mary)))&
((generous(alice)&rich(alice)))&
((~old(fred)|~wise(fred)))&
(~humble(alice)) | ~patient(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7992027349352600486788597
% SZS output start Proof for 7992027349352600486788597
9. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~patient(X0) | rich(X0))) [input p8]
23. ~patient(alice) [input hypothesis]
55. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 9]
56. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | tall(X0) | ~patient(X0))) [flattening 55]
111. patient(X0) | patient(X0) [cnf transformation 56]
147. ~patient(alice) [cnf transformation 23]
150. patient(X0) [duplicate literal removal 111]
341. $false [subsumption resolution 147,150]
% SZS output end Proof for 7992027349352600486788597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not patient is both not old and rich.
If someone is both rich and strong then alice is happy and vice versa.
Everyone who is creative or generous is old or not wise.
If someone is either not kind or strong then someone is both generous and tall and vice versa.
Everyone who is funny or not funny is not tall.
Everyone who is curious or patient is either not patient or strong and vice versa.
If someone is kind or quiet then fred is creative or not tall and vice versa.
Everyone who is either calm or tall is creative and vice versa.
Everyone who is patient is patient or not happy.
Everyone who is either calm or not funny is either brave or happy.
If someone is either old or kind then someone is kind or not wise.
If someone is both not patient and not brave then lucy is not tall or happy and vice versa.
Everyone who is not tall is humble and vice versa.
Everyone who is happy or humble is not rich and vice versa.
Everyone who is both strong and humble is old or wise.
Someone is either tall or not creative.
Fred is either not generous or patient.
Alice is either not curious or quiet.
Someone is generous or not rich.
Someone is not brave or not happy.
Susan is generous.
Someone is both not tall and not rich.
John is both not creative and wise. | John is not rich. | entailment | (![X]:((~generous(X)<~>~patient(X))=>(~old(X)&rich(X))))&
((?[X]:((rich(X)&strong(X))))<=>(happy(alice)))&
(![X]:((creative(X)|generous(X))=>(old(X)|~wise(X))))&
((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((funny(X)|~funny(X))=>~tall(X)))&
(![X]:((curious(X)|patient(X))<=>(~patient(X)<~>strong(X))))&
((?[X]:((kind(X)|quiet(X))))<=>((creative(fred)|~tall(fred))))&
(![X]:((calm(X)<~>tall(X))<=>creative(X)))&
(![X]:(patient(X)=>(patient(X)|~happy(X))))&
(![X]:((calm(X)<~>~funny(X))=>(brave(X)<~>happy(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:((~patient(X)&~brave(X))))<=>((~tall(lucy)|happy(lucy))))&
(![X]:(~tall(X)<=>humble(X)))&
(![X]:((happy(X)|humble(X))<=>~rich(X)))&
(![X]:((strong(X)&humble(X))=>(old(X)|wise(X))))&
(?[X]:((tall(X)<~>~creative(X))))&
((~generous(fred)<~>patient(fred)))&
((~curious(alice)<~>quiet(alice)))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((~brave(X)|~happy(X))))&
(generous(susan))&
(?[X]:((~tall(X)&~rich(X))))&
((~creative(john)&wise(john))) | ~rich(john) | [
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8486777423817629906109847
% SZS output start Proof for 8486777423817629906109847
5. ! [X0] : ((~funny(X0) | funny(X0)) => ~tall(X0)) [input p4]
13. ! [X0] : (~tall(X0) <=> humble(X0)) [input p12]
14. ! [X0] : ((humble(X0) | happy(X0)) <=> ~rich(X0)) [input p13]
24. rich(john) [input hypothesis]
30. ! [X0] : (~tall(X0) | (funny(X0) & ~funny(X0))) [ennf transformation 5]
65. ! [X0] : ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0))) [nnf transformation 13]
66. ! [X0] : (((humble(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (~humble(X0) & ~happy(X0)))) [nnf transformation 14]
67. ! [X0] : ((humble(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (~humble(X0) & ~happy(X0)))) [flattening 66]
94. ~tall(X0) | ~funny(X0) [cnf transformation 30]
95. ~tall(X0) | funny(X0) [cnf transformation 30]
122. humble(X0) | tall(X0) [cnf transformation 65]
125. ~rich(X0) | ~humble(X0) [cnf transformation 67]
141. rich(john) [cnf transformation 24]
193. ~tall(X0) [subsumption resolution 94,95]
245. humble(X0) [subsumption resolution 122,193]
246. ~rich(X0) [subsumption resolution 125,245]
278. $false [subsumption resolution 141,246]
% SZS output end Proof for 8486777423817629906109847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not generous then lucy is happy. If someone is old or not brave then fred is not quiet or old. Everyone who is either rich or kind is not patient or not curious and vice versa. If mary is not humble or not patient then someone is either curious or not strong and vice versa. If susan is curious or not patient then fred is not rich or not patient and vice versa. Everyone who is either curious or calm is both old and not calm and vice versa. Everyone who is funny or kind is not happy or not funny. Everyone who is curious is not old or strong. If lucy is not creative then susan is not brave or not strong and vice versa. Everyone who is happy or not old is quiet. If mary is either not curious or not old then alice is creative and vice versa. Everyone who is either patient or wise is both not patient and not curious and vice versa. Everyone who is happy is not wise or not humble. Everyone who is not kind is funny or brave. Everyone who is not generous or quiet is either generous or not funny. Everyone who is both not quiet and strong is strong or curious and vice versa. Someone is both not tall and not quiet. Mary is not generous or not calm. Fred is not funny. Someone is either not calm or old. John is not generous. Someone is not rich. Susan is humble. | Susan is kind. | neutral | ((?[X]:((~creative(X)<~>~generous(X))))=>(happy(lucy)))&
((?[X]:((old(X)|~brave(X))))=>((~quiet(fred)|old(fred))))&
(![X]:((rich(X)<~>kind(X))<=>(~patient(X)|~curious(X))))&
(((~humble(mary)|~patient(mary)))<=>(?[X]:((curious(X)<~>~strong(X)))))&
(((curious(susan)|~patient(susan)))<=>((~rich(fred)|~patient(fred))))&
(![X]:((curious(X)<~>calm(X))<=>(old(X)&~calm(X))))&
(![X]:((funny(X)|kind(X))=>(~happy(X)|~funny(X))))&
(![X]:(curious(X)=>(~old(X)|strong(X))))&
((~creative(lucy))<=>((~brave(susan)|~strong(susan))))&
(![X]:((happy(X)|~old(X))=>quiet(X)))&
(((~curious(mary)<~>~old(mary)))<=>(creative(alice)))&
(![X]:((patient(X)<~>wise(X))<=>(~patient(X)&~curious(X))))&
(![X]:(happy(X)=>(~wise(X)|~humble(X))))&
(![X]:(~kind(X)=>(funny(X)|brave(X))))&
(![X]:((~generous(X)|quiet(X))=>(generous(X)<~>~funny(X))))&
(![X]:((~quiet(X)&strong(X))<=>(strong(X)|curious(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
((~generous(mary)|~calm(mary)))&
(~funny(fred))&
(?[X]:((~calm(X)<~>old(X))))&
(~generous(john))&
(?[X]:(~rich(X)))&
(humble(susan)) | kind(susan) | [] | null | 0 |
If someone is either wise or not curious then paul is not brave or not happy and vice versa.
If fred is strong then alice is not kind and vice versa.
Everyone who is either patient or brave is both humble and curious and vice versa.
Everyone who is brave is both tall and humble.
If susan is both happy and curious then john is not happy or not patient.
Everyone who is not brave or not curious is not quiet or calm.
Everyone who is both calm and kind is curious.
If lucy is not funny then someone is both not wise and brave and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
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.
If someone is not wise or calm then john is both not calm and not funny and vice versa.
If someone is not old then someone is not tall and vice versa.
Everyone who is either not kind or wise is either not brave or not creative and vice versa.
Everyone who is both rich and calm is both not quiet and not funny and vice versa.
Someone is both wise and not old.
John is either not generous or funny.
Someone is both not calm and rich.
Alice is both not old and tall.
Someone is strong.
Someone is brave or not curious.
Someone is either not calm or tall. | Paul is not humble. | contradiction | ((?[X]:((wise(X)<~>~curious(X))))<=>((~brave(paul)|~happy(paul))))&
((strong(fred))<=>(~kind(alice)))&
(![X]:((patient(X)<~>brave(X))<=>(humble(X)&curious(X))))&
(![X]:(brave(X)=>(tall(X)&humble(X))))&
(((happy(susan)&curious(susan)))=>((~happy(john)|~patient(john))))&
(![X]:((~brave(X)|~curious(X))=>(~quiet(X)|calm(X))))&
(![X]:((calm(X)&kind(X))=>curious(X)))&
((~funny(lucy))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
(((~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))))&
((?[X]:((~wise(X)|calm(X))))<=>((~calm(john)&~funny(john))))&
((?[X]:(~old(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(~brave(X)<~>~creative(X))))&
(![X]:((rich(X)&calm(X))<=>(~quiet(X)&~funny(X))))&
(?[X]:((wise(X)&~old(X))))&
((~generous(john)<~>funny(john)))&
(?[X]:((~calm(X)&rich(X))))&
((~old(alice)&tall(alice)))&
(?[X]:(strong(X)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((~calm(X)<~>tall(X)))) | ~humble(paul) | [
"p2",
"p3",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4586742048004782610938151
% SZS output start Proof for 4586742048004782610938151
3. ! [X0] : ((patient(X0) <~> brave(X0)) <=> (curious(X0) & humble(X0))) [input p2]
4. ! [X0] : (brave(X0) => (humble(X0) & tall(X0))) [input p3]
9. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p8]
11. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~old(X0) & ~creative(X0))) [input p10]
12. ? [X0] : calm(X0) => (~humble(susan) & creative(susan)) [input p11]
24. ~humble(paul) [input hypothesis]
26. ! [X0] : ((humble(X0) & tall(X0)) | ~brave(X0)) [ennf transformation 4]
33. (~humble(susan) & creative(susan)) | ! [X0] : ~calm(X0) [ennf transformation 12]
40. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [flattening 40]
46. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 46]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 11]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [flattening 53]
88. ~patient(X0) | brave(X0) | humble(X0) [cnf transformation 41]
95. ~brave(X0) | humble(X0) [cnf transformation 26]
104. calm(X0) | patient(X0) [cnf transformation 47]
112. ~creative(X0) | humble(X0) [cnf transformation 54]
117. creative(susan) | ~calm(X0) [cnf transformation 33]
118. ~humble(susan) | ~calm(X0) [cnf transformation 33]
150. ~humble(paul) [cnf transformation 24]
253. 23 <=> ! [X0] : ~calm(X0) [avatar definition]
254. ~calm(X0) <- (23) [avatar component clause 253]
256. 24 <=> humble(susan) [avatar definition]
258. ~humble(susan) <- (~24) [avatar component clause 256]
259. 23 | ~24 [avatar split clause 118,256,253]
261. 25 <=> creative(susan) [avatar definition]
263. creative(susan) <- (25) [avatar component clause 261]
264. 23 | 25 [avatar split clause 117,261,253]
330. patient(X0) <- (23) [resolution 104,254]
337. brave(X1) | humble(X1) <- (23) [resolution 88,330]
339. humble(X1) <- (23) [subsumption resolution 337,95]
340. $false <- (23) [resolution 339,150]
341. ~23 [avatar contradiction clause 340]
345. humble(susan) <- (25) [resolution 263,112]
348. $false <- (~24, 25) [subsumption resolution 345,258]
349. 24 | ~25 [avatar contradiction clause 348]
350. $false [avatar sat refutation 259,264,341,349]
% SZS output end Proof for 4586742048004782610938151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not patient is both tall and curious.
Everyone who is not old is not humble.
Everyone who is both strong and not strong is both not humble and not funny.
If someone is both not funny and not rich then someone is both not kind and not rich.
If mary is calm or curious then someone is not kind and vice versa.
Everyone who is not tall or patient is old or kind.
Everyone who is not curious or not creative is not calm.
Everyone who is not generous is either tall or not happy.
If paul is brave then mary is not creative or strong.
Everyone who is not tall is tall or calm.
If someone is tall or not generous then someone is either not old or not humble.
Everyone who is either quiet or old is not creative.
Everyone who is both brave and generous is both not kind and not strong and vice versa.
Everyone who is either not happy or not humble is both not creative and humble and vice versa.
Everyone who is both not kind and not strong is either not strong or not quiet and vice versa.
Everyone who is generous or funny is both not patient and calm and vice versa.
Someone is both not strong and happy.
John is not patient or not calm.
Fred is not humble or not patient.
Fred is both not wise and quiet.
Susan is tall.
Someone is either patient or funny. | Fred is patient. | neutral | (![X]:((~humble(X)&~patient(X))=>(tall(X)&curious(X))))&
(![X]:(~old(X)=>~humble(X)))&
(![X]:((strong(X)&~strong(X))=>(~humble(X)&~funny(X))))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~kind(X)&~rich(X)))))&
(((calm(mary)|curious(mary)))<=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)|patient(X))=>(old(X)|kind(X))))&
(![X]:((~curious(X)|~creative(X))=>~calm(X)))&
(![X]:(~generous(X)=>(tall(X)<~>~happy(X))))&
((brave(paul))=>((~creative(mary)|strong(mary))))&
(![X]:(~tall(X)=>(tall(X)|calm(X))))&
((?[X]:((tall(X)|~generous(X))))=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((quiet(X)<~>old(X))=>~creative(X)))&
(![X]:((brave(X)&generous(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~creative(X)&humble(X))))&
(![X]:((~kind(X)&~strong(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(~patient(X)&calm(X))))&
(?[X]:((~strong(X)&happy(X))))&
((~patient(john)|~calm(john)))&
((~humble(fred)|~patient(fred)))&
((~wise(fred)&quiet(fred)))&
(tall(susan))&
(?[X]:((patient(X)<~>funny(X)))) | patient(fred) | [] | null | 0 |
If alice is creative or curious then fred is both curious and strong.
Everyone who is either rich or not rich is not humble or wise and vice versa.
If someone is brave then alice is both patient and not rich and vice versa.
Everyone who is humble or not brave is rich.
If susan is either calm or happy then susan is both quiet and happy and vice versa.
Everyone who is both not humble and creative is not happy or quiet.
Everyone who is either not old or generous is both humble and quiet and vice versa.
Everyone who is either humble or happy is both patient and kind and vice versa.
Everyone who is both tall and not humble is not generous.
Everyone who is both curious and not quiet is old or creative.
If someone is both tall and not funny then someone is either quiet or wise.
Everyone who is not rich is not quiet or brave.
If someone is quiet or not kind then john is creative or not funny and vice versa.
Everyone who is funny is not generous.
Everyone who is both brave and not generous is quiet or brave.
Everyone who is not wise is not kind or brave.
Someone is either not curious or creative.
Mary is wise or not tall.
Someone is either not strong or brave.
Mary is either strong or not strong.
Someone is either not creative or humble.
Alice is not old.
Someone is both old and curious.
Someone is funny. | Susan is calm. | neutral | (((creative(alice)|curious(alice)))=>((curious(fred)&strong(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>(~humble(X)|wise(X))))&
((?[X]:(brave(X)))<=>((patient(alice)&~rich(alice))))&
(![X]:((humble(X)|~brave(X))=>rich(X)))&
(((calm(susan)<~>happy(susan)))<=>((quiet(susan)&happy(susan))))&
(![X]:((~humble(X)&creative(X))=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>generous(X))<=>(humble(X)&quiet(X))))&
(![X]:((humble(X)<~>happy(X))<=>(patient(X)&kind(X))))&
(![X]:((tall(X)&~humble(X))=>~generous(X)))&
(![X]:((curious(X)&~quiet(X))=>(old(X)|creative(X))))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:(~rich(X)=>(~quiet(X)|brave(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((creative(john)|~funny(john))))&
(![X]:(funny(X)=>~generous(X)))&
(![X]:((brave(X)&~generous(X))=>(quiet(X)|brave(X))))&
(![X]:(~wise(X)=>(~kind(X)|brave(X))))&
(?[X]:((~curious(X)<~>creative(X))))&
((wise(mary)|~tall(mary)))&
(?[X]:((~strong(X)<~>brave(X))))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((~creative(X)<~>humble(X))))&
(~old(alice))&
(?[X]:((old(X)&curious(X))))&
(?[X]:(funny(X))) | calm(susan) | [] | null | 0 |
Everyone who is curious is both wise and not creative and vice versa.
Everyone who is both not generous and tall is both not strong and not old and vice versa.
Everyone who is calm is both not quiet and patient and vice versa.
If mary is both happy and funny then someone is not funny or not humble and vice versa.
If paul is wise or not calm then someone is not kind or not happy.
If someone is both not calm and not old then fred is old.
If lucy is both patient and not strong then someone is not wise.
Everyone who is both curious and not rich is tall or rich.
Everyone who is either strong or generous is both tall and not generous.
If someone is happy or not calm then someone is kind or not humble and vice versa.
Everyone who is not strong is old or not curious.
If susan is both wise and quiet then mary is quiet or strong and vice versa.
Everyone who is strong or rich is either not wise or not kind and vice versa.
If lucy is either not wise or old then john is both not brave and generous.
Everyone who is not calm or creative is kind and vice versa.
Everyone who is not curious or wise is both not generous and not creative.
Someone is both not old and funny.
Someone is either not funny or tall.
Someone is both not funny and not humble.
Someone is not rich.
Paul is not funny or not happy.
Mary is either patient or not patient.
Lucy is not creative or not generous. | John is generous. | contradiction | (![X]:(curious(X)<=>(wise(X)&~creative(X))))&
(![X]:((~generous(X)&tall(X))<=>(~strong(X)&~old(X))))&
(![X]:(calm(X)<=>(~quiet(X)&patient(X))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~funny(X)|~humble(X)))))&
(((wise(paul)|~calm(paul)))=>(?[X]:((~kind(X)|~happy(X)))))&
((?[X]:((~calm(X)&~old(X))))=>(old(fred)))&
(((patient(lucy)&~strong(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((curious(X)&~rich(X))=>(tall(X)|rich(X))))&
(![X]:((strong(X)<~>generous(X))=>(tall(X)&~generous(X))))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:(~strong(X)=>(old(X)|~curious(X))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(((~wise(lucy)<~>old(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((~calm(X)|creative(X))<=>kind(X)))&
(![X]:((~curious(X)|wise(X))=>(~generous(X)&~creative(X))))&
(?[X]:((~old(X)&funny(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:(~rich(X)))&
((~funny(paul)|~happy(paul)))&
((patient(mary)<~>~patient(mary)))&
((~creative(lucy)|~generous(lucy))) | generous(john) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4164382050799514954860692
% SZS output start Proof for 4164382050799514954860692
1. ! [X0] : (curious(X0) <=> (~creative(X0) & wise(X0))) [input p0]
16. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & ~generous(X0))) [input p15]
24. generous(john) [input hypothesis]
37. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 16]
38. ! [X0] : ((curious(X0) | (creative(X0) | ~wise(X0))) & ((~creative(X0) & wise(X0)) | ~curious(X0))) [nnf transformation 1]
39. ! [X0] : ((curious(X0) | creative(X0) | ~wise(X0)) & ((~creative(X0) & wise(X0)) | ~curious(X0))) [flattening 38]
76. ~curious(X0) | wise(X0) [cnf transformation 39]
121. ~generous(X0) | curious(X0) [cnf transformation 37]
122. ~generous(X0) | ~wise(X0) [cnf transformation 37]
136. generous(john) [cnf transformation 24]
265. 29 <=> generous(john) [avatar definition]
267. generous(john) <- (29) [avatar component clause 265]
290. 29 [avatar split clause 136,265]
293. curious(john) <- (29) [resolution 121,267]
294. wise(john) <- (29) [resolution 293,76]
295. ~wise(john) <- (29) [resolution 122,267]
296. $false <- (29) [subsumption resolution 295,294]
297. ~29 [avatar contradiction clause 296]
298. $false [avatar sat refutation 290,297]
% SZS output end Proof for 4164382050799514954860692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not calm or creative then paul is either quiet or humble and vice versa. If alice is not wise then susan is not old. If someone is either patient or old then someone is brave or not brave and vice versa. Everyone who is old is both not rich and funny. If mary is generous then mary is wise or not generous. Everyone who is both not rich and not happy is humble or not old and vice versa. Everyone who is both wise and not happy is not rich and vice versa. Everyone who is generous or not kind is either not happy or not wise. Everyone who is funny is either generous or not funny. Everyone who is creative or rich is either not wise or not quiet. Everyone who is not funny is either not funny or generous. Everyone who is not old is either brave or not kind and vice versa. If someone is either not tall or brave then paul is not calm or not tall and vice versa. Everyone who is both humble and happy is old and vice versa. If someone is tall then someone is wise or not old and vice versa. If someone is not curious or old then someone is either not wise or not rich and vice versa. Susan is patient. Mary is curious or not humble. Someone is not calm. Fred is either not brave or not tall. Someone is curious. Someone is either patient or happy. Someone is not generous or not old. | Alice is curious. | neutral | (((~calm(paul)<~>creative(paul)))<=>((quiet(paul)<~>humble(paul))))&
((~wise(alice))=>(~old(susan)))&
((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:(old(X)=>(~rich(X)&funny(X))))&
((generous(mary))=>((wise(mary)|~generous(mary))))&
(![X]:((~rich(X)&~happy(X))<=>(humble(X)|~old(X))))&
(![X]:((wise(X)&~happy(X))<=>~rich(X)))&
(![X]:((generous(X)|~kind(X))=>(~happy(X)<~>~wise(X))))&
(![X]:(funny(X)=>(generous(X)<~>~funny(X))))&
(![X]:((creative(X)|rich(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~funny(X)<~>generous(X))))&
(![X]:(~old(X)<=>(brave(X)<~>~kind(X))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((~calm(paul)|~tall(paul))))&
(![X]:((humble(X)&happy(X))<=>old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(patient(susan))&
((curious(mary)|~humble(mary)))&
(?[X]:(~calm(X)))&
((~brave(fred)<~>~tall(fred)))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((~generous(X)|~old(X)))) | curious(alice) | [] | null | 0 |
If susan is either happy or kind then paul is both not generous and not patient and vice versa.
If someone is either funny or not kind then someone is generous or not brave.
If someone is not happy or not brave then paul is not wise and vice versa.
If someone is not generous or rich then someone is either happy or curious.
If someone is either funny or humble then fred is either curious or funny.
If lucy is both not happy and old then someone is creative.
Everyone who is not creative is funny or not generous.
Everyone who is not strong is either kind or strong and vice versa.
Everyone who is not old or kind is not happy or strong.
If paul is either kind or rich then someone is both humble and not calm and vice versa.
If someone is not kind then someone is both humble and quiet.
If someone is both not rich and not old then paul is calm and vice versa.
If fred is either not old or not quiet then paul is either not happy or patient and vice versa.
If fred is both not tall and not kind then someone is not humble or not wise and vice versa.
Everyone who is rich or old is not wise.
If mary is not old or not strong then someone is not funny.
Susan is not funny or not old.
Fred is not patient or not funny.
Mary is calm or curious.
Fred is both not rich and not funny.
Lucy is not curious or quiet.
John is not generous or not brave. | Mary is old. | contradiction | (((happy(susan)<~>kind(susan)))<=>((~generous(paul)&~patient(paul))))&
((?[X]:((funny(X)<~>~kind(X))))=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~happy(X)|~brave(X))))<=>(~wise(paul)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((happy(X)<~>curious(X)))))&
((?[X]:((funny(X)<~>humble(X))))=>((curious(fred)<~>funny(fred))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(kind(X)<~>strong(X))))&
(![X]:((~old(X)|kind(X))=>(~happy(X)|strong(X))))&
(((kind(paul)<~>rich(paul)))<=>(?[X]:((humble(X)&~calm(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((humble(X)&quiet(X)))))&
((?[X]:((~rich(X)&~old(X))))<=>(calm(paul)))&
(((~old(fred)<~>~quiet(fred)))<=>((~happy(paul)<~>patient(paul))))&
(((~tall(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((rich(X)|old(X))=>~wise(X)))&
(((~old(mary)|~strong(mary)))=>(?[X]:(~funny(X))))&
((~funny(susan)|~old(susan)))&
((~patient(fred)|~funny(fred)))&
((calm(mary)|curious(mary)))&
((~rich(fred)&~funny(fred)))&
((~curious(lucy)|quiet(lucy)))&
((~generous(john)|~brave(john))) | old(mary) | [
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1613518452223597943427289
% SZS output start Proof for 1613518452223597943427289
8. ! [X0] : (~strong(X0) <=> (kind(X0) <~> strong(X0))) [input p7]
14. (~kind(fred) & ~tall(fred)) <=> ? [X0] : (~wise(X0) | ~humble(X0)) [input p13]
15. ! [X0] : ((old(X0) | rich(X0)) => ~wise(X0)) [input p14]
23. old(mary) [input hypothesis]
35. ! [X0] : (~wise(X0) | (~old(X0) & ~rich(X0))) [ennf transformation 15]
52. ! [X0] : ((~strong(X0) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0)))) & (((~strong(X0) | ~kind(X0)) & (strong(X0) | kind(X0))) | strong(X0))) [nnf transformation 8]
65. ((~kind(fred) & ~tall(fred)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X0] : (~wise(X0) | ~humble(X0)) | (kind(fred) | tall(fred))) [nnf transformation 14]
66. ((~kind(fred) & ~tall(fred)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X0] : (~wise(X0) | ~humble(X0)) | kind(fred) | tall(fred)) [flattening 65]
67. ((~kind(fred) & ~tall(fred)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X1] : (~wise(X1) | ~humble(X1)) | kind(fred) | tall(fred)) [rectify 66]
68. ? [X1] : (~wise(X1) | ~humble(X1)) => (~wise(sK6) | ~humble(sK6)) [choice axiom]
69. ((~kind(fred) & ~tall(fred)) | ! [X0] : (wise(X0) & humble(X0))) & ((~wise(sK6) | ~humble(sK6)) | kind(fred) | tall(fred)) [skolemisation 67,68]
91. strong(X0) | kind(X0) | strong(X0) [cnf transformation 52]
94. ~strong(X0) | kind(X0) | ~strong(X0) [cnf transformation 52]
120. ~kind(fred) | wise(X0) [cnf transformation 69]
122. ~wise(X0) | ~old(X0) [cnf transformation 35]
132. old(mary) [cnf transformation 23]
133. strong(X0) | kind(X0) [duplicate literal removal 91]
134. ~strong(X0) | kind(X0) [duplicate literal removal 94]
230. kind(X0) [subsumption resolution 133,134]
291. wise(X0) [subsumption resolution 120,230]
293. ~old(X0) [subsumption resolution 122,291]
340. $false [subsumption resolution 132,293]
% SZS output end Proof for 1613518452223597943427289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not humble is both strong and not curious.
Everyone who is either not rich or not kind is both not patient and calm.
Everyone who is curious or patient is not patient or not tall and vice versa.
If john is either not tall or not old then someone is not tall and vice versa.
Everyone who is either calm or not curious is not quiet.
Everyone who is generous is both not curious and humble.
If someone is not brave then susan is old and vice versa.
Everyone who is not calm is both not tall and not patient and vice versa.
Everyone who is either tall or not quiet is either not tall or rich and vice versa.
Everyone who is either not happy or not calm is not humble or calm.
If lucy is either not quiet or creative then susan is both not happy and quiet.
Everyone who is either not creative or rich is either not funny or not strong.
Everyone who is both not calm and not generous is generous.
If susan is wise or old then lucy is not brave and vice versa.
If john is both generous and not humble then alice is both not creative and not kind.
If paul is not generous or brave then someone is tall or not curious and vice versa.
Lucy is happy.
John is rich.
Someone is both not generous and not old.
Paul is either wise or not curious.
Susan is not tall.
Someone is not curious.
Mary is not curious or not brave.
John is patient or wise. | Paul is not calm. | contradiction | (![X]:((~rich(X)&~humble(X))=>(strong(X)&~curious(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(~patient(X)&calm(X))))&
(![X]:((curious(X)|patient(X))<=>(~patient(X)|~tall(X))))&
(((~tall(john)<~>~old(john)))<=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>~curious(X))=>~quiet(X)))&
(![X]:(generous(X)=>(~curious(X)&humble(X))))&
((?[X]:(~brave(X)))<=>(old(susan)))&
(![X]:(~calm(X)<=>(~tall(X)&~patient(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(~humble(X)|calm(X))))&
(((~quiet(lucy)<~>creative(lucy)))=>((~happy(susan)&quiet(susan))))&
(![X]:((~creative(X)<~>rich(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)&~generous(X))=>generous(X)))&
(((wise(susan)|old(susan)))<=>(~brave(lucy)))&
(((generous(john)&~humble(john)))=>((~creative(alice)&~kind(alice))))&
(((~generous(paul)|brave(paul)))<=>(?[X]:((tall(X)|~curious(X)))))&
(happy(lucy))&
(rich(john))&
(?[X]:((~generous(X)&~old(X))))&
((wise(paul)<~>~curious(paul)))&
(~tall(susan))&
(?[X]:(~curious(X)))&
((~curious(mary)|~brave(mary)))&
((patient(john)|wise(john))) | ~calm(paul) | [
"p2",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 418241650494531101920823
% SZS output start Proof for 418241650494531101920823
3. ! [X0] : ((patient(X0) | curious(X0)) <=> (~tall(X0) | ~patient(X0))) [input p2]
6. ! [X0] : (generous(X0) => (humble(X0) & ~curious(X0))) [input p5]
8. ! [X0] : (~calm(X0) <=> (~patient(X0) & ~tall(X0))) [input p7]
13. ! [X0] : ((~generous(X0) & ~calm(X0)) => generous(X0)) [input p12]
25. ~calm(paul) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~curious(X0)) | ~generous(X0)) [ennf transformation 6]
35. ! [X0] : (generous(X0) | (generous(X0) | calm(X0))) [ennf transformation 13]
36. ! [X0] : (generous(X0) | generous(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (((patient(X0) | curious(X0)) | (tall(X0) & patient(X0))) & ((~tall(X0) | ~patient(X0)) | (~patient(X0) & ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : ((patient(X0) | curious(X0) | (tall(X0) & patient(X0))) & (~tall(X0) | ~patient(X0) | (~patient(X0) & ~curious(X0)))) [flattening 40]
51. ! [X0] : ((~calm(X0) | (patient(X0) | tall(X0))) & ((~patient(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 8]
52. ! [X0] : ((~calm(X0) | patient(X0) | tall(X0)) & ((~patient(X0) & ~tall(X0)) | calm(X0))) [flattening 51]
77. patient(X0) | curious(X0) | patient(X0) [cnf transformation 41]
85. ~generous(X0) | ~curious(X0) [cnf transformation 30]
90. ~patient(X0) | calm(X0) [cnf transformation 52]
110. generous(X0) | generous(X0) | calm(X0) [cnf transformation 36]
130. ~calm(paul) [cnf transformation 25]
131. generous(X0) | calm(X0) [duplicate literal removal 110]
138. patient(X0) | curious(X0) [duplicate literal removal 77]
263. calm(X1) | ~curious(X1) [resolution 131,85]
272. curious(X0) | calm(X0) [resolution 138,90]
274. calm(X0) [subsumption resolution 272,263]
276. $false [resolution 274,130]
% SZS output end Proof for 418241650494531101920823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or tall is generous or not calm.
If susan is both kind and curious then someone is either curious or not patient.
Everyone who is both patient and strong is happy or not kind.
Everyone who is both not quiet and rich is both brave and old.
Everyone who is not patient or not creative is both generous and not generous.
Everyone who is either not creative or not generous is not rich and vice versa.
Everyone who is curious or creative is both not curious and wise and vice versa.
If someone is quiet then someone is not patient or wise.
Everyone who is both not strong and strong is tall and vice versa.
If someone is both curious and wise then someone is not wise.
Everyone who is quiet is strong.
Everyone who is humble or not humble is creative.
Everyone who is either not curious or not funny is both not quiet and old.
Everyone who is either tall or creative is both calm and wise.
Everyone who is generous or not quiet is not quiet or kind.
Everyone who is both not old and calm is both not curious and not funny and vice versa.
Paul is both strong and generous.
Someone is kind or not creative.
Fred is humble.
Fred is strong.
Someone is either not strong or humble. | Paul is happy. | neutral | (![X]:((~rich(X)<~>tall(X))=>(generous(X)|~calm(X))))&
(((kind(susan)&curious(susan)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((patient(X)&strong(X))=>(happy(X)|~kind(X))))&
(![X]:((~quiet(X)&rich(X))=>(brave(X)&old(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)&~generous(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((curious(X)|creative(X))<=>(~curious(X)&wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
((strong(paul)&generous(paul)))&
(?[X]:((kind(X)|~creative(X))))&
(humble(fred))&
(strong(fred))&
(?[X]:((~strong(X)<~>humble(X)))) | happy(paul) | [] | null | 0 |
Everyone who is both not brave and not curious is both rich and funny. Everyone who is not old is either not brave or generous and vice versa. If lucy is not kind then someone is either not brave or not strong. Everyone who is both not wise and tall is humble and vice versa. If someone is rich then fred is both generous and curious. Everyone who is generous is not humble and vice versa. Everyone who is both calm and not calm is either old or patient. Everyone who is either not kind or wise is quiet or not wise and vice versa. If someone is curious or not tall then someone is both old and generous. Everyone who is curious is either strong or humble and vice versa. If someone is not quiet then someone is both generous and not quiet and vice versa. Everyone who is not tall or tall is either patient or not happy. Everyone who is either curious or happy is both brave and not brave and vice versa. Everyone who is both not happy and old is happy or quiet and vice versa. If mary is not creative then mary is either brave or tall and vice versa. Everyone who is not creative is generous. Paul is both strong and not kind. Someone is generous. Someone is not quiet. Someone is both not happy and not strong. Someone is not humble or not creative. | Lucy is not generous. | neutral | (![X]:((~brave(X)&~curious(X))=>(rich(X)&funny(X))))&
(![X]:(~old(X)<=>(~brave(X)<~>generous(X))))&
((~kind(lucy))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((~wise(X)&tall(X))<=>humble(X)))&
((?[X]:(rich(X)))=>((generous(fred)&curious(fred))))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((calm(X)&~calm(X))=>(old(X)<~>patient(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(quiet(X)|~wise(X))))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((old(X)&generous(X)))))&
(![X]:(curious(X)<=>(strong(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
(![X]:((~happy(X)&old(X))<=>(happy(X)|quiet(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((strong(paul)&~kind(paul)))&
(?[X]:(generous(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~humble(X)|~creative(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is both not generous and not wise is not rich or not wise. If someone is either not strong or not rich then susan is not happy or not generous. Everyone who is either not kind or calm is either patient or not funny. Everyone who is not generous or kind is not quiet. If fred is both happy and not patient then alice is either funny or kind and vice versa. If fred is not kind then someone is both tall and humble and vice versa. If someone is either not brave or not kind then susan is both rich and creative and vice versa. If someone is both not quiet and not wise then someone is not tall or rich and vice versa. Everyone who is not quiet or generous is strong or not funny and vice versa. If someone is either not kind or not brave then someone is either brave or not quiet and vice versa. Everyone who is either not old or kind is humble. Everyone who is either not strong or quiet is not happy or not strong and vice versa. Everyone who is either not humble or not tall is both curious and not old and vice versa. Everyone who is not wise or wise is both rich and not patient. If someone is either kind or funny then john is not creative. If someone is quiet then someone is either not tall or not generous and vice versa. Someone is old or not curious. Someone is both quiet and wise. Someone is not wise. Someone is not calm or wise. Susan is either not funny or happy. Lucy is both not calm and creative. Lucy is both tall and happy. | Alice is not rich. | contradiction | (![X]:((~generous(X)&~wise(X))=>(~rich(X)|~wise(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>((~happy(susan)|~generous(susan))))&
(![X]:((~kind(X)<~>calm(X))=>(patient(X)<~>~funny(X))))&
(![X]:((~generous(X)|kind(X))=>~quiet(X)))&
(((happy(fred)&~patient(fred)))<=>((funny(alice)<~>kind(alice))))&
((~kind(fred))<=>(?[X]:((tall(X)&humble(X)))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((rich(susan)&creative(susan))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(strong(X)|~funny(X))))&
((?[X]:((~kind(X)<~>~brave(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((~old(X)<~>kind(X))=>humble(X)))&
(![X]:((~strong(X)<~>quiet(X))<=>(~happy(X)|~strong(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>(curious(X)&~old(X))))&
(![X]:((~wise(X)|wise(X))=>(rich(X)&~patient(X))))&
((?[X]:((kind(X)<~>funny(X))))=>(~creative(john)))&
((?[X]:(quiet(X)))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(?[X]:((old(X)|~curious(X))))&
(?[X]:((quiet(X)&wise(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~calm(X)|wise(X))))&
((~funny(susan)<~>happy(susan)))&
((~calm(lucy)&creative(lucy)))&
((tall(lucy)&happy(lucy))) | ~rich(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6491617155319337861268082
% SZS output start Proof for 6491617155319337861268082
14. ! [X0] : ((wise(X0) | ~wise(X0)) => (~patient(X0) & rich(X0))) [input p13]
24. ~rich(alice) [input hypothesis]
35. ! [X0] : ((~patient(X0) & rich(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 14]
137. rich(X0) | wise(X0) [cnf transformation 35]
138. rich(X0) | ~wise(X0) [cnf transformation 35]
158. ~rich(alice) [cnf transformation 24]
307. rich(X0) [subsumption resolution 137,138]
369. $false [subsumption resolution 158,307]
% SZS output end Proof for 6491617155319337861268082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Lucy is not calm.
Mary is either tall or quiet.
Someone is either brave or not curious.
Paul is either not calm or not kind.
Paul is either not wise or not kind.
Someone is not patient or brave. | Susan is not wise. | contradiction | (![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(~calm(lucy))&
((tall(mary)<~>quiet(mary)))&
(?[X]:((brave(X)<~>~curious(X))))&
((~calm(paul)<~>~kind(paul)))&
((~wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)|brave(X)))) | ~wise(susan) | [
"p0",
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7867963648818083157485191
% SZS output start Proof for 7867963648818083157485191
1. ! [X0] : (~kind(X0) => (wise(X0) & creative(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p3]
12. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (wise(X0) | ~creative(X0))) [input p11]
16. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | kind(X0)) [input p15]
23. ~wise(susan) [input hypothesis]
24. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | kind(X1)) [rectify 16]
25. ! [X0] : ((wise(X0) & creative(X0)) | kind(X0)) [ennf transformation 1]
27. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 4]
56. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 12]
57. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 56]
60. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X1] : (humble(X1) | kind(X1)) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 24]
61. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X2] : (humble(X2) | kind(X2)) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 60]
62. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK3) & ~kind(sK3)) [choice axiom]
63. ? [X2] : (humble(X2) | kind(X2)) => (humble(sK4) | kind(sK4)) [choice axiom]
64. ((curious(sK3) & ~kind(sK3)) | ! [X1] : (~humble(X1) & ~kind(X1))) & ((humble(sK4) | kind(sK4)) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 61,63,62]
74. wise(X0) | kind(X0) [cnf transformation 25]
81. quiet(X0) | wise(X0) [cnf transformation 27]
83. ~curious(X0) | quiet(X0) [cnf transformation 27]
111. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 57]
113. curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 57]
124. ~kind(sK3) | ~kind(X1) [cnf transformation 64]
126. curious(sK3) | ~kind(X1) [cnf transformation 64]
138. ~wise(susan) [cnf transformation 23]
183. quiet(X0) | ~wise(X0) [subsumption resolution 113,83]
184. quiet(X0) [subsumption resolution 183,81]
185. ~curious(X0) | ~wise(X0) [subsumption resolution 111,184]
194. 11 <=> curious(sK3) [avatar definition]
196. curious(sK3) <- (11) [avatar component clause 194]
199. 12 <=> ! [X1] : ~kind(X1) [avatar definition]
200. ~kind(X1) <- (12) [avatar component clause 199]
201. 12 | 11 [avatar split clause 126,194,199]
203. 13 <=> kind(sK3) [avatar definition]
205. ~kind(sK3) <- (~13) [avatar component clause 203]
207. 12 | ~13 [avatar split clause 124,203,199]
255. kind(susan) [resolution 74,138]
259. ~wise(sK3) <- (11) [resolution 185,196]
261. kind(sK3) <- (11) [resolution 259,74]
262. $false <- (11, ~13) [subsumption resolution 261,205]
263. ~11 | 13 [avatar contradiction clause 262]
264. $false <- (12) [resolution 200,255]
265. ~12 [avatar contradiction clause 264]
266. $false [avatar sat refutation 201,207,263,265]
% SZS output end Proof for 7867963648818083157485191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not creative is both wise and old and vice versa.
Everyone who is happy or strong is either not generous or not patient.
Everyone who is not patient is both not funny and tall.
Everyone who is not patient or not old is kind.
If someone is either quiet or not funny then susan is either calm or not brave and vice versa.
If paul is not strong or kind then someone is both not tall and generous.
Everyone who is either not calm or not quiet is both not humble and humble.
Everyone who is not strong is not happy and vice versa.
Everyone who is not humble is humble.
Everyone who is both not happy and creative is either funny or brave and vice versa.
If someone is not patient then paul is happy or kind and vice versa.
Everyone who is both not patient and not funny is either calm or happy and vice versa.
Everyone who is both not funny and kind is not quiet or not curious.
Everyone who is humble is either not tall or creative.
Alice is either kind or patient.
Someone is wise.
Someone is creative.
Paul is either calm or not curious.
Someone is either not humble or happy.
Lucy is kind or rich. | Lucy is not patient. | neutral | (![X]:((strong(X)&~creative(X))<=>(wise(X)&old(X))))&
(![X]:((happy(X)|strong(X))=>(~generous(X)<~>~patient(X))))&
(![X]:(~patient(X)=>(~funny(X)&tall(X))))&
(![X]:((~patient(X)|~old(X))=>kind(X)))&
((?[X]:((quiet(X)<~>~funny(X))))<=>((calm(susan)<~>~brave(susan))))&
(((~strong(paul)|kind(paul)))=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~humble(X)&humble(X))))&
(![X]:(~strong(X)<=>~happy(X)))&
(![X]:(~humble(X)=>humble(X)))&
(![X]:((~happy(X)&creative(X))<=>(funny(X)<~>brave(X))))&
((?[X]:(~patient(X)))<=>((happy(paul)|kind(paul))))&
(![X]:((~patient(X)&~funny(X))<=>(calm(X)<~>happy(X))))&
(![X]:((~funny(X)&kind(X))=>(~quiet(X)|~curious(X))))&
(![X]:(humble(X)=>(~tall(X)<~>creative(X))))&
((kind(alice)<~>patient(alice)))&
(?[X]:(wise(X)))&
(?[X]:(creative(X)))&
((calm(paul)<~>~curious(paul)))&
(?[X]:((~humble(X)<~>happy(X))))&
((kind(lucy)|rich(lucy))) | ~patient(lucy) | [] | null | 0 |
Everyone who is not brave is not kind or happy. If someone is wise then john is both not creative and kind. If someone is not creative or not quiet then paul is both happy and old and vice versa. Everyone who is either rich or wise is either not tall or happy. If someone is quiet or tall then someone is both curious and funny and vice versa. If fred is either not curious or not happy then someone is not rich or humble and vice versa. Everyone who is both not kind and quiet is funny and vice versa. Everyone who is either not brave or creative is both funny and rich and vice versa. Everyone who is not wise or creative is not kind or strong. If fred is either generous or not kind then alice is curious or tall and vice versa. If someone is both happy and not brave then someone is both not happy and calm. Everyone who is not funny or not wise is not funny. Everyone who is creative or patient is both kind and creative and vice versa. If alice is both tall and old then mary is both not brave and not rich and vice versa. If paul is either tall or brave then mary is both humble and not old. Everyone who is either not wise or funny is not brave and vice versa. Someone is either happy or generous. Someone is either strong or humble. Someone is not tall or curious. John is either not old or happy. Someone is not curious or not quiet. Mary is funny. Susan is happy. Someone is either happy or not curious. | Mary is rich. | entailment | (![X]:(~brave(X)=>(~kind(X)|happy(X))))&
((?[X]:(wise(X)))=>((~creative(john)&kind(john))))&
((?[X]:((~creative(X)|~quiet(X))))<=>((happy(paul)&old(paul))))&
(![X]:((rich(X)<~>wise(X))=>(~tall(X)<~>happy(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:((curious(X)&funny(X)))))&
(((~curious(fred)<~>~happy(fred)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((~kind(X)&quiet(X))<=>funny(X)))&
(![X]:((~brave(X)<~>creative(X))<=>(funny(X)&rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~kind(X)|strong(X))))&
(((generous(fred)<~>~kind(fred)))<=>((curious(alice)|tall(alice))))&
((?[X]:((happy(X)&~brave(X))))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((~funny(X)|~wise(X))=>~funny(X)))&
(![X]:((creative(X)|patient(X))<=>(kind(X)&creative(X))))&
(((tall(alice)&old(alice)))<=>((~brave(mary)&~rich(mary))))&
(((tall(paul)<~>brave(paul)))=>((humble(mary)&~old(mary))))&
(![X]:((~wise(X)<~>funny(X))<=>~brave(X)))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:((~tall(X)|curious(X))))&
((~old(john)<~>happy(john)))&
(?[X]:((~curious(X)|~quiet(X))))&
(funny(mary))&
(happy(susan))&
(?[X]:((happy(X)<~>~curious(X)))) | rich(mary) | [
"p6",
"p7",
"p11",
"p12",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2980881392481276548263080
% SZS output start Proof for 2980881392481276548263080
7. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> funny(X0)) [input p6]
8. ! [X0] : ((~brave(X0) <~> creative(X0)) <=> (rich(X0) & funny(X0))) [input p7]
12. ! [X0] : ((~wise(X0) | ~funny(X0)) => ~funny(X0)) [input p11]
13. ! [X0] : ((patient(X0) | creative(X0)) <=> (creative(X0) & kind(X0))) [input p12]
16. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> ~brave(X0)) [input p15]
22. funny(mary) [input p21]
25. ~rich(mary) [input hypothesis]
36. ! [X0] : (~funny(X0) | (wise(X0) & funny(X0))) [ennf transformation 12]
53. ! [X0] : (((quiet(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | (~quiet(X0) | kind(X0)))) [nnf transformation 7]
54. ! [X0] : (((quiet(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | ~quiet(X0) | kind(X0))) [flattening 53]
55. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [flattening 55]
62. ! [X0] : (((patient(X0) | creative(X0)) | (~creative(X0) | ~kind(X0))) & ((creative(X0) & kind(X0)) | (~patient(X0) & ~creative(X0)))) [nnf transformation 13]
63. ! [X0] : ((patient(X0) | creative(X0) | ~creative(X0) | ~kind(X0)) & ((creative(X0) & kind(X0)) | (~patient(X0) & ~creative(X0)))) [flattening 62]
67. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | brave(X0)) & (~brave(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 16]
106. ~funny(X0) | ~kind(X0) [cnf transformation 54]
110. rich(X0) | creative(X0) | brave(X0) [cnf transformation 56]
124. ~funny(X0) | wise(X0) [cnf transformation 36]
125. ~creative(X0) | kind(X0) [cnf transformation 63]
139. ~brave(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 67]
150. funny(mary) [cnf transformation 22]
154. ~rich(mary) [cnf transformation 25]
284. 29 <=> brave(mary) [avatar definition]
285. ~brave(mary) <- (~29) [avatar component clause 284]
288. 30 <=> rich(mary) [avatar definition]
289. ~rich(mary) <- (~30) [avatar component clause 288]
319. ~funny(X0) | ~brave(X0) [subsumption resolution 139,124]
379. ~30 [avatar split clause 154,288]
382. ~kind(mary) [resolution 106,150]
396. ~brave(mary) [resolution 319,150]
400. ~29 [avatar split clause 396,284]
426. creative(mary) | brave(mary) <- (~30) [resolution 110,289]
436. creative(mary) <- (~29, ~30) [subsumption resolution 426,285]
442. kind(mary) <- (~29, ~30) [resolution 436,125]
443. $false <- (~29, ~30) [subsumption resolution 442,382]
444. 29 | 30 [avatar contradiction clause 443]
445. $false [avatar sat refutation 379,400,444]
% SZS output end Proof for 2980881392481276548263080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is not happy or not patient then someone is not rich or not wise.
If someone is both kind and not quiet then someone is not brave.
If paul is both generous and humble then someone is not curious or not happy and vice versa.
If mary is either not wise or not old then someone is either old or not funny.
If someone is calm or not creative then paul is both not old and calm and vice versa.
If someone is humble or not humble then fred is both generous and not funny and vice versa.
Everyone who is both not rich and not calm is generous or not strong.
If alice is curious or not creative then alice is both not calm and quiet and vice versa.
If someone is not quiet then lucy is generous or not generous.
Everyone who is funny is not generous and vice versa.
Everyone who is not calm or not creative is both rich and brave and vice versa.
Everyone who is both not wise and not patient is not funny or happy and vice versa.
Everyone who is either calm or creative is both kind and creative.
Everyone who is patient is either quiet or strong.
Everyone who is either not strong or not wise is either not strong or not generous.
Everyone who is kind is either generous or wise and vice versa.
Alice is not humble.
Susan is not strong.
Someone is not rich or not quiet.
Someone is patient.
Mary is either curious or not strong.
Fred is either not creative or not rich.
Mary is both quiet and generous. | Fred is strong. | contradiction | (((~happy(lucy)|~patient(lucy)))=>(?[X]:((~rich(X)|~wise(X)))))&
((?[X]:((kind(X)&~quiet(X))))=>(?[X]:(~brave(X))))&
(((generous(paul)&humble(paul)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(((~wise(mary)<~>~old(mary)))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((calm(X)|~creative(X))))<=>((~old(paul)&calm(paul))))&
((?[X]:((humble(X)|~humble(X))))<=>((generous(fred)&~funny(fred))))&
(![X]:((~rich(X)&~calm(X))=>(generous(X)|~strong(X))))&
(((curious(alice)|~creative(alice)))<=>((~calm(alice)&quiet(alice))))&
((?[X]:(~quiet(X)))=>((generous(lucy)|~generous(lucy))))&
(![X]:(funny(X)<=>~generous(X)))&
(![X]:((~calm(X)|~creative(X))<=>(rich(X)&brave(X))))&
(![X]:((~wise(X)&~patient(X))<=>(~funny(X)|happy(X))))&
(![X]:((calm(X)<~>creative(X))=>(kind(X)&creative(X))))&
(![X]:(patient(X)=>(quiet(X)<~>strong(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(~strong(X)<~>~generous(X))))&
(![X]:(kind(X)<=>(generous(X)<~>wise(X))))&
(~humble(alice))&
(~strong(susan))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:(patient(X)))&
((curious(mary)<~>~strong(mary)))&
((~creative(fred)<~>~rich(fred)))&
((quiet(mary)&generous(mary))) | strong(fred) | [
"p5",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 16072136184729716843919
% SZS output start Proof for 16072136184729716843919
6. ? [X0] : (~humble(X0) | humble(X0)) <=> (~funny(fred) & generous(fred)) [input p5]
12. ! [X0] : ((~patient(X0) & ~wise(X0)) <=> (happy(X0) | ~funny(X0))) [input p11]
15. ! [X0] : ((~strong(X0) <~> ~wise(X0)) => (~strong(X0) <~> ~generous(X0))) [input p14]
24. strong(fred) [input hypothesis]
35. ! [X0] : ((~strong(X0) <~> ~generous(X0)) | (~strong(X0) <=> ~wise(X0))) [ennf transformation 15]
54. (? [X0] : (~humble(X0) | humble(X0)) | (funny(fred) | ~generous(fred))) & ((~funny(fred) & generous(fred)) | ! [X0] : (humble(X0) & ~humble(X0))) [nnf transformation 6]
55. (? [X0] : (~humble(X0) | humble(X0)) | funny(fred) | ~generous(fred)) & ((~funny(fred) & generous(fred)) | ! [X0] : (humble(X0) & ~humble(X0))) [flattening 54]
56. (? [X0] : (~humble(X0) | humble(X0)) | funny(fred) | ~generous(fred)) & ((~funny(fred) & generous(fred)) | ! [X1] : (humble(X1) & ~humble(X1))) [rectify 55]
57. ? [X0] : (~humble(X0) | humble(X0)) => (~humble(sK5) | humble(sK5)) [choice axiom]
58. ((~humble(sK5) | humble(sK5)) | funny(fred) | ~generous(fred)) & ((~funny(fred) & generous(fred)) | ! [X1] : (humble(X1) & ~humble(X1))) [skolemisation 56,57]
64. ! [X0] : (((~patient(X0) & ~wise(X0)) | (~happy(X0) & funny(X0))) & ((happy(X0) | ~funny(X0)) | (patient(X0) | wise(X0)))) [nnf transformation 12]
65. ! [X0] : (((~patient(X0) & ~wise(X0)) | (~happy(X0) & funny(X0))) & (happy(X0) | ~funny(X0) | patient(X0) | wise(X0))) [flattening 64]
68. ! [X0] : (((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) [nnf transformation 35]
93. generous(fred) | ~humble(X1) [cnf transformation 58]
94. generous(fred) | humble(X1) [cnf transformation 58]
95. ~funny(fred) | ~humble(X1) [cnf transformation 58]
96. ~funny(fred) | humble(X1) [cnf transformation 58]
113. ~wise(X0) | funny(X0) [cnf transformation 65]
124. ~generous(X0) | ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 68]
141. strong(fred) [cnf transformation 24]
142. ~strong(X0) | ~generous(X0) | wise(X0) [duplicate literal removal 124]
246. 23 <=> ! [X1] : humble(X1) [avatar definition]
247. humble(X1) <- (23) [avatar component clause 246]
249. 24 <=> funny(fred) [avatar definition]
251. ~funny(fred) <- (~24) [avatar component clause 249]
252. 23 | ~24 [avatar split clause 96,249,246]
254. 25 <=> ! [X1] : ~humble(X1) [avatar definition]
255. ~humble(X1) <- (25) [avatar component clause 254]
256. 25 | ~24 [avatar split clause 95,249,254]
258. 26 <=> generous(fred) [avatar definition]
260. generous(fred) <- (26) [avatar component clause 258]
261. 23 | 26 [avatar split clause 94,258,246]
262. 25 | 26 [avatar split clause 93,258,254]
312. $false <- (23, 25) [subsumption resolution 247,255]
313. ~23 | ~25 [avatar contradiction clause 312]
383. 44 <=> wise(fred) [avatar definition]
384. wise(fred) <- (44) [avatar component clause 383]
397. ~generous(fred) | wise(fred) [resolution 142,141]
400. wise(fred) <- (26) [subsumption resolution 397,260]
413. 44 | ~26 [avatar split clause 400,258,383]
426. funny(fred) <- (44) [resolution 384,113]
427. $false <- (~24, 44) [subsumption resolution 426,251]
428. 24 | ~44 [avatar contradiction clause 427]
429. $false [avatar sat refutation 252,256,261,262,313,413,428]
% SZS output end Proof for 16072136184729716843919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not rich is either kind or not quiet and vice versa.
If paul is not kind or old then john is rich and vice versa.
Everyone who is quiet is either not happy or generous and vice versa.
Everyone who is both not old and not tall is either not calm or curious and vice versa.
If someone is either not quiet or funny then mary is not brave.
Everyone who is both old and not strong is not wise or old and vice versa.
If paul is either wise or not rich then someone is either not tall or kind.
If someone is wise then someone is not generous.
Everyone who is not calm or kind is generous or brave.
If someone is either not brave or not wise then lucy is not curious or not generous.
Everyone who is both not generous and not quiet is not rich or old and vice versa.
Everyone who is not rich or kind is both not calm and not tall.
If lucy is either not brave or wise then someone is patient or not calm and vice versa.
Everyone who is humble or patient is funny or not happy and vice versa.
Everyone who is not strong or generous is wise or calm and vice versa.
If someone is both funny and quiet then someone is brave or not generous and vice versa.
Someone is either not humble or generous.
Someone is both happy and not funny.
Paul is happy or creative.
Someone is both not brave and not quiet.
John is either wise or not curious.
Susan is either funny or not funny.
Someone is humble or quiet.
Someone is quiet or tall. | Lucy is wise. | entailment | (![X]:((brave(X)<~>~rich(X))<=>(kind(X)<~>~quiet(X))))&
(((~kind(paul)|old(paul)))<=>(rich(john)))&
(![X]:(quiet(X)<=>(~happy(X)<~>generous(X))))&
(![X]:((~old(X)&~tall(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((~quiet(X)<~>funny(X))))=>(~brave(mary)))&
(![X]:((old(X)&~strong(X))<=>(~wise(X)|old(X))))&
(((wise(paul)<~>~rich(paul)))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(wise(X)))=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)|kind(X))=>(generous(X)|brave(X))))&
((?[X]:((~brave(X)<~>~wise(X))))=>((~curious(lucy)|~generous(lucy))))&
(![X]:((~generous(X)&~quiet(X))<=>(~rich(X)|old(X))))&
(![X]:((~rich(X)|kind(X))=>(~calm(X)&~tall(X))))&
(((~brave(lucy)<~>wise(lucy)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((humble(X)|patient(X))<=>(funny(X)|~happy(X))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)|calm(X))))&
((?[X]:((funny(X)&quiet(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((happy(X)&~funny(X))))&
((happy(paul)|creative(paul)))&
(?[X]:((~brave(X)&~quiet(X))))&
((wise(john)<~>~curious(john)))&
((funny(susan)<~>~funny(susan)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((quiet(X)|tall(X)))) | wise(lucy) | [
"p0",
"p5",
"p10",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5870112198959586389128480
% SZS output start Proof for 5870112198959586389128480
1. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (kind(X0) <~> ~quiet(X0))) [input p0]
6. ! [X0] : ((~strong(X0) & old(X0)) <=> (old(X0) | ~wise(X0))) [input p5]
11. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (old(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((kind(X0) | ~rich(X0)) => (~tall(X0) & ~calm(X0))) [input p11]
13. (~brave(lucy) <~> wise(lucy)) <=> ? [X0] : (~calm(X0) | patient(X0)) [input p12]
15. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (calm(X0) | wise(X0))) [input p14]
20. ? [X0] : (~quiet(X0) & ~brave(X0)) [input p19]
25. ~wise(lucy) [input hypothesis]
36. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~kind(X0) & rich(X0))) [ennf transformation 12]
37. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 1]
44. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | strong(X0) | ~old(X0))) [flattening 44]
53. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | quiet(X0) | generous(X0))) [flattening 53]
55. (((~wise(lucy) | brave(lucy)) & (wise(lucy) | ~brave(lucy))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | ((~brave(lucy) | ~wise(lucy)) & (wise(lucy) | brave(lucy)))) [nnf transformation 13]
56. (((~wise(lucy) | brave(lucy)) & (wise(lucy) | ~brave(lucy))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X1] : (~calm(X1) | patient(X1)) | ((~brave(lucy) | ~wise(lucy)) & (wise(lucy) | brave(lucy)))) [rectify 55]
57. ? [X1] : (~calm(X1) | patient(X1)) => (~calm(sK2) | patient(sK2)) [choice axiom]
58. (((~wise(lucy) | brave(lucy)) & (wise(lucy) | ~brave(lucy))) | ! [X0] : (calm(X0) & ~patient(X0))) & ((~calm(sK2) | patient(sK2)) | ((~brave(lucy) | ~wise(lucy)) & (wise(lucy) | brave(lucy)))) [skolemisation 56,57]
61. ! [X0] : (((generous(X0) | ~strong(X0)) | (~calm(X0) & ~wise(X0))) & ((calm(X0) | wise(X0)) | (~generous(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((generous(X0) | ~strong(X0) | (~calm(X0) & ~wise(X0))) & (calm(X0) | wise(X0) | (~generous(X0) & strong(X0)))) [flattening 61]
73. ? [X0] : (~quiet(X0) & ~brave(X0)) => (~quiet(sK7) & ~brave(sK7)) [choice axiom]
74. ~quiet(sK7) & ~brave(sK7) [skolemisation 20,73]
86. ~rich(X0) | brave(X0) | kind(X0) | quiet(X0) [cnf transformation 37]
105. wise(X0) | old(X0) [cnf transformation 45]
107. ~strong(X0) | wise(X0) [cnf transformation 45]
122. ~old(X0) | ~quiet(X0) [cnf transformation 54]
123. ~calm(X0) | rich(X0) [cnf transformation 36]
124. ~calm(X0) | ~kind(X0) [cnf transformation 36]
130. wise(lucy) | ~brave(lucy) | calm(X0) [cnf transformation 58]
137. calm(X0) | wise(X0) | strong(X0) [cnf transformation 62]
150. ~brave(sK7) [cnf transformation 74]
151. ~quiet(sK7) [cnf transformation 74]
158. ~wise(lucy) [cnf transformation 25]
231. 17 <=> ! [X0] : calm(X0) [avatar definition]
232. calm(X0) <- (17) [avatar component clause 231]
234. 18 <=> brave(lucy) [avatar definition]
238. 19 <=> wise(lucy) [avatar definition]
240. ~wise(lucy) <- (~19) [avatar component clause 238]
246. 17 | ~18 | 19 [avatar split clause 130,238,234,231]
259. wise(X0) | calm(X0) [subsumption resolution 137,107]
325. ~19 [avatar split clause 158,238]
331. old(lucy) <- (~19) [resolution 105,240]
337. ~quiet(lucy) <- (~19) [resolution 122,331]
340. calm(lucy) <- (~19) [resolution 259,240]
355. ~kind(lucy) <- (~19) [resolution 340,124]
356. rich(lucy) <- (~19) [resolution 340,123]
409. ~kind(X0) <- (17) [resolution 232,124]
410. rich(X1) <- (17) [resolution 232,123]
487. brave(X0) | kind(X0) | quiet(X0) <- (17) [resolution 86,410]
489. brave(lucy) | kind(lucy) | quiet(lucy) <- (~19) [resolution 86,356]
492. quiet(X0) | brave(X0) <- (17) [subsumption resolution 487,409]
525. brave(sK7) <- (17) [resolution 492,151]
529. $false <- (17) [subsumption resolution 525,150]
530. ~17 [avatar contradiction clause 529]
586. brave(lucy) | quiet(lucy) <- (~19) [subsumption resolution 489,355]
587. brave(lucy) <- (~19) [subsumption resolution 586,337]
588. 18 | 19 [avatar split clause 587,238,234]
591. $false [avatar sat refutation 246,325,530,588]
% SZS output end Proof for 5870112198959586389128480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not tall then someone is rich.
Everyone who is not kind or generous is generous and vice versa.
Everyone who is either old or kind is not wise or rich and vice versa.
If john is either humble or not strong then paul is both rich and not funny.
If mary is not generous then someone is either calm or humble.
If alice is either quiet or tall then someone is either wise or kind and vice versa.
If someone is not wise then someone is either not strong or patient and vice versa.
Everyone who is strong is generous and vice versa.
Everyone who is kind is both curious and humble and vice versa.
If someone is brave or not generous then someone is either strong or rich and vice versa.
If someone is both not happy and not generous then someone is not kind or old and vice versa.
Everyone who is both not generous and old is either generous or not wise and vice versa.
If someone is either not patient or not strong then someone is not calm.
Everyone who is tall or funny is old and vice versa.
Everyone who is funny or generous is both not happy and rich and vice versa.
If fred is either not humble or not patient then lucy is both creative and not old.
Alice is both brave and not patient.
Someone is generous or not patient.
Someone is both wise and not brave.
Someone is not strong.
Fred is brave or wise. | Mary is not old. | entailment | ((?[X]:((generous(X)|~tall(X))))=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|generous(X))<=>generous(X)))&
(![X]:((old(X)<~>kind(X))<=>(~wise(X)|rich(X))))&
(((humble(john)<~>~strong(john)))=>((rich(paul)&~funny(paul))))&
((~generous(mary))=>(?[X]:((calm(X)<~>humble(X)))))&
(((quiet(alice)<~>tall(alice)))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(![X]:(strong(X)<=>generous(X)))&
(![X]:(kind(X)<=>(curious(X)&humble(X))))&
((?[X]:((brave(X)|~generous(X))))<=>(?[X]:((strong(X)<~>rich(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>~wise(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:(~calm(X))))&
(![X]:((tall(X)|funny(X))<=>old(X)))&
(![X]:((funny(X)|generous(X))<=>(~happy(X)&rich(X))))&
(((~humble(fred)<~>~patient(fred)))=>((creative(lucy)&~old(lucy))))&
((brave(alice)&~patient(alice)))&
(?[X]:((generous(X)|~patient(X))))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:(~strong(X)))&
((brave(fred)|wise(fred))) | ~old(mary) | [
"p1",
"p2",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4789749397687639350775097
% SZS output start Proof for 4789749397687639350775097
2. ! [X0] : ((generous(X0) | ~kind(X0)) <=> generous(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> kind(X0)) <=> (rich(X0) | ~wise(X0))) [input p2]
11. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X0] : (old(X0) | ~kind(X0)) [input p10]
12. ! [X0] : ((old(X0) & ~generous(X0)) <=> (generous(X0) <~> ~wise(X0))) [input p11]
14. ! [X0] : ((funny(X0) | tall(X0)) <=> old(X0)) [input p13]
15. ! [X0] : ((generous(X0) | funny(X0)) <=> (rich(X0) & ~happy(X0))) [input p14]
22. old(mary) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X1] : (old(X1) | ~kind(X1)) [rectify 11]
37. ! [X0] : (((generous(X0) | ~kind(X0)) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [nnf transformation 2]
38. ! [X0] : ((generous(X0) | ~kind(X0) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [flattening 39]
62. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X1] : (old(X1) | ~kind(X1)) | ! [X0] : (generous(X0) | happy(X0))) [nnf transformation 26]
63. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X2] : (old(X2) | ~kind(X2)) | ! [X3] : (generous(X3) | happy(X3))) [rectify 62]
64. ? [X0] : (~generous(X0) & ~happy(X0)) => (~generous(sK7) & ~happy(sK7)) [choice axiom]
65. ? [X2] : (old(X2) | ~kind(X2)) => (old(sK8) | ~kind(sK8)) [choice axiom]
66. ((~generous(sK7) & ~happy(sK7)) | ! [X1] : (~old(X1) & kind(X1))) & ((old(sK8) | ~kind(sK8)) | ! [X3] : (generous(X3) | happy(X3))) [skolemisation 63,65,64]
67. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (~old(X0) | generous(X0)))) [nnf transformation 12]
68. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ~old(X0) | generous(X0))) [flattening 67]
73. ! [X0] : (((funny(X0) | tall(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [nnf transformation 14]
74. ! [X0] : ((funny(X0) | tall(X0) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [flattening 73]
75. ! [X0] : (((generous(X0) | funny(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 15]
76. ! [X0] : ((generous(X0) | funny(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [flattening 75]
86. kind(X0) | generous(X0) [cnf transformation 38]
90. ~wise(X0) | rich(X0) | old(X0) | ~kind(X0) [cnf transformation 40]
93. ~old(X0) | ~kind(X0) | wise(X0) [cnf transformation 40]
94. ~old(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 40]
126. ~happy(sK7) | ~old(X1) [cnf transformation 66]
128. ~generous(sK7) | ~old(X1) [cnf transformation 66]
129. ~wise(X0) | generous(X0) | ~old(X0) | generous(X0) [cnf transformation 68]
131. ~generous(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 68]
134. wise(X0) | generous(X0) | old(X0) [cnf transformation 68]
137. ~tall(X0) | old(X0) [cnf transformation 74]
138. ~funny(X0) | old(X0) [cnf transformation 74]
139. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 74]
142. ~funny(X0) | rich(X0) [cnf transformation 76]
143. ~generous(X0) | rich(X0) [cnf transformation 76]
144. ~rich(X0) | funny(X0) | generous(X0) | happy(X0) [cnf transformation 76]
154. old(mary) [cnf transformation 22]
155. ~wise(X0) | generous(X0) | ~old(X0) [duplicate literal removal 129]
156. ~wise(X0) | ~generous(X0) [duplicate literal removal 131]
293. 31 <=> ! [X1] : ~old(X1) [avatar definition]
294. ~old(X1) <- (31) [avatar component clause 293]
296. 32 <=> generous(sK7) [avatar definition]
298. ~generous(sK7) <- (~32) [avatar component clause 296]
299. 31 | ~32 [avatar split clause 128,296,293]
305. 34 <=> happy(sK7) [avatar definition]
307. ~happy(sK7) <- (~34) [avatar component clause 305]
308. 31 | ~34 [avatar split clause 126,305,293]
322. ~wise(X0) | ~old(X0) [subsumption resolution 155,156]
462. rich(X0) | old(X0) | ~kind(X0) | generous(X0) | old(X0) [resolution 90,134]
465. rich(X0) | old(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 462]
663. 71 <=> tall(sK7) [avatar definition]
665. tall(sK7) <- (71) [avatar component clause 663]
667. 72 <=> funny(sK7) [avatar definition]
668. ~funny(sK7) <- (~72) [avatar component clause 667]
669. funny(sK7) <- (72) [avatar component clause 667]
690. $false <- (31) [resolution 294,154]
693. ~31 [avatar contradiction clause 690]
836. old(sK7) <- (72) [resolution 669,138]
842. ~kind(sK7) | ~rich(sK7) <- (72) [resolution 836,94]
854. 82 <=> kind(sK7) [avatar definition]
855. kind(sK7) <- (82) [avatar component clause 854]
856. ~kind(sK7) <- (~82) [avatar component clause 854]
859. 83 <=> rich(sK7) [avatar definition]
861. ~rich(sK7) <- (~83) [avatar component clause 859]
862. ~83 | ~82 | ~72 [avatar split clause 842,667,854,859]
873. rich(X0) | old(X0) | generous(X0) [subsumption resolution 465,86]
874. old(X0) | rich(X0) [subsumption resolution 873,143]
892. rich(X0) | tall(X0) | funny(X0) [resolution 874,139]
894. ~kind(X2) | rich(X2) | wise(X2) [resolution 874,93]
897. rich(X0) | tall(X0) [subsumption resolution 892,142]
919. happy(X0) | funny(X0) | generous(X0) | tall(X0) [resolution 897,144]
922. rich(X0) | wise(X0) | generous(X0) [resolution 894,86]
927. wise(X0) | rich(X0) [subsumption resolution 922,143]
935. generous(sK7) <- (~82) [resolution 856,86]
936. $false <- (~32, ~82) [subsumption resolution 935,298]
937. 32 | 82 [avatar contradiction clause 936]
941. rich(X3) | ~old(X3) [resolution 927,322]
949. rich(X3) [subsumption resolution 941,874]
953. funny(sK7) | generous(sK7) | tall(sK7) <- (~34) [resolution 919,307]
955. generous(sK7) | tall(sK7) <- (~34, ~72) [subsumption resolution 953,668]
956. tall(sK7) <- (~32, ~34, ~72) [subsumption resolution 955,298]
959. 71 | 32 | 34 | 72 [avatar split clause 956,667,305,296,663]
960. old(sK7) <- (71) [resolution 665,137]
964. ~kind(sK7) | ~rich(sK7) <- (71) [resolution 960,94]
966. ~rich(sK7) <- (71, 82) [subsumption resolution 964,855]
971. $false <- (71, 82) [subsumption resolution 966,949]
972. ~71 | ~82 [avatar contradiction clause 971]
973. $false <- (~83) [subsumption resolution 861,949]
974. 83 [avatar contradiction clause 973]
975. $false [avatar sat refutation 299,308,693,862,937,959,972,974]
% SZS output end Proof for 4789749397687639350775097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or calm then someone is not wise and vice versa. Everyone who is kind is creative and vice versa. Everyone who is not wise or not rich is both wise and not generous. Everyone who is kind or generous is both rich and tall and vice versa. If fred is both not tall and not brave then someone is either generous or not creative and vice versa. If someone is generous then someone is either not creative or calm and vice versa. If john is either calm or humble then john is either generous or not rich. If someone is not quiet then lucy is either kind or not curious. Everyone who is either not humble or not brave is either not quiet or kind. Everyone who is either not happy or humble is either happy or quiet. Everyone who is not happy or strong is happy and vice versa. If mary is rich then someone is humble and vice versa. If someone is both not funny and not happy then lucy is not generous and vice versa. Everyone who is either curious or quiet is either not quiet or not rich. Everyone who is not generous is both not patient and not creative and vice versa. If john is either humble or not calm then someone is quiet and vice versa. Susan is curious or not humble. Mary is not old. Paul is both humble and wise. Someone is not humble. Someone is either quiet or curious. | Lucy is not calm. | entailment | ((?[X]:((~tall(X)|calm(X))))<=>(?[X]:(~wise(X))))&
(![X]:(kind(X)<=>creative(X)))&
(![X]:((~wise(X)|~rich(X))=>(wise(X)&~generous(X))))&
(![X]:((kind(X)|generous(X))<=>(rich(X)&tall(X))))&
(((~tall(fred)&~brave(fred)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((calm(john)<~>humble(john)))=>((generous(john)<~>~rich(john))))&
((?[X]:(~quiet(X)))=>((kind(lucy)<~>~curious(lucy))))&
(![X]:((~humble(X)<~>~brave(X))=>(~quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>humble(X))=>(happy(X)<~>quiet(X))))&
(![X]:((~happy(X)|strong(X))<=>happy(X)))&
((rich(mary))<=>(?[X]:(humble(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>(~generous(lucy)))&
(![X]:((curious(X)<~>quiet(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~patient(X)&~creative(X))))&
(((humble(john)<~>~calm(john)))<=>(?[X]:(quiet(X))))&
((curious(susan)|~humble(susan)))&
(~old(mary))&
((humble(paul)&wise(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)<~>curious(X)))) | ~calm(lucy) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3988823163928582656228240
% SZS output start Proof for 3988823163928582656228240
1. ? [X0] : (calm(X0) | ~tall(X0)) <=> ? [X0] : ~wise(X0) [input p0]
3. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~generous(X0) & wise(X0))) [input p2]
22. calm(lucy) [input hypothesis]
23. ? [X0] : (calm(X0) | ~tall(X0)) <=> ? [X1] : ~wise(X1) [rectify 1]
26. ! [X0] : ((~generous(X0) & wise(X0)) | (rich(X0) & wise(X0))) [ennf transformation 3]
32. (? [X0] : (calm(X0) | ~tall(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~calm(X0) & tall(X0))) [nnf transformation 23]
33. (? [X0] : (calm(X0) | ~tall(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~calm(X3) & tall(X3))) [rectify 32]
34. ? [X0] : (calm(X0) | ~tall(X0)) => (calm(sK0) | ~tall(sK0)) [choice axiom]
35. ? [X2] : ~wise(X2) => ~wise(sK1) [choice axiom]
36. ((calm(sK0) | ~tall(sK0)) | ! [X1] : wise(X1)) & (~wise(sK1) | ! [X3] : (~calm(X3) & tall(X3))) [skolemisation 33,35,34]
77. ~wise(sK1) | ~calm(X3) [cnf transformation 36]
81. wise(X0) | wise(X0) [cnf transformation 26]
139. calm(lucy) [cnf transformation 22]
146. wise(X0) [duplicate literal removal 81]
148. 1 <=> ! [X1] : wise(X1) [avatar definition]
149. wise(X1) <- (1) [avatar component clause 148]
160. 4 <=> ! [X3] : ~calm(X3) [avatar definition]
161. ~calm(X3) <- (4) [avatar component clause 160]
163. 5 <=> wise(sK1) [avatar definition]
165. ~wise(sK1) <- (~5) [avatar component clause 163]
166. 4 | ~5 [avatar split clause 77,163,160]
171. 1 [avatar split clause 146,148]
302. $false <- (1, ~5) [resolution 165,149]
303. ~1 | 5 [avatar contradiction clause 302]
304. $false <- (4) [resolution 161,139]
305. ~4 [avatar contradiction clause 304]
306. $false [avatar sat refutation 166,171,303,305]
% SZS output end Proof for 3988823163928582656228240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and curious then lucy is both not rich and calm and vice versa. Everyone who is not humble or wise is calm and vice versa. If someone is not strong then susan is not patient or not rich. If alice is both not curious and not humble then someone is either wise or not happy. Everyone who is not generous is either not kind or not happy. If alice is either brave or wise then someone is either not creative or not happy. If someone is both old and not generous then paul is either not creative or not humble and vice versa. If someone is humble or not kind then someone is not curious or not quiet and vice versa. If john is not funny then someone is either not rich or not funny. If john is rich then someone is either happy or old. Everyone who is curious is generous and vice versa. If mary is patient then someone is creative or curious and vice versa. If someone is not kind or tall then john is not old and vice versa. If someone is not rich then alice is calm or generous and vice versa. Everyone who is either humble or not tall is not kind and vice versa. If someone is not curious then someone is both not old and not happy. Someone is either funny or curious. Someone is either not patient or old. Someone is happy or not funny. Someone is funny or not old. Susan is both old and creative. Susan is either not creative or strong. Someone is strong or quiet. Paul is not generous or not happy. | Mary is not patient. | contradiction | ((?[X]:((old(X)&curious(X))))<=>((~rich(lucy)&calm(lucy))))&
(![X]:((~humble(X)|wise(X))<=>calm(X)))&
((?[X]:(~strong(X)))=>((~patient(susan)|~rich(susan))))&
(((~curious(alice)&~humble(alice)))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~happy(X))))&
(((brave(alice)<~>wise(alice)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((old(X)&~generous(X))))<=>((~creative(paul)<~>~humble(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~curious(X)|~quiet(X)))))&
((~funny(john))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((rich(john))=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:(curious(X)<=>generous(X)))&
((patient(mary))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((~kind(X)|tall(X))))<=>(~old(john)))&
((?[X]:(~rich(X)))<=>((calm(alice)|generous(alice))))&
(![X]:((humble(X)<~>~tall(X))<=>~kind(X)))&
((?[X]:(~curious(X)))=>(?[X]:((~old(X)&~happy(X)))))&
(?[X]:((funny(X)<~>curious(X))))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((funny(X)|~old(X))))&
((old(susan)&creative(susan)))&
((~creative(susan)<~>strong(susan)))&
(?[X]:((strong(X)|quiet(X))))&
((~generous(paul)|~happy(paul))) | ~patient(mary) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1575983896401404136485061
% SZS output start Proof for 1575983896401404136485061
12. patient(mary) <=> ? [X0] : (curious(X0) | creative(X0)) [input p11]
21. creative(susan) & old(susan) [input p20]
25. ~patient(mary) [input hypothesis]
67. (patient(mary) | ! [X0] : (~curious(X0) & ~creative(X0))) & (? [X0] : (curious(X0) | creative(X0)) | ~patient(mary)) [nnf transformation 12]
68. (patient(mary) | ! [X0] : (~curious(X0) & ~creative(X0))) & (? [X1] : (curious(X1) | creative(X1)) | ~patient(mary)) [rectify 67]
69. ? [X1] : (curious(X1) | creative(X1)) => (curious(sK8) | creative(sK8)) [choice axiom]
70. (patient(mary) | ! [X0] : (~curious(X0) & ~creative(X0))) & ((curious(sK8) | creative(sK8)) | ~patient(mary)) [skolemisation 68,69]
130. patient(mary) | ~creative(X0) [cnf transformation 70]
151. creative(susan) [cnf transformation 21]
156. ~patient(mary) [cnf transformation 25]
319. 37 <=> patient(mary) [avatar definition]
324. 38 <=> ! [X0] : ~creative(X0) [avatar definition]
325. ~creative(X0) <- (38) [avatar component clause 324]
326. 38 | 37 [avatar split clause 130,319,324]
439. ~37 [avatar split clause 156,319]
440. $false <- (38) [resolution 325,151]
441. ~38 [avatar contradiction clause 440]
442. $false [avatar sat refutation 326,439,441]
% SZS output end Proof for 1575983896401404136485061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or strong then someone is both not tall and kind and vice versa. Everyone who is patient is both not generous and humble and vice versa. Everyone who is humble is either not strong or not humble and vice versa. Everyone who is both not generous and not strong is either not creative or not funny and vice versa. If someone is creative then alice is wise and vice versa. If someone is creative or not wise then john is rich and vice versa. If paul is either not rich or not old then someone is either generous or not wise and vice versa. If lucy is not happy or kind then john is either curious or not curious. Everyone who is either quiet or kind is calm. If mary is either humble or not rich then someone is both quiet and not rich. Everyone who is funny is not patient or not tall and vice versa. If someone is either kind or not old then alice is old. Everyone who is both not brave and calm is both not strong and wise and vice versa. If susan is either funny or not generous then someone is both not curious and not strong. If someone is not calm then susan is not patient or not calm and vice versa. Everyone who is not wise is not patient. Alice is not tall or happy. Mary is not calm. Someone is not calm. Someone is either strong or creative. Someone is not humble or not tall. Someone is either patient or creative. Someone is not tall. Fred is both not creative and not generous. | Alice is old. | neutral | ((?[X]:((~curious(X)|strong(X))))<=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:(patient(X)<=>(~generous(X)&humble(X))))&
(![X]:(humble(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((~generous(X)&~strong(X))<=>(~creative(X)<~>~funny(X))))&
((?[X]:(creative(X)))<=>(wise(alice)))&
((?[X]:((creative(X)|~wise(X))))<=>(rich(john)))&
(((~rich(paul)<~>~old(paul)))<=>(?[X]:((generous(X)<~>~wise(X)))))&
(((~happy(lucy)|kind(lucy)))=>((curious(john)<~>~curious(john))))&
(![X]:((quiet(X)<~>kind(X))=>calm(X)))&
(((humble(mary)<~>~rich(mary)))=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:(funny(X)<=>(~patient(X)|~tall(X))))&
((?[X]:((kind(X)<~>~old(X))))=>(old(alice)))&
(![X]:((~brave(X)&calm(X))<=>(~strong(X)&wise(X))))&
(((funny(susan)<~>~generous(susan)))=>(?[X]:((~curious(X)&~strong(X)))))&
((?[X]:(~calm(X)))<=>((~patient(susan)|~calm(susan))))&
(![X]:(~wise(X)=>~patient(X)))&
((~tall(alice)|happy(alice)))&
(~calm(mary))&
(?[X]:(~calm(X)))&
(?[X]:((strong(X)<~>creative(X))))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:(~tall(X)))&
((~creative(fred)&~generous(fred))) | old(alice) | [] | null | 0 |
Everyone who is not happy is not curious and vice versa.
Everyone who is both funny and strong is either patient or generous and vice versa.
Everyone who is both strong and not kind is either brave or kind.
If paul is both not funny and kind then john is either strong or quiet.
If someone is either rich or generous then someone is rich and vice versa.
Everyone who is strong is both not strong and not generous.
Everyone who is either not tall or old is calm.
Everyone who is both rich and not patient is not funny.
Everyone who is both kind and not curious is not funny and vice versa.
Everyone who is patient is happy or not patient.
Everyone who is both not curious and creative is either creative or not patient and vice versa.
If alice is not curious or humble then paul is not quiet and vice versa.
Everyone who is not funny or curious is not wise or not kind.
Everyone who is both curious and not funny is either not quiet or creative.
If fred is not humble then someone is humble or not kind and vice versa.
Everyone who is not generous is both old and tall and vice versa.
Someone is generous or not wise.
Mary is rich.
Someone is humble.
John is curious or not old.
Mary is not rich or rich.
Someone is not humble.
Alice is funny or not strong. | Fred is not calm. | neutral | (![X]:(~happy(X)<=>~curious(X)))&
(![X]:((funny(X)&strong(X))<=>(patient(X)<~>generous(X))))&
(![X]:((strong(X)&~kind(X))=>(brave(X)<~>kind(X))))&
(((~funny(paul)&kind(paul)))=>((strong(john)<~>quiet(john))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:(rich(X))))&
(![X]:(strong(X)=>(~strong(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>calm(X)))&
(![X]:((rich(X)&~patient(X))=>~funny(X)))&
(![X]:((kind(X)&~curious(X))<=>~funny(X)))&
(![X]:(patient(X)=>(happy(X)|~patient(X))))&
(![X]:((~curious(X)&creative(X))<=>(creative(X)<~>~patient(X))))&
(((~curious(alice)|humble(alice)))<=>(~quiet(paul)))&
(![X]:((~funny(X)|curious(X))=>(~wise(X)|~kind(X))))&
(![X]:((curious(X)&~funny(X))=>(~quiet(X)<~>creative(X))))&
((~humble(fred))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:(~generous(X)<=>(old(X)&tall(X))))&
(?[X]:((generous(X)|~wise(X))))&
(rich(mary))&
(?[X]:(humble(X)))&
((curious(john)|~old(john)))&
((~rich(mary)|rich(mary)))&
(?[X]:(~humble(X)))&
((funny(alice)|~strong(alice))) | ~calm(fred) | [] | null | 0 |
Everyone who is both not happy and not rich is not happy or not patient.
If mary is not happy then someone is funny and vice versa.
Everyone who is not kind is either not tall or not funny.
If susan is humble then someone is either not curious or curious.
Everyone who is not wise is not patient and vice versa.
If someone is either not patient or funny then someone is either not rich or funny.
Everyone who is not strong or old is both calm and not happy.
If paul is not rich then lucy is both not humble and rich.
If someone is both not happy and not brave then john is either not kind or happy and vice versa.
If someone is both strong and happy then lucy is either not curious or not brave.
Everyone who is not strong is both creative and not tall.
Everyone who is either kind or strong is either not humble or tall.
If someone is generous or quiet then lucy is calm and vice versa.
If susan is not calm or not humble then someone is both curious and kind.
If someone is rich then susan is either wise or not patient.
Everyone who is rich or not quiet is rich or not patient.
Someone is tall.
Someone is both rich and not tall.
Someone is either not curious or curious.
Someone is tall or not happy.
Alice is not old.
Susan is not quiet or not calm.
Someone is patient or not strong.
Alice is both not strong and not funny. | Alice is not happy. | entailment | (![X]:((~happy(X)&~rich(X))=>(~happy(X)|~patient(X))))&
((~happy(mary))<=>(?[X]:(funny(X))))&
(![X]:(~kind(X)=>(~tall(X)<~>~funny(X))))&
((humble(susan))=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:(~wise(X)<=>~patient(X)))&
((?[X]:((~patient(X)<~>funny(X))))=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((~strong(X)|old(X))=>(calm(X)&~happy(X))))&
((~rich(paul))=>((~humble(lucy)&rich(lucy))))&
((?[X]:((~happy(X)&~brave(X))))<=>((~kind(john)<~>happy(john))))&
((?[X]:((strong(X)&happy(X))))=>((~curious(lucy)<~>~brave(lucy))))&
(![X]:(~strong(X)=>(creative(X)&~tall(X))))&
(![X]:((kind(X)<~>strong(X))=>(~humble(X)<~>tall(X))))&
((?[X]:((generous(X)|quiet(X))))<=>(calm(lucy)))&
(((~calm(susan)|~humble(susan)))=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:(rich(X)))=>((wise(susan)<~>~patient(susan))))&
(![X]:((rich(X)|~quiet(X))=>(rich(X)|~patient(X))))&
(?[X]:(tall(X)))&
(?[X]:((rich(X)&~tall(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
(?[X]:((tall(X)|~happy(X))))&
(~old(alice))&
((~quiet(susan)|~calm(susan)))&
(?[X]:((patient(X)|~strong(X))))&
((~strong(alice)&~funny(alice))) | ~happy(alice) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8368269805962137209770635
% SZS output start Proof for 8368269805962137209770635
7. ! [X0] : ((old(X0) | ~strong(X0)) => (~happy(X0) & calm(X0))) [input p6]
24. ~funny(alice) & ~strong(alice) [input p23]
25. happy(alice) [input hypothesis]
29. ! [X0] : (~strong(X0) => (~happy(X0) & calm(X0))) [pure predicate removal 7]
35. ! [X0] : ((~happy(X0) & calm(X0)) | strong(X0)) [ennf transformation 29]
95. ~happy(X0) | strong(X0) [cnf transformation 35]
130. ~strong(alice) [cnf transformation 24]
132. happy(alice) [cnf transformation 25]
286. strong(alice) [resolution 95,132]
287. $false [subsumption resolution 286,130]
% SZS output end Proof for 8368269805962137209770635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not happy is not generous or humble.
Everyone who is not happy is not curious or brave and vice versa.
If someone is either calm or generous then alice is both tall and not humble.
Everyone who is generous or old is both not calm and old and vice versa.
If someone is both humble and funny then someone is not generous.
Everyone who is either quiet or creative is not rich or brave and vice versa.
Everyone who is not calm is tall.
If someone is kind then susan is either quiet or rich and vice versa.
Everyone who is not creative or generous is either not old or not patient and vice versa.
Everyone who is rich is not wise or not happy and vice versa.
If susan is kind or not happy then someone is calm or patient and vice versa.
If fred is either old or humble then someone is generous or strong and vice versa.
If susan is either old or quiet then someone is rich.
Everyone who is both not old and humble is calm and vice versa.
Everyone who is either wise or not curious is both tall and not curious and vice versa.
If susan is either not rich or strong then someone is both calm and not humble and vice versa.
Fred is either creative or generous.
Someone is not quiet.
Paul is creative.
Someone is either strong or not humble.
Fred is both brave and kind.
Someone is not creative.
Someone is either not strong or not humble.
John is either funny or not humble. | Fred is generous. | contradiction | (![X]:((~curious(X)|~happy(X))=>(~generous(X)|humble(X))))&
(![X]:(~happy(X)<=>(~curious(X)|brave(X))))&
((?[X]:((calm(X)<~>generous(X))))=>((tall(alice)&~humble(alice))))&
(![X]:((generous(X)|old(X))<=>(~calm(X)&old(X))))&
((?[X]:((humble(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(~rich(X)|brave(X))))&
(![X]:(~calm(X)=>tall(X)))&
((?[X]:(kind(X)))<=>((quiet(susan)<~>rich(susan))))&
(![X]:((~creative(X)|generous(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(rich(X)<=>(~wise(X)|~happy(X))))&
(((kind(susan)|~happy(susan)))<=>(?[X]:((calm(X)|patient(X)))))&
(((old(fred)<~>humble(fred)))<=>(?[X]:((generous(X)|strong(X)))))&
(((old(susan)<~>quiet(susan)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)&humble(X))<=>calm(X)))&
(![X]:((wise(X)<~>~curious(X))<=>(tall(X)&~curious(X))))&
(((~rich(susan)<~>strong(susan)))<=>(?[X]:((calm(X)&~humble(X)))))&
((creative(fred)<~>generous(fred)))&
(?[X]:(~quiet(X)))&
(creative(paul))&
(?[X]:((strong(X)<~>~humble(X))))&
((brave(fred)&kind(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~strong(X)<~>~humble(X))))&
((funny(john)<~>~humble(john))) | generous(fred) | [
"p0",
"p1",
"p3",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 228022308710627678593797
% SZS output start Proof for 228022308710627678593797
1. ! [X0] : ((~happy(X0) | ~curious(X0)) => (humble(X0) | ~generous(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (brave(X0) | ~curious(X0))) [input p1]
4. ! [X0] : ((old(X0) | generous(X0)) <=> (old(X0) & ~calm(X0))) [input p3]
12. (old(fred) <~> humble(fred)) <=> ? [X0] : (strong(X0) | generous(X0)) [input p11]
21. kind(fred) & brave(fred) [input p20]
25. generous(fred) [input hypothesis]
27. ! [X0] : ((humble(X0) | ~generous(X0)) | (happy(X0) & curious(X0))) [ennf transformation 1]
28. ! [X0] : (humble(X0) | ~generous(X0) | (happy(X0) & curious(X0))) [flattening 27]
33. ! [X0] : ((~happy(X0) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | happy(X0))) [nnf transformation 2]
34. ! [X0] : ((~happy(X0) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | happy(X0))) [flattening 33]
36. ! [X0] : (((old(X0) | generous(X0)) | (~old(X0) | calm(X0))) & ((old(X0) & ~calm(X0)) | (~old(X0) & ~generous(X0)))) [nnf transformation 4]
37. ! [X0] : ((old(X0) | generous(X0) | ~old(X0) | calm(X0)) & ((old(X0) & ~calm(X0)) | (~old(X0) & ~generous(X0)))) [flattening 36]
56. (((~humble(fred) | ~old(fred)) & (humble(fred) | old(fred))) | ! [X0] : (~strong(X0) & ~generous(X0))) & (? [X0] : (strong(X0) | generous(X0)) | ((old(fred) | ~humble(fred)) & (humble(fred) | ~old(fred)))) [nnf transformation 12]
57. (((~humble(fred) | ~old(fred)) & (humble(fred) | old(fred))) | ! [X0] : (~strong(X0) & ~generous(X0))) & (? [X1] : (strong(X1) | generous(X1)) | ((old(fred) | ~humble(fred)) & (humble(fred) | ~old(fred)))) [rectify 56]
58. ? [X1] : (strong(X1) | generous(X1)) => (strong(sK3) | generous(sK3)) [choice axiom]
59. (((~humble(fred) | ~old(fred)) & (humble(fred) | old(fred))) | ! [X0] : (~strong(X0) & ~generous(X0))) & ((strong(sK3) | generous(sK3)) | ((old(fred) | ~humble(fred)) & (humble(fred) | ~old(fred)))) [skolemisation 57,58]
84. ~generous(X0) | humble(X0) | happy(X0) [cnf transformation 28]
87. ~brave(X0) | ~happy(X0) [cnf transformation 34]
94. ~generous(X0) | old(X0) [cnf transformation 37]
126. ~humble(fred) | ~old(fred) | ~generous(X0) [cnf transformation 59]
151. brave(fred) [cnf transformation 21]
158. generous(fred) [cnf transformation 25]
238. 18 <=> old(fred) [avatar definition]
242. 19 <=> humble(fred) [avatar definition]
247. 20 <=> ! [X0] : ~generous(X0) [avatar definition]
248. ~generous(X0) <- (20) [avatar component clause 247]
249. 20 | ~18 | ~19 [avatar split clause 126,242,238,247]
293. 29 <=> generous(fred) [avatar definition]
294. generous(fred) <- (29) [avatar component clause 293]
328. 29 [avatar split clause 158,293]
329. $false <- (20, 29) [resolution 294,248]
330. ~20 | ~29 [avatar contradiction clause 329]
334. ~happy(fred) [resolution 87,151]
336. old(fred) <- (29) [resolution 94,294]
352. humble(fred) | happy(fred) <- (29) [resolution 84,294]
362. 18 | ~29 [avatar split clause 336,293,238]
363. humble(fred) <- (29) [subsumption resolution 352,334]
364. 19 | ~29 [avatar split clause 363,293,242]
370. $false [avatar sat refutation 249,328,330,362,364]
% SZS output end Proof for 228022308710627678593797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is calm or tall is either not old or not brave and vice versa. Everyone who is patient is both not curious and not rich and vice versa. Everyone who is either not curious or curious is either old or not rich and vice versa. If someone is calm or not brave then someone is not rich or patient. Everyone who is old is not patient and vice versa. Everyone who is not humble or not curious is either not brave or wise. Everyone who is not patient is either not kind or funny and vice versa. If lucy is not quiet or curious then susan is creative. If john is both tall and old then someone is not curious and vice versa. Everyone who is either not kind or not calm is both not patient and rich. Everyone who is not wise or calm is both old and patient. If mary is either not curious or kind then lucy is old. If fred is either not funny or funny then susan is not curious or not rich and vice versa. Everyone who is both wise and calm is both not creative and tall. Everyone who is either not happy or brave is not curious and vice versa. If someone is both funny and brave then fred is curious or not rich. John is not strong or funny. Alice is either not quiet or not brave. Someone is both not curious and not strong. Someone is not old or humble. Someone is either creative or not tall. John is either not patient or not old. Someone is both funny and wise. Mary is not wise or quiet. | John is not patient. | entailment | (![X]:((calm(X)|tall(X))<=>(~old(X)<~>~brave(X))))&
(![X]:(patient(X)<=>(~curious(X)&~rich(X))))&
(![X]:((~curious(X)<~>curious(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((~humble(X)|~curious(X))=>(~brave(X)<~>wise(X))))&
(![X]:(~patient(X)<=>(~kind(X)<~>funny(X))))&
(((~quiet(lucy)|curious(lucy)))=>(creative(susan)))&
(((tall(john)&old(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)<~>~calm(X))=>(~patient(X)&rich(X))))&
(![X]:((~wise(X)|calm(X))=>(old(X)&patient(X))))&
(((~curious(mary)<~>kind(mary)))=>(old(lucy)))&
(((~funny(fred)<~>funny(fred)))<=>((~curious(susan)|~rich(susan))))&
(![X]:((wise(X)&calm(X))=>(~creative(X)&tall(X))))&
(![X]:((~happy(X)<~>brave(X))<=>~curious(X)))&
((?[X]:((funny(X)&brave(X))))=>((curious(fred)|~rich(fred))))&
((~strong(john)|funny(john)))&
((~quiet(alice)<~>~brave(alice)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
((~patient(john)<~>~old(john)))&
(?[X]:((funny(X)&wise(X))))&
((~wise(mary)|quiet(mary))) | ~patient(john) | [
"p4",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 408987412729662042943282
% SZS output start Proof for 408987412729662042943282
5. ! [X0] : (old(X0) <=> ~patient(X0)) [input p4]
9. (old(john) & tall(john)) <=> ? [X0] : ~curious(X0) [input p8]
19. ? [X0] : (~strong(X0) & ~curious(X0)) [input p18]
25. patient(john) [input hypothesis]
27. ? [X0] : ~curious(X0) [pure predicate removal 19]
49. ! [X0] : ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))) [nnf transformation 5]
52. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~old(john) | ~tall(john))) [nnf transformation 9]
53. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~old(john) | ~tall(john)) [flattening 52]
54. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~old(john) | ~tall(john)) [rectify 53]
55. ? [X1] : ~curious(X1) => ~curious(sK1) [choice axiom]
56. ((old(john) & tall(john)) | ! [X0] : curious(X0)) & (~curious(sK1) | ~old(john) | ~tall(john)) [skolemisation 54,55]
63. ? [X0] : ~curious(X0) => ~curious(sK2) [choice axiom]
64. ~curious(sK2) [skolemisation 27,63]
90. ~patient(X0) | ~old(X0) [cnf transformation 49]
102. old(john) | curious(X0) [cnf transformation 56]
128. ~curious(sK2) [cnf transformation 64]
136. patient(john) [cnf transformation 25]
174. 7 <=> ! [X0] : curious(X0) [avatar definition]
175. curious(X0) <- (7) [avatar component clause 174]
177. 8 <=> old(john) [avatar definition]
179. old(john) <- (8) [avatar component clause 177]
180. 7 | 8 [avatar split clause 102,177,174]
260. $false <- (7) [resolution 175,128]
261. ~7 [avatar contradiction clause 260]
262. ~old(john) [resolution 90,136]
263. $false <- (8) [subsumption resolution 262,179]
264. ~8 [avatar contradiction clause 263]
265. $false [avatar sat refutation 180,261,264]
% SZS output end Proof for 408987412729662042943282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not patient is not brave or not patient. Everyone who is humble or creative is not curious or patient. Everyone who is both brave and strong is either curious or creative and vice versa. Everyone who is both kind and brave is either not generous or quiet and vice versa. Everyone who is rich is tall or generous and vice versa. If someone is not kind or not tall then someone is either generous or curious. If lucy is both curious and old then someone is not creative and vice versa. Everyone who is not happy is not old. If someone is either quiet or calm then someone is not generous or not kind and vice versa. Everyone who is creative is not quiet and vice versa. Everyone who is not patient or generous is not kind. If someone is either not rich or funny then someone is both not old and not quiet and vice versa. If mary is either not calm or happy then paul is calm. Everyone who is either not wise or not old is both patient and rich and vice versa. Everyone who is generous or not creative is either not curious or not brave and vice versa. Everyone who is wise is not calm or funny and vice versa. Lucy is both kind and not wise. Mary is kind or quiet. Someone is either not curious or rich. Mary is not funny or not wise. Mary is either not humble or humble. Someone is either rich or humble. Someone is both not brave and patient. John is not kind or not rich. | Lucy is not strong. | entailment | (![X]:((~old(X)<~>~patient(X))=>(~brave(X)|~patient(X))))&
(![X]:((humble(X)|creative(X))=>(~curious(X)|patient(X))))&
(![X]:((brave(X)&strong(X))<=>(curious(X)<~>creative(X))))&
(![X]:((kind(X)&brave(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|generous(X))))&
((?[X]:((~kind(X)|~tall(X))))=>(?[X]:((generous(X)<~>curious(X)))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)=>~old(X)))&
((?[X]:((quiet(X)<~>calm(X))))<=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:(creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
(((~calm(mary)<~>happy(mary)))=>(calm(paul)))&
(![X]:((~wise(X)<~>~old(X))<=>(patient(X)&rich(X))))&
(![X]:((generous(X)|~creative(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~calm(X)|funny(X))))&
((kind(lucy)&~wise(lucy)))&
((kind(mary)|quiet(mary)))&
(?[X]:((~curious(X)<~>rich(X))))&
((~funny(mary)|~wise(mary)))&
((~humble(mary)<~>humble(mary)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((~brave(X)&patient(X))))&
((~kind(john)|~rich(john))) | ~strong(lucy) | [
"p2",
"p3",
"p6",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2562973284638662997314528
% SZS output start Proof for 2562973284638662997314528
3. ! [X0] : ((strong(X0) & brave(X0)) <=> (curious(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((brave(X0) & kind(X0)) <=> (~generous(X0) <~> quiet(X0))) [input p3]
7. (old(lucy) & curious(lucy)) <=> ? [X0] : ~creative(X0) [input p6]
10. ! [X0] : (creative(X0) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((generous(X0) | ~patient(X0)) => ~kind(X0)) [input p10]
15. ! [X0] : ((~creative(X0) | generous(X0)) <=> (~curious(X0) <~> ~brave(X0))) [input p14]
17. ~wise(lucy) & kind(lucy) [input p16]
25. strong(lucy) [input hypothesis]
35. ! [X0] : (~kind(X0) | (~generous(X0) & patient(X0))) [ennf transformation 11]
38. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~strong(X0) | ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~strong(X0) | ~brave(X0))) [flattening 38]
40. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (~brave(X0) | ~kind(X0)))) [nnf transformation 4]
41. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | ~brave(X0) | ~kind(X0))) [flattening 40]
48. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~old(lucy) | ~curious(lucy))) [nnf transformation 7]
49. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~old(lucy) | ~curious(lucy)) [flattening 48]
50. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~old(lucy) | ~curious(lucy)) [rectify 49]
51. ? [X1] : ~creative(X1) => ~creative(sK1) [choice axiom]
52. ((old(lucy) & curious(lucy)) | ! [X0] : creative(X0)) & (~creative(sK1) | ~old(lucy) | ~curious(lucy)) [skolemisation 50,51]
58. ! [X0] : ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0))) [nnf transformation 10]
67. ! [X0] : (((~creative(X0) | generous(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [nnf transformation 15]
68. ! [X0] : ((~creative(X0) | generous(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [flattening 67]
85. ~strong(X0) | ~curious(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
86. ~curious(X0) | creative(X0) | brave(X0) [cnf transformation 39]
87. ~creative(X0) | curious(X0) | brave(X0) [cnf transformation 39]
91. ~quiet(X0) | generous(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 41]
93. ~quiet(X0) | ~generous(X0) | kind(X0) [cnf transformation 41]
94. quiet(X0) | brave(X0) | generous(X0) [cnf transformation 41]
104. curious(lucy) | creative(X0) [cnf transformation 52]
113. ~quiet(X0) | ~creative(X0) [cnf transformation 58]
114. quiet(X0) | creative(X0) [cnf transformation 58]
116. ~generous(X0) | ~kind(X0) [cnf transformation 35]
134. brave(X0) | curious(X0) | creative(X0) [cnf transformation 68]
135. ~creative(X0) | generous(X0) | ~brave(X0) | curious(X0) [cnf transformation 68]
140. kind(lucy) [cnf transformation 17]
153. strong(lucy) [cnf transformation 25]
174. 5 <=> ! [X0] : creative(X0) [avatar definition]
175. creative(X0) <- (5) [avatar component clause 174]
182. 7 <=> curious(lucy) [avatar definition]
183. ~curious(lucy) <- (~7) [avatar component clause 182]
185. 5 | 7 [avatar split clause 104,182,174]
268. ~creative(X0) | generous(X0) | curious(X0) [subsumption resolution 135,87]
269. creative(X0) | brave(X0) [subsumption resolution 134,86]
367. ~generous(X2) | kind(X2) | creative(X2) [resolution 93,114]
372. ~generous(X2) | creative(X2) [subsumption resolution 367,116]
375. brave(X1) | generous(X1) | ~creative(X1) [resolution 94,113]
376. generous(X1) | brave(X1) [subsumption resolution 375,269]
435. 44 <=> generous(lucy) [avatar definition]
436. ~generous(lucy) <- (~44) [avatar component clause 435]
437. generous(lucy) <- (44) [avatar component clause 435]
542. ~curious(lucy) | ~creative(lucy) | ~brave(lucy) [resolution 85,153]
550. generous(X3) | ~brave(X3) | ~kind(X3) | creative(X3) [resolution 91,114]
557. generous(X3) | ~kind(X3) | creative(X3) [subsumption resolution 550,269]
558. ~kind(X3) | creative(X3) [subsumption resolution 557,372]
588. ~kind(lucy) <- (44) [resolution 437,116]
590. $false <- (44) [subsumption resolution 588,140]
591. ~44 [avatar contradiction clause 590]
716. creative(lucy) [resolution 558,140]
815. brave(lucy) <- (~44) [resolution 436,376]
818. ~curious(lucy) | ~brave(lucy) [subsumption resolution 542,716]
819. ~curious(lucy) <- (~44) [subsumption resolution 818,815]
820. ~7 | 44 [avatar split clause 819,435,182]
823. generous(X2) | curious(X2) <- (5) [resolution 175,268]
884. curious(lucy) <- (5, ~44) [resolution 823,436]
891. $false <- (5, ~7, ~44) [subsumption resolution 884,183]
892. ~5 | 7 | 44 [avatar contradiction clause 891]
894. $false [avatar sat refutation 185,591,820,892]
% SZS output end Proof for 2562973284638662997314528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is generous then lucy is not happy or quiet.
Everyone who is creative or patient is either old or generous and vice versa.
Everyone who is either not old or not generous is either not quiet or curious and vice versa.
Everyone who is patient or brave is not happy or not rich.
If alice is not strong or not curious then lucy is patient and vice versa.
If someone is either creative or not wise then someone is kind.
Everyone who is not wise is patient.
If mary is humble then someone is both rich and curious.
If lucy is not tall then alice is curious and vice versa.
Everyone who is happy or brave is either not quiet or not kind.
Everyone who is old is not happy or brave.
Everyone who is happy is either brave or not kind.
Everyone who is generous or kind is both calm and tall.
Everyone who is calm is both patient and tall and vice versa.
Everyone who is not creative or not patient is kind.
Everyone who is quiet or not creative is rich or not strong.
Susan is strong or generous.
Someone is patient or not funny.
Someone is both creative and not strong.
Mary is rich or curious.
John is either humble or tall.
Someone is both not old and not strong.
Someone is not kind.
Fred is either not generous or not wise. | Mary is humble. | neutral | ((generous(mary))=>((~happy(lucy)|quiet(lucy))))&
(![X]:((creative(X)|patient(X))<=>(old(X)<~>generous(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((patient(X)|brave(X))=>(~happy(X)|~rich(X))))&
(((~strong(alice)|~curious(alice)))<=>(patient(lucy)))&
((?[X]:((creative(X)<~>~wise(X))))=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>patient(X)))&
((humble(mary))=>(?[X]:((rich(X)&curious(X)))))&
((~tall(lucy))<=>(curious(alice)))&
(![X]:((happy(X)|brave(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(old(X)=>(~happy(X)|brave(X))))&
(![X]:(happy(X)=>(brave(X)<~>~kind(X))))&
(![X]:((generous(X)|kind(X))=>(calm(X)&tall(X))))&
(![X]:(calm(X)<=>(patient(X)&tall(X))))&
(![X]:((~creative(X)|~patient(X))=>kind(X)))&
(![X]:((quiet(X)|~creative(X))=>(rich(X)|~strong(X))))&
((strong(susan)|generous(susan)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((creative(X)&~strong(X))))&
((rich(mary)|curious(mary)))&
((humble(john)<~>tall(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>~wise(fred))) | humble(mary) | [] | null | 0 |
Everyone who is both strong and not quiet is either not old or patient and vice versa. If susan is quiet then alice is both not quiet and not strong and vice versa. Everyone who is not creative or not quiet is kind or not quiet and vice versa. If fred is happy then someone is happy and vice versa. Everyone who is both not patient and creative is both calm and not old. If mary is humble then lucy is patient or rich and vice versa. If someone is either not old or not kind then someone is funny and vice versa. If someone is not old or not funny then mary is both kind and rich and vice versa. Everyone who is either not brave or old is not wise or quiet and vice versa. Everyone who is either generous or kind is both not rich and not brave. Everyone who is both not calm and creative is not funny. If someone is humble or tall then someone is creative. Everyone who is not patient is either not quiet or creative and vice versa. If alice is tall or wise then susan is creative or not strong. Everyone who is both tall and not strong is strong and vice versa. If john is both not old and calm then someone is either not curious or not old. Someone is either tall or not generous. Susan is either patient or rich. Susan is both not kind and not patient. Paul is both not brave and not quiet. Alice is both generous and not curious. Mary is not old. | Susan is funny. | neutral | (![X]:((strong(X)&~quiet(X))<=>(~old(X)<~>patient(X))))&
((quiet(susan))<=>((~quiet(alice)&~strong(alice))))&
(![X]:((~creative(X)|~quiet(X))<=>(kind(X)|~quiet(X))))&
((happy(fred))<=>(?[X]:(happy(X))))&
(![X]:((~patient(X)&creative(X))=>(calm(X)&~old(X))))&
((humble(mary))<=>((patient(lucy)|rich(lucy))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~old(X)|~funny(X))))<=>((kind(mary)&rich(mary))))&
(![X]:((~brave(X)<~>old(X))<=>(~wise(X)|quiet(X))))&
(![X]:((generous(X)<~>kind(X))=>(~rich(X)&~brave(X))))&
(![X]:((~calm(X)&creative(X))=>~funny(X)))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)<=>(~quiet(X)<~>creative(X))))&
(((tall(alice)|wise(alice)))=>((creative(susan)|~strong(susan))))&
(![X]:((tall(X)&~strong(X))<=>strong(X)))&
(((~old(john)&calm(john)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(?[X]:((tall(X)<~>~generous(X))))&
((patient(susan)<~>rich(susan)))&
((~kind(susan)&~patient(susan)))&
((~brave(paul)&~quiet(paul)))&
((generous(alice)&~curious(alice)))&
(~old(mary)) | funny(susan) | [] | null | 0 |
Everyone who is calm or not generous is either not humble or not patient.
If paul is either old or wise then someone is either not patient or not creative and vice versa.
If someone is tall or not calm then someone is either creative or not curious.
Everyone who is not wise is both kind and not tall.
If someone is either not generous or not curious then someone is either not funny or not wise and vice versa.
If fred is either not kind or not humble then someone is both curious and patient.
If someone is both not generous and not rich then someone is either not generous or not strong.
Everyone who is old or brave is both strong and not old and vice versa.
If mary is both funny and not brave then someone is tall.
Everyone who is both tall and not funny is rich or not rich and vice versa.
Everyone who is either not kind or creative is either not patient or not creative and vice versa.
Everyone who is both quiet and rich is both not creative and rich and vice versa.
Everyone who is either not happy or humble is not humble.
If alice is either not wise or calm then someone is both wise and patient and vice versa.
Everyone who is either calm or rich is either curious or not quiet.
Everyone who is strong or humble is either wise or not creative and vice versa.
Someone is not quiet or creative.
Someone is either patient or creative.
Mary is not curious.
Someone is not patient.
Someone is not funny.
Someone is wise or not generous. | Alice is patient. | neutral | (![X]:((calm(X)|~generous(X))=>(~humble(X)<~>~patient(X))))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((~patient(X)<~>~creative(X)))))&
((?[X]:((tall(X)|~calm(X))))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(~wise(X)=>(kind(X)&~tall(X))))&
((?[X]:((~generous(X)<~>~curious(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(((~kind(fred)<~>~humble(fred)))=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((old(X)|brave(X))<=>(strong(X)&~old(X))))&
(((funny(mary)&~brave(mary)))=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((quiet(X)&rich(X))<=>(~creative(X)&rich(X))))&
(![X]:((~happy(X)<~>humble(X))=>~humble(X)))&
(((~wise(alice)<~>calm(alice)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)|humble(X))<=>(wise(X)<~>~creative(X))))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((patient(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:(~patient(X)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)|~generous(X)))) | patient(alice) | [] | null | 0 |
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