premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either kind or tall is tall.
If someone is either not brave or curious then someone is both not wise and wise and vice versa.
Everyone who is not brave is tall or not funny.
Everyone who is either creative or tall is wise or tall and vice versa.
Everyone who is either kind or not strong is both old and not old.
If someone is not tall then lucy is both old and creative and vice versa.
If mary is both not brave and not rich then paul is not happy or rich and vice versa.
If someone is rich then someone is old or not humble.
If someone is both not brave and not quiet then someone is not generous and vice versa.
Everyone who is either not funny or not patient is both strong and not tall.
Everyone who is both creative and quiet is funny and vice versa.
If fred is either not kind or quiet then someone is both not wise and funny.
If someone is either not tall or not creative then someone is both generous and not curious.
Everyone who is quiet or tall is strong and vice versa.
If lucy is quiet then someone is strong and vice versa.
If someone is either not brave or calm then paul is either not creative or not curious.
Fred is both quiet and strong.
Alice is either patient or not calm.
Someone is both old and not brave.
John is rich.
Alice is brave or rich.
John is not calm or not patient.
Someone is either creative or not brave.
Someone is not humble or not curious. | Alice is strong. | entailment | (![X]:((kind(X)<~>tall(X))=>tall(X)))&
((?[X]:((~brave(X)<~>curious(X))))<=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:(~brave(X)=>(tall(X)|~funny(X))))&
(![X]:((creative(X)<~>tall(X))<=>(wise(X)|tall(X))))&
(![X]:((kind(X)<~>~strong(X))=>(old(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((old(lucy)&creative(lucy))))&
(((~brave(mary)&~rich(mary)))<=>((~happy(paul)|rich(paul))))&
((?[X]:(rich(X)))=>(?[X]:((old(X)|~humble(X)))))&
((?[X]:((~brave(X)&~quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(strong(X)&~tall(X))))&
(![X]:((creative(X)&quiet(X))<=>funny(X)))&
(((~kind(fred)<~>quiet(fred)))=>(?[X]:((~wise(X)&funny(X)))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((quiet(X)|tall(X))<=>strong(X)))&
((quiet(lucy))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>((~creative(paul)<~>~curious(paul))))&
((quiet(fred)&strong(fred)))&
((patient(alice)<~>~calm(alice)))&
(?[X]:((old(X)&~brave(X))))&
(rich(john))&
((brave(alice)|rich(alice)))&
((~calm(john)|~patient(john)))&
(?[X]:((creative(X)<~>~brave(X))))&
(?[X]:((~humble(X)|~curious(X)))) | strong(alice) | [
"p0",
"p4",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5002951687656357674566683
% SZS output start Proof for 5002951687656357674566683
1. ! [X0] : ((kind(X0) <~> tall(X0)) => tall(X0)) [input p0]
5. ! [X0] : ((kind(X0) <~> ~strong(X0)) => (~old(X0) & old(X0))) [input p4]
14. ! [X0] : ((tall(X0) | quiet(X0)) <=> strong(X0)) [input p13]
25. ~strong(alice) [input hypothesis]
32. ! [X0] : (tall(X0) | (kind(X0) <=> tall(X0))) [ennf transformation 1]
35. ! [X0] : ((~old(X0) & old(X0)) | (kind(X0) <=> ~strong(X0))) [ennf transformation 5]
40. ! [X0] : (tall(X0) | ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0)))) [nnf transformation 32]
48. ! [X0] : ((~old(X0) & old(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) [nnf transformation 35]
71. ! [X0] : (((tall(X0) | quiet(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 14]
72. ! [X0] : ((tall(X0) | quiet(X0) | ~strong(X0)) & (strong(X0) | (~tall(X0) & ~quiet(X0)))) [flattening 71]
84. tall(X0) | tall(X0) | ~kind(X0) [cnf transformation 40]
100. old(X0) | kind(X0) | strong(X0) [cnf transformation 48]
102. ~old(X0) | kind(X0) | strong(X0) [cnf transformation 48]
130. ~tall(X0) | strong(X0) [cnf transformation 72]
149. ~strong(alice) [cnf transformation 25]
152. ~kind(X0) | tall(X0) [duplicate literal removal 84]
168. strong(X0) | kind(X0) [subsumption resolution 100,102]
362. kind(alice) [resolution 168,149]
367. tall(alice) [resolution 362,152]
371. strong(alice) [resolution 367,130]
372. $false [subsumption resolution 371,149]
% SZS output end Proof for 5002951687656357674566683
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not quiet or not generous.
Everyone who is not strong is both not happy and not rich and vice versa.
If fred is both creative and not happy then someone is either calm or old.
If someone is both not old and old then someone is both humble and not quiet and vice versa.
If susan is not brave or curious then someone is not happy and vice versa.
If lucy is both not kind and not patient then someone is both wise and not wise and vice versa.
If susan is kind or not strong then susan is not wise.
Everyone who is not rich is brave and vice versa.
Everyone who is not wise is either not brave or strong.
Everyone who is both patient and calm is not calm or rich and vice versa.
Everyone who is wise is both not quiet and tall and vice versa.
Everyone who is happy or not tall is either not rich or not strong and vice versa.
If paul is either not strong or curious then someone is not calm or happy.
Everyone who is not curious or calm is not wise and vice versa.
If paul is both curious and humble then mary is humble or not tall.
Someone is either not funny or tall.
Someone is either not quiet or generous.
Alice is not wise or rich.
Paul is not brave or not rich.
Someone is either not tall or tall.
Someone is either kind or not generous.
Someone is kind or wise. | Lucy is not patient. | entailment | (![X]:(~patient(X)=>(~quiet(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~happy(X)&~rich(X))))&
(((creative(fred)&~happy(fred)))=>(?[X]:((calm(X)<~>old(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((humble(X)&~quiet(X)))))&
(((~brave(susan)|curious(susan)))<=>(?[X]:(~happy(X))))&
(((~kind(lucy)&~patient(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(((kind(susan)|~strong(susan)))=>(~wise(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:(~wise(X)=>(~brave(X)<~>strong(X))))&
(![X]:((patient(X)&calm(X))<=>(~calm(X)|rich(X))))&
(![X]:(wise(X)<=>(~quiet(X)&tall(X))))&
(![X]:((happy(X)|~tall(X))<=>(~rich(X)<~>~strong(X))))&
(((~strong(paul)<~>curious(paul)))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~curious(X)|calm(X))<=>~wise(X)))&
(((curious(paul)&humble(paul)))=>((humble(mary)|~tall(mary))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((~quiet(X)<~>generous(X))))&
((~wise(alice)|rich(alice)))&
((~brave(paul)|~rich(paul)))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((kind(X)<~>~generous(X))))&
(?[X]:((kind(X)|wise(X)))) | ~patient(lucy) | [
"p1",
"p7",
"p8",
"p9",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5954342423001221123279563
% SZS output start Proof for 5954342423001221123279563
2. ! [X0] : (~strong(X0) <=> (~rich(X0) & ~happy(X0))) [input p1]
8. ! [X0] : (~rich(X0) <=> brave(X0)) [input p7]
9. ! [X0] : (~wise(X0) => (~brave(X0) <~> strong(X0))) [input p8]
10. ! [X0] : ((calm(X0) & patient(X0)) <=> (rich(X0) | ~calm(X0))) [input p9]
14. ! [X0] : ((calm(X0) | ~curious(X0)) <=> ~wise(X0)) [input p13]
23. patient(lucy) [input hypothesis]
29. ! [X0] : ((~brave(X0) <~> strong(X0)) | wise(X0)) [ennf transformation 9]
33. ! [X0] : ((~strong(X0) | (rich(X0) | happy(X0))) & ((~rich(X0) & ~happy(X0)) | strong(X0))) [nnf transformation 2]
34. ! [X0] : ((~strong(X0) | rich(X0) | happy(X0)) & ((~rich(X0) & ~happy(X0)) | strong(X0))) [flattening 33]
50. ! [X0] : ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))) [nnf transformation 8]
51. ! [X0] : (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | wise(X0)) [nnf transformation 29]
52. ! [X0] : (((calm(X0) & patient(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~calm(X0) | ~patient(X0)))) [nnf transformation 10]
53. ! [X0] : (((calm(X0) & patient(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~calm(X0) | ~patient(X0))) [flattening 52]
61. ! [X0] : (((calm(X0) | ~curious(X0)) | wise(X0)) & (~wise(X0) | (~calm(X0) & curious(X0)))) [nnf transformation 14]
62. ! [X0] : ((calm(X0) | ~curious(X0) | wise(X0)) & (~wise(X0) | (~calm(X0) & curious(X0)))) [flattening 61]
79. ~rich(X0) | strong(X0) [cnf transformation 34]
94. brave(X0) | rich(X0) [cnf transformation 50]
95. ~brave(X0) | ~rich(X0) [cnf transformation 50]
96. ~brave(X0) | strong(X0) | wise(X0) [cnf transformation 51]
97. ~strong(X0) | brave(X0) | wise(X0) [cnf transformation 51]
98. rich(X0) | ~calm(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 53]
101. calm(X0) | calm(X0) [cnf transformation 53]
115. ~wise(X0) | ~calm(X0) [cnf transformation 62]
129. patient(lucy) [cnf transformation 23]
130. rich(X0) | ~calm(X0) | ~patient(X0) [duplicate literal removal 98]
131. calm(X0) [duplicate literal removal 101]
164. 8 <=> patient(lucy) [avatar definition]
166. patient(lucy) <- (8) [avatar component clause 164]
187. ~patient(X0) | rich(X0) [subsumption resolution 130,131]
207. ~wise(X0) [subsumption resolution 115,131]
252. 8 [avatar split clause 129,164]
261. rich(lucy) <- (8) [resolution 187,166]
279. strong(X0) | wise(X0) | rich(X0) [resolution 96,94]
281. strong(X0) | rich(X0) [subsumption resolution 279,207]
282. strong(X0) [subsumption resolution 281,79]
286. brave(X0) | wise(X0) [resolution 282,97]
289. brave(X0) [subsumption resolution 286,207]
291. ~rich(X1) [resolution 289,95]
305. $false <- (8) [resolution 291,261]
307. ~8 [avatar contradiction clause 305]
309. $false [avatar sat refutation 252,307]
% SZS output end Proof for 5954342423001221123279563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or generous then someone is both humble and patient and vice versa.
Everyone who is brave or not humble is both not creative and not quiet and vice versa.
If john is either not curious or not wise then someone is not generous and vice versa.
Everyone who is creative or funny is curious and vice versa.
Everyone who is rich is calm and vice versa.
Everyone who is not rich or not creative is both not calm and wise and vice versa.
Everyone who is both not humble and tall is not patient or tall.
If someone is both kind and not creative then lucy is both kind and curious and vice versa.
Everyone who is not creative or tall is either calm or not happy.
If mary is either old or generous then fred is either creative or not brave.
If someone is not brave or strong then john is rich and vice versa.
If someone is kind or creative then someone is rich and vice versa.
Everyone who is not creative or not calm is either calm or tall.
Everyone who is either rich or not kind is both not humble and not calm and vice versa.
If someone is generous or patient then lucy is not wise or funny and vice versa.
Everyone who is both funny and humble is both calm and quiet and vice versa.
Susan is both not curious and not generous.
Someone is both strong and not funny.
Paul is happy or brave.
Someone is both not old and not patient.
Paul is either curious or not kind.
Alice is not patient. | Susan is not kind. | entailment | ((?[X]:((~wise(X)|generous(X))))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((brave(X)|~humble(X))<=>(~creative(X)&~quiet(X))))&
(((~curious(john)<~>~wise(john)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|funny(X))<=>curious(X)))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((~rich(X)|~creative(X))<=>(~calm(X)&wise(X))))&
(![X]:((~humble(X)&tall(X))=>(~patient(X)|tall(X))))&
((?[X]:((kind(X)&~creative(X))))<=>((kind(lucy)&curious(lucy))))&
(![X]:((~creative(X)|tall(X))=>(calm(X)<~>~happy(X))))&
(((old(mary)<~>generous(mary)))=>((creative(fred)<~>~brave(fred))))&
((?[X]:((~brave(X)|strong(X))))<=>(rich(john)))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)|~calm(X))=>(calm(X)<~>tall(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~wise(lucy)|funny(lucy))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&quiet(X))))&
((~curious(susan)&~generous(susan)))&
(?[X]:((strong(X)&~funny(X))))&
((happy(paul)|brave(paul)))&
(?[X]:((~old(X)&~patient(X))))&
((curious(paul)<~>~kind(paul)))&
(~patient(alice)) | ~kind(susan) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p7",
"p10",
"p13",
"p14",
"p15",
"p16",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 2251278020697272979681637
% SZS output start Proof for 2251278020697272979681637
1. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X0] : (patient(X0) & humble(X0)) [input p0]
3. (~curious(john) <~> ~wise(john)) <=> ? [X0] : ~generous(X0) [input p2]
4. ! [X0] : ((funny(X0) | creative(X0)) <=> curious(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> calm(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (wise(X0) & ~calm(X0))) [input p5]
8. ? [X0] : (~creative(X0) & kind(X0)) <=> (curious(lucy) & kind(lucy)) [input p7]
11. ? [X0] : (strong(X0) | ~brave(X0)) <=> rich(john) [input p10]
14. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> (~calm(X0) & ~humble(X0))) [input p13]
15. ? [X0] : (patient(X0) | generous(X0)) <=> (funny(lucy) | ~wise(lucy)) [input p14]
16. ! [X0] : ((humble(X0) & funny(X0)) <=> (quiet(X0) & calm(X0))) [input p15]
17. ~generous(susan) & ~curious(susan) [input p16]
18. ? [X0] : (~funny(X0) & strong(X0)) [input p17]
23. kind(susan) [input hypothesis]
24. ? [X0] : (generous(X0) | ~wise(X0)) <=> ? [X1] : (patient(X1) & humble(X1)) [rectify 1]
31. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X1] : (patient(X1) & humble(X1)) | ! [X0] : (~generous(X0) & wise(X0))) [nnf transformation 24]
32. (? [X0] : (generous(X0) | ~wise(X0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X2] : (patient(X2) & humble(X2)) | ! [X3] : (~generous(X3) & wise(X3))) [rectify 31]
33. ? [X0] : (generous(X0) | ~wise(X0)) => (generous(sK0) | ~wise(sK0)) [choice axiom]
34. ? [X2] : (patient(X2) & humble(X2)) => (patient(sK1) & humble(sK1)) [choice axiom]
35. ((generous(sK0) | ~wise(sK0)) | ! [X1] : (~patient(X1) | ~humble(X1))) & ((patient(sK1) & humble(sK1)) | ! [X3] : (~generous(X3) & wise(X3))) [skolemisation 32,34,33]
38. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [nnf transformation 3]
39. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [rectify 38]
40. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
41. (((wise(john) | curious(john)) & (~wise(john) | ~curious(john))) | ! [X0] : generous(X0)) & (~generous(sK2) | ((~curious(john) | wise(john)) & (~wise(john) | curious(john)))) [skolemisation 39,40]
42. ! [X0] : (((funny(X0) | creative(X0)) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [nnf transformation 4]
43. ! [X0] : ((funny(X0) | creative(X0) | ~curious(X0)) & (curious(X0) | (~funny(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))) [nnf transformation 5]
45. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~rich(X0) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | (creative(X0) & rich(X0)))) [flattening 45]
47. (? [X0] : (~creative(X0) & kind(X0)) | (~curious(lucy) | ~kind(lucy))) & ((curious(lucy) & kind(lucy)) | ! [X0] : (creative(X0) | ~kind(X0))) [nnf transformation 8]
48. (? [X0] : (~creative(X0) & kind(X0)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X0] : (creative(X0) | ~kind(X0))) [flattening 47]
49. (? [X0] : (~creative(X0) & kind(X0)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X1] : (creative(X1) | ~kind(X1))) [rectify 48]
50. ? [X0] : (~creative(X0) & kind(X0)) => (~creative(sK3) & kind(sK3)) [choice axiom]
51. ((~creative(sK3) & kind(sK3)) | ~curious(lucy) | ~kind(lucy)) & ((curious(lucy) & kind(lucy)) | ! [X1] : (creative(X1) | ~kind(X1))) [skolemisation 49,50]
54. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X0] : (~strong(X0) & brave(X0))) [nnf transformation 11]
55. (? [X0] : (strong(X0) | ~brave(X0)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (strong(X0) | ~brave(X0)) => (strong(sK4) | ~brave(sK4)) [choice axiom]
57. ((strong(sK4) | ~brave(sK4)) | ~rich(john)) & (rich(john) | ! [X1] : (~strong(X1) & brave(X1))) [skolemisation 55,56]
64. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (calm(X0) | humble(X0))) & ((~calm(X0) & ~humble(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 14]
65. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | calm(X0) | humble(X0)) & ((~calm(X0) & ~humble(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [flattening 64]
66. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & ((funny(lucy) | ~wise(lucy)) | ! [X0] : (~patient(X0) & ~generous(X0))) [nnf transformation 15]
67. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X0] : (~patient(X0) & ~generous(X0))) [flattening 66]
68. (? [X0] : (patient(X0) | generous(X0)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [rectify 67]
69. ? [X0] : (patient(X0) | generous(X0)) => (patient(sK7) | generous(sK7)) [choice axiom]
70. ((patient(sK7) | generous(sK7)) | (~funny(lucy) & wise(lucy))) & (funny(lucy) | ~wise(lucy) | ! [X1] : (~patient(X1) & ~generous(X1))) [skolemisation 68,69]
71. ! [X0] : (((humble(X0) & funny(X0)) | (~quiet(X0) | ~calm(X0))) & ((quiet(X0) & calm(X0)) | (~humble(X0) | ~funny(X0)))) [nnf transformation 16]
72. ! [X0] : (((humble(X0) & funny(X0)) | ~quiet(X0) | ~calm(X0)) & ((quiet(X0) & calm(X0)) | ~humble(X0) | ~funny(X0))) [flattening 71]
73. ? [X0] : (~funny(X0) & strong(X0)) => (~funny(sK8) & strong(sK8)) [choice axiom]
74. ~funny(sK8) & strong(sK8) [skolemisation 18,73]
80. patient(sK1) | wise(X3) [cnf transformation 35]
90. ~wise(john) | ~curious(john) | generous(X0) [cnf transformation 41]
92. ~creative(X0) | curious(X0) [cnf transformation 43]
95. ~rich(X0) | calm(X0) [cnf transformation 44]
96. ~calm(X0) | rich(X0) [cnf transformation 44]
98. ~calm(X0) | creative(X0) [cnf transformation 46]
99. rich(X0) | wise(X0) [cnf transformation 46]
103. kind(lucy) | creative(X1) | ~kind(X1) [cnf transformation 51]
116. rich(john) | ~strong(X1) [cnf transformation 57]
127. ~calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 65]
129. ~kind(X0) | rich(X0) | calm(X0) | humble(X0) [cnf transformation 65]
132. funny(lucy) | ~wise(lucy) | ~patient(X1) [cnf transformation 70]
135. ~funny(X0) | ~humble(X0) | calm(X0) [cnf transformation 72]
139. ~curious(susan) [cnf transformation 17]
140. ~generous(susan) [cnf transformation 17]
141. strong(sK8) [cnf transformation 74]
149. kind(susan) [cnf transformation 23]
167. 5 <=> patient(sK1) [avatar definition]
169. patient(sK1) <- (5) [avatar component clause 167]
172. 6 <=> ! [X3] : wise(X3) [avatar definition]
173. wise(X3) <- (6) [avatar component clause 172]
174. 6 | 5 [avatar split clause 80,167,172]
182. 8 <=> ! [X0] : generous(X0) [avatar definition]
183. generous(X0) <- (8) [avatar component clause 182]
185. 9 <=> curious(john) [avatar definition]
189. 10 <=> wise(john) [avatar definition]
190. ~wise(john) <- (~10) [avatar component clause 189]
193. 8 | ~9 | ~10 [avatar split clause 90,189,185,182]
201. 12 <=> kind(lucy) [avatar definition]
202. kind(lucy) <- (12) [avatar component clause 201]
219. 16 <=> ! [X1] : (creative(X1) | ~kind(X1)) [avatar definition]
220. ~kind(X1) | creative(X1) <- (16) [avatar component clause 219]
222. 16 | 12 [avatar split clause 103,201,219]
249. 21 <=> rich(john) [avatar definition]
250. rich(john) <- (21) [avatar component clause 249]
262. 24 <=> ! [X1] : ~strong(X1) [avatar definition]
263. ~strong(X1) <- (24) [avatar component clause 262]
264. 24 | 21 [avatar split clause 116,249,262]
293. ~kind(X0) | calm(X0) | humble(X0) [subsumption resolution 129,95]
294. ~kind(X0) | ~rich(X0) [subsumption resolution 127,95]
296. 32 <=> funny(lucy) [avatar definition]
297. funny(lucy) <- (32) [avatar component clause 296]
309. 35 <=> wise(lucy) [avatar definition]
310. ~wise(lucy) <- (~35) [avatar component clause 309]
314. 36 <=> ! [X1] : ~patient(X1) [avatar definition]
315. ~patient(X1) <- (36) [avatar component clause 314]
316. 36 | ~35 | 32 [avatar split clause 132,296,309,314]
343. $false <- (8) [resolution 183,140]
344. ~8 [avatar contradiction clause 343]
345. $false <- (24) [resolution 263,141]
346. ~24 [avatar contradiction clause 345]
349. calm(john) <- (21) [resolution 95,250]
353. creative(john) <- (21) [resolution 98,349]
355. curious(john) <- (21) [resolution 353,92]
375. ~rich(lucy) <- (12) [resolution 294,202]
379. wise(lucy) <- (12) [resolution 375,99]
380. $false <- (12, ~35) [subsumption resolution 379,310]
381. ~12 | 35 [avatar contradiction clause 380]
383. creative(susan) <- (16) [resolution 220,149]
400. curious(susan) <- (16) [resolution 383,92]
403. $false <- (16) [subsumption resolution 400,139]
404. ~16 [avatar contradiction clause 403]
405. ~rich(lucy) <- (12) [resolution 202,294]
422. ~humble(lucy) | calm(lucy) <- (32) [resolution 135,297]
424. 44 <=> calm(lucy) [avatar definition]
426. calm(lucy) <- (44) [avatar component clause 424]
428. 45 <=> humble(lucy) [avatar definition]
431. 44 | ~45 | ~32 [avatar split clause 422,296,428,424]
460. calm(lucy) | humble(lucy) <- (12) [resolution 293,202]
484. 45 | 44 | ~12 [avatar split clause 460,201,424,428]
510. rich(lucy) <- (44) [resolution 426,96]
513. $false <- (12, 44) [subsumption resolution 510,405]
514. ~12 | ~44 [avatar contradiction clause 513]
517. $false <- (5, 36) [resolution 315,169]
518. ~5 | ~36 [avatar contradiction clause 517]
521. $false <- (6, ~10) [resolution 173,190]
522. ~6 | 10 [avatar contradiction clause 521]
523. 9 | ~21 [avatar split clause 355,249,185]
524. $false [avatar sat refutation 174,193,222,264,316,344,346,381,404,431,484,514,518,522,523]
% SZS output end Proof for 2251278020697272979681637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not quiet and rich then someone is not patient or not strong and vice versa.
If lucy is curious then susan is both humble and not calm.
Everyone who is both quiet and not rich is calm and vice versa.
If susan is either not strong or wise then someone is either not happy or old and vice versa.
Everyone who is both calm and curious is kind or curious.
If someone is old then fred is either humble or quiet and vice versa.
Everyone who is both brave and kind is not calm or strong and vice versa.
Everyone who is brave is either wise or humble.
Everyone who is not old or humble is strong or not rich.
Everyone who is humble is old or not curious.
Everyone who is either patient or not humble is not patient.
Everyone who is not patient is humble.
Everyone who is kind is either not quiet or creative and vice versa.
Everyone who is not wise or not quiet is both happy and not curious and vice versa.
If mary is calm or not patient then someone is either calm or not tall.
Everyone who is not curious or not strong is either patient or strong and vice versa.
Someone is either creative or humble.
Paul is not humble or creative.
Susan is either patient or curious.
Paul is either humble or happy.
Someone is happy. | Paul is not happy. | contradiction | (((~quiet(fred)&rich(fred)))<=>(?[X]:((~patient(X)|~strong(X)))))&
((curious(lucy))=>((humble(susan)&~calm(susan))))&
(![X]:((quiet(X)&~rich(X))<=>calm(X)))&
(((~strong(susan)<~>wise(susan)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((calm(X)&curious(X))=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>((humble(fred)<~>quiet(fred))))&
(![X]:((brave(X)&kind(X))<=>(~calm(X)|strong(X))))&
(![X]:(brave(X)=>(wise(X)<~>humble(X))))&
(![X]:((~old(X)|humble(X))=>(strong(X)|~rich(X))))&
(![X]:(humble(X)=>(old(X)|~curious(X))))&
(![X]:((patient(X)<~>~humble(X))=>~patient(X)))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(kind(X)<=>(~quiet(X)<~>creative(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(happy(X)&~curious(X))))&
(((calm(mary)|~patient(mary)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((~curious(X)|~strong(X))<=>(patient(X)<~>strong(X))))&
(?[X]:((creative(X)<~>humble(X))))&
((~humble(paul)|creative(paul)))&
((patient(susan)<~>curious(susan)))&
((humble(paul)<~>happy(paul)))&
(?[X]:(happy(X))) | ~happy(paul) | [
"p6",
"p7",
"p10",
"p13",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 461521570745752603283119
% SZS output start Proof for 461521570745752603283119
7. ! [X0] : ((kind(X0) & brave(X0)) <=> (strong(X0) | ~calm(X0))) [input p6]
8. ! [X0] : (brave(X0) => (wise(X0) <~> humble(X0))) [input p7]
11. ! [X0] : ((patient(X0) <~> ~humble(X0)) => ~patient(X0)) [input p10]
14. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (~curious(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | ~curious(X0)) <=> (patient(X0) <~> strong(X0))) [input p15]
20. humble(paul) <~> happy(paul) [input p19]
22. ~happy(paul) [input hypothesis]
26. ! [X0] : ((wise(X0) <~> humble(X0)) | ~brave(X0)) [ennf transformation 8]
31. ! [X0] : (~patient(X0) | (patient(X0) <=> ~humble(X0))) [ennf transformation 11]
49. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 7]
50. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | ~kind(X0) | ~brave(X0))) [flattening 49]
51. ! [X0] : (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | ~brave(X0)) [nnf transformation 26]
52. ! [X0] : (~patient(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) [nnf transformation 31]
54. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 14]
55. ! [X0] : ((~quiet(X0) | ~wise(X0) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | (quiet(X0) & wise(X0)))) [flattening 54]
59. ! [X0] : (((~strong(X0) | ~curious(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (strong(X0) & curious(X0)))) [nnf transformation 16]
60. ! [X0] : ((~strong(X0) | ~curious(X0) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (strong(X0) & curious(X0)))) [flattening 59]
65. (~happy(paul) | ~humble(paul)) & (happy(paul) | humble(paul)) [nnf transformation 20]
93. ~strong(X0) | brave(X0) [cnf transformation 50]
97. ~brave(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 51]
101. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 52]
108. happy(X0) | wise(X0) [cnf transformation 55]
118. strong(X0) | patient(X0) | strong(X0) [cnf transformation 60]
128. happy(paul) | humble(paul) [cnf transformation 65]
131. ~happy(paul) [cnf transformation 22]
132. strong(X0) | patient(X0) [duplicate literal removal 118]
134. ~humble(X0) | ~patient(X0) [duplicate literal removal 101]
252. 25 <=> humble(paul) [avatar definition]
253. humble(paul) <- (25) [avatar component clause 252]
271. 29 <=> happy(paul) [avatar definition]
273. ~happy(paul) <- (~29) [avatar component clause 271]
275. 25 | 29 [avatar split clause 128,271,252]
276. ~29 [avatar split clause 131,271]
279. wise(paul) <- (~29) [resolution 108,273]
284. brave(X1) | patient(X1) [resolution 132,93]
447. patient(X1) | ~wise(X1) | ~humble(X1) [resolution 284,97]
449. ~wise(X1) | ~humble(X1) [subsumption resolution 447,134]
498. ~humble(paul) <- (~29) [resolution 449,279]
500. $false <- (25, ~29) [subsumption resolution 498,253]
501. ~25 | 29 [avatar contradiction clause 500]
502. $false [avatar sat refutation 275,276,501]
% SZS output end Proof for 461521570745752603283119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or calm is not kind or not rich.
Everyone who is either creative or wise is either old or not brave.
If fred is either not old or wise then someone is both not humble and not happy.
Everyone who is quiet or not brave is not funny and vice versa.
Everyone who is either not creative or not quiet is either calm or not rich and vice versa.
Everyone who is either patient or creative is either quiet or not rich and vice versa.
If someone is not patient then someone is patient and vice versa.
Everyone who is not generous is not wise or creative.
If mary is brave then someone is humble or rich and vice versa.
Everyone who is both calm and rich is either quiet or not calm and vice versa.
Everyone who is not humble is both not quiet and humble and vice versa.
If someone is not happy or generous then mary is funny or not happy and vice versa.
If someone is both not kind and not quiet then lucy is not generous and vice versa.
If fred is funny or not generous then someone is funny or happy and vice versa.
Everyone who is not creative is curious and vice versa.
If mary is curious or not happy then paul is both not funny and not brave and vice versa.
Alice is rich.
Fred is not kind or not tall.
Someone is not funny or not happy.
Someone is either not curious or not creative.
Paul is not old.
Alice is happy or strong.
Susan is rich or not wise. | Susan is old. | neutral | (![X]:((~patient(X)<~>calm(X))=>(~kind(X)|~rich(X))))&
(![X]:((creative(X)<~>wise(X))=>(old(X)<~>~brave(X))))&
(((~old(fred)<~>wise(fred)))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((quiet(X)|~brave(X))<=>~funny(X)))&
(![X]:((~creative(X)<~>~quiet(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((patient(X)<~>creative(X))<=>(quiet(X)<~>~rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(patient(X))))&
(![X]:(~generous(X)=>(~wise(X)|creative(X))))&
((brave(mary))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:((calm(X)&rich(X))<=>(quiet(X)<~>~calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)&humble(X))))&
((?[X]:((~happy(X)|generous(X))))<=>((funny(mary)|~happy(mary))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(~generous(lucy)))&
(((funny(fred)|~generous(fred)))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:(~creative(X)<=>curious(X)))&
(((curious(mary)|~happy(mary)))<=>((~funny(paul)&~brave(paul))))&
(rich(alice))&
((~kind(fred)|~tall(fred)))&
(?[X]:((~funny(X)|~happy(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
(~old(paul))&
((happy(alice)|strong(alice)))&
((rich(susan)|~wise(susan))) | old(susan) | []
| null | 0 |
Everyone who is either not wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Mary is humble. | entailment | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | humble(mary) | [
"p5",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6860900770238912196204981
% SZS output start Proof for 6860900770238912196204981
6. ! [X0] : ((brave(X0) | ~strong(X0)) <=> (~happy(X0) | ~humble(X0))) [input p5]
11. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p10]
12. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p11]
20. ~humble(mary) [input hypothesis]
25. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 11]
38. ! [X0] : (((brave(X0) | ~strong(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (~brave(X0) & strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((brave(X0) | ~strong(X0) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | (~brave(X0) & strong(X0)))) [flattening 38]
48. ! [X0] : ((strong(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [flattening 48]
80. ~strong(X0) | brave(X0) | humble(X0) [cnf transformation 39]
100. strong(X0) | brave(X0) [cnf transformation 25]
101. ~brave(X0) | strong(X0) [cnf transformation 25]
103. ~brave(X0) | ~strong(X0) [cnf transformation 49]
123. ~humble(mary) [cnf transformation 20]
125. 1 <=> humble(mary) [avatar definition]
126. ~humble(mary) <- (~1) [avatar component clause 125]
205. strong(X0) [subsumption resolution 100,101]
207. ~brave(X0) [subsumption resolution 103,205]
227. ~1 [avatar split clause 123,125]
236. brave(X0) | humble(X0) [resolution 80,205]
237. humble(X0) [subsumption resolution 236,207]
238. $false <- (~1) [resolution 237,126]
240. 1 [avatar contradiction clause 238]
241. $false [avatar sat refutation 227,240]
% SZS output end Proof for 6860900770238912196204981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not happy then paul is quiet.
Everyone who is not wise or not creative is both old and not creative and vice versa.
If someone is both not patient and calm then john is both rich and not generous.
If someone is either not patient or creative then someone is not funny.
Everyone who is both not brave and kind is funny.
If susan is both curious and happy then alice is either quiet or not old.
Everyone who is humble or kind is generous or not patient.
Everyone who is not humble is both kind and not rich and vice versa.
Everyone who is not patient or not creative is either brave or not funny.
If someone is either not tall or not strong then someone is both not wise and not old.
Everyone who is not funny or curious is calm.
Everyone who is not brave is not strong.
Everyone who is either tall or kind is generous or humble and vice versa.
If someone is both patient and not funny then someone is happy and vice versa.
Everyone who is not old or humble is both not humble and creative and vice versa.
Everyone who is old or calm is not kind.
Fred is generous or curious.
Someone is either curious or tall.
Alice is either not curious or old.
Fred is funny.
John is wise.
Fred is kind or not quiet.
Someone is strong. | Paul is not quiet. | contradiction | ((?[X]:((funny(X)&~happy(X))))=>(quiet(paul)))&
(![X]:((~wise(X)|~creative(X))<=>(old(X)&~creative(X))))&
((?[X]:((~patient(X)&calm(X))))=>((rich(john)&~generous(john))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&kind(X))=>funny(X)))&
(((curious(susan)&happy(susan)))=>((quiet(alice)<~>~old(alice))))&
(![X]:((humble(X)|kind(X))=>(generous(X)|~patient(X))))&
(![X]:(~humble(X)<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)|~creative(X))=>(brave(X)<~>~funny(X))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((~funny(X)|curious(X))=>calm(X)))&
(![X]:(~brave(X)=>~strong(X)))&
(![X]:((tall(X)<~>kind(X))<=>(generous(X)|humble(X))))&
((?[X]:((patient(X)&~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~humble(X)&creative(X))))&
(![X]:((old(X)|calm(X))=>~kind(X)))&
((generous(fred)|curious(fred)))&
(?[X]:((curious(X)<~>tall(X))))&
((~curious(alice)<~>old(alice)))&
(funny(fred))&
(wise(john))&
((kind(fred)|~quiet(fred)))&
(?[X]:(strong(X))) | ~quiet(paul) | [
"p0",
"p7",
"p10",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7490312336968179000634209
% SZS output start Proof for 7490312336968179000634209
1. ? [X0] : (~happy(X0) & funny(X0)) => quiet(paul) [input p0]
8. ! [X0] : (~humble(X0) <=> (~rich(X0) & kind(X0))) [input p7]
11. ! [X0] : ((curious(X0) | ~funny(X0)) => calm(X0)) [input p10]
14. ? [X0] : (~funny(X0) & patient(X0)) <=> ? [X0] : happy(X0) [input p13]
15. ! [X0] : ((humble(X0) | ~old(X0)) <=> (creative(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((calm(X0) | old(X0)) => ~kind(X0)) [input p15]
20. funny(fred) [input p19]
24. ~quiet(paul) [input hypothesis]
27. ? [X0] : (~funny(X0) & patient(X0)) <=> ? [X1] : happy(X1) [rectify 14]
28. quiet(paul) | ! [X0] : (happy(X0) | ~funny(X0)) [ennf transformation 1]
39. ! [X0] : (calm(X0) | (~curious(X0) & funny(X0))) [ennf transformation 11]
41. ! [X0] : (~kind(X0) | (~calm(X0) & ~old(X0))) [ennf transformation 16]
49. ! [X0] : ((~humble(X0) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | humble(X0))) [nnf transformation 8]
50. ! [X0] : ((~humble(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | humble(X0))) [flattening 49]
58. (? [X0] : (~funny(X0) & patient(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (funny(X0) | ~patient(X0))) [nnf transformation 27]
59. (? [X0] : (~funny(X0) & patient(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (funny(X3) | ~patient(X3))) [rectify 58]
60. ? [X0] : (~funny(X0) & patient(X0)) => (~funny(sK2) & patient(sK2)) [choice axiom]
61. ? [X2] : happy(X2) => happy(sK3) [choice axiom]
62. ((~funny(sK2) & patient(sK2)) | ! [X1] : ~happy(X1)) & (happy(sK3) | ! [X3] : (funny(X3) | ~patient(X3))) [skolemisation 59,61,60]
63. ! [X0] : (((humble(X0) | ~old(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((humble(X0) | ~old(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [flattening 63]
71. quiet(paul) | happy(X0) | ~funny(X0) [cnf transformation 28]
86. humble(X0) | kind(X0) [cnf transformation 50]
97. calm(X0) | funny(X0) [cnf transformation 39]
108. ~funny(sK2) | ~happy(X1) [cnf transformation 62]
110. ~humble(X0) | ~humble(X0) [cnf transformation 64]
115. ~kind(X0) | ~calm(X0) [cnf transformation 41]
121. funny(fred) [cnf transformation 20]
125. ~quiet(paul) [cnf transformation 24]
126. ~humble(X0) [duplicate literal removal 110]
129. 1 <=> ! [X0] : (happy(X0) | ~funny(X0)) [avatar definition]
130. ~funny(X0) | happy(X0) <- (1) [avatar component clause 129]
132. 2 <=> quiet(paul) [avatar definition]
135. 1 | 2 [avatar split clause 71,132,129]
200. 17 <=> ! [X1] : ~happy(X1) [avatar definition]
201. ~happy(X1) <- (17) [avatar component clause 200]
203. 18 <=> funny(sK2) [avatar definition]
205. ~funny(sK2) <- (~18) [avatar component clause 203]
206. 17 | ~18 [avatar split clause 108,203,200]
254. ~2 [avatar split clause 125,132]
255. ~funny(X0) <- (1, 17) [subsumption resolution 130,201]
256. $false <- (1, 17) [resolution 255,121]
257. ~1 | ~17 [avatar contradiction clause 256]
264. kind(X0) [resolution 86,126]
276. ~calm(X0) [resolution 115,264]
277. funny(X0) [resolution 276,97]
292. $false <- (~18) [resolution 277,205]
294. 18 [avatar contradiction clause 292]
296. $false [avatar sat refutation 135,206,254,257,294]
% SZS output end Proof for 7490312336968179000634209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy then lucy is both creative and not funny. Everyone who is patient or not humble is not funny and vice versa. Everyone who is not wise or humble is both curious and kind and vice versa. If someone is both not kind and quiet then fred is strong. If lucy is both not calm and not funny then someone is quiet or not tall. Everyone who is either not kind or tall is not curious or quiet and vice versa. If john is not happy then someone is either not happy or not calm. Everyone who is both not happy and not generous is tall or quiet and vice versa. If paul is either not quiet or curious then someone is not patient or wise and vice versa. If john is both calm and patient then someone is brave or generous. Everyone who is either not happy or not patient is either strong or not kind. If alice is tall then fred is both not strong and wise and vice versa. Everyone who is humble or wise is both generous and tall and vice versa. If someone is both funny and wise then john is both not strong and not happy. Everyone who is not tall is either wise or creative and vice versa. Everyone who is both brave and kind is both not quiet and not calm and vice versa. Mary is calm or not humble. Someone is both not happy and patient. Someone is either old or strong. Someone is not generous. Fred is both not quiet and not calm. Someone is either creative or not rich. Someone is kind. | Paul is funny. | contradiction | ((happy(mary))=>((creative(lucy)&~funny(lucy))))&
(![X]:((patient(X)|~humble(X))<=>~funny(X)))&
(![X]:((~wise(X)|humble(X))<=>(curious(X)&kind(X))))&
((?[X]:((~kind(X)&quiet(X))))=>(strong(fred)))&
(((~calm(lucy)&~funny(lucy)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~kind(X)<~>tall(X))<=>(~curious(X)|quiet(X))))&
((~happy(john))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~happy(X)&~generous(X))<=>(tall(X)|quiet(X))))&
(((~quiet(paul)<~>curious(paul)))<=>(?[X]:((~patient(X)|wise(X)))))&
(((calm(john)&patient(john)))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:((~happy(X)<~>~patient(X))=>(strong(X)<~>~kind(X))))&
((tall(alice))<=>((~strong(fred)&wise(fred))))&
(![X]:((humble(X)|wise(X))<=>(generous(X)&tall(X))))&
((?[X]:((funny(X)&wise(X))))=>((~strong(john)&~happy(john))))&
(![X]:(~tall(X)<=>(wise(X)<~>creative(X))))&
(![X]:((brave(X)&kind(X))<=>(~quiet(X)&~calm(X))))&
((calm(mary)|~humble(mary)))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:((old(X)<~>strong(X))))&
(?[X]:(~generous(X)))&
((~quiet(fred)&~calm(fred)))&
(?[X]:((creative(X)<~>~rich(X))))&
(?[X]:(kind(X))) | funny(paul) | [
"p1",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 862148943117153832858856
% SZS output start Proof for 862148943117153832858856
2. ! [X0] : ((~humble(X0) | patient(X0)) <=> ~funny(X0)) [input p1]
8. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> (quiet(X0) | tall(X0))) [input p7]
13. ! [X0] : ((wise(X0) | humble(X0)) <=> (tall(X0) & generous(X0))) [input p12]
24. funny(paul) [input hypothesis]
34. ! [X0] : (((~humble(X0) | patient(X0)) | funny(X0)) & (~funny(X0) | (humble(X0) & ~patient(X0)))) [nnf transformation 2]
35. ! [X0] : ((~humble(X0) | patient(X0) | funny(X0)) & (~funny(X0) | (humble(X0) & ~patient(X0)))) [flattening 34]
45. ! [X0] : (((~generous(X0) & ~happy(X0)) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | (generous(X0) | happy(X0)))) [nnf transformation 8]
46. ! [X0] : (((~generous(X0) & ~happy(X0)) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | generous(X0) | happy(X0))) [flattening 45]
56. ! [X0] : (((wise(X0) | humble(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (~wise(X0) & ~humble(X0)))) [nnf transformation 13]
57. ! [X0] : ((wise(X0) | humble(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (~wise(X0) & ~humble(X0)))) [flattening 56]
76. ~funny(X0) | humble(X0) [cnf transformation 35]
96. ~generous(X0) | ~tall(X0) [cnf transformation 46]
112. ~humble(X0) | generous(X0) [cnf transformation 57]
114. ~humble(X0) | tall(X0) [cnf transformation 57]
138. funny(paul) [cnf transformation 24]
285. humble(paul) [resolution 76,138]
293. generous(paul) [resolution 112,285]
295. ~tall(paul) [resolution 293,96]
304. tall(paul) [resolution 114,285]
305. $false [subsumption resolution 304,295]
% SZS output end Proof for 862148943117153832858856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and generous then paul is both humble and not curious.
Everyone who is not happy or creative is not funny.
If someone is either not strong or not kind then someone is not quiet and vice versa.
Everyone who is both not old and brave is either not calm or not kind.
If alice is either not tall or quiet then mary is either calm or tall and vice versa.
Everyone who is generous or not old is tall or not patient.
Everyone who is either curious or not patient is both not patient and brave.
Everyone who is either calm or not patient is either not strong or not patient and vice versa.
Everyone who is quiet is both kind and curious.
If susan is not strong then someone is both tall and not rich and vice versa.
Everyone who is both not quiet and not humble is not calm and vice versa.
If mary is both humble and funny then lucy is either old or not calm.
If lucy is either humble or creative then alice is both not old and funny.
Everyone who is not humble is not wise or not generous.
If paul is creative or strong then fred is either brave or not brave.
If john is either not tall or quiet then fred is not old and vice versa.
Susan is not curious or generous.
Fred is both not strong and creative.
Someone is both not brave and not kind.
Mary is strong.
Susan is old.
Someone is not old or kind.
John is either not old or generous.
Fred is patient. | Fred is curious. | contradiction | ((?[X]:((~kind(X)&generous(X))))=>((humble(paul)&~curious(paul))))&
(![X]:((~happy(X)|creative(X))=>~funny(X)))&
((?[X]:((~strong(X)<~>~kind(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~old(X)&brave(X))=>(~calm(X)<~>~kind(X))))&
(((~tall(alice)<~>quiet(alice)))<=>((calm(mary)<~>tall(mary))))&
(![X]:((generous(X)|~old(X))=>(tall(X)|~patient(X))))&
(![X]:((curious(X)<~>~patient(X))=>(~patient(X)&brave(X))))&
(![X]:((calm(X)<~>~patient(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:(quiet(X)=>(kind(X)&curious(X))))&
((~strong(susan))<=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>~calm(X)))&
(((humble(mary)&funny(mary)))=>((old(lucy)<~>~calm(lucy))))&
(((humble(lucy)<~>creative(lucy)))=>((~old(alice)&funny(alice))))&
(![X]:(~humble(X)=>(~wise(X)|~generous(X))))&
(((creative(paul)|strong(paul)))=>((brave(fred)<~>~brave(fred))))&
(((~tall(john)<~>quiet(john)))<=>(~old(fred)))&
((~curious(susan)|generous(susan)))&
((~strong(fred)&creative(fred)))&
(?[X]:((~brave(X)&~kind(X))))&
(strong(mary))&
(old(susan))&
(?[X]:((~old(X)|kind(X))))&
((~old(john)<~>generous(john)))&
(patient(fred)) | curious(fred) | [
"p6",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 974989666672792500929222
% SZS output start Proof for 974989666672792500929222
7. ! [X0] : ((curious(X0) <~> ~patient(X0)) => (brave(X0) & ~patient(X0))) [input p6]
24. patient(fred) [input p23]
25. curious(fred) [input hypothesis]
35. ! [X0] : ((brave(X0) & ~patient(X0)) | (curious(X0) <=> ~patient(X0))) [ennf transformation 7]
48. ! [X0] : ((brave(X0) & ~patient(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) [nnf transformation 35]
84. ~patient(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 48]
128. patient(fred) [cnf transformation 24]
129. curious(fred) [cnf transformation 25]
134. ~patient(X0) | ~curious(X0) [duplicate literal removal 84]
319. ~curious(fred) [resolution 134,128]
320. $false [subsumption resolution 319,129]
% SZS output end Proof for 974989666672792500929222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or patient is not strong or not creative and vice versa.
Everyone who is kind or not rich is either not curious or curious.
If susan is both calm and not creative then paul is creative.
Everyone who is both not curious and curious is quiet.
If someone is quiet or funny then someone is rich and vice versa.
Everyone who is either funny or tall is rich or brave and vice versa.
Everyone who is either wise or not calm is not quiet and vice versa.
Everyone who is either not quiet or not creative is generous.
Everyone who is creative is either funny or old and vice versa.
If someone is not old or creative then someone is either tall or not kind and vice versa.
Everyone who is both creative and calm is old.
If someone is both not quiet and not calm then fred is not old or calm and vice versa.
Everyone who is both not creative and kind is not calm or rich and vice versa.
If alice is both old and not calm then someone is quiet or happy and vice versa.
Everyone who is kind is both quiet and generous.
If someone is both not kind and not calm then someone is both not curious and not tall and vice versa.
Paul is both quiet and funny.
Lucy is strong or not patient.
Someone is strong or not humble.
Fred is both brave and not calm.
John is both curious and not kind.
John is not quiet.
Someone is generous.
Paul is not brave or not tall. | Alice is generous. | entailment | (![X]:((old(X)<~>patient(X))<=>(~strong(X)|~creative(X))))&
(![X]:((kind(X)|~rich(X))=>(~curious(X)<~>curious(X))))&
(((calm(susan)&~creative(susan)))=>(creative(paul)))&
(![X]:((~curious(X)&curious(X))=>quiet(X)))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)<~>tall(X))<=>(rich(X)|brave(X))))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~creative(X))=>generous(X)))&
(![X]:(creative(X)<=>(funny(X)<~>old(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((quiet(paul)&funny(paul)))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((strong(X)|~humble(X))))&
((brave(fred)&~calm(fred)))&
((curious(john)&~kind(john)))&
(~quiet(john))&
(?[X]:(generous(X)))&
((~brave(paul)|~tall(paul))) | generous(alice) | [
"p12",
"p13",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 192566611147777565916067
% SZS output start Proof for 192566611147777565916067
13. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p12]
14. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p13]
15. ! [X0] : (kind(X0) => (generous(X0) & quiet(X0))) [input p14]
17. funny(paul) & quiet(paul) [input p16]
25. ~generous(alice) [input hypothesis]
38. ! [X0] : ((generous(X0) & quiet(X0)) | ~kind(X0)) [ennf transformation 15]
62. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 13]
63. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 62]
64. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 14]
65. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 64]
66. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 65]
67. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK5) | quiet(sK5)) [choice axiom]
68. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK5) | quiet(sK5)) | calm(alice) | ~old(alice)) [skolemisation 66,67]
122. calm(X0) | kind(X0) [cnf transformation 63]
127. ~calm(alice) | ~quiet(X0) [cnf transformation 68]
130. ~kind(X0) | generous(X0) [cnf transformation 38]
135. quiet(paul) [cnf transformation 17]
145. ~generous(alice) [cnf transformation 25]
180. 9 <=> ! [X3] : ~quiet(X3) [avatar definition]
181. ~quiet(X3) <- (9) [avatar component clause 180]
245. 24 <=> calm(alice) [avatar definition]
247. ~calm(alice) <- (~24) [avatar component clause 245]
249. 9 | ~24 [avatar split clause 127,245,180]
303. $false <- (9) [resolution 181,135]
304. ~9 [avatar contradiction clause 303]
308. kind(alice) <- (~24) [resolution 122,247]
318. generous(alice) <- (~24) [resolution 308,130]
320. $false <- (~24) [subsumption resolution 318,145]
321. 24 [avatar contradiction clause 320]
322. $false [avatar sat refutation 249,304,321]
% SZS output end Proof for 192566611147777565916067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not brave then someone is creative or curious and vice versa.
Everyone who is either quiet or humble is either strong or not humble and vice versa.
If lucy is both not funny and generous then fred is both not generous and not happy and vice versa.
If lucy is both not rich and curious then mary is not kind.
If someone is brave or kind then someone is not humble or not calm.
Everyone who is either happy or not brave is either not wise or curious and vice versa.
Everyone who is either not generous or not humble is both not rich and patient.
If someone is not calm then someone is either not happy or not brave.
If someone is not humble then lucy is both not calm and tall.
Everyone who is not happy or not kind is not creative and vice versa.
If fred is kind or generous then lucy is rich and vice versa.
Everyone who is both not old and old is happy or kind.
Everyone who is both funny and quiet is curious and vice versa.
If someone is either generous or brave then mary is not calm and vice versa.
Everyone who is either not curious or strong is not creative or old.
If mary is both rich and strong then someone is creative or not rich and vice versa.
Someone is either strong or tall.
Someone is brave.
Someone is either not curious or not calm.
Mary is not strong or creative.
Fred is calm.
Someone is either not generous or not funny.
Someone is not brave or kind.
Mary is both quiet and not happy. | Lucy is brave. | neutral | ((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:((creative(X)|curious(X)))))&
(![X]:((quiet(X)<~>humble(X))<=>(strong(X)<~>~humble(X))))&
(((~funny(lucy)&generous(lucy)))<=>((~generous(fred)&~happy(fred))))&
(((~rich(lucy)&curious(lucy)))=>(~kind(mary)))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((happy(X)<~>~brave(X))<=>(~wise(X)<~>curious(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(~rich(X)&patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~happy(X)<~>~brave(X)))))&
((?[X]:(~humble(X)))=>((~calm(lucy)&tall(lucy))))&
(![X]:((~happy(X)|~kind(X))<=>~creative(X)))&
(((kind(fred)|generous(fred)))<=>(rich(lucy)))&
(![X]:((~old(X)&old(X))=>(happy(X)|kind(X))))&
(![X]:((funny(X)&quiet(X))<=>curious(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>(~calm(mary)))&
(![X]:((~curious(X)<~>strong(X))=>(~creative(X)|old(X))))&
(((rich(mary)&strong(mary)))<=>(?[X]:((creative(X)|~rich(X)))))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:(brave(X)))&
(?[X]:((~curious(X)<~>~calm(X))))&
((~strong(mary)|creative(mary)))&
(calm(fred))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:((~brave(X)|kind(X))))&
((quiet(mary)&~happy(mary))) | brave(lucy) | []
| null | 0 |
If someone is happy then paul is either humble or not wise and vice versa. If someone is not wise then alice is both not patient and quiet. If someone is not humble then someone is both generous and not brave. Everyone who is both calm and brave is both not patient and not humble and vice versa. Everyone who is not generous or humble is happy or wise and vice versa. Everyone who is both not wise and not happy is either patient or curious and vice versa. Everyone who is not strong is not humble or humble and vice versa. Everyone who is both not happy and not curious is both calm and brave. If someone is both not patient and not strong then someone is calm. If lucy is both brave and not kind then someone is both not rich and not generous and vice versa. If someone is not kind or not happy then someone is both old and not generous. If mary is happy then someone is either not kind or not creative and vice versa. If someone is not creative or not generous then someone is either curious or calm and vice versa. If someone is not generous or old then susan is not generous or rich. If john is not strong or not creative then someone is either patient or wise and vice versa. If someone is not quiet then someone is both strong and tall. Someone is curious. Someone is both humble and quiet. Someone is funny or not happy. Fred is not brave. Someone is not rich or humble. Someone is curious or happy. Someone is not creative or humble. Someone is brave. | Susan is strong. | contradiction | ((?[X]:(happy(X)))<=>((humble(paul)<~>~wise(paul))))&
((?[X]:(~wise(X)))=>((~patient(alice)&quiet(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((calm(X)&brave(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~generous(X)|humble(X))<=>(happy(X)|wise(X))))&
(![X]:((~wise(X)&~happy(X))<=>(patient(X)<~>curious(X))))&
(![X]:(~strong(X)<=>(~humble(X)|humble(X))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)&brave(X))))&
((?[X]:((~patient(X)&~strong(X))))=>(?[X]:(calm(X))))&
(((brave(lucy)&~kind(lucy)))<=>(?[X]:((~rich(X)&~generous(X)))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:((old(X)&~generous(X)))))&
((happy(mary))<=>(?[X]:((~kind(X)<~>~creative(X)))))&
((?[X]:((~creative(X)|~generous(X))))<=>(?[X]:((curious(X)<~>calm(X)))))&
((?[X]:((~generous(X)|old(X))))=>((~generous(susan)|rich(susan))))&
(((~strong(john)|~creative(john)))<=>(?[X]:((patient(X)<~>wise(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)&tall(X)))))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)&quiet(X))))&
(?[X]:((funny(X)|~happy(X))))&
(~brave(fred))&
(?[X]:((~rich(X)|humble(X))))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:(brave(X))) | strong(susan) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 238172528167226970731022
% SZS output start Proof for 238172528167226970731022
7. ! [X0] : (~strong(X0) <=> (humble(X0) | ~humble(X0))) [input p6]
25. strong(susan) [input hypothesis]
57. ! [X0] : ((~strong(X0) | (~humble(X0) & humble(X0))) & ((humble(X0) | ~humble(X0)) | strong(X0))) [nnf transformation 7]
58. ! [X0] : ((~strong(X0) | (~humble(X0) & humble(X0))) & (humble(X0) | ~humble(X0) | strong(X0))) [flattening 57]
118. ~strong(X0) | humble(X0) [cnf transformation 58]
119. ~strong(X0) | ~humble(X0) [cnf transformation 58]
156. strong(susan) [cnf transformation 25]
197. ~strong(X0) [subsumption resolution 118,119]
362. $false [subsumption resolution 156,197]
% SZS output end Proof for 238172528167226970731022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not strong.
If alice is not funny then someone is both brave and funny and vice versa.
Everyone who is humble or not kind is humble or tall and vice versa.
Everyone who is not generous or old is not kind.
Everyone who is funny or creative is old.
Everyone who is both not kind and tall is either old or not creative.
If someone is funny or not calm then fred is either quiet or generous and vice versa.
If someone is both not wise and calm then fred is both not quiet and not humble and vice versa.
Everyone who is generous or not kind is patient and vice versa.
Everyone who is not humble or tall is brave or not kind.
If someone is either quiet or not wise then john is either not brave or calm and vice versa.
Everyone who is generous or creative is both not quiet and not rich.
Everyone who is not strong or not rich is both generous and not patient.
Everyone who is both not funny and not tall is wise.
If mary is either calm or not wise then someone is not kind.
If someone is not strong then john is not happy or tall and vice versa.
Paul is both wise and happy.
Fred is both not generous and not funny.
Someone is either not funny or not old.
Alice is brave or not strong.
Lucy is old.
Someone is not funny or quiet. | Fred is rich. | entailment | (![X]:(~rich(X)=>~strong(X)))&
((~funny(alice))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((humble(X)|~kind(X))<=>(humble(X)|tall(X))))&
(![X]:((~generous(X)|old(X))=>~kind(X)))&
(![X]:((funny(X)|creative(X))=>old(X)))&
(![X]:((~kind(X)&tall(X))=>(old(X)<~>~creative(X))))&
((?[X]:((funny(X)|~calm(X))))<=>((quiet(fred)<~>generous(fred))))&
((?[X]:((~wise(X)&calm(X))))<=>((~quiet(fred)&~humble(fred))))&
(![X]:((generous(X)|~kind(X))<=>patient(X)))&
(![X]:((~humble(X)|tall(X))=>(brave(X)|~kind(X))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>((~brave(john)<~>calm(john))))&
(![X]:((generous(X)|creative(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~strong(X)|~rich(X))=>(generous(X)&~patient(X))))&
(![X]:((~funny(X)&~tall(X))=>wise(X)))&
(((calm(mary)<~>~wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>((~happy(john)|tall(john))))&
((wise(paul)&happy(paul)))&
((~generous(fred)&~funny(fred)))&
(?[X]:((~funny(X)<~>~old(X))))&
((brave(alice)|~strong(alice)))&
(old(lucy))&
(?[X]:((~funny(X)|quiet(X)))) | rich(fred) | [
"p0",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 5945059713861167757532794
% SZS output start Proof for 5945059713861167757532794
1. ! [X0] : (~rich(X0) => ~strong(X0)) [input p0]
9. ! [X0] : ((~kind(X0) | generous(X0)) <=> patient(X0)) [input p8]
13. ! [X0] : ((~rich(X0) | ~strong(X0)) => (~patient(X0) & generous(X0))) [input p12]
23. ~rich(fred) [input hypothesis]
24. ! [X0] : ((~kind(X0) | generous(X0)) => patient(X0)) [unused predicate definition removal 9]
25. ! [X0] : (~strong(X0) | rich(X0)) [ennf transformation 1]
30. ! [X0] : (patient(X0) | (kind(X0) & ~generous(X0))) [ennf transformation 24]
34. ! [X0] : ((~patient(X0) & generous(X0)) | (rich(X0) & strong(X0))) [ennf transformation 13]
71. ~strong(X0) | rich(X0) [cnf transformation 25]
95. ~generous(X0) | patient(X0) [cnf transformation 30]
111. generous(X0) | strong(X0) [cnf transformation 34]
113. ~patient(X0) | strong(X0) [cnf transformation 34]
130. ~rich(fred) [cnf transformation 23]
256. 27 <=> ! [X1] : strong(X1) [avatar definition]
257. strong(X1) <- (27) [avatar component clause 256]
293. strong(X1) | patient(X1) [resolution 111,95]
294. strong(X1) [subsumption resolution 293,113]
295. 27 [avatar split clause 294,256]
298. rich(X0) <- (27) [resolution 257,71]
305. $false <- (27) [resolution 298,130]
306. ~27 [avatar contradiction clause 305]
307. $false [avatar sat refutation 295,306]
% SZS output end Proof for 5945059713861167757532794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not rich then susan is generous and vice versa.
Everyone who is generous is funny.
Everyone who is wise is both not kind and brave.
Everyone who is both wise and funny is both strong and wise and vice versa.
Everyone who is not rich is either not curious or quiet.
If someone is calm then alice is both not calm and not quiet.
Everyone who is not happy is not rich and vice versa.
If mary is either strong or old then someone is not happy.
If someone is funny then john is not brave or quiet and vice versa.
Everyone who is not brave or not patient is not patient or calm and vice versa.
If paul is not creative or not wise then john is rich and vice versa.
Everyone who is not old or wise is kind and vice versa.
Everyone who is not calm or curious is not funny.
Everyone who is either not humble or funny is happy and vice versa.
Everyone who is quiet or not brave is not humble or patient.
Everyone who is not quiet or not brave is either brave or humble and vice versa.
Someone is not quiet.
Mary is both generous and kind.
Lucy is either not creative or humble.
Paul is generous.
Someone is old or not tall.
Someone is both not rich and brave. | Alice is not curious. | neutral | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(?[X]:(~quiet(X)))&
((generous(mary)&kind(mary)))&
((~creative(lucy)<~>humble(lucy)))&
(generous(paul))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~rich(X)&brave(X)))) | ~curious(alice) | []
| null | 0 |
Everyone who is funny or not tall is either strong or not generous and vice versa.
Everyone who is funny is not kind or not calm.
If paul is either patient or not curious then someone is creative or strong.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If mary is not curious then mary is not quiet and vice versa.
If someone is not brave then someone is both happy and rich.
Everyone who is both not humble and not funny is humble.
Everyone who is kind is not strong or rich.
If john is both not funny and not kind then john is both not humble and curious and vice versa.
Someone is old.
Paul is rich or not generous.
Mary is not funny.
Lucy is both not patient and not generous.
Someone is not humble or patient. | Lucy is quiet. | neutral | (![X]:((funny(X)|~tall(X))<=>(strong(X)<~>~generous(X))))&
(![X]:(funny(X)=>(~kind(X)|~calm(X))))&
(((patient(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((~curious(mary))<=>(~quiet(mary)))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((~humble(X)&~funny(X))=>humble(X)))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(((~funny(john)&~kind(john)))<=>((~humble(john)&curious(john))))&
(?[X]:(old(X)))&
((rich(paul)|~generous(paul)))&
(~funny(mary))&
((~patient(lucy)&~generous(lucy)))&
(?[X]:((~humble(X)|patient(X)))) | quiet(lucy) | []
| null | 0 |
If fred is not kind then fred is not strong and vice versa.
Everyone who is either not humble or not rich is both quiet and not generous.
If fred is not curious then alice is wise or not rich and vice versa.
Everyone who is both not humble and not rich is not strong and vice versa.
If lucy is either quiet or not humble then mary is either old or generous and vice versa.
If someone is either not calm or kind then john is tall or not rich.
If john is happy or strong then someone is both not calm and wise and vice versa.
If someone is either wise or patient then fred is not kind.
If someone is not old then someone is either not patient or not wise.
Everyone who is rich is not strong and vice versa.
Everyone who is both brave and not wise is not brave or not kind and vice versa.
Everyone who is not wise or not brave is quiet or calm.
Everyone who is either not funny or patient is either patient or calm.
If someone is curious then mary is either kind or calm and vice versa.
If someone is both not brave and not wise then someone is either not humble or rich.
If someone is both quiet and tall then lucy is either not curious or not creative and vice versa.
Someone is either wise or not humble.
John is either not curious or old.
Someone is either not humble or not wise.
Someone is both brave and not tall. | Mary is quiet. | entailment | ((~kind(fred))<=>(~strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))=>(quiet(X)&~generous(X))))&
((~curious(fred))<=>((wise(alice)|~rich(alice))))&
(![X]:((~humble(X)&~rich(X))<=>~strong(X)))&
(((quiet(lucy)<~>~humble(lucy)))<=>((old(mary)<~>generous(mary))))&
((?[X]:((~calm(X)<~>kind(X))))=>((tall(john)|~rich(john))))&
(((happy(john)|strong(john)))<=>(?[X]:((~calm(X)&wise(X)))))&
((?[X]:((wise(X)<~>patient(X))))=>(~kind(fred)))&
((?[X]:(~old(X)))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:(rich(X)<=>~strong(X)))&
(![X]:((brave(X)&~wise(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~wise(X)|~brave(X))=>(quiet(X)|calm(X))))&
(![X]:((~funny(X)<~>patient(X))=>(patient(X)<~>calm(X))))&
((?[X]:(curious(X)))<=>((kind(mary)<~>calm(mary))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
((?[X]:((quiet(X)&tall(X))))<=>((~curious(lucy)<~>~creative(lucy))))&
(?[X]:((wise(X)<~>~humble(X))))&
((~curious(john)<~>old(john)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((brave(X)&~tall(X)))) | quiet(mary) | [
"p1",
"p3",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 5569531433949883230114626
% SZS output start Proof for 5569531433949883230114626
2. ! [X0] : ((~humble(X0) <~> ~rich(X0)) => (~generous(X0) & quiet(X0))) [input p1]
4. ! [X0] : ((~rich(X0) & ~humble(X0)) <=> ~strong(X0)) [input p3]
10. ! [X0] : (rich(X0) <=> ~strong(X0)) [input p9]
21. ~quiet(mary) [input hypothesis]
24. ! [X0] : ((~generous(X0) & quiet(X0)) | (~humble(X0) <=> ~rich(X0))) [ennf transformation 2]
34. ! [X0] : ((~generous(X0) & quiet(X0)) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) [nnf transformation 24]
37. ! [X0] : (((~rich(X0) & ~humble(X0)) | strong(X0)) & (~strong(X0) | (rich(X0) | humble(X0)))) [nnf transformation 4]
38. ! [X0] : (((~rich(X0) & ~humble(X0)) | strong(X0)) & (~strong(X0) | rich(X0) | humble(X0))) [flattening 37]
51. ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))) [nnf transformation 10]
79. ~humble(X0) | quiet(X0) | rich(X0) [cnf transformation 34]
85. ~strong(X0) | rich(X0) | humble(X0) [cnf transformation 38]
87. ~rich(X0) | strong(X0) [cnf transformation 38]
107. ~strong(X0) | ~rich(X0) [cnf transformation 51]
108. rich(X0) | strong(X0) [cnf transformation 51]
140. ~quiet(mary) [cnf transformation 21]
255. strong(X0) [subsumption resolution 108,87]
256. ~rich(X0) [subsumption resolution 107,255]
357. rich(X0) | humble(X0) [resolution 85,255]
358. humble(X0) [subsumption resolution 357,256]
362. quiet(X0) | rich(X0) [resolution 358,79]
366. quiet(X0) [subsumption resolution 362,256]
375. $false [resolution 366,140]
% SZS output end Proof for 5569531433949883230114626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or funny is curious and vice versa. If someone is not humble or happy then alice is creative. If alice is not wise or wise then someone is both not creative and humble. Everyone who is calm or not creative is not wise and vice versa. Everyone who is patient is quiet. Everyone who is both curious and not patient is either kind or not humble and vice versa. Everyone who is quiet is both creative and not curious and vice versa. If mary is both not calm and not wise then lucy is patient or not tall and vice versa. Everyone who is not strong or not wise is either kind or not calm. If someone is strong or brave then alice is generous and vice versa. If mary is not curious then someone is not curious or humble. If alice is either not funny or generous then someone is both not curious and not happy. Everyone who is not generous or tall is both old and not strong. If someone is both not happy and brave then fred is either not patient or not rich. Everyone who is both not old and old is old. If someone is either strong or not old then fred is curious and vice versa. Someone is tall. Lucy is patient. Fred is both not patient and tall. Mary is not funny. Someone is not creative or quiet. Someone is not tall. Someone is both generous and not calm. Fred is calm. | Fred is rich. | neutral | (![X]:((~creative(X)|funny(X))<=>curious(X)))&
((?[X]:((~humble(X)|happy(X))))=>(creative(alice)))&
(((~wise(alice)|wise(alice)))=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((calm(X)|~creative(X))<=>~wise(X)))&
(![X]:(patient(X)=>quiet(X)))&
(![X]:((curious(X)&~patient(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(quiet(X)<=>(creative(X)&~curious(X))))&
(((~calm(mary)&~wise(mary)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((~strong(X)|~wise(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((strong(X)|brave(X))))<=>(generous(alice)))&
((~curious(mary))=>(?[X]:((~curious(X)|humble(X)))))&
(((~funny(alice)<~>generous(alice)))=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((~generous(X)|tall(X))=>(old(X)&~strong(X))))&
((?[X]:((~happy(X)&brave(X))))=>((~patient(fred)<~>~rich(fred))))&
(![X]:((~old(X)&old(X))=>old(X)))&
((?[X]:((strong(X)<~>~old(X))))<=>(curious(fred)))&
(?[X]:(tall(X)))&
(patient(lucy))&
((~patient(fred)&tall(fred)))&
(~funny(mary))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:((generous(X)&~calm(X))))&
(calm(fred)) | rich(fred) | []
| null | 0 |
Everyone who is not quiet is happy or not happy and vice versa.
Everyone who is both not calm and not generous is either not creative or curious and vice versa.
Everyone who is either calm or not happy is both not old and wise and vice versa.
If someone is not happy then someone is either brave or not strong and vice versa.
If someone is not humble then someone is both not humble and not patient.
If john is both old and not tall then someone is not strong or generous.
If susan is tall or not tall then fred is tall or funny and vice versa.
If paul is either patient or rich then someone is not funny or not old and vice versa.
If someone is both humble and old then mary is both quiet and not brave.
Everyone who is either rich or quiet is both not quiet and patient and vice versa.
If john is not creative or not strong then alice is either not brave or brave and vice versa.
Everyone who is either not humble or not quiet is both not brave and kind and vice versa.
If paul is quiet then someone is either kind or not kind.
Everyone who is either kind or patient is both not rich and not funny.
Everyone who is either kind or quiet is not happy or not strong and vice versa.
Everyone who is either not curious or not creative is either wise or generous.
John is rich or tall.
Susan is brave.
Someone is either not strong or rich.
John is not happy or not rich.
Lucy is both not quiet and not brave.
Someone is either brave or quiet.
Someone is both not creative and kind.
Mary is not tall or rich. | Lucy is not calm. | entailment | (![X]:(~quiet(X)<=>(happy(X)|~happy(X))))&
(![X]:((~calm(X)&~generous(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((calm(X)<~>~happy(X))<=>(~old(X)&wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((~humble(X)&~patient(X)))))&
(((old(john)&~tall(john)))=>(?[X]:((~strong(X)|generous(X)))))&
(((tall(susan)|~tall(susan)))<=>((tall(fred)|funny(fred))))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)|~old(X)))))&
((?[X]:((humble(X)&old(X))))=>((quiet(mary)&~brave(mary))))&
(![X]:((rich(X)<~>quiet(X))<=>(~quiet(X)&patient(X))))&
(((~creative(john)|~strong(john)))<=>((~brave(alice)<~>brave(alice))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((quiet(paul))=>(?[X]:((kind(X)<~>~kind(X)))))&
(![X]:((kind(X)<~>patient(X))=>(~rich(X)&~funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(~happy(X)|~strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(wise(X)<~>generous(X))))&
((rich(john)|tall(john)))&
(brave(susan))&
(?[X]:((~strong(X)<~>rich(X))))&
((~happy(john)|~rich(john)))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((~creative(X)&kind(X))))&
((~tall(mary)|rich(mary))) | ~calm(lucy) | [
"p0",
"p2",
"p7",
"p8",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 9191273280976570191589679
% SZS output start Proof for 9191273280976570191589679
1. ! [X0] : (~quiet(X0) <=> (~happy(X0) | happy(X0))) [input p0]
3. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> (wise(X0) & ~old(X0))) [input p2]
8. (patient(paul) <~> rich(paul)) <=> ? [X0] : (~old(X0) | ~funny(X0)) [input p7]
9. ? [X0] : (old(X0) & humble(X0)) => (~brave(mary) & quiet(mary)) [input p8]
10. ! [X0] : ((rich(X0) <~> quiet(X0)) <=> (patient(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> ~quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p11]
15. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> (~strong(X0) | ~happy(X0))) [input p14]
21. ~brave(lucy) & ~quiet(lucy) [input p20]
25. calm(lucy) [input hypothesis]
31. (~brave(mary) & quiet(mary)) | ! [X0] : (~old(X0) | ~humble(X0)) [ennf transformation 9]
35. ! [X0] : ((~quiet(X0) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | quiet(X0))) [nnf transformation 1]
36. ! [X0] : ((~quiet(X0) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | quiet(X0))) [flattening 35]
39. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 3]
40. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [flattening 39]
53. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & (? [X0] : (~old(X0) | ~funny(X0)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [nnf transformation 8]
54. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & (? [X1] : (~old(X1) | ~funny(X1)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [rectify 53]
55. ? [X1] : (~old(X1) | ~funny(X1)) => (~old(sK4) | ~funny(sK4)) [choice axiom]
56. (((~rich(paul) | ~patient(paul)) & (rich(paul) | patient(paul))) | ! [X0] : (old(X0) & funny(X0))) & ((~old(sK4) | ~funny(sK4)) | ((patient(paul) | ~rich(paul)) & (rich(paul) | ~patient(paul)))) [skolemisation 54,55]
57. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [nnf transformation 10]
58. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [flattening 57]
61. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [nnf transformation 12]
62. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [flattening 61]
67. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (strong(X0) & happy(X0))) & ((~strong(X0) | ~happy(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (strong(X0) & happy(X0))) & (~strong(X0) | ~happy(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [flattening 67]
79. ~quiet(X0) | ~happy(X0) [cnf transformation 36]
80. ~quiet(X0) | happy(X0) [cnf transformation 36]
87. ~old(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 40]
107. rich(paul) | patient(paul) | old(X0) [cnf transformation 56]
109. ~rich(paul) | ~patient(paul) | old(X0) [cnf transformation 56]
110. quiet(mary) | ~old(X0) | ~humble(X0) [cnf transformation 31]
114. patient(X0) | quiet(X0) | ~rich(X0) [cnf transformation 58]
116. quiet(X0) | rich(X0) | ~patient(X0) | quiet(X0) [cnf transformation 58]
129. quiet(X0) | humble(X0) | ~kind(X0) | brave(X0) [cnf transformation 62]
138. quiet(X0) | kind(X0) | happy(X0) [cnf transformation 68]
152. ~brave(lucy) [cnf transformation 21]
158. calm(lucy) [cnf transformation 25]
162. quiet(X0) | rich(X0) | ~patient(X0) [duplicate literal removal 116]
163. ~quiet(X0) [subsumption resolution 79,80]
234. 17 <=> ! [X0] : old(X0) [avatar definition]
235. old(X0) <- (17) [avatar component clause 234]
237. 18 <=> patient(paul) [avatar definition]
238. patient(paul) <- (18) [avatar component clause 237]
239. ~patient(paul) <- (~18) [avatar component clause 237]
241. 19 <=> rich(paul) [avatar definition]
242. rich(paul) <- (19) [avatar component clause 241]
243. ~rich(paul) <- (~19) [avatar component clause 241]
244. 17 | ~18 | ~19 [avatar split clause 109,241,237,234]
249. 17 | 18 | 19 [avatar split clause 107,241,237,234]
262. 23 <=> ! [X0] : (~old(X0) | ~humble(X0)) [avatar definition]
263. ~humble(X0) | ~old(X0) <- (23) [avatar component clause 262]
269. ~old(X0) | ~humble(X0) [subsumption resolution 110,163]
270. 23 [avatar split clause 269,262]
271. ~patient(X0) | rich(X0) [subsumption resolution 162,163]
272. ~rich(X0) | patient(X0) [subsumption resolution 114,163]
287. ~kind(X0) | humble(X0) | brave(X0) [subsumption resolution 129,163]
292. kind(X0) | happy(X0) [subsumption resolution 138,163]
327. rich(paul) <- (18) [resolution 271,238]
328. $false <- (18, ~19) [subsumption resolution 327,243]
329. ~18 | 19 [avatar contradiction clause 328]
330. patient(paul) <- (19) [resolution 272,242]
331. $false <- (~18, 19) [subsumption resolution 330,239]
332. 18 | ~19 [avatar contradiction clause 331]
349. ~calm(X0) | ~happy(X0) <- (17) [resolution 87,235]
350. ~happy(lucy) <- (17) [resolution 349,158]
366. humble(X0) | brave(X0) | happy(X0) [resolution 287,292]
427. brave(X2) | happy(X2) | ~old(X2) <- (23) [resolution 366,263]
428. brave(X2) | happy(X2) <- (17, 23) [subsumption resolution 427,235]
474. happy(lucy) <- (17, 23) [resolution 428,152]
475. $false <- (17, 23) [subsumption resolution 474,350]
476. ~17 | ~23 [avatar contradiction clause 475]
477. $false [avatar sat refutation 244,249,270,329,332,476]
% SZS output end Proof for 9191273280976570191589679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not kind or not funny and vice versa.
If lucy is kind then fred is either not old or not rich and vice versa.
If someone is strong then fred is both not patient and quiet and vice versa.
Everyone who is either calm or not patient is not rich or happy and vice versa.
Everyone who is both tall and generous is both kind and wise.
If someone is either not funny or not tall then someone is either creative or not calm.
Everyone who is tall or brave is not funny.
If someone is both funny and not old then fred is either not brave or tall.
Everyone who is kind is both curious and not patient and vice versa.
Everyone who is humble is both generous and not generous.
Everyone who is not brave is either not generous or not humble.
If someone is not happy or rich then fred is rich or not quiet.
Everyone who is either patient or not creative is either kind or funny.
If lucy is not humble then paul is old or kind.
Everyone who is not funny or not brave is either not quiet or not curious.
Everyone who is either not patient or not creative is both brave and creative and vice versa.
Mary is both not old and not funny.
Mary is not calm.
Lucy is both happy and generous.
Susan is humble or not generous.
John is both not generous and wise.
Someone is either not quiet or tall.
Paul is creative or funny. | Susan is not curious. | contradiction | (![X]:(~creative(X)<=>(~kind(X)|~funny(X))))&
((kind(lucy))<=>((~old(fred)<~>~rich(fred))))&
((?[X]:(strong(X)))<=>((~patient(fred)&quiet(fred))))&
(![X]:((calm(X)<~>~patient(X))<=>(~rich(X)|happy(X))))&
(![X]:((tall(X)&generous(X))=>(kind(X)&wise(X))))&
((?[X]:((~funny(X)<~>~tall(X))))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((tall(X)|brave(X))=>~funny(X)))&
((?[X]:((funny(X)&~old(X))))=>((~brave(fred)<~>tall(fred))))&
(![X]:(kind(X)<=>(curious(X)&~patient(X))))&
(![X]:(humble(X)=>(generous(X)&~generous(X))))&
(![X]:(~brave(X)=>(~generous(X)<~>~humble(X))))&
((?[X]:((~happy(X)|rich(X))))=>((rich(fred)|~quiet(fred))))&
(![X]:((patient(X)<~>~creative(X))=>(kind(X)<~>funny(X))))&
((~humble(lucy))=>((old(paul)|kind(paul))))&
(![X]:((~funny(X)|~brave(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>(brave(X)&creative(X))))&
((~old(mary)&~funny(mary)))&
(~calm(mary))&
((happy(lucy)&generous(lucy)))&
((humble(susan)|~generous(susan)))&
((~generous(john)&wise(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((creative(paul)|funny(paul))) | ~curious(susan) | [
"p0",
"p6",
"p8",
"p9",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 9125638405173566007954121
% SZS output start Proof for 9125638405173566007954121
1. ! [X0] : (~creative(X0) <=> (~funny(X0) | ~kind(X0))) [input p0]
7. ! [X0] : ((brave(X0) | tall(X0)) => ~funny(X0)) [input p6]
9. ! [X0] : (kind(X0) <=> (~patient(X0) & curious(X0))) [input p8]
10. ! [X0] : (humble(X0) => (~generous(X0) & generous(X0))) [input p9]
11. ! [X0] : (~brave(X0) => (~generous(X0) <~> ~humble(X0))) [input p10]
13. ! [X0] : ((patient(X0) <~> ~creative(X0)) => (kind(X0) <~> funny(X0))) [input p12]
16. ! [X0] : ((~patient(X0) <~> ~creative(X0)) <=> (creative(X0) & brave(X0))) [input p15]
20. ~generous(susan) | humble(susan) [input p19]
24. ~curious(susan) [input hypothesis]
31. ! [X0] : (~funny(X0) | (~brave(X0) & ~tall(X0))) [ennf transformation 7]
33. ! [X0] : ((~generous(X0) & generous(X0)) | ~humble(X0)) [ennf transformation 10]
34. ! [X0] : ((~generous(X0) <~> ~humble(X0)) | brave(X0)) [ennf transformation 11]
37. ! [X0] : ((kind(X0) <~> funny(X0)) | (patient(X0) <=> ~creative(X0))) [ennf transformation 13]
41. ! [X0] : ((~creative(X0) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | creative(X0))) [nnf transformation 1]
42. ! [X0] : ((~creative(X0) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | creative(X0))) [flattening 41]
56. ! [X0] : ((kind(X0) | (patient(X0) | ~curious(X0))) & ((~patient(X0) & curious(X0)) | ~kind(X0))) [nnf transformation 9]
57. ! [X0] : ((kind(X0) | patient(X0) | ~curious(X0)) & ((~patient(X0) & curious(X0)) | ~kind(X0))) [flattening 56]
58. ! [X0] : (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | brave(X0)) [nnf transformation 34]
59. ! [X0] : (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) [nnf transformation 37]
61. ! [X0] : ((((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))))) [nnf transformation 16]
62. ! [X0] : ((((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))))) [flattening 61]
67. ~creative(X0) | kind(X0) [cnf transformation 42]
68. ~creative(X0) | funny(X0) [cnf transformation 42]
88. ~brave(X0) | ~funny(X0) [cnf transformation 31]
91. ~kind(X0) | curious(X0) [cnf transformation 57]
94. generous(X0) | ~humble(X0) [cnf transformation 33]
95. ~humble(X0) | ~generous(X0) [cnf transformation 33]
97. humble(X0) | generous(X0) | brave(X0) [cnf transformation 58]
101. funny(X0) | kind(X0) | patient(X0) | creative(X0) [cnf transformation 59]
112. creative(X0) | ~patient(X0) | creative(X0) [cnf transformation 62]
120. ~generous(susan) | humble(susan) [cnf transformation 20]
125. ~curious(susan) [cnf transformation 24]
126. ~patient(X0) | creative(X0) [duplicate literal removal 112]
193. ~humble(X0) [subsumption resolution 94,95]
194. brave(X0) | generous(X0) [subsumption resolution 97,193]
203. patient(X0) | kind(X0) | funny(X0) [subsumption resolution 101,67]
214. ~generous(susan) [subsumption resolution 120,193]
227. ~funny(X0) | generous(X0) [resolution 194,88]
259. 24 <=> funny(susan) [avatar definition]
260. ~funny(susan) <- (~24) [avatar component clause 259]
261. funny(susan) <- (24) [avatar component clause 259]
277. generous(susan) <- (24) [resolution 261,227]
279. $false <- (24) [subsumption resolution 277,214]
280. ~24 [avatar contradiction clause 279]
286. 28 <=> kind(susan) [avatar definition]
287. kind(susan) <- (28) [avatar component clause 286]
293. kind(X1) | funny(X1) | creative(X1) [resolution 203,126]
296. funny(X1) | kind(X1) [subsumption resolution 293,68]
301. kind(susan) <- (~24) [resolution 296,260]
302. 28 | 24 [avatar split clause 301,259,286]
303. curious(susan) <- (28) [resolution 287,91]
304. $false <- (28) [subsumption resolution 303,125]
305. ~28 [avatar contradiction clause 304]
306. $false [avatar sat refutation 280,302,305]
% SZS output end Proof for 9125638405173566007954121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or old is both strong and not tall. Everyone who is patient or not calm is both not wise and old. If john is funny or curious then lucy is either generous or tall. If someone is not patient then someone is not generous. If someone is kind then someone is either not happy or not strong. Everyone who is either old or not humble is both not curious and not patient and vice versa. If lucy is both curious and creative then someone is either not rich or not generous. If mary is rich then mary is both generous and not calm. Everyone who is curious or calm is not wise. Everyone who is both strong and not wise is patient or wise and vice versa. If someone is rich then someone is both not funny and not calm and vice versa. Everyone who is curious or not wise is creative or tall. Everyone who is both not kind and not calm is both strong and not quiet. Everyone who is rich is not patient or happy and vice versa. If someone is both curious and not old then alice is calm or not brave and vice versa. Everyone who is brave is either not brave or not generous and vice versa. Fred is not curious or not kind. Someone is both not rich and not happy. Someone is either not happy or not tall. Someone is not calm or tall. Someone is strong. Alice is not humble. | Alice is funny. | neutral | (![X]:((~strong(X)<~>old(X))=>(strong(X)&~tall(X))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
((?[X]:(kind(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(~curious(X)&~patient(X))))&
(((curious(lucy)&creative(lucy)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
((rich(mary))=>((generous(mary)&~calm(mary))))&
(![X]:((curious(X)|calm(X))=>~wise(X)))&
(![X]:((strong(X)&~wise(X))<=>(patient(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((curious(X)|~wise(X))=>(creative(X)|tall(X))))&
(![X]:((~kind(X)&~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:(rich(X)<=>(~patient(X)|happy(X))))&
((?[X]:((curious(X)&~old(X))))<=>((calm(alice)|~brave(alice))))&
(![X]:(brave(X)<=>(~brave(X)<~>~generous(X))))&
((~curious(fred)|~kind(fred)))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:(strong(X)))&
(~humble(alice)) | funny(alice) | []
| null | 0 |
Everyone who is both creative and happy is tall. If someone is either wise or kind then john is either not humble or patient. Everyone who is not tall or patient is either not patient or rich. Everyone who is either not quiet or not patient is either wise or not tall and vice versa. Everyone who is either not funny or brave is either not calm or strong. Everyone who is either not brave or not funny is creative or patient. Everyone who is not old is tall or patient. If someone is both tall and funny then someone is not kind. If john is either not curious or not calm then mary is both not kind and not strong. Everyone who is both not humble and not funny is either curious or wise and vice versa. If mary is either generous or not creative then alice is not quiet and vice versa. Everyone who is both generous and curious is either not strong or not funny and vice versa. If susan is old or not creative then paul is generous and vice versa. If lucy is either not quiet or not humble then someone is either not happy or curious. If susan is not happy then someone is not wise and vice versa. If paul is not brave or tall then someone is not generous. Someone is either not tall or strong. Susan is brave. Someone is humble or wise. Someone is both not funny and not brave. Paul is old or happy. Someone is happy. Paul is wise. Fred is not quiet or not creative. | Susan is brave. | entailment | (![X]:((creative(X)&happy(X))=>tall(X)))&
((?[X]:((wise(X)<~>kind(X))))=>((~humble(john)<~>patient(john))))&
(![X]:((~tall(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((~funny(X)<~>brave(X))=>(~calm(X)<~>strong(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(creative(X)|patient(X))))&
(![X]:(~old(X)=>(tall(X)|patient(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:(~kind(X))))&
(((~curious(john)<~>~calm(john)))=>((~kind(mary)&~strong(mary))))&
(![X]:((~humble(X)&~funny(X))<=>(curious(X)<~>wise(X))))&
(((generous(mary)<~>~creative(mary)))<=>(~quiet(alice)))&
(![X]:((generous(X)&curious(X))<=>(~strong(X)<~>~funny(X))))&
(((old(susan)|~creative(susan)))<=>(generous(paul)))&
(((~quiet(lucy)<~>~humble(lucy)))=>(?[X]:((~happy(X)<~>curious(X)))))&
((~happy(susan))<=>(?[X]:(~wise(X))))&
(((~brave(paul)|tall(paul)))=>(?[X]:(~generous(X))))&
(?[X]:((~tall(X)<~>strong(X))))&
(brave(susan))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((~funny(X)&~brave(X))))&
((old(paul)|happy(paul)))&
(?[X]:(happy(X)))&
(wise(paul))&
((~quiet(fred)|~creative(fred))) | brave(susan) | [
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 3399311360483901765935044
% SZS output start Proof for 3399311360483901765935044
18. brave(susan) [input p17]
25. ~brave(susan) [input hypothesis]
132. brave(susan) [cnf transformation 18]
140. ~brave(susan) [cnf transformation 25]
303. $false [subsumption resolution 140,132]
% SZS output end Proof for 3399311360483901765935044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or patient is either calm or funny.
If paul is either quiet or not generous then paul is rich.
Everyone who is either strong or curious is not creative.
If alice is both generous and curious then someone is creative.
If someone is either not humble or not tall then someone is both generous and not calm and vice versa.
If susan is not quiet or not wise then someone is either not tall or brave and vice versa.
If mary is not generous then alice is both not generous and tall and vice versa.
Everyone who is quiet or generous is either patient or humble and vice versa.
Everyone who is not rich or happy is curious or rich.
If someone is either not patient or old then someone is either rich or creative and vice versa.
If someone is either rich or brave then susan is either not patient or funny and vice versa.
Everyone who is either not humble or not generous is either calm or kind.
If someone is strong or calm then someone is either kind or not generous and vice versa.
Everyone who is either not old or not humble is not quiet or not rich and vice versa.
Everyone who is not kind or not old is either happy or curious.
Everyone who is funny is quiet or creative and vice versa.
Someone is either humble or not quiet.
Alice is not humble.
Susan is not patient.
Susan is either not kind or not wise.
Mary is patient.
Mary is not kind.
John is quiet.
Mary is both generous and not tall. | Mary is not calm. | contradiction | (![X]:((quiet(X)|patient(X))=>(calm(X)<~>funny(X))))&
(((quiet(paul)<~>~generous(paul)))=>(rich(paul)))&
(![X]:((strong(X)<~>curious(X))=>~creative(X)))&
(((generous(alice)&curious(alice)))=>(?[X]:(creative(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:((generous(X)&~calm(X)))))&
(((~quiet(susan)|~wise(susan)))<=>(?[X]:((~tall(X)<~>brave(X)))))&
((~generous(mary))<=>((~generous(alice)&tall(alice))))&
(![X]:((quiet(X)|generous(X))<=>(patient(X)<~>humble(X))))&
(![X]:((~rich(X)|happy(X))=>(curious(X)|rich(X))))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:((rich(X)<~>brave(X))))<=>((~patient(susan)<~>funny(susan))))&
(![X]:((~humble(X)<~>~generous(X))=>(calm(X)<~>kind(X))))&
((?[X]:((strong(X)|calm(X))))<=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((~old(X)<~>~humble(X))<=>(~quiet(X)|~rich(X))))&
(![X]:((~kind(X)|~old(X))=>(happy(X)<~>curious(X))))&
(![X]:(funny(X)<=>(quiet(X)|creative(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(~humble(alice))&
(~patient(susan))&
((~kind(susan)<~>~wise(susan)))&
(patient(mary))&
(~kind(mary))&
(quiet(john))&
((generous(mary)&~tall(mary))) | ~calm(mary) | [
"p7",
"p11",
"p20",
"p21",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 3437567853986673038100522
% SZS output start Proof for 3437567853986673038100522
8. ! [X0] : ((generous(X0) | quiet(X0)) <=> (patient(X0) <~> humble(X0))) [input p7]
12. ! [X0] : ((~humble(X0) <~> ~generous(X0)) => (calm(X0) <~> kind(X0))) [input p11]
21. patient(mary) [input p20]
22. ~kind(mary) [input p21]
24. ~tall(mary) & generous(mary) [input p23]
25. ~calm(mary) [input hypothesis]
36. ! [X0] : ((calm(X0) <~> kind(X0)) | (~humble(X0) <=> ~generous(X0))) [ennf transformation 12]
55. ! [X0] : (((generous(X0) | quiet(X0)) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 8]
56. ! [X0] : ((generous(X0) | quiet(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (~generous(X0) & ~quiet(X0)))) [flattening 55]
66. ! [X0] : (((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) [nnf transformation 36]
108. ~humble(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 56]
129. ~generous(X0) | calm(X0) | kind(X0) | humble(X0) [cnf transformation 66]
158. patient(mary) [cnf transformation 21]
159. ~kind(mary) [cnf transformation 22]
161. generous(mary) [cnf transformation 24]
163. ~calm(mary) [cnf transformation 25]
256. 21 <=> generous(mary) [avatar definition]
257. generous(mary) <- (21) [avatar component clause 256]
379. 21 [avatar split clause 161,256]
559. calm(mary) | kind(mary) | humble(mary) <- (21) [resolution 129,257]
561. kind(mary) | humble(mary) <- (21) [subsumption resolution 559,163]
562. humble(mary) <- (21) [subsumption resolution 561,159]
564. ~patient(mary) | ~generous(mary) <- (21) [resolution 562,108]
567. ~generous(mary) <- (21) [subsumption resolution 564,158]
568. $false <- (21) [subsumption resolution 567,257]
569. ~21 [avatar contradiction clause 568]
574. $false [avatar sat refutation 379,569]
% SZS output end Proof for 3437567853986673038100522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and strong is quiet. If someone is either not funny or not quiet then susan is both old and not strong and vice versa. If john is not patient or funny then someone is generous or patient. Everyone who is both brave and not curious is not patient or not brave and vice versa. If paul is either humble or not happy then someone is both happy and kind. Everyone who is curious or not kind is not kind and vice versa. If someone is both old and humble then paul is either generous or not kind and vice versa. If susan is not generous or old then someone is not brave or not curious. Everyone who is calm is both not creative and funny and vice versa. Everyone who is kind is not humble and vice versa. If someone is wise or not wise then someone is rich. Everyone who is rich or old is both patient and not old. Everyone who is not quiet is curious and vice versa. If someone is both funny and not calm then someone is both not rich and not creative and vice versa. Susan is both not humble and not happy. Someone is both tall and not rich. Paul is generous or brave. Someone is either wise or kind. Someone is not tall. | Paul is creative. | neutral | (![X]:((~happy(X)&strong(X))=>quiet(X)))&
((?[X]:((~funny(X)<~>~quiet(X))))<=>((old(susan)&~strong(susan))))&
(((~patient(john)|funny(john)))=>(?[X]:((generous(X)|patient(X)))))&
(![X]:((brave(X)&~curious(X))<=>(~patient(X)|~brave(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((curious(X)|~kind(X))<=>~kind(X)))&
((?[X]:((old(X)&humble(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~generous(susan)|old(susan)))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(calm(X)<=>(~creative(X)&funny(X))))&
(![X]:(kind(X)<=>~humble(X)))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|old(X))=>(patient(X)&~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
((~humble(susan)&~happy(susan)))&
(?[X]:((tall(X)&~rich(X))))&
((generous(paul)|brave(paul)))&
(?[X]:((wise(X)<~>kind(X))))&
(?[X]:(~tall(X))) | creative(paul) | []
| null | 0 |
If alice is either not kind or calm then someone is not rich or not tall and vice versa.
If someone is tall then someone is either funny or brave.
Everyone who is not rich is curious and vice versa.
If someone is generous then someone is both brave and not brave and vice versa.
Everyone who is not generous is both funny and not humble.
Everyone who is either funny or happy is not tall or not patient and vice versa.
Everyone who is brave is both not calm and not kind and vice versa.
Everyone who is rich or not humble is both not generous and not happy and vice versa.
If someone is either not wise or calm then fred is not rich.
Everyone who is both calm and strong is both not generous and not strong.
If someone is both not rich and not wise then fred is not old.
If john is either happy or not brave then paul is both not creative and quiet.
If someone is creative then susan is creative.
If fred is not calm or quiet then someone is either not generous or not happy and vice versa.
If fred is either happy or not tall then susan is not rich or not brave.
If john is either generous or curious then susan is both old and not happy and vice versa.
Lucy is both not generous and not wise.
Paul is calm or not old.
Lucy is kind.
Mary is not happy or rich.
Someone is either not quiet or not old.
Paul is kind or not tall.
Someone is not happy or curious.
Mary is either not kind or not quiet. | Lucy is brave. | contradiction | (((~kind(alice)<~>calm(alice)))<=>(?[X]:((~rich(X)|~tall(X)))))&
((?[X]:(tall(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(~rich(X)<=>curious(X)))&
((?[X]:(generous(X)))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~generous(X)=>(funny(X)&~humble(X))))&
(![X]:((funny(X)<~>happy(X))<=>(~tall(X)|~patient(X))))&
(![X]:(brave(X)<=>(~calm(X)&~kind(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(~rich(fred)))&
(![X]:((calm(X)&strong(X))=>(~generous(X)&~strong(X))))&
((?[X]:((~rich(X)&~wise(X))))=>(~old(fred)))&
(((happy(john)<~>~brave(john)))=>((~creative(paul)&quiet(paul))))&
((?[X]:(creative(X)))=>(creative(susan)))&
(((~calm(fred)|quiet(fred)))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(((happy(fred)<~>~tall(fred)))=>((~rich(susan)|~brave(susan))))&
(((generous(john)<~>curious(john)))<=>((old(susan)&~happy(susan))))&
((~generous(lucy)&~wise(lucy)))&
((calm(paul)|~old(paul)))&
(kind(lucy))&
((~happy(mary)|rich(mary)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((kind(paul)|~tall(paul)))&
(?[X]:((~happy(X)|curious(X))))&
((~kind(mary)<~>~quiet(mary))) | brave(lucy) | [
"p6",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7668518285358612936208651
% SZS output start Proof for 7668518285358612936208651
7. ! [X0] : (brave(X0) <=> (~kind(X0) & ~calm(X0))) [input p6]
19. kind(lucy) [input p18]
25. brave(lucy) [input hypothesis]
53. ! [X0] : ((brave(X0) | (kind(X0) | calm(X0))) & ((~kind(X0) & ~calm(X0)) | ~brave(X0))) [nnf transformation 7]
54. ! [X0] : ((brave(X0) | kind(X0) | calm(X0)) & ((~kind(X0) & ~calm(X0)) | ~brave(X0))) [flattening 53]
95. ~brave(X0) | ~kind(X0) [cnf transformation 54]
127. kind(lucy) [cnf transformation 19]
135. brave(lucy) [cnf transformation 25]
357. ~kind(lucy) [resolution 95,135]
359. $false [subsumption resolution 357,127]
% SZS output end Proof for 7668518285358612936208651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or quiet is not strong or not happy and vice versa.
Everyone who is not brave is both happy and generous and vice versa.
Everyone who is either not generous or not creative is both humble and tall.
Everyone who is either not funny or brave is curious or not curious and vice versa.
Everyone who is not strong or generous is not humble or not curious.
Everyone who is either not quiet or calm is both old and calm and vice versa.
If someone is either humble or brave then mary is humble or not kind.
Everyone who is both not rich and calm is strong or not rich and vice versa.
If mary is not patient or not kind then mary is not generous.
Everyone who is both not humble and not old is both not calm and brave.
Everyone who is tall is not brave or happy.
If mary is both curious and not quiet then lucy is not wise or not creative.
Everyone who is either rich or not creative is generous and vice versa.
If john is generous then someone is both not calm and patient and vice versa.
Everyone who is not funny or tall is not calm or rich and vice versa.
If paul is not rich then someone is both not kind and not generous and vice versa.
Someone is brave.
Alice is creative.
Someone is happy or not calm.
Someone is not curious or not patient.
Someone is either not creative or rich.
Mary is both patient and not humble.
Someone is not quiet or not wise.
Fred is strong or not funny. | Mary is kind. | entailment | (![X]:((humble(X)<~>quiet(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)&generous(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(humble(X)&tall(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)|~curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)|~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(old(X)&calm(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((humble(mary)|~kind(mary))))&
(![X]:((~rich(X)&calm(X))<=>(strong(X)|~rich(X))))&
(((~patient(mary)|~kind(mary)))=>(~generous(mary)))&
(![X]:((~humble(X)&~old(X))=>(~calm(X)&brave(X))))&
(![X]:(tall(X)=>(~brave(X)|happy(X))))&
(((curious(mary)&~quiet(mary)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:((rich(X)<~>~creative(X))<=>generous(X)))&
((generous(john))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~calm(X)|rich(X))))&
((~rich(paul))<=>(?[X]:((~kind(X)&~generous(X)))))&
(?[X]:(brave(X)))&
(creative(alice))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((patient(mary)&~humble(mary)))&
(?[X]:((~quiet(X)|~wise(X))))&
((strong(fred)|~funny(fred))) | kind(mary) | [
"p2",
"p7",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 5806672126069208029216899
% SZS output start Proof for 5806672126069208029216899
3. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (tall(X0) & humble(X0))) [input p2]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~rich(X0) | strong(X0))) [input p7]
9. (~kind(mary) | ~patient(mary)) => ~generous(mary) [input p8]
13. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> generous(X0)) [input p12]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
16. ~rich(paul) <=> ? [X0] : (~generous(X0) & ~kind(X0)) [input p15]
25. ~kind(mary) [input hypothesis]
28. ! [X0] : ((tall(X0) & humble(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 3]
33. ~generous(mary) | (kind(mary) & patient(mary)) [ennf transformation 9]
42. ! [X0] : ((tall(X0) & humble(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 28]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : (((tall(X0) | ~funny(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | ~funny(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | (~tall(X0) & funny(X0)))) [flattening 55]
57. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X0] : (~generous(X0) & ~kind(X0)) | rich(paul)) [nnf transformation 16]
58. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X1] : (~generous(X1) & ~kind(X1)) | rich(paul)) [rectify 57]
59. ? [X1] : (~generous(X1) & ~kind(X1)) => (~generous(sK1) & ~kind(sK1)) [choice axiom]
60. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & ((~generous(sK1) & ~kind(sK1)) | rich(paul)) [skolemisation 58,59]
81. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 42]
82. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 42]
103. rich(X0) | calm(X0) [cnf transformation 49]
105. ~generous(mary) | kind(mary) [cnf transformation 33]
110. rich(X0) | generous(X0) | creative(X0) [cnf transformation 50]
111. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
117. rich(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 56]
122. ~rich(paul) | generous(X0) | kind(X0) [cnf transformation 60]
132. ~kind(mary) [cnf transformation 25]
145. 3 <=> kind(mary) [avatar definition]
147. ~kind(mary) <- (~3) [avatar component clause 145]
154. 5 <=> generous(mary) [avatar definition]
156. ~generous(mary) <- (~5) [avatar component clause 154]
157. 3 | ~5 [avatar split clause 105,154,145]
182. ~tall(X0) | rich(X0) [subsumption resolution 117,103]
185. 11 <=> ! [X0] : (generous(X0) | kind(X0)) [avatar definition]
186. kind(X0) | generous(X0) <- (11) [avatar component clause 185]
188. 12 <=> rich(paul) [avatar definition]
190. ~rich(paul) <- (~12) [avatar component clause 188]
191. 11 | ~12 [avatar split clause 122,188,185]
241. ~3 [avatar split clause 132,145]
452. 48 <=> creative(paul) [avatar definition]
453. ~creative(paul) <- (~48) [avatar component clause 452]
454. creative(paul) <- (48) [avatar component clause 452]
456. 49 <=> generous(paul) [avatar definition]
458. generous(paul) <- (49) [avatar component clause 456]
465. generous(mary) <- (~3, 11) [resolution 186,147]
467. $false <- (~3, ~5, 11) [subsumption resolution 465,156]
468. 3 | 5 | ~11 [avatar contradiction clause 467]
471. generous(paul) | creative(paul) <- (~12) [resolution 190,110]
542. rich(paul) | ~generous(paul) <- (48) [resolution 454,111]
543. tall(paul) | generous(paul) <- (48) [resolution 454,81]
545. ~generous(paul) <- (~12, 48) [subsumption resolution 542,190]
546. ~49 | 12 | ~48 [avatar split clause 545,452,188,456]
548. 58 <=> tall(paul) [avatar definition]
550. tall(paul) <- (58) [avatar component clause 548]
551. 49 | 58 | ~48 [avatar split clause 543,452,548,456]
553. 48 | 49 | 12 [avatar split clause 471,188,456,452]
561. tall(paul) | creative(paul) <- (49) [resolution 458,82]
564. tall(paul) <- (~48, 49) [subsumption resolution 561,453]
565. 58 | 48 | ~49 [avatar split clause 564,456,452,548]
758. rich(paul) <- (58) [resolution 550,182]
760. $false <- (~12, 58) [subsumption resolution 758,190]
761. 12 | ~58 [avatar contradiction clause 760]
762. $false [avatar sat refutation 157,191,241,468,546,551,553,565,761]
% SZS output end Proof for 5806672126069208029216899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa.
If fred is not happy or not rich then someone is quiet and vice versa.
Everyone who is both not humble and calm is kind or calm.
If someone is calm or not curious then someone is wise and vice versa.
Everyone who is both not humble and not funny is both tall and not funny.
If someone is either not tall or old then someone is brave or humble and vice versa.
If lucy is tall or brave then someone is both patient and not patient.
If mary is old then john is either not old or funny and vice versa.
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 old or not wise is both not curious and not generous and vice versa.
Everyone who is either not kind or tall is not wise and vice versa.
If paul is both not wise and not happy then someone is kind or tall and vice versa.
Someone is either humble or happy.
Someone is tall or patient.
Someone is not generous or generous.
Someone is either not strong or not happy.
Someone is happy or rich.
Someone is not funny. | Fred is not generous. | neutral | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((~happy(fred)|~rich(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)&calm(X))=>(kind(X)|calm(X))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~funny(X))=>(tall(X)&~funny(X))))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(((tall(lucy)|brave(lucy)))=>(?[X]:((patient(X)&~patient(X)))))&
((old(mary))<=>((~old(john)<~>funny(john))))&
(![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]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(((~wise(paul)&~happy(paul)))<=>(?[X]:((kind(X)|tall(X)))))&
(?[X]:((humble(X)<~>happy(X))))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(~funny(X))) | ~generous(fred) | []
| null | 0 |
Everyone who is strong is both strong and not funny.
Everyone who is both not old and not quiet is strong.
If susan is brave then someone is not old or not calm and vice versa.
Everyone who is both creative and quiet is old or not quiet and vice versa.
Everyone who is not old or not calm is calm and vice versa.
Everyone who is calm or not strong is either humble or not generous and vice versa.
Everyone who is both not tall and quiet is both not strong and patient.
Everyone who is both not kind and not creative is happy or not calm.
If john is either old or not tall then paul is not curious.
Everyone who is old or not kind is not rich or not tall.
If alice is both not creative and generous then paul is both not generous and not kind.
If someone is rich then alice is not rich or not old.
If someone is not quiet then john is not tall.
Everyone who is not wise or strong is both not strong and patient and vice versa.
Everyone who is both funny and quiet is both patient and not strong.
If someone is not funny then fred is both not wise and not happy and vice versa.
Alice is both wise and not generous.
Someone is either humble or not strong.
Susan is curious.
Lucy is calm or patient.
Someone is not wise or not strong.
Paul is calm. | Lucy is not strong. | entailment | (![X]:(strong(X)=>(strong(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))=>strong(X)))&
((brave(susan))<=>(?[X]:((~old(X)|~calm(X)))))&
(![X]:((creative(X)&quiet(X))<=>(old(X)|~quiet(X))))&
(![X]:((~old(X)|~calm(X))<=>calm(X)))&
(![X]:((calm(X)|~strong(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((~tall(X)&quiet(X))=>(~strong(X)&patient(X))))&
(![X]:((~kind(X)&~creative(X))=>(happy(X)|~calm(X))))&
(((old(john)<~>~tall(john)))=>(~curious(paul)))&
(![X]:((old(X)|~kind(X))=>(~rich(X)|~tall(X))))&
(((~creative(alice)&generous(alice)))=>((~generous(paul)&~kind(paul))))&
((?[X]:(rich(X)))=>((~rich(alice)|~old(alice))))&
((?[X]:(~quiet(X)))=>(~tall(john)))&
(![X]:((~wise(X)|strong(X))<=>(~strong(X)&patient(X))))&
(![X]:((funny(X)&quiet(X))=>(patient(X)&~strong(X))))&
((?[X]:(~funny(X)))<=>((~wise(fred)&~happy(fred))))&
((wise(alice)&~generous(alice)))&
(?[X]:((humble(X)<~>~strong(X))))&
(curious(susan))&
((calm(lucy)|patient(lucy)))&
(?[X]:((~wise(X)|~strong(X))))&
(calm(paul)) | ~strong(lucy) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 4730617754491742766430131
% SZS output start Proof for 4730617754491742766430131
14. ! [X0] : ((strong(X0) | ~wise(X0)) <=> (patient(X0) & ~strong(X0))) [input p13]
23. strong(lucy) [input hypothesis]
50. ! [X0] : (((strong(X0) | ~wise(X0)) | (~patient(X0) | strong(X0))) & ((patient(X0) & ~strong(X0)) | (~strong(X0) & wise(X0)))) [nnf transformation 14]
51. ! [X0] : ((strong(X0) | ~wise(X0) | ~patient(X0) | strong(X0)) & ((patient(X0) & ~strong(X0)) | (~strong(X0) & wise(X0)))) [flattening 50]
91. ~strong(X0) | ~strong(X0) [cnf transformation 51]
108. strong(lucy) [cnf transformation 23]
109. ~strong(X0) [duplicate literal removal 91]
202. $false [subsumption resolution 108,109]
% SZS output end Proof for 4730617754491742766430131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is either funny or not rich. Everyone who is not brave is patient and vice versa. If john is either not generous or not tall then fred is old or not kind and vice versa. Everyone who is quiet is not quiet or not creative. If someone is either patient or curious then someone is both happy and not funny and vice versa. If mary is humble or not brave then someone is quiet and vice versa. If susan is quiet then someone is quiet or calm and vice versa. Everyone who is rich or not quiet is humble or not old and vice versa. Everyone who is not quiet or not tall is creative. If someone is not kind or not wise then fred is either patient or not tall. Everyone who is either not creative or creative is either curious or creative. If someone is either not wise or not patient then someone is both not tall and creative. Everyone who is either calm or not quiet is both generous and not quiet. Everyone who is both quiet and not tall is happy and vice versa. If mary is patient or not wise then someone is either rich or old. Everyone who is both not creative and not humble is either generous or wise. Someone is not kind or creative. Fred is both generous and quiet. Lucy is both wise and not tall. Someone is tall. Fred is both not rich and patient. | Lucy is brave. | entailment | (![X]:(quiet(X)=>(funny(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>patient(X)))&
(((~generous(john)<~>~tall(john)))<=>((old(fred)|~kind(fred))))&
(![X]:(quiet(X)=>(~quiet(X)|~creative(X))))&
((?[X]:((patient(X)<~>curious(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(((humble(mary)|~brave(mary)))<=>(?[X]:(quiet(X))))&
((quiet(susan))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((rich(X)|~quiet(X))<=>(humble(X)|~old(X))))&
(![X]:((~quiet(X)|~tall(X))=>creative(X)))&
((?[X]:((~kind(X)|~wise(X))))=>((patient(fred)<~>~tall(fred))))&
(![X]:((~creative(X)<~>creative(X))=>(curious(X)<~>creative(X))))&
((?[X]:((~wise(X)<~>~patient(X))))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:((calm(X)<~>~quiet(X))=>(generous(X)&~quiet(X))))&
(![X]:((quiet(X)&~tall(X))<=>happy(X)))&
(((patient(mary)|~wise(mary)))=>(?[X]:((rich(X)<~>old(X)))))&
(![X]:((~creative(X)&~humble(X))=>(generous(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((generous(fred)&quiet(fred)))&
((wise(lucy)&~tall(lucy)))&
(?[X]:(tall(X)))&
((~rich(fred)&patient(fred))) | brave(lucy) | [
"p1",
"p3",
"p4",
"p8",
"p10",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 1965023236781502748359609
% SZS output start Proof for 1965023236781502748359609
2. ! [X0] : (~brave(X0) <=> patient(X0)) [input p1]
4. ! [X0] : (quiet(X0) => (~creative(X0) | ~quiet(X0))) [input p3]
5. ? [X0] : (patient(X0) <~> curious(X0)) <=> ? [X0] : (~funny(X0) & happy(X0)) [input p4]
9. ! [X0] : ((~tall(X0) | ~quiet(X0)) => creative(X0)) [input p8]
11. ! [X0] : ((~creative(X0) <~> creative(X0)) => (curious(X0) <~> creative(X0))) [input p10]
14. ! [X0] : ((~tall(X0) & quiet(X0)) <=> happy(X0)) [input p13]
19. ~tall(lucy) & wise(lucy) [input p18]
22. ~brave(lucy) [input hypothesis]
23. ? [X0] : (patient(X0) <~> curious(X0)) <=> ? [X1] : (~funny(X1) & happy(X1)) [rectify 5]
26. ! [X0] : ((~creative(X0) | ~quiet(X0)) | ~quiet(X0)) [ennf transformation 4]
27. ! [X0] : (~creative(X0) | ~quiet(X0) | ~quiet(X0)) [flattening 26]
28. ! [X0] : (creative(X0) | (tall(X0) & quiet(X0))) [ennf transformation 9]
30. ! [X0] : ((curious(X0) <~> creative(X0)) | (~creative(X0) <=> creative(X0))) [ennf transformation 11]
37. ! [X0] : ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))) [nnf transformation 2]
40. (? [X0] : ((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X1] : (~funny(X1) & happy(X1)) | ! [X0] : ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) [nnf transformation 23]
41. (? [X0] : ((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X2] : (~funny(X2) & happy(X2)) | ! [X3] : ((patient(X3) | ~curious(X3)) & (curious(X3) | ~patient(X3)))) [rectify 40]
42. ? [X0] : ((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) => ((~curious(sK0) | ~patient(sK0)) & (curious(sK0) | patient(sK0))) [choice axiom]
43. ? [X2] : (~funny(X2) & happy(X2)) => (~funny(sK1) & happy(sK1)) [choice axiom]
44. (((~curious(sK0) | ~patient(sK0)) & (curious(sK0) | patient(sK0))) | ! [X1] : (funny(X1) | ~happy(X1))) & ((~funny(sK1) & happy(sK1)) | ! [X3] : ((patient(X3) | ~curious(X3)) & (curious(X3) | ~patient(X3)))) [skolemisation 41,43,42]
57. ! [X0] : (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 30]
63. ! [X0] : (((~tall(X0) & quiet(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) | ~quiet(X0)))) [nnf transformation 14]
64. ! [X0] : (((~tall(X0) & quiet(X0)) | ~happy(X0)) & (happy(X0) | tall(X0) | ~quiet(X0))) [flattening 63]
75. patient(X0) | brave(X0) [cnf transformation 37]
83. ~creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 27]
84. happy(sK1) | curious(X3) | ~patient(X3) [cnf transformation 44]
101. creative(X0) | tall(X0) [cnf transformation 28]
109. ~creative(X0) | ~curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 57]
119. ~happy(X0) | quiet(X0) [cnf transformation 64]
120. ~happy(X0) | ~tall(X0) [cnf transformation 64]
131. ~tall(lucy) [cnf transformation 19]
135. ~brave(lucy) [cnf transformation 22]
140. ~curious(X0) | ~creative(X0) [duplicate literal removal 109]
141. ~creative(X0) | ~quiet(X0) [duplicate literal removal 83]
186. 10 <=> ! [X3] : (curious(X3) | ~patient(X3)) [avatar definition]
187. ~patient(X3) | curious(X3) <- (10) [avatar component clause 186]
190. 11 <=> happy(sK1) [avatar definition]
192. happy(sK1) <- (11) [avatar component clause 190]
194. 10 | 11 [avatar split clause 84,190,186]
307. ~quiet(X0) | tall(X0) [resolution 141,101]
311. curious(X0) | brave(X0) <- (10) [resolution 187,75]
469. ~creative(X1) | brave(X1) <- (10) [resolution 311,140]
498. tall(X1) | brave(X1) <- (10) [resolution 469,101]
505. brave(lucy) <- (10) [resolution 498,131]
507. $false <- (10) [subsumption resolution 505,135]
508. ~10 [avatar contradiction clause 507]
528. ~tall(sK1) <- (11) [resolution 192,120]
529. quiet(sK1) <- (11) [resolution 192,119]
537. tall(sK1) <- (11) [resolution 529,307]
540. $false <- (11) [subsumption resolution 537,528]
541. ~11 [avatar contradiction clause 540]
551. $false [avatar sat refutation 194,508,541]
% SZS output end Proof for 1965023236781502748359609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and humble then someone is not generous and vice versa. If someone is patient then someone is either creative or generous and vice versa. If someone is both not funny and not happy then someone is brave or not creative and vice versa. If lucy is not happy or not kind then someone is both brave and not funny. If john is both generous and not generous then someone is either not kind or rich. If alice is not generous or not brave then paul is patient and vice versa. If someone is not strong then someone is patient. If alice is either creative or not creative then fred is either not quiet or creative. If someone is either generous or not creative then susan is not quiet or old. Everyone who is either not happy or tall is either old or quiet and vice versa. Everyone who is creative is either brave or creative. Everyone who is either not happy or humble is either not quiet or not old and vice versa. Everyone who is either brave or quiet is either old or humble. If someone is either not kind or not brave then paul is either not strong or not calm. If mary is not patient or brave then someone is happy or rich. Everyone who is tall or not wise is both not tall and not rich. Mary is both kind and not tall. Someone is both happy and curious. Paul is either not humble or strong. Alice is wise. Someone is not wise or not humble. Someone is kind. | Fred is not generous. | contradiction | ((?[X]:((~quiet(X)&humble(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(patient(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(((~happy(lucy)|~kind(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(((generous(john)&~generous(john)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(((~generous(alice)|~brave(alice)))<=>(patient(paul)))&
((?[X]:(~strong(X)))=>(?[X]:(patient(X))))&
(((creative(alice)<~>~creative(alice)))=>((~quiet(fred)<~>creative(fred))))&
((?[X]:((generous(X)<~>~creative(X))))=>((~quiet(susan)|old(susan))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)<~>quiet(X))))&
(![X]:(creative(X)=>(brave(X)<~>creative(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((brave(X)<~>quiet(X))=>(old(X)<~>humble(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>((~strong(paul)<~>~calm(paul))))&
(((~patient(mary)|brave(mary)))=>(?[X]:((happy(X)|rich(X)))))&
(![X]:((tall(X)|~wise(X))=>(~tall(X)&~rich(X))))&
((kind(mary)&~tall(mary)))&
(?[X]:((happy(X)&curious(X))))&
((~humble(paul)<~>strong(paul)))&
(wise(alice))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:(kind(X))) | ~generous(fred) | [
"p0",
"p9",
"p11",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7079830264647479280196494
% SZS output start Proof for 7079830264647479280196494
1. ? [X0] : (humble(X0) & ~quiet(X0)) <=> ? [X0] : ~generous(X0) [input p0]
10. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (old(X0) <~> quiet(X0))) [input p9]
12. ! [X0] : ((~happy(X0) <~> humble(X0)) <=> (~quiet(X0) <~> ~old(X0))) [input p11]
16. ! [X0] : ((~wise(X0) | tall(X0)) => (~rich(X0) & ~tall(X0))) [input p15]
23. ~generous(fred) [input hypothesis]
24. ? [X0] : (humble(X0) & ~quiet(X0)) <=> ? [X1] : ~generous(X1) [rectify 1]
40. ! [X0] : ((~rich(X0) & ~tall(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 16]
41. (? [X0] : (humble(X0) & ~quiet(X0)) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : (~humble(X0) | quiet(X0))) [nnf transformation 24]
42. (? [X0] : (humble(X0) & ~quiet(X0)) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : (~humble(X3) | quiet(X3))) [rectify 41]
43. ? [X0] : (humble(X0) & ~quiet(X0)) => (humble(sK0) & ~quiet(sK0)) [choice axiom]
44. ? [X2] : ~generous(X2) => ~generous(sK1) [choice axiom]
45. ((humble(sK0) & ~quiet(sK0)) | ! [X1] : generous(X1)) & (~generous(sK1) | ! [X3] : (~humble(X3) | quiet(X3))) [skolemisation 42,44,43]
68. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0)))) & (((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 10]
70. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [nnf transformation 12]
83. ~quiet(sK0) | generous(X1) [cnf transformation 45]
84. humble(sK0) | generous(X1) [cnf transformation 45]
110. tall(X0) | old(X0) | quiet(X0) | happy(X0) [cnf transformation 68]
114. ~old(X0) | ~happy(X0) | quiet(X0) | tall(X0) [cnf transformation 68]
123. ~happy(X0) | quiet(X0) | old(X0) | ~humble(X0) [cnf transformation 70]
126. ~old(X0) | happy(X0) | ~humble(X0) | quiet(X0) [cnf transformation 70]
138. ~tall(X0) | ~tall(X0) [cnf transformation 40]
150. ~generous(fred) [cnf transformation 23]
151. ~tall(X0) [duplicate literal removal 138]
158. 1 <=> ! [X1] : generous(X1) [avatar definition]
159. generous(X1) <- (1) [avatar component clause 158]
161. 2 <=> humble(sK0) [avatar definition]
163. humble(sK0) <- (2) [avatar component clause 161]
164. 1 | 2 [avatar split clause 84,161,158]
166. 3 <=> quiet(sK0) [avatar definition]
168. ~quiet(sK0) <- (~3) [avatar component clause 166]
169. 1 | ~3 [avatar split clause 83,166,158]
373. old(X2) | quiet(X2) | happy(X2) [resolution 110,151]
457. happy(X1) | ~humble(X1) | quiet(X1) | quiet(X1) | happy(X1) [resolution 126,373]
458. ~humble(X1) | happy(X1) | quiet(X1) [duplicate literal removal 457]
460. happy(sK0) | quiet(sK0) <- (2) [resolution 458,163]
461. happy(sK0) <- (2, ~3) [subsumption resolution 460,168]
464. quiet(sK0) | old(sK0) | ~humble(sK0) <- (2, ~3) [resolution 461,123]
466. old(sK0) | ~humble(sK0) <- (2, ~3) [subsumption resolution 464,168]
467. old(sK0) <- (2, ~3) [subsumption resolution 466,163]
472. ~happy(sK0) | quiet(sK0) | tall(sK0) <- (2, ~3) [resolution 467,114]
474. quiet(sK0) | tall(sK0) <- (2, ~3) [subsumption resolution 472,461]
475. tall(sK0) <- (2, ~3) [subsumption resolution 474,168]
476. $false <- (2, ~3) [subsumption resolution 475,151]
477. ~2 | 3 [avatar contradiction clause 476]
490. $false <- (1) [resolution 159,150]
493. ~1 [avatar contradiction clause 490]
495. $false [avatar sat refutation 164,169,477,493]
% SZS output end Proof for 7079830264647479280196494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not humble is both creative and patient.
Everyone who is calm or rich is both not calm and creative.
If lucy is not funny then someone is old.
If someone is rich then john is not creative or happy and vice versa.
Everyone who is either calm or not rich is not old or funny and vice versa.
Everyone who is either not brave or not funny is either kind or not calm.
Everyone who is not tall or kind is either not generous or brave.
Everyone who is not wise or brave is not funny and vice versa.
Everyone who is not tall is either kind or not quiet.
Everyone who is not tall or old is funny.
If someone is both rich and not humble then alice is either curious or not quiet and vice versa.
Everyone who is generous or not patient is not creative.
Everyone who is both not creative and not brave is brave and vice versa.
Everyone who is either wise or humble is both not curious and generous.
If fred is not tall or tall then someone is brave or humble.
If lucy is both not wise and not old then fred is either calm or not humble and vice versa.
Lucy is wise or old.
Someone is both not brave and creative.
John is either not patient or quiet.
Fred is not happy.
Someone is either funny or not strong.
Someone is not wise. | Alice is not happy. | neutral | (![X]:((humble(X)<~>~humble(X))=>(creative(X)&patient(X))))&
(![X]:((calm(X)|rich(X))=>(~calm(X)&creative(X))))&
((~funny(lucy))=>(?[X]:(old(X))))&
((?[X]:(rich(X)))<=>((~creative(john)|happy(john))))&
(![X]:((calm(X)<~>~rich(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~tall(X)|kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~wise(X)|brave(X))<=>~funny(X)))&
(![X]:(~tall(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((~tall(X)|old(X))=>funny(X)))&
((?[X]:((rich(X)&~humble(X))))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((generous(X)|~patient(X))=>~creative(X)))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
(![X]:((wise(X)<~>humble(X))=>(~curious(X)&generous(X))))&
(((~tall(fred)|tall(fred)))=>(?[X]:((brave(X)|humble(X)))))&
(((~wise(lucy)&~old(lucy)))<=>((calm(fred)<~>~humble(fred))))&
((wise(lucy)|old(lucy)))&
(?[X]:((~brave(X)&creative(X))))&
((~patient(john)<~>quiet(john)))&
(~happy(fred))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:(~wise(X))) | ~happy(alice) | []
| null | 0 |
Everyone who is either not generous or not brave is not patient.
Everyone who is both not brave and tall is both curious and strong and vice versa.
Everyone who is either not curious or not humble is either not humble or rich.
If someone is not quiet or not rich then someone is curious or not tall.
Everyone who is either strong or generous is both kind and not strong and vice versa.
Everyone who is not wise is both not generous and not quiet and vice versa.
Everyone who is both not humble and brave is either not kind or wise.
Everyone who is either not calm or calm is not strong and vice versa.
Everyone who is not generous or curious is old or strong.
Everyone who is funny or not rich is creative.
Everyone who is old is either not happy or patient and vice versa.
If john is old then someone is either not patient or wise and vice versa.
If fred is both happy and not generous then alice is brave.
If someone is not generous then someone is not quiet or strong and vice versa.
Everyone who is not wise is not old or old.
Everyone who is funny or not quiet is not curious.
Someone is either tall or generous.
Lucy is either not humble or not old.
Someone is not patient or not kind.
Someone is either not calm or not quiet.
Alice is tall or not generous.
Alice is funny.
Susan is either not generous or not wise. | Susan is not strong. | entailment | (![X]:((~generous(X)<~>~brave(X))=>~patient(X)))&
(![X]:((~brave(X)&tall(X))<=>(curious(X)&strong(X))))&
(![X]:((~curious(X)<~>~humble(X))=>(~humble(X)<~>rich(X))))&
((?[X]:((~quiet(X)|~rich(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)&~strong(X))))&
(![X]:(~wise(X)<=>(~generous(X)&~quiet(X))))&
(![X]:((~humble(X)&brave(X))=>(~kind(X)<~>wise(X))))&
(![X]:((~calm(X)<~>calm(X))<=>~strong(X)))&
(![X]:((~generous(X)|curious(X))=>(old(X)|strong(X))))&
(![X]:((funny(X)|~rich(X))=>creative(X)))&
(![X]:(old(X)<=>(~happy(X)<~>patient(X))))&
((old(john))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(((happy(fred)&~generous(fred)))=>(brave(alice)))&
((?[X]:(~generous(X)))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:(~wise(X)=>(~old(X)|old(X))))&
(![X]:((funny(X)|~quiet(X))=>~curious(X)))&
(?[X]:((tall(X)<~>generous(X))))&
((~humble(lucy)<~>~old(lucy)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((tall(alice)|~generous(alice)))&
(funny(alice))&
((~generous(susan)<~>~wise(susan))) | ~strong(susan) | [
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 9093064925713436622901111
% SZS output start Proof for 9093064925713436622901111
8. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> ~strong(X0)) [input p7]
24. strong(susan) [input hypothesis]
52. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | strong(X0)) & (~strong(X0) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 8]
96. ~strong(X0) | calm(X0) | calm(X0) [cnf transformation 52]
97. ~strong(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 52]
128. strong(susan) [cnf transformation 24]
129. ~strong(X0) | calm(X0) [duplicate literal removal 96]
130. ~strong(X0) | ~calm(X0) [duplicate literal removal 97]
151. ~strong(X0) [subsumption resolution 129,130]
253. $false [subsumption resolution 128,151]
% SZS output end Proof for 9093064925713436622901111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either quiet or wise. If susan is either tall or not rich then someone is either not happy or creative. If alice is both not funny and not kind then someone is not old and vice versa. Everyone who is brave is not kind and vice versa. Everyone who is both curious and not funny is curious or happy. Everyone who is brave or calm is both not brave and not quiet and vice versa. If someone is either not calm or not curious then susan is not creative or not old and vice versa. Everyone who is both kind and not calm is rich or kind. Everyone who is rich or not wise is generous. Everyone who is not strong is not tall or patient. Everyone who is both not creative and not generous is not calm and vice versa. If mary is both kind and happy then susan is either not kind or quiet and vice versa. Everyone who is not tall or not quiet is funny or rich and vice versa. Everyone who is not creative is old or tall and vice versa. If mary is either wise or not patient then john is either old or not old and vice versa. Everyone who is not funny or not wise is curious or not wise and vice versa. Someone is either not rich or tall. Someone is quiet. Someone is either not creative or not wise. Someone is either not wise or calm. Someone is not wise. Someone is either not humble or calm. | Mary is tall. | neutral | (![X]:((~tall(X)<~>~humble(X))=>(quiet(X)<~>wise(X))))&
(((tall(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~funny(alice)&~kind(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:((curious(X)&~funny(X))=>(curious(X)|happy(X))))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~creative(susan)|~old(susan))))&
(![X]:((kind(X)&~calm(X))=>(rich(X)|kind(X))))&
(![X]:((rich(X)|~wise(X))=>generous(X)))&
(![X]:(~strong(X)=>(~tall(X)|patient(X))))&
(![X]:((~creative(X)&~generous(X))<=>~calm(X)))&
(((kind(mary)&happy(mary)))<=>((~kind(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(funny(X)|rich(X))))&
(![X]:(~creative(X)<=>(old(X)|tall(X))))&
(((wise(mary)<~>~patient(mary)))<=>((old(john)<~>~old(john))))&
(![X]:((~funny(X)|~wise(X))<=>(curious(X)|~wise(X))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((~wise(X)<~>calm(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~humble(X)<~>calm(X)))) | tall(mary) | []
| null | 0 |
If fred is either generous or not curious then someone is not generous and vice versa.
Everyone who is either brave or rich is strong and vice versa.
Everyone who is both tall and not old is not humble or not tall.
If someone is either not curious or not kind then someone is tall.
If lucy is both curious and not wise then john is not happy and vice versa.
If alice is both not strong and not happy then someone is creative or not funny and vice versa.
If someone is either brave or not calm then john is not old or not kind and vice versa.
Everyone who is both brave and happy is not funny and vice versa.
Everyone who is both not old and not humble is not happy and vice versa.
Everyone who is not old or not calm is both not old and not strong.
If someone is both not generous and not curious then someone is not happy or not rich.
Everyone who is either happy or not creative is not humble or rich and vice versa.
Everyone who is strong is not strong or happy.
If fred is humble then someone is not kind.
If lucy is not patient then lucy is either kind or happy.
Everyone who is not quiet or not strong is either happy or calm.
Someone is both not wise and not happy.
Lucy is both happy and patient.
Lucy is not funny or creative.
Mary is generous or brave.
Susan is not curious or not patient.
Susan is not funny or strong.
Mary is old.
John is both kind and not creative. | Mary is not old. | contradiction | (((generous(fred)<~>~curious(fred)))<=>(?[X]:(~generous(X))))&
(![X]:((brave(X)<~>rich(X))<=>strong(X)))&
(![X]:((tall(X)&~old(X))=>(~humble(X)|~tall(X))))&
((?[X]:((~curious(X)<~>~kind(X))))=>(?[X]:(tall(X))))&
(((curious(lucy)&~wise(lucy)))<=>(~happy(john)))&
(((~strong(alice)&~happy(alice)))<=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:((brave(X)<~>~calm(X))))<=>((~old(john)|~kind(john))))&
(![X]:((brave(X)&happy(X))<=>~funny(X)))&
(![X]:((~old(X)&~humble(X))<=>~happy(X)))&
(![X]:((~old(X)|~calm(X))=>(~old(X)&~strong(X))))&
((?[X]:((~generous(X)&~curious(X))))=>(?[X]:((~happy(X)|~rich(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~humble(X)|rich(X))))&
(![X]:(strong(X)=>(~strong(X)|happy(X))))&
((humble(fred))=>(?[X]:(~kind(X))))&
((~patient(lucy))=>((kind(lucy)<~>happy(lucy))))&
(![X]:((~quiet(X)|~strong(X))=>(happy(X)<~>calm(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((happy(lucy)&patient(lucy)))&
((~funny(lucy)|creative(lucy)))&
((generous(mary)|brave(mary)))&
((~curious(susan)|~patient(susan)))&
((~funny(susan)|strong(susan)))&
(old(mary))&
((kind(john)&~creative(john))) | ~old(mary) | [
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 1257370725169135991601967
% SZS output start Proof for 1257370725169135991601967
23. old(mary) [input p22]
25. ~old(mary) [input hypothesis]
131. old(mary) [cnf transformation 23]
134. ~old(mary) [cnf transformation 25]
315. $false [subsumption resolution 134,131]
% SZS output end Proof for 1257370725169135991601967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then mary is not curious or funny and vice versa. Everyone who is not happy is either kind or generous. Everyone who is not rich or not patient is either not brave or generous. Everyone who is both not curious and rich is not rich or not funny. Everyone who is both not rich and quiet is both happy and old and vice versa. Everyone who is not creative or creative is not old or quiet and vice versa. Everyone who is quiet is curious or not brave and vice versa. Everyone who is creative or not kind is not wise or not curious. If lucy is wise or not brave then someone is not happy or not funny and vice versa. Everyone who is not creative or strong is both not tall and patient. If someone is old or not funny then mary is old. If alice is both generous and old then susan is humble and vice versa. Everyone who is wise or not old is either rich or not humble. Everyone who is both not strong and brave is strong or old. If someone is either patient or not rich then john is both not quiet and not patient. If alice is either rich or creative then mary is either not generous or humble. Fred is both not old and funny. Paul is not kind or happy. Fred is quiet or generous. John is not creative. Alice is not strong or patient. Someone is both not generous and kind. Alice is patient or rich. | Paul is patient. | neutral | ((?[X]:(curious(X)))<=>((~curious(mary)|funny(mary))))&
(![X]:(~happy(X)=>(kind(X)<~>generous(X))))&
(![X]:((~rich(X)|~patient(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&rich(X))=>(~rich(X)|~funny(X))))&
(![X]:((~rich(X)&quiet(X))<=>(happy(X)&old(X))))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~creative(X)|strong(X))=>(~tall(X)&patient(X))))&
((?[X]:((old(X)|~funny(X))))=>(old(mary)))&
(((generous(alice)&old(alice)))<=>(humble(susan)))&
(![X]:((wise(X)|~old(X))=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)&brave(X))=>(strong(X)|old(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>((~quiet(john)&~patient(john))))&
(((rich(alice)<~>creative(alice)))=>((~generous(mary)<~>humble(mary))))&
((~old(fred)&funny(fred)))&
((~kind(paul)|happy(paul)))&
((quiet(fred)|generous(fred)))&
(~creative(john))&
((~strong(alice)|patient(alice)))&
(?[X]:((~generous(X)&kind(X))))&
((patient(alice)|rich(alice))) | patient(paul) | []
| null | 0 |
Everyone who is both not calm and curious is both wise and tall.
If someone is both generous and not happy then someone is not strong.
If john is both not happy and happy then someone is kind or tall.
If fred is both not patient and brave then someone is both not quiet and wise.
Everyone who is not wise or not curious is not humble or quiet.
If fred is either not strong or not tall then fred is both funny and not brave and vice versa.
If someone is both generous and funny then someone is both not brave and curious.
If someone is either not funny or funny then someone is not patient and vice versa.
Everyone who is calm or not patient is not calm.
Everyone who is either curious or calm is both not funny and not tall.
If someone is calm or not humble then someone is both creative and curious and vice versa.
Everyone who is not humble is strong or rich and vice versa.
If someone is wise or not happy then john is tall or not calm.
If lucy is brave or not strong then fred is old and vice versa.
Everyone who is not patient or happy is not kind and vice versa.
If john is humble or not kind then alice is not old or not strong.
Someone is brave or not happy.
John is not happy.
Someone is either not old or creative.
Paul is both funny and brave.
Someone is either calm or not curious.
Someone is not creative.
Alice is both old and kind.
Paul is not curious. | Lucy is rich. | contradiction | (![X]:((~calm(X)&curious(X))=>(wise(X)&tall(X))))&
((?[X]:((generous(X)&~happy(X))))=>(?[X]:(~strong(X))))&
(((~happy(john)&happy(john)))=>(?[X]:((kind(X)|tall(X)))))&
(((~patient(fred)&brave(fred)))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)|~curious(X))=>(~humble(X)|quiet(X))))&
(((~strong(fred)<~>~tall(fred)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~patient(X))=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))=>(~funny(X)&~tall(X))))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(~humble(X)<=>(strong(X)|rich(X))))&
((?[X]:((wise(X)|~happy(X))))=>((tall(john)|~calm(john))))&
(((brave(lucy)|~strong(lucy)))<=>(old(fred)))&
(![X]:((~patient(X)|happy(X))<=>~kind(X)))&
(((humble(john)|~kind(john)))=>((~old(alice)|~strong(alice))))&
(?[X]:((brave(X)|~happy(X))))&
(~happy(john))&
(?[X]:((~old(X)<~>creative(X))))&
((funny(paul)&brave(paul)))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:(~creative(X)))&
((old(alice)&kind(alice)))&
(~curious(paul)) | rich(lucy) | [
"p0",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6790143313351020768290675
% SZS output start Proof for 6790143313351020768290675
1. ! [X0] : ((curious(X0) & ~calm(X0)) => (tall(X0) & wise(X0))) [input p0]
9. ! [X0] : ((~patient(X0) | calm(X0)) => ~calm(X0)) [input p8]
10. ! [X0] : ((curious(X0) <~> calm(X0)) => (~tall(X0) & ~funny(X0))) [input p9]
11. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X0] : (curious(X0) & creative(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (rich(X0) | strong(X0))) [input p11]
25. rich(lucy) [input hypothesis]
29. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X1] : (curious(X1) & creative(X1)) [rectify 11]
33. ! [X0] : ((tall(X0) & wise(X0)) | (~curious(X0) | calm(X0))) [ennf transformation 1]
34. ! [X0] : ((tall(X0) & wise(X0)) | ~curious(X0) | calm(X0)) [flattening 33]
41. ! [X0] : (~calm(X0) | (patient(X0) & ~calm(X0))) [ennf transformation 9]
42. ! [X0] : ((~tall(X0) & ~funny(X0)) | (curious(X0) <=> calm(X0))) [ennf transformation 10]
59. ! [X0] : ((~tall(X0) & ~funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) [nnf transformation 42]
60. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X1] : (curious(X1) & creative(X1)) | ! [X0] : (humble(X0) & ~calm(X0))) [nnf transformation 29]
61. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X2] : (curious(X2) & creative(X2)) | ! [X3] : (humble(X3) & ~calm(X3))) [rectify 60]
62. ? [X0] : (~humble(X0) | calm(X0)) => (~humble(sK4) | calm(sK4)) [choice axiom]
63. ? [X2] : (curious(X2) & creative(X2)) => (curious(sK5) & creative(sK5)) [choice axiom]
64. ((~humble(sK4) | calm(sK4)) | ! [X1] : (~curious(X1) | ~creative(X1))) & ((curious(sK5) & creative(sK5)) | ! [X3] : (humble(X3) & ~calm(X3))) [skolemisation 61,63,62]
65. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | humble(X0))) [nnf transformation 12]
66. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | humble(X0))) [flattening 65]
80. ~curious(X0) | tall(X0) | calm(X0) [cnf transformation 34]
96. ~calm(X0) | ~calm(X0) [cnf transformation 41]
100. ~tall(X0) | calm(X0) | ~curious(X0) [cnf transformation 59]
105. curious(sK5) | humble(X3) [cnf transformation 64]
109. ~rich(X0) | ~humble(X0) [cnf transformation 66]
131. rich(lucy) [cnf transformation 25]
132. ~calm(X0) [duplicate literal removal 96]
183. ~tall(X0) | ~curious(X0) [subsumption resolution 100,132]
195. 13 <=> ! [X3] : humble(X3) [avatar definition]
196. humble(X3) <- (13) [avatar component clause 195]
198. 14 <=> curious(sK5) [avatar definition]
200. curious(sK5) <- (14) [avatar component clause 198]
201. 13 | 14 [avatar split clause 105,198,195]
264. ~humble(lucy) [resolution 109,131]
265. $false <- (13) [subsumption resolution 264,196]
266. ~13 [avatar contradiction clause 265]
276. tall(sK5) | calm(sK5) <- (14) [resolution 80,200]
277. tall(sK5) <- (14) [subsumption resolution 276,132]
278. ~curious(sK5) <- (14) [resolution 277,183]
279. $false <- (14) [subsumption resolution 278,200]
280. ~14 [avatar contradiction clause 279]
281. $false [avatar sat refutation 201,266,280]
% SZS output end Proof for 6790143313351020768290675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not quiet or strong then someone is tall and vice versa.
If someone is both generous and old then susan is not happy or not strong.
If fred is both curious and not curious then someone is either not generous or brave.
Everyone who is either old or not patient is strong.
If fred is either funny or not happy then lucy is either old or strong.
Everyone who is either not kind or rich is creative and vice versa.
Everyone who is either creative or not generous is not funny.
If mary is old or not generous then susan is either not old or not strong.
If lucy is either tall or not generous then someone is not creative.
Everyone who is either patient or not old is either not old or not humble.
If paul is not calm then susan is either wise or curious.
Everyone who is either not quiet or not creative is both not humble and curious and vice versa.
Everyone who is both not brave and wise is not humble and vice versa.
If john is either not strong or not patient then lucy is both quiet and not funny.
Everyone who is not humble is either old or brave.
If paul is both tall and not wise then john is not generous or not tall and vice versa.
Fred is either quiet or rich.
Paul is both patient and old.
Someone is not curious.
Mary is either not funny or not quiet.
John is not strong.
Someone is either not happy or patient.
Someone is both not humble and creative.
Someone is old or not strong. | Mary is not funny. | neutral | (((~quiet(lucy)<~>strong(lucy)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)&old(X))))=>((~happy(susan)|~strong(susan))))&
(((curious(fred)&~curious(fred)))=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:((old(X)<~>~patient(X))=>strong(X)))&
(((funny(fred)<~>~happy(fred)))=>((old(lucy)<~>strong(lucy))))&
(![X]:((~kind(X)<~>rich(X))<=>creative(X)))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(((old(mary)|~generous(mary)))=>((~old(susan)<~>~strong(susan))))&
(((tall(lucy)<~>~generous(lucy)))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~old(X))=>(~old(X)<~>~humble(X))))&
((~calm(paul))=>((wise(susan)<~>curious(susan))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~humble(X)&curious(X))))&
(![X]:((~brave(X)&wise(X))<=>~humble(X)))&
(((~strong(john)<~>~patient(john)))=>((quiet(lucy)&~funny(lucy))))&
(![X]:(~humble(X)=>(old(X)<~>brave(X))))&
(((tall(paul)&~wise(paul)))<=>((~generous(john)|~tall(john))))&
((quiet(fred)<~>rich(fred)))&
((patient(paul)&old(paul)))&
(?[X]:(~curious(X)))&
((~funny(mary)<~>~quiet(mary)))&
(~strong(john))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((~humble(X)&creative(X))))&
(?[X]:((old(X)|~strong(X)))) | ~funny(mary) | []
| null | 0 |
If someone is funny then paul is both not happy and not humble and vice versa.
If someone is generous then someone is either not strong or not calm.
If john is either not kind or tall then someone is not curious.
Everyone who is generous is either calm or wise and vice versa.
Everyone who is both not creative and not tall is not creative and vice versa.
If someone is funny then paul is not humble or quiet.
Everyone who is calm or curious is funny or not calm and vice versa.
If paul is both quiet and calm then paul is not generous or not wise.
Everyone who is both not brave and not old is both creative and not patient.
Everyone who is not quiet or funny is humble or not funny.
If someone is not rich or humble then someone is both not generous and not kind.
If someone is not funny or kind then fred is either calm or not tall.
Everyone who is either strong or generous is not happy and vice versa.
Everyone who is generous is brave and vice versa.
If someone is quiet or not tall then john is either happy or not rich and vice versa.
Everyone who is happy is not calm and vice versa.
John is not funny.
Someone is either not strong or not happy.
Alice is either patient or not brave.
Paul is curious.
John is not rich or not funny.
Someone is patient.
Alice is not patient.
Fred is either old or not old. | Paul is strong. | neutral | ((?[X]:(funny(X)))<=>((~happy(paul)&~humble(paul))))&
((?[X]:(generous(X)))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(((~kind(john)<~>tall(john)))=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(calm(X)<~>wise(X))))&
(![X]:((~creative(X)&~tall(X))<=>~creative(X)))&
((?[X]:(funny(X)))=>((~humble(paul)|quiet(paul))))&
(![X]:((calm(X)|curious(X))<=>(funny(X)|~calm(X))))&
(((quiet(paul)&calm(paul)))=>((~generous(paul)|~wise(paul))))&
(![X]:((~brave(X)&~old(X))=>(creative(X)&~patient(X))))&
(![X]:((~quiet(X)|funny(X))=>(humble(X)|~funny(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~funny(X)|kind(X))))=>((calm(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>generous(X))<=>~happy(X)))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((quiet(X)|~tall(X))))<=>((happy(john)<~>~rich(john))))&
(![X]:(happy(X)<=>~calm(X)))&
(~funny(john))&
(?[X]:((~strong(X)<~>~happy(X))))&
((patient(alice)<~>~brave(alice)))&
(curious(paul))&
((~rich(john)|~funny(john)))&
(?[X]:(patient(X)))&
(~patient(alice))&
((old(fred)<~>~old(fred))) | strong(paul) | []
| null | 0 |
If someone is either not patient or not curious then lucy is funny and vice versa.
If john is patient or not rich then someone is curious or kind.
Everyone who is either generous or old is either not happy or humble and vice versa.
Everyone who is happy or curious is either not creative or not curious and vice versa.
Everyone who is both brave and not kind is kind and vice versa.
Everyone who is wise is quiet.
If someone is both brave and not calm then someone is either not patient or not old and vice versa.
Everyone who is either patient or funny is patient and vice versa.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
Someone is either curious or not rich.
Susan is curious.
Someone is either generous or happy.
John is either not strong or not humble.
Alice is both strong and not kind.
Lucy is not happy or old.
Someone is not kind. | Susan is not old. | contradiction | ((?[X]:((~patient(X)<~>~curious(X))))<=>(funny(lucy)))&
(((patient(john)|~rich(john)))=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((happy(X)|curious(X))<=>(~creative(X)<~>~curious(X))))&
(![X]:((brave(X)&~kind(X))<=>kind(X)))&
(![X]:(wise(X)=>quiet(X)))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((patient(X)<~>funny(X))<=>patient(X)))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
(?[X]:((curious(X)<~>~rich(X))))&
(curious(susan))&
(?[X]:((generous(X)<~>happy(X))))&
((~strong(john)<~>~humble(john)))&
((strong(alice)&~kind(alice)))&
((~happy(lucy)|old(lucy)))&
(?[X]:(~kind(X))) | ~old(susan) | [
"p0",
"p4",
"p6",
"p7",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 175657215594068803181240
% SZS output start Proof for 175657215594068803181240
1. ? [X0] : (~patient(X0) <~> ~curious(X0)) <=> funny(lucy) [input p0]
5. ! [X0] : ((~kind(X0) & brave(X0)) <=> kind(X0)) [input p4]
7. ? [X0] : (~calm(X0) & brave(X0)) <=> ? [X0] : (~patient(X0) <~> ~old(X0)) [input p6]
8. ! [X0] : ((patient(X0) <~> funny(X0)) <=> patient(X0)) [input p7]
18. curious(susan) [input p17]
24. ~old(susan) [input hypothesis]
25. ? [X0] : (~calm(X0) & brave(X0)) <=> ? [X1] : (~patient(X1) <~> ~old(X1)) [rectify 7]
35. (? [X0] : ((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ~funny(lucy)) & (funny(lucy) | ! [X0] : ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) [nnf transformation 1]
36. (? [X0] : ((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ~funny(lucy)) & (funny(lucy) | ! [X1] : ((~patient(X1) | curious(X1)) & (~curious(X1) | patient(X1)))) [rectify 35]
37. ? [X0] : ((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) => ((curious(sK0) | patient(sK0)) & (~curious(sK0) | ~patient(sK0))) [choice axiom]
38. (((curious(sK0) | patient(sK0)) & (~curious(sK0) | ~patient(sK0))) | ~funny(lucy)) & (funny(lucy) | ! [X1] : ((~patient(X1) | curious(X1)) & (~curious(X1) | patient(X1)))) [skolemisation 36,37]
44. ! [X0] : (((~kind(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~brave(X0)))) [nnf transformation 5]
45. ! [X0] : (((~kind(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~brave(X0))) [flattening 44]
46. (? [X0] : (~calm(X0) & brave(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X1] : ((old(X1) | patient(X1)) & (~old(X1) | ~patient(X1))) | ! [X0] : (calm(X0) | ~brave(X0))) [nnf transformation 25]
47. (? [X0] : (~calm(X0) & brave(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) | ! [X3] : (calm(X3) | ~brave(X3))) [rectify 46]
48. ? [X0] : (~calm(X0) & brave(X0)) => (~calm(sK2) & brave(sK2)) [choice axiom]
49. ? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) => ((old(sK3) | patient(sK3)) & (~old(sK3) | ~patient(sK3))) [choice axiom]
50. ((~calm(sK2) & brave(sK2)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (((old(sK3) | patient(sK3)) & (~old(sK3) | ~patient(sK3))) | ! [X3] : (calm(X3) | ~brave(X3))) [skolemisation 47,49,48]
51. ! [X0] : ((((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ~patient(X0)) & (patient(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0))))) [nnf transformation 8]
73. funny(lucy) | ~curious(X1) | patient(X1) [cnf transformation 38]
93. kind(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
95. ~kind(X0) | ~kind(X0) [cnf transformation 45]
99. brave(sK2) | ~patient(X1) | old(X1) [cnf transformation 50]
103. patient(X0) | patient(X0) | ~funny(X0) [cnf transformation 51]
105. ~funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
134. curious(susan) [cnf transformation 18]
143. ~old(susan) [cnf transformation 24]
146. patient(X0) | ~funny(X0) [duplicate literal removal 103]
147. ~funny(X0) | ~patient(X0) [duplicate literal removal 105]
148. kind(X0) | ~brave(X0) [duplicate literal removal 93]
149. ~kind(X0) [duplicate literal removal 95]
153. 1 <=> funny(lucy) [avatar definition]
154. funny(lucy) <- (1) [avatar component clause 153]
171. 5 <=> ! [X1] : (~curious(X1) | patient(X1)) [avatar definition]
172. ~curious(X1) | patient(X1) <- (5) [avatar component clause 171]
173. 5 | 1 [avatar split clause 73,153,171]
192. ~brave(X0) [subsumption resolution 148,149]
194. 10 <=> ! [X1] : (~patient(X1) | old(X1)) [avatar definition]
195. ~patient(X1) | old(X1) <- (10) [avatar component clause 194]
205. ~patient(X1) | old(X1) [subsumption resolution 99,192]
206. 10 [avatar split clause 205,194]
209. ~funny(X0) [subsumption resolution 146,147]
265. patient(susan) <- (5) [resolution 172,134]
266. old(susan) <- (5, 10) [resolution 265,195]
268. $false <- (5, 10) [subsumption resolution 266,143]
269. ~5 | ~10 [avatar contradiction clause 268]
270. $false <- (1) [subsumption resolution 154,209]
271. ~1 [avatar contradiction clause 270]
272. $false [avatar sat refutation 173,206,269,271]
% SZS output end Proof for 175657215594068803181240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is either rich or not creative and vice versa.
Everyone who is either not generous or patient is not kind.
If alice is generous then alice is quiet or not brave.
If someone is old then someone is not patient and vice versa.
Everyone who is not patient is both funny and calm.
Everyone who is either wise or not strong is creative or not happy.
Everyone who is either old or kind is wise or not humble.
Everyone who is either humble or not tall is both not kind and not patient.
Everyone who is both generous and rich is not curious.
Everyone who is both not strong and not tall is both not rich and not patient and vice versa.
If mary is both not kind and generous then someone is strong or calm.
Everyone who is brave or strong is either not kind or creative.
If susan is either not calm or curious then someone is not strong.
Everyone who is rich is both not curious and not brave and vice versa.
Everyone who is either not kind or not tall is either not strong or humble and vice versa.
Everyone who is humble or not wise is both not generous and funny.
Someone is either wise or generous.
Someone is either not curious or not brave.
Someone is old or not quiet.
Alice is both not generous and not kind.
Someone is not happy.
Someone is not kind or happy.
Someone is either not brave or not funny. | Alice is creative. | contradiction | (![X]:(curious(X)<=>(rich(X)<~>~creative(X))))&
(![X]:((~generous(X)<~>patient(X))=>~kind(X)))&
((generous(alice))=>((quiet(alice)|~brave(alice))))&
((?[X]:(old(X)))<=>(?[X]:(~patient(X))))&
(![X]:(~patient(X)=>(funny(X)&calm(X))))&
(![X]:((wise(X)<~>~strong(X))=>(creative(X)|~happy(X))))&
(![X]:((old(X)<~>kind(X))=>(wise(X)|~humble(X))))&
(![X]:((humble(X)<~>~tall(X))=>(~kind(X)&~patient(X))))&
(![X]:((generous(X)&rich(X))=>~curious(X)))&
(![X]:((~strong(X)&~tall(X))<=>(~rich(X)&~patient(X))))&
(((~kind(mary)&generous(mary)))=>(?[X]:((strong(X)|calm(X)))))&
(![X]:((brave(X)|strong(X))=>(~kind(X)<~>creative(X))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:(~strong(X))))&
(![X]:(rich(X)<=>(~curious(X)&~brave(X))))&
(![X]:((~kind(X)<~>~tall(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((humble(X)|~wise(X))=>(~generous(X)&funny(X))))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((old(X)|~quiet(X))))&
((~generous(alice)&~kind(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((~kind(X)|happy(X))))&
(?[X]:((~brave(X)<~>~funny(X)))) | creative(alice) | [
"p0",
"p11",
"p13",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3534006061792470164864458
% SZS output start Proof for 3534006061792470164864458
1. ! [X0] : (curious(X0) <=> (rich(X0) <~> ~creative(X0))) [input p0]
12. ! [X0] : ((strong(X0) | brave(X0)) => (~kind(X0) <~> creative(X0))) [input p11]
14. ! [X0] : (rich(X0) <=> (~brave(X0) & ~curious(X0))) [input p13]
20. ~kind(alice) & ~generous(alice) [input p19]
24. creative(alice) [input hypothesis]
39. ! [X0] : ((~kind(X0) <~> creative(X0)) | (~strong(X0) & ~brave(X0))) [ennf transformation 12]
42. ! [X0] : ((curious(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~curious(X0))) [nnf transformation 1]
56. ! [X0] : (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | (~strong(X0) & ~brave(X0))) [nnf transformation 39]
60. ! [X0] : ((rich(X0) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [nnf transformation 14]
61. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [flattening 60]
78. ~creative(X0) | rich(X0) | ~curious(X0) [cnf transformation 42]
80. ~creative(X0) | curious(X0) | ~rich(X0) [cnf transformation 42]
105. ~brave(X0) | kind(X0) | ~creative(X0) [cnf transformation 56]
109. ~rich(X0) | ~curious(X0) [cnf transformation 61]
111. brave(X0) | rich(X0) | curious(X0) [cnf transformation 61]
130. ~kind(alice) [cnf transformation 20]
135. creative(alice) [cnf transformation 24]
246. rich(alice) | ~curious(alice) [resolution 78,135]
247. ~curious(alice) [subsumption resolution 246,109]
265. rich(X0) | curious(X0) | kind(X0) | ~creative(X0) [resolution 111,105]
269. ~creative(X0) | kind(X0) | curious(X0) [subsumption resolution 265,80]
319. kind(alice) | curious(alice) [resolution 269,135]
322. curious(alice) [subsumption resolution 319,130]
323. $false [subsumption resolution 322,247]
% SZS output end Proof for 3534006061792470164864458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and rich is both not patient and not old.
Everyone who is either old or quiet is either not patient or not funny and vice versa.
If mary is not wise then alice is generous.
Everyone who is rich or calm is not rich and vice versa.
Everyone who is either kind or old is either rich or patient and vice versa.
If alice is either not happy or patient then someone is either not curious or tall and vice versa.
Everyone who is not kind or not curious is either not happy or funny and vice versa.
Everyone who is not tall or not brave is both not patient and tall and vice versa.
Everyone who is brave or not tall is both not brave and not quiet and vice versa.
If someone is both not old and not humble then paul is not funny or not quiet.
If lucy is either not kind or calm then susan is both funny and not kind and vice versa.
If someone is either not creative or not brave then someone is not quiet.
Everyone who is either funny or not rich is both not wise and not rich.
Everyone who is not rich is not wise and vice versa.
Everyone who is strong is not wise.
Susan is kind or happy.
Susan is curious or not brave.
Someone is either kind or tall.
John is humble or generous. | Susan is kind. | neutral | (![X]:((~quiet(X)&rich(X))=>(~patient(X)&~old(X))))&
(![X]:((old(X)<~>quiet(X))<=>(~patient(X)<~>~funny(X))))&
((~wise(mary))=>(generous(alice)))&
(![X]:((rich(X)|calm(X))<=>~rich(X)))&
(![X]:((kind(X)<~>old(X))<=>(rich(X)<~>patient(X))))&
(((~happy(alice)<~>patient(alice)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)&tall(X))))&
(![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~old(X)&~humble(X))))=>((~funny(paul)|~quiet(paul))))&
(((~kind(lucy)<~>calm(lucy)))<=>((funny(susan)&~kind(susan))))&
((?[X]:((~creative(X)<~>~brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>~wise(X)))&
(![X]:(strong(X)=>~wise(X)))&
((kind(susan)|happy(susan)))&
((curious(susan)|~brave(susan)))&
(?[X]:((kind(X)<~>tall(X))))&
((humble(john)|generous(john))) | kind(susan) | []
| null | 0 |
Everyone who is not strong is generous and vice versa. If lucy is old or creative then someone is both not creative and quiet and vice versa. If alice is both old and brave then john is either tall or humble. If fred is not patient or not strong then lucy is not patient and vice versa. Everyone who is both not rich and not calm is both creative and patient and vice versa. If someone is kind or old then someone is quiet or strong. If lucy is not tall then someone is both quiet and old and vice versa. Everyone who is both wise and humble is generous and vice versa. Everyone who is either quiet or tall is both rich and kind and vice versa. If someone is both not kind and rich then john is both tall and strong and vice versa. Everyone who is not curious is either not curious or not generous and vice versa. Everyone who is tall or not quiet is brave. If someone is not calm or not patient then susan is generous or not old and vice versa. Everyone who is quiet is patient or not kind and vice versa. If someone is either calm or humble then someone is either happy or quiet and vice versa. If mary is both not generous and quiet then someone is either not creative or kind. Someone is either kind or not rich. Mary is generous. Mary is both generous and not creative. John is not creative. Someone is not creative. Susan is strong or funny. | Mary is humble. | entailment | (![X]:(~strong(X)<=>generous(X)))&
(((old(lucy)|creative(lucy)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((old(alice)&brave(alice)))=>((tall(john)<~>humble(john))))&
(((~patient(fred)|~strong(fred)))<=>(~patient(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)&patient(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(lucy))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((wise(X)&humble(X))<=>generous(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(rich(X)&kind(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((tall(john)&strong(john))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~generous(X))))&
(![X]:((tall(X)|~quiet(X))=>brave(X)))&
((?[X]:((~calm(X)|~patient(X))))<=>((generous(susan)|~old(susan))))&
(![X]:(quiet(X)<=>(patient(X)|~kind(X))))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(((~generous(mary)&quiet(mary)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(?[X]:((kind(X)<~>~rich(X))))&
(generous(mary))&
((generous(mary)&~creative(mary)))&
(~creative(john))&
(?[X]:(~creative(X)))&
((strong(susan)|funny(susan))) | humble(mary) | [
"p0",
"p7",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 3678154794297518468515144
% SZS output start Proof for 3678154794297518468515144
1. ! [X0] : (~strong(X0) <=> generous(X0)) [input p0]
8. ! [X0] : ((humble(X0) & wise(X0)) <=> generous(X0)) [input p7]
11. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~generous(X0))) [input p10]
23. ~humble(mary) [input hypothesis]
33. ! [X0] : ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))) [nnf transformation 1]
51. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~humble(X0) | ~wise(X0))) [flattening 51]
60. ! [X0] : ((~curious(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 11]
81. generous(X0) | strong(X0) [cnf transformation 33]
82. ~generous(X0) | ~strong(X0) [cnf transformation 33]
104. ~generous(X0) | humble(X0) [cnf transformation 52]
116. generous(X0) | curious(X0) | curious(X0) [cnf transformation 60]
118. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 60]
145. ~humble(mary) [cnf transformation 23]
146. generous(X0) | curious(X0) [duplicate literal removal 116]
147. ~curious(X0) | generous(X0) [duplicate literal removal 118]
258. generous(X0) [subsumption resolution 146,147]
321. ~strong(X1) [resolution 82,258]
327. humble(X0) | strong(X0) [resolution 104,81]
329. humble(X0) [subsumption resolution 327,321]
332. $false [resolution 329,145]
% SZS output end Proof for 3678154794297518468515144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not wise and not calm then susan is tall or not creative.
If paul is old or generous then someone is not generous and vice versa.
Everyone who is creative or not wise is happy or not old and vice versa.
Everyone who is both strong and patient is old and vice versa.
Everyone who is both happy and not calm is brave or humble and vice versa.
Everyone who is both rich and calm is not wise or not happy.
Everyone who is both not humble and not rich is both not patient and not curious.
Everyone who is strong is not wise or generous.
Everyone who is tall is both not generous and not calm and vice versa.
If someone is either humble or kind then susan is creative.
Everyone who is both tall and strong is not curious.
Everyone who is both brave and not generous is either not kind or tall and vice versa.
If someone is quiet or not patient then paul is not quiet or not creative.
Everyone who is both not tall and strong is not rich.
Everyone who is not happy is not strong or not wise and vice versa.
Everyone who is both rich and not strong is not humble.
Lucy is not curious.
Susan is either humble or old.
Someone is either not quiet or not calm.
Susan is patient or brave.
Mary is not humble.
Susan is either not old or tall.
Susan is both not tall and funny.
Someone is either kind or not calm. | Susan is brave. | entailment | (((~wise(john)&~calm(john)))=>((tall(susan)|~creative(susan))))&
(((old(paul)|generous(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~wise(X))<=>(happy(X)|~old(X))))&
(![X]:((strong(X)&patient(X))<=>old(X)))&
(![X]:((happy(X)&~calm(X))<=>(brave(X)|humble(X))))&
(![X]:((rich(X)&calm(X))=>(~wise(X)|~happy(X))))&
(![X]:((~humble(X)&~rich(X))=>(~patient(X)&~curious(X))))&
(![X]:(strong(X)=>(~wise(X)|generous(X))))&
(![X]:(tall(X)<=>(~generous(X)&~calm(X))))&
((?[X]:((humble(X)<~>kind(X))))=>(creative(susan)))&
(![X]:((tall(X)&strong(X))=>~curious(X)))&
(![X]:((brave(X)&~generous(X))<=>(~kind(X)<~>tall(X))))&
((?[X]:((quiet(X)|~patient(X))))=>((~quiet(paul)|~creative(paul))))&
(![X]:((~tall(X)&strong(X))=>~rich(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&~strong(X))=>~humble(X)))&
(~curious(lucy))&
((humble(susan)<~>old(susan)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((patient(susan)|brave(susan)))&
(~humble(mary))&
((~old(susan)<~>tall(susan)))&
((~tall(susan)&funny(susan)))&
(?[X]:((kind(X)<~>~calm(X)))) | brave(susan) | [
"p3",
"p4",
"p14",
"p17",
"p19",
"p21",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4914117240598247130164973
% SZS output start Proof for 4914117240598247130164973
4. ! [X0] : ((patient(X0) & strong(X0)) <=> old(X0)) [input p3]
5. ! [X0] : ((~calm(X0) & happy(X0)) <=> (humble(X0) | brave(X0))) [input p4]
15. ! [X0] : (~happy(X0) <=> (~wise(X0) | ~strong(X0))) [input p14]
18. humble(susan) <~> old(susan) [input p17]
20. brave(susan) | patient(susan) [input p19]
22. ~old(susan) <~> tall(susan) [input p21]
23. funny(susan) & ~tall(susan) [input p22]
25. ~brave(susan) [input hypothesis]
26. ~tall(susan) [pure predicate removal 23]
52. ! [X0] : (((patient(X0) & strong(X0)) | ~old(X0)) & (old(X0) | (~patient(X0) | ~strong(X0)))) [nnf transformation 4]
53. ! [X0] : (((patient(X0) & strong(X0)) | ~old(X0)) & (old(X0) | ~patient(X0) | ~strong(X0))) [flattening 52]
54. ! [X0] : (((~calm(X0) & happy(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (calm(X0) | ~happy(X0)))) [nnf transformation 5]
55. ! [X0] : (((~calm(X0) & happy(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | calm(X0) | ~happy(X0))) [flattening 54]
61. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 15]
62. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | happy(X0))) [flattening 61]
63. (~old(susan) | ~humble(susan)) & (old(susan) | humble(susan)) [nnf transformation 18]
67. (~tall(susan) | old(susan)) & (tall(susan) | ~old(susan)) [nnf transformation 22]
79. ~patient(X0) | old(X0) | ~strong(X0) [cnf transformation 53]
84. ~humble(X0) | happy(X0) [cnf transformation 55]
105. ~happy(X0) | strong(X0) [cnf transformation 62]
108. old(susan) | humble(susan) [cnf transformation 63]
112. brave(susan) | patient(susan) [cnf transformation 20]
114. tall(susan) | ~old(susan) [cnf transformation 67]
116. ~tall(susan) [cnf transformation 26]
119. ~brave(susan) [cnf transformation 25]
129. 3 <=> tall(susan) [avatar definition]
182. 15 <=> humble(susan) [avatar definition]
183. humble(susan) <- (15) [avatar component clause 182]
186. 16 <=> old(susan) [avatar definition]
188. ~old(susan) <- (~16) [avatar component clause 186]
190. 15 | 16 [avatar split clause 108,186,182]
202. 19 <=> patient(susan) [avatar definition]
204. patient(susan) <- (19) [avatar component clause 202]
206. 20 <=> brave(susan) [avatar definition]
209. 19 | 20 [avatar split clause 112,206,202]
211. ~16 | 3 [avatar split clause 114,129,186]
212. ~3 [avatar split clause 116,129]
223. ~20 [avatar split clause 119,206]
228. happy(susan) <- (15) [resolution 84,183]
231. strong(susan) <- (15) [resolution 105,228]
236. old(susan) | ~strong(susan) <- (19) [resolution 79,204]
237. ~strong(susan) <- (~16, 19) [subsumption resolution 236,188]
238. $false <- (15, ~16, 19) [subsumption resolution 237,231]
239. ~15 | 16 | ~19 [avatar contradiction clause 238]
240. $false [avatar sat refutation 190,209,211,212,223,239]
% SZS output end Proof for 4914117240598247130164973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or happy is not old or calm and vice versa.
If mary is rich or kind then john is either not kind or not curious and vice versa.
If paul is both not calm and strong then mary is both rich and not tall.
Everyone who is either not kind or not funny is either curious or not calm.
Everyone who is both generous and not patient is both tall and not strong.
Everyone who is kind or calm is not tall or tall and vice versa.
Everyone who is not strong is not tall or quiet and vice versa.
Everyone who is both calm and strong is rich.
Everyone who is brave or not creative is old and vice versa.
If susan is kind then someone is tall.
If alice is patient or not funny then someone is not old and vice versa.
Everyone who is not funny or not curious is not generous.
Everyone who is not old or rich is both not brave and not tall and vice versa.
If someone is either not funny or old then someone is either brave or not rich.
If alice is either strong or brave then fred is not funny and vice versa.
If paul is either not tall or not brave then fred is generous or happy and vice versa.
Someone is humble or wise.
Mary is patient.
Susan is either quiet or not strong.
Someone is wise or funny.
Someone is tall or wise.
Lucy is not old.
John is both curious and kind. | Mary is old. | neutral | (![X]:((~tall(X)<~>happy(X))<=>(~old(X)|calm(X))))&
(((rich(mary)|kind(mary)))<=>((~kind(john)<~>~curious(john))))&
(((~calm(paul)&strong(paul)))=>((rich(mary)&~tall(mary))))&
(![X]:((~kind(X)<~>~funny(X))=>(curious(X)<~>~calm(X))))&
(![X]:((generous(X)&~patient(X))=>(tall(X)&~strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~tall(X)|tall(X))))&
(![X]:(~strong(X)<=>(~tall(X)|quiet(X))))&
(![X]:((calm(X)&strong(X))=>rich(X)))&
(![X]:((brave(X)|~creative(X))<=>old(X)))&
((kind(susan))=>(?[X]:(tall(X))))&
(((patient(alice)|~funny(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)|~curious(X))=>~generous(X)))&
(![X]:((~old(X)|rich(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(((strong(alice)<~>brave(alice)))<=>(~funny(fred)))&
(((~tall(paul)<~>~brave(paul)))<=>((generous(fred)|happy(fred))))&
(?[X]:((humble(X)|wise(X))))&
(patient(mary))&
((quiet(susan)<~>~strong(susan)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:((tall(X)|wise(X))))&
(~old(lucy))&
((curious(john)&kind(john))) | old(mary) | []
| null | 0 |
If someone is either funny or not strong then alice is not brave or funny and vice versa.
Everyone who is not kind is not wise or rich.
Everyone who is either happy or not wise is either happy or generous.
Everyone who is either not wise or not old is not old.
If someone is not wise or happy then someone is either funny or calm.
If lucy is generous or creative then someone is both not tall and not brave.
If someone is either not generous or patient then paul is either not patient or not tall and vice versa.
Everyone who is calm is both not wise and rich and vice versa.
Everyone who is tall or kind is calm.
If someone is either not curious or quiet then john is not creative.
If john is patient then paul is not kind or not calm and vice versa.
If mary is not quiet or not generous then someone is both not patient and patient.
Everyone who is both not generous and wise is not old and vice versa.
Everyone who is either not humble or not strong is tall or generous and vice versa.
Everyone who is not rich or strong is old and vice versa.
Everyone who is either tall or quiet is not funny or strong.
Fred is not humble.
Mary is both brave and not curious.
Mary is either not kind or not brave.
Someone is quiet or not creative.
Someone is both wise and not brave.
Someone is either not creative or not quiet.
Someone is either not brave or curious.
Someone is not curious. | Lucy is not tall. | entailment | ((?[X]:((funny(X)<~>~strong(X))))<=>((~brave(alice)|funny(alice))))&
(![X]:(~kind(X)=>(~wise(X)|rich(X))))&
(![X]:((happy(X)<~>~wise(X))=>(happy(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~old(X))=>~old(X)))&
((?[X]:((~wise(X)|happy(X))))=>(?[X]:((funny(X)<~>calm(X)))))&
(((generous(lucy)|creative(lucy)))=>(?[X]:((~tall(X)&~brave(X)))))&
((?[X]:((~generous(X)<~>patient(X))))<=>((~patient(paul)<~>~tall(paul))))&
(![X]:(calm(X)<=>(~wise(X)&rich(X))))&
(![X]:((tall(X)|kind(X))=>calm(X)))&
((?[X]:((~curious(X)<~>quiet(X))))=>(~creative(john)))&
((patient(john))<=>((~kind(paul)|~calm(paul))))&
(((~quiet(mary)|~generous(mary)))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~generous(X)&wise(X))<=>~old(X)))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)|generous(X))))&
(![X]:((~rich(X)|strong(X))<=>old(X)))&
(![X]:((tall(X)<~>quiet(X))=>(~funny(X)|strong(X))))&
(~humble(fred))&
((brave(mary)&~curious(mary)))&
((~kind(mary)<~>~brave(mary)))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:(~curious(X))) | ~tall(lucy) | [
"p3",
"p7",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 206595578124930750159222
% SZS output start Proof for 206595578124930750159222
4. ! [X0] : ((~wise(X0) <~> ~old(X0)) => ~old(X0)) [input p3]
8. ! [X0] : (calm(X0) <=> (rich(X0) & ~wise(X0))) [input p7]
9. ! [X0] : ((kind(X0) | tall(X0)) => calm(X0)) [input p8]
13. ! [X0] : ((wise(X0) & ~generous(X0)) <=> ~old(X0)) [input p12]
25. tall(lucy) [input hypothesis]
30. ! [X0] : (~old(X0) | (~wise(X0) <=> ~old(X0))) [ennf transformation 4]
33. ! [X0] : (calm(X0) | (~kind(X0) & ~tall(X0))) [ennf transformation 9]
44. ! [X0] : (~old(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) [nnf transformation 30]
55. ! [X0] : ((calm(X0) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | ~calm(X0))) [nnf transformation 8]
56. ! [X0] : ((calm(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | ~calm(X0))) [flattening 55]
62. ! [X0] : (((wise(X0) & ~generous(X0)) | old(X0)) & (~old(X0) | (~wise(X0) | generous(X0)))) [nnf transformation 13]
63. ! [X0] : (((wise(X0) & ~generous(X0)) | old(X0)) & (~old(X0) | ~wise(X0) | generous(X0))) [flattening 62]
93. ~old(X0) | ~old(X0) | wise(X0) [cnf transformation 44]
111. ~calm(X0) | ~wise(X0) [cnf transformation 56]
114. ~tall(X0) | calm(X0) [cnf transformation 33]
127. wise(X0) | old(X0) [cnf transformation 63]
152. tall(lucy) [cnf transformation 25]
153. ~old(X0) | wise(X0) [duplicate literal removal 93]
197. 10 <=> ! [X1] : wise(X1) [avatar definition]
198. wise(X1) <- (10) [avatar component clause 197]
296. wise(X0) [subsumption resolution 127,153]
297. 10 [avatar split clause 296,197]
329. calm(lucy) [resolution 114,152]
333. ~wise(lucy) [resolution 329,111]
334. $false <- (10) [subsumption resolution 333,198]
335. ~10 [avatar contradiction clause 334]
336. $false [avatar sat refutation 297,335]
% SZS output end Proof for 206595578124930750159222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not funny then someone is either not funny or generous and vice versa.
If susan is not patient then lucy is both not rich and old.
Everyone who is not brave or creative is tall.
Everyone who is not generous or tall is not old or not wise.
Everyone who is either not happy or curious is both patient and not generous.
Everyone who is old is either not strong or not humble and vice versa.
Everyone who is either rich or funny is both not strong and strong.
Everyone who is both not generous and not tall is strong or generous.
Everyone who is not brave is not wise or curious.
Everyone who is not creative or not old is curious.
Everyone who is kind or not calm is rich and vice versa.
If paul is curious or not generous then someone is either creative or not brave and vice versa.
Everyone who is either not strong or tall is either not old or kind and vice versa.
If mary is either not rich or not patient then someone is not funny or strong.
Everyone who is both not wise and not old is both not calm and not rich.
If someone is both curious and strong then someone is both not creative and not rich and vice versa.
Someone is happy.
Someone is either not brave or not funny.
Alice is not wise.
Paul is kind.
Alice is both strong and creative.
Someone is not tall or not funny.
Alice is both strong and funny.
Paul is either not old or wise. | Paul is not happy. | entailment | ((?[X]:((~patient(X)|~funny(X))))<=>(?[X]:((~funny(X)<~>generous(X)))))&
((~patient(susan))=>((~rich(lucy)&old(lucy))))&
(![X]:((~brave(X)|creative(X))=>tall(X)))&
(![X]:((~generous(X)|tall(X))=>(~old(X)|~wise(X))))&
(![X]:((~happy(X)<~>curious(X))=>(patient(X)&~generous(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~tall(X))=>(strong(X)|generous(X))))&
(![X]:(~brave(X)=>(~wise(X)|curious(X))))&
(![X]:((~creative(X)|~old(X))=>curious(X)))&
(![X]:((kind(X)|~calm(X))<=>rich(X)))&
(((curious(paul)|~generous(paul)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((~strong(X)<~>tall(X))<=>(~old(X)<~>kind(X))))&
(((~rich(mary)<~>~patient(mary)))=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:((~wise(X)&~old(X))=>(~calm(X)&~rich(X))))&
((?[X]:((curious(X)&strong(X))))<=>(?[X]:((~creative(X)&~rich(X)))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(~wise(alice))&
(kind(paul))&
((strong(alice)&creative(alice)))&
(?[X]:((~tall(X)|~funny(X))))&
((strong(alice)&funny(alice)))&
((~old(paul)<~>wise(paul))) | ~happy(paul) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p14",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 3436357751466208034671955
% SZS output start Proof for 3436357751466208034671955
3. ! [X0] : ((creative(X0) | ~brave(X0)) => tall(X0)) [input p2]
4. ! [X0] : ((tall(X0) | ~generous(X0)) => (~wise(X0) | ~old(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> curious(X0)) => (~generous(X0) & patient(X0))) [input p4]
10. ! [X0] : ((~old(X0) | ~creative(X0)) => curious(X0)) [input p9]
11. ! [X0] : ((~calm(X0) | kind(X0)) <=> rich(X0)) [input p10]
15. ! [X0] : ((~old(X0) & ~wise(X0)) => (~rich(X0) & ~calm(X0))) [input p14]
24. ~old(paul) <~> wise(paul) [input p23]
25. happy(paul) [input hypothesis]
29. ! [X0] : (tall(X0) | (~creative(X0) & brave(X0))) [ennf transformation 3]
30. ! [X0] : ((~wise(X0) | ~old(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 4]
31. ! [X0] : (~wise(X0) | ~old(X0) | (~tall(X0) & generous(X0))) [flattening 30]
32. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) <=> curious(X0))) [ennf transformation 5]
38. ! [X0] : (curious(X0) | (old(X0) & creative(X0))) [ennf transformation 10]
40. ! [X0] : ((~rich(X0) & ~calm(X0)) | (old(X0) | wise(X0))) [ennf transformation 15]
41. ! [X0] : ((~rich(X0) & ~calm(X0)) | old(X0) | wise(X0)) [flattening 40]
47. ! [X0] : ((~generous(X0) & patient(X0)) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0)))) [nnf transformation 32]
50. ! [X0] : (((~calm(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (calm(X0) & ~kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((~calm(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (calm(X0) & ~kind(X0)))) [flattening 50]
73. (~wise(paul) | old(paul)) & (wise(paul) | ~old(paul)) [nnf transformation 24]
83. ~creative(X0) | tall(X0) [cnf transformation 29]
84. ~wise(X0) | ~old(X0) | generous(X0) [cnf transformation 31]
85. ~wise(X0) | ~old(X0) | ~tall(X0) [cnf transformation 31]
89. ~curious(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 47]
100. curious(X0) | creative(X0) [cnf transformation 38]
103. calm(X0) | rich(X0) [cnf transformation 51]
121. ~calm(X0) | old(X0) | wise(X0) [cnf transformation 41]
122. ~rich(X0) | old(X0) | wise(X0) [cnf transformation 41]
137. wise(paul) | ~old(paul) [cnf transformation 73]
138. ~wise(paul) | old(paul) [cnf transformation 73]
139. happy(paul) [cnf transformation 25]
195. 13 <=> curious(paul) [avatar definition]
196. ~curious(paul) <- (~13) [avatar component clause 195]
197. curious(paul) <- (13) [avatar component clause 195]
199. 14 <=> generous(paul) [avatar definition]
283. 32 <=> old(paul) [avatar definition]
284. ~old(paul) <- (~32) [avatar component clause 283]
285. old(paul) <- (32) [avatar component clause 283]
287. 33 <=> wise(paul) [avatar definition]
288. wise(paul) <- (33) [avatar component clause 287]
289. ~wise(paul) <- (~33) [avatar component clause 287]
290. 32 | ~33 [avatar split clause 138,287,283]
291. ~32 | 33 [avatar split clause 137,287,283]
375. ~happy(paul) | ~generous(paul) <- (13) [resolution 197,89]
377. ~generous(paul) <- (13) [subsumption resolution 375,139]
381. ~14 | ~13 [avatar split clause 377,195,199]
431. old(X0) | wise(X0) | rich(X0) [resolution 121,103]
432. wise(X0) | old(X0) [subsumption resolution 431,122]
439. old(paul) <- (~33) [resolution 432,289]
442. $false <- (~32, ~33) [subsumption resolution 439,284]
443. 32 | 33 [avatar contradiction clause 442]
447. ~old(paul) | ~tall(paul) <- (33) [resolution 288,85]
448. ~old(paul) | generous(paul) <- (33) [resolution 288,84]
449. ~tall(paul) <- (32, 33) [subsumption resolution 447,285]
450. generous(paul) <- (32, 33) [subsumption resolution 448,285]
458. 14 | ~32 | ~33 [avatar split clause 450,287,283,199]
461. creative(paul) <- (~13) [resolution 196,100]
481. tall(paul) <- (~13) [resolution 461,83]
484. $false <- (~13, 32, 33) [subsumption resolution 481,449]
485. 13 | ~32 | ~33 [avatar contradiction clause 484]
486. $false [avatar sat refutation 290,291,381,443,458,485]
% SZS output end Proof for 3436357751466208034671955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and not rich is generous or not kind.
Everyone who is either calm or brave is not funny or not strong.
Everyone who is not happy or not kind is not calm.
Everyone who is either not funny or wise is both wise and not rich and vice versa.
Everyone who is not creative or not humble is rich and vice versa.
If susan is both generous and not rich then fred is either humble or happy.
If someone is either not kind or not wise then someone is not patient and vice versa.
If someone is not creative then someone is both funny and not quiet.
If alice is both not brave and not wise then someone is both not creative and quiet and vice versa.
If someone is not wise or wise then someone is not rich and vice versa.
Everyone who is not curious is quiet and vice versa.
Everyone who is both not quiet and happy is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Mary is either tall or not quiet.
Mary is creative or brave.
Alice is happy or tall.
Someone is patient or not brave.
Someone is brave or patient. | Alice is not strong. | entailment | (![X]:((happy(X)&~rich(X))=>(generous(X)|~kind(X))))&
(![X]:((calm(X)<~>brave(X))=>(~funny(X)|~strong(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((~funny(X)<~>wise(X))<=>(wise(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>rich(X)))&
(((generous(susan)&~rich(susan)))=>((humble(fred)<~>happy(fred))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)&~quiet(X)))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:((~quiet(X)&happy(X))<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
((tall(mary)<~>~quiet(mary)))&
((creative(mary)|brave(mary)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((brave(X)|patient(X)))) | ~strong(alice) | [
"p1",
"p2",
"p3",
"p10",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3682691931402339725400228
% SZS output start Proof for 3682691931402339725400228
2. ! [X0] : ((calm(X0) <~> brave(X0)) => (~strong(X0) | ~funny(X0))) [input p1]
3. ! [X0] : ((~kind(X0) | ~happy(X0)) => ~calm(X0)) [input p2]
4. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> (~rich(X0) & wise(X0))) [input p3]
11. ! [X0] : (~curious(X0) <=> quiet(X0)) [input p10]
14. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p13]
15. ! [X0] : (brave(X0) <=> (~generous(X0) | funny(X0))) [input p14]
22. strong(alice) [input hypothesis]
28. ! [X0] : ((~strong(X0) | ~funny(X0)) | (calm(X0) <=> brave(X0))) [ennf transformation 2]
29. ! [X0] : (~strong(X0) | ~funny(X0) | (calm(X0) <=> brave(X0))) [flattening 28]
30. ! [X0] : (~calm(X0) | (kind(X0) & happy(X0))) [ennf transformation 3]
35. ! [X0] : (~strong(X0) | ~funny(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) [nnf transformation 29]
36. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 4]
37. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [flattening 36]
59. ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))) [nnf transformation 11]
64. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 14]
65. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 64]
66. ! [X0] : ((brave(X0) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | ~brave(X0))) [nnf transformation 15]
67. ! [X0] : ((brave(X0) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ~brave(X0))) [flattening 66]
76. ~strong(X0) | ~funny(X0) | calm(X0) | ~brave(X0) [cnf transformation 35]
78. ~calm(X0) | kind(X0) [cnf transformation 30]
79. wise(X0) | wise(X0) | funny(X0) [cnf transformation 37]
84. ~wise(X0) | funny(X0) | rich(X0) | ~wise(X0) [cnf transformation 37]
103. curious(X0) | quiet(X0) [cnf transformation 59]
113. ~quiet(X0) | ~kind(X0) [cnf transformation 65]
114. ~curious(X0) | ~kind(X0) [cnf transformation 65]
115. ~quiet(X0) | ~rich(X0) [cnf transformation 65]
116. ~curious(X0) | ~rich(X0) [cnf transformation 65]
118. ~funny(X0) | brave(X0) [cnf transformation 67]
130. strong(alice) [cnf transformation 22]
131. wise(X0) | funny(X0) [duplicate literal removal 79]
132. ~wise(X0) | funny(X0) | rich(X0) [duplicate literal removal 84]
198. 16 <=> brave(alice) [avatar definition]
199. brave(alice) <- (16) [avatar component clause 198]
200. ~brave(alice) <- (~16) [avatar component clause 198]
293. ~kind(X0) | quiet(X0) [resolution 114,103]
294. ~kind(X0) [subsumption resolution 293,113]
298. ~rich(X0) | quiet(X0) [resolution 116,103]
299. ~rich(X0) [subsumption resolution 298,115]
341. funny(X0) | rich(X0) | funny(X0) [resolution 132,131]
342. funny(X0) | rich(X0) [duplicate literal removal 341]
346. funny(X0) [subsumption resolution 342,299]
352. brave(X0) [resolution 346,118]
354. ~funny(alice) | calm(alice) | ~brave(alice) [resolution 76,130]
355. calm(alice) | ~brave(alice) [subsumption resolution 354,346]
356. calm(alice) <- (16) [subsumption resolution 355,199]
357. kind(alice) <- (16) [resolution 356,78]
359. $false <- (16) [subsumption resolution 357,294]
360. ~16 [avatar contradiction clause 359]
364. $false <- (~16) [subsumption resolution 200,352]
365. 16 [avatar contradiction clause 364]
366. $false [avatar sat refutation 360,365]
% SZS output end Proof for 3682691931402339725400228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not old then paul is not kind and vice versa.
Everyone who is not generous or calm is both happy and quiet and vice versa.
If someone is both brave and wise then someone is strong and vice versa.
If lucy is quiet or not strong then someone is not tall or not creative.
Everyone who is not curious or not patient is both not patient and strong and vice versa.
Everyone who is either funny or not calm is both not quiet and not calm and vice versa.
Everyone who is brave or kind is not strong.
If someone is either not humble or humble then fred is both humble and quiet.
Everyone who is either brave or not calm is not brave and vice versa.
Everyone who is either quiet or creative is not patient and vice versa.
Everyone who is both not quiet and not brave is both not brave and funny and vice versa.
If someone is either humble or not quiet then mary is calm or not quiet.
If mary is quiet then someone is either quiet or not brave.
Everyone who is either generous or not humble is both not rich and calm and vice versa.
Everyone who is not generous is happy.
If lucy is both rich and old then someone is kind.
John is both not calm and quiet.
Someone is humble.
Someone is either not patient or not old.
Someone is not quiet or curious.
Someone is not kind or kind.
Susan is old or not kind.
Someone is curious. | Lucy is calm. | contradiction | ((?[X]:((brave(X)<~>~old(X))))<=>(~kind(paul)))&
(![X]:((~generous(X)|calm(X))<=>(happy(X)&quiet(X))))&
((?[X]:((brave(X)&wise(X))))<=>(?[X]:(strong(X))))&
(((quiet(lucy)|~strong(lucy)))=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((~curious(X)|~patient(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)<~>~calm(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((brave(X)|kind(X))=>~strong(X)))&
((?[X]:((~humble(X)<~>humble(X))))=>((humble(fred)&quiet(fred))))&
(![X]:((brave(X)<~>~calm(X))<=>~brave(X)))&
(![X]:((quiet(X)<~>creative(X))<=>~patient(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>((calm(mary)|~quiet(mary))))&
((quiet(mary))=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>(~rich(X)&calm(X))))&
(![X]:(~generous(X)=>happy(X)))&
(((rich(lucy)&old(lucy)))=>(?[X]:(kind(X))))&
((~calm(john)&quiet(john)))&
(?[X]:(humble(X)))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((~kind(X)|kind(X))))&
((old(susan)|~kind(susan)))&
(?[X]:(curious(X))) | calm(lucy) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 6733409134449808599926329
% SZS output start Proof for 6733409134449808599926329
9. ! [X0] : ((brave(X0) <~> ~calm(X0)) <=> ~brave(X0)) [input p8]
24. calm(lucy) [input hypothesis]
51. ! [X0] : ((((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | brave(X0)) & (~brave(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0))))) [nnf transformation 9]
103. ~brave(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 51]
105. ~calm(X0) | brave(X0) | brave(X0) [cnf transformation 51]
136. calm(lucy) [cnf transformation 24]
137. ~brave(X0) | ~calm(X0) [duplicate literal removal 103]
138. ~calm(X0) | brave(X0) [duplicate literal removal 105]
207. ~calm(X0) [subsumption resolution 137,138]
279. $false [subsumption resolution 136,207]
% SZS output end Proof for 6733409134449808599926329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient is either curious or not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is either creative or brave is either rich or not happy and vice versa. Alice is either not patient or not old. John is not calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | Mary is patient. | entailment | (![X]:((rich(X)|patient(X))=>(curious(X)<~>~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~patient(alice)<~>~old(alice)))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | patient(mary) | [
"p3",
"p7",
"p9",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 659899538739399586206234
% SZS output start Proof for 659899538739399586206234
4. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p3]
8. ! [X0] : (~quiet(X0) => patient(X0)) [input p7]
10. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p9]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
21. ~patient(mary) [input hypothesis]
23. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 4]
26. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 23]
30. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 8]
48. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 10]
49. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 48]
55. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
56. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~wise(X0) | ~creative(X0))) [flattening 55]
77. ~quiet(X0) | ~funny(X0) [cnf transformation 26]
87. quiet(X0) | patient(X0) [cnf transformation 30]
89. ~wise(X0) | funny(X0) [cnf transformation 49]
101. wise(X0) | funny(X0) [cnf transformation 56]
118. ~patient(mary) [cnf transformation 21]
205. funny(X0) [subsumption resolution 101,89]
230. patient(X0) | ~funny(X0) [resolution 87,77]
231. patient(X0) [subsumption resolution 230,205]
232. $false [resolution 231,118]
% SZS output end Proof for 659899538739399586206234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not strong is either not strong or rich and vice versa.
Everyone who is curious or strong is not quiet and vice versa.
Everyone who is calm is both kind and strong and vice versa.
If paul is humble or creative then someone is not rich or patient.
If someone is both not wise and not creative then susan is both not humble and not rich and vice versa.
If someone is not wise or strong then someone is not curious or patient.
Everyone who is not strong is both not happy and kind and vice versa.
Everyone who is both old and not wise is both not calm and happy.
Everyone who is both humble and not generous is curious.
Everyone who is not wise or tall is either old or patient and vice versa.
If someone is both not funny and curious then fred is not curious or kind and vice versa.
If paul is not calm or creative then paul is not patient or not curious.
Everyone who is not happy or not quiet is either not tall or generous.
If someone is not quiet then someone is not calm or calm.
Everyone who is either not creative or strong is happy or not happy and vice versa.
Everyone who is creative is not wise or kind.
Susan is either kind or not curious.
Someone is both not quiet and old.
Someone is either tall or not funny.
Someone is patient or not tall.
Fred is not funny.
Alice is tall or rich.
Someone is either not curious or calm.
Someone is either curious or old. | Susan is wise. | neutral | (![X]:((~curious(X)&~strong(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((curious(X)|strong(X))<=>~quiet(X)))&
(![X]:(calm(X)<=>(kind(X)&strong(X))))&
(((humble(paul)|creative(paul)))=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((~wise(X)&~creative(X))))<=>((~humble(susan)&~rich(susan))))&
((?[X]:((~wise(X)|strong(X))))=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:(~strong(X)<=>(~happy(X)&kind(X))))&
(![X]:((old(X)&~wise(X))=>(~calm(X)&happy(X))))&
(![X]:((humble(X)&~generous(X))=>curious(X)))&
(![X]:((~wise(X)|tall(X))<=>(old(X)<~>patient(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~curious(fred)|kind(fred))))&
(((~calm(paul)|creative(paul)))=>((~patient(paul)|~curious(paul))))&
(![X]:((~happy(X)|~quiet(X))=>(~tall(X)<~>generous(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((~creative(X)<~>strong(X))<=>(happy(X)|~happy(X))))&
(![X]:(creative(X)=>(~wise(X)|kind(X))))&
((kind(susan)<~>~curious(susan)))&
(?[X]:((~quiet(X)&old(X))))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((patient(X)|~tall(X))))&
(~funny(fred))&
((tall(alice)|rich(alice)))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((curious(X)<~>old(X)))) | wise(susan) | []
| null | 0 |
Everyone who is not humble is calm.
If someone is brave then alice is funny or not creative and vice versa.
Everyone who is generous is kind and vice versa.
Everyone who is both funny and brave is either not tall or not old.
If mary is not tall or quiet then someone is either not creative or patient.
If paul is funny or generous then paul is not wise or not patient.
Everyone who is both not wise and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Lucy is not old or tall.
Alice is not humble or kind.
Paul is both not quiet and not wise.
Paul is both not curious and not rich.
Paul is humble or not wise.
Someone is either not happy or not creative.
Alice is rich.
John is either not humble or kind. | Alice is wise. | entailment | (![X]:(~humble(X)=>calm(X)))&
((?[X]:(brave(X)))<=>((funny(alice)|~creative(alice))))&
(![X]:(generous(X)<=>kind(X)))&
(![X]:((funny(X)&brave(X))=>(~tall(X)<~>~old(X))))&
(((~tall(mary)|quiet(mary)))=>(?[X]:((~creative(X)<~>patient(X)))))&
(((funny(paul)|generous(paul)))=>((~wise(paul)|~patient(paul))))&
(![X]:((~wise(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
((~old(lucy)|tall(lucy)))&
((~humble(alice)|kind(alice)))&
((~quiet(paul)&~wise(paul)))&
((~curious(paul)&~rich(paul)))&
((humble(paul)|~wise(paul)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(rich(alice))&
((~humble(john)<~>kind(john))) | wise(alice) | [
"p6",
"p8",
"p13",
"p14",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 2794615485810852583555153
% SZS output start Proof for 2794615485810852583555153
7. ! [X0] : ((creative(X0) & ~wise(X0)) <=> ~wise(X0)) [input p6]
9. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p8]
14. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p13]
15. ! [X0] : (rich(X0) => ~kind(X0)) [input p14]
16. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p15]
23. rich(alice) [input p22]
25. ~wise(alice) [input hypothesis]
34. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 14]
35. ! [X0] : (~kind(X0) | ~rich(X0)) [ennf transformation 15]
45. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) | wise(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | ~creative(X0) | wise(X0))) [flattening 45]
48. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 9]
49. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 48]
59. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 16]
78. wise(X0) | creative(X0) [cnf transformation 46]
81. ~old(X0) | tall(X0) [cnf transformation 49]
82. ~curious(X0) | ~old(X0) [cnf transformation 49]
85. ~tall(X0) | curious(X0) | kind(X0) | old(X0) [cnf transformation 49]
105. tall(X0) | old(X0) [cnf transformation 34]
107. ~rich(X0) | ~kind(X0) [cnf transformation 35]
108. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 59]
110. ~creative(X0) | curious(X0) | ~old(X0) [cnf transformation 59]
121. rich(alice) [cnf transformation 23]
124. ~wise(alice) [cnf transformation 25]
130. 1 <=> creative(alice) [avatar definition]
132. creative(alice) <- (1) [avatar component clause 130]
216. tall(X0) [subsumption resolution 105,81]
217. ~old(X0) | ~creative(X0) [subsumption resolution 110,82]
218. ~curious(X0) | ~creative(X0) [subsumption resolution 108,82]
224. 20 <=> kind(alice) [avatar definition]
225. ~kind(alice) <- (~20) [avatar component clause 224]
256. creative(alice) [resolution 78,124]
262. 1 [avatar split clause 256,130]
269. ~kind(alice) [resolution 107,121]
270. ~20 [avatar split clause 269,224]
320. curious(X0) | kind(X0) | old(X0) [resolution 85,216]
328. kind(X0) | old(X0) | ~creative(X0) [resolution 320,218]
340. ~creative(X0) | kind(X0) [subsumption resolution 328,217]
358. kind(alice) <- (1) [resolution 340,132]
361. $false <- (1, ~20) [subsumption resolution 358,225]
362. ~1 | 20 [avatar contradiction clause 361]
363. $false [avatar sat refutation 262,270,362]
% SZS output end Proof for 2794615485810852583555153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is both not brave and curious and vice versa.
If mary is not strong then someone is quiet and vice versa.
Everyone who is not generous or not patient is either patient or generous.
If someone is not kind then someone is both patient and humble.
If someone is not curious then someone is calm or not humble and vice versa.
If susan is both not strong and not generous then lucy is either not rich or not wise and vice versa.
Everyone who is old or quiet is either rich or not old and vice versa.
If susan is not calm or not strong then someone is strong or not quiet.
If someone is either not humble or not generous then someone is both rich and not quiet and vice versa.
Everyone who is either wise or generous is either strong or not brave and vice versa.
Everyone who is not tall or not strong is either rich or old and vice versa.
Everyone who is happy or not strong is both not calm and brave.
If someone is brave then someone is not humble and vice versa.
Everyone who is strong or not rich is humble or not rich.
Everyone who is both not generous and not wise is not calm or not old.
Everyone who is not rich or strong is brave or not happy.
Susan is not curious.
Lucy is either patient or not creative.
John is not tall.
Fred is either not curious or not patient.
Someone is either patient or tall.
Susan is old.
Mary is either not humble or not strong.
Someone is either not rich or not tall. | Susan is not tall. | contradiction | (![X]:((~creative(X)&patient(X))<=>(~brave(X)&curious(X))))&
((~strong(mary))<=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)|~patient(X))=>(patient(X)<~>generous(X))))&
((?[X]:(~kind(X)))=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((calm(X)|~humble(X)))))&
(((~strong(susan)&~generous(susan)))<=>((~rich(lucy)<~>~wise(lucy))))&
(![X]:((old(X)|quiet(X))<=>(rich(X)<~>~old(X))))&
(((~calm(susan)|~strong(susan)))=>(?[X]:((strong(X)|~quiet(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((wise(X)<~>generous(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~tall(X)|~strong(X))<=>(rich(X)<~>old(X))))&
(![X]:((happy(X)|~strong(X))=>(~calm(X)&brave(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~humble(X))))&
(![X]:((strong(X)|~rich(X))=>(humble(X)|~rich(X))))&
(![X]:((~generous(X)&~wise(X))=>(~calm(X)|~old(X))))&
(![X]:((~rich(X)|strong(X))=>(brave(X)|~happy(X))))&
(~curious(susan))&
((patient(lucy)<~>~creative(lucy)))&
(~tall(john))&
((~curious(fred)<~>~patient(fred)))&
(?[X]:((patient(X)<~>tall(X))))&
(old(susan))&
((~humble(mary)<~>~strong(mary)))&
(?[X]:((~rich(X)<~>~tall(X)))) | ~tall(susan) | [
"p6",
"p10",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 3024025651425358140967286
% SZS output start Proof for 3024025651425358140967286
7. ! [X0] : ((quiet(X0) | old(X0)) <=> (rich(X0) <~> ~old(X0))) [input p6]
11. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (rich(X0) <~> old(X0))) [input p10]
22. old(susan) [input p21]
25. ~tall(susan) [input hypothesis]
54. ! [X0] : (((quiet(X0) | old(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | (~quiet(X0) & ~old(X0)))) [nnf transformation 7]
55. ! [X0] : ((quiet(X0) | old(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | (~quiet(X0) & ~old(X0)))) [flattening 54]
64. ! [X0] : (((~strong(X0) | ~tall(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (strong(X0) & tall(X0)))) [nnf transformation 11]
65. ! [X0] : ((~strong(X0) | ~tall(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (strong(X0) & tall(X0)))) [flattening 64]
99. ~old(X0) | rich(X0) | ~old(X0) [cnf transformation 55]
123. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 65]
142. old(susan) [cnf transformation 22]
147. ~tall(susan) [cnf transformation 25]
148. ~old(X0) | rich(X0) [duplicate literal removal 99]
257. ~old(X0) | tall(X0) [subsumption resolution 123,148]
341. tall(susan) [resolution 257,142]
342. $false [subsumption resolution 341,147]
% SZS output end Proof for 3024025651425358140967286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not rich then susan is happy or not creative.
Everyone who is funny or calm is both wise and happy and vice versa.
If someone is either curious or not humble then susan is both not happy and happy.
Everyone who is both humble and not brave is creative or brave.
If mary is not wise then someone is not old and vice versa.
Everyone who is either wise or not strong is not curious or curious and vice versa.
If someone is not humble or old then someone is tall or not old and vice versa.
Everyone who is either not curious or not quiet is patient.
Everyone who is either not wise or generous is both not wise and not funny and vice versa.
Everyone who is both tall and not wise is not generous or tall and vice versa.
Everyone who is either patient or happy is either happy or wise.
Everyone who is either patient or humble is not funny or quiet and vice versa.
If susan is either not quiet or calm then someone is not kind and vice versa.
If someone is kind then mary is not calm and vice versa.
If someone is not wise or not creative then someone is either happy or old and vice versa.
Someone is either wise or old.
Someone is not old or generous.
Someone is either brave or not humble.
Lucy is kind.
Alice is both patient and not strong.
Someone is not happy or kind.
Mary is either not quiet or curious. | Mary is not calm. | entailment | ((~rich(lucy))=>((happy(susan)|~creative(susan))))&
(![X]:((funny(X)|calm(X))<=>(wise(X)&happy(X))))&
((?[X]:((curious(X)<~>~humble(X))))=>((~happy(susan)&happy(susan))))&
(![X]:((humble(X)&~brave(X))=>(creative(X)|brave(X))))&
((~wise(mary))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~strong(X))<=>(~curious(X)|curious(X))))&
((?[X]:((~humble(X)|old(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>patient(X)))&
(![X]:((~wise(X)<~>generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:((tall(X)&~wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((patient(X)<~>happy(X))=>(happy(X)<~>wise(X))))&
(![X]:((patient(X)<~>humble(X))<=>(~funny(X)|quiet(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(kind(X)))<=>(~calm(mary)))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((happy(X)<~>old(X)))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
(kind(lucy))&
((patient(alice)&~strong(alice)))&
(?[X]:((~happy(X)|kind(X))))&
((~quiet(mary)<~>curious(mary))) | ~calm(mary) | [
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 1059182518343421135237755
% SZS output start Proof for 1059182518343421135237755
14. ? [X0] : kind(X0) <=> ~calm(mary) [input p13]
19. kind(lucy) [input p18]
23. calm(mary) [input hypothesis]
58. (? [X0] : kind(X0) | calm(mary)) & (~calm(mary) | ! [X0] : ~kind(X0)) [nnf transformation 14]
59. (? [X0] : kind(X0) | calm(mary)) & (~calm(mary) | ! [X1] : ~kind(X1)) [rectify 58]
60. ? [X0] : kind(X0) => kind(sK4) [choice axiom]
61. (kind(sK4) | calm(mary)) & (~calm(mary) | ! [X1] : ~kind(X1)) [skolemisation 59,60]
127. ~calm(mary) | ~kind(X1) [cnf transformation 61]
140. kind(lucy) [cnf transformation 19]
146. calm(mary) [cnf transformation 23]
236. 18 <=> calm(mary) [avatar definition]
245. 20 <=> ! [X1] : ~kind(X1) [avatar definition]
246. ~kind(X1) <- (20) [avatar component clause 245]
247. 20 | ~18 [avatar split clause 127,236,245]
296. 18 [avatar split clause 146,236]
297. $false <- (20) [resolution 246,140]
298. ~20 [avatar contradiction clause 297]
299. $false [avatar sat refutation 247,296,298]
% SZS output end Proof for 1059182518343421135237755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong is both not tall and not rich.
If someone is not calm or humble then someone is both old and not rich and vice versa.
If someone is either tall or old then someone is either brave or rich and vice versa.
If someone is not happy then someone is both not calm and not rich and vice versa.
If alice is either not rich or tall then someone is either creative or not humble.
Everyone who is strong or calm is not tall or not kind.
Everyone who is either not wise or not happy is not generous.
If someone is both curious and not kind then someone is either rich or not curious.
Everyone who is calm is either not generous or not creative and vice versa.
If someone is both brave and not kind then someone is curious.
If someone is not wise then someone is not happy and vice versa.
If paul is either quiet or not strong then someone is both not wise and strong.
Everyone who is both not brave and not strong is either not quiet or humble.
Everyone who is not happy is either humble or tall.
Everyone who is either not patient or funny is either rich or not generous and vice versa.
If someone is either patient or happy then someone is humble and vice versa.
Susan is not patient.
Someone is either not quiet or creative.
Fred is both humble and not creative.
Fred is both not funny and curious.
Fred is either not wise or not quiet.
Someone is both not kind and tall.
Mary is both calm and not curious.
Someone is either not kind or quiet. | Fred is not brave. | neutral | (![X]:((~rich(X)<~>~strong(X))=>(~tall(X)&~rich(X))))&
((?[X]:((~calm(X)|humble(X))))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)&~rich(X)))))&
(((~rich(alice)<~>tall(alice)))=>(?[X]:((creative(X)<~>~humble(X)))))&
(![X]:((strong(X)|calm(X))=>(~tall(X)|~kind(X))))&
(![X]:((~wise(X)<~>~happy(X))=>~generous(X)))&
((?[X]:((curious(X)&~kind(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:(calm(X)<=>(~generous(X)<~>~creative(X))))&
((?[X]:((brave(X)&~kind(X))))=>(?[X]:(curious(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~happy(X))))&
(((quiet(paul)<~>~strong(paul)))=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:(~happy(X)=>(humble(X)<~>tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(~patient(susan))&
(?[X]:((~quiet(X)<~>creative(X))))&
((humble(fred)&~creative(fred)))&
((~funny(fred)&curious(fred)))&
((~wise(fred)<~>~quiet(fred)))&
(?[X]:((~kind(X)&tall(X))))&
((calm(mary)&~curious(mary)))&
(?[X]:((~kind(X)<~>quiet(X)))) | ~brave(fred) | []
| null | 0 |
Everyone who is either humble or not creative is happy or not patient and vice versa.
Everyone who is not wise is both patient and not funny and vice versa.
Everyone who is brave is both not creative and not humble and vice versa.
Everyone who is strong or not kind is either not calm or patient.
If someone is wise or not brave then lucy is not calm and vice versa.
Everyone who is both curious and creative is either wise or not wise and vice versa.
If lucy is patient or not curious then lucy is both rich and curious and vice versa.
Everyone who is strong or not rich is both old and tall.
If fred is both patient and strong then john is curious or not kind.
If paul is not tall or not old then someone is either not wise or calm and vice versa.
Everyone who is either not wise or not funny is both not brave and humble.
Everyone who is not brave is either not curious or generous and vice versa.
Everyone who is either strong or not tall is not quiet or not kind and vice versa.
Everyone who is patient is either not funny or not curious and vice versa.
If someone is both not old and funny then someone is either kind or quiet.
Someone is generous.
Alice is either not curious or old.
Paul is either humble or tall.
Paul is either rich or not brave.
Someone is not rich.
Alice is rich or not creative. | Lucy is tall. | entailment | (![X]:((humble(X)<~>~creative(X))<=>(happy(X)|~patient(X))))&
(![X]:(~wise(X)<=>(patient(X)&~funny(X))))&
(![X]:(brave(X)<=>(~creative(X)&~humble(X))))&
(![X]:((strong(X)|~kind(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((wise(X)|~brave(X))))<=>(~calm(lucy)))&
(![X]:((curious(X)&creative(X))<=>(wise(X)<~>~wise(X))))&
(((patient(lucy)|~curious(lucy)))<=>((rich(lucy)&curious(lucy))))&
(![X]:((strong(X)|~rich(X))=>(old(X)&tall(X))))&
(((patient(fred)&strong(fred)))=>((curious(john)|~kind(john))))&
(((~tall(paul)|~old(paul)))<=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((~wise(X)<~>~funny(X))=>(~brave(X)&humble(X))))&
(![X]:(~brave(X)<=>(~curious(X)<~>generous(X))))&
(![X]:((strong(X)<~>~tall(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(?[X]:(generous(X)))&
((~curious(alice)<~>old(alice)))&
((humble(paul)<~>tall(paul)))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(~rich(X)))&
((rich(alice)|~creative(alice))) | tall(lucy) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 2857031134459435431552735
% SZS output start Proof for 2857031134459435431552735
2. ! [X0] : (~wise(X0) <=> (~funny(X0) & patient(X0))) [input p1]
3. ! [X0] : (brave(X0) <=> (~humble(X0) & ~creative(X0))) [input p2]
5. ? [X0] : (~brave(X0) | wise(X0)) <=> ~calm(lucy) [input p4]
6. ! [X0] : ((creative(X0) & curious(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p5]
7. (~curious(lucy) | patient(lucy)) <=> (curious(lucy) & rich(lucy)) [input p6]
8. ! [X0] : ((~rich(X0) | strong(X0)) => (tall(X0) & old(X0))) [input p7]
10. (~old(paul) | ~tall(paul)) <=> ? [X0] : (~wise(X0) <~> calm(X0)) [input p9]
14. ! [X0] : (patient(X0) <=> (~funny(X0) <~> ~curious(X0))) [input p13]
19. rich(paul) <~> ~brave(paul) [input p18]
22. ~tall(lucy) [input hypothesis]
25. ! [X0] : ((tall(X0) & old(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 8]
32. ! [X0] : ((~wise(X0) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | wise(X0))) [nnf transformation 2]
33. ! [X0] : ((~wise(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | wise(X0))) [flattening 32]
34. ! [X0] : ((brave(X0) | (humble(X0) | creative(X0))) & ((~humble(X0) & ~creative(X0)) | ~brave(X0))) [nnf transformation 3]
35. ! [X0] : ((brave(X0) | humble(X0) | creative(X0)) & ((~humble(X0) & ~creative(X0)) | ~brave(X0))) [flattening 34]
37. (? [X0] : (~brave(X0) | wise(X0)) | calm(lucy)) & (~calm(lucy) | ! [X0] : (brave(X0) & ~wise(X0))) [nnf transformation 5]
38. (? [X0] : (~brave(X0) | wise(X0)) | calm(lucy)) & (~calm(lucy) | ! [X1] : (brave(X1) & ~wise(X1))) [rectify 37]
39. ? [X0] : (~brave(X0) | wise(X0)) => (~brave(sK0) | wise(sK0)) [choice axiom]
40. ((~brave(sK0) | wise(sK0)) | calm(lucy)) & (~calm(lucy) | ! [X1] : (brave(X1) & ~wise(X1))) [skolemisation 38,39]
41. ! [X0] : (((creative(X0) & curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~creative(X0) | ~curious(X0)))) [nnf transformation 6]
42. ! [X0] : (((creative(X0) & curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~creative(X0) | ~curious(X0))) [flattening 41]
43. ((~curious(lucy) | patient(lucy)) | (~curious(lucy) | ~rich(lucy))) & ((curious(lucy) & rich(lucy)) | (curious(lucy) & ~patient(lucy))) [nnf transformation 7]
44. (~curious(lucy) | patient(lucy) | ~curious(lucy) | ~rich(lucy)) & ((curious(lucy) & rich(lucy)) | (curious(lucy) & ~patient(lucy))) [flattening 43]
45. ((~old(paul) | ~tall(paul)) | ! [X0] : ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (? [X0] : ((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (old(paul) & tall(paul))) [nnf transformation 10]
46. (~old(paul) | ~tall(paul) | ! [X0] : ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (? [X0] : ((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (old(paul) & tall(paul))) [flattening 45]
47. (~old(paul) | ~tall(paul) | ! [X0] : ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (? [X1] : ((~calm(X1) | wise(X1)) & (calm(X1) | ~wise(X1))) | (old(paul) & tall(paul))) [rectify 46]
48. ? [X1] : ((~calm(X1) | wise(X1)) & (calm(X1) | ~wise(X1))) => ((~calm(sK1) | wise(sK1)) & (calm(sK1) | ~wise(sK1))) [choice axiom]
49. (~old(paul) | ~tall(paul) | ! [X0] : ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(sK1) | wise(sK1)) & (calm(sK1) | ~wise(sK1))) | (old(paul) & tall(paul))) [skolemisation 47,48]
54. ! [X0] : ((patient(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | ~patient(X0))) [nnf transformation 14]
63. (brave(paul) | ~rich(paul)) & (~brave(paul) | rich(paul)) [nnf transformation 19]
74. ~wise(X0) | funny(X0) | ~patient(X0) [cnf transformation 33]
75. ~brave(X0) | ~creative(X0) [cnf transformation 35]
83. ~calm(lucy) | brave(X1) [cnf transformation 40]
87. curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 42]
88. curious(X0) | wise(X0) | wise(X0) [cnf transformation 42]
89. creative(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 42]
90. creative(X0) | wise(X0) | wise(X0) [cnf transformation 42]
95. ~curious(lucy) | patient(lucy) | ~curious(lucy) | ~rich(lucy) [cnf transformation 44]
97. old(X0) | rich(X0) [cnf transformation 25]
99. tall(X0) | rich(X0) [cnf transformation 25]
105. ~old(paul) | ~tall(paul) | calm(X0) | wise(X0) [cnf transformation 49]
121. ~curious(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 54]
133. brave(paul) | ~rich(paul) [cnf transformation 63]
136. ~tall(lucy) [cnf transformation 22]
138. ~curious(lucy) | patient(lucy) | ~rich(lucy) [duplicate literal removal 95]
139. curious(X0) | ~wise(X0) [duplicate literal removal 87]
140. curious(X0) | wise(X0) [duplicate literal removal 88]
141. creative(X0) | ~wise(X0) [duplicate literal removal 89]
142. wise(X0) | creative(X0) [duplicate literal removal 90]
144. 1 <=> calm(lucy) [avatar definition]
145. ~calm(lucy) <- (~1) [avatar component clause 144]
157. 4 <=> ! [X1] : brave(X1) [avatar definition]
158. brave(X1) <- (4) [avatar component clause 157]
159. 4 | ~1 [avatar split clause 83,144,157]
164. creative(X0) [subsumption resolution 141,142]
165. curious(X0) [subsumption resolution 139,140]
166. patient(lucy) | ~rich(lucy) [subsumption resolution 138,165]
168. 6 <=> rich(lucy) [avatar definition]
172. 7 <=> patient(lucy) [avatar definition]
174. patient(lucy) <- (7) [avatar component clause 172]
175. ~6 | 7 [avatar split clause 166,172,168]
181. 9 <=> tall(paul) [avatar definition]
183. ~tall(paul) <- (~9) [avatar component clause 181]
185. 10 <=> old(paul) [avatar definition]
187. ~old(paul) <- (~10) [avatar component clause 185]
190. 11 <=> ! [X0] : (calm(X0) | wise(X0)) [avatar definition]
191. calm(X0) | wise(X0) <- (11) [avatar component clause 190]
192. 11 | ~9 | ~10 [avatar split clause 105,185,181,190]
210. ~funny(X0) | ~patient(X0) [subsumption resolution 121,165]
232. 18 <=> rich(paul) [avatar definition]
234. ~rich(paul) <- (~18) [avatar component clause 232]
236. 19 <=> brave(paul) [avatar definition]
238. brave(paul) <- (19) [avatar component clause 236]
239. ~18 | 19 [avatar split clause 133,236,232]
243. rich(paul) <- (~10) [resolution 97,187]
244. $false <- (~10, ~18) [subsumption resolution 243,234]
245. 10 | 18 [avatar contradiction clause 244]
246. rich(lucy) [resolution 99,136]
249. 6 [avatar split clause 246,168]
251. wise(lucy) <- (~1, 11) [resolution 191,145]
266. funny(lucy) | ~patient(lucy) <- (~1, 11) [resolution 74,251]
268. funny(lucy) <- (~1, 7, 11) [subsumption resolution 266,174]
279. ~patient(lucy) <- (~1, 7, 11) [resolution 268,210]
281. $false <- (~1, 7, 11) [subsumption resolution 279,174]
282. 1 | ~7 | ~11 [avatar contradiction clause 281]
283. rich(paul) <- (~9) [resolution 183,99]
284. $false <- (~9, ~18) [subsumption resolution 283,234]
285. 9 | 18 [avatar contradiction clause 284]
291. ~creative(paul) <- (19) [resolution 238,75]
292. $false <- (19) [subsumption resolution 291,164]
293. ~19 [avatar contradiction clause 292]
297. ~creative(X1) <- (4) [resolution 158,75]
302. $false <- (4) [subsumption resolution 297,164]
303. ~4 [avatar contradiction clause 302]
304. $false [avatar sat refutation 159,175,192,239,245,249,282,285,293,303]
% SZS output end Proof for 2857031134459435431552735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not brave and brave and vice versa.
If someone is either not humble or not happy then mary is not funny or not happy.
If someone is both not rich and calm then paul is both not wise and generous and vice versa.
Everyone who is both not calm and quiet is both not curious and humble and vice versa.
Everyone who is not quiet or not creative is either calm or not strong and vice versa.
If susan is both rich and funny then someone is not brave or calm.
Everyone who is kind is both not strong and calm.
Everyone who is both generous and old is not kind and vice versa.
If someone is both humble and old then someone is either calm or happy and vice versa.
If alice is both not quiet and not kind then john is both not curious and strong and vice versa.
If alice is rich or not creative then fred is both wise and not tall.
If someone is both humble and not funny then john is rich and vice versa.
If someone is both generous and not generous then john is kind.
If someone is kind or patient then someone is either not happy or not curious.
Everyone who is strong or patient is both happy and not funny.
Everyone who is either old or not tall is both not brave and not old.
Fred is both tall and not rich.
Someone is wise.
Alice is funny.
Someone is both wise and brave.
Someone is old or curious.
Someone is either not curious or brave. | Fred is tall. | entailment | (![X]:(~curious(X)<=>(~brave(X)&brave(X))))&
((?[X]:((~humble(X)<~>~happy(X))))=>((~funny(mary)|~happy(mary))))&
((?[X]:((~rich(X)&calm(X))))<=>((~wise(paul)&generous(paul))))&
(![X]:((~calm(X)&quiet(X))<=>(~curious(X)&humble(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(calm(X)<~>~strong(X))))&
(((rich(susan)&funny(susan)))=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:(kind(X)=>(~strong(X)&calm(X))))&
(![X]:((generous(X)&old(X))<=>~kind(X)))&
((?[X]:((humble(X)&old(X))))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~quiet(alice)&~kind(alice)))<=>((~curious(john)&strong(john))))&
(((rich(alice)|~creative(alice)))=>((wise(fred)&~tall(fred))))&
((?[X]:((humble(X)&~funny(X))))<=>(rich(john)))&
((?[X]:((generous(X)&~generous(X))))=>(kind(john)))&
((?[X]:((kind(X)|patient(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:((strong(X)|patient(X))=>(happy(X)&~funny(X))))&
(![X]:((old(X)<~>~tall(X))=>(~brave(X)&~old(X))))&
((tall(fred)&~rich(fred)))&
(?[X]:(wise(X)))&
(funny(alice))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~curious(X)<~>brave(X)))) | tall(fred) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8582953286186512253699463
% SZS output start Proof for 8582953286186512253699463
17. ~rich(fred) & tall(fred) [input p16]
23. ~tall(fred) [input hypothesis]
130. tall(fred) [cnf transformation 17]
139. ~tall(fred) [cnf transformation 23]
252. 25 <=> tall(fred) [avatar definition]
294. 25 [avatar split clause 130,252]
296. ~25 [avatar split clause 139,252]
297. $false [avatar sat refutation 294,296]
% SZS output end Proof for 8582953286186512253699463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either tall or rich then fred is either not happy or not creative and vice versa. Everyone who is patient or creative is both not generous and humble. Everyone who is not wise or humble is generous and vice versa. If lucy is generous or not quiet then lucy is not tall. If fred is either patient or not generous then alice is rich. Everyone who is not curious or not patient is both not wise and not calm. If alice is either wise or brave then someone is both not happy and not brave. Everyone who is wise is both strong and humble. Everyone who is rich is both not strong and not calm and vice versa. Everyone who is either strong or not funny is not happy or not funny and vice versa. Everyone who is brave or not calm is kind or not funny. If someone is humble then alice is not happy and vice versa. If john is not brave then mary is either old or not kind and vice versa. Everyone who is either not rich or funny is either not kind or old. Everyone who is both not old and not generous is patient or not kind. Someone is humble. Someone is either not humble or not funny. Someone is not old. Paul is kind. Fred is not creative or not brave. Susan is either not strong or old. | Alice is not generous. | contradiction | (((tall(john)<~>rich(john)))<=>((~happy(fred)<~>~creative(fred))))&
(![X]:((patient(X)|creative(X))=>(~generous(X)&humble(X))))&
(![X]:((~wise(X)|humble(X))<=>generous(X)))&
(((generous(lucy)|~quiet(lucy)))=>(~tall(lucy)))&
(((patient(fred)<~>~generous(fred)))=>(rich(alice)))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)&~calm(X))))&
(((wise(alice)<~>brave(alice)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)=>(strong(X)&humble(X))))&
(![X]:(rich(X)<=>(~strong(X)&~calm(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~happy(X)|~funny(X))))&
(![X]:((brave(X)|~calm(X))=>(kind(X)|~funny(X))))&
((?[X]:(humble(X)))<=>(~happy(alice)))&
((~brave(john))<=>((old(mary)<~>~kind(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>old(X))))&
(![X]:((~old(X)&~generous(X))=>(patient(X)|~kind(X))))&
(?[X]:(humble(X)))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:(~old(X)))&
(kind(paul))&
((~creative(fred)|~brave(fred)))&
((~strong(susan)<~>old(susan))) | ~generous(alice) | [
"p2",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 86305636018147322790974
% SZS output start Proof for 86305636018147322790974
3. ! [X0] : ((humble(X0) | ~wise(X0)) <=> generous(X0)) [input p2]
8. ! [X0] : (wise(X0) => (humble(X0) & strong(X0))) [input p7]
22. ~generous(alice) [input hypothesis]
30. ! [X0] : ((humble(X0) & strong(X0)) | ~wise(X0)) [ennf transformation 8]
37. ! [X0] : (((humble(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & wise(X0)))) [nnf transformation 3]
38. ! [X0] : ((humble(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & wise(X0)))) [flattening 37]
73. wise(X0) | generous(X0) [cnf transformation 38]
74. ~humble(X0) | generous(X0) [cnf transformation 38]
86. ~wise(X0) | humble(X0) [cnf transformation 30]
117. ~generous(alice) [cnf transformation 22]
260. humble(X0) | generous(X0) [resolution 86,73]
262. generous(X0) [subsumption resolution 260,74]
267. $false [resolution 262,117]
% SZS output end Proof for 86305636018147322790974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not strong is not happy. Everyone who is both patient and not rich is not happy. Everyone who is either not kind or not curious is either not patient or not old. If alice is kind or not humble then lucy is patient. If someone is either kind or patient then someone is either not kind or tall. Everyone who is both old and curious is both not patient and not funny. Everyone who is not happy is both wise and kind and vice versa. If lucy is happy or brave then lucy is rich and vice versa. If someone is either not kind or not creative then susan is old and vice versa. Everyone who is either funny or not brave is either tall or not calm and vice versa. Everyone who is either brave or patient is curious or quiet. Everyone who is both funny and not generous is not brave and vice versa. If fred is both old and not wise then paul is either quiet or wise. If someone is happy then someone is both not generous and creative and vice versa. Everyone who is not kind is not patient and vice versa. Everyone who is both not kind and curious is both patient and not generous and vice versa. Mary is both not tall and humble. Fred is not quiet. Mary is kind or not happy. Someone is both not strong and not tall. Lucy is patient or not generous. | Mary is rich. | neutral | (![X]:((creative(X)|~strong(X))=>~happy(X)))&
(![X]:((patient(X)&~rich(X))=>~happy(X)))&
(![X]:((~kind(X)<~>~curious(X))=>(~patient(X)<~>~old(X))))&
(((kind(alice)|~humble(alice)))=>(patient(lucy)))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((old(X)&curious(X))=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>(wise(X)&kind(X))))&
(((happy(lucy)|brave(lucy)))<=>(rich(lucy)))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(old(susan)))&
(![X]:((funny(X)<~>~brave(X))<=>(tall(X)<~>~calm(X))))&
(![X]:((brave(X)<~>patient(X))=>(curious(X)|quiet(X))))&
(![X]:((funny(X)&~generous(X))<=>~brave(X)))&
(((old(fred)&~wise(fred)))=>((quiet(paul)<~>wise(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(patient(X)&~generous(X))))&
((~tall(mary)&humble(mary)))&
(~quiet(fred))&
((kind(mary)|~happy(mary)))&
(?[X]:((~strong(X)&~tall(X))))&
((patient(lucy)|~generous(lucy))) | rich(mary) | []
| null | 0 |
If john is calm or not old then someone is both not funny and not rich and vice versa. If someone is not humble or not creative then lucy is either tall or not strong. Everyone who is not old or quiet is not old or rich. If john is either quiet or creative then paul is kind or not calm. If someone is both not curious and patient then paul is both kind and funny and vice versa. Everyone who is not creative or not generous is not funny or not kind. If susan is not curious or wise then alice is humble. Everyone who is either wise or not rich is both patient and creative. If someone is not funny then alice is both not brave and old. Everyone who is patient is creative and vice versa. If someone is generous or creative then mary is happy. If someone is both brave and generous then john is not kind or not wise. Everyone who is not strong is both not patient and not kind and vice versa. Everyone who is curious is both tall and not tall. Everyone who is humble is both not generous and calm and vice versa. Everyone who is creative or not quiet is both happy and quiet and vice versa. Someone is either not generous or not curious. Someone is funny or not strong. Susan is not funny. Someone is either not tall or strong. John is either brave or kind. Someone is not tall or not calm. Someone is both not humble and quiet. | Paul is calm. | neutral | (((calm(john)|~old(john)))<=>(?[X]:((~funny(X)&~rich(X)))))&
((?[X]:((~humble(X)|~creative(X))))=>((tall(lucy)<~>~strong(lucy))))&
(![X]:((~old(X)|quiet(X))=>(~old(X)|rich(X))))&
(((quiet(john)<~>creative(john)))=>((kind(paul)|~calm(paul))))&
((?[X]:((~curious(X)&patient(X))))<=>((kind(paul)&funny(paul))))&
(![X]:((~creative(X)|~generous(X))=>(~funny(X)|~kind(X))))&
(((~curious(susan)|wise(susan)))=>(humble(alice)))&
(![X]:((wise(X)<~>~rich(X))=>(patient(X)&creative(X))))&
((?[X]:(~funny(X)))=>((~brave(alice)&old(alice))))&
(![X]:(patient(X)<=>creative(X)))&
((?[X]:((generous(X)|creative(X))))=>(happy(mary)))&
((?[X]:((brave(X)&generous(X))))=>((~kind(john)|~wise(john))))&
(![X]:(~strong(X)<=>(~patient(X)&~kind(X))))&
(![X]:(curious(X)=>(tall(X)&~tall(X))))&
(![X]:(humble(X)<=>(~generous(X)&calm(X))))&
(![X]:((creative(X)|~quiet(X))<=>(happy(X)&quiet(X))))&
(?[X]:((~generous(X)<~>~curious(X))))&
(?[X]:((funny(X)|~strong(X))))&
(~funny(susan))&
(?[X]:((~tall(X)<~>strong(X))))&
((brave(john)<~>kind(john)))&
(?[X]:((~tall(X)|~calm(X))))&
(?[X]:((~humble(X)&quiet(X)))) | calm(paul) | []
| null | 0 |
Everyone who is generous or not happy is not humble.
Everyone who is old is not patient and vice versa.
Everyone who is both not rich and not curious is not happy or curious and vice versa.
If someone is not old then someone is not humble or tall and vice versa.
Everyone who is either strong or tall is not rich and vice versa.
If lucy is not quiet then someone is funny and vice versa.
Everyone who is calm or not strong is not quiet or not wise and vice versa.
If lucy is humble or strong then someone is either not curious or not happy.
Everyone who is not strong is calm or tall and vice versa.
If john is not funny then alice is not curious.
If someone is both not generous and humble then fred is creative.
If someone is kind then someone is calm.
If someone is strong then someone is both not happy and kind.
If john is strong or not generous then fred is both not wise and kind.
Everyone who is not calm is kind or not old and vice versa.
Everyone who is both not curious and not old is both not calm and strong.
Someone is not kind or not brave.
Fred is both not old and not curious.
Someone is both rich and happy.
Alice is either creative or not tall.
Alice is brave or not patient.
Mary is either not calm or not strong. | Lucy is strong. | neutral | (![X]:((generous(X)|~happy(X))=>~humble(X)))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((~rich(X)&~curious(X))<=>(~happy(X)|curious(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
((~quiet(lucy))<=>(?[X]:(funny(X))))&
(![X]:((calm(X)|~strong(X))<=>(~quiet(X)|~wise(X))))&
(((humble(lucy)|strong(lucy)))=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:(~strong(X)<=>(calm(X)|tall(X))))&
((~funny(john))=>(~curious(alice)))&
((?[X]:((~generous(X)&humble(X))))=>(creative(fred)))&
((?[X]:(kind(X)))=>(?[X]:(calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~happy(X)&kind(X)))))&
(((strong(john)|~generous(john)))=>((~wise(fred)&kind(fred))))&
(![X]:(~calm(X)<=>(kind(X)|~old(X))))&
(![X]:((~curious(X)&~old(X))=>(~calm(X)&strong(X))))&
(?[X]:((~kind(X)|~brave(X))))&
((~old(fred)&~curious(fred)))&
(?[X]:((rich(X)&happy(X))))&
((creative(alice)<~>~tall(alice)))&
((brave(alice)|~patient(alice)))&
((~calm(mary)<~>~strong(mary))) | strong(lucy) | []
| null | 0 |
Everyone who is both not creative and humble is both quiet and not curious and vice versa. If someone is not creative or old then someone is either not patient or wise. Everyone who is both not generous and not old is either quiet or humble. If fred is tall or patient then someone is both not strong and not wise. Everyone who is both patient and not kind is creative. Everyone who is creative or not patient is both not brave and quiet and vice versa. Everyone who is both calm and not creative is both not humble and strong and vice versa. If someone is not funny or calm then fred is both creative and not brave and vice versa. If paul is not generous or brave then someone is not kind or not funny and vice versa. Everyone who is tall is not quiet or not tall. If someone is not curious or wise then someone is curious or not happy and vice versa. If paul is either calm or strong then someone is either happy or brave and vice versa. If paul is not creative then someone is not kind or not calm and vice versa. Everyone who is either strong or kind is funny or not old. If someone is both humble and brave then someone is both brave and strong and vice versa. Everyone who is both brave and humble is rich or not generous. Someone is either not kind or happy. Someone is curious or not patient. Lucy is calm or curious. Someone is kind or not patient. Paul is either tall or calm. Someone is either happy or brave. Lucy is not quiet. Mary is kind or not funny. | Mary is not calm. | contradiction | (![X]:((~creative(X)&humble(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((~creative(X)|old(X))))=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((~generous(X)&~old(X))=>(quiet(X)<~>humble(X))))&
(((tall(fred)|patient(fred)))=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((patient(X)&~kind(X))=>creative(X)))&
(![X]:((creative(X)|~patient(X))<=>(~brave(X)&quiet(X))))&
(![X]:((calm(X)&~creative(X))<=>(~humble(X)&strong(X))))&
((?[X]:((~funny(X)|calm(X))))<=>((creative(fred)&~brave(fred))))&
(((~generous(paul)|brave(paul)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(tall(X)=>(~quiet(X)|~tall(X))))&
((?[X]:((~curious(X)|wise(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(((calm(paul)<~>strong(paul)))<=>(?[X]:((happy(X)<~>brave(X)))))&
((~creative(paul))<=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:((strong(X)<~>kind(X))=>(funny(X)|~old(X))))&
((?[X]:((humble(X)&brave(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((brave(X)&humble(X))=>(rich(X)|~generous(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((curious(X)|~patient(X))))&
((calm(lucy)|curious(lucy)))&
(?[X]:((kind(X)|~patient(X))))&
((tall(paul)<~>calm(paul)))&
(?[X]:((happy(X)<~>brave(X))))&
(~quiet(lucy))&
((kind(mary)|~funny(mary))) | ~calm(mary) | [
"p0",
"p6",
"p9",
"p11",
"p12",
"p20",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 8524737038956158616523291
% SZS output start Proof for 8524737038956158616523291
1. ! [X0] : ((humble(X0) & ~creative(X0)) <=> (~curious(X0) & quiet(X0))) [input p0]
7. ! [X0] : ((~creative(X0) & calm(X0)) <=> (strong(X0) & ~humble(X0))) [input p6]
10. ! [X0] : (tall(X0) => (~tall(X0) | ~quiet(X0))) [input p9]
12. (calm(paul) <~> strong(paul)) <=> ? [X0] : (happy(X0) <~> brave(X0)) [input p11]
13. ~creative(paul) <=> ? [X0] : (~calm(X0) | ~kind(X0)) [input p12]
21. tall(paul) <~> calm(paul) [input p20]
22. ? [X0] : (happy(X0) <~> brave(X0)) [input p21]
25. ~calm(mary) [input hypothesis]
36. ! [X0] : ((~tall(X0) | ~quiet(X0)) | ~tall(X0)) [ennf transformation 10]
37. ! [X0] : (~tall(X0) | ~quiet(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : (((humble(X0) & ~creative(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (~humble(X0) | creative(X0)))) [nnf transformation 1]
41. ! [X0] : (((humble(X0) & ~creative(X0)) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ~humble(X0) | creative(X0))) [flattening 40]
51. ! [X0] : (((~creative(X0) & calm(X0)) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | (creative(X0) | ~calm(X0)))) [nnf transformation 7]
52. ! [X0] : (((~creative(X0) & calm(X0)) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | creative(X0) | ~calm(X0))) [flattening 51]
68. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [nnf transformation 12]
69. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [rectify 68]
70. ? [X1] : ((~brave(X1) | ~happy(X1)) & (brave(X1) | happy(X1))) => ((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) [choice axiom]
71. (((~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul))) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(sK6) | ~happy(sK6)) & (brave(sK6) | happy(sK6))) | ((calm(paul) | ~strong(paul)) & (strong(paul) | ~calm(paul)))) [skolemisation 69,70]
72. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X0] : (~calm(X0) | ~kind(X0)) | creative(paul)) [nnf transformation 13]
73. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & (? [X1] : (~calm(X1) | ~kind(X1)) | creative(paul)) [rectify 72]
74. ? [X1] : (~calm(X1) | ~kind(X1)) => (~calm(sK7) | ~kind(sK7)) [choice axiom]
75. (~creative(paul) | ! [X0] : (calm(X0) & kind(X0))) & ((~calm(sK7) | ~kind(sK7)) | creative(paul)) [skolemisation 73,74]
89. (~calm(paul) | ~tall(paul)) & (calm(paul) | tall(paul)) [nnf transformation 21]
90. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) [nnf transformation 22]
91. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13))) [choice axiom]
92. (~brave(sK13) | ~happy(sK13)) & (brave(sK13) | happy(sK13)) [skolemisation 90,91]
93. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 41]
113. ~calm(X0) | creative(X0) | ~humble(X0) [cnf transformation 52]
114. ~calm(X0) | creative(X0) | strong(X0) [cnf transformation 52]
115. ~strong(X0) | calm(X0) | humble(X0) [cnf transformation 52]
126. ~tall(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 37]
135. strong(paul) | calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
136. strong(paul) | calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
137. ~strong(paul) | ~calm(paul) | brave(X0) | ~happy(X0) [cnf transformation 71]
138. ~strong(paul) | ~calm(paul) | happy(X0) | ~brave(X0) [cnf transformation 71]
141. ~creative(paul) | calm(X0) [cnf transformation 75]
153. calm(paul) | tall(paul) [cnf transformation 89]
155. brave(sK13) | happy(sK13) [cnf transformation 92]
156. ~brave(sK13) | ~happy(sK13) [cnf transformation 92]
159. ~calm(mary) [cnf transformation 25]
160. ~tall(X0) | ~quiet(X0) [duplicate literal removal 126]
283. 28 <=> ! [X0] : (happy(X0) | ~brave(X0)) [avatar definition]
284. ~brave(X0) | happy(X0) <- (28) [avatar component clause 283]
286. 29 <=> calm(paul) [avatar definition]
287. calm(paul) <- (29) [avatar component clause 286]
288. ~calm(paul) <- (~29) [avatar component clause 286]
290. 30 <=> strong(paul) [avatar definition]
291. strong(paul) <- (30) [avatar component clause 290]
292. ~strong(paul) <- (~30) [avatar component clause 290]
293. 28 | ~29 | ~30 [avatar split clause 138,290,286,283]
295. 31 <=> ! [X0] : (brave(X0) | ~happy(X0)) [avatar definition]
296. ~happy(X0) | brave(X0) <- (31) [avatar component clause 295]
297. 31 | ~29 | ~30 [avatar split clause 137,290,286,295]
298. 28 | 29 | 30 [avatar split clause 136,290,286,283]
299. 31 | 29 | 30 [avatar split clause 135,290,286,295]
313. 34 <=> ! [X0] : calm(X0) [avatar definition]
314. calm(X0) <- (34) [avatar component clause 313]
316. 35 <=> creative(paul) [avatar definition]
318. ~creative(paul) <- (~35) [avatar component clause 316]
319. 34 | ~35 [avatar split clause 141,316,313]
394. 52 <=> tall(paul) [avatar definition]
395. tall(paul) <- (52) [avatar component clause 394]
398. 52 | 29 [avatar split clause 153,286,394]
400. 53 <=> happy(sK13) [avatar definition]
401. happy(sK13) <- (53) [avatar component clause 400]
402. ~happy(sK13) <- (~53) [avatar component clause 400]
404. 54 <=> brave(sK13) [avatar definition]
405. brave(sK13) <- (54) [avatar component clause 404]
406. ~brave(sK13) <- (~54) [avatar component clause 404]
407. ~53 | ~54 [avatar split clause 156,404,400]
408. 53 | 54 [avatar split clause 155,404,400]
422. brave(sK13) <- (31, 53) [resolution 296,401]
423. $false <- (31, 53, ~54) [subsumption resolution 422,406]
424. ~31 | ~53 | 54 [avatar contradiction clause 423]
480. creative(paul) | ~humble(paul) <- (29) [resolution 113,287]
492. creative(paul) | strong(paul) <- (29) [resolution 114,287]
502. creative(paul) <- (29, ~30) [subsumption resolution 492,292]
503. 35 | ~29 | 30 [avatar split clause 502,290,286,316]
505. 68 <=> humble(paul) [avatar definition]
506. humble(paul) <- (68) [avatar component clause 505]
508. ~68 | 35 | ~29 [avatar split clause 480,286,316,505]
513. $false <- (34) [resolution 314,159]
518. ~34 [avatar contradiction clause 513]
520. ~quiet(paul) <- (52) [resolution 395,160]
521. calm(paul) | humble(paul) <- (30) [resolution 115,291]
522. humble(paul) <- (~29, 30) [subsumption resolution 521,288]
523. 68 | 29 | ~30 [avatar split clause 522,290,286,505]
524. quiet(paul) | creative(paul) <- (68) [resolution 506,93]
525. creative(paul) <- (52, 68) [subsumption resolution 524,520]
526. $false <- (~35, 52, 68) [subsumption resolution 525,318]
527. 35 | ~52 | ~68 [avatar contradiction clause 526]
530. happy(sK13) <- (28, 54) [resolution 405,284]
533. $false <- (28, ~53, 54) [subsumption resolution 530,402]
534. ~28 | 53 | ~54 [avatar contradiction clause 533]
535. $false [avatar sat refutation 293,297,298,299,319,398,407,408,424,503,508,518,523,527,534]
% SZS output end Proof for 8524737038956158616523291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or funny is generous and vice versa.
Everyone who is both creative and kind is not creative or not happy and vice versa.
If susan is not humble or not generous then someone is both funny and not patient.
Everyone who is either strong or brave is funny and vice versa.
If fred is kind then john is either funny or calm.
If someone is both funny and not rich then someone is either old or not strong and vice versa.
Everyone who is either not funny or creative is not happy or kind.
Everyone who is both brave and strong is both not old and not strong and vice versa.
Everyone who is either not curious or not calm is either not kind or not funny.
If someone is both creative and not calm then fred is old.
Everyone who is not quiet or not generous is both calm and not old.
If someone is not humble or not strong then someone is not happy and vice versa.
If alice is happy then someone is both not rich and not quiet.
Everyone who is creative or brave is wise or not brave.
Fred is not rich.
Fred is calm or tall.
Susan is either curious or not generous.
Susan is either humble or not humble. | Alice is not funny. | contradiction | (![X]:((~creative(X)<~>funny(X))<=>generous(X)))&
(![X]:((creative(X)&kind(X))<=>(~creative(X)|~happy(X))))&
(((~humble(susan)|~generous(susan)))=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:((strong(X)<~>brave(X))<=>funny(X)))&
((kind(fred))=>((funny(john)<~>calm(john))))&
((?[X]:((funny(X)&~rich(X))))<=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((~funny(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~old(X)&~strong(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>(old(fred)))&
(![X]:((~quiet(X)|~generous(X))=>(calm(X)&~old(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:(~happy(X))))&
((happy(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>(wise(X)|~brave(X))))&
(~rich(fred))&
((calm(fred)|tall(fred)))&
((curious(susan)<~>~generous(susan)))&
((humble(susan)<~>~humble(susan))) | ~funny(alice) | [
"p0",
"p1",
"p3",
"p7",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 8936092392702225727944820
% SZS output start Proof for 8936092392702225727944820
1. ! [X0] : ((~creative(X0) <~> funny(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : ((kind(X0) & creative(X0)) <=> (~happy(X0) | ~creative(X0))) [input p1]
4. ! [X0] : ((strong(X0) <~> brave(X0)) <=> funny(X0)) [input p3]
8. ! [X0] : ((strong(X0) & brave(X0)) <=> (~strong(X0) & ~old(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (~old(X0) & calm(X0))) [input p10]
19. ~funny(alice) [input hypothesis]
31. ! [X0] : ((~old(X0) & calm(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 11]
33. ! [X0] : ((((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | ~generous(X0)) & (generous(X0) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0))))) [nnf transformation 1]
34. ! [X0] : (((kind(X0) & creative(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~kind(X0) | ~creative(X0)))) [nnf transformation 2]
35. ! [X0] : (((kind(X0) & creative(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~kind(X0) | ~creative(X0))) [flattening 34]
38. ! [X0] : ((((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ~funny(X0)) & (funny(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))))) [nnf transformation 4]
46. ! [X0] : (((strong(X0) & brave(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 8]
47. ! [X0] : (((strong(X0) & brave(X0)) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | ~strong(X0) | ~brave(X0))) [flattening 46]
60. ~generous(X0) | ~creative(X0) | funny(X0) [cnf transformation 33]
63. creative(X0) | creative(X0) [cnf transformation 35]
69. ~strong(X0) | brave(X0) | funny(X0) [cnf transformation 38]
84. ~strong(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 47]
86. strong(X0) | strong(X0) | old(X0) [cnf transformation 47]
95. ~old(X0) | generous(X0) [cnf transformation 31]
106. ~funny(alice) [cnf transformation 19]
107. ~brave(X0) | ~strong(X0) [duplicate literal removal 84]
108. strong(X0) | old(X0) [duplicate literal removal 86]
110. creative(X0) [duplicate literal removal 63]
141. 7 <=> ! [X1] : (old(X1) | strong(X1)) [avatar definition]
142. old(X1) | strong(X1) <- (7) [avatar component clause 141]
173. 7 [avatar split clause 108,141]
235. strong(X0) | generous(X0) <- (7) [resolution 142,95]
261. brave(X0) | funny(X0) | generous(X0) <- (7) [resolution 69,235]
337. funny(X2) | generous(X2) | ~strong(X2) <- (7) [resolution 261,107]
339. generous(X2) | funny(X2) <- (7) [subsumption resolution 337,235]
341. funny(X1) | ~creative(X1) | funny(X1) <- (7) [resolution 339,60]
343. funny(X1) | ~creative(X1) <- (7) [duplicate literal removal 341]
344. funny(X1) <- (7) [subsumption resolution 343,110]
345. $false <- (7) [resolution 344,106]
352. ~7 [avatar contradiction clause 345]
354. $false [avatar sat refutation 173,352]
% SZS output end Proof for 8936092392702225727944820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble then fred is both not happy and rich.
If someone is creative or funny then someone is both not kind and tall.
Everyone who is tall or not brave is not funny or not old.
If fred is creative or patient then susan is old and vice versa.
If someone is not quiet or humble then mary is not tall or not strong.
If someone is either not curious or funny then someone is patient or quiet and vice versa.
Everyone who is not wise or not funny is humble.
Everyone who is both not curious and not brave is strong or funny.
If paul is both rich and not old then mary is not rich or strong and vice versa.
Everyone who is either brave or not creative is not rich.
Everyone who is brave or not rich is not brave.
Everyone who is not old is both not kind and kind.
If someone is not wise or calm then paul is not patient.
If mary is both not strong and not calm then someone is tall or brave.
Everyone who is generous or kind is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Someone is not curious or calm.
Someone is either humble or calm.
Someone is wise.
John is patient or quiet.
Mary is both creative and not wise.
Someone is not patient. | Fred is rich. | entailment | ((humble(john))=>((~happy(fred)&rich(fred))))&
((?[X]:((creative(X)|funny(X))))=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((tall(X)|~brave(X))=>(~funny(X)|~old(X))))&
(((creative(fred)|patient(fred)))<=>(old(susan)))&
((?[X]:((~quiet(X)|humble(X))))=>((~tall(mary)|~strong(mary))))&
((?[X]:((~curious(X)<~>funny(X))))<=>(?[X]:((patient(X)|quiet(X)))))&
(![X]:((~wise(X)|~funny(X))=>humble(X)))&
(![X]:((~curious(X)&~brave(X))=>(strong(X)|funny(X))))&
(((rich(paul)&~old(paul)))<=>((~rich(mary)|strong(mary))))&
(![X]:((brave(X)<~>~creative(X))=>~rich(X)))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~kind(X)&kind(X))))&
((?[X]:((~wise(X)|calm(X))))=>(~patient(paul)))&
(((~strong(mary)&~calm(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((generous(X)|kind(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:(wise(X)))&
((patient(john)|quiet(john)))&
((creative(mary)&~wise(mary)))&
(?[X]:(~patient(X))) | rich(fred) | [
"p0",
"p2",
"p6",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 5023715389877399647863130
% SZS output start Proof for 5023715389877399647863130
1. humble(john) => (rich(fred) & ~happy(fred)) [input p0]
3. ! [X0] : ((~brave(X0) | tall(X0)) => (~old(X0) | ~funny(X0))) [input p2]
7. ! [X0] : ((~funny(X0) | ~wise(X0)) => humble(X0)) [input p6]
11. ! [X0] : ((~rich(X0) | brave(X0)) => ~brave(X0)) [input p10]
12. ! [X0] : (~old(X0) => (kind(X0) & ~kind(X0))) [input p11]
23. ~rich(fred) [input hypothesis]
27. (rich(fred) & ~happy(fred)) | ~humble(john) [ennf transformation 1]
29. ! [X0] : ((~old(X0) | ~funny(X0)) | (brave(X0) & ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~old(X0) | ~funny(X0) | (brave(X0) & ~tall(X0))) [flattening 29]
33. ! [X0] : (humble(X0) | (funny(X0) & wise(X0))) [ennf transformation 7]
37. ! [X0] : (~brave(X0) | (rich(X0) & ~brave(X0))) [ennf transformation 11]
38. ! [X0] : ((kind(X0) & ~kind(X0)) | old(X0)) [ennf transformation 12]
73. rich(fred) | ~humble(john) [cnf transformation 27]
79. ~old(X0) | ~funny(X0) | brave(X0) [cnf transformation 30]
92. funny(X0) | humble(X0) [cnf transformation 33]
101. ~brave(X0) | ~brave(X0) [cnf transformation 37]
103. ~kind(X0) | old(X0) [cnf transformation 38]
104. old(X0) | kind(X0) [cnf transformation 38]
121. ~rich(fred) [cnf transformation 23]
122. ~brave(X0) [duplicate literal removal 101]
124. 1 <=> humble(john) [avatar definition]
126. ~humble(john) <- (~1) [avatar component clause 124]
128. 2 <=> rich(fred) [avatar definition]
131. ~1 | 2 [avatar split clause 73,128,124]
138. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
139. ~funny(X1) <- (4) [avatar component clause 138]
237. old(X0) [subsumption resolution 103,104]
307. ~2 [avatar split clause 121,128]
327. ~funny(X1) | brave(X1) [resolution 79,237]
331. ~funny(X1) [subsumption resolution 327,122]
332. 4 [avatar split clause 331,138]
333. humble(X0) <- (4) [resolution 139,92]
334. $false <- (~1, 4) [resolution 333,126]
335. 1 | ~4 [avatar contradiction clause 334]
336. $false [avatar sat refutation 131,307,332,335]
% SZS output end Proof for 5023715389877399647863130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both humble and not humble then someone is either happy or not funny and vice versa.
Everyone who is not old or not tall is calm or funny and vice versa.
If someone is either rich or brave then alice is either funny or wise.
Everyone who is not strong is both wise and not kind.
Everyone who is either not quiet or not creative is either quiet or humble and vice versa.
If someone is not wise then someone is either not brave or creative.
Everyone who is rich is either wise or happy and vice versa.
Everyone who is not rich is not old and vice versa.
If someone is not generous then someone is either not generous or not strong and vice versa.
Everyone who is not wise is not generous and vice versa.
If lucy is both funny and not funny then alice is not kind or not tall.
If someone is both not quiet and generous then someone is both generous and not humble.
Everyone who is either funny or not humble is funny or humble.
Everyone who is happy or not curious is tall and vice versa.
If paul is both generous and wise then someone is not humble.
Everyone who is not generous or tall is both not funny and not strong.
John is curious or creative.
John is not patient or patient.
Lucy is wise or not kind.
Someone is not funny or old.
Mary is both funny and not creative.
Someone is quiet or calm.
Mary is both brave and generous. | Mary is curious. | entailment | (((humble(john)&~humble(john)))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~old(X)|~tall(X))<=>(calm(X)|funny(X))))&
((?[X]:((rich(X)<~>brave(X))))=>((funny(alice)<~>wise(alice))))&
(![X]:(~strong(X)=>(wise(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:(rich(X)<=>(wise(X)<~>happy(X))))&
(![X]:(~rich(X)<=>~old(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>~generous(X)))&
(((funny(lucy)&~funny(lucy)))=>((~kind(alice)|~tall(alice))))&
((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(funny(X)|humble(X))))&
(![X]:((happy(X)|~curious(X))<=>tall(X)))&
(((generous(paul)&wise(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|tall(X))=>(~funny(X)&~strong(X))))&
((curious(john)|creative(john)))&
((~patient(john)|patient(john)))&
((wise(lucy)|~kind(lucy)))&
(?[X]:((~funny(X)|old(X))))&
((funny(mary)&~creative(mary)))&
(?[X]:((quiet(X)|calm(X))))&
((brave(mary)&generous(mary))) | curious(mary) | [
"p13",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1650366270936240058319595
% SZS output start Proof for 1650366270936240058319595
14. ! [X0] : ((~curious(X0) | happy(X0)) <=> tall(X0)) [input p13]
16. ! [X0] : ((tall(X0) | ~generous(X0)) => (~strong(X0) & ~funny(X0))) [input p15]
21. ~creative(mary) & funny(mary) [input p20]
24. ~curious(mary) [input hypothesis]
39. ! [X0] : ((~strong(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 16]
65. ! [X0] : (((~curious(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 14]
66. ! [X0] : ((~curious(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~happy(X0)))) [flattening 65]
115. curious(X0) | tall(X0) [cnf transformation 66]
119. ~tall(X0) | ~funny(X0) [cnf transformation 39]
125. funny(mary) [cnf transformation 21]
130. ~curious(mary) [cnf transformation 24]
271. tall(mary) [resolution 115,130]
274. ~funny(mary) [resolution 119,271]
275. $false [subsumption resolution 274,125]
% SZS output end Proof for 1650366270936240058319595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or not old then someone is either tall or patient.
If someone is both not patient and happy then john is not strong or quiet and vice versa.
Everyone who is not generous is either not curious or creative and vice versa.
Everyone who is either not curious or not generous is either generous or not wise and vice versa.
Everyone who is patient is brave or not patient and vice versa.
If alice is both patient and humble then lucy is not generous or not happy and vice versa.
If someone is not patient then mary is not quiet or funny.
If lucy is both creative and calm then someone is either generous or not creative and vice versa.
If someone is both not creative and not quiet then someone is kind or tall and vice versa.
If someone is old then paul is patient or happy.
If someone is both curious and not creative then paul is either creative or generous.
If john is old or not happy then someone is not happy or generous and vice versa.
If someone is either not curious or not generous then someone is not patient or not old.
Everyone who is patient is creative or not strong.
Everyone who is both funny and generous is either funny or rich and vice versa.
If lucy is both not quiet and not creative then someone is both rich and not tall.
Fred is either not happy or quiet.
Mary is either not happy or old.
Someone is not happy.
Someone is quiet.
Someone is both brave and kind.
Paul is either quiet or not quiet. | Susan is kind. | neutral | (((~funny(susan)|~old(susan)))=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:((~patient(X)&happy(X))))<=>((~strong(john)|quiet(john))))&
(![X]:(~generous(X)<=>(~curious(X)<~>creative(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>(generous(X)<~>~wise(X))))&
(![X]:(patient(X)<=>(brave(X)|~patient(X))))&
(((patient(alice)&humble(alice)))<=>((~generous(lucy)|~happy(lucy))))&
((?[X]:(~patient(X)))=>((~quiet(mary)|funny(mary))))&
(((creative(lucy)&calm(lucy)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
((?[X]:((~creative(X)&~quiet(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:(old(X)))=>((patient(paul)|happy(paul))))&
((?[X]:((curious(X)&~creative(X))))=>((creative(paul)<~>generous(paul))))&
(((old(john)|~happy(john)))<=>(?[X]:((~happy(X)|generous(X)))))&
((?[X]:((~curious(X)<~>~generous(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(patient(X)=>(creative(X)|~strong(X))))&
(![X]:((funny(X)&generous(X))<=>(funny(X)<~>rich(X))))&
(((~quiet(lucy)&~creative(lucy)))=>(?[X]:((rich(X)&~tall(X)))))&
((~happy(fred)<~>quiet(fred)))&
((~happy(mary)<~>old(mary)))&
(?[X]:(~happy(X)))&
(?[X]:(quiet(X)))&
(?[X]:((brave(X)&kind(X))))&
((quiet(paul)<~>~quiet(paul))) | kind(susan) | []
| null | 0 |
Everyone who is either not kind or not wise is not funny.
If alice is not quiet then susan is not brave and vice versa.
Everyone who is not funny or not brave is not rich or not calm and vice versa.
Everyone who is not generous or not creative is not wise or not tall and vice versa.
Everyone who is happy or brave is either not calm or tall.
If susan is not funny then john is not quiet and vice versa.
If someone is both creative and funny then someone is both not creative and not quiet.
Everyone who is not kind or not tall is not curious or creative and vice versa.
Everyone who is both not humble and not happy is old or not strong.
Everyone who is both not happy and humble is both funny and not happy.
Everyone who is either not calm or not wise is old or not generous and vice versa.
If someone is either not rich or kind then someone is not funny or tall and vice versa.
If someone is both kind and not kind then someone is either wise or kind and vice versa.
Everyone who is not rich is both not generous and generous and vice versa.
If someone is both kind and humble then someone is both not rich and not quiet and vice versa.
Everyone who is not creative or not old is both not creative and creative.
Paul is not generous.
Someone is generous or quiet.
Mary is not curious.
Someone is not happy or not brave.
Someone is either strong or not humble.
Someone is strong or quiet.
Someone is either old or generous. | John is not strong. | neutral | (![X]:((~kind(X)<~>~wise(X))=>~funny(X)))&
((~quiet(alice))<=>(~brave(susan)))&
(![X]:((~funny(X)|~brave(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(~wise(X)|~tall(X))))&
(![X]:((happy(X)|brave(X))=>(~calm(X)<~>tall(X))))&
((~funny(susan))<=>(~quiet(john)))&
((?[X]:((creative(X)&funny(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~kind(X)|~tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((~humble(X)&~happy(X))=>(old(X)|~strong(X))))&
(![X]:((~happy(X)&humble(X))=>(funny(X)&~happy(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(old(X)|~generous(X))))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
((?[X]:((kind(X)&~kind(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(~rich(X)<=>(~generous(X)&generous(X))))&
((?[X]:((kind(X)&humble(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)|~old(X))=>(~creative(X)&creative(X))))&
(~generous(paul))&
(?[X]:((generous(X)|quiet(X))))&
(~curious(mary))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((old(X)<~>generous(X)))) | ~strong(john) | []
| null | 0 |
If alice is both not humble and calm then someone is not strong and vice versa.
Everyone who is both not tall and calm is either not humble or humble and vice versa.
Everyone who is both not wise and not rich is calm or rich.
Everyone who is quiet or patient is not curious or not humble and vice versa.
If mary is wise then paul is both not kind and funny and vice versa.
Everyone who is either creative or not curious is both rich and not humble.
If john is not humble or not happy then someone is kind and vice versa.
Everyone who is strong or not wise is either not brave or not curious.
If alice is wise or not strong then john is not wise.
Everyone who is not wise or not patient is calm and vice versa.
Everyone who is either not brave or not happy is patient or not funny.
If john is both creative and not curious then someone is both not strong and calm and vice versa.
Everyone who is both not quiet and quiet is old and vice versa.
If alice is both rich and wise then paul is both creative and rich and vice versa.
If someone is not strong then someone is not generous and vice versa.
Paul is generous or not tall.
John is both curious and not rich.
Susan is either creative or not curious.
Someone is not brave or not strong.
John is both humble and not patient.
John is kind or wise. | Alice is not generous. | contradiction | (((~humble(alice)&calm(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~wise(X)&~rich(X))=>(calm(X)|rich(X))))&
(![X]:((quiet(X)|patient(X))<=>(~curious(X)|~humble(X))))&
((wise(mary))<=>((~kind(paul)&funny(paul))))&
(![X]:((creative(X)<~>~curious(X))=>(rich(X)&~humble(X))))&
(((~humble(john)|~happy(john)))<=>(?[X]:(kind(X))))&
(![X]:((strong(X)|~wise(X))=>(~brave(X)<~>~curious(X))))&
(((wise(alice)|~strong(alice)))=>(~wise(john)))&
(![X]:((~wise(X)|~patient(X))<=>calm(X)))&
(![X]:((~brave(X)<~>~happy(X))=>(patient(X)|~funny(X))))&
(((creative(john)&~curious(john)))<=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((~quiet(X)&quiet(X))<=>old(X)))&
(((rich(alice)&wise(alice)))<=>((creative(paul)&rich(paul))))&
((?[X]:(~strong(X)))<=>(?[X]:(~generous(X))))&
((generous(paul)|~tall(paul)))&
((curious(john)&~rich(john)))&
((creative(susan)<~>~curious(susan)))&
(?[X]:((~brave(X)|~strong(X))))&
((humble(john)&~patient(john)))&
((kind(john)|wise(john))) | ~generous(alice) | [
"p1",
"p11",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 1202417746340102273273575
% SZS output start Proof for 1202417746340102273273575
2. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~humble(X0) <~> humble(X0))) [input p1]
12. (~curious(john) & creative(john)) <=> ? [X0] : (calm(X0) & ~strong(X0)) [input p11]
15. ? [X0] : ~strong(X0) <=> ? [X0] : ~generous(X0) [input p14]
17. ~rich(john) & curious(john) [input p16]
22. ~generous(alice) [input hypothesis]
23. ? [X0] : ~strong(X0) <=> ? [X1] : ~generous(X1) [rectify 15]
36. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~calm(X0) | tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~calm(X0) | tall(X0))) [flattening 36]
52. ((~curious(john) & creative(john)) | ! [X0] : (~calm(X0) | strong(X0))) & (? [X0] : (calm(X0) & ~strong(X0)) | (curious(john) | ~creative(john))) [nnf transformation 12]
53. ((~curious(john) & creative(john)) | ! [X0] : (~calm(X0) | strong(X0))) & (? [X0] : (calm(X0) & ~strong(X0)) | curious(john) | ~creative(john)) [flattening 52]
54. ((~curious(john) & creative(john)) | ! [X0] : (~calm(X0) | strong(X0))) & (? [X1] : (calm(X1) & ~strong(X1)) | curious(john) | ~creative(john)) [rectify 53]
55. ? [X1] : (calm(X1) & ~strong(X1)) => (calm(sK2) & ~strong(sK2)) [choice axiom]
56. ((~curious(john) & creative(john)) | ! [X0] : (~calm(X0) | strong(X0))) & ((calm(sK2) & ~strong(sK2)) | curious(john) | ~creative(john)) [skolemisation 54,55]
59. (? [X0] : ~strong(X0) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : strong(X0)) [nnf transformation 23]
60. (? [X0] : ~strong(X0) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : strong(X3)) [rectify 59]
61. ? [X0] : ~strong(X0) => ~strong(sK3) [choice axiom]
62. ? [X2] : ~generous(X2) => ~generous(sK4) [choice axiom]
63. (~strong(sK3) | ! [X1] : generous(X1)) & (~generous(sK4) | ! [X3] : strong(X3)) [skolemisation 60,62,61]
74. calm(X0) | humble(X0) | humble(X0) [cnf transformation 37]
75. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 37]
105. ~curious(john) | ~calm(X0) | strong(X0) [cnf transformation 56]
111. ~strong(sK3) | generous(X1) [cnf transformation 63]
113. curious(john) [cnf transformation 17]
121. ~generous(alice) [cnf transformation 22]
125. calm(X0) | humble(X0) [duplicate literal removal 74]
126. calm(X0) | ~humble(X0) [duplicate literal removal 75]
128. 1 <=> ! [X0] : strong(X0) [avatar definition]
129. strong(X0) <- (1) [avatar component clause 128]
145. calm(X0) [subsumption resolution 125,126]
195. ~curious(john) | strong(X0) [subsumption resolution 105,145]
197. 15 <=> curious(john) [avatar definition]
200. 1 | ~15 [avatar split clause 195,197,128]
229. 21 <=> ! [X1] : generous(X1) [avatar definition]
230. generous(X1) <- (21) [avatar component clause 229]
232. 22 <=> strong(sK3) [avatar definition]
234. ~strong(sK3) <- (~22) [avatar component clause 232]
235. 21 | ~22 [avatar split clause 111,232,229]
241. 15 [avatar split clause 113,197]
271. $false <- (1, ~22) [resolution 234,129]
272. ~1 | 22 [avatar contradiction clause 271]
273. $false <- (21) [resolution 230,121]
274. ~21 [avatar contradiction clause 273]
275. $false [avatar sat refutation 200,235,241,272,274]
% SZS output end Proof for 1202417746340102273273575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not kind is not creative. Everyone who is not humble or not rich is both patient and not old. If someone is not calm then lucy is not tall or not kind and vice versa. Everyone who is not curious is either not generous or not funny. If someone is either not rich or not tall then paul is both not funny and kind. If someone is both not old and not strong then someone is not strong and vice versa. Everyone who is not kind is not curious and vice versa. If fred is either not quiet or humble then someone is either humble or not brave and vice versa. If someone is wise then paul is humble and vice versa. Everyone who is both not curious and curious is either not quiet or not kind. Everyone who is rich or old is not curious or strong and vice versa. If someone is not quiet then paul is not tall or not funny. Everyone who is both brave and strong is not brave or patient. Everyone who is calm or patient is humble and vice versa. Everyone who is both not curious and not generous is kind and vice versa. If alice is either not happy or not brave then someone is not rich or tall and vice versa. Someone is not patient or tall. Someone is either not rich or not curious. Someone is not humble or humble. Mary is either not brave or not strong. Someone is not calm or patient. Someone is not happy. Someone is either not patient or curious. Lucy is either brave or not quiet. | Mary is generous. | entailment | (![X]:((~calm(X)<~>~kind(X))=>~creative(X)))&
(![X]:((~humble(X)|~rich(X))=>(patient(X)&~old(X))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)|~kind(lucy))))&
(![X]:(~curious(X)=>(~generous(X)<~>~funny(X))))&
((?[X]:((~rich(X)<~>~tall(X))))=>((~funny(paul)&kind(paul))))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~kind(X)<=>~curious(X)))&
(((~quiet(fred)<~>humble(fred)))<=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:(wise(X)))<=>(humble(paul)))&
(![X]:((~curious(X)&curious(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:((rich(X)|old(X))<=>(~curious(X)|strong(X))))&
((?[X]:(~quiet(X)))=>((~tall(paul)|~funny(paul))))&
(![X]:((brave(X)&strong(X))=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|patient(X))<=>humble(X)))&
(![X]:((~curious(X)&~generous(X))<=>kind(X)))&
(((~happy(alice)<~>~brave(alice)))<=>(?[X]:((~rich(X)|tall(X)))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~rich(X)<~>~curious(X))))&
(?[X]:((~humble(X)|humble(X))))&
((~brave(mary)<~>~strong(mary)))&
(?[X]:((~calm(X)|patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~patient(X)<~>curious(X))))&
((brave(lucy)<~>~quiet(lucy))) | generous(mary) | [
"p6",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 338908290650550130831710
% SZS output start Proof for 338908290650550130831710
7. ! [X0] : (~kind(X0) <=> ~curious(X0)) [input p6]
15. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> kind(X0)) [input p14]
25. ~generous(mary) [input hypothesis]
49. ! [X0] : ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))) [nnf transformation 7]
63. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~kind(X0)) & (kind(X0) | (generous(X0) | curious(X0)))) [nnf transformation 15]
64. ! [X0] : (((~generous(X0) & ~curious(X0)) | ~kind(X0)) & (kind(X0) | generous(X0) | curious(X0))) [flattening 63]
101. ~curious(X0) | kind(X0) [cnf transformation 49]
102. ~kind(X0) | curious(X0) [cnf transformation 49]
124. kind(X0) | generous(X0) | curious(X0) [cnf transformation 64]
125. ~curious(X0) | ~kind(X0) [cnf transformation 64]
145. ~generous(mary) [cnf transformation 25]
259. ~curious(X0) [subsumption resolution 125,101]
260. generous(X0) | kind(X0) [subsumption resolution 124,259]
350. kind(mary) [resolution 260,145]
356. curious(mary) [resolution 350,102]
357. $false [subsumption resolution 356,259]
% SZS output end Proof for 338908290650550130831710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not calm is kind or tall and vice versa.
Everyone who is curious or not kind is creative.
Everyone who is either curious or kind is not calm.
If mary is either humble or not funny then someone is either old or happy and vice versa.
If someone is both strong and rich then susan is both not rich and not tall.
Everyone who is kind or happy is not brave and vice versa.
If alice is humble then alice is not old.
Everyone who is both quiet and not strong is either not curious or not tall.
Everyone who is happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
If someone is either tall or not curious then someone is either not curious or strong and vice versa.
Everyone who is curious or generous is either not old or not quiet.
Everyone who is calm is not quiet or old and vice versa.
Everyone who is both wise and not wise is not happy.
Lucy is creative.
Someone is either not wise or brave.
Someone is both rich and quiet.
Paul is either not curious or not calm.
Someone is either quiet or not strong. | Susan is not quiet. | contradiction | (![X]:((brave(X)&~calm(X))<=>(kind(X)|tall(X))))&
(![X]:((curious(X)|~kind(X))=>creative(X)))&
(![X]:((curious(X)<~>kind(X))=>~calm(X)))&
(((humble(mary)<~>~funny(mary)))<=>(?[X]:((old(X)<~>happy(X)))))&
((?[X]:((strong(X)&rich(X))))=>((~rich(susan)&~tall(susan))))&
(![X]:((kind(X)|happy(X))<=>~brave(X)))&
((humble(alice))=>(~old(alice)))&
(![X]:((quiet(X)&~strong(X))=>(~curious(X)<~>~tall(X))))&
(![X]:(happy(X)<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((curious(X)|generous(X))=>(~old(X)<~>~quiet(X))))&
(![X]:(calm(X)<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)&~wise(X))=>~happy(X)))&
(creative(lucy))&
(?[X]:((~wise(X)<~>brave(X))))&
(?[X]:((rich(X)&quiet(X))))&
((~curious(paul)<~>~calm(paul)))&
(?[X]:((quiet(X)<~>~strong(X)))) | ~quiet(susan) | [
"p0",
"p1",
"p5",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1984399561740056849563151
% SZS output start Proof for 1984399561740056849563151
1. ! [X0] : ((~calm(X0) & brave(X0)) <=> (tall(X0) | kind(X0))) [input p0]
2. ! [X0] : ((~kind(X0) | curious(X0)) => creative(X0)) [input p1]
6. ! [X0] : ((happy(X0) | kind(X0)) <=> ~brave(X0)) [input p5]
11. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (~happy(X0) | creative(X0))) [input p10]
15. ! [X0] : (calm(X0) <=> (old(X0) | ~quiet(X0))) [input p14]
22. ~quiet(susan) [input hypothesis]
25. ! [X0] : (creative(X0) | (kind(X0) & ~curious(X0))) [ennf transformation 2]
38. ! [X0] : (((~calm(X0) & brave(X0)) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 1]
39. ! [X0] : (((~calm(X0) & brave(X0)) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | calm(X0) | ~brave(X0))) [flattening 38]
45. ! [X0] : (((happy(X0) | kind(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((happy(X0) | kind(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & ~kind(X0)))) [flattening 45]
51. ! [X0] : (((happy(X0) & ~calm(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 11]
52. ! [X0] : (((happy(X0) & ~calm(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | ~happy(X0) | calm(X0))) [flattening 51]
59. ! [X0] : ((calm(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | ~calm(X0))) [nnf transformation 15]
60. ! [X0] : ((calm(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~calm(X0))) [flattening 59]
71. ~kind(X0) | brave(X0) [cnf transformation 39]
76. creative(X0) | kind(X0) [cnf transformation 25]
89. ~brave(X0) | ~kind(X0) [cnf transformation 46]
101. ~creative(X0) | ~calm(X0) [cnf transformation 52]
117. quiet(X0) | calm(X0) [cnf transformation 60]
129. ~quiet(susan) [cnf transformation 22]
177. ~kind(X0) [subsumption resolution 89,71]
270. ~calm(X0) | kind(X0) [resolution 101,76]
272. ~calm(X0) [subsumption resolution 270,177]
273. calm(susan) [resolution 117,129]
275. $false [subsumption resolution 273,272]
% SZS output end Proof for 1984399561740056849563151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous and not creative then mary is not brave and vice versa.
If someone is either not humble or not curious then fred is both patient and brave.
Everyone who is not wise is not patient or old and vice versa.
Everyone who is humble or not patient is both strong and not funny and vice versa.
Everyone who is not rich or not kind is both not kind and happy.
If someone is both old and not creative then lucy is happy.
If someone is either kind or not humble then someone is curious.
Everyone who is not creative or funny is either old or strong and vice versa.
Everyone who is both not brave and creative is not creative.
Everyone who is either brave or not tall is either quiet or not humble and vice versa.
Everyone who is both patient and wise is both not patient and patient.
If someone is not wise or not brave then alice is both not calm and brave and vice versa.
If susan is not kind or wise then lucy is not generous.
Everyone who is either not strong or not old is patient or old and vice versa.
Everyone who is both not old and not patient is either quiet or not old and vice versa.
Everyone who is not patient or quiet is not happy and vice versa.
Someone is both patient and not generous.
Mary is either happy or not generous.
Someone is both not quiet and not humble.
Someone is happy or not old.
Mary is either quiet or not curious.
Mary is either calm or creative.
John is wise or not humble. | Fred is calm. | neutral | (((~generous(paul)&~creative(paul)))<=>(~brave(mary)))&
((?[X]:((~humble(X)<~>~curious(X))))=>((patient(fred)&brave(fred))))&
(![X]:(~wise(X)<=>(~patient(X)|old(X))))&
(![X]:((humble(X)|~patient(X))<=>(strong(X)&~funny(X))))&
(![X]:((~rich(X)|~kind(X))=>(~kind(X)&happy(X))))&
((?[X]:((old(X)&~creative(X))))=>(happy(lucy)))&
((?[X]:((kind(X)<~>~humble(X))))=>(?[X]:(curious(X))))&
(![X]:((~creative(X)|funny(X))<=>(old(X)<~>strong(X))))&
(![X]:((~brave(X)&creative(X))=>~creative(X)))&
(![X]:((brave(X)<~>~tall(X))<=>(quiet(X)<~>~humble(X))))&
(![X]:((patient(X)&wise(X))=>(~patient(X)&patient(X))))&
((?[X]:((~wise(X)|~brave(X))))<=>((~calm(alice)&brave(alice))))&
(((~kind(susan)|wise(susan)))=>(~generous(lucy)))&
(![X]:((~strong(X)<~>~old(X))<=>(patient(X)|old(X))))&
(![X]:((~old(X)&~patient(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|quiet(X))<=>~happy(X)))&
(?[X]:((patient(X)&~generous(X))))&
((happy(mary)<~>~generous(mary)))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:((happy(X)|~old(X))))&
((quiet(mary)<~>~curious(mary)))&
((calm(mary)<~>creative(mary)))&
((wise(john)|~humble(john))) | calm(fred) | []
| null | 0 |
If mary is not quiet or not old then someone is not generous or strong and vice versa. Everyone who is either not wise or tall is either not funny or patient and vice versa. If john is both not humble and not curious then john is brave. Everyone who is strong is both funny and wise and vice versa. If someone is brave or creative then someone is either not calm or strong. Everyone who is not strong or not creative is old. If mary is both wise and tall then someone is not quiet or not curious and vice versa. Everyone who is brave or strong is not happy or not tall. If lucy is old or brave then lucy is not kind. Everyone who is both not curious and not creative is either not patient or not brave and vice versa. If someone is not curious then someone is either brave or not wise and vice versa. Everyone who is not generous is either not old or tall. Everyone who is not strong is not funny or not rich and vice versa. If someone is not happy or rich then fred is either humble or not strong. Everyone who is both not wise and old is generous or brave and vice versa. Everyone who is not quiet is not kind. Lucy is either not calm or not generous. Susan is tall. Someone is patient. Someone is calm or not calm. Someone is not funny or not generous. Someone is either generous or not funny. Someone is either not wise or patient. Alice is either not curious or not brave. | Mary is old. | entailment | (((~quiet(mary)|~old(mary)))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((~wise(X)<~>tall(X))<=>(~funny(X)<~>patient(X))))&
(((~humble(john)&~curious(john)))=>(brave(john)))&
(![X]:(strong(X)<=>(funny(X)&wise(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~strong(X)|~creative(X))=>old(X)))&
(((wise(mary)&tall(mary)))<=>(?[X]:((~quiet(X)|~curious(X)))))&
(![X]:((brave(X)|strong(X))=>(~happy(X)|~tall(X))))&
(((old(lucy)|brave(lucy)))=>(~kind(lucy)))&
(![X]:((~curious(X)&~creative(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(~funny(X)|~rich(X))))&
((?[X]:((~happy(X)|rich(X))))=>((humble(fred)<~>~strong(fred))))&
(![X]:((~wise(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
((~calm(lucy)<~>~generous(lucy)))&
(tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
((~curious(alice)<~>~brave(alice))) | old(mary) | [
"p3",
"p5",
"p6",
"p9",
"p10",
"p11",
"p14",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 237495476755508270789930
% SZS output start Proof for 237495476755508270789930
4. ! [X0] : (strong(X0) <=> (wise(X0) & funny(X0))) [input p3]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) => old(X0)) [input p5]
7. (tall(mary) & wise(mary)) <=> ? [X0] : (~curious(X0) | ~quiet(X0)) [input p6]
10. ! [X0] : ((~creative(X0) & ~curious(X0)) <=> (~patient(X0) <~> ~brave(X0))) [input p9]
11. ? [X0] : ~curious(X0) <=> ? [X0] : (brave(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : (~generous(X0) => (~old(X0) <~> tall(X0))) [input p11]
15. ! [X0] : ((old(X0) & ~wise(X0)) <=> (brave(X0) | generous(X0))) [input p14]
23. ? [X0] : (~wise(X0) <~> patient(X0)) [input p22]
25. ~old(mary) [input hypothesis]
27. ? [X0] : ~curious(X0) <=> ? [X1] : (brave(X1) <~> ~wise(X1)) [rectify 11]
33. ! [X0] : (old(X0) | (creative(X0) & strong(X0))) [ennf transformation 6]
36. ! [X0] : ((~old(X0) <~> tall(X0)) | generous(X0)) [ennf transformation 12]
44. ! [X0] : ((strong(X0) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | ~strong(X0))) [nnf transformation 4]
45. ! [X0] : ((strong(X0) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | ~strong(X0))) [flattening 44]
50. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | (~tall(mary) | ~wise(mary))) [nnf transformation 7]
51. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | ~tall(mary) | ~wise(mary)) [flattening 50]
52. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X1] : (~curious(X1) | ~quiet(X1)) | ~tall(mary) | ~wise(mary)) [rectify 51]
53. ? [X1] : (~curious(X1) | ~quiet(X1)) => (~curious(sK2) | ~quiet(sK2)) [choice axiom]
54. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & ((~curious(sK2) | ~quiet(sK2)) | ~tall(mary) | ~wise(mary)) [skolemisation 52,53]
55. ! [X0] : (((~creative(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (creative(X0) | curious(X0)))) [nnf transformation 10]
56. ! [X0] : (((~creative(X0) & ~curious(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | creative(X0) | curious(X0))) [flattening 55]
57. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X1] : ((wise(X1) | ~brave(X1)) & (~wise(X1) | brave(X1))) | ! [X0] : curious(X0)) [nnf transformation 27]
58. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) | ! [X3] : curious(X3)) [rectify 57]
59. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
60. ? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) => ((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) [choice axiom]
61. (~curious(sK3) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) | ! [X3] : curious(X3)) [skolemisation 58,60,59]
62. ! [X0] : (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | generous(X0)) [nnf transformation 36]
66. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 15]
67. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | wise(X0))) [flattening 66]
78. ? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) [nnf transformation 23]
79. ? [X0] : ((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) => ((~patient(sK9) | wise(sK9)) & (patient(sK9) | ~wise(sK9))) [choice axiom]
80. (~patient(sK9) | wise(sK9)) & (patient(sK9) | ~wise(sK9)) [skolemisation 78,79]
96. ~strong(X0) | wise(X0) [cnf transformation 45]
102. strong(X0) | old(X0) [cnf transformation 33]
108. tall(mary) | curious(X0) [cnf transformation 54]
113. ~brave(X0) | ~curious(X0) | patient(X0) [cnf transformation 56]
114. ~curious(X0) | ~patient(X0) | brave(X0) [cnf transformation 56]
120. ~curious(sK3) | brave(X1) | wise(X1) [cnf transformation 61]
122. ~tall(X0) | old(X0) | generous(X0) [cnf transformation 62]
131. ~wise(X0) | ~generous(X0) [cnf transformation 67]
132. ~wise(X0) | ~brave(X0) [cnf transformation 67]
143. patient(sK9) | ~wise(sK9) [cnf transformation 80]
144. ~patient(sK9) | wise(sK9) [cnf transformation 80]
147. ~old(mary) [cnf transformation 25]
156. 3 <=> old(mary) [avatar definition]
158. ~old(mary) <- (~3) [avatar component clause 156]
206. 14 <=> ! [X0] : curious(X0) [avatar definition]
207. curious(X0) <- (14) [avatar component clause 206]
209. 15 <=> tall(mary) [avatar definition]
211. tall(mary) <- (15) [avatar component clause 209]
212. 14 | 15 [avatar split clause 108,209,206]
218. 17 <=> wise(mary) [avatar definition]
219. ~wise(mary) <- (~17) [avatar component clause 218]
220. wise(mary) <- (17) [avatar component clause 218]
233. 20 <=> ! [X1] : (brave(X1) | wise(X1)) [avatar definition]
234. brave(X1) | wise(X1) <- (20) [avatar component clause 233]
236. 21 <=> curious(sK3) [avatar definition]
238. ~curious(sK3) <- (~21) [avatar component clause 236]
239. 20 | ~21 [avatar split clause 120,236,233]
241. 22 <=> ! [X1] : (~wise(X1) | ~brave(X1)) [avatar definition]
242. ~brave(X1) | ~wise(X1) <- (22) [avatar component clause 241]
272. 22 [avatar split clause 132,241]
303. 35 <=> wise(sK9) [avatar definition]
304. ~wise(sK9) <- (~35) [avatar component clause 303]
305. wise(sK9) <- (35) [avatar component clause 303]
307. 36 <=> patient(sK9) [avatar definition]
308. patient(sK9) <- (36) [avatar component clause 307]
309. ~patient(sK9) <- (~36) [avatar component clause 307]
310. 35 | ~36 [avatar split clause 144,307,303]
311. ~35 | 36 [avatar split clause 143,307,303]
322. ~3 [avatar split clause 147,156]
323. $false <- (14, ~21) [resolution 238,207]
324. ~14 | 21 [avatar contradiction clause 323]
327. wise(X0) | old(X0) [resolution 102,96]
330. ~generous(mary) <- (17) [resolution 131,220]
386. ~patient(X0) | brave(X0) <- (14) [resolution 207,114]
401. wise(X0) | ~curious(X0) | patient(X0) <- (20) [resolution 234,113]
404. patient(X0) | wise(X0) <- (14, 20) [subsumption resolution 401,207]
408. old(mary) | generous(mary) <- (15) [resolution 122,211]
410. generous(mary) <- (~3, 15) [subsumption resolution 408,158]
411. $false <- (~3, 15, 17) [subsumption resolution 410,330]
412. 3 | ~15 | ~17 [avatar contradiction clause 411]
413. old(mary) <- (~17) [resolution 219,327]
414. $false <- (~3, ~17) [subsumption resolution 413,158]
415. 3 | 17 [avatar contradiction clause 414]
602. wise(sK9) <- (14, 20, ~36) [resolution 309,404]
603. $false <- (14, 20, ~35, ~36) [subsumption resolution 602,304]
604. ~14 | ~20 | 35 | 36 [avatar contradiction clause 603]
607. brave(sK9) <- (14, 36) [resolution 308,386]
626. ~wise(sK9) <- (14, 22, 36) [resolution 607,242]
628. $false <- (14, 22, 35, 36) [subsumption resolution 626,305]
629. ~14 | ~22 | ~35 | ~36 [avatar contradiction clause 628]
630. $false [avatar sat refutation 212,239,272,310,311,322,324,412,415,604,629]
% SZS output end Proof for 237495476755508270789930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is curious or not brave then someone is not old or generous.
If lucy is not calm or not generous then fred is both not creative and not brave and vice versa.
Everyone who is both tall and not happy is not happy or not patient and vice versa.
Everyone who is both not creative and not brave is both not creative and quiet and vice versa.
If someone is not old then someone is old.
If someone is not quiet then alice is both wise and curious.
If someone is both not quiet and not funny then fred is either not generous or rich.
If mary is happy or humble then susan is kind.
Everyone who is either quiet or not tall is either curious or quiet and vice versa.
Everyone who is both humble and rich is not happy or not curious.
Everyone who is tall is not creative.
Everyone who is old is both calm and not generous and vice versa.
Everyone who is both patient and calm is either not calm or not curious.
If alice is either funny or humble then someone 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.
Someone is either tall or creative.
Someone is not happy or not humble.
John is curious.
Someone is both not strong and wise.
Someone is not patient.
Someone is both curious and not old.
Someone is generous or curious. | Susan is kind. | neutral | ((?[X]:((curious(X)|~brave(X))))=>(?[X]:((~old(X)|generous(X)))))&
(((~calm(lucy)|~generous(lucy)))<=>((~creative(fred)&~brave(fred))))&
(![X]:((tall(X)&~happy(X))<=>(~happy(X)|~patient(X))))&
(![X]:((~creative(X)&~brave(X))<=>(~creative(X)&quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(old(X))))&
((?[X]:(~quiet(X)))=>((wise(alice)&curious(alice))))&
((?[X]:((~quiet(X)&~funny(X))))=>((~generous(fred)<~>rich(fred))))&
(((happy(mary)|humble(mary)))=>(kind(susan)))&
(![X]:((quiet(X)<~>~tall(X))<=>(curious(X)<~>quiet(X))))&
(![X]:((humble(X)&rich(X))=>(~happy(X)|~curious(X))))&
(![X]:(tall(X)=>~creative(X)))&
(![X]:(old(X)<=>(calm(X)&~generous(X))))&
(![X]:((patient(X)&calm(X))=>(~calm(X)<~>~curious(X))))&
(((funny(alice)<~>humble(alice)))=>(?[X]:((old(X)|~curious(X)))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(?[X]:((tall(X)<~>creative(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(curious(john))&
(?[X]:((~strong(X)&wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&~old(X))))&
(?[X]:((generous(X)|curious(X)))) | kind(susan) | []
| null | 0 |
If susan is not creative then fred is both not generous and wise.
Everyone who is either not generous or strong is both not curious and funny and vice versa.
Everyone who is creative or kind is curious.
Everyone who is not funny or tall is both not brave and strong and vice versa.
If fred is either not calm or not humble then john is not wise and vice versa.
If lucy is old then someone is both calm and not wise.
If fred is either calm or funny then someone is either not humble or not quiet.
Everyone who is calm or not generous is either quiet or wise.
Everyone who is not calm or funny is not tall.
If someone is patient or not funny then fred is kind and vice versa.
If lucy is both rich and curious then someone is either wise or not brave.
Everyone who is either rich or happy is both not calm and funny.
Everyone who is calm or not patient is not brave and vice versa.
Everyone who is patient or humble is either not generous or not quiet and vice versa.
Everyone who is either kind or funny is not strong.
Everyone who is either not tall or quiet is both not patient and wise.
Someone is either not generous or quiet.
Alice is both quiet and not generous.
Someone is not old or not funny.
Someone is both not kind and funny.
Someone is both calm and generous.
Alice is curious.
Mary is wise.
Someone is not curious or not calm. | Mary is patient. | contradiction | ((~creative(susan))=>((~generous(fred)&wise(fred))))&
(![X]:((~generous(X)<~>strong(X))<=>(~curious(X)&funny(X))))&
(![X]:((creative(X)|kind(X))=>curious(X)))&
(![X]:((~funny(X)|tall(X))<=>(~brave(X)&strong(X))))&
(((~calm(fred)<~>~humble(fred)))<=>(~wise(john)))&
((old(lucy))=>(?[X]:((calm(X)&~wise(X)))))&
(((calm(fred)<~>funny(fred)))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((calm(X)|~generous(X))=>(quiet(X)<~>wise(X))))&
(![X]:((~calm(X)|funny(X))=>~tall(X)))&
((?[X]:((patient(X)|~funny(X))))<=>(kind(fred)))&
(((rich(lucy)&curious(lucy)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((rich(X)<~>happy(X))=>(~calm(X)&funny(X))))&
(![X]:((calm(X)|~patient(X))<=>~brave(X)))&
(![X]:((patient(X)|humble(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>funny(X))=>~strong(X)))&
(![X]:((~tall(X)<~>quiet(X))=>(~patient(X)&wise(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((quiet(alice)&~generous(alice)))&
(?[X]:((~old(X)|~funny(X))))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:((calm(X)&generous(X))))&
(curious(alice))&
(wise(mary))&
(?[X]:((~curious(X)|~calm(X)))) | patient(mary) | [
"p1",
"p3",
"p7",
"p8",
"p13",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 138705905275504068778461
% SZS output start Proof for 138705905275504068778461
2. ! [X0] : ((~generous(X0) <~> strong(X0)) <=> (funny(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (strong(X0) & ~brave(X0))) [input p3]
8. ! [X0] : ((~generous(X0) | calm(X0)) => (quiet(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((funny(X0) | ~calm(X0)) => ~tall(X0)) [input p8]
14. ! [X0] : ((humble(X0) | patient(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p13]
16. ! [X0] : ((~tall(X0) <~> quiet(X0)) => (wise(X0) & ~patient(X0))) [input p15]
23. wise(mary) [input p22]
25. patient(mary) [input hypothesis]
31. ! [X0] : ((quiet(X0) <~> wise(X0)) | (generous(X0) & ~calm(X0))) [ennf transformation 8]
32. ! [X0] : (~tall(X0) | (~funny(X0) & calm(X0))) [ennf transformation 9]
37. ! [X0] : ((wise(X0) & ~patient(X0)) | (~tall(X0) <=> quiet(X0))) [ennf transformation 16]
38. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0))))) [flattening 38]
40. ! [X0] : (((tall(X0) | ~funny(X0)) | (~strong(X0) | brave(X0))) & ((strong(X0) & ~brave(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | ~funny(X0) | ~strong(X0) | brave(X0)) & ((strong(X0) & ~brave(X0)) | (~tall(X0) & funny(X0)))) [flattening 40]
46. ! [X0] : (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (generous(X0) & ~calm(X0))) [nnf transformation 31]
57. ! [X0] : (((humble(X0) | patient(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~humble(X0) & ~patient(X0)))) [nnf transformation 14]
58. ! [X0] : ((humble(X0) | patient(X0) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~humble(X0) & ~patient(X0)))) [flattening 57]
60. ! [X0] : ((wise(X0) & ~patient(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0)))) [nnf transformation 37]
75. ~strong(X0) | ~generous(X0) | funny(X0) [cnf transformation 39]
83. ~tall(X0) | strong(X0) [cnf transformation 41]
96. ~quiet(X0) | ~wise(X0) | generous(X0) [cnf transformation 46]
98. ~tall(X0) | ~funny(X0) [cnf transformation 32]
111. ~patient(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 58]
113. ~patient(X0) | generous(X0) | quiet(X0) [cnf transformation 58]
119. ~patient(X0) | quiet(X0) | tall(X0) [cnf transformation 60]
132. wise(mary) [cnf transformation 23]
134. patient(mary) [cnf transformation 25]
302. ~generous(mary) | ~quiet(mary) [resolution 111,134]
304. 29 <=> quiet(mary) [avatar definition]
305. quiet(mary) <- (29) [avatar component clause 304]
306. ~quiet(mary) <- (~29) [avatar component clause 304]
308. 30 <=> generous(mary) [avatar definition]
309. generous(mary) <- (30) [avatar component clause 308]
310. ~generous(mary) <- (~30) [avatar component clause 308]
311. ~29 | ~30 [avatar split clause 302,308,304]
315. generous(mary) | quiet(mary) [resolution 113,134]
318. 29 | 30 [avatar split clause 315,308,304]
320. ~wise(mary) | generous(mary) <- (29) [resolution 305,96]
322. generous(mary) <- (29) [subsumption resolution 320,132]
323. $false <- (29, ~30) [subsumption resolution 322,310]
324. ~29 | 30 [avatar contradiction clause 323]
335. quiet(mary) | tall(mary) [resolution 119,134]
336. tall(mary) <- (~29) [subsumption resolution 335,306]
385. ~funny(mary) <- (~29) [resolution 336,98]
387. strong(mary) <- (~29) [resolution 336,83]
513. ~generous(mary) | funny(mary) <- (~29) [resolution 387,75]
514. funny(mary) <- (~29, 30) [subsumption resolution 513,309]
515. $false <- (~29, 30) [subsumption resolution 514,385]
516. 29 | ~30 [avatar contradiction clause 515]
517. $false [avatar sat refutation 311,318,324,516]
% SZS output end Proof for 138705905275504068778461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both curious and not funny then fred is generous and vice versa.
Everyone who is both not generous and not tall is both humble and not happy.
If alice is both rich and not generous then john is both calm and not kind.
If fred is both calm and not generous then someone is either rich or not curious and vice versa.
Everyone who is either not old or happy is either not curious or creative and vice versa.
Everyone who is tall or not rich is not kind.
If someone is patient then susan is either rich or strong.
If fred is both not strong and not patient then alice is either not calm or not generous and vice versa.
Everyone who is either old or tall is not humble and vice versa.
If someone is old then someone is not happy and vice versa.
Everyone who is creative or quiet is not strong.
Everyone who is not happy is either not generous or kind and vice versa.
Everyone who is either not wise or generous is both not calm and not wise and vice versa.
Everyone who is both humble and not funny is either humble or rich.
If someone is both patient and not creative then fred is happy and vice versa.
Everyone who is quiet or not old is both not generous and not quiet and vice versa.
Someone is curious or rich.
Mary is both not funny and not tall.
Someone is happy.
Someone is not rich or not brave.
Lucy is funny.
Someone is calm.
Someone is not tall.
Someone is both kind and not funny. | Fred is not kind. | neutral | (((curious(alice)&~funny(alice)))<=>(generous(fred)))&
(![X]:((~generous(X)&~tall(X))=>(humble(X)&~happy(X))))&
(((rich(alice)&~generous(alice)))=>((calm(john)&~kind(john))))&
(((calm(fred)&~generous(fred)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((~old(X)<~>happy(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)|~rich(X))=>~kind(X)))&
((?[X]:(patient(X)))=>((rich(susan)<~>strong(susan))))&
(((~strong(fred)&~patient(fred)))<=>((~calm(alice)<~>~generous(alice))))&
(![X]:((old(X)<~>tall(X))<=>~humble(X)))&
((?[X]:(old(X)))<=>(?[X]:(~happy(X))))&
(![X]:((creative(X)|quiet(X))=>~strong(X)))&
(![X]:(~happy(X)<=>(~generous(X)<~>kind(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~calm(X)&~wise(X))))&
(![X]:((humble(X)&~funny(X))=>(humble(X)<~>rich(X))))&
((?[X]:((patient(X)&~creative(X))))<=>(happy(fred)))&
(![X]:((quiet(X)|~old(X))<=>(~generous(X)&~quiet(X))))&
(?[X]:((curious(X)|rich(X))))&
((~funny(mary)&~tall(mary)))&
(?[X]:(happy(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(funny(lucy))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
(?[X]:((kind(X)&~funny(X)))) | ~kind(fred) | []
| null | 0 |
If mary is either not curious or not kind then alice is either calm or not creative and vice versa. Everyone who is both not creative and not funny is both not wise and not funny. If someone is not generous or not kind then alice is patient or not generous. If john is both brave and not wise then someone is rich. Everyone who is not patient or not curious is either not brave or not funny and vice versa. Everyone who is either not happy or patient is both kind and not wise. If fred is either strong or tall then someone is both not old and creative. If fred is either rich or not rich then someone is not happy. Everyone who is old is both kind and not tall. Everyone who is old or humble is either not calm or not tall and vice versa. If someone is creative or not humble then paul is not brave or brave. Everyone who is not calm is either not wise or rich. Everyone who is calm or humble is both not strong and not tall. Everyone who is not strong is both patient and funny. Everyone who is both not funny and not patient is either patient or brave. Everyone who is either quiet or tall is both not calm and brave. Someone is not funny or not brave. Susan is not rich or not generous. Fred is wise. Someone is not brave or calm. Someone is either happy or not quiet. Mary is rich. Fred is creative. Susan is either humble or not tall. | Susan is not tall. | entailment | (((~curious(mary)<~>~kind(mary)))<=>((calm(alice)<~>~creative(alice))))&
(![X]:((~creative(X)&~funny(X))=>(~wise(X)&~funny(X))))&
((?[X]:((~generous(X)|~kind(X))))=>((patient(alice)|~generous(alice))))&
(((brave(john)&~wise(john)))=>(?[X]:(rich(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>patient(X))=>(kind(X)&~wise(X))))&
(((strong(fred)<~>tall(fred)))=>(?[X]:((~old(X)&creative(X)))))&
(((rich(fred)<~>~rich(fred)))=>(?[X]:(~happy(X))))&
(![X]:(old(X)=>(kind(X)&~tall(X))))&
(![X]:((old(X)|humble(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:((creative(X)|~humble(X))))=>((~brave(paul)|brave(paul))))&
(![X]:(~calm(X)=>(~wise(X)<~>rich(X))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)&~tall(X))))&
(![X]:(~strong(X)=>(patient(X)&funny(X))))&
(![X]:((~funny(X)&~patient(X))=>(patient(X)<~>brave(X))))&
(![X]:((quiet(X)<~>tall(X))=>(~calm(X)&brave(X))))&
(?[X]:((~funny(X)|~brave(X))))&
((~rich(susan)|~generous(susan)))&
(wise(fred))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:((happy(X)<~>~quiet(X))))&
(rich(mary))&
(creative(fred))&
((humble(susan)<~>~tall(susan))) | ~tall(susan) | [
"p12",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 3459981428191508104424902
% SZS output start Proof for 3459981428191508104424902
13. ! [X0] : ((humble(X0) | calm(X0)) => (~tall(X0) & ~strong(X0))) [input p12]
24. humble(susan) <~> ~tall(susan) [input p23]
25. tall(susan) [input hypothesis]
39. ! [X0] : ((~tall(X0) & ~strong(X0)) | (~humble(X0) & ~calm(X0))) [ennf transformation 13]
68. (tall(susan) | ~humble(susan)) & (~tall(susan) | humble(susan)) [nnf transformation 24]
113. ~tall(X0) | ~humble(X0) [cnf transformation 39]
130. ~tall(susan) | humble(susan) [cnf transformation 68]
131. tall(susan) | ~humble(susan) [cnf transformation 68]
132. tall(susan) [cnf transformation 25]
259. ~humble(susan) [subsumption resolution 131,113]
260. ~tall(susan) [subsumption resolution 130,259]
261. $false [subsumption resolution 132,260]
% SZS output end Proof for 3459981428191508104424902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not patient and happy then john is either brave or humble and vice versa. If someone is either not tall or not strong then someone is either happy or patient. Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. Someone is either humble or funny. Susan is both happy and not funny. Paul is not funny. Someone is both humble and happy. Alice is generous or not curious. Someone is not rich or wise. Someone is tall or not wise. Mary is either strong or not curious. | Alice is quiet. | contradiction | (((~patient(paul)&happy(paul)))<=>((brave(john)<~>humble(john))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
(?[X]:((humble(X)<~>funny(X))))&
((happy(susan)&~funny(susan)))&
(~funny(paul))&
(?[X]:((humble(X)&happy(X))))&
((generous(alice)|~curious(alice)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((tall(X)|~wise(X))))&
((strong(mary)<~>~curious(mary))) | quiet(alice) | [
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 2504414896570039502158341
% SZS output start Proof for 2504414896570039502158341
8. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p7]
24. quiet(alice) [input hypothesis]
53. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 8]
54. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 53]
91. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
120. quiet(alice) [cnf transformation 24]
121. ~quiet(X0) [duplicate literal removal 91]
269. $false [subsumption resolution 120,121]
% SZS output end Proof for 2504414896570039502158341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or humble is not humble or not creative.
If susan is funny or not kind then someone is either not patient or wise.
If fred is both not strong and quiet then paul is not brave or funny and vice versa.
If fred is quiet or generous then someone is both not patient and kind and vice versa.
Everyone who is both not calm and brave is both not patient and not curious.
Everyone who is either not rich or not patient is either not tall or calm and vice versa.
If lucy is not kind or happy then someone is either not generous or humble and vice versa.
Everyone who is not generous or not funny is not funny or funny and vice versa.
If lucy is not curious or not patient then paul is calm.
If someone is not generous then paul is either strong or wise and vice versa.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
Someone is either calm or not strong.
Lucy is either not curious or not quiet.
Lucy is not quiet or strong.
Someone is both curious and not brave.
Someone is old.
Someone is kind or not happy.
Fred is not calm.
Lucy is either creative or not curious. | Fred is not brave. | entailment | (![X]:((generous(X)|humble(X))=>(~humble(X)|~creative(X))))&
(((funny(susan)|~kind(susan)))=>(?[X]:((~patient(X)<~>wise(X)))))&
(((~strong(fred)&quiet(fred)))<=>((~brave(paul)|funny(paul))))&
(((quiet(fred)|generous(fred)))<=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:((~calm(X)&brave(X))=>(~patient(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~tall(X)<~>calm(X))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:((~generous(X)|~funny(X))<=>(~funny(X)|funny(X))))&
(((~curious(lucy)|~patient(lucy)))=>(calm(paul)))&
((?[X]:(~generous(X)))<=>((strong(paul)<~>wise(paul))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(?[X]:((calm(X)<~>~strong(X))))&
((~curious(lucy)<~>~quiet(lucy)))&
((~quiet(lucy)|strong(lucy)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((kind(X)|~happy(X))))&
(~calm(fred))&
((creative(lucy)<~>~curious(lucy))) | ~brave(fred) | [
"p0",
"p10",
"p12",
"p14",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 876063483676723847466350
% SZS output start Proof for 876063483676723847466350
1. ! [X0] : ((humble(X0) | generous(X0)) => (~creative(X0) | ~humble(X0))) [input p0]
11. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (funny(X0) | brave(X0))) [input p10]
13. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~tall(X0)) [input p12]
15. ! [X0] : ((calm(X0) | ~humble(X0)) <=> ~tall(X0)) [input p14]
23. ~calm(fred) [input p22]
25. brave(fred) [input hypothesis]
28. ! [X0] : ((~creative(X0) | ~humble(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 1]
29. ! [X0] : (~creative(X0) | ~humble(X0) | (~humble(X0) & ~generous(X0))) [flattening 28]
58. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 11]
59. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 58]
64. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 13]
65. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | creative(X0))) [flattening 64]
66. ! [X0] : (((calm(X0) | ~humble(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [nnf transformation 15]
67. ! [X0] : ((calm(X0) | ~humble(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [flattening 66]
80. ~creative(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 29]
125. ~brave(X0) | calm(X0) | creative(X0) [cnf transformation 59]
132. ~creative(X0) | tall(X0) [cnf transformation 65]
136. ~tall(X0) | humble(X0) [cnf transformation 67]
150. ~calm(fred) [cnf transformation 23]
153. brave(fred) [cnf transformation 25]
156. ~creative(X0) | ~humble(X0) [duplicate literal removal 80]
355. calm(fred) | creative(fred) [resolution 125,153]
357. creative(fred) [subsumption resolution 355,150]
358. ~humble(fred) [resolution 357,156]
359. tall(fred) [resolution 357,132]
378. humble(fred) [resolution 359,136]
379. $false [subsumption resolution 378,358]
% SZS output end Proof for 876063483676723847466350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not old is not generous.
If paul is rich or old then alice is either not brave or not kind and vice versa.
If someone is generous or not tall then fred is either calm or not strong and vice versa.
Everyone who is not wise or calm is wise and vice versa.
If someone is both brave and not strong then someone is either not happy or tall and vice versa.
Everyone who is either not brave or not patient is quiet.
Everyone who is wise is either not curious or tall and vice versa.
Everyone who is not wise is happy and vice versa.
Everyone who is happy is not quiet and vice versa.
If someone is brave or old then lucy is not old or wise and vice versa.
If john is funny or brave then mary is not happy or old and vice versa.
If someone is both not wise and not calm then alice is both not humble and not old.
If someone is either kind or patient then someone is not kind or tall.
If john is brave then paul is patient or quiet and vice versa.
If paul is either humble or brave then someone is either quiet or not happy and vice versa.
If someone is both not tall and tall then lucy is happy and vice versa.
Someone is either not tall or not strong.
Someone is wise or not generous.
Fred is either not wise or rich.
Someone is either not funny or not creative.
Paul is both creative and not tall.
John is either not quiet or rich.
Paul is humble or funny. | John is not brave. | contradiction | (![X]:((~curious(X)&~old(X))=>~generous(X)))&
(((rich(paul)|old(paul)))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((generous(X)|~tall(X))))<=>((calm(fred)<~>~strong(fred))))&
(![X]:((~wise(X)|calm(X))<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&tall(X))))<=>(happy(lucy)))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~wise(fred)<~>rich(fred)))&
(?[X]:((~funny(X)<~>~creative(X))))&
((creative(paul)&~tall(paul)))&
((~quiet(john)<~>rich(john)))&
((humble(paul)|funny(paul))) | ~brave(john) | [
"p3",
"p7",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 307092744870898267299137
% SZS output start Proof for 307092744870898267299137
4. ! [X0] : ((calm(X0) | ~wise(X0)) <=> wise(X0)) [input p3]
8. ! [X0] : (~wise(X0) <=> happy(X0)) [input p7]
9. ! [X0] : (happy(X0) <=> ~quiet(X0)) [input p8]
14. brave(john) <=> (quiet(paul) | patient(paul)) [input p13]
24. ~brave(john) [input hypothesis]
38. ! [X0] : (((calm(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [nnf transformation 4]
39. ! [X0] : ((calm(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [flattening 38]
47. ! [X0] : ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))) [nnf transformation 9]
60. (brave(john) | (~quiet(paul) & ~patient(paul))) & ((quiet(paul) | patient(paul)) | ~brave(john)) [nnf transformation 14]
61. (brave(john) | (~quiet(paul) & ~patient(paul))) & (quiet(paul) | patient(paul) | ~brave(john)) [flattening 60]
93. wise(X0) | wise(X0) [cnf transformation 39]
109. ~wise(X0) | ~happy(X0) [cnf transformation 47]
111. happy(X0) | quiet(X0) [cnf transformation 48]
126. brave(john) | ~quiet(paul) [cnf transformation 61]
150. ~brave(john) [cnf transformation 24]
151. wise(X0) [duplicate literal removal 93]
236. ~happy(X0) [subsumption resolution 109,151]
237. quiet(X0) [subsumption resolution 111,236]
262. 23 <=> brave(john) [avatar definition]
284. brave(john) [subsumption resolution 126,237]
285. 23 [avatar split clause 284,262]
332. ~23 [avatar split clause 150,262]
333. $false [avatar sat refutation 285,332]
% SZS output end Proof for 307092744870898267299137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or generous then someone is not funny or funny.
Everyone who is quiet is not brave or calm.
If mary is either wise or not calm then someone is either humble or creative.
Everyone who is not brave or generous is both not humble and not curious.
Everyone who is both curious and not patient is not wise or not brave and vice versa.
Everyone who is either not tall or strong is both strong and funny.
Everyone who is humble or not brave is both not generous and calm.
Everyone who is brave is creative or brave.
Everyone who is both tall and calm is either not patient or patient and vice versa.
If susan is both creative and humble then someone is not funny or not rich.
If someone is either not funny or not rich then someone is both not funny and quiet and vice versa.
If susan is rich then someone is both kind and not wise and vice versa.
If fred is both generous and not tall then paul is both curious and not calm and vice versa.
Everyone who is either not kind or generous is not quiet.
Everyone who is both not strong and humble is not strong and vice versa.
Mary is not happy or not old.
Someone is either not kind or not creative.
Fred is both not generous and not humble.
Someone is either not humble or humble.
Someone is either not happy or strong.
Someone is not happy or generous.
Someone is both tall and not generous. | Fred is not creative. | neutral | ((?[X]:((old(X)|generous(X))))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:(quiet(X)=>(~brave(X)|calm(X))))&
(((wise(mary)<~>~calm(mary)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~brave(X)|generous(X))=>(~humble(X)&~curious(X))))&
(![X]:((curious(X)&~patient(X))<=>(~wise(X)|~brave(X))))&
(![X]:((~tall(X)<~>strong(X))=>(strong(X)&funny(X))))&
(![X]:((humble(X)|~brave(X))=>(~generous(X)&calm(X))))&
(![X]:(brave(X)=>(creative(X)|brave(X))))&
(![X]:((tall(X)&calm(X))<=>(~patient(X)<~>patient(X))))&
(((creative(susan)&humble(susan)))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:((~funny(X)&quiet(X)))))&
((rich(susan))<=>(?[X]:((kind(X)&~wise(X)))))&
(((generous(fred)&~tall(fred)))<=>((curious(paul)&~calm(paul))))&
(![X]:((~kind(X)<~>generous(X))=>~quiet(X)))&
(![X]:((~strong(X)&humble(X))<=>~strong(X)))&
((~happy(mary)|~old(mary)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~generous(fred)&~humble(fred)))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:((tall(X)&~generous(X)))) | ~creative(fred) | []
| null | 0 |
Everyone who is either not curious or brave is not funny.
Everyone who is both old and not patient is humble.
Everyone who is either patient or tall is both patient and not generous.
If someone is not kind then someone is either funny or not strong and vice versa.
Everyone who is not wise is rich and vice versa.
Everyone who is both curious and not wise is not quiet and vice versa.
Everyone who is strong is either not brave or not quiet and vice versa.
Everyone who is either not creative or curious is not quiet and vice versa.
Everyone who is wise or not wise is curious and vice versa.
Everyone who is not tall is patient or not happy and vice versa.
If fred is tall then paul is either curious or generous and vice versa.
If susan is not patient or not tall then lucy is not patient or not strong.
Everyone who is either not strong or kind is happy.
If someone is brave then susan is both patient and curious.
If mary is either not curious or tall then john is both not calm and generous and vice versa.
If someone is either generous or old then lucy is either not creative or funny.
Alice is calm.
Someone is both strong and not kind.
Someone is creative.
Someone is both not patient and not funny.
Paul is brave.
Someone is either brave or not tall.
Someone is both happy and curious. | Susan is old. | neutral | (![X]:((~curious(X)<~>brave(X))=>~funny(X)))&
(![X]:((old(X)&~patient(X))=>humble(X)))&
(![X]:((patient(X)<~>tall(X))=>(patient(X)&~generous(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>rich(X)))&
(![X]:((curious(X)&~wise(X))<=>~quiet(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>curious(X))<=>~quiet(X)))&
(![X]:((wise(X)|~wise(X))<=>curious(X)))&
(![X]:(~tall(X)<=>(patient(X)|~happy(X))))&
((tall(fred))<=>((curious(paul)<~>generous(paul))))&
(((~patient(susan)|~tall(susan)))=>((~patient(lucy)|~strong(lucy))))&
(![X]:((~strong(X)<~>kind(X))=>happy(X)))&
((?[X]:(brave(X)))=>((patient(susan)&curious(susan))))&
(((~curious(mary)<~>tall(mary)))<=>((~calm(john)&generous(john))))&
((?[X]:((generous(X)<~>old(X))))=>((~creative(lucy)<~>funny(lucy))))&
(calm(alice))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)&~funny(X))))&
(brave(paul))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:((happy(X)&curious(X)))) | old(susan) | []
| null | 0 |
Everyone who is both not quiet and happy is either not kind or not humble. Everyone who is curious or not brave is both not funny and tall. If mary is tall or not rich then someone is patient or kind and vice versa. Everyone who is either not funny or not quiet is not kind or not happy and vice versa. If fred is not kind or wise then someone is both not old and not patient. Everyone who is not strong is not quiet or generous. If someone is not brave then someone is both not tall and funny. Everyone who is not generous or not wise is old or not rich and vice versa. If someone is calm or kind then susan is both curious and not patient. Everyone who is rich or old is not calm. Everyone who is tall or generous is both not kind and funny and vice versa. If someone is not generous then lucy is not patient. If someone is not tall then someone is old and vice versa. If someone is calm or funny then fred is either not funny or happy. If alice is not creative then someone is not calm and vice versa. Everyone who is not kind or tall is either curious or not strong and vice versa. Someone is rich or strong. John is both humble and not curious. Mary is either not happy or not kind. John is not old. Someone is either not wise or not rich. | John is strong. | contradiction | (![X]:((~quiet(X)&happy(X))=>(~kind(X)<~>~humble(X))))&
(![X]:((curious(X)|~brave(X))=>(~funny(X)&tall(X))))&
(((tall(mary)|~rich(mary)))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(((~kind(fred)|wise(fred)))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:(~strong(X)=>(~quiet(X)|generous(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)&funny(X)))))&
(![X]:((~generous(X)|~wise(X))<=>(old(X)|~rich(X))))&
((?[X]:((calm(X)|kind(X))))=>((curious(susan)&~patient(susan))))&
(![X]:((rich(X)|old(X))=>~calm(X)))&
(![X]:((tall(X)|generous(X))<=>(~kind(X)&funny(X))))&
((?[X]:(~generous(X)))=>(~patient(lucy)))&
((?[X]:(~tall(X)))<=>(?[X]:(old(X))))&
((?[X]:((calm(X)|funny(X))))=>((~funny(fred)<~>happy(fred))))&
((~creative(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)|tall(X))<=>(curious(X)<~>~strong(X))))&
(?[X]:((rich(X)|strong(X))))&
((humble(john)&~curious(john)))&
((~happy(mary)<~>~kind(mary)))&
(~old(john))&
(?[X]:((~wise(X)<~>~rich(X)))) | strong(john) | [
"p1",
"p8",
"p10",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 8853929196387914782750245
% SZS output start Proof for 8853929196387914782750245
2. ! [X0] : ((~brave(X0) | curious(X0)) => (tall(X0) & ~funny(X0))) [input p1]
9. ? [X0] : (kind(X0) | calm(X0)) => (~patient(susan) & curious(susan)) [input p8]
11. ! [X0] : ((generous(X0) | tall(X0)) <=> (funny(X0) & ~kind(X0))) [input p10]
16. ! [X0] : ((tall(X0) | ~kind(X0)) <=> (curious(X0) <~> ~strong(X0))) [input p15]
18. ~curious(john) & humble(john) [input p17]
22. strong(john) [input hypothesis]
25. ! [X0] : (curious(X0) => (tall(X0) & ~funny(X0))) [pure predicate removal 2]
29. ! [X0] : ((tall(X0) & ~funny(X0)) | ~curious(X0)) [ennf transformation 25]
33. (~patient(susan) & curious(susan)) | ! [X0] : (~kind(X0) & ~calm(X0)) [ennf transformation 9]
49. ! [X0] : (((generous(X0) | tall(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (~generous(X0) & ~tall(X0)))) [nnf transformation 11]
50. ! [X0] : ((generous(X0) | tall(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | (~generous(X0) & ~tall(X0)))) [flattening 49]
61. ! [X0] : (((tall(X0) | ~kind(X0)) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (~tall(X0) & kind(X0)))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | ~kind(X0) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (~tall(X0) & kind(X0)))) [flattening 61]
71. ~funny(X0) | ~curious(X0) [cnf transformation 29]
72. ~curious(X0) | tall(X0) [cnf transformation 29]
93. curious(susan) | ~kind(X0) [cnf transformation 33]
100. ~tall(X0) | funny(X0) [cnf transformation 50]
112. ~strong(X0) | curious(X0) | kind(X0) [cnf transformation 62]
120. ~curious(john) [cnf transformation 18]
126. strong(john) [cnf transformation 22]
128. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
129. ~kind(X0) <- (1) [avatar component clause 128]
183. 13 <=> curious(susan) [avatar definition]
185. curious(susan) <- (13) [avatar component clause 183]
186. 1 | 13 [avatar split clause 93,183,128]
273. tall(susan) <- (13) [resolution 72,185]
279. funny(susan) <- (13) [resolution 100,273]
280. ~curious(susan) <- (13) [resolution 279,71]
281. $false <- (13) [subsumption resolution 280,185]
282. ~13 [avatar contradiction clause 281]
331. curious(john) | kind(john) [resolution 112,126]
333. kind(john) [subsumption resolution 331,120]
334. $false <- (1) [subsumption resolution 333,129]
335. ~1 [avatar contradiction clause 334]
337. $false [avatar sat refutation 186,282,335]
% SZS output end Proof for 8853929196387914782750245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and tall is both not generous and not creative.
Everyone who is happy or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Someone is both patient and not quiet.
John is not rich or not creative.
Paul is either not brave or happy.
Susan is either happy or not generous.
Someone is both tall and kind.
Susan is not creative. | John is not happy. | neutral | (![X]:((humble(X)&tall(X))=>(~generous(X)&~creative(X))))&
(![X]:((happy(X)|~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X))))&
(~creative(susan)) | ~happy(john) | []
| null | 0 |
Everyone who is both not generous and not funny is not patient. Everyone who is either old or not strong is not strong or happy. If someone is creative then susan is not calm and vice versa. Everyone who is both quiet and not creative is quiet and vice versa. Everyone who is either strong or tall is old and vice versa. If someone is either not funny or not wise then fred is both generous and not happy and vice versa. If mary is either rich or not strong then someone is not wise and vice versa. Everyone who is both patient and old is both not old and not calm. If someone is not patient or curious then someone is creative. If someone is both not rich and not wise then someone is rich or funny and vice versa. If someone is both patient and happy then paul is both creative and not generous and vice versa. Everyone who is both kind and rich is either patient or not humble and vice versa. If someone is not generous then someone is not strong and vice versa. Everyone who is generous is not happy or strong and vice versa. Everyone who is not calm or not tall is not calm or not quiet. Everyone who is both not tall and not old is patient or not happy. Lucy is not humble or not happy. Someone is not creative or not wise. Someone is not kind or rich. Paul is either not tall or tall. Someone is either not rich or not happy. Someone is both creative and not calm. Fred is either not happy or calm. Someone is either rich or calm. | Fred is tall. | neutral | (![X]:((~generous(X)&~funny(X))=>~patient(X)))&
(![X]:((old(X)<~>~strong(X))=>(~strong(X)|happy(X))))&
((?[X]:(creative(X)))<=>(~calm(susan)))&
(![X]:((quiet(X)&~creative(X))<=>quiet(X)))&
(![X]:((strong(X)<~>tall(X))<=>old(X)))&
((?[X]:((~funny(X)<~>~wise(X))))<=>((generous(fred)&~happy(fred))))&
(((rich(mary)<~>~strong(mary)))<=>(?[X]:(~wise(X))))&
(![X]:((patient(X)&old(X))=>(~old(X)&~calm(X))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:(creative(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>(?[X]:((rich(X)|funny(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((creative(paul)&~generous(paul))))&
(![X]:((kind(X)&rich(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(~happy(X)|strong(X))))&
(![X]:((~calm(X)|~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~happy(X))))&
((~humble(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~wise(X))))&
(?[X]:((~kind(X)|rich(X))))&
((~tall(paul)<~>tall(paul)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~happy(fred)<~>calm(fred)))&
(?[X]:((rich(X)<~>calm(X)))) | tall(fred) | []
| null | 0 |
Everyone who is not old is either brave or not kind and vice versa.
Everyone who is either not curious or strong is either not brave or wise and vice versa.
If mary is not patient or not quiet then susan is old.
Everyone who is not brave or old is not brave and vice versa.
Everyone who is happy is rich or not generous and vice versa.
Everyone who is not tall is not kind and vice versa.
Everyone who is not tall is not humble.
Everyone who is not humble is both happy and strong and vice versa.
Everyone who is generous or humble is tall or quiet and vice versa.
Everyone who is funny is both not quiet and not humble and vice versa.
If alice is not calm then alice is strong or not quiet and vice versa.
Everyone who is patient is both not calm and kind.
If someone is creative or not rich then fred is either rich or funny and vice versa.
If someone is not brave then lucy is not kind or humble and vice versa.
Everyone who is tall or not rich is funny and vice versa.
Everyone who is both not curious and curious is both brave and rich and vice versa.
Someone is calm or not generous.
Someone is either calm or generous.
Paul is calm or not generous.
Someone is either not brave or brave.
Someone is either not kind or not happy.
Someone is not humble.
John is humble or not curious.
Someone is not quiet or wise. | Susan is kind. | entailment | (![X]:(~old(X)<=>(brave(X)<~>~kind(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~brave(X)<~>wise(X))))&
(((~patient(mary)|~quiet(mary)))=>(old(susan)))&
(![X]:((~brave(X)|old(X))<=>~brave(X)))&
(![X]:(happy(X)<=>(rich(X)|~generous(X))))&
(![X]:(~tall(X)<=>~kind(X)))&
(![X]:(~tall(X)=>~humble(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
(![X]:((generous(X)|humble(X))<=>(tall(X)|quiet(X))))&
(![X]:(funny(X)<=>(~quiet(X)&~humble(X))))&
((~calm(alice))<=>((strong(alice)|~quiet(alice))))&
(![X]:(patient(X)=>(~calm(X)&kind(X))))&
((?[X]:((creative(X)|~rich(X))))<=>((rich(fred)<~>funny(fred))))&
((?[X]:(~brave(X)))<=>((~kind(lucy)|humble(lucy))))&
(![X]:((tall(X)|~rich(X))<=>funny(X)))&
(![X]:((~curious(X)&curious(X))<=>(brave(X)&rich(X))))&
(?[X]:((calm(X)|~generous(X))))&
(?[X]:((calm(X)<~>generous(X))))&
((calm(paul)|~generous(paul)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
(?[X]:(~humble(X)))&
((humble(john)|~curious(john)))&
(?[X]:((~quiet(X)|wise(X)))) | kind(susan) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2547787889410873336909617
% SZS output start Proof for 2547787889410873336909617
1. ! [X0] : (~old(X0) <=> (brave(X0) <~> ~kind(X0))) [input p0]
3. (~quiet(mary) | ~patient(mary)) => old(susan) [input p2]
4. ! [X0] : ((old(X0) | ~brave(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : (~tall(X0) <=> ~kind(X0)) [input p5]
10. ! [X0] : (funny(X0) <=> (~humble(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : (patient(X0) => (kind(X0) & ~calm(X0))) [input p11]
15. ! [X0] : ((~rich(X0) | tall(X0)) <=> funny(X0)) [input p14]
25. ~kind(susan) [input hypothesis]
26. old(susan) | (quiet(mary) & patient(mary)) [ennf transformation 3]
28. ! [X0] : ((kind(X0) & ~calm(X0)) | ~patient(X0)) [ennf transformation 12]
29. ! [X0] : ((~old(X0) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0)))) & (((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | old(X0))) [nnf transformation 1]
31. ! [X0] : (((old(X0) | ~brave(X0)) | brave(X0)) & (~brave(X0) | (~old(X0) & brave(X0)))) [nnf transformation 4]
32. ! [X0] : ((old(X0) | ~brave(X0) | brave(X0)) & (~brave(X0) | (~old(X0) & brave(X0)))) [flattening 31]
35. ! [X0] : ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))) [nnf transformation 6]
40. ! [X0] : ((funny(X0) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | ~funny(X0))) [nnf transformation 10]
41. ! [X0] : ((funny(X0) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | ~funny(X0))) [flattening 40]
53. ! [X0] : (((~rich(X0) | tall(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) & ~tall(X0)))) [nnf transformation 15]
54. ! [X0] : ((~rich(X0) | tall(X0) | ~funny(X0)) & (funny(X0) | (rich(X0) & ~tall(X0)))) [flattening 53]
75. ~old(X0) | brave(X0) | kind(X0) [cnf transformation 29]
84. old(susan) | patient(mary) [cnf transformation 26]
85. old(susan) | quiet(mary) [cnf transformation 26]
87. ~brave(X0) | ~old(X0) [cnf transformation 32]
92. ~kind(X0) | tall(X0) [cnf transformation 35]
102. ~funny(X0) | ~quiet(X0) [cnf transformation 41]
109. ~patient(X0) | kind(X0) [cnf transformation 28]
119. ~tall(X0) | funny(X0) [cnf transformation 54]
137. ~kind(susan) [cnf transformation 25]
139. 1 <=> quiet(mary) [avatar definition]
141. quiet(mary) <- (1) [avatar component clause 139]
143. 2 <=> old(susan) [avatar definition]
145. old(susan) <- (2) [avatar component clause 143]
146. 1 | 2 [avatar split clause 85,143,139]
148. 3 <=> patient(mary) [avatar definition]
150. patient(mary) <- (3) [avatar component clause 148]
151. 3 | 2 [avatar split clause 84,143,148]
306. brave(susan) | kind(susan) <- (2) [resolution 75,145]
307. brave(susan) <- (2) [subsumption resolution 306,137]
309. ~old(susan) <- (2) [resolution 307,87]
310. $false <- (2) [subsumption resolution 309,145]
311. ~2 [avatar contradiction clause 310]
312. kind(mary) <- (3) [resolution 150,109]
315. tall(mary) <- (3) [resolution 312,92]
328. funny(mary) <- (3) [resolution 315,119]
345. ~quiet(mary) <- (3) [resolution 328,102]
348. $false <- (1, 3) [subsumption resolution 345,141]
349. ~1 | ~3 [avatar contradiction clause 348]
350. $false [avatar sat refutation 146,151,311,349]
% SZS output end Proof for 2547787889410873336909617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both patient and not wise then someone is rich. Everyone who is both happy and not generous is either calm or not old and vice versa. If someone is happy or not tall then someone is both not old and quiet and vice versa. Everyone who is generous is either old or not rich and vice versa. Everyone who is not curious is both funny and not brave and vice versa. Everyone who is either not happy or not funny is brave. Everyone who is either not happy or calm is happy. If fred is both curious and not rich then someone is either not creative or strong and vice versa. If alice is brave or not brave then someone is wise and vice versa. Everyone who is not funny is both brave and not curious. If someone is calm then someone is either not old or funny and vice versa. Everyone who is either creative or not happy is both humble and not old. Everyone who is both not funny and happy is not kind or happy. Everyone who is creative is either not patient or not brave and vice versa. Everyone who is either not kind or not old is either kind or brave and vice versa. Lucy is not humble or not curious. Someone is either quiet or not rich. Someone is both not patient and not generous. Someone is not curious or tall. Someone is generous. Mary is either creative or patient. Someone is both rich and patient. | Mary is not tall. | neutral | (((patient(lucy)&~wise(lucy)))=>(?[X]:(rich(X))))&
(![X]:((happy(X)&~generous(X))<=>(calm(X)<~>~old(X))))&
((?[X]:((happy(X)|~tall(X))))<=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~rich(X))))&
(![X]:(~curious(X)<=>(funny(X)&~brave(X))))&
(![X]:((~happy(X)<~>~funny(X))=>brave(X)))&
(![X]:((~happy(X)<~>calm(X))=>happy(X)))&
(((curious(fred)&~rich(fred)))<=>(?[X]:((~creative(X)<~>strong(X)))))&
(((brave(alice)|~brave(alice)))<=>(?[X]:(wise(X))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(kind(X)<~>brave(X))))&
((~humble(lucy)|~curious(lucy)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:(generous(X)))&
((creative(mary)<~>patient(mary)))&
(?[X]:((rich(X)&patient(X)))) | ~tall(mary) | []
| null | 0 |
Everyone who is patient or not tall is brave.
Everyone who is not tall or not kind is either not strong or not calm.
Everyone who is strong or brave is both not strong and creative.
If john is not kind or tall then john is both not brave and generous.
Everyone who is both not generous and wise is not calm and vice versa.
If someone is both humble and rich then john is not old and vice versa.
If mary is either funny or not curious then someone is not creative and vice versa.
Everyone who is both not strong and rich is strong.
Everyone who is calm or creative is old or brave and vice versa.
Everyone who is not funny is not curious.
Everyone who is not calm or not patient is either not old or not curious and vice versa.
Everyone who is not quiet or not rich is either not tall or rich.
Everyone who is either happy or not funny is both not patient and old and vice versa.
If someone is not brave or generous then john is not calm and vice versa.
Everyone who is quiet or old is not curious.
Everyone who is both not happy and humble is either not brave or not generous and vice versa.
Paul is not generous.
Someone is not quiet or not patient.
Lucy is both not rich and kind.
Someone is either patient or not strong.
Someone is either curious or not happy. | John is patient. | contradiction | (![X]:((patient(X)|~tall(X))=>brave(X)))&
(![X]:((~tall(X)|~kind(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|brave(X))=>(~strong(X)&creative(X))))&
(((~kind(john)|tall(john)))=>((~brave(john)&generous(john))))&
(![X]:((~generous(X)&wise(X))<=>~calm(X)))&
((?[X]:((humble(X)&rich(X))))<=>(~old(john)))&
(((funny(mary)<~>~curious(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&rich(X))=>strong(X)))&
(![X]:((calm(X)|creative(X))<=>(old(X)|brave(X))))&
(![X]:(~funny(X)=>~curious(X)))&
(![X]:((~calm(X)|~patient(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~tall(X)<~>rich(X))))&
(![X]:((happy(X)<~>~funny(X))<=>(~patient(X)&old(X))))&
((?[X]:((~brave(X)|generous(X))))<=>(~calm(john)))&
(![X]:((quiet(X)|old(X))=>~curious(X)))&
(![X]:((~happy(X)&humble(X))<=>(~brave(X)<~>~generous(X))))&
(~generous(paul))&
(?[X]:((~quiet(X)|~patient(X))))&
((~rich(lucy)&kind(lucy)))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:((curious(X)<~>~happy(X)))) | patient(john) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3142933464577175674516873
% SZS output start Proof for 3142933464577175674516873
2. ! [X0] : ((~kind(X0) | ~tall(X0)) => (~strong(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((brave(X0) | strong(X0)) => (creative(X0) & ~strong(X0))) [input p2]
6. ? [X0] : (rich(X0) & humble(X0)) <=> ~old(john) [input p5]
8. ! [X0] : ((rich(X0) & ~strong(X0)) => strong(X0)) [input p7]
11. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p10]
12. ! [X0] : ((~rich(X0) | ~quiet(X0)) => (~tall(X0) <~> rich(X0))) [input p11]
15. ! [X0] : ((old(X0) | quiet(X0)) => ~curious(X0)) [input p14]
22. patient(john) [input hypothesis]
23. ! [X0] : (~tall(X0) => (~strong(X0) <~> ~calm(X0))) [pure predicate removal 2]
27. ! [X0] : ((~strong(X0) <~> ~calm(X0)) | tall(X0)) [ennf transformation 23]
28. ! [X0] : ((creative(X0) & ~strong(X0)) | (~brave(X0) & ~strong(X0))) [ennf transformation 3]
30. ! [X0] : (strong(X0) | (~rich(X0) | strong(X0))) [ennf transformation 8]
31. ! [X0] : (strong(X0) | ~rich(X0) | strong(X0)) [flattening 30]
33. ! [X0] : ((~tall(X0) <~> rich(X0)) | (rich(X0) & quiet(X0))) [ennf transformation 12]
34. ! [X0] : (~curious(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 15]
35. ! [X0] : (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | tall(X0)) [nnf transformation 27]
38. (? [X0] : (rich(X0) & humble(X0)) | old(john)) & (~old(john) | ! [X0] : (~rich(X0) | ~humble(X0))) [nnf transformation 6]
39. (? [X0] : (rich(X0) & humble(X0)) | old(john)) & (~old(john) | ! [X1] : (~rich(X1) | ~humble(X1))) [rectify 38]
40. ? [X0] : (rich(X0) & humble(X0)) => (rich(sK0) & humble(sK0)) [choice axiom]
41. ((rich(sK0) & humble(sK0)) | old(john)) & (~old(john) | ! [X1] : (~rich(X1) | ~humble(X1))) [skolemisation 39,40]
48. ! [X0] : (((~patient(X0) | ~calm(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (patient(X0) & calm(X0)))) [nnf transformation 11]
49. ! [X0] : ((~patient(X0) | ~calm(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (patient(X0) & calm(X0)))) [flattening 48]
50. ! [X0] : (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (rich(X0) & quiet(X0))) [nnf transformation 33]
70. calm(X0) | strong(X0) | tall(X0) [cnf transformation 35]
71. ~strong(X0) | ~strong(X0) [cnf transformation 28]
82. rich(sK0) | old(john) [cnf transformation 41]
87. strong(X0) | ~rich(X0) | strong(X0) [cnf transformation 31]
98. ~old(X0) | ~calm(X0) | ~patient(X0) | curious(X0) [cnf transformation 49]
100. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 50]
113. ~curious(X0) | ~old(X0) [cnf transformation 34]
127. patient(john) [cnf transformation 22]
128. rich(X0) | ~tall(X0) [duplicate literal removal 100]
129. strong(X0) | ~rich(X0) [duplicate literal removal 87]
130. ~strong(X0) [duplicate literal removal 71]
146. 4 <=> old(john) [avatar definition]
148. old(john) <- (4) [avatar component clause 146]
150. 5 <=> rich(sK0) [avatar definition]
152. rich(sK0) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 82,150,146]
182. ~rich(X0) [subsumption resolution 129,130]
183. ~tall(X0) [subsumption resolution 128,182]
185. 12 <=> calm(john) [avatar definition]
186. ~calm(john) <- (~12) [avatar component clause 185]
187. calm(john) <- (12) [avatar component clause 185]
225. $false <- (5) [subsumption resolution 152,182]
226. ~5 [avatar contradiction clause 225]
241. strong(john) | tall(john) <- (~12) [resolution 70,186]
244. tall(john) <- (~12) [subsumption resolution 241,130]
245. $false <- (~12) [subsumption resolution 244,183]
246. 12 [avatar contradiction clause 245]
363. ~calm(john) | ~patient(john) | curious(john) <- (4) [resolution 98,148]
366. ~patient(john) | curious(john) <- (4, 12) [subsumption resolution 363,187]
367. curious(john) <- (4, 12) [subsumption resolution 366,127]
379. ~old(john) <- (4, 12) [resolution 367,113]
381. $false <- (4, 12) [subsumption resolution 379,148]
382. ~4 | ~12 [avatar contradiction clause 381]
383. $false [avatar sat refutation 153,226,246,382]
% SZS output end Proof for 3142933464577175674516873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and generous then lucy is not brave or curious and vice versa. Everyone who is both curious and generous is either quiet or not happy. Everyone who is not happy or kind is both not quiet and old. Everyone who is generous is either curious or strong. Everyone who is both not humble and not curious is brave. Everyone who is funny is both not brave and patient and vice versa. Everyone who is humble is creative and vice versa. Everyone who is either patient or funny is both not calm and tall. Everyone who is either not old or creative is kind or not old and vice versa. Everyone who is not strong is not old or not kind. If someone is either not generous or strong then someone is either patient or strong. Everyone who is not patient or strong is both not happy and not kind. Everyone who is not curious or tall is both not generous and not strong and vice versa. Everyone who is not tall is both not kind and brave. Everyone who is either strong or patient is not tall or not kind and vice versa. Someone is funny or wise. Fred is old or quiet. Someone is rich. Fred is not brave. | Fred is curious. | entailment | ((?[X]:((~creative(X)&generous(X))))<=>((~brave(lucy)|curious(lucy))))&
(![X]:((curious(X)&generous(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((~happy(X)|kind(X))=>(~quiet(X)&old(X))))&
(![X]:(generous(X)=>(curious(X)<~>strong(X))))&
(![X]:((~humble(X)&~curious(X))=>brave(X)))&
(![X]:(funny(X)<=>(~brave(X)&patient(X))))&
(![X]:(humble(X)<=>creative(X)))&
(![X]:((patient(X)<~>funny(X))=>(~calm(X)&tall(X))))&
(![X]:((~old(X)<~>creative(X))<=>(kind(X)|~old(X))))&
(![X]:(~strong(X)=>(~old(X)|~kind(X))))&
((?[X]:((~generous(X)<~>strong(X))))=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:((~patient(X)|strong(X))=>(~happy(X)&~kind(X))))&
(![X]:((~curious(X)|tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~tall(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~tall(X)|~kind(X))))&
(?[X]:((funny(X)|wise(X))))&
((old(fred)|quiet(fred)))&
(?[X]:(rich(X)))&
(~brave(fred)) | curious(fred) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p11",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6554587240069213817758320
% SZS output start Proof for 6554587240069213817758320
3. ! [X0] : ((kind(X0) | ~happy(X0)) => (old(X0) & ~quiet(X0))) [input p2]
5. ! [X0] : ((~curious(X0) & ~humble(X0)) => brave(X0)) [input p4]
7. ! [X0] : (humble(X0) <=> creative(X0)) [input p6]
9. ! [X0] : ((~old(X0) <~> creative(X0)) <=> (~old(X0) | kind(X0))) [input p8]
10. ! [X0] : (~strong(X0) => (~kind(X0) | ~old(X0))) [input p9]
12. ! [X0] : ((strong(X0) | ~patient(X0)) => (~kind(X0) & ~happy(X0))) [input p11]
19. ~brave(fred) [input p18]
20. ~curious(fred) [input hypothesis]
22. ! [X0] : (humble(X0) => creative(X0)) [unused predicate definition removal 7]
28. ! [X0] : ((old(X0) & ~quiet(X0)) | (~kind(X0) & happy(X0))) [ennf transformation 3]
30. ! [X0] : (brave(X0) | (curious(X0) | humble(X0))) [ennf transformation 5]
31. ! [X0] : (brave(X0) | curious(X0) | humble(X0)) [flattening 30]
32. ! [X0] : (creative(X0) | ~humble(X0)) [ennf transformation 22]
34. ! [X0] : ((~kind(X0) | ~old(X0)) | strong(X0)) [ennf transformation 10]
35. ! [X0] : (~kind(X0) | ~old(X0) | strong(X0)) [flattening 34]
37. ! [X0] : ((~kind(X0) & ~happy(X0)) | (~strong(X0) & patient(X0))) [ennf transformation 12]
49. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | (old(X0) & ~kind(X0))) & ((~old(X0) | kind(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | (old(X0) & ~kind(X0))) & (~old(X0) | kind(X0) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [flattening 49]
69. ~kind(X0) | old(X0) [cnf transformation 28]
72. humble(X0) | curious(X0) | brave(X0) [cnf transformation 31]
76. ~humble(X0) | creative(X0) [cnf transformation 32]
80. ~old(X0) | kind(X0) | ~old(X0) | ~creative(X0) [cnf transformation 50]
84. ~creative(X0) | old(X0) | old(X0) [cnf transformation 50]
85. ~kind(X0) | ~old(X0) | strong(X0) [cnf transformation 35]
93. ~kind(X0) | ~strong(X0) [cnf transformation 37]
108. ~brave(fred) [cnf transformation 19]
109. ~curious(fred) [cnf transformation 20]
110. ~old(X0) | kind(X0) | ~creative(X0) [duplicate literal removal 80]
111. ~creative(X0) | old(X0) [duplicate literal removal 84]
137. ~creative(X0) | kind(X0) [subsumption resolution 110,111]
138. ~kind(X0) | strong(X0) [subsumption resolution 85,69]
157. ~kind(X0) [subsumption resolution 93,138]
176. curious(X0) | brave(X0) | creative(X0) [resolution 72,76]
230. brave(fred) | creative(fred) [resolution 176,109]
233. creative(fred) [subsumption resolution 230,108]
235. kind(fred) [resolution 233,137]
237. $false [subsumption resolution 235,157]
% SZS output end Proof for 6554587240069213817758320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not calm.
Everyone who is calm is either calm or humble and vice versa.
If someone is not quiet then fred is wise or not calm and vice versa.
If someone is both kind and not rich then someone is either not funny or not rich.
If fred is both calm and wise then someone is not creative or not quiet.
Everyone who is brave or not wise is curious and vice versa.
Everyone who is either rich or not kind is not strong.
If lucy is not wise or funny then someone is curious.
If fred is either patient or not curious then someone is tall and vice versa.
If someone is not funny then someone is patient.
If someone is both rich and not wise then someone is not kind and vice versa.
Everyone who is not strong or brave is not patient and vice versa.
If fred is both not humble and strong then someone is not wise and vice versa.
Everyone who is either not strong or not humble is both tall and wise and vice versa.
If someone is both not generous and rich then paul is both not calm and not old and vice versa.
If someone is not brave or kind then someone is not humble or not curious.
Someone is either brave or funny.
Someone is quiet.
Someone is either not generous or not patient.
Alice is generous or not tall.
Someone is kind or not curious.
Paul is generous or patient. | Lucy is not kind. | contradiction | (![X]:(tall(X)=>~calm(X)))&
(![X]:(calm(X)<=>(calm(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>((wise(fred)|~calm(fred))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(((calm(fred)&wise(fred)))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((brave(X)|~wise(X))<=>curious(X)))&
(![X]:((rich(X)<~>~kind(X))=>~strong(X)))&
(((~wise(lucy)|funny(lucy)))=>(?[X]:(curious(X))))&
(((patient(fred)<~>~curious(fred)))<=>(?[X]:(tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>~patient(X)))&
(((~humble(fred)&strong(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)&wise(X))))&
((?[X]:((~generous(X)&rich(X))))<=>((~calm(paul)&~old(paul))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
((generous(alice)|~tall(alice)))&
(?[X]:((kind(X)|~curious(X))))&
((generous(paul)|patient(paul))) | ~kind(lucy) | [
"p1",
"p5",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5537646888395105633788292
% SZS output start Proof for 5537646888395105633788292
2. ! [X0] : (calm(X0) <=> (calm(X0) <~> humble(X0))) [input p1]
6. ! [X0] : ((~wise(X0) | brave(X0)) <=> curious(X0)) [input p5]
9. (patient(fred) <~> ~curious(fred)) <=> ? [X0] : tall(X0) [input p8]
11. ? [X0] : (~wise(X0) & rich(X0)) <=> ? [X0] : ~kind(X0) [input p10]
12. ! [X0] : ((brave(X0) | ~strong(X0)) <=> ~patient(X0)) [input p11]
13. (strong(fred) & ~humble(fred)) <=> ? [X0] : ~wise(X0) [input p12]
14. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (wise(X0) & tall(X0))) [input p13]
23. ~kind(lucy) [input hypothesis]
26. ? [X0] : (~wise(X0) & rich(X0)) <=> ? [X1] : ~kind(X1) [rectify 11]
35. ! [X0] : ((calm(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ~calm(X0))) [nnf transformation 2]
45. ! [X0] : (((~wise(X0) | brave(X0)) | ~curious(X0)) & (curious(X0) | (wise(X0) & ~brave(X0)))) [nnf transformation 6]
46. ! [X0] : ((~wise(X0) | brave(X0) | ~curious(X0)) & (curious(X0) | (wise(X0) & ~brave(X0)))) [flattening 45]
50. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [nnf transformation 9]
51. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [rectify 50]
52. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
53. (((curious(fred) | ~patient(fred)) & (~curious(fred) | patient(fred))) | ! [X0] : ~tall(X0)) & (tall(sK3) | ((patient(fred) | curious(fred)) & (~curious(fred) | ~patient(fred)))) [skolemisation 51,52]
57. (? [X0] : (~wise(X0) & rich(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (wise(X0) | ~rich(X0))) [nnf transformation 26]
58. (? [X0] : (~wise(X0) & rich(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (wise(X3) | ~rich(X3))) [rectify 57]
59. ? [X0] : (~wise(X0) & rich(X0)) => (~wise(sK5) & rich(sK5)) [choice axiom]
60. ? [X2] : ~kind(X2) => ~kind(sK6) [choice axiom]
61. ((~wise(sK5) & rich(sK5)) | ! [X1] : kind(X1)) & (~kind(sK6) | ! [X3] : (wise(X3) | ~rich(X3))) [skolemisation 58,60,59]
62. ! [X0] : (((brave(X0) | ~strong(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 12]
63. ! [X0] : ((brave(X0) | ~strong(X0) | patient(X0)) & (~patient(X0) | (~brave(X0) & strong(X0)))) [flattening 62]
64. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~strong(fred) | humble(fred))) [nnf transformation 13]
65. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~strong(fred) | humble(fred)) [flattening 64]
66. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~strong(fred) | humble(fred)) [rectify 65]
67. ? [X1] : ~wise(X1) => ~wise(sK7) [choice axiom]
68. ((strong(fred) & ~humble(fred)) | ! [X0] : wise(X0)) & (~wise(sK7) | ~strong(fred) | humble(fred)) [skolemisation 66,67]
69. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 14]
70. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 69]
91. ~humble(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 35]
93. calm(X0) | calm(X0) | ~humble(X0) [cnf transformation 35]
99. ~brave(X0) | curious(X0) [cnf transformation 46]
101. ~curious(X0) | brave(X0) | ~wise(X0) [cnf transformation 46]
108. ~curious(fred) | patient(fred) | ~tall(X0) [cnf transformation 53]
109. curious(fred) | ~patient(fred) | ~tall(X0) [cnf transformation 53]
113. ~wise(sK5) | kind(X1) [cnf transformation 61]
115. ~patient(X0) | ~brave(X0) [cnf transformation 63]
116. ~strong(X0) | brave(X0) | patient(X0) [cnf transformation 63]
119. strong(fred) | wise(X0) [cnf transformation 68]
121. tall(X0) | ~strong(X0) | humble(X0) [cnf transformation 70]
123. wise(X0) | ~strong(X0) | humble(X0) [cnf transformation 70]
140. ~kind(lucy) [cnf transformation 23]
141. ~humble(X0) | ~calm(X0) [duplicate literal removal 91]
142. ~humble(X0) | calm(X0) [duplicate literal removal 93]
143. ~humble(X0) [subsumption resolution 141,142]
154. 3 <=> wise(fred) [avatar definition]
155. wise(fred) <- (3) [avatar component clause 154]
190. 11 <=> ! [X0] : ~tall(X0) [avatar definition]
191. ~tall(X0) <- (11) [avatar component clause 190]
193. 12 <=> patient(fred) [avatar definition]
194. patient(fred) <- (12) [avatar component clause 193]
195. ~patient(fred) <- (~12) [avatar component clause 193]
197. 13 <=> curious(fred) [avatar definition]
198. ~curious(fred) <- (~13) [avatar component clause 197]
199. curious(fred) <- (13) [avatar component clause 197]
200. 11 | ~12 | 13 [avatar split clause 109,197,193,190]
201. 11 | 12 | ~13 [avatar split clause 108,197,193,190]
217. 17 <=> ! [X1] : kind(X1) [avatar definition]
218. kind(X1) <- (17) [avatar component clause 217]
220. 18 <=> wise(sK5) [avatar definition]
222. ~wise(sK5) <- (~18) [avatar component clause 220]
223. 17 | ~18 [avatar split clause 113,220,217]
238. 22 <=> ! [X0] : wise(X0) [avatar definition]
239. wise(X0) <- (22) [avatar component clause 238]
241. 23 <=> strong(fred) [avatar definition]
243. strong(fred) <- (23) [avatar component clause 241]
244. 22 | 23 [avatar split clause 119,241,238]
252. ~strong(X0) | wise(X0) [subsumption resolution 123,143]
253. ~strong(X0) | tall(X0) [subsumption resolution 121,143]
325. $false <- (17) [resolution 218,140]
326. ~17 [avatar contradiction clause 325]
327. $false <- (~18, 22) [subsumption resolution 222,239]
328. 18 | ~22 [avatar contradiction clause 327]
337. wise(fred) <- (23) [resolution 252,243]
339. 3 | ~23 [avatar split clause 337,241,154]
340. tall(fred) <- (23) [resolution 253,243]
342. $false <- (11, 23) [subsumption resolution 340,191]
343. ~11 | ~23 [avatar contradiction clause 342]
346. ~brave(fred) <- (12) [resolution 194,115]
349. brave(fred) | ~wise(fred) <- (13) [resolution 101,199]
352. ~wise(fred) <- (12, 13) [subsumption resolution 349,346]
353. $false <- (3, 12, 13) [subsumption resolution 352,155]
354. ~3 | ~12 | ~13 [avatar contradiction clause 353]
373. brave(fred) | patient(fred) <- (23) [resolution 116,243]
375. brave(fred) <- (~12, 23) [subsumption resolution 373,195]
376. curious(fred) <- (~12, 23) [resolution 375,99]
377. $false <- (~12, ~13, 23) [subsumption resolution 376,198]
378. 12 | 13 | ~23 [avatar contradiction clause 377]
379. $false [avatar sat refutation 200,201,223,244,326,328,339,343,354,378]
% SZS output end Proof for 5537646888395105633788292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not 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. | Mary is happy. | 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)))) | happy(mary) | [
"p2",
"p6",
"p9",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 448727819577511922648794
% SZS output start Proof for 448727819577511922648794
3. ! [X0] : ((~strong(X0) <~> ~old(X0)) => (wise(X0) & ~creative(X0))) [input p2]
7. (~creative(mary) <~> ~strong(mary)) => ~strong(lucy) [input p6]
10. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (wise(X0) & funny(X0))) [input p9]
12. ! [X0] : ((rich(X0) | funny(X0)) <=> (strong(X0) & ~old(X0))) [input p11]
13. ! [X0] : (rich(X0) <=> ~strong(X0)) [input p12]
25. happy(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~creative(X0)) | (~strong(X0) <=> ~old(X0))) [ennf transformation 3]
31. ~strong(lucy) | (~creative(mary) <=> ~strong(mary)) [ennf transformation 7]
40. ! [X0] : ((wise(X0) & ~creative(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) [nnf transformation 29]
47. ~strong(lucy) | ((~creative(mary) | strong(mary)) & (~strong(mary) | creative(mary))) [nnf transformation 31]
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]
56. ! [X0] : (((rich(X0) | funny(X0)) | (~strong(X0) | old(X0))) & ((strong(X0) & ~old(X0)) | (~rich(X0) & ~funny(X0)))) [nnf transformation 12]
57. ! [X0] : ((rich(X0) | funny(X0) | ~strong(X0) | old(X0)) & ((strong(X0) & ~old(X0)) | (~rich(X0) & ~funny(X0)))) [flattening 56]
58. ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))) [nnf transformation 13]
81. ~creative(X0) | ~strong(X0) | old(X0) [cnf transformation 40]
93. ~strong(lucy) | ~strong(mary) | creative(mary) [cnf transformation 47]
102. ~happy(X0) | funny(X0) [cnf transformation 55]
109. ~funny(X0) | ~old(X0) [cnf transformation 57]
112. ~rich(X0) | strong(X0) [cnf transformation 57]
115. rich(X0) | strong(X0) [cnf transformation 58]
137. happy(mary) [cnf transformation 25]
183. 11 <=> strong(mary) [avatar definition]
184. ~strong(mary) <- (~11) [avatar component clause 183]
187. 12 <=> creative(mary) [avatar definition]
188. creative(mary) <- (12) [avatar component clause 187]
191. 13 <=> strong(lucy) [avatar definition]
193. ~strong(lucy) <- (~13) [avatar component clause 191]
195. 12 | ~11 | ~13 [avatar split clause 93,191,183,187]
243. strong(X0) [subsumption resolution 115,112]
307. $false <- (~13) [subsumption resolution 193,243]
308. 13 [avatar contradiction clause 307]
309. $false <- (~11) [subsumption resolution 184,243]
310. 11 [avatar contradiction clause 309]
311. funny(mary) [resolution 102,137]
323. ~old(mary) [resolution 109,311]
350. ~strong(mary) | old(mary) <- (12) [resolution 81,188]
352. old(mary) <- (12) [subsumption resolution 350,243]
353. $false <- (12) [subsumption resolution 352,323]
354. ~12 [avatar contradiction clause 353]
356. $false [avatar sat refutation 195,308,310,354]
% SZS output end Proof for 448727819577511922648794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both not quiet and not kind.
If mary is both not old and creative then someone is not patient or not quiet and vice versa.
If someone is generous then paul is both not rich and patient.
Everyone who is humble is rich and vice versa.
If someone is either not kind or not quiet then paul is not rich and vice versa.
Everyone who is either happy or not curious is both not wise and not strong and vice versa.
Everyone who is tall or not generous is not brave or generous and vice versa.
If someone is quiet or calm then someone is patient or not quiet.
Everyone who is kind is not old or not curious.
Everyone who is both quiet and not old is both old and not happy.
If fred is either kind or not happy then mary is both not humble and not calm and vice versa.
Everyone who is both tall and old is both curious and kind and vice versa.
If mary is not funny then fred is both not rich and kind.
If alice is funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy.
Lucy is not kind. | Fred is tall. | contradiction | (![X]:(curious(X)=>(~quiet(X)&~kind(X))))&
(((~old(mary)&creative(mary)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:(generous(X)))=>((~rich(paul)&patient(paul))))&
(![X]:(humble(X)<=>rich(X)))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(~rich(paul)))&
(![X]:((happy(X)<~>~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((tall(X)|~generous(X))<=>(~brave(X)|generous(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:(kind(X)=>(~old(X)|~curious(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)&~happy(X))))&
(((kind(fred)<~>~happy(fred)))<=>((~humble(mary)&~calm(mary))))&
(![X]:((tall(X)&old(X))<=>(curious(X)&kind(X))))&
((~funny(mary))=>((~rich(fred)&kind(fred))))&
((funny(alice))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy)))&
(~kind(lucy)) | tall(fred) | [
"p0",
"p1",
"p9",
"p11",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 1818104845191311240237687
% SZS output start Proof for 1818104845191311240237687
1. ! [X0] : (curious(X0) => (~kind(X0) & ~quiet(X0))) [input p0]
2. (creative(mary) & ~old(mary)) <=> ? [X0] : (~quiet(X0) | ~patient(X0)) [input p1]
10. ! [X0] : ((~old(X0) & quiet(X0)) => (~happy(X0) & old(X0))) [input p9]
12. ! [X0] : ((old(X0) & tall(X0)) <=> (kind(X0) & curious(X0))) [input p11]
17. quiet(mary) [input p16]
25. tall(fred) [input hypothesis]
27. ! [X0] : ((~kind(X0) & ~quiet(X0)) | ~curious(X0)) [ennf transformation 1]
32. ! [X0] : ((~happy(X0) & old(X0)) | (old(X0) | ~quiet(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & old(X0)) | old(X0) | ~quiet(X0)) [flattening 32]
37. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | (~creative(mary) | old(mary))) [nnf transformation 2]
38. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | ~creative(mary) | old(mary)) [flattening 37]
39. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X1] : (~quiet(X1) | ~patient(X1)) | ~creative(mary) | old(mary)) [rectify 38]
40. ? [X1] : (~quiet(X1) | ~patient(X1)) => (~quiet(sK0) | ~patient(sK0)) [choice axiom]
41. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & ((~quiet(sK0) | ~patient(sK0)) | ~creative(mary) | old(mary)) [skolemisation 39,40]
56. ! [X0] : (((old(X0) & tall(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (~old(X0) | ~tall(X0)))) [nnf transformation 12]
57. ! [X0] : (((old(X0) & tall(X0)) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | ~old(X0) | ~tall(X0))) [flattening 56]
73. ~quiet(X0) | ~curious(X0) [cnf transformation 27]
77. ~old(mary) | quiet(X0) [cnf transformation 41]
101. old(X0) | old(X0) | ~quiet(X0) [cnf transformation 33]
109. ~tall(X0) | ~old(X0) | curious(X0) [cnf transformation 57]
123. quiet(mary) [cnf transformation 17]
134. tall(fred) [cnf transformation 25]
135. ~quiet(X0) | old(X0) [duplicate literal removal 101]
139. 1 <=> ! [X0] : quiet(X0) [avatar definition]
140. quiet(X0) <- (1) [avatar component clause 139]
151. 4 <=> old(mary) [avatar definition]
154. 1 | ~4 [avatar split clause 77,151,139]
298. old(mary) [resolution 135,123]
302. 4 [avatar split clause 298,151]
305. old(X0) <- (1) [resolution 140,135]
306. ~curious(X1) <- (1) [resolution 140,73]
320. ~old(fred) | curious(fred) [resolution 109,134]
321. curious(fred) <- (1) [subsumption resolution 320,305]
324. $false <- (1) [subsumption resolution 321,306]
325. ~1 [avatar contradiction clause 324]
326. $false [avatar sat refutation 154,302,325]
% SZS output end Proof for 1818104845191311240237687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not old then someone is either not rich or not old. If someone is kind or creative then mary is either strong or not funny and vice versa. Everyone who is patient or humble is strong or not strong and vice versa. Everyone who is both not generous and wise is either humble or patient and vice versa. Everyone who is patient is either funny or not quiet. If someone is either wise or not humble then someone is funny or kind and vice versa. If susan is either quiet or not brave then someone is not happy or not calm and vice versa. Everyone who is either not calm or quiet is not curious and vice versa. Everyone who is not quiet is either brave or kind and vice versa. Everyone who is either generous or not funny is not brave or not generous and vice versa. Everyone who is not curious or tall is either humble or not curious. Everyone who is curious is both patient and not quiet. Everyone who is not wise is both kind and creative and vice versa. If john is creative then someone is either not kind or tall and vice versa. If someone is both old and rich then someone is both not rich and not wise. Everyone who is either curious or happy is both generous and not wise. Someone is not old or not patient. Someone is either happy or not creative. Someone is not kind or not humble. Someone is not curious or not quiet. John is either not kind or happy. Someone is not creative or generous. John is rich. Alice is either not strong or happy. | Alice is happy. | neutral | ((?[X]:((~humble(X)&~old(X))))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((kind(X)|creative(X))))<=>((strong(mary)<~>~funny(mary))))&
(![X]:((patient(X)|humble(X))<=>(strong(X)|~strong(X))))&
(![X]:((~generous(X)&wise(X))<=>(humble(X)<~>patient(X))))&
(![X]:(patient(X)=>(funny(X)<~>~quiet(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(((quiet(susan)<~>~brave(susan)))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~quiet(X)<=>(brave(X)<~>kind(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|tall(X))=>(humble(X)<~>~curious(X))))&
(![X]:(curious(X)=>(patient(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(kind(X)&creative(X))))&
((creative(john))<=>(?[X]:((~kind(X)<~>tall(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~wise(X))))&
(?[X]:((~old(X)|~patient(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
((~kind(john)<~>happy(john)))&
(?[X]:((~creative(X)|generous(X))))&
(rich(john))&
((~strong(alice)<~>happy(alice))) | happy(alice) | []
| null | 0 |
Everyone who is rich is both not humble and humble and vice versa.
Everyone who is either kind or not old is generous.
Everyone who is both funny and tall is either not creative or not rich and vice versa.
Everyone who is both generous and not kind is either not brave or not strong and vice versa.
Everyone who is both not creative and patient is tall or patient.
If lucy is strong then someone is curious and vice versa.
Everyone who is both funny and curious is not kind.
Everyone who is not creative or curious is both not quiet and patient.
Everyone who is either not patient or kind is both not patient and old.
If someone is either happy or generous then someone is not generous and vice versa.
If someone is both old and happy then someone is generous or happy and vice versa.
If someone is not calm then susan is either not kind or not happy.
Everyone who is not quiet is both old and brave.
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.
Someone is either not patient or not funny.
Someone is both not strong and brave.
Susan is either patient or not calm.
Someone is quiet.
Someone is tall or not curious.
Lucy is not curious or patient.
Susan is humble or curious. | Susan is patient. | entailment | (![X]:(rich(X)<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>~old(X))=>generous(X)))&
(![X]:((funny(X)&tall(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((generous(X)&~kind(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~creative(X)&patient(X))=>(tall(X)|patient(X))))&
((strong(lucy))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)&curious(X))=>~kind(X)))&
(![X]:((~creative(X)|curious(X))=>(~quiet(X)&patient(X))))&
(![X]:((~patient(X)<~>kind(X))=>(~patient(X)&old(X))))&
((?[X]:((happy(X)<~>generous(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((old(X)&happy(X))))<=>(?[X]:((generous(X)|happy(X)))))&
((?[X]:(~calm(X)))=>((~kind(susan)<~>~happy(susan))))&
(![X]:(~quiet(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]:((~patient(X)<~>~funny(X))))&
(?[X]:((~strong(X)&brave(X))))&
((patient(susan)<~>~calm(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((tall(X)|~curious(X))))&
((~curious(lucy)|patient(lucy)))&
((humble(susan)|curious(susan))) | patient(susan) | [
"p0",
"p7",
"p9",
"p13",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 753333725756018451643584
% SZS output start Proof for 753333725756018451643584
1. ! [X0] : (rich(X0) <=> (humble(X0) & ~humble(X0))) [input p0]
8. ! [X0] : ((curious(X0) | ~creative(X0)) => (patient(X0) & ~quiet(X0))) [input p7]
10. ? [X0] : (happy(X0) <~> generous(X0)) <=> ? [X0] : ~generous(X0) [input p9]
14. ? [X0] : (kind(X0) | ~generous(X0)) => ~creative(susan) [input p13]
16. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (wise(X0) | ~rich(X0))) [input p15]
18. ? [X0] : (brave(X0) & ~strong(X0)) [input p17]
24. ~patient(susan) [input hypothesis]
25. ? [X0] : (happy(X0) <~> generous(X0)) <=> ? [X1] : ~generous(X1) [rectify 10]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~curious(X0) & creative(X0))) [ennf transformation 8]
36. ~creative(susan) | ! [X0] : (~kind(X0) & generous(X0)) [ennf transformation 14]
37. ! [X0] : ((rich(X0) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | ~rich(X0))) [nnf transformation 1]
38. ! [X0] : ((rich(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | ~rich(X0))) [flattening 37]
49. (? [X0] : ((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) [nnf transformation 25]
50. (? [X0] : ((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : ((happy(X3) | ~generous(X3)) & (generous(X3) | ~happy(X3)))) [rectify 49]
51. ? [X0] : ((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) => ((~generous(sK1) | ~happy(sK1)) & (generous(sK1) | happy(sK1))) [choice axiom]
52. ? [X2] : ~generous(X2) => ~generous(sK2) [choice axiom]
53. (((~generous(sK1) | ~happy(sK1)) & (generous(sK1) | happy(sK1))) | ! [X1] : generous(X1)) & (~generous(sK2) | ! [X3] : ((happy(X3) | ~generous(X3)) & (generous(X3) | ~happy(X3)))) [skolemisation 50,52,51]
64. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 16]
65. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 64]
69. ? [X0] : (brave(X0) & ~strong(X0)) => (brave(sK7) & ~strong(sK7)) [choice axiom]
70. brave(sK7) & ~strong(sK7) [skolemisation 18,69]
76. ~humble(X0) | ~rich(X0) [cnf transformation 38]
77. ~rich(X0) | humble(X0) [cnf transformation 38]
99. patient(X0) | creative(X0) [cnf transformation 32]
106. ~generous(sK2) | happy(X3) | ~generous(X3) [cnf transformation 53]
118. ~creative(susan) | generous(X0) [cnf transformation 36]
126. ~happy(X0) | strong(X0) | rich(X0) [cnf transformation 65]
130. ~strong(sK7) [cnf transformation 70]
138. ~patient(susan) [cnf transformation 24]
140. ~rich(X0) [subsumption resolution 76,77]
158. 4 <=> ! [X1] : generous(X1) [avatar definition]
159. generous(X1) <- (4) [avatar component clause 158]
171. 7 <=> ! [X3] : (happy(X3) | ~generous(X3)) [avatar definition]
172. happy(X3) | ~generous(X3) <- (7) [avatar component clause 171]
174. 8 <=> generous(sK2) [avatar definition]
176. ~generous(sK2) <- (~8) [avatar component clause 174]
177. 7 | ~8 [avatar split clause 106,174,171]
229. 21 <=> creative(susan) [avatar definition]
233. 4 | ~21 [avatar split clause 118,229,158]
247. ~happy(X0) | strong(X0) [subsumption resolution 126,140]
260. 27 <=> patient(susan) [avatar definition]
262. ~patient(susan) <- (~27) [avatar component clause 260]
287. ~27 [avatar split clause 138,260]
290. $false <- (4, ~8) [subsumption resolution 176,159]
291. ~4 | 8 [avatar contradiction clause 290]
294. happy(X3) <- (4, 7) [subsumption resolution 172,159]
301. creative(susan) <- (~27) [resolution 99,262]
304. 21 | 27 [avatar split clause 301,260,229]
326. strong(X0) <- (4, 7) [resolution 247,294]
329. $false <- (4, 7) [resolution 326,130]
331. ~4 | ~7 [avatar contradiction clause 329]
332. $false [avatar sat refutation 177,233,287,291,304,331]
% SZS output end Proof for 753333725756018451643584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not calm is not old or curious and vice versa.
Everyone who is both not happy and not funny is either not brave or strong.
If someone is kind or not humble then john is patient and vice versa.
Everyone who is not humble is not kind or old.
If someone is either not happy or tall then fred is rich.
Everyone who is both not calm and not funny is not old.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Everyone who is either quiet or not creative is either rich or old and vice versa.
If someone is either not quiet or quiet then fred is not tall or tall and vice versa.
If someone is humble or not funny then someone is not patient or quiet.
Everyone who is brave or curious is not brave.
Everyone who is curious or not old is either wise or not curious and vice versa.
Everyone who is wise or not funny is both brave and not curious.
Everyone who is either not strong or funny is either not wise or not funny and vice versa.
Someone is not generous.
Someone is either quiet or kind.
Paul is happy or not curious.
Fred is humble or not calm.
Paul is both funny and not old.
Someone is strong. | Lucy is strong. | entailment | (![X]:((curious(X)<~>~calm(X))<=>(~old(X)|curious(X))))&
(![X]:((~happy(X)&~funny(X))=>(~brave(X)<~>strong(X))))&
((?[X]:((kind(X)|~humble(X))))<=>(patient(john)))&
(![X]:(~humble(X)=>(~kind(X)|old(X))))&
((?[X]:((~happy(X)<~>tall(X))))=>(rich(fred)))&
(![X]:((~calm(X)&~funny(X))=>~old(X)))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~tall(fred)|tall(fred))))&
((?[X]:((humble(X)|~funny(X))))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((brave(X)|curious(X))=>~brave(X)))&
(![X]:((curious(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>kind(X))))&
((happy(paul)|~curious(paul)))&
((humble(fred)|~calm(fred)))&
((funny(paul)&~old(paul)))&
(?[X]:(strong(X))) | strong(lucy) | [
"p12",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8784893781414218866538732
% SZS output start Proof for 8784893781414218866538732
13. ! [X0] : ((curious(X0) | brave(X0)) => ~brave(X0)) [input p12]
15. ! [X0] : ((~funny(X0) | wise(X0)) => (~curious(X0) & brave(X0))) [input p14]
16. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (~wise(X0) <~> ~funny(X0))) [input p15]
23. ~strong(lucy) [input hypothesis]
35. ! [X0] : (~brave(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 13]
36. ! [X0] : ((~curious(X0) & brave(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 15]
60. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) & (((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 16]
110. ~brave(X0) | ~brave(X0) [cnf transformation 35]
118. brave(X0) | ~wise(X0) [cnf transformation 36]
124. funny(X0) | wise(X0) | funny(X0) | strong(X0) [cnf transformation 60]
128. ~funny(X0) | strong(X0) | ~funny(X0) | wise(X0) [cnf transformation 60]
137. ~strong(lucy) [cnf transformation 23]
139. funny(X0) | wise(X0) | strong(X0) [duplicate literal removal 124]
141. ~funny(X0) | strong(X0) | wise(X0) [duplicate literal removal 128]
144. ~brave(X0) [duplicate literal removal 110]
223. ~wise(X0) [subsumption resolution 118,144]
224. ~funny(X0) | strong(X0) [subsumption resolution 141,223]
225. funny(X0) | strong(X0) [subsumption resolution 139,223]
226. strong(X0) [subsumption resolution 225,224]
246. $false [subsumption resolution 137,226]
% SZS output end Proof for 8784893781414218866538732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not humble or not kind then paul is both not calm and tall and vice versa.
Everyone who is strong or happy is both calm and funny.
Everyone who is not curious is not funny or wise.
Everyone who is not humble is not tall or not brave.
If paul is either strong or not quiet then someone is both calm and not generous.
If someone is either not patient or strong then someone is not patient or not creative.
If someone is both quiet and not curious then someone is not funny or not happy and vice versa.
If someone is strong then lucy is both patient and not funny.
Everyone who is not happy or rich is creative or not curious and vice versa.
Everyone who is old is not quiet.
If someone is either rich or not rich then john is wise and vice versa.
If someone is not humble then lucy is not brave and vice versa.
If alice is both not funny and not tall then someone is humble and vice versa.
If lucy is tall or not patient then mary is patient and vice versa.
If someone is wise then john is both kind and humble.
If alice is both generous and not generous then fred is not patient or not tall.
Susan is strong.
Someone is either not tall or curious.
Mary is both not tall and not happy.
John is brave or patient.
Someone is tall.
Someone is not calm or not kind.
Susan is either not old or curious.
Someone is not quiet. | Susan is not calm. | contradiction | (((~humble(fred)|~kind(fred)))<=>((~calm(paul)&tall(paul))))&
(![X]:((strong(X)|happy(X))=>(calm(X)&funny(X))))&
(![X]:(~curious(X)=>(~funny(X)|wise(X))))&
(![X]:(~humble(X)=>(~tall(X)|~brave(X))))&
(((strong(paul)<~>~quiet(paul)))=>(?[X]:((calm(X)&~generous(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:((~patient(X)|~creative(X)))))&
((?[X]:((quiet(X)&~curious(X))))<=>(?[X]:((~funny(X)|~happy(X)))))&
((?[X]:(strong(X)))=>((patient(lucy)&~funny(lucy))))&
(![X]:((~happy(X)|rich(X))<=>(creative(X)|~curious(X))))&
(![X]:(old(X)=>~quiet(X)))&
((?[X]:((rich(X)<~>~rich(X))))<=>(wise(john)))&
((?[X]:(~humble(X)))<=>(~brave(lucy)))&
(((~funny(alice)&~tall(alice)))<=>(?[X]:(humble(X))))&
(((tall(lucy)|~patient(lucy)))<=>(patient(mary)))&
((?[X]:(wise(X)))=>((kind(john)&humble(john))))&
(((generous(alice)&~generous(alice)))=>((~patient(fred)|~tall(fred))))&
(strong(susan))&
(?[X]:((~tall(X)<~>curious(X))))&
((~tall(mary)&~happy(mary)))&
((brave(john)|patient(john)))&
(?[X]:(tall(X)))&
(?[X]:((~calm(X)|~kind(X))))&
((~old(susan)<~>curious(susan)))&
(?[X]:(~quiet(X))) | ~calm(susan) | [
"p1",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 570039729584254179200095
% SZS output start Proof for 570039729584254179200095
2. ! [X0] : ((happy(X0) | strong(X0)) => (funny(X0) & calm(X0))) [input p1]
17. strong(susan) [input p16]
25. ~calm(susan) [input hypothesis]
28. ! [X0] : ((funny(X0) & calm(X0)) | (~happy(X0) & ~strong(X0))) [ennf transformation 2]
86. ~strong(X0) | calm(X0) [cnf transformation 28]
125. strong(susan) [cnf transformation 17]
136. ~calm(susan) [cnf transformation 25]
351. calm(susan) [resolution 86,125]
352. $false [subsumption resolution 351,136]
% SZS output end Proof for 570039729584254179200095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 7867963648818083157297620
% SZS output start Proof for 7867963648818083157297620
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 7867963648818083157297620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong then someone is both not tall and brave and vice versa.
If someone is humble or quiet then mary is either not curious or tall and vice versa.
If fred is brave or not old then fred is strong.
If someone is brave or not happy then someone is either humble or not calm and vice versa.
Everyone who is either not humble or rich is both calm and strong and vice versa.
If someone is wise then lucy is either not calm or not old and vice versa.
Everyone who is either not generous or not quiet is either brave or not quiet and vice versa.
If someone is not quiet or wise then mary is either kind or tall.
If alice is not patient or not happy then john is brave and vice versa.
Everyone who is not calm is both not strong and not wise and vice versa.
If someone is not patient then fred is either not quiet or wise.
Everyone who is kind or generous is not rich or wise.
If fred is either not patient or not funny then someone is wise and vice versa.
Everyone who is either not tall or not strong is both not creative and calm.
Everyone who is both tall and calm is not tall or not funny and vice versa.
Someone is either not curious or not rich.
Someone is either humble or not patient.
Lucy is kind.
Someone is not wise.
Paul is not old.
Lucy is old or funny.
Someone is not patient or not curious.
Susan is not curious or not patient. | Susan is not brave. | neutral | ((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((~tall(X)&brave(X)))))&
((?[X]:((humble(X)|quiet(X))))<=>((~curious(mary)<~>tall(mary))))&
(((brave(fred)|~old(fred)))=>(strong(fred)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>(calm(X)&strong(X))))&
((?[X]:(wise(X)))<=>((~calm(lucy)<~>~old(lucy))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|wise(X))))=>((kind(mary)<~>tall(mary))))&
(((~patient(alice)|~happy(alice)))<=>(brave(john)))&
(![X]:(~calm(X)<=>(~strong(X)&~wise(X))))&
((?[X]:(~patient(X)))=>((~quiet(fred)<~>wise(fred))))&
(![X]:((kind(X)|generous(X))=>(~rich(X)|wise(X))))&
(((~patient(fred)<~>~funny(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~creative(X)&calm(X))))&
(![X]:((tall(X)&calm(X))<=>(~tall(X)|~funny(X))))&
(?[X]:((~curious(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
(kind(lucy))&
(?[X]:(~wise(X)))&
(~old(paul))&
((old(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|~curious(X))))&
((~curious(susan)|~patient(susan))) | ~brave(susan) | []
| null | 0 |
If alice is patient then someone is creative or not funny. If someone is either rich or humble then john is either not quiet or not rich. Everyone who is both not old and funny is both not tall and wise and vice versa. If someone is rich or old then alice is wise or not strong and vice versa. Everyone who is both creative and not generous is not humble or strong and vice versa. Everyone who is not curious or humble is not strong or humble and vice versa. If someone is funny then alice is either strong or creative and vice versa. Everyone who is creative is either not patient or not kind. Everyone who is creative or not brave is either strong or not brave and vice versa. If someone is old then alice is calm. Everyone who is either kind or funny is both curious and tall and vice versa. Everyone who is both not old and generous is curious or not wise and vice versa. Everyone who is strong is happy and vice versa. If john is both curious and rich then fred is not patient or calm. If someone is both not patient and tall then john is both not wise and humble. If someone is not tall or wise then lucy is both curious and not curious and vice versa. Someone is not old or not tall. Someone is either not curious or humble. Someone is not creative. Someone is either calm or not rich. Someone is both generous and patient. Someone is either not humble or not wise. Someone is not quiet or calm. John is funny or creative. | John is not brave. | entailment | ((patient(alice))=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:((rich(X)<~>humble(X))))=>((~quiet(john)<~>~rich(john))))&
(![X]:((~old(X)&funny(X))<=>(~tall(X)&wise(X))))&
((?[X]:((rich(X)|old(X))))<=>((wise(alice)|~strong(alice))))&
(![X]:((creative(X)&~generous(X))<=>(~humble(X)|strong(X))))&
(![X]:((~curious(X)|humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(![X]:((creative(X)|~brave(X))<=>(strong(X)<~>~brave(X))))&
((?[X]:(old(X)))=>(calm(alice)))&
(![X]:((kind(X)<~>funny(X))<=>(curious(X)&tall(X))))&
(![X]:((~old(X)&generous(X))<=>(curious(X)|~wise(X))))&
(![X]:(strong(X)<=>happy(X)))&
(((curious(john)&rich(john)))=>((~patient(fred)|calm(fred))))&
((?[X]:((~patient(X)&tall(X))))=>((~wise(john)&humble(john))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)<~>~rich(X))))&
(?[X]:((generous(X)&patient(X))))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((funny(john)|creative(john))) | ~brave(john) | [
"p2",
"p4",
"p6",
"p8",
"p11",
"p15",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 7070916661264764961509009
% SZS output start Proof for 7070916661264764961509009
3. ! [X0] : ((funny(X0) & ~old(X0)) <=> (wise(X0) & ~tall(X0))) [input p2]
5. ! [X0] : ((~generous(X0) & creative(X0)) <=> (strong(X0) | ~humble(X0))) [input p4]
7. ? [X0] : funny(X0) <=> (strong(alice) <~> creative(alice)) [input p6]
9. ! [X0] : ((~brave(X0) | creative(X0)) <=> (strong(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((generous(X0) & ~old(X0)) <=> (~wise(X0) | curious(X0))) [input p11]
16. ? [X0] : (wise(X0) | ~tall(X0)) <=> (~curious(lucy) & curious(lucy)) [input p15]
24. creative(john) | funny(john) [input p23]
25. brave(john) [input hypothesis]
36. ! [X0] : (((funny(X0) & ~old(X0)) | (~wise(X0) | tall(X0))) & ((wise(X0) & ~tall(X0)) | (~funny(X0) | old(X0)))) [nnf transformation 3]
37. ! [X0] : (((funny(X0) & ~old(X0)) | ~wise(X0) | tall(X0)) & ((wise(X0) & ~tall(X0)) | ~funny(X0) | old(X0))) [flattening 36]
43. ! [X0] : (((~generous(X0) & creative(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (generous(X0) | ~creative(X0)))) [nnf transformation 5]
44. ! [X0] : (((~generous(X0) & creative(X0)) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | generous(X0) | ~creative(X0))) [flattening 43]
47. (? [X0] : funny(X0) | ((strong(alice) | ~creative(alice)) & (creative(alice) | ~strong(alice)))) & (((~creative(alice) | ~strong(alice)) & (creative(alice) | strong(alice))) | ! [X0] : ~funny(X0)) [nnf transformation 7]
48. (? [X0] : funny(X0) | ((strong(alice) | ~creative(alice)) & (creative(alice) | ~strong(alice)))) & (((~creative(alice) | ~strong(alice)) & (creative(alice) | strong(alice))) | ! [X1] : ~funny(X1)) [rectify 47]
49. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
50. (funny(sK2) | ((strong(alice) | ~creative(alice)) & (creative(alice) | ~strong(alice)))) & (((~creative(alice) | ~strong(alice)) & (creative(alice) | strong(alice))) | ! [X1] : ~funny(X1)) [skolemisation 48,49]
52. ! [X0] : (((~brave(X0) | creative(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (brave(X0) & ~creative(X0)))) [nnf transformation 9]
53. ! [X0] : ((~brave(X0) | creative(X0) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (brave(X0) & ~creative(X0)))) [flattening 52]
56. ! [X0] : (((generous(X0) & ~old(X0)) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | (~generous(X0) | old(X0)))) [nnf transformation 12]
57. ! [X0] : (((generous(X0) & ~old(X0)) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | ~generous(X0) | old(X0))) [flattening 56]
59. (? [X0] : (wise(X0) | ~tall(X0)) | (curious(lucy) | ~curious(lucy))) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [nnf transformation 16]
60. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [flattening 59]
61. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [rectify 60]
62. ? [X0] : (wise(X0) | ~tall(X0)) => (wise(sK3) | ~tall(sK3)) [choice axiom]
63. ((wise(sK3) | ~tall(sK3)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [skolemisation 61,62]
87. ~funny(X0) | wise(X0) | old(X0) [cnf transformation 37]
96. ~strong(X0) | creative(X0) [cnf transformation 44]
98. ~generous(X0) | ~strong(X0) [cnf transformation 44]
103. creative(alice) | strong(alice) | ~funny(X1) [cnf transformation 50]
106. funny(sK2) | strong(alice) | ~creative(alice) [cnf transformation 50]
109. ~brave(X0) | strong(X0) | ~creative(X0) [cnf transformation 53]
124. ~old(X0) | wise(X0) [cnf transformation 57]
126. generous(X0) | wise(X0) [cnf transformation 57]
133. curious(lucy) | ~wise(X1) [cnf transformation 63]
135. ~curious(lucy) | ~wise(X1) [cnf transformation 63]
148. creative(john) | funny(john) [cnf transformation 24]
149. brave(john) [cnf transformation 25]
184. 8 <=> strong(alice) [avatar definition]
186. strong(alice) <- (8) [avatar component clause 184]
210. 14 <=> creative(alice) [avatar definition]
214. 15 <=> funny(sK2) [avatar definition]
216. funny(sK2) <- (15) [avatar component clause 214]
217. ~14 | 8 | 15 [avatar split clause 106,214,184,210]
220. 16 <=> ! [X1] : ~funny(X1) [avatar definition]
221. ~funny(X1) <- (16) [avatar component clause 220]
223. creative(alice) | ~funny(X1) [subsumption resolution 103,96]
224. 16 | 14 [avatar split clause 223,210,220]
257. 24 <=> ! [X1] : ~wise(X1) [avatar definition]
258. ~wise(X1) <- (24) [avatar component clause 257]
260. 25 <=> curious(lucy) [avatar definition]
263. 24 | ~25 [avatar split clause 135,260,257]
268. 24 | 25 [avatar split clause 133,260,257]
319. 37 <=> funny(john) [avatar definition]
321. funny(john) <- (37) [avatar component clause 319]
323. 38 <=> creative(john) [avatar definition]
325. creative(john) <- (38) [avatar component clause 323]
326. 37 | 38 [avatar split clause 148,323,319]
333. wise(X0) | ~strong(X0) [resolution 126,98]
335. ~strong(X0) <- (24) [subsumption resolution 333,258]
344. wise(sK2) | old(sK2) <- (15) [resolution 87,216]
346. old(sK2) <- (15, 24) [subsumption resolution 344,258]
348. wise(sK2) <- (15, 24) [resolution 346,124]
349. $false <- (15, 24) [subsumption resolution 348,258]
350. ~15 | ~24 [avatar contradiction clause 349]
353. $false <- (8, 24) [subsumption resolution 186,335]
354. ~8 | ~24 [avatar contradiction clause 353]
355. $false <- (16, 37) [resolution 221,321]
356. ~16 | ~37 [avatar contradiction clause 355]
359. strong(john) | ~creative(john) [resolution 109,149]
360. ~creative(john) <- (24) [subsumption resolution 359,335]
361. $false <- (24, 38) [subsumption resolution 360,325]
362. ~24 | ~38 [avatar contradiction clause 361]
363. $false [avatar sat refutation 217,224,263,268,326,350,354,356,362]
% SZS output end Proof for 7070916661264764961509009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not brave then mary is either tall or kind and vice versa.
Everyone who is not old is kind or old and vice versa.
Everyone who is quiet or happy is either patient or old and vice versa.
If fred is either tall or humble then susan is kind or brave and vice versa.
Everyone who is both not rich and quiet is either strong or not curious and vice versa.
If lucy is funny then paul is tall.
If someone is generous then lucy is both not generous and brave.
Everyone who is either old or kind is happy and vice versa.
Everyone who is either curious or not rich is either brave or not wise and vice versa.
If fred is not humble or not patient then someone is not curious or not tall.
Everyone who is both quiet and tall is either calm or quiet and vice versa.
Everyone who is either funny or strong is either not patient or humble.
If someone is not curious then lucy is both quiet and wise and vice versa.
If someone is both not rich and not strong then someone is either happy or not kind.
Everyone who is both happy and not old is not patient or calm.
Everyone who is both not brave and not generous is either not curious or happy.
Susan is not kind or not old.
Someone is both rich and not curious.
Someone is brave.
Someone is creative or generous.
Paul is either funny or not wise. | Mary is creative. | neutral | ((~brave(mary))<=>((tall(mary)<~>kind(mary))))&
(![X]:(~old(X)<=>(kind(X)|old(X))))&
(![X]:((quiet(X)|happy(X))<=>(patient(X)<~>old(X))))&
(((tall(fred)<~>humble(fred)))<=>((kind(susan)|brave(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(strong(X)<~>~curious(X))))&
((funny(lucy))=>(tall(paul)))&
((?[X]:(generous(X)))=>((~generous(lucy)&brave(lucy))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(brave(X)<~>~wise(X))))&
(((~humble(fred)|~patient(fred)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((quiet(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((funny(X)<~>strong(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)&wise(lucy))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((happy(X)&~old(X))=>(~patient(X)|calm(X))))&
(![X]:((~brave(X)&~generous(X))=>(~curious(X)<~>happy(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)|generous(X))))&
((funny(paul)<~>~wise(paul))) | creative(mary) | []
| null | 0 |
If john is either not kind or creative then someone is either not kind or not rich.
Everyone who is old or quiet is both not old and curious and vice versa.
If john is not quiet then someone is not generous or not brave and vice versa.
If someone is not quiet then someone is either not quiet or wise and vice versa.
If susan is both humble and not happy then mary is quiet or not brave.
If fred is either strong or tall then john is not quiet.
Everyone who is either happy or not creative is quiet.
Everyone who is either old or not generous is either not brave or patient.
Everyone who is either happy or curious is generous or happy and vice versa.
Everyone who is not rich is both patient and kind and vice versa.
Everyone who is either not funny or calm is funny or not funny and vice versa.
Everyone who is either not brave or not kind is either strong or patient.
Everyone who is either not funny or creative is either old or funny and vice versa.
If someone is quiet then lucy is old or not quiet and vice versa.
Everyone who is either calm or happy is either creative or humble.
If alice is not tall then mary is not humble and vice versa.
Someone is not brave.
Someone is strong or quiet.
Someone is not happy or brave.
Mary is not generous.
Someone is both not old and not calm.
Someone is both creative and not brave.
Someone is either not patient or creative.
Someone is not curious. | Fred is not happy. | entailment | (((~kind(john)<~>creative(john)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((old(X)|quiet(X))<=>(~old(X)&curious(X))))&
((~quiet(john))<=>(?[X]:((~generous(X)|~brave(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(((humble(susan)&~happy(susan)))=>((quiet(mary)|~brave(mary))))&
(((strong(fred)<~>tall(fred)))=>(~quiet(john)))&
(![X]:((happy(X)<~>~creative(X))=>quiet(X)))&
(![X]:((old(X)<~>~generous(X))=>(~brave(X)<~>patient(X))))&
(![X]:((happy(X)<~>curious(X))<=>(generous(X)|happy(X))))&
(![X]:(~rich(X)<=>(patient(X)&kind(X))))&
(![X]:((~funny(X)<~>calm(X))<=>(funny(X)|~funny(X))))&
(![X]:((~brave(X)<~>~kind(X))=>(strong(X)<~>patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(old(X)<~>funny(X))))&
((?[X]:(quiet(X)))<=>((old(lucy)|~quiet(lucy))))&
(![X]:((calm(X)<~>happy(X))=>(creative(X)<~>humble(X))))&
((~tall(alice))<=>(~humble(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((~happy(X)|brave(X))))&
(~generous(mary))&
(?[X]:((~old(X)&~calm(X))))&
(?[X]:((creative(X)&~brave(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
(?[X]:(~curious(X))) | ~happy(fred) | [
"p1",
"p6",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 1336269418557377746183918
% SZS output start Proof for 1336269418557377746183918
2. ! [X0] : ((quiet(X0) | old(X0)) <=> (curious(X0) & ~old(X0))) [input p1]
7. ! [X0] : ((happy(X0) <~> ~creative(X0)) => quiet(X0)) [input p6]
9. ! [X0] : ((happy(X0) <~> curious(X0)) <=> (happy(X0) | generous(X0))) [input p8]
13. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> (old(X0) <~> funny(X0))) [input p12]
25. happy(fred) [input hypothesis]
31. ! [X0] : (quiet(X0) | (happy(X0) <=> ~creative(X0))) [ennf transformation 7]
38. ! [X0] : (((quiet(X0) | old(X0)) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 2]
39. ! [X0] : ((quiet(X0) | old(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 38]
50. ! [X0] : (quiet(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) [nnf transformation 31]
52. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [flattening 52]
59. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) & (((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 13]
86. ~old(X0) | ~old(X0) [cnf transformation 39]
89. ~quiet(X0) | curious(X0) [cnf transformation 39]
101. ~happy(X0) | ~creative(X0) | quiet(X0) [cnf transformation 50]
112. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 53]
126. funny(X0) | old(X0) | creative(X0) | funny(X0) [cnf transformation 59]
131. creative(X0) | ~funny(X0) | old(X0) | ~funny(X0) [cnf transformation 59]
154. happy(fred) [cnf transformation 25]
155. funny(X0) | old(X0) | creative(X0) [duplicate literal removal 126]
157. creative(X0) | ~funny(X0) | old(X0) [duplicate literal removal 131]
164. ~happy(X0) | ~curious(X0) [duplicate literal removal 112]
165. ~old(X0) [duplicate literal removal 86]
263. ~funny(X0) | creative(X0) [subsumption resolution 157,165]
264. funny(X0) | creative(X0) [subsumption resolution 155,165]
265. creative(X0) [subsumption resolution 264,263]
316. ~curious(fred) [resolution 164,154]
318. ~creative(fred) | quiet(fred) [resolution 101,154]
319. quiet(fred) [subsumption resolution 318,265]
320. curious(fred) [resolution 319,89]
322. $false [subsumption resolution 320,316]
% SZS output end Proof for 1336269418557377746183918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is not patient.
If someone is wise or rich then someone is both rich and not quiet.
If alice is not wise or quiet then someone is both generous and not brave and vice versa.
Everyone who is not brave or not old is both creative and patient.
Everyone who is generous or brave is not rich and vice versa.
Everyone who is both not funny and not generous is rich or not curious.
If someone is not old then someone is both not strong and not creative.
If paul is humble then someone is brave.
Everyone who is either not patient or not brave is both quiet and not kind.
If someone is either not tall or kind then lucy is generous and vice versa.
If someone is both not tall and rich then john is either tall or old.
Everyone who is both not happy and wise is both rich and not rich.
Everyone who is not brave or not happy is both happy and not wise and vice versa.
Everyone who is creative or curious is happy and vice versa.
If john is calm or not brave then john is creative.
Paul is either generous or funny.
Someone is either not quiet or not tall.
Lucy is either not strong or creative.
Someone is either not quiet or not humble.
Someone is quiet or curious.
Mary is not strong. | Lucy is not calm. | entailment | (![X]:(calm(X)=>~patient(X)))&
((?[X]:((wise(X)|rich(X))))=>(?[X]:((rich(X)&~quiet(X)))))&
(((~wise(alice)|quiet(alice)))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((~brave(X)|~old(X))=>(creative(X)&patient(X))))&
(![X]:((generous(X)|brave(X))<=>~rich(X)))&
(![X]:((~funny(X)&~generous(X))=>(rich(X)|~curious(X))))&
((?[X]:(~old(X)))=>(?[X]:((~strong(X)&~creative(X)))))&
((humble(paul))=>(?[X]:(brave(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(quiet(X)&~kind(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(generous(lucy)))&
((?[X]:((~tall(X)&rich(X))))=>((tall(john)<~>old(john))))&
(![X]:((~happy(X)&wise(X))=>(rich(X)&~rich(X))))&
(![X]:((~brave(X)|~happy(X))<=>(happy(X)&~wise(X))))&
(![X]:((creative(X)|curious(X))<=>happy(X)))&
(((calm(john)|~brave(john)))=>(creative(john)))&
((generous(paul)<~>funny(paul)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
((~strong(lucy)<~>creative(lucy)))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((quiet(X)|curious(X))))&
(~strong(mary)) | ~calm(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3214593067808626271309646
% SZS output start Proof for 3214593067808626271309646
1. ! [X0] : (calm(X0) => ~patient(X0)) [input p0]
2. ? [X0] : (rich(X0) | wise(X0)) => ? [X0] : (~quiet(X0) & rich(X0)) [input p1]
4. ! [X0] : ((~old(X0) | ~brave(X0)) => (patient(X0) & creative(X0))) [input p3]
5. ! [X0] : ((brave(X0) | generous(X0)) <=> ~rich(X0)) [input p4]
9. ! [X0] : ((~patient(X0) <~> ~brave(X0)) => (~kind(X0) & quiet(X0))) [input p8]
13. ! [X0] : ((~happy(X0) | ~brave(X0)) <=> (~wise(X0) & happy(X0))) [input p12]
22. calm(lucy) [input hypothesis]
23. ? [X0] : (rich(X0) | wise(X0)) => ? [X1] : (~quiet(X1) & rich(X1)) [rectify 2]
25. ! [X0] : (~patient(X0) | ~calm(X0)) [ennf transformation 1]
26. ? [X1] : (~quiet(X1) & rich(X1)) | ! [X0] : (~rich(X0) & ~wise(X0)) [ennf transformation 23]
27. ! [X0] : ((patient(X0) & creative(X0)) | (old(X0) & brave(X0))) [ennf transformation 4]
32. ! [X0] : ((~kind(X0) & quiet(X0)) | (~patient(X0) <=> ~brave(X0))) [ennf transformation 9]
37. ? [X0] : (~quiet(X0) & rich(X0)) | ! [X1] : (~rich(X1) & ~wise(X1)) [rectify 26]
38. ? [X0] : (~quiet(X0) & rich(X0)) => (~quiet(sK0) & rich(sK0)) [choice axiom]
39. (~quiet(sK0) & rich(sK0)) | ! [X1] : (~rich(X1) & ~wise(X1)) [skolemisation 37,38]
45. ! [X0] : (((brave(X0) | generous(X0)) | rich(X0)) & (~rich(X0) | (~brave(X0) & ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : ((brave(X0) | generous(X0) | rich(X0)) & (~rich(X0) | (~brave(X0) & ~generous(X0)))) [flattening 45]
52. ! [X0] : ((~kind(X0) & quiet(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) [nnf transformation 32]
58. ! [X0] : (((~happy(X0) | ~brave(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (happy(X0) & brave(X0)))) [nnf transformation 13]
59. ! [X0] : ((~happy(X0) | ~brave(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (happy(X0) & brave(X0)))) [flattening 58]
72. ~patient(X0) | ~calm(X0) [cnf transformation 25]
73. rich(sK0) | ~wise(X1) [cnf transformation 39]
75. ~quiet(sK0) | ~wise(X1) [cnf transformation 39]
84. brave(X0) | patient(X0) [cnf transformation 27]
87. ~brave(X0) | ~rich(X0) [cnf transformation 46]
94. quiet(X0) | ~patient(X0) | brave(X0) [cnf transformation 52]
106. happy(X0) | happy(X0) [cnf transformation 59]
109. ~happy(X0) | ~brave(X0) | wise(X0) | ~happy(X0) [cnf transformation 59]
125. calm(lucy) [cnf transformation 22]
126. happy(X0) [duplicate literal removal 106]
127. ~happy(X0) | ~brave(X0) | wise(X0) [duplicate literal removal 109]
132. 2 <=> quiet(sK0) [avatar definition]
137. 3 <=> ! [X1] : ~wise(X1) [avatar definition]
138. ~wise(X1) <- (3) [avatar component clause 137]
139. 3 | ~2 [avatar split clause 75,132,137]
141. 4 <=> rich(sK0) [avatar definition]
143. rich(sK0) <- (4) [avatar component clause 141]
145. 3 | 4 [avatar split clause 73,141,137]
194. brave(X0) | quiet(X0) [subsumption resolution 94,84]
305. ~rich(X0) | quiet(X0) [resolution 194,87]
315. ~brave(X0) | wise(X0) [resolution 127,126]
316. quiet(sK0) <- (4) [resolution 305,143]
319. 2 | ~4 [avatar split clause 316,141,132]
336. wise(X2) | patient(X2) [resolution 315,84]
342. patient(X2) <- (3) [subsumption resolution 336,138]
351. ~calm(X0) <- (3) [resolution 342,72]
352. $false <- (3) [resolution 351,125]
353. ~3 [avatar contradiction clause 352]
354. $false [avatar sat refutation 139,145,319,353]
% SZS output end Proof for 3214593067808626271309646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. If someone is creative then someone is not curious or not kind and vice versa. Everyone who is both not generous and not strong is either not humble or not rich. Alice is brave or strong. Alice is not quiet or not rich. Someone is rich. Paul is curious or not patient. Paul is either old or quiet. Someone is both not old and kind. Paul is not old or calm. | Alice is quiet. | contradiction | (![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((~generous(X)&~strong(X))=>(~humble(X)<~>~rich(X))))&
((brave(alice)|strong(alice)))&
((~quiet(alice)|~rich(alice)))&
(?[X]:(rich(X)))&
((curious(paul)|~patient(paul)))&
((old(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&kind(X))))&
((~old(paul)|calm(paul))) | quiet(alice) | [
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 1558902836225688912610425
% SZS output start Proof for 1558902836225688912610425
6. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p5]
23. quiet(alice) [input hypothesis]
48. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 48]
77. ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
108. quiet(alice) [cnf transformation 23]
109. ~quiet(X0) [duplicate literal removal 77]
202. $false [subsumption resolution 108,109]
% SZS output end Proof for 1558902836225688912610425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.